LMFDB - Embedded newform 7.12.c.a.2.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7,12,Mod(2,7)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 12, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("7.2");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	7.c (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.37840226392$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 1846 x^{10} + 9475 x^{9} + 2735534 x^{8} + 11305015 x^{7} + 1247863105 x^{6} + \cdots + 4089842896896 $ x^12 - x^11 + 1846x^10 + 9475x^9 + 2735534x^8 + 11305015x^7 + 1247863105x^6 + 8299724444x^5 + 456730004116x^4 + 1967575859568x^3 + 7281700309008x^2 + 5939576563968x + 4089842896896
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{20}\cdot 3^{3}\cdot 7^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2.3
Root			$-0.427084 + 0.739732i$ of defining polynomial
Character	$\chi$	$=$	7.2
Dual form			7.12.c.a.4.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.85417 - 4.94356i) q^{2} +(-366.163 - 634.213i) q^{3} +(1007.71 + 1745.40i) q^{4} +(-4491.11 + 7778.83i) q^{5} -4180.36 q^{6} +(-43014.2 - 11274.1i) q^{7} +23195.3 q^{8} +(-179577. + 311037. i) q^{9} +O(q^{10})$	\(q+(2.85417 - 4.94356i) q^{2} +(-366.163 - 634.213i) q^{3} +(1007.71 + 1745.40i) q^{4} +(-4491.11 + 7778.83i) q^{5} -4180.36 q^{6} +(-43014.2 - 11274.1i) q^{7} +23195.3 q^{8} +(-179577. + 311037. i) q^{9} +(25636.8 + 44404.2i) q^{10} +(-45694.4 - 79145.1i) q^{11} +(737970. - 1.27820e6i) q^{12} -775221. q^{13} +(-178504. + 180465. i) q^{14} +6.57792e6 q^{15} +(-1.99758e6 + 3.45991e6i) q^{16} +(-4.63726e6 - 8.03198e6i) q^{17} +(1.02509e6 + 1.77550e6i) q^{18} +(1.43623e6 - 2.48762e6i) q^{19} -1.81029e7 q^{20} +(8.60003e6 + 3.14083e7i) q^{21} -521678. q^{22} +(-5.26756e6 + 9.12369e6i) q^{23} +(-8.49327e6 - 1.47108e7i) q^{24} +(-1.59261e7 - 2.75848e7i) q^{25} +(-2.21261e6 + 3.83236e6i) q^{26} +1.33289e8 q^{27} +(-2.36679e7 - 8.64380e7i) q^{28} -4.24570e7 q^{29} +(1.87745e7 - 3.25184e7i) q^{30} +(5.29120e7 + 9.16463e7i) q^{31} +(3.51549e7 + 6.08901e7i) q^{32} +(-3.34632e7 + 5.79600e7i) q^{33} -5.29421e7 q^{34} +(2.80881e8 - 2.83967e8i) q^{35} -7.23845e8 q^{36} +(-1.54843e8 + 2.68196e8i) q^{37} +(-8.19848e6 - 1.42002e7i) q^{38} +(2.83857e8 + 4.91655e8i) q^{39} +(-1.04173e8 + 1.80433e8i) q^{40} -1.19606e8 q^{41} +(1.79815e8 + 4.71298e7i) q^{42} +1.16451e9 q^{43} +(9.20932e7 - 1.59510e8i) q^{44} +(-1.61300e9 - 2.79380e9i) q^{45} +(3.00690e7 + 5.20811e7i) q^{46} +(1.25006e8 - 2.16517e8i) q^{47} +2.92576e9 q^{48} +(1.72312e9 + 9.69892e8i) q^{49} -1.81823e8 q^{50} +(-3.39599e9 + 5.88203e9i) q^{51} +(-7.81196e8 - 1.35307e9i) q^{52} +(-1.73284e9 - 3.00136e9i) q^{53} +(3.80428e8 - 6.58921e8i) q^{54} +8.20875e8 q^{55} +(-9.97729e8 - 2.61506e8i) q^{56} -2.10358e9 q^{57} +(-1.21180e8 + 2.09889e8i) q^{58} +(-3.01421e9 - 5.22077e9i) q^{59} +(6.62861e9 + 1.14811e10i) q^{60} +(-5.31834e9 + 9.21163e9i) q^{61} +6.04079e8 q^{62} +(1.12310e10 - 1.13544e10i) q^{63} -7.78074e9 q^{64} +(3.48161e9 - 6.03032e9i) q^{65} +(1.91019e8 + 3.30855e8i) q^{66} +(-1.10439e9 - 1.91285e9i) q^{67} +(9.34601e9 - 1.61878e10i) q^{68} +7.71514e9 q^{69} +(-6.02129e8 - 2.19904e9i) q^{70} -1.34122e10 q^{71} +(-4.16535e9 + 7.21460e9i) q^{72} +(8.02494e9 + 1.38996e10i) q^{73} +(8.83897e8 + 1.53095e9i) q^{74} +(-1.16631e10 + 2.02011e10i) q^{75} +5.78919e9 q^{76} +(1.07322e9 + 3.91953e9i) q^{77} +3.24071e9 q^{78} +(-8.41954e9 + 1.45831e10i) q^{79} +(-1.79427e10 - 3.10777e10i) q^{80} +(-1.69938e10 - 2.94341e10i) q^{81} +(-3.41376e8 + 5.91281e8i) q^{82} -1.25839e10 q^{83} +(-4.61538e10 + 4.66609e10i) q^{84} +8.33059e10 q^{85} +(3.32372e9 - 5.75684e9i) q^{86} +(1.55462e10 + 2.69268e10i) q^{87} +(-1.05990e9 - 1.83580e9i) q^{88} +(3.02118e10 - 5.23283e10i) q^{89} -1.84151e10 q^{90} +(3.33455e10 + 8.73991e9i) q^{91} -2.12326e10 q^{92} +(3.87488e10 - 6.71149e10i) q^{93} +(-7.13578e8 - 1.23595e9i) q^{94} +(1.29005e10 + 2.23444e10i) q^{95} +(2.57448e10 - 4.45914e10i) q^{96} -1.39153e11 q^{97} +(9.71279e9 - 5.75010e9i) q^{98} +3.28227e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 22 q^{2} - 244 q^{3} - 2556 q^{4} - 8782 q^{5} + 38140 q^{6} - 504 q^{7} + 97008 q^{8} - 172348 q^{9}+O(q^{10}) $ 12 * q + 22 * q^2 - 244 * q^3 - 2556 * q^4 - 8782 * q^5 + 38140 * q^6 - 504 * q^7 + 97008 * q^8 - 172348 * q^9	\( 12 q + 22 q^{2} - 244 q^{3} - 2556 q^{4} - 8782 q^{5} + 38140 q^{6} - 504 q^{7} + 97008 q^{8} - 172348 q^{9} + 111546 q^{10} - 1001572 q^{11} - 173684 q^{12} + 3864504 q^{13} - 1302994 q^{14} - 1286512 q^{15} + 39120 q^{16} - 6704802 q^{17} + 3768052 q^{18} + 4192212 q^{19} - 17646776 q^{20} + 44745358 q^{21} - 8505684 q^{22} - 33871872 q^{23} - 15734760 q^{24} + 13695456 q^{25} + 29350300 q^{26} + 73859384 q^{27} + 181285692 q^{28} - 255125224 q^{29} - 336068498 q^{30} - 331783920 q^{31} + 163252640 q^{32} - 80899438 q^{33} + 1853334396 q^{34} + 1407354844 q^{35} - 2197352048 q^{36} - 833082774 q^{37} - 2086458338 q^{38} + 737605904 q^{39} - 1219023432 q^{40} + 3104076808 q^{41} + 5982095000 q^{42} - 1722177552 q^{43} - 5105122436 q^{44} - 7406493484 q^{45} + 3435559326 q^{46} - 1327587552 q^{47} + 14535793696 q^{48} + 11976558636 q^{49} - 12237094384 q^{50} - 13921261140 q^{51} - 17237001432 q^{52} + 6725755626 q^{53} - 1674595226 q^{54} + 26323921200 q^{55} + 28163516640 q^{56} - 16884487756 q^{57} - 20073189204 q^{58} - 26237179548 q^{59} + 13611677716 q^{60} - 14411013726 q^{61} + 46185665964 q^{62} + 45955779184 q^{63} - 46365999744 q^{64} - 16224702172 q^{65} - 40938633602 q^{66} - 4241860068 q^{67} - 6528332916 q^{68} + 46750854252 q^{69} + 55705143270 q^{70} - 37335334656 q^{71} - 30237166608 q^{72} + 6005568990 q^{73} + 21663581922 q^{74} + 17116276792 q^{75} - 28817353320 q^{76} - 51928077698 q^{77} + 42636498520 q^{78} + 11712395640 q^{79} + 41748525232 q^{80} - 12455008366 q^{81} + 52795921668 q^{82} - 100821781200 q^{83} - 155783007940 q^{84} + 138884613396 q^{85} + 110437384472 q^{86} + 119455310144 q^{87} - 105039956616 q^{88} - 48633519778 q^{89} - 361508123864 q^{90} - 160908361488 q^{91} + 242956324248 q^{92} + 266530114134 q^{93} + 368497095702 q^{94} - 72161225128 q^{95} + 124456168928 q^{96} - 401308415928 q^{97} - 582375436706 q^{98} + 367357472240 q^{99}+O(q^{100}) \) 12 * q + 22 * q^2 - 244 * q^3 - 2556 * q^4 - 8782 * q^5 + 38140 * q^6 - 504 * q^7 + 97008 * q^8 - 172348 * q^9 + 111546 * q^10 - 1001572 * q^11 - 173684 * q^12 + 3864504 * q^13 - 1302994 * q^14 - 1286512 * q^15 + 39120 * q^16 - 6704802 * q^17 + 3768052 * q^18 + 4192212 * q^19 - 17646776 * q^20 + 44745358 * q^21 - 8505684 * q^22 - 33871872 * q^23 - 15734760 * q^24 + 13695456 * q^25 + 29350300 * q^26 + 73859384 * q^27 + 181285692 * q^28 - 255125224 * q^29 - 336068498 * q^30 - 331783920 * q^31 + 163252640 * q^32 - 80899438 * q^33 + 1853334396 * q^34 + 1407354844 * q^35 - 2197352048 * q^36 - 833082774 * q^37 - 2086458338 * q^38 + 737605904 * q^39 - 1219023432 * q^40 + 3104076808 * q^41 + 5982095000 * q^42 - 1722177552 * q^43 - 5105122436 * q^44 - 7406493484 * q^45 + 3435559326 * q^46 - 1327587552 * q^47 + 14535793696 * q^48 + 11976558636 * q^49 - 12237094384 * q^50 - 13921261140 * q^51 - 17237001432 * q^52 + 6725755626 * q^53 - 1674595226 * q^54 + 26323921200 * q^55 + 28163516640 * q^56 - 16884487756 * q^57 - 20073189204 * q^58 - 26237179548 * q^59 + 13611677716 * q^60 - 14411013726 * q^61 + 46185665964 * q^62 + 45955779184 * q^63 - 46365999744 * q^64 - 16224702172 * q^65 - 40938633602 * q^66 - 4241860068 * q^67 - 6528332916 * q^68 + 46750854252 * q^69 + 55705143270 * q^70 - 37335334656 * q^71 - 30237166608 * q^72 + 6005568990 * q^73 + 21663581922 * q^74 + 17116276792 * q^75 - 28817353320 * q^76 - 51928077698 * q^77 + 42636498520 * q^78 + 11712395640 * q^79 + 41748525232 * q^80 - 12455008366 * q^81 + 52795921668 * q^82 - 100821781200 * q^83 - 155783007940 * q^84 + 138884613396 * q^85 + 110437384472 * q^86 + 119455310144 * q^87 - 105039956616 * q^88 - 48633519778 * q^89 - 361508123864 * q^90 - 160908361488 * q^91 + 242956324248 * q^92 + 266530114134 * q^93 + 368497095702 * q^94 - 72161225128 * q^95 + 124456168928 * q^96 - 401308415928 * q^97 - 582375436706 * q^98 + 367357472240 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/7\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.85417	−	4.94356i	0.0630688	−	0.109238i	−0.832767	−	0.553624i	$-0.813245\pi$
$2$	2.85417	−	4.94356i	0.0630688	−	0.109238i	0.895836	+	0.444385i	$0.146578\pi$
$3$	−366.163	−	634.213i	−0.869976	−	1.50684i	−0.862020	−	0.506875i	$-0.830801\pi$
$3$	−366.163	−	634.213i	−0.869976	−	1.50684i	−0.00795684	−	0.999968i	$-0.502533\pi$
$4$	1007.71	+	1745.40i	0.492045	+	0.852246i
$5$	−4491.11	+	7778.83i	−0.642716	+	1.11322i	0.342108	+	0.939661i	$0.388859\pi$
$5$	−4491.11	+	7778.83i	−0.642716	+	1.11322i	−0.984824	+	0.173556i	$0.944474\pi$
$6$	−4180.36			−0.219473
$7$	−43014.2	−	11274.1i	−0.967326	−	0.253538i
$7$	−43014.2	−	11274.1i	−0.967326	−	0.253538i
$8$	23195.3			0.250268
$9$	−179577.	+	311037.i	−1.01372	+	1.75581i
$10$	25636.8	+	44404.2i	0.0810706	+	0.140418i
$11$	−45694.4	−	79145.1i	−0.0855468	−	0.148171i	0.820077	−	0.572253i	$-0.193930\pi$
$11$	−45694.4	−	79145.1i	−0.0855468	−	0.148171i	−0.905624	+	0.424081i	$0.860597\pi$
$12$	737970.	−	1.27820e6i	0.856134	−	1.48287i
$13$	−775221.			−0.579078			−0.289539	−	0.957166i	$-0.593502\pi$
$13$	−775221.			−0.579078			−0.289539	+	0.957166i	$0.593502\pi$
$14$	−178504.	+	180465.i	−0.0887041	+	0.0896788i
$15$	6.57792e6			2.23659
$16$	−1.99758e6	+	3.45991e6i	−0.476261	+	0.824907i
$17$	−4.63726e6	−	8.03198e6i	−0.792123	−	1.37200i	−0.924650	−	0.380818i	$-0.875642\pi$
$17$	−4.63726e6	−	8.03198e6i	−0.792123	−	1.37200i	0.132527	−	0.991179i	$-0.457691\pi$
$18$	1.02509e6	+	1.77550e6i	0.127868	+	0.221474i
$19$	1.43623e6	−	2.48762e6i	0.133070	−	0.230483i	−0.791789	−	0.610795i	$-0.790850\pi$
$19$	1.43623e6	−	2.48762e6i	0.133070	−	0.230483i	0.924858	+	0.380312i	$0.124183\pi$
$20$	−1.81029e7			−1.26498
$21$	8.60003e6	+	3.14083e7i	0.459509	+	1.67818i
$22$	−521678.			−0.0215813
$23$	−5.26756e6	+	9.12369e6i	−0.170650	+	0.295575i	−0.938647	−	0.344879i	$-0.887920\pi$
$23$	−5.26756e6	+	9.12369e6i	−0.170650	+	0.295575i	0.767997	+	0.640453i	$0.221253\pi$
$24$	−8.49327e6	−	1.47108e7i	−0.217728	−	0.377115i
$25$	−1.59261e7	−	2.75848e7i	−0.326167	−	0.564938i
$26$	−2.21261e6	+	3.83236e6i	−0.0365218	+	0.0632576i
$27$	1.33289e8			1.78769
$28$	−2.36679e7	−	8.64380e7i	−0.259891	−	0.949151i
$29$	−4.24570e7			−0.384380			−0.192190	−	0.981358i	$-0.561559\pi$
$29$	−4.24570e7			−0.384380			−0.192190	+	0.981358i	$0.561559\pi$
$30$	1.87745e7	−	3.25184e7i	0.141059	−	0.244321i
$31$	5.29120e7	+	9.16463e7i	0.331944	+	0.574944i	0.982893	−	0.184178i	$-0.0589622\pi$
$31$	5.29120e7	+	9.16463e7i	0.331944	+	0.574944i	−0.650949	+	0.759121i	$0.725629\pi$
$32$	3.51549e7	+	6.08901e7i	0.185209	+	0.320791i
$33$	−3.34632e7	+	5.79600e7i	−0.148847	+	0.257811i
$34$	−5.29421e7			−0.199833
$35$	2.80881e8	−	2.83967e8i	0.903957	−	0.913890i
$36$	−7.23845e8			−1.99518
$37$	−1.54843e8	+	2.68196e8i	−0.367099	+	0.635833i	−0.989111	−	0.147174i	$-0.952982\pi$
$37$	−1.54843e8	+	2.68196e8i	−0.367099	+	0.635833i	0.622012	+	0.783008i	$0.286315\pi$
$38$	−8.19848e6	−	1.42002e7i	−0.0167851	−	0.0290726i
$39$	2.83857e8	+	4.91655e8i	0.503784	+	0.872580i
$40$	−1.04173e8	+	1.80433e8i	−0.160851	+	0.278603i
$41$	−1.19606e8			−0.161229			−0.0806144	−	0.996745i	$-0.525688\pi$
$41$	−1.19606e8			−0.161229			−0.0806144	+	0.996745i	$0.525688\pi$
$42$	1.79815e8	+	4.71298e7i	0.212302	+	0.0556448i
$43$	1.16451e9			1.20800			0.604001	−	0.796983i	$-0.293572\pi$
$43$	1.16451e9			1.20800			0.604001	+	0.796983i	$0.293572\pi$
$44$	9.20932e7	−	1.59510e8i	0.0841856	−	0.145814i
$45$	−1.61300e9	−	2.79380e9i	−1.30306	−	2.25697i
$46$	3.00690e7	+	5.20811e7i	0.0215254	+	0.0372831i
$47$	1.25006e8	−	2.16517e8i	0.0795048	−	0.137706i	−0.823532	−	0.567270i	$-0.807999\pi$
$47$	1.25006e8	−	2.16517e8i	0.0795048	−	0.137706i	0.903036	+	0.429564i	$0.141333\pi$
$48$	2.92576e9			1.65734
$49$	1.72312e9	+	9.69892e8i	0.871437	+	0.490507i
$50$	−1.81823e8			−0.0822838
$51$	−3.39599e9	+	5.88203e9i	−1.37826	+	2.38721i
$52$	−7.81196e8	−	1.35307e9i	−0.284932	−	0.493517i
$53$	−1.73284e9	−	3.00136e9i	−0.569168	−	0.985829i	−0.996648	−	0.0818038i	$-0.973932\pi$
$53$	−1.73284e9	−	3.00136e9i	−0.569168	−	0.985829i	0.427480	−	0.904025i	$-0.359401\pi$
$54$	3.80428e8	−	6.58921e8i	0.112747	−	0.195284i
$55$	8.20875e8			0.219929
$56$	−9.97729e8	−	2.61506e8i	−0.242091	−	0.0634524i
$57$	−2.10358e9			−0.463070
$58$	−1.21180e8	+	2.09889e8i	−0.0242424	+	0.0419890i
$59$	−3.01421e9	−	5.22077e9i	−0.548893	−	0.950711i	−0.998351	−	0.0574095i	$-0.981716\pi$
$59$	−3.01421e9	−	5.22077e9i	−0.548893	−	0.950711i	0.449457	−	0.893302i	$-0.351617\pi$
$60$	6.62861e9	+	1.14811e10i	1.10050	+	1.90613i
$61$	−5.31834e9	+	9.21163e9i	−0.806236	+	1.39644i	0.109218	+	0.994018i	$0.465165\pi$
$61$	−5.31834e9	+	9.21163e9i	−0.806236	+	1.39644i	−0.915454	+	0.402423i	$0.868168\pi$
$62$	6.04079e8			0.0837412
$63$	1.12310e10	−	1.13544e10i	1.42576	−	1.44143i
$64$	−7.78074e9			−0.905798
$65$	3.48161e9	−	6.03032e9i	0.372183	−	0.644639i
$66$	1.91019e8	+	3.30855e8i	0.0187752	+	0.0325197i
$67$	−1.10439e9	−	1.91285e9i	−0.0999332	−	0.173089i	0.811724	−	0.584042i	$-0.198530\pi$
$67$	−1.10439e9	−	1.91285e9i	−0.0999332	−	0.173089i	−0.911657	+	0.410952i	$0.865196\pi$
$68$	9.34601e9	−	1.61878e10i	0.779520	−	1.35017i
$69$	7.71514e9			0.593846
$70$	−6.02129e8	−	2.19904e9i	−0.0428203	−	0.156385i
$71$	−1.34122e10			−0.882223			−0.441111	−	0.897452i	$-0.645416\pi$
$71$	−1.34122e10			−0.882223			−0.441111	+	0.897452i	$0.645416\pi$
$72$	−4.16535e9	+	7.21460e9i	−0.253701	+	0.439424i
$73$	8.02494e9	+	1.38996e10i	0.453071	+	0.784742i	0.998575	−	0.0533664i	$-0.0169951\pi$
$73$	8.02494e9	+	1.38996e10i	0.453071	+	0.784742i	−0.545504	+	0.838108i	$0.683662\pi$
$74$	8.83897e8	+	1.53095e9i	0.0463049	+	0.0802025i
$75$	−1.16631e10	+	2.02011e10i	−0.567515	+	0.982965i
$76$	5.78919e9			0.261905
$77$	1.07322e9	+	3.91953e9i	0.0451846	+	0.165019i
$78$	3.24071e9			0.127092
$79$	−8.41954e9	+	1.45831e10i	−0.307850	+	0.533212i	−0.977892	−	0.209111i	$-0.932943\pi$
$79$	−8.41954e9	+	1.45831e10i	−0.307850	+	0.533212i	0.670042	+	0.742323i	$0.266276\pi$
$80$	−1.79427e10	−	3.10777e10i	−0.612200	−	1.06036i
$81$	−1.69938e10	−	2.94341e10i	−0.541530	−	0.937958i
$82$	−3.41376e8	+	5.91281e8i	−0.0101685	+	0.0176124i
$83$	−1.25839e10			−0.350659			−0.175329	−	0.984510i	$-0.556099\pi$
$83$	−1.25839e10			−0.350659			−0.175329	+	0.984510i	$0.556099\pi$
$84$	−4.61538e10	+	4.66609e10i	−1.20412	+	1.21735i
$85$	8.33059e10			2.03644
$86$	3.32372e9	−	5.75684e9i	0.0761873	−	0.131960i
$87$	1.55462e10	+	2.69268e10i	0.334402	+	0.579200i
$88$	−1.05990e9	−	1.83580e9i	−0.0214096	−	0.0370826i
$89$	3.02118e10	−	5.23283e10i	0.573497	−	0.993326i	−0.422706	−	0.906267i	$-0.638920\pi$
$89$	3.02118e10	−	5.23283e10i	0.573497	−	0.993326i	0.996203	−	0.0870594i	$-0.0277470\pi$
$90$	−1.84151e10			−0.328731
$91$	3.33455e10	+	8.73991e9i	0.560157	+	0.146818i
$92$	−2.12326e10			−0.335870
$93$	3.87488e10	−	6.71149e10i	0.577567	−	1.00038i
$94$	−7.13578e8	−	1.23595e9i	−0.0100286	−	0.0173700i
$95$	1.29005e10	+	2.23444e10i	0.171052	+	0.296270i
$96$	2.57448e10	−	4.45914e10i	0.322254	−	0.558160i
$97$	−1.39153e11			−1.64531			−0.822654	−	0.568542i	$-0.807508\pi$
$97$	−1.39153e11			−1.64531			−0.822654	+	0.568542i	$0.807508\pi$
$98$	9.71279e9	−	5.75010e9i	0.108543	−	0.0642587i
$99$	3.28227e10			0.346881
$100$	3.20977e10	−	5.55949e10i	0.320977	−	0.555949i
$101$	7.27138e10	+	1.25944e11i	0.688413	+	1.19237i	0.972351	+	0.233524i	$0.0750258\pi$
$101$	7.27138e10	+	1.25944e11i	0.688413	+	1.19237i	−0.283938	+	0.958843i	$0.591641\pi$
$102$	1.93854e10	+	3.35766e10i	0.173850	+	0.301117i
$103$	−9.52360e10	+	1.64954e11i	−0.809462	+	1.40203i	0.103775	+	0.994601i	$0.466908\pi$
$103$	−9.52360e10	+	1.64954e11i	−0.809462	+	1.40203i	−0.913237	+	0.407429i	$0.866425\pi$
$104$	−1.79815e10			−0.144925
$105$	−2.82944e11	−	7.41600e10i	−2.16351	−	0.567060i
$106$	−1.97833e10			−0.143587
$107$	2.98014e10	−	5.16176e10i	0.205412	−	0.355785i	−0.744852	−	0.667230i	$-0.767480\pi$
$107$	2.98014e10	−	5.16176e10i	0.205412	−	0.355785i	0.950264	+	0.311445i	$0.100813\pi$
$108$	1.34316e11	+	2.32642e11i	0.879623	+	1.52355i
$109$	−7.38720e10	−	1.27950e11i	−0.459869	−	0.796517i	0.539084	−	0.842252i	$-0.318770\pi$
$109$	−7.38720e10	−	1.27950e11i	−0.459869	−	0.796517i	−0.998954	+	0.0457350i	$0.985437\pi$
$110$	2.34292e9	−	4.05805e9i	0.0138707	−	0.0240247i
$111$	2.26791e11			1.27747
$112$	1.24932e11	−	1.26304e11i	0.669844	−	0.677204i
$113$	−2.11327e11			−1.07901			−0.539503	−	0.841984i	$-0.681388\pi$
$113$	−2.11327e11			−1.07901			−0.539503	+	0.841984i	$0.681388\pi$
$114$	−6.00396e9	+	1.03992e10i	−0.0292052	+	0.0505850i
$115$	−4.73144e10	−	8.19510e10i	−0.219359	−	0.379941i
$116$	−4.27843e10	−	7.41046e10i	−0.189132	−	0.327586i
$117$	1.39212e11	−	2.41122e11i	0.587022	−	1.01675i
$118$	−3.44123e10			−0.138472
$119$	1.08915e11	+	3.97770e11i	0.418388	+	1.52800i
$120$	1.52577e11			0.559748
$121$	1.38480e11	−	2.39854e11i	0.485364	−	0.840674i
$122$	3.03589e10	+	5.25831e10i	0.101697	+	0.176144i
$123$	4.37954e10	+	7.58558e10i	0.140265	+	0.242946i
$124$	−1.06640e11	+	1.84705e11i	−0.326663	+	0.565796i
$125$	−1.52481e11			−0.446901
$126$	−2.40761e10	−	8.79287e10i	−0.0675380	−	0.246657i
$127$	3.51747e11			0.944735			0.472367	−	0.881402i	$-0.343400\pi$
$127$	3.51747e11			0.944735			0.472367	+	0.881402i	$0.343400\pi$
$128$	−9.42048e10	+	1.63167e11i	−0.242336	+	0.419738i
$129$	−4.26401e11	−	7.38549e11i	−1.05093	−	1.82027i
$130$	−1.98742e10	−	3.44231e10i	−0.0469462	−	0.0813132i
$131$	2.15308e10	−	3.72924e10i	0.0487604	−	0.0844556i	−0.840615	−	0.541633i	$-0.817806\pi$
$131$	2.15308e10	−	3.72924e10i	0.0487604	−	0.0844556i	0.889375	+	0.457177i	$0.151140\pi$
$132$	−1.34885e11			−0.292958
$133$	−8.98239e10	+	9.08109e10i	−0.187158	+	0.189214i
$134$	−1.26084e10			−0.0252107
$135$	−5.98614e11	+	1.03683e12i	−1.14898	+	1.99009i
$136$	−1.07563e11	−	1.86304e11i	−0.198243	−	0.343368i
$137$	4.92302e11	+	8.52692e11i	0.871502	+	1.50949i	0.860443	+	0.509547i	$0.170187\pi$
$137$	4.92302e11	+	8.52692e11i	0.871502	+	1.50949i	0.0110587	+	0.999939i	$0.496480\pi$
$138$	2.20203e10	−	3.81403e10i	0.0374532	−	0.0648708i
$139$	−7.31783e10			−0.119619			−0.0598096	−	0.998210i	$-0.519049\pi$
$139$	−7.31783e10			−0.119619			−0.0598096	+	0.998210i	$0.519049\pi$
$140$	7.78682e11	+	2.04094e11i	1.22365	+	0.320720i
$141$	−1.83091e11			−0.276669
$142$	−3.82806e10	+	6.63040e10i	−0.0556407	+	0.0963726i
$143$	3.54233e10	+	6.13549e10i	0.0495383	+	0.0858028i
$144$	−7.17440e11	−	1.24264e12i	−0.965588	−	1.67245i
$145$	1.90679e11	−	3.30266e11i	0.247047	−	0.427898i
$146$	9.16181e10			0.114299
$147$	−1.58233e10	−	1.44796e12i	−0.0190130	−	1.73985i
$148$	−6.24147e11			−0.722515
$149$	2.21679e11	−	3.83960e11i	0.247287	−	0.428313i	−0.715485	−	0.698628i	$-0.753794\pi$
$149$	2.21679e11	−	3.83960e11i	0.247287	−	0.428313i	0.962772	+	0.270314i	$0.0871277\pi$
$150$	6.65769e10	+	1.15315e11i	0.0715850	+	0.123989i
$151$	6.38440e11	+	1.10581e12i	0.661830	+	1.14632i	0.980134	+	0.198335i	$0.0635534\pi$
$151$	6.38440e11	+	1.10581e12i	0.661830	+	1.14632i	−0.318304	+	0.947989i	$0.603113\pi$
$152$	3.33138e10	−	5.77012e10i	0.0333031	−	0.0576827i
$153$	3.33099e12			3.21196
$154$	2.24396e10	+	5.88145e9i	0.0208762	+	0.00547168i
$155$	−9.50535e11			−0.853382
$156$	−5.72090e11	+	9.90889e11i	−0.495769	+	0.858697i
$157$	−4.66854e11	−	8.08615e11i	−0.390601	−	0.676541i	0.601928	−	0.798550i	$-0.294399\pi$
$157$	−4.66854e11	−	8.08615e11i	−0.390601	−	0.676541i	−0.992529	+	0.122010i	$0.961066\pi$
$158$	4.80616e10	+	8.32451e10i	0.0388315	+	0.0672581i
$159$	−1.26900e12	+	2.19798e12i	−0.990326	+	1.71530i
$160$	−6.31538e11			−0.476146
$161$	3.29441e11	−	3.33061e11i	0.240014	−	0.242651i
$162$	−1.94013e11			−0.136615
$163$	1.23921e12	−	2.14638e12i	0.843556	−	1.46108i	−0.0433132	−	0.999062i	$-0.513791\pi$
$163$	1.23921e12	−	2.14638e12i	0.843556	−	1.46108i	0.886869	−	0.462020i	$-0.152875\pi$
$164$	−1.20528e11	−	2.08761e11i	−0.0793317	−	0.137407i
$165$	−3.00574e11	−	5.20610e11i	−0.191333	−	0.331398i
$166$	−3.59165e10	+	6.22092e10i	−0.0221156	+	0.0383054i
$167$	−2.38715e12			−1.42213			−0.711065	−	0.703126i	$-0.751787\pi$
$167$	−2.38715e12			−1.42213			−0.711065	+	0.703126i	$0.751787\pi$
$168$	1.99481e11	+	7.28527e11i	0.115001	+	0.419995i
$169$	−1.19119e12			−0.664669
$170$	2.37769e11	−	4.11828e11i	0.128436	−	0.222457i
$171$	5.15828e11	+	8.93440e11i	0.269790	+	0.467290i
$172$	1.17349e12	+	2.03254e12i	0.594391	+	1.02952i
$173$	−2.71347e11	+	4.69988e11i	−0.133129	+	0.230586i	−0.924881	−	0.380256i	$-0.875836\pi$
$173$	−2.71347e11	+	4.69988e11i	−0.133129	+	0.230586i	0.791752	+	0.610842i	$0.209169\pi$
$174$	1.77486e11			0.0843612
$175$	3.74055e11	+	1.36609e12i	0.172277	+	0.629174i
$176$	3.65113e11			0.162970
$177$	−2.20739e12	+	3.82331e12i	−0.955049	+	1.65419i
$178$	−1.72459e11	−	2.98708e11i	−0.0723396	−	0.125296i
$179$	−1.65743e12	−	2.87075e12i	−0.674128	−	1.16762i	−0.976723	−	0.214505i	$-0.931186\pi$
$179$	−1.65743e12	−	2.87075e12i	−0.674128	−	1.16762i	0.302594	−	0.953119i	$-0.402147\pi$
$180$	3.25087e12	−	5.63067e12i	1.28233	−	2.22106i
$181$	−7.57463e11			−0.289821			−0.144910	−	0.989445i	$-0.546289\pi$
$181$	−7.57463e11			−0.289821			−0.144910	+	0.989445i	$0.546289\pi$
$182$	1.38380e11	−	1.39901e11i	0.0513666	−	0.0519310i
$183$	7.78952e12			2.80562
$184$	−1.22183e11	+	2.11627e11i	−0.0427083	+	0.0739730i
$185$	−1.39084e12	−	2.40900e12i	−0.471880	−	0.817320i
$186$	−2.21191e11	−	3.83115e11i	−0.0728529	−	0.126185i
$187$	−4.23794e11	+	7.34033e11i	−0.135527	+	0.234740i
$188$	5.03879e11			0.156480
$189$	−5.73330e12	−	1.50271e12i	−1.72928	−	0.453247i
$190$	1.47281e11			0.0431521
$191$	2.41197e12	−	4.17765e12i	0.686575	−	1.18918i	−0.286364	−	0.958121i	$-0.592447\pi$
$191$	2.41197e12	−	4.17765e12i	0.686575	−	1.18918i	0.972939	−	0.231062i	$-0.0742199\pi$
$192$	2.84902e12	+	4.93465e12i	0.788022	+	1.36489i
$193$	3.50989e11	+	6.07931e11i	0.0943471	+	0.163414i	0.909336	−	0.416063i	$-0.136590\pi$
$193$	3.50989e11	+	6.07931e11i	0.0943471	+	0.163414i	−0.814989	+	0.579477i	$0.803257\pi$
$194$	−3.97166e11	+	6.87911e11i	−0.103768	+	0.179731i
$195$	−5.09934e12			−1.29516
$196$	4.35469e10	+	3.98490e12i	0.0107535	+	0.984031i
$197$	3.47030e12			0.833302			0.416651	−	0.909066i	$-0.363204\pi$
$197$	3.47030e12			0.833302			0.416651	+	0.909066i	$0.363204\pi$
$198$	9.36815e10	−	1.62261e11i	0.0218774	−	0.0378927i
$199$	1.44819e12	+	2.50834e12i	0.328953	+	0.569764i	0.982304	−	0.187291i	$-0.0599708\pi$
$199$	1.44819e12	+	2.50834e12i	0.328953	+	0.569764i	−0.653351	+	0.757055i	$0.726637\pi$
$200$	−3.69412e11	−	6.39840e11i	−0.0816292	−	0.141386i
$201$	−8.08771e11	+	1.40083e12i	−0.173879	+	0.301167i
$202$	8.30150e11			0.173670
$203$	1.82626e12	+	4.78665e11i	0.371821	+	0.0974548i
$204$	−1.36887e13			−2.71266
$205$	5.37165e11	−	9.30397e11i	0.103624	−	0.179482i
$206$	5.43639e11	+	9.41611e11i	0.102104	+	0.176849i
$207$	−1.89187e12	−	3.27681e12i	−0.345982	−	0.599259i
$208$	1.54857e12	−	2.68220e12i	0.275792	−	0.477686i
$209$	−2.62511e11			−0.0455347
$210$	−1.17418e12	+	1.18709e12i	−0.198395	+	0.200575i
$211$	−2.99203e10			−0.00492508			−0.00246254	−	0.999997i	$-0.500784\pi$
$211$	−2.99203e10			−0.00492508			−0.00246254	+	0.999997i	$0.500784\pi$
$212$	3.49239e12	−	6.04899e12i	0.560113	−	0.970143i
$213$	4.91104e12	+	8.50617e12i	0.767513	+	1.32937i
$214$	−1.70117e11	−	2.94651e11i	−0.0259102	−	0.0448778i
$215$	−5.22996e12	+	9.05855e12i	−0.776402	+	1.34477i
$216$	3.09167e12			0.447402
$217$	−1.24274e12	−	4.53863e12i	−0.175328	−	0.640318i
$218$	−8.43373e11			−0.116014
$219$	5.87687e12	−	1.01790e13i	0.788322	−	1.36541i
$220$	8.27202e11	+	1.43276e12i	0.108215	+	0.187434i
$221$	3.59491e12	+	6.22656e12i	0.458701	+	0.794494i
$222$	6.47301e11	−	1.12116e12i	0.0805684	−	0.139549i
$223$	−2.52256e12			−0.306312			−0.153156	−	0.988202i	$-0.548944\pi$
$223$	−2.52256e12			−0.306312			−0.153156	+	0.988202i	$0.548944\pi$
$224$	−8.25680e11	−	3.01548e12i	−0.0978245	−	0.357266i
$225$	1.14399e13			1.32256
$226$	−6.03163e11	+	1.04471e12i	−0.0680516	+	0.117869i
$227$	−6.08276e12	−	1.05356e13i	−0.669820	−	1.16016i	−0.977954	−	0.208820i	$-0.933038\pi$
$227$	−6.08276e12	−	1.05356e13i	−0.669820	−	1.16016i	0.308134	−	0.951343i	$-0.400296\pi$
$228$	−2.11979e12	−	3.67158e12i	−0.227851	−	0.394649i
$229$	2.17759e12	−	3.77170e12i	0.228497	−	0.395769i	−0.728866	−	0.684657i	$-0.759952\pi$
$229$	2.17759e12	−	3.77170e12i	0.228497	−	0.395769i	0.957363	+	0.288888i	$0.0932854\pi$
$230$	−5.40173e11			−0.0553388
$231$	2.09284e12	−	2.11584e12i	0.209349	−	0.211649i
$232$	−9.84806e11			−0.0961981
$233$	−8.54463e12	+	1.47997e13i	−0.815147	+	1.41188i	0.0940755	+	0.995565i	$0.470010\pi$
$233$	−8.54463e12	+	1.47997e13i	−0.815147	+	1.41188i	−0.909222	+	0.416311i	$0.863323\pi$
$234$	−7.94669e11	−	1.37641e12i	−0.0740455	−	0.128251i
$235$	1.12283e12	+	1.94481e12i	0.102198	+	0.177012i
$236$	6.07489e12	−	1.05220e13i	0.540160	−	0.935585i
$237$	1.23317e13			1.07129
$238$	2.27726e12	+	5.96875e11i	0.193304	+	0.0506652i
$239$	−3.04856e11			−0.0252876			−0.0126438	−	0.999920i	$-0.504025\pi$
$239$	−3.04856e11			−0.0252876			−0.0126438	+	0.999920i	$0.504025\pi$
$240$	−1.31399e13	+	2.27590e13i	−1.06520	+	1.84498i
$241$	−8.33995e11	−	1.44452e12i	−0.0660800	−	0.114454i	0.831093	−	0.556134i	$-0.187716\pi$
$241$	−8.33995e11	−	1.44452e12i	−0.0660800	−	0.114454i	−0.897173	+	0.441680i	$0.854383\pi$
$242$	−7.90490e11	−	1.36917e12i	−0.0612226	−	0.106041i
$243$	−6.39156e11	+	1.10705e12i	−0.0483919	+	0.0838172i
$244$	−2.14373e13			−1.58682
$245$	−1.52833e13	+	9.04794e12i	−1.10613	+	0.654842i
$246$	4.99997e11			0.0353854
$247$	−1.11339e12	+	1.92846e12i	−0.0770577	+	0.133468i
$248$	1.22731e12	+	2.12577e12i	0.0830751	+	0.143890i
$249$	4.60775e12	+	7.98085e12i	0.305065	+	0.528388i
$250$	−4.35207e11	+	7.53801e11i	−0.0281855	+	0.0488187i
$251$	1.29045e13			0.817590			0.408795	−	0.912626i	$-0.365949\pi$
$251$	1.29045e13			0.817590			0.408795	+	0.912626i	$0.365949\pi$
$252$	3.11356e13	+	8.16069e12i	1.92999	+	0.505853i
$253$	9.62793e11			0.0583943
$254$	1.00395e12	−	1.73888e12i	0.0595833	−	0.103201i
$255$	−3.05035e13	−	5.28337e13i	−1.77166	−	3.06860i
$256$	−7.42973e12	−	1.28687e13i	−0.422331	−	0.731499i
$257$	−1.15462e13	+	1.99986e13i	−0.642402	+	1.11267i	0.342493	+	0.939520i	$0.388729\pi$
$257$	−1.15462e13	+	1.99986e13i	−0.642402	+	1.11267i	−0.984895	+	0.173152i	$0.944605\pi$
$258$	−4.86809e12			−0.265124
$259$	9.68413e12	−	9.79053e12i	0.516311	−	0.521985i
$260$	1.40338e13			0.732522
$261$	7.62431e12	−	1.32057e13i	0.389653	−	0.674899i
$262$	−1.22905e11	−	2.12878e11i	−0.00615053	−	0.0106530i
$263$	1.41565e13	+	2.45199e13i	0.693746	+	1.20160i	0.970601	+	0.240692i	$0.0773744\pi$
$263$	1.41565e13	+	2.45199e13i	0.693746	+	1.20160i	−0.276855	+	0.960912i	$0.589292\pi$
$264$	−7.76191e11	+	1.34440e12i	−0.0372518	+	0.0645219i
$265$	3.11295e13			1.46325
$266$	1.92557e11	+	7.03240e11i	0.00886564	+	0.0323783i
$267$	−4.42497e13			−1.99572
$268$	2.22580e12	−	3.85519e12i	0.0983432	−	0.170335i
$269$	1.38564e13	+	2.39999e13i	0.599807	+	1.03890i	0.992849	+	0.119376i	$0.0380894\pi$
$269$	1.38564e13	+	2.39999e13i	0.599807	+	1.03890i	−0.393042	+	0.919521i	$0.628577\pi$
$270$	3.41709e12	+	5.91857e12i	0.144929	+	0.251025i
$271$	2.41659e12	−	4.18566e12i	0.100432	−	0.173954i	−0.811431	−	0.584449i	$-0.801311\pi$
$271$	2.41659e12	−	4.18566e12i	0.100432	−	0.173954i	0.911863	+	0.410495i	$0.134644\pi$
$272$	3.70533e13			1.50903
$273$	−6.66693e12	−	2.43484e13i	−0.266092	−	0.971797i
$274$	5.62045e12			0.219858
$275$	−1.45547e12	+	2.52095e12i	−0.0558050	+	0.0966572i
$276$	7.77461e12	+	1.34660e13i	0.292199	+	0.506103i
$277$	−1.89204e13	−	3.27711e13i	−0.697094	−	1.20740i	−0.969470	−	0.245211i	$-0.921143\pi$
$277$	−1.89204e13	−	3.27711e13i	−0.697094	−	1.20740i	0.272376	−	0.962191i	$-0.412191\pi$
$278$	−2.08863e11	+	3.61762e11i	−0.00754424	+	0.0130670i
$279$	−3.80071e13			−1.34599
$280$	6.51513e12	−	6.58671e12i	0.226232	−	0.228718i
$281$	−3.89411e13			−1.32594			−0.662969	−	0.748647i	$-0.730704\pi$
$281$	−3.89411e13			−1.32594			−0.662969	+	0.748647i	$0.730704\pi$
$282$	−5.22572e11	+	9.05120e11i	−0.0174492	+	0.0302229i
$283$	1.01150e13	+	1.75197e13i	0.331238	+	0.573722i	0.982755	−	0.184913i	$-0.0592002\pi$
$283$	1.01150e13	+	1.75197e13i	0.331238	+	0.573722i	−0.651516	+	0.758634i	$0.725867\pi$
$284$	−1.35156e13	−	2.34096e13i	−0.434093	−	0.751871i
$285$	9.44739e12	−	1.63634e13i	0.297622	−	0.515497i
$286$	4.04416e11			0.0124973
$287$	5.14477e12	+	1.34845e12i	0.155961	+	0.0408776i
$288$	−2.52521e13			−0.750997
$289$	−2.58725e13	+	4.48125e13i	−0.754919	+	1.30756i
$290$	−1.08846e12	−	1.88527e12i	−0.0311619	−	0.0539740i
$291$	5.09526e13	+	8.82525e13i	1.43138	+	2.47922i
$292$	−1.61736e13	+	2.80135e13i	−0.445862	+	0.772256i
$293$	1.09986e13			0.297554			0.148777	−	0.988871i	$-0.452466\pi$
$293$	1.09986e13			0.297554			0.148777	+	0.988871i	$0.452466\pi$
$294$	−7.20325e12	−	4.05450e12i	−0.191257	−	0.107653i
$295$	5.41487e13			1.41113
$296$	−3.59164e12	+	6.22090e12i	−0.0918731	+	0.159129i
$297$	−6.09055e12	−	1.05491e13i	−0.152931	−	0.264884i
$298$	−1.26542e12	−	2.19177e12i	−0.0311922	−	0.0540264i
$299$	4.08353e12	−	7.07287e12i	0.0988197	−	0.171161i
$300$	−4.70120e13			−1.11697
$301$	−5.00906e13	−	1.31288e13i	−1.16853	−	0.306274i
$302$	7.28886e12			0.166963
$303$	5.32502e13	−	9.22321e13i	1.19781	−	2.07466i
$304$	5.73797e12	+	9.93845e12i	0.126752	+	0.219540i
$305$	−4.77705e13	−	8.27410e13i	−1.03636	−	1.79503i
$306$	9.50719e12	−	1.64669e13i	0.202574	−	0.350869i
$307$	−1.77123e13			−0.370692			−0.185346	−	0.982673i	$-0.559341\pi$
$307$	−1.77123e13			−0.370692			−0.185346	+	0.982673i	$0.559341\pi$
$308$	−5.75965e12	+	5.82293e12i	−0.118404	+	0.119705i
$309$	1.39488e14			2.81685
$310$	−2.71299e12	+	4.69903e12i	−0.0538218	+	0.0932221i
$311$	−7.97859e12	−	1.38193e13i	−0.155505	−	0.269342i	0.777738	−	0.628589i	$-0.216367\pi$
$311$	−7.97859e12	−	1.38193e13i	−0.155505	−	0.269342i	−0.933243	+	0.359246i	$0.883034\pi$
$312$	6.58417e12	+	1.14041e13i	0.126081	+	0.218379i
$313$	1.52684e13	−	2.64456e13i	0.287276	−	0.497577i	−0.685882	−	0.727712i	$-0.740584\pi$
$313$	1.52684e13	−	2.64456e13i	0.287276	−	0.497577i	0.973159	+	0.230136i	$0.0739169\pi$
$314$	−5.32992e12			−0.0985389
$315$	3.78844e13	+	1.38358e14i	0.688260	+	2.51360i
$316$	−3.39377e13			−0.605904
$317$	−1.70577e13	+	2.95449e13i	−0.299292	+	0.518390i	−0.975974	−	0.217886i	$-0.930084\pi$
$317$	−1.70577e13	+	2.95449e13i	−0.299292	+	0.518390i	0.676682	+	0.736276i	$0.263417\pi$
$318$	7.24389e12	+	1.25468e13i	0.124917	+	0.216363i
$319$	1.94005e12	+	3.36027e12i	0.0328825	+	0.0569541i
$320$	3.49442e13	−	6.05251e13i	0.582170	−	1.00835i
$321$	−4.36487e13			−0.714816
$322$	−7.06228e11	−	2.57923e12i	−0.0113694	−	0.0415224i
$323$	−2.66407e13			−0.421630
$324$	3.42495e13	−	5.93219e13i	0.532914	−	0.923034i
$325$	1.23463e13	+	2.13844e13i	0.188876	+	0.327143i
$326$	−7.07384e12	−	1.22523e13i	−0.106404	−	0.184297i
$327$	−5.40984e13	+	9.37012e13i	−0.800151	+	1.38590i
$328$	−2.77431e12			−0.0403504
$329$	−7.81808e12	+	7.90398e12i	−0.111821	+	0.113049i
$330$	−3.43156e12			−0.0482686
$331$	1.39115e13	−	2.40955e13i	0.192451	−	0.333335i	−0.753611	−	0.657321i	$-0.771690\pi$
$331$	1.39115e13	−	2.40955e13i	0.192451	−	0.333335i	0.946062	+	0.323986i	$0.105023\pi$
$332$	−1.26809e13	−	2.19639e13i	−0.172540	−	0.298848i
$333$	−5.56126e13	−	9.63238e13i	−0.744269	−	1.28911i
$334$	−6.81333e12	+	1.18010e13i	−0.0896920	+	0.155351i
$335$	1.98397e13			0.256914
$336$	−1.25849e14	−	3.29853e13i	−1.60319	−	0.420198i
$337$	8.74273e12			0.109568			0.0547839	−	0.998498i	$-0.482553\pi$
$337$	8.74273e12			0.109568			0.0547839	+	0.998498i	$0.482553\pi$
$338$	−3.39986e12	+	5.88874e12i	−0.0419199	+	0.0726073i
$339$	7.73801e13	+	1.34026e14i	0.938709	+	1.62589i
$340$	8.39480e13	+	1.45402e14i	1.00202	+	1.73555i
$341$	4.83557e12	−	8.37545e12i	0.0567935	−	0.0983692i
$342$	5.88904e12			0.0680614
$343$	−6.31838e13	−	6.11457e13i	−0.718602	−	0.695422i
$344$	2.70113e13			0.302325
$345$	−3.46496e13	+	6.00148e13i	−0.381674	+	0.661079i
$346$	1.54894e12	+	2.68285e12i	0.0167926	+	0.0290856i
$347$	−5.57163e13	−	9.65034e13i	−0.594525	−	1.02975i	−0.993614	−	0.112835i	$-0.964007\pi$
$347$	−5.57163e13	−	9.65034e13i	−0.594525	−	1.02975i	0.399089	−	0.916912i	$-0.369326\pi$
$348$	−3.13320e13	+	5.42687e13i	−0.329081	+	0.569985i
$349$	2.49619e13			0.258070			0.129035	−	0.991640i	$-0.458812\pi$
$349$	2.49619e13			0.258070			0.129035	+	0.991640i	$0.458812\pi$
$350$	7.82098e12	+	2.04989e12i	0.0795952	+	0.0208620i
$351$	−1.03328e14			−1.03521
$352$	3.21277e12	−	5.56467e12i	0.0316880	−	0.0548852i
$353$	4.46527e13	+	7.73407e13i	0.433597	+	0.751012i	0.997180	−	0.0750472i	$-0.0239107\pi$
$353$	4.46527e13	+	7.73407e13i	0.433597	+	0.751012i	−0.563583	+	0.826060i	$0.690577\pi$
$354$	1.26005e13	+	2.18247e13i	0.120468	+	0.208656i
$355$	6.02356e13	−	1.04331e14i	0.567019	−	0.982105i
$356$	1.21779e14			1.12874
$357$	2.12390e14	−	2.14724e14i	1.93847	−	1.95977i
$358$	−1.89223e13			−0.170066
$359$	8.39570e13	−	1.45418e14i	0.743083	−	1.28706i	−0.208002	−	0.978128i	$-0.566696\pi$
$359$	8.39570e13	−	1.45418e14i	0.743083	−	1.28706i	0.951085	−	0.308929i	$-0.0999707\pi$
$360$	−3.74141e13	−	6.48032e13i	−0.326116	−	0.564849i
$361$	5.41196e13	+	9.37379e13i	0.464585	+	0.804685i
$362$	−2.16193e12	+	3.74457e12i	−0.0182786	+	0.0316595i
$363$	−2.02825e14			−1.68902
$364$	1.83479e13	+	6.70086e13i	0.150497	+	0.549633i
$365$	−1.44164e14			−1.16478
$366$	2.22326e13	−	3.85080e13i	0.176947	−	0.306482i
$367$	−1.03952e13	−	1.80050e13i	−0.0815021	−	0.141166i	0.822393	−	0.568919i	$-0.192638\pi$
$367$	−1.03952e13	−	1.80050e13i	−0.0815021	−	0.141166i	−0.903895	+	0.427754i	$0.859305\pi$
$368$	−2.10448e13	−	3.64506e13i	−0.162548	−	0.281541i
$369$	2.14785e13	−	3.72019e13i	0.163440	−	0.283087i
$370$	−1.58787e13			−0.119044
$371$	4.06990e13	+	1.48637e14i	0.300627	+	1.09792i
$372$	1.56190e14			1.13675
$373$	−6.86233e13	+	1.18859e14i	−0.492122	+	0.852381i	−0.999959	−	0.00907250i	$-0.997112\pi$
$373$	−6.86233e13	+	1.18859e14i	−0.492122	+	0.852381i	0.507836	+	0.861454i	$0.330445\pi$
$374$	2.41916e12	+	4.19011e12i	0.0170951	+	0.0296095i
$375$	5.58330e13	+	9.67056e13i	0.388793	+	0.673410i
$376$	2.89956e12	−	5.02219e12i	0.0198975	−	0.0344635i
$377$	3.29136e13			0.222586
$378$	−2.37925e13	+	2.40540e13i	−0.158575	+	0.160318i
$379$	−5.43469e12			−0.0356992			−0.0178496	−	0.999841i	$-0.505682\pi$
$379$	−5.43469e12			−0.0356992			−0.0178496	+	0.999841i	$0.505682\pi$
$380$	−2.59999e13	+	4.50332e13i	−0.168330	+	0.291557i
$381$	−1.28797e14	−	2.23082e14i	−0.821897	−	1.42357i
$382$	−1.37683e13	−	2.38474e13i	−0.0866029	−	0.150001i
$383$	−1.10671e14	+	1.91687e14i	−0.686183	+	1.18850i	0.286881	+	0.957966i	$0.407382\pi$
$383$	−1.10671e14	+	1.91687e14i	−0.686183	+	1.18850i	−0.973063	+	0.230537i	$0.925952\pi$
$384$	1.37977e14			0.843307
$385$	−3.53093e13	−	9.25462e12i	−0.212743	−	0.0557603i
$386$	4.00713e12			0.0238014
$387$	−2.09120e14	+	3.62206e14i	−1.22457	+	2.12102i
$388$	−1.40225e14	−	2.42877e14i	−0.809565	−	1.40221i
$389$	−5.67324e13	−	9.82634e13i	−0.322930	−	0.559331i	0.658161	−	0.752877i	$-0.271334\pi$
$389$	−5.67324e13	−	9.82634e13i	−0.322930	−	0.559331i	−0.981091	+	0.193546i	$0.938001\pi$
$390$	−1.45544e13	+	2.52089e13i	−0.0816842	+	0.141481i
$391$	9.77083e13			0.540704
$392$	3.99683e13	+	2.24970e13i	0.218093	+	0.122758i
$393$	−3.15351e13			−0.169682
$394$	9.90481e12	−	1.71556e13i	0.0525554	−	0.0910286i
$395$	−7.56262e13	−	1.30988e14i	−0.395720	−	0.685407i
$396$	3.30757e13	+	5.72887e13i	0.170681	+	0.295628i
$397$	6.27094e13	−	1.08616e14i	0.319143	−	0.552771i	−0.661167	−	0.750239i	$-0.729938\pi$
$397$	6.27094e13	−	1.08616e14i	0.319143	−	0.552771i	0.980309	+	0.197468i	$0.0632718\pi$
$398$	1.65335e13			0.0829868
$399$	9.04836e13	+	2.37159e13i	0.447939	+	0.117406i
$400$	1.27255e14			0.621362
$401$	2.01310e13	−	3.48679e13i	0.0969552	−	0.167931i	−0.813468	−	0.581610i	$-0.802423\pi$
$401$	2.01310e13	−	3.48679e13i	0.0969552	−	0.167931i	0.910423	+	0.413679i	$0.135756\pi$
$402$	4.61674e12	+	7.99642e12i	0.0219327	+	0.0379885i
$403$	−4.10185e13	−	7.10461e13i	−0.192222	−	0.332937i
$404$	−1.46548e14	+	2.53829e14i	−0.677460	+	1.17340i
$405$	3.05284e14			1.39220
$406$	7.57875e12	−	7.66202e12i	0.0340961	−	0.0344707i
$407$	2.83019e13			0.125616
$408$	−7.87711e13	+	1.36436e14i	−0.344934	+	0.597443i
$409$	9.79564e13	+	1.69665e14i	0.423209	+	0.733019i	0.996251	−	0.0865068i	$-0.0275704\pi$
$409$	9.79564e13	+	1.69665e14i	0.423209	+	0.733019i	−0.573043	+	0.819525i	$0.694237\pi$
$410$	−3.06632e12	−	5.31102e12i	−0.0130709	−	0.0226395i
$411$	3.60525e14	−	6.24448e14i	1.51637	−	2.62643i
$412$	−3.83880e14			−1.59317
$413$	7.07945e13	+	2.58550e14i	0.289918	+	1.05881i
$414$	−2.15988e13			−0.0872827
$415$	5.65156e13	−	9.78878e13i	0.225374	−	0.390359i
$416$	−2.72528e13	−	4.72033e13i	−0.107250	−	0.185763i
$417$	2.67952e13	+	4.64106e13i	0.104066	+	0.180247i
$418$	−7.49250e11	+	1.29774e12i	−0.00287182	+	0.00497414i
$419$	3.11107e14			1.17688			0.588441	−	0.808541i	$-0.299742\pi$
$419$	3.11107e14			1.17688			0.588441	+	0.808541i	$0.299742\pi$
$420$	−1.55686e14	−	5.68582e14i	−0.581269	−	2.12286i
$421$	−3.15409e14			−1.16231			−0.581155	−	0.813793i	$-0.697399\pi$
$421$	−3.15409e14			−1.16231			−0.581155	+	0.813793i	$0.697399\pi$
$422$	−8.53977e10	+	1.47913e11i	−0.000310619	+	0.000538008i
$423$	4.48965e13	+	7.77631e13i	0.161191	+	0.279191i
$424$	−4.01938e13	−	6.96177e13i	−0.142445	−	0.246722i
$425$	−1.47707e14	+	2.55836e14i	−0.516729	+	0.895001i
$426$	5.60678e13			0.193625
$427$	3.32617e14	−	3.36272e14i	1.13394	−	1.14640i
$428$	1.20125e14			0.404288
$429$	2.59414e13	−	4.49318e13i	0.0861942	−	0.149293i
$430$	2.98544e13	+	5.17093e13i	0.0979335	+	0.169626i
$431$	2.45551e14	+	4.25307e14i	0.795274	+	1.37746i	0.922665	+	0.385603i	$0.126006\pi$
$431$	2.45551e14	+	4.25307e14i	0.795274	+	1.37746i	−0.127391	+	0.991853i	$0.540660\pi$
$432$	−2.66255e14	+	4.61167e14i	−0.851406	+	1.47468i
$433$	−4.66688e14			−1.47348			−0.736739	−	0.676178i	$-0.763635\pi$
$433$	−4.66688e14			−1.47348			−0.736739	+	0.676178i	$0.763635\pi$
$434$	−2.59840e13	−	6.81044e12i	−0.0810050	−	0.0212316i
$435$	−2.79279e14			−0.859700
$436$	1.48883e14	−	2.57873e14i	0.452552	−	0.783844i
$437$	1.51309e13	+	2.62074e13i	0.0454167	+	0.0786640i
$438$	−3.35472e13	−	5.81054e13i	−0.0994370	−	0.172230i
$439$	−1.39073e14	+	2.40882e14i	−0.407088	+	0.705098i	−0.994562	−	0.104145i	$-0.966789\pi$
$439$	−1.39073e14	+	2.40882e14i	−0.407088	+	0.705098i	0.587474	+	0.809243i	$0.300123\pi$
$440$	1.90405e13			0.0550412
$441$	−6.11104e14	+	3.61782e14i	−1.74463	+	1.03284i
$442$	4.10419e13			0.115719
$443$	2.19620e14	−	3.80393e14i	0.611578	−	1.05928i	−0.379397	−	0.925234i	$-0.623869\pi$
$443$	2.19620e14	−	3.80393e14i	0.611578	−	1.05928i	0.990975	−	0.134049i	$-0.0427981\pi$
$444$	2.28539e14	+	3.95842e14i	0.628571	+	1.08872i
$445$	2.71369e14	+	4.70025e14i	0.737191	+	1.27685i
$446$	−7.19980e12	+	1.24704e13i	−0.0193187	+	0.0334611i
$447$	−3.24683e14			−0.860535
$448$	3.34682e14	+	8.77208e13i	0.876201	+	0.229654i
$449$	−8.42239e13			−0.217811			−0.108906	−	0.994052i	$-0.534735\pi$
$449$	−8.42239e13			−0.217811			−0.108906	+	0.994052i	$0.534735\pi$
$450$	3.26513e13	−	5.65537e13i	0.0834126	−	0.144475i
$451$	5.46534e12	+	9.46624e12i	0.0137926	+	0.0238895i
$452$	−2.12956e14	−	3.68850e14i	−0.530919	−	0.919578i
$453$	4.67546e14	−	8.09813e14i	1.15155	−	1.99455i
$454$	−6.94449e13			−0.168979
$455$	−2.17745e14	+	2.20137e14i	−0.523462	+	0.529214i
$456$	−4.87931e13			−0.115892
$457$	−9.06110e13	+	1.56943e14i	−0.212638	+	0.368300i	−0.952539	−	0.304415i	$-0.901539\pi$
$457$	−9.06110e13	+	1.56943e14i	−0.212638	+	0.368300i	0.739901	+	0.672716i	$0.234872\pi$
$458$	−1.24304e13	−	2.15301e13i	−0.0288221	−	0.0499214i
$459$	−6.18094e14	−	1.07057e15i	−1.41607	−	2.45271i
$460$	9.53582e13	−	1.65165e14i	0.215869	−	0.373896i
$461$	2.32317e14			0.519668			0.259834	−	0.965653i	$-0.416332\pi$
$461$	2.32317e14			0.519668			0.259834	+	0.965653i	$0.416332\pi$
$462$	−4.48645e12	−	1.63850e13i	−0.00991681	−	0.0362173i
$463$	4.85865e14			1.06126			0.530628	−	0.847605i	$-0.321956\pi$
$463$	4.85865e14			1.06126			0.530628	+	0.847605i	$0.321956\pi$
$464$	8.48114e13	−	1.46898e14i	0.183065	−	0.317078i
$465$	3.48051e14	+	6.02841e14i	0.742423	+	1.28591i
$466$	4.87756e13	+	8.44819e13i	0.102821	+	0.178091i
$467$	−4.71057e13	+	8.15895e13i	−0.0981365	+	0.169977i	−0.910913	−	0.412598i	$-0.864622\pi$
$467$	−4.71057e13	+	8.15895e13i	−0.0981365	+	0.169977i	0.812777	+	0.582575i	$0.197955\pi$
$468$	5.61140e14			1.15536
$469$	2.59386e13	+	9.47308e13i	0.0527832	+	0.192771i
$470$	1.28190e13			0.0257820
$471$	−3.41889e14	+	5.92170e14i	−0.679627	+	1.17715i
$472$	−6.99157e13	−	1.21098e14i	−0.137371	−	0.237933i
$473$	−5.32118e13	−	9.21655e13i	−0.103341	−	0.178991i
$474$	3.51967e13	−	6.09625e13i	0.0675649	−	0.117026i
$475$	−9.14942e13			−0.173612
$476$	−5.84514e14	+	5.90936e14i	−1.09637	+	1.10841i
$477$	1.24471e15			2.30790
$478$	−8.70111e11	+	1.50708e12i	−0.00159486	+	0.00276237i
$479$	−3.21363e14	−	5.56617e14i	−0.582305	−	1.00858i	−0.995205	−	0.0978061i	$-0.968817\pi$
$479$	−3.21363e14	−	5.56617e14i	−0.582305	−	1.00858i	0.412900	−	0.910776i	$-0.364516\pi$
$480$	2.31246e14	+	4.00530e14i	0.414235	+	0.717477i
$481$	1.20038e14	−	2.07911e14i	0.212579	−	0.368197i
$482$	−9.52145e12			−0.0166703
$483$	−3.31861e14	−	8.69813e13i	−0.574443	−	0.150562i
$484$	5.58189e14			0.955282
$485$	6.24951e14	−	1.08245e15i	1.05747	−	1.83158i
$486$	3.64852e12	+	6.31942e12i	0.00610404	+	0.0105725i
$487$	−4.11872e14	−	7.13383e14i	−0.681323	−	1.18009i	−0.974577	−	0.224051i	$-0.928072\pi$
$487$	−4.11872e14	−	7.13383e14i	−0.681323	−	1.18009i	0.293255	−	0.956034i	$-0.405262\pi$
$488$	−1.23361e14	+	2.13667e14i	−0.201775	+	0.349485i
$489$	−1.81501e15			−2.93550
$490$	1.10786e12	+	1.01379e14i	0.00177177	+	0.162132i
$491$	−7.05003e14			−1.11492			−0.557459	−	0.830204i	$-0.688224\pi$
$491$	−7.05003e14			−1.11492			−0.557459	+	0.830204i	$0.688224\pi$
$492$	−8.82658e13	+	1.52881e14i	−0.138033	+	0.239081i
$493$	1.96885e14	+	3.41014e14i	0.304476	+	0.527369i
$494$	6.35563e12	+	1.10083e13i	0.00971987	+	0.0168353i
$495$	−1.47410e14	+	2.55322e14i	−0.222946	+	0.386154i
$496$	−4.22784e14			−0.632367
$497$	5.76914e14	+	1.51210e14i	0.853397	+	0.223677i
$498$	5.26051e13			0.0769603
$499$	−4.11492e14	+	7.12725e14i	−0.595399	+	1.03126i	0.398091	+	0.917346i	$0.369673\pi$
$499$	−4.11492e14	+	7.12725e14i	−0.595399	+	1.03126i	−0.993490	+	0.113916i	$0.963661\pi$
$500$	−1.53657e14	−	2.66141e14i	−0.219895	−	0.380870i
$501$	8.74086e14	+	1.51396e15i	1.23722	+	2.14293i
$502$	3.68316e13	−	6.37942e13i	0.0515644	−	0.0893122i
$503$	1.18063e15			1.63489			0.817445	−	0.576007i	$-0.195390\pi$
$503$	1.18063e15			1.63489			0.817445	+	0.576007i	$0.195390\pi$
$504$	2.60507e14	−	2.63370e14i	0.356822	−	0.360743i
$505$	−1.30626e15			−1.76982
$506$	2.74797e12	−	4.75963e12i	0.00368286	−	0.00637889i
$507$	4.36171e14	+	7.55470e14i	0.578246	+	1.00155i
$508$	3.54458e14	+	6.13939e14i	0.464852	+	0.805147i
$509$	−3.07502e14	+	5.32609e14i	−0.398933	+	0.690972i	−0.993595	−	0.113004i	$-0.963953\pi$
$509$	−3.07502e14	+	5.32609e14i	−0.398933	+	0.690972i	0.594661	+	0.803976i	$0.297286\pi$
$510$	−3.48249e14			−0.446945
$511$	−1.88481e14	−	6.88354e14i	−0.239305	−	0.873971i
$512$	−4.70686e14			−0.591216
$513$	1.91433e14	−	3.31571e14i	0.237887	−	0.412033i
$514$	6.59096e13	+	1.14159e14i	0.0810310	+	0.140350i
$515$	−8.55431e14	−	1.48165e15i	−1.04051	−	1.80221i
$516$	8.59376e14	−	1.48848e15i	1.03421	−	1.79131i
$517$	−2.28484e13			−0.0272055
$518$	−2.07600e13	−	7.58179e13i	−0.0244576	−	0.0893220i
$519$	3.97430e14			0.463276
$520$	8.07570e13	−	1.39875e14i	0.0931455	−	0.161333i
$521$	−1.98750e14	−	3.44245e14i	−0.226830	−	0.392880i	0.730037	−	0.683407i	$-0.239503\pi$
$521$	−1.98750e14	−	3.44245e14i	−0.226830	−	0.392880i	−0.956867	+	0.290527i	$0.906169\pi$
$522$	−4.35221e13	−	7.53826e13i	−0.0491499	−	0.0851301i
$523$	−4.29122e14	+	7.43262e14i	−0.479537	+	0.830582i	−0.999725	−	0.0234698i	$-0.992529\pi$
$523$	−4.29122e14	+	7.43262e14i	−0.479537	+	0.830582i	0.520188	+	0.854052i	$0.325862\pi$
$524$	8.67869e13			0.0959693
$525$	7.29428e14	−	7.37443e14i	0.798190	−	0.806961i
$526$	1.61621e14			0.175015
$527$	4.90734e14	−	8.49976e14i	0.525881	−	0.910853i
$528$	−1.33691e14	−	2.31560e14i	−0.141780	−	0.245571i
$529$	4.20910e14	+	7.29038e14i	0.441757	+	0.765146i
$530$	8.88488e13	−	1.53891e14i	0.0922857	−	0.159843i
$531$	2.16514e15			2.22569
$532$	−2.49018e14	−	6.52679e13i	−0.253347	−	0.0664027i
$533$	9.27213e13			0.0933640
$534$	−1.26296e14	+	2.18751e14i	−0.125867	+	0.218009i
$535$	2.67683e14	+	4.63641e14i	0.264044	+	0.457337i
$536$	−2.56166e13	−	4.43693e13i	−0.0250101	−	0.0433188i
$537$	−1.21378e15	+	2.10232e15i	−1.17295	+	2.03161i
$538$	1.58194e14			0.151316
$539$	−1.97463e12	−	1.80695e14i	−0.00186960	−	0.171083i
$540$	−2.41291e15			−2.26139
$541$	−3.29697e13	+	5.71052e13i	−0.0305865	+	0.0529774i	−0.880913	−	0.473277i	$-0.843071\pi$
$541$	−3.29697e13	+	5.71052e13i	−0.0305865	+	0.0529774i	0.850327	+	0.526255i	$0.176404\pi$
$542$	−1.37947e13	−	2.38932e13i	−0.0126683	−	0.0219421i
$543$	2.77355e14	+	4.80393e14i	0.252137	+	0.436714i
$544$	3.26045e14	−	5.64727e14i	0.293416	−	0.508211i
$545$	1.32707e15			1.18226
$546$	−1.39396e14	−	3.65360e13i	−0.122940	−	0.0322227i
$547$	1.54397e15			1.34805			0.674027	−	0.738706i	$-0.264563\pi$
$547$	1.54397e15			1.34805			0.674027	+	0.738706i	$0.264563\pi$
$548$	−9.92192e14	+	1.71853e15i	−0.857636	+	1.48547i
$549$	−1.91010e15	−	3.30840e15i	−1.63459	−	2.83119i
$550$	8.30831e12	+	1.43904e13i	0.00703911	+	0.0121921i
$551$	−6.09780e13	+	1.05617e14i	−0.0511493	+	0.0885932i
$552$	1.78955e14			0.148621
$553$	5.26571e14	−	5.32356e14i	0.432981	−	0.437738i
$554$	−2.16008e14			−0.175859
$555$	−1.01855e15	+	1.76417e15i	−0.821049	+	1.42210i
$556$	−7.37423e13	−	1.27725e14i	−0.0588580	−	0.101945i
$557$	−1.07657e15	−	1.86467e15i	−0.850822	−	1.47367i	−0.880468	−	0.474106i	$-0.842771\pi$
$557$	−1.07657e15	−	1.86467e15i	−0.850822	−	1.47367i	0.0296461	−	0.999560i	$-0.490562\pi$
$558$	−1.08479e14	+	1.87891e14i	−0.0848900	+	0.147034i
$559$	−9.02755e14			−0.699528
$560$	4.21419e14	+	1.53907e15i	0.323355	+	1.18093i
$561$	6.20711e14			0.471622
$562$	−1.11144e14	+	1.92508e14i	−0.0836253	+	0.144843i
$563$	7.40273e14	+	1.28219e15i	0.551564	+	0.955336i	0.998162	+	0.0606018i	$0.0193020\pi$
$563$	7.40273e14	+	1.28219e15i	0.551564	+	0.955336i	−0.446598	+	0.894735i	$0.647365\pi$
$564$	−1.84502e14	−	3.19566e14i	−0.136134	−	0.235790i
$565$	9.49094e14	−	1.64388e15i	0.693494	−	1.20117i
$566$	1.15480e14			0.0835633
$567$	3.99131e14	+	1.45767e15i	0.286028	+	1.04461i
$568$	−3.11100e14			−0.220792
$569$	−7.54590e14	+	1.30699e15i	−0.530388	+	0.918659i	0.468984	+	0.883207i	$0.344620\pi$
$569$	−7.54590e14	+	1.30699e15i	−0.530388	+	0.918659i	−0.999371	+	0.0354518i	$0.988713\pi$
$570$	−5.39289e13	−	9.34076e13i	−0.0375413	−	0.0650235i
$571$	1.11735e15	+	1.93530e15i	0.770352	+	1.33429i	0.937370	+	0.348335i	$0.113253\pi$
$571$	1.11735e15	+	1.93530e15i	0.770352	+	1.33429i	−0.167018	+	0.985954i	$0.553414\pi$
$572$	−7.13926e13	+	1.23656e14i	−0.0487501	+	0.0844376i
$573$	−3.53269e15			−2.38922
$574$	2.13502e13	−	2.15848e13i	0.0143017	−	0.0144588i
$575$	3.35567e14			0.222642
$576$	1.39724e15	−	2.42010e15i	0.918223	−	1.59041i
$577$	−1.10810e15	−	1.91928e15i	−0.721293	−	1.24932i	−0.960482	−	0.278343i	$-0.910215\pi$
$577$	−1.10810e15	−	1.91928e15i	−0.721293	−	1.24932i	0.239189	−	0.970973i	$-0.423119\pi$
$578$	1.47689e14	+	2.55805e14i	0.0952237	+	0.164932i
$579$	2.57038e14	−	4.45204e14i	0.164159	−	0.284333i
$580$	7.68596e14			0.486233
$581$	5.41285e14	+	1.41872e14i	0.339201	+	0.0889052i
$582$	5.81709e14			0.361102
$583$	−1.58362e14	+	2.74291e14i	−0.0973810	+	0.168669i
$584$	1.86141e14	+	3.22406e14i	0.113389	+	0.196396i
$585$	1.25043e15	+	2.16581e15i	0.754576	+	1.30696i
$586$	3.13919e13	−	5.43724e13i	0.0187664	−	0.0325043i
$587$	9.98055e14			0.591078			0.295539	−	0.955331i	$-0.404501\pi$
$587$	9.98055e14			0.591078			0.295539	+	0.955331i	$0.404501\pi$
$588$	2.51133e15	−	1.48674e15i	1.47342	−	0.872287i
$589$	3.03975e14			0.176687
$590$	1.54549e14	−	2.67688e14i	0.0889983	−	0.154150i
$591$	−1.27069e15	−	2.20091e15i	−0.724953	−	1.25566i
$592$	−6.18624e14	−	1.07149e15i	−0.349669	−	0.605645i
$593$	4.92960e13	−	8.53833e13i	0.0276065	−	0.0478159i	−0.851892	−	0.523717i	$-0.824545\pi$
$593$	4.92960e13	−	8.53833e13i	0.0276065	−	0.0478159i	0.879499	+	0.475902i	$0.157878\pi$
$594$	−6.95338e13			−0.0385807
$595$	−3.58334e15	−	9.39198e14i	−1.96990	−	0.516314i
$596$	8.93552e14			0.486705
$597$	1.06055e15	−	1.83692e15i	0.572363	−	0.991362i
$598$	−2.33101e13	−	4.03743e13i	−0.0124649	−	0.0215898i
$599$	−2.95594e14	−	5.11985e14i	−0.156621	−	0.271275i	0.777027	−	0.629467i	$-0.216727\pi$
$599$	−2.95594e14	−	5.11985e14i	−0.156621	−	0.271275i	−0.933648	+	0.358192i	$0.883393\pi$
$600$	−2.70530e14	+	4.68571e14i	−0.142031	+	0.246005i
$601$	7.05336e14			0.366932			0.183466	−	0.983026i	$-0.441268\pi$
$601$	7.05336e14			0.366932			0.183466	+	0.983026i	$0.441268\pi$
$602$	−2.07870e14	+	2.10154e14i	−0.107155	+	0.108332i
$603$	7.93290e14			0.405216
$604$	−1.28672e15	+	2.22867e15i	−0.651300	+	1.12808i
$605$	1.24386e15	+	2.15442e15i	0.623901	+	1.08063i
$606$	−3.03970e14	−	5.26492e14i	−0.151089	−	0.261693i
$607$	9.23697e13	−	1.59989e14i	0.0454980	−	0.0788048i	−0.842380	−	0.538885i	$-0.818846\pi$
$607$	9.23697e13	−	1.59989e14i	0.0454980	−	0.0788048i	0.887878	+	0.460080i	$0.152179\pi$
$608$	2.01962e14			0.0985825
$609$	−3.65132e14	−	1.33350e15i	−0.176626	−	0.645059i
$610$	−5.45380e14			−0.261448
$611$	−9.69075e13	+	1.67849e14i	−0.0460395	+	0.0797428i
$612$	3.35666e15	+	5.81390e15i	1.58043	+	2.73738i
$613$	−6.30271e14	−	1.09166e15i	−0.294100	−	0.509396i	0.680675	−	0.732585i	$-0.261687\pi$
$613$	−6.30271e14	−	1.09166e15i	−0.294100	−	0.509396i	−0.974775	+	0.223189i	$0.928353\pi$
$614$	−5.05539e13	+	8.75618e13i	−0.0233791	+	0.0404938i
$615$	−7.86759e14			−0.360603
$616$	2.48937e13	+	9.09147e13i	0.0113083	+	0.0412991i
$617$	−3.07915e15			−1.38632			−0.693159	−	0.720784i	$-0.743782\pi$
$617$	−3.07915e15			−1.38632			−0.693159	+	0.720784i	$0.743782\pi$
$618$	3.98121e14	−	6.89566e14i	0.177655	−	0.307708i
$619$	1.11640e15	+	1.93367e15i	0.493768	+	0.855230i	0.999974	−	0.00718174i	$-0.00228604\pi$
$619$	1.11640e15	+	1.93367e15i	0.493768	+	0.855230i	−0.506207	+	0.862412i	$0.668953\pi$
$620$	−9.57861e14	−	1.65906e15i	−0.419902	−	0.727292i
$621$	−7.02106e14	+	1.21608e15i	−0.305069	+	0.528396i
$622$	−9.10889e13			−0.0392300
$623$	−1.88949e15	+	1.91025e15i	−0.806604	+	0.815467i
$624$	−2.26811e15			−0.959730
$625$	1.46245e15	−	2.53304e15i	0.613397	−	1.06244i
$626$	−8.71571e13	−	1.50961e14i	−0.0362363	−	0.0627631i
$627$	9.61217e13	+	1.66488e14i	0.0396141	+	0.0686136i
$628$	9.40905e14	−	1.62970e15i	0.384386	−	0.665776i
$629$	2.87220e15			1.16315
$630$	7.92111e14	+	2.07614e14i	0.317990	+	0.0833457i
$631$	−3.18888e15			−1.26905			−0.634523	−	0.772904i	$-0.718803\pi$
$631$	−3.18888e15			−1.26905			−0.634523	+	0.772904i	$0.718803\pi$
$632$	−1.95294e14	+	3.38259e14i	−0.0770451	+	0.133446i
$633$	1.09557e13	+	1.89759e13i	0.00428470	+	0.00742132i
$634$	9.73713e13	+	1.68652e14i	0.0377520	+	0.0653884i
$635$	−1.57974e15	+	2.73618e15i	−0.607196	+	1.05169i
$636$	−5.11513e15			−1.94914
$637$	−1.33580e15	−	7.51881e14i	−0.504630	−	0.284042i
$638$	2.21489e13			0.00829543
$639$	2.40852e15	−	4.17168e15i	0.894325	−	1.54902i
$640$	−8.46168e14	−	1.46561e15i	−0.311506	−	0.539545i
$641$	5.28395e14	+	9.15207e14i	0.192859	+	0.334041i	0.946196	−	0.323593i	$-0.104891\pi$
$641$	5.28395e14	+	9.15207e14i	0.192859	+	0.334041i	−0.753338	+	0.657634i	$0.771557\pi$
$642$	−1.24581e14	+	2.15780e14i	−0.0450826	+	0.0780853i
$643$	2.86505e15			1.02795			0.513975	−	0.857805i	$-0.328172\pi$
$643$	2.86505e15			1.02795			0.513975	+	0.857805i	$0.328172\pi$
$644$	9.13305e14	+	2.39379e14i	0.324896	+	0.0851557i
$645$	7.66007e15			2.70181
$646$	−7.60370e13	+	1.31700e14i	−0.0265917	+	0.0460582i
$647$	−2.19873e14	−	3.80831e14i	−0.0762428	−	0.132056i	0.825383	−	0.564573i	$-0.190959\pi$
$647$	−2.19873e14	−	3.80831e14i	−0.0762428	−	0.132056i	−0.901626	+	0.432516i	$0.857626\pi$
$648$	−3.94177e14	−	6.82734e14i	−0.135528	−	0.234741i
$649$	−2.75466e14	+	4.77120e14i	−0.0939121	+	0.162661i
$650$	1.40953e14			0.0476488
$651$	−2.42341e15	+	2.45004e15i	−0.812328	+	0.821254i
$652$	4.99505e15			1.66027
$653$	2.92912e14	−	5.07338e14i	0.0965415	−	0.167215i	−0.813709	−	0.581272i	$-0.802555\pi$
$653$	2.92912e14	−	5.07338e14i	0.0965415	−	0.167215i	0.910251	+	0.414057i	$0.135889\pi$
$654$	3.08812e14	+	5.34878e14i	0.100929	+	0.174814i
$655$	1.93394e14	+	3.34969e14i	0.0626782	+	0.108562i
$656$	2.38923e14	−	4.13827e14i	0.0767869	−	0.132999i
$657$	−5.76438e15			−1.83714
$658$	1.67597e13	+	6.12085e13i	0.00529694	+	0.0193450i
$659$	−5.89551e14			−0.184779			−0.0923893	−	0.995723i	$-0.529450\pi$
$659$	−5.89551e14			−0.184779			−0.0923893	+	0.995723i	$0.529450\pi$
$660$	6.05782e14	−	1.04924e15i	0.188289	−	0.326126i
$661$	2.16762e15	+	3.75442e15i	0.668151	+	1.15727i	0.978421	+	0.206623i	$0.0662474\pi$
$661$	2.16762e15	+	3.75442e15i	0.668151	+	1.15727i	−0.310269	+	0.950649i	$0.600419\pi$
$662$	−7.94117e13	−	1.37545e14i	−0.0242753	−	0.0420461i
$663$	2.63264e15	−	4.55987e15i	0.798119	−	1.38238i
$664$	−2.91887e14			−0.0877588
$665$	−3.02993e14	−	1.10657e15i	−0.0903471	−	0.329958i
$666$	−6.34911e14			−0.187761
$667$	2.23645e14	−	3.87365e14i	0.0655945	−	0.113613i
$668$	−2.40555e15	−	4.16653e15i	−0.699751	−	1.21200i
$669$	9.23667e14	+	1.59984e15i	0.266484	+	0.461565i
$670$	5.66258e13	−	9.80788e13i	0.0162033	−	0.0280649i
$671$	9.72074e14			0.275883
$672$	−1.61012e15	+	1.62781e15i	−0.453239	+	0.458219i
$673$	1.69410e15			0.472994			0.236497	−	0.971632i	$-0.424001\pi$
$673$	1.69410e15			0.472994			0.236497	+	0.971632i	$0.424001\pi$
$674$	2.49532e13	−	4.32202e13i	0.00691030	−	0.0119690i
$675$	−2.12277e15	−	3.67674e15i	−0.583085	−	1.00993i
$676$	−1.20037e15	−	2.07911e15i	−0.327047	−	0.566461i
$677$	2.59774e15	−	4.49941e15i	0.702033	−	1.21596i	−0.265718	−	0.964051i	$-0.585609\pi$
$677$	2.59774e15	−	4.49941e15i	0.702033	−	1.21596i	0.967752	−	0.251907i	$-0.0810576\pi$
$678$	8.83424e14			0.236813
$679$	5.98555e15	+	1.56882e15i	1.59155	+	0.417148i
$680$	1.93231e15			0.509656
$681$	−4.45456e15	+	7.71553e15i	−1.16546	+	2.01863i
$682$	−2.76030e13	−	4.78099e13i	−0.00716379	−	0.0124081i
$683$	1.70845e14	+	2.95913e14i	0.0439834	+	0.0761815i	0.887179	−	0.461425i	$-0.152662\pi$
$683$	1.70845e14	+	2.95913e14i	0.0439834	+	0.0761815i	−0.843196	+	0.537607i	$0.819328\pi$
$684$	−1.03961e15	+	1.80065e15i	−0.265498	+	0.459855i
$685$	−8.84393e15			−2.24051
$686$	−4.82615e14	+	1.37833e14i	−0.121288	+	0.0346395i
$687$	−3.18941e15			−0.795149
$688$	−2.32621e15	+	4.02911e15i	−0.575324	+	0.996490i
$689$	1.34333e15	+	2.32672e15i	0.329593	+	0.570872i
$690$	1.97791e14	+	3.42585e14i	0.0481435	+	0.0833870i
$691$	−2.58334e15	+	4.47447e15i	−0.623810	+	1.08047i	0.364960	+	0.931023i	$0.381083\pi$
$691$	−2.58334e15	+	4.47447e15i	−0.623810	+	1.08047i	−0.988770	+	0.149447i	$0.952251\pi$
$692$	−1.09376e15			−0.262021
$693$	−1.41184e15	−	3.70046e14i	−0.335547	−	0.0879474i
$694$	−6.36094e14			−0.149984
$695$	3.28652e14	−	5.69242e14i	0.0768811	−	0.133162i
$696$	3.60599e14	+	6.24576e14i	0.0836901	+	0.144956i
$697$	5.54646e14	+	9.60674e14i	0.127713	+	0.221206i
$698$	7.12455e13	−	1.23401e14i	0.0162762	−	0.0281912i
$699$	1.25149e16			2.83663
$700$	−2.00744e15	+	2.02950e15i	−0.451444	+	0.456404i
$701$	3.33033e15			0.743084			0.371542	−	0.928416i	$-0.378829\pi$
$701$	3.33033e15			0.743084			0.371542	+	0.928416i	$0.378829\pi$
$702$	−2.94916e14	+	5.10809e14i	−0.0652896	+	0.113085i
$703$	4.44781e14	+	7.70382e14i	0.0976993	+	0.169220i
$704$	3.55537e14	+	6.15807e14i	0.0774880	+	0.134213i
$705$	8.22281e14	−	1.42423e15i	0.177820	−	0.307993i
$706$	5.09785e14			0.109386
$707$	−1.70782e15	−	6.23716e15i	−0.363610	−	1.32795i
$708$	−8.89760e15			−1.87971
$709$	7.09927e14	−	1.22963e15i	0.148819	−	0.257763i	−0.781972	−	0.623313i	$-0.785786\pi$
$709$	7.09927e14	−	1.22963e15i	0.148819	−	0.257763i	0.930791	+	0.365551i	$0.119119\pi$
$710$	−3.43845e14	−	5.95557e14i	−0.0715224	−	0.123880i
$711$	−3.02391e15	−	5.23757e15i	−0.624146	−	1.08105i
$712$	7.00773e14	−	1.21377e15i	0.143528	−	0.248598i
$713$	−1.11487e15			−0.226585
$714$	−4.55304e14	−	1.66282e15i	−0.0918251	−	0.335356i
$715$	−6.36360e14			−0.127356
$716$	3.34040e15	−	5.78575e15i	0.663403	−	1.14905i
$717$	1.11627e14	+	1.93344e14i	0.0219996	+	0.0381044i
$718$	−4.79255e14	−	8.30094e14i	−0.0937307	−	0.162346i
$719$	−4.37317e15	+	7.57456e15i	−0.848765	+	1.47010i	0.0335454	+	0.999437i	$0.489320\pi$
$719$	−4.37317e15	+	7.57456e15i	−0.848765	+	1.47010i	−0.882311	+	0.470667i	$0.844013\pi$
$720$	1.28884e16			2.48239
$721$	5.95620e15	−	6.02165e15i	1.13848	−	1.15099i
$722$	6.17866e14			0.117203
$723$	−6.10756e14	+	1.05786e15i	−0.114976	+	0.199144i
$724$	−7.63301e14	−	1.32208e15i	−0.142605	−	0.246999i
$725$	6.76176e14	+	1.17117e15i	0.125372	+	0.217151i
$726$	−5.78896e14	+	1.00268e15i	−0.106524	+	0.184506i
$727$	−7.92864e14			−0.144797			−0.0723984	−	0.997376i	$-0.523065\pi$
$727$	−7.92864e14			−0.144797			−0.0723984	+	0.997376i	$0.523065\pi$
$728$	7.73461e14	+	2.02725e14i	0.140190	+	0.0367439i
$729$	−5.08466e15			−0.914661
$730$	−4.11467e14	+	7.12682e14i	−0.0734615	+	0.127239i
$731$	−5.40015e15	−	9.35334e15i	−0.956887	−	1.65738i
$732$	7.84955e15	+	1.35958e16i	1.38049	+	2.39108i
$733$	−1.71682e15	+	2.97363e15i	−0.299678	+	0.519057i	−0.976062	−	0.217492i	$-0.930212\pi$
$733$	−1.71682e15	+	2.97363e15i	−0.299678	+	0.519057i	0.676385	+	0.736549i	$0.263546\pi$
$734$	−1.18678e14			−0.0205610
$735$	1.13345e16	+	6.37987e15i	1.94905	+	1.09706i
$736$	−7.40722e14			−0.126423
$737$	−1.00929e14	+	1.74813e14i	−0.0170979	+	0.0296145i
$738$	−1.22607e14	−	2.12361e14i	−0.0206160	−	0.0357079i
$739$	−1.17677e15	−	2.03823e15i	−0.196403	−	0.340180i	0.750957	−	0.660351i	$-0.229593\pi$
$739$	−1.17677e15	−	2.03823e15i	−0.196403	−	0.340180i	−0.947359	+	0.320172i	$0.896259\pi$
$740$	2.80311e15	−	4.85513e15i	0.464372	−	0.804316i
$741$	1.63074e15			0.268154
$742$	8.50961e14	+	2.23038e14i	0.138895	+	0.0364047i
$743$	−1.13067e16			−1.83188			−0.915940	−	0.401316i	$-0.868553\pi$
$743$	−1.13067e16			−1.83188			−0.915940	+	0.401316i	$0.868553\pi$
$744$	8.98792e14	−	1.55675e15i	0.144547	−	0.250362i
$745$	1.99117e15	+	3.44882e15i	0.317870	+	0.550567i
$746$	3.91725e14	+	6.78488e14i	0.0620751	+	0.107517i
$747$	2.25977e15	−	3.91404e15i	0.355469	−	0.615690i
$748$	−1.70824e15			−0.266742
$749$	−1.86383e15	+	1.88431e15i	−0.288905	+	0.292080i
$750$	6.37427e14			0.0980829
$751$	2.89693e15	−	5.01763e15i	0.442505	−	0.766441i	−0.555370	−	0.831603i	$-0.687423\pi$
$751$	2.89693e15	−	5.01763e15i	0.442505	−	0.766441i	0.997875	+	0.0651627i	$0.0207566\pi$
$752$	4.99420e14	+	8.65021e14i	0.0757300	+	0.131168i
$753$	−4.72515e15	−	8.18420e15i	−0.711284	−	1.23198i
$754$	9.39410e13	−	1.62711e14i	0.0140382	−	0.0243149i
$755$	−1.14692e16			−1.70147
$756$	−3.15466e15	−	1.15212e16i	−0.464604	−	1.69679i
$757$	−3.69592e15			−0.540374			−0.270187	−	0.962808i	$-0.587086\pi$
$757$	−3.69592e15			−0.540374			−0.270187	+	0.962808i	$0.587086\pi$
$758$	−1.55115e13	+	2.68667e13i	−0.00225151	+	0.00389973i
$759$	−3.52539e14	−	6.10616e14i	−0.0508016	−	0.0879910i
$760$	2.99232e14	+	5.18285e14i	0.0428088	+	0.0741471i
$761$	−7.85569e14	+	1.36065e15i	−0.111575	+	0.193254i	−0.916406	−	0.400251i	$-0.868923\pi$
$761$	−7.85569e14	+	1.36065e15i	−0.111575	+	0.193254i	0.804830	+	0.593505i	$0.202256\pi$
$762$	−1.47043e15			−0.207344
$763$	1.73503e15	+	6.33651e15i	0.242896	+	0.887085i
$764$	9.72223e15			1.35130
$765$	−1.49598e16	+	2.59112e16i	−2.06438	+	3.57560i
$766$	6.31746e14	+	1.09422e15i	0.0865535	+	0.149915i
$767$	2.33668e15	+	4.04725e15i	0.317852	+	0.550536i
$768$	−5.44098e15	+	9.42406e15i	−0.734836	+	1.27277i
$769$	1.12892e16			1.51380			0.756902	−	0.653529i	$-0.226712\pi$
$769$	1.12892e16			1.51380			0.756902	+	0.653529i	$0.226712\pi$
$770$	−1.46530e14	+	1.48140e14i	−0.0195086	+	0.0197230i
$771$	1.69112e16			2.23550
$772$	−7.07389e14	+	1.22523e15i	−0.0928460	+	0.160814i
$773$	−9.91548e14	−	1.71741e15i	−0.129219	−	0.223814i	0.794155	−	0.607715i	$-0.207914\pi$
$773$	−9.91548e14	−	1.71741e15i	−0.129219	−	0.223814i	−0.923374	+	0.383901i	$0.874580\pi$
$774$	1.19373e15	+	2.06759e15i	0.154465	+	0.267541i
$775$	1.68537e15	−	2.91914e15i	0.216538	−	0.375055i
$776$	−3.22770e15			−0.411769
$777$	−9.75525e15	−	2.55687e15i	−1.23573	−	0.323886i
$778$	−6.47695e14			−0.0814672
$779$	−1.71782e14	+	2.97535e14i	−0.0214546	+	0.0371605i
$780$	−5.13864e15	−	8.90039e15i	−0.637277	−	1.10380i
$781$	6.12862e14	+	1.06151e15i	0.0754713	+	0.130720i
$782$	2.78876e14	−	4.83027e14i	0.0341015	−	0.0590656i
$783$	−5.65904e15			−0.687152
$784$	−6.79781e15	+	4.02439e15i	−0.819654	+	0.485246i
$785$	8.38678e15			1.00418
$786$	−9.00065e13	+	1.55896e14i	−0.0107016	+	0.0185358i
$787$	−6.95413e15	−	1.20449e16i	−0.821073	−	1.42214i	−0.904884	−	0.425658i	$-0.860043\pi$
$787$	−6.95413e15	−	1.20449e16i	−0.821073	−	1.42214i	0.0838114	−	0.996482i	$-0.473291\pi$
$788$	3.49705e15	+	6.05706e15i	0.410022	+	0.710179i
$789$	1.03672e16	−	1.79565e16i	1.20709	−	2.09073i
$790$	−8.63399e14			−0.0998304
$791$	9.09006e15	+	2.38252e15i	1.04375	+	0.273568i
$792$	7.61334e14			0.0868133
$793$	4.12289e15	−	7.14105e15i	0.466873	−	0.808648i
$794$	−3.57966e14	−	6.20016e14i	−0.0402559	−	0.0697252i
$795$	−1.13985e16	−	1.97427e16i	−1.27300	−	2.20489i
$796$	−2.91871e15	+	5.05535e15i	−0.323719	+	0.560699i
$797$	6.82904e15			0.752210			0.376105	−	0.926577i	$-0.377263\pi$
$797$	6.82904e15			0.752210			0.376105	+	0.926577i	$0.377263\pi$
$798$	3.75497e14	−	3.79622e14i	0.0410762	−	0.0415275i
$799$	−2.31875e15			−0.251911
$800$	1.11976e15	−	1.93948e15i	0.120818	−	0.209263i
$801$	1.08507e16	+	1.87939e16i	1.16273	+	2.01391i
$802$	−1.14914e14	−	1.99038e14i	−0.0122297	−	0.0211825i
$803$	7.33390e14	−	1.27027e15i	0.0775175	−	0.134264i
$804$	−3.26002e15			−0.342225
$805$	1.11127e15	+	4.05848e15i	0.115862	+	0.423142i
$806$	−4.68295e14			−0.0484927
$807$	1.01474e16	−	1.75758e16i	1.04364	−	1.80763i
$808$	1.68662e15	+	2.92131e15i	0.172288	+	0.298412i
$809$	8.33703e15	+	1.44402e16i	0.845852	+	1.46506i	0.884879	+	0.465820i	$0.154241\pi$
$809$	8.33703e15	+	1.44402e16i	0.845852	+	1.46506i	−0.0390274	+	0.999238i	$0.512426\pi$
$810$	8.71332e14	−	1.50919e15i	0.0878044	−	0.152082i
$811$	−5.16144e15			−0.516602			−0.258301	−	0.966065i	$-0.583163\pi$
$811$	−5.16144e15			−0.516602			−0.258301	+	0.966065i	$0.583163\pi$
$812$	1.00487e15	+	3.66990e15i	0.0998969	+	0.364835i
$813$	−3.53947e15			−0.349494
$814$	8.07784e13	−	1.39912e14i	0.00792247	−	0.0137221i
$815$	1.11309e16	+	1.92793e16i	1.08433	+	1.87812i
$816$	−1.35675e16	−	2.34996e16i	−1.31282	−	2.27387i
$817$	1.67251e15	−	2.89687e15i	0.160748	−	0.278424i
$818$	1.11834e15			0.106765
$819$	−8.70652e15	+	8.80219e15i	−0.825626	+	0.834698i
$820$	2.16522e15			0.203951
$821$	−5.05873e15	+	8.76198e15i	−0.473319	+	0.819813i	−0.999534	−	0.0305391i	$-0.990278\pi$
$821$	−5.05873e15	+	8.76198e15i	−0.473319	+	0.819813i	0.526214	+	0.850352i	$0.323611\pi$
$822$	−2.05800e15	−	3.56456e15i	−0.191272	−	0.331292i
$823$	3.99868e15	+	6.92593e15i	0.369163	+	0.639409i	0.989435	−	0.144978i	$-0.0463111\pi$
$823$	3.99868e15	+	6.92593e15i	0.369163	+	0.639409i	−0.620272	+	0.784387i	$0.712978\pi$
$824$	−2.20903e15	+	3.82616e15i	−0.202583	+	0.350884i
$825$	2.13176e15			0.194196
$826$	1.48022e15	+	3.87967e14i	0.133948	+	0.0351079i
$827$	−1.50295e16			−1.35102			−0.675512	−	0.737349i	$-0.736077\pi$
$827$	−1.50295e16			−1.35102			−0.675512	+	0.737349i	$0.736077\pi$
$828$	3.81290e15	−	6.60413e15i	0.340477	−	0.589724i
$829$	−6.43760e15	−	1.11502e16i	−0.571050	−	0.989087i	−0.996459	−	0.0840857i	$-0.973203\pi$
$829$	−6.43760e15	−	1.11502e16i	−0.571050	−	0.989087i	0.425409	−	0.905001i	$-0.360130\pi$
$830$	−3.22610e14	−	5.58777e14i	−0.0284281	−	0.0492390i
$831$	−1.38559e16	+	2.39991e16i	−1.21291	+	2.10082i
$832$	6.03180e15			0.524528
$833$	−2.00394e14	−	1.83377e16i	−0.0173116	−	1.58415i
$834$	3.05912e14			0.0262532
$835$	1.07210e16	−	1.85692e16i	0.914025	−	1.58314i
$836$	−2.64534e14	−	4.58186e14i	−0.0224051	−	0.0388068i
$837$	7.05256e15	+	1.22154e16i	0.593413	+	1.02782i
$838$	8.87952e14	−	1.53798e15i	0.0742245	−	0.128561i
$839$	−1.90314e16			−1.58045			−0.790225	−	0.612817i	$-0.790036\pi$
$839$	−1.90314e16			−1.58045			−0.790225	+	0.612817i	$0.790036\pi$
$840$	−6.56298e15	−	1.72017e15i	−0.541458	−	0.141917i
$841$	−1.03979e16			−0.852252
$842$	−9.00229e14	+	1.55924e15i	−0.0733055	+	0.126969i
$843$	1.42588e16	+	2.46969e16i	1.15353	+	1.99798i
$844$	−3.01510e13	−	5.22230e13i	−0.00242336	−	0.00419738i
$845$	5.34978e15	−	9.26609e15i	0.427193	−	0.739920i
$846$	5.12569e14			0.0406645
$847$	−8.66074e15	+	8.75590e15i	−0.682647	+	0.690148i
$848$	1.38459e16			1.08429
$849$	7.40748e15	−	1.28301e16i	0.576339	−	0.998249i
$850$	8.43163e14	+	1.46040e15i	0.0651789	+	0.112893i
$851$	−1.63129e15	−	2.82548e15i	−0.125291	−	0.217010i
$852$	−9.89779e15	+	1.71435e16i	−0.755302	+	1.30822i
$853$	−5.80889e15			−0.440427			−0.220213	−	0.975452i	$-0.570675\pi$
$853$	−5.80889e15			−0.440427			−0.220213	+	0.975452i	$0.570675\pi$
$854$	−7.13036e14	−	2.60409e15i	−0.0537147	−	0.196172i
$855$	−9.26656e15			−0.693593
$856$	6.91255e14	−	1.19729e15i	0.0514082	−	0.0890416i
$857$	5.44606e15	+	9.43285e15i	0.402428	+	0.697025i	0.994018	−	0.109213i	$-0.0348331\pi$
$857$	5.44606e15	+	9.43285e15i	0.402428	+	0.697025i	−0.591591	+	0.806239i	$0.701500\pi$
$858$	−1.48082e14	−	2.56486e14i	−0.0108723	−	0.0188314i
$859$	4.88936e15	−	8.46862e15i	0.356689	−	0.617803i	−0.630717	−	0.776013i	$-0.717239\pi$
$859$	4.88936e15	−	8.46862e15i	0.356689	−	0.617803i	0.987406	+	0.158210i	$0.0505723\pi$
$860$	−2.10811e16			−1.52810
$861$	−1.02862e15	−	3.75663e15i	−0.0740861	−	0.270571i
$862$	2.80338e15			0.200628
$863$	−3.21366e15	+	5.56622e15i	−0.228529	+	0.395823i	−0.957372	−	0.288857i	$-0.906725\pi$
$863$	−3.21366e15	+	5.56622e15i	−0.228529	+	0.395823i	0.728844	+	0.684680i	$0.240058\pi$
$864$	4.68575e15	+	8.11595e15i	0.331095	+	0.573474i
$865$	−2.43730e15	−	4.22153e15i	−0.171128	−	0.296402i
$866$	−1.33201e15	+	2.30710e15i	−0.0929305	+	0.160960i
$867$	3.78942e16			2.62705
$868$	6.66940e15	−	6.74268e15i	0.459440	−	0.464488i
$869$	1.53890e15			0.105342
$870$	−7.97109e14	+	1.38063e15i	−0.0542203	+	0.0939123i
$871$	8.56144e14	+	1.48288e15i	0.0578691	+	0.100232i
$872$	−1.71349e15	−	2.96785e15i	−0.115091	−	0.199343i
$873$	2.49887e16	−	4.32816e16i	1.66788	−	2.88885i
$874$	1.72744e14			0.0114575
$875$	6.55886e15	+	1.71909e15i	0.432299	+	0.113306i
$876$	2.36887e16			1.55156
$877$	−1.22064e16	+	2.11421e16i	−0.794491	+	1.37610i	0.128670	+	0.991687i	$0.458929\pi$
$877$	−1.22064e16	+	2.11421e16i	−0.794491	+	1.37610i	−0.923162	+	0.384412i	$0.874404\pi$
$878$	7.93877e14	+	1.37504e15i	0.0513492	+	0.0889394i
$879$	−4.02729e15	−	6.97546e15i	−0.258865	−	0.448368i
$880$	−1.63977e15	+	2.84016e15i	−0.104743	+	0.181421i
$881$	−2.26230e16			−1.43609			−0.718045	−	0.695996i	$-0.754963\pi$
$881$	−2.26230e16			−1.43609			−0.718045	+	0.695996i	$0.754963\pi$
$882$	4.42979e13	+	4.05362e15i	0.00279451	+	0.255721i
$883$	2.40396e14			0.0150711			0.00753554	−	0.999972i	$-0.497601\pi$
$883$	2.40396e14			0.0150711			0.00753554	+	0.999972i	$0.497601\pi$
$884$	−7.24523e15	+	1.25491e16i	−0.451403	+	0.781853i
$885$	−1.98272e16	−	3.43418e16i	−1.22765	−	2.12635i
$886$	−1.25367e15	−	2.17141e15i	−0.0771429	−	0.133615i
$887$	7.90944e15	−	1.36996e16i	0.483689	−	0.837773i	−0.516136	−	0.856507i	$-0.672630\pi$
$887$	7.90944e15	−	1.36996e16i	0.483689	−	0.837773i	0.999825	+	0.0187334i	$0.00596339\pi$
$888$	5.26050e15			0.319710
$889$	−1.51301e16	−	3.96563e15i	−0.913866	−	0.239526i
$890$	3.09813e15			0.185975
$891$	−1.55304e15	+	2.68995e15i	−0.0926523	+	0.160478i
$892$	−2.54200e15	−	4.40287e15i	−0.150719	−	0.261054i
$893$	−3.59075e14	−	6.21937e14i	−0.0211594	−	0.0366491i
$894$	−9.26701e14	+	1.60509e15i	−0.0542729	+	0.0940034i
$895$	2.97748e16			1.73309
$896$	5.89171e15	−	5.95644e15i	0.340837	−	0.344582i
$897$	−5.98094e15			−0.343883
$898$	−2.40389e14	+	4.16366e14i	−0.0137371	+	0.0237934i
$899$	−2.24649e15	−	3.89103e15i	−0.127593	−	0.220997i
$900$	1.15280e16	+	1.99671e16i	0.650761	+	1.12715i
$901$	−1.60713e16	+	2.78362e16i	−0.901703	+	1.56180i
$902$	6.23960e13			0.00347953
$903$	1.00148e16	+	3.65754e16i	0.555088	+	2.02724i
$904$	−4.90180e15			−0.270041
$905$	3.40185e15	−	5.89218e15i	0.186272	−	0.322633i
$906$	−2.66891e15	−	4.62269e15i	−0.145254	−	0.251588i
$907$	−2.57501e15	−	4.46004e15i	−0.139296	−	0.241267i	0.787934	−	0.615759i	$-0.211151\pi$
$907$	−2.57501e15	−	4.46004e15i	−0.139296	−	0.241267i	−0.927230	+	0.374492i	$0.877817\pi$
$908$	1.22593e16	−	2.12337e16i	0.659163	−	1.14170i
$909$	−5.22309e16			−2.79143
$910$	4.66783e14	+	1.70474e15i	0.0247963	+	0.0905590i
$911$	2.54507e16			1.34384			0.671922	−	0.740622i	$-0.265469\pi$
$911$	2.54507e16			1.34384			0.671922	+	0.740622i	$0.265469\pi$
$912$	4.20206e15	−	7.27819e15i	0.220542	−	0.381990i
$913$	5.75013e14	+	9.95951e14i	0.0299977	+	0.0519576i
$914$	5.17238e14	+	8.95882e14i	0.0268217	+	0.0464565i
$915$	−3.49836e16	+	6.05934e16i	−1.80322	+	3.12327i
$916$	8.77750e15			0.449724
$917$	−1.34657e15	+	1.36136e15i	−0.0685799	+	0.0693334i
$918$	−7.05658e15			−0.357240
$919$	−3.49711e15	+	6.05718e15i	−0.175984	+	0.304814i	−0.940502	−	0.339789i	$-0.889644\pi$
$919$	−3.49711e15	+	6.05718e15i	−0.175984	+	0.304814i	0.764517	+	0.644604i	$0.222978\pi$
$920$	−1.09747e15	−	1.90088e15i	−0.0548986	−	0.0950872i
$921$	6.48558e15	+	1.12334e16i	0.322494	+	0.558575i
$922$	6.63072e14	−	1.14848e15i	0.0327749	−	0.0567677i
$923$	1.03974e16			0.510876
$924$	5.80195e15	+	1.52070e15i	0.283386	+	0.0742759i
$925$	9.86420e15			0.478942
$926$	1.38674e15	−	2.40191e15i	0.0669322	−	0.115930i
$927$	−3.42044e16	−	5.92438e16i	−1.64113	−	2.84253i
$928$	−1.49257e15	−	2.58521e15i	−0.0711904	−	0.123305i
$929$	6.32951e15	−	1.09630e16i	0.300112	−	0.519810i	−0.676049	−	0.736857i	$-0.736309\pi$
$929$	6.32951e15	−	1.09630e16i	0.300112	−	0.519810i	0.976161	+	0.217047i	$0.0696425\pi$
$930$	3.97358e15			0.187295
$931$	4.88751e15	−	2.89347e15i	0.229015	−	0.135580i
$932$	−3.44420e16			−1.60435
$933$	−5.84292e15	+	1.01202e16i	−0.270571	+	0.468643i
$934$	2.68895e14	+	4.65740e14i	0.0123787	+	0.0214405i
$935$	−3.80662e15	−	6.59325e15i	−0.174211	−	0.301742i
$936$	3.22907e15	−	5.59291e15i	0.146913	−	0.254461i
$937$	2.80207e16			1.26739			0.633697	−	0.773582i	$-0.281537\pi$
$937$	2.80207e16			1.26739			0.633697	+	0.773582i	$0.281537\pi$
$938$	5.42341e14	+	1.42148e14i	0.0243869	+	0.00639185i
$939$	−2.23629e16			−0.999694
$940$	−2.26298e15	+	3.91959e15i	−0.100572	+	0.174196i
$941$	2.38780e15	+	4.13578e15i	0.105500	+	0.182732i	0.913943	−	0.405844i	$-0.133022\pi$
$941$	2.38780e15	+	4.13578e15i	0.105500	+	0.182732i	−0.808442	+	0.588576i	$0.799689\pi$
$942$	1.95162e15	+	3.38031e15i	0.0857266	+	0.148483i
$943$	6.30033e14	−	1.09125e15i	0.0275137	−	0.0476551i
$944$	2.40846e16			1.04567
$945$	3.74382e16	−	3.78496e16i	1.61600	−	1.63375i
$946$	−6.07501e14			−0.0260703
$947$	−1.48624e16	+	2.57425e16i	−0.634110	+	1.09831i	0.352593	+	0.935777i	$0.385300\pi$
$947$	−1.48624e16	+	2.57425e16i	−0.634110	+	1.09831i	−0.986703	+	0.162534i	$0.948033\pi$
$948$	1.24267e16	+	2.15237e16i	0.527122	+	0.913002i
$949$	−6.22110e15	−	1.07753e16i	−0.262363	−	0.454427i
$950$	−2.61140e14	+	4.52307e14i	−0.0109495	+	0.0189650i
$951$	2.49837e16			1.04151
$952$	2.52632e15	+	9.22641e15i	0.104709	+	0.382410i
$953$	4.28873e15			0.176733			0.0883665	−	0.996088i	$-0.471835\pi$
$953$	4.28873e15			0.176733			0.0883665	+	0.996088i	$0.471835\pi$
$954$	3.55262e15	−	6.15332e15i	0.145557	−	0.252112i
$955$	2.16648e16	+	3.75246e16i	0.882545	+	1.52861i
$956$	−3.07206e14	−	5.32096e14i	−0.0124426	−	0.0215512i
$957$	1.42075e15	−	2.46081e15i	0.0572139	−	0.0990974i
$958$	−3.66890e15			−0.146901
$959$	−1.15626e16	−	4.22281e16i	−0.460315	−	1.68112i
$960$	−5.11811e16			−2.02590
$961$	7.10488e15	−	1.23060e16i	0.279626	−	0.484327i
$962$	−6.85216e14	−	1.18683e15i	−0.0268142	−	0.0464435i
$963$	1.07033e16	+	1.85387e16i	0.416460	+	0.721331i
$964$	1.68085e15	−	2.91131e15i	0.0650286	−	0.112633i
$965$	−6.30533e15			−0.242553
$966$	−1.37718e15	+	1.39232e15i	−0.0526766	+	0.0532554i
$967$	8.30400e15			0.315822			0.157911	−	0.987453i	$-0.449524\pi$
$967$	8.30400e15			0.315822			0.157911	+	0.987453i	$0.449524\pi$
$968$	3.21209e15	−	5.56350e15i	0.121471	−	0.210394i
$969$	9.75483e15	+	1.68959e16i	0.366808	+	0.635331i
$970$	−3.56743e15	−	6.17897e15i	−0.133386	−	0.231032i
$971$	1.68239e16	−	2.91399e16i	0.625491	−	1.08338i	−0.362954	−	0.931807i	$-0.618232\pi$
$971$	1.68239e16	−	2.91399e16i	0.625491	−	1.08338i	0.988446	−	0.151576i	$-0.0484348\pi$
$972$	−2.57633e15			−0.0952439
$973$	3.14771e15	+	8.25019e14i	0.115711	+	0.0303280i
$974$	−4.70221e15			−0.171881
$975$	9.04149e15	−	1.56603e16i	0.328636	−	0.569213i
$976$	−2.12476e16	−	3.68020e16i	−0.767956	−	1.33014i
$977$	1.98072e16	+	3.43071e16i	0.711875	+	1.23300i	0.964152	+	0.265349i	$0.0854871\pi$
$977$	1.98072e16	+	3.43071e16i	0.711875	+	1.23300i	−0.252277	+	0.967655i	$0.581180\pi$
$978$	−5.18036e15	+	8.97264e15i	−0.185138	+	0.320669i
$979$	−5.52204e15			−0.196243
$980$	−3.11934e16	−	1.75579e16i	−1.10235	−	0.620481i
$981$	5.30629e16			1.86471
$982$	−2.01220e15	+	3.48523e15i	−0.0703166	+	0.121792i
$983$	−1.53479e16	−	2.65834e16i	−0.533342	−	0.923775i	−0.999242	−	0.0389378i	$-0.987603\pi$
$983$	−1.53479e16	−	2.65834e16i	−0.533342	−	0.923775i	0.465900	−	0.884838i	$-0.345731\pi$
$984$	1.01585e15	+	1.75950e15i	0.0351039	+	0.0608018i
$985$	−1.55855e16	+	2.69949e16i	−0.535576	+	0.927646i
$986$	2.24777e15			0.0768118
$987$	7.87550e15	+	2.06418e15i	0.267629	+	0.0701461i
$988$	−4.48791e15			−0.151663
$989$	−6.13414e15	+	1.06246e16i	−0.206146	+	0.357055i
$990$	8.41468e14	+	1.45747e15i	0.0281219	+	0.0487085i
$991$	−7.01280e15	−	1.21465e16i	−0.233070	−	0.403689i	0.725640	−	0.688075i	$-0.241544\pi$
$991$	−7.01280e15	−	1.21465e16i	−0.233070	−	0.403689i	−0.958710	+	0.284385i	$0.908211\pi$
$992$	−3.72023e15	+	6.44363e15i	−0.122958	+	0.212969i
$993$	−2.03755e16			−0.669712
$994$	2.39413e15	−	2.42043e15i	0.0782568	−	0.0791167i
$995$	−2.60160e16			−0.845694
$996$	−9.28652e15	+	1.60847e16i	−0.300211	+	0.519981i
$997$	1.01222e16	+	1.75321e16i	0.325424	+	0.563651i	0.981598	−	0.190959i	$-0.0611596\pi$
$997$	1.01222e16	+	1.75321e16i	0.325424	+	0.563651i	−0.656174	+	0.754610i	$0.727826\pi$
$998$	2.34893e15	+	4.06847e15i	0.0751023	+	0.130081i
$999$	−2.06388e16	+	3.57475e16i	−0.656258	+	1.13667i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.12.c.a.2.3	✓	12
3.2	odd	2		63.12.e.b.37.4		12
4.3	odd	2		112.12.i.c.65.6		12
7.2	even	3		49.12.a.g.1.4		6
7.3	odd	6		49.12.c.i.18.3		12
7.4	even	3	inner	7.12.c.a.4.3	yes	12
7.5	odd	6		49.12.a.f.1.4		6
7.6	odd	2		49.12.c.i.30.3		12
21.11	odd	6		63.12.e.b.46.4		12
28.11	odd	6		112.12.i.c.81.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.12.c.a.2.3	✓	12	1.1	even	1	trivial
7.12.c.a.4.3	yes	12	7.4	even	3	inner
49.12.a.f.1.4		6	7.5	odd	6
49.12.a.g.1.4		6	7.2	even	3
49.12.c.i.18.3		12	7.3	odd	6
49.12.c.i.30.3		12	7.6	odd	2
63.12.e.b.37.4		12	3.2	odd	2
63.12.e.b.46.4		12	21.11	odd	6
112.12.i.c.65.6		12	4.3	odd	2
112.12.i.c.81.6		12	28.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	7.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.85417 - 4.94356i) q^{2} +(-366.163 - 634.213i) q^{3} +(1007.71 + 1745.40i) q^{4} +(-4491.11 + 7778.83i) q^{5} -4180.36 q^{6} +(-43014.2 - 11274.1i) q^{7} +23195.3 q^{8} +(-179577. + 311037. i) q^{9} +O(q^{10})\)	\(q+(2.85417 - 4.94356i) q^{2} +(-366.163 - 634.213i) q^{3} +(1007.71 + 1745.40i) q^{4} +(-4491.11 + 7778.83i) q^{5} -4180.36 q^{6} +(-43014.2 - 11274.1i) q^{7} +23195.3 q^{8} +(-179577. + 311037. i) q^{9} +(25636.8 + 44404.2i) q^{10} +(-45694.4 - 79145.1i) q^{11} +(737970. - 1.27820e6i) q^{12} -775221. q^{13} +(-178504. + 180465. i) q^{14} +6.57792e6 q^{15} +(-1.99758e6 + 3.45991e6i) q^{16} +(-4.63726e6 - 8.03198e6i) q^{17} +(1.02509e6 + 1.77550e6i) q^{18} +(1.43623e6 - 2.48762e6i) q^{19} -1.81029e7 q^{20} +(8.60003e6 + 3.14083e7i) q^{21} -521678. q^{22} +(-5.26756e6 + 9.12369e6i) q^{23} +(-8.49327e6 - 1.47108e7i) q^{24} +(-1.59261e7 - 2.75848e7i) q^{25} +(-2.21261e6 + 3.83236e6i) q^{26} +1.33289e8 q^{27} +(-2.36679e7 - 8.64380e7i) q^{28} -4.24570e7 q^{29} +(1.87745e7 - 3.25184e7i) q^{30} +(5.29120e7 + 9.16463e7i) q^{31} +(3.51549e7 + 6.08901e7i) q^{32} +(-3.34632e7 + 5.79600e7i) q^{33} -5.29421e7 q^{34} +(2.80881e8 - 2.83967e8i) q^{35} -7.23845e8 q^{36} +(-1.54843e8 + 2.68196e8i) q^{37} +(-8.19848e6 - 1.42002e7i) q^{38} +(2.83857e8 + 4.91655e8i) q^{39} +(-1.04173e8 + 1.80433e8i) q^{40} -1.19606e8 q^{41} +(1.79815e8 + 4.71298e7i) q^{42} +1.16451e9 q^{43} +(9.20932e7 - 1.59510e8i) q^{44} +(-1.61300e9 - 2.79380e9i) q^{45} +(3.00690e7 + 5.20811e7i) q^{46} +(1.25006e8 - 2.16517e8i) q^{47} +2.92576e9 q^{48} +(1.72312e9 + 9.69892e8i) q^{49} -1.81823e8 q^{50} +(-3.39599e9 + 5.88203e9i) q^{51} +(-7.81196e8 - 1.35307e9i) q^{52} +(-1.73284e9 - 3.00136e9i) q^{53} +(3.80428e8 - 6.58921e8i) q^{54} +8.20875e8 q^{55} +(-9.97729e8 - 2.61506e8i) q^{56} -2.10358e9 q^{57} +(-1.21180e8 + 2.09889e8i) q^{58} +(-3.01421e9 - 5.22077e9i) q^{59} +(6.62861e9 + 1.14811e10i) q^{60} +(-5.31834e9 + 9.21163e9i) q^{61} +6.04079e8 q^{62} +(1.12310e10 - 1.13544e10i) q^{63} -7.78074e9 q^{64} +(3.48161e9 - 6.03032e9i) q^{65} +(1.91019e8 + 3.30855e8i) q^{66} +(-1.10439e9 - 1.91285e9i) q^{67} +(9.34601e9 - 1.61878e10i) q^{68} +7.71514e9 q^{69} +(-6.02129e8 - 2.19904e9i) q^{70} -1.34122e10 q^{71} +(-4.16535e9 + 7.21460e9i) q^{72} +(8.02494e9 + 1.38996e10i) q^{73} +(8.83897e8 + 1.53095e9i) q^{74} +(-1.16631e10 + 2.02011e10i) q^{75} +5.78919e9 q^{76} +(1.07322e9 + 3.91953e9i) q^{77} +3.24071e9 q^{78} +(-8.41954e9 + 1.45831e10i) q^{79} +(-1.79427e10 - 3.10777e10i) q^{80} +(-1.69938e10 - 2.94341e10i) q^{81} +(-3.41376e8 + 5.91281e8i) q^{82} -1.25839e10 q^{83} +(-4.61538e10 + 4.66609e10i) q^{84} +8.33059e10 q^{85} +(3.32372e9 - 5.75684e9i) q^{86} +(1.55462e10 + 2.69268e10i) q^{87} +(-1.05990e9 - 1.83580e9i) q^{88} +(3.02118e10 - 5.23283e10i) q^{89} -1.84151e10 q^{90} +(3.33455e10 + 8.73991e9i) q^{91} -2.12326e10 q^{92} +(3.87488e10 - 6.71149e10i) q^{93} +(-7.13578e8 - 1.23595e9i) q^{94} +(1.29005e10 + 2.23444e10i) q^{95} +(2.57448e10 - 4.45914e10i) q^{96} -1.39153e11 q^{97} +(9.71279e9 - 5.75010e9i) q^{98} +3.28227e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 22 q^{2} - 244 q^{3} - 2556 q^{4} - 8782 q^{5} + 38140 q^{6} - 504 q^{7} + 97008 q^{8} - 172348 q^{9}+O(q^{10}) \) 12 * q + 22 * q^2 - 244 * q^3 - 2556 * q^4 - 8782 * q^5 + 38140 * q^6 - 504 * q^7 + 97008 * q^8 - 172348 * q^9	\( 12 q + 22 q^{2} - 244 q^{3} - 2556 q^{4} - 8782 q^{5} + 38140 q^{6} - 504 q^{7} + 97008 q^{8} - 172348 q^{9} + 111546 q^{10} - 1001572 q^{11} - 173684 q^{12} + 3864504 q^{13} - 1302994 q^{14} - 1286512 q^{15} + 39120 q^{16} - 6704802 q^{17} + 3768052 q^{18} + 4192212 q^{19} - 17646776 q^{20} + 44745358 q^{21} - 8505684 q^{22} - 33871872 q^{23} - 15734760 q^{24} + 13695456 q^{25} + 29350300 q^{26} + 73859384 q^{27} + 181285692 q^{28} - 255125224 q^{29} - 336068498 q^{30} - 331783920 q^{31} + 163252640 q^{32} - 80899438 q^{33} + 1853334396 q^{34} + 1407354844 q^{35} - 2197352048 q^{36} - 833082774 q^{37} - 2086458338 q^{38} + 737605904 q^{39} - 1219023432 q^{40} + 3104076808 q^{41} + 5982095000 q^{42} - 1722177552 q^{43} - 5105122436 q^{44} - 7406493484 q^{45} + 3435559326 q^{46} - 1327587552 q^{47} + 14535793696 q^{48} + 11976558636 q^{49} - 12237094384 q^{50} - 13921261140 q^{51} - 17237001432 q^{52} + 6725755626 q^{53} - 1674595226 q^{54} + 26323921200 q^{55} + 28163516640 q^{56} - 16884487756 q^{57} - 20073189204 q^{58} - 26237179548 q^{59} + 13611677716 q^{60} - 14411013726 q^{61} + 46185665964 q^{62} + 45955779184 q^{63} - 46365999744 q^{64} - 16224702172 q^{65} - 40938633602 q^{66} - 4241860068 q^{67} - 6528332916 q^{68} + 46750854252 q^{69} + 55705143270 q^{70} - 37335334656 q^{71} - 30237166608 q^{72} + 6005568990 q^{73} + 21663581922 q^{74} + 17116276792 q^{75} - 28817353320 q^{76} - 51928077698 q^{77} + 42636498520 q^{78} + 11712395640 q^{79} + 41748525232 q^{80} - 12455008366 q^{81} + 52795921668 q^{82} - 100821781200 q^{83} - 155783007940 q^{84} + 138884613396 q^{85} + 110437384472 q^{86} + 119455310144 q^{87} - 105039956616 q^{88} - 48633519778 q^{89} - 361508123864 q^{90} - 160908361488 q^{91} + 242956324248 q^{92} + 266530114134 q^{93} + 368497095702 q^{94} - 72161225128 q^{95} + 124456168928 q^{96} - 401308415928 q^{97} - 582375436706 q^{98} + 367357472240 q^{99}+O(q^{100}) \) 12 * q + 22 * q^2 - 244 * q^3 - 2556 * q^4 - 8782 * q^5 + 38140 * q^6 - 504 * q^7 + 97008 * q^8 - 172348 * q^9 + 111546 * q^10 - 1001572 * q^11 - 173684 * q^12 + 3864504 * q^13 - 1302994 * q^14 - 1286512 * q^15 + 39120 * q^16 - 6704802 * q^17 + 3768052 * q^18 + 4192212 * q^19 - 17646776 * q^20 + 44745358 * q^21 - 8505684 * q^22 - 33871872 * q^23 - 15734760 * q^24 + 13695456 * q^25 + 29350300 * q^26 + 73859384 * q^27 + 181285692 * q^28 - 255125224 * q^29 - 336068498 * q^30 - 331783920 * q^31 + 163252640 * q^32 - 80899438 * q^33 + 1853334396 * q^34 + 1407354844 * q^35 - 2197352048 * q^36 - 833082774 * q^37 - 2086458338 * q^38 + 737605904 * q^39 - 1219023432 * q^40 + 3104076808 * q^41 + 5982095000 * q^42 - 1722177552 * q^43 - 5105122436 * q^44 - 7406493484 * q^45 + 3435559326 * q^46 - 1327587552 * q^47 + 14535793696 * q^48 + 11976558636 * q^49 - 12237094384 * q^50 - 13921261140 * q^51 - 17237001432 * q^52 + 6725755626 * q^53 - 1674595226 * q^54 + 26323921200 * q^55 + 28163516640 * q^56 - 16884487756 * q^57 - 20073189204 * q^58 - 26237179548 * q^59 + 13611677716 * q^60 - 14411013726 * q^61 + 46185665964 * q^62 + 45955779184 * q^63 - 46365999744 * q^64 - 16224702172 * q^65 - 40938633602 * q^66 - 4241860068 * q^67 - 6528332916 * q^68 + 46750854252 * q^69 + 55705143270 * q^70 - 37335334656 * q^71 - 30237166608 * q^72 + 6005568990 * q^73 + 21663581922 * q^74 + 17116276792 * q^75 - 28817353320 * q^76 - 51928077698 * q^77 + 42636498520 * q^78 + 11712395640 * q^79 + 41748525232 * q^80 - 12455008366 * q^81 + 52795921668 * q^82 - 100821781200 * q^83 - 155783007940 * q^84 + 138884613396 * q^85 + 110437384472 * q^86 + 119455310144 * q^87 - 105039956616 * q^88 - 48633519778 * q^89 - 361508123864 * q^90 - 160908361488 * q^91 + 242956324248 * q^92 + 266530114134 * q^93 + 368497095702 * q^94 - 72161225128 * q^95 + 124456168928 * q^96 - 401308415928 * q^97 - 582375436706 * q^98 + 367357472240 * q^99

Introduction

L-functions

Modular forms

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