LMFDB - Embedded newform 63.12.e.b.46.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,12,Mod(37,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("63.37");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	63.e (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:	$48.4056203753$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{20}\cdot 3^{5}\cdot 7^{6} $
Twist minimal:	no (minimal twist has level 7)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			46.4
Root			$-0.427084 - 0.739732i$ of defining polynomial
Character	$\chi$	$=$	63.46
Dual form			63.12.e.b.37.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.85417 - 4.94356i) q^{2} +(1007.71 - 1745.40i) q^{4} +(4491.11 + 7778.83i) q^{5} +(-43014.2 + 11274.1i) q^{7} -23195.3 q^{8} +O(q^{10})$	\(q+(-2.85417 - 4.94356i) q^{2} +(1007.71 - 1745.40i) q^{4} +(4491.11 + 7778.83i) q^{5} +(-43014.2 + 11274.1i) q^{7} -23195.3 q^{8} +(25636.8 - 44404.2i) q^{10} +(45694.4 - 79145.1i) q^{11} -775221. q^{13} +(178504. + 180465. i) q^{14} +(-1.99758e6 - 3.45991e6i) q^{16} +(4.63726e6 - 8.03198e6i) q^{17} +(1.43623e6 + 2.48762e6i) q^{19} +1.81029e7 q^{20} -521678. q^{22} +(5.26756e6 + 9.12369e6i) q^{23} +(-1.59261e7 + 2.75848e7i) q^{25} +(2.21261e6 + 3.83236e6i) q^{26} +(-2.36679e7 + 8.64380e7i) q^{28} +4.24570e7 q^{29} +(5.29120e7 - 9.16463e7i) q^{31} +(-3.51549e7 + 6.08901e7i) q^{32} -5.29421e7 q^{34} +(-2.80881e8 - 2.83967e8i) q^{35} +(-1.54843e8 - 2.68196e8i) q^{37} +(8.19848e6 - 1.42002e7i) q^{38} +(-1.04173e8 - 1.80433e8i) q^{40} +1.19606e8 q^{41} +1.16451e9 q^{43} +(-9.20932e7 - 1.59510e8i) q^{44} +(3.00690e7 - 5.20811e7i) q^{46} +(-1.25006e8 - 2.16517e8i) q^{47} +(1.72312e9 - 9.69892e8i) q^{49} +1.81823e8 q^{50} +(-7.81196e8 + 1.35307e9i) q^{52} +(1.73284e9 - 3.00136e9i) q^{53} +8.20875e8 q^{55} +(9.97729e8 - 2.61506e8i) q^{56} +(-1.21180e8 - 2.09889e8i) q^{58} +(3.01421e9 - 5.22077e9i) q^{59} +(-5.31834e9 - 9.21163e9i) q^{61} -6.04079e8 q^{62} -7.78074e9 q^{64} +(-3.48161e9 - 6.03032e9i) q^{65} +(-1.10439e9 + 1.91285e9i) q^{67} +(-9.34601e9 - 1.61878e10i) q^{68} +(-6.02129e8 + 2.19904e9i) q^{70} +1.34122e10 q^{71} +(8.02494e9 - 1.38996e10i) q^{73} +(-8.83897e8 + 1.53095e9i) q^{74} +5.78919e9 q^{76} +(-1.07322e9 + 3.91953e9i) q^{77} +(-8.41954e9 - 1.45831e10i) q^{79} +(1.79427e10 - 3.10777e10i) q^{80} +(-3.41376e8 - 5.91281e8i) q^{82} +1.25839e10 q^{83} +8.33059e10 q^{85} +(-3.32372e9 - 5.75684e9i) q^{86} +(-1.05990e9 + 1.83580e9i) q^{88} +(-3.02118e10 - 5.23283e10i) q^{89} +(3.33455e10 - 8.73991e9i) q^{91} +2.12326e10 q^{92} +(-7.13578e8 + 1.23595e9i) q^{94} +(-1.29005e10 + 2.23444e10i) q^{95} -1.39153e11 q^{97} +(-9.71279e9 - 5.75010e9i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 22 q^{2} - 2556 q^{4} + 8782 q^{5} - 504 q^{7} - 97008 q^{8}+O(q^{10}) $ 12 * q - 22 * q^2 - 2556 * q^4 + 8782 * q^5 - 504 * q^7 - 97008 * q^8	\( 12 q - 22 q^{2} - 2556 q^{4} + 8782 q^{5} - 504 q^{7} - 97008 q^{8} + 111546 q^{10} + 1001572 q^{11} + 3864504 q^{13} + 1302994 q^{14} + 39120 q^{16} + 6704802 q^{17} + 4192212 q^{19} + 17646776 q^{20} - 8505684 q^{22} + 33871872 q^{23} + 13695456 q^{25} - 29350300 q^{26} + 181285692 q^{28} + 255125224 q^{29} - 331783920 q^{31} - 163252640 q^{32} + 1853334396 q^{34} - 1407354844 q^{35} - 833082774 q^{37} + 2086458338 q^{38} - 1219023432 q^{40} - 3104076808 q^{41} - 1722177552 q^{43} + 5105122436 q^{44} + 3435559326 q^{46} + 1327587552 q^{47} + 11976558636 q^{49} + 12237094384 q^{50} - 17237001432 q^{52} - 6725755626 q^{53} + 26323921200 q^{55} - 28163516640 q^{56} - 20073189204 q^{58} + 26237179548 q^{59} - 14411013726 q^{61} - 46185665964 q^{62} - 46365999744 q^{64} + 16224702172 q^{65} - 4241860068 q^{67} + 6528332916 q^{68} + 55705143270 q^{70} + 37335334656 q^{71} + 6005568990 q^{73} - 21663581922 q^{74} - 28817353320 q^{76} + 51928077698 q^{77} + 11712395640 q^{79} - 41748525232 q^{80} + 52795921668 q^{82} + 100821781200 q^{83} + 138884613396 q^{85} - 110437384472 q^{86} - 105039956616 q^{88} + 48633519778 q^{89} - 160908361488 q^{91} - 242956324248 q^{92} + 368497095702 q^{94} + 72161225128 q^{95} - 401308415928 q^{97} + 582375436706 q^{98}+O(q^{100}) \) 12 * q - 22 * q^2 - 2556 * q^4 + 8782 * q^5 - 504 * q^7 - 97008 * q^8 + 111546 * q^10 + 1001572 * q^11 + 3864504 * q^13 + 1302994 * q^14 + 39120 * q^16 + 6704802 * q^17 + 4192212 * q^19 + 17646776 * q^20 - 8505684 * q^22 + 33871872 * q^23 + 13695456 * q^25 - 29350300 * q^26 + 181285692 * q^28 + 255125224 * q^29 - 331783920 * q^31 - 163252640 * q^32 + 1853334396 * q^34 - 1407354844 * q^35 - 833082774 * q^37 + 2086458338 * q^38 - 1219023432 * q^40 - 3104076808 * q^41 - 1722177552 * q^43 + 5105122436 * q^44 + 3435559326 * q^46 + 1327587552 * q^47 + 11976558636 * q^49 + 12237094384 * q^50 - 17237001432 * q^52 - 6725755626 * q^53 + 26323921200 * q^55 - 28163516640 * q^56 - 20073189204 * q^58 + 26237179548 * q^59 - 14411013726 * q^61 - 46185665964 * q^62 - 46365999744 * q^64 + 16224702172 * q^65 - 4241860068 * q^67 + 6528332916 * q^68 + 55705143270 * q^70 + 37335334656 * q^71 + 6005568990 * q^73 - 21663581922 * q^74 - 28817353320 * q^76 + 51928077698 * q^77 + 11712395640 * q^79 - 41748525232 * q^80 + 52795921668 * q^82 + 100821781200 * q^83 + 138884613396 * q^85 - 110437384472 * q^86 - 105039956616 * q^88 + 48633519778 * q^89 - 160908361488 * q^91 - 242956324248 * q^92 + 368497095702 * q^94 + 72161225128 * q^95 - 401308415928 * q^97 + 582375436706 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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	$-0.186755\pi$
$2$	−2.85417	−	4.94356i	−0.0630688	−	0.109238i	−0.895836	+	0.444385i	$0.853422\pi$
$3$		0			0
$3$		0			0
$4$	1007.71	−	1745.40i	0.492045	−	0.852246i
$5$	4491.11	+	7778.83i	0.642716	+	1.11322i	0.984824	+	0.173556i	$0.0555257\pi$
$5$	4491.11	+	7778.83i	0.642716	+	1.11322i	−0.342108	+	0.939661i	$0.611141\pi$
$6$		0			0
$7$	−43014.2	+	11274.1i	−0.967326	+	0.253538i
$7$	−43014.2	+	11274.1i	−0.967326	+	0.253538i
$8$	−23195.3			−0.250268
$9$		0			0
$10$	25636.8	−	44404.2i	0.0810706	−	0.140418i
$11$	45694.4	−	79145.1i	0.0855468	−	0.148171i	−0.820077	−	0.572253i	$-0.806070\pi$
$11$	45694.4	−	79145.1i	0.0855468	−	0.148171i	0.905624	+	0.424081i	$0.139403\pi$
$12$		0			0
$13$	−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
$15$		0			0
$16$	−1.99758e6	−	3.45991e6i	−0.476261	−	0.824907i
$17$	4.63726e6	−	8.03198e6i	0.792123	−	1.37200i	−0.132527	−	0.991179i	$-0.542309\pi$
$17$	4.63726e6	−	8.03198e6i	0.792123	−	1.37200i	0.924650	−	0.380818i	$-0.124358\pi$
$18$		0			0
$19$	1.43623e6	+	2.48762e6i	0.133070	+	0.230483i	0.924858	−	0.380312i	$-0.124183\pi$
$19$	1.43623e6	+	2.48762e6i	0.133070	+	0.230483i	−0.791789	+	0.610795i	$0.790850\pi$
$20$	1.81029e7			1.26498
$21$		0			0
$22$	−521678.			−0.0215813
$23$	5.26756e6	+	9.12369e6i	0.170650	+	0.295575i	0.938647	−	0.344879i	$-0.112080\pi$
$23$	5.26756e6	+	9.12369e6i	0.170650	+	0.295575i	−0.767997	+	0.640453i	$0.778747\pi$
$24$		0			0
$25$	−1.59261e7	+	2.75848e7i	−0.326167	+	0.564938i
$26$	2.21261e6	+	3.83236e6i	0.0365218	+	0.0632576i
$27$		0			0
$28$	−2.36679e7	+	8.64380e7i	−0.259891	+	0.949151i
$29$	4.24570e7			0.384380			0.192190	−	0.981358i	$-0.438441\pi$
$29$	4.24570e7			0.384380			0.192190	+	0.981358i	$0.438441\pi$
$30$		0			0
$31$	5.29120e7	−	9.16463e7i	0.331944	−	0.574944i	−0.650949	−	0.759121i	$-0.725629\pi$
$31$	5.29120e7	−	9.16463e7i	0.331944	−	0.574944i	0.982893	+	0.184178i	$0.0589622\pi$
$32$	−3.51549e7	+	6.08901e7i	−0.185209	+	0.320791i
$33$		0			0
$34$	−5.29421e7			−0.199833
$35$	−2.80881e8	−	2.83967e8i	−0.903957	−	0.913890i
$36$		0			0
$37$	−1.54843e8	−	2.68196e8i	−0.367099	−	0.635833i	0.622012	−	0.783008i	$-0.286315\pi$
$37$	−1.54843e8	−	2.68196e8i	−0.367099	−	0.635833i	−0.989111	+	0.147174i	$0.952982\pi$
$38$	8.19848e6	−	1.42002e7i	0.0167851	−	0.0290726i
$39$		0			0
$40$	−1.04173e8	−	1.80433e8i	−0.160851	−	0.278603i
$41$	1.19606e8			0.161229			0.0806144	−	0.996745i	$-0.474312\pi$
$41$	1.19606e8			0.161229			0.0806144	+	0.996745i	$0.474312\pi$
$42$		0			0
$43$	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
$45$		0			0
$46$	3.00690e7	−	5.20811e7i	0.0215254	−	0.0372831i
$47$	−1.25006e8	−	2.16517e8i	−0.0795048	−	0.137706i	0.823532	−	0.567270i	$-0.192001\pi$
$47$	−1.25006e8	−	2.16517e8i	−0.0795048	−	0.137706i	−0.903036	+	0.429564i	$0.858667\pi$
$48$		0			0
$49$	1.72312e9	−	9.69892e8i	0.871437	−	0.490507i
$50$	1.81823e8			0.0822838
$51$		0			0
$52$	−7.81196e8	+	1.35307e9i	−0.284932	+	0.493517i
$53$	1.73284e9	−	3.00136e9i	0.569168	−	0.985829i	−0.427480	−	0.904025i	$-0.640599\pi$
$53$	1.73284e9	−	3.00136e9i	0.569168	−	0.985829i	0.996648	−	0.0818038i	$-0.0260681\pi$
$54$		0			0
$55$	8.20875e8			0.219929
$56$	9.97729e8	−	2.61506e8i	0.242091	−	0.0634524i
$57$		0			0
$58$	−1.21180e8	−	2.09889e8i	−0.0242424	−	0.0419890i
$59$	3.01421e9	−	5.22077e9i	0.548893	−	0.950711i	−0.449457	−	0.893302i	$-0.648383\pi$
$59$	3.01421e9	−	5.22077e9i	0.548893	−	0.950711i	0.998351	−	0.0574095i	$-0.0182841\pi$
$60$		0			0
$61$	−5.31834e9	−	9.21163e9i	−0.806236	−	1.39644i	−0.915454	−	0.402423i	$-0.868168\pi$
$61$	−5.31834e9	−	9.21163e9i	−0.806236	−	1.39644i	0.109218	−	0.994018i	$-0.465165\pi$
$62$	−6.04079e8			−0.0837412
$63$		0			0
$64$	−7.78074e9			−0.905798
$65$	−3.48161e9	−	6.03032e9i	−0.372183	−	0.644639i
$66$		0			0
$67$	−1.10439e9	+	1.91285e9i	−0.0999332	+	0.173089i	−0.911657	−	0.410952i	$-0.865196\pi$
$67$	−1.10439e9	+	1.91285e9i	−0.0999332	+	0.173089i	0.811724	+	0.584042i	$0.198530\pi$
$68$	−9.34601e9	−	1.61878e10i	−0.779520	−	1.35017i
$69$		0			0
$70$	−6.02129e8	+	2.19904e9i	−0.0428203	+	0.156385i
$71$	1.34122e10			0.882223			0.441111	−	0.897452i	$-0.354584\pi$
$71$	1.34122e10			0.882223			0.441111	+	0.897452i	$0.354584\pi$
$72$		0			0
$73$	8.02494e9	−	1.38996e10i	0.453071	−	0.784742i	−0.545504	−	0.838108i	$-0.683662\pi$
$73$	8.02494e9	−	1.38996e10i	0.453071	−	0.784742i	0.998575	+	0.0533664i	$0.0169951\pi$
$74$	−8.83897e8	+	1.53095e9i	−0.0463049	+	0.0802025i
$75$		0			0
$76$	5.78919e9			0.261905
$77$	−1.07322e9	+	3.91953e9i	−0.0451846	+	0.165019i
$78$		0			0
$79$	−8.41954e9	−	1.45831e10i	−0.307850	−	0.533212i	0.670042	−	0.742323i	$-0.266276\pi$
$79$	−8.41954e9	−	1.45831e10i	−0.307850	−	0.533212i	−0.977892	+	0.209111i	$0.932943\pi$
$80$	1.79427e10	−	3.10777e10i	0.612200	−	1.06036i
$81$		0			0
$82$	−3.41376e8	−	5.91281e8i	−0.0101685	−	0.0176124i
$83$	1.25839e10			0.350659			0.175329	−	0.984510i	$-0.443901\pi$
$83$	1.25839e10			0.350659			0.175329	+	0.984510i	$0.443901\pi$
$84$		0			0
$85$	8.33059e10			2.03644
$86$	−3.32372e9	−	5.75684e9i	−0.0761873	−	0.131960i
$87$		0			0
$88$	−1.05990e9	+	1.83580e9i	−0.0214096	+	0.0370826i
$89$	−3.02118e10	−	5.23283e10i	−0.573497	−	0.993326i	−0.996203	−	0.0870594i	$-0.972253\pi$
$89$	−3.02118e10	−	5.23283e10i	−0.573497	−	0.993326i	0.422706	−	0.906267i	$-0.361080\pi$
$90$		0			0
$91$	3.33455e10	−	8.73991e9i	0.560157	−	0.146818i
$92$	2.12326e10			0.335870
$93$		0			0
$94$	−7.13578e8	+	1.23595e9i	−0.0100286	+	0.0173700i
$95$	−1.29005e10	+	2.23444e10i	−0.171052	+	0.296270i
$96$		0			0
$97$	−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
$99$		0			0
$100$	3.20977e10	+	5.55949e10i	0.320977	+	0.555949i
$101$	−7.27138e10	+	1.25944e11i	−0.688413	+	1.19237i	0.283938	+	0.958843i	$0.408359\pi$
$101$	−7.27138e10	+	1.25944e11i	−0.688413	+	1.19237i	−0.972351	+	0.233524i	$0.924974\pi$
$102$		0			0
$103$	−9.52360e10	−	1.64954e11i	−0.809462	−	1.40203i	−0.913237	−	0.407429i	$-0.866425\pi$
$103$	−9.52360e10	−	1.64954e11i	−0.809462	−	1.40203i	0.103775	−	0.994601i	$-0.466908\pi$
$104$	1.79815e10			0.144925
$105$		0			0
$106$	−1.97833e10			−0.143587
$107$	−2.98014e10	−	5.16176e10i	−0.205412	−	0.355785i	0.744852	−	0.667230i	$-0.232520\pi$
$107$	−2.98014e10	−	5.16176e10i	−0.205412	−	0.355785i	−0.950264	+	0.311445i	$0.899187\pi$
$108$		0			0
$109$	−7.38720e10	+	1.27950e11i	−0.459869	+	0.796517i	−0.998954	−	0.0457350i	$-0.985437\pi$
$109$	−7.38720e10	+	1.27950e11i	−0.459869	+	0.796517i	0.539084	+	0.842252i	$0.318770\pi$
$110$	−2.34292e9	−	4.05805e9i	−0.0138707	−	0.0240247i
$111$		0			0
$112$	1.24932e11	+	1.26304e11i	0.669844	+	0.677204i
$113$	2.11327e11			1.07901			0.539503	−	0.841984i	$-0.318612\pi$
$113$	2.11327e11			1.07901			0.539503	+	0.841984i	$0.318612\pi$
$114$		0			0
$115$	−4.73144e10	+	8.19510e10i	−0.219359	+	0.379941i
$116$	4.27843e10	−	7.41046e10i	0.189132	−	0.327586i
$117$		0			0
$118$	−3.44123e10			−0.138472
$119$	−1.08915e11	+	3.97770e11i	−0.418388	+	1.52800i
$120$		0			0
$121$	1.38480e11	+	2.39854e11i	0.485364	+	0.840674i
$122$	−3.03589e10	+	5.25831e10i	−0.101697	+	0.176144i
$123$		0			0
$124$	−1.06640e11	−	1.84705e11i	−0.326663	−	0.565796i
$125$	1.52481e11			0.446901
$126$		0			0
$127$	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
$129$		0			0
$130$	−1.98742e10	+	3.44231e10i	−0.0469462	+	0.0813132i
$131$	−2.15308e10	−	3.72924e10i	−0.0487604	−	0.0844556i	0.840615	−	0.541633i	$-0.182194\pi$
$131$	−2.15308e10	−	3.72924e10i	−0.0487604	−	0.0844556i	−0.889375	+	0.457177i	$0.848860\pi$
$132$		0			0
$133$	−8.98239e10	−	9.08109e10i	−0.187158	−	0.189214i
$134$	1.26084e10			0.0252107
$135$		0			0
$136$	−1.07563e11	+	1.86304e11i	−0.198243	+	0.343368i
$137$	−4.92302e11	+	8.52692e11i	−0.871502	+	1.50949i	−0.0110587	+	0.999939i	$0.503520\pi$
$137$	−4.92302e11	+	8.52692e11i	−0.871502	+	1.50949i	−0.860443	+	0.509547i	$0.829813\pi$
$138$		0			0
$139$	−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
$141$		0			0
$142$	−3.82806e10	−	6.63040e10i	−0.0556407	−	0.0963726i
$143$	−3.54233e10	+	6.13549e10i	−0.0495383	+	0.0858028i
$144$		0			0
$145$	1.90679e11	+	3.30266e11i	0.247047	+	0.427898i
$146$	−9.16181e10			−0.114299
$147$		0			0
$148$	−6.24147e11			−0.722515
$149$	−2.21679e11	−	3.83960e11i	−0.247287	−	0.428313i	0.715485	−	0.698628i	$-0.246206\pi$
$149$	−2.21679e11	−	3.83960e11i	−0.247287	−	0.428313i	−0.962772	+	0.270314i	$0.912872\pi$
$150$		0			0
$151$	6.38440e11	−	1.10581e12i	0.661830	−	1.14632i	−0.318304	−	0.947989i	$-0.603113\pi$
$151$	6.38440e11	−	1.10581e12i	0.661830	−	1.14632i	0.980134	−	0.198335i	$-0.0635534\pi$
$152$	−3.33138e10	−	5.77012e10i	−0.0333031	−	0.0576827i
$153$		0			0
$154$	2.24396e10	−	5.88145e9i	0.0208762	−	0.00547168i
$155$	9.50535e11			0.853382
$156$		0			0
$157$	−4.66854e11	+	8.08615e11i	−0.390601	+	0.676541i	−0.992529	−	0.122010i	$-0.961066\pi$
$157$	−4.66854e11	+	8.08615e11i	−0.390601	+	0.676541i	0.601928	+	0.798550i	$0.294399\pi$
$158$	−4.80616e10	+	8.32451e10i	−0.0388315	+	0.0672581i
$159$		0			0
$160$	−6.31538e11			−0.476146
$161$	−3.29441e11	−	3.33061e11i	−0.240014	−	0.242651i
$162$		0			0
$163$	1.23921e12	+	2.14638e12i	0.843556	+	1.46108i	0.886869	+	0.462020i	$0.152875\pi$
$163$	1.23921e12	+	2.14638e12i	0.843556	+	1.46108i	−0.0433132	+	0.999062i	$0.513791\pi$
$164$	1.20528e11	−	2.08761e11i	0.0793317	−	0.137407i
$165$		0			0
$166$	−3.59165e10	−	6.22092e10i	−0.0221156	−	0.0383054i
$167$	2.38715e12			1.42213			0.711065	−	0.703126i	$-0.248213\pi$
$167$	2.38715e12			1.42213			0.711065	+	0.703126i	$0.248213\pi$
$168$		0			0
$169$	−1.19119e12			−0.664669
$170$	−2.37769e11	−	4.11828e11i	−0.128436	−	0.222457i
$171$		0			0
$172$	1.17349e12	−	2.03254e12i	0.594391	−	1.02952i
$173$	2.71347e11	+	4.69988e11i	0.133129	+	0.230586i	0.924881	−	0.380256i	$-0.124164\pi$
$173$	2.71347e11	+	4.69988e11i	0.133129	+	0.230586i	−0.791752	+	0.610842i	$0.790831\pi$
$174$		0			0
$175$	3.74055e11	−	1.36609e12i	0.172277	−	0.629174i
$176$	−3.65113e11			−0.162970
$177$		0			0
$178$	−1.72459e11	+	2.98708e11i	−0.0723396	+	0.125296i
$179$	1.65743e12	−	2.87075e12i	0.674128	−	1.16762i	−0.302594	−	0.953119i	$-0.597853\pi$
$179$	1.65743e12	−	2.87075e12i	0.674128	−	1.16762i	0.976723	−	0.214505i	$-0.0688139\pi$
$180$		0			0
$181$	−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
$183$		0			0
$184$	−1.22183e11	−	2.11627e11i	−0.0427083	−	0.0739730i
$185$	1.39084e12	−	2.40900e12i	0.471880	−	0.817320i
$186$		0			0
$187$	−4.23794e11	−	7.34033e11i	−0.135527	−	0.234740i
$188$	−5.03879e11			−0.156480
$189$		0			0
$190$	1.47281e11			0.0431521
$191$	−2.41197e12	−	4.17765e12i	−0.686575	−	1.18918i	−0.972939	−	0.231062i	$-0.925780\pi$
$191$	−2.41197e12	−	4.17765e12i	−0.686575	−	1.18918i	0.286364	−	0.958121i	$-0.407553\pi$
$192$		0			0
$193$	3.50989e11	−	6.07931e11i	0.0943471	−	0.163414i	−0.814989	−	0.579477i	$-0.803257\pi$
$193$	3.50989e11	−	6.07931e11i	0.0943471	−	0.163414i	0.909336	+	0.416063i	$0.136590\pi$
$194$	3.97166e11	+	6.87911e11i	0.103768	+	0.179731i
$195$		0			0
$196$	4.35469e10	−	3.98490e12i	0.0107535	−	0.984031i
$197$	−3.47030e12			−0.833302			−0.416651	−	0.909066i	$-0.636796\pi$
$197$	−3.47030e12			−0.833302			−0.416651	+	0.909066i	$0.636796\pi$
$198$		0			0
$199$	1.44819e12	−	2.50834e12i	0.328953	−	0.569764i	−0.653351	−	0.757055i	$-0.726637\pi$
$199$	1.44819e12	−	2.50834e12i	0.328953	−	0.569764i	0.982304	+	0.187291i	$0.0599708\pi$
$200$	3.69412e11	−	6.39840e11i	0.0816292	−	0.141386i
$201$		0			0
$202$	8.30150e11			0.173670
$203$	−1.82626e12	+	4.78665e11i	−0.371821	+	0.0974548i
$204$		0			0
$205$	5.37165e11	+	9.30397e11i	0.103624	+	0.179482i
$206$	−5.43639e11	+	9.41611e11i	−0.102104	+	0.176849i
$207$		0			0
$208$	1.54857e12	+	2.68220e12i	0.275792	+	0.477686i
$209$	2.62511e11			0.0455347
$210$		0			0
$211$	−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
$213$		0			0
$214$	−1.70117e11	+	2.94651e11i	−0.0259102	+	0.0448778i
$215$	5.22996e12	+	9.05855e12i	0.776402	+	1.34477i
$216$		0			0
$217$	−1.24274e12	+	4.53863e12i	−0.175328	+	0.640318i
$218$	8.43373e11			0.116014
$219$		0			0
$220$	8.27202e11	−	1.43276e12i	0.108215	−	0.187434i
$221$	−3.59491e12	+	6.22656e12i	−0.458701	+	0.794494i
$222$		0			0
$223$	−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
$225$		0			0
$226$	−6.03163e11	−	1.04471e12i	−0.0680516	−	0.117869i
$227$	6.08276e12	−	1.05356e13i	0.669820	−	1.16016i	−0.308134	−	0.951343i	$-0.599704\pi$
$227$	6.08276e12	−	1.05356e13i	0.669820	−	1.16016i	0.977954	−	0.208820i	$-0.0669622\pi$
$228$		0			0
$229$	2.17759e12	+	3.77170e12i	0.228497	+	0.395769i	0.957363	−	0.288888i	$-0.0932854\pi$
$229$	2.17759e12	+	3.77170e12i	0.228497	+	0.395769i	−0.728866	+	0.684657i	$0.759952\pi$
$230$	5.40173e11			0.0553388
$231$		0			0
$232$	−9.84806e11			−0.0961981
$233$	8.54463e12	+	1.47997e13i	0.815147	+	1.41188i	0.909222	+	0.416311i	$0.136677\pi$
$233$	8.54463e12	+	1.47997e13i	0.815147	+	1.41188i	−0.0940755	+	0.995565i	$0.529990\pi$
$234$		0			0
$235$	1.12283e12	−	1.94481e12i	0.102198	−	0.177012i
$236$	−6.07489e12	−	1.05220e13i	−0.540160	−	0.935585i
$237$		0			0
$238$	2.27726e12	−	5.96875e11i	0.193304	−	0.0506652i
$239$	3.04856e11			0.0252876			0.0126438	−	0.999920i	$-0.495975\pi$
$239$	3.04856e11			0.0252876			0.0126438	+	0.999920i	$0.495975\pi$
$240$		0			0
$241$	−8.33995e11	+	1.44452e12i	−0.0660800	+	0.114454i	−0.897173	−	0.441680i	$-0.854383\pi$
$241$	−8.33995e11	+	1.44452e12i	−0.0660800	+	0.114454i	0.831093	+	0.556134i	$0.187716\pi$
$242$	7.90490e11	−	1.36917e12i	0.0612226	−	0.106041i
$243$		0			0
$244$	−2.14373e13			−1.58682
$245$	1.52833e13	+	9.04794e12i	1.10613	+	0.654842i
$246$		0			0
$247$	−1.11339e12	−	1.92846e12i	−0.0770577	−	0.133468i
$248$	−1.22731e12	+	2.12577e12i	−0.0830751	+	0.143890i
$249$		0			0
$250$	−4.35207e11	−	7.53801e11i	−0.0281855	−	0.0488187i
$251$	−1.29045e13			−0.817590			−0.408795	−	0.912626i	$-0.634051\pi$
$251$	−1.29045e13			−0.817590			−0.408795	+	0.912626i	$0.634051\pi$
$252$		0			0
$253$	9.62793e11			0.0583943
$254$	−1.00395e12	−	1.73888e12i	−0.0595833	−	0.103201i
$255$		0			0
$256$	−7.42973e12	+	1.28687e13i	−0.422331	+	0.731499i
$257$	1.15462e13	+	1.99986e13i	0.642402	+	1.11267i	0.984895	+	0.173152i	$0.0553953\pi$
$257$	1.15462e13	+	1.99986e13i	0.642402	+	1.11267i	−0.342493	+	0.939520i	$0.611271\pi$
$258$		0			0
$259$	9.68413e12	+	9.79053e12i	0.516311	+	0.521985i
$260$	−1.40338e13			−0.732522
$261$		0			0
$262$	−1.22905e11	+	2.12878e11i	−0.00615053	+	0.0106530i
$263$	−1.41565e13	+	2.45199e13i	−0.693746	+	1.20160i	0.276855	+	0.960912i	$0.410708\pi$
$263$	−1.41565e13	+	2.45199e13i	−0.693746	+	1.20160i	−0.970601	+	0.240692i	$0.922626\pi$
$264$		0			0
$265$	3.11295e13			1.46325
$266$	−1.92557e11	+	7.03240e11i	−0.00886564	+	0.0323783i
$267$		0			0
$268$	2.22580e12	+	3.85519e12i	0.0983432	+	0.170335i
$269$	−1.38564e13	+	2.39999e13i	−0.599807	+	1.03890i	0.393042	+	0.919521i	$0.371423\pi$
$269$	−1.38564e13	+	2.39999e13i	−0.599807	+	1.03890i	−0.992849	+	0.119376i	$0.961911\pi$
$270$		0			0
$271$	2.41659e12	+	4.18566e12i	0.100432	+	0.173954i	0.911863	−	0.410495i	$-0.134644\pi$
$271$	2.41659e12	+	4.18566e12i	0.100432	+	0.173954i	−0.811431	+	0.584449i	$0.801311\pi$
$272$	−3.70533e13			−1.50903
$273$		0			0
$274$	5.62045e12			0.219858
$275$	1.45547e12	+	2.52095e12i	0.0558050	+	0.0966572i
$276$		0			0
$277$	−1.89204e13	+	3.27711e13i	−0.697094	+	1.20740i	0.272376	+	0.962191i	$0.412191\pi$
$277$	−1.89204e13	+	3.27711e13i	−0.697094	+	1.20740i	−0.969470	+	0.245211i	$0.921143\pi$
$278$	2.08863e11	+	3.61762e11i	0.00754424	+	0.0130670i
$279$		0			0
$280$	6.51513e12	+	6.58671e12i	0.226232	+	0.228718i
$281$	3.89411e13			1.32594			0.662969	−	0.748647i	$-0.269296\pi$
$281$	3.89411e13			1.32594			0.662969	+	0.748647i	$0.269296\pi$
$282$		0			0
$283$	1.01150e13	−	1.75197e13i	0.331238	−	0.573722i	−0.651516	−	0.758634i	$-0.725867\pi$
$283$	1.01150e13	−	1.75197e13i	0.331238	−	0.573722i	0.982755	+	0.184913i	$0.0592002\pi$
$284$	1.35156e13	−	2.34096e13i	0.434093	−	0.751871i
$285$		0			0
$286$	4.04416e11			0.0124973
$287$	−5.14477e12	+	1.34845e12i	−0.155961	+	0.0408776i
$288$		0			0
$289$	−2.58725e13	−	4.48125e13i	−0.754919	−	1.30756i
$290$	1.08846e12	−	1.88527e12i	0.0311619	−	0.0539740i
$291$		0			0
$292$	−1.61736e13	−	2.80135e13i	−0.445862	−	0.772256i
$293$	−1.09986e13			−0.297554			−0.148777	−	0.988871i	$-0.547534\pi$
$293$	−1.09986e13			−0.297554			−0.148777	+	0.988871i	$0.547534\pi$
$294$		0			0
$295$	5.41487e13			1.41113
$296$	3.59164e12	+	6.22090e12i	0.0918731	+	0.159129i
$297$		0			0
$298$	−1.26542e12	+	2.19177e12i	−0.0311922	+	0.0540264i
$299$	−4.08353e12	−	7.07287e12i	−0.0988197	−	0.171161i
$300$		0			0
$301$	−5.00906e13	+	1.31288e13i	−1.16853	+	0.306274i
$302$	−7.28886e12			−0.166963
$303$		0			0
$304$	5.73797e12	−	9.93845e12i	0.126752	−	0.219540i
$305$	4.77705e13	−	8.27410e13i	1.03636	−	1.79503i
$306$		0			0
$307$	−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
$309$		0			0
$310$	−2.71299e12	−	4.69903e12i	−0.0538218	−	0.0932221i
$311$	7.97859e12	−	1.38193e13i	0.155505	−	0.269342i	−0.777738	−	0.628589i	$-0.783633\pi$
$311$	7.97859e12	−	1.38193e13i	0.155505	−	0.269342i	0.933243	+	0.359246i	$0.116966\pi$
$312$		0			0
$313$	1.52684e13	+	2.64456e13i	0.287276	+	0.497577i	0.973159	−	0.230136i	$-0.0739169\pi$
$313$	1.52684e13	+	2.64456e13i	0.287276	+	0.497577i	−0.685882	+	0.727712i	$0.740584\pi$
$314$	5.32992e12			0.0985389
$315$		0			0
$316$	−3.39377e13			−0.605904
$317$	1.70577e13	+	2.95449e13i	0.299292	+	0.518390i	0.975974	−	0.217886i	$-0.0699161\pi$
$317$	1.70577e13	+	2.95449e13i	0.299292	+	0.518390i	−0.676682	+	0.736276i	$0.736583\pi$
$318$		0			0
$319$	1.94005e12	−	3.36027e12i	0.0328825	−	0.0569541i
$320$	−3.49442e13	−	6.05251e13i	−0.582170	−	1.00835i
$321$		0			0
$322$	−7.06228e11	+	2.57923e12i	−0.0113694	+	0.0415224i
$323$	2.66407e13			0.421630
$324$		0			0
$325$	1.23463e13	−	2.13844e13i	0.188876	−	0.327143i
$326$	7.07384e12	−	1.22523e13i	0.106404	−	0.184297i
$327$		0			0
$328$	−2.77431e12			−0.0403504
$329$	7.81808e12	+	7.90398e12i	0.111821	+	0.113049i
$330$		0			0
$331$	1.39115e13	+	2.40955e13i	0.192451	+	0.333335i	0.946062	−	0.323986i	$-0.105023\pi$
$331$	1.39115e13	+	2.40955e13i	0.192451	+	0.333335i	−0.753611	+	0.657321i	$0.771690\pi$
$332$	1.26809e13	−	2.19639e13i	0.172540	−	0.298848i
$333$		0			0
$334$	−6.81333e12	−	1.18010e13i	−0.0896920	−	0.155351i
$335$	−1.98397e13			−0.256914
$336$		0			0
$337$	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
$339$		0			0
$340$	8.39480e13	−	1.45402e14i	1.00202	−	1.73555i
$341$	−4.83557e12	−	8.37545e12i	−0.0567935	−	0.0983692i
$342$		0			0
$343$	−6.31838e13	+	6.11457e13i	−0.718602	+	0.695422i
$344$	−2.70113e13			−0.302325
$345$		0			0
$346$	1.54894e12	−	2.68285e12i	0.0167926	−	0.0290856i
$347$	5.57163e13	−	9.65034e13i	0.594525	−	1.02975i	−0.399089	−	0.916912i	$-0.630674\pi$
$347$	5.57163e13	−	9.65034e13i	0.594525	−	1.02975i	0.993614	−	0.112835i	$-0.0359931\pi$
$348$		0			0
$349$	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
$351$		0			0
$352$	3.21277e12	+	5.56467e12i	0.0316880	+	0.0548852i
$353$	−4.46527e13	+	7.73407e13i	−0.433597	+	0.751012i	−0.997180	−	0.0750472i	$-0.976089\pi$
$353$	−4.46527e13	+	7.73407e13i	−0.433597	+	0.751012i	0.563583	+	0.826060i	$0.309423\pi$
$354$		0			0
$355$	6.02356e13	+	1.04331e14i	0.567019	+	0.982105i
$356$	−1.21779e14			−1.12874
$357$		0			0
$358$	−1.89223e13			−0.170066
$359$	−8.39570e13	−	1.45418e14i	−0.743083	−	1.28706i	−0.951085	−	0.308929i	$-0.900029\pi$
$359$	−8.39570e13	−	1.45418e14i	−0.743083	−	1.28706i	0.208002	−	0.978128i	$-0.433304\pi$
$360$		0			0
$361$	5.41196e13	−	9.37379e13i	0.464585	−	0.804685i
$362$	2.16193e12	+	3.74457e12i	0.0182786	+	0.0316595i
$363$		0			0
$364$	1.83479e13	−	6.70086e13i	0.150497	−	0.549633i
$365$	1.44164e14			1.16478
$366$		0			0
$367$	−1.03952e13	+	1.80050e13i	−0.0815021	+	0.141166i	−0.903895	−	0.427754i	$-0.859305\pi$
$367$	−1.03952e13	+	1.80050e13i	−0.0815021	+	0.141166i	0.822393	+	0.568919i	$0.192638\pi$
$368$	2.10448e13	−	3.64506e13i	0.162548	−	0.281541i
$369$		0			0
$370$	−1.58787e13			−0.119044
$371$	−4.06990e13	+	1.48637e14i	−0.300627	+	1.09792i
$372$		0			0
$373$	−6.86233e13	−	1.18859e14i	−0.492122	−	0.852381i	0.507836	−	0.861454i	$-0.330445\pi$
$373$	−6.86233e13	−	1.18859e14i	−0.492122	−	0.852381i	−0.999959	+	0.00907250i	$0.997112\pi$
$374$	−2.41916e12	+	4.19011e12i	−0.0170951	+	0.0296095i
$375$		0			0
$376$	2.89956e12	+	5.02219e12i	0.0198975	+	0.0344635i
$377$	−3.29136e13			−0.222586
$378$		0			0
$379$	−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
$381$		0			0
$382$	−1.37683e13	+	2.38474e13i	−0.0866029	+	0.150001i
$383$	1.10671e14	+	1.91687e14i	0.686183	+	1.18850i	0.973063	+	0.230537i	$0.0740484\pi$
$383$	1.10671e14	+	1.91687e14i	0.686183	+	1.18850i	−0.286881	+	0.957966i	$0.592618\pi$
$384$		0			0
$385$	−3.53093e13	+	9.25462e12i	−0.212743	+	0.0557603i
$386$	−4.00713e12			−0.0238014
$387$		0			0
$388$	−1.40225e14	+	2.42877e14i	−0.809565	+	1.40221i
$389$	5.67324e13	−	9.82634e13i	0.322930	−	0.559331i	−0.658161	−	0.752877i	$-0.728666\pi$
$389$	5.67324e13	−	9.82634e13i	0.322930	−	0.559331i	0.981091	+	0.193546i	$0.0619989\pi$
$390$		0			0
$391$	9.77083e13			0.540704
$392$	−3.99683e13	+	2.24970e13i	−0.218093	+	0.122758i
$393$		0			0
$394$	9.90481e12	+	1.71556e13i	0.0525554	+	0.0910286i
$395$	7.56262e13	−	1.30988e14i	0.395720	−	0.685407i
$396$		0			0
$397$	6.27094e13	+	1.08616e14i	0.319143	+	0.552771i	0.980309	−	0.197468i	$-0.0632718\pi$
$397$	6.27094e13	+	1.08616e14i	0.319143	+	0.552771i	−0.661167	+	0.750239i	$0.729938\pi$
$398$	−1.65335e13			−0.0829868
$399$		0			0
$400$	1.27255e14			0.621362
$401$	−2.01310e13	−	3.48679e13i	−0.0969552	−	0.167931i	0.813468	−	0.581610i	$-0.197577\pi$
$401$	−2.01310e13	−	3.48679e13i	−0.0969552	−	0.167931i	−0.910423	+	0.413679i	$0.864244\pi$
$402$		0			0
$403$	−4.10185e13	+	7.10461e13i	−0.192222	+	0.332937i
$404$	1.46548e14	+	2.53829e14i	0.677460	+	1.17340i
$405$		0			0
$406$	7.57875e12	+	7.66202e12i	0.0340961	+	0.0344707i
$407$	−2.83019e13			−0.125616
$408$		0			0
$409$	9.79564e13	−	1.69665e14i	0.423209	−	0.733019i	−0.573043	−	0.819525i	$-0.694237\pi$
$409$	9.79564e13	−	1.69665e14i	0.423209	−	0.733019i	0.996251	+	0.0865068i	$0.0275704\pi$
$410$	3.06632e12	−	5.31102e12i	0.0130709	−	0.0226395i
$411$		0			0
$412$	−3.83880e14			−1.59317
$413$	−7.07945e13	+	2.58550e14i	−0.289918	+	1.05881i
$414$		0			0
$415$	5.65156e13	+	9.78878e13i	0.225374	+	0.390359i
$416$	2.72528e13	−	4.72033e13i	0.107250	−	0.185763i
$417$		0			0
$418$	−7.49250e11	−	1.29774e12i	−0.00287182	−	0.00497414i
$419$	−3.11107e14			−1.17688			−0.588441	−	0.808541i	$-0.700258\pi$
$419$	−3.11107e14			−1.17688			−0.588441	+	0.808541i	$0.700258\pi$
$420$		0			0
$421$	−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
$423$		0			0
$424$	−4.01938e13	+	6.96177e13i	−0.142445	+	0.246722i
$425$	1.47707e14	+	2.55836e14i	0.516729	+	0.895001i
$426$		0			0
$427$	3.32617e14	+	3.36272e14i	1.13394	+	1.14640i
$428$	−1.20125e14			−0.404288
$429$		0			0
$430$	2.98544e13	−	5.17093e13i	0.0979335	−	0.169626i
$431$	−2.45551e14	+	4.25307e14i	−0.795274	+	1.37746i	0.127391	+	0.991853i	$0.459340\pi$
$431$	−2.45551e14	+	4.25307e14i	−0.795274	+	1.37746i	−0.922665	+	0.385603i	$0.873994\pi$
$432$		0			0
$433$	−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
$435$		0			0
$436$	1.48883e14	+	2.57873e14i	0.452552	+	0.783844i
$437$	−1.51309e13	+	2.62074e13i	−0.0454167	+	0.0786640i
$438$		0			0
$439$	−1.39073e14	−	2.40882e14i	−0.407088	−	0.705098i	0.587474	−	0.809243i	$-0.300123\pi$
$439$	−1.39073e14	−	2.40882e14i	−0.407088	−	0.705098i	−0.994562	+	0.104145i	$0.966789\pi$
$440$	−1.90405e13			−0.0550412
$441$		0			0
$442$	4.10419e13			0.115719
$443$	−2.19620e14	−	3.80393e14i	−0.611578	−	1.05928i	−0.990975	−	0.134049i	$-0.957202\pi$
$443$	−2.19620e14	−	3.80393e14i	−0.611578	−	1.05928i	0.379397	−	0.925234i	$-0.376131\pi$
$444$		0			0
$445$	2.71369e14	−	4.70025e14i	0.737191	−	1.27685i
$446$	7.19980e12	+	1.24704e13i	0.0193187	+	0.0334611i
$447$		0			0
$448$	3.34682e14	−	8.77208e13i	0.876201	−	0.229654i
$449$	8.42239e13			0.217811			0.108906	−	0.994052i	$-0.465265\pi$
$449$	8.42239e13			0.217811			0.108906	+	0.994052i	$0.465265\pi$
$450$		0			0
$451$	5.46534e12	−	9.46624e12i	0.0137926	−	0.0238895i
$452$	2.12956e14	−	3.68850e14i	0.530919	−	0.919578i
$453$		0			0
$454$	−6.94449e13			−0.168979
$455$	2.17745e14	+	2.20137e14i	0.523462	+	0.529214i
$456$		0			0
$457$	−9.06110e13	−	1.56943e14i	−0.212638	−	0.368300i	0.739901	−	0.672716i	$-0.234872\pi$
$457$	−9.06110e13	−	1.56943e14i	−0.212638	−	0.368300i	−0.952539	+	0.304415i	$0.901539\pi$
$458$	1.24304e13	−	2.15301e13i	0.0288221	−	0.0499214i
$459$		0			0
$460$	9.53582e13	+	1.65165e14i	0.215869	+	0.373896i
$461$	−2.32317e14			−0.519668			−0.259834	−	0.965653i	$-0.583668\pi$
$461$	−2.32317e14			−0.519668			−0.259834	+	0.965653i	$0.583668\pi$
$462$		0			0
$463$	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
$465$		0			0
$466$	4.87756e13	−	8.44819e13i	0.102821	−	0.178091i
$467$	4.71057e13	+	8.15895e13i	0.0981365	+	0.169977i	0.910913	−	0.412598i	$-0.135378\pi$
$467$	4.71057e13	+	8.15895e13i	0.0981365	+	0.169977i	−0.812777	+	0.582575i	$0.802045\pi$
$468$		0			0
$469$	2.59386e13	−	9.47308e13i	0.0527832	−	0.192771i
$470$	−1.28190e13			−0.0257820
$471$		0			0
$472$	−6.99157e13	+	1.21098e14i	−0.137371	+	0.237933i
$473$	5.32118e13	−	9.21655e13i	0.103341	−	0.178991i
$474$		0			0
$475$	−9.14942e13			−0.173612
$476$	5.84514e14	+	5.90936e14i	1.09637	+	1.10841i
$477$		0			0
$478$	−8.70111e11	−	1.50708e12i	−0.00159486	−	0.00276237i
$479$	3.21363e14	−	5.56617e14i	0.582305	−	1.00858i	−0.412900	−	0.910776i	$-0.635484\pi$
$479$	3.21363e14	−	5.56617e14i	0.582305	−	1.00858i	0.995205	−	0.0978061i	$-0.0311825\pi$
$480$		0			0
$481$	1.20038e14	+	2.07911e14i	0.212579	+	0.368197i
$482$	9.52145e12			0.0166703
$483$		0			0
$484$	5.58189e14			0.955282
$485$	−6.24951e14	−	1.08245e15i	−1.05747	−	1.83158i
$486$		0			0
$487$	−4.11872e14	+	7.13383e14i	−0.681323	+	1.18009i	0.293255	+	0.956034i	$0.405262\pi$
$487$	−4.11872e14	+	7.13383e14i	−0.681323	+	1.18009i	−0.974577	+	0.224051i	$0.928072\pi$
$488$	1.23361e14	+	2.13667e14i	0.201775	+	0.349485i
$489$		0			0
$490$	1.10786e12	−	1.01379e14i	0.00177177	−	0.162132i
$491$	7.05003e14			1.11492			0.557459	−	0.830204i	$-0.311776\pi$
$491$	7.05003e14			1.11492			0.557459	+	0.830204i	$0.311776\pi$
$492$		0			0
$493$	1.96885e14	−	3.41014e14i	0.304476	−	0.527369i
$494$	−6.35563e12	+	1.10083e13i	−0.00971987	+	0.0168353i
$495$		0			0
$496$	−4.22784e14			−0.632367
$497$	−5.76914e14	+	1.51210e14i	−0.853397	+	0.223677i
$498$		0			0
$499$	−4.11492e14	−	7.12725e14i	−0.595399	−	1.03126i	−0.993490	−	0.113916i	$-0.963661\pi$
$499$	−4.11492e14	−	7.12725e14i	−0.595399	−	1.03126i	0.398091	−	0.917346i	$-0.369673\pi$
$500$	1.53657e14	−	2.66141e14i	0.219895	−	0.380870i
$501$		0			0
$502$	3.68316e13	+	6.37942e13i	0.0515644	+	0.0893122i
$503$	−1.18063e15			−1.63489			−0.817445	−	0.576007i	$-0.804610\pi$
$503$	−1.18063e15			−1.63489			−0.817445	+	0.576007i	$0.804610\pi$
$504$		0			0
$505$	−1.30626e15			−1.76982
$506$	−2.74797e12	−	4.75963e12i	−0.00368286	−	0.00637889i
$507$		0			0
$508$	3.54458e14	−	6.13939e14i	0.464852	−	0.805147i
$509$	3.07502e14	+	5.32609e14i	0.398933	+	0.690972i	0.993595	−	0.113004i	$-0.0360472\pi$
$509$	3.07502e14	+	5.32609e14i	0.398933	+	0.690972i	−0.594661	+	0.803976i	$0.702714\pi$
$510$		0			0
$511$	−1.88481e14	+	6.88354e14i	−0.239305	+	0.873971i
$512$	4.70686e14			0.591216
$513$		0			0
$514$	6.59096e13	−	1.14159e14i	0.0810310	−	0.140350i
$515$	8.55431e14	−	1.48165e15i	1.04051	−	1.80221i
$516$		0			0
$517$	−2.28484e13			−0.0272055
$518$	2.07600e13	−	7.58179e13i	0.0244576	−	0.0893220i
$519$		0			0
$520$	8.07570e13	+	1.39875e14i	0.0931455	+	0.161333i
$521$	1.98750e14	−	3.44245e14i	0.226830	−	0.392880i	−0.730037	−	0.683407i	$-0.760497\pi$
$521$	1.98750e14	−	3.44245e14i	0.226830	−	0.392880i	0.956867	+	0.290527i	$0.0938306\pi$
$522$		0			0
$523$	−4.29122e14	−	7.43262e14i	−0.479537	−	0.830582i	0.520188	−	0.854052i	$-0.325862\pi$
$523$	−4.29122e14	−	7.43262e14i	−0.479537	−	0.830582i	−0.999725	+	0.0234698i	$0.992529\pi$
$524$	−8.67869e13			−0.0959693
$525$		0			0
$526$	1.61621e14			0.175015
$527$	−4.90734e14	−	8.49976e14i	−0.525881	−	0.910853i
$528$		0			0
$529$	4.20910e14	−	7.29038e14i	0.441757	−	0.765146i
$530$	−8.88488e13	−	1.53891e14i	−0.0922857	−	0.159843i
$531$		0			0
$532$	−2.49018e14	+	6.52679e13i	−0.253347	+	0.0664027i
$533$	−9.27213e13			−0.0933640
$534$		0			0
$535$	2.67683e14	−	4.63641e14i	0.264044	−	0.457337i
$536$	2.56166e13	−	4.43693e13i	0.0250101	−	0.0433188i
$537$		0			0
$538$	1.58194e14			0.151316
$539$	1.97463e12	−	1.80695e14i	0.00186960	−	0.171083i
$540$		0			0
$541$	−3.29697e13	−	5.71052e13i	−0.0305865	−	0.0529774i	0.850327	−	0.526255i	$-0.176404\pi$
$541$	−3.29697e13	−	5.71052e13i	−0.0305865	−	0.0529774i	−0.880913	+	0.473277i	$0.843071\pi$
$542$	1.37947e13	−	2.38932e13i	0.0126683	−	0.0219421i
$543$		0			0
$544$	3.26045e14	+	5.64727e14i	0.293416	+	0.508211i
$545$	−1.32707e15			−1.18226
$546$		0			0
$547$	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
$549$		0			0
$550$	8.30831e12	−	1.43904e13i	0.00703911	−	0.0121921i
$551$	6.09780e13	+	1.05617e14i	0.0511493	+	0.0885932i
$552$		0			0
$553$	5.26571e14	+	5.32356e14i	0.432981	+	0.437738i
$554$	2.16008e14			0.175859
$555$		0			0
$556$	−7.37423e13	+	1.27725e14i	−0.0588580	+	0.101945i
$557$	1.07657e15	−	1.86467e15i	0.850822	−	1.47367i	−0.0296461	−	0.999560i	$-0.509438\pi$
$557$	1.07657e15	−	1.86467e15i	0.850822	−	1.47367i	0.880468	−	0.474106i	$-0.157229\pi$
$558$		0			0
$559$	−9.02755e14			−0.699528
$560$	−4.21419e14	+	1.53907e15i	−0.323355	+	1.18093i
$561$		0			0
$562$	−1.11144e14	−	1.92508e14i	−0.0836253	−	0.144843i
$563$	−7.40273e14	+	1.28219e15i	−0.551564	+	0.955336i	0.446598	+	0.894735i	$0.352635\pi$
$563$	−7.40273e14	+	1.28219e15i	−0.551564	+	0.955336i	−0.998162	+	0.0606018i	$0.980698\pi$
$564$		0			0
$565$	9.49094e14	+	1.64388e15i	0.693494	+	1.20117i
$566$	−1.15480e14			−0.0835633
$567$		0			0
$568$	−3.11100e14			−0.220792
$569$	7.54590e14	+	1.30699e15i	0.530388	+	0.918659i	0.999371	+	0.0354518i	$0.0112870\pi$
$569$	7.54590e14	+	1.30699e15i	0.530388	+	0.918659i	−0.468984	+	0.883207i	$0.655380\pi$
$570$		0			0
$571$	1.11735e15	−	1.93530e15i	0.770352	−	1.33429i	−0.167018	−	0.985954i	$-0.553414\pi$
$571$	1.11735e15	−	1.93530e15i	0.770352	−	1.33429i	0.937370	−	0.348335i	$-0.113253\pi$
$572$	7.13926e13	+	1.23656e14i	0.0487501	+	0.0844376i
$573$		0			0
$574$	2.13502e13	+	2.15848e13i	0.0143017	+	0.0144588i
$575$	−3.35567e14			−0.222642
$576$		0			0
$577$	−1.10810e15	+	1.91928e15i	−0.721293	+	1.24932i	0.239189	+	0.970973i	$0.423119\pi$
$577$	−1.10810e15	+	1.91928e15i	−0.721293	+	1.24932i	−0.960482	+	0.278343i	$0.910215\pi$
$578$	−1.47689e14	+	2.55805e14i	−0.0952237	+	0.164932i
$579$		0			0
$580$	7.68596e14			0.486233
$581$	−5.41285e14	+	1.41872e14i	−0.339201	+	0.0889052i
$582$		0			0
$583$	−1.58362e14	−	2.74291e14i	−0.0973810	−	0.168669i
$584$	−1.86141e14	+	3.22406e14i	−0.113389	+	0.196396i
$585$		0			0
$586$	3.13919e13	+	5.43724e13i	0.0187664	+	0.0325043i
$587$	−9.98055e14			−0.591078			−0.295539	−	0.955331i	$-0.595499\pi$
$587$	−9.98055e14			−0.591078			−0.295539	+	0.955331i	$0.595499\pi$
$588$		0			0
$589$	3.03975e14			0.176687
$590$	−1.54549e14	−	2.67688e14i	−0.0889983	−	0.154150i
$591$		0			0
$592$	−6.18624e14	+	1.07149e15i	−0.349669	+	0.605645i
$593$	−4.92960e13	−	8.53833e13i	−0.0276065	−	0.0478159i	0.851892	−	0.523717i	$-0.175455\pi$
$593$	−4.92960e13	−	8.53833e13i	−0.0276065	−	0.0478159i	−0.879499	+	0.475902i	$0.842122\pi$
$594$		0			0
$595$	−3.58334e15	+	9.39198e14i	−1.96990	+	0.516314i
$596$	−8.93552e14			−0.486705
$597$		0			0
$598$	−2.33101e13	+	4.03743e13i	−0.0124649	+	0.0215898i
$599$	2.95594e14	−	5.11985e14i	0.156621	−	0.271275i	−0.777027	−	0.629467i	$-0.783273\pi$
$599$	2.95594e14	−	5.11985e14i	0.156621	−	0.271275i	0.933648	+	0.358192i	$0.116607\pi$
$600$		0			0
$601$	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
$603$		0			0
$604$	−1.28672e15	−	2.22867e15i	−0.651300	−	1.12808i
$605$	−1.24386e15	+	2.15442e15i	−0.623901	+	1.08063i
$606$		0			0
$607$	9.23697e13	+	1.59989e14i	0.0454980	+	0.0788048i	0.887878	−	0.460080i	$-0.152179\pi$
$607$	9.23697e13	+	1.59989e14i	0.0454980	+	0.0788048i	−0.842380	+	0.538885i	$0.818846\pi$
$608$	−2.01962e14			−0.0985825
$609$		0			0
$610$	−5.45380e14			−0.261448
$611$	9.69075e13	+	1.67849e14i	0.0460395	+	0.0797428i
$612$		0			0
$613$	−6.30271e14	+	1.09166e15i	−0.294100	+	0.509396i	−0.974775	−	0.223189i	$-0.928353\pi$
$613$	−6.30271e14	+	1.09166e15i	−0.294100	+	0.509396i	0.680675	+	0.732585i	$0.261687\pi$
$614$	5.05539e13	+	8.75618e13i	0.0233791	+	0.0404938i
$615$		0			0
$616$	2.48937e13	−	9.09147e13i	0.0113083	−	0.0412991i
$617$	3.07915e15			1.38632			0.693159	−	0.720784i	$-0.256218\pi$
$617$	3.07915e15			1.38632			0.693159	+	0.720784i	$0.256218\pi$
$618$		0			0
$619$	1.11640e15	−	1.93367e15i	0.493768	−	0.855230i	−0.506207	−	0.862412i	$-0.668953\pi$
$619$	1.11640e15	−	1.93367e15i	0.493768	−	0.855230i	0.999974	+	0.00718174i	$0.00228604\pi$
$620$	9.57861e14	−	1.65906e15i	0.419902	−	0.727292i
$621$		0			0
$622$	−9.10889e13			−0.0392300
$623$	1.88949e15	+	1.91025e15i	0.806604	+	0.815467i
$624$		0			0
$625$	1.46245e15	+	2.53304e15i	0.613397	+	1.06244i
$626$	8.71571e13	−	1.50961e14i	0.0362363	−	0.0627631i
$627$		0			0
$628$	9.40905e14	+	1.62970e15i	0.384386	+	0.665776i
$629$	−2.87220e15			−1.16315
$630$		0			0
$631$	−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
$633$		0			0
$634$	9.73713e13	−	1.68652e14i	0.0377520	−	0.0653884i
$635$	1.57974e15	+	2.73618e15i	0.607196	+	1.05169i
$636$		0			0
$637$	−1.33580e15	+	7.51881e14i	−0.504630	+	0.284042i
$638$	−2.21489e13			−0.00829543
$639$		0			0
$640$	−8.46168e14	+	1.46561e15i	−0.311506	+	0.539545i
$641$	−5.28395e14	+	9.15207e14i	−0.192859	+	0.334041i	−0.946196	−	0.323593i	$-0.895109\pi$
$641$	−5.28395e14	+	9.15207e14i	−0.192859	+	0.334041i	0.753338	+	0.657634i	$0.228443\pi$
$642$		0			0
$643$	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
$645$		0			0
$646$	−7.60370e13	−	1.31700e14i	−0.0265917	−	0.0460582i
$647$	2.19873e14	−	3.80831e14i	0.0762428	−	0.132056i	−0.825383	−	0.564573i	$-0.809041\pi$
$647$	2.19873e14	−	3.80831e14i	0.0762428	−	0.132056i	0.901626	+	0.432516i	$0.142374\pi$
$648$		0			0
$649$	−2.75466e14	−	4.77120e14i	−0.0939121	−	0.162661i
$650$	−1.40953e14			−0.0476488
$651$		0			0
$652$	4.99505e15			1.66027
$653$	−2.92912e14	−	5.07338e14i	−0.0965415	−	0.167215i	0.813709	−	0.581272i	$-0.197445\pi$
$653$	−2.92912e14	−	5.07338e14i	−0.0965415	−	0.167215i	−0.910251	+	0.414057i	$0.864111\pi$
$654$		0			0
$655$	1.93394e14	−	3.34969e14i	0.0626782	−	0.108562i
$656$	−2.38923e14	−	4.13827e14i	−0.0767869	−	0.132999i
$657$		0			0
$658$	1.67597e13	−	6.12085e13i	0.00529694	−	0.0193450i
$659$	5.89551e14			0.184779			0.0923893	−	0.995723i	$-0.470550\pi$
$659$	5.89551e14			0.184779			0.0923893	+	0.995723i	$0.470550\pi$
$660$		0			0
$661$	2.16762e15	−	3.75442e15i	0.668151	−	1.15727i	−0.310269	−	0.950649i	$-0.600419\pi$
$661$	2.16762e15	−	3.75442e15i	0.668151	−	1.15727i	0.978421	−	0.206623i	$-0.0662474\pi$
$662$	7.94117e13	−	1.37545e14i	0.0242753	−	0.0420461i
$663$		0			0
$664$	−2.91887e14			−0.0877588
$665$	3.02993e14	−	1.10657e15i	0.0903471	−	0.329958i
$666$		0			0
$667$	2.23645e14	+	3.87365e14i	0.0655945	+	0.113613i
$668$	2.40555e15	−	4.16653e15i	0.699751	−	1.21200i
$669$		0			0
$670$	5.66258e13	+	9.80788e13i	0.0162033	+	0.0280649i
$671$	−9.72074e14			−0.275883
$672$		0			0
$673$	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
$675$		0			0
$676$	−1.20037e15	+	2.07911e15i	−0.327047	+	0.566461i
$677$	−2.59774e15	−	4.49941e15i	−0.702033	−	1.21596i	−0.967752	−	0.251907i	$-0.918942\pi$
$677$	−2.59774e15	−	4.49941e15i	−0.702033	−	1.21596i	0.265718	−	0.964051i	$-0.414391\pi$
$678$		0			0
$679$	5.98555e15	−	1.56882e15i	1.59155	−	0.417148i
$680$	−1.93231e15			−0.509656
$681$		0			0
$682$	−2.76030e13	+	4.78099e13i	−0.00716379	+	0.0124081i
$683$	−1.70845e14	+	2.95913e14i	−0.0439834	+	0.0761815i	−0.887179	−	0.461425i	$-0.847338\pi$
$683$	−1.70845e14	+	2.95913e14i	−0.0439834	+	0.0761815i	0.843196	+	0.537607i	$0.180672\pi$
$684$		0			0
$685$	−8.84393e15			−2.24051
$686$	4.82615e14	+	1.37833e14i	0.121288	+	0.0346395i
$687$		0			0
$688$	−2.32621e15	−	4.02911e15i	−0.575324	−	0.996490i
$689$	−1.34333e15	+	2.32672e15i	−0.329593	+	0.570872i
$690$		0			0
$691$	−2.58334e15	−	4.47447e15i	−0.623810	−	1.08047i	−0.988770	−	0.149447i	$-0.952251\pi$
$691$	−2.58334e15	−	4.47447e15i	−0.623810	−	1.08047i	0.364960	−	0.931023i	$-0.381083\pi$
$692$	1.09376e15			0.262021
$693$		0			0
$694$	−6.36094e14			−0.149984
$695$	−3.28652e14	−	5.69242e14i	−0.0768811	−	0.133162i
$696$		0			0
$697$	5.54646e14	−	9.60674e14i	0.127713	−	0.221206i
$698$	−7.12455e13	−	1.23401e14i	−0.0162762	−	0.0281912i
$699$		0			0
$700$	−2.00744e15	−	2.02950e15i	−0.451444	−	0.456404i
$701$	−3.33033e15			−0.743084			−0.371542	−	0.928416i	$-0.621171\pi$
$701$	−3.33033e15			−0.743084			−0.371542	+	0.928416i	$0.621171\pi$
$702$		0			0
$703$	4.44781e14	−	7.70382e14i	0.0976993	−	0.169220i
$704$	−3.55537e14	+	6.15807e14i	−0.0774880	+	0.134213i
$705$		0			0
$706$	5.09785e14			0.109386
$707$	1.70782e15	−	6.23716e15i	0.363610	−	1.32795i
$708$		0			0
$709$	7.09927e14	+	1.22963e15i	0.148819	+	0.257763i	0.930791	−	0.365551i	$-0.119119\pi$
$709$	7.09927e14	+	1.22963e15i	0.148819	+	0.257763i	−0.781972	+	0.623313i	$0.785786\pi$
$710$	3.43845e14	−	5.95557e14i	0.0715224	−	0.123880i
$711$		0			0
$712$	7.00773e14	+	1.21377e15i	0.143528	+	0.248598i
$713$	1.11487e15			0.226585
$714$		0			0
$715$	−6.36360e14			−0.127356
$716$	−3.34040e15	−	5.78575e15i	−0.663403	−	1.14905i
$717$		0			0
$718$	−4.79255e14	+	8.30094e14i	−0.0937307	+	0.162346i
$719$	4.37317e15	+	7.57456e15i	0.848765	+	1.47010i	0.882311	+	0.470667i	$0.155987\pi$
$719$	4.37317e15	+	7.57456e15i	0.848765	+	1.47010i	−0.0335454	+	0.999437i	$0.510680\pi$
$720$		0			0
$721$	5.95620e15	+	6.02165e15i	1.13848	+	1.15099i
$722$	−6.17866e14			−0.117203
$723$		0			0
$724$	−7.63301e14	+	1.32208e15i	−0.142605	+	0.246999i
$725$	−6.76176e14	+	1.17117e15i	−0.125372	+	0.217151i
$726$		0			0
$727$	−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
$729$		0			0
$730$	−4.11467e14	−	7.12682e14i	−0.0734615	−	0.127239i
$731$	5.40015e15	−	9.35334e15i	0.956887	−	1.65738i
$732$		0			0
$733$	−1.71682e15	−	2.97363e15i	−0.299678	−	0.519057i	0.676385	−	0.736549i	$-0.263546\pi$
$733$	−1.71682e15	−	2.97363e15i	−0.299678	−	0.519057i	−0.976062	+	0.217492i	$0.930212\pi$
$734$	1.18678e14			0.0205610
$735$		0			0
$736$	−7.40722e14			−0.126423
$737$	1.00929e14	+	1.74813e14i	0.0170979	+	0.0296145i
$738$		0			0
$739$	−1.17677e15	+	2.03823e15i	−0.196403	+	0.340180i	−0.947359	−	0.320172i	$-0.896259\pi$
$739$	−1.17677e15	+	2.03823e15i	−0.196403	+	0.340180i	0.750957	+	0.660351i	$0.229593\pi$
$740$	−2.80311e15	−	4.85513e15i	−0.464372	−	0.804316i
$741$		0			0
$742$	8.50961e14	−	2.23038e14i	0.138895	−	0.0364047i
$743$	1.13067e16			1.83188			0.915940	−	0.401316i	$-0.131447\pi$
$743$	1.13067e16			1.83188			0.915940	+	0.401316i	$0.131447\pi$
$744$		0			0
$745$	1.99117e15	−	3.44882e15i	0.317870	−	0.550567i
$746$	−3.91725e14	+	6.78488e14i	−0.0620751	+	0.107517i
$747$		0			0
$748$	−1.70824e15			−0.266742
$749$	1.86383e15	+	1.88431e15i	0.288905	+	0.292080i
$750$		0			0
$751$	2.89693e15	+	5.01763e15i	0.442505	+	0.766441i	0.997875	−	0.0651627i	$-0.0207566\pi$
$751$	2.89693e15	+	5.01763e15i	0.442505	+	0.766441i	−0.555370	+	0.831603i	$0.687423\pi$
$752$	−4.99420e14	+	8.65021e14i	−0.0757300	+	0.131168i
$753$		0			0
$754$	9.39410e13	+	1.62711e14i	0.0140382	+	0.0243149i
$755$	1.14692e16			1.70147
$756$		0			0
$757$	−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
$759$		0			0
$760$	2.99232e14	−	5.18285e14i	0.0428088	−	0.0741471i
$761$	7.85569e14	+	1.36065e15i	0.111575	+	0.193254i	0.916406	−	0.400251i	$-0.131077\pi$
$761$	7.85569e14	+	1.36065e15i	0.111575	+	0.193254i	−0.804830	+	0.593505i	$0.797744\pi$
$762$		0			0
$763$	1.73503e15	−	6.33651e15i	0.242896	−	0.887085i
$764$	−9.72223e15			−1.35130
$765$		0			0
$766$	6.31746e14	−	1.09422e15i	0.0865535	−	0.149915i
$767$	−2.33668e15	+	4.04725e15i	−0.317852	+	0.550536i
$768$		0			0
$769$	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
$771$		0			0
$772$	−7.07389e14	−	1.22523e15i	−0.0928460	−	0.160814i
$773$	9.91548e14	−	1.71741e15i	0.129219	−	0.223814i	−0.794155	−	0.607715i	$-0.792086\pi$
$773$	9.91548e14	−	1.71741e15i	0.129219	−	0.223814i	0.923374	+	0.383901i	$0.125420\pi$
$774$		0			0
$775$	1.68537e15	+	2.91914e15i	0.216538	+	0.375055i
$776$	3.22770e15			0.411769
$777$		0			0
$778$	−6.47695e14			−0.0814672
$779$	1.71782e14	+	2.97535e14i	0.0214546	+	0.0371605i
$780$		0			0
$781$	6.12862e14	−	1.06151e15i	0.0754713	−	0.130720i
$782$	−2.78876e14	−	4.83027e14i	−0.0341015	−	0.0590656i
$783$		0			0
$784$	−6.79781e15	−	4.02439e15i	−0.819654	−	0.485246i
$785$	−8.38678e15			−1.00418
$786$		0			0
$787$	−6.95413e15	+	1.20449e16i	−0.821073	+	1.42214i	0.0838114	+	0.996482i	$0.473291\pi$
$787$	−6.95413e15	+	1.20449e16i	−0.821073	+	1.42214i	−0.904884	+	0.425658i	$0.860043\pi$
$788$	−3.49705e15	+	6.05706e15i	−0.410022	+	0.710179i
$789$		0			0
$790$	−8.63399e14			−0.0998304
$791$	−9.09006e15	+	2.38252e15i	−1.04375	+	0.273568i
$792$		0			0
$793$	4.12289e15	+	7.14105e15i	0.466873	+	0.808648i
$794$	3.57966e14	−	6.20016e14i	0.0402559	−	0.0697252i
$795$		0			0
$796$	−2.91871e15	−	5.05535e15i	−0.323719	−	0.560699i
$797$	−6.82904e15			−0.752210			−0.376105	−	0.926577i	$-0.622737\pi$
$797$	−6.82904e15			−0.752210			−0.376105	+	0.926577i	$0.622737\pi$
$798$		0			0
$799$	−2.31875e15			−0.251911
$800$	−1.11976e15	−	1.93948e15i	−0.120818	−	0.209263i
$801$		0			0
$802$	−1.14914e14	+	1.99038e14i	−0.0122297	+	0.0211825i
$803$	−7.33390e14	−	1.27027e15i	−0.0775175	−	0.134264i
$804$		0			0
$805$	1.11127e15	−	4.05848e15i	0.115862	−	0.423142i
$806$	4.68295e14			0.0484927
$807$		0			0
$808$	1.68662e15	−	2.92131e15i	0.172288	−	0.298412i
$809$	−8.33703e15	+	1.44402e16i	−0.845852	+	1.46506i	0.0390274	+	0.999238i	$0.487574\pi$
$809$	−8.33703e15	+	1.44402e16i	−0.845852	+	1.46506i	−0.884879	+	0.465820i	$0.845759\pi$
$810$		0			0
$811$	−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
$813$		0			0
$814$	8.07784e13	+	1.39912e14i	0.00792247	+	0.0137221i
$815$	−1.11309e16	+	1.92793e16i	−1.08433	+	1.87812i
$816$		0			0
$817$	1.67251e15	+	2.89687e15i	0.160748	+	0.278424i
$818$	−1.11834e15			−0.106765
$819$		0			0
$820$	2.16522e15			0.203951
$821$	5.05873e15	+	8.76198e15i	0.473319	+	0.819813i	0.999534	−	0.0305391i	$-0.00972241\pi$
$821$	5.05873e15	+	8.76198e15i	0.473319	+	0.819813i	−0.526214	+	0.850352i	$0.676389\pi$
$822$		0			0
$823$	3.99868e15	−	6.92593e15i	0.369163	−	0.639409i	−0.620272	−	0.784387i	$-0.712978\pi$
$823$	3.99868e15	−	6.92593e15i	0.369163	−	0.639409i	0.989435	+	0.144978i	$0.0463111\pi$
$824$	2.20903e15	+	3.82616e15i	0.202583	+	0.350884i
$825$		0			0
$826$	1.48022e15	−	3.87967e14i	0.133948	−	0.0351079i
$827$	1.50295e16			1.35102			0.675512	−	0.737349i	$-0.263923\pi$
$827$	1.50295e16			1.35102			0.675512	+	0.737349i	$0.263923\pi$
$828$		0			0
$829$	−6.43760e15	+	1.11502e16i	−0.571050	+	0.989087i	0.425409	+	0.905001i	$0.360130\pi$
$829$	−6.43760e15	+	1.11502e16i	−0.571050	+	0.989087i	−0.996459	+	0.0840857i	$0.973203\pi$
$830$	3.22610e14	−	5.58777e14i	0.0284281	−	0.0492390i
$831$		0			0
$832$	6.03180e15			0.524528
$833$	2.00394e14	−	1.83377e16i	0.0173116	−	1.58415i
$834$		0			0
$835$	1.07210e16	+	1.85692e16i	0.914025	+	1.58314i
$836$	2.64534e14	−	4.58186e14i	0.0224051	−	0.0388068i
$837$		0			0
$838$	8.87952e14	+	1.53798e15i	0.0742245	+	0.128561i
$839$	1.90314e16			1.58045			0.790225	−	0.612817i	$-0.209964\pi$
$839$	1.90314e16			1.58045			0.790225	+	0.612817i	$0.209964\pi$
$840$		0			0
$841$	−1.03979e16			−0.852252
$842$	9.00229e14	+	1.55924e15i	0.0733055	+	0.126969i
$843$		0			0
$844$	−3.01510e13	+	5.22230e13i	−0.00242336	+	0.00419738i
$845$	−5.34978e15	−	9.26609e15i	−0.427193	−	0.739920i
$846$		0			0
$847$	−8.66074e15	−	8.75590e15i	−0.682647	−	0.690148i
$848$	−1.38459e16			−1.08429
$849$		0			0
$850$	8.43163e14	−	1.46040e15i	0.0651789	−	0.112893i
$851$	1.63129e15	−	2.82548e15i	0.125291	−	0.217010i
$852$		0			0
$853$	−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
$855$		0			0
$856$	6.91255e14	+	1.19729e15i	0.0514082	+	0.0890416i
$857$	−5.44606e15	+	9.43285e15i	−0.402428	+	0.697025i	−0.994018	−	0.109213i	$-0.965167\pi$
$857$	−5.44606e15	+	9.43285e15i	−0.402428	+	0.697025i	0.591591	+	0.806239i	$0.298500\pi$
$858$		0			0
$859$	4.88936e15	+	8.46862e15i	0.356689	+	0.617803i	0.987406	−	0.158210i	$-0.0505723\pi$
$859$	4.88936e15	+	8.46862e15i	0.356689	+	0.617803i	−0.630717	+	0.776013i	$0.717239\pi$
$860$	2.10811e16			1.52810
$861$		0			0
$862$	2.80338e15			0.200628
$863$	3.21366e15	+	5.56622e15i	0.228529	+	0.395823i	0.957372	−	0.288857i	$-0.0932752\pi$
$863$	3.21366e15	+	5.56622e15i	0.228529	+	0.395823i	−0.728844	+	0.684680i	$0.759942\pi$
$864$		0			0
$865$	−2.43730e15	+	4.22153e15i	−0.171128	+	0.296402i
$866$	1.33201e15	+	2.30710e15i	0.0929305	+	0.160960i
$867$		0			0
$868$	6.66940e15	+	6.74268e15i	0.459440	+	0.464488i
$869$	−1.53890e15			−0.105342
$870$		0			0
$871$	8.56144e14	−	1.48288e15i	0.0578691	−	0.100232i
$872$	1.71349e15	−	2.96785e15i	0.115091	−	0.199343i
$873$		0			0
$874$	1.72744e14			0.0114575
$875$	−6.55886e15	+	1.71909e15i	−0.432299	+	0.113306i
$876$		0			0
$877$	−1.22064e16	−	2.11421e16i	−0.794491	−	1.37610i	−0.923162	−	0.384412i	$-0.874404\pi$
$877$	−1.22064e16	−	2.11421e16i	−0.794491	−	1.37610i	0.128670	−	0.991687i	$-0.458929\pi$
$878$	−7.93877e14	+	1.37504e15i	−0.0513492	+	0.0889394i
$879$		0			0
$880$	−1.63977e15	−	2.84016e15i	−0.104743	−	0.181421i
$881$	2.26230e16			1.43609			0.718045	−	0.695996i	$-0.245037\pi$
$881$	2.26230e16			1.43609			0.718045	+	0.695996i	$0.245037\pi$
$882$		0			0
$883$	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
$885$		0			0
$886$	−1.25367e15	+	2.17141e15i	−0.0771429	+	0.133615i
$887$	−7.90944e15	−	1.36996e16i	−0.483689	−	0.837773i	0.516136	−	0.856507i	$-0.327370\pi$
$887$	−7.90944e15	−	1.36996e16i	−0.483689	−	0.837773i	−0.999825	+	0.0187334i	$0.994037\pi$
$888$		0			0
$889$	−1.51301e16	+	3.96563e15i	−0.913866	+	0.239526i
$890$	−3.09813e15			−0.185975
$891$		0			0
$892$	−2.54200e15	+	4.40287e15i	−0.150719	+	0.261054i
$893$	3.59075e14	−	6.21937e14i	0.0211594	−	0.0366491i
$894$		0			0
$895$	2.97748e16			1.73309
$896$	−5.89171e15	−	5.95644e15i	−0.340837	−	0.344582i
$897$		0			0
$898$	−2.40389e14	−	4.16366e14i	−0.0137371	−	0.0237934i
$899$	2.24649e15	−	3.89103e15i	0.127593	−	0.220997i
$900$		0			0
$901$	−1.60713e16	−	2.78362e16i	−0.901703	−	1.56180i
$902$	−6.23960e13			−0.00347953
$903$		0			0
$904$	−4.90180e15			−0.270041
$905$	−3.40185e15	−	5.89218e15i	−0.186272	−	0.322633i
$906$		0			0
$907$	−2.57501e15	+	4.46004e15i	−0.139296	+	0.241267i	−0.927230	−	0.374492i	$-0.877817\pi$
$907$	−2.57501e15	+	4.46004e15i	−0.139296	+	0.241267i	0.787934	+	0.615759i	$0.211151\pi$
$908$	−1.22593e16	−	2.12337e16i	−0.659163	−	1.14170i
$909$		0			0
$910$	4.66783e14	−	1.70474e15i	0.0247963	−	0.0905590i
$911$	−2.54507e16			−1.34384			−0.671922	−	0.740622i	$-0.734531\pi$
$911$	−2.54507e16			−1.34384			−0.671922	+	0.740622i	$0.734531\pi$
$912$		0			0
$913$	5.75013e14	−	9.95951e14i	0.0299977	−	0.0519576i
$914$	−5.17238e14	+	8.95882e14i	−0.0268217	+	0.0464565i
$915$		0			0
$916$	8.77750e15			0.449724
$917$	1.34657e15	+	1.36136e15i	0.0685799	+	0.0693334i
$918$		0			0
$919$	−3.49711e15	−	6.05718e15i	−0.175984	−	0.304814i	0.764517	−	0.644604i	$-0.222978\pi$
$919$	−3.49711e15	−	6.05718e15i	−0.175984	−	0.304814i	−0.940502	+	0.339789i	$0.889644\pi$
$920$	1.09747e15	−	1.90088e15i	0.0548986	−	0.0950872i
$921$		0			0
$922$	6.63072e14	+	1.14848e15i	0.0327749	+	0.0567677i
$923$	−1.03974e16			−0.510876
$924$		0			0
$925$	9.86420e15			0.478942
$926$	−1.38674e15	−	2.40191e15i	−0.0669322	−	0.115930i
$927$		0			0
$928$	−1.49257e15	+	2.58521e15i	−0.0711904	+	0.123305i
$929$	−6.32951e15	−	1.09630e16i	−0.300112	−	0.519810i	0.676049	−	0.736857i	$-0.263691\pi$
$929$	−6.32951e15	−	1.09630e16i	−0.300112	−	0.519810i	−0.976161	+	0.217047i	$0.930358\pi$
$930$		0			0
$931$	4.88751e15	+	2.89347e15i	0.229015	+	0.135580i
$932$	3.44420e16			1.60435
$933$		0			0
$934$	2.68895e14	−	4.65740e14i	0.0123787	−	0.0214405i
$935$	3.80662e15	−	6.59325e15i	0.174211	−	0.301742i
$936$		0			0
$937$	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
$939$		0			0
$940$	−2.26298e15	−	3.91959e15i	−0.100572	−	0.174196i
$941$	−2.38780e15	+	4.13578e15i	−0.105500	+	0.182732i	−0.913943	−	0.405844i	$-0.866978\pi$
$941$	−2.38780e15	+	4.13578e15i	−0.105500	+	0.182732i	0.808442	+	0.588576i	$0.200311\pi$
$942$		0			0
$943$	6.30033e14	+	1.09125e15i	0.0275137	+	0.0476551i
$944$	−2.40846e16			−1.04567
$945$		0			0
$946$	−6.07501e14			−0.0260703
$947$	1.48624e16	+	2.57425e16i	0.634110	+	1.09831i	0.986703	+	0.162534i	$0.0519668\pi$
$947$	1.48624e16	+	2.57425e16i	0.634110	+	1.09831i	−0.352593	+	0.935777i	$0.614700\pi$
$948$		0			0
$949$	−6.22110e15	+	1.07753e16i	−0.262363	+	0.454427i
$950$	2.61140e14	+	4.52307e14i	0.0109495	+	0.0189650i
$951$		0			0
$952$	2.52632e15	−	9.22641e15i	0.104709	−	0.382410i
$953$	−4.28873e15			−0.176733			−0.0883665	−	0.996088i	$-0.528165\pi$
$953$	−4.28873e15			−0.176733			−0.0883665	+	0.996088i	$0.528165\pi$
$954$		0			0
$955$	2.16648e16	−	3.75246e16i	0.882545	−	1.52861i
$956$	3.07206e14	−	5.32096e14i	0.0124426	−	0.0215512i
$957$		0			0
$958$	−3.66890e15			−0.146901
$959$	1.15626e16	−	4.22281e16i	0.460315	−	1.68112i
$960$		0			0
$961$	7.10488e15	+	1.23060e16i	0.279626	+	0.484327i
$962$	6.85216e14	−	1.18683e15i	0.0268142	−	0.0464435i
$963$		0			0
$964$	1.68085e15	+	2.91131e15i	0.0650286	+	0.112633i
$965$	6.30533e15			0.242553
$966$		0			0
$967$	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
$969$		0			0
$970$	−3.56743e15	+	6.17897e15i	−0.133386	+	0.231032i
$971$	−1.68239e16	−	2.91399e16i	−0.625491	−	1.08338i	−0.988446	−	0.151576i	$-0.951565\pi$
$971$	−1.68239e16	−	2.91399e16i	−0.625491	−	1.08338i	0.362954	−	0.931807i	$-0.381768\pi$
$972$		0			0
$973$	3.14771e15	−	8.25019e14i	0.115711	−	0.0303280i
$974$	4.70221e15			0.171881
$975$		0			0
$976$	−2.12476e16	+	3.68020e16i	−0.767956	+	1.33014i
$977$	−1.98072e16	+	3.43071e16i	−0.711875	+	1.23300i	0.252277	+	0.967655i	$0.418820\pi$
$977$	−1.98072e16	+	3.43071e16i	−0.711875	+	1.23300i	−0.964152	+	0.265349i	$0.914513\pi$
$978$		0			0
$979$	−5.52204e15			−0.196243
$980$	3.11934e16	−	1.75579e16i	1.10235	−	0.620481i
$981$		0			0
$982$	−2.01220e15	−	3.48523e15i	−0.0703166	−	0.121792i
$983$	1.53479e16	−	2.65834e16i	0.533342	−	0.923775i	−0.465900	−	0.884838i	$-0.654269\pi$
$983$	1.53479e16	−	2.65834e16i	0.533342	−	0.923775i	0.999242	−	0.0389378i	$-0.0123974\pi$
$984$		0			0
$985$	−1.55855e16	−	2.69949e16i	−0.535576	−	0.927646i
$986$	−2.24777e15			−0.0768118
$987$		0			0
$988$	−4.48791e15			−0.151663
$989$	6.13414e15	+	1.06246e16i	0.206146	+	0.357055i
$990$		0			0
$991$	−7.01280e15	+	1.21465e16i	−0.233070	+	0.403689i	−0.958710	−	0.284385i	$-0.908211\pi$
$991$	−7.01280e15	+	1.21465e16i	−0.233070	+	0.403689i	0.725640	+	0.688075i	$0.241544\pi$
$992$	3.72023e15	+	6.44363e15i	0.122958	+	0.212969i
$993$		0			0
$994$	2.39413e15	+	2.42043e15i	0.0782568	+	0.0791167i
$995$	2.60160e16			0.845694
$996$		0			0
$997$	1.01222e16	−	1.75321e16i	0.325424	−	0.563651i	−0.656174	−	0.754610i	$-0.727826\pi$
$997$	1.01222e16	−	1.75321e16i	0.325424	−	0.563651i	0.981598	+	0.190959i	$0.0611596\pi$
$998$	−2.34893e15	+	4.06847e15i	−0.0751023	+	0.130081i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.12.c.a.2.3	✓	12	21.2	odd	6
7.12.c.a.4.3	yes	12	3.2	odd	2
49.12.a.f.1.4		6	21.17	even	6
49.12.a.g.1.4		6	21.11	odd	6
49.12.c.i.18.3		12	21.20	even	2
49.12.c.i.30.3		12	21.5	even	6
63.12.e.b.37.4		12	7.2	even	3	inner
63.12.e.b.46.4		12	1.1	even	1	trivial
112.12.i.c.65.6		12	84.23	even	6
112.12.i.c.81.6		12	12.11	even	2

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	63.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.85417 - 4.94356i) q^{2} +(1007.71 - 1745.40i) q^{4} +(4491.11 + 7778.83i) q^{5} +(-43014.2 + 11274.1i) q^{7} -23195.3 q^{8} +O(q^{10})\)	\(q+(-2.85417 - 4.94356i) q^{2} +(1007.71 - 1745.40i) q^{4} +(4491.11 + 7778.83i) q^{5} +(-43014.2 + 11274.1i) q^{7} -23195.3 q^{8} +(25636.8 - 44404.2i) q^{10} +(45694.4 - 79145.1i) q^{11} -775221. q^{13} +(178504. + 180465. i) q^{14} +(-1.99758e6 - 3.45991e6i) q^{16} +(4.63726e6 - 8.03198e6i) q^{17} +(1.43623e6 + 2.48762e6i) q^{19} +1.81029e7 q^{20} -521678. q^{22} +(5.26756e6 + 9.12369e6i) q^{23} +(-1.59261e7 + 2.75848e7i) q^{25} +(2.21261e6 + 3.83236e6i) q^{26} +(-2.36679e7 + 8.64380e7i) q^{28} +4.24570e7 q^{29} +(5.29120e7 - 9.16463e7i) q^{31} +(-3.51549e7 + 6.08901e7i) q^{32} -5.29421e7 q^{34} +(-2.80881e8 - 2.83967e8i) q^{35} +(-1.54843e8 - 2.68196e8i) q^{37} +(8.19848e6 - 1.42002e7i) q^{38} +(-1.04173e8 - 1.80433e8i) q^{40} +1.19606e8 q^{41} +1.16451e9 q^{43} +(-9.20932e7 - 1.59510e8i) q^{44} +(3.00690e7 - 5.20811e7i) q^{46} +(-1.25006e8 - 2.16517e8i) q^{47} +(1.72312e9 - 9.69892e8i) q^{49} +1.81823e8 q^{50} +(-7.81196e8 + 1.35307e9i) q^{52} +(1.73284e9 - 3.00136e9i) q^{53} +8.20875e8 q^{55} +(9.97729e8 - 2.61506e8i) q^{56} +(-1.21180e8 - 2.09889e8i) q^{58} +(3.01421e9 - 5.22077e9i) q^{59} +(-5.31834e9 - 9.21163e9i) q^{61} -6.04079e8 q^{62} -7.78074e9 q^{64} +(-3.48161e9 - 6.03032e9i) q^{65} +(-1.10439e9 + 1.91285e9i) q^{67} +(-9.34601e9 - 1.61878e10i) q^{68} +(-6.02129e8 + 2.19904e9i) q^{70} +1.34122e10 q^{71} +(8.02494e9 - 1.38996e10i) q^{73} +(-8.83897e8 + 1.53095e9i) q^{74} +5.78919e9 q^{76} +(-1.07322e9 + 3.91953e9i) q^{77} +(-8.41954e9 - 1.45831e10i) q^{79} +(1.79427e10 - 3.10777e10i) q^{80} +(-3.41376e8 - 5.91281e8i) q^{82} +1.25839e10 q^{83} +8.33059e10 q^{85} +(-3.32372e9 - 5.75684e9i) q^{86} +(-1.05990e9 + 1.83580e9i) q^{88} +(-3.02118e10 - 5.23283e10i) q^{89} +(3.33455e10 - 8.73991e9i) q^{91} +2.12326e10 q^{92} +(-7.13578e8 + 1.23595e9i) q^{94} +(-1.29005e10 + 2.23444e10i) q^{95} -1.39153e11 q^{97} +(-9.71279e9 - 5.75010e9i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 22 q^{2} - 2556 q^{4} + 8782 q^{5} - 504 q^{7} - 97008 q^{8}+O(q^{10}) \) 12 * q - 22 * q^2 - 2556 * q^4 + 8782 * q^5 - 504 * q^7 - 97008 * q^8	\( 12 q - 22 q^{2} - 2556 q^{4} + 8782 q^{5} - 504 q^{7} - 97008 q^{8} + 111546 q^{10} + 1001572 q^{11} + 3864504 q^{13} + 1302994 q^{14} + 39120 q^{16} + 6704802 q^{17} + 4192212 q^{19} + 17646776 q^{20} - 8505684 q^{22} + 33871872 q^{23} + 13695456 q^{25} - 29350300 q^{26} + 181285692 q^{28} + 255125224 q^{29} - 331783920 q^{31} - 163252640 q^{32} + 1853334396 q^{34} - 1407354844 q^{35} - 833082774 q^{37} + 2086458338 q^{38} - 1219023432 q^{40} - 3104076808 q^{41} - 1722177552 q^{43} + 5105122436 q^{44} + 3435559326 q^{46} + 1327587552 q^{47} + 11976558636 q^{49} + 12237094384 q^{50} - 17237001432 q^{52} - 6725755626 q^{53} + 26323921200 q^{55} - 28163516640 q^{56} - 20073189204 q^{58} + 26237179548 q^{59} - 14411013726 q^{61} - 46185665964 q^{62} - 46365999744 q^{64} + 16224702172 q^{65} - 4241860068 q^{67} + 6528332916 q^{68} + 55705143270 q^{70} + 37335334656 q^{71} + 6005568990 q^{73} - 21663581922 q^{74} - 28817353320 q^{76} + 51928077698 q^{77} + 11712395640 q^{79} - 41748525232 q^{80} + 52795921668 q^{82} + 100821781200 q^{83} + 138884613396 q^{85} - 110437384472 q^{86} - 105039956616 q^{88} + 48633519778 q^{89} - 160908361488 q^{91} - 242956324248 q^{92} + 368497095702 q^{94} + 72161225128 q^{95} - 401308415928 q^{97} + 582375436706 q^{98}+O(q^{100}) \) 12 * q - 22 * q^2 - 2556 * q^4 + 8782 * q^5 - 504 * q^7 - 97008 * q^8 + 111546 * q^10 + 1001572 * q^11 + 3864504 * q^13 + 1302994 * q^14 + 39120 * q^16 + 6704802 * q^17 + 4192212 * q^19 + 17646776 * q^20 - 8505684 * q^22 + 33871872 * q^23 + 13695456 * q^25 - 29350300 * q^26 + 181285692 * q^28 + 255125224 * q^29 - 331783920 * q^31 - 163252640 * q^32 + 1853334396 * q^34 - 1407354844 * q^35 - 833082774 * q^37 + 2086458338 * q^38 - 1219023432 * q^40 - 3104076808 * q^41 - 1722177552 * q^43 + 5105122436 * q^44 + 3435559326 * q^46 + 1327587552 * q^47 + 11976558636 * q^49 + 12237094384 * q^50 - 17237001432 * q^52 - 6725755626 * q^53 + 26323921200 * q^55 - 28163516640 * q^56 - 20073189204 * q^58 + 26237179548 * q^59 - 14411013726 * q^61 - 46185665964 * q^62 - 46365999744 * q^64 + 16224702172 * q^65 - 4241860068 * q^67 + 6528332916 * q^68 + 55705143270 * q^70 + 37335334656 * q^71 + 6005568990 * q^73 - 21663581922 * q^74 - 28817353320 * q^76 + 51928077698 * q^77 + 11712395640 * q^79 - 41748525232 * q^80 + 52795921668 * q^82 + 100821781200 * q^83 + 138884613396 * q^85 - 110437384472 * q^86 - 105039956616 * q^88 + 48633519778 * q^89 - 160908361488 * q^91 - 242956324248 * q^92 + 368497095702 * q^94 + 72161225128 * q^95 - 401308415928 * q^97 + 582375436706 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more