LMFDB - Embedded newform 8.10.b.a.5.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,10,Mod(5,8)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("8.5");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	8.b (of order $2$, degree $1$, 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:	$4.12028668931$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 59x^{6} - 313x^{5} - 315x^{4} - 92091x^{3} + 1261649x^{2} - 16074123x + 251007534 $ x^8 - x^7 + 59x^6 - 313x^5 - 315x^4 - 92091x^3 + 1261649x^2 - 16074123x + 251007534
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{28}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.4
Root			$3.68032 - 10.3002i$ of defining polynomial
Character	$\chi$	$=$	8.5
Dual form			8.10.b.a.5.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-9.36065 + 20.6004i) q^{2} +150.106i q^{3} +(-336.757 - 385.667i) q^{4} -292.339i q^{5} +(-3092.24 - 1405.08i) q^{6} -9955.46 q^{7} +(11097.2 - 3327.24i) q^{8} -2848.66 q^{9} +O(q^{10})$	\(q+(-9.36065 + 20.6004i) q^{2} +150.106i q^{3} +(-336.757 - 385.667i) q^{4} -292.339i q^{5} +(-3092.24 - 1405.08i) q^{6} -9955.46 q^{7} +(11097.2 - 3327.24i) q^{8} -2848.66 q^{9} +(6022.31 + 2736.48i) q^{10} +65874.1i q^{11} +(57890.7 - 50549.0i) q^{12} +44990.6i q^{13} +(93189.6 - 205087. i) q^{14} +43881.7 q^{15} +(-35334.0 + 259752. i) q^{16} -469098. q^{17} +(26665.3 - 58683.7i) q^{18} +438793. i q^{19} +(-112745. + 98447.0i) q^{20} -1.49437e6i q^{21} +(-1.35703e6 - 616624. i) q^{22} +1.14082e6 q^{23} +(499437. + 1.66575e6i) q^{24} +1.86766e6 q^{25} +(-926827. - 421141. i) q^{26} +2.52693e6i q^{27} +(3.35257e6 + 3.83949e6i) q^{28} -5.39024e6i q^{29} +(-410761. + 903982. i) q^{30} +1.85181e6 q^{31} +(-5.02025e6 - 3.15934e6i) q^{32} -9.88806e6 q^{33} +(4.39106e6 - 9.66363e6i) q^{34} +2.91037e6i q^{35} +(959306. + 1.09863e6i) q^{36} +1.45757e7i q^{37} +(-9.03933e6 - 4.10739e6i) q^{38} -6.75334e6 q^{39} +(-972682. - 3.24413e6i) q^{40} +5.45239e6 q^{41} +(3.07847e7 + 1.39883e7i) q^{42} -5.79053e6i q^{43} +(2.54054e7 - 2.21835e7i) q^{44} +832774. i q^{45} +(-1.06788e7 + 2.35013e7i) q^{46} -1.69791e7 q^{47} +(-3.89902e7 - 5.30383e6i) q^{48} +5.87576e7 q^{49} +(-1.74825e7 + 3.84747e7i) q^{50} -7.04142e7i q^{51} +(1.73514e7 - 1.51509e7i) q^{52} +4.94827e7i q^{53} +(-5.20558e7 - 2.36537e7i) q^{54} +1.92575e7 q^{55} +(-1.10477e8 + 3.31242e7i) q^{56} -6.58652e7 q^{57} +(1.11041e8 + 5.04561e7i) q^{58} -4.70612e7i q^{59} +(-1.47774e7 - 1.69237e7i) q^{60} -7.39468e7i q^{61} +(-1.73342e7 + 3.81481e7i) q^{62} +2.83597e7 q^{63} +(1.12077e8 - 7.38460e7i) q^{64} +1.31525e7 q^{65} +(9.25586e7 - 2.03698e8i) q^{66} +2.37554e8i q^{67} +(1.57972e8 + 1.80916e8i) q^{68} +1.71243e8i q^{69} +(-5.99549e7 - 2.72429e7i) q^{70} -6.33394e7 q^{71} +(-3.16121e7 + 9.47819e6i) q^{72} -2.73992e7 q^{73} +(-3.00266e8 - 1.36438e8i) q^{74} +2.80346e8i q^{75} +(1.69228e8 - 1.47766e8i) q^{76} -6.55807e8i q^{77} +(6.32157e7 - 1.39122e8i) q^{78} -1.20924e8 q^{79} +(7.59355e7 + 1.03295e7i) q^{80} -4.35376e8 q^{81} +(-5.10379e7 + 1.12322e8i) q^{82} -1.31132e8i q^{83} +(-5.76329e8 + 5.03239e8i) q^{84} +1.37136e8i q^{85} +(1.19288e8 + 5.42031e7i) q^{86} +8.09104e8 q^{87} +(2.19179e8 + 7.31016e8i) q^{88} +6.90156e8 q^{89} +(-1.71555e7 - 7.79531e6i) q^{90} -4.47903e8i q^{91} +(-3.84177e8 - 4.39975e8i) q^{92} +2.77967e8i q^{93} +(1.58935e8 - 3.49777e8i) q^{94} +1.28276e8 q^{95} +(4.74234e8 - 7.53568e8i) q^{96} +1.17879e8 q^{97} +(-5.50009e8 + 1.21043e9i) q^{98} -1.87653e8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 18 q^{2} - 428 q^{4} + 4684 q^{6} + 4800 q^{7} - 3384 q^{8} - 39368 q^{9}+O(q^{10}) $ 8 * q - 18 * q^2 - 428 * q^4 + 4684 * q^6 + 4800 * q^7 - 3384 * q^8 - 39368 * q^9	\( 8 q - 18 q^{2} - 428 q^{4} + 4684 q^{6} + 4800 q^{7} - 3384 q^{8} - 39368 q^{9} + 26392 q^{10} + 54760 q^{12} - 72336 q^{14} - 163136 q^{15} + 185616 q^{16} - 102000 q^{17} - 23614 q^{18} + 1245264 q^{20} - 2373124 q^{22} + 3412032 q^{23} - 3961456 q^{24} - 2423384 q^{25} + 4551240 q^{26} + 7509920 q^{28} - 15284368 q^{30} + 803584 q^{31} - 14113248 q^{32} + 58272 q^{33} + 27757244 q^{34} + 57226188 q^{36} - 63661140 q^{38} - 17590208 q^{39} - 93063648 q^{40} - 2180784 q^{41} + 127541344 q^{42} + 114013320 q^{44} - 131840944 q^{46} + 7432320 q^{47} - 217917408 q^{48} + 24436680 q^{49} + 231784902 q^{50} + 219270896 q^{52} - 362934280 q^{54} + 7056832 q^{55} - 358503360 q^{56} + 134003744 q^{57} + 375425192 q^{58} + 516952992 q^{60} - 344291904 q^{62} - 223198400 q^{63} - 316815296 q^{64} - 146501760 q^{65} + 239713176 q^{66} + 79875048 q^{68} - 56202048 q^{70} + 560234688 q^{71} + 112273016 q^{72} - 523987120 q^{73} - 65773608 q^{74} - 87532760 q^{76} + 318117968 q^{78} - 248943744 q^{79} + 890441280 q^{80} + 231960296 q^{81} - 1051981172 q^{82} - 1275608768 q^{84} + 1492810428 q^{86} + 540527424 q^{87} + 1544767952 q^{88} + 744827856 q^{89} - 3218579800 q^{90} - 2959012128 q^{92} + 3068552352 q^{94} - 1465245504 q^{95} + 4296343616 q^{96} - 9932784 q^{97} - 3062604162 q^{98}+O(q^{100}) \) 8 * q - 18 * q^2 - 428 * q^4 + 4684 * q^6 + 4800 * q^7 - 3384 * q^8 - 39368 * q^9 + 26392 * q^10 + 54760 * q^12 - 72336 * q^14 - 163136 * q^15 + 185616 * q^16 - 102000 * q^17 - 23614 * q^18 + 1245264 * q^20 - 2373124 * q^22 + 3412032 * q^23 - 3961456 * q^24 - 2423384 * q^25 + 4551240 * q^26 + 7509920 * q^28 - 15284368 * q^30 + 803584 * q^31 - 14113248 * q^32 + 58272 * q^33 + 27757244 * q^34 + 57226188 * q^36 - 63661140 * q^38 - 17590208 * q^39 - 93063648 * q^40 - 2180784 * q^41 + 127541344 * q^42 + 114013320 * q^44 - 131840944 * q^46 + 7432320 * q^47 - 217917408 * q^48 + 24436680 * q^49 + 231784902 * q^50 + 219270896 * q^52 - 362934280 * q^54 + 7056832 * q^55 - 358503360 * q^56 + 134003744 * q^57 + 375425192 * q^58 + 516952992 * q^60 - 344291904 * q^62 - 223198400 * q^63 - 316815296 * q^64 - 146501760 * q^65 + 239713176 * q^66 + 79875048 * q^68 - 56202048 * q^70 + 560234688 * q^71 + 112273016 * q^72 - 523987120 * q^73 - 65773608 * q^74 - 87532760 * q^76 + 318117968 * q^78 - 248943744 * q^79 + 890441280 * q^80 + 231960296 * q^81 - 1051981172 * q^82 - 1275608768 * q^84 + 1492810428 * q^86 + 540527424 * q^87 + 1544767952 * q^88 + 744827856 * q^89 - 3218579800 * q^90 - 2959012128 * q^92 + 3068552352 * q^94 - 1465245504 * q^95 + 4296343616 * q^96 - 9932784 * q^97 - 3062604162 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/8\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$1$

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 $

$2$	−9.36065	+	20.6004i	−0.413686	+	0.910420i
$2$	−9.36065	+	20.6004i	−0.413686	+	0.910420i
$3$			150.106i			1.06992i	0.844878	+	0.534960i	$0.179673\pi$
$3$			150.106i			1.06992i	−0.844878	+	0.534960i	$0.820327\pi$
$4$	−336.757	−	385.667i	−0.657728	−	0.753256i
$5$		−	292.339i		−	0.209181i	−0.994515	−	0.104590i	$-0.966647\pi$
$5$		−	292.339i		−	0.209181i	0.994515	−	0.104590i	$-0.0333531\pi$
$6$	−3092.24	−	1405.08i	−0.974075	−	0.442611i
$7$	−9955.46			−1.56718			−0.783592	−	0.621275i	$-0.786615\pi$
$7$	−9955.46			−1.56718			−0.783592	+	0.621275i	$0.786615\pi$
$8$	11097.2	−	3327.24i	0.957872	−	0.287197i
$9$	−2848.66			−0.144727
$10$	6022.31	+	2736.48i	0.190442	+	0.0865351i
$11$			65874.1i			1.35659i	0.734791	+	0.678293i	$0.237280\pi$
$11$			65874.1i			1.35659i	−0.734791	+	0.678293i	$0.762720\pi$
$12$	57890.7	−	50549.0i	0.805923	−	0.703715i
$13$			44990.6i			0.436895i	0.975849	+	0.218447i	$0.0700992\pi$
$13$			44990.6i			0.436895i	−0.975849	+	0.218447i	$0.929901\pi$
$14$	93189.6	−	205087.i	0.648322	−	1.42680i
$15$	43881.7			0.223806
$16$	−35334.0	+	259752.i	−0.134789	+	0.990874i
$17$	−469098.			−1.36221			−0.681104	−	0.732187i	$-0.738500\pi$
$17$	−469098.			−1.36221			−0.681104	+	0.732187i	$0.738500\pi$
$18$	26665.3	−	58683.7i	0.0598716	−	0.131762i
$19$			438793.i			0.772447i	0.922405	+	0.386223i	$0.126221\pi$
$19$			438793.i			0.772447i	−0.922405	+	0.386223i	$0.873779\pi$
$20$	−112745.	+	98447.0i	−0.157567	+	0.137584i
$21$		−	1.49437e6i		−	1.67676i
$22$	−1.35703e6	−	616624.i	−1.23506	−	0.561201i
$23$	1.14082e6			0.850041			0.425021	−	0.905184i	$-0.360267\pi$
$23$	1.14082e6			0.850041			0.425021	+	0.905184i	$0.360267\pi$
$24$	499437.	+	1.66575e6i	0.307277	+	1.02485i
$25$	1.86766e6			0.956243
$26$	−926827.	−	421141.i	−0.397758	−	0.180737i
$27$			2.52693e6i			0.915073i
$28$	3.35257e6	+	3.83949e6i	1.03078	+	1.18049i
$29$		−	5.39024e6i		−	1.41520i	−0.706615	−	0.707598i	$-0.749779\pi$
$29$		−	5.39024e6i		−	1.41520i	0.706615	−	0.707598i	$-0.250221\pi$
$30$	−410761.	+	903982.i	−0.0925856	+	0.203758i
$31$	1.85181e6			0.360138			0.180069	−	0.983654i	$-0.442368\pi$
$31$	1.85181e6			0.360138			0.180069	+	0.983654i	$0.442368\pi$
$32$	−5.02025e6	−	3.15934e6i	−0.846351	−	0.532625i
$33$	−9.88806e6			−1.45144
$34$	4.39106e6	−	9.66363e6i	0.563526	−	1.24018i
$35$			2.91037e6i			0.327825i
$36$	959306.	+	1.09863e6i	0.0951910	+	0.109016i
$37$			1.45757e7i			1.27856i	0.768972	+	0.639282i	$0.220768\pi$
$37$			1.45757e7i			1.27856i	−0.768972	+	0.639282i	$0.779232\pi$
$38$	−9.03933e6	−	4.10739e6i	−0.703250	−	0.319550i
$39$	−6.75334e6			−0.467442
$40$	−972682.	−	3.24413e6i	−0.0600760	−	0.200368i
$41$	5.45239e6			0.301342			0.150671	−	0.988584i	$-0.451857\pi$
$41$	5.45239e6			0.301342			0.150671	+	0.988584i	$0.451857\pi$
$42$	3.07847e7	+	1.39883e7i	1.52656	+	0.693653i
$43$		−	5.79053e6i		−	0.258292i	−0.991626	−	0.129146i	$-0.958776\pi$
$43$		−	5.79053e6i		−	0.258292i	0.991626	−	0.129146i	$-0.0412235\pi$
$44$	2.54054e7	−	2.21835e7i	1.02186	−	0.892264i
$45$			832774.i			0.0302741i
$46$	−1.06788e7	+	2.35013e7i	−0.351650	+	0.773894i
$47$	−1.69791e7			−0.507544			−0.253772	−	0.967264i	$-0.581671\pi$
$47$	−1.69791e7			−0.507544			−0.253772	+	0.967264i	$0.581671\pi$
$48$	−3.89902e7	−	5.30383e6i	−1.06016	−	0.144213i
$49$	5.87576e7			1.45607
$50$	−1.74825e7	+	3.84747e7i	−0.395585	+	0.870583i
$51$		−	7.04142e7i		−	1.45745i
$52$	1.73514e7	−	1.51509e7i	0.329094	−	0.287358i
$53$			4.94827e7i			0.861415i	0.902492	+	0.430707i	$0.141736\pi$
$53$			4.94827e7i			0.861415i	−0.902492	+	0.430707i	$0.858264\pi$
$54$	−5.20558e7	−	2.36537e7i	−0.833100	−	0.378553i
$55$	1.92575e7			0.283772
$56$	−1.10477e8	+	3.31242e7i	−1.50116	+	0.450090i
$57$	−6.58652e7			−0.826455
$58$	1.11041e8	+	5.04561e7i	1.28842	+	0.585447i
$59$		−	4.70612e7i		−	0.505625i	−0.967515	−	0.252813i	$-0.918644\pi$
$59$		−	4.70612e7i		−	0.505625i	0.967515	−	0.252813i	$-0.0813556\pi$
$60$	−1.47774e7	−	1.69237e7i	−0.147204	−	0.168583i
$61$		−	7.39468e7i		−	0.683810i	−0.939735	−	0.341905i	$-0.888928\pi$
$61$		−	7.39468e7i		−	0.683810i	0.939735	−	0.341905i	$-0.111072\pi$
$62$	−1.73342e7	+	3.81481e7i	−0.148984	+	0.327877i
$63$	2.83597e7			0.226814
$64$	1.12077e8	−	7.38460e7i	0.835036	−	0.550195i
$65$	1.31525e7			0.0913900
$66$	9.25586e7	−	2.03698e8i	0.600439	−	1.32142i
$67$			2.37554e8i			1.44021i	0.693866	+	0.720104i	$0.255906\pi$
$67$			2.37554e8i			1.44021i	−0.693866	+	0.720104i	$0.744094\pi$
$68$	1.57972e8	+	1.80916e8i	0.895962	+	1.02609i
$69$			1.71243e8i			0.909476i
$70$	−5.99549e7	−	2.72429e7i	−0.298458	−	0.135616i
$71$	−6.33394e7			−0.295809			−0.147904	−	0.989002i	$-0.547253\pi$
$71$	−6.33394e7			−0.295809			−0.147904	+	0.989002i	$0.547253\pi$
$72$	−3.16121e7	+	9.47819e6i	−0.138630	+	0.0415651i
$73$	−2.73992e7			−0.112924			−0.0564618	−	0.998405i	$-0.517982\pi$
$73$	−2.73992e7			−0.112924			−0.0564618	+	0.998405i	$0.517982\pi$
$74$	−3.00266e8	−	1.36438e8i	−1.16403	−	0.528924i
$75$			2.80346e8i			1.02310i
$76$	1.69228e8	−	1.47766e8i	0.581850	−	0.508059i
$77$		−	6.55807e8i		−	2.12602i
$78$	6.32157e7	−	1.39122e8i	0.193374	−	0.425569i
$79$	−1.20924e8			−0.349294			−0.174647	−	0.984631i	$-0.555878\pi$
$79$	−1.20924e8			−0.349294			−0.174647	+	0.984631i	$0.555878\pi$
$80$	7.59355e7	+	1.03295e7i	0.207272	+	0.0281952i
$81$	−4.35376e8			−1.12378
$82$	−5.10379e7	+	1.12322e8i	−0.124661	+	0.274348i
$83$		−	1.31132e8i		−	0.303290i	−0.988435	−	0.151645i	$-0.951543\pi$
$83$		−	1.31132e8i		−	0.303290i	0.988435	−	0.151645i	$-0.0484570\pi$
$84$	−5.76329e8	+	5.03239e8i	−1.26303	+	1.10285i
$85$			1.37136e8i			0.284947i
$86$	1.19288e8	+	5.42031e7i	0.235154	+	0.106852i
$87$	8.09104e8			1.51415
$88$	2.19179e8	+	7.31016e8i	0.389607	+	1.29944i
$89$	6.90156e8			1.16598			0.582991	−	0.812478i	$-0.301882\pi$
$89$	6.90156e8			1.16598			0.582991	+	0.812478i	$0.301882\pi$
$90$	−1.71555e7	−	7.79531e6i	−0.0275621	−	0.0125240i
$91$		−	4.47903e8i		−	0.684695i
$92$	−3.84177e8	−	4.39975e8i	−0.559096	−	0.640299i
$93$			2.77967e8i			0.385319i
$94$	1.58935e8	−	3.49777e8i	0.209964	−	0.462078i
$95$	1.28276e8			0.161581
$96$	4.74234e8	−	7.53568e8i	0.569866	−	0.905527i
$97$	1.17879e8			0.135196			0.0675982	−	0.997713i	$-0.478466\pi$
$97$	1.17879e8			0.135196			0.0675982	+	0.997713i	$0.478466\pi$
$98$	−5.50009e8	+	1.21043e9i	−0.602355	+	1.32563i
$99$		−	1.87653e8i		−	0.196335i
$100$	−6.28948e8	−	7.20296e8i	−0.628948	−	0.720296i
$101$		−	9.55963e7i		−	0.0914103i	−0.998955	−	0.0457051i	$-0.985447\pi$
$101$		−	9.55963e7i		−	0.0914103i	0.998955	−	0.0457051i	$-0.0145535\pi$
$102$	1.45056e9	+	6.59122e8i	1.32689	+	0.602928i
$103$	−1.83082e9			−1.60280			−0.801399	−	0.598130i	$-0.795910\pi$
$103$	−1.83082e9			−1.60280			−0.801399	+	0.598130i	$0.795910\pi$
$104$	1.49695e8	+	4.99269e8i	0.125475	+	0.418489i
$105$	−4.36862e8			−0.350746
$106$	−1.01937e9	−	4.63191e8i	−0.784249	−	0.356355i
$107$		−	3.98905e8i		−	0.294200i	−0.989122	−	0.147100i	$-0.953006\pi$
$107$		−	3.98905e8i		−	0.294200i	0.989122	−	0.147100i	$-0.0469939\pi$
$108$	9.74552e8	−	8.50959e8i	0.689284	−	0.601869i
$109$			2.62653e9i			1.78223i	0.453782	+	0.891113i	$0.350074\pi$
$109$			2.62653e9i			1.78223i	−0.453782	+	0.891113i	$0.649926\pi$
$110$	−1.80263e8	+	3.96714e8i	−0.117392	+	0.258351i
$111$	−2.18790e9			−1.36796
$112$	3.51766e8	−	2.58595e9i	0.211239	−	1.55288i
$113$	1.25718e9			0.725343			0.362672	−	0.931917i	$-0.381865\pi$
$113$	1.25718e9			0.725343			0.362672	+	0.931917i	$0.381865\pi$
$114$	6.16541e8	−	1.35685e9i	0.341893	−	0.752421i
$115$		−	3.33505e8i		−	0.177812i
$116$	−2.07884e9	+	1.81520e9i	−1.06601	+	0.930814i
$117$		−	1.28163e8i		−	0.0632305i
$118$	9.69481e8	+	4.40523e8i	0.460331	+	0.209170i
$119$	4.67009e9			2.13483
$120$	4.86962e8	−	1.46005e8i	0.214378	−	0.0642765i
$121$	−1.98144e9			−0.840326
$122$	1.52334e9	+	6.92190e8i	0.622554	+	0.282883i
$123$			8.18434e8i			0.322412i
$124$	−6.23610e8	−	7.14183e8i	−0.236873	−	0.271276i
$125$		−	1.11696e9i		−	0.409208i
$126$	−2.65466e8	+	5.84223e8i	−0.0938298	+	0.206496i
$127$	−2.41608e8			−0.0824129			−0.0412065	−	0.999151i	$-0.513120\pi$
$127$	−2.41608e8			−0.0824129			−0.0412065	+	0.999151i	$0.513120\pi$
$128$	4.72150e8	+	3.00007e9i	0.155466	+	0.987841i
$129$	8.69191e8			0.276351
$130$	−1.23116e8	+	2.70948e8i	−0.0378068	+	0.0832032i
$131$		−	1.35260e9i		−	0.401281i	−0.979665	−	0.200641i	$-0.935698\pi$
$131$		−	1.35260e9i		−	0.401281i	0.979665	−	0.200641i	$-0.0643023\pi$
$132$	3.32987e9	+	3.81350e9i	0.954651	+	1.09330i
$133$		−	4.36839e9i		−	1.21057i
$134$	−4.89371e9	−	2.22366e9i	−1.31119	−	0.595794i
$135$	7.38719e8			0.191416
$136$	−5.20566e9	+	1.56080e9i	−1.30482	+	0.391222i
$137$	6.09544e8			0.147830			0.0739150	−	0.997265i	$-0.476451\pi$
$137$	6.09544e8			0.147830			0.0739150	+	0.997265i	$0.476451\pi$
$138$	−3.52767e9	−	1.60294e9i	−0.828004	−	0.376237i
$139$			2.13256e9i			0.484546i	0.970208	+	0.242273i	$0.0778929\pi$
$139$			2.13256e9i			0.484546i	−0.970208	+	0.242273i	$0.922107\pi$
$140$	1.12243e9	−	9.80085e8i	0.246936	−	0.215619i
$141$		−	2.54865e9i		−	0.543031i
$142$	5.92897e8	−	1.30482e9i	0.122372	−	0.269310i
$143$	−2.96372e9			−0.592686
$144$	1.00655e8	−	7.39945e8i	0.0195076	−	0.143406i
$145$	−1.57578e9			−0.296032
$146$	2.56474e8	−	5.64436e8i	0.0467149	−	0.102808i
$147$			8.81984e9i			1.55787i
$148$	5.62138e9	−	4.90847e9i	0.963086	−	0.840947i
$149$		−	5.25087e9i		−	0.872757i	−0.899763	−	0.436378i	$-0.856261\pi$
$149$		−	5.25087e9i		−	0.872757i	0.899763	−	0.436378i	$-0.143739\pi$
$150$	−5.77526e9	−	2.62422e9i	−0.931453	−	0.423244i
$151$	5.75614e9			0.901022			0.450511	−	0.892771i	$-0.351242\pi$
$151$	5.75614e9			0.901022			0.450511	+	0.892771i	$0.351242\pi$
$152$	1.45997e9	+	4.86936e9i	0.221844	+	0.739905i
$153$	1.33630e9			0.197148
$154$	1.35099e10	+	6.13877e9i	1.93557	+	0.879505i
$155$		−	5.41356e8i		−	0.0753339i
$156$	2.27423e9	+	2.60454e9i	0.307450	+	0.352104i
$157$			1.51315e10i			1.98763i	0.111070	+	0.993813i	$0.464572\pi$
$157$			1.51315e10i			1.98763i	−0.111070	+	0.993813i	$0.535428\pi$
$158$	1.13193e9	−	2.49109e9i	0.144498	−	0.318004i
$159$	−7.42763e9			−0.921644
$160$	−9.23598e8	+	1.46761e9i	−0.111415	+	0.177040i
$161$	−1.13573e10			−1.33217
$162$	4.07540e9	−	8.96894e9i	0.464893	−	1.02311i
$163$		−	1.00347e10i		−	1.11343i	−0.830705	−	0.556713i	$-0.812062\pi$
$163$		−	1.00347e10i		−	1.11343i	0.830705	−	0.556713i	$-0.187938\pi$
$164$	−1.83613e9	−	2.10281e9i	−0.198201	−	0.226988i
$165$			2.89066e9i			0.303613i
$166$	2.70138e9	+	1.22748e9i	0.276121	+	0.125467i
$167$	9.12880e9			0.908217			0.454108	−	0.890946i	$-0.349958\pi$
$167$	9.12880e9			0.908217			0.454108	+	0.890946i	$0.349958\pi$
$168$	−4.97213e9	−	1.65833e10i	−0.481560	−	1.60612i
$169$	8.58034e9			0.809123
$170$	−2.82505e9	−	1.28368e9i	−0.259422	−	0.117879i
$171$		−	1.24997e9i		−	0.111794i
$172$	−2.23322e9	+	1.95000e9i	−0.194560	+	0.169886i
$173$		−	6.47969e9i		−	0.549980i	−0.961447	−	0.274990i	$-0.911325\pi$
$173$		−	6.47969e9i		−	0.549980i	0.961447	−	0.274990i	$-0.0886746\pi$
$174$	−7.57374e9	+	1.66679e10i	−0.626381	+	1.37851i
$175$	−1.85934e10			−1.49861
$176$	−1.71109e10	−	2.32760e9i	−1.34421	−	0.182852i
$177$	7.06414e9			0.540978
$178$	−6.46030e9	+	1.42175e10i	−0.482351	+	1.06153i
$179$		−	1.37068e9i		−	0.0997923i	−0.998754	−	0.0498962i	$-0.984111\pi$
$179$		−	1.37068e9i		−	0.0997923i	0.998754	−	0.0498962i	$-0.0158890\pi$
$180$	3.21174e8	−	2.80442e8i	0.0228041	−	0.0199121i
$181$			1.85728e10i			1.28625i	0.765763	+	0.643123i	$0.222362\pi$
$181$			1.85728e10i			1.28625i	−0.765763	+	0.643123i	$0.777638\pi$
$182$	9.22699e9	+	4.19266e9i	0.623360	+	0.283249i
$183$	1.10998e10			0.731621
$184$	1.26598e10	−	3.79577e9i	0.814230	−	0.244129i
$185$	4.26105e9			0.267451
$186$	−5.72625e9	−	2.60195e9i	−0.350802	−	0.159401i
$187$		−	3.09014e10i		−	1.84795i
$188$	5.71782e9	+	6.54827e9i	0.333826	+	0.382311i
$189$		−	2.51567e10i		−	1.43409i
$190$	−1.20075e9	+	2.64255e9i	−0.0668437	+	0.147106i
$191$	−1.73970e10			−0.945852			−0.472926	−	0.881102i	$-0.656802\pi$
$191$	−1.73970e10			−0.945852			−0.472926	+	0.881102i	$0.656802\pi$
$192$	1.10847e10	+	1.68233e10i	0.588664	+	0.893421i
$193$	3.11955e10			1.61839			0.809197	−	0.587538i	$-0.199903\pi$
$193$	3.11955e10			1.61839			0.809197	+	0.587538i	$0.199903\pi$
$194$	−1.10343e9	+	2.42837e9i	−0.0559288	+	0.123085i
$195$			1.97426e9i			0.0977799i
$196$	−1.97870e10	−	2.26609e10i	−0.957696	−	1.09679i
$197$			1.86636e10i			0.882872i	0.897293	+	0.441436i	$0.145531\pi$
$197$			1.86636e10i			0.882872i	−0.897293	+	0.441436i	$0.854469\pi$
$198$	3.86573e9	+	1.75655e9i	0.178747	+	0.0812209i
$199$	3.27467e10			1.48023			0.740115	−	0.672481i	$-0.234771\pi$
$199$	3.27467e10			1.48023			0.740115	+	0.672481i	$0.234771\pi$
$200$	2.07258e10	−	6.21417e9i	0.915958	−	0.274630i
$201$	−3.56581e10			−1.54091
$202$	1.96933e9	+	8.94844e8i	0.0832217	+	0.0378152i
$203$			5.36623e10i			2.21788i
$204$	−2.71564e10	+	2.37124e10i	−1.09783	+	0.958607i
$205$		−	1.59395e9i		−	0.0630349i
$206$	1.71377e10	−	3.77158e10i	0.663055	−	1.45922i
$207$	−3.24980e9			−0.123024
$208$	−1.16864e10	−	1.58970e9i	−0.432908	−	0.0588885i
$209$	−2.89051e10			−1.04789
$210$	4.08931e9	−	8.99955e9i	0.145099	−	0.319326i
$211$		−	6.63427e9i		−	0.230421i	−0.993341	−	0.115210i	$-0.963246\pi$
$211$		−	6.63427e9i		−	0.230421i	0.993341	−	0.115210i	$-0.0367543\pi$
$212$	1.90839e10	−	1.66636e10i	0.648866	−	0.566576i
$213$		−	9.50759e9i		−	0.316491i
$214$	8.21763e9	+	3.73401e9i	0.267846	+	0.121707i
$215$	−1.69280e9			−0.0540296
$216$	8.40770e9	+	2.80417e10i	0.262806	+	0.876522i
$217$	−1.84356e10			−0.564403
$218$	−5.41076e10	−	2.45860e10i	−1.62257	−	0.737282i
$219$		−	4.11277e9i		−	0.120819i
$220$	−6.48510e9	−	7.42700e9i	−0.186644	−	0.213753i
$221$		−	2.11050e10i		−	0.595142i
$222$	2.04801e10	−	4.50716e10i	0.565906	−	1.24542i
$223$	−6.34852e10			−1.71910			−0.859549	−	0.511053i	$-0.829256\pi$
$223$	−6.34852e10			−1.71910			−0.859549	+	0.511053i	$0.829256\pi$
$224$	4.99789e10	+	3.14527e10i	1.32639	+	0.834722i
$225$	−5.32034e9			−0.138394
$226$	−1.17680e10	+	2.58984e10i	−0.300064	+	0.660367i
$227$			5.09567e10i			1.27375i	0.770966	+	0.636877i	$0.219774\pi$
$227$			5.09567e10i			1.27375i	−0.770966	+	0.636877i	$0.780226\pi$
$228$	2.21806e10	+	2.54020e10i	0.543583	+	0.622532i
$229$		−	1.53720e10i		−	0.369377i	−0.982797	−	0.184689i	$-0.940872\pi$
$229$		−	1.53720e10i		−	0.369377i	0.982797	−	0.184689i	$-0.0591277\pi$
$230$	6.87034e9	+	3.12182e9i	0.161884	+	0.0735584i
$231$	9.84402e10			2.27467
$232$	−1.79346e10	−	5.98164e10i	−0.406440	−	1.35558i
$233$	5.78808e10			1.28657			0.643284	−	0.765628i	$-0.277571\pi$
$233$	5.78808e10			1.28657			0.643284	+	0.765628i	$0.277571\pi$
$234$	2.64022e9	+	1.19969e9i	0.0575663	+	0.0261576i
$235$			4.96365e9i			0.106168i
$236$	−1.81499e10	+	1.58482e10i	−0.380865	+	0.332564i
$237$		−	1.81514e10i		−	0.373716i
$238$	−4.37150e10	+	9.62058e10i	−0.883150	+	1.94359i
$239$	−5.44879e9			−0.108021			−0.0540106	−	0.998540i	$-0.517200\pi$
$239$	−5.44879e9			−0.108021			−0.0540106	+	0.998540i	$0.517200\pi$
$240$	−1.55052e9	+	1.13983e10i	−0.0301665	+	0.221764i
$241$	3.35748e10			0.641116			0.320558	−	0.947229i	$-0.396130\pi$
$241$	3.35748e10			0.641116			0.320558	+	0.947229i	$0.396130\pi$
$242$	1.85476e10	−	4.08186e10i	0.347631	−	0.765049i
$243$		−	1.56148e10i		−	0.287282i
$244$	−2.85188e10	+	2.49021e10i	−0.515084	+	0.449761i
$245$		−	1.71771e10i		−	0.304581i
$246$	−1.68601e10	−	7.66107e9i	−0.293530	−	0.133377i
$247$	−1.97416e10			−0.337478
$248$	2.05499e10	−	6.16143e9i	0.344966	−	0.103431i
$249$	1.96836e10			0.324495
$250$	2.30100e10	+	1.04555e10i	0.372551	+	0.169284i
$251$		−	8.11855e10i		−	1.29106i	−0.763734	−	0.645531i	$-0.776636\pi$
$251$		−	8.11855e10i		−	1.29106i	0.763734	−	0.645531i	$-0.223364\pi$
$252$	−9.55033e9	−	1.09374e10i	−0.149182	−	0.170849i
$253$			7.51501e10i			1.15315i
$254$	2.26161e9	−	4.97724e9i	0.0340931	−	0.0750303i
$255$	−2.05848e10			−0.304871
$256$	−6.62225e10	−	1.83561e10i	−0.963664	−	0.267117i
$257$	−1.18704e11			−1.69733			−0.848666	−	0.528930i	$-0.822594\pi$
$257$	−1.18704e11			−1.69733			−0.848666	+	0.528930i	$0.822594\pi$
$258$	−8.13619e9	+	1.79057e10i	−0.114323	+	0.251596i
$259$		−	1.45108e11i		−	2.00375i
$260$	−4.42919e9	−	5.07249e9i	−0.0601097	−	0.0688400i
$261$			1.53550e10i			0.204817i
$262$	2.78642e10	+	1.26612e10i	0.365334	+	0.166004i
$263$	1.49616e10			0.192832			0.0964158	−	0.995341i	$-0.469262\pi$
$263$	1.49616e10			0.192832			0.0964158	+	0.995341i	$0.469262\pi$
$264$	−1.09729e11	+	3.29000e10i	−1.39029	+	0.416848i
$265$	1.44657e10			0.180191
$266$	8.99907e10	+	4.08909e10i	1.10212	+	0.500794i
$267$			1.03596e11i			1.24751i
$268$	9.16166e10	−	7.99978e10i	1.08484	−	0.947265i
$269$			6.60058e10i			0.768594i	0.923210	+	0.384297i	$0.125556\pi$
$269$			6.60058e10i			0.768594i	−0.923210	+	0.384297i	$0.874444\pi$
$270$	−6.91489e9	+	1.52179e10i	−0.0791859	+	0.174268i
$271$	−5.96531e10			−0.671849			−0.335924	−	0.941889i	$-0.609049\pi$
$271$	−5.96531e10			−0.671849			−0.335924	+	0.941889i	$0.609049\pi$
$272$	1.65751e10	−	1.21849e11i	0.183610	−	1.34978i
$273$	6.72326e10			0.732568
$274$	−5.70572e9	+	1.25569e10i	−0.0611552	+	0.134587i
$275$			1.23031e11i			1.29723i
$276$	6.60426e10	−	5.76671e10i	0.685068	−	0.598187i
$277$			8.76886e10i			0.894920i	0.894304	+	0.447460i	$0.147671\pi$
$277$			8.76886e10i			0.894920i	−0.894304	+	0.447460i	$0.852329\pi$
$278$	−4.39317e10	−	1.99621e10i	−0.441140	−	0.200450i
$279$	−5.27519e9			−0.0521217
$280$	9.68350e9	+	3.22968e10i	0.0941502	+	0.314014i
$281$	2.36402e10			0.226189			0.113095	−	0.993584i	$-0.463924\pi$
$281$	2.36402e10			0.226189			0.113095	+	0.993584i	$0.463924\pi$
$282$	5.25034e10	+	2.38571e10i	0.494387	+	0.224645i
$283$		−	1.27110e11i		−	1.17799i	−0.808138	−	0.588993i	$-0.799525\pi$
$283$		−	1.27110e11i		−	1.17799i	0.808138	−	0.588993i	$-0.200475\pi$
$284$	2.13299e10	+	2.44279e10i	0.194562	+	0.222820i
$285$			1.92550e10i			0.172878i
$286$	2.77423e10	−	6.10539e10i	0.245186	−	0.539593i
$287$	−5.42811e10			−0.472259
$288$	1.43010e10	+	8.99990e9i	0.122490	+	0.0770852i
$289$	1.01465e11			0.855610
$290$	1.47503e10	−	3.24617e10i	0.122464	−	0.269513i
$291$			1.76943e10i			0.144649i
$292$	9.22686e9	+	1.05670e10i	0.0742730	+	0.0850604i
$293$		−	1.89715e11i		−	1.50383i	−0.659261	−	0.751914i	$-0.729131\pi$
$293$		−	1.89715e11i		−	1.50383i	0.659261	−	0.751914i	$-0.270869\pi$
$294$	−1.81693e11	−	8.25594e10i	−1.41832	−	0.644471i
$295$	−1.37578e10			−0.105767
$296$	4.84970e10	+	1.61749e11i	0.367199	+	1.22470i
$297$	−1.66459e11			−1.24138
$298$	1.08170e11	+	4.91515e10i	0.794575	+	0.361047i
$299$			5.13260e10i			0.371379i
$300$	1.08120e11	−	9.44085e10i	0.770658	−	0.672923i
$301$			5.76474e10i			0.404791i
$302$	−5.38812e10	+	1.18579e11i	−0.372740	+	0.820308i
$303$	1.43495e10			0.0978016
$304$	−1.13977e11	−	1.55043e10i	−0.765397	−	0.104117i
$305$	−2.16175e10			−0.143040
$306$	−1.25086e10	+	2.75284e10i	−0.0815575	+	0.179488i
$307$			1.07930e11i			0.693457i	0.937966	+	0.346729i	$0.112707\pi$
$307$			1.07930e11i			0.693457i	−0.937966	+	0.346729i	$0.887293\pi$
$308$	−2.52923e11	+	2.20847e11i	−1.60144	+	1.39834i
$309$		−	2.74816e11i		−	1.71486i
$310$	1.11522e10	+	5.06745e9i	0.0685855	+	0.0311646i
$311$	2.31164e11			1.40120			0.700598	−	0.713556i	$-0.252917\pi$
$311$	2.31164e11			1.40120			0.700598	+	0.713556i	$0.252917\pi$
$312$	−7.49430e10	+	2.24700e10i	−0.447750	+	0.134248i
$313$	−1.20963e11			−0.712367			−0.356183	−	0.934416i	$-0.615922\pi$
$313$	−1.20963e11			−0.712367			−0.356183	+	0.934416i	$0.615922\pi$
$314$	−3.11716e11	−	1.41641e11i	−1.80957	−	0.822253i
$315$		−	8.29065e9i		−	0.0474451i
$316$	4.07220e10	+	4.66364e10i	0.229740	+	0.263108i
$317$		−	5.78132e10i		−	0.321559i	−0.986990	−	0.160779i	$-0.948599\pi$
$317$		−	5.78132e10i		−	0.321559i	0.986990	−	0.160779i	$-0.0514008\pi$
$318$	6.95274e10	−	1.53013e11i	0.381271	−	0.839083i
$319$	3.55077e11			1.91984
$320$	−2.15880e10	−	3.27644e10i	−0.115090	−	0.174673i
$321$	5.98779e10			0.314770
$322$	1.06312e11	−	2.33966e11i	0.551101	−	1.21284i
$323$		−	2.05837e11i		−	1.05223i
$324$	1.46616e11	+	1.67910e11i	0.739142	+	0.846495i
$325$			8.40273e10i			0.417778i
$326$	2.06720e11	+	9.39315e10i	1.01368	+	0.460609i
$327$	−3.94256e11			−1.90684
$328$	6.05061e10	−	1.81414e10i	0.288647	−	0.0865444i
$329$	1.69035e11			0.795416
$330$	−5.95489e10	−	2.70585e10i	−0.276415	−	0.125600i
$331$			2.91884e11i			1.33655i	0.743915	+	0.668274i	$0.232967\pi$
$331$			2.91884e11i			1.33655i	−0.743915	+	0.668274i	$0.767033\pi$
$332$	−5.05733e10	+	4.41596e10i	−0.228455	+	0.199482i
$333$		−	4.15213e10i		−	0.185043i
$334$	−8.54515e10	+	1.88057e11i	−0.375717	+	0.826858i
$335$	6.94462e10			0.301264
$336$	3.88165e11	+	5.28021e10i	1.66146	+	0.226008i
$337$	−1.08867e11			−0.459791			−0.229895	−	0.973215i	$-0.573838\pi$
$337$	−1.08867e11			−0.459791			−0.229895	+	0.973215i	$0.573838\pi$
$338$	−8.03176e10	+	1.76759e11i	−0.334723	+	0.736641i
$339$			1.88709e11i			0.776059i
$340$	5.28886e10	−	4.61813e10i	0.214638	−	0.187418i
$341$			1.21986e11i			0.488558i
$342$	2.57500e10	+	1.17006e10i	0.101779	+	0.0462476i
$343$	−1.83220e11			−0.714743
$344$	−1.92665e10	−	6.42585e10i	−0.0741806	−	0.247410i
$345$	5.00609e10			0.190245
$346$	1.33485e11	+	6.06541e10i	0.500713	+	0.227519i
$347$		−	1.21916e11i		−	0.451416i	−0.974195	−	0.225708i	$-0.927530\pi$
$347$		−	1.21916e11i		−	0.451416i	0.974195	−	0.225708i	$-0.0724696\pi$
$348$	−2.72471e11	−	3.12045e11i	−0.995896	−	1.14054i
$349$		−	2.36404e11i		−	0.852983i	−0.904492	−	0.426491i	$-0.859749\pi$
$349$		−	2.36404e11i		−	0.852983i	0.904492	−	0.426491i	$-0.140251\pi$
$350$	1.74047e11	−	3.83033e11i	0.619954	−	1.36436i
$351$	−1.13688e11			−0.399791
$352$	2.08119e11	−	3.30704e11i	0.722552	−	1.14815i
$353$	−1.76095e11			−0.603616			−0.301808	−	0.953369i	$-0.597590\pi$
$353$	−1.76095e11			−0.603616			−0.301808	+	0.953369i	$0.597590\pi$
$354$	−6.61250e10	+	1.45525e11i	−0.223795	+	0.492517i
$355$			1.85166e10i			0.0618775i
$356$	−2.32414e11	−	2.66170e11i	−0.766899	−	0.878283i
$357$			7.01006e11i			2.28410i
$358$	2.82366e10	+	1.28304e10i	0.0908529	+	0.0412827i
$359$	−2.58619e11			−0.821743			−0.410872	−	0.911693i	$-0.634776\pi$
$359$	−2.58619e11			−0.821743			−0.410872	+	0.911693i	$0.634776\pi$
$360$	2.77084e9	+	9.24144e9i	0.00869462	+	0.0289987i
$361$	1.30148e11			0.403326
$362$	−3.82608e11	−	1.73854e11i	−1.17102	−	0.532102i
$363$		−	2.97426e11i		−	0.899081i
$364$	−1.72741e11	+	1.50834e11i	−0.515751	+	0.450343i
$365$			8.00985e9i			0.0236214i
$366$	−1.03902e11	+	2.28661e11i	−0.302661	+	0.666082i
$367$	2.80806e10			0.0807997			0.0403998	−	0.999184i	$-0.487137\pi$
$367$	2.80806e10			0.0807997			0.0403998	+	0.999184i	$0.487137\pi$
$368$	−4.03096e10	+	2.96329e11i	−0.114576	+	0.842284i
$369$	−1.55320e10			−0.0436123
$370$	−3.98862e10	+	8.77795e10i	−0.110641	+	0.243492i
$371$		−	4.92624e11i		−	1.35000i
$372$	1.07203e11	−	9.36072e10i	0.290244	−	0.253435i
$373$			2.27140e11i			0.607582i	0.952739	+	0.303791i	$0.0982524\pi$
$373$			2.27140e11i			0.607582i	−0.952739	+	0.303791i	$0.901748\pi$
$374$	6.36582e11	+	2.89257e11i	1.68241	+	0.764472i
$375$	1.67663e11			0.437820
$376$	−1.88420e11	+	5.64936e10i	−0.486162	+	0.145765i
$377$	2.42510e11			0.618292
$378$	5.18240e11	+	2.35483e11i	1.30562	+	0.593262i
$379$		−	7.70802e10i		−	0.191896i	−0.995386	−	0.0959481i	$-0.969412\pi$
$379$		−	7.70802e10i		−	0.191896i	0.995386	−	0.0959481i	$-0.0305883\pi$
$380$	−4.31979e10	−	4.94719e10i	−0.106276	−	0.121712i
$381$		−	3.62667e10i		−	0.0881752i
$382$	1.62847e11	−	3.58385e11i	0.391286	−	0.861122i
$383$	6.86276e11			1.62969			0.814844	−	0.579680i	$-0.196822\pi$
$383$	6.86276e11			1.62969			0.814844	+	0.579680i	$0.196822\pi$
$384$	−4.50328e11	+	7.08722e10i	−1.05691	+	0.166336i
$385$	−1.91718e11			−0.444722
$386$	−2.92010e11	+	6.42641e11i	−0.669507	+	1.47342i
$387$			1.64953e10i			0.0373818i
$388$	−3.96966e10	−	4.54622e10i	−0.0889224	−	0.101837i
$389$		−	3.92836e11i		−	0.869837i	−0.900470	−	0.434919i	$-0.856777\pi$
$389$		−	3.92836e11i		−	0.869837i	0.900470	−	0.434919i	$-0.143223\pi$
$390$	−4.06707e10	−	1.84804e10i	−0.0890207	−	0.0404502i
$391$	−5.35154e11			−1.15793
$392$	6.52043e11	−	1.95501e11i	1.39473	−	0.418178i
$393$	2.03033e11			0.429338
$394$	−3.84479e11	−	1.74703e11i	−0.803784	−	0.365232i
$395$			3.53508e10i			0.0730655i
$396$	−7.23715e10	+	6.31934e10i	−0.147890	+	0.129135i
$397$		−	3.27648e11i		−	0.661988i	−0.943633	−	0.330994i	$-0.892616\pi$
$397$		−	3.27648e11i		−	0.661988i	0.943633	−	0.330994i	$-0.107384\pi$
$398$	−3.06531e11	+	6.74597e11i	−0.612350	+	1.34763i
$399$	6.55719e11			1.29521
$400$	−6.59920e10	+	4.85129e11i	−0.128891	+	0.947517i
$401$	8.62754e11			1.66624			0.833120	−	0.553093i	$-0.186553\pi$
$401$	8.62754e11			1.66624			0.833120	+	0.553093i	$0.186553\pi$
$402$	3.33783e11	−	7.34573e11i	0.637451	−	1.40287i
$403$			8.33142e10i			0.157343i
$404$	−3.68683e10	+	3.21927e10i	−0.0688553	+	0.0601231i
$405$			1.27277e11i			0.235073i
$406$	−1.10547e12	−	5.02314e11i	−2.01920	−	0.917504i
$407$	−9.60162e11			−1.73448
$408$	−2.34285e11	−	7.81398e11i	−0.418576	−	1.39605i
$409$	−7.29199e11			−1.28852			−0.644260	−	0.764807i	$-0.722834\pi$
$409$	−7.29199e11			−1.28852			−0.644260	+	0.764807i	$0.722834\pi$
$410$	3.28360e10	+	1.49204e10i	0.0573882	+	0.0260767i
$411$			9.14959e10i			0.158166i
$412$	6.16541e11	+	7.06088e11i	1.05420	+	1.20732i
$413$			4.68516e11i			0.792408i
$414$	3.04202e10	−	6.69473e10i	0.0508933	−	0.112003i
$415$	−3.83350e10			−0.0634423
$416$	1.42141e11	−	2.25864e11i	0.232701	−	0.369767i
$417$	−3.20109e11			−0.518425
$418$	2.70570e11	−	5.95457e11i	0.433498	−	0.954020i
$419$			9.24005e11i			1.46457i	0.680997	+	0.732286i	$0.261547\pi$
$419$			9.24005e11i			1.46457i	−0.680997	+	0.732286i	$0.738453\pi$
$420$	1.47116e11	+	1.68483e11i	0.230695	+	0.264201i
$421$		−	9.91623e11i		−	1.53843i	−0.638991	−	0.769214i	$-0.720648\pi$
$421$		−	9.91623e11i		−	1.53843i	0.638991	−	0.769214i	$-0.279352\pi$
$422$	1.36669e11	+	6.21010e10i	0.209780	+	0.0953219i
$423$	4.83677e10			0.0734554
$424$	1.64641e11	+	5.49118e11i	0.247396	+	0.825125i
$425$	−8.76117e11			−1.30260
$426$	1.95860e11	+	8.89972e10i	0.288140	+	0.130928i
$427$			7.36175e11i			1.07166i
$428$	−1.53845e11	+	1.34334e11i	−0.221608	+	0.193504i
$429$		−	4.44870e11i		−	0.634126i
$430$	1.58457e10	−	3.48724e10i	0.0223513	−	0.0491896i
$431$	9.73542e10			0.135896			0.0679481	−	0.997689i	$-0.478355\pi$
$431$	9.73542e10			0.135896			0.0679481	+	0.997689i	$0.478355\pi$
$432$	−6.56374e11	−	8.92865e10i	−0.906722	−	0.123341i
$433$	1.47830e11			0.202100			0.101050	−	0.994881i	$-0.467780\pi$
$433$	1.47830e11			0.202100			0.101050	+	0.994881i	$0.467780\pi$
$434$	1.72569e11	−	3.79782e11i	0.233486	−	0.513844i
$435$		−	2.36533e11i		−	0.316730i
$436$	1.01296e12	−	8.84500e11i	1.34247	−	1.17222i
$437$			5.00582e11i			0.656611i
$438$	8.47249e10	+	3.84982e10i	0.109996	+	0.0499812i
$439$	4.93675e11			0.634381			0.317191	−	0.948362i	$-0.397260\pi$
$439$	4.93675e11			0.634381			0.317191	+	0.948362i	$0.397260\pi$
$440$	2.13704e11	−	6.40745e10i	0.271817	−	0.0814983i
$441$	−1.67381e11			−0.210732
$442$	4.34773e11	+	1.97557e11i	0.541829	+	0.246202i
$443$			3.53853e10i			0.0436522i	0.999762	+	0.0218261i	$0.00694801\pi$
$443$			3.53853e10i			0.0436522i	−0.999762	+	0.0218261i	$0.993052\pi$
$444$	7.36789e11	+	8.43800e11i	0.899745	+	1.03042i
$445$		−	2.01759e11i		−	0.243901i
$446$	5.94263e11	−	1.30782e12i	0.711167	−	1.56510i
$447$	7.88185e11			0.933779
$448$	−1.11577e12	+	7.35170e11i	−1.30866	+	0.862258i
$449$	−2.44259e11			−0.283623			−0.141812	−	0.989894i	$-0.545293\pi$
$449$	−2.44259e11			−0.283623			−0.141812	+	0.989894i	$0.545293\pi$
$450$	4.98018e10	−	1.09601e11i	0.0572518	−	0.125997i
$451$			3.59171e11i			0.408796i
$452$	−4.23363e11	−	4.84852e11i	−0.477078	−	0.546369i
$453$			8.64029e11i			0.964021i
$454$	−1.04973e12	−	4.76988e11i	−1.15965	−	0.526934i
$455$	−1.30939e11			−0.143225
$456$	−7.30918e11	+	2.19150e11i	−0.791638	+	0.237355i
$457$	1.16957e12			1.25431			0.627154	−	0.778895i	$-0.284220\pi$
$457$	1.16957e12			1.25431			0.627154	+	0.778895i	$0.284220\pi$
$458$	3.16670e11	+	1.43892e11i	0.336288	+	0.152806i
$459$		−	1.18538e12i		−	1.24652i
$460$	−1.28622e11	+	1.12310e11i	−0.133938	+	0.116952i
$461$			8.92772e11i			0.920633i	0.887755	+	0.460317i	$0.152264\pi$
$461$			8.92772e11i			0.920633i	−0.887755	+	0.460317i	$0.847736\pi$
$462$	−9.21464e11	+	2.02791e12i	−0.941000	+	2.07090i
$463$	7.55549e11			0.764097			0.382048	−	0.924142i	$-0.375219\pi$
$463$	7.55549e11			0.764097			0.382048	+	0.924142i	$0.375219\pi$
$464$	1.40012e12	+	1.90459e11i	1.40228	+	0.190752i
$465$	8.12606e10			0.0806012
$466$	−5.41802e11	+	1.19237e12i	−0.532235	+	1.17132i
$467$		−	7.06860e11i		−	0.687713i	−0.939022	−	0.343857i	$-0.888267\pi$
$467$		−	7.06860e11i		−	0.687713i	0.939022	−	0.343857i	$-0.111733\pi$
$468$	−4.94283e10	+	4.31598e10i	−0.0476287	+	0.0415885i
$469$		−	2.36496e12i		−	2.25707i
$470$	−1.02253e11	−	4.64629e10i	−0.0966578	−	0.0439204i
$471$	−2.27133e12			−2.12660
$472$	−1.56584e11	−	5.22246e11i	−0.145214	−	0.484324i
$473$	3.81446e11			0.350395
$474$	3.73926e11	+	1.69909e11i	0.340239	+	0.154601i
$475$			8.19517e11i			0.738647i
$476$	−1.57268e12	−	1.80110e12i	−1.40414	−	1.60807i
$477$		−	1.40960e11i		−	0.124670i
$478$	5.10042e10	−	1.12247e11i	0.0446869	−	0.0983447i
$479$	−1.32511e12			−1.15012			−0.575061	−	0.818111i	$-0.695022\pi$
$479$	−1.32511e12			−1.15012			−0.575061	+	0.818111i	$0.695022\pi$
$480$	−2.20297e11	−	1.38637e11i	−0.189419	−	0.119205i
$481$	−6.55771e11			−0.558598
$482$	−3.14282e11	+	6.91656e11i	−0.265221	+	0.583685i
$483$		−	1.70480e12i		−	1.42532i
$484$	6.67264e11	+	7.64178e11i	0.552706	+	0.632980i
$485$		−	3.44607e10i		−	0.0282805i
$486$	3.21672e11	+	1.46165e11i	0.261547	+	0.118845i
$487$	1.69922e12			1.36889			0.684446	−	0.729064i	$-0.260044\pi$
$487$	1.69922e12			1.36889			0.684446	+	0.729064i	$0.260044\pi$
$488$	−2.46039e11	−	8.20601e11i	−0.196388	−	0.655002i
$489$	1.50627e12			1.19128
$490$	3.53856e11	+	1.60789e11i	0.277297	+	0.126001i
$491$		−	1.61014e12i		−	1.25025i	−0.780525	−	0.625125i	$-0.785048\pi$
$491$		−	1.61014e12i		−	1.25025i	0.780525	−	0.625125i	$-0.214952\pi$
$492$	3.15643e11	−	2.75613e11i	0.242858	−	0.212059i
$493$			2.52855e12i			1.92779i
$494$	1.84794e11	−	4.06685e11i	0.139610	−	0.307247i
$495$	−5.48582e10			−0.0410694
$496$	−6.54319e10	+	4.81011e11i	−0.0485425	+	0.356852i
$497$	6.30572e11			0.463587
$498$	−1.84252e11	+	4.05492e11i	−0.134239	+	0.295427i
$499$			1.12530e12i			0.812489i	0.913764	+	0.406244i	$0.133162\pi$
$499$			1.12530e12i			0.812489i	−0.913764	+	0.406244i	$0.866838\pi$
$500$	−4.30776e11	+	3.76145e11i	−0.308238	+	0.269148i
$501$			1.37028e12i			0.971718i
$502$	1.67246e12	+	7.59949e11i	1.17541	+	0.534094i
$503$	−3.27201e11			−0.227908			−0.113954	−	0.993486i	$-0.536352\pi$
$503$	−3.27201e11			−0.227908			−0.113954	+	0.993486i	$0.536352\pi$
$504$	3.14713e11	−	9.43597e10i	0.217259	−	0.0651402i
$505$	−2.79465e10			−0.0191213
$506$	−1.54813e12	−	7.03454e11i	−1.04985	−	0.477044i
$507$			1.28796e12i			0.865696i
$508$	8.13632e10	+	9.31804e10i	0.0542053	+	0.0620780i
$509$			1.78571e12i			1.17918i	0.807701	+	0.589592i	$0.200711\pi$
$509$			1.78571e12i			1.17918i	−0.807701	+	0.589592i	$0.799289\pi$
$510$	1.92687e11	−	4.24056e11i	0.126121	−	0.277560i
$511$	2.72772e11			0.176972
$512$	9.98030e11	−	1.19239e12i	0.641843	−	0.766836i
$513$	−1.10880e12			−0.706845
$514$	1.11115e12	−	2.44536e12i	0.702162	−	1.54528i
$515$			5.35220e11i			0.335274i
$516$	−2.92706e11	−	3.35218e11i	−0.181764	−	0.208163i
$517$		−	1.11848e12i		−	0.688528i
$518$	2.98929e12	+	1.35831e12i	1.82425	+	0.828922i
$519$	9.72637e11			0.588434
$520$	1.45956e11	−	4.37616e10i	0.0875398	−	0.0262469i
$521$	−2.62743e12			−1.56229			−0.781145	−	0.624350i	$-0.785364\pi$
$521$	−2.62743e12			−1.56229			−0.781145	+	0.624350i	$0.785364\pi$
$522$	−3.16319e11	−	1.43732e11i	−0.186470	−	0.0847300i
$523$		−	1.74460e12i		−	1.01962i	−0.860288	−	0.509808i	$-0.829716\pi$
$523$		−	1.74460e12i		−	1.01962i	0.860288	−	0.509808i	$-0.170284\pi$
$524$	−5.21653e11	+	4.55497e11i	−0.302267	+	0.263934i
$525$		−	2.79098e12i		−	1.60339i
$526$	−1.40051e11	+	3.08216e11i	−0.0797717	+	0.175558i
$527$	−8.68681e11			−0.490583
$528$	3.49385e11	−	2.56844e12i	0.195637	−	1.43819i
$529$	−4.99693e11			−0.277430
$530$	−1.35409e11	+	2.98000e11i	−0.0745426	+	0.164050i
$531$			1.34061e11i			0.0731777i
$532$	−1.68474e12	+	1.47108e12i	−0.911866	+	0.796223i
$533$			2.45307e11i			0.131655i
$534$	−2.13413e12	−	9.69727e11i	−1.13575	−	0.516076i
$535$	−1.16616e11			−0.0615410
$536$	7.90399e11	+	2.63617e12i	0.413623	+	1.37953i
$537$	2.05746e11			0.106770
$538$	−1.35975e12	−	6.17857e11i	−0.699743	−	0.317957i
$539$			3.87060e12i			1.97528i
$540$	−2.48768e11	−	2.84899e11i	−0.125899	−	0.144185i
$541$		−	4.60286e11i		−	0.231015i	−0.993307	−	0.115508i	$-0.963151\pi$
$541$		−	4.60286e11i		−	0.231015i	0.993307	−	0.115508i	$-0.0368495\pi$
$542$	5.58392e11	−	1.22888e12i	0.277934	−	0.611664i
$543$	−2.78788e12			−1.37618
$544$	2.35499e12	+	1.48204e12i	1.15291	+	0.725546i
$545$	7.67836e11			0.372807
$546$	−6.29341e11	+	1.38502e12i	−0.303053	+	0.666945i
$547$		−	5.60408e11i		−	0.267646i	−0.991005	−	0.133823i	$-0.957275\pi$
$547$		−	5.60408e11i		−	0.267646i	0.991005	−	0.133823i	$-0.0427254\pi$
$548$	−2.05268e11	−	2.35081e11i	−0.0972318	−	0.111354i
$549$			2.10650e11i			0.0989658i
$550$	−2.53448e12	−	1.15165e12i	−1.18102	−	0.536645i
$551$	2.36520e12			1.09316
$552$	5.69766e11	+	1.90031e12i	0.261198	+	0.871161i
$553$	1.20386e12			0.547408
$554$	−1.80642e12	−	8.20822e11i	−0.814753	−	0.370216i
$555$			6.39607e11i			0.286151i
$556$	8.22458e11	−	7.18154e11i	0.364987	−	0.318699i
$557$		−	3.67343e12i		−	1.61705i	−0.588462	−	0.808525i	$-0.700266\pi$
$557$		−	3.67343e12i		−	1.61705i	0.588462	−	0.808525i	$-0.299734\pi$
$558$	4.93791e10	−	1.08671e11i	0.0215620	−	0.0474526i
$559$	2.60520e11			0.112846
$560$	−7.55973e11	−	1.02835e11i	−0.324833	−	0.0441870i
$561$	4.63847e12			1.97716
$562$	−2.21287e11	+	4.86998e11i	−0.0935713	+	0.205927i
$563$		−	7.28222e11i		−	0.305475i	−0.988267	−	0.152738i	$-0.951191\pi$
$563$		−	7.28222e11i		−	0.305475i	0.988267	−	0.152738i	$-0.0488089\pi$
$564$	−9.82932e11	+	8.58276e11i	−0.409042	+	0.357167i
$565$		−	3.67522e11i		−	0.151728i
$566$	2.61852e12	+	1.18983e12i	1.07246	+	0.487316i
$567$	4.33437e12			1.76117
$568$	−7.02888e11	+	2.10745e11i	−0.283347	+	0.0849553i
$569$	−3.21622e12			−1.28629			−0.643147	−	0.765742i	$-0.722372\pi$
$569$	−3.21622e12			−1.28629			−0.643147	+	0.765742i	$0.722372\pi$
$570$	−3.96661e11	−	1.80239e11i	−0.157392	−	0.0715174i
$571$		−	9.17863e11i		−	0.361339i	−0.983544	−	0.180670i	$-0.942174\pi$
$571$		−	9.17863e11i		−	0.361339i	0.983544	−	0.180670i	$-0.0578265\pi$
$572$	9.98051e11	+	1.14301e12i	0.389826	+	0.446444i
$573$		−	2.61138e12i		−	1.01199i
$574$	5.08106e11	−	1.11821e12i	0.195367	−	0.429953i
$575$	2.13066e12			0.812846
$576$	−3.19268e11	+	2.10362e11i	−0.120852	+	0.0796281i
$577$	−3.29707e12			−1.23833			−0.619167	−	0.785260i	$-0.712529\pi$
$577$	−3.29707e12			−1.23833			−0.619167	+	0.785260i	$0.712529\pi$
$578$	−9.49778e11	+	2.09022e12i	−0.353954	+	0.778964i
$579$			4.68262e12i			1.73155i
$580$	5.30653e11	+	6.07725e11i	0.194708	+	0.222988i
$581$			1.30548e12i			0.475311i
$582$	−3.64511e11	−	1.65630e11i	−0.131691	−	0.0598393i
$583$	−3.25963e12			−1.16858
$584$	−3.04054e11	+	9.11638e10i	−0.108166	+	0.0324313i
$585$	−3.74671e10			−0.0132266
$586$	3.90822e12	+	1.77586e12i	1.36911	+	0.622113i
$587$		−	4.56218e12i		−	1.58599i	−0.609227	−	0.792996i	$-0.708520\pi$
$587$		−	4.56218e12i		−	1.58599i	0.609227	−	0.792996i	$-0.291480\pi$
$588$	3.40152e12	−	2.97014e12i	1.17348	−	1.02466i
$589$			8.12562e11i			0.278187i
$590$	1.28782e11	−	2.83417e11i	0.0437543	−	0.0962924i
$591$	−2.80151e12			−0.944602
$592$	−3.78607e12	−	5.15019e11i	−1.26690	−	0.172336i
$593$	3.34603e12			1.11118			0.555590	−	0.831457i	$-0.312493\pi$
$593$	3.34603e12			1.11118			0.555590	+	0.831457i	$0.312493\pi$
$594$	1.55816e12	−	3.42913e12i	0.513540	−	1.13017i
$595$		−	1.36525e12i		−	0.446565i
$596$	−2.02509e12	+	1.76827e12i	−0.657409	+	0.574036i
$597$			4.91546e12i			1.58373i
$598$	−1.05734e12	−	4.80445e11i	−0.338111	−	0.153634i
$599$	3.92344e12			1.24522			0.622610	−	0.782532i	$-0.286072\pi$
$599$	3.92344e12			1.24522			0.622610	+	0.782532i	$0.286072\pi$
$600$	9.32781e11	+	3.11105e12i	0.293832	+	0.980002i
$601$	−1.68334e12			−0.526305			−0.263153	−	0.964754i	$-0.584762\pi$
$601$	−1.68334e12			−0.526305			−0.263153	+	0.964754i	$0.584762\pi$
$602$	−1.18756e12	−	5.39617e11i	−0.368530	−	0.167456i
$603$		−	6.76710e11i		−	0.208437i
$604$	−1.93842e12	−	2.21995e12i	−0.592627	−	0.678700i
$605$			5.79253e11i			0.175780i
$606$	−1.34321e11	+	2.95607e11i	−0.0404592	+	0.0890405i
$607$	−4.88789e12			−1.46141			−0.730706	−	0.682692i	$-0.760809\pi$
$607$	−4.88789e12			−1.46141			−0.730706	+	0.682692i	$0.760809\pi$
$608$	1.38630e12	−	2.20285e12i	0.411424	−	0.653761i
$609$	−8.05501e12			−2.37295
$610$	2.02354e11	−	4.45331e11i	0.0591736	−	0.130226i
$611$		−	7.63900e11i		−	0.221744i
$612$	−4.50008e11	−	5.15367e11i	−0.129670	−	0.148503i
$613$			3.80258e12i			1.08769i	0.839185	+	0.543846i	$0.183033\pi$
$613$			3.80258e12i			1.08769i	−0.839185	+	0.543846i	$0.816967\pi$
$614$	−2.22341e12	−	1.01029e12i	−0.631337	−	0.286874i
$615$	2.39260e11			0.0674423
$616$	−2.18203e12	−	7.27760e12i	−0.610586	−	2.03646i
$617$	7.15842e12			1.98854			0.994270	−	0.106902i	$-0.0340932\pi$
$617$	7.15842e12			1.98854			0.994270	+	0.106902i	$0.0340932\pi$
$618$	5.66134e12	+	2.57246e12i	1.56125	+	0.709415i
$619$			4.99966e12i			1.36878i	0.729118	+	0.684388i	$0.239930\pi$
$619$			4.99966e12i			1.36878i	−0.729118	+	0.684388i	$0.760070\pi$
$620$	−2.08783e11	+	1.82305e11i	−0.0567457	+	0.0495492i
$621$			2.88276e12i			0.777850i
$622$	−2.16385e12	+	4.76209e12i	−0.579655	+	1.27568i
$623$	−6.87082e12			−1.82731
$624$	2.38623e11	−	1.75419e12i	0.0630059	−	0.463177i
$625$	3.32125e12			0.870645
$626$	1.13229e12	−	2.49190e12i	0.294696	−	0.648553i
$627$		−	4.33881e12i		−	1.12116i
$628$	5.83573e12	−	5.09564e12i	1.49719	−	1.30732i
$629$		−	6.83744e12i		−	1.74167i
$630$	1.70791e11	+	7.76059e10i	0.0431949	+	0.0196274i
$631$	3.31885e12			0.833403			0.416702	−	0.909043i	$-0.363186\pi$
$631$	3.31885e12			0.833403			0.416702	+	0.909043i	$0.363186\pi$
$632$	−1.34192e12	+	4.02344e11i	−0.334579	+	0.100316i
$633$	9.95840e11			0.246532
$634$	1.19098e12	+	5.41169e11i	0.292753	+	0.133024i
$635$			7.06315e10i			0.0172392i
$636$	2.50130e12	+	2.86459e12i	0.606191	+	0.694234i
$637$			2.64354e12i			0.636149i
$638$	−3.32375e12	+	7.31474e12i	−0.794210	+	1.74786i
$639$	1.80432e11			0.0428115
$640$	8.77038e11	−	1.38028e11i	0.206637	−	0.0325204i
$641$	−6.76534e11			−0.158281			−0.0791404	−	0.996863i	$-0.525218\pi$
$641$	−6.76534e11			−0.158281			−0.0791404	+	0.996863i	$0.525218\pi$
$642$	−5.60496e11	+	1.23351e12i	−0.130216	+	0.286573i
$643$		−	2.51359e12i		−	0.579889i	−0.957044	−	0.289944i	$-0.906363\pi$
$643$		−	2.51359e12i		−	0.579889i	0.957044	−	0.289944i	$-0.0936368\pi$
$644$	3.82466e12	+	4.38015e12i	0.876206	+	1.00347i
$645$		−	2.54098e11i		−	0.0578073i
$646$	4.24033e12	+	1.92677e12i	0.957973	+	0.435294i
$647$	1.44698e12			0.324634			0.162317	−	0.986739i	$-0.448103\pi$
$647$	1.44698e12			0.324634			0.162317	+	0.986739i	$0.448103\pi$
$648$	−4.83144e12	+	1.44860e12i	−1.07644	+	0.322746i
$649$	3.10011e12			0.685924
$650$	−1.73100e12	−	7.86550e11i	−0.380353	−	0.172829i
$651$		−	2.76729e12i		−	0.603866i
$652$	−3.87006e12	+	3.37926e12i	−0.838694	+	0.732331i
$653$			3.39613e12i			0.730928i	0.930825	+	0.365464i	$0.119090\pi$
$653$			3.39613e12i			0.730928i	−0.930825	+	0.365464i	$0.880910\pi$
$654$	3.69049e12	−	8.12185e12i	0.788832	−	1.73602i
$655$	−3.95418e11			−0.0839402
$656$	−1.92655e11	+	1.41627e12i	−0.0406175	+	0.298592i
$657$	7.80510e10			0.0163431
$658$	−1.58227e12	+	3.48219e12i	−0.329052	+	0.724162i
$659$			2.73212e12i			0.564308i	0.959369	+	0.282154i	$0.0910489\pi$
$659$			2.73212e12i			0.564308i	−0.959369	+	0.282154i	$0.908951\pi$
$660$	1.11483e12	−	9.73450e11i	0.228698	−	0.199694i
$661$			3.29057e12i			0.670448i	0.942138	+	0.335224i	$0.108812\pi$
$661$			3.29057e12i			0.670448i	−0.942138	+	0.335224i	$0.891188\pi$
$662$	−6.01294e12	−	2.73222e12i	−1.21682	−	0.552911i
$663$	3.16798e12			0.636754
$664$	−4.36308e11	−	1.45519e12i	−0.0871038	−	0.290512i
$665$	−1.27705e12			−0.253227
$666$	8.55358e11	+	3.88666e11i	0.168467	+	0.0765496i
$667$		−	6.14926e12i		−	1.20298i
$668$	−3.07418e12	−	3.52068e12i	−0.597359	−	0.684119i
$669$		−	9.52948e12i		−	1.83930i
$670$	−6.50061e11	+	1.43062e12i	−0.124629	+	0.274276i
$671$	4.87118e12			0.927647
$672$	−4.72122e12	+	7.50211e12i	−0.893085	+	1.41913i
$673$	3.00500e11			0.0564646			0.0282323	−	0.999601i	$-0.491012\pi$
$673$	3.00500e11			0.0564646			0.0282323	+	0.999601i	$0.491012\pi$
$674$	1.01906e12	−	2.24270e12i	0.190209	−	0.418602i
$675$			4.71945e12i			0.875033i
$676$	−2.88949e12	−	3.30915e12i	−0.532182	−	0.609476i
$677$		−	8.63566e12i		−	1.57996i	−0.613132	−	0.789981i	$-0.710091\pi$
$677$		−	8.63566e12i		−	1.57996i	0.613132	−	0.789981i	$-0.289909\pi$
$678$	−3.88750e12	−	1.76644e12i	−0.706539	−	0.321045i
$679$	−1.17354e12			−0.211878
$680$	4.56283e11	+	1.52182e12i	0.0818360	+	0.272943i
$681$	−7.64889e12			−1.36281
$682$	−2.51297e12	−	1.14187e12i	−0.444793	−	0.202110i
$683$			4.86440e12i			0.855335i	0.903936	+	0.427668i	$0.140665\pi$
$683$			4.86440e12i			0.855335i	−0.903936	+	0.427668i	$0.859335\pi$
$684$	−4.82073e11	+	4.20937e11i	−0.0842094	+	0.0735299i
$685$		−	1.78193e11i		−	0.0309232i
$686$	1.71506e12	−	3.77442e12i	0.295679	−	0.650716i
$687$	2.30742e12			0.395204
$688$	1.50410e12	+	2.04603e11i	0.255935	+	0.0348148i
$689$	−2.22626e12			−0.376348
$690$	−4.68602e11	+	1.03128e12i	−0.0787016	+	0.173202i
$691$		−	8.78244e11i		−	0.146543i	−0.997312	−	0.0732713i	$-0.976656\pi$
$691$		−	8.78244e11i		−	0.146543i	0.997312	−	0.0732713i	$-0.0233439\pi$
$692$	−2.49900e12	+	2.18208e12i	−0.414276	+	0.361737i
$693$			1.86817e12i			0.307693i
$694$	2.51152e12	+	1.14121e12i	0.410978	+	0.186745i
$695$	6.23430e11			0.101358
$696$	8.97877e12	−	2.69209e12i	1.45036	−	0.434858i
$697$	−2.55771e12			−0.410490
$698$	4.87003e12	+	2.21289e12i	0.776572	+	0.352867i
$699$			8.68822e12i			1.37652i
$700$	6.26147e12	+	7.17088e12i	0.985677	+	1.12884i
$701$			3.76755e12i			0.589288i	0.955607	+	0.294644i	$0.0952011\pi$
$701$			3.76755e12i			0.589288i	−0.955607	+	0.294644i	$0.904799\pi$
$702$	1.06419e12	−	2.34202e12i	0.165388	−	0.363977i
$703$	−6.39573e12			−0.987622
$704$	4.86453e12	+	7.38294e12i	0.746387	+	1.13280i
$705$	−7.45071e11			−0.113592
$706$	1.64836e12	−	3.62764e12i	0.249708	−	0.549544i
$707$			9.51706e11i			0.143257i
$708$	−2.37890e12	−	2.72441e12i	−0.355816	−	0.407495i
$709$		−	6.49276e11i		−	0.0964986i	−0.998835	−	0.0482493i	$-0.984636\pi$
$709$		−	6.49276e11i		−	0.0964986i	0.998835	−	0.0482493i	$-0.0153642\pi$
$710$	−3.81449e11	−	1.73327e11i	−0.0563345	−	0.0255978i
$711$	3.44472e11			0.0505523
$712$	7.65878e12	−	2.29632e12i	1.11686	−	0.334866i
$713$	2.11257e12			0.306132
$714$	−1.44410e13	−	6.56187e12i	−2.07949	−	0.944899i
$715$			8.66409e11i			0.123978i
$716$	−5.28626e11	+	4.61585e11i	−0.0751691	+	0.0656362i
$717$		−	8.17893e11i		−	0.115574i
$718$	2.42084e12	−	5.32767e12i	0.339944	−	0.748131i
$719$	−3.35865e12			−0.468689			−0.234344	−	0.972154i	$-0.575294\pi$
$719$	−3.35865e12			−0.468689			−0.234344	+	0.972154i	$0.575294\pi$
$720$	−2.16315e11	−	2.94253e10i	−0.0299978	−	0.00408060i
$721$	1.82267e13			2.51188
$722$	−1.21827e12	+	2.68112e12i	−0.166850	+	0.367196i
$723$			5.03976e12i			0.685942i
$724$	7.16292e12	−	6.25452e12i	0.968873	−	0.846000i
$725$		−	1.00671e13i		−	1.35327i
$726$	6.12710e12	+	2.78410e12i	0.818541	+	0.371937i
$727$	7.42904e11			0.0986342			0.0493171	−	0.998783i	$-0.484296\pi$
$727$	7.42904e11			0.0986342			0.0493171	+	0.998783i	$0.484296\pi$
$728$	−1.49028e12	−	4.97045e12i	−0.196642	−	0.655850i
$729$	−6.22563e12			−0.816413
$730$	−1.65006e11	−	7.49774e10i	−0.0215054	−	0.00977186i
$731$			2.71633e12i			0.351847i
$732$	−3.73794e12	−	4.28084e12i	−0.481208	−	0.551098i
$733$			1.31480e13i			1.68226i	0.540832	+	0.841130i	$0.318109\pi$
$733$			1.31480e13i			1.68226i	−0.540832	+	0.841130i	$0.681891\pi$
$734$	−2.62853e11	+	5.78474e11i	−0.0334257	+	0.0735616i
$735$	2.57838e12			0.325877
$736$	−5.72718e12	−	3.60422e12i	−0.719434	−	0.452753i
$737$	−1.56486e13			−1.95377
$738$	1.45390e11	−	3.19966e11i	0.0180418	−	0.0397055i
$739$		−	4.12361e12i		−	0.508602i	−0.967125	−	0.254301i	$-0.918155\pi$
$739$		−	4.12361e12i		−	0.508602i	0.967125	−	0.254301i	$-0.0818454\pi$
$740$	−1.43494e12	−	1.64335e12i	−0.175910	−	0.201459i
$741$		−	2.96332e12i		−	0.361074i
$742$	1.01483e13	+	4.61127e12i	1.22906	+	0.558475i
$743$	−8.36687e11			−0.100719			−0.0503597	−	0.998731i	$-0.516037\pi$
$743$	−8.36687e11			−0.100719			−0.0503597	+	0.998731i	$0.516037\pi$
$744$	9.24864e11	+	3.08465e12i	0.110662	+	0.369086i
$745$	−1.53503e12			−0.182564
$746$	−4.67919e12	−	2.12618e12i	−0.553154	−	0.251348i
$747$			3.73551e11i			0.0438942i
$748$	−1.19176e13	+	1.04062e13i	−1.39198	+	1.21545i
$749$			3.97129e12i			0.461066i
$750$	−1.56943e12	+	3.45392e12i	−0.181120	+	0.398600i
$751$	5.28606e12			0.606390			0.303195	−	0.952928i	$-0.401947\pi$
$751$	5.28606e12			0.606390			0.303195	+	0.952928i	$0.401947\pi$
$752$	5.99939e11	−	4.41035e12i	0.0684112	−	0.502913i
$753$	1.21864e13			1.38133
$754$	−2.27005e12	+	4.99582e12i	−0.255779	+	0.562906i
$755$		−	1.68274e12i		−	0.188476i
$756$	−9.70212e12	+	8.47169e12i	−1.08024	+	0.943240i
$757$		−	1.04605e12i		−	0.115777i	−0.998323	−	0.0578884i	$-0.981563\pi$
$757$		−	1.04605e12i		−	0.115777i	0.998323	−	0.0578884i	$-0.0184368\pi$
$758$	1.58789e12	+	7.21521e11i	0.174706	+	0.0793848i
$759$	−1.12804e13			−1.23378
$760$	1.42350e12	−	4.26806e11i	0.154774	−	0.0464055i
$761$	−6.96339e11			−0.0752644			−0.0376322	−	0.999292i	$-0.511982\pi$
$761$	−6.96339e11			−0.0752644			−0.0376322	+	0.999292i	$0.511982\pi$
$762$	7.47111e11	+	3.39480e11i	0.0802764	+	0.0364768i
$763$		−	2.61483e13i		−	2.79308i
$764$	5.85854e12	+	6.70943e12i	0.622113	+	0.712468i
$765$		−	3.90653e11i		−	0.0412396i
$766$	−6.42399e12	+	1.41376e13i	−0.674179	+	1.48370i
$767$	2.11731e12			0.220905
$768$	2.75536e12	−	9.94036e12i	0.285794	−	1.03104i
$769$	−1.48499e13			−1.53128			−0.765642	−	0.643267i	$-0.777579\pi$
$769$	−1.48499e13			−1.53128			−0.765642	+	0.643267i	$0.777579\pi$
$770$	1.79460e12	−	3.94947e12i	0.183975	−	0.404884i
$771$		−	1.78181e13i		−	1.81601i
$772$	−1.05053e13	−	1.20311e13i	−1.06446	−	1.21906i
$773$			1.26481e13i			1.27414i	0.770804	+	0.637072i	$0.219855\pi$
$773$			1.26481e13i			1.27414i	−0.770804	+	0.637072i	$0.780145\pi$
$774$	−3.39810e11	−	1.54406e11i	−0.0340331	−	0.0154643i
$775$	3.45856e12			0.344380
$776$	1.30813e12	−	3.92213e11i	0.129501	−	0.0388280i
$777$	2.17815e13			2.14385
$778$	8.09260e12	+	3.67720e12i	0.791917	+	0.359840i
$779$			2.39247e12i			0.232771i
$780$	7.61408e11	−	6.64846e11i	0.0736533	−	0.0643125i
$781$		−	4.17242e12i		−	0.401290i
$782$	5.00939e12	−	1.10244e13i	0.479021	−	1.05420i
$783$	1.36207e13			1.29501
$784$	−2.07614e12	+	1.52624e13i	−0.196261	+	1.44278i
$785$	4.42353e12			0.415773
$786$	−1.90052e12	+	4.18257e12i	−0.177611	+	0.390878i
$787$			1.55699e13i			1.44677i	0.690446	+	0.723383i	$0.257414\pi$
$787$			1.55699e13i			1.44677i	−0.690446	+	0.723383i	$0.742586\pi$
$788$	7.19794e12	−	6.28509e12i	0.665028	−	0.580689i
$789$			2.24582e12i			0.206314i
$790$	−7.28242e11	−	3.30906e11i	−0.0665203	−	0.0302262i
$791$	−1.25158e13			−1.13675
$792$	−6.24367e11	−	2.08242e12i	−0.0563867	−	0.188063i
$793$	3.32691e12			0.298753
$794$	6.74969e12	+	3.06700e12i	0.602687	+	0.273855i
$795$			2.17139e12i			0.192790i
$796$	−1.10277e13	−	1.26293e13i	−0.973588	−	1.11499i
$797$		−	1.00331e12i		−	0.0880792i	−0.999030	−	0.0440396i	$-0.985977\pi$
$797$		−	1.00331e12i		−	0.0880792i	0.999030	−	0.0440396i	$-0.0140228\pi$
$798$	−6.13795e12	+	1.35081e13i	−0.535810	+	1.17918i
$799$	7.96486e12			0.691381
$800$	−9.37614e12	−	5.90058e12i	−0.809318	−	0.509319i
$801$	−1.96602e12			−0.168749
$802$	−8.07594e12	+	1.77731e13i	−0.689300	+	1.51698i
$803$		−	1.80490e12i		−	0.153191i
$804$	1.20081e13	+	1.37522e13i	1.01350	+	1.16070i
$805$			3.32019e12i			0.278665i
$806$	−1.71631e12	−	7.79875e11i	−0.143248	−	0.0650904i
$807$	−9.90784e12			−0.822333
$808$	−3.18072e11	−	1.06085e12i	−0.0262527	−	0.0875593i
$809$	1.16269e13			0.954327			0.477164	−	0.878815i	$-0.341665\pi$
$809$	1.16269e13			0.954327			0.477164	+	0.878815i	$0.341665\pi$
$810$	−2.62197e12	−	1.19140e12i	−0.214015	−	0.0972465i
$811$			1.45881e13i			1.18415i	0.805884	+	0.592074i	$0.201691\pi$
$811$			1.45881e13i			1.18415i	−0.805884	+	0.592074i	$0.798309\pi$
$812$	2.06958e13	−	1.80711e13i	1.67063	−	1.45876i
$813$		−	8.95427e12i		−	0.718824i
$814$	8.98774e12	−	1.97798e13i	0.717531	−	1.57911i
$815$	−2.93354e12			−0.232907
$816$	1.82902e13	+	2.48802e12i	1.44415	+	0.196448i
$817$	2.54085e12			0.199517
$818$	6.82577e12	−	1.50218e13i	0.533043	−	1.17309i
$819$			1.27592e12i			0.0990939i
$820$	−6.14732e11	+	5.36772e11i	−0.0474814	+	0.0414598i
$821$			2.01173e13i			1.54534i	0.634805	+	0.772672i	$0.281080\pi$
$821$			2.01173e13i			1.54534i	−0.634805	+	0.772672i	$0.718920\pi$
$822$	−1.88486e12	−	8.56461e11i	−0.143997	−	0.0654311i
$823$	−1.80557e13			−1.37188			−0.685939	−	0.727659i	$-0.740608\pi$
$823$	−1.80557e13			−1.37188			−0.685939	+	0.727659i	$0.740608\pi$
$824$	−2.03169e13	+	6.09159e12i	−1.53527	+	0.460318i
$825$	−1.84676e13			−1.38793
$826$	−9.65163e12	−	4.38561e12i	−0.721424	−	0.327808i
$827$		−	5.41935e12i		−	0.402877i	−0.979501	−	0.201438i	$-0.935438\pi$
$827$		−	5.41935e12i		−	0.402877i	0.979501	−	0.201438i	$-0.0645616\pi$
$828$	1.09439e12	+	1.25334e12i	0.0809163	+	0.0926685i
$829$		−	1.93367e13i		−	1.42196i	−0.703213	−	0.710980i	$-0.748252\pi$
$829$		−	1.93367e13i		−	1.42196i	0.703213	−	0.710980i	$-0.251748\pi$
$830$	3.58840e11	−	7.89718e11i	0.0262452	−	0.0577591i
$831$	−1.31625e13			−0.957492
$832$	3.32238e12	+	5.04240e12i	0.240378	+	0.364823i
$833$	−2.75631e13			−1.98347
$834$	2.99643e12	−	6.59439e12i	0.214465	−	0.471984i
$835$		−	2.66870e12i		−	0.189981i
$836$	9.73397e12	+	1.11477e13i	0.689226	+	0.789329i
$837$			4.67939e12i			0.329553i
$838$	−1.90349e13	−	8.64928e12i	−1.33338	−	0.605873i
$839$	1.70460e13			1.18766			0.593831	−	0.804590i	$-0.297615\pi$
$839$	1.70460e13			1.18766			0.593831	+	0.804590i	$0.297615\pi$
$840$	−4.84793e12	+	1.45355e12i	−0.335970	+	0.100733i
$841$	−1.45475e13			−1.00278
$842$	2.04279e13	+	9.28223e12i	1.40062	+	0.636426i
$843$			3.54852e12i			0.242004i
$844$	−2.55862e12	+	2.23413e12i	−0.173566	+	0.151554i
$845$		−	2.50837e12i		−	0.169253i
$846$	−4.52753e11	+	9.96396e11i	−0.0303875	+	0.0668752i
$847$	1.97262e13			1.31695
$848$	−1.28532e13	−	1.74842e12i	−0.853554	−	0.116109i
$849$	1.90799e13			1.26035
$850$	8.20102e12	−	1.80484e13i	0.538868	−	1.18591i
$851$			1.66282e13i			1.08683i
$852$	−3.66676e12	+	3.20174e12i	−0.238399	+	0.208165i
$853$		−	1.12979e13i		−	0.730677i	−0.930875	−	0.365339i	$-0.880953\pi$
$853$		−	1.12979e13i		−	0.730677i	0.930875	−	0.365339i	$-0.119047\pi$
$854$	−1.51655e13	−	6.89107e12i	−0.975657	−	0.443329i
$855$	−3.65416e11			−0.0233851
$856$	−1.32726e12	−	4.42672e12i	−0.0844933	−	0.281806i
$857$	−2.94210e12			−0.186313			−0.0931567	−	0.995651i	$-0.529696\pi$
$857$	−2.94210e12			−0.186313			−0.0931567	+	0.995651i	$0.529696\pi$
$858$	9.16452e12	+	4.16427e12i	0.577320	+	0.262329i
$859$			7.27946e12i			0.456173i	0.973641	+	0.228087i	$0.0732470\pi$
$859$			7.27946e12i			0.456173i	−0.973641	+	0.228087i	$0.926753\pi$
$860$	5.70061e11	+	6.52856e11i	0.0355368	+	0.0406981i
$861$		−	8.14789e12i		−	0.505278i
$862$	−9.11298e11	+	2.00554e12i	−0.0562183	+	0.123722i
$863$	2.79331e13			1.71424			0.857118	−	0.515120i	$-0.172253\pi$
$863$	2.79331e13			1.71424			0.857118	+	0.515120i	$0.172253\pi$
$864$	7.98342e12	−	1.26858e13i	0.487391	−	0.774473i
$865$	−1.89427e12			−0.115045
$866$	−1.38378e12	+	3.04536e12i	−0.0836061	+	0.183996i
$867$			1.52305e13i			0.915434i
$868$	6.20832e12	+	7.11002e12i	0.371223	+	0.425140i
$869$		−	7.96576e12i		−	0.473847i
$870$	4.87268e12	+	2.21410e12i	0.288357	+	0.131027i
$871$	−1.06877e13			−0.629220
$872$	8.73909e12	+	2.91470e13i	0.511849	+	1.70714i
$873$	−3.35798e11			−0.0195666
$874$	−1.03122e13	−	4.68577e12i	−0.597792	−	0.271631i
$875$			1.11199e13i			0.641305i
$876$	−1.58616e12	+	1.38500e12i	−0.0910078	+	0.0794661i
$877$			7.87352e12i			0.449439i	0.974424	+	0.224719i	$0.0721465\pi$
$877$			7.87352e12i			0.449439i	−0.974424	+	0.224719i	$0.927853\pi$
$878$	−4.62111e12	+	1.01699e13i	−0.262435	+	0.577553i
$879$	2.84773e13			1.60897
$880$	−6.80446e11	+	5.00218e12i	−0.0382492	+	0.281182i
$881$	2.87110e13			1.60567			0.802837	−	0.596198i	$-0.203323\pi$
$881$	2.87110e13			1.60567			0.802837	+	0.596198i	$0.203323\pi$
$882$	1.56679e12	−	3.44811e12i	0.0871770	−	0.191855i
$883$		−	2.78143e13i		−	1.53973i	−0.638207	−	0.769865i	$-0.720324\pi$
$883$		−	2.78143e13i		−	1.53973i	0.638207	−	0.769865i	$-0.279676\pi$
$884$	−8.13951e12	+	7.10725e12i	−0.448294	+	0.391441i
$885$		−	2.06512e12i		−	0.113162i
$886$	−7.28953e11	−	3.31229e11i	−0.0397418	−	0.0180583i
$887$	−2.72103e13			−1.47597			−0.737985	−	0.674817i	$-0.764223\pi$
$887$	−2.72103e13			−1.47597			−0.737985	+	0.674817i	$0.764223\pi$
$888$	−2.42795e13	+	7.27966e12i	−1.31033	+	0.392874i
$889$	2.40532e12			0.129156
$890$	4.15633e12	+	1.88860e12i	0.222052	+	0.100898i
$891$		−	2.86800e13i		−	1.52451i
$892$	2.13791e13	+	2.44841e13i	1.13070	+	1.29492i
$893$		−	7.45030e12i		−	0.392051i
$894$	−7.37792e12	+	1.62370e13i	−0.386291	+	0.850131i
$895$	−4.00703e11			−0.0208746
$896$	−4.70047e12	−	2.98671e13i	−0.243644	−	1.54813i
$897$	−7.70432e12			−0.397345
$898$	2.28642e12	−	5.03184e12i	0.117331	−	0.258216i
$899$		−	9.98170e12i		−	0.509666i
$900$	1.79166e12	+	2.05188e12i	0.0910257	+	0.104246i
$901$		−	2.32123e13i		−	1.17343i
$902$	−7.39909e12	−	3.36207e12i	−0.372176	−	0.169113i
$903$	−8.65320e12			−0.433094
$904$	1.39511e13	−	4.18294e12i	0.694786	−	0.208316i
$905$	5.42955e12			0.269058
$906$	−1.77994e13	−	8.08787e12i	−0.877663	−	0.398802i
$907$			2.32280e13i			1.13967i	0.821760	+	0.569834i	$0.192993\pi$
$907$			2.32280e13i			1.13967i	−0.821760	+	0.569834i	$0.807007\pi$
$908$	1.96523e13	−	1.71600e13i	0.959462	−	0.837783i
$909$			2.72322e11i			0.0132295i
$910$	1.22568e12	−	2.69741e12i	0.0592502	−	0.130395i
$911$	−3.33123e13			−1.60240			−0.801201	−	0.598396i	$-0.795805\pi$
$911$	−3.33123e13			−1.60240			−0.801201	+	0.598396i	$0.795805\pi$
$912$	2.32728e12	−	1.71086e13i	0.111397	−	0.818913i
$913$	8.63820e12			0.411438
$914$	−1.09480e13	+	2.40937e13i	−0.518890	+	1.14195i
$915$		−	3.24491e12i		−	0.153041i
$916$	−5.92847e12	+	5.17662e12i	−0.278236	+	0.242950i
$917$			1.34658e13i			0.628882i
$918$	2.44193e13	+	1.10959e13i	1.13486	+	0.515668i
$919$	1.19970e13			0.554822			0.277411	−	0.960751i	$-0.410524\pi$
$919$	1.19970e13			0.554822			0.277411	+	0.960751i	$0.410524\pi$
$920$	−1.10965e12	−	3.70096e12i	−0.0510671	−	0.170321i
$921$	−1.62009e13			−0.741943
$922$	−1.83915e13	−	8.35693e12i	−0.838162	−	0.380853i
$923$		−	2.84968e12i		−	0.129237i
$924$	−3.31504e13	−	3.79651e13i	−1.49611	−	1.71341i
$925$			2.72225e13i			1.22262i
$926$	−7.07243e12	+	1.55646e13i	−0.316096	+	0.695649i
$927$	5.21539e12			0.231968
$928$	−1.70296e13	+	2.70604e13i	−0.753769	+	1.19775i
$929$	2.87066e11			0.0126448			0.00632238	−	0.999980i	$-0.497988\pi$
$929$	2.87066e11			0.0126448			0.00632238	+	0.999980i	$0.497988\pi$
$930$	−7.60651e11	+	1.67400e12i	−0.0333436	+	0.0733809i
$931$			2.57824e13i			1.12473i
$932$	−1.94917e13	−	2.23227e13i	−0.846211	−	0.969115i
$933$			3.46990e13i			1.49917i
$934$	1.45616e13	+	6.61667e12i	0.626108	+	0.284497i
$935$	−9.03367e12			−0.386556
$936$	−4.26430e11	−	1.42225e12i	−0.0181596	−	0.0605667i
$937$	4.23141e12			0.179332			0.0896659	−	0.995972i	$-0.471420\pi$
$937$	4.23141e12			0.179332			0.0896659	+	0.995972i	$0.471420\pi$
$938$	4.87192e13	+	2.21375e13i	2.05488	+	0.933719i
$939$		−	1.81572e13i		−	0.762175i
$940$	1.91431e12	−	1.67154e12i	0.0799720	−	0.0698299i
$941$			6.44282e10i			0.00267869i	0.999999	+	0.00133935i	$0.000426327\pi$
$941$			6.44282e10i			0.00267869i	−0.999999	+	0.00133935i	$0.999574\pi$
$942$	2.12611e13	−	4.67903e13i	0.879744	−	1.93610i
$943$	6.22017e12			0.256153
$944$	1.22242e13	+	1.66286e12i	0.501011	+	0.0681525i
$945$	−7.35429e12			−0.299983
$946$	−3.57058e12	+	7.85796e12i	−0.144954	+	0.319006i
$947$		−	4.05102e13i		−	1.63678i	−0.574667	−	0.818388i	$-0.694868\pi$
$947$		−	4.05102e13i		−	1.63678i	0.574667	−	0.818388i	$-0.305132\pi$
$948$	−7.00038e12	+	6.11259e12i	−0.281504	+	0.245803i
$949$		−	1.23271e12i		−	0.0493358i
$950$	−1.68824e13	−	7.67121e12i	−0.672479	−	0.305568i
$951$	8.67808e12			0.344042
$952$	5.18247e13	−	1.55385e13i	2.04489	−	0.613117i
$953$	8.30603e11			0.0326194			0.0163097	−	0.999867i	$-0.494808\pi$
$953$	8.30603e11			0.0326194			0.0163097	+	0.999867i	$0.494808\pi$
$954$	2.90383e12	+	1.31947e12i	0.113502	+	0.0515742i
$955$			5.08581e12i			0.197854i
$956$	1.83492e12	+	2.10142e12i	0.0710486	+	0.0813677i
$957$			5.32990e13i			2.05407i
$958$	1.24039e13	−	2.72979e13i	0.475789	−	1.04709i
$959$	−6.06829e12			−0.231677
$960$	4.91811e12	−	3.24048e12i	0.186886	−	0.123137i
$961$	−2.30104e13			−0.870300
$962$	6.13844e12	−	1.35092e13i	0.231084	−	0.508559i
$963$			1.13635e12i			0.0425787i
$964$	−1.13065e13	−	1.29487e13i	−0.421680	−	0.482924i
$965$		−	9.11966e12i		−	0.338537i
$966$	3.51196e13	+	1.59580e13i	1.29764	+	0.589633i
$967$	−2.92619e13			−1.07618			−0.538088	−	0.842889i	$-0.680853\pi$
$967$	−2.92619e13			−1.07618			−0.538088	+	0.842889i	$0.680853\pi$
$968$	−2.19884e13	+	6.59275e12i	−0.804924	+	0.241339i
$969$	3.08972e13			1.12580
$970$	7.09906e11	+	3.22575e11i	0.0257471	+	0.0116992i
$971$		−	4.12204e13i		−	1.48808i	−0.668136	−	0.744039i	$-0.732907\pi$
$971$		−	4.12204e13i		−	1.48808i	0.668136	−	0.744039i	$-0.267093\pi$
$972$	−6.02212e12	+	5.25839e12i	−0.216397	+	0.188953i
$973$		−	2.12306e13i		−	0.759373i
$974$	−1.59058e13	+	3.50047e13i	−0.566291	+	1.24627i
$975$	−1.26130e13			−0.446989
$976$	1.92078e13	+	2.61284e12i	0.677570	+	0.0921698i
$977$	6.53429e12			0.229442			0.114721	−	0.993398i	$-0.463403\pi$
$977$	6.53429e12			0.229442			0.114721	+	0.993398i	$0.463403\pi$
$978$	−1.40996e13	+	3.10298e13i	−0.492814	+	1.08456i
$979$			4.54634e13i			1.58176i
$980$	−6.62465e12	+	5.78451e12i	−0.229428	+	0.200331i
$981$		−	7.48209e12i		−	0.257936i
$982$	3.31696e13	+	1.50720e13i	1.13825	+	0.517211i
$983$	4.98970e13			1.70445			0.852224	−	0.523178i	$-0.175254\pi$
$983$	4.98970e13			1.70445			0.852224	+	0.523178i	$0.175254\pi$
$984$	2.72313e12	+	9.08230e12i	0.0925956	+	0.308829i
$985$	5.45610e12			0.184680
$986$	−5.20892e13	−	2.36689e13i	−1.75510	−	0.797501i
$987$			2.53730e13i			0.851031i
$988$	6.64810e12	+	7.61367e12i	0.221969	+	0.254207i
$989$		−	6.60593e12i		−	0.219559i
$990$	5.13509e11	−	1.13010e12i	0.0169898	−	0.0373904i
$991$	3.03676e13			1.00018			0.500090	−	0.865973i	$-0.333300\pi$
$991$	3.03676e13			1.00018			0.500090	+	0.865973i	$0.333300\pi$
$992$	−9.29656e12	−	5.85050e12i	−0.304803	−	0.191819i
$993$	−4.38134e13			−1.43000
$994$	−5.90257e12	+	1.29901e13i	−0.191779	+	0.422059i
$995$		−	9.57314e12i		−	0.309635i
$996$	−6.62860e12	−	7.59133e12i	−0.213430	−	0.244428i
$997$		−	3.60157e13i		−	1.15442i	−0.816596	−	0.577209i	$-0.804142\pi$
$997$		−	3.60157e13i		−	1.15442i	0.816596	−	0.577209i	$-0.195858\pi$
$998$	−2.31818e13	−	1.05336e13i	−0.739706	−	0.336115i
$999$	−3.68318e13			−1.16998

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.10.b.a.5.4	yes	8
3.2	odd	2		72.10.d.b.37.5		8
4.3	odd	2		32.10.b.a.17.2		8
8.3	odd	2		32.10.b.a.17.7		8
8.5	even	2	inner	8.10.b.a.5.3	✓	8
12.11	even	2		288.10.d.b.145.5		8
16.3	odd	4		256.10.a.s.1.7		8
16.5	even	4		256.10.a.p.1.7		8
16.11	odd	4		256.10.a.s.1.2		8
16.13	even	4		256.10.a.p.1.2		8
24.5	odd	2		72.10.d.b.37.6		8
24.11	even	2		288.10.d.b.145.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.10.b.a.5.3	✓	8	8.5	even	2	inner
8.10.b.a.5.4	yes	8	1.1	even	1	trivial
32.10.b.a.17.2		8	4.3	odd	2
32.10.b.a.17.7		8	8.3	odd	2
72.10.d.b.37.5		8	3.2	odd	2
72.10.d.b.37.6		8	24.5	odd	2
256.10.a.p.1.2		8	16.13	even	4
256.10.a.p.1.7		8	16.5	even	4
256.10.a.s.1.2		8	16.11	odd	4
256.10.a.s.1.7		8	16.3	odd	4
288.10.d.b.145.4		8	24.11	even	2
288.10.d.b.145.5		8	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:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	8.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-9.36065 + 20.6004i) q^{2} +150.106i q^{3} +(-336.757 - 385.667i) q^{4} -292.339i q^{5} +(-3092.24 - 1405.08i) q^{6} -9955.46 q^{7} +(11097.2 - 3327.24i) q^{8} -2848.66 q^{9} +O(q^{10})\)	\(q+(-9.36065 + 20.6004i) q^{2} +150.106i q^{3} +(-336.757 - 385.667i) q^{4} -292.339i q^{5} +(-3092.24 - 1405.08i) q^{6} -9955.46 q^{7} +(11097.2 - 3327.24i) q^{8} -2848.66 q^{9} +(6022.31 + 2736.48i) q^{10} +65874.1i q^{11} +(57890.7 - 50549.0i) q^{12} +44990.6i q^{13} +(93189.6 - 205087. i) q^{14} +43881.7 q^{15} +(-35334.0 + 259752. i) q^{16} -469098. q^{17} +(26665.3 - 58683.7i) q^{18} +438793. i q^{19} +(-112745. + 98447.0i) q^{20} -1.49437e6i q^{21} +(-1.35703e6 - 616624. i) q^{22} +1.14082e6 q^{23} +(499437. + 1.66575e6i) q^{24} +1.86766e6 q^{25} +(-926827. - 421141. i) q^{26} +2.52693e6i q^{27} +(3.35257e6 + 3.83949e6i) q^{28} -5.39024e6i q^{29} +(-410761. + 903982. i) q^{30} +1.85181e6 q^{31} +(-5.02025e6 - 3.15934e6i) q^{32} -9.88806e6 q^{33} +(4.39106e6 - 9.66363e6i) q^{34} +2.91037e6i q^{35} +(959306. + 1.09863e6i) q^{36} +1.45757e7i q^{37} +(-9.03933e6 - 4.10739e6i) q^{38} -6.75334e6 q^{39} +(-972682. - 3.24413e6i) q^{40} +5.45239e6 q^{41} +(3.07847e7 + 1.39883e7i) q^{42} -5.79053e6i q^{43} +(2.54054e7 - 2.21835e7i) q^{44} +832774. i q^{45} +(-1.06788e7 + 2.35013e7i) q^{46} -1.69791e7 q^{47} +(-3.89902e7 - 5.30383e6i) q^{48} +5.87576e7 q^{49} +(-1.74825e7 + 3.84747e7i) q^{50} -7.04142e7i q^{51} +(1.73514e7 - 1.51509e7i) q^{52} +4.94827e7i q^{53} +(-5.20558e7 - 2.36537e7i) q^{54} +1.92575e7 q^{55} +(-1.10477e8 + 3.31242e7i) q^{56} -6.58652e7 q^{57} +(1.11041e8 + 5.04561e7i) q^{58} -4.70612e7i q^{59} +(-1.47774e7 - 1.69237e7i) q^{60} -7.39468e7i q^{61} +(-1.73342e7 + 3.81481e7i) q^{62} +2.83597e7 q^{63} +(1.12077e8 - 7.38460e7i) q^{64} +1.31525e7 q^{65} +(9.25586e7 - 2.03698e8i) q^{66} +2.37554e8i q^{67} +(1.57972e8 + 1.80916e8i) q^{68} +1.71243e8i q^{69} +(-5.99549e7 - 2.72429e7i) q^{70} -6.33394e7 q^{71} +(-3.16121e7 + 9.47819e6i) q^{72} -2.73992e7 q^{73} +(-3.00266e8 - 1.36438e8i) q^{74} +2.80346e8i q^{75} +(1.69228e8 - 1.47766e8i) q^{76} -6.55807e8i q^{77} +(6.32157e7 - 1.39122e8i) q^{78} -1.20924e8 q^{79} +(7.59355e7 + 1.03295e7i) q^{80} -4.35376e8 q^{81} +(-5.10379e7 + 1.12322e8i) q^{82} -1.31132e8i q^{83} +(-5.76329e8 + 5.03239e8i) q^{84} +1.37136e8i q^{85} +(1.19288e8 + 5.42031e7i) q^{86} +8.09104e8 q^{87} +(2.19179e8 + 7.31016e8i) q^{88} +6.90156e8 q^{89} +(-1.71555e7 - 7.79531e6i) q^{90} -4.47903e8i q^{91} +(-3.84177e8 - 4.39975e8i) q^{92} +2.77967e8i q^{93} +(1.58935e8 - 3.49777e8i) q^{94} +1.28276e8 q^{95} +(4.74234e8 - 7.53568e8i) q^{96} +1.17879e8 q^{97} +(-5.50009e8 + 1.21043e9i) q^{98} -1.87653e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 18 q^{2} - 428 q^{4} + 4684 q^{6} + 4800 q^{7} - 3384 q^{8} - 39368 q^{9}+O(q^{10}) \) 8 * q - 18 * q^2 - 428 * q^4 + 4684 * q^6 + 4800 * q^7 - 3384 * q^8 - 39368 * q^9	\( 8 q - 18 q^{2} - 428 q^{4} + 4684 q^{6} + 4800 q^{7} - 3384 q^{8} - 39368 q^{9} + 26392 q^{10} + 54760 q^{12} - 72336 q^{14} - 163136 q^{15} + 185616 q^{16} - 102000 q^{17} - 23614 q^{18} + 1245264 q^{20} - 2373124 q^{22} + 3412032 q^{23} - 3961456 q^{24} - 2423384 q^{25} + 4551240 q^{26} + 7509920 q^{28} - 15284368 q^{30} + 803584 q^{31} - 14113248 q^{32} + 58272 q^{33} + 27757244 q^{34} + 57226188 q^{36} - 63661140 q^{38} - 17590208 q^{39} - 93063648 q^{40} - 2180784 q^{41} + 127541344 q^{42} + 114013320 q^{44} - 131840944 q^{46} + 7432320 q^{47} - 217917408 q^{48} + 24436680 q^{49} + 231784902 q^{50} + 219270896 q^{52} - 362934280 q^{54} + 7056832 q^{55} - 358503360 q^{56} + 134003744 q^{57} + 375425192 q^{58} + 516952992 q^{60} - 344291904 q^{62} - 223198400 q^{63} - 316815296 q^{64} - 146501760 q^{65} + 239713176 q^{66} + 79875048 q^{68} - 56202048 q^{70} + 560234688 q^{71} + 112273016 q^{72} - 523987120 q^{73} - 65773608 q^{74} - 87532760 q^{76} + 318117968 q^{78} - 248943744 q^{79} + 890441280 q^{80} + 231960296 q^{81} - 1051981172 q^{82} - 1275608768 q^{84} + 1492810428 q^{86} + 540527424 q^{87} + 1544767952 q^{88} + 744827856 q^{89} - 3218579800 q^{90} - 2959012128 q^{92} + 3068552352 q^{94} - 1465245504 q^{95} + 4296343616 q^{96} - 9932784 q^{97} - 3062604162 q^{98}+O(q^{100}) \) 8 * q - 18 * q^2 - 428 * q^4 + 4684 * q^6 + 4800 * q^7 - 3384 * q^8 - 39368 * q^9 + 26392 * q^10 + 54760 * q^12 - 72336 * q^14 - 163136 * q^15 + 185616 * q^16 - 102000 * q^17 - 23614 * q^18 + 1245264 * q^20 - 2373124 * q^22 + 3412032 * q^23 - 3961456 * q^24 - 2423384 * q^25 + 4551240 * q^26 + 7509920 * q^28 - 15284368 * q^30 + 803584 * q^31 - 14113248 * q^32 + 58272 * q^33 + 27757244 * q^34 + 57226188 * q^36 - 63661140 * q^38 - 17590208 * q^39 - 93063648 * q^40 - 2180784 * q^41 + 127541344 * q^42 + 114013320 * q^44 - 131840944 * q^46 + 7432320 * q^47 - 217917408 * q^48 + 24436680 * q^49 + 231784902 * q^50 + 219270896 * q^52 - 362934280 * q^54 + 7056832 * q^55 - 358503360 * q^56 + 134003744 * q^57 + 375425192 * q^58 + 516952992 * q^60 - 344291904 * q^62 - 223198400 * q^63 - 316815296 * q^64 - 146501760 * q^65 + 239713176 * q^66 + 79875048 * q^68 - 56202048 * q^70 + 560234688 * q^71 + 112273016 * q^72 - 523987120 * q^73 - 65773608 * q^74 - 87532760 * q^76 + 318117968 * q^78 - 248943744 * q^79 + 890441280 * q^80 + 231960296 * q^81 - 1051981172 * q^82 - 1275608768 * q^84 + 1492810428 * q^86 + 540527424 * q^87 + 1544767952 * q^88 + 744827856 * q^89 - 3218579800 * q^90 - 2959012128 * q^92 + 3068552352 * q^94 - 1465245504 * q^95 + 4296343616 * q^96 - 9932784 * q^97 - 3062604162 * q^98

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