LMFDB - Embedded newform 403.2.f.c.94.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(94,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("403.94");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.f (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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			94.8
Character	$\chi$	$=$	403.94
Dual form			403.2.f.c.373.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.683087 - 1.18314i) q^{2} +(1.43249 + 2.48115i) q^{3} +(0.0667843 - 0.115674i) q^{4} -1.11791 q^{5} +(1.95703 - 3.38968i) q^{6} +(-1.05496 + 1.82724i) q^{7} -2.91483 q^{8} +(-2.60407 + 4.51038i) q^{9} +O(q^{10})$	\(q+(-0.683087 - 1.18314i) q^{2} +(1.43249 + 2.48115i) q^{3} +(0.0667843 - 0.115674i) q^{4} -1.11791 q^{5} +(1.95703 - 3.38968i) q^{6} +(-1.05496 + 1.82724i) q^{7} -2.91483 q^{8} +(-2.60407 + 4.51038i) q^{9} +(0.763627 + 1.32264i) q^{10} +(1.52097 + 2.63439i) q^{11} +0.382672 q^{12} +(3.51884 + 0.785991i) q^{13} +2.88252 q^{14} +(-1.60139 - 2.77369i) q^{15} +(1.85751 + 3.21730i) q^{16} +(-2.97802 + 5.15809i) q^{17} +7.11522 q^{18} +(2.32004 - 4.01843i) q^{19} +(-0.0746586 + 0.129313i) q^{20} -6.04488 q^{21} +(2.07790 - 3.59903i) q^{22} +(1.63787 + 2.83687i) q^{23} +(-4.17546 - 7.23212i) q^{24} -3.75029 q^{25} +(-1.47373 - 4.70018i) q^{26} -6.32626 q^{27} +(0.140909 + 0.244062i) q^{28} +(2.64492 + 4.58114i) q^{29} +(-2.18778 + 3.78935i) q^{30} +1.00000 q^{31} +(-0.377143 + 0.653230i) q^{32} +(-4.35754 + 7.54748i) q^{33} +8.13699 q^{34} +(1.17935 - 2.04269i) q^{35} +(0.347822 + 0.602445i) q^{36} +(-2.94288 - 5.09722i) q^{37} -6.33916 q^{38} +(3.09054 + 9.85669i) q^{39} +3.25850 q^{40} +(-1.74317 - 3.01925i) q^{41} +(4.12918 + 7.15195i) q^{42} +(2.17102 - 3.76031i) q^{43} +0.406307 q^{44} +(2.91110 - 5.04218i) q^{45} +(2.23762 - 3.87566i) q^{46} -7.36211 q^{47} +(-5.32174 + 9.21752i) q^{48} +(1.27412 + 2.20684i) q^{49} +(2.56177 + 4.43712i) q^{50} -17.0640 q^{51} +(0.325922 - 0.354545i) q^{52} +11.5305 q^{53} +(4.32139 + 7.48486i) q^{54} +(-1.70030 - 2.94500i) q^{55} +(3.07502 - 5.32610i) q^{56} +13.2938 q^{57} +(3.61343 - 6.25864i) q^{58} +(2.32101 - 4.02011i) q^{59} -0.427791 q^{60} +(7.39115 - 12.8018i) q^{61} +(-0.683087 - 1.18314i) q^{62} +(-5.49437 - 9.51652i) q^{63} +8.46053 q^{64} +(-3.93373 - 0.878665i) q^{65} +11.9063 q^{66} +(2.33745 + 4.04858i) q^{67} +(0.397770 + 0.688959i) q^{68} +(-4.69247 + 8.12760i) q^{69} -3.22238 q^{70} +(4.57872 - 7.93057i) q^{71} +(7.59040 - 13.1470i) q^{72} +1.93507 q^{73} +(-4.02049 + 6.96369i) q^{74} +(-5.37225 - 9.30502i) q^{75} +(-0.309885 - 0.536736i) q^{76} -6.41823 q^{77} +(9.55074 - 10.3895i) q^{78} -10.5516 q^{79} +(-2.07652 - 3.59664i) q^{80} +(-1.25012 - 2.16528i) q^{81} +(-2.38147 + 4.12483i) q^{82} +0.540055 q^{83} +(-0.403703 + 0.699235i) q^{84} +(3.32915 - 5.76626i) q^{85} -5.93198 q^{86} +(-7.57766 + 13.1249i) q^{87} +(-4.43335 - 7.67879i) q^{88} +(-2.98295 - 5.16662i) q^{89} -7.95415 q^{90} +(-5.14843 + 5.60058i) q^{91} +0.437536 q^{92} +(1.43249 + 2.48115i) q^{93} +(5.02896 + 8.71042i) q^{94} +(-2.59359 + 4.49223i) q^{95} -2.16102 q^{96} +(-8.09934 + 14.0285i) q^{97} +(1.74067 - 3.01493i) q^{98} -15.8428 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9}+O(q^{10}) $ 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9	\( 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9} - 3 q^{10} - 17 q^{11} + 8 q^{12} + 8 q^{13} + 4 q^{14} - 12 q^{15} - 17 q^{16} + 7 q^{17} - 14 q^{18} - 4 q^{19} - 15 q^{20} + 28 q^{21} - 30 q^{22} + 4 q^{23} - 48 q^{24} + 24 q^{25} + 25 q^{26} - 6 q^{27} - q^{28} + 15 q^{29} + 35 q^{30} + 36 q^{31} - 35 q^{32} - 17 q^{33} - 6 q^{34} - 17 q^{35} - 35 q^{36} - 3 q^{37} + 14 q^{38} + 3 q^{39} - 2 q^{40} - 44 q^{41} + 57 q^{42} + 4 q^{43} + 64 q^{44} + 5 q^{45} - 13 q^{46} + 24 q^{47} - 89 q^{48} - 44 q^{49} - 84 q^{50} - 28 q^{51} + 50 q^{52} - 28 q^{53} - 21 q^{54} + 29 q^{55} + 11 q^{56} + 32 q^{57} + 49 q^{58} - 11 q^{59} + 54 q^{60} - 4 q^{61} - 5 q^{62} - 9 q^{63} + 34 q^{64} - 5 q^{65} + 52 q^{66} - 16 q^{67} + 53 q^{68} + 4 q^{69} - 44 q^{70} - 5 q^{71} - 27 q^{72} + 64 q^{73} + q^{74} - 98 q^{75} - 42 q^{76} - 22 q^{77} + 143 q^{78} - 6 q^{79} - 2 q^{80} + 10 q^{81} + 22 q^{82} + 36 q^{83} + 38 q^{84} + 2 q^{85} + 84 q^{86} - 34 q^{87} - 69 q^{88} - 54 q^{89} - 32 q^{90} - 43 q^{91} - 86 q^{92} + 44 q^{94} - 2 q^{95} + 170 q^{96} - 28 q^{97} - 29 q^{98} + 154 q^{99}+O(q^{100}) \) 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9 - 3 * q^10 - 17 * q^11 + 8 * q^12 + 8 * q^13 + 4 * q^14 - 12 * q^15 - 17 * q^16 + 7 * q^17 - 14 * q^18 - 4 * q^19 - 15 * q^20 + 28 * q^21 - 30 * q^22 + 4 * q^23 - 48 * q^24 + 24 * q^25 + 25 * q^26 - 6 * q^27 - q^28 + 15 * q^29 + 35 * q^30 + 36 * q^31 - 35 * q^32 - 17 * q^33 - 6 * q^34 - 17 * q^35 - 35 * q^36 - 3 * q^37 + 14 * q^38 + 3 * q^39 - 2 * q^40 - 44 * q^41 + 57 * q^42 + 4 * q^43 + 64 * q^44 + 5 * q^45 - 13 * q^46 + 24 * q^47 - 89 * q^48 - 44 * q^49 - 84 * q^50 - 28 * q^51 + 50 * q^52 - 28 * q^53 - 21 * q^54 + 29 * q^55 + 11 * q^56 + 32 * q^57 + 49 * q^58 - 11 * q^59 + 54 * q^60 - 4 * q^61 - 5 * q^62 - 9 * q^63 + 34 * q^64 - 5 * q^65 + 52 * q^66 - 16 * q^67 + 53 * q^68 + 4 * q^69 - 44 * q^70 - 5 * q^71 - 27 * q^72 + 64 * q^73 + q^74 - 98 * q^75 - 42 * q^76 - 22 * q^77 + 143 * q^78 - 6 * q^79 - 2 * q^80 + 10 * q^81 + 22 * q^82 + 36 * q^83 + 38 * q^84 + 2 * q^85 + 84 * q^86 - 34 * q^87 - 69 * q^88 - 54 * q^89 - 32 * q^90 - 43 * q^91 - 86 * q^92 + 44 * q^94 - 2 * q^95 + 170 * q^96 - 28 * q^97 - 29 * q^98 + 154 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.683087	−	1.18314i	−0.483015	−	0.836607i	0.516794	−	0.856110i	$-0.327125\pi$
$2$	−0.683087	−	1.18314i	−0.483015	−	0.836607i	−0.999810	+	0.0195023i	$0.993792\pi$
$3$	1.43249	+	2.48115i	0.827050	+	1.43249i	0.900343	+	0.435181i	$0.143316\pi$
$3$	1.43249	+	2.48115i	0.827050	+	1.43249i	−0.0732932	+	0.997310i	$0.523351\pi$
$4$	0.0667843	−	0.115674i	0.0333922	−	0.0578369i
$5$	−1.11791			−0.499943			−0.249971	−	0.968253i	$-0.580421\pi$
$5$	−1.11791			−0.499943			−0.249971	+	0.968253i	$0.580421\pi$
$6$	1.95703	−	3.38968i	0.798955	−	1.38383i
$7$	−1.05496	+	1.82724i	−0.398737	+	0.690633i	−0.993570	−	0.113216i	$-0.963885\pi$
$7$	−1.05496	+	1.82724i	−0.398737	+	0.690633i	0.594833	+	0.803849i	$0.297218\pi$
$8$	−2.91483			−1.03055
$9$	−2.60407	+	4.51038i	−0.868022	+	1.50346i
$10$	0.763627	+	1.32264i	0.241480	+	0.418256i
$11$	1.52097	+	2.63439i	0.458588	+	0.794298i	0.998887	−	0.0471752i	$-0.0150219\pi$
$11$	1.52097	+	2.63439i	0.458588	+	0.794298i	−0.540298	+	0.841474i	$0.681689\pi$
$12$	0.382672			0.110468
$13$	3.51884	+	0.785991i	0.975950	+	0.217995i
$13$	3.51884	+	0.785991i	0.975950	+	0.217995i
$14$	2.88252			0.770385
$15$	−1.60139	−	2.77369i	−0.413478	−	0.716164i
$16$	1.85751	+	3.21730i	0.464378	+	0.804326i
$17$	−2.97802	+	5.15809i	−0.722277	+	1.25102i	0.237809	+	0.971312i	$0.423571\pi$
$17$	−2.97802	+	5.15809i	−0.722277	+	1.25102i	−0.960085	+	0.279708i	$0.909762\pi$
$18$	7.11522			1.67707
$19$	2.32004	−	4.01843i	0.532254	−	0.921891i	−0.467037	−	0.884238i	$-0.654678\pi$
$19$	2.32004	−	4.01843i	0.532254	−	0.921891i	0.999291	−	0.0376531i	$-0.0119882\pi$
$20$	−0.0746586	+	0.129313i	−0.0166942	+	0.0289152i
$21$	−6.04488			−1.31910
$22$	2.07790	−	3.59903i	0.443011	−	0.767317i
$23$	1.63787	+	2.83687i	0.341520	+	0.591529i	0.984715	−	0.174173i	$-0.0557251\pi$
$23$	1.63787	+	2.83687i	0.341520	+	0.591529i	−0.643196	+	0.765702i	$0.722392\pi$
$24$	−4.17546	−	7.23212i	−0.852313	−	1.47625i
$25$	−3.75029			−0.750057
$26$	−1.47373	−	4.70018i	−0.289023	−	0.921782i
$27$	−6.32626			−1.21749
$28$	0.140909	+	0.244062i	0.0266294	+	0.0461234i
$29$	2.64492	+	4.58114i	0.491150	+	0.850697i	0.999948	−	0.0101890i	$-0.00324333\pi$
$29$	2.64492	+	4.58114i	0.491150	+	0.850697i	−0.508798	+	0.860886i	$0.669910\pi$
$30$	−2.18778	+	3.78935i	−0.399432	+	0.691837i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	−0.377143	+	0.653230i	−0.0666700	+	0.115476i
$33$	−4.35754	+	7.54748i	−0.758551	+	1.31385i
$34$	8.13699			1.39548
$35$	1.17935	−	2.04269i	0.199346	−	0.345277i
$36$	0.347822	+	0.602445i	0.0579703	+	0.100407i
$37$	−2.94288	−	5.09722i	−0.483806	−	0.837977i	0.516021	−	0.856576i	$-0.327413\pi$
$37$	−2.94288	−	5.09722i	−0.483806	−	0.837977i	−0.999827	+	0.0185988i	$0.994079\pi$
$38$	−6.33916			−1.02835
$39$	3.09054	+	9.85669i	0.494883	+	1.57833i
$40$	3.25850			0.515215
$41$	−1.74317	−	3.01925i	−0.272237	−	0.471528i	0.697197	−	0.716879i	$-0.254430\pi$
$41$	−1.74317	−	3.01925i	−0.272237	−	0.471528i	−0.969434	+	0.245351i	$0.921097\pi$
$42$	4.12918	+	7.15195i	0.637146	+	1.10357i
$43$	2.17102	−	3.76031i	0.331077	−	0.573443i	−0.651646	−	0.758523i	$-0.725921\pi$
$43$	2.17102	−	3.76031i	0.331077	−	0.573443i	0.982723	+	0.185081i	$0.0592546\pi$
$44$	0.406307			0.0612530
$45$	2.91110	−	5.04218i	0.433962	−	0.751643i
$46$	2.23762	−	3.87566i	0.329918	−	0.571435i
$47$	−7.36211			−1.07387			−0.536937	−	0.843622i	$-0.680419\pi$
$47$	−7.36211			−1.07387			−0.536937	+	0.843622i	$0.680419\pi$
$48$	−5.32174	+	9.21752i	−0.768127	+	1.33043i
$49$	1.27412	+	2.20684i	0.182017	+	0.315263i
$50$	2.56177	+	4.43712i	0.362289	+	0.627503i
$51$	−17.0640			−2.38943
$52$	0.325922	−	0.354545i	0.0451972	−	0.0491666i
$53$	11.5305			1.58383			0.791916	−	0.610630i	$-0.209084\pi$
$53$	11.5305			1.58383			0.791916	+	0.610630i	$0.209084\pi$
$54$	4.32139	+	7.48486i	0.588067	+	1.01856i
$55$	−1.70030	−	2.94500i	−0.229268	−	0.397104i
$56$	3.07502	−	5.32610i	0.410917	−	0.711729i
$57$	13.2938			1.76080
$58$	3.61343	−	6.25864i	0.474466	−	0.821799i
$59$	2.32101	−	4.02011i	0.302170	−	0.523373i	−0.674457	−	0.738314i	$-0.735622\pi$
$59$	2.32101	−	4.02011i	0.302170	−	0.523373i	0.976627	+	0.214940i	$0.0689557\pi$
$60$	−0.427791			−0.0552276
$61$	7.39115	−	12.8018i	0.946340	−	1.63911i	0.193293	−	0.981141i	$-0.438083\pi$
$61$	7.39115	−	12.8018i	0.946340	−	1.63911i	0.753047	−	0.657967i	$-0.228583\pi$
$62$	−0.683087	−	1.18314i	−0.0867521	−	0.150259i
$63$	−5.49437	−	9.51652i	−0.692225	−	1.19897i
$64$	8.46053			1.05757
$65$	−3.93373	−	0.878665i	−0.487919	−	0.108985i
$66$	11.9063			1.46557
$67$	2.33745	+	4.04858i	0.285565	+	0.494612i	0.972746	−	0.231874i	$-0.0744855\pi$
$67$	2.33745	+	4.04858i	0.285565	+	0.494612i	−0.687181	+	0.726486i	$0.741152\pi$
$68$	0.397770	+	0.688959i	0.0482367	+	0.0835485i
$69$	−4.69247	+	8.12760i	−0.564907	+	0.978448i
$70$	−3.22238			−0.385148
$71$	4.57872	−	7.93057i	0.543394	−	0.941186i	−0.455312	−	0.890332i	$-0.650472\pi$
$71$	4.57872	−	7.93057i	0.543394	−	0.941186i	0.998706	−	0.0508539i	$-0.0161943\pi$
$72$	7.59040	−	13.1470i	0.894537	−	1.54938i
$73$	1.93507			0.226482			0.113241	−	0.993568i	$-0.463877\pi$
$73$	1.93507			0.226482			0.113241	+	0.993568i	$0.463877\pi$
$74$	−4.02049	+	6.96369i	−0.467372	+	0.809512i
$75$	−5.37225	−	9.30502i	−0.620334	−	1.07445i
$76$	−0.309885	−	0.536736i	−0.0355462	−	0.0615678i
$77$	−6.41823			−0.731425
$78$	9.55074	−	10.3895i	1.08141	−	1.17638i
$79$	−10.5516			−1.18715			−0.593576	−	0.804778i	$-0.702284\pi$
$79$	−10.5516			−1.18715			−0.593576	+	0.804778i	$0.702284\pi$
$80$	−2.07652	−	3.59664i	−0.232162	−	0.402117i
$81$	−1.25012	−	2.16528i	−0.138903	−	0.240586i
$82$	−2.38147	+	4.12483i	−0.262989	+	0.455511i
$83$	0.540055			0.0592788			0.0296394	−	0.999561i	$-0.490564\pi$
$83$	0.540055			0.0592788			0.0296394	+	0.999561i	$0.490564\pi$
$84$	−0.403703	+	0.699235i	−0.0440476	+	0.0762928i
$85$	3.32915	−	5.76626i	0.361097	−	0.625439i
$86$	−5.93198			−0.639662
$87$	−7.57766	+	13.1249i	−0.812411	+	1.40714i
$88$	−4.43335	−	7.67879i	−0.472597	−	0.818561i
$89$	−2.98295	−	5.16662i	−0.316192	−	0.547660i	0.663498	−	0.748178i	$-0.269071\pi$
$89$	−2.98295	−	5.16662i	−0.316192	−	0.547660i	−0.979690	+	0.200517i	$0.935738\pi$
$90$	−7.95415			−0.838441
$91$	−5.14843	+	5.60058i	−0.539702	+	0.587101i
$92$	0.437536			0.0456163
$93$	1.43249	+	2.48115i	0.148542	+	0.257283i
$94$	5.02896	+	8.71042i	0.518698	+	0.898412i
$95$	−2.59359	+	4.49223i	−0.266097	+	0.460893i
$96$	−2.16102			−0.220558
$97$	−8.09934	+	14.0285i	−0.822364	+	1.42438i	0.0815540	+	0.996669i	$0.474012\pi$
$97$	−8.09934	+	14.0285i	−0.822364	+	1.42438i	−0.903918	+	0.427707i	$0.859322\pi$
$98$	1.74067	−	3.01493i	0.175834	−	0.304554i
$99$	−15.8428			−1.59226
$100$	−0.250460	+	0.433810i	−0.0250460	+	0.0433810i
$101$	1.89832	+	3.28798i	0.188890	+	0.327166i	0.944880	−	0.327416i	$-0.106178\pi$
$101$	1.89832	+	3.28798i	0.188890	+	0.327166i	−0.755991	+	0.654582i	$0.772845\pi$
$102$	11.6562	+	20.1891i	1.15413	+	1.99902i
$103$	14.3699			1.41591			0.707954	−	0.706259i	$-0.249618\pi$
$103$	14.3699			1.41591			0.707954	+	0.706259i	$0.249618\pi$
$104$	−10.2568	−	2.29103i	−1.00576	−	0.224654i
$105$	6.75761			0.659476
$106$	−7.87632	−	13.6422i	−0.765016	−	1.32505i
$107$	−6.07478	−	10.5218i	−0.587272	−	1.01718i	−0.994588	−	0.103897i	$-0.966869\pi$
$107$	−6.07478	−	10.5218i	−0.587272	−	1.01718i	0.407316	−	0.913287i	$-0.366465\pi$
$108$	−0.422495	+	0.731783i	−0.0406546	+	0.0704159i
$109$	4.40994			0.422396			0.211198	−	0.977443i	$-0.432264\pi$
$109$	4.40994			0.422396			0.211198	+	0.977443i	$0.432264\pi$
$110$	−2.32290	+	4.02338i	−0.221480	+	0.383615i
$111$	8.43130	−	14.6034i	0.800264	−	1.38610i
$112$	−7.83839			−0.740659
$113$	−5.38674	+	9.33011i	−0.506742	+	0.877703i	0.493227	+	0.869900i	$0.335817\pi$
$113$	−5.38674	+	9.33011i	−0.506742	+	0.877703i	−0.999970	+	0.00780263i	$0.997516\pi$
$114$	−9.08080	−	15.7284i	−0.850494	−	1.47310i
$115$	−1.83099	−	3.17136i	−0.170740	−	0.295731i
$116$	0.706558			0.0656022
$117$	−12.7084	+	13.8245i	−1.17489	+	1.27808i
$118$	−6.34181			−0.583811
$119$	−6.28339	−	10.8831i	−0.575997	−	0.997656i
$120$	4.66778	+	8.08483i	0.426108	+	0.738041i
$121$	0.873328	−	1.51265i	0.0793934	−	0.137513i
$122$	−20.1952			−1.82839
$123$	4.99414	−	8.65011i	0.450307	−	0.779954i
$124$	0.0667843	−	0.115674i	0.00599741	−	0.0103878i
$125$	9.78200			0.874929
$126$	−7.50626	+	13.0012i	−0.668711	+	1.15824i
$127$	−4.42737	−	7.66842i	−0.392865	−	0.680462i	0.599961	−	0.800029i	$-0.295183\pi$
$127$	−4.42737	−	7.66842i	−0.392865	−	0.680462i	−0.992826	+	0.119567i	$0.961849\pi$
$128$	−5.02499	−	8.70354i	−0.444151	−	0.769292i
$129$	12.4399			1.09527
$130$	1.64750	+	5.25437i	0.144495	+	0.460838i
$131$	−12.2706			−1.07209			−0.536044	−	0.844190i	$-0.680082\pi$
$131$	−12.2706			−1.07209			−0.536044	+	0.844190i	$0.680082\pi$
$132$	0.582031	+	1.00811i	0.0506593	+	0.0877444i
$133$	4.89510	+	8.47856i	0.424459	+	0.735184i
$134$	3.19336	−	5.53106i	0.275864	−	0.477811i
$135$	7.07217			0.608676
$136$	8.68042	−	15.0349i	0.744340	−	1.28923i
$137$	3.43914	−	5.95676i	0.293825	−	0.508921i	−0.680886	−	0.732390i	$-0.738405\pi$
$137$	3.43914	−	5.95676i	0.293825	−	0.508921i	0.974711	+	0.223469i	$0.0717382\pi$
$138$	12.8215			1.09144
$139$	6.56953	−	11.3788i	0.557220	−	0.965133i	−0.440507	−	0.897749i	$-0.645201\pi$
$139$	6.56953	−	11.3788i	0.557220	−	0.965133i	0.997727	−	0.0673841i	$-0.0214653\pi$
$140$	−0.157524	−	0.272839i	−0.0133132	−	0.0230591i
$141$	−10.5462	−	18.2665i	−0.888148	−	1.53832i
$142$	−12.5107			−1.04987
$143$	3.28142	+	10.4655i	0.274406	+	0.875165i
$144$	−19.3483			−1.61236
$145$	−2.95678	−	5.12129i	−0.245547	−	0.425300i
$146$	−1.32182	−	2.28946i	−0.109395	−	0.189477i
$147$	−3.65034	+	6.32257i	−0.301075	+	0.521477i
$148$	−0.786153			−0.0646214
$149$	4.28859	−	7.42805i	0.351335	−	0.608530i	−0.635149	−	0.772390i	$-0.719061\pi$
$149$	4.28859	−	7.42805i	0.351335	−	0.608530i	0.986484	+	0.163860i	$0.0523945\pi$
$150$	−7.33943	+	12.7123i	−0.599262	+	1.03795i
$151$	15.8910			1.29319			0.646597	−	0.762832i	$-0.276192\pi$
$151$	15.8910			1.29319			0.646597	+	0.762832i	$0.276192\pi$
$152$	−6.76252	+	11.7130i	−0.548512	+	0.950052i
$153$	−15.5099	−	26.8640i	−1.25390	−	2.17183i
$154$	4.38421	+	7.59367i	0.353289	+	0.611915i
$155$	−1.11791			−0.0897924
$156$	1.34656	+	0.300777i	0.107811	+	0.0240814i
$157$	13.7584			1.09804			0.549019	−	0.835810i	$-0.315002\pi$
$157$	13.7584			1.09804			0.549019	+	0.835810i	$0.315002\pi$
$158$	7.20768	+	12.4841i	0.573412	+	0.993180i
$159$	16.5173	+	28.6088i	1.30991	+	2.26883i
$160$	0.421610	−	0.730250i	0.0333312	−	0.0577314i
$161$	−6.91154			−0.544706
$162$	−1.70789	+	2.95815i	−0.134184	+	0.232414i
$163$	−5.95625	+	10.3165i	−0.466529	+	0.808052i	−0.999269	−	0.0382267i	$-0.987829\pi$
$163$	−5.95625	+	10.3165i	−0.466529	+	0.808052i	0.532740	+	0.846279i	$0.321162\pi$
$164$	−0.465665			−0.0363623
$165$	4.87132	−	8.43738i	0.379232	−	0.656849i
$166$	−0.368905	−	0.638962i	−0.0286326	−	0.0495930i
$167$	−2.89782	−	5.01917i	−0.224240	−	0.388395i	0.731851	−	0.681464i	$-0.238657\pi$
$167$	−2.89782	−	5.01917i	−0.224240	−	0.388395i	−0.956091	+	0.293070i	$0.905323\pi$
$168$	17.6198			1.35940
$169$	11.7644	+	5.53155i	0.904957	+	0.425504i
$170$	−9.09640			−0.697662
$171$	12.0831	+	20.9285i	0.924016	+	1.60044i
$172$	−0.289980	−	0.502260i	−0.0221108	−	0.0382970i
$173$	−1.92974	+	3.34241i	−0.146715	+	0.254118i	−0.930012	−	0.367530i	$-0.880203\pi$
$173$	−1.92974	+	3.34241i	−0.146715	+	0.254118i	0.783296	+	0.621649i	$0.213537\pi$
$174$	20.7048			1.56963
$175$	3.95640	−	6.85268i	0.299076	−	0.518014i
$176$	−5.65042	+	9.78682i	−0.425916	+	0.737709i
$177$	13.2993			0.999638
$178$	−4.07523	+	7.05850i	−0.305451	+	0.529057i
$179$	−6.15924	−	10.6681i	−0.460363	−	0.797372i	0.538616	−	0.842551i	$-0.318947\pi$
$179$	−6.15924	−	10.6681i	−0.460363	−	0.797372i	−0.998979	+	0.0451795i	$0.985614\pi$
$180$	−0.388832	−	0.673477i	−0.0289818	−	0.0501980i
$181$	−1.30104			−0.0967056			−0.0483528	−	0.998830i	$-0.515397\pi$
$181$	−1.30104			−0.0967056			−0.0483528	+	0.998830i	$0.515397\pi$
$182$	10.1431	+	2.26563i	0.751857	+	0.167940i
$183$	42.3510			3.13068
$184$	−4.77411	−	8.26899i	−0.351952	−	0.609598i
$185$	3.28986	+	5.69821i	0.241876	+	0.418941i
$186$	1.95703	−	3.38968i	0.143497	−	0.248543i
$187$	−18.1179			−1.32491
$188$	−0.491674	+	0.851604i	−0.0358590	+	0.0621096i
$189$	6.67395	−	11.5596i	0.485458	−	0.840839i
$190$	7.08659			0.514115
$191$	−5.13564	+	8.89518i	−0.371602	+	0.643633i	−0.989812	−	0.142380i	$-0.954525\pi$
$191$	−5.13564	+	8.89518i	−0.371602	+	0.643633i	0.618210	+	0.786013i	$0.287858\pi$
$192$	12.1196	+	20.9918i	0.874660	+	1.51495i
$193$	−10.0020	−	17.3240i	−0.719960	−	1.24701i	−0.961015	−	0.276496i	$-0.910827\pi$
$193$	−10.0020	−	17.3240i	−0.719960	−	1.24701i	0.241055	−	0.970511i	$-0.422506\pi$
$194$	22.1302			1.58886
$195$	−3.45494	−	11.0189i	−0.247413	−	0.789076i
$196$	0.340365			0.0243118
$197$	13.5726	+	23.5084i	0.967007	+	1.67490i	0.704124	+	0.710077i	$0.251340\pi$
$197$	13.5726	+	23.5084i	0.967007	+	1.67490i	0.262882	+	0.964828i	$0.415327\pi$
$198$	10.8220	+	18.7442i	0.769086	+	1.33210i
$199$	−13.4485	+	23.2935i	−0.953338	+	1.65123i	−0.215213	+	0.976567i	$0.569045\pi$
$199$	−13.4485	+	23.2935i	−0.953338	+	1.65123i	−0.738125	+	0.674664i	$0.764289\pi$
$200$	10.9314			0.772969
$201$	−6.69675	+	11.5991i	−0.472352	+	0.818138i
$202$	2.59343	−	4.49195i	0.182473	−	0.316053i
$203$	−11.1611			−0.783359
$204$	−1.13961	+	1.97386i	−0.0797884	+	0.138197i
$205$	1.94870	+	3.37524i	0.136103	+	0.235737i
$206$	−9.81589	−	17.0016i	−0.683905	−	1.18456i
$207$	−17.0605			−1.18579
$208$	4.00751	+	12.7812i	0.277871	+	0.886214i
$209$	14.1148			0.976342
$210$	−4.61604	−	7.99521i	−0.318537	−	0.551722i
$211$	−3.28733	−	5.69383i	−0.226309	−	0.391979i	0.730402	−	0.683017i	$-0.239333\pi$
$211$	−3.28733	−	5.69383i	−0.226309	−	0.391979i	−0.956711	+	0.291038i	$0.905999\pi$
$212$	0.770055	−	1.33377i	0.0528876	−	0.0916040i
$213$	26.2359			1.79765
$214$	−8.29921	+	14.3747i	−0.567323	+	0.982631i
$215$	−2.42700	+	4.20368i	−0.165520	+	0.286689i
$216$	18.4400			1.25468
$217$	−1.05496	+	1.82724i	−0.0716153	+	0.124041i
$218$	−3.01237	−	5.21758i	−0.204024	−	0.353379i
$219$	2.77197	+	4.80119i	0.187312	+	0.324434i
$220$	−0.454213			−0.0306230
$221$	−14.5334	+	15.8098i	−0.977622	+	1.06348i
$222$	−23.0373			−1.54616
$223$	6.35876	+	11.0137i	0.425814	+	0.737532i	0.996496	−	0.0836392i	$-0.0266543\pi$
$223$	6.35876	+	11.0137i	0.425814	+	0.737532i	−0.570682	+	0.821171i	$0.693321\pi$
$224$	−0.795740	−	1.37826i	−0.0531676	−	0.0920890i
$225$	9.76599	−	16.9152i	0.651066	−	1.12768i
$226$	14.7185			0.979057
$227$	−7.65183	+	13.2534i	−0.507870	+	0.879656i	0.492089	+	0.870545i	$0.336233\pi$
$227$	−7.65183	+	13.2534i	−0.507870	+	0.879656i	−0.999958	+	0.00911100i	$0.997100\pi$
$228$	0.887815	−	1.53774i	0.0587970	−	0.101839i
$229$	20.0213			1.32304			0.661522	−	0.749926i	$-0.269911\pi$
$229$	20.0213			1.32304			0.661522	+	0.749926i	$0.269911\pi$
$230$	−2.50144	+	4.33263i	−0.164940	+	0.285685i
$231$	−9.19406	−	15.9246i	−0.604925	−	1.04776i
$232$	−7.70949	−	13.3532i	−0.506153	−	0.876683i
$233$	17.9735			1.17748			0.588741	−	0.808322i	$-0.299624\pi$
$233$	17.9735			1.17748			0.588741	+	0.808322i	$0.299624\pi$
$234$	25.0373	+	5.59250i	1.63674	+	0.365593i
$235$	8.23016			0.536876
$236$	−0.310014	−	0.536960i	−0.0201802	−	0.0349531i
$237$	−15.1151	−	26.1802i	−0.981833	−	1.70058i
$238$	−8.58420	+	14.8683i	−0.556431	+	0.963767i
$239$	8.58498			0.555316			0.277658	−	0.960680i	$-0.410442\pi$
$239$	8.58498			0.555316			0.277658	+	0.960680i	$0.410442\pi$
$240$	5.94921	−	10.3043i	0.384020	−	0.665142i
$241$	−9.03416	+	15.6476i	−0.581941	+	1.00795i	0.413308	+	0.910591i	$0.364373\pi$
$241$	−9.03416	+	15.6476i	−0.581941	+	1.00795i	−0.995249	+	0.0973608i	$0.968960\pi$
$242$	−2.38624			−0.153393
$243$	−5.90781	+	10.2326i	−0.378986	+	0.656424i
$244$	−0.987225	−	1.70992i	−0.0632006	−	0.109467i
$245$	−1.42435	−	2.46704i	−0.0909983	−	0.157614i
$246$	−13.6457			−0.870021
$247$	11.3223	−	12.3167i	0.720421	−	0.783691i
$248$	−2.91483			−0.185092
$249$	0.773625	+	1.33996i	0.0490265	+	0.0849163i
$250$	−6.68196	−	11.5735i	−0.422604	−	0.731972i
$251$	−3.85602	+	6.67882i	−0.243390	+	0.421563i	−0.961678	−	0.274183i	$-0.911593\pi$
$251$	−3.85602	+	6.67882i	−0.243390	+	0.421563i	0.718288	+	0.695746i	$0.244926\pi$
$252$	−1.46775			−0.0924596
$253$	−4.98229	+	8.62958i	−0.313234	+	0.542537i
$254$	−6.04855	+	10.4764i	−0.379520	+	0.657348i
$255$	19.0759			1.19458
$256$	1.59552	−	2.76351i	0.0997197	−	0.172720i
$257$	−6.98247	−	12.0940i	−0.435555	−	0.754403i	0.561786	−	0.827283i	$-0.310114\pi$
$257$	−6.98247	−	12.0940i	−0.435555	−	0.754403i	−0.997341	+	0.0728798i	$0.976781\pi$
$258$	−8.49751	−	14.7181i	−0.529032	−	0.916310i
$259$	12.4185			0.771646
$260$	−0.364350	+	0.396349i	−0.0225960	+	0.0245805i
$261$	−27.5502			−1.70532
$262$	8.38189	+	14.5179i	0.517835	+	0.896917i
$263$	−5.95774	−	10.3191i	−0.367370	−	0.636303i	0.621784	−	0.783189i	$-0.286408\pi$
$263$	−5.95774	−	10.3191i	−0.367370	−	0.636303i	−0.989153	+	0.146886i	$0.953075\pi$
$264$	12.7015	−	21.9996i	0.781722	−	1.35398i
$265$	−12.8900			−0.791826
$266$	6.68756	−	11.5832i	0.410040	−	0.710211i
$267$	8.54610	−	14.8023i	0.523013	−	0.905884i
$268$	0.624419			0.0381425
$269$	8.23284	−	14.2597i	0.501965	−	0.869429i	−0.498032	−	0.867158i	$-0.665944\pi$
$269$	8.23284	−	14.2597i	0.501965	−	0.869429i	0.999997	−	0.00227045i	$-0.000722707\pi$
$270$	−4.83091	−	8.36738i	−0.294000	−	0.509222i
$271$	11.9038	+	20.6179i	0.723102	+	1.25245i	0.959750	+	0.280854i	$0.0906178\pi$
$271$	11.9038	+	20.6179i	0.723102	+	1.25245i	−0.236648	+	0.971595i	$0.576049\pi$
$272$	−22.1268			−1.34164
$273$	−21.2710	−	4.75123i	−1.28738	−	0.287557i
$274$	−9.39692			−0.567689
$275$	−5.70405	−	9.87971i	−0.343967	−	0.595769i
$276$	0.626767	+	1.08559i	0.0377269	+	0.0653450i
$277$	8.91810	−	15.4466i	0.535837	−	0.928097i	−0.463286	−	0.886209i	$-0.653330\pi$
$277$	8.91810	−	15.4466i	0.535837	−	0.928097i	0.999122	−	0.0418875i	$-0.0133371\pi$
$278$	−17.9502			−1.07658
$279$	−2.60407	+	4.51038i	−0.155901	+	0.270029i
$280$	−3.43759	+	5.95408i	−0.205435	+	0.355824i
$281$	2.15513			0.128564			0.0642822	−	0.997932i	$-0.479524\pi$
$281$	2.15513			0.128564			0.0642822	+	0.997932i	$0.479524\pi$
$282$	−14.4079	+	24.9552i	−0.857978	+	1.48606i
$283$	8.24208	+	14.2757i	0.489941	+	0.848603i	0.999933	−	0.0115766i	$-0.00368501\pi$
$283$	8.24208	+	14.2757i	0.489941	+	0.848603i	−0.509992	+	0.860179i	$0.670352\pi$
$284$	−0.611573	−	1.05928i	−0.0362902	−	0.0628564i
$285$	−14.8612			−0.880300
$286$	10.1406	−	11.0312i	0.599627	−	0.652289i
$287$	7.35588			0.434204
$288$	−1.96421	−	3.40211i	−0.115742	−	0.200471i
$289$	−9.23724	−	15.9994i	−0.543367	−	0.941139i
$290$	−4.03947	+	6.99657i	−0.237206	+	0.410853i
$291$	−46.4090			−2.72054
$292$	0.129232	−	0.223837i	0.00756274	−	0.0130990i
$293$	−12.7527	+	22.0884i	−0.745023	+	1.29042i	0.205161	+	0.978728i	$0.434228\pi$
$293$	−12.7527	+	22.0884i	−0.745023	+	1.29042i	−0.950184	+	0.311689i	$0.899105\pi$
$294$	9.97399			0.581695
$295$	−2.59467	+	4.49410i	−0.151068	+	0.261657i
$296$	8.57798	+	14.8575i	0.498585	+	0.863575i
$297$	−9.62203	−	16.6658i	−0.558327	−	0.967050i
$298$	−11.7179			−0.678801
$299$	3.53364	+	11.2699i	0.204356	+	0.651752i
$300$	−1.43513			−0.0828572
$301$	4.58067	+	7.93396i	0.264026	+	0.457306i
$302$	−10.8550	−	18.8013i	−0.624633	−	1.08190i
$303$	−5.43865	+	9.42001i	−0.312442	+	0.541166i
$304$	17.2380			0.988668
$305$	−8.26261	+	14.3113i	−0.473116	+	0.819461i
$306$	−21.1893	+	36.7009i	−1.21131	+	2.09805i
$307$	3.74295			0.213621			0.106811	−	0.994279i	$-0.465936\pi$
$307$	3.74295			0.213621			0.106811	+	0.994279i	$0.465936\pi$
$308$	−0.428637	+	0.742421i	−0.0244239	+	0.0423034i
$309$	20.5848	+	35.6538i	1.17103	+	2.02828i
$310$	0.763627	+	1.32264i	0.0433711	+	0.0751210i
$311$	−8.65529			−0.490796			−0.245398	−	0.969422i	$-0.578919\pi$
$311$	−8.65529			−0.490796			−0.245398	+	0.969422i	$0.578919\pi$
$312$	−9.00840	−	28.7305i	−0.510000	−	1.62655i
$313$	9.20783			0.520457			0.260229	−	0.965547i	$-0.416202\pi$
$313$	9.20783			0.520457			0.260229	+	0.965547i	$0.416202\pi$
$314$	−9.39816	−	16.2781i	−0.530369	−	0.918626i
$315$	6.14219	+	10.6386i	0.346073	+	0.599416i
$316$	−0.704684	+	1.22055i	−0.0396415	+	0.0686612i
$317$	6.90984			0.388095			0.194048	−	0.980992i	$-0.437838\pi$
$317$	6.90984			0.388095			0.194048	+	0.980992i	$0.437838\pi$
$318$	22.5655	−	39.0846i	1.26541	−	2.19176i
$319$	−8.04568	+	13.9355i	−0.450471	+	0.780239i
$320$	−9.45808			−0.528723
$321$	17.4042	−	30.1449i	0.971405	−	1.68252i
$322$	4.72119	+	8.17733i	0.263101	+	0.455705i
$323$	13.8183	+	23.9339i	0.768869	+	1.33172i
$324$	−0.333954			−0.0185530
$325$	−13.1966	−	2.94769i	−0.732018	−	0.163509i
$326$	16.2745			0.901363
$327$	6.31720	+	10.9417i	0.349342	+	0.605078i
$328$	5.08103	+	8.80060i	0.280553	+	0.485932i
$329$	7.76673	−	13.4524i	0.428194	−	0.741653i
$330$	−13.3102			−0.732700
$331$	−10.9610	+	18.9850i	−0.602470	+	1.04351i	0.389976	+	0.920825i	$0.372483\pi$
$331$	−10.9610	+	18.9850i	−0.602470	+	1.04351i	−0.992446	+	0.122683i	$0.960850\pi$
$332$	0.0360672	−	0.0624702i	0.00197945	−	0.00342850i
$333$	30.6538			1.67982
$334$	−3.95892	+	6.85705i	−0.216623	+	0.375201i
$335$	−2.61305	−	4.52593i	−0.142766	−	0.247278i
$336$	−11.2284	−	19.4482i	−0.612561	−	1.06099i
$337$	−29.3055			−1.59637			−0.798186	−	0.602410i	$-0.794207\pi$
$337$	−29.3055			−1.59637			−0.798186	+	0.602410i	$0.794207\pi$
$338$	−1.49152	−	17.6975i	−0.0811282	−	0.962618i
$339$	−30.8659			−1.67640
$340$	−0.444670	−	0.770191i	−0.0241156	−	0.0417695i
$341$	1.52097	+	2.63439i	0.0823649	+	0.142660i
$342$	16.5076	−	28.5920i	0.892628	−	1.54608i
$343$	−20.1460			−1.08778
$344$	−6.32814	+	10.9607i	−0.341190	+	0.590959i
$345$	5.24574	−	9.08590i	0.282421	−	0.489168i
$346$	5.27272			0.283463
$347$	18.0098	−	31.1940i	0.966819	−	1.67458i	0.262174	−	0.965021i	$-0.415561\pi$
$347$	18.0098	−	31.1940i	0.966819	−	1.67458i	0.704645	−	0.709560i	$-0.251106\pi$
$348$	1.01214	+	1.75307i	0.0542563	+	0.0939747i
$349$	−14.7519	−	25.5511i	−0.789652	−	1.36772i	−0.926180	−	0.377082i	$-0.876928\pi$
$349$	−14.7519	−	25.5511i	−0.789652	−	1.36772i	0.136528	−	0.990636i	$-0.456406\pi$
$350$	−10.8103			−0.577832
$351$	−22.2611	−	4.97239i	−1.18821	−	0.265407i
$352$	−2.29448			−0.122296
$353$	2.22615	+	3.85580i	0.118486	+	0.205224i	0.919168	−	0.393866i	$-0.128863\pi$
$353$	2.22615	+	3.85580i	0.118486	+	0.205224i	−0.800682	+	0.599090i	$0.795529\pi$
$354$	−9.08459	−	15.7350i	−0.482840	−	0.836304i
$355$	−5.11858	+	8.86564i	−0.271666	+	0.470539i
$356$	−0.796856			−0.0422333
$357$	18.0018	−	31.1800i	0.952756	−	1.65022i
$358$	−8.41459	+	14.5745i	−0.444725	+	0.770286i
$359$	−4.87356			−0.257217			−0.128608	−	0.991695i	$-0.541051\pi$
$359$	−4.87356			−0.257217			−0.128608	+	0.991695i	$0.541051\pi$
$360$	−8.48536	+	14.6971i	−0.447218	+	0.774604i
$361$	−1.26518	−	2.19136i	−0.0665885	−	0.115335i
$362$	0.888724	+	1.53932i	0.0467103	+	0.0809046i
$363$	5.00414			0.262649
$364$	0.304007	+	0.969569i	0.0159343	+	0.0508192i
$365$	−2.16322			−0.113228
$366$	−28.9294	−	50.1073i	−1.51217	−	2.61915i
$367$	10.8518	+	18.7958i	0.566457	+	0.981132i	0.996912	+	0.0785206i	$0.0250196\pi$
$367$	10.8518	+	18.7958i	0.566457	+	0.981132i	−0.430455	+	0.902612i	$0.641647\pi$
$368$	−6.08472	+	10.5391i	−0.317188	+	0.549386i
$369$	18.1573			0.945231
$370$	4.49453	−	7.78475i	0.233659	−	0.404710i
$371$	−12.1642	+	21.0690i	−0.631533	+	1.09385i
$372$	0.382672			0.0198406
$373$	1.27562	−	2.20944i	0.0660492	−	0.114401i	−0.831110	−	0.556108i	$-0.812294\pi$
$373$	1.27562	−	2.20944i	0.0660492	−	0.114401i	0.897159	+	0.441708i	$0.145627\pi$
$374$	12.3761	+	21.4360i	0.639952	+	1.10843i
$375$	14.0126	+	24.2706i	0.723609	+	1.25333i
$376$	21.4593			1.10668
$377$	5.70632	+	18.1992i	0.293890	+	0.937306i
$378$	−18.2356			−0.937936
$379$	−3.79317	−	6.56996i	−0.194842	−	0.337476i	0.752007	−	0.659155i	$-0.229086\pi$
$379$	−3.79317	−	6.56996i	−0.194842	−	0.337476i	−0.946849	+	0.321679i	$0.895753\pi$
$380$	0.346422	+	0.600021i	0.0177711	+	0.0307804i
$381$	12.6843	−	21.9699i	0.649838	−	1.12555i
$382$	14.0323			0.717957
$383$	7.34893	−	12.7287i	0.375513	−	0.650407i	−0.614891	−	0.788612i	$-0.710800\pi$
$383$	7.34893	−	12.7287i	0.375513	−	0.650407i	0.990404	+	0.138205i	$0.0441333\pi$
$384$	14.3965	−	24.9355i	0.734669	−	1.27248i
$385$	7.17498			0.365671
$386$	−13.6645	+	23.6676i	−0.695503	+	1.20465i
$387$	11.3070	+	19.5842i	0.574765	+	0.995522i
$388$	1.08182	+	1.87376i	0.0549210	+	0.0951259i
$389$	5.17416			0.262340			0.131170	−	0.991360i	$-0.458127\pi$
$389$	5.17416			0.262340			0.131170	+	0.991360i	$0.458127\pi$
$390$	−10.6768	+	11.6145i	−0.540643	+	0.588124i
$391$	−19.5105			−0.986686
$392$	−3.71384	−	6.43257i	−0.187577	−	0.324894i
$393$	−17.5775	−	30.4452i	−0.886670	−	1.53576i
$394$	18.5425	−	32.1166i	0.934158	−	1.61801i
$395$	11.7957			0.593508
$396$	−1.05805	+	1.83259i	−0.0531690	+	0.0920914i
$397$	−11.1141	+	19.2501i	−0.557798	+	0.966135i	0.439882	+	0.898056i	$0.355020\pi$
$397$	−11.1141	+	19.2501i	−0.557798	+	0.966135i	−0.997680	+	0.0680793i	$0.978313\pi$
$398$	36.7460			1.84191
$399$	−14.0244	+	24.2909i	−0.702097	+	1.21607i
$400$	−6.96620	−	12.0658i	−0.348310	−	0.603290i
$401$	−7.31913	−	12.6771i	−0.365500	−	0.633064i	0.623356	−	0.781938i	$-0.285769\pi$
$401$	−7.31913	−	12.6771i	−0.365500	−	0.633064i	−0.988856	+	0.148873i	$0.952435\pi$
$402$	18.2978			0.912614
$403$	3.51884	+	0.785991i	0.175286	+	0.0391530i
$404$	0.507111			0.0252297
$405$	1.39752	+	2.42058i	0.0694434	+	0.120279i
$406$	7.62404	+	13.2052i	0.378375	+	0.655364i
$407$	8.95204	−	15.5054i	0.443736	−	0.768573i
$408$	49.7385			2.46242
$409$	9.03698	−	15.6525i	0.446850	−	0.773967i	−0.551329	−	0.834288i	$-0.685879\pi$
$409$	9.03698	−	15.6525i	0.446850	−	0.773967i	0.998179	+	0.0603211i	$0.0192125\pi$
$410$	2.66226	−	4.61117i	0.131480	−	0.227729i
$411$	19.7061			0.972033
$412$	0.959684	−	1.66222i	0.0472802	−	0.0818917i
$413$	4.89714	+	8.48210i	0.240973	+	0.417377i
$414$	11.6538	+	20.1850i	0.572753	+	0.992037i
$415$	−0.603731			−0.0296360
$416$	−1.84054	+	2.00218i	−0.0902397	+	0.0981650i
$417$	37.6432			1.84339
$418$	−9.64164	−	16.6998i	−0.471588	−	0.816815i
$419$	−10.5901	−	18.3427i	−0.517362	−	0.896097i	−0.999797	−	0.0201653i	$-0.993581\pi$
$419$	−10.5901	−	18.3427i	−0.517362	−	0.896097i	0.482435	−	0.875932i	$-0.339753\pi$
$420$	0.451303	−	0.781679i	0.0220213	−	0.0381420i
$421$	−21.1422			−1.03041			−0.515204	−	0.857068i	$-0.672284\pi$
$421$	−21.1422			−1.03041			−0.515204	+	0.857068i	$0.672284\pi$
$422$	−4.49107	+	7.77876i	−0.218622	+	0.378664i
$423$	19.1714	−	33.2059i	0.932147	−	1.61453i
$424$	−33.6093			−1.63221
$425$	11.1684	−	19.3443i	0.541749	−	0.938336i
$426$	−17.9214	−	31.0408i	−0.868295	−	1.50393i
$427$	15.5947	+	27.0108i	0.754681	+	1.30715i
$428$	−1.62280			−0.0784411
$429$	−21.2657	+	23.1334i	−1.02672	+	1.11689i
$430$	6.63140			0.319794
$431$	−13.1725	−	22.8155i	−0.634498	−	1.09898i	−0.986621	−	0.163029i	$-0.947874\pi$
$431$	−13.1725	−	22.8155i	−0.634498	−	1.09898i	0.352124	−	0.935953i	$-0.385460\pi$
$432$	−11.7511	−	20.3535i	−0.565375	−	0.979259i
$433$	4.41465	−	7.64640i	0.212155	−	0.367463i	−0.740234	−	0.672349i	$-0.765285\pi$
$433$	4.41465	−	7.64640i	0.212155	−	0.367463i	0.952389	+	0.304887i	$0.0986186\pi$
$434$	2.88252			0.138365
$435$	8.47112	−	14.6724i	0.406159	−	0.703488i
$436$	0.294515	−	0.510115i	0.0141047	−	0.0244301i
$437$	15.1997			0.727100
$438$	3.78699	−	6.55926i	0.180949	−	0.313413i
$439$	−1.37660	−	2.38435i	−0.0657017	−	0.113799i	0.831303	−	0.555819i	$-0.187595\pi$
$439$	−1.37660	−	2.38435i	−0.0657017	−	0.113799i	−0.897005	+	0.442020i	$0.854262\pi$
$440$	4.95607	+	8.58417i	0.236271	+	0.409234i
$441$	−13.2716			−0.631980
$442$	28.6328	+	6.39561i	1.36192	+	0.304208i
$443$	39.2598			1.86529			0.932645	−	0.360796i	$-0.117495\pi$
$443$	39.2598			1.86529			0.932645	+	0.360796i	$0.117495\pi$
$444$	−1.12616	−	1.95056i	−0.0534451	−	0.0925696i
$445$	3.33466	+	5.77579i	0.158078	+	0.273799i
$446$	8.68718	−	15.0466i	0.411350	−	0.712479i
$447$	24.5735			1.16229
$448$	−8.92551	+	15.4594i	−0.421691	+	0.730390i
$449$	−7.69492	+	13.3280i	−0.363146	+	0.628987i	−0.988477	−	0.151373i	$-0.951631\pi$
$449$	−7.69492	+	13.3280i	−0.363146	+	0.628987i	0.625331	+	0.780360i	$0.284964\pi$
$450$	−26.6841			−1.25790
$451$	5.30259	−	9.18436i	0.249689	−	0.432475i
$452$	0.719500	+	1.24621i	0.0338424	+	0.0586168i
$453$	22.7638	+	39.4280i	1.06954	+	1.85249i
$454$	20.9075			0.981235
$455$	5.75546	−	6.26093i	0.269820	−	0.293517i
$456$	−38.7490			−1.81459
$457$	6.99831	+	12.1214i	0.327367	+	0.567016i	0.981989	−	0.188940i	$-0.0605053\pi$
$457$	6.99831	+	12.1214i	0.327367	+	0.567016i	−0.654621	+	0.755957i	$0.727172\pi$
$458$	−13.6763	−	23.6880i	−0.639051	−	1.10687i
$459$	18.8398	−	32.6314i	0.879365	−	1.52310i
$460$	−0.489124			−0.0228055
$461$	8.22288	−	14.2424i	0.382978	−	0.663337i	−0.608509	−	0.793547i	$-0.708232\pi$
$461$	8.22288	−	14.2424i	0.382978	−	0.663337i	0.991486	+	0.130210i	$0.0415653\pi$
$462$	−12.5607	+	21.7557i	−0.584376	+	1.01217i
$463$	7.57938			0.352244			0.176122	−	0.984368i	$-0.443645\pi$
$463$	7.57938			0.352244			0.176122	+	0.984368i	$0.443645\pi$
$464$	−9.82595	+	17.0190i	−0.456158	+	0.790089i
$465$	−1.60139	−	2.77369i	−0.0742628	−	0.128627i
$466$	−12.2774	−	21.2652i	−0.568742	−	0.985090i
$467$	10.2278			0.473284			0.236642	−	0.971597i	$-0.423953\pi$
$467$	10.2278			0.473284			0.236642	+	0.971597i	$0.423953\pi$
$468$	0.750411	+	2.39329i	0.0346878	+	0.110630i
$469$	−9.86365			−0.455461
$470$	−5.62191	−	9.73744i	−0.259319	−	0.449155i
$471$	19.7087	+	34.1366i	0.908131	+	1.57293i
$472$	−6.76534	+	11.7179i	−0.311400	+	0.539361i
$473$	13.2082			0.607313
$474$	−20.6499	+	35.7667i	−0.948481	+	1.64282i
$475$	−8.70082	+	15.0703i	−0.399221	+	0.691471i
$476$	−1.67853			−0.0769351
$477$	−30.0261	+	52.0068i	−1.37480	+	2.38123i
$478$	−5.86429	−	10.1572i	−0.268226	−	0.464582i
$479$	−16.0382	−	27.7789i	−0.732802	−	1.26925i	−0.955681	−	0.294404i	$-0.904879\pi$
$479$	−16.0382	−	27.7789i	−0.732802	−	1.26925i	0.222879	−	0.974846i	$-0.428455\pi$
$480$	2.41581			0.110266
$481$	−6.34915	−	20.2494i	−0.289496	−	0.923291i
$482$	24.6845			1.12435
$483$	−9.90073	−	17.1486i	−0.450499	−	0.780287i
$484$	−0.116649	−	0.202042i	−0.00530224	−	0.00918374i
$485$	9.05431	−	15.6825i	0.411135	−	0.712107i
$486$	16.1422			0.732225
$487$	−14.2634	+	24.7049i	−0.646334	+	1.11948i	0.337657	+	0.941269i	$0.390366\pi$
$487$	−14.2634	+	24.7049i	−0.646334	+	1.11948i	−0.983992	+	0.178215i	$0.942968\pi$
$488$	−21.5439	+	37.3151i	−0.975247	+	1.68918i
$489$	−34.1291			−1.54337
$490$	−1.94591	+	3.37041i	−0.0879072	+	0.152260i
$491$	0.784490	+	1.35878i	0.0354035	+	0.0613207i	0.883184	−	0.469026i	$-0.155395\pi$
$491$	0.784490	+	1.35878i	0.0354035	+	0.0613207i	−0.847781	+	0.530347i	$0.822062\pi$
$492$	−0.667061	−	1.15538i	−0.0300734	−	0.0520887i
$493$	−31.5066			−1.41898
$494$	−22.3065	−	4.98253i	−1.00362	−	0.224174i
$495$	17.7107			0.796039
$496$	1.85751	+	3.21730i	0.0834047	+	0.144461i
$497$	9.66072	+	16.7329i	0.433343	+	0.750571i
$498$	1.05691	−	1.83061i	0.0473611	−	0.0820318i
$499$	−29.2842			−1.31094			−0.655470	−	0.755221i	$-0.727530\pi$
$499$	−29.2842			−1.31094			−0.655470	+	0.755221i	$0.727530\pi$
$500$	0.653284	−	1.13152i	0.0292158	−	0.0506032i
$501$	8.30220	−	14.3798i	0.370915	−	0.642443i
$502$	10.5360			0.470244
$503$	19.6034	−	33.9541i	0.874074	−	1.51394i	0.0163276	−	0.999867i	$-0.494803\pi$
$503$	19.6034	−	33.9541i	0.874074	−	1.51394i	0.857746	−	0.514074i	$-0.171864\pi$
$504$	16.0151	+	27.7390i	0.713370	+	1.23559i
$505$	−2.12214	−	3.67566i	−0.0944340	−	0.163565i
$506$	13.6133			0.605187
$507$	3.12785	+	37.1132i	0.138913	+	1.64826i
$508$	−1.18271			−0.0524745
$509$	15.7219	+	27.2311i	0.696859	+	1.20700i	0.969550	+	0.244894i	$0.0787532\pi$
$509$	15.7219	+	27.2311i	0.696859	+	1.20700i	−0.272691	+	0.962102i	$0.587914\pi$
$510$	−13.0305	−	22.5695i	−0.577001	−	0.999395i
$511$	−2.04142	+	3.53584i	−0.0903069	+	0.156416i
$512$	−24.4595			−1.08097
$513$	−14.6772	+	25.4216i	−0.648014	+	1.12239i
$514$	−9.53927	+	16.5225i	−0.420759	+	0.728776i
$515$	−16.0642			−0.707873
$516$	0.830788	−	1.43897i	0.0365734	−	0.0633470i
$517$	−11.1975	−	19.3947i	−0.492466	−	0.852977i
$518$	−8.48290	−	14.6928i	−0.372717	−	0.645565i
$519$	−11.0573			−0.485363
$520$	11.4661	+	2.56116i	0.502824	+	0.112314i
$521$	−24.7527			−1.08443			−0.542217	−	0.840238i	$-0.682415\pi$
$521$	−24.7527			−1.08443			−0.542217	+	0.840238i	$0.682415\pi$
$522$	18.8192	+	32.5958i	0.823694	+	1.42668i
$523$	−8.31684	−	14.4052i	−0.363670	−	0.629895i	0.624892	−	0.780711i	$-0.285143\pi$
$523$	−8.31684	−	14.4052i	−0.363670	−	0.629895i	−0.988562	+	0.150816i	$0.951810\pi$
$524$	−0.819484	+	1.41939i	−0.0357993	+	0.0620062i
$525$	22.6700			0.989401
$526$	−8.13930	+	14.0977i	−0.354891	+	0.614688i
$527$	−2.97802	+	5.15809i	−0.129725	+	0.224690i
$528$	−32.3767			−1.40902
$529$	6.13476	−	10.6257i	0.266729	−	0.461988i
$530$	8.80499	+	15.2507i	0.382464	+	0.662447i
$531$	12.0881	+	20.9373i	0.524580	+	0.908599i
$532$	1.30766			0.0566944
$533$	−3.76081	−	11.9944i	−0.162899	−	0.519534i
$534$	−23.3509			−1.01049
$535$	6.79104	+	11.7624i	0.293602	+	0.508534i
$536$	−6.81325	−	11.8009i	−0.294288	−	0.509721i
$537$	17.6461	−	30.5640i	0.761486	−	1.31893i
$538$	−22.4950			−0.969827
$539$	−3.87579	+	6.71307i	−0.166942	+	0.289152i
$540$	0.472310	−	0.818065i	0.0203250	−	0.0352039i
$541$	9.33405			0.401302			0.200651	−	0.979663i	$-0.435694\pi$
$541$	9.33405			0.401302			0.200651	+	0.979663i	$0.435694\pi$
$542$	16.2626	−	28.1677i	0.698539	−	1.20991i
$543$	−1.86373	−	3.22808i	−0.0799804	−	0.138530i
$544$	−2.24628	−	3.89067i	−0.0963084	−	0.166811i
$545$	−4.92990			−0.211174
$546$	8.90854	+	28.4121i	0.381250	+	1.21592i
$547$	−20.6064			−0.881064			−0.440532	−	0.897737i	$-0.645210\pi$
$547$	−20.6064			−0.881064			−0.440532	+	0.897737i	$0.645210\pi$
$548$	−0.459361	−	0.795636i	−0.0196229	−	0.0339879i
$549$	38.4941	+	66.6737i	1.64289	+	2.84556i
$550$	−7.79273	+	13.4974i	−0.332283	+	0.575531i
$551$	24.5453			1.04567
$552$	13.6777	−	23.6905i	0.582163	−	1.00834i
$553$	11.1315	−	19.2804i	0.473361	−	0.819886i
$554$	−24.3674			−1.03527
$555$	−9.42541	+	16.3253i	−0.400086	+	0.692970i
$556$	−0.877483	−	1.51984i	−0.0372135	−	0.0644558i
$557$	−11.6681	−	20.2097i	−0.494392	−	0.856311i	0.505588	−	0.862775i	$-0.331276\pi$
$557$	−11.6681	−	20.2097i	−0.494392	−	0.856311i	−0.999979	+	0.00646397i	$0.997942\pi$
$558$	7.11522			0.301211
$559$	10.5950	−	11.5255i	0.448122	−	0.487478i
$560$	8.76259			0.370287
$561$	−25.9537	−	44.9532i	−1.09577	−	1.89792i
$562$	−1.47214	−	2.54983i	−0.0620986	−	0.107558i
$563$	1.81516	−	3.14396i	0.0765000	−	0.132502i	−0.825238	−	0.564786i	$-0.808959\pi$
$563$	1.81516	−	3.14396i	0.0765000	−	0.132502i	0.901738	+	0.432284i	$0.142292\pi$
$564$	−2.81727			−0.118629
$565$	6.02187	−	10.4302i	0.253342	−	0.438801i
$566$	11.2601	−	19.5031i	0.473298	−	0.819776i
$567$	5.27532			0.221542
$568$	−13.3462	+	23.1162i	−0.559993	+	0.969936i
$569$	−15.4875	−	26.8251i	−0.649268	−	1.12457i	−0.983298	−	0.182003i	$-0.941742\pi$
$569$	−15.4875	−	26.8251i	−0.649268	−	1.12457i	0.334030	−	0.942562i	$-0.391591\pi$
$570$	10.1515	+	17.5829i	0.425199	+	0.736466i
$571$	−25.2221			−1.05551			−0.527756	−	0.849396i	$-0.676966\pi$
$571$	−25.2221			−1.05551			−0.527756	+	0.849396i	$0.676966\pi$
$572$	1.42973	+	0.319353i	0.0597799	+	0.0133528i
$573$	−29.4270			−1.22933
$574$	−5.02471	−	8.70305i	−0.209727	−	0.363258i
$575$	−6.14248	−	10.6391i	−0.256159	−	0.443681i
$576$	−22.0318	+	38.1602i	−0.917991	+	1.59001i
$577$	−9.37505			−0.390288			−0.195144	−	0.980775i	$-0.562518\pi$
$577$	−9.37505			−0.390288			−0.195144	+	0.980775i	$0.562518\pi$
$578$	−12.6197	+	21.8579i	−0.524909	+	0.909170i
$579$	28.6556	−	49.6329i	1.19089	−	2.06267i
$580$	−0.789865			−0.0327974
$581$	−0.569736	+	0.986812i	−0.0236366	+	0.0409399i
$582$	31.7014	+	54.9084i	1.31406	+	2.27603i
$583$	17.5375	+	30.3758i	0.726327	+	1.25804i
$584$	−5.64038			−0.233401
$585$	14.2068	−	15.4545i	0.587379	−	0.638965i
$586$	34.8449			1.43943
$587$	−0.840587	−	1.45594i	−0.0346947	−	0.0600931i	0.848157	−	0.529746i	$-0.177713\pi$
$587$	−0.840587	−	1.45594i	−0.0346947	−	0.0600931i	−0.882851	+	0.469652i	$0.844379\pi$
$588$	0.487571	+	0.844497i	0.0201071	+	0.0348265i
$589$	2.32004	−	4.01843i	0.0955956	−	0.165576i
$590$	7.08955			0.291872
$591$	−38.8852	+	67.3512i	−1.59952	+	2.77046i
$592$	10.9329	−	18.9363i	0.449338	−	0.778276i
$593$	25.8643			1.06212			0.531060	−	0.847334i	$-0.321794\pi$
$593$	25.8643			1.06212			0.531060	+	0.847334i	$0.321794\pi$
$594$	−13.1454	+	22.7684i	−0.539361	+	0.934200i
$595$	7.02424	+	12.1663i	0.287966	+	0.498771i
$596$	−0.572821	−	0.992155i	−0.0234637	−	0.0406402i
$597$	−77.0594			−3.15383
$598$	10.9200	−	11.8791i	0.446554	−	0.485772i
$599$	1.79594			0.0733800			0.0366900	−	0.999327i	$-0.488319\pi$
$599$	1.79594			0.0733800			0.0366900	+	0.999327i	$0.488319\pi$
$600$	15.6592	+	27.1225i	0.639283	+	1.10727i
$601$	−2.24387	−	3.88650i	−0.0915294	−	0.158534i	0.816625	−	0.577168i	$-0.195842\pi$
$601$	−2.24387	−	3.88650i	−0.0915294	−	0.158534i	−0.908155	+	0.418634i	$0.862509\pi$
$602$	6.25799	−	10.8392i	0.255057	−	0.441771i
$603$	−24.3475			−0.991506
$604$	1.06127	−	1.83818i	0.0431825	−	0.0747944i
$605$	−0.976299	+	1.69100i	−0.0396922	+	0.0687489i
$606$	14.8603			0.603657
$607$	15.0996	−	26.1533i	0.612874	−	1.06153i	−0.377879	−	0.925855i	$-0.623347\pi$
$607$	15.0996	−	26.1533i	0.612874	−	1.06153i	0.990753	−	0.135675i	$-0.0433201\pi$
$608$	1.74997	+	3.03104i	0.0709708	+	0.122925i
$609$	−15.9883	−	27.6925i	−0.647877	−	1.12216i
$610$	22.5763			0.914089
$611$	−25.9061	−	5.78656i	−1.04805	−	0.234099i
$612$	−4.14328			−0.167482
$613$	5.87419	+	10.1744i	0.237256	+	0.410940i	0.959926	−	0.280254i	$-0.0904186\pi$
$613$	5.87419	+	10.1744i	0.237256	+	0.410940i	−0.722670	+	0.691193i	$0.757085\pi$
$614$	−2.55676	−	4.42844i	−0.103182	−	0.178717i
$615$	−5.58299	+	9.67002i	−0.225128	+	0.389933i
$616$	18.7080			0.753767
$617$	17.6219	−	30.5221i	0.709432	−	1.22877i	−0.255636	−	0.966773i	$-0.582285\pi$
$617$	17.6219	−	30.5221i	0.709432	−	1.22877i	0.965068	−	0.262000i	$-0.0843819\pi$
$618$	28.1224	−	48.7094i	1.13125	−	1.95938i
$619$	−8.55565			−0.343881			−0.171940	−	0.985107i	$-0.555004\pi$
$619$	−8.55565			−0.343881			−0.171940	+	0.985107i	$0.555004\pi$
$620$	−0.0746586	+	0.129313i	−0.00299836	+	0.00519332i
$621$	−10.3616	−	17.9468i	−0.415797	−	0.720181i
$622$	5.91231	+	10.2404i	0.237062	+	0.410604i
$623$	12.5876			0.504310
$624$	−25.9712	+	28.2521i	−1.03968	+	1.13099i
$625$	7.81606			0.312643
$626$	−6.28975	−	10.8942i	−0.251389	−	0.435419i
$627$	20.2194	+	35.0209i	0.807483	+	1.39860i
$628$	0.918843	−	1.59148i	0.0366658	−	0.0635071i
$629$	35.0559			1.39777
$630$	8.39130	−	14.5342i	0.334317	−	0.579055i
$631$	21.6388	−	37.4796i	0.861428	−	1.49204i	−0.00912241	−	0.999958i	$-0.502904\pi$
$631$	21.6388	−	37.4796i	0.861428	−	1.49204i	0.870551	−	0.492079i	$-0.163763\pi$
$632$	30.7562			1.22341
$633$	9.41816	−	16.3127i	0.374338	−	0.648373i
$634$	−4.72002	−	8.17532i	−0.187456	−	0.324683i
$635$	4.94938	+	8.57258i	0.196410	+	0.340192i
$636$	4.41239			0.174963
$637$	2.74887	+	8.76697i	0.108914	+	0.347360i
$638$	21.9836			0.870339
$639$	23.8466	+	41.3035i	0.943356	+	1.63394i
$640$	5.61747	+	9.72975i	0.222050	+	0.384602i
$641$	5.41310	−	9.37576i	0.213804	−	0.370320i	−0.739098	−	0.673598i	$-0.764748\pi$
$641$	5.41310	−	9.37576i	0.213804	−	0.370320i	0.952902	+	0.303278i	$0.0980811\pi$
$642$	−47.5542			−1.87682
$643$	5.76329	−	9.98232i	0.227282	−	0.393664i	−0.729720	−	0.683747i	$-0.760349\pi$
$643$	5.76329	−	9.98232i	0.227282	−	0.393664i	0.957002	+	0.290082i	$0.0936827\pi$
$644$	−0.461583	+	0.799485i	−0.0181889	+	0.0315041i
$645$	−13.9066			−0.547572
$646$	18.8782	−	32.6979i	0.742751	−	1.28648i
$647$	6.44020	+	11.1548i	0.253191	+	0.438539i	0.964402	−	0.264439i	$-0.0851867\pi$
$647$	6.44020	+	11.1548i	0.253191	+	0.438539i	−0.711212	+	0.702978i	$0.751853\pi$
$648$	3.64389	+	6.31141i	0.143146	+	0.247935i
$649$	14.1207			0.554286
$650$	5.52692	+	17.6270i	0.216784	+	0.691389i
$651$	−6.04488			−0.236918
$652$	0.795568	+	1.37796i	0.0311568	+	0.0539652i
$653$	−17.1054	−	29.6275i	−0.669387	−	1.15941i	−0.978076	−	0.208250i	$-0.933223\pi$
$653$	−17.1054	−	29.6275i	−0.669387	−	1.15941i	0.308688	−	0.951163i	$-0.400110\pi$
$654$	8.63040	−	14.9483i	0.337475	−	0.584524i
$655$	13.7174			0.535983
$656$	6.47590	−	11.2166i	0.252842	−	0.437934i
$657$	−5.03904	+	8.72788i	−0.196592	+	0.340507i
$658$	−21.2214			−0.827297
$659$	−19.0063	+	32.9199i	−0.740381	+	1.28238i	0.211941	+	0.977282i	$0.432021\pi$
$659$	−19.0063	+	32.9199i	−0.740381	+	1.28238i	−0.952322	+	0.305095i	$0.901312\pi$
$660$	−0.650656	−	1.12697i	−0.0253268	−	0.0438672i
$661$	11.0755	+	19.1833i	0.430786	+	0.746144i	0.996941	−	0.0781549i	$-0.0249029\pi$
$661$	11.0755	+	19.1833i	0.430786	+	0.746144i	−0.566155	+	0.824299i	$0.691570\pi$
$662$	29.9492			1.16401
$663$	−60.0454	−	13.4121i	−2.33197	−	0.520884i
$664$	−1.57417			−0.0610895
$665$	−5.47226	−	9.47824i	−0.212205	−	0.367550i
$666$	−20.9392	−	36.2678i	−0.811378	−	1.40535i
$667$	−8.66408	+	15.0066i	−0.335475	+	0.581059i
$668$	−0.774115			−0.0299514
$669$	−18.2178	+	31.5541i	−0.704339	+	1.21995i
$670$	−3.56988	+	6.18321i	−0.137916	+	0.238878i
$671$	44.9667			1.73592
$672$	2.27978	−	3.94870i	0.0879445	−	0.152324i
$673$	−20.3727	−	35.2866i	−0.785310	−	1.36020i	−0.928813	−	0.370548i	$-0.879170\pi$
$673$	−20.3727	−	35.2866i	−0.785310	−	1.36020i	0.143503	−	0.989650i	$-0.454163\pi$
$674$	20.0182	+	34.6726i	0.771073	+	1.33554i
$675$	23.7253			0.913187
$676$	1.42554	−	0.991416i	0.0548283	−	0.0381314i
$677$	14.8127			0.569298			0.284649	−	0.958632i	$-0.408123\pi$
$677$	14.8127			0.569298			0.284649	+	0.958632i	$0.408123\pi$
$678$	21.0841	+	36.5187i	0.809729	+	1.40249i
$679$	−17.0890	−	29.5989i	−0.655814	−	1.13590i
$680$	−9.70390	+	16.8076i	−0.372127	+	0.644544i
$681$	−43.8447			−1.68013
$682$	2.07790	−	3.59903i	0.0795670	−	0.137814i
$683$	−23.2958	+	40.3494i	−0.891388	+	1.54393i	−0.0531749	+	0.998585i	$0.516934\pi$
$683$	−23.2958	+	40.3494i	−0.891388	+	1.54393i	−0.838213	+	0.545343i	$0.816399\pi$
$684$	3.22784			0.123420
$685$	−3.84463	+	6.65910i	−0.146896	+	0.254431i
$686$	13.7615	+	23.8356i	0.525416	+	0.910047i
$687$	28.6803	+	49.6758i	1.09422	+	1.89525i
$688$	16.1308			0.614980
$689$	40.5739	+	9.06286i	1.54574	+	0.345267i
$690$	−14.3332			−0.545656
$691$	8.96252	+	15.5235i	0.340950	+	0.590543i	0.984609	−	0.174769i	$-0.0559178\pi$
$691$	8.96252	+	15.5235i	0.340950	+	0.590543i	−0.643659	+	0.765312i	$0.722584\pi$
$692$	0.257753	+	0.446440i	0.00979828	+	0.0169711i
$693$	16.7135	−	28.9486i	0.634893	−	1.09967i
$694$	−49.2092			−1.86795
$695$	−7.34412	+	12.7204i	−0.278578	+	0.482512i
$696$	22.0876	−	38.2568i	0.837227	−	1.45012i
$697$	20.7648			0.786521
$698$	−20.1537	+	34.9072i	−0.762828	+	1.32126i
$699$	25.7469	+	44.5949i	0.973836	+	1.68673i
$700$	−0.528451	−	0.915303i	−0.0199736	−	0.0345952i
$701$	22.0032			0.831050			0.415525	−	0.909582i	$-0.363598\pi$
$701$	22.0032			0.831050			0.415525	+	0.909582i	$0.363598\pi$
$702$	9.32323	+	29.7346i	0.351882	+	1.12226i
$703$	−27.3104			−1.03003
$704$	12.8682	+	22.2883i	0.484988	+	0.840023i
$705$	11.7896	+	20.4202i	0.444023	+	0.769071i
$706$	3.04131	−	5.26770i	0.114461	−	0.198253i
$707$	−8.01059			−0.301269
$708$	0.888185	−	1.53838i	0.0333801	−	0.0578159i
$709$	−3.89003	+	6.73773i	−0.146093	+	0.253041i	−0.929780	−	0.368115i	$-0.880003\pi$
$709$	−3.89003	+	6.73773i	−0.146093	+	0.253041i	0.783687	+	0.621156i	$0.213337\pi$
$710$	13.9857			0.524875
$711$	27.4772	−	47.5918i	1.03047	−	1.78483i
$712$	8.69477	+	15.0598i	0.325850	+	0.564389i
$713$	1.63787	+	2.83687i	0.0613387	+	0.106242i
$714$	−49.1872			−1.84078
$715$	−3.66832	−	11.6994i	−0.137188	−	0.437533i
$716$	−1.64536			−0.0614900
$717$	12.2979	+	21.3006i	0.459274	+	0.795486i
$718$	3.32907	+	5.76611i	0.124240	+	0.215189i
$719$	−14.6812	+	25.4286i	−0.547516	+	0.948326i	0.450928	+	0.892560i	$0.351093\pi$
$719$	−14.6812	+	25.4286i	−0.547516	+	0.948326i	−0.998444	+	0.0557651i	$0.982240\pi$
$720$	21.6296			0.806088
$721$	−15.1597	+	26.2573i	−0.564575	+	0.977873i
$722$	−1.72846	+	2.99378i	−0.0643266	+	0.111417i
$723$	−51.7655			−1.92518
$724$	−0.0868891	+	0.150496i	−0.00322921	+	0.00559315i
$725$	−9.91922	−	17.1806i	−0.368391	−	0.638071i
$726$	−3.41826	−	5.92061i	−0.126864	−	0.219734i
$727$	−46.8248			−1.73664			−0.868318	−	0.496008i	$-0.834799\pi$
$727$	−46.8248			−1.73664			−0.868318	+	0.496008i	$0.834799\pi$
$728$	15.0068	−	16.3247i	0.556188	−	0.605035i
$729$	−41.3523			−1.53157
$730$	1.47767	+	2.55940i	0.0546910	+	0.0947276i
$731$	12.9307	+	22.3966i	0.478259	+	0.828368i
$732$	2.82839	−	4.89891i	0.104540	−	0.181069i
$733$	6.43934			0.237842			0.118921	−	0.992904i	$-0.462056\pi$
$733$	6.43934			0.237842			0.118921	+	0.992904i	$0.462056\pi$
$734$	14.8254	−	25.6783i	0.547215	−	0.947804i
$735$	4.08074	−	7.06804i	0.150520	−	0.260709i
$736$	−2.47084			−0.0910765
$737$	−7.11035	+	12.3155i	−0.261913	+	0.453647i
$738$	−12.4030	−	21.4826i	−0.456561	−	0.790787i
$739$	−22.6737	−	39.2719i	−0.834064	−	1.44464i	−0.894790	−	0.446487i	$-0.852675\pi$
$739$	−22.6737	−	39.2719i	−0.834064	−	1.44464i	0.0607262	−	0.998154i	$-0.480658\pi$
$740$	0.878845			0.0323070
$741$	46.7786	+	10.4488i	1.71845	+	0.383846i
$742$	33.2368			1.22016
$743$	−18.4962	−	32.0364i	−0.678560	−	1.17530i	−0.975415	−	0.220377i	$-0.929271\pi$
$743$	−18.4962	−	32.0364i	−0.678560	−	1.17530i	0.296855	−	0.954923i	$-0.404062\pi$
$744$	−4.17546	−	7.23212i	−0.153080	−	0.265142i
$745$	−4.79424	+	8.30387i	−0.175647	+	0.304230i
$746$	−3.48544			−0.127611
$747$	−1.40634	+	2.43585i	−0.0514553	+	0.0891231i
$748$	−1.20999	+	2.09576i	−0.0442416	+	0.0766287i
$749$	25.6346			0.936668
$750$	19.1437	−	33.1579i	0.699029	−	1.21075i
$751$	−13.5444	−	23.4597i	−0.494244	−	0.856055i	0.505734	−	0.862689i	$-0.331222\pi$
$751$	−13.5444	−	23.4597i	−0.494244	−	0.856055i	−0.999978	+	0.00663391i	$0.997888\pi$
$752$	−13.6752	−	23.6862i	−0.498684	−	0.863745i
$753$	−22.0949			−0.805181
$754$	17.6343	−	19.1830i	0.642203	−	0.698604i
$755$	−17.7647			−0.646523
$756$	−0.891430	−	1.54400i	−0.0324210	−	0.0561548i
$757$	1.49511	+	2.58960i	0.0543406	+	0.0941207i	0.891916	−	0.452201i	$-0.149361\pi$
$757$	1.49511	+	2.58960i	0.0543406	+	0.0941207i	−0.837576	+	0.546322i	$0.816028\pi$
$758$	−5.18213	+	8.97571i	−0.188223	+	0.326012i
$759$	−28.5483			−1.03624
$760$	7.55986	−	13.0941i	0.274225	−	0.474972i
$761$	−23.6134	+	40.8997i	−0.855987	+	1.48261i	0.0197400	+	0.999805i	$0.493716\pi$
$761$	−23.6134	+	40.8997i	−0.855987	+	1.48261i	−0.875727	+	0.482807i	$0.839617\pi$
$762$	−34.6580			−1.25553
$763$	−4.65231	+	8.05803i	−0.168425	+	0.291720i
$764$	0.685960	+	1.18812i	0.0248172	+	0.0429846i
$765$	17.3387	+	30.0314i	0.626881	+	1.08579i
$766$	−20.0798			−0.725514
$767$	11.3270	−	12.3218i	0.408995	−	0.444915i
$768$	9.14225			0.329893
$769$	3.32873	+	5.76553i	0.120037	+	0.207910i	0.919782	−	0.392430i	$-0.128365\pi$
$769$	3.32873	+	5.76553i	0.120037	+	0.207910i	−0.799745	+	0.600340i	$0.795032\pi$
$770$	−4.90113	−	8.48901i	−0.176625	−	0.305923i
$771$	20.0047	−	34.6491i	0.720451	−	1.24786i
$772$	−2.67191			−0.0961640
$773$	−14.4401	+	25.0109i	−0.519373	+	0.899580i	0.480374	+	0.877064i	$0.340501\pi$
$773$	−14.4401	+	25.0109i	−0.519373	+	0.899580i	−0.999746	+	0.0225158i	$0.992832\pi$
$774$	15.4473	−	26.7554i	0.555240	−	0.961705i
$775$	−3.75029			−0.134714
$776$	23.6082	−	40.8906i	0.847484	−	1.46789i
$777$	17.7894	+	30.8121i	0.638190	+	1.10538i
$778$	−3.53440	−	6.12176i	−0.126714	−	0.219476i
$779$	−16.1769			−0.579597
$780$	−1.50533	−	0.336240i	−0.0538994	−	0.0120393i
$781$	27.8563			0.996776
$782$	13.3273	+	23.0836i	0.476585	+	0.825469i
$783$	−16.7325	−	28.9815i	−0.597970	−	1.03572i
$784$	−4.73339	+	8.19847i	−0.169050	+	0.292803i
$785$	−15.3806			−0.548956
$786$	−24.0140	+	41.5934i	−0.856550	+	1.48359i
$787$	25.1587	−	43.5761i	0.896809	−	1.55332i	0.0652603	−	0.997868i	$-0.479212\pi$
$787$	25.1587	−	43.5761i	0.896809	−	1.55332i	0.831549	−	0.555451i	$-0.187454\pi$
$788$	3.62574			0.129162
$789$	17.0688	−	29.5641i	0.607666	−	1.05251i
$790$	−8.05752	−	13.9560i	−0.286674	−	0.496533i
$791$	−11.3656	−	19.6858i	−0.404114	−	0.699946i
$792$	46.1789			1.64090
$793$	36.0704	−	39.2382i	1.28090	−	1.39339i
$794$	30.3675			1.07770
$795$	−18.4648	−	31.9820i	−0.654879	−	1.13428i
$796$	1.79630	+	3.11128i	0.0636681	+	0.110276i
$797$	9.93134	−	17.2016i	0.351786	−	0.609311i	−0.634776	−	0.772696i	$-0.718908\pi$
$797$	9.93134	−	17.2016i	0.351786	−	0.609311i	0.986562	+	0.163385i	$0.0522411\pi$
$798$	38.3195			1.35649
$799$	21.9245	−	37.9744i	0.775635	−	1.34344i
$800$	1.41439	−	2.44980i	0.0500063	−	0.0866135i
$801$	31.0712			1.09785
$802$	−9.99921	+	17.3191i	−0.353084	+	0.611560i
$803$	2.94317	+	5.09772i	0.103862	+	0.179895i
$804$	0.894475	+	1.54928i	0.0315457	+	0.0546388i
$805$	7.72646			0.272322
$806$	−1.47373	−	4.70018i	−0.0519100	−	0.165557i
$807$	47.1739			1.66060
$808$	−5.53326	−	9.58389i	−0.194660	−	0.337160i
$809$	23.8164	+	41.2512i	0.837341	+	1.45032i	0.892110	+	0.451817i	$0.149224\pi$
$809$	23.8164	+	41.2512i	0.837341	+	1.45032i	−0.0547699	+	0.998499i	$0.517443\pi$
$810$	1.90926	−	3.30693i	0.0670844	−	0.116194i
$811$	−8.54395			−0.300019			−0.150009	−	0.988685i	$-0.547930\pi$
$811$	−8.54395			−0.300019			−0.150009	+	0.988685i	$0.547930\pi$
$812$	−0.745390	+	1.29105i	−0.0261580	+	0.0453071i
$813$	−34.1041	+	59.0700i	−1.19608	+	2.07168i
$814$	−24.4601			−0.857325
$815$	6.65853	−	11.5329i	0.233238	−	0.403980i
$816$	−31.6965	−	54.9000i	−1.10960	−	1.92188i
$817$	−10.0737	−	17.4482i	−0.352434	−	0.610434i
$818$	−24.6922			−0.863342
$819$	−11.8539	−	37.8056i	−0.414208	−	1.32104i
$820$	0.520570			0.0181791
$821$	−13.7604	−	23.8337i	−0.480241	−	0.831801i	0.519502	−	0.854469i	$-0.326117\pi$
$821$	−13.7604	−	23.8337i	−0.480241	−	0.831801i	−0.999743	+	0.0226678i	$0.992784\pi$
$822$	−13.4610	−	23.3152i	−0.469507	−	0.813210i
$823$	−25.9128	+	44.8823i	−0.903263	+	1.56450i	−0.0800316	+	0.996792i	$0.525502\pi$
$823$	−25.9128	+	44.8823i	−0.903263	+	1.56450i	−0.823232	+	0.567706i	$0.807831\pi$
$824$	−41.8857			−1.45916
$825$	16.3420	−	28.3052i	0.568956	−	0.985461i
$826$	6.69035	−	11.5880i	0.232787	−	0.403199i
$827$	3.45561			0.120163			0.0600817	−	0.998193i	$-0.480864\pi$
$827$	3.45561			0.120163			0.0600817	+	0.998193i	$0.480864\pi$
$828$	−1.13937	+	1.97345i	−0.0395959	+	0.0685822i
$829$	10.1672	+	17.6102i	0.353123	+	0.611627i	0.986795	−	0.161975i	$-0.0517864\pi$
$829$	10.1672	+	17.6102i	0.353123	+	0.611627i	−0.633672	+	0.773602i	$0.718453\pi$
$830$	0.412401	+	0.714299i	0.0143146	+	0.0247937i
$831$	51.1004			1.77265
$832$	29.7712	+	6.64990i	1.03213	+	0.230544i
$833$	−15.1775			−0.525868
$834$	−25.7136	−	44.5372i	−0.890388	−	1.54220i
$835$	3.23949	+	5.61096i	0.112107	+	0.194175i
$836$	0.942648	−	1.63271i	0.0326022	−	0.0564686i
$837$	−6.32626			−0.218668
$838$	−14.4680	+	25.0593i	−0.499788	+	0.865658i
$839$	−1.59940	+	2.77024i	−0.0552173	+	0.0956392i	−0.892313	−	0.451418i	$-0.850918\pi$
$839$	−1.59940	+	2.77024i	−0.0552173	+	0.0956392i	0.837095	+	0.547057i	$0.184252\pi$
$840$	−19.6973			−0.679620
$841$	0.508753	−	0.881186i	0.0175432	−	0.0303857i
$842$	14.4420	+	25.0142i	0.497703	+	0.862047i
$843$	3.08721	+	5.34721i	0.106329	+	0.184168i
$844$	−0.878169			−0.0302278
$845$	−13.1515	−	6.18376i	−0.452427	−	0.212728i
$846$	−52.3830			−1.80097
$847$	1.84265	+	3.19156i	0.0633142	+	0.109663i
$848$	21.4180	+	37.0970i	0.735497	+	1.27392i
$849$	−23.6134	+	40.8997i	−0.810411	+	1.40367i
$850$	−30.5160			−1.04669
$851$	9.64011	−	16.6972i	0.330459	−	0.572371i
$852$	1.75215	−	3.03481i	0.0600276	−	0.103971i
$853$	−17.2610			−0.591005			−0.295503	−	0.955342i	$-0.595487\pi$
$853$	−17.2610			−0.591005			−0.295503	+	0.955342i	$0.595487\pi$
$854$	21.3051	−	36.9015i	0.729046	−	1.26274i
$855$	−13.5078	−	23.3961i	−0.461956	−	0.800130i
$856$	17.7069	+	30.6693i	0.605211	+	1.04826i
$857$	40.0707			1.36879			0.684395	−	0.729111i	$-0.260066\pi$
$857$	40.0707			1.36879			0.684395	+	0.729111i	$0.260066\pi$
$858$	41.8964	+	9.35827i	1.43032	+	0.319486i
$859$	−43.2804			−1.47671			−0.738354	−	0.674413i	$-0.764397\pi$
$859$	−43.2804			−1.47671			−0.738354	+	0.674413i	$0.764397\pi$
$860$	0.324170	+	0.561480i	0.0110541	+	0.0191463i
$861$	10.5372	+	18.2510i	0.359108	+	0.621993i
$862$	−17.9959	+	31.1699i	−0.612944	+	1.06165i
$863$	6.89674			0.234768			0.117384	−	0.993087i	$-0.462549\pi$
$863$	6.89674			0.234768			0.117384	+	0.993087i	$0.462549\pi$
$864$	2.38590	−	4.13251i	0.0811701	−	0.140591i
$865$	2.15727	−	3.73650i	0.0733493	−	0.127045i
$866$	−12.0624			−0.409896
$867$	26.4645	−	45.8379i	0.898783	−	1.55674i
$868$	0.140909	+	0.244062i	0.00478278	+	0.00828402i
$869$	−16.0487	−	27.7971i	−0.544414	−	0.942952i
$870$	−23.1461			−0.784725
$871$	5.04295	+	16.0835i	0.170874	+	0.544969i
$872$	−12.8542			−0.435298
$873$	−42.1824	−	73.0621i	−1.42766	−	2.47278i
$874$	−10.3827	−	17.9834i	−0.351201	−	0.608298i
$875$	−10.3196	+	17.8741i	−0.348867	+	0.604255i
$876$	0.740496			0.0250190
$877$	12.4464	−	21.5577i	0.420284	−	0.727953i	−0.575683	−	0.817673i	$-0.695264\pi$
$877$	12.4464	−	21.5577i	0.420284	−	0.727953i	0.995967	+	0.0897201i	$0.0285973\pi$
$878$	−1.88068	+	3.25743i	−0.0634698	+	0.109933i
$879$	−73.0728			−2.46468
$880$	6.31664	−	10.9407i	0.212934	−	0.368812i
$881$	16.0671	+	27.8290i	0.541314	+	0.937583i	0.998829	+	0.0483809i	$0.0154061\pi$
$881$	16.0671	+	27.8290i	0.541314	+	0.937583i	−0.457515	+	0.889202i	$0.651261\pi$
$882$	9.06565	+	15.7022i	0.305256	+	0.528719i
$883$	−8.48864			−0.285666			−0.142833	−	0.989747i	$-0.545621\pi$
$883$	−8.48864			−0.285666			−0.142833	+	0.989747i	$0.545621\pi$
$884$	0.858174	+	2.73698i	0.0288635	+	0.0920545i
$885$	−14.8674			−0.499762
$886$	−26.8179	−	46.4499i	−0.900964	−	1.56052i
$887$	−12.6267	−	21.8700i	−0.423962	−	0.734324i	0.572361	−	0.820002i	$-0.306028\pi$
$887$	−12.6267	−	21.8700i	−0.423962	−	0.734324i	−0.996323	+	0.0856779i	$0.972694\pi$
$888$	−24.5758	+	42.5665i	−0.824709	+	1.42844i
$889$	18.6828			0.626600
$890$	4.55572	−	7.89074i	0.152708	−	0.264498i
$891$	3.80279	−	6.58662i	0.127398	−	0.220660i
$892$	1.69866			0.0568754
$893$	−17.0804	+	29.5841i	−0.571574	+	0.989995i
$894$	−16.7858	−	29.0739i	−0.561402	−	0.972376i
$895$	6.88545	+	11.9259i	0.230155	+	0.398640i
$896$	21.2046			0.708398
$897$	−22.9003	+	24.9115i	−0.764618	+	0.831769i
$898$	21.0252			0.701620
$899$	2.64492	+	4.58114i	0.0882132	+	0.152790i
$900$	−1.30443	−	2.25934i	−0.0434810	−	0.0753113i
$901$	−34.3380	+	59.4752i	−1.14397	+	1.98141i
$902$	−14.4885			−0.482415
$903$	−13.1236	+	22.7307i	−0.436724	+	0.756429i
$904$	15.7014	−	27.1956i	0.522221	−	0.904514i
$905$	1.45444			0.0483473
$906$	31.0993	−	53.8655i	1.03320	−	1.78956i
$907$	−15.1350	−	26.2145i	−0.502548	−	0.870439i	−0.999996	−	0.00294461i	$-0.999063\pi$
$907$	−15.1350	−	26.2145i	−0.502548	−	0.870439i	0.497448	−	0.867494i	$-0.334271\pi$
$908$	1.02204	+	1.77023i	0.0339177	+	0.0587472i
$909$	−19.7734			−0.655841
$910$	−11.3390	−	2.53277i	−0.375886	−	0.0839604i
$911$	8.35528			0.276823			0.138411	−	0.990375i	$-0.455800\pi$
$911$	8.35528			0.276823			0.138411	+	0.990375i	$0.455800\pi$
$912$	24.6933	+	42.7701i	0.817677	+	1.41626i
$913$	0.821405	+	1.42272i	0.0271845	+	0.0470850i
$914$	9.56091	−	16.5600i	0.316247	−	0.547755i
$915$	−47.3445			−1.56516
$916$	1.33711	−	2.31594i	0.0441793	−	0.0765208i
$917$	12.9450	−	22.4214i	0.427481	−	0.740419i
$918$	−51.4768			−1.69899
$919$	14.8823	−	25.7768i	0.490920	−	0.850299i	−0.509025	−	0.860752i	$-0.669994\pi$
$919$	14.8823	−	25.7768i	0.490920	−	0.850299i	0.999945	+	0.0104528i	$0.00332730\pi$
$920$	5.33700	+	9.24396i	0.175956	+	0.304764i
$921$	5.36174	+	9.28681i	0.176675	+	0.306011i
$922$	−22.4678			−0.739937
$923$	22.3451	−	24.3076i	0.735499	−	0.800093i
$924$	−2.45608			−0.0807989
$925$	11.0366	+	19.1160i	0.362882	+	0.628531i
$926$	−5.17737	−	8.96748i	−0.170139	−	0.294690i
$927$	−37.4202	+	64.8136i	−1.22904	+	2.12876i
$928$	−3.99005			−0.130980
$929$	−29.6892	+	51.4233i	−0.974073	+	1.68714i	−0.291110	+	0.956690i	$0.594025\pi$
$929$	−29.6892	+	51.4233i	−0.974073	+	1.68714i	−0.682962	+	0.730454i	$0.739309\pi$
$930$	−2.18778	+	3.78935i	−0.0717401	+	0.124258i
$931$	11.8241			0.387518
$932$	1.20035	−	2.07906i	0.0393186	−	0.0681019i
$933$	−12.3986	−	21.4751i	−0.405913	−	0.703062i
$934$	−6.98645	−	12.1009i	−0.228604	−	0.395953i
$935$	20.2541			0.662380
$936$	37.0428	−	40.2960i	1.21078	−	1.31712i
$937$	−15.7956			−0.516020			−0.258010	−	0.966142i	$-0.583067\pi$
$937$	−15.7956			−0.516020			−0.258010	+	0.966142i	$0.583067\pi$
$938$	6.73773	+	11.6701i	0.219995	+	0.381042i
$939$	13.1901	+	22.8460i	0.430444	+	0.745551i
$940$	0.549645	−	0.952014i	0.0179275	−	0.0310513i
$941$	−26.6027			−0.867223			−0.433611	−	0.901100i	$-0.642761\pi$
$941$	−26.6027			−0.867223			−0.433611	+	0.901100i	$0.642761\pi$
$942$	26.9256	−	46.6365i	0.877283	−	1.51950i
$943$	5.71016	−	9.89029i	0.185948	−	0.322072i
$944$	17.2452			0.561284
$945$	−7.46085	+	12.9226i	−0.242702	+	0.420371i
$946$	−9.02233	−	15.6271i	−0.293341	−	0.508082i
$947$	−10.8966	−	18.8734i	−0.354091	−	0.613304i	0.632871	−	0.774257i	$-0.281876\pi$
$947$	−10.8966	−	18.8734i	−0.354091	−	0.613304i	−0.986962	+	0.160953i	$0.948543\pi$
$948$	−4.03781			−0.131142
$949$	6.80918	+	1.52095i	0.221035	+	0.0493720i
$950$	23.7737			0.771319
$951$	9.89829	+	17.1443i	0.320974	+	0.555943i
$952$	18.3150	+	31.7225i	0.593592	+	1.02813i
$953$	−4.47999	+	7.75958i	−0.145121	+	0.251357i	−0.929418	−	0.369028i	$-0.879691\pi$
$953$	−4.47999	+	7.75958i	−0.145121	+	0.251357i	0.784297	+	0.620386i	$0.213024\pi$
$954$	82.0418			2.65620
$955$	5.74116	−	9.94399i	0.185780	−	0.321780i
$956$	0.573342	−	0.993058i	0.0185432	−	0.0321178i
$957$	−46.1015			−1.49025
$958$	−21.9109	+	37.9508i	−0.707909	+	1.22614i
$959$	7.25630	+	12.5683i	0.234318	+	0.405851i
$960$	−13.5486	−	23.4669i	−0.437280	−	0.757391i
$961$	1.00000			0.0322581
$962$	−19.6208	+	21.3440i	−0.632601	+	0.688159i
$963$	63.2766			2.03906
$964$	1.20668	+	2.09003i	0.0388646	+	0.0673154i
$965$	11.1813	+	19.3666i	0.359939	+	0.623432i
$966$	−13.5261	+	23.4279i	−0.435196	+	0.753781i
$967$	8.89357			0.285998			0.142999	−	0.989723i	$-0.454325\pi$
$967$	8.89357			0.285998			0.142999	+	0.989723i	$0.454325\pi$
$968$	−2.54560	+	4.40911i	−0.0818186	+	0.141714i
$969$	−39.5891	+	68.5704i	−1.27179	+	2.20280i
$970$	−24.7395			−0.794338
$971$	30.4454	−	52.7330i	0.977040	−	1.69228i	0.304007	−	0.952670i	$-0.401675\pi$
$971$	30.4454	−	52.7330i	0.977040	−	1.69228i	0.673033	−	0.739613i	$-0.264991\pi$
$972$	0.789098	+	1.36676i	0.0253103	+	0.0438388i
$973$	13.8612	+	24.0082i	0.444369	+	0.769669i
$974$	38.9725			1.24876
$975$	−11.5904	−	36.9654i	−0.371191	−	1.18384i
$976$	54.9166			1.75784
$977$	−26.3864	−	45.7026i	−0.844176	−	1.46216i	−0.886335	−	0.463045i	$-0.846757\pi$
$977$	−26.3864	−	45.7026i	−0.844176	−	1.46216i	0.0421585	−	0.999111i	$-0.486577\pi$
$978$	23.3131	+	40.3796i	0.745472	+	1.29120i
$979$	9.07392	−	15.7165i	0.290004	−	0.502301i
$980$	−0.380497			−0.0121545
$981$	−11.4838	+	19.8905i	−0.366649	+	0.635054i
$982$	1.07175	−	1.85632i	0.0342009	−	0.0592377i
$983$	−40.8576			−1.30316			−0.651578	−	0.758581i	$-0.725893\pi$
$983$	−40.8576			−1.30316			−0.651578	+	0.758581i	$0.725893\pi$
$984$	−14.5571	+	25.2136i	−0.464062	+	0.803779i
$985$	−15.1729	−	26.2802i	−0.483448	−	0.837357i
$986$	21.5217	+	37.2767i	0.685392	+	1.18713i
$987$	44.5031			1.41655
$988$	−0.668564	−	2.13225i	−0.0212699	−	0.0678360i
$989$	14.2234			0.452277
$990$	−12.0980	−	20.9543i	−0.384499	−	0.665972i
$991$	7.24680	+	12.5518i	0.230202	+	0.398722i	0.957867	−	0.287210i	$-0.0927279\pi$
$991$	7.24680	+	12.5518i	0.230202	+	0.398722i	−0.727665	+	0.685932i	$0.759395\pi$
$992$	−0.377143	+	0.653230i	−0.0119743	+	0.0207401i
$993$	−62.8060			−1.99309
$994$	13.1982	−	22.8600i	0.418622	−	0.725075i
$995$	15.0342	−	26.0399i	0.476615	−	0.825521i
$996$	0.206664			0.00654840
$997$	−12.3028	+	21.3091i	−0.389634	+	0.674866i	−0.992400	−	0.123052i	$-0.960732\pi$
$997$	−12.3028	+	21.3091i	−0.389634	+	0.674866i	0.602766	+	0.797918i	$0.294065\pi$
$998$	20.0037	+	34.6473i	0.633205	+	1.09674i
$999$	18.6174	+	32.2463i	0.589030	+	1.02023i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.f.c.94.8	✓	36
13.3	even	3		5239.2.a.p.1.11		18
13.9	even	3	inner	403.2.f.c.373.8	yes	36
13.10	even	6		5239.2.a.o.1.8		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.f.c.94.8	✓	36	1.1	even	1	trivial
403.2.f.c.373.8	yes	36	13.9	even	3	inner
5239.2.a.o.1.8		18	13.10	even	6
5239.2.a.p.1.11		18	13.3	even	3

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.683087 - 1.18314i) q^{2} +(1.43249 + 2.48115i) q^{3} +(0.0667843 - 0.115674i) q^{4} -1.11791 q^{5} +(1.95703 - 3.38968i) q^{6} +(-1.05496 + 1.82724i) q^{7} -2.91483 q^{8} +(-2.60407 + 4.51038i) q^{9} +O(q^{10})\)	\(q+(-0.683087 - 1.18314i) q^{2} +(1.43249 + 2.48115i) q^{3} +(0.0667843 - 0.115674i) q^{4} -1.11791 q^{5} +(1.95703 - 3.38968i) q^{6} +(-1.05496 + 1.82724i) q^{7} -2.91483 q^{8} +(-2.60407 + 4.51038i) q^{9} +(0.763627 + 1.32264i) q^{10} +(1.52097 + 2.63439i) q^{11} +0.382672 q^{12} +(3.51884 + 0.785991i) q^{13} +2.88252 q^{14} +(-1.60139 - 2.77369i) q^{15} +(1.85751 + 3.21730i) q^{16} +(-2.97802 + 5.15809i) q^{17} +7.11522 q^{18} +(2.32004 - 4.01843i) q^{19} +(-0.0746586 + 0.129313i) q^{20} -6.04488 q^{21} +(2.07790 - 3.59903i) q^{22} +(1.63787 + 2.83687i) q^{23} +(-4.17546 - 7.23212i) q^{24} -3.75029 q^{25} +(-1.47373 - 4.70018i) q^{26} -6.32626 q^{27} +(0.140909 + 0.244062i) q^{28} +(2.64492 + 4.58114i) q^{29} +(-2.18778 + 3.78935i) q^{30} +1.00000 q^{31} +(-0.377143 + 0.653230i) q^{32} +(-4.35754 + 7.54748i) q^{33} +8.13699 q^{34} +(1.17935 - 2.04269i) q^{35} +(0.347822 + 0.602445i) q^{36} +(-2.94288 - 5.09722i) q^{37} -6.33916 q^{38} +(3.09054 + 9.85669i) q^{39} +3.25850 q^{40} +(-1.74317 - 3.01925i) q^{41} +(4.12918 + 7.15195i) q^{42} +(2.17102 - 3.76031i) q^{43} +0.406307 q^{44} +(2.91110 - 5.04218i) q^{45} +(2.23762 - 3.87566i) q^{46} -7.36211 q^{47} +(-5.32174 + 9.21752i) q^{48} +(1.27412 + 2.20684i) q^{49} +(2.56177 + 4.43712i) q^{50} -17.0640 q^{51} +(0.325922 - 0.354545i) q^{52} +11.5305 q^{53} +(4.32139 + 7.48486i) q^{54} +(-1.70030 - 2.94500i) q^{55} +(3.07502 - 5.32610i) q^{56} +13.2938 q^{57} +(3.61343 - 6.25864i) q^{58} +(2.32101 - 4.02011i) q^{59} -0.427791 q^{60} +(7.39115 - 12.8018i) q^{61} +(-0.683087 - 1.18314i) q^{62} +(-5.49437 - 9.51652i) q^{63} +8.46053 q^{64} +(-3.93373 - 0.878665i) q^{65} +11.9063 q^{66} +(2.33745 + 4.04858i) q^{67} +(0.397770 + 0.688959i) q^{68} +(-4.69247 + 8.12760i) q^{69} -3.22238 q^{70} +(4.57872 - 7.93057i) q^{71} +(7.59040 - 13.1470i) q^{72} +1.93507 q^{73} +(-4.02049 + 6.96369i) q^{74} +(-5.37225 - 9.30502i) q^{75} +(-0.309885 - 0.536736i) q^{76} -6.41823 q^{77} +(9.55074 - 10.3895i) q^{78} -10.5516 q^{79} +(-2.07652 - 3.59664i) q^{80} +(-1.25012 - 2.16528i) q^{81} +(-2.38147 + 4.12483i) q^{82} +0.540055 q^{83} +(-0.403703 + 0.699235i) q^{84} +(3.32915 - 5.76626i) q^{85} -5.93198 q^{86} +(-7.57766 + 13.1249i) q^{87} +(-4.43335 - 7.67879i) q^{88} +(-2.98295 - 5.16662i) q^{89} -7.95415 q^{90} +(-5.14843 + 5.60058i) q^{91} +0.437536 q^{92} +(1.43249 + 2.48115i) q^{93} +(5.02896 + 8.71042i) q^{94} +(-2.59359 + 4.49223i) q^{95} -2.16102 q^{96} +(-8.09934 + 14.0285i) q^{97} +(1.74067 - 3.01493i) q^{98} -15.8428 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9}+O(q^{10}) \) 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9	\( 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9} - 3 q^{10} - 17 q^{11} + 8 q^{12} + 8 q^{13} + 4 q^{14} - 12 q^{15} - 17 q^{16} + 7 q^{17} - 14 q^{18} - 4 q^{19} - 15 q^{20} + 28 q^{21} - 30 q^{22} + 4 q^{23} - 48 q^{24} + 24 q^{25} + 25 q^{26} - 6 q^{27} - q^{28} + 15 q^{29} + 35 q^{30} + 36 q^{31} - 35 q^{32} - 17 q^{33} - 6 q^{34} - 17 q^{35} - 35 q^{36} - 3 q^{37} + 14 q^{38} + 3 q^{39} - 2 q^{40} - 44 q^{41} + 57 q^{42} + 4 q^{43} + 64 q^{44} + 5 q^{45} - 13 q^{46} + 24 q^{47} - 89 q^{48} - 44 q^{49} - 84 q^{50} - 28 q^{51} + 50 q^{52} - 28 q^{53} - 21 q^{54} + 29 q^{55} + 11 q^{56} + 32 q^{57} + 49 q^{58} - 11 q^{59} + 54 q^{60} - 4 q^{61} - 5 q^{62} - 9 q^{63} + 34 q^{64} - 5 q^{65} + 52 q^{66} - 16 q^{67} + 53 q^{68} + 4 q^{69} - 44 q^{70} - 5 q^{71} - 27 q^{72} + 64 q^{73} + q^{74} - 98 q^{75} - 42 q^{76} - 22 q^{77} + 143 q^{78} - 6 q^{79} - 2 q^{80} + 10 q^{81} + 22 q^{82} + 36 q^{83} + 38 q^{84} + 2 q^{85} + 84 q^{86} - 34 q^{87} - 69 q^{88} - 54 q^{89} - 32 q^{90} - 43 q^{91} - 86 q^{92} + 44 q^{94} - 2 q^{95} + 170 q^{96} - 28 q^{97} - 29 q^{98} + 154 q^{99}+O(q^{100}) \) 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9 - 3 * q^10 - 17 * q^11 + 8 * q^12 + 8 * q^13 + 4 * q^14 - 12 * q^15 - 17 * q^16 + 7 * q^17 - 14 * q^18 - 4 * q^19 - 15 * q^20 + 28 * q^21 - 30 * q^22 + 4 * q^23 - 48 * q^24 + 24 * q^25 + 25 * q^26 - 6 * q^27 - q^28 + 15 * q^29 + 35 * q^30 + 36 * q^31 - 35 * q^32 - 17 * q^33 - 6 * q^34 - 17 * q^35 - 35 * q^36 - 3 * q^37 + 14 * q^38 + 3 * q^39 - 2 * q^40 - 44 * q^41 + 57 * q^42 + 4 * q^43 + 64 * q^44 + 5 * q^45 - 13 * q^46 + 24 * q^47 - 89 * q^48 - 44 * q^49 - 84 * q^50 - 28 * q^51 + 50 * q^52 - 28 * q^53 - 21 * q^54 + 29 * q^55 + 11 * q^56 + 32 * q^57 + 49 * q^58 - 11 * q^59 + 54 * q^60 - 4 * q^61 - 5 * q^62 - 9 * q^63 + 34 * q^64 - 5 * q^65 + 52 * q^66 - 16 * q^67 + 53 * q^68 + 4 * q^69 - 44 * q^70 - 5 * q^71 - 27 * q^72 + 64 * q^73 + q^74 - 98 * q^75 - 42 * q^76 - 22 * q^77 + 143 * q^78 - 6 * q^79 - 2 * q^80 + 10 * q^81 + 22 * q^82 + 36 * q^83 + 38 * q^84 + 2 * q^85 + 84 * q^86 - 34 * q^87 - 69 * q^88 - 54 * q^89 - 32 * q^90 - 43 * q^91 - 86 * q^92 + 44 * q^94 - 2 * q^95 + 170 * q^96 - 28 * q^97 - 29 * q^98 + 154 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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