LMFDB - Embedded newform 403.2.k.e.287.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(66,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("403.66");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.k (of order $5$, degree $4$, 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:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			287.3
Character	$\chi$	$=$	403.287
Dual form			403.2.k.e.66.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.651553 + 2.00527i) q^{2} +(-0.602423 - 1.85407i) q^{3} +(-1.97856 - 1.43751i) q^{4} +2.75944 q^{5} +4.11042 q^{6} +(-1.61436 - 1.17290i) q^{7} +(0.760164 - 0.552291i) q^{8} +(-0.647600 + 0.470509i) q^{9} +O(q^{10})$	\(q+(-0.651553 + 2.00527i) q^{2} +(-0.602423 - 1.85407i) q^{3} +(-1.97856 - 1.43751i) q^{4} +2.75944 q^{5} +4.11042 q^{6} +(-1.61436 - 1.17290i) q^{7} +(0.760164 - 0.552291i) q^{8} +(-0.647600 + 0.470509i) q^{9} +(-1.79792 + 5.53344i) q^{10} +(-1.52627 - 1.10890i) q^{11} +(-1.47331 + 4.53438i) q^{12} +(0.309017 + 0.951057i) q^{13} +(3.40383 - 2.47302i) q^{14} +(-1.66235 - 5.11620i) q^{15} +(-0.899280 - 2.76770i) q^{16} +(5.81579 - 4.22542i) q^{17} +(-0.521553 - 1.60518i) q^{18} +(1.47010 - 4.52451i) q^{19} +(-5.45973 - 3.96673i) q^{20} +(-1.20211 + 3.69971i) q^{21} +(3.21809 - 2.33808i) q^{22} +(0.365759 - 0.265740i) q^{23} +(-1.48192 - 1.07668i) q^{24} +2.61454 q^{25} -2.10847 q^{26} +(-3.46901 - 2.52038i) q^{27} +(1.50806 + 4.64132i) q^{28} +(1.43621 - 4.42019i) q^{29} +11.3425 q^{30} +(-0.697017 + 5.52396i) q^{31} +8.01515 q^{32} +(-1.13651 + 3.49783i) q^{33} +(4.68382 + 14.4153i) q^{34} +(-4.45474 - 3.23656i) q^{35} +1.95768 q^{36} +11.6410 q^{37} +(8.11502 + 5.89591i) q^{38} +(1.57716 - 1.14588i) q^{39} +(2.09763 - 1.52402i) q^{40} +(0.313473 - 0.964771i) q^{41} +(-6.63570 - 4.82111i) q^{42} +(-2.62766 + 8.08711i) q^{43} +(1.42577 + 4.38805i) q^{44} +(-1.78702 + 1.29834i) q^{45} +(0.294569 + 0.906591i) q^{46} +(0.618792 + 1.90445i) q^{47} +(-4.58975 + 3.33465i) q^{48} +(-0.932659 - 2.87043i) q^{49} +(-1.70351 + 5.24286i) q^{50} +(-11.3378 - 8.23738i) q^{51} +(0.755744 - 2.32594i) q^{52} +(-0.445724 + 0.323837i) q^{53} +(7.31429 - 5.31414i) q^{54} +(-4.21165 - 3.05995i) q^{55} -1.87496 q^{56} -9.27436 q^{57} +(7.92791 + 5.75997i) q^{58} +(-2.42331 - 7.45817i) q^{59} +(-4.06551 + 12.5124i) q^{60} -9.19132 q^{61} +(-10.6229 - 4.99686i) q^{62} +1.59732 q^{63} +(-3.42373 + 10.5372i) q^{64} +(0.852715 + 2.62439i) q^{65} +(-6.27361 - 4.55804i) q^{66} +6.19938 q^{67} -17.5810 q^{68} +(-0.713041 - 0.518055i) q^{69} +(9.39267 - 6.82417i) q^{70} +(-3.23916 + 2.35339i) q^{71} +(-0.232424 + 0.715327i) q^{72} +(8.87119 + 6.44530i) q^{73} +(-7.58474 + 23.3434i) q^{74} +(-1.57506 - 4.84752i) q^{75} +(-9.41271 + 6.83874i) q^{76} +(1.16332 + 3.58032i) q^{77} +(1.27019 + 3.90924i) q^{78} +(6.94872 - 5.04854i) q^{79} +(-2.48151 - 7.63731i) q^{80} +(-3.32523 + 10.2340i) q^{81} +(1.73038 + 1.25720i) q^{82} +(-2.88738 + 8.88644i) q^{83} +(7.69682 - 5.59207i) q^{84} +(16.0484 - 11.6598i) q^{85} +(-14.5048 - 10.5384i) q^{86} -9.06052 q^{87} -1.77265 q^{88} +(-4.91459 - 3.57066i) q^{89} +(-1.43920 - 4.42939i) q^{90} +(0.616630 - 1.89779i) q^{91} -1.10568 q^{92} +(10.6617 - 2.03545i) q^{93} -4.22211 q^{94} +(4.05666 - 12.4851i) q^{95} +(-4.82851 - 14.8606i) q^{96} +(-6.66010 - 4.83885i) q^{97} +6.36367 q^{98} +1.51016 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9}+O(q^{10}) $ 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9	\( 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9} - 13 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 3 q^{14} - 14 q^{15} + 9 q^{16} + 12 q^{17} - 19 q^{18} - 4 q^{19} - 53 q^{20} - 13 q^{21} - 14 q^{22} - 9 q^{23} + 2 q^{24} + 96 q^{25} + 12 q^{26} + 25 q^{27} - 25 q^{28} - 78 q^{30} - 2 q^{31} + 76 q^{32} + 29 q^{33} - 15 q^{34} - 36 q^{35} + 52 q^{36} + 24 q^{37} - 19 q^{38} + 3 q^{39} - 12 q^{40} - 40 q^{41} + 11 q^{42} - 22 q^{43} + 4 q^{44} + 63 q^{45} - 24 q^{46} + 3 q^{47} + 68 q^{48} + 33 q^{49} - 76 q^{50} - 59 q^{51} - 13 q^{52} - q^{53} + 18 q^{54} - 22 q^{55} + 78 q^{56} - 16 q^{57} + 5 q^{58} - 18 q^{59} + 43 q^{60} - 32 q^{61} - 39 q^{62} + 20 q^{63} + 23 q^{64} + 2 q^{65} + 11 q^{66} + 114 q^{67} + 98 q^{68} - 46 q^{69} + 32 q^{70} - 2 q^{71} + 28 q^{72} + 10 q^{73} - 43 q^{74} - 12 q^{75} - 35 q^{76} - 3 q^{77} - 6 q^{78} - 10 q^{79} + 68 q^{80} - 54 q^{81} - 80 q^{82} - 22 q^{83} - 14 q^{84} - 50 q^{85} - 66 q^{86} + 76 q^{87} - 34 q^{88} - 10 q^{89} - 63 q^{90} - 8 q^{91} - 64 q^{92} - 16 q^{93} + 30 q^{94} + 15 q^{95} + 34 q^{96} - 7 q^{97} + 138 q^{98} - 48 q^{99}+O(q^{100}) \) 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9 - 13 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 3 * q^14 - 14 * q^15 + 9 * q^16 + 12 * q^17 - 19 * q^18 - 4 * q^19 - 53 * q^20 - 13 * q^21 - 14 * q^22 - 9 * q^23 + 2 * q^24 + 96 * q^25 + 12 * q^26 + 25 * q^27 - 25 * q^28 - 78 * q^30 - 2 * q^31 + 76 * q^32 + 29 * q^33 - 15 * q^34 - 36 * q^35 + 52 * q^36 + 24 * q^37 - 19 * q^38 + 3 * q^39 - 12 * q^40 - 40 * q^41 + 11 * q^42 - 22 * q^43 + 4 * q^44 + 63 * q^45 - 24 * q^46 + 3 * q^47 + 68 * q^48 + 33 * q^49 - 76 * q^50 - 59 * q^51 - 13 * q^52 - q^53 + 18 * q^54 - 22 * q^55 + 78 * q^56 - 16 * q^57 + 5 * q^58 - 18 * q^59 + 43 * q^60 - 32 * q^61 - 39 * q^62 + 20 * q^63 + 23 * q^64 + 2 * q^65 + 11 * q^66 + 114 * q^67 + 98 * q^68 - 46 * q^69 + 32 * q^70 - 2 * q^71 + 28 * q^72 + 10 * q^73 - 43 * q^74 - 12 * q^75 - 35 * q^76 - 3 * q^77 - 6 * q^78 - 10 * q^79 + 68 * q^80 - 54 * q^81 - 80 * q^82 - 22 * q^83 - 14 * q^84 - 50 * q^85 - 66 * q^86 + 76 * q^87 - 34 * q^88 - 10 * q^89 - 63 * q^90 - 8 * q^91 - 64 * q^92 - 16 * q^93 + 30 * q^94 + 15 * q^95 + 34 * q^96 - 7 * q^97 + 138 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−0.651553	+	2.00527i	−0.460717	+	1.41794i	0.403573	+	0.914948i	$0.367768\pi$
$2$	−0.651553	+	2.00527i	−0.460717	+	1.41794i	−0.864290	+	0.502994i	$0.832232\pi$
$3$	−0.602423	−	1.85407i	−0.347809	−	1.07045i	−0.960063	−	0.279785i	$-0.909737\pi$
$3$	−0.602423	−	1.85407i	−0.347809	−	1.07045i	0.612254	−	0.790661i	$-0.290263\pi$
$4$	−1.97856	−	1.43751i	−0.989281	−	0.718755i
$5$	2.75944			1.23406			0.617031	−	0.786939i	$-0.288335\pi$
$5$	2.75944			1.23406			0.617031	+	0.786939i	$0.288335\pi$
$6$	4.11042			1.67807
$7$	−1.61436	−	1.17290i	−0.610171	−	0.443315i	0.239304	−	0.970945i	$-0.423081\pi$
$7$	−1.61436	−	1.17290i	−0.610171	−	0.443315i	−0.849474	+	0.527630i	$0.823081\pi$
$8$	0.760164	−	0.552291i	0.268758	−	0.195264i
$9$	−0.647600	+	0.470509i	−0.215867	+	0.156836i
$10$	−1.79792	+	5.53344i	−0.568553	+	1.74983i
$11$	−1.52627	−	1.10890i	−0.460187	−	0.334346i	0.333417	−	0.942779i	$-0.391798\pi$
$11$	−1.52627	−	1.10890i	−0.460187	−	0.334346i	−0.793605	+	0.608434i	$0.791798\pi$
$12$	−1.47331	+	4.53438i	−0.425307	+	1.30896i
$13$	0.309017	+	0.951057i	0.0857059	+	0.263776i
$13$	0.309017	+	0.951057i	0.0857059	+	0.263776i
$14$	3.40383	−	2.47302i	0.909711	−	0.660944i
$15$	−1.66235	−	5.11620i	−0.429218	−	1.32100i
$16$	−0.899280	−	2.76770i	−0.224820	−	0.691925i
$17$	5.81579	−	4.22542i	1.41054	−	1.02481i	0.417292	−	0.908772i	$-0.362979\pi$
$17$	5.81579	−	4.22542i	1.41054	−	1.02481i	0.993244	−	0.116043i	$-0.0370209\pi$
$18$	−0.521553	−	1.60518i	−0.122931	−	0.378343i
$19$	1.47010	−	4.52451i	0.337264	−	1.03799i	−0.628331	−	0.777946i	$-0.716262\pi$
$19$	1.47010	−	4.52451i	0.337264	−	1.03799i	0.965596	−	0.260047i	$-0.0837382\pi$
$20$	−5.45973	−	3.96673i	−1.22083	−	0.886988i
$21$	−1.20211	+	3.69971i	−0.262322	+	0.807344i
$22$	3.21809	−	2.33808i	0.686099	−	0.498480i
$23$	0.365759	−	0.265740i	0.0762661	−	0.0554106i	−0.548999	−	0.835823i	$-0.684991\pi$
$23$	0.365759	−	0.265740i	0.0762661	−	0.0554106i	0.625265	+	0.780413i	$0.284991\pi$
$24$	−1.48192	−	1.07668i	−0.302497	−	0.219777i
$25$	2.61454			0.522907
$26$	−2.10847			−0.413505
$27$	−3.46901	−	2.52038i	−0.667611	−	0.485048i
$28$	1.50806	+	4.64132i	0.284996	+	0.877126i
$29$	1.43621	−	4.42019i	0.266697	−	0.820808i	−0.724601	−	0.689169i	$-0.757976\pi$
$29$	1.43621	−	4.42019i	0.266697	−	0.820808i	0.991298	−	0.131639i	$-0.0420240\pi$
$30$	11.3425			2.07084
$31$	−0.697017	+	5.52396i	−0.125188	+	0.992133i
$31$	−0.697017	+	5.52396i	−0.125188	+	0.992133i
$32$	8.01515			1.41689
$33$	−1.13651	+	3.49783i	−0.197842	+	0.608894i
$34$	4.68382	+	14.4153i	0.803269	+	2.47221i
$35$	−4.45474	−	3.23656i	−0.752988	−	0.547078i
$36$	1.95768			0.326280
$37$	11.6410			1.91377			0.956886	−	0.290463i	$-0.0938094\pi$
$37$	11.6410			1.91377			0.956886	+	0.290463i	$0.0938094\pi$
$38$	8.11502	+	5.89591i	1.31643	+	0.956443i
$39$	1.57716	−	1.14588i	0.252548	−	0.183487i
$40$	2.09763	−	1.52402i	0.331664	−	0.240968i
$41$	0.313473	−	0.964771i	0.0489563	−	0.150672i	−0.923590	−	0.383382i	$-0.874759\pi$
$41$	0.313473	−	0.964771i	0.0489563	−	0.150672i	0.972546	+	0.232710i	$0.0747593\pi$
$42$	−6.63570	−	4.82111i	−1.02391	−	0.743914i
$43$	−2.62766	+	8.08711i	−0.400714	+	1.23327i	0.523707	+	0.851899i	$0.324549\pi$
$43$	−2.62766	+	8.08711i	−0.400714	+	1.23327i	−0.924421	+	0.381374i	$0.875451\pi$
$44$	1.42577	+	4.38805i	0.214942	+	0.661524i
$45$	−1.78702	+	1.29834i	−0.266393	+	0.193546i
$46$	0.294569	+	0.906591i	0.0434319	+	0.133670i
$47$	0.618792	+	1.90445i	0.0902601	+	0.277792i	0.985989	−	0.166808i	$-0.0533459\pi$
$47$	0.618792	+	1.90445i	0.0902601	+	0.277792i	−0.895729	+	0.444600i	$0.853346\pi$
$48$	−4.58975	+	3.33465i	−0.662474	+	0.481315i
$49$	−0.932659	−	2.87043i	−0.133237	−	0.410061i
$50$	−1.70351	+	5.24286i	−0.240912	+	0.741452i
$51$	−11.3378	−	8.23738i	−1.58761	−	1.15346i
$52$	0.755744	−	2.32594i	0.104803	−	0.322550i
$53$	−0.445724	+	0.323837i	−0.0612249	+	0.0444825i	−0.617977	−	0.786196i	$-0.712047\pi$
$53$	−0.445724	+	0.323837i	−0.0612249	+	0.0444825i	0.556752	+	0.830679i	$0.312047\pi$
$54$	7.31429	−	5.31414i	0.995349	−	0.723163i
$55$	−4.21165	−	3.05995i	−0.567899	−	0.412603i
$56$	−1.87496			−0.250552
$57$	−9.27436			−1.22842
$58$	7.92791	+	5.75997i	1.04099	+	0.756321i
$59$	−2.42331	−	7.45817i	−0.315487	−	0.970971i	−0.975553	−	0.219763i	$-0.929472\pi$
$59$	−2.42331	−	7.45817i	−0.315487	−	0.970971i	0.660066	−	0.751208i	$-0.270528\pi$
$60$	−4.06551	+	12.5124i	−0.524855	+	1.61534i
$61$	−9.19132			−1.17683			−0.588414	−	0.808560i	$-0.700247\pi$
$61$	−9.19132			−1.17683			−0.588414	+	0.808560i	$0.700247\pi$
$62$	−10.6229	−	4.99686i	−1.34911	−	0.634602i
$63$	1.59732			0.201243
$64$	−3.42373	+	10.5372i	−0.427966	+	1.31714i
$65$	0.852715	+	2.62439i	0.105766	+	0.325515i
$66$	−6.27361	−	4.55804i	−0.772227	−	0.561056i
$67$	6.19938			0.757375			0.378687	−	0.925525i	$-0.376376\pi$
$67$	6.19938			0.757375			0.378687	+	0.925525i	$0.376376\pi$
$68$	−17.5810			−2.13201
$69$	−0.713041	−	0.518055i	−0.0858401	−	0.0623665i
$70$	9.39267	−	6.82417i	1.12264	−	0.815645i
$71$	−3.23916	+	2.35339i	−0.384417	+	0.279295i	−0.763164	−	0.646205i	$-0.776355\pi$
$71$	−3.23916	+	2.35339i	−0.384417	+	0.279295i	0.378747	+	0.925500i	$0.376355\pi$
$72$	−0.232424	+	0.715327i	−0.0273914	+	0.0843021i
$73$	8.87119	+	6.44530i	1.03829	+	0.754365i	0.969952	−	0.243297i	$-0.0782289\pi$
$73$	8.87119	+	6.44530i	1.03829	+	0.754365i	0.0683426	+	0.997662i	$0.478229\pi$
$74$	−7.58474	+	23.3434i	−0.881708	+	2.71362i
$75$	−1.57506	−	4.84752i	−0.181872	−	0.559744i
$76$	−9.41271	+	6.83874i	−1.07971	+	0.784457i
$77$	1.16332	+	3.58032i	0.132572	+	0.408016i
$78$	1.27019	+	3.90924i	0.143821	+	0.442634i
$79$	6.94872	−	5.04854i	0.781792	−	0.568005i	−0.123725	−	0.992317i	$-0.539484\pi$
$79$	6.94872	−	5.04854i	0.781792	−	0.568005i	0.905516	+	0.424312i	$0.139484\pi$
$80$	−2.48151	−	7.63731i	−0.277442	−	0.853877i
$81$	−3.32523	+	10.2340i	−0.369470	+	1.13711i
$82$	1.73038	+	1.25720i	0.191089	+	0.138834i
$83$	−2.88738	+	8.88644i	−0.316931	+	0.975413i	0.658021	+	0.752999i	$0.271394\pi$
$83$	−2.88738	+	8.88644i	−0.316931	+	0.975413i	−0.974952	+	0.222414i	$0.928606\pi$
$84$	7.69682	−	5.59207i	0.839792	−	0.610145i
$85$	16.0484	−	11.6598i	1.74069	−	1.26468i
$86$	−14.5048	−	10.5384i	−1.56409	−	1.13638i
$87$	−9.06052			−0.971390
$88$	−1.77265			−0.188965
$89$	−4.91459	−	3.57066i	−0.520946	−	0.378489i	0.296014	−	0.955183i	$-0.404342\pi$
$89$	−4.91459	−	3.57066i	−0.520946	−	0.378489i	−0.816960	+	0.576694i	$0.804342\pi$
$90$	−1.43920	−	4.42939i	−0.151705	−	0.466899i
$91$	0.616630	−	1.89779i	0.0646404	−	0.198943i
$92$	−1.10568			−0.115275
$93$	10.6617	−	2.03545i	1.10557	−	0.211066i
$94$	−4.22211			−0.435477
$95$	4.05666	−	12.4851i	0.416205	−	1.28095i
$96$	−4.82851	−	14.8606i	−0.492807	−	1.51671i
$97$	−6.66010	−	4.83885i	−0.676231	−	0.491310i	0.195874	−	0.980629i	$-0.437246\pi$
$97$	−6.66010	−	4.83885i	−0.676231	−	0.491310i	−0.872105	+	0.489319i	$0.837246\pi$
$98$	6.36367			0.642827
$99$	1.51016			0.151777
$100$	−5.17302	−	3.75842i	−0.517302	−	0.375842i
$101$	−11.9511	+	8.68296i	−1.18918	+	0.863987i	−0.993177	−	0.116617i	$-0.962795\pi$
$101$	−11.9511	+	8.68296i	−1.18918	+	0.863987i	−0.195999	+	0.980604i	$0.562795\pi$
$102$	23.9053	−	17.3682i	2.36698	−	1.71971i
$103$	−0.367779	+	1.13191i	−0.0362384	+	0.111530i	−0.967539	−	0.252720i	$-0.918675\pi$
$103$	−0.367779	+	1.13191i	−0.0362384	+	0.111530i	0.931301	+	0.364250i	$0.118675\pi$
$104$	0.760164	+	0.552291i	0.0745402	+	0.0541566i
$105$	−3.31716	+	10.2092i	−0.323721	+	0.996311i
$106$	−0.358970	−	1.10480i	−0.0348662	−	0.107307i
$107$	2.27782	−	1.65493i	0.220205	−	0.159988i	−0.472214	−	0.881484i	$-0.656545\pi$
$107$	2.27782	−	1.65493i	0.220205	−	0.159988i	0.692419	+	0.721496i	$0.256545\pi$
$108$	3.24057	+	9.97346i	0.311824	+	0.959697i
$109$	4.22451	+	13.0017i	0.404635	+	1.24534i	0.921200	+	0.389090i	$0.127210\pi$
$109$	4.22451	+	13.0017i	0.404635	+	1.24534i	−0.516565	+	0.856248i	$0.672790\pi$
$110$	8.88014	−	6.45180i	0.846688	−	0.615155i
$111$	−7.01282	−	21.5832i	−0.665627	−	2.04859i
$112$	−1.79448	+	5.52283i	−0.169562	+	0.521858i
$113$	−12.0099	−	8.72573i	−1.12980	−	0.820847i	−0.144134	−	0.989558i	$-0.546040\pi$
$113$	−12.0099	−	8.72573i	−1.12980	−	0.820847i	−0.985666	+	0.168711i	$0.946040\pi$
$114$	6.04273	−	18.5976i	0.565954	−	1.74183i
$115$	1.00929	−	0.733294i	0.0941171	−	0.0683801i
$116$	−9.19568	+	6.68105i	−0.853798	+	0.620320i
$117$	−0.647600	−	0.470509i	−0.0598706	−	0.0434986i
$118$	16.5346			1.52213
$119$	−14.3448			−1.31498
$120$	−4.08929	−	2.97104i	−0.373299	−	0.271218i
$121$	−2.29935	−	7.07666i	−0.209032	−	0.643333i
$122$	5.98863	−	18.4311i	0.542185	−	1.66867i
$123$	−1.97759			−0.178314
$124$	9.31984	−	9.92754i	0.836947	−	0.891519i
$125$	−6.58256			−0.588762
$126$	−1.04074	+	3.20306i	−0.0927163	+	0.285351i
$127$	3.44172	+	10.5925i	0.305403	+	0.939933i	0.979527	+	0.201315i	$0.0645215\pi$
$127$	3.44172	+	10.5925i	0.305403	+	0.939933i	−0.674124	+	0.738618i	$0.735479\pi$
$128$	−5.93035	−	4.30865i	−0.524173	−	0.380834i
$129$	16.5770			1.45952
$130$	−5.81820			−0.510290
$131$	1.59688	+	1.16020i	0.139520	+	0.101367i	0.655356	−	0.755320i	$-0.272519\pi$
$131$	1.59688	+	1.16020i	0.139520	+	0.101367i	−0.515836	+	0.856687i	$0.672519\pi$
$132$	7.27683	−	5.28693i	0.633367	−	0.460168i
$133$	−7.68007	+	5.57990i	−0.665947	+	0.483839i
$134$	−4.03922	+	12.4314i	−0.348936	+	1.07391i
$135$	−9.57253	−	6.95485i	−0.823872	−	0.598578i
$136$	2.08729	−	6.42402i	0.178984	−	0.550855i
$137$	6.64952	+	20.4651i	0.568107	+	1.74845i	0.658535	+	0.752551i	$0.271177\pi$
$137$	6.64952	+	20.4651i	0.568107	+	1.74845i	−0.0904275	+	0.995903i	$0.528823\pi$
$138$	1.50342	−	1.09230i	0.127980	−	0.0929829i
$139$	3.93123	+	12.0991i	0.333443	+	1.02623i	0.967484	+	0.252932i	$0.0813949\pi$
$139$	3.93123	+	12.0991i	0.333443	+	1.02623i	−0.634041	+	0.773299i	$0.718605\pi$
$140$	4.16139	+	12.8075i	0.351702	+	1.08243i
$141$	3.15820	−	2.29456i	0.265968	−	0.193237i
$142$	−2.60870	−	8.02875i	−0.218917	−	0.673757i
$143$	0.582983	−	1.79424i	0.0487515	−	0.150042i
$144$	1.88460	+	1.36924i	0.157050	+	0.114104i
$145$	3.96313	−	12.1973i	0.329120	−	1.01293i
$146$	−18.7046	+	13.5897i	−1.54801	+	1.12469i
$147$	−4.76011	+	3.45842i	−0.392607	+	0.285246i
$148$	−23.0325	−	16.7341i	−1.89326	−	1.37553i
$149$	4.85360			0.397623			0.198811	−	0.980038i	$-0.436292\pi$
$149$	4.85360			0.397623			0.198811	+	0.980038i	$0.436292\pi$
$150$	10.7468			0.877476
$151$	9.56919	+	6.95242i	0.778730	+	0.565780i	0.904597	−	0.426267i	$-0.140172\pi$
$151$	9.56919	+	6.95242i	0.778730	+	0.565780i	−0.125868	+	0.992047i	$0.540172\pi$
$152$	−1.38133	−	4.25129i	−0.112040	−	0.344825i
$153$	−1.77821	+	5.47276i	−0.143760	+	0.442447i
$154$	−7.93749			−0.639621
$155$	−1.92338	+	15.2431i	−0.154490	+	1.22435i
$156$	−4.76773			−0.381724
$157$	0.789172	−	2.42882i	0.0629828	−	0.193841i	−0.914614	−	0.404329i	$-0.867505\pi$
$157$	0.789172	−	2.42882i	0.0629828	−	0.193841i	0.977597	+	0.210488i	$0.0675052\pi$
$158$	5.59624	+	17.2235i	0.445213	+	1.37022i
$159$	0.868931	+	0.631315i	0.0689107	+	0.0500665i
$160$	22.1174			1.74853
$161$	−0.902154			−0.0710997
$162$	−18.3554	−	13.3360i	−1.44214	−	1.04777i
$163$	−11.6625	+	8.47330i	−0.913477	+	0.663680i	−0.941892	−	0.335916i	$-0.890954\pi$
$163$	−11.6625	+	8.47330i	−0.913477	+	0.663680i	0.0284148	+	0.999596i	$0.490954\pi$
$164$	−2.00709	+	1.45824i	−0.156728	+	0.113869i
$165$	−3.13615	+	9.65207i	−0.244149	+	0.751413i
$166$	−15.9384	−	11.5800i	−1.23706	−	0.898779i
$167$	−0.711704	+	2.19040i	−0.0550733	+	0.169498i	−0.974810	−	0.223039i	$-0.928402\pi$
$167$	−0.711704	+	2.19040i	−0.0550733	+	0.169498i	0.919736	+	0.392537i	$0.128402\pi$
$168$	1.12952	+	3.47630i	0.0871443	+	0.268203i
$169$	−0.809017	+	0.587785i	−0.0622321	+	0.0452143i
$170$	12.9248	+	39.7783i	0.991283	+	3.05086i
$171$	1.17678	+	3.62177i	0.0899909	+	0.276963i
$172$	16.8243	−	12.2236i	1.28284	−	0.932038i
$173$	−1.11902	−	3.44399i	−0.0850776	−	0.261842i	0.899463	−	0.436996i	$-0.143958\pi$
$173$	−1.11902	−	3.44399i	−0.0850776	−	0.261842i	−0.984541	+	0.175154i	$0.943958\pi$
$174$	5.90341	−	18.1688i	0.447536	−	1.37737i
$175$	−4.22080	−	3.06659i	−0.319063	−	0.231813i
$176$	−1.69656	+	5.22146i	−0.127883	+	0.393583i
$177$	−12.3681	+	8.98594i	−0.929642	+	0.675425i
$178$	10.3623	−	7.52862i	0.776684	−	0.564294i
$179$	−6.33474	−	4.60246i	−0.473481	−	0.344004i	0.325315	−	0.945606i	$-0.394530\pi$
$179$	−6.33474	−	4.60246i	−0.473481	−	0.344004i	−0.798796	+	0.601602i	$0.794530\pi$
$180$	5.40211			0.402649
$181$	−6.01306			−0.446947			−0.223474	−	0.974710i	$-0.571740\pi$
$181$	−6.01306			−0.446947			−0.223474	+	0.974710i	$0.571740\pi$
$182$	3.40383	+	2.47302i	0.252308	+	0.183313i
$183$	5.53706	+	17.0413i	0.409311	+	1.25973i
$184$	0.131271	−	0.404011i	0.00967745	−	0.0297841i
$185$	32.1228			2.36171
$186$	−2.86503	+	22.7058i	−0.210074	+	1.66487i
$187$	−13.5620			−0.991754
$188$	1.51334	−	4.65759i	0.110372	−	0.339689i
$189$	2.64407	+	8.13760i	0.192328	+	0.591923i
$190$	22.3930	+	16.2694i	1.62456	+	1.18031i
$191$	3.61561			0.261616			0.130808	−	0.991408i	$-0.458243\pi$
$191$	3.61561			0.261616			0.130808	+	0.991408i	$0.458243\pi$
$192$	21.5991			1.55878
$193$	−4.84862	−	3.52273i	−0.349012	−	0.253572i	0.399443	−	0.916758i	$-0.369204\pi$
$193$	−4.84862	−	3.52273i	−0.349012	−	0.253572i	−0.748454	+	0.663186i	$0.769204\pi$
$194$	14.0426	−	10.2026i	1.00820	−	0.732501i
$195$	4.35210	−	3.16198i	0.311660	−	0.226434i
$196$	−2.28095	+	7.02003i	−0.162925	+	0.501431i
$197$	9.17880	+	6.66879i	0.653962	+	0.475131i	0.864619	−	0.502429i	$-0.167560\pi$
$197$	9.17880	+	6.66879i	0.653962	+	0.475131i	−0.210656	+	0.977560i	$0.567560\pi$
$198$	−0.983948	+	3.02828i	−0.0699261	+	0.215210i
$199$	−0.753172	−	2.31802i	−0.0533909	−	0.164320i	0.920806	−	0.390022i	$-0.127533\pi$
$199$	−0.753172	−	2.31802i	−0.0533909	−	0.164320i	−0.974196	+	0.225702i	$0.927533\pi$
$200$	1.98747	−	1.44398i	0.140536	−	0.102105i
$201$	−3.73465	−	11.4941i	−0.263422	−	0.810729i
$202$	−9.62495	−	29.6226i	−0.677209	−	2.08424i
$203$	−7.50299	+	5.45124i	−0.526607	+	0.382602i
$204$	10.5912	+	32.5963i	0.741532	+	2.28220i
$205$	0.865012	−	2.66223i	0.0604150	−	0.185938i
$206$	−2.03016	−	1.47500i	−0.141448	−	0.102768i
$207$	−0.111833	+	0.344186i	−0.00777292	+	0.0239226i
$208$	2.35434	−	1.71053i	0.163244	−	0.118604i
$209$	−7.26099	+	5.27542i	−0.502253	+	0.364908i
$210$	−18.3108	−	13.3036i	−1.26357	−	0.918036i
$211$	12.6919			0.873748			0.436874	−	0.899523i	$-0.356086\pi$
$211$	12.6919			0.873748			0.436874	+	0.899523i	$0.356086\pi$
$212$	1.34741			0.0925407
$213$	6.31468	+	4.58788i	0.432674	+	0.314356i
$214$	1.83447	+	5.64592i	0.125402	+	0.385947i
$215$	−7.25088	+	22.3159i	−0.494506	+	1.52193i
$216$	−4.02900			−0.274139
$217$	7.60430	−	8.10013i	0.516213	−	0.549873i
$218$	−28.8245			−1.95224
$219$	6.60581	−	20.3306i	0.446379	−	1.37381i
$220$	3.93432	+	12.1086i	0.265252	+	0.816361i
$221$	5.81579	+	4.22542i	0.391212	+	0.284233i
$222$	47.8495			3.21145
$223$	16.0899			1.07746			0.538730	−	0.842479i	$-0.318904\pi$
$223$	16.0899			1.07746			0.538730	+	0.842479i	$0.318904\pi$
$224$	−12.9393	−	9.40097i	−0.864545	−	0.628129i
$225$	−1.69317	+	1.23016i	−0.112878	+	0.0820108i
$226$	25.3226	−	18.3979i	1.68443	−	1.22381i
$227$	8.25262	−	25.3990i	0.547746	−	1.68579i	−0.166625	−	0.986020i	$-0.553287\pi$
$227$	8.25262	−	25.3990i	0.547746	−	1.68579i	0.714370	−	0.699768i	$-0.246713\pi$
$228$	18.3499	+	13.3320i	1.21525	+	0.882932i
$229$	−4.75170	+	14.6242i	−0.314001	+	0.966397i	0.662162	+	0.749361i	$0.269639\pi$
$229$	−4.75170	+	14.6242i	−0.314001	+	0.966397i	−0.976164	+	0.217036i	$0.930361\pi$
$230$	0.812848	+	2.50169i	0.0535976	+	0.164956i
$231$	5.93735	−	4.31374i	0.390649	−	0.283823i
$232$	−1.34948	−	4.15327i	−0.0885976	−	0.272675i
$233$	3.44604	+	10.6058i	0.225757	+	0.694809i	0.998214	+	0.0597419i	$0.0190278\pi$
$233$	3.44604	+	10.6058i	0.225757	+	0.694809i	−0.772457	+	0.635068i	$0.780972\pi$
$234$	1.36544	−	0.992053i	0.0892619	−	0.0648525i
$235$	1.70752	+	5.25522i	0.111387	+	0.342812i
$236$	−5.92653	+	18.2400i	−0.385784	+	1.18732i
$237$	−13.5464	−	9.84203i	−0.879933	−	0.639308i
$238$	9.34638	−	28.7652i	0.605836	−	1.86457i
$239$	23.0355	−	16.7363i	1.49005	−	1.08258i	0.515902	−	0.856647i	$-0.327457\pi$
$239$	23.0355	−	16.7363i	1.49005	−	1.08258i	0.974143	−	0.225934i	$-0.0725433\pi$
$240$	−12.6652	+	9.20178i	−0.817533	+	0.593972i
$241$	15.9625	+	11.5974i	1.02823	+	0.747055i	0.967954	−	0.251127i	$-0.0808011\pi$
$241$	15.9625	+	11.5974i	1.02823	+	0.747055i	0.0602784	+	0.998182i	$0.480801\pi$
$242$	15.6888			1.00851
$243$	8.11394			0.520509
$244$	18.1856	+	13.2126i	1.16421	+	0.845851i
$245$	−2.57362	−	7.92079i	−0.164423	−	0.506041i
$246$	1.28851	−	3.96561i	0.0821521	−	0.252838i
$247$	4.75735			0.302703
$248$	2.52099	+	4.58407i	0.160083	+	0.291089i
$249$	18.2155			1.15436
$250$	4.28888	−	13.1998i	0.271253	−	0.834830i
$251$	−7.40108	−	22.7782i	−0.467152	−	1.43775i	−0.856255	−	0.516553i	$-0.827215\pi$
$251$	−7.40108	−	22.7782i	−0.467152	−	1.43775i	0.389103	−	0.921194i	$-0.372785\pi$
$252$	−3.16040	−	2.29616i	−0.199086	−	0.144645i
$253$	−0.852926			−0.0536230
$254$	−23.4833			−1.47348
$255$	−31.2860	−	22.7306i	−1.95920	−	1.42344i
$256$	−5.42293	+	3.93999i	−0.338933	+	0.246249i
$257$	−15.7744	+	11.4608i	−0.983980	+	0.714904i	−0.958595	−	0.284774i	$-0.908081\pi$
$257$	−15.7744	+	11.4608i	−0.983980	+	0.714904i	−0.0253857	+	0.999678i	$0.508081\pi$
$258$	−10.8008	+	33.2414i	−0.672428	+	2.06952i
$259$	−18.7928	−	13.6538i	−1.16773	−	0.848404i
$260$	2.08543	−	6.41830i	0.129333	−	0.398046i
$261$	1.14965	+	3.53826i	0.0711615	+	0.219013i
$262$	−3.36697	+	2.44625i	−0.208012	+	0.151130i
$263$	5.02433	+	15.4633i	0.309813	+	0.953507i	0.977837	+	0.209367i	$0.0671405\pi$
$263$	5.02433	+	15.4633i	0.309813	+	0.953507i	−0.668024	+	0.744140i	$0.732860\pi$
$264$	1.06788	+	3.28661i	0.0657237	+	0.202277i
$265$	−1.22995	+	0.893612i	−0.0755553	+	0.0548941i
$266$	−6.18525	−	19.0362i	−0.379242	−	1.16719i
$267$	−3.65958	+	11.2630i	−0.223963	+	0.689286i
$268$	−12.2659	−	8.91167i	−0.749257	−	0.544367i
$269$	2.83591	−	8.72803i	0.172908	−	0.532157i	−0.826623	−	0.562756i	$-0.809741\pi$
$269$	2.83591	−	8.72803i	0.172908	−	0.532157i	0.999532	+	0.0305981i	$0.00974121\pi$
$270$	20.1834	−	14.6641i	1.22832	−	0.892428i
$271$	−17.3079	+	12.5749i	−1.05138	+	0.763872i	−0.972474	−	0.233010i	$-0.925143\pi$
$271$	−17.3079	+	12.5749i	−1.05138	+	0.763872i	−0.0789058	+	0.996882i	$0.525143\pi$
$272$	−16.9247	−	12.2965i	−1.02621	−	0.745586i
$273$	−3.89011			−0.235440
$274$	−45.3707			−2.74094
$275$	−3.99048	−	2.89926i	−0.240635	−	0.174832i
$276$	0.666088	+	2.05001i	0.0400938	+	0.123396i
$277$	−2.54260	+	7.82532i	−0.152770	+	0.470178i	−0.997928	−	0.0643386i	$-0.979506\pi$
$277$	−2.54260	+	7.82532i	−0.152770	+	0.470178i	0.845158	+	0.534516i	$0.179506\pi$
$278$	−26.8234			−1.60876
$279$	−2.14769	−	3.90527i	−0.128579	−	0.233802i
$280$	−5.17385			−0.309197
$281$	4.47438	−	13.7707i	0.266919	−	0.821493i	−0.724326	−	0.689458i	$-0.757849\pi$
$281$	4.47438	−	13.7707i	0.266919	−	0.821493i	0.991245	−	0.132035i	$-0.0421511\pi$
$282$	2.54350	+	7.82807i	0.151463	+	0.466155i
$283$	24.4108	+	17.7355i	1.45107	+	1.05427i	0.985579	+	0.169215i	$0.0541231\pi$
$283$	24.4108	+	17.7355i	1.45107	+	1.05427i	0.465493	+	0.885051i	$0.345877\pi$
$284$	9.79189			0.581042
$285$	−25.5921			−1.51594
$286$	3.21809	+	2.33808i	0.190290	+	0.138254i
$287$	−1.63764	+	1.18981i	−0.0966668	+	0.0702325i
$288$	−5.19061	+	3.77120i	−0.305859	+	0.222220i
$289$	10.7160	−	32.9804i	0.630351	−	1.94002i
$290$	21.8766	+	15.8943i	1.28464	+	0.933346i
$291$	−4.95935	+	15.2633i	−0.290722	+	0.894751i
$292$	−8.28703	−	25.5049i	−0.484962	−	1.49256i
$293$	16.6432	−	12.0920i	0.972305	−	0.706421i	0.0163295	−	0.999867i	$-0.494802\pi$
$293$	16.6432	−	12.0920i	0.972305	−	0.706421i	0.955976	+	0.293446i	$0.0948019\pi$
$294$	−3.83362	−	11.7987i	−0.223581	−	0.688112i
$295$	−6.68698	−	20.5804i	−0.389331	−	1.19824i
$296$	8.84908	−	6.42923i	0.514342	−	0.373692i
$297$	2.49979	+	7.69356i	0.145052	+	0.446426i
$298$	−3.16238	+	9.73280i	−0.183192	+	0.563806i
$299$	0.365759	+	0.265740i	0.0211524	+	0.0153681i
$300$	−3.85202	+	11.8553i	−0.222396	+	0.684465i
$301$	13.7274	−	9.97351i	0.791232	−	0.574864i
$302$	−20.1763	+	14.6590i	−1.16102	+	0.843529i
$303$	23.2984	+	16.9273i	1.33846	+	0.972446i
$304$	−13.8445			−0.794037
$305$	−25.3629			−1.45228
$306$	−9.81578	−	7.13158i	−0.561131	−	0.407686i
$307$	−0.0670593	−	0.206387i	−0.00382728	−	0.0117791i	0.949125	−	0.314901i	$-0.101971\pi$
$307$	−0.0670593	−	0.206387i	−0.00382728	−	0.0117791i	−0.952952	+	0.303121i	$0.901971\pi$
$308$	2.84505	−	8.75618i	0.162112	−	0.498930i
$309$	2.32019			0.131991
$310$	−29.3133	−	13.7886i	−1.66489	−	0.783138i
$311$	17.3936			0.986302			0.493151	−	0.869944i	$-0.335845\pi$
$311$	17.3936			0.986302			0.493151	+	0.869944i	$0.335845\pi$
$312$	0.566045	−	1.74211i	0.0320460	−	0.0986274i
$313$	−1.02916	−	3.16742i	−0.0581715	−	0.179033i	0.917749	−	0.397162i	$-0.130005\pi$
$313$	−1.02916	−	3.16742i	−0.0581715	−	0.179033i	−0.975920	+	0.218128i	$0.930005\pi$
$314$	4.35626	+	3.16501i	0.245838	+	0.178612i
$315$	4.40771			0.248347
$316$	−21.0058			−1.18167
$317$	−4.71486	−	3.42555i	−0.264813	−	0.192398i	0.447453	−	0.894307i	$-0.352331\pi$
$317$	−4.71486	−	3.42555i	−0.264813	−	0.192398i	−0.712266	+	0.701909i	$0.752331\pi$
$318$	−1.83211	+	1.33111i	−0.102740	+	0.0746448i
$319$	−7.09358	+	5.15378i	−0.397164	+	0.288557i
$320$	−9.44759	+	29.0767i	−0.528136	+	1.62544i
$321$	−4.44057	−	3.22626i	−0.247848	−	0.180072i
$322$	0.587801	−	1.80906i	0.0327568	−	0.100815i
$323$	−10.5681	−	32.5254i	−0.588027	−	1.80976i
$324$	21.2907	−	15.4686i	1.18281	−	0.859365i
$325$	0.807936	+	2.48657i	0.0448162	+	0.137930i
$326$	−9.39254	−	28.9073i	−0.520205	−	1.60103i
$327$	21.5611	−	15.6650i	1.19233	−	0.866279i
$328$	−0.294544	−	0.906512i	−0.0162635	−	0.0500538i
$329$	1.23477	−	3.80024i	0.0680753	−	0.209514i
$330$	−17.3117	−	12.5777i	−0.952976	−	0.692378i
$331$	9.62018	−	29.6079i	0.528773	−	1.62739i	−0.227960	−	0.973670i	$-0.573206\pi$
$331$	9.62018	−	29.6079i	0.528773	−	1.62739i	0.756733	−	0.653724i	$-0.226794\pi$
$332$	18.4872	−	13.4317i	1.01462	−	0.737162i
$333$	−7.53872	+	5.47720i	−0.413120	+	0.300149i
$334$	−3.92863	−	2.85432i	−0.214965	−	0.156181i
$335$	17.1068			0.934647
$336$	11.3207			0.617596
$337$	24.7691	+	17.9958i	1.34926	+	0.980294i	0.999048	+	0.0436237i	$0.0138903\pi$
$337$	24.7691	+	17.9958i	1.34926	+	0.980294i	0.350211	+	0.936671i	$0.386110\pi$
$338$	−0.651553	−	2.00527i	−0.0354398	−	0.109072i
$339$	−8.94302	+	27.5238i	−0.485718	+	1.49489i
$340$	−48.5138			−2.63103
$341$	7.18935	−	7.65813i	0.389325	−	0.414711i
$342$	−8.02936			−0.434178
$343$	−6.17749	+	19.0124i	−0.333553	+	1.02657i
$344$	2.46899	+	7.59876i	0.133119	+	0.409698i
$345$	−1.96760	−	1.42954i	−0.105932	−	0.0769640i
$346$	7.63524			0.410473
$347$	7.62556			0.409361			0.204681	−	0.978829i	$-0.434384\pi$
$347$	7.62556			0.409361			0.204681	+	0.978829i	$0.434384\pi$
$348$	17.9268	+	13.0246i	0.960978	+	0.698191i
$349$	−27.5445	+	20.0122i	−1.47442	+	1.07123i	−0.495119	+	0.868825i	$0.664876\pi$
$349$	−27.5445	+	20.0122i	−1.47442	+	1.07123i	−0.979302	+	0.202404i	$0.935124\pi$
$350$	8.89942	−	6.46581i	0.475694	−	0.345612i
$351$	1.32504	−	4.07806i	0.0707255	−	0.217671i
$352$	−12.2333	−	8.88799i	−0.652035	−	0.473731i
$353$	5.25902	−	16.1856i	0.279910	−	0.861473i	−0.707969	−	0.706244i	$-0.750388\pi$
$353$	5.25902	−	16.1856i	0.279910	−	0.861473i	0.987878	−	0.155229i	$-0.0496116\pi$
$354$	−9.96080	−	30.6562i	−0.529411	−	1.62936i
$355$	−8.93827	+	6.49404i	−0.474394	+	0.344668i
$356$	4.59097	+	14.1296i	0.243321	+	0.748865i
$357$	8.64162	+	26.5962i	0.457363	+	1.40762i
$358$	13.3566	−	9.70414i	0.705918	−	0.512880i
$359$	−0.651246	−	2.00433i	−0.0343715	−	0.105784i	0.932399	−	0.361431i	$-0.117712\pi$
$359$	−0.651246	−	2.00433i	−0.0343715	−	0.105784i	−0.966770	+	0.255647i	$0.917712\pi$
$360$	−0.641361	+	1.97391i	−0.0338027	+	0.104034i
$361$	−2.93864	−	2.13505i	−0.154665	−	0.112371i
$362$	3.91783	−	12.0578i	0.205916	−	0.633745i
$363$	−11.7354	+	8.52629i	−0.615950	+	0.447514i
$364$	−3.94814	+	2.86849i	−0.206939	+	0.150350i
$365$	24.4796	+	17.7854i	1.28132	+	0.930933i
$366$	−37.7802			−1.97480
$367$	24.3785			1.27255			0.636274	−	0.771463i	$-0.280475\pi$
$367$	24.3785			1.27255			0.636274	+	0.771463i	$0.280475\pi$
$368$	−1.06441	−	0.773338i	−0.0554861	−	0.0403130i
$369$	0.250928	+	0.772277i	0.0130628	+	0.0402032i
$370$	−20.9297	+	64.4149i	−1.08808	+	3.34877i
$371$	1.09939			0.0570774
$372$	−24.0208	−	11.2990i	−1.24542	−	0.585828i
$373$	15.4558			0.800273			0.400137	−	0.916456i	$-0.368963\pi$
$373$	15.4558			0.800273			0.400137	+	0.916456i	$0.368963\pi$
$374$	8.83637	−	27.1956i	0.456918	−	1.40625i
$375$	3.96548	+	12.2045i	0.204777	+	0.630238i
$376$	1.52219	+	1.10594i	0.0785011	+	0.0570344i
$377$	4.64766			0.239367
$378$	−18.0409			−0.927922
$379$	13.7678	+	10.0029i	0.707203	+	0.513813i	0.882270	−	0.470744i	$-0.156014\pi$
$379$	13.7678	+	10.0029i	0.707203	+	0.513813i	−0.175067	+	0.984556i	$0.556014\pi$
$380$	−25.9739	+	18.8711i	−1.33243	+	0.968068i
$381$	17.5659	−	12.7623i	0.899926	−	0.653835i
$382$	−2.35576	+	7.25028i	−0.120531	+	0.370957i
$383$	12.5273	+	9.10162i	0.640115	+	0.465071i	0.859890	−	0.510480i	$-0.170532\pi$
$383$	12.5273	+	9.10162i	0.640115	+	0.465071i	−0.219774	+	0.975551i	$0.570532\pi$
$384$	−4.41595	+	13.5909i	−0.225350	+	0.693557i
$385$	3.21011	+	9.87971i	0.163602	+	0.503517i
$386$	10.2232	−	7.42757i	0.520346	−	0.378053i
$387$	−2.10338	−	6.47355i	−0.106921	−	0.329069i
$388$	6.22154	+	19.1479i	0.315851	+	0.972088i
$389$	−27.0772	+	19.6728i	−1.37287	+	0.997449i	−0.375364	+	0.926877i	$0.622482\pi$
$389$	−27.0772	+	19.6728i	−1.37287	+	0.997449i	−0.997507	+	0.0705718i	$0.977518\pi$
$390$	3.50502	+	10.7873i	0.177483	+	0.546238i
$391$	1.00432	−	3.09098i	0.0507906	−	0.156317i
$392$	−2.29429	−	1.66690i	−0.115879	−	0.0841909i
$393$	1.18909	−	3.65966i	0.0599819	−	0.184605i
$394$	−19.3532	+	14.0609i	−0.975000	+	0.708379i
$395$	19.1746	−	13.9312i	0.964779	−	0.700953i
$396$	−2.98794	−	2.17087i	−0.150150	−	0.109090i
$397$	−14.4099			−0.723214			−0.361607	−	0.932331i	$-0.617772\pi$
$397$	−14.4099			−0.723214			−0.361607	+	0.932331i	$0.617772\pi$
$398$	5.13900			0.257595
$399$	14.9722	+	10.8779i	0.749545	+	0.544576i
$400$	−2.35120	−	7.23625i	−0.117560	−	0.361812i
$401$	−1.86933	+	5.75321i	−0.0933500	+	0.287302i	−0.986820	−	0.161821i	$-0.948263\pi$
$401$	−1.86933	+	5.75321i	−0.0933500	+	0.287302i	0.893470	+	0.449123i	$0.148263\pi$
$402$	25.4820			1.27093
$403$	−5.46899	+	1.04410i	−0.272430	+	0.0520101i
$404$	36.1278			1.79742
$405$	−9.17579	+	28.2402i	−0.455949	+	1.40327i
$406$	−6.04263	−	18.5973i	−0.299891	−	0.922969i
$407$	−17.7673	−	12.9087i	−0.880694	−	0.639862i
$408$	−13.1680			−0.651913
$409$	−11.5955			−0.573359			−0.286680	−	0.958027i	$-0.592551\pi$
$409$	−11.5955			−0.573359			−0.286680	+	0.958027i	$0.592551\pi$
$410$	4.77490	+	3.46917i	0.235816	+	0.171330i
$411$	33.9379	−	24.6573i	1.67403	−	1.21626i
$412$	2.35480	−	1.71087i	0.116013	−	0.0842883i
$413$	−4.83560	+	14.8825i	−0.237945	+	0.732318i
$414$	−0.617322	−	0.448511i	−0.0303397	−	0.0220431i
$415$	−7.96756	+	24.5216i	−0.391112	+	1.20372i
$416$	2.47682	+	7.62286i	0.121436	+	0.373741i
$417$	20.0643	−	14.5775i	0.982551	−	0.713865i
$418$	−5.84774	−	17.9975i	−0.286022	−	0.880286i
$419$	−7.40511	−	22.7906i	−0.361763	−	1.11339i	−0.951983	−	0.306150i	$-0.900959\pi$
$419$	−7.40511	−	22.7906i	−0.361763	−	1.11339i	0.590220	−	0.807242i	$-0.299041\pi$
$420$	21.2390	−	15.4310i	1.03636	−	0.752956i
$421$	−3.92072	−	12.0667i	−0.191084	−	0.588096i	−1.00000		0.000171941i	$-0.999945\pi$
$421$	−3.92072	−	12.0667i	−0.191084	−	0.588096i	0.808916	−	0.587924i	$-0.200055\pi$
$422$	−8.26945	+	25.4508i	−0.402551	+	1.23892i
$423$	−1.29679	−	0.942172i	−0.0630520	−	0.0458100i
$424$	−0.159971	+	0.492339i	−0.00776886	+	0.0239101i
$425$	15.2056	−	11.0475i	0.737580	−	0.535883i
$426$	−13.3143	+	9.67340i	−0.645080	+	0.468678i
$427$	14.8381	+	10.7805i	0.718066	+	0.521705i
$428$	−6.88579			−0.332837
$429$	−3.67784			−0.177568
$430$	−40.0252	−	29.0800i	−1.93019	−	1.40236i
$431$	3.84416	+	11.8311i	0.185167	+	0.569884i	0.999951	−	0.00987969i	$-0.00314485\pi$
$431$	3.84416	+	11.8311i	0.185167	+	0.569884i	−0.814785	+	0.579764i	$0.803145\pi$
$432$	−3.85605	+	11.8677i	−0.185524	+	0.570985i
$433$	−6.94571			−0.333790			−0.166895	−	0.985975i	$-0.553374\pi$
$433$	−6.94571			−0.333790			−0.166895	+	0.985975i	$0.553374\pi$
$434$	11.2884	+	20.5263i	0.541859	+	0.985296i
$435$	−25.0020			−1.19875
$436$	10.3316	−	31.7975i	0.494795	−	1.52282i
$437$	−0.664638	−	2.04555i	−0.0317940	−	0.0978517i
$438$	36.4643	+	26.4929i	1.74233	+	1.26588i
$439$	−11.2778			−0.538259			−0.269129	−	0.963104i	$-0.586736\pi$
$439$	−11.2778			−0.538259			−0.269129	+	0.963104i	$0.586736\pi$
$440$	−4.89153			−0.233194
$441$	1.95455	+	1.42006i	0.0930739	+	0.0676221i
$442$	−12.2624	+	8.90916i	−0.583263	+	0.423766i
$443$	−20.1795	+	14.6613i	−0.958756	+	0.696577i	−0.952862	−	0.303405i	$-0.901876\pi$
$443$	−20.1795	+	14.6613i	−0.958756	+	0.696577i	−0.00589468	+	0.999983i	$0.501876\pi$
$444$	−17.1508	+	52.7848i	−0.813942	+	2.50505i
$445$	−13.5615	−	9.85304i	−0.642879	−	0.467079i
$446$	−10.4834	+	32.2646i	−0.496404	+	1.52777i
$447$	−2.92392	−	8.99891i	−0.138297	−	0.425634i
$448$	17.8862	−	12.9951i	0.845042	−	0.613959i
$449$	−7.77100	−	23.9167i	−0.366736	−	1.12870i	−0.948887	−	0.315617i	$-0.897788\pi$
$449$	−7.77100	−	23.9167i	−0.366736	−	1.12870i	0.582150	−	0.813081i	$-0.302212\pi$
$450$	−1.36362	−	4.19679i	−0.0642816	−	0.197839i
$451$	−1.54828	+	1.12489i	−0.0729056	+	0.0529690i
$452$	11.2191	+	34.5288i	0.527702	+	1.62410i
$453$	7.12556	−	21.9302i	0.334788	−	1.03037i
$454$	45.5548	+	33.0975i	2.13799	+	1.55334i
$455$	1.70156	−	5.23686i	0.0797703	−	0.245508i
$456$	−7.05003	+	5.12215i	−0.330148	+	0.239867i
$457$	−27.8367	+	20.2245i	−1.30215	+	0.946064i	−0.999974	−	0.00718919i	$-0.997712\pi$
$457$	−27.8367	+	20.2245i	−1.30215	+	0.946064i	−0.302172	+	0.953254i	$0.597712\pi$
$458$	−26.2296	−	19.0569i	−1.22563	−	0.890471i
$459$	−30.8247			−1.43877
$460$	−3.05107			−0.142257
$461$	−9.19325	−	6.67928i	−0.428172	−	0.311085i	0.352745	−	0.935719i	$-0.385248\pi$
$461$	−9.19325	−	6.67928i	−0.428172	−	0.311085i	−0.780918	+	0.624634i	$0.785248\pi$
$462$	4.78172	+	14.7166i	0.222466	+	0.684680i
$463$	9.82826	−	30.2483i	0.456758	−	1.40576i	−0.412301	−	0.911048i	$-0.635275\pi$
$463$	9.82826	−	30.2483i	0.456758	−	1.40576i	0.869059	−	0.494709i	$-0.164725\pi$
$464$	−13.5253			−0.627896
$465$	29.4204	−	5.61670i	1.36434	−	0.260468i
$466$	−23.5128			−1.08921
$467$	8.52189	−	26.2277i	0.394346	−	1.21367i	−0.535123	−	0.844774i	$-0.679735\pi$
$467$	8.52189	−	26.2277i	0.394346	−	1.21367i	0.929470	−	0.368899i	$-0.120265\pi$
$468$	0.604956	+	1.86186i	0.0279641	+	0.0860646i
$469$	−10.0080	−	7.27126i	−0.462128	−	0.335755i
$470$	−11.6507			−0.537406
$471$	−4.97861			−0.229402
$472$	−5.96119	−	4.33106i	−0.274386	−	0.199353i
$473$	12.9783	−	9.42929i	0.596743	−	0.433559i
$474$	28.5621	−	20.7516i	1.31190	−	0.953153i
$475$	3.84363	−	11.8295i	0.176358	−	0.542774i
$476$	28.3820	+	20.6208i	1.30089	+	0.945151i
$477$	0.136282	−	0.419434i	0.00623994	−	0.0192046i
$478$	18.5520	+	57.0971i	0.848548	+	2.61156i
$479$	20.9372	−	15.2118i	0.956647	−	0.695045i	0.00427758	−	0.999991i	$-0.498638\pi$
$479$	20.9372	−	15.2118i	0.956647	−	0.695045i	0.952370	+	0.304946i	$0.0986384\pi$
$480$	−13.3240	−	41.0070i	−0.608154	−	1.87171i
$481$	3.59727	+	11.0713i	0.164022	+	0.504806i
$482$	−33.6563	+	24.4528i	−1.53300	+	1.11379i
$483$	0.543478	+	1.67265i	0.0247291	+	0.0761084i
$484$	−5.62337	+	17.3070i	−0.255608	+	0.786680i
$485$	−18.3782	−	13.3525i	−0.834510	−	0.606307i
$486$	−5.28666	+	16.2707i	−0.239808	+	0.738052i
$487$	−20.4557	+	14.8620i	−0.926938	+	0.673460i	−0.945241	−	0.326373i	$-0.894174\pi$
$487$	−20.4557	+	14.8620i	−0.926938	+	0.673460i	0.0183034	+	0.999832i	$0.494174\pi$
$488$	−6.98691	+	5.07628i	−0.316282	+	0.229793i
$489$	22.7358	+	16.5185i	1.02815	+	0.746994i
$490$	17.5602			0.793288
$491$	−14.1436			−0.638290			−0.319145	−	0.947706i	$-0.603396\pi$
$491$	−14.1436			−0.638290			−0.319145	+	0.947706i	$0.603396\pi$
$492$	3.91279	+	2.84281i	0.176402	+	0.128164i
$493$	−10.3245	−	31.7754i	−0.464991	−	1.43109i
$494$	−3.09966	+	9.53978i	−0.139460	+	0.429215i
$495$	4.16720			0.187302
$496$	15.9155	−	3.03845i	0.714626	−	0.136431i
$497$	7.98945			0.358376
$498$	−11.8683	+	36.5270i	−0.531833	+	1.63681i
$499$	9.54126	+	29.3650i	0.427126	+	1.31456i	0.900944	+	0.433935i	$0.142875\pi$
$499$	9.54126	+	29.3650i	0.427126	+	1.31456i	−0.473819	+	0.880622i	$0.657125\pi$
$500$	13.0240	+	9.46249i	0.582451	+	0.423176i
$501$	4.48989			0.200594
$502$	50.4987			2.25387
$503$	22.0543	+	16.0234i	0.983353	+	0.714448i	0.958455	−	0.285242i	$-0.0920741\pi$
$503$	22.0543	+	16.0234i	0.983353	+	0.714448i	0.0248974	+	0.999690i	$0.492074\pi$
$504$	1.21422	−	0.882185i	0.0540858	−	0.0392957i
$505$	−32.9783	+	23.9602i	−1.46752	+	1.06621i
$506$	0.555726	−	1.71035i	0.0247050	−	0.0760343i
$507$	1.57716	+	1.14588i	0.0700443	+	0.0508902i
$508$	8.41719	−	25.9054i	0.373452	−	1.14937i
$509$	5.90346	+	18.1690i	0.261666	+	0.805325i	0.992443	+	0.122709i	$0.0391581\pi$
$509$	5.90346	+	18.1690i	0.261666	+	0.805325i	−0.730777	+	0.682617i	$0.760842\pi$
$510$	65.9655	−	47.9267i	2.92100	−	2.12223i
$511$	−6.76160	−	20.8101i	−0.299115	−	0.920583i
$512$	−8.89781	−	27.3846i	−0.393231	−	1.21024i
$513$	−16.5033	+	11.9903i	−0.728637	+	0.529386i
$514$	−12.7041	−	39.0993i	−0.560355	−	1.72460i
$515$	−1.01487	+	3.12344i	−0.0447204	+	0.137635i
$516$	−32.7986	−	23.8296i	−1.44388	−	1.04904i
$517$	1.16740	−	3.59288i	0.0513420	−	0.158014i
$518$	39.6240	−	28.7885i	1.74098	−	1.26490i
$519$	−5.71127	+	4.14948i	−0.250697	+	0.182142i
$520$	2.09763	+	1.52402i	0.0919871	+	0.0668326i
$521$	24.6713			1.08087			0.540435	−	0.841386i	$-0.318260\pi$
$521$	24.6713			1.08087			0.540435	+	0.841386i	$0.318260\pi$
$522$	−7.84423			−0.343333
$523$	−2.66849	−	1.93877i	−0.116685	−	0.0847767i	0.527912	−	0.849299i	$-0.322975\pi$
$523$	−2.66849	−	1.93877i	−0.116685	−	0.0847767i	−0.644597	+	0.764522i	$0.722975\pi$
$524$	−1.49173	−	4.59107i	−0.0651664	−	0.200562i
$525$	−3.14296	+	9.67303i	−0.137170	+	0.422166i
$526$	−34.2817			−1.49475
$527$	19.2874	+	35.0714i	0.840170	+	1.52773i
$528$	10.7030			0.465788
$529$	−7.04423	+	21.6799i	−0.306271	+	0.942605i
$530$	−0.990557	−	3.04862i	−0.0430271	−	0.132424i
$531$	5.07847	+	3.68972i	0.220387	+	0.160120i
$532$	23.2167			1.00657
$533$	1.01442			0.0439394
$534$	−20.2010	−	14.6769i	−0.874184	−	0.635132i
$535$	6.28552	−	4.56670i	0.271747	−	0.197435i
$536$	4.71254	−	3.42386i	0.203551	−	0.147888i
$537$	−4.71708	+	14.5177i	−0.203557	+	0.626483i
$538$	15.6543	+	11.3735i	0.674906	+	0.490348i
$539$	−1.75953	+	5.41527i	−0.0757882	+	0.233252i
$540$	8.94219	+	27.5212i	0.384810	+	1.18432i
$541$	25.1128	−	18.2455i	1.07969	−	0.784437i	0.102057	−	0.994779i	$-0.467458\pi$
$541$	25.1128	−	18.2455i	1.07969	−	0.784437i	0.977628	+	0.210341i	$0.0674575\pi$
$542$	−13.9391	−	42.9003i	−0.598738	−	1.84273i
$543$	3.62241	+	11.1486i	0.155452	+	0.478433i
$544$	46.6144	−	33.8674i	1.99858	−	1.45205i
$545$	11.6573	+	35.8775i	0.499344	+	1.53682i
$546$	2.53461	−	7.80073i	0.108471	−	0.333840i
$547$	−31.6328	−	22.9825i	−1.35252	−	0.982663i	−0.998882	−	0.0472802i	$-0.984945\pi$
$547$	−31.6328	−	22.9825i	−1.35252	−	0.982663i	−0.353638	−	0.935383i	$-0.615055\pi$
$548$	16.2623	−	50.0503i	0.694692	−	2.13804i
$549$	5.95230	−	4.32460i	0.254038	−	0.184569i
$550$	8.41381	−	6.11299i	0.358766	−	0.260659i
$551$	−17.8878	−	12.9962i	−0.762046	−	0.553658i
$552$	−0.828145			−0.0352482
$553$	−17.1392			−0.728831
$554$	−14.0353	−	10.1972i	−0.596301	−	0.433238i
$555$	−19.3515	−	59.5577i	−0.821425	−	2.52809i
$556$	9.61437	−	29.5900i	0.407740	−	1.25490i
$557$	−26.3462			−1.11632			−0.558162	−	0.829732i	$-0.688493\pi$
$557$	−26.3462			−1.11632			−0.558162	+	0.829732i	$0.688493\pi$
$558$	9.23046	−	1.76221i	0.390757	−	0.0746001i
$559$	−8.50329			−0.359651
$560$	−4.95176	+	15.2399i	−0.209250	+	0.644005i
$561$	8.17008	+	25.1449i	0.344941	+	1.06162i
$562$	24.6988	+	17.9447i	1.04185	+	0.756952i
$563$	9.54590			0.402312			0.201156	−	0.979559i	$-0.435530\pi$
$563$	9.54590			0.402312			0.201156	+	0.979559i	$0.435530\pi$
$564$	−9.54715			−0.402008
$565$	−33.1408	−	24.0782i	−1.39424	−	1.01298i
$566$	−51.4694	+	37.3947i	−2.16342	+	1.57182i
$567$	17.3716	−	12.6212i	0.729538	−	0.530040i
$568$	−1.16254	+	3.57792i	−0.0487789	+	0.150126i
$569$	−28.6495	−	20.8151i	−1.20105	−	0.872615i	−0.206664	−	0.978412i	$-0.566261\pi$
$569$	−28.6495	−	20.8151i	−1.20105	−	0.872615i	−0.994388	+	0.105797i	$0.966261\pi$
$570$	16.6746	−	51.3191i	0.698422	−	2.14952i
$571$	−5.87529	−	18.0823i	−0.245873	−	0.756720i	−0.995492	−	0.0948498i	$-0.969763\pi$
$571$	−5.87529	−	18.0823i	−0.245873	−	0.756720i	0.749618	−	0.661870i	$-0.230237\pi$
$572$	−3.73270	+	2.71197i	−0.156072	+	0.113393i
$573$	−2.17813	−	6.70358i	−0.0909925	−	0.280046i
$574$	−1.31889	−	4.05914i	−0.0550496	−	0.169425i
$575$	0.956291	−	0.694786i	0.0398801	−	0.0289746i
$576$	−2.74062	−	8.43475i	−0.114192	−	0.351448i
$577$	−5.79191	+	17.8257i	−0.241120	+	0.742092i	0.755130	+	0.655575i	$0.227574\pi$
$577$	−5.79191	+	17.8257i	−0.241120	+	0.742092i	−0.996250	+	0.0865171i	$0.972426\pi$
$578$	59.1526	+	42.9769i	2.46042	+	1.78760i
$579$	−3.61046	+	11.1118i	−0.150045	+	0.461793i
$580$	−25.3750	+	18.4360i	−1.05364	+	0.765513i
$581$	15.0842	−	10.9593i	0.625797	−	0.454668i
$582$	−27.3758	−	19.8897i	−1.13476	−	0.824454i
$583$	1.03940			0.0430475
$584$	10.3032			0.426351
$585$	−1.78702	−	1.29834i	−0.0738840	−	0.0536799i
$586$	13.4038	+	41.2527i	0.553706	+	1.70413i
$587$	0.729391	−	2.24484i	0.0301052	−	0.0926543i	−0.934875	−	0.354977i	$-0.884489\pi$
$587$	0.729391	−	2.24484i	0.0301052	−	0.0926543i	0.964980	+	0.262323i	$0.0844886\pi$
$588$	14.3897			0.593421
$589$	23.9685	+	11.2744i	0.987606	+	0.464555i
$590$	45.6262			1.87840
$591$	6.83486	−	21.0355i	0.281149	−	0.865286i
$592$	−10.4685	−	32.2188i	−0.430254	−	1.32419i
$593$	18.7746	+	13.6406i	0.770981	+	0.560151i	0.902259	−	0.431195i	$-0.141908\pi$
$593$	18.7746	+	13.6406i	0.770981	+	0.560151i	−0.131278	+	0.991346i	$0.541908\pi$
$594$	−17.0564			−0.699834
$595$	−39.5836			−1.62277
$596$	−9.60316	−	6.97711i	−0.393361	−	0.285793i
$597$	−3.84405	+	2.79286i	−0.157326	+	0.114304i
$598$	−0.771192	+	0.560304i	−0.0315364	+	0.0229125i
$599$	14.9570	−	46.0330i	0.611128	−	1.88086i	0.163787	−	0.986496i	$-0.447629\pi$
$599$	14.9570	−	46.0330i	0.611128	−	1.88086i	0.447341	−	0.894363i	$-0.352371\pi$
$600$	−3.87455	−	2.81502i	−0.158178	−	0.114923i
$601$	−8.26433	+	25.4350i	−0.337109	+	1.03752i	0.628565	+	0.777757i	$0.283643\pi$
$601$	−8.26433	+	25.4350i	−0.337109	+	1.03752i	−0.965674	+	0.259758i	$0.916357\pi$
$602$	11.0555	+	34.0254i	0.450589	+	1.38677i
$603$	−4.01472	+	2.91686i	−0.163492	+	0.118784i
$604$	−8.93907	−	27.5116i	−0.363725	−	1.11943i
$605$	−6.34492	−	19.5277i	−0.257958	−	0.793912i
$606$	−49.1239	+	35.6906i	−1.99552	+	1.44983i
$607$	0.0268380	+	0.0825990i	0.00108932	+	0.00335259i	0.951600	−	0.307340i	$-0.0994390\pi$
$607$	0.0268380	+	0.0825990i	0.00108932	+	0.00335259i	−0.950510	+	0.310693i	$0.899439\pi$
$608$	11.7831	−	36.2646i	0.477867	−	1.47072i
$609$	14.6269	+	10.6271i	0.592714	+	0.430632i
$610$	16.5253	−	50.8596i	0.669089	−	2.05924i
$611$	−1.62002	+	1.17701i	−0.0655390	+	0.0476168i
$612$	11.3854	−	8.27201i	0.460230	−	0.334376i
$613$	2.03426	+	1.47797i	0.0821628	+	0.0596948i	0.628108	−	0.778126i	$-0.283829\pi$
$613$	2.03426	+	1.47797i	0.0821628	+	0.0596948i	−0.545946	+	0.837821i	$0.683829\pi$
$614$	0.457556			0.0184654
$615$	−5.45706			−0.220050
$616$	2.86169	+	2.07914i	0.115301	+	0.0837710i
$617$	4.64464	+	14.2947i	0.186986	+	0.575484i	0.999977	−	0.00679259i	$-0.00216217\pi$
$617$	4.64464	+	14.2947i	0.186986	+	0.575484i	−0.812991	+	0.582276i	$0.802162\pi$
$618$	−1.51173	+	4.65262i	−0.0608106	+	0.187156i
$619$	−11.6483			−0.468186			−0.234093	−	0.972214i	$-0.575212\pi$
$619$	−11.6483			−0.468186			−0.234093	+	0.972214i	$0.575212\pi$
$620$	25.7176	−	27.3945i	1.03284	−	1.10019i
$621$	−1.93859			−0.0777928
$622$	−11.3329	+	34.8790i	−0.454406	+	1.39852i
$623$	3.74589	+	11.5287i	0.150076	+	0.461886i
$624$	−4.58975	−	3.33465i	−0.183737	−	0.133493i
$625$	−31.2369			−1.24948
$626$	7.02210			0.280660
$627$	14.1552	+	10.2843i	0.565303	+	0.410717i
$628$	−5.05288	+	3.67113i	−0.201632	+	0.146494i
$629$	67.7018	−	49.1882i	2.69945	−	1.96126i
$630$	−2.87186	+	8.83867i	−0.114418	+	0.352141i
$631$	3.25497	+	2.36487i	0.129578	+	0.0941441i	0.650687	−	0.759346i	$-0.274481\pi$
$631$	3.25497	+	2.36487i	0.129578	+	0.0941441i	−0.521108	+	0.853491i	$0.674481\pi$
$632$	2.49390	−	7.67543i	0.0992019	−	0.305312i
$633$	−7.64590	−	23.5317i	−0.303897	−	0.935300i
$634$	9.94113	−	7.22265i	0.394813	−	0.286848i
$635$	9.49722	+	29.2295i	0.376886	+	1.15994i
$636$	−0.811712	−	2.49819i	−0.0321865	−	0.0990598i
$637$	2.44173	−	1.77402i	0.0967449	−	0.0702893i
$638$	−5.71290	−	17.5825i	−0.226176	−	0.696098i
$639$	0.990389	−	3.04810i	0.0391792	−	0.120581i
$640$	−16.3645	−	11.8895i	−0.646862	−	0.469973i
$641$	−13.0044	+	40.0233i	−0.513641	+	1.58082i	0.272100	+	0.962269i	$0.412282\pi$
$641$	−13.0044	+	40.0233i	−0.513641	+	1.58082i	−0.785741	+	0.618556i	$0.787718\pi$
$642$	9.36279	−	6.80247i	0.369520	−	0.268472i
$643$	−19.9826	+	14.5182i	−0.788038	+	0.572543i	−0.907381	−	0.420310i	$-0.861921\pi$
$643$	−19.9826	+	14.5182i	−0.788038	+	0.572543i	0.119343	+	0.992853i	$0.461921\pi$
$644$	1.78497	+	1.29686i	0.0703376	+	0.0511033i
$645$	45.7433			1.80114
$646$	72.1080			2.83705
$647$	−16.6577	−	12.1025i	−0.654881	−	0.475799i	0.210050	−	0.977691i	$-0.432637\pi$
$647$	−16.6577	−	12.1025i	−0.654881	−	0.475799i	−0.864930	+	0.501892i	$0.832637\pi$
$648$	3.12443	+	9.61601i	0.122739	+	0.377753i
$649$	−4.57174	+	14.0704i	−0.179457	+	0.552310i
$650$	−5.51267			−0.216225
$651$	−19.5992	−	9.21917i	−0.768153	−	0.361328i
$652$	35.2554			1.38071
$653$	6.78935	−	20.8955i	0.265688	−	0.817702i	−0.725847	−	0.687857i	$-0.758552\pi$
$653$	6.78935	−	20.8955i	0.265688	−	0.817702i	0.991534	−	0.129846i	$-0.0414482\pi$
$654$	17.3645	+	53.4425i	0.679006	+	2.08977i
$655$	4.40651	+	3.20151i	0.172176	+	0.125093i
$656$	−2.95210			−0.115260
$657$	−8.77755			−0.342445
$658$	6.81600	+	4.95212i	0.265715	+	0.193054i
$659$	7.36917	−	5.35401i	0.287062	−	0.208563i	−0.434930	−	0.900464i	$-0.643227\pi$
$659$	7.36917	−	5.35401i	0.287062	−	0.208563i	0.721992	+	0.691902i	$0.243227\pi$
$660$	20.0800	−	14.5890i	0.781614	−	0.567876i
$661$	−9.80595	+	30.1796i	−0.381407	+	1.17385i	0.557646	+	0.830079i	$0.311705\pi$
$661$	−9.80595	+	30.1796i	−0.381407	+	1.17385i	−0.939053	+	0.343772i	$0.888295\pi$
$662$	53.1038	+	38.5821i	2.06394	+	1.49954i
$663$	4.33065	−	13.3284i	0.168188	−	0.517630i
$664$	2.71302	+	8.34982i	0.105286	+	0.324036i
$665$	−21.1927	+	15.3974i	−0.821819	+	0.597086i
$666$	−6.07141	−	18.6859i	−0.235262	−	0.724063i
$667$	−0.649314	−	1.99838i	−0.0251415	−	0.0773776i
$668$	4.55687	−	3.31076i	0.176311	−	0.128097i
$669$	−9.69292	−	29.8318i	−0.374750	−	1.15336i
$670$	−11.1460	+	34.3039i	−0.430608	+	1.32527i
$671$	14.0284	+	10.1922i	0.541561	+	0.393467i
$672$	−9.63508	+	29.6537i	−0.371681	+	1.14392i
$673$	−18.1872	+	13.2138i	−0.701066	+	0.509354i	−0.880279	−	0.474456i	$-0.842645\pi$
$673$	−18.1872	+	13.2138i	−0.701066	+	0.509354i	0.179213	+	0.983810i	$0.442645\pi$
$674$	−52.2249	+	37.9436i	−2.01163	+	1.46153i
$675$	−9.06984	−	6.58963i	−0.349098	−	0.253635i
$676$	2.44564			0.0940630
$677$	24.2154			0.930673			0.465336	−	0.885134i	$-0.345933\pi$
$677$	24.2154			0.930673			0.465336	+	0.885134i	$0.345933\pi$
$678$	−49.3659	−	35.8664i	−1.89588	−	1.37744i
$679$	5.07631	+	15.6233i	0.194811	+	0.599566i
$680$	5.75976	−	17.7267i	0.220877	−	0.679789i
$681$	−52.0629			−1.99506
$682$	10.6724	+	19.4063i	0.408667	+	0.743105i
$683$	−43.6989			−1.67209			−0.836046	−	0.548659i	$-0.815138\pi$
$683$	−43.6989			−1.67209			−0.836046	+	0.548659i	$0.815138\pi$
$684$	2.87799	−	8.85753i	0.110043	−	0.338676i
$685$	18.3490	+	56.4724i	0.701079	+	2.15770i
$686$	−34.1000	−	24.7751i	−1.30195	−	0.945918i
$687$	29.9769			1.14369
$688$	24.7457			0.943420
$689$	−0.445724	−	0.323837i	−0.0169807	−	0.0123372i
$690$	4.14862	−	3.01415i	0.157935	−	0.114747i
$691$	−1.69123	+	1.22875i	−0.0643375	+	0.0467440i	−0.619489	−	0.785005i	$-0.712660\pi$
$691$	−1.69123	+	1.22875i	−0.0643375	+	0.0467440i	0.555152	+	0.831749i	$0.312660\pi$
$692$	−2.73672	+	8.42276i	−0.104034	+	0.320185i
$693$	−2.43794	−	1.77127i	−0.0926096	−	0.0672848i
$694$	−4.96845	+	15.2913i	−0.188600	+	0.580450i
$695$	10.8480	+	33.3868i	0.411489	+	1.26643i
$696$	−6.88748	+	5.00405i	−0.261069	+	0.189678i
$697$	−2.25347	−	6.93546i	−0.0853562	−	0.262699i
$698$	−22.1833	−	68.2732i	−0.839650	−	2.58418i
$699$	17.5879	−	12.7784i	0.665236	−	0.483322i
$700$	3.94286	+	12.1349i	0.149026	+	0.458656i
$701$	0.688551	−	2.11914i	0.0260062	−	0.0800389i	−0.937211	−	0.348763i	$-0.886602\pi$
$701$	0.688551	−	2.11914i	0.0260062	−	0.0800389i	0.963217	+	0.268724i	$0.0866019\pi$
$702$	7.31429	+	5.31414i	0.276060	+	0.200569i
$703$	17.1135	−	52.6699i	0.645447	−	1.98648i
$704$	16.9102	−	12.2860i	0.637326	−	0.463044i
$705$	8.71487	−	6.33172i	0.328221	−	0.238466i
$706$	29.0300	+	21.0915i	1.09256	+	0.793791i
$707$	29.4776			1.10862
$708$	37.3884			1.40514
$709$	42.6350	+	30.9761i	1.60119	+	1.16333i	0.885188	+	0.465234i	$0.154030\pi$
$709$	42.6350	+	30.9761i	1.60119	+	1.16333i	0.716002	+	0.698098i	$0.245970\pi$
$710$	−7.19856	−	22.1549i	−0.270157	−	0.831458i
$711$	−2.12461	+	6.53886i	−0.0796789	+	0.245227i
$712$	−5.70794			−0.213914
$713$	1.21300	+	2.20567i	0.0454271	+	0.0826029i
$714$	−58.9631			−2.20664
$715$	1.60871	−	4.95110i	0.0601623	−	0.185161i
$716$	5.91760	+	18.2125i	0.221151	+	0.680634i
$717$	−44.9074	−	32.6271i	−1.67710	−	1.21848i
$718$	4.44355			0.165832
$719$	0.782506			0.0291825			0.0145913	−	0.999894i	$-0.495355\pi$
$719$	0.782506			0.0291825			0.0145913	+	0.999894i	$0.495355\pi$
$720$	5.20045	+	3.77835i	0.193809	+	0.140811i
$721$	1.92134	−	1.39594i	0.0715546	−	0.0519875i
$722$	6.19603	−	4.50168i	0.230592	−	0.167535i
$723$	11.8862	−	36.5820i	0.442053	−	1.36050i
$724$	11.8972	+	8.64384i	0.442157	+	0.321246i
$725$	3.75501	−	11.5567i	0.139458	−	0.429206i
$726$	−9.45128	−	29.0881i	−0.350770	−	1.07956i
$727$	−7.84178	+	5.69738i	−0.290835	+	0.211304i	−0.723630	−	0.690188i	$-0.757528\pi$
$727$	−7.84178	+	5.69738i	−0.290835	+	0.211304i	0.432794	+	0.901493i	$0.357528\pi$
$728$	−0.579395	−	1.78319i	−0.0214738	−	0.0660895i
$729$	5.08767	+	15.6582i	0.188432	+	0.579934i
$730$	−51.6144	+	37.5000i	−1.91033	+	1.38794i
$731$	18.8895	+	58.1359i	0.698653	+	2.15023i
$732$	13.5416	−	41.6769i	0.500514	−	1.54042i
$733$	−7.86856	−	5.71684i	−0.290632	−	0.211156i	0.432910	−	0.901437i	$-0.357487\pi$
$733$	−7.86856	−	5.71684i	−0.290632	−	0.211156i	−0.723541	+	0.690281i	$0.757487\pi$
$734$	−15.8839	+	48.8855i	−0.586284	+	1.80440i
$735$	−13.1353	+	9.54333i	−0.484501	+	0.352011i
$736$	2.93162	−	2.12994i	0.108061	−	0.0785108i
$737$	−9.46192	−	6.87449i	−0.348534	−	0.253225i
$738$	−1.71212			−0.0630240
$739$	46.4766			1.70967			0.854834	−	0.518901i	$-0.173659\pi$
$739$	46.4766			1.70967			0.854834	+	0.518901i	$0.173659\pi$
$740$	−63.5569	−	46.1768i	−2.33640	−	1.69749i
$741$	−2.86594	−	8.82044i	−0.105283	−	0.324027i
$742$	−0.716309	+	2.20457i	−0.0262965	+	0.0809324i
$743$	−22.1138			−0.811276			−0.405638	−	0.914034i	$-0.632951\pi$
$743$	−22.1138			−0.811276			−0.405638	+	0.914034i	$0.632951\pi$
$744$	6.98047	−	7.43563i	0.255917	−	0.272603i
$745$	13.3933			0.490691
$746$	−10.0703	+	30.9932i	−0.368700	+	1.13474i
$747$	−2.31128	−	7.11339i	−0.0845654	−	0.260265i
$748$	26.8333	+	19.4956i	0.981124	+	0.712828i
$749$	−5.61829			−0.205288
$750$	−27.0571			−0.987985
$751$	−27.3007	−	19.8351i	−0.996218	−	0.723795i	−0.0349439	−	0.999389i	$-0.511125\pi$
$751$	−27.3007	−	19.8351i	−0.996218	−	0.723795i	−0.961274	+	0.275595i	$0.911125\pi$
$752$	4.71447	−	3.42526i	0.171919	−	0.124906i
$753$	−37.7737	+	27.4442i	−1.37655	+	1.00012i
$754$	−3.02819	+	9.31982i	−0.110280	+	0.339408i
$755$	26.4057	+	19.1848i	0.961000	+	0.698207i
$756$	6.46643	−	19.9016i	0.235182	−	0.723815i
$757$	−7.57030	−	23.2990i	−0.275147	−	0.846816i	−0.989180	−	0.146704i	$-0.953133\pi$
$757$	−7.57030	−	23.2990i	−0.275147	−	0.846816i	0.714033	−	0.700112i	$-0.246867\pi$
$758$	−29.0289	+	21.0907i	−1.05438	+	0.766050i
$759$	0.513822	+	1.58138i	0.0186506	+	0.0574005i
$760$	−3.81170	−	11.7312i	−0.138265	−	0.425535i
$761$	−34.9386	+	25.3844i	−1.26652	+	0.920183i	−0.999058	−	0.0433840i	$-0.986186\pi$
$761$	−34.9386	+	25.3844i	−1.26652	+	0.920183i	−0.267465	+	0.963567i	$0.586186\pi$
$762$	14.1469	+	43.5397i	0.512488	+	1.57728i
$763$	8.42983	−	25.9444i	0.305180	−	0.939249i
$764$	−7.15371	−	5.19747i	−0.258812	−	0.188038i
$765$	−4.90687	+	15.1018i	−0.177408	+	0.546006i
$766$	−26.4134	+	19.1905i	−0.954356	+	0.693380i
$767$	6.34430	−	4.60940i	0.229079	−	0.166436i
$768$	10.5719	+	7.68094i	0.381481	+	0.277162i
$769$	20.7960			0.749924			0.374962	−	0.927040i	$-0.377656\pi$
$769$	20.7960			0.749924			0.374962	+	0.927040i	$0.377656\pi$
$770$	−21.9031			−0.789332
$771$	30.7519	+	22.3426i	1.10750	+	0.804648i
$772$	4.52934	+	13.9399i	0.163015	+	0.501708i
$773$	0.700196	−	2.15498i	0.0251843	−	0.0775094i	−0.937674	−	0.347515i	$-0.887026\pi$
$773$	0.700196	−	2.15498i	0.0251843	−	0.0775094i	0.962859	+	0.270006i	$0.0870256\pi$
$774$	14.3517			0.515861
$775$	−1.82238	+	14.4426i	−0.0654617	+	0.518793i
$776$	−7.73522			−0.277678
$777$	−13.9938	+	43.0684i	−0.502024	+	1.54507i
$778$	−21.8070	−	67.1151i	−0.781820	−	2.40619i
$779$	−3.90428	−	2.83662i	−0.139885	−	0.101633i
$780$	−13.1563			−0.471070
$781$	7.55349			0.270285
$782$	5.54388	+	4.02787i	0.198249	+	0.144036i
$783$	−16.1228	+	11.7139i	−0.576180	+	0.418619i
$784$	−7.10576	+	5.16264i	−0.253777	+	0.184380i
$785$	2.17768	−	6.70220i	0.0777246	−	0.239212i
$786$	6.56385	+	4.76892i	0.234125	+	0.170102i
$787$	−2.56980	+	7.90903i	−0.0916035	+	0.281926i	−0.986354	−	0.164641i	$-0.947354\pi$
$787$	−2.56980	+	7.90903i	−0.0916035	+	0.281926i	0.894750	+	0.446567i	$0.147354\pi$
$788$	−8.57438	−	26.3892i	−0.305450	−	0.940077i
$789$	25.6432	−	18.6309i	0.912922	−	0.663277i
$790$	15.4425	+	47.5272i	0.549420	+	1.69094i
$791$	9.15394	+	28.1729i	0.325477	+	1.00171i
$792$	1.14797	−	0.834047i	0.0407913	−	0.0296366i
$793$	−2.84027	−	8.74146i	−0.100861	−	0.310418i
$794$	9.38883	−	28.8959i	0.333197	−	1.02548i
$795$	2.39777	+	1.74208i	0.0850400	+	0.0617852i
$796$	−1.84199	+	5.66905i	−0.0652875	+	0.200934i
$797$	22.5596	−	16.3905i	0.799102	−	0.580582i	−0.111549	−	0.993759i	$-0.535581\pi$
$797$	22.5596	−	16.3905i	0.799102	−	0.580582i	0.910651	+	0.413177i	$0.135581\pi$
$798$	−31.5683	+	22.9357i	−1.11751	+	0.811916i
$799$	11.6459	+	8.46121i	0.412001	+	0.299336i
$800$	20.9559			0.740902
$801$	4.86272			0.171816
$802$	−10.3188	−	7.49704i	−0.364369	−	0.264730i
$803$	−6.39264	−	19.6745i	−0.225591	−	0.694299i
$804$	−9.13360	+	28.1103i	−0.322117	+	0.991375i
$805$	−2.48944			−0.0877414
$806$	1.46964	−	11.6471i	0.0517658	−	0.410252i
$807$	−17.8908			−0.629785
$808$	−4.28925	+	13.2009i	−0.150895	+	0.464408i
$809$	−3.57831	−	11.0129i	−0.125807	−	0.387193i	0.868240	−	0.496144i	$-0.165251\pi$
$809$	−3.57831	−	11.0129i	−0.125807	−	0.387193i	−0.994047	+	0.108950i	$0.965251\pi$
$810$	−50.6507	−	36.7999i	−1.77969	−	1.29302i
$811$	−39.2821			−1.37938			−0.689691	−	0.724104i	$-0.742254\pi$
$811$	−39.2821			−1.37938			−0.689691	+	0.724104i	$0.742254\pi$
$812$	22.6814			0.795959
$813$	33.7414	+	24.5146i	1.18336	+	0.859764i
$814$	37.4619	−	27.2176i	1.31304	−	0.953977i
$815$	−32.1820	+	23.3816i	−1.12729	+	0.819022i
$816$	−12.6027	+	38.7873i	−0.441184	+	1.35783i
$817$	32.7272	+	23.7777i	1.14498	+	0.831878i
$818$	7.55506	−	23.2521i	0.264156	−	0.812990i
$819$	0.493599	+	1.51914i	0.0172477	+	0.0530831i
$820$	−5.53847	+	4.02393i	−0.193412	+	0.140522i
$821$	2.61835	+	8.05844i	0.0913809	+	0.281242i	0.986294	−	0.165000i	$-0.0527623\pi$
$821$	2.61835	+	8.05844i	0.0913809	+	0.281242i	−0.894913	+	0.446241i	$0.852762\pi$
$822$	27.3323	+	84.1202i	0.953324	+	2.93403i
$823$	−3.24811	+	2.35989i	−0.113222	+	0.0822607i	−0.642956	−	0.765904i	$-0.722292\pi$
$823$	−3.24811	+	2.35989i	−0.113222	+	0.0822607i	0.529733	+	0.848164i	$0.322292\pi$
$824$	0.345571	+	1.06356i	0.0120385	+	0.0370508i
$825$	−2.97146	+	9.14520i	−0.103453	+	0.318395i
$826$	−26.6927	−	19.3934i	−0.928759	−	0.674783i
$827$	3.35688	−	10.3314i	0.116730	−	0.359258i	−0.875574	−	0.483084i	$-0.839516\pi$
$827$	3.35688	−	10.3314i	0.116730	−	0.359258i	0.992304	+	0.123826i	$0.0395165\pi$
$828$	0.716039	−	0.520233i	0.0248841	−	0.0180793i
$829$	12.1198	−	8.80555i	0.420938	−	0.305829i	−0.357077	−	0.934075i	$-0.616227\pi$
$829$	12.1198	−	8.80555i	0.420938	−	0.305829i	0.778015	+	0.628245i	$0.216227\pi$
$830$	−43.9813	−	31.9543i	−1.52661	−	1.10915i
$831$	16.0404			0.556435
$832$	−11.0794			−0.384110
$833$	−17.5529	−	12.7529i	−0.608172	−	0.441863i
$834$	16.1590	+	49.7323i	0.559541	+	1.72209i
$835$	−1.96391	+	6.04428i	−0.0679638	+	0.209171i
$836$	21.9498			0.759150
$837$	16.3404	−	17.4059i	0.564809	−	0.601636i
$838$	50.5261			1.74540
$839$	−11.7865	+	36.2752i	−0.406916	+	1.25236i	0.512369	+	0.858765i	$0.328768\pi$
$839$	−11.7865	+	36.2752i	−0.406916	+	1.25236i	−0.919285	+	0.393593i	$0.871232\pi$
$840$	3.11685	+	9.59266i	0.107541	+	0.330978i
$841$	5.98614	+	4.34919i	0.206419	+	0.149972i
$842$	26.7516			0.921922
$843$	−28.2273			−0.972201
$844$	−25.1118	−	18.2448i	−0.864383	−	0.628011i
$845$	−2.23244	+	1.62196i	−0.0767982	+	0.0557972i
$846$	2.73424	−	1.98654i	0.0940050	−	0.0682987i
$847$	−4.58825	+	14.1212i	−0.157654	+	0.485210i
$848$	1.29712	+	0.942409i	0.0445431	+	0.0323625i
$849$	18.1772	−	55.9436i	0.623839	−	1.91998i
$850$	12.2460	+	37.6894i	0.420035	+	1.29274i
$851$	4.25781	−	3.09348i	0.145956	−	0.106043i
$852$	−5.89886	−	18.1548i	−0.202092	−	0.621974i
$853$	−15.8360	−	48.7383i	−0.542215	−	1.66877i	−0.727521	−	0.686086i	$-0.759327\pi$
$853$	−15.8360	−	48.7383i	−0.542215	−	1.66877i	0.185306	−	0.982681i	$-0.440673\pi$
$854$	−31.2856	+	22.7304i	−1.07057	+	0.777817i
$855$	3.24727	+	9.99406i	0.111054	+	0.341790i
$856$	0.817511	−	2.51604i	0.0279419	−	0.0859965i
$857$	21.0462	+	15.2910i	0.718926	+	0.522330i	0.886041	−	0.463607i	$-0.153445\pi$
$857$	21.0462	+	15.2910i	0.718926	+	0.522330i	−0.167115	+	0.985937i	$0.553445\pi$
$858$	2.39630	−	7.37507i	0.0818085	−	0.251781i
$859$	25.6256	−	18.6181i	0.874334	−	0.635241i	−0.0574123	−	0.998351i	$-0.518285\pi$
$859$	25.6256	−	18.6181i	0.874334	−	0.635241i	0.931746	+	0.363110i	$0.118285\pi$
$860$	46.4257	−	33.7302i	1.58310	−	1.15019i
$861$	3.19255	+	2.31952i	0.108802	+	0.0790491i
$862$	−26.2292			−0.893372
$863$	21.2135			0.722116			0.361058	−	0.932543i	$-0.382416\pi$
$863$	21.2135			0.722116			0.361058	+	0.932543i	$0.382416\pi$
$864$	−27.8046	−	20.2012i	−0.945931	−	0.687259i
$865$	−3.08788	−	9.50351i	−0.104991	−	0.323129i
$866$	4.52550	−	13.9280i	0.153783	−	0.473294i
$867$	−67.6034			−2.29593
$868$	−26.6896	+	5.09536i	−0.905904	+	0.172948i
$869$	−16.2039			−0.549681
$870$	16.2901	−	50.1358i	0.552287	−	1.69976i
$871$	1.91571	+	5.89596i	0.0649115	+	0.199777i
$872$	10.3920	+	7.55026i	0.351919	+	0.255684i
$873$	6.58980			0.223031
$874$	4.53492			0.153396
$875$	10.6266	+	7.72069i	0.359245	+	0.261007i
$876$	−42.2954	+	30.7294i	−1.42903	+	1.03825i
$877$	26.0113	−	18.8983i	0.878340	−	0.638151i	−0.0544718	−	0.998515i	$-0.517348\pi$
$877$	26.0113	−	18.8983i	0.878340	−	0.638151i	0.932812	+	0.360364i	$0.117348\pi$
$878$	7.34806	−	22.6150i	0.247985	−	0.763219i
$879$	−32.4456	−	23.5731i	−1.09436	−	0.795101i
$880$	−4.68155	+	14.4083i	−0.157815	+	0.485705i
$881$	−13.0183	−	40.0661i	−0.438597	−	1.34986i	−0.889355	−	0.457217i	$-0.848846\pi$
$881$	−13.0183	−	40.0661i	−0.438597	−	1.34986i	0.450758	−	0.892646i	$-0.351154\pi$
$882$	−4.12111	+	2.99416i	−0.138765	+	0.100819i
$883$	6.46170	+	19.8871i	0.217454	+	0.669253i	0.998970	+	0.0453689i	$0.0144463\pi$
$883$	6.46170	+	19.8871i	0.217454	+	0.669253i	−0.781517	+	0.623884i	$0.785554\pi$
$884$	−5.43283	−	16.7205i	−0.182726	−	0.562372i
$885$	−34.1291	+	24.7962i	−1.14724	+	0.833515i
$886$	−16.2518	−	50.0179i	−0.545990	−	1.68039i
$887$	1.60074	−	4.92656i	0.0537475	−	0.165418i	−0.920580	−	0.390555i	$-0.872283\pi$
$887$	1.60074	−	4.92656i	0.0537475	−	0.165418i	0.974327	+	0.225137i	$0.0722831\pi$
$888$	−17.2511	−	12.5337i	−0.578910	−	0.420602i
$889$	6.86780	−	21.1369i	0.230339	−	0.708909i
$890$	28.5941	−	20.7748i	0.958476	−	0.696374i
$891$	16.4237	−	11.9325i	0.550214	−	0.399754i
$892$	−31.8349	−	23.1294i	−1.06591	−	0.774429i
$893$	9.52637			0.318788
$894$	19.9504			0.667240
$895$	−17.4804	−	12.7002i	−0.584304	−	0.424522i
$896$	4.52009	+	13.9114i	0.151006	+	0.464748i
$897$	0.272358	−	0.838230i	0.00909375	−	0.0279877i
$898$	53.0227			1.76939
$899$	23.4159	+	11.0145i	0.780963	+	0.367354i
$900$	5.11842			0.170614
$901$	−1.22389	+	3.76674i	−0.0407737	+	0.125488i
$902$	−1.24693	−	3.83764i	−0.0415181	−	0.127780i
$903$	−26.7612	−	19.4432i	−0.890558	−	0.647029i
$904$	−13.9487			−0.463925
$905$	−16.5927			−0.551560
$906$	39.3334	+	28.5774i	1.30676	+	0.949420i
$907$	−17.3674	+	12.6182i	−0.576676	+	0.418980i	−0.837524	−	0.546400i	$-0.815998\pi$
$907$	−17.3674	+	12.6182i	−0.576676	+	0.418980i	0.260848	+	0.965380i	$0.415998\pi$
$908$	−52.8396	+	38.3902i	−1.75354	+	1.27402i
$909$	3.65410	−	11.2462i	0.121199	−	0.373012i
$910$	9.39267	+	6.82417i	0.311364	+	0.226219i
$911$	−3.63142	+	11.1763i	−0.120314	+	0.370289i	−0.993018	−	0.117960i	$-0.962364\pi$
$911$	−3.63142	+	11.1763i	−0.120314	+	0.370289i	0.872704	+	0.488249i	$0.162364\pi$
$912$	8.34025	+	25.6686i	0.276173	+	0.849973i
$913$	14.2611	−	10.3613i	0.471973	−	0.342908i
$914$	−22.4187	−	68.9975i	−0.741543	−	2.28224i
$915$	15.2792	+	47.0246i	0.505115	+	1.55458i
$916$	30.4240	−	22.1044i	1.00524	−	0.730348i
$917$	−1.21714	−	3.74597i	−0.0401934	−	0.123703i
$918$	20.0839	−	61.8119i	0.662868	−	2.04010i
$919$	−27.1636	−	19.7355i	−0.896045	−	0.651014i	0.0414024	−	0.999143i	$-0.486817\pi$
$919$	−27.1636	−	19.7355i	−0.896045	−	0.651014i	−0.937447	+	0.348128i	$0.886817\pi$
$920$	0.362236	−	1.11485i	0.0119426	−	0.0367554i
$921$	−0.342258	+	0.248665i	−0.0112778	+	0.00819379i
$922$	19.3837	−	14.0831i	0.638367	−	0.463801i
$923$	−3.23916	−	2.35339i	−0.106618	−	0.0774626i
$924$	−17.9485			−0.590461
$925$	30.4359			1.00073
$926$	54.2524	+	39.4167i	1.78285	+	1.29531i
$927$	−0.294399	−	0.906067i	−0.00966934	−	0.0297592i
$928$	11.5114	−	35.4284i	0.377880	−	1.16300i
$929$	−3.65878			−0.120041			−0.0600204	−	0.998197i	$-0.519117\pi$
$929$	−3.65878			−0.120041			−0.0600204	+	0.998197i	$0.519117\pi$
$930$	−7.90590	+	62.6554i	−0.259245	+	2.05455i
$931$	−14.3584			−0.470577
$932$	8.42776	−	25.9380i	0.276060	−	0.849626i
$933$	−10.4783	−	32.2490i	−0.343045	−	1.05578i
$934$	47.0412	+	34.1774i	1.53923	+	1.11832i
$935$	−37.4237			−1.22388
$936$	−0.752140			−0.0245845
$937$	17.7341	+	12.8846i	0.579348	+	0.420921i	0.838489	−	0.544918i	$-0.183439\pi$
$937$	17.7341	+	12.8846i	0.579348	+	0.420921i	−0.259141	+	0.965840i	$0.583439\pi$
$938$	21.1016	−	15.3312i	0.688992	−	0.500582i
$939$	−5.25263	+	3.81626i	−0.171413	+	0.124539i
$940$	4.17598	−	12.8524i	0.136206	−	0.419198i
$941$	−39.2115	−	28.4888i	−1.27826	−	0.928709i	−0.278760	−	0.960361i	$-0.589923\pi$
$941$	−39.2115	−	28.4888i	−1.27826	−	0.928709i	−0.999499	+	0.0316513i	$0.989923\pi$
$942$	3.24383	−	9.98347i	0.105690	−	0.325279i
$943$	−0.141722	−	0.436176i	−0.00461511	−	0.0142039i
$944$	−18.4627	+	13.4140i	−0.600911	+	0.436587i
$945$	7.29616	+	22.4553i	0.237344	+	0.730470i
$946$	10.4522	+	32.1687i	0.339832	+	1.04590i
$947$	42.8226	−	31.1125i	1.39155	−	1.01102i	0.395855	−	0.918313i	$-0.370448\pi$
$947$	42.8226	−	31.1125i	1.39155	−	1.01102i	0.995694	−	0.0927056i	$-0.0295515\pi$
$948$	12.6544	+	38.9461i	0.410995	+	1.26491i
$949$	−3.38849	+	10.4287i	−0.109995	+	0.338530i
$950$	21.2170	+	15.4151i	0.688371	+	0.500131i
$951$	−3.51085	+	10.8053i	−0.113847	+	0.350386i
$952$	−10.9044	+	7.92249i	−0.353413	+	0.256770i
$953$	5.33012	−	3.87256i	0.172659	−	0.125444i	−0.498099	−	0.867120i	$-0.665969\pi$
$953$	5.33012	−	3.87256i	0.172659	−	0.125444i	0.670759	+	0.741675i	$0.265969\pi$
$954$	0.752285	+	0.546567i	0.0243561	+	0.0176958i
$955$	9.97707			0.322851
$956$	−69.6359			−2.25218
$957$	13.8288	+	10.0472i	0.447021	+	0.324780i
$958$	16.8621	+	51.8962i	0.544789	+	1.67669i
$959$	13.2688	−	40.8373i	0.428473	−	1.31871i
$960$	59.6016			1.92363
$961$	−30.0283	−	7.70059i	−0.968656	−	0.248406i
$962$	−24.5447			−0.791354
$963$	−0.696455	+	2.14347i	−0.0224430	+	0.0690723i
$964$	−14.9113	−	45.8924i	−0.480262	−	1.47809i
$965$	−13.3795	−	9.72078i	−0.430702	−	0.312923i
$966$	−3.70823			−0.119310
$967$	3.61677			0.116307			0.0581537	−	0.998308i	$-0.481479\pi$
$967$	3.61677			0.116307			0.0581537	+	0.998308i	$0.481479\pi$
$968$	−5.65626	−	4.10951i	−0.181799	−	0.132085i
$969$	−53.9378	+	39.1881i	−1.73273	+	1.25890i
$970$	38.7498	−	28.1534i	1.24418	−	0.903951i
$971$	−15.4790	+	47.6396i	−0.496746	+	1.52883i	0.317472	+	0.948268i	$0.397166\pi$
$971$	−15.4790	+	47.6396i	−0.496746	+	1.52883i	−0.814218	+	0.580559i	$0.802834\pi$
$972$	−16.0539	−	11.6639i	−0.514930	−	0.374119i
$973$	7.84461	−	24.1432i	0.251487	−	0.773996i
$974$	−16.4743	−	50.7027i	−0.527870	−	1.62462i
$975$	4.12355	−	2.99593i	0.132059	−	0.0959467i
$976$	8.26557	+	25.4388i	0.264574	+	0.814276i
$977$	−5.70793	−	17.5672i	−0.182613	−	0.562025i	0.817286	−	0.576232i	$-0.195478\pi$
$977$	−5.70793	−	17.5672i	−0.182613	−	0.562025i	−0.999899	+	0.0142071i	$0.995478\pi$
$978$	−47.9377	+	34.8288i	−1.53288	+	1.11370i
$979$	3.54149	+	10.8996i	0.113186	+	0.348352i
$980$	−6.29414	+	19.3714i	−0.201059	+	0.618796i
$981$	−8.85321	−	6.43223i	−0.282661	−	0.205365i
$982$	9.21527	−	28.3617i	0.294071	−	0.905058i
$983$	−34.8683	+	25.3333i	−1.11212	+	0.808006i	−0.982997	−	0.183622i	$-0.941218\pi$
$983$	−34.8683	+	25.3333i	−1.11212	+	0.808006i	−0.129128	+	0.991628i	$0.541218\pi$
$984$	−1.50329	+	1.09221i	−0.0479233	+	0.0348183i
$985$	25.3284	+	18.4021i	0.807029	+	0.586341i
$986$	70.4454			2.24344
$987$	−7.78976			−0.247951
$988$	−9.41271	−	6.83874i	−0.299458	−	0.217569i
$989$	1.18797	+	3.65621i	0.0377754	+	0.116261i
$990$	−2.71515	+	8.35637i	−0.0862931	+	0.265583i
$991$	45.5312			1.44635			0.723174	−	0.690666i	$-0.242683\pi$
$991$	45.5312			1.44635			0.723174	+	0.690666i	$0.242683\pi$
$992$	−5.58669	+	44.2754i	−0.177378	+	1.40574i
$993$	−60.6904			−1.92595
$994$	−5.20555	+	16.0210i	−0.165110	+	0.508156i
$995$	−2.07834	−	6.39646i	−0.0658877	−	0.202781i
$996$	−36.0405	−	26.1849i	−1.14199	−	0.829701i
$997$	−56.7180			−1.79628			−0.898139	−	0.439712i	$-0.855081\pi$
$997$	−56.7180			−1.79628			−0.898139	+	0.439712i	$0.855081\pi$
$998$	−65.1014			−2.06075
$999$	−40.3828	−	29.3398i	−1.27765	−	0.928270i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.k.e.287.3	yes	68
31.4	even	5	inner	403.2.k.e.66.3	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.k.e.66.3	✓	68	31.4	even	5	inner
403.2.k.e.287.3	yes	68	1.1	even	1	trivial

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.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.651553 + 2.00527i) q^{2} +(-0.602423 - 1.85407i) q^{3} +(-1.97856 - 1.43751i) q^{4} +2.75944 q^{5} +4.11042 q^{6} +(-1.61436 - 1.17290i) q^{7} +(0.760164 - 0.552291i) q^{8} +(-0.647600 + 0.470509i) q^{9} +O(q^{10})\)	\(q+(-0.651553 + 2.00527i) q^{2} +(-0.602423 - 1.85407i) q^{3} +(-1.97856 - 1.43751i) q^{4} +2.75944 q^{5} +4.11042 q^{6} +(-1.61436 - 1.17290i) q^{7} +(0.760164 - 0.552291i) q^{8} +(-0.647600 + 0.470509i) q^{9} +(-1.79792 + 5.53344i) q^{10} +(-1.52627 - 1.10890i) q^{11} +(-1.47331 + 4.53438i) q^{12} +(0.309017 + 0.951057i) q^{13} +(3.40383 - 2.47302i) q^{14} +(-1.66235 - 5.11620i) q^{15} +(-0.899280 - 2.76770i) q^{16} +(5.81579 - 4.22542i) q^{17} +(-0.521553 - 1.60518i) q^{18} +(1.47010 - 4.52451i) q^{19} +(-5.45973 - 3.96673i) q^{20} +(-1.20211 + 3.69971i) q^{21} +(3.21809 - 2.33808i) q^{22} +(0.365759 - 0.265740i) q^{23} +(-1.48192 - 1.07668i) q^{24} +2.61454 q^{25} -2.10847 q^{26} +(-3.46901 - 2.52038i) q^{27} +(1.50806 + 4.64132i) q^{28} +(1.43621 - 4.42019i) q^{29} +11.3425 q^{30} +(-0.697017 + 5.52396i) q^{31} +8.01515 q^{32} +(-1.13651 + 3.49783i) q^{33} +(4.68382 + 14.4153i) q^{34} +(-4.45474 - 3.23656i) q^{35} +1.95768 q^{36} +11.6410 q^{37} +(8.11502 + 5.89591i) q^{38} +(1.57716 - 1.14588i) q^{39} +(2.09763 - 1.52402i) q^{40} +(0.313473 - 0.964771i) q^{41} +(-6.63570 - 4.82111i) q^{42} +(-2.62766 + 8.08711i) q^{43} +(1.42577 + 4.38805i) q^{44} +(-1.78702 + 1.29834i) q^{45} +(0.294569 + 0.906591i) q^{46} +(0.618792 + 1.90445i) q^{47} +(-4.58975 + 3.33465i) q^{48} +(-0.932659 - 2.87043i) q^{49} +(-1.70351 + 5.24286i) q^{50} +(-11.3378 - 8.23738i) q^{51} +(0.755744 - 2.32594i) q^{52} +(-0.445724 + 0.323837i) q^{53} +(7.31429 - 5.31414i) q^{54} +(-4.21165 - 3.05995i) q^{55} -1.87496 q^{56} -9.27436 q^{57} +(7.92791 + 5.75997i) q^{58} +(-2.42331 - 7.45817i) q^{59} +(-4.06551 + 12.5124i) q^{60} -9.19132 q^{61} +(-10.6229 - 4.99686i) q^{62} +1.59732 q^{63} +(-3.42373 + 10.5372i) q^{64} +(0.852715 + 2.62439i) q^{65} +(-6.27361 - 4.55804i) q^{66} +6.19938 q^{67} -17.5810 q^{68} +(-0.713041 - 0.518055i) q^{69} +(9.39267 - 6.82417i) q^{70} +(-3.23916 + 2.35339i) q^{71} +(-0.232424 + 0.715327i) q^{72} +(8.87119 + 6.44530i) q^{73} +(-7.58474 + 23.3434i) q^{74} +(-1.57506 - 4.84752i) q^{75} +(-9.41271 + 6.83874i) q^{76} +(1.16332 + 3.58032i) q^{77} +(1.27019 + 3.90924i) q^{78} +(6.94872 - 5.04854i) q^{79} +(-2.48151 - 7.63731i) q^{80} +(-3.32523 + 10.2340i) q^{81} +(1.73038 + 1.25720i) q^{82} +(-2.88738 + 8.88644i) q^{83} +(7.69682 - 5.59207i) q^{84} +(16.0484 - 11.6598i) q^{85} +(-14.5048 - 10.5384i) q^{86} -9.06052 q^{87} -1.77265 q^{88} +(-4.91459 - 3.57066i) q^{89} +(-1.43920 - 4.42939i) q^{90} +(0.616630 - 1.89779i) q^{91} -1.10568 q^{92} +(10.6617 - 2.03545i) q^{93} -4.22211 q^{94} +(4.05666 - 12.4851i) q^{95} +(-4.82851 - 14.8606i) q^{96} +(-6.66010 - 4.83885i) q^{97} +6.36367 q^{98} +1.51016 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9}+O(q^{10}) \) 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9	\( 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9} - 13 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 3 q^{14} - 14 q^{15} + 9 q^{16} + 12 q^{17} - 19 q^{18} - 4 q^{19} - 53 q^{20} - 13 q^{21} - 14 q^{22} - 9 q^{23} + 2 q^{24} + 96 q^{25} + 12 q^{26} + 25 q^{27} - 25 q^{28} - 78 q^{30} - 2 q^{31} + 76 q^{32} + 29 q^{33} - 15 q^{34} - 36 q^{35} + 52 q^{36} + 24 q^{37} - 19 q^{38} + 3 q^{39} - 12 q^{40} - 40 q^{41} + 11 q^{42} - 22 q^{43} + 4 q^{44} + 63 q^{45} - 24 q^{46} + 3 q^{47} + 68 q^{48} + 33 q^{49} - 76 q^{50} - 59 q^{51} - 13 q^{52} - q^{53} + 18 q^{54} - 22 q^{55} + 78 q^{56} - 16 q^{57} + 5 q^{58} - 18 q^{59} + 43 q^{60} - 32 q^{61} - 39 q^{62} + 20 q^{63} + 23 q^{64} + 2 q^{65} + 11 q^{66} + 114 q^{67} + 98 q^{68} - 46 q^{69} + 32 q^{70} - 2 q^{71} + 28 q^{72} + 10 q^{73} - 43 q^{74} - 12 q^{75} - 35 q^{76} - 3 q^{77} - 6 q^{78} - 10 q^{79} + 68 q^{80} - 54 q^{81} - 80 q^{82} - 22 q^{83} - 14 q^{84} - 50 q^{85} - 66 q^{86} + 76 q^{87} - 34 q^{88} - 10 q^{89} - 63 q^{90} - 8 q^{91} - 64 q^{92} - 16 q^{93} + 30 q^{94} + 15 q^{95} + 34 q^{96} - 7 q^{97} + 138 q^{98} - 48 q^{99}+O(q^{100}) \) 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9 - 13 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 3 * q^14 - 14 * q^15 + 9 * q^16 + 12 * q^17 - 19 * q^18 - 4 * q^19 - 53 * q^20 - 13 * q^21 - 14 * q^22 - 9 * q^23 + 2 * q^24 + 96 * q^25 + 12 * q^26 + 25 * q^27 - 25 * q^28 - 78 * q^30 - 2 * q^31 + 76 * q^32 + 29 * q^33 - 15 * q^34 - 36 * q^35 + 52 * q^36 + 24 * q^37 - 19 * q^38 + 3 * q^39 - 12 * q^40 - 40 * q^41 + 11 * q^42 - 22 * q^43 + 4 * q^44 + 63 * q^45 - 24 * q^46 + 3 * q^47 + 68 * q^48 + 33 * q^49 - 76 * q^50 - 59 * q^51 - 13 * q^52 - q^53 + 18 * q^54 - 22 * q^55 + 78 * q^56 - 16 * q^57 + 5 * q^58 - 18 * q^59 + 43 * q^60 - 32 * q^61 - 39 * q^62 + 20 * q^63 + 23 * q^64 + 2 * q^65 + 11 * q^66 + 114 * q^67 + 98 * q^68 - 46 * q^69 + 32 * q^70 - 2 * q^71 + 28 * q^72 + 10 * q^73 - 43 * q^74 - 12 * q^75 - 35 * q^76 - 3 * q^77 - 6 * q^78 - 10 * q^79 + 68 * q^80 - 54 * q^81 - 80 * q^82 - 22 * q^83 - 14 * q^84 - 50 * q^85 - 66 * q^86 + 76 * q^87 - 34 * q^88 - 10 * q^89 - 63 * q^90 - 8 * q^91 - 64 * q^92 - 16 * q^93 + 30 * q^94 + 15 * q^95 + 34 * q^96 - 7 * q^97 + 138 * q^98 - 48 * q^99

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