LMFDB - Embedded newform 201.2.d.a.200.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,2,Mod(200,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("201.200");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	201.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.60499308063$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 7 x^{18} + 32 x^{16} + 128 x^{14} + 423 x^{12} + 1186 x^{10} + 3807 x^{8} + 10368 x^{6} + \cdots + 59049 $ x^20 + 7x^18 + 32x^16 + 128x^14 + 423x^12 + 1186x^10 + 3807x^8 + 10368x^6 + 23328x^4 + 45927*x^2 + 59049
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			200.12
Root			$0.421281 - 1.68004i$ of defining polynomial
Character	$\chi$	$=$	201.200
Dual form			201.2.d.a.200.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.598526 q^{2} +(0.421281 + 1.68004i) q^{3} -1.64177 q^{4} -3.30634 q^{5} +(0.252148 + 1.00555i) q^{6} +2.20280i q^{7} -2.17969 q^{8} +(-2.64504 + 1.41554i) q^{9} +O(q^{10})$	\(q+0.598526 q^{2} +(0.421281 + 1.68004i) q^{3} -1.64177 q^{4} -3.30634 q^{5} +(0.252148 + 1.00555i) q^{6} +2.20280i q^{7} -2.17969 q^{8} +(-2.64504 + 1.41554i) q^{9} -1.97893 q^{10} +4.09110 q^{11} +(-0.691645 - 2.75823i) q^{12} +5.23566i q^{13} +1.31843i q^{14} +(-1.39290 - 5.55476i) q^{15} +1.97893 q^{16} -3.25197i q^{17} +(-1.58313 + 0.847235i) q^{18} -0.137471 q^{19} +5.42823 q^{20} +(-3.70078 + 0.927997i) q^{21} +2.44863 q^{22} -3.21123i q^{23} +(-0.918263 - 3.66196i) q^{24} +5.93186 q^{25} +3.13368i q^{26} +(-3.49246 - 3.84743i) q^{27} -3.61648i q^{28} +9.21673i q^{29} +(-0.833685 - 3.32467i) q^{30} -1.43807i q^{31} +5.54383 q^{32} +(1.72350 + 6.87320i) q^{33} -1.94639i q^{34} -7.28319i q^{35} +(4.34254 - 2.32398i) q^{36} +6.90219 q^{37} -0.0822798 q^{38} +(-8.79611 + 2.20569i) q^{39} +7.20680 q^{40} -8.31041 q^{41} +(-2.21501 + 0.555430i) q^{42} +9.13293i q^{43} -6.71663 q^{44} +(8.74540 - 4.68023i) q^{45} -1.92201i q^{46} +12.5055i q^{47} +(0.833685 + 3.32467i) q^{48} +2.14769 q^{49} +3.55037 q^{50} +(5.46344 - 1.37000i) q^{51} -8.59574i q^{52} -2.45213 q^{53} +(-2.09033 - 2.30279i) q^{54} -13.5265 q^{55} -4.80142i q^{56} +(-0.0579138 - 0.230956i) q^{57} +5.51645i q^{58} -9.02089i q^{59} +(2.28681 + 9.11962i) q^{60} -10.2902i q^{61} -0.860720i q^{62} +(-3.11814 - 5.82650i) q^{63} -0.639731 q^{64} -17.3109i q^{65} +(1.03156 + 4.11379i) q^{66} +(7.09695 - 4.07839i) q^{67} +5.33898i q^{68} +(5.39499 - 1.35283i) q^{69} -4.35918i q^{70} -0.302613i q^{71} +(5.76538 - 3.08543i) q^{72} -3.46215 q^{73} +4.13114 q^{74} +(2.49898 + 9.96573i) q^{75} +0.225695 q^{76} +9.01186i q^{77} +(-5.26470 + 1.32016i) q^{78} +5.02568i q^{79} -6.54300 q^{80} +(4.99252 - 7.48831i) q^{81} -4.97400 q^{82} -0.995273i q^{83} +(6.07581 - 1.52355i) q^{84} +10.7521i q^{85} +5.46630i q^{86} +(-15.4844 + 3.88283i) q^{87} -8.91734 q^{88} +5.26307i q^{89} +(5.23435 - 2.80124i) q^{90} -11.5331 q^{91} +5.27209i q^{92} +(2.41600 - 0.605830i) q^{93} +7.48488i q^{94} +0.454524 q^{95} +(2.33551 + 9.31383i) q^{96} -2.53000i q^{97} +1.28545 q^{98} +(-10.8211 + 5.79109i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 12 q^{4} - 4 q^{6} - 14 q^{9}+O(q^{10}) $ 20 * q + 12 * q^4 - 4 * q^6 - 14 * q^9	$ 20 q + 12 q^{4} - 4 q^{6} - 14 q^{9} - 12 q^{10} + 2 q^{15} + 12 q^{16} + 24 q^{19} + 12 q^{21} - 28 q^{22} + 2 q^{24} - 4 q^{25} + 10 q^{33} - 44 q^{36} + 24 q^{37} - 8 q^{39} - 32 q^{40} - 48 q^{49} - 26 q^{54} - 8 q^{55} - 38 q^{60} - 16 q^{64} + 32 q^{67} + 4 q^{73} + 116 q^{76} - 30 q^{81} - 32 q^{82} + 90 q^{84} - 40 q^{88} + 74 q^{90} + 20 q^{91} - 2 q^{93} + 30 q^{96}+O(q^{100}) $ 20 * q + 12 * q^4 - 4 * q^6 - 14 * q^9 - 12 * q^10 + 2 * q^15 + 12 * q^16 + 24 * q^19 + 12 * q^21 - 28 * q^22 + 2 * q^24 - 4 * q^25 + 10 * q^33 - 44 * q^36 + 24 * q^37 - 8 * q^39 - 32 * q^40 - 48 * q^49 - 26 * q^54 - 8 * q^55 - 38 * q^60 - 16 * q^64 + 32 * q^67 + 4 * q^73 + 116 * q^76 - 30 * q^81 - 32 * q^82 + 90 * q^84 - 40 * q^88 + 74 * q^90 + 20 * q^91 - 2 * q^93 + 30 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.598526			0.423222			0.211611	−	0.977354i	$-0.432129\pi$
$2$	0.598526			0.423222			0.211611	+	0.977354i	$0.432129\pi$
$3$	0.421281	+	1.68004i	0.243227	+	0.969969i
$3$	0.421281	+	1.68004i	0.243227	+	0.969969i
$4$	−1.64177			−0.820883
$5$	−3.30634			−1.47864			−0.739319	−	0.673355i	$-0.764852\pi$
$5$	−3.30634			−1.47864			−0.739319	+	0.673355i	$0.764852\pi$
$6$	0.252148	+	1.00555i	0.102939	+	0.410512i
$7$			2.20280i			0.832579i	0.909232	+	0.416289i	$0.136670\pi$
$7$			2.20280i			0.832579i	−0.909232	+	0.416289i	$0.863330\pi$
$8$	−2.17969			−0.770638
$9$	−2.64504	+	1.41554i	−0.881681	+	0.471845i
$10$	−1.97893			−0.625792
$11$	4.09110			1.23351			0.616756	−	0.787154i	$-0.288446\pi$
$11$	4.09110			1.23351			0.616756	+	0.787154i	$0.288446\pi$
$12$	−0.691645	−	2.75823i	−0.199661	−	0.796232i
$13$			5.23566i			1.45211i	0.687636	+	0.726056i	$0.258649\pi$
$13$			5.23566i			1.45211i	−0.687636	+	0.726056i	$0.741351\pi$
$14$			1.31843i			0.352366i
$15$	−1.39290	−	5.55476i	−0.359644	−	1.43423i
$16$	1.97893			0.494732
$17$		−	3.25197i		−	0.788720i	−0.918956	−	0.394360i	$-0.870966\pi$
$17$		−	3.25197i		−	0.788720i	0.918956	−	0.394360i	$-0.129034\pi$
$18$	−1.58313	+	0.847235i	−0.373147	+	0.199695i
$19$	−0.137471			−0.0315379			−0.0157690	−	0.999876i	$-0.505020\pi$
$19$	−0.137471			−0.0315379			−0.0157690	+	0.999876i	$0.505020\pi$
$20$	5.42823			1.21379
$21$	−3.70078	+	0.927997i	−0.807576	+	0.202505i
$22$	2.44863			0.522050
$23$		−	3.21123i		−	0.669588i	−0.942291	−	0.334794i	$-0.891333\pi$
$23$		−	3.21123i		−	0.669588i	0.942291	−	0.334794i	$-0.108667\pi$
$24$	−0.918263	−	3.66196i	−0.187440	−	0.747495i
$25$	5.93186			1.18637
$26$			3.13368i			0.614566i
$27$	−3.49246	−	3.84743i	−0.672124	−	0.740439i
$28$		−	3.61648i		−	0.683450i
$29$			9.21673i			1.71150i	0.517387	+	0.855752i	$0.326905\pi$
$29$			9.21673i			1.71150i	−0.517387	+	0.855752i	$0.673095\pi$
$30$	−0.833685	−	3.32467i	−0.152209	−	0.606999i
$31$		−	1.43807i		−	0.258284i	−0.991626	−	0.129142i	$-0.958778\pi$
$31$		−	1.43807i		−	0.258284i	0.991626	−	0.129142i	$-0.0412223\pi$
$32$	5.54383			0.980019
$33$	1.72350	+	6.87320i	0.300023	+	1.19647i
$34$		−	1.94639i		−	0.333804i
$35$		−	7.28319i		−	1.23108i
$36$	4.34254	−	2.32398i	0.723757	−	0.387330i
$37$	6.90219			1.13471			0.567357	−	0.823472i	$-0.307966\pi$
$37$	6.90219			1.13471			0.567357	+	0.823472i	$0.307966\pi$
$38$	−0.0822798			−0.0133475
$39$	−8.79611	+	2.20569i	−1.40850	+	0.353192i
$40$	7.20680			1.13949
$41$	−8.31041			−1.29787			−0.648934	−	0.760845i	$-0.724785\pi$
$41$	−8.31041			−1.29787			−0.648934	+	0.760845i	$0.724785\pi$
$42$	−2.21501	+	0.555430i	−0.341784	+	0.0857048i
$43$			9.13293i			1.39276i	0.717674	+	0.696379i	$0.245207\pi$
$43$			9.13293i			1.39276i	−0.717674	+	0.696379i	$0.754793\pi$
$44$	−6.71663			−1.01257
$45$	8.74540	−	4.68023i	1.30369	−	0.697688i
$46$		−	1.92201i		−	0.283384i
$47$			12.5055i			1.82412i	0.410061	+	0.912058i	$0.365507\pi$
$47$			12.5055i			1.82412i	−0.410061	+	0.912058i	$0.634493\pi$
$48$	0.833685	+	3.32467i	0.120332	+	0.479875i
$49$	2.14769			0.306812
$50$	3.55037			0.502098
$51$	5.46344	−	1.37000i	0.765034	−	0.191838i
$52$		−	8.59574i		−	1.19201i
$53$	−2.45213			−0.336827			−0.168413	−	0.985716i	$-0.553864\pi$
$53$	−2.45213			−0.336827			−0.168413	+	0.985716i	$0.553864\pi$
$54$	−2.09033	−	2.30279i	−0.284458	−	0.313370i
$55$	−13.5265			−1.82392
$56$		−	4.80142i		−	0.641617i
$57$	−0.0579138	−	0.230956i	−0.00767087	−	0.0305908i
$58$			5.51645i			0.724346i
$59$		−	9.02089i		−	1.17442i	−0.809435	−	0.587210i	$-0.800226\pi$
$59$		−	9.02089i		−	1.17442i	0.809435	−	0.587210i	$-0.199774\pi$
$60$	2.28681	+	9.11962i	0.295226	+	1.17734i
$61$		−	10.2902i		−	1.31753i	−0.752351	−	0.658763i	$-0.771080\pi$
$61$		−	10.2902i		−	1.31753i	0.752351	−	0.658763i	$-0.228920\pi$
$62$		−	0.860720i		−	0.109312i
$63$	−3.11814	−	5.82650i	−0.392848	−	0.734069i
$64$	−0.639731			−0.0799664
$65$		−	17.3109i		−	2.14715i
$66$	1.03156	+	4.11379i	0.126976	+	0.506372i
$67$	7.09695	−	4.07839i	0.867031	−	0.498254i
$67$	7.09695	−	4.07839i	0.867031	−	0.498254i
$68$			5.33898i			0.647447i
$69$	5.39499	−	1.35283i	0.649480	−	0.162862i
$70$		−	4.35918i		−	0.521021i
$71$		−	0.302613i		−	0.0359135i	−0.999839	−	0.0179568i	$-0.994284\pi$
$71$		−	0.302613i		−	0.0359135i	0.999839	−	0.0179568i	$-0.00571612\pi$
$72$	5.76538	−	3.08543i	0.679457	−	0.363622i
$73$	−3.46215			−0.405214			−0.202607	−	0.979260i	$-0.564941\pi$
$73$	−3.46215			−0.405214			−0.202607	+	0.979260i	$0.564941\pi$
$74$	4.13114			0.480236
$75$	2.49898	+	9.96573i	0.288557	+	1.15074i
$76$	0.225695			0.0258889
$77$			9.01186i			1.02700i
$78$	−5.26470	+	1.32016i	−0.596110	+	0.149479i
$79$			5.02568i			0.565433i	0.959204	+	0.282716i	$0.0912355\pi$
$79$			5.02568i			0.565433i	−0.959204	+	0.282716i	$0.908764\pi$
$80$	−6.54300			−0.731530
$81$	4.99252	−	7.48831i	0.554725	−	0.832034i
$82$	−4.97400			−0.549286
$83$		−	0.995273i		−	0.109245i	−0.998507	−	0.0546227i	$-0.982604\pi$
$83$		−	0.995273i		−	0.109245i	0.998507	−	0.0546227i	$-0.0173956\pi$
$84$	6.07581	−	1.52355i	0.662926	−	0.166233i
$85$			10.7521i			1.16623i
$86$			5.46630i			0.589446i
$87$	−15.4844	+	3.88283i	−1.66011	+	0.416283i
$88$	−8.91734			−0.950592
$89$			5.26307i			0.557884i	0.960308	+	0.278942i	$0.0899837\pi$
$89$			5.26307i			0.557884i	−0.960308	+	0.278942i	$0.910016\pi$
$90$	5.23435	−	2.80124i	0.551749	−	0.295277i
$91$	−11.5331			−1.20900
$92$			5.27209i			0.549654i
$93$	2.41600	−	0.605830i	0.250528	−	0.0628216i
$94$			7.48488i			0.772006i
$95$	0.454524			0.0466332
$96$	2.33551	+	9.31383i	0.238367	+	0.950589i
$97$		−	2.53000i		−	0.256883i	−0.991717	−	0.128441i	$-0.959003\pi$
$97$		−	2.53000i		−	0.256883i	0.991717	−	0.128441i	$-0.0409974\pi$
$98$	1.28545			0.129850
$99$	−10.8211	+	5.79109i	−1.08757	+	0.582027i
$100$	−9.73872			−0.973872
$101$	0.546843			0.0544129			0.0272064	−	0.999630i	$-0.491339\pi$
$101$	0.546843			0.0544129			0.0272064	+	0.999630i	$0.491339\pi$
$102$	3.27001	−	0.819978i	0.323779	−	0.0811899i
$103$	7.18228			0.707691			0.353846	−	0.935304i	$-0.384874\pi$
$103$	7.18228			0.707691			0.353846	+	0.935304i	$0.384874\pi$
$104$		−	11.4121i		−	1.11905i
$105$	12.2360	−	3.06827i	1.19411	−	0.299432i
$106$	−1.46767			−0.142552
$107$			5.10797i			0.493806i	0.969040	+	0.246903i	$0.0794129\pi$
$107$			5.10797i			0.493806i	−0.969040	+	0.246903i	$0.920587\pi$
$108$	5.73380	+	6.31659i	0.551735	+	0.607814i
$109$			6.38085i			0.611175i	0.952164	+	0.305587i	$0.0988528\pi$
$109$			6.38085i			0.611175i	−0.952164	+	0.305587i	$0.901147\pi$
$110$	−8.09599			−0.771923
$111$	2.90776	+	11.5959i	0.275993	+	1.10064i
$112$			4.35918i			0.411904i
$113$	10.5353			0.991076			0.495538	−	0.868586i	$-0.334971\pi$
$113$	10.5353			0.991076			0.495538	+	0.868586i	$0.334971\pi$
$114$	−0.0346629	−	0.138233i	−0.00324648	−	0.0129467i
$115$			10.6174i			0.990079i
$116$		−	15.1317i		−	1.40494i
$117$	−7.41127	−	13.8486i	−0.685172	−	1.28030i
$118$		−	5.39924i		−	0.497040i
$119$	7.16344			0.656671
$120$	3.03609	+	12.1077i	0.277156	+	1.10527i
$121$	5.73709			0.521554
$122$		−	6.15896i		−	0.557606i
$123$	−3.50102	−	13.9618i	−0.315676	−	1.25889i
$124$			2.36097i			0.212021i
$125$	−3.08103			−0.275575
$126$	−1.86629	−	3.48731i	−0.166262	−	0.310674i
$127$	−9.22194			−0.818315			−0.409158	−	0.912464i	$-0.634177\pi$
$127$	−9.22194			−0.818315			−0.409158	+	0.912464i	$0.634177\pi$
$128$	−11.4705			−1.01386
$129$	−15.3437	+	3.84753i	−1.35093	+	0.338756i
$130$		−	10.3610i		−	0.908720i
$131$			3.91292i			0.341873i	0.985282	+	0.170937i	$0.0546794\pi$
$131$			3.91292i			0.341873i	−0.985282	+	0.170937i	$0.945321\pi$
$132$	−2.82959	−	11.2842i	−0.246284	−	0.982162i
$133$		−	0.302820i		−	0.0262578i
$134$	4.24771	−	2.44102i	0.366947	−	0.210872i
$135$	11.5472	+	12.7209i	0.993828	+	1.09484i
$136$			7.08831i			0.607817i
$137$	7.07762			0.604682			0.302341	−	0.953200i	$-0.402232\pi$
$137$	7.07762			0.604682			0.302341	+	0.953200i	$0.402232\pi$
$138$	3.22904	−	0.809705i	0.274874	−	0.0689267i
$139$		−	14.5047i		−	1.23028i	−0.788420	−	0.615138i	$-0.789100\pi$
$139$		−	14.5047i		−	1.23028i	0.788420	−	0.615138i	$-0.210900\pi$
$140$			11.9573i			1.01058i
$141$	−21.0097	+	5.26833i	−1.76934	+	0.443674i
$142$		−	0.181122i		−	0.0151994i
$143$			21.4196i			1.79120i
$144$	−5.23435	+	2.80124i	−0.436196	+	0.233437i
$145$		−	30.4736i		−	2.53069i
$146$	−2.07219			−0.171496
$147$	0.904780	+	3.60819i	0.0746250	+	0.297599i
$148$	−11.3318			−0.931467
$149$		−	16.0700i		−	1.31650i	−0.752798	−	0.658252i	$-0.771296\pi$
$149$		−	16.0700i		−	1.31650i	0.752798	−	0.658252i	$-0.228704\pi$
$150$	1.49570	+	5.96475i	0.122124	+	0.487020i
$151$	3.48688			0.283759			0.141879	−	0.989884i	$-0.454686\pi$
$151$	3.48688			0.283759			0.141879	+	0.989884i	$0.454686\pi$
$152$	0.299644			0.0243043
$153$	4.60328	+	8.60162i	0.372153	+	0.695400i
$154$			5.39384i			0.434648i
$155$			4.75473i			0.381909i
$156$	14.4412	−	3.62122i	1.15622	−	0.289930i
$157$	18.5468			1.48019			0.740097	−	0.672501i	$-0.234780\pi$
$157$	18.5468			1.48019			0.740097	+	0.672501i	$0.234780\pi$
$158$			3.00800i			0.239304i
$159$	−1.03304	−	4.11968i	−0.0819252	−	0.326711i
$160$	−18.3298			−1.44909
$161$	7.07369			0.557485
$162$	2.98816	−	4.48195i	0.234772	−	0.352135i
$163$	13.5039			1.05770			0.528852	−	0.848714i	$-0.322623\pi$
$163$	13.5039			1.05770			0.528852	+	0.848714i	$0.322623\pi$
$164$	13.6437			1.06540
$165$	−5.69848	−	22.7251i	−0.443626	−	1.76915i
$166$		−	0.595697i		−	0.0462351i
$167$			9.79110i			0.757658i	0.925467	+	0.378829i	$0.123673\pi$
$167$			9.79110i			0.757658i	−0.925467	+	0.378829i	$0.876327\pi$
$168$	8.06656	−	2.02275i	0.622349	−	0.156058i
$169$	−14.4122			−1.10863
$170$			6.43543i			0.493575i
$171$	0.363616	−	0.194594i	0.0278064	−	0.0148810i
$172$		−	14.9941i		−	1.14329i
$173$		−	1.82677i		−	0.138887i	−0.997586	−	0.0694434i	$-0.977878\pi$
$173$		−	1.82677i		−	0.138887i	0.997586	−	0.0694434i	$-0.0221223\pi$
$174$	−9.26784	+	2.32398i	−0.702593	+	0.176180i
$175$			13.0667i			0.987747i
$176$	8.09599			0.610259
$177$	15.1554	−	3.80033i	1.13915	−	0.285650i
$178$			3.15008i			0.236109i
$179$	−14.9298			−1.11591			−0.557953	−	0.829873i	$-0.688413\pi$
$179$	−14.9298			−1.11591			−0.557953	+	0.829873i	$0.688413\pi$
$180$	−14.3579	+	7.68385i	−1.07018	+	0.572720i
$181$	−6.45722			−0.479962			−0.239981	−	0.970778i	$-0.577141\pi$
$181$	−6.45722			−0.479962			−0.239981	+	0.970778i	$0.577141\pi$
$182$	−6.90287			−0.511675
$183$	17.2879	−	4.33507i	1.27796	−	0.320458i
$184$			6.99950i			0.516010i
$185$	−22.8210			−1.67783
$186$	1.44604	−	0.362605i	0.106029	−	0.0265875i
$187$		−	13.3042i		−	0.972896i
$188$		−	20.5311i		−	1.49739i
$189$	8.47511	−	7.69317i	0.616474	−	0.559596i
$190$	0.272045			0.0197362
$191$	8.09404			0.585664			0.292832	−	0.956164i	$-0.405402\pi$
$191$	8.09404			0.585664			0.292832	+	0.956164i	$0.405402\pi$
$192$	−0.269507	−	1.07477i	−0.0194500	−	0.0775650i
$193$	9.78924			0.704645			0.352322	−	0.935879i	$-0.385392\pi$
$193$	9.78924			0.704645			0.352322	+	0.935879i	$0.385392\pi$
$194$		−	1.51427i		−	0.108718i
$195$	29.0829	−	7.29274i	2.08267	−	0.522244i
$196$	−3.52600			−0.251857
$197$	24.0360			1.71249			0.856247	−	0.516566i	$-0.172790\pi$
$197$	24.0360			1.71249			0.856247	+	0.516566i	$0.172790\pi$
$198$	−6.47674	+	3.46612i	−0.460282	+	0.246327i
$199$	−3.58407			−0.254068			−0.127034	−	0.991898i	$-0.540546\pi$
$199$	−3.58407			−0.254068			−0.127034	+	0.991898i	$0.540546\pi$
$200$	−12.9296			−0.914262
$201$	9.84165	+	10.2050i	0.694177	+	0.719805i
$202$	0.327300			0.0230287
$203$	−20.3026			−1.42496
$204$	−8.96968	+	2.24921i	−0.628003	+	0.157476i
$205$	27.4770			1.91908
$206$	4.29878			0.299510
$207$	4.54561	+	8.49385i	0.315942	+	0.590364i
$208$			10.3610i			0.718407i
$209$	−0.562406			−0.0389024
$210$	7.32358	−	1.83644i	0.505375	−	0.126726i
$211$	5.93412			0.408522			0.204261	−	0.978917i	$-0.434521\pi$
$211$	5.93412			0.408522			0.204261	+	0.978917i	$0.434521\pi$
$212$	4.02583			0.276495
$213$	0.508401	−	0.127485i	0.0348350	−	0.00873513i
$214$			3.05725i			0.208990i
$215$		−	30.1965i		−	2.05939i
$216$	7.61249	+	8.38622i	0.517964	+	0.570610i
$217$	3.16777			0.215042
$218$			3.81911i			0.258663i
$219$	−1.45854	−	5.81654i	−0.0985590	−	0.393046i
$220$	22.2074			1.49722
$221$	17.0262			1.14531
$222$	1.74037	+	6.94047i	0.116806	+	0.465814i
$223$	−29.2041			−1.95565			−0.977825	−	0.209423i	$-0.932842\pi$
$223$	−29.2041			−1.95565			−0.977825	+	0.209423i	$0.932842\pi$
$224$			12.2119i			0.815943i
$225$	−15.6900	+	8.39675i	−1.04600	+	0.559783i
$226$	6.30565			0.419445
$227$		−	9.76187i		−	0.647918i	−0.946071	−	0.323959i	$-0.894986\pi$
$227$		−	9.76187i		−	0.647918i	0.946071	−	0.323959i	$-0.105014\pi$
$228$	0.0950809	+	0.379175i	0.00629688	+	0.0251115i
$229$			7.62407i			0.503812i	0.967752	+	0.251906i	$0.0810574\pi$
$229$			7.62407i			0.503812i	−0.967752	+	0.251906i	$0.918943\pi$
$230$			6.35480i			0.419023i
$231$	−15.1403	+	3.79653i	−0.996156	+	0.249793i
$232$		−	20.0896i		−	1.31895i
$233$	9.61325			0.629785			0.314892	−	0.949127i	$-0.398032\pi$
$233$	9.61325			0.629785			0.314892	+	0.949127i	$0.398032\pi$
$234$	−4.43584	−	8.28873i	−0.289980	−	0.541851i
$235$		−	41.3474i		−	2.69721i
$236$			14.8102i			0.964061i
$237$	−8.44332	+	2.11722i	−0.548452	+	0.137528i
$238$	4.28751			0.277918
$239$	−21.6171			−1.39829			−0.699146	−	0.714979i	$-0.746436\pi$
$239$	−21.6171			−1.39829			−0.699146	+	0.714979i	$0.746436\pi$
$240$	−2.75644	−	10.9925i	−0.177928	−	0.709562i
$241$	−16.4316			−1.05845			−0.529227	−	0.848480i	$-0.677518\pi$
$241$	−16.4316			−1.05845			−0.529227	+	0.848480i	$0.677518\pi$
$242$	3.43380			0.220733
$243$	14.6839	+	5.23293i	0.941971	+	0.335693i
$244$			16.8941i			1.08153i
$245$	−7.10097			−0.453665
$246$	−2.09545	−	8.35650i	−0.133601	−	0.532791i
$247$		−	0.719750i		−	0.0457966i
$248$			3.13454i			0.199044i
$249$	1.67209	−	0.419290i	0.105965	−	0.0265714i
$250$	−1.84408			−0.116630
$251$	16.7116			1.05483			0.527415	−	0.849608i	$-0.323161\pi$
$251$	16.7116			1.05483			0.527415	+	0.849608i	$0.323161\pi$
$252$	5.11925	+	9.56574i	0.322482	+	0.602585i
$253$		−	13.1375i		−	0.825946i
$254$	−5.51958			−0.346329
$255$	−18.0640	+	4.52966i	−1.13121	+	0.283659i
$256$	−5.58596			−0.349123
$257$		−	16.1091i		−	1.00486i	−0.864619	−	0.502429i	$-0.832440\pi$
$257$		−	16.1091i		−	1.00486i	0.864619	−	0.502429i	$-0.167560\pi$
$258$	−9.18358	+	2.30285i	−0.571745	+	0.143369i
$259$			15.2041i			0.944738i
$260$			28.4204i			1.76256i
$261$	−13.0466	−	24.3787i	−0.807564	−	1.50900i
$262$			2.34199i			0.144688i
$263$		−	1.16843i		−	0.0720482i	−0.999351	−	0.0360241i	$-0.988531\pi$
$263$		−	1.16843i		−	0.0720482i	0.999351	−	0.0360241i	$-0.0114693\pi$
$264$	−3.75671	−	14.9815i	−0.231209	−	0.922045i
$265$	8.10758			0.498045
$266$		−	0.181246i		−	0.0111129i
$267$	−8.84214	+	2.21723i	−0.541130	+	0.135692i
$268$	−11.6515	+	6.69576i	−0.711731	+	0.409009i
$269$			29.7872i			1.81615i	0.418803	+	0.908077i	$0.362450\pi$
$269$			29.7872i			1.81615i	−0.418803	+	0.908077i	$0.637550\pi$
$270$	6.91133	+	7.61380i	0.420610	+	0.463361i
$271$			18.5656i			1.12778i	0.825849	+	0.563891i	$0.190696\pi$
$271$			18.5656i			1.12778i	−0.825849	+	0.563891i	$0.809304\pi$
$272$		−	6.43543i		−	0.390205i
$273$	−4.85868	−	19.3760i	−0.294061	−	1.17269i
$274$	4.23614			0.255915
$275$	24.2678			1.46340
$276$	−8.85731	+	2.22103i	−0.533147	+	0.133690i
$277$	23.5051			1.41228			0.706141	−	0.708071i	$-0.250434\pi$
$277$	23.5051			1.41228			0.706141	+	0.708071i	$0.250434\pi$
$278$		−	8.68147i		−	0.520680i
$279$	2.03563	+	3.80375i	0.121870	+	0.227724i
$280$			15.8751i			0.948719i
$281$	−12.2237			−0.729206			−0.364603	−	0.931163i	$-0.618795\pi$
$281$	−12.2237			−0.729206			−0.364603	+	0.931163i	$0.618795\pi$
$282$	−12.5749	+	3.15324i	−0.748822	+	0.187773i
$283$	−14.3637			−0.853834			−0.426917	−	0.904291i	$-0.640400\pi$
$283$	−14.3637			−0.853834			−0.426917	+	0.904291i	$0.640400\pi$
$284$			0.496819i			0.0294808i
$285$	0.191482	+	0.763617i	0.0113424	+	0.0452328i
$286$			12.8202i			0.758075i
$287$		−	18.3061i		−	1.08058i
$288$	−14.6637	+	7.84748i	−0.864065	+	0.462417i
$289$	6.42466			0.377921
$290$		−	18.2392i		−	1.07105i
$291$	4.25049	−	1.06584i	0.249168	−	0.0624808i
$292$	5.68405			0.332634
$293$		−	21.2049i		−	1.23880i	−0.785075	−	0.619401i	$-0.787376\pi$
$293$		−	21.2049i		−	1.23880i	0.785075	−	0.619401i	$-0.212624\pi$
$294$	0.541535	+	2.15960i	0.0315829	+	0.125950i
$295$			29.8261i			1.73654i
$296$	−15.0447			−0.874453
$297$	−14.2880	−	15.7402i	−0.829073	−	0.913341i
$298$		−	9.61831i		−	0.557174i
$299$	16.8129			0.972317
$300$	−4.10274	−	16.3614i	−0.236872	−	0.944626i
$301$	−20.1180			−1.15958
$302$	2.08699			0.120093
$303$	0.230374	+	0.918716i	0.0132347	+	0.0527788i
$304$	−0.272045			−0.0156028
$305$			34.0229i			1.94814i
$306$	2.75519	+	5.14829i	0.157504	+	0.294308i
$307$	10.0437			0.573226			0.286613	−	0.958046i	$-0.407471\pi$
$307$	10.0437			0.573226			0.286613	+	0.958046i	$0.407471\pi$
$308$		−	14.7954i		−	0.843044i
$309$	3.02576	+	12.0665i	0.172129	+	0.686439i
$310$			2.84583i			0.161632i
$311$	−22.8440			−1.29536			−0.647681	−	0.761911i	$-0.724261\pi$
$311$	−22.8440			−1.29536			−0.647681	+	0.761911i	$0.724261\pi$
$312$	19.1728	−	4.80772i	1.08545	−	0.272184i
$313$		−	0.971672i		−	0.0549222i	−0.999623	−	0.0274611i	$-0.991258\pi$
$313$		−	0.971672i		−	0.0549222i	0.999623	−	0.0274611i	$-0.00874223\pi$
$314$	11.1007			0.626450
$315$	10.3096	+	19.2643i	0.580880	+	1.08542i
$316$		−	8.25098i		−	0.464154i
$317$			13.8721i			0.779133i	0.920998	+	0.389567i	$0.127375\pi$
$317$			13.8721i			0.779133i	−0.920998	+	0.389567i	$0.872625\pi$
$318$	−0.618300	−	2.46573i	−0.0346726	−	0.138271i
$319$			37.7065i			2.11116i
$320$	2.11517			0.118241
$321$	−8.58157	+	2.15189i	−0.478977	+	0.120107i
$322$	4.23379			0.235940
$323$			0.447051i			0.0248746i
$324$	−8.19655	+	12.2940i	−0.455364	+	0.683003i
$325$			31.0572i			1.72274i
$326$	8.08241			0.447643
$327$	−10.7201	+	2.68813i	−0.592821	+	0.148654i
$328$	18.1141			1.00019
$329$	−27.5471			−1.51872
$330$	−3.41069	−	13.6016i	−0.187752	−	0.748742i
$331$		−	27.5115i		−	1.51217i	−0.654473	−	0.756085i	$-0.727110\pi$
$331$		−	27.5115i		−	1.51217i	0.654473	−	0.756085i	$-0.272890\pi$
$332$			1.63401i			0.0896777i
$333$	−18.2566	+	9.77030i	−1.00046	+	0.535409i
$334$			5.86023i			0.320657i
$335$	−23.4649	+	13.4845i	−1.28202	+	0.736738i
$336$	−7.32358	+	1.83644i	−0.399534	+	0.100186i
$337$			13.0378i			0.710214i	0.934826	+	0.355107i	$0.115556\pi$
$337$			13.0378i			0.710214i	−0.934826	+	0.355107i	$0.884444\pi$
$338$	−8.62607			−0.469196
$339$	4.43832	+	17.6997i	0.241056	+	0.961314i
$340$		−	17.6525i		−	0.957339i
$341$		−	5.88327i		−	0.318597i
$342$	0.217634	−	0.116470i	0.0117683	−	0.00629797i
$343$			20.1505i			1.08802i
$344$		−	19.9070i		−	1.07331i
$345$	−17.8376	+	4.47291i	−0.960346	+	0.240814i
$346$		−	1.09337i		−	0.0587799i
$347$	−10.2576			−0.550654			−0.275327	−	0.961351i	$-0.588786\pi$
$347$	−10.2576			−0.550654			−0.275327	+	0.961351i	$0.588786\pi$
$348$	25.4218	−	6.37470i	1.36275	−	0.341720i
$349$	27.3420			1.46358			0.731792	−	0.681528i	$-0.238684\pi$
$349$	27.3420			1.46358			0.731792	+	0.681528i	$0.238684\pi$
$350$			7.82075i			0.418036i
$351$	20.1439	−	18.2853i	1.07520	−	0.975999i
$352$	22.6803			1.20887
$353$	14.0470			0.747645			0.373822	−	0.927500i	$-0.378047\pi$
$353$	14.0470			0.747645			0.373822	+	0.927500i	$0.378047\pi$
$354$	9.07092	−	2.27460i	0.482114	−	0.120893i
$355$			1.00054i			0.0531031i
$356$		−	8.64072i		−	0.457957i
$357$	3.01782	+	12.0348i	0.159720	+	0.636951i
$358$	−8.93588			−0.472276
$359$			2.43036i			0.128270i	0.997941	+	0.0641348i	$0.0204288\pi$
$359$			2.43036i			0.128270i	−0.997941	+	0.0641348i	$0.979571\pi$
$360$	−19.0623	+	10.2015i	−1.00467	+	0.537665i
$361$	−18.9811			−0.999005
$362$	−3.86482			−0.203130
$363$	2.41693	+	9.63853i	0.126856	+	0.505892i
$364$	18.9347			0.992446
$365$	11.4470			0.599166
$366$	10.3473	−	2.59465i	0.540861	−	0.135625i
$367$			1.52946i			0.0798373i	0.999203	+	0.0399186i	$0.0127099\pi$
$367$			1.52946i			0.0798373i	−0.999203	+	0.0399186i	$0.987290\pi$
$368$		−	6.35480i		−	0.331267i
$369$	21.9814	−	11.7637i	1.14431	−	0.612392i
$370$	−13.6589			−0.710095
$371$		−	5.40155i		−	0.280435i
$372$	−3.96651	+	0.994631i	−0.205654	+	0.0515692i
$373$		−	16.0645i		−	0.831788i	−0.909413	−	0.415894i	$-0.863469\pi$
$373$		−	16.0645i		−	0.831788i	0.909413	−	0.415894i	$-0.136531\pi$
$374$		−	7.96288i		−	0.411751i
$375$	−1.29798	−	5.17624i	−0.0670273	−	0.267300i
$376$		−	27.2582i		−	1.40573i
$377$	−48.2557			−2.48529
$378$	5.07258	−	4.60457i	0.260905	−	0.236833i
$379$			4.61702i			0.237160i	0.992944	+	0.118580i	$0.0378342\pi$
$379$			4.61702i			0.237160i	−0.992944	+	0.118580i	$0.962166\pi$
$380$	−0.746222			−0.0382804
$381$	−3.88503	−	15.4932i	−0.199036	−	0.793741i
$382$	4.84449			0.247866
$383$	4.90587			0.250678			0.125339	−	0.992114i	$-0.459998\pi$
$383$	4.90587			0.250678			0.125339	+	0.992114i	$0.459998\pi$
$384$	−4.83233	−	19.2709i	−0.246599	−	0.983416i
$385$		−	29.7962i		−	1.51856i
$386$	5.85912			0.298221
$387$	−12.9280	−	24.1570i	−0.657166	−	1.22797i
$388$			4.15367i			0.210871i
$389$			26.3278i			1.33487i	0.744667	+	0.667437i	$0.232609\pi$
$389$			26.3278i			1.33487i	−0.744667	+	0.667437i	$0.767391\pi$
$390$	17.4069	−	4.36490i	0.881431	−	0.221025i
$391$	−10.4428			−0.528117
$392$	−4.68130			−0.236441
$393$	−6.57385	+	1.64844i	−0.331607	+	0.0831527i
$394$	14.3862			0.724765
$395$		−	16.6166i		−	0.836070i
$396$	17.7658	−	9.50762i	0.892764	−	0.477776i
$397$	3.07652			0.154406			0.0772031	−	0.997015i	$-0.475401\pi$
$397$	3.07652			0.154406			0.0772031	+	0.997015i	$0.475401\pi$
$398$	−2.14516			−0.107527
$399$	0.508748	−	0.127572i	0.0254693	−	0.00638660i
$400$	11.7387			0.586936
$401$	34.5943			1.72756			0.863779	−	0.503871i	$-0.168091\pi$
$401$	34.5943			1.72756			0.863779	+	0.503871i	$0.168091\pi$
$402$	5.89049	+	6.10796i	0.293791	+	0.304637i
$403$	7.52923			0.375058
$404$	−0.897788			−0.0446666
$405$	−16.5069	+	24.7589i	−0.820237	+	1.23028i
$406$	−12.1516			−0.603075
$407$	28.2376			1.39968
$408$	−11.9086	+	2.98617i	−0.589564	+	0.147837i
$409$			11.1257i			0.550132i	0.961425	+	0.275066i	$0.0886998\pi$
$409$			11.1257i			0.550132i	−0.961425	+	0.275066i	$0.911300\pi$
$410$	16.4457			0.812195
$411$	2.98167	+	11.8907i	0.147075	+	0.586523i
$412$	−11.7916			−0.580932
$413$	19.8712			0.977797
$414$	2.72067	+	5.08379i	0.133714	+	0.249855i
$415$			3.29071i			0.161534i
$416$			29.0256i			1.42310i
$417$	24.3685	−	6.11057i	1.19333	−	0.299236i
$418$	−0.336615			−0.0164644
$419$			4.67554i			0.228415i	0.993457	+	0.114208i	$0.0364329\pi$
$419$			4.67554i			0.228415i	−0.993457	+	0.114208i	$0.963567\pi$
$420$	−20.0887	+	5.03738i	−0.980227	+	0.245799i
$421$	−16.0392			−0.781704			−0.390852	−	0.920454i	$-0.627820\pi$
$421$	−16.0392			−0.781704			−0.390852	+	0.920454i	$0.627820\pi$
$422$	3.55173			0.172895
$423$	−17.7020	−	33.0776i	−0.860700	−	1.60829i
$424$	5.34490			0.259571
$425$		−	19.2902i		−	0.935714i
$426$	0.304291	−	0.0763032i	0.0147430	−	0.00369690i
$427$	22.6672			1.09694
$428$		−	8.38609i		−	0.405357i
$429$	−35.9857	+	9.02368i	−1.73741	+	0.435668i
$430$		−	18.0734i		−	0.871578i
$431$		−	27.0652i		−	1.30368i	−0.758355	−	0.651841i	$-0.773997\pi$
$431$		−	27.0652i		−	1.30368i	0.758355	−	0.651841i	$-0.226003\pi$
$432$	−6.91133	−	7.61380i	−0.332521	−	0.366319i
$433$		−	16.2168i		−	0.779327i	−0.920957	−	0.389664i	$-0.872591\pi$
$433$		−	16.2168i		−	0.779327i	0.920957	−	0.389664i	$-0.127409\pi$
$434$	1.89599			0.0910105
$435$	51.1967	−	12.8379i	2.45470	−	0.615533i
$436$		−	10.4759i		−	0.501703i
$437$			0.441450i			0.0211174i
$438$	−0.872974	−	3.48135i	−0.0417123	−	0.166346i
$439$	−12.6014			−0.601434			−0.300717	−	0.953713i	$-0.597226\pi$
$439$	−12.6014			−0.601434			−0.300717	+	0.953713i	$0.597226\pi$
$440$	29.4837			1.40558
$441$	−5.68073	+	3.04013i	−0.270511	+	0.144768i
$442$	10.1907			0.484720
$443$	−3.38360			−0.160760			−0.0803799	−	0.996764i	$-0.525613\pi$
$443$	−3.38360			−0.160760			−0.0803799	+	0.996764i	$0.525613\pi$
$444$	−4.77387	−	19.0378i	−0.226558	−	0.903495i
$445$		−	17.4015i		−	0.824908i
$446$	−17.4794			−0.827674
$447$	26.9982	−	6.76998i	1.27697	−	0.320209i
$448$		−	1.40920i		−	0.0665784i
$449$		−	26.4461i		−	1.24807i	−0.781397	−	0.624034i	$-0.785492\pi$
$449$		−	26.4461i		−	1.24807i	0.781397	−	0.624034i	$-0.214508\pi$
$450$	−9.39089	+	5.02568i	−0.442691	+	0.236913i
$451$	−33.9987			−1.60094
$452$	−17.2965			−0.813558
$453$	1.46896	+	5.85809i	0.0690177	+	0.275237i
$454$		−	5.84274i		−	0.274213i
$455$	38.1323			1.78767
$456$	0.126234	+	0.503412i	0.00591146	+	0.0235744i
$457$	−29.3610			−1.37345			−0.686725	−	0.726917i	$-0.740952\pi$
$457$	−29.3610			−1.37345			−0.686725	+	0.726917i	$0.740952\pi$
$458$			4.56320i			0.213225i
$459$	−12.5118	+	11.3574i	−0.583999	+	0.530117i
$460$		−	17.4313i		−	0.812739i
$461$			16.2860i			0.758515i	0.925291	+	0.379258i	$0.123821\pi$
$461$			16.2860i			0.758515i	−0.925291	+	0.379258i	$0.876179\pi$
$462$	−9.06184	+	2.27232i	−0.421595	+	0.105718i
$463$		−	33.8458i		−	1.57295i	−0.617625	−	0.786473i	$-0.711905\pi$
$463$		−	33.8458i		−	1.57295i	0.617625	−	0.786473i	$-0.288095\pi$
$464$			18.2392i			0.846736i
$465$	−7.98812	+	2.00308i	−0.370440	+	0.0928905i
$466$	5.75378			0.266539
$467$			30.6656i			1.41903i	0.704689	+	0.709517i	$0.251087\pi$
$467$			30.6656i			1.41903i	−0.704689	+	0.709517i	$0.748913\pi$
$468$	12.1676	+	22.7361i	0.562446	+	1.05098i
$469$	8.98386	+	15.6331i	0.414836	+	0.721872i
$470$		−	24.7475i		−	1.14152i
$471$	7.81340	+	31.1592i	0.360023	+	1.43574i
$472$			19.6628i			0.905052i
$473$			37.3637i			1.71799i
$474$	−5.05355	+	1.26721i	−0.232117	+	0.0582050i
$475$	−0.815456			−0.0374157
$476$	−11.7607			−0.539050
$477$	6.48600	−	3.47108i	0.296974	−	0.158930i
$478$	−12.9384			−0.591788
$479$			0.663438i			0.0303132i	0.999885	+	0.0151566i	$0.00482469\pi$
$479$			0.663438i			0.0303132i	−0.999885	+	0.0151566i	$0.995175\pi$
$480$	−7.72198	−	30.7947i	−0.352458	−	1.40558i
$481$			36.1376i			1.64773i
$482$	−9.83477			−0.447961
$483$	2.98001	+	11.8841i	0.135595	+	0.540743i
$484$	−9.41897			−0.428135
$485$			8.36503i			0.379837i
$486$	8.78869	+	3.13205i	0.398663	+	0.142073i
$487$		−	38.9864i		−	1.76664i	−0.468766	−	0.883322i	$-0.655301\pi$
$487$		−	38.9864i		−	1.76664i	0.468766	−	0.883322i	$-0.344699\pi$
$488$			22.4295i			1.01534i
$489$	5.68892	+	22.6870i	0.257262	+	1.02594i
$490$	−4.25012			−0.192001
$491$			30.7725i			1.38875i	0.719616	+	0.694373i	$0.244318\pi$
$491$			30.7725i			1.38875i	−0.719616	+	0.694373i	$0.755682\pi$
$492$	5.74785	+	22.9220i	0.259133	+	1.03340i
$493$	29.9726			1.34990
$494$		−	0.430789i		−	0.0193821i
$495$	35.7783	−	19.1473i	1.60812	−	0.860607i
$496$		−	2.84583i		−	0.127782i
$497$	0.666594			0.0299008
$498$	1.00079	−	0.250956i	0.0448466	−	0.0112456i
$499$		−	31.4902i		−	1.40970i	−0.709358	−	0.704849i	$-0.751015\pi$
$499$		−	31.4902i		−	1.40970i	0.709358	−	0.704849i	$-0.248985\pi$
$500$	5.05832			0.226215
$501$	−16.4494	+	4.12480i	−0.734905	+	0.184283i
$502$	10.0024			0.446427
$503$	−37.9687			−1.69294			−0.846471	−	0.532434i	$-0.821277\pi$
$503$	−37.9687			−1.69294			−0.846471	+	0.532434i	$0.821277\pi$
$504$	6.79658	+	12.7000i	0.302744	+	0.565702i
$505$	−1.80805			−0.0804570
$506$		−	7.86312i		−	0.349558i
$507$	−6.07158	−	24.2130i	−0.269648	−	1.07534i
$508$	15.1403			0.671741
$509$			14.7116i			0.652079i	0.945356	+	0.326040i	$0.105714\pi$
$509$			14.7116i			0.652079i	−0.945356	+	0.326040i	$0.894286\pi$
$510$	−10.8117	+	2.71112i	−0.478752	+	0.120051i
$511$		−	7.62642i		−	0.337373i
$512$	19.5978			0.866107
$513$	0.480110	+	0.528909i	0.0211974	+	0.0233519i
$514$		−	9.64171i		−	0.425278i
$515$	−23.7470			−1.04642
$516$	25.1907	−	6.31675i	1.10896	−	0.278079i
$517$			51.1613i			2.25007i
$518$			9.10007i			0.399834i
$519$	3.06904	−	0.769584i	0.134716	−	0.0337810i
$520$			37.7324i			1.65467i
$521$	20.9758			0.918966			0.459483	−	0.888186i	$-0.348035\pi$
$521$	20.9758			0.918966			0.459483	+	0.888186i	$0.348035\pi$
$522$	−7.80873	−	14.5913i	−0.341779	−	0.638642i
$523$	−12.1671			−0.532032			−0.266016	−	0.963969i	$-0.585707\pi$
$523$	−12.1671			−0.532032			−0.266016	+	0.963969i	$0.585707\pi$
$524$		−	6.42410i		−	0.280638i
$525$	−21.9525	+	5.50474i	−0.958085	+	0.240247i
$526$		−	0.699333i		−	0.0304924i
$527$	−4.67655			−0.203714
$528$	3.41069	+	13.6016i	0.148431	+	0.591932i
$529$	12.6880			0.551652
$530$	4.85260			0.210783
$531$	12.7694	+	23.8606i	0.554144	+	1.03546i
$532$			0.497159i			0.0215546i
$533$		−	43.5105i		−	1.88465i
$534$	−5.29226	+	1.32707i	−0.229018	+	0.0574280i
$535$		−	16.8887i		−	0.730160i
$536$	−15.4692	+	8.88963i	−0.668167	+	0.383974i
$537$	−6.28964	−	25.0826i	−0.271418	−	1.08239i
$538$			17.8284i			0.768637i
$539$	8.78640			0.378457
$540$	−18.9579	−	20.8848i	−0.815817	−	0.898737i
$541$			1.43117i			0.0615308i	0.999527	+	0.0307654i	$0.00979448\pi$
$541$			1.43117i			0.0615308i	−0.999527	+	0.0307654i	$0.990206\pi$
$542$			11.1120i			0.477302i
$543$	−2.72031	−	10.8484i	−0.116739	−	0.465548i
$544$		−	18.0284i		−	0.772961i
$545$		−	21.0972i		−	0.903707i
$546$	−2.90805	−	11.5971i	−0.124453	−	0.496309i
$547$		−	17.8923i		−	0.765019i	−0.923951	−	0.382510i	$-0.875060\pi$
$547$		−	17.8923i		−	0.765019i	0.923951	−	0.382510i	$-0.124940\pi$
$548$	−11.6198			−0.496373
$549$	14.5661	+	27.2181i	0.621668	+	1.16164i
$550$	14.5249			0.619345
$551$		−	1.26703i		−	0.0539773i
$552$	−11.7594	+	2.94876i	−0.500514	+	0.125507i
$553$	−11.0705			−0.470767
$554$	14.0684			0.597709
$555$	−9.61404	−	38.3401i	−0.408093	−	1.62744i
$556$			23.8134i			1.00991i
$557$		−	25.2745i		−	1.07092i	−0.844562	−	0.535458i	$-0.820139\pi$
$557$		−	25.2745i		−	1.07092i	0.844562	−	0.535458i	$-0.179861\pi$
$558$	1.21838	+	2.27664i	0.0515781	+	0.0963780i
$559$	−47.8170			−2.02244
$560$		−	14.4129i		−	0.609056i
$561$	22.3515	−	5.60479i	0.943679	−	0.236634i
$562$	−7.31622			−0.308616
$563$	25.6547			1.08122			0.540608	−	0.841275i	$-0.318194\pi$
$563$	25.6547			1.08122			0.540608	+	0.841275i	$0.318194\pi$
$564$	34.4930	−	8.64937i	1.45242	−	0.364204i
$565$	−34.8332			−1.46544
$566$	−8.59706			−0.361361
$567$	16.4952	+	10.9975i	0.692734	+	0.461852i
$568$			0.659603i			0.0276763i
$569$		−	27.7162i		−	1.16192i	−0.813931	−	0.580962i	$-0.802676\pi$
$569$		−	27.7162i		−	1.16192i	0.813931	−	0.580962i	$-0.197324\pi$
$570$	0.114607	+	0.457045i	0.00480037	+	0.0191435i
$571$	−34.1820			−1.43047			−0.715236	−	0.698883i	$-0.753681\pi$
$571$	−34.1820			−1.43047			−0.715236	+	0.698883i	$0.753681\pi$
$572$		−	35.1660i		−	1.47036i
$573$	3.40986	+	13.5983i	0.142449	+	0.568076i
$574$		−	10.9567i		−	0.457324i
$575$		−	19.0486i		−	0.794380i
$576$	1.69212	−	0.905562i	0.0705049	−	0.0377318i
$577$			29.5552i			1.23040i	0.788371	+	0.615200i	$0.210925\pi$
$577$			29.5552i			1.23040i	−0.788371	+	0.615200i	$0.789075\pi$
$578$	3.84533			0.159945
$579$	4.12402	+	16.4463i	0.171388	+	0.683484i
$580$			50.0305i			2.07740i
$581$	2.19238			0.0909554
$582$	2.54403	−	0.637934i	0.105454	−	0.0264432i
$583$	−10.0319			−0.415480
$584$	7.54643			0.312274
$585$	24.5041	+	45.7880i	1.01312	+	1.89310i
$586$		−	12.6917i		−	0.524288i
$587$	2.71773			0.112173			0.0560864	−	0.998426i	$-0.482138\pi$
$587$	2.71773			0.112173			0.0560864	+	0.998426i	$0.482138\pi$
$588$	−1.48544	−	5.92381i	−0.0612584	−	0.244294i
$589$			0.197692i			0.00814575i
$590$			17.8517i			0.734943i
$591$	10.1259	+	40.3814i	0.416524	+	1.66107i
$592$	13.6589			0.561379
$593$	−32.7701			−1.34571			−0.672853	−	0.739776i	$-0.734931\pi$
$593$	−32.7701			−1.34571			−0.672853	+	0.739776i	$0.734931\pi$
$594$	−8.55174	−	9.42094i	−0.350882	−	0.386546i
$595$	−23.6847			−0.970979
$596$			26.3832i			1.08070i
$597$	−1.50990	−	6.02136i	−0.0617961	−	0.246438i
$598$	10.0630			0.411506
$599$	5.02427			0.205286			0.102643	−	0.994718i	$-0.467270\pi$
$599$	5.02427			0.205286			0.102643	+	0.994718i	$0.467270\pi$
$600$	−5.44701	−	21.7222i	−0.222373	−	0.886807i
$601$	19.1043			0.779282			0.389641	−	0.920967i	$-0.372599\pi$
$601$	19.1043			0.779282			0.389641	+	0.920967i	$0.372599\pi$
$602$	−12.0411			−0.490761
$603$	−12.9987	+	20.8335i	−0.529346	+	0.848406i
$604$	−5.72465			−0.232933
$605$	−18.9688			−0.771190
$606$	0.137885	+	0.549875i	0.00560120	+	0.0223372i
$607$	−24.9631			−1.01322			−0.506610	−	0.862175i	$-0.669102\pi$
$607$	−24.9631			−1.01322			−0.506610	+	0.862175i	$0.669102\pi$
$608$	−0.762113			−0.0309078
$609$	−8.55309	−	34.1091i	−0.346589	−	1.38217i
$610$			20.3636i			0.824498i
$611$	−65.4747			−2.64882
$612$	−7.55752	−	14.1218i	−0.305494	−	0.570842i
$613$	16.6039			0.670624			0.335312	−	0.942107i	$-0.391158\pi$
$613$	16.6039			0.670624			0.335312	+	0.942107i	$0.391158\pi$
$614$	6.01144			0.242602
$615$	11.5755	+	46.1624i	0.466771	+	1.86145i
$616$		−	19.6431i		−	0.791443i
$617$			25.9935i			1.04646i	0.852192	+	0.523229i	$0.175273\pi$
$617$			25.9935i			1.04646i	−0.852192	+	0.523229i	$0.824727\pi$
$618$	1.81100	+	7.22211i	0.0728490	+	0.290516i
$619$	1.36231			0.0547559			0.0273780	−	0.999625i	$-0.491284\pi$
$619$	1.36231			0.0547559			0.0273780	+	0.999625i	$0.491284\pi$
$620$		−	7.80615i		−	0.313503i
$621$	−12.3550	+	11.2151i	−0.495789	+	0.450046i
$622$	−13.6727			−0.548226
$623$	−11.5935			−0.464482
$624$	−17.4069	+	4.36490i	−0.696832	+	0.174736i
$625$	−19.4724			−0.778895
$626$		−	0.581571i		−	0.0232443i
$627$	−0.236931	−	0.944862i	−0.00946211	−	0.0377342i
$628$	−30.4495			−1.21507
$629$		−	22.4458i		−	0.894971i
$630$	6.17057	+	11.5302i	0.245841	+	0.459375i
$631$		−	33.0377i		−	1.31521i	−0.753364	−	0.657604i	$-0.771570\pi$
$631$		−	33.0377i		−	1.31521i	0.753364	−	0.657604i	$-0.228430\pi$
$632$		−	10.9544i		−	0.435744i
$633$	2.49993	+	9.96954i	0.0993634	+	0.396253i
$634$			8.30280i			0.329746i
$635$	30.4908			1.20999
$636$	1.69601	+	6.76354i	0.0672510	+	0.268192i
$637$			11.2446i			0.445526i
$638$			22.5684i			0.893490i
$639$	0.428359	+	0.800424i	0.0169456	+	0.0316643i
$640$	37.9255			1.49914
$641$	14.5251			0.573708			0.286854	−	0.957974i	$-0.407391\pi$
$641$	14.5251			0.573708			0.286854	+	0.957974i	$0.407391\pi$
$642$	−5.13630	+	1.28796i	−0.202713	+	0.0508318i
$643$	38.8448			1.53189			0.765944	−	0.642907i	$-0.222272\pi$
$643$	38.8448			1.53189			0.765944	+	0.642907i	$0.222272\pi$
$644$	−11.6133			−0.457630
$645$	50.7313	−	12.7212i	1.99754	−	0.500898i
$646$			0.267572i			0.0105275i
$647$	5.01987			0.197351			0.0986756	−	0.995120i	$-0.468539\pi$
$647$	5.01987			0.197351			0.0986756	+	0.995120i	$0.468539\pi$
$648$	−10.8822	+	16.3222i	−0.427492	+	0.641197i
$649$		−	36.9053i		−	1.44866i
$650$			18.5886i			0.729103i
$651$	1.33452	+	5.32196i	0.0523040	+	0.208584i
$652$	−22.1702			−0.868251
$653$	8.84563			0.346156			0.173078	−	0.984908i	$-0.444629\pi$
$653$	8.84563			0.346156			0.173078	+	0.984908i	$0.444629\pi$
$654$	−6.41624	+	1.60892i	−0.250895	+	0.0629137i
$655$		−	12.9374i		−	0.505507i
$656$	−16.4457			−0.642097
$657$	9.15755	−	4.90080i	0.357270	−	0.191198i
$658$	−16.4877			−0.642756
$659$			22.2697i			0.867504i	0.901032	+	0.433752i	$0.142811\pi$
$659$			22.2697i			0.867504i	−0.901032	+	0.433752i	$0.857189\pi$
$660$	9.35557	+	37.3093i	0.364165	+	1.45226i
$661$		−	12.4861i		−	0.485653i	−0.970070	−	0.242827i	$-0.921925\pi$
$661$		−	12.4861i		−	0.485653i	0.970070	−	0.242827i	$-0.0780746\pi$
$662$		−	16.4664i		−	0.639984i
$663$	7.17284	+	28.6047i	0.278570	+	1.11092i
$664$			2.16939i			0.0841886i
$665$			1.00122i			0.0388258i
$666$	−10.9271	+	5.84778i	−0.423415	+	0.226597i
$667$	29.5971			1.14600
$668$		−	16.0747i		−	0.621948i
$669$	−12.3031	−	49.0639i	−0.475667	−	1.89692i
$670$	−14.0444	+	8.07084i	−0.542581	+	0.311804i
$671$		−	42.0983i		−	1.62519i
$672$	−20.5165	+	5.14465i	−0.791440	+	0.198459i
$673$			39.8887i			1.53760i	0.639490	+	0.768799i	$0.279145\pi$
$673$			39.8887i			1.53760i	−0.639490	+	0.768799i	$0.720855\pi$
$674$			7.80347i			0.300578i
$675$	−20.7168	−	22.8224i	−0.797388	−	0.878435i
$676$	23.6614			0.910055
$677$	4.01578			0.154339			0.0771694	−	0.997018i	$-0.475412\pi$
$677$	4.01578			0.154339			0.0771694	+	0.997018i	$0.475412\pi$
$678$	2.65645	+	10.5937i	0.102020	+	0.406849i
$679$	5.57308			0.213875
$680$		−	23.4363i		−	0.898742i
$681$	16.4003	−	4.11249i	0.628461	−	0.157591i
$682$		−	3.52129i		−	0.134837i
$683$	0.785853			0.0300698			0.0150349	−	0.999887i	$-0.495214\pi$
$683$	0.785853			0.0300698			0.0150349	+	0.999887i	$0.495214\pi$
$684$	−0.596972	+	0.319479i	−0.0228258	+	0.0122156i
$685$	−23.4010			−0.894105
$686$			12.0606i			0.460476i
$687$	−12.8087	+	3.21187i	−0.488683	+	0.122541i
$688$			18.0734i			0.689043i
$689$		−	12.8386i		−	0.489110i
$690$	−10.6763	+	2.67716i	−0.406440	+	0.101918i
$691$	37.9676			1.44436			0.722178	−	0.691707i	$-0.243141\pi$
$691$	37.9676			1.44436			0.722178	+	0.691707i	$0.243141\pi$
$692$			2.99913i			0.114010i
$693$	−12.7566	−	23.8368i	−0.484583	−	0.905484i
$694$	−6.13941			−0.233049
$695$			47.9575i			1.81913i
$696$	33.7513	−	8.46338i	1.27934	−	0.320804i
$697$			27.0252i			1.02365i
$698$	16.3649			0.619421
$699$	4.04988	+	16.1506i	0.153181	+	0.610872i
$700$		−	21.4524i		−	0.810825i
$701$	−34.2754			−1.29457			−0.647283	−	0.762250i	$-0.724095\pi$
$701$	−34.2754			−1.29457			−0.647283	+	0.762250i	$0.724095\pi$
$702$	12.0566	−	10.9443i	0.455048	−	0.413064i
$703$	−0.948849			−0.0357865
$704$	−2.61720			−0.0986396
$705$	69.4652	−	17.4189i	2.61621	−	0.656033i
$706$	8.40748			0.316420
$707$			1.20458i			0.0453030i
$708$	−24.8817	+	6.23925i	−0.935110	+	0.234485i
$709$	5.02636			0.188769			0.0943844	−	0.995536i	$-0.469912\pi$
$709$	5.02636			0.188769			0.0943844	+	0.995536i	$0.469912\pi$
$710$			0.598849i			0.0224744i
$711$	−7.11402	−	13.2931i	−0.266797	−	0.498532i
$712$		−	11.4719i		−	0.429926i
$713$	−4.61796			−0.172944
$714$	1.80625	+	7.20317i	0.0675970	+	0.269572i
$715$		−	70.8205i		−	2.64854i
$716$	24.5113			0.916028
$717$	−9.10686	−	36.3174i	−0.340102	−	1.35630i
$718$			1.45464i			0.0542865i
$719$			0.487793i			0.0181916i	0.999959	+	0.00909580i	$0.00289532\pi$
$719$			0.487793i			0.0181916i	−0.999959	+	0.00909580i	$0.997105\pi$
$720$	17.3065	−	9.26185i	0.644976	−	0.345169i
$721$			15.8211i			0.589209i
$722$	−11.3607			−0.422801
$723$	−6.92234	−	27.6057i	−0.257445	−	1.02667i
$724$	10.6012			0.393992
$725$			54.6723i			2.03048i
$726$	1.44660	+	5.76891i	0.0536882	+	0.214104i
$727$			27.4132i			1.01670i	0.861150	+	0.508350i	$0.169744\pi$
$727$			27.4132i			1.01670i	−0.861150	+	0.508350i	$0.830256\pi$
$728$	25.1386			0.931699
$729$	−2.60548	+	26.8740i	−0.0964992	+	0.995333i
$730$	6.85136			0.253580
$731$	29.7001			1.09850
$732$	−28.3827	+	7.11717i	−1.04906	+	0.263058i
$733$		−	50.0017i		−	1.84685i	−0.383775	−	0.923427i	$-0.625376\pi$
$733$		−	50.0017i		−	1.84685i	0.383775	−	0.923427i	$-0.374624\pi$
$734$			0.915423i			0.0337889i
$735$	−2.99151	−	11.9299i	−0.110343	−	0.440041i
$736$		−	17.8025i		−	0.656209i
$737$	29.0343	−	16.6851i	1.06949	−	0.614603i
$738$	13.1564	−	7.04087i	0.484295	−	0.259178i
$739$		−	25.0485i		−	0.921425i	−0.887549	−	0.460713i	$-0.847594\pi$
$739$		−	25.0485i		−	0.921425i	0.887549	−	0.460713i	$-0.152406\pi$
$740$	37.4667			1.37730
$741$	1.20921	−	0.303217i	0.0444213	−	0.0111390i
$742$		−	3.23297i		−	0.118686i
$743$		−	15.3006i		−	0.561326i	−0.959806	−	0.280663i	$-0.909446\pi$
$743$		−	15.3006i		−	0.561326i	0.959806	−	0.280663i	$-0.0905543\pi$
$744$	−5.26614	+	1.32052i	−0.193066	+	0.0484127i
$745$			53.1328i			1.94663i
$746$		−	9.61503i		−	0.352031i
$747$	1.40884	+	2.63254i	0.0515469	+	0.0963197i
$748$			21.8423i			0.798634i
$749$	−11.2518			−0.411132
$750$	−0.776874	−	3.09811i	−0.0283674	−	0.113127i
$751$	−12.0775			−0.440713			−0.220357	−	0.975419i	$-0.570722\pi$
$751$	−12.0775			−0.440713			−0.220357	+	0.975419i	$0.570722\pi$
$752$			24.7475i			0.902449i
$753$	7.04030	+	28.0762i	0.256563	+	1.02315i
$754$	−28.8823			−1.05183
$755$	−11.5288			−0.419576
$756$	−13.9142	+	12.6304i	−0.506053	+	0.459363i
$757$			37.4830i			1.36234i	0.732123	+	0.681172i	$0.238529\pi$
$757$			37.4830i			1.36234i	−0.732123	+	0.681172i	$0.761471\pi$
$758$			2.76341i			0.100371i
$759$	22.0714	−	5.53457i	0.801142	−	0.200892i
$760$	−0.990723			−0.0359373
$761$			7.01014i			0.254118i	0.991895	+	0.127059i	$0.0405537\pi$
$761$			7.01014i			0.254118i	−0.991895	+	0.127059i	$0.959446\pi$
$762$	−2.32529	−	9.27309i	−0.0842365	−	0.335929i
$763$	−14.0557			−0.508851
$764$	−13.2885			−0.480762
$765$	−15.2200	−	28.4398i	−0.550280	−	1.02824i
$766$	2.93629			0.106093
$767$	47.2303			1.70539
$768$	−2.35326	−	9.38462i	−0.0849160	−	0.338638i
$769$		−	39.7862i		−	1.43473i	−0.696699	−	0.717364i	$-0.745349\pi$
$769$		−	39.7862i		−	1.43473i	0.696699	−	0.717364i	$-0.254651\pi$
$770$		−	17.8338i		−	0.642687i
$771$	27.0639	−	6.78645i	0.974681	−	0.244408i
$772$	−16.0716			−0.578431
$773$			4.93991i			0.177676i	0.996046	+	0.0888381i	$0.0283154\pi$
$773$			4.93991i			0.177676i	−0.996046	+	0.0888381i	$0.971685\pi$
$774$	−7.73774	−	14.4586i	−0.278127	−	0.519704i
$775$		−	8.53040i		−	0.306421i
$776$			5.51463i			0.197964i
$777$	−25.5435	+	6.40521i	−0.916367	+	0.229786i
$778$			15.7579i			0.564948i
$779$	1.14244			0.0409320
$780$	−47.7473	+	11.9730i	−1.70963	+	0.428701i
$781$		−	1.23802i		−	0.0442998i
$782$	−6.25032			−0.223511
$783$	35.4607	−	32.1890i	1.26726	−	1.15034i
$784$	4.25012			0.151790
$785$	−61.3218			−2.18867
$786$	−3.93462	+	0.986634i	−0.140343	+	0.0351921i
$787$		−	8.72525i		−	0.311022i	−0.987834	−	0.155511i	$-0.950298\pi$
$787$		−	8.72525i		−	0.311022i	0.987834	−	0.155511i	$-0.0497023\pi$
$788$	−39.4615			−1.40576
$789$	1.96300	−	0.492235i	0.0698845	−	0.0175240i
$790$		−	9.94545i		−	0.353843i
$791$			23.2071i			0.825149i
$792$	23.5868	−	12.6228i	0.838119	−	0.448532i
$793$	53.8761			1.91320
$794$	1.84138			0.0653481
$795$	3.41557	+	13.6210i	0.121138	+	0.483088i
$796$	5.88420			0.208560
$797$			2.53173i			0.0896783i	0.998994	+	0.0448392i	$0.0142775\pi$
$797$			2.53173i			0.0896783i	−0.998994	+	0.0448392i	$0.985722\pi$
$798$	0.304499	−	0.0763553i	0.0107792	−	0.00270295i
$799$	40.6676			1.43872
$800$	32.8852			1.16267
$801$	−7.45006	−	13.9210i	−0.263235	−	0.491876i
$802$	20.7056			0.731141
$803$	−14.1640			−0.499837
$804$	−16.1577	−	16.7542i	−0.569838	−	0.590875i
$805$	−23.3880			−0.824319
$806$	4.50644			0.158733
$807$	−50.0435	+	12.5488i	−1.76161	+	0.441737i
$808$	−1.19195			−0.0419326
$809$	16.1523			0.567885			0.283943	−	0.958841i	$-0.408357\pi$
$809$	16.1523			0.567885			0.283943	+	0.958841i	$0.408357\pi$
$810$	−9.87984	+	14.8188i	−0.347142	+	0.520680i
$811$		−	14.7422i		−	0.517669i	−0.965922	−	0.258835i	$-0.916662\pi$
$811$		−	14.7422i		−	0.517669i	0.965922	−	0.258835i	$-0.0833385\pi$
$812$	33.3321			1.16973
$813$	−31.1909	+	7.82135i	−1.09391	+	0.274307i
$814$	16.9009			0.592377
$815$	−44.6483			−1.56396
$816$	10.8117	−	2.71112i	0.378487	−	0.0949083i
$817$		−	1.25551i		−	0.0439247i
$818$			6.65905i			0.232828i
$819$	30.5056	−	16.3255i	1.06595	−	0.570460i
$820$	−45.1108			−1.57534
$821$		−	28.6113i		−	0.998541i	−0.866446	−	0.499271i	$-0.833601\pi$
$821$		−	28.6113i		−	0.998541i	0.866446	−	0.499271i	$-0.166399\pi$
$822$	1.78461	+	7.11687i	0.0622453	+	0.248229i
$823$	27.7892			0.968671			0.484335	−	0.874882i	$-0.339061\pi$
$823$	27.7892			0.968671			0.484335	+	0.874882i	$0.339061\pi$
$824$	−15.6552			−0.545374
$825$	10.2236	+	40.7708i	0.355939	+	1.41946i
$826$	11.8934			0.413825
$827$			27.3097i			0.949653i	0.880079	+	0.474826i	$0.157489\pi$
$827$			27.3097i			0.949653i	−0.880079	+	0.474826i	$0.842511\pi$
$828$	−7.46283	−	13.9449i	−0.259351	−	0.484619i
$829$	−13.8737			−0.481854			−0.240927	−	0.970543i	$-0.577451\pi$
$829$	−13.8737			−0.481854			−0.240927	+	0.970543i	$0.577451\pi$
$830$			1.96957i			0.0683649i
$831$	9.90224	+	39.4894i	0.343505	+	1.36987i
$832$		−	3.34942i		−	0.116120i
$833$		−	6.98422i		−	0.241989i
$834$	14.5852	−	3.65734i	0.505043	−	0.126643i
$835$		−	32.3727i		−	1.12030i
$836$	0.923339			0.0319343
$837$	−5.53286	+	5.02238i	−0.191244	+	0.173599i
$838$			2.79844i			0.0966704i
$839$		−	13.9332i		−	0.481028i	−0.970646	−	0.240514i	$-0.922684\pi$
$839$		−	13.9332i		−	0.481028i	0.970646	−	0.240514i	$-0.0773159\pi$
$840$	−26.6708	+	6.68788i	−0.920229	+	0.230754i
$841$	−55.9481			−1.92924
$842$	−9.59989			−0.330834
$843$	−5.14962	−	20.5363i	−0.177362	−	0.707308i
$844$	−9.74244			−0.335348
$845$	47.6515			1.63926
$846$	−10.5951	−	19.7978i	−0.364267	−	0.680663i
$847$			12.6377i			0.434235i
$848$	−4.85260			−0.166639
$849$	−6.05116	−	24.1316i	−0.207675	−	0.828193i
$850$		−	11.5457i		−	0.396015i
$851$		−	22.1645i		−	0.759791i
$852$	−0.834675	+	0.209301i	−0.0285955	+	0.00717052i
$853$	43.6961			1.49612			0.748062	−	0.663629i	$-0.230984\pi$
$853$	43.6961			1.49612			0.748062	+	0.663629i	$0.230984\pi$
$854$	13.5669			0.464251
$855$	−1.20224	+	0.643395i	−0.0411156	+	0.0220036i
$856$		−	11.1338i		−	0.380545i
$857$	10.4761			0.357857			0.178929	−	0.983862i	$-0.442737\pi$
$857$	10.4761			0.357857			0.178929	+	0.983862i	$0.442737\pi$
$858$	−21.5384	+	5.40091i	−0.735309	+	0.184384i
$859$	13.3052			0.453968			0.226984	−	0.973898i	$-0.427114\pi$
$859$	13.3052			0.453968			0.226984	+	0.973898i	$0.427114\pi$
$860$			49.5757i			1.69052i
$861$	30.7550	−	7.71203i	1.04813	−	0.262825i
$862$		−	16.1992i		−	0.551747i
$863$		−	46.3186i		−	1.57670i	−0.615225	−	0.788352i	$-0.710935\pi$
$863$		−	46.3186i		−	1.57670i	0.615225	−	0.788352i	$-0.289065\pi$
$864$	−19.3616	−	21.3295i	−0.658694	−	0.725644i
$865$			6.03992i			0.205363i
$866$		−	9.70615i		−	0.329829i
$867$	2.70659	+	10.7937i	0.0919206	+	0.366572i
$868$	−5.20073			−0.176524
$869$			20.5605i			0.697468i
$870$	30.6426	−	7.68385i	1.03888	−	0.260507i
$871$	21.3531	+	37.1573i	0.723521	+	1.25903i
$872$		−	13.9083i		−	0.470994i
$873$	3.58131	+	6.69197i	0.121209	+	0.226489i
$874$			0.264219i			0.00893736i
$875$		−	6.78687i		−	0.229438i
$876$	2.39458	+	9.54941i	0.0809054	+	0.322644i
$877$	19.8348			0.669774			0.334887	−	0.942258i	$-0.391302\pi$
$877$	19.8348			0.669774			0.334887	+	0.942258i	$0.391302\pi$
$878$	−7.54229			−0.254540
$879$	35.6250	−	8.93321i	1.20160	−	0.301310i
$880$	−26.7681			−0.902352
$881$			32.6660i			1.10055i	0.834985	+	0.550273i	$0.185476\pi$
$881$			32.6660i			1.10055i	−0.834985	+	0.550273i	$0.814524\pi$
$882$	−3.40006	+	1.81960i	−0.114486	+	0.0612690i
$883$			14.8729i			0.500513i	0.968180	+	0.250256i	$0.0805149\pi$
$883$			14.8729i			0.500513i	−0.968180	+	0.250256i	$0.919485\pi$
$884$	−27.9531			−0.940165
$885$	−50.1089	+	12.5652i	−1.68439	+	0.422373i
$886$	−2.02517			−0.0680371
$887$		−	49.9663i		−	1.67770i	−0.544359	−	0.838852i	$-0.683227\pi$
$887$		−	49.9663i		−	1.67770i	0.544359	−	0.838852i	$-0.316773\pi$
$888$	−6.33803	−	25.2756i	−0.212690	−	0.848193i
$889$		−	20.3141i		−	0.681312i
$890$		−	10.4152i		−	0.349119i
$891$	20.4249	−	30.6354i	0.684260	−	1.02632i
$892$	47.9463			1.60536
$893$		−	1.71914i		−	0.0575288i
$894$	16.1591	−	4.05201i	0.540441	−	0.135520i
$895$	49.3629			1.65002
$896$		−	25.2673i		−	0.844121i
$897$	7.08297	+	28.2463i	0.236494	+	0.943118i
$898$		−	15.8287i		−	0.528210i
$899$	13.2543			0.442054
$900$	25.7593	−	13.7855i	0.858645	−	0.459517i
$901$			7.97428i			0.265662i
$902$	−20.3491			−0.677552
$903$	−8.47533	−	33.7990i	−0.282041	−	1.12476i
$904$	−22.9637			−0.763761
$905$	21.3497			0.709689
$906$	0.879210	+	3.50622i	0.0292098	+	0.116486i
$907$	43.8545			1.45616			0.728082	−	0.685490i	$-0.240412\pi$
$907$	43.8545			1.45616			0.728082	+	0.685490i	$0.240412\pi$
$908$			16.0267i			0.531865i
$909$	−1.44642	+	0.774075i	−0.0479748	+	0.0256744i
$910$	22.8232			0.756581
$911$		−	21.2493i		−	0.704020i	−0.935996	−	0.352010i	$-0.885498\pi$
$911$		−	21.2493i		−	0.704020i	0.935996	−	0.352010i	$-0.114502\pi$
$912$	−0.114607	−	0.457045i	−0.00379502	−	0.0151343i
$913$		−	4.07176i		−	0.134756i
$914$	−17.5733			−0.581274
$915$	−57.1597	+	14.3332i	−1.88964	+	0.473841i
$916$		−	12.5169i		−	0.413571i
$917$	−8.61937			−0.284637
$918$	−7.48861	+	6.79769i	−0.247161	+	0.224357i
$919$			33.0135i			1.08902i	0.838756	+	0.544508i	$0.183284\pi$
$919$			33.0135i			1.08902i	−0.838756	+	0.544508i	$0.816716\pi$
$920$		−	23.1427i		−	0.762992i
$921$	4.23123	+	16.8738i	0.139424	+	0.556012i
$922$			9.74761i			0.321020i
$923$	1.58438			0.0521505
$924$	24.8568	−	6.23301i	0.817727	−	0.205051i
$925$	40.9428			1.34619
$926$		−	20.2576i		−	0.665705i
$927$	−18.9975	+	10.1668i	−0.623958	+	0.333921i
$928$			51.0959i			1.67731i
$929$	5.10398			0.167456			0.0837280	−	0.996489i	$-0.473317\pi$
$929$	5.10398			0.167456			0.0837280	+	0.996489i	$0.473317\pi$
$930$	−4.78110	+	1.19889i	−0.156778	+	0.0393133i
$931$	−0.295244			−0.00967623
$932$	−15.7827			−0.516980
$933$	−9.62373	−	38.3787i	−0.315067	−	1.25646i
$934$			18.3542i			0.600566i
$935$			43.9880i			1.43856i
$936$	16.1543	+	30.1856i	0.528019	+	0.986648i
$937$			21.0220i			0.686758i	0.939197	+	0.343379i	$0.111571\pi$
$937$			21.0220i			0.686758i	−0.939197	+	0.343379i	$0.888429\pi$
$938$	5.37708	+	9.35685i	0.175568	+	0.305512i
$939$	1.63244	−	0.409347i	0.0532728	−	0.0133585i
$940$			67.8828i			2.21409i
$941$	0.118666			0.00386840			0.00193420	−	0.999998i	$-0.499384\pi$
$941$	0.118666			0.00386840			0.00193420	+	0.999998i	$0.499384\pi$
$942$	4.67653	+	18.6496i	0.152369	+	0.607638i
$943$			26.6866i			0.869037i
$944$		−	17.8517i		−	0.581023i
$945$	−28.0216	+	25.4362i	−0.911542	+	0.827440i
$946$			22.3632i			0.727090i
$947$			20.2733i			0.658795i	0.944191	+	0.329397i	$0.106846\pi$
$947$			20.2733i			0.658795i	−0.944191	+	0.329397i	$0.893154\pi$
$948$	13.8620	−	3.47598i	0.450215	−	0.112895i
$949$		−	18.1267i		−	0.588417i
$950$	−0.488072			−0.0158351
$951$	−23.3056	+	5.84404i	−0.755736	+	0.189506i
$952$	−15.6141			−0.506056
$953$			15.5577i			0.503964i	0.967732	+	0.251982i	$0.0810823\pi$
$953$			15.5577i			0.503964i	−0.967732	+	0.251982i	$0.918918\pi$
$954$	3.88204	−	2.07753i	0.125686	−	0.0672627i
$955$	−26.7616			−0.865985
$956$	35.4902			1.14783
$957$	−63.3484	+	15.8851i	−2.04776	+	0.513491i
$958$			0.397085i			0.0128292i
$959$			15.5905i			0.503445i
$960$	0.891080	+	3.55356i	0.0287595	+	0.114691i
$961$	28.9320			0.933289
$962$			21.6293i			0.697356i
$963$	−7.23051	−	13.5108i	−0.233000	−	0.435379i
$964$	26.9769			0.868868
$965$	−32.3665			−1.04191
$966$	1.78362	+	7.11292i	0.0573869	+	0.228855i
$967$	−32.3047			−1.03885			−0.519425	−	0.854516i	$-0.673854\pi$
$967$	−32.3047			−1.03885			−0.519425	+	0.854516i	$0.673854\pi$
$968$	−12.5051			−0.401929
$969$	−0.751062	+	0.188334i	−0.0241276	+	0.00605016i
$970$			5.00669i			0.160755i
$971$			41.9132i			1.34506i	0.740071	+	0.672529i	$0.234792\pi$
$971$			41.9132i			1.34506i	−0.740071	+	0.672529i	$0.765208\pi$
$972$	−24.1075	−	8.59126i	−0.773248	−	0.275565i
$973$	31.9510			1.02430
$974$		−	23.3344i		−	0.747683i
$975$	−52.1772	+	13.0838i	−1.67101	+	0.419017i
$976$		−	20.3636i		−	0.651823i
$977$			15.6622i			0.501079i	0.968106	+	0.250540i	$0.0806080\pi$
$977$			15.6622i			0.501079i	−0.968106	+	0.250540i	$0.919392\pi$
$978$	3.40497	+	13.5787i	0.108879	+	0.434200i
$979$			21.5317i			0.688157i
$980$	11.6581			0.372406
$981$	−9.03232	−	16.8776i	−0.288380	−	0.538862i
$982$			18.4182i			0.587748i
$983$	31.7322			1.01210			0.506050	−	0.862504i	$-0.331105\pi$
$983$	31.7322			1.01210			0.506050	+	0.862504i	$0.331105\pi$
$984$	7.63114	+	30.4324i	0.243272	+	0.970150i
$985$	−79.4711			−2.53216
$986$	17.9394			0.571306
$987$	−11.6051	−	46.2801i	−0.369393	−	1.47311i
$988$			1.18166i			0.0375937i
$989$	29.3280			0.932575
$990$	21.4143	−	11.4602i	0.680590	−	0.364228i
$991$		−	13.5300i		−	0.429795i	−0.976637	−	0.214898i	$-0.931058\pi$
$991$		−	13.5300i		−	0.429795i	0.976637	−	0.214898i	$-0.0689418\pi$
$992$		−	7.97239i		−	0.253124i
$993$	46.2204	−	11.5901i	1.46676	−	0.367800i
$994$	0.398974			0.0126547
$995$	11.8501			0.375674
$996$	−2.74519	+	0.688376i	−0.0869846	+	0.0218120i
$997$	−10.0198			−0.317329			−0.158665	−	0.987333i	$-0.550719\pi$
$997$	−10.0198			−0.317329			−0.158665	+	0.987333i	$0.550719\pi$
$998$		−	18.8477i		−	0.596615i
$999$	−24.1056	−	26.5557i	−0.762668	−	0.840186i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.2.d.a.200.12	yes	20
3.2	odd	2	inner	201.2.d.a.200.10	yes	20
67.66	odd	2	inner	201.2.d.a.200.9	✓	20
201.200	even	2	inner	201.2.d.a.200.11	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.2.d.a.200.9	✓	20	67.66	odd	2	inner
201.2.d.a.200.10	yes	20	3.2	odd	2	inner
201.2.d.a.200.11	yes	20	201.200	even	2	inner
201.2.d.a.200.12	yes	20	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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	201.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.598526 q^{2} +(0.421281 + 1.68004i) q^{3} -1.64177 q^{4} -3.30634 q^{5} +(0.252148 + 1.00555i) q^{6} +2.20280i q^{7} -2.17969 q^{8} +(-2.64504 + 1.41554i) q^{9} +O(q^{10})\)	\(q+0.598526 q^{2} +(0.421281 + 1.68004i) q^{3} -1.64177 q^{4} -3.30634 q^{5} +(0.252148 + 1.00555i) q^{6} +2.20280i q^{7} -2.17969 q^{8} +(-2.64504 + 1.41554i) q^{9} -1.97893 q^{10} +4.09110 q^{11} +(-0.691645 - 2.75823i) q^{12} +5.23566i q^{13} +1.31843i q^{14} +(-1.39290 - 5.55476i) q^{15} +1.97893 q^{16} -3.25197i q^{17} +(-1.58313 + 0.847235i) q^{18} -0.137471 q^{19} +5.42823 q^{20} +(-3.70078 + 0.927997i) q^{21} +2.44863 q^{22} -3.21123i q^{23} +(-0.918263 - 3.66196i) q^{24} +5.93186 q^{25} +3.13368i q^{26} +(-3.49246 - 3.84743i) q^{27} -3.61648i q^{28} +9.21673i q^{29} +(-0.833685 - 3.32467i) q^{30} -1.43807i q^{31} +5.54383 q^{32} +(1.72350 + 6.87320i) q^{33} -1.94639i q^{34} -7.28319i q^{35} +(4.34254 - 2.32398i) q^{36} +6.90219 q^{37} -0.0822798 q^{38} +(-8.79611 + 2.20569i) q^{39} +7.20680 q^{40} -8.31041 q^{41} +(-2.21501 + 0.555430i) q^{42} +9.13293i q^{43} -6.71663 q^{44} +(8.74540 - 4.68023i) q^{45} -1.92201i q^{46} +12.5055i q^{47} +(0.833685 + 3.32467i) q^{48} +2.14769 q^{49} +3.55037 q^{50} +(5.46344 - 1.37000i) q^{51} -8.59574i q^{52} -2.45213 q^{53} +(-2.09033 - 2.30279i) q^{54} -13.5265 q^{55} -4.80142i q^{56} +(-0.0579138 - 0.230956i) q^{57} +5.51645i q^{58} -9.02089i q^{59} +(2.28681 + 9.11962i) q^{60} -10.2902i q^{61} -0.860720i q^{62} +(-3.11814 - 5.82650i) q^{63} -0.639731 q^{64} -17.3109i q^{65} +(1.03156 + 4.11379i) q^{66} +(7.09695 - 4.07839i) q^{67} +5.33898i q^{68} +(5.39499 - 1.35283i) q^{69} -4.35918i q^{70} -0.302613i q^{71} +(5.76538 - 3.08543i) q^{72} -3.46215 q^{73} +4.13114 q^{74} +(2.49898 + 9.96573i) q^{75} +0.225695 q^{76} +9.01186i q^{77} +(-5.26470 + 1.32016i) q^{78} +5.02568i q^{79} -6.54300 q^{80} +(4.99252 - 7.48831i) q^{81} -4.97400 q^{82} -0.995273i q^{83} +(6.07581 - 1.52355i) q^{84} +10.7521i q^{85} +5.46630i q^{86} +(-15.4844 + 3.88283i) q^{87} -8.91734 q^{88} +5.26307i q^{89} +(5.23435 - 2.80124i) q^{90} -11.5331 q^{91} +5.27209i q^{92} +(2.41600 - 0.605830i) q^{93} +7.48488i q^{94} +0.454524 q^{95} +(2.33551 + 9.31383i) q^{96} -2.53000i q^{97} +1.28545 q^{98} +(-10.8211 + 5.79109i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 12 q^{4} - 4 q^{6} - 14 q^{9}+O(q^{10}) \) 20 * q + 12 * q^4 - 4 * q^6 - 14 * q^9	\( 20 q + 12 q^{4} - 4 q^{6} - 14 q^{9} - 12 q^{10} + 2 q^{15} + 12 q^{16} + 24 q^{19} + 12 q^{21} - 28 q^{22} + 2 q^{24} - 4 q^{25} + 10 q^{33} - 44 q^{36} + 24 q^{37} - 8 q^{39} - 32 q^{40} - 48 q^{49} - 26 q^{54} - 8 q^{55} - 38 q^{60} - 16 q^{64} + 32 q^{67} + 4 q^{73} + 116 q^{76} - 30 q^{81} - 32 q^{82} + 90 q^{84} - 40 q^{88} + 74 q^{90} + 20 q^{91} - 2 q^{93} + 30 q^{96}+O(q^{100}) \) 20 * q + 12 * q^4 - 4 * q^6 - 14 * q^9 - 12 * q^10 + 2 * q^15 + 12 * q^16 + 24 * q^19 + 12 * q^21 - 28 * q^22 + 2 * q^24 - 4 * q^25 + 10 * q^33 - 44 * q^36 + 24 * q^37 - 8 * q^39 - 32 * q^40 - 48 * q^49 - 26 * q^54 - 8 * q^55 - 38 * q^60 - 16 * q^64 + 32 * q^67 + 4 * q^73 + 116 * q^76 - 30 * q^81 - 32 * q^82 + 90 * q^84 - 40 * q^88 + 74 * q^90 + 20 * q^91 - 2 * q^93 + 30 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more