LMFDB - Embedded newform 171.2.x.a.14.16

Error: no document with id 276274424 found in table mf_hecke_traces.

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [171,2,Mod(14,171)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("171.14"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(171, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([15, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	171.x (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.36544187456$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			14.16
Character	$\chi$	$=$	171.14
Dual form			171.2.x.a.110.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.42288 + 1.19394i) q^{2} +(-1.62073 + 0.610926i) q^{3} +(0.251804 + 1.42805i) q^{4} +(0.629748 + 1.73022i) q^{5} +(-3.03552 - 1.06578i) q^{6} +(-1.66649 + 2.88644i) q^{7} +(0.510719 - 0.884592i) q^{8} +(2.25354 - 1.98029i) q^{9} +(-1.16972 + 3.21378i) q^{10} +2.01233i q^{11} +(-1.28054 - 2.16066i) q^{12} +(-0.355101 + 0.975632i) q^{13} +(-5.81744 + 2.11738i) q^{14} +(-2.07769 - 2.41949i) q^{15} +(4.50811 - 1.64082i) q^{16} +(-2.49671 - 6.85966i) q^{17} +(5.57087 - 0.127133i) q^{18} +(4.33498 + 0.456034i) q^{19} +(-2.31227 + 1.33499i) q^{20} +(0.937526 - 5.69624i) q^{21} +(-2.40260 + 2.86331i) q^{22} +(5.68790 - 1.00293i) q^{23} +(-0.287319 + 1.74570i) q^{24} +(1.23315 - 1.03473i) q^{25} +(-1.67011 + 0.964239i) q^{26} +(-2.44257 + 4.58627i) q^{27} +(-4.54161 - 1.65301i) q^{28} +(-0.250256 - 1.41927i) q^{29} +(-0.0675790 - 5.92328i) q^{30} +3.08283i q^{31} +(6.45386 + 2.34901i) q^{32} +(-1.22938 - 3.26144i) q^{33} +(4.63749 - 12.7414i) q^{34} +(-6.04364 - 1.06566i) q^{35} +(3.39541 + 2.71953i) q^{36} -2.56367i q^{37} +(5.62368 + 5.82458i) q^{38} +(-0.0205155 - 1.79818i) q^{39} +(1.85216 + 0.326586i) q^{40} +(-6.61929 - 5.55425i) q^{41} +(8.13495 - 6.98572i) q^{42} +(-0.553471 + 3.13889i) q^{43} +(-2.87371 + 0.506713i) q^{44} +(4.84550 + 2.65203i) q^{45} +(9.29064 + 5.36395i) q^{46} +(-8.65752 + 1.52655i) q^{47} +(-6.30401 + 5.41344i) q^{48} +(-2.05435 - 3.55824i) q^{49} +2.99003 q^{50} +(8.23725 + 9.59236i) q^{51} +(-1.48267 - 0.261435i) q^{52} +(-4.17870 + 3.50634i) q^{53} +(-8.95121 + 3.60944i) q^{54} +(-3.48177 + 1.26726i) q^{55} +(1.70221 + 2.94832i) q^{56} +(-7.30444 + 1.90924i) q^{57} +(1.33844 - 2.31825i) q^{58} +(1.40063 - 7.94334i) q^{59} +(2.93199 - 3.57629i) q^{60} +(10.4732 + 3.81194i) q^{61} +(-3.68071 + 4.38650i) q^{62} +(1.96050 + 9.80483i) q^{63} +(1.58107 + 2.73850i) q^{64} -1.91168 q^{65} +(2.14470 - 6.10846i) q^{66} +(-5.53209 - 6.59289i) q^{67} +(9.16728 - 5.29273i) q^{68} +(-8.60584 + 5.10036i) q^{69} +(-7.32705 - 8.73204i) q^{70} +(4.33638 + 3.63865i) q^{71} +(-0.600825 - 3.00484i) q^{72} +(-2.19677 + 12.4585i) q^{73} +(3.06087 - 3.64780i) q^{74} +(-1.36645 + 2.43038i) q^{75} +(0.440324 + 6.30541i) q^{76} +(-5.80846 - 3.35352i) q^{77} +(2.11772 - 2.58309i) q^{78} +(-3.44685 - 9.47013i) q^{79} +(5.67794 + 6.76671i) q^{80} +(1.15688 - 8.92534i) q^{81} +(-2.78704 - 15.8061i) q^{82} +(-7.44260 - 4.29699i) q^{83} +(8.37060 - 0.0955007i) q^{84} +(10.2964 - 8.63972i) q^{85} +(-4.53517 + 3.80546i) q^{86} +(1.27267 + 2.14737i) q^{87} +(1.78009 + 1.02773i) q^{88} +(-1.35261 - 7.67105i) q^{89} +(3.72821 + 9.55876i) q^{90} +(-2.22433 - 2.65085i) q^{91} +(2.86447 + 7.87007i) q^{92} +(-1.88338 - 4.99643i) q^{93} +(-14.1412 - 8.16445i) q^{94} +(1.94091 + 7.78765i) q^{95} +(-11.8950 + 0.135711i) q^{96} +(-10.2106 + 12.1685i) q^{97} +(1.32522 - 7.51572i) q^{98} +(3.98500 + 4.53486i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9} - 12 q^{10} - 9 q^{12} - 6 q^{13} - 9 q^{14} - 36 q^{15} - 9 q^{16} + 27 q^{17} + 36 q^{18} - 15 q^{19} - 18 q^{20} + 3 q^{21} + 30 q^{22} - 45 q^{23}+ \cdots + 39 q^{99}+O(q^{100}) $ 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9 - 12 * q^10 - 9 * q^12 - 6 * q^13 - 9 * q^14 - 36 * q^15 - 9 * q^16 + 27 * q^17 + 36 * q^18 - 15 * q^19 - 18 * q^20 + 3 * q^21 + 30 * q^22 - 45 * q^23 - 21 * q^24 - 3 * q^25 - 72 * q^26 - 36 * q^28 - 9 * q^29 - 21 * q^30 - 9 * q^32 - 6 * q^33 + 33 * q^34 + 45 * q^35 + 18 * q^36 - 9 * q^38 - 18 * q^39 + 15 * q^40 - 9 * q^41 + 15 * q^42 + 9 * q^43 - 63 * q^44 + 33 * q^45 - 18 * q^46 - 9 * q^47 + 3 * q^48 - 15 * q^49 + 126 * q^50 + 39 * q^51 - 39 * q^52 - 51 * q^54 + 3 * q^55 + 63 * q^56 - 78 * q^57 - 6 * q^58 + 36 * q^59 - 75 * q^60 - 24 * q^61 + 18 * q^62 - 9 * q^63 - 18 * q^65 + 159 * q^66 - 63 * q^67 + 54 * q^68 - 9 * q^69 + 39 * q^70 + 141 * q^72 - 45 * q^73 - 117 * q^74 - 3 * q^76 - 18 * q^77 + 27 * q^78 + 3 * q^79 + 126 * q^80 - 60 * q^81 - 3 * q^82 + 27 * q^83 - 117 * q^84 - 3 * q^85 - 171 * q^86 + 15 * q^87 - 9 * q^88 + 54 * q^89 - 21 * q^90 - 9 * q^91 - 27 * q^92 + 42 * q^93 + 99 * q^95 + 207 * q^96 - 57 * q^97 - 27 * q^98 + 39 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{18}\right)$

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 $

$2$	1.42288	+	1.19394i	1.00613	+	0.844243i	0.987822	−	0.155590i	$-0.0497278\pi$
$2$	1.42288	+	1.19394i	1.00613	+	0.844243i	0.0183074	+	0.999832i	$0.494172\pi$
$3$	−1.62073	+	0.610926i	−0.935730	+	0.352718i
$3$	−1.62073	+	0.610926i	−0.935730	+	0.352718i
$4$	0.251804	+	1.42805i	0.125902	+	0.714026i
$5$	0.629748	+	1.73022i	0.281632	+	0.773778i	0.997168	+	0.0752020i	$0.0239602\pi$
$5$	0.629748	+	1.73022i	0.281632	+	0.773778i	−0.715536	+	0.698576i	$0.753818\pi$
$6$	−3.03552	−	1.06578i	−1.23924	−	0.435103i
$7$	−1.66649	+	2.88644i	−0.629872	+	1.09097i	0.357705	+	0.933835i	$0.383560\pi$
$7$	−1.66649	+	2.88644i	−0.629872	+	1.09097i	−0.987577	+	0.157136i	$0.949774\pi$
$8$	0.510719	−	0.884592i	0.180567	−	0.312750i
$9$	2.25354	−	1.98029i	0.751180	−	0.660098i
$10$	−1.16972	+	3.21378i	−0.369898	+	1.01629i
$11$			2.01233i			0.606740i	0.952873	+	0.303370i	$0.0981118\pi$
$11$			2.01233i			0.606740i	−0.952873	+	0.303370i	$0.901888\pi$
$12$	−1.28054	−	2.16066i	−0.369660	−	0.623728i
$13$	−0.355101	+	0.975632i	−0.0984873	+	0.270592i	−0.979145	−	0.203161i	$-0.934879\pi$
$13$	−0.355101	+	0.975632i	−0.0984873	+	0.270592i	0.880658	+	0.473752i	$0.157101\pi$
$14$	−5.81744	+	2.11738i	−1.55478	+	0.565893i
$15$	−2.07769	−	2.41949i	−0.536457	−	0.624710i
$16$	4.50811	−	1.64082i	1.12703	−	0.410204i
$17$	−2.49671	−	6.85966i	−0.605542	−	1.66371i	−0.739849	−	0.672773i	$-0.765103\pi$
$17$	−2.49671	−	6.85966i	−0.605542	−	1.66371i	0.134307	−	0.990940i	$-0.457119\pi$
$18$	5.57087	−	0.127133i	1.31307	−	0.0299656i
$19$	4.33498	+	0.456034i	0.994512	+	0.104621i
$19$	4.33498	+	0.456034i	0.994512	+	0.104621i
$20$	−2.31227	+	1.33499i	−0.517039	+	0.298513i
$21$	0.937526	−	5.69624i	0.204585	−	1.24302i
$22$	−2.40260	+	2.86331i	−0.512236	+	0.610459i
$23$	5.68790	−	1.00293i	1.18601	−	0.209125i	0.454367	−	0.890815i	$-0.349866\pi$
$23$	5.68790	−	1.00293i	1.18601	−	0.209125i	0.731642	+	0.681689i	$0.238754\pi$
$24$	−0.287319	+	1.74570i	−0.0586487	+	0.356339i
$25$	1.23315	−	1.03473i	0.246629	−	0.206947i
$26$	−1.67011	+	0.964239i	−0.327536	+	0.189103i
$27$	−2.44257	+	4.58627i	−0.470073	+	0.882628i
$28$	−4.54161	−	1.65301i	−0.858284	−	0.312390i
$29$	−0.250256	−	1.41927i	−0.0464715	−	0.263553i	0.952716	−	0.303863i	$-0.0982765\pi$
$29$	−0.250256	−	1.41927i	−0.0464715	−	0.263553i	−0.999187	+	0.0403102i	$0.987165\pi$
$30$	−0.0675790	−	5.92328i	−0.0123382	−	1.08144i
$31$			3.08283i			0.553692i	0.960914	+	0.276846i	$0.0892892\pi$
$31$			3.08283i			0.553692i	−0.960914	+	0.276846i	$0.910711\pi$
$32$	6.45386	+	2.34901i	1.14089	+	0.415251i
$33$	−1.22938	−	3.26144i	−0.214008	−	0.567745i
$34$	4.63749	−	12.7414i	0.795324	−	2.18513i
$35$	−6.04364	−	1.06566i	−1.02156	−	0.180129i
$36$	3.39541	+	2.71953i	0.565902	+	0.453254i
$37$		−	2.56367i		−	0.421465i	−0.977544	−	0.210733i	$-0.932415\pi$
$37$		−	2.56367i		−	0.421465i	0.977544	−	0.210733i	$-0.0675849\pi$
$38$	5.62368	+	5.82458i	0.912282	+	0.944872i
$39$	−0.0205155	−	1.79818i	−0.00328511	−	0.287939i
$40$	1.85216	+	0.326586i	0.292853	+	0.0516378i
$41$	−6.61929	−	5.55425i	−1.03376	−	0.867428i	−0.0424664	−	0.999098i	$-0.513522\pi$
$41$	−6.61929	−	5.55425i	−1.03376	−	0.867428i	−0.991294	+	0.131670i	$0.957966\pi$
$42$	8.13495	−	6.98572i	1.25525	−	1.07792i
$43$	−0.553471	+	3.13889i	−0.0844035	+	0.478676i	0.913080	+	0.407780i	$0.133697\pi$
$43$	−0.553471	+	3.13889i	−0.0844035	+	0.478676i	−0.997484	+	0.0708960i	$0.977414\pi$
$44$	−2.87371	+	0.506713i	−0.433228	+	0.0763898i
$45$	4.84550	+	2.65203i	0.722325	+	0.395341i
$46$	9.29064	+	5.36395i	1.36983	+	0.790872i
$47$	−8.65752	+	1.52655i	−1.26283	+	0.222671i	−0.764674	−	0.644417i	$-0.777100\pi$
$47$	−8.65752	+	1.52655i	−1.26283	+	0.222671i	−0.498155	+	0.867088i	$0.665989\pi$
$48$	−6.30401	+	5.41344i	−0.909905	+	0.781363i
$49$	−2.05435	−	3.55824i	−0.293479	−	0.508320i
$50$	2.99003			0.422854
$51$	8.23725	+	9.59236i	1.15345	+	1.34320i
$52$	−1.48267	−	0.261435i	−0.205609	−	0.0362544i
$53$	−4.17870	+	3.50634i	−0.573988	+	0.481633i	−0.882967	−	0.469436i	$-0.844457\pi$
$53$	−4.17870	+	3.50634i	−0.573988	+	0.481633i	0.308978	+	0.951069i	$0.400013\pi$
$54$	−8.95121	+	3.60944i	−1.21811	+	0.491182i
$55$	−3.48177	+	1.26726i	−0.469482	+	0.170877i
$56$	1.70221	+	2.94832i	0.227468	+	0.393986i
$57$	−7.30444	+	1.90924i	−0.967496	+	0.252885i
$58$	1.33844	−	2.31825i	0.175746	−	0.304401i
$59$	1.40063	−	7.94334i	0.182346	−	1.03414i	−0.746972	−	0.664855i	$-0.768493\pi$
$59$	1.40063	−	7.94334i	0.182346	−	1.03414i	0.929318	−	0.369280i	$-0.120396\pi$
$60$	2.93199	−	3.57629i	0.378518	−	0.461697i
$61$	10.4732	+	3.81194i	1.34096	+	0.488069i	0.910115	−	0.414357i	$-0.135993\pi$
$61$	10.4732	+	3.81194i	1.34096	+	0.488069i	0.430845	+	0.902426i	$0.358216\pi$
$62$	−3.68071	+	4.38650i	−0.467450	+	0.557086i
$63$	1.96050	+	9.80483i	0.247000	+	1.23529i
$64$	1.58107	+	2.73850i	0.197634	+	0.342312i
$65$	−1.91168			−0.237115
$66$	2.14470	−	6.10846i	0.263994	−	0.751899i
$67$	−5.53209	−	6.59289i	−0.675852	−	0.805449i	0.313716	−	0.949517i	$-0.398426\pi$
$67$	−5.53209	−	6.59289i	−0.675852	−	0.805449i	−0.989568	+	0.144068i	$0.953982\pi$
$68$	9.16728	−	5.29273i	1.11170	−	0.641838i
$69$	−8.60584	+	5.10036i	−1.03602	+	0.614012i
$70$	−7.32705	−	8.73204i	−0.875750	−	1.04368i
$71$	4.33638	+	3.63865i	0.514633	+	0.431829i	0.862756	−	0.505620i	$-0.168736\pi$
$71$	4.33638	+	3.63865i	0.514633	+	0.431829i	−0.348123	+	0.937449i	$0.613181\pi$
$72$	−0.600825	−	3.00484i	−0.0708079	−	0.354123i
$73$	−2.19677	+	12.4585i	−0.257112	+	1.45816i	0.533480	+	0.845813i	$0.320884\pi$
$73$	−2.19677	+	12.4585i	−0.257112	+	1.45816i	−0.790592	+	0.612343i	$0.790227\pi$
$74$	3.06087	−	3.64780i	0.355819	−	0.424048i
$75$	−1.36645	+	2.43038i	−0.157784	+	0.280637i
$76$	0.440324	+	6.30541i	0.0505087	+	0.723280i
$77$	−5.80846	−	3.35352i	−0.661936	−	0.382169i
$78$	2.11772	−	2.58309i	0.239785	−	0.292477i
$79$	−3.44685	−	9.47013i	−0.387800	−	1.06547i	−0.967989	−	0.250991i	$-0.919244\pi$
$79$	−3.44685	−	9.47013i	−0.387800	−	1.06547i	0.580189	−	0.814482i	$-0.302979\pi$
$80$	5.67794	+	6.76671i	0.634813	+	0.756541i
$81$	1.15688	−	8.92534i	0.128542	−	0.991704i
$82$	−2.78704	−	15.8061i	−0.307777	−	1.74549i
$83$	−7.44260	−	4.29699i	−0.816932	−	0.471656i	0.0324254	−	0.999474i	$-0.489677\pi$
$83$	−7.44260	−	4.29699i	−0.816932	−	0.471656i	−0.849357	+	0.527818i	$0.823010\pi$
$84$	8.37060	−	0.0955007i	0.913308	−	0.0104200i
$85$	10.2964	−	8.63972i	1.11680	−	0.937109i
$86$	−4.53517	+	3.80546i	−0.489039	+	0.410353i
$87$	1.27267	+	2.14737i	0.136445	+	0.230223i
$88$	1.78009	+	1.02773i	0.189758	+	0.109557i
$89$	−1.35261	−	7.67105i	−0.143377	−	0.813130i	−0.968656	−	0.248405i	$-0.920094\pi$
$89$	−1.35261	−	7.67105i	−0.143377	−	0.813130i	0.825280	−	0.564724i	$-0.191018\pi$
$90$	3.72821	+	9.55876i	0.392988	+	1.00758i
$91$	−2.22433	−	2.65085i	−0.233173	−	0.277885i
$92$	2.86447	+	7.87007i	0.298642	+	0.820512i
$93$	−1.88338	−	4.99643i	−0.195297	−	0.518106i
$94$	−14.1412	−	8.16445i	−1.45856	−	0.842098i
$95$	1.94091	+	7.78765i	0.199133	+	0.798996i
$96$	−11.8950	+	0.135711i	−1.21403	+	0.0138510i
$97$	−10.2106	+	12.1685i	−1.03673	+	1.23552i	−0.0653807	+	0.997860i	$0.520826\pi$
$97$	−10.2106	+	12.1685i	−1.03673	+	1.23552i	−0.971347	+	0.237664i	$0.923618\pi$
$98$	1.32522	−	7.51572i	0.133868	−	0.759202i
$99$	3.98500	+	4.53486i	0.400508	+	0.455771i
$100$	1.78816	+	1.50045i	0.178816	+	0.150045i
$101$	3.65665	+	4.35782i	0.363850	+	0.433620i	0.916648	−	0.399696i	$-0.130884\pi$
$101$	3.65665	+	4.35782i	0.363850	+	0.433620i	−0.552798	+	0.833315i	$0.686440\pi$
$102$	0.267925	+	23.4836i	0.0265286	+	2.32522i
$103$	−3.51204	+	2.02767i	−0.346051	+	0.199793i	−0.662945	−	0.748668i	$-0.730694\pi$
$103$	−3.51204	+	2.02767i	−0.346051	+	0.199793i	0.316894	+	0.948461i	$0.397360\pi$
$104$	0.681679	+	0.812393i	0.0668441	+	0.0796617i
$105$	10.4461	−	1.96507i	1.01944	−	0.191771i
$106$	−10.1322			−0.984122
$107$	−1.89059	−	3.27459i	−0.182770	−	0.316567i	0.760053	−	0.649861i	$-0.225173\pi$
$107$	−1.89059	−	3.27459i	−0.182770	−	0.316567i	−0.942823	+	0.333295i	$0.891840\pi$
$108$	−7.16448	−	2.33328i	−0.689403	−	0.224520i
$109$	−4.65575	+	5.54851i	−0.445940	+	0.531451i	−0.941450	−	0.337151i	$-0.890537\pi$
$109$	−4.65575	+	5.54851i	−0.445940	+	0.531451i	0.495510	+	0.868602i	$0.334981\pi$
$110$	−6.46718	−	2.35386i	−0.616621	−	0.224432i
$111$	1.56621	+	4.15502i	0.148658	+	0.394377i
$112$	−2.77658	+	15.7468i	−0.262362	+	1.48793i
$113$	7.23693	−	12.5347i	0.680793	−	1.17917i	−0.293946	−	0.955822i	$-0.594969\pi$
$113$	7.23693	−	12.5347i	0.680793	−	1.17917i	0.974739	−	0.223346i	$-0.0716981\pi$
$114$	−12.6729	−	6.00443i	−1.18692	−	0.562367i
$115$	5.31723	+	9.20972i	0.495834	+	0.858810i
$116$	1.96378	−	0.714759i	0.182333	−	0.0663637i
$117$	1.13180	+	2.90183i	0.104635	+	0.268274i
$118$	11.4768	−	9.63017i	1.05652	−	0.886529i
$119$	23.9607	+	4.22492i	2.19648	+	0.387298i
$120$	−3.20138	+	0.602225i	−0.292244	+	0.0549754i
$121$	6.95053			0.631867
$122$	10.3509	+	17.9283i	0.937129	+	1.62316i
$123$	14.1213	+	4.95804i	1.27328	+	0.447052i
$124$	−4.40244	+	0.776269i	−0.395351	+	0.0697110i
$125$	10.5398	+	6.08514i	0.942707	+	0.544272i
$126$	−8.91681	+	16.2918i	−0.794373	+	1.45139i
$127$	−1.28938	+	0.227353i	−0.114414	+	0.0201743i	−0.230562	−	0.973058i	$-0.574056\pi$
$127$	−1.28938	+	0.227353i	−0.114414	+	0.0201743i	0.116148	+	0.993232i	$0.462945\pi$
$128$	1.36533	−	7.74316i	0.120679	−	0.684406i
$129$	−1.02060	−	5.42542i	−0.0898589	−	0.477682i
$130$	−2.72009	−	2.28243i	−0.238568	−	0.200182i
$131$	5.10663	+	0.900436i	0.446168	+	0.0786715i	0.392218	−	0.919872i	$-0.371708\pi$
$131$	5.10663	+	0.900436i	0.446168	+	0.0786715i	0.0539498	+	0.998544i	$0.482819\pi$
$132$	4.34795	−	2.57687i	0.378440	−	0.224288i
$133$	−8.54049	+	11.7527i	−0.740555	+	1.01909i
$134$		−	15.9859i		−	1.38097i
$135$	−9.47345	−	1.33799i	−0.815345	−	0.115155i
$136$	−7.34312	−	1.29479i	−0.629667	−	0.111027i
$137$	4.70095	−	12.9158i	0.401629	−	1.10347i	−0.559851	−	0.828593i	$-0.689142\pi$
$137$	4.70095	−	12.9158i	0.401629	−	1.10347i	0.961480	−	0.274874i	$-0.0886362\pi$
$138$	−18.3346	−	3.01764i	−1.56075	−	0.256878i
$139$	−4.91514	−	1.78896i	−0.416896	−	0.151738i	0.125051	−	0.992150i	$-0.460091\pi$
$139$	−4.91514	−	1.78896i	−0.416896	−	0.151738i	−0.541947	+	0.840412i	$0.682313\pi$
$140$		−	8.89897i		−	0.752100i
$141$	13.0989	−	7.76323i	1.10313	−	0.653782i
$142$	1.82582	+	10.3547i	0.153219	+	0.868951i
$143$	−1.96329	−	0.714580i	−0.164179	−	0.0597561i
$144$	6.90990	−	12.6250i	0.575825	−	1.05208i
$145$	2.29806	−	1.32678i	0.190843	−	0.110183i
$146$	−18.0004	+	15.1041i	−1.48973	+	1.25003i
$147$	5.50337	+	4.51189i	0.453910	+	0.372135i
$148$	3.66106	−	0.645544i	0.300937	−	0.0530634i
$149$	1.95002	−	2.32394i	0.159752	−	0.190385i	−0.680231	−	0.732998i	$-0.738121\pi$
$149$	1.95002	−	2.32394i	0.159752	−	0.190385i	0.839983	+	0.542613i	$0.182565\pi$
$150$	−4.84603	+	1.82669i	−0.395677	+	0.149148i
$151$	−15.6433	+	9.03169i	−1.27304	+	0.734988i	−0.975558	−	0.219740i	$-0.929479\pi$
$151$	−15.6433	+	9.03169i	−1.27304	+	0.734988i	−0.297478	+	0.954729i	$0.596146\pi$
$152$	2.61736	−	3.60178i	0.212296	−	0.292143i
$153$	−19.2106	−	10.5143i	−1.55308	−	0.850030i
$154$	−4.26086	−	11.7066i	−0.343350	−	0.943345i
$155$	−5.33397	+	1.94141i	−0.428435	+	0.155937i
$156$	2.56273	−	0.482086i	0.205182	−	0.0385977i
$157$	21.8184	−	7.94124i	1.74130	−	0.633780i	0.741968	−	0.670435i	$-0.233892\pi$
$157$	21.8184	−	7.94124i	1.74130	−	0.633780i	0.999328	+	0.0366550i	$0.0116703\pi$
$158$	6.40231	−	17.5902i	0.509340	−	1.39940i
$159$	4.63043	−	8.23572i	0.367217	−	0.653135i
$160$			12.6459i			0.999744i
$161$	−6.58391	+	18.0891i	−0.518884	+	1.42562i
$162$	12.3024	−	11.3185i	0.966569	−	0.889262i
$163$	−1.87789	+	3.25259i	−0.147087	+	0.254763i	−0.930150	−	0.367180i	$-0.880323\pi$
$163$	−1.87789	+	3.25259i	−0.147087	+	0.254763i	0.783062	+	0.621943i	$0.213657\pi$
$164$	6.26499	−	10.8513i	0.489214	−	0.847343i
$165$	4.86881	−	4.18099i	0.379036	−	0.325490i
$166$	−5.45960	−	15.0001i	−0.423747	−	1.16424i
$167$	−0.900611	−	5.10762i	−0.0696914	−	0.395239i	−0.999622	−	0.0275037i	$-0.991244\pi$
$167$	−0.900611	−	5.10762i	−0.0696914	−	0.395239i	0.929930	−	0.367736i	$-0.119867\pi$
$168$	−4.56003	−	3.73851i	−0.351814	−	0.288432i
$169$	9.13282	+	7.66334i	0.702524	+	0.589488i
$170$	24.9659			1.91480
$171$	10.6721	−	7.55684i	0.816118	−	0.577886i
$172$	−4.62186			−0.352414
$173$	0.795445	+	0.667458i	0.0604766	+	0.0507459i	0.672525	−	0.740074i	$-0.265210\pi$
$173$	0.795445	+	0.667458i	0.0604766	+	0.0507459i	−0.612048	+	0.790820i	$0.709654\pi$
$174$	−0.752977	+	4.57495i	−0.0570830	+	0.346826i
$175$	0.931671	+	5.28377i	0.0704277	+	0.399415i
$176$	3.30186	+	9.07179i	0.248887	+	0.683812i
$177$	2.58276	+	13.7297i	0.194132	+	1.03199i
$178$	7.23416	−	12.5299i	0.542223	−	0.939158i
$179$	5.29472	−	9.17073i	0.395746	−	0.685453i	−0.597450	−	0.801906i	$-0.703819\pi$
$179$	5.29472	−	9.17073i	0.395746	−	0.685453i	0.993196	+	0.116454i	$0.0371527\pi$
$180$	−2.56712	+	7.58743i	−0.191342	+	0.565533i
$181$	8.27035	−	22.7226i	0.614730	−	1.68896i	−0.104798	−	0.994494i	$-0.533419\pi$
$181$	8.27035	−	22.7226i	0.614730	−	1.68896i	0.719528	−	0.694464i	$-0.244358\pi$
$182$		−	6.42756i		−	0.476443i
$183$	−19.3031	+	0.220230i	−1.42693	+	0.0162799i
$184$	2.01774	−	5.54368i	0.148749	−	0.408686i
$185$	4.43572	−	1.61447i	0.326120	−	0.118698i
$186$	3.28561	−	9.35797i	0.240913	−	0.686160i
$187$	13.8039	−	5.02421i	1.00944	−	0.367406i
$188$	−4.36000	−	11.9790i	−0.317986	−	0.873658i
$189$	−9.16747	−	14.6933i	−0.666835	−	1.06878i
$190$	−6.53630	+	13.3982i	−0.474193	+	0.972009i
$191$	−9.40161	+	5.42802i	−0.680277	+	0.392758i	−0.799959	−	0.600054i	$-0.795146\pi$
$191$	−9.40161	+	5.42802i	−0.680277	+	0.392758i	0.119683	+	0.992812i	$0.461812\pi$
$192$	−4.23551	−	3.47245i	−0.305672	−	0.250602i
$193$	1.57956	−	1.88245i	0.113699	−	0.135502i	−0.706193	−	0.708020i	$-0.749589\pi$
$193$	1.57956	−	1.88245i	0.113699	−	0.135502i	0.819892	+	0.572518i	$0.194033\pi$
$194$	−29.0569	+	5.12352i	−2.08616	+	0.367847i
$195$	3.09832	−	1.16790i	0.221875	−	0.0836347i
$196$	4.56406	−	3.82970i	0.326004	−	0.273550i
$197$	−14.2423	+	8.22281i	−1.01472	+	0.585851i	−0.912571	−	0.408918i	$-0.865906\pi$
$197$	−14.2423	+	8.22281i	−1.01472	+	0.585851i	−0.102153	+	0.994769i	$0.532573\pi$
$198$	0.255834	+	11.2104i	0.0181813	+	0.796690i
$199$	−12.8946	−	4.69326i	−0.914077	−	0.332697i	−0.158197	−	0.987408i	$-0.550568\pi$
$199$	−12.8946	−	4.69326i	−0.914077	−	0.332697i	−0.755879	+	0.654711i	$0.772790\pi$
$200$	−0.285524	−	1.61929i	−0.0201896	−	0.114501i
$201$	12.9938	+	7.30560i	0.916512	+	0.515297i
$202$			10.5665i			0.743455i
$203$	4.51370	+	1.64285i	0.316799	+	0.115306i
$204$	−11.6242	+	14.1786i	−0.813859	+	0.992702i
$205$	5.44158	−	14.9506i	0.380056	−	1.04420i
$206$	−7.41813	−	1.30802i	−0.516846	−	0.0911338i
$207$	10.8318	−	13.5238i	0.752862	−	0.939972i
$208$			4.98091i			0.345364i
$209$	−0.917691	+	8.72340i	−0.0634780	+	0.603410i
$210$	17.2098	+	9.67600i	1.18759	+	0.667708i
$211$	7.95554	+	1.40278i	0.547682	+	0.0965712i	0.440641	−	0.897683i	$-0.354751\pi$
$211$	7.95554	+	1.40278i	0.547682	+	0.0965712i	0.107041	+	0.994255i	$0.465862\pi$
$212$	−6.05946	−	5.08449i	−0.416165	−	0.349204i
$213$	−9.25105	−	3.24807i	−0.633871	−	0.222554i
$214$	1.21958	−	6.91660i	0.0833690	−	0.472809i
$215$	−5.77951	+	1.01908i	−0.394159	+	0.0695010i
$216$	2.80951	+	4.50297i	0.191163	+	0.306388i
$217$	−8.89839	−	5.13749i	−0.604062	−	0.348755i
$218$	−13.2492	+	2.33618i	−0.897346	+	0.158226i
$219$	−4.05084	−	21.5339i	−0.273731	−	1.45513i
$220$	−2.68644	−	4.65305i	−0.181120	−	0.313709i
$221$	7.57909			0.509825
$222$	−2.73231	+	7.78207i	−0.183381	+	0.522298i
$223$	−15.5123	−	2.73524i	−1.03878	−	0.183165i	−0.371857	−	0.928290i	$-0.621279\pi$
$223$	−15.5123	−	2.73524i	−1.03878	−	0.183165i	−0.666925	+	0.745125i	$0.732390\pi$
$224$	−17.5355	+	14.7141i	−1.17164	+	0.983125i
$225$	0.729870	−	4.77380i	0.0486580	−	0.318253i
$226$	25.2630	−	9.19498i	1.68047	−	0.611641i
$227$	13.8297	+	23.9537i	0.917909	+	1.58986i	0.802586	+	0.596537i	$0.203457\pi$
$227$	13.8297	+	23.9537i	0.917909	+	1.58986i	0.115323	+	0.993328i	$0.463210\pi$
$228$	−4.56578	−	9.95037i	−0.302376	−	0.658979i
$229$	−4.51331	+	7.81728i	−0.298248	+	0.516580i	−0.975735	−	0.218954i	$-0.929735\pi$
$229$	−4.51331	+	7.81728i	−0.298248	+	0.516580i	0.677487	+	0.735534i	$0.263069\pi$
$230$	−3.43005	+	19.4528i	−0.226171	+	1.28268i
$231$	11.4627	+	1.88661i	0.754191	+	0.124130i
$232$	−1.38329	−	0.503476i	−0.0908174	−	0.0330548i
$233$	−13.7138	+	16.3435i	−0.898420	+	1.07070i	0.0987193	+	0.995115i	$0.468525\pi$
$233$	−13.7138	+	16.3435i	−0.898420	+	1.07070i	−0.997140	+	0.0755804i	$0.975919\pi$
$234$	−1.85419	+	5.48026i	−0.121212	+	0.358256i
$235$	−8.09333	−	14.0181i	−0.527951	−	0.914437i
$236$	11.6962			0.761358
$237$	11.3720	+	13.2428i	0.738688	+	0.860210i
$238$	29.0490	+	34.6192i	1.88297	+	2.24403i
$239$	−7.11510	+	4.10790i	−0.460237	+	0.265718i	−0.712144	−	0.702033i	$-0.752276\pi$
$239$	−7.11510	+	4.10790i	−0.460237	+	0.265718i	0.251907	+	0.967752i	$0.418942\pi$
$240$	−13.3364	−	7.49822i	−0.860860	−	0.484008i
$241$	−15.7245	−	18.7397i	−1.01290	−	1.20713i	−0.978186	−	0.207732i	$-0.933392\pi$
$241$	−15.7245	−	18.7397i	−1.01290	−	1.20713i	−0.0347155	−	0.999397i	$-0.511052\pi$
$242$	9.88978	+	8.29851i	0.635739	+	0.533449i
$243$	3.57773	+	15.1723i	0.229511	+	0.973306i
$244$	−2.80645	+	15.9162i	−0.179665	+	1.01893i
$245$	4.86281	−	5.79527i	0.310673	−	0.370246i
$246$	14.1734	+	23.9147i	0.903661	+	1.52475i
$247$	−1.98428	+	4.06740i	−0.126256	+	0.258803i
$248$	2.72704	+	1.57446i	0.173167	+	0.0999783i
$249$	14.6876	+	2.41739i	0.930789	+	0.153196i
$250$	7.73156	+	21.2423i	0.488987	+	1.34348i
$251$	−8.54330	−	10.1815i	−0.539248	−	0.642651i	0.425771	−	0.904831i	$-0.360003\pi$
$251$	−8.54330	−	10.1815i	−0.539248	−	0.642651i	−0.965019	+	0.262180i	$0.915559\pi$
$252$	−13.5082	+	5.26860i	−0.850934	+	0.331890i
$253$	2.01822	+	11.4459i	0.126885	+	0.719599i
$254$	−2.10608	−	1.21595i	−0.132147	−	0.0762953i
$255$	−11.4095	+	20.2930i	−0.714491	+	1.27080i
$256$	16.0323	−	13.4527i	1.00202	−	0.840791i
$257$	−15.4469	+	12.9615i	−0.963551	+	0.808516i	−0.981527	−	0.191323i	$-0.938722\pi$
$257$	−15.4469	+	12.9615i	−0.963551	+	0.808516i	0.0179757	+	0.999838i	$0.494278\pi$
$258$	5.02543	−	8.93827i	0.312870	−	0.556472i
$259$	7.39988	+	4.27232i	0.459806	+	0.265469i
$260$	−0.481369	−	2.72998i	−0.0298533	−	0.169306i
$261$	−3.37454	−	2.70281i	−0.208879	−	0.167300i
$262$	6.19106	+	7.37822i	0.382485	+	0.455828i
$263$	−7.51651	−	20.6514i	−0.463488	−	1.27342i	−0.922845	−	0.385170i	$-0.874143\pi$
$263$	−7.51651	−	20.6514i	−0.463488	−	1.27342i	0.459358	−	0.888251i	$-0.348080\pi$
$264$	−3.51292	−	0.578180i	−0.216205	−	0.0355845i
$265$	−8.69827	−	5.02195i	−0.534331	−	0.308496i
$266$	−26.1841	+	6.52582i	−1.60545	+	0.400124i
$267$	6.87866	+	11.6064i	0.420967	+	0.710298i
$268$	8.02199	−	9.56023i	0.490021	−	0.583984i
$269$	−1.76467	+	10.0079i	−0.107594	+	0.610194i	0.882559	+	0.470202i	$0.155819\pi$
$269$	−1.76467	+	10.0079i	−0.107594	+	0.610194i	−0.990153	+	0.139992i	$0.955292\pi$
$270$	−11.8821	−	13.2145i	−0.723123	−	0.804210i
$271$	11.1890	+	9.38869i	0.679683	+	0.570322i	0.915914	−	0.401375i	$-0.131468\pi$
$271$	11.1890	+	9.38869i	0.679683	+	0.570322i	−0.236230	+	0.971697i	$0.575912\pi$
$272$	−22.5109	−	26.8274i	−1.36492	−	1.62665i
$273$	5.22451	+	2.93742i	0.316202	+	0.177781i
$274$	22.1095	−	12.7649i	1.33569	−	0.771158i
$275$	2.08222	+	2.48150i	0.125563	+	0.149640i
$276$	−9.45057	−	11.0053i	−0.568858	−	0.662441i
$277$	8.81336			0.529543			0.264772	−	0.964311i	$-0.414703\pi$
$277$	8.81336			0.529543			0.264772	+	0.964311i	$0.414703\pi$
$278$	−4.85774	−	8.41386i	−0.291348	−	0.504629i
$279$	6.10490	+	6.94727i	0.365491	+	0.415922i
$280$	−4.02927	+	4.80190i	−0.240795	+	0.286968i
$281$	1.36960	+	0.498492i	0.0817032	+	0.0297376i	0.382548	−	0.923935i	$-0.375047\pi$
$281$	1.36960	+	0.498492i	0.0817032	+	0.0297376i	−0.300845	+	0.953673i	$0.597269\pi$
$282$	27.9070	+	4.59313i	1.66184	+	0.273517i
$283$	−5.63746	+	31.9716i	−0.335112	+	1.90052i	0.0910081	+	0.995850i	$0.470991\pi$
$283$	−5.63746	+	31.9716i	−0.335112	+	1.90052i	−0.426120	+	0.904666i	$0.640120\pi$
$284$	−4.10427	+	7.10880i	−0.243544	+	0.421830i
$285$	−7.90336	−	11.4359i	−0.468155	−	0.677406i
$286$	−1.94037	−	3.36081i	−0.114736	−	0.198729i
$287$	27.0629	−	9.85011i	1.59748	−	0.581433i
$288$	19.1958	−	7.48694i	1.13112	−	0.441172i
$289$	−27.7986	+	23.3258i	−1.63521	+	1.37211i
$290$	4.85396	+	0.855885i	0.285035	+	0.0502593i
$291$	9.11456	−	25.9598i	0.534305	−	1.52179i
$292$	−18.3445			−1.07353
$293$	0.195948	+	0.339392i	0.0114474	+	0.0198275i	0.871692	−	0.490053i	$-0.163023\pi$
$293$	0.195948	+	0.339392i	0.0114474	+	0.0198275i	−0.860245	+	0.509881i	$0.829689\pi$
$294$	2.44372	+	12.9906i	0.142520	+	0.757626i
$295$	14.6258	−	2.57892i	0.851545	−	0.150150i
$296$	−2.26780	−	1.30932i	−0.131813	−	0.0761025i
$297$	−9.22908	−	4.91525i	−0.535525	−	0.285212i
$298$	5.54929	−	0.978490i	0.321462	−	0.0566824i
$299$	−1.04129	+	5.90543i	−0.0602192	+	0.341520i
$300$	−3.81480	−	1.33939i	−0.220247	−	0.0773295i
$301$	−8.13786	−	6.82847i	−0.469058	−	0.393587i
$302$	−33.0419	−	5.82618i	−1.90135	−	0.335259i
$303$	−8.58875	−	4.82892i	−0.493411	−	0.277414i
$304$	20.2908	−	5.05705i	1.16376	−	0.290042i
$305$			20.5215i			1.17506i
$306$	−14.7810	−	37.8969i	−0.844971	−	2.16642i
$307$	−5.80729	−	1.02398i	−0.331440	−	0.0584417i	0.00545214	−	0.999985i	$-0.498265\pi$
$307$	−5.80729	−	1.02398i	−0.331440	−	0.0584417i	−0.336892	+	0.941543i	$0.609376\pi$
$308$	3.32640	−	9.13922i	0.189539	−	0.520755i
$309$	4.45331	−	5.43191i	0.253340	−	0.309011i
$310$	−9.90752	−	3.60604i	−0.562709	−	0.204810i
$311$		−	2.19354i		−	0.124384i	−0.998064	−	0.0621921i	$-0.980191\pi$
$311$		−	2.19354i		−	0.124384i	0.998064	−	0.0621921i	$-0.0198092\pi$
$312$	−1.60113	−	0.900216i	−0.0906461	−	0.0509647i
$313$	−3.72184	−	21.1076i	−0.210371	−	1.19307i	−0.888761	−	0.458371i	$-0.848433\pi$
$313$	−3.72184	−	21.1076i	−0.210371	−	1.19307i	0.678390	−	0.734702i	$-0.262678\pi$
$314$	40.5263	+	14.7504i	2.28703	+	0.832412i
$315$	−15.7299	+	9.56668i	−0.886279	+	0.539021i
$316$	12.6559	−	7.30690i	0.711951	−	0.411045i
$317$	−7.32717	+	6.14822i	−0.411535	+	0.345319i	−0.824932	−	0.565232i	$-0.808787\pi$
$317$	−7.32717	+	6.14822i	−0.411535	+	0.345319i	0.413397	+	0.910551i	$0.364342\pi$
$318$	16.4215	−	6.19000i	0.920872	−	0.347118i
$319$	2.85605	−	0.503598i	0.159908	−	0.0281961i
$320$	−3.74252	+	4.46016i	−0.209213	+	0.249331i
$321$	5.06466	+	4.15222i	0.282682	+	0.231755i
$322$	−30.9654	+	17.8779i	−1.72564	+	0.996297i
$323$	−7.69495	−	30.8751i	−0.428159	−	1.71793i
$324$	13.0372	−	0.595354i	0.724286	−	0.0330752i
$325$	0.571626	+	1.57053i	0.0317081	+	0.0871174i
$326$	−6.55541	+	2.38597i	−0.363070	+	0.132147i
$327$	4.15599	−	11.8370i	0.229827	−	0.654585i
$328$	−8.29384	+	3.01871i	−0.457951	+	0.166680i
$329$	10.0213	−	27.5334i	0.552494	−	1.51796i
$330$	11.9196	−	0.135991i	0.656152	−	0.00748607i
$331$			7.67688i			0.421959i	0.977490	+	0.210980i	$0.0676654\pi$
$331$			7.67688i			0.421959i	−0.977490	+	0.210980i	$0.932335\pi$
$332$	4.26225	−	11.7104i	0.233921	−	0.642693i
$333$	−5.07682	−	5.77734i	−0.278208	−	0.316596i
$334$	4.81672	−	8.34281i	0.263559	−	0.456498i
$335$	7.92332	−	13.7236i	0.432897	−	0.749800i
$336$	−5.12002	−	27.2176i	−0.279320	−	1.48484i
$337$	−2.77732	−	7.63062i	−0.151290	−	0.415667i	0.840776	−	0.541383i	$-0.182099\pi$
$337$	−2.77732	−	7.63062i	−0.151290	−	0.415667i	−0.992066	+	0.125717i	$0.959877\pi$
$338$	3.84535	+	21.8081i	0.209159	+	1.18620i
$339$	−4.07133	+	24.7367i	−0.221124	+	1.34351i
$340$	14.9307	+	12.5283i	0.809729	+	0.679443i
$341$	−6.20366			−0.335947
$342$	24.2076	+	1.98939i	1.30900	+	0.107574i
$343$	−9.63662			−0.520329
$344$	2.49397	+	2.09269i	0.134466	+	0.112830i
$345$	−14.2443	−	11.6780i	−0.766885	−	0.628725i
$346$	0.334920	+	1.89943i	0.0180054	+	0.102114i
$347$	4.50145	+	12.3676i	0.241650	+	0.663929i	0.999928	+	0.0119971i	$0.00381890\pi$
$347$	4.50145	+	12.3676i	0.241650	+	0.663929i	−0.758278	+	0.651932i	$0.773959\pi$
$348$	−2.74610	+	2.35816i	−0.147206	+	0.126411i
$349$	−2.14047	+	3.70740i	−0.114577	+	0.198452i	−0.917610	−	0.397481i	$-0.869884\pi$
$349$	−2.14047	+	3.70740i	−0.114577	+	0.198452i	0.803034	+	0.595933i	$0.203218\pi$
$350$	−4.98284	+	8.63053i	−0.266344	+	0.461321i
$351$	−3.60715	−	4.01164i	−0.192535	−	0.214125i
$352$	−4.72698	+	12.9873i	−0.251949	+	0.692225i
$353$			23.1211i			1.23061i	0.788288	+	0.615307i	$0.210968\pi$
$353$			23.1211i			1.23061i	−0.788288	+	0.615307i	$0.789032\pi$
$354$	−12.7175	+	22.6194i	−0.675926	+	1.20221i
$355$	−3.56484	+	9.79432i	−0.189202	+	0.519829i
$356$	10.6141	−	3.86320i	0.562544	−	0.204749i
$357$	−41.4150	+	7.79076i	−2.19191	+	0.412331i
$358$	18.4831	−	6.72728i	0.976860	−	0.355548i
$359$	1.03497	+	2.84356i	0.0546238	+	0.150078i	0.964004	−	0.265889i	$-0.0856655\pi$
$359$	1.03497	+	2.84356i	0.0546238	+	0.150078i	−0.909380	+	0.415967i	$0.863443\pi$
$360$	4.82066	−	2.93185i	0.254071	−	0.154522i
$361$	18.5841	+	3.95380i	0.978109	+	0.208095i
$362$	38.8971	−	22.4573i	2.04439	−	1.18033i
$363$	−11.2649	+	4.24626i	−0.591256	+	0.222871i
$364$	3.22546	−	3.84396i	0.169060	−	0.201478i
$365$	−22.9393	+	4.04482i	−1.20070	+	0.211716i
$366$	−27.7290	−	22.7334i	−1.44942	−	1.18829i
$367$	22.1772	−	18.6089i	1.15764	−	0.971376i	0.157771	−	0.987476i	$-0.449569\pi$
$367$	22.1772	−	18.6089i	1.15764	−	0.971376i	0.999870	+	0.0160993i	$0.00512480\pi$
$368$	23.9960	−	13.8541i	1.25088	−	0.722195i
$369$	−25.9159	+	0.591428i	−1.34913	+	0.0307885i
$370$	8.23908	+	2.99878i	0.428329	+	0.155899i
$371$	−3.15710	−	17.9048i	−0.163909	−	0.929572i
$372$	6.66093	−	3.94769i	0.345353	−	0.204678i
$373$			5.02370i			0.260117i	0.991506	+	0.130059i	$0.0415166\pi$
$373$			5.02370i			0.260117i	−0.991506	+	0.130059i	$0.958483\pi$
$374$	25.6399	+	9.33216i	1.32581	+	0.482555i
$375$	−20.7997	−	3.42336i	−1.07409	−	0.176782i
$376$	−3.07118	+	8.43801i	−0.158384	+	0.435157i
$377$	1.47356	+	0.259828i	0.0758920	+	0.0133818i
$378$	4.49865	−	31.8522i	0.231386	−	1.63830i
$379$		−	10.9355i		−	0.561718i	−0.959749	−	0.280859i	$-0.909381\pi$
$379$		−	10.9355i		−	0.561718i	0.959749	−	0.280859i	$-0.0906193\pi$
$380$	−10.6324	+	4.73268i	−0.545433	+	0.242781i
$381$	1.95085	−	1.15619i	0.0999449	−	0.0592336i
$382$	−19.8581	−	3.50152i	−1.01603	−	0.179153i
$383$	3.19500	+	2.68092i	0.163257	+	0.136989i	0.720756	−	0.693189i	$-0.243795\pi$
$383$	3.19500	+	2.68092i	0.163257	+	0.136989i	−0.557500	+	0.830177i	$0.688239\pi$
$384$	2.51767	+	13.3837i	0.128479	+	0.682984i
$385$	2.14445	−	12.1618i	0.109291	−	0.619822i
$386$	4.49506	−	0.792600i	0.228793	−	0.0403423i
$387$	4.96865	+	8.16964i	0.252571	+	0.415286i
$388$	−19.9483	−	11.5172i	−1.01272	−	0.584696i
$389$	9.04539	−	1.59495i	0.458619	−	0.0808670i	0.0604345	−	0.998172i	$-0.480751\pi$
$389$	9.04539	−	1.59495i	0.458619	−	0.0808670i	0.398185	+	0.917305i	$0.369640\pi$
$390$	5.80294	+	2.03743i	0.293843	+	0.103169i
$391$	−21.0808	−	36.5130i	−1.06610	−	1.84654i
$392$	−4.19678			−0.211970
$393$	−8.82657	+	1.66041i	−0.445241	+	0.0837564i
$394$	−30.0827	−	5.30439i	−1.51554	−	0.267231i
$395$	14.2148	−	11.9276i	0.715222	−	0.600143i
$396$	−5.47258	+	6.83269i	−0.275008	+	0.343355i
$397$	34.6905	−	12.6263i	1.74106	−	0.633696i	0.741749	−	0.670678i	$-0.233997\pi$
$397$	34.6905	−	12.6263i	1.74106	−	0.633696i	0.999316	+	0.0369820i	$0.0117744\pi$
$398$	−12.7441	−	22.0734i	−0.638802	−	1.10644i
$399$	6.66184	−	24.2655i	0.333509	−	1.21480i
$400$	3.86135	−	6.68805i	0.193067	−	0.334403i
$401$	−4.78032	+	27.1106i	−0.238718	+	1.35384i	0.595923	+	0.803042i	$0.296786\pi$
$401$	−4.78032	+	27.1106i	−0.238718	+	1.35384i	−0.834641	+	0.550795i	$0.814325\pi$
$402$	9.76619	+	25.9088i	0.487093	+	1.29221i
$403$	−3.00770	−	1.09471i	−0.149824	−	0.0545316i
$404$	−5.30244	+	6.31921i	−0.263806	+	0.314392i
$405$	16.1713	−	3.61906i	0.803560	−	0.179833i
$406$	4.46099	+	7.72666i	0.221395	+	0.383468i
$407$	5.15895			0.255720
$408$	12.6922	−	2.38759i	0.628360	−	0.118204i
$409$	−8.63679	−	10.2929i	−0.427062	−	0.508952i	0.509011	−	0.860760i	$-0.330011\pi$
$409$	−8.63679	−	10.2929i	−0.427062	−	0.508952i	−0.936072	+	0.351808i	$0.885567\pi$
$410$	25.5928	−	14.7760i	1.26394	−	0.729736i
$411$	0.271591	+	23.8049i	0.0133966	+	1.17421i
$412$	−3.77997	−	4.50479i	−0.186226	−	0.221935i
$413$	20.5938	+	17.2803i	1.01336	+	0.850307i
$414$	31.5590	−	6.31031i	1.55104	−	0.310135i
$415$	2.74777	−	15.5834i	0.134883	−	0.764957i
$416$	−4.58354	+	5.46245i	−0.224727	+	0.267819i
$417$	9.05904	−	0.103355i	0.443623	−	0.00506132i
$418$	−11.7210	+	11.3167i	−0.573292	+	0.553518i
$419$	−28.4986	−	16.4537i	−1.39225	−	0.803814i	−0.398683	−	0.917089i	$-0.630532\pi$
$419$	−28.4986	−	16.4537i	−1.39225	−	0.803814i	−0.993564	+	0.113275i	$0.963866\pi$
$420$	5.43661	+	14.4228i	0.265279	+	0.703762i
$421$	9.94232	+	27.3163i	0.484559	+	1.33131i	0.905546	+	0.424248i	$0.139462\pi$
$421$	9.94232	+	27.3163i	0.484559	+	1.33131i	−0.420987	+	0.907067i	$0.638316\pi$
$422$	9.64496	+	11.4944i	0.469510	+	0.559540i
$423$	−16.4870	+	20.5846i	−0.801627	+	1.00086i
$424$	0.967541	+	5.48720i	0.0469880	+	0.266482i
$425$	−10.1767	−	5.87554i	−0.493644	−	0.285005i
$426$	−9.28514	−	15.6668i	−0.449867	−	0.759060i
$427$	−28.4564	+	23.8778i	−1.37710	+	1.15553i
$428$	4.20023	−	3.52441i	0.203026	−	0.170359i
$429$	3.61852	−	0.0412839i	0.174704	−	0.00199321i
$430$	−9.44029	−	5.45035i	−0.455251	−	0.262839i
$431$	6.81517	+	38.6508i	0.328275	+	1.86174i	0.485581	+	0.874192i	$0.338608\pi$
$431$	6.81517	+	38.6508i	0.328275	+	1.86174i	−0.157306	+	0.987550i	$0.550281\pi$
$432$	−3.48614	+	24.6832i	−0.167727	+	1.18757i
$433$	21.1600	+	25.2175i	1.01689	+	1.21188i	0.977124	+	0.212668i	$0.0682154\pi$
$433$	21.1600	+	25.2175i	1.01689	+	1.21188i	0.0397614	+	0.999209i	$0.487340\pi$
$434$	−6.52751	−	17.9342i	−0.313330	−	0.860868i
$435$	−2.91397	+	3.55430i	−0.139714	+	0.170416i
$436$	−9.09590	−	5.25152i	−0.435614	−	0.251502i
$437$	25.1143	−	1.75380i	1.20138	−	0.0838957i
$438$	19.9463	−	35.4767i	0.953073	−	1.69514i
$439$	−2.47542	+	2.95009i	−0.118145	+	0.140800i	−0.821875	−	0.569667i	$-0.807072\pi$
$439$	−2.47542	+	2.95009i	−0.118145	+	0.140800i	0.703730	+	0.710467i	$0.251516\pi$
$440$	−0.657199	+	3.72716i	−0.0313307	+	0.177685i
$441$	−11.6759	−	3.95041i	−0.555996	−	0.188115i
$442$	10.7841	+	9.04897i	0.512949	+	0.430416i
$443$	20.1469	+	24.0101i	0.957207	+	1.14075i	0.989968	+	0.141292i	$0.0451255\pi$
$443$	20.1469	+	24.0101i	0.957207	+	1.14075i	−0.0327611	+	0.999463i	$0.510430\pi$
$444$	−5.53921	+	3.28289i	−0.262879	+	0.155799i
$445$	12.4208	−	7.17115i	0.588802	−	0.339945i
$446$	−18.8065	−	22.4127i	−0.890513	−	1.06127i
$447$	−1.74070	+	4.95780i	−0.0823323	+	0.234496i
$448$	−10.5393			−0.497937
$449$	−6.48937	−	11.2399i	−0.306252	−	0.530444i	0.671287	−	0.741197i	$-0.265742\pi$
$449$	−6.48937	−	11.2399i	−0.306252	−	0.530444i	−0.977539	+	0.210753i	$0.932408\pi$
$450$	6.73815	−	5.92113i	0.317639	−	0.279125i
$451$	11.1770	−	13.3202i	0.526303	−	0.627223i
$452$	19.7225	+	7.17842i	0.927670	+	0.337644i
$453$	19.8360	−	24.1949i	0.931974	−	1.13677i
$454$	−8.92129	+	50.5951i	−0.418697	+	2.37455i
$455$	3.18579	−	5.51795i	0.149352	−	0.258685i
$456$	−2.04162	+	7.43653i	−0.0956075	+	0.348247i
$457$	1.27172	+	2.20269i	0.0594886	+	0.103037i	0.894236	−	0.447596i	$-0.147720\pi$
$457$	1.27172	+	2.20269i	0.0594886	+	0.103037i	−0.834747	+	0.550633i	$0.814386\pi$
$458$	−15.7553	+	5.73444i	−0.736195	+	0.267953i
$459$	37.5586	+	5.30461i	1.75309	+	0.247598i
$460$	−11.8131	+	9.91233i	−0.550787	+	0.462165i
$461$	19.3059	+	3.40415i	0.899166	+	0.158547i	0.604080	−	0.796924i	$-0.293541\pi$
$461$	19.3059	+	3.40415i	0.899166	+	0.158547i	0.295086	+	0.955471i	$0.404652\pi$
$462$	14.0576	+	16.3702i	0.654018	+	0.761611i
$463$	11.1887			0.519984			0.259992	−	0.965611i	$-0.416280\pi$
$463$	11.1887			0.519984			0.259992	+	0.965611i	$0.416280\pi$
$464$	−3.45695	−	5.98762i	−0.160485	−	0.277968i
$465$	7.45887	−	6.40515i	0.345897	−	0.297032i
$466$	−39.0262	+	6.88137i	−1.80785	+	0.318773i
$467$	−12.7064	−	7.33603i	−0.587981	−	0.339471i	0.176318	−	0.984333i	$-0.443581\pi$
$467$	−12.7064	−	7.33603i	−0.587981	−	0.339471i	−0.764299	+	0.644862i	$0.776915\pi$
$468$	−3.85897	+	2.34697i	−0.178381	+	0.108489i
$469$	28.2491	−	4.98108i	1.30442	−	0.230005i
$470$	5.22086	−	29.6090i	0.240820	−	1.36576i
$471$	−30.5102	+	26.2000i	−1.40584	+	1.20723i
$472$	−6.31129	−	5.29580i	−0.290501	−	0.243759i
$473$	−6.31648	−	1.11377i	−0.290432	−	0.0512110i
$474$	0.369885	+	32.4203i	0.0169894	+	1.48911i
$475$	5.81754	−	3.92319i	0.266927	−	0.180008i
$476$			35.2810i			1.61710i
$477$	−2.47327	+	16.1767i	−0.113243	+	0.740682i
$478$	−15.0285	−	2.64993i	−0.687389	−	0.121205i
$479$	−1.26216	+	3.46776i	−0.0576697	+	0.158446i	−0.965182	−	0.261579i	$-0.915757\pi$
$479$	−1.26216	+	3.46776i	−0.0576697	+	0.158446i	0.907512	+	0.420026i	$0.137979\pi$
$480$	−7.72569	−	20.4956i	−0.352628	−	0.935490i
$481$	2.50120	+	0.910362i	0.114045	+	0.0415089i
$482$		−	45.4384i		−	2.06966i
$483$	−0.380377	−	33.3399i	−0.0173077	−	1.51702i
$484$	1.75017	+	9.92573i	0.0795533	+	0.451169i
$485$	−27.4843	−	10.0035i	−1.24800	−	0.454234i
$486$	−13.0242	+	25.8600i	−0.590788	+	1.17303i
$487$	−26.5090	+	15.3050i	−1.20124	+	0.693534i	−0.960830	−	0.277138i	$-0.910614\pi$
$487$	−26.5090	+	15.3050i	−1.20124	+	0.693534i	−0.240407	+	0.970672i	$0.577281\pi$
$488$	8.72089	−	7.31770i	0.394776	−	0.331257i
$489$	1.05645	−	6.41883i	0.0477745	−	0.290269i
$490$	13.8384	−	2.44008i	0.625155	−	0.110232i
$491$	−4.36948	+	5.20734i	−0.197192	+	0.235004i	−0.855575	−	0.517679i	$-0.826796\pi$
$491$	−4.36948	+	5.20734i	−0.197192	+	0.235004i	0.658383	+	0.752683i	$0.271241\pi$
$492$	−3.52454	+	21.4145i	−0.158898	+	0.965438i
$493$	−9.11093	+	5.26020i	−0.410336	+	0.236907i
$494$	−7.67962	+	3.41833i	−0.345522	+	0.153798i
$495$	−5.33676	+	9.75075i	−0.239869	+	0.438263i
$496$	5.05835	+	13.8977i	0.227127	+	0.624026i
$497$	−17.7293	+	6.45292i	−0.795266	+	0.289453i
$498$	18.0125	+	20.9758i	0.807160	+	0.939946i
$499$	2.92874	−	1.06598i	0.131109	−	0.0477196i	−0.275633	−	0.961263i	$-0.588887\pi$
$499$	2.92874	−	1.06598i	0.131109	−	0.0477196i	0.406741	+	0.913543i	$0.366665\pi$
$500$	−6.03595	+	16.5836i	−0.269936	+	0.741642i
$501$	4.58002	+	7.72787i	0.204620	+	0.345256i
$502$		−	24.6873i		−	1.10185i
$503$	13.2963	−	36.5314i	0.592854	−	1.62885i	−0.172329	−	0.985040i	$-0.555129\pi$
$503$	13.2963	−	36.5314i	0.592854	−	1.62885i	0.765183	−	0.643813i	$-0.222649\pi$
$504$	9.67454	+	3.27327i	0.430938	+	0.145803i
$505$	−5.23722	+	9.07114i	−0.233053	+	0.403660i
$506$	−10.7940	+	18.6958i	−0.479854	+	0.831131i
$507$	−19.4836	−	6.84075i	−0.865296	−	0.303808i
$508$	−0.649344	−	1.78406i	−0.0288100	−	0.0791547i
$509$	−0.768996	−	4.36119i	−0.0340852	−	0.193307i	0.963011	−	0.269463i	$-0.0868462\pi$
$509$	−0.768996	−	4.36119i	−0.0340852	−	0.193307i	−0.997096	+	0.0761566i	$0.975735\pi$
$510$	−40.4630	+	15.2523i	−1.79173	+	0.675383i
$511$	−32.2998	−	27.1027i	−1.42886	−	1.19895i
$512$	23.1484			1.02303
$513$	−12.6800	+	18.7675i	−0.559835	+	0.828604i
$514$	−37.4543			−1.65204
$515$	−5.72002	−	4.79967i	−0.252054	−	0.211499i
$516$	7.49080	−	2.82362i	0.329764	−	0.124303i
$517$	−3.07193	−	17.4218i	−0.135103	−	0.766209i
$518$	5.42826	+	14.9140i	0.238504	+	0.655284i
$519$	−1.69697	−	0.595812i	−0.0744887	−	0.0261532i
$520$	−0.976332	+	1.69106i	−0.0428150	+	0.0741577i
$521$	5.51847	−	9.55828i	0.241769	−	0.418756i	−0.719449	−	0.694545i	$-0.755606\pi$
$521$	5.51847	−	9.55828i	0.241769	−	0.418756i	0.961218	+	0.275789i	$0.0889391\pi$
$522$	−1.57458	−	7.87478i	−0.0689176	−	0.344670i
$523$	6.63357	−	18.2256i	0.290066	−	0.796949i	−0.705990	−	0.708222i	$-0.749498\pi$
$523$	6.63357	−	18.2256i	0.290066	−	0.796949i	0.996056	−	0.0887276i	$-0.0282801\pi$
$524$			7.51926i			0.328481i
$525$	−4.73798	−	7.99439i	−0.206782	−	0.348904i
$526$	13.9615	−	38.3588i	0.608748	−	1.67252i
$527$	21.1472	−	7.69693i	0.921185	−	0.335284i
$528$	−10.8936	−	12.6857i	−0.474084	−	0.552076i
$529$	9.73338	−	3.54266i	0.423190	−	0.154029i
$530$	−6.38071	−	17.5308i	−0.277160	−	0.761491i
$531$	−12.5738	−	20.6743i	−0.545656	−	0.897188i
$532$	−18.9340	−	9.23690i	−0.820891	−	0.400471i
$533$	7.76941	−	4.48567i	0.336531	−	0.194296i
$534$	−4.06977	+	24.7272i	−0.176116	+	1.07005i
$535$	4.47517	−	5.33330i	0.193478	−	0.230578i
$536$	−8.65736	+	1.52653i	−0.373941	+	0.0659359i
$537$	−2.97869	+	18.0980i	−0.128540	+	0.780985i
$538$	−14.4598	+	12.1332i	−0.623405	+	0.523099i
$539$	7.16034	−	4.13403i	0.308418	−	0.178065i
$540$	−0.474742	−	13.8655i	−0.0204296	−	0.596676i
$541$	−12.3864	−	4.50828i	−0.532533	−	0.193826i	0.0617360	−	0.998093i	$-0.480336\pi$
$541$	−12.3864	−	4.50828i	−0.532533	−	0.193826i	−0.594269	+	0.804266i	$0.702559\pi$
$542$	4.71110	+	26.7180i	0.202359	+	1.14764i
$543$	0.477809	+	41.8798i	0.0205047	+	1.79723i
$544$		−	50.1361i		−	2.14957i
$545$	−12.5321	−	4.56131i	−0.536815	−	0.195385i
$546$	3.92676	+	10.4174i	0.168050	+	0.445822i
$547$	7.71585	−	21.1991i	0.329906	−	0.906409i	−0.658229	−	0.752818i	$-0.728694\pi$
$547$	7.71585	−	21.1991i	0.329906	−	0.906409i	0.988135	−	0.153591i	$-0.0490838\pi$
$548$	19.6281	+	3.46096i	0.838471	+	0.147845i
$549$	31.1506	−	12.1497i	1.32947	−	0.518536i
$550$			6.01692i			0.256562i
$551$	−0.437618	−	6.26665i	−0.0186431	−	0.266968i
$552$	0.116572	+	10.2175i	0.00496164	+	0.434886i
$553$	33.0791	+	5.83273i	1.40667	+	0.248033i
$554$	12.5404	+	10.5226i	0.532789	+	0.447063i
$555$	−6.20278	+	5.32651i	−0.263293	+	0.226098i
$556$	1.31708	−	7.46954i	0.0558567	−	0.316779i
$557$	−6.75730	+	1.19149i	−0.286316	+	0.0504853i	−0.314962	−	0.949104i	$-0.601992\pi$
$557$	−6.75730	+	1.19149i	−0.286316	+	0.0504853i	0.0286456	+	0.999590i	$0.490881\pi$
$558$	0.391930	+	17.1740i	0.0165917	+	0.727035i
$559$	−2.86586	−	1.65461i	−0.121213	−	0.0699824i
$560$	−28.9939	+	5.11241i	−1.22522	+	0.216039i
$561$	−19.3030	+	16.5760i	−0.814973	+	0.699841i
$562$	1.35360	+	2.34451i	0.0570983	+	0.0988972i
$563$	14.3595			0.605181			0.302590	−	0.953121i	$-0.402149\pi$
$563$	14.3595			0.605181			0.302590	+	0.953121i	$0.402149\pi$
$564$	14.3847	+	16.7511i	0.605704	+	0.705349i
$565$	26.2453	+	4.62775i	1.10415	+	0.194691i
$566$	−46.1936	+	38.7611i	−1.94166	+	1.62925i
$567$	23.8345	+	18.2132i	1.00096	+	0.764883i
$568$	5.43339	−	1.97759i	0.227980	−	0.0829780i
$569$	−10.6542	−	18.4536i	−0.446647	−	0.773616i	0.551518	−	0.834163i	$-0.314049\pi$
$569$	−10.6542	−	18.4536i	−0.446647	−	0.773616i	−0.998165	+	0.0605472i	$0.980715\pi$
$570$	2.40827	−	25.7081i	0.100871	−	1.07679i
$571$	−0.953898	+	1.65220i	−0.0399194	+	0.0691424i	−0.885295	−	0.465030i	$-0.846043\pi$
$571$	−0.953898	+	1.65220i	−0.0399194	+	0.0691424i	0.845375	+	0.534173i	$0.179377\pi$
$572$	0.526092	−	2.98362i	0.0219970	−	0.124751i
$573$	11.9214	−	14.5411i	0.498022	−	0.607461i
$574$	50.2678	+	18.2960i	2.09814	+	0.763659i
$575$	5.97625	−	7.12221i	0.249227	−	0.297017i
$576$	8.98603	+	3.04032i	0.374418	+	0.126680i
$577$	−15.3988	−	26.6715i	−0.641061	−	1.11035i	−0.985196	−	0.171430i	$-0.945161\pi$
$577$	−15.3988	−	26.6715i	−0.641061	−	1.11035i	0.344135	−	0.938920i	$-0.388172\pi$
$578$	−67.4038			−2.80363
$579$	−1.41001	+	4.01594i	−0.0585980	+	0.166897i
$580$	2.47338	+	2.94766i	0.102701	+	0.122395i
$581$	24.8060	−	14.3217i	1.02913	−	0.594166i
$582$	43.9634	−	26.0555i	1.82234	−	1.08003i
$583$	−7.05592	−	8.40892i	−0.292226	−	0.348262i
$584$	9.89875	+	8.30603i	0.409613	+	0.343706i
$585$	−4.30805	+	3.78569i	−0.178116	+	0.156519i
$586$	−0.126403	+	0.716864i	−0.00522164	+	0.0296134i
$587$	−6.60180	+	7.86771i	−0.272485	+	0.324735i	−0.884882	−	0.465815i	$-0.845761\pi$
$587$	−6.60180	+	7.86771i	−0.272485	+	0.324735i	0.612397	+	0.790551i	$0.290206\pi$
$588$	−5.05745	+	8.99521i	−0.208566	+	0.370956i
$589$	−1.40588	+	13.3640i	−0.0579281	+	0.550654i
$590$	23.8898	+	13.7928i	0.983528	+	0.567840i
$591$	18.0595	−	22.0280i	0.742867	−	0.906110i
$592$	−4.20652	−	11.5573i	−0.172887	−	0.475002i
$593$	5.84464	+	6.96537i	0.240011	+	0.286033i	0.872581	−	0.488469i	$-0.162445\pi$
$593$	5.84464	+	6.96537i	0.240011	+	0.286033i	−0.632571	+	0.774503i	$0.718000\pi$
$594$	−7.26337	−	18.0128i	−0.298020	−	0.739073i
$595$	7.77919	+	44.1180i	0.318915	+	1.80866i
$596$	3.80973	+	2.19955i	0.156053	+	0.0900971i
$597$	23.7660	−	0.271147i	0.972677	−	0.0110973i
$598$	−8.53236	+	7.15950i	−0.348914	+	0.292774i
$599$	−9.99737	+	8.38879i	−0.408482	+	0.342757i	−0.823761	−	0.566937i	$-0.808128\pi$
$599$	−9.99737	+	8.38879i	−0.408482	+	0.342757i	0.415279	+	0.909694i	$0.363684\pi$
$600$	1.45202	+	2.45000i	0.0592786	+	0.100021i
$601$	−3.33374	−	1.92474i	−0.135986	−	0.0785117i	0.430463	−	0.902608i	$-0.358350\pi$
$601$	−3.33374	−	1.92474i	−0.135986	−	0.0785117i	−0.566450	+	0.824096i	$0.691683\pi$
$602$	−3.42642	−	19.4322i	−0.139651	−	0.791998i
$603$	−25.5226	−	3.90217i	−1.03936	−	0.158909i
$604$	−16.8368	−	20.0653i	−0.685079	−	0.816445i
$605$	4.37709	+	12.0259i	0.177954	+	0.488924i
$606$	−6.45534	−	17.1254i	−0.262230	−	0.695673i
$607$	27.0590	+	15.6225i	1.09829	+	0.634098i	0.935771	−	0.352607i	$-0.114705\pi$
$607$	27.0590	+	15.6225i	1.09829	+	0.634098i	0.162519	+	0.986705i	$0.448038\pi$
$608$	26.9061	+	13.1261i	1.09119	+	0.532334i
$609$	−8.31915	+	0.0949136i	−0.337109	+	0.00384609i
$610$	−24.5015	+	29.1997i	−0.992036	+	1.18226i
$611$	1.58494	−	8.98863i	0.0641197	−	0.363641i
$612$	10.1777	−	30.0813i	0.411408	−	1.21596i
$613$	−15.2044	−	12.7580i	−0.614101	−	0.515292i	0.281842	−	0.959461i	$-0.409055\pi$
$613$	−15.2044	−	12.7580i	−0.614101	−	0.515292i	−0.895943	+	0.444169i	$0.853499\pi$
$614$	−7.04051	−	8.39056i	−0.284132	−	0.338615i
$615$	0.314380	+	27.5553i	0.0126770	+	1.11114i
$616$	−5.93299	+	3.42541i	−0.239047	+	0.138014i
$617$	9.67497	+	11.5302i	0.389500	+	0.464188i	0.924789	−	0.380481i	$-0.124242\pi$
$617$	9.67497	+	11.5302i	0.389500	+	0.464188i	−0.535289	+	0.844669i	$0.679797\pi$
$618$	12.8219	−	2.41198i	0.515772	−	0.0970242i
$619$	−6.02193			−0.242042			−0.121021	−	0.992650i	$-0.538617\pi$
$619$	−6.02193			−0.242042			−0.121021	+	0.992650i	$0.538617\pi$
$620$	−4.11554	−	7.12833i	−0.165284	−	0.286281i
$621$	−9.29338	+	28.5359i	−0.372930	+	1.14511i
$622$	2.61895	−	3.12115i	0.105010	−	0.125147i
$623$	24.3961	+	8.87946i	0.977410	+	0.355748i
$624$	−3.04296	−	8.07271i	−0.121816	−	0.323167i
$625$	−2.49357	+	14.1417i	−0.0997427	+	0.565669i
$626$	19.9055	−	34.4773i	0.795583	−	1.37799i
$627$	−3.84202	−	14.6989i	−0.153435	−	0.587019i
$628$	16.8345	+	29.1582i	0.671768	+	1.16354i
$629$	−17.5859	+	6.40075i	−0.701197	+	0.255215i
$630$	−33.8038	−	5.16828i	−1.34678	−	0.205909i
$631$	29.0095	−	24.3418i	1.15485	−	0.969033i	0.155026	−	0.987910i	$-0.450454\pi$
$631$	29.0095	−	24.3418i	1.15485	−	0.969033i	0.999822	+	0.0188777i	$0.00600933\pi$
$632$	−10.1376	−	1.78753i	−0.403251	−	0.0711040i
$633$	−13.7508	+	2.58672i	−0.546545	+	0.102813i
$634$	−17.7663			−0.705590
$635$	−1.20536	−	2.08774i	−0.0478331	−	0.0828494i
$636$	12.9270	+	4.53871i	0.512589	+	0.179972i
$637$	4.20103	−	0.740755i	0.166451	−	0.0293498i
$638$	4.66508	+	2.69339i	0.184692	+	0.106632i
$639$	16.9778	−	0.387452i	0.671631	−	0.0153273i
$640$	14.2572	−	2.51393i	0.563565	−	0.0993717i
$641$	−4.09124	+	23.2026i	−0.161594	+	0.916447i	0.790912	+	0.611929i	$0.209606\pi$
$641$	−4.09124	+	23.2026i	−0.161594	+	0.916447i	−0.952507	+	0.304518i	$0.901505\pi$
$642$	2.24891	+	11.9550i	0.0887575	+	0.471827i
$643$	−11.3449	−	9.51952i	−0.447400	−	0.375413i	0.391070	−	0.920361i	$-0.372105\pi$
$643$	−11.3449	−	9.51952i	−0.447400	−	0.375413i	−0.838470	+	0.544948i	$0.816549\pi$
$644$	−27.4901	−	4.84724i	−1.08326	−	0.191008i
$645$	8.74445	−	5.18251i	0.344312	−	0.204061i
$646$	25.9140	−	53.1189i	1.01957	−	2.08993i
$647$		−	15.6034i		−	0.613433i	−0.951801	−	0.306716i	$-0.900770\pi$
$647$		−	15.6034i		−	0.613433i	0.951801	−	0.306716i	$-0.0992303\pi$
$648$	−7.30444	−	5.58171i	−0.286945	−	0.219270i
$649$	15.9846	+	2.81852i	0.627451	+	0.110637i
$650$	−1.06176	+	2.91717i	−0.0416457	+	0.114421i
$651$	17.5605	+	2.89023i	0.688251	+	0.113277i
$652$	−5.11773	−	1.86270i	−0.200426	−	0.0729491i
$653$			18.6660i			0.730459i	0.930918	+	0.365229i	$0.119009\pi$
$653$			18.6660i			0.730459i	−0.930918	+	0.365229i	$0.880991\pi$
$654$	20.0461	−	11.8806i	0.783864	−	0.464567i
$655$	1.65794	+	9.40263i	0.0647810	+	0.367391i
$656$	−38.9540	−	14.1781i	−1.52090	−	0.553561i
$657$	19.7210	+	32.4259i	0.769388	+	1.26506i
$658$	47.1323	−	27.2119i	1.83741	−	1.06083i
$659$	1.37276	−	1.15188i	0.0534752	−	0.0448710i	−0.615658	−	0.788013i	$-0.711110\pi$
$659$	1.37276	−	1.15188i	0.0534752	−	0.0448710i	0.669134	+	0.743142i	$0.266665\pi$
$660$	7.19666	+	5.90013i	0.280130	+	0.229662i
$661$	17.2956	−	3.04967i	0.672719	−	0.118619i	0.173154	−	0.984895i	$-0.444604\pi$
$661$	17.2956	−	3.04967i	0.672719	−	0.118619i	0.499565	+	0.866276i	$0.333493\pi$
$662$	−9.16573	+	10.9233i	−0.356236	+	0.424546i
$663$	−12.2837	+	4.63026i	−0.477058	+	0.179824i
$664$	−7.60216	+	4.38911i	−0.295021	+	0.170330i
$665$	−25.7131	−	7.37570i	−0.997110	−	0.286018i
$666$	−0.325928	−	14.2819i	−0.0126295	−	0.553412i
$667$	−2.84687	−	7.82170i	−0.110231	−	0.302857i
$668$	7.06717	−	2.57224i	0.273437	−	0.0995229i
$669$	26.8123	−	5.04379i	1.03662	−	0.195004i
$670$	27.6591	−	10.0671i	1.06856	−	0.388925i
$671$	−7.67088	+	21.0756i	−0.296131	+	0.813614i
$672$	19.4312	−	34.5605i	0.749575	−	1.33320i
$673$			27.5490i			1.06194i	0.847392	+	0.530968i	$0.178172\pi$
$673$			27.5490i			1.06194i	−0.847392	+	0.530968i	$0.821828\pi$
$674$	5.15870	−	14.1734i	0.198706	−	0.545940i
$675$	1.73352	+	8.18295i	0.0667231	+	0.314962i
$676$	−8.64398	+	14.9718i	−0.332461	+	0.575839i
$677$	6.64844	−	11.5154i	0.255520	−	0.442574i	−0.709516	−	0.704689i	$-0.751087\pi$
$677$	6.64844	−	11.5154i	0.255520	−	0.442574i	0.965037	+	0.262115i	$0.0844199\pi$
$678$	−35.3271	+	30.3364i	−1.35673	+	1.16506i
$679$	−18.1078	−	49.7509i	−0.694915	−	1.90926i
$680$	−2.38405	−	13.5206i	−0.0914240	−	0.518491i
$681$	−37.0482	−	30.3736i	−1.41969	−	1.16392i
$682$	−8.82708	−	7.40680i	−0.338006	−	0.283621i
$683$	22.0982			0.845566			0.422783	−	0.906231i	$-0.361053\pi$
$683$	22.0982			0.845566			0.422783	+	0.906231i	$0.361053\pi$
$684$	13.4788	+	13.3375i	0.515376	+	0.509973i
$685$	25.3075			0.966950
$686$	−13.7118	−	11.5055i	−0.523518	−	0.439284i
$687$	2.53908	−	15.4270i	0.0968720	−	0.588577i
$688$	2.65523	+	15.0586i	0.101230	+	0.574103i
$689$	−1.93704	−	5.32198i	−0.0737954	−	0.202751i
$690$	−6.32502	−	33.6232i	−0.240789	−	1.28002i
$691$	−11.6378	+	20.1573i	−0.442724	+	0.766821i	−0.997891	−	0.0649186i	$-0.979321\pi$
$691$	−11.6378	+	20.1573i	−0.442724	+	0.766821i	0.555166	+	0.831739i	$0.312655\pi$
$692$	−0.752868	+	1.30401i	−0.0286198	+	0.0495709i
$693$	−19.7305	+	3.94517i	−0.749501	+	0.149865i
$694$	−8.36117	+	22.9721i	−0.317386	+	0.872010i
$695$		−	9.63086i		−	0.365319i
$696$	2.54953	−	0.0290877i	0.0966396	−	0.00110257i
$697$	−21.5738	+	59.2735i	−0.817165	+	2.24514i
$698$	−7.47204	+	2.71960i	−0.282821	+	0.102938i
$699$	12.2417	−	34.8665i	0.463025	−	1.31877i
$700$	−7.31090	+	2.66095i	−0.276326	+	0.100574i
$701$	7.58127	+	20.8294i	0.286341	+	0.786715i	0.996571	+	0.0827450i	$0.0263687\pi$
$701$	7.58127	+	20.8294i	0.286341	+	0.786715i	−0.710230	+	0.703970i	$0.751409\pi$
$702$	−0.342897	−	10.0148i	−0.0129418	−	0.377984i
$703$	1.16912	−	11.1135i	0.0440943	−	0.419152i
$704$	−5.51075	+	3.18164i	−0.207694	+	0.119912i
$705$	21.6811	+	17.7751i	0.816558	+	0.669448i
$706$	−27.6052	+	32.8986i	−1.03894	+	1.23816i
$707$	−18.6723	+	3.29244i	−0.702246	+	0.123825i
$708$	−18.9564	+	7.14551i	−0.712425	+	0.268545i
$709$	−24.2283	+	20.3300i	−0.909915	+	0.763509i	−0.972103	−	0.234555i	$-0.924637\pi$
$709$	−24.2283	+	20.3300i	−0.909915	+	0.763509i	0.0621881	+	0.998064i	$0.480192\pi$
$710$	−16.7662	+	9.67995i	−0.629223	+	0.363282i
$711$	−26.5212	−	14.5155i	−0.994624	−	0.544376i
$712$	−7.47655	−	2.72124i	−0.280196	−	0.101983i
$713$	3.09186	+	17.5348i	0.115791	+	0.656684i
$714$	−68.2304	−	38.3617i	−2.55346	−	1.43565i
$715$		−	3.84693i		−	0.143867i
$716$	14.4295	+	5.25192i	0.539256	+	0.196273i
$717$	9.02203	−	11.0046i	0.336934	−	0.410974i
$718$	−1.92240	+	5.28175i	−0.0717433	+	0.197113i
$719$	31.0491	+	5.47480i	1.15794	+	0.204176i	0.719438	−	0.694556i	$-0.244399\pi$
$719$	31.0491	+	5.47480i	1.15794	+	0.204176i	0.438499	+	0.898732i	$0.355510\pi$
$720$	26.1955	+	4.00505i	0.976250	+	0.149260i
$721$		−	13.5164i		−	0.503376i
$722$	21.7223	+	27.8140i	0.808421	+	1.03513i
$723$	36.9337	+	20.7655i	1.37358	+	0.772277i
$724$	34.5316	+	6.08885i	1.28336	+	0.226290i
$725$	−1.77717	−	1.49122i	−0.0660025	−	0.0553827i
$726$	−21.0985	−	7.40774i	−0.783037	−	0.274927i
$727$	6.35871	−	36.0620i	0.235831	−	1.33747i	−0.605024	−	0.796207i	$-0.706837\pi$
$727$	6.35871	−	36.0620i	0.235831	−	1.33747i	0.840856	−	0.541260i	$-0.182052\pi$
$728$	−3.48093	+	0.613782i	−0.129012	+	0.0227483i
$729$	−15.0677	−	22.4046i	−0.558063	−	0.829798i
$730$	−37.4692	−	21.6329i	−1.38680	−	0.800668i
$731$	22.9136	−	4.04028i	0.847489	−	0.149435i
$732$	−5.17510	−	27.5104i	−0.191277	−	1.01681i
$733$	14.7002	+	25.4615i	0.542964	+	0.940442i	0.998732	+	0.0503430i	$0.0160314\pi$
$733$	14.7002	+	25.4615i	0.542964	+	0.940442i	−0.455768	+	0.890099i	$0.650635\pi$
$734$	53.7734			1.98481
$735$	−4.34083	+	12.3634i	−0.160114	+	0.456031i
$736$	39.0648	+	6.88817i	1.43995	+	0.253901i
$737$	13.2671	−	11.1324i	0.488698	−	0.410067i
$738$	−37.5813	−	30.1004i	−1.38339	−	1.10801i
$739$	−45.1726	+	16.4415i	−1.66170	+	0.604810i	−0.990629	−	0.136583i	$-0.956388\pi$
$739$	−45.1726	+	16.4415i	−1.66170	+	0.604810i	−0.671072	+	0.741392i	$0.734166\pi$
$740$	3.42248	+	5.92791i	0.125813	+	0.217914i
$741$	0.731096	−	7.80441i	0.0268575	−	0.286702i
$742$	16.8851	−	29.2458i	0.619871	−	1.07365i
$743$	−0.262367	+	1.48796i	−0.00962530	+	0.0545878i	−0.989242	−	0.146288i	$-0.953268\pi$
$743$	−0.262367	+	1.48796i	−0.00962530	+	0.0545878i	0.979617	+	0.200875i	$0.0643786\pi$
$744$	−5.38168	−	0.885754i	−0.197302	−	0.0324733i
$745$	5.24895	+	1.91046i	0.192307	+	0.0699939i
$746$	−5.99799	+	7.14813i	−0.219602	+	0.261712i
$747$	−25.2815	+	5.05510i	−0.925002	+	0.184957i
$748$	10.6507	+	18.4476i	0.389429	+	0.674510i
$749$	12.6025			0.460487
$750$	−25.5083	−	29.7046i	−0.931430	−	1.08466i
$751$	15.4593	+	18.4237i	0.564118	+	0.672290i	0.970413	−	0.241452i	$-0.0776237\pi$
$751$	15.4593	+	18.4237i	0.564118	+	0.672290i	−0.406295	+	0.913742i	$0.633179\pi$
$752$	−36.5242	+	21.0873i	−1.33190	+	0.768973i
$753$	20.0665	+	11.2822i	0.731265	+	0.411145i
$754$	1.78648	+	2.12904i	0.0650596	+	0.0775350i
$755$	−25.4782	−	21.3787i	−0.927245	−	0.778051i
$756$	18.6744	−	16.7915i	0.679180	−	0.610700i
$757$	−2.26718	+	12.8578i	−0.0824019	+	0.467325i	0.915485	+	0.402352i	$0.131807\pi$
$757$	−2.26718	+	12.8578i	−0.0824019	+	0.467325i	−0.997887	+	0.0649728i	$0.979304\pi$
$758$	13.0563	−	15.5599i	0.474226	−	0.565161i
$759$	−10.2636	−	17.3178i	−0.372545	−	0.628595i
$760$	7.88015	+	2.26039i	0.285843	+	0.0819931i
$761$	−27.7682	−	16.0320i	−1.00660	−	0.581159i	−0.0964035	−	0.995342i	$-0.530734\pi$
$761$	−27.7682	−	16.0320i	−1.00660	−	0.581159i	−0.910193	+	0.414183i	$0.864067\pi$
$762$	4.15625	+	0.684064i	0.150565	+	0.0247810i
$763$	−8.25668	−	22.6850i	−0.298912	−	0.821254i
$764$	−10.1189	−	12.0592i	−0.366088	−	0.436286i
$765$	6.09420	−	39.8599i	0.220336	−	1.44114i
$766$	1.34525	+	7.62927i	0.0486057	+	0.275657i
$767$	7.25241	+	4.18718i	0.261869	+	0.151190i
$768$	−17.7654	+	31.5977i	−0.641054	+	1.14018i
$769$	−1.31313	+	1.10185i	−0.0473528	+	0.0397337i	−0.666157	−	0.745812i	$-0.732062\pi$
$769$	−1.31313	+	1.10185i	−0.0473528	+	0.0397337i	0.618804	+	0.785545i	$0.287617\pi$
$770$	17.5717	−	14.7444i	0.633241	−	0.531353i
$771$	17.1168	−	30.4440i	0.616445	−	1.09641i
$772$	3.08598	+	1.78169i	0.111067	+	0.0641244i
$773$	0.312006	+	1.76948i	0.0112221	+	0.0636436i	0.989905	−	0.141736i	$-0.0452683\pi$
$773$	0.312006	+	1.76948i	0.0112221	+	0.0636436i	−0.978682	+	0.205379i	$0.934157\pi$
$774$	−2.68426	+	17.5567i	−0.0964836	+	0.631063i
$775$	3.18990	+	3.80158i	0.114585	+	0.136557i
$776$	5.54941	+	15.2469i	0.199212	+	0.547331i
$777$	−14.6033	−	2.40351i	−0.523890	−	0.0862254i
$778$	14.7748	+	8.53022i	0.529702	+	0.305823i
$779$	−26.1616	−	27.0962i	−0.937335	−	0.970821i
$780$	2.44799	+	4.13048i	0.0876520	+	0.147895i
$781$	−7.32217	+	8.72622i	−0.262008	+	0.312249i
$782$	13.5988	−	77.1229i	0.486294	−	2.75791i
$783$	7.12044	+	2.31893i	0.254464	+	0.0828719i
$784$	−15.0996	−	12.6701i	−0.539273	−	0.452504i
$785$	27.4802	+	32.7496i	0.980810	+	1.16888i
$786$	−14.5416	−	8.17583i	−0.518681	−	0.291622i
$787$	17.9663	−	10.3728i	0.640429	−	0.369752i	−0.144351	−	0.989527i	$-0.546109\pi$
$787$	17.9663	−	10.3728i	0.640429	−	0.369752i	0.784780	+	0.619775i	$0.212776\pi$
$788$	−15.3289	−	18.2683i	−0.546069	−	0.650780i
$789$	24.7987	+	28.8784i	0.882858	+	1.02810i
$790$	34.4667			1.22627
$791$	24.1205	+	41.7779i	0.857626	+	1.48545i
$792$	6.04672	−	1.20906i	0.214861	−	0.0429620i
$793$	−7.43810	+	8.86439i	−0.264135	+	0.314784i
$794$	64.4355	+	23.4526i	2.28673	+	0.832301i
$795$	17.1656	+	2.82523i	0.608801	+	0.100201i
$796$	3.45530	−	19.5960i	0.122470	−	0.694562i
$797$	5.52208	−	9.56452i	0.195602	−	0.338793i	−0.751496	−	0.659738i	$-0.770667\pi$
$797$	5.52208	−	9.56452i	0.195602	−	0.338793i	0.947098	+	0.320945i	$0.104001\pi$
$798$	38.4506	−	26.5731i	1.36114	−	0.940679i
$799$	32.0870	+	55.5763i	1.13516	+	1.96615i
$800$	10.3892	−	3.78134i	0.367312	−	0.133691i
$801$	−18.2391	−	14.6084i	−0.644447	−	0.516164i
$802$	−39.1702	+	32.8677i	−1.38315	+	1.16060i
$803$	−25.0706	−	4.42062i	−0.884722	−	0.156000i
$804$	−7.16089	+	20.3954i	−0.252545	+	0.719291i
$805$	−35.4444			−1.24925
$806$	−2.97258	−	5.14866i	−0.104705	−	0.181354i
$807$	−3.25405	−	17.2982i	−0.114548	−	0.608927i
$808$	5.72242	−	1.00902i	0.201314	−	0.0354971i
$809$	−25.4076	−	14.6691i	−0.893285	−	0.515738i	−0.0182691	−	0.999833i	$-0.505816\pi$
$809$	−25.4076	−	14.6691i	−0.893285	−	0.515738i	−0.875015	+	0.484095i	$0.839149\pi$
$810$	27.3308	+	14.1581i	0.960307	+	0.497465i
$811$	8.54494	−	1.50670i	0.300054	−	0.0529075i	−0.0215946	−	0.999767i	$-0.506874\pi$
$811$	8.54494	−	1.50670i	0.300054	−	0.0529075i	0.321648	+	0.946859i	$0.395763\pi$
$812$	−1.20951	+	6.85947i	−0.0424455	+	0.240720i
$813$	−23.8702	−	8.38089i	−0.837163	−	0.293931i
$814$	7.34058	+	6.15948i	0.257287	+	0.215890i
$815$	−6.81029	−	1.20084i	−0.238554	−	0.0420635i
$816$	52.8737	+	29.7276i	1.85095	+	1.04067i
$817$	−3.83072	+	13.3546i	−0.134020	+	0.467219i
$818$		−	24.9574i		−	0.872615i
$819$	−10.2621	−	1.56898i	−0.358586	−	0.0548245i
$820$	22.7205	+	4.00623i	0.793433	+	0.139904i
$821$	8.98230	−	24.6787i	0.313484	−	0.861291i	−0.678462	−	0.734635i	$-0.737353\pi$
$821$	8.98230	−	24.6787i	0.313484	−	0.861291i	0.991947	−	0.126656i	$-0.0404245\pi$
$822$	−28.0352	+	34.1958i	−0.977839	+	1.19272i
$823$	5.00326	+	1.82104i	0.174403	+	0.0634774i	0.427746	−	0.903899i	$-0.359308\pi$
$823$	5.00326	+	1.82104i	0.174403	+	0.0634774i	−0.253343	+	0.967377i	$0.581530\pi$
$824$			4.14229i			0.144304i
$825$	−4.89073	−	2.74975i	−0.170273	−	0.0957342i
$826$	8.67099	+	49.1756i	0.301702	+	1.71104i
$827$	−32.9464	−	11.9915i	−1.14566	−	0.416986i	−0.301705	−	0.953401i	$-0.597556\pi$
$827$	−32.9464	−	11.9915i	−1.14566	−	0.416986i	−0.843954	+	0.536415i	$0.819778\pi$
$828$	22.0403	+	12.0630i	0.765952	+	0.419219i
$829$	−13.7150	+	7.91834i	−0.476340	+	0.275015i	−0.718890	−	0.695124i	$-0.755350\pi$
$829$	−13.7150	+	7.91834i	−0.476340	+	0.275015i	0.242550	+	0.970139i	$0.422016\pi$
$830$	22.5153	−	18.8926i	0.781518	−	0.655772i
$831$	−14.2841	+	5.38431i	−0.495509	+	0.186780i
$832$	−3.23320	+	0.570101i	−0.112091	+	0.0197647i
$833$	−19.2792	+	22.9760i	−0.667984	+	0.796073i
$834$	13.0133	+	10.6689i	0.450615	+	0.369433i
$835$	8.27014	−	4.77477i	0.286200	−	0.165238i
$836$	−12.6886	+	0.886078i	−0.438843	+	0.0306456i
$837$	−14.1387	−	7.53002i	−0.488704	−	0.260276i
$838$	−20.9054	−	57.4372i	−0.722166	−	1.98413i
$839$	−9.96452	+	3.62679i	−0.344013	+	0.125211i	−0.508248	−	0.861211i	$-0.669707\pi$
$839$	−9.96452	+	3.62679i	−0.344013	+	0.125211i	0.164235	+	0.986421i	$0.447485\pi$
$840$	3.59676	−	10.2442i	0.124100	−	0.353458i
$841$	25.2994	−	9.20822i	0.872392	−	0.317525i
$842$	−18.4673	+	50.7384i	−0.636424	+	1.74856i
$843$	−2.52429	+	0.0287997i	−0.0869411	+	0.000991916i
$844$			11.7142i			0.403218i
$845$	−7.50789	+	20.6278i	−0.258279	+	0.709616i
$846$	−48.0358	+	9.60489i	−1.65151	+	0.330223i
$847$	−11.5830	+	20.0623i	−0.397995	+	0.689348i
$848$	−13.0847	+	22.6634i	−0.449332	+	0.778266i
$849$	−10.3955	−	55.2615i	−0.356772	−	1.89657i
$850$	−7.46524	−	20.5106i	−0.256056	−	0.703507i
$851$	−2.57118	−	14.5819i	−0.0881390	−	0.499861i
$852$	2.30897	−	14.0289i	0.0791039	−	0.480621i
$853$	−38.6369	−	32.4202i	−1.32290	−	1.11005i	−0.985681	−	0.168621i	$-0.946068\pi$
$853$	−38.6369	−	32.4202i	−1.32290	−	1.11005i	−0.337221	−	0.941425i	$-0.609487\pi$
$854$	−68.9987			−2.36109
$855$	19.7957	+	13.7062i	0.677000	+	0.468743i
$856$	−3.86223			−0.132008
$857$	−12.1949	−	10.2327i	−0.416569	−	0.349543i	0.410287	−	0.911956i	$-0.365428\pi$
$857$	−12.1949	−	10.2327i	−0.416569	−	0.349543i	−0.826856	+	0.562414i	$0.809873\pi$
$858$	5.19802	+	4.26155i	0.177457	+	0.145487i
$859$	1.96954	+	11.1698i	0.0671997	+	0.381108i	0.999796	+	0.0201877i	$0.00642638\pi$
$859$	1.96954	+	11.1698i	0.0671997	+	0.381108i	−0.932597	+	0.360921i	$0.882463\pi$
$860$	−2.91061	−	7.99684i	−0.0992510	−	0.272690i
$861$	−37.8441	+	32.4978i	−1.28972	+	1.10752i
$862$	−36.4495	+	63.1323i	−1.24147	+	2.15030i
$863$	−11.5167	+	19.9475i	−0.392032	+	0.679020i	−0.992717	−	0.120466i	$-0.961561\pi$
$863$	−11.5167	+	19.9475i	−0.392032	+	0.679020i	0.600685	+	0.799486i	$0.294895\pi$
$864$	−26.5372	+	23.8615i	−0.902814	+	0.811785i
$865$	−0.653918	+	1.79663i	−0.0222339	+	0.0610871i
$866$			61.1453i			2.07780i
$867$	30.8038	−	54.7878i	1.04615	−	1.86069i
$868$	5.09595	−	14.0010i	0.172968	−	0.475225i
$869$	19.0570	−	6.93619i	0.646465	−	0.235294i
$870$	−8.38985	+	1.57825i	−0.284443	+	0.0535078i
$871$	8.39668	−	3.05614i	0.284511	−	0.103553i
$872$	2.53038	+	6.95217i	0.0856895	+	0.235430i
$873$	1.08725	+	47.6422i	0.0367977	+	1.61244i
$874$	37.8286	+	27.4895i	1.27957	+	0.929845i
$875$	−35.1288	+	20.2816i	−1.18757	+	0.685644i
$876$	29.7316	−	11.2072i	1.00454	−	0.378655i
$877$	−17.2014	+	20.4998i	−0.580849	+	0.692228i	−0.973820	−	0.227322i	$-0.927003\pi$
$877$	−17.2014	+	20.4998i	−0.580849	+	0.692228i	0.392971	+	0.919551i	$0.371447\pi$
$878$	−7.04445	+	1.24213i	−0.237739	+	0.0419197i
$879$	−0.524922	−	0.430353i	−0.0177052	−	0.0145155i
$880$	−13.6168	+	11.4259i	−0.459024	+	0.385167i
$881$	−15.6752	+	9.05009i	−0.528111	+	0.304905i	−0.740247	−	0.672335i	$-0.765291\pi$
$881$	−15.6752	+	9.05009i	−0.528111	+	0.304905i	0.212136	+	0.977240i	$0.431958\pi$
$882$	−11.8969	−	19.5613i	−0.400589	−	0.658663i
$883$	−4.14247	−	1.50773i	−0.139405	−	0.0507393i	0.271375	−	0.962474i	$-0.412522\pi$
$883$	−4.14247	−	1.50773i	−0.139405	−	0.0507393i	−0.410780	+	0.911734i	$0.634744\pi$
$884$	1.90845	+	10.8233i	0.0641880	+	0.364028i
$885$	−22.1289	+	13.1150i	−0.743855	+	0.440856i
$886$			58.2177i			1.95586i
$887$	39.7578	+	14.4706i	1.33494	+	0.485877i	0.908214	−	0.418506i	$-0.137446\pi$
$887$	39.7578	+	14.4706i	1.33494	+	0.485877i	0.426721	+	0.904383i	$0.359668\pi$
$888$	4.47540	+	0.736591i	0.150184	+	0.0247184i
$889$	1.49250	−	4.10060i	0.0500567	−	0.137530i
$890$	26.2352	+	4.62598i	0.879407	+	0.155063i
$891$	17.9607	+	2.32802i	0.601706	+	0.0779916i
$892$		−	22.8412i		−	0.764778i
$893$	−38.2263	+	2.66945i	−1.27919	+	0.0893298i
$894$	−8.39612	+	4.97607i	−0.280808	+	0.166425i
$895$	19.2017	+	3.38578i	0.641843	+	0.113174i
$896$	20.0749	+	16.8448i	0.670654	+	0.562746i
$897$	−1.92013	−	10.2073i	−0.0641114	−	0.340811i
$898$	4.18617	−	23.7410i	0.139694	−	0.792246i
$899$	4.37538	−	0.771497i	0.145927	−	0.0257309i
$900$	7.00102	−	0.159771i	0.233367	−	0.00532570i
$901$	34.4853	+	19.9101i	1.14887	+	0.663302i
$902$	31.8070	−	5.60843i	1.05906	−	0.186740i
$903$	17.3610	+	6.09549i	0.577737	+	0.202845i
$904$	−7.39208	−	12.8035i	−0.245857	−	0.425837i
$905$	44.5233			1.48000
$906$	57.1114	−	10.7435i	1.89740	−	0.356928i
$907$	−6.73516	−	1.18759i	−0.223637	−	0.0394333i	0.0607065	−	0.998156i	$-0.480665\pi$
$907$	−6.73516	−	1.18759i	−0.223637	−	0.0394333i	−0.284344	+	0.958722i	$0.591776\pi$
$908$	−30.7248	+	25.7812i	−1.01964	+	0.855578i
$909$	16.8702	+	2.57929i	0.559548	+	0.0855497i
$910$	11.1211	−	4.04775i	0.368661	−	0.134182i
$911$	−22.1214	−	38.3154i	−0.732915	−	1.26945i	−0.955632	−	0.294563i	$-0.904826\pi$
$911$	−22.1214	−	38.3154i	−0.732915	−	1.26945i	0.222717	−	0.974883i	$-0.428507\pi$
$912$	−29.7965	+	20.5923i	−0.986659	+	0.681879i
$913$	8.64695	−	14.9770i	0.286172	−	0.495665i
$914$	−0.820365	+	4.65252i	−0.0271353	+	0.153892i
$915$	−12.5371	−	33.2599i	−0.414465	−	1.09954i
$916$	−12.2999	−	4.47682i	−0.406402	−	0.147918i
$917$	−11.1092	+	13.2394i	−0.366857	+	0.437203i
$918$	47.1081	+	52.3906i	1.55480	+	1.72915i
$919$	5.00958	+	8.67685i	0.165251	+	0.286223i	0.936744	−	0.350014i	$-0.113823\pi$
$919$	5.00958	+	8.67685i	0.165251	+	0.286223i	−0.771494	+	0.636237i	$0.780490\pi$
$920$	10.8625			0.358124
$921$	10.0376	−	1.88822i	0.330751	−	0.0622191i
$922$	23.4057	+	27.8938i	0.770824	+	0.918633i
$923$	−5.08984	+	2.93862i	−0.167534	+	0.0967258i
$924$	0.192179	+	16.8444i	0.00632222	+	0.554140i
$925$	−2.65272	−	3.16138i	−0.0872208	−	0.103946i
$926$	15.9202	+	13.3586i	0.523171	+	0.438992i
$927$	−3.89912	+	11.5243i	−0.128064	+	0.378508i
$928$	1.71877	−	9.74765i	0.0564215	−	0.319982i
$929$	−23.2675	+	27.7292i	−0.763383	+	0.909764i	−0.998057	−	0.0623098i	$-0.980153\pi$
$929$	−23.2675	+	27.7292i	−0.763383	+	0.909764i	0.234674	+	0.972074i	$0.424598\pi$
$930$	18.2605	−	0.208335i	0.598784	−	0.00683156i
$931$	−7.28288	−	16.3617i	−0.238687	−	0.536234i
$932$	−26.7925	−	15.4687i	−0.877618	−	0.506693i
$933$	1.34009	+	3.55514i	0.0438726	+	0.116390i
$934$	−9.32089	−	25.6089i	−0.304989	−	0.837950i
$935$	17.3860	+	20.7198i	0.568582	+	0.677609i
$936$	3.14497	+	0.480836i	0.102796	+	0.0157166i
$937$	−4.25208	−	24.1147i	−0.138909	−	0.787794i	−0.972057	−	0.234744i	$-0.924575\pi$
$937$	−4.25208	−	24.1147i	−0.138909	−	0.787794i	0.833148	−	0.553050i	$-0.186536\pi$
$938$	46.1422	+	26.6402i	1.50660	+	0.869835i
$939$	18.9273	+	31.9360i	0.617669	+	1.04219i
$940$	17.9806	−	15.0875i	0.586462	−	0.492100i
$941$	−1.59941	+	1.34207i	−0.0521394	+	0.0437501i	−0.668485	−	0.743726i	$-0.733057\pi$
$941$	−1.59941	+	1.34207i	−0.0521394	+	0.0437501i	0.616346	+	0.787476i	$0.288612\pi$
$942$	−74.6937	+	0.852184i	−2.43365	+	0.0277657i
$943$	−43.2204	−	24.9533i	−1.40745	−	0.812591i
$944$	−6.71940	−	38.1076i	−0.218698	−	1.24030i
$945$	19.6494	−	25.1148i	0.639195	−	0.816985i
$946$	−7.65783	−	9.12624i	−0.248977	−	0.296720i
$947$	−11.4363	−	31.4208i	−0.371628	−	1.02104i	−0.974732	−	0.223378i	$-0.928292\pi$
$947$	−11.4363	−	31.4208i	−0.371628	−	1.02104i	0.603104	−	0.797663i	$-0.293930\pi$
$948$	−16.0479	+	19.5743i	−0.521210	+	0.635745i
$949$	−11.3748	−	6.56726i	−0.369242	−	0.213182i
$950$	12.9617	+	1.36356i	0.420533	+	0.0442396i
$951$	8.11926	−	14.4410i	0.263285	−	0.468281i
$952$	15.9745	−	19.0377i	0.517738	−	0.617016i
$953$	0.455320	−	2.58225i	0.0147492	−	0.0836471i	−0.976545	−	0.215315i	$-0.930922\pi$
$953$	0.455320	−	2.58225i	0.0147492	−	0.0836471i	0.991294	+	0.131668i	$0.0420333\pi$
$954$	−22.8332	+	20.0646i	−0.739252	+	0.649617i
$955$	−15.3123	−	12.8486i	−0.495495	−	0.415770i
$956$	−7.65791	−	9.12634i	−0.247675	−	0.295167i
$957$	−4.32122	+	2.56103i	−0.139685	+	0.0827864i
$958$	−5.93621	+	3.42727i	−0.191790	+	0.110730i
$959$	29.4465	+	35.0929i	0.950876	+	1.13321i
$960$	3.34079	−	9.51513i	0.107824	−	0.307099i
$961$	21.4962			0.693425
$962$	2.47199	+	4.28162i	0.0797003	+	0.138045i
$963$	−10.7452	−	3.63550i	−0.346258	−	0.117152i
$964$	22.8018	−	27.1741i	0.734395	−	0.875218i
$965$	4.25178	+	1.54752i	0.136870	+	0.0498164i
$966$	39.2646	−	47.8929i	1.26332	−	1.54093i
$967$	4.00168	−	22.6946i	0.128685	−	0.729810i	−0.850365	−	0.526193i	$-0.823619\pi$
$967$	4.00168	−	22.6946i	0.128685	−	0.729810i	0.979051	−	0.203617i	$-0.0652699\pi$
$968$	3.54977	−	6.14838i	0.114094	−	0.197617i
$969$	31.3338	+	45.3391i	1.00659	+	1.45650i
$970$	−27.1633	−	47.0483i	−0.872163	−	1.51063i
$971$	30.0218	−	10.9270i	0.963446	−	0.350666i	0.188063	−	0.982157i	$-0.439779\pi$
$971$	30.0218	−	10.9270i	0.963446	−	0.350666i	0.775383	+	0.631491i	$0.217557\pi$
$972$	−20.7660	+	8.92964i	−0.666070	+	0.286418i
$973$	13.3547	−	11.2060i	0.428133	−	0.359246i
$974$	−55.9923	−	9.87296i	−1.79411	−	0.316350i
$975$	−1.88593	−	2.19619i	−0.0603981	−	0.0703343i
$976$	53.4691			1.71150
$977$	−14.5029	−	25.1198i	−0.463990	−	0.803654i	0.535166	−	0.844747i	$-0.320249\pi$
$977$	−14.5029	−	25.1198i	−0.463990	−	0.803654i	−0.999155	+	0.0410934i	$0.986916\pi$
$978$	9.16690	−	7.87189i	0.293125	−	0.251715i
$979$	15.4367	−	2.72190i	0.493358	−	0.0869924i
$980$	9.50043	+	5.48507i	0.303480	+	0.175214i
$981$	0.495754	+	21.7235i	0.0158282	+	0.693579i
$982$	−12.4345	+	2.19254i	−0.396801	+	0.0699667i
$983$	6.90713	−	39.1723i	0.220303	−	1.24940i	−0.651160	−	0.758940i	$-0.725717\pi$
$983$	6.90713	−	39.1723i	0.220303	−	1.24940i	0.871463	−	0.490461i	$-0.163171\pi$
$984$	11.5979	−	9.95944i	0.369727	−	0.317495i
$985$	−23.1963	−	19.4640i	−0.739097	−	0.620176i
$986$	−19.2441	−	3.39326i	−0.612858	−	0.108063i
$987$	0.578969	+	50.7465i	0.0184288	+	1.61528i
$988$	−6.30811	−	1.80946i	−0.200688	−	0.0575666i
$989$			18.4088i			0.585365i
$990$	−19.2354	+	7.50239i	−0.611340	+	0.238442i
$991$	22.8844	+	4.03514i	0.726947	+	0.128180i	0.524861	−	0.851188i	$-0.324117\pi$
$991$	22.8844	+	4.03514i	0.726947	+	0.128180i	0.202085	+	0.979368i	$0.435228\pi$
$992$	−7.24160	+	19.8961i	−0.229921	+	0.631703i
$993$	−4.69000	−	12.4422i	−0.148833	−	0.394840i
$994$	−32.9310	−	11.9859i	−1.04451	−	0.380170i
$995$		−	25.2661i		−	0.800990i
$996$	0.246246	+	21.5834i	0.00780260	+	0.683895i
$997$	−5.47066	−	31.0257i	−0.173258	−	0.982593i	−0.940136	−	0.340800i	$-0.889302\pi$
$997$	−5.47066	−	31.0257i	−0.173258	−	0.982593i	0.766878	−	0.641793i	$-0.221809\pi$
$998$	5.43997	+	1.97999i	0.172199	+	0.0626754i
$999$	11.7577	+	6.26195i	0.371997	+	0.198119i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.2.x.a.14.16	✓	108
3.2	odd	2		513.2.bo.a.71.3		108
9.2	odd	6		171.2.bd.a.128.3	yes	108
9.7	even	3		513.2.cd.a.413.16		108
19.15	odd	18		171.2.bd.a.167.3	yes	108
57.53	even	18		513.2.cd.a.395.16		108
171.34	odd	18		513.2.bo.a.224.3		108
171.110	even	18	inner	171.2.x.a.110.16	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.x.a.14.16	✓	108	1.1	even	1	trivial
171.2.x.a.110.16	yes	108	171.110	even	18	inner
171.2.bd.a.128.3	yes	108	9.2	odd	6
171.2.bd.a.167.3	yes	108	19.15	odd	18
513.2.bo.a.71.3		108	3.2	odd	2
513.2.bo.a.224.3		108	171.34	odd	18
513.2.cd.a.395.16		108	57.53	even	18
513.2.cd.a.413.16		108	9.7	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.x (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.42288 + 1.19394i) q^{2} +(-1.62073 + 0.610926i) q^{3} +(0.251804 + 1.42805i) q^{4} +(0.629748 + 1.73022i) q^{5} +(-3.03552 - 1.06578i) q^{6} +(-1.66649 + 2.88644i) q^{7} +(0.510719 - 0.884592i) q^{8} +(2.25354 - 1.98029i) q^{9} +(-1.16972 + 3.21378i) q^{10} +2.01233i q^{11} +(-1.28054 - 2.16066i) q^{12} +(-0.355101 + 0.975632i) q^{13} +(-5.81744 + 2.11738i) q^{14} +(-2.07769 - 2.41949i) q^{15} +(4.50811 - 1.64082i) q^{16} +(-2.49671 - 6.85966i) q^{17} +(5.57087 - 0.127133i) q^{18} +(4.33498 + 0.456034i) q^{19} +(-2.31227 + 1.33499i) q^{20} +(0.937526 - 5.69624i) q^{21} +(-2.40260 + 2.86331i) q^{22} +(5.68790 - 1.00293i) q^{23} +(-0.287319 + 1.74570i) q^{24} +(1.23315 - 1.03473i) q^{25} +(-1.67011 + 0.964239i) q^{26} +(-2.44257 + 4.58627i) q^{27} +(-4.54161 - 1.65301i) q^{28} +(-0.250256 - 1.41927i) q^{29} +(-0.0675790 - 5.92328i) q^{30} +3.08283i q^{31} +(6.45386 + 2.34901i) q^{32} +(-1.22938 - 3.26144i) q^{33} +(4.63749 - 12.7414i) q^{34} +(-6.04364 - 1.06566i) q^{35} +(3.39541 + 2.71953i) q^{36} -2.56367i q^{37} +(5.62368 + 5.82458i) q^{38} +(-0.0205155 - 1.79818i) q^{39} +(1.85216 + 0.326586i) q^{40} +(-6.61929 - 5.55425i) q^{41} +(8.13495 - 6.98572i) q^{42} +(-0.553471 + 3.13889i) q^{43} +(-2.87371 + 0.506713i) q^{44} +(4.84550 + 2.65203i) q^{45} +(9.29064 + 5.36395i) q^{46} +(-8.65752 + 1.52655i) q^{47} +(-6.30401 + 5.41344i) q^{48} +(-2.05435 - 3.55824i) q^{49} +2.99003 q^{50} +(8.23725 + 9.59236i) q^{51} +(-1.48267 - 0.261435i) q^{52} +(-4.17870 + 3.50634i) q^{53} +(-8.95121 + 3.60944i) q^{54} +(-3.48177 + 1.26726i) q^{55} +(1.70221 + 2.94832i) q^{56} +(-7.30444 + 1.90924i) q^{57} +(1.33844 - 2.31825i) q^{58} +(1.40063 - 7.94334i) q^{59} +(2.93199 - 3.57629i) q^{60} +(10.4732 + 3.81194i) q^{61} +(-3.68071 + 4.38650i) q^{62} +(1.96050 + 9.80483i) q^{63} +(1.58107 + 2.73850i) q^{64} -1.91168 q^{65} +(2.14470 - 6.10846i) q^{66} +(-5.53209 - 6.59289i) q^{67} +(9.16728 - 5.29273i) q^{68} +(-8.60584 + 5.10036i) q^{69} +(-7.32705 - 8.73204i) q^{70} +(4.33638 + 3.63865i) q^{71} +(-0.600825 - 3.00484i) q^{72} +(-2.19677 + 12.4585i) q^{73} +(3.06087 - 3.64780i) q^{74} +(-1.36645 + 2.43038i) q^{75} +(0.440324 + 6.30541i) q^{76} +(-5.80846 - 3.35352i) q^{77} +(2.11772 - 2.58309i) q^{78} +(-3.44685 - 9.47013i) q^{79} +(5.67794 + 6.76671i) q^{80} +(1.15688 - 8.92534i) q^{81} +(-2.78704 - 15.8061i) q^{82} +(-7.44260 - 4.29699i) q^{83} +(8.37060 - 0.0955007i) q^{84} +(10.2964 - 8.63972i) q^{85} +(-4.53517 + 3.80546i) q^{86} +(1.27267 + 2.14737i) q^{87} +(1.78009 + 1.02773i) q^{88} +(-1.35261 - 7.67105i) q^{89} +(3.72821 + 9.55876i) q^{90} +(-2.22433 - 2.65085i) q^{91} +(2.86447 + 7.87007i) q^{92} +(-1.88338 - 4.99643i) q^{93} +(-14.1412 - 8.16445i) q^{94} +(1.94091 + 7.78765i) q^{95} +(-11.8950 + 0.135711i) q^{96} +(-10.2106 + 12.1685i) q^{97} +(1.32522 - 7.51572i) q^{98} +(3.98500 + 4.53486i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9} - 12 q^{10} - 9 q^{12} - 6 q^{13} - 9 q^{14} - 36 q^{15} - 9 q^{16} + 27 q^{17} + 36 q^{18} - 15 q^{19} - 18 q^{20} + 3 q^{21} + 30 q^{22} - 45 q^{23}+ \cdots + 39 q^{99}+O(q^{100}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9 - 12 * q^10 - 9 * q^12 - 6 * q^13 - 9 * q^14 - 36 * q^15 - 9 * q^16 + 27 * q^17 + 36 * q^18 - 15 * q^19 - 18 * q^20 + 3 * q^21 + 30 * q^22 - 45 * q^23 - 21 * q^24 - 3 * q^25 - 72 * q^26 - 36 * q^28 - 9 * q^29 - 21 * q^30 - 9 * q^32 - 6 * q^33 + 33 * q^34 + 45 * q^35 + 18 * q^36 - 9 * q^38 - 18 * q^39 + 15 * q^40 - 9 * q^41 + 15 * q^42 + 9 * q^43 - 63 * q^44 + 33 * q^45 - 18 * q^46 - 9 * q^47 + 3 * q^48 - 15 * q^49 + 126 * q^50 + 39 * q^51 - 39 * q^52 - 51 * q^54 + 3 * q^55 + 63 * q^56 - 78 * q^57 - 6 * q^58 + 36 * q^59 - 75 * q^60 - 24 * q^61 + 18 * q^62 - 9 * q^63 - 18 * q^65 + 159 * q^66 - 63 * q^67 + 54 * q^68 - 9 * q^69 + 39 * q^70 + 141 * q^72 - 45 * q^73 - 117 * q^74 - 3 * q^76 - 18 * q^77 + 27 * q^78 + 3 * q^79 + 126 * q^80 - 60 * q^81 - 3 * q^82 + 27 * q^83 - 117 * q^84 - 3 * q^85 - 171 * q^86 + 15 * q^87 - 9 * q^88 + 54 * q^89 - 21 * q^90 - 9 * q^91 - 27 * q^92 + 42 * q^93 + 99 * q^95 + 207 * q^96 - 57 * q^97 - 27 * q^98 + 39 * q^99

Introduction

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