LMFDB - Embedded newform 546.2.bv.a.317.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(317,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 4, 9]))

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

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

chi := DirichletCharacter("546.317");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bv (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			317.10
Character	$\chi$	$=$	546.317
Dual form			546.2.bv.a.515.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(0.0392246 - 1.73161i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.98929 - 0.533030i) q^{5} +(0.410285 + 1.68276i) q^{6} +(-2.22758 + 1.42754i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.99692 - 0.135843i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(0.0392246 - 1.73161i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.98929 - 0.533030i) q^{5} +(0.410285 + 1.68276i) q^{6} +(-2.22758 + 1.42754i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.99692 - 0.135843i) q^{9} +(-1.78355 + 1.02973i) q^{10} +(-3.44459 - 0.922976i) q^{11} +(-0.831834 - 1.51923i) q^{12} +(-3.26173 - 1.53659i) q^{13} +(1.78221 - 1.95544i) q^{14} +(-0.844969 - 3.46558i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-3.54630 - 6.14237i) q^{17} +(2.92996 - 0.644446i) q^{18} +(1.49254 + 5.57022i) q^{19} +(1.45626 - 1.45626i) q^{20} +(2.38456 + 3.91329i) q^{21} +3.56611 q^{22} +(3.12969 - 5.42078i) q^{23} +(1.19669 + 1.25217i) q^{24} +(-0.656955 + 0.379293i) q^{25} +(3.54829 + 0.640028i) q^{26} +(-0.352780 + 5.18416i) q^{27} +(-1.21537 + 2.35008i) q^{28} +0.340291i q^{29} +(1.71314 + 3.12880i) q^{30} +(-8.31053 - 2.22680i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-1.73334 + 5.92848i) q^{33} +(5.01522 + 5.01522i) q^{34} +(-3.67040 + 4.02717i) q^{35} +(-2.66333 + 1.38082i) q^{36} +(7.50999 - 2.01230i) q^{37} +(-2.88336 - 4.99412i) q^{38} +(-2.78870 + 5.58777i) q^{39} +(-1.02973 + 1.78355i) q^{40} +(-5.27007 - 5.27007i) q^{41} +(-3.31615 - 3.16278i) q^{42} +0.428508i q^{43} +(-3.44459 + 0.922976i) q^{44} +(-6.03417 + 1.32722i) q^{45} +(-1.62005 + 6.04610i) q^{46} +(0.403284 + 1.50508i) q^{47} +(-1.48000 - 0.899773i) q^{48} +(2.92426 - 6.35993i) q^{49} +(0.536402 - 0.536402i) q^{50} +(-10.7753 + 5.89986i) q^{51} +(-3.59304 + 0.300145i) q^{52} +(5.74215 - 3.31523i) q^{53} +(-1.00100 - 5.09882i) q^{54} -7.34429 q^{55} +(0.565716 - 2.58456i) q^{56} +(9.70397 - 2.36599i) q^{57} +(-0.0880738 - 0.328696i) q^{58} +(1.94912 + 0.522265i) q^{59} +(-2.46456 - 2.57880i) q^{60} +(-0.887540 + 1.53726i) q^{61} +8.60369 q^{62} +(6.86982 - 3.97563i) q^{63} -1.00000i q^{64} +(-7.30759 - 1.31812i) q^{65} +(0.139879 - 6.17509i) q^{66} +(-11.7315 - 3.14344i) q^{67} +(-6.14237 - 3.54630i) q^{68} +(-9.26390 - 5.63202i) q^{69} +(2.50302 - 4.83991i) q^{70} +(1.49159 + 1.49159i) q^{71} +(2.21520 - 2.02309i) q^{72} +(-1.14879 + 4.28734i) q^{73} +(-6.73327 + 3.88746i) q^{74} +(0.631018 + 1.15247i) q^{75} +(4.07768 + 4.07768i) q^{76} +(8.99071 - 2.86129i) q^{77} +(1.24746 - 6.11914i) q^{78} +(-4.48152 + 7.76223i) q^{79} +(0.533030 - 1.98929i) q^{80} +(8.96309 + 0.814222i) q^{81} +(6.45449 + 3.72650i) q^{82} +(8.13092 + 8.13092i) q^{83} +(4.02174 + 2.19673i) q^{84} +(-10.3287 - 10.3287i) q^{85} +(-0.110906 - 0.413907i) q^{86} +(0.589250 + 0.0133478i) q^{87} +(3.08834 - 1.78305i) q^{88} +(0.601969 + 2.24658i) q^{89} +(5.48505 - 2.84375i) q^{90} +(9.45932 - 1.23338i) q^{91} -6.25938i q^{92} +(-4.18192 + 14.3032i) q^{93} +(-0.779084 - 1.34941i) q^{94} +(5.93818 + 10.2852i) q^{95} +(1.66245 + 0.486061i) q^{96} +(11.9267 - 11.9267i) q^{97} +(-1.17854 + 6.90007i) q^{98} +(10.1978 + 3.23401i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 16 q^{7}+O(q^{10}) $ 144 * q - 16 * q^7	$ 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99}+O(q^{100}) $ 144 * q - 16 * q^7 + 72 * q^16 + 16 * q^18 + 8 * q^19 + 8 * q^21 + 24 * q^27 - 8 * q^28 - 8 * q^31 + 12 * q^33 - 8 * q^37 + 16 * q^39 - 40 * q^45 + 8 * q^46 + 8 * q^52 - 12 * q^54 - 32 * q^55 + 16 * q^57 + 8 * q^58 - 32 * q^61 - 40 * q^63 - 32 * q^66 - 8 * q^67 + 16 * q^72 + 80 * q^73 - 16 * q^76 + 16 * q^78 - 112 * q^79 - 48 * q^81 + 16 * q^84 - 80 * q^85 + 96 * q^87 - 32 * q^91 + 36 * q^93 - 64 * q^94 - 144 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$	0.0392246	−	1.73161i	0.0226463	−	0.999744i
$3$	0.0392246	−	1.73161i	0.0226463	−	0.999744i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	1.98929	−	0.533030i	0.889640	−	0.238378i	0.215078	−	0.976597i	$-0.430999\pi$
$5$	1.98929	−	0.533030i	0.889640	−	0.238378i	0.674561	+	0.738219i	$0.264333\pi$
$6$	0.410285	+	1.68276i	0.167498	+	0.686982i
$7$	−2.22758	+	1.42754i	−0.841947	+	0.539560i
$7$	−2.22758	+	1.42754i	−0.841947	+	0.539560i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−2.99692	−	0.135843i	−0.998974	−	0.0452810i
$10$	−1.78355	+	1.02973i	−0.564009	+	0.325631i
$11$	−3.44459	−	0.922976i	−1.03858	−	0.278288i	−0.301058	−	0.953606i	$-0.597340\pi$
$11$	−3.44459	−	0.922976i	−1.03858	−	0.278288i	−0.737527	+	0.675318i	$0.764006\pi$
$12$	−0.831834	−	1.51923i	−0.240130	−	0.438563i
$13$	−3.26173	−	1.53659i	−0.904642	−	0.426172i
$13$	−3.26173	−	1.53659i	−0.904642	−	0.426172i
$14$	1.78221	−	1.95544i	0.476315	−	0.522613i
$15$	−0.844969	−	3.46558i	−0.218170	−	0.894810i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−3.54630	−	6.14237i	−0.860104	−	1.48974i	−0.871828	−	0.489812i	$-0.837065\pi$
$17$	−3.54630	−	6.14237i	−0.860104	−	1.48974i	0.0117245	−	0.999931i	$-0.496268\pi$
$18$	2.92996	−	0.644446i	0.690599	−	0.151897i
$19$	1.49254	+	5.57022i	0.342411	+	1.27790i	0.895608	+	0.444845i	$0.146741\pi$
$19$	1.49254	+	5.57022i	0.342411	+	1.27790i	−0.553197	+	0.833051i	$0.686592\pi$
$20$	1.45626	−	1.45626i	0.325631	−	0.325631i
$21$	2.38456	+	3.91329i	0.520354	+	0.853951i
$22$	3.56611			0.760297
$23$	3.12969	−	5.42078i	0.652585	−	1.13031i	−0.329908	−	0.944013i	$-0.607018\pi$
$23$	3.12969	−	5.42078i	0.652585	−	1.13031i	0.982493	−	0.186298i	$-0.0596490\pi$
$24$	1.19669	+	1.25217i	0.244274	+	0.255597i
$25$	−0.656955	+	0.379293i	−0.131391	+	0.0758587i
$26$	3.54829	+	0.640028i	0.695877	+	0.125520i
$27$	−0.352780	+	5.18416i	−0.0678925	+	0.997693i
$28$	−1.21537	+	2.35008i	−0.229684	+	0.444123i
$29$			0.340291i			0.0631904i	0.999501	+	0.0315952i	$0.0100587\pi$
$29$			0.340291i			0.0631904i	−0.999501	+	0.0315952i	$0.989941\pi$
$30$	1.71314	+	3.12880i	0.312774	+	0.571239i
$31$	−8.31053	−	2.22680i	−1.49261	−	0.399945i	−0.581996	−	0.813192i	$-0.697728\pi$
$31$	−8.31053	−	2.22680i	−1.49261	−	0.399945i	−0.910619	+	0.413247i	$0.864395\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	−1.73334	+	5.92848i	−0.301737	+	1.03202i
$34$	5.01522	+	5.01522i	0.860104	+	0.860104i
$35$	−3.67040	+	4.02717i	−0.620410	+	0.680715i
$36$	−2.66333	+	1.38082i	−0.443889	+	0.230136i
$37$	7.50999	−	2.01230i	1.23463	−	0.330819i	0.418252	−	0.908331i	$-0.362643\pi$
$37$	7.50999	−	2.01230i	1.23463	−	0.330819i	0.816382	+	0.577512i	$0.195976\pi$
$38$	−2.88336	−	4.99412i	−0.467742	−	0.810153i
$39$	−2.78870	+	5.58777i	−0.446550	+	0.894759i
$40$	−1.02973	+	1.78355i	−0.162815	+	0.282004i
$41$	−5.27007	−	5.27007i	−0.823047	−	0.823047i	0.163497	−	0.986544i	$-0.447723\pi$
$41$	−5.27007	−	5.27007i	−0.823047	−	0.823047i	−0.986544	+	0.163497i	$0.947723\pi$
$42$	−3.31615	−	3.16278i	−0.511692	−	0.488028i
$43$			0.428508i			0.0653469i	0.999466	+	0.0326735i	$0.0104021\pi$
$43$			0.428508i			0.0653469i	−0.999466	+	0.0326735i	$0.989598\pi$
$44$	−3.44459	+	0.922976i	−0.519292	+	0.139144i
$45$	−6.03417	+	1.32722i	−0.899521	+	0.197850i
$46$	−1.62005	+	6.04610i	−0.238863	+	0.891448i
$47$	0.403284	+	1.50508i	0.0588250	+	0.219538i	0.989081	−	0.147373i	$-0.0470819\pi$
$47$	0.403284	+	1.50508i	0.0588250	+	0.219538i	−0.930256	+	0.366911i	$0.880415\pi$
$48$	−1.48000	−	0.899773i	−0.213620	−	0.129871i
$49$	2.92426	−	6.35993i	0.417751	−	0.908562i
$50$	0.536402	−	0.536402i	0.0758587	−	0.0758587i
$51$	−10.7753	+	5.89986i	−1.50884	+	0.826146i
$52$	−3.59304	+	0.300145i	−0.498265	+	0.0416226i
$53$	5.74215	−	3.31523i	0.788745	−	0.455382i	−0.0507753	−	0.998710i	$-0.516169\pi$
$53$	5.74215	−	3.31523i	0.788745	−	0.455382i	0.839521	+	0.543328i	$0.182836\pi$
$54$	−1.00100	−	5.09882i	−0.136219	−	0.693862i
$55$	−7.34429			−0.990303
$56$	0.565716	−	2.58456i	0.0755970	−	0.345377i
$57$	9.70397	−	2.36599i	1.28532	−	0.313384i
$58$	−0.0880738	−	0.328696i	−0.0115647	−	0.0431599i
$59$	1.94912	+	0.522265i	0.253754	+	0.0679931i	0.383453	−	0.923560i	$-0.374735\pi$
$59$	1.94912	+	0.522265i	0.253754	+	0.0679931i	−0.129700	+	0.991553i	$0.541401\pi$
$60$	−2.46456	−	2.57880i	−0.318173	−	0.332921i
$61$	−0.887540	+	1.53726i	−0.113638	+	0.196827i	−0.917234	−	0.398348i	$-0.869584\pi$
$61$	−0.887540	+	1.53726i	−0.113638	+	0.196827i	0.803597	+	0.595174i	$0.202917\pi$
$62$	8.60369			1.09267
$63$	6.86982	−	3.97563i	0.865516	−	0.500882i
$64$		−	1.00000i		−	0.125000i
$65$	−7.30759	−	1.31812i	−0.906396	−	0.163493i
$66$	0.139879	−	6.17509i	0.0172179	−	0.760102i
$67$	−11.7315	−	3.14344i	−1.43323	−	0.384032i	−0.543070	−	0.839688i	$-0.682738\pi$
$67$	−11.7315	−	3.14344i	−1.43323	−	0.384032i	−0.890156	+	0.455656i	$0.849405\pi$
$68$	−6.14237	−	3.54630i	−0.744872	−	0.430052i
$69$	−9.26390	−	5.63202i	−1.11524	−	0.678015i
$70$	2.50302	−	4.83991i	0.299169	−	0.578480i
$71$	1.49159	+	1.49159i	0.177020	+	0.177020i	0.790055	−	0.613036i	$-0.210052\pi$
$71$	1.49159	+	1.49159i	0.177020	+	0.177020i	−0.613036	+	0.790055i	$0.710052\pi$
$72$	2.21520	−	2.02309i	0.261064	−	0.238423i
$73$	−1.14879	+	4.28734i	−0.134455	+	0.501795i	0.865544	+	0.500833i	$0.166973\pi$
$73$	−1.14879	+	4.28734i	−0.134455	+	0.501795i	−1.00000		0.000961865i	$0.999694\pi$
$74$	−6.73327	+	3.88746i	−0.782727	+	0.451908i
$75$	0.631018	+	1.15247i	0.0728637	+	0.133075i
$76$	4.07768	+	4.07768i	0.467742	+	0.467742i
$77$	8.99071	−	2.86129i	1.02459	−	0.326074i
$78$	1.24746	−	6.11914i	0.141247	−	0.692856i
$79$	−4.48152	+	7.76223i	−0.504211	+	0.873319i	0.495777	+	0.868450i	$0.334883\pi$
$79$	−4.48152	+	7.76223i	−0.504211	+	0.873319i	−0.999988	+	0.00486899i	$0.998450\pi$
$80$	0.533030	−	1.98929i	0.0595945	−	0.222410i
$81$	8.96309	+	0.814222i	0.995899	+	0.0904692i
$82$	6.45449	+	3.72650i	0.712779	+	0.411523i
$83$	8.13092	+	8.13092i	0.892484	+	0.892484i	0.994756	−	0.102272i	$-0.0326113\pi$
$83$	8.13092	+	8.13092i	0.892484	+	0.892484i	−0.102272	+	0.994756i	$0.532611\pi$
$84$	4.02174	+	2.19673i	0.438808	+	0.239683i
$85$	−10.3287	−	10.3287i	−1.12030	−	1.12030i
$86$	−0.110906	−	0.413907i	−0.0119593	−	0.0446328i
$87$	0.589250	+	0.0133478i	0.0631742	+	0.00143103i
$88$	3.08834	−	1.78305i	0.329218	−	0.190074i
$89$	0.601969	+	2.24658i	0.0638085	+	0.238137i	0.990463	−	0.137777i	$-0.0439957\pi$
$89$	0.601969	+	2.24658i	0.0638085	+	0.238137i	−0.926655	+	0.375913i	$0.877329\pi$
$90$	5.48505	−	2.84375i	0.578175	−	0.299758i
$91$	9.45932	−	1.23338i	0.991606	−	0.129294i
$92$		−	6.25938i		−	0.652585i
$93$	−4.18192	+	14.3032i	−0.433645	+	1.48317i
$94$	−0.779084	−	1.34941i	−0.0803564	−	0.139181i
$95$	5.93818	+	10.2852i	0.609245	+	1.05524i
$96$	1.66245	+	0.486061i	0.169673	+	0.0496084i
$97$	11.9267	−	11.9267i	1.21097	−	1.21097i	0.240261	−	0.970708i	$-0.422767\pi$
$97$	11.9267	−	11.9267i	1.21097	−	1.21097i	0.970708	−	0.240261i	$-0.0772332\pi$
$98$	−1.17854	+	6.90007i	−0.119051	+	0.697013i
$99$	10.1978	+	3.23401i	1.02492	+	0.325031i
$100$	−0.379293	+	0.656955i	−0.0379293	+	0.0656955i
$101$	−9.58488	−	16.6015i	−0.953731	−	1.65191i	−0.737246	−	0.675624i	$-0.763874\pi$
$101$	−9.58488	−	16.6015i	−0.953731	−	1.65191i	−0.216484	−	0.976286i	$-0.569459\pi$
$102$	8.88111	−	8.48767i	0.879361	−	0.840405i
$103$	−6.96843	−	4.02323i	−0.686620	−	0.396420i	0.115724	−	0.993281i	$-0.463081\pi$
$103$	−6.96843	−	4.02323i	−0.686620	−	0.396420i	−0.802345	+	0.596861i	$0.796414\pi$
$104$	3.39292	−	1.21986i	0.332704	−	0.119618i
$105$	6.82950	+	6.51365i	0.666491	+	0.635667i
$106$	−4.68845	+	4.68845i	−0.455382	+	0.455382i
$107$	0.729345	+	0.421088i	0.0705085	+	0.0407081i	0.534840	−	0.844954i	$-0.320372\pi$
$107$	0.729345	+	0.421088i	0.0705085	+	0.0407081i	−0.464331	+	0.885662i	$0.653705\pi$
$108$	2.28657	+	4.66601i	0.220025	+	0.448987i
$109$	12.8052	+	3.43114i	1.22651	+	0.328643i	0.813221	−	0.581955i	$-0.197712\pi$
$109$	12.8052	+	3.43114i	1.22651	+	0.328643i	0.413293	+	0.910598i	$0.364379\pi$
$110$	7.09404	−	1.90084i	0.676390	−	0.181238i
$111$	−3.18993	−	13.0833i	−0.302775	−	1.24181i
$112$	0.122494	+	2.64291i	0.0115746	+	0.249732i
$113$		−	2.28160i		−	0.214635i	−0.994225	−	0.107317i	$-0.965774\pi$
$113$		−	2.28160i		−	0.214635i	0.994225	−	0.107317i	$-0.0342261\pi$
$114$	−8.76095	+	4.79695i	−0.820538	+	0.449275i
$115$	3.33644	−	12.4517i	0.311124	−	1.16113i
$116$	0.170145	+	0.294701i	0.0157976	+	0.0273623i
$117$	9.56643	+	5.04811i	0.884417	+	0.466698i
$118$	−2.01788			−0.185761
$119$	16.6682	+	8.62016i	1.52797	+	0.790208i
$120$	3.04802	+	1.85305i	0.278245	+	0.169160i
$121$	1.48707	+	0.858559i	0.135188	+	0.0780508i
$122$	0.459425	−	1.71460i	0.0415943	−	0.155232i
$123$	−9.33240	+	8.91897i	−0.841475	+	0.804197i
$124$	−8.31053	+	2.22680i	−0.746307	+	0.199972i
$125$	−8.38603	+	8.38603i	−0.750069	+	0.750069i
$126$	−5.60677	+	5.61820i	−0.499490	+	0.500509i
$127$			7.84238i			0.695899i	0.937513	+	0.347949i	$0.113122\pi$
$127$			7.84238i			0.695899i	−0.937513	+	0.347949i	$0.886878\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	0.742008	+	0.0168081i	0.0653302	+	0.00147987i
$130$	7.39975	−	0.618140i	0.649001	−	0.0542144i
$131$	−11.9026	−	6.87197i	−1.03994	−	0.600407i	−0.120120	−	0.992759i	$-0.538328\pi$
$131$	−11.9026	−	6.87197i	−1.03994	−	0.600407i	−0.919815	+	0.392352i	$0.871661\pi$
$132$	1.46312	+	6.00089i	0.127348	+	0.522310i
$133$	−11.2765	−	10.2775i	−0.977793	−	0.891170i
$134$	12.1453			1.04919
$135$	2.06153	+	10.5009i	0.177428	+	0.903771i
$136$	6.85092	+	1.83570i	0.587462	+	0.157410i
$137$	11.2765	+	3.02154i	0.963419	+	0.258147i	0.706047	−	0.708165i	$-0.250477\pi$
$137$	11.2765	+	3.02154i	0.963419	+	0.258147i	0.257372	+	0.966312i	$0.417143\pi$
$138$	10.4059	+	3.04244i	0.885810	+	0.258990i
$139$	21.4052			1.81557			0.907784	−	0.419437i	$-0.137773\pi$
$139$	21.4052			1.81557			0.907784	+	0.419437i	$0.137773\pi$
$140$	−1.16507	+	5.32283i	−0.0984668	+	0.449861i
$141$	2.62202	−	0.639293i	0.220814	−	0.0538382i
$142$	−1.82682	−	1.05472i	−0.153303	−	0.0885098i
$143$	9.81712	+	8.30342i	0.820949	+	0.694367i
$144$	−1.61610	+	2.52749i	−0.134675	+	0.210624i
$145$	0.181385	+	0.676939i	0.0150632	+	0.0562167i
$146$		−	4.43858i		−	0.367339i
$147$	−10.8982	−	5.31313i	−0.898868	−	0.438219i
$148$	5.49769	−	5.49769i	0.451908	−	0.451908i
$149$	−8.39308	+	2.24892i	−0.687588	+	0.184239i	−0.585665	−	0.810554i	$-0.699166\pi$
$149$	−8.39308	+	2.24892i	−0.687588	+	0.184239i	−0.101924	+	0.994792i	$0.532500\pi$
$150$	−0.907797	−	0.949877i	−0.0741213	−	0.0775572i
$151$	1.18588	−	4.42576i	0.0965055	−	0.360163i	−0.900738	−	0.434363i	$-0.856974\pi$
$151$	1.18588	−	4.42576i	0.0965055	−	0.360163i	0.997243	+	0.0741996i	$0.0236402\pi$
$152$	−4.99412	−	2.88336i	−0.405077	−	0.233871i
$153$	9.79358	+	18.8899i	0.791764	+	1.52716i
$154$	−7.94380	+	5.09076i	−0.640130	+	0.410225i
$155$	−17.7190			−1.42323
$156$	0.378798	+	6.23350i	0.0303281	+	0.499079i
$157$	−0.998255	−	1.72903i	−0.0796694	−	0.137992i	0.823438	−	0.567406i	$-0.192053\pi$
$157$	−0.998255	−	1.72903i	−0.0796694	−	0.137992i	−0.903107	+	0.429415i	$0.858720\pi$
$158$	2.31981	−	8.65764i	0.184554	−	0.688765i
$159$	−5.51545	−	10.0732i	−0.437403	−	0.798856i
$160$			2.05947i			0.162815i
$161$	0.766739	+	16.5430i	0.0604275	+	1.30377i
$162$	−8.86842	+	1.53334i	−0.696769	+	0.120471i
$163$	16.3399	−	4.37826i	1.27984	−	0.342932i	0.446046	−	0.895010i	$-0.352832\pi$
$163$	16.3399	−	4.37826i	1.27984	−	0.342932i	0.833792	+	0.552078i	$0.186165\pi$
$164$	−7.19905	−	1.92898i	−0.562151	−	0.150628i
$165$	−0.288077	+	12.7174i	−0.0224267	+	0.990049i
$166$	−9.95830	−	5.74943i	−0.772914	−	0.446242i
$167$	5.20220	−	5.20220i	0.402558	−	0.402558i	−0.476575	−	0.879134i	$-0.658122\pi$
$167$	5.20220	−	5.20220i	0.402558	−	0.402558i	0.879134	+	0.476575i	$0.158122\pi$
$168$	−4.45326	−	1.08098i	−0.343576	−	0.0833991i
$169$	8.27781	+	10.0239i	0.636755	+	0.771066i
$170$	12.6500	+	7.30349i	0.970212	+	0.560152i
$171$	−3.71634	−	16.8963i	−0.284195	−	1.29209i
$172$	0.214254	+	0.371099i	0.0163367	+	0.0282960i
$173$	7.84476	−	13.5875i	0.596426	−	1.03304i	−0.396918	−	0.917854i	$-0.629920\pi$
$173$	7.84476	−	13.5875i	0.596426	−	1.03304i	0.993344	−	0.115186i	$-0.0367465\pi$
$174$	−0.572627	+	0.139616i	−0.0434107	+	0.0105843i
$175$	0.921967	−	1.78274i	0.0696941	−	0.134762i
$176$	−2.52162	+	2.52162i	−0.190074	+	0.190074i
$177$	0.980811	−	3.35462i	0.0737223	−	0.252149i
$178$	−1.16291	−	2.01423i	−0.0871641	−	0.150973i
$179$	−1.69754	−	2.94023i	−0.126880	−	0.219763i	0.795586	−	0.605841i	$-0.207163\pi$
$179$	−1.69754	−	2.94023i	−0.126880	−	0.219763i	−0.922466	+	0.386078i	$0.873830\pi$
$180$	−4.56214	+	4.16649i	−0.340042	+	0.310552i
$181$		−	21.4107i		−	1.59145i	−0.605661	−	0.795723i	$-0.707091\pi$
$181$		−	21.4107i		−	1.59145i	0.605661	−	0.795723i	$-0.292909\pi$
$182$	−8.81778	+	3.63961i	−0.653617	+	0.269786i
$183$	2.62712	+	1.59717i	0.194203	+	0.118066i
$184$	1.62005	+	6.04610i	0.119431	+	0.445724i
$185$	13.8670	−	8.00610i	1.01952	−	0.588620i
$186$	0.337476	−	14.8982i	0.0247449	−	1.09239i
$187$	6.54630	+	24.4311i	0.478713	+	1.78658i
$188$	1.10179	+	1.10179i	0.0803564	+	0.0803564i
$189$	−6.61476	−	12.0518i	−0.481153	−	0.876637i
$190$	−8.39786	−	8.39786i	−0.609245	−	0.609245i
$191$	6.36942	+	3.67739i	0.460875	+	0.266086i	0.712412	−	0.701761i	$-0.247603\pi$
$191$	6.36942	+	3.67739i	0.460875	+	0.266086i	−0.251537	+	0.967848i	$0.580936\pi$
$192$	−1.73161	−	0.0392246i	−0.124968	−	0.00283079i
$193$	2.39902	−	8.95326i	0.172685	−	0.644470i	−0.824249	−	0.566227i	$-0.808402\pi$
$193$	2.39902	−	8.95326i	0.172685	−	0.644470i	0.996934	−	0.0782426i	$-0.0249309\pi$
$194$	−8.43343	+	14.6071i	−0.605485	+	1.04873i
$195$	−2.56910	+	12.6022i	−0.183977	+	0.902461i
$196$	−0.647484	−	6.96999i	−0.0462489	−	0.497856i
$197$	−13.6917	−	13.6917i	−0.975490	−	0.975490i	0.0242167	−	0.999707i	$-0.492291\pi$
$197$	−13.6917	−	13.6917i	−0.975490	−	0.975490i	−0.999707	+	0.0242167i	$0.992291\pi$
$198$	−10.6873	−	0.484431i	−0.759517	−	0.0344270i
$199$	−5.65413	+	3.26442i	−0.400811	+	0.231408i	−0.686834	−	0.726814i	$-0.741000\pi$
$199$	−5.65413	+	3.26442i	−0.400811	+	0.231408i	0.286023	+	0.958223i	$0.407667\pi$
$200$	0.196337	−	0.732739i	0.0138831	−	0.0518124i
$201$	−5.90335	+	20.1910i	−0.416391	+	1.42416i
$202$	13.5551	+	13.5551i	0.953731	+	0.953731i
$203$	−0.485779	−	0.758027i	−0.0340950	−	0.0532030i
$204$	−6.38173	+	10.4971i	−0.446810	+	0.734941i
$205$	−13.2928	−	7.67462i	−0.928411	−	0.536018i
$206$	7.77228	+	2.08258i	0.541520	+	0.145100i
$207$	−10.1158	+	15.8205i	−0.703098	+	1.09960i
$208$	−2.96159	+	2.05645i	−0.205349	+	0.142589i
$209$		−	20.5647i		−	1.42249i
$210$	−8.28265	−	4.52410i	−0.571557	−	0.312192i
$211$	−8.69638			−0.598683			−0.299342	−	0.954146i	$-0.596767\pi$
$211$	−8.69638			−0.598683			−0.299342	+	0.954146i	$0.596767\pi$
$212$	3.31523	−	5.74215i	0.227691	−	0.394373i
$213$	2.64136	−	2.52435i	0.180983	−	0.172965i
$214$	−0.813479	−	0.217971i	−0.0556083	−	0.0149002i
$215$	0.228408	+	0.852429i	0.0155773	+	0.0581352i
$216$	−3.41630	−	3.91521i	−0.232450	−	0.266396i
$217$	21.6912	−	6.90323i	1.47250	−	0.468622i
$218$	−13.2569			−0.897870
$219$	7.37892	+	2.15742i	0.498621	+	0.145785i
$220$	−6.36034	+	3.67214i	−0.428814	+	0.247576i
$221$	2.12881	+	25.4840i	0.143199	+	1.71424i
$222$	6.46744	+	11.8119i	0.434066	+	0.792760i
$223$	2.74582	−	2.74582i	0.183874	−	0.183874i	−0.609168	−	0.793041i	$-0.708496\pi$
$223$	2.74582	−	2.74582i	0.183874	−	0.183874i	0.793041	+	0.609168i	$0.208496\pi$
$224$	−0.802357	−	2.52116i	−0.0536097	−	0.168452i
$225$	2.02037	−	1.04747i	0.134691	−	0.0698314i
$226$	0.590522	+	2.20386i	0.0392809	+	0.146598i
$227$	3.90799	−	14.5848i	0.259383	−	0.968029i	−0.706217	−	0.707996i	$-0.749600\pi$
$227$	3.90799	−	14.5848i	0.259383	−	0.968029i	0.965600	−	0.260034i	$-0.0837337\pi$
$228$	7.22089	−	6.90100i	0.478215	−	0.457030i
$229$	1.17491	−	0.314817i	0.0776406	−	0.0208037i	−0.219790	−	0.975547i	$-0.570537\pi$
$229$	1.17491	−	0.314817i	0.0776406	−	0.0208037i	0.297430	+	0.954744i	$0.403870\pi$
$230$			12.8910i			0.850007i
$231$	−4.60197	−	15.6806i	−0.302788	−	1.03171i
$232$	−0.240622	−	0.240622i	−0.0157976	−	0.0157976i
$233$	3.06855	−	5.31488i	0.201027	−	0.348189i	−0.747833	−	0.663887i	$-0.768905\pi$
$233$	3.06855	−	5.31488i	0.201027	−	0.348189i	0.948860	+	0.315698i	$0.102239\pi$
$234$	−10.5470	−	2.40013i	−0.689480	−	0.156901i
$235$	1.60450	+	2.77908i	0.104666	+	0.181287i
$236$	1.94912	−	0.522265i	0.126877	−	0.0339966i
$237$	13.2653	+	8.06471i	0.861676	+	0.523859i
$238$	−18.3313	−	4.01240i	−1.18824	−	0.260085i
$239$	−2.53094	−	2.53094i	−0.163713	−	0.163713i	0.620496	−	0.784209i	$-0.286931\pi$
$239$	−2.53094	−	2.53094i	−0.163713	−	0.163713i	−0.784209	+	0.620496i	$0.786931\pi$
$240$	−3.42377	−	1.00103i	−0.221003	−	0.0646160i
$241$	−2.81958	+	10.5228i	−0.181625	+	0.677834i	0.813703	+	0.581281i	$0.197448\pi$
$241$	−2.81958	+	10.5228i	−0.181625	+	0.677834i	−0.995328	+	0.0965526i	$0.969218\pi$
$242$	−1.65861	−	0.444423i	−0.106619	−	0.0285686i
$243$	1.76149	−	15.4886i	0.112999	−	0.993595i
$244$			1.77508i			0.113638i
$245$	2.42718	−	14.2105i	0.155067	−	0.907875i
$246$	6.70601	−	11.0305i	0.427560	−	0.703277i
$247$	3.69086	−	20.4620i	0.234844	−	1.30196i
$248$	7.45101	−	4.30184i	0.473140	−	0.273167i
$249$	14.3985	−	13.7606i	0.912467	−	0.872044i
$250$	5.92982	−	10.2707i	0.375034	−	0.649579i
$251$	−11.3906			−0.718967			−0.359483	−	0.933151i	$-0.617047\pi$
$251$	−11.3906			−0.718967			−0.359483	+	0.933151i	$0.617047\pi$
$252$	3.96162	−	6.87790i	0.249559	−	0.433267i
$253$	−15.7838	+	15.7838i	−0.992317	+	0.992317i
$254$	−2.02976	−	7.57516i	−0.127358	−	0.475308i
$255$	−18.2904	+	17.4801i	−1.14539	+	1.09465i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.02138	−	5.23318i	0.188468	−	0.326437i	−0.756271	−	0.654258i	$-0.772981\pi$
$257$	3.02138	−	5.23318i	0.188468	−	0.326437i	0.944740	+	0.327821i	$0.106314\pi$
$258$	−0.721075	+	0.175810i	−0.0448922	+	0.0109455i
$259$	−13.8565	+	15.2034i	−0.861001	+	0.944691i
$260$	−6.98762	+	2.51227i	−0.433354	+	0.155805i
$261$	0.0462262	−	1.01983i	0.00286133	−	0.0631256i
$262$	13.2756	+	3.55719i	0.820171	+	0.219764i
$263$	−11.9684	+	6.90998i	−0.738006	+	0.426088i	−0.821344	−	0.570434i	$-0.806775\pi$
$263$	−11.9684	+	6.90998i	−0.738006	+	0.426088i	0.0833381	+	0.996521i	$0.473442\pi$
$264$	−2.96641	−	5.41773i	−0.182570	−	0.333438i
$265$	9.65571	−	9.65571i	0.593146	−	0.593146i
$266$	13.5522	+	7.00871i	0.830940	+	0.429732i
$267$	3.91380	−	0.954252i	0.239521	−	0.0583993i
$268$	−11.7315	+	3.14344i	−0.716613	+	0.192016i
$269$	−18.7675	+	10.8354i	−1.14428	+	0.660648i	−0.947486	−	0.319798i	$-0.896385\pi$
$269$	−18.7675	+	10.8354i	−1.14428	+	0.660648i	−0.196790	+	0.980446i	$0.563052\pi$
$270$	−4.70911	−	9.60950i	−0.286587	−	0.584815i
$271$	−2.53065	+	0.678087i	−0.153726	+	0.0411908i	−0.334861	−	0.942267i	$-0.608690\pi$
$271$	−2.53065	+	0.678087i	−0.153726	+	0.0411908i	0.181135	+	0.983458i	$0.442023\pi$
$272$	−7.09260			−0.430052
$273$	−1.76470	−	16.4282i	−0.106804	−	0.994280i
$274$	−11.6743			−0.705271
$275$	2.61302	−	0.700158i	0.157571	−	0.0422211i
$276$	−10.8388	−	0.245522i	−0.652418	−	0.0147787i
$277$	−1.39339	+	0.804475i	−0.0837208	+	0.0483362i	−0.541276	−	0.840845i	$-0.682059\pi$
$277$	−1.39339	+	0.804475i	−0.0837208	+	0.0483362i	0.457555	+	0.889181i	$0.348725\pi$
$278$	−20.6759	+	5.54008i	−1.24006	+	0.332272i
$279$	24.6035	+	7.80247i	1.47297	+	0.467122i
$280$	−0.252273	−	5.44300i	−0.0150762	−	0.325281i
$281$	−7.24549	+	7.24549i	−0.432230	+	0.432230i	−0.889386	−	0.457156i	$-0.848868\pi$
$281$	−7.24549	+	7.24549i	−0.432230	+	0.432230i	0.457156	+	0.889386i	$0.348868\pi$
$282$	−2.36721	+	1.29614i	−0.140965	+	0.0771838i
$283$	−9.21099	+	5.31797i	−0.547537	+	0.316120i	−0.748128	−	0.663555i	$-0.769047\pi$
$283$	−9.21099	+	5.31797i	−0.547537	+	0.316120i	0.200591	+	0.979675i	$0.435714\pi$
$284$	2.03755	+	0.545961i	0.120907	+	0.0323968i
$285$	18.0429	−	9.87917i	1.06877	−	0.585191i
$286$	−11.6317	−	5.47963i	−0.687796	−	0.324017i
$287$	19.2628	+	4.21628i	1.13704	+	0.248879i
$288$	0.906875	−	2.85965i	0.0534381	−	0.168506i
$289$	−16.6525	+	28.8429i	−0.979557	+	1.69664i
$290$	−0.350409	−	0.606927i	−0.0205767	−	0.0356400i
$291$	−20.1845	−	21.1201i	−1.18324	−	1.23808i
$292$	1.14879	+	4.28734i	0.0672277	+	0.250897i
$293$	−13.4623	+	13.4623i	−0.786477	+	0.786477i	−0.980915	−	0.194438i	$-0.937712\pi$
$293$	−13.4623	+	13.4623i	−0.786477	+	0.786477i	0.194438	+	0.980915i	$0.437712\pi$
$294$	11.9020	+	2.31143i	0.694138	+	0.134805i
$295$	4.15576			0.241957
$296$	−3.88746	+	6.73327i	−0.225954	+	0.391363i
$297$	6.00004	−	17.5317i	0.348158	−	1.01729i
$298$	7.52503	−	4.34458i	0.435913	−	0.251675i
$299$	−18.5377	+	12.8721i	−1.07206	+	0.744413i
$300$	1.12271	+	0.682556i	0.0648197	+	0.0394074i
$301$	−0.611713	−	0.954538i	−0.0352586	−	0.0550187i
$302$			4.58188i			0.263658i
$303$	−29.1232	+	15.9460i	−1.67308	+	0.916076i
$304$	5.57022	+	1.49254i	0.319474	+	0.0856028i
$305$	−0.946171	+	3.53116i	−0.0541776	+	0.202193i
$306$	−14.3490	−	15.7115i	−0.820275	−	0.898168i
$307$	−19.3297	−	19.3297i	−1.10320	−	1.10320i	−0.994022	−	0.109180i	$-0.965178\pi$
$307$	−19.3297	−	19.3297i	−1.10320	−	1.10320i	−0.109180	−	0.994022i	$-0.534822\pi$
$308$	6.35554	−	6.97330i	0.362140	−	0.397341i
$309$	−7.23998	+	11.9088i	−0.411868	+	0.677467i
$310$	17.1153	−	4.58602i	0.972082	−	0.260469i
$311$	−3.15032	−	5.45652i	−0.178639	−	0.309411i	0.762776	−	0.646663i	$-0.223836\pi$
$311$	−3.15032	−	5.45652i	−0.178639	−	0.309411i	−0.941414	+	0.337252i	$0.890503\pi$
$312$	−1.97924	−	5.92306i	−0.112052	−	0.335327i
$313$	11.4585	−	19.8468i	0.647675	−	1.12181i	−0.336002	−	0.941861i	$-0.609075\pi$
$313$	11.4585	−	19.8468i	0.647675	−	1.12181i	0.983677	−	0.179945i	$-0.0575919\pi$
$314$	1.41175	+	1.41175i	0.0796694	+	0.0796694i
$315$	11.5470	−	11.5705i	0.650598	−	0.651924i
$316$			8.96305i			0.504211i
$317$	2.54191	−	0.681102i	0.142768	−	0.0382545i	−0.186727	−	0.982412i	$-0.559788\pi$
$317$	2.54191	−	0.681102i	0.142768	−	0.0382545i	0.329495	+	0.944157i	$0.393121\pi$
$318$	7.93465	+	8.30245i	0.444953	+	0.465578i
$319$	0.314081	−	1.17216i	0.0175851	−	0.0656286i
$320$	−0.533030	−	1.98929i	−0.0297973	−	0.111205i
$321$	0.757766	−	1.24642i	0.0422944	−	0.0695685i
$322$	−5.02226	−	15.7809i	−0.279879	−	0.879433i
$323$	28.9214	−	28.9214i	1.60923	−	1.60923i
$324$	8.16938	−	3.77641i	0.453854	−	0.209801i
$325$	2.72563	−	0.227686i	0.151191	−	0.0126298i
$326$	−14.6499	+	8.45814i	−0.811385	+	0.468453i
$327$	6.44366	−	22.0389i	0.356335	−	1.21876i
$328$	7.45300			0.411523
$329$	−3.04690	−	2.77698i	−0.167981	−	0.153100i
$330$	−3.01325	−	12.3586i	−0.165874	−	0.680321i
$331$	−5.34427	−	19.9451i	−0.293748	−	1.09628i	−0.942207	−	0.335032i	$-0.891253\pi$
$331$	−5.34427	−	19.9451i	−0.293748	−	1.09628i	0.648459	−	0.761250i	$-0.275414\pi$
$332$	11.1070	+	2.97612i	0.609578	+	0.163336i
$333$	−22.7802	+	5.01051i	−1.24835	+	0.274574i
$334$	−3.67851	+	6.37136i	−0.201279	+	0.348626i
$335$	−25.0129			−1.36660
$336$	4.58129	−	0.108445i	0.249930	−	0.00591616i
$337$			34.3237i			1.86973i	0.354999	+	0.934867i	$0.384481\pi$
$337$			34.3237i			1.86973i	−0.354999	+	0.934867i	$0.615519\pi$
$338$	−10.5901	−	7.53985i	−0.576027	−	0.410114i
$339$	−3.95084	−	0.0894948i	−0.214580	−	0.00486069i
$340$	−14.1093	−	3.78057i	−0.765182	−	0.205030i
$341$	26.5711	+	15.3408i	1.43891	+	0.830753i
$342$	7.96278	+	15.3587i	0.430578	+	0.830502i
$343$	2.56503	+	18.3418i	0.138499	+	0.990363i
$344$	−0.303001	−	0.303001i	−0.0163367	−	0.0163367i
$345$	−21.4307	−	6.26581i	−1.15379	−	0.337340i
$346$	−4.06075	+	15.1549i	−0.218307	+	0.814733i
$347$	−11.7055	+	6.75818i	−0.628385	+	0.362798i	−0.780126	−	0.625622i	$-0.784845\pi$
$347$	−11.7055	+	6.75818i	−0.628385	+	0.362798i	0.151741	+	0.988420i	$0.451512\pi$
$348$	0.516979	−	0.283066i	0.0277130	−	0.0151739i
$349$	6.08708	+	6.08708i	0.325834	+	0.325834i	0.851000	−	0.525166i	$-0.175997\pi$
$349$	6.08708	+	6.08708i	0.325834	+	0.325834i	−0.525166	+	0.851000i	$0.675997\pi$
$350$	−0.429145	+	1.96062i	−0.0229388	+	0.104799i
$351$	9.11658	−	16.3673i	0.486607	−	0.873621i
$352$	1.78305	−	3.08834i	0.0950371	−	0.164609i
$353$	6.18263	−	23.0739i	0.329068	−	1.22810i	−0.581090	−	0.813839i	$-0.697374\pi$
$353$	6.18263	−	23.0739i	0.329068	−	1.22810i	0.910159	−	0.414260i	$-0.135960\pi$
$354$	−0.0791504	+	3.49417i	−0.00420680	+	0.185713i
$355$	3.76228	+	2.17215i	0.199681	+	0.115286i
$356$	1.64461	+	1.64461i	0.0871641	+	0.0871641i
$357$	15.5805	−	28.5246i	0.824609	−	1.50968i
$358$	2.40069	+	2.40069i	0.126880	+	0.126880i
$359$	−1.96581	−	7.33651i	−0.103752	−	0.387206i	0.894449	−	0.447170i	$-0.147568\pi$
$359$	−1.96581	−	7.33651i	−0.103752	−	0.387206i	−0.998201	+	0.0599637i	$0.980901\pi$
$360$	3.32832	−	5.20529i	0.175418	−	0.274343i
$361$	−12.3452	+	7.12749i	−0.649746	+	0.375131i
$362$	5.54150	+	20.6812i	0.291255	+	1.08698i
$363$	1.54502	−	2.54134i	0.0810923	−	0.133386i
$364$	7.57532	−	5.79780i	0.397055	−	0.303887i
$365$			9.14111i			0.478468i
$366$	−2.95098	−	0.862797i	−0.154250	−	0.0450991i
$367$	6.10777	+	10.5790i	0.318823	+	0.552218i	0.980243	−	0.197798i	$-0.0633791\pi$
$367$	6.10777	+	10.5790i	0.318823	+	0.552218i	−0.661420	+	0.750016i	$0.730046\pi$
$368$	−3.12969	−	5.42078i	−0.163146	−	0.282578i
$369$	15.0781	+	16.5099i	0.784934	+	0.859471i
$370$	−11.3223	+	11.3223i	−0.588620	+	0.588620i
$371$	−8.05850	+	15.5821i	−0.418376	+	0.808983i
$372$	3.52996	+	14.4779i	0.183020	+	0.750644i
$373$	2.63091	−	4.55686i	0.136223	−	0.235945i	−0.789841	−	0.613312i	$-0.789837\pi$
$373$	2.63091	−	4.55686i	0.136223	−	0.235945i	0.926064	+	0.377366i	$0.123170\pi$
$374$	−12.6465	−	21.9043i	−0.653934	−	1.13265i
$375$	14.1924	+	14.8502i	0.732890	+	0.766863i
$376$	−1.34941	−	0.779084i	−0.0695907	−	0.0401782i
$377$	0.522886	−	1.10994i	0.0269300	−	0.0571647i
$378$	9.50859	+	9.92909i	0.489069	+	0.510697i
$379$	−10.6483	+	10.6483i	−0.546967	+	0.546967i	−0.925562	−	0.378595i	$-0.876407\pi$
$379$	−10.6483	+	10.6483i	−0.546967	+	0.546967i	0.378595	+	0.925562i	$0.376407\pi$
$380$	10.2852	+	5.93818i	0.527622	+	0.304622i
$381$	13.5799	+	0.307614i	0.695720	+	0.0157595i
$382$	−7.10416	−	1.90355i	−0.363481	−	0.0973943i
$383$	−15.2019	+	4.07334i	−0.776781	+	0.208138i	−0.625365	−	0.780332i	$-0.715050\pi$
$383$	−15.2019	+	4.07334i	−0.776781	+	0.208138i	−0.151416	+	0.988470i	$0.548383\pi$
$384$	1.68276	−	0.410285i	0.0858728	−	0.0209373i
$385$	16.3600	−	10.4843i	0.833783	−	0.534328i
$386$			9.26910i			0.471785i
$387$	0.0582099	−	1.28421i	0.00295898	−	0.0652799i
$388$	4.36546	−	16.2921i	0.221623	−	0.827108i
$389$	7.87823	+	13.6455i	0.399442	+	0.691854i	0.993657	−	0.112452i	$-0.0358705\pi$
$389$	7.87823	+	13.6455i	0.399442	+	0.691854i	−0.594215	+	0.804306i	$0.702537\pi$
$390$	−0.780122	−	12.8377i	−0.0395030	−	0.650062i
$391$	−44.3953			−2.24516
$392$	2.42939	+	6.56491i	0.122703	+	0.331578i
$393$	−12.3664	+	20.3411i	−0.623804	+	1.02607i
$394$	16.7688	+	9.68146i	0.844799	+	0.487745i
$395$	−4.77757	+	17.8301i	−0.240386	+	0.897132i
$396$	10.4486	−	2.29816i	0.525060	−	0.115487i
$397$	9.76195	−	2.61571i	0.489938	−	0.131279i	−0.00538814	−	0.999985i	$-0.501715\pi$
$397$	9.76195	−	2.61571i	0.489938	−	0.131279i	0.495326	+	0.868707i	$0.335048\pi$
$398$	4.61658	−	4.61658i	0.231408	−	0.231408i
$399$	−18.2389	+	19.1233i	−0.913085	+	0.957360i
$400$			0.758587i			0.0379293i
$401$	8.56867	+	31.9787i	0.427899	+	1.59694i	0.757510	+	0.652824i	$0.226416\pi$
$401$	8.56867	+	31.9787i	0.427899	+	1.59694i	−0.329611	+	0.944117i	$0.606918\pi$
$402$	0.476394	−	21.0309i	0.0237604	−	1.04893i
$403$	23.6851	+	20.0331i	1.17984	+	0.997918i
$404$	−16.6015	−	9.58488i	−0.825955	−	0.476865i
$405$	18.2642	−	3.15787i	0.907557	−	0.156916i
$406$	0.665418	+	0.606469i	0.0330242	+	0.0300985i
$407$	−27.7262			−1.37434
$408$	3.44743	−	11.7911i	0.170673	−	0.583746i
$409$	21.5139	+	5.76463i	1.06379	+	0.285042i	0.747940	−	0.663766i	$-0.231043\pi$
$409$	21.5139	+	5.76463i	1.06379	+	0.285042i	0.315852	+	0.948808i	$0.397710\pi$
$410$	14.8262	+	3.97267i	0.732215	+	0.196196i
$411$	5.67443	−	19.4080i	0.279899	−	0.957326i
$412$	−8.04646			−0.396420
$413$	−5.08738	+	1.61906i	−0.250334	+	0.0796686i
$414$	5.67648	−	17.8996i	0.278984	−	0.879718i
$415$	20.5088	+	11.8408i	1.00674	+	0.581240i
$416$	2.32843	−	2.75290i	0.114160	−	0.134972i
$417$	0.839611	−	37.0655i	0.0411160	−	1.81510i
$418$	5.32254	+	19.8640i	0.260334	+	0.971580i
$419$		−	2.14134i		−	0.104611i	−0.998631	−	0.0523057i	$-0.983343\pi$
$419$		−	2.14134i		−	0.104611i	0.998631	−	0.0523057i	$-0.0166570\pi$
$420$	9.17134	+	2.22624i	0.447516	+	0.108629i
$421$	−4.67526	+	4.67526i	−0.227858	+	0.227858i	−0.811797	−	0.583939i	$-0.801511\pi$
$421$	−4.67526	+	4.67526i	−0.227858	+	0.227858i	0.583939	+	0.811797i	$0.301511\pi$
$422$	8.40006	−	2.25079i	0.408908	−	0.109567i
$423$	−1.00416	−	4.56538i	−0.0488237	−	0.221976i
$424$	−1.71609	+	6.40454i	−0.0833408	+	0.311032i
$425$	4.65952	+	2.69018i	0.226020	+	0.130493i
$426$	−1.89801	+	3.12197i	−0.0919589	+	0.151260i
$427$	−0.217437	−	4.69138i	−0.0105225	−	0.227032i
$428$	0.842175			0.0407081
$429$	14.7633	−	16.6737i	0.712780	−	0.805013i
$430$	−0.441250	−	0.764267i	−0.0212790	−	0.0368562i
$431$	−5.81075	+	21.6860i	−0.279894	+	1.04458i	0.672596	+	0.740009i	$0.265179\pi$
$431$	−5.81075	+	21.6860i	−0.279894	+	1.04458i	−0.952490	+	0.304569i	$0.901488\pi$
$432$	4.31323	+	2.89760i	0.207520	+	0.139411i
$433$			21.9443i			1.05458i	0.849687	+	0.527288i	$0.176791\pi$
$433$			21.9443i			1.05458i	−0.849687	+	0.527288i	$0.823209\pi$
$434$	−19.1654	+	12.2821i	−0.919970	+	0.589560i
$435$	1.17931	−	0.287535i	0.0565434	−	0.0137863i
$436$	12.8052	−	3.43114i	0.613257	−	0.164322i
$437$	34.8661	+	9.34235i	1.66787	+	0.446905i
$438$	−7.68587	−	0.174101i	−0.367245	−	0.00831888i
$439$	−5.76484	−	3.32833i	−0.275141	−	0.158853i	0.356081	−	0.934455i	$-0.384113\pi$
$439$	−5.76484	−	3.32833i	−0.275141	−	0.158853i	−0.631222	+	0.775603i	$0.717446\pi$
$440$	5.19319	−	5.19319i	0.247576	−	0.247576i
$441$	−9.62773	+	18.6630i	−0.458463	+	0.888713i
$442$	−8.65200	−	24.0646i	−0.411534	−	1.14464i
$443$	−12.0003	−	6.92836i	−0.570150	−	0.329176i	0.187059	−	0.982349i	$-0.440104\pi$
$443$	−12.0003	−	6.92836i	−0.570150	−	0.329176i	−0.757209	+	0.653172i	$0.773438\pi$
$444$	−9.30420	−	9.73549i	−0.441558	−	0.462026i
$445$	2.39499	+	4.14824i	0.113533	+	0.196645i
$446$	−1.94159	+	3.36293i	−0.0919369	+	0.159239i
$447$	3.56503	+	14.6217i	0.168620	+	0.691584i
$448$	1.42754	+	2.22758i	0.0674449	+	0.105243i
$449$	−0.760702	+	0.760702i	−0.0358998	+	0.0358998i	−0.724829	−	0.688929i	$-0.758081\pi$
$449$	−0.760702	+	0.760702i	−0.0358998	+	0.0358998i	0.688929	+	0.724829i	$0.258081\pi$
$450$	−1.68042	+	1.53469i	−0.0792158	+	0.0723459i
$451$	13.2891	+	23.0174i	0.625759	+	1.08385i
$452$	−1.14080	−	1.97592i	−0.0536587	−	0.0929397i
$453$	−7.61716	−	2.22707i	−0.357885	−	0.104637i
$454$			15.0993i			0.708647i
$455$	18.1599	−	7.49567i	0.851351	−	0.351402i
$456$	−5.18873	+	8.53475i	−0.242985	+	0.399676i
$457$	−4.74912	−	17.7240i	−0.222155	−	0.829092i	−0.983525	−	0.180775i	$-0.942140\pi$
$457$	−4.74912	−	17.7240i	−0.222155	−	0.829092i	0.761370	−	0.648318i	$-0.224527\pi$
$458$	−1.05340	+	0.608181i	−0.0492221	+	0.0284184i
$459$	33.0941	−	16.2177i	1.54470	−	0.756977i
$460$	−3.33644	−	12.4517i	−0.155562	−	0.580566i
$461$	12.6810	+	12.6810i	0.590615	+	0.590615i	0.937797	−	0.347183i	$-0.112862\pi$
$461$	12.6810	+	12.6810i	0.590615	+	0.590615i	−0.347183	+	0.937797i	$0.612862\pi$
$462$	8.50360	+	13.9552i	0.395623	+	0.649256i
$463$	−18.1175	−	18.1175i	−0.841992	−	0.841992i	0.147126	−	0.989118i	$-0.452998\pi$
$463$	−18.1175	−	18.1175i	−0.841992	−	0.841992i	−0.989118	+	0.147126i	$0.952998\pi$
$464$	0.294701	+	0.170145i	0.0136811	+	0.00789881i
$465$	−0.695022	+	30.6824i	−0.0322309	+	1.42286i
$466$	−1.58840	+	5.92797i	−0.0735810	+	0.274608i
$467$	12.7135	−	22.0204i	0.588310	−	1.01898i	−0.406144	−	0.913809i	$-0.633127\pi$
$467$	12.7135	−	22.0204i	0.588310	−	1.01898i	0.994454	−	0.105174i	$-0.0335399\pi$
$468$	10.8088	−	0.411422i	0.499638	−	0.0190180i
$469$	30.6202	−	9.74487i	1.41391	−	0.449976i
$470$	−2.26911	−	2.26911i	−0.104666	−	0.104666i
$471$	−3.03315	+	1.66076i	−0.139760	+	0.0765240i
$472$	−1.74753	+	1.00894i	−0.0804367	+	0.0464402i
$473$	0.395503	−	1.47604i	0.0181853	−	0.0678683i
$474$	−14.9006	−	4.35659i	−0.684409	−	0.200105i
$475$	−3.09328	−	3.09328i	−0.141929	−	0.141929i
$476$	18.7451	−	0.868803i	0.859181	−	0.0398215i
$477$	−17.6591	+	9.15547i	−0.808557	+	0.419200i
$478$	3.09975	+	1.78964i	0.141779	+	0.0818564i
$479$	−13.3811	−	3.58545i	−0.611397	−	0.163823i	−0.0601830	−	0.998187i	$-0.519168\pi$
$479$	−13.3811	−	3.58545i	−0.611397	−	0.163823i	−0.551214	+	0.834364i	$0.685835\pi$
$480$	3.56619	+	0.0807818i	0.162774	+	0.00368717i
$481$	−27.5876	−	4.97617i	−1.25789	−	0.226894i
$482$		−	10.8940i		−	0.496209i
$483$	28.6760	−	0.678798i	1.30481	−	0.0308864i
$484$	1.71712			0.0780508
$485$	17.3684	−	30.0829i	0.788658	−	1.36600i
$486$	2.30728	+	15.4168i	0.104660	+	0.699318i
$487$	13.6294	+	3.65198i	0.617606	+	0.165487i	0.554039	−	0.832490i	$-0.313086\pi$
$487$	13.6294	+	3.65198i	0.617606	+	0.165487i	0.0635670	+	0.997978i	$0.479752\pi$
$488$	−0.459425	−	1.71460i	−0.0207972	−	0.0776161i
$489$	−6.94050	−	28.4660i	−0.313860	−	1.28728i
$490$	1.33347	+	14.3545i	0.0602402	+	0.648469i
$491$	33.7611			1.52362			0.761809	−	0.647802i	$-0.224312\pi$
$491$	33.7611			1.52362			0.761809	+	0.647802i	$0.224312\pi$
$492$	−3.62261	+	12.3903i	−0.163320	+	0.558596i
$493$	2.09019	−	1.20677i	0.0941375	−	0.0543503i
$494$	1.73085	+	20.7200i	0.0778747	+	0.932237i
$495$	22.0103	+	0.997671i	0.989288	+	0.0448420i
$496$	−6.08373	+	6.08373i	−0.273167	+	0.273167i
$497$	−5.45196	−	1.19334i	−0.244554	−	0.0535286i
$498$	−10.3464	+	17.0183i	−0.463631	+	0.762610i
$499$	2.17585	+	8.12039i	0.0974045	+	0.363519i	0.997373	−	0.0724362i	$-0.0230774\pi$
$499$	2.17585	+	8.12039i	0.0974045	+	0.363519i	−0.899968	+	0.435955i	$0.856411\pi$
$500$	−3.06950	+	11.4555i	−0.137272	+	0.512307i
$501$	−8.80410	−	9.21221i	−0.393338	−	0.411571i
$502$	11.0025	−	2.94810i	0.491064	−	0.131580i
$503$		−	15.3123i		−	0.682741i	−0.939929	−	0.341371i	$-0.889109\pi$
$503$		−	15.3123i		−	0.682741i	0.939929	−	0.341371i	$-0.110891\pi$
$504$	−2.04650	+	7.66889i	−0.0911585	+	0.341599i
$505$	−27.9162	−	27.9162i	−1.24226	−	1.24226i
$506$	11.1608	−	19.3311i	0.496158	−	0.859372i
$507$	17.6821	−	13.9407i	0.785289	−	0.619130i
$508$	3.92119	+	6.79170i	0.173975	+	0.301333i
$509$	−38.1303	+	10.2170i	−1.69010	+	0.452860i	−0.970415	−	0.241444i	$-0.922379\pi$
$509$	−38.1303	+	10.2170i	−1.69010	+	0.452860i	−0.719681	+	0.694304i	$0.755712\pi$
$510$	13.1430	−	21.6184i	0.581980	−	0.957278i
$511$	−3.56132	−	11.1903i	−0.157544	−	0.495031i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−29.4035	+	5.77249i	−1.29819	+	0.254861i
$514$	−1.56398	+	5.83685i	−0.0689842	+	0.257452i
$515$	−16.0068	−	4.28900i	−0.705343	−	0.188996i
$516$	0.651002	−	0.356448i	0.0286588	−	0.0156917i
$517$		−	5.55660i		−	0.244379i
$518$	9.44943	−	18.2717i	0.415184	−	0.802810i
$519$	−23.2205	−	14.1170i	−1.01927	−	0.619668i
$520$	6.09930	−	4.23520i	0.267472	−	0.185726i
$521$	−4.76089	+	2.74870i	−0.208579	+	0.120423i	−0.600651	−	0.799512i	$-0.705092\pi$
$521$	−4.76089	+	2.74870i	−0.208579	+	0.120423i	0.392072	+	0.919935i	$0.371758\pi$
$522$	0.219299	+	0.997040i	0.00959847	+	0.0436393i
$523$	19.2984	−	33.4258i	0.843860	−	1.46161i	−0.0427471	−	0.999086i	$-0.513611\pi$
$523$	19.2984	−	33.4258i	0.843860	−	1.46161i	0.886607	−	0.462523i	$-0.153056\pi$
$524$	−13.7439			−0.600407
$525$	−3.05084	−	1.66641i	−0.133149	−	0.0727281i
$526$	9.77219	−	9.77219i	0.426088	−	0.426088i
$527$	15.7938	+	58.9432i	0.687988	+	2.56761i
$528$	4.26754	+	4.46536i	0.185721	+	0.194330i
$529$	−8.08992	−	14.0121i	−0.351736	−	0.609224i
$530$	−6.82762	+	11.8258i	−0.296573	+	0.513679i
$531$	−5.77042	−	1.82996i	−0.250415	−	0.0794136i
$532$	−14.9044	−	3.26232i	−0.646189	−	0.141440i
$533$	9.09165	+	25.2875i	0.393803	+	1.09532i
$534$	−3.53346	+	1.93470i	−0.152908	+	0.0837228i
$535$	1.67533	+	0.448905i	0.0724310	+	0.0194078i
$536$	10.5181	−	6.07265i	0.454314	−	0.262299i
$537$	−5.15790	+	2.82415i	−0.222580	+	0.121871i
$538$	15.3236	−	15.3236i	0.660648	−	0.660648i
$539$	−15.9429	+	19.2084i	−0.686711	+	0.827363i
$540$	7.03577	+	8.06325i	0.302771	+	0.346987i
$541$	−29.9159	+	8.01593i	−1.28618	+	0.344632i	−0.836209	−	0.548410i	$-0.815233\pi$
$541$	−29.9159	+	8.01593i	−1.28618	+	0.344632i	−0.449973	+	0.893042i	$0.648567\pi$
$542$	2.26892	−	1.30996i	0.0974586	−	0.0562677i
$543$	−37.0749	−	0.839826i	−1.59104	−	0.0360404i
$544$	6.85092	−	1.83570i	0.293731	−	0.0787049i
$545$	27.3022			1.16950
$546$	5.95650	+	15.4117i	0.254915	+	0.659559i
$547$	31.8987			1.36389			0.681944	−	0.731404i	$-0.261135\pi$
$547$	31.8987			1.36389			0.681944	+	0.731404i	$0.261135\pi$
$548$	11.2765	−	3.02154i	0.481709	−	0.129074i
$549$	2.86872	−	4.48650i	0.122434	−	0.191479i
$550$	−2.34277	+	1.35260i	−0.0998962	+	0.0576751i
$551$	−1.89549	+	0.507896i	−0.0807508	+	0.0216371i
$552$	10.5330	−	2.56813i	0.448315	−	0.109307i
$553$	−1.09792	−	23.6886i	−0.0466884	−	1.00734i
$554$	1.13770	−	1.13770i	0.0483362	−	0.0483362i
$555$	−13.3195	−	24.3262i	−0.565381	−	1.03259i
$556$	18.5375	−	10.7026i	0.786164	−	0.453892i
$557$	25.1839	+	6.74800i	1.06708	+	0.285922i	0.749291	−	0.662241i	$-0.230395\pi$
$557$	25.1839	+	6.74800i	1.06708	+	0.285922i	0.317784	+	0.948163i	$0.397061\pi$
$558$	−25.7846	−	1.16875i	−1.09155	−	0.0494772i
$559$	0.658440	−	1.39768i	0.0278490	−	0.0591156i
$560$	1.65243	+	5.19224i	0.0698279	+	0.219412i
$561$	42.5619	−	10.3773i	1.79696	−	0.438131i
$562$	5.12334	−	8.87388i	0.216115	−	0.374322i
$563$	16.1891	+	28.0403i	0.682289	+	1.18176i	0.974281	+	0.225339i	$0.0723488\pi$
$563$	16.1891	+	28.0403i	0.682289	+	1.18176i	−0.291991	+	0.956421i	$0.594318\pi$
$564$	1.95109	−	1.86465i	0.0821556	−	0.0785160i
$565$	−1.21616	−	4.53878i	−0.0511643	−	0.190948i
$566$	7.52074	−	7.52074i	0.316120	−	0.316120i
$567$	−21.1284	+	10.9814i	−0.887308	+	0.461177i
$568$	−2.10943			−0.0885098
$569$	7.24779	−	12.5535i	0.303843	−	0.526272i	−0.673160	−	0.739497i	$-0.735063\pi$
$569$	7.24779	−	12.5535i	0.303843	−	0.526272i	0.977003	+	0.213225i	$0.0683967\pi$
$570$	−14.8712	+	14.2124i	−0.622886	+	0.595291i
$571$	15.0070	−	8.66430i	0.628024	−	0.362590i	−0.151963	−	0.988386i	$-0.548559\pi$
$571$	15.0070	−	8.66430i	0.628024	−	0.362590i	0.779986	+	0.625797i	$0.215226\pi$
$572$	12.6536	+	2.28241i	0.529073	+	0.0954323i
$573$	6.61762	−	10.8851i	0.276455	−	0.454731i
$574$	−19.6976	+	0.912951i	−0.822164	+	0.0381059i
$575$			4.74828i			0.198017i
$576$	−0.135843	+	2.99692i	−0.00566013	+	0.124872i
$577$	−44.5096	−	11.9263i	−1.85296	−	0.496498i	−0.853269	−	0.521471i	$-0.825383\pi$
$577$	−44.5096	−	11.9263i	−1.85296	−	0.496498i	−0.999688	+	0.0249728i	$0.992050\pi$
$578$	8.61995	−	32.1701i	0.358543	−	1.33810i
$579$	−15.4094	−	4.50535i	−0.640394	−	0.187236i
$580$	0.495554	+	0.495554i	0.0205767	+	0.0205767i
$581$	−29.7195	−	6.50509i	−1.23297	−	0.269876i
$582$	24.9630	+	15.1763i	1.03475	+	0.629079i
$583$	−22.8393	+	6.11976i	−0.945906	+	0.253455i
$584$	−2.21929	−	3.84392i	−0.0918348	−	0.159063i
$585$	21.7212	+	4.94299i	0.898063	+	0.204367i
$586$	9.51930	−	16.4879i	0.393239	−	0.681109i
$587$	−18.9172	−	18.9172i	−0.780798	−	0.780798i	0.199168	−	0.979965i	$-0.436176\pi$
$587$	−18.9172	−	18.9172i	−0.780798	−	0.780798i	−0.979965	+	0.199168i	$0.936176\pi$
$588$	−12.0947	+	0.847793i	−0.498776	+	0.0349624i
$589$		−	49.6150i		−	2.04435i
$590$	−4.01415	+	1.07559i	−0.165260	+	0.0442813i
$591$	−24.2456	+	23.1715i	−0.997331	+	0.953149i
$592$	2.01230	−	7.50999i	0.0827048	−	0.308659i
$593$	3.72678	+	13.9085i	0.153041	+	0.571156i	0.999265	+	0.0383291i	$0.0122035\pi$
$593$	3.72678	+	13.9085i	0.153041	+	0.571156i	−0.846224	+	0.532827i	$0.821130\pi$
$594$	−1.25805	+	18.4873i	−0.0516184	+	0.758542i
$595$	37.7527	+	8.26340i	1.54771	+	0.338767i
$596$	−6.14416	+	6.14416i	−0.251675	+	0.251675i
$597$	5.43090	+	9.91878i	0.222272	+	0.405949i
$598$	14.5745	−	17.2314i	0.595996	−	0.704645i
$599$	21.9183	−	12.6546i	0.895559	−	0.517051i	0.0198021	−	0.999804i	$-0.493696\pi$
$599$	21.9183	−	12.6546i	0.895559	−	0.517051i	0.875757	+	0.482753i	$0.160363\pi$
$600$	−1.26111	−	0.368719i	−0.0514848	−	0.0150529i
$601$	7.33163			0.299063			0.149532	−	0.988757i	$-0.452223\pi$
$601$	7.33163			0.299063			0.149532	+	0.988757i	$0.452223\pi$
$602$	0.837922	+	0.763690i	0.0341512	+	0.0311257i
$603$	34.7313	+	11.0143i	1.41437	+	0.448536i
$604$	−1.18588	−	4.42576i	−0.0482527	−	0.180082i
$605$	3.41585	+	0.915275i	0.138874	+	0.0372112i
$606$	24.0037	−	22.9403i	0.975085	−	0.931888i
$607$	−10.8473	+	18.7881i	−0.440279	+	0.762585i	−0.997710	−	0.0676378i	$-0.978454\pi$
$607$	−10.8473	+	18.7881i	−0.440279	+	0.762585i	0.557431	+	0.830223i	$0.311787\pi$
$608$	−5.76671			−0.233871
$609$	−1.33166	+	0.811445i	−0.0539615	+	0.0328814i
$610$		−	3.65572i		−	0.148016i
$611$	0.997272	−	5.52883i	0.0403453	−	0.223673i
$612$	17.9265	+	11.4624i	0.724634	+	0.463339i
$613$	−23.3751	−	6.26334i	−0.944111	−	0.252974i	−0.246250	−	0.969206i	$-0.579198\pi$
$613$	−23.3751	−	6.26334i	−0.944111	−	0.252974i	−0.697862	+	0.716233i	$0.745865\pi$
$614$	23.6739	+	13.6681i	0.955401	+	0.551601i
$615$	−13.8108	+	22.7169i	−0.556906	+	0.916034i
$616$	−4.33415	+	8.38063i	−0.174628	+	0.337665i
$617$	25.9111	+	25.9111i	1.04314	+	1.04314i	0.999026	+	0.0441149i	$0.0140468\pi$
$617$	25.9111	+	25.9111i	1.04314	+	1.04314i	0.0441149	+	0.999026i	$0.485953\pi$
$618$	3.91107	−	13.3768i	0.157326	−	0.538095i
$619$	8.48353	−	31.6610i	0.340982	−	1.27256i	−0.556255	−	0.831012i	$-0.687762\pi$
$619$	8.48353	−	31.6610i	0.340982	−	1.27256i	0.897237	−	0.441550i	$-0.145571\pi$
$620$	−15.3451	+	8.85952i	−0.616275	+	0.355807i
$621$	26.9981	+	18.1372i	1.08340	+	0.727819i
$622$	4.45523	+	4.45523i	0.178639	+	0.178639i
$623$	−4.54801	−	4.14510i	−0.182212	−	0.166070i
$624$	3.44480	+	5.20897i	0.137902	+	0.208526i
$625$	−10.3158	+	17.8675i	−0.412632	+	0.714700i
$626$	−5.93138	+	22.1362i	−0.237066	+	0.884741i
$627$	−35.6100	−	0.806642i	−1.42213	−	0.0322142i
$628$	−1.72903	−	0.998255i	−0.0689958	−	0.0398347i
$629$	−38.9929	−	38.9929i	−1.55475	−	1.55475i
$630$	−8.15884	+	14.1648i	−0.325056	+	0.564340i
$631$	28.5560	+	28.5560i	1.13680	+	1.13680i	0.989021	+	0.147776i	$0.0472116\pi$
$631$	28.5560	+	28.5560i	1.13680	+	1.13680i	0.147776	+	0.989021i	$0.452788\pi$
$632$	−2.31981	−	8.65764i	−0.0922770	−	0.344382i
$633$	−0.341112	+	15.0587i	−0.0135580	+	0.598530i
$634$	−2.27901	+	1.31579i	−0.0905111	+	0.0522566i
$635$	4.18022	+	15.6008i	0.165887	+	0.619099i
$636$	−9.81311	−	5.96591i	−0.389115	−	0.236564i
$637$	−19.3107	+	16.2510i	−0.765119	+	0.643889i
$638$			1.21351i			0.0480435i
$639$	−4.26757	−	4.67281i	−0.168822	−	0.184854i
$640$	1.02973	+	1.78355i	0.0407038	+	0.0705011i
$641$	−18.5105	−	32.0611i	−0.731121	−	1.26634i	−0.956405	−	0.292045i	$-0.905664\pi$
$641$	−18.5105	−	32.0611i	−0.731121	−	1.26634i	0.225284	−	0.974293i	$-0.427669\pi$
$642$	−0.409348	+	1.40008i	−0.0161557	+	0.0552566i
$643$	−19.7152	+	19.7152i	−0.777493	+	0.777493i	−0.979404	−	0.201911i	$-0.935285\pi$
$643$	−19.7152	+	19.7152i	−0.777493	+	0.777493i	0.201911	+	0.979404i	$0.435285\pi$
$644$	8.93552	+	13.9433i	0.352109	+	0.549443i
$645$	1.48503	−	0.362076i	0.0584731	−	0.0142567i
$646$	−20.4505	+	35.4213i	−0.804614	+	1.39363i
$647$	−11.4313	−	19.7996i	−0.449412	−	0.778404i	0.548936	−	0.835864i	$-0.315033\pi$
$647$	−11.4313	−	19.7996i	−0.449412	−	0.778404i	−0.998348	+	0.0574606i	$0.981700\pi$
$648$	−6.91361	+	5.76212i	−0.271592	+	0.226358i
$649$	−6.23189	−	3.59798i	−0.244623	−	0.141233i
$650$	−2.57383	+	0.925373i	−0.100954	+	0.0362961i
$651$	−11.1029	−	37.8315i	−0.435155	−	1.48273i
$652$	11.9616	−	11.9616i	0.468453	−	0.468453i
$653$	17.2294	+	9.94739i	0.674238	+	0.389271i	0.797680	−	0.603080i	$-0.206060\pi$
$653$	17.2294	+	9.94739i	0.674238	+	0.389271i	−0.123443	+	0.992352i	$0.539394\pi$
$654$	−0.519996	+	22.9557i	−0.0203335	+	0.897640i
$655$	−27.3408	−	7.32593i	−1.06829	−	0.286248i
$656$	−7.19905	+	1.92898i	−0.281076	+	0.0753140i
$657$	4.02523	−	12.6928i	0.157039	−	0.495192i
$658$	3.66182	+	1.89376i	0.142753	+	0.0738263i
$659$		−	26.2057i		−	1.02083i	−0.859929	−	0.510414i	$-0.829492\pi$
$659$		−	26.2057i		−	1.02083i	0.859929	−	0.510414i	$-0.170508\pi$
$660$	6.10923	+	11.1576i	0.237801	+	0.434311i
$661$	4.35027	−	16.2354i	0.169206	−	0.631485i	−0.828260	−	0.560343i	$-0.810669\pi$
$661$	4.35027	−	16.2354i	0.169206	−	0.631485i	0.997466	−	0.0711414i	$-0.0226642\pi$
$662$	10.3243	+	17.8823i	0.401267	+	0.695015i
$663$	44.2117	−	2.68666i	1.71704	−	0.104341i
$664$	−11.4989			−0.446242
$665$	−27.9104	−	14.4342i	−1.08232	−	0.559735i
$666$	20.7072	−	10.7357i	0.802387	−	0.416001i
$667$	1.84464	+	1.06501i	0.0714249	+	0.0412372i
$668$	1.90414	−	7.10633i	0.0736732	−	0.274952i
$669$	−4.64698	−	4.86239i	−0.179663	−	0.187991i
$670$	24.1606	−	6.47381i	0.933405	−	0.250105i
$671$	4.47607	−	4.47607i	0.172797	−	0.172797i
$672$	−4.39712	+	1.29048i	−0.169623	+	0.0497812i
$673$			22.4111i			0.863885i	0.901901	+	0.431942i	$0.142172\pi$
$673$			22.4111i			0.863885i	−0.901901	+	0.431942i	$0.857828\pi$
$674$	−8.88364	−	33.1542i	−0.342185	−	1.27705i
$675$	−1.73456	−	3.53957i	−0.0667632	−	0.136238i
$676$	12.1807	+	4.54201i	0.468490	+	0.174693i
$677$	−37.5970	−	21.7066i	−1.44497	−	0.834253i	−0.446793	−	0.894637i	$-0.647434\pi$
$677$	−37.5970	−	21.7066i	−1.44497	−	0.834253i	−0.998175	+	0.0603842i	$0.980767\pi$
$678$	3.83938	−	0.936106i	0.147450	−	0.0359509i
$679$	−9.54185	+	43.5934i	−0.366183	+	1.67296i
$680$	14.6070			0.560152
$681$	−25.1019	−	7.33919i	−0.961907	−	0.281238i
$682$	−29.6362	−	7.94100i	−1.13483	−	0.304077i
$683$	−22.7552	−	6.09725i	−0.870705	−	0.233305i	−0.204312	−	0.978906i	$-0.565496\pi$
$683$	−22.7552	−	6.09725i	−0.870705	−	0.233305i	−0.666392	+	0.745601i	$0.732162\pi$
$684$	−11.6666	−	12.7744i	−0.446083	−	0.488442i
$685$	24.0429			0.918632
$686$	−7.22483	−	17.0529i	−0.275845	−	0.651083i
$687$	−0.499055	−	2.04684i	−0.0190401	−	0.0780918i
$688$	0.371099	+	0.214254i	0.0141480	+	0.00816836i
$689$	−23.8235	+	1.99010i	−0.907604	+	0.0758169i
$690$	22.3221	+	0.505644i	0.849789	+	0.0192495i
$691$	−0.745645	−	2.78278i	−0.0283657	−	0.105862i	0.950292	−	0.311361i	$-0.100785\pi$
$691$	−0.745645	−	2.78278i	−0.0283657	−	0.105862i	−0.978657	+	0.205499i	$0.934118\pi$
$692$		−	15.6895i		−	0.596426i
$693$	−27.3331	+	7.35374i	−1.03830	+	0.279346i
$694$	9.55751	−	9.55751i	0.362798	−	0.362798i
$695$	42.5813	−	11.4096i	1.61520	−	0.432792i
$696$	−0.426101	+	0.407224i	−0.0161513	+	0.0154358i
$697$	−13.6815	+	51.0599i	−0.518223	+	1.93403i
$698$	−7.45512	−	4.30422i	−0.282181	−	0.162917i
$699$	−9.08291	−	5.52199i	−0.343547	−	0.208861i
$700$	−0.0929227	−	2.00488i	−0.00351215	−	0.0757773i
$701$	−26.3344			−0.994636			−0.497318	−	0.867568i	$-0.665682\pi$
$701$	−26.3344			−0.994636			−0.497318	+	0.867568i	$0.665682\pi$
$702$	−4.56978	+	18.1691i	−0.172475	+	0.685749i
$703$	22.4178	+	38.8289i	0.845505	+	1.46446i
$704$	−0.922976	+	3.44459i	−0.0347860	+	0.129823i
$705$	4.87520	−	2.66935i	0.183611	−	0.100534i
$706$			23.8878i			0.899031i
$707$	45.0504	+	23.2984i	1.69429	+	0.876227i
$708$	−0.827904	−	3.39559i	−0.0311145	−	0.127614i
$709$	−18.1689	+	4.86834i	−0.682347	+	0.182834i	−0.583310	−	0.812249i	$-0.698243\pi$
$709$	−18.1689	+	4.86834i	−0.682347	+	0.182834i	−0.0990370	+	0.995084i	$0.531576\pi$
$710$	−4.19628	−	1.12439i	−0.157484	−	0.0421976i
$711$	14.4852	−	22.6540i	0.543238	−	0.849592i
$712$	−2.01423	−	1.16291i	−0.0754863	−	0.0435820i
$713$	−38.0804	+	38.0804i	−1.42612	+	1.42612i
$714$	−7.66693	+	31.5851i	−0.286927	+	1.18204i
$715$	23.9551	+	11.2851i	0.895870	+	0.422040i
$716$	−2.94023	−	1.69754i	−0.109882	−	0.0634401i
$717$	−4.48186	+	4.28331i	−0.167378	+	0.159963i
$718$	3.79766	+	6.57774i	0.141727	+	0.245479i
$719$	10.3763	−	17.9723i	0.386971	−	0.670253i	−0.605070	−	0.796172i	$-0.706855\pi$
$719$	10.3763	−	17.9723i	0.386971	−	0.670253i	0.992040	+	0.125920i	$0.0401881\pi$
$720$	−1.86768	+	5.88935i	−0.0696044	+	0.219483i
$721$	21.2661	−	0.985646i	0.791991	−	0.0367074i
$722$	10.0798	−	10.0798i	0.375131	−	0.375131i
$723$	18.1108	+	5.29515i	0.673547	+	0.196929i
$724$	−10.7054	−	18.5422i	−0.397862	−	0.689116i
$725$	−0.129070	−	0.223556i	−0.00479354	−	0.00830266i
$726$	−0.834623	+	2.85462i	−0.0309758	+	0.105945i
$727$			0.874759i			0.0324430i	0.999868	+	0.0162215i	$0.00516369\pi$
$727$			0.874759i			0.0324430i	−0.999868	+	0.0162215i	$0.994836\pi$
$728$	−5.81662	+	7.56088i	−0.215578	+	0.280225i
$729$	−26.7511	−	3.65774i	−0.990781	−	0.135472i
$730$	−2.36589	−	8.82963i	−0.0875656	−	0.326799i
$731$	2.63206	−	1.51962i	0.0973501	−	0.0562051i
$732$	3.07374	+	0.0696268i	0.113609	+	0.00257348i
$733$	6.74247	+	25.1633i	0.249039	+	0.929426i	0.971310	+	0.237816i	$0.0764315\pi$
$733$	6.74247	+	25.1633i	0.249039	+	0.929426i	−0.722271	+	0.691610i	$0.756902\pi$
$734$	−8.63769	−	8.63769i	−0.318823	−	0.318823i
$735$	−24.5118	−	4.76031i	−0.904130	−	0.175587i
$736$	4.42605	+	4.42605i	0.163146	+	0.163146i
$737$	37.5088	+	21.6557i	1.38165	+	0.797699i
$738$	−18.8374	−	12.0448i	−0.693414	−	0.443377i
$739$	−1.26454	+	4.71934i	−0.0465169	+	0.173604i	−0.985276	−	0.170970i	$-0.945310\pi$
$739$	−1.26454	+	4.71934i	−0.0465169	+	0.173604i	0.938759	+	0.344574i	$0.111977\pi$
$740$	8.00610	−	13.8670i	0.294310	−	0.509760i
$741$	−35.2873	−	7.19373i	−1.29631	−	0.264268i
$742$	3.75096	−	17.1369i	0.137702	−	0.629114i
$743$	−1.07143	−	1.07143i	−0.0393071	−	0.0393071i	0.687180	−	0.726487i	$-0.258848\pi$
$743$	−1.07143	−	1.07143i	−0.0393071	−	0.0393071i	−0.726487	+	0.687180i	$0.758848\pi$
$744$	−7.15684	−	13.0710i	−0.262382	−	0.479205i
$745$	−15.4976	+	8.94753i	−0.567787	+	0.327812i
$746$	−1.36186	+	5.08252i	−0.0498611	+	0.186084i
$747$	−23.2632	−	25.4723i	−0.851156	−	0.931981i
$748$	17.8848	+	17.8848i	0.653934	+	0.653934i
$749$	−2.22580	+	0.103162i	−0.0813288	+	0.00376945i
$750$	−17.5523	−	10.6710i	−0.640919	−	0.389649i
$751$	−11.9427	−	6.89510i	−0.435794	−	0.251606i	0.266018	−	0.963968i	$-0.414292\pi$
$751$	−11.9427	−	6.89510i	−0.435794	−	0.251606i	−0.701812	+	0.712362i	$0.747625\pi$
$752$	1.50508	+	0.403284i	0.0548844	+	0.0147062i
$753$	−0.446791	+	19.7240i	−0.0162820	+	0.718783i
$754$	−0.217796	+	1.20745i	−0.00793166	+	0.0439728i
$755$		−	9.43625i		−	0.343420i
$756$	−11.7544	−	7.12976i	−0.427504	−	0.259307i
$757$	19.3286			0.702509			0.351254	−	0.936280i	$-0.385755\pi$
$757$	19.3286			0.702509			0.351254	+	0.936280i	$0.385755\pi$
$758$	7.52949	−	13.0415i	0.273484	−	0.473687i
$759$	26.7122	+	27.9504i	0.969590	+	1.01453i
$760$	−11.4717	−	3.07383i	−0.416122	−	0.111500i
$761$	−5.56192	−	20.7574i	−0.201620	−	0.752455i	−0.990453	−	0.137848i	$-0.955981\pi$
$761$	−5.56192	−	20.7574i	−0.201620	−	0.752455i	0.788834	−	0.614607i	$-0.210685\pi$
$762$	−13.1968	+	3.21761i	−0.478070	+	0.116562i
$763$	−33.4227	+	10.6368i	−1.20998	+	0.385077i
$764$	7.35477			0.266086
$765$	29.5512	+	32.3574i	1.06843	+	1.16988i
$766$	13.6297	−	7.86909i	0.492460	−	0.284322i
$767$	−5.55500	−	4.69848i	−0.200580	−	0.169652i
$768$	−1.51923	+	0.831834i	−0.0548204	+	0.0300162i
$769$	4.93994	−	4.93994i	0.178139	−	0.178139i	−0.612405	−	0.790544i	$-0.709798\pi$
$769$	4.93994	−	4.93994i	0.178139	−	0.178139i	0.790544	+	0.612405i	$0.209798\pi$
$770$	−13.0890	+	14.3613i	−0.471696	+	0.517546i
$771$	−8.94329	−	5.43710i	−0.322085	−	0.195812i
$772$	−2.39902	−	8.95326i	−0.0863426	−	0.322235i
$773$	−3.76207	+	14.0402i	−0.135312	+	0.504992i	0.864684	+	0.502316i	$0.167518\pi$
$773$	−3.76207	+	14.0402i	−0.135312	+	0.504992i	−0.999996	+	0.00267596i	$0.999148\pi$
$774$	0.276151	+	1.25551i	0.00992603	+	0.0451285i
$775$	6.30426	−	1.68922i	0.226456	−	0.0606786i
$776$			16.8669i			0.605485i
$777$	25.7827	+	24.5903i	0.924951	+	0.882174i
$778$	−11.1415	−	11.1415i	−0.399442	−	0.399442i
$779$	21.4897	−	37.2212i	0.769947	−	1.33359i
$780$	4.07618	+	12.1984i	0.145951	+	0.436771i
$781$	−3.76123	−	6.51464i	−0.134587	−	0.233112i
$782$	42.8825	−	11.4903i	1.53348	−	0.410894i
$783$	−1.76412	−	0.120048i	−0.0630446	−	0.00429016i
$784$	−4.04573	−	5.71245i	−0.144490	−	0.204016i
$785$	−2.90745	−	2.90745i	−0.103771	−	0.103771i
$786$	6.68039	−	22.8486i	0.238282	−	0.814984i
$787$	−5.60464	+	20.9168i	−0.199784	+	0.745603i	0.791193	+	0.611567i	$0.209461\pi$
$787$	−5.60464	+	20.9168i	−0.199784	+	0.745603i	−0.990976	+	0.134036i	$0.957206\pi$
$788$	−18.7031	−	5.01149i	−0.666272	−	0.178527i
$789$	11.4959	+	20.9957i	0.409265	+	0.747466i
$790$		−	18.4591i		−	0.656746i
$791$	3.25708	+	5.08246i	0.115808	+	0.180711i
$792$	−9.49773	+	4.92414i	−0.337487	+	0.174972i
$793$	5.25706	−	3.65037i	0.186684	−	0.129628i
$794$	−8.75233	+	5.05316i	−0.310608	+	0.179330i
$795$	−16.3412	−	17.0986i	−0.579561	−	0.606426i
$796$	−3.26442	+	5.65413i	−0.115704	+	0.200405i
$797$	−37.9629			−1.34472			−0.672358	−	0.740226i	$-0.734718\pi$
$797$	−37.9629			−1.34472			−0.672358	+	0.740226i	$0.734718\pi$
$798$	12.6679	−	23.1922i	0.448439	−	0.820995i
$799$	7.81456	−	7.81456i	0.276459	−	0.276459i
$800$	−0.196337	−	0.732739i	−0.00694155	−	0.0259062i
$801$	−1.49887	−	6.81459i	−0.0529600	−	0.240782i
$802$	−16.5534	−	28.6713i	−0.584521	−	1.01242i
$803$	7.91422	−	13.7078i	0.279287	−	0.483739i
$804$	4.98303	+	20.4376i	0.175738	+	0.720778i
$805$	10.3432	+	32.5002i	0.364549	+	1.14548i
$806$	−28.0629	−	13.2203i	−0.988475	−	0.465665i
$807$	18.0266	+	32.9230i	0.634565	+	1.15894i
$808$	18.5166	+	4.96150i	0.651410	+	0.174545i
$809$	−28.4508	+	16.4261i	−1.00028	+	0.577510i	−0.908330	−	0.418254i	$-0.862642\pi$
$809$	−28.4508	+	16.4261i	−1.00028	+	0.577510i	−0.0919465	+	0.995764i	$0.529309\pi$
$810$	−16.8246	+	7.77740i	−0.591156	+	0.273270i
$811$	−1.93172	+	1.93172i	−0.0678318	+	0.0678318i	−0.740209	−	0.672377i	$-0.765273\pi$
$811$	−1.93172	+	1.93172i	−0.0678318	+	0.0678318i	0.672377	+	0.740209i	$0.265273\pi$
$812$	−0.799710	−	0.413581i	−0.0280643	−	0.0145138i
$813$	1.07492	+	4.40870i	0.0376989	+	0.154620i
$814$	26.7814	−	7.17606i	0.938688	−	0.251521i
$815$	30.1711	−	17.4193i	1.05685	−	0.610171i
$816$	−0.278204	+	12.2816i	−0.00973909	+	0.429942i
$817$	−2.38688	+	0.639564i	−0.0835065	+	0.0223755i
$818$	−22.2728			−0.778750
$819$	−28.5164	+	2.41138i	−0.996444	+	0.0842603i
$820$	−15.3492			−0.536018
$821$	15.7970	−	4.23278i	0.551318	−	0.147725i	0.0276033	−	0.999619i	$-0.491212\pi$
$821$	15.7970	−	4.23278i	0.551318	−	0.147725i	0.523715	+	0.851894i	$0.324546\pi$
$822$	−0.457920	+	20.2153i	−0.0159718	+	0.705091i
$823$	9.88506	−	5.70714i	0.344572	−	0.198939i	−0.317720	−	0.948185i	$-0.602917\pi$
$823$	9.88506	−	5.70714i	0.344572	−	0.198939i	0.662292	+	0.749246i	$0.269584\pi$
$824$	7.77228	−	2.08258i	0.270760	−	0.0725500i
$825$	−1.10990	−	4.55219i	−0.0386419	−	0.158487i
$826$	4.49499	−	2.88060i	0.156401	−	0.100229i
$827$	8.33815	−	8.33815i	0.289946	−	0.289946i	−0.547113	−	0.837059i	$-0.684273\pi$
$827$	8.33815	−	8.33815i	0.289946	−	0.289946i	0.837059	+	0.547113i	$0.184273\pi$
$828$	−0.850293	+	18.7589i	−0.0295497	+	0.651916i
$829$	−27.7331	+	16.0117i	−0.963210	+	0.556109i	−0.897159	−	0.441707i	$-0.854373\pi$
$829$	−27.7331	+	16.0117i	−0.963210	+	0.556109i	−0.0660503	+	0.997816i	$0.521040\pi$
$830$	−22.8746	−	6.12923i	−0.793989	−	0.212749i
$831$	1.33838	+	2.44436i	0.0464279	+	0.0847940i
$832$	−1.53659	+	3.26173i	−0.0532715	+	0.113080i
$833$	−49.4353	+	4.59235i	−1.71283	+	0.159115i
$834$	8.78224	+	36.0198i	0.304104	+	1.24726i
$835$	7.57578	−	13.1216i	0.262171	−	0.454093i
$836$	−10.2824	−	17.8096i	−0.355623	−	0.615957i
$837$	14.4759	−	42.2976i	0.500359	−	1.46202i
$838$	0.554221	+	2.06838i	0.0191452	+	0.0714510i
$839$	2.99573	−	2.99573i	0.103424	−	0.103424i	−0.653501	−	0.756925i	$-0.726701\pi$
$839$	2.99573	−	2.99573i	0.103424	−	0.103424i	0.756925	+	0.653501i	$0.226701\pi$
$840$	−9.43503	+	0.223339i	−0.325539	+	0.00770593i
$841$	28.8842			0.996007
$842$	3.30591	−	5.72600i	0.113929	−	0.197331i
$843$	12.2621	+	12.8305i	0.422331	+	0.441907i
$844$	−7.53128	+	4.34819i	−0.259238	+	0.149671i
$845$	21.8100	+	15.5281i	0.750288	+	0.534183i
$846$	2.15155	+	4.14992i	0.0739717	+	0.142677i
$847$	−4.53819	+	0.210337i	−0.155934	+	0.00722727i
$848$		−	6.63047i		−	0.227691i
$849$	8.84733	+	16.1584i	0.303640	+	0.554555i
$850$	−5.19702	−	1.39254i	−0.178256	−	0.0477636i
$851$	12.5957	−	47.0079i	0.431776	−	1.61141i
$852$	1.02531	−	3.50683i	0.0351266	−	0.120142i
$853$	−11.0400	−	11.0400i	−0.378003	−	0.378003i	0.492378	−	0.870381i	$-0.336128\pi$
$853$	−11.0400	−	11.0400i	−0.378003	−	0.378003i	−0.870381	+	0.492378i	$0.836128\pi$
$854$	1.42425	+	4.47525i	0.0487368	+	0.153140i
$855$	−16.3991	−	31.6307i	−0.560837	−	1.08175i
$856$	−0.813479	+	0.217971i	−0.0278041	+	0.00745010i
$857$	−11.9240	−	20.6529i	−0.407315	−	0.705491i	0.587273	−	0.809389i	$-0.300202\pi$
$857$	−11.9240	−	20.6529i	−0.407315	−	0.705491i	−0.994588	+	0.103899i	$0.966868\pi$
$858$	−9.94481	+	19.9266i	−0.339510	+	0.680282i
$859$	3.71653	−	6.43722i	0.126806	−	0.219635i	−0.795631	−	0.605781i	$-0.792861\pi$
$859$	3.71653	−	6.43722i	0.126806	−	0.219635i	0.922438	+	0.386146i	$0.126194\pi$
$860$	0.624022	+	0.624022i	0.0212790	+	0.0212790i
$861$	8.05652	−	33.1901i	0.274565	−	1.13112i
$862$		−	22.4510i		−	0.764684i
$863$	−39.0162	+	10.4544i	−1.32813	+	0.355871i	−0.852017	−	0.523514i	$-0.824621\pi$
$863$	−39.0162	+	10.4544i	−1.32813	+	0.355871i	−0.476111	+	0.879385i	$0.657954\pi$
$864$	−4.91621	−	1.68252i	−0.167253	−	0.0572405i
$865$	8.36298	−	31.2111i	0.284350	−	1.06121i
$866$	−5.67961	−	21.1966i	−0.193001	−	0.720289i
$867$	49.2914	+	29.9669i	1.67402	+	1.01773i
$868$	15.3335	−	16.8240i	0.520454	−	0.571043i
$869$	22.6014	−	22.6014i	0.766699	−	0.766699i
$870$	−1.06470	+	0.582965i	−0.0360968	+	0.0197644i
$871$	33.4347	+	28.2794i	1.13289	+	0.958212i
$872$	−11.4808	+	6.62845i	−0.388789	+	0.224468i
$873$	−37.3635	+	34.1231i	−1.26456	+	1.15489i
$874$	−36.0961			−1.22097
$875$	6.70918	−	30.6520i	0.226812	−	1.03623i
$876$	7.46904	−	1.82108i	0.252355	−	0.0615286i
$877$	−6.57892	−	24.5529i	−0.222154	−	0.829091i	−0.983525	−	0.180774i	$-0.942140\pi$
$877$	−6.57892	−	24.5529i	−0.222154	−	0.829091i	0.761370	−	0.648317i	$-0.224527\pi$
$878$	6.42984	+	1.72287i	0.216997	+	0.0581441i
$879$	22.7834	+	23.8395i	0.768465	+	0.804086i
$880$	−3.67214	+	6.36034i	−0.123788	+	0.214407i
$881$	28.5207			0.960888			0.480444	−	0.877025i	$-0.340476\pi$
$881$	28.5207			0.960888			0.480444	+	0.877025i	$0.340476\pi$
$882$	4.46933	−	20.5189i	0.150490	−	0.690907i
$883$		−	3.85564i		−	0.129753i	−0.997893	−	0.0648763i	$-0.979335\pi$
$883$		−	3.85564i		−	0.129753i	0.997893	−	0.0648763i	$-0.0206653\pi$
$884$	14.5856	+	21.0054i	0.490566	+	0.706486i
$885$	0.163008	−	7.19613i	0.00547945	−	0.241895i
$886$	13.3846	+	3.58638i	0.449663	+	0.120487i
$887$	10.1210	+	5.84334i	0.339829	+	0.196200i	0.660196	−	0.751093i	$-0.270473\pi$
$887$	10.1210	+	5.84334i	0.339829	+	0.196200i	−0.320368	+	0.947293i	$0.603806\pi$
$888$	11.5069	+	6.99565i	0.386146	+	0.234759i
$889$	−11.1953	−	17.4696i	−0.375479	−	0.585910i
$890$	−3.38702	−	3.38702i	−0.113533	−	0.113533i
$891$	−30.1227	−	11.0774i	−1.00915	−	0.371107i
$892$	1.00504	−	3.75086i	0.0336512	−	0.125588i
$893$	−7.78168	+	4.49276i	−0.260404	+	0.150344i
$894$	−7.22794	−	13.2008i	−0.241738	−	0.441501i
$895$	−4.94414	−	4.94414i	−0.165264	−	0.165264i
$896$	−1.95544	−	1.78221i	−0.0653266	−	0.0595393i
$897$	21.5623	+	32.6049i	0.719944	+	1.08865i
$898$	0.537898	−	0.931666i	0.0179499	−	0.0310901i
$899$	0.757759	−	2.82800i	0.0252727	−	0.0943190i
$900$	1.22596	−	1.91732i	0.0408652	−	0.0639107i
$901$	−40.7268	−	23.5136i	−1.35681	−	0.783352i
$902$	−18.7936	−	18.7936i	−0.625759	−	0.625759i
$903$	−1.67688	+	1.02180i	−0.0558030	+	0.0340035i
$904$	1.61334	+	1.61334i	0.0536587	+	0.0536587i
$905$	−11.4126	−	42.5922i	−0.379366	−	1.41581i
$906$	7.93402	+	0.179722i	0.263590	+	0.00597088i
$907$	45.8562	−	26.4751i	1.52263	−	0.879090i	0.522986	−	0.852341i	$-0.324818\pi$
$907$	45.8562	−	26.4751i	1.52263	−	0.879090i	0.999642	−	0.0267491i	$-0.00851552\pi$
$908$	−3.90799	−	14.5848i	−0.129691	−	0.484015i
$909$	26.4699	+	51.0554i	0.877952	+	1.69340i
$910$	−15.6011	+	11.9404i	−0.517173	+	0.395820i
$911$			43.7366i			1.44906i	0.689244	+	0.724529i	$0.257943\pi$
$911$			43.7366i			1.44906i	−0.689244	+	0.724529i	$0.742057\pi$
$912$	2.80297	−	9.58688i	0.0928157	−	0.317453i
$913$	−20.5031	−	35.5124i	−0.678553	−	1.17529i
$914$	9.17460	+	15.8909i	0.303469	+	0.525623i
$915$	6.07746	+	1.77690i	0.200915	+	0.0587426i
$916$	0.860097	−	0.860097i	0.0284184	−	0.0284184i
$917$	36.3241	−	1.68356i	1.19953	−	0.0555959i
$918$	−27.7690	+	24.2305i	−0.916514	+	0.799724i
$919$	2.43706	−	4.22111i	0.0803912	−	0.139242i	−0.823027	−	0.568003i	$-0.807716\pi$
$919$	2.43706	−	4.22111i	0.0803912	−	0.139242i	0.903418	+	0.428761i	$0.141050\pi$
$920$	6.44550	+	11.1639i	0.212502	+	0.368064i
$921$	−34.2296	+	32.7132i	−1.12790	+	1.07794i
$922$	−15.5310	−	8.96685i	−0.511487	−	0.295307i
$923$	−2.57322	−	7.15714i	−0.0846986	−	0.235580i
$924$	−11.8257	−	11.2788i	−0.389038	−	0.371046i
$925$	−4.17048	+	4.17048i	−0.137124	+	0.137124i
$926$	22.1893	+	12.8110i	0.729186	+	0.420996i
$927$	20.3373	+	13.0039i	0.667966	+	0.427105i
$928$	−0.328696	−	0.0880738i	−0.0107900	−	0.00289116i
$929$	22.4127	−	6.00546i	0.735336	−	0.197033i	0.128332	−	0.991731i	$-0.459038\pi$
$929$	22.4127	−	6.00546i	0.735336	−	0.197033i	0.607004	+	0.794699i	$0.292371\pi$
$930$	−7.26985	−	29.8168i	−0.238388	−	0.977731i
$931$	39.7908	+	6.79633i	1.30409	+	0.222741i
$932$		−	6.13709i		−	0.201027i
$933$	−9.57212	+	5.24109i	−0.313377	+	0.171586i
$934$	−6.58099	+	24.5606i	−0.215336	+	0.803647i
$935$	26.0450	+	45.1113i	0.851764	+	1.47530i
$936$	−10.3340	+	3.19493i	−0.337779	+	0.104430i
$937$	30.5321			0.997439			0.498719	−	0.866763i	$-0.333804\pi$
$937$	30.5321			0.997439			0.498719	+	0.866763i	$0.333804\pi$
$938$	−27.0547	+	17.3379i	−0.883366	+	0.566103i
$939$	−33.9174	−	20.6202i	−1.10685	−	0.672914i
$940$	2.77908	+	1.60450i	0.0906434	+	0.0523330i
$941$	−12.4338	+	46.4035i	−0.405330	+	1.51271i	0.398117	+	0.917335i	$0.369664\pi$
$941$	−12.4338	+	46.4035i	−0.405330	+	1.51271i	−0.803447	+	0.595377i	$0.797003\pi$
$942$	2.49996	−	2.38921i	0.0814532	−	0.0778448i
$943$	−45.0616	+	12.0742i	−1.46741	+	0.393191i
$944$	1.42685	−	1.42685i	0.0464402	−	0.0464402i
$945$	−19.5826	−	20.4486i	−0.637024	−	0.665194i
$946$			1.52811i			0.0496830i
$947$	−12.7734	−	47.6710i	−0.415080	−	1.54910i	−0.784675	−	0.619907i	$-0.787170\pi$
$947$	−12.7734	−	47.6710i	−0.415080	−	1.54910i	0.369595	−	0.929193i	$-0.379497\pi$
$948$	15.5205	+	0.351572i	0.504081	+	0.0114185i
$949$	10.3349	−	12.2189i	0.335485	−	0.396643i
$950$	3.78847	+	2.18728i	0.122914	+	0.0709646i
$951$	−1.07970	−	4.42830i	−0.0350115	−	0.143597i
$952$	−17.8815	+	5.69079i	−0.579544	+	0.184440i
$953$	36.8202			1.19272			0.596362	−	0.802716i	$-0.296612\pi$
$953$	36.8202			1.19272			0.596362	+	0.802716i	$0.296612\pi$
$954$	14.6878	−	13.4140i	0.475535	−	0.434295i
$955$	14.6308	+	3.92031i	0.473442	+	0.126858i
$956$	−3.45732	−	0.926387i	−0.111818	−	0.0299615i
$957$	−2.01741	−	0.589842i	−0.0652135	−	0.0190669i
$958$	13.8531			0.447573
$959$	−29.4328	+	9.36697i	−0.950434	+	0.302475i
$960$	−3.46558	+	0.844969i	−0.111851	+	0.0272712i
$961$	37.2594	+	21.5117i	1.20192	+	0.693927i
$962$	27.9355	−	2.33360i	0.900678	−	0.0752383i
$963$	−2.12859	−	1.36104i	−0.0685928	−	0.0438590i
$964$	2.81958	+	10.5228i	0.0908125	+	0.338917i
$965$		−	19.0894i		−	0.614510i
$966$	−27.5233	+	8.07758i	−0.885546	+	0.259892i
$967$	−6.82936	+	6.82936i	−0.219617	+	0.219617i	−0.808337	−	0.588720i	$-0.799632\pi$
$967$	−6.82936	+	6.82936i	−0.219617	+	0.219617i	0.588720	+	0.808337i	$0.299632\pi$
$968$	−1.65861	+	0.444423i	−0.0533097	+	0.0142843i
$969$	−48.9460	−	51.2148i	−1.57237	−	1.64526i
$970$	−8.99054	+	33.5531i	−0.288669	+	1.07733i
$971$	13.2249	+	7.63541i	0.424408	+	0.245032i	0.696961	−	0.717109i	$-0.254535\pi$
$971$	13.2249	+	7.63541i	0.424408	+	0.245032i	−0.272554	+	0.962141i	$0.587868\pi$
$972$	−6.21881	−	14.2943i	−0.199469	−	0.458489i
$973$	−47.6820	+	30.5568i	−1.52861	+	0.979607i
$974$	−14.1102			−0.452119
$975$	−0.287351	−	4.72865i	−0.00920260	−	0.151438i
$976$	0.887540	+	1.53726i	0.0284095	+	0.0492066i
$977$	7.03681	−	26.2617i	0.225128	−	0.840187i	−0.757226	−	0.653153i	$-0.773446\pi$
$977$	7.03681	−	26.2617i	0.225128	−	0.840187i	0.982353	−	0.187034i	$-0.0598875\pi$
$978$	14.0715	+	25.6997i	0.449958	+	0.821786i
$979$		−	8.29415i		−	0.265082i
$980$	−5.00325	−	13.5202i	−0.159823	−	0.431888i
$981$	−37.9100	−	12.0223i	−1.21037	−	0.383844i
$982$	−32.6107	+	8.73802i	−1.04065	+	0.278841i
$983$	−32.3308	−	8.66300i	−1.03119	−	0.276307i	−0.296733	−	0.954961i	$-0.595897\pi$
$983$	−32.3308	−	8.66300i	−1.03119	−	0.276307i	−0.734458	+	0.678654i	$0.762564\pi$
$984$	0.292341	−	12.9057i	0.00931949	−	0.411418i
$985$	−34.5348	−	19.9387i	−1.10037	−	0.635299i
$986$	−1.70664	+	1.70664i	−0.0543503	+	0.0543503i
$987$	−4.92815	+	5.16711i	−0.156865	+	0.164471i
$988$	−7.03461	−	19.5660i	−0.223801	−	0.622478i
$989$	2.32285	+	1.34110i	0.0738623	+	0.0426444i
$990$	−21.5185	+	4.73300i	−0.683903	+	0.150425i
$991$	2.49678	+	4.32455i	0.0793129	+	0.137374i	0.902954	−	0.429738i	$-0.141394\pi$
$991$	2.49678	+	4.32455i	0.0793129	+	0.137374i	−0.823641	+	0.567112i	$0.808061\pi$
$992$	4.30184	−	7.45101i	0.136584	−	0.236570i
$993$	−34.7467	+	8.47184i	−1.10265	+	0.268846i
$994$	5.57505	−	0.258394i	0.176830	−	0.00819575i
$995$	−9.50771	+	9.50771i	−0.301415	+	0.301415i
$996$	5.58914	−	19.1163i	0.177099	−	0.605723i
$997$	−7.91540	−	13.7099i	−0.250683	−	0.434196i	0.713031	−	0.701133i	$-0.247322\pi$
$997$	−7.91540	−	13.7099i	−0.250683	−	0.434196i	−0.963714	+	0.266936i	$0.913989\pi$
$998$	−4.20342	−	7.28055i	−0.133057	−	0.230462i
$999$	7.78270	+	39.6429i	0.246234	+	1.25425i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bv.a.317.10	✓	144
3.2	odd	2	inner	546.2.bv.a.317.21	yes	144
7.4	even	3	inner	546.2.bv.a.473.21	yes	144
13.8	odd	4	inner	546.2.bv.a.359.10	yes	144
21.11	odd	6	inner	546.2.bv.a.473.10	yes	144
39.8	even	4	inner	546.2.bv.a.359.21	yes	144
91.60	odd	12	inner	546.2.bv.a.515.21	yes	144
273.242	even	12	inner	546.2.bv.a.515.10	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bv.a.317.10	✓	144	1.1	even	1	trivial
546.2.bv.a.317.21	yes	144	3.2	odd	2	inner
546.2.bv.a.359.10	yes	144	13.8	odd	4	inner
546.2.bv.a.359.21	yes	144	39.8	even	4	inner
546.2.bv.a.473.10	yes	144	21.11	odd	6	inner
546.2.bv.a.473.21	yes	144	7.4	even	3	inner
546.2.bv.a.515.10	yes	144	273.242	even	12	inner
546.2.bv.a.515.21	yes	144	91.60	odd	12	inner

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.0392246 - 1.73161i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.98929 - 0.533030i) q^{5} +(0.410285 + 1.68276i) q^{6} +(-2.22758 + 1.42754i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.99692 - 0.135843i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.0392246 - 1.73161i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.98929 - 0.533030i) q^{5} +(0.410285 + 1.68276i) q^{6} +(-2.22758 + 1.42754i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.99692 - 0.135843i) q^{9} +(-1.78355 + 1.02973i) q^{10} +(-3.44459 - 0.922976i) q^{11} +(-0.831834 - 1.51923i) q^{12} +(-3.26173 - 1.53659i) q^{13} +(1.78221 - 1.95544i) q^{14} +(-0.844969 - 3.46558i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-3.54630 - 6.14237i) q^{17} +(2.92996 - 0.644446i) q^{18} +(1.49254 + 5.57022i) q^{19} +(1.45626 - 1.45626i) q^{20} +(2.38456 + 3.91329i) q^{21} +3.56611 q^{22} +(3.12969 - 5.42078i) q^{23} +(1.19669 + 1.25217i) q^{24} +(-0.656955 + 0.379293i) q^{25} +(3.54829 + 0.640028i) q^{26} +(-0.352780 + 5.18416i) q^{27} +(-1.21537 + 2.35008i) q^{28} +0.340291i q^{29} +(1.71314 + 3.12880i) q^{30} +(-8.31053 - 2.22680i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-1.73334 + 5.92848i) q^{33} +(5.01522 + 5.01522i) q^{34} +(-3.67040 + 4.02717i) q^{35} +(-2.66333 + 1.38082i) q^{36} +(7.50999 - 2.01230i) q^{37} +(-2.88336 - 4.99412i) q^{38} +(-2.78870 + 5.58777i) q^{39} +(-1.02973 + 1.78355i) q^{40} +(-5.27007 - 5.27007i) q^{41} +(-3.31615 - 3.16278i) q^{42} +0.428508i q^{43} +(-3.44459 + 0.922976i) q^{44} +(-6.03417 + 1.32722i) q^{45} +(-1.62005 + 6.04610i) q^{46} +(0.403284 + 1.50508i) q^{47} +(-1.48000 - 0.899773i) q^{48} +(2.92426 - 6.35993i) q^{49} +(0.536402 - 0.536402i) q^{50} +(-10.7753 + 5.89986i) q^{51} +(-3.59304 + 0.300145i) q^{52} +(5.74215 - 3.31523i) q^{53} +(-1.00100 - 5.09882i) q^{54} -7.34429 q^{55} +(0.565716 - 2.58456i) q^{56} +(9.70397 - 2.36599i) q^{57} +(-0.0880738 - 0.328696i) q^{58} +(1.94912 + 0.522265i) q^{59} +(-2.46456 - 2.57880i) q^{60} +(-0.887540 + 1.53726i) q^{61} +8.60369 q^{62} +(6.86982 - 3.97563i) q^{63} -1.00000i q^{64} +(-7.30759 - 1.31812i) q^{65} +(0.139879 - 6.17509i) q^{66} +(-11.7315 - 3.14344i) q^{67} +(-6.14237 - 3.54630i) q^{68} +(-9.26390 - 5.63202i) q^{69} +(2.50302 - 4.83991i) q^{70} +(1.49159 + 1.49159i) q^{71} +(2.21520 - 2.02309i) q^{72} +(-1.14879 + 4.28734i) q^{73} +(-6.73327 + 3.88746i) q^{74} +(0.631018 + 1.15247i) q^{75} +(4.07768 + 4.07768i) q^{76} +(8.99071 - 2.86129i) q^{77} +(1.24746 - 6.11914i) q^{78} +(-4.48152 + 7.76223i) q^{79} +(0.533030 - 1.98929i) q^{80} +(8.96309 + 0.814222i) q^{81} +(6.45449 + 3.72650i) q^{82} +(8.13092 + 8.13092i) q^{83} +(4.02174 + 2.19673i) q^{84} +(-10.3287 - 10.3287i) q^{85} +(-0.110906 - 0.413907i) q^{86} +(0.589250 + 0.0133478i) q^{87} +(3.08834 - 1.78305i) q^{88} +(0.601969 + 2.24658i) q^{89} +(5.48505 - 2.84375i) q^{90} +(9.45932 - 1.23338i) q^{91} -6.25938i q^{92} +(-4.18192 + 14.3032i) q^{93} +(-0.779084 - 1.34941i) q^{94} +(5.93818 + 10.2852i) q^{95} +(1.66245 + 0.486061i) q^{96} +(11.9267 - 11.9267i) q^{97} +(-1.17854 + 6.90007i) q^{98} +(10.1978 + 3.23401i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 16 q^{7}+O(q^{10}) \) 144 * q - 16 * q^7	\( 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99}+O(q^{100}) \) 144 * q - 16 * q^7 + 72 * q^16 + 16 * q^18 + 8 * q^19 + 8 * q^21 + 24 * q^27 - 8 * q^28 - 8 * q^31 + 12 * q^33 - 8 * q^37 + 16 * q^39 - 40 * q^45 + 8 * q^46 + 8 * q^52 - 12 * q^54 - 32 * q^55 + 16 * q^57 + 8 * q^58 - 32 * q^61 - 40 * q^63 - 32 * q^66 - 8 * q^67 + 16 * q^72 + 80 * q^73 - 16 * q^76 + 16 * q^78 - 112 * q^79 - 48 * q^81 + 16 * q^84 - 80 * q^85 + 96 * q^87 - 32 * q^91 + 36 * q^93 - 64 * q^94 - 144 * q^97 - 32 * q^99

Introduction

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