LMFDB - Embedded newform 546.2.ch.a.275.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(137,546)]

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, 8, 11]))

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

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

chi := DirichletCharacter("546.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.ch (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:	$152$
Relative dimension:	$38$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			275.2
Character	$\chi$	$=$	546.275
Dual form			546.2.ch.a.137.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-1.72614 - 0.143006i) q^{3} +1.00000i q^{4} +(-1.09645 + 0.293793i) q^{5} +(1.11944 + 1.32168i) q^{6} +(-0.0234379 - 2.64565i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.95910 + 0.493697i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.72614 - 0.143006i) q^{3} +1.00000i q^{4} +(-1.09645 + 0.293793i) q^{5} +(1.11944 + 1.32168i) q^{6} +(-0.0234379 - 2.64565i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.95910 + 0.493697i) q^{9} +(0.983052 + 0.567565i) q^{10} +(-0.882338 - 3.29293i) q^{11} +(0.143006 - 1.72614i) q^{12} +(2.35322 + 2.73173i) q^{13} +(-1.85418 + 1.88733i) q^{14} +(1.93464 - 0.350328i) q^{15} -1.00000 q^{16} +2.19941 q^{17} +(-1.74330 - 2.44150i) q^{18} +(-2.74521 - 0.735577i) q^{19} +(-0.293793 - 1.09645i) q^{20} +(-0.337887 + 4.57010i) q^{21} +(-1.70455 + 2.95236i) q^{22} -8.10303 q^{23} +(-1.32168 + 1.11944i) q^{24} +(-3.21423 + 1.85574i) q^{25} +(0.267648 - 3.59560i) q^{26} +(-5.03721 - 1.27536i) q^{27} +(2.64565 - 0.0234379i) q^{28} +(-4.77468 + 2.75666i) q^{29} +(-1.61572 - 1.12028i) q^{30} +(5.48451 + 1.46957i) q^{31} +(0.707107 + 0.707107i) q^{32} +(1.05213 + 5.81023i) q^{33} +(-1.55521 - 1.55521i) q^{34} +(0.802972 + 2.89394i) q^{35} +(-0.493697 + 2.95910i) q^{36} +(-8.14758 - 8.14758i) q^{37} +(1.42102 + 2.46129i) q^{38} +(-3.67132 - 5.05187i) q^{39} +(-0.567565 + 0.983052i) q^{40} +(-1.60050 + 5.97315i) q^{41} +(3.47047 - 2.99263i) q^{42} +(-6.18316 - 3.56985i) q^{43} +(3.29293 - 0.882338i) q^{44} +(-3.38955 + 0.328048i) q^{45} +(5.72971 + 5.72971i) q^{46} +(2.43712 + 9.09544i) q^{47} +(1.72614 + 0.143006i) q^{48} +(-6.99890 + 0.124017i) q^{49} +(3.58501 + 0.960601i) q^{50} +(-3.79648 - 0.314529i) q^{51} +(-2.73173 + 2.35322i) q^{52} +(-1.67323 + 0.966043i) q^{53} +(2.66003 + 4.46366i) q^{54} +(1.93488 + 3.35131i) q^{55} +(-1.88733 - 1.85418i) q^{56} +(4.63342 + 1.66229i) q^{57} +(5.32546 + 1.42695i) q^{58} +(-0.878024 + 0.878024i) q^{59} +(0.350328 + 1.93464i) q^{60} +(1.71921 + 2.97776i) q^{61} +(-2.83899 - 4.91728i) q^{62} +(1.23679 - 7.84030i) q^{63} -1.00000i q^{64} +(-3.38276 - 2.30385i) q^{65} +(3.36449 - 4.85242i) q^{66} +(2.31020 + 8.62180i) q^{67} +2.19941i q^{68} +(13.9869 + 1.15878i) q^{69} +(1.47854 - 2.61411i) q^{70} +(4.82231 - 1.29213i) q^{71} +(2.44150 - 1.74330i) q^{72} +(4.09203 - 15.2717i) q^{73} +11.5224i q^{74} +(5.81359 - 2.74360i) q^{75} +(0.735577 - 2.74521i) q^{76} +(-8.69125 + 2.41153i) q^{77} +(-0.976192 + 6.16823i) q^{78} +(-2.69940 + 4.67549i) q^{79} +(1.09645 - 0.293793i) q^{80} +(8.51253 + 2.92180i) q^{81} +(5.35538 - 3.09193i) q^{82} +(-9.78838 - 9.78838i) q^{83} +(-4.57010 - 0.337887i) q^{84} +(-2.41154 + 0.646171i) q^{85} +(1.84789 + 6.89642i) q^{86} +(8.63597 - 4.07557i) q^{87} +(-2.95236 - 1.70455i) q^{88} +(-11.4221 + 11.4221i) q^{89} +(2.62874 + 2.16481i) q^{90} +(7.17204 - 6.28982i) q^{91} -8.10303i q^{92} +(-9.25686 - 3.32100i) q^{93} +(4.70815 - 8.15475i) q^{94} +3.22610 q^{95} +(-1.11944 - 1.32168i) q^{96} +(-1.01235 - 3.77815i) q^{97} +(5.03666 + 4.86128i) q^{98} +(-0.985214 - 10.1797i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q + 8 q^{7}+O(q^{10}) $ 152 * q + 8 * q^7	$ 152 q + 8 q^{7} - 152 q^{16} - 8 q^{18} + 36 q^{19} + 8 q^{21} + 24 q^{27} - 12 q^{28} - 24 q^{30} - 36 q^{31} + 12 q^{33} + 24 q^{36} - 12 q^{37} - 8 q^{39} - 36 q^{42} + 84 q^{43} - 40 q^{45} + 8 q^{46} + 4 q^{49} - 20 q^{52} - 12 q^{54} + 16 q^{55} - 8 q^{57} + 8 q^{58} + 24 q^{60} - 32 q^{61} - 28 q^{63} + 16 q^{66} + 92 q^{67} + 84 q^{69} - 8 q^{72} + 84 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} - 24 q^{81} - 48 q^{82} - 8 q^{84} - 152 q^{85} - 96 q^{87} - 88 q^{91} - 48 q^{93} + 32 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) $ 152 * q + 8 * q^7 - 152 * q^16 - 8 * q^18 + 36 * q^19 + 8 * q^21 + 24 * q^27 - 12 * q^28 - 24 * q^30 - 36 * q^31 + 12 * q^33 + 24 * q^36 - 12 * q^37 - 8 * q^39 - 36 * q^42 + 84 * q^43 - 40 * q^45 + 8 * q^46 + 4 * q^49 - 20 * q^52 - 12 * q^54 + 16 * q^55 - 8 * q^57 + 8 * q^58 + 24 * q^60 - 32 * q^61 - 28 * q^63 + 16 * q^66 + 92 * q^67 + 84 * q^69 - 8 * q^72 + 84 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 - 24 * q^81 - 48 * q^82 - 8 * q^84 - 152 * q^85 - 96 * q^87 - 88 * q^91 - 48 * q^93 + 32 * q^94 - 100 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{12}\right)$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−1.72614	−	0.143006i	−0.996586	−	0.0825648i
$3$	−1.72614	−	0.143006i	−0.996586	−	0.0825648i
$4$			1.00000i			0.500000i
$5$	−1.09645	+	0.293793i	−0.490348	+	0.131388i	−0.495517	−	0.868598i	$-0.665021\pi$
$5$	−1.09645	+	0.293793i	−0.490348	+	0.131388i	0.00516881	+	0.999987i	$0.498355\pi$
$6$	1.11944	+	1.32168i	0.457010	+	0.539575i
$7$	−0.0234379	−	2.64565i	−0.00885869	−	0.999961i
$7$	−0.0234379	−	2.64565i	−0.00885869	−	0.999961i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	2.95910	+	0.493697i	0.986366	+	0.164566i
$10$	0.983052	+	0.567565i	0.310868	+	0.179480i
$11$	−0.882338	−	3.29293i	−0.266035	−	0.992856i	−0.961614	−	0.274406i	$-0.911519\pi$
$11$	−0.882338	−	3.29293i	−0.266035	−	0.992856i	0.695579	−	0.718450i	$-0.255148\pi$
$12$	0.143006	−	1.72614i	0.0412824	−	0.498293i
$13$	2.35322	+	2.73173i	0.652666	+	0.757646i
$13$	2.35322	+	2.73173i	0.652666	+	0.757646i
$14$	−1.85418	+	1.88733i	−0.495551	+	0.504410i
$15$	1.93464	−	0.350328i	0.499522	−	0.0904543i
$16$	−1.00000			−0.250000
$17$	2.19941			0.533434			0.266717	−	0.963775i	$-0.414061\pi$
$17$	2.19941			0.533434			0.266717	+	0.963775i	$0.414061\pi$
$18$	−1.74330	−	2.44150i	−0.410900	−	0.575466i
$19$	−2.74521	−	0.735577i	−0.629794	−	0.168753i	−0.0702179	−	0.997532i	$-0.522369\pi$
$19$	−2.74521	−	0.735577i	−0.629794	−	0.168753i	−0.559576	+	0.828779i	$0.689036\pi$
$20$	−0.293793	−	1.09645i	−0.0656942	−	0.245174i
$21$	−0.337887	+	4.57010i	−0.0737331	+	0.997278i
$22$	−1.70455	+	2.95236i	−0.363410	+	0.629445i
$23$	−8.10303			−1.68960			−0.844799	−	0.535084i	$-0.820280\pi$
$23$	−8.10303			−1.68960			−0.844799	+	0.535084i	$0.820280\pi$
$24$	−1.32168	+	1.11944i	−0.269788	+	0.228505i
$25$	−3.21423	+	1.85574i	−0.642847	+	0.371148i
$26$	0.267648	−	3.59560i	0.0524901	−	0.705156i
$27$	−5.03721	−	1.27536i	−0.969411	−	0.245443i
$28$	2.64565	−	0.0234379i	0.499980	−	0.00442934i
$29$	−4.77468	+	2.75666i	−0.886636	+	0.511899i	−0.872841	−	0.488005i	$-0.837725\pi$
$29$	−4.77468	+	2.75666i	−0.886636	+	0.511899i	−0.0137951	+	0.999905i	$0.504391\pi$
$30$	−1.61572	−	1.12028i	−0.294988	−	0.204534i
$31$	5.48451	+	1.46957i	0.985047	+	0.263942i	0.715169	−	0.698952i	$-0.246350\pi$
$31$	5.48451	+	1.46957i	0.985047	+	0.263942i	0.269878	+	0.962894i	$0.413017\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	1.05213	+	5.81023i	0.183152	+	1.01143i
$34$	−1.55521	−	1.55521i	−0.266717	−	0.266717i
$35$	0.802972	+	2.89394i	0.135727	+	0.489165i
$36$	−0.493697	+	2.95910i	−0.0822829	+	0.493183i
$37$	−8.14758	−	8.14758i	−1.33945	−	1.33945i	−0.896588	−	0.442866i	$-0.853962\pi$
$37$	−8.14758	−	8.14758i	−1.33945	−	1.33945i	−0.442866	−	0.896588i	$-0.646038\pi$
$38$	1.42102	+	2.46129i	0.230521	+	0.399274i
$39$	−3.67132	−	5.05187i	−0.587882	−	0.808946i
$40$	−0.567565	+	0.983052i	−0.0897399	+	0.155434i
$41$	−1.60050	+	5.97315i	−0.249956	+	0.932849i	0.720871	+	0.693069i	$0.243742\pi$
$41$	−1.60050	+	5.97315i	−0.249956	+	0.932849i	−0.970827	+	0.239780i	$0.922925\pi$
$42$	3.47047	−	2.99263i	0.535506	−	0.461772i
$43$	−6.18316	−	3.56985i	−0.942924	−	0.544397i	−0.0520480	−	0.998645i	$-0.516575\pi$
$43$	−6.18316	−	3.56985i	−0.942924	−	0.544397i	−0.890876	+	0.454247i	$0.849908\pi$
$44$	3.29293	−	0.882338i	0.496428	−	0.133017i
$45$	−3.38955	+	0.328048i	−0.505285	+	0.0489026i
$46$	5.72971	+	5.72971i	0.844799	+	0.844799i
$47$	2.43712	+	9.09544i	0.355490	+	1.32671i	0.879867	+	0.475220i	$0.157632\pi$
$47$	2.43712	+	9.09544i	0.355490	+	1.32671i	−0.524377	+	0.851486i	$0.675702\pi$
$48$	1.72614	+	0.143006i	0.249146	+	0.0206412i
$49$	−6.99890	+	0.124017i	−0.999843	+	0.0177167i
$50$	3.58501	+	0.960601i	0.506997	+	0.135850i
$51$	−3.79648	−	0.314529i	−0.531613	−	0.0440429i
$52$	−2.73173	+	2.35322i	−0.378823	+	0.326333i
$53$	−1.67323	+	0.966043i	−0.229836	+	0.132696i	−0.610497	−	0.792019i	$-0.709030\pi$
$53$	−1.67323	+	0.966043i	−0.229836	+	0.132696i	0.380660	+	0.924715i	$0.375697\pi$
$54$	2.66003	+	4.46366i	0.361984	+	0.607427i
$55$	1.93488	+	3.35131i	0.260899	+	0.451891i
$56$	−1.88733	−	1.85418i	−0.252205	−	0.247776i
$57$	4.63342	+	1.66229i	0.613711	+	0.220175i
$58$	5.32546	+	1.42695i	0.699268	+	0.187368i
$59$	−0.878024	+	0.878024i	−0.114309	+	0.114309i	−0.761948	−	0.647639i	$-0.775757\pi$
$59$	−0.878024	+	0.878024i	−0.114309	+	0.114309i	0.647639	+	0.761948i	$0.275757\pi$
$60$	0.350328	+	1.93464i	0.0452272	+	0.249761i
$61$	1.71921	+	2.97776i	0.220122	+	0.381263i	0.954845	−	0.297105i	$-0.0960210\pi$
$61$	1.71921	+	2.97776i	0.220122	+	0.381263i	−0.734723	+	0.678368i	$0.762688\pi$
$62$	−2.83899	−	4.91728i	−0.360552	−	0.624495i
$63$	1.23679	−	7.84030i	0.155821	−	0.987785i
$64$		−	1.00000i		−	0.125000i
$65$	−3.38276	−	2.30385i	−0.419579	−	0.285758i
$66$	3.36449	−	4.85242i	0.414140	−	0.597291i
$67$	2.31020	+	8.62180i	0.282236	+	1.05332i	0.950835	+	0.309697i	$0.100228\pi$
$67$	2.31020	+	8.62180i	0.282236	+	1.05332i	−0.668599	+	0.743623i	$0.733106\pi$
$68$			2.19941i			0.266717i
$69$	13.9869	+	1.15878i	1.68383	+	0.139501i
$70$	1.47854	−	2.61411i	0.176719	−	0.312446i
$71$	4.82231	−	1.29213i	0.572303	−	0.153348i	0.0389505	−	0.999241i	$-0.487599\pi$
$71$	4.82231	−	1.29213i	0.572303	−	0.153348i	0.533353	+	0.845893i	$0.320932\pi$
$72$	2.44150	−	1.74330i	0.287733	−	0.205450i
$73$	4.09203	−	15.2717i	0.478936	−	1.78741i	−0.127005	−	0.991902i	$-0.540536\pi$
$73$	4.09203	−	15.2717i	0.478936	−	1.78741i	0.605940	−	0.795510i	$-0.292797\pi$
$74$			11.5224i			1.33945i
$75$	5.81359	−	2.74360i	0.671296	−	0.316804i
$76$	0.735577	−	2.74521i	0.0843764	−	0.314897i
$77$	−8.69125	+	2.41153i	−0.990460	+	0.274820i
$78$	−0.976192	+	6.16823i	−0.110532	+	0.698414i
$79$	−2.69940	+	4.67549i	−0.303706	+	0.526034i	−0.976972	−	0.213366i	$-0.931557\pi$
$79$	−2.69940	+	4.67549i	−0.303706	+	0.526034i	0.673266	+	0.739400i	$0.264891\pi$
$80$	1.09645	−	0.293793i	0.122587	−	0.0328471i
$81$	8.51253	+	2.92180i	0.945836	+	0.324644i
$82$	5.35538	−	3.09193i	0.591403	−	0.341447i
$83$	−9.78838	−	9.78838i	−1.07441	−	1.07441i	−0.996999	−	0.0774152i	$-0.975333\pi$
$83$	−9.78838	−	9.78838i	−1.07441	−	1.07441i	−0.0774152	−	0.996999i	$-0.524667\pi$
$84$	−4.57010	−	0.337887i	−0.498639	−	0.0368665i
$85$	−2.41154	+	0.646171i	−0.261569	+	0.0700871i
$86$	1.84789	+	6.89642i	0.199263	+	0.743660i
$87$	8.63597	−	4.07557i	0.925873	−	0.436947i
$88$	−2.95236	−	1.70455i	−0.314723	−	0.181705i
$89$	−11.4221	+	11.4221i	−1.21074	+	1.21074i	−0.239952	+	0.970785i	$0.577132\pi$
$89$	−11.4221	+	11.4221i	−1.21074	+	1.21074i	−0.970785	+	0.239952i	$0.922868\pi$
$90$	2.62874	+	2.16481i	0.277094	+	0.228191i
$91$	7.17204	−	6.28982i	0.751834	−	0.659352i
$92$		−	8.10303i		−	0.844799i
$93$	−9.25686	−	3.32100i	−0.959891	−	0.344371i
$94$	4.70815	−	8.15475i	0.485608	−	0.841098i
$95$	3.22610			0.330991
$96$	−1.11944	−	1.32168i	−0.114253	−	0.134894i
$97$	−1.01235	−	3.77815i	−0.102789	−	0.383614i	0.895296	−	0.445472i	$-0.146964\pi$
$97$	−1.01235	−	3.77815i	−0.102789	−	0.383614i	−0.998085	+	0.0618582i	$0.980297\pi$
$98$	5.03666	+	4.86128i	0.508780	+	0.491063i
$99$	−0.985214	−	10.1797i	−0.0990178	−	1.02310i
$100$	−1.85574	−	3.21423i	−0.185574	−	0.321423i
$101$	−2.65255	+	4.59436i	−0.263939	+	0.457156i	−0.967285	−	0.253692i	$-0.918355\pi$
$101$	−2.65255	+	4.59436i	−0.263939	+	0.457156i	0.703346	+	0.710848i	$0.251688\pi$
$102$	2.46211	+	2.90692i	0.243785	+	0.287828i
$103$	−8.48228	−	4.89724i	−0.835784	−	0.482540i	0.0200453	−	0.999799i	$-0.493619\pi$
$103$	−8.48228	−	4.89724i	−0.835784	−	0.482540i	−0.855829	+	0.517259i	$0.826952\pi$
$104$	3.59560	+	0.267648i	0.352578	+	0.0262451i
$105$	−0.972188	−	5.11017i	−0.0948759	−	0.498701i
$106$	1.86625	+	0.500060i	0.181266	+	0.0485702i
$107$		−	17.4080i		−	1.68290i	−0.540339	−	0.841448i	$-0.681704\pi$
$107$		−	17.4080i		−	1.68290i	0.540339	−	0.841448i	$-0.318296\pi$
$108$	1.27536	−	5.03721i	0.122721	−	0.484706i
$109$	0.490152	+	0.131336i	0.0469480	+	0.0125797i	0.282217	−	0.959351i	$-0.408930\pi$
$109$	0.490152	+	0.131336i	0.0469480	+	0.0125797i	−0.235269	+	0.971930i	$0.575597\pi$
$110$	1.00157	−	3.73791i	0.0954958	−	0.356395i
$111$	12.8987	+	15.2290i	1.22429	+	1.44547i
$112$	0.0234379	+	2.64565i	0.00221467	+	0.249990i
$113$	6.92105	+	3.99587i	0.651078	+	0.375900i	0.788869	−	0.614561i	$-0.210667\pi$
$113$	6.92105	+	3.99587i	0.651078	+	0.375900i	−0.137791	+	0.990461i	$0.544000\pi$
$114$	−2.10090	−	4.45173i	−0.196768	−	0.416943i
$115$	8.88458	−	2.38062i	0.828491	−	0.221994i
$116$	−2.75666	−	4.77468i	−0.255950	−	0.443318i
$117$	5.61476	+	9.24524i	0.519085	+	0.854723i
$118$	1.24171			0.114309
$119$	−0.0515494	−	5.81885i	−0.00472553	−	0.533413i
$120$	1.12028	−	1.61572i	0.102267	−	0.147494i
$121$	−0.538590	+	0.310955i	−0.0489627	+	0.0282686i
$122$	0.889929	−	3.32126i	0.0805704	−	0.300693i
$123$	3.61688	−	10.0816i	0.326123	−	0.909027i
$124$	−1.46957	+	5.48451i	−0.131971	+	0.492523i
$125$	6.99234	−	6.99234i	0.625414	−	0.625414i
$126$	−6.41848	+	4.66939i	−0.571803	+	0.415982i
$127$	−3.49351	+	2.01698i	−0.309999	+	0.178978i	−0.646926	−	0.762553i	$-0.723946\pi$
$127$	−3.49351	+	2.01698i	−0.309999	+	0.178978i	0.336927	+	0.941531i	$0.390612\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	10.1625	+	7.04628i	0.894756	+	0.620391i
$130$	0.762901	+	4.02104i	0.0669109	+	0.352668i
$131$	−3.20932	−	1.85290i	−0.280400	−	0.161889i	0.353205	−	0.935546i	$-0.385092\pi$
$131$	−3.20932	−	1.85290i	−0.280400	−	0.161889i	−0.633604	+	0.773657i	$0.718425\pi$
$132$	−5.81023	+	1.05213i	−0.505716	+	0.0915758i
$133$	−1.88173	+	7.28010i	−0.163167	+	0.631264i
$134$	4.46297	−	7.73009i	0.385542	−	0.667778i
$135$	5.89775	−	0.0815285i	0.507597	−	0.00701686i
$136$	1.55521	−	1.55521i	0.133359	−	0.133359i
$137$	−3.91063	+	3.91063i	−0.334107	+	0.334107i	−0.854144	−	0.520037i	$-0.825918\pi$
$137$	−3.91063	+	3.91063i	−0.334107	+	0.334107i	0.520037	+	0.854144i	$0.325918\pi$
$138$	−9.07087	−	10.7096i	−0.772164	−	0.911665i
$139$	−0.515944	+	0.893641i	−0.0437618	+	0.0757976i	−0.887077	−	0.461622i	$-0.847268\pi$
$139$	−0.515944	+	0.893641i	−0.0437618	+	0.0757976i	0.843315	+	0.537420i	$0.180601\pi$
$140$	−2.89394	+	0.802972i	−0.244583	+	0.0678635i
$141$	−2.90609	−	16.0485i	−0.244737	−	1.35153i
$142$	−4.32357	−	2.49621i	−0.362826	−	0.209477i
$143$	6.91907	−	10.1593i	0.578601	−	0.849563i
$144$	−2.95910	−	0.493697i	−0.246592	−	0.0411414i
$145$	4.42532	−	4.42532i	0.367503	−	0.367503i
$146$	−13.6922	+	7.90519i	−1.13317	+	0.654238i
$147$	12.0988	+	0.786818i	0.997892	+	0.0648956i
$148$	8.14758	−	8.14758i	0.669727	−	0.669727i
$149$	1.23665	−	4.61525i	0.101310	−	0.378096i	−0.896590	−	0.442862i	$-0.853963\pi$
$149$	1.23665	−	4.61525i	0.101310	−	0.378096i	0.997900	+	0.0647657i	$0.0206300\pi$
$150$	−6.05085	−	2.17081i	−0.494050	−	0.177246i
$151$	3.51554	−	13.1202i	0.286091	−	1.06770i	−0.661948	−	0.749550i	$-0.730270\pi$
$151$	3.51554	−	13.1202i	0.286091	−	1.06770i	0.948039	−	0.318155i	$-0.103063\pi$
$152$	−2.46129	+	1.42102i	−0.199637	+	0.115260i
$153$	6.50826	+	1.08584i	0.526161	+	0.0877850i
$154$	7.85086	+	4.44043i	0.632640	+	0.357820i
$155$	−6.44525			−0.517695
$156$	5.05187	−	3.67132i	0.404473	−	0.293941i
$157$	−10.7094	−	18.5493i	−0.854704	−	1.48039i	−0.876919	−	0.480638i	$-0.840405\pi$
$157$	−10.7094	−	18.5493i	−0.854704	−	1.48039i	0.0222145	−	0.999753i	$-0.492928\pi$
$158$	5.21483	−	1.39731i	0.414870	−	0.111164i
$159$	3.02638	−	1.42824i	0.240008	−	0.113267i
$160$	−0.983052	−	0.567565i	−0.0777171	−	0.0448700i
$161$	0.189918	+	21.4378i	0.0149676	+	1.68953i
$162$	−3.95324	−	8.08529i	−0.310596	−	0.635240i
$163$	−5.37671	+	20.0661i	−0.421136	+	1.57170i	0.351083	+	0.936344i	$0.385814\pi$
$163$	−5.37671	+	20.0661i	−0.421136	+	1.57170i	−0.772219	+	0.635357i	$0.780853\pi$
$164$	−5.97315	−	1.60050i	−0.466425	−	0.124978i
$165$	−2.86061	−	6.06153i	−0.222698	−	0.471889i
$166$			13.8429i			1.07441i
$167$	3.23111	+	0.865773i	0.250031	+	0.0669955i	0.381657	−	0.924304i	$-0.375353\pi$
$167$	3.23111	+	0.865773i	0.250031	+	0.0669955i	−0.131627	+	0.991299i	$0.542020\pi$
$168$	2.99263	+	3.47047i	0.230886	+	0.267753i
$169$	−1.92471	+	12.8567i	−0.148055	+	0.988979i
$170$	2.16213	+	1.24831i	0.165828	+	0.0957407i
$171$	−7.76019	−	3.53195i	−0.593437	−	0.270095i
$172$	3.56985	−	6.18316i	0.272199	−	0.471462i
$173$	4.94260	+	8.56083i	0.375779	+	0.650868i	0.990443	−	0.137921i	$-0.0440419\pi$
$173$	4.94260	+	8.56083i	0.375779	+	0.650868i	−0.614665	+	0.788789i	$0.710709\pi$
$174$	−8.98842	−	3.22469i	−0.681410	−	0.244463i
$175$	4.98497	+	8.46024i	0.376828	+	0.639534i
$176$	0.882338	+	3.29293i	0.0665087	+	0.248214i
$177$	1.64115	−	1.39003i	0.123357	−	0.104481i
$178$	16.1532			1.21074
$179$	−2.39361	+	4.14586i	−0.178907	+	0.309876i	−0.941506	−	0.336995i	$-0.890589\pi$
$179$	−2.39361	+	4.14586i	−0.178907	+	0.309876i	0.762599	+	0.646871i	$0.223923\pi$
$180$	−0.328048	−	3.38955i	−0.0244513	−	0.252642i
$181$			24.1509i			1.79512i	0.440891	+	0.897561i	$0.354663\pi$
$181$			24.1509i			1.79512i	−0.440891	+	0.897561i	$0.645337\pi$
$182$	−9.51897	−	0.623829i	−0.705593	−	0.0462413i
$183$	−2.54175	−	5.38588i	−0.187892	−	0.398136i
$184$	−5.72971	+	5.72971i	−0.422399	+	0.422399i
$185$	11.3271	+	6.53972i	0.832787	+	0.480810i
$186$	4.19728	+	8.89389i	0.307760	+	0.652131i
$187$	−1.94062	−	7.24249i	−0.141912	−	0.529623i
$188$	−9.09544	+	2.43712i	−0.663353	+	0.177745i
$189$	−3.25609	+	13.3566i	−0.236846	+	0.971547i
$190$	−2.28120	−	2.28120i	−0.165495	−	0.165495i
$191$	19.8360	−	11.4523i	1.43528	−	0.828662i	0.437768	−	0.899088i	$-0.355769\pi$
$191$	19.8360	−	11.4523i	1.43528	−	0.828662i	0.997517	+	0.0704260i	$0.0224359\pi$
$192$	−0.143006	+	1.72614i	−0.0103206	+	0.124573i
$193$	−1.44565	+	0.387362i	−0.104060	+	0.0278829i	−0.310474	−	0.950582i	$-0.600488\pi$
$193$	−1.44565	+	0.387362i	−0.104060	+	0.0278829i	0.206413	+	0.978465i	$0.433821\pi$
$194$	−1.95572	+	3.38740i	−0.140412	+	0.243201i
$195$	5.50964	+	4.46052i	0.394553	+	0.319424i
$196$	−0.124017	−	6.99890i	−0.00885834	−	0.499922i
$197$	2.72299	−	10.1623i	0.194005	−	0.724037i	−0.798517	−	0.601972i	$-0.794382\pi$
$197$	2.72299	−	10.1623i	0.194005	−	0.724037i	0.992522	−	0.122065i	$-0.0389516\pi$
$198$	−6.50149	+	7.89480i	−0.462041	+	0.561059i
$199$		−	2.79028i		−	0.197797i	−0.995098	−	0.0988987i	$-0.968468\pi$
$199$		−	2.79028i		−	0.197797i	0.995098	−	0.0988987i	$-0.0315320\pi$
$200$	−0.960601	+	3.58501i	−0.0679248	+	0.253499i
$201$	−2.75476	−	15.2128i	−0.194306	−	1.07303i
$202$	5.12434	−	1.37306i	0.360547	−	0.0966084i
$203$	7.40507	+	12.5675i	0.519734	+	0.882066i
$204$	0.314529	−	3.79648i	0.0220214	−	0.265806i
$205$		−	7.01949i		−	0.490262i
$206$	2.53500	+	9.46075i	0.176622	+	0.659162i
$207$	−23.9777	−	4.00044i	−1.66656	−	0.278050i
$208$	−2.35322	−	2.73173i	−0.163166	−	0.189411i
$209$			9.68881i			0.670189i
$210$	−2.92599	+	4.30087i	−0.201913	+	0.296789i
$211$	−5.39798	−	9.34957i	−0.371612	−	0.643651i	0.618202	−	0.786020i	$-0.287862\pi$
$211$	−5.39798	−	9.34957i	−0.371612	−	0.643651i	−0.989814	+	0.142369i	$0.954528\pi$
$212$	−0.966043	−	1.67323i	−0.0663481	−	0.114918i
$213$	−8.50875	+	1.54078i	−0.583010	+	0.105573i
$214$	−12.3093	+	12.3093i	−0.841448	+	0.841448i
$215$	7.82834	+	2.09760i	0.533888	+	0.143055i
$216$	−4.46366	+	2.66003i	−0.303713	+	0.180992i
$217$	3.75942	−	14.5445i	0.255206	−	0.987346i
$218$	−0.253721	−	0.439458i	−0.0171842	−	0.0297639i
$219$	−9.24735	+	25.7758i	−0.624878	+	1.74177i
$220$	−3.35131	+	1.93488i	−0.225946	+	0.130450i
$221$	5.17569	+	6.00819i	0.348154	+	0.404154i
$222$	1.64778	−	19.8893i	0.110592	−	1.33488i
$223$	12.1140	+	3.24593i	0.811211	+	0.217363i	0.640500	−	0.767958i	$-0.278727\pi$
$223$	12.1140	+	3.24593i	0.811211	+	0.217363i	0.170711	+	0.985321i	$0.445394\pi$
$224$	1.85418	−	1.88733i	0.123888	−	0.126102i
$225$	−10.4274	+	3.90446i	−0.695161	+	0.260297i
$226$	−2.06842	−	7.71943i	−0.137589	−	0.513489i
$227$	−10.8731	−	10.8731i	−0.721674	−	0.721674i	0.247272	−	0.968946i	$-0.420466\pi$
$227$	−10.8731	−	10.8731i	−0.721674	−	0.721674i	−0.968946	+	0.247272i	$0.920466\pi$
$228$	−1.66229	+	4.63342i	−0.110088	+	0.306855i
$229$	−7.97981	+	2.13818i	−0.527321	+	0.141295i	−0.512651	−	0.858597i	$-0.671336\pi$
$229$	−7.97981	+	2.13818i	−0.527321	+	0.141295i	−0.0146699	+	0.999892i	$0.504670\pi$
$230$	−7.96570	−	4.59900i	−0.525242	−	0.303249i
$231$	15.3472	−	2.91973i	1.00977	−	0.192104i
$232$	−1.42695	+	5.32546i	−0.0936841	+	0.349634i
$233$	7.01132	−	12.1440i	0.459327	−	0.795577i	−0.539599	−	0.841922i	$-0.681424\pi$
$233$	7.01132	−	12.1440i	0.459327	−	0.795577i	0.998925	+	0.0463453i	$0.0147574\pi$
$234$	2.56714	−	10.5076i	0.167819	−	0.686904i
$235$	−5.34436	−	9.25670i	−0.348628	−	0.603841i
$236$	−0.878024	−	0.878024i	−0.0571545	−	0.0571545i
$237$	5.32815	−	7.68451i	0.346101	−	0.499163i
$238$	−4.07810	+	4.15100i	−0.264344	+	0.269069i
$239$	−4.81026	−	4.81026i	−0.311150	−	0.311150i	0.534205	−	0.845355i	$-0.320611\pi$
$239$	−4.81026	−	4.81026i	−0.311150	−	0.311150i	−0.845355	+	0.534205i	$0.820611\pi$
$240$	−1.93464	+	0.350328i	−0.124881	+	0.0226136i
$241$	6.70462	+	6.70462i	0.431883	+	0.431883i	0.889268	−	0.457386i	$-0.151214\pi$
$241$	6.70462	+	6.70462i	0.431883	+	0.431883i	−0.457386	+	0.889268i	$0.651214\pi$
$242$	0.600719	+	0.160962i	0.0386157	+	0.0103470i
$243$	−14.2760	−	6.26077i	−0.915803	−	0.401628i
$244$	−2.97776	+	1.71921i	−0.190632	+	0.110061i
$245$	7.63752	−	2.19221i	0.487943	−	0.140055i
$246$	−9.68629	+	4.57124i	−0.617575	+	0.291452i
$247$	−4.45068	−	9.23015i	−0.283190	−	0.587300i
$248$	4.91728	−	2.83899i	0.312247	−	0.180276i
$249$	15.4963	+	18.2959i	0.982037	+	1.15945i
$250$	−9.88867			−0.625414
$251$	−5.88964	+	10.2012i	−0.371751	+	0.643892i	−0.989835	−	0.142220i	$-0.954576\pi$
$251$	−5.88964	+	10.2012i	−0.371751	+	0.643892i	0.618084	+	0.786112i	$0.287909\pi$
$252$	7.84030	+	1.23679i	0.493893	+	0.0779107i
$253$	7.14961	+	26.6827i	0.449492	+	1.67753i
$254$	3.89651	+	1.04407i	0.244489	+	0.0655106i
$255$	4.25506	−	0.770514i	0.266462	−	0.0482514i
$256$	1.00000			0.0625000
$257$	1.82609			0.113908			0.0569541	−	0.998377i	$-0.481861\pi$
$257$	1.82609			0.113908			0.0569541	+	0.998377i	$0.481861\pi$
$258$	−2.20348	−	12.1684i	−0.137183	−	0.757573i
$259$	−21.3647	+	21.7466i	−1.32754	+	1.35127i
$260$	2.30385	−	3.38276i	0.142879	−	0.209790i
$261$	−15.4897	+	5.79999i	−0.958789	+	0.359010i
$262$	0.959133	+	3.57953i	0.0592554	+	0.221144i
$263$	−18.0199	−	10.4038i	−1.11115	−	0.641525i	−0.172025	−	0.985093i	$-0.555031\pi$
$263$	−18.0199	−	10.4038i	−1.11115	−	0.641525i	−0.939128	+	0.343568i	$0.888364\pi$
$264$	4.85242	+	3.36449i	0.298646	+	0.207070i
$265$	1.55080	−	1.55080i	0.0952652	−	0.0952652i
$266$	6.47839	−	3.81722i	0.397216	−	0.234049i
$267$	21.3495	−	18.0826i	1.30657	−	1.10664i
$268$	−8.62180	+	2.31020i	−0.526660	+	0.141118i
$269$			13.5716i			0.827474i	0.910396	+	0.413737i	$0.135777\pi$
$269$			13.5716i			0.827474i	−0.910396	+	0.413737i	$0.864223\pi$
$270$	−4.22799	−	4.11269i	−0.257307	−	0.250290i
$271$	9.76531	+	9.76531i	0.593200	+	0.593200i	0.938495	−	0.345294i	$-0.112221\pi$
$271$	9.76531	+	9.76531i	0.593200	+	0.593200i	−0.345294	+	0.938495i	$0.612221\pi$
$272$	−2.19941			−0.133359
$273$	−13.2794	+	9.83144i	−0.803707	+	0.595026i
$274$	5.53046			0.334107
$275$	8.94686	+	8.94686i	0.539516	+	0.539516i
$276$	−1.15878	+	13.9869i	−0.0697506	+	0.841915i
$277$		−	6.39491i		−	0.384233i	−0.981372	−	0.192116i	$-0.938465\pi$
$277$		−	6.39491i		−	0.384233i	0.981372	−	0.192116i	$-0.0615351\pi$
$278$	0.996727	−	0.267072i	0.0597797	−	0.0160179i
$279$	15.5037	+	7.05629i	0.928181	+	0.422449i
$280$	2.61411	+	1.47854i	0.156223	+	0.0883595i
$281$	13.8916	−	13.8916i	0.828701	−	0.828701i	−0.158636	−	0.987337i	$-0.550710\pi$
$281$	13.8916	−	13.8916i	0.828701	−	0.828701i	0.987337	+	0.158636i	$0.0507097\pi$
$282$	−9.29309	+	13.4029i	−0.553395	+	0.798132i
$283$	−3.82165	−	2.20643i	−0.227174	−	0.131159i	0.382094	−	0.924124i	$-0.375203\pi$
$283$	−3.82165	−	2.20643i	−0.227174	−	0.131159i	−0.609267	+	0.792965i	$0.708536\pi$
$284$	1.29213	+	4.82231i	0.0766741	+	0.286152i
$285$	−5.56869	−	0.461352i	−0.329860	−	0.0273282i
$286$	−12.0762	+	2.29119i	−0.714082	+	0.135481i
$287$	15.8404	+	4.09436i	0.935027	+	0.241683i
$288$	1.74330	+	2.44150i	0.102725	+	0.143866i
$289$	−12.1626			−0.715448
$290$	−6.25834			−0.367503
$291$	1.20716	+	6.66639i	0.0707650	+	0.390790i
$292$	15.2717	+	4.09203i	0.893706	+	0.239468i
$293$	−1.20732	−	4.50577i	−0.0705323	−	0.263230i	0.921651	−	0.388020i	$-0.126841\pi$
$293$	−1.20732	−	4.50577i	−0.0705323	−	0.263230i	−0.992183	+	0.124790i	$0.960174\pi$
$294$	−7.99878	−	9.11151i	−0.466498	−	0.531394i
$295$	0.704753	−	1.22067i	0.0410323	−	0.0710701i
$296$	−11.5224			−0.669727
$297$	0.244851	+	17.7125i	0.0142077	+	1.02778i
$298$	−4.13792	+	2.38903i	−0.239703	+	0.138393i
$299$	−19.0682	−	22.1353i	−1.10274	−	1.28012i
$300$	2.74360	+	5.81359i	0.158402	+	0.335648i
$301$	−9.29965	+	16.4421i	−0.536023	+	0.947709i
$302$	−11.7632	+	6.79150i	−0.676898	+	0.390807i
$303$	5.23570	−	7.55116i	0.300783	−	0.433803i
$304$	2.74521	+	0.735577i	0.157449	+	0.0421882i
$305$	−2.75988	−	2.75988i	−0.158030	−	0.158030i
$306$	−3.83423	−	5.36984i	−0.219188	−	0.306973i
$307$	14.8782	+	14.8782i	0.849146	+	0.849146i	0.990027	−	0.140881i	$-0.0449933\pi$
$307$	14.8782	+	14.8782i	0.849146	+	0.849146i	−0.140881	+	0.990027i	$0.544993\pi$
$308$	−2.41153	−	8.69125i	−0.137410	−	0.495230i
$309$	13.9412	+	9.66633i	0.793089	+	0.549899i
$310$	4.55748	+	4.55748i	0.258847	+	0.258847i
$311$	−7.60179	−	13.1667i	−0.431058	−	0.746614i	0.565907	−	0.824469i	$-0.308526\pi$
$311$	−7.60179	−	13.1667i	−0.431058	−	0.746614i	−0.996965	+	0.0778549i	$0.975193\pi$
$312$	−6.16823	−	0.976192i	−0.349207	−	0.0552660i
$313$	−1.79003	+	3.10042i	−0.101178	+	0.175246i	−0.912170	−	0.409811i	$-0.865595\pi$
$313$	−1.79003	+	3.10042i	−0.101178	+	0.175246i	0.810992	+	0.585057i	$0.198928\pi$
$314$	−5.54360	+	20.6890i	−0.312844	+	1.16755i
$315$	0.947344	+	8.95988i	0.0533768	+	0.504832i
$316$	−4.67549	−	2.69940i	−0.263017	−	0.151853i
$317$	19.0265	−	5.09812i	1.06863	−	0.286339i	0.318701	−	0.947855i	$-0.396753\pi$
$317$	19.0265	−	5.09812i	1.06863	−	0.286339i	0.749931	+	0.661516i	$0.230087\pi$
$318$	−3.14989	−	1.13006i	−0.176637	−	0.0633705i
$319$	13.2904	+	13.2904i	0.744118	+	0.744118i
$320$	0.293793	+	1.09645i	0.0164235	+	0.0612935i
$321$	−2.48946	+	30.0486i	−0.138948	+	1.67715i
$322$	15.0245	−	15.2931i	0.837282	−	0.852250i
$323$	−6.03783	−	1.61783i	−0.335954	−	0.0900185i
$324$	−2.92180	+	8.51253i	−0.162322	+	0.472918i
$325$	−12.6332	−	4.41346i	−0.700763	−	0.244815i
$326$	17.9908	−	10.3870i	0.996419	−	0.575283i
$327$	−0.827287	−	0.296798i	−0.0457491	−	0.0164130i
$328$	3.09193	+	5.35538i	0.170723	+	0.295701i
$329$	24.0062	−	6.66093i	1.32351	−	0.367229i
$330$	−2.26339	+	6.30891i	−0.124595	+	0.347294i
$331$	−29.0774	−	7.79128i	−1.59824	−	0.428247i	−0.653730	−	0.756728i	$-0.726797\pi$
$331$	−29.0774	−	7.79128i	−1.59824	−	0.428247i	−0.944511	+	0.328480i	$0.893464\pi$
$332$	9.78838	−	9.78838i	0.537207	−	0.537207i
$333$	−20.0871	−	28.1319i	−1.10076	−	1.54162i
$334$	−1.67254	−	2.89693i	−0.0915176	−	0.158513i
$335$	−5.06605	−	8.77466i	−0.276788	−	0.479411i
$336$	0.337887	−	4.57010i	0.0184333	−	0.249320i
$337$		−	10.1673i		−	0.553846i	−0.960892	−	0.276923i	$-0.910685\pi$
$337$		−	10.1673i		−	0.553846i	0.960892	−	0.276923i	$-0.0893147\pi$
$338$	10.4521	−	7.73010i	0.568517	−	0.420462i
$339$	−11.3752	−	7.88718i	−0.617819	−	0.428373i
$340$	−0.646171	−	2.41154i	−0.0350435	−	0.130784i
$341$		−	19.3568i		−	1.04823i
$342$	2.98982	+	7.98475i	0.161671	+	0.431766i
$343$	0.492144	+	18.5137i	0.0265733	+	0.999647i
$344$	−6.89642	+	1.84789i	−0.371830	+	0.0996316i
$345$	−15.6764	+	2.83872i	−0.843991	+	0.152831i
$346$	2.55848	−	9.54836i	0.137545	−	0.513323i
$347$			10.1547i			0.545132i	0.962137	+	0.272566i	$0.0878723\pi$
$347$			10.1547i			0.545132i	−0.962137	+	0.272566i	$0.912128\pi$
$348$	4.07557	+	8.63597i	0.218473	+	0.462937i
$349$	4.73132	−	17.6575i	0.253262	−	0.945186i	−0.715787	−	0.698318i	$-0.753932\pi$
$349$	4.73132	−	17.6575i	0.253262	−	0.945186i	0.969049	−	0.246868i	$-0.0794013\pi$
$350$	2.45739	−	9.50720i	0.131353	−	0.508181i
$351$	−8.36972	−	16.7615i	−0.446743	−	0.894663i
$352$	1.70455	−	2.95236i	0.0908526	−	0.157361i
$353$	−3.27176	+	0.876666i	−0.174138	+	0.0466602i	−0.344835	−	0.938663i	$-0.612065\pi$
$353$	−3.27176	+	0.876666i	−0.174138	+	0.0466602i	0.170696	+	0.985324i	$0.445398\pi$
$354$	−2.14337	−	0.177573i	−0.113919	−	0.00943790i
$355$	−4.90781	+	2.83353i	−0.260480	+	0.150388i
$356$	−11.4221	−	11.4221i	−0.605368	−	0.605368i
$357$	−0.743152	+	10.0515i	−0.0393318	+	0.531982i
$358$	4.62411	−	1.23903i	0.244392	−	0.0654845i
$359$	4.51245	+	16.8407i	0.238158	+	0.888818i	0.976700	+	0.214610i	$0.0688480\pi$
$359$	4.51245	+	16.8407i	0.238158	+	0.888818i	−0.738542	+	0.674208i	$0.764485\pi$
$360$	−2.16481	+	2.62874i	−0.114096	+	0.138547i
$361$	−9.45938	−	5.46138i	−0.497862	−	0.287441i
$362$	17.0773	−	17.0773i	0.897561	−	0.897561i
$363$	0.974148	−	0.459729i	0.0511295	−	0.0241295i
$364$	6.28982	+	7.17204i	0.329676	+	0.375917i
$365$			17.9468i			0.939381i
$366$	−2.01110	+	5.60568i	−0.105122	+	0.293014i
$367$	2.50704	−	4.34231i	0.130866	−	0.226667i	−0.793144	−	0.609033i	$-0.791557\pi$
$367$	2.50704	−	4.34231i	0.130866	−	0.226667i	0.924011	+	0.382367i	$0.124891\pi$
$368$	8.10303			0.422399
$369$	−7.68497	+	16.8850i	−0.400063	+	0.878997i
$370$	−3.38521	−	12.6338i	−0.175989	−	0.656799i
$371$	2.59503	+	4.40415i	0.134727	+	0.228652i
$372$	3.32100	−	9.25686i	0.172186	−	0.479946i
$373$	−0.939328	−	1.62696i	−0.0486366	−	0.0842410i	0.840682	−	0.541529i	$-0.182154\pi$
$373$	−0.939328	−	1.62696i	−0.0486366	−	0.0842410i	−0.889319	+	0.457288i	$0.848821\pi$
$374$	−3.74899	+	6.49344i	−0.193856	+	0.335768i
$375$	−13.0697	+	11.0698i	−0.674916	+	0.571642i
$376$	8.15475	+	4.70815i	0.420549	+	0.242804i
$377$	−18.7663	−	6.55611i	−0.966515	−	0.337657i
$378$	11.7469	−	7.14212i	0.604196	−	0.367351i
$379$	8.19927	+	2.19699i	0.421168	+	0.112852i	0.463177	−	0.886266i	$-0.346709\pi$
$379$	8.19927	+	2.19699i	0.421168	+	0.112852i	−0.0420093	+	0.999117i	$0.513376\pi$
$380$			3.22610i			0.165495i
$381$	6.31873	−	2.98199i	0.323718	−	0.152772i
$382$	−22.1242	−	5.92817i	−1.13197	−	0.303311i
$383$	−0.714682	+	2.66723i	−0.0365186	+	0.136289i	−0.981778	−	0.190030i	$-0.939142\pi$
$383$	−0.714682	+	2.66723i	−0.0365186	+	0.136289i	0.945260	+	0.326319i	$0.105808\pi$
$384$	1.32168	−	1.11944i	0.0674469	−	0.0571263i
$385$	8.82105	−	5.19756i	0.449562	−	0.264892i
$386$	1.29614	+	0.748325i	0.0659717	+	0.0380888i
$387$	−16.5342	−	13.6162i	−0.840479	−	0.692148i
$388$	3.77815	−	1.01235i	0.191807	−	0.0513945i
$389$	−16.2841	−	28.2049i	−0.825636	−	1.43004i	−0.901432	−	0.432920i	$-0.857483\pi$
$389$	−16.2841	−	28.2049i	−0.825636	−	1.43004i	0.0757963	−	0.997123i	$-0.475850\pi$
$390$	−0.741838	−	7.04996i	−0.0375644	−	0.356989i
$391$	−17.8218			−0.901289
$392$	−4.86128	+	5.03666i	−0.245532	+	0.254390i
$393$	5.27475	+	3.65732i	0.266076	+	0.184487i
$394$	−9.11131	+	5.26042i	−0.459021	+	0.265016i
$395$	1.58613	−	5.91952i	0.0798069	−	0.297843i
$396$	10.1797	−	0.985214i	0.511550	−	0.0495089i
$397$	5.88680	−	21.9698i	0.295450	−	1.10263i	−0.645410	−	0.763837i	$-0.723313\pi$
$397$	5.88680	−	21.9698i	0.295450	−	1.10263i	0.940859	−	0.338797i	$-0.110020\pi$
$398$	−1.97302	+	1.97302i	−0.0988987	+	0.0988987i
$399$	4.28923	−	12.2973i	0.214730	−	0.615637i
$400$	3.21423	−	1.85574i	0.160712	−	0.0927870i
$401$	27.1884	−	27.1884i	1.35772	−	1.35772i	0.481007	−	0.876717i	$-0.340271\pi$
$401$	27.1884	−	27.1884i	1.35772	−	1.35772i	0.876717	−	0.481007i	$-0.159729\pi$
$402$	−8.80915	+	12.7050i	−0.439361	+	0.633666i
$403$	8.89178	+	18.4404i	0.442931	+	0.918583i
$404$	−4.59436	−	2.65255i	−0.228578	−	0.131970i
$405$	−10.1920	−	0.702686i	−0.506444	−	0.0349168i
$406$	3.65040	−	14.1227i	0.181166	−	0.700900i
$407$	−19.6405	+	34.0183i	−0.973543	+	1.68623i
$408$	−2.90692	+	2.46211i	−0.143914	+	0.121893i
$409$	1.28701	−	1.28701i	0.0636386	−	0.0636386i	−0.674571	−	0.738210i	$-0.735671\pi$
$409$	1.28701	−	1.28701i	0.0636386	−	0.0636386i	0.738210	+	0.674571i	$0.235671\pi$
$410$	−4.96353	+	4.96353i	−0.245131	+	0.245131i
$411$	7.30952	−	6.19103i	0.360552	−	0.305381i
$412$	4.89724	−	8.48228i	0.241270	−	0.417892i
$413$	2.34352	+	2.30236i	0.115317	+	0.113292i
$414$	14.1260	+	19.7835i	0.694256	+	0.972306i
$415$	13.6082	+	7.85673i	0.668003	+	0.385671i
$416$	−0.267648	+	3.59560i	−0.0131225	+	0.176289i
$417$	1.01839	−	1.46876i	0.0498706	−	0.0719257i
$418$	6.85102	−	6.85102i	0.335094	−	0.335094i
$419$	34.5179	−	19.9289i	1.68631	−	0.973592i	0.729007	−	0.684506i	$-0.239982\pi$
$419$	34.5179	−	19.9289i	1.68631	−	0.973592i	0.957303	−	0.289086i	$-0.0933512\pi$
$420$	5.11017	−	0.972188i	0.249351	−	0.0474379i
$421$	−1.40551	+	1.40551i	−0.0685005	+	0.0685005i	−0.740527	−	0.672027i	$-0.765424\pi$
$421$	−1.40551	+	1.40551i	−0.0685005	+	0.0685005i	0.672027	+	0.740527i	$0.265424\pi$
$422$	−2.79420	+	10.4281i	−0.136019	+	0.507632i
$423$	2.72127	+	28.1175i	0.132313	+	1.36712i
$424$	−0.500060	+	1.86625i	−0.0242851	+	0.0906332i
$425$	−7.06941	+	4.08152i	−0.342917	+	0.197983i
$426$	7.10609	+	4.92710i	0.344291	+	0.238719i
$427$	7.83781	−	4.61822i	0.379298	−	0.223491i
$428$	17.4080			0.841448
$429$	−13.3961	+	16.5469i	−0.646770	+	0.798891i
$430$	−4.05225	−	7.01870i	−0.195417	−	0.338472i
$431$	1.64141	−	0.439813i	0.0790637	−	0.0211851i	−0.219070	−	0.975709i	$-0.570302\pi$
$431$	1.64141	−	0.439813i	0.0790637	−	0.0211851i	0.298134	+	0.954524i	$0.403636\pi$
$432$	5.03721	+	1.27536i	0.242353	+	0.0613607i
$433$	−26.9379	−	15.5526i	−1.29455	−	0.747410i	−0.315094	−	0.949061i	$-0.602036\pi$
$433$	−26.9379	−	15.5526i	−1.29455	−	0.747410i	−0.979457	+	0.201651i	$0.935369\pi$
$434$	−12.9428	+	7.62622i	−0.621276	+	0.366070i
$435$	−8.27155	+	7.00586i	−0.396591	+	0.335905i
$436$	−0.131336	+	0.490152i	−0.00628984	+	0.0234740i
$437$	22.2445	+	5.96040i	1.06410	+	0.285124i
$438$	24.7651	−	11.6874i	1.18332	−	0.558444i
$439$			28.8836i			1.37854i	0.724504	+	0.689270i	$0.242069\pi$
$439$			28.8836i			1.37854i	−0.724504	+	0.689270i	$0.757931\pi$
$440$	3.73791	+	1.00157i	0.178198	+	0.0477479i
$441$	−20.7717	−	3.08836i	−0.989127	−	0.147065i
$442$	0.588667	−	7.90819i	0.0280000	−	0.376154i
$443$	−6.01738	−	3.47414i	−0.285894	−	0.165061i	0.350194	−	0.936677i	$-0.386116\pi$
$443$	−6.01738	−	3.47414i	−0.285894	−	0.165061i	−0.636089	+	0.771616i	$0.719449\pi$
$444$	−15.2290	+	12.8987i	−0.722736	+	0.612144i
$445$	9.16802	−	15.8795i	0.434606	−	0.752759i
$446$	−6.27065	−	10.8611i	−0.296924	−	0.514287i
$447$	−2.79464	+	7.78970i	−0.132182	+	0.368440i
$448$	−2.64565	+	0.0234379i	−0.124995	+	0.00110734i
$449$	−0.550451	−	2.05431i	−0.0259774	−	0.0969490i	0.951720	−	0.306967i	$-0.0993143\pi$
$449$	−0.550451	−	2.05431i	−0.0259774	−	0.0969490i	−0.977697	+	0.210018i	$0.932648\pi$
$450$	10.1342	+	4.61242i	0.477729	+	0.217432i
$451$	21.0814			0.992682
$452$	−3.99587	+	6.92105i	−0.187950	+	0.325539i
$453$	−7.94457	+	22.1445i	−0.373269	+	1.04044i
$454$			15.3769i			0.721674i
$455$	−6.01589	+	9.00358i	−0.282029	+	0.422094i
$456$	4.45173	−	2.10090i	0.208472	−	0.0983838i
$457$	12.2243	−	12.2243i	0.571829	−	0.571829i	−0.360810	−	0.932639i	$-0.617500\pi$
$457$	12.2243	−	12.2243i	0.571829	−	0.571829i	0.932639	+	0.360810i	$0.117500\pi$
$458$	7.15450	+	4.13065i	0.334308	+	0.193013i
$459$	−11.0789	−	2.80503i	−0.517117	−	0.130928i
$460$	2.38062	+	8.88458i	0.110997	+	0.414246i
$461$	−2.26528	+	0.606980i	−0.105505	+	0.0282699i	−0.311185	−	0.950349i	$-0.600726\pi$
$461$	−2.26528	+	0.606980i	−0.105505	+	0.0282699i	0.205680	+	0.978619i	$0.434059\pi$
$462$	−12.9166	−	8.78752i	−0.600937	−	0.408832i
$463$	−9.55924	−	9.55924i	−0.444256	−	0.444256i	0.449184	−	0.893439i	$-0.351715\pi$
$463$	−9.55924	−	9.55924i	−0.444256	−	0.444256i	−0.893439	+	0.449184i	$0.851715\pi$
$464$	4.77468	−	2.75666i	0.221659	−	0.127975i
$465$	11.1254	+	0.921712i	0.515927	+	0.0427434i
$466$	−13.5448	+	3.62932i	−0.627452	+	0.168125i
$467$	−8.47142	+	14.6729i	−0.392010	+	0.678982i	−0.992715	−	0.120489i	$-0.961554\pi$
$467$	−8.47142	+	14.6729i	−0.392010	+	0.678982i	0.600704	+	0.799471i	$0.294887\pi$
$468$	−9.24524	+	5.61476i	−0.427361	+	0.259542i
$469$	22.7561	−	6.31406i	1.05078	−	0.291556i
$470$	−2.76644	+	10.3245i	−0.127607	+	0.476234i
$471$	15.8333	+	33.5501i	0.729558	+	1.54591i
$472$			1.24171i			0.0571545i
$473$	−6.29963	+	23.5105i	−0.289657	+	1.08102i
$474$	−9.20134	+	1.66620i	−0.422632	+	0.0765309i
$475$	10.1888	−	2.73008i	0.467494	−	0.125265i
$476$	5.81885	−	0.0515494i	0.266707	−	0.00236276i
$477$	−5.42820	+	2.03254i	−0.248540	+	0.0930638i
$478$			6.80274i			0.311150i
$479$	−9.96678	−	37.1965i	−0.455394	−	1.69955i	−0.686928	−	0.726726i	$-0.741041\pi$
$479$	−9.96678	−	37.1965i	−0.455394	−	1.69955i	0.231534	−	0.972827i	$-0.425626\pi$
$480$	1.61572	+	1.12028i	0.0737470	+	0.0511335i
$481$	3.08395	−	41.4300i	0.140616	−	1.88905i
$482$		−	9.48177i		−	0.431883i
$483$	2.73791	−	37.0317i	0.124579	−	1.68500i
$484$	−0.310955	−	0.538590i	−0.0141343	−	0.0244813i
$485$	2.21999	+	3.84514i	0.100805	+	0.174599i
$486$	5.66759	+	14.5217i	0.257087	+	0.658716i
$487$	22.4005	−	22.4005i	1.01506	−	1.01506i	0.0151799	−	0.999885i	$-0.495168\pi$
$487$	22.4005	−	22.4005i	1.01506	−	1.01506i	0.999885	−	0.0151799i	$-0.00483211\pi$
$488$	3.32126	+	0.889929i	0.150346	+	0.0402852i
$489$	12.1505	−	33.8680i	0.549465	−	1.53156i
$490$	−6.95067	−	3.85042i	−0.313999	−	0.173944i
$491$	−5.71235	−	9.89407i	−0.257795	−	0.446513i	0.707856	−	0.706357i	$-0.249662\pi$
$491$	−5.71235	−	9.89407i	−0.257795	−	0.446513i	−0.965651	+	0.259843i	$0.916329\pi$
$492$	10.0816	+	3.61688i	0.454513	+	0.163062i
$493$	−10.5015	+	6.06302i	−0.472962	+	0.273065i
$494$	−3.37959	+	9.67381i	−0.152055	+	0.435245i
$495$	4.07097	+	10.8721i	0.182977	+	0.488665i
$496$	−5.48451	−	1.46957i	−0.246262	−	0.0659856i
$497$	−3.53156	−	12.7279i	−0.158412	−	0.570922i
$498$	1.97962	−	23.8947i	0.0887088	−	1.07075i
$499$	−0.649442	−	2.42375i	−0.0290730	−	0.108502i	0.949865	−	0.312661i	$-0.101221\pi$
$499$	−0.649442	−	2.42375i	−0.0290730	−	0.108502i	−0.978938	+	0.204160i	$0.934554\pi$
$500$	6.99234	+	6.99234i	0.312707	+	0.312707i
$501$	−5.45352	−	1.95651i	−0.243646	−	0.0874105i
$502$	11.3779	−	3.04870i	0.507821	−	0.136070i
$503$	11.4480	+	6.60949i	0.510440	+	0.294703i	0.733015	−	0.680213i	$-0.238113\pi$
$503$	11.4480	+	6.60949i	0.510440	+	0.294703i	−0.222574	+	0.974916i	$0.571446\pi$
$504$	−4.66939	−	6.41848i	−0.207991	−	0.285902i
$505$	1.55861	−	5.81680i	0.0693571	−	0.258844i
$506$	13.8120	−	23.9231i	0.614018	−	1.06351i
$507$	5.16091	−	21.9172i	0.229204	−	0.973378i
$508$	−2.01698	−	3.49351i	−0.0894891	−	0.155000i
$509$	−5.74526	−	5.74526i	−0.254654	−	0.254654i	0.568221	−	0.822876i	$-0.307632\pi$
$509$	−5.74526	−	5.74526i	−0.254654	−	0.254654i	−0.822876	+	0.568221i	$0.807632\pi$
$510$	−3.55362	−	2.46395i	−0.157357	−	0.109105i
$511$	−40.4993	−	10.4681i	−1.79158	−	0.463083i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	12.8901	+	7.20638i	0.569110	+	0.318169i
$514$	−1.29124	−	1.29124i	−0.0569541	−	0.0569541i
$515$	10.7392	+	2.87756i	0.473225	+	0.126800i
$516$	−7.04628	+	10.1625i	−0.310195	+	0.447378i
$517$	27.8003	−	16.0505i	1.22266	−	0.705900i
$518$	30.4843	−	0.270061i	1.33940	−	0.0118658i
$519$	−7.30735	−	15.4840i	−0.320757	−	0.679672i
$520$	−4.02104	+	0.762901i	−0.176334	+	0.0334554i
$521$	28.1014	−	16.2244i	1.23115	−	0.710802i	0.263877	−	0.964556i	$-0.414999\pi$
$521$	28.1014	−	16.2244i	1.23115	−	0.710802i	0.967269	+	0.253754i	$0.0816655\pi$
$522$	15.0541	+	6.85166i	0.658899	+	0.299889i
$523$	4.99027			0.218209			0.109105	−	0.994030i	$-0.465202\pi$
$523$	4.99027			0.218209			0.109105	+	0.994030i	$0.465202\pi$
$524$	1.85290	−	3.20932i	0.0809444	−	0.140200i
$525$	−7.39487	−	15.3164i	−0.322739	−	0.668463i
$526$	5.38539	+	20.0986i	0.234814	+	0.876339i
$527$	12.0627	+	3.23218i	0.525458	+	0.140796i
$528$	−1.05213	−	5.81023i	−0.0457879	−	0.252858i
$529$	42.6590			1.85474
$530$	−2.19317			−0.0952652
$531$	−3.03164	+	2.16468i	−0.131562	+	0.0939392i
$532$	−7.28010	−	1.88173i	−0.315632	−	0.0815835i
$533$	−20.0834	+	9.68400i	−0.869908	+	0.419461i
$534$	−27.8827	−	2.31002i	−1.20660	−	0.0999642i
$535$	5.11436	+	19.0870i	0.221113	+	0.825205i
$536$	7.73009	+	4.46297i	0.333889	+	0.192771i
$537$	4.72459	−	6.81402i	0.203881	−	0.294047i
$538$	9.59656	−	9.59656i	0.413737	−	0.413737i
$539$	6.58377	+	22.9375i	0.283583	+	0.987987i
$540$	0.0815285	+	5.89775i	0.00350843	+	0.253799i
$541$	38.7325	−	10.3784i	1.66524	−	0.446200i	0.701420	−	0.712748i	$-0.252550\pi$
$541$	38.7325	−	10.3784i	1.66524	−	0.446200i	0.963822	+	0.266548i	$0.0858831\pi$
$542$		−	13.8102i		−	0.593200i
$543$	3.45373	−	41.6877i	0.148214	−	1.78899i
$544$	1.55521	+	1.55521i	0.0666793	+	0.0666793i
$545$	−0.576013			−0.0246737
$546$	16.3418	+	2.43809i	0.699366	+	0.104341i
$547$	−13.6896			−0.585325			−0.292663	−	0.956216i	$-0.594541\pi$
$547$	−13.6896			−0.585325			−0.292663	+	0.956216i	$0.594541\pi$
$548$	−3.91063	−	3.91063i	−0.167054	−	0.167054i
$549$	3.61720	+	9.66025i	0.154378	+	0.412289i
$550$		−	12.6528i		−	0.539516i
$551$	15.1352	−	4.05547i	0.644782	−	0.172769i
$552$	10.7096	−	9.07087i	0.455833	−	0.386082i
$553$	12.4330	+	7.03207i	0.528704	+	0.299034i
$554$	−4.52188	+	4.52188i	−0.192116	+	0.192116i
$555$	−18.6170	−	12.9083i	−0.790246	−	0.547927i
$556$	−0.893641	−	0.515944i	−0.0378988	−	0.0218809i
$557$	6.65086	+	24.8213i	0.281806	+	1.05171i	0.951142	+	0.308754i	$0.0999120\pi$
$557$	6.65086	+	24.8213i	0.281806	+	1.05171i	−0.669336	+	0.742960i	$0.733421\pi$
$558$	−5.97321	−	15.9523i	−0.252866	−	0.675315i
$559$	−4.79847	−	25.2914i	−0.202954	−	1.06971i
$560$	−0.802972	−	2.89394i	−0.0339318	−	0.122291i
$561$	2.31405	+	12.7791i	0.0976994	+	0.539532i
$562$	−19.6456			−0.828701
$563$	−11.0916			−0.467454			−0.233727	−	0.972302i	$-0.575092\pi$
$563$	−11.0916			−0.467454			−0.233727	+	0.972302i	$0.575092\pi$
$564$	16.0485	−	2.90609i	0.675764	−	0.122368i
$565$	−8.76256	−	2.34792i	−0.368644	−	0.0987778i
$566$	1.14213	+	4.26250i	0.0480074	+	0.179166i
$567$	7.53053	−	22.5896i	0.316253	−	0.948675i
$568$	2.49621	−	4.32357i	0.104739	−	0.181413i
$569$	−7.24611			−0.303773			−0.151886	−	0.988398i	$-0.548535\pi$
$569$	−7.24611			−0.303773			−0.151886	+	0.988398i	$0.548535\pi$
$570$	3.61143	+	4.26388i	0.151266	+	0.178594i
$571$	−8.26580	+	4.77226i	−0.345913	+	0.199713i	−0.662884	−	0.748722i	$-0.730668\pi$
$571$	−8.26580	+	4.77226i	−0.345913	+	0.199713i	0.316971	+	0.948435i	$0.397334\pi$
$572$	10.1593	+	6.91907i	0.424782	+	0.289301i
$573$	−35.8775	+	16.9316i	−1.49880	+	0.707329i
$574$	−8.30568	−	14.0960i	−0.346672	−	0.588355i
$575$	26.0450	−	15.0371i	1.08615	−	0.627091i
$576$	0.493697	−	2.95910i	0.0205707	−	0.123296i
$577$	−9.45512	−	2.53349i	−0.393622	−	0.105471i	0.0565786	−	0.998398i	$-0.481981\pi$
$577$	−9.45512	−	2.53349i	−0.393622	−	0.105471i	−0.450201	+	0.892927i	$0.648648\pi$
$578$	8.60027	+	8.60027i	0.357724	+	0.357724i
$579$	2.55079	−	0.461902i	0.106007	−	0.0191960i
$580$	4.42532	+	4.42532i	0.183751	+	0.183751i
$581$	−25.6672	+	26.1260i	−1.06485	+	1.08389i
$582$	3.86026	−	5.56744i	0.160013	−	0.230778i
$583$	4.65747	+	4.65747i	0.192893	+	0.192893i
$584$	−7.90519	−	13.6922i	−0.327119	−	0.566587i
$585$	−8.87251	−	8.48738i	−0.366833	−	0.350910i
$586$	−2.33236	+	4.03977i	−0.0963489	+	0.166881i
$587$	−0.00331697	+	0.0123791i	−0.000136906	+	0.000510940i	−0.965994	−	0.258564i	$-0.916751\pi$
$587$	−0.00331697	+	0.0123791i	−0.000136906	+	0.000510940i	0.965857	+	0.259075i	$0.0834175\pi$
$588$	−0.786818	+	12.0988i	−0.0324478	+	0.498946i
$589$	−13.9751	−	8.06855i	−0.575836	−	0.332459i
$590$	−1.36148	+	0.364807i	−0.0560512	+	0.0150189i
$591$	−6.15354	+	17.1522i	−0.253123	+	0.705547i
$592$	8.14758	+	8.14758i	0.334863	+	0.334863i
$593$	7.35053	+	27.4325i	0.301850	+	1.12652i	0.935623	+	0.353001i	$0.114839\pi$
$593$	7.35053	+	27.4325i	0.301850	+	1.12652i	−0.633773	+	0.773519i	$0.718495\pi$
$594$	12.3515	−	12.6977i	0.506787	−	0.520995i
$595$	1.76606	+	6.36495i	0.0724015	+	0.260937i
$596$	4.61525	+	1.23665i	0.189048	+	0.0506552i
$597$	−0.399027	+	4.81640i	−0.0163311	+	0.197122i
$598$	−2.16876	+	29.1353i	−0.0886872	+	1.19143i
$599$	12.1259	−	7.00089i	0.495451	−	0.286049i	−0.231382	−	0.972863i	$-0.574325\pi$
$599$	12.1259	−	7.00089i	0.495451	−	0.286049i	0.726833	+	0.686814i	$0.240991\pi$
$600$	2.17081	−	6.05085i	0.0886229	−	0.247025i
$601$	8.32868	+	14.4257i	0.339734	+	0.588436i	0.984383	−	0.176043i	$-0.0563297\pi$
$601$	8.32868	+	14.4257i	0.339734	+	0.588436i	−0.644649	+	0.764479i	$0.722996\pi$
$602$	18.2022	−	5.05051i	0.741866	−	0.205843i
$603$	2.57956	+	26.6533i	0.105048	+	1.08541i
$604$	13.1202	+	3.51554i	0.533852	+	0.143045i
$605$	0.499181	−	0.499181i	0.0202946	−	0.0202946i
$606$	−9.04167	+	1.63728i	−0.367293	+	0.0665100i
$607$	−7.38332	−	12.7883i	−0.299680	−	0.519061i	0.676383	−	0.736550i	$-0.263547\pi$
$607$	−7.38332	−	12.7883i	−0.299680	−	0.519061i	−0.976063	+	0.217490i	$0.930213\pi$
$608$	−1.42102	−	2.46129i	−0.0576302	−	0.0998184i
$609$	−10.9849	−	22.7522i	−0.445132	−	0.921966i
$610$			3.90306i			0.158030i
$611$	−19.1112	+	28.0611i	−0.773158	+	1.13523i
$612$	−1.08584	+	6.50826i	−0.0438925	+	0.263081i
$613$	10.1851	+	38.0111i	0.411370	+	1.53526i	0.791996	+	0.610526i	$0.209042\pi$
$613$	10.1851	+	38.0111i	0.411370	+	1.53526i	−0.380626	+	0.924729i	$0.624291\pi$
$614$		−	21.0410i		−	0.849146i
$615$	−1.00383	+	12.1166i	−0.0404784	+	0.488589i
$616$	−4.44043	+	7.85086i	−0.178910	+	0.316320i
$617$	−45.4152	+	12.1690i	−1.82835	+	0.489904i	−0.997754	−	0.0669776i	$-0.978664\pi$
$617$	−45.4152	+	12.1690i	−1.82835	+	0.489904i	−0.830592	+	0.556882i	$0.811998\pi$
$618$	−3.02281	−	16.6931i	−0.121595	−	0.671494i
$619$	−5.15227	+	19.2285i	−0.207087	+	0.772859i	0.781716	+	0.623634i	$0.214345\pi$
$619$	−5.15227	+	19.2285i	−0.207087	+	0.772859i	−0.988803	+	0.149225i	$0.952322\pi$
$620$		−	6.44525i		−	0.258847i
$621$	40.8166	+	10.3343i	1.63791	+	0.414700i
$622$	−3.93498	+	14.6855i	−0.157778	+	0.588836i
$623$	30.4865	+	29.9511i	1.22141	+	1.19996i
$624$	3.67132	+	5.05187i	0.146971	+	0.202237i
$625$	3.66623	−	6.35010i	0.146649	−	0.254004i
$626$	3.45807	−	0.926586i	0.138212	−	0.0370338i
$627$	1.38556	−	16.7242i	0.0553340	−	0.667901i
$628$	18.5493	−	10.7094i	0.740196	−	0.427352i
$629$	−17.9198	−	17.9198i	−0.714511	−	0.714511i
$630$	5.66572	−	7.00546i	0.225728	−	0.279104i
$631$	−19.1615	+	5.13431i	−0.762808	+	0.204394i	−0.619192	−	0.785240i	$-0.712540\pi$
$631$	−19.1615	+	5.13431i	−0.762808	+	0.204394i	−0.143616	+	0.989633i	$0.545873\pi$
$632$	1.39731	+	5.21483i	0.0555820	+	0.207435i
$633$	7.98060	+	16.9106i	0.317200	+	0.672135i
$634$	−17.0587	−	9.84882i	−0.677486	−	0.391146i
$635$	3.23790	−	3.23790i	0.128492	−	0.128492i
$636$	1.42824	+	3.02638i	0.0566334	+	0.120004i
$637$	−16.8087	−	18.8273i	−0.665986	−	0.745964i
$638$		−	18.7954i		−	0.744118i
$639$	14.9076	−	1.44279i	0.589736	−	0.0570759i
$640$	0.567565	−	0.983052i	0.0224350	−	0.0388585i
$641$	−31.8755			−1.25901			−0.629503	−	0.776998i	$-0.716741\pi$
$641$	−31.8755			−1.25901			−0.629503	+	0.776998i	$0.716741\pi$
$642$	23.0079	−	19.4873i	0.908049	−	0.769101i
$643$	−6.13525	−	22.8971i	−0.241951	−	0.902972i	−0.974892	−	0.222680i	$-0.928520\pi$
$643$	−6.13525	−	22.8971i	−0.241951	−	0.902972i	0.732941	−	0.680292i	$-0.238147\pi$
$644$	−21.4378	+	0.189918i	−0.844766	+	0.00748381i
$645$	−13.2128	−	4.74024i	−0.520254	−	0.186647i
$646$	3.12541	+	5.41337i	0.122968	+	0.212986i
$647$	−16.8878	+	29.2505i	−0.663927	+	1.14995i	0.315649	+	0.948876i	$0.397778\pi$
$647$	−16.8878	+	29.2505i	−0.663927	+	1.14995i	−0.979575	+	0.201078i	$0.935555\pi$
$648$	8.08529	−	3.95324i	0.317620	−	0.155298i
$649$	3.66599	+	2.11656i	0.143903	+	0.0830822i
$650$	5.81222	+	12.0538i	0.227974	+	0.472789i
$651$	−8.56923	+	24.5682i	−0.335855	+	0.962904i
$652$	−20.0661	−	5.37671i	−0.785851	−	0.210568i
$653$			9.87342i			0.386377i	0.981162	+	0.193188i	$0.0618828\pi$
$653$			9.87342i			0.386377i	−0.981162	+	0.193188i	$0.938117\pi$
$654$	0.375112	+	0.794848i	0.0146681	+	0.0310810i
$655$	4.06324	+	1.08874i	0.158764	+	0.0425406i
$656$	1.60050	−	5.97315i	0.0624891	−	0.233212i
$657$	19.6483	−	43.1701i	0.766553	−	1.68423i
$658$	−21.6849	−	12.2650i	−0.845367	−	0.478138i
$659$	−31.8025	−	18.3612i	−1.23885	−	0.715250i	−0.269991	−	0.962863i	$-0.587021\pi$
$659$	−31.8025	−	18.3612i	−1.23885	−	0.715250i	−0.968859	+	0.247613i	$0.920354\pi$
$660$	6.06153	−	2.86061i	0.235945	−	0.111349i
$661$	3.05787	−	0.819354i	0.118937	−	0.0318692i	−0.198859	−	0.980028i	$-0.563724\pi$
$661$	3.05787	−	0.819354i	0.118937	−	0.0318692i	0.317797	+	0.948159i	$0.397057\pi$
$662$	15.0516	+	26.0701i	0.584997	+	1.01324i
$663$	−8.07473	−	11.1111i	−0.313597	−	0.431520i
$664$	−13.8429			−0.537207
$665$	−0.0756129	−	8.53512i	−0.00293214	−	0.330978i
$666$	−5.68859	+	34.0960i	−0.220428	+	1.32119i
$667$	38.6894	−	22.3373i	1.49806	−	0.864904i
$668$	−0.865773	+	3.23111i	−0.0334978	+	0.125015i
$669$	−20.4462	−	7.33529i	−0.790495	−	0.283599i
$670$	−2.62238	+	9.78687i	−0.101311	+	0.378100i
$671$	8.28863	−	8.28863i	0.319979	−	0.319979i
$672$	−3.47047	+	2.99263i	−0.133876	+	0.115443i
$673$	−15.1252	+	8.73251i	−0.583032	+	0.336614i	−0.762337	−	0.647180i	$-0.775948\pi$
$673$	−15.1252	+	8.73251i	−0.583032	+	0.336614i	0.179306	+	0.983793i	$0.442615\pi$
$674$	−7.18934	+	7.18934i	−0.276923	+	0.276923i
$675$	18.5575	−	5.24844i	0.714279	−	0.202013i
$676$	−12.8567	−	1.92471i	−0.494490	−	0.0740274i
$677$	22.2255	+	12.8319i	0.854194	+	0.493169i	0.862064	−	0.506800i	$-0.169172\pi$
$677$	22.2255	+	12.8319i	0.854194	+	0.493169i	−0.00786981	+	0.999969i	$0.502505\pi$
$678$	2.46644	+	13.6206i	0.0947231	+	0.523096i
$679$	−9.97194	+	2.76688i	−0.382688	+	0.106183i
$680$	−1.24831	+	2.16213i	−0.0478704	+	0.0829139i
$681$	17.2136	+	20.3234i	0.659625	+	0.778795i
$682$	−13.6873	+	13.6873i	−0.524114	+	0.524114i
$683$	−26.5156	+	26.5156i	−1.01459	+	1.01459i	−0.0146999	+	0.999892i	$0.504679\pi$
$683$	−26.5156	+	26.5156i	−1.01459	+	1.01459i	−0.999892	+	0.0146999i	$0.995321\pi$
$684$	3.53195	−	7.76019i	0.135047	−	0.296718i
$685$	3.13890	−	5.43673i	0.119931	−	0.207727i
$686$	12.7432	−	13.4392i	0.486537	−	0.513110i
$687$	14.0800	−	2.54963i	0.537186	−	0.0972746i
$688$	6.18316	+	3.56985i	0.235731	+	0.136099i
$689$	−6.57646	−	2.29752i	−0.250543	−	0.0875285i
$690$	13.0922	+	9.07764i	0.498411	+	0.345580i
$691$	−5.52542	+	5.52542i	−0.210197	+	0.210197i	−0.804351	−	0.594154i	$-0.797487\pi$
$691$	−5.52542	+	5.52542i	−0.210197	+	0.210197i	0.594154	+	0.804351i	$0.297487\pi$
$692$	−8.56083	+	4.94260i	−0.325434	+	0.187889i
$693$	−26.9088	+	2.84512i	−1.02218	+	0.108077i
$694$	7.18044	−	7.18044i	0.272566	−	0.272566i
$695$	0.303162	−	1.13142i	0.0114996	−	0.0429170i
$696$	3.22469	−	8.98842i	0.122232	−	0.340705i
$697$	−3.52015	+	13.1374i	−0.133335	+	0.497614i
$698$	−15.8313	+	9.14021i	−0.599224	+	0.345962i
$699$	−13.8392	+	19.9595i	−0.523445	+	0.754936i
$700$	−8.46024	+	4.98497i	−0.319767	+	0.188414i
$701$	6.30897			0.238286			0.119143	−	0.992877i	$-0.461985\pi$
$701$	6.30897			0.238286			0.119143	+	0.992877i	$0.461985\pi$
$702$	−5.93388	+	17.7705i	−0.223960	+	0.670703i
$703$	16.3736	+	28.3600i	0.617544	+	1.06962i
$704$	−3.29293	+	0.882338i	−0.124107	+	0.0332544i
$705$	7.90133	+	16.7426i	0.297581	+	0.630564i
$706$	2.93338	+	1.69359i	0.110399	+	0.0637390i
$707$	12.2172	+	6.91004i	0.459476	+	0.259879i
$708$	1.39003	+	1.64115i	0.0522404	+	0.0616783i
$709$	−0.109223	+	0.407624i	−0.00410194	+	0.0153086i	−0.967946	−	0.251157i	$-0.919189\pi$
$709$	−0.109223	+	0.407624i	−0.00410194	+	0.0153086i	0.963845	+	0.266465i	$0.0858558\pi$
$710$	5.47395	+	1.46674i	0.205434	+	0.0550458i
$711$	−10.2961	+	12.5026i	−0.386132	+	0.468883i
$712$			16.1532i			0.605368i
$713$	−44.4411	−	11.9080i	−1.66433	−	0.445957i
$714$	7.63298	−	6.58200i	0.285657	−	0.246325i
$715$	−4.60169	+	13.1720i	−0.172093	+	0.492603i
$716$	−4.14586	−	2.39361i	−0.154938	−	0.0894535i
$717$	7.61528	+	8.99107i	0.284398	+	0.335778i
$718$	8.71738	−	15.0989i	0.325330	−	0.563488i
$719$	1.66002	+	2.87524i	0.0619084	+	0.107228i	0.895318	−	0.445427i	$-0.146948\pi$
$719$	1.66002	+	2.87524i	0.0619084	+	0.107228i	−0.833410	+	0.552655i	$0.813615\pi$
$720$	3.38955	−	0.328048i	0.126321	−	0.0122256i
$721$	−12.7576	+	22.5559i	−0.475117	+	0.840025i
$722$	2.82702	+	10.5506i	0.105211	+	0.392652i
$723$	−10.6143	−	12.5319i	−0.394750	−	0.466067i
$724$	−24.1509			−0.897561
$725$	10.2313	−	17.7211i	0.379981	−	0.658146i
$726$	−1.01390	−	0.363749i	−0.0376295	−	0.0135000i
$727$			26.2230i			0.972558i	0.873804	+	0.486279i	$0.161646\pi$
$727$			26.2230i			0.972558i	−0.873804	+	0.486279i	$0.838354\pi$
$728$	0.623829	−	9.51897i	0.0231206	−	0.352797i
$729$	23.7469	+	12.8485i	0.879516	+	0.475870i
$730$	12.6903	−	12.6903i	0.469690	−	0.469690i
$731$	−13.5993	−	7.85155i	−0.502988	−	0.290400i
$732$	5.38588	−	2.54175i	0.199068	−	0.0939459i
$733$	1.76070	+	6.57101i	0.0650328	+	0.242706i	0.990789	−	0.135415i	$-0.0432369\pi$
$733$	1.76070	+	6.57101i	0.0650328	+	0.242706i	−0.925756	+	0.378121i	$0.876570\pi$
$734$	−4.84322	+	1.29774i	−0.178767	+	0.0479004i
$735$	−13.4969	+	2.69184i	−0.497841	+	0.0992900i
$736$	−5.72971	−	5.72971i	−0.211200	−	0.211200i
$737$	26.3526	−	15.2147i	0.970710	−	0.560440i
$738$	17.3736	−	6.50539i	0.639530	−	0.239467i
$739$	−2.03194	+	0.544457i	−0.0747462	+	0.0200282i	−0.295998	−	0.955188i	$-0.595652\pi$
$739$	−2.03194	+	0.544457i	−0.0747462	+	0.0200282i	0.221252	+	0.975217i	$0.428986\pi$
$740$	−6.53972	+	11.3271i	−0.240405	+	0.416394i
$741$	6.36252	+	16.5690i	0.233733	+	0.608677i
$742$	1.27924	−	4.94916i	0.0469625	−	0.181689i
$743$	5.99415	−	22.3705i	0.219904	−	0.820693i	−0.764478	−	0.644650i	$-0.777003\pi$
$743$	5.99415	−	22.3705i	0.219904	−	0.820693i	0.984382	−	0.176044i	$-0.0563300\pi$
$744$	−8.89389	+	4.19728i	−0.326066	+	0.153880i
$745$			5.42372i			0.198710i
$746$	−0.486232	+	1.81464i	−0.0178022	+	0.0664388i
$747$	−24.1323	−	33.7973i	−0.882954	−	1.23658i
$748$	7.24249	−	1.94062i	0.264812	−	0.0709561i
$749$	−46.0554	+	0.408007i	−1.68283	+	0.0149082i
$750$	17.0692	+	1.41414i	0.623279	+	0.0516372i
$751$		−	10.5262i		−	0.384106i	−0.981385	−	0.192053i	$-0.938485\pi$
$751$		−	10.5262i		−	0.384106i	0.981385	−	0.192053i	$-0.0615146\pi$
$752$	−2.43712	−	9.09544i	−0.0888725	−	0.331677i
$753$	11.6252	−	16.7664i	0.423645	−	0.611000i
$754$	8.63393	+	17.9057i	0.314429	+	0.652086i
$755$			15.4185i			0.561136i
$756$	−13.3566	−	3.25609i	−0.485774	−	0.118423i
$757$	20.4922	+	35.4936i	0.744802	+	1.29004i	0.950287	+	0.311375i	$0.100790\pi$
$757$	20.4922	+	35.4936i	0.744802	+	1.29004i	−0.205485	+	0.978660i	$0.565877\pi$
$758$	−4.24425	−	7.35126i	−0.154158	−	0.267010i
$759$	−8.52541	−	47.0804i	−0.309453	−	1.70891i
$760$	2.28120	−	2.28120i	0.0827476	−	0.0827476i
$761$	−10.3869	−	2.78316i	−0.376525	−	0.100890i	0.0655929	−	0.997846i	$-0.479106\pi$
$761$	−10.3869	−	2.78316i	−0.376525	−	0.100890i	−0.442118	+	0.896957i	$0.645773\pi$
$762$	−6.57660	−	2.35943i	−0.238245	−	0.0854731i
$763$	0.335980	−	1.29985i	0.0121633	−	0.0470576i
$764$	11.4523	+	19.8360i	0.414331	+	0.717642i
$765$	−7.45500	+	0.721511i	−0.269536	+	0.0260863i
$766$	2.39137	−	1.38066i	0.0864038	−	0.0498853i
$767$	−4.46471	−	0.332342i	−0.161211	−	0.0120002i
$768$	−1.72614	−	0.143006i	−0.0622866	−	0.00516030i
$769$	−50.4265	−	13.5117i	−1.81843	−	0.487246i	−0.821833	−	0.569728i	$-0.807049\pi$
$769$	−50.4265	−	13.5117i	−1.81843	−	0.487246i	−0.996593	+	0.0824820i	$0.973715\pi$
$770$	−9.91266	−	2.56219i	−0.357227	−	0.0923349i
$771$	−3.15208	−	0.261142i	−0.113519	−	0.00940480i
$772$	−0.387362	−	1.44565i	−0.0139415	−	0.0520302i
$773$	−6.25076	−	6.25076i	−0.224824	−	0.224824i	0.585702	−	0.810526i	$-0.300819\pi$
$773$	−6.25076	−	6.25076i	−0.224824	−	0.224824i	−0.810526	+	0.585702i	$0.800819\pi$
$774$	2.06335	+	21.3195i	0.0741654	+	0.766313i
$775$	−20.3556	+	5.45428i	−0.731196	+	0.195923i
$776$	−3.38740	−	1.95572i	−0.121601	−	0.0702061i
$777$	39.9882	−	34.4823i	1.43457	−	1.23705i
$778$	−8.42926	+	31.4584i	−0.302204	+	1.12784i
$779$	8.78742	−	15.2203i	0.314842	−	0.545322i
$780$	−4.46052	+	5.50964i	−0.159712	+	0.197277i
$781$	−8.50982	−	14.7394i	−0.304505	−	0.527419i
$782$	12.6019	+	12.6019i	0.450645	+	0.450645i
$783$	27.5668	−	7.79645i	0.985157	−	0.278622i
$784$	6.99890	−	0.124017i	0.249961	−	0.00442917i
$785$	17.1920	+	17.1920i	0.613609	+	0.613609i
$786$	−1.14370	−	6.31593i	−0.0407944	−	0.225282i
$787$	−21.7967	−	21.7967i	−0.776970	−	0.776970i	0.202344	−	0.979314i	$-0.435144\pi$
$787$	−21.7967	−	21.7967i	−0.776970	−	0.776970i	−0.979314	+	0.202344i	$0.935144\pi$
$788$	10.1623	+	2.72299i	0.362019	+	0.0970026i
$789$	29.6170	+	20.5353i	1.05439	+	0.731076i
$790$	−5.30729	+	3.06417i	−0.188825	+	0.109018i
$791$	10.4095	−	18.4043i	0.370117	−	0.654382i
$792$	−7.89480	−	6.50149i	−0.280529	−	0.231020i
$793$	−4.08876	+	11.7037i	−0.145196	+	0.415612i
$794$	−19.6976	+	11.3724i	−0.699042	+	0.403592i
$795$	−2.89868	+	2.45513i	−0.102805	+	0.0870744i
$796$	2.79028			0.0988987
$797$	15.6716	−	27.1440i	0.555117	−	0.961491i	−0.442777	−	0.896632i	$-0.646007\pi$
$797$	15.6716	−	27.1440i	0.555117	−	0.961491i	0.997894	−	0.0648595i	$-0.0206599\pi$
$798$	−11.7285	+	5.66259i	−0.415184	+	0.200454i
$799$	5.36021	+	20.0046i	0.189631	+	0.707711i
$800$	−3.58501	−	0.960601i	−0.126749	−	0.0339624i
$801$	−39.4381	+	28.1600i	−1.39348	+	0.994984i
$802$	−38.4502			−1.35772
$803$	−53.8991			−1.90206
$804$	15.2128	−	2.75476i	0.536513	−	0.0971528i
$805$	−6.50651	−	23.4497i	−0.229324	−	0.826492i
$806$	6.75191	−	19.3268i	0.237826	−	0.680757i
$807$	1.94082	−	23.4264i	0.0683202	−	0.824649i
$808$	1.37306	+	5.12434i	0.0483042	+	0.180274i
$809$	5.60435	+	3.23568i	0.197039	+	0.113760i	0.595273	−	0.803523i	$-0.297044\pi$
$809$	5.60435	+	3.23568i	0.197039	+	0.113760i	−0.398235	+	0.917284i	$0.630377\pi$
$810$	6.70994	+	7.70369i	0.235763	+	0.270680i
$811$	22.2009	−	22.2009i	0.779581	−	0.779581i	−0.200179	−	0.979759i	$-0.564152\pi$
$811$	22.2009	−	22.2009i	0.779581	−	0.779581i	0.979759	+	0.200179i	$0.0641523\pi$
$812$	−12.5675	+	7.40507i	−0.441033	+	0.259867i
$813$	−15.4598	−	18.2528i	−0.542198	−	0.640152i
$814$	37.9425	−	10.1667i	1.32988	−	0.356341i
$815$		−	23.5812i		−	0.826013i
$816$	3.79648	+	0.314529i	0.132903	+	0.0110107i
$817$	14.3482	+	14.3482i	0.501979	+	0.501979i
$818$	−1.82011			−0.0636386
$819$	24.3280	−	15.0714i	0.850091	−	0.526636i
$820$	7.01949			0.245131
$821$	−38.0323	−	38.0323i	−1.32734	−	1.32734i	−0.907685	−	0.419651i	$-0.862152\pi$
$821$	−38.0323	−	38.0323i	−1.32734	−	1.32734i	−0.419651	−	0.907685i	$-0.637848\pi$
$822$	−9.54633	−	0.790891i	−0.332967	−	0.0275855i
$823$			22.4357i			0.782059i	0.920378	+	0.391030i	$0.127881\pi$
$823$			22.4357i			0.782059i	−0.920378	+	0.391030i	$0.872119\pi$
$824$	−9.46075	+	2.53500i	−0.329581	+	0.0883109i
$825$	−14.1641	−	16.7230i	−0.493129	−	0.582219i
$826$	−0.0291031	−	3.28514i	−0.00101263	−	0.114304i
$827$	1.82433	−	1.82433i	0.0634380	−	0.0634380i	−0.674676	−	0.738114i	$-0.735717\pi$
$827$	1.82433	−	1.82433i	0.0634380	−	0.0634380i	0.738114	+	0.674676i	$0.235717\pi$
$828$	4.00044	−	23.9777i	0.139025	−	0.833281i
$829$	25.7118	+	14.8447i	0.893009	+	0.515579i	0.874925	−	0.484258i	$-0.160910\pi$
$829$	25.7118	+	14.8447i	0.893009	+	0.515579i	0.0180832	+	0.999836i	$0.494244\pi$
$830$	−4.06694	−	15.1780i	−0.141166	−	0.526837i
$831$	−0.914512	+	11.0385i	−0.0317241	+	0.382921i
$832$	2.73173	−	2.35322i	0.0947057	−	0.0815832i
$833$	−15.3934	+	0.272763i	−0.533351	+	0.00945068i
$834$	−1.75868	+	0.318465i	−0.0608981	+	0.0110275i
$835$	−3.79711			−0.131405
$836$	−9.68881			−0.335094
$837$	−25.7524	−	14.3972i	−0.890132	−	0.497642i
$838$	−38.4997	−	10.3160i	−1.32995	−	0.356359i
$839$	−2.47094	−	9.22166i	−0.0853062	−	0.318367i	0.910066	−	0.414464i	$-0.136031\pi$
$839$	−2.47094	−	9.22166i	−0.0853062	−	0.318367i	−0.995372	+	0.0960968i	$0.969364\pi$
$840$	−4.30087	−	2.92599i	−0.148394	−	0.100956i
$841$	0.698376	−	1.20962i	0.0240819	−	0.0417111i
$842$	1.98770			0.0685005
$843$	−25.9653	+	21.9922i	−0.894293	+	0.757450i
$844$	9.34957	−	5.39798i	0.321825	−	0.185806i
$845$	−1.66687	−	14.6623i	−0.0573420	−	0.504397i
$846$	17.9578	−	21.8063i	0.617403	−	0.749716i
$847$	0.835300	+	1.41763i	0.0287013	+	0.0487103i
$848$	1.67323	−	0.966043i	0.0574591	−	0.0331740i
$849$	6.28116	+	4.35512i	0.215569	+	0.149467i
$850$	7.88490	+	2.11275i	0.270450	+	0.0724668i
$851$	66.0201	+	66.0201i	2.26314	+	2.26314i
$852$	−1.54078	−	8.50875i	−0.0527863	−	0.291505i
$853$	13.9116	+	13.9116i	0.476325	+	0.476325i	0.903954	−	0.427629i	$-0.140651\pi$
$853$	13.9116	+	13.9116i	0.476325	+	0.476325i	−0.427629	+	0.903954i	$0.640651\pi$
$854$	−8.80774	−	2.27659i	−0.301395	−	0.0779034i
$855$	9.54634	+	1.59272i	0.326478	+	0.0544697i
$856$	−12.3093	−	12.3093i	−0.420724	−	0.420724i
$857$	−17.8521	−	30.9207i	−0.609816	−	1.05623i	−0.991270	−	0.131844i	$-0.957910\pi$
$857$	−17.8521	−	30.9207i	−0.609816	−	1.05623i	0.381455	−	0.924387i	$-0.375423\pi$
$858$	21.1729	−	2.22793i	0.722830	−	0.0760604i
$859$	−16.9244	+	29.3139i	−0.577453	+	1.00018i	0.418317	+	0.908301i	$0.362620\pi$
$859$	−16.9244	+	29.3139i	−0.577453	+	1.00018i	−0.995770	+	0.0918774i	$0.970713\pi$
$860$	−2.09760	+	7.82834i	−0.0715275	+	0.266944i
$861$	−26.7571	−	9.33271i	−0.911880	−	0.318058i
$862$	−1.47164	−	0.849654i	−0.0501244	−	0.0289393i
$863$	6.02265	−	1.61376i	0.205013	−	0.0549331i	−0.154851	−	0.987938i	$-0.549490\pi$
$863$	6.02265	−	1.61376i	0.205013	−	0.0549331i	0.359864	+	0.933005i	$0.382823\pi$
$864$	−2.66003	−	4.46366i	−0.0904960	−	0.151857i
$865$	−7.93443	−	7.93443i	−0.269779	−	0.269779i
$866$	8.05061	+	30.0453i	0.273571	+	1.02098i
$867$	20.9943	+	1.73933i	0.713005	+	0.0590708i
$868$	14.5445	+	3.75942i	0.493673	+	0.127603i
$869$	17.7779	+	4.76356i	0.603072	+	0.161593i
$870$	10.8028	+	0.894983i	0.366248	+	0.0303428i
$871$	−18.1160	+	26.5998i	−0.613838	+	0.901301i
$872$	0.439458	−	0.253721i	0.0148819	−	0.00859208i
$873$	−1.13039	−	11.6797i	−0.0382579	−	0.395299i
$874$	−11.5146	−	19.9439i	−0.389487	−	0.674612i
$875$	−18.6632	−	18.3354i	−0.630930	−	0.619849i
$876$	−25.7758	−	9.24735i	−0.870883	−	0.312439i
$877$	25.6699	+	6.87822i	0.866809	+	0.232261i	0.664708	−	0.747104i	$-0.268556\pi$
$877$	25.6699	+	6.87822i	0.866809	+	0.232261i	0.202102	+	0.979365i	$0.435223\pi$
$878$	20.4238	−	20.4238i	0.689270	−	0.689270i
$879$	1.43964	+	7.95024i	0.0485579	+	0.268155i
$880$	−1.93488	−	3.35131i	−0.0652249	−	0.112973i
$881$	−12.2623	−	21.2389i	−0.413127	−	0.715557i	0.582103	−	0.813115i	$-0.302230\pi$
$881$	−12.2623	−	21.2389i	−0.413127	−	0.715557i	−0.995230	+	0.0975584i	$0.968897\pi$
$882$	12.5040	+	16.8716i	0.421031	+	0.568096i
$883$			15.4617i			0.520327i	0.965565	+	0.260163i	$0.0837765\pi$
$883$			15.4617i			0.520327i	−0.965565	+	0.260163i	$0.916224\pi$
$884$	−6.00819	+	5.17569i	−0.202077	+	0.174077i
$885$	−1.39106	+	2.00626i	−0.0467601	+	0.0674396i
$886$	1.79835	+	6.71152i	0.0604166	+	0.225478i
$887$			9.39683i			0.315515i	0.987478	+	0.157757i	$0.0504264\pi$
$887$			9.39683i			0.315515i	−0.987478	+	0.157757i	$0.949574\pi$
$888$	19.8893	+	1.64778i	0.667440	+	0.0552958i
$889$	5.41810	+	9.19534i	0.181717	+	0.308402i
$890$	−17.7113	+	4.74572i	−0.593682	+	0.159077i
$891$	2.11035	−	30.6092i	0.0706994	−	1.02545i
$892$	−3.24593	+	12.1140i	−0.108682	+	0.405606i
$893$		−	26.7616i		−	0.895542i
$894$	7.48426	−	3.53204i	0.250311	−	0.118129i
$895$	1.40646	−	5.24896i	0.0470126	−	0.175454i
$896$	1.88733	+	1.85418i	0.0630512	+	0.0619439i
$897$	29.7488	+	40.9354i	0.993285	+	1.36679i
$898$	−1.06339	+	1.84185i	−0.0354858	+	0.0614632i
$899$	−30.2379	+	8.10221i	−1.00849	+	0.270224i
$900$	−3.90446	−	10.4274i	−0.130149	−	0.347580i
$901$	−3.68012	+	2.12472i	−0.122603	+	0.0707847i
$902$	−14.9068	−	14.9068i	−0.496341	−	0.496341i
$903$	18.4038	−	27.0515i	0.612440	−	0.900217i
$904$	7.71943	−	2.06842i	0.256744	−	0.0687945i
$905$	−7.09537	−	26.4803i	−0.235858	−	0.880234i
$906$	21.2762	−	10.0408i	0.706853	−	0.333585i
$907$	−41.1368	−	23.7504i	−1.36593	−	0.788618i	−0.375521	−	0.926814i	$-0.622536\pi$
$907$	−41.1368	−	23.7504i	−1.36593	−	0.788618i	−0.990405	+	0.138196i	$0.955870\pi$
$908$	10.8731	−	10.8731i	0.360837	−	0.360837i
$909$	−10.1174	+	12.2856i	−0.335573	+	0.407488i
$910$	10.6204	−	2.11261i	0.352062	−	0.0700324i
$911$			32.4090i			1.07376i	0.843659	+	0.536879i	$0.180397\pi$
$911$			32.4090i			1.07376i	−0.843659	+	0.536879i	$0.819603\pi$
$912$	−4.63342	−	1.66229i	−0.153428	−	0.0550439i
$913$	−23.5958	+	40.8691i	−0.780907	+	1.35257i
$914$	−17.2878			−0.571829
$915$	4.36925	+	5.15861i	0.144443	+	0.170538i
$916$	−2.13818	−	7.97981i	−0.0706476	−	0.263660i
$917$	−4.82691	+	8.53416i	−0.159398	+	0.281823i
$918$	5.85048	+	9.81740i	0.193095	+	0.324022i
$919$	29.5986	+	51.2662i	0.976367	+	1.69112i	0.675350	+	0.737498i	$0.263993\pi$
$919$	29.5986	+	51.2662i	0.976367	+	1.69112i	0.301017	+	0.953619i	$0.402674\pi$
$920$	4.59900	−	7.96570i	0.151624	−	0.262621i
$921$	−23.5542	−	27.8096i	−0.776137	−	0.916356i
$922$	2.03100	+	1.17260i	0.0668873	+	0.0386174i
$923$	14.8777	+	10.1326i	0.489706	+	0.333518i
$924$	2.91973	+	15.3472i	0.0960522	+	0.504884i
$925$	41.3080	+	11.0684i	1.35820	+	0.363928i
$926$			13.5188i			0.444256i
$927$	−22.6821	−	18.6791i	−0.744979	−	0.613502i
$928$	−5.32546	−	1.42695i	−0.174817	−	0.0468420i
$929$	−12.0261	+	44.8820i	−0.394563	+	1.47253i	0.427960	+	0.903798i	$0.359232\pi$
$929$	−12.0261	+	44.8820i	−0.394563	+	1.47253i	−0.822523	+	0.568732i	$0.807434\pi$
$930$	−7.21509	−	8.51858i	−0.236592	−	0.279335i
$931$	19.3047	+	4.80778i	0.632685	+	0.157568i
$932$	12.1440	+	7.01132i	0.397788	+	0.229663i
$933$	11.2388	+	23.8146i	0.367942	+	0.779655i
$934$	16.3655	−	4.38513i	0.535496	−	0.143486i
$935$	4.25559	+	7.37090i	0.139173	+	0.241054i
$936$	10.5076	+	2.56714i	0.343452	+	0.0839095i
$937$	−1.30841			−0.0427438			−0.0213719	−	0.999772i	$-0.506803\pi$
$937$	−1.30841			−0.0427438			−0.0213719	+	0.999772i	$0.506803\pi$
$938$	−20.5557	−	11.6263i	−0.671168	−	0.379611i
$939$	3.53321	−	5.09576i	0.115302	−	0.166294i
$940$	9.25670	−	5.34436i	0.301920	−	0.174314i
$941$	−11.2314	+	41.9163i	−0.366135	+	1.36643i	0.499741	+	0.866175i	$0.333428\pi$
$941$	−11.2314	+	41.9163i	−0.366135	+	1.36643i	−0.865876	+	0.500259i	$0.833238\pi$
$942$	12.5277	−	34.9193i	0.408174	−	1.13773i
$943$	12.9689	−	48.4006i	0.422326	−	1.57614i
$944$	0.878024	−	0.878024i	0.0285772	−	0.0285772i
$945$	−0.353926	−	15.6015i	−0.0115132	−	0.507515i
$946$	21.0790	−	12.1700i	0.685337	−	0.395679i
$947$	−32.1616	+	32.1616i	−1.04511	+	1.04511i	−0.0461769	+	0.998933i	$0.514704\pi$
$947$	−32.1616	+	32.1616i	−1.04511	+	1.04511i	−0.998933	+	0.0461769i	$0.985296\pi$
$948$	7.68451	+	5.32815i	0.249581	+	0.173050i
$949$	51.3475	−	24.7592i	1.66681	−	0.803719i
$950$	−9.13502	−	5.27410i	−0.296379	−	0.171115i
$951$	−33.5713	+	6.07915i	−1.08862	+	0.197130i
$952$	−4.15100	−	4.07810i	−0.134535	−	0.132172i
$953$	13.6389	−	23.6233i	0.441808	−	0.765234i	−0.556016	−	0.831172i	$-0.687671\pi$
$953$	13.6389	−	23.6233i	0.441808	−	0.765234i	0.997824	+	0.0659379i	$0.0210039\pi$
$954$	5.27554	+	2.40109i	0.170802	+	0.0777382i
$955$	−18.3846	+	18.3846i	−0.594913	+	0.594913i
$956$	4.81026	−	4.81026i	0.155575	−	0.155575i
$957$	−21.0404	−	24.8416i	−0.680140	−	0.803016i
$958$	−19.2543	+	33.3495i	−0.622079	+	1.07747i
$959$	10.4378	+	10.2545i	0.337054	+	0.331135i
$960$	−0.350328	−	1.93464i	−0.0113068	−	0.0624403i
$961$	1.07341	+	0.619734i	0.0346261	+	0.0199914i
$962$	−31.4761	+	27.1148i	−1.01483	+	0.874216i
$963$	8.59428	−	51.5120i	0.276947	−	1.65995i
$964$	−6.70462	+	6.70462i	−0.215941	+	0.215941i
$965$	1.47129	−	0.849447i	0.0473624	−	0.0273447i
$966$	−28.1213	+	24.2493i	−0.904789	+	0.780210i
$967$	43.4225	−	43.4225i	1.39637	−	1.39637i	0.586231	−	0.810144i	$-0.300611\pi$
$967$	43.4225	−	43.4225i	1.39637	−	1.39637i	0.810144	−	0.586231i	$-0.199389\pi$
$968$	−0.160962	+	0.600719i	−0.00517352	+	0.0193078i
$969$	10.1908	+	3.65605i	0.327374	+	0.117449i
$970$	1.14915	−	4.28870i	0.0368971	−	0.137702i
$971$	−8.25135	+	4.76392i	−0.264798	+	0.152881i	−0.626521	−	0.779404i	$-0.715522\pi$
$971$	−8.25135	+	4.76392i	−0.264798	+	0.152881i	0.361723	+	0.932286i	$0.382189\pi$
$972$	6.26077	−	14.2760i	0.200814	−	0.457901i
$973$	2.37635	+	1.34406i	0.0761823	+	0.0430886i
$974$	−31.6791			−1.01506
$975$	21.1755	+	9.42487i	0.678157	+	0.301837i
$976$	−1.71921	−	2.97776i	−0.0550306	−	0.0953158i
$977$	44.6865	−	11.9737i	1.42965	−	0.383073i	0.540752	−	0.841182i	$-0.318140\pi$
$977$	44.6865	−	11.9737i	1.42965	−	0.383073i	0.888896	+	0.458109i	$0.151473\pi$
$978$	−32.5400	+	15.3566i	−1.04051	+	0.491049i
$979$	47.6902	+	27.5339i	1.52419	+	0.879989i
$980$	2.19221	+	7.63752i	0.0700276	+	0.243972i
$981$	1.38557	+	0.630622i	0.0442378	+	0.0201342i
$982$	−2.95693	+	11.0354i	−0.0943594	+	0.352154i
$983$	−1.66915	−	0.447247i	−0.0532375	−	0.0142650i	0.232102	−	0.972691i	$-0.425440\pi$
$983$	−1.66915	−	0.447247i	−0.0532375	−	0.0142650i	−0.285340	+	0.958427i	$0.592106\pi$
$984$	−4.57124	−	9.68629i	−0.145726	−	0.308788i
$985$			11.9425i			0.380520i
$986$	11.7129	+	3.13845i	0.373013	+	0.0999486i
$987$	−42.3906	+	8.06463i	−1.34931	+	0.256700i
$988$	9.23015	−	4.45068i	0.293650	−	0.141595i
$989$	50.1023	+	28.9266i	1.59316	+	0.919812i
$990$	4.80913	−	10.5664i	0.152844	−	0.335821i
$991$	−19.9945	+	34.6315i	−0.635147	+	1.10011i	0.351337	+	0.936249i	$0.385727\pi$
$991$	−19.9945	+	34.6315i	−0.635147	+	1.10011i	−0.986484	+	0.163858i	$0.947606\pi$
$992$	2.83899	+	4.91728i	0.0901380	+	0.156124i
$993$	49.0775	+	17.6071i	1.55743	+	0.558744i
$994$	−6.50276	+	11.4971i	−0.206255	+	0.364667i
$995$	0.819764	+	3.05940i	0.0259883	+	0.0969896i
$996$	−18.2959	+	15.4963i	−0.579727	+	0.491019i
$997$	−42.5321			−1.34701			−0.673503	−	0.739184i	$-0.735211\pi$
$997$	−42.5321			−1.34701			−0.673503	+	0.739184i	$0.735211\pi$
$998$	−1.25462	+	2.17307i	−0.0397145	+	0.0687875i
$999$	30.6500	+	51.4321i	0.969722	+	1.62724i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.ch.a.275.2	yes	152
3.2	odd	2	inner	546.2.ch.a.275.33	yes	152
7.4	even	3		546.2.bw.a.431.31	yes	152
13.7	odd	12		546.2.bw.a.527.12	yes	152
21.11	odd	6		546.2.bw.a.431.12	✓	152
39.20	even	12		546.2.bw.a.527.31	yes	152
91.46	odd	12	inner	546.2.ch.a.137.33	yes	152
273.137	even	12	inner	546.2.ch.a.137.2	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bw.a.431.12	✓	152	21.11	odd	6
546.2.bw.a.431.31	yes	152	7.4	even	3
546.2.bw.a.527.12	yes	152	13.7	odd	12
546.2.bw.a.527.31	yes	152	39.20	even	12
546.2.ch.a.137.2	yes	152	273.137	even	12	inner
546.2.ch.a.137.33	yes	152	91.46	odd	12	inner
546.2.ch.a.275.2	yes	152	1.1	even	1	trivial
546.2.ch.a.275.33	yes	152	3.2	odd	2	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.ch (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.72614 - 0.143006i) q^{3} +1.00000i q^{4} +(-1.09645 + 0.293793i) q^{5} +(1.11944 + 1.32168i) q^{6} +(-0.0234379 - 2.64565i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.95910 + 0.493697i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.72614 - 0.143006i) q^{3} +1.00000i q^{4} +(-1.09645 + 0.293793i) q^{5} +(1.11944 + 1.32168i) q^{6} +(-0.0234379 - 2.64565i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.95910 + 0.493697i) q^{9} +(0.983052 + 0.567565i) q^{10} +(-0.882338 - 3.29293i) q^{11} +(0.143006 - 1.72614i) q^{12} +(2.35322 + 2.73173i) q^{13} +(-1.85418 + 1.88733i) q^{14} +(1.93464 - 0.350328i) q^{15} -1.00000 q^{16} +2.19941 q^{17} +(-1.74330 - 2.44150i) q^{18} +(-2.74521 - 0.735577i) q^{19} +(-0.293793 - 1.09645i) q^{20} +(-0.337887 + 4.57010i) q^{21} +(-1.70455 + 2.95236i) q^{22} -8.10303 q^{23} +(-1.32168 + 1.11944i) q^{24} +(-3.21423 + 1.85574i) q^{25} +(0.267648 - 3.59560i) q^{26} +(-5.03721 - 1.27536i) q^{27} +(2.64565 - 0.0234379i) q^{28} +(-4.77468 + 2.75666i) q^{29} +(-1.61572 - 1.12028i) q^{30} +(5.48451 + 1.46957i) q^{31} +(0.707107 + 0.707107i) q^{32} +(1.05213 + 5.81023i) q^{33} +(-1.55521 - 1.55521i) q^{34} +(0.802972 + 2.89394i) q^{35} +(-0.493697 + 2.95910i) q^{36} +(-8.14758 - 8.14758i) q^{37} +(1.42102 + 2.46129i) q^{38} +(-3.67132 - 5.05187i) q^{39} +(-0.567565 + 0.983052i) q^{40} +(-1.60050 + 5.97315i) q^{41} +(3.47047 - 2.99263i) q^{42} +(-6.18316 - 3.56985i) q^{43} +(3.29293 - 0.882338i) q^{44} +(-3.38955 + 0.328048i) q^{45} +(5.72971 + 5.72971i) q^{46} +(2.43712 + 9.09544i) q^{47} +(1.72614 + 0.143006i) q^{48} +(-6.99890 + 0.124017i) q^{49} +(3.58501 + 0.960601i) q^{50} +(-3.79648 - 0.314529i) q^{51} +(-2.73173 + 2.35322i) q^{52} +(-1.67323 + 0.966043i) q^{53} +(2.66003 + 4.46366i) q^{54} +(1.93488 + 3.35131i) q^{55} +(-1.88733 - 1.85418i) q^{56} +(4.63342 + 1.66229i) q^{57} +(5.32546 + 1.42695i) q^{58} +(-0.878024 + 0.878024i) q^{59} +(0.350328 + 1.93464i) q^{60} +(1.71921 + 2.97776i) q^{61} +(-2.83899 - 4.91728i) q^{62} +(1.23679 - 7.84030i) q^{63} -1.00000i q^{64} +(-3.38276 - 2.30385i) q^{65} +(3.36449 - 4.85242i) q^{66} +(2.31020 + 8.62180i) q^{67} +2.19941i q^{68} +(13.9869 + 1.15878i) q^{69} +(1.47854 - 2.61411i) q^{70} +(4.82231 - 1.29213i) q^{71} +(2.44150 - 1.74330i) q^{72} +(4.09203 - 15.2717i) q^{73} +11.5224i q^{74} +(5.81359 - 2.74360i) q^{75} +(0.735577 - 2.74521i) q^{76} +(-8.69125 + 2.41153i) q^{77} +(-0.976192 + 6.16823i) q^{78} +(-2.69940 + 4.67549i) q^{79} +(1.09645 - 0.293793i) q^{80} +(8.51253 + 2.92180i) q^{81} +(5.35538 - 3.09193i) q^{82} +(-9.78838 - 9.78838i) q^{83} +(-4.57010 - 0.337887i) q^{84} +(-2.41154 + 0.646171i) q^{85} +(1.84789 + 6.89642i) q^{86} +(8.63597 - 4.07557i) q^{87} +(-2.95236 - 1.70455i) q^{88} +(-11.4221 + 11.4221i) q^{89} +(2.62874 + 2.16481i) q^{90} +(7.17204 - 6.28982i) q^{91} -8.10303i q^{92} +(-9.25686 - 3.32100i) q^{93} +(4.70815 - 8.15475i) q^{94} +3.22610 q^{95} +(-1.11944 - 1.32168i) q^{96} +(-1.01235 - 3.77815i) q^{97} +(5.03666 + 4.86128i) q^{98} +(-0.985214 - 10.1797i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 8 q^{7}+O(q^{10}) \) 152 * q + 8 * q^7	\( 152 q + 8 q^{7} - 152 q^{16} - 8 q^{18} + 36 q^{19} + 8 q^{21} + 24 q^{27} - 12 q^{28} - 24 q^{30} - 36 q^{31} + 12 q^{33} + 24 q^{36} - 12 q^{37} - 8 q^{39} - 36 q^{42} + 84 q^{43} - 40 q^{45} + 8 q^{46} + 4 q^{49} - 20 q^{52} - 12 q^{54} + 16 q^{55} - 8 q^{57} + 8 q^{58} + 24 q^{60} - 32 q^{61} - 28 q^{63} + 16 q^{66} + 92 q^{67} + 84 q^{69} - 8 q^{72} + 84 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} - 24 q^{81} - 48 q^{82} - 8 q^{84} - 152 q^{85} - 96 q^{87} - 88 q^{91} - 48 q^{93} + 32 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) \) 152 * q + 8 * q^7 - 152 * q^16 - 8 * q^18 + 36 * q^19 + 8 * q^21 + 24 * q^27 - 12 * q^28 - 24 * q^30 - 36 * q^31 + 12 * q^33 + 24 * q^36 - 12 * q^37 - 8 * q^39 - 36 * q^42 + 84 * q^43 - 40 * q^45 + 8 * q^46 + 4 * q^49 - 20 * q^52 - 12 * q^54 + 16 * q^55 - 8 * q^57 + 8 * q^58 + 24 * q^60 - 32 * q^61 - 28 * q^63 + 16 * q^66 + 92 * q^67 + 84 * q^69 - 8 * q^72 + 84 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 - 24 * q^81 - 48 * q^82 - 8 * q^84 - 152 * q^85 - 96 * q^87 - 88 * q^91 - 48 * q^93 + 32 * q^94 - 100 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more