LMFDB - Embedded newform 546.2.bu.a.197.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(71,546)]

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, 0, 5]))

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

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

chi := DirichletCharacter("546.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bu (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:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			197.8
Character	$\chi$	$=$	546.197
Dual form			546.2.bu.a.449.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(-1.72641 + 0.139688i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.05727 + 1.05727i) q^{5} +(-0.311899 + 1.70374i) q^{6} +(-0.965926 + 0.258819i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.96097 - 0.482317i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(-1.72641 + 0.139688i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.05727 + 1.05727i) q^{5} +(-0.311899 + 1.70374i) q^{6} +(-0.965926 + 0.258819i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.96097 - 0.482317i) q^{9} +(1.29489 - 0.747605i) q^{10} +(-2.11737 - 0.567347i) q^{11} +(1.56496 + 0.742231i) q^{12} +(-1.77553 - 3.13807i) q^{13} +1.00000i q^{14} +(-1.97297 - 1.67760i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.61760 - 4.53382i) q^{17} +(0.300474 - 2.98491i) q^{18} +(-2.01058 - 7.50359i) q^{19} +(-0.386989 - 1.44426i) q^{20} +(1.63143 - 0.581756i) q^{21} +(-1.09603 + 1.89838i) q^{22} +(1.89764 + 3.28680i) q^{23} +(1.12198 - 1.31953i) q^{24} -2.76435i q^{25} +(-3.49069 + 0.902835i) q^{26} +(-5.04448 + 1.24629i) q^{27} +(0.965926 + 0.258819i) q^{28} +(-6.69332 + 3.86439i) q^{29} +(-2.13108 + 1.47155i) q^{30} +(-3.28024 + 3.28024i) q^{31} +(0.965926 - 0.258819i) q^{32} +(3.73469 + 0.683702i) q^{33} +(-3.70185 - 3.70185i) q^{34} +(-1.29489 - 0.747605i) q^{35} +(-2.80544 - 1.06279i) q^{36} +(0.896760 - 3.34675i) q^{37} -7.76829 q^{38} +(3.50364 + 5.16958i) q^{39} -1.49521 q^{40} +(2.92345 - 10.9105i) q^{41} +(-0.139688 - 1.72641i) q^{42} +(-8.42241 - 4.86268i) q^{43} +(1.55002 + 1.55002i) q^{44} +(3.64050 + 2.62062i) q^{45} +(3.66595 - 0.982289i) q^{46} +(-1.61934 + 1.61934i) q^{47} +(-0.984178 - 1.42527i) q^{48} +(0.866025 - 0.500000i) q^{49} +(-2.67015 - 0.715466i) q^{50} +(-3.88573 + 8.19287i) q^{51} +(-0.0313841 + 3.60541i) q^{52} +7.90385i q^{53} +(-0.101785 + 5.19516i) q^{54} +(-1.63879 - 2.83848i) q^{55} +(0.500000 - 0.866025i) q^{56} +(4.51925 + 12.6734i) q^{57} +(2.00035 + 7.46542i) q^{58} +(-3.07907 - 11.4912i) q^{59} +(0.869847 + 2.43933i) q^{60} +(3.28906 - 5.69681i) q^{61} +(2.31948 + 4.01746i) q^{62} +(-2.73525 + 1.23224i) q^{63} -1.00000i q^{64} +(1.44058 - 5.19502i) q^{65} +(1.62702 - 3.43048i) q^{66} +(15.4661 + 4.14413i) q^{67} +(-4.53382 + 2.61760i) q^{68} +(-3.73522 - 5.40929i) q^{69} +(-1.05727 + 1.05727i) q^{70} +(-9.79449 + 2.62443i) q^{71} +(-1.75268 + 2.43477i) q^{72} +(1.17055 + 1.17055i) q^{73} +(-3.00062 - 1.73241i) q^{74} +(0.386146 + 4.77239i) q^{75} +(-2.01058 + 7.50359i) q^{76} +2.19206 q^{77} +(5.90024 - 2.04627i) q^{78} +15.2544 q^{79} +(-0.386989 + 1.44426i) q^{80} +(8.53474 - 2.85626i) q^{81} +(-9.78207 - 5.64768i) q^{82} +(-1.82647 - 1.82647i) q^{83} +(-1.70374 - 0.311899i) q^{84} +(7.56100 - 2.02596i) q^{85} +(-6.87687 + 6.87687i) q^{86} +(11.0156 - 7.60649i) q^{87} +(1.89838 - 1.09603i) q^{88} +(-2.44499 - 0.655132i) q^{89} +(3.47355 - 2.83819i) q^{90} +(2.52722 + 2.57161i) q^{91} -3.79527i q^{92} +(5.20483 - 6.12125i) q^{93} +(1.14504 + 1.98327i) q^{94} +(5.80761 - 10.0591i) q^{95} +(-1.63143 + 0.581756i) q^{96} +(3.53642 + 13.1981i) q^{97} +(-0.258819 - 0.965926i) q^{98} +(-6.54311 - 0.658658i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{6} + 24 q^{9}+O(q^{10}) $ 56 * q - 8 * q^6 + 24 * q^9	$ 56 q - 8 q^{6} + 24 q^{9} + 24 q^{10} - 8 q^{11} + 24 q^{13} - 4 q^{15} + 28 q^{16} + 4 q^{17} + 8 q^{19} + 4 q^{21} + 8 q^{23} + 8 q^{24} + 4 q^{26} - 24 q^{27} - 16 q^{30} - 8 q^{31} - 32 q^{33} - 24 q^{34} - 24 q^{35} - 12 q^{36} - 8 q^{37} - 60 q^{39} + 28 q^{41} - 8 q^{44} - 40 q^{45} - 20 q^{46} - 64 q^{50} + 8 q^{54} + 8 q^{55} + 28 q^{56} + 40 q^{57} + 4 q^{58} + 8 q^{59} + 4 q^{60} + 8 q^{61} + 32 q^{62} + 24 q^{65} + 32 q^{66} - 56 q^{69} + 112 q^{71} + 16 q^{72} + 8 q^{73} - 48 q^{74} - 40 q^{75} + 8 q^{76} - 8 q^{78} + 16 q^{79} + 12 q^{81} + 4 q^{83} - 4 q^{84} + 32 q^{85} + 16 q^{86} + 144 q^{87} - 88 q^{89} + 8 q^{90} - 8 q^{91} - 76 q^{93} - 8 q^{94} + 48 q^{95} - 4 q^{96} - 64 q^{97} - 40 q^{99}+O(q^{100}) $ 56 * q - 8 * q^6 + 24 * q^9 + 24 * q^10 - 8 * q^11 + 24 * q^13 - 4 * q^15 + 28 * q^16 + 4 * q^17 + 8 * q^19 + 4 * q^21 + 8 * q^23 + 8 * q^24 + 4 * q^26 - 24 * q^27 - 16 * q^30 - 8 * q^31 - 32 * q^33 - 24 * q^34 - 24 * q^35 - 12 * q^36 - 8 * q^37 - 60 * q^39 + 28 * q^41 - 8 * q^44 - 40 * q^45 - 20 * q^46 - 64 * q^50 + 8 * q^54 + 8 * q^55 + 28 * q^56 + 40 * q^57 + 4 * q^58 + 8 * q^59 + 4 * q^60 + 8 * q^61 + 32 * q^62 + 24 * q^65 + 32 * q^66 - 56 * q^69 + 112 * q^71 + 16 * q^72 + 8 * q^73 - 48 * q^74 - 40 * q^75 + 8 * q^76 - 8 * q^78 + 16 * q^79 + 12 * q^81 + 4 * q^83 - 4 * q^84 + 32 * q^85 + 16 * q^86 + 144 * q^87 - 88 * q^89 + 8 * q^90 - 8 * q^91 - 76 * q^93 - 8 * q^94 + 48 * q^95 - 4 * q^96 - 64 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$	−1.72641	+	0.139688i	−0.996743	+	0.0806489i
$3$	−1.72641	+	0.139688i	−0.996743	+	0.0806489i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	1.05727	+	1.05727i	0.472827	+	0.472827i	0.902828	−	0.430001i	$-0.141487\pi$
$5$	1.05727	+	1.05727i	0.472827	+	0.472827i	−0.430001	+	0.902828i	$0.641487\pi$
$6$	−0.311899	+	1.70374i	−0.127332	+	0.695548i
$7$	−0.965926	+	0.258819i	−0.365086	+	0.0978244i
$7$	−0.965926	+	0.258819i	−0.365086	+	0.0978244i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	2.96097	−	0.482317i	0.986992	−	0.160772i
$10$	1.29489	−	0.747605i	0.409480	−	0.236413i
$11$	−2.11737	−	0.567347i	−0.638410	−	0.171062i	−0.0749271	−	0.997189i	$-0.523872\pi$
$11$	−2.11737	−	0.567347i	−0.638410	−	0.171062i	−0.563483	+	0.826127i	$0.690539\pi$
$12$	1.56496	+	0.742231i	0.451764	+	0.214264i
$13$	−1.77553	−	3.13807i	−0.492443	−	0.870345i
$13$	−1.77553	−	3.13807i	−0.492443	−	0.870345i
$14$			1.00000i			0.267261i
$15$	−1.97297	−	1.67760i	−0.509420	−	0.433154i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	2.61760	−	4.53382i	0.634861	−	1.09961i	−0.351683	−	0.936119i	$-0.614391\pi$
$17$	2.61760	−	4.53382i	0.634861	−	1.09961i	0.986545	−	0.163493i	$-0.0522761\pi$
$18$	0.300474	−	2.98491i	0.0708225	−	0.703551i
$19$	−2.01058	−	7.50359i	−0.461259	−	1.72144i	−0.669004	−	0.743259i	$-0.733279\pi$
$19$	−2.01058	−	7.50359i	−0.461259	−	1.72144i	0.207745	−	0.978183i	$-0.433387\pi$
$20$	−0.386989	−	1.44426i	−0.0865333	−	0.322947i
$21$	1.63143	−	0.581756i	0.356007	−	0.126949i
$22$	−1.09603	+	1.89838i	−0.233674	+	0.404736i
$23$	1.89764	+	3.28680i	0.395684	+	0.685346i	0.993188	−	0.116520i	$-0.0371741\pi$
$23$	1.89764	+	3.28680i	0.395684	+	0.685346i	−0.597504	+	0.801866i	$0.703841\pi$
$24$	1.12198	−	1.31953i	0.229023	−	0.269348i
$25$		−	2.76435i		−	0.552869i
$26$	−3.49069	+	0.902835i	−0.684580	+	0.177061i
$27$	−5.04448	+	1.24629i	−0.970810	+	0.239848i
$28$	0.965926	+	0.258819i	0.182543	+	0.0489122i
$29$	−6.69332	+	3.86439i	−1.24292	+	0.717599i	−0.969687	−	0.244350i	$-0.921425\pi$
$29$	−6.69332	+	3.86439i	−1.24292	+	0.717599i	−0.273230	+	0.961949i	$0.588092\pi$
$30$	−2.13108	+	1.47155i	−0.389080	+	0.268667i
$31$	−3.28024	+	3.28024i	−0.589149	+	0.589149i	−0.937401	−	0.348252i	$-0.886775\pi$
$31$	−3.28024	+	3.28024i	−0.589149	+	0.589149i	0.348252	+	0.937401i	$0.386775\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	3.73469	+	0.683702i	0.650127	+	0.119017i
$34$	−3.70185	−	3.70185i	−0.634861	−	0.634861i
$35$	−1.29489	−	0.747605i	−0.218876	−	0.126368i
$36$	−2.80544	−	1.06279i	−0.467573	−	0.177131i
$37$	0.896760	−	3.34675i	0.147426	−	0.550203i	−0.852209	−	0.523202i	$-0.824738\pi$
$37$	0.896760	−	3.34675i	0.147426	−	0.550203i	0.999635	−	0.0270013i	$-0.00859582\pi$
$38$	−7.76829			−1.26018
$39$	3.50364	+	5.16958i	0.561031	+	0.827795i
$40$	−1.49521			−0.236413
$41$	2.92345	−	10.9105i	0.456567	−	1.70393i	−0.226873	−	0.973924i	$-0.572850\pi$
$41$	2.92345	−	10.9105i	0.456567	−	1.70393i	0.683440	−	0.730007i	$-0.260483\pi$
$42$	−0.139688	−	1.72641i	−0.0215543	−	0.266391i
$43$	−8.42241	−	4.86268i	−1.28440	−	0.741552i	−0.306755	−	0.951789i	$-0.599243\pi$
$43$	−8.42241	−	4.86268i	−1.28440	−	0.741552i	−0.977650	+	0.210237i	$0.932576\pi$
$44$	1.55002	+	1.55002i	0.233674	+	0.233674i
$45$	3.64050	+	2.62062i	0.542694	+	0.390659i
$46$	3.66595	−	0.982289i	0.540515	−	0.144831i
$47$	−1.61934	+	1.61934i	−0.236205	+	0.236205i	−0.815276	−	0.579072i	$-0.803415\pi$
$47$	−1.61934	+	1.61934i	−0.236205	+	0.236205i	0.579072	+	0.815276i	$0.303415\pi$
$48$	−0.984178	−	1.42527i	−0.142054	−	0.205720i
$49$	0.866025	−	0.500000i	0.123718	−	0.0714286i
$50$	−2.67015	−	0.715466i	−0.377617	−	0.101182i
$51$	−3.88573	+	8.19287i	−0.544111	+	1.14723i
$52$	−0.0313841	+	3.60541i	−0.00435219	+	0.499981i
$53$			7.90385i			1.08568i	0.839837	+	0.542838i	$0.182650\pi$
$53$			7.90385i			1.08568i	−0.839837	+	0.542838i	$0.817350\pi$
$54$	−0.101785	+	5.19516i	−0.0138512	+	0.706971i
$55$	−1.63879	−	2.83848i	−0.220975	−	0.382740i
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$	4.51925	+	12.6734i	0.598589	+	1.67863i
$58$	2.00035	+	7.46542i	0.262659	+	0.980258i
$59$	−3.07907	−	11.4912i	−0.400861	−	1.49603i	−0.811564	−	0.584263i	$-0.801384\pi$
$59$	−3.07907	−	11.4912i	−0.400861	−	1.49603i	0.410703	−	0.911769i	$-0.365283\pi$
$60$	0.869847	+	2.43933i	0.112297	+	0.314916i
$61$	3.28906	−	5.69681i	0.421120	−	0.729402i	−0.574929	−	0.818203i	$-0.694970\pi$
$61$	3.28906	−	5.69681i	0.421120	−	0.729402i	0.996049	+	0.0888014i	$0.0283037\pi$
$62$	2.31948	+	4.01746i	0.294574	+	0.510218i
$63$	−2.73525	+	1.23224i	−0.344609	+	0.155248i
$64$		−	1.00000i		−	0.125000i
$65$	1.44058	−	5.19502i	0.178682	−	0.644363i
$66$	1.62702	−	3.43048i	0.200272	−	0.422263i
$67$	15.4661	+	4.14413i	1.88949	+	0.506286i	0.998649	+	0.0519651i	$0.0165485\pi$
$67$	15.4661	+	4.14413i	1.88949	+	0.506286i	0.890838	+	0.454321i	$0.150118\pi$
$68$	−4.53382	+	2.61760i	−0.549806	+	0.317431i
$69$	−3.73522	−	5.40929i	−0.449668	−	0.651202i
$70$	−1.05727	+	1.05727i	−0.126368	+	0.126368i
$71$	−9.79449	+	2.62443i	−1.16239	+	0.311462i	−0.787921	−	0.615776i	$-0.788842\pi$
$71$	−9.79449	+	2.62443i	−1.16239	+	0.311462i	−0.374471	+	0.927238i	$0.622176\pi$
$72$	−1.75268	+	2.43477i	−0.206555	+	0.286941i
$73$	1.17055	+	1.17055i	0.137003	+	0.137003i	0.772282	−	0.635280i	$-0.219115\pi$
$73$	1.17055	+	1.17055i	0.137003	+	0.137003i	−0.635280	+	0.772282i	$0.719115\pi$
$74$	−3.00062	−	1.73241i	−0.348815	−	0.201388i
$75$	0.386146	+	4.77239i	0.0445883	+	0.551069i
$76$	−2.01058	+	7.50359i	−0.230629	+	0.860721i
$77$	2.19206			0.249808
$78$	5.90024	−	2.04627i	0.668070	−	0.231694i
$79$	15.2544			1.71626			0.858130	−	0.513433i	$-0.171626\pi$
$79$	15.2544			1.71626			0.858130	+	0.513433i	$0.171626\pi$
$80$	−0.386989	+	1.44426i	−0.0432667	+	0.161473i
$81$	8.53474	−	2.85626i	0.948305	−	0.317362i
$82$	−9.78207	−	5.64768i	−1.08025	−	0.623682i
$83$	−1.82647	−	1.82647i	−0.200482	−	0.200482i	0.599725	−	0.800206i	$-0.295277\pi$
$83$	−1.82647	−	1.82647i	−0.200482	−	0.200482i	−0.800206	+	0.599725i	$0.795277\pi$
$84$	−1.70374	−	0.311899i	−0.185893	−	0.0340310i
$85$	7.56100	−	2.02596i	0.820106	−	0.219747i
$86$	−6.87687	+	6.87687i	−0.741552	+	0.741552i
$87$	11.0156	−	7.60649i	1.18100	−	0.815501i
$88$	1.89838	−	1.09603i	0.202368	−	0.116837i
$89$	−2.44499	−	0.655132i	−0.259168	−	0.0694439i	0.126895	−	0.991916i	$-0.459499\pi$
$89$	−2.44499	−	0.655132i	−0.259168	−	0.0694439i	−0.386063	+	0.922472i	$0.626165\pi$
$90$	3.47355	−	2.83819i	0.366145	−	0.299171i
$91$	2.52722	+	2.57161i	0.264925	+	0.269577i
$92$		−	3.79527i		−	0.395684i
$93$	5.20483	−	6.12125i	0.539715	−	0.634744i
$94$	1.14504	+	1.98327i	0.118102	+	0.204559i
$95$	5.80761	−	10.0591i	0.595848	−	1.03204i
$96$	−1.63143	+	0.581756i	−0.166507	+	0.0593752i
$97$	3.53642	+	13.1981i	0.359070	+	1.34007i	0.875285	+	0.483607i	$0.160674\pi$
$97$	3.53642	+	13.1981i	0.359070	+	1.34007i	−0.516216	+	0.856459i	$0.672660\pi$
$98$	−0.258819	−	0.965926i	−0.0261447	−	0.0975732i
$99$	−6.54311	−	0.658658i	−0.657608	−	0.0661976i
$100$	−1.38217	+	2.39399i	−0.138217	+	0.239399i
$101$	4.30170	+	7.45077i	0.428035	+	0.741379i	0.996699	−	0.0811915i	$-0.0258725\pi$
$101$	4.30170	+	7.45077i	0.428035	+	0.741379i	−0.568663	+	0.822570i	$0.692539\pi$
$102$	6.90800	+	5.87380i	0.683994	+	0.581592i
$103$			6.73155i			0.663280i	0.943406	+	0.331640i	$0.107602\pi$
$103$			6.73155i			0.663280i	−0.943406	+	0.331640i	$0.892398\pi$
$104$	3.47444	+	0.963465i	0.340697	+	0.0944755i
$105$	2.33994	+	1.10979i	0.228355	+	0.108305i
$106$	7.63453	+	2.04567i	0.741531	+	0.198693i
$107$	−0.624663	+	0.360649i	−0.0603884	+	0.0348653i	−0.529890	−	0.848066i	$-0.677767\pi$
$107$	−0.624663	+	0.360649i	−0.0603884	+	0.0348653i	0.469502	+	0.882932i	$0.344434\pi$
$108$	4.99179	+	1.44292i	0.480335	+	0.138845i
$109$	1.35124	−	1.35124i	0.129426	−	0.129426i	−0.639427	−	0.768852i	$-0.720828\pi$
$109$	1.35124	−	1.35124i	0.129426	−	0.129426i	0.768852	+	0.639427i	$0.220828\pi$
$110$	−3.16591	+	0.848303i	−0.301858	+	0.0808825i
$111$	−1.08067	+	5.90313i	−0.102573	+	0.560300i
$112$	−0.707107	−	0.707107i	−0.0668153	−	0.0668153i
$113$	−2.21231	−	1.27728i	−0.208117	−	0.120156i	0.392319	−	0.919829i	$-0.371673\pi$
$113$	−2.21231	−	1.27728i	−0.208117	−	0.120156i	−0.600436	+	0.799673i	$0.705006\pi$
$114$	13.4112	−	1.08514i	1.25608	−	0.101632i
$115$	−1.46873	+	5.48137i	−0.136960	+	0.511140i
$116$	7.72878			0.717599
$117$	−6.77084	−	8.43539i	−0.625964	−	0.779852i
$118$	−11.8966			−1.09517
$119$	−1.35497	+	5.05682i	−0.124210	+	0.463557i
$120$	2.58134	−	0.208863i	0.235643	−	0.0190665i
$121$	−5.36492	−	3.09744i	−0.487720	−	0.281585i
$122$	−4.65143	−	4.65143i	−0.421120	−	0.421120i
$123$	−3.52302	+	19.2443i	−0.317660	+	1.73520i
$124$	4.48089	−	1.20065i	0.402396	−	0.107822i
$125$	8.20904	−	8.20904i	0.734238	−	0.734238i
$126$	0.482317	+	2.96097i	0.0429682	+	0.263785i
$127$	−1.26873	+	0.732503i	−0.112582	+	0.0649992i	−0.555234	−	0.831694i	$-0.687371\pi$
$127$	−1.26873	+	0.732503i	−0.112582	+	0.0649992i	0.442652	+	0.896694i	$0.354038\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	15.2198	+	7.21846i	1.34003	+	0.635550i
$130$	−4.64515	−	2.73606i	−0.407407	−	0.239969i
$131$			3.47622i			0.303719i	0.988402	+	0.151859i	$0.0485261\pi$
$131$			3.47622i			0.303719i	−0.988402	+	0.151859i	$0.951474\pi$
$132$	−2.89249	−	2.45945i	−0.251759	−	0.214068i
$133$	3.88414	+	6.72753i	0.336798	+	0.583351i
$134$	8.00585	−	13.8665i	0.691600	−	1.19789i
$135$	−6.65106	−	4.01572i	−0.572432	−	0.345619i
$136$	1.35497	+	5.05682i	0.116188	+	0.433618i
$137$	1.32711	+	4.95285i	0.113383	+	0.423151i	0.999161	−	0.0409586i	$-0.0130412\pi$
$137$	1.32711	+	4.95285i	0.113383	+	0.423151i	−0.885778	+	0.464109i	$0.846375\pi$
$138$	−6.19172	+	2.20792i	−0.527074	+	0.187951i
$139$	7.55192	−	13.0803i	0.640546	−	1.10946i	−0.344765	−	0.938689i	$-0.612042\pi$
$139$	7.55192	−	13.0803i	0.640546	−	1.10946i	0.985311	−	0.170769i	$-0.0546251\pi$
$140$	0.747605	+	1.29489i	0.0631842	+	0.109438i
$141$	2.56944	−	3.02184i	0.216386	−	0.254485i
$142$			10.1400i			0.850930i
$143$	1.97907	+	7.65179i	0.165498	+	0.639875i
$144$	1.89819	+	2.32312i	0.158182	+	0.193593i
$145$	−11.1624	−	2.99095i	−0.926985	−	0.248385i
$146$	1.43363	−	0.827705i	0.118648	−	0.0685013i
$147$	−1.42527	+	0.984178i	−0.117554	+	0.0811736i
$148$	−2.44999	+	2.44999i	−0.201388	+	0.201388i
$149$	14.0304	−	3.75943i	1.14941	−	0.307985i	0.366684	−	0.930346i	$-0.380493\pi$
$149$	14.0304	−	3.75943i	1.14941	−	0.307985i	0.782730	+	0.622361i	$0.213826\pi$
$150$	4.70972	+	0.862198i	0.384547	+	0.0703982i
$151$	−5.31083	−	5.31083i	−0.432189	−	0.432189i	0.457183	−	0.889372i	$-0.348858\pi$
$151$	−5.31083	−	5.31083i	−0.432189	−	0.432189i	−0.889372	+	0.457183i	$0.848858\pi$
$152$	6.72753	+	3.88414i	0.545675	+	0.315046i
$153$	5.56391	−	14.6870i	0.449816	−	1.18738i
$154$	0.567347	−	2.11737i	0.0457181	−	0.170622i
$155$	−6.93622			−0.557131
$156$	−0.449451	−	6.22880i	−0.0359849	−	0.498703i
$157$	−21.4186			−1.70939			−0.854695	−	0.519130i	$-0.826256\pi$
$157$	−21.4186			−1.70939			−0.854695	+	0.519130i	$0.826256\pi$
$158$	3.94814	−	14.7347i	0.314097	−	1.17223i
$159$	−1.10407	−	13.6453i	−0.0875586	−	1.08214i
$160$	1.29489	+	0.747605i	0.102370	+	0.0591034i
$161$	−2.68366	−	2.68366i	−0.211502	−	0.211502i
$162$	−0.549978	−	8.98318i	−0.0432104	−	0.705785i
$163$	4.07472	−	1.09182i	0.319157	−	0.0855177i	−0.0956843	−	0.995412i	$-0.530504\pi$
$163$	4.07472	−	1.09182i	0.319157	−	0.0855177i	0.414841	+	0.909894i	$0.363837\pi$
$164$	−7.98703	+	7.98703i	−0.623682	+	0.623682i
$165$	3.22573	+	4.67145i	0.251123	+	0.363672i
$166$	−2.23696	+	1.29151i	−0.173622	+	0.100241i
$167$	−12.0719	−	3.23465i	−0.934149	−	0.250305i	−0.240526	−	0.970643i	$-0.577320\pi$
$167$	−12.0719	−	3.23465i	−0.934149	−	0.250305i	−0.693623	+	0.720338i	$0.743987\pi$
$168$	−0.742231	+	1.56496i	−0.0572644	+	0.120739i
$169$	−6.69500	+	11.1435i	−0.515000	+	0.857190i
$170$		−	7.82772i		−	0.600359i
$171$	−9.57239	−	21.2482i	−0.732019	−	1.62489i
$172$	4.86268	+	8.42241i	0.370776	+	0.642202i
$173$	−7.59905	+	13.1619i	−0.577745	+	1.00068i	0.417993	+	0.908450i	$0.362734\pi$
$173$	−7.59905	+	13.1619i	−0.577745	+	1.00068i	−0.995737	+	0.0922329i	$0.970600\pi$
$174$	−4.49626	−	12.6089i	−0.340861	−	0.955882i
$175$	0.715466	+	2.67015i	0.0540841	+	0.201845i
$176$	−0.567347	−	2.11737i	−0.0427654	−	0.159603i
$177$	6.92092	+	19.4085i	0.520208	+	1.45883i
$178$	−1.26562	+	2.19211i	−0.0948621	+	0.164306i
$179$	−8.74705	−	15.1503i	−0.653785	−	1.13239i	−0.982197	−	0.187855i	$-0.939847\pi$
$179$	−8.74705	−	15.1503i	−0.653785	−	1.13239i	0.328412	−	0.944535i	$-0.393487\pi$
$180$	−1.84246	−	4.08977i	−0.137329	−	0.304834i
$181$			2.69032i			0.199970i	0.994989	+	0.0999849i	$0.0318795\pi$
$181$			2.69032i			0.199970i	−0.994989	+	0.0999849i	$0.968121\pi$
$182$	3.13807	−	1.77553i	0.232609	−	0.131611i
$183$	−4.88248	+	10.2945i	−0.360923	+	0.760989i
$184$	−3.66595	−	0.982289i	−0.270257	−	0.0724153i
$185$	4.48655	−	2.59031i	0.329858	−	0.190444i
$186$	−4.56556	−	6.61177i	−0.334763	−	0.484799i
$187$	−8.11467	+	8.11467i	−0.593403	+	0.593403i
$188$	2.21206	−	0.592719i	0.161331	−	0.0432284i
$189$	4.55003	−	2.50943i	0.330966	−	0.182534i
$190$	−8.21320	−	8.21320i	−0.595848	−	0.595848i
$191$	−6.61189	−	3.81738i	−0.478420	−	0.276216i	0.241338	−	0.970441i	$-0.422414\pi$
$191$	−6.61189	−	3.81738i	−0.478420	−	0.276216i	−0.719758	+	0.694225i	$0.755747\pi$
$192$	0.139688	+	1.72641i	0.0100811	+	0.124593i
$193$	0.149710	−	0.558725i	0.0107764	−	0.0402179i	−0.960328	−	0.278872i	$-0.910040\pi$
$193$	0.149710	−	0.558725i	0.0107764	−	0.0402179i	0.971105	+	0.238654i	$0.0767062\pi$
$194$	13.6637			0.980996
$195$	−1.76135	+	9.16996i	−0.126133	+	0.656674i
$196$	−1.00000			−0.0714286
$197$	−2.62767	+	9.80658i	−0.187213	+	0.698690i	0.806932	+	0.590644i	$0.201126\pi$
$197$	−2.62767	+	9.80658i	−0.187213	+	0.698690i	−0.994146	+	0.108046i	$0.965541\pi$
$198$	−2.32970	+	6.14969i	−0.165564	+	0.437039i
$199$	14.7885	+	8.53813i	1.04833	+	0.605252i	0.922181	−	0.386759i	$-0.126406\pi$
$199$	14.7885	+	8.53813i	1.04833	+	0.605252i	0.126147	+	0.992012i	$0.459739\pi$
$200$	1.95469	+	1.95469i	0.138217	+	0.138217i
$201$	−27.2797	−	4.99404i	−1.92416	−	0.352252i
$202$	8.31025	−	2.22672i	0.584707	−	0.156672i
$203$	5.46507	−	5.46507i	0.383573	−	0.383573i
$204$	7.46157	−	5.15237i	0.522415	−	0.360738i
$205$	14.6262	−	8.44447i	1.02154	−	0.589787i
$206$	6.50218	+	1.74225i	0.453028	+	0.121389i
$207$	7.20413	+	8.81687i	0.500722	+	0.612815i
$208$	1.82989	−	3.10669i	0.126880	−	0.215410i
$209$			17.0286i			1.17789i
$210$	1.67760	−	1.97297i	0.115765	−	0.136148i
$211$	4.90384	+	8.49369i	0.337594	+	0.584730i	0.983980	−	0.178281i	$-0.0570536\pi$
$211$	4.90384	+	8.49369i	0.337594	+	0.584730i	−0.646386	+	0.763011i	$0.723720\pi$
$212$	3.95192	−	6.84493i	0.271419	−	0.470112i
$213$	16.5427	−	5.89901i	1.13349	−	0.404193i
$214$	0.186686	+	0.696721i	0.0127616	+	0.0476268i
$215$	−3.76360	−	14.0460i	−0.256676	−	0.957927i
$216$	2.68573	−	4.44824i	0.182741	−	0.302665i
$217$	2.31948	−	4.01746i	0.157457	−	0.272723i
$218$	−0.955472	−	1.65493i	−0.0647128	−	0.112086i
$219$	−2.18436	−	1.85734i	−0.147606	−	0.125507i
$220$			3.27759i			0.220975i
$221$	−18.8751	−	0.164302i	−1.26967	−	0.0110521i
$222$	5.42229	+	2.57169i	0.363920	+	0.172601i
$223$	2.80512	+	0.751631i	0.187845	+	0.0503329i	0.351515	−	0.936182i	$-0.385667\pi$
$223$	2.80512	+	0.751631i	0.187845	+	0.0503329i	−0.163670	+	0.986515i	$0.552333\pi$
$224$	−0.866025	+	0.500000i	−0.0578638	+	0.0334077i
$225$	−1.33329	−	8.18516i	−0.0888861	−	0.545677i
$226$	−1.80635	+	1.80635i	−0.120156	+	0.120156i
$227$	2.49159	−	0.667619i	0.165373	−	0.0443115i	−0.175183	−	0.984536i	$-0.556052\pi$
$227$	2.49159	−	0.667619i	0.165373	−	0.0443115i	0.340555	+	0.940224i	$0.389385\pi$
$228$	2.42292	−	13.2351i	0.160462	−	0.876517i
$229$	−15.0557	−	15.0557i	−0.994910	−	0.994910i	0.00507662	−	0.999987i	$-0.498384\pi$
$229$	−15.0557	−	15.0557i	−0.994910	−	0.994910i	−0.999987	+	0.00507662i	$0.998384\pi$
$230$	4.91446	+	2.83736i	0.324050	+	0.187090i
$231$	−3.78439	+	0.306204i	−0.248995	+	0.0201468i
$232$	2.00035	−	7.46542i	0.131330	−	0.490129i
$233$	26.4704			1.73413			0.867067	−	0.498191i	$-0.166002\pi$
$233$	26.4704			1.73413			0.867067	+	0.498191i	$0.166002\pi$
$234$	−9.90038	+	4.35689i	−0.647208	+	0.284819i
$235$	−3.42416			−0.223368
$236$	−3.07907	+	11.4912i	−0.200430	+	0.748016i
$237$	−26.3354	+	2.13086i	−1.71067	+	0.138414i
$238$	4.53382	+	2.61760i	0.293884	+	0.169674i
$239$	13.5227	+	13.5227i	0.874713	+	0.874713i	0.992982	−	0.118269i	$-0.0377344\pi$
$239$	13.5227	+	13.5227i	0.874713	+	0.874713i	−0.118269	+	0.992982i	$0.537734\pi$
$240$	0.466355	−	2.54744i	0.0301031	−	0.164437i
$241$	16.2783	−	4.36174i	1.04857	−	0.280965i	0.306912	−	0.951738i	$-0.400704\pi$
$241$	16.2783	−	4.36174i	1.04857	−	0.280965i	0.741662	+	0.670773i	$0.234038\pi$
$242$	−4.38044	+	4.38044i	−0.281585	+	0.281585i
$243$	−14.3355	+	6.12327i	−0.919621	+	0.392808i
$244$	−5.69681	+	3.28906i	−0.364701	+	0.210560i
$245$	1.44426	+	0.386989i	0.0922705	+	0.0247238i
$246$	17.6768	+	8.38377i	1.12703	+	0.534530i
$247$	−19.9770	+	19.6322i	−1.27110	+	1.24917i
$248$		−	4.63896i		−	0.294574i
$249$	3.40838	+	2.89810i	0.215997	+	0.183660i
$250$	−5.80466	−	10.0540i	−0.367119	−	0.635869i
$251$	−6.50358	+	11.2645i	−0.410502	+	0.711010i	−0.994945	−	0.100425i	$-0.967980\pi$
$251$	−6.50358	+	11.2645i	−0.410502	+	0.711010i	0.584443	+	0.811435i	$0.301313\pi$
$252$	2.98491	+	0.300474i	0.188032	+	0.0189281i
$253$	−2.15324	−	8.03598i	−0.135373	−	0.505218i
$254$	0.379172	+	1.41509i	0.0237913	+	0.0887905i
$255$	−12.7704	+	4.55382i	−0.799712	+	0.285171i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	14.6976	+	25.4570i	0.916812	+	1.58797i	0.804226	+	0.594324i	$0.202580\pi$
$257$	14.6976	+	25.4570i	0.916812	+	1.58797i	0.112587	+	0.993642i	$0.464086\pi$
$258$	10.9117	−	12.8329i	0.679331	−	0.798941i
$259$			3.46481i			0.215293i
$260$	−3.84509	+	3.77873i	−0.238462	+	0.234347i
$261$	−17.9549	+	14.6707i	−1.11138	+	0.908091i
$262$	3.35777	+	0.899712i	0.207444	+	0.0555844i
$263$	−14.1187	+	8.15141i	−0.870594	+	0.502638i	−0.867546	−	0.497358i	$-0.834304\pi$
$263$	−14.1187	+	8.15141i	−0.870594	+	0.502638i	−0.00304826	+	0.999995i	$0.500970\pi$
$264$	−3.12428	+	2.15738i	−0.192286	+	0.132777i
$265$	−8.35652	+	8.35652i	−0.513337	+	0.513337i
$266$	7.50359	−	2.01058i	0.460075	−	0.123277i
$267$	4.31256	+	0.789491i	0.263924	+	0.0483160i
$268$	−11.3220	−	11.3220i	−0.691600	−	0.691600i
$269$	−12.4541	−	7.19038i	−0.759340	−	0.438405i	0.0697188	−	0.997567i	$-0.477790\pi$
$269$	−12.4541	−	7.19038i	−0.759340	−	0.438405i	−0.829059	+	0.559162i	$0.811123\pi$
$270$	−5.60031	+	5.38508i	−0.340824	+	0.327726i
$271$	6.12198	−	22.8476i	0.371884	−	1.38789i	−0.485960	−	0.873981i	$-0.661530\pi$
$271$	6.12198	−	22.8476i	0.371884	−	1.38789i	0.857844	−	0.513909i	$-0.171803\pi$
$272$	5.23520			0.317431
$273$	−4.72224	−	4.08662i	−0.285803	−	0.247333i
$274$	5.12757			0.309768
$275$	−1.56834	+	5.85314i	−0.0945747	+	0.352958i
$276$	0.530154	+	6.55219i	0.0319115	+	0.394396i
$277$	6.24900	+	3.60786i	0.375466	+	0.216775i	0.675844	−	0.737045i	$-0.263779\pi$
$277$	6.24900	+	3.60786i	0.375466	+	0.216775i	−0.300378	+	0.953820i	$0.597113\pi$
$278$	−10.6800	−	10.6800i	−0.640546	−	0.640546i
$279$	−8.13059	+	11.2948i	−0.486766	+	0.676203i
$280$	1.44426	−	0.386989i	0.0863112	−	0.0231270i
$281$	−7.15417	+	7.15417i	−0.426782	+	0.426782i	−0.887531	−	0.460749i	$-0.847581\pi$
$281$	−7.15417	+	7.15417i	−0.426782	+	0.426782i	0.460749	+	0.887531i	$0.347581\pi$
$282$	−2.25385	−	3.26399i	−0.134215	−	0.194368i
$283$	16.0304	−	9.25515i	0.952908	−	0.550162i	0.0589247	−	0.998262i	$-0.481233\pi$
$283$	16.0304	−	9.25515i	0.952908	−	0.550162i	0.893983	+	0.448101i	$0.147899\pi$
$284$	9.79449	+	2.62443i	0.581196	+	0.155731i
$285$	−8.62118	+	18.1773i	−0.510675	+	1.07673i
$286$	7.90329	+	0.0687958i	0.467331	+	0.00406798i
$287$			11.2954i			0.666744i
$288$	2.73525	−	1.23224i	0.161176	−	0.0726104i
$289$	−5.20366	−	9.01301i	−0.306098	−	0.530177i
$290$	−5.77807	+	10.0079i	−0.339300	+	0.587685i
$291$	−7.94893	−	22.2913i	−0.465975	−	1.30674i
$292$	−0.428452	−	1.59900i	−0.0250732	−	0.0935746i
$293$	−0.127883	−	0.477267i	−0.00747102	−	0.0278822i	0.962090	−	0.272733i	$-0.0879276\pi$
$293$	−0.127883	−	0.477267i	−0.00747102	−	0.0278822i	−0.969561	+	0.244851i	$0.921261\pi$
$294$	0.581756	+	1.63143i	0.0339287	+	0.0951469i
$295$	8.89396	−	15.4048i	0.517827	−	0.896902i
$296$	1.73241	+	3.00062i	0.100694	+	0.174407i
$297$	11.3881	+	0.223119i	0.660804	+	0.0129467i
$298$		−	14.5253i		−	0.841429i
$299$	6.94492	−	11.7907i	0.401635	−	0.681875i
$300$	2.05178	−	4.32609i	0.118460	−	0.249767i
$301$	9.39397	+	2.51711i	0.541460	+	0.145084i
$302$	−6.50441	+	3.75532i	−0.374287	+	0.216094i
$303$	−8.46728	−	12.2622i	−0.486432	−	0.704443i
$304$	5.49301	−	5.49301i	0.315046	−	0.315046i
$305$	9.50051	−	2.54566i	0.543998	−	0.145764i
$306$	−12.7465	−	9.17561i	−0.728671	−	0.524535i
$307$	−8.78623	−	8.78623i	−0.501456	−	0.501456i	0.410434	−	0.911890i	$-0.365377\pi$
$307$	−8.78623	−	8.78623i	−0.501456	−	0.501456i	−0.911890	+	0.410434i	$0.865377\pi$
$308$	−1.89838	−	1.09603i	−0.108170	−	0.0624521i
$309$	−0.940317	−	11.6214i	−0.0534927	−	0.661119i
$310$	−1.79523	+	6.69987i	−0.101962	+	0.380527i
$311$	−20.5980			−1.16800			−0.584002	−	0.811752i	$-0.698514\pi$
$311$	−20.5980			−1.16800			−0.584002	+	0.811752i	$0.698514\pi$
$312$	−6.13289	−	1.17800i	−0.347206	−	0.0666909i
$313$	−8.51802			−0.481467			−0.240733	−	0.970591i	$-0.577388\pi$
$313$	−8.51802			−0.481467			−0.240733	+	0.970591i	$0.577388\pi$
$314$	−5.54354	+	20.6888i	−0.312840	+	1.16754i
$315$	−4.19472	−	1.58909i	−0.236346	−	0.0895352i
$316$	−13.2107	−	7.62722i	−0.743162	−	0.429065i
$317$	−3.30217	−	3.30217i	−0.185468	−	0.185468i	0.608265	−	0.793734i	$-0.291866\pi$
$317$	−3.30217	−	3.30217i	−0.185468	−	0.185468i	−0.793734	+	0.608265i	$0.791866\pi$
$318$	−13.4661	−	2.46520i	−0.755140	−	0.138242i
$319$	16.3647	−	4.38490i	0.916245	−	0.245507i
$320$	1.05727	−	1.05727i	0.0591034	−	0.0591034i
$321$	1.02804	−	0.709886i	0.0573799	−	0.0396219i
$322$	−3.28680	+	1.89764i	−0.183166	+	0.105751i
$323$	−39.2828	−	10.5258i	−2.18575	−	0.585671i
$324$	−8.81943	−	1.79378i	−0.489968	−	0.0996544i
$325$	−8.67472	+	4.90818i	−0.481187	+	0.272257i
$326$		−	4.21846i		−	0.233639i
$327$	−2.14404	+	2.52155i	−0.118566	+	0.139442i
$328$	5.64768	+	9.78207i	0.311841	+	0.540124i
$329$	1.14504	−	1.98327i	0.0631283	−	0.109341i
$330$	5.34716	−	1.90676i	0.294351	−	0.104963i
$331$	4.49742	+	16.7846i	0.247200	+	0.922564i	0.972265	+	0.233883i	$0.0751433\pi$
$331$	4.49742	+	16.7846i	0.247200	+	0.922564i	−0.725064	+	0.688681i	$0.758190\pi$
$332$	0.668536	+	2.49501i	0.0366907	+	0.136931i
$333$	1.04109	−	10.3422i	0.0570512	−	0.566748i
$334$	−6.24886	+	10.8233i	−0.341922	+	0.592227i
$335$	11.9704	+	20.7334i	0.654014	+	1.13279i
$336$	1.31953	+	1.12198i	0.0719862	+	0.0612091i
$337$		−	10.3172i		−	0.562015i	−0.959706	−	0.281007i	$-0.909331\pi$
$337$		−	10.3172i		−	0.562015i	0.959706	−	0.281007i	$-0.0906685\pi$
$338$	9.03097	+	9.35102i	0.491220	+	0.508628i
$339$	3.99778	+	1.89607i	0.217129	+	0.102981i
$340$	−7.56100	−	2.02596i	−0.410053	−	0.109873i
$341$	8.80651	−	5.08444i	0.476899	−	0.275338i
$342$	−23.0017	+	3.74678i	−1.24379	+	0.202602i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	9.39397	−	2.51711i	0.506489	−	0.135713i
$345$	1.76994	−	9.66824i	0.0952906	−	0.520521i
$346$	10.7467	+	10.7467i	0.577745	+	0.577745i
$347$	8.16834	+	4.71599i	0.438500	+	0.253168i	0.702961	−	0.711228i	$-0.251861\pi$
$347$	8.16834	+	4.71599i	0.438500	+	0.253168i	−0.264461	+	0.964396i	$0.585194\pi$
$348$	−13.3430	+	1.07962i	−0.715261	+	0.0578735i
$349$	1.56809	−	5.85220i	0.0839381	−	0.313261i	−0.911173	−	0.412024i	$-0.864822\pi$
$349$	1.56809	−	5.85220i	0.0839381	−	0.313261i	0.995111	+	0.0987631i	$0.0314886\pi$
$350$	2.76435			0.147761
$351$	12.8676	+	13.6171i	0.686819	+	0.726828i
$352$	−2.19206			−0.116837
$353$	7.41629	−	27.6780i	0.394729	−	1.47315i	−0.427512	−	0.904010i	$-0.640610\pi$
$353$	7.41629	−	27.6780i	0.394729	−	1.47315i	0.822241	−	0.569139i	$-0.192723\pi$
$354$	20.5384	−	1.66181i	1.09160	−	0.0883243i
$355$	−13.1302	−	7.58072i	−0.696878	−	0.402343i
$356$	1.78985	+	1.78985i	0.0948621	+	0.0948621i
$357$	1.63286	−	8.91940i	0.0864199	−	0.472065i
$358$	−16.8980	+	4.52781i	−0.893087	+	0.239302i
$359$	19.0129	−	19.0129i	1.00346	−	1.00346i	0.00346917	−	0.999994i	$-0.498896\pi$
$359$	19.0129	−	19.0129i	1.00346	−	1.00346i	0.999994	−	0.00346917i	$-0.00110427\pi$
$360$	−4.42728	+	0.721165i	−0.233338	+	0.0380087i
$361$	−35.8069	+	20.6731i	−1.88458	+	1.08806i
$362$	2.59865	+	0.696306i	0.136582	+	0.0365970i
$363$	9.69471	+	4.59803i	0.508841	+	0.241334i
$364$	−0.902835	−	3.49069i	−0.0473214	−	0.182962i
$365$			2.47518i			0.129557i
$366$	8.68001	+	7.38052i	0.453711	+	0.385786i
$367$	−6.01301	−	10.4148i	−0.313876	−	0.543650i	0.665322	−	0.746557i	$-0.268294\pi$
$367$	−6.01301	−	10.4148i	−0.313876	−	0.543650i	−0.979198	+	0.202907i	$0.934961\pi$
$368$	−1.89764	+	3.28680i	−0.0989211	+	0.171336i
$369$	3.39397	−	33.7157i	0.176683	−	1.75517i
$370$	−1.34084	−	5.00410i	−0.0697072	−	0.260151i
$371$	−2.04567	−	7.63453i	−0.106206	−	0.396365i
$372$	−7.56813	+	2.69874i	−0.392389	+	0.139923i
$373$	6.81210	−	11.7989i	0.352717	−	0.610924i	−0.634007	−	0.773327i	$-0.718591\pi$
$373$	6.81210	−	11.7989i	0.352717	−	0.610924i	0.986725	+	0.162403i	$0.0519244\pi$
$374$	5.73794	+	9.93840i	0.296702	+	0.513902i
$375$	−13.0254	+	15.3189i	−0.672631	+	0.791062i
$376$		−	2.29009i		−	0.118102i
$377$	24.0109	+	14.1428i	1.23662	+	0.728390i
$378$	−1.24629	−	5.04448i	−0.0641022	−	0.259460i
$379$	2.25845	+	0.605151i	0.116009	+	0.0310845i	0.316356	−	0.948640i	$-0.397540\pi$
$379$	2.25845	+	0.605151i	0.116009	+	0.0310845i	−0.200347	+	0.979725i	$0.564207\pi$
$380$	−10.0591	+	5.80761i	−0.516020	+	0.297924i
$381$	2.08803	−	1.44183i	0.106973	−	0.0738670i
$382$	−5.39858	+	5.39858i	−0.276216	+	0.276216i
$383$	26.5611	−	7.11702i	1.35721	−	0.363663i	0.494417	−	0.869225i	$-0.335381\pi$
$383$	26.5611	−	7.11702i	1.35721	−	0.363663i	0.862790	+	0.505562i	$0.168715\pi$
$384$	1.70374	+	0.311899i	0.0869435	+	0.0159165i
$385$	2.31761	+	2.31761i	0.118116	+	0.118116i
$386$	−0.500939	−	0.289217i	−0.0254971	−	0.0147208i
$387$	−27.2839	−	10.3360i	−1.38692	−	0.525408i
$388$	3.53642	−	13.1981i	0.179535	−	0.670033i
$389$	−9.53986			−0.483690			−0.241845	−	0.970315i	$-0.577753\pi$
$389$	−9.53986			−0.483690			−0.241845	+	0.970315i	$0.577753\pi$
$390$	8.40163	+	4.07469i	0.425433	+	0.206330i
$391$	19.8690			1.00482
$392$	−0.258819	+	0.965926i	−0.0130723	+	0.0487866i
$393$	−0.485586	−	6.00138i	−0.0244946	−	0.302730i
$394$	8.79234	+	5.07626i	0.442952	+	0.255738i
$395$	16.1281	+	16.1281i	0.811494	+	0.811494i
$396$	5.33717	+	3.84197i	0.268203	+	0.193066i
$397$	15.9389	−	4.27081i	0.799950	−	0.214346i	0.164388	−	0.986396i	$-0.447435\pi$
$397$	15.9389	−	4.27081i	0.799950	−	0.214346i	0.635562	+	0.772050i	$0.280768\pi$
$398$	12.0747	−	12.0747i	0.605252	−	0.605252i
$399$	−7.64538	−	11.0719i	−0.382748	−	0.554289i
$400$	2.39399	−	1.38217i	0.119700	−	0.0691087i
$401$	−0.207374	−	0.0555657i	−0.0103558	−	0.00277482i	0.253637	−	0.967299i	$-0.418373\pi$
$401$	−0.207374	−	0.0555657i	−0.0103558	−	0.00277482i	−0.263993	+	0.964525i	$0.585040\pi$
$402$	−11.8844	+	25.0576i	−0.592739	+	1.24976i
$403$	16.1178	+	4.46947i	0.802884	+	0.222640i
$404$		−	8.60340i		−	0.428035i
$405$	12.0434	+	6.00371i	0.598441	+	0.298327i
$406$	−3.86439	−	6.69332i	−0.191786	−	0.332184i
$407$	−3.79754	+	6.57753i	−0.188237	+	0.326036i
$408$	−3.04561	−	8.54086i	−0.150780	−	0.422835i
$409$	−5.26447	−	19.6473i	−0.260311	−	0.971495i	−0.965058	−	0.262036i	$-0.915606\pi$
$409$	−5.26447	−	19.6473i	−0.260311	−	0.971495i	0.704747	−	0.709459i	$-0.251061\pi$
$410$	−4.37118	−	16.3135i	−0.215877	−	0.805664i
$411$	−2.98299	−	8.36526i	−0.147140	−	0.412628i
$412$	3.36578	−	5.82970i	0.165820	−	0.287208i
$413$	5.94830	+	10.3028i	0.292697	+	0.506966i
$414$	10.3810	−	4.67668i	0.510199	−	0.229846i
$415$		−	3.86216i		−	0.189586i
$416$	−2.52722	−	2.57161i	−0.123907	−	0.126083i
$417$	−11.2105	+	23.6369i	−0.548983	+	1.15750i
$418$	16.4483	+	4.40731i	0.804514	+	0.215569i
$419$	15.8894	−	9.17374i	0.776248	−	0.448167i	−0.0588512	−	0.998267i	$-0.518744\pi$
$419$	15.8894	−	9.17374i	0.776248	−	0.448167i	0.835099	+	0.550100i	$0.185410\pi$
$420$	−1.47155	−	2.13108i	−0.0718044	−	0.103986i
$421$	−11.3194	+	11.3194i	−0.551676	+	0.551676i	−0.926924	−	0.375249i	$-0.877557\pi$
$421$	−11.3194	+	11.3194i	−0.551676	+	0.551676i	0.375249	+	0.926924i	$0.377557\pi$
$422$	9.47349	−	2.53841i	0.461162	−	0.123568i
$423$	−4.01378	+	5.57585i	−0.195157	+	0.271107i
$424$	−5.58886	−	5.58886i	−0.271419	−	0.271419i
$425$	−12.5330	−	7.23596i	−0.607942	−	0.350995i
$426$	−1.41644	−	17.5058i	−0.0686266	−	0.848158i
$427$	−1.70254	+	6.35397i	−0.0823917	+	0.307490i
$428$	0.721298			0.0348653
$429$	−4.48555	−	12.9337i	−0.216564	−	0.624444i
$430$	−14.5415			−0.701251
$431$	1.65888	−	6.19103i	0.0799055	−	0.298211i	−0.914395	−	0.404822i	$-0.867333\pi$
$431$	1.65888	−	6.19103i	0.0799055	−	0.298211i	0.994301	+	0.106611i	$0.0340000\pi$
$432$	−3.60156	−	3.74550i	−0.173280	−	0.180206i
$433$	15.7024	+	9.06580i	0.754610	+	0.435675i	0.827357	−	0.561676i	$-0.189843\pi$
$433$	15.7024	+	9.06580i	0.754610	+	0.435675i	−0.0727469	+	0.997350i	$0.523177\pi$
$434$	−3.28024	−	3.28024i	−0.157457	−	0.157457i
$435$	19.6886	+	3.60435i	0.943997	+	0.172815i
$436$	−1.84583	+	0.494589i	−0.0883993	+	0.0236865i
$437$	20.8475	−	20.8475i	0.997269	−	0.997269i
$438$	−2.35941	+	1.62922i	−0.112737	+	0.0778470i
$439$	9.34753	−	5.39680i	0.446133	−	0.257575i	−0.260063	−	0.965592i	$-0.583743\pi$
$439$	9.34753	−	5.39680i	0.446133	−	0.257575i	0.706196	+	0.708017i	$0.250410\pi$
$440$	3.16591	+	0.848303i	0.150929	+	0.0404412i
$441$	2.32312	−	1.89819i	0.110625	−	0.0903898i
$442$	−5.04393	+	18.1894i	−0.239915	+	0.865181i
$443$		−	4.50677i		−	0.214123i	−0.994252	−	0.107061i	$-0.965856\pi$
$443$		−	4.50677i		−	0.214123i	0.994252	−	0.107061i	$-0.0341442\pi$
$444$	3.88746	−	4.57192i	0.184490	−	0.216974i
$445$	−1.89236	−	3.27767i	−0.0897067	−	0.155377i
$446$	1.45204	−	2.51501i	0.0687560	−	0.119089i
$447$	−23.6970	+	8.45019i	−1.12083	+	0.399680i
$448$	0.258819	+	0.965926i	0.0122281	+	0.0456357i
$449$	−8.97347	−	33.4894i	−0.423484	−	1.58046i	−0.767211	−	0.641395i	$-0.778356\pi$
$449$	−8.97347	−	33.4894i	−0.423484	−	1.58046i	0.343727	−	0.939070i	$-0.388311\pi$
$450$	−8.25134	−	0.830615i	−0.388972	−	0.0391556i
$451$	−12.3801	+	21.4429i	−0.582954	+	1.00971i
$452$	1.27728	+	2.21231i	0.0600782	+	0.104058i
$453$	9.91052	+	8.42680i	0.465637	+	0.395926i
$454$		−	2.57948i		−	0.121061i
$455$	−0.0469258	+	5.39085i	−0.00219991	+	0.252727i
$456$	−12.1570	−	5.76586i	−0.569306	−	0.270011i
$457$	0.0420261	+	0.0112609i	0.00196590	+	0.000526761i	0.259802	−	0.965662i	$-0.416343\pi$
$457$	0.0420261	+	0.0112609i	0.00196590	+	0.000526761i	−0.257836	+	0.966189i	$0.583009\pi$
$458$	−18.4394	+	10.6460i	−0.861618	+	0.497455i
$459$	−7.55398	+	26.1330i	−0.352590	+	1.21979i
$460$	4.01264	−	4.01264i	0.187090	−	0.187090i
$461$	−24.1897	+	6.48161i	−1.12663	+	0.301879i	−0.773562	−	0.633720i	$-0.781527\pi$
$461$	−24.1897	+	6.48161i	−1.12663	+	0.301879i	−0.353065	+	0.935599i	$0.614860\pi$
$462$	−0.683702	+	3.73469i	−0.0318087	+	0.173754i
$463$	−2.17087	−	2.17087i	−0.100889	−	0.100889i	0.654861	−	0.755750i	$-0.272727\pi$
$463$	−2.17087	−	2.17087i	−0.100889	−	0.100889i	−0.755750	+	0.654861i	$0.772727\pi$
$464$	−6.69332	−	3.86439i	−0.310729	−	0.179400i
$465$	11.9747	−	0.968906i	0.555316	−	0.0449319i
$466$	6.85105	−	25.5685i	0.317369	−	1.18444i
$467$	13.9572			0.645863			0.322932	−	0.946422i	$-0.395332\pi$
$467$	13.9572			0.645863			0.322932	+	0.946422i	$0.395332\pi$
$468$	1.64602	+	10.6907i	0.0760875	+	0.494177i
$469$	−16.0117			−0.739352
$470$	−0.886239	+	3.30749i	−0.0408791	+	0.152563i
$471$	36.9773	−	2.99192i	1.70382	−	0.137860i
$472$	10.3028	+	5.94830i	0.474223	+	0.273793i
$473$	15.0745	+	15.0745i	0.693126	+	0.693126i
$474$	−4.75785	+	25.9896i	−0.218535	+	1.19374i
$475$	−20.7425	+	5.55794i	−0.951732	+	0.255016i
$476$	3.70185	−	3.70185i	0.169674	−	0.169674i
$477$	3.81216	+	23.4031i	0.174547	+	1.07155i
$478$	16.5619	−	9.56202i	0.757524	−	0.437356i
$479$	7.42991	+	1.99084i	0.339481	+	0.0909637i	0.424532	−	0.905413i	$-0.360439\pi$
$479$	7.42991	+	1.99084i	0.339481	+	0.0909637i	−0.0850508	+	0.996377i	$0.527105\pi$
$480$	−2.33994	−	1.10979i	−0.106803	−	0.0506548i
$481$	−12.0946	+	3.12816i	−0.551465	+	0.142632i
$482$		−	16.8525i		−	0.767610i
$483$	5.00797	+	4.25822i	0.227871	+	0.193756i
$484$	3.09744	+	5.36492i	0.140793	+	0.243860i
$485$	−10.2150	+	17.6930i	−0.463841	+	0.803397i
$486$	2.20433	+	15.4318i	0.0999904	+	0.700001i
$487$	−3.78272	−	14.1173i	−0.171411	−	0.639716i	−0.997135	−	0.0756411i	$-0.975900\pi$
$487$	−3.78272	−	14.1173i	−0.171411	−	0.639716i	0.825724	−	0.564075i	$-0.190767\pi$
$488$	1.70254	+	6.35397i	0.0770704	+	0.287631i
$489$	−6.88212	+	2.45411i	−0.311220	+	0.110979i
$490$	0.747605	−	1.29489i	0.0337733	−	0.0584972i
$491$	−12.3616	−	21.4109i	−0.557871	−	0.966261i	−0.997674	−	0.0681669i	$-0.978285\pi$
$491$	−12.3616	−	21.4109i	−0.557871	−	0.966261i	0.439803	−	0.898094i	$-0.355048\pi$
$492$	12.6732	−	14.9046i	0.571351	−	0.671950i
$493$			40.4617i			1.82230i
$494$	13.7928	+	24.3775i	0.620568	+	1.09679i
$495$	−6.22148	−	7.61424i	−0.279635	−	0.342235i
$496$	−4.48089	−	1.20065i	−0.201198	−	0.0539108i
$497$	8.78150	−	5.07000i	0.393904	−	0.227421i
$498$	3.68151	−	2.54215i	0.164972	−	0.113917i
$499$	27.5916	−	27.5916i	1.23517	−	1.23517i	0.273218	−	0.961952i	$-0.411912\pi$
$499$	27.5916	−	27.5916i	1.23517	−	1.23517i	0.961952	−	0.273218i	$-0.0880879\pi$
$500$	−11.2138	+	3.00472i	−0.501494	+	0.134375i
$501$	21.2928	+	3.89803i	0.951293	+	0.174151i
$502$	9.19745	+	9.19745i	0.410502	+	0.410502i
$503$	18.9750	+	10.9552i	0.846053	+	0.488469i	0.859317	−	0.511443i	$-0.170889\pi$
$503$	18.9750	+	10.9552i	0.846053	+	0.488469i	−0.0132638	+	0.999912i	$0.504222\pi$
$504$	1.06279	−	2.80544i	0.0473404	−	0.124964i
$505$	−3.32942	+	12.4256i	−0.148157	+	0.552931i
$506$	−8.31946			−0.369845
$507$	10.0017	−	20.1734i	0.444191	−	0.895932i
$508$	1.46501			0.0649992
$509$	2.86121	−	10.6782i	0.126821	−	0.473303i	−0.873077	−	0.487582i	$-0.837879\pi$
$509$	2.86121	−	10.6782i	0.126821	−	0.473303i	0.999898	+	0.0142796i	$0.00454550\pi$
$510$	1.09344	+	13.5139i	0.0484183	+	0.598403i
$511$	−1.43363	−	0.827705i	−0.0634199	−	0.0366155i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	19.4940	+	35.3459i	0.860680	+	1.56056i
$514$	28.3936	−	7.60805i	1.25239	−	0.335577i
$515$	−7.11709	+	7.11709i	−0.313616	+	0.313616i
$516$	−9.57148	−	13.8613i	−0.421361	−	0.610208i
$517$	4.34746	−	2.51001i	0.191201	−	0.110390i
$518$	3.34675	+	0.896760i	0.147048	+	0.0394014i
$519$	11.2805	−	23.7844i	0.495159	−	1.04402i
$520$	2.65479	+	4.69208i	0.116420	+	0.205761i
$521$			14.8404i			0.650169i	0.945685	+	0.325084i	$0.105393\pi$
$521$			14.8404i			0.650169i	−0.945685	+	0.325084i	$0.894607\pi$
$522$	9.52370	+	21.1401i	0.416841	+	0.925278i
$523$	11.7259	+	20.3098i	0.512736	+	0.888085i	0.999891	+	0.0147693i	$0.00470140\pi$
$523$	11.7259	+	20.3098i	0.512736	+	0.888085i	−0.487155	+	0.873316i	$0.661965\pi$
$524$	1.73811	−	3.01050i	0.0759297	−	0.131514i
$525$	−1.60817	−	4.50984i	−0.0701865	−	0.196825i
$526$	4.21948	+	15.7473i	0.183978	+	0.686616i
$527$	6.28565	+	23.4584i	0.273807	+	1.02186i
$528$	1.27524	+	3.57619i	0.0554978	+	0.155634i
$529$	4.29796	−	7.44428i	0.186868	−	0.323664i
$530$	5.90896	+	10.2346i	0.256669	+	0.444563i
$531$	−14.6595	−	32.5402i	−0.636167	−	1.41212i
$532$		−	7.76829i		−	0.336798i
$533$	−39.4286	+	10.1979i	−1.70784	+	0.441718i
$534$	1.87876	−	3.96128i	0.0813020	−	0.171421i
$535$	−1.04174	−	0.279134i	−0.0450385	−	0.0120680i
$536$	−13.8665	+	8.00585i	−0.598943	+	0.345800i
$537$	17.2173	+	24.9338i	0.742981	+	1.07597i
$538$	−10.1687	+	10.1687i	−0.438405	+	0.438405i
$539$	−2.11737	+	0.567347i	−0.0912015	+	0.0244374i
$540$	3.75212	+	6.80325i	0.161466	+	0.292765i
$541$	−19.4313	−	19.4313i	−0.835415	−	0.835415i	0.152836	−	0.988252i	$-0.451159\pi$
$541$	−19.4313	−	19.4313i	−0.835415	−	0.835415i	−0.988252	+	0.152836i	$0.951159\pi$
$542$	−20.4846	−	11.8268i	−0.879887	−	0.508003i
$543$	−0.375805	−	4.64459i	−0.0161273	−	0.199318i
$544$	1.35497	−	5.05682i	0.0580938	−	0.216809i
$545$	2.85726			0.122392
$546$	−5.16958	+	3.50364i	−0.221237	+	0.149942i
$547$	−14.9433			−0.638931			−0.319466	−	0.947598i	$-0.603503\pi$
$547$	−14.9433			−0.638931			−0.319466	+	0.947598i	$0.603503\pi$
$548$	1.32711	−	4.95285i	0.0566914	−	0.211575i
$549$	6.99114	−	18.4545i	0.298375	−	0.787618i
$550$	5.24778	+	3.02981i	0.223766	+	0.129191i
$551$	42.4542	+	42.4542i	1.80861	+	1.80861i
$552$	6.46614	+	1.18374i	0.275217	+	0.0503834i
$553$	−14.7347	+	3.94814i	−0.626582	+	0.167892i
$554$	5.10229	−	5.10229i	0.216775	−	0.216775i
$555$	−7.38379	+	5.09865i	−0.313424	+	0.216426i
$556$	−13.0803	+	7.55192i	−0.554729	+	0.320273i
$557$	−8.34550	−	2.23617i	−0.353610	−	0.0947496i	0.0776412	−	0.996981i	$-0.475261\pi$
$557$	−8.34550	−	2.23617i	−0.353610	−	0.0947496i	−0.431251	+	0.902232i	$0.641928\pi$
$558$	8.80561	+	10.7769i	0.372771	+	0.456221i
$559$	−0.305221	+	35.0639i	−0.0129095	+	1.48305i
$560$		−	1.49521i		−	0.0631842i
$561$	12.8757	−	15.1428i	0.543613	−	0.639328i
$562$	5.05876	+	8.76203i	0.213391	+	0.369604i
$563$	−3.12728	+	5.41660i	−0.131799	+	0.228283i	−0.924370	−	0.381497i	$-0.875409\pi$
$563$	−3.12728	+	5.41660i	−0.131799	+	0.228283i	0.792571	+	0.609779i	$0.208742\pi$
$564$	−3.73612	+	1.33227i	−0.157319	+	0.0560988i
$565$	−0.988586	−	3.68945i	−0.0415901	−	0.155216i
$566$	−4.79082	−	17.8796i	−0.201373	−	0.751535i
$567$	−7.50467	+	4.96789i	−0.315167	+	0.208632i
$568$	5.07000	−	8.78150i	0.212733	−	0.368464i
$569$	8.52745	+	14.7700i	0.357489	+	0.619189i	0.987541	−	0.157364i	$-0.0502996\pi$
$569$	8.52745	+	14.7700i	0.357489	+	0.619189i	−0.630052	+	0.776553i	$0.716966\pi$
$570$	15.3266	+	13.0321i	0.641962	+	0.545853i
$571$			30.4744i			1.27531i	0.770320	+	0.637657i	$0.220096\pi$
$571$			30.4744i			1.27531i	−0.770320	+	0.637657i	$0.779904\pi$
$572$	2.11197	−	7.61618i	0.0883060	−	0.318449i
$573$	11.9481	+	5.66675i	0.499138	+	0.236732i
$574$	10.9105	+	2.92345i	0.455395	+	0.122023i
$575$	9.08586	−	5.24572i	0.378907	−	0.218762i
$576$	−0.482317	−	2.96097i	−0.0200965	−	0.123374i
$577$	17.6984	−	17.6984i	0.736796	−	0.736796i	−0.235161	−	0.971957i	$-0.575562\pi$
$577$	17.6984	−	17.6984i	0.736796	−	0.736796i	0.971957	+	0.235161i	$0.0755616\pi$
$578$	−10.0527	+	2.69361i	−0.418137	+	0.112040i
$579$	−0.180413	+	0.985501i	−0.00749773	+	0.0409560i
$580$	8.17143	+	8.17143i	0.339300	+	0.339300i
$581$	2.23696	+	1.29151i	0.0928049	+	0.0535810i
$582$	−23.5891	+	1.90865i	−0.977801	+	0.0791162i
$583$	4.48422	−	16.7353i	0.185718	−	0.693107i
$584$	−1.65541			−0.0685013
$585$	1.75988	−	16.0771i	0.0727622	−	0.664708i
$586$	−0.494103			−0.0204112
$587$	−0.843372	+	3.14751i	−0.0348097	+	0.129912i	−0.981144	−	0.193277i	$-0.938088\pi$
$587$	−0.843372	+	3.14751i	−0.0348097	+	0.129912i	0.946334	+	0.323189i	$0.104755\pi$
$588$	1.72641	−	0.139688i	0.0711959	−	0.00576063i
$589$	31.2088	+	18.0184i	1.28593	+	0.742435i
$590$	−12.5780	−	12.5780i	−0.517827	−	0.517827i
$591$	3.16656	−	17.2972i	0.130255	−	0.711513i
$592$	3.34675	−	0.896760i	0.137551	−	0.0368566i
$593$	5.03998	−	5.03998i	0.206967	−	0.206967i	−0.596010	−	0.802977i	$-0.703248\pi$
$593$	5.03998	−	5.03998i	0.206967	−	0.206967i	0.802977	+	0.596010i	$0.203248\pi$
$594$	3.16297	−	10.9423i	0.129778	−	0.448968i
$595$	−6.77901	+	3.91386i	−0.277912	+	0.160453i
$596$	−14.0304	−	3.75943i	−0.574707	−	0.153992i
$597$	−26.7236	−	12.6745i	−1.09373	−	0.518734i
$598$	−9.59149	−	9.75994i	−0.392225	−	0.399114i
$599$		−	26.5579i		−	1.08513i	−0.840015	−	0.542564i	$-0.817454\pi$
$599$		−	26.5579i		−	1.08513i	0.840015	−	0.542564i	$-0.182546\pi$
$600$	−3.64764	−	3.10155i	−0.148914	−	0.126620i
$601$	2.35032	+	4.07088i	0.0958716	+	0.166055i	0.909972	−	0.414670i	$-0.136103\pi$
$601$	2.35032	+	4.07088i	0.0958716	+	0.166055i	−0.814100	+	0.580724i	$0.802770\pi$
$602$	4.86268	−	8.42241i	0.198188	−	0.343272i
$603$	47.7936	+	4.81110i	1.94630	+	0.195923i
$604$	1.94390	+	7.25472i	0.0790961	+	0.295191i
$605$	−2.39735	−	8.94702i	−0.0974660	−	0.363748i
$606$	−14.0358	+	5.00508i	−0.570167	+	0.203317i
$607$	−7.50564	+	13.0002i	−0.304645	+	0.527660i	−0.977182	−	0.212403i	$-0.931871\pi$
$607$	−7.50564	+	13.0002i	−0.304645	+	0.527660i	0.672537	+	0.740063i	$0.265204\pi$
$608$	−3.88414	−	6.72753i	−0.157523	−	0.272838i
$609$	−8.67154	+	10.1983i	−0.351389	+	0.413258i
$610$		−	9.83566i		−	0.398234i
$611$	7.95678	+	2.20642i	0.321897	+	0.0892622i
$612$	−12.1620	+	9.93738i	−0.491620	+	0.401695i
$613$	10.7055	+	2.86853i	0.432391	+	0.115859i	0.468448	−	0.883491i	$-0.344813\pi$
$613$	10.7055	+	2.86853i	0.432391	+	0.115859i	−0.0360574	+	0.999350i	$0.511480\pi$
$614$	−10.7609	+	6.21280i	−0.434274	+	0.250728i
$615$	−24.0713	+	16.6217i	−0.970648	+	0.670252i
$616$	−1.55002	+	1.55002i	−0.0624521	+	0.0624521i
$617$	17.9156	−	4.80046i	0.721253	−	0.193259i	0.120522	−	0.992711i	$-0.461543\pi$
$617$	17.9156	−	4.80046i	0.721253	−	0.193259i	0.600731	+	0.799451i	$0.294876\pi$
$618$	−11.4688	−	2.09957i	−0.461343	−	0.0844570i
$619$	3.05190	+	3.05190i	0.122666	+	0.122666i	0.765775	−	0.643109i	$-0.222356\pi$
$619$	3.05190	+	3.05190i	0.122666	+	0.122666i	−0.643109	+	0.765775i	$0.722356\pi$
$620$	6.00694	+	3.46811i	0.241245	+	0.139283i
$621$	−13.6689	−	14.2152i	−0.548514	−	0.570436i
$622$	−5.33115	+	19.8961i	−0.213760	+	0.797761i
$623$	2.53124			0.101412
$624$	−2.72517	+	5.61903i	−0.109094	+	0.224941i
$625$	3.53665			0.141466
$626$	−2.20463	+	8.22777i	−0.0881145	+	0.328848i
$627$	−2.37868	−	29.3982i	−0.0949955	−	1.17405i
$628$	18.5490	+	10.7093i	0.740188	+	0.427347i
$629$	−12.8262	−	12.8262i	−0.511414	−	0.511414i
$630$	−2.62062	+	3.64050i	−0.104408	+	0.145041i
$631$	31.3247	−	8.39342i	1.24702	−	0.334137i	0.425833	−	0.904802i	$-0.359981\pi$
$631$	31.3247	−	8.39342i	1.24702	−	0.334137i	0.821183	+	0.570665i	$0.193314\pi$
$632$	−10.7865	+	10.7865i	−0.429065	+	0.429065i
$633$	−9.65249	−	13.9786i	−0.383652	−	0.555599i
$634$	−4.04431	+	2.33499i	−0.160620	+	0.0927341i
$635$	−2.11585	−	0.566941i	−0.0839651	−	0.0224984i
$636$	−5.86648	+	12.3692i	−0.232621	+	0.490470i
$637$	−3.10669	−	1.82989i	−0.123091	−	0.0725028i
$638$		−	16.9419i		−	0.670738i
$639$	−27.7354	+	12.4949i	−1.09720	+	0.494291i
$640$	−0.747605	−	1.29489i	−0.0295517	−	0.0511850i
$641$	−2.85713	+	4.94869i	−0.112850	+	0.195462i	−0.916918	−	0.399075i	$-0.869331\pi$
$641$	−2.85713	+	4.94869i	−0.112850	+	0.195462i	0.804068	+	0.594537i	$0.202665\pi$
$642$	−0.419619	−	1.17675i	−0.0165611	−	0.0464425i
$643$	−5.82709	−	21.7470i	−0.229798	−	0.857618i	−0.980425	−	0.196892i	$-0.936915\pi$
$643$	−5.82709	−	21.7470i	−0.229798	−	0.857618i	0.750627	−	0.660726i	$-0.229752\pi$
$644$	0.982289	+	3.66595i	0.0387076	+	0.144459i
$645$	8.45957	+	23.7233i	0.333095	+	0.934106i
$646$	−20.3343	+	35.2200i	−0.800041	+	1.38571i
$647$	−9.23303	−	15.9921i	−0.362988	−	0.628713i	0.625463	−	0.780254i	$-0.284910\pi$
$647$	−9.23303	−	15.9921i	−0.362988	−	0.628713i	−0.988451	+	0.151540i	$0.951577\pi$
$648$	−4.01529	+	8.05465i	−0.157736	+	0.316417i
$649$			26.0781i			1.02365i
$650$	2.49575	+	9.64947i	0.0978914	+	0.378483i
$651$	−3.44318	+	7.25978i	−0.134949	+	0.284533i
$652$	−4.07472	−	1.09182i	−0.159578	−	0.0427589i
$653$	33.4295	−	19.3005i	1.30820	−	0.755288i	0.326402	−	0.945231i	$-0.394164\pi$
$653$	33.4295	−	19.3005i	1.30820	−	0.755288i	0.981795	+	0.189943i	$0.0608303\pi$
$654$	1.88071	+	2.72361i	0.0735416	+	0.106502i
$655$	−3.67532	+	3.67532i	−0.143606	+	0.143606i
$656$	10.9105	−	2.92345i	0.425983	−	0.114142i
$657$	4.03055	+	2.90140i	0.157247	+	0.113194i
$658$	−1.61934	−	1.61934i	−0.0631283	−	0.0631283i
$659$	−17.6399	−	10.1844i	−0.687152	−	0.396727i	0.115393	−	0.993320i	$-0.463187\pi$
$659$	−17.6399	−	10.1844i	−0.687152	−	0.396727i	−0.802544	+	0.596593i	$0.796521\pi$
$660$	−0.457840	−	5.65846i	−0.0178214	−	0.220255i
$661$	6.08781	−	22.7200i	0.236788	−	0.883706i	−0.740546	−	0.672005i	$-0.765433\pi$
$661$	6.08781	−	22.7200i	0.236788	−	0.883706i	0.977335	−	0.211701i	$-0.0679002\pi$
$662$	17.3767			0.675364
$663$	32.6090	−	2.35297i	1.26643	−	0.0913817i
$664$	2.58302			0.100241
$665$	−3.00624	+	11.2194i	−0.116577	+	0.435071i
$666$	−9.72032	−	3.68236i	−0.376655	−	0.142689i
$667$	−25.4030	−	14.6664i	−0.983606	−	0.567885i
$668$	8.83722	+	8.83722i	0.341922	+	0.341922i
$669$	−4.94778	−	0.905780i	−0.191292	−	0.0350195i
$670$	23.1251	−	6.19635i	0.893400	−	0.239386i
$671$	−10.1962	+	10.1962i	−0.393620	+	0.393620i
$672$	1.42527	−	0.984178i	0.0549810	−	0.0379655i
$673$	−21.4656	+	12.3932i	−0.827437	+	0.477721i	−0.852974	−	0.521953i	$-0.825204\pi$
$673$	−21.4656	+	12.3932i	−0.827437	+	0.477721i	0.0255373	+	0.999674i	$0.491870\pi$
$674$	−9.96567	−	2.67029i	−0.383863	−	0.102856i
$675$	3.44517	+	13.9447i	0.132605	+	0.536731i
$676$	11.3698	−	6.30303i	0.437299	−	0.242424i
$677$		−	2.09995i		−	0.0807078i	−0.999185	−	0.0403539i	$-0.987151\pi$
$677$		−	2.09995i		−	0.0807078i	0.999185	−	0.0403539i	$-0.0128485\pi$
$678$	2.86617	−	3.37082i	0.110074	−	0.129455i
$679$	−6.83185	−	11.8331i	−0.262182	−	0.454113i
$680$	−3.91386	+	6.77901i	−0.150090	+	0.259963i
$681$	−4.20824	+	1.50063i	−0.161260	+	0.0575042i
$682$	−2.63190	−	9.82238i	−0.100781	−	0.376118i
$683$	−0.477606	−	1.78245i	−0.0182751	−	0.0682036i	0.956186	−	0.292759i	$-0.0945735\pi$
$683$	−0.477606	−	1.78245i	−0.0182751	−	0.0682036i	−0.974461	+	0.224556i	$0.927907\pi$
$684$	−2.33417	+	23.1877i	−0.0892492	+	0.886603i
$685$	−3.83340	+	6.63964i	−0.146467	+	0.253687i
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$	28.0954	+	23.8892i	1.07191	+	0.911431i
$688$		−	9.72536i		−	0.370776i
$689$	24.8028	−	14.0335i	0.944913	−	0.534634i
$690$	−8.88071	−	4.21196i	−0.338083	−	0.160347i
$691$	32.5237	+	8.71469i	1.23726	+	0.331523i	0.817402	−	0.576068i	$-0.195414\pi$
$691$	32.5237	+	8.71469i	1.23726	+	0.331523i	0.419857	+	0.907590i	$0.362080\pi$
$692$	13.1619	−	7.59905i	0.500342	−	0.288872i
$693$	6.49063	−	1.05727i	0.246559	−	0.0401623i
$694$	6.66942	−	6.66942i	0.253168	−	0.253168i
$695$	21.8139	−	5.84502i	0.827449	−	0.221714i
$696$	−2.41060	+	13.1678i	−0.0913735	+	0.499124i
$697$	−41.8137	−	41.8137i	−1.58381	−	1.58381i
$698$	−5.24694	−	3.02932i	−0.198600	−	0.114662i
$699$	−45.6988	+	3.69760i	−1.72849	+	0.139856i
$700$	0.715466	−	2.67015i	0.0270421	−	0.100922i
$701$	27.4857			1.03812			0.519060	−	0.854738i	$-0.326282\pi$
$701$	27.4857			1.03812			0.519060	+	0.854738i	$0.326282\pi$
$702$	16.4835	−	8.90474i	0.622130	−	0.336088i
$703$	−26.9157			−1.01514
$704$	−0.567347	+	2.11737i	−0.0213827	+	0.0798013i
$705$	5.91151	−	0.478314i	0.222640	−	0.0180144i
$706$	−24.8154	−	14.3272i	−0.933939	−	0.539210i
$707$	−6.08353	−	6.08353i	−0.228795	−	0.228795i
$708$	3.71054	−	20.2687i	0.139451	−	0.761744i
$709$	−21.1952	+	5.67924i	−0.796003	+	0.213288i	−0.633828	−	0.773474i	$-0.718517\pi$
$709$	−21.1952	+	5.67924i	−0.796003	+	0.213288i	−0.162175	+	0.986762i	$0.551851\pi$
$710$	−10.7208	+	10.7208i	−0.402343	+	0.402343i
$711$	45.1680	−	7.35748i	1.69393	−	0.275927i
$712$	2.19211	−	1.26562i	0.0821530	−	0.0474310i
$713$	−17.0062	−	4.55680i	−0.636887	−	0.170653i
$714$	−8.19287	−	3.88573i	−0.306610	−	0.145420i
$715$	−5.99762	+	10.1825i	−0.224298	+	0.380802i
$716$			17.4941i			0.653785i
$717$	−25.2347	−	21.4568i	−0.942408	−	0.801319i
$718$	−13.4442	−	23.2860i	−0.501732	−	0.869025i
$719$	4.65122	−	8.05614i	0.173461	−	0.300443i	−0.766167	−	0.642642i	$-0.777838\pi$
$719$	4.65122	−	8.05614i	0.173461	−	0.300443i	0.939628	+	0.342199i	$0.111172\pi$
$720$	−0.449272	+	4.46307i	−0.0167434	+	0.166329i
$721$	−1.74225	−	6.50218i	−0.0648849	−	0.242154i
$722$	10.7012	+	39.9375i	0.398258	+	1.48632i
$723$	−27.4936	+	9.80403i	−1.02250	+	0.364616i
$724$	1.34516	−	2.32988i	0.0499925	−	0.0865895i
$725$	10.6825	+	18.5027i	0.396738	+	0.687171i
$726$	6.95053	−	8.17432i	0.257958	−	0.303377i
$727$		−	13.3586i		−	0.495442i	−0.968831	−	0.247721i	$-0.920318\pi$
$727$		−	13.3586i		−	0.495442i	0.968831	−	0.247721i	$-0.0796817\pi$
$728$	−3.60541	−	0.0313841i	−0.133626	−	0.00116317i
$729$	23.8935	−	12.5738i	0.884946	−	0.465695i
$730$	2.39084	+	0.640625i	0.0884891	+	0.0237106i
$731$	−44.0930	+	25.4571i	−1.63084	+	0.941565i
$732$	9.37558	−	6.47403i	0.346532	−	0.239287i
$733$	−29.4010	+	29.4010i	−1.08595	+	1.08595i	−0.0900086	+	0.995941i	$0.528689\pi$
$733$	−29.4010	+	29.4010i	−1.08595	+	1.08595i	−0.995941	+	0.0900086i	$0.971311\pi$
$734$	−11.6162	+	3.11256i	−0.428763	+	0.114887i
$735$	−2.54744	−	0.466355i	−0.0939639	−	0.0172018i
$736$	2.68366	+	2.68366i	0.0989211	+	0.0989211i
$737$	−30.3963	−	17.5493i	−1.11966	−	0.646437i
$738$	−31.6884	−	12.0046i	−1.16647	−	0.441895i
$739$	0.0453794	−	0.169358i	0.00166931	−	0.00622994i	−0.965086	−	0.261933i	$-0.915640\pi$
$739$	0.0453794	−	0.169358i	0.00166931	−	0.00622994i	0.966755	+	0.255703i	$0.0823068\pi$
$740$	−5.18062			−0.190444
$741$	31.7460	−	36.6837i	1.16622	−	1.34761i
$742$	−7.90385			−0.290159
$743$	4.57687	−	17.0811i	0.167909	−	0.626645i	−0.829742	−	0.558147i	$-0.811513\pi$
$743$	4.57687	−	17.0811i	0.167909	−	0.626645i	0.997651	−	0.0684983i	$-0.0218208\pi$
$744$	0.648007	+	8.00874i	0.0237571	+	0.293615i
$745$	18.8087	+	10.8592i	0.689097	+	0.397850i
$746$	−9.63377	−	9.63377i	−0.352717	−	0.352717i
$747$	−6.28908	−	4.52720i	−0.230105	−	0.165642i
$748$	11.0848	−	2.97017i	0.405302	−	0.108600i
$749$	0.510035	−	0.510035i	0.0186363	−	0.0186363i
$750$	11.4256	+	16.5464i	0.417205	+	0.604190i
$751$	43.7692	−	25.2702i	1.59716	−	0.922121i	0.605130	−	0.796126i	$-0.293121\pi$
$751$	43.7692	−	25.2702i	1.59716	−	0.922121i	0.992031	−	0.125995i	$-0.0402124\pi$
$752$	−2.21206	−	0.592719i	−0.0806654	−	0.0216142i
$753$	9.65431	−	20.3556i	0.351823	−	0.741801i
$754$	19.8754	−	19.5323i	0.723818	−	0.711325i
$755$		−	11.2300i		−	0.408701i
$756$	−5.19516	−	0.101785i	−0.188946	−	0.00370188i
$757$	4.39379	+	7.61027i	0.159695	+	0.276600i	0.934759	−	0.355283i	$-0.115616\pi$
$757$	4.39379	+	7.61027i	0.159695	+	0.276600i	−0.775064	+	0.631883i	$0.782282\pi$
$758$	1.16906	−	2.02487i	0.0424622	−	0.0735467i
$759$	4.83989	+	13.5726i	0.175677	+	0.492655i
$760$	3.00624	+	11.2194i	0.109048	+	0.406972i
$761$	−6.04253	−	22.5510i	−0.219041	−	0.817474i	−0.984705	−	0.174232i	$-0.944256\pi$
$761$	−6.04253	−	22.5510i	−0.219041	−	0.817474i	0.765663	−	0.643242i	$-0.222411\pi$
$762$	−0.852276	−	2.39005i	−0.0308747	−	0.0865825i
$763$	−0.955472	+	1.65493i	−0.0345904	+	0.0599124i
$764$	3.81738	+	6.61189i	0.138108	+	0.239210i
$765$	21.4108	−	9.64563i	0.774108	−	0.348738i
$766$		−	27.4981i		−	0.993545i
$767$	−30.5934	+	30.0654i	−1.10466	+	1.08560i
$768$	0.742231	−	1.56496i	0.0267830	−	0.0564706i
$769$	−4.62655	−	1.23968i	−0.166838	−	0.0447040i	0.174433	−	0.984669i	$-0.444191\pi$
$769$	−4.62655	−	1.23968i	−0.166838	−	0.0447040i	−0.341271	+	0.939965i	$0.610857\pi$
$770$	2.83848	−	1.63879i	0.102292	−	0.0590581i
$771$	−28.9301	−	41.8962i	−1.04189	−	1.50885i
$772$	−0.409015	+	0.409015i	−0.0147208	+	0.0147208i
$773$	0.359233	−	0.0962561i	0.0129207	−	0.00346209i	−0.252353	−	0.967635i	$-0.581204\pi$
$773$	0.359233	−	0.0962561i	0.0129207	−	0.00346209i	0.265274	+	0.964173i	$0.414538\pi$
$774$	−17.0454	+	23.6791i	−0.612684	+	0.851126i
$775$	9.06772	+	9.06772i	0.325722	+	0.325722i
$776$	−11.8331	−	6.83185i	−0.424784	−	0.245249i
$777$	−0.483993	−	5.98168i	−0.0173631	−	0.214592i
$778$	−2.46910	+	9.21480i	−0.0885214	+	0.330366i
$779$	−87.7456			−3.14381
$780$	6.11035	−	7.06074i	0.218786	−	0.252815i
$781$	22.2275			0.795362
$782$	5.14248	−	19.1920i	0.183895	−	0.686304i
$783$	28.9481	−	27.8356i	1.03452	−	0.994764i
$784$	0.866025	+	0.500000i	0.0309295	+	0.0178571i
$785$	−22.6453	−	22.6453i	−0.808246	−	0.808246i
$786$	−5.92257	−	1.08423i	−0.211251	−	0.0386732i
$787$	−48.7819	+	13.0711i	−1.73889	+	0.465933i	−0.982199	−	0.187843i	$-0.939850\pi$
$787$	−48.7819	+	13.0711i	−1.73889	+	0.465933i	−0.756688	+	0.653777i	$0.773184\pi$
$788$	7.17892	−	7.17892i	0.255738	−	0.255738i
$789$	23.2359	−	16.0449i	0.827221	−	0.571213i
$790$	19.7528	−	11.4043i	0.702774	−	0.405747i
$791$	2.46751	+	0.661169i	0.0877347	+	0.0235084i
$792$	5.09242	−	4.16094i	0.180951	−	0.147852i
$793$	−23.7168	−	0.206448i	−0.842209	−	0.00733118i
$794$		−	16.5012i		−	0.585604i
$795$	13.2595	−	15.5941i	0.470265	−	0.553065i
$796$	−8.53813	−	14.7885i	−0.302626	−	0.524164i
$797$	2.60079	−	4.50470i	0.0921247	−	0.159565i	−0.816280	−	0.577656i	$-0.803967\pi$
$797$	2.60079	−	4.50470i	0.0921247	−	0.159565i	0.908405	+	0.418091i	$0.137301\pi$
$798$	−12.6734	+	4.51925i	−0.448634	+	0.159980i
$799$	3.10300	+	11.5806i	0.109776	+	0.409691i
$800$	−0.715466	−	2.67015i	−0.0252955	−	0.0944042i
$801$	−7.55552	−	0.760571i	−0.266961	−	0.0268735i
$802$	−0.107345	+	0.185926i	−0.00379047	+	0.00656529i
$803$	−1.81438	−	3.14260i	−0.0640280	−	0.110900i
$804$	21.1279	+	17.9648i	0.745124	+	0.633571i
$805$		−	5.67473i		−	0.200008i
$806$	8.48877	−	14.4118i	0.299004	−	0.507634i
$807$	22.5053	+	10.6738i	0.792223	+	0.375737i
$808$	−8.31025	−	2.22672i	−0.292354	−	0.0783359i
$809$	−22.1006	+	12.7598i	−0.777015	+	0.448610i	−0.835371	−	0.549686i	$-0.814747\pi$
$809$	−22.1006	+	12.7598i	−0.777015	+	0.448610i	0.0583563	+	0.998296i	$0.481414\pi$
$810$	8.91620	−	10.0792i	0.313283	−	0.354145i
$811$	0.105980	−	0.105980i	0.00372145	−	0.00372145i	−0.705244	−	0.708965i	$-0.749162\pi$
$811$	0.105980	−	0.105980i	0.00372145	−	0.00372145i	0.708965	+	0.705244i	$0.249162\pi$
$812$	−7.46542	+	2.00035i	−0.261985	+	0.0701987i
$813$	−7.37752	+	40.2994i	−0.258741	+	1.41336i
$814$	5.37053	+	5.37053i	0.188237	+	0.188237i
$815$	5.46244	+	3.15374i	0.191341	+	0.110471i
$816$	−9.03810	+	0.731294i	−0.316397	+	0.0256004i
$817$	−19.5536	+	72.9751i	−0.684094	+	2.55308i
$818$	−20.3404			−0.711184
$819$	8.72337	+	6.39554i	0.304819	+	0.223478i
$820$	−16.8889			−0.589787
$821$	−1.67018	+	6.23320i	−0.0582897	+	0.217540i	−0.988927	−	0.148403i	$-0.952587\pi$
$821$	−1.67018	+	6.23320i	−0.0582897	+	0.217540i	0.930637	+	0.365943i	$0.119253\pi$
$822$	−8.85228	+	0.716259i	−0.308759	+	0.0249824i
$823$	−7.94559	−	4.58739i	−0.276966	−	0.159906i	0.355083	−	0.934835i	$-0.384453\pi$
$823$	−7.94559	−	4.58739i	−0.276966	−	0.159906i	−0.632049	+	0.774928i	$0.717786\pi$
$824$	−4.75993	−	4.75993i	−0.165820	−	0.165820i
$825$	1.88999	−	10.3240i	0.0658010	−	0.359435i
$826$	11.4912	−	3.07907i	0.399831	−	0.107135i
$827$	3.21828	−	3.21828i	0.111910	−	0.111910i	−0.648934	−	0.760845i	$-0.724785\pi$
$827$	3.21828	−	3.21828i	0.111910	−	0.111910i	0.760845	+	0.648934i	$0.224785\pi$
$828$	−1.83052	−	11.2377i	−0.0636151	−	0.390537i
$829$	−25.7343	+	14.8577i	−0.893788	+	0.516029i	−0.875180	−	0.483798i	$-0.839257\pi$
$829$	−25.7343	+	14.8577i	−0.893788	+	0.516029i	−0.0186086	+	0.999827i	$0.505924\pi$
$830$	−3.73056	−	0.999602i	−0.129490	−	0.0346967i
$831$	−11.2923	−	5.35573i	−0.391726	−	0.185788i
$832$	−3.13807	+	1.77553i	−0.108793	+	0.0615554i
$833$		−	5.23520i		−	0.181389i
$834$	19.9300	+	16.9462i	0.690118	+	0.586800i
$835$	−9.34336	−	16.1832i	−0.323340	−	0.560042i
$836$	8.51428	−	14.7472i	0.294472	−	0.510041i
$837$	12.4590	−	20.6352i	0.430645	−	0.713258i
$838$	−4.74868	−	17.7223i	−0.164040	−	0.612207i
$839$	−5.02107	−	18.7389i	−0.173347	−	0.646938i	−0.996827	−	0.0795942i	$-0.974638\pi$
$839$	−5.02107	−	18.7389i	−0.173347	−	0.646938i	0.823481	−	0.567344i	$-0.192029\pi$
$840$	−2.43933	+	0.869847i	−0.0841648	+	0.0300126i
$841$	15.3670	−	26.6164i	0.529896	−	0.917807i
$842$	8.00405	+	13.8634i	0.275838	+	0.477765i
$843$	11.3517	−	13.3504i	0.390972	−	0.459811i
$844$		−	9.80767i		−	0.337594i
$845$	−18.8601	+	4.70325i	−0.648808	+	0.161797i
$846$	4.34701	+	5.32015i	0.149453	+	0.182911i
$847$	5.98379	+	1.60335i	0.205605	+	0.0550918i
$848$	−6.84493	+	3.95192i	−0.235056	+	0.135710i
$849$	−26.3822	+	18.2174i	−0.905434	+	0.625220i
$850$	−10.2332	+	10.2332i	−0.350995	+	0.350995i
$851$	12.7018	−	3.40345i	0.435413	−	0.116669i
$852$	−17.2759	−	3.16266i	−0.591863	−	0.108351i
$853$	−2.39984	−	2.39984i	−0.0821689	−	0.0821689i	0.664828	−	0.746997i	$-0.268505\pi$
$853$	−2.39984	−	2.39984i	−0.0821689	−	0.0821689i	−0.746997	+	0.664828i	$0.768505\pi$
$854$	5.69681	+	3.28906i	0.194941	+	0.112549i
$855$	12.3445	−	32.5858i	0.422174	−	1.11441i
$856$	0.186686	−	0.696721i	0.00638079	−	0.0238134i
$857$	−12.8743			−0.439777			−0.219889	−	0.975525i	$-0.570569\pi$
$857$	−12.8743			−0.439777			−0.219889	+	0.975525i	$0.570569\pi$
$858$	−13.6539	+	0.985224i	−0.466137	+	0.0336350i
$859$	39.6930			1.35431			0.677154	−	0.735841i	$-0.263213\pi$
$859$	39.6930			1.35431			0.677154	+	0.735841i	$0.263213\pi$
$860$	−3.76360	+	14.0460i	−0.128338	+	0.478963i
$861$	−1.57783	−	19.5004i	−0.0537722	−	0.664572i
$862$	−5.55072	−	3.20471i	−0.189058	−	0.109153i
$863$	22.1953	+	22.1953i	0.755537	+	0.755537i	0.975507	−	0.219969i	$-0.0705957\pi$
$863$	22.1953	+	22.1953i	0.755537	+	0.755537i	−0.219969	+	0.975507i	$0.570596\pi$
$864$	−4.55003	+	2.50943i	−0.154795	+	0.0853725i
$865$	−21.9500	+	5.88149i	−0.746323	+	0.199977i
$866$	12.8210	−	12.8210i	0.435675	−	0.435675i
$867$	10.2427	+	14.8332i	0.347859	+	0.503763i
$868$	−4.01746	+	2.31948i	−0.136361	+	0.0787283i
$869$	−32.2993	−	8.65456i	−1.09568	−	0.293586i
$870$	8.57733	−	18.0849i	0.290799	−	0.613135i
$871$	−14.4559	−	55.8918i	−0.489820	−	1.89382i
$872$			1.91094i			0.0647128i
$873$	16.8369	+	37.3736i	0.569844	+	1.26490i
$874$	−14.7414	−	25.5328i	−0.498635	−	0.863661i
$875$	−5.80466	+	10.0540i	−0.196233	+	0.339886i
$876$	0.963044	+	2.70068i	0.0325382	+	0.0912476i
$877$	1.66095	+	6.19873i	0.0560862	+	0.209316i	0.988282	−	0.152637i	$-0.0487766\pi$
$877$	1.66095	+	6.19873i	0.0560862	+	0.209316i	−0.932196	+	0.361954i	$0.882110\pi$
$878$	−2.79359	−	10.4258i	−0.0942790	−	0.351854i
$879$	0.287447	+	0.806094i	0.00969535	+	0.0271889i
$880$	1.63879	−	2.83848i	0.0552438	−	0.0956850i
$881$	−13.5259	−	23.4275i	−0.455699	−	0.789294i	0.543029	−	0.839714i	$-0.317277\pi$
$881$	−13.5259	−	23.4275i	−0.455699	−	0.789294i	−0.998728	+	0.0504200i	$0.983944\pi$
$882$	−1.23224	−	2.73525i	−0.0414916	−	0.0921006i
$883$		−	4.71053i		−	0.158522i	−0.996854	−	0.0792610i	$-0.974744\pi$
$883$		−	4.71053i		−	0.158522i	0.996854	−	0.0792610i	$-0.0252561\pi$
$884$	16.2641	+	9.57982i	0.547022	+	0.322204i
$885$	−13.2028	+	27.8374i	−0.443806	+	0.935743i
$886$	−4.35320	−	1.16644i	−0.146249	−	0.0391872i
$887$	42.6265	−	24.6104i	1.43126	−	0.826337i	0.434041	−	0.900893i	$-0.357087\pi$
$887$	42.6265	−	24.6104i	1.43126	−	0.826337i	0.997217	+	0.0745559i	$0.0237539\pi$
$888$	−3.40999	−	4.93829i	−0.114432	−	0.165718i
$889$	1.03592	−	1.03592i	0.0347435	−	0.0347435i
$890$	−3.65577	+	0.979560i	−0.122542	+	0.0328349i
$891$	−19.6917	+	1.20559i	−0.659696	+	0.0403886i
$892$	−2.05349	−	2.05349i	−0.0687560	−	0.0687560i
$893$	15.4067	+	8.89503i	0.515564	+	0.297661i
$894$	2.02901	+	25.0766i	0.0678603	+	0.838688i
$895$	6.77002	−	25.2661i	0.226297	−	0.844551i
$896$	1.00000			0.0334077
$897$	−10.3427	+	21.3257i	−0.345334	+	0.712046i
$898$	−34.6708			−1.15698
$899$	9.27956	−	34.6318i	0.309491	−	1.15504i
$900$	−2.93792	+	7.75520i	−0.0979306	+	0.258507i
$901$	35.8346	+	20.6891i	1.19382	+	0.689254i
$902$	17.5080	+	17.5080i	0.582954	+	0.582954i
$903$	−16.5694	−	3.03333i	−0.551397	−	0.100943i
$904$	2.46751	−	0.661169i	0.0820683	−	0.0219901i
$905$	−2.84440	+	2.84440i	−0.0945511	+	0.0945511i
$906$	10.7047	−	7.39181i	0.355640	−	0.245576i
$907$	−15.7623	+	9.10039i	−0.523380	+	0.302173i	−0.738316	−	0.674455i	$-0.764379\pi$
$907$	−15.7623	+	9.10039i	−0.523380	+	0.302173i	0.214937	+	0.976628i	$0.431046\pi$
$908$	−2.49159	−	0.667619i	−0.0826863	−	0.0221557i
$909$	16.3309	+	19.9867i	0.541660	+	0.662919i
$910$	5.19502	+	1.44058i	0.172213	+	0.0477548i
$911$			1.11524i			0.0369497i	0.999829	+	0.0184748i	$0.00588106\pi$
$911$			1.11524i			0.0369497i	−0.999829	+	0.0184748i	$0.994119\pi$
$912$	−8.71587	+	10.2505i	−0.288611	+	0.339428i
$913$	2.83107	+	4.90356i	0.0936948	+	0.162284i
$914$	0.0217543	−	0.0376796i	0.000719569	−	0.00124633i
$915$	−16.0462	+	5.72195i	−0.530470	+	0.189162i
$916$	5.51078	+	20.5665i	0.182081	+	0.679537i
$917$	−0.899712	−	3.35777i	−0.0297111	−	0.110883i
$918$	23.2874	+	14.0603i	0.768600	+	0.464060i
$919$	3.76940	−	6.52880i	0.124341	−	0.215365i	−0.797134	−	0.603802i	$-0.793652\pi$
$919$	3.76940	−	6.52880i	0.124341	−	0.215365i	0.921475	+	0.388437i	$0.126985\pi$
$920$	−2.83736	−	4.91446i	−0.0935451	−	0.162025i
$921$	16.3959	+	13.9413i	0.540265	+	0.459381i
$922$			25.0430i			0.824748i
$923$	25.6260	+	26.0761i	0.843491	+	0.858305i
$924$	3.43048	+	1.62702i	0.112855	+	0.0535249i
$925$	−9.25159	−	2.47896i	−0.304190	−	0.0815076i
$926$	−2.65876	+	1.53504i	−0.0873723	+	0.0504444i
$927$	3.24674	+	19.9320i	0.106637	+	0.654651i
$928$	−5.46507	+	5.46507i	−0.179400	+	0.179400i
$929$	−38.0943	+	10.2073i	−1.24983	+	0.334892i	−0.822272	−	0.569095i	$-0.807294\pi$
$929$	−38.0943	+	10.2073i	−1.24983	+	0.334892i	−0.427561	+	0.903986i	$0.640627\pi$
$930$	2.16340	−	11.8175i	0.0709407	−	0.387511i
$931$	−5.49301	−	5.49301i	−0.180026	−	0.180026i
$932$	−22.9241	−	13.2352i	−0.750902	−	0.433534i
$933$	35.5605	−	2.87729i	1.16420	−	0.0941982i
$934$	3.61239	−	13.4816i	0.118201	−	0.441133i
$935$	−17.1588			−0.561154
$936$	10.7524	+	1.17701i	0.351454	+	0.0384719i
$937$	13.3455			0.435977			0.217989	−	0.975951i	$-0.430050\pi$
$937$	13.3455			0.435977			0.217989	+	0.975951i	$0.430050\pi$
$938$	−4.14413	+	15.4661i	−0.135311	+	0.504987i
$939$	14.7056	−	1.18986i	0.479898	−	0.0388297i
$940$	2.96541	+	1.71208i	0.0967211	+	0.0558419i
$941$	−0.510723	−	0.510723i	−0.0166491	−	0.0166491i	0.698733	−	0.715382i	$-0.253747\pi$
$941$	−0.510723	−	0.510723i	−0.0166491	−	0.0166491i	−0.715382	+	0.698733i	$0.753747\pi$
$942$	6.68044	−	36.4916i	0.217661	−	1.18896i
$943$	41.4082	−	11.0953i	1.34844	−	0.361313i
$944$	8.41217	−	8.41217i	0.273793	−	0.273793i
$945$	7.46378	+	2.15747i	0.242797	+	0.0701825i
$946$	18.4624	−	10.6593i	0.600265	−	0.346563i
$947$	−19.9919	−	5.35680i	−0.649648	−	0.174073i	−0.0810782	−	0.996708i	$-0.525836\pi$
$947$	−19.9919	−	5.35680i	−0.649648	−	0.174073i	−0.568570	+	0.822635i	$0.692503\pi$
$948$	23.8726	+	11.3223i	0.775345	+	0.367732i
$949$	1.59493	−	5.75162i	0.0517736	−	0.186706i
$950$			21.4742i			0.696717i
$951$	6.16217	+	5.23962i	0.199822	+	0.169906i
$952$	−2.61760	−	4.53382i	−0.0848369	−	0.146942i
$953$	−23.3641	+	40.4678i	−0.756837	+	1.31088i	0.187619	+	0.982242i	$0.439923\pi$
$953$	−23.3641	+	40.4678i	−0.756837	+	1.31088i	−0.944456	+	0.328638i	$0.893410\pi$
$954$	23.5923	+	2.37490i	0.763829	+	0.0768903i
$955$	−2.95456	−	11.0266i	−0.0956074	−	0.356812i
$956$	−4.94966	−	18.4724i	−0.160084	−	0.597440i
$957$	−27.6396	+	9.85607i	−0.893460	+	0.318601i
$958$	3.84600	−	6.66148i	0.124259	−	0.215223i
$959$	−2.56378	−	4.44060i	−0.0827889	−	0.143395i
$960$	−1.67760	+	1.97297i	−0.0541442	+	0.0636775i
$961$			9.48005i			0.305808i
$962$	−0.108740	+	12.4921i	−0.00350592	+	0.402761i
$963$	−1.67566	+	1.36916i	−0.0539975	+	0.0441205i
$964$	−16.2783	−	4.36174i	−0.524287	−	0.140482i
$965$	0.749010	−	0.432441i	0.0241115	−	0.0139208i
$966$	5.40929	−	3.73522i	0.174041	−	0.120179i
$967$	8.29925	−	8.29925i	0.266886	−	0.266886i	−0.560958	−	0.827844i	$-0.689567\pi$
$967$	8.29925	−	8.29925i	0.266886	−	0.266886i	0.827844	+	0.560958i	$0.189567\pi$
$968$	5.98379	−	1.60335i	0.192326	−	0.0515337i
$969$	69.2885	+	12.6845i	2.22587	+	0.407485i
$970$	14.4463	+	14.4463i	0.463841	+	0.463841i
$971$	52.5330	+	30.3300i	1.68587	+	0.973335i	0.957627	+	0.288010i	$0.0929937\pi$
$971$	52.5330	+	30.3300i	1.68587	+	0.973335i	0.728238	+	0.685325i	$0.240340\pi$
$972$	15.4765	+	1.86483i	0.496409	+	0.0598144i
$973$	−3.90916	+	14.5892i	−0.125322	+	0.467708i
$974$	−14.6153			−0.468304
$975$	14.2905	−	9.68527i	0.457662	−	0.310177i
$976$	6.57811			0.210560
$977$	−6.61197	+	24.6762i	−0.211536	+	0.789461i	0.775822	+	0.630952i	$0.217335\pi$
$977$	−6.61197	+	24.6762i	−0.211536	+	0.789461i	−0.987357	+	0.158509i	$0.949331\pi$
$978$	0.589268	+	7.28278i	0.0188427	+	0.232878i
$979$	4.80525	+	2.77431i	0.153576	+	0.0886673i
$980$	−1.05727	−	1.05727i	−0.0337733	−	0.0337733i
$981$	3.34927	−	4.65272i	0.106934	−	0.148550i
$982$	−23.8808	+	6.39884i	−0.762066	+	0.204195i
$983$	−25.4534	+	25.4534i	−0.811838	+	0.811838i	−0.984909	−	0.173071i	$-0.944631\pi$
$983$	−25.4534	+	25.4534i	−0.811838	+	0.811838i	0.173071	+	0.984909i	$0.444631\pi$
$984$	−11.1166	−	16.0989i	−0.354386	−	0.513215i
$985$	−13.1464	+	7.59008i	−0.418879	+	0.241840i
$986$	39.0830	+	10.4723i	1.24466	+	0.333505i
$987$	−1.69978	+	3.58389i	−0.0541044	+	0.114077i
$988$	27.1167	−	7.01348i	0.862696	−	0.223129i
$989$		−	36.9104i		−	1.17368i
$990$	−8.96502	+	4.03877i	−0.284927	+	0.128361i
$991$	28.7710	+	49.8328i	0.913941	+	1.58299i	0.808444	+	0.588573i	$0.200310\pi$
$991$	28.7710	+	49.8328i	0.913941	+	1.58299i	0.105497	+	0.994420i	$0.466357\pi$
$992$	−2.31948	+	4.01746i	−0.0736436	+	0.127554i
$993$	−10.1090	−	28.3488i	−0.320799	−	0.899623i
$994$	−2.62443	−	9.79449i	−0.0832418	−	0.310662i
$995$	6.60832	+	24.6626i	0.209498	+	0.781857i
$996$	−1.50269	−	4.21402i	−0.0476145	−	0.133526i
$997$	−17.4383	+	30.2040i	−0.552275	+	0.956569i	0.445835	+	0.895115i	$0.352907\pi$
$997$	−17.4383	+	30.2040i	−0.552275	+	0.956569i	−0.998110	+	0.0614535i	$0.980426\pi$
$998$	−19.5102	−	33.7927i	−0.617585	−	1.06969i
$999$	−0.352666	+	18.0002i	−0.0111578	+	0.569503i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bu.a.197.8	✓	56
3.2	odd	2		546.2.bu.b.197.5	yes	56
13.7	odd	12		546.2.bu.b.449.5	yes	56
39.20	even	12	inner	546.2.bu.a.449.8	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bu.a.197.8	✓	56	1.1	even	1	trivial
546.2.bu.a.449.8	yes	56	39.20	even	12	inner
546.2.bu.b.197.5	yes	56	3.2	odd	2
546.2.bu.b.449.5	yes	56	13.7	odd	12

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.bu (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-1.72641 + 0.139688i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.05727 + 1.05727i) q^{5} +(-0.311899 + 1.70374i) q^{6} +(-0.965926 + 0.258819i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.96097 - 0.482317i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(-1.72641 + 0.139688i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.05727 + 1.05727i) q^{5} +(-0.311899 + 1.70374i) q^{6} +(-0.965926 + 0.258819i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.96097 - 0.482317i) q^{9} +(1.29489 - 0.747605i) q^{10} +(-2.11737 - 0.567347i) q^{11} +(1.56496 + 0.742231i) q^{12} +(-1.77553 - 3.13807i) q^{13} +1.00000i q^{14} +(-1.97297 - 1.67760i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.61760 - 4.53382i) q^{17} +(0.300474 - 2.98491i) q^{18} +(-2.01058 - 7.50359i) q^{19} +(-0.386989 - 1.44426i) q^{20} +(1.63143 - 0.581756i) q^{21} +(-1.09603 + 1.89838i) q^{22} +(1.89764 + 3.28680i) q^{23} +(1.12198 - 1.31953i) q^{24} -2.76435i q^{25} +(-3.49069 + 0.902835i) q^{26} +(-5.04448 + 1.24629i) q^{27} +(0.965926 + 0.258819i) q^{28} +(-6.69332 + 3.86439i) q^{29} +(-2.13108 + 1.47155i) q^{30} +(-3.28024 + 3.28024i) q^{31} +(0.965926 - 0.258819i) q^{32} +(3.73469 + 0.683702i) q^{33} +(-3.70185 - 3.70185i) q^{34} +(-1.29489 - 0.747605i) q^{35} +(-2.80544 - 1.06279i) q^{36} +(0.896760 - 3.34675i) q^{37} -7.76829 q^{38} +(3.50364 + 5.16958i) q^{39} -1.49521 q^{40} +(2.92345 - 10.9105i) q^{41} +(-0.139688 - 1.72641i) q^{42} +(-8.42241 - 4.86268i) q^{43} +(1.55002 + 1.55002i) q^{44} +(3.64050 + 2.62062i) q^{45} +(3.66595 - 0.982289i) q^{46} +(-1.61934 + 1.61934i) q^{47} +(-0.984178 - 1.42527i) q^{48} +(0.866025 - 0.500000i) q^{49} +(-2.67015 - 0.715466i) q^{50} +(-3.88573 + 8.19287i) q^{51} +(-0.0313841 + 3.60541i) q^{52} +7.90385i q^{53} +(-0.101785 + 5.19516i) q^{54} +(-1.63879 - 2.83848i) q^{55} +(0.500000 - 0.866025i) q^{56} +(4.51925 + 12.6734i) q^{57} +(2.00035 + 7.46542i) q^{58} +(-3.07907 - 11.4912i) q^{59} +(0.869847 + 2.43933i) q^{60} +(3.28906 - 5.69681i) q^{61} +(2.31948 + 4.01746i) q^{62} +(-2.73525 + 1.23224i) q^{63} -1.00000i q^{64} +(1.44058 - 5.19502i) q^{65} +(1.62702 - 3.43048i) q^{66} +(15.4661 + 4.14413i) q^{67} +(-4.53382 + 2.61760i) q^{68} +(-3.73522 - 5.40929i) q^{69} +(-1.05727 + 1.05727i) q^{70} +(-9.79449 + 2.62443i) q^{71} +(-1.75268 + 2.43477i) q^{72} +(1.17055 + 1.17055i) q^{73} +(-3.00062 - 1.73241i) q^{74} +(0.386146 + 4.77239i) q^{75} +(-2.01058 + 7.50359i) q^{76} +2.19206 q^{77} +(5.90024 - 2.04627i) q^{78} +15.2544 q^{79} +(-0.386989 + 1.44426i) q^{80} +(8.53474 - 2.85626i) q^{81} +(-9.78207 - 5.64768i) q^{82} +(-1.82647 - 1.82647i) q^{83} +(-1.70374 - 0.311899i) q^{84} +(7.56100 - 2.02596i) q^{85} +(-6.87687 + 6.87687i) q^{86} +(11.0156 - 7.60649i) q^{87} +(1.89838 - 1.09603i) q^{88} +(-2.44499 - 0.655132i) q^{89} +(3.47355 - 2.83819i) q^{90} +(2.52722 + 2.57161i) q^{91} -3.79527i q^{92} +(5.20483 - 6.12125i) q^{93} +(1.14504 + 1.98327i) q^{94} +(5.80761 - 10.0591i) q^{95} +(-1.63143 + 0.581756i) q^{96} +(3.53642 + 13.1981i) q^{97} +(-0.258819 - 0.965926i) q^{98} +(-6.54311 - 0.658658i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{6} + 24 q^{9}+O(q^{10}) \) 56 * q - 8 * q^6 + 24 * q^9	\( 56 q - 8 q^{6} + 24 q^{9} + 24 q^{10} - 8 q^{11} + 24 q^{13} - 4 q^{15} + 28 q^{16} + 4 q^{17} + 8 q^{19} + 4 q^{21} + 8 q^{23} + 8 q^{24} + 4 q^{26} - 24 q^{27} - 16 q^{30} - 8 q^{31} - 32 q^{33} - 24 q^{34} - 24 q^{35} - 12 q^{36} - 8 q^{37} - 60 q^{39} + 28 q^{41} - 8 q^{44} - 40 q^{45} - 20 q^{46} - 64 q^{50} + 8 q^{54} + 8 q^{55} + 28 q^{56} + 40 q^{57} + 4 q^{58} + 8 q^{59} + 4 q^{60} + 8 q^{61} + 32 q^{62} + 24 q^{65} + 32 q^{66} - 56 q^{69} + 112 q^{71} + 16 q^{72} + 8 q^{73} - 48 q^{74} - 40 q^{75} + 8 q^{76} - 8 q^{78} + 16 q^{79} + 12 q^{81} + 4 q^{83} - 4 q^{84} + 32 q^{85} + 16 q^{86} + 144 q^{87} - 88 q^{89} + 8 q^{90} - 8 q^{91} - 76 q^{93} - 8 q^{94} + 48 q^{95} - 4 q^{96} - 64 q^{97} - 40 q^{99}+O(q^{100}) \) 56 * q - 8 * q^6 + 24 * q^9 + 24 * q^10 - 8 * q^11 + 24 * q^13 - 4 * q^15 + 28 * q^16 + 4 * q^17 + 8 * q^19 + 4 * q^21 + 8 * q^23 + 8 * q^24 + 4 * q^26 - 24 * q^27 - 16 * q^30 - 8 * q^31 - 32 * q^33 - 24 * q^34 - 24 * q^35 - 12 * q^36 - 8 * q^37 - 60 * q^39 + 28 * q^41 - 8 * q^44 - 40 * q^45 - 20 * q^46 - 64 * q^50 + 8 * q^54 + 8 * q^55 + 28 * q^56 + 40 * q^57 + 4 * q^58 + 8 * q^59 + 4 * q^60 + 8 * q^61 + 32 * q^62 + 24 * q^65 + 32 * q^66 - 56 * q^69 + 112 * q^71 + 16 * q^72 + 8 * q^73 - 48 * q^74 - 40 * q^75 + 8 * q^76 - 8 * q^78 + 16 * q^79 + 12 * q^81 + 4 * q^83 - 4 * q^84 + 32 * q^85 + 16 * q^86 + 144 * q^87 - 88 * q^89 + 8 * q^90 - 8 * q^91 - 76 * q^93 - 8 * q^94 + 48 * q^95 - 4 * q^96 - 64 * q^97 - 40 * q^99

Introduction

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