LMFDB - Embedded newform 546.2.cg.a.271.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(145,546)]

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([0, 10, 1]))

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

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

chi := DirichletCharacter("546.145");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.cg (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:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			271.1
Character	$\chi$	$=$	546.271
Dual form			546.2.cg.a.409.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-0.866025 - 0.500000i) q^{3} +1.00000i q^{4} +(-0.765779 - 2.85793i) q^{5} +(0.258819 + 0.965926i) q^{6} +(-1.78167 - 1.95592i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.866025 - 0.500000i) q^{3} +1.00000i q^{4} +(-0.765779 - 2.85793i) q^{5} +(0.258819 + 0.965926i) q^{6} +(-1.78167 - 1.95592i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.47937 + 2.56235i) q^{10} +(-1.13023 - 4.21807i) q^{11} +(0.500000 - 0.866025i) q^{12} +(1.11321 + 3.42940i) q^{13} +(-0.123214 + 2.64288i) q^{14} +(-0.765779 + 2.85793i) q^{15} -1.00000 q^{16} -0.928803 q^{17} +(0.258819 - 0.965926i) q^{18} +(0.161344 + 0.0432320i) q^{19} +(2.85793 - 0.765779i) q^{20} +(0.565013 + 2.58472i) q^{21} +(-2.18344 + 3.78182i) q^{22} +1.61325i q^{23} +(-0.965926 + 0.258819i) q^{24} +(-3.25120 + 1.87708i) q^{25} +(1.63780 - 3.21211i) q^{26} -1.00000i q^{27} +(1.95592 - 1.78167i) q^{28} +(1.94582 + 3.37026i) q^{29} +(2.56235 - 1.47937i) q^{30} +(-8.33172 - 2.23248i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-1.13023 + 4.21807i) q^{33} +(0.656763 + 0.656763i) q^{34} +(-4.22552 + 6.58970i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(-4.92659 + 4.92659i) q^{37} +(-0.0835178 - 0.144657i) q^{38} +(0.750635 - 3.52655i) q^{39} +(-2.56235 - 1.47937i) q^{40} +(-9.71078 - 2.60200i) q^{41} +(1.42815 - 2.22720i) q^{42} +(4.51157 + 2.60476i) q^{43} +(4.21807 - 1.13023i) q^{44} +(2.09215 - 2.09215i) q^{45} +(1.14074 - 1.14074i) q^{46} +(8.74657 - 2.34364i) q^{47} +(0.866025 + 0.500000i) q^{48} +(-0.651277 + 6.96964i) q^{49} +(3.62625 + 0.971650i) q^{50} +(0.804367 + 0.464402i) q^{51} +(-3.42940 + 1.11321i) q^{52} +(1.13857 + 1.97205i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(-11.1894 + 6.46023i) q^{55} +(-2.64288 - 0.123214i) q^{56} +(-0.118112 - 0.118112i) q^{57} +(1.00723 - 3.75904i) q^{58} +(-2.46741 - 2.46741i) q^{59} +(-2.85793 - 0.765779i) q^{60} +(-8.49717 + 4.90584i) q^{61} +(4.31282 + 7.47002i) q^{62} +(0.803043 - 2.52094i) q^{63} -1.00000i q^{64} +(8.94850 - 5.80762i) q^{65} +(3.78182 - 2.18344i) q^{66} +(-5.27908 + 1.41452i) q^{67} -0.928803i q^{68} +(0.806627 - 1.39712i) q^{69} +(7.64751 - 1.67173i) q^{70} +(7.17756 - 1.92322i) q^{71} +(0.965926 + 0.258819i) q^{72} +(1.66618 - 6.21826i) q^{73} +6.96725 q^{74} +3.75417 q^{75} +(-0.0432320 + 0.161344i) q^{76} +(-6.23653 + 9.72588i) q^{77} +(-3.02443 + 1.96287i) q^{78} +(4.30390 - 7.45458i) q^{79} +(0.765779 + 2.85793i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.02667 + 8.70645i) q^{82} +(-1.81174 + 1.81174i) q^{83} +(-2.58472 + 0.565013i) q^{84} +(0.711258 + 2.65445i) q^{85} +(-1.34832 - 5.03200i) q^{86} -3.89165i q^{87} +(-3.78182 - 2.18344i) q^{88} +(-8.59688 - 8.59688i) q^{89} -2.95874 q^{90} +(4.72427 - 8.28741i) q^{91} -1.61325 q^{92} +(6.09924 + 6.09924i) q^{93} +(-7.84196 - 4.52756i) q^{94} -0.494215i q^{95} +(-0.258819 - 0.965926i) q^{96} +(2.87536 + 10.7310i) q^{97} +(5.38880 - 4.46775i) q^{98} +(3.08784 - 3.08784i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{7} + 16 q^{9}+O(q^{10}) $ 32 * q - 4 * q^7 + 16 * q^9	$ 32 q - 4 q^{7} + 16 q^{9} + 8 q^{11} + 16 q^{12} + 4 q^{14} - 32 q^{16} - 16 q^{17} + 24 q^{19} + 8 q^{21} - 4 q^{22} + 24 q^{25} - 8 q^{26} + 8 q^{28} - 12 q^{29} + 4 q^{31} + 8 q^{33} + 8 q^{34} + 40 q^{35} - 12 q^{37} - 8 q^{38} + 28 q^{39} + 28 q^{41} - 12 q^{42} + 84 q^{43} - 4 q^{44} - 40 q^{46} - 4 q^{47} - 36 q^{49} - 16 q^{50} - 20 q^{52} - 4 q^{53} - 48 q^{55} + 12 q^{56} + 12 q^{57} + 12 q^{58} - 24 q^{59} - 36 q^{61} + 40 q^{62} + 4 q^{63} + 44 q^{65} - 16 q^{67} + 8 q^{69} + 40 q^{70} + 20 q^{71} - 16 q^{73} - 40 q^{74} + 16 q^{75} - 36 q^{76} + 12 q^{77} - 20 q^{78} - 16 q^{81} - 24 q^{82} - 12 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 60 q^{89} - 48 q^{91} - 16 q^{92} - 32 q^{93} - 76 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) $ 32 * q - 4 * q^7 + 16 * q^9 + 8 * q^11 + 16 * q^12 + 4 * q^14 - 32 * q^16 - 16 * q^17 + 24 * q^19 + 8 * q^21 - 4 * q^22 + 24 * q^25 - 8 * q^26 + 8 * q^28 - 12 * q^29 + 4 * q^31 + 8 * q^33 + 8 * q^34 + 40 * q^35 - 12 * q^37 - 8 * q^38 + 28 * q^39 + 28 * q^41 - 12 * q^42 + 84 * q^43 - 4 * q^44 - 40 * q^46 - 4 * q^47 - 36 * q^49 - 16 * q^50 - 20 * q^52 - 4 * q^53 - 48 * q^55 + 12 * q^56 + 12 * q^57 + 12 * q^58 - 24 * q^59 - 36 * q^61 + 40 * q^62 + 4 * q^63 + 44 * q^65 - 16 * q^67 + 8 * q^69 + 40 * q^70 + 20 * q^71 - 16 * q^73 - 40 * q^74 + 16 * q^75 - 36 * q^76 + 12 * q^77 - 20 * q^78 - 16 * q^81 - 24 * q^82 - 12 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 60 * q^89 - 48 * q^91 - 16 * q^92 - 32 * q^93 - 76 * q^97 - 8 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{7}{12}\right)$

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
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$			1.00000i			0.500000i
$5$	−0.765779	−	2.85793i	−0.342467	−	1.27810i	−0.895544	−	0.444974i	$-0.853213\pi$
$5$	−0.765779	−	2.85793i	−0.342467	−	1.27810i	0.553077	−	0.833130i	$-0.313454\pi$
$6$	0.258819	+	0.965926i	0.105662	+	0.394338i
$7$	−1.78167	−	1.95592i	−0.673409	−	0.739270i
$7$	−1.78167	−	1.95592i	−0.673409	−	0.739270i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−1.47937	+	2.56235i	−0.467818	+	0.810285i
$11$	−1.13023	−	4.21807i	−0.340777	−	1.27180i	−0.897469	−	0.441078i	$-0.854596\pi$
$11$	−1.13023	−	4.21807i	−0.340777	−	1.27180i	0.556692	−	0.830719i	$-0.312070\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	1.11321	+	3.42940i	0.308748	+	0.951144i
$13$	1.11321	+	3.42940i	0.308748	+	0.951144i
$14$	−0.123214	+	2.64288i	−0.0329302	+	0.706340i
$15$	−0.765779	+	2.85793i	−0.197723	+	0.737914i
$16$	−1.00000			−0.250000
$17$	−0.928803			−0.225268			−0.112634	−	0.993637i	$-0.535929\pi$
$17$	−0.928803			−0.225268			−0.112634	+	0.993637i	$0.535929\pi$
$18$	0.258819	−	0.965926i	0.0610042	−	0.227671i
$19$	0.161344	+	0.0432320i	0.0370148	+	0.00991809i	0.277279	−	0.960789i	$-0.410567\pi$
$19$	0.161344	+	0.0432320i	0.0370148	+	0.00991809i	−0.240264	+	0.970708i	$0.577234\pi$
$20$	2.85793	−	0.765779i	0.639052	−	0.171233i
$21$	0.565013	+	2.58472i	0.123296	+	0.564031i
$22$	−2.18344	+	3.78182i	−0.465510	+	0.806287i
$23$			1.61325i			0.336387i	0.985754	+	0.168193i	$0.0537933\pi$
$23$			1.61325i			0.336387i	−0.985754	+	0.168193i	$0.946207\pi$
$24$	−0.965926	+	0.258819i	−0.197169	+	0.0528312i
$25$	−3.25120	+	1.87708i	−0.650241	+	0.375417i
$26$	1.63780	−	3.21211i	0.321198	−	0.629946i
$27$		−	1.00000i		−	0.192450i
$28$	1.95592	−	1.78167i	0.369635	−	0.336705i
$29$	1.94582	+	3.37026i	0.361330	+	0.625842i	0.988180	−	0.153298i	$-0.0489894\pi$
$29$	1.94582	+	3.37026i	0.361330	+	0.625842i	−0.626850	+	0.779140i	$0.715656\pi$
$30$	2.56235	−	1.47937i	0.467818	−	0.270095i
$31$	−8.33172	−	2.23248i	−1.49642	−	0.400965i	−0.584521	−	0.811378i	$-0.698718\pi$
$31$	−8.33172	−	2.23248i	−1.49642	−	0.400965i	−0.911900	+	0.410413i	$0.865384\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−1.13023	+	4.21807i	−0.196748	+	0.734272i
$34$	0.656763	+	0.656763i	0.112634	+	0.112634i
$35$	−4.22552	+	6.58970i	−0.714243	+	1.11386i
$36$	−0.866025	+	0.500000i	−0.144338	+	0.0833333i
$37$	−4.92659	+	4.92659i	−0.809927	+	0.809927i	−0.984622	−	0.174696i	$-0.944106\pi$
$37$	−4.92659	+	4.92659i	−0.809927	+	0.809927i	0.174696	+	0.984622i	$0.444106\pi$
$38$	−0.0835178	−	0.144657i	−0.0135484	−	0.0234665i
$39$	0.750635	−	3.52655i	0.120198	−	0.564700i
$40$	−2.56235	−	1.47937i	−0.405143	−	0.233909i
$41$	−9.71078	−	2.60200i	−1.51657	−	0.406363i	−0.597958	−	0.801527i	$-0.704021\pi$
$41$	−9.71078	−	2.60200i	−1.51657	−	0.406363i	−0.918611	+	0.395164i	$0.870688\pi$
$42$	1.42815	−	2.22720i	0.220368	−	0.343664i
$43$	4.51157	+	2.60476i	0.688008	+	0.397222i	0.802865	−	0.596160i	$-0.203308\pi$
$43$	4.51157	+	2.60476i	0.688008	+	0.397222i	−0.114857	+	0.993382i	$0.536641\pi$
$44$	4.21807	−	1.13023i	0.635899	−	0.170389i
$45$	2.09215	−	2.09215i	0.311879	−	0.311879i
$46$	1.14074	−	1.14074i	0.168193	−	0.168193i
$47$	8.74657	−	2.34364i	1.27582	−	0.341854i	0.443561	−	0.896244i	$-0.353715\pi$
$47$	8.74657	−	2.34364i	1.27582	−	0.341854i	0.832257	+	0.554390i	$0.187048\pi$
$48$	0.866025	+	0.500000i	0.125000	+	0.0721688i
$49$	−0.651277	+	6.96964i	−0.0930396	+	0.995662i
$50$	3.62625	+	0.971650i	0.512829	+	0.137412i
$51$	0.804367	+	0.464402i	0.112634	+	0.0650292i
$52$	−3.42940	+	1.11321i	−0.475572	+	0.154374i
$53$	1.13857	+	1.97205i	0.156394	+	0.270882i	0.933566	−	0.358406i	$-0.116680\pi$
$53$	1.13857	+	1.97205i	0.156394	+	0.270882i	−0.777172	+	0.629289i	$0.783346\pi$
$54$	−0.707107	+	0.707107i	−0.0962250	+	0.0962250i
$55$	−11.1894	+	6.46023i	−1.50878	+	0.871097i
$56$	−2.64288	−	0.123214i	−0.353170	−	0.0164651i
$57$	−0.118112	−	0.118112i	−0.0156443	−	0.0156443i
$58$	1.00723	−	3.75904i	0.132256	−	0.493586i
$59$	−2.46741	−	2.46741i	−0.321229	−	0.321229i	0.528009	−	0.849238i	$-0.322939\pi$
$59$	−2.46741	−	2.46741i	−0.321229	−	0.321229i	−0.849238	+	0.528009i	$0.822939\pi$
$60$	−2.85793	−	0.765779i	−0.368957	−	0.0988617i
$61$	−8.49717	+	4.90584i	−1.08795	+	0.628129i	−0.933030	−	0.359798i	$-0.882845\pi$
$61$	−8.49717	+	4.90584i	−1.08795	+	0.628129i	−0.154920	+	0.987927i	$0.549512\pi$
$62$	4.31282	+	7.47002i	0.547728	+	0.948693i
$63$	0.803043	−	2.52094i	0.101174	−	0.317608i
$64$		−	1.00000i		−	0.125000i
$65$	8.94850	−	5.80762i	1.10992	−	0.720347i
$66$	3.78182	−	2.18344i	0.465510	−	0.268762i
$67$	−5.27908	+	1.41452i	−0.644942	+	0.172812i	−0.566441	−	0.824102i	$-0.691680\pi$
$67$	−5.27908	+	1.41452i	−0.644942	+	0.172812i	−0.0785011	+	0.996914i	$0.525013\pi$
$68$		−	0.928803i		−	0.112634i
$69$	0.806627	−	1.39712i	0.0971065	−	0.168193i
$70$	7.64751	−	1.67173i	0.914053	−	0.199810i
$71$	7.17756	−	1.92322i	0.851820	−	0.228244i	0.193610	−	0.981079i	$-0.437980\pi$
$71$	7.17756	−	1.92322i	0.851820	−	0.228244i	0.658210	+	0.752834i	$0.271314\pi$
$72$	0.965926	+	0.258819i	0.113835	+	0.0305021i
$73$	1.66618	−	6.21826i	0.195011	−	0.727792i	−0.797253	−	0.603646i	$-0.793714\pi$
$73$	1.66618	−	6.21826i	0.195011	−	0.727792i	0.992264	−	0.124146i	$-0.0396192\pi$
$74$	6.96725			0.809927
$75$	3.75417			0.433494
$76$	−0.0432320	+	0.161344i	−0.00495905	+	0.0185074i
$77$	−6.23653	+	9.72588i	−0.710719	+	1.10837i
$78$	−3.02443	+	1.96287i	−0.342449	+	0.222251i
$79$	4.30390	−	7.45458i	0.484227	−	0.838705i	−0.515609	−	0.856824i	$-0.672434\pi$
$79$	4.30390	−	7.45458i	0.484227	−	0.838705i	0.999836	+	0.0181185i	$0.00576761\pi$
$80$	0.765779	+	2.85793i	0.0856167	+	0.319526i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	5.02667	+	8.70645i	0.555103	+	0.961466i
$83$	−1.81174	+	1.81174i	−0.198864	+	0.198864i	−0.799513	−	0.600649i	$-0.794909\pi$
$83$	−1.81174	+	1.81174i	−0.198864	+	0.198864i	0.600649	+	0.799513i	$0.294909\pi$
$84$	−2.58472	+	0.565013i	−0.282016	+	0.0616479i
$85$	0.711258	+	2.65445i	0.0771468	+	0.287916i
$86$	−1.34832	−	5.03200i	−0.145393	−	0.542615i
$87$		−	3.89165i		−	0.417228i
$88$	−3.78182	−	2.18344i	−0.403144	−	0.232755i
$89$	−8.59688	−	8.59688i	−0.911268	−	0.911268i	0.0851044	−	0.996372i	$-0.472878\pi$
$89$	−8.59688	−	8.59688i	−0.911268	−	0.911268i	−0.996372	+	0.0851044i	$0.972878\pi$
$90$	−2.95874			−0.311879
$91$	4.72427	−	8.28741i	0.495238	−	0.868757i
$92$	−1.61325			−0.168193
$93$	6.09924	+	6.09924i	0.632462	+	0.632462i
$94$	−7.84196	−	4.52756i	−0.808836	−	0.466982i
$95$		−	0.494215i		−	0.0507054i
$96$	−0.258819	−	0.965926i	−0.0264156	−	0.0985844i
$97$	2.87536	+	10.7310i	0.291948	+	1.08957i	0.943611	+	0.331056i	$0.107405\pi$
$97$	2.87536	+	10.7310i	0.291948	+	1.08957i	−0.651663	+	0.758509i	$0.725928\pi$
$98$	5.38880	−	4.46775i	0.544351	−	0.451311i
$99$	3.08784	−	3.08784i	0.310340	−	0.310340i
$100$	−1.87708	−	3.25120i	−0.187708	−	0.325120i
$101$	3.88637	−	6.73139i	0.386708	−	0.669798i	−0.605296	−	0.796000i	$-0.706945\pi$
$101$	3.88637	−	6.73139i	0.386708	−	0.669798i	0.992005	+	0.126202i	$0.0402787\pi$
$102$	−0.240392	−	0.897155i	−0.0238024	−	0.0888316i
$103$	4.87420	−	8.44236i	0.480269	−	0.831850i	−0.519475	−	0.854486i	$-0.673872\pi$
$103$	4.87420	−	8.44236i	0.480269	−	0.831850i	0.999744	+	0.0226355i	$0.00720571\pi$
$104$	3.21211	+	1.63780i	0.314973	+	0.160599i
$105$	6.95426	−	3.59409i	0.678666	−	0.350747i
$106$	0.589365	−	2.19954i	0.0572442	−	0.213638i
$107$	−8.33119			−0.805407			−0.402703	−	0.915330i	$-0.631929\pi$
$107$	−8.33119			−0.805407			−0.402703	+	0.915330i	$0.631929\pi$
$108$	1.00000			0.0962250
$109$	1.76584	−	6.59020i	0.169137	−	0.631227i	−0.828339	−	0.560226i	$-0.810714\pi$
$109$	1.76584	−	6.59020i	0.169137	−	0.631227i	0.997476	−	0.0710006i	$-0.0226192\pi$
$110$	12.4802	+	3.34406i	1.18994	+	0.318844i
$111$	6.72985	−	1.80326i	0.638769	−	0.171158i
$112$	1.78167	+	1.95592i	0.168352	+	0.184817i
$113$	0.175357	−	0.303727i	0.0164962	−	0.0285722i	−0.857659	−	0.514218i	$-0.828082\pi$
$113$	0.175357	−	0.303727i	0.0164962	−	0.0285722i	0.874156	+	0.485646i	$0.161416\pi$
$114$			0.167036i			0.0156443i
$115$	4.61056	−	1.23540i	0.429937	−	0.115201i
$116$	−3.37026	+	1.94582i	−0.312921	+	0.180665i
$117$	−2.41334	+	2.67876i	−0.223114	+	0.247652i
$118$			3.48944i			0.321229i
$119$	1.65482	+	1.81667i	0.151698	+	0.166534i
$120$	1.47937	+	2.56235i	0.135048	+	0.233909i
$121$	−6.98845	+	4.03478i	−0.635314	+	0.366799i
$122$	9.47736	+	2.53945i	0.858040	+	0.229911i
$123$	7.10878	+	7.10878i	0.640978	+	0.640978i
$124$	2.23248	−	8.33172i	0.200482	−	0.748211i
$125$	−2.60647	−	2.60647i	−0.233130	−	0.233130i
$126$	−2.35041	+	1.21473i	−0.209391	+	0.108217i
$127$	18.1902	−	10.5021i	1.61412	−	0.931914i	0.625722	−	0.780046i	$-0.284804\pi$
$127$	18.1902	−	10.5021i	1.61412	−	0.931914i	0.988401	−	0.151868i	$-0.0485289\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−2.60476	−	4.51157i	−0.229336	−	0.397222i
$130$	−10.4342	−	2.22094i	−0.915136	−	0.194789i
$131$	−17.8105	−	10.2829i	−1.55611	−	0.898420i	−0.997623	−	0.0689054i	$-0.978049\pi$
$131$	−17.8105	−	10.2829i	−1.55611	−	0.898420i	−0.558485	−	0.829514i	$-0.688617\pi$
$132$	−4.21807	−	1.13023i	−0.367136	−	0.0983739i
$133$	−0.202904	−	0.392602i	−0.0175940	−	0.0340429i
$134$	4.73309	+	2.73265i	0.408877	+	0.236065i
$135$	−2.85793	+	0.765779i	−0.245971	+	0.0659078i
$136$	−0.656763	+	0.656763i	−0.0563170	+	0.0563170i
$137$	9.08049	−	9.08049i	0.775799	−	0.775799i	−0.203315	−	0.979113i	$-0.565172\pi$
$137$	9.08049	−	9.08049i	0.775799	−	0.775799i	0.979113	+	0.203315i	$0.0651715\pi$
$138$	−1.55828	+	0.417541i	−0.132650	+	0.0355435i
$139$	−17.3133	−	9.99586i	−1.46850	−	0.847838i	−0.469121	−	0.883134i	$-0.655429\pi$
$139$	−17.3133	−	9.99586i	−1.46850	−	0.847838i	−0.999377	+	0.0352960i	$0.988763\pi$
$140$	−6.58970	−	4.22552i	−0.556931	−	0.357122i
$141$	−8.74657	−	2.34364i	−0.736594	−	0.197370i
$142$	−6.43523	−	3.71538i	−0.540032	−	0.311788i
$143$	13.2073	−	8.57159i	1.10445	−	0.716792i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	8.14190	−	8.14190i	0.676148	−	0.676148i
$146$	−5.57514	+	3.21881i	−0.461402	+	0.266390i
$147$	4.04884	−	5.71024i	0.333943	−	0.470973i
$148$	−4.92659	−	4.92659i	−0.404963	−	0.404963i
$149$	−2.46393	+	9.19552i	−0.201853	+	0.753326i	0.788533	+	0.614993i	$0.210841\pi$
$149$	−2.46393	+	9.19552i	−0.201853	+	0.753326i	−0.990386	+	0.138333i	$0.955826\pi$
$150$	−2.65460	−	2.65460i	−0.216747	−	0.216747i
$151$	−14.6710	−	3.93110i	−1.19391	−	0.319908i	−0.393482	−	0.919332i	$-0.628730\pi$
$151$	−14.6710	−	3.93110i	−1.19391	−	0.319908i	−0.800431	+	0.599424i	$0.795396\pi$
$152$	0.144657	−	0.0835178i	0.0117332	−	0.00677418i
$153$	−0.464402	−	0.804367i	−0.0375446	−	0.0650292i
$154$	11.2871	−	2.46734i	0.909543	−	0.198824i
$155$			25.5210i			2.04990i
$156$	3.52655	+	0.750635i	0.282350	+	0.0600989i
$157$	13.1171	−	7.57314i	1.04686	−	0.604403i	0.125089	−	0.992146i	$-0.460079\pi$
$157$	13.1171	−	7.57314i	1.04686	−	0.604403i	0.921768	+	0.387743i	$0.126745\pi$
$158$	−8.31450	+	2.22786i	−0.661466	+	0.177239i
$159$		−	2.27713i		−	0.180588i
$160$	1.47937	−	2.56235i	0.116955	−	0.202571i
$161$	3.15540	−	2.87429i	0.248681	−	0.226526i
$162$	0.965926	−	0.258819i	0.0758903	−	0.0203347i
$163$	−7.55672	−	2.02482i	−0.591888	−	0.158596i	−0.0495721	−	0.998771i	$-0.515786\pi$
$163$	−7.55672	−	2.02482i	−0.591888	−	0.158596i	−0.542316	+	0.840175i	$0.682452\pi$
$164$	2.60200	−	9.71078i	0.203182	−	0.758285i
$165$	12.9205			1.00586
$166$	2.56219			0.198864
$167$	1.05970	−	3.95484i	0.0820018	−	0.306035i	−0.912728	−	0.408568i	$-0.866028\pi$
$167$	1.05970	−	3.95484i	0.0820018	−	0.306035i	0.994730	+	0.102533i	$0.0326948\pi$
$168$	2.22720	+	1.42815i	0.171832	+	0.110184i
$169$	−10.5215	+	7.63525i	−0.809350	+	0.587327i
$170$	1.37405	−	2.37992i	0.105384	−	0.182531i
$171$	0.0432320	+	0.161344i	0.00330603	+	0.0123383i
$172$	−2.60476	+	4.51157i	−0.198611	+	0.344004i
$173$	−12.1513	−	21.0467i	−0.923846	−	1.60015i	−0.793406	−	0.608692i	$-0.791694\pi$
$173$	−12.1513	−	21.0467i	−0.923846	−	1.60015i	−0.130440	−	0.991456i	$-0.541639\pi$
$174$	−2.75181	+	2.75181i	−0.208614	+	0.208614i
$175$	9.46401	+	3.01476i	0.715412	+	0.227894i
$176$	1.13023	+	4.21807i	0.0851943	+	0.317949i
$177$	0.903133	+	3.37054i	0.0678837	+	0.253345i
$178$			12.1578i			0.911268i
$179$	7.28059	+	4.20345i	0.544177	+	0.314180i	0.746770	−	0.665082i	$-0.231604\pi$
$179$	7.28059	+	4.20345i	0.544177	+	0.314180i	−0.202593	+	0.979263i	$0.564937\pi$
$180$	2.09215	+	2.09215i	0.155939	+	0.155939i
$181$	16.6914			1.24066			0.620330	−	0.784341i	$-0.286999\pi$
$181$	16.6914			1.24066			0.620330	+	0.784341i	$0.286999\pi$
$182$	−9.20065	+	2.51952i	−0.681998	+	0.186759i
$183$	9.81168			0.725300
$184$	1.14074	+	1.14074i	0.0840967	+	0.0840967i
$185$	17.8525	+	10.3072i	1.31254	+	0.757797i
$186$		−	8.62563i		−	0.632462i
$187$	1.04976	+	3.91776i	0.0767661	+	0.286495i
$188$	2.34364	+	8.74657i	0.170927	+	0.637909i
$189$	−1.95592	+	1.78167i	−0.142273	+	0.129598i
$190$	−0.349463	+	0.349463i	−0.0253527	+	0.0253527i
$191$	−7.39879	−	12.8151i	−0.535358	−	0.927266i	−0.999146	−	0.0413204i	$-0.986844\pi$
$191$	−7.39879	−	12.8151i	−0.535358	−	0.927266i	0.463788	−	0.885946i	$-0.346490\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	6.40813	+	23.9155i	0.461267	+	1.72147i	0.668977	+	0.743283i	$0.266732\pi$
$193$	6.40813	+	23.9155i	0.461267	+	1.72147i	−0.207710	+	0.978191i	$0.566601\pi$
$194$	5.55476	−	9.62113i	0.398809	−	0.690757i
$195$	−10.6534	+	0.555299i	−0.762909	+	0.0397658i
$196$	−6.96964	−	0.651277i	−0.497831	−	0.0465198i
$197$	−4.85782	+	18.1296i	−0.346105	+	1.29168i	0.545211	+	0.838299i	$0.316450\pi$
$197$	−4.85782	+	18.1296i	−0.346105	+	1.29168i	−0.891316	+	0.453383i	$0.850217\pi$
$198$	−4.36687			−0.310340
$199$	−10.9923			−0.779224			−0.389612	−	0.920979i	$-0.627391\pi$
$199$	−10.9923			−0.779224			−0.389612	+	0.920979i	$0.627391\pi$
$200$	−0.971650	+	3.62625i	−0.0687060	+	0.256414i
$201$	5.27908	+	1.41452i	0.372357	+	0.0997729i
$202$	−7.50789	+	2.01173i	−0.528253	+	0.141545i
$203$	3.12516	−	9.81059i	0.219343	−	0.688569i
$204$	−0.464402	+	0.804367i	−0.0325146	+	0.0563170i
$205$			29.7453i			2.07750i
$206$	−9.41623	+	2.52307i	−0.656060	+	0.175791i
$207$	−1.39712	+	0.806627i	−0.0971065	+	0.0560645i
$208$	−1.11321	−	3.42940i	−0.0771869	−	0.237786i
$209$		−	0.729423i		−	0.0504552i
$210$	−7.45881	−	2.37600i	−0.514707	−	0.163959i
$211$	4.81334	+	8.33694i	0.331364	+	0.573939i	0.982780	−	0.184782i	$-0.0591579\pi$
$211$	4.81334	+	8.33694i	0.331364	+	0.573939i	−0.651416	+	0.758721i	$0.725825\pi$
$212$	−1.97205	+	1.13857i	−0.135441	+	0.0781970i
$213$	−7.17756	−	1.92322i	−0.491799	−	0.131777i
$214$	5.89104	+	5.89104i	0.402703	+	0.402703i
$215$	3.98934	−	14.8884i	0.272071	−	1.01538i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	10.4778	+	20.2738i	0.711283	+	1.37627i
$218$	−5.90862	+	3.41134i	−0.400182	+	0.231045i
$219$	−4.55208	+	4.55208i	−0.307601	+	0.307601i
$220$	−6.46023	−	11.1894i	−0.435548	−	0.754392i
$221$	−1.03395	−	3.18524i	−0.0695509	−	0.214262i
$222$	−6.03382	−	3.48363i	−0.404963	−	0.233806i
$223$	−4.61883	−	1.23761i	−0.309300	−	0.0828767i	0.100830	−	0.994904i	$-0.467850\pi$
$223$	−4.61883	−	1.23761i	−0.309300	−	0.0828767i	−0.410130	+	0.912027i	$0.634517\pi$
$224$	0.123214	−	2.64288i	0.00823255	−	0.176585i
$225$	−3.25120	−	1.87708i	−0.216747	−	0.125139i
$226$	−0.338763	+	0.0907714i	−0.0225342	+	0.00603802i
$227$	−17.7081	+	17.7081i	−1.17533	+	1.17533i	−0.194411	+	0.980920i	$0.562279\pi$
$227$	−17.7081	+	17.7081i	−1.17533	+	1.17533i	−0.980920	+	0.194411i	$0.937721\pi$
$228$	0.118112	−	0.118112i	0.00782215	−	0.00782215i
$229$	14.8062	−	3.96732i	0.978424	−	0.262168i	0.266043	−	0.963961i	$-0.414284\pi$
$229$	14.8062	−	3.96732i	0.978424	−	0.262168i	0.712381	+	0.701793i	$0.247617\pi$
$230$	−4.13372	−	2.38660i	−0.272569	−	0.157368i
$231$	10.2639	−	5.30459i	0.675317	−	0.349016i
$232$	3.75904	+	1.00723i	0.246793	+	0.0661280i
$233$	10.5926	+	6.11566i	0.693947	+	0.400650i	0.805089	−	0.593154i	$-0.202117\pi$
$233$	10.5926	+	6.11566i	0.693947	+	0.400650i	−0.111142	+	0.993805i	$0.535451\pi$
$234$	3.60066	−	0.187680i	0.235383	−	0.0122691i
$235$	−13.3959	−	23.2023i	−0.873851	−	1.51355i
$236$	2.46741	−	2.46741i	0.160614	−	0.160614i
$237$	−7.45458	+	4.30390i	−0.484227	+	0.279568i
$238$	0.114441	−	2.45472i	0.00741812	−	0.159116i
$239$	−17.9887	−	17.9887i	−1.16359	−	1.16359i	−0.983683	−	0.179909i	$-0.942420\pi$
$239$	−17.9887	−	17.9887i	−1.16359	−	1.16359i	−0.179909	−	0.983683i	$-0.557580\pi$
$240$	0.765779	−	2.85793i	0.0494308	−	0.184478i
$241$	16.2898	+	16.2898i	1.04932	+	1.04932i	0.998719	+	0.0506008i	$0.0161136\pi$
$241$	16.2898	+	16.2898i	1.04932	+	1.04932i	0.0506008	+	0.998719i	$0.483886\pi$
$242$	7.79460	+	2.08856i	0.501056	+	0.134258i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−4.90584	−	8.49717i	−0.314064	−	0.543975i
$245$	20.4174	−	3.47590i	1.30442	−	0.222067i
$246$		−	10.0533i		−	0.640978i
$247$	0.0313493	+	0.601439i	0.00199471	+	0.0382686i
$248$	−7.47002	+	4.31282i	−0.474346	+	0.273864i
$249$	2.47488	−	0.663142i	0.156839	−	0.0420249i
$250$			3.68611i			0.233130i
$251$	−10.6293	+	18.4105i	−0.670915	+	1.16206i	0.306730	+	0.951797i	$0.400765\pi$
$251$	−10.6293	+	18.4105i	−0.670915	+	1.16206i	−0.977645	+	0.210263i	$0.932568\pi$
$252$	2.52094	+	0.803043i	0.158804	+	0.0505870i
$253$	6.80483	−	1.82335i	0.427816	−	0.114633i
$254$	−20.2886	−	5.43631i	−1.27302	−	0.341104i
$255$	0.711258	−	2.65445i	0.0445407	−	0.166228i
$256$	1.00000			0.0625000
$257$	−17.1939			−1.07252			−0.536262	−	0.844052i	$-0.680164\pi$
$257$	−17.1939			−1.07252			−0.536262	+	0.844052i	$0.680164\pi$
$258$	−1.34832	+	5.03200i	−0.0839428	+	0.313279i
$259$	18.4136	+	0.858460i	1.14417	+	0.0533421i
$260$	5.80762	+	8.94850i	0.360173	+	0.554962i
$261$	−1.94582	+	3.37026i	−0.120443	+	0.208614i
$262$	5.32281	+	19.8650i	0.328844	+	1.22726i
$263$	−4.30618	+	7.45852i	−0.265530	+	0.459912i	−0.967702	−	0.252095i	$-0.918880\pi$
$263$	−4.30618	+	7.45852i	−0.265530	+	0.459912i	0.702172	+	0.712007i	$0.252214\pi$
$264$	2.18344	+	3.78182i	0.134381	+	0.232755i
$265$	4.76410	−	4.76410i	0.292656	−	0.292656i
$266$	−0.134137	+	0.421086i	−0.00822445	+	0.0258184i
$267$	3.14668	+	11.7436i	0.192574	+	0.718694i
$268$	−1.41452	−	5.27908i	−0.0864059	−	0.322471i
$269$		−	7.63892i		−	0.465753i	−0.972506	−	0.232876i	$-0.925186\pi$
$269$		−	7.63892i		−	0.465753i	0.972506	−	0.232876i	$-0.0748138\pi$
$270$	2.56235	+	1.47937i	0.155939	+	0.0900317i
$271$	11.6956	+	11.6956i	0.710454	+	0.710454i	0.966630	−	0.256176i	$-0.0824626\pi$
$271$	11.6956	+	11.6956i	0.710454	+	0.710454i	−0.256176	+	0.966630i	$0.582463\pi$
$272$	0.928803			0.0563170
$273$	−8.23505	+	4.81497i	−0.498408	+	0.291416i
$274$	−12.8418			−0.775799
$275$	11.5923	+	11.5923i	0.699041	+	0.699041i
$276$	1.39712	+	0.806627i	0.0840967	+	0.0485533i
$277$		−	23.7783i		−	1.42870i	−0.699788	−	0.714350i	$-0.746722\pi$
$277$		−	23.7783i		−	1.42870i	0.699788	−	0.714350i	$-0.253278\pi$
$278$	5.17424	+	19.3105i	0.310330	+	1.15817i
$279$	−2.23248	−	8.33172i	−0.133655	−	0.498807i
$280$	1.67173	+	7.64751i	0.0999048	+	0.457026i
$281$	−2.54618	+	2.54618i	−0.151893	+	0.151893i	−0.778963	−	0.627070i	$-0.784254\pi$
$281$	−2.54618	+	2.54618i	−0.151893	+	0.151893i	0.627070	+	0.778963i	$0.284254\pi$
$282$	4.52756	+	7.84196i	0.269612	+	0.466982i
$283$	−0.894922	+	1.55005i	−0.0531976	+	0.0921409i	−0.891398	−	0.453222i	$-0.850275\pi$
$283$	−0.894922	+	1.55005i	−0.0531976	+	0.0921409i	0.838200	+	0.545362i	$0.183608\pi$
$284$	1.92322	+	7.17756i	0.114122	+	0.425910i
$285$	−0.247108	+	0.428003i	−0.0146374	+	0.0253527i
$286$	−15.4000	−	3.27793i	−0.910620	−	0.193828i
$287$	12.2121	+	23.6295i	0.720860	+	1.39480i
$288$	−0.258819	+	0.965926i	−0.0152511	+	0.0569177i
$289$	−16.1373			−0.949254
$290$	−11.5144			−0.676148
$291$	2.87536	−	10.7310i	0.168556	−	0.629061i
$292$	6.21826	+	1.66618i	0.363896	+	0.0975056i
$293$	4.02574	−	1.07869i	0.235186	−	0.0630179i	−0.139301	−	0.990250i	$-0.544486\pi$
$293$	4.02574	−	1.07869i	0.235186	−	0.0630179i	0.374487	+	0.927232i	$0.377819\pi$
$294$	−6.90072	+	1.17479i	−0.402458	+	0.0685151i
$295$	−5.16218	+	8.94116i	−0.300554	+	0.520574i
$296$			6.96725i			0.404963i
$297$	−4.21807	+	1.13023i	−0.244757	+	0.0655826i
$298$	8.24448	−	4.75995i	0.477590	−	0.275737i
$299$	−5.53249	+	1.79588i	−0.319952	+	0.103859i
$300$			3.75417i			0.216747i
$301$	−2.94344	−	13.4651i	−0.169657	−	0.776117i
$302$	7.59429	+	13.1537i	0.437002	+	0.756910i
$303$	−6.73139	+	3.88637i	−0.386708	+	0.223266i
$304$	−0.161344	−	0.0432320i	−0.00925371	−	0.00247952i
$305$	20.5275	+	20.5275i	1.17540	+	1.17540i
$306$	−0.240392	+	0.897155i	−0.0137423	+	0.0512869i
$307$	4.14745	+	4.14745i	0.236708	+	0.236708i	0.815485	−	0.578778i	$-0.196470\pi$
$307$	4.14745	+	4.14745i	0.236708	+	0.236708i	−0.578778	+	0.815485i	$0.696470\pi$
$308$	−9.72588	−	6.23653i	−0.554183	−	0.355359i
$309$	−8.44236	+	4.87420i	−0.480269	+	0.277283i
$310$	18.0461	−	18.0461i	1.02495	−	1.02495i
$311$	−16.7488	−	29.0098i	−0.949737	−	1.64499i	−0.745977	−	0.665971i	$-0.768017\pi$
$311$	−16.7488	−	29.0098i	−0.949737	−	1.64499i	−0.203759	−	0.979021i	$-0.565316\pi$
$312$	−1.96287	−	3.02443i	−0.111126	−	0.171224i
$313$	−13.8517	−	7.99730i	−0.782946	−	0.452034i	0.0545271	−	0.998512i	$-0.482635\pi$
$313$	−13.8517	−	7.99730i	−0.782946	−	0.452034i	−0.837473	+	0.546478i	$0.815968\pi$
$314$	−14.6302	−	3.92015i	−0.825629	−	0.221227i
$315$	−7.81961	−	0.364557i	−0.440585	−	0.0205405i
$316$	7.45458	+	4.30390i	0.419353	+	0.242113i
$317$	−11.9966	+	3.21447i	−0.673794	+	0.180543i	−0.579463	−	0.814998i	$-0.696738\pi$
$317$	−11.9966	+	3.21447i	−0.673794	+	0.180543i	−0.0943308	+	0.995541i	$0.530071\pi$
$318$	−1.61018	+	1.61018i	−0.0902942	+	0.0902942i
$319$	12.0168	−	12.0168i	0.672812	−	0.672812i
$320$	−2.85793	+	0.765779i	−0.159763	+	0.0428084i
$321$	7.21503	+	4.16560i	0.402703	+	0.232501i
$322$	−4.26364	−	0.198775i	−0.237603	−	0.0110773i
$323$	−0.149857	−	0.0401540i	−0.00833825	−	0.00223423i
$324$	−0.866025	−	0.500000i	−0.0481125	−	0.0277778i
$325$	−10.0565	−	9.06009i	−0.557835	−	0.502563i
$326$	3.91165	+	6.77517i	0.216646	+	0.375242i
$327$	−4.82436	+	4.82436i	−0.266788	+	0.266788i
$328$	−8.70645	+	5.02667i	−0.480733	+	0.277551i
$329$	−20.1675	−	12.9320i	−1.11187	−	0.712966i
$330$	−9.13614	−	9.13614i	−0.502928	−	0.502928i
$331$	0.162687	−	0.607156i	0.00894208	−	0.0333723i	−0.961311	−	0.275467i	$-0.911168\pi$
$331$	0.162687	−	0.607156i	0.00894208	−	0.0333723i	0.970253	+	0.242094i	$0.0778343\pi$
$332$	−1.81174	−	1.81174i	−0.0994321	−	0.0994321i
$333$	−6.72985	−	1.80326i	−0.368793	−	0.0988179i
$334$	−3.54582	+	2.04718i	−0.194018	+	0.112017i
$335$	8.08522	+	14.0040i	0.441743	+	0.765121i
$336$	−0.565013	−	2.58472i	−0.0308240	−	0.141008i
$337$		−	0.617536i		−	0.0336393i	−0.999859	−	0.0168197i	$-0.994646\pi$
$337$		−	0.617536i		−	0.0336393i	0.999859	−	0.0168197i	$-0.00535412\pi$
$338$	12.8388	+	2.04092i	0.698338	+	0.111011i
$339$	−0.303727	+	0.175357i	−0.0164962	+	0.00952408i
$340$	−2.65445	+	0.711258i	−0.143958	+	0.0385734i
$341$			37.6670i			2.03978i
$342$	0.0835178	−	0.144657i	0.00451612	−	0.00782215i
$343$	14.7924	−	11.1438i	0.798717	−	0.601707i
$344$	5.03200	−	1.34832i	0.271308	−	0.0726966i
$345$	−4.61056	−	1.23540i	−0.248224	−	0.0665115i
$346$	−6.28998	+	23.4745i	−0.338151	+	1.26200i
$347$	−19.5585			−1.04995			−0.524976	−	0.851117i	$-0.675926\pi$
$347$	−19.5585			−1.04995			−0.524976	+	0.851117i	$0.675926\pi$
$348$	3.89165			0.208614
$349$	3.35788	−	12.5318i	0.179743	−	0.670810i	−0.815952	−	0.578120i	$-0.803787\pi$
$349$	3.35788	−	12.5318i	0.179743	−	0.670810i	0.995695	−	0.0926905i	$-0.0295467\pi$
$350$	−4.56031	−	8.82382i	−0.243759	−	0.471653i
$351$	3.42940	−	1.11321i	0.183048	−	0.0594185i
$352$	2.18344	−	3.78182i	0.116378	−	0.201572i
$353$	−2.99703	−	11.1851i	−0.159516	−	0.595321i	−0.998676	−	0.0514371i	$-0.983620\pi$
$353$	−2.99703	−	11.1851i	−0.159516	−	0.595321i	0.839160	−	0.543884i	$-0.183047\pi$
$354$	1.74472	−	3.02194i	0.0927308	−	0.160614i
$355$	−10.9929	−	19.0402i	−0.583440	−	1.01055i
$356$	8.59688	−	8.59688i	0.455634	−	0.455634i
$357$	−0.524786	−	2.40069i	−0.0277746	−	0.127058i
$358$	−2.17586	−	8.12044i	−0.114998	−	0.429179i
$359$	3.37607	+	12.5996i	0.178182	+	0.664984i	0.995988	+	0.0894898i	$0.0285236\pi$
$359$	3.37607	+	12.5996i	0.178182	+	0.664984i	−0.817806	+	0.575494i	$0.804810\pi$
$360$		−	2.95874i		−	0.155939i
$361$	−16.4303	−	9.48605i	−0.864754	−	0.499266i
$362$	−11.8026	−	11.8026i	−0.620330	−	0.620330i
$363$	8.06957			0.423543
$364$	8.28741	+	4.72427i	0.434379	+	0.247619i
$365$	−19.0473			−0.996979
$366$	−6.93791	−	6.93791i	−0.362650	−	0.362650i
$367$	21.7395	+	12.5513i	1.13479	+	0.655174i	0.945136	−	0.326677i	$-0.105929\pi$
$367$	21.7395	+	12.5513i	1.13479	+	0.655174i	0.189658	+	0.981850i	$0.439262\pi$
$368$		−	1.61325i		−	0.0840967i
$369$	−2.60200	−	9.71078i	−0.135454	−	0.505523i
$370$	−5.33538	−	19.9119i	−0.277373	−	1.03517i
$371$	1.82864	−	5.74051i	0.0949380	−	0.298032i
$372$	−6.09924	+	6.09924i	−0.316231	+	0.316231i
$373$	−8.26440	−	14.3144i	−0.427915	−	0.741170i	0.568773	−	0.822494i	$-0.307418\pi$
$373$	−8.26440	−	14.3144i	−0.427915	−	0.741170i	−0.996688	+	0.0813247i	$0.974085\pi$
$374$	2.02798	−	3.51257i	0.104864	−	0.181631i
$375$	0.954034	+	3.56050i	0.0492661	+	0.183864i
$376$	4.52756	−	7.84196i	0.233491	−	0.404418i
$377$	−9.39188	+	10.4248i	−0.483706	+	0.536905i
$378$	2.64288	+	0.123214i	0.135935	+	0.00633742i
$379$	5.26805	−	19.6606i	0.270602	−	1.00990i	−0.688130	−	0.725587i	$-0.741568\pi$
$379$	5.26805	−	19.6606i	0.270602	−	1.00990i	0.958732	−	0.284312i	$-0.0917651\pi$
$380$	0.494215			0.0253527
$381$	−21.0043			−1.07608
$382$	−3.82989	+	14.2934i	−0.195954	+	0.731312i
$383$	2.64931	+	0.709879i	0.135373	+	0.0362731i	0.325869	−	0.945415i	$-0.394343\pi$
$383$	2.64931	+	0.709879i	0.135373	+	0.0362731i	−0.190496	+	0.981688i	$0.561010\pi$
$384$	0.965926	−	0.258819i	0.0492922	−	0.0132078i
$385$	32.5716	+	10.3757i	1.66000	+	0.528794i
$386$	12.3796	−	21.4420i	0.630103	−	1.09137i
$387$			5.20951i			0.264815i
$388$	−10.7310	+	2.87536i	−0.544783	+	0.145974i
$389$	2.29812	−	1.32682i	0.116519	−	0.0672724i	−0.440608	−	0.897700i	$-0.645237\pi$
$389$	2.29812	−	1.32682i	0.116519	−	0.0672724i	0.557127	+	0.830427i	$0.311904\pi$
$390$	7.92578	+	7.14046i	0.401337	+	0.361571i
$391$		−	1.49840i		−	0.0757772i
$392$	4.46775	+	5.38880i	0.225656	+	0.272176i
$393$	10.2829	+	17.8105i	0.518703	+	0.898420i
$394$	16.2546	−	9.38458i	0.818894	−	0.472788i
$395$	−24.6005	−	6.59168i	−1.23778	−	0.331663i
$396$	3.08784	+	3.08784i	0.155170	+	0.155170i
$397$	−3.27175	+	12.2104i	−0.164205	+	0.612820i	0.833936	+	0.551862i	$0.186082\pi$
$397$	−3.27175	+	12.2104i	−0.164205	+	0.612820i	−0.998140	+	0.0609584i	$0.980584\pi$
$398$	7.77274	+	7.77274i	0.389612	+	0.389612i
$399$	−0.0205810	+	0.441455i	−0.00103034	+	0.0221004i
$400$	3.25120	−	1.87708i	0.162560	−	0.0938541i
$401$	17.1138	−	17.1138i	0.854623	−	0.854623i	−0.136075	−	0.990698i	$-0.543449\pi$
$401$	17.1138	−	17.1138i	0.854623	−	0.854623i	0.990698	+	0.136075i	$0.0434489\pi$
$402$	−2.73265	−	4.73309i	−0.136292	−	0.236065i
$403$	−1.61886	−	31.0580i	−0.0806413	−	1.54711i
$404$	6.73139	+	3.88637i	0.334899	+	0.193354i
$405$	2.85793	+	0.765779i	0.142012	+	0.0380519i
$406$	−9.14696	+	4.72732i	−0.453956	+	0.234613i
$407$	26.3489	+	15.2125i	1.30607	+	0.754058i
$408$	0.897155	−	0.240392i	0.0444158	−	0.0119012i
$409$	−20.5637	+	20.5637i	−1.01681	+	1.01681i	−0.0169533	+	0.999856i	$0.505397\pi$
$409$	−20.5637	+	20.5637i	−1.01681	+	1.01681i	−0.999856	+	0.0169533i	$0.994603\pi$
$410$	21.0331	−	21.0331i	1.03875	−	1.03875i
$411$	−12.4042	+	3.32369i	−0.611853	+	0.163946i
$412$	8.44236	+	4.87420i	0.415925	+	0.240134i
$413$	−0.429946	+	9.22217i	−0.0211563	+	0.453793i
$414$	1.55828	+	0.417541i	0.0765855	+	0.0205210i
$415$	6.56521	+	3.79042i	0.322273	+	0.186065i
$416$	−1.63780	+	3.21211i	−0.0802995	+	0.157486i
$417$	9.99586	+	17.3133i	0.489499	+	0.847838i
$418$	−0.515780	+	0.515780i	−0.0252276	+	0.0252276i
$419$	1.80135	−	1.04001i	0.0880017	−	0.0508078i	−0.455353	−	0.890311i	$-0.650487\pi$
$419$	1.80135	−	1.04001i	0.0880017	−	0.0508078i	0.543355	+	0.839503i	$0.317154\pi$
$420$	3.59409	+	6.95426i	0.175374	+	0.339333i
$421$	23.4430	+	23.4430i	1.14254	+	1.14254i	0.987984	+	0.154559i	$0.0493958\pi$
$421$	23.4430	+	23.4430i	1.14254	+	1.14254i	0.154559	+	0.987984i	$0.450604\pi$
$422$	2.49157	−	9.29865i	0.121288	−	0.452651i
$423$	6.40293	+	6.40293i	0.311321	+	0.311321i
$424$	2.19954	+	0.589365i	0.106819	+	0.0286221i
$425$	3.01973	−	1.74344i	0.146478	−	0.0845693i
$426$	3.71538	+	6.43523i	0.180011	+	0.311788i
$427$	24.7346	+	7.87920i	1.19699	+	0.381301i
$428$		−	8.33119i		−	0.402703i
$429$	−15.7236	+	0.819577i	−0.759144	+	0.0395695i
$430$	−13.3486	+	7.70681i	−0.643726	+	0.371655i
$431$	19.0336	−	5.10004i	0.916816	−	0.245660i	0.230592	−	0.973051i	$-0.425934\pi$
$431$	19.0336	−	5.10004i	0.916816	−	0.245660i	0.686224	+	0.727390i	$0.259267\pi$
$432$			1.00000i			0.0481125i
$433$	10.1105	−	17.5119i	0.485879	−	0.841566i	−0.513990	−	0.857796i	$-0.671833\pi$
$433$	10.1105	−	17.5119i	0.485879	−	0.841566i	0.999868	+	0.0162300i	$0.00516638\pi$
$434$	6.92675	−	21.7447i	0.332495	−	1.04378i
$435$	−11.1220	+	2.98014i	−0.533261	+	0.142887i
$436$	6.59020	+	1.76584i	0.315614	+	0.0845684i
$437$	−0.0697442	+	0.260289i	−0.00333632	+	0.0124513i
$438$	6.43761			0.307601
$439$	33.4309			1.59557			0.797784	−	0.602943i	$-0.206006\pi$
$439$	33.4309			1.59557			0.797784	+	0.602943i	$0.206006\pi$
$440$	−3.34406	+	12.4802i	−0.159422	+	0.594970i
$441$	−6.36152	+	2.92080i	−0.302930	+	0.139086i
$442$	−1.52119	+	2.98341i	−0.0723556	+	0.141907i
$443$	−0.726887	+	1.25900i	−0.0345354	+	0.0598171i	−0.882777	−	0.469793i	$-0.844328\pi$
$443$	−0.726887	+	1.25900i	−0.0345354	+	0.0598171i	0.848241	+	0.529610i	$0.177662\pi$
$444$	1.80326	+	6.72985i	0.0855788	+	0.319384i
$445$	−17.9859	+	31.1526i	−0.852616	+	1.47677i
$446$	2.39088	+	4.14113i	0.113212	+	0.196088i
$447$	6.73159	−	6.73159i	0.318393	−	0.318393i
$448$	−1.95592	+	1.78167i	−0.0924087	+	0.0841762i
$449$	−6.78725	−	25.3304i	−0.320310	−	1.19541i	−0.918943	−	0.394390i	$-0.870956\pi$
$449$	−6.78725	−	25.3304i	−0.320310	−	1.19541i	0.598633	−	0.801023i	$-0.295711\pi$
$450$	0.971650	+	3.62625i	0.0458040	+	0.170943i
$451$			43.9016i			2.06725i
$452$	0.303727	+	0.175357i	0.0142861	+	0.00824809i
$453$	10.7400	+	10.7400i	0.504607	+	0.504607i
$454$	25.0431			1.17533
$455$	−27.3026	−	7.15530i	−1.27996	−	0.335446i
$456$	−0.167036			−0.00782215
$457$	−18.1140	−	18.1140i	−0.847336	−	0.847336i	0.142464	−	0.989800i	$-0.454498\pi$
$457$	−18.1140	−	18.1140i	−0.847336	−	0.847336i	−0.989800	+	0.142464i	$0.954498\pi$
$458$	−13.2749	−	7.66427i	−0.620296	−	0.358128i
$459$			0.928803i			0.0433528i
$460$	1.23540	+	4.61056i	0.0576007	+	0.214969i
$461$	−3.62598	−	13.5323i	−0.168879	−	0.630264i	−0.997514	−	0.0704742i	$-0.977549\pi$
$461$	−3.62598	−	13.5323i	−0.168879	−	0.630264i	0.828635	−	0.559789i	$-0.189118\pi$
$462$	−11.0086	−	3.50679i	−0.512167	−	0.163150i
$463$	18.1441	−	18.1441i	0.843229	−	0.843229i	−0.146048	−	0.989277i	$-0.546655\pi$
$463$	18.1441	−	18.1441i	0.843229	−	0.843229i	0.989277	+	0.146048i	$0.0466554\pi$
$464$	−1.94582	−	3.37026i	−0.0903326	−	0.156461i
$465$	12.7605	−	22.1019i	0.591755	−	1.02495i
$466$	−3.16570	−	11.8146i	−0.146648	−	0.547299i
$467$	−4.26229	+	7.38250i	−0.197235	+	0.341621i	−0.947631	−	0.319367i	$-0.896530\pi$
$467$	−4.26229	+	7.38250i	−0.197235	+	0.341621i	0.750396	+	0.660989i	$0.229863\pi$
$468$	−2.67876	−	2.41334i	−0.123826	−	0.111557i
$469$	12.1723	+	7.80525i	0.562065	+	0.360413i
$470$	−6.93422	+	25.8789i	−0.319852	+	1.19370i
$471$	−15.1463			−0.697904
$472$	−3.48944			−0.160614
$473$	5.88795	−	21.9741i	0.270728	−	1.01037i
$474$	8.31450	+	2.22786i	0.381898	+	0.102329i
$475$	−0.605712	+	0.162300i	−0.0277920	+	0.00744683i
$476$	−1.81667	+	1.65482i	−0.0832669	+	0.0758488i
$477$	−1.13857	+	1.97205i	−0.0521314	+	0.0902942i
$478$			25.4399i			1.16359i
$479$	23.3016	−	6.24364i	1.06468	−	0.285279i	0.316372	−	0.948635i	$-0.397535\pi$
$479$	23.3016	−	6.24364i	1.06468	−	0.285279i	0.748304	+	0.663356i	$0.230869\pi$
$480$	−2.56235	+	1.47937i	−0.116955	+	0.0675238i
$481$	−22.3796	−	11.4109i	−1.02042	−	0.520294i
$482$		−	23.0373i		−	1.04932i
$483$	−4.16981	+	0.911509i	−0.189733	+	0.0414751i
$484$	−4.03478	−	6.98845i	−0.183399	−	0.317657i
$485$	28.4665	−	16.4351i	1.29260	−	0.746280i
$486$	−0.965926	−	0.258819i	−0.0438153	−	0.0117403i
$487$	−17.6862	−	17.6862i	−0.801438	−	0.801438i	0.181883	−	0.983320i	$-0.441781\pi$
$487$	−17.6862	−	17.6862i	−0.801438	−	0.801438i	−0.983320	+	0.181883i	$0.941781\pi$
$488$	−2.53945	+	9.47736i	−0.114955	+	0.429020i
$489$	5.53190	+	5.53190i	0.250161	+	0.250161i
$490$	−16.8951	−	11.9795i	−0.763245	−	0.541178i
$491$	24.9338	−	14.3955i	1.12525	−	0.649661i	0.182511	−	0.983204i	$-0.441578\pi$
$491$	24.9338	−	14.3955i	1.12525	−	0.649661i	0.942735	+	0.333543i	$0.108244\pi$
$492$	−7.10878	+	7.10878i	−0.320489	+	0.320489i
$493$	−1.80729	−	3.13031i	−0.0813961	−	0.140982i
$494$	0.403114	−	0.447449i	0.0181370	−	0.0201317i
$495$	−11.1894	−	6.46023i	−0.502928	−	0.290366i
$496$	8.33172	+	2.23248i	0.374105	+	0.100241i
$497$	−16.5498	−	10.6122i	−0.742358	−	0.476023i
$498$	−2.21892	−	1.28109i	−0.0994321	−	0.0574071i
$499$	11.0345	−	2.95669i	0.493972	−	0.132360i	−0.00322879	−	0.999995i	$-0.501028\pi$
$499$	11.0345	−	2.95669i	0.493972	−	0.132360i	0.497201	+	0.867635i	$0.334361\pi$
$500$	2.60647	−	2.60647i	0.116565	−	0.116565i
$501$	−2.89515	+	2.89515i	−0.129346	+	0.129346i
$502$	20.5342	−	5.50213i	0.916487	−	0.245572i
$503$	−20.5073	−	11.8399i	−0.914374	−	0.527914i	−0.0325383	−	0.999470i	$-0.510359\pi$
$503$	−20.5073	−	11.8399i	−0.914374	−	0.527914i	−0.881836	+	0.471556i	$0.843692\pi$
$504$	−1.21473	−	2.35041i	−0.0541086	−	0.104696i
$505$	−22.2139	−	5.95220i	−0.988507	−	0.264870i
$506$	−6.10104	−	3.52244i	−0.271224	−	0.156591i
$507$	12.9296	−	1.35155i	0.574222	−	0.0600244i
$508$	10.5021	+	18.1902i	0.465957	+	0.807061i
$509$	−13.6787	+	13.6787i	−0.606300	+	0.606300i	−0.941977	−	0.335677i	$-0.891035\pi$
$509$	−13.6787	+	13.6787i	−0.606300	+	0.606300i	0.335677	+	0.941977i	$0.391035\pi$
$510$	−2.37992	+	1.37405i	−0.105384	+	0.0608438i
$511$	−15.1310	+	7.81999i	−0.669357	+	0.345936i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	0.0432320	−	0.161344i	0.00190874	−	0.00712351i
$514$	12.1579	+	12.1579i	0.536262	+	0.536262i
$515$	−27.8602	−	7.46512i	−1.22767	−	0.328952i
$516$	4.51157	−	2.60476i	0.198611	−	0.114668i
$517$	−19.7713	−	34.2448i	−0.869539	−	1.50609i
$518$	−12.4134	−	13.6274i	−0.545412	−	0.598754i
$519$			24.3026i			1.06677i
$520$	2.22094	−	10.4342i	0.0973945	−	0.457568i
$521$	31.7915	−	18.3549i	1.39281	−	0.804141i	0.399187	−	0.916870i	$-0.369293\pi$
$521$	31.7915	−	18.3549i	1.39281	−	0.804141i	0.993626	+	0.112729i	$0.0359592\pi$
$522$	3.75904	−	1.00723i	0.164529	−	0.0440854i
$523$			3.93552i			0.172088i	0.996291	+	0.0860441i	$0.0274226\pi$
$523$			3.93552i			0.172088i	−0.996291	+	0.0860441i	$0.972577\pi$
$524$	10.2829	−	17.8105i	0.449210	−	0.778054i
$525$	−6.68870	−	7.34286i	−0.291919	−	0.320469i
$526$	8.31889	−	2.22904i	0.362721	−	0.0971908i
$527$	7.73853	+	2.07353i	0.337096	+	0.0903245i
$528$	1.13023	−	4.21807i	0.0491869	−	0.183568i
$529$	20.3974			0.886844
$530$	−6.73745			−0.292656
$531$	0.903133	−	3.37054i	0.0391927	−	0.146269i
$532$	0.392602	−	0.202904i	0.0170214	−	0.00879699i
$533$	−1.88682	−	36.1987i	−0.0817271	−	1.56794i
$534$	6.07891	−	10.5290i	0.263060	−	0.455634i
$535$	6.37986	+	23.8099i	0.275825	+	1.02939i
$536$	−2.73265	+	4.73309i	−0.118033	+	0.204438i
$537$	−4.20345	−	7.28059i	−0.181392	−	0.314180i
$538$	−5.40153	+	5.40153i	−0.232876	+	0.232876i
$539$	30.1345	−	5.13015i	1.29799	−	0.220971i
$540$	−0.765779	−	2.85793i	−0.0329539	−	0.122986i
$541$	−7.68661	−	28.6868i	−0.330473	−	1.23334i	−0.908694	−	0.417462i	$-0.862920\pi$
$541$	−7.68661	−	28.6868i	−0.330473	−	1.23334i	0.578221	−	0.815880i	$-0.303747\pi$
$542$		−	16.5400i		−	0.710454i
$543$	−14.4552	−	8.34569i	−0.620330	−	0.358148i
$544$	−0.656763	−	0.656763i	−0.0281585	−	0.0281585i
$545$	−20.1866			−0.864698
$546$	9.22776	+	2.41836i	0.394912	+	0.103496i
$547$	19.7265			0.843446			0.421723	−	0.906725i	$-0.361426\pi$
$547$	19.7265			0.843446			0.421723	+	0.906725i	$0.361426\pi$
$548$	9.08049	+	9.08049i	0.387899	+	0.387899i
$549$	−8.49717	−	4.90584i	−0.362650	−	0.209376i
$550$		−	16.3940i		−	0.699041i
$551$	0.168244	+	0.627893i	0.00716742	+	0.0267492i
$552$	−0.417541	−	1.55828i	−0.0177717	−	0.0663250i
$553$	−22.2487	+	4.86352i	−0.946113	+	0.206818i
$554$	−16.8138	+	16.8138i	−0.714350	+	0.714350i
$555$	−10.3072	−	17.8525i	−0.437514	−	0.757797i
$556$	9.99586	−	17.3133i	0.423919	−	0.734249i
$557$	10.9843	+	40.9939i	0.465419	+	1.73697i	0.655497	+	0.755198i	$0.272459\pi$
$557$	10.9843	+	40.9939i	0.465419	+	1.73697i	−0.190078	+	0.981769i	$0.560874\pi$
$558$	−4.31282	+	7.47002i	−0.182576	+	0.316231i
$559$	−3.91044	+	18.3716i	−0.165394	+	0.777036i
$560$	4.22552	−	6.58970i	0.178561	−	0.278466i
$561$	1.04976	−	3.91776i	0.0443209	−	0.165408i
$562$	3.60085			0.151893
$563$	−2.49590			−0.105190			−0.0525949	−	0.998616i	$-0.516749\pi$
$563$	−2.49590			−0.105190			−0.0525949	+	0.998616i	$0.516749\pi$
$564$	2.34364	−	8.74657i	0.0986849	−	0.368297i
$565$	−1.00231	−	0.268569i	−0.0421677	−	0.0112988i
$566$	1.72886	−	0.463246i	0.0726693	−	0.0194717i
$567$	2.58472	−	0.565013i	0.108548	−	0.0237283i
$568$	3.71538	−	6.43523i	0.155894	−	0.270016i
$569$		−	22.3881i		−	0.938557i	−0.883050	−	0.469278i	$-0.844514\pi$
$569$		−	22.3881i		−	0.938557i	0.883050	−	0.469278i	$-0.155486\pi$
$570$	0.477375	−	0.127912i	0.0199951	−	0.00535766i
$571$	−29.1379	+	16.8228i	−1.21938	+	0.704011i	−0.964786	−	0.263036i	$-0.915276\pi$
$571$	−29.1379	+	16.8228i	−1.21938	+	0.704011i	−0.254597	+	0.967047i	$0.581943\pi$
$572$	8.57159	+	13.2073i	0.358396	+	0.552224i
$573$			14.7976i			0.618178i
$574$	8.07326	−	25.3438i	0.336972	−	1.05783i
$575$	−3.02821	−	5.24502i	−0.126285	−	0.218732i
$576$	0.866025	−	0.500000i	0.0360844	−	0.0208333i
$577$	25.0543	+	6.71327i	1.04302	+	0.279477i	0.739366	−	0.673304i	$-0.235126\pi$
$577$	25.0543	+	6.71327i	1.04302	+	0.279477i	0.303657	+	0.952781i	$0.401792\pi$
$578$	11.4108	+	11.4108i	0.474627	+	0.474627i
$579$	6.40813	−	23.9155i	0.266313	−	0.993893i
$580$	8.14190	+	8.14190i	0.338074	+	0.338074i
$581$	6.77155	+	0.315696i	0.280931	+	0.0130973i
$582$	−9.62113	+	5.55476i	−0.398809	+	0.230252i
$583$	7.03143	−	7.03143i	0.291212	−	0.291212i
$584$	−3.21881	−	5.57514i	−0.133195	−	0.230701i
$585$	9.50380	+	4.84582i	0.392934	+	0.200350i
$586$	−3.60938	−	2.08388i	−0.149102	−	0.0860841i
$587$	−34.8159	−	9.32890i	−1.43701	−	0.385045i	−0.545522	−	0.838096i	$-0.683669\pi$
$587$	−34.8159	−	9.32890i	−1.43701	−	0.385045i	−0.891484	+	0.453052i	$0.850335\pi$
$588$	5.71024	+	4.04884i	0.235486	+	0.166971i
$589$	−1.24776	−	0.720393i	−0.0514130	−	0.0296833i
$590$	9.97256	−	2.67214i	0.410564	−	0.110010i
$591$	13.2718	−	13.2718i	0.545929	−	0.545929i
$592$	4.92659	−	4.92659i	0.202482	−	0.202482i
$593$	24.5090	−	6.56716i	1.00646	−	0.269681i	0.282312	−	0.959323i	$-0.408899\pi$
$593$	24.5090	−	6.56716i	1.00646	−	0.269681i	0.724151	+	0.689642i	$0.242232\pi$
$594$	3.78182	+	2.18344i	0.155170	+	0.0895875i
$595$	3.92468	−	6.12054i	0.160896	−	0.250917i
$596$	−9.19552	−	2.46393i	−0.376663	−	0.100927i
$597$	9.51962	+	5.49616i	0.389612	+	0.224943i
$598$	5.18194	+	2.64218i	0.211905	+	0.108047i
$599$	24.4230	+	42.3019i	0.997897	+	1.72841i	0.555089	+	0.831791i	$0.312684\pi$
$599$	24.4230	+	42.3019i	0.997897	+	1.72841i	0.442808	+	0.896617i	$0.353982\pi$
$600$	2.65460	−	2.65460i	0.108373	−	0.108373i
$601$	20.2207	−	11.6744i	0.824820	−	0.476210i	−0.0272557	−	0.999628i	$-0.508677\pi$
$601$	20.2207	−	11.6744i	0.824820	−	0.476210i	0.852076	+	0.523418i	$0.175343\pi$
$602$	−7.43995	+	11.6026i	−0.303230	+	0.472887i
$603$	−3.86455	−	3.86455i	−0.157377	−	0.157377i
$604$	3.93110	−	14.6710i	0.159954	−	0.596956i
$605$	16.8827	+	16.8827i	0.686381	+	0.686381i
$606$	7.50789	+	2.01173i	0.304987	+	0.0817211i
$607$	−33.7948	+	19.5115i	−1.37169	+	0.791946i	−0.991141	−	0.132815i	$-0.957598\pi$
$607$	−33.7948	+	19.5115i	−1.37169	+	0.791946i	−0.380549	+	0.924761i	$0.624265\pi$
$608$	0.0835178	+	0.144657i	0.00338709	+	0.00586662i
$609$	−7.61176	+	6.93364i	−0.308444	+	0.280965i
$610$		−	29.0303i		−	1.17540i
$611$	17.7740	+	27.3865i	0.719059	+	1.10794i
$612$	0.804367	−	0.464402i	0.0325146	−	0.0187723i
$613$	−6.99504	+	1.87432i	−0.282527	+	0.0757029i	−0.397300	−	0.917689i	$-0.630053\pi$
$613$	−6.99504	+	1.87432i	−0.282527	+	0.0757029i	0.114773	+	0.993392i	$0.463386\pi$
$614$		−	5.86538i		−	0.236708i
$615$	14.8726	−	25.7601i	0.599722	−	1.03875i
$616$	2.46734	+	11.2871i	0.0994119	+	0.454771i
$617$	−8.86874	+	2.37637i	−0.357042	+	0.0956691i	−0.432881	−	0.901451i	$-0.642503\pi$
$617$	−8.86874	+	2.37637i	−0.357042	+	0.0956691i	0.0758393	+	0.997120i	$0.475836\pi$
$618$	9.41623	+	2.52307i	0.378776	+	0.101493i
$619$	−1.36204	+	5.08319i	−0.0547449	+	0.204311i	−0.987881	−	0.155212i	$-0.950394\pi$
$619$	−1.36204	+	5.08319i	−0.0547449	+	0.204311i	0.933136	+	0.359523i	$0.117061\pi$
$620$	−25.5210			−1.02495
$621$	1.61325			0.0647377
$622$	−8.66981	+	32.3562i	−0.347628	+	1.29736i
$623$	−1.49801	+	32.1317i	−0.0600165	+	1.28733i
$624$	−0.750635	+	3.52655i	−0.0300494	+	0.141175i
$625$	−14.8385	+	25.7011i	−0.593541	+	1.02804i
$626$	4.13971	+	15.4496i	0.165456	+	0.617490i
$627$	−0.364711	+	0.631699i	−0.0145652	+	0.0252276i
$628$	7.57314	+	13.1171i	0.302201	+	0.523428i
$629$	4.57583	−	4.57583i	0.182450	−	0.182450i
$630$	5.27152	+	5.78708i	0.210022	+	0.230563i
$631$	−6.94295	−	25.9114i	−0.276394	−	1.03152i	−0.954901	−	0.296924i	$-0.904039\pi$
$631$	−6.94295	−	25.9114i	−0.276394	−	1.03152i	0.678507	−	0.734594i	$-0.262627\pi$
$632$	−2.22786	−	8.31450i	−0.0886197	−	0.330733i
$633$		−	9.62667i		−	0.382626i
$634$	10.7558	+	6.20988i	0.427168	+	0.246626i
$635$	−43.9441	−	43.9441i	−1.74387	−	1.74387i
$636$	2.27713			0.0902942
$637$	−24.6267	+	5.52515i	−0.975744	+	0.218914i
$638$	−16.9943			−0.672812
$639$	5.25434	+	5.25434i	0.207859	+	0.207859i
$640$	2.56235	+	1.47937i	0.101286	+	0.0584773i
$641$			9.50092i			0.375264i	0.982239	+	0.187632i	$0.0600812\pi$
$641$			9.50092i			0.375264i	−0.982239	+	0.187632i	$0.939919\pi$
$642$	−2.15627	−	8.04732i	−0.0851013	−	0.317602i
$643$	1.89475	+	7.07129i	0.0747215	+	0.278865i	0.993170	−	0.116676i	$-0.0372239\pi$
$643$	1.89475	+	7.07129i	0.0747215	+	0.278865i	−0.918448	+	0.395541i	$0.870557\pi$
$644$	2.87429	+	3.15540i	0.113263	+	0.124340i
$645$	−10.8991	+	10.8991i	−0.429151	+	0.429151i
$646$	0.0775716	+	0.134358i	0.00305201	+	0.00528624i
$647$	−2.16942	+	3.75755i	−0.0852887	+	0.147724i	−0.905514	−	0.424316i	$-0.860515\pi$
$647$	−2.16942	+	3.75755i	−0.0852887	+	0.147724i	0.820225	+	0.572040i	$0.193848\pi$
$648$	0.258819	+	0.965926i	0.0101674	+	0.0379452i
$649$	−7.61897	+	13.1964i	−0.299071	+	0.518006i
$650$	0.704584	+	13.5175i	0.0276360	+	0.530199i
$651$	1.06279	−	22.7965i	0.0416542	−	0.893466i
$652$	2.02482	−	7.55672i	0.0792980	−	0.295944i
$653$	32.7081			1.27997			0.639983	−	0.768389i	$-0.278941\pi$
$653$	32.7081			1.27997			0.639983	+	0.768389i	$0.278941\pi$
$654$	6.82268			0.266788
$655$	−15.7488	+	58.7755i	−0.615358	+	2.29655i
$656$	9.71078	+	2.60200i	0.379142	+	0.101591i
$657$	6.21826	−	1.66618i	0.242597	−	0.0650038i
$658$	5.11625	+	23.4049i	0.199452	+	0.912418i
$659$	−16.4529	+	28.4972i	−0.640913	+	1.11009i	0.344316	+	0.938854i	$0.388111\pi$
$659$	−16.4529	+	28.4972i	−0.640913	+	1.11009i	−0.985229	+	0.171241i	$0.945222\pi$
$660$			12.9205i			0.502928i
$661$	−33.0964	+	8.86814i	−1.28730	+	0.344931i	−0.836634	−	0.547762i	$-0.815480\pi$
$661$	−33.0964	+	8.86814i	−1.28730	+	0.344931i	−0.450665	+	0.892693i	$0.648813\pi$
$662$	−0.544361	+	0.314287i	−0.0211572	+	0.0122151i
$663$	−0.697192	+	3.27547i	−0.0270767	+	0.127209i
$664$			2.56219i			0.0994321i
$665$	−0.966648	+	0.880530i	−0.0374850	+	0.0341455i
$666$	3.48363	+	6.03382i	0.134988	+	0.233806i
$667$	−5.43709	+	3.13911i	−0.210525	+	0.121547i
$668$	3.95484	+	1.05970i	0.153018	+	0.0410009i
$669$	3.38122	+	3.38122i	0.130726	+	0.130726i
$670$	4.18522	−	15.6194i	0.161689	−	0.603432i
$671$	30.2969	+	30.2969i	1.16960	+	1.16960i
$672$	−1.42815	+	2.22720i	−0.0550919	+	0.0859159i
$673$	26.3740	−	15.2270i	1.01664	−	0.586959i	0.103513	−	0.994628i	$-0.466992\pi$
$673$	26.3740	−	15.2270i	1.01664	−	0.586959i	0.913130	+	0.407669i	$0.133658\pi$
$674$	−0.436664	+	0.436664i	−0.0168197	+	0.0168197i
$675$	1.87708	+	3.25120i	0.0722489	+	0.125139i
$676$	−7.63525	−	10.5215i	−0.293664	−	0.404675i
$677$	24.6190	+	14.2138i	0.946185	+	0.546280i	0.891894	−	0.452245i	$-0.149377\pi$
$677$	24.6190	+	14.2138i	0.946185	+	0.546280i	0.0542912	+	0.998525i	$0.482710\pi$
$678$	0.338763	+	0.0907714i	0.0130101	+	0.00348605i
$679$	15.8660	−	24.7431i	0.608882	−	0.949552i
$680$	2.37992	+	1.37405i	0.0912656	+	0.0526922i
$681$	24.1898	−	6.48163i	0.926954	−	0.248377i
$682$	26.6346	−	26.6346i	1.01989	−	1.01989i
$683$	31.2496	−	31.2496i	1.19573	−	1.19573i	0.220299	−	0.975432i	$-0.429297\pi$
$683$	31.2496	−	31.2496i	1.19573	−	1.19573i	0.975432	−	0.220299i	$-0.0707035\pi$
$684$	−0.161344	+	0.0432320i	−0.00616914	+	0.00165302i
$685$	−32.9050	−	18.9977i	−1.25724	−	0.725866i
$686$	−18.3397	−	2.58000i	−0.700212	−	0.0985049i
$687$	−14.8062	−	3.96732i	−0.564893	−	0.151363i
$688$	−4.51157	−	2.60476i	−0.172002	−	0.0993054i
$689$	−5.49550	+	6.09990i	−0.209362	+	0.232388i
$690$	2.38660	+	4.13372i	0.0908564	+	0.157368i
$691$	−5.76245	+	5.76245i	−0.219214	+	0.219214i	−0.808167	−	0.588953i	$-0.799540\pi$
$691$	−5.76245	+	5.76245i	−0.219214	+	0.219214i	0.588953	+	0.808167i	$0.299540\pi$
$692$	21.0467	−	12.1513i	0.800074	−	0.461923i
$693$	−11.5411	−	0.538058i	−0.438411	−	0.0204391i
$694$	13.8299	+	13.8299i	0.524976	+	0.524976i
$695$	−15.3092	+	57.1349i	−0.580713	+	2.16725i
$696$	−2.75181	−	2.75181i	−0.104307	−	0.104307i
$697$	9.01941	+	2.41674i	0.341634	+	0.0915406i
$698$	−11.2357	+	6.48692i	−0.425277	+	0.245534i
$699$	−6.11566	−	10.5926i	−0.231316	−	0.400650i
$700$	−3.01476	+	9.46401i	−0.113947	+	0.357706i
$701$		−	15.6543i		−	0.591254i	−0.955303	−	0.295627i	$-0.904471\pi$
$701$		−	15.6543i		−	0.591254i	0.955303	−	0.295627i	$-0.0955286\pi$
$702$	−3.21211	−	1.63780i	−0.121233	−	0.0618146i
$703$	−1.00786	+	0.581889i	−0.0380122	+	0.0219464i
$704$	−4.21807	+	1.13023i	−0.158975	+	0.0425971i
$705$			26.7918i			1.00904i
$706$	−5.78982	+	10.0283i	−0.217903	+	0.377418i
$707$	−20.0903	+	4.39170i	−0.755575	+	0.165167i
$708$	−3.37054	+	0.903133i	−0.126673	+	0.0339418i
$709$	2.80232	+	0.750881i	0.105244	+	0.0281999i	0.311056	−	0.950391i	$-0.399317\pi$
$709$	2.80232	+	0.750881i	0.105244	+	0.0281999i	−0.205813	+	0.978591i	$0.565984\pi$
$710$	−5.69032	+	21.2366i	−0.213554	+	0.796994i
$711$	8.60780			0.322818
$712$	−12.1578			−0.455634
$713$	3.60155	−	13.4412i	0.134879	−	0.503376i
$714$	−1.32647	+	2.06863i	−0.0496418	+	0.0774164i
$715$	−34.6108	−	31.1815i	−1.29437	−	1.16612i
$716$	−4.20345	+	7.28059i	−0.157090	+	0.272088i
$717$	6.58432	+	24.5730i	0.245896	+	0.917697i
$718$	6.52206	−	11.2965i	0.243401	−	0.421583i
$719$	4.43820	+	7.68719i	0.165517	+	0.286684i	0.936839	−	0.349762i	$-0.113737\pi$
$719$	4.43820	+	7.68719i	0.165517	+	0.286684i	−0.771322	+	0.636445i	$0.780404\pi$
$720$	−2.09215	+	2.09215i	−0.0779697	+	0.0779697i
$721$	−25.1968	+	5.50797i	−0.938379	+	0.205127i
$722$	4.91034	+	18.3256i	0.182744	+	0.682010i
$723$	−5.96249	−	22.2523i	−0.221747	−	0.827572i
$724$			16.6914i			0.620330i
$725$	−12.6525	−	7.30494i	−0.469903	−	0.271299i
$726$	−5.70605	−	5.70605i	−0.211771	−	0.211771i
$727$	7.55567			0.280224			0.140112	−	0.990136i	$-0.455254\pi$
$727$	7.55567			0.280224			0.140112	+	0.990136i	$0.455254\pi$
$728$	−2.51952	−	9.20065i	−0.0933797	−	0.340999i
$729$	−1.00000			−0.0370370
$730$	13.4684	+	13.4684i	0.498489	+	0.498489i
$731$	−4.19036	−	2.41931i	−0.154986	−	0.0894813i
$732$			9.81168i			0.362650i
$733$	2.17425	+	8.11440i	0.0803076	+	0.299712i	0.994384	−	0.105829i	$-0.0337497\pi$
$733$	2.17425	+	8.11440i	0.0803076	+	0.299712i	−0.914077	+	0.405541i	$0.867083\pi$
$734$	−6.49704	−	24.2473i	−0.239810	−	0.894984i
$735$	−19.4200	−	7.19851i	−0.716317	−	0.265521i
$736$	−1.14074	+	1.14074i	−0.0420484	+	0.0420484i
$737$	11.9331	+	20.6688i	0.439563	+	0.761345i
$738$	−5.02667	+	8.70645i	−0.185034	+	0.320489i
$739$	8.32388	+	31.0652i	0.306199	+	1.14275i	0.931908	+	0.362694i	$0.118143\pi$
$739$	8.32388	+	31.0652i	0.306199	+	1.14275i	−0.625709	+	0.780056i	$0.715190\pi$
$740$	−10.3072	+	17.8525i	−0.378899	+	0.656272i
$741$	0.273570	−	0.536536i	0.0100498	−	0.0197101i
$742$	−5.35219	+	2.76611i	−0.196485	+	0.101547i
$743$	9.74900	−	36.3837i	0.357656	−	1.33479i	−0.519453	−	0.854499i	$-0.673864\pi$
$743$	9.74900	−	36.3837i	0.357656	−	1.33479i	0.877109	−	0.480291i	$-0.159469\pi$
$744$	8.62563			0.316231
$745$	28.1669			1.03196
$746$	−4.27797	+	15.9656i	−0.156628	+	0.584542i
$747$	−2.47488	−	0.663142i	−0.0905512	−	0.0242631i
$748$	−3.91776	+	1.04976i	−0.143248	+	0.0383831i
$749$	14.8435	+	16.2952i	0.542369	+	0.595413i
$750$	1.84305	−	3.19226i	0.0672988	−	0.116565i
$751$			5.65198i			0.206244i	0.994669	+	0.103122i	$0.0328831\pi$
$751$			5.65198i			0.206244i	−0.994669	+	0.103122i	$0.967117\pi$
$752$	−8.74657	+	2.34364i	−0.318954	+	0.0854636i
$753$	18.4105	−	10.6293i	0.670915	−	0.387353i
$754$	14.0125	−	0.730386i	0.510305	−	0.0265991i
$755$			44.9391i			1.63550i
$756$	−1.78167	−	1.95592i	−0.0647988	−	0.0711363i
$757$	−14.4076	−	24.9546i	−0.523652	−	0.906991i	−0.999621	−	0.0275293i	$-0.991236\pi$
$757$	−14.4076	−	24.9546i	−0.523652	−	0.906991i	0.475969	−	0.879462i	$-0.342097\pi$
$758$	−17.6272	+	10.1771i	−0.640250	+	0.369649i
$759$	−6.80483	−	1.82335i	−0.247000	−	0.0661833i
$760$	−0.349463	−	0.349463i	−0.0126764	−	0.0126764i
$761$	−9.31258	+	34.7550i	−0.337581	+	1.25987i	0.563464	+	0.826141i	$0.309468\pi$
$761$	−9.31258	+	34.7550i	−0.337581	+	1.25987i	−0.901044	+	0.433727i	$0.857198\pi$
$762$	14.8523	+	14.8523i	0.538041	+	0.538041i
$763$	−16.0361	+	8.28774i	−0.580545	+	0.300037i
$764$	12.8151	−	7.39879i	0.463633	−	0.267679i
$765$	−1.94319	+	1.94319i	−0.0702563	+	0.0702563i
$766$	−1.37138	−	2.37530i	−0.0495500	−	0.0858232i
$767$	5.71499	−	11.2085i	0.206356	−	0.404714i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	−4.05486	−	1.08650i	−0.146222	−	0.0391801i	0.184966	−	0.982745i	$-0.440783\pi$
$769$	−4.05486	−	1.08650i	−0.146222	−	0.0391801i	−0.331188	+	0.943565i	$0.607449\pi$
$770$	−15.6949	−	30.3683i	−0.565606	−	1.09440i
$771$	14.8903	+	8.59693i	0.536262	+	0.309611i
$772$	−23.9155	+	6.40813i	−0.860737	+	0.230634i
$773$	20.2779	−	20.2779i	0.729345	−	0.729345i	−0.241144	−	0.970489i	$-0.577523\pi$
$773$	20.2779	−	20.2779i	0.729345	−	0.729345i	0.970489	+	0.241144i	$0.0775226\pi$
$774$	3.68368	−	3.68368i	0.132407	−	0.132407i
$775$	31.2787	−	8.38109i	1.12356	−	0.301058i
$776$	9.62113	+	5.55476i	0.345378	+	0.199404i
$777$	−15.5174	−	9.95026i	−0.556685	−	0.356963i
$778$	−2.56322	−	0.686812i	−0.0918959	−	0.0246234i
$779$	−1.45429	−	0.839632i	−0.0521052	−	0.0300830i
$780$	−0.555299	−	10.6534i	−0.0198829	−	0.381454i
$781$	−16.2246	−	28.1018i	−0.580561	−	1.00556i
$782$	−1.05953	+	1.05953i	−0.0378886	+	0.0378886i
$783$	3.37026	−	1.94582i	0.120443	−	0.0695380i
$784$	0.651277	−	6.96964i	0.0232599	−	0.248916i
$785$	−31.6883	−	31.6883i	−1.13100	−	1.13100i
$786$	5.32281	−	19.8650i	0.189858	−	0.708561i
$787$	−19.2514	−	19.2514i	−0.686239	−	0.686239i	0.275159	−	0.961399i	$-0.411269\pi$
$787$	−19.2514	−	19.2514i	−0.686239	−	0.686239i	−0.961399	+	0.275159i	$0.911269\pi$
$788$	−18.1296	−	4.85782i	−0.645841	−	0.173053i
$789$	7.45852	−	4.30618i	0.265530	−	0.153304i
$790$	12.7341	+	22.0562i	0.453061	+	0.784724i
$791$	−0.906496	+	0.198158i	−0.0322313	+	0.00704568i
$792$		−	4.36687i		−	0.155170i
$793$	−26.2832	−	23.6790i	−0.933343	−	0.840864i
$794$	10.9475	−	6.32054i	0.388512	−	0.224308i
$795$	−6.50788	+	1.74378i	−0.230811	+	0.0618455i
$796$		−	10.9923i		−	0.389612i
$797$	7.28549	−	12.6188i	0.258065	−	0.446982i	−0.707658	−	0.706555i	$-0.750248\pi$
$797$	7.28549	−	12.6188i	0.258065	−	0.446982i	0.965724	+	0.259572i	$0.0835816\pi$
$798$	0.326709	−	0.297603i	0.0115654	−	0.0105350i
$799$	−8.12384	+	2.17678i	−0.287401	+	0.0770088i
$800$	−3.62625	−	0.971650i	−0.128207	−	0.0343530i
$801$	3.14668	−	11.7436i	0.111182	−	0.414938i
$802$	−24.2026			−0.854623
$803$	−28.1122			−0.992059
$804$	−1.41452	+	5.27908i	−0.0498864	+	0.186179i
$805$	−10.6309	−	6.81684i	−0.374689	−	0.240262i
$806$	−20.8166	+	23.1060i	−0.733234	+	0.813875i
$807$	−3.81946	+	6.61549i	−0.134451	+	0.232876i
$808$	−2.01173	−	7.50789i	−0.0707725	−	0.264127i
$809$	7.58990	−	13.1461i	0.266847	−	0.462192i	−0.701199	−	0.712965i	$-0.747352\pi$
$809$	7.58990	−	13.1461i	0.266847	−	0.462192i	0.968046	+	0.250774i	$0.0806850\pi$
$810$	−1.47937	−	2.56235i	−0.0519798	−	0.0900317i
$811$	3.93386	−	3.93386i	0.138136	−	0.138136i	−0.634657	−	0.772794i	$-0.718859\pi$
$811$	3.93386	−	3.93386i	0.138136	−	0.138136i	0.772794	+	0.634657i	$0.218859\pi$
$812$	9.81059	+	3.12516i	0.344284	+	0.109672i
$813$	−4.28087	−	15.9764i	−0.150137	−	0.560318i
$814$	−7.87459	−	29.3884i	−0.276004	−	1.03006i
$815$			23.1471i			0.810808i
$816$	−0.804367	−	0.464402i	−0.0281585	−	0.0162573i
$817$	0.615306	+	0.615306i	0.0215268	+	0.0215268i
$818$	29.0815			1.01681
$819$	9.53925	−	0.0523666i	0.333328	−	0.00182984i
$820$	−29.7453			−1.03875
$821$	−3.76251	−	3.76251i	−0.131313	−	0.131313i	0.638396	−	0.769708i	$-0.279598\pi$
$821$	−3.76251	−	3.76251i	−0.131313	−	0.131313i	−0.769708	+	0.638396i	$0.779598\pi$
$822$	11.1213	+	6.42088i	0.387899	+	0.223954i
$823$			9.98294i			0.347984i	0.984747	+	0.173992i	$0.0556666\pi$
$823$			9.98294i			0.347984i	−0.984747	+	0.173992i	$0.944333\pi$
$824$	−2.52307	−	9.41623i	−0.0878953	−	0.328030i
$825$	−4.24307	−	15.8353i	−0.147725	−	0.551316i
$826$	6.82508	−	6.21704i	0.237475	−	0.216319i
$827$	−26.7429	+	26.7429i	−0.929943	+	0.929943i	−0.997702	−	0.0677589i	$-0.978415\pi$
$827$	−26.7429	+	26.7429i	−0.929943	+	0.929943i	0.0677589	+	0.997702i	$0.478415\pi$
$828$	−0.806627	−	1.39712i	−0.0280322	−	0.0485533i
$829$	−2.85762	+	4.94955i	−0.0992494	+	0.171905i	−0.911374	−	0.411579i	$-0.864978\pi$
$829$	−2.85762	+	4.94955i	−0.0992494	+	0.171905i	0.812125	+	0.583484i	$0.198311\pi$
$830$	−1.96207	−	7.32254i	−0.0681044	−	0.254169i
$831$	−11.8892	+	20.5926i	−0.412430	+	0.714350i
$832$	3.42940	−	1.11321i	0.118893	−	0.0385935i
$833$	0.604909	−	6.47342i	0.0209588	−	0.224291i
$834$	5.17424	−	19.3105i	0.179169	−	0.668669i
$835$	−12.1141			−0.419227
$836$	0.729423			0.0252276
$837$	−2.23248	+	8.33172i	−0.0771657	+	0.287986i
$838$	−2.00914	−	0.538349i	−0.0694048	−	0.0185969i
$839$	24.9742	−	6.69183i	0.862206	−	0.231027i	0.199492	−	0.979900i	$-0.436071\pi$
$839$	24.9742	−	6.69183i	0.862206	−	0.231027i	0.662715	+	0.748872i	$0.269404\pi$
$840$	2.37600	−	7.45881i	0.0819797	−	0.257353i
$841$	6.92755	−	11.9989i	0.238881	−	0.413754i
$842$		−	33.1534i		−	1.14254i
$843$	3.47815	−	0.931968i	0.119794	−	0.0320987i
$844$	−8.33694	+	4.81334i	−0.286969	+	0.165682i
$845$	29.8782	+	24.2229i	1.02784	+	0.833293i
$846$		−	9.05511i		−	0.311321i
$847$	20.3429	+	6.48021i	0.698989	+	0.222663i
$848$	−1.13857	−	1.97205i	−0.0390985	−	0.0677206i
$849$	1.55005	−	0.894922i	0.0531976	−	0.0307136i
$850$	−3.36807	−	0.902471i	−0.115524	−	0.0309545i
$851$	−7.94785	−	7.94785i	−0.272449	−	0.272449i
$852$	1.92322	−	7.17756i	0.0658885	−	0.245899i
$853$	30.2068	+	30.2068i	1.03426	+	1.03426i	0.999392	+	0.0348675i	$0.0111009\pi$
$853$	30.2068	+	30.2068i	1.03426	+	1.03426i	0.0348675	+	0.999392i	$0.488899\pi$
$854$	−11.9186	−	23.0615i	−0.407846	−	0.789147i
$855$	0.428003	−	0.247108i	0.0146374	−	0.00845090i
$856$	−5.89104	+	5.89104i	−0.201352	+	0.201352i
$857$	6.20537	+	10.7480i	0.211971	+	0.367145i	0.952331	−	0.305065i	$-0.0986783\pi$
$857$	6.20537	+	10.7480i	0.211971	+	0.367145i	−0.740360	+	0.672211i	$0.765345\pi$
$858$	11.6978	+	10.5388i	0.399357	+	0.359787i
$859$	−39.8604	−	23.0134i	−1.36002	−	0.785207i	−0.370393	−	0.928875i	$-0.620777\pi$
$859$	−39.8604	−	23.0134i	−1.36002	−	0.785207i	−0.989626	+	0.143668i	$0.954110\pi$
$860$	14.8884	+	3.98934i	0.507691	+	0.136035i
$861$	1.23871	−	26.5698i	0.0422150	−	0.905496i
$862$	−17.0651	−	9.85251i	−0.581238	−	0.335578i
$863$	−17.3840	+	4.65804i	−0.591760	+	0.158562i	−0.542257	−	0.840212i	$-0.682430\pi$
$863$	−17.3840	+	4.65804i	−0.591760	+	0.158562i	−0.0495024	+	0.998774i	$0.515764\pi$
$864$	0.707107	−	0.707107i	0.0240563	−	0.0240563i
$865$	−50.8446	+	50.8446i	−1.72877	+	1.72877i
$866$	−19.5319	+	5.23357i	−0.663722	+	0.177844i
$867$	13.9753	+	8.06866i	0.474627	+	0.274026i
$868$	−20.2738	+	10.4778i	−0.688136	+	0.355641i
$869$	−36.3084	−	9.72880i	−1.23168	−	0.330027i
$870$	9.97175	+	5.75719i	0.338074	+	0.195187i
$871$	−10.7277	−	16.5294i	−0.363493	−	0.560078i
$872$	−3.41134	−	5.90862i	−0.115523	−	0.200091i
$873$	−7.85562	+	7.85562i	−0.265872	+	0.265872i
$874$	0.233369	−	0.134735i	0.00789381	−	0.00455749i
$875$	−0.454178	+	9.74194i	−0.0153540	+	0.329338i
$876$	−4.55208	−	4.55208i	−0.153801	−	0.153801i
$877$	−9.75638	+	36.4113i	−0.329450	+	1.22952i	0.580313	+	0.814393i	$0.302930\pi$
$877$	−9.75638	+	36.4113i	−0.329450	+	1.22952i	−0.909763	+	0.415129i	$0.863736\pi$
$878$	−23.6392	−	23.6392i	−0.797784	−	0.797784i
$879$	−4.02574	−	1.07869i	−0.135785	−	0.0363834i
$880$	11.1894	−	6.46023i	0.377196	−	0.217774i
$881$	6.87680	+	11.9110i	0.231685	+	0.401291i	0.958304	−	0.285750i	$-0.0922427\pi$
$881$	6.87680	+	11.9110i	0.231685	+	0.401291i	−0.726619	+	0.687041i	$0.758909\pi$
$882$	6.56359	+	2.43296i	0.221008	+	0.0819220i
$883$		−	15.0786i		−	0.507437i	−0.967278	−	0.253718i	$-0.918346\pi$
$883$		−	15.0786i		−	0.507437i	0.967278	−	0.253718i	$-0.0816537\pi$
$884$	3.18524	−	1.03395i	0.107131	−	0.0347755i
$885$	8.94116	−	5.16218i	0.300554	−	0.173525i
$886$	1.40424	−	0.376264i	0.0471763	−	0.0126408i
$887$			42.8002i			1.43709i	0.695480	+	0.718545i	$0.255192\pi$
$887$			42.8002i			1.43709i	−0.695480	+	0.718545i	$0.744808\pi$
$888$	3.48363	−	6.03382i	0.116903	−	0.202482i
$889$	−52.9505	−	16.8673i	−1.77590	−	0.565712i
$890$	34.7462	−	9.31021i	1.16469	−	0.312079i
$891$	4.21807	+	1.13023i	0.141311	+	0.0378641i
$892$	1.23761	−	4.61883i	0.0414383	−	0.154650i
$893$	1.51253			0.0506147
$894$	−9.51990			−0.318393
$895$	6.43783	−	24.0263i	0.215193	−	0.803111i
$896$	2.64288	+	0.123214i	0.0882924	+	0.00411628i
$897$	5.68922	+	1.21097i	0.189958	+	0.0404329i
$898$	−13.1120	+	22.7106i	−0.437552	+	0.757862i
$899$	−8.68801	−	32.4241i	−0.289761	−	1.08140i
$900$	1.87708	−	3.25120i	0.0625694	−	0.108373i
$901$	−1.05750	−	1.83165i	−0.0352306	−	0.0610211i
$902$	31.0432	−	31.0432i	1.03362	−	1.03362i
$903$	−4.18346	+	13.1329i	−0.139217	+	0.437034i
$904$	−0.0907714	−	0.338763i	−0.00301901	−	0.0112671i
$905$	−12.7819	−	47.7027i	−0.424885	−	1.58569i
$906$		−	15.1886i		−	0.504607i
$907$	6.25564	+	3.61169i	0.207715	+	0.119924i	0.600249	−	0.799813i	$-0.295068\pi$
$907$	6.25564	+	3.61169i	0.207715	+	0.119924i	−0.392534	+	0.919737i	$0.628401\pi$
$908$	−17.7081	−	17.7081i	−0.587665	−	0.587665i
$909$	7.77274			0.257806
$910$	14.2463	+	24.3654i	0.472260	+	0.807705i
$911$	19.7139			0.653149			0.326575	−	0.945171i	$-0.394106\pi$
$911$	19.7139			0.653149			0.326575	+	0.945171i	$0.394106\pi$
$912$	0.118112	+	0.118112i	0.00391108	+	0.00391108i
$913$	9.68973	+	5.59437i	0.320683	+	0.185147i
$914$			25.6170i			0.847336i
$915$	−7.51358	−	28.0411i	−0.248391	−	0.927009i
$916$	3.96732	+	14.8062i	0.131084	+	0.489212i
$917$	11.6199	+	53.1567i	0.383724	+	1.75539i
$918$	0.656763	−	0.656763i	0.0216764	−	0.0216764i
$919$	13.4774	+	23.3436i	0.444580	+	0.770034i	0.998023	−	0.0628525i	$-0.0200198\pi$
$919$	13.4774	+	23.3436i	0.444580	+	0.770034i	−0.553443	+	0.832887i	$0.686686\pi$
$920$	2.38660	−	4.13372i	0.0786840	−	0.136285i
$921$	−1.51807	−	5.66552i	−0.0500222	−	0.186685i
$922$	−7.00485	+	12.1328i	−0.230692	+	0.399571i
$923$	14.5856	+	22.4738i	0.480091	+	0.739734i
$924$	5.30459	+	10.2639i	0.174508	+	0.337659i
$925$	6.76973	−	25.2650i	0.222587	−	0.830707i
$926$	−25.6597			−0.843229
$927$	9.74840			0.320179
$928$	−1.00723	+	3.75904i	−0.0330640	+	0.123397i
$929$	0.573832	+	0.153758i	0.0188268	+	0.00504463i	0.268220	−	0.963358i	$-0.413565\pi$
$929$	0.573832	+	0.153758i	0.0188268	+	0.00504463i	−0.249393	+	0.968402i	$0.580231\pi$
$930$	−24.6514	+	6.60533i	−0.808352	+	0.216597i
$931$	−0.406391	+	1.09635i	−0.0133189	+	0.0359315i
$932$	−6.11566	+	10.5926i	−0.200325	+	0.346974i
$933$			33.4976i			1.09666i
$934$	8.23411	−	2.20632i	0.269428	−	0.0721931i
$935$	10.3928	−	6.00028i	0.339881	−	0.196230i
$936$	0.187680	+	3.60066i	0.00613453	+	0.117691i
$937$		−	6.82244i		−	0.222879i	−0.993771	−	0.111440i	$-0.964454\pi$
$937$		−	6.82244i		−	0.222879i	0.993771	−	0.111440i	$-0.0355462\pi$
$938$	−3.08797	−	14.1263i	−0.100826	−	0.461239i
$939$	7.99730	+	13.8517i	0.260982	+	0.452034i
$940$	23.2023	−	13.3959i	0.756777	−	0.436925i
$941$	20.5995	+	5.51963i	0.671526	+	0.179935i	0.578442	−	0.815723i	$-0.303661\pi$
$941$	20.5995	+	5.51963i	0.671526	+	0.179935i	0.0930839	+	0.995658i	$0.470328\pi$
$942$	10.7100	+	10.7100i	0.348952	+	0.348952i
$943$	4.19768	−	15.6660i	0.136695	−	0.510154i
$944$	2.46741	+	2.46741i	0.0803072	+	0.0803072i
$945$	6.58970	+	4.22552i	0.214363	+	0.137456i
$946$	−19.7015	+	11.3746i	−0.640550	+	0.369821i
$947$	−13.2782	+	13.2782i	−0.431484	+	0.431484i	−0.889133	−	0.457649i	$-0.848692\pi$
$947$	−13.2782	+	13.2782i	−0.431484	+	0.431484i	0.457649	+	0.889133i	$0.348692\pi$
$948$	−4.30390	−	7.45458i	−0.139784	−	0.242113i
$949$	23.1797	−	1.20821i	0.752444	−	0.0392203i
$950$	0.543066	+	0.313539i	0.0176194	+	0.0101726i
$951$	11.9966	+	3.21447i	0.389015	+	0.104236i
$952$	2.45472	+	0.114441i	0.0795578	+	0.00370906i
$953$	14.2393	+	8.22104i	0.461255	+	0.266306i	0.712572	−	0.701599i	$-0.247530\pi$
$953$	14.2393	+	8.22104i	0.461255	+	0.266306i	−0.251317	+	0.967905i	$0.580864\pi$
$954$	2.19954	−	0.589365i	0.0712128	−	0.0190814i
$955$	−30.9587	+	30.9587i	−1.00180	+	1.00180i
$956$	17.9887	−	17.9887i	0.581796	−	0.581796i
$957$	−16.4153	+	4.39845i	−0.530630	+	0.142182i
$958$	−20.8916	−	12.0618i	−0.674978	−	0.389698i
$959$	−33.9392	−	1.58228i	−1.09595	−	0.0510944i
$960$	2.85793	+	0.765779i	0.0922392	+	0.0247154i
$961$	37.5868	+	21.7008i	1.21248	+	0.700024i
$962$	7.75598	+	23.8935i	0.250063	+	0.770357i
$963$	−4.16560	−	7.21503i	−0.134234	−	0.232501i
$964$	−16.2898	+	16.2898i	−0.524660	+	0.524660i
$965$	63.4415	−	36.6279i	2.04225	−	1.17910i
$966$	3.59303	+	2.30396i	0.115604	+	0.0741288i
$967$	30.3414	+	30.3414i	0.975713	+	0.975713i	0.999712	−	0.0239988i	$-0.00763980\pi$
$967$	30.3414	+	30.3414i	0.975713	+	0.975713i	−0.0239988	+	0.999712i	$0.507640\pi$
$968$	−2.08856	+	7.79460i	−0.0671288	+	0.250528i
$969$	0.109703	+	0.109703i	0.00352416	+	0.00352416i
$970$	−31.7502	−	8.50744i	−1.01944	−	0.273157i
$971$	46.0534	−	26.5889i	1.47792	−	0.853280i	0.478235	−	0.878232i	$-0.341277\pi$
$971$	46.0534	−	26.5889i	1.47792	−	0.853280i	0.999689	+	0.0249520i	$0.00794330\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	11.2956	+	51.6729i	0.362120	+	1.65656i
$974$			25.0120i			0.801438i
$975$	4.17916	+	12.8745i	0.133840	+	0.412315i
$976$	8.49717	−	4.90584i	0.271988	−	0.157032i
$977$	−20.1081	+	5.38794i	−0.643314	+	0.172376i	−0.565704	−	0.824608i	$-0.691396\pi$
$977$	−20.1081	+	5.38794i	−0.643314	+	0.172376i	−0.0776101	+	0.996984i	$0.524729\pi$
$978$		−	7.82329i		−	0.250161i
$979$	−26.5458	+	45.9787i	−0.848409	+	1.46949i
$980$	3.47590	+	20.4174i	0.111034	+	0.652211i
$981$	6.59020	−	1.76584i	0.210409	−	0.0563789i
$982$	−27.8100	−	7.45167i	−0.887453	−	0.237792i
$983$	−10.4897	+	39.1482i	−0.334571	+	1.24863i	0.569763	+	0.821809i	$0.307035\pi$
$983$	−10.4897	+	39.1482i	−0.334571	+	1.24863i	−0.904334	+	0.426826i	$0.859632\pi$
$984$	10.0533			0.320489
$985$	55.5332			1.76943
$986$	−0.935521	+	3.49141i	−0.0297930	+	0.111189i
$987$	10.9996	+	21.2832i	0.350120	+	0.677452i
$988$	−0.601439	+	0.0313493i	−0.0191343	+	0.000997354i
$989$	−4.20214	+	7.27831i	−0.133620	+	0.231437i
$990$	3.34406	+	12.4802i	0.106281	+	0.396647i
$991$	11.6094	−	20.1081i	0.368785	−	0.638755i	−0.620591	−	0.784135i	$-0.713107\pi$
$991$	11.6094	−	20.1081i	0.368785	−	0.638755i	0.989376	+	0.145380i	$0.0464404\pi$
$992$	−4.31282	−	7.47002i	−0.136932	−	0.237173i
$993$	−0.444469	+	0.444469i	−0.0141048	+	0.0141048i
$994$	4.19847	+	19.2064i	0.133168	+	0.609190i
$995$	8.41768	+	31.4152i	0.266859	+	0.995930i
$996$	0.663142	+	2.47488i	0.0210125	+	0.0784196i
$997$			4.69984i			0.148845i	0.997227	+	0.0744227i	$0.0237114\pi$
$997$			4.69984i			0.148845i	−0.997227	+	0.0744227i	$0.976289\pi$
$998$	−9.89327	−	5.71188i	−0.313166	−	0.180806i
$999$	4.92659	+	4.92659i	0.155870	+	0.155870i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.cg.a.271.1	yes	32
7.3	odd	6		546.2.by.a.115.5	yes	32
13.6	odd	12		546.2.by.a.19.5	✓	32
91.45	even	12	inner	546.2.cg.a.409.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.a.19.5	✓	32	13.6	odd	12
546.2.by.a.115.5	yes	32	7.3	odd	6
546.2.cg.a.271.1	yes	32	1.1	even	1	trivial
546.2.cg.a.409.1	yes	32	91.45	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.866025 - 0.500000i) q^{3} +1.00000i q^{4} +(-0.765779 - 2.85793i) q^{5} +(0.258819 + 0.965926i) q^{6} +(-1.78167 - 1.95592i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.866025 - 0.500000i) q^{3} +1.00000i q^{4} +(-0.765779 - 2.85793i) q^{5} +(0.258819 + 0.965926i) q^{6} +(-1.78167 - 1.95592i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.47937 + 2.56235i) q^{10} +(-1.13023 - 4.21807i) q^{11} +(0.500000 - 0.866025i) q^{12} +(1.11321 + 3.42940i) q^{13} +(-0.123214 + 2.64288i) q^{14} +(-0.765779 + 2.85793i) q^{15} -1.00000 q^{16} -0.928803 q^{17} +(0.258819 - 0.965926i) q^{18} +(0.161344 + 0.0432320i) q^{19} +(2.85793 - 0.765779i) q^{20} +(0.565013 + 2.58472i) q^{21} +(-2.18344 + 3.78182i) q^{22} +1.61325i q^{23} +(-0.965926 + 0.258819i) q^{24} +(-3.25120 + 1.87708i) q^{25} +(1.63780 - 3.21211i) q^{26} -1.00000i q^{27} +(1.95592 - 1.78167i) q^{28} +(1.94582 + 3.37026i) q^{29} +(2.56235 - 1.47937i) q^{30} +(-8.33172 - 2.23248i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-1.13023 + 4.21807i) q^{33} +(0.656763 + 0.656763i) q^{34} +(-4.22552 + 6.58970i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(-4.92659 + 4.92659i) q^{37} +(-0.0835178 - 0.144657i) q^{38} +(0.750635 - 3.52655i) q^{39} +(-2.56235 - 1.47937i) q^{40} +(-9.71078 - 2.60200i) q^{41} +(1.42815 - 2.22720i) q^{42} +(4.51157 + 2.60476i) q^{43} +(4.21807 - 1.13023i) q^{44} +(2.09215 - 2.09215i) q^{45} +(1.14074 - 1.14074i) q^{46} +(8.74657 - 2.34364i) q^{47} +(0.866025 + 0.500000i) q^{48} +(-0.651277 + 6.96964i) q^{49} +(3.62625 + 0.971650i) q^{50} +(0.804367 + 0.464402i) q^{51} +(-3.42940 + 1.11321i) q^{52} +(1.13857 + 1.97205i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(-11.1894 + 6.46023i) q^{55} +(-2.64288 - 0.123214i) q^{56} +(-0.118112 - 0.118112i) q^{57} +(1.00723 - 3.75904i) q^{58} +(-2.46741 - 2.46741i) q^{59} +(-2.85793 - 0.765779i) q^{60} +(-8.49717 + 4.90584i) q^{61} +(4.31282 + 7.47002i) q^{62} +(0.803043 - 2.52094i) q^{63} -1.00000i q^{64} +(8.94850 - 5.80762i) q^{65} +(3.78182 - 2.18344i) q^{66} +(-5.27908 + 1.41452i) q^{67} -0.928803i q^{68} +(0.806627 - 1.39712i) q^{69} +(7.64751 - 1.67173i) q^{70} +(7.17756 - 1.92322i) q^{71} +(0.965926 + 0.258819i) q^{72} +(1.66618 - 6.21826i) q^{73} +6.96725 q^{74} +3.75417 q^{75} +(-0.0432320 + 0.161344i) q^{76} +(-6.23653 + 9.72588i) q^{77} +(-3.02443 + 1.96287i) q^{78} +(4.30390 - 7.45458i) q^{79} +(0.765779 + 2.85793i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.02667 + 8.70645i) q^{82} +(-1.81174 + 1.81174i) q^{83} +(-2.58472 + 0.565013i) q^{84} +(0.711258 + 2.65445i) q^{85} +(-1.34832 - 5.03200i) q^{86} -3.89165i q^{87} +(-3.78182 - 2.18344i) q^{88} +(-8.59688 - 8.59688i) q^{89} -2.95874 q^{90} +(4.72427 - 8.28741i) q^{91} -1.61325 q^{92} +(6.09924 + 6.09924i) q^{93} +(-7.84196 - 4.52756i) q^{94} -0.494215i q^{95} +(-0.258819 - 0.965926i) q^{96} +(2.87536 + 10.7310i) q^{97} +(5.38880 - 4.46775i) q^{98} +(3.08784 - 3.08784i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{7} + 16 q^{9}+O(q^{10}) \) 32 * q - 4 * q^7 + 16 * q^9	\( 32 q - 4 q^{7} + 16 q^{9} + 8 q^{11} + 16 q^{12} + 4 q^{14} - 32 q^{16} - 16 q^{17} + 24 q^{19} + 8 q^{21} - 4 q^{22} + 24 q^{25} - 8 q^{26} + 8 q^{28} - 12 q^{29} + 4 q^{31} + 8 q^{33} + 8 q^{34} + 40 q^{35} - 12 q^{37} - 8 q^{38} + 28 q^{39} + 28 q^{41} - 12 q^{42} + 84 q^{43} - 4 q^{44} - 40 q^{46} - 4 q^{47} - 36 q^{49} - 16 q^{50} - 20 q^{52} - 4 q^{53} - 48 q^{55} + 12 q^{56} + 12 q^{57} + 12 q^{58} - 24 q^{59} - 36 q^{61} + 40 q^{62} + 4 q^{63} + 44 q^{65} - 16 q^{67} + 8 q^{69} + 40 q^{70} + 20 q^{71} - 16 q^{73} - 40 q^{74} + 16 q^{75} - 36 q^{76} + 12 q^{77} - 20 q^{78} - 16 q^{81} - 24 q^{82} - 12 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 60 q^{89} - 48 q^{91} - 16 q^{92} - 32 q^{93} - 76 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) \) 32 * q - 4 * q^7 + 16 * q^9 + 8 * q^11 + 16 * q^12 + 4 * q^14 - 32 * q^16 - 16 * q^17 + 24 * q^19 + 8 * q^21 - 4 * q^22 + 24 * q^25 - 8 * q^26 + 8 * q^28 - 12 * q^29 + 4 * q^31 + 8 * q^33 + 8 * q^34 + 40 * q^35 - 12 * q^37 - 8 * q^38 + 28 * q^39 + 28 * q^41 - 12 * q^42 + 84 * q^43 - 4 * q^44 - 40 * q^46 - 4 * q^47 - 36 * q^49 - 16 * q^50 - 20 * q^52 - 4 * q^53 - 48 * q^55 + 12 * q^56 + 12 * q^57 + 12 * q^58 - 24 * q^59 - 36 * q^61 + 40 * q^62 + 4 * q^63 + 44 * q^65 - 16 * q^67 + 8 * q^69 + 40 * q^70 + 20 * q^71 - 16 * q^73 - 40 * q^74 + 16 * q^75 - 36 * q^76 + 12 * q^77 - 20 * q^78 - 16 * q^81 - 24 * q^82 - 12 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 60 * q^89 - 48 * q^91 - 16 * q^92 - 32 * q^93 - 76 * q^97 - 8 * q^98 + 4 * q^99

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