LMFDB - Embedded newform 546.2.bx.b.223.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(97,546)]

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, 6, 5]))

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

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

chi := DirichletCharacter("546.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bx (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:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			223.10
Character	$\chi$	$=$	546.223
Dual form			546.2.bx.b.475.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(3.01404 + 3.01404i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(0.900010 - 2.48797i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(3.01404 + 3.01404i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(0.900010 - 2.48797i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +(2.13125 + 3.69143i) q^{10} +(1.34862 - 5.03311i) q^{11} -1.00000 q^{12} +(2.96038 + 2.05819i) q^{13} +(1.51328 - 2.17025i) q^{14} +(-4.11725 - 1.10321i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.0243803 + 0.0422279i) q^{17} +(0.707107 - 0.707107i) q^{18} +(-7.20556 + 1.93072i) q^{19} +(1.10321 + 4.11725i) q^{20} +(0.464552 + 2.60465i) q^{21} +(2.60533 - 4.51256i) q^{22} +(-2.01393 + 1.16275i) q^{23} +(-0.965926 - 0.258819i) q^{24} +13.1688i q^{25} +(2.32681 + 2.75426i) q^{26} +1.00000i q^{27} +(2.02342 - 1.70464i) q^{28} +(-0.957176 - 1.65788i) q^{29} +(-3.69143 - 2.13125i) q^{30} +(0.0635996 + 0.0635996i) q^{31} +(0.258819 + 0.965926i) q^{32} +(1.34862 + 5.03311i) q^{33} +(-0.0344789 + 0.0344789i) q^{34} +(10.2115 - 4.78616i) q^{35} +(0.866025 - 0.500000i) q^{36} +(0.134039 - 0.500239i) q^{37} -7.45974 q^{38} +(-3.59286 - 0.302250i) q^{39} +4.26249i q^{40} +(2.12899 - 7.94548i) q^{41} +(-0.225410 + 2.63613i) q^{42} +(1.94416 + 1.12246i) q^{43} +(3.68449 - 3.68449i) q^{44} +(4.11725 - 1.10321i) q^{45} +(-2.24625 + 0.601881i) q^{46} +(-7.47665 + 7.47665i) q^{47} +(-0.866025 - 0.500000i) q^{48} +(-5.37996 - 4.47839i) q^{49} +(-3.40835 + 12.7201i) q^{50} -0.0487606i q^{51} +(1.53467 + 3.26263i) q^{52} -6.42739 q^{53} +(-0.258819 + 0.965926i) q^{54} +(19.2348 - 11.1052i) q^{55} +(2.39566 - 1.12286i) q^{56} +(5.27483 - 5.27483i) q^{57} +(-0.495471 - 1.84912i) q^{58} +(-3.02700 - 11.2969i) q^{59} +(-3.01404 - 3.01404i) q^{60} +(0.783854 + 0.452558i) q^{61} +(0.0449717 + 0.0778933i) q^{62} +(-1.70464 - 2.02342i) q^{63} +1.00000i q^{64} +(2.71926 + 15.1262i) q^{65} +5.21066i q^{66} +(-5.54850 - 1.48672i) q^{67} +(-0.0422279 + 0.0243803i) q^{68} +(1.16275 - 2.01393i) q^{69} +(11.1023 - 1.98015i) q^{70} +(4.13049 + 15.4152i) q^{71} +(0.965926 - 0.258819i) q^{72} +(4.68392 - 4.68392i) q^{73} +(0.258943 - 0.448502i) q^{74} +(-6.58442 - 11.4045i) q^{75} +(-7.20556 - 1.93072i) q^{76} +(-11.3084 - 7.88516i) q^{77} +(-3.39221 - 1.22185i) q^{78} +10.1690 q^{79} +(-1.10321 + 4.11725i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.11288 - 7.12372i) q^{82} +(-4.50530 - 4.50530i) q^{83} +(-0.900010 + 2.48797i) q^{84} +(-0.200760 + 0.0537934i) q^{85} +(1.58740 + 1.58740i) q^{86} +(1.65788 + 0.957176i) q^{87} +(4.51256 - 2.60533i) q^{88} +(-7.26476 - 1.94659i) q^{89} +4.26249 q^{90} +(7.78507 - 5.51295i) q^{91} -2.32549 q^{92} +(-0.0868787 - 0.0232791i) q^{93} +(-9.15699 + 5.28679i) q^{94} +(-27.5371 - 15.8985i) q^{95} +(-0.707107 - 0.707107i) q^{96} +(-4.37727 + 1.17289i) q^{97} +(-4.03755 - 5.71823i) q^{98} +(-3.68449 - 3.68449i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 8 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q + 8 * q^7 + 20 * q^9	$ 40 q + 8 q^{7} + 20 q^{9} + 8 q^{11} - 40 q^{12} - 8 q^{14} + 20 q^{16} - 16 q^{17} - 16 q^{19} + 4 q^{21} + 8 q^{22} - 32 q^{26} - 8 q^{28} + 8 q^{33} - 16 q^{34} + 40 q^{35} + 40 q^{37} + 16 q^{38} - 16 q^{39} + 4 q^{41} - 12 q^{42} + 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} - 20 q^{49} - 16 q^{50} + 8 q^{52} + 32 q^{53} + 72 q^{55} + 12 q^{56} + 8 q^{57} - 36 q^{58} - 84 q^{59} + 48 q^{61} + 4 q^{62} + 4 q^{63} - 16 q^{65} - 12 q^{68} + 8 q^{69} - 20 q^{70} - 40 q^{71} + 48 q^{73} + 8 q^{74} - 36 q^{75} - 16 q^{76} + 24 q^{77} - 8 q^{78} - 48 q^{79} - 20 q^{81} - 36 q^{83} - 8 q^{84} + 8 q^{85} - 8 q^{86} - 12 q^{89} + 32 q^{91} - 16 q^{92} - 24 q^{93} - 96 q^{95} - 8 q^{98} - 8 q^{99}+O(q^{100}) $ 40 * q + 8 * q^7 + 20 * q^9 + 8 * q^11 - 40 * q^12 - 8 * q^14 + 20 * q^16 - 16 * q^17 - 16 * q^19 + 4 * q^21 + 8 * q^22 - 32 * q^26 - 8 * q^28 + 8 * q^33 - 16 * q^34 + 40 * q^35 + 40 * q^37 + 16 * q^38 - 16 * q^39 + 4 * q^41 - 12 * q^42 + 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 - 20 * q^49 - 16 * q^50 + 8 * q^52 + 32 * q^53 + 72 * q^55 + 12 * q^56 + 8 * q^57 - 36 * q^58 - 84 * q^59 + 48 * q^61 + 4 * q^62 + 4 * q^63 - 16 * q^65 - 12 * q^68 + 8 * q^69 - 20 * q^70 - 40 * q^71 + 48 * q^73 + 8 * q^74 - 36 * q^75 - 16 * q^76 + 24 * q^77 - 8 * q^78 - 48 * q^79 - 20 * q^81 - 36 * q^83 - 8 * q^84 + 8 * q^85 - 8 * q^86 - 12 * q^89 + 32 * q^91 - 16 * q^92 - 24 * q^93 - 96 * q^95 - 8 * q^98 - 8 * 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 $

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	3.01404	+	3.01404i	1.34792	+	1.34792i	0.887920	+	0.459999i	$0.152150\pi$
$5$	3.01404	+	3.01404i	1.34792	+	1.34792i	0.459999	+	0.887920i	$0.347850\pi$
$6$	−0.965926	+	0.258819i	−0.394338	+	0.105662i
$7$	0.900010	−	2.48797i	0.340172	−	0.940363i
$7$	0.900010	−	2.48797i	0.340172	−	0.940363i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	2.13125	+	3.69143i	0.673959	+	1.16733i
$11$	1.34862	−	5.03311i	0.406623	−	1.51754i	−0.394419	−	0.918931i	$-0.629054\pi$
$11$	1.34862	−	5.03311i	0.406623	−	1.51754i	0.801042	−	0.598608i	$-0.204279\pi$
$12$	−1.00000			−0.288675
$13$	2.96038	+	2.05819i	0.821063	+	0.570838i
$13$	2.96038	+	2.05819i	0.821063	+	0.570838i
$14$	1.51328	−	2.17025i	0.404440	−	0.580024i
$15$	−4.11725	−	1.10321i	−1.06307	−	0.284849i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.0243803	+	0.0422279i	−0.00591309	+	0.0102418i	−0.868967	−	0.494870i	$-0.835216\pi$
$17$	−0.0243803	+	0.0422279i	−0.00591309	+	0.0102418i	0.863054	+	0.505112i	$0.168549\pi$
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$	−7.20556	+	1.93072i	−1.65307	+	0.442938i	−0.960470	−	0.278385i	$-0.910201\pi$
$19$	−7.20556	+	1.93072i	−1.65307	+	0.442938i	−0.692599	+	0.721323i	$0.743534\pi$
$20$	1.10321	+	4.11725i	0.246686	+	0.920645i
$21$	0.464552	+	2.60465i	0.101374	+	0.568381i
$22$	2.60533	−	4.51256i	0.555458	−	0.962081i
$23$	−2.01393	+	1.16275i	−0.419934	+	0.242449i	−0.695049	−	0.718962i	$-0.744617\pi$
$23$	−2.01393	+	1.16275i	−0.419934	+	0.242449i	0.275115	+	0.961411i	$0.411284\pi$
$24$	−0.965926	−	0.258819i	−0.197169	−	0.0528312i
$25$			13.1688i			2.63377i
$26$	2.32681	+	2.75426i	0.456326	+	0.540155i
$27$			1.00000i			0.192450i
$28$	2.02342	−	1.70464i	0.382390	−	0.322146i
$29$	−0.957176	−	1.65788i	−0.177743	−	0.307860i	0.763364	−	0.645969i	$-0.223546\pi$
$29$	−0.957176	−	1.65788i	−0.177743	−	0.307860i	−0.941107	+	0.338108i	$0.890213\pi$
$30$	−3.69143	−	2.13125i	−0.673959	−	0.389110i
$31$	0.0635996	+	0.0635996i	0.0114228	+	0.0114228i	0.712795	−	0.701372i	$-0.247429\pi$
$31$	0.0635996	+	0.0635996i	0.0114228	+	0.0114228i	−0.701372	+	0.712795i	$0.747429\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	1.34862	+	5.03311i	0.234764	+	0.876152i
$34$	−0.0344789	+	0.0344789i	−0.00591309	+	0.00591309i
$35$	10.2115	−	4.78616i	1.72606	−	0.809009i
$36$	0.866025	−	0.500000i	0.144338	−	0.0833333i
$37$	0.134039	−	0.500239i	0.0220358	−	0.0822387i	−0.954032	−	0.299704i	$-0.903112\pi$
$37$	0.134039	−	0.500239i	0.0220358	−	0.0822387i	0.976068	+	0.217465i	$0.0697788\pi$
$38$	−7.45974			−1.21013
$39$	−3.59286	−	0.302250i	−0.575318	−	0.0483987i
$40$			4.26249i			0.673959i
$41$	2.12899	−	7.94548i	0.332492	−	1.24088i	−0.574071	−	0.818805i	$-0.694637\pi$
$41$	2.12899	−	7.94548i	0.332492	−	1.24088i	0.906563	−	0.422070i	$-0.138696\pi$
$42$	−0.225410	+	2.63613i	−0.0347814	+	0.406764i
$43$	1.94416	+	1.12246i	0.296482	+	0.171174i	0.640861	−	0.767657i	$-0.278577\pi$
$43$	1.94416	+	1.12246i	0.296482	+	0.171174i	−0.344380	+	0.938831i	$0.611911\pi$
$44$	3.68449	−	3.68449i	0.555458	−	0.555458i
$45$	4.11725	−	1.10321i	0.613764	−	0.164457i
$46$	−2.24625	+	0.601881i	−0.331192	+	0.0887426i
$47$	−7.47665	+	7.47665i	−1.09058	+	1.09058i	−0.0951153	+	0.995466i	$0.530322\pi$
$47$	−7.47665	+	7.47665i	−1.09058	+	1.09058i	−0.995466	+	0.0951153i	$0.969678\pi$
$48$	−0.866025	−	0.500000i	−0.125000	−	0.0721688i
$49$	−5.37996	−	4.47839i	−0.768566	−	0.639770i
$50$	−3.40835	+	12.7201i	−0.482013	+	1.79890i
$51$		−	0.0487606i		−	0.00682785i
$52$	1.53467	+	3.26263i	0.212821	+	0.452446i
$53$	−6.42739			−0.882870			−0.441435	−	0.897293i	$-0.645530\pi$
$53$	−6.42739			−0.882870			−0.441435	+	0.897293i	$0.645530\pi$
$54$	−0.258819	+	0.965926i	−0.0352208	+	0.131446i
$55$	19.2348	−	11.1052i	2.59361	−	1.49742i
$56$	2.39566	−	1.12286i	0.320134	−	0.150048i
$57$	5.27483	−	5.27483i	0.698669	−	0.698669i
$58$	−0.495471	−	1.84912i	−0.0650585	−	0.242802i
$59$	−3.02700	−	11.2969i	−0.394082	−	1.47073i	−0.823338	−	0.567551i	$-0.807891\pi$
$59$	−3.02700	−	11.2969i	−0.394082	−	1.47073i	0.429256	−	0.903183i	$-0.358776\pi$
$60$	−3.01404	−	3.01404i	−0.389110	−	0.389110i
$61$	0.783854	+	0.452558i	0.100362	+	0.0579441i	0.549341	−	0.835598i	$-0.314879\pi$
$61$	0.783854	+	0.452558i	0.100362	+	0.0579441i	−0.448979	+	0.893542i	$0.648212\pi$
$62$	0.0449717	+	0.0778933i	0.00571141	+	0.00989246i
$63$	−1.70464	−	2.02342i	−0.214764	−	0.254926i
$64$			1.00000i			0.125000i
$65$	2.71926	+	15.1262i	0.337282	+	1.87617i
$66$			5.21066i			0.641388i
$67$	−5.54850	−	1.48672i	−0.677857	−	0.181631i	−0.0965654	−	0.995327i	$-0.530786\pi$
$67$	−5.54850	−	1.48672i	−0.677857	−	0.181631i	−0.581291	+	0.813695i	$0.697452\pi$
$68$	−0.0422279	+	0.0243803i	−0.00512089	+	0.00295655i
$69$	1.16275	−	2.01393i	0.139978	−	0.242449i
$70$	11.1023	−	1.98015i	1.32698	−	0.236673i
$71$	4.13049	+	15.4152i	0.490199	+	1.82945i	0.555409	+	0.831577i	$0.312562\pi$
$71$	4.13049	+	15.4152i	0.490199	+	1.82945i	−0.0652099	+	0.997872i	$0.520772\pi$
$72$	0.965926	−	0.258819i	0.113835	−	0.0305021i
$73$	4.68392	−	4.68392i	0.548212	−	0.548212i	−0.377712	−	0.925923i	$-0.623289\pi$
$73$	4.68392	−	4.68392i	0.548212	−	0.548212i	0.925923	+	0.377712i	$0.123289\pi$
$74$	0.258943	−	0.448502i	0.0301015	−	0.0521373i
$75$	−6.58442	−	11.4045i	−0.760303	−	1.31688i
$76$	−7.20556	−	1.93072i	−0.826534	−	0.221469i
$77$	−11.3084	−	7.88516i	−1.28872	−	0.898598i
$78$	−3.39221	−	1.22185i	−0.384092	−	0.138347i
$79$	10.1690			1.14410			0.572052	−	0.820218i	$-0.306148\pi$
$79$	10.1690			1.14410			0.572052	+	0.820218i	$0.306148\pi$
$80$	−1.10321	+	4.11725i	−0.123343	+	0.460323i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	4.11288	−	7.12372i	0.454192	−	0.786684i
$83$	−4.50530	−	4.50530i	−0.494521	−	0.494521i	0.415206	−	0.909727i	$-0.363709\pi$
$83$	−4.50530	−	4.50530i	−0.494521	−	0.494521i	−0.909727	+	0.415206i	$0.863709\pi$
$84$	−0.900010	+	2.48797i	−0.0981991	+	0.271460i
$85$	−0.200760	+	0.0537934i	−0.0217754	+	0.00583471i
$86$	1.58740	+	1.58740i	0.171174	+	0.171174i
$87$	1.65788	+	0.957176i	0.177743	+	0.102620i
$88$	4.51256	−	2.60533i	0.481041	−	0.277729i
$89$	−7.26476	−	1.94659i	−0.770063	−	0.206338i	−0.147664	−	0.989038i	$-0.547175\pi$
$89$	−7.26476	−	1.94659i	−0.770063	−	0.206338i	−0.622399	+	0.782700i	$0.713842\pi$
$90$	4.26249			0.449306
$91$	7.78507	−	5.51295i	0.816098	−	0.577914i
$92$	−2.32549			−0.242449
$93$	−0.0868787	−	0.0232791i	−0.00900890	−	0.00241393i
$94$	−9.15699	+	5.28679i	−0.944471	+	0.545291i
$95$	−27.5371	−	15.8985i	−2.82525	−	1.63116i
$96$	−0.707107	−	0.707107i	−0.0721688	−	0.0721688i
$97$	−4.37727	+	1.17289i	−0.444445	+	0.119089i	−0.474099	−	0.880472i	$-0.657226\pi$
$97$	−4.37727	+	1.17289i	−0.444445	+	0.119089i	0.0296541	+	0.999560i	$0.490559\pi$
$98$	−4.03755	−	5.71823i	−0.407854	−	0.577629i
$99$	−3.68449	−	3.68449i	−0.370305	−	0.370305i
$100$	−6.58442	+	11.4045i	−0.658442	+	1.14045i
$101$	1.27577	+	2.20970i	0.126944	+	0.219873i	0.922491	−	0.386018i	$-0.126150\pi$
$101$	1.27577	+	2.20970i	0.126944	+	0.219873i	−0.795547	+	0.605892i	$0.792816\pi$
$102$	0.0126202	−	0.0470991i	0.00124958	−	0.00466351i
$103$	10.0249			0.987783			0.493892	−	0.869523i	$-0.335574\pi$
$103$	10.0249			0.987783			0.493892	+	0.869523i	$0.335574\pi$
$104$	0.637950	+	3.54866i	0.0625561	+	0.347975i
$105$	−6.45033	+	9.25068i	−0.629488	+	0.902774i
$106$	−6.20838	−	1.66353i	−0.603011	−	0.161576i
$107$	−5.31879	−	9.21242i	−0.514187	−	0.890598i	−0.999865	−	0.0164600i	$-0.994760\pi$
$107$	−5.31879	−	9.21242i	−0.514187	−	0.890598i	0.485677	−	0.874138i	$-0.338573\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−8.98687	+	8.98687i	−0.860786	+	0.860786i	−0.991429	−	0.130644i	$-0.958296\pi$
$109$	−8.98687	+	8.98687i	−0.860786	+	0.860786i	0.130644	+	0.991429i	$0.458296\pi$
$110$	21.4536	−	5.74847i	2.04552	−	0.548095i
$111$	0.134039	+	0.500239i	0.0127224	+	0.0474806i
$112$	2.60465	−	0.464552i	0.246116	−	0.0438961i
$113$	7.83188	−	13.5652i	0.736762	−	1.27611i	−0.217184	−	0.976131i	$-0.569687\pi$
$113$	7.83188	−	13.5652i	0.736762	−	1.27611i	0.953946	−	0.299978i	$-0.0969794\pi$
$114$	6.46033	−	3.72987i	0.605065	−	0.349334i
$115$	−9.57463	−	2.56551i	−0.892839	−	0.239235i
$116$		−	1.91435i		−	0.177743i
$117$	3.26263	−	1.53467i	0.301631	−	0.141881i
$118$		−	11.6954i		−	1.07665i
$119$	0.0831192	+	0.0986629i	0.00761952	+	0.00904442i
$120$	−2.13125	−	3.69143i	−0.194555	−	0.336980i
$121$	−13.9871	−	8.07547i	−1.27156	−	0.734134i
$122$	0.640014	+	0.640014i	0.0579441	+	0.0579441i
$123$	2.12899	+	7.94548i	0.191964	+	0.716420i
$124$	0.0232791	+	0.0868787i	0.00209052	+	0.00780194i
$125$	−24.6212	+	24.6212i	−2.20218	+	2.20218i
$126$	−1.12286	−	2.39566i	−0.100032	−	0.213423i
$127$	−0.0431590	+	0.0249178i	−0.00382974	+	0.00221110i	−0.501914	−	0.864918i	$-0.667370\pi$
$127$	−0.0431590	+	0.0249178i	−0.00382974	+	0.00221110i	0.498084	+	0.867129i	$0.334037\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$	−2.24492			−0.197655
$130$	−1.28834	+	15.3145i	−0.112995	+	1.34317i
$131$		−	14.5562i		−	1.27178i	−0.771780	−	0.635890i	$-0.780633\pi$
$131$		−	14.5562i		−	1.27178i	0.771780	−	0.635890i	$-0.219367\pi$
$132$	−1.34862	+	5.03311i	−0.117382	+	0.438076i
$133$	−1.68150	+	19.6649i	−0.145804	+	1.70516i
$134$	−4.97465	−	2.87211i	−0.429744	−	0.248113i
$135$	−3.01404	+	3.01404i	−0.259407	+	0.259407i
$136$	−0.0470991	+	0.0126202i	−0.00403872	+	0.00108217i
$137$	4.92230	−	1.31893i	0.420540	−	0.112683i	−0.0423420	−	0.999103i	$-0.513482\pi$
$137$	4.92230	−	1.31893i	0.420540	−	0.112683i	0.462882	+	0.886420i	$0.346815\pi$
$138$	1.64437	−	1.64437i	0.139978	−	0.139978i
$139$	−0.168450	−	0.0972545i	−0.0142877	−	0.00824902i	0.492839	−	0.870120i	$-0.335959\pi$
$139$	−0.168450	−	0.0972545i	−0.0142877	−	0.00824902i	−0.507127	+	0.861871i	$0.669292\pi$
$140$	11.2365	+	0.960806i	0.949657	+	0.0812030i
$141$	2.73664	−	10.2133i	0.230467	−	0.860115i
$142$			15.9590i			1.33925i
$143$	14.3515	−	12.1242i	1.20013	−	1.01388i
$144$	1.00000			0.0833333
$145$	2.11194	−	7.88187i	0.175387	−	0.654553i
$146$	5.73661	−	3.31203i	0.474765	−	0.274106i
$147$	6.89838	+	1.18842i	0.568969	+	0.0980191i
$148$	0.366200	−	0.366200i	0.0301015	−	0.0301015i
$149$	−3.21737	−	12.0074i	−0.263577	−	0.983683i	−0.963116	−	0.269088i	$-0.913278\pi$
$149$	−3.21737	−	12.0074i	−0.263577	−	0.983683i	0.699538	−	0.714595i	$-0.253389\pi$
$150$	−3.40835	−	12.7201i	−0.278290	−	1.03859i
$151$	4.15720	+	4.15720i	0.338308	+	0.338308i	0.855730	−	0.517422i	$-0.173108\pi$
$151$	4.15720	+	4.15720i	0.338308	+	0.338308i	−0.517422	+	0.855730i	$0.673108\pi$
$152$	−6.46033	−	3.72987i	−0.524002	−	0.302533i
$153$	0.0243803	+	0.0422279i	0.00197103	+	0.00341392i
$154$	−8.88228	−	10.5433i	−0.715755	−	0.849605i
$155$			0.383383i			0.0307941i
$156$	−2.96038	−	2.05819i	−0.237020	−	0.164787i
$157$			1.58290i			0.126330i	0.998003	+	0.0631648i	$0.0201194\pi$
$157$			1.58290i			0.126330i	−0.998003	+	0.0631648i	$0.979881\pi$
$158$	9.82251	+	2.63193i	0.781437	+	0.209385i
$159$	5.56628	−	3.21369i	0.441435	−	0.254863i
$160$	−2.13125	+	3.69143i	−0.168490	+	0.291833i
$161$	1.08031	+	6.05708i	0.0851405	+	0.477365i
$162$	−0.258819	−	0.965926i	−0.0203347	−	0.0758903i
$163$	21.8401	−	5.85204i	1.71065	−	0.458367i	0.735065	−	0.677996i	$-0.237151\pi$
$163$	21.8401	−	5.85204i	1.71065	−	0.458367i	0.975583	+	0.219629i	$0.0704847\pi$
$164$	5.81650	−	5.81650i	0.454192	−	0.454192i
$165$	−11.1052	+	19.2348i	−0.864538	+	1.49742i
$166$	−3.18573	−	5.51784i	−0.247260	−	0.428268i
$167$	17.6596	+	4.73188i	1.36654	+	0.366164i	0.866215	−	0.499672i	$-0.166546\pi$
$167$	17.6596	+	4.73188i	1.36654	+	0.366164i	0.500328	+	0.865836i	$0.333213\pi$
$168$	−1.51328	+	2.17025i	−0.116752	+	0.167439i
$169$	4.52774	+	12.1860i	0.348288	+	0.937388i
$170$	−0.207842			−0.0159407
$171$	−1.93072	+	7.20556i	−0.147646	+	0.551023i
$172$	1.12246	+	1.94416i	0.0855869	+	0.148241i
$173$	1.65399	−	2.86479i	0.125750	−	0.217806i	−0.796276	−	0.604934i	$-0.793200\pi$
$173$	1.65399	−	2.86479i	0.125750	−	0.217806i	0.922026	+	0.387128i	$0.126533\pi$
$174$	1.35365	+	1.35365i	0.102620	+	0.102620i
$175$	32.7636	+	11.8521i	2.47670	+	0.895933i
$176$	5.03311	−	1.34862i	0.379385	−	0.101656i
$177$	8.26992	+	8.26992i	0.621605	+	0.621605i
$178$	−6.51341	−	3.76052i	−0.488200	−	0.281863i
$179$	−16.2842	+	9.40166i	−1.21714	+	0.702713i	−0.964304	−	0.264797i	$-0.914695\pi$
$179$	−16.2842	+	9.40166i	−1.21714	+	0.702713i	−0.252831	+	0.967510i	$0.581362\pi$
$180$	4.11725	+	1.10321i	0.306882	+	0.0822287i
$181$	8.02259			0.596315			0.298157	−	0.954517i	$-0.403628\pi$
$181$	8.02259			0.596315			0.298157	+	0.954517i	$0.403628\pi$
$182$	8.94666	−	3.31018i	0.663171	−	0.245367i
$183$	−0.905116			−0.0669081
$184$	−2.24625	−	0.601881i	−0.165596	−	0.0443713i
$185$	1.91173	−	1.10374i	0.140554	−	0.0811486i
$186$	−0.0778933	−	0.0449717i	−0.00571141	−	0.00329749i
$187$	0.179658	+	0.179658i	0.0131379	+	0.0131379i
$188$	−10.2133	+	2.73664i	−0.744881	+	0.199590i
$189$	2.48797	+	0.900010i	0.180973	+	0.0654661i
$190$	−22.4839	−	22.4839i	−1.63116	−	1.63116i
$191$	−3.66177	+	6.34237i	−0.264956	+	0.458917i	−0.967552	−	0.252671i	$-0.918691\pi$
$191$	−3.66177	+	6.34237i	−0.264956	+	0.458917i	0.702596	+	0.711589i	$0.252024\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	3.37529	−	12.5967i	0.242958	−	0.906733i	−0.731440	−	0.681906i	$-0.761151\pi$
$193$	3.37529	−	12.5967i	0.242958	−	0.906733i	0.974399	−	0.224828i	$-0.0721819\pi$
$194$	−4.53169			−0.325356
$195$	−9.91802	−	11.7400i	−0.710244	−	0.840719i
$196$	−2.41999	−	6.56838i	−0.172856	−	0.469170i
$197$	7.03375	+	1.88469i	0.501134	+	0.134278i	0.500526	−	0.865721i	$-0.333140\pi$
$197$	7.03375	+	1.88469i	0.501134	+	0.134278i	0.000607778		1.00000i	$0.499807\pi$
$198$	−2.60533	−	4.51256i	−0.185153	−	0.320694i
$199$	−6.95882	+	12.0530i	−0.493298	+	0.854417i	−0.999970	−	0.00772168i	$-0.997542\pi$
$199$	−6.95882	+	12.0530i	−0.493298	+	0.854417i	0.506672	+	0.862139i	$0.330875\pi$
$200$	−9.31177	+	9.31177i	−0.658442	+	0.658442i
$201$	5.54850	−	1.48672i	0.391361	−	0.104865i
$202$	0.660388	+	2.46460i	0.0464647	+	0.173409i
$203$	−4.98621	+	0.889316i	−0.349964	+	0.0624178i
$204$	0.0243803	−	0.0422279i	0.00170696	−	0.00295655i
$205$	30.3648	−	17.5311i	2.12077	−	1.22443i
$206$	9.68332	+	2.59464i	0.674669	+	0.180777i
$207$			2.32549i			0.161633i
$208$	−0.302250	+	3.59286i	−0.0209572	+	0.249120i
$209$			38.8702i			2.68871i
$210$	−8.62479	+	7.26601i	−0.595167	+	0.501402i
$211$	2.92279	+	5.06242i	0.201213	+	0.348511i	0.948920	−	0.315518i	$-0.102178\pi$
$211$	2.92279	+	5.06242i	0.201213	+	0.348511i	−0.747707	+	0.664029i	$0.768845\pi$
$212$	−5.56628	−	3.21369i	−0.382294	−	0.220717i
$213$	−11.2847	−	11.2847i	−0.773216	−	0.773216i
$214$	−2.75321	−	10.2751i	−0.188206	−	0.702393i
$215$	2.47663	+	9.24291i	0.168905	+	0.630362i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$	0.215474	−	0.100993i	0.0146273	−	0.00685588i
$218$	−11.0066	+	6.35467i	−0.745462	+	0.430393i
$219$	−1.71443	+	6.39836i	−0.115851	+	0.432361i
$220$	22.2104			1.49742
$221$	−0.159088	+	0.0748316i	−0.0107014	+	0.00503372i
$222$			0.517885i			0.0347582i
$223$	−2.68964	+	10.0379i	−0.180112	+	0.672186i	0.815513	+	0.578739i	$0.196455\pi$
$223$	−2.68964	+	10.0379i	−0.180112	+	0.672186i	−0.995624	+	0.0934466i	$0.970212\pi$
$224$	2.63613	+	0.225410i	0.176134	+	0.0150608i
$225$	11.4045	+	6.58442i	0.760303	+	0.438961i
$226$	11.0760	−	11.0760i	0.736762	−	0.736762i
$227$	−3.69249	+	0.989401i	−0.245079	+	0.0656688i	−0.379268	−	0.925287i	$-0.623824\pi$
$227$	−3.69249	+	0.989401i	−0.245079	+	0.0656688i	0.134188	+	0.990956i	$0.457157\pi$
$228$	7.20556	−	1.93072i	0.477200	−	0.127865i
$229$	−6.26815	+	6.26815i	−0.414211	+	0.414211i	−0.883203	−	0.468991i	$-0.844618\pi$
$229$	−6.26815	+	6.26815i	−0.414211	+	0.414211i	0.468991	+	0.883203i	$0.344618\pi$
$230$	−8.58438	−	4.95619i	−0.566037	−	0.326802i
$231$	13.7360	+	1.17453i	0.903761	+	0.0772785i
$232$	0.495471	−	1.84912i	0.0325292	−	0.121401i
$233$		−	12.3663i		−	0.810141i	−0.914285	−	0.405071i	$-0.867247\pi$
$233$		−	12.3663i		−	0.810141i	0.914285	−	0.405071i	$-0.132753\pi$
$234$	3.54866	−	0.637950i	0.231983	−	0.0417041i
$235$	−45.0698			−2.94003
$236$	3.02700	−	11.2969i	0.197041	−	0.735367i
$237$	−8.80662	+	5.08451i	−0.572052	+	0.330274i
$238$	0.0547511	+	0.116814i	0.00354899	+	0.00757192i
$239$	−3.99366	+	3.99366i	−0.258328	+	0.258328i	−0.824374	−	0.566046i	$-0.808473\pi$
$239$	−3.99366	+	3.99366i	−0.258328	+	0.258328i	0.566046	+	0.824374i	$0.308473\pi$
$240$	−1.10321	−	4.11725i	−0.0712122	−	0.265767i
$241$	2.36063	+	8.81001i	0.152062	+	0.567502i	0.999339	+	0.0363516i	$0.0115736\pi$
$241$	2.36063	+	8.81001i	0.152062	+	0.567502i	−0.847277	+	0.531151i	$0.821760\pi$
$242$	−11.4204	−	11.4204i	−0.734134	−	0.734134i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	0.452558	+	0.783854i	0.0289721	+	0.0501811i
$245$	−2.71737	−	29.7134i	−0.173607	−	1.89832i
$246$			8.22577i			0.524456i
$247$	−25.3050	−	9.11470i	−1.61012	−	0.579954i
$248$			0.0899434i			0.00571141i
$249$	6.15435	+	1.64905i	0.390016	+	0.104505i
$250$	−30.1547	+	17.4098i	−1.90715	+	1.10109i
$251$	−5.83885	+	10.1132i	−0.368545	+	0.638339i	−0.989338	−	0.145636i	$-0.953477\pi$
$251$	−5.83885	+	10.1132i	−0.368545	+	0.638339i	0.620793	+	0.783974i	$0.286811\pi$
$252$	−0.464552	−	2.60465i	−0.0292640	−	0.164077i
$253$	3.13620	+	11.7044i	0.197171	+	0.735852i
$254$	−0.0481376	+	0.0128984i	−0.00302042	+	0.000809319i
$255$	0.146966	−	0.146966i	0.00920338	−	0.00920338i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	0.0151525	+	0.0262448i	0.000945184	+	0.00163711i	0.866498	−	0.499181i	$-0.166366\pi$
$257$	0.0151525	+	0.0262448i	0.000945184	+	0.00163711i	−0.865552	+	0.500818i	$0.833032\pi$
$258$	−2.16843	−	0.581029i	−0.135001	−	0.0361733i
$259$	−1.12394	−	0.783703i	−0.0698383	−	0.0486970i
$260$	−5.20813	+	14.4593i	−0.322995	+	0.896725i
$261$	−1.91435			−0.118495
$262$	3.76742	−	14.0602i	0.232752	−	0.868642i
$263$	8.46547	+	14.6626i	0.522003	+	0.904136i	0.999672	+	0.0255963i	$0.00814844\pi$
$263$	8.46547	+	14.6626i	0.522003	+	0.904136i	−0.477669	+	0.878540i	$0.658518\pi$
$264$	−2.60533	+	4.51256i	−0.160347	+	0.277729i
$265$	−19.3724	−	19.3724i	−1.19004	−	1.19004i
$266$	−6.71384	+	18.5596i	−0.411652	+	1.13796i
$267$	7.26476	−	1.94659i	0.444596	−	0.119129i
$268$	−4.06178	−	4.06178i	−0.248113	−	0.248113i
$269$	−5.19218	−	2.99771i	−0.316573	−	0.182774i	0.333291	−	0.942824i	$-0.391841\pi$
$269$	−5.19218	−	2.99771i	−0.316573	−	0.182774i	−0.649864	+	0.760050i	$0.725174\pi$
$270$	−3.69143	+	2.13125i	−0.224653	+	0.129703i
$271$	−16.3576	−	4.38299i	−0.993651	−	0.266248i	−0.274867	−	0.961482i	$-0.588634\pi$
$271$	−16.3576	−	4.38299i	−0.993651	−	0.266248i	−0.718783	+	0.695234i	$0.755301\pi$
$272$	−0.0487606			−0.00295655
$273$	−3.98560	+	8.66689i	−0.241219	+	0.524544i
$274$	5.09594			0.307857
$275$	66.2802	+	17.7597i	3.99684	+	1.07095i
$276$	2.01393	−	1.16275i	0.121225	−	0.0699890i
$277$	−5.27184	−	3.04370i	−0.316754	−	0.182878i	0.333191	−	0.942859i	$-0.391875\pi$
$277$	−5.27184	−	3.04370i	−0.316754	−	0.182878i	−0.649945	+	0.759981i	$0.725208\pi$
$278$	−0.137539	−	0.137539i	−0.00824902	−	0.00824902i
$279$	0.0868787	−	0.0232791i	0.00520129	−	0.00139368i
$280$	10.6049	+	3.83629i	0.633766	+	0.229262i
$281$	−16.6513	−	16.6513i	−0.993336	−	0.993336i	0.00664213	−	0.999978i	$-0.497886\pi$
$281$	−16.6513	−	16.6513i	−0.993336	−	0.993336i	−0.999978	+	0.00664213i	$0.997886\pi$
$282$	5.28679	−	9.15699i	0.314824	−	0.545291i
$283$	10.9988	+	19.0504i	0.653809	+	1.13243i	0.982191	+	0.187886i	$0.0601635\pi$
$283$	10.9988	+	19.0504i	0.653809	+	1.13243i	−0.328382	+	0.944545i	$0.606503\pi$
$284$	−4.13049	+	15.4152i	−0.245100	+	0.914724i
$285$	31.7971			1.88350
$286$	17.0005	−	7.99666i	1.00526	−	0.472852i
$287$	−17.8520	−	12.4479i	−1.05377	−	0.734774i
$288$	0.965926	+	0.258819i	0.0569177	+	0.0152511i
$289$	8.49881	+	14.7204i	0.499930	+	0.865904i
$290$	4.07995	−	7.06669i	0.239583	−	0.414970i
$291$	3.20439	−	3.20439i	0.187844	−	0.187844i
$292$	6.39836	−	1.71443i	0.374435	−	0.100330i
$293$	−2.27353	−	8.48492i	−0.132821	−	0.495695i	0.867176	−	0.498001i	$-0.165932\pi$
$293$	−2.27353	−	8.48492i	−0.132821	−	0.495695i	−0.999997	+	0.00230655i	$0.999266\pi$
$294$	6.35574	+	2.93336i	0.370674	+	0.171077i
$295$	24.9258	−	43.1728i	1.45124	−	2.51362i
$296$	0.448502	−	0.258943i	0.0260686	−	0.0150507i
$297$	5.03311	+	1.34862i	0.292051	+	0.0782547i
$298$		−	12.4310i		−	0.720106i
$299$	−8.35516	−	0.702879i	−0.483192	−	0.0406485i
$300$		−	13.1688i		−	0.760303i
$301$	4.54241	−	3.82678i	0.261820	−	0.220572i
$302$	2.93958	+	5.09151i	0.169154	+	0.292983i
$303$	−2.20970	−	1.27577i	−0.126944	−	0.0732911i
$304$	−5.27483	−	5.27483i	−0.302533	−	0.302533i
$305$	0.998537	+	3.72659i	0.0571761	+	0.213384i
$306$	0.0126202	+	0.0470991i	0.000721447	+	0.00269248i
$307$	13.6193	−	13.6193i	0.777292	−	0.777292i	−0.202077	−	0.979370i	$-0.564769\pi$
$307$	13.6193	−	13.6193i	0.777292	−	0.777292i	0.979370	+	0.202077i	$0.0647693\pi$
$308$	−5.85081	−	12.4830i	−0.333381	−	0.711283i
$309$	−8.68182	+	5.01245i	−0.493892	+	0.285148i
$310$	−0.0992269	+	0.370320i	−0.00563571	+	0.0210327i
$311$	17.5285			0.993952			0.496976	−	0.867764i	$-0.334444\pi$
$311$	17.5285			0.993952			0.496976	+	0.867764i	$0.334444\pi$
$312$	−2.32681	−	2.75426i	−0.131730	−	0.155929i
$313$			6.10565i			0.345112i	0.985000	+	0.172556i	$0.0552025\pi$
$313$			6.10565i			0.345112i	−0.985000	+	0.172556i	$0.944797\pi$
$314$	−0.409686	+	1.52897i	−0.0231199	+	0.0862847i
$315$	0.960806	−	11.2365i	0.0541353	−	0.633104i
$316$	8.80662	+	5.08451i	0.495411	+	0.286026i
$317$	3.34794	−	3.34794i	0.188039	−	0.188039i	−0.606809	−	0.794848i	$-0.707551\pi$
$317$	3.34794	−	3.34794i	0.188039	−	0.188039i	0.794848	+	0.606809i	$0.207551\pi$
$318$	6.20838	−	1.66353i	0.348149	−	0.0932862i
$319$	−9.63514	+	2.58173i	−0.539464	+	0.144549i
$320$	−3.01404	+	3.01404i	−0.168490	+	0.168490i
$321$	9.21242	+	5.31879i	0.514187	+	0.296866i
$322$	−0.524188	+	6.13030i	−0.0292118	+	0.341628i
$323$	0.0941432	−	0.351347i	0.00523827	−	0.0195495i
$324$		−	1.00000i		−	0.0555556i
$325$	−27.1039	+	38.9848i	−1.50345	+	2.16249i
$326$	22.6105			1.25228
$327$	3.28942	−	12.2763i	0.181905	−	0.678880i
$328$	7.12372	−	4.11288i	0.393342	−	0.227096i
$329$	11.8726	+	25.3307i	0.654558	+	1.39653i
$330$	−15.7051	+	15.7051i	−0.864538	+	0.864538i
$331$	−3.07253	−	11.4669i	−0.168882	−	0.630275i	−0.997513	−	0.0704806i	$-0.977547\pi$
$331$	−3.07253	−	11.4669i	−0.168882	−	0.630275i	0.828631	−	0.559795i	$-0.189120\pi$
$332$	−1.64905	−	6.15435i	−0.0905036	−	0.337764i
$333$	−0.366200	−	0.366200i	−0.0200676	−	0.0200676i
$334$	15.8332	+	9.14129i	0.866353	+	0.500189i
$335$	−12.2424	−	21.2044i	−0.668872	−	1.15852i
$336$	−2.02342	+	1.70464i	−0.110386	+	0.0929956i
$337$			20.5099i			1.11725i	0.829421	+	0.558624i	$0.188670\pi$
$337$			20.5099i			1.11725i	−0.829421	+	0.558624i	$0.811330\pi$
$338$	1.21948	+	12.9427i	0.0663311	+	0.703989i
$339$			15.6638i			0.850739i
$340$	−0.200760	−	0.0537934i	−0.0108877	−	0.00291736i
$341$	0.405875	−	0.234332i	0.0219794	−	0.0126898i
$342$	−3.72987	+	6.46033i	−0.201688	+	0.349334i
$343$	−15.9841	+	9.35458i	−0.863061	+	0.505100i
$344$	0.581029	+	2.16843i	0.0313270	+	0.116914i
$345$	9.57463	−	2.56551i	0.515481	−	0.138123i
$346$	2.33909	−	2.33909i	0.125750	−	0.125750i
$347$	−1.19412	+	2.06827i	−0.0641035	+	0.111030i	−0.896296	−	0.443456i	$-0.853752\pi$
$347$	−1.19412	+	2.06827i	−0.0641035	+	0.111030i	0.832192	+	0.554487i	$0.187085\pi$
$348$	0.957176	+	1.65788i	0.0513100	+	0.0888716i
$349$	−1.85462	−	0.496943i	−0.0992753	−	0.0266007i	0.208839	−	0.977950i	$-0.433031\pi$
$349$	−1.85462	−	0.496943i	−0.0992753	−	0.0266007i	−0.308115	+	0.951349i	$0.599698\pi$
$350$	28.5797	+	19.9281i	1.52765	+	1.06520i
$351$	−2.05819	+	2.96038i	−0.109858	+	0.158014i
$352$	5.21066			0.277729
$353$	2.04294	−	7.62435i	0.108735	−	0.405803i	−0.890007	−	0.455946i	$-0.849301\pi$
$353$	2.04294	−	7.62435i	0.108735	−	0.405803i	0.998742	+	0.0501428i	$0.0159677\pi$
$354$	5.84772	+	10.1285i	0.310803	+	0.538326i
$355$	−34.0126	+	58.9115i	−1.80520	+	3.12670i
$356$	−5.31817	−	5.31817i	−0.281863	−	0.281863i
$357$	−0.121315	−	0.0438850i	−0.00642066	−	0.00232264i
$358$	−18.1626	+	4.86666i	−0.959924	+	0.257211i
$359$	−1.24104	−	1.24104i	−0.0654994	−	0.0654994i	0.673598	−	0.739098i	$-0.264748\pi$
$359$	−1.24104	−	1.24104i	−0.0654994	−	0.0654994i	−0.739098	+	0.673598i	$0.764748\pi$
$360$	3.69143	+	2.13125i	0.194555	+	0.112327i
$361$	31.7379	−	18.3239i	1.67042	−	0.964415i
$362$	7.74923	+	2.07640i	0.407290	+	0.109133i
$363$	16.1509			0.847705
$364$	9.49855	−	0.881817i	0.497859	−	0.0462198i
$365$	28.2350			1.47789
$366$	−0.874275	−	0.234261i	−0.0456991	−	0.0122450i
$367$	−4.81952	+	2.78255i	−0.251577	+	0.145248i	−0.620486	−	0.784217i	$-0.713065\pi$
$367$	−4.81952	+	2.78255i	−0.251577	+	0.145248i	0.368909	+	0.929465i	$0.379731\pi$
$368$	−2.01393	−	1.16275i	−0.104984	−	0.0606123i
$369$	−5.81650	−	5.81650i	−0.302795	−	0.302795i
$370$	2.13226	−	0.571338i	0.110851	−	0.0297025i
$371$	−5.78471	+	15.9911i	−0.300327	+	0.830218i
$372$	−0.0635996	−	0.0635996i	−0.00329749	−	0.00329749i
$373$	−12.5991	+	21.8222i	−0.652356	+	1.12991i	0.330194	+	0.943913i	$0.392886\pi$
$373$	−12.5991	+	21.8222i	−0.652356	+	1.12991i	−0.982550	+	0.186000i	$0.940448\pi$
$374$	0.127037	+	0.220035i	0.00656895	+	0.0113777i
$375$	9.01197	−	33.6331i	0.465376	−	1.73681i
$376$	−10.5736			−0.545291
$377$	0.578612	−	6.87800i	0.0298000	−	0.354235i
$378$	2.17025	+	1.51328i	0.111626	+	0.0778345i
$379$	−11.7156	−	3.13917i	−0.601788	−	0.161249i	−0.0549527	−	0.998489i	$-0.517501\pi$
$379$	−11.7156	−	3.13917i	−0.601788	−	0.161249i	−0.546835	+	0.837240i	$0.684167\pi$
$380$	−15.8985	−	27.5371i	−0.815578	−	1.41262i
$381$	0.0249178	−	0.0431590i	0.00127658	−	0.00221110i
$382$	−5.17852	+	5.17852i	−0.264956	+	0.264956i
$383$	2.48689	−	0.666359i	0.127074	−	0.0340493i	−0.194722	−	0.980859i	$-0.562380\pi$
$383$	2.48689	−	0.666359i	0.127074	−	0.0340493i	0.321795	+	0.946809i	$0.395714\pi$
$384$	−0.258819	−	0.965926i	−0.0132078	−	0.0492922i
$385$	−10.3179	−	57.8502i	−0.525848	−	2.94832i
$386$	6.52055	−	11.2939i	0.331887	−	0.574846i
$387$	1.94416	−	1.12246i	0.0988273	−	0.0570579i
$388$	−4.37727	−	1.17289i	−0.222222	−	0.0595443i
$389$			38.1327i			1.93341i	0.255902	+	0.966703i	$0.417628\pi$
$389$			38.1327i			1.93341i	−0.255902	+	0.966703i	$0.582372\pi$
$390$	−6.54154	−	13.9069i	−0.331244	−	0.704206i
$391$		−	0.113392i		−	0.00573450i
$392$	−0.637508	−	6.97091i	−0.0321990	−	0.352084i
$393$	7.27810	+	12.6060i	0.367131	+	0.635890i
$394$	6.30629	+	3.64094i	0.317706	+	0.183428i
$395$	30.6498	+	30.6498i	1.54216	+	1.54216i
$396$	−1.34862	−	5.03311i	−0.0677706	−	0.252923i
$397$	2.76645	+	10.3245i	0.138844	+	0.518173i	0.999952	+	0.00975161i	$0.00310408\pi$
$397$	2.76645	+	10.3245i	0.138844	+	0.518173i	−0.861108	+	0.508421i	$0.830229\pi$
$398$	−9.84126	+	9.84126i	−0.493298	+	0.493298i
$399$	−8.37621	−	17.8710i	−0.419335	−	0.894670i
$400$	−11.4045	+	6.58442i	−0.570227	+	0.329221i
$401$	1.28227	−	4.78549i	0.0640334	−	0.238976i	−0.926490	−	0.376319i	$-0.877190\pi$
$401$	1.28227	−	4.78549i	0.0640334	−	0.238976i	0.990524	+	0.137343i	$0.0438563\pi$
$402$	5.74423			0.286496
$403$	0.0573794	+	0.319179i	0.00285827	+	0.0158994i
$404$			2.55154i			0.126944i
$405$	1.10321	−	4.11725i	0.0548191	−	0.204588i
$406$	−5.04648	−	0.431513i	−0.250453	−	0.0214156i
$407$	−2.33699	−	1.34926i	−0.115840	−	0.0668804i
$408$	0.0344789	−	0.0344789i	0.00170696	−	0.00170696i
$409$	−7.87188	+	2.10926i	−0.389239	+	0.104296i	−0.448131	−	0.893968i	$-0.647910\pi$
$409$	−7.87188	+	2.10926i	−0.389239	+	0.104296i	0.0588914	+	0.998264i	$0.481243\pi$
$410$	33.8675	−	9.07478i	1.67260	−	0.448172i
$411$	−3.60337	+	3.60337i	−0.177741	+	0.177741i
$412$	8.68182	+	5.01245i	0.427723	+	0.246946i
$413$	−30.8307	−	2.63626i	−1.51708	−	0.129722i
$414$	−0.601881	+	2.24625i	−0.0295809	+	0.110397i
$415$		−	27.1583i		−	1.33315i
$416$	−1.22185	+	3.39221i	−0.0599062	+	0.166317i
$417$	0.194509			0.00952515
$418$	−10.0603	+	37.5457i	−0.492067	+	1.83642i
$419$	−6.03311	+	3.48322i	−0.294737	+	0.170166i	−0.640076	−	0.768312i	$-0.721097\pi$
$419$	−6.03311	+	3.48322i	−0.294737	+	0.170166i	0.345339	+	0.938478i	$0.387764\pi$
$420$	−10.2115	+	4.78616i	−0.498270	+	0.233541i
$421$	−15.8352	+	15.8352i	−0.771760	+	0.771760i	−0.978414	−	0.206654i	$-0.933743\pi$
$421$	−15.8352	+	15.8352i	−0.771760	+	0.771760i	0.206654	+	0.978414i	$0.433743\pi$
$422$	1.51295	+	5.64639i	0.0736491	+	0.274862i
$423$	2.73664	+	10.2133i	0.133060	+	0.496587i
$424$	−4.54485	−	4.54485i	−0.220717	−	0.220717i
$425$	−0.556092	−	0.321060i	−0.0269744	−	0.0155737i
$426$	−7.97950	−	13.8209i	−0.386608	−	0.669625i
$427$	1.83143	−	1.54290i	0.0886289	−	0.0746660i
$428$		−	10.6376i		−	0.514187i
$429$	−6.36665	+	17.6756i	−0.307385	+	0.853388i
$430$			9.56897i			0.461457i
$431$	−15.7679	−	4.22500i	−0.759513	−	0.203511i	−0.141779	−	0.989898i	$-0.545282\pi$
$431$	−15.7679	−	4.22500i	−0.759513	−	0.203511i	−0.617734	+	0.786387i	$0.711949\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$	5.01068	−	8.67875i	0.240798	−	0.417074i	−0.720144	−	0.693825i	$-0.755924\pi$
$433$	5.01068	−	8.67875i	0.240798	−	0.417074i	0.960942	+	0.276750i	$0.0892576\pi$
$434$	0.234271	−	0.0417834i	0.0112454	−	0.00200567i
$435$	2.11194	+	7.88187i	0.101260	+	0.377907i
$436$	−12.2763	+	3.28942i	−0.587928	+	0.157535i
$437$	12.2666	−	12.2666i	0.586790	−	0.586790i
$438$	−3.31203	+	5.73661i	−0.158255	+	0.274106i
$439$	−0.672328	−	1.16451i	−0.0320885	−	0.0555788i	0.849535	−	0.527532i	$-0.176882\pi$
$439$	−0.672328	−	1.16451i	−0.0320885	−	0.0555788i	−0.881624	+	0.471953i	$0.843549\pi$
$440$	21.4536	+	5.74847i	1.02276	+	0.274048i
$441$	−6.56838	+	2.41999i	−0.312780	+	0.115238i
$442$	−0.173035	+	0.0311068i	−0.00823044	+	0.00147960i
$443$	−8.80913			−0.418534			−0.209267	−	0.977859i	$-0.567108\pi$
$443$	−8.80913			−0.418534			−0.209267	+	0.977859i	$0.567108\pi$
$444$	−0.134039	+	0.500239i	−0.00636119	+	0.0237403i
$445$	−16.0292	−	27.7633i	−0.759856	−	1.31611i
$446$	−5.19599	+	8.99971i	−0.246037	+	0.426149i
$447$	8.79002	+	8.79002i	0.415753	+	0.415753i
$448$	2.48797	+	0.900010i	0.117545	+	0.0425215i
$449$	7.15942	−	1.91836i	0.337874	−	0.0905330i	−0.0858929	−	0.996304i	$-0.527374\pi$
$449$	7.15942	−	1.91836i	0.337874	−	0.0905330i	0.423767	+	0.905771i	$0.360708\pi$
$450$	9.31177	+	9.31177i	0.438961	+	0.438961i
$451$	−37.1193	−	21.4308i	−1.74788	−	1.00914i
$452$	13.5652	−	7.83188i	0.638054	−	0.368381i
$453$	−5.67884	−	1.52164i	−0.266815	−	0.0714929i
$454$	−3.82275			−0.179411
$455$	40.0807	+	6.84827i	1.87901	+	0.321052i
$456$	7.45974			0.349334
$457$	32.4340	+	8.69067i	1.51720	+	0.406532i	0.918819	−	0.394680i	$-0.129145\pi$
$457$	32.4340	+	8.69067i	1.51720	+	0.406532i	0.598380	+	0.801212i	$0.295811\pi$
$458$	−7.67689	+	4.43225i	−0.358718	+	0.207106i
$459$	−0.0422279	−	0.0243803i	−0.00197103	−	0.00113797i
$460$	−7.00911	−	7.00911i	−0.326802	−	0.326802i
$461$	35.1799	−	9.42643i	1.63849	−	0.439033i	0.682133	−	0.731228i	$-0.261052\pi$
$461$	35.1799	−	9.42643i	1.63849	−	0.439033i	0.956359	+	0.292195i	$0.0943858\pi$
$462$	12.9639	+	4.68964i	0.603137	+	0.218182i
$463$	−2.84290	−	2.84290i	−0.132121	−	0.132121i	0.637954	−	0.770075i	$-0.279781\pi$
$463$	−2.84290	−	2.84290i	−0.132121	−	0.132121i	−0.770075	+	0.637954i	$0.779781\pi$
$464$	0.957176	−	1.65788i	0.0444358	−	0.0769650i
$465$	−0.191692	−	0.332020i	−0.00888948	−	0.0153970i
$466$	3.20063	−	11.9449i	0.148266	−	0.553337i
$467$	24.4581			1.13179			0.565893	−	0.824479i	$-0.308531\pi$
$467$	24.4581			1.13179			0.565893	+	0.824479i	$0.308531\pi$
$468$	3.59286	+	0.302250i	0.166080	+	0.0139715i
$469$	−8.69260	+	12.4664i	−0.401387	+	0.575646i
$470$	−43.5341	−	11.6649i	−2.00808	−	0.538063i
$471$	−0.791452	−	1.37084i	−0.0364682	−	0.0631648i
$472$	5.84772	−	10.1285i	0.269163	−	0.466204i
$473$	8.27140	−	8.27140i	0.380319	−	0.380319i
$474$	−9.82251	+	2.63193i	−0.451163	+	0.120889i
$475$	−25.4254	−	94.8888i	−1.16660	−	4.35380i
$476$	0.0226518	+	0.127004i	0.00103825	+	0.00582123i
$477$	−3.21369	+	5.56628i	−0.147145	+	0.254863i
$478$	−4.89122	+	2.82394i	−0.223719	+	0.129164i
$479$	−24.8772	−	6.66582i	−1.13667	−	0.304569i	−0.359057	−	0.933316i	$-0.616902\pi$
$479$	−24.8772	−	6.66582i	−1.13667	−	0.304569i	−0.777610	+	0.628747i	$0.783568\pi$
$480$		−	4.26249i		−	0.194555i
$481$	1.42639	−	1.20502i	0.0650378	−	0.0549443i
$482$			9.12079i			0.415441i
$483$	−3.96412	−	4.70543i	−0.180374	−	0.214105i
$484$	−8.07547	−	13.9871i	−0.367067	−	0.635779i
$485$	−16.7284	−	9.65814i	−0.759597	−	0.438554i
$486$	0.707107	+	0.707107i	0.0320750	+	0.0320750i
$487$	−5.95026	−	22.2067i	−0.269632	−	1.00628i	−0.959354	−	0.282206i	$-0.908934\pi$
$487$	−5.95026	−	22.2067i	−0.269632	−	1.00628i	0.689722	−	0.724075i	$-0.257733\pi$
$488$	0.234261	+	0.874275i	0.0106045	+	0.0395766i
$489$	−15.9881	+	15.9881i	−0.723005	+	0.723005i
$490$	5.06562	−	29.4043i	0.228842	−	1.32835i
$491$	−10.7629	+	6.21397i	−0.485724	+	0.280433i	−0.722799	−	0.691059i	$-0.757145\pi$
$491$	−10.7629	+	6.21397i	−0.485724	+	0.280433i	0.237075	+	0.971491i	$0.423811\pi$
$492$	−2.12899	+	7.94548i	−0.0959821	+	0.358210i
$493$	0.0933449			0.00420404
$494$	−22.0837	−	15.3535i	−0.993593	−	0.690788i
$495$		−	22.2104i		−	0.998282i
$496$	−0.0232791	+	0.0868787i	−0.00104526	+	0.00390097i
$497$	42.0700	+	3.59731i	1.88710	+	0.161361i
$498$	5.51784	+	3.18573i	0.247260	+	0.142756i
$499$	11.7362	−	11.7362i	0.525383	−	0.525383i	−0.393809	−	0.919192i	$-0.628843\pi$
$499$	11.7362	−	11.7362i	0.525383	−	0.525383i	0.919192	+	0.393809i	$0.128843\pi$
$500$	−33.6331	+	9.01197i	−1.50412	+	0.403028i
$501$	−17.6596	+	4.73188i	−0.788973	+	0.211405i
$502$	−8.25738	+	8.25738i	−0.368545	+	0.368545i
$503$	16.9363	+	9.77818i	0.755153	+	0.435988i	0.827553	−	0.561388i	$-0.189732\pi$
$503$	16.9363	+	9.77818i	0.755153	+	0.435988i	−0.0723999	+	0.997376i	$0.523066\pi$
$504$	0.225410	−	2.63613i	0.0100405	−	0.117423i
$505$	−2.81490	+	10.5053i	−0.125261	+	0.467482i
$506$			12.1173i			0.538681i
$507$	−10.0142	−	8.28955i	−0.444744	−	0.368152i
$508$	−0.0498357			−0.00221110
$509$	10.4715	−	39.0800i	0.464139	−	1.73219i	−0.195588	−	0.980686i	$-0.562662\pi$
$509$	10.4715	−	39.0800i	0.464139	−	1.73219i	0.659727	−	0.751505i	$-0.270672\pi$
$510$	0.179996	−	0.103921i	0.00797036	−	0.00460169i
$511$	−7.43787	−	15.8690i	−0.329032	−	0.702004i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−1.93072	−	7.20556i	−0.0852435	−	0.318133i
$514$	0.00784349	+	0.0292723i	0.000345961	+	0.00129115i
$515$	30.2154	+	30.2154i	1.33145	+	1.33145i
$516$	−1.94416	−	1.12246i	−0.0855869	−	0.0494136i
$517$	27.5476	+	47.7139i	1.21154	+	2.09846i
$518$	−0.882807	−	1.04790i	−0.0387883	−	0.0460419i
$519$			3.30797i			0.145204i
$520$	−8.77300	+	12.6186i	−0.384722	+	0.553363i
$521$		−	9.06412i		−	0.397106i	−0.980090	−	0.198553i	$-0.936376\pi$
$521$		−	9.06412i		−	0.397106i	0.980090	−	0.198553i	$-0.0636242\pi$
$522$	−1.84912	−	0.495471i	−0.0809339	−	0.0216862i
$523$	−16.8690	+	9.73931i	−0.737629	+	0.425870i	−0.821206	−	0.570631i	$-0.806699\pi$
$523$	−16.8690	+	9.73931i	−0.737629	+	0.425870i	0.0835778	+	0.996501i	$0.473365\pi$
$524$	7.27810	−	12.6060i	0.317945	−	0.550697i
$525$	−34.3002	+	6.11761i	−1.49698	+	0.266994i
$526$	4.38205	+	16.3540i	0.191066	+	0.713070i
$527$	−0.00423626	+	0.00113510i	−0.000184534	+	4.94458e-5i
$528$	−3.68449	+	3.68449i	−0.160347	+	0.160347i
$529$	−8.79605	+	15.2352i	−0.382437	+	0.662400i
$530$	−13.6983	−	23.7262i	−0.595018	−	1.03060i
$531$	−11.2969	−	3.02700i	−0.490245	−	0.131361i
$532$	−11.2887	+	16.1895i	−0.489425	+	0.701905i
$533$	22.6559	−	19.1398i	0.981335	−	0.829038i
$534$	7.52103			0.325467
$535$	11.7355	−	43.7976i	0.507371	−	1.89354i
$536$	−2.87211	−	4.97465i	−0.124056	−	0.214872i
$537$	9.40166	−	16.2842i	0.405712	−	0.702713i
$538$	−4.23940	−	4.23940i	−0.182774	−	0.182774i
$539$	−29.7957	+	21.0383i	−1.28339	+	0.906184i
$540$	−4.11725	+	1.10321i	−0.177178	+	0.0474748i
$541$	−11.7771	−	11.7771i	−0.506336	−	0.506336i	0.407064	−	0.913400i	$-0.366553\pi$
$541$	−11.7771	−	11.7771i	−0.506336	−	0.506336i	−0.913400	+	0.407064i	$0.866553\pi$
$542$	−14.6658	−	8.46729i	−0.629949	−	0.363701i
$543$	−6.94777	+	4.01130i	−0.298157	+	0.172141i
$544$	−0.0470991	−	0.0126202i	−0.00201936	−	0.000541085i
$545$	−54.1735			−2.32054
$546$	−6.09295	+	7.34003i	−0.260754	+	0.314124i
$547$	−29.2355			−1.25002			−0.625009	−	0.780618i	$-0.714905\pi$
$547$	−29.2355			−1.25002			−0.625009	+	0.780618i	$0.714905\pi$
$548$	4.92230	+	1.31893i	0.210270	+	0.0563417i
$549$	0.783854	−	0.452558i	0.0334541	−	0.0193147i
$550$	59.4252	+	34.3091i	2.53390	+	1.46295i
$551$	10.0979	+	10.0979i	0.430185	+	0.430185i
$552$	2.24625	−	0.601881i	0.0956068	−	0.0256178i
$553$	9.15221	−	25.3002i	0.389192	−	1.07587i
$554$	−4.30444	−	4.30444i	−0.182878	−	0.182878i
$555$	−1.10374	+	1.91173i	−0.0468512	+	0.0811486i
$556$	−0.0972545	−	0.168450i	−0.00412451	−	0.00714386i
$557$	−0.459813	+	1.71604i	−0.0194829	+	0.0727111i	−0.974983	−	0.222280i	$-0.928650\pi$
$557$	−0.459813	+	1.71604i	−0.0194829	+	0.0727111i	0.955500	+	0.294991i	$0.0953167\pi$
$558$	0.0899434			0.00380761
$559$	3.44523	+	7.32436i	0.145718	+	0.309788i
$560$	9.25068	+	6.45033i	0.390913	+	0.272576i
$561$	−0.245417	−	0.0657594i	−0.0103615	−	0.00277636i
$562$	−11.7743	−	20.3936i	−0.496668	−	0.860254i
$563$	14.7835	−	25.6057i	0.623049	−	1.07915i	−0.365866	−	0.930667i	$-0.619227\pi$
$563$	14.7835	−	25.6057i	0.623049	−	1.07915i	0.988915	−	0.148484i	$-0.0474394\pi$
$564$	7.47665	−	7.47665i	0.314824	−	0.314824i
$565$	64.4917	−	17.2805i	2.71318	−	0.726996i
$566$	5.69338	+	21.2480i	0.239311	+	0.893120i
$567$	−2.60465	+	0.464552i	−0.109385	+	0.0195094i
$568$	−7.97950	+	13.8209i	−0.334812	+	0.579912i
$569$	8.69495	−	5.02003i	0.364511	−	0.210451i	−0.306547	−	0.951856i	$-0.599174\pi$
$569$	8.69495	−	5.02003i	0.364511	−	0.210451i	0.671058	+	0.741405i	$0.265840\pi$
$570$	30.7136	+	8.22969i	1.28645	+	0.344704i
$571$			32.0900i			1.34293i	0.741038	+	0.671463i	$0.234334\pi$
$571$			32.0900i			1.34293i	−0.741038	+	0.671463i	$0.765666\pi$
$572$	18.4909	−	3.32414i	0.773142	−	0.138989i
$573$		−	7.32353i		−	0.305945i
$574$	−14.0220	−	16.6441i	−0.585265	−	0.694713i
$575$	−15.3120	−	26.5212i	−0.638555	−	1.10601i
$576$	0.866025	+	0.500000i	0.0360844	+	0.0208333i
$577$	31.2900	+	31.2900i	1.30262	+	1.30262i	0.926620	+	0.375999i	$0.122700\pi$
$577$	31.2900	+	31.2900i	1.30262	+	1.30262i	0.375999	+	0.926620i	$0.377300\pi$
$578$	4.39931	+	16.4184i	0.182987	+	0.682917i
$579$	3.37529	+	12.5967i	0.140272	+	0.523503i
$580$	5.76993	−	5.76993i	0.239583	−	0.239583i
$581$	−15.2639	+	7.15423i	−0.633251	+	0.296807i
$582$	3.92456	−	2.26584i	0.162678	−	0.0939222i
$583$	−8.66809	+	32.3497i	−0.358995	+	1.33979i
$584$	6.62407			0.274106
$585$	14.4593	+	5.20813i	0.597817	+	0.215330i
$586$		−	8.78424i		−	0.362874i
$587$	−1.35057	+	5.04040i	−0.0557441	+	0.208040i	−0.988181	−	0.153294i	$-0.951012\pi$
$587$	−1.35057	+	5.04040i	−0.0557441	+	0.208040i	0.932437	+	0.361334i	$0.117679\pi$
$588$	5.37996	+	4.47839i	0.221866	+	0.184686i
$589$	−0.581064	−	0.335477i	−0.0239423	−	0.0138231i
$590$	35.2505	−	35.2505i	1.45124	−	1.45124i
$591$	−7.03375	+	1.88469i	−0.289330	+	0.0775257i
$592$	0.500239	−	0.134039i	0.0205597	−	0.00550895i
$593$	1.41136	−	1.41136i	0.0579578	−	0.0579578i	−0.677534	−	0.735492i	$-0.736951\pi$
$593$	1.41136	−	1.41136i	0.0579578	−	0.0579578i	0.735492	+	0.677534i	$0.236951\pi$
$594$	4.51256	+	2.60533i	0.185153	+	0.106898i
$595$	−0.0468495	+	0.547898i	−0.00192064	+	0.0224616i
$596$	3.21737	−	12.0074i	0.131789	−	0.491842i
$597$		−	13.9176i		−	0.569611i
$598$	−7.88855	−	2.84140i	−0.322587	−	0.116194i
$599$	−8.01399			−0.327443			−0.163721	−	0.986507i	$-0.552350\pi$
$599$	−8.01399			−0.327443			−0.163721	+	0.986507i	$0.552350\pi$
$600$	3.40835	−	12.7201i	0.139145	−	0.519297i
$601$	−12.2866	+	7.09367i	−0.501181	+	0.289357i	−0.729201	−	0.684300i	$-0.760108\pi$
$601$	−12.2866	+	7.09367i	−0.501181	+	0.289357i	0.228020	+	0.973656i	$0.426775\pi$
$602$	5.37808	−	2.52073i	0.219194	−	0.102737i
$603$	−4.06178	+	4.06178i	−0.165409	+	0.165409i
$604$	1.52164	+	5.67884i	0.0619146	+	0.231069i
$605$	−17.8179	−	66.4975i	−0.724403	−	2.70351i
$606$	−1.80421	−	1.80421i	−0.0732911	−	0.0732911i
$607$	−18.2115	−	10.5144i	−0.739181	−	0.426766i	0.0825907	−	0.996584i	$-0.473681\pi$
$607$	−18.2115	−	10.5144i	−0.739181	−	0.426766i	−0.821771	+	0.569817i	$0.807014\pi$
$608$	−3.72987	−	6.46033i	−0.151266	−	0.262001i
$609$	3.87353	−	3.26328i	0.156963	−	0.132235i
$610$			3.85805i			0.156208i
$611$	−37.5221	+	6.74542i	−1.51798	+	0.272890i
$612$			0.0487606i			0.00197103i
$613$	21.1108	+	5.65662i	0.852657	+	0.228469i	0.658574	−	0.752516i	$-0.271160\pi$
$613$	21.1108	+	5.65662i	0.852657	+	0.228469i	0.194083	+	0.980985i	$0.437827\pi$
$614$	16.6801	−	9.63027i	0.673155	−	0.388646i
$615$	−17.5311	+	30.3648i	−0.706923	+	1.22443i
$616$	−2.42062	−	13.5719i	−0.0975296	−	0.546829i
$617$	−5.29389	−	19.7571i	−0.213124	−	0.795390i	−0.986819	−	0.161831i	$-0.948260\pi$
$617$	−5.29389	−	19.7571i	−0.213124	−	0.795390i	0.773694	−	0.633559i	$-0.218407\pi$
$618$	−9.68332	+	2.59464i	−0.389520	+	0.104372i
$619$	3.17121	−	3.17121i	0.127462	−	0.127462i	−0.640498	−	0.767960i	$-0.721272\pi$
$619$	3.17121	−	3.17121i	0.127462	−	0.127462i	0.767960	+	0.640498i	$0.221272\pi$
$620$	−0.191692	+	0.332020i	−0.00769852	+	0.0133342i
$621$	−1.16275	−	2.01393i	−0.0466594	−	0.0808164i
$622$	16.9313	+	4.53672i	0.678882	+	0.181906i
$623$	−11.3814	+	16.3225i	−0.455986	+	0.653949i
$624$	−1.53467	−	3.26263i	−0.0614361	−	0.130610i
$625$	−82.5741			−3.30296
$626$	−1.58026	+	5.89760i	−0.0631598	+	0.235716i
$627$	−19.4351	−	33.6625i	−0.776162	−	1.34435i
$628$	−0.791452	+	1.37084i	−0.0315824	+	0.0547023i
$629$	0.0178561	+	0.0178561i	0.000711971	+	0.000711971i
$630$	3.83629	−	10.6049i	0.152841	−	0.422511i
$631$	17.5117	−	4.69225i	0.697130	−	0.186796i	0.107185	−	0.994239i	$-0.465816\pi$
$631$	17.5117	−	4.69225i	0.697130	−	0.186796i	0.589945	+	0.807444i	$0.299149\pi$
$632$	7.19058	+	7.19058i	0.286026	+	0.286026i
$633$	−5.06242	−	2.92279i	−0.201213	−	0.116170i
$634$	4.10038	−	2.36735i	0.162847	−	0.0940196i
$635$	−0.205186	−	0.0549794i	−0.00814256	−	0.00218179i
$636$	6.42739			0.254863
$637$	−6.70939	−	24.3307i	−0.265836	−	0.964018i
$638$	−9.97503			−0.394915
$639$	15.4152	+	4.13049i	0.609816	+	0.163400i
$640$	−3.69143	+	2.13125i	−0.145916	+	0.0842449i
$641$	−23.0338	−	13.2986i	−0.909779	−	0.525261i	−0.0294191	−	0.999567i	$-0.509366\pi$
$641$	−23.0338	−	13.2986i	−0.909779	−	0.525261i	−0.880360	+	0.474306i	$0.842699\pi$
$642$	7.52191	+	7.52191i	0.296866	+	0.296866i
$643$	−11.8505	+	3.17532i	−0.467336	+	0.125222i	−0.484800	−	0.874625i	$-0.661108\pi$
$643$	−11.8505	+	3.17532i	−0.467336	+	0.125222i	0.0174636	+	0.999848i	$0.494441\pi$
$644$	−2.09296	+	5.78575i	−0.0824744	+	0.227990i
$645$	−6.76628	−	6.76628i	−0.266422	−	0.266422i
$646$	0.181871	−	0.315009i	0.00715561	−	0.0123939i
$647$	6.62125	+	11.4683i	0.260308	+	0.450867i	0.966324	−	0.257329i	$-0.0828425\pi$
$647$	6.62125	+	11.4683i	0.260308	+	0.450867i	−0.706016	+	0.708196i	$0.749509\pi$
$648$	0.258819	−	0.965926i	0.0101674	−	0.0379452i
$649$	−60.9409			−2.39214
$650$	−36.2704	+	30.6414i	−1.42264	+	1.20186i
$651$	−0.136109	+	0.195200i	−0.00533454	+	0.00765049i
$652$	21.8401	+	5.85204i	0.855324	+	0.229183i
$653$	−15.7843	−	27.3391i	−0.617686	−	1.06986i	−0.989907	−	0.141719i	$-0.954737\pi$
$653$	−15.7843	−	27.3391i	−0.617686	−	1.06986i	0.372221	−	0.928144i	$-0.378596\pi$
$654$	6.35467	−	11.0066i	0.248487	−	0.430393i
$655$	43.8729	−	43.8729i	1.71426	−	1.71426i
$656$	7.94548	−	2.12899i	0.310219	−	0.0831229i
$657$	−1.71443	−	6.39836i	−0.0668864	−	0.249624i
$658$	4.91198	+	27.5405i	0.191489	+	1.07364i
$659$	−11.1598	+	19.3294i	−0.434725	+	0.752966i	−0.997273	−	0.0737987i	$-0.976488\pi$
$659$	−11.1598	+	19.3294i	−0.434725	+	0.752966i	0.562548	+	0.826765i	$0.309821\pi$
$660$	−19.2348	+	11.1052i	−0.748712	+	0.432269i
$661$	7.19487	+	1.92786i	0.279848	+	0.0749850i	0.396013	−	0.918245i	$-0.370394\pi$
$661$	7.19487	+	1.92786i	0.279848	+	0.0749850i	−0.116165	+	0.993230i	$0.537060\pi$
$662$		−	11.8714i		−	0.461393i
$663$	0.100358	−	0.144350i	0.00389760	−	0.00560609i
$664$		−	6.37146i		−	0.247260i
$665$	−64.3387	+	54.2025i	−2.49495	+	2.10188i
$666$	−0.258943	−	0.448502i	−0.0100338	−	0.0173791i
$667$	3.85538	+	2.22590i	0.149281	+	0.0861873i
$668$	12.9277	+	12.9277i	0.500189	+	0.500189i
$669$	−2.68964	−	10.0379i	−0.103988	−	0.388087i
$670$	−6.33711	−	23.6504i	−0.244824	−	0.913696i
$671$	3.33489	−	3.33489i	0.128742	−	0.128742i
$672$	−2.39566	+	1.12286i	−0.0924147	+	0.0433151i
$673$	−19.9491	+	11.5176i	−0.768980	+	0.443971i	−0.832511	−	0.554009i	$-0.813097\pi$
$673$	−19.9491	+	11.5176i	−0.768980	+	0.443971i	0.0635306	+	0.997980i	$0.479764\pi$
$674$	−5.30836	+	19.8111i	−0.204470	+	0.763094i
$675$	−13.1688			−0.506869
$676$	−2.17188	+	12.8173i	−0.0835339	+	0.492973i
$677$			43.4641i			1.67046i	0.549899	+	0.835231i	$0.314666\pi$
$677$			43.4641i			1.67046i	−0.549899	+	0.835231i	$0.685334\pi$
$678$	−4.05408	+	15.1300i	−0.155696	+	0.581066i
$679$	−1.02149	+	11.9461i	−0.0392010	+	0.458450i
$680$	−0.179996	−	0.103921i	−0.00690254	−	0.00398518i
$681$	2.70309	−	2.70309i	0.103583	−	0.103583i
$682$	0.452695	−	0.121299i	0.0173346	−	0.00464479i
$683$	−0.866927	+	0.232292i	−0.0331720	+	0.00888842i	−0.275367	−	0.961339i	$-0.588799\pi$
$683$	−0.866927	+	0.232292i	−0.0331720	+	0.00888842i	0.242195	+	0.970228i	$0.422133\pi$
$684$	−5.27483	+	5.27483i	−0.201688	+	0.201688i
$685$	18.8113	+	10.8607i	0.718742	+	0.414966i
$686$	−17.8606	+	4.89884i	−0.681921	+	0.187038i
$687$	2.29430	−	8.56246i	0.0875332	−	0.326678i
$688$			2.24492i			0.0855869i
$689$	−19.0275	−	13.2288i	−0.724891	−	0.503976i
$690$	9.91238			0.377358
$691$	−1.96610	+	7.33759i	−0.0747940	+	0.279135i	−0.993187	−	0.116536i	$-0.962821\pi$
$691$	−1.96610	+	7.33759i	−0.0747940	+	0.279135i	0.918393	+	0.395671i	$0.129488\pi$
$692$	2.86479	−	1.65399i	0.108903	−	0.0628751i
$693$	−12.4830	+	5.85081i	−0.474189	+	0.222254i
$694$	−1.68873	+	1.68873i	−0.0641035	+	0.0641035i
$695$	−0.214585	−	0.800843i	−0.00813968	−	0.0303777i
$696$	0.495471	+	1.84912i	0.0187808	+	0.0700908i
$697$	0.283616	+	0.283616i	0.0107427	+	0.0107427i
$698$	−1.66280	−	0.960019i	−0.0629380	−	0.0363373i
$699$	6.18314	+	10.7095i	0.233868	+	0.405071i
$700$	22.4481	+	26.6460i	0.848458	+	1.00713i
$701$			13.3276i			0.503375i	0.967809	+	0.251688i	$0.0809856\pi$
$701$			13.3276i			0.503375i	−0.967809	+	0.251688i	$0.919014\pi$
$702$	−2.75426	+	2.32681i	−0.103953	+	0.0878199i
$703$			3.86329i			0.145707i
$704$	5.03311	+	1.34862i	0.189692	+	0.0508279i
$705$	39.0316	−	22.5349i	1.47001	−	0.848713i
$706$	3.94665	−	6.83581i	0.148534	−	0.257269i
$707$	6.64587	−	1.18532i	0.249944	−	0.0445787i
$708$	3.02700	+	11.2969i	0.113762	+	0.424564i
$709$	14.3757	−	3.85196i	0.539891	−	0.144663i	0.0214389	−	0.999770i	$-0.493175\pi$
$709$	14.3757	−	3.85196i	0.539891	−	0.144663i	0.518452	+	0.855107i	$0.326509\pi$
$710$	−48.1010	+	48.1010i	−1.80520	+	1.80520i
$711$	5.08451	−	8.80662i	0.190684	−	0.330274i
$712$	−3.76052	−	6.51341i	−0.140931	−	0.244100i
$713$	−0.202036	−	0.0541353i	−0.00756629	−	0.00202738i
$714$	−0.105823	−	0.0737882i	−0.00396032	−	0.00276146i
$715$	79.7988	+	6.71308i	2.98431	+	0.251055i
$716$	−18.8033			−0.702713
$717$	1.46178	−	5.45544i	0.0545912	−	0.203737i
$718$	−0.877546	−	1.51995i	−0.0327497	−	0.0567242i
$719$	21.3794	−	37.0303i	0.797319	−	1.38100i	−0.124038	−	0.992278i	$-0.539584\pi$
$719$	21.3794	−	37.0303i	0.797319	−	1.38100i	0.921356	−	0.388719i	$-0.127082\pi$
$720$	3.01404	+	3.01404i	0.112327	+	0.112327i
$721$	9.02252	−	24.9416i	0.336016	−	0.928875i
$722$	35.3990	−	9.48514i	1.31742	−	0.353000i
$723$	−6.44937	−	6.44937i	−0.239855	−	0.239855i
$724$	6.94777	+	4.01130i	0.258212	+	0.149079i
$725$	21.8323	−	12.6049i	0.810832	−	0.468134i
$726$	15.6006	+	4.18017i	0.578993	+	0.155141i
$727$	43.5219			1.61414			0.807069	−	0.590457i	$-0.201052\pi$
$727$	43.5219			1.61414			0.807069	+	0.590457i	$0.201052\pi$
$728$	9.40312	+	1.60663i	0.348503	+	0.0595458i
$729$	−1.00000			−0.0370370
$730$	27.2729	+	7.30776i	1.00942	+	0.270472i
$731$	−0.0947985	+	0.0547319i	−0.00350625	+	0.00202433i
$732$	−0.783854	−	0.452558i	−0.0289721	−	0.0167270i
$733$	33.6698	+	33.6698i	1.24362	+	1.24362i	0.958487	+	0.285137i	$0.0920391\pi$
$733$	33.6698	+	33.6698i	1.24362	+	1.24362i	0.285137	+	0.958487i	$0.407961\pi$
$734$	−5.37548	+	1.44035i	−0.198413	+	0.0531645i
$735$	17.2100	+	24.3739i	0.634802	+	0.899045i
$736$	−1.64437	−	1.64437i	−0.0606123	−	0.0606123i
$737$	−14.9656	+	25.9212i	−0.551265	+	0.954819i
$738$	−4.11288	−	7.12372i	−0.151397	−	0.262228i
$739$	−11.1104	+	41.4645i	−0.408702	+	1.52530i	0.388423	+	0.921481i	$0.373020\pi$
$739$	−11.1104	+	41.4645i	−0.408702	+	1.52530i	−0.797125	+	0.603815i	$0.793647\pi$
$740$	2.20748			0.0811486
$741$	26.4721	−	4.75894i	0.972478	−	0.174824i
$742$	−9.72641	+	13.9491i	−0.357068	+	0.512086i
$743$	49.8437	+	13.3556i	1.82859	+	0.489968i	0.997780	−	0.0665921i	$-0.0212126\pi$
$743$	49.8437	+	13.3556i	1.82859	+	0.489968i	0.830807	+	0.556561i	$0.187879\pi$
$744$	−0.0449717	−	0.0778933i	−0.00164874	−	0.00285571i
$745$	26.4934	−	45.8880i	0.970644	−	1.68121i
$746$	−17.8178	+	17.8178i	−0.652356	+	0.652356i
$747$	−6.15435	+	1.64905i	−0.225176	+	0.0603357i
$748$	0.0657594	+	0.245417i	0.00240440	+	0.00897335i
$749$	−27.7072	+	4.94171i	−1.01240	+	0.180566i
$750$	17.4098	−	30.1547i	0.635716	−	1.10109i
$751$	11.7824	−	6.80258i	0.429946	−	0.248229i	−0.269378	−	0.963035i	$-0.586818\pi$
$751$	11.7824	−	6.80258i	0.429946	−	0.248229i	0.699324	+	0.714805i	$0.253485\pi$
$752$	−10.2133	−	2.73664i	−0.372441	−	0.0997951i
$753$		−	11.6777i		−	0.425559i
$754$	2.33905	−	6.49388i	0.0851833	−	0.236493i
$755$			25.0599i			0.912023i
$756$	1.70464	+	2.02342i	0.0619971	+	0.0735909i
$757$	16.0569	+	27.8114i	0.583599	+	1.01082i	0.995048	+	0.0993907i	$0.0316894\pi$
$757$	16.0569	+	27.8114i	0.583599	+	1.01082i	−0.411449	+	0.911433i	$0.634977\pi$
$758$	−10.5039	−	6.06442i	−0.381518	−	0.220270i
$759$	−8.56825	−	8.56825i	−0.311008	−	0.311008i
$760$	−8.22969	−	30.7136i	−0.298522	−	1.11410i
$761$	0.503892	+	1.88055i	0.0182661	+	0.0681699i	0.974457	−	0.224573i	$-0.0720987\pi$
$761$	0.503892	+	1.88055i	0.0182661	+	0.0681699i	−0.956191	+	0.292743i	$0.905432\pi$
$762$	0.0352392	−	0.0352392i	0.00127658	−	0.00127658i
$763$	14.2708	+	30.4473i	0.516636	+	1.10227i
$764$	−6.34237	+	3.66177i	−0.229459	+	0.132478i
$765$	−0.0537934	+	0.200760i	−0.00194490	+	0.00725848i
$766$	2.57461			0.0930246
$767$	14.2901	−	39.6733i	0.515985	−	1.43252i
$768$		−	1.00000i		−	0.0360844i
$769$	5.19927	−	19.4039i	0.187491	−	0.699724i	−0.806593	−	0.591107i	$-0.798691\pi$
$769$	5.19927	−	19.4039i	0.187491	−	0.699724i	0.994084	−	0.108617i	$-0.0346423\pi$
$770$	5.00643	−	58.5495i	0.180419	−	2.10998i
$771$	−0.0262448	−	0.0151525i	−0.000945184	−	0.000545702i
$772$	9.22145	−	9.22145i	0.331887	−	0.331887i
$773$	−46.9245	+	12.5734i	−1.68776	+	0.452233i	−0.969809	−	0.243865i	$-0.921585\pi$
$773$	−46.9245	+	12.5734i	−1.68776	+	0.452233i	−0.717947	+	0.696098i	$0.754918\pi$
$774$	2.16843	−	0.581029i	0.0779426	−	0.0208847i
$775$	−0.837533	+	0.837533i	−0.0300851	+	0.0300851i
$776$	−3.92456	−	2.26584i	−0.140883	−	0.0813390i
$777$	1.36521	+	0.116736i	0.0489768	+	0.00418789i
$778$	−9.86947	+	36.8334i	−0.353838	+	1.32054i
$779$			61.3621i			2.19853i
$780$	−2.71926	−	15.1262i	−0.0973650	−	0.541603i
$781$	83.1569			2.97559
$782$	0.0293481	−	0.109529i	0.00104949	−	0.00391673i
$783$	1.65788	−	0.957176i	0.0592477	−	0.0342067i
$784$	1.18842	−	6.89838i	0.0424435	−	0.246371i
$785$	−4.77093	+	4.77093i	−0.170282	+	0.170282i
$786$	3.76742	+	14.0602i	0.134379	+	0.501511i
$787$	9.36734	+	34.9594i	0.333910	+	1.24617i	0.905046	+	0.425313i	$0.139836\pi$
$787$	9.36734	+	34.9594i	0.333910	+	1.24617i	−0.571137	+	0.820855i	$0.693497\pi$
$788$	5.14906	+	5.14906i	0.183428	+	0.183428i
$789$	−14.6626	−	8.46547i	−0.522003	−	0.301379i
$790$	21.6727	+	37.5382i	0.771079	+	1.33555i
$791$	−26.7011	−	31.6943i	−0.949380	−	1.12692i
$792$		−	5.21066i		−	0.185153i
$793$	1.38906	+	2.95306i	0.0493269	+	0.104866i
$794$			10.6887i			0.379329i
$795$	26.4632	+	7.09079i	0.938552	+	0.251484i
$796$	−12.0530	+	6.95882i	−0.427209	+	0.246649i
$797$	24.8284	−	43.0040i	0.879467	−	1.52328i	0.0275395	−	0.999621i	$-0.491233\pi$
$797$	24.8284	−	43.0040i	0.879467	−	1.52328i	0.851927	−	0.523660i	$-0.175434\pi$
$798$	−3.46544	−	19.4300i	−0.122675	−	0.687815i
$799$	−0.133440	−	0.498006i	−0.00472078	−	0.0176182i
$800$	−12.7201	+	3.40835i	−0.449724	+	0.120503i
$801$	−5.31817	+	5.31817i	−0.187908	+	0.187908i
$802$	2.47715	−	4.29055i	0.0874712	−	0.151505i
$803$	−17.2579	−	29.8915i	−0.609017	−	1.05485i
$804$	5.54850	+	1.48672i	0.195680	+	0.0524324i
$805$	−15.0002	+	21.5124i	−0.528687	+	0.758212i
$806$	−0.0271854	+	0.323154i	−0.000957564	+	0.0113826i
$807$	5.99542			0.211049
$808$	−0.660388	+	2.46460i	−0.0232324	+	0.0867044i
$809$	16.7921	+	29.0848i	0.590380	+	1.02257i	0.994181	+	0.107721i	$0.0343555\pi$
$809$	16.7921	+	29.0848i	0.590380	+	1.02257i	−0.403801	+	0.914847i	$0.632311\pi$
$810$	2.13125	−	3.69143i	0.0748843	−	0.129703i
$811$	31.3548	+	31.3548i	1.10102	+	1.10102i	0.994288	+	0.106727i	$0.0340370\pi$
$811$	31.3548	+	31.3548i	1.10102	+	1.10102i	0.106727	+	0.994288i	$0.465963\pi$
$812$	−4.76284	−	1.72294i	−0.167143	−	0.0604632i
$813$	16.3576	−	4.38299i	0.573685	−	0.153718i
$814$	−1.90814	−	1.90814i	−0.0668804	−	0.0668804i
$815$	83.4651	+	48.1886i	2.92366	+	1.68797i
$816$	0.0422279	−	0.0243803i	0.00147827	−	0.000853481i
$817$	−16.1759	−	4.33433i	−0.565924	−	0.151639i
$818$	−8.14957			−0.284943
$819$	−0.881817	−	9.49855i	−0.0308132	−	0.331906i
$820$	35.0623			1.22443
$821$	−32.6396	−	8.74576i	−1.13913	−	0.305229i	−0.360530	−	0.932748i	$-0.617404\pi$
$821$	−32.6396	−	8.74576i	−1.13913	−	0.305229i	−0.778602	+	0.627518i	$0.784071\pi$
$822$	−4.41321	+	2.54797i	−0.153928	+	0.0888706i
$823$	−32.3079	−	18.6530i	−1.12618	−	0.650202i	−0.183211	−	0.983074i	$-0.558649\pi$
$823$	−32.3079	−	18.6530i	−1.12618	−	0.650202i	−0.942972	+	0.332871i	$0.891982\pi$
$824$	7.08868	+	7.08868i	0.246946	+	0.246946i
$825$	−66.2802	+	17.7597i	−2.30758	+	0.618314i
$826$	−29.0979	−	10.5260i	−1.01244	−	0.366247i
$827$	21.7373	+	21.7373i	0.755880	+	0.755880i	0.975570	−	0.219690i	$-0.0705046\pi$
$827$	21.7373	+	21.7373i	0.755880	+	0.755880i	−0.219690	+	0.975570i	$0.570505\pi$
$828$	−1.16275	+	2.01393i	−0.0404082	+	0.0699890i
$829$	−2.03760	−	3.52923i	−0.0707689	−	0.122575i	0.828470	−	0.560034i	$-0.189212\pi$
$829$	−2.03760	−	3.52923i	−0.0707689	−	0.122575i	−0.899239	+	0.437459i	$0.855879\pi$
$830$	7.02908	−	26.2329i	0.243983	−	0.910557i
$831$	6.08740			0.211170
$832$	−2.05819	+	2.96038i	−0.0713548	+	0.102633i
$833$	0.320278	−	0.118000i	0.0110970	−	0.00408846i
$834$	0.187881	+	0.0503427i	0.00650580	+	0.00174322i
$835$	38.9647	+	67.4888i	1.34843	+	2.33555i
$836$	−19.4351	+	33.6625i	−0.672176	+	1.16424i
$837$	−0.0635996	+	0.0635996i	−0.00219832	+	0.00219832i
$838$	−6.72906	+	1.80305i	−0.232451	+	0.0622852i
$839$	−0.743066	−	2.77316i	−0.0256535	−	0.0957401i	0.951912	−	0.306371i	$-0.0991148\pi$
$839$	−0.743066	−	2.77316i	−0.0256535	−	0.0957401i	−0.977566	+	0.210631i	$0.932448\pi$
$840$	−11.1023	+	1.98015i	−0.383065	+	0.0683217i
$841$	12.6676	−	21.9410i	0.436815	−	0.756585i
$842$	−19.3941	+	11.1972i	−0.668364	+	0.385880i
$843$	22.7462	+	6.09481i	0.783419	+	0.209917i
$844$			5.84558i			0.201213i
$845$	−23.0824	+	50.3760i	−0.794058	+	1.73299i
$846$			10.5736i			0.363527i
$847$	−32.6801	+	27.5315i	−1.12290	+	0.945994i
$848$	−3.21369	−	5.56628i	−0.110359	−	0.191147i
$849$	−19.0504	−	10.9988i	−0.653809	−	0.377477i
$850$	−0.454048	−	0.454048i	−0.0155737	−	0.0155737i
$851$	0.311705	+	1.16330i	0.0106851	+	0.0398774i
$852$	−4.13049	−	15.4152i	−0.141508	−	0.528116i
$853$	25.0363	−	25.0363i	0.857226	−	0.857226i	−0.133785	−	0.991010i	$-0.542713\pi$
$853$	25.0363	−	25.0363i	0.857226	−	0.857226i	0.991010	+	0.133785i	$0.0427131\pi$
$854$	2.16835	−	1.01631i	0.0741995	−	0.0347776i
$855$	−27.5371	+	15.8985i	−0.941749	+	0.543719i
$856$	2.75321	−	10.2751i	0.0941028	−	0.351196i
$857$	41.9562			1.43320			0.716598	−	0.697486i	$-0.245698\pi$
$857$	41.9562			1.43320			0.716598	+	0.697486i	$0.245698\pi$
$858$	−10.7245	+	15.4255i	−0.366128	+	0.526619i
$859$		−	28.7997i		−	0.982634i	−0.870981	−	0.491317i	$-0.836516\pi$
$859$		−	28.7997i		−	0.982634i	0.870981	−	0.491317i	$-0.163484\pi$
$860$	−2.47663	+	9.24291i	−0.0844524	+	0.315181i
$861$	21.6842	+	1.85417i	0.738996	+	0.0631898i
$862$	−14.1371	−	8.16207i	−0.481512	−	0.278001i
$863$	12.6000	−	12.6000i	0.428908	−	0.428908i	−0.459348	−	0.888256i	$-0.651917\pi$
$863$	12.6000	−	12.6000i	0.428908	−	0.428908i	0.888256	+	0.459348i	$0.151917\pi$
$864$	−0.965926	+	0.258819i	−0.0328615	+	0.00880520i
$865$	13.6198	−	3.64940i	0.463085	−	0.124083i
$866$	7.08617	−	7.08617i	0.240798	−	0.240798i
$867$	−14.7204	−	8.49881i	−0.499930	−	0.288635i
$868$	0.237103	+	0.0202741i	0.00804779	+	0.000688148i
$869$	13.7141	−	51.1817i	0.465219	−	1.73622i
$870$			8.15991i			0.276647i
$871$	−13.3657	−	15.8211i	−0.452881	−	0.536077i
$872$	−12.7093			−0.430393
$873$	−1.17289	+	4.37727i	−0.0396962	+	0.148148i
$874$	15.0234	−	8.67378i	0.508175	−	0.293395i
$875$	39.0974	+	83.4160i	1.32173	+	2.81997i
$876$	−4.68392	+	4.68392i	−0.158255	+	0.158255i
$877$	−9.68146	−	36.1317i	−0.326920	−	1.22008i	−0.912368	−	0.409371i	$-0.865748\pi$
$877$	−9.68146	−	36.1317i	−0.326920	−	1.22008i	0.585448	−	0.810710i	$-0.300919\pi$
$878$	−0.348022	−	1.29884i	−0.0117452	−	0.0438336i
$879$	6.21140	+	6.21140i	0.209505	+	0.209505i
$880$	19.2348	+	11.1052i	0.648403	+	0.374356i
$881$	22.0492	+	38.1903i	0.742855	+	1.28666i	0.951190	+	0.308606i	$0.0998624\pi$
$881$	22.0492	+	38.1903i	0.742855	+	1.28666i	−0.208335	+	0.978058i	$0.566804\pi$
$882$	−6.97091	+	0.637508i	−0.234723	+	0.0214660i
$883$		−	46.2522i		−	1.55651i	−0.627949	−	0.778254i	$-0.716105\pi$
$883$		−	46.2522i		−	1.55651i	0.627949	−	0.778254i	$-0.283895\pi$
$884$	−0.175190	−	0.0147379i	−0.00589228	−	0.000495688i
$885$			49.8517i			1.67575i
$886$	−8.50896	−	2.27997i	−0.285864	−	0.0765971i
$887$	0.770990	−	0.445131i	0.0258873	−	0.0149460i	−0.487000	−	0.873402i	$-0.661909\pi$
$887$	0.770990	−	0.445131i	0.0258873	−	0.0149460i	0.512888	+	0.858456i	$0.328576\pi$
$888$	−0.258943	+	0.448502i	−0.00868954	+	0.0150507i
$889$	0.0231513	+	0.129804i	0.000776469	+	0.00435350i
$890$	−8.29731	−	30.9660i	−0.278126	−	1.03798i
$891$	−5.03311	+	1.34862i	−0.168615	+	0.0451804i
$892$	−7.34823	+	7.34823i	−0.246037	+	0.246037i
$893$	39.4381	−	68.3088i	1.31975	−	2.28587i
$894$	6.21548	+	10.7655i	0.207877	+	0.360053i
$895$	−77.4180	−	20.7441i	−2.58780	−	0.693399i
$896$	2.17025	+	1.51328i	0.0725030	+	0.0505550i
$897$	7.58722	−	3.56887i	0.253330	−	0.119161i
$898$	7.41198			0.247341
$899$	0.0445643	−	0.166316i	0.00148630	−	0.00554696i
$900$	6.58442	+	11.4045i	0.219481	+	0.380152i
$901$	0.156702	−	0.271415i	0.00522049	−	0.00904215i
$902$	−30.3078	−	30.3078i	−1.00914	−	1.00914i
$903$	−2.02045	+	5.58530i	−0.0672365	+	0.185867i
$904$	15.1300	−	4.05408i	0.503218	−	0.134837i
$905$	24.1804	+	24.1804i	0.803783	+	0.803783i
$906$	−5.09151	−	2.93958i	−0.169154	−	0.0976611i
$907$	−40.8144	+	23.5642i	−1.35522	+	0.782437i	−0.988975	−	0.148082i	$-0.952690\pi$
$907$	−40.8144	+	23.5642i	−1.35522	+	0.782437i	−0.366245	+	0.930518i	$0.619357\pi$
$908$	−3.69249	−	0.989401i	−0.122540	−	0.0328344i
$909$	2.55154			0.0846293
$910$	36.9426	+	16.9886i	1.22463	+	0.563166i
$911$	−23.8066			−0.788747			−0.394373	−	0.918950i	$-0.629038\pi$
$911$	−23.8066			−0.788747			−0.394373	+	0.918950i	$0.629038\pi$
$912$	7.20556	+	1.93072i	0.238600	+	0.0639326i
$913$	−28.7516	+	16.5997i	−0.951539	+	0.549371i
$914$	29.0795	+	16.7891i	0.961866	+	0.555333i
$915$	−2.72805	−	2.72805i	−0.0901867	−	0.0901867i
$916$	−8.56246	+	2.29430i	−0.282912	+	0.0758059i
$917$	−36.2153	−	13.1007i	−1.19594	−	0.432624i
$918$	−0.0344789	−	0.0344789i	−0.00113797	−	0.00113797i
$919$	−14.0633	+	24.3583i	−0.463905	+	0.803506i	−0.999151	−	0.0411895i	$-0.986885\pi$
$919$	−14.0633	+	24.3583i	−0.463905	+	0.803506i	0.535247	+	0.844696i	$0.320219\pi$
$920$	−4.95619	−	8.58438i	−0.163401	−	0.283019i
$921$	−4.98499	+	18.6043i	−0.164261	+	0.613031i
$922$	36.4209			1.19946
$923$	−19.4995	+	54.1363i	−0.641835	+	1.78192i
$924$	11.3084	+	7.88516i	0.372020	+	0.259403i
$925$	6.58756	+	1.76513i	0.216598	+	0.0580372i
$926$	−2.01023	−	3.48183i	−0.0660604	−	0.114420i
$927$	5.01245	−	8.68182i	0.164631	−	0.285148i
$928$	1.35365	−	1.35365i	0.0444358	−	0.0444358i
$929$	−15.1367	+	4.05587i	−0.496619	+	0.133069i	−0.498430	−	0.866930i	$-0.666090\pi$
$929$	−15.1367	+	4.05587i	−0.496619	+	0.133069i	0.00181137	+	0.999998i	$0.499423\pi$
$930$	−0.0992269	−	0.370320i	−0.00325378	−	0.0121433i
$931$	47.4122	+	21.8821i	1.55387	+	0.717156i
$932$	6.18314	−	10.7095i	0.202535	−	0.350802i
$933$	−15.1801	+	8.76426i	−0.496976	+	0.286929i
$934$	23.6247	+	6.33022i	0.773024	+	0.207131i
$935$			1.08299i			0.0354176i
$936$	3.39221	+	1.22185i	0.110878	+	0.0399375i
$937$		−	55.3888i		−	1.80947i	−0.425971	−	0.904737i	$-0.640068\pi$
$937$		−	55.3888i		−	1.80947i	0.425971	−	0.904737i	$-0.359932\pi$
$938$	−11.6230	+	9.79183i	−0.379503	+	0.319715i
$939$	−3.05282	−	5.28765i	−0.0996251	−	0.172556i
$940$	−39.0316	−	22.5349i	−1.27307	−	0.735007i
$941$	−2.93637	−	2.93637i	−0.0957229	−	0.0957229i	0.657624	−	0.753347i	$-0.271562\pi$
$941$	−2.93637	−	2.93637i	−0.0957229	−	0.0957229i	−0.753347	+	0.657624i	$0.771562\pi$
$942$	−0.409686	−	1.52897i	−0.0133483	−	0.0498165i
$943$	4.95094	+	18.4771i	0.161225	+	0.601699i
$944$	8.26992	−	8.26992i	0.269163	−	0.269163i
$945$	4.78616	+	10.2115i	0.155694	+	0.332180i
$946$	10.1304	−	5.84876i	0.329366	−	0.190160i
$947$	8.95002	−	33.4019i	0.290836	−	1.08542i	−0.653631	−	0.756813i	$-0.726755\pi$
$947$	8.95002	−	33.4019i	0.290836	−	1.08542i	0.944468	−	0.328604i	$-0.106578\pi$
$948$	−10.1690			−0.330274
$949$	23.5066	−	4.22582i	0.763056	−	0.137176i
$950$		−	98.2361i		−	3.18720i
$951$	−1.22543	+	4.57338i	−0.0397374	+	0.148302i
$952$	−0.0109911	+	0.128539i	−0.000356224	+	0.00416598i
$953$	−0.340028	−	0.196315i	−0.0110146	−	0.00635927i	0.494483	−	0.869188i	$-0.335358\pi$
$953$	−0.340028	−	0.196315i	−0.0110146	−	0.00635927i	−0.505497	+	0.862828i	$0.668691\pi$
$954$	−4.54485	+	4.54485i	−0.147145	+	0.147145i
$955$	−30.1528	+	8.07942i	−0.975722	+	0.261444i
$956$	−5.45544	+	1.46178i	−0.176442	+	0.0472774i
$957$	7.05341	−	7.05341i	0.228004	−	0.228004i
$958$	−22.3043	−	12.8774i	−0.720618	−	0.416049i
$959$	1.14867	−	13.4336i	0.0370926	−	0.433792i
$960$	1.10321	−	4.11725i	0.0356061	−	0.132884i
$961$		−	30.9919i		−	0.999739i
$962$	1.68967	−	0.794785i	0.0544771	−	0.0256249i
$963$	−10.6376			−0.342791
$964$	−2.36063	+	8.81001i	−0.0760309	+	0.283751i
$965$	48.1403	−	27.7938i	1.54969	−	0.894714i
$966$	−2.61119	−	5.57109i	−0.0840137	−	0.179247i
$967$	32.1160	−	32.1160i	1.03278	−	1.03278i	0.0333375	−	0.999444i	$-0.489386\pi$
$967$	32.1160	−	32.1160i	1.03278	−	1.03278i	0.999444	−	0.0333375i	$-0.0106136\pi$
$968$	−4.18017	−	15.6006i	−0.134356	−	0.501423i
$969$	0.0941432	+	0.351347i	0.00302432	+	0.0112869i
$970$	−13.6587	−	13.6587i	−0.438554	−	0.438554i
$971$	9.18369	+	5.30221i	0.294719	+	0.170156i	0.640068	−	0.768318i	$-0.278906\pi$
$971$	9.18369	+	5.30221i	0.294719	+	0.170156i	−0.345349	+	0.938474i	$0.612240\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−0.393573	+	0.331568i	−0.0126174	+	0.0106296i
$974$		−	22.9901i		−	0.736649i
$975$	3.98028	−	47.3138i	0.127471	−	1.51525i
$976$			0.905116i			0.0289721i
$977$	−18.6664	−	5.00166i	−0.597192	−	0.160017i	−0.0524542	−	0.998623i	$-0.516704\pi$
$977$	−18.6664	−	5.00166i	−0.597192	−	0.160017i	−0.544738	+	0.838606i	$0.683371\pi$
$978$	−19.5813	+	11.3053i	−0.626141	+	0.361503i
$979$	−19.5948	+	33.9391i	−0.626251	+	1.08470i
$980$	12.5034	−	27.0913i	0.399407	−	0.865399i
$981$	3.28942	+	12.2763i	0.105023	+	0.391952i
$982$	−12.0045	+	3.21659i	−0.383078	+	0.102645i
$983$	3.03269	−	3.03269i	0.0967278	−	0.0967278i	−0.657087	−	0.753815i	$-0.728212\pi$
$983$	3.03269	−	3.03269i	0.0967278	−	0.0967278i	0.753815	+	0.657087i	$0.228212\pi$
$984$	−4.11288	+	7.12372i	−0.131114	+	0.227096i
$985$	15.5195	+	26.8805i	0.494491	+	0.856484i
$986$	0.0901643	+	0.0241594i	0.00287142	+	0.000769393i
$987$	−22.9473	−	16.0007i	−0.730422	−	0.509309i
$988$	−17.3574	−	20.5461i	−0.552213	−	0.653657i
$989$	−5.22055			−0.166004
$990$	5.74847	−	21.4536i	0.182698	−	0.681840i
$991$	11.6311	+	20.1456i	0.369474	+	0.639948i	0.989483	−	0.144647i	$-0.0462046\pi$
$991$	11.6311	+	20.1456i	0.369474	+	0.639948i	−0.620009	+	0.784594i	$0.712871\pi$
$992$	−0.0449717	+	0.0778933i	−0.00142785	+	0.00247311i
$993$	8.39432	+	8.39432i	0.266386	+	0.266386i
$994$	39.7055	+	14.3633i	1.25938	+	0.455575i
$995$	−57.3024	+	15.3541i	−1.81661	+	0.486759i
$996$	4.50530	+	4.50530i	0.142756	+	0.142756i
$997$	−27.6342	−	15.9546i	−0.875185	−	0.505288i	−0.00611697	−	0.999981i	$-0.501947\pi$
$997$	−27.6342	−	15.9546i	−0.875185	−	0.505288i	−0.869068	+	0.494693i	$0.835280\pi$
$998$	14.3738	−	8.29872i	0.454995	−	0.262691i
$999$	0.500239	+	0.134039i	0.0158269	+	0.00424079i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bx.b.223.10	yes	40
7.6	odd	2		546.2.bx.a.223.6	✓	40
13.7	odd	12		546.2.bx.a.475.6	yes	40
91.20	even	12	inner	546.2.bx.b.475.10	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bx.a.223.6	✓	40	7.6	odd	2
546.2.bx.a.475.6	yes	40	13.7	odd	12
546.2.bx.b.223.10	yes	40	1.1	even	1	trivial
546.2.bx.b.475.10	yes	40	91.20	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.bx (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(3.01404 + 3.01404i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(0.900010 - 2.48797i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(3.01404 + 3.01404i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(0.900010 - 2.48797i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +(2.13125 + 3.69143i) q^{10} +(1.34862 - 5.03311i) q^{11} -1.00000 q^{12} +(2.96038 + 2.05819i) q^{13} +(1.51328 - 2.17025i) q^{14} +(-4.11725 - 1.10321i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.0243803 + 0.0422279i) q^{17} +(0.707107 - 0.707107i) q^{18} +(-7.20556 + 1.93072i) q^{19} +(1.10321 + 4.11725i) q^{20} +(0.464552 + 2.60465i) q^{21} +(2.60533 - 4.51256i) q^{22} +(-2.01393 + 1.16275i) q^{23} +(-0.965926 - 0.258819i) q^{24} +13.1688i q^{25} +(2.32681 + 2.75426i) q^{26} +1.00000i q^{27} +(2.02342 - 1.70464i) q^{28} +(-0.957176 - 1.65788i) q^{29} +(-3.69143 - 2.13125i) q^{30} +(0.0635996 + 0.0635996i) q^{31} +(0.258819 + 0.965926i) q^{32} +(1.34862 + 5.03311i) q^{33} +(-0.0344789 + 0.0344789i) q^{34} +(10.2115 - 4.78616i) q^{35} +(0.866025 - 0.500000i) q^{36} +(0.134039 - 0.500239i) q^{37} -7.45974 q^{38} +(-3.59286 - 0.302250i) q^{39} +4.26249i q^{40} +(2.12899 - 7.94548i) q^{41} +(-0.225410 + 2.63613i) q^{42} +(1.94416 + 1.12246i) q^{43} +(3.68449 - 3.68449i) q^{44} +(4.11725 - 1.10321i) q^{45} +(-2.24625 + 0.601881i) q^{46} +(-7.47665 + 7.47665i) q^{47} +(-0.866025 - 0.500000i) q^{48} +(-5.37996 - 4.47839i) q^{49} +(-3.40835 + 12.7201i) q^{50} -0.0487606i q^{51} +(1.53467 + 3.26263i) q^{52} -6.42739 q^{53} +(-0.258819 + 0.965926i) q^{54} +(19.2348 - 11.1052i) q^{55} +(2.39566 - 1.12286i) q^{56} +(5.27483 - 5.27483i) q^{57} +(-0.495471 - 1.84912i) q^{58} +(-3.02700 - 11.2969i) q^{59} +(-3.01404 - 3.01404i) q^{60} +(0.783854 + 0.452558i) q^{61} +(0.0449717 + 0.0778933i) q^{62} +(-1.70464 - 2.02342i) q^{63} +1.00000i q^{64} +(2.71926 + 15.1262i) q^{65} +5.21066i q^{66} +(-5.54850 - 1.48672i) q^{67} +(-0.0422279 + 0.0243803i) q^{68} +(1.16275 - 2.01393i) q^{69} +(11.1023 - 1.98015i) q^{70} +(4.13049 + 15.4152i) q^{71} +(0.965926 - 0.258819i) q^{72} +(4.68392 - 4.68392i) q^{73} +(0.258943 - 0.448502i) q^{74} +(-6.58442 - 11.4045i) q^{75} +(-7.20556 - 1.93072i) q^{76} +(-11.3084 - 7.88516i) q^{77} +(-3.39221 - 1.22185i) q^{78} +10.1690 q^{79} +(-1.10321 + 4.11725i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.11288 - 7.12372i) q^{82} +(-4.50530 - 4.50530i) q^{83} +(-0.900010 + 2.48797i) q^{84} +(-0.200760 + 0.0537934i) q^{85} +(1.58740 + 1.58740i) q^{86} +(1.65788 + 0.957176i) q^{87} +(4.51256 - 2.60533i) q^{88} +(-7.26476 - 1.94659i) q^{89} +4.26249 q^{90} +(7.78507 - 5.51295i) q^{91} -2.32549 q^{92} +(-0.0868787 - 0.0232791i) q^{93} +(-9.15699 + 5.28679i) q^{94} +(-27.5371 - 15.8985i) q^{95} +(-0.707107 - 0.707107i) q^{96} +(-4.37727 + 1.17289i) q^{97} +(-4.03755 - 5.71823i) q^{98} +(-3.68449 - 3.68449i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 8 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q + 8 * q^7 + 20 * q^9	\( 40 q + 8 q^{7} + 20 q^{9} + 8 q^{11} - 40 q^{12} - 8 q^{14} + 20 q^{16} - 16 q^{17} - 16 q^{19} + 4 q^{21} + 8 q^{22} - 32 q^{26} - 8 q^{28} + 8 q^{33} - 16 q^{34} + 40 q^{35} + 40 q^{37} + 16 q^{38} - 16 q^{39} + 4 q^{41} - 12 q^{42} + 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} - 20 q^{49} - 16 q^{50} + 8 q^{52} + 32 q^{53} + 72 q^{55} + 12 q^{56} + 8 q^{57} - 36 q^{58} - 84 q^{59} + 48 q^{61} + 4 q^{62} + 4 q^{63} - 16 q^{65} - 12 q^{68} + 8 q^{69} - 20 q^{70} - 40 q^{71} + 48 q^{73} + 8 q^{74} - 36 q^{75} - 16 q^{76} + 24 q^{77} - 8 q^{78} - 48 q^{79} - 20 q^{81} - 36 q^{83} - 8 q^{84} + 8 q^{85} - 8 q^{86} - 12 q^{89} + 32 q^{91} - 16 q^{92} - 24 q^{93} - 96 q^{95} - 8 q^{98} - 8 q^{99}+O(q^{100}) \) 40 * q + 8 * q^7 + 20 * q^9 + 8 * q^11 - 40 * q^12 - 8 * q^14 + 20 * q^16 - 16 * q^17 - 16 * q^19 + 4 * q^21 + 8 * q^22 - 32 * q^26 - 8 * q^28 + 8 * q^33 - 16 * q^34 + 40 * q^35 + 40 * q^37 + 16 * q^38 - 16 * q^39 + 4 * q^41 - 12 * q^42 + 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 - 20 * q^49 - 16 * q^50 + 8 * q^52 + 32 * q^53 + 72 * q^55 + 12 * q^56 + 8 * q^57 - 36 * q^58 - 84 * q^59 + 48 * q^61 + 4 * q^62 + 4 * q^63 - 16 * q^65 - 12 * q^68 + 8 * q^69 - 20 * q^70 - 40 * q^71 + 48 * q^73 + 8 * q^74 - 36 * q^75 - 16 * q^76 + 24 * q^77 - 8 * q^78 - 48 * q^79 - 20 * q^81 - 36 * q^83 - 8 * q^84 + 8 * q^85 - 8 * q^86 - 12 * q^89 + 32 * q^91 - 16 * q^92 - 24 * q^93 - 96 * q^95 - 8 * q^98 - 8 * q^99

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