LMFDB - Embedded newform 546.2.bg.a.467.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(311,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 3]))

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

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

chi := DirichletCharacter("546.311");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bg (of order $6$, degree $2$, 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:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			467.2
Character	$\chi$	$=$	546.467
Dual form			546.2.bg.a.311.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-1.63622 + 0.568150i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.08726 - 0.627730i) q^{5} +(0.326076 - 1.70108i) q^{6} +(1.14208 + 2.38656i) q^{7} +1.00000 q^{8} +(2.35441 - 1.85923i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.63622 + 0.568150i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.08726 - 0.627730i) q^{5} +(0.326076 - 1.70108i) q^{6} +(1.14208 + 2.38656i) q^{7} +1.00000 q^{8} +(2.35441 - 1.85923i) q^{9} +(1.08726 - 0.627730i) q^{10} +(0.900851 + 1.56032i) q^{11} +(1.31014 + 1.13293i) q^{12} +(-0.657649 + 3.54507i) q^{13} +(-2.63786 - 0.204205i) q^{14} +(2.13564 + 0.409376i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.12649 - 1.95113i) q^{17} +(0.432936 + 2.96860i) q^{18} +(-2.46356 + 4.26702i) q^{19} +1.25546i q^{20} +(-3.22462 - 3.25605i) q^{21} -1.80170 q^{22} +(-7.93452 - 4.58100i) q^{23} +(-1.63622 + 0.568150i) q^{24} +(-1.71191 - 2.96512i) q^{25} +(-2.74129 - 2.34207i) q^{26} +(-2.79601 + 4.37977i) q^{27} +(1.49578 - 2.18235i) q^{28} -6.62631i q^{29} +(-1.42235 + 1.64483i) q^{30} +(2.39209 + 4.14321i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.36048 - 2.04120i) q^{33} +2.25297 q^{34} +(0.256371 - 3.31172i) q^{35} +(-2.78735 - 1.10936i) q^{36} +(-4.77663 - 2.75779i) q^{37} +(-2.46356 - 4.26702i) q^{38} +(-0.938072 - 6.17414i) q^{39} +(-1.08726 - 0.627730i) q^{40} +9.52690i q^{41} +(4.43213 - 1.16458i) q^{42} +3.14581 q^{43} +(0.900851 - 1.56032i) q^{44} +(-3.72695 + 0.543534i) q^{45} +(7.93452 - 4.58100i) q^{46} +(-8.20429 - 4.73675i) q^{47} +(0.326076 - 1.70108i) q^{48} +(-4.39129 + 5.45129i) q^{49} +3.42382 q^{50} +(2.95171 + 2.55246i) q^{51} +(3.39894 - 1.20299i) q^{52} +(-11.2966 + 6.52211i) q^{53} +(-2.39498 - 4.61130i) q^{54} -2.26196i q^{55} +(1.14208 + 2.38656i) q^{56} +(1.60662 - 8.38144i) q^{57} +(5.73855 + 3.31315i) q^{58} +(4.80116 - 2.77195i) q^{59} +(-0.713289 - 2.05420i) q^{60} +(2.64951 + 1.52970i) q^{61} -4.78417 q^{62} +(7.12609 + 3.49554i) q^{63} +1.00000 q^{64} +(2.94038 - 3.44158i) q^{65} +(2.94797 - 1.02364i) q^{66} +(-11.4400 + 6.60487i) q^{67} +(-1.12649 + 1.95113i) q^{68} +(15.5853 + 2.98751i) q^{69} +(2.73985 + 1.87789i) q^{70} +9.21344 q^{71} +(2.35441 - 1.85923i) q^{72} +(-7.95079 - 13.7712i) q^{73} +(4.77663 - 2.75779i) q^{74} +(4.48569 + 3.87895i) q^{75} +4.92713 q^{76} +(-2.69494 + 3.93194i) q^{77} +(5.81600 + 2.27468i) q^{78} +(-0.323763 + 0.560775i) q^{79} +(1.08726 - 0.627730i) q^{80} +(2.08651 - 8.75480i) q^{81} +(-8.25053 - 4.76345i) q^{82} +11.3503i q^{83} +(-1.20751 + 4.42062i) q^{84} +2.82851i q^{85} +(-1.57290 + 2.72435i) q^{86} +(3.76474 + 10.8421i) q^{87} +(0.900851 + 1.56032i) q^{88} +(-11.1220 - 6.42131i) q^{89} +(1.39276 - 3.49940i) q^{90} +(-9.21159 + 2.47924i) q^{91} +9.16199i q^{92} +(-6.26793 - 5.42013i) q^{93} +(8.20429 - 4.73675i) q^{94} +(5.35707 - 3.09290i) q^{95} +(1.31014 + 1.13293i) q^{96} -1.48848 q^{97} +(-2.52531 - 6.52862i) q^{98} +(5.02197 + 1.99874i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 18 q^{2} - 18 q^{4} + 36 q^{8} + 4 q^{9}+O(q^{10}) $ 36 * q - 18 * q^2 - 18 * q^4 + 36 * q^8 + 4 * q^9	$ 36 q - 18 q^{2} - 18 q^{4} + 36 q^{8} + 4 q^{9} - 14 q^{15} - 18 q^{16} + 4 q^{18} + 23 q^{21} + 14 q^{25} - 6 q^{26} + 7 q^{30} - 18 q^{32} + 24 q^{33} - 8 q^{36} - 10 q^{39} - 16 q^{42} - 16 q^{43} - 9 q^{45} + 72 q^{47} + 12 q^{49} - 28 q^{50} - 3 q^{51} + 6 q^{52} + 9 q^{54} - 8 q^{57} + 24 q^{59} + 7 q^{60} - 36 q^{61} - 39 q^{63} + 36 q^{64} + 18 q^{65} - 24 q^{66} - 72 q^{71} + 4 q^{72} + 54 q^{75} + 20 q^{78} + 20 q^{79} - 20 q^{81} - 24 q^{82} - 7 q^{84} + 8 q^{86} - 24 q^{87} - 72 q^{89} - 2 q^{91} - 14 q^{93} - 72 q^{94} - 12 q^{98} + 72 q^{99}+O(q^{100}) $ 36 * q - 18 * q^2 - 18 * q^4 + 36 * q^8 + 4 * q^9 - 14 * q^15 - 18 * q^16 + 4 * q^18 + 23 * q^21 + 14 * q^25 - 6 * q^26 + 7 * q^30 - 18 * q^32 + 24 * q^33 - 8 * q^36 - 10 * q^39 - 16 * q^42 - 16 * q^43 - 9 * q^45 + 72 * q^47 + 12 * q^49 - 28 * q^50 - 3 * q^51 + 6 * q^52 + 9 * q^54 - 8 * q^57 + 24 * q^59 + 7 * q^60 - 36 * q^61 - 39 * q^63 + 36 * q^64 + 18 * q^65 - 24 * q^66 - 72 * q^71 + 4 * q^72 + 54 * q^75 + 20 * q^78 + 20 * q^79 - 20 * q^81 - 24 * q^82 - 7 * q^84 + 8 * q^86 - 24 * q^87 - 72 * q^89 - 2 * q^91 - 14 * q^93 - 72 * q^94 - 12 * q^98 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−1.63622	+	0.568150i	−0.944670	+	0.328021i
$3$	−1.63622	+	0.568150i	−0.944670	+	0.328021i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.08726	−	0.627730i	−0.486237	−	0.280729i	0.236775	−	0.971565i	$-0.423910\pi$
$5$	−1.08726	−	0.627730i	−0.486237	−	0.280729i	−0.723012	+	0.690835i	$0.757243\pi$
$6$	0.326076	−	1.70108i	0.133120	−	0.694463i
$7$	1.14208	+	2.38656i	0.431667	+	0.902033i
$7$	1.14208	+	2.38656i	0.431667	+	0.902033i
$8$	1.00000			0.353553
$9$	2.35441	−	1.85923i	0.784804	−	0.619744i
$10$	1.08726	−	0.627730i	0.343822	−	0.198506i
$11$	0.900851	+	1.56032i	0.271617	+	0.470454i	0.969276	−	0.245976i	$-0.0791084\pi$
$11$	0.900851	+	1.56032i	0.271617	+	0.470454i	−0.697659	+	0.716430i	$0.745775\pi$
$12$	1.31014	+	1.13293i	0.378205	+	0.327049i
$13$	−0.657649	+	3.54507i	−0.182399	+	0.983225i
$13$	−0.657649	+	3.54507i	−0.182399	+	0.983225i
$14$	−2.63786	−	0.204205i	−0.704997	−	0.0545760i
$15$	2.13564	+	0.409376i	0.551419	+	0.105700i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.12649	−	1.95113i	−0.273213	−	0.473218i	0.696470	−	0.717586i	$-0.254753\pi$
$17$	−1.12649	−	1.95113i	−0.273213	−	0.473218i	−0.969683	+	0.244368i	$0.921420\pi$
$18$	0.432936	+	2.96860i	0.102044	+	0.699705i
$19$	−2.46356	+	4.26702i	−0.565180	+	0.978921i	0.431853	+	0.901944i	$0.357860\pi$
$19$	−2.46356	+	4.26702i	−0.565180	+	0.978921i	−0.997033	+	0.0769769i	$0.975473\pi$
$20$			1.25546i			0.280729i
$21$	−3.22462	−	3.25605i	−0.703669	−	0.710528i
$22$	−1.80170			−0.384124
$23$	−7.93452	−	4.58100i	−1.65446	−	0.955204i	−0.975205	−	0.221302i	$-0.928969\pi$
$23$	−7.93452	−	4.58100i	−1.65446	−	0.955204i	−0.679256	−	0.733901i	$-0.737697\pi$
$24$	−1.63622	+	0.568150i	−0.333991	+	0.115973i
$25$	−1.71191	−	2.96512i	−0.342382	−	0.593023i
$26$	−2.74129	−	2.34207i	−0.537612	−	0.459319i
$27$	−2.79601	+	4.37977i	−0.538092	+	0.842886i
$28$	1.49578	−	2.18235i	0.282675	−	0.412425i
$29$		−	6.62631i		−	1.23047i	−0.788342	−	0.615237i	$-0.789060\pi$
$29$		−	6.62631i		−	1.23047i	0.788342	−	0.615237i	$-0.210940\pi$
$30$	−1.42235	+	1.64483i	−0.259684	+	0.300303i
$31$	2.39209	+	4.14321i	0.429631	+	0.744143i	0.996840	−	0.0794307i	$-0.0253103\pi$
$31$	2.39209	+	4.14321i	0.429631	+	0.744143i	−0.567209	+	0.823574i	$0.691977\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−2.36048	−	2.04120i	−0.410907	−	0.355328i
$34$	2.25297			0.386381
$35$	0.256371	−	3.31172i	0.0433346	−	0.559784i
$36$	−2.78735	−	1.10936i	−0.464558	−	0.184894i
$37$	−4.77663	−	2.75779i	−0.785274	−	0.453378i	0.0530223	−	0.998593i	$-0.483115\pi$
$37$	−4.77663	−	2.75779i	−0.785274	−	0.453378i	−0.838296	+	0.545215i	$0.816448\pi$
$38$	−2.46356	−	4.26702i	−0.399643	−	0.692202i
$39$	−0.938072	−	6.17414i	−0.150212	−	0.988654i
$40$	−1.08726	−	0.627730i	−0.171911	−	0.0992528i
$41$			9.52690i			1.48785i	0.668262	+	0.743926i	$0.267038\pi$
$41$			9.52690i			1.48785i	−0.668262	+	0.743926i	$0.732962\pi$
$42$	4.43213	−	1.16458i	0.683892	−	0.179698i
$43$	3.14581			0.479731			0.239866	−	0.970806i	$-0.422897\pi$
$43$	3.14581			0.479731			0.239866	+	0.970806i	$0.422897\pi$
$44$	0.900851	−	1.56032i	0.135808	−	0.235227i
$45$	−3.72695	+	0.543534i	−0.555581	+	0.0810252i
$46$	7.93452	−	4.58100i	1.16988	−	0.675431i
$47$	−8.20429	−	4.73675i	−1.19672	−	0.690926i	−0.236896	−	0.971535i	$-0.576130\pi$
$47$	−8.20429	−	4.73675i	−1.19672	−	0.690926i	−0.959822	+	0.280609i	$0.909463\pi$
$48$	0.326076	−	1.70108i	0.0470651	−	0.245530i
$49$	−4.39129	+	5.45129i	−0.627328	+	0.778756i
$50$	3.42382			0.484202
$51$	2.95171	+	2.55246i	0.413322	+	0.357416i
$52$	3.39894	−	1.20299i	0.471349	−	0.166825i
$53$	−11.2966	+	6.52211i	−1.55171	+	0.895881i	−0.553709	+	0.832710i	$0.686788\pi$
$53$	−11.2966	+	6.52211i	−1.55171	+	0.895881i	−0.998003	+	0.0631707i	$0.979879\pi$
$54$	−2.39498	−	4.61130i	−0.325916	−	0.627518i
$55$		−	2.26196i		−	0.305003i
$56$	1.14208	+	2.38656i	0.152617	+	0.318917i
$57$	1.60662	−	8.38144i	0.212802	−	1.11015i
$58$	5.73855	+	3.31315i	0.753509	+	0.435039i
$59$	4.80116	−	2.77195i	0.625058	−	0.360877i	−0.153778	−	0.988105i	$-0.549144\pi$
$59$	4.80116	−	2.77195i	0.625058	−	0.360877i	0.778836	+	0.627228i	$0.215811\pi$
$60$	−0.713289	−	2.05420i	−0.0920852	−	0.265197i
$61$	2.64951	+	1.52970i	0.339236	+	0.195858i	0.659934	−	0.751324i	$-0.270584\pi$
$61$	2.64951	+	1.52970i	0.339236	+	0.195858i	−0.320698	+	0.947181i	$0.603918\pi$
$62$	−4.78417			−0.607590
$63$	7.12609	+	3.49554i	0.897804	+	0.440396i
$64$	1.00000			0.125000
$65$	2.94038	−	3.44158i	0.364709	−	0.426876i
$66$	2.94797	−	1.02364i	0.362871	−	0.126001i
$67$	−11.4400	+	6.60487i	−1.39761	+	0.806913i	−0.994142	−	0.108079i	$-0.965530\pi$
$67$	−11.4400	+	6.60487i	−1.39761	+	0.806913i	−0.403472	+	0.914992i	$0.632197\pi$
$68$	−1.12649	+	1.95113i	−0.136606	+	0.236609i
$69$	15.5853	+	2.98751i	1.87625	+	0.359654i
$70$	2.73985	+	1.87789i	0.327475	+	0.224450i
$71$	9.21344			1.09343			0.546717	−	0.837318i	$-0.315877\pi$
$71$	9.21344			1.09343			0.546717	+	0.837318i	$0.315877\pi$
$72$	2.35441	−	1.85923i	0.277470	−	0.219113i
$73$	−7.95079	−	13.7712i	−0.930570	−	1.61179i	−0.782350	−	0.622839i	$-0.785979\pi$
$73$	−7.95079	−	13.7712i	−0.930570	−	1.61179i	−0.148220	−	0.988954i	$-0.547354\pi$
$74$	4.77663	−	2.75779i	0.555272	−	0.320587i
$75$	4.48569	+	3.87895i	0.517963	+	0.447903i
$76$	4.92713			0.565180
$77$	−2.69494	+	3.93194i	−0.307117	+	0.448087i
$78$	5.81600	+	2.27468i	0.658532	+	0.257556i
$79$	−0.323763	+	0.560775i	−0.0364262	+	0.0630921i	−0.883664	−	0.468122i	$-0.844931\pi$
$79$	−0.323763	+	0.560775i	−0.0364262	+	0.0630921i	0.847238	+	0.531214i	$0.178264\pi$
$80$	1.08726	−	0.627730i	0.121559	−	0.0701823i
$81$	2.08651	−	8.75480i	0.231835	−	0.972755i
$82$	−8.25053	−	4.76345i	−0.911119	−	0.526035i
$83$			11.3503i			1.24585i	0.782280	+	0.622926i	$0.214056\pi$
$83$			11.3503i			1.24585i	−0.782280	+	0.622926i	$0.785944\pi$
$84$	−1.20751	+	4.42062i	−0.131750	+	0.482330i
$85$			2.82851i			0.306795i
$86$	−1.57290	+	2.72435i	−0.169611	+	0.293774i
$87$	3.76474	+	10.8421i	0.403622	+	1.16239i
$88$	0.900851	+	1.56032i	0.0960310	+	0.166331i
$89$	−11.1220	−	6.42131i	−1.17893	−	0.680657i	−0.223165	−	0.974781i	$-0.571639\pi$
$89$	−11.1220	−	6.42131i	−1.17893	−	0.680657i	−0.955767	+	0.294124i	$0.904972\pi$
$90$	1.39276	−	3.49940i	0.146810	−	0.368869i
$91$	−9.21159	+	2.47924i	−0.965637	+	0.259895i
$92$			9.16199i			0.955204i
$93$	−6.26793	−	5.42013i	−0.649955	−	0.562042i
$94$	8.20429	−	4.73675i	0.846208	−	0.488558i
$95$	5.35707	−	3.09290i	0.549623	−	0.317325i
$96$	1.31014	+	1.13293i	0.133716	+	0.115629i
$97$	−1.48848			−0.151132			−0.0755661	−	0.997141i	$-0.524076\pi$
$97$	−1.48848			−0.151132			−0.0755661	+	0.997141i	$0.524076\pi$
$98$	−2.52531	−	6.52862i	−0.255095	−	0.659490i
$99$	5.02197	+	1.99874i	0.504727	+	0.200881i
$100$	−1.71191	+	2.96512i	−0.171191	+	0.296512i
$101$	0.424346	+	0.734989i	0.0422240	+	0.0731342i	0.886365	−	0.462987i	$-0.153222\pi$
$101$	0.424346	+	0.734989i	0.0422240	+	0.0731342i	−0.844141	+	0.536121i	$0.819889\pi$
$102$	−3.68635	+	1.28002i	−0.365003	+	0.126741i
$103$	5.30846	+	3.06484i	0.523058	+	0.301988i	0.738185	−	0.674599i	$-0.235683\pi$
$103$	5.30846	+	3.06484i	0.523058	+	0.301988i	−0.215127	+	0.976586i	$0.569017\pi$
$104$	−0.657649	+	3.54507i	−0.0644878	+	0.347622i
$105$	1.46208	+	5.56436i	0.142684	+	0.543026i
$106$		−	13.0442i		−	1.26697i
$107$	9.73051	+	5.61791i	0.940684	+	0.543104i	0.890175	−	0.455620i	$-0.150582\pi$
$107$	9.73051	+	5.61791i	0.940684	+	0.543104i	0.0505092	+	0.998724i	$0.483916\pi$
$108$	5.19099	+	0.231530i	0.499503	+	0.0222790i
$109$	−2.01838	+	1.16531i	−0.193326	+	0.111617i	−0.593539	−	0.804806i	$-0.702270\pi$
$109$	−2.01838	+	1.16531i	−0.193326	+	0.111617i	0.400213	+	0.916422i	$0.368936\pi$
$110$	1.95892	+	1.13098i	0.186775	+	0.107835i
$111$	9.38245	+	1.79850i	0.890543	+	0.170706i
$112$	−2.63786	−	0.204205i	−0.249254	−	0.0192955i
$113$			9.43789i			0.887842i	0.896066	+	0.443921i	$0.146413\pi$
$113$			9.43789i			0.887842i	−0.896066	+	0.443921i	$0.853587\pi$
$114$	6.45523	+	5.58209i	0.604588	+	0.522811i
$115$	5.75125	+	9.96146i	0.536307	+	0.928911i
$116$	−5.73855	+	3.31315i	−0.532811	+	0.307619i
$117$	5.04272	+	9.56927i	0.466200	+	0.884679i
$118$			5.54390i			0.510357i
$119$	3.36994	−	4.91677i	0.308922	−	0.450720i
$120$	2.13564	+	0.409376i	0.194956	+	0.0373707i
$121$	3.87694	−	6.71505i	0.352449	−	0.610459i
$122$	−2.64951	+	1.52970i	−0.239876	+	0.138492i
$123$	−5.41270	−	15.5881i	−0.488047	−	1.40553i
$124$	2.39209	−	4.14321i	0.214816	−	0.372071i
$125$			10.5758i			0.945925i
$126$	−6.59027	+	4.42361i	−0.587108	+	0.394087i
$127$	9.66003			0.857189			0.428594	−	0.903497i	$-0.359009\pi$
$127$	9.66003			0.857189			0.428594	+	0.903497i	$0.359009\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−5.14723	+	1.78729i	−0.453188	+	0.157362i
$130$	1.51031	+	4.26723i	0.132463	+	0.374261i
$131$	−9.71936	+	16.8344i	−0.849184	+	1.47083i	0.0327529	+	0.999463i	$0.489573\pi$
$131$	−9.71936	+	16.8344i	−0.849184	+	1.47083i	−0.881937	+	0.471367i	$0.843761\pi$
$132$	−0.587492	+	3.06484i	−0.0511347	+	0.266760i
$133$	−12.9971	−	1.00614i	−1.12699	−	0.0872437i
$134$		−	13.2097i		−	1.14115i
$135$	5.78929	−	3.00681i	0.498263	−	0.258785i
$136$	−1.12649	−	1.95113i	−0.0965953	−	0.167308i
$137$	5.51288	+	9.54858i	0.470997	+	0.815790i	0.999450	−	0.0331723i	$-0.0105610\pi$
$137$	5.51288	+	9.54858i	0.470997	+	0.815790i	−0.528453	+	0.848963i	$0.677228\pi$
$138$	−10.3799	+	12.0035i	−0.883596	+	1.02181i
$139$		−	9.08904i		−	0.770922i	−0.922724	−	0.385461i	$-0.874042\pi$
$139$		−	9.08904i		−	0.770922i	0.922724	−	0.385461i	$-0.125958\pi$
$140$	−2.99622	+	1.43384i	−0.253227	+	0.121181i
$141$	16.1152	+	3.08908i	1.35714	+	0.260148i
$142$	−4.60672	+	7.97907i	−0.386587	+	0.669589i
$143$	−6.12388	+	2.16743i	−0.512105	+	0.181250i
$144$	0.432936	+	2.96860i	0.0360780	+	0.247383i
$145$	−4.15953	+	7.20452i	−0.345430	+	0.598303i
$146$	15.9016			1.31602
$147$	4.08796	−	11.4144i	0.337169	−	0.941444i
$148$			5.51558i			0.453378i
$149$	−4.17530	+	7.23183i	−0.342054	+	0.592455i	−0.984814	−	0.173613i	$-0.944456\pi$
$149$	−4.17530	+	7.23183i	−0.342054	+	0.592455i	0.642760	+	0.766068i	$0.277789\pi$
$150$	−5.60212	+	1.94524i	−0.457411	+	0.158828i
$151$	9.67867	−	5.58798i	0.787639	−	0.454744i	−0.0514918	−	0.998673i	$-0.516398\pi$
$151$	9.67867	−	5.58798i	0.787639	−	0.454744i	0.839131	+	0.543930i	$0.183064\pi$
$152$	−2.46356	+	4.26702i	−0.199821	+	0.346101i
$153$	−6.27981	−	2.49937i	−0.507693	−	0.202062i
$154$	−2.05769	−	4.29986i	−0.165814	−	0.346493i
$155$		−	6.00633i		−	0.482440i
$156$	−4.87793	+	3.89946i	−0.390547	+	0.312207i
$157$	6.53612	−	3.77363i	0.521639	−	0.301168i	−0.215966	−	0.976401i	$-0.569290\pi$
$157$	6.53612	−	3.77363i	0.521639	−	0.301168i	0.737605	+	0.675232i	$0.235957\pi$
$158$	−0.323763	−	0.560775i	−0.0257572	−	0.0446128i
$159$	14.7782	−	17.0898i	1.17199	−	1.35531i
$160$			1.25546i			0.0992528i
$161$	1.87092	−	24.1680i	0.147449	−	1.90471i
$162$	6.53862	+	6.18437i	0.513723	+	0.485890i
$163$	10.1935	+	5.88520i	0.798414	+	0.460965i	0.842916	−	0.538045i	$-0.180837\pi$
$163$	10.1935	+	5.88520i	0.798414	+	0.460965i	−0.0445021	+	0.999009i	$0.514170\pi$
$164$	8.25053	−	4.76345i	0.644258	−	0.371963i
$165$	1.28513	+	3.70106i	0.100047	+	0.288127i
$166$	−9.82961	−	5.67513i	−0.762926	−	0.440475i
$167$		−	8.30092i		−	0.642344i	−0.947021	−	0.321172i	$-0.895923\pi$
$167$		−	8.30092i		−	0.642344i	0.947021	−	0.321172i	$-0.104077\pi$
$168$	−3.22462	−	3.25605i	−0.248785	−	0.251210i
$169$	−12.1350	−	4.66282i	−0.933461	−	0.358678i
$170$	−2.44956	−	1.41426i	−0.187873	−	0.108468i
$171$	2.13313	+	14.6267i	0.163125	+	1.11853i
$172$	−1.57290	−	2.72435i	−0.119933	−	0.207730i
$173$	9.17486	−	15.8913i	0.697552	−	1.20819i	−0.271761	−	0.962365i	$-0.587606\pi$
$173$	9.17486	−	15.8913i	0.697552	−	1.20819i	0.969313	−	0.245830i	$-0.0790605\pi$
$174$	−11.2719	−	2.16068i	−0.854519	−	0.163801i
$175$	5.12127	−	7.47198i	0.387132	−	0.564829i
$176$	−1.80170			−0.135808
$177$	−6.28086	+	7.26329i	−0.472098	+	0.545942i
$178$	11.1220	−	6.42131i	0.833631	−	0.481297i
$179$	3.45299	−	1.99358i	0.258088	−	0.149007i	−0.365374	−	0.930861i	$-0.619059\pi$
$179$	3.45299	−	1.99358i	0.258088	−	0.149007i	0.623462	+	0.781853i	$0.285725\pi$
$180$	2.33419	+	2.95587i	0.173980	+	0.220317i
$181$			13.2147i			0.982244i	0.871091	+	0.491122i	$0.163413\pi$
$181$			13.2147i			0.982244i	−0.871091	+	0.491122i	$0.836587\pi$
$182$	2.45871	−	9.21709i	0.182251	−	0.683216i
$183$	−5.20428	−	0.997597i	−0.384711	−	0.0737445i
$184$	−7.93452	−	4.58100i	−0.584940	−	0.337716i
$185$	3.46229	+	5.99687i	0.254553	+	0.440899i
$186$	7.82794	−	2.71812i	0.573972	−	0.199303i
$187$	2.02959	−	3.51535i	0.148418	−	0.257068i
$188$			9.47349i			0.690926i
$189$	−13.6458	−	1.67077i	−0.992588	−	0.121531i
$190$			6.18581i			0.448766i
$191$	−4.46998	−	2.58075i	−0.323437	−	0.186736i	0.329487	−	0.944160i	$-0.393124\pi$
$191$	−4.46998	−	2.58075i	−0.323437	−	0.186736i	−0.652923	+	0.757424i	$0.726458\pi$
$192$	−1.63622	+	0.568150i	−0.118084	+	0.0410027i
$193$	2.77221	−	1.60054i	0.199548	−	0.115209i	−0.396896	−	0.917863i	$-0.629913\pi$
$193$	2.77221	−	1.60054i	0.199548	−	0.115209i	0.596445	+	0.802654i	$0.296579\pi$
$194$	0.744240	−	1.28906i	0.0534333	−	0.0925492i
$195$	−2.85576	+	7.30175i	−0.204505	+	0.522889i
$196$	6.91660	+	1.07733i	0.494043	+	0.0769519i
$197$	3.52408			0.251081			0.125540	−	0.992089i	$-0.459934\pi$
$197$	3.52408			0.251081			0.125540	+	0.992089i	$0.459934\pi$
$198$	−4.24195	+	3.34978i	−0.301462	+	0.238059i
$199$	−8.99539	+	5.19349i	−0.637666	+	0.368157i	−0.783715	−	0.621121i	$-0.786678\pi$
$199$	−8.99539	+	5.19349i	−0.637666	+	0.368157i	0.146049	+	0.989277i	$0.453344\pi$
$200$	−1.71191	−	2.96512i	−0.121050	−	0.209665i
$201$	14.9657	−	17.3066i	1.05560	−	1.22071i
$202$	−0.848692			−0.0597138
$203$	15.8141	−	7.56780i	1.10993	−	0.531155i
$204$	0.734641	−	3.83248i	0.0514351	−	0.268328i
$205$	5.98031	−	10.3582i	0.417683	−	0.723449i
$206$	−5.30846	+	3.06484i	−0.369858	+	0.213537i
$207$	−27.1983	+	3.96656i	−1.89041	+	0.275695i
$208$	−2.74129	−	2.34207i	−0.190074	−	0.162394i
$209$	−8.87721			−0.614050
$210$	−5.54991	−	1.51598i	−0.382980	−	0.104613i
$211$	7.62625			0.525013			0.262506	−	0.964930i	$-0.415451\pi$
$211$	7.62625			0.525013			0.262506	+	0.964930i	$0.415451\pi$
$212$	11.2966	+	6.52211i	0.775856	+	0.447941i
$213$	−15.0752	+	5.23461i	−1.03293	+	0.358670i
$214$	−9.73051	+	5.61791i	−0.665164	+	0.384033i
$215$	−3.42031	−	1.97472i	−0.233263	−	0.134675i
$216$	−2.79601	+	4.37977i	−0.190244	+	0.298005i
$217$	−7.15605	+	10.4407i	−0.485784	+	0.708763i
$218$		−	2.33062i		−	0.157850i
$219$	20.8333	+	18.0154i	1.40778	+	1.21737i
$220$	−1.95892	+	1.13098i	−0.132070	+	0.0762507i
$221$	7.65772	−	2.71031i	0.515114	−	0.182315i
$222$	−6.24877	+	7.22619i	−0.419390	+	0.484990i
$223$	−0.159812			−0.0107018			−0.00535090	−	0.999986i	$-0.501703\pi$
$223$	−0.159812			−0.0107018			−0.00535090	+	0.999986i	$0.501703\pi$
$224$	1.49578	−	2.18235i	0.0999407	−	0.145814i
$225$	−9.54339	−	3.79827i	−0.636226	−	0.253218i
$226$	−8.17345	−	4.71894i	−0.543690	−	0.313900i
$227$	−7.71498	+	4.45425i	−0.512061	+	0.295639i	−0.733681	−	0.679495i	$-0.762199\pi$
$227$	−7.71498	+	4.45425i	−0.512061	+	0.295639i	0.221619	+	0.975133i	$0.428866\pi$
$228$	−8.06185	+	2.79935i	−0.533909	+	0.185391i
$229$	2.78489	−	4.82358i	0.184031	−	0.318751i	−0.759219	−	0.650836i	$-0.774419\pi$
$229$	2.78489	−	4.82358i	0.184031	−	0.318751i	0.943250	+	0.332085i	$0.107752\pi$
$230$	−11.5025			−0.758453
$231$	2.17558	−	7.96464i	0.143142	−	0.524035i
$232$		−	6.62631i		−	0.435039i
$233$	−4.99084	−	2.88146i	−0.326961	−	0.188771i	0.327530	−	0.944841i	$-0.393784\pi$
$233$	−4.99084	−	2.88146i	−0.326961	−	0.188771i	−0.654491	+	0.756070i	$0.727117\pi$
$234$	−10.8086	−	0.417507i	−0.706580	−	0.0272933i
$235$	5.94679	+	10.3001i	0.387926	+	0.671907i
$236$	−4.80116	−	2.77195i	−0.312529	−	0.180439i
$237$	0.211143	−	1.10150i	0.0137152	−	0.0715498i
$238$	2.57308	+	5.37684i	0.166788	+	0.348529i
$239$	−12.0528			−0.779630			−0.389815	−	0.920893i	$-0.627461\pi$
$239$	−12.0528			−0.779630			−0.389815	+	0.920893i	$0.627461\pi$
$240$	−1.42235	+	1.64483i	−0.0918122	+	0.106173i
$241$	7.40564	+	12.8269i	0.477039	+	0.826256i	0.999654	−	0.0263129i	$-0.00837662\pi$
$241$	7.40564	+	12.8269i	0.477039	+	0.826256i	−0.522615	+	0.852569i	$0.675043\pi$
$242$	3.87694	+	6.71505i	0.249219	+	0.431660i
$243$	1.56005	+	15.5102i	0.100077	+	0.994980i
$244$		−	3.05940i		−	0.195858i
$245$	8.19641	−	3.17042i	0.523649	−	0.202551i
$246$	16.2060	+	3.10650i	1.03326	+	0.198063i
$247$	−13.5067	−	11.5397i	−0.859411	−	0.734254i
$248$	2.39209	+	4.14321i	0.151898	+	0.263094i
$249$	−6.44865	−	18.5715i	−0.408666	−	1.17692i
$250$	−9.15888	−	5.28788i	−0.579258	−	0.334435i
$251$	9.87047			0.623019			0.311509	−	0.950243i	$-0.399165\pi$
$251$	9.87047			0.623019			0.311509	+	0.950243i	$0.399165\pi$
$252$	−0.535824	−	7.91915i	−0.0337537	−	0.498859i
$253$		−	16.5072i		−	1.03780i
$254$	−4.83001	+	8.36583i	−0.303062	+	0.524919i
$255$	−1.60702	−	4.62806i	−0.100635	−	0.289820i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.00565	+	6.93799i	−0.249866	+	0.432780i	−0.963488	−	0.267750i	$-0.913720\pi$
$257$	−4.00565	+	6.93799i	−0.249866	+	0.432780i	0.713623	+	0.700530i	$0.247053\pi$
$258$	1.02577	−	5.35127i	0.0638619	−	0.333156i
$259$	1.12631	−	14.5493i	0.0699854	−	0.904051i
$260$	−4.45069	−	0.825652i	−0.276020	−	0.0512047i
$261$	−12.3198	−	15.6011i	−0.762579	−	0.965682i
$262$	−9.71936	−	16.8344i	−0.600464	−	1.04003i
$263$	9.16411	−	5.29090i	0.565083	−	0.326251i	−0.190100	−	0.981765i	$-0.560881\pi$
$263$	9.16411	−	5.29090i	0.565083	−	0.326251i	0.755183	+	0.655514i	$0.227548\pi$
$264$	−2.36048	−	2.04120i	−0.145278	−	0.125627i
$265$	16.3765			1.00600
$266$	7.36988	−	10.7527i	0.451876	−	0.659292i
$267$	21.8463	+	4.18767i	1.33697	+	0.256281i
$268$	11.4400	+	6.60487i	0.698807	+	0.403457i
$269$	−5.38350	−	9.32450i	−0.328238	−	0.568525i	0.653924	−	0.756560i	$-0.273121\pi$
$269$	−5.38350	−	9.32450i	−0.328238	−	0.568525i	−0.982162	+	0.188035i	$0.939788\pi$
$270$	−0.290676	+	6.51708i	−0.0176900	+	0.396617i
$271$	0.888146	−	1.53831i	0.0539510	−	0.0934459i	−0.837789	−	0.545995i	$-0.816152\pi$
$271$	0.888146	−	1.53831i	0.0539510	−	0.0934459i	0.891740	+	0.452549i	$0.149485\pi$
$272$	2.25297			0.136606
$273$	13.6636	−	9.29014i	0.826957	−	0.562265i
$274$	−11.0258			−0.666090
$275$	3.08435	−	5.34226i	0.185993	−	0.322150i
$276$	−5.20538	−	14.9910i	−0.313327	−	0.902353i
$277$	8.32192	+	14.4140i	0.500016	+	0.866053i	1.00000		1.81111e-5i	$5.76495e-6\pi$
$277$	8.32192	+	14.4140i	0.500016	+	0.866053i	−0.499984	+	0.866034i	$0.666661\pi$
$278$	7.87134	+	4.54452i	0.472091	+	0.272562i
$279$	13.3351	+	5.30739i	0.798354	+	0.317745i
$280$	0.256371	−	3.31172i	0.0153211	−	0.197913i
$281$	−17.4383			−1.04028			−0.520140	−	0.854081i	$-0.674120\pi$
$281$	−17.4383			−1.04028			−0.520140	+	0.854081i	$0.674120\pi$
$282$	−10.7328	+	12.4116i	−0.639130	+	0.739101i
$283$	−22.7964	+	13.1615i	−1.35510	+	0.782369i	−0.988959	−	0.148189i	$-0.952656\pi$
$283$	−22.7964	+	13.1615i	−1.35510	+	0.782369i	−0.366144	+	0.930558i	$0.619322\pi$
$284$	−4.60672	−	7.97907i	−0.273358	−	0.473471i
$285$	−7.00809	+	8.10428i	−0.415123	+	0.480056i
$286$	1.18489	−	6.38715i	0.0700639	−	0.377680i
$287$	−22.7365	+	10.8805i	−1.34209	+	0.642256i
$288$	−2.78735	−	1.10936i	−0.164246	−	0.0653699i
$289$	5.96206	−	10.3266i	0.350710	−	0.607447i
$290$	−4.15953	−	7.20452i	−0.244256	−	0.423064i
$291$	2.43548	−	0.845679i	0.142770	−	0.0495746i
$292$	−7.95079	+	13.7712i	−0.465285	+	0.805897i
$293$			6.46090i			0.377450i	0.982030	+	0.188725i	$0.0604355\pi$
$293$			6.46090i			0.377450i	−0.982030	+	0.188725i	$0.939565\pi$
$294$	7.84118	+	9.24748i	0.457307	+	0.539324i
$295$	−6.96014			−0.405235
$296$	−4.77663	−	2.75779i	−0.277636	−	0.160293i
$297$	−9.35262	−	0.417148i	−0.542694	−	0.0242054i
$298$	−4.17530	−	7.23183i	−0.241869	−	0.418929i
$299$	21.4581	−	25.1157i	1.24095	−	1.45248i
$300$	1.11643	−	5.82420i	0.0644570	−	0.336260i
$301$	3.59277	+	7.50765i	0.207084	+	0.432734i
$302$			11.1760i			0.643104i
$303$	−1.11191	−	0.961510i	−0.0638773	−	0.0552373i
$304$	−2.46356	−	4.26702i	−0.141295	−	0.244730i
$305$	−1.92047	−	3.32636i	−0.109966	−	0.190467i
$306$	5.30442	−	4.18880i	0.303234	−	0.239458i
$307$	−3.11265			−0.177648			−0.0888242	−	0.996047i	$-0.528311\pi$
$307$	−3.11265			−0.177648			−0.0888242	+	0.996047i	$0.528311\pi$
$308$	4.75263	+	0.367916i	0.270806	+	0.0209640i
$309$	−10.4271	−	1.99874i	−0.593176	−	0.113705i
$310$	5.20163	+	3.00316i	0.295433	+	0.170568i
$311$	6.28396	+	10.8841i	0.356330	+	0.617182i	0.987345	−	0.158589i	$-0.0506944\pi$
$311$	6.28396	+	10.8841i	0.356330	+	0.617182i	−0.631014	+	0.775771i	$0.717361\pi$
$312$	−0.938072	−	6.17414i	−0.0531078	−	0.349542i
$313$	−1.20941	−	0.698253i	−0.0683598	−	0.0394676i	0.465431	−	0.885084i	$-0.345900\pi$
$313$	−1.20941	−	0.698253i	−0.0683598	−	0.0394676i	−0.533790	+	0.845617i	$0.679233\pi$
$314$			7.54726i			0.425916i
$315$	−5.55366	−	8.27382i	−0.312913	−	0.466177i
$316$	0.647527			0.0364262
$317$	−0.992390	+	1.71887i	−0.0557382	+	0.0965414i	−0.892548	−	0.450952i	$-0.851085\pi$
$317$	−0.992390	+	1.71887i	−0.0557382	+	0.0965414i	0.836810	+	0.547493i	$0.184418\pi$
$318$	7.41107	+	21.3432i	0.415592	+	1.19687i
$319$	10.3392	−	5.96932i	0.578882	−	0.334218i
$320$	−1.08726	−	0.627730i	−0.0607797	−	0.0350911i
$321$	−19.1130	−	3.66374i	−1.06679	−	0.204490i
$322$	19.9947	+	13.7043i	1.11426	+	0.763710i
$323$	11.1007			0.617658
$324$	−8.62513	+	2.57043i	−0.479174	+	0.142801i
$325$	11.6374	−	4.11883i	0.645525	−	0.228472i
$326$	−10.1935	+	5.88520i	−0.564564	+	0.325951i
$327$	2.64044	−	3.05345i	0.146016	−	0.168856i
$328$			9.52690i			0.526035i
$329$	1.93453	−	24.9897i	0.106654	−	1.37773i
$330$	−3.84778	−	0.737573i	−0.211813	−	0.0406020i
$331$	−1.38896	−	0.801918i	−0.0763443	−	0.0440774i	0.461342	−	0.887222i	$-0.347368\pi$
$331$	−1.38896	−	0.801918i	−0.0763443	−	0.0440774i	−0.537686	+	0.843145i	$0.680701\pi$
$332$	9.82961	−	5.67513i	0.539470	−	0.311463i
$333$	−16.3735	+	2.38790i	−0.897264	+	0.130856i
$334$	7.18880	+	4.15046i	0.393354	+	0.227103i
$335$	16.5843			0.906096
$336$	4.43213	−	1.16458i	0.241792	−	0.0635328i
$337$	19.0094			1.03551			0.517754	−	0.855529i	$-0.326768\pi$
$337$	19.0094			1.03551			0.517754	+	0.855529i	$0.326768\pi$
$338$	10.1056	−	8.17780i	0.549673	−	0.444814i
$339$	−5.36213	−	15.4424i	−0.291231	−	0.838718i
$340$	2.44956	−	1.41426i	0.132846	−	0.0766988i
$341$	−4.30982	+	7.46483i	−0.233390	+	0.404243i
$342$	−13.7336	−	5.46598i	−0.742629	−	0.295566i
$343$	−18.0250	−	4.25424i	−0.973260	−	0.229707i
$344$	3.14581			0.169611
$345$	−15.0699	−	13.0315i	−0.811336	−	0.701595i
$346$	9.17486	+	15.8913i	0.493243	+	0.854323i
$347$	−22.0055	+	12.7049i	−1.18132	+	0.682033i	−0.956319	−	0.292326i	$-0.905571\pi$
$347$	−22.0055	+	12.7049i	−1.18132	+	0.682033i	−0.224997	+	0.974359i	$0.572237\pi$
$348$	7.50715	−	8.68140i	0.402425	−	0.465372i
$349$	−16.8298			−0.900881			−0.450440	−	0.892807i	$-0.648733\pi$
$349$	−16.8298			−0.900881			−0.450440	+	0.892807i	$0.648733\pi$
$350$	3.91029	+	8.17114i	0.209014	+	0.436766i
$351$	−13.6878	−	12.7924i	−0.730599	−	0.682807i
$352$	0.900851	−	1.56032i	0.0480155	−	0.0831653i
$353$	11.7823	−	6.80251i	0.627109	−	0.362061i	−0.152523	−	0.988300i	$-0.548740\pi$
$353$	11.7823	−	6.80251i	0.627109	−	0.362061i	0.779631	+	0.626239i	$0.215406\pi$
$354$	−3.14977	−	9.07102i	−0.167408	−	0.482120i
$355$	−10.0174	−	5.78355i	−0.531668	−	0.306959i
$356$			12.8426i			0.680657i
$357$	−2.72049	+	9.95954i	−0.143984	+	0.527115i
$358$			3.98717i			0.210728i
$359$	−14.3788	+	24.9048i	−0.758884	+	1.31443i	0.184536	+	0.982826i	$0.440922\pi$
$359$	−14.3788	+	24.9048i	−0.758884	+	1.31443i	−0.943420	+	0.331600i	$0.892412\pi$
$360$	−3.72695	+	0.543534i	−0.196428	+	0.0286468i
$361$	−2.63830	−	4.56966i	−0.138858	−	0.240509i
$362$	−11.4443	−	6.60737i	−0.601499	−	0.347276i
$363$	−2.52835	+	13.1900i	−0.132704	+	0.692293i
$364$	6.75288	+	6.73785i	0.353947	+	0.353159i
$365$			19.9638i			1.04495i
$366$	3.46608	−	4.00824i	0.181175	−	0.209514i
$367$	−17.7774	+	10.2638i	−0.927970	+	0.535764i	−0.886169	−	0.463362i	$-0.846643\pi$
$367$	−17.7774	+	10.2638i	−0.927970	+	0.535764i	−0.0418014	+	0.999126i	$0.513310\pi$
$368$	7.93452	−	4.58100i	0.413615	−	0.238801i
$369$	17.7127	+	22.4302i	0.922087	+	1.16767i
$370$	−6.92459			−0.359992
$371$	−28.4671	−	19.5112i	−1.47794	−	1.01297i
$372$	−1.56001	+	8.13826i	−0.0808825	+	0.421949i
$373$	6.93995	−	12.0203i	0.359337	−	0.622390i	−0.628513	−	0.777799i	$-0.716336\pi$
$373$	6.93995	−	12.0203i	0.359337	−	0.622390i	0.987850	+	0.155409i	$0.0496695\pi$
$374$	2.02959	+	3.51535i	0.104948	+	0.181775i
$375$	−6.00862	−	17.3042i	−0.310284	−	0.893587i
$376$	−8.20429	−	4.73675i	−0.423104	−	0.244279i
$377$	23.4907	+	4.35779i	1.20983	+	0.224437i
$378$	8.26984	−	10.9822i	0.425355	−	0.564866i
$379$			30.4541i			1.56432i	0.623075	+	0.782162i	$0.285883\pi$
$379$			30.4541i			1.56432i	−0.623075	+	0.782162i	$0.714117\pi$
$380$	−5.35707	−	3.09290i	−0.274812	−	0.158663i
$381$	−15.8059	+	5.48834i	−0.809761	+	0.281176i
$382$	4.46998	−	2.58075i	0.228704	−	0.132042i
$383$	1.33536	+	0.770971i	0.0682338	+	0.0393948i	0.533729	−	0.845656i	$-0.320790\pi$
$383$	1.33536	+	0.770971i	0.0682338	+	0.0393948i	−0.465495	+	0.885051i	$0.654124\pi$
$384$	0.326076	−	1.70108i	0.0166400	−	0.0868079i
$385$	5.39830	−	2.58335i	0.275123	−	0.131660i
$386$			3.20108i			0.162931i
$387$	7.40653	−	5.84879i	0.376495	−	0.297311i
$388$	0.744240	+	1.28906i	0.0377831	+	0.0654422i
$389$	24.9269	−	14.3916i	1.26385	−	0.729682i	0.290029	−	0.957018i	$-0.406335\pi$
$389$	24.9269	−	14.3916i	1.26385	−	0.729682i	0.973816	+	0.227336i	$0.0730016\pi$
$390$	−4.89562	−	6.12404i	−0.247899	−	0.310103i
$391$			20.6417i			1.04390i
$392$	−4.39129	+	5.45129i	−0.221794	+	0.275332i
$393$	6.33851	−	33.0668i	0.319735	−	1.66800i
$394$	−1.76204	+	3.05195i	−0.0887704	+	0.153755i
$395$	0.704030	−	0.406472i	0.0354236	−	0.0204518i
$396$	−0.780022	−	5.34853i	−0.0391976	−	0.268774i
$397$	−6.83724	+	11.8425i	−0.343151	+	0.594356i	−0.985016	−	0.172462i	$-0.944828\pi$
$397$	−6.83724	+	11.8425i	−0.343151	+	0.594356i	0.641865	+	0.766818i	$0.278161\pi$
$398$		−	10.3870i		−	0.520652i
$399$	21.8377	−	5.73801i	1.09325	−	0.287260i
$400$	3.42382			0.171191
$401$	−16.5303	+	28.6313i	−0.825483	+	1.42978i	0.0760665	+	0.997103i	$0.475764\pi$
$401$	−16.5303	+	28.6313i	−0.825483	+	1.42978i	−0.901550	+	0.432676i	$0.857569\pi$
$402$	7.50511	+	21.6140i	0.374321	+	1.07801i
$403$	−16.2611	+	5.75532i	−0.810024	+	0.286693i
$404$	0.424346	−	0.734989i	0.0211120	−	0.0365671i
$405$	−7.76422	+	8.20897i	−0.385807	+	0.407907i
$406$	−1.35312	+	17.4793i	−0.0671544	+	0.867482i
$407$		−	9.93743i		−	0.492580i
$408$	2.95171	+	2.55246i	0.146131	+	0.126366i
$409$	0.635322	+	1.10041i	0.0314146	+	0.0544117i	0.881305	−	0.472547i	$-0.156665\pi$
$409$	0.635322	+	1.10041i	0.0314146	+	0.0544117i	−0.849891	+	0.526959i	$0.823332\pi$
$410$	5.98031	+	10.3582i	0.295347	+	0.511555i
$411$	−14.4453	−	12.4914i	−0.712533	−	0.616156i
$412$		−	6.12968i		−	0.301988i
$413$	12.0987	+	8.29243i	0.595340	+	0.408044i
$414$	10.1640	−	25.5377i	0.499533	−	1.25511i
$415$	7.12489	−	12.3407i	0.349747	−	0.605780i
$416$	3.39894	−	1.20299i	0.166647	−	0.0589816i
$417$	5.16393	+	14.8716i	0.252879	+	0.728267i
$418$	4.43861	−	7.68789i	0.217099	−	0.376027i
$419$	−12.8180			−0.626202			−0.313101	−	0.949720i	$-0.601368\pi$
$419$	−12.8180			−0.626202			−0.313101	+	0.949720i	$0.601368\pi$
$420$	4.08784	−	4.04837i	0.199466	−	0.197540i
$421$			24.3303i			1.18579i	0.805281	+	0.592894i	$0.202015\pi$
$421$			24.3303i			1.18579i	−0.805281	+	0.592894i	$0.797985\pi$
$422$	−3.81313	+	6.60453i	−0.185620	+	0.321503i
$423$	−28.1230	+	4.10142i	−1.36739	+	0.199418i
$424$	−11.2966	+	6.52211i	−0.548613	+	0.316742i
$425$	−3.85689	+	6.68032i	−0.187086	+	0.324043i
$426$	3.00428	−	15.6728i	0.145558	−	0.759349i
$427$	−0.624743	+	8.07026i	−0.0302334	+	0.390547i
$428$		−	11.2358i		−	0.543104i
$429$	8.78857	−	7.02567i	0.424316	−	0.339203i
$430$	3.42031	−	1.97472i	0.164942	−	0.0952293i
$431$	6.41225	+	11.1063i	0.308867	+	0.534974i	0.978115	−	0.208066i	$-0.0667168\pi$
$431$	6.41225	+	11.1063i	0.308867	+	0.534974i	−0.669248	+	0.743039i	$0.733383\pi$
$432$	−2.39498	−	4.61130i	−0.115229	−	0.221861i
$433$		−	24.6486i		−	1.18454i	−0.805741	−	0.592268i	$-0.798233\pi$
$433$		−	24.6486i		−	1.18454i	0.805741	−	0.592268i	$-0.201767\pi$
$434$	−5.46392	−	11.4177i	−0.262277	−	0.548066i
$435$	2.71265	−	14.1514i	0.130062	−	0.678507i
$436$	2.01838	+	1.16531i	0.0966629	+	0.0558083i
$437$	39.0944	−	22.5712i	1.87014	−	1.07972i
$438$	−26.0184	+	9.03448i	−1.24321	+	0.431684i
$439$	6.57463	+	3.79586i	0.313790	+	0.181167i	0.648621	−	0.761111i	$-0.275346\pi$
$439$	6.57463	+	3.79586i	0.313790	+	0.181167i	−0.334831	+	0.942278i	$0.608679\pi$
$440$		−	2.26196i		−	0.107835i
$441$	−0.203700	+	20.9990i	−0.00970002	+	0.999953i
$442$	−1.48166	+	7.98693i	−0.0704756	+	0.379900i
$443$	20.0410	+	11.5707i	0.952176	+	0.549739i	0.893756	−	0.448553i	$-0.148060\pi$
$443$	20.0410	+	11.5707i	0.952176	+	0.549739i	0.0584201	+	0.998292i	$0.481394\pi$
$444$	−3.13368	−	9.02469i	−0.148718	−	0.428293i
$445$	8.06169	+	13.9632i	0.382161	+	0.661922i
$446$	0.0799060	−	0.138401i	0.00378366	−	0.00655349i
$447$	2.72293	−	14.2050i	0.128790	−	0.671875i
$448$	1.14208	+	2.38656i	0.0539584	+	0.112754i
$449$	20.1099			0.949047			0.474523	−	0.880243i	$-0.342620\pi$
$449$	20.1099			0.949047			0.474523	+	0.880243i	$0.342620\pi$
$450$	8.06109	−	6.36568i	0.380003	−	0.300081i
$451$	−14.8650	+	8.58231i	−0.699966	+	0.404125i
$452$	8.17345	−	4.71894i	0.384447	−	0.221960i
$453$	−12.6616	+	14.6421i	−0.594893	+	0.687945i
$454$		−	8.90849i		−	0.418096i
$455$	11.5717	+	3.08680i	0.542489	+	0.144712i
$456$	1.60662	−	8.38144i	0.0752369	−	0.392497i
$457$	29.4354	+	16.9945i	1.37693	+	0.794970i	0.991789	−	0.127887i	$-0.0408196\pi$
$457$	29.4354	+	16.9945i	1.37693	+	0.794970i	0.385141	+	0.922858i	$0.374153\pi$
$458$	2.78489	+	4.82358i	0.130130	+	0.225391i
$459$	11.6952	+	0.521630i	0.545883	+	0.0243476i
$460$	5.75125	−	9.96146i	0.268154	−	0.464456i
$461$		−	32.1844i		−	1.49898i	−0.662016	−	0.749489i	$-0.730299\pi$
$461$		−	32.1844i		−	1.49898i	0.662016	−	0.749489i	$-0.269701\pi$
$462$	5.80980	+	5.86643i	0.270296	+	0.272931i
$463$		−	31.4752i		−	1.46278i	−0.681962	−	0.731388i	$-0.738873\pi$
$463$		−	31.4752i		−	1.46278i	0.681962	−	0.731388i	$-0.261127\pi$
$464$	5.73855	+	3.31315i	0.266406	+	0.153809i
$465$	3.41249	+	9.82766i	0.158251	+	0.455747i
$466$	4.99084	−	2.88146i	0.231196	−	0.133481i
$467$	−4.80726	+	8.32642i	−0.222453	+	0.385301i	−0.955552	−	0.294821i	$-0.904740\pi$
$467$	−4.80726	+	8.32642i	−0.222453	+	0.385301i	0.733099	+	0.680122i	$0.238073\pi$
$468$	5.76587	−	9.15176i	0.266527	−	0.423040i
$469$	−28.8283	−	19.7588i	−1.33117	−	0.912377i
$470$	−11.8936			−0.548610
$471$	−8.55052	+	9.88797i	−0.393987	+	0.455614i
$472$	4.80116	−	2.77195i	0.220991	−	0.127589i
$473$	2.83390	+	4.90847i	0.130303	+	0.225692i
$474$	0.848351	+	0.733603i	0.0389661	+	0.0336955i
$475$	16.8696			0.774031
$476$	−5.94302	−	0.460067i	−0.272398	−	0.0210872i
$477$	−14.4708	+	36.3588i	−0.662572	+	1.66476i
$478$	6.02639	−	10.4380i	0.275641	−	0.477424i
$479$	23.5767	−	13.6120i	1.07725	−	0.621948i	0.147094	−	0.989123i	$-0.453008\pi$
$479$	23.5767	−	13.6120i	1.07725	−	0.621948i	0.930152	+	0.367174i	$0.119675\pi$
$480$	−0.713289	−	2.05420i	−0.0325570	−	0.0937611i
$481$	12.9179	−	15.1198i	0.589006	−	0.689405i
$482$	−14.8113			−0.674635
$483$	10.6698	+	40.6071i	0.485494	+	1.84769i
$484$	−7.75387			−0.352449
$485$	1.61836	+	0.934363i	0.0734861	+	0.0424272i
$486$	−14.2123	−	6.40406i	−0.644681	−	0.290494i
$487$	−9.99814	+	5.77243i	−0.453059	+	0.261574i	−0.709121	−	0.705087i	$-0.750908\pi$
$487$	−9.99814	+	5.77243i	−0.453059	+	0.261574i	0.256062	+	0.966660i	$0.417575\pi$
$488$	2.64951	+	1.52970i	0.119938	+	0.0692462i
$489$	−20.0224	−	3.83805i	−0.905444	−	0.173563i
$490$	−1.35254	+	8.68351i	−0.0611015	+	0.392281i
$491$			8.30353i			0.374733i	0.982290	+	0.187367i	$0.0599952\pi$
$491$			8.30353i			0.374733i	−0.982290	+	0.187367i	$0.940005\pi$
$492$	−10.7933	+	12.4816i	−0.486600	+	0.562713i
$493$	−12.9288	+	7.46444i	−0.582283	+	0.336181i
$494$	16.7470	−	5.92730i	0.753484	−	0.266682i
$495$	−4.20551	−	5.32559i	−0.189024	−	0.239368i
$496$	−4.78417			−0.214816
$497$	10.5225	+	21.9884i	0.471999	+	0.986313i
$498$	19.3077	+	3.70105i	0.865199	+	0.165848i
$499$	−8.26470	−	4.77163i	−0.369979	−	0.213607i	0.303470	−	0.952841i	$-0.401855\pi$
$499$	−8.26470	−	4.77163i	−0.369979	−	0.213607i	−0.673449	+	0.739234i	$0.735188\pi$
$500$	9.15888	−	5.28788i	0.409598	−	0.236481i
$501$	4.71616	+	13.5821i	0.210703	+	0.606804i
$502$	−4.93524	+	8.54808i	−0.220270	+	0.381519i
$503$	−9.19561			−0.410012			−0.205006	−	0.978761i	$-0.565721\pi$
$503$	−9.19561			−0.410012			−0.205006	+	0.978761i	$0.565721\pi$
$504$	7.12609	+	3.49554i	0.317421	+	0.155704i
$505$		−	1.06550i		−	0.0474141i
$506$	14.2956	+	8.25359i	0.635518	+	0.366917i
$507$	22.5047	+	0.734893i	0.999467	+	0.0326377i
$508$	−4.83001	−	8.36583i	−0.214297	−	0.371174i
$509$	−21.0228	−	12.1375i	−0.931821	−	0.537987i	−0.0444338	−	0.999012i	$-0.514148\pi$
$509$	−21.0228	−	12.1375i	−0.931821	−	0.537987i	−0.887387	+	0.461025i	$0.847482\pi$
$510$	4.81153	+	0.922311i	0.213058	+	0.0408406i
$511$	23.7852	−	34.7028i	1.05220	−	1.53516i
$512$	1.00000			0.0441942
$513$	−11.8004	−	22.7204i	−0.521000	−	1.00313i
$514$	−4.00565	−	6.93799i	−0.176682	−	0.306022i
$515$	−3.84778	−	6.66455i	−0.169553	−	0.293675i
$516$	4.12145	+	3.56398i	0.181437	+	0.156896i
$517$		−	17.0684i		−	0.750668i
$518$	12.0369	+	8.25008i	0.528872	+	0.362487i
$519$	−5.98341	+	31.2143i	−0.262643	+	1.37016i
$520$	2.94038	−	3.44158i	0.128944	−	0.150923i
$521$	11.6545	+	20.1861i	0.510591	+	0.884370i	0.999925	+	0.0122733i	$0.00390682\pi$
$521$	11.6545	+	20.1861i	0.510591	+	0.884370i	−0.489333	+	0.872097i	$0.662760\pi$
$522$	19.6708	−	2.86877i	0.860969	−	0.125563i
$523$	26.9553	+	15.5627i	1.17867	+	0.680508i	0.955707	−	0.294318i	$-0.0950926\pi$
$523$	26.9553	+	15.5627i	1.17867	+	0.680508i	0.222967	+	0.974826i	$0.428426\pi$
$524$	19.4387			0.849184
$525$	−4.13431	+	15.1354i	−0.180436	+	0.660564i
$526$			10.5818i			0.461389i
$527$	5.38930	−	9.33454i	0.234761	−	0.406619i
$528$	2.94797	−	1.02364i	0.128294	−	0.0445480i
$529$	30.4710	+	52.7774i	1.32483	+	2.29467i
$530$	−8.18825	+	14.1825i	−0.355675	+	0.616047i
$531$	6.15021	−	15.4528i	0.266896	−	0.670594i
$532$	5.62719	+	11.7589i	0.243970	+	0.509811i
$533$	−33.7735	−	6.26536i	−1.46289	−	0.271383i
$534$	−14.5498	+	16.8256i	−0.629631	+	0.728116i
$535$	−7.05306	−	12.2163i	−0.304930	−	0.528155i
$536$	−11.4400	+	6.60487i	−0.494131	+	0.285287i
$537$	−4.51718	+	5.22375i	−0.194931	+	0.225421i
$538$	10.7670			0.464199
$539$	−12.4617	−	1.94102i	−0.536761	−	0.0836057i
$540$	−5.49862	−	3.51027i	−0.236623	−	0.151058i
$541$	2.26719	+	1.30896i	0.0974740	+	0.0562766i	0.547945	−	0.836515i	$-0.315410\pi$
$541$	2.26719	+	1.30896i	0.0974740	+	0.0562766i	−0.450471	+	0.892791i	$0.648744\pi$
$542$	0.888146	+	1.53831i	0.0381491	+	0.0660762i
$543$	−7.50795	−	21.6222i	−0.322197	−	0.927897i
$544$	−1.12649	+	1.95113i	−0.0482977	+	0.0836540i
$545$	2.92600			0.125336
$546$	1.21371	+	16.4781i	0.0519421	+	0.705196i
$547$	23.2307			0.993272			0.496636	−	0.867959i	$-0.334568\pi$
$547$	23.2307			0.993272			0.496636	+	0.867959i	$0.334568\pi$
$548$	5.51288	−	9.54858i	0.235498	−	0.407895i
$549$	9.08211	−	1.32452i	0.387615	−	0.0565293i
$550$	3.08435	+	5.34226i	0.131517	+	0.227795i
$551$	28.2746	+	16.3243i	1.20454	+	0.695440i
$552$	15.5853	+	2.98751i	0.663354	+	0.127157i
$553$	−1.70808	−	0.132228i	−0.0726351	−	0.00562291i
$554$	−16.6438			−0.707129
$555$	−9.07218	−	7.84508i	−0.385093	−	0.333005i
$556$	−7.87134	+	4.54452i	−0.333819	+	0.192730i
$557$	21.0588	+	36.4749i	0.892290	+	1.54549i	0.837123	+	0.547015i	$0.184236\pi$
$557$	21.0588	+	36.4749i	0.892290	+	1.54549i	0.0551670	+	0.998477i	$0.482431\pi$
$558$	−11.2639	+	8.89488i	−0.476839	+	0.376550i
$559$	−2.06884	+	11.1521i	−0.0875026	+	0.471684i
$560$	2.73985	+	1.87789i	0.115780	+	0.0793551i
$561$	−1.32360	+	6.90499i	−0.0558826	+	0.291529i
$562$	8.71914	−	15.1020i	0.367795	−	0.637039i
$563$	4.75102	+	8.22901i	0.200232	+	0.346811i	0.948603	−	0.316469i	$-0.102497\pi$
$563$	4.75102	+	8.22901i	0.200232	+	0.346811i	−0.748371	+	0.663280i	$0.769164\pi$
$564$	−5.38236	−	15.5007i	−0.226638	−	0.652697i
$565$	5.92444	−	10.2614i	0.249243	−	0.431702i
$566$		−	26.3230i		−	1.10644i
$567$	23.2768	−	5.01913i	0.977533	−	0.210784i
$568$	9.21344			0.386587
$569$	23.5732	+	13.6100i	0.988238	+	0.570560i	0.904747	−	0.425949i	$-0.140060\pi$
$569$	23.5732	+	13.6100i	0.988238	+	0.570560i	0.0834912	+	0.996509i	$0.473393\pi$
$570$	−3.51446	−	10.1213i	−0.147205	−	0.423936i
$571$	−10.1291	−	17.5442i	−0.423891	−	0.734200i	0.572425	−	0.819957i	$-0.306003\pi$
$571$	−10.1291	−	17.5442i	−0.423891	−	0.734200i	−0.996316	+	0.0857564i	$0.972669\pi$
$572$	4.93899	+	4.21972i	0.206510	+	0.176435i
$573$	8.78012	+	1.68304i	0.366795	+	0.0703101i
$574$	1.94544	−	25.1306i	0.0812010	−	1.04893i
$575$			31.3690i			1.30818i
$576$	2.35441	−	1.85923i	0.0981005	−	0.0774680i
$577$	10.6054	+	18.3692i	0.441511	+	0.764719i	0.997802	−	0.0662687i	$-0.0211095\pi$
$577$	10.6054	+	18.3692i	0.441511	+	0.764719i	−0.556291	+	0.830987i	$0.687776\pi$
$578$	5.96206	+	10.3266i	0.247989	+	0.429530i
$579$	−3.62660	+	4.19386i	−0.150716	+	0.174291i
$580$	8.31906			0.345430
$581$	−27.0880	+	12.9629i	−1.12380	+	0.537793i
$582$	−0.485358	+	2.53202i	−0.0201187	+	0.104956i
$583$	−20.3532	−	11.7509i	−0.842942	−	0.486673i
$584$	−7.95079	−	13.7712i	−0.329006	−	0.569855i
$585$	0.524163	−	13.5697i	0.0216715	−	0.561040i
$586$	−5.59531	−	3.23045i	−0.231140	−	0.133449i
$587$			9.30051i			0.383873i	0.981407	+	0.191937i	$0.0614768\pi$
$587$			9.30051i			0.383873i	−0.981407	+	0.191937i	$0.938523\pi$
$588$	−11.9291	+	2.16692i	−0.491950	+	0.0893624i
$589$	−23.5722			−0.971276
$590$	3.48007	−	6.02766i	0.143272	−	0.248155i
$591$	−5.76617	+	2.00221i	−0.237188	+	0.0823598i
$592$	4.77663	−	2.75779i	0.196318	−	0.113345i
$593$	−18.3797	−	10.6115i	−0.754765	−	0.435764i	0.0726480	−	0.997358i	$-0.476855\pi$
$593$	−18.3797	−	10.6115i	−0.754765	−	0.435764i	−0.827413	+	0.561594i	$0.810188\pi$
$594$	5.03757	−	7.89103i	0.206694	−	0.323773i
$595$	−6.75040	+	3.23040i	−0.276739	+	0.132433i
$596$	8.35060			0.342054
$597$	11.7677	−	13.6084i	0.481621	−	0.556955i
$598$	11.0218	+	31.1411i	0.450715	+	1.27345i
$599$	−4.28246	+	2.47248i	−0.174976	+	0.101023i	−0.584930	−	0.811084i	$-0.698878\pi$
$599$	−4.28246	+	2.47248i	−0.174976	+	0.101023i	0.409954	+	0.912106i	$0.365545\pi$
$600$	4.48569	+	3.87895i	0.183127	+	0.158358i
$601$		−	30.0304i		−	1.22496i	−0.790484	−	0.612482i	$-0.790171\pi$
$601$		−	30.0304i		−	1.22496i	0.790484	−	0.612482i	$-0.209829\pi$
$602$	−8.29820	−	0.642389i	−0.338209	−	0.0261818i
$603$	−14.6544	+	36.8201i	−0.596774	+	1.49943i
$604$	−9.67867	−	5.58798i	−0.393819	−	0.227372i
$605$	−8.43047	+	4.86733i	−0.342747	+	0.197885i
$606$	1.38864	−	0.482184i	0.0564098	−	0.0195874i
$607$	−12.2846	−	7.09250i	−0.498616	−	0.287876i	0.229526	−	0.973303i	$-0.426282\pi$
$607$	−12.2846	−	7.09250i	−0.498616	−	0.287876i	−0.728142	+	0.685427i	$0.759616\pi$
$608$	4.92713			0.199821
$609$	−21.5756	+	21.3673i	−0.874287	+	0.865847i
$610$	3.84095			0.155515
$611$	22.1876	−	25.9696i	0.897615	−	1.05062i
$612$	0.975393	+	6.68816i	0.0394279	+	0.270353i
$613$	25.9439	−	14.9787i	1.04787	−	0.604985i	0.125814	−	0.992054i	$-0.459846\pi$
$613$	25.9439	−	14.9787i	1.04787	−	0.604985i	0.922051	+	0.387068i	$0.126512\pi$
$614$	1.55633	−	2.69563i	0.0628082	−	0.108787i
$615$	−3.90008	+	20.3460i	−0.157266	+	0.820429i
$616$	−2.69494	+	3.93194i	−0.108582	+	0.158423i
$617$	−18.3153			−0.737348			−0.368674	−	0.929559i	$-0.620188\pi$
$617$	−18.3153			−0.737348			−0.368674	+	0.929559i	$0.620188\pi$
$618$	6.94450	−	8.03074i	0.279349	−	0.323044i
$619$	0.162214	+	0.280963i	0.00651994	+	0.0112929i	0.869267	−	0.494343i	$-0.164591\pi$
$619$	0.162214	+	0.280963i	0.00651994	+	0.0112929i	−0.862747	+	0.505636i	$0.831258\pi$
$620$	−5.20163	+	3.00316i	−0.208903	+	0.120610i
$621$	42.2487	−	21.9428i	1.69538	−	0.880536i
$622$	−12.5679			−0.503927
$623$	2.62252	−	33.8770i	0.105069	−	1.35725i
$624$	5.81600	+	2.27468i	0.232826	+	0.0910600i
$625$	−1.92084	+	3.32699i	−0.0768335	+	0.133079i
$626$	1.20941	−	0.698253i	0.0483377	−	0.0279078i
$627$	14.5250	−	5.04359i	0.580075	−	0.201421i
$628$	−6.53612	−	3.77363i	−0.260819	−	0.150584i
$629$			12.4264i			0.495475i
$630$	9.94217	−	0.672705i	0.396105	−	0.0268012i
$631$		−	38.0843i		−	1.51611i	−0.652190	−	0.758056i	$-0.726150\pi$
$631$		−	38.0843i		−	1.51611i	0.652190	−	0.758056i	$-0.273850\pi$
$632$	−0.323763	+	0.560775i	−0.0128786	+	0.0223064i
$633$	−12.4782	+	4.33285i	−0.495964	+	0.172215i
$634$	−0.992390	−	1.71887i	−0.0394128	−	0.0682651i
$635$	−10.5030	−	6.06388i	−0.416797	−	0.240638i
$636$	−22.1893	−	4.25341i	−0.879862	−	0.168659i
$637$	−16.4373	−	19.1525i	−0.651268	−	0.758848i
$638$			11.9386i			0.472655i
$639$	21.6922	−	17.1299i	0.858131	−	0.677649i
$640$	1.08726	−	0.627730i	0.0429777	−	0.0248132i
$641$	27.9073	−	16.1123i	1.10227	−	0.636396i	0.165454	−	0.986217i	$-0.447091\pi$
$641$	27.9073	−	16.1123i	1.10227	−	0.636396i	0.936816	+	0.349821i	$0.113758\pi$
$642$	12.7294	−	14.7205i	0.502390	−	0.580972i
$643$	−44.5662			−1.75752			−0.878760	−	0.477264i	$-0.841628\pi$
$643$	−44.5662			−1.75752			−0.878760	+	0.477264i	$0.841628\pi$
$644$	−21.8656	+	10.4638i	−0.861625	+	0.412330i
$645$	6.71830	+	1.28782i	0.264533	+	0.0507078i
$646$	−5.55034	+	9.61347i	−0.218375	+	0.378237i
$647$	−4.35837	−	7.54892i	−0.171345	−	0.296779i	0.767545	−	0.640995i	$-0.221478\pi$
$647$	−4.35837	−	7.54892i	−0.171345	−	0.296779i	−0.938890	+	0.344216i	$0.888145\pi$
$648$	2.08651	−	8.75480i	0.0819659	−	0.343921i
$649$	8.65026	+	4.99423i	0.339552	+	0.196041i
$650$	−2.25167	+	12.1377i	−0.0883179	+	0.476079i
$651$	5.77694	−	21.1490i	0.226416	−	0.828895i
$652$		−	11.7704i		−	0.460965i
$653$	−17.3737	−	10.0307i	−0.679884	−	0.392531i	0.119928	−	0.992783i	$-0.461734\pi$
$653$	−17.3737	−	10.0307i	−0.679884	−	0.392531i	−0.799811	+	0.600252i	$0.795067\pi$
$654$	1.32414	+	3.81341i	0.0517781	+	0.149116i
$655$	21.1349	−	12.2023i	0.825810	−	0.476782i
$656$	−8.25053	−	4.76345i	−0.322129	−	0.185981i
$657$	−44.3232	−	17.6406i	−1.72921	−	0.688227i
$658$	20.6745	+	14.1702i	0.805975	+	0.552413i
$659$		−	26.2428i		−	1.02227i	−0.859500	−	0.511136i	$-0.829225\pi$
$659$		−	26.2428i		−	1.02227i	0.859500	−	0.511136i	$-0.170775\pi$
$660$	2.56265	−	2.96349i	0.0997509	−	0.115354i
$661$	−15.1199	−	26.1885i	−0.588098	−	1.01862i	−0.994481	−	0.104913i	$-0.966544\pi$
$661$	−15.1199	−	26.1885i	−0.588098	−	1.01862i	0.406384	−	0.913703i	$-0.366790\pi$
$662$	1.38896	−	0.801918i	0.0539836	−	0.0311674i
$663$	−10.9898	+	8.78538i	−0.426810	+	0.341196i
$664$			11.3503i			0.440475i
$665$	13.4996	+	9.25258i	0.523492	+	0.358800i
$666$	6.11879	−	15.3738i	0.237098	−	0.595725i
$667$	−30.3551	+	52.5766i	−1.17535	+	2.03577i
$668$	−7.18880	+	4.15046i	−0.278143	+	0.160586i
$669$	0.261487	−	0.0907971i	0.0101097	−	0.00351042i
$670$	−8.29214	+	14.3624i	−0.320353	+	0.554868i
$671$			5.51212i			0.212793i
$672$	−1.20751	+	4.42062i	−0.0465808	+	0.170529i
$673$	−8.54206			−0.329272			−0.164636	−	0.986354i	$-0.552645\pi$
$673$	−8.54206			−0.329272			−0.164636	+	0.986354i	$0.552645\pi$
$674$	−9.50471	+	16.4626i	−0.366108	+	0.634117i
$675$	17.7730	+	0.792718i	0.684084	+	0.0305117i
$676$	2.02938	+	12.8406i	0.0780529	+	0.493870i
$677$	−5.08564	+	8.80859i	−0.195457	+	0.338542i	−0.947050	−	0.321085i	$-0.895952\pi$
$677$	−5.08564	+	8.80859i	−0.195457	+	0.338542i	0.751593	+	0.659627i	$0.229286\pi$
$678$	16.0546	+	3.07747i	0.616573	+	0.118190i
$679$	−1.69997	−	3.55234i	−0.0652388	−	0.136326i
$680$			2.82851i			0.108468i
$681$	10.0927	−	11.6714i	0.386753	−	0.447248i
$682$	−4.30982	−	7.46483i	−0.165032	−	0.285843i
$683$	13.6076	+	23.5691i	0.520682	+	0.901848i	0.999711	+	0.0240486i	$0.00765566\pi$
$683$	13.6076	+	23.5691i	0.520682	+	0.901848i	−0.479029	+	0.877799i	$0.659011\pi$
$684$	11.6005	−	9.16068i	0.443556	−	0.350267i
$685$		−	13.8424i		−	0.528890i
$686$	12.6968	−	13.4830i	0.484766	−	0.514784i
$687$	−1.81618	+	9.47466i	−0.0692915	+	0.361481i
$688$	−1.57290	+	2.72435i	−0.0599664	+	0.103865i
$689$	−15.6921	−	44.3366i	−0.597822	−	1.68909i
$690$	18.8206	−	6.53514i	0.716488	−	0.248789i
$691$	−23.0089	+	39.8526i	−0.875300	+	1.51606i	−0.0188577	+	0.999822i	$0.506003\pi$
$691$	−23.0089	+	39.8526i	−0.875300	+	1.51606i	−0.856443	+	0.516242i	$0.827330\pi$
$692$	−18.3497			−0.697552
$693$	0.965394	+	14.2679i	0.0366723	+	0.541994i
$694$		−	25.4097i		−	0.964540i
$695$	−5.70546	+	9.88214i	−0.216420	+	0.374851i
$696$	3.76474	+	10.8421i	0.142702	+	0.410968i
$697$	18.5882	−	10.7319i	0.704079	−	0.406500i
$698$	8.41492	−	14.5751i	0.318509	−	0.551675i
$699$	9.80321	+	1.87916i	0.370791	+	0.0710762i
$700$	−9.03156	−	0.699161i	−0.341361	−	0.0264258i
$701$		−	19.8971i		−	0.751505i	−0.926720	−	0.375752i	$-0.877384\pi$
$701$		−	19.8971i		−	0.751505i	0.926720	−	0.375752i	$-0.122616\pi$
$702$	17.9224	−	5.45777i	0.676438	−	0.205990i
$703$	23.5351	−	13.5880i	0.887643	−	0.512481i
$704$	0.900851	+	1.56032i	0.0339521	+	0.0588067i
$705$	−15.5823	−	13.4746i	−0.586862	−	0.507483i
$706$			13.6050i			0.512032i
$707$	−1.26945	+	1.85214i	−0.0477427	+	0.0696571i
$708$	9.43062	+	1.80774i	0.354424	+	0.0679389i
$709$	−13.9224	−	8.03812i	−0.522868	−	0.301878i	0.215239	−	0.976561i	$-0.430947\pi$
$709$	−13.9224	−	8.03812i	−0.522868	−	0.301878i	−0.738107	+	0.674683i	$0.764280\pi$
$710$	10.0174	−	5.78355i	0.375946	−	0.217053i
$711$	0.280338	+	1.92225i	0.0105135	+	0.0720899i
$712$	−11.1220	−	6.42131i	−0.416816	−	0.240649i
$713$		−	43.8325i		−	1.64154i
$714$	−7.26497	−	7.33578i	−0.271885	−	0.274535i
$715$	8.01881	+	1.48758i	0.299886	+	0.0556323i
$716$	−3.45299	−	1.99358i	−0.129044	−	0.0745037i
$717$	19.7210	−	6.84779i	0.736493	−	0.255735i
$718$	−14.3788	−	24.9048i	−0.536612	−	0.929439i
$719$	0.367826	−	0.637094i	0.0137176	−	0.0237596i	−0.859085	−	0.511833i	$-0.828967\pi$
$719$	0.367826	−	0.637094i	0.0137176	−	0.0237596i	0.872803	+	0.488073i	$0.162300\pi$
$720$	1.39276	−	3.49940i	0.0519052	−	0.130415i
$721$	−1.25171	+	16.1692i	−0.0466161	+	0.602173i
$722$	5.27659			0.196374
$723$	−19.4049	−	16.7802i	−0.721674	−	0.624061i
$724$	11.4443	−	6.60737i	0.425324	−	0.245561i
$725$	−19.6478	+	11.3437i	−0.729700	+	0.421293i
$726$	−10.1587	−	8.78460i	−0.377023	−	0.326027i
$727$			30.0123i			1.11310i	0.830815	+	0.556548i	$0.187875\pi$
$727$			30.0123i			1.11310i	−0.830815	+	0.556548i	$0.812125\pi$
$728$	−9.21159	+	2.47924i	−0.341404	+	0.0918869i
$729$	−11.3647	−	24.4917i	−0.420915	−	0.907100i
$730$	−17.2891	−	9.98189i	−0.639900	−	0.369446i
$731$	−3.54371	−	6.13788i	−0.131069	−	0.227018i
$732$	1.73819	+	5.00584i	0.0642455	+	0.185021i
$733$	10.5944	−	18.3500i	0.391313	−	0.677774i	−0.601310	−	0.799016i	$-0.705354\pi$
$733$	10.5944	−	18.3500i	0.391313	−	0.677774i	0.992623	+	0.121242i	$0.0386876\pi$
$734$		−	20.5275i		−	0.757685i
$735$	−11.6098	+	9.84428i	−0.428235	+	0.363112i
$736$			9.16199i			0.337716i
$737$	−20.6114	−	11.9000i	−0.759231	−	0.438342i
$738$	−28.2815	+	4.12454i	−1.04106	+	0.151826i
$739$	−27.6117	+	15.9416i	−1.01571	+	0.586422i	−0.912859	−	0.408274i	$-0.866131\pi$
$739$	−27.6117	+	15.9416i	−1.01571	+	0.586422i	−0.102854	+	0.994696i	$0.532797\pi$
$740$	3.46229	−	5.99687i	0.127276	−	0.220449i
$741$	28.6562	+	11.2076i	1.05271	+	0.411722i
$742$	31.1308	−	14.8976i	1.14285	−	0.546908i
$743$	−52.2488			−1.91682			−0.958411	−	0.285393i	$-0.907876\pi$
$743$	−52.2488			−1.91682			−0.958411	+	0.285393i	$0.907876\pi$
$744$	−6.26793	−	5.42013i	−0.229794	−	0.198712i
$745$	9.07927	−	5.24192i	0.332639	−	0.192049i
$746$	6.93995	+	12.0203i	0.254090	+	0.440096i
$747$	21.1028	+	26.7232i	0.772110	+	0.977750i
$748$	−4.05918			−0.148418
$749$	−2.29441	+	29.6385i	−0.0838359	+	1.08297i
$750$	17.9902	+	3.44851i	0.656910	+	0.125922i
$751$	−1.47301	+	2.55132i	−0.0537508	+	0.0930991i	−0.891649	−	0.452728i	$-0.850451\pi$
$751$	−1.47301	+	2.55132i	−0.0537508	+	0.0930991i	0.837898	+	0.545827i	$0.183784\pi$
$752$	8.20429	−	4.73675i	0.299180	−	0.172731i
$753$	−16.1502	+	5.60791i	−0.588547	+	0.204363i
$754$	−15.5193	+	18.1647i	−0.565180	+	0.661518i
$755$	−14.0310			−0.510639
$756$	5.37598	+	12.6530i	0.195523	+	0.460186i
$757$	−6.17064			−0.224276			−0.112138	−	0.993693i	$-0.535770\pi$
$757$	−6.17064			−0.224276			−0.112138	+	0.993693i	$0.535770\pi$
$758$	−26.3741	−	15.2271i	−0.957949	−	0.553072i
$759$	9.37855	+	27.0093i	0.340420	+	0.980376i
$760$	5.35707	−	3.09290i	0.194321	−	0.112191i
$761$	21.9711	+	12.6850i	0.796453	+	0.459833i	0.842230	−	0.539119i	$-0.181243\pi$
$761$	21.9711	+	12.6850i	0.796453	+	0.459833i	−0.0457761	+	0.998952i	$0.514576\pi$
$762$	3.14991	−	16.4325i	0.114109	−	0.595286i
$763$	−5.08624	−	3.48609i	−0.184134	−	0.126205i
$764$			5.16149i			0.186736i
$765$	5.25886	+	6.65948i	0.190135	+	0.240774i
$766$	−1.33536	+	0.770971i	−0.0482486	+	0.0278563i
$767$	6.66927	+	18.8434i	0.240813	+	0.680396i
$768$	1.31014	+	1.13293i	0.0472756	+	0.0408811i
$769$	44.5230			1.60554			0.802771	−	0.596288i	$-0.203358\pi$
$769$	44.5230			1.60554			0.802771	+	0.596288i	$0.203358\pi$
$770$	−0.461903	+	5.96674i	−0.0166458	+	0.215026i
$771$

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.bg (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.63622 + 0.568150i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.08726 - 0.627730i) q^{5} +(0.326076 - 1.70108i) q^{6} +(1.14208 + 2.38656i) q^{7} +1.00000 q^{8} +(2.35441 - 1.85923i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.63622 + 0.568150i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.08726 - 0.627730i) q^{5} +(0.326076 - 1.70108i) q^{6} +(1.14208 + 2.38656i) q^{7} +1.00000 q^{8} +(2.35441 - 1.85923i) q^{9} +(1.08726 - 0.627730i) q^{10} +(0.900851 + 1.56032i) q^{11} +(1.31014 + 1.13293i) q^{12} +(-0.657649 + 3.54507i) q^{13} +(-2.63786 - 0.204205i) q^{14} +(2.13564 + 0.409376i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.12649 - 1.95113i) q^{17} +(0.432936 + 2.96860i) q^{18} +(-2.46356 + 4.26702i) q^{19} +1.25546i q^{20} +(-3.22462 - 3.25605i) q^{21} -1.80170 q^{22} +(-7.93452 - 4.58100i) q^{23} +(-1.63622 + 0.568150i) q^{24} +(-1.71191 - 2.96512i) q^{25} +(-2.74129 - 2.34207i) q^{26} +(-2.79601 + 4.37977i) q^{27} +(1.49578 - 2.18235i) q^{28} -6.62631i q^{29} +(-1.42235 + 1.64483i) q^{30} +(2.39209 + 4.14321i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.36048 - 2.04120i) q^{33} +2.25297 q^{34} +(0.256371 - 3.31172i) q^{35} +(-2.78735 - 1.10936i) q^{36} +(-4.77663 - 2.75779i) q^{37} +(-2.46356 - 4.26702i) q^{38} +(-0.938072 - 6.17414i) q^{39} +(-1.08726 - 0.627730i) q^{40} +9.52690i q^{41} +(4.43213 - 1.16458i) q^{42} +3.14581 q^{43} +(0.900851 - 1.56032i) q^{44} +(-3.72695 + 0.543534i) q^{45} +(7.93452 - 4.58100i) q^{46} +(-8.20429 - 4.73675i) q^{47} +(0.326076 - 1.70108i) q^{48} +(-4.39129 + 5.45129i) q^{49} +3.42382 q^{50} +(2.95171 + 2.55246i) q^{51} +(3.39894 - 1.20299i) q^{52} +(-11.2966 + 6.52211i) q^{53} +(-2.39498 - 4.61130i) q^{54} -2.26196i q^{55} +(1.14208 + 2.38656i) q^{56} +(1.60662 - 8.38144i) q^{57} +(5.73855 + 3.31315i) q^{58} +(4.80116 - 2.77195i) q^{59} +(-0.713289 - 2.05420i) q^{60} +(2.64951 + 1.52970i) q^{61} -4.78417 q^{62} +(7.12609 + 3.49554i) q^{63} +1.00000 q^{64} +(2.94038 - 3.44158i) q^{65} +(2.94797 - 1.02364i) q^{66} +(-11.4400 + 6.60487i) q^{67} +(-1.12649 + 1.95113i) q^{68} +(15.5853 + 2.98751i) q^{69} +(2.73985 + 1.87789i) q^{70} +9.21344 q^{71} +(2.35441 - 1.85923i) q^{72} +(-7.95079 - 13.7712i) q^{73} +(4.77663 - 2.75779i) q^{74} +(4.48569 + 3.87895i) q^{75} +4.92713 q^{76} +(-2.69494 + 3.93194i) q^{77} +(5.81600 + 2.27468i) q^{78} +(-0.323763 + 0.560775i) q^{79} +(1.08726 - 0.627730i) q^{80} +(2.08651 - 8.75480i) q^{81} +(-8.25053 - 4.76345i) q^{82} +11.3503i q^{83} +(-1.20751 + 4.42062i) q^{84} +2.82851i q^{85} +(-1.57290 + 2.72435i) q^{86} +(3.76474 + 10.8421i) q^{87} +(0.900851 + 1.56032i) q^{88} +(-11.1220 - 6.42131i) q^{89} +(1.39276 - 3.49940i) q^{90} +(-9.21159 + 2.47924i) q^{91} +9.16199i q^{92} +(-6.26793 - 5.42013i) q^{93} +(8.20429 - 4.73675i) q^{94} +(5.35707 - 3.09290i) q^{95} +(1.31014 + 1.13293i) q^{96} -1.48848 q^{97} +(-2.52531 - 6.52862i) q^{98} +(5.02197 + 1.99874i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 18 q^{2} - 18 q^{4} + 36 q^{8} + 4 q^{9}+O(q^{10}) \) 36 * q - 18 * q^2 - 18 * q^4 + 36 * q^8 + 4 * q^9	\( 36 q - 18 q^{2} - 18 q^{4} + 36 q^{8} + 4 q^{9} - 14 q^{15} - 18 q^{16} + 4 q^{18} + 23 q^{21} + 14 q^{25} - 6 q^{26} + 7 q^{30} - 18 q^{32} + 24 q^{33} - 8 q^{36} - 10 q^{39} - 16 q^{42} - 16 q^{43} - 9 q^{45} + 72 q^{47} + 12 q^{49} - 28 q^{50} - 3 q^{51} + 6 q^{52} + 9 q^{54} - 8 q^{57} + 24 q^{59} + 7 q^{60} - 36 q^{61} - 39 q^{63} + 36 q^{64} + 18 q^{65} - 24 q^{66} - 72 q^{71} + 4 q^{72} + 54 q^{75} + 20 q^{78} + 20 q^{79} - 20 q^{81} - 24 q^{82} - 7 q^{84} + 8 q^{86} - 24 q^{87} - 72 q^{89} - 2 q^{91} - 14 q^{93} - 72 q^{94} - 12 q^{98} + 72 q^{99}+O(q^{100}) \) 36 * q - 18 * q^2 - 18 * q^4 + 36 * q^8 + 4 * q^9 - 14 * q^15 - 18 * q^16 + 4 * q^18 + 23 * q^21 + 14 * q^25 - 6 * q^26 + 7 * q^30 - 18 * q^32 + 24 * q^33 - 8 * q^36 - 10 * q^39 - 16 * q^42 - 16 * q^43 - 9 * q^45 + 72 * q^47 + 12 * q^49 - 28 * q^50 - 3 * q^51 + 6 * q^52 + 9 * q^54 - 8 * q^57 + 24 * q^59 + 7 * q^60 - 36 * q^61 - 39 * q^63 + 36 * q^64 + 18 * q^65 - 24 * q^66 - 72 * q^71 + 4 * q^72 + 54 * q^75 + 20 * q^78 + 20 * q^79 - 20 * q^81 - 24 * q^82 - 7 * q^84 + 8 * q^86 - 24 * q^87 - 72 * q^89 - 2 * q^91 - 14 * q^93 - 72 * q^94 - 12 * q^98 + 72 * q^99

Introduction

L-functions

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