LMFDB - Embedded newform 546.2.bg.b.467.5

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			467.5
Character	$\chi$	$=$	546.467
Dual form			546.2.bg.b.311.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-1.31014 + 1.13293i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.08726 + 0.627730i) q^{5} +(0.326076 + 1.70108i) q^{6} +(1.14208 + 2.38656i) q^{7} -1.00000 q^{8} +(0.432936 - 2.96860i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.31014 + 1.13293i) 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} +(0.432936 - 2.96860i) q^{9} +(1.08726 - 0.627730i) q^{10} +(-0.900851 - 1.56032i) q^{11} +(1.63622 + 0.568150i) 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} +(-2.35441 - 1.85923i) q^{18} +(-2.46356 + 4.26702i) q^{19} -1.25546i q^{20} +(-4.20009 - 1.83282i) q^{21} -1.80170 q^{22} +(7.93452 + 4.58100i) q^{23} +(1.31014 - 1.13293i) 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} +(-0.713289 + 2.05420i) q^{30} +(2.39209 + 4.14321i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.94797 + 1.02364i) 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} +(-3.15470 - 5.38961i) q^{39} +(-1.08726 - 0.627730i) q^{40} -9.52690i q^{41} +(-3.68732 + 2.72097i) q^{42} +3.14581 q^{43} +(-0.900851 + 1.56032i) q^{44} +(2.33419 - 2.95587i) 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} +(-3.68635 - 1.28002i) q^{51} +(3.39894 - 1.20299i) q^{52} +(11.2966 - 6.52211i) q^{53} +(5.19099 - 0.231530i) 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} +(1.42235 + 1.64483i) q^{60} +(2.64951 + 1.52970i) q^{61} +4.78417 q^{62} +(7.57917 - 2.35716i) q^{63} +1.00000 q^{64} +(-2.94038 + 3.44158i) q^{65} +(2.36048 - 2.04120i) 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} +(-0.432936 + 2.96860i) q^{72} +(-7.95079 - 13.7712i) q^{73} +(-4.77663 + 2.75779i) q^{74} +(5.60212 + 1.94524i) q^{75} +4.92713 q^{76} +(2.69494 - 3.93194i) q^{77} +(-6.24489 + 0.0372487i) q^{78} +(-0.323763 + 0.560775i) q^{79} +(-1.08726 + 0.627730i) q^{80} +(-8.62513 - 2.57043i) q^{81} +(-8.25053 - 4.76345i) q^{82} -11.3503i q^{83} +(0.512775 + 4.55380i) q^{84} +2.82851i q^{85} +(1.57290 - 2.72435i) q^{86} +(-7.50715 - 8.68140i) 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} +(-7.82794 - 2.71812i) q^{93} +(8.20429 - 4.73675i) q^{94} +(-5.35707 + 3.09290i) q^{95} +(-1.63622 - 0.568150i) 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
$3$	−1.31014	+	1.13293i	−0.756410	+	0.654098i
$3$	−1.31014	+	1.13293i	−0.756410	+	0.654098i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.08726	+	0.627730i	0.486237	+	0.280729i	0.723012	−	0.690835i	$-0.242757\pi$
$5$	1.08726	+	0.627730i	0.486237	+	0.280729i	−0.236775	+	0.971565i	$0.576090\pi$
$6$	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
$9$	0.432936	−	2.96860i	0.144312	−	0.989532i
$10$	1.08726	−	0.627730i	0.343822	−	0.198506i
$11$	−0.900851	−	1.56032i	−0.271617	−	0.470454i	0.697659	−	0.716430i	$-0.254225\pi$
$11$	−0.900851	−	1.56032i	−0.271617	−	0.470454i	−0.969276	+	0.245976i	$0.920892\pi$
$12$	1.63622	+	0.568150i	0.472335	+	0.164011i
$13$	−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	0.969683	−	0.244368i	$-0.0785803\pi$
$17$	1.12649	+	1.95113i	0.273213	+	0.473218i	−0.696470	+	0.717586i	$0.745247\pi$
$18$	−2.35441	−	1.85923i	−0.554940	−	0.438225i
$19$	−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
$21$	−4.20009	−	1.83282i	−0.916535	−	0.399955i
$22$	−1.80170			−0.384124
$23$	7.93452	+	4.58100i	1.65446	+	0.955204i	0.975205	+	0.221302i	$0.0710308\pi$
$23$	7.93452	+	4.58100i	1.65446	+	0.955204i	0.679256	+	0.733901i	$0.262303\pi$
$24$	1.31014	−	1.13293i	0.267431	−	0.231258i
$25$	−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	$0.210940\pi$
$29$			6.62631i			1.23047i	−0.788342	+	0.615237i	$0.789060\pi$
$30$	−0.713289	+	2.05420i	−0.130228	+	0.375045i
$31$	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
$33$	2.94797	+	1.02364i	0.513177	+	0.178192i
$34$	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
$39$	−3.15470	−	5.38961i	−0.505157	−	0.863028i
$40$	−1.08726	−	0.627730i	−0.171911	−	0.0992528i
$41$		−	9.52690i		−	1.48785i	−0.668262	−	0.743926i	$-0.732962\pi$
$41$		−	9.52690i		−	1.48785i	0.668262	−	0.743926i	$-0.267038\pi$
$42$	−3.68732	+	2.72097i	−0.568965	+	0.419855i
$43$	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
$45$	2.33419	−	2.95587i	0.347960	−	0.440635i
$46$	7.93452	−	4.58100i	1.16988	−	0.675431i
$47$	8.20429	+	4.73675i	1.19672	+	0.690926i	0.959822	−	0.280609i	$-0.0905365\pi$
$47$	8.20429	+	4.73675i	1.19672	+	0.690926i	0.236896	+	0.971535i	$0.423870\pi$
$48$	−0.326076	−	1.70108i	−0.0470651	−	0.245530i
$49$	−4.39129	+	5.45129i	−0.627328	+	0.778756i
$50$	−3.42382			−0.484202
$51$	−3.68635	−	1.28002i	−0.516192	−	0.179239i
$52$	3.39894	−	1.20299i	0.471349	−	0.166825i
$53$	11.2966	−	6.52211i	1.55171	−	0.895881i	0.553709	−	0.832710i	$-0.313212\pi$
$53$	11.2966	−	6.52211i	1.55171	−	0.895881i	0.998003	−	0.0631707i	$-0.0201213\pi$
$54$	5.19099	−	0.231530i	0.706404	−	0.0315072i
$55$		−	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	−0.778836	−	0.627228i	$-0.784189\pi$
$59$	−4.80116	+	2.77195i	−0.625058	+	0.360877i	0.153778	+	0.988105i	$0.450856\pi$
$60$	1.42235	+	1.64483i	0.183624	+	0.212346i
$61$	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
$63$	7.57917	−	2.35716i	0.954886	−	0.296974i
$64$	1.00000			0.125000
$65$	−2.94038	+	3.44158i	−0.364709	+	0.426876i
$66$	2.36048	−	2.04120i	0.290555	−	0.251255i
$67$	−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	$-0.684123\pi$
$71$	−9.21344			−1.09343			−0.546717	+	0.837318i	$0.684123\pi$
$72$	−0.432936	+	2.96860i	−0.0510220	+	0.349852i
$73$	−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
$75$	5.60212	+	1.94524i	0.646877	+	0.224617i
$76$	4.92713			0.565180
$77$	2.69494	−	3.93194i	0.307117	−	0.448087i
$78$	−6.24489	+	0.0372487i	−0.707094	+	0.00421758i
$79$	−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
$81$	−8.62513	−	2.57043i	−0.958348	−	0.285603i
$82$	−8.25053	−	4.76345i	−0.911119	−	0.526035i
$83$		−	11.3503i		−	1.24585i	−0.782280	−	0.622926i	$-0.785944\pi$
$83$		−	11.3503i		−	1.24585i	0.782280	−	0.622926i	$-0.214056\pi$
$84$	0.512775	+	4.55380i	0.0559483	+	0.496860i
$85$			2.82851i			0.306795i
$86$	1.57290	−	2.72435i	0.169611	−	0.293774i
$87$	−7.50715	−	8.68140i	−0.804851	−	0.930743i
$88$	0.900851	+	1.56032i	0.0960310	+	0.166331i
$89$	11.1220	+	6.42131i	1.17893	+	0.680657i	0.955767	−	0.294124i	$-0.0950277\pi$
$89$	11.1220	+	6.42131i	1.17893	+	0.680657i	0.223165	+	0.974781i	$0.428361\pi$
$90$	−1.39276	−	3.49940i	−0.146810	−	0.368869i
$91$	−9.21159	+	2.47924i	−0.965637	+	0.259895i
$92$		−	9.16199i		−	0.955204i
$93$	−7.82794	−	2.71812i	−0.811720	−	0.281856i
$94$	8.20429	−	4.73675i	0.846208	−	0.488558i
$95$	−5.35707	+	3.09290i	−0.549623	+	0.317325i
$96$	−1.63622	−	0.568150i	−0.166996	−	0.0579865i
$97$	−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	0.844141	−	0.536121i	$-0.180111\pi$
$101$	−0.424346	−	0.734989i	−0.0422240	−	0.0731342i	−0.886365	+	0.462987i	$0.846778\pi$
$102$	−2.95171	+	2.55246i	−0.292263	+	0.252731i
$103$	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
$105$	−3.41607	−	4.62927i	−0.333374	−	0.451771i
$106$		−	13.0442i		−	1.26697i
$107$	−9.73051	−	5.61791i	−0.940684	−	0.543104i	−0.0505092	−	0.998724i	$-0.516084\pi$
$107$	−9.73051	−	5.61791i	−0.940684	−	0.543104i	−0.890175	+	0.455620i	$0.849418\pi$
$108$	2.39498	−	4.61130i	0.230458	−	0.443722i
$109$	−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	$-0.853587\pi$
$113$		−	9.43789i		−	0.887842i	0.896066	−	0.443921i	$-0.146413\pi$
$114$	−8.06185	−	2.79935i	−0.755061	−	0.262183i
$115$	5.75125	+	9.96146i	0.536307	+	0.928911i
$116$	5.73855	−	3.31315i	0.532811	−	0.307619i
$117$	10.2392	+	3.48708i	0.946610	+	0.322381i
$118$			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
$123$	10.7933	+	12.4816i	0.973200	+	1.12543i
$124$	2.39209	−	4.14321i	0.214816	−	0.372071i
$125$		−	10.5758i		−	0.945925i
$126$	1.74823	−	7.74233i	0.155744	−	0.689742i
$127$	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
$129$	−4.12145	+	3.56398i	−0.362874	+	0.313791i
$130$	1.51031	+	4.26723i	0.132463	+	0.374261i
$131$	9.71936	−	16.8344i	0.849184	−	1.47083i	−0.0327529	−	0.999463i	$-0.510427\pi$
$131$	9.71936	−	16.8344i	0.849184	−	1.47083i	0.881937	−	0.471367i	$-0.156239\pi$
$132$	−0.587492	−	3.06484i	−0.0511347	−	0.266760i
$133$	−12.9971	−	1.00614i	−1.12699	−	0.0872437i
$134$			13.2097i			1.14115i
$135$	0.290676	+	6.51708i	0.0250174	+	0.560901i
$136$	−1.12649	−	1.95113i	−0.0965953	−	0.167308i
$137$	−5.51288	−	9.54858i	−0.470997	−	0.815790i	0.528453	−	0.848963i	$-0.322772\pi$
$137$	−5.51288	−	9.54858i	−0.470997	−	0.815790i	−0.999450	+	0.0331723i	$0.989439\pi$
$138$	−5.20538	+	14.9910i	−0.443112	+	1.27612i
$139$		−	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
$144$	2.35441	+	1.85923i	0.196201	+	0.154936i
$145$	−4.15953	+	7.20452i	−0.345430	+	0.598303i
$146$	−15.9016			−1.31602
$147$	−0.422721	−	12.1170i	−0.0348655	−	0.999392i
$148$			5.51558i			0.453378i
$149$	4.17530	−	7.23183i	0.342054	−	0.592455i	−0.642760	−	0.766068i	$-0.722211\pi$
$149$	4.17530	−	7.23183i	0.342054	−	0.592455i	0.984814	+	0.173613i	$0.0555441\pi$
$150$	4.48569	−	3.87895i	0.366255	−	0.316715i
$151$	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
$156$	−3.09019	+	5.42686i	−0.247413	+	0.434496i
$157$	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
$159$	−7.41107	+	21.3432i	−0.587736	+	1.69262i
$160$			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
$165$	2.56265	+	2.96349i	0.199502	+	0.230707i
$166$	−9.82961	−	5.67513i	−0.762926	−	0.440475i
$167$			8.30092i			0.642344i	0.947021	+	0.321172i	$0.104077\pi$
$167$			8.30092i			0.642344i	−0.947021	+	0.321172i	$0.895923\pi$
$168$	4.20009	+	1.83282i	0.324044	+	0.141405i
$169$	−12.1350	−	4.66282i	−0.933461	−	0.358678i
$170$	2.44956	+	1.41426i	0.187873	+	0.108468i
$171$	11.6005	+	9.16068i	0.887112	+	0.700534i
$172$	−1.57290	−	2.72435i	−0.119933	−	0.207730i
$173$	−9.17486	+	15.8913i	−0.697552	+	1.20819i	0.271761	+	0.962365i	$0.412394\pi$
$173$	−9.17486	+	15.8913i	−0.697552	+	1.20819i	−0.969313	+	0.245830i	$0.920939\pi$
$174$	−11.2719	+	2.16068i	−0.854519	+	0.163801i
$175$	5.12127	−	7.47198i	0.387132	−	0.564829i
$176$	1.80170			0.135808
$177$	3.14977	−	9.07102i	0.236751	−	0.681820i
$178$	11.1220	−	6.42131i	0.833631	−	0.481297i
$179$	−3.45299	+	1.99358i	−0.258088	+	0.149007i	−0.623462	−	0.781853i	$-0.714275\pi$
$179$	−3.45299	+	1.99358i	−0.258088	+	0.149007i	0.365374	+	0.930861i	$0.380941\pi$
$180$	−3.72695	−	0.543534i	−0.277791	−	0.0405126i
$181$			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
$186$	−6.26793	+	5.42013i	−0.459587	+	0.397423i
$187$	2.02959	−	3.51535i	0.148418	−	0.257068i
$188$		−	9.47349i		−	0.690926i
$189$	−7.25928	+	11.6749i	−0.528035	+	0.849223i
$190$			6.18581i			0.448766i
$191$	4.46998	+	2.58075i	0.323437	+	0.186736i	0.652923	−	0.757424i	$-0.273542\pi$
$191$	4.46998	+	2.58075i	0.323437	+	0.186736i	−0.329487	+	0.944160i	$0.606876\pi$
$192$	−1.31014	+	1.13293i	−0.0945512	+	0.0817622i
$193$	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
$195$	−0.0467642	−	7.84020i	−0.00334885	−	0.561448i
$196$	6.91660	+	1.07733i	0.494043	+	0.0769519i
$197$	−3.52408			−0.251081			−0.125540	−	0.992089i	$-0.540066\pi$
$197$	−3.52408			−0.251081			−0.125540	+	0.992089i	$0.540066\pi$
$198$	−0.780022	+	5.34853i	−0.0554338	+	0.380103i
$199$	−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
$201$	7.50511	−	21.6140i	0.529370	−	1.52453i
$202$	−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
$207$	17.0343	−	21.5711i	1.18396	−	1.49930i
$208$	−2.74129	−	2.34207i	−0.190074	−	0.162394i
$209$	8.87721			0.614050
$210$	−5.71710	+	0.643768i	−0.394518	+	0.0444242i
$211$	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
$213$	12.0709	−	10.4382i	0.827084	−	0.715213i
$214$	−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
$219$	26.0184	+	9.03448i	1.75816	+	0.610493i
$220$	−1.95892	+	1.13098i	−0.132070	+	0.0762507i
$221$	−7.65772	+	2.71031i	−0.515114	+	0.182315i
$222$	3.13368	−	9.02469i	0.210319	−	0.605697i
$223$	−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	−0.221619	−	0.975133i	$-0.571134\pi$
$227$	7.71498	−	4.45425i	0.512061	−	0.295639i	0.733681	+	0.679495i	$0.237801\pi$
$228$	−6.45523	+	5.58209i	−0.427508	+	0.369683i
$229$	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
$231$	0.923868	+	8.20458i	0.0607860	+	0.539822i
$232$		−	6.62631i		−	0.435039i
$233$	4.99084	+	2.88146i	0.326961	+	0.188771i	0.654491	−	0.756070i	$-0.272883\pi$
$233$	4.99084	+	2.88146i	0.326961	+	0.188771i	−0.327530	+	0.944841i	$0.606216\pi$
$234$	8.13948	−	7.12382i	0.532094	−	0.465699i
$235$	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	$-0.372539\pi$
$239$	12.0528			0.779630			0.389815	+	0.920893i	$0.372539\pi$
$240$	0.713289	−	2.05420i	0.0460426	−	0.132598i
$241$	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
$243$	14.2123	−	6.40406i	0.911716	−	0.410820i
$244$		−	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
$249$	12.8591	+	14.8704i	0.814910	+	0.942375i
$250$	−9.15888	−	5.28788i	−0.579258	−	0.334435i
$251$	−9.87047			−0.623019			−0.311509	−	0.950243i	$-0.600835\pi$
$251$	−9.87047			−0.623019			−0.311509	+	0.950243i	$0.600835\pi$
$252$	−5.83094	−	5.38517i	−0.367315	−	0.339234i
$253$		−	16.5072i		−	1.03780i
$254$	4.83001	−	8.36583i	0.303062	−	0.524919i
$255$	−3.20451	−	3.70575i	−0.200674	−	0.232063i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	4.00565	−	6.93799i	0.249866	−	0.432780i	−0.713623	−	0.700530i	$-0.752947\pi$
$257$	4.00565	−	6.93799i	0.249866	−	0.432780i	0.963488	+	0.267750i	$0.0862802\pi$
$258$	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
$261$	19.6708	+	2.86877i	1.21759	+	0.177572i
$262$	−9.71936	−	16.8344i	−0.600464	−	1.04003i
$263$	−9.16411	+	5.29090i	−0.565083	+	0.326251i	−0.755183	−	0.655514i	$-0.772452\pi$
$263$	−9.16411	+	5.29090i	−0.565083	+	0.326251i	0.190100	+	0.981765i	$0.439119\pi$
$264$	−2.94797	−	1.02364i	−0.181435	−	0.0630004i
$265$	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	0.982162	−	0.188035i	$-0.0602119\pi$
$269$	5.38350	+	9.32450i	0.328238	+	0.568525i	−0.653924	+	0.756560i	$0.726879\pi$
$270$	5.78929	+	3.00681i	0.352325	+	0.182988i
$271$	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
$273$	9.25966	−	13.6842i	0.560420	−	0.828208i
$274$	−11.0258			−0.666090
$275$	−3.08435	+	5.34226i	−0.185993	+	0.322150i
$276$	10.3799	+	12.0035i	0.624797	+	0.722526i
$277$	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	$-0.325880\pi$
$281$	17.4383			1.04028			0.520140	+	0.854081i	$0.325880\pi$
$282$	−5.38236	+	15.5007i	−0.320515	+	0.923053i
$283$	−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
$285$	3.51446	−	10.1213i	0.208179	−	0.599535i
$286$	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
$291$	1.95012	−	1.68634i	0.114318	−	0.0988553i
$292$	−7.95079	+	13.7712i	−0.465285	+	0.805897i
$293$		−	6.46090i		−	0.377450i	−0.982030	−	0.188725i	$-0.939565\pi$
$293$		−	6.46090i		−	0.377450i	0.982030	−	0.188725i	$-0.0604355\pi$
$294$	−10.7050	−	5.69240i	−0.624327	−	0.331988i
$295$	−6.96014			−0.405235
$296$	4.77663	+	2.75779i	0.277636	+	0.160293i
$297$	4.31505	−	8.30818i	0.250384	−	0.482089i
$298$	−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
$303$	1.38864	+	0.482184i	0.0797756	+	0.0277008i
$304$	−2.46356	−	4.26702i	−0.141295	−	0.244730i
$305$	1.92047	+	3.32636i	0.109966	+	0.190467i
$306$	0.975393	−	6.68816i	0.0557595	−	0.382337i
$307$	−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	0.631014	−	0.775771i	$-0.282639\pi$
$311$	−6.28396	−	10.8841i	−0.356330	−	0.617182i	−0.987345	+	0.158589i	$0.949306\pi$
$312$	3.15470	+	5.38961i	0.178600	+	0.305126i
$313$	−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
$315$	9.72018	+	2.19483i	0.547670	+	0.123664i
$316$	0.647527			0.0364262
$317$	0.992390	−	1.71887i	0.0557382	−	0.0965414i	−0.836810	−	0.547493i	$-0.815582\pi$
$317$	0.992390	−	1.71887i	0.0557382	−	0.0965414i	0.892548	+	0.450952i	$0.148915\pi$
$318$	14.7782	+	17.0898i	0.828720	+	0.958347i
$319$	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
$324$	2.08651	+	8.75480i	0.115917	+	0.486378i
$325$	11.6374	−	4.11883i	0.645525	−	0.228472i
$326$	10.1935	−	5.88520i	0.564564	−	0.325951i
$327$	1.32414	−	3.81341i	0.0732253	−	0.210882i
$328$			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
$333$	−10.2547	+	12.9860i	−0.561957	+	0.711626i
$334$	7.18880	+	4.15046i	0.393354	+	0.227103i
$335$	−16.5843			−0.906096
$336$	3.68732	−	2.72097i	0.201160	−	0.148441i
$337$	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
$339$	10.6925	+	12.3650i	0.580735	+	0.671572i
$340$	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
$345$	−18.8206	−	6.53514i	−1.01327	−	0.351840i
$346$	9.17486	+	15.8913i	0.493243	+	0.854323i
$347$	22.0055	−	12.7049i	1.18132	−	0.682033i	0.224997	−	0.974359i	$-0.427763\pi$
$347$	22.0055	−	12.7049i	1.18132	−	0.682033i	0.956319	+	0.292326i	$0.0944293\pi$
$348$	−3.76474	+	10.8421i	−0.201811	+	0.581197i
$349$	−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
$351$	−17.3654	+	7.03168i	−0.926894	+	0.375323i
$352$	0.900851	−	1.56032i	0.0480155	−	0.0831653i
$353$	−11.7823	+	6.80251i	−0.627109	+	0.362061i	−0.779631	−	0.626239i	$-0.784594\pi$
$353$	−11.7823	+	6.80251i	−0.627109	+	0.362061i	0.152523	+	0.988300i	$0.451260\pi$
$354$	−6.28086	−	7.26329i	−0.333824	−	0.386039i
$355$	−10.0174	−	5.78355i	−0.531668	−	0.306959i
$356$		−	12.8426i		−	0.680657i
$357$	−1.15527	−	10.2596i	−0.0611432	−	0.542994i
$358$			3.98717i			0.210728i
$359$	14.3788	−	24.9048i	0.758884	−	1.31443i	−0.184536	−	0.982826i	$-0.559078\pi$
$359$	14.3788	−	24.9048i	0.758884	−	1.31443i	0.943420	−	0.331600i	$-0.107588\pi$
$360$	−2.33419	+	2.95587i	−0.123023	+	0.155788i
$361$	−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
$366$	−1.73819	+	5.00584i	−0.0908569	+	0.261659i
$367$	−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
$369$	−28.2815	−	4.12454i	−1.47228	−	0.214715i
$370$	−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
$375$	11.9816	+	13.8557i	0.618728	+	0.715507i
$376$	−8.20429	−	4.73675i	−0.423104	−	0.244279i
$377$	−23.4907	−	4.35779i	−1.20983	−	0.224437i
$378$	6.48110	+	12.1242i	0.333352	+	0.623600i
$379$			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
$381$	−12.6560	+	10.9441i	−0.648386	+	0.560685i
$382$	4.46998	−	2.58075i	0.228704	−	0.132042i
$383$	−1.33536	−	0.770971i	−0.0682338	−	0.0393948i	0.465495	−	0.885051i	$-0.345876\pi$
$383$	−1.33536	−	0.770971i	−0.0682338	−	0.0393948i	−0.533729	+	0.845656i	$0.679210\pi$
$384$	0.326076	+	1.70108i	0.0166400	+	0.0868079i
$385$	5.39830	−	2.58335i	0.275123	−	0.131660i
$386$		−	3.20108i		−	0.162931i
$387$	1.36193	−	9.33864i	0.0692310	−	0.474710i
$388$	0.744240	+	1.28906i	0.0377831	+	0.0654422i
$389$	−24.9269	+	14.3916i	−1.26385	+	0.729682i	−0.973816	−	0.227336i	$-0.926998\pi$
$389$	−24.9269	+	14.3916i	−1.26385	+	0.729682i	−0.290029	+	0.957018i	$0.593665\pi$
$390$	−6.81319	−	3.87960i	−0.345000	−	0.196451i
$391$			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
$396$	4.24195	+	3.34978i	0.213166	+	0.168333i
$397$	−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
$399$	18.1679	−	13.4066i	0.909532	−	0.671169i
$400$	3.42382			0.171191
$401$	16.5303	−	28.6313i	0.825483	−	1.42978i	−0.0760665	−	0.997103i	$-0.524236\pi$
$401$	16.5303	−	28.6313i	0.825483	−	1.42978i	0.901550	−	0.432676i	$-0.142431\pi$
$402$	−14.9657	−	17.3066i	−0.746422	−	0.863176i
$403$	−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
$408$	3.68635	+	1.28002i	0.182501	+	0.0633707i
$409$	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
$411$	18.0405	+	6.26428i	0.889873	+	0.308994i
$412$		−	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
$417$	10.2972	+	11.9079i	0.504258	+	0.583133i
$418$	4.43861	−	7.68789i	0.217099	−	0.376027i
$419$	12.8180			0.626202			0.313101	−	0.949720i	$-0.398632\pi$
$419$	12.8180			0.626202			0.313101	+	0.949720i	$0.398632\pi$
$420$	−2.30103	+	5.27304i	−0.112279	+	0.257298i
$421$			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
$423$	17.6134	−	22.3045i	0.856394	−	1.08448i
$424$	−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
$429$	−5.56759	+	9.77757i	−0.268806	+	0.472066i
$430$	3.42031	−	1.97472i	0.164942	−	0.0952293i
$431$	−6.41225	−	11.1063i	−0.308867	−	0.534974i	0.669248	−	0.743039i	$-0.266617\pi$
$431$	−6.41225	−	11.1063i	−0.308867	−	0.534974i	−0.978115	+	0.208066i	$0.933283\pi$
$432$	−5.19099	+	0.231530i	−0.249752	+	0.0111395i
$433$		−	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
$438$	20.8333	−	18.0154i	0.995454	−	0.860808i
$439$	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
$441$	14.2815	+	15.3960i	0.680073	+	0.733145i
$442$	−1.48166	+	7.98693i	−0.0704756	+	0.379900i
$443$	−20.0410	−	11.5707i	−0.952176	−	0.549739i	−0.0584201	−	0.998292i	$-0.518606\pi$
$443$	−20.0410	−	11.5707i	−0.952176	−	0.549739i	−0.893756	+	0.448553i	$0.851940\pi$
$444$	−6.24877	−	7.22619i	−0.296554	−	0.342940i
$445$	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	$-0.657380\pi$
$449$	−20.1099			−0.949047			−0.474523	+	0.880243i	$0.657380\pi$
$450$	−1.48230	+	10.1639i	−0.0698762	+	0.479133i
$451$	−14.8650	+	8.58231i	−0.699966	+	0.404125i
$452$	−8.17345	+	4.71894i	−0.384447	+	0.221960i
$453$	−6.34962	+	18.2863i	−0.298331	+	0.859165i
$454$		−	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
$459$	−5.39583	+	10.3891i	−0.251856	+	0.484922i
$460$	5.75125	−	9.96146i	0.268154	−	0.464456i
$461$			32.1844i			1.49898i	0.662016	+	0.749489i	$0.269701\pi$
$461$			32.1844i			1.49898i	−0.662016	+	0.749489i	$0.730299\pi$
$462$	7.56731	+	3.30220i	0.352063	+	0.153632i
$463$		−	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
$465$	−6.80475	−	7.86914i	−0.315563	−	0.364922i
$466$	4.99084	−	2.88146i	0.231196	−	0.133481i
$467$	4.80726	−	8.32642i	0.222453	−	0.385301i	−0.733099	−	0.680122i	$-0.761927\pi$
$467$	4.80726	−	8.32642i	0.222453	−	0.385301i	0.955552	+	0.294821i	$0.0952601\pi$
$468$	−2.09967	−	10.6109i	−0.0970574	−	0.490489i
$469$	−28.8283	−	19.7588i	−1.33117	−	0.912377i
$470$	11.8936			0.548610
$471$	−4.28797	+	12.3490i	−0.197579	+	0.569010i
$472$	4.80116	−	2.77195i	0.220991	−	0.127589i
$473$	−2.83390	−	4.90847i	−0.130303	−	0.225692i
$474$	−1.05949	−	0.367892i	−0.0486642	−	0.0168978i
$475$	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	−0.930152	−	0.367174i	$-0.880325\pi$
$479$	−23.5767	+	13.6120i	−1.07725	+	0.621948i	−0.147094	+	0.989123i	$0.546992\pi$
$480$	−1.42235	−	1.64483i	−0.0649210	−	0.0750758i
$481$	12.9179	−	15.1198i	0.589006	−	0.689405i
$482$	14.8113			0.674635
$483$	−24.9295	−	33.7832i	−1.13433	−	1.53719i
$484$	−7.75387			−0.352449
$485$	−1.61836	−	0.934363i	−0.0734861	−	0.0424272i
$486$	1.56005	−	15.5102i	0.0707653	−	0.703557i
$487$	−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	$-0.940005\pi$
$491$		−	8.30353i		−	0.374733i	0.982290	−	0.187367i	$-0.0599952\pi$
$492$	5.41270	−	15.5881i	0.244023	−	0.702764i
$493$	−12.9288	+	7.46444i	−0.582283	+	0.336181i
$494$	−16.7470	+	5.92730i	−0.753484	+	0.266682i
$495$	−6.71485	−	0.979286i	−0.301810	−	0.0440156i
$496$	−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
$501$	−9.40436	−	10.8754i	−0.420156	−	0.485876i
$502$	−4.93524	+	8.54808i	−0.220270	+	0.381519i
$503$	9.19561			0.410012			0.205006	−	0.978761i	$-0.434279\pi$
$503$	9.19561			0.410012			0.205006	+	0.978761i	$0.434279\pi$
$504$	−7.57917	+	2.35716i	−0.337603	+	0.104996i
$505$		−	1.06550i		−	0.0474141i
$506$	−14.2956	−	8.25359i	−0.635518	−	0.366917i
$507$	21.1812	−	7.63916i	0.940690	−	0.339267i
$508$	−4.83001	−	8.36583i	−0.214297	−	0.371174i
$509$	21.0228	+	12.1375i	0.931821	+	0.537987i	0.887387	−	0.461025i	$-0.152518\pi$
$509$	21.0228	+	12.1375i	0.931821	+	0.537987i	0.0444338	+	0.999012i	$0.485852\pi$
$510$	−4.81153	+	0.922311i	−0.213058	+	0.0408406i
$511$	23.7852	−	34.7028i	1.05220	−	1.53516i
$512$	−1.00000			−0.0441942
$513$	−25.5767	+	1.14078i	−1.12924	+	0.0503666i
$514$	−4.00565	−	6.93799i	−0.176682	−	0.306022i
$515$	3.84778	+	6.66455i	0.169553	+	0.293675i
$516$	5.14723	+	1.78729i	0.226594	+	0.0786811i
$517$		−	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	$-0.996093\pi$
$521$	−11.6545	−	20.1861i	−0.510591	−	0.884370i	0.489333	−	0.872097i	$-0.337240\pi$
$522$	12.3198	−	15.6011i	0.539225	−	0.682840i
$523$	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
$525$	1.75565	+	15.5914i	0.0766229	+	0.680464i
$526$			10.5818i			0.461389i
$527$	−5.38930	+	9.33454i	−0.234761	+	0.406619i
$528$	−2.36048	+	2.04120i	−0.102727	+	0.0888320i
$529$	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
$534$	−7.29652	+	21.0133i	−0.315752	+	0.909334i
$535$	−7.05306	−	12.2163i	−0.304930	−	0.528155i
$536$	11.4400	−	6.60487i	0.494131	−	0.285287i
$537$	2.26531	−	6.52387i	0.0977552	−	0.281526i
$538$	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
$543$	−14.9714	−	17.3132i	−0.642484	−	0.742979i
$544$	−1.12649	+	1.95113i	−0.0482977	+	0.0836540i
$545$	−2.92600			−0.125336
$546$	−7.22108	−	14.8612i	−0.309033	−	0.636002i
$547$	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
$549$	5.68813	−	7.20308i	0.242763	−	0.307420i
$550$	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
$555$	11.3301	+	3.93420i	0.480937	+	0.166998i
$556$	−7.87134	+	4.54452i	−0.333819	+	0.192730i
$557$	−21.0588	−	36.4749i	−0.892290	−	1.54549i	−0.837123	−	0.547015i	$-0.815764\pi$
$557$	−21.0588	−	36.4749i	−0.892290	−	1.54549i	−0.0551670	−	0.998477i	$-0.517569\pi$
$558$	2.07124	−	14.2023i	0.0876826	−	0.601230i
$559$	−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	0.748371	−	0.663280i	$-0.230836\pi$
$563$	−4.75102	−	8.22901i	−0.200232	−	0.346811i	−0.948603	+	0.316469i	$0.897503\pi$
$564$	10.7328	+	12.4116i	0.451933	+	0.522623i
$565$	5.92444	−	10.2614i	0.249243	−	0.431702i
$566$			26.3230i			1.10644i
$567$	−3.71615	−	23.5200i	−0.156064	−	0.987747i
$568$	9.21344			0.386587
$569$	−23.5732	−	13.6100i	−0.988238	−	0.570560i	−0.0834912	−	0.996509i	$-0.526607\pi$
$569$	−23.5732	−	13.6100i	−0.988238	−	0.570560i	−0.904747	+	0.425949i	$0.859940\pi$
$570$	−7.00809	−	8.10428i	−0.293537	−	0.339451i
$571$	−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
$576$	0.432936	−	2.96860i	0.0180390	−	0.123692i
$577$	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
$579$	−1.81869	+	5.23766i	−0.0755822	+	0.217670i
$580$	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
$585$	8.94367	+	10.2188i	0.369775	+	0.422495i
$586$	−5.59531	−	3.23045i	−0.231140	−	0.133449i
$587$		−	9.30051i		−	0.383873i	−0.981407	−	0.191937i	$-0.938523\pi$
$587$		−	9.30051i		−	0.383873i	0.981407	−	0.191937i	$-0.0614768\pi$
$588$	−10.2823	+	6.42458i	−0.424033	+	0.264945i
$589$	−23.5722			−0.971276
$590$	−3.48007	+	6.02766i	−0.143272	+	0.248155i
$591$	4.61705	−	3.99254i	0.189920	−	0.164231i
$592$	4.77663	−	2.75779i	0.196318	−	0.113345i
$593$	18.3797	+	10.6115i	0.754765	+	0.435764i	0.827413	−	0.561594i	$-0.189812\pi$
$593$	18.3797	+	10.6115i	0.754765	+	0.435764i	−0.0726480	+	0.997358i	$0.523145\pi$
$594$	−5.03757	−	7.89103i	−0.206694	−	0.323773i
$595$	−6.75040	+	3.23040i	−0.276739	+	0.132433i
$596$	−8.35060			−0.342054
$597$	5.90136	−	16.9954i	0.241527	−	0.695574i
$598$	11.0218	+	31.1411i	0.450715	+	1.27345i
$599$	4.28246	−	2.47248i	0.174976	−	0.101023i	−0.409954	−	0.912106i	$-0.634455\pi$
$599$	4.28246	−	2.47248i	0.174976	−	0.101023i	0.584930	+	0.811084i	$0.301122\pi$
$600$	−5.60212	−	1.94524i	−0.228705	−	0.0794142i
$601$		−	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
$606$	1.11191	−	0.961510i	0.0451681	−	0.0390587i
$607$	−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
$609$	12.1448	−	27.8311i	0.492134	−	1.12777i
$610$	3.84095			0.155515
$611$	−22.1876	+	25.9696i	−0.897615	+	1.05062i
$612$	−5.30442	−	4.18880i	−0.214419	−	0.169322i
$613$	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	$-0.379812\pi$
$617$	18.3153			0.737348			0.368674	+	0.929559i	$0.379812\pi$
$618$	−3.48257	+	10.0295i	−0.140090	+	0.403445i
$619$	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
$621$	2.12128	+	47.5598i	0.0851239	+	1.90851i
$622$	−12.5679			−0.503927
$623$	−2.62252	+	33.8770i	−0.105069	+	1.35725i
$624$	6.24489	−	0.0372487i	0.249996	−	0.00149114i
$625$	−1.92084	+	3.32699i	−0.0768335	+	0.133079i
$626$	−1.20941	+	0.698253i	−0.0483377	+	0.0279078i
$627$	−11.6304	+	10.0573i	−0.464473	+	0.401649i
$628$	−6.53612	−	3.77363i	−0.260819	−	0.150584i
$629$		−	12.4264i		−	0.495475i
$630$	6.76087	−	7.32051i	0.269359	−	0.291656i
$631$		−	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
$633$	−9.99146	+	8.64002i	−0.397125	+	0.343410i
$634$	−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
$639$	−3.98883	+	27.3510i	−0.157796	+	1.08199i
$640$	1.08726	−	0.627730i	0.0429777	−	0.0248132i
$641$	−27.9073	+	16.1123i	−1.10227	+	0.636396i	−0.936816	−	0.349821i	$-0.886242\pi$
$641$	−27.9073	+	16.1123i	−1.10227	+	0.636396i	−0.165454	+	0.986217i	$0.552909\pi$
$642$	6.38363	−	18.3842i	0.251942	−	0.725568i
$643$	−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	0.938890	−	0.344216i	$-0.111855\pi$
$647$	4.35837	+	7.54892i	0.171345	+	0.296779i	−0.767545	+	0.640995i	$0.778522\pi$
$648$	8.62513	+	2.57043i	0.338827	+	0.100976i
$649$	8.65026	+	4.99423i	0.339552	+	0.196041i
$650$	2.25167	−	12.1377i	0.0883179	−	0.476079i
$651$	−2.45320	−	21.7861i	−0.0961486	−	0.853866i
$652$		−	11.7704i		−	0.460965i
$653$	17.3737	+	10.0307i	0.679884	+	0.392531i	0.799811	−	0.600252i	$-0.204933\pi$
$653$	17.3737	+	10.0307i	0.679884	+	0.392531i	−0.119928	+	0.992783i	$0.538266\pi$
$654$	−2.64044	−	3.05345i	−0.103249	−	0.119399i
$655$	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	$0.170775\pi$
$659$			26.2428i			1.02227i	−0.859500	+	0.511136i	$0.829225\pi$
$660$	1.28513	−	3.70106i	0.0500237	−	0.144064i
$661$	−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
$663$	6.96210	−	12.2265i	0.270385	−	0.474840i
$664$			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
$669$	0.209376	−	0.181056i	0.00809495	−	0.00700002i
$670$	−8.29214	+	14.3624i	−0.320353	+	0.554868i
$671$		−	5.51212i		−	0.212793i
$672$	−0.512775	−	4.55380i	−0.0197807	−	0.175667i
$673$	−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
$675$	8.20000	−	15.7883i	0.315618	−	0.607690i
$676$	2.02938	+	12.8406i	0.0780529	+	0.493870i
$677$	5.08564	−	8.80859i	0.195457	−	0.338542i	−0.751593	−	0.659627i	$-0.770714\pi$
$677$	5.08564	−	8.80859i	0.195457	−	0.338542i	0.947050	+	0.321085i	$0.104048\pi$
$678$	16.0546	−	3.07747i	0.616573	−	0.118190i
$679$	−1.69997	−	3.55234i	−0.0652388	−	0.136326i
$680$		−	2.82851i		−	0.108468i
$681$	−5.06136	+	14.5762i	−0.193952	+	0.558562i
$682$	−4.30982	−	7.46483i	−0.165032	−	0.285843i
$683$	−13.6076	−	23.5691i	−0.520682	−	0.901848i	−0.999711	−	0.0240486i	$-0.992344\pi$
$683$	−13.6076	−	23.5691i	−0.520682	−	0.901848i	0.479029	−	0.877799i	$-0.340989\pi$
$684$	2.13313	−	14.6267i	0.0815624	−	0.559264i
$685$		−	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
$690$	−15.0699	+	13.0315i	−0.573701	+	0.496102i
$691$	−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
$693$	−10.5056	−	9.70248i	−0.399075	−	0.368567i
$694$		−	25.4097i		−	0.964540i
$695$	5.70546	−	9.88214i	0.216420	−	0.374851i
$696$	7.50715	+	8.68140i	0.284558	+	0.329067i
$697$	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	$0.122616\pi$
$701$			19.8971i			0.751505i	−0.926720	+	0.375752i	$0.877384\pi$
$702$	−2.59306	+	18.5547i	−0.0978688	+	0.700301i
$703$	23.5351	−	13.5880i	0.887643	−	0.512481i
$704$	−0.900851	−	1.56032i	−0.0339521	−	0.0588067i
$705$	−19.4605	−	6.75734i	−0.732924	−	0.254496i
$706$			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
$711$	1.52454	+	1.20390i	0.0571749	+	0.0451499i
$712$	−11.1220	−	6.42131i	−0.416816	−	0.240649i
$713$			43.8325i			1.64154i
$714$	−9.46268	−	4.12929i	−0.354132	−	0.154535i
$715$	8.01881	+	1.48758i	0.299886	+	0.0556323i
$716$	3.45299	+	1.99358i	0.129044	+	0.0745037i
$717$	−15.7908	+	13.6550i	−0.589720	+	0.509954i
$718$	−14.3788	−	24.9048i	−0.536612	−	0.929439i
$719$	−0.367826	+	0.637094i	−0.0137176	+	0.0237596i	−0.872803	−	0.488073i	$-0.837700\pi$
$719$	−0.367826	+	0.637094i	−0.0137176	+	0.0237596i	0.859085	+	0.511833i	$0.171033\pi$
$720$	1.39276	+	3.49940i	0.0519052	+	0.130415i
$721$	−1.25171	+	16.1692i	−0.0466161	+	0.602173i
$722$	−5.27659			−0.196374
$723$	−24.2345	−	8.41502i	−0.901290	−	0.312958i
$724$	11.4443	−	6.60737i	0.425324	−	0.245561i
$725$	19.6478	−	11.3437i	0.729700	−	0.421293i
$726$	12.6870	+	4.40536i	0.470859	+	0.163498i
$727$			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
$732$	3.46608	+	4.00824i	0.128110	+	0.148149i
$733$	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
$735$	7.14658	−	13.4397i	0.263606	−	0.495729i
$736$			9.16199i			0.337716i
$737$	20.6114	+	11.9000i	0.759231	+	0.438342i
$738$	−17.7127	+	22.4302i	−0.652014	+	0.825668i
$739$	−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
$741$	30.7694	−	0.183529i	1.13034	−	0.00674210i
$742$	31.1308	−	14.8976i	1.14285	−	0.546908i
$743$	52.2488			1.91682			0.958411	−	0.285393i	$-0.0921240\pi$
$743$	52.2488			1.91682			0.958411	+	0.285393i	$0.0921240\pi$
$744$	7.82794	+	2.71812i	0.286986	+	0.0996513i
$745$	9.07927	−	5.24192i	0.332639	−	0.192049i
$746$	−6.93995	−	12.0203i	−0.254090	−	0.440096i
$747$	−33.6943	−	4.91394i	−1.23281	−	0.179792i
$748$	−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
$753$	12.9317	−	11.1826i	0.471258	−	0.407515i
$754$	−15.5193	+	18.1647i	−0.565180	+	0.661518i
$755$	14.0310			0.510639
$756$	13.7404	+	0.449282i	0.499733	+	0.0163402i
$757$	−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
$759$	18.7015	+	21.6267i	0.678821	+	0.785000i
$760$	5.35707	−	3.09290i	0.194321	−	0.112191i
$761$	−21.9711	−	12.6850i	−0.796453	−	0.459833i	0.0457761	−	0.998952i	$-0.485424\pi$
$761$	−21.9711	−	12.6850i	−0.796453	−	0.459833i	−0.842230	+	0.539119i	$0.818757\pi$
$762$	3.14991	+	16.4325i	0.114109	+	0.595286i
$763$	−5.08624	−	3.48609i	−0.184134	−	0.126205i
$764$		−	5.16149i		−	0.186736i
$765$	8.39671	+	1.22457i	0.303584	+	0.0442743i
$766$	−1.33536	+	0.770971i	−0.0482486	+	0.0278563i
$767$	−6.66927	−	18.8434i	−0.240813	−	0.680396i
$768$	1.63622	+	0.568150i	0.0590419	+	0.0205013i
$769$	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

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)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.31014 + 1.13293i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.08726 + 0.627730i) q^{5} +(0.326076 + 1.70108i) q^{6} +(1.14208 + 2.38656i) q^{7} -1.00000 q^{8} +(0.432936 - 2.96860i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.31014 + 1.13293i) 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} +(0.432936 - 2.96860i) q^{9} +(1.08726 - 0.627730i) q^{10} +(-0.900851 - 1.56032i) q^{11} +(1.63622 + 0.568150i) 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} +(-2.35441 - 1.85923i) q^{18} +(-2.46356 + 4.26702i) q^{19} -1.25546i q^{20} +(-4.20009 - 1.83282i) q^{21} -1.80170 q^{22} +(7.93452 + 4.58100i) q^{23} +(1.31014 - 1.13293i) 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} +(-0.713289 + 2.05420i) q^{30} +(2.39209 + 4.14321i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.94797 + 1.02364i) 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} +(-3.15470 - 5.38961i) q^{39} +(-1.08726 - 0.627730i) q^{40} -9.52690i q^{41} +(-3.68732 + 2.72097i) q^{42} +3.14581 q^{43} +(-0.900851 + 1.56032i) q^{44} +(2.33419 - 2.95587i) 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} +(-3.68635 - 1.28002i) q^{51} +(3.39894 - 1.20299i) q^{52} +(11.2966 - 6.52211i) q^{53} +(5.19099 - 0.231530i) 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} +(1.42235 + 1.64483i) q^{60} +(2.64951 + 1.52970i) q^{61} +4.78417 q^{62} +(7.57917 - 2.35716i) q^{63} +1.00000 q^{64} +(-2.94038 + 3.44158i) q^{65} +(2.36048 - 2.04120i) 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} +(-0.432936 + 2.96860i) q^{72} +(-7.95079 - 13.7712i) q^{73} +(-4.77663 + 2.75779i) q^{74} +(5.60212 + 1.94524i) q^{75} +4.92713 q^{76} +(2.69494 - 3.93194i) q^{77} +(-6.24489 + 0.0372487i) q^{78} +(-0.323763 + 0.560775i) q^{79} +(-1.08726 + 0.627730i) q^{80} +(-8.62513 - 2.57043i) q^{81} +(-8.25053 - 4.76345i) q^{82} -11.3503i q^{83} +(0.512775 + 4.55380i) q^{84} +2.82851i q^{85} +(1.57290 - 2.72435i) q^{86} +(-7.50715 - 8.68140i) 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} +(-7.82794 - 2.71812i) q^{93} +(8.20429 - 4.73675i) q^{94} +(-5.35707 + 3.09290i) q^{95} +(-1.63622 - 0.568150i) 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

Modular forms

Varieties

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Representations

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