LMFDB - Embedded newform 930.2.o.e.161.14

Newspace parameters

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.o (of order $6$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			161.14
Character	$\chi$	$=$	930.161
Dual form			930.2.o.e.491.4

$q$-expansion

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.449207 + 1.67279i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(-1.67279 - 0.449207i) q^{6} +(-1.32225 - 2.29021i) q^{7} -1.00000i q^{8} +(-2.59643 - 1.50285i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.449207 + 1.67279i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(-1.67279 - 0.449207i) q^{6} +(-1.32225 - 2.29021i) q^{7} -1.00000i q^{8} +(-2.59643 - 1.50285i) q^{9} +(0.500000 - 0.866025i) q^{10} +(1.35563 - 2.34802i) q^{11} +(0.449207 - 1.67279i) q^{12} +(3.49868 + 2.01996i) q^{13} +(2.29021 - 1.32225i) q^{14} +(1.22542 - 1.22407i) q^{15} +1.00000 q^{16} +(-0.370882 - 0.642386i) q^{17} +(1.50285 - 2.59643i) q^{18} +(1.17674 + 2.03818i) q^{19} +(0.866025 + 0.500000i) q^{20} +(4.42499 - 1.18307i) q^{21} +(2.34802 + 1.35563i) q^{22} +3.17723 q^{23} +(1.67279 + 0.449207i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-2.01996 + 3.49868i) q^{26} +(3.68029 - 3.66817i) q^{27} +(1.32225 + 2.29021i) q^{28} -1.11630 q^{29} +(1.22407 + 1.22542i) q^{30} +(4.10522 + 3.76128i) q^{31} +1.00000i q^{32} +(3.31878 + 3.32243i) q^{33} +(0.642386 - 0.370882i) q^{34} +2.64450i q^{35} +(2.59643 + 1.50285i) q^{36} +(8.66260 - 5.00135i) q^{37} +(-2.03818 + 1.17674i) q^{38} +(-4.95060 + 4.94516i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-4.56104 - 2.63332i) q^{41} +(1.18307 + 4.42499i) q^{42} +(4.20794 - 2.42945i) q^{43} +(-1.35563 + 2.34802i) q^{44} +(1.49714 + 2.59972i) q^{45} +3.17723i q^{46} +3.29156i q^{47} +(-0.449207 + 1.67279i) q^{48} +(0.00329675 - 0.00571013i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(1.24118 - 0.331842i) q^{51} +(-3.49868 - 2.01996i) q^{52} +(-0.432136 + 0.748481i) q^{53} +(3.66817 + 3.68029i) q^{54} +(-2.34802 + 1.35563i) q^{55} +(-2.29021 + 1.32225i) q^{56} +(-3.93803 + 1.05287i) q^{57} -1.11630i q^{58} +(0.0673682 - 0.0388951i) q^{59} +(-1.22542 + 1.22407i) q^{60} -8.21375i q^{61} +(-3.76128 + 4.10522i) q^{62} +(-0.00871827 + 7.93351i) q^{63} -1.00000 q^{64} +(-2.01996 - 3.49868i) q^{65} +(-3.32243 + 3.31878i) q^{66} +(4.09060 - 7.08512i) q^{67} +(0.370882 + 0.642386i) q^{68} +(-1.42723 + 5.31482i) q^{69} -2.64450 q^{70} +(-11.6252 - 6.71183i) q^{71} +(-1.50285 + 2.59643i) q^{72} +(9.24020 + 5.33483i) q^{73} +(5.00135 + 8.66260i) q^{74} +(-1.67328 + 0.447368i) q^{75} +(-1.17674 - 2.03818i) q^{76} -7.16994 q^{77} +(-4.94516 - 4.95060i) q^{78} +(-10.5492 + 6.09057i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(4.48286 + 7.80410i) q^{81} +(2.63332 - 4.56104i) q^{82} +(2.44932 - 4.24235i) q^{83} +(-4.42499 + 1.18307i) q^{84} +0.741764i q^{85} +(2.42945 + 4.20794i) q^{86} +(0.501450 - 1.86733i) q^{87} +(-2.34802 - 1.35563i) q^{88} +17.1663 q^{89} +(-2.59972 + 1.49714i) q^{90} -10.6836i q^{91} -3.17723 q^{92} +(-8.13590 + 5.17756i) q^{93} -3.29156 q^{94} -2.35348i q^{95} +(-1.67279 - 0.449207i) q^{96} +12.4034 q^{97} +(0.00571013 + 0.00329675i) q^{98} +(-7.04853 + 4.05915i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40q + 6q^{3} - 40q^{4} - 12q^{7} - 2q^{9} + O(q^{10}) $	$ 40q + 6q^{3} - 40q^{4} - 12q^{7} - 2q^{9} + 20q^{10} - 6q^{12} - 12q^{13} + 40q^{16} - 12q^{18} - 12q^{19} + 12q^{21} - 24q^{22} + 20q^{25} + 12q^{28} + 8q^{31} + 52q^{33} + 24q^{34} + 2q^{36} + 60q^{37} - 8q^{39} - 20q^{40} + 12q^{42} + 24q^{43} - 12q^{45} + 6q^{48} - 4q^{49} + 14q^{51} + 12q^{52} + 24q^{55} - 12q^{57} - 40q^{64} + 8q^{66} + 64q^{67} - 26q^{69} - 24q^{70} + 12q^{72} + 6q^{75} + 12q^{76} - 68q^{78} - 48q^{79} + 2q^{81} + 4q^{82} - 12q^{84} + 36q^{87} + 24q^{88} + 2q^{90} - 22q^{93} - 40q^{94} + 8q^{97} - 90q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−0.449207	+	1.67279i	−0.259350	+	0.965783i
$3$	−0.449207	+	1.67279i	−0.259350	+	0.965783i
$4$	−1.00000			−0.500000
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$	−1.67279	−	0.449207i	−0.682912	−	0.183388i
$7$	−1.32225	−	2.29021i	−0.499764	−	0.865617i	0.500236	−	0.865889i	$-0.333247\pi$
$7$	−1.32225	−	2.29021i	−0.499764	−	0.865617i	−1.00000		0.000271954i	$0.999913\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−2.59643	−	1.50285i	−0.865475	−	0.500951i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	1.35563	−	2.34802i	0.408738	−	0.707955i	−0.586011	−	0.810303i	$-0.699302\pi$
$11$	1.35563	−	2.34802i	0.408738	−	0.707955i	0.994749	+	0.102348i	$0.0326356\pi$
$12$	0.449207	−	1.67279i	0.129675	−	0.482892i
$13$	3.49868	+	2.01996i	0.970359	+	0.560237i	0.899346	−	0.437238i	$-0.144043\pi$
$13$	3.49868	+	2.01996i	0.970359	+	0.560237i	0.0710136	+	0.997475i	$0.477377\pi$
$14$	2.29021	−	1.32225i	0.612084	−	0.353387i
$15$	1.22542	−	1.22407i	0.316401	−	0.316054i
$16$	1.00000			0.250000
$17$	−0.370882	−	0.642386i	−0.0899521	−	0.155802i	0.817539	−	0.575874i	$-0.195338\pi$
$17$	−0.370882	−	0.642386i	−0.0899521	−	0.155802i	−0.907491	+	0.420072i	$0.862005\pi$
$18$	1.50285	−	2.59643i	0.354226	−	0.611984i
$19$	1.17674	+	2.03818i	0.269963	+	0.467590i	0.968852	−	0.247641i	$-0.0796552\pi$
$19$	1.17674	+	2.03818i	0.269963	+	0.467590i	−0.698889	+	0.715230i	$0.746322\pi$
$20$	0.866025	+	0.500000i	0.193649	+	0.111803i
$21$	4.42499	−	1.18307i	0.965613	−	0.258167i
$22$	2.34802	+	1.35563i	0.500600	+	0.289021i
$23$	3.17723			0.662498			0.331249	−	0.943543i	$-0.392530\pi$
$23$	3.17723			0.662498			0.331249	+	0.943543i	$0.392530\pi$
$24$	1.67279	+	0.449207i	0.341456	+	0.0916940i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−2.01996	+	3.49868i	−0.396148	+	0.686148i
$27$	3.68029	−	3.66817i	0.708271	−	0.705940i
$28$	1.32225	+	2.29021i	0.249882	+	0.432809i
$29$	−1.11630			−0.207292			−0.103646	−	0.994614i	$-0.533051\pi$
$29$	−1.11630			−0.207292			−0.103646	+	0.994614i	$0.533051\pi$
$30$	1.22407	+	1.22542i	0.223484	+	0.223730i
$31$	4.10522	+	3.76128i	0.737319	+	0.675545i
$31$	4.10522	+	3.76128i	0.737319	+	0.675545i
$32$			1.00000i			0.176777i
$33$	3.31878	+	3.32243i	0.577725	+	0.578360i
$34$	0.642386	−	0.370882i	0.110168	−	0.0636057i
$35$			2.64450i			0.447003i
$36$	2.59643	+	1.50285i	0.432738	+	0.250476i
$37$	8.66260	−	5.00135i	1.42412	−	0.822218i	0.427475	−	0.904027i	$-0.359403\pi$
$37$	8.66260	−	5.00135i	1.42412	−	0.822218i	0.996648	+	0.0818097i	$0.0260700\pi$
$38$	−2.03818	+	1.17674i	−0.330636	+	0.190893i
$39$	−4.95060	+	4.94516i	−0.792730	+	0.791860i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	−4.56104	−	2.63332i	−0.712315	−	0.411255i	0.0996025	−	0.995027i	$-0.468243\pi$
$41$	−4.56104	−	2.63332i	−0.712315	−	0.411255i	−0.811918	+	0.583772i	$0.801576\pi$
$42$	1.18307	+	4.42499i	0.182551	+	0.682791i
$43$	4.20794	−	2.42945i	0.641704	−	0.370488i	−0.143567	−	0.989641i	$-0.545857\pi$
$43$	4.20794	−	2.42945i	0.641704	−	0.370488i	0.785271	+	0.619153i	$0.212524\pi$
$44$	−1.35563	+	2.34802i	−0.204369	+	0.353978i
$45$	1.49714	+	2.59972i	0.223181	+	0.387544i
$46$			3.17723i			0.468457i
$47$			3.29156i			0.480123i	0.970758	+	0.240061i	$0.0771676\pi$
$47$			3.29156i			0.480123i	−0.970758	+	0.240061i	$0.922832\pi$
$48$	−0.449207	+	1.67279i	−0.0648374	+	0.241446i
$49$	0.00329675	−	0.00571013i	0.000470964	−	0.000815734i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$	1.24118	−	0.331842i	0.173800	−	0.0464671i
$52$	−3.49868	−	2.01996i	−0.485180	−	0.280119i
$53$	−0.432136	+	0.748481i	−0.0593584	+	0.102812i	−0.894178	−	0.447712i	$-0.852239\pi$
$53$	−0.432136	+	0.748481i	−0.0593584	+	0.102812i	0.834819	+	0.550524i	$0.185572\pi$
$54$	3.66817	+	3.68029i	0.499175	+	0.500824i
$55$	−2.34802	+	1.35563i	−0.316607	+	0.182793i
$56$	−2.29021	+	1.32225i	−0.306042	+	0.176693i
$57$	−3.93803	+	1.05287i	−0.521605	+	0.139457i
$58$		−	1.11630i		−	0.146577i
$59$	0.0673682	−	0.0388951i	0.00877060	−	0.00506371i	−0.495608	−	0.868546i	$-0.665055\pi$
$59$	0.0673682	−	0.0388951i	0.00877060	−	0.00506371i	0.504379	+	0.863482i	$0.331721\pi$
$60$	−1.22542	+	1.22407i	−0.158201	+	0.158027i
$61$		−	8.21375i		−	1.05166i	−0.850589	−	0.525832i	$-0.823754\pi$
$61$		−	8.21375i		−	1.05166i	0.850589	−	0.525832i	$-0.176246\pi$
$62$	−3.76128	+	4.10522i	−0.477682	+	0.521363i
$63$	−0.00871827	+	7.93351i	−0.00109840	+	0.999528i
$64$	−1.00000			−0.125000
$65$	−2.01996	−	3.49868i	−0.250546	−	0.433958i
$66$	−3.32243	+	3.31878i	−0.408963	+	0.408513i
$67$	4.09060	−	7.08512i	0.499746	−	0.865586i	−0.500254	−	0.865879i	$-0.666760\pi$
$67$	4.09060	−	7.08512i	0.499746	−	0.865586i	1.00000		0.000293150i	$9.33126e-5\pi$
$68$	0.370882	+	0.642386i	0.0449760	+	0.0779008i
$69$	−1.42723	+	5.31482i	−0.171819	+	0.639830i
$70$	−2.64450			−0.316079
$71$	−11.6252	−	6.71183i	−1.37966	−	0.796548i	−0.387543	−	0.921852i	$-0.626676\pi$
$71$	−11.6252	−	6.71183i	−1.37966	−	0.796548i	−0.992118	+	0.125304i	$0.960009\pi$
$72$	−1.50285	+	2.59643i	−0.177113	+	0.305992i
$73$	9.24020	+	5.33483i	1.08148	+	0.624395i	0.931296	−	0.364262i	$-0.118679\pi$
$73$	9.24020	+	5.33483i	1.08148	+	0.624395i	0.150188	+	0.988657i	$0.452012\pi$
$74$	5.00135	+	8.66260i	0.581396	+	1.00701i
$75$	−1.67328	+	0.447368i	−0.193214	+	0.0516577i
$76$	−1.17674	−	2.03818i	−0.134982	−	0.233795i
$77$	−7.16994			−0.817091
$78$	−4.94516	−	4.95060i	−0.559929	−	0.560545i
$79$	−10.5492	+	6.09057i	−1.18688	+	0.685243i	−0.957595	−	0.288118i	$-0.906971\pi$
$79$	−10.5492	+	6.09057i	−1.18688	+	0.685243i	−0.229280	+	0.973360i	$0.573637\pi$
$80$	−0.866025	−	0.500000i	−0.0968246	−	0.0559017i
$81$	4.48286	+	7.80410i	0.498095	+	0.867122i
$82$	2.63332	−	4.56104i	0.290801	−	0.503683i
$83$	2.44932	−	4.24235i	0.268848	−	0.465659i	−0.699716	−	0.714421i	$-0.746690\pi$
$83$	2.44932	−	4.24235i	0.268848	−	0.465659i	0.968565	+	0.248762i	$0.0800237\pi$
$84$	−4.42499	+	1.18307i	−0.482806	+	0.129083i
$85$			0.741764i			0.0804556i
$86$	2.42945	+	4.20794i	0.261975	+	0.453753i
$87$	0.501450	−	1.86733i	0.0537611	−	0.200199i
$88$	−2.34802	−	1.35563i	−0.250300	−	0.144511i
$89$	17.1663			1.81962			0.909811	−	0.415022i	$-0.136226\pi$
$89$	17.1663			1.81962			0.909811	+	0.415022i	$0.136226\pi$
$90$	−2.59972	+	1.49714i	−0.274035	+	0.157813i
$91$		−	10.6836i		−	1.11995i
$92$	−3.17723			−0.331249
$93$	−8.13590	+	5.17756i	−0.843654	+	0.536888i
$94$	−3.29156			−0.339498
$95$		−	2.35348i		−	0.241462i
$96$	−1.67279	−	0.449207i	−0.170728	−	0.0458470i
$97$	12.4034			1.25938			0.629689	−	0.776847i	$-0.283182\pi$
$97$	12.4034			1.25938			0.629689	+	0.776847i	$0.283182\pi$
$98$	0.00571013	+	0.00329675i	0.000576811	+	0.000333022i
$99$	−7.04853	+	4.05915i	−0.708404	+	0.407960i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$			0.291018i			0.0289574i	0.999895	+	0.0144787i	$0.00460888\pi$
$101$			0.291018i			0.0289574i	−0.999895	+	0.0144787i	$0.995391\pi$
$102$	0.331842	+	1.24118i	0.0328572	+	0.122895i
$103$	3.02724	−	5.24333i	0.298283	−	0.516641i	−0.677460	−	0.735559i	$-0.736919\pi$
$103$	3.02724	−	5.24333i	0.298283	−	0.516641i	0.975743	+	0.218918i	$0.0702528\pi$
$104$	2.01996	−	3.49868i	0.198074	−	0.343074i
$105$	−4.42369	−	1.18793i	−0.431708	−	0.115930i
$106$	−0.748481	−	0.432136i	−0.0726989	−	0.0419727i
$107$	−4.83678	+	2.79252i	−0.467590	+	0.269963i	−0.715230	−	0.698889i	$-0.753678\pi$
$107$	−4.83678	+	2.79252i	−0.467590	+	0.269963i	0.247641	+	0.968852i	$0.420345\pi$
$108$	−3.68029	+	3.66817i	−0.354136	+	0.352970i
$109$	7.74239			0.741587			0.370793	−	0.928715i	$-0.379086\pi$
$109$	7.74239			0.741587			0.370793	+	0.928715i	$0.379086\pi$
$110$	−1.35563	−	2.34802i	−0.129254	−	0.223875i
$111$	4.47490	+	16.7373i	0.424738	+	1.58864i
$112$	−1.32225	−	2.29021i	−0.124941	−	0.216404i
$113$	5.97390	+	3.44903i	0.561978	+	0.324458i	0.753939	−	0.656945i	$-0.228151\pi$
$113$	5.97390	+	3.44903i	0.561978	+	0.324458i	−0.191961	+	0.981402i	$0.561485\pi$
$114$	−1.05287	−	3.93803i	−0.0986107	−	0.368831i
$115$	−2.75156	−	1.58861i	−0.256584	−	0.148139i
$116$	1.11630			0.103646
$117$	−6.04835	−	10.5027i	−0.559171	−	0.970974i
$118$	0.0388951	+	0.0673682i	0.00358058	+	0.00620175i
$119$	−0.980799	+	1.69879i	−0.0899097	+	0.155728i
$120$	−1.22407	−	1.22542i	−0.111742	−	0.111865i
$121$	1.82453	+	3.16018i	0.165866	+	0.287289i
$122$	8.21375			0.743638
$123$	6.45383	−	6.44674i	0.581922	−	0.581283i
$124$	−4.10522	−	3.76128i	−0.368659	−	0.337772i
$125$		−	1.00000i		−	0.0894427i
$126$	−7.93351	−	0.00871827i	−0.706773	−	0.000776685i
$127$	6.24347	−	3.60467i	0.554019	−	0.319863i	−0.196723	−	0.980459i	$-0.563030\pi$
$127$	6.24347	−	3.60467i	0.554019	−	0.319863i	0.750741	+	0.660596i	$0.229696\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	2.17372	+	8.13030i	0.191385	+	0.715833i
$130$	3.49868	−	2.01996i	0.306855	−	0.177163i
$131$	−13.4418	+	7.76065i	−1.17442	+	0.678051i	−0.954717	−	0.297516i	$-0.903842\pi$
$131$	−13.4418	+	7.76065i	−1.17442	+	0.678051i	−0.219702	+	0.975567i	$0.570509\pi$
$132$	−3.31878	−	3.32243i	−0.288863	−	0.289180i
$133$	3.11190	−	5.38997i	0.269836	−	0.467369i
$134$	7.08512	+	4.09060i	0.612061	+	0.353374i
$135$	−5.02131	+	1.33659i	−0.432165	+	0.115035i
$136$	−0.642386	+	0.370882i	−0.0550842	+	0.0318029i
$137$	9.07490	−	15.7182i	0.775321	−	1.34290i	−0.159293	−	0.987231i	$-0.550921\pi$
$137$	9.07490	−	15.7182i	0.775321	−	1.34290i	0.934614	−	0.355664i	$-0.115745\pi$
$138$	−5.31482	−	1.42723i	−0.452428	−	0.121494i
$139$			20.3716i			1.72789i	0.503583	+	0.863947i	$0.332015\pi$
$139$			20.3716i			1.72789i	−0.503583	+	0.863947i	$0.667985\pi$
$140$		−	2.64450i		−	0.223501i
$141$	−5.50607	−	1.47859i	−0.463695	−	0.124520i
$142$	6.71183	−	11.6252i	0.563244	−	0.975568i
$143$	9.48584	−	5.47665i	0.793246	−	0.457981i
$144$	−2.59643	−	1.50285i	−0.216369	−	0.125238i
$145$	0.966745	+	0.558150i	0.0802838	+	0.0463519i
$146$	−5.33483	+	9.24020i	−0.441514	+	0.764725i
$147$	0.00807091	+	0.00807979i	0.000665678	+	0.000666410i
$148$	−8.66260	+	5.00135i	−0.712061	+	0.411109i
$149$	6.93481	−	4.00381i	0.568122	−	0.328005i	−0.188277	−	0.982116i	$-0.560290\pi$
$149$	6.93481	−	4.00381i	0.568122	−	0.328005i	0.756399	+	0.654111i	$0.226957\pi$
$150$	−0.447368	−	1.67328i	−0.0365275	−	0.136623i
$151$		−	7.40096i		−	0.602282i	−0.953580	−	0.301141i	$-0.902633\pi$
$151$		−	7.40096i		−	0.602282i	0.953580	−	0.301141i	$-0.0973674\pi$
$152$	2.03818	−	1.17674i	0.165318	−	0.0954463i
$153$	−0.00244541	+	2.22529i	−0.000197700	+	0.179904i
$154$		−	7.16994i		−	0.577771i
$155$	−1.67459	−	5.30997i	−0.134506	−	0.426507i
$156$	4.95060	−	4.94516i	0.396365	−	0.395930i
$157$	2.41698			0.192896			0.0964482	−	0.995338i	$-0.469252\pi$
$157$	2.41698			0.192896			0.0964482	+	0.995338i	$0.469252\pi$
$158$	−6.09057	−	10.5492i	−0.484540	−	0.839247i
$159$	−1.05793	−	1.05909i	−0.0838993	−	0.0839916i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−4.20110	−	7.27652i	−0.331093	−	0.573470i
$162$	−7.80410	+	4.48286i	−0.613148	+	0.352207i
$163$	−25.1648			−1.97106			−0.985532	−	0.169492i	$-0.945787\pi$
$163$	−25.1648			−1.97106			−0.985532	+	0.169492i	$0.945787\pi$
$164$	4.56104	+	2.63332i	0.356158	+	0.205628i
$165$	−1.21293	−	4.53670i	−0.0944267	−	0.353181i
$166$	4.24235	+	2.44932i	0.329270	+	0.190104i
$167$	−11.2639	−	19.5096i	−0.871624	−	1.50970i	−0.860316	−	0.509762i	$-0.829734\pi$
$167$	−11.2639	−	19.5096i	−0.871624	−	1.50970i	−0.0113086	−	0.999936i	$-0.503600\pi$
$168$	−1.18307	−	4.42499i	−0.0912757	−	0.341396i
$169$	1.66051	+	2.87609i	0.127731	+	0.221237i
$170$	−0.741764			−0.0568907
$171$	0.00775884	−	7.06044i	0.000593333	−	0.539926i
$172$	−4.20794	+	2.42945i	−0.320852	+	0.185244i
$173$	7.33403	+	4.23431i	0.557596	+	0.321928i	0.752180	−	0.658958i	$-0.229002\pi$
$173$	7.33403	+	4.23431i	0.557596	+	0.321928i	−0.194584	+	0.980886i	$0.562336\pi$
$174$	1.86733	+	0.501450i	0.141562	+	0.0380148i
$175$	1.32225	−	2.29021i	0.0999529	−	0.173123i
$176$	1.35563	−	2.34802i	0.102185	−	0.176989i
$177$	0.0348009	+	0.130165i	0.00261579	+	0.00978377i
$178$			17.1663i			1.28667i
$179$	−8.32290	−	14.4157i	−0.622083	−	1.07748i	−0.989097	−	0.147264i	$-0.952953\pi$
$179$	−8.32290	−	14.4157i	−0.622083	−	1.07748i	0.367014	−	0.930215i	$-0.380380\pi$
$180$	−1.49714	−	2.59972i	−0.111591	−	0.193772i
$181$	−2.86960	−	1.65676i	−0.213296	−	0.123146i	0.389547	−	0.921007i	$-0.372632\pi$
$181$	−2.86960	−	1.65676i	−0.213296	−	0.123146i	−0.602842	+	0.797861i	$0.705965\pi$
$182$	10.6836			0.791922
$183$	13.7399	+	3.68968i	1.01568	+	0.272749i
$184$		−	3.17723i		−	0.234228i
$185$	−10.0027			−0.735414
$186$	−5.17756	−	8.13590i	−0.379637	−	0.596553i
$187$	−2.01112			−0.147067
$188$		−	3.29156i		−	0.240061i
$189$	−13.2671	−	3.57837i	−0.965043	−	0.260288i
$190$	2.35348			0.170740
$191$	−2.56932	−	1.48340i	−0.185909	−	0.107335i	0.404157	−	0.914690i	$-0.367565\pi$
$191$	−2.56932	−	1.48340i	−0.185909	−	0.107335i	−0.590066	+	0.807355i	$0.700898\pi$
$192$	0.449207	−	1.67279i	0.0324187	−	0.120723i
$193$	6.42312	+	11.1252i	0.462346	+	0.800807i	0.999077	−	0.0429465i	$-0.0136745\pi$
$193$	6.42312	+	11.1252i	0.462346	+	0.800807i	−0.536731	+	0.843753i	$0.680341\pi$
$194$			12.4034i			0.890515i
$195$	6.75993	−	1.80734i	0.484088	−	0.129426i
$196$	−0.00329675	+	0.00571013i	−0.000235482	+	0.000407867i
$197$	6.44071	−	11.1556i	0.458881	−	0.794806i	−0.540021	−	0.841652i	$-0.681584\pi$
$197$	6.44071	−	11.1556i	0.458881	−	0.794806i	0.998902	+	0.0468458i	$0.0149169\pi$
$198$	−4.05915	−	7.04853i	−0.288471	−	0.500917i
$199$	8.97201	+	5.17999i	0.636009	+	0.367200i	0.783075	−	0.621927i	$-0.213650\pi$
$199$	8.97201	+	5.17999i	0.636009	+	0.367200i	−0.147067	+	0.989127i	$0.546983\pi$
$200$	0.866025	−	0.500000i	0.0612372	−	0.0353553i
$201$	10.0144	+	10.0254i	0.706359	+	0.707136i
$202$	−0.291018			−0.0204760
$203$	1.47603	+	2.55656i	0.103597	+	0.179435i
$204$	−1.24118	+	0.331842i	−0.0868998	+	0.0232336i
$205$	2.63332	+	4.56104i	0.183919	+	0.318557i
$206$	5.24333	+	3.02724i	0.365320	+	0.210918i
$207$	−8.24944	−	4.77491i	−0.573376	−	0.331879i
$208$	3.49868	+	2.01996i	0.242590	+	0.140059i
$209$	6.38091			0.441377
$210$	1.18793	−	4.42369i	0.0819750	−	0.305264i
$211$	2.42025	+	4.19199i	0.166617	+	0.288588i	0.937228	−	0.348717i	$-0.113382\pi$
$211$	2.42025	+	4.19199i	0.166617	+	0.288588i	−0.770612	+	0.637305i	$0.780049\pi$
$212$	0.432136	−	0.748481i	0.0296792	−	0.0514059i
$213$	16.4496	−	16.4315i	1.12711	−	1.12587i
$214$	−2.79252	−	4.83678i	−0.190893	−	0.330636i
$215$	−4.85891			−0.331375
$216$	−3.66817	−	3.68029i	−0.249588	−	0.250412i
$217$	3.18597	−	14.3752i	0.216278	−	0.975849i
$218$			7.74239i			0.524381i
$219$	−13.0748	+	13.0604i	−0.883513	+	0.882543i
$220$	2.34802	−	1.35563i	0.158304	−	0.0913966i
$221$		−	2.99667i		−	0.201578i
$222$	−16.7373	+	4.47490i	−1.12334	+	0.300335i
$223$	7.55204	−	4.36017i	0.505722	−	0.291979i	−0.225351	−	0.974278i	$-0.572353\pi$
$223$	7.55204	−	4.36017i	0.505722	−	0.291979i	0.731073	+	0.682299i	$0.239020\pi$
$224$	2.29021	−	1.32225i	0.153021	−	0.0883467i
$225$	0.00329675	−	3.00000i	0.000219783	−	0.200000i
$226$	−3.44903	+	5.97390i	−0.229426	+	0.397378i
$227$	11.0216	+	6.36331i	0.731528	+	0.422348i	0.818981	−	0.573821i	$-0.194539\pi$
$227$	11.0216	+	6.36331i	0.731528	+	0.422348i	−0.0874527	+	0.996169i	$0.527873\pi$
$228$	3.93803	−	1.05287i	0.260803	−	0.0697283i
$229$	−0.300311	+	0.173385i	−0.0198451	+	0.0114576i	−0.509890	−	0.860240i	$-0.670314\pi$
$229$	−0.300311	+	0.173385i	−0.0198451	+	0.0114576i	0.490045	+	0.871697i	$0.336980\pi$
$230$	1.58861	−	2.75156i	0.104750	−	0.181433i
$231$	3.22079	−	11.9938i	0.211912	−	0.789133i
$232$			1.11630i			0.0732887i
$233$			3.05182i			0.199931i	0.994991	+	0.0999657i	$0.0318733\pi$
$233$			3.05182i			0.199931i	−0.994991	+	0.0999657i	$0.968127\pi$
$234$	10.5027	−	6.04835i	0.686583	−	0.395393i
$235$	1.64578	−	2.85057i	0.107359	−	0.185951i
$236$	−0.0673682	+	0.0388951i	−0.00438530	+	0.00253185i
$237$	−5.44946	−	20.3824i	−0.353980	−	1.32398i
$238$	−1.69879	−	0.980799i	−0.110116	−	0.0635758i
$239$	−6.34019	+	10.9815i	−0.410113	+	0.710336i	−0.994902	−	0.100850i	$-0.967844\pi$
$239$	−6.34019	+	10.9815i	−0.410113	+	0.710336i	0.584789	+	0.811185i	$0.301177\pi$
$240$	1.22542	−	1.22407i	0.0791004	−	0.0790135i
$241$	−17.6091	+	10.1666i	−1.13430	+	0.654890i	−0.945013	−	0.327032i	$-0.893952\pi$
$241$	−17.6091	+	10.1666i	−1.13430	+	0.654890i	−0.189289	+	0.981921i	$0.560618\pi$
$242$	−3.16018	+	1.82453i	−0.203144	+	0.117285i
$243$	−15.0683	+	3.99321i	−0.966633	+	0.256164i
$244$			8.21375i			0.525832i
$245$	−0.00571013	+	0.00329675i	−0.000364807	+	0.000210621i
$246$	6.44674	+	6.45383i	0.411029	+	0.411481i
$247$			9.50790i			0.604973i
$248$	3.76128	−	4.10522i	0.238841	−	0.260682i
$249$	5.99630	+	6.00289i	0.380000	+	0.380418i
$250$	1.00000			0.0632456
$251$	−8.05449	−	13.9508i	−0.508395	−	0.880565i	−0.999953	−	0.00972062i	$-0.996906\pi$
$251$	−8.05449	−	13.9508i	−0.508395	−	0.880565i	0.491558	−	0.870845i	$-0.336428\pi$
$252$	0.00871827	−	7.93351i	0.000549199	−	0.499764i
$253$	4.30715	−	7.46020i	0.270788	−	0.469019i
$254$	3.60467	+	6.24347i	0.226177	+	0.391750i
$255$	−1.24081	−	0.333205i	−0.0777027	−	0.0208661i
$256$	1.00000			0.0625000
$257$	−17.9053	−	10.3376i	−1.11690	−	0.644843i	−0.176293	−	0.984338i	$-0.556411\pi$
$257$	−17.9053	−	10.3376i	−1.11690	−	0.644843i	−0.940608	+	0.339494i	$0.889744\pi$
$258$	−8.13030	+	2.17372i	−0.506171	+	0.135330i
$259$	−22.9083	−	13.2261i	−1.42345	−	0.821830i
$260$	2.01996	+	3.49868i	0.125273	+	0.216979i
$261$	2.89839	+	1.67764i	0.179406	+	0.103843i
$262$	−7.76065	−	13.4418i	−0.479455	−	0.830440i
$263$	−16.8210			−1.03723			−0.518613	−	0.855009i	$-0.673551\pi$
$263$	−16.8210			−1.03723			−0.518613	+	0.855009i	$0.673551\pi$
$264$	3.32243	−	3.31878i	0.204481	−	0.204257i
$265$	0.748481	−	0.432136i	0.0459788	−	0.0265459i
$266$	5.38997	+	3.11190i	0.330480	+	0.190803i
$267$	−7.71121	+	28.7155i	−0.471919	+	1.75736i
$268$	−4.09060	+	7.08512i	−0.249873	+	0.432793i
$269$	3.65752	−	6.33501i	0.223003	−	0.386252i	−0.732716	−	0.680535i	$-0.761747\pi$
$269$	3.65752	−	6.33501i	0.223003	−	0.386252i	0.955718	+	0.294283i	$0.0950807\pi$
$270$	−1.33659	−	5.02131i	−0.0813422	−	0.305587i
$271$		−	4.32372i		−	0.262647i	−0.991340	−	0.131324i	$-0.958077\pi$
$271$		−	4.32372i		−	0.262647i	0.991340	−	0.131324i	$-0.0419227\pi$
$272$	−0.370882	−	0.642386i	−0.0224880	−	0.0389504i
$273$	17.8714	+	4.79915i	1.08163	+	0.290458i
$274$	15.7182	+	9.07490i	0.949570	+	0.548235i
$275$	2.71126			0.163495
$276$	1.42723	−	5.31482i	0.0859093	−	0.319915i
$277$		−	12.3568i		−	0.742447i	−0.928544	−	0.371223i	$-0.878938\pi$
$277$		−	12.3568i		−	0.742447i	0.928544	−	0.371223i	$-0.121062\pi$
$278$	−20.3716			−1.22181
$279$	−5.00625	−	15.9354i	−0.299716	−	0.954028i
$280$	2.64450			0.158039
$281$		−	2.26737i		−	0.135260i	−0.997710	−	0.0676300i	$-0.978456\pi$
$281$		−	2.26737i		−	0.135260i	0.997710	−	0.0676300i	$-0.0215437\pi$
$282$	1.47859	−	5.50607i	0.0880488	−	0.327882i
$283$	4.78042			0.284166			0.142083	−	0.989855i	$-0.454620\pi$
$283$	4.78042			0.284166			0.142083	+	0.989855i	$0.454620\pi$
$284$	11.6252	+	6.71183i	0.689831	+	0.398274i
$285$	3.93687	+	1.05720i	0.233200	+	0.0626232i
$286$	5.47665	+	9.48584i	0.323841	+	0.560909i
$287$			13.9277i			0.822123i
$288$	1.50285	−	2.59643i	0.0885565	−	0.152996i
$289$	8.22489	−	14.2459i	0.483817	−	0.837996i
$290$	−0.558150	+	0.966745i	−0.0327757	+	0.0567692i
$291$	−5.57171	+	20.7483i	−0.326619	+	1.21629i
$292$	−9.24020	−	5.33483i	−0.540742	−	0.312198i
$293$	−16.4722	+	9.51024i	−0.962318	+	0.555594i	−0.896886	−	0.442263i	$-0.854176\pi$
$293$	−16.4722	+	9.51024i	−0.962318	+	0.555594i	−0.0654320	+	0.997857i	$0.520843\pi$
$294$	−0.00807979	+	0.00807091i	−0.000471223	+	0.000470705i
$295$	−0.0777901			−0.00452912
$296$	−5.00135	−	8.66260i	−0.290698	−	0.503503i
$297$	−3.62384	−	13.6141i	−0.210277	−	0.789969i
$298$	4.00381	+	6.93481i	0.231935	+	0.401723i
$299$	11.1161	+	6.41789i	0.642861	+	0.371156i
$300$	1.67328	−	0.447368i	0.0966068	−	0.0258288i
$301$	−11.1279	−	6.42470i	−0.641402	−	0.370314i
$302$	7.40096			0.425877
$303$	−0.486812	−	0.130728i	−0.0279666	−	0.00751010i
$304$	1.17674	+	2.03818i	0.0674908	+	0.116897i
$305$	−4.10688	+	7.11332i	−0.235159	+	0.407308i
$306$	−2.22529	−	0.00244541i	−0.127211	−	0.000139795i
$307$	−14.0713	−	24.3721i	−0.803089	−	1.39099i	−0.917574	−	0.397566i	$-0.869855\pi$
$307$	−14.0713	−	24.3721i	−0.803089	−	1.39099i	0.114485	−	0.993425i	$-0.463478\pi$
$308$	7.16994			0.408546
$309$	7.41112	+	7.41927i	0.421604	+	0.422067i
$310$	5.30997	−	1.67459i	0.301586	−	0.0951100i
$311$			34.7697i			1.97161i	0.167895	+	0.985805i	$0.446303\pi$
$311$			34.7697i			1.97161i	−0.167895	+	0.985805i	$0.553697\pi$
$312$	4.94516	+	4.95060i	0.279965	+	0.280272i
$313$	−13.4245	+	7.75065i	−0.758799	+	0.438093i	−0.828864	−	0.559450i	$-0.811013\pi$
$313$	−13.4245	+	7.75065i	−0.758799	+	0.438093i	0.0700654	+	0.997542i	$0.477679\pi$
$314$			2.41698i			0.136398i
$315$	3.97431	−	6.86626i	0.223927	−	0.386870i
$316$	10.5492	−	6.09057i	0.593438	−	0.342621i
$317$	4.29014	−	2.47691i	0.240958	−	0.139117i	−0.374659	−	0.927163i	$-0.622240\pi$
$317$	4.29014	−	2.47691i	0.240958	−	0.139117i	0.615617	+	0.788045i	$0.288907\pi$
$318$	1.05909	−	1.05793i	0.0593910	−	0.0593258i
$319$	−1.51329	+	2.62110i	−0.0847281	+	0.146753i
$320$	0.866025	+	0.500000i	0.0484123	+	0.0279508i
$321$	−2.49857	−	9.34533i	−0.139457	−	0.521605i
$322$	7.27652	−	4.20110i	0.405504	−	0.234118i
$323$	0.872864	−	1.51185i	0.0485675	−	0.0841213i
$324$	−4.48286	−	7.80410i	−0.249048	−	0.433561i
$325$			4.03993i			0.224095i
$326$		−	25.1648i		−	1.39375i
$327$	−3.47794	+	12.9514i	−0.192330	+	0.716212i
$328$	−2.63332	+	4.56104i	−0.145401	+	0.251841i
$329$	7.53835	−	4.35227i	0.415603	−	0.239948i
$330$	4.53670	−	1.21293i	0.249737	−	0.0667698i
$331$	−1.63849	−	0.945983i	−0.0900596	−	0.0519959i	0.454294	−	0.890852i	$-0.349892\pi$
$331$	−1.63849	−	0.945983i	−0.0900596	−	0.0519959i	−0.544353	+	0.838856i	$0.683225\pi$
$332$	−2.44932	+	4.24235i	−0.134424	+	0.232829i
$333$	−30.0081	−	0.0329764i	−1.64443	−	0.00180710i
$334$	19.5096	−	11.2639i	1.06752	−	0.616331i
$335$	−7.08512	+	4.09060i	−0.387102	+	0.223493i
$336$	4.42499	−	1.18307i	0.241403	−	0.0645416i
$337$			27.5245i			1.49936i	0.661802	+	0.749678i	$0.269792\pi$
$337$			27.5245i			1.49936i	−0.661802	+	0.749678i	$0.730208\pi$
$338$	−2.87609	+	1.66051i	−0.156438	+	0.0903198i
$339$	−8.45302	+	8.44373i	−0.459105	+	0.458601i
$340$		−	0.741764i		−	0.0402278i
$341$	14.3967	−	4.54024i	0.779626	−	0.245868i
$342$	7.06044	+	0.00775884i	0.381785	+	0.000419550i
$343$	−18.5290			−1.00047
$344$	−2.42945	−	4.20794i	−0.130987	−	0.226877i
$345$	3.89343	−	3.88916i	0.209615	−	0.209385i
$346$	−4.23431	+	7.33403i	−0.227638	+	0.394280i
$347$	12.1983	+	21.1281i	0.654841	+	1.13422i	0.981934	+	0.189226i	$0.0605978\pi$
$347$	12.1983	+	21.1281i	0.654841	+	1.13422i	−0.327092	+	0.944992i	$0.606069\pi$
$348$	−0.501450	+	1.86733i	−0.0268805	+	0.100100i
$349$	−7.97476			−0.426879			−0.213440	−	0.976956i	$-0.568467\pi$
$349$	−7.97476			−0.426879			−0.213440	+	0.976956i	$0.568467\pi$
$350$	2.29021	+	1.32225i	0.122417	+	0.0706774i
$351$	20.2857	−	5.39972i	1.08277	−	0.288216i
$352$	2.34802	+	1.35563i	0.125150	+	0.0722554i
$353$	17.7462	+	30.7372i	0.944533	+	1.63598i	0.756684	+	0.653781i	$0.226818\pi$
$353$	17.7462	+	30.7372i	0.944533	+	1.63598i	0.187848	+	0.982198i	$0.439849\pi$
$354$	−0.130165	+	0.0348009i	−0.00691817	+	0.00184964i
$355$	6.71183	+	11.6252i	0.356227	+	0.617003i
$356$	−17.1663			−0.909811
$357$	−2.40114	−	2.40378i	−0.127082	−	0.127221i
$358$	14.4157	−	8.32290i	0.761893	−	0.439879i
$359$	−8.61779	−	4.97548i	−0.454830	−	0.262596i	0.255038	−	0.966931i	$-0.417912\pi$
$359$	−8.61779	−	4.97548i	−0.454830	−	0.262596i	−0.709868	+	0.704335i	$0.751245\pi$
$360$	2.59972	−	1.49714i	0.137017	−	0.0789064i
$361$	6.73056	−	11.6577i	0.354240	−	0.613562i
$362$	1.65676	−	2.86960i	0.0870775	−	0.150823i
$363$	−6.10590	+	1.63247i	−0.320476	+	0.0856827i
$364$			10.6836i			0.559973i
$365$	−5.33483	−	9.24020i	−0.279238	−	0.483654i
$366$	−3.68968	+	13.7399i	−0.192862	+	0.718194i
$367$	4.15155	+	2.39690i	0.216709	+	0.125117i	0.604426	−	0.796662i	$-0.293403\pi$
$367$	4.15155	+	2.39690i	0.216709	+	0.125117i	−0.387716	+	0.921779i	$0.626736\pi$
$368$	3.17723			0.165624
$369$	7.88492	+	13.6918i	0.410472	+	0.712767i
$370$		−	10.0027i		−	0.520016i
$371$	2.28557			0.118661
$372$	8.13590	−	5.17756i	0.421827	−	0.268444i
$373$	−23.1098			−1.19658			−0.598289	−	0.801280i	$-0.704153\pi$
$373$	−23.1098			−1.19658			−0.598289	+	0.801280i	$0.704153\pi$
$374$		−	2.01112i		−	0.103992i
$375$	1.67279	+	0.449207i	0.0863823	+	0.0231969i
$376$	3.29156			0.169749
$377$	−3.90558	−	2.25489i	−0.201148	−	0.116133i
$378$	3.57837	−	13.2671i	0.184052	−	0.682388i
$379$	−0.565702	−	0.979824i	−0.0290582	−	0.0503302i	0.851131	−	0.524954i	$-0.175917\pi$
$379$	−0.565702	−	0.979824i	−0.0290582	−	0.0503302i	−0.880189	+	0.474624i	$0.842584\pi$
$380$			2.35348i			0.120731i
$381$	3.22523	+	12.0632i	0.165234	+	0.618018i
$382$	1.48340	−	2.56932i	0.0758971	−	0.131458i
$383$	1.85664	−	3.21579i	0.0948697	−	0.164319i	−0.814685	−	0.579904i	$-0.803090\pi$
$383$	1.85664	−	3.21579i	0.0948697	−	0.164319i	0.909554	+	0.415585i	$0.136423\pi$
$384$	1.67279	+	0.449207i	0.0853640	+	0.0229235i
$385$	6.20935	+	3.58497i	0.316458	+	0.182707i
$386$	−11.1252	+	6.42312i	−0.566256	+	0.326928i
$387$	−14.5767	−	0.0160186i	−0.740976	−	0.000814271i
$388$	−12.4034			−0.629689
$389$	4.87542	+	8.44448i	0.247194	+	0.428152i	0.962746	−	0.270407i	$-0.0871583\pi$
$389$	4.87542	+	8.44448i	0.247194	+	0.428152i	−0.715552	+	0.698559i	$0.753825\pi$
$390$	1.80734	+	6.75993i	0.0915180	+	0.342302i
$391$	−1.17838	−	2.04101i	−0.0595931	−	0.103218i
$392$	−0.00571013	−	0.00329675i	−0.000288405	−	0.000166511i
$393$	−6.94374	−	25.9715i	−0.350265	−	1.31009i
$394$	11.1556	+	6.44071i	0.562013	+	0.324478i
$395$	12.1811			0.612900
$396$	7.04853	−	4.05915i	0.354202	−	0.203980i
$397$	−5.53921	−	9.59420i	−0.278005	−	0.481519i	0.692884	−	0.721049i	$-0.256340\pi$
$397$	−5.53921	−	9.59420i	−0.278005	−	0.481519i	−0.970889	+	0.239530i	$0.923007\pi$
$398$	−5.17999	+	8.97201i	−0.259650	+	0.449726i
$399$	7.61837	+	7.62675i	0.381396	+	0.381815i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	0.963613			0.0481205			0.0240603	−	0.999711i	$-0.492341\pi$
$401$	0.963613			0.0481205			0.0240603	+	0.999711i	$0.492341\pi$
$402$	−10.0254	+	10.0144i	−0.500021	+	0.499471i
$403$	6.76520	+	21.4519i	0.336999	+	1.06859i
$404$		−	0.291018i		−	0.0144787i
$405$	0.0197805	−	8.99998i	0.000982900	−	0.447213i
$406$	−2.55656	+	1.47603i	−0.126880	+	0.0732542i
$407$		−	27.1200i		−	1.34429i
$408$	−0.331842	−	1.24118i	−0.0164286	−	0.0614474i
$409$	−3.39020	+	1.95733i	−0.167635	+	0.0967838i	−0.581470	−	0.813568i	$-0.697522\pi$
$409$	−3.39020	+	1.95733i	−0.167635	+	0.0967838i	0.413835	+	0.910352i	$0.364189\pi$
$410$	−4.56104	+	2.63332i	−0.225254	+	0.130050i
$411$	22.2167	+	22.2411i	1.09587	+	1.09707i
$412$	−3.02724	+	5.24333i	−0.149141	+	0.258321i
$413$	−0.178156	−	0.102858i	−0.00876647	−	0.00506132i
$414$	4.77491	−	8.24944i	0.234674	−	0.405438i
$415$	−4.24235	+	2.44932i	−0.208249	+	0.120233i
$416$	−2.01996	+	3.49868i	−0.0990369	+	0.171537i
$417$	−34.0773	−	9.15105i	−1.66877	−	0.448129i
$418$			6.38091i			0.312100i
$419$			6.12859i			0.299401i	0.988731	+	0.149701i	$0.0478310\pi$
$419$			6.12859i			0.299401i	−0.988731	+	0.149701i	$0.952169\pi$
$420$	4.42369	+	1.18793i	0.215854	+	0.0579650i
$421$	−6.31725	+	10.9418i	−0.307884	+	0.533271i	−0.977899	−	0.209077i	$-0.932954\pi$
$421$	−6.31725	+	10.9418i	−0.307884	+	0.533271i	0.670015	+	0.742347i	$0.266288\pi$
$422$	−4.19199	+	2.42025i	−0.204063	+	0.117816i
$423$	4.94673	−	8.54629i	0.240518	−	0.415535i
$424$	0.748481	+	0.432136i	0.0363495	+	0.0209864i
$425$	0.370882	−	0.642386i	0.0179904	−	0.0311603i
$426$	16.4315	+	16.4496i	0.796110	+	0.796985i
$427$	−18.8112	+	10.8607i	−0.910338	+	0.525584i
$428$	4.83678	−	2.79252i	0.233795	−	0.134982i
$429$	4.90016	+	18.3279i	0.236582	+	0.884881i
$430$		−	4.85891i		−	0.234317i
$431$	24.8975	−	14.3746i	1.19927	−	0.692399i	0.238878	−	0.971050i	$-0.423220\pi$
$431$	24.8975	−	14.3746i	1.19927	−	0.692399i	0.960393	+	0.278650i	$0.0898871\pi$
$432$	3.68029	−	3.66817i	0.177068	−	0.176485i
$433$		−	7.12270i		−	0.342295i	−0.985245	−	0.171148i	$-0.945252\pi$
$433$		−	7.12270i		−	0.342295i	0.985245	−	0.171148i	$-0.0547475\pi$
$434$	14.3752	+	3.18597i	0.690030	+	0.152931i
$435$	−1.36793	+	1.36643i	−0.0655874	+	0.0655154i
$436$	−7.74239			−0.370793
$437$	3.73878	+	6.47575i	0.178850	+	0.309777i
$438$	−13.0604	−	13.0748i	−0.624052	−	0.624738i
$439$	16.5785	−	28.7148i	0.791248	−	1.37048i	−0.133946	−	0.990989i	$-0.542765\pi$
$439$	16.5785	−	28.7148i	0.791248	−	1.37048i	0.925194	−	0.379494i	$-0.123902\pi$
$440$	1.35563	+	2.34802i	0.0646272	+	0.111938i
$441$	−0.0171413	+	0.00987141i	−0.000816251	+	0.000470067i
$442$	2.99667			0.142537
$443$	23.1960	+	13.3922i	1.10207	+	0.636283i	0.936765	−	0.349959i	$-0.113804\pi$
$443$	23.1960	+	13.3922i	1.10207	+	0.636283i	0.165310	+	0.986242i	$0.447138\pi$
$444$	−4.47490	−	16.7373i	−0.212369	−	0.794318i
$445$	−14.8664	−	8.58314i	−0.704737	−	0.406880i
$446$	4.36017	+	7.55204i	0.206460	+	0.357599i
$447$	3.58236	+	13.3990i	0.169440	+	0.633751i
$448$	1.32225	+	2.29021i	0.0624706	+	0.108202i
$449$	−24.5175			−1.15705			−0.578527	−	0.815663i	$-0.696372\pi$
$449$	−24.5175			−1.15705			−0.578527	+	0.815663i	$0.696372\pi$
$450$	3.00000	+	0.00329675i	0.141421	+	0.000155410i
$451$	−12.3662	+	7.13962i	−0.582301	+	0.336191i
$452$	−5.97390	−	3.44903i	−0.280989	−	0.162229i
$453$	12.3802	+	3.32456i	0.581674	+	0.156202i
$454$	−6.36331	+	11.0216i	−0.298645	+	0.517269i
$455$	−5.34180	+	9.25228i	−0.250428	+	0.433753i
$456$	1.05287	+	3.93803i	0.0493053	+	0.184415i
$457$			8.46145i			0.395810i	0.980221	+	0.197905i	$0.0634137\pi$
$457$			8.46145i			0.395810i	−0.980221	+	0.197905i	$0.936586\pi$
$458$	−0.173385	−	0.300311i	−0.00810174	−	0.0140326i
$459$	−3.72134	−	1.00371i	−0.173697	−	0.0468490i
$460$	2.75156	+	1.58861i	0.128292	+	0.0740695i
$461$	10.2584			0.477779			0.238890	−	0.971047i	$-0.423217\pi$
$461$	10.2584			0.477779			0.238890	+	0.971047i	$0.423217\pi$
$462$	11.9938	+	3.22079i	0.558001	+	0.149845i
$463$			16.4580i			0.764870i	0.923982	+	0.382435i	$0.124914\pi$
$463$			16.4580i			0.764870i	−0.923982	+	0.382435i	$0.875086\pi$
$464$	−1.11630			−0.0518230
$465$	9.63468	−	0.415948i	0.446797	−	0.0192891i
$466$	−3.05182			−0.141373
$467$			21.7403i			1.00602i	0.864281	+	0.503010i	$0.167774\pi$
$467$			21.7403i			1.00602i	−0.864281	+	0.503010i	$0.832226\pi$
$468$	6.04835	+	10.5027i	0.279585	+	0.485487i
$469$	−21.6352			−0.999021
$470$	2.85057	+	1.64578i	0.131487	+	0.0759141i
$471$	−1.08573	+	4.04310i	−0.0500276	+	0.186296i
$472$	−0.0388951	−	0.0673682i	−0.00179029	−	0.00310087i
$473$		−	13.1738i		−	0.605730i
$474$	20.3824	−	5.44946i	0.936197	−	0.250302i
$475$	−1.17674	+	2.03818i	−0.0539926	+	0.0935179i
$476$	0.980799	−	1.69879i	0.0449548	−	0.0778641i
$477$	2.24687	−	1.29394i	0.102877	−	0.0592454i
$478$	−10.9815	−	6.34019i	−0.502283	−	0.289993i
$479$	16.4488	−	9.49670i	0.751563	−	0.433915i	−0.0746954	−	0.997206i	$-0.523798\pi$
$479$	16.4488	−	9.49670i	0.751563	−	0.433915i	0.826258	+	0.563291i	$0.190465\pi$
$480$	1.22407	+	1.22542i	0.0558710	+	0.0559324i
$481$	40.4102			1.84255
$482$	−10.1666	−	17.6091i	−0.463077	−	0.802073i
$483$	14.0592	−	3.75888i	0.639716	−	0.171035i
$484$	−1.82453	−	3.16018i	−0.0829332	−	0.143645i
$485$	−10.7417	−	6.20172i	−0.487755	−	0.281606i
$486$	−3.99321	−	15.0683i	−0.181136	−	0.683513i
$487$	21.3554	+	12.3295i	0.967704	+	0.558704i	0.898535	−	0.438901i	$-0.144632\pi$
$487$	21.3554	+	12.3295i	0.967704	+	0.558704i	0.0691683	+	0.997605i	$0.477965\pi$
$488$	−8.21375			−0.371819
$489$	11.3042	−	42.0954i	0.511195	−	1.90362i
$490$	−0.00329675	−	0.00571013i	−0.000148932	−	0.000257958i
$491$	−13.0832	+	22.6608i	−0.590438	+	1.02267i	0.403735	+	0.914876i	$0.367712\pi$
$491$	−13.0832	+	22.6608i	−0.590438	+	1.02267i	−0.994173	+	0.107793i	$0.965622\pi$
$492$	−6.45383	+	6.44674i	−0.290961	+	0.290642i
$493$	0.414016	+	0.717096i	0.0186463	+	0.0322964i
$494$	−9.50790			−0.427781
$495$	8.13378	+	0.00893835i	0.365586	+	0.000401749i
$496$	4.10522	+	3.76128i	0.184330	+	0.168886i
$497$			35.4989i			1.59235i
$498$	−6.00289	+	5.99630i	−0.268996	+	0.268700i
$499$	−25.4093	+	14.6701i	−1.13748	+	0.656722i	−0.945804	−	0.324737i	$-0.894724\pi$
$499$	−25.4093	+	14.6701i	−1.13748	+	0.656722i	−0.191672	+	0.981459i	$0.561391\pi$
$500$			1.00000i			0.0447214i
$501$	37.6952	−	10.0782i	1.68410	−	0.450261i
$502$	13.9508	−	8.05449i	0.622654	−	0.359489i
$503$	6.14219	−	3.54620i	0.273867	−	0.158117i	−0.356777	−	0.934190i	$-0.616124\pi$
$503$	6.14219	−	3.54620i	0.273867	−	0.158117i	0.630644	+	0.776073i	$0.282791\pi$
$504$	7.93351	+	0.00871827i	0.353387	+	0.000388342i
$505$	0.145509	−	0.252029i	0.00647508	−	0.0112152i
$506$	7.46020	+	4.30715i	0.331646	+	0.191476i
$507$	−5.55699	+	1.48572i	−0.246795	+	0.0659831i
$508$	−6.24347	+	3.60467i	−0.277009	+	0.159931i
$509$	−11.2332	+	19.4565i	−0.497903	+	0.862393i	−0.999997	−	0.00241974i	$-0.999230\pi$
$509$	−11.2332	+	19.4565i	−0.497903	+	0.862393i	0.502094	+	0.864813i	$0.332563\pi$
$510$	0.333205	−	1.24081i	0.0147546	−	0.0549441i
$511$		−	28.2160i		−	1.24820i
$512$			1.00000i			0.0441942i
$513$	11.8071	+	3.18458i	0.521297	+	0.140603i
$514$	10.3376	−	17.9053i	0.455973	−	0.789769i
$515$	−5.24333	+	3.02724i	−0.231049	+	0.133396i
$516$	−2.17372	−	8.13030i	−0.0956927	−	0.357917i
$517$	7.72865	+	4.46214i	0.339905	+	0.196245i
$518$	13.2261	−	22.9083i	0.581122	−	1.00653i
$519$	−10.3776	+	10.3662i	−0.455525	+	0.455025i
$520$	−3.49868	+	2.01996i	−0.153427	+	0.0885813i
$521$	−24.2738	+	14.0145i	−1.06346	+	0.613986i	−0.926386	−	0.376575i	$-0.877102\pi$
$521$	−24.2738	+	14.0145i	−1.06346	+	0.613986i	−0.137069	+	0.990561i	$0.543768\pi$
$522$	−1.67764	+	2.89839i	−0.0734282	+	0.126859i
$523$		−	22.8974i		−	1.00123i	−0.865669	−	0.500617i	$-0.833107\pi$
$523$		−	22.8974i		−	1.00123i	0.865669	−	0.500617i	$-0.166893\pi$
$524$	13.4418	−	7.76065i	0.587210	−	0.339026i
$525$	3.23706	+	3.24062i	0.141277	+	0.141432i
$526$		−	16.8210i		−	0.733429i
$527$	0.893641	−	4.03212i	0.0389276	−	0.175642i
$528$	3.31878	+	3.32243i	0.144431	+	0.144590i
$529$	−12.9052			−0.561097
$530$	0.432136	+	0.748481i	0.0187708	+	0.0325119i
$531$	−0.233370		0.000256455i	−0.0101274		1.11292e-5i
$532$	−3.11190	+	5.38997i	−0.134918	+	0.233685i
$533$	−10.6384	−	18.4263i	−0.460801	−	0.798131i
$534$	−28.7155	−	7.71121i	−1.24264	−	0.333697i
$535$	5.58504			0.241462
$536$	−7.08512	−	4.09060i	−0.306031	−	0.176687i
$537$	27.8531	−	7.44681i	1.20195	−	0.321353i
$538$	6.33501	+	3.65752i	0.273122	+	0.157687i
$539$	−0.00893835	−	0.0154817i	−0.000385002	−	0.000666843i
$540$	5.02131	−	1.33659i	0.216083	−	0.0575176i
$541$	−6.55194	−	11.3483i	−0.281690	−	0.487901i	0.690111	−	0.723703i	$-0.257562\pi$
$541$	−6.55194	−	11.3483i	−0.281690	−	0.487901i	−0.971801	+	0.235802i	$0.924228\pi$
$542$	4.32372			0.185720
$543$	4.06045	−	4.05599i	0.174251	−	0.174059i
$544$	0.642386	−	0.370882i	0.0275421	−	0.0159014i
$545$	−6.70511	−	3.87120i	−0.287215	−	0.165824i
$546$	−4.79915	+	17.8714i	−0.205385	+	0.764825i
$547$	−23.1238	+	40.0517i	−0.988704	+	1.71249i	−0.364552	+	0.931183i	$0.618778\pi$
$547$	−23.1238	+	40.0517i	−0.988704	+	1.71249i	−0.624153	+	0.781302i	$0.714556\pi$
$548$	−9.07490	+	15.7182i	−0.387661	+	0.671448i
$549$	−12.3441	+	21.3264i	−0.526832	+	0.910189i
$550$			2.71126i			0.115609i
$551$	−1.31360	−	2.27522i	−0.0559611	−	0.0969275i
$552$	5.31482	+	1.42723i	0.226214	+	0.0607471i
$553$	27.8974	+	16.1065i	1.18632	+	0.684920i
$554$	12.3568			0.524989
$555$	4.49329	−	16.7324i	0.190729	−	0.710250i
$556$		−	20.3716i		−	0.863947i
$557$	36.3726			1.54116			0.770579	−	0.637345i	$-0.219967\pi$
$557$	36.3726			1.54116			0.770579	+	0.637345i	$0.219967\pi$
$558$	15.9354	−	5.00625i	0.674600	−	0.211931i
$559$	19.6296			0.830245
$560$			2.64450i			0.111751i
$561$	0.903407	−	3.36417i	0.0381419	−	0.142035i
$562$	2.26737			0.0956432
$563$	19.8508	+	11.4609i	0.836613	+	0.483019i	0.856112	−	0.516791i	$-0.172874\pi$
$563$	19.8508	+	11.4609i	0.836613	+	0.483019i	−0.0194982	+	0.999810i	$0.506207\pi$
$564$	5.50607	+	1.47859i	0.231847	+	0.0622599i
$565$	−3.44903	−	5.97390i	−0.145102	−	0.251324i
$566$			4.78042i			0.200936i
$567$	11.9455	−	20.5857i	0.501666	−	0.864517i
$568$	−6.71183	+	11.6252i	−0.281622	+	0.487784i
$569$	−6.04836	+	10.4761i	−0.253561	+	0.439180i	−0.964504	−	0.264070i	$-0.914935\pi$
$569$	−6.04836	+	10.4761i	−0.253561	+	0.439180i	0.710943	+	0.703250i	$0.248268\pi$
$570$	−1.05720	+	3.93687i	−0.0442813	+	0.164897i
$571$	32.0896	+	18.5270i	1.34291	+	0.775329i	0.987233	−	0.159281i	$-0.0509175\pi$
$571$	32.0896	+	18.5270i	1.34291	+	0.775329i	0.355676	+	0.934609i	$0.384251\pi$
$572$	−9.48584	+	5.47665i	−0.396623	+	0.228990i
$573$	3.63556	−	3.63157i	0.151878	−	0.151711i
$574$	−13.9277			−0.581329
$575$	1.58861	+	2.75156i	0.0662498	+	0.114748i
$576$	2.59643	+	1.50285i	0.108184	+	0.0626189i
$577$	10.8409	+	18.7769i	0.451311	+	0.781693i	0.998468	−	0.0553370i	$-0.0176233\pi$
$577$	10.8409	+	18.7769i	0.451311	+	0.781693i	−0.547157	+	0.837030i	$0.684290\pi$
$578$	14.2459	+	8.22489i	0.592553	+	0.342110i
$579$	−21.4953	+	5.74700i	−0.893315	+	0.238837i
$580$	−0.966745	−	0.558150i	−0.0401419	−	0.0231759i
$581$	−12.9545			−0.537443
$582$	−20.7483	−	5.57171i	−0.860045	−	0.230955i
$583$	1.17163	+	2.02933i	0.0485241	+	0.0840462i
$584$	5.33483	−	9.24020i	0.220757	−	0.382362i
$585$	−0.0133186	+	12.1198i	−0.000550657	+	0.501091i
$586$	−9.51024	−	16.4722i	−0.392864	−	0.680461i
$587$	−34.2190			−1.41237			−0.706185	−	0.708027i	$-0.749585\pi$
$587$	−34.2190			−1.41237			−0.706185	+	0.708027i	$0.749585\pi$
$588$	−0.00807091	−	0.00807979i	−0.000332839	−	0.000333205i
$589$	−2.83536	+	12.7932i	−0.116829	+	0.527135i
$590$		−	0.0777901i		−	0.00320257i
$591$	15.7678	+	15.7851i	0.648600	+	0.649313i
$592$	8.66260	−	5.00135i	0.356031	−	0.205554i
$593$			22.8931i			0.940105i	0.882638	+	0.470053i	$0.155765\pi$
$593$			22.8931i			0.940105i	−0.882638	+	0.470053i	$0.844235\pi$
$594$	13.6141	−	3.62384i	0.558592	−	0.148688i
$595$	1.69879	−	0.980799i	0.0696437	−	0.0402088i
$596$	−6.93481	+	4.00381i	−0.284061	+	0.164003i
$597$	−12.6953	+	12.6814i	−0.519584	+	0.519014i
$598$	−6.41789	+	11.1161i	−0.262447	+	0.454571i
$599$	−34.1667	−	19.7261i	−1.39601	−	0.805988i	−0.402041	−	0.915622i	$-0.631699\pi$
$599$	−34.1667	−	19.7261i	−1.39601	−	0.805988i	−0.993972	+	0.109634i	$0.965032\pi$
$600$	0.447368	+	1.67328i	0.0182637	+	0.0683113i
$601$	28.0179	−	16.1761i	1.14287	−	0.659838i	0.195732	−	0.980657i	$-0.437292\pi$
$601$	28.0179	−	16.1761i	1.14287	−	0.659838i	0.947140	+	0.320820i	$0.103958\pi$
$602$	6.42470	−	11.1279i	0.261851	−	0.453540i
$603$	−21.2688	+	12.2484i	−0.866134	+	0.498795i
$604$			7.40096i			0.301141i
$605$		−	3.64906i		−	0.148355i
$606$	0.130728	−	0.486812i	0.00531044	−	0.0197754i
$607$	−7.33156	+	12.6986i	−0.297579	+	0.515422i	−0.975582	−	0.219638i	$-0.929513\pi$
$607$	−7.33156	+	12.6986i	−0.297579	+	0.515422i	0.678002	+	0.735060i	$0.262846\pi$
$608$	−2.03818	+	1.17674i	−0.0826590	+	0.0477232i
$609$	−4.93962	+	1.32066i	−0.200164	+	0.0535158i
$610$	−7.11332	−	4.10688i	−0.288010	−	0.166283i
$611$	−6.64883	+	11.5161i	−0.268983	+	0.465892i
$612$	0.00244541	−	2.22529i	9.88498e−5	−	0.0899520i
$613$	−9.31317	+	5.37696i	−0.376155	+	0.217173i	−0.676144	−	0.736769i	$-0.736350\pi$
$613$	−9.31317	+	5.37696i	−0.376155	+	0.217173i	0.299989	+	0.953943i	$0.403017\pi$
$614$	24.3721	−	14.0713i	0.983579	−	0.567870i
$615$	−8.81255	+	2.35613i	−0.355356	+	0.0950082i
$616$			7.16994i			0.288885i
$617$	38.3757	−	22.1562i	1.54495	−	0.891975i	0.546431	−	0.837504i	$-0.315986\pi$
$617$	38.3757	−	22.1562i	1.54495	−	0.891975i	0.998515	−	0.0544716i	$-0.0173474\pi$
$618$	−7.41927	+	7.41112i	−0.298447	+	0.298119i
$619$			31.8706i			1.28099i	0.767963	+	0.640495i	$0.221271\pi$
$619$			31.8706i			1.28099i	−0.767963	+	0.640495i	$0.778729\pi$
$620$	1.67459	+	5.30997i	0.0672530	+	0.213253i
$621$	11.6931	−	11.6546i	0.469228	−	0.467684i
$622$	−34.7697			−1.39414
$623$	−22.6982	−	39.3144i	−0.909383	−	1.57510i
$624$	−4.95060	+	4.94516i	−0.198183	+	0.197965i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−7.75065	−	13.4245i	−0.309778	−	0.536552i
$627$	−2.86635	+	10.6739i	−0.114471	+	0.426274i
$628$	−2.41698			−0.0964482
$629$	−6.42560	−	3.70982i	−0.256206	−	0.147920i
$630$	6.86626	+	3.97431i	0.273558	+	0.158340i
$631$	−30.4987	−	17.6084i	−1.21413	−	0.700980i	−0.250476	−	0.968123i	$-0.580587\pi$
$631$	−30.4987	−	17.6084i	−1.21413	−	0.700980i	−0.963657	+	0.267143i	$0.913920\pi$
$632$	6.09057	+	10.5492i	0.242270	+	0.419624i
$633$	−8.09949	+	2.16548i	−0.321926	+	0.0860702i
$634$	2.47691	+	4.29014i	0.0983708	+	0.170383i
$635$	−7.20934			−0.286094
$636$	1.05793	+	1.05909i	0.0419497	+	0.0419958i
$637$	0.0230685	−	0.0133186i	0.000914009	−	0.000527703i
$638$	−2.62110	−	1.51329i	−0.103770	−	0.0599118i
$639$	20.0972	+	34.8978i	0.795031	+	1.38054i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−2.24960	+	3.89643i	−0.0888540	+	0.153900i	−0.907027	−	0.421073i	$-0.861654\pi$
$641$	−2.24960	+	3.89643i	−0.0888540	+	0.153900i	0.818173	+	0.574972i	$0.194987\pi$
$642$	9.34533	−	2.49857i	0.368831	−	0.0986107i
$643$			7.11918i			0.280753i	0.990098	+	0.140376i	$0.0448313\pi$
$643$			7.11918i			0.280753i	−0.990098	+	0.140376i	$0.955169\pi$
$644$	4.20110	+	7.27652i	0.165546	+	0.286735i
$645$	2.18265	−	8.12791i	0.0859419	−	0.320036i
$646$	1.51185	+	0.872864i	0.0594827	+	0.0343424i
$647$	38.1767			1.50088			0.750441	−	0.660937i	$-0.229841\pi$
$647$	38.1767			1.50088			0.750441	+	0.660937i	$0.229841\pi$
$648$	7.80410	−	4.48286i	0.306574	−	0.176103i
$649$		−	0.210909i		−	0.00827892i
$650$	−4.03993			−0.158459
$651$	22.6154	+	11.7869i	0.886368	+	0.461964i
$652$	25.1648			0.985532
$653$		−	31.6623i		−	1.23904i	−0.784981	−	0.619520i	$-0.787327\pi$
$653$		−	31.6623i		−	1.23904i	0.784981	−	0.619520i	$-0.212673\pi$
$654$	−12.9514	−	3.47794i	−0.506439	−	0.135998i
$655$	15.5213			0.606468
$656$	−4.56104	−	2.63332i	−0.178079	−	0.102814i
$657$	−15.9740	−	27.7382i	−0.623206	−	1.08217i
$658$	4.35227	+	7.53835i	0.169669	+	0.293876i
$659$		−	23.6853i		−	0.922648i	−0.887232	−	0.461324i	$-0.847375\pi$
$659$		−	23.6853i		−	0.922648i	0.887232	−	0.461324i	$-0.152625\pi$
$660$	1.21293	+	4.53670i	0.0472133	+	0.176591i
$661$	4.12220	−	7.13985i	0.160335	−	0.277708i	−0.774654	−	0.632385i	$-0.782076\pi$
$661$	4.12220	−	7.13985i	0.160335	−	0.277708i	0.934989	+	0.354677i	$0.115409\pi$
$662$	0.945983	−	1.63849i	0.0367667	−	0.0636818i
$663$	5.01279	+	1.34613i	0.194681	+	0.0522792i
$664$	−4.24235	−	2.44932i	−0.164635	−	0.0950522i
$665$	−5.38997	+	3.11190i	−0.209014	+	0.120674i
$666$	0.0329764	−	30.0081i	0.00127781	−	1.16279i
$667$	−3.54674			−0.137330
$668$	11.2639	+	19.5096i	0.435812	+	0.754849i
$669$	3.90121	+	14.5916i	0.150829	+	0.564142i
$670$	−4.09060	−	7.08512i	−0.158034	−	0.273722i
$671$	−19.2861	−	11.1348i	−0.744531	−	0.429855i
$672$	1.18307	+	4.42499i	0.0456378	+	0.170698i
$673$	9.26140	+	5.34707i	0.357001	+	0.206114i	0.667764	−	0.744373i	$-0.267251\pi$
$673$	9.26140	+	5.34707i	0.357001	+	0.206114i	−0.310764	+	0.950487i	$0.600585\pi$
$674$	−27.5245			−1.06021
$675$	5.01687	+	1.35313i	0.193100	+	0.0520822i
$676$	−1.66051	−	2.87609i	−0.0638657	−	0.110619i
$677$	7.89992	−	13.6831i	0.303619	−	0.525883i	−0.673334	−	0.739338i	$-0.735138\pi$
$677$	7.89992	−	13.6831i	0.303619	−	0.525883i	0.976953	+	0.213455i	$0.0684718\pi$
$678$	−8.44373	−	8.45302i	−0.324280	−	0.324636i
$679$	−16.4005	−	28.4065i	−0.629393	−	1.09014i
$680$	0.741764			0.0284453
$681$	−15.5954	+	15.5783i	−0.597618	+	0.596962i
$682$	4.54024	+	14.3967i	0.173855	+	0.551279i
$683$			34.5090i			1.32045i	0.751068	+	0.660224i	$0.229539\pi$
$683$			34.5090i			1.32045i	−0.751068	+	0.660224i	$0.770461\pi$
$684$	−0.00775884	+	7.06044i	−0.000296667	+	0.269963i
$685$	−15.7182	+	9.07490i	−0.600561	+	0.346734i
$686$		−	18.5290i		−	0.707439i
$687$	−0.155134	−	0.580242i	−0.00591872	−	0.0221376i
$688$	4.20794	−	2.42945i	0.160426	−	0.0926220i
$689$	−3.02381	+	1.74580i	−0.115198	+	0.0665096i
$690$	3.88916	+	3.89343i	0.148058	+	0.148220i
$691$	8.69755	−	15.0646i	0.330870	−	0.573084i	−0.651813	−	0.758380i	$-0.725991\pi$
$691$	8.69755	−	15.0646i	0.330870	−	0.573084i	0.982683	+	0.185296i	$0.0593244\pi$
$692$	−7.33403	−	4.23431i	−0.278798	−	0.160964i
$693$	18.6162	+	10.7754i	0.707172	+	0.409323i
$694$	−21.1281	+	12.1983i	−0.802013	+	0.463043i
$695$	10.1858	−	17.6423i	0.386369	−	0.669210i
$696$	−1.86733	−	0.501450i	−0.0707810	−	0.0190074i
$697$			3.90660i			0.147973i
$698$		−	7.97476i		−	0.301849i
$699$	−5.10504	−	1.37090i	−0.193090	−	0.0518522i
$700$	−1.32225	+	2.29021i	−0.0499764	+	0.0865617i
$701$	−14.1135	+	8.14843i	−0.533060	+	0.307762i	−0.742261	−	0.670110i	$-0.766247\pi$
$701$	−14.1135	+	8.14843i	−0.533060	+	0.307762i	0.209202	+	0.977872i	$0.432913\pi$
$702$	5.39972	+	20.2857i	0.203799	+	0.765635i
$703$	20.3873	+	11.7706i	0.768921	+	0.443937i
$704$	−1.35563	+	2.34802i	−0.0510923	+	0.0884944i
$705$	4.02910	+	4.03353i	0.151745	+	0.151912i
$706$	−30.7372	+	17.7462i	−1.15681	+	0.667885i
$707$	0.666493	−	0.384800i	0.0250660	−	0.0144719i
$708$	−0.0348009	−	0.130165i	−0.00130790	−	0.00489189i
$709$			34.3386i			1.28961i	0.764346	+	0.644807i	$0.223062\pi$
$709$			34.3386i			1.28961i	−0.764346	+	0.644807i	$0.776938\pi$
$710$	−11.6252	+	6.71183i	−0.436287	+	0.251891i
$711$	36.5434	+	0.0401581i	1.37048	+	0.00150605i
$712$		−	17.1663i		−	0.643334i
$713$	13.0432	+	11.9504i	0.488472	+	0.447547i
$714$	2.40378	−	2.40114i	0.0899591	−	0.0898603i
$715$	−10.9533			−0.409630
$716$	8.32290	+	14.4157i	0.311041	+	0.538739i
$717$	−15.5217	−	15.5388i	−0.579668	−	0.580305i
$718$	4.97548	−	8.61779i	0.185683	−	0.321613i
$719$	−12.9598	−	22.4470i	−0.483319	−	0.837133i	0.516497	−	0.856289i	$-0.327236\pi$
$719$	−12.9598	−	22.4470i	−0.483319	−	0.837133i	−0.999817	+	0.0191556i	$0.993902\pi$
$720$	1.49714	+	2.59972i	0.0557953	+	0.0968860i
$721$	−16.0111			−0.596285
$722$	11.6577	+	6.73056i	0.433854	+	0.250485i
$723$	−9.09645	−	34.0232i	−0.338301	−	1.26534i
$724$	2.86960	+	1.65676i	0.106648	+	0.0615731i
$725$	−0.558150	−	0.966745i	−0.0207292	−	0.0359040i
$726$	−1.63247	−	6.10590i	−0.0605868	−	0.226611i
$727$	−5.51137	−	9.54597i	−0.204405	−	0.354040i	0.745538	−	0.666463i	$-0.232193\pi$
$727$	−5.51137	−	9.54597i	−0.204405	−	0.354040i	−0.949943	+	0.312423i	$0.898859\pi$
$728$	−10.6836			−0.395961
$729$	0.0890120	−	26.9999i	0.00329674	−	0.999995i
$730$	9.24020	−	5.33483i	0.341995	−	0.197451i
$731$	−3.12129	−	1.80208i	−0.115445	−	0.0666523i
$732$	−13.7399	−	3.68968i	−0.507840	−	0.136374i
$733$	23.9907	−	41.5531i	0.886116	−	1.53480i	0.0416867	−	0.999131i	$-0.486727\pi$
$733$	23.9907	−	41.5531i	0.886116	−	1.53480i	0.844429	−	0.535667i	$-0.179940\pi$
$734$	−2.39690	+	4.15155i	−0.0884711	+	0.153236i
$735$	−0.00294972	−	0.0110328i	−0.000108802	−	0.000406949i
$736$			3.17723i			0.117114i
$737$	−11.0907	−	19.2096i	−0.408531	−	0.707596i
$738$	−13.6918	+	7.88492i	−0.504002	+	0.290248i
$739$	27.7681	+	16.0319i	1.02147	+	0.589745i	0.914529	−	0.404521i	$-0.132562\pi$
$739$	27.7681	+	16.0319i	1.02147	+	0.589745i	0.106939	+	0.994266i	$0.465895\pi$
$740$	10.0027			0.367707
$741$	−15.9047	−	4.27102i	−0.584273	−	0.156900i
$742$			2.28557i			0.0839059i
$743$	−25.3947			−0.931641			−0.465821	−	0.884879i	$-0.654241\pi$
$743$	−25.3947			−0.931641			−0.465821	+	0.884879i	$0.654241\pi$
$744$	5.17756	+	8.13590i	0.189819	+	0.298277i
$745$	−8.00763			−0.293377
$746$		−	23.1098i		−	0.846109i
$747$	−12.7351	+	7.33398i	−0.465954	+	0.268336i
$748$	2.01112			0.0735337
$749$	12.7909	+	7.38483i	0.467369	+	0.269836i
$750$	−0.449207	+	1.67279i	−0.0164027	+	0.0610815i
$751$	9.23056	+	15.9878i	0.336828	+	0.583403i	0.983834	−	0.179082i	$-0.0573126\pi$
$751$	9.23056	+	15.9878i	0.336828	+	0.583403i	−0.647006	+	0.762485i	$0.723979\pi$
$752$			3.29156i			0.120031i
$753$	26.9548	−	7.20665i	0.982288	−	0.262625i
$754$	2.25489	−	3.90558i	0.0821181	−	0.142233i
$755$	−3.70048	+	6.40942i	−0.134674	+	0.233263i
$756$	13.2671	+	3.57837i	0.482522	+	0.130144i
$757$	−36.5554	−	21.1053i	−1.32863	−	0.767084i	−0.343541	−	0.939138i	$-0.611627\pi$
$757$	−36.5554	−	21.1053i	−1.32863	−	0.767084i	−0.985088	+	0.172053i	$0.944960\pi$
$758$	0.979824	−	0.565702i	0.0355888	−	0.0205472i
$759$	10.5445	+	10.5561i	0.382742	+	0.383163i
$760$	−2.35348			−0.0853698
$761$	−0.562411	−	0.974124i	−0.0203874	−	0.0353120i	0.855652	−	0.517552i	$-0.173157\pi$
$761$	−0.562411	−	0.974124i	−0.0203874	−	0.0353120i	−0.876039	+	0.482240i	$0.839823\pi$
$762$	−12.0632	+	3.22523i	−0.437005	+	0.116838i
$763$	−10.2374	−	17.7317i	−0.370619	−	0.641930i
$764$	2.56932	+	1.48340i	0.0929546	+	0.0536674i
$765$	1.11476	−	1.92593i	0.0403043	−	0.0696323i
$766$	3.21579	+	1.85664i	0.116191	+	0.0670830i
$767$	0.314267			0.0113475
$768$	−0.449207	+	1.67279i	−0.0162094	+	0.0603615i
$769$	−18.7708	−	32.5120i	−0.676892	−	1.17241i	−0.975912	−	0.218165i	$-0.929993\pi$
$769$	−18.7708	−	32.5120i	−0.676892	−	1.17241i	0.299020	−	0.954247i	$-0.403340\pi$
$770$	−3.58497	+	6.20935i	−0.129193	+	0.223770i
$771$	25.3358	−	25.3080i	0.912447	−	0.911445i
$772$	−6.42312	−	11.1252i	−0.231173	−	0.400403i
$773$	−13.0451			−0.469198			−0.234599	−	0.972092i	$-0.575378\pi$
$773$	−13.0451			−0.469198			−0.234599	+	0.972092i	$0.575378\pi$
$774$	0.0160186	−	14.5767i	0.000575776	−	0.523949i
$775$	−1.20475	+	5.43586i	−0.0432759	+	0.195262i
$776$		−

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.449207 + 1.67279i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(-1.67279 - 0.449207i) q^{6} +(-1.32225 - 2.29021i) q^{7} -1.00000i q^{8} +(-2.59643 - 1.50285i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.449207 + 1.67279i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(-1.67279 - 0.449207i) q^{6} +(-1.32225 - 2.29021i) q^{7} -1.00000i q^{8} +(-2.59643 - 1.50285i) q^{9} +(0.500000 - 0.866025i) q^{10} +(1.35563 - 2.34802i) q^{11} +(0.449207 - 1.67279i) q^{12} +(3.49868 + 2.01996i) q^{13} +(2.29021 - 1.32225i) q^{14} +(1.22542 - 1.22407i) q^{15} +1.00000 q^{16} +(-0.370882 - 0.642386i) q^{17} +(1.50285 - 2.59643i) q^{18} +(1.17674 + 2.03818i) q^{19} +(0.866025 + 0.500000i) q^{20} +(4.42499 - 1.18307i) q^{21} +(2.34802 + 1.35563i) q^{22} +3.17723 q^{23} +(1.67279 + 0.449207i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-2.01996 + 3.49868i) q^{26} +(3.68029 - 3.66817i) q^{27} +(1.32225 + 2.29021i) q^{28} -1.11630 q^{29} +(1.22407 + 1.22542i) q^{30} +(4.10522 + 3.76128i) q^{31} +1.00000i q^{32} +(3.31878 + 3.32243i) q^{33} +(0.642386 - 0.370882i) q^{34} +2.64450i q^{35} +(2.59643 + 1.50285i) q^{36} +(8.66260 - 5.00135i) q^{37} +(-2.03818 + 1.17674i) q^{38} +(-4.95060 + 4.94516i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-4.56104 - 2.63332i) q^{41} +(1.18307 + 4.42499i) q^{42} +(4.20794 - 2.42945i) q^{43} +(-1.35563 + 2.34802i) q^{44} +(1.49714 + 2.59972i) q^{45} +3.17723i q^{46} +3.29156i q^{47} +(-0.449207 + 1.67279i) q^{48} +(0.00329675 - 0.00571013i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(1.24118 - 0.331842i) q^{51} +(-3.49868 - 2.01996i) q^{52} +(-0.432136 + 0.748481i) q^{53} +(3.66817 + 3.68029i) q^{54} +(-2.34802 + 1.35563i) q^{55} +(-2.29021 + 1.32225i) q^{56} +(-3.93803 + 1.05287i) q^{57} -1.11630i q^{58} +(0.0673682 - 0.0388951i) q^{59} +(-1.22542 + 1.22407i) q^{60} -8.21375i q^{61} +(-3.76128 + 4.10522i) q^{62} +(-0.00871827 + 7.93351i) q^{63} -1.00000 q^{64} +(-2.01996 - 3.49868i) q^{65} +(-3.32243 + 3.31878i) q^{66} +(4.09060 - 7.08512i) q^{67} +(0.370882 + 0.642386i) q^{68} +(-1.42723 + 5.31482i) q^{69} -2.64450 q^{70} +(-11.6252 - 6.71183i) q^{71} +(-1.50285 + 2.59643i) q^{72} +(9.24020 + 5.33483i) q^{73} +(5.00135 + 8.66260i) q^{74} +(-1.67328 + 0.447368i) q^{75} +(-1.17674 - 2.03818i) q^{76} -7.16994 q^{77} +(-4.94516 - 4.95060i) q^{78} +(-10.5492 + 6.09057i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(4.48286 + 7.80410i) q^{81} +(2.63332 - 4.56104i) q^{82} +(2.44932 - 4.24235i) q^{83} +(-4.42499 + 1.18307i) q^{84} +0.741764i q^{85} +(2.42945 + 4.20794i) q^{86} +(0.501450 - 1.86733i) q^{87} +(-2.34802 - 1.35563i) q^{88} +17.1663 q^{89} +(-2.59972 + 1.49714i) q^{90} -10.6836i q^{91} -3.17723 q^{92} +(-8.13590 + 5.17756i) q^{93} -3.29156 q^{94} -2.35348i q^{95} +(-1.67279 - 0.449207i) q^{96} +12.4034 q^{97} +(0.00571013 + 0.00329675i) q^{98} +(-7.04853 + 4.05915i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40q + 6q^{3} - 40q^{4} - 12q^{7} - 2q^{9} + O(q^{10}) \)	\( 40q + 6q^{3} - 40q^{4} - 12q^{7} - 2q^{9} + 20q^{10} - 6q^{12} - 12q^{13} + 40q^{16} - 12q^{18} - 12q^{19} + 12q^{21} - 24q^{22} + 20q^{25} + 12q^{28} + 8q^{31} + 52q^{33} + 24q^{34} + 2q^{36} + 60q^{37} - 8q^{39} - 20q^{40} + 12q^{42} + 24q^{43} - 12q^{45} + 6q^{48} - 4q^{49} + 14q^{51} + 12q^{52} + 24q^{55} - 12q^{57} - 40q^{64} + 8q^{66} + 64q^{67} - 26q^{69} - 24q^{70} + 12q^{72} + 6q^{75} + 12q^{76} - 68q^{78} - 48q^{79} + 2q^{81} + 4q^{82} - 12q^{84} + 36q^{87} + 24q^{88} + 2q^{90} - 22q^{93} - 40q^{94} + 8q^{97} - 90q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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