LMFDB - Embedded newform 234.2.z.a.227.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(41,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 1]))

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

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

chi := DirichletCharacter("234.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.z (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			227.14
Character	$\chi$	$=$	234.227
Dual form			234.2.z.a.167.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(1.71941 + 0.208859i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.406496 - 1.51706i) q^{5} +(0.646759 - 1.60677i) q^{6} +(-3.31317 - 3.31317i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.91276 + 0.718230i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(1.71941 + 0.208859i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.406496 - 1.51706i) q^{5} +(0.646759 - 1.60677i) q^{6} +(-3.31317 - 3.31317i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.91276 + 0.718230i) q^{9} +(-1.36016 - 0.785290i) q^{10} +(-1.47782 - 0.395981i) q^{11} +(-1.38462 - 1.04058i) q^{12} +(3.50315 + 0.853192i) q^{13} +(-4.05778 + 2.34276i) q^{14} +(1.01579 - 2.52356i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.99188 + 5.18209i) q^{17} +(1.44763 - 2.62761i) q^{18} +(5.70943 + 1.52984i) q^{19} +(-1.11057 + 1.11057i) q^{20} +(-5.00471 - 6.38869i) q^{21} +(-0.764977 + 1.32498i) q^{22} -4.97403 q^{23} +(-1.36349 + 1.06812i) q^{24} +(2.19388 + 1.26664i) q^{25} +(1.73080 - 3.16296i) q^{26} +(4.85822 + 1.84329i) q^{27} +(1.21270 + 4.52587i) q^{28} +(-5.94907 + 3.43470i) q^{29} +(-2.17466 - 1.63432i) q^{30} +(1.01253 + 0.271305i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-2.45828 - 0.989512i) q^{33} +(5.77988 - 1.54871i) q^{34} +(-6.37308 + 3.67950i) q^{35} +(-2.16341 - 2.07838i) q^{36} +(-6.94881 + 1.86193i) q^{37} +(2.95542 - 5.11893i) q^{38} +(5.84516 + 2.19865i) q^{39} +(0.785290 + 1.36016i) q^{40} +(-3.66574 - 3.66574i) q^{41} +(-7.46631 + 3.18067i) q^{42} -12.2587i q^{43} +(1.08184 + 1.08184i) q^{44} +(2.27362 - 4.12688i) q^{45} +(-1.28737 + 4.80455i) q^{46} +(1.64560 + 6.14146i) q^{47} +(0.678829 + 1.59348i) q^{48} +14.9542i q^{49} +(1.79130 - 1.79130i) q^{50} +(4.06195 + 9.53504i) q^{51} +(-2.60722 - 2.49046i) q^{52} -2.78130i q^{53} +(3.03788 - 4.21560i) q^{54} +(-1.20146 + 2.08099i) q^{55} +4.68553 q^{56} +(9.49734 + 3.82288i) q^{57} +(1.77793 + 6.63533i) q^{58} +(1.54597 + 5.76965i) q^{59} +(-2.14148 + 1.67757i) q^{60} +4.37246 q^{61} +(0.524122 - 0.907805i) q^{62} +(-7.27083 - 12.0301i) q^{63} -1.00000i q^{64} +(2.71836 - 4.96768i) q^{65} +(-1.59205 + 2.11841i) q^{66} +(3.96548 - 3.96548i) q^{67} -5.98377i q^{68} +(-8.55241 - 1.03887i) q^{69} +(1.90465 + 7.10824i) q^{70} +(-0.0745019 + 0.278045i) q^{71} +(-2.56749 + 1.55176i) q^{72} +(0.964880 + 0.964880i) q^{73} +7.19393i q^{74} +(3.50764 + 2.63609i) q^{75} +(-4.17959 - 4.17959i) q^{76} +(3.58432 + 6.20823i) q^{77} +(3.63658 - 5.07694i) q^{78} +(-0.0673941 + 0.116730i) q^{79} +(1.51706 - 0.406496i) q^{80} +(7.96829 + 4.18406i) q^{81} +(-4.48960 + 2.59207i) q^{82} +(-11.2043 + 3.00217i) q^{83} +(1.13987 + 8.03512i) q^{84} +(9.07776 - 2.43238i) q^{85} +(-11.8410 - 3.17279i) q^{86} +(-10.9463 + 4.66314i) q^{87} +(1.32498 - 0.764977i) q^{88} +(-1.46167 - 5.45501i) q^{89} +(-3.39780 - 3.26427i) q^{90} +(-8.77976 - 14.4333i) q^{91} +(4.30764 + 2.48702i) q^{92} +(1.68428 + 0.677961i) q^{93} +6.35810 q^{94} +(4.64172 - 8.03969i) q^{95} +(1.71488 - 0.243274i) q^{96} +(-4.71824 + 4.71824i) q^{97} +(14.4446 + 3.87042i) q^{98} +(-4.02013 - 2.21481i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{7}+O(q^{10}) $ 56 * q - 8 * q^7	$ 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47} - 24 q^{50} + 8 q^{52} - 36 q^{54} + 36 q^{57} + 24 q^{60} - 48 q^{63} - 36 q^{65} + 28 q^{67} + 84 q^{69} - 24 q^{71} - 24 q^{72} + 28 q^{73} + 4 q^{76} + 24 q^{77} - 60 q^{78} - 24 q^{79} + 24 q^{81} - 96 q^{83} - 72 q^{85} + 4 q^{91} - 24 q^{92} - 36 q^{93} - 52 q^{97} + 48 q^{98} + 60 q^{99}+O(q^{100}) $ 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$	1.71941	+	0.208859i	0.992703	+	0.120585i
$3$	1.71941	+	0.208859i	0.992703	+	0.120585i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	0.406496	−	1.51706i	0.181791	−	0.678452i	−0.813504	−	0.581559i	$-0.802443\pi$
$5$	0.406496	−	1.51706i	0.181791	−	0.678452i	0.995295	−	0.0968927i	$-0.0308904\pi$
$6$	0.646759	−	1.60677i	0.264038	−	0.655960i
$7$	−3.31317	−	3.31317i	−1.25226	−	1.25226i	−0.954705	−	0.297555i	$-0.903829\pi$
$7$	−3.31317	−	3.31317i	−1.25226	−	1.25226i	−0.297555	−	0.954705i	$-0.596171\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	2.91276	+	0.718230i	0.970919	+	0.239410i
$10$	−1.36016	−	0.785290i	−0.430121	−	0.248331i
$11$	−1.47782	−	0.395981i	−0.445580	−	0.119393i	0.0290504	−	0.999578i	$-0.490752\pi$
$11$	−1.47782	−	0.395981i	−0.445580	−	0.119393i	−0.474631	+	0.880185i	$0.657418\pi$
$12$	−1.38462	−	1.04058i	−0.399707	−	0.300391i
$13$	3.50315	+	0.853192i	0.971599	+	0.236633i
$13$	3.50315	+	0.853192i	0.971599	+	0.236633i
$14$	−4.05778	+	2.34276i	−1.08449	+	0.626130i
$15$	1.01579	−	2.52356i	0.262275	−	0.651580i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	2.99188	+	5.18209i	0.725638	+	1.25684i	0.958711	+	0.284383i	$0.0917888\pi$
$17$	2.99188	+	5.18209i	0.725638	+	1.25684i	−0.233072	+	0.972459i	$0.574878\pi$
$18$	1.44763	−	2.62761i	0.341210	−	0.619335i
$19$	5.70943	+	1.52984i	1.30983	+	0.350968i	0.845160	−	0.534514i	$-0.179505\pi$
$19$	5.70943	+	1.52984i	1.30983	+	0.350968i	0.464673	+	0.885483i	$0.346172\pi$
$20$	−1.11057	+	1.11057i	−0.248331	+	0.248331i
$21$	−5.00471	−	6.38869i	−1.09212	−	1.39413i
$22$	−0.764977	+	1.32498i	−0.163094	+	0.282487i
$23$	−4.97403			−1.03716			−0.518579	−	0.855030i	$-0.673539\pi$
$23$	−4.97403			−1.03716			−0.518579	+	0.855030i	$0.673539\pi$
$24$	−1.36349	+	1.06812i	−0.278322	+	0.218030i
$25$	2.19388	+	1.26664i	0.438777	+	0.253328i
$26$	1.73080	−	3.16296i	0.339438	−	0.620308i
$27$	4.85822	+	1.84329i	0.934965	+	0.354741i
$28$	1.21270	+	4.52587i	0.229179	+	0.855309i
$29$	−5.94907	+	3.43470i	−1.10471	+	0.637807i	−0.937455	−	0.348106i	$-0.886825\pi$
$29$	−5.94907	+	3.43470i	−1.10471	+	0.637807i	−0.167259	+	0.985913i	$0.553492\pi$
$30$	−2.17466	−	1.63432i	−0.397038	−	0.298385i
$31$	1.01253	+	0.271305i	0.181855	+	0.0487279i	0.348597	−	0.937273i	$-0.386658\pi$
$31$	1.01253	+	0.271305i	0.181855	+	0.0487279i	−0.166742	+	0.986001i	$0.553325\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	−2.45828	−	0.989512i	−0.427932	−	0.172252i
$34$	5.77988	−	1.54871i	0.991240	−	0.265602i
$35$	−6.37308	+	3.67950i	−1.07725	+	0.621949i
$36$	−2.16341	−	2.07838i	−0.360568	−	0.346397i
$37$	−6.94881	+	1.86193i	−1.14238	+	0.306099i	−0.779906	−	0.625896i	$-0.784733\pi$
$37$	−6.94881	+	1.86193i	−1.14238	+	0.306099i	−0.362471	+	0.931995i	$0.618067\pi$
$38$	2.95542	−	5.11893i	0.479432	−	0.830400i
$39$	5.84516	+	2.19865i	0.935975	+	0.352066i
$40$	0.785290	+	1.36016i	0.124165	+	0.215061i
$41$	−3.66574	−	3.66574i	−0.572493	−	0.572493i	0.360331	−	0.932824i	$-0.382664\pi$
$41$	−3.66574	−	3.66574i	−0.572493	−	0.572493i	−0.932824	+	0.360331i	$0.882664\pi$
$42$	−7.46631	+	3.18067i	−1.15208	+	0.490788i
$43$		−	12.2587i		−	1.86944i	−0.355391	−	0.934718i	$-0.615652\pi$
$43$		−	12.2587i		−	1.86944i	0.355391	−	0.934718i	$-0.384348\pi$
$44$	1.08184	+	1.08184i	0.163094	+	0.163094i
$45$	2.27362	−	4.12688i	0.338932	−	0.615199i
$46$	−1.28737	+	4.80455i	−0.189813	+	0.708392i
$47$	1.64560	+	6.14146i	0.240035	+	0.895823i	0.975814	+	0.218602i	$0.0701495\pi$
$47$	1.64560	+	6.14146i	0.240035	+	0.895823i	−0.735779	+	0.677222i	$0.763184\pi$
$48$	0.678829	+	1.59348i	0.0979805	+	0.230000i
$49$			14.9542i			2.13631i
$50$	1.79130	−	1.79130i	0.253328	−	0.253328i
$51$	4.06195	+	9.53504i	0.568787	+	1.33517i
$52$	−2.60722	−	2.49046i	−0.361557	−	0.345365i
$53$		−	2.78130i		−	0.382041i	−0.981586	−	0.191021i	$-0.938820\pi$
$53$		−	2.78130i		−	0.382041i	0.981586	−	0.191021i	$-0.0611798\pi$
$54$	3.03788	−	4.21560i	0.413403	−	0.573671i
$55$	−1.20146	+	2.08099i	−0.162005	+	0.280600i
$56$	4.68553			0.626130
$57$	9.49734	+	3.82288i	1.25795	+	0.506353i
$58$	1.77793	+	6.63533i	0.233454	+	0.871261i
$59$	1.54597	+	5.76965i	0.201268	+	0.751144i	0.990555	+	0.137118i	$0.0437841\pi$
$59$	1.54597	+	5.76965i	0.201268	+	0.751144i	−0.789286	+	0.614025i	$0.789549\pi$
$60$	−2.14148	+	1.67757i	−0.276463	+	0.216574i
$61$	4.37246			0.559836			0.279918	−	0.960024i	$-0.409693\pi$
$61$	4.37246			0.559836			0.279918	+	0.960024i	$0.409693\pi$
$62$	0.524122	−	0.907805i	0.0665635	−	0.115291i
$63$	−7.27083	−	12.0301i	−0.916039	−	1.51565i
$64$		−	1.00000i		−	0.125000i
$65$	2.71836	−	4.96768i	0.337172	−	0.616165i
$66$	−1.59205	+	2.11841i	−0.195967	+	0.260759i
$67$	3.96548	−	3.96548i	0.484460	−	0.484460i	−0.422092	−	0.906553i	$-0.638704\pi$
$67$	3.96548	−	3.96548i	0.484460	−	0.484460i	0.906553	+	0.422092i	$0.138704\pi$
$68$		−	5.98377i		−	0.725638i
$69$	−8.55241	−	1.03887i	−1.02959	−	0.125065i
$70$	1.90465	+	7.10824i	0.227649	+	0.849598i
$71$	−0.0745019	+	0.278045i	−0.00884175	+	0.0329979i	−0.970206	−	0.242282i	$-0.922104\pi$
$71$	−0.0745019	+	0.278045i	−0.00884175	+	0.0329979i	0.961364	+	0.275280i	$0.0887706\pi$
$72$	−2.56749	+	1.55176i	−0.302582	+	0.182877i
$73$	0.964880	+	0.964880i	0.112931	+	0.112931i	0.761314	−	0.648383i	$-0.224555\pi$
$73$	0.964880	+	0.964880i	0.112931	+	0.112931i	−0.648383	+	0.761314i	$0.724555\pi$
$74$			7.19393i			0.836278i
$75$	3.50764	+	2.63609i	0.405027	+	0.304389i
$76$	−4.17959	−	4.17959i	−0.479432	−	0.479432i
$77$	3.58432	+	6.20823i	0.408471	+	0.707493i
$78$	3.63658	−	5.07694i	0.411761	−	0.574850i
$79$	−0.0673941	+	0.116730i	−0.00758243	+	0.0131331i	−0.869792	−	0.493419i	$-0.835747\pi$
$79$	−0.0673941	+	0.116730i	−0.00758243	+	0.0131331i	0.862209	+	0.506552i	$0.169080\pi$
$80$	1.51706	−	0.406496i	0.169613	−	0.0454476i
$81$	7.96829	+	4.18406i	0.885366	+	0.464895i
$82$	−4.48960	+	2.59207i	−0.495794	+	0.286247i
$83$	−11.2043	+	3.00217i	−1.22983	+	0.329531i	−0.814512	−	0.580147i	$-0.802995\pi$
$83$	−11.2043	+	3.00217i	−1.22983	+	0.329531i	−0.415314	+	0.909678i	$0.636328\pi$
$84$	1.13987	+	8.03512i	0.124370	+	0.876704i
$85$	9.07776	−	2.43238i	0.984621	−	0.263828i
$86$	−11.8410	−	3.17279i	−1.27685	−	0.342130i
$87$	−10.9463	+	4.66314i	−1.17356	+	0.499941i
$88$	1.32498	−	0.764977i	0.141243	−	0.0815468i
$89$	−1.46167	−	5.45501i	−0.154936	−	0.578230i	−0.999111	−	0.0421616i	$-0.986576\pi$
$89$	−1.46167	−	5.45501i	−0.154936	−	0.578230i	0.844175	−	0.536068i	$-0.180091\pi$
$90$	−3.39780	−	3.26427i	−0.358160	−	0.344084i
$91$	−8.77976	−	14.4333i	−0.920368	−	1.51302i
$92$	4.30764	+	2.48702i	0.449102	+	0.259289i
$93$	1.68428	+	0.677961i	0.174652	+	0.0703013i
$94$	6.35810			0.655788
$95$	4.64172	−	8.03969i	0.476230	−	0.824855i
$96$	1.71488	−	0.243274i	0.175024	−	0.0248291i
$97$	−4.71824	+	4.71824i	−0.479064	+	0.479064i	−0.904832	−	0.425768i	$-0.860004\pi$
$97$	−4.71824	+	4.71824i	−0.479064	+	0.479064i	0.425768	+	0.904832i	$0.360004\pi$
$98$	14.4446	+	3.87042i	1.45913	+	0.390972i
$99$	−4.02013	−	2.21481i	−0.404038	−	0.222597i
$100$	−1.26664	−	2.19388i	−0.126664	−	0.219388i
$101$	3.82995	+	6.63367i	0.381094	+	0.660075i	0.991219	−	0.132231i	$-0.0422140\pi$
$101$	3.82995	+	6.63367i	0.381094	+	0.660075i	−0.610125	+	0.792305i	$0.708881\pi$
$102$	10.2615	−	1.45570i	1.01603	−	0.144135i
$103$	2.46359	−	1.42235i	0.242744	−	0.140149i	−0.373693	−	0.927552i	$-0.621909\pi$
$103$	2.46359	−	1.42235i	0.242744	−	0.140149i	0.616437	+	0.787404i	$0.288575\pi$
$104$	−3.08040	+	1.87380i	−0.302058	+	0.183742i
$105$	−11.7264	+	4.99550i	−1.14438	+	0.487511i
$106$	−2.68653	−	0.719854i	−0.260939	−	0.0699184i
$107$	−14.7551	−	8.51888i	−1.42643	−	0.823551i	−0.429595	−	0.903022i	$-0.641344\pi$
$107$	−14.7551	−	8.51888i	−1.42643	−	0.823551i	−0.996837	+	0.0794704i	$0.974677\pi$
$108$	−3.28570	−	4.02544i	−0.316166	−	0.387349i
$109$	−1.44362	+	1.44362i	−0.138274	+	0.138274i	−0.772856	−	0.634582i	$-0.781172\pi$
$109$	−1.44362	+	1.44362i	−0.138274	+	0.138274i	0.634582	+	0.772856i	$0.281172\pi$
$110$	1.69912	+	1.69912i	0.162005	+	0.162005i
$111$	−12.3367	+	1.75010i	−1.17095	+	0.166112i
$112$	1.21270	−	4.52587i	0.114590	−	0.427655i
$113$	7.19725	+	4.15533i	0.677060	+	0.390901i	0.798746	−	0.601668i	$-0.205497\pi$
$113$	7.19725	+	4.15533i	0.677060	+	0.390901i	−0.121686	+	0.992569i	$0.538830\pi$
$114$	6.15071	−	8.18429i	0.576067	−	0.766529i
$115$	−2.02192	+	7.54592i	−0.188545	+	0.703661i
$116$	6.86939			0.637807
$117$	9.59103	+	5.00121i	0.886691	+	0.462362i
$118$	5.97318			0.549875
$119$	7.25654	−	27.0818i	0.665205	−	2.48258i
$120$	1.06615	+	2.50269i	0.0973262	+	0.228464i
$121$	−7.49912	−	4.32962i	−0.681738	−	0.393602i
$122$	1.13168	−	4.22347i	0.102457	−	0.382375i
$123$	−5.53730	−	7.06855i	−0.499282	−	0.637350i
$124$	−0.741220	−	0.741220i	−0.0665635	−	0.0665635i
$125$	8.36622	−	8.36622i	0.748297	−	0.748297i
$126$	−13.5020	+	3.90948i	−1.20285	+	0.348284i
$127$	−10.0790	−	5.81914i	−0.894371	−	0.516365i	−0.0190013	−	0.999819i	$-0.506049\pi$
$127$	−10.0790	−	5.81914i	−0.894371	−	0.516365i	−0.875370	+	0.483454i	$0.839382\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	2.56034	−	21.0778i	0.225426	−	1.85579i
$130$	−4.09485	−	3.91147i	−0.359142	−	0.343059i
$131$	4.72499	−	2.72798i	0.412825	−	0.238344i	−0.279178	−	0.960239i	$-0.590062\pi$
$131$	4.72499	−	2.72798i	0.412825	−	0.238344i	0.692003	+	0.721895i	$0.256729\pi$
$132$	1.63418	+	2.08608i	0.142237	+	0.181570i
$133$	−13.8477	−	23.9849i	−1.20075	−	2.07975i
$134$	−2.80402	−	4.85670i	−0.242230	−	0.419555i
$135$	4.77123	−	6.62094i	0.410642	−	0.569840i
$136$	−5.77988	−	1.54871i	−0.495620	−	0.132801i
$137$	−1.03545	+	1.03545i	−0.0884647	+	0.0884647i	−0.749954	−	0.661490i	$-0.769925\pi$
$137$	−1.03545	+	1.03545i	−0.0884647	+	0.0884647i	0.661490	+	0.749954i	$0.269925\pi$
$138$	−3.21700	+	7.99211i	−0.273849	+	0.680334i
$139$	3.74702	−	6.49002i	0.317818	−	0.550477i	−0.662215	−	0.749314i	$-0.730383\pi$
$139$	3.74702	−	6.49002i	0.317818	−	0.550477i	0.980032	+	0.198838i	$0.0637166\pi$
$140$	7.35899			0.621949
$141$	1.54676	+	10.9034i	0.130261	+	0.918231i
$142$	0.249288	+	0.143927i	0.0209198	+	0.0120781i
$143$	−4.83919	−	2.64805i	−0.404673	−	0.221441i
$144$	0.834373	+	2.88164i	0.0695311	+	0.240136i
$145$	2.79238	+	10.4213i	0.231895	+	0.865443i
$146$	1.18173	−	0.682273i	0.0978008	−	0.0564653i
$147$	−3.12331	+	25.7124i	−0.257606	+	2.12072i
$148$	6.94881	+	1.86193i	0.571188	+	0.153049i
$149$	−0.579672	+	0.155323i	−0.0474886	+	0.0127245i	−0.282485	−	0.959272i	$-0.591159\pi$
$149$	−0.579672	+	0.155323i	−0.0474886	+	0.0127245i	0.234997	+	0.971996i	$0.424492\pi$
$150$	3.45411	−	2.70585i	0.282027	−	0.220932i
$151$	−1.75756	+	0.470936i	−0.143028	+	0.0383242i	−0.329623	−	0.944113i	$-0.606922\pi$
$151$	−1.75756	+	0.470936i	−0.143028	+	0.0383242i	0.186595	+	0.982437i	$0.440255\pi$
$152$	−5.11893	+	2.95542i	−0.415200	+	0.239716i
$153$	4.99269	+	17.2430i	0.403635	+	1.39402i
$154$	6.92438	−	1.85538i	0.557982	−	0.149511i
$155$	0.823175	−	1.42578i	0.0661190	−	0.114521i
$156$	−3.96273	−	4.82667i	−0.317272	−	0.386443i
$157$	−1.01577	−	1.75937i	−0.0810676	−	0.140413i	0.822641	−	0.568561i	$-0.192500\pi$
$157$	−1.01577	−	1.75937i	−0.0810676	−	0.140413i	−0.903709	+	0.428148i	$0.859166\pi$
$158$	0.0953096	+	0.0953096i	0.00758243	+	0.00758243i
$159$	0.580901	−	4.78221i	0.0460684	−	0.379254i
$160$		−	1.57058i		−	0.124165i
$161$	16.4798	+	16.4798i	1.29879	+	1.29879i
$162$	6.10383	−	6.61387i	0.479562	−	0.519634i
$163$	−2.35591	+	8.79238i	−0.184529	+	0.688672i	0.810202	+	0.586151i	$0.199358\pi$
$163$	−2.35591	+	8.79238i	−0.184529	+	0.688672i	−0.994731	+	0.102521i	$0.967309\pi$
$164$	1.34176	+	5.00750i	0.104774	+	0.391020i
$165$	−2.50043	+	3.32714i	−0.194659	+	0.259017i
$166$			11.5995i			0.900295i
$167$	2.64522	−	2.64522i	0.204694	−	0.204694i	−0.597314	−	0.802008i	$-0.703765\pi$
$167$	2.64522	−	2.64522i	0.204694	−	0.204694i	0.802008	+	0.597314i	$0.203765\pi$
$168$	8.05635	+	0.978615i	0.621561	+	0.0755018i
$169$	11.5441	+	5.97772i	0.888010	+	0.459825i
$170$		−	9.39799i		−	0.720793i
$171$	15.5314	+	8.55672i	1.18772	+	0.654349i
$172$	−6.12935	+	10.6164i	−0.467359	+	0.809489i
$173$	1.01425			0.0771122			0.0385561	−	0.999256i	$-0.487724\pi$
$173$	1.01425			0.0771122			0.0385561	+	0.999256i	$0.487724\pi$
$174$	1.67115	+	11.7802i	0.126689	+	0.893054i
$175$	−3.07211	−	11.4653i	−0.232230	−	0.866694i
$176$	−0.395981	−	1.47782i	−0.0298482	−	0.111395i
$177$	1.45312	+	10.2433i	0.109223	+	0.769933i
$178$	−5.64744			−0.423294
$179$	−11.6793	+	20.2291i	−0.872951	+	1.51200i	−0.0140213	+	0.999902i	$0.504463\pi$
$179$	−11.6793	+	20.2291i	−0.872951	+	1.51200i	−0.858930	+	0.512094i	$0.828870\pi$
$180$	−4.03246	+	2.43717i	−0.300562	+	0.181656i
$181$		−	8.51778i		−	0.633122i	−0.948572	−	0.316561i	$-0.897472\pi$
$181$		−	8.51778i		−	0.633122i	0.948572	−	0.316561i	$-0.102528\pi$
$182$	−16.2139	+	4.74498i	−1.20185	+	0.351721i
$183$	7.51806	+	0.913228i	0.555751	+	0.0675078i
$184$	3.51717	−	3.51717i	0.259289	−	0.259289i
$185$			11.2987i			0.830693i
$186$	1.09078	−	1.45142i	0.0799802	−	0.106424i
$187$	−2.36946	−	8.84295i	−0.173272	−	0.646660i
$188$	1.64560	−	6.14146i	0.120018	−	0.447912i
$189$	−9.98897	−	22.2032i	−0.726591	−	1.61505i
$190$	−6.56438	−	6.56438i	−0.476230	−	0.476230i
$191$			15.6305i			1.13098i	0.824754	+	0.565492i	$0.191314\pi$
$191$			15.6305i			1.13098i	−0.824754	+	0.565492i	$0.808686\pi$
$192$	0.208859	−	1.71941i	0.0150731	−	0.124088i
$193$	−11.1792	−	11.1792i	−0.804697	−	0.804697i	0.179129	−	0.983826i	$-0.442672\pi$
$193$	−11.1792	−	11.1792i	−0.804697	−	0.804697i	−0.983826	+	0.179129i	$0.942672\pi$
$194$	3.33630	+	5.77864i	0.239532	+	0.414882i
$195$	5.71153	−	7.97374i	0.409011	−	0.571011i
$196$	7.47708	−	12.9507i	0.534077	−	0.925049i
$197$	13.3907	−	3.58802i	0.954045	−	0.255635i	0.251967	−	0.967736i	$-0.418923\pi$
$197$	13.3907	−	3.58802i	0.954045	−	0.255635i	0.702078	+	0.712100i	$0.252256\pi$
$198$	−3.17983	+	3.30991i	−0.225981	+	0.235225i
$199$	−10.8199	+	6.24687i	−0.767002	+	0.442829i	−0.831804	−	0.555069i	$-0.812692\pi$
$199$	−10.8199	+	6.24687i	−0.767002	+	0.442829i	0.0648021	+	0.997898i	$0.479358\pi$
$200$	−2.44696	+	0.655661i	−0.173026	+	0.0463622i
$201$	7.64652	−	5.99007i	0.539344	−	0.422507i
$202$	7.39889	−	1.98253i	0.520584	−	0.139490i
$203$	31.0900	+	8.33054i	2.18209	+	0.584689i
$204$	1.24976	−	10.2886i	0.0875010	−	0.720343i
$205$	−7.05128	+	4.07106i	−0.492483	+	0.284335i
$206$	−0.736264	−	2.74777i	−0.0512979	−	0.191446i
$207$	−14.4881	−	3.57250i	−1.00700	−	0.248306i
$208$	1.01269	+	3.46041i	0.0702174	+	0.239936i
$209$	−7.83173	−	4.52165i	−0.541732	−	0.312769i
$210$	1.79025	+	12.6198i	0.123539	+	0.870849i
$211$	7.81897			0.538280			0.269140	−	0.963101i	$-0.413261\pi$
$211$	7.81897			0.538280			0.269140	+	0.963101i	$0.413261\pi$
$212$	−1.39065	+	2.40868i	−0.0955104	+	0.165429i
$213$	−0.186172	+	0.462513i	−0.0127563	+	0.0316909i
$214$	−12.0475	+	12.0475i	−0.823551	+	0.823551i
$215$	−18.5972	−	4.98312i	−1.26832	−	0.339846i
$216$	−4.73868	+	2.13188i	−0.322426	+	0.145056i
$217$	−2.45579	−	4.25355i	−0.166710	−	0.288750i
$218$	1.02079	+	1.76807i	0.0691369	+	0.119749i
$219$	1.45750	+	1.86055i	0.0984889	+	0.125724i
$220$	2.08099	−	1.20146i	0.140300	−	0.0810023i
$221$	6.05970	+	20.7063i	0.407619	+	1.39286i
$222$	−1.50252	+	12.3693i	−0.100842	+	0.830176i
$223$	2.05177	+	0.549769i	0.137396	+	0.0368153i	0.326862	−	0.945072i	$-0.394009\pi$
$223$	2.05177	+	0.549769i	0.137396	+	0.0368153i	−0.189465	+	0.981887i	$0.560675\pi$
$224$	−4.05778	−	2.34276i	−0.271122	−	0.156532i
$225$	5.48051	+	5.26512i	0.365367	+	0.351008i
$226$	5.87653	−	5.87653i	0.390901	−	0.390901i
$227$	−13.2579	−	13.2579i	−0.879960	−	0.879960i	0.113570	−	0.993530i	$-0.463771\pi$
$227$	−13.2579	−	13.2579i	−0.879960	−	0.879960i	−0.993530	+	0.113570i	$0.963771\pi$
$228$	−6.31349	−	8.05938i	−0.418121	−	0.533746i
$229$	−5.74509	+	21.4410i	−0.379646	+	1.41686i	0.466789	+	0.884369i	$0.345411\pi$
$229$	−5.74509	+	21.4410i	−0.379646	+	1.41686i	−0.846436	+	0.532491i	$0.821256\pi$
$230$	6.76549	+	3.90606i	0.446103	+	0.257558i
$231$	4.86628	+	11.4231i	0.320178	+	0.751586i
$232$	1.77793	−	6.63533i	0.116727	−	0.435630i
$233$	−18.3697			−1.20344			−0.601721	−	0.798707i	$-0.705518\pi$
$233$	−18.3697			−1.20344			−0.601721	+	0.798707i	$0.705518\pi$
$234$	7.31314	−	7.96982i	0.478075	−	0.521003i
$235$	9.98591			0.651409
$236$	1.54597	−	5.76965i	0.100634	−	0.375572i
$237$	−0.140258	+	0.186631i	−0.00911076	+	0.0121230i
$238$	−24.2808	−	14.0185i	−1.57389	−	0.908688i
$239$	2.32455	−	8.67535i	0.150363	−	0.561161i	−0.849095	−	0.528240i	$-0.822852\pi$
$239$	2.32455	−	8.67535i	0.150363	−	0.561161i	0.999458	−	0.0329216i	$-0.0104812\pi$
$240$	2.69336	−	0.382082i	0.173856	−	0.0246633i
$241$	2.98745	+	2.98745i	0.192439	+	0.192439i	0.796749	−	0.604310i	$-0.206551\pi$
$241$	2.98745	+	2.98745i	0.192439	+	0.192439i	−0.604310	+	0.796749i	$0.706551\pi$
$242$	−6.12301	+	6.12301i	−0.393602	+	0.393602i
$243$	12.8269	+	8.85837i	0.822846	+	0.568264i
$244$	−3.78666	−	2.18623i	−0.242416	−	0.139959i
$245$	22.6864	+	6.07881i	1.44938	+	0.388361i
$246$	−8.26085	+	3.51915i	−0.526693	+	0.224373i
$247$	18.6957	+	10.2305i	1.18958	+	0.650950i
$248$	−0.907805	+	0.524122i	−0.0576457	+	0.0332818i
$249$	−19.8918	+	2.82186i	−1.26059	+	0.178828i
$250$	−5.91581	−	10.2465i	−0.374149	−	0.648044i
$251$	−0.0344162	−	0.0596107i	−0.00217233	−	0.00376259i	0.864937	−	0.501880i	$-0.167358\pi$
$251$	−0.0344162	−	0.0596107i	−0.00217233	−	0.00376259i	−0.867110	+	0.498118i	$0.834025\pi$
$252$	0.281694	+	14.0538i	0.0177450	+	0.885303i
$253$	7.35074	+	1.96962i	0.462137	+	0.123829i
$254$	−8.22951	+	8.22951i	−0.516365	+	0.516365i
$255$	16.1164	−	2.28629i	1.00925	−	0.143173i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−13.9678			−0.871287			−0.435643	−	0.900119i	$-0.643479\pi$
$257$	−13.9678			−0.871287			−0.435643	+	0.900119i	$0.643479\pi$
$258$	−19.6969	−	7.92843i	−1.22628	−	0.493602i
$259$	29.1914	+	16.8537i	1.81387	+	1.04724i
$260$	−4.83801	+	2.94296i	−0.300041	+	0.182515i
$261$	−19.7951	+	5.73163i	−1.22529	+	0.354779i
$262$	−1.41210	−	5.27005i	−0.0872401	−	0.325584i
$263$	20.7579	−	11.9846i	1.27999	−	0.739001i	0.303141	−	0.952946i	$-0.401965\pi$
$263$	20.7579	−	11.9846i	1.27999	−	0.739001i	0.976846	+	0.213945i	$0.0686313\pi$
$264$	2.43796	−	1.03858i	0.150046	−	0.0639200i
$265$	−4.21942	−	1.13059i	−0.259197	−	0.0694515i
$266$	−26.7517	+	7.16809i	−1.64025	+	0.439504i
$267$	−1.37388	−	9.68469i	−0.0840799	−	0.592694i
$268$	−5.41695	+	1.45147i	−0.330893	+	0.0886624i
$269$	22.7826	−	13.1536i	1.38908	−	0.801987i	0.395870	−	0.918307i	$-0.370443\pi$
$269$	22.7826	−	13.1536i	1.38908	−	0.801987i	0.993212	+	0.116320i	$0.0371099\pi$
$270$	−5.16045	−	6.32228i	−0.314055	−	0.384762i
$271$	4.66870	−	1.25097i	0.283603	−	0.0759913i	−0.114213	−	0.993456i	$-0.536435\pi$
$271$	4.66870	−	1.25097i	0.283603	−	0.0759913i	0.397817	+	0.917465i	$0.369768\pi$
$272$	−2.99188	+	5.18209i	−0.181410	+	0.314211i
$273$	−12.0815	−	26.6505i	−0.731205	−	1.61296i
$274$	0.732176	+	1.26817i	0.0442324	+	0.0766127i
$275$	−2.74060	−	2.74060i	−0.165265	−	0.165265i
$276$	6.88717	+	5.17589i	0.414559	+	0.311552i
$277$			14.5756i			0.875764i	0.899032	+	0.437882i	$0.144271\pi$
$277$			14.5756i			0.875764i	−0.899032	+	0.437882i	$0.855729\pi$
$278$	−5.29908	−	5.29908i	−0.317818	−	0.317818i
$279$	2.75438	+	1.51747i	0.164900	+	0.0908487i
$280$	1.90465	−	7.10824i	0.113824	−	0.424799i
$281$	−5.95459	−	22.2228i	−0.355221	−	1.32570i	−0.880206	−	0.474592i	$-0.842596\pi$
$281$	−5.95459	−	22.2228i	−0.355221	−	1.32570i	0.524985	−	0.851112i	$-0.324071\pi$
$282$	10.9322	+	1.32795i	0.651003	+	0.0790781i
$283$			14.3645i			0.853878i	0.904280	+	0.426939i	$0.140408\pi$
$283$			14.3645i			0.853878i	−0.904280	+	0.426939i	$0.859592\pi$
$284$	0.203543	−	0.203543i	0.0120781	−	0.0120781i
$285$	9.66019	−	12.8541i	0.572220	−	0.761410i
$286$	−3.81029	+	3.98893i	−0.225307	+	0.235870i
$287$			24.2905i			1.43382i
$288$	2.99940	−	0.0601200i	0.176741	−	0.00354261i
$289$	−9.40274	+	16.2860i	−0.553102	+	0.958001i
$290$	10.7889			0.633548
$291$	−9.09804	+	7.12715i	−0.533337	+	0.417801i
$292$	−0.353171	−	1.31805i	−0.0206678	−	0.0771331i
$293$	−3.15243	−	11.7650i	−0.184167	−	0.687320i	−0.994807	−	0.101776i	$-0.967548\pi$
$293$	−3.15243	−	11.7650i	−0.184167	−	0.687320i	0.810640	−	0.585544i	$-0.199119\pi$
$294$	24.0279	+	9.67174i	1.40133	+	0.564067i
$295$	9.38135			0.546203
$296$	3.59697	−	6.23013i	0.209069	−	0.362119i
$297$	−6.44968	−	4.64782i	−0.374248	−	0.269694i
$298$			0.600121i			0.0347641i
$299$	−17.4248	−	4.24380i	−1.00770	−	0.245426i
$300$	−1.71966	−	4.03674i	−0.0992847	−	0.233061i
$301$	−40.6151	+	40.6151i	−2.34102	+	2.34102i
$302$			1.81956i			0.104704i
$303$	5.19976	+	12.2059i	0.298718	+	0.701212i
$304$	1.52984	+	5.70943i	0.0877421	+	0.327458i
$305$	1.77739	−	6.63330i	0.101773	−	0.379822i
$306$	17.9477	−	0.359744i	1.02600	−	0.0205652i
$307$	−6.82241	−	6.82241i	−0.389375	−	0.389375i	0.485089	−	0.874465i	$-0.338787\pi$
$307$	−6.82241	−	6.82241i	−0.389375	−	0.389375i	−0.874465	+	0.485089i	$0.838787\pi$
$308$		−	7.16864i		−	0.408471i
$309$	4.53299	−	1.93107i	0.257873	−	0.109855i
$310$	−1.16415	−	1.16415i	−0.0661190	−	0.0661190i
$311$	−7.73754	−	13.4018i	−0.438756	−	0.759947i	0.558838	−	0.829277i	$-0.311247\pi$
$311$	−7.73754	−	13.4018i	−0.438756	−	0.759947i	−0.997594	+	0.0693297i	$0.977914\pi$
$312$	−5.68784	+	2.57847i	−0.322010	+	0.145977i
$313$	13.3960	−	23.2026i	0.757189	−	1.31149i	−0.187090	−	0.982343i	$-0.559906\pi$
$313$	13.3960	−	23.2026i	0.757189	−	1.31149i	0.944279	−	0.329146i	$-0.106761\pi$
$314$	−1.96232	+	0.525803i	−0.110740	+	0.0296728i
$315$	−21.2059	+	6.14014i	−1.19482	+	0.345958i
$316$	0.116730	−	0.0673941i	0.00656657	−	0.00379121i
$317$	13.9142	−	3.72829i	0.781498	−	0.209402i	0.154053	−	0.988063i	$-0.450767\pi$
$317$	13.9142	−	3.72829i	0.781498	−	0.209402i	0.627445	+	0.778661i	$0.284101\pi$
$318$	−4.46891	−	1.79883i	−0.250604	−	0.100874i
$319$	10.1517	−	2.72015i	0.568389	−	0.152299i
$320$	−1.51706	−	0.406496i	−0.0848065	−	0.0227238i
$321$	−23.5909	−	17.7292i	−1.31672	−	0.989548i
$322$	20.1835	−	11.6530i	1.12479	−	0.649395i
$323$	9.15418	+	34.1639i	0.509352	+	1.90093i
$324$	−4.80872	−	7.60764i	−0.267151	−	0.422647i
$325$	6.60482	+	6.30903i	0.366369	+	0.349962i
$326$	7.88303	+	4.55127i	0.436601	+	0.252072i
$327$	−2.78369	+	2.18067i	−0.153939	+	0.120591i
$328$	5.18415			0.286247
$329$	14.8955	−	25.7998i	0.821217	−	1.42239i
$330$	2.56661	+	3.27636i	0.141287	+	0.180358i
$331$	−21.7375	+	21.7375i	−1.19480	+	1.19480i	−0.219098	+	0.975703i	$0.570311\pi$
$331$	−21.7375	+	21.7375i	−1.19480	+	1.19480i	−0.975703	+	0.219098i	$0.929689\pi$
$332$	11.2043	+	3.00217i	0.614913	+	0.164765i
$333$	−21.5775	+	0.432499i	−1.18244	+	0.0237008i
$334$	−1.87046	−	3.23973i	−0.102347	−	0.177270i
$335$	−4.40393	−	7.62784i	−0.240613	−	0.416753i
$336$	3.03041	−	7.52855i	0.165322	−	0.410716i
$337$	26.0523	−	15.0413i	1.41916	−	0.819353i	0.422936	−	0.906159i	$-0.360999\pi$
$337$	26.0523	−	15.0413i	1.41916	−	0.819353i	0.996225	+	0.0868060i	$0.0276660\pi$
$338$	8.76188	−	9.60362i	0.476583	−	0.522368i
$339$	11.5072	+	8.64794i	0.624983	+	0.469692i
$340$	−9.07776	−	2.43238i	−0.492311	−	0.131914i
$341$	−1.38890	−	0.801882i	−0.0752132	−	0.0434244i
$342$	12.2850	−	12.7875i	0.664295	−	0.691470i
$343$	26.3535	−	26.3535i	1.42295	−	1.42295i
$344$	8.66821	+	8.66821i	0.467359	+	0.467359i
$345$	−5.05256	+	12.5523i	−0.272020	+	0.675791i
$346$	0.262508	−	0.979692i	0.0141125	−	0.0526686i
$347$	−14.8126	−	8.55203i	−0.795179	−	0.459097i	0.0466034	−	0.998913i	$-0.485160\pi$
$347$	−14.8126	−	8.55203i	−0.795179	−	0.459097i	−0.841783	+	0.539816i	$0.818494\pi$
$348$	11.8113	+	1.43474i	0.633153	+	0.0769099i
$349$	−0.723680	+	2.70081i	−0.0387377	+	0.144571i	−0.982586	−	0.185808i	$-0.940510\pi$
$349$	−0.723680	+	2.70081i	−0.0387377	+	0.144571i	0.943848	+	0.330379i	$0.107177\pi$
$350$	−11.8697			−0.634464
$351$	15.4464	+	10.6023i	0.824467	+	0.565910i
$352$	−1.52995			−0.0815468
$353$	8.65669	−	32.3072i	0.460749	−	1.71954i	−0.209862	−	0.977731i	$-0.567302\pi$
$353$	8.65669	−	32.3072i	0.460749	−	1.71954i	0.670612	−	0.741809i	$-0.266032\pi$
$354$	10.2704	+	1.24755i	0.545863	+	0.0663067i
$355$	0.391527	+	0.226048i	0.0207801	+	0.0119974i
$356$	−1.46167	+	5.45501i	−0.0774681	+	0.289115i
$357$	18.1332	−	45.0491i	0.959713	−	2.38425i
$358$	16.5170	+	16.5170i	0.872951	+	0.872951i
$359$	−4.06738	+	4.06738i	−0.214668	+	0.214668i	−0.806247	−	0.591579i	$-0.798505\pi$
$359$	−4.06738	+	4.06738i	−0.214668	+	0.214668i	0.591579	+	0.806247i	$0.298505\pi$
$360$	1.31045	+	4.52584i	0.0690667	+	0.238533i
$361$	13.8027	+	7.96897i	0.726456	+	0.419420i
$362$	−8.22755	−	2.20456i	−0.432430	−	0.115869i
$363$	−11.9898	−	9.01066i	−0.629301	−	0.472937i
$364$	0.386845	+	16.8895i	0.0202762	+	0.885249i
$365$	1.85601	−	1.07157i	0.0971477	−	0.0560883i
$366$	2.82793	−	7.02553i	0.147818	−	0.367230i
$367$	−1.43997	−	2.49409i	−0.0751656	−	0.130191i	0.825993	−	0.563681i	$-0.190615\pi$
$367$	−1.43997	−	2.49409i	−0.0751656	−	0.130191i	−0.901158	+	0.433490i	$0.857282\pi$
$368$	−2.48702	−	4.30764i	−0.129645	−	0.224551i
$369$	−8.04457	−	13.3103i	−0.418784	−	0.692905i
$370$	10.9137	+	2.92431i	0.567374	+	0.152027i
$371$	−9.21493	+	9.21493i	−0.478415	+	0.478415i
$372$	−1.11965	−	1.42927i	−0.0580513	−	0.0741044i
$373$	8.54896	−	14.8072i	0.442648	−	0.766689i	−0.555237	−	0.831692i	$-0.687372\pi$
$373$	8.54896	−	14.8072i	0.442648	−	0.766689i	0.997885	+	0.0650030i	$0.0207057\pi$
$374$	−9.15489			−0.473388
$375$	16.1323	−	12.6376i	0.833070	−	0.652604i
$376$	−5.50628	−	3.17905i	−0.283965	−	0.163947i
$377$	−23.7709	+	6.95656i	−1.22427	+	0.358281i
$378$	−24.0320	+	3.90199i	−1.23607	+	0.200697i
$379$	5.27326	+	19.6801i	0.270869	+	1.01090i	0.958559	+	0.284893i	$0.0919581\pi$
$379$	5.27326	+	19.6801i	0.270869	+	1.01090i	−0.687690	+	0.726004i	$0.741375\pi$
$380$	−8.03969	+	4.64172i	−0.412428	+	0.238115i
$381$	−16.1147	−	12.1106i	−0.825579	−	0.620445i
$382$	15.0979	+	4.04547i	0.772476	+	0.206984i
$383$	−15.5784	+	4.17422i	−0.796018	+	0.213293i	−0.633835	−	0.773468i	$-0.718520\pi$
$383$	−15.5784	+	4.17422i	−0.796018	+	0.213293i	−0.162183	+	0.986761i	$0.551854\pi$
$384$	−1.60677	−	0.646759i	−0.0819950	−	0.0330048i
$385$	10.8753	−	2.91402i	0.554256	−	0.148512i
$386$	−13.6917	+	7.90489i	−0.696888	+	0.402348i
$387$	8.80457	−	35.7066i	0.447561	−	1.81507i
$388$	6.44523	−	1.72699i	0.327207	−	0.0876749i
$389$	−18.1024	+	31.3543i	−0.917828	+	1.58972i	−0.115121	+	0.993351i	$0.536726\pi$
$389$	−18.1024	+	31.3543i	−0.917828	+	1.58972i	−0.802707	+	0.596373i	$0.796608\pi$
$390$	−6.22379	−	7.58067i	−0.315154	−	0.383862i
$391$	−14.8817	−	25.7759i	−0.752601	−	1.30354i
$392$	−10.5742	−	10.5742i	−0.534077	−	0.534077i
$393$	8.69397	−	3.70366i	0.438553	−	0.186825i
$394$		−	13.8630i		−	0.698409i
$395$	0.149691	+	0.149691i	0.00753179	+	0.00753179i
$396$	2.37413	+	3.92815i	0.119304	+	0.197397i
$397$	−0.170003	+	0.634461i	−0.00853223	+	0.0318427i	−0.970061	−	0.242863i	$-0.921914\pi$
$397$	−0.170003	+	0.634461i	−0.00853223	+	0.0318427i	0.961528	+	0.274705i	$0.0885803\pi$
$398$	3.23362	+	12.0680i	0.162087	+	0.604915i
$399$	−18.8004	−	44.1321i	−0.941198	−	2.20937i
$400$			2.53328i			0.126664i
$401$	−2.13312	+	2.13312i	−0.106523	+	0.106523i	−0.758360	−	0.651836i	$-0.773999\pi$
$401$	−2.13312	+	2.13312i	−0.106523	+	0.106523i	0.651836	+	0.758360i	$0.273999\pi$
$402$	−3.80690	−	8.93631i	−0.189871	−	0.445703i
$403$	3.31555	+	1.81430i	0.165159	+	0.0903768i
$404$		−	7.65990i		−	0.381094i
$405$	9.58656	−	10.3876i	0.476360	−	0.516164i
$406$	16.0934	−	27.8745i	0.798700	−	1.38339i
$407$	11.0064			0.545567
$408$	−9.61452	−	3.87006i	−0.475990	−	0.191596i
$409$	0.610760	+	2.27939i	0.0302001	+	0.112708i	0.979381	−	0.202024i	$-0.0647519\pi$
$409$	0.610760	+	2.27939i	0.0302001	+	0.112708i	−0.949180	+	0.314732i	$0.898085\pi$
$410$	2.10733	+	7.86468i	0.104074	+	0.388409i
$411$	−1.99663	+	1.56411i	−0.0984867	+	0.0771517i
$412$	−2.84470			−0.140149
$413$	13.9937	−	24.2379i	0.688587	−	1.19267i
$414$	−7.20057	+	13.0698i	−0.353889	+	0.642347i
$415$			18.2179i			0.894283i
$416$	3.60461	−	0.0825616i	0.176730	−	0.00404792i
$417$	7.79817	−	10.3764i	0.381878	−	0.508136i
$418$	−6.39458	+	6.39458i	−0.312769	+	0.312769i
$419$			22.7695i			1.11236i	0.831061	+	0.556181i	$0.187734\pi$
$419$			22.7695i			1.11236i	−0.831061	+	0.556181i	$0.812266\pi$
$420$	12.6531	+	1.53699i	0.617410	+	0.0749976i
$421$	8.84164	+	32.9974i	0.430915	+	1.60820i	0.750657	+	0.660692i	$0.229737\pi$
$421$	8.84164	+	32.9974i	0.430915	+	1.60820i	−0.319742	+	0.947505i	$0.603596\pi$
$422$	2.02370	−	7.55254i	0.0985121	−	0.367652i
$423$	0.382249	+	19.0705i	0.0185856	+	0.927238i
$424$	1.96668	+	1.96668i	0.0955104	+	0.0955104i
$425$			15.1585i			0.735297i
$426$	0.398569	+	0.299535i	0.0193107	+	0.0145125i
$427$	−14.4867	−	14.4867i	−0.701060	−	0.701060i
$428$	8.51888	+	14.7551i	0.411776	+	0.713216i
$429$	−7.76749	−	5.56380i	−0.375018	−	0.268623i
$430$	−9.62664	+	16.6738i	−0.464238	+	0.804084i
$431$	6.97762	−	1.86965i	0.336100	−	0.0900578i	−0.0868218	−	0.996224i	$-0.527671\pi$
$431$	6.97762	−	1.86965i	0.336100	−	0.0900578i	0.422922	+	0.906166i	$0.361004\pi$
$432$	0.832775	+	5.12898i	0.0400669	+	0.246768i
$433$	16.0208	−	9.24961i	0.769910	−	0.444508i	−0.0629325	−	0.998018i	$-0.520045\pi$
$433$	16.0208	−	9.24961i	0.769910	−	0.444508i	0.832842	+	0.553510i	$0.186712\pi$
$434$	−4.74421	+	1.27121i	−0.227730	+	0.0610200i
$435$	2.62467	+	18.5017i	0.125843	+	0.887091i
$436$	1.97202	−	0.528402i	0.0944428	−	0.0253059i
$437$	−28.3989	−	7.60945i	−1.35850	−	0.364010i
$438$	2.17438	−	0.926294i	0.103896	−	0.0442600i
$439$	−17.5983	+	10.1604i	−0.839919	+	0.484927i	−0.857237	−	0.514923i	$-0.827821\pi$
$439$	−17.5983	+	10.1604i	−0.839919	+	0.484927i	0.0173179	+	0.999850i	$0.494487\pi$
$440$	−0.621920	−	2.32104i	−0.0296489	−	0.110651i
$441$	−10.7405	+	43.5578i	−0.511453	+	2.07418i
$442$	21.5691	−	0.494029i	1.02594	−	0.0234986i
$443$	8.71411	+	5.03109i	0.414020	+	0.239034i	0.692515	−	0.721403i	$-0.256502\pi$
$443$	8.71411	+	5.03109i	0.414020	+	0.239034i	−0.278496	+	0.960437i	$0.589836\pi$
$444$	11.5590	+	4.65274i	0.548565	+	0.220809i
$445$	−8.86976			−0.420467
$446$	1.06207	−	1.83956i	0.0502906	−	0.0871058i
$447$	−1.02914	+	0.145994i	−0.0486764	+	0.00690527i
$448$	−3.31317	+	3.31317i	−0.156532	+	0.156532i
$449$	−22.3408	−	5.98619i	−1.05433	−	0.282506i	−0.310288	−	0.950643i	$-0.600426\pi$
$449$	−22.3408	−	5.98619i	−1.05433	−	0.282506i	−0.744039	+	0.668137i	$0.767092\pi$
$450$	6.50418	−	3.93105i	0.306610	−	0.185311i
$451$	3.96575	+	6.86889i	0.186740	+	0.323443i
$452$	−4.15533	−	7.19725i	−0.195450	−	0.338530i
$453$	−3.12032	+	0.442651i	−0.146606	+	0.0207976i
$454$	−16.2376	+	9.37478i	−0.762068	+	0.439980i
$455$	−25.4652	+	7.45237i	−1.19383	+	0.349373i
$456$	−9.41882	+	4.01244i	−0.441077	+	0.187900i
$457$	−21.4539	−	5.74857i	−1.00357	−	0.268907i	−0.280632	−	0.959816i	$-0.590544\pi$
$457$	−21.4539	−	5.74857i	−1.00357	−	0.268907i	−0.722942	+	0.690909i	$0.757211\pi$
$458$	19.2235	+	11.0987i	0.898253	+	0.518607i
$459$	4.98313	+	30.6907i	0.232593	+	1.43252i
$460$	5.52400	−	5.52400i	0.257558	−	0.257558i
$461$	16.9087	+	16.9087i	0.787517	+	0.787517i	0.981087	−	0.193570i	$-0.0620066\pi$
$461$	16.9087	+	16.9087i	0.787517	+	0.787517i	−0.193570	+	0.981087i	$0.562007\pi$
$462$	12.2934	−	1.74395i	0.571939	−	0.0811357i
$463$	3.99959	−	14.9267i	0.185877	−	0.693702i	−0.808564	−	0.588408i	$-0.799755\pi$
$463$	3.99959	−	14.9267i	0.185877	−	0.693702i	0.994441	−	0.105294i	$-0.0335783\pi$
$464$	−5.94907	−	3.43470i	−0.276179	−	0.159452i
$465$	1.71316	−	2.27958i	0.0794461	−	0.105713i
$466$	−4.75444	+	17.7438i	−0.220245	+	0.821966i
$467$	30.0205			1.38918			0.694591	−	0.719405i	$-0.255585\pi$
$467$	30.0205			1.38918			0.694591	+	0.719405i	$0.255585\pi$
$468$	−5.80547	−	9.12669i	−0.268358	−	0.421881i
$469$	−26.2766			−1.21334
$470$	2.58454	−	9.64565i	0.119216	−	0.444921i
$471$	−1.37907	−	3.23724i	−0.0635443	−	0.149164i
$472$	−5.17292	−	2.98659i	−0.238103	−	0.137469i
$473$	−4.85422	+	18.1162i	−0.223197	+	0.832983i
$474$	0.143970	+	0.183783i	0.00661277	+	0.00844142i
$475$	10.5881	+	10.5881i	0.485814	+	0.485814i
$476$	−19.8252	+	19.8252i	−0.908688	+	0.908688i
$477$	1.99762	−	8.10126i	0.0914645	−	0.370931i
$478$	−7.77810	−	4.49069i	−0.355762	−	0.205399i
$479$	−0.481177	−	0.128931i	−0.0219855	−	0.00589100i	0.247810	−	0.968809i	$-0.420289\pi$
$479$	−0.481177	−	0.128931i	−0.0219855	−	0.00589100i	−0.269795	+	0.962918i	$0.586956\pi$
$480$	0.328030	−	2.70047i	0.0149725	−	0.123259i
$481$	−25.9313	+	0.593943i	−1.18237	+	0.0270815i
$482$	3.65887	−	2.11245i	0.166657	−	0.0962194i
$483$	24.8936	+	31.7775i	1.13270	+	1.44593i
$484$	4.32962	+	7.49912i	0.196801	+	0.340869i
$485$	5.23992	+	9.07581i	0.237933	+	0.412111i
$486$	11.8764	−	10.0971i	0.538723	−	0.458015i
$487$	22.2998	+	5.97522i	1.01050	+	0.270763i	0.725839	−	0.687865i	$-0.241452\pi$
$487$	22.2998	+	5.97522i	1.01050	+	0.270763i	0.284663	+	0.958628i	$0.408118\pi$
$488$	−3.09180	+	3.09180i	−0.139959	+	0.139959i
$489$	−5.88715	+	14.6257i	−0.266226	+	0.661396i
$490$	11.7434	−	20.3401i	0.530511	−	0.918871i
$491$	3.19722			0.144288			0.0721442	−	0.997394i	$-0.477016\pi$
$491$	3.19722			0.144288			0.0721442	+	0.997394i	$0.477016\pi$
$492$	1.26117	+	8.89019i	0.0568579	+	0.400801i
$493$	−35.5978	−	20.5524i	−1.60325	−	0.925635i
$494$	14.7207	−	15.4108i	0.662316	−	0.693367i
$495$	−4.99418	+	5.19848i	−0.224472	+	0.233654i
$496$	0.271305	+	1.01253i	0.0121820	+	0.0454637i
$497$	1.16805	−	0.674372i	0.0523940	−	0.0302497i
$498$	−2.42266	+	19.9443i	−0.108562	+	0.893726i
$499$	−32.9338	−	8.82459i	−1.47432	−	0.395043i	−0.569910	−	0.821707i	$-0.693022\pi$
$499$	−32.9338	−	8.82459i	−1.47432	−	0.395043i	−0.904410	+	0.426664i	$0.859689\pi$
$500$	−11.4285	+	3.06225i	−0.511096	+	0.136948i
$501$	5.10071	−	3.99575i	0.227883	−	0.178517i
$502$	−0.0664871	+	0.0178152i	−0.00296746	+	0.000795129i
$503$	0.778425	−	0.449424i	0.0347083	−	0.0200388i	−0.482545	−	0.875871i	$-0.660288\pi$
$503$	0.778425	−	0.449424i	0.0347083	−	0.0200388i	0.517254	+	0.855832i	$0.326954\pi$
$504$	13.6478	+	3.36528i	0.607921	+	0.149902i
$505$	11.6206	−	3.11372i	0.517108	−	0.138559i
$506$	3.80502	−	6.59049i	0.169154	−	0.292983i
$507$	18.6006	+	12.6893i	0.826082	+	0.563550i
$508$	5.81914	+	10.0790i	0.258183	+	0.447185i
$509$	3.43391	+	3.43391i	0.152205	+	0.152205i	0.779102	−	0.626897i	$-0.215675\pi$
$509$	3.43391	+	3.43391i	0.152205	+	0.152205i	−0.626897	+	0.779102i	$0.715675\pi$
$510$	1.96286	−	16.1590i	0.0869167	−	0.715533i
$511$		−	6.39362i		−	0.282837i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	24.9177	+	17.9564i	1.10014	+	0.792794i
$514$	−3.61513	+	13.4918i	−0.159457	+	0.595100i
$515$	−1.15636	−	4.31560i	−0.0509554	−	0.190168i
$516$	−12.7562	+	16.9737i	−0.561561	+	0.747226i
$517$		−	9.72761i		−	0.427820i
$518$	23.8347	−	23.8347i	1.04724	−	1.04724i
$519$	1.74392	+	0.211836i	0.0765495	+	0.00929856i
$520$	1.59051	+	5.43486i	0.0697484	+	0.238334i
$521$		−	14.7602i		−	0.646655i	−0.946287	−	0.323327i	$-0.895198\pi$
$521$		−	14.7602i		−	0.646655i	0.946287	−	0.323327i	$-0.104802\pi$
$522$	0.412988	+	20.6040i	0.0180760	+	0.901814i
$523$	−7.04052	+	12.1945i	−0.307860	+	0.533230i	−0.977894	−	0.209101i	$-0.932946\pi$
$523$	−7.04052	+	12.1945i	−0.307860	+	0.533230i	0.670034	+	0.742331i	$0.266280\pi$
$524$	−5.45595			−0.238344
$525$	−2.88760	−	20.3552i	−0.126025	−	0.888374i
$526$	−6.20367	−	23.1524i	−0.270493	−	1.00949i
$527$	1.62343	+	6.05872i	0.0707176	+	0.263922i
$528$	−0.372198	−	2.62369i	−0.0161979	−	0.114181i
$529$	1.74099			0.0756951
$530$	−2.18413	+	3.78302i	−0.0948726	+	0.164324i
$531$	0.359107	+	17.9159i	0.0155839	+	0.777485i
$532$			27.6954i			1.20075i
$533$	−9.71407	−	15.9692i	−0.420763	−	0.691705i
$534$	−9.71028	−	1.17952i	−0.420205	−	0.0510428i
$535$	−18.9216	+	18.9216i	−0.818052	+	0.818052i
$536$			5.60804i			0.242230i
$537$	−24.3065	+	32.3429i	−1.04890	+	1.39570i
$538$	−6.80878	−	25.4107i	−0.293547	−	1.09553i
$539$	5.92157	−	22.0996i	0.255060	−	0.951897i
$540$	−7.44248	+	3.34828i	−0.320273	+	0.144087i
$541$	22.4390	+	22.4390i	0.964730	+	0.964730i	0.999399	−	0.0346688i	$-0.0110376\pi$
$541$	22.4390	+	22.4390i	0.964730	+	0.964730i	−0.0346688	+	0.999399i	$0.511038\pi$
$542$		−	4.83340i		−	0.207612i
$543$	1.77902	−	14.6456i	0.0763449	−	0.628502i
$544$	4.23116	+	4.23116i	0.181410	+	0.181410i
$545$	1.60324	+	2.77689i	0.0686752	+	0.118949i
$546$	−28.8693	+	4.77217i	−1.23549	+	0.204230i
$547$	1.46832	−	2.54321i	0.0627810	−	0.108740i	−0.832927	−	0.553384i	$-0.813336\pi$
$547$	1.46832	−	2.54321i	0.0627810	−	0.108740i	0.895708	+	0.444644i	$0.146670\pi$
$548$	1.41446	−	0.379002i	0.0604225	−	0.0161902i
$549$	12.7359	+	3.14043i	0.543556	+	0.134030i
$550$	−3.35654	+	1.93790i	−0.143123	+	0.0826323i
$551$	−39.2203	+	10.5090i	−1.67084	+	0.447700i
$552$	6.78206	−	5.31287i	0.288664	−	0.226131i
$553$	0.610034	−	0.163458i	0.0259413	−	0.00695094i
$554$	14.0790	+	3.77245i	0.598158	+	0.160276i
$555$	−2.35983	+	19.4270i	−0.100169	+	0.824632i
$556$	−6.49002	+	3.74702i	−0.275238	+	0.158909i
$557$	3.80383	+	14.1961i	0.161173	+	0.601507i	0.998497	+	0.0548002i	$0.0174522\pi$
$557$	3.80383	+	14.1961i	0.161173	+	0.601507i	−0.837324	+	0.546707i	$0.815881\pi$
$558$	2.17865	−	2.26778i	0.0922297	−	0.0960026i
$559$	10.4590	−	42.9441i	0.442370	−	1.81634i
$560$	−6.37308	−	3.67950i	−0.269312	−	0.155487i
$561$	−2.22715	−	15.6996i	−0.0940303	−	0.662836i
$562$	−23.0068			−0.970482
$563$	14.3608	−	24.8737i	0.605237	−	1.04830i	−0.386777	−	0.922173i	$-0.626412\pi$
$563$	14.3608	−	24.8737i	0.605237	−	1.04830i	0.992014	−	0.126128i	$-0.0402551\pi$
$564$	4.11216	−	10.2160i	0.173153	−	0.430171i
$565$	9.22956	−	9.22956i	0.388290	−	0.388290i
$566$	13.8750	+	3.71780i	0.583210	+	0.156271i
$567$	−12.5378	−	40.2628i	−0.526538	−	1.69088i
$568$	−0.143927	−	0.249288i	−0.00603903	−	0.0104599i
$569$	−5.61525	−	9.72590i	−0.235403	−	0.407731i	0.723986	−	0.689814i	$-0.242308\pi$
$569$	−5.61525	−	9.72590i	−0.235403	−	0.407731i	−0.959390	+	0.282083i	$0.908974\pi$
$570$	−9.91585	−	12.6579i	−0.415329	−	0.530181i
$571$	35.2056	−	20.3260i	1.47331	−	0.850615i	0.473760	−	0.880654i	$-0.342897\pi$
$571$	35.2056	−	20.3260i	1.47331	−	0.850615i	0.999549	+	0.0300392i	$0.00956322\pi$
$572$	2.86683	+	4.71287i	0.119868	+	0.197055i
$573$	−3.26457	+	26.8753i	−0.136380	+	1.12273i
$574$	23.4628	+	6.28683i	0.979317	+	0.262407i
$575$	−10.9124	−	6.30030i	−0.455080	−	0.262741i
$576$	0.718230	−	2.91276i	0.0299262	−	0.121365i
$577$	−9.12182	+	9.12182i	−0.379746	+	0.379746i	−0.871011	−	0.491264i	$-0.836535\pi$
$577$	−9.12182	+	9.12182i	−0.379746	+	0.379746i	0.491264	+	0.871011i	$0.336535\pi$
$578$	13.2975	+	13.2975i	0.553102	+	0.553102i
$579$	−16.8868	−	21.5565i	−0.701791	−	0.895859i
$580$	2.79238	−	10.4213i	0.115947	−	0.432721i
$581$	47.0683	+	27.1749i	1.95272	+	1.12740i
$582$	4.52955	+	10.6327i	0.187756	+	0.440739i
$583$	−1.10134	+	4.11027i	−0.0456130	+	0.170230i
$584$	−1.36455			−0.0564653
$585$	11.4859	−	12.5172i	0.474882	−	0.517524i
$586$	−12.1801			−0.503153
$587$	−9.50777	+	35.4835i	−0.392427	+	1.46456i	0.433690	+	0.901062i	$0.357211\pi$
$587$	−9.50777	+	35.4835i	−0.392427	+	1.46456i	−0.826118	+	0.563497i	$0.809456\pi$
$588$	15.5610	−	20.7059i	0.641727	−	0.853897i
$589$	5.36589	+	3.09800i	0.221097	+	0.127651i
$590$	2.42807	−	9.06169i	0.0999622	−	0.373064i
$591$	23.7734	−	3.37252i	0.977909	−	0.138727i
$592$	−5.08688	−	5.08688i	−0.209069	−	0.209069i
$593$	27.5996	−	27.5996i	1.13338	−	1.13338i	0.143768	−	0.989611i	$-0.454078\pi$
$593$	27.5996	−	27.5996i	1.13338	−	1.13338i	0.989611	−	0.143768i	$-0.0459219\pi$
$594$	−6.15875	+	5.02697i	−0.252696	+	0.206259i
$595$	−38.1350	−	22.0173i	−1.56338	−	0.902619i
$596$	0.579672	+	0.155323i	0.0237443	+	0.00636226i
$597$	−19.9086	+	8.48111i	−0.814804	+	0.347109i
$598$	−8.60907	+	15.7327i	−0.352051	+	0.643357i
$599$	40.1298	−	23.1689i	1.63966	−	0.946657i	0.658708	−	0.752399i	$-0.271103\pi$
$599$	40.1298	−	23.1689i	1.63966	−	0.946657i	0.980950	−	0.194259i	$-0.0622301\pi$
$600$	−4.34427	+	0.616281i	−0.177354	+	0.0251596i
$601$	10.5451	+	18.2647i	0.430145	+	0.745032i	0.996885	−	0.0788639i	$-0.0251293\pi$
$601$	10.5451	+	18.2647i	0.430145	+	0.745032i	−0.566741	+	0.823896i	$0.691796\pi$
$602$	28.7192	+	49.7432i	1.17051	+	2.02738i
$603$	14.3986	−	8.70235i	0.586356	−	0.354387i
$604$	1.75756	+	0.470936i	0.0715140	+	0.0191621i
$605$	−9.61667	+	9.61667i	−0.390973	+	0.390973i
$606$	13.1358	−	1.86346i	0.533606	−	0.0756977i
$607$	−5.11412	+	8.85791i	−0.207576	+	0.359532i	−0.950950	−	0.309344i	$-0.899891\pi$
$607$	−5.11412	+	8.85791i	−0.207576	+	0.359532i	0.743375	+	0.668875i	$0.233224\pi$
$608$	5.91083			0.239716
$609$	51.7166	+	20.8171i	2.09566	+	0.843550i
$610$	−5.94726	−	3.43365i	−0.240797	−	0.139024i
$611$	0.524935	+	22.9185i	0.0212366	+	0.927182i
$612$	4.29772	−	17.4293i	0.173725	−	0.704536i
$613$	−12.0361	−	44.9194i	−0.486134	−	1.81428i	−0.574900	−	0.818224i	$-0.694959\pi$
$613$	−12.0361	−	44.9194i	−0.486134	−	1.81428i	0.0887657	−	0.996053i	$-0.471708\pi$
$614$	−8.35571	+	4.82417i	−0.337209	+	0.194688i
$615$	−12.9743	+	5.52710i	−0.523176	+	0.222874i
$616$	−6.92438	−	1.85538i	−0.278991	−	0.0747554i
$617$	−22.0098	+	5.89751i	−0.886081	+	0.237425i	−0.673029	−	0.739616i	$-0.735007\pi$
$617$	−22.0098	+	5.89751i	−0.886081	+	0.237425i	−0.213052	+	0.977041i	$0.568340\pi$
$618$	−0.692043	−	4.87833i	−0.0278381	−	0.196235i
$619$	28.4902	−	7.63393i	1.14512	−	0.306834i	0.364111	−	0.931355i	$-0.381373\pi$
$619$	28.4902	−	7.63393i	1.14512	−	0.306834i	0.781007	+	0.624522i	$0.214706\pi$
$620$	−1.42578	+	0.823175i	−0.0572607	+	0.0330595i
$621$	−24.1649	−	9.16857i	−0.969705	−	0.367922i
$622$	−14.9478	+	4.00525i	−0.599351	+	0.160596i
$623$	−13.2306	+	22.9161i	−0.530074	+	0.918115i
$624$	1.01849	+	6.16139i	0.0407723	+	0.246653i
$625$	−2.95806	−	5.12350i	−0.118322	−	0.204940i
$626$	−18.9449	−	18.9449i	−0.757189	−	0.757189i
$627$	−12.5216	−	9.41031i	−0.500064	−	0.375812i
$628$			2.03155i			0.0810676i
$629$	−30.4387	−	30.4387i	−1.21367	−	1.21367i
$630$	0.442423	+	22.0726i	0.0176265	+	0.879391i
$631$	11.3620	−	42.4037i	0.452315	−	1.68806i	−0.243548	−	0.969889i	$-0.578311\pi$
$631$	11.3620	−	42.4037i	0.452315	−	1.68806i	0.695863	−	0.718174i	$-0.255022\pi$
$632$	−0.0348857	−	0.130195i	−0.00138768	−	0.00517889i
$633$	13.4440	+	1.63306i	0.534352	+	0.0649084i
$634$		−	14.4050i		−	0.572096i
$635$	−12.9251	+	12.9251i	−0.512917	+	0.512917i
$636$	−2.89418	+	3.85106i	−0.114762	+	0.152705i
$637$	−12.7588	+	52.3867i	−0.505521	+	2.07564i
$638$		−	10.5099i		−	0.416089i
$639$	−0.416706	+	0.756367i	−0.0164846	+	0.0299214i
$640$	−0.785290	+	1.36016i	−0.0310413	+	0.0537651i
$641$	45.3709			1.79204			0.896022	−	0.444009i	$-0.146444\pi$
$641$	45.3709			1.79204			0.896022	+	0.444009i	$0.146444\pi$
$642$	−23.2309	+	18.1984i	−0.916850	+	0.718234i
$643$	7.11309	+	26.5464i	0.280513	+	1.04689i	0.952056	+	0.305923i	$0.0989649\pi$
$643$	7.11309	+	26.5464i	0.280513	+	1.04689i	−0.671544	+	0.740965i	$0.734368\pi$
$644$	−6.03202	−	22.5118i	−0.237695	−	0.887090i
$645$	−30.9356	−	12.4522i	−1.21809	−	0.490306i
$646$	35.3691			1.39158
$647$	1.29346	−	2.24034i	0.0508513	−	0.0880770i	−0.839479	−	0.543392i	$-0.817140\pi$
$647$	1.29346	−	2.24034i	0.0508513	−	0.0880770i	0.890331	+	0.455315i	$0.150473\pi$
$648$	−8.59301	+	2.67586i	−0.337565	+	0.105118i
$649$		−	9.13869i		−	0.358725i
$650$	7.80351	−	4.74686i	0.306079	−	0.186187i
$651$	−3.33412	−	7.82651i	−0.130674	−	0.306745i
$652$	6.43647	−	6.43647i	0.252072	−	0.252072i
$653$		−	2.19250i		−	0.0857991i	−0.999079	−	0.0428995i	$-0.986340\pi$
$653$		−	2.19250i		−	0.0857991i	0.999079	−	0.0428995i	$-0.0136595\pi$
$654$	1.38589	+	3.25324i	0.0541926	+	0.127212i
$655$	−2.21782	−	8.27703i	−0.0866575	−	0.323410i
$656$	1.34176	−	5.00750i	0.0523868	−	0.195510i
$657$	2.11745	+	3.50347i	0.0826098	+	0.136683i
$658$	−21.0655	−	21.0655i	−0.821217	−	0.821217i
$659$		−	22.2888i		−	0.868248i	−0.900853	−	0.434124i	$-0.857058\pi$
$659$		−	22.2888i		−	0.868248i	0.900853	−	0.434124i	$-0.142942\pi$
$660$	3.82901	−	1.63117i	0.149044	−	0.0634932i
$661$	18.0417	+	18.0417i	0.701741	+	0.701741i	0.964784	−	0.263043i	$-0.0847261\pi$
$661$	18.0417	+	18.0417i	0.701741	+	0.701741i	−0.263043	+	0.964784i	$0.584726\pi$
$662$	15.3707	+	26.6229i	0.597400	+	1.03473i
$663$	6.09441	+	36.8683i	0.236687	+	1.43185i
$664$	5.79975	−	10.0455i	0.225074	−	0.389839i
$665$	−42.0156	+	11.2581i	−1.62930	+	0.436569i
$666$	−5.16690	+	20.9542i	−0.200213	+	0.811958i
$667$	29.5909	−	17.0843i	1.14576	−	0.661506i
$668$	−3.61344	+	0.968219i	−0.139808	+	0.0374615i
$669$	3.41301	+	1.37381i	0.131954	+	0.0531145i
$670$	−8.50775	+	2.27964i	−0.328683	+	0.0880703i
$671$	−6.46172	−	1.73141i	−0.249452	−	0.0668405i
$672$	−6.48770	−	4.87568i	−0.250268	−	0.188083i
$673$	15.0426	−	8.68484i	0.579849	−	0.334776i	−0.181225	−	0.983442i	$-0.558006\pi$
$673$	15.0426	−	8.68484i	0.579849	−	0.334776i	0.761073	+	0.648666i	$0.224673\pi$
$674$	−7.78596	−	29.0576i	−0.299904	−	1.11926i
$675$	8.32358	+	10.1976i	0.320375	+	0.392505i
$676$	−7.00865	−	10.9489i	−0.269563	−	0.421112i
$677$	−1.50598	−	0.869476i	−0.0578794	−	0.0334167i	0.470781	−	0.882250i	$-0.343972\pi$
$677$	−1.50598	−	0.869476i	−0.0578794	−	0.0334167i	−0.528660	+	0.848833i	$0.677306\pi$
$678$	11.3315	−	8.87681i	0.435185	−	0.340912i
$679$	31.2646			1.19983
$680$	−4.69899	+	8.13889i	−0.180198	+	0.312112i
$681$	−20.0268	−	25.5649i	−0.767429	−	0.979649i
$682$	−1.13403	+	1.13403i	−0.0434244	+	0.0434244i
$683$	40.4081	+	10.8273i	1.54617	+	0.414296i	0.928254	−	0.371947i	$-0.121310\pi$
$683$	40.4081	+	10.8273i	1.54617	+	0.414296i	0.617918	+	0.786243i	$0.287976\pi$
$684$	−9.17222	−	15.1760i	−0.350709	−	0.580270i
$685$	1.14994	+	1.99176i	0.0439370	+	0.0761011i
$686$	−18.6347	−	32.2763i	−0.711476	−	1.23231i
$687$	−14.3563	+	35.6660i	−0.547728	+	1.36074i
$688$	10.6164	−	6.12935i	0.404745	−	0.233679i
$689$	2.37299	−	9.74333i	0.0904036	−	0.371191i
$690$	10.8168	+	8.12916i	0.411790	+	0.309472i
$691$	−9.52423	−	2.55201i	−0.362319	−	0.0970830i	0.0730670	−	0.997327i	$-0.476721\pi$
$691$	−9.52423	−	2.55201i	−0.362319	−	0.0970830i	−0.435386	+	0.900244i	$0.643388\pi$
$692$	−0.878368	−	0.507126i	−0.0333905	−	0.0192780i
$693$	5.98132	+	20.6574i	0.227212	+	0.784710i
$694$	−12.0944	+	12.0944i	−0.459097	+	0.459097i
$695$	−8.32263	−	8.32263i	−0.315695	−	0.315695i
$696$	4.44284	−	11.0375i	0.168406	−	0.418376i
$697$	8.02875	−	29.9637i	0.304111	−	1.13496i
$698$	2.42148	+	1.39804i	0.0916544	+	0.0529167i
$699$	−31.5851	−	3.83669i	−1.19466	−	0.145117i
$700$	−3.07211	+	11.4653i	−0.116115	+	0.433347i
$701$	9.99927			0.377667			0.188834	−	0.982009i	$-0.439529\pi$
$701$	9.99927			0.377667			0.188834	+	0.982009i	$0.439529\pi$
$702$	14.2389	−	12.1760i	0.537411	−	0.459553i
$703$	−42.5221			−1.60375
$704$	−0.395981	+	1.47782i	−0.0149241	+	0.0556975i
$705$	17.1699	+	2.08565i	0.646656	+	0.0785501i
$706$	−28.9659	−	16.7234i	−1.09014	−	0.629395i
$707$	9.28919	−	34.6677i	0.349356	−	1.30381i
$708$	3.86321	−	9.59751i	0.145188	−	0.360696i
$709$	−14.4105	−	14.4105i	−0.541199	−	0.541199i	0.382682	−	0.923880i	$-0.375001\pi$
$709$	−14.4105	−	14.4105i	−0.541199	−	0.541199i	−0.923880	+	0.382682i	$0.875001\pi$
$710$	0.319681	−	0.319681i	0.0119974	−	0.0119974i
$711$	−0.280141	+	0.291601i	−0.0105061	+	0.0109359i
$712$	4.89083	+	2.82372i	0.183292	+	0.105823i
$713$	−5.03633	−	1.34948i	−0.188612	−	0.0505385i
$714$	−38.8209	−	29.1749i	−1.45283	−	1.09184i
$715$	−5.98437	+	6.26493i	−0.223803	+	0.234295i
$716$	20.2291	−	11.6793i	0.755998	−	0.436475i
$717$	5.80879	−	14.4310i	0.216933	−	0.538935i
$718$	2.87607	+	4.98150i	0.107334	+	0.185908i
$719$	−9.70859	−	16.8158i	−0.362069	−	0.627123i	0.626232	−	0.779637i	$-0.284596\pi$
$719$	−9.70859	−	16.8158i	−0.362069	−	0.627123i	−0.988301	+	0.152514i	$0.951263\pi$
$720$	4.71079	−	0.0944233i	0.175561	−	0.00351895i
$721$	−12.8748	−	3.44978i	−0.479481	−	0.128477i
$722$	11.2698	−	11.2698i	0.419420	−	0.419420i
$723$	4.51271	+	5.76062i	0.167829	+	0.214240i
$724$	−4.25889	+	7.37662i	−0.158280	+	0.274150i
$725$	−17.4021			−0.646297
$726$	−11.8068	+	9.24913i	−0.438192	+	0.343267i
$727$	−38.1818	−	22.0442i	−1.41608	−	0.817576i	−0.420131	−	0.907464i	$-0.638016\pi$
$727$	−38.1818	−	22.0442i	−1.41608	−	0.817576i	−0.995952	+	0.0898878i	$0.971349\pi$
$728$	16.4141	+	3.99765i	0.608347	+	0.148163i
$729$	20.2046	+	17.9102i	0.748318	+	0.663341i
$730$	−0.554683	−	2.07010i	−0.0205297	−	0.0766180i
$731$	63.5258	−	36.6766i	2.34959	−	1.35653i
$732$	−6.05422	−	4.54991i	−0.223770	−	0.168170i
$733$	−34.7355	−	9.30736i	−1.28299	−	0.343775i	−0.447994	−	0.894037i	$-0.647861\pi$
$733$	−34.7355	−	9.30736i	−1.28299	−	0.343775i	−0.834992	+	0.550261i	$0.814528\pi$
$734$	−2.78180	+	0.745381i	−0.102678	+	0.0275125i
$735$	37.7377	+	15.1902i	1.39198	+	0.560300i
$736$	−4.80455	+	1.28737i	−0.177098	+	0.0474532i
$737$	−7.43053	+	4.29002i	−0.273707	+	0.158025i
$738$	−14.9388	+	4.32551i	−0.549905	+	0.159224i
$739$	−40.1431	+	10.7563i	−1.47669	+	0.395677i	−0.905219	−	0.424946i	$-0.860293\pi$
$739$	−40.1431	+	10.7563i	−1.47669	+	0.395677i	−0.571470	+	0.820623i	$0.693627\pi$
$740$	5.64933	−	9.78492i	0.207673	−	0.359701i
$741$	30.0089	+	21.4952i	1.10241	+	0.789646i
$742$	6.51594	+	11.2859i	0.239208	+	0.414320i
$743$	18.8687	+	18.8687i	0.692224	+	0.692224i	0.962721	−	0.270497i	$-0.0871879\pi$
$743$	18.8687	+	18.8687i	0.692224	+	0.692224i	−0.270497	+	0.962721i	$0.587188\pi$
$744$	−1.67036	+	0.711578i	−0.0612383	+	0.0260877i
$745$			0.942538i			0.0345319i
$746$	−12.0901	−	12.0901i	−0.442648	−	0.442648i
$747$	−34.7915	+	0.697362i	−1.27295	+	0.0255151i
$748$	−2.36946	+	8.84295i	−0.0866360	+	0.323330i
$749$	20.6617	+	77.1107i	0.754964	+	2.81756i
$750$	−8.03164	−	18.8535i	−0.293274	−	0.688432i
$751$			4.26755i			0.155725i	0.996964	+	0.0778626i	$0.0248096\pi$
$751$			4.26755i			0.155725i	−0.996964	+	0.0778626i	$0.975190\pi$
$752$	−4.49586	+	4.49586i	−0.163947	+	0.163947i
$753$	−0.0467255	−	0.109683i	−0.00170277	−	0.00399709i
$754$	0.567148	+	24.7615i	0.0206543	+	0.901759i
$755$			2.85776i			0.104005i
$756$	−2.45091	+	24.2230i	−0.0891386	+	0.880983i
$757$	8.81337	−	15.2652i	0.320327	−	0.554823i	−0.660228	−	0.751065i	$-0.729540\pi$
$757$	8.81337	−	15.2652i	0.320327	−	0.554823i	0.980556	+	0.196242i	$0.0628738\pi$
$758$	20.3743			0.740028
$759$	12.2276	+	4.92186i	0.443833	+	0.178652i
$760$	2.40273	+	8.96711i	0.0871562	+	0.325271i
$761$	1.90621	+	7.11408i	0.0691002	+	0.257885i	0.991831	−	0.127560i	$-0.0407145\pi$
$761$	1.90621	+	7.11408i	0.0691002	+	0.257885i	−0.922731	+	0.385445i	$0.874048\pi$
$762$	−15.8687	+	12.4311i	−0.574863	+	0.450332i
$763$	9.56592			0.346310
$764$	7.81525	−	13.5364i	0.282746	−	0.489730i
$765$	28.1883	−	0.565007i	1.01915	−	0.0204279i
$766$			16.1279i			0.582726i
$767$	0.493155	+	21.5309i	0.0178068	+	0.777437i
$768$	−1.04058	+	1.38462i	−0.0375488	+	0.0499634i
$769$	8.31352	−	8.31352i	0.299793	−	0.299793i	−0.541140	−

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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.z (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(1.71941 + 0.208859i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.406496 - 1.51706i) q^{5} +(0.646759 - 1.60677i) q^{6} +(-3.31317 - 3.31317i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.91276 + 0.718230i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(1.71941 + 0.208859i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.406496 - 1.51706i) q^{5} +(0.646759 - 1.60677i) q^{6} +(-3.31317 - 3.31317i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.91276 + 0.718230i) q^{9} +(-1.36016 - 0.785290i) q^{10} +(-1.47782 - 0.395981i) q^{11} +(-1.38462 - 1.04058i) q^{12} +(3.50315 + 0.853192i) q^{13} +(-4.05778 + 2.34276i) q^{14} +(1.01579 - 2.52356i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.99188 + 5.18209i) q^{17} +(1.44763 - 2.62761i) q^{18} +(5.70943 + 1.52984i) q^{19} +(-1.11057 + 1.11057i) q^{20} +(-5.00471 - 6.38869i) q^{21} +(-0.764977 + 1.32498i) q^{22} -4.97403 q^{23} +(-1.36349 + 1.06812i) q^{24} +(2.19388 + 1.26664i) q^{25} +(1.73080 - 3.16296i) q^{26} +(4.85822 + 1.84329i) q^{27} +(1.21270 + 4.52587i) q^{28} +(-5.94907 + 3.43470i) q^{29} +(-2.17466 - 1.63432i) q^{30} +(1.01253 + 0.271305i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-2.45828 - 0.989512i) q^{33} +(5.77988 - 1.54871i) q^{34} +(-6.37308 + 3.67950i) q^{35} +(-2.16341 - 2.07838i) q^{36} +(-6.94881 + 1.86193i) q^{37} +(2.95542 - 5.11893i) q^{38} +(5.84516 + 2.19865i) q^{39} +(0.785290 + 1.36016i) q^{40} +(-3.66574 - 3.66574i) q^{41} +(-7.46631 + 3.18067i) q^{42} -12.2587i q^{43} +(1.08184 + 1.08184i) q^{44} +(2.27362 - 4.12688i) q^{45} +(-1.28737 + 4.80455i) q^{46} +(1.64560 + 6.14146i) q^{47} +(0.678829 + 1.59348i) q^{48} +14.9542i q^{49} +(1.79130 - 1.79130i) q^{50} +(4.06195 + 9.53504i) q^{51} +(-2.60722 - 2.49046i) q^{52} -2.78130i q^{53} +(3.03788 - 4.21560i) q^{54} +(-1.20146 + 2.08099i) q^{55} +4.68553 q^{56} +(9.49734 + 3.82288i) q^{57} +(1.77793 + 6.63533i) q^{58} +(1.54597 + 5.76965i) q^{59} +(-2.14148 + 1.67757i) q^{60} +4.37246 q^{61} +(0.524122 - 0.907805i) q^{62} +(-7.27083 - 12.0301i) q^{63} -1.00000i q^{64} +(2.71836 - 4.96768i) q^{65} +(-1.59205 + 2.11841i) q^{66} +(3.96548 - 3.96548i) q^{67} -5.98377i q^{68} +(-8.55241 - 1.03887i) q^{69} +(1.90465 + 7.10824i) q^{70} +(-0.0745019 + 0.278045i) q^{71} +(-2.56749 + 1.55176i) q^{72} +(0.964880 + 0.964880i) q^{73} +7.19393i q^{74} +(3.50764 + 2.63609i) q^{75} +(-4.17959 - 4.17959i) q^{76} +(3.58432 + 6.20823i) q^{77} +(3.63658 - 5.07694i) q^{78} +(-0.0673941 + 0.116730i) q^{79} +(1.51706 - 0.406496i) q^{80} +(7.96829 + 4.18406i) q^{81} +(-4.48960 + 2.59207i) q^{82} +(-11.2043 + 3.00217i) q^{83} +(1.13987 + 8.03512i) q^{84} +(9.07776 - 2.43238i) q^{85} +(-11.8410 - 3.17279i) q^{86} +(-10.9463 + 4.66314i) q^{87} +(1.32498 - 0.764977i) q^{88} +(-1.46167 - 5.45501i) q^{89} +(-3.39780 - 3.26427i) q^{90} +(-8.77976 - 14.4333i) q^{91} +(4.30764 + 2.48702i) q^{92} +(1.68428 + 0.677961i) q^{93} +6.35810 q^{94} +(4.64172 - 8.03969i) q^{95} +(1.71488 - 0.243274i) q^{96} +(-4.71824 + 4.71824i) q^{97} +(14.4446 + 3.87042i) q^{98} +(-4.02013 - 2.21481i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{7}+O(q^{10}) \) 56 * q - 8 * q^7	\( 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47} - 24 q^{50} + 8 q^{52} - 36 q^{54} + 36 q^{57} + 24 q^{60} - 48 q^{63} - 36 q^{65} + 28 q^{67} + 84 q^{69} - 24 q^{71} - 24 q^{72} + 28 q^{73} + 4 q^{76} + 24 q^{77} - 60 q^{78} - 24 q^{79} + 24 q^{81} - 96 q^{83} - 72 q^{85} + 4 q^{91} - 24 q^{92} - 36 q^{93} - 52 q^{97} + 48 q^{98} + 60 q^{99}+O(q^{100}) \) 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

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