LMFDB - Embedded newform 690.2.n.a.659.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(89,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 5]))

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

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

chi := DirichletCharacter("690.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.n (of order $22$, degree $10$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			659.20
Character	$\chi$	$=$	690.659
Dual form			690.2.n.a.89.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 + 0.989821i) q^{2} +(1.53419 + 0.803900i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(1.22793 - 1.86874i) q^{5} +(-1.01406 + 1.40417i) q^{6} +(4.08214 + 2.62343i) q^{7} +(0.415415 - 0.909632i) q^{8} +(1.70749 + 2.46667i) q^{9} +O(q^{10})$	\(q+(-0.142315 + 0.989821i) q^{2} +(1.53419 + 0.803900i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(1.22793 - 1.86874i) q^{5} +(-1.01406 + 1.40417i) q^{6} +(4.08214 + 2.62343i) q^{7} +(0.415415 - 0.909632i) q^{8} +(1.70749 + 2.46667i) q^{9} +(1.67496 + 1.48138i) q^{10} +(-0.475030 - 3.30390i) q^{11} +(-1.24556 - 1.20357i) q^{12} +(0.660771 + 1.02818i) q^{13} +(-3.17768 + 3.66723i) q^{14} +(3.38616 - 1.87987i) q^{15} +(0.841254 + 0.540641i) q^{16} +(-1.75177 - 5.96599i) q^{17} +(-2.68457 + 1.33906i) q^{18} +(0.670285 - 2.28278i) q^{19} +(-1.70468 + 1.44709i) q^{20} +(4.15380 + 7.30648i) q^{21} +3.33788 q^{22} +(-4.18997 - 2.33328i) q^{23} +(1.36858 - 1.06160i) q^{24} +(-1.98436 - 4.58937i) q^{25} +(-1.11175 + 0.507720i) q^{26} +(0.636654 + 5.15700i) q^{27} +(-3.17768 - 3.66723i) q^{28} +(1.83741 + 6.25766i) q^{29} +(1.37883 + 3.61923i) q^{30} +(-2.18940 + 4.79412i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(1.92722 - 5.45070i) q^{33} +(6.15457 - 0.884894i) q^{34} +(9.91509 - 4.40704i) q^{35} +(-0.943381 - 2.84781i) q^{36} +(-0.549311 + 0.633939i) q^{37} +(2.16415 + 0.988336i) q^{38} +(0.187195 + 2.10862i) q^{39} +(-1.18976 - 1.89327i) q^{40} +(-4.44117 + 3.84830i) q^{41} +(-7.82325 + 3.07170i) q^{42} +(-0.0334887 - 0.0733301i) q^{43} +(-0.475030 + 3.30390i) q^{44} +(6.70625 - 0.161935i) q^{45} +(2.90582 - 3.81526i) q^{46} +4.46884 q^{47} +(0.856023 + 1.50573i) q^{48} +(6.87355 + 15.0510i) q^{49} +(4.82506 - 1.31102i) q^{50} +(2.10851 - 10.5612i) q^{51} +(-0.344333 - 1.17269i) q^{52} +(-5.83690 + 9.08239i) q^{53} +(-5.19512 - 0.103744i) q^{54} +(-6.75743 - 3.16927i) q^{55} +(4.08214 - 2.62343i) q^{56} +(2.86347 - 2.96338i) q^{57} +(-6.45546 + 0.928154i) q^{58} +(2.51261 + 3.90970i) q^{59} +(-3.77862 + 0.849725i) q^{60} +(-9.97373 - 4.55485i) q^{61} +(-4.43374 - 2.84939i) q^{62} +(0.499054 + 14.5488i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(2.73278 + 0.0277290i) q^{65} +(5.12094 + 2.68332i) q^{66} +(0.376968 - 2.62187i) q^{67} +6.21786i q^{68} +(-4.55249 - 6.94801i) q^{69} +(2.95112 + 10.4414i) q^{70} +(-8.42268 - 1.21100i) q^{71} +(2.95308 - 0.528493i) q^{72} +(-0.938954 + 3.19778i) q^{73} +(-0.549311 - 0.633939i) q^{74} +(0.645010 - 8.63620i) q^{75} +(-1.28627 + 2.00147i) q^{76} +(6.72842 - 14.7332i) q^{77} +(-2.11380 - 0.114798i) q^{78} +(-3.34150 - 5.19947i) q^{79} +(2.04332 - 0.908211i) q^{80} +(-3.16897 + 8.42364i) q^{81} +(-3.17708 - 4.94364i) q^{82} +(-10.3554 - 8.97304i) q^{83} +(-1.92707 - 8.18077i) q^{84} +(-13.2999 - 4.05224i) q^{85} +(0.0773497 - 0.0227119i) q^{86} +(-2.21159 + 11.0775i) q^{87} +(-3.20267 - 0.940389i) q^{88} +(-2.16744 - 4.74603i) q^{89} +(-0.794112 + 6.66103i) q^{90} +5.93065i q^{91} +(3.36288 + 3.41921i) q^{92} +(-7.21296 + 5.59504i) q^{93} +(-0.635982 + 4.42335i) q^{94} +(-3.44285 - 4.05569i) q^{95} +(-1.61223 + 0.633022i) q^{96} +(4.90317 + 5.65856i) q^{97} +(-15.8760 + 4.66161i) q^{98} +(7.33855 - 6.81312i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 24 q^{2} + 2 q^{3} - 24 q^{4} + 2 q^{6} - 24 q^{8} - 6 q^{9}+O(q^{10}) $ 240 * q - 24 * q^2 + 2 * q^3 - 24 * q^4 + 2 * q^6 - 24 * q^8 - 6 * q^9	$ 240 q - 24 q^{2} + 2 q^{3} - 24 q^{4} + 2 q^{6} - 24 q^{8} - 6 q^{9} - 9 q^{12} + 11 q^{15} - 24 q^{16} - 6 q^{18} - 4 q^{23} + 2 q^{24} - 12 q^{25} + 2 q^{27} + 22 q^{30} + 28 q^{31} - 24 q^{32} - 36 q^{35} - 6 q^{36} - 4 q^{46} + 104 q^{47} - 9 q^{48} + 70 q^{49} + 54 q^{50} - 9 q^{54} - 26 q^{55} - 44 q^{57} - 11 q^{60} + 44 q^{61} + 28 q^{62} - 121 q^{63} - 24 q^{64} + 44 q^{65} + 44 q^{66} - 102 q^{69} - 36 q^{70} + 16 q^{72} - 82 q^{75} + 8 q^{77} - 44 q^{79} + 74 q^{81} - 11 q^{84} + 22 q^{85} - 93 q^{87} - 4 q^{92} + 172 q^{93} + 16 q^{94} + 26 q^{95} + 2 q^{96} + 4 q^{98}+O(q^{100}) $ 240 * q - 24 * q^2 + 2 * q^3 - 24 * q^4 + 2 * q^6 - 24 * q^8 - 6 * q^9 - 9 * q^12 + 11 * q^15 - 24 * q^16 - 6 * q^18 - 4 * q^23 + 2 * q^24 - 12 * q^25 + 2 * q^27 + 22 * q^30 + 28 * q^31 - 24 * q^32 - 36 * q^35 - 6 * q^36 - 4 * q^46 + 104 * q^47 - 9 * q^48 + 70 * q^49 + 54 * q^50 - 9 * q^54 - 26 * q^55 - 44 * q^57 - 11 * q^60 + 44 * q^61 + 28 * q^62 - 121 * q^63 - 24 * q^64 + 44 * q^65 + 44 * q^66 - 102 * q^69 - 36 * q^70 + 16 * q^72 - 82 * q^75 + 8 * q^77 - 44 * q^79 + 74 * q^81 - 11 * q^84 + 22 * q^85 - 93 * q^87 - 4 * q^92 + 172 * q^93 + 16 * q^94 + 26 * q^95 + 2 * q^96 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{17}{22}\right)$

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 $

$2$	−0.142315	+	0.989821i	−0.100632	+	0.699909i
$2$	−0.142315	+	0.989821i	−0.100632	+	0.699909i
$3$	1.53419	+	0.803900i	0.885766	+	0.464132i
$3$	1.53419	+	0.803900i	0.885766	+	0.464132i
$4$	−0.959493	−	0.281733i	−0.479746	−	0.140866i
$5$	1.22793	−	1.86874i	0.549149	−	0.835725i
$5$	1.22793	−	1.86874i	0.549149	−	0.835725i
$6$	−1.01406	+	1.40417i	−0.413987	+	0.573250i
$7$	4.08214	+	2.62343i	1.54290	+	0.991563i	0.987074	+	0.160267i	$0.0512354\pi$
$7$	4.08214	+	2.62343i	1.54290	+	0.991563i	0.555829	+	0.831297i	$0.312401\pi$
$8$	0.415415	−	0.909632i	0.146871	−	0.321603i
$9$	1.70749	+	2.46667i	0.569163	+	0.822225i
$10$	1.67496	+	1.48138i	0.529670	+	0.468455i
$11$	−0.475030	−	3.30390i	−0.143227	−	0.996164i	−0.926985	−	0.375098i	$-0.877609\pi$
$11$	−0.475030	−	3.30390i	−0.143227	−	0.996164i	0.783758	−	0.621066i	$-0.213300\pi$
$12$	−1.24556	−	1.20357i	−0.359563	−	0.347440i
$13$	0.660771	+	1.02818i	0.183265	+	0.285166i	0.920715	−	0.390236i	$-0.127607\pi$
$13$	0.660771	+	1.02818i	0.183265	+	0.285166i	−0.737450	+	0.675402i	$0.763970\pi$
$14$	−3.17768	+	3.66723i	−0.849270	+	0.980109i
$15$	3.38616	−	1.87987i	0.874304	−	0.485379i
$16$	0.841254	+	0.540641i	0.210313	+	0.135160i
$17$	−1.75177	−	5.96599i	−0.424867	−	1.44697i	−0.842671	−	0.538428i	$-0.819018\pi$
$17$	−1.75177	−	5.96599i	−0.424867	−	1.44697i	0.417804	−	0.908537i	$-0.362800\pi$
$18$	−2.68457	+	1.33906i	−0.632759	+	0.315621i
$19$	0.670285	−	2.28278i	0.153774	−	0.523706i	−0.846184	−	0.532891i	$-0.821106\pi$
$19$	0.670285	−	2.28278i	0.153774	−	0.523706i	0.999958	+	0.00918523i	$0.00292379\pi$
$20$	−1.70468	+	1.44709i	−0.381178	+	0.323579i
$21$	4.15380	+	7.30648i	0.906434	+	1.59440i
$22$	3.33788			0.711638
$23$	−4.18997	−	2.33328i	−0.873668	−	0.486522i
$23$	−4.18997	−	2.33328i	−0.873668	−	0.486522i
$24$	1.36858	−	1.06160i	0.279360	−	0.216698i
$25$	−1.98436	−	4.58937i	−0.396872	−	0.917874i
$26$	−1.11175	+	0.507720i	−0.218032	+	0.0995720i
$27$	0.636654	+	5.15700i	0.122524	+	0.992466i
$28$	−3.17768	−	3.66723i	−0.600524	−	0.693042i
$29$	1.83741	+	6.25766i	0.341199	+	1.16202i	0.934180	+	0.356801i	$0.116133\pi$
$29$	1.83741	+	6.25766i	0.341199	+	1.16202i	−0.592981	+	0.805216i	$0.702049\pi$
$30$	1.37883	+	3.61923i	0.251739	+	0.660778i
$31$	−2.18940	+	4.79412i	−0.393228	+	0.861050i	0.604684	+	0.796466i	$0.293299\pi$
$31$	−2.18940	+	4.79412i	−0.393228	+	0.861050i	−0.997912	+	0.0645844i	$0.979428\pi$
$32$	−0.654861	+	0.755750i	−0.115764	+	0.133599i
$33$	1.92722	−	5.45070i	0.335486	−	0.948845i
$34$	6.15457	−	0.884894i	1.05550	−	0.151758i
$35$	9.91509	−	4.40704i	1.67596	−	0.744926i
$36$	−0.943381	−	2.84781i	−0.157230	−	0.474635i
$37$	−0.549311	+	0.633939i	−0.0903062	+	0.104219i	−0.799104	−	0.601193i	$-0.794692\pi$
$37$	−0.549311	+	0.633939i	−0.0903062	+	0.104219i	0.708798	+	0.705412i	$0.249238\pi$
$38$	2.16415	+	0.988336i	0.351072	+	0.160329i
$39$	0.187195	+	2.10862i	0.0299752	+	0.337649i
$40$	−1.18976	−	1.89327i	−0.188118	−	0.299352i
$41$	−4.44117	+	3.84830i	−0.693595	+	0.601003i	−0.928640	−	0.370981i	$-0.879021\pi$
$41$	−4.44117	+	3.84830i	−0.693595	+	0.601003i	0.235046	+	0.971984i	$0.424476\pi$
$42$	−7.82325	+	3.07170i	−1.20715	+	0.473974i
$43$	−0.0334887	−	0.0733301i	−0.00510699	−	0.0111827i	0.907061	−	0.420999i	$-0.138320\pi$
$43$	−0.0334887	−	0.0733301i	−0.00510699	−	0.0111827i	−0.912168	+	0.409816i	$0.865593\pi$
$44$	−0.475030	+	3.30390i	−0.0716134	+	0.498082i
$45$	6.70625	−	0.161935i	0.999709	−	0.0241399i
$46$	2.90582	−	3.81526i	0.428440	−	0.562529i
$47$	4.46884			0.651847			0.325923	−	0.945396i	$-0.394325\pi$
$47$	4.46884			0.651847			0.325923	+	0.945396i	$0.394325\pi$
$48$	0.856023	+	1.50573i	0.123556	+	0.217334i
$49$	6.87355	+	15.0510i	0.981936	+	2.15014i
$50$	4.82506	−	1.31102i	0.682367	−	0.185407i
$51$	2.10851	−	10.5612i	0.295250	−	1.47887i
$52$	−0.344333	−	1.17269i	−0.0477504	−	0.162623i
$53$	−5.83690	+	9.08239i	−0.801760	+	1.24756i	0.163570	+	0.986532i	$0.447699\pi$
$53$	−5.83690	+	9.08239i	−0.801760	+	1.24756i	−0.965330	+	0.261031i	$0.915937\pi$
$54$	−5.19512	−	0.103744i	−0.706966	−	0.0141177i
$55$	−6.75743	−	3.16927i	−0.911172	−	0.427344i
$56$	4.08214	−	2.62343i	0.545498	−	0.350571i
$57$	2.86347	−	2.96338i	0.379276	−	0.392509i
$58$	−6.45546	+	0.928154i	−0.847643	+	0.121873i
$59$	2.51261	+	3.90970i	0.327114	+	0.509000i	0.965391	−	0.260807i	$-0.0839887\pi$
$59$	2.51261	+	3.90970i	0.327114	+	0.509000i	−0.638277	+	0.769807i	$0.720352\pi$
$60$	−3.77862	+	0.849725i	−0.487818	+	0.109699i
$61$	−9.97373	−	4.55485i	−1.27701	−	0.583189i	−0.342627	−	0.939472i	$-0.611317\pi$
$61$	−9.97373	−	4.55485i	−1.27701	−	0.583189i	−0.934378	+	0.356283i	$0.884044\pi$
$62$	−4.43374	−	2.84939i	−0.563086	−	0.361873i
$63$	0.499054	+	14.5488i	0.0628749	+	1.83297i
$64$	−0.654861	−	0.755750i	−0.0818576	−	0.0944687i
$65$	2.73278	+	0.0277290i	0.338960	+	0.00343936i
$66$	5.12094	+	2.68332i	0.630345	+	0.330294i
$67$	0.376968	−	2.62187i	0.0460540	−	0.320312i	−0.953752	−	0.300596i	$-0.902814\pi$
$67$	0.376968	−	2.62187i	0.0460540	−	0.320312i	0.999806	−	0.0197167i	$-0.00627642\pi$
$68$			6.21786i			0.754026i
$69$	−4.55249	−	6.94801i	−0.548055	−	0.836442i
$70$	2.95112	+	10.4414i	0.352726	+	1.24798i
$71$	−8.42268	−	1.21100i	−0.999589	−	0.143719i	−0.376954	−	0.926232i	$-0.623029\pi$
$71$	−8.42268	−	1.21100i	−0.999589	−	0.143719i	−0.622634	+	0.782513i	$0.713938\pi$
$72$	2.95308	−	0.528493i	0.348024	−	0.0622835i
$73$	−0.938954	+	3.19778i	−0.109896	+	0.374272i	−0.996015	−	0.0891860i	$-0.971573\pi$
$73$	−0.938954	+	3.19778i	−0.109896	+	0.374272i	0.886119	+	0.463458i	$0.153392\pi$
$74$	−0.549311	−	0.633939i	−0.0638562	−	0.0736939i
$75$	0.645010	−	8.63620i	0.0744794	−	0.997223i
$76$	−1.28627	+	2.00147i	−0.147545	+	0.229584i
$77$	6.72842	−	14.7332i	0.766775	−	1.67900i
$78$	−2.11380	−	0.114798i	−0.239340	−	0.0129983i
$79$	−3.34150	−	5.19947i	−0.375948	−	0.584986i	0.600794	−	0.799404i	$-0.294851\pi$
$79$	−3.34150	−	5.19947i	−0.375948	−	0.584986i	−0.976742	+	0.214417i	$0.931215\pi$
$80$	2.04332	−	0.908211i	0.228450	−	0.101541i
$81$	−3.16897	+	8.42364i	−0.352107	+	0.935960i
$82$	−3.17708	−	4.94364i	−0.350850	−	0.545933i
$83$	−10.3554	−	8.97304i	−1.13666	−	0.984919i	−0.136674	−	0.990616i	$-0.543641\pi$
$83$	−10.3554	−	8.97304i	−1.13666	−	0.984919i	−0.999984	+	0.00569681i	$0.998187\pi$
$84$	−1.92707	−	8.18077i	−0.210261	−	0.892596i
$85$	−13.2999	−	4.05224i	−1.44258	−	0.439527i
$86$	0.0773497	−	0.0227119i	0.00834083	−	0.00244909i
$87$	−2.21159	+	11.0775i	−0.237107	+	1.18764i
$88$	−3.20267	−	0.940389i	−0.341406	−	0.100246i
$89$	−2.16744	−	4.74603i	−0.229748	−	0.503078i	0.759288	−	0.650755i	$-0.225548\pi$
$89$	−2.16744	−	4.74603i	−0.229748	−	0.503078i	−0.989036	+	0.147677i	$0.952820\pi$
$90$	−0.794112	+	6.66103i	−0.0837067	+	0.702135i
$91$			5.93065i			0.621701i
$92$	3.36288	+	3.41921i	0.350605	+	0.356478i
$93$	−7.21296	+	5.59504i	−0.747949	+	0.580179i
$94$	−0.635982	+	4.42335i	−0.0655965	+	0.456234i
$95$	−3.44285	−	4.05569i	−0.353229	−	0.416105i
$96$	−1.61223	+	0.633022i	−0.164547	+	0.0646075i
$97$	4.90317	+	5.65856i	0.497841	+	0.574539i	0.947944	−	0.318437i	$-0.103158\pi$
$97$	4.90317	+	5.65856i	0.497841	+	0.574539i	−0.450103	+	0.892977i	$0.648613\pi$
$98$	−15.8760	+	4.66161i	−1.60372	+	0.470894i
$99$	7.33855	−	6.81312i	0.737552	−	0.684744i
$100$	0.611003	+	4.96253i	0.0611003	+	0.496253i
$101$	12.7588	+	11.0556i	1.26955	+	1.10007i	0.990167	+	0.139893i	$0.0446760\pi$
$101$	12.7588	+	11.0556i	1.26955	+	1.10007i	0.279385	+	0.960179i	$0.409869\pi$
$102$	10.1537	+	3.59006i	1.00536	+	0.355469i
$103$	−2.50854	−	17.4473i	−0.247174	−	1.71913i	−0.614394	−	0.788999i	$-0.710600\pi$
$103$	−2.50854	−	17.4473i	−0.247174	−	1.71913i	0.367220	−	0.930134i	$-0.380310\pi$
$104$	1.20976	−	0.173937i	0.118627	−	0.0170559i
$105$	18.7545	+	1.20950i	1.83025	+	0.118035i
$106$	−8.15927	−	7.07005i	−0.792498	−	0.686704i
$107$	−4.12405	−	1.88339i	−0.398687	−	0.182074i	0.205974	−	0.978558i	$-0.433964\pi$
$107$	−4.12405	−	1.88339i	−0.398687	−	0.182074i	−0.604660	+	0.796483i	$0.706691\pi$
$108$	0.842030	−	5.12747i	0.0810244	−	0.493391i
$109$	4.14943	+	14.1317i	0.397443	+	1.35357i	0.878861	+	0.477077i	$0.158304\pi$
$109$	4.14943	+	14.1317i	0.397443	+	1.35357i	−0.481418	+	0.876491i	$0.659878\pi$
$110$	4.09869	−	6.23762i	0.390795	−	0.594733i
$111$	−1.35237	+	0.530993i	−0.128362	+	0.0503996i
$112$	2.01578	+	4.41394i	0.190473	+	0.417078i
$113$	5.57471	+	0.801522i	0.524425	+	0.0754009i	0.399443	−	0.916758i	$-0.369204\pi$
$113$	5.57471	+	0.801522i	0.524425	+	0.0754009i	0.124982	+	0.992159i	$0.460113\pi$
$114$	2.52570	+	3.25606i	0.236554	+	0.304958i
$115$	−9.50528	+	4.96484i	−0.886372	+	0.462974i
$116$		−	6.52184i		−	0.605537i
$117$	−1.40793	+	3.38551i	−0.130163	+	0.312991i
$118$	−4.22749	+	1.93063i	−0.389172	+	0.177729i
$119$	8.50038	−	28.9496i	0.779229	−	2.65381i
$120$	−0.303322	−	3.86109i	−0.0276894	−	0.352467i
$121$	−0.135698	+	0.0398446i	−0.0123362	+	0.00362224i
$122$	5.92790	−	9.22399i	0.536687	−	0.835101i
$123$	−9.90726	+	2.33377i	−0.893307	+	0.210429i
$124$	3.45138	−	3.98310i	0.309943	−	0.357693i
$125$	−11.0130	−	1.92720i	−0.985032	−	0.172374i
$126$	−14.4717	−	1.57653i	−1.28924	−	0.140449i
$127$	17.5969	−	2.53005i	1.56147	−	0.224506i	0.693255	−	0.720692i	$-0.256176\pi$
$127$	17.5969	−	2.53005i	1.56147	−	0.224506i	0.868216	+	0.496186i	$0.165267\pi$
$128$	0.841254	−	0.540641i	0.0743570	−	0.0477863i
$129$	0.00757195	−	0.139424i	0.000666673	−	0.0122756i
$130$	−0.416362	+	2.70102i	−0.0365173	+	0.236895i
$131$	−4.82999	+	7.51561i	−0.421998	+	0.656642i	−0.985540	−	0.169446i	$-0.945802\pi$
$131$	−4.82999	+	7.51561i	−0.421998	+	0.656642i	0.563541	+	0.826088i	$0.309439\pi$
$132$	−3.38479	+	4.68694i	−0.294609	+	0.407946i
$133$	8.72491	−	7.56018i	0.756545	−	0.655550i
$134$	2.54154	+	0.746262i	0.219555	+	0.0644672i
$135$	10.4189	+	5.14272i	0.896712	+	0.442615i
$136$	−6.15457	−	0.884894i	−0.527750	−	0.0758790i
$137$		−	11.0512i		−	0.944166i	−0.881554	−	0.472083i	$-0.843502\pi$
$137$		−	11.0512i		−	0.944166i	0.881554	−	0.472083i	$-0.156498\pi$
$138$	7.52518	−	3.51735i	0.640585	−	0.299417i
$139$	3.22829			0.273820			0.136910	−	0.990583i	$-0.456283\pi$
$139$	3.22829			0.273820			0.136910	+	0.990583i	$0.456283\pi$
$140$	−10.7551	+	1.43512i	−0.908969	+	0.121290i
$141$	6.85605	+	3.59250i	0.577384	+	0.302543i
$142$	2.39735	−	8.16461i	0.201181	−	0.685159i
$143$	3.08312	−	2.67154i	0.257823	−	0.223405i
$144$	0.102846	+	2.99824i	0.00857049	+	0.249853i
$145$	13.9501	+	4.25034i	1.15850	+	0.352972i
$146$	−3.03161	−	1.38449i	−0.250898	−	0.114581i
$147$	−1.55414	+	28.6167i	−0.128183	+	2.36027i
$148$	0.705662	−	0.453501i	0.0580050	−	0.0372776i
$149$	−1.45183	−	10.0977i	−0.118939	−	0.827238i	−0.958728	−	0.284325i	$-0.908230\pi$
$149$	−1.45183	−	10.0977i	−0.118939	−	0.827238i	0.839789	−	0.542913i	$-0.182679\pi$
$150$	8.45650	+	1.86750i	0.690470	+	0.152481i
$151$	−7.84078	+	5.03896i	−0.638073	+	0.410065i	−0.819291	−	0.573378i	$-0.805633\pi$
$151$	−7.84078	+	5.03896i	−0.638073	+	0.410065i	0.181217	+	0.983443i	$0.441996\pi$
$152$	−1.79804	−	1.55801i	−0.145841	−	0.126372i
$153$	11.7250	−	14.5079i	0.947912	−	1.17290i
$154$	13.6257	+	8.75669i	1.09799	+	0.705634i
$155$	6.27052	+	9.97828i	0.503660	+	0.801475i
$156$	0.414454	−	2.07594i	0.0331829	−	0.166208i
$157$	10.2815	+	3.01891i	0.820549	+	0.240935i	0.664952	−	0.746886i	$-0.268452\pi$
$157$	10.2815	+	3.01891i	0.820549	+	0.240935i	0.155597	+	0.987821i	$0.450270\pi$
$158$	5.62209	−	2.56752i	0.447270	−	0.204261i
$159$	−16.2563	+	9.24185i	−1.28921	+	0.732926i
$160$	0.608172	+	2.15177i	0.0480802	+	0.170113i
$161$	−10.9828	−	20.5168i	−0.865568	−	1.61695i
$162$	−7.88691	−	4.33552i	−0.619654	−	0.340631i
$163$	−14.9453	−	2.14881i	−1.17061	−	0.168308i	−0.470536	−	0.882381i	$-0.655939\pi$
$163$	−14.9453	−	2.14881i	−1.17061	−	0.168308i	−0.700071	+	0.714073i	$0.746848\pi$
$164$	5.34546	−	2.44119i	0.417411	−	0.190625i
$165$	−7.81942	−	10.2946i	−0.608741	−	0.801431i
$166$	10.3554	−	8.97304i	0.803738	−	0.696443i
$167$	8.63720	−	2.53611i	0.668367	−	0.196250i	0.0700912	−	0.997541i	$-0.477671\pi$
$167$	8.63720	−	2.53611i	0.668367	−	0.196250i	0.598276	+	0.801290i	$0.295853\pi$
$168$	8.37176	−	0.743214i	0.645895	−	0.0573402i
$169$	4.77986	−	10.4664i	0.367682	−	0.805110i
$170$	5.90377	−	12.5879i	0.452798	−	0.965445i
$171$	6.77538	−	2.24445i	0.518126	−	0.171637i
$172$	0.0114727	+	0.0797946i	0.000874788	+	0.00608428i
$173$	−1.70696	−	11.8722i	−0.129778	−	0.902625i	−0.945834	−	0.324652i	$-0.894753\pi$
$173$	−1.70696	−	11.8722i	−0.129778	−	0.902625i	0.816056	−	0.577973i	$-0.196156\pi$
$174$	−10.6500	−	3.76558i	−0.807378	−	0.285468i
$175$	3.93947	−	23.9403i	0.297796	−	1.80971i
$176$	1.38660	−	3.03624i	0.104519	−	0.228865i
$177$	0.711819	+	8.01812i	0.0535036	+	0.602679i
$178$	5.00618	−	1.46995i	0.375229	−	0.110177i
$179$	−10.7953	+	9.35422i	−0.806882	+	0.699167i	−0.957186	−	0.289473i	$-0.906520\pi$
$179$	−10.7953	+	9.35422i	−0.806882	+	0.699167i	0.150304	+	0.988640i	$0.451975\pi$
$180$	−6.48022	−	1.73399i	−0.483007	−	0.129244i
$181$	−2.43796	+	1.11338i	−0.181212	+	0.0827569i	−0.503955	−	0.863730i	$-0.668122\pi$
$181$	−2.43796	+	1.11338i	−0.181212	+	0.0827569i	0.322743	+	0.946487i	$0.395395\pi$
$182$	−5.87029	−	0.844020i	−0.435135	−	0.0625629i
$183$	−11.6400	−	15.0059i	−0.860451	−	1.10927i
$184$	−3.86300	+	2.84205i	−0.284784	+	0.209519i
$185$	0.510148	+	1.80495i	0.0375068	+	0.132703i
$186$	−4.51158	−	7.93580i	−0.330805	−	0.581881i
$187$	−18.8789	+	8.62171i	−1.38056	+	0.630482i
$188$	−4.28782	−	1.25902i	−0.312721	−	0.0918232i
$189$	−10.9301	+	22.7218i	−0.795049	+	1.65277i
$190$	4.50438	−	2.83062i	0.326782	−	0.205355i
$191$	20.2556	+	13.0175i	1.46564	+	0.941911i	0.998327	+	0.0578200i	$0.0184150\pi$
$191$	20.2556	+	13.0175i	1.46564	+	0.941911i	0.467315	+	0.884091i	$0.345221\pi$
$192$	−0.397135	−	1.68591i	−0.0286607	−	0.121670i
$193$	−17.2773	−	14.9708i	−1.24364	−	1.07762i	−0.994011	−	0.109284i	$-0.965144\pi$
$193$	−17.2773	−	14.9708i	−1.24364	−	1.07762i	−0.249634	−	0.968340i	$-0.580310\pi$
$194$	−6.29875	+	4.04796i	−0.452224	+	0.290627i
$195$	4.17032	+	2.23942i	0.298643	+	0.160368i
$196$	−2.35477	−	16.3778i	−0.168198	−	1.16984i
$197$	2.03675	−	1.30894i	0.145112	−	0.0932579i	−0.466070	−	0.884748i	$-0.654331\pi$
$197$	2.03675	−	1.30894i	0.145112	−	0.0932579i	0.611182	+	0.791490i	$0.290694\pi$
$198$	5.69939	+	8.23346i	0.405038	+	0.585126i
$199$	−9.03682	−	4.12698i	−0.640603	−	0.292554i	0.0685079	−	0.997651i	$-0.478176\pi$
$199$	−9.03682	−	4.12698i	−0.640603	−	0.292554i	−0.709111	+	0.705097i	$0.750903\pi$
$200$	−4.99897	−	0.101458i	−0.353481	−	0.00717414i
$201$	2.68606	−	3.71941i	0.189460	−	0.262347i
$202$	−12.7588	+	11.0556i	−0.897708	+	0.777869i
$203$	−8.91595	+	30.3649i	−0.625777	+	2.13120i
$204$	−4.99854	+	9.53939i	−0.349968	+	0.667891i
$205$	1.73799	+	13.0248i	0.121387	+	0.909694i
$206$	17.6267			1.22811
$207$	−1.39889	−	14.3193i	−0.0972293	−	0.995262i
$208$			1.22220i			0.0847443i
$209$	−7.86049	−	1.13017i	−0.543721	−	0.0781753i
$210$	−3.86623	+	18.3915i	−0.266795	+	1.26913i
$211$	−11.1065	−	3.26116i	−0.764603	−	0.224508i	−0.123898	−	0.992295i	$-0.539540\pi$
$211$	−11.1065	−	3.26116i	−0.764603	−	0.224508i	−0.640705	+	0.767787i	$0.721358\pi$
$212$	8.15927	−	7.07005i	0.560381	−	0.485573i
$213$	−11.9485	−	8.62890i	−0.818697	−	0.591243i
$214$	2.45113	−	3.81404i	0.167556	−	0.260722i
$215$	−0.178157	−	0.0274628i	−0.0121502	−	0.00187295i
$216$	4.95545	+	1.56317i	0.337176	+	0.106361i
$217$	−21.5145	+	13.8265i	−1.46050	+	0.938605i
$218$	−14.5784	+	2.09605i	−0.987371	+	0.141962i
$219$	−4.01124	+	4.15119i	−0.271054	+	0.280511i
$220$	5.59082	+	4.94468i	0.376933	+	0.333370i
$221$	4.97659	−	5.74329i	0.334762	−	0.386335i
$222$	−0.333125	−	1.41418i	−0.0223579	−	0.0949133i
$223$	0.894659	−	1.39212i	0.0599108	−	0.0932231i	−0.810006	−	0.586422i	$-0.800536\pi$
$223$	0.894659	−	1.39212i	0.0599108	−	0.0932231i	0.869917	+	0.493199i	$0.164172\pi$
$224$	−4.65589	+	1.36709i	−0.311085	+	0.0913427i
$225$	7.93221	−	12.7311i	0.528814	−	0.848738i
$226$	−1.58673	+	5.40390i	−0.105548	+	0.359462i
$227$	−11.5296	+	5.26541i	−0.765250	+	0.349478i	−0.759501	−	0.650506i	$-0.774557\pi$
$227$	−11.5296	+	5.26541i	−0.765250	+	0.349478i	−0.00574819	+	0.999983i	$0.501830\pi$
$228$	−3.58236	+	2.03661i	−0.237248	+	0.134878i
$229$		−	16.1083i		−	1.06447i	−0.846597	−	0.532234i	$-0.821353\pi$
$229$		−	16.1083i		−	1.06447i	0.846597	−	0.532234i	$-0.178647\pi$
$230$	−3.56156	−	10.1151i	−0.234842	−	0.666970i
$231$	22.1667	−	17.1946i	1.45846	−	1.13132i
$232$	6.45546	+	0.928154i	0.423821	+	0.0609363i
$233$	−2.35607	−	5.15907i	−0.154351	−	0.337982i	0.816621	−	0.577174i	$-0.195845\pi$
$233$	−2.35607	−	5.15907i	−0.154351	−	0.337982i	−0.970972	+	0.239192i	$0.923117\pi$
$234$	−3.15068	−	1.87540i	−0.205967	−	0.122599i
$235$	5.48743	−	8.35108i	0.357961	−	0.544764i
$236$	−1.30934	−	4.45922i	−0.0852310	−	0.290270i
$237$	−0.946641	−	10.6632i	−0.0614909	−	0.692650i
$238$	27.4453	+	12.5338i	1.77901	+	0.812447i
$239$	5.58674	+	4.84094i	0.361376	+	0.313134i	0.816557	−	0.577265i	$-0.195880\pi$
$239$	5.58674	+	4.84094i	0.361376	+	0.313134i	−0.455181	+	0.890399i	$0.650425\pi$
$240$	3.86495	+	0.249255i	0.249482	+	0.0160894i
$241$	10.2681	−	1.47633i	0.661425	−	0.0950986i	0.196576	−	0.980489i	$-0.437018\pi$
$241$	10.2681	−	1.47633i	0.661425	−	0.0950986i	0.464849	+	0.885390i	$0.346109\pi$
$242$	−0.0201272	−	0.139988i	−0.00129382	−	0.00899874i
$243$	−11.6336	+	10.3759i	−0.746294	+	0.665617i
$244$	8.28647	+	7.18027i	0.530487	+	0.459670i
$245$	36.5666	+	5.63674i	2.33615	+	0.360118i
$246$	−0.900063	−	10.1385i	−0.0573859	−	0.646410i
$247$	2.79001	−	0.819221i	0.177524	−	0.0521258i
$248$	3.45138	+	3.98310i	0.219163	+	0.252927i
$249$	−8.67380	−	22.0911i	−0.549680	−	1.39997i
$250$	3.47489	−	10.6266i	0.219772	−	0.672087i
$251$	0.398058	−	2.76855i	0.0251252	−	0.174749i	−0.973395	−	0.229134i	$-0.926411\pi$
$251$	0.398058	−	2.76855i	0.0251252	−	0.174749i	0.998520	+	0.0543845i	$0.0173197\pi$
$252$	3.62003	−	14.1001i	0.228040	−	0.888220i
$253$	−5.71856	+	14.9516i	−0.359523	+	0.940000i
$254$			17.7778i			1.11548i
$255$	−17.1471	−	16.9087i	−1.07379	−	1.05887i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	22.0394	+	6.47135i	1.37478	+	0.403672i	0.883949	−	0.467583i	$-0.154875\pi$
$257$	22.0394	+	6.47135i	1.37478	+	0.403672i	0.490831	+	0.871255i	$0.336693\pi$
$258$	0.136927	+	0.0273370i	0.00852472	+	0.00170193i
$259$	−3.90546	+	1.14675i	−0.242673	+	0.0712553i
$260$	−2.61427	−	0.796519i	−0.162130	−	0.0493980i
$261$	−12.2982	+	15.2172i	−0.761242	+	0.941920i
$262$	−6.75174	−	5.85041i	−0.417124	−	0.361440i
$263$	6.44216	+	10.0242i	0.397241	+	0.618119i	0.981046	−	0.193775i	$-0.0620732\pi$
$263$	6.44216	+	10.0242i	0.397241	+	0.618119i	−0.583805	+	0.811894i	$0.698437\pi$
$264$	−4.15753	−	4.01736i	−0.255878	−	0.247252i
$265$	9.80528	+	22.0602i	0.602334	+	1.35515i
$266$	6.24154	+	9.71203i	0.382693	+	0.595482i
$267$	0.490067	−	9.02372i	0.0299916	−	0.552243i
$268$	−1.10036	+	2.40946i	−0.0672155	+	0.147181i
$269$	−3.21489	+	5.00247i	−0.196016	+	0.305006i	−0.925323	−	0.379180i	$-0.876206\pi$
$269$	−3.21489	+	5.00247i	−0.196016	+	0.305006i	0.729307	+	0.684186i	$0.239842\pi$
$270$	−6.57313	+	9.58092i	−0.400028	+	0.583076i
$271$	2.07086	+	2.38989i	0.125796	+	0.145176i	0.815153	−	0.579245i	$-0.196653\pi$
$271$	2.07086	+	2.38989i	0.125796	+	0.145176i	−0.689358	+	0.724421i	$0.742107\pi$
$272$	1.75177	−	5.96599i	0.106217	−	0.361741i
$273$	−4.76765	+	9.09876i	−0.288552	+	0.550682i
$274$	10.9387	+	1.57275i	0.660830	+	0.0950131i
$275$	−14.2202	+	8.73621i	−0.857511	+	0.526813i
$276$	2.41060	+	7.94915i	0.145101	+	0.478483i
$277$		−	32.3648i		−	1.94462i	−0.233705	−	0.972308i	$-0.575085\pi$
$277$		−	32.3648i		−	1.94462i	0.233705	−	0.972308i	$-0.424915\pi$
$278$	−0.459434	+	3.19543i	−0.0275550	+	0.191649i
$279$	−15.5639	+	2.78537i	−0.931788	+	0.166756i
$280$	0.110091	−	10.8498i	0.00657921	−	0.648402i
$281$	3.09085	+	3.56703i	0.184385	+	0.212791i	0.840415	−	0.541943i	$-0.182311\pi$
$281$	3.09085	+	3.56703i	0.184385	+	0.212791i	−0.656031	+	0.754734i	$0.727766\pi$
$282$	−4.53165	+	6.27500i	−0.269856	+	0.373671i
$283$	−9.86425	−	6.33937i	−0.586369	−	0.376837i	0.213561	−	0.976930i	$-0.431494\pi$
$283$	−9.86425	−	6.33937i	−0.586369	−	0.376837i	−0.799930	+	0.600093i	$0.795130\pi$
$284$	7.74033	+	3.53489i	0.459304	+	0.209757i
$285$	−2.02162	−	8.98991i	−0.119751	−	0.532516i
$286$	2.20557	+	3.43194i	0.130418	+	0.202935i
$287$	−28.2252	+	4.05817i	−1.66608	+	0.239546i
$288$	−2.98236	−	0.324895i	−0.175737	−	0.0191446i
$289$	−18.2230	+	11.7112i	−1.07194	+	0.688896i
$290$	−6.19239	+	13.2033i	−0.363630	+	0.775322i
$291$	2.97348	+	12.6230i	0.174309	+	0.739971i
$292$	1.80184	−	2.80372i	0.105445	−	0.164075i
$293$	−0.449712	−	1.53158i	−0.0262725	−	0.0894758i	0.945313	−	0.326164i	$-0.105756\pi$
$293$	−0.449712	−	1.53158i	−0.0262725	−	0.0894758i	−0.971586	+	0.236688i	$0.923938\pi$
$294$	−28.1043	−	5.61091i	−1.63907	−	0.327235i
$295$	10.3915	+	0.105441i	0.605018	+	0.00613900i
$296$	0.348459	+	0.763019i	0.0202538	+	0.0443496i
$297$	16.7358	−	4.55317i	0.971110	−	0.264202i
$298$	10.2016			0.590961
$299$	−0.369581	−	5.84980i	−0.0213734	−	0.338303i
$300$	−3.05198	+	8.10465i	−0.176206	+	0.467922i
$301$	0.0556708	−	0.387199i	0.00320881	−	0.0223178i
$302$	−3.87181	−	8.47809i	−0.222798	−	0.487859i
$303$	10.6869	+	27.2182i	0.613947	+	1.56365i
$304$	1.79804	−	1.55801i	0.103125	−	0.0893582i
$305$	−20.7589	+	13.0452i	−1.18865	+	0.746967i
$306$	12.6916	+	13.6704i	0.725531	+	0.781483i
$307$	0.772740	+	0.352899i	0.0441026	+	0.0201410i	0.437344	−	0.899294i	$-0.355919\pi$
$307$	0.772740	+	0.352899i	0.0441026	+	0.0201410i	−0.393242	+	0.919435i	$0.628646\pi$
$308$	−10.6067	+	12.2408i	−0.604372	+	0.697483i
$309$	10.1773	−	28.7841i	0.578966	−	1.63747i
$310$	−10.7691	+	4.78663i	−0.611644	+	0.271863i
$311$	−14.6416	+	2.10514i	−0.830248	+	0.119372i	−0.544318	−	0.838879i	$-0.683211\pi$
$311$	−14.6416	+	2.10514i	−0.830248	+	0.119372i	−0.285930	+	0.958251i	$0.592302\pi$
$312$	1.99583	+	0.705673i	0.112992	+	0.0399508i
$313$	21.6863	−	25.0273i	1.22578	−	1.41463i	0.346686	−	0.937981i	$-0.387307\pi$
$313$	21.6863	−	25.0273i	1.22578	−	1.41463i	0.879095	−	0.476646i	$-0.158148\pi$
$314$	−4.45138	+	9.74717i	−0.251206	+	0.550064i
$315$	27.8007	+	16.9323i	1.56639	+	0.954029i
$316$	1.74128	+	5.93026i	0.0979548	+	0.333603i
$317$	13.6650	+	15.7702i	0.767501	+	0.885744i	0.996141	−	0.0877675i	$-0.0279732\pi$
$317$	13.6650	+	15.7702i	0.767501	+	0.885744i	−0.228640	+	0.973511i	$0.573428\pi$
$318$	−6.83427	−	17.4061i	−0.383247	−	0.976083i
$319$	19.8019	−	9.04321i	1.10869	−	0.506323i
$320$	−2.21642	+	0.295752i	−0.123902	+	0.0165331i
$321$	−4.81302	−	6.20480i	−0.268637	−	0.346318i
$322$	21.8710	−	7.95119i	1.21882	−	0.443102i
$323$	−14.7932			−0.823118
$324$	5.41381	−	7.18962i	0.300767	−	0.399423i
$325$	3.40749	−	5.07280i	0.189014	−	0.281388i
$326$	4.25388	−	14.4874i	0.235601	−	0.802382i
$327$	−4.99443	+	25.0164i	−0.276192	+	1.38341i
$328$	1.65561	+	5.63847i	0.0914155	+	0.311333i
$329$	18.2424	+	11.7237i	1.00574	+	0.646347i
$330$	11.3026	−	6.27476i	0.622188	−	0.345414i
$331$	19.0804	−	22.0199i	1.04875	−	1.21032i	0.0716761	−	0.997428i	$-0.477165\pi$
$331$	19.0804	−	22.0199i	1.04875	−	1.21032i	0.977075	−	0.212895i	$-0.0682893\pi$
$332$	7.40798	+	11.5270i	0.406566	+	0.632628i
$333$	−2.50166	−	0.272529i	−0.137090	−	0.0149345i
$334$	1.28110	+	8.91022i	0.0700984	+	0.487545i
$335$	−4.43670	−	3.92394i	−0.242403	−	0.214388i
$336$	−0.455776	+	8.39231i	−0.0248646	+	0.457838i
$337$	−12.9115	+	28.2722i	−0.703333	+	1.54009i	0.132549	+	0.991176i	$0.457684\pi$
$337$	−12.9115	+	28.2722i	−0.703333	+	1.54009i	−0.835882	+	0.548909i	$0.815043\pi$
$338$	9.67966	+	6.22074i	0.526504	+	0.338364i
$339$	7.90833	+	5.71120i	0.429521	+	0.310190i
$340$	11.6195	+	7.63512i	0.630158	+	0.414072i
$341$	16.8793	+	4.95622i	0.914068	+	0.268395i
$342$	1.25736	+	7.02583i	0.0679905	+	0.379914i
$343$	−6.59238	+	45.8510i	−0.355955	+	2.47572i
$344$	−0.0806151			−0.00434648
$345$	−18.5742	−	0.0242850i	−0.999999	−	0.00130746i
$346$	11.9943			0.644815
$347$	−3.14886	+	21.9008i	−0.169040	+	1.17570i	0.711835	+	0.702347i	$0.247864\pi$
$347$	−3.14886	+	21.9008i	−0.169040	+	1.17570i	−0.880874	+	0.473350i	$0.843045\pi$
$348$	5.24291	−	10.0058i	0.281049	−	0.536365i
$349$	13.3853	+	3.93029i	0.716501	+	0.210384i	0.619608	−	0.784911i	$-0.287291\pi$
$349$	13.3853	+	3.93029i	0.716501	+	0.210384i	0.0968927	+	0.995295i	$0.469110\pi$
$350$	23.1359	+	7.30643i	1.23667	+	0.390545i
$351$	−4.88164	+	4.06219i	−0.260563	+	0.216824i
$352$	2.80800	+	1.80459i	0.149667	+	0.0961851i
$353$	10.1537	−	22.2336i	0.540429	−	1.18338i	−0.420680	−	0.907209i	$-0.638209\pi$
$353$	10.1537	−	22.2336i	0.540429	−	1.18338i	0.961110	−	0.276166i	$-0.0890641\pi$
$354$	−8.03781	−	0.436524i	−0.427205	−	0.0232010i
$355$	−12.6055	+	14.2528i	−0.669032	+	0.756458i
$356$	0.742531	+	5.16442i	0.0393541	+	0.273714i
$357$	36.3138	−	37.5808i	1.92193	−	1.98899i
$358$	−7.72267	−	12.0167i	−0.408156	−	0.635103i
$359$	14.6951	−	16.9591i	0.775579	−	0.895066i	−0.221202	−	0.975228i	$-0.570998\pi$
$359$	14.6951	−	16.9591i	0.775579	−	0.895066i	0.996782	+	0.0801615i	$0.0255436\pi$
$360$	2.63858	−	6.16749i	0.139065	−	0.325055i
$361$	11.2220	+	7.21195i	0.590632	+	0.379576i
$362$	−0.755089	−	2.57160i	−0.0396866	−	0.135160i
$363$	−0.240218	−	0.0479586i	−0.0126082	−	0.00251717i
$364$	1.67086	−	5.69042i	0.0875768	−	0.298259i
$365$	4.82285	+	5.68133i	0.252439	+	0.297374i
$366$	16.5097	−	9.38593i	0.862976	−	0.490610i
$367$	−18.1073			−0.945192			−0.472596	−	0.881279i	$-0.656683\pi$
$367$	−18.1073			−0.945192			−0.472596	+	0.881279i	$0.656683\pi$
$368$	−2.26336	−	4.22814i	−0.117986	−	0.220407i
$369$	−17.0757	−	4.38400i	−0.888928	−	0.228222i
$370$	−1.85918	+	0.248084i	−0.0966544	+	0.0128972i
$371$	−47.6540	+	21.7629i	−2.47407	+	1.12987i
$372$	8.49709	−	3.33628i	0.440554	−	0.172978i
$373$	12.3454	+	14.2473i	0.639219	+	0.737698i	0.979236	−	0.202721i	$-0.0649786\pi$
$373$	12.3454	+	14.2473i	0.639219	+	0.737698i	−0.340018	+	0.940419i	$0.610433\pi$
$374$	−5.84720	−	19.9137i	−0.302352	−	1.02972i
$375$	−15.3468	−	11.8100i	−0.792503	−	0.609868i
$376$	1.85642	−	4.06500i	0.0957376	−	0.209636i
$377$	−5.21988	+	6.02407i	−0.268838	+	0.310255i
$378$	−20.9350	−	14.0525i	−1.07678	−	0.722784i
$379$	13.8020	−	1.98442i	0.708959	−	0.101933i	0.221604	−	0.975137i	$-0.428871\pi$
$379$	13.8020	−	1.98442i	0.708959	−	0.101933i	0.487355	+	0.873204i	$0.337962\pi$
$380$	2.16077	+	4.86137i	0.110845	+	0.249383i
$381$	29.0309	+	10.2646i	1.48730	+	0.525869i
$382$	−15.7676	+	18.1968i	−0.806743	+	0.931031i
$383$	21.4044	+	9.77508i	1.09372	+	0.499483i	0.878820	−	0.477154i	$-0.158332\pi$
$383$	21.4044	+	9.77508i	1.09372	+	0.499483i	0.214896	+	0.976637i	$0.431059\pi$
$384$	1.72527	−	0.153163i	0.0880421	−	0.00781605i
$385$	−19.2704	−	30.6650i	−0.982111	−	1.56283i
$386$	17.2773	−	14.9708i	0.879390	−	0.761996i
$387$	0.123700	−	0.207816i	0.00628802	−	0.0105639i
$388$	−3.11035	−	6.81073i	−0.157904	−	0.345762i
$389$	−3.01858	+	20.9947i	−0.153048	+	1.06447i	0.758024	+	0.652227i	$0.226165\pi$
$389$	−3.01858	+	20.9947i	−0.153048	+	1.06447i	−0.911072	+	0.412247i	$0.864744\pi$
$390$	−2.81013	+	3.80917i	−0.142296	+	0.192885i
$391$	−6.58044	+	29.0847i	−0.332787	+	1.47088i
$392$	16.5462			0.835710
$393$	−13.4519	+	7.64756i	−0.678561	+	0.385768i
$394$	1.00575	+	2.20230i	0.0506692	+	0.110950i
$395$	−13.8196	−	0.140225i	−0.695339	−	0.00705547i
$396$	−8.96076	+	4.46963i	−0.450295	+	0.224608i
$397$	0.194218	+	0.661447i	0.00974755	+	0.0331971i	0.964223	−	0.265092i	$-0.0854023\pi$
$397$	0.194218	+	0.661447i	0.00974755	+	0.0331971i	−0.954476	+	0.298289i	$0.903584\pi$
$398$	5.37104	−	8.35750i	0.269226	−	0.418924i
$399$	19.4633	−	4.58480i	0.974384	−	0.229527i
$400$	0.811853	−	4.93365i	0.0405926	−	0.246682i
$401$	−10.8465	+	6.97064i	−0.541650	+	0.348097i	−0.782684	−	0.622419i	$-0.786150\pi$
$401$	−10.8465	+	6.97064i	−0.541650	+	0.348097i	0.241034	+	0.970517i	$0.422513\pi$
$402$	3.29928	+	3.18805i	0.164553	+	0.159005i
$403$	−6.37591	+	0.916718i	−0.317607	+	0.0456650i
$404$	−9.12729	−	14.2023i	−0.454100	−	0.706593i
$405$	11.8503	+	16.2656i	0.588845	+	0.808246i
$406$	−28.7870	−	13.1466i	−1.42867	−	0.652454i
$407$	2.35541	+	1.51373i	0.116753	+	0.0750329i
$408$	−8.73092	−	6.30526i	−0.432245	−	0.312157i
$409$	19.9229	+	22.9923i	0.985125	+	1.13689i	0.990584	+	0.136909i	$0.0437169\pi$
$409$	19.9229	+	22.9923i	0.985125	+	1.13689i	−0.00545882	+	0.999985i	$0.501738\pi$
$410$	−13.1396	−	0.133325i	−0.648919	−	0.00658445i
$411$	8.88404	−	16.9546i	0.438218	−	0.836310i
$412$	−2.50854	+	17.4473i	−0.123587	+	0.859567i
$413$			22.5516i			1.10969i
$414$	14.3727	+	0.653205i	0.706378	+	0.0321033i
$415$	−29.4841	+	8.33330i	−1.44732	+	0.409066i
$416$	−1.20976	−	0.173937i	−0.0593133	−	0.00852797i
$417$	4.95282	+	2.59522i	0.242541	+	0.127089i
$418$	2.23733	−	7.61964i	0.109431	−	0.372689i
$419$	11.9438	+	13.7838i	0.583491	+	0.673384i	0.968352	−	0.249590i	$-0.0802960\pi$
$419$	11.9438	+	13.7838i	0.583491	+	0.673384i	−0.384861	+	0.922975i	$0.625751\pi$
$420$	−17.6540	−	6.44425i	−0.861429	−	0.314447i
$421$	−7.44535	+	11.5852i	−0.362864	+	0.564627i	−0.973901	−	0.226975i	$-0.927116\pi$
$421$	−7.44535	+	11.5852i	−0.362864	+	0.564627i	0.611037	+	0.791602i	$0.290753\pi$
$422$	4.80859	−	10.5293i	0.234078	−	0.512560i
$423$	7.63049	+	11.0232i	0.371007	+	0.535964i
$424$	5.83690	+	9.08239i	0.283465	+	0.441080i
$425$	−23.9040	+	19.8782i	−1.15951	+	0.964234i
$426$	10.2415	−	10.5988i	0.496203	−	0.513516i
$427$	−28.7648	−	44.7589i	−1.39203	−	2.16603i
$428$	3.42638	+	2.96898i	0.165620	+	0.143511i
$429$	6.87775	−	1.62013i	0.332061	−	0.0782206i
$430$	0.0525377	−	0.172435i	0.00253359	−	0.00831555i
$431$	−15.1604	+	4.45149i	−0.730249	+	0.214421i	−0.625661	−	0.780095i	$-0.715171\pi$
$431$	−15.1604	+	4.45149i	−0.730249	+	0.214421i	−0.104588	+	0.994516i	$0.533352\pi$
$432$	−2.25250	+	4.68255i	−0.108373	+	0.225289i
$433$	−7.25996	−	2.13172i	−0.348892	−	0.102444i	0.102591	−	0.994724i	$-0.467287\pi$
$433$	−7.25996	−	2.13172i	−0.348892	−	0.102444i	−0.451483	+	0.892280i	$0.649105\pi$
$434$	−10.6240	−	23.2632i	−0.509966	−	1.11667i
$435$	17.9853	+	17.7354i	0.862331	+	0.850346i
$436$		−	14.7283i		−	0.705356i
$437$	−8.13483	+	8.00081i	−0.389142	+	0.382731i
$438$	−3.53808	−	4.56118i	−0.169056	−	0.217942i
$439$	−0.819397	+	5.69903i	−0.0391077	+	0.272000i	−0.999988	−	0.00496511i	$-0.998420\pi$
$439$	−0.819397	+	5.69903i	−0.0391077	+	0.272000i	0.960880	+	0.276965i	$0.0893286\pi$
$440$	−5.69001	+	4.83021i	−0.271260	+	0.230271i
$441$	−25.3893	+	42.6542i	−1.20902	+	2.03115i
$442$	4.97659	+	5.74329i	0.236712	+	0.273180i
$443$	5.18802	−	1.52334i	0.246490	−	0.0723760i	−0.156154	−	0.987733i	$-0.549910\pi$
$443$	5.18802	−	1.52334i	0.246490	−	0.0723760i	0.402644	+	0.915357i	$0.368091\pi$
$444$	1.44719	−	0.128476i	0.0686806	−	0.00609721i
$445$	−11.5305	−	1.77743i	−0.546600	−	0.0842584i
$446$	1.25062	+	1.08367i	0.0592188	+	0.0513134i
$447$	5.89018	−	16.6590i	0.278596	−	0.787943i
$448$	−0.690575	−	4.80305i	−0.0326266	−	0.226923i
$449$	−17.6544	+	2.53831i	−0.833160	+	0.119790i	−0.545677	−	0.837995i	$-0.683728\pi$
$449$	−17.6544	+	2.53831i	−0.833160	+	0.119790i	−0.287483	+	0.957786i	$0.592819\pi$
$450$	11.4726	+	9.66329i	0.540824	+	0.455532i
$451$	14.8241	+	12.8451i	0.698039	+	0.604854i
$452$	−5.12308	−	2.33963i	−0.240969	−	0.110047i
$453$	−16.0801	+	1.42753i	−0.755508	+	0.0670712i
$454$	−3.57098	−	12.1616i	−0.167594	−	0.570774i
$455$	11.0828	+	7.28245i	0.519571	+	0.341406i
$456$	−1.50606	−	3.83574i	−0.0705275	−	0.179625i
$457$	9.77133	+	21.3962i	0.457083	+	1.00087i	0.988143	+	0.153538i	$0.0490668\pi$
$457$	9.77133	+	21.3962i	0.457083	+	1.00087i	−0.531059	+	0.847335i	$0.678206\pi$
$458$	15.9444	+	2.29245i	0.745031	+	0.107119i
$459$	29.6514	−	12.8322i	1.38401	−	0.598955i
$460$	10.5190	−	2.08578i	0.490451	−	0.0972500i
$461$		−	1.49932i		−	0.0698304i	−0.999390	−	0.0349152i	$-0.988884\pi$
$461$		−	1.49932i		−	0.0698304i	0.999390	−	0.0349152i	$-0.0111161\pi$
$462$	13.8649	+	24.3881i	0.645053	+	1.13464i
$463$	1.31129	−	0.598848i	0.0609410	−	0.0278308i	−0.384711	−	0.923037i	$-0.625699\pi$
$463$	1.31129	−	0.598848i	0.0609410	−	0.0278308i	0.445652	+	0.895206i	$0.352972\pi$
$464$	−1.83741	+	6.25766i	−0.0852998	+	0.290504i
$465$	1.59863	+	20.3495i	0.0741346	+	0.943684i
$466$	5.44186	−	1.59787i	0.252089	−	0.0740201i
$467$	15.2039	−	23.6578i	0.703555	−	1.09475i	−0.287039	−	0.957919i	$-0.592671\pi$
$467$	15.2039	−	23.6578i	0.703555	−	1.09475i	0.990594	−	0.136834i	$-0.0436926\pi$
$468$	2.30470	−	2.85172i	0.106535	−	0.131821i
$469$	8.41713	−	9.71388i	0.388667	−	0.448545i
$470$	7.48513	+	6.62006i	0.345263	+	0.305361i
$471$	13.3468	+	12.8968i	0.614989	+	0.594255i
$472$	4.60017	−	0.661404i	0.211740	−	0.0304436i
$473$	−0.226367	+	0.145478i	−0.0104084	+	0.00668906i
$474$	10.6894	+	0.580528i	0.490980	+	0.0266646i
$475$	−11.8066	+	1.45367i	−0.541724	+	0.0666989i
$476$	−16.3121	+	25.3821i	−0.747665	+	1.16339i
$477$	−32.3697	+	1.11035i	−1.48211	+	0.0508395i
$478$	−5.58674	+	4.84094i	−0.255532	+	0.221419i
$479$	−28.1512	−	8.26594i	−1.28626	−	0.377680i	−0.434055	−	0.900886i	$-0.642918\pi$
$479$	−28.1512	−	8.26594i	−1.28626	−	0.377680i	−0.852206	+	0.523206i	$0.824736\pi$
$480$	−0.796759	+	3.79014i	−0.0363669	+	0.172996i
$481$	−1.01477	−	0.145902i	−0.0462696	−	0.00665257i
$482$			10.3737i			0.472508i
$483$	−0.356273	−	40.3059i	−0.0162110	−	1.83398i
$484$	0.141427			0.00642850
$485$	16.5951	−	2.21440i	0.753545	−	0.100551i
$486$	−8.61470	−	12.9918i	−0.390771	−	0.589320i
$487$	10.5266	−	35.8502i	0.477005	−	1.62453i	−0.272235	−	0.962231i	$-0.587763\pi$
$487$	10.5266	−	35.8502i	0.477005	−	1.62453i	0.749240	−	0.662298i	$-0.230419\pi$
$488$	−8.28647	+	7.18027i	−0.375111	+	0.325036i
$489$	−21.2015	−	15.3112i	−0.958767	−	0.692398i
$490$	−10.7833	+	35.3922i	−0.487141	+	1.59886i
$491$	−3.12892	−	1.42893i	−0.141206	−	0.0644867i	0.343559	−	0.939131i	$-0.388368\pi$
$491$	−3.12892	−	1.42893i	−0.141206	−	0.0644867i	−0.484765	+	0.874645i	$0.661095\pi$
$492$	10.1634	+	0.551964i	0.458203	+	0.0248845i
$493$	34.1144	−	21.9240i	1.53644	−	0.987407i
$494$	0.413823	+	2.87820i	0.0186188	+	0.129496i
$495$	−3.72068	−	22.0799i	−0.167232	−	0.992416i
$496$	−4.43374	+	2.84939i	−0.199081	+	0.127942i
$497$	−31.2056	−	27.0398i	−1.39976	−	1.21290i
$498$	23.1007	−	5.44162i	1.03517	−	0.243845i
$499$	−34.7028	−	22.3022i	−1.55351	−	0.998382i	−0.984364	−	0.176147i	$-0.943637\pi$
$499$	−34.7028	−	22.3022i	−1.55351	−	0.998382i	−0.569148	−	0.822235i	$-0.692727\pi$
$500$	10.0239	+	4.95185i	0.448284	+	0.221453i
$501$	15.2899	+	3.05257i	0.683103	+	0.136379i
$502$	2.68372	+	0.788012i	0.119780	+	0.0351707i
$503$	15.8125	−	7.22133i	0.705045	−	0.321983i	−0.0304282	−	0.999537i	$-0.509687\pi$
$503$	15.8125	−	7.22133i	0.705045	−	0.321983i	0.735473	+	0.677554i	$0.236960\pi$
$504$	13.4413	+	5.58983i	0.598725	+	0.248991i
$505$	36.3270	−	10.2674i	1.61653	−	0.456892i
$506$	−13.9856	−	7.78819i	−0.621736	−	0.346227i
$507$	15.7472	−	12.2150i	0.699357	−	0.542487i
$508$	−17.5969	−	2.53005i	−0.780736	−	0.112253i
$509$	0.466876	−	0.213215i	0.0206939	−	0.00945060i	−0.405041	−	0.914298i	$-0.632743\pi$
$509$	0.466876	−	0.213215i	0.0206939	−	0.00945060i	0.425735	+	0.904848i	$0.360016\pi$
$510$	19.1769	−	14.5662i	0.849168	−	0.645000i
$511$	−12.2221	+	10.5905i	−0.540674	+	0.468497i
$512$	−0.959493	+	0.281733i	−0.0424040	+	0.0124509i
$513$	12.1990	+	2.00332i	0.538601	+	0.0884486i
$514$	−9.54202	+	20.8941i	−0.420880	+	0.921599i
$515$	−35.6847	−	16.7363i	−1.57246	−	0.737490i
$516$	−0.0465455	+	0.131643i	−0.00204905	+	0.00579527i
$517$	−2.12283	−	14.7646i	−0.0933619	−	0.649346i
$518$	−0.579269	−	4.02891i	−0.0254516	−	0.177020i
$519$	6.92524	−	19.5864i	0.303984	−	0.859748i
$520$	1.16046	−	2.47430i	0.0508896	−	0.108505i
$521$	8.65873	−	18.9600i	0.379346	−	0.830652i	−0.619607	−	0.784912i	$-0.712708\pi$
$521$	8.65873	−	18.9600i	0.379346	−	0.830652i	0.998953	−	0.0457398i	$-0.0145645\pi$
$522$	−13.3121	−	14.3387i	−0.582653	−	0.627588i
$523$	−9.22426	+	2.70849i	−0.403349	+	0.118434i	−0.477113	−	0.878842i	$-0.658317\pi$
$523$	−9.22426	+	2.70849i	−0.403349	+	0.118434i	0.0737644	+	0.997276i	$0.476499\pi$
$524$	6.75174	−	5.85041i	0.294951	−	0.255576i
$525$	25.2895	−	33.5620i	1.10372	−	1.46477i
$526$	−10.8390	+	4.95000i	−0.472602	+	0.215830i
$527$	32.4370	+	4.66374i	1.41298	+	0.203156i
$528$	4.56815	−	3.54348i	0.198803	−	0.154210i
$529$	12.1116	+	19.5527i	0.526593	+	0.850117i
$530$	−23.2311	+	6.56598i	−1.00909	+	0.285208i
$531$	−5.35370	+	12.8736i	−0.232331	+	0.558665i
$532$	−10.5014	+	4.79584i	−0.455295	+	0.207926i
$533$	−6.89134	−	2.02348i	−0.298497	−	0.0876466i
$534$	8.86213	+	1.76929i	0.383502	+	0.0765646i
$535$	−8.58362	+	5.39408i	−0.371102	+	0.233207i
$536$	−2.22834	−	1.43207i	−0.0962496	−	0.0618559i
$537$	−24.0820	+	5.67278i	−1.03921	+	0.244799i
$538$	−4.49403	−	3.89410i	−0.193751	−	0.167886i
$539$	46.4618	−	29.8592i	2.00125	−	1.28613i
$540$	−8.54794	−	7.86973i	−0.367845	−	0.338659i
$541$	−1.91788	−	13.3391i	−0.0824561	−	0.573495i	−0.988605	−	0.150535i	$-0.951900\pi$
$541$	−1.91788	−	13.3391i	−0.0824561	−	0.573495i	0.906149	−	0.422959i	$-0.139009\pi$
$542$	−2.66028	+	1.70966i	−0.114269	+	0.0734362i
$543$	−4.63535	−	0.251740i	−0.198922	−	0.0108032i
$544$	5.65596	+	2.58299i	0.242497	+	0.110745i
$545$	31.5036	+	9.59855i	1.34947	+	0.411157i
$546$	−8.32764	−	6.01401i	−0.356390	−	0.257376i
$547$	−13.1168	+	11.3658i	−0.560834	+	0.485965i	−0.888530	−	0.458818i	$-0.848273\pi$
$547$	−13.1168	+	11.3658i	−0.560834	+	0.485965i	0.327697	+	0.944783i	$0.393728\pi$
$548$	−3.11348	+	10.6035i	−0.133001	+	0.452960i
$549$	−5.79470	−	32.3793i	−0.247312	−	1.38191i
$550$	−6.62355	−	15.3188i	−0.282429	−	0.653194i
$551$	15.5164			0.661023
$552$	−8.21130	+	1.25478i	−0.349496	+	0.0534071i
$553$		−	29.9911i		−	1.27535i
$554$	32.0354	+	4.60600i	1.36105	+	0.195690i
$555$	−0.668338	+	3.17925i	−0.0283694	+	0.134952i
$556$	−3.09752	−	0.909515i	−0.131364	−	0.0385720i
$557$	−1.24654	+	1.08014i	−0.0528178	+	0.0457669i	−0.680870	−	0.732405i	$-0.738398\pi$
$557$	−1.24654	+	1.08014i	−0.0528178	+	0.0457669i	0.628052	+	0.778171i	$0.283853\pi$
$558$	−0.542039	−	15.8019i	−0.0229463	−	0.668948i
$559$	0.0532681	−	0.0828868i	0.00225300	−	0.00350574i
$560$	10.7237	+	1.65306i	0.453161	+	0.0698547i
$561$	−35.8949	−	1.94941i	−1.51548	−	0.0823040i
$562$	−3.97060	+	2.55175i	−0.167489	+	0.107639i
$563$	10.1569	−	1.46034i	0.428061	−	0.0615458i	0.0750823	−	0.997177i	$-0.476078\pi$
$563$	10.1569	−	1.46034i	0.428061	−	0.0615458i	0.352978	+	0.935632i	$0.385169\pi$
$564$	−5.56621	−	5.37855i	−0.234380	−	0.226478i
$565$	8.34321	−	9.43345i	0.351001	−	0.396868i
$566$	7.67868	−	8.86166i	0.322759	−	0.372484i
$567$	−35.0350	+	26.0729i	−1.47133	+	1.09496i
$568$	−4.60047	+	7.15847i	−0.193032	+	0.300363i
$569$	−8.71612	+	2.55928i	−0.365399	+	0.107291i	−0.459277	−	0.888293i	$-0.651892\pi$
$569$	−8.71612	+	2.55928i	−0.365399	+	0.107291i	0.0938787	+	0.995584i	$0.470073\pi$
$570$	9.18612	−	0.721650i	0.384764	−	0.0302266i
$571$	−0.652046	+	2.22066i	−0.0272873	+	0.0929319i	−0.972011	−	0.234936i	$-0.924512\pi$
$571$	−0.652046	+	2.22066i	−0.0272873	+	0.0929319i	0.944724	+	0.327868i	$0.106330\pi$
$572$	−3.71089	+	1.69471i	−0.155160	+	0.0708592i
$573$	20.6112	+	36.2548i	0.861045	+	1.51456i
$574$		−	28.5155i		−	1.19021i
$575$	−2.39388	+	23.8594i	−0.0998315	+	0.995004i
$576$	0.746021	−	2.90576i	0.0310842	−	0.121073i
$577$	46.6498	+	6.70723i	1.94206	+	0.279226i	0.998629	−	0.0523524i	$-0.0166719\pi$
$577$	46.6498	+	6.70723i	1.94206	+	0.279226i	0.943428	+	0.331578i	$0.107581\pi$
$578$	−8.99862	−	19.7042i	−0.374293	−	0.819588i
$579$	−14.4716	−	36.8573i	−0.601418	−	1.53174i
$580$	−12.1876	−	8.00838i	−0.506063	−	0.332530i
$581$	−18.7322	−	63.7960i	−0.777142	−	2.64670i
$582$	−12.9177	+	1.14678i	−0.535454	+	0.0475356i
$583$	32.7800	+	14.9701i	1.35761	+	0.620000i
$584$	2.51875	+	2.18251i	0.104227	+	0.0903129i
$585$	4.59779	+	6.78822i	0.190095	+	0.280659i
$586$	1.57999	−	0.227168i	0.0652688	−	0.00938424i
$587$	−3.64962	−	25.3837i	−0.150636	−	1.04770i	−0.915157	−	0.403097i	$-0.867934\pi$
$587$	−3.64962	−	25.3837i	−0.150636	−	1.04770i	0.764521	−	0.644599i	$-0.222976\pi$
$588$	9.55345	−	27.0197i	0.393978	−	1.11427i
$589$	9.47641	+	8.21135i	0.390469	+	0.338343i
$590$	−1.58324	+	10.2708i	−0.0651808	+	0.422840i
$591$	4.17701	−	0.370820i	0.171819	−	0.0152535i
$592$	−0.804844	+	0.236323i	−0.0330789	+	0.00971283i
$593$	−0.557126	−	0.642958i	−0.0228784	−	0.0264031i	0.744195	−	0.667962i	$-0.232833\pi$
$593$	−0.557126	−	0.642958i	−0.0228784	−	0.0264031i	−0.767073	+	0.641559i	$0.778288\pi$
$594$	2.12507	+	17.2134i	0.0871929	+	0.706276i
$595$	−43.6614	−	51.4332i	−1.78994	−	2.10856i
$596$	−1.45183	+	10.0977i	−0.0594694	+	0.413619i
$597$	−10.5465	−	13.5963i	−0.431641	−	0.556458i
$598$	5.84285	+	0.466694i	0.238932	+	0.0190845i
$599$		−	0.0217945i		−	0.000890501i	−1.00000		0.000445250i	$-0.999858\pi$
$599$		−	0.0217945i		−	0.000890501i	1.00000		0.000445250i	$-0.000141728\pi$
$600$	−7.58782	−	4.17433i	−0.309771	−	0.170416i
$601$	6.82025	+	14.9343i	0.278204	+	0.609181i	0.996222	−	0.0868431i	$-0.0276779\pi$
$601$	6.82025	+	14.9343i	0.278204	+	0.609181i	−0.718018	+	0.696024i	$0.754951\pi$
$602$	0.375335	+	0.110208i	0.0152975	+	0.00449175i
$603$	7.11097	−	3.54696i	0.289581	−	0.144443i
$604$	8.94281	−	2.62585i	0.363878	−	0.106844i
$605$	−0.0921694	+	0.302511i	−0.00374722	+	0.0122988i
$606$	−28.4621	+	6.70457i	−1.15619	+	0.272354i
$607$	19.5482	+	16.9386i	0.793435	+	0.687516i	0.954098	−	0.299494i	$-0.0968178\pi$
$607$	19.5482	+	16.9386i	0.793435	+	0.687516i	−0.160663	+	0.987009i	$0.551363\pi$
$608$	1.28627	+	2.00147i	0.0521650	+	0.0811703i
$609$	−38.0892	+	39.4181i	−1.54345	+	1.59730i
$610$	−9.95815	−	22.4041i	−0.403194	−	0.907117i
$611$	2.95288	+	4.59476i	0.119461	+	0.185884i
$612$	−15.3374	+	10.6169i	−0.619979	+	0.429164i
$613$	−15.0218	+	32.8931i	−0.606724	+	1.32854i	0.318068	+	0.948068i	$0.396966\pi$
$613$	−15.0218	+	32.8931i	−0.606724	+	1.32854i	−0.924792	+	0.380472i	$0.875761\pi$
$614$	−0.459279	+	0.714652i	−0.0185350	+	0.0288410i
$615$	−7.80426	+	21.3798i	−0.314698	+	0.862116i
$616$	−10.6067	−	12.2408i	−0.427356	−	0.493195i
$617$	−5.79065	+	19.7211i	−0.233123	+	0.793943i	0.756961	+	0.653461i	$0.226683\pi$
$617$	−5.79065	+	19.7211i	−0.233123	+	0.793943i	−0.990083	+	0.140482i	$0.955135\pi$
$618$	27.0428	+	14.1701i	1.08782	+	0.570006i
$619$	−11.4223	−	1.64227i	−0.459099	−	0.0660085i	−0.0911146	−	0.995840i	$-0.529043\pi$
$619$	−11.4223	−	1.64227i	−0.459099	−	0.0660085i	−0.367985	+	0.929832i	$0.619952\pi$
$620$	−3.20531	−	11.3407i	−0.128728	−	0.455454i
$621$	9.36515	−	23.0932i	0.375811	−	0.926696i
$622$		−	14.7921i		−	0.593111i
$623$	3.60309	−	25.0600i	0.144355	−	1.00401i
$624$	−0.982526	+	1.87509i	−0.0393325	+	0.0750636i
$625$	−17.1246	+	18.2139i	−0.684986	+	0.728556i
$626$	21.6863	+	25.0273i	0.866758	+	1.00029i
$627$	−11.1510	−	8.05294i	−0.445326	−	0.321604i
$628$	−9.01446	−	5.79324i	−0.359716	−	0.231175i
$629$	4.74434	+	2.16667i	0.189169	+	0.0863908i
$630$	−20.7164	+	25.1080i	−0.825362	+	1.00032i
$631$	−1.42084	−	2.21088i	−0.0565629	−	0.0880136i	0.811820	−	0.583907i	$-0.198477\pi$
$631$	−1.42084	−	2.21088i	−0.0565629	−	0.0880136i	−0.868383	+	0.495894i	$0.834841\pi$
$632$	−6.11771	+	0.879594i	−0.243350	+	0.0349884i
$633$	−14.4178	−	13.9318i	−0.573058	−	0.553738i
$634$	−17.5544	+	11.2815i	−0.697175	+	0.448047i
$635$	16.8798	−	35.9907i	0.669855	−	1.42825i
$636$	18.2015	−	4.28757i	0.721736	−	0.170013i
$637$	−10.9333	+	17.0125i	−0.433191	+	0.674059i
$638$	6.13306	+	20.8873i	0.242810	+	0.826936i
$639$	−11.3945	−	22.8438i	−0.450759	−	0.903686i
$640$	0.0226878	−	2.23595i	0.000896813	−	0.0883838i
$641$	16.0864	+	35.2243i	0.635375	+	1.39128i	0.903791	+	0.427973i	$0.140772\pi$
$641$	16.0864	+	35.2243i	0.635375	+	1.39128i	−0.268417	+	0.963303i	$0.586500\pi$
$642$	6.82661	−	3.88100i	0.269425	−	0.153171i
$643$	26.9435			1.06255			0.531275	−	0.847200i	$-0.321713\pi$
$643$	26.9435			1.06255			0.531275	+	0.847200i	$0.321713\pi$
$644$	4.75769	+	22.7800i	0.187479	+	0.897657i
$645$	−0.251249	−	0.185353i	−0.00989292	−	0.00729829i
$646$	2.10530	−	14.6427i	0.0828318	−	0.576108i
$647$	−18.5997	−	40.7277i	−0.731230	−	1.60117i	−0.797464	−	0.603366i	$-0.793826\pi$
$647$	−18.5997	−	40.7277i	−0.731230	−	1.60117i	0.0662342	−	0.997804i	$-0.478902\pi$
$648$	6.34597	+	6.38190i	0.249293	+	0.250705i
$649$	11.7237	−	10.1587i	0.460196	−	0.398762i
$650$	4.53623	+	4.09474i	0.177925	+	0.160609i
$651$	−44.1225	+	3.91703i	−1.72930	+	0.153521i
$652$	13.7345	+	6.27235i	0.537886	+	0.245644i
$653$	6.13103	−	7.07558i	0.239926	−	0.276889i	−0.622998	−	0.782224i	$-0.714085\pi$
$653$	6.13103	−	7.07558i	0.239926	−	0.276889i	0.862923	+	0.505335i	$0.168631\pi$
$654$	−24.0510	−	8.50380i	−0.940469	−	0.332525i
$655$	8.11380	+	18.2547i	0.317032	+	0.713269i
$656$	−5.81670	+	0.836315i	−0.227104	+	0.0326526i
$657$	−9.49115	+	3.14409i	−0.370285	+	0.122662i
$658$	−14.2005	+	16.3883i	−0.553594	+	0.638881i
$659$	−12.1960	+	26.7055i	−0.475088	+	1.04030i	0.508697	+	0.860946i	$0.330127\pi$
$659$	−12.1960	+	26.7055i	−0.475088	+	1.04030i	−0.983785	+	0.179352i	$0.942600\pi$
$660$	4.60236	+	12.0805i	0.179147	+	0.470235i
$661$	1.95949	+	6.67340i	0.0762152	+	0.259565i	0.988783	−	0.149361i	$-0.0477216\pi$
$661$	1.95949	+	6.67340i	0.0762152	+	0.259565i	−0.912568	+	0.408926i	$0.865903\pi$
$662$	19.0804	+	22.0199i	0.741579	+	0.855828i
$663$	12.2521	−	4.81063i	0.475831	−	0.186829i
$664$	−12.4640	+	5.69211i	−0.483696	+	0.220897i
$665$	−3.41438	−	25.5880i	−0.132404	−	0.992258i
$666$	0.625779	−	2.43742i	0.0242484	−	0.0944480i
$667$	6.90214	−	30.5066i	0.267252	−	1.18122i
$668$	−9.00184			−0.348292
$669$	2.49170	−	1.41656i	0.0963348	−	0.0547673i
$670$	4.51540	−	3.83310i	0.174445	−	0.148086i
$671$	−10.3110	+	35.1159i	−0.398050	+	1.35563i
$672$	−8.24203	−	1.64549i	−0.317943	−	0.0634761i
$673$	−7.36965	−	25.0987i	−0.284079	−	0.967485i	−0.970665	−	0.240436i	$-0.922709\pi$
$673$	−7.36965	−	25.0987i	−0.284079	−	0.967485i	0.686586	−	0.727049i	$-0.259109\pi$
$674$	−26.1469	−	16.8036i	−1.00714	−	0.647251i
$675$	22.4040	−	13.1552i	0.862332	−	0.506343i
$676$	−7.53498	+	8.69583i	−0.289807	+	0.334455i
$677$	25.1682	+	39.1626i	0.967294	+	1.50514i	0.859608	+	0.510954i	$0.170708\pi$
$677$	25.1682	+	39.1626i	0.967294	+	1.50514i	0.107686	+	0.994185i	$0.465656\pi$
$678$	−6.77854	+	7.01505i	−0.260328	+	0.269411i
$679$	5.17057	+	35.9621i	0.198428	+	1.38010i
$680$	−9.21104	+	10.4147i	−0.353227	+	0.399385i
$681$	−21.9216	−	1.19053i	−0.840036	−	0.0456213i
$682$	−7.30796	+	16.0022i	−0.279836	+	0.612756i
$683$	11.6957	+	7.51640i	0.447525	+	0.287607i	0.744928	−	0.667145i	$-0.232484\pi$
$683$	11.6957	+	7.51640i	0.447525	+	0.287607i	−0.297403	+	0.954752i	$0.596120\pi$
$684$	−7.13326	+	0.244686i	−0.272747	+	0.00935580i
$685$	−20.6517	−	13.5701i	−0.789063	−	0.518487i
$686$	−44.4461	−	13.0506i	−1.69696	−	0.498273i
$687$	12.9495	−	24.7132i	0.494054	−	0.942869i
$688$	0.0114727	−	0.0797946i	0.000437394	−	0.00304214i
$689$	−13.1952			−0.502696
$690$	2.66742	−	18.3816i	0.101547	−	0.699777i
$691$	−48.1594			−1.83207			−0.916035	−	0.401099i	$-0.868628\pi$
$691$	−48.1594			−1.83207			−0.916035	+	0.401099i	$0.868628\pi$
$692$	−1.70696	+	11.8722i	−0.0648889	+	0.451312i
$693$	47.8307	−	8.55992i	1.81694	−	0.325165i
$694$	−21.2298	−	6.23362i	−0.805871	−	0.236625i
$695$	3.96413	−	6.03283i	0.150368	−	0.228838i
$696$	9.15776	+	6.61351i	0.347124	+	0.250684i
$697$	30.7388	+	19.7547i	1.16432	+	0.748261i
$698$	−5.79522	+	12.6898i	−0.219352	+	0.480315i
$699$	0.532717	−	9.80904i	0.0201492	−	0.371012i
$700$	−10.5246	+	21.8606i	−0.397794	+	0.826254i
$701$	−3.67381	−	25.5519i	−0.138758	−	0.965083i	−0.933613	−	0.358283i	$-0.883362\pi$
$701$	−3.67381	−	25.5519i	−0.138758	−	0.965083i	0.794855	−	0.606799i	$-0.207547\pi$
$702$	−3.32611	−	5.41006i	−0.125536	−	0.204190i
$703$	1.07895	+	1.67888i	0.0406933	+	0.0633200i
$704$	−2.18584	+	2.52260i	−0.0823821	+	0.0950740i
$705$	15.1322	−	8.40081i	0.569912	−	0.316393i
$706$	20.5623	+	13.2146i	0.773871	+	0.497337i
$707$	23.0797	+	78.6023i	0.868003	+	2.95615i
$708$	1.57598	−	7.89387i	0.0592290	−	0.296670i
$709$	−1.69608	+	5.77633i	−0.0636977	+	0.216934i	−0.985191	−	0.171459i	$-0.945152\pi$
$709$	−1.69608	+	5.77633i	−0.0636977	+	0.216934i	0.921493	+	0.388394i	$0.126970\pi$
$710$	−12.3137	−	14.5056i	−0.462126	−	0.544386i
$711$	7.11983	−	17.1204i	0.267015	−	0.642066i
$712$	−5.21752			−0.195535
$713$	20.3595	−	14.9787i	0.762471	−	0.560958i
$714$	32.0303	+	41.2925i	1.19870	+	1.54533i
$715$	−1.20654	−	9.04201i	−0.0451219	−	0.338152i
$716$	12.9934	−	5.93391i	0.485588	−	0.221761i
$717$	4.67950	+	11.9181i	0.174759	+	0.445090i
$718$	14.6951	+	16.9591i	0.548418	+	0.632908i
$719$	9.67608	+	32.9537i	0.360857	+	1.22897i	0.917339	+	0.398106i	$0.130332\pi$
$719$	9.67608	+	32.9537i	0.360857	+	1.22897i	−0.556482	+	0.830859i	$0.687849\pi$
$720$	5.72920	+	3.48944i	0.213515	+	0.130044i
$721$	35.5315	−	77.8032i	1.32326	−	2.89754i
$722$	−8.73560	+	10.0814i	−0.325105	+	0.375192i
$723$	16.9400	+	5.98955i	0.630006	+	0.222754i
$724$	2.65288	−	0.381427i	0.0985936	−	0.0141756i
$725$	25.0726	−	20.8500i	0.931174	−	0.774350i
$726$	0.0816571	−	0.230948i	0.00303058	−	0.00857128i
$727$	−1.34472	+	1.55190i	−0.0498731	+	0.0575566i	−0.780138	−	0.625607i	$-0.784851\pi$
$727$	−1.34472	+	1.55190i	−0.0498731	+	0.0575566i	0.730265	+	0.683164i	$0.239397\pi$
$728$	5.39471	+	2.46368i	0.199941	+	0.0913101i
$729$	−26.1893	+	6.56646i	−0.969976	+	0.243202i
$730$	−6.30986	+	3.96522i	−0.233538	+	0.146759i
$731$	−0.378822	+	0.328251i	−0.0140112	+	0.0121408i
$732$	6.94082	+	17.6774i	0.256540	+	0.653376i
$733$	17.4106	+	38.1240i	0.643076	+	1.40814i	0.897485	+	0.441044i	$0.145392\pi$
$733$	17.4106	+	38.1240i	0.643076	+	1.40814i	−0.254409	+	0.967097i	$0.581881\pi$
$734$	2.57694	−	17.9230i	0.0951164	−	0.661549i
$735$	51.5688	+	38.0437i	1.90214	+	1.40326i
$736$	4.50722	−	1.63859i	0.166138	−	0.0603994i
$737$	−8.84148			−0.325680
$738$	6.76951	−	16.2780i	0.249189	−	0.599203i
$739$	−8.05339	−	17.6345i	−0.296249	−	0.648694i	0.701716	−	0.712456i	$-0.252417\pi$
$739$	−8.05339	−	17.6345i	−0.296249	−	0.648694i	−0.997965	+	0.0637622i	$0.979690\pi$
$740$	0.0190310	−	1.87557i	0.000699594	−	0.0689472i
$741$	4.93898	+	0.986049i	0.181438	+	0.0362234i
$742$	−14.7595	−	50.2662i	−0.541838	−	1.84533i
$743$	13.6799	−	21.2864i	0.501867	−	0.780921i	−0.494216	−	0.869339i	$-0.664545\pi$
$743$	13.6799	−	21.2864i	0.501867	−	0.780921i	0.996083	+	0.0884183i	$0.0281812\pi$
$744$	2.09306	+	8.88540i	0.0767352	+	0.325755i
$745$	−20.6528	−	9.68624i	−0.756659	−	0.354876i
$746$	−15.8592	+	10.1921i	−0.580647	+	0.373159i
$747$	4.45177	−	40.8649i	0.162882	−	1.49517i
$748$	20.5432	−	2.95367i	0.751134	−	0.107997i
$749$	−11.8940	−	18.5074i	−0.434597	−	0.676246i
$750$	13.8739	−	13.5098i	0.506603	−	0.493308i
$751$	−30.8269	−	14.0782i	−1.12489	−	0.513720i	−0.235960	−	0.971763i	$-0.575824\pi$
$751$	−30.8269	−	14.0782i	−1.12489	−	0.513720i	−0.888930	+	0.458042i	$0.848551\pi$
$752$	3.75942	+	2.41603i	0.137092	+	0.0881037i
$753$	2.83634	−	3.92749i	0.103362	−	0.143126i
$754$	−5.21988	−	6.02407i	−0.190097	−	0.219384i
$755$	−0.211458	+	20.8399i	−0.00769575	+	0.758440i
$756$	16.8888	−	18.7220i	0.614241	−	0.680914i
$757$	6.15408	−	42.8025i	0.223674	−	1.55568i	−0.500297	−	0.865854i	$-0.666776\pi$
$757$	6.15408	−	42.8025i	0.223674	−	1.55568i	0.723971	−	0.689831i	$-0.242315\pi$
$758$			13.9439i			0.506465i
$759$	−20.7930	+	18.3415i	−0.754737	+	0.665754i
$760$	−5.11940	+	1.44693i	−0.185700	+	0.0524858i
$761$	4.51009	+	0.648452i	0.163490	+	0.0235064i	0.223574	−	0.974687i	$-0.428228\pi$
$761$	4.51009	+	0.648452i	0.163490	+	0.0235064i	−0.0600834	+	0.998193i	$0.519137\pi$
$762$	−14.2916	+	27.2746i	−0.517731	+	0.988055i
$763$	−20.1349	+	68.5731i	−0.728932	+	2.48251i
$764$	−15.7676	−	18.1968i	−0.570453	−	0.658338i
$765$	−12.7139	−	39.7258i	−0.459673	−	1.43629i
$766$	−12.7217	+	19.7954i	−0.459655	+	0.715238i
$767$	−2.35961	+	5.16683i	−0.0852007	+	0.186564i
$768$	−0.0939272	+	1.72950i	−0.00338931	+	0.0624080i
$769$	21.6637	+	33.7093i	0.781212	+	1.21559i	0.972236	+	0.234004i	$0.0751828\pi$
$769$	21.6637	+	33.7093i	0.781212	+	1.21559i	−0.191024	+	0.981585i	$0.561181\pi$
$770$	33.0954	−	14.7102i	1.19267	−	0.530118i
$771$	28.6103	+	27.6458i	1.03038	+	0.995638i
$772$	12.3596	+	19.2320i	0.444833	+	0.692174i
$773$	3.63972	+	3.15384i	0.130912	+	0.113436i	0.717856	−	0.696192i	$-0.245124\pi$
$773$	3.63972	+	3.15384i	0.130912	+	0.113436i	−0.586944	+	0.809627i	$0.699669\pi$
$774$	0.188097	+	0.152016i	0.00676099	+	0.00546411i
$775$	26.3466	+	0.534722i	0.946397	+	0.0192078i
$776$	7.18405	−	2.10943i	0.257892	−	0.0757241i
$777$	−6.91359	−	1.38027i	−0.248024	−	0.0495170i
$778$	−20.3514	−	5.97572i	−0.729634	−	0.214240i
$779$	5.80797	+	12.7177i	0.208092	+	0.455658i
$780$	−3.37047	−	3.32363i	−0.120682	−	0.119005i
$781$			28.4030i			1.01634i
$782$	−27.8521	−	10.6526i	−0.995991	−	0.380938i
$783$	−31.1010	+	13.4595i	−1.11146	+	0.481004i
$784$	−2.35477	+	16.3778i	−0.0840990	+	0.584922i
$785$	18.2665	−	15.5063i	0.651959	−	0.553444i
$786$	−5.65531	−	14.4034i	−0.201718	−	0.513751i
$787$	−2.55237	−	2.94559i	−0.0909820	−	0.104999i	0.708433	−	0.705778i	$-0.249402\pi$
$787$	−2.55237	−	2.94559i	−0.0909820	−	0.104999i	−0.799415	+	0.600779i	$0.794857\pi$
$788$	−2.32301	+	0.682098i	−0.0827539	+	0.0242987i
$789$	1.82505	+	20.5579i	0.0649737	+	0.731881i
$790$	2.10553	−	13.6590i	0.0749114	−	0.485964i
$791$	20.6540	+	17.8968i	0.734371	+	0.636336i
$792$	−3.14889	−	9.50565i	−0.111891	−	0.337768i
$793$	−1.90715	−	13.2645i	−0.0677247	−	0.471036i
$794$	−0.682355	+	0.0981078i	−0.0242159	+	0.00348172i
$795$	−2.69103	+	41.7271i	−0.0954408	+	1.47991i
$796$	7.50806	+	6.50577i	0.266116	+	0.230591i
$797$	−35.6636	−	16.2870i	−1.26327	−	0.576916i	−0.332701	−	0.943032i	$-0.607960\pi$
$797$	−35.6636	−	16.2870i	−1.26327	−	0.576916i	−0.930569	+	0.366116i	$0.880687\pi$
$798$	1.76822	+	19.9177i	0.0625942	+	0.705078i
$799$	−7.82839	−	26.6610i	−0.276948	−	0.943200i
$800$	4.76789	+	1.50572i	0.168570	+	0.0532353i
$801$	8.00603	−	13.4501i	0.282879	−	0.475238i
$802$	−5.35607	−	11.7282i	−0.189129	−	0.414135i
$803$	11.0112	+	1.58317i	0.388577	+	0.0558689i
$804$	−3.62514	+	2.81199i	−0.127849	+	0.0991714i
$805$	−51.8268	−	4.66929i	−1.82665	−	0.164571i
$806$		−	6.44148i		−	0.226891i
$807$	−8.95375	+	5.09030i	−0.315187	+	0.179187i
$808$	15.3567	−	7.01318i	0.540248	−	0.246723i
$809$	−2.94322	+	10.0237i	−0.103478	+	0.352414i	−0.994913	−	0.100734i	$-0.967881\pi$
$809$	−2.94322	+	10.0237i	−0.103478	+	0.352414i	0.891435	+	0.453148i	$0.149699\pi$
$810$	−17.7865	+	9.41483i	−0.624955	+	0.330803i
$811$	−2.41772	+	0.709907i	−0.0848977	+	0.0249282i	−0.323906	−	0.946089i	$-0.604996\pi$
$811$	−2.41772	+	0.709907i	−0.0848977	+	0.0249282i	0.239008	+	0.971018i	$0.423178\pi$
$812$	17.1096	−	26.6230i	0.600429	−	0.934285i
$813$	1.25585	+	5.33132i	0.0440447	+	0.186977i
$814$	−1.83353	+	2.11601i	−0.0642653	+	0.0741662i
$815$	−22.3674	+	25.2903i	−0.783496	+	0.885879i
$816$	7.48362	−	7.74472i	0.261979	−	0.271120i
$817$	−0.189844	+	0.0272954i	−0.00664178	+	0.000954944i
$818$	−25.5936	+	16.4480i	−0.894858	+	0.575090i
$819$	−14.6290	+	10.1265i	−0.511178	+	0.353849i
$820$	2.00193	−	12.9869i	0.0699104	−	0.453522i
$821$	4.25616	−	6.62271i	0.148541	−	0.231134i	−0.759007	−	0.651082i	$-0.774315\pi$
$821$	4.25616	−	6.62271i	0.148541	−	0.231134i	0.907548	+	0.419948i	$0.137952\pi$
$822$	15.5177	+	11.2065i	0.541242	+	0.390872i
$823$	−0.779323	+	0.675287i	−0.0271655	+	0.0235390i	−0.668338	−	0.743858i	$-0.732994\pi$
$823$	−0.779323	+	0.675287i	−0.0271655	+	0.0235390i	0.641172	+	0.767397i	$0.278448\pi$
$824$	−16.9127	−	4.96602i	−0.589182	−	0.172999i
$825$	−28.8396	+	1.97140i	−1.00406	+	0.0686353i
$826$	−22.3221	−	3.20943i	−0.776684	−	0.111670i
$827$			15.4463i			0.537121i	0.963263	+	0.268560i	$0.0865479\pi$
$827$			15.4463i			0.537121i	−0.963263	+	0.268560i	$0.913452\pi$
$828$	−2.69200	+	14.1334i	−0.0935534	+	0.491170i
$829$	21.4942			0.746524			0.373262	−	0.927726i	$-0.378239\pi$
$829$	21.4942			0.746524			0.373262	+	0.927726i	$0.378239\pi$
$830$	−4.05246	−	30.3699i	−0.140663	−	1.05415i
$831$	26.0181	−	49.6539i	0.902558	−	1.72247i
$832$	0.344333	−	1.17269i	0.0119376	−	0.0406558i
$833$	77.7531	−	67.3734i	2.69398	−	2.33435i
$834$	−3.27367	+	4.53307i	−0.113358	+	0.156967i
$835$	5.86659	−	19.2548i	0.203022	−	0.666341i
$836$	7.22368	+	3.29894i	0.249836	+	0.114096i
$837$	−26.1172	−	8.23856i	−0.902742	−	0.284766i
$838$	−15.3433	+	9.86055i	−0.530026	+	0.340627i
$839$	0.0621969	+	0.432589i	0.00214728	+	0.0149346i	0.990867	−	0.134843i	$-0.0430532\pi$
$839$	0.0621969	+	0.432589i	0.00214728	+	0.0149346i	−0.988720	+	0.149778i	$0.952144\pi$
$840$	8.89109	−	16.5572i	0.306772	−	0.571279i
$841$	−11.3858	+	7.31723i	−0.392615	+	0.252318i
$842$	−10.4077	−	9.01831i	−0.358672	−	0.310791i
$843$	1.87442	+	7.95724i	0.0645584	+	0.274062i
$844$	9.73783	+	6.25812i	0.335190	+	0.215413i
$845$	−13.6897	−	21.7844i	−0.470939	−	0.749406i
$846$	−11.9969	+	5.98406i	−0.412462	+	0.205736i
$847$	−0.658469	−	0.193344i	−0.0226252	−	0.00664337i
$848$	−9.82063	+	4.48493i	−0.337242	+	0.154013i
$849$	−10.0374	−	17.6557i	−0.344484	−	0.605942i
$850$	−16.2740	−	26.4897i	−0.558193	−	0.908588i
$851$	3.78075	−	1.37449i	0.129603	−	0.0471169i
$852$	9.03345	+	11.6456i	0.309481	+	0.398973i
$853$	−32.4840	−	4.67050i	−1.11223	−	0.159915i	−0.438386	−	0.898787i	$-0.644450\pi$
$853$	−32.4840	−	4.67050i	−1.11223	−	0.159915i	−0.673846	+	0.738872i	$0.735359\pi$
$854$	48.3970	−	22.1022i	1.65611	−	0.756320i
$855$	4.12543	−	15.4174i	0.141087	−	0.527265i
$856$	−3.42638	+	2.96898i	−0.117111	+	0.101478i
$857$	−29.9628	+	8.79789i	−1.02351	+	0.300530i	−0.750070	−	0.661359i	$-0.769980\pi$
$857$	−29.9628	+	8.79789i	−1.02351	+	0.300530i	−0.273441	+	0.961889i	$0.588162\pi$
$858$	0.624835	+	7.03831i	0.0213315	+	0.240284i
$859$	−1.02094	+	2.23555i	−0.0348340	+	0.0762759i	−0.926249	−	0.376912i	$-0.876986\pi$
$859$	−1.02094	+	2.23555i	−0.0348340	+	0.0762759i	0.891415	+	0.453188i	$0.149713\pi$
$860$	0.163203	+	0.0765429i	0.00556517	+	0.00261009i
$861$	−46.5653	−	16.4642i	−1.58694	−	0.561100i
$862$	−2.24863	−	15.6396i	−0.0765887	−	0.532686i
$863$	−2.99165	−	20.8074i	−0.101837	−	0.708292i	−0.975217	−	0.221252i	$-0.928986\pi$
$863$	−2.99165	−	20.8074i	−0.101837	−	0.708292i	0.873380	−	0.487040i	$-0.161923\pi$
$864$	−4.31432	−	2.89597i	−0.146776	−	0.0985228i
$865$	−24.2820	−	11.3884i	−0.825613	−	0.387217i
$866$	3.14322	−	6.88269i	0.106811	−	0.233883i
$867$	−37.3723	+	3.31777i	−1.26923	+	0.112678i
$868$	24.5384	−	7.20512i	0.832887	−	0.244558i
$869$	−15.5912	+	13.5099i	−0.528896	+	0.458291i
$870$	−20.1144	+	15.2783i	−0.681943	+	0.517982i
$871$	2.94484	−	1.34486i	0.0997822	−	0.0455690i
$872$	14.5784	+	2.09605i	0.493685	+	0.0709812i
$873$	−5.58571	+	21.7564i	−0.189048	+	0.736344i
$874$	−6.76167	−	9.19066i	−0.228717	−	0.310879i
$875$	−39.9007	−	36.7589i	−1.34889	−	1.24268i
$876$	5.01828	−	2.85294i	0.169552	−	0.0963919i
$877$	28.0338	−	12.8026i	0.946635	−	0.432314i	0.118570	−	0.992946i	$-0.462169\pi$
$877$	28.0338	−	12.8026i	0.946635	−	0.432314i	0.828065	+	0.560632i	$0.189442\pi$
$878$	−5.52441	−	1.62211i	−0.186440	−	0.0547437i
$879$	0.541292	−	2.71126i	0.0182573	−	0.0914485i
$880$	−3.97128	−	6.31950i	−0.133872	−	0.213030i
$881$	−40.1117	−	25.7782i	−1.35140	−	0.868491i	−0.353638	−	0.935382i	$-0.615056\pi$
$881$	−40.1117	−	25.7782i	−1.35140	−	0.868491i	−0.997760	+	0.0668911i	$0.978692\pi$
$882$	−38.6067	−	31.2012i	−1.29996	−	1.05060i
$883$	5.31685	+	4.60707i	0.178926	+	0.155040i	0.739719	−	0.672916i	$-0.234958\pi$
$883$	5.31685	+	4.60707i	0.178926	+	0.155040i	−0.560793	+	0.827956i	$0.689504\pi$
$884$	−6.39307	+	4.10858i	−0.215022	+	0.138186i
$885$	15.8578	+	8.51552i	0.533055	+	0.286246i
$886$	0.769502	+	5.35200i	0.0258519	+	0.179804i
$887$	40.2287	−	25.8534i	1.35075	−	0.868073i	0.353031	−	0.935611i	$-0.385151\pi$
$887$	40.2287	−	25.8534i	1.35075	−	0.868073i	0.997717	+	0.0675383i	$0.0215145\pi$
$888$	−0.0787882	+	1.45074i	−0.00264396	+	0.0486838i
$889$	78.4703	+	35.8362i	2.63181	+	1.20191i
$890$	3.40031	−	11.1602i	0.113979	−	0.374092i
$891$	29.3362	+	6.46848i	0.982801	+	0.216702i
$892$	−1.25062	+	1.08367i	−0.0418740	+	0.0362840i
$893$	2.99539	−	10.2014i	0.100237	−	0.341376i
$894$	15.6512	+	8.20104i	0.523453	+	0.274284i
$895$	4.22461	+	31.6600i	0.141213	+	1.05828i
$896$	4.85245			0.162109
$897$	4.13565	−	9.27182i	0.138085	−	0.309577i
$898$		−	17.8359i		−	0.595192i
$899$	−34.0228	−	4.89174i	−1.13472	−	0.163149i
$900$	−11.1977	+	9.98060i	−0.373255	+	0.332687i
$901$	64.4104	+	18.9126i	2.14582	+	0.630070i
$902$	−14.8241	+	12.8451i	−0.493588	+	0.427697i
$903$	0.396679	−	0.549284i	0.0132007	−	0.0182790i
$904$	3.04491	−	4.73797i	0.101272	−	0.157583i
$905$	−0.913041	+	5.92307i	−0.0303505	+	0.196889i
$906$	0.875434	−	16.1196i	0.0290844	−	0.535537i
$907$	3.61375	−	2.32241i	0.119992	−	0.0771145i	−0.479268	−	0.877669i	$-0.659098\pi$
$907$	3.61375	−	2.32241i	0.119992	−	0.0771145i	0.599260	+	0.800554i	$0.295461\pi$
$908$	12.5461	−	1.80385i	0.416355	−	0.0598629i
$909$	−5.48499	+	50.3492i	−0.181925	+	1.66998i
$910$	−8.78558	+	9.93363i	−0.291239	+	0.329296i
$911$	10.4131	−	12.0174i	0.345001	−	0.398153i	−0.556558	−	0.830809i	$-0.687878\pi$
$911$	10.4131	−	12.0174i	0.345001	−	0.398153i	0.901559	+	0.432656i	$0.142424\pi$
$912$	4.01103	−	0.944844i	0.132819	−	0.0312869i
$913$	−24.7269	+	38.4758i	−0.818342	+	1.27336i
$914$	−22.5690	+	6.62687i	−0.746517	+	0.219197i
$915$	−42.3352	+	3.32580i	−1.39956	+	0.109947i
$916$	−4.53824	+	15.4558i	−0.149948	+	0.510675i
$917$	−39.4334	+	18.0086i	−1.30220	+	0.594697i
$918$	8.48173	+	31.1758i	0.279939	+	1.02895i
$919$		−	40.9080i		−	1.34943i	−0.738079	−	0.674715i	$-0.764267\pi$
$919$		−	40.9080i		−	1.34943i	0.738079	−	0.674715i	$-0.235733\pi$
$920$	0.567539	+	10.7088i	0.0187112	+	0.353058i
$921$	0.901836	+	1.16262i	0.0297165	+	0.0383096i
$922$	1.48406	+	0.213376i	0.0488749	+	0.00702715i
$923$	−4.32034	−	9.46022i	−0.142206	−	0.311387i
$924$	−26.1131	+	10.2530i	−0.859057	+	0.337298i
$925$	3.99941	+	1.26303i	0.131500	+	0.0415282i
$926$	0.406136	+	1.38317i	0.0133465	+	0.0454539i
$927$	38.7535	−	35.9788i	1.27283	−	1.18170i
$928$	−5.93247	−	2.70927i	−0.194743	−	0.0889361i
$929$	11.4904	+	9.95647i	0.376987	+	0.326661i	0.822659	−	0.568535i	$-0.192490\pi$
$929$	11.4904	+	9.95647i	0.376987	+	0.326661i	−0.445672	+	0.895196i	$0.647035\pi$
$930$	−20.3699	−	1.31367i	−0.667954	−	0.0430771i
$931$	38.9653	−	5.60236i	1.27704	−	0.183610i
$932$	0.807152	+	5.61387i	0.0264392	+	0.183888i
$933$	−24.1553	−	8.54068i	−0.790809	−	0.279609i
$934$	21.2532	+	18.4160i	0.695428	+	0.602591i
$935$	−7.07034	+	45.8666i	−0.231225	+	1.50000i
$936$	2.49470	+	2.68709i	0.0815417	+	0.0878301i
$937$	−33.0757	+	9.71190i	−1.08054	+	0.317274i	−0.773093	−	0.634292i	$-0.781292\pi$
$937$	−33.0757	+	9.71190i	−1.08054	+	0.317274i	−0.307443	+	0.951566i	$0.599473\pi$
$938$	8.41713	+	9.71388i	0.274829	+	0.317170i
$939$	53.3904	−	20.9631i	1.74233	−	0.684104i
$940$	−7.61792	+	6.46681i	−0.248469	+	0.210924i
$941$	−5.15384	+	35.8458i	−0.168011	+	1.16854i	0.714979	+	0.699146i	$0.246436\pi$
$941$	−5.15384	+	35.8458i	−0.168011	+	1.16854i	−0.882989	+	0.469393i	$0.844473\pi$
$942$	−14.6650	+	11.3756i	−0.477812	+	0.370636i
$943$	27.5875	−	5.76176i	0.898373	−	0.187629i
$944$			4.64747i			0.151262i
$945$	29.0396	+	48.3264i	0.944659	+	1.57206i
$946$	−0.111781	−	0.244767i	−0.00363432	−	0.00795806i
$947$	−47.2606	−	13.8770i	−1.53576	−	0.450941i	−0.598954	−	0.800783i	$-0.704417\pi$
$947$	−47.2606	−	13.8770i	−1.53576	−	0.450941i	−0.936808	+	0.349843i	$0.886235\pi$
$948$	−2.09588	+	10.4980i	−0.0680710	+	0.340959i
$949$	−3.90833	+	1.14759i	−0.126870	+	0.0372523i
$950$	0.241383	−	11.8933i	0.00783150	−	0.385870i
$951$	8.28700	+	35.1798i	0.268724	+	1.14078i
$952$	−22.8023	−	19.7583i	−0.739028	−	0.640371i
$953$	−21.7497	−	33.8431i	−0.704541	−	1.09629i	−0.990429	−	0.138024i	$-0.955925\pi$
$953$	−21.7497	−	33.8431i	−0.704541	−	1.09629i	0.285888	−	0.958263i	$-0.407711\pi$
$954$	3.50765	−	32.1983i	0.113564	−	1.04246i
$955$	49.1987	−	21.8678i	1.59203	−	0.707624i
$956$	−3.99659	−	6.21881i	−0.129259	−	0.201131i
$957$	37.6497	+	2.04471i	1.21704	+	0.0660961i
$958$	12.1881	−	26.6883i	0.393781	−	0.862260i
$959$	28.9920	−	45.1124i	0.936200	−	1.45676i
$960$	−3.63817	−	1.32804i	−0.117422	−	0.0428624i
$961$	2.11055	+	2.43570i	0.0680822	+	0.0785711i
$962$	0.288834	−	0.983679i	0.00931239	−	0.0317151i
$963$	−2.39606	−	13.3885i	−0.0772118	−	0.431440i
$964$	−10.2681	−	1.47633i	−0.330713	−	0.0475493i
$965$	−49.1919	+	13.9035i	−1.58354	+	0.447569i
$966$	39.9463	+	5.38348i	1.28525	+	0.173210i
$967$			43.4317i			1.39667i	0.715772	+	0.698335i	$0.246075\pi$
$967$			43.4317i			1.39667i	−0.715772	+	0.698335i	$0.753925\pi$
$968$	−0.0201272	+	0.139988i	−0.000646912	+	0.00449937i
$969$	−22.6957	−	11.8923i	−0.729090	−	0.382035i
$970$	−0.169871	+	16.7413i	−0.00545423	+	0.537532i
$971$	−13.1848	−	15.2160i	−0.423119	−	0.488305i	0.503666	−	0.863899i	$-0.331984\pi$
$971$	−13.1848	−	15.2160i	−0.423119	−	0.488305i	−0.926785	+	0.375593i	$0.877439\pi$
$972$	14.0856	−	6.67809i	0.451795	−	0.214200i
$973$	13.1783	+	8.46920i	0.422478	+	0.271510i
$974$	33.9872	+	15.5215i	1.08902	+	0.497339i
$975$	9.30577	−	5.04336i	0.298023	−	0.161517i
$976$	−5.92790	−	9.22399i	−0.189747	−	0.295253i
$977$	−30.8721	+	4.43874i	−0.987687	+	0.142008i	−0.617180	−	0.786822i	$-0.711725\pi$
$977$	−30.8721	+	4.43874i	−0.987687	+	0.142008i	−0.370507	+	0.928830i	$0.620816\pi$
$978$	18.1727	−	18.8067i	0.581098	−	0.601373i
$979$	−14.6508	+	9.41551i	−0.468242	+	0.300921i
$980$	−33.4973	−	15.7104i	−1.07003	−	0.501851i
$981$	−27.7731	+	34.3650i	−0.886727	+	1.09719i
$982$	1.85968	−	2.89371i	0.0593447	−	0.0923421i
$983$	−4.67730	−	15.9294i	−0.149183	−	0.508070i	0.850662	−	0.525714i	$-0.176202\pi$
$983$	−4.67730	−	15.9294i	−0.149183	−	0.508070i	−0.999844	+	0.0176438i	$0.994384\pi$
$984$	−1.99275	+	9.98144i	−0.0635267	+	0.318197i
$985$	0.0549290	−	5.41343i	0.00175018	−	0.172486i
$986$	16.8459	+	36.8873i	0.536481	+	1.17473i
$987$	18.5627	+	32.6514i	0.590856	+	1.03931i
$988$	−2.90780			−0.0925094
$989$	−0.0307827	+	0.385389i	−0.000978834	+	0.0122547i
$990$	22.3846	−	0.540520i	0.711431	−	0.0171788i
$991$	0.894086	−	6.21851i	0.0284016	−	0.197537i	−0.970681	−	0.240373i	$-0.922730\pi$
$991$	0.894086	−	6.21851i	0.0284016	−	0.197537i	0.999082	+	0.0428359i	$0.0136393\pi$
$992$	−2.18940	−	4.79412i	−0.0695136	−	0.152214i
$993$	46.9747	−	18.4440i	1.49070	−	0.585304i
$994$	31.2056	−	27.0398i	0.989781	−	0.857650i
$995$	−18.8088	+	11.8198i	−0.596280	+	0.374712i
$996$	2.09867	+	23.6400i	0.0664988	+	0.749061i
$997$	−15.6127	−	7.13008i	−0.494459	−	0.225812i	0.152548	−	0.988296i	$-0.451252\pi$
$997$	−15.6127	−	7.13008i	−0.494459	−	0.225812i	−0.647007	+	0.762484i	$0.723979\pi$
$998$	27.0139	−	31.1757i	0.855109	−	0.986849i
$999$	−3.61895	−	2.42920i	−0.114498	−	0.0768565i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.n.a.659.20	yes	240
3.2	odd	2		690.2.n.b.659.14	yes	240
5.4	even	2		690.2.n.b.659.5	yes	240
15.14	odd	2	inner	690.2.n.a.659.11	yes	240
23.20	odd	22	inner	690.2.n.a.89.11	✓	240
69.20	even	22		690.2.n.b.89.5	yes	240
115.89	odd	22		690.2.n.b.89.14	yes	240
345.89	even	22	inner	690.2.n.a.89.20	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.n.a.89.11	✓	240	23.20	odd	22	inner
690.2.n.a.89.20	yes	240	345.89	even	22	inner
690.2.n.a.659.11	yes	240	15.14	odd	2	inner
690.2.n.a.659.20	yes	240	1.1	even	1	trivial
690.2.n.b.89.5	yes	240	69.20	even	22
690.2.n.b.89.14	yes	240	115.89	odd	22
690.2.n.b.659.5	yes	240	5.4	even	2
690.2.n.b.659.14	yes	240	3.2	odd	2

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.n (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 + 0.989821i) q^{2} +(1.53419 + 0.803900i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(1.22793 - 1.86874i) q^{5} +(-1.01406 + 1.40417i) q^{6} +(4.08214 + 2.62343i) q^{7} +(0.415415 - 0.909632i) q^{8} +(1.70749 + 2.46667i) q^{9} +O(q^{10})\)	\(q+(-0.142315 + 0.989821i) q^{2} +(1.53419 + 0.803900i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(1.22793 - 1.86874i) q^{5} +(-1.01406 + 1.40417i) q^{6} +(4.08214 + 2.62343i) q^{7} +(0.415415 - 0.909632i) q^{8} +(1.70749 + 2.46667i) q^{9} +(1.67496 + 1.48138i) q^{10} +(-0.475030 - 3.30390i) q^{11} +(-1.24556 - 1.20357i) q^{12} +(0.660771 + 1.02818i) q^{13} +(-3.17768 + 3.66723i) q^{14} +(3.38616 - 1.87987i) q^{15} +(0.841254 + 0.540641i) q^{16} +(-1.75177 - 5.96599i) q^{17} +(-2.68457 + 1.33906i) q^{18} +(0.670285 - 2.28278i) q^{19} +(-1.70468 + 1.44709i) q^{20} +(4.15380 + 7.30648i) q^{21} +3.33788 q^{22} +(-4.18997 - 2.33328i) q^{23} +(1.36858 - 1.06160i) q^{24} +(-1.98436 - 4.58937i) q^{25} +(-1.11175 + 0.507720i) q^{26} +(0.636654 + 5.15700i) q^{27} +(-3.17768 - 3.66723i) q^{28} +(1.83741 + 6.25766i) q^{29} +(1.37883 + 3.61923i) q^{30} +(-2.18940 + 4.79412i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(1.92722 - 5.45070i) q^{33} +(6.15457 - 0.884894i) q^{34} +(9.91509 - 4.40704i) q^{35} +(-0.943381 - 2.84781i) q^{36} +(-0.549311 + 0.633939i) q^{37} +(2.16415 + 0.988336i) q^{38} +(0.187195 + 2.10862i) q^{39} +(-1.18976 - 1.89327i) q^{40} +(-4.44117 + 3.84830i) q^{41} +(-7.82325 + 3.07170i) q^{42} +(-0.0334887 - 0.0733301i) q^{43} +(-0.475030 + 3.30390i) q^{44} +(6.70625 - 0.161935i) q^{45} +(2.90582 - 3.81526i) q^{46} +4.46884 q^{47} +(0.856023 + 1.50573i) q^{48} +(6.87355 + 15.0510i) q^{49} +(4.82506 - 1.31102i) q^{50} +(2.10851 - 10.5612i) q^{51} +(-0.344333 - 1.17269i) q^{52} +(-5.83690 + 9.08239i) q^{53} +(-5.19512 - 0.103744i) q^{54} +(-6.75743 - 3.16927i) q^{55} +(4.08214 - 2.62343i) q^{56} +(2.86347 - 2.96338i) q^{57} +(-6.45546 + 0.928154i) q^{58} +(2.51261 + 3.90970i) q^{59} +(-3.77862 + 0.849725i) q^{60} +(-9.97373 - 4.55485i) q^{61} +(-4.43374 - 2.84939i) q^{62} +(0.499054 + 14.5488i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(2.73278 + 0.0277290i) q^{65} +(5.12094 + 2.68332i) q^{66} +(0.376968 - 2.62187i) q^{67} +6.21786i q^{68} +(-4.55249 - 6.94801i) q^{69} +(2.95112 + 10.4414i) q^{70} +(-8.42268 - 1.21100i) q^{71} +(2.95308 - 0.528493i) q^{72} +(-0.938954 + 3.19778i) q^{73} +(-0.549311 - 0.633939i) q^{74} +(0.645010 - 8.63620i) q^{75} +(-1.28627 + 2.00147i) q^{76} +(6.72842 - 14.7332i) q^{77} +(-2.11380 - 0.114798i) q^{78} +(-3.34150 - 5.19947i) q^{79} +(2.04332 - 0.908211i) q^{80} +(-3.16897 + 8.42364i) q^{81} +(-3.17708 - 4.94364i) q^{82} +(-10.3554 - 8.97304i) q^{83} +(-1.92707 - 8.18077i) q^{84} +(-13.2999 - 4.05224i) q^{85} +(0.0773497 - 0.0227119i) q^{86} +(-2.21159 + 11.0775i) q^{87} +(-3.20267 - 0.940389i) q^{88} +(-2.16744 - 4.74603i) q^{89} +(-0.794112 + 6.66103i) q^{90} +5.93065i q^{91} +(3.36288 + 3.41921i) q^{92} +(-7.21296 + 5.59504i) q^{93} +(-0.635982 + 4.42335i) q^{94} +(-3.44285 - 4.05569i) q^{95} +(-1.61223 + 0.633022i) q^{96} +(4.90317 + 5.65856i) q^{97} +(-15.8760 + 4.66161i) q^{98} +(7.33855 - 6.81312i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 24 q^{2} + 2 q^{3} - 24 q^{4} + 2 q^{6} - 24 q^{8} - 6 q^{9}+O(q^{10}) \) 240 * q - 24 * q^2 + 2 * q^3 - 24 * q^4 + 2 * q^6 - 24 * q^8 - 6 * q^9	\( 240 q - 24 q^{2} + 2 q^{3} - 24 q^{4} + 2 q^{6} - 24 q^{8} - 6 q^{9} - 9 q^{12} + 11 q^{15} - 24 q^{16} - 6 q^{18} - 4 q^{23} + 2 q^{24} - 12 q^{25} + 2 q^{27} + 22 q^{30} + 28 q^{31} - 24 q^{32} - 36 q^{35} - 6 q^{36} - 4 q^{46} + 104 q^{47} - 9 q^{48} + 70 q^{49} + 54 q^{50} - 9 q^{54} - 26 q^{55} - 44 q^{57} - 11 q^{60} + 44 q^{61} + 28 q^{62} - 121 q^{63} - 24 q^{64} + 44 q^{65} + 44 q^{66} - 102 q^{69} - 36 q^{70} + 16 q^{72} - 82 q^{75} + 8 q^{77} - 44 q^{79} + 74 q^{81} - 11 q^{84} + 22 q^{85} - 93 q^{87} - 4 q^{92} + 172 q^{93} + 16 q^{94} + 26 q^{95} + 2 q^{96} + 4 q^{98}+O(q^{100}) \) 240 * q - 24 * q^2 + 2 * q^3 - 24 * q^4 + 2 * q^6 - 24 * q^8 - 6 * q^9 - 9 * q^12 + 11 * q^15 - 24 * q^16 - 6 * q^18 - 4 * q^23 + 2 * q^24 - 12 * q^25 + 2 * q^27 + 22 * q^30 + 28 * q^31 - 24 * q^32 - 36 * q^35 - 6 * q^36 - 4 * q^46 + 104 * q^47 - 9 * q^48 + 70 * q^49 + 54 * q^50 - 9 * q^54 - 26 * q^55 - 44 * q^57 - 11 * q^60 + 44 * q^61 + 28 * q^62 - 121 * q^63 - 24 * q^64 + 44 * q^65 + 44 * q^66 - 102 * q^69 - 36 * q^70 + 16 * q^72 - 82 * q^75 + 8 * q^77 - 44 * q^79 + 74 * q^81 - 11 * q^84 + 22 * q^85 - 93 * q^87 - 4 * q^92 + 172 * q^93 + 16 * q^94 + 26 * q^95 + 2 * q^96 + 4 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more