LMFDB - Embedded newform 690.2.n.a.659.11

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			659.11
Character	$\chi$	$=$	690.659
Dual form			690.2.n.a.89.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 + 0.989821i) q^{2} +(-0.397135 + 1.68591i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(2.02447 - 0.949486i) q^{5} +(-1.61223 - 0.633022i) q^{6} +(-4.08214 - 2.62343i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-2.68457 - 1.33906i) q^{9} +O(q^{10})$	\(q+(-0.142315 + 0.989821i) q^{2} +(-0.397135 + 1.68591i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(2.02447 - 0.949486i) q^{5} +(-1.61223 - 0.633022i) q^{6} +(-4.08214 - 2.62343i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-2.68457 - 1.33906i) q^{9} +(0.651709 + 2.13899i) q^{10} +(0.475030 + 3.30390i) q^{11} +(0.856023 - 1.50573i) q^{12} +(-0.660771 - 1.02818i) q^{13} +(3.17768 - 3.66723i) q^{14} +(0.796759 + 3.79014i) q^{15} +(0.841254 + 0.540641i) q^{16} +(-1.75177 - 5.96599i) q^{17} +(1.70749 - 2.46667i) q^{18} +(0.670285 - 2.28278i) q^{19} +(-2.20997 + 0.340666i) q^{20} +(6.04402 - 5.84025i) q^{21} -3.33788 q^{22} +(-4.18997 - 2.33328i) q^{23} +(1.36858 + 1.06160i) q^{24} +(3.19695 - 3.84441i) q^{25} +(1.11175 - 0.507720i) q^{26} +(3.32367 - 3.99414i) q^{27} +(3.17768 + 3.66723i) q^{28} +(-1.83741 - 6.25766i) q^{29} +(-3.86495 + 0.249255i) q^{30} +(-2.18940 + 4.79412i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(-5.75873 - 0.511238i) q^{33} +(6.15457 - 0.884894i) q^{34} +(-10.7551 - 1.43512i) q^{35} +(2.19857 + 2.04115i) q^{36} +(0.549311 - 0.633939i) q^{37} +(2.16415 + 0.988336i) q^{38} +(1.99583 - 0.705673i) q^{39} +(-0.0226878 - 2.23595i) q^{40} +(4.44117 - 3.84830i) q^{41} +(4.92065 + 6.81365i) 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} +(-1.24556 + 1.20357i) q^{48} +(6.87355 + 15.0510i) q^{49} +(3.35031 + 3.71153i) q^{50} +(10.7538 - 0.584026i) q^{51} +(0.344333 + 1.17269i) q^{52} +(-5.83690 + 9.08239i) q^{53} +(3.48048 + 3.85827i) q^{54} +(4.09869 + 6.23762i) q^{55} +(-4.08214 + 2.62343i) q^{56} +(3.58236 + 2.03661i) q^{57} +(6.45546 - 0.928154i) q^{58} +(-2.51261 - 3.90970i) q^{59} +(0.303322 - 3.86109i) q^{60} +(-9.97373 - 4.55485i) q^{61} +(-4.43374 - 2.84939i) q^{62} +(7.44583 + 12.5090i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(-2.31395 - 1.45412i) q^{65} +(1.32559 - 5.62735i) q^{66} +(-0.376968 + 2.62187i) q^{67} +6.21786i q^{68} +(5.59767 - 6.13727i) q^{69} +(2.95112 - 10.4414i) q^{70} +(8.42268 + 1.21100i) q^{71} +(-2.33327 + 1.88570i) q^{72} +(0.938954 - 3.19778i) q^{73} +(0.549311 + 0.633939i) q^{74} +(5.21170 + 6.91652i) q^{75} +(-1.28627 + 2.00147i) q^{76} +(6.72842 - 14.7332i) q^{77} +(0.414454 + 2.07594i) q^{78} +(-3.34150 - 5.19947i) q^{79} +(2.21642 + 0.295752i) q^{80} +(5.41381 + 7.18962i) q^{81} +(3.17708 + 4.94364i) q^{82} +(-10.3554 - 8.97304i) q^{83} +(-7.44458 + 3.90088i) q^{84} +(-9.21104 - 10.4147i) q^{85} +(-0.0773497 + 0.0227119i) q^{86} +(11.2795 - 0.612578i) q^{87} +(3.20267 + 0.940389i) q^{88} +(2.16744 + 4.74603i) q^{89} +(1.11469 - 6.61494i) q^{90} +5.93065i q^{91} +(3.36288 + 3.41921i) q^{92} +(-7.21296 - 5.59504i) q^{93} +(-0.635982 + 4.42335i) q^{94} +(-0.810497 - 5.25784i) q^{95} +(-1.01406 - 1.40417i) q^{96} +(-4.90317 - 5.65856i) q^{97} +(-15.8760 + 4.66161i) q^{98} +(3.14889 - 9.50565i) 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
$3$	−0.397135	+	1.68591i	−0.229286	+	0.973359i
$3$	−0.397135	+	1.68591i	−0.229286	+	0.973359i
$4$	−0.959493	−	0.281733i	−0.479746	−	0.140866i
$5$	2.02447	−	0.949486i	0.905370	−	0.424623i
$5$	2.02447	−	0.949486i	0.905370	−	0.424623i
$6$	−1.61223	−	0.633022i	−0.658190	−	0.258430i
$7$	−4.08214	−	2.62343i	−1.54290	−	0.991563i	−0.987074	−	0.160267i	$-0.948765\pi$
$7$	−4.08214	−	2.62343i	−1.54290	−	0.991563i	−0.555829	−	0.831297i	$-0.687599\pi$
$8$	0.415415	−	0.909632i	0.146871	−	0.321603i
$9$	−2.68457	−	1.33906i	−0.894856	−	0.446355i
$10$	0.651709	+	2.13899i	0.206089	+	0.676408i
$11$	0.475030	+	3.30390i	0.143227	+	0.996164i	0.926985	+	0.375098i	$0.122391\pi$
$11$	0.475030	+	3.30390i	0.143227	+	0.996164i	−0.783758	+	0.621066i	$0.786700\pi$
$12$	0.856023	−	1.50573i	0.247113	−	0.434667i
$13$	−0.660771	−	1.02818i	−0.183265	−	0.285166i	0.737450	−	0.675402i	$-0.236030\pi$
$13$	−0.660771	−	1.02818i	−0.183265	−	0.285166i	−0.920715	+	0.390236i	$0.872393\pi$
$14$	3.17768	−	3.66723i	0.849270	−	0.980109i
$15$	0.796759	+	3.79014i	0.205722	+	0.978610i
$16$	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	$-0.362800\pi$
$18$	1.70749	−	2.46667i	0.402459	−	0.581401i
$19$	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	$0.00292379\pi$
$20$	−2.20997	+	0.340666i	−0.494163	+	0.0761753i
$21$	6.04402	−	5.84025i	1.31891	−	1.27445i
$22$	−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
$25$	3.19695	−	3.84441i	0.639391	−	0.768882i
$26$	1.11175	−	0.507720i	0.218032	−	0.0995720i
$27$	3.32367	−	3.99414i	0.639641	−	0.768674i
$28$	3.17768	+	3.66723i	0.600524	+	0.693042i
$29$	−1.83741	−	6.25766i	−0.341199	−	1.16202i	−0.934180	−	0.356801i	$-0.883867\pi$
$29$	−1.83741	−	6.25766i	−0.341199	−	1.16202i	0.592981	−	0.805216i	$-0.297951\pi$
$30$	−3.86495	+	0.249255i	−0.705641	+	0.0455076i
$31$	−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
$33$	−5.75873	−	0.511238i	−1.00247	−	0.0889952i
$34$	6.15457	−	0.884894i	1.05550	−	0.151758i
$35$	−10.7551	−	1.43512i	−1.81794	−	0.242580i
$36$	2.19857	+	2.04115i	0.366428	+	0.340192i
$37$	0.549311	−	0.633939i	0.0903062	−	0.104219i	−0.708798	−	0.705412i	$-0.750762\pi$
$37$	0.549311	−	0.633939i	0.0903062	−	0.104219i	0.799104	+	0.601193i	$0.205308\pi$
$38$	2.16415	+	0.988336i	0.351072	+	0.160329i
$39$	1.99583	−	0.705673i	0.319589	−	0.112998i
$40$	−0.0226878	−	2.23595i	−0.00358725	−	0.353535i
$41$	4.44117	−	3.84830i	0.693595	−	0.601003i	−0.235046	−	0.971984i	$-0.575524\pi$
$41$	4.44117	−	3.84830i	0.693595	−	0.601003i	0.928640	+	0.370981i	$0.120979\pi$
$42$	4.92065	+	6.81365i	0.759273	+	1.05137i
$43$	0.0334887	+	0.0733301i	0.00510699	+	0.0111827i	0.912168	−	0.409816i	$-0.134407\pi$
$43$	0.0334887	+	0.0733301i	0.00510699	+	0.0111827i	−0.907061	+	0.420999i	$0.861680\pi$
$44$	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	$0.394325\pi$
$48$	−1.24556	+	1.20357i	−0.179781	+	0.173720i
$49$	6.87355	+	15.0510i	0.981936	+	2.15014i
$50$	3.35031	+	3.71153i	0.473805	+	0.524889i
$51$	10.7538	−	0.584026i	1.50583	−	0.0817800i
$52$	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	$0.915937\pi$
$54$	3.48048	+	3.85827i	0.473634	+	0.525044i
$55$	4.09869	+	6.23762i	0.552668	+	0.841080i
$56$	−4.08214	+	2.62343i	−0.545498	+	0.350571i
$57$	3.58236	+	2.03661i	0.474496	+	0.269755i
$58$	6.45546	−	0.928154i	0.847643	−	0.121873i
$59$	−2.51261	−	3.90970i	−0.327114	−	0.509000i	0.638277	−	0.769807i	$-0.279648\pi$
$59$	−2.51261	−	3.90970i	−0.327114	−	0.509000i	−0.965391	+	0.260807i	$0.916011\pi$
$60$	0.303322	−	3.86109i	0.0391587	−	0.498464i
$61$	−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
$63$	7.44583	+	12.5090i	0.938087	+	1.57599i
$64$	−0.654861	−	0.755750i	−0.0818576	−	0.0944687i
$65$	−2.31395	−	1.45412i	−0.287010	−	0.180362i
$66$	1.32559	−	5.62735i	0.163168	−	0.692679i
$67$	−0.376968	+	2.62187i	−0.0460540	+	0.320312i	0.953752	+	0.300596i	$0.0971855\pi$
$67$	−0.376968	+	2.62187i	−0.0460540	+	0.320312i	−0.999806	+	0.0197167i	$0.993724\pi$
$68$			6.21786i			0.754026i
$69$	5.59767	−	6.13727i	0.673880	−	0.738841i
$70$	2.95112	−	10.4414i	0.352726	−	1.24798i
$71$	8.42268	+	1.21100i	0.999589	+	0.143719i	0.622634	−	0.782513i	$-0.286062\pi$
$71$	8.42268	+	1.21100i	0.999589	+	0.143719i	0.376954	+	0.926232i	$0.376971\pi$
$72$	−2.33327	+	1.88570i	−0.274978	+	0.222232i
$73$	0.938954	−	3.19778i	0.109896	−	0.374272i	−0.886119	−	0.463458i	$-0.846608\pi$
$73$	0.938954	−	3.19778i	0.109896	−	0.374272i	0.996015	+	0.0891860i	$0.0284266\pi$
$74$	0.549311	+	0.633939i	0.0638562	+	0.0736939i
$75$	5.21170	+	6.91652i	0.601795	+	0.798650i
$76$	−1.28627	+	2.00147i	−0.147545	+	0.229584i
$77$	6.72842	−	14.7332i	0.766775	−	1.67900i
$78$	0.414454	+	2.07594i	0.0469276	+	0.235054i
$79$	−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	$0.931215\pi$
$80$	2.21642	+	0.295752i	0.247804	+	0.0330661i
$81$	5.41381	+	7.18962i	0.601535	+	0.798847i
$82$	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	$0.998187\pi$
$84$	−7.44458	+	3.90088i	−0.812270	+	0.425621i
$85$	−9.21104	−	10.4147i	−0.999077	−	1.12963i
$86$	−0.0773497	+	0.0227119i	−0.00834083	+	0.00244909i
$87$	11.2795	−	0.612578i	1.20929	−	0.0656752i
$88$	3.20267	+	0.940389i	0.341406	+	0.100246i
$89$	2.16744	+	4.74603i	0.229748	+	0.503078i	0.989036	−	0.147677i	$-0.0471797\pi$
$89$	2.16744	+	4.74603i	0.229748	+	0.503078i	−0.759288	+	0.650755i	$0.774452\pi$
$90$	1.11469	−	6.61494i	0.117498	−	0.697276i
$91$			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
$95$	−0.810497	−	5.25784i	−0.0831552	−	0.539443i
$96$	−1.01406	−	1.40417i	−0.103497	−	0.143312i
$97$	−4.90317	−	5.65856i	−0.497841	−	0.574539i	0.450103	−	0.892977i	$-0.351387\pi$
$97$	−4.90317	−	5.65856i	−0.497841	−	0.574539i	−0.947944	+	0.318437i	$0.896842\pi$
$98$	−15.8760	+	4.66161i	−1.60372	+	0.470894i
$99$	3.14889	−	9.50565i	0.316475	−	0.955354i
$100$	−4.15055	+	2.78800i	−0.415055	+	0.278800i
$101$	−12.7588	−	11.0556i	−1.26955	−	1.10007i	−0.990167	−	0.139893i	$-0.955324\pi$
$101$	−12.7588	−	11.0556i	−1.26955	−	1.10007i	−0.279385	−	0.960179i	$-0.590131\pi$
$102$	−0.952344	+	10.7275i	−0.0942961	+	1.06218i
$103$	2.50854	+	17.4473i	0.247174	+	1.71913i	0.614394	+	0.788999i	$0.289400\pi$
$103$	2.50854	+	17.4473i	0.247174	+	1.71913i	−0.367220	+	0.930134i	$0.619690\pi$
$104$	−1.20976	+	0.173937i	−0.118627	+	0.0170559i
$105$	6.69069	−	17.5621i	0.652945	−	1.71389i
$106$	−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	$0.706691\pi$
$108$	−4.31432	+	2.89597i	−0.415146	+	0.278665i
$109$	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	$0.659878\pi$
$110$	−6.75743	+	3.16927i	−0.644296	+	0.302178i
$111$	0.850612	+	1.17785i	0.0807365	+	0.111796i
$112$	−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
$115$	−10.6979	−	0.745333i	−0.997582	−	0.0695026i
$116$			6.52184i			0.605537i
$117$	0.397086	+	3.64503i	0.0367106	+	0.336983i
$118$	4.22749	−	1.93063i	0.389172	−	0.177729i
$119$	−8.50038	+	28.9496i	−0.779229	+	2.65381i
$120$	3.77862	+	0.849725i	0.344939	+	0.0775689i
$121$	−0.135698	+	0.0398446i	−0.0123362	+	0.00362224i
$122$	5.92790	−	9.22399i	0.536687	−	0.835101i
$123$	4.72413	+	9.01570i	0.425961	+	0.812918i
$124$	3.45138	−	3.98310i	0.309943	−	0.357693i
$125$	2.82192	−	10.8184i	0.252400	−	0.967623i
$126$	−13.4413	+	5.58983i	−1.19745	+	0.497981i
$127$	−17.5969	+	2.53005i	−1.56147	+	0.224506i	−0.868216	−	0.496186i	$-0.834733\pi$
$127$	−17.5969	+	2.53005i	−1.56147	+	0.224506i	−0.693255	+	0.720692i	$0.743824\pi$
$128$	0.841254	−	0.540641i	0.0743570	−	0.0477863i
$129$	−0.136927	+	0.0273370i	−0.0120558	+	0.00240689i
$130$	1.76863	−	2.08346i	0.155119	−	0.182731i
$131$	4.82999	−	7.51561i	0.421998	−	0.656642i	−0.563541	−	0.826088i	$-0.690561\pi$
$131$	4.82999	−	7.51561i	0.421998	−	0.656642i	0.985540	+	0.169446i	$0.0541977\pi$
$132$	5.38142	+	2.11295i	0.468393	+	0.183909i
$133$	−8.72491	+	7.56018i	−0.756545	+	0.655550i
$134$	−2.54154	−	0.746262i	−0.219555	−	0.0644672i
$135$	2.93629	−	11.2418i	0.252716	−	0.967541i
$136$	−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	$-0.156498\pi$
$138$	5.27817	+	6.41412i	0.449308	+	0.546006i
$139$	3.22829			0.273820			0.136910	−	0.990583i	$-0.456283\pi$
$139$	3.22829			0.273820			0.136910	+	0.990583i	$0.456283\pi$
$140$	9.91509	+	4.40704i	0.837978	+	0.372463i
$141$	−1.77473	+	7.53404i	−0.149459	+	0.634481i
$142$	−2.39735	+	8.16461i	−0.201181	+	0.685159i
$143$	3.08312	−	2.67154i	0.257823	−	0.223405i
$144$	−1.53445	−	2.57788i	−0.127871	−	0.214823i
$145$	−9.66135	−	10.9238i	−0.802331	−	0.907175i
$146$	3.03161	+	1.38449i	0.250898	+	0.114581i
$147$	−28.1043	+	5.61091i	−2.31800	+	0.462780i
$148$	−0.705662	+	0.453501i	−0.0580050	+	0.0372776i
$149$	1.45183	+	10.0977i	0.118939	+	0.827238i	0.958728	+	0.284325i	$0.0917695\pi$
$149$	1.45183	+	10.0977i	0.118939	+	0.827238i	−0.839789	+	0.542913i	$0.817321\pi$
$150$	−7.58782	+	4.17433i	−0.619543	+	0.340833i
$151$	−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
$153$	−3.28609	+	18.3618i	−0.265665	+	1.48447i
$154$	13.6257	+	8.75669i	1.09799	+	0.705634i
$155$	0.119574	+	11.7844i	0.00960439	+	0.946543i
$156$	−2.11380	+	0.114798i	−0.169239	+	0.00919117i
$157$	−10.2815	−	3.01891i	−0.820549	−	0.240935i	−0.155597	−	0.987821i	$-0.549730\pi$
$157$	−10.2815	−	3.01891i	−0.820549	−	0.240935i	−0.664952	+	0.746886i	$0.731548\pi$
$158$	5.62209	−	2.56752i	0.447270	−	0.204261i
$159$	−12.9940	−	13.4474i	−1.03049	−	1.06645i
$160$	−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	0.700071	−	0.714073i	$-0.253152\pi$
$163$	14.9453	+	2.14881i	1.17061	+	0.168308i	0.470536	+	0.882381i	$0.344061\pi$
$164$	−5.34546	+	2.44119i	−0.417411	+	0.190625i
$165$	−12.1438	+	4.43284i	−0.945392	+	0.345096i
$166$	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	$0.295853\pi$
$168$	−2.80170	−	7.92396i	−0.216156	−	0.611347i
$169$	4.77986	−	10.4664i	0.367682	−	0.805110i
$170$	11.6195	−	7.63512i	0.891178	−	0.585587i
$171$	−4.85621	+	5.23072i	−0.371364	+	0.400004i
$172$	−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	$-0.196156\pi$
$174$	−0.998902	+	11.2519i	−0.0757266	+	0.853005i
$175$	−23.1359	+	7.30643i	−1.74891	+	0.552314i
$176$	−1.38660	+	3.03624i	−0.104519	+	0.228865i
$177$	7.58924	−	2.68335i	0.570442	−	0.201693i
$178$	−5.00618	+	1.46995i	−0.375229	+	0.110177i
$179$	10.7953	−	9.35422i	0.806882	−	0.699167i	−0.150304	−	0.988640i	$-0.548025\pi$
$179$	10.7953	−	9.35422i	0.806882	−	0.699167i	0.957186	+	0.289473i	$0.0934799\pi$
$180$	6.38898	+	2.04474i	0.476206	+	0.152406i
$181$	−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
$186$	6.56460	−	6.34329i	0.481340	−	0.465112i
$187$	18.8789	−	8.62171i	1.38056	−	0.630482i
$188$	−4.28782	−	1.25902i	−0.312721	−	0.0918232i
$189$	−24.0460	+	7.58522i	−1.74909	+	0.551744i
$190$	5.31967	−	0.0539777i	0.385930	−	0.00391595i
$191$	−20.2556	−	13.0175i	−1.46564	−	0.941911i	−0.998327	−	0.0578200i	$-0.981585\pi$
$191$	−20.2556	−	13.0175i	−1.46564	−	0.941911i	−0.467315	−	0.884091i	$-0.654779\pi$
$192$	1.53419	−	0.803900i	0.110721	−	0.0580165i
$193$	17.2773	+	14.9708i	1.24364	+	1.07762i	0.994011	+	0.109284i	$0.0348559\pi$
$193$	17.2773	+	14.9708i	1.24364	+	1.07762i	0.249634	+	0.968340i	$0.419690\pi$
$194$	6.29875	−	4.04796i	0.452224	−	0.290627i
$195$	3.37047	−	3.32363i	0.241364	−	0.238010i
$196$	−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	$0.290694\pi$
$198$	8.96076	+	4.46963i	0.636814	+	0.317643i
$199$	−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	$0.750903\pi$
$200$	−2.16894	−	4.50508i	−0.153367	−	0.318557i
$201$	−4.27052	−	1.67677i	−0.301220	−	0.118270i
$202$	12.7588	−	11.0556i	0.897708	−	0.777869i
$203$	−8.91595	+	30.3649i	−0.625777	+	2.13120i
$204$	−10.4827	−	2.46933i	−0.733938	−	0.172887i
$205$	5.33711	−	12.0076i	0.372760	−	0.838647i
$206$	−17.6267			−1.22811
$207$	8.12384	+	11.8745i	0.564646	+	0.825333i
$208$		−	1.22220i		−	0.0847443i
$209$	7.86049	+	1.13017i	0.543721	+	0.0781753i
$210$	16.4312	+	9.12194i	1.13386	+	0.629474i
$211$	−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
$213$	−5.38657	+	13.7189i	−0.369082	+	0.940006i
$214$	2.45113	−	3.81404i	0.167556	−	0.260722i
$215$	0.137423	+	0.116657i	0.00937216	+	0.00795597i
$216$	−2.25250	−	4.68255i	−0.153263	−	0.318607i
$217$	21.5145	−	13.8265i	1.46050	−	0.938605i
$218$	−14.5784	+	2.09605i	−0.987371	+	0.141962i
$219$	5.01828	+	2.85294i	0.339104	+	0.192784i
$220$	−2.17533	−	7.13968i	−0.146660	−	0.481357i
$221$	−4.97659	+	5.74329i	−0.334762	+	0.386335i
$222$	−1.28691	+	0.674329i	−0.0863720	+	0.0452580i
$223$	−0.894659	+	1.39212i	−0.0599108	+	0.0932231i	−0.869917	−	0.493199i	$-0.835828\pi$
$223$	−0.894659	+	1.39212i	−0.0599108	+	0.0932231i	0.810006	+	0.586422i	$0.199464\pi$
$224$	4.65589	−	1.36709i	0.311085	−	0.0913427i
$225$	−13.7304	+	6.03966i	−0.915357	+	0.402644i
$226$	−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	$0.501830\pi$
$228$	−2.86347	−	2.96338i	−0.189638	−	0.196255i
$229$		−	16.1083i		−	1.06447i	−0.846597	−	0.532234i	$-0.821353\pi$
$229$		−	16.1083i		−	1.06447i	0.846597	−	0.532234i	$-0.178647\pi$
$230$	2.26021	−	10.4829i	0.149034	−	0.691223i
$231$	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	$0.923117\pi$
$234$	−3.66444	−	0.125698i	−0.239552	−	0.00821714i
$235$	9.04702	−	4.24310i	0.590163	−	0.276789i
$236$	1.30934	+	4.45922i	0.0852310	+	0.290270i
$237$	10.0929	−	3.56857i	0.655601	−	0.231803i
$238$	−27.4453	−	12.5338i	−1.77901	−	0.812447i
$239$	−5.58674	−	4.84094i	−0.361376	−	0.313134i	0.455181	−	0.890399i	$-0.349575\pi$
$239$	−5.58674	−	4.84094i	−0.361376	−	0.313134i	−0.816557	+	0.577265i	$0.804120\pi$
$240$	−1.37883	+	3.61923i	−0.0890031	+	0.233620i
$241$	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
$243$	−14.2710	+	6.27194i	−0.915488	+	0.402345i
$244$	8.28647	+	7.18027i	0.530487	+	0.459670i
$245$	28.2060	+	23.9439i	1.80201	+	1.52972i
$246$	−9.59624	+	3.39298i	−0.611834	+	0.216328i
$247$	−2.79001	+	0.819221i	−0.177524	+	0.0521258i
$248$	3.45138	+	3.98310i	0.219163	+	0.252927i
$249$	19.2402	−	13.8948i	1.21930	−	0.880548i
$250$	10.3066	+	4.33281i	0.651849	+	0.274031i
$251$	−0.398058	+	2.76855i	−0.0251252	+	0.174749i	−0.998520	−	0.0543845i	$-0.982680\pi$
$251$	−0.398058	+	2.76855i	−0.0251252	+	0.174749i	0.973395	+	0.229134i	$0.0735894\pi$
$252$	−3.62003	−	14.1001i	−0.228040	−	0.888220i
$253$	5.71856	−	14.9516i	0.359523	−	0.940000i
$254$		−	17.7778i		−	1.11548i
$255$	21.2162	−	11.3929i	1.32861	−	0.713453i
$256$	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	$0.336693\pi$
$258$	−0.00757195	−	0.139424i	−0.000471409	−	0.00868016i
$259$	−3.90546	+	1.14675i	−0.242673	+	0.0712553i
$260$	1.81055	+	2.04714i	0.112285	+	0.126958i
$261$	−3.44674	+	19.2595i	−0.213348	+	1.19213i
$262$	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	$0.698437\pi$
$264$	−2.85730	+	5.02594i	−0.175855	+	0.309326i
$265$	−3.19302	+	23.9291i	−0.196146	+	1.46995i
$266$	−6.24154	−	9.71203i	−0.382693	−	0.595482i
$267$	−8.86213	+	1.76929i	−0.542353	+	0.108279i
$268$	1.10036	−	2.40946i	0.0672155	−	0.147181i
$269$	3.21489	−	5.00247i	0.196016	−	0.305006i	−0.729307	−	0.684186i	$-0.760158\pi$
$269$	3.21489	−	5.00247i	0.196016	−	0.305006i	0.925323	+	0.379180i	$0.123794\pi$
$270$	10.7095	+	4.50628i	0.651760	+	0.274243i
$271$	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
$273$	−9.99853	−	2.35527i	−0.605139	−	0.142547i
$274$	10.9387	+	1.57275i	0.660830	+	0.0950131i
$275$	14.2202	+	8.73621i	0.857511	+	0.526813i
$276$	−7.09999	+	4.31162i	−0.427369	+	0.259529i
$277$			32.3648i			1.94462i	0.233705	+	0.972308i	$0.424915\pi$
$277$			32.3648i			1.94462i	−0.233705	+	0.972308i	$0.575085\pi$
$278$	−0.459434	+	3.19543i	−0.0275550	+	0.191649i
$279$	12.2972	−	9.93840i	0.736217	−	0.594996i
$280$	−5.77325	+	9.18698i	−0.345018	+	0.549027i
$281$	−3.09085	−	3.56703i	−0.184385	−	0.212791i	0.656031	−	0.754734i	$-0.272234\pi$
$281$	−3.09085	−	3.56703i	−0.184385	−	0.212791i	−0.840415	+	0.541943i	$0.817689\pi$
$282$	−7.20479	−	2.82887i	−0.429039	−	0.168457i
$283$	9.86425	+	6.33937i	0.586369	+	0.376837i	0.799930	−	0.600093i	$-0.204870\pi$
$283$	9.86425	+	6.33937i	0.586369	+	0.376837i	−0.213561	+	0.976930i	$0.568506\pi$
$284$	−7.74033	−	3.53489i	−0.459304	−	0.209757i
$285$	9.18612	+	0.721650i	0.544139	+	0.0427468i
$286$	2.20557	+	3.43194i	0.130418	+	0.202935i
$287$	−28.2252	+	4.05817i	−1.66608	+	0.239546i
$288$	2.77002	−	1.15196i	0.163225	−	0.0678799i
$289$	−18.2230	+	11.7112i	−1.07194	+	0.688896i
$290$	12.1876	−	8.00838i	0.715681	−	0.470269i
$291$	11.4870	−	6.01908i	0.673381	−	0.352845i
$292$	−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	$0.923938\pi$
$294$	−1.55414	−	28.6167i	−0.0906393	−	1.66896i
$295$	−8.79891	−	5.52938i	−0.512293	−	0.321933i
$296$	−0.348459	−	0.763019i	−0.0202538	−	0.0443496i
$297$	14.7751	+	9.08376i	0.857339	+	0.527093i
$298$	−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
$303$	23.7057	−	17.1197i	1.36186	−	0.983499i
$304$	1.79804	−	1.55801i	0.103125	−	0.0893582i
$305$	−24.5163	+	0.248762i	−1.40380	+	0.0142441i
$306$	−17.7073	−	5.86581i	−1.01226	−	0.335326i
$307$	−0.772740	−	0.352899i	−0.0441026	−	0.0201410i	0.393242	−	0.919435i	$-0.371354\pi$
$307$	−0.772740	−	0.352899i	−0.0441026	−	0.0201410i	−0.437344	+	0.899294i	$0.644081\pi$
$308$	−10.6067	+	12.2408i	−0.604372	+	0.697483i
$309$	−30.4108	−	2.69975i	−1.73001	−	0.153584i
$310$	−11.6814	−	1.55873i	−0.663461	−	0.0885301i
$311$	14.6416	−	2.10514i	0.830248	−	0.119372i	0.285930	−	0.958251i	$-0.407698\pi$
$311$	14.6416	−	2.10514i	0.830248	−	0.119372i	0.544318	+	0.838879i	$0.316789\pi$
$312$	0.187195	−	2.10862i	0.0105978	−	0.119377i
$313$	−21.6863	+	25.0273i	−1.22578	+	1.41463i	−0.346686	+	0.937981i	$0.612693\pi$
$313$	−21.6863	+	25.0273i	−1.22578	+	1.41463i	−0.879095	+	0.476646i	$0.841852\pi$
$314$	4.45138	−	9.74717i	0.251206	−	0.550064i
$315$	26.9510	+	18.2544i	1.51852	+	1.02852i
$316$	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	$0.573428\pi$
$318$	15.1598	−	10.9480i	0.850118	−	0.613934i
$319$	19.8019	−	9.04321i	1.10869	−	0.506323i
$320$	−2.04332	−	0.908211i	−0.114225	−	0.0507705i
$321$	4.81302	−	6.20480i	0.268637	−	0.346318i
$322$	−21.8710	+	7.95119i	−1.21882	+	0.443102i
$323$	−14.7932			−0.823118
$324$	−3.16897	−	8.42364i	−0.176054	−	0.467980i
$325$	−6.06520	−	0.746767i	−0.336437	−	0.0414232i
$326$	−4.25388	+	14.4874i	−0.235601	+	0.802382i
$327$	−25.4726	+	1.38338i	−1.40864	+	0.0765013i
$328$	−1.65561	−	5.63847i	−0.0914155	−	0.311333i
$329$	−18.2424	−	11.7237i	−1.00574	−	0.646347i
$330$	−2.65948	−	12.6510i	−0.146400	−	0.696416i
$331$	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
$333$	−2.32355	+	0.966290i	−0.127330	+	0.0529523i
$334$	1.28110	+	8.91022i	0.0700984	+	0.487545i
$335$	1.72627	+	5.66582i	0.0943161	+	0.309557i
$336$	8.24203	−	1.64549i	0.449640	−	0.0897687i
$337$	12.9115	−	28.2722i	0.703333	−	1.54009i	−0.132549	−	0.991176i	$-0.542316\pi$
$337$	12.9115	−	28.2722i	0.703333	−	1.54009i	0.835882	−	0.548909i	$-0.184957\pi$
$338$	9.67966	+	6.22074i	0.526504	+	0.338364i
$339$	−3.56520	+	9.08013i	−0.193635	+	0.493165i
$340$	5.90377	+	12.5879i	0.320177	+	0.682673i
$341$	−16.8793	−	4.95622i	−0.914068	−	0.268395i
$342$	−4.48637	−	5.55120i	−0.242595	−	0.300174i
$343$	6.59238	−	45.8510i	0.355955	−	2.47572i
$344$	0.0806151			0.00434648
$345$	5.50506	−	17.7396i	0.296382	−	0.955069i
$346$	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	$0.843045\pi$
$348$	−10.9952	−	2.59005i	−0.589405	−	0.138841i
$349$	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	$0.469110\pi$
$350$	−3.93947	−	23.9403i	−0.210574	−	1.27966i
$351$	−6.30288	−	0.778118i	−0.336423	−	0.0415329i
$352$	−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	$-0.0890641\pi$
$354$	1.57598	+	7.89387i	0.0837624	+	0.419555i
$355$	18.2013	−	5.54559i	0.966024	−	0.294329i
$356$	−0.742531	−	5.16442i	−0.0393541	−	0.273714i
$357$	−45.4306	−	25.8278i	−2.40444	−	1.36695i
$358$	7.72267	+	12.0167i	0.408156	+	0.635103i
$359$	−14.6951	+	16.9591i	−0.775579	+	0.895066i	−0.996782	−	0.0801615i	$-0.974456\pi$
$359$	−14.6951	+	16.9591i	−0.775579	+	0.895066i	0.221202	+	0.975228i	$0.429002\pi$
$360$	−2.93318	+	6.03295i	−0.154592	+	0.317964i
$361$	11.2220	+	7.21195i	0.590632	+	0.379576i
$362$	−0.755089	−	2.57160i	−0.0396866	−	0.135160i
$363$	−0.0132838	−	0.244598i	−0.000697221	−	0.0128381i
$364$	1.67086	−	5.69042i	0.0875768	−	0.298259i
$365$	−1.13537	−	7.36534i	−0.0594278	−	0.385520i
$366$	13.1966	+	13.6570i	0.689798	+	0.713865i
$367$	18.1073			0.945192			0.472596	−	0.881279i	$-0.343317\pi$
$367$	18.1073			0.945192			0.472596	+	0.881279i	$0.343317\pi$
$368$	−2.26336	−	4.22814i	−0.117986	−	0.220407i
$369$	−17.0757	+	4.38400i	−0.888928	+	0.228222i
$370$	1.71398	+	0.761827i	0.0891056	+	0.0396055i
$371$	47.6540	−	21.7629i	2.47407	−	1.12987i
$372$	5.34448	+	7.40053i	0.277098	+	0.383700i
$373$	−12.3454	−	14.2473i	−0.639219	−	0.737698i	0.340018	−	0.940419i	$-0.389567\pi$
$373$	−12.3454	−	14.2473i	−0.639219	−	0.737698i	−0.979236	+	0.202721i	$0.935021\pi$
$374$	5.84720	+	19.9137i	0.302352	+	1.02972i
$375$	17.1181	+	9.05384i	0.883973	+	0.467538i
$376$	1.85642	−	4.06500i	0.0957376	−	0.209636i
$377$	−5.21988	+	6.02407i	−0.268838	+	0.310255i
$378$	−4.08590	−	24.8808i	−0.210156	−	1.27973i
$379$	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	$0.337962\pi$
$380$	−0.703640	+	5.27321i	−0.0360960	+	0.270510i
$381$	2.72290	−	30.6715i	0.139499	−	1.57135i
$382$	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	$0.431059\pi$
$384$	0.577380	+	1.63298i	0.0294643	+	0.0833328i
$385$	−0.367471	−	36.2154i	−0.0187281	−	1.84571i
$386$	−17.2773	+	14.9708i	−0.879390	+	0.761996i
$387$	0.00829093	−	0.241703i	0.000421452	−	0.0122865i
$388$	3.11035	+	6.81073i	0.157904	+	0.345762i
$389$	3.01858	−	20.9947i	0.153048	−	1.06447i	−0.758024	−	0.652227i	$-0.773835\pi$
$389$	3.01858	−	20.9947i	0.153048	−	1.06447i	0.911072	−	0.412247i	$-0.135256\pi$
$390$	2.81013	+	3.80917i	0.142296	+	0.192885i
$391$	−6.58044	+	29.0847i	−0.332787	+	1.47088i
$392$	16.5462			0.835710
$393$	10.7525	+	11.1276i	0.542391	+	0.561315i
$394$	1.00575	+	2.20230i	0.0506692	+	0.110950i
$395$	−11.7016	−	7.35347i	−0.588771	−	0.369993i
$396$	−5.69939	+	8.23346i	−0.286405	+	0.413747i
$397$	−0.194218	−	0.661447i	−0.00974755	−	0.0331971i	0.954476	−	0.298289i	$-0.0964159\pi$
$397$	−0.194218	−	0.661447i	−0.00974755	−	0.0331971i	−0.964223	+	0.265092i	$0.914598\pi$
$398$	5.37104	−	8.35750i	0.269226	−	0.418924i
$399$	−9.28079	−	17.7118i	−0.464621	−	0.886699i
$400$	4.76789	−	1.50572i	0.238395	−	0.0752860i
$401$	10.8465	−	6.97064i	0.541650	−	0.348097i	−0.241034	−	0.970517i	$-0.577487\pi$
$401$	10.8465	−	6.97064i	0.541650	−	0.348097i	0.782684	+	0.622419i	$0.213850\pi$
$402$	2.26746	−	3.98843i	0.113091	−	0.198925i
$403$	6.37591	−	0.916718i	0.317607	−	0.0456650i
$404$	9.12729	+	14.2023i	0.454100	+	0.706593i
$405$	17.7865	+	9.41483i	0.883820	+	0.467826i
$406$	−28.7870	−	13.1466i	−1.42867	−	0.652454i
$407$	2.35541	+	1.51373i	0.116753	+	0.0750329i
$408$	3.93604	−	10.0246i	0.194863	−	0.496292i
$409$	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	$0.501738\pi$
$410$	11.1258	+	6.99165i	0.549465	+	0.345293i
$411$	18.6313	+	4.38880i	0.919012	+	0.216484i
$412$	2.50854	−	17.4473i	0.123587	−	0.859567i
$413$			22.5516i			1.10969i
$414$	−12.9098	+	6.35124i	−0.634480	+	0.312146i
$415$	−29.4841	−	8.33330i	−1.44732	−	0.409066i
$416$	1.20976	+	0.173937i	0.0593133	+	0.00852797i
$417$	−1.28207	+	5.44260i	−0.0627830	+	0.266525i
$418$	−2.23733	+	7.61964i	−0.109431	+	0.372689i
$419$	−11.9438	−	13.7838i	−0.583491	−	0.673384i	0.384861	−	0.922975i	$-0.374249\pi$
$419$	−11.9438	−	13.7838i	−0.583491	−	0.673384i	−0.968352	+	0.249590i	$0.919704\pi$
$420$	−11.3675	+	14.9657i	−0.554677	+	0.730253i
$421$	−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
$423$	−11.9969	−	5.98406i	−0.583309	−	0.290955i
$424$	5.83690	+	9.08239i	0.283465	+	0.441080i
$425$	−28.5361	−	12.3385i	−1.38420	−	0.598503i
$426$	−12.8127	−	7.28415i	−0.620778	−	0.352918i
$427$	28.7648	+	44.7589i	1.39203	+	2.16603i
$428$	3.42638	+	2.96898i	0.165620	+	0.143511i
$429$	3.27955	+	6.25881i	0.158338	+	0.302178i
$430$	−0.135027	+	0.119422i	−0.00651160	+	0.00575904i
$431$	15.1604	−	4.45149i	0.730249	−	0.214421i	0.104588	−	0.994516i	$-0.466648\pi$
$431$	15.1604	−	4.45149i	0.730249	−	0.214421i	0.625661	+	0.780095i	$0.284829\pi$
$432$	4.95545	−	1.56317i	0.238419	−	0.0752083i
$433$	7.25996	+	2.13172i	0.348892	+	0.102444i	0.451483	−	0.892280i	$-0.350895\pi$
$433$	7.25996	+	2.13172i	0.348892	+	0.102444i	−0.102591	+	0.994724i	$0.532713\pi$
$434$	10.6240	+	23.2632i	0.509966	+	1.11667i
$435$	22.2534	−	11.9499i	1.06697	−	0.572954i
$436$		−	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	$0.0893286\pi$
$440$	7.37659	−	1.13710i	0.351665	−	0.0542092i
$441$	1.70171	−	49.6095i	0.0810338	−	2.36236i
$442$	−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	$0.368091\pi$
$444$	−0.484318	−	1.36978i	−0.0229847	−	0.0650069i
$445$	8.89420	+	7.55023i	0.421625	+	0.357915i
$446$	−1.25062	−	1.08367i	−0.0592188	−	0.0513134i
$447$	−17.6004	−	1.56250i	−0.832471	−	0.0739037i
$448$	0.690575	+	4.80305i	0.0326266	+	0.226923i
$449$	17.6544	−	2.53831i	0.833160	−	0.119790i	0.287483	−	0.957786i	$-0.407181\pi$
$449$	17.6544	−	2.53831i	0.833160	−	0.119790i	0.545677	+	0.837995i	$0.316272\pi$
$450$	−4.02415	−	14.4501i	−0.189700	−	0.681186i
$451$	14.8241	+	12.8451i	0.698039	+	0.604854i
$452$	−5.12308	−	2.33963i	−0.240969	−	0.110047i
$453$	−5.38138	−	15.2200i	−0.252839	−	0.715097i
$454$	−3.57098	−	12.1616i	−0.167594	−	0.570774i
$455$	5.63107	+	12.0064i	0.263989	+	0.562870i
$456$	3.34073	−	2.41259i	0.156444	−	0.112980i
$457$	−9.77133	−	21.3962i	−0.457083	−	1.00087i	−0.988143	−	0.153538i	$-0.950933\pi$
$457$	−9.77133	−	21.3962i	−0.457083	−	1.00087i	0.531059	−	0.847335i	$-0.321794\pi$
$458$	15.9444	+	2.29245i	0.745031	+	0.107119i
$459$	−29.6514	−	12.8322i	−1.38401	−	0.598955i
$460$	10.0545	+	3.72908i	0.468796	+	0.173869i
$461$			1.49932i			0.0698304i	0.999390	+	0.0349152i	$0.0111161\pi$
$461$			1.49932i			0.0698304i	−0.999390	+	0.0349152i	$0.988884\pi$
$462$	−20.1742	+	19.4940i	−0.938588	+	0.906945i
$463$	−1.31129	+	0.598848i	−0.0609410	+	0.0278308i	−0.445652	−	0.895206i	$-0.647028\pi$
$463$	−1.31129	+	0.598848i	−0.0609410	+	0.0278308i	0.384711	+	0.923037i	$0.374301\pi$
$464$	1.83741	−	6.25766i	0.0852998	−	0.290504i
$465$	−19.9148	−	4.47839i	−0.923528	−	0.207680i
$466$	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	$-0.0436926\pi$
$468$	0.645923	−	3.60925i	0.0298578	−	0.166838i
$469$	8.41713	−	9.71388i	0.388667	−	0.448545i
$470$	2.91238	+	9.55879i	0.134338	+	0.440914i
$471$	9.17272	−	16.1347i	0.422657	−	0.743446i
$472$	−4.60017	+	0.661404i	−0.211740	+	0.0304436i
$473$	−0.226367	+	0.145478i	−0.0104084	+	0.00668906i
$474$	2.09588	+	10.4980i	0.0962669	+	0.482188i
$475$	−6.63307	−	9.87479i	−0.304346	−	0.453086i
$476$	16.3121	−	25.3821i	0.747665	−	1.16339i
$477$	27.8315	−	16.5663i	1.27432	−	0.758520i
$478$	5.58674	−	4.84094i	0.255532	−	0.221419i
$479$	28.1512	+	8.26594i	1.28626	+	0.377680i	0.852206	−	0.523206i	$-0.175264\pi$
$479$	28.1512	+	8.26594i	1.28626	+	0.377680i	0.434055	+	0.900886i	$0.357082\pi$
$480$	−3.38616	−	1.87987i	−0.154557	−	0.0858037i
$481$	−1.01477	−	0.145902i	−0.0462696	−	0.00665257i
$482$			10.3737i			0.472508i
$483$	−38.9512	+	10.3681i	−1.77234	+	0.471764i
$484$	0.141427			0.00642850
$485$	−15.2990	−	6.80009i	−0.694693	−	0.308776i
$486$	−4.17712	−	15.0184i	−0.189478	−	0.681247i
$487$	−10.5266	+	35.8502i	−0.477005	+	1.62453i	0.272235	+	0.962231i	$0.412237\pi$
$487$	−10.5266	+	35.8502i	−0.477005	+	1.62453i	−0.749240	+	0.662298i	$0.769581\pi$
$488$	−8.28647	+	7.18027i	−0.375111	+	0.325036i
$489$	−9.55800	+	24.3430i	−0.432228	+	1.10083i
$490$	−27.7143	+	24.5113i	−1.25201	+	1.10731i
$491$	3.12892	+	1.42893i	0.141206	+	0.0644867i	0.484765	−	0.874645i	$-0.338905\pi$
$491$	3.12892	+	1.42893i	0.141206	+	0.0644867i	−0.343559	+	0.939131i	$0.611632\pi$
$492$	−1.99275	−	9.98144i	−0.0898403	−	0.449998i
$493$	−34.1144	+	21.9240i	−1.53644	+	0.987407i
$494$	−0.413823	−	2.87820i	−0.0186188	−	0.129496i
$495$	−2.65065	−	22.2337i	−0.119138	−	0.999331i
$496$	−4.43374	+	2.84939i	−0.199081	+	0.127942i
$497$	−31.2056	−	27.0398i	−1.39976	−	1.21290i
$498$	11.0152	+	21.0218i	0.493604	+	0.942010i
$499$	−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	$-0.692727\pi$
$500$	−5.75549	+	9.58511i	−0.257394	+	0.428659i
$501$	0.845518	+	15.5687i	0.0377749	+	0.695558i
$502$	−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	$0.236960\pi$
$504$	14.4717	−	1.57653i	0.644621	−	0.0702244i
$505$	−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	−0.425735	−	0.904848i	$-0.639984\pi$
$509$	−0.466876	+	0.213215i	−0.0206939	+	0.00945060i	0.405041	+	0.914298i	$0.367257\pi$
$510$	8.25758	+	22.6216i	0.365652	+	1.00170i
$511$	−12.2221	+	10.5905i	−0.540674	+	0.468497i
$512$	−0.959493	+	0.281733i	−0.0424040	+	0.0124509i
$513$	−6.88995	−	10.2644i	−0.304199	−	0.453186i
$514$	−9.54202	+	20.8941i	−0.420880	+	0.921599i
$515$	21.6444	+	32.9397i	0.953768	+	1.45150i
$516$	0.139083	+	0.0123472i	0.00612277	+	0.000543557i
$517$	2.12283	+	14.7646i	0.0933619	+	0.649346i
$518$	−0.579269	−	4.02891i	−0.0254516	−	0.177020i
$519$	20.6933	+	1.83707i	0.908334	+	0.0806386i
$520$	−2.28397	+	1.50078i	−0.100159	+	0.0658135i
$521$	−8.65873	+	18.9600i	−0.379346	+	0.830652i	0.619607	+	0.784912i	$0.287292\pi$
$521$	−8.65873	+	18.9600i	−0.379346	+	0.830652i	−0.998953	+	0.0457398i	$0.985435\pi$
$522$	−18.5730	−	6.15258i	−0.812917	−	0.269291i
$523$	9.22426	−	2.70849i	0.403349	−	0.118434i	−0.0737644	−	0.997276i	$-0.523501\pi$
$523$	9.22426	−	2.70849i	0.403349	−	0.118434i	0.477113	+	0.878842i	$0.341683\pi$
$524$	−6.75174	+	5.85041i	−0.294951	+	0.255576i
$525$	−3.12988	−	41.9067i	−0.136599	−	1.82896i
$526$	−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
$531$	1.50994	+	13.8604i	0.0655257	+	0.601491i
$532$	10.5014	−	4.79584i	0.455295	−	0.207926i
$533$	−6.89134	−	2.02348i	−0.298497	−	0.0876466i
$534$	−0.490067	−	9.02372i	−0.0212073	−	0.390494i
$535$	−10.1373	+	0.102861i	−0.438272	+	0.00444706i
$536$	2.22834	+	1.43207i	0.0962496	+	0.0618559i
$537$	11.4831	+	21.9148i	0.495534	+	0.945695i
$538$	4.49403	+	3.89410i	0.193751	+	0.167886i
$539$	−46.4618	+	29.8592i	−2.00125	+	1.28613i
$540$	−5.98453	+	9.95918i	−0.257533	+	0.428575i
$541$	−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
$543$	−0.908857	−	4.55234i	−0.0390028	−	0.195360i
$544$	5.65596	+	2.58299i	0.242497	+	0.110745i
$545$	21.8182	+	24.6693i	0.934590	+	1.05672i
$546$	3.75423	−	9.56157i	0.160666	−	0.409198i
$547$	13.1168	−	11.3658i	0.560834	−	0.485965i	−0.327697	−	0.944783i	$-0.606272\pi$
$547$	13.1168	−	11.3658i	0.560834	−	0.485965i	0.888530	+	0.458818i	$0.151727\pi$
$548$	−3.11348	+	10.6035i	−0.133001	+	0.452960i
$549$	20.6759	+	25.5833i	0.882427	+	1.09187i
$550$	−10.6710	+	12.8322i	−0.455015	+	0.547166i
$551$	−15.5164			−0.661023
$552$	−3.25730	−	7.64133i	−0.138640	−	0.325237i
$553$			29.9911i			1.27535i
$554$	−32.0354	−	4.60600i	−1.36105	−	0.195690i
$555$	2.84039	+	1.57687i	0.120568	+	0.0669345i
$556$	−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	$0.283853\pi$
$558$	8.08716	+	13.5865i	0.342357	+	0.575160i
$559$	0.0532681	−	0.0828868i	0.00225300	−	0.00350574i
$560$	−8.27186	−	7.02193i	−0.349550	−	0.296731i
$561$	7.03794	+	35.2521i	0.297142	+	1.48834i
$562$	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	$0.385169\pi$
$564$	3.82543	−	6.72886i	0.161079	−	0.283336i
$565$	12.0469	−	3.67045i	0.506815	−	0.154417i
$566$	−7.67868	+	8.86166i	−0.322759	+	0.372484i
$567$	−3.23846	−	43.5518i	−0.136003	−	1.82900i
$568$	4.60047	−	7.15847i	0.193032	−	0.300363i
$569$	8.71612	−	2.55928i	0.365399	−	0.107291i	−0.0938787	−	0.995584i	$-0.529927\pi$
$569$	8.71612	−	2.55928i	0.365399	−	0.107291i	0.459277	+	0.888293i	$0.348108\pi$
$570$	−2.02162	+	8.98991i	−0.0846765	+	0.376546i
$571$	−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
$573$	29.9904	−	28.9793i	1.25287	−	1.21063i
$574$		−	28.5155i		−	1.19021i
$575$	−22.3652	+	8.64858i	−0.932693	+	0.360671i
$576$	0.746021	+	2.90576i	0.0310842	+	0.121073i
$577$	−46.6498	−	6.70723i	−1.94206	−	0.279226i	−0.943428	−	0.331578i	$-0.892419\pi$
$577$	−46.6498	−	6.70723i	−1.94206	−	0.279226i	−0.998629	+	0.0523524i	$0.983328\pi$
$578$	−8.99862	−	19.7042i	−0.374293	−	0.819588i
$579$	−32.1008	+	23.1824i	−1.33407	+	0.963429i
$580$	6.19239	+	13.2033i	0.257125	+	0.548236i
$581$	18.7322	+	63.7960i	0.777142	+	2.64670i
$582$	4.32304	+	12.2267i	0.179196	+	0.506813i
$583$	−32.7800	−	14.9701i	−1.35761	−	0.620000i
$584$	−2.51875	−	2.18251i	−0.104227	−	0.0903129i
$585$	4.26479	+	7.00223i	0.176328	+	0.289506i
$586$	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	$-0.222976\pi$
$588$	28.5466	+	2.53426i	1.17724	+	0.104511i
$589$	9.47641	+	8.21135i	0.390469	+	0.338343i
$590$	6.72532	−	7.92244i	0.276877	−	0.326162i
$591$	1.39788	+	3.95359i	0.0575013	+	0.162629i
$592$	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	$0.778288\pi$
$594$	−11.0940	+	13.3320i	−0.455193	+	0.547017i
$595$	10.2785	+	66.6787i	0.421378	+	2.73356i
$596$	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	$0.000141728\pi$
$599$			0.0217945i			0.000890501i	−1.00000		0.000445250i	$0.999858\pi$
$600$	8.45650	−	1.86750i	0.345235	−	0.0762406i
$601$	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
$603$	4.52285	−	6.53381i	0.184185	−	0.266077i
$604$	8.94281	−	2.62585i	0.363878	−	0.106844i
$605$	−0.236885	+	0.209508i	−0.00963075	+	0.00851770i
$606$	13.5717	+	25.9008i	0.551314	+	1.05215i
$607$	−19.5482	−	16.9386i	−0.793435	−	0.687516i	0.160663	−	0.987009i	$-0.448637\pi$
$607$	−19.5482	−	16.9386i	−0.793435	−	0.687516i	−0.954098	+	0.299494i	$0.903182\pi$
$608$	1.28627	+	2.00147i	0.0521650	+	0.0811703i
$609$	−47.6517	−	27.0904i	−1.93094	−	1.09776i
$610$	3.24280	−	24.3021i	0.131297	−	0.983965i
$611$	−2.95288	−	4.59476i	−0.119461	−	0.185884i
$612$	8.32611	−	16.6923i	0.336563	−	0.674745i
$613$	15.0218	−	32.8931i	0.606724	−	1.32854i	−0.318068	−	0.948068i	$-0.603034\pi$
$613$	15.0218	−	32.8931i	0.606724	−	1.32854i	0.924792	−	0.380472i	$-0.124239\pi$
$614$	0.459279	−	0.714652i	0.0185350	−	0.0288410i
$615$	18.1241	+	13.7665i	0.730836	+	0.555119i
$616$	−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	$0.955135\pi$
$618$	7.00018	−	29.7170i	0.281588	−	1.19539i
$619$	−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
$621$	−23.2455	+	8.98028i	−0.932811	+	0.360366i
$622$			14.7921i			0.593111i
$623$	3.60309	−	25.0600i	0.144355	−	1.00401i
$624$	2.06051	+	0.485378i	0.0824866	+	0.0194307i
$625$	−4.55898	−	24.5808i	−0.182359	−	0.983232i
$626$	−21.6863	−	25.0273i	−0.866758	−	1.00029i
$627$	−5.02703	+	12.8032i	−0.200760	+	0.511312i
$628$	9.01446	+	5.79324i	0.359716	+	0.231175i
$629$	−4.74434	−	2.16667i	−0.189169	−	0.0863908i
$630$	−21.9041	+	24.0788i	−0.872682	+	0.959322i
$631$	−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
$633$	9.90879	−	17.4294i	0.393839	−	0.692757i
$634$	−17.5544	+	11.2815i	−0.697175	+	0.448047i
$635$	−33.2221	+	21.8300i	−1.31838	+	0.866298i
$636$	8.67912	+	16.5635i	0.344149	+	0.656787i
$637$	10.9333	−	17.0125i	0.433191	−	0.674059i
$638$	6.13306	+	20.8873i	0.242810	+	0.826936i
$639$	−20.9897	−	14.5295i	−0.830338	−	0.574779i
$640$	1.18976	−	1.89327i	0.0470294	−	0.0748380i
$641$	−16.0864	−	35.2243i	−0.635375	−	1.39128i	−0.903791	−	0.427973i	$-0.859228\pi$
$641$	−16.0864	−	35.2243i	−0.635375	−	1.39128i	0.268417	−	0.963303i	$-0.413500\pi$
$642$	5.45668	+	5.64707i	0.215358	+	0.222872i
$643$	−26.9435			−1.06255			−0.531275	−	0.847200i	$-0.678287\pi$
$643$	−26.9435			−1.06255			−0.531275	+	0.847200i	$0.678287\pi$
$644$	−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	$-0.478902\pi$
$648$	8.78889	−	1.93790i	0.345260	−	0.0761280i
$649$	11.7237	−	10.1587i	0.460196	−	0.398762i
$650$	1.60233	−	5.89718i	0.0628487	−	0.231307i
$651$	14.7661	+	41.7624i	0.578729	+	1.63680i
$652$	−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	$0.168631\pi$
$654$	2.25582	−	25.4102i	0.0882096	−	0.993616i
$655$	2.64220	−	19.8011i	0.103239	−	0.773695i
$656$	5.81670	−	0.836315i	0.227104	−	0.0326526i
$657$	−6.80273	+	7.32735i	−0.265400	+	0.285867i
$658$	14.2005	−	16.3883i	0.553594	−	0.638881i
$659$	12.1960	−	26.7055i	0.475088	−	1.04030i	−0.508697	−	0.860946i	$-0.669873\pi$
$659$	12.1960	−	26.7055i	0.475088	−	1.04030i	0.983785	−	0.179352i	$-0.0574001\pi$
$660$	12.9007	−	0.831984i	0.502161	−	0.0323849i
$661$	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
$663$	−7.70628	−	10.6709i	−0.299287	−	0.414424i
$664$	−12.4640	+	5.69211i	−0.483696	+	0.220897i
$665$	−10.4850	+	23.5895i	−0.406592	+	0.914762i
$666$	−0.625779	−	2.43742i	−0.0242484	−	0.0944480i
$667$	−6.90214	+	30.5066i	−0.267252	+	1.18122i
$668$	−9.00184			−0.348292
$669$	−1.99168	−	2.06117i	−0.0770028	−	0.0796895i
$670$	−5.85383	+	0.902367i	−0.226153	+	0.0348615i
$671$	10.3110	−	35.1159i	0.398050	−	1.35563i
$672$	0.455776	+	8.39231i	0.0175820	+	0.323741i
$673$	7.36965	+	25.0987i	0.284079	+	0.967485i	0.970665	+	0.240436i	$0.0772905\pi$
$673$	7.36965	+	25.0987i	0.284079	+	0.967485i	−0.686586	+	0.727049i	$0.740891\pi$
$674$	26.1469	+	16.8036i	1.00714	+	0.647251i
$675$	−4.72950	−	25.5467i	−0.182039	−	0.983291i
$676$	−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	$0.465656\pi$
$678$	−8.48033	−	4.82115i	−0.325685	−	0.185155i
$679$	5.17057	+	35.9621i	0.198428	+	1.38010i
$680$	−13.2999	+	4.05224i	−0.510029	+	0.155396i
$681$	−4.29818	−	21.5290i	−0.164707	−	0.824993i
$682$	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	$0.596120\pi$
$684$	6.13317	−	3.65069i	0.234508	−	0.139588i
$685$	−10.4929	−	22.3728i	−0.400914	−	0.854819i
$686$	44.4461	+	13.0506i	1.69696	+	0.498273i
$687$	27.1571	+	6.39717i	1.03611	+	0.244067i
$688$	−0.0114727	+	0.0797946i	−0.000437394	+	0.00304214i
$689$	13.1952			0.502696
$690$	16.7756	+	7.97364i	0.638637	+	0.303551i
$691$	−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
$693$	−37.7916	+	30.5425i	−1.43558	+	1.16021i
$694$	−21.2298	−	6.23362i	−0.805871	−	0.236625i
$695$	6.53558	−	3.06522i	0.247909	−	0.116270i
$696$	4.12847	−	10.5147i	0.156489	−	0.398559i
$697$	−30.7388	−	19.7547i	−1.16432	−	0.748261i
$698$	−5.79522	+	12.6898i	−0.219352	+	0.480315i
$699$	9.63338	−	1.92327i	0.364368	−	0.0727446i
$700$	24.2572	−	0.492318i	0.916837	−	0.0186079i
$701$	3.67381	+	25.5519i	0.138758	+	0.965083i	0.933613	+	0.358283i	$0.116638\pi$
$701$	3.67381	+	25.5519i	0.138758	+	0.965083i	−0.794855	+	0.606799i	$0.792453\pi$
$702$	1.66719	−	6.12799i	0.0629241	−	0.231286i
$703$	−1.07895	−	1.67888i	−0.0406933	−	0.0633200i
$704$	2.18584	−	2.52260i	0.0823821	−	0.0950740i
$705$	3.56058	+	16.9375i	0.134099	+	0.637904i
$706$	20.5623	+	13.2146i	0.773871	+	0.497337i
$707$	23.0797	+	78.6023i	0.868003	+	2.95615i
$708$	−8.03781	+	0.436524i	−0.302079	+	0.0164056i
$709$	−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	$0.126970\pi$
$710$	2.89883	+	18.8052i	0.108791	+	0.705748i
$711$	2.00805	+	18.4328i	0.0753078	+	0.691285i
$712$	5.21752			0.195535
$713$	20.3595	−	14.9787i	0.762471	−	0.560958i
$714$	32.0303	−	41.2925i	1.19870	−	1.54533i
$715$	3.70509	−	8.33582i	0.138563	−	0.311742i
$716$	−12.9934	+	5.93391i	−0.485588	+	0.221761i
$717$	10.3801	−	7.49622i	0.387651	−	0.279952i
$718$	−14.6951	−	16.9591i	−0.548418	−	0.632908i
$719$	−9.67608	−	32.9537i	−0.360857	−	1.22897i	−0.917339	−	0.398106i	$-0.869668\pi$
$719$	−9.67608	−	32.9537i	−0.360857	−	1.22897i	0.556482	−	0.830859i	$-0.312151\pi$
$720$	−5.55411	−	3.76190i	−0.206989	−	0.140198i
$721$	35.5315	−	77.8032i	1.32326	−	2.89754i
$722$	−8.73560	+	10.0814i	−0.325105	+	0.375192i
$723$	−1.58886	+	17.8973i	−0.0590903	+	0.665609i
$724$	2.65288	−	0.381427i	0.0985936	−	0.0141756i
$725$	−29.9311	−	12.9417i	−1.11161	−	0.480641i
$726$	0.243999	+	0.0216614i	0.00905566	+	0.000803928i
$727$	1.34472	−	1.55190i	0.0498731	−	0.0575566i	−0.730265	−	0.683164i	$-0.760603\pi$
$727$	1.34472	−	1.55190i	0.0498731	−	0.0575566i	0.780138	+	0.625607i	$0.215149\pi$
$728$	5.39471	+	2.46368i	0.199941	+	0.0913101i
$729$	−4.90639	−	26.5505i	−0.181718	−	0.983351i
$730$	7.45195	−	0.0756135i	0.275809	−	0.00279858i
$731$	0.378822	−	0.328251i	0.0140112	−	0.0121408i
$732$	−15.3961	+	11.1187i	−0.569057	+	0.410959i
$733$	−17.4106	−	38.1240i	−0.643076	−	1.40814i	−0.897485	−	0.441044i	$-0.854608\pi$
$733$	−17.4106	−	38.1240i	−0.643076	−	1.40814i	0.254409	−	0.967097i	$-0.418119\pi$
$734$	−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
$738$	−1.90925	−	17.5259i	−0.0702803	−	0.645135i
$739$	−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	$0.979690\pi$
$740$	−0.997998	+	1.58812i	−0.0366871	+	0.0583803i
$741$	−0.273121	−	5.02904i	−0.0100334	−	0.184746i
$742$	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	$0.0281812\pi$
$744$	−8.08580	+	4.23688i	−0.296440	+	0.155331i
$745$	12.5268	+	19.0640i	0.458948	+	0.698453i
$746$	15.8592	−	10.1921i	0.580647	−	0.373159i
$747$	15.7844	+	37.9553i	0.577521	+	1.38871i
$748$	−20.5432	+	2.95367i	−0.751134	+	0.107997i
$749$	11.8940	+	18.5074i	0.434597	+	0.676246i
$750$	−11.3978	+	15.6553i	−0.416190	+	0.571652i
$751$	−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
$753$	−4.50944	−	1.77058i	−0.164333	−	0.0645234i
$754$	−5.21988	−	6.02407i	−0.190097	−	0.219384i
$755$	−11.0890	+	17.6459i	−0.403570	+	0.642201i
$756$	25.2090	−	0.503411i	0.916843	−	0.0183089i
$757$	−6.15408	+	42.8025i	−0.223674	+	1.55568i	0.500297	+	0.865854i	$0.333224\pi$
$757$	−6.15408	+	42.8025i	−0.223674	+	1.55568i	−0.723971	+	0.689831i	$0.757685\pi$
$758$			13.9439i			0.506465i
$759$	22.9360	+	15.5788i	0.832524	+	0.565474i
$760$	−5.11940	−	1.44693i	−0.185700	−	0.0524858i
$761$	−4.51009	−	0.648452i	−0.163490	−	0.0235064i	0.0600834	−	0.998193i	$-0.480863\pi$
$761$	−4.51009	−	0.648452i	−0.163490	−	0.0235064i	−0.223574	+	0.974687i	$0.571772\pi$
$762$	29.9718	+	7.06020i	1.08576	+	0.255764i
$763$	20.1349	−	68.5731i	0.728932	−	2.48251i
$764$	15.7676	+	18.1968i	0.570453	+	0.658338i
$765$	10.7817	+	40.2931i	0.389814	+	1.45680i
$766$	−12.7217	+	19.7954i	−0.459655	+	0.715238i
$767$	−2.35961	+	5.16683i	−0.0852007	+	0.186564i
$768$	−1.69853	+	0.339105i	−0.0612905	+	0.0122364i
$769$	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	$0.561181\pi$
$770$	35.8991	+	4.79026i	1.29371	+	0.172629i
$771$	−19.6627	+	34.5864i	−0.708135	+	1.24560i
$772$	−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	$0.699669\pi$
$774$	0.238063	+	0.0426045i	0.00855700	+	0.00153139i
$775$	11.4312	+	23.7435i	0.410619	+	0.852893i
$776$	−7.18405	+	2.10943i	−0.257892	+	0.0757241i
$777$	−0.382315	−	7.03966i	−0.0137155	−	0.252546i
$778$	20.3514	+	5.97572i	0.729634	+	0.214240i
$779$	−5.80797	−	12.7177i	−0.208092	−	0.455658i
$780$	−4.17032	+	2.23942i	−0.149321	+	0.0801842i
$781$			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
$785$	−23.6809	+	3.65041i	−0.845207	+	0.130289i
$786$	−12.5446	+	9.05940i	−0.447451	+	0.323138i
$787$	2.55237	+	2.94559i	0.0909820	+	0.104999i	0.799415	−	0.600779i	$-0.205143\pi$
$787$	2.55237	+	2.94559i	0.0909820	+	0.104999i	−0.708433	+	0.705778i	$0.750598\pi$
$788$	−2.32301	+	0.682098i	−0.0827539	+	0.0242987i
$789$	−19.4583	+	6.87993i	−0.692733	+	0.244932i
$790$	8.94393	−	10.5360i	0.318211	−	0.374853i
$791$	−20.6540	−	17.8968i	−0.734371	−	0.636336i
$792$	−7.33855	−	6.81312i	−0.260764	−	0.242094i
$793$	1.90715	+	13.2645i	0.0677247	+	0.471036i
$794$	0.682355	−	0.0981078i	0.0242159	−	0.00348172i
$795$	−39.0742	−	14.8862i	−1.38582	−	0.527959i
$796$	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	$0.880687\pi$
$798$	18.8523	−	6.66568i	0.667364	−	0.235962i
$799$	−7.82839	−	26.6610i	−0.276948	−	0.943200i
$800$	0.811853	+	4.93365i	0.0287033	+	0.174431i
$801$	0.536601	−	15.6434i	0.0189599	−	0.552731i
$802$	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
$805$	41.7148	+	31.1077i	1.47026	+	1.09640i
$806$			6.44148i			0.226891i
$807$	7.15696	+	7.40667i	0.251937	+	0.260727i
$808$	−15.3567	+	7.01318i	−0.540248	+	0.246723i
$809$	2.94322	−	10.0237i	0.103478	−	0.352414i	−0.891435	−	0.453148i	$-0.850301\pi$
$809$	2.94322	−	10.0237i	0.103478	−	0.352414i	0.994913	+	0.100734i	$0.0321190\pi$
$810$	−11.8503	+	16.2656i	−0.416377	+	0.571516i
$811$	−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
$813$	−4.85155	+	2.54216i	−0.170151	+	0.0891575i
$814$	−1.83353	+	2.11601i	−0.0642653	+	0.0741662i
$815$	32.2966	−	9.84016i	1.13130	−	0.344686i
$816$	9.36242	+	5.32263i	0.327750	+	0.186329i
$817$	0.189844	−	0.0272954i	0.00664178	−	0.000954944i
$818$	−25.5936	+	16.4480i	−0.894858	+	0.575090i
$819$	7.94153	−	15.9212i	0.277499	−	0.556333i
$820$	−8.50385	+	10.0176i	−0.296967	+	0.349828i
$821$	−4.25616	+	6.62271i	−0.148541	+	0.231134i	−0.907548	−	0.419948i	$-0.862048\pi$
$821$	−4.25616	+	6.62271i	−0.148541	+	0.231134i	0.759007	+	0.651082i	$0.225685\pi$
$822$	−6.99564	+	17.8170i	−0.244001	+	0.621440i
$823$	0.779323	−	0.675287i	0.0271655	−	0.0235390i	−0.641172	−	0.767397i	$-0.721552\pi$
$823$	0.779323	−	0.675287i	0.0271655	−	0.0235390i	0.668338	+	0.743858i	$0.267006\pi$
$824$	16.9127	+	4.96602i	0.589182	+	0.172999i
$825$	−20.3758	+	20.5045i	−0.709394	+	0.713875i
$826$	−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	$0.913452\pi$
$828$	−4.44934	−	13.6822i	−0.154625	−	0.475490i
$829$	21.4942			0.746524			0.373262	−	0.927726i	$-0.378239\pi$
$829$	21.4942			0.746524			0.373262	+	0.927726i	$0.378239\pi$
$830$	12.4445	−	27.9980i	0.431955	−	0.971825i
$831$	−54.5641	−	12.8532i	−1.89281	−	0.445873i
$832$	−0.344333	+	1.17269i	−0.0119376	+	0.0406558i
$833$	77.7531	−	67.3734i	2.69398	−	2.33435i
$834$	−5.20475	−	2.04358i	−0.180226	−	0.0707634i
$835$	15.0778	−	13.3352i	0.521787	−	0.461483i
$836$	−7.22368	−	3.29894i	−0.249836	−	0.114096i
$837$	11.8716	+	24.6789i	0.410341	+	0.853027i
$838$	15.3433	−	9.86055i	0.530026	−	0.340627i
$839$	−0.0621969	−	0.432589i	−0.00214728	−	0.0149346i	0.988720	−	0.149778i	$-0.0478559\pi$
$839$	−0.0621969	−	0.432589i	−0.00214728	−	0.0149346i	−0.990867	+	0.134843i	$0.956947\pi$
$840$	−13.1956	−	13.3816i	−0.455293	−	0.461710i
$841$	−11.3858	+	7.31723i	−0.392615	+	0.252318i
$842$	−10.4077	−	9.01831i	−0.358672	−	0.310791i
$843$	7.24116	−	3.79429i	0.249399	−	0.130682i
$844$	9.73783	+	6.25812i	0.335190	+	0.215413i
$845$	−0.261051	−	25.7274i	−0.00898042	−	0.885049i
$846$	7.63049	−	11.0232i	0.262341	−	0.378984i
$847$	0.658469	+	0.193344i	0.0226252	+	0.00664337i
$848$	−9.82063	+	4.48493i	−0.337242	+	0.154013i
$849$	−14.6050	+	14.1126i	−0.501243	+	0.484344i
$850$	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	0.673846	−	0.738872i	$-0.264641\pi$
$853$	32.4840	+	4.67050i	1.11223	+	0.159915i	0.438386	+	0.898787i	$0.355550\pi$
$854$	−48.3970	+	22.1022i	−1.65611	+	0.756320i
$855$	−4.86476	+	15.2003i	−0.166371	+	0.519841i
$856$	−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	$0.588162\pi$
$858$	−6.66184	+	2.35545i	−0.227431	+	0.0804137i
$859$	−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	$0.149713\pi$
$860$	−0.0989900	−	0.150649i	−0.00337553	−	0.00513707i
$861$	4.36750	−	49.1967i	0.148844	−	1.67662i
$862$	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	$-0.161923\pi$
$864$	0.842030	+	5.12747i	0.0286464	+	0.174440i
$865$	−14.7282	−	22.4141i	−0.500772	−	0.762103i
$866$	−3.14322	+	6.88269i	−0.106811	+	0.233883i
$867$	−12.5071	−	35.3733i	−0.424762	−	1.20134i
$868$	−24.5384	+	7.20512i	−0.832887	+	0.244558i
$869$	15.5912	−	13.5099i	0.528896	−	0.458291i
$870$	8.66128	+	23.7276i	0.293645	+	0.804440i
$871$	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
$876$	−4.01124	−	4.15119i	−0.135527	−	0.140256i
$877$	−28.0338	+	12.8026i	−0.946635	+	0.432314i	−0.828065	−	0.560632i	$-0.810558\pi$
$877$	−28.0338	+	12.8026i	−0.946635	+	0.432314i	−0.118570	+	0.992946i	$0.537831\pi$
$878$	−5.52441	−	1.62211i	−0.186440	−	0.0547437i
$879$	2.76070	−	0.149930i	0.0931160	−	0.00505702i
$880$	0.0757290	+	7.46334i	0.00255283	+	0.251589i
$881$	40.1117	+	25.7782i	1.35140	+	0.868491i	0.997760	−	0.0668911i	$-0.0213080\pi$
$881$	40.1117	+	25.7782i	1.35140	+	0.868491i	0.353638	+	0.935382i	$0.384944\pi$
$882$	48.8624	+	8.74456i	1.64528	+	0.294445i
$883$	−5.31685	−	4.60707i	−0.178926	−	0.155040i	0.560793	−	0.827956i	$-0.310496\pi$
$883$	−5.31685	−	4.60707i	−0.178926	−	0.155040i	−0.739719	+	0.672916i	$0.765042\pi$
$884$	6.39307	−	4.10858i	0.215022	−	0.138186i
$885$	12.8164	−	12.6382i	0.430818	−	0.424830i
$886$	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	$0.0215145\pi$
$888$	1.42476	−	0.284449i	0.0478120	−	0.00954547i
$889$	78.4703	+	35.8362i	2.63181	+	1.20191i
$890$	−8.73916	+	7.72916i	−0.292937	+	0.259082i
$891$	−21.1821	+	21.3020i	−0.709626	+	0.713644i
$892$	1.25062	−	1.08367i	0.0418740	−	0.0362840i
$893$	2.99539	−	10.2014i	0.100237	−	0.341376i
$894$	4.05139	−	17.1989i	0.135499	−	0.575217i
$895$	12.9731	−	29.1874i	0.433644	−	0.975626i
$896$	−4.85245			−0.162109
$897$	−10.0090	−	1.70008i	−0.334190	−	0.0567640i
$898$			17.8359i			0.595192i
$899$	34.0228	+	4.89174i	1.13472	+	0.163149i
$900$	14.8757	−	1.92672i	0.495858	−	0.0642240i
$901$	64.4104	+	18.9126i	2.14582	+	0.630070i
$902$	−14.8241	+	12.8451i	−0.493588	+	0.427697i
$903$	0.630673	+	0.247626i	0.0209875	+	0.00824047i
$904$	3.04491	−	4.73797i	0.101272	−	0.157583i
$905$	−3.87844	+	4.56881i	−0.128924	+	0.151873i
$906$	15.8309	−	3.16058i	0.525947	−	0.105003i
$907$	−3.61375	+	2.32241i	−0.119992	+	0.0771145i	−0.599260	−	0.800554i	$-0.704539\pi$
$907$	−3.61375	+	2.32241i	−0.119992	+	0.0771145i	0.479268	+	0.877669i	$0.340902\pi$
$908$	12.5461	−	1.80385i	0.416355	−	0.0598629i
$909$	19.4478	+	46.7644i	0.645043	+	1.55108i
$910$	−12.6856	+	3.86506i	−0.420524	+	0.128126i
$911$	−10.4131	+	12.0174i	−0.345001	+	0.398153i	−0.901559	−	0.432656i	$-0.857576\pi$
$911$	−10.4131	+	12.0174i	−0.345001	+	0.398153i	0.556558	+	0.830809i	$0.312122\pi$
$912$	1.91260	+	3.65008i	0.0633326	+	0.120866i
$913$	24.7269	−	38.4758i	0.818342	−	1.27336i
$914$	22.5690	−	6.62687i	0.746517	−	0.219197i
$915$	9.31687	−	41.4310i	0.308006	−	1.36967i
$916$	−4.53824	+	15.4558i	−0.149948	+	0.510675i
$917$	−39.4334	+	18.0086i	−1.30220	+	0.594697i
$918$	16.9214	−	27.5233i	0.558489	−	0.908406i
$919$		−	40.9080i		−	1.34943i	−0.738079	−	0.674715i	$-0.764267\pi$
$919$		−	40.9080i		−	1.34943i	0.738079	−	0.674715i	$-0.235733\pi$
$920$	−5.12204	+	9.42150i	−0.168869	+	0.310618i
$921$	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
$924$	−16.4245	−	22.7431i	−0.540327	−	0.748194i
$925$	−0.681000	−	4.13845i	−0.0223911	−	0.136071i
$926$	−0.406136	−	1.38317i	−0.0133465	−	0.0454539i
$927$	16.6287	−	50.1976i	0.546158	−	1.64870i
$928$	5.93247	+	2.70927i	0.194743	+	0.0889361i
$929$	−11.4904	−	9.95647i	−0.376987	−	0.326661i	0.445672	−	0.895196i	$-0.352965\pi$
$929$	−11.4904	−	9.95647i	−0.376987	−	0.326661i	−0.822659	+	0.568535i	$0.807510\pi$
$930$	7.26698	−	19.0748i	0.238294	−	0.625487i
$931$	38.9653	−	5.60236i	1.27704	−	0.183610i
$932$	0.807152	+	5.61387i	0.0264392	+	0.183888i
$933$	−2.26560	+	25.5204i	−0.0741725	+	0.835499i
$934$	21.2532	+	18.4160i	0.695428	+	0.602591i
$935$	30.0336	−	35.3797i	0.982203	−	1.15704i
$936$	3.48059	+	1.15300i	0.113767	+	0.0376870i
$937$	33.0757	−	9.71190i	1.08054	−	0.317274i	0.307443	−	0.951566i	$-0.400527\pi$
$937$	33.0757	−	9.71190i	1.08054	−	0.317274i	0.773093	+	0.634292i	$0.218708\pi$
$938$	8.41713	+	9.71388i	0.274829	+	0.317170i
$939$	−33.5814	−	46.5003i	−1.09589	−	1.51748i
$940$	−9.87597	+	1.52238i	−0.322119	+	0.0496546i
$941$	5.15384	−	35.8458i	0.168011	−	1.16854i	−0.714979	−	0.699146i	$-0.753564\pi$
$941$	5.15384	−	35.8458i	0.168011	−	1.16854i	0.882989	−	0.469393i	$-0.155527\pi$
$942$	14.6650	+	11.3756i	0.477812	+	0.370636i
$943$	−27.5875	+	5.76176i	−0.898373	+	0.187629i
$944$		−	4.64747i		−	0.151262i
$945$	−41.4784	+	38.1874i	−1.34929	+	1.24224i
$946$	−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	$0.886235\pi$
$948$	−10.6894	+	0.580528i	−0.347176	+	0.0188547i
$949$	−3.90833	+	1.14759i	−0.126870	+	0.0372523i
$950$	10.7183	−	5.16023i	0.347746	−	0.167420i
$951$	−32.0140	+	16.7750i	−1.03812	+	0.543966i
$952$	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	$-0.407711\pi$
$954$	12.4369	+	29.9058i	0.402659	+	0.968237i
$955$	−53.3667	−	7.12108i	−1.72691	−	0.230433i
$956$	3.99659	+	6.21881i	0.129259	+	0.201131i
$957$	7.38201	+	36.9755i	0.238626	+	1.19525i
$958$	−12.1881	+	26.6883i	−0.393781	+	0.862260i
$959$	−28.9920	+	45.1124i	−0.936200	+	1.45676i
$960$	2.34263	−	3.08417i	0.0756081	−	0.0995410i
$961$	2.11055	+	2.43570i	0.0680822	+	0.0785711i
$962$	0.288834	−	0.983679i	0.00931239	−	0.0317151i
$963$	8.54931	+	10.5785i	0.275498	+	0.340886i
$964$	−10.2681	−	1.47633i	−0.330713	−	0.0475493i
$965$	49.1919	+	13.9035i	1.58354	+	0.447569i
$966$	−4.71923	−	40.0302i	−0.151839	−	1.28795i
$967$		−	43.4317i		−	1.39667i	−0.715772	−	0.698335i	$-0.753925\pi$
$967$		−	43.4317i		−	1.39667i	0.715772	−	0.698335i	$-0.246075\pi$
$968$	−0.0201272	+	0.139988i	−0.000646912	+	0.00449937i
$969$	5.87490	−	24.9400i	0.188729	−	0.801189i
$970$	8.90815	−	14.1756i	0.286023	−	0.455150i
$971$	13.1848	+	15.2160i	0.423119	+	0.488305i	0.926785	−	0.375593i	$-0.122561\pi$
$971$	13.1848	+	15.2160i	0.423119	+	0.488305i	−0.503666	+	0.863899i	$0.668016\pi$
$972$	15.4600	−	1.99727i	0.495879	−	0.0640623i
$973$	−13.1783	−	8.46920i	−0.422478	−	0.271510i
$974$	−33.9872	−	15.5215i	−1.08902	−	0.497339i
$975$	3.66768	−	9.92879i	0.117460	−	0.317976i
$976$	−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	$0.620816\pi$
$978$	−22.7350	−	12.9251i	−0.726986	−	0.413299i
$979$	−14.6508	+	9.41551i	−0.468242	+	0.300921i
$980$	−20.3177	−	30.9205i	−0.649024	−	0.987721i
$981$	7.78378	−	43.4938i	0.248517	−	1.38865i
$982$	−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	$0.994384\pi$
$984$	10.1634	−	0.551964i	0.323999	−	0.0175960i
$985$	2.88051	−	4.58376i	0.0917808	−	0.146051i
$986$	−16.8459	−	36.8873i	−0.536481	−	1.17473i
$987$	27.0097	−	26.0991i	0.859729	−	0.830744i
$988$	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
$993$	29.5460	+	40.9126i	0.937616	+	1.29832i
$994$	31.2056	−	27.0398i	0.989781	−	0.857650i
$995$	−22.2133	+	0.225394i	−0.704208	+	0.00714546i
$996$	−22.3755	+	7.91138i	−0.708994	+	0.250682i
$997$	15.6127	+	7.13008i	0.494459	+	0.225812i	0.647007	−	0.762484i	$-0.276021\pi$
$997$	15.6127	+	7.13008i	0.494459	+	0.225812i	−0.152548	+	0.988296i	$0.548748\pi$
$998$	27.0139	−	31.1757i	0.855109	−	0.986849i
$999$	−0.706313	−	4.30104i	−0.0223468	−	0.136079i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.142315 + 0.989821i) q^{2} +(-0.397135 + 1.68591i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(2.02447 - 0.949486i) q^{5} +(-1.61223 - 0.633022i) q^{6} +(-4.08214 - 2.62343i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-2.68457 - 1.33906i) q^{9} +O(q^{10})\)	\(q+(-0.142315 + 0.989821i) q^{2} +(-0.397135 + 1.68591i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(2.02447 - 0.949486i) q^{5} +(-1.61223 - 0.633022i) q^{6} +(-4.08214 - 2.62343i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-2.68457 - 1.33906i) q^{9} +(0.651709 + 2.13899i) q^{10} +(0.475030 + 3.30390i) q^{11} +(0.856023 - 1.50573i) q^{12} +(-0.660771 - 1.02818i) q^{13} +(3.17768 - 3.66723i) q^{14} +(0.796759 + 3.79014i) q^{15} +(0.841254 + 0.540641i) q^{16} +(-1.75177 - 5.96599i) q^{17} +(1.70749 - 2.46667i) q^{18} +(0.670285 - 2.28278i) q^{19} +(-2.20997 + 0.340666i) q^{20} +(6.04402 - 5.84025i) q^{21} -3.33788 q^{22} +(-4.18997 - 2.33328i) q^{23} +(1.36858 + 1.06160i) q^{24} +(3.19695 - 3.84441i) q^{25} +(1.11175 - 0.507720i) q^{26} +(3.32367 - 3.99414i) q^{27} +(3.17768 + 3.66723i) q^{28} +(-1.83741 - 6.25766i) q^{29} +(-3.86495 + 0.249255i) q^{30} +(-2.18940 + 4.79412i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(-5.75873 - 0.511238i) q^{33} +(6.15457 - 0.884894i) q^{34} +(-10.7551 - 1.43512i) q^{35} +(2.19857 + 2.04115i) q^{36} +(0.549311 - 0.633939i) q^{37} +(2.16415 + 0.988336i) q^{38} +(1.99583 - 0.705673i) q^{39} +(-0.0226878 - 2.23595i) q^{40} +(4.44117 - 3.84830i) q^{41} +(4.92065 + 6.81365i) 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} +(-1.24556 + 1.20357i) q^{48} +(6.87355 + 15.0510i) q^{49} +(3.35031 + 3.71153i) q^{50} +(10.7538 - 0.584026i) q^{51} +(0.344333 + 1.17269i) q^{52} +(-5.83690 + 9.08239i) q^{53} +(3.48048 + 3.85827i) q^{54} +(4.09869 + 6.23762i) q^{55} +(-4.08214 + 2.62343i) q^{56} +(3.58236 + 2.03661i) q^{57} +(6.45546 - 0.928154i) q^{58} +(-2.51261 - 3.90970i) q^{59} +(0.303322 - 3.86109i) q^{60} +(-9.97373 - 4.55485i) q^{61} +(-4.43374 - 2.84939i) q^{62} +(7.44583 + 12.5090i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(-2.31395 - 1.45412i) q^{65} +(1.32559 - 5.62735i) q^{66} +(-0.376968 + 2.62187i) q^{67} +6.21786i q^{68} +(5.59767 - 6.13727i) q^{69} +(2.95112 - 10.4414i) q^{70} +(8.42268 + 1.21100i) q^{71} +(-2.33327 + 1.88570i) q^{72} +(0.938954 - 3.19778i) q^{73} +(0.549311 + 0.633939i) q^{74} +(5.21170 + 6.91652i) q^{75} +(-1.28627 + 2.00147i) q^{76} +(6.72842 - 14.7332i) q^{77} +(0.414454 + 2.07594i) q^{78} +(-3.34150 - 5.19947i) q^{79} +(2.21642 + 0.295752i) q^{80} +(5.41381 + 7.18962i) q^{81} +(3.17708 + 4.94364i) q^{82} +(-10.3554 - 8.97304i) q^{83} +(-7.44458 + 3.90088i) q^{84} +(-9.21104 - 10.4147i) q^{85} +(-0.0773497 + 0.0227119i) q^{86} +(11.2795 - 0.612578i) q^{87} +(3.20267 + 0.940389i) q^{88} +(2.16744 + 4.74603i) q^{89} +(1.11469 - 6.61494i) q^{90} +5.93065i q^{91} +(3.36288 + 3.41921i) q^{92} +(-7.21296 - 5.59504i) q^{93} +(-0.635982 + 4.42335i) q^{94} +(-0.810497 - 5.25784i) q^{95} +(-1.01406 - 1.40417i) q^{96} +(-4.90317 - 5.65856i) q^{97} +(-15.8760 + 4.66161i) q^{98} +(3.14889 - 9.50565i) 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

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