LMFDB - Embedded newform 690.2.n.b.89.14

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			89.14
Character	$\chi$	$=$	690.89
Dual form			690.2.n.b.659.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 + 0.989821i) q^{2} +(0.397135 + 1.68591i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-1.22793 - 1.86874i) q^{5} +(-1.61223 + 0.633022i) q^{6} +(4.08214 - 2.62343i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-2.68457 + 1.33906i) q^{9} +O(q^{10})$	\(q+(0.142315 + 0.989821i) q^{2} +(0.397135 + 1.68591i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-1.22793 - 1.86874i) 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} +(1.67496 - 1.48138i) 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} +(2.66286 - 2.81232i) 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} +(1.70468 + 1.44709i) q^{20} +(6.04402 + 5.84025i) 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} +(-3.32367 - 3.99414i) q^{27} +(-3.17768 + 3.66723i) q^{28} +(-1.83741 + 6.25766i) q^{29} +(3.16266 + 2.23552i) 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} +(-9.91509 - 4.40704i) 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} +(-1.18976 + 1.89327i) 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} +(5.79883 + 3.37247i) q^{45} +(2.90582 + 3.81526i) q^{46} -4.46884 q^{47} +(1.24556 + 1.20357i) q^{48} +(6.87355 - 15.0510i) q^{49} +(-4.82506 - 1.31102i) 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} +(-6.75743 + 3.16927i) 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} +(-1.76268 + 3.44862i) 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} +(-2.73278 + 0.0277290i) 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} +(-8.52531 - 1.52285i) 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} +(-2.04332 - 0.908211i) 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} +(-13.2999 + 4.05224i) 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} +(-2.51288 + 6.21976i) 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} +(-1.01406 + 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} - 102 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 - 102 * 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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{22}\right)$

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
$5$	−1.22793	−	1.86874i	−0.549149	−	0.835725i
$5$	−1.22793	−	1.86874i	−0.549149	−	0.835725i
$6$	−1.61223	+	0.633022i	−0.658190	+	0.258430i
$7$	4.08214	−	2.62343i	1.54290	−	0.991563i	0.555829	−	0.831297i	$-0.312401\pi$
$7$	4.08214	−	2.62343i	1.54290	−	0.991563i	0.987074	−	0.160267i	$-0.0512354\pi$
$8$	−0.415415	−	0.909632i	−0.146871	−	0.321603i
$9$	−2.68457	+	1.33906i	−0.894856	+	0.446355i
$10$	1.67496	−	1.48138i	0.529670	−	0.468455i
$11$	0.475030	−	3.30390i	0.143227	−	0.996164i	−0.783758	−	0.621066i	$-0.786700\pi$
$11$	0.475030	−	3.30390i	0.143227	−	0.996164i	0.926985	−	0.375098i	$-0.122391\pi$
$12$	−0.856023	−	1.50573i	−0.247113	−	0.434667i
$13$	0.660771	−	1.02818i	0.183265	−	0.285166i	−0.737450	−	0.675402i	$-0.763970\pi$
$13$	0.660771	−	1.02818i	0.183265	−	0.285166i	0.920715	+	0.390236i	$0.127607\pi$
$14$	3.17768	+	3.66723i	0.849270	+	0.980109i
$15$	2.66286	−	2.81232i	0.687548	−	0.726139i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	1.75177	−	5.96599i	0.424867	−	1.44697i	−0.417804	−	0.908537i	$-0.637200\pi$
$17$	1.75177	−	5.96599i	0.424867	−	1.44697i	0.842671	−	0.538428i	$-0.180982\pi$
$18$	−1.70749	−	2.46667i	−0.402459	−	0.581401i
$19$	0.670285	+	2.28278i	0.153774	+	0.523706i	0.999958	−	0.00918523i	$-0.00292379\pi$
$19$	0.670285	+	2.28278i	0.153774	+	0.523706i	−0.846184	+	0.532891i	$0.821106\pi$
$20$	1.70468	+	1.44709i	0.381178	+	0.323579i
$21$	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
$25$	−1.98436	+	4.58937i	−0.396872	+	0.917874i
$26$	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	0.592981	+	0.805216i	$0.297951\pi$
$29$	−1.83741	+	6.25766i	−0.341199	+	1.16202i	−0.934180	+	0.356801i	$0.883867\pi$
$30$	3.16266	+	2.23552i	0.577420	+	0.408149i
$31$	−2.18940	−	4.79412i	−0.393228	−	0.861050i	−0.997912	−	0.0645844i	$-0.979428\pi$
$31$	−2.18940	−	4.79412i	−0.393228	−	0.861050i	0.604684	−	0.796466i	$-0.293299\pi$
$32$	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
$35$	−9.91509	−	4.40704i	−1.67596	−	0.744926i
$36$	2.19857	−	2.04115i	0.366428	−	0.340192i
$37$	−0.549311	−	0.633939i	−0.0903062	−	0.104219i	0.708798	−	0.705412i	$-0.249238\pi$
$37$	−0.549311	−	0.633939i	−0.0903062	−	0.104219i	−0.799104	+	0.601193i	$0.794692\pi$
$38$	−2.16415	+	0.988336i	−0.351072	+	0.160329i
$39$	1.99583	+	0.705673i	0.319589	+	0.112998i
$40$	−1.18976	+	1.89327i	−0.188118	+	0.299352i
$41$	4.44117	+	3.84830i	0.693595	+	0.601003i	0.928640	−	0.370981i	$-0.120979\pi$
$41$	4.44117	+	3.84830i	0.693595	+	0.601003i	−0.235046	+	0.971984i	$0.575524\pi$
$42$	−4.92065	+	6.81365i	−0.759273	+	1.05137i
$43$	−0.0334887	+	0.0733301i	−0.00510699	+	0.0111827i	−0.912168	−	0.409816i	$-0.865593\pi$
$43$	−0.0334887	+	0.0733301i	−0.00510699	+	0.0111827i	0.907061	+	0.420999i	$0.138320\pi$
$44$	0.475030	+	3.30390i	0.0716134	+	0.498082i
$45$	5.79883	+	3.37247i	0.864439	+	0.502738i
$46$	2.90582	+	3.81526i	0.428440	+	0.562529i
$47$	−4.46884			−0.651847			−0.325923	−	0.945396i	$-0.605675\pi$
$47$	−4.46884			−0.651847			−0.325923	+	0.945396i	$0.605675\pi$
$48$	1.24556	+	1.20357i	0.179781	+	0.173720i
$49$	6.87355	−	15.0510i	0.981936	−	2.15014i
$50$	−4.82506	−	1.31102i	−0.682367	−	0.185407i
$51$	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	0.965330	+	0.261031i	$0.0840625\pi$
$53$	5.83690	+	9.08239i	0.801760	+	1.24756i	−0.163570	+	0.986532i	$0.552301\pi$
$54$	3.48048	−	3.85827i	0.473634	−	0.525044i
$55$	−6.75743	+	3.16927i	−0.911172	+	0.427344i
$56$	−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	−0.965391	−	0.260807i	$-0.916011\pi$
$59$	−2.51261	+	3.90970i	−0.327114	+	0.509000i	0.638277	+	0.769807i	$0.279648\pi$
$60$	−1.76268	+	3.44862i	−0.227560	+	0.445215i
$61$	−9.97373	+	4.55485i	−1.27701	+	0.583189i	−0.934378	−	0.356283i	$-0.884044\pi$
$61$	−9.97373	+	4.55485i	−1.27701	+	0.583189i	−0.342627	+	0.939472i	$0.611317\pi$
$62$	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
$65$	−2.73278	+	0.0277290i	−0.338960	+	0.00343936i
$66$	1.32559	+	5.62735i	0.163168	+	0.692679i
$67$	0.376968	+	2.62187i	0.0460540	+	0.320312i	0.999806	+	0.0197167i	$0.00627642\pi$
$67$	0.376968	+	2.62187i	0.0460540	+	0.320312i	−0.953752	+	0.300596i	$0.902814\pi$
$68$			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	0.376954	−	0.926232i	$-0.376971\pi$
$71$	8.42268	−	1.21100i	0.999589	−	0.143719i	0.622634	+	0.782513i	$0.286062\pi$
$72$	2.33327	+	1.88570i	0.274978	+	0.222232i
$73$	−0.938954	−	3.19778i	−0.109896	−	0.374272i	0.886119	−	0.463458i	$-0.153392\pi$
$73$	−0.938954	−	3.19778i	−0.109896	−	0.374272i	−0.996015	+	0.0891860i	$0.971573\pi$
$74$	0.549311	−	0.633939i	0.0638562	−	0.0736939i
$75$	−8.52531	−	1.52285i	−0.984418	−	0.175843i
$76$	−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	−0.976742	−	0.214417i	$-0.931215\pi$
$79$	−3.34150	+	5.19947i	−0.375948	+	0.584986i	0.600794	+	0.799404i	$0.294851\pi$
$80$	−2.04332	−	0.908211i	−0.228450	−	0.101541i
$81$	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	$-0.456359\pi$
$83$	10.3554	−	8.97304i	1.13666	−	0.984919i	0.999984	+	0.00569681i	$0.00181336\pi$
$84$	−7.44458	−	3.90088i	−0.812270	−	0.425621i
$85$	−13.2999	+	4.05224i	−1.44258	+	0.439527i
$86$	−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	−0.759288	−	0.650755i	$-0.774452\pi$
$89$	2.16744	−	4.74603i	0.229748	−	0.503078i	0.989036	+	0.147677i	$0.0471797\pi$
$90$	−2.51288	+	6.21976i	−0.264881	+	0.655620i
$91$		−	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
$96$	−1.01406	+	1.40417i	−0.103497	+	0.143312i
$97$	4.90317	−	5.65856i	0.497841	−	0.574539i	−0.450103	−	0.892977i	$-0.648613\pi$
$97$	4.90317	−	5.65856i	0.497841	−	0.574539i	0.947944	+	0.318437i	$0.103158\pi$
$98$	15.8760	+	4.66161i	1.60372	+	0.470894i
$99$	3.14889	+	9.50565i	0.316475	+	0.955354i
$100$	0.611003	−	4.96253i	0.0611003	−	0.496253i
$101$	−12.7588	+	11.0556i	−1.26955	+	1.10007i	−0.279385	+	0.960179i	$0.590131\pi$
$101$	−12.7588	+	11.0556i	−1.26955	+	1.10007i	−0.990167	+	0.139893i	$0.955324\pi$
$102$	0.952344	+	10.7275i	0.0942961	+	1.06218i
$103$	−2.50854	+	17.4473i	−0.247174	+	1.71913i	0.367220	+	0.930134i	$0.380310\pi$
$103$	−2.50854	+	17.4473i	−0.247174	+	1.71913i	−0.614394	+	0.788999i	$0.710600\pi$
$104$	−1.20976	−	0.173937i	−0.118627	−	0.0170559i
$105$	3.49224	−	18.4661i	0.340808	−	1.80211i
$106$	−8.15927	+	7.07005i	−0.792498	+	0.686704i
$107$	4.12405	−	1.88339i	0.398687	−	0.182074i	−0.205974	−	0.978558i	$-0.566036\pi$
$107$	4.12405	−	1.88339i	0.398687	−	0.182074i	0.604660	+	0.796483i	$0.293309\pi$
$108$	4.31432	+	2.89597i	0.415146	+	0.278665i
$109$	4.14943	−	14.1317i	0.397443	−	1.35357i	−0.481418	−	0.876491i	$-0.659878\pi$
$109$	4.14943	−	14.1317i	0.397443	−	1.35357i	0.878861	−	0.477077i	$-0.158304\pi$
$110$	−4.09869	−	6.23762i	−0.390795	−	0.594733i
$111$	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	$-0.630796\pi$
$113$	−5.57471	+	0.801522i	−0.524425	+	0.0754009i	−0.124982	+	0.992159i	$0.539887\pi$
$114$	−2.52570	−	3.25606i	−0.236554	−	0.304958i
$115$	−9.50528	−	4.96484i	−0.886372	−	0.462974i
$116$		−	6.52184i		−	0.605537i
$117$	−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
$120$	−3.66437	−	1.25394i	−0.334510	−	0.114469i
$121$	−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
$125$	11.0130	−	1.92720i	0.985032	−	0.172374i
$126$	−13.4413	−	5.58983i	−1.19745	−	0.497981i
$127$	17.5969	+	2.53005i	1.56147	+	0.224506i	0.868216	−	0.496186i	$-0.165267\pi$
$127$	17.5969	+	2.53005i	1.56147	+	0.224506i	0.693255	+	0.720692i	$0.256176\pi$
$128$	−0.841254	−	0.540641i	−0.0743570	−	0.0477863i
$129$	−0.136927	−	0.0273370i	−0.0120558	−	0.00240689i
$130$	−0.416362	−	2.70102i	−0.0365173	−	0.236895i
$131$	4.82999	+	7.51561i	0.421998	+	0.656642i	0.985540	−	0.169446i	$-0.0541977\pi$
$131$	4.82999	+	7.51561i	0.421998	+	0.656642i	−0.563541	+	0.826088i	$0.690561\pi$
$132$	−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
$135$	−3.38276	+	11.1156i	−0.291141	+	0.956680i
$136$	−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	$0.456283\pi$
$140$	10.7551	+	1.43512i	0.908969	+	0.121290i
$141$	−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
$145$	13.9501	−	4.25034i	1.15850	−	0.352972i
$146$	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	−0.839789	−	0.542913i	$-0.817321\pi$
$149$	1.45183	−	10.0977i	0.118939	−	0.827238i	0.958728	−	0.284325i	$-0.0917695\pi$
$150$	0.294068	−	8.65526i	0.0240106	−	0.706699i
$151$	−7.84078	−	5.03896i	−0.638073	−	0.410065i	0.181217	−	0.983443i	$-0.441996\pi$
$151$	−7.84078	−	5.03896i	−0.638073	−	0.410065i	−0.819291	+	0.573378i	$0.805633\pi$
$152$	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
$155$	−6.27052	+	9.97828i	−0.503660	+	0.801475i
$156$	−2.11380	−	0.114798i	−0.169239	−	0.00919117i
$157$	10.2815	−	3.01891i	0.820549	−	0.240935i	0.155597	−	0.987821i	$-0.450270\pi$
$157$	10.2815	−	3.01891i	0.820549	−	0.240935i	0.664952	+	0.746886i	$0.268452\pi$
$158$	−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	$-0.746848\pi$
$163$	−14.9453	+	2.14881i	−1.17061	+	0.168308i	−0.470536	+	0.882381i	$0.655939\pi$
$164$	−5.34546	−	2.44119i	−0.417411	−	0.190625i
$165$	−8.02670	−	10.1338i	−0.624878	−	0.788914i
$166$	10.3554	+	8.97304i	0.803738	+	0.696443i
$167$	−8.63720	−	2.53611i	−0.668367	−	0.196250i	−0.0700912	−	0.997541i	$-0.522329\pi$
$167$	−8.63720	−	2.53611i	−0.668367	−	0.196250i	−0.598276	+	0.801290i	$0.704147\pi$
$168$	2.80170	−	7.92396i	0.216156	−	0.611347i
$169$	4.77986	+	10.4664i	0.367682	+	0.805110i
$170$	−5.90377	−	12.5879i	−0.452798	−	0.965445i
$171$	−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	−0.816056	−	0.577973i	$-0.803844\pi$
$173$	1.70696	−	11.8722i	0.129778	−	0.902625i	0.945834	−	0.324652i	$-0.105247\pi$
$174$	−0.998902	−	11.2519i	−0.0757266	−	0.853005i
$175$	3.93947	+	23.9403i	0.297796	+	1.80971i
$176$	−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	0.957186	−	0.289473i	$-0.0934799\pi$
$179$	10.7953	+	9.35422i	0.806882	+	0.699167i	−0.150304	+	0.988640i	$0.548025\pi$
$180$	−6.51407	−	1.60214i	−0.485530	−	0.119417i
$181$	−2.43796	−	1.11338i	−0.181212	−	0.0827569i	0.322743	−	0.946487i	$-0.395395\pi$
$181$	−2.43796	−	1.11338i	−0.181212	−	0.0827569i	−0.503955	+	0.863730i	$0.668122\pi$
$182$	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
$190$	4.50438	+	2.83062i	0.326782	+	0.205355i
$191$	−20.2556	+	13.0175i	−1.46564	+	0.941911i	−0.467315	+	0.884091i	$0.654779\pi$
$191$	−20.2556	+	13.0175i	−1.46564	+	0.941911i	−0.998327	+	0.0578200i	$0.981585\pi$
$192$	−1.53419	−	0.803900i	−0.110721	−	0.0580165i
$193$	−17.2773	+	14.9708i	−1.24364	+	1.07762i	−0.249634	+	0.968340i	$0.580310\pi$
$193$	−17.2773	+	14.9708i	−1.24364	+	1.07762i	−0.994011	+	0.109284i	$0.965144\pi$
$194$	6.29875	+	4.04796i	0.452224	+	0.290627i
$195$	−1.13203	−	4.59620i	−0.0810663	−	0.329141i
$196$	−2.35477	+	16.3778i	−0.168198	+	1.16984i
$197$	−2.03675	−	1.30894i	−0.145112	−	0.0932579i	0.466070	−	0.884748i	$-0.345669\pi$
$197$	−2.03675	−	1.30894i	−0.145112	−	0.0932579i	−0.611182	+	0.791490i	$0.709306\pi$
$198$	−8.96076	+	4.46963i	−0.636814	+	0.317643i
$199$	−9.03682	+	4.12698i	−0.640603	+	0.292554i	−0.709111	−	0.705097i	$-0.750903\pi$
$199$	−9.03682	+	4.12698i	−0.640603	+	0.292554i	0.0685079	+	0.997651i	$0.478176\pi$
$200$	4.99897	−	0.101458i	0.353481	−	0.00717414i
$201$	−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
$205$	1.73799	−	13.0248i	0.121387	−	0.909694i
$206$	−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
$210$	18.7752	+	0.828692i	1.29561	+	0.0571852i
$211$	−11.1065	+	3.26116i	−0.764603	+	0.224508i	−0.640705	−	0.767787i	$-0.721358\pi$
$211$	−11.1065	+	3.26116i	−0.764603	+	0.224508i	−0.123898	+	0.992295i	$0.539540\pi$
$212$	−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
$215$	0.178157	−	0.0274628i	0.0121502	−	0.00187295i
$216$	−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
$220$	5.59082	−	4.94468i	0.376933	−	0.333370i
$221$	−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	$-0.164172\pi$
$223$	0.894659	+	1.39212i	0.0599108	+	0.0932231i	−0.810006	+	0.586422i	$0.800536\pi$
$224$	4.65589	+	1.36709i	0.311085	+	0.0913427i
$225$	−0.818317	−	14.9777i	−0.0545545	−	0.998511i
$226$	−1.58673	−	5.40390i	−0.105548	−	0.359462i
$227$	11.5296	+	5.26541i	0.765250	+	0.349478i	0.759501	−	0.650506i	$-0.225443\pi$
$227$	11.5296	+	5.26541i	0.765250	+	0.349478i	0.00574819	+	0.999983i	$0.498170\pi$
$228$	2.86347	−	2.96338i	0.189638	−	0.196255i
$229$			16.1083i			1.06447i	0.846597	+	0.532234i	$0.178647\pi$
$229$			16.1083i			1.06447i	−0.846597	+	0.532234i	$0.821353\pi$
$230$	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	$-0.804155\pi$
$233$	2.35607	−	5.15907i	0.154351	−	0.337982i	0.970972	+	0.239192i	$0.0768827\pi$
$234$	−3.66444	+	0.125698i	−0.239552	+	0.00821714i
$235$	5.48743	+	8.35108i	0.357961	+	0.544764i
$236$	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	−0.816557	−	0.577265i	$-0.804120\pi$
$239$	−5.58674	+	4.84094i	−0.361376	+	0.313134i	0.455181	+	0.890399i	$0.349575\pi$
$240$	0.719687	−	3.80553i	0.0464556	−	0.245646i
$241$	10.2681	+	1.47633i	0.661425	+	0.0950986i	0.464849	−	0.885390i	$-0.346109\pi$
$241$	10.2681	+	1.47633i	0.661425	+	0.0950986i	0.196576	+	0.980489i	$0.437018\pi$
$242$	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
$245$	−36.5666	+	5.63674i	−2.33615	+	0.360118i
$246$	−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
$250$	3.47489	+	10.6266i	0.219772	+	0.672087i
$251$	−0.398058	−	2.76855i	−0.0251252	−	0.174749i	0.973395	−	0.229134i	$-0.0735894\pi$
$251$	−0.398058	−	2.76855i	−0.0251252	−	0.174749i	−0.998520	+	0.0543845i	$0.982680\pi$
$252$	3.62003	−	14.1001i	0.228040	−	0.888220i
$253$	−5.71856	−	14.9516i	−0.359523	−	0.940000i
$254$			17.7778i			1.11548i
$255$	−12.1136	−	20.8132i	−0.758581	−	1.30337i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	−22.0394	+	6.47135i	−1.37478	+	0.403672i	−0.883949	−	0.467583i	$-0.845125\pi$
$257$	−22.0394	+	6.47135i	−1.37478	+	0.403672i	−0.490831	+	0.871255i	$0.663307\pi$
$258$	0.00757195	−	0.139424i	0.000471409	−	0.00868016i
$259$	−3.90546	−	1.14675i	−0.242673	−	0.0712553i
$260$	2.61427	−	0.796519i	0.162130	−	0.0493980i
$261$	−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	$-0.937927\pi$
$263$	−6.44216	+	10.0242i	−0.397241	+	0.618119i	0.583805	+	0.811894i	$0.301563\pi$
$264$	−2.85730	−	5.02594i	−0.175855	−	0.309326i
$265$	9.80528	−	22.0602i	0.602334	−	1.35515i
$266$	−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	0.925323	−	0.379180i	$-0.123794\pi$
$269$	3.21489	+	5.00247i	0.196016	+	0.305006i	−0.729307	+	0.684186i	$0.760158\pi$
$270$	−11.4839	−	1.76641i	−0.698887	−	0.107500i
$271$	2.07086	−	2.38989i	0.125796	−	0.145176i	−0.689358	−	0.724421i	$-0.742107\pi$
$271$	2.07086	−	2.38989i	0.125796	−	0.145176i	0.815153	+	0.579245i	$0.196653\pi$
$272$	−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
$280$	0.110091	+	10.8498i	0.00657921	+	0.648402i
$281$	−3.09085	+	3.56703i	−0.184385	+	0.212791i	−0.840415	−	0.541943i	$-0.817689\pi$
$281$	−3.09085	+	3.56703i	−0.184385	+	0.212791i	0.656031	+	0.754734i	$0.272234\pi$
$282$	7.20479	−	2.82887i	0.429039	−	0.168457i
$283$	−9.86425	+	6.33937i	−0.586369	+	0.376837i	−0.799930	−	0.600093i	$-0.795130\pi$
$283$	−9.86425	+	6.33937i	−0.586369	+	0.376837i	0.213561	+	0.976930i	$0.431494\pi$
$284$	−7.74033	+	3.53489i	−0.459304	+	0.209757i
$285$	8.20479	+	4.19367i	0.486010	+	0.248412i
$286$	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
$290$	6.19239	+	13.2033i	0.363630	+	0.775322i
$291$	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	$-0.894244\pi$
$293$	0.449712	−	1.53158i	0.0262725	−	0.0894758i	0.971586	+	0.236688i	$0.0760620\pi$
$294$	−1.55414	+	28.6167i	−0.0906393	+	1.66896i
$295$	10.3915	−	0.105441i	0.605018	−	0.00613900i
$296$	−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
$300$	8.60901	−	0.940697i	0.497042	−	0.0543112i
$301$	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
$305$	20.7589	+	13.0452i	1.18865	+	0.746967i
$306$	−17.7073	+	5.86581i	−1.01226	+	0.335326i
$307$	0.772740	−	0.352899i	0.0441026	−	0.0201410i	−0.393242	−	0.919435i	$-0.628646\pi$
$307$	0.772740	−	0.352899i	0.0441026	−	0.0201410i	0.437344	+	0.899294i	$0.355919\pi$
$308$	10.6067	+	12.2408i	0.604372	+	0.697483i
$309$	−30.4108	+	2.69975i	−1.73001	+	0.153584i
$310$	−10.7691	−	4.78663i	−0.611644	−	0.271863i
$311$	14.6416	+	2.10514i	0.830248	+	0.119372i	0.544318	−	0.838879i	$-0.316789\pi$
$311$	14.6416	+	2.10514i	0.830248	+	0.119372i	0.285930	+	0.958251i	$0.407698\pi$
$312$	−0.187195	−	2.10862i	−0.0105978	−	0.119377i
$313$	21.6863	+	25.0273i	1.22578	+	1.41463i	0.879095	+	0.476646i	$0.158148\pi$
$313$	21.6863	+	25.0273i	1.22578	+	1.41463i	0.346686	+	0.937981i	$0.387307\pi$
$314$	4.45138	+	9.74717i	0.251206	+	0.550064i
$315$	32.5191	−	1.44594i	1.83224	−	0.0814695i
$316$	1.74128	−	5.93026i	0.0979548	−	0.333603i
$317$	−13.6650	+	15.7702i	−0.767501	+	0.885744i	−0.996141	−	0.0877675i	$-0.972027\pi$
$317$	−13.6650	+	15.7702i	−0.767501	+	0.885744i	0.228640	+	0.973511i	$0.426572\pi$
$318$	−15.1598	−	10.9480i	−0.850118	−	0.613934i
$319$	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
$324$	−3.16897	+	8.42364i	−0.176054	+	0.467980i
$325$	3.40749	+	5.07280i	0.189014	+	0.281388i
$326$	−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
$330$	8.88831	−	9.38719i	0.489285	−	0.516748i
$331$	19.0804	+	22.0199i	1.04875	+	1.21032i	0.977075	+	0.212895i	$0.0682893\pi$
$331$	19.0804	+	22.0199i	1.04875	+	1.21032i	0.0716761	+	0.997428i	$0.477165\pi$
$332$	−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
$335$	4.43670	−	3.92394i	0.242403	−	0.214388i
$336$	8.24203	+	1.64549i	0.449640	+	0.0897687i
$337$	−12.9115	−	28.2722i	−0.703333	−	1.54009i	−0.835882	−	0.548909i	$-0.815043\pi$
$337$	−12.9115	−	28.2722i	−0.703333	−	1.54009i	0.132549	−	0.991176i	$-0.457684\pi$
$338$	−9.67966	+	6.22074i	−0.526504	+	0.338364i
$339$	−3.56520	−	9.08013i	−0.193635	−	0.493165i
$340$	11.6195	−	7.63512i	0.630158	−	0.414072i
$341$	−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
$345$	4.59538	−	17.9967i	0.247407	−	0.968912i
$346$	11.9943			0.644815
$347$	3.14886	+	21.9008i	0.169040	+	1.17570i	0.880874	+	0.473350i	$0.156955\pi$
$347$	3.14886	+	21.9008i	0.169040	+	1.17570i	−0.711835	+	0.702347i	$0.752136\pi$
$348$	10.9952	−	2.59005i	0.589405	−	0.138841i
$349$	13.3853	−	3.93029i	0.716501	−	0.210384i	0.0968927	−	0.995295i	$-0.469110\pi$
$349$	13.3853	−	3.93029i	0.716501	−	0.210384i	0.619608	+	0.784911i	$0.287291\pi$
$350$	−23.1359	+	7.30643i	−1.23667	+	0.390545i
$351$	−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	−0.961110	−	0.276166i	$-0.910936\pi$
$353$	−10.1537	−	22.2336i	−0.540429	−	1.18338i	0.420680	−	0.907209i	$-0.361791\pi$
$354$	1.57598	−	7.89387i	0.0837624	−	0.419555i
$355$	−12.6055	−	14.2528i	−0.669032	−	0.756458i
$356$	−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	0.221202	−	0.975228i	$-0.429002\pi$
$359$	−14.6951	−	16.9591i	−0.775579	−	0.895066i	−0.996782	+	0.0801615i	$0.974456\pi$
$360$	0.658786	−	6.67578i	0.0347211	−	0.351844i
$361$	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
$365$	−4.82285	+	5.68133i	−0.252439	+	0.297374i
$366$	13.1966	−	13.6570i	0.689798	−	0.713865i
$367$	−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
$372$	−5.34448	+	7.40053i	−0.277098	+	0.383700i
$373$	12.3454	−	14.2473i	0.639219	−	0.737698i	−0.340018	−	0.940419i	$-0.610433\pi$
$373$	12.3454	−	14.2473i	0.639219	−	0.737698i	0.979236	+	0.202721i	$0.0649786\pi$
$374$	5.84720	−	19.9137i	0.302352	−	1.02972i
$375$	7.62272	+	17.8015i	0.393635	+	0.919267i
$376$	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	0.487355	−	0.873204i	$-0.337962\pi$
$379$	13.8020	+	1.98442i	0.708959	+	0.101933i	0.221604	+	0.975137i	$0.428871\pi$
$380$	−2.16077	+	4.86137i	−0.110845	+	0.249383i
$381$	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	$-0.841668\pi$
$383$	−21.4044	+	9.77508i	−1.09372	+	0.499483i	−0.214896	+	0.976637i	$0.568941\pi$
$384$	0.577380	−	1.63298i	0.0294643	−	0.0833328i
$385$	−19.2704	+	30.6650i	−0.982111	+	1.56283i
$386$	−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	0.911072	+	0.412247i	$0.135256\pi$
$389$	3.01858	+	20.9947i	0.153048	+	1.06447i	−0.758024	+	0.652227i	$0.773835\pi$
$390$	4.38831	−	1.77461i	0.222211	−	0.0898611i
$391$	−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
$395$	13.8196	−	0.140225i	0.695339	−	0.00705547i
$396$	−5.69939	−	8.23346i	−0.286405	−	0.413747i
$397$	0.194218	−	0.661447i	0.00974755	−	0.0331971i	−0.954476	−	0.298289i	$-0.903584\pi$
$397$	0.194218	−	0.661447i	0.00974755	−	0.0331971i	0.964223	+	0.265092i	$0.0854023\pi$
$398$	−5.37104	−	8.35750i	−0.269226	−	0.418924i
$399$	−9.28079	+	17.7118i	−0.464621	+	0.886699i
$400$	0.811853	+	4.93365i	0.0405926	+	0.246682i
$401$	10.8465	+	6.97064i	0.541650	+	0.348097i	0.782684	−	0.622419i	$-0.213850\pi$
$401$	10.8465	+	6.97064i	0.541650	+	0.348097i	−0.241034	+	0.970517i	$0.577487\pi$
$402$	−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
$405$	−20.0833	−	1.28862i	−0.997948	−	0.0640320i
$406$	−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	−0.00545882	−	0.999985i	$-0.501738\pi$
$409$	19.9229	−	22.9923i	0.985125	−	1.13689i	0.990584	−	0.136909i	$-0.0437169\pi$
$410$	13.1396	−	0.133325i	0.648919	−	0.00658445i
$411$	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	−0.968352	−	0.249590i	$-0.919704\pi$
$419$	−11.9438	+	13.7838i	−0.583491	+	0.673384i	0.384861	+	0.922975i	$0.374249\pi$
$420$	1.85173	+	18.7020i	0.0903550	+	0.912564i
$421$	−7.44535	−	11.5852i	−0.362864	−	0.564627i	0.611037	−	0.791602i	$-0.290753\pi$
$421$	−7.44535	−	11.5852i	−0.362864	−	0.564627i	−0.973901	+	0.226975i	$0.927116\pi$
$422$	−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
$425$	23.9040	+	19.8782i	1.15951	+	0.964234i
$426$	−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
$430$	0.0525377	+	0.172435i	0.00253359	+	0.00831555i
$431$	15.1604	+	4.45149i	0.730249	+	0.214421i	0.625661	−	0.780095i	$-0.284829\pi$
$431$	15.1604	+	4.45149i	0.730249	+	0.214421i	0.104588	+	0.994516i	$0.466648\pi$
$432$	−4.95545	−	1.56317i	−0.238419	−	0.0752083i
$433$	−7.25996	+	2.13172i	−0.348892	+	0.102444i	−0.451483	−	0.892280i	$-0.649105\pi$
$433$	−7.25996	+	2.13172i	−0.348892	+	0.102444i	0.102591	+	0.994724i	$0.467287\pi$
$434$	10.6240	−	23.2632i	0.509966	−	1.11667i
$435$	12.7058	+	21.8307i	0.609195	+	1.04670i
$436$			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	0.960880	−	0.276965i	$-0.0893286\pi$
$439$	−0.819397	−	5.69903i	−0.0391077	−	0.272000i	−0.999988	+	0.00496511i	$0.998420\pi$
$440$	5.69001	+	4.83021i	0.271260	+	0.230271i
$441$	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	$-0.450090\pi$
$443$	−5.18802	−	1.52334i	−0.246490	−	0.0723760i	−0.402644	+	0.915357i	$0.631909\pi$
$444$	−0.484318	+	1.36978i	−0.0229847	+	0.0650069i
$445$	−11.5305	+	1.77743i	−0.546600	+	0.0842584i
$446$	−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	0.545677	−	0.837995i	$-0.316272\pi$
$449$	17.6544	+	2.53831i	0.833160	+	0.119790i	0.287483	+	0.957786i	$0.407181\pi$
$450$	14.7088	−	2.94153i	0.693377	−	0.138665i
$451$	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
$455$	−11.0828	+	7.28245i	−0.519571	+	0.341406i
$456$	3.34073	+	2.41259i	0.156444	+	0.112980i
$457$	9.77133	−	21.3962i	0.457083	−	1.00087i	−0.531059	−	0.847335i	$-0.678206\pi$
$457$	9.77133	−	21.3962i	0.457083	−	1.00087i	0.988143	−	0.153538i	$-0.0490668\pi$
$458$	−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	$-0.0111161\pi$
$462$	20.1742	+	19.4940i	0.938588	+	0.906945i
$463$	1.31129	+	0.598848i	0.0609410	+	0.0278308i	0.445652	−	0.895206i	$-0.352972\pi$
$463$	1.31129	+	0.598848i	0.0609410	+	0.0278308i	−0.384711	+	0.923037i	$0.625699\pi$
$464$	1.83741	+	6.25766i	0.0852998	+	0.290504i
$465$	−19.3127	−	6.60879i	−0.895605	−	0.306475i
$466$	5.44186	+	1.59787i	0.252089	+	0.0740201i
$467$	−15.2039	−	23.6578i	−0.703555	−	1.09475i	−0.990594	−	0.136834i	$-0.956307\pi$
$467$	−15.2039	−	23.6578i	−0.703555	−	1.09475i	0.287039	−	0.957919i	$-0.407329\pi$
$468$	−0.645923	−	3.60925i	−0.0298578	−	0.166838i
$469$	8.41713	+	9.71388i	0.388667	+	0.448545i
$470$	−7.48513	+	6.62006i	−0.345263	+	0.305361i
$471$	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
$475$	−11.8066	−	1.45367i	−0.541724	−	0.0666989i
$476$	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	0.434055	−	0.900886i	$-0.357082\pi$
$479$	28.1512	−	8.26594i	1.28626	−	0.377680i	0.852206	+	0.523206i	$0.175264\pi$
$480$	3.86922	+	0.170778i	0.176605	+	0.00779492i
$481$	−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
$485$	−16.5951	−	2.21440i	−0.753545	−	0.100551i
$486$	−4.17712	+	15.0184i	−0.189478	+	0.681247i
$487$	10.5266	+	35.8502i	0.477005	+	1.62453i	0.749240	+	0.662298i	$0.230419\pi$
$487$	10.5266	+	35.8502i	0.477005	+	1.62453i	−0.272235	+	0.962231i	$0.587763\pi$
$488$	8.28647	+	7.18027i	0.375111	+	0.325036i
$489$	−9.55800	−	24.3430i	−0.432228	−	1.10083i
$490$	−10.7833	−	35.3922i	−0.487141	−	1.59886i
$491$	3.12892	−	1.42893i	0.141206	−	0.0644867i	−0.343559	−	0.939131i	$-0.611632\pi$
$491$	3.12892	−	1.42893i	0.141206	−	0.0644867i	0.484765	+	0.874645i	$0.338905\pi$
$492$	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
$495$	13.8969	−	17.5568i	0.624621	−	0.789117i
$496$	−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	−0.569148	+	0.822235i	$0.692727\pi$
$499$	−34.7028	+	22.3022i	−1.55351	+	0.998382i	−0.984364	+	0.176147i	$0.943637\pi$
$500$	−10.0239	+	4.95185i	−0.448284	+	0.221453i
$501$	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	$-0.490313\pi$
$503$	−15.8125	−	7.22133i	−0.705045	−	0.321983i	−0.735473	+	0.677554i	$0.763040\pi$
$504$	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	0.405041	−	0.914298i	$-0.367257\pi$
$509$	−0.466876	−	0.213215i	−0.0206939	−	0.00945060i	−0.425735	+	0.904848i	$0.639984\pi$
$510$	18.8774	−	14.9523i	0.835905	−	0.662098i
$511$	−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
$515$	35.6847	−	16.7363i	1.57246	−	0.737490i
$516$	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
$520$	1.16046	+	2.47430i	0.0508896	+	0.108505i
$521$	−8.65873	−	18.9600i	−0.379346	−	0.830652i	−0.998953	−	0.0457398i	$-0.985435\pi$
$521$	−8.65873	−	18.9600i	−0.379346	−	0.830652i	0.619607	−	0.784912i	$-0.287292\pi$
$522$	18.5730	−	6.15258i	0.812917	−	0.269291i
$523$	−9.22426	−	2.70849i	−0.403349	−	0.118434i	0.0737644	−	0.997276i	$-0.476499\pi$
$523$	−9.22426	−	2.70849i	−0.403349	−	0.118434i	−0.477113	+	0.878842i	$0.658317\pi$
$524$	−6.75174	−	5.85041i	−0.294951	−	0.255576i
$525$	−38.7966	+	16.1491i	−1.69322	+	0.704804i
$526$	−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
$535$	−8.58362	−	5.39408i	−0.371102	−	0.233207i
$536$	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
$540$	0.114100	−	11.6184i	0.00491010	−	0.499976i
$541$	−1.91788	+	13.3391i	−0.0824561	+	0.573495i	0.906149	+	0.422959i	$0.139009\pi$
$541$	−1.91788	+	13.3391i	−0.0824561	+	0.573495i	−0.988605	+	0.150535i	$0.951900\pi$
$542$	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
$545$	−31.5036	+	9.59855i	−1.34947	+	0.411157i
$546$	3.75423	+	9.56157i	0.160666	+	0.409198i
$547$	−13.1168	−	11.3658i	−0.560834	−	0.485965i	0.327697	−	0.944783i	$-0.393728\pi$
$547$	−13.1168	−	11.3658i	−0.560834	−	0.485965i	−0.888530	+	0.458818i	$0.848273\pi$
$548$	3.11348	+	10.6035i	0.133001	+	0.452960i
$549$	20.6759	−	25.5833i	0.882427	−	1.09187i
$550$	−6.62355	+	15.3188i	−0.282429	+	0.653194i
$551$	−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
$555$	−3.24558	−	0.143252i	−0.137767	−	0.00608073i
$556$	−3.09752	+	0.909515i	−0.131364	+	0.0385720i
$557$	1.24654	+	1.08014i	0.0528178	+	0.0457669i	0.680870	−	0.732405i	$-0.261602\pi$
$557$	1.24654	+	1.08014i	0.0528178	+	0.0457669i	−0.628052	+	0.778171i	$0.716147\pi$
$558$	−8.08716	+	13.5865i	−0.342357	+	0.575160i
$559$	0.0532681	+	0.0828868i	0.00225300	+	0.00350574i
$560$	−10.7237	+	1.65306i	−0.453161	+	0.0698547i
$561$	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	$-0.523922\pi$
$563$	−10.1569	−	1.46034i	−0.428061	−	0.0615458i	−0.352978	+	0.935632i	$0.614831\pi$
$564$	3.82543	+	6.72886i	0.161079	+	0.283336i
$565$	8.34321	+	9.43345i	0.351001	+	0.396868i
$566$	−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	0.459277	−	0.888293i	$-0.348108\pi$
$569$	8.71612	+	2.55928i	0.365399	+	0.107291i	−0.0938787	+	0.995584i	$0.529927\pi$
$570$	−2.98333	+	8.71810i	−0.124958	+	0.365161i
$571$	−0.652046	−	2.22066i	−0.0272873	−	0.0929319i	0.944724	−	0.327868i	$-0.106330\pi$
$571$	−0.652046	−	2.22066i	−0.0272873	−	0.0929319i	−0.972011	+	0.234936i	$0.924512\pi$
$572$	3.71089	+	1.69471i	0.155160	+	0.0708592i
$573$	−29.9904	−	28.9793i	−1.25287	−	1.21063i
$574$			28.5155i			1.19021i
$575$	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	0.943428	−	0.331578i	$-0.107581\pi$
$577$	46.6498	−	6.70723i	1.94206	−	0.279226i	0.998629	+	0.0523524i	$0.0166719\pi$
$578$	8.99862	−	19.7042i	0.374293	−	0.819588i
$579$	−32.1008	−	23.1824i	−1.33407	−	0.963429i
$580$	−12.1876	+	8.00838i	−0.506063	+	0.332530i
$581$	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
$585$	7.29920	−	3.73381i	0.301785	−	0.154374i
$586$	1.57999	+	0.227168i	0.0652688	+	0.00938424i
$587$	3.64962	−	25.3837i	0.150636	−	1.04770i	−0.764521	−	0.644599i	$-0.777024\pi$
$587$	3.64962	−	25.3837i	0.150636	−	1.04770i	0.915157	−	0.403097i	$-0.132066\pi$
$588$	−28.5466	+	2.53426i	−1.17724	+	0.104511i
$589$	9.47641	−	8.21135i	0.390469	−	0.338343i
$590$	1.58324	+	10.2708i	0.0651808	+	0.422840i
$591$	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	$-0.767167\pi$
$593$	0.557126	−	0.642958i	0.0228784	−	0.0264031i	0.767073	+	0.641559i	$0.221712\pi$
$594$	−11.0940	−	13.3320i	−0.455193	−	0.547017i
$595$	−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	$-0.000141728\pi$
$600$	2.15631	+	8.38751i	0.0880311	+	0.342419i
$601$	6.82025	−	14.9343i	0.278204	−	0.609181i	−0.718018	−	0.696024i	$-0.754951\pi$
$601$	6.82025	−	14.9343i	0.278204	−	0.609181i	0.996222	+	0.0868431i	$0.0276779\pi$
$602$	−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
$605$	0.0921694	+	0.302511i	0.00374722	+	0.0122988i
$606$	13.5717	−	25.9008i	0.551314	−	1.05215i
$607$	19.5482	−	16.9386i	0.793435	−	0.687516i	−0.160663	−	0.987009i	$-0.551363\pi$
$607$	19.5482	−	16.9386i	0.793435	−	0.687516i	0.954098	+	0.299494i	$0.0968178\pi$
$608$	−1.28627	+	2.00147i	−0.0521650	+	0.0811703i
$609$	−47.6517	+	27.0904i	−1.93094	+	1.09776i
$610$	−9.95815	+	22.4041i	−0.403194	+	0.907117i
$611$	−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	−0.924792	−	0.380472i	$-0.875761\pi$
$613$	−15.0218	−	32.8931i	−0.606724	−	1.32854i	0.318068	−	0.948068i	$-0.396966\pi$
$614$	0.459279	+	0.714652i	0.0185350	+	0.0288410i
$615$	22.6489	−	2.24252i	0.913291	−	0.0904271i
$616$	−10.6067	+	12.2408i	−0.427356	+	0.493195i
$617$	5.79065	+	19.7211i	0.233123	+	0.793943i	0.990083	+	0.140482i	$0.0448653\pi$
$617$	5.79065	+	19.7211i	0.233123	+	0.793943i	−0.756961	+	0.653461i	$0.773317\pi$
$618$	−7.00018	−	29.7170i	−0.281588	−	1.19539i
$619$	−11.4223	+	1.64227i	−0.459099	+	0.0660085i	−0.367985	−	0.929832i	$-0.619952\pi$
$619$	−11.4223	+	1.64227i	−0.459099	+	0.0660085i	−0.0911146	+	0.995840i	$0.529043\pi$
$620$	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
$625$	−17.1246	−	18.2139i	−0.684986	−	0.728556i
$626$	−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
$630$	6.05917	+	31.9823i	0.241403	+	1.27420i
$631$	−1.42084	+	2.21088i	−0.0565629	+	0.0880136i	−0.868383	−	0.495894i	$-0.834841\pi$
$631$	−1.42084	+	2.21088i	−0.0565629	+	0.0880136i	0.811820	+	0.583907i	$0.198477\pi$
$632$	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
$635$	−16.8798	−	35.9907i	−0.669855	−	1.42825i
$636$	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
$640$	0.0226878	+	2.23595i	0.000896813	+	0.0883838i
$641$	−16.0864	+	35.2243i	−0.635375	+	1.39128i	0.268417	+	0.963303i	$0.413500\pi$
$641$	−16.0864	+	35.2243i	−0.635375	+	1.39128i	−0.903791	+	0.427973i	$0.859228\pi$
$642$	−5.45668	+	5.64707i	−0.215358	+	0.222872i
$643$	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
$645$	0.117052	+	0.289449i	0.00460892	+	0.0113971i
$646$	2.10530	+	14.6427i	0.0828318	+	0.576108i
$647$	18.5997	−	40.7277i	0.731230	−	1.60117i	−0.0662342	−	0.997804i	$-0.521098\pi$
$647$	18.5997	−	40.7277i	0.731230	−	1.60117i	0.797464	−	0.603366i	$-0.206174\pi$
$648$	−8.78889	−	1.93790i	−0.345260	−	0.0761280i
$649$	11.7237	+	10.1587i	0.460196	+	0.398762i
$650$	−4.53623	+	4.09474i	−0.177925	+	0.160609i
$651$	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	$-0.285915\pi$
$653$	−6.13103	−	7.07558i	−0.239926	−	0.276889i	−0.862923	+	0.505335i	$0.831369\pi$
$654$	2.25582	+	25.4102i	0.0882096	+	0.993616i
$655$	8.11380	−	18.2547i	0.317032	−	0.713269i
$656$	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	0.983785	+	0.179352i	$0.0574001\pi$
$659$	12.1960	+	26.7055i	0.475088	+	1.04030i	−0.508697	+	0.860946i	$0.669873\pi$
$660$	10.5566	+	7.46191i	0.410914	+	0.290454i
$661$	1.95949	−	6.67340i	0.0762152	−	0.259565i	−0.912568	−	0.408926i	$-0.865903\pi$
$661$	1.95949	−	6.67340i	0.0762152	−	0.259565i	0.988783	+	0.149361i	$0.0477216\pi$
$662$	−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
$665$	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
$669$	−1.99168	+	2.06117i	−0.0770028	+	0.0796895i
$670$	4.51540	+	3.83310i	0.174445	+	0.148086i
$671$	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	0.686586	+	0.727049i	$0.259109\pi$
$673$	−7.36965	+	25.0987i	−0.284079	+	0.967485i	−0.970665	+	0.240436i	$0.922709\pi$
$674$	26.1469	−	16.8036i	1.00714	−	0.647251i
$675$	24.9260	−	7.32776i	0.959401	−	0.282045i
$676$	−7.53498	−	8.69583i	−0.289807	−	0.334455i
$677$	−25.1682	+	39.1626i	−0.967294	+	1.50514i	−0.107686	+	0.994185i	$0.534344\pi$
$677$	−25.1682	+	39.1626i	−0.967294	+	1.50514i	−0.859608	+	0.510954i	$0.829292\pi$
$678$	8.48033	−	4.82115i	0.325685	−	0.185155i
$679$	5.17057	−	35.9621i	0.198428	−	1.38010i
$680$	9.21104	+	10.4147i	0.353227	+	0.399385i
$681$	−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	$-0.767516\pi$
$683$	−11.6957	+	7.51640i	−0.447525	+	0.287607i	0.297403	+	0.954752i	$0.403880\pi$
$684$	6.13317	+	3.65069i	0.234508	+	0.139588i
$685$	−20.6517	+	13.5701i	−0.789063	+	0.518487i
$686$	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
$690$	18.4675	+	1.98741i	0.703047	+	0.0756592i
$691$	−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
$695$	−3.96413	−	6.03283i	−0.150368	−	0.228838i
$696$	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
$700$	−10.5246	−	21.8606i	−0.397794	−	0.826254i
$701$	3.67381	−	25.5519i	0.138758	−	0.965083i	−0.794855	−	0.606799i	$-0.792453\pi$
$701$	3.67381	−	25.5519i	0.138758	−	0.965083i	0.933613	−	0.358283i	$-0.116638\pi$
$702$	−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
$705$	−11.8999	+	12.5678i	−0.448176	+	0.473331i
$706$	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	0.921493	−	0.388394i	$-0.126970\pi$
$709$	−1.69608	−	5.77633i	−0.0636977	−	0.216934i	−0.985191	+	0.171459i	$0.945152\pi$
$710$	12.3137	−	14.5056i	0.462126	−	0.544386i
$711$	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
$715$	−1.20654	+	9.04201i	−0.0451219	+	0.338152i
$716$	−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	0.556482	+	0.830859i	$0.312151\pi$
$719$	−9.67608	+	32.9537i	−0.360857	+	1.22897i	−0.917339	+	0.398106i	$0.869668\pi$
$720$	6.70158	−	0.297982i	0.249753	−	0.0111051i
$721$	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
$725$	−25.0726	−	20.8500i	−0.931174	−	0.774350i
$726$	0.243999	−	0.0216614i	0.00905566	−	0.000803928i
$727$	−1.34472	−	1.55190i	−0.0498731	−	0.0575566i	0.730265	−	0.683164i	$-0.239397\pi$
$727$	−1.34472	−	1.55190i	−0.0498731	−	0.0575566i	−0.780138	+	0.625607i	$0.784851\pi$
$728$	−5.39471	+	2.46368i	−0.199941	+	0.0913101i
$729$	−4.90639	+	26.5505i	−0.181718	+	0.983351i
$730$	−6.30986	−	3.96522i	−0.233538	−	0.146759i
$731$	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	−0.254409	−	0.967097i	$-0.581881\pi$
$733$	17.4106	−	38.1240i	0.643076	−	1.40814i	0.897485	−	0.441044i	$-0.145392\pi$
$734$	−2.57694	−	17.9230i	−0.0951164	−	0.661549i
$735$	−24.0249	−	59.4093i	−0.886171	−	2.19135i
$736$	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	−0.997965	−	0.0637622i	$-0.979690\pi$
$739$	−8.05339	+	17.6345i	−0.296249	+	0.648694i	0.701716	+	0.712456i	$0.252417\pi$
$740$	−0.0190310	−	1.87557i	−0.000699594	−	0.0689472i
$741$	−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	$-0.335455\pi$
$743$	−13.6799	−	21.2864i	−0.501867	−	0.780921i	−0.996083	+	0.0884183i	$0.971819\pi$
$744$	−8.08580	−	4.23688i	−0.296440	−	0.155331i
$745$	−20.6528	+	9.68624i	−0.756659	+	0.354876i
$746$	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
$750$	−16.5355	+	10.0785i	−0.603791	+	0.368017i
$751$	−30.8269	+	14.0782i	−1.12489	+	0.513720i	−0.888930	−	0.458042i	$-0.848551\pi$
$751$	−30.8269	+	14.0782i	−1.12489	+	0.513720i	−0.235960	+	0.971763i	$0.575824\pi$
$752$	−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
$755$	0.211458	+	20.8399i	0.00769575	+	0.758440i
$756$	25.2090	+	0.503411i	0.916843	+	0.0183089i
$757$	6.15408	+	42.8025i	0.223674	+	1.55568i	0.723971	+	0.689831i	$0.242315\pi$
$757$	6.15408	+	42.8025i	0.223674	+	1.55568i	−0.500297	+	0.865854i	$0.666776\pi$
$758$			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	−0.223574	−	0.974687i	$-0.571772\pi$
$761$	−4.51009	+	0.648452i	−0.163490	+	0.0235064i	0.0600834	+	0.998193i	$0.480863\pi$
$762$	−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
$765$	30.2784	−	28.6880i	1.09472	−	1.03722i
$766$	−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	−0.191024	−	0.981585i	$-0.561181\pi$
$769$	21.6637	−	33.7093i	0.781212	−	1.21559i	0.972236	−	0.234004i	$-0.0751828\pi$
$770$	−33.0954	−	14.7102i	−1.19267	−	0.530118i
$771$	−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	$-0.754876\pi$
$773$	−3.63972	+	3.15384i	−0.130912	+	0.113436i	0.586944	+	0.809627i	$0.300331\pi$
$774$	0.238063	−	0.0426045i	0.00855700	−	0.00153139i
$775$	26.3466	−	0.534722i	0.946397	−	0.0192078i
$776$	−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
$780$	2.38107	+	4.09109i	0.0852561	+	0.146485i
$781$		−	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
$786$	−12.5446	−	9.05940i	−0.447451	−	0.323138i
$787$	−2.55237	+	2.94559i	−0.0909820	+	0.104999i	−0.799415	−	0.600779i	$-0.794857\pi$
$787$	−2.55237	+	2.94559i	−0.0909820	+	0.104999i	0.708433	+	0.705778i	$0.249402\pi$
$788$	2.32301	+	0.682098i	0.0827539	+	0.0242987i
$789$	−19.4583	−	6.87993i	−0.692733	−	0.244932i
$790$	2.10553	+	13.6590i	0.0749114	+	0.485964i
$791$	−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
$795$	41.0855	+	7.76993i	1.45715	+	0.275571i
$796$	7.50806	−	6.50577i	0.266116	−	0.230591i
$797$	35.6636	−	16.2870i	1.26327	−	0.576916i	0.332701	−	0.943032i	$-0.392040\pi$
$797$	35.6636	−	16.2870i	1.26327	−	0.576916i	0.930569	+	0.366116i	$0.119313\pi$
$798$	−18.8523	−	6.66568i	−0.667364	−	0.235962i
$799$	−7.82839	+	26.6610i	−0.276948	+	0.943200i
$800$	−4.76789	+	1.50572i	−0.168570	+	0.0532353i
$801$	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
$805$	−51.8268	+	4.66929i	−1.82665	+	0.164571i
$806$		−	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	0.994913	−	0.100734i	$-0.0321190\pi$
$809$	2.94322	+	10.0237i	0.103478	+	0.352414i	−0.891435	+	0.453148i	$0.850301\pi$
$810$	−1.58265	−	20.0623i	−0.0556087	−	0.704917i
$811$	−2.41772	−	0.709907i	−0.0848977	−	0.0249282i	0.239008	−	0.971018i	$-0.423178\pi$
$811$	−2.41772	−	0.709907i	−0.0848977	−	0.0249282i	−0.323906	+	0.946089i	$0.604996\pi$
$812$	−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
$815$	22.3674	+	25.2903i	0.783496	+	0.885879i
$816$	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
$820$	2.00193	+	12.9869i	0.0699104	+	0.453522i
$821$	−4.25616	−	6.62271i	−0.148541	−	0.231134i	0.759007	−	0.651082i	$-0.225685\pi$
$821$	−4.25616	−	6.62271i	−0.148541	−	0.231134i	−0.907548	+	0.419948i	$0.862048\pi$
$822$	6.99564	+	17.8170i	0.244001	+	0.621440i
$823$	−0.779323	−	0.675287i	−0.0271655	−	0.0235390i	0.641172	−	0.767397i	$-0.278448\pi$
$823$	−0.779323	−	0.675287i	−0.0271655	−	0.0235390i	−0.668338	+	0.743858i	$0.732994\pi$
$824$	16.9127	−	4.96602i	0.589182	−	0.172999i
$825$	−9.08111	+	27.4434i	−0.316164	+	0.955457i
$826$	−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	$0.378239\pi$
$830$	4.05246	−	30.3699i	0.140663	−	1.05415i
$831$	−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
$835$	5.86659	+	19.2548i	0.203022	+	0.666341i
$836$	−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	−0.990867	−	0.134843i	$-0.956947\pi$
$839$	−0.0621969	+	0.432589i	−0.00214728	+	0.0149346i	0.988720	+	0.149778i	$0.0478559\pi$
$840$	−18.2481	+	4.49445i	−0.629619	+	0.155073i
$841$	−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
$845$	13.6897	−	21.7844i	0.470939	−	0.749406i
$846$	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	$-0.735359\pi$
$853$	−32.4840	+	4.67050i	−1.11223	+	0.159915i	−0.438386	+	0.898787i	$0.644450\pi$
$854$	−48.3970	−	22.1022i	−1.65611	−	0.756320i
$855$	−3.81174	+	15.4980i	−0.130359	+	0.530019i
$856$	−3.42638	−	2.96898i	−0.117111	−	0.101478i
$857$	29.9628	+	8.79789i	1.02351	+	0.300530i	0.750070	−	0.661359i	$-0.230020\pi$
$857$	29.9628	+	8.79789i	1.02351	+	0.300530i	0.273441	+	0.961889i	$0.411838\pi$
$858$	6.66184	+	2.35545i	0.227431	+	0.0804137i
$859$	−1.02094	−	2.23555i	−0.0348340	−	0.0762759i	0.891415	−	0.453188i	$-0.149713\pi$
$859$	−1.02094	−	2.23555i	−0.0348340	−	0.0762759i	−0.926249	+	0.376912i	$0.876986\pi$
$860$	−0.163203	+	0.0765429i	−0.00556517	+	0.00261009i
$861$	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	−0.873380	−	0.487040i	$-0.838077\pi$
$863$	2.99165	−	20.8074i	0.101837	−	0.708292i	0.975217	−	0.221252i	$-0.0710143\pi$
$864$	0.842030	−	5.12747i	0.0286464	−	0.174440i
$865$	−24.2820	+	11.3884i	−0.825613	+	0.387217i
$866$	−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
$870$	−19.8003	+	15.6833i	−0.671292	+	0.531713i
$871$	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	$-0.189442\pi$
$877$	28.0338	+	12.8026i	0.946635	+	0.432314i	0.118570	+	0.992946i	$0.462169\pi$
$878$	5.52441	−	1.62211i	0.186440	−	0.0547437i
$879$	2.76070	+	0.149930i	0.0931160	+	0.00505702i
$880$	−3.97128	+	6.31950i	−0.133872	+	0.213030i
$881$	40.1117	−	25.7782i	1.35140	−	0.868491i	0.353638	−	0.935382i	$-0.384944\pi$
$881$	40.1117	−	25.7782i	1.35140	−	0.868491i	0.997760	+	0.0668911i	$0.0213080\pi$
$882$	−48.8624	+	8.74456i	−1.64528	+	0.294445i
$883$	5.31685	−	4.60707i	0.178926	−	0.155040i	−0.560793	−	0.827956i	$-0.689504\pi$
$883$	5.31685	−	4.60707i	0.178926	−	0.155040i	0.739719	+	0.672916i	$0.234958\pi$
$884$	6.39307	+	4.10858i	0.215022	+	0.138186i
$885$	4.30460	+	17.4773i	0.144697	+	0.587492i
$886$	0.769502	−	5.35200i	0.0258519	−	0.179804i
$887$	−40.2287	−	25.8534i	−1.35075	−	0.868073i	−0.353031	−	0.935611i	$-0.614849\pi$
$887$	−40.2287	−	25.8534i	−1.35075	−	0.868073i	−0.997717	+	0.0675383i	$0.978486\pi$
$888$	−1.42476	−	0.284449i	−0.0478120	−	0.00954547i
$889$	78.4703	−	35.8362i	2.63181	−	1.20191i
$890$	−3.40031	−	11.1602i	−0.113979	−	0.374092i
$891$	−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
$895$	4.22461	−	31.6600i	0.141213	−	1.05828i
$896$	−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
$900$	5.00486	+	14.1404i	0.166829	+	0.471347i
$901$	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
$905$	0.913041	+	5.92307i	0.0303505	+	0.196889i
$906$	15.8309	+	3.16058i	0.525947	+	0.105003i
$907$	3.61375	+	2.32241i	0.119992	+	0.0771145i	0.599260	−	0.800554i	$-0.295461\pi$
$907$	3.61375	+	2.32241i	0.119992	+	0.0771145i	−0.479268	+	0.877669i	$0.659098\pi$
$908$	−12.5461	−	1.80385i	−0.416355	−	0.0598629i
$909$	19.4478	−	46.7644i	0.645043	−	1.55108i
$910$	−8.78558	−	9.93363i	−0.291239	−	0.329296i
$911$	−10.4131	−	12.0174i	−0.345001	−	0.398153i	0.556558	−	0.830809i	$-0.312122\pi$
$911$	−10.4131	−	12.0174i	−0.345001	−	0.398153i	−0.901559	+	0.432656i	$0.857576\pi$
$912$	−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
$915$	−13.7490	+	40.1783i	−0.454527	+	1.32825i
$916$	−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	$0.235733\pi$
$919$			40.9080i			1.34943i	−0.738079	+	0.674715i	$0.764267\pi$
$920$	−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
$924$	−16.4245	+	22.7431i	−0.540327	+	0.748194i
$925$	3.99941	−	1.26303i	0.131500	−	0.0415282i
$926$	−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	−0.822659	−	0.568535i	$-0.807510\pi$
$929$	−11.4904	+	9.95647i	−0.376987	+	0.326661i	0.445672	+	0.895196i	$0.352965\pi$
$930$	3.79304	−	20.0567i	0.124379	−	0.657684i
$931$	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
$935$	7.07034	+	45.8666i	0.231225	+	1.50000i
$936$	3.48059	−	1.15300i	0.113767	−	0.0376870i
$937$	−33.0757	−	9.71190i	−1.08054	−	0.317274i	−0.307443	−	0.951566i	$-0.599473\pi$
$937$	−33.0757	−	9.71190i	−1.08054	−	0.317274i	−0.773093	+	0.634292i	$0.781292\pi$
$938$	−8.41713	+	9.71388i	−0.274829	+	0.317170i
$939$	−33.5814	+	46.5003i	−1.09589	+	1.51748i
$940$	−7.61792	−	6.46681i	−0.248469	−	0.210924i
$941$	5.15384	+	35.8458i	0.168011	+	1.16854i	0.882989	+	0.469393i	$0.155527\pi$
$941$	5.15384	+	35.8458i	0.168011	+	1.16854i	−0.714979	+	0.699146i	$0.753564\pi$
$942$	−14.6650	+	11.3756i	−0.477812	+	0.370636i
$943$	27.5875	+	5.76176i	0.898373	+	0.187629i
$944$			4.64747i			0.151262i
$945$	15.3522	+	54.2499i	0.499406	+	1.76475i
$946$	−0.111781	+	0.244767i	−0.00363432	+	0.00795806i
$947$	47.2606	−	13.8770i	1.53576	−	0.450941i	0.598954	−	0.800783i	$-0.295583\pi$
$947$	47.2606	−	13.8770i	1.53576	−	0.450941i	0.936808	+	0.349843i	$0.113765\pi$
$948$	10.6894	+	0.580528i	0.347176	+	0.0188547i
$949$	−3.90833	−	1.14759i	−0.126870	−	0.0372523i
$950$	−0.241383	−	11.8933i	−0.00783150	−	0.385870i
$951$	−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	−0.285888	−	0.958263i	$-0.592289\pi$
$953$	21.7497	−	33.8431i	0.704541	−	1.09629i	0.990429	−	0.138024i	$-0.0440751\pi$
$954$	12.4369	−	29.9058i	0.402659	−	0.968237i
$955$	49.1987	+	21.8678i	1.59203	+	0.707624i
$956$	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
$960$	0.381607	+	3.85414i	0.0123163	+	0.124392i
$961$	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
$970$	−0.169871	−	16.7413i	−0.00545423	−	0.537532i
$971$	13.1848	−	15.2160i	0.423119	−	0.488305i	−0.503666	−	0.863899i	$-0.668016\pi$
$971$	13.1848	−	15.2160i	0.423119	−	0.488305i	0.926785	+	0.375593i	$0.122561\pi$
$972$	−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
$975$	−7.19904	+	7.75930i	−0.230554	+	0.248496i
$976$	−5.92790	+	9.22399i	−0.189747	+	0.295253i
$977$	30.8721	+	4.43874i	0.987687	+	0.142008i	0.617180	−	0.786822i	$-0.288275\pi$
$977$	30.8721	+	4.43874i	0.987687	+	0.142008i	0.370507	+	0.928830i	$0.379184\pi$
$978$	22.7350	−	12.9251i	0.726986	−	0.413299i
$979$	−14.6508	−	9.41551i	−0.468242	−	0.300921i
$980$	33.4973	−	15.7104i	1.07003	−	0.501851i
$981$	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	$-0.823798\pi$
$983$	4.67730	−	15.9294i	0.149183	−	0.508070i	0.999844	+	0.0176438i	$0.00561649\pi$
$984$	10.1634	+	0.551964i	0.323999	+	0.0175960i
$985$	0.0549290	+	5.41343i	0.00175018	+	0.172486i
$986$	−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
$990$	19.3558	+	11.2569i	0.615167	+	0.357768i
$991$	0.894086	+	6.21851i	0.0284016	+	0.197537i	0.999082	−	0.0428359i	$-0.0136393\pi$
$991$	0.894086	+	6.21851i	0.0284016	+	0.197537i	−0.970681	+	0.240373i	$0.922730\pi$
$992$	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
$995$	18.8088	+	11.8198i	0.596280	+	0.374712i
$996$	−22.3755	−	7.91138i	−0.708994	−	0.250682i
$997$	−15.6127	+	7.13008i	−0.494459	+	0.225812i	−0.647007	−	0.762484i	$-0.723979\pi$
$997$	−15.6127	+	7.13008i	−0.494459	+	0.225812i	0.152548	+	0.988296i	$0.451252\pi$
$998$	−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.b.89.14	yes	240
3.2	odd	2		690.2.n.a.89.20	yes	240
5.4	even	2		690.2.n.a.89.11	✓	240
15.14	odd	2	inner	690.2.n.b.89.5	yes	240
23.15	odd	22	inner	690.2.n.b.659.5	yes	240
69.38	even	22		690.2.n.a.659.11	yes	240
115.84	odd	22		690.2.n.a.659.20	yes	240
345.314	even	22	inner	690.2.n.b.659.14	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.n.a.89.11	✓	240	5.4	even	2
690.2.n.a.89.20	yes	240	3.2	odd	2
690.2.n.a.659.11	yes	240	69.38	even	22
690.2.n.a.659.20	yes	240	115.84	odd	22
690.2.n.b.89.5	yes	240	15.14	odd	2	inner
690.2.n.b.89.14	yes	240	1.1	even	1	trivial
690.2.n.b.659.5	yes	240	23.15	odd	22	inner
690.2.n.b.659.14	yes	240	345.314	even	22	inner

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)

\(f(q)\)	\(=\)	\(q+(0.142315 + 0.989821i) q^{2} +(0.397135 + 1.68591i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-1.22793 - 1.86874i) q^{5} +(-1.61223 + 0.633022i) q^{6} +(4.08214 - 2.62343i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-2.68457 + 1.33906i) q^{9} +O(q^{10})\)	\(q+(0.142315 + 0.989821i) q^{2} +(0.397135 + 1.68591i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-1.22793 - 1.86874i) 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} +(1.67496 - 1.48138i) 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} +(2.66286 - 2.81232i) 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} +(1.70468 + 1.44709i) q^{20} +(6.04402 + 5.84025i) 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} +(-3.32367 - 3.99414i) q^{27} +(-3.17768 + 3.66723i) q^{28} +(-1.83741 + 6.25766i) q^{29} +(3.16266 + 2.23552i) 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} +(-9.91509 - 4.40704i) 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} +(-1.18976 + 1.89327i) 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} +(5.79883 + 3.37247i) q^{45} +(2.90582 + 3.81526i) q^{46} -4.46884 q^{47} +(1.24556 + 1.20357i) q^{48} +(6.87355 - 15.0510i) q^{49} +(-4.82506 - 1.31102i) 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} +(-6.75743 + 3.16927i) 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} +(-1.76268 + 3.44862i) 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} +(-2.73278 + 0.0277290i) 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} +(-8.52531 - 1.52285i) 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} +(-2.04332 - 0.908211i) 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} +(-13.2999 + 4.05224i) 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} +(-2.51288 + 6.21976i) 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} +(-1.01406 + 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	\( 240 q + 24 q^{2} - 2 q^{3} - 24 q^{4} + 2 q^{6} + 24 q^{8} - 6 q^{9} + 9 q^{12} + 11 q^{15} - 24 q^{16} + 6 q^{18} + 4 q^{23} + 2 q^{24} - 12 q^{25} - 2 q^{27} + 22 q^{30} + 28 q^{31} + 24 q^{32} + 36 q^{35} - 6 q^{36} - 4 q^{46} - 104 q^{47} + 9 q^{48} + 70 q^{49} - 54 q^{50} - 9 q^{54} - 26 q^{55} + 44 q^{57} - 11 q^{60} + 44 q^{61} - 28 q^{62} + 121 q^{63} - 24 q^{64} - 44 q^{65} + 44 q^{66} - 102 q^{69} - 36 q^{70} - 16 q^{72} - 102 q^{75} - 8 q^{77} - 44 q^{79} + 74 q^{81} - 11 q^{84} + 22 q^{85} + 93 q^{87} + 4 q^{92} - 172 q^{93} + 16 q^{94} - 26 q^{95} + 2 q^{96} - 4 q^{98}+O(q^{100}) \) 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 - 102 * 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

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