LMFDB - Embedded newform 138.2.f.a.11.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,2,Mod(5,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 1]))

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

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

chi := DirichletCharacter("138.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	138.f (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:	$1.10193554789$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			11.8
Character	$\chi$	$=$	138.11
Dual form			138.2.f.a.113.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.540641 + 0.841254i) q^{2} +(1.34287 + 1.09394i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-1.80115 + 0.528864i) q^{5} +(-0.194269 + 1.72112i) q^{6} +(1.49075 - 1.29175i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(0.606601 + 2.93803i) q^{9} +O(q^{10})$	\(q+(0.540641 + 0.841254i) q^{2} +(1.34287 + 1.09394i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-1.80115 + 0.528864i) q^{5} +(-0.194269 + 1.72112i) q^{6} +(1.49075 - 1.29175i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(0.606601 + 2.93803i) q^{9} +(-1.41868 - 1.22930i) q^{10} +(-1.85571 - 1.19259i) q^{11} +(-1.55293 + 0.767080i) q^{12} +(2.95529 - 3.41059i) q^{13} +(1.89265 + 0.555732i) q^{14} +(-2.99725 - 1.26015i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-0.301664 - 0.660552i) q^{17} +(-2.14368 + 2.09873i) q^{18} +(-0.501549 - 0.229050i) q^{19} +(0.267151 - 1.85808i) q^{20} +(3.41498 - 0.103855i) q^{21} -2.20589i q^{22} +(3.69884 - 3.05263i) q^{23} +(-1.48489 - 0.891693i) q^{24} +(-1.24184 + 0.798080i) q^{25} +(4.46692 + 0.642246i) q^{26} +(-2.39944 + 4.60898i) q^{27} +(0.555732 + 1.89265i) q^{28} +(-1.91619 + 0.875096i) q^{29} +(-0.560334 - 3.20273i) q^{30} +(0.655155 + 4.55670i) q^{31} +(0.281733 - 0.959493i) q^{32} +(-1.18736 - 3.63153i) q^{33} +(0.392600 - 0.610897i) q^{34} +(-2.00191 + 3.11503i) q^{35} +(-2.92452 - 0.668720i) q^{36} +(2.84409 - 9.68610i) q^{37} +(-0.0784689 - 0.545763i) q^{38} +(7.69954 - 1.34707i) q^{39} +(1.70755 - 0.779811i) q^{40} +(-3.00908 - 10.2480i) q^{41} +(1.93365 + 2.81672i) q^{42} +(-10.2475 - 1.47337i) q^{43} +(1.85571 - 1.19259i) q^{44} +(-2.64640 - 4.97102i) q^{45} +(4.56778 + 1.46129i) q^{46} +10.8344i q^{47} +(-0.0526500 - 1.73125i) q^{48} +(-0.442463 + 3.07740i) q^{49} +(-1.34277 - 0.613225i) q^{50} +(0.317507 - 1.21704i) q^{51} +(1.87471 + 4.10503i) q^{52} +(1.98330 + 2.28885i) q^{53} +(-5.17455 + 0.473266i) q^{54} +(3.97313 + 1.16662i) q^{55} +(-1.29175 + 1.49075i) q^{56} +(-0.422949 - 0.856247i) q^{57} +(-1.77215 - 1.13889i) q^{58} +(4.87697 + 4.22592i) q^{59} +(2.39137 - 2.20291i) q^{60} +(-14.8890 + 2.14072i) q^{61} +(-3.47914 + 3.01469i) q^{62} +(4.69948 + 3.59631i) q^{63} +(0.959493 - 0.281733i) q^{64} +(-3.51917 + 7.70591i) q^{65} +(2.41310 - 2.96222i) q^{66} +(3.42273 + 5.32586i) q^{67} +0.726175 q^{68} +(8.30645 - 0.0529805i) q^{69} -3.70284 q^{70} +(1.36094 + 2.11766i) q^{71} +(-1.01855 - 2.82180i) q^{72} +(-2.06209 + 4.51534i) q^{73} +(9.68610 - 2.84409i) q^{74} +(-2.54067 - 0.286774i) q^{75} +(0.416702 - 0.361074i) q^{76} +(-4.30694 + 0.619244i) q^{77} +(5.29591 + 5.74898i) q^{78} +(10.6252 + 9.20675i) q^{79} +(1.57919 + 1.01488i) q^{80} +(-8.26407 + 3.56442i) q^{81} +(6.99432 - 8.07188i) q^{82} +(-10.5768 - 3.10563i) q^{83} +(-1.32416 + 3.14952i) q^{84} +(0.892684 + 1.03021i) q^{85} +(-4.30074 - 9.41731i) q^{86} +(-3.53050 - 0.921055i) q^{87} +(2.00655 + 0.916359i) q^{88} +(0.391167 - 2.72063i) q^{89} +(2.75114 - 4.91383i) q^{90} -8.90183i q^{91} +(1.24021 + 4.63270i) q^{92} +(-4.10496 + 6.83576i) q^{93} +(-9.11445 + 5.85750i) q^{94} +(1.02450 + 0.147301i) q^{95} +(1.42796 - 0.980277i) q^{96} +(1.95701 + 6.66496i) q^{97} +(-2.82809 + 1.29154i) q^{98} +(2.37820 - 6.17557i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6}+O(q^{10}) $ 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6	$ 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6} - 4 q^{12} + 8 q^{13} - 22 q^{15} - 8 q^{16} - 28 q^{18} - 66 q^{21} - 4 q^{24} - 48 q^{25} - 38 q^{27} - 44 q^{30} - 16 q^{31} - 22 q^{33} - 44 q^{37} - 24 q^{39} - 44 q^{43} - 16 q^{46} + 4 q^{48} - 76 q^{49} - 8 q^{52} - 6 q^{54} + 64 q^{55} + 66 q^{57} + 36 q^{58} + 22 q^{60} + 88 q^{61} + 110 q^{63} + 8 q^{64} + 88 q^{66} + 44 q^{67} + 82 q^{69} + 112 q^{70} + 28 q^{72} + 52 q^{73} + 136 q^{75} + 82 q^{78} + 88 q^{79} + 36 q^{81} + 44 q^{82} + 22 q^{84} + 20 q^{85} - 10 q^{87} + 8 q^{93} - 56 q^{94} + 4 q^{96} - 132 q^{97} - 66 q^{99}+O(q^{100}) $ 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6 - 4 * q^12 + 8 * q^13 - 22 * q^15 - 8 * q^16 - 28 * q^18 - 66 * q^21 - 4 * q^24 - 48 * q^25 - 38 * q^27 - 44 * q^30 - 16 * q^31 - 22 * q^33 - 44 * q^37 - 24 * q^39 - 44 * q^43 - 16 * q^46 + 4 * q^48 - 76 * q^49 - 8 * q^52 - 6 * q^54 + 64 * q^55 + 66 * q^57 + 36 * q^58 + 22 * q^60 + 88 * q^61 + 110 * q^63 + 8 * q^64 + 88 * q^66 + 44 * q^67 + 82 * q^69 + 112 * q^70 + 28 * q^72 + 52 * q^73 + 136 * q^75 + 82 * q^78 + 88 * q^79 + 36 * q^81 + 44 * q^82 + 22 * q^84 + 20 * q^85 - 10 * q^87 + 8 * q^93 - 56 * q^94 + 4 * q^96 - 132 * q^97 - 66 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$-1$	$e\left(\frac{9}{22}\right)$

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 $

$2$	0.540641	+	0.841254i	0.382291	+	0.594856i
$2$	0.540641	+	0.841254i	0.382291	+	0.594856i
$3$	1.34287	+	1.09394i	0.775306	+	0.631585i
$3$	1.34287	+	1.09394i	0.775306	+	0.631585i
$4$	−0.415415	+	0.909632i	−0.207708	+	0.454816i
$5$	−1.80115	+	0.528864i	−0.805497	+	0.236515i	−0.658460	−	0.752616i	$-0.728792\pi$
$5$	−1.80115	+	0.528864i	−0.805497	+	0.236515i	−0.147037	+	0.989131i	$0.546974\pi$
$6$	−0.194269	+	1.72112i	−0.0793098	+	0.702645i
$7$	1.49075	−	1.29175i	0.563452	−	0.488234i	−0.325933	−	0.945393i	$-0.605678\pi$
$7$	1.49075	−	1.29175i	0.563452	−	0.488234i	0.889385	+	0.457159i	$0.151133\pi$
$8$	−0.989821	+	0.142315i	−0.349955	+	0.0503159i
$9$	0.606601	+	2.93803i	0.202200	+	0.979344i
$10$	−1.41868	−	1.22930i	−0.448627	−	0.388737i
$11$	−1.85571	−	1.19259i	−0.559518	−	0.359580i	0.230112	−	0.973164i	$-0.426091\pi$
$11$	−1.85571	−	1.19259i	−0.559518	−	0.359580i	−0.789630	+	0.613584i	$0.789727\pi$
$12$	−1.55293	+	0.767080i	−0.448292	+	0.221437i
$13$	2.95529	−	3.41059i	0.819650	−	0.945926i	−0.179635	−	0.983733i	$-0.557492\pi$
$13$	2.95529	−	3.41059i	0.819650	−	0.945926i	0.999285	+	0.0378070i	$0.0120372\pi$
$14$	1.89265	+	0.555732i	0.505832	+	0.148526i
$15$	−2.99725	−	1.26015i	−0.773887	−	0.325368i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	−0.301664	−	0.660552i	−0.0731643	−	0.160207i	0.869516	−	0.493905i	$-0.164431\pi$
$17$	−0.301664	−	0.660552i	−0.0731643	−	0.160207i	−0.942680	+	0.333697i	$0.891704\pi$
$18$	−2.14368	+	2.09873i	−0.505270	+	0.494674i
$19$	−0.501549	−	0.229050i	−0.115063	−	0.0525476i	0.357052	−	0.934085i	$-0.383782\pi$
$19$	−0.501549	−	0.229050i	−0.115063	−	0.0525476i	−0.472115	+	0.881537i	$0.656509\pi$
$20$	0.267151	−	1.85808i	0.0597369	−	0.415479i
$21$	3.41498	−	0.103855i	0.745210	−	0.0226630i
$22$		−	2.20589i		−	0.470297i
$23$	3.69884	−	3.05263i	0.771262	−	0.636517i
$23$	3.69884	−	3.05263i	0.771262	−	0.636517i
$24$	−1.48489	−	0.891693i	−0.303101	−	0.182016i
$25$	−1.24184	+	0.798080i	−0.248367	+	0.159616i
$26$	4.46692	+	0.642246i	0.876035	+	0.125955i
$27$	−2.39944	+	4.60898i	−0.461772	+	0.886999i
$28$	0.555732	+	1.89265i	0.105023	+	0.357677i
$29$	−1.91619	+	0.875096i	−0.355828	+	0.162501i	−0.585306	−	0.810813i	$-0.699025\pi$
$29$	−1.91619	+	0.875096i	−0.355828	+	0.162501i	0.229478	+	0.973314i	$0.426298\pi$
$30$	−0.560334	−	3.20273i	−0.102302	−	0.584737i
$31$	0.655155	+	4.55670i	0.117669	+	0.818408i	0.960111	+	0.279620i	$0.0902084\pi$
$31$	0.655155	+	4.55670i	0.117669	+	0.818408i	−0.842442	+	0.538788i	$0.818882\pi$
$32$	0.281733	−	0.959493i	0.0498038	−	0.169616i
$33$	−1.18736	−	3.63153i	−0.206692	−	0.632168i
$34$	0.392600	−	0.610897i	0.0673303	−	0.104768i
$35$	−2.00191	+	3.11503i	−0.338384	+	0.526536i
$36$	−2.92452	−	0.668720i	−0.487420	−	0.111453i
$37$	2.84409	−	9.68610i	0.467566	−	1.59238i	−0.301665	−	0.953414i	$-0.597542\pi$
$37$	2.84409	−	9.68610i	0.467566	−	1.59238i	0.769231	−	0.638970i	$-0.220639\pi$
$38$	−0.0784689	−	0.545763i	−0.0127293	−	0.0885345i
$39$	7.69954	−	1.34707i	1.23291	−	0.215704i
$40$	1.70755	−	0.779811i	0.269987	−	0.123299i
$41$	−3.00908	−	10.2480i	−0.469940	−	1.60047i	−0.764359	−	0.644791i	$-0.776945\pi$
$41$	−3.00908	−	10.2480i	−0.469940	−	1.60047i	0.294420	−	0.955676i	$-0.404874\pi$
$42$	1.93365	+	2.81672i	0.298368	+	0.434629i
$43$	−10.2475	−	1.47337i	−1.56273	−	0.224687i	−0.694000	−	0.719975i	$-0.744153\pi$
$43$	−10.2475	−	1.47337i	−1.56273	−	0.224687i	−0.868729	+	0.495288i	$0.835063\pi$
$44$	1.85571	−	1.19259i	0.279759	−	0.179790i
$45$	−2.64640	−	4.97102i	−0.394502	−	0.741036i
$46$	4.56778	+	1.46129i	0.673483	+	0.215455i
$47$			10.8344i			1.58035i	0.612878	+	0.790177i	$0.290012\pi$
$47$			10.8344i			1.58035i	−0.612878	+	0.790177i	$0.709988\pi$
$48$	−0.0526500	−	1.73125i	−0.00759937	−	0.249884i
$49$	−0.442463	+	3.07740i	−0.0632090	+	0.439628i
$50$	−1.34277	−	0.613225i	−0.189897	−	0.0867231i
$51$	0.317507	−	1.21704i	0.0444599	−	0.170419i
$52$	1.87471	+	4.10503i	0.259975	+	0.569266i
$53$	1.98330	+	2.28885i	0.272428	+	0.314398i	0.875434	−	0.483338i	$-0.160576\pi$
$53$	1.98330	+	2.28885i	0.272428	+	0.314398i	−0.603006	+	0.797737i	$0.706030\pi$
$54$	−5.17455	+	0.473266i	−0.704168	+	0.0644034i
$55$	3.97313	+	1.16662i	0.535737	+	0.157306i
$56$	−1.29175	+	1.49075i	−0.172617	+	0.199210i
$57$	−0.422949	−	0.856247i	−0.0560210	−	0.113413i
$58$	−1.77215	−	1.13889i	−0.232695	−	0.149544i
$59$	4.87697	+	4.22592i	0.634927	+	0.550168i	0.911746	−	0.410755i	$-0.134735\pi$
$59$	4.87697	+	4.22592i	0.634927	+	0.550168i	−0.276819	+	0.960922i	$0.589280\pi$
$60$	2.39137	−	2.20291i	0.308725	−	0.284395i
$61$	−14.8890	+	2.14072i	−1.90634	+	0.274091i	−0.991539	−	0.129807i	$-0.958564\pi$
$61$	−14.8890	+	2.14072i	−1.90634	+	0.274091i	−0.914804	+	0.403898i	$0.867655\pi$
$62$	−3.47914	+	3.01469i	−0.441851	+	0.382866i
$63$	4.69948	+	3.59631i	0.592079	+	0.453093i
$64$	0.959493	−	0.281733i	0.119937	−	0.0352166i
$65$	−3.51917	+	7.70591i	−0.436500	+	0.955801i
$66$	2.41310	−	2.96222i	0.297033	−	0.364624i
$67$	3.42273	+	5.32586i	0.418152	+	0.650658i	0.984878	−	0.173249i	$-0.0554264\pi$
$67$	3.42273	+	5.32586i	0.418152	+	0.650658i	−0.566726	+	0.823907i	$0.691790\pi$
$68$	0.726175			0.0880617
$69$	8.30645	−	0.0529805i	0.999980	−	0.00637811i
$70$	−3.70284			−0.442575
$71$	1.36094	+	2.11766i	0.161514	+	0.251320i	0.912572	−	0.408915i	$-0.134093\pi$
$71$	1.36094	+	2.11766i	0.161514	+	0.251320i	−0.751059	+	0.660235i	$0.770457\pi$
$72$	−1.01855	−	2.82180i	−0.120037	−	0.332552i
$73$	−2.06209	+	4.51534i	−0.241349	+	0.528481i	−0.991081	−	0.133261i	$-0.957455\pi$
$73$	−2.06209	+	4.51534i	−0.241349	+	0.528481i	0.749732	+	0.661742i	$0.230182\pi$
$74$	9.68610	−	2.84409i	1.12599	−	0.330619i
$75$	−2.54067	−	0.286774i	−0.293372	−	0.0331138i
$76$	0.416702	−	0.361074i	0.0477990	−	0.0414181i
$77$	−4.30694	+	0.619244i	−0.490821	+	0.0705694i
$78$	5.29591	+	5.74898i	0.599644	+	0.650944i
$79$	10.6252	+	9.20675i	1.19542	+	1.03584i	0.998463	+	0.0554287i	$0.0176526\pi$
$79$	10.6252	+	9.20675i	1.19542	+	1.03584i	0.196961	+	0.980411i	$0.436893\pi$
$80$	1.57919	+	1.01488i	0.176559	+	0.113467i
$81$	−8.26407	+	3.56442i	−0.918230	+	0.396047i
$82$	6.99432	−	8.07188i	0.772394	−	0.891390i
$83$	−10.5768	−	3.10563i	−1.16095	−	0.340887i	−0.356151	−	0.934428i	$-0.615911\pi$
$83$	−10.5768	−	3.10563i	−1.16095	−	0.340887i	−0.804803	+	0.593542i	$0.797729\pi$
$84$	−1.32416	+	3.14952i	−0.144478	+	0.343641i
$85$	0.892684	+	1.03021i	0.0968251	+	0.111742i
$86$	−4.30074	−	9.41731i	−0.463761	−	1.01549i
$87$	−3.53050	−	0.921055i	−0.378509	−	0.0987475i
$88$	2.00655	+	0.916359i	0.213899	+	0.0976842i
$89$	0.391167	−	2.72063i	0.0414636	−	0.288386i	−0.958531	−	0.284990i	$-0.908010\pi$
$89$	0.391167	−	2.72063i	0.0414636	−	0.288386i	0.999994	−	0.00339624i	$-0.00108106\pi$
$90$	2.75114	−	4.91383i	0.289995	−	0.517963i
$91$		−	8.90183i		−	0.933165i
$92$	1.24021	+	4.63270i	0.129301	+	0.482992i
$93$	−4.10496	+	6.83576i	−0.425664	+	0.708835i
$94$	−9.11445	+	5.85750i	−0.940083	+	0.604155i
$95$	1.02450	+	0.147301i	0.105111	+	0.0151127i
$96$	1.42796	−	0.980277i	0.145740	−	0.100049i
$97$	1.95701	+	6.66496i	0.198704	+	0.676724i	0.997204	+	0.0747288i	$0.0238091\pi$
$97$	1.95701	+	6.66496i	0.198704	+	0.676724i	−0.798500	+	0.601995i	$0.794373\pi$
$98$	−2.82809	+	1.29154i	−0.285680	+	0.130466i
$99$	2.37820	−	6.17557i	0.239018	−	0.620668i
$100$	−0.210081	−	1.46115i	−0.0210081	−	0.146115i
$101$	5.08531	−	17.3190i	0.506008	−	1.72330i	−0.169114	−	0.985597i	$-0.554090\pi$
$101$	5.08531	−	17.3190i	0.506008	−	1.72330i	0.675121	−	0.737707i	$-0.264091\pi$
$102$	1.19549	−	0.390876i	0.118372	−	0.0387025i
$103$	−4.85874	+	7.56034i	−0.478745	+	0.744943i	−0.993676	−	0.112290i	$-0.964182\pi$
$103$	−4.85874	+	7.56034i	−0.478745	+	0.744943i	0.514930	+	0.857232i	$0.327818\pi$
$104$	−2.43983	+	3.79645i	−0.239245	+	0.372273i
$105$	−6.09595	+	1.99312i	−0.594904	+	0.194508i
$106$	−0.853252	+	2.90591i	−0.0828752	+	0.282247i
$107$	0.913030	+	6.35026i	0.0882659	+	0.613903i	0.985158	+	0.171653i	$0.0549106\pi$
$107$	0.913030	+	6.35026i	0.0882659	+	0.613903i	−0.896892	+	0.442250i	$0.854180\pi$
$108$	−3.19571	−	4.09725i	−0.307508	−	0.394258i
$109$	13.5637	−	6.19435i	1.29917	−	0.593311i	0.358784	−	0.933421i	$-0.383192\pi$
$109$	13.5637	−	6.19435i	1.29917	−	0.593311i	0.940386	+	0.340110i	$0.110464\pi$
$110$	1.16662	+	3.97313i	0.111232	+	0.378823i
$111$	14.4152	−	9.89591i	1.36823	−	0.939278i
$112$	−1.95247	−	0.280723i	−0.184491	−	0.0265259i
$113$	3.07687	−	1.97738i	0.289447	−	0.186016i	−0.387857	−	0.921720i	$-0.626785\pi$
$113$	3.07687	−	1.97738i	0.289447	−	0.186016i	0.677304	+	0.735703i	$0.263148\pi$
$114$	0.491658	−	0.818730i	0.0460480	−	0.0766811i
$115$	−5.04773	+	7.45442i	−0.470704	+	0.695128i
$116$		−	2.10656i		−	0.195589i
$117$	11.8131	+	6.61387i	1.09212	+	0.611453i
$118$	−0.918379	+	6.38747i	−0.0845437	+	0.588014i
$119$	−1.30297	−	0.595048i	−0.119443	−	0.0545479i
$120$	3.14608	+	0.820766i	0.287197	+	0.0749254i
$121$	−2.54818	−	5.57973i	−0.231653	−	0.507248i
$122$	−9.85050	−	11.3681i	−0.891822	−	1.02922i
$123$	7.16986	−	17.0535i	0.646484	−	1.53766i
$124$	−4.41708	−	1.29697i	−0.396666	−	0.116472i
$125$	7.96113	−	9.18763i	0.712065	−	0.821767i
$126$	−0.484676	+	5.89777i	−0.0431784	+	0.525415i
$127$	−5.77176	−	3.70929i	−0.512161	−	0.329146i	0.258903	−	0.965903i	$-0.416639\pi$
$127$	−5.77176	−	3.70929i	−0.512161	−	0.329146i	−0.771064	+	0.636757i	$0.780275\pi$
$128$	0.755750	+	0.654861i	0.0667995	+	0.0578821i
$129$	−12.1493	−	13.1887i	−1.06969	−	1.16120i
$130$	−8.38523	+	1.20561i	−0.735434	+	0.105739i
$131$	3.70085	−	3.20680i	0.323344	−	0.280179i	−0.478029	−	0.878344i	$-0.658649\pi$
$131$	3.70085	−	3.20680i	0.323344	−	0.280179i	0.801373	+	0.598165i	$0.204103\pi$
$132$	3.79660	+	0.428535i	0.330452	+	0.0372992i
$133$	−1.04356	+	0.306417i	−0.0904882	+	0.0265697i
$134$	−2.62994	+	5.75876i	−0.227192	+	0.497481i
$135$	1.88422	−	9.57043i	0.162167	−	0.823691i
$136$	0.392600	+	0.610897i	0.0336652	+	0.0523840i
$137$	12.1765			1.04031			0.520154	−	0.854073i	$-0.325875\pi$
$137$	12.1765			1.04031			0.520154	+	0.854073i	$0.325875\pi$
$138$	4.53538	+	6.95919i	0.386077	+	0.592406i
$139$	−18.0035			−1.52703			−0.763517	−	0.645788i	$-0.776529\pi$
$139$	−18.0035			−1.52703			−0.763517	+	0.645788i	$0.776529\pi$
$140$	−2.00191	−	3.11503i	−0.169192	−	0.263268i
$141$	−11.8521	+	14.5491i	−0.998128	+	1.22526i
$142$	−1.04571	+	2.28979i	−0.0877541	+	0.192155i
$143$	−9.55161	+	2.80460i	−0.798745	+	0.234533i
$144$	1.82318	−	2.38244i	0.151932	−	0.198537i
$145$	2.98854	−	2.58958i	0.248184	−	0.215053i
$146$	−4.91340	+	0.706440i	−0.406635	+	0.0584654i
$147$	−3.96065	+	3.64852i	−0.326669	+	0.300925i
$148$	7.62930	+	6.61083i	0.627125	+	0.543407i
$149$	−0.413148	−	0.265514i	−0.0338464	−	0.0217517i	0.523608	−	0.851959i	$-0.324586\pi$
$149$	−0.413148	−	0.265514i	−0.0338464	−	0.0217517i	−0.557455	+	0.830207i	$0.688222\pi$
$150$	−1.13234	−	2.29239i	−0.0924554	−	0.187173i
$151$	9.05009	−	10.4444i	0.736486	−	0.849950i	−0.256700	−	0.966491i	$-0.582635\pi$
$151$	9.05009	−	10.4444i	0.736486	−	0.849950i	0.993186	+	0.116541i	$0.0371806\pi$
$152$	0.529041	+	0.155340i	0.0429109	+	0.0125998i
$153$	1.75773	−	1.28699i	0.142104	−	0.104047i
$154$	−2.84945	−	3.28844i	−0.229615	−	0.264990i
$155$	−3.58991	−	7.86080i	−0.288348	−	0.631394i
$156$	−1.97316	+	7.56334i	−0.157980	+	0.605552i
$157$	−2.69059	−	1.22875i	−0.214733	−	0.0980651i	0.305145	−	0.952306i	$-0.401295\pi$
$157$	−2.69059	−	1.22875i	−0.214733	−	0.0980651i	−0.519877	+	0.854241i	$0.674022\pi$
$158$	−2.00082	+	13.9160i	−0.159177	+	1.10710i
$159$	0.159455	+	5.24324i	0.0126456	+	0.415816i
$160$			1.87719i			0.148405i
$161$	1.57085	−	9.32869i	0.123800	−	0.735204i
$162$	−7.46648	−	5.02511i	−0.586622	−	0.394810i
$163$	10.9082	−	7.01027i	0.854395	−	0.549087i	−0.0385473	−	0.999257i	$-0.512273\pi$
$163$	10.9082	−	7.01027i	0.854395	−	0.549087i	0.892943	+	0.450170i	$0.148637\pi$
$164$	10.5719	+	1.52001i	0.825528	+	0.118693i
$165$	4.05919	+	5.91297i	0.316008	+	0.460324i
$166$	−3.10563	−	10.5768i	−0.241043	−	0.820919i
$167$	5.47008	−	2.49810i	0.423288	−	0.193309i	−0.192370	−	0.981322i	$-0.561618\pi$
$167$	5.47008	−	2.49810i	0.423288	−	0.193309i	0.615658	+	0.788013i	$0.288890\pi$
$168$	−3.36544	+	0.588800i	−0.259649	+	0.0454269i
$169$	−1.04827	−	7.29086i	−0.0806359	−	0.560835i
$170$	−0.384048	+	1.30795i	−0.0294551	+	0.100315i
$171$	0.368716	−	1.61251i	0.0281964	−	0.123312i
$172$	5.59719	−	8.70940i	0.426782	−	0.664085i
$173$	−1.30500	+	2.03062i	−0.0992176	+	0.154386i	−0.887313	−	0.461167i	$-0.847431\pi$
$173$	−1.30500	+	2.03062i	−0.0992176	+	0.154386i	0.788096	+	0.615553i	$0.211067\pi$
$174$	−1.13389	−	3.46800i	−0.0859600	−	0.262909i
$175$	−0.820357	+	2.79388i	−0.0620131	+	0.211197i
$176$	0.313931	+	2.18344i	0.0236634	+	0.164583i
$177$	1.92625	+	11.0100i	0.144785	+	0.827559i
$178$	2.50022	−	1.14181i	0.187399	−	0.0855824i
$179$	5.42051	+	18.4606i	0.405148	+	1.37981i	0.869402	+	0.494105i	$0.164504\pi$
$179$	5.42051	+	18.4606i	0.405148	+	1.37981i	−0.464254	+	0.885702i	$0.653678\pi$
$180$	5.62115	−	0.342212i	0.418976	−	0.0255070i
$181$	0.494499	+	0.0710982i	0.0367558	+	0.00528469i	0.160668	−	0.987008i	$-0.448635\pi$
$181$	0.494499	+	0.0710982i	0.0367558	+	0.00528469i	−0.123912	+	0.992293i	$0.539544\pi$
$182$	7.48870	−	4.81269i	0.555099	−	0.356740i
$183$	−22.3358	−	13.4130i	−1.65111	−	0.991514i
$184$	−3.22676	+	3.54796i	−0.237880	+	0.261559i
$185$			18.9502i			1.39325i
$186$	−7.96991	+	0.242377i	−0.584382	+	0.0177720i
$187$	−0.227969	+	1.58556i	−0.0166707	+	0.115947i
$188$	−9.85528	−	4.50076i	−0.718770	−	0.328251i
$189$	2.37666	+	9.97032i	0.172876	+	0.725234i
$190$	0.429969	+	0.941501i	0.0311932	+	0.0683036i
$191$	−7.04339	−	8.12851i	−0.509642	−	0.588158i	0.441365	−	0.897328i	$-0.354494\pi$
$191$	−7.04339	−	8.12851i	−0.509642	−	0.588158i	−0.951007	+	0.309169i	$0.899949\pi$
$192$	1.59667	+	0.671295i	0.115230	+	0.0484466i
$193$	8.38831	+	2.46303i	0.603803	+	0.177293i	0.569325	−	0.822113i	$-0.307205\pi$
$193$	8.38831	+	2.46303i	0.603803	+	0.177293i	0.0344787	+	0.999405i	$0.489023\pi$
$194$	−4.54888	+	5.24969i	−0.326591	+	0.376906i
$195$	−13.1556	+	6.49828i	−0.942091	+	0.465352i
$196$	−2.61549	−	1.68088i	−0.186821	−	0.120063i
$197$	−0.639673	−	0.554280i	−0.0455748	−	0.0394908i	0.631776	−	0.775151i	$-0.282326\pi$
$197$	−0.639673	−	0.554280i	−0.0455748	−	0.0394908i	−0.677350	+	0.735661i	$0.736872\pi$
$198$	6.48097	−	1.33809i	0.460583	−	0.0950941i
$199$	11.5796	−	1.66489i	0.820855	−	0.118021i	0.280924	−	0.959730i	$-0.409359\pi$
$199$	11.5796	−	1.66489i	0.820855	−	0.118021i	0.539932	+	0.841709i	$0.318450\pi$
$200$	1.11562	−	0.966688i	0.0788861	−	0.0683552i
$201$	−1.22989	+	10.8962i	−0.0867496	+	0.768558i
$202$	17.3190	−	5.08531i	1.21856	−	0.357801i
$203$	−1.72617	+	3.77979i	−0.121153	+	0.265289i
$204$	0.975159	+	0.794390i	0.0682748	+	0.0556185i
$205$	10.8396	+	16.8667i	0.757070	+	1.17802i
$206$	−8.98699			−0.626154
$207$	11.2124	+	9.01560i	0.779319	+	0.626627i
$208$	−4.51285			−0.312910
$209$	0.657567	+	1.02319i	0.0454849	+	0.0707758i
$210$	−4.97244	−	4.05068i	−0.343131	−	0.279524i
$211$	4.28128	−	9.37470i	0.294735	−	0.645381i	−0.703104	−	0.711088i	$-0.748203\pi$
$211$	4.28128	−	9.37470i	0.294735	−	0.645381i	0.997839	+	0.0657069i	$0.0209302\pi$
$212$	−2.90591	+	0.853252i	−0.199579	+	0.0586016i
$213$	−0.489026	+	4.33252i	−0.0335075	+	0.296860i
$214$	−4.84856	+	4.20130i	−0.331441	+	0.287195i
$215$	19.2365	−	2.76579i	1.31192	−	0.188625i
$216$	1.71909	−	4.90354i	0.116969	−	0.333644i
$217$	6.86277	+	5.94663i	0.465876	+	0.403683i
$218$	12.5441	+	8.06161i	0.849595	+	0.546001i
$219$	−7.70862	+	3.80772i	−0.520900	+	0.257302i
$220$	−2.71169	+	3.12946i	−0.182822	+	0.210988i
$221$	−3.14437	−	0.923272i	−0.211514	−	0.0621060i
$222$	16.1184	+	6.77674i	1.08180	+	0.454825i
$223$	2.77177	+	3.19880i	0.185612	+	0.214207i	0.840928	−	0.541148i	$-0.182010\pi$
$223$	2.77177	+	3.19880i	0.185612	+	0.214207i	−0.655316	+	0.755355i	$0.727465\pi$
$224$	−0.819427	−	1.79430i	−0.0547503	−	0.119886i
$225$	−3.09808	−	3.16444i	−0.206539	−	0.210963i
$226$	3.32696	+	1.51937i	0.221306	+	0.101067i
$227$	−3.50584	+	24.3836i	−0.232690	+	1.61840i	0.453693	+	0.891158i	$0.350106\pi$
$227$	−3.50584	+	24.3836i	−0.232690	+	1.61840i	−0.686383	+	0.727240i	$0.740803\pi$
$228$	0.954569	−	0.0290299i	0.0632179	−	0.00192255i
$229$		−	5.57118i		−	0.368154i	−0.982912	−	0.184077i	$-0.941070\pi$
$229$		−	5.57118i		−	0.368154i	0.982912	−	0.184077i	$-0.0589295\pi$
$230$	−9.00007	−	0.216259i	−0.593447	−	0.0142597i
$231$	−6.46107	−	3.87996i	−0.425107	−	0.255282i
$232$	1.77215	−	1.13889i	0.116347	−	0.0747719i
$233$	16.4214	+	2.36103i	1.07580	+	0.154676i	0.657366	−	0.753571i	$-0.271671\pi$
$233$	16.4214	+	2.36103i	1.07580	+	0.154676i	0.418433	+	0.908248i	$0.362580\pi$
$234$	0.822696	+	13.5135i	0.0537813	+	0.883407i
$235$	−5.72991	−	19.5143i	−0.373778	−	1.27297i
$236$	−5.86999	+	2.68074i	−0.382104	+	0.174501i
$237$	4.19659	+	23.9867i	0.272598	+	1.55811i
$238$	−0.203854	−	1.41784i	−0.0132139	−	0.0919047i
$239$	2.18966	−	7.45730i	0.141637	−	0.482373i	−0.857866	−	0.513873i	$-0.828210\pi$
$239$	2.18966	−	7.45730i	0.141637	−	0.482373i	0.999504	+	0.0315001i	$0.0100285\pi$
$240$	1.01043	+	3.09039i	0.0652228	+	0.199484i
$241$	−5.14277	+	8.00230i	−0.331275	+	0.515474i	−0.966437	−	0.256905i	$-0.917297\pi$
$241$	−5.14277	+	8.00230i	−0.331275	+	0.515474i	0.635162	+	0.772379i	$0.280933\pi$
$242$	3.31632	−	5.16030i	0.213181	−	0.331716i
$243$	−14.9968	−	4.25382i	−0.962047	−	0.272883i
$244$	4.23786	−	14.4328i	0.271301	−	0.923966i
$245$	−0.830585	−	5.77685i	−0.0530641	−	0.369069i
$246$	18.2226	−	3.18813i	1.16183	−	0.203268i
$247$	−2.26342	+	1.03367i	−0.144018	+	0.0657707i
$248$	−1.29697	−	4.41708i	−0.0823578	−	0.280485i
$249$	−10.8059	−	15.7408i	−0.684796	−	0.997533i
$250$	12.0332	+	1.73012i	0.761049	+	0.109422i
$251$	−17.0589	+	10.9631i	−1.07675	+	0.691983i	−0.953804	−	0.300431i	$-0.902870\pi$
$251$	−17.0589	+	10.9631i	−1.07675	+	0.691983i	−0.122943	+	0.992414i	$0.539233\pi$
$252$	−5.22356	+	2.78084i	−0.329053	+	0.175176i
$253$	−10.5045	+	1.25358i	−0.660414	+	0.0788121i
$254$		−	6.86091i		−	0.430492i
$255$	0.0717707	+	2.35998i	0.00449445	+	0.147788i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	19.7198	+	9.00572i	1.23009	+	0.561761i	0.921108	−	0.389308i	$-0.127286\pi$
$257$	19.7198	+	9.00572i	1.23009	+	0.561761i	0.308978	+	0.951069i	$0.400013\pi$
$258$	4.52661	−	17.3510i	0.281815	−	1.08022i
$259$	−8.27213	−	18.1134i	−0.514005	−	1.12551i
$260$	−5.54763	−	6.40230i	−0.344049	−	0.397054i
$261$	−3.73342	−	5.09900i	−0.231093	−	0.315620i
$262$	4.69856	+	1.37962i	0.290278	+	0.0852333i
$263$	1.26151	−	1.45586i	0.0777878	−	0.0897719i	−0.715522	−	0.698591i	$-0.753811\pi$
$263$	1.26151	−	1.45586i	0.0777878	−	0.0897719i	0.793309	+	0.608819i	$0.208356\pi$
$264$	1.69209	+	3.42559i	0.104141	+	0.210830i
$265$	−4.78271	−	3.07366i	−0.293800	−	0.188814i
$266$	−0.821966	−	0.712237i	−0.0503980	−	0.0436701i
$267$	3.50148	−	3.22554i	0.214287	−	0.197400i
$268$	−6.26643	+	0.900976i	−0.382783	+	0.0550359i
$269$	−11.1453	+	9.65750i	−0.679544	+	0.588828i	−0.924719	−	0.380651i	$-0.875700\pi$
$269$	−11.1453	+	9.65750i	−0.679544	+	0.588828i	0.245175	+	0.969479i	$0.421155\pi$
$270$	9.06984	−	3.58906i	0.551973	−	0.218423i
$271$	−0.732230	+	0.215002i	−0.0444798	+	0.0130604i	−0.303897	−	0.952705i	$-0.598288\pi$
$271$	−0.732230	+	0.215002i	−0.0444798	+	0.0130604i	0.259417	+	0.965765i	$0.416470\pi$
$272$	−0.301664	+	0.660552i	−0.0182911	+	0.0400519i
$273$	9.73805	−	11.9540i	0.589373	−	0.723489i
$274$	6.58311	+	10.2435i	0.397700	+	0.618833i
$275$	3.25628			0.196361
$276$	−3.40243	+	7.57783i	−0.204802	+	0.456132i
$277$	−15.9124			−0.956085			−0.478043	−	0.878337i	$-0.658654\pi$
$277$	−15.9124			−0.956085			−0.478043	+	0.878337i	$0.658654\pi$
$278$	−9.73341	−	15.1455i	−0.583771	−	0.908366i
$279$	−12.9903	+	4.68896i	−0.777710	+	0.280721i
$280$	1.53822	−	3.36823i	0.0919260	−	0.201290i
$281$	−11.4144	+	3.35157i	−0.680927	+	0.199938i	−0.603863	−	0.797088i	$-0.706373\pi$
$281$	−11.4144	+	3.35157i	−0.680927	+	0.199938i	−0.0770637	+	0.997026i	$0.524554\pi$
$282$	−18.6473	−	2.10478i	−1.11043	−	0.125338i
$283$	6.15227	−	5.33097i	0.365715	−	0.316894i	−0.452546	−	0.891741i	$-0.649484\pi$
$283$	6.15227	−	5.33097i	0.365715	−	0.316894i	0.818260	+	0.574848i	$0.194939\pi$
$284$	−2.49164	+	0.358244i	−0.147852	+	0.0212579i
$285$	1.21463	+	1.31854i	0.0719486	+	0.0781038i
$286$	−7.52337	−	6.51904i	−0.444866	−	0.385479i
$287$	−17.7236	−	11.3903i	−1.04619	−	0.672346i
$288$	2.98992	+	0.245710i	0.176183	+	0.0144786i
$289$	10.7873	−	12.4492i	0.634547	−	0.732307i
$290$	3.79422	+	1.11408i	0.222804	+	0.0654212i
$291$	−4.66304	+	11.0910i	−0.273352	+	0.650167i
$292$	−3.25068	−	3.75148i	−0.190231	−	0.219539i
$293$	−12.1468	−	26.5979i	−0.709626	−	1.55386i	−0.827895	−	0.560883i	$-0.810462\pi$
$293$	−12.1468	−	26.5979i	−0.709626	−	1.55386i	0.118269	−	0.992982i	$-0.462266\pi$
$294$	−5.21062	−	1.35937i	−0.303890	−	0.0792803i
$295$	−11.0191	−	5.03224i	−0.641555	−	0.292988i
$296$	−1.43667	+	9.99226i	−0.0835048	+	0.580788i
$297$	9.94931	−	5.69138i	0.577317	−	0.330247i
$298$		−	0.491110i		−	0.0284492i
$299$	0.519899	−	21.6366i	0.0300665	−	1.25128i
$300$	1.31629	−	2.19195i	0.0759962	−	0.126552i
$301$	−17.1797	+	11.0407i	−0.990223	+	0.636378i
$302$	13.6792	+	1.96677i	0.787150	+	0.113175i
$303$	25.7748	−	17.6941i	1.48072	−	1.01650i
$304$	0.155340	+	0.529041i	0.00890939	+	0.0303426i
$305$	25.6852	−	11.7300i	1.47073	−	0.671659i
$306$	2.03299	+	0.782901i	0.116218	+	0.0447555i
$307$	0.616673	+	4.28905i	0.0351954	+	0.244789i	0.999823	−	0.0188280i	$-0.00599350\pi$
$307$	0.616673	+	4.28905i	0.0351954	+	0.244789i	−0.964627	+	0.263617i	$0.915084\pi$
$308$	1.22588	−	4.17497i	0.0698511	−	0.237891i
$309$	−14.7952	+	4.83740i	−0.841669	+	0.275190i
$310$	4.67207	−	7.26989i	0.265356	−	0.412902i
$311$	6.44713	−	10.0319i	0.365583	−	0.568859i	−0.608920	−	0.793232i	$-0.708397\pi$
$311$	6.44713	−	10.0319i	0.365583	−	0.568859i	0.974503	+	0.224373i	$0.0720333\pi$
$312$	−7.42946	+	2.42912i	−0.420610	+	0.137522i
$313$	−6.80062	+	23.1608i	−0.384394	+	1.30913i	0.509354	+	0.860557i	$0.329884\pi$
$313$	−6.80062	+	23.1608i	−0.384394	+	1.30913i	−0.893748	+	0.448569i	$0.851934\pi$
$314$	−0.420952	−	2.92778i	−0.0237557	−	0.165224i
$315$	−10.3664	−	3.99209i	−0.584082	−	0.224929i
$316$	−12.7886	+	5.84036i	−0.719415	+	0.328546i
$317$	−4.19170	−	14.2756i	−0.235429	−	0.801798i	−0.989441	−	0.144937i	$-0.953702\pi$
$317$	−4.19170	−	14.2756i	−0.235429	−	0.801798i	0.754012	−	0.656861i	$-0.228116\pi$
$318$	−4.32469	+	2.96885i	−0.242517	+	0.166485i
$319$	4.59953	+	0.661313i	0.257524	+	0.0370264i
$320$	−1.57919	+	1.01488i	−0.0882794	+	0.0567337i
$321$	−5.72071	+	9.52637i	−0.319299	+	0.531710i
$322$	8.69706	−	3.72199i	0.484668	−	0.207418i
$323$			0.400395i			0.0222786i
$324$	0.190705	−	8.99798i	0.0105947	−	0.499888i
$325$	−0.948066	+	6.59395i	−0.0525893	+	0.365766i
$326$	11.7948	+	5.38652i	0.653255	+	0.298332i
$327$	24.9905	+	6.51967i	1.38198	+	0.360538i
$328$	4.43689	+	9.71544i	0.244986	+	0.536446i
$329$	13.9952	+	16.1514i	0.771583	+	0.890454i
$330$	−2.77974	+	6.61160i	−0.153020	+	0.363957i
$331$	−2.16524	−	0.635773i	−0.119012	−	0.0349452i	0.221684	−	0.975119i	$-0.428845\pi$
$331$	−2.16524	−	0.635773i	−0.119012	−	0.0349452i	−0.340696	+	0.940173i	$0.610663\pi$
$332$	7.21874	−	8.33087i	0.396180	−	0.457216i
$333$	30.1833	+	2.48045i	1.65403	+	0.135928i
$334$	5.05889	+	3.25115i	0.276810	+	0.177895i
$335$	−8.98149	−	7.78251i	−0.490711	−	0.425204i
$336$	−2.31482	−	2.51286i	−0.126284	−	0.137088i
$337$	7.99532	−	1.14955i	0.435533	−	0.0626202i	0.0789386	−	0.996879i	$-0.474847\pi$
$337$	7.99532	−	1.14955i	0.435533	−	0.0626202i	0.356594	+	0.934259i	$0.383938\pi$
$338$	5.56672	−	4.82359i	0.302790	−	0.262369i
$339$	6.29496	+	0.710533i	0.341896	+	0.0385908i
$340$	−1.30795	+	0.384048i	−0.0709334	+	0.0208279i
$341$	4.21851	−	9.23726i	0.228445	−	0.500225i
$342$	1.55587	−	0.561605i	0.0841319	−	0.0303681i
$343$	10.7807	+	16.7751i	0.582103	+	0.905770i
$344$	10.3529			0.558190
$345$	−14.9331	+	4.48841i	−0.803972	+	0.241648i
$346$	−2.41381			−0.129767
$347$	12.0071	+	18.6834i	0.644574	+	1.00298i	0.997725	+	0.0674109i	$0.0214738\pi$
$347$	12.0071	+	18.6834i	0.644574	+	1.00298i	−0.353151	+	0.935566i	$0.614890\pi$
$348$	2.30444	−	2.82883i	0.123531	−	0.151641i
$349$	−5.62869	+	12.3251i	−0.301297	+	0.659748i	−0.998359	−	0.0572626i	$-0.981763\pi$
$349$	−5.62869	+	12.3251i	−0.301297	+	0.659748i	0.697062	+	0.717010i	$0.254490\pi$
$350$	−2.79388	+	0.820357i	−0.149339	+	0.0438499i
$351$	8.62828	+	21.8044i	0.460544	+	1.16383i
$352$	−1.66710	+	1.44455i	−0.0888567	+	0.0769948i
$353$	−35.6857	+	5.13083i	−1.89936	+	0.273087i	−0.989798	−	0.142481i	$-0.954492\pi$
$353$	−35.6857	+	5.13083i	−1.89936	+	0.273087i	−0.909562	+	0.415568i	$0.863583\pi$
$354$	−8.22076	+	7.57289i	−0.436928	+	0.402495i
$355$	−3.57120	−	3.09446i	−0.189540	−	0.164237i
$356$	2.31227	+	1.48601i	0.122550	+	0.0787582i
$357$	−1.09878	−	2.22444i	−0.0581535	−	0.117730i
$358$	−12.5995	+	14.5406i	−0.665902	+	0.768492i
$359$	10.3735	+	3.04593i	0.547492	+	0.160758i	0.543769	−	0.839235i	$-0.316997\pi$
$359$	10.3735	+	3.04593i	0.547492	+	0.160758i	0.00372270	+	0.999993i	$0.498815\pi$
$360$	3.32691	+	4.54380i	0.175344	+	0.239479i
$361$	−12.2433	−	14.1295i	−0.644382	−	0.743657i
$362$	0.207535	+	0.454438i	0.0109078	+	0.0238847i
$363$	2.68201	−	10.2804i	0.140769	−	0.539581i
$364$	8.09739	+	3.69795i	0.424418	+	0.193825i
$365$	1.32612	−	9.22335i	0.0694122	−	0.482772i
$366$	−0.791968	−	26.0417i	−0.0413968	−	1.36122i
$367$			6.90386i			0.360379i	0.983632	+	0.180189i	$0.0576711\pi$
$367$			6.90386i			0.360379i	−0.983632	+	0.180189i	$0.942329\pi$
$368$	−4.72925	−	0.796352i	−0.246529	−	0.0415127i
$369$	28.2836	−	15.0572i	1.47239	−	0.783847i
$370$	−15.9419	+	10.2453i	−0.828782	+	0.532626i
$371$	5.91324	+	0.850195i	0.307000	+	0.0441399i
$372$	−4.51276	−	6.57368i	−0.233976	−	0.340829i
$373$	8.09640	+	27.5738i	0.419216	+	1.42772i	0.850726	+	0.525610i	$0.176163\pi$
$373$	8.09640	+	27.5738i	0.419216	+	1.42772i	−0.431510	+	0.902108i	$0.642019\pi$
$374$	−1.45710	+	0.665437i	−0.0753451	+	0.0344089i
$375$	20.7415	−	3.62882i	1.07108	−	0.187391i
$376$	−1.54189	−	10.7241i	−0.0795169	−	0.553052i
$377$	−2.67831	+	9.12150i	−0.137940	+	0.469781i
$378$	−7.10265	+	7.38973i	−0.365321	+	0.380087i
$379$	4.37766	−	6.81177i	0.224865	−	0.349897i	−0.710429	−	0.703769i	$-0.751499\pi$
$379$	4.37766	−	6.81177i	0.224865	−	0.349897i	0.935294	+	0.353872i	$0.115135\pi$
$380$	−0.559582	+	0.870726i	−0.0287059	+	0.0446673i
$381$	−3.69300	−	11.2950i	−0.189198	−	0.578662i
$382$	3.03019	−	10.3199i	0.155038	−	0.528011i
$383$	1.82924	+	12.7226i	0.0934696	+	0.650096i	0.981663	+	0.190625i	$0.0610516\pi$
$383$	1.82924	+	12.7226i	0.0934696	+	0.650096i	−0.888193	+	0.459470i	$0.848039\pi$
$384$	0.298497	+	1.70614i	0.0152326	+	0.0870659i
$385$	7.42993	−	3.39314i	0.378664	−	0.172930i
$386$	2.46303	+	8.38831i	0.125365	+	0.426954i
$387$	−1.88734	−	31.0012i	−0.0959387	−	1.57588i
$388$	−6.87563	−	0.988566i	−0.349057	−	0.0501868i
$389$	−28.9931	+	18.6327i	−1.47001	+	0.944717i	−0.472003	+	0.881597i	$0.656469\pi$
$389$	−28.9931	+	18.6327i	−1.47001	+	0.944717i	−0.998006	+	0.0631206i	$0.979895\pi$
$390$	−12.5791	−	7.55394i	−0.636970	−	0.382509i
$391$	−3.13223	−	1.52241i	−0.158404	−	0.0769916i
$392$		−	3.10904i		−	0.157030i
$393$	8.47779	−	0.257823i	0.427648	−	0.0130054i
$394$	0.120457	−	0.837794i	0.00606852	−	0.0422074i
$395$	−24.0066	−	10.9634i	−1.20790	−	0.551630i
$396$	4.62955	+	4.72871i	0.232644	+	0.237627i
$397$	−5.26485	−	11.5284i	−0.264235	−	0.578595i	0.730285	−	0.683143i	$-0.239387\pi$
$397$	−5.26485	−	11.5284i	−0.264235	−	0.578595i	−0.994520	+	0.104549i	$0.966660\pi$
$398$	7.66100	+	8.84126i	0.384011	+	0.443172i
$399$	−1.73657	−	0.730112i	−0.0869371	−	0.0365513i
$400$	1.41638	+	0.415886i	0.0708189	+	0.0207943i
$401$	−1.78297	+	2.05766i	−0.0890373	+	0.102755i	−0.798520	−	0.601968i	$-0.794383\pi$
$401$	−1.78297	+	2.05766i	−0.0890373	+	0.102755i	0.709483	+	0.704723i	$0.248929\pi$
$402$	−9.83139	+	4.85628i	−0.490345	+	0.242209i
$403$	17.4772	+	11.2319i	0.870601	+	0.559501i
$404$	13.6414	+	11.8203i	0.678684	+	0.588083i
$405$	12.9997	−	10.7906i	0.645961	−	0.536190i
$406$	−4.11300	+	0.591360i	−0.204125	+	0.0293487i
$407$	−16.8294	+	14.5828i	−0.834202	+	0.722840i
$408$	−0.141073	+	1.24984i	−0.00698415	+	0.0618761i
$409$	−4.24238	+	1.24568i	−0.209772	+	0.0615947i	−0.384930	−	0.922946i	$-0.625775\pi$
$409$	−4.24238	+	1.24568i	−0.209772	+	0.0615947i	0.175158	+	0.984540i	$0.443956\pi$
$410$	−8.32887	+	18.2377i	−0.411334	+	0.900695i
$411$	16.3514	+	13.3203i	0.806557	+	0.657043i
$412$	−4.85874	−	7.56034i	−0.239373	−	0.372471i
$413$	12.7292			0.626362
$414$	−1.52250	+	14.3067i	−0.0748266	+	0.703137i
$415$	20.6928			1.01577
$416$	−2.43983	−	3.79645i	−0.119623	−	0.186136i
$417$	−24.1763	−	19.6947i	−1.18392	−	0.964452i
$418$	−0.505258	+	1.10636i	−0.0247130	+	0.0541139i
$419$	−35.5048	+	10.4252i	−1.73452	+	0.509302i	−0.987786	−	0.155816i	$-0.950199\pi$
$419$	−35.5048	+	10.4252i	−1.73452	+	0.509302i	−0.746738	+	0.665118i	$0.768381\pi$
$420$	0.719346	−	6.37305i	0.0351005	−	0.310973i
$421$	24.3165	−	21.0704i	1.18511	−	1.02691i	0.186098	−	0.982531i	$-0.440416\pi$
$421$	24.3165	−	21.0704i	1.18511	−	1.02691i	0.999015	−	0.0443749i	$-0.0141296\pi$
$422$	10.2011	−	1.46670i	0.496583	−	0.0713979i
$423$	−31.8317	+	6.57213i	−1.54771	+	0.319548i
$424$	−2.28885	−	1.98330i	−0.111157	−	0.0963177i
$425$	0.901791	+	0.579546i	0.0437433	+	0.0281121i
$426$	−3.90914	+	1.93094i	−0.189398	+	0.0935545i
$427$	−19.4306	+	22.4241i	−0.940313	+	1.08518i
$428$	−6.15569	−	1.80747i	−0.297546	−	0.0873675i
$429$	−15.8946	−	6.68264i	−0.767400	−	0.322641i
$430$	12.7267	+	14.6874i	0.613738	+	0.708291i
$431$	6.22902	+	13.6396i	0.300041	+	0.656999i	0.998265	−	0.0588809i	$-0.0187532\pi$
$431$	6.22902	+	13.6396i	0.300041	+	0.656999i	−0.698224	+	0.715880i	$0.746026\pi$
$432$	5.05453	−	1.20486i	0.243186	−	0.0579691i
$433$	10.1351	+	4.62854i	0.487061	+	0.222433i	0.643781	−	0.765210i	$-0.277365\pi$
$433$	10.1351	+	4.62854i	0.487061	+	0.222433i	−0.156720	+	0.987643i	$0.550092\pi$
$434$	−1.29233	+	8.98832i	−0.0620336	+	0.431453i
$435$	6.84606	−	0.208199i	0.328243	−	0.00998238i
$436$			14.9112i			0.714118i
$437$	−2.55436	+	0.683824i	−0.122191	+	0.0327117i
$438$	−7.37085	−	4.42629i	−0.352193	−	0.211496i
$439$	12.1521	−	7.80970i	0.579990	−	0.372737i	−0.217508	−	0.976058i	$-0.569793\pi$
$439$	12.1521	−	7.80970i	0.579990	−	0.372737i	0.797498	+	0.603322i	$0.206157\pi$
$440$	−4.09871	−	0.589306i	−0.195399	−	0.0280941i
$441$	−9.30989	+	0.566781i	−0.443328	+	0.0269896i
$442$	−0.923272	−	3.14437i	−0.0439156	−	0.149563i
$443$	17.2153	−	7.86195i	0.817922	−	0.373532i	0.0378976	−	0.999282i	$-0.487934\pi$
$443$	17.2153	−	7.86195i	0.817922	−	0.373532i	0.780024	+	0.625749i	$0.215207\pi$
$444$	3.01333	+	17.2235i	0.143006	+	0.817390i
$445$	0.734293	+	5.10712i	0.0348088	+	0.242101i
$446$	−1.19246	+	4.06116i	−0.0564649	+	0.192302i
$447$	−0.264348	−	0.808508i	−0.0125032	−	0.0382411i
$448$	1.06644	−	1.65942i	0.0503846	−	0.0784000i
$449$	12.1071	−	18.8391i	0.571371	−	0.889071i	−0.428524	−	0.903530i	$-0.640966\pi$
$449$	12.1071	−	18.8391i	0.571371	−	0.889071i	0.999895	+	0.0144592i	$0.00460268\pi$
$450$	0.987146	−	4.31710i	0.0465345	−	0.203510i
$451$	−6.63770	+	22.6059i	−0.312557	+	1.06447i
$452$	0.520513	+	3.62025i	0.0244829	+	0.170282i
$453$	23.5786	−	4.12519i	1.10782	−	0.193818i
$454$	−22.4082	+	10.2335i	−1.05167	+	0.480281i
$455$	4.70786	+	16.0335i	0.220708	+	0.751662i
$456$	0.540501	+	0.787340i	0.0253113	+	0.0368706i
$457$	−23.0174	−	3.30940i	−1.07671	−	0.154807i	−0.418929	−	0.908019i	$-0.637594\pi$
$457$	−23.0174	−	3.30940i	−1.07671	−	0.154807i	−0.657778	+	0.753212i	$0.728503\pi$
$458$	4.68677	−	3.01201i	0.218999	−	0.140742i
$459$	3.76830	+	0.194591i	0.175889	+	0.00908273i
$460$	−4.68388	−	7.68826i	−0.218387	−	0.358467i
$461$			25.8406i			1.20352i	0.798679	+	0.601758i	$0.205533\pi$
$461$			25.8406i			1.20352i	−0.798679	+	0.601758i	$0.794467\pi$
$462$	−0.229092	−	7.53306i	−0.0106583	−	0.350470i
$463$	2.22872	−	15.5011i	0.103577	−	0.720395i	−0.870168	−	0.492755i	$-0.835990\pi$
$463$	2.22872	−	15.5011i	0.103577	−	0.720395i	0.973745	−	0.227640i	$-0.0731010\pi$
$464$	1.91619	+	0.875096i	0.0889570	+	0.0406253i
$465$	3.77845	−	14.4832i	0.175221	−	0.671641i
$466$	6.89183	+	15.0910i	0.319258	+	0.699077i
$467$	−19.3933	−	22.3810i	−0.897414	−	1.03567i	−0.999165	−	0.0408613i	$-0.986990\pi$
$467$	−19.3933	−	22.3810i	−0.897414	−	1.03567i	0.101751	−	0.994810i	$-0.467556\pi$
$468$	−10.9235	+	7.99806i	−0.504940	+	0.369711i
$469$	11.9821	+	3.51826i	0.553282	+	0.162458i
$470$	13.3186	−	15.3705i	0.614343	−	0.708989i
$471$	−2.26894	−	4.59340i	−0.104547	−	0.211652i
$472$	−5.42874	−	3.48884i	−0.249878	−	0.160587i
$473$	17.2593	+	14.9552i	0.793582	+	0.687643i
$474$	−17.9101	+	16.4986i	−0.822637	+	0.757806i
$475$	0.805642	−	0.115834i	0.0369654	−	0.00531482i
$476$	1.08255	−	0.938034i	0.0496185	−	0.0429947i
$477$	−5.52166	+	7.21543i	−0.252819	+	0.330372i
$478$	7.45730	−	2.18966i	0.341089	−	0.100153i
$479$	7.46364	−	16.3431i	0.341022	−	0.746735i	−0.658963	−	0.752176i	$-0.729005\pi$
$479$	7.46364	−	16.3431i	0.341022	−	0.746735i	0.999985	+	0.00544059i	$0.00173180\pi$
$480$	−2.05352	+	2.52082i	−0.0937301	+	0.115059i
$481$	−24.6301	−	38.3252i	−1.12304	−	1.74748i
$482$	−9.51236			−0.433276
$483$	12.3144	−	10.8088i	0.560327	−	0.491818i
$484$	6.13406			0.278821
$485$	−7.04972	−	10.9696i	−0.320111	−	0.498103i
$486$	−4.52936	−	14.9159i	−0.205456	−	0.676600i
$487$	0.316253	−	0.692497i	0.0143308	−	0.0313800i	−0.902331	−	0.431043i	$-0.858146\pi$
$487$	0.316253	−	0.692497i	0.0143308	−	0.0313800i	0.916662	+	0.399663i	$0.130873\pi$
$488$	14.4328	−	4.23786i	0.653343	−	0.191839i
$489$	22.3171	+	2.51900i	1.00921	+	0.113913i
$490$	4.41075	−	3.82193i	0.199257	−	0.172657i
$491$	34.5209	−	4.96336i	1.55791	−	0.223993i	0.691146	−	0.722715i	$-0.257106\pi$
$491$	34.5209	−	4.96336i	1.55791	−	0.223993i	0.866762	+	0.498722i	$0.166197\pi$
$492$	12.5339	+	13.6062i	0.565072	+	0.613415i
$493$	1.15609	+	1.00176i	0.0520678	+	0.0451170i
$494$	−2.09327	−	1.34526i	−0.0941807	−	0.0605263i
$495$	−1.01745	+	12.3809i	−0.0457311	+	0.556478i
$496$	3.01469	−	3.47914i	0.135364	−	0.156218i
$497$	4.76430	+	1.39893i	0.213708	+	0.0627504i
$498$	7.39990	−	17.6006i	0.331597	−	0.788703i
$499$	0.823674	+	0.950570i	0.0368727	+	0.0425534i	0.773886	−	0.633324i	$-0.218310\pi$
$499$	0.823674	+	0.950570i	0.0368727	+	0.0425534i	−0.737014	+	0.675878i	$0.763765\pi$
$500$	5.05019	+	11.0584i	0.225851	+	0.494546i
$501$	10.0784	+	2.62930i	0.450269	+	0.117469i
$502$	−18.4454	−	8.42375i	−0.823260	−	0.375970i
$503$	0.121216	−	0.843078i	0.00540477	−	0.0375910i	−0.986941	−	0.161085i	$-0.948501\pi$
$503$	0.121216	−	0.843078i	0.00540477	−	0.0375910i	0.992345	+	0.123494i	$0.0394099\pi$
$504$	−5.16346	−	2.89090i	−0.229999	−	0.128771i
$505$			33.8835i			1.50779i
$506$	−6.73376	−	8.15924i	−0.299352	−	0.362722i
$507$	6.56806	−	10.9374i	0.291698	−	0.485748i
$508$	5.77176	−	3.70929i	0.256081	−	0.164573i
$509$	25.1088	+	3.61010i	1.11293	+	0.160015i	0.674159	−	0.738586i	$-0.264506\pi$
$509$	25.1088	+	3.61010i	1.11293	+	0.160015i	0.438767	+	0.898601i	$0.355415\pi$
$510$	−1.94654	+	1.33628i	−0.0861943	+	0.0591714i
$511$	2.75861	+	9.39496i	0.122034	+	0.415608i
$512$	−0.909632	+	0.415415i	−0.0402004	+	0.0183589i
$513$	2.25912	−	1.76204i	0.0997427	−	0.0777959i
$514$	3.08522	+	21.4582i	0.136083	+	0.946480i
$515$	4.75290	−	16.1869i	0.209438	−	0.713280i
$516$	17.0438	−	5.57261i	0.750313	−	0.245321i
$517$	12.9210	−	20.1055i	0.568265	−	0.884237i
$518$	10.7657	−	16.7518i	0.473020	−	0.736033i
$519$	−3.97383	+	1.29927i	−0.174432	+	0.0570318i
$520$	2.38669	−	8.12831i	0.104663	−	0.356450i
$521$	−2.84880	−	19.8138i	−0.124808	−	0.868059i	−0.951991	−	0.306126i	$-0.900967\pi$
$521$	−2.84880	−	19.8138i	−0.124808	−	0.868059i	0.827183	−	0.561933i	$-0.189942\pi$
$522$	2.27111	−	5.89748i	0.0994039	−	0.258126i
$523$	−26.7190	+	12.2021i	−1.16834	+	0.533563i	−0.902599	−	0.430482i	$-0.858344\pi$
$523$	−26.7190	+	12.2021i	−1.16834	+	0.533563i	−0.265740	+	0.964045i	$0.585616\pi$
$524$	1.37962	+	4.69856i	0.0602691	+	0.205258i
$525$	−4.15796	+	2.85440i	−0.181468	+	0.124576i
$526$	1.90677	+	0.274152i	0.0831389	+	0.0119536i
$527$	2.81230	−	1.80736i	0.122506	−	0.0787297i
$528$	−1.96697	+	3.27549i	−0.0856016	+	0.142547i
$529$	4.36290	−	22.5824i	0.189691	−	0.981844i
$530$		−	5.68522i		−	0.246950i
$531$	−9.45751	+	16.8921i	−0.410421	+	0.733056i
$532$	0.154784	−	1.07655i	0.00671074	−	0.0466742i
$533$	−43.8444	−	20.0230i	−1.89911	−	0.867294i
$534$	4.60654	+	1.20178i	0.199344	+	0.0520060i
$535$	−5.00293	−	10.9549i	−0.216295	−	0.473621i
$536$	−4.14584	−	4.78455i	−0.179073	−	0.206661i
$537$	−12.9157	+	30.7198i	−0.557352	+	1.32566i
$538$	−14.1500	−	4.15482i	−0.610051	−	0.179127i
$539$	4.49117	−	5.18308i	0.193448	−	0.223251i
$540$	7.92283	+	5.68964i	0.340944	+	0.244843i
$541$	−14.6045	−	9.38573i	−0.627896	−	0.403524i	0.187634	−	0.982239i	$-0.439918\pi$
$541$	−14.6045	−	9.38573i	−0.627896	−	0.403524i	−0.815530	+	0.578715i	$0.803554\pi$
$542$	−0.576745	−	0.499752i	−0.0247733	−	0.0214662i
$543$	0.586271	+	0.636427i	0.0251593	+	0.0273117i
$544$	−0.718784	+	0.103346i	−0.0308176	+	0.00443090i
$545$	−21.1543	+	18.3303i	−0.906150	+	0.785183i
$546$	15.3211	+	1.72935i	0.655684	+	0.0740091i
$547$	−11.0586	+	3.24711i	−0.472833	+	0.138836i	−0.509463	−	0.860493i	$-0.670156\pi$
$547$	−11.0586	+	3.24711i	−0.472833	+	0.138836i	0.0366299	+	0.999329i	$0.488338\pi$
$548$	−5.05830	+	11.0761i	−0.216080	+	0.473148i
$549$	−15.3212	−	42.4459i	−0.653892	−	1.81155i
$550$	1.76048	+	2.73935i	0.0750669	+	0.116806i
$551$	1.16150			0.0494818
$552$	−8.21437	+	1.23457i	−0.349627	+	0.0525469i
$553$	27.7323			1.17930
$554$	−8.60291	−	13.3864i	−0.365503	−	0.568733i
$555$	−20.7304	+	25.4477i	−0.879955	+	1.08019i
$556$	7.47891	−	16.3765i	0.317176	−	0.694520i
$557$	−17.4775	+	5.13187i	−0.740547	+	0.217444i	−0.630183	−	0.776447i	$-0.717020\pi$
$557$	−17.4775	+	5.13187i	−0.740547	+	0.217444i	−0.110364	+	0.993891i	$0.535202\pi$
$558$	−10.9677	−	8.39311i	−0.464300	−	0.355309i
$559$	−35.3094	+	30.5958i	−1.49343	+	1.29406i
$560$	3.66515	−	0.526970i	0.154881	−	0.0222685i
$561$	−2.04063	+	1.87981i	−0.0861556	+	0.0793658i
$562$	−8.99062	−	7.79042i	−0.379247	−	0.328619i
$563$	−2.07744	−	1.33509i	−0.0875537	−	0.0562673i	0.496131	−	0.868247i	$-0.334753\pi$
$563$	−2.07744	−	1.33509i	−0.0875537	−	0.0562673i	−0.583685	+	0.811980i	$0.698390\pi$
$564$	−8.31082	−	16.8250i	−0.349949	−	0.708460i
$565$	−4.49612	+	5.18880i	−0.189153	+	0.218294i
$566$	7.81087	+	2.29348i	0.328315	+	0.0964021i
$567$	−7.71537	+	15.9888i	−0.324015	+	0.671465i
$568$	−1.64846	−	1.90242i	−0.0691678	−	0.0798239i
$569$	2.72157	+	5.95940i	0.114094	+	0.249831i	0.958061	−	0.286564i	$-0.0925130\pi$
$569$	2.72157	+	5.95940i	0.114094	+	0.249831i	−0.843967	+	0.536395i	$0.819786\pi$
$570$	−0.452551	+	1.73467i	−0.0189553	+	0.0726574i
$571$	29.2972	+	13.3796i	1.22605	+	0.559917i	0.919932	−	0.392077i	$-0.128243\pi$
$571$	29.2972	+	13.3796i	1.22605	+	0.559917i	0.306115	+	0.951994i	$0.400971\pi$
$572$	1.41672	−	9.85352i	0.0592361	−	0.411996i
$573$	−0.566280	−	18.6206i	−0.0236567	−	0.777885i
$574$		−	21.0681i		−	0.879365i
$575$	−2.15712	+	6.74284i	−0.0899580	+	0.281196i
$576$	1.40977	+	2.64812i	0.0587404	+	0.110338i
$577$	17.1921	−	11.0487i	0.715716	−	0.459962i	−0.131429	−	0.991326i	$-0.541956\pi$
$577$	17.1921	−	11.0487i	0.715716	−	0.459962i	0.847144	+	0.531363i	$0.178320\pi$
$578$	16.3050	+	2.34431i	0.678199	+	0.0975102i
$579$	8.57001	+	12.4838i	0.356157	+	0.518810i
$580$	1.11408	+	3.79422i	0.0462598	+	0.157546i
$581$	−19.7791	+	9.03281i	−0.820575	+	0.374744i
$582$	−11.8514	+	2.07346i	−0.491256	+	0.0859476i
$583$	−0.950767	−	6.61273i	−0.0393767	−	0.273871i
$584$	1.39850	−	4.76285i	0.0578703	−	0.197088i
$585$	−24.7750	−	5.66503i	−1.02432	−	0.234220i
$586$	15.8085	−	24.5985i	0.653042	−	1.01615i
$587$	11.7978	−	18.3578i	0.486948	−	0.757706i	−0.507644	−	0.861567i	$-0.669483\pi$
$587$	11.7978	−	18.3578i	0.486948	−	0.757706i	0.994592	+	0.103861i	$0.0331197\pi$
$588$	−1.67350	−	5.11839i	−0.0690138	−	0.211079i
$589$	0.715119	−	2.43547i	0.0294660	−	0.100352i
$590$	−1.72397	−	11.9905i	−0.0709747	−	0.493640i
$591$	−0.252650	−	1.44409i	−0.0103926	−	0.0594019i
$592$	−9.18275	+	4.19362i	−0.377409	+	0.172357i
$593$	−2.22412	−	7.57465i	−0.0913336	−	0.311054i	0.901137	−	0.433534i	$-0.142733\pi$
$593$	−2.22412	−	7.57465i	−0.0913336	−	0.311054i	−0.992471	+	0.122480i	$0.960915\pi$
$594$	10.1669	+	5.29289i	0.417153	+	0.217170i
$595$	2.66154	+	0.382672i	0.109113	+	0.0156880i
$596$	0.413148	−	0.265514i	0.0169232	−	0.0108759i
$597$	17.3712	+	10.4316i	0.710955	+	0.426938i
$598$	18.4830	−	11.2603i	0.755825	−	0.460467i
$599$		−	46.0220i		−	1.88041i	−0.340609	−	0.940205i	$-0.610633\pi$
$599$		−	46.0220i		−	1.88041i	0.340609	−	0.940205i	$-0.389367\pi$
$600$	2.55563	−	0.0777205i	0.104333	−	0.00317293i
$601$	6.54719	−	45.5367i	0.267065	−	1.85748i	−0.208793	−	0.977960i	$-0.566954\pi$
$601$	6.54719	−	45.5367i	0.267065	−	1.85748i	0.475859	−	0.879522i	$-0.342137\pi$
$602$	−18.5761	−	8.48343i	−0.757106	−	0.345759i
$603$	−13.5713	+	13.2868i	−0.552668	+	0.541078i
$604$	5.74098	+	12.5710i	0.233597	+	0.511507i
$605$	7.54057	+	8.70228i	0.306568	+	0.353798i
$606$	28.8202	+	12.1170i	1.17074	+	0.492219i
$607$	−20.0415	−	5.88471i	−0.813458	−	0.238853i	−0.151561	−	0.988448i	$-0.548430\pi$
$607$	−20.0415	−	5.88471i	−0.813458	−	0.238853i	−0.661897	+	0.749595i	$0.730248\pi$
$608$	−0.361074	+	0.416702i	−0.0146435	+	0.0168995i
$609$	−6.45287	+	3.18744i	−0.261484	+	0.129162i
$610$	23.7544	+	15.2660i	0.961786	+	0.618102i
$611$	36.9515	+	32.0187i	1.49490	+	1.29534i
$612$	0.440498	+	2.13353i	0.0178061	+	0.0862427i
$613$	15.4837	−	2.22621i	0.625379	−	0.0899160i	0.177663	−	0.984091i	$-0.443146\pi$
$613$	15.4837	−	2.22621i	0.625379	−	0.0899160i	0.447717	+	0.894175i	$0.352237\pi$
$614$	−3.27478	+	2.83762i	−0.132159	+	0.114517i
$615$	−3.89499	+	34.5077i	−0.157061	+	1.39148i
$616$	4.17497	−	1.22588i	0.168214	−	0.0493922i
$617$	−16.7198	+	36.6113i	−0.673115	+	1.47392i	0.196663	+	0.980471i	$0.436990\pi$
$617$	−16.7198	+	36.6113i	−0.673115	+	1.47392i	−0.869777	+	0.493444i	$0.835738\pi$
$618$	−12.0684	−	9.83121i	−0.485461	−	0.395469i
$619$	−17.4352	−	27.1298i	−0.700782	−	1.09044i	−0.991050	−	0.133492i	$-0.957381\pi$
$619$	−17.4352	−	27.1298i	−0.700782	−	1.09044i	0.290268	−	0.956945i	$-0.406255\pi$
$620$	8.64173			0.347060
$621$	5.19436	+	24.3725i	0.208442	+	0.978035i
$622$	11.9250			0.478148
$623$	−2.93122	−	4.56107i	−0.117437	−	0.182736i
$624$	−6.06017	−	4.93678i	−0.242601	−	0.197629i
$625$	−6.41402	+	14.0448i	−0.256561	+	0.561790i
$626$	−23.1608	+	6.80062i	−0.925691	+	0.271808i
$627$	−0.236284	+	2.09335i	−0.00943626	+	0.0836005i
$628$	2.23543	−	1.93701i	0.0892032	−	0.0772950i
$629$	−7.25613	+	1.04327i	−0.289321	+	0.0415981i
$630$	−2.24615	−	10.8791i	−0.0894887	−	0.433433i
$631$	−28.0739	−	24.3262i	−1.11760	−	0.968409i	−0.117907	−	0.993025i	$-0.537619\pi$
$631$	−28.0739	−	24.3262i	−1.11760	−	0.968409i	−0.999697	+	0.0246152i	$0.992164\pi$
$632$	−11.8273	−	7.60092i	−0.470463	−	0.302348i
$633$	16.0045	−	7.90555i	0.636123	−	0.314217i
$634$	9.74320	−	11.2443i	0.386952	−	0.446566i
$635$	12.3575	+	3.62849i	0.490392	+	0.143992i
$636$	−4.83566	−	2.03308i	−0.191747	−	0.0806167i
$637$	9.18812	+	10.6037i	0.364047	+	0.420132i
$638$	1.93036	+	4.22691i	0.0764238	+	0.167345i
$639$	−5.39621	+	5.28305i	−0.213471	+	0.208994i
$640$	−1.70755	−	0.779811i	−0.0674968	−	0.0308247i
$641$	−1.62988	+	11.3361i	−0.0643763	+	0.447747i	0.931984	+	0.362501i	$0.118077\pi$
$641$	−1.62988	+	11.3361i	−0.0643763	+	0.447747i	−0.996360	+	0.0852466i	$0.972832\pi$
$642$	−11.1069	+	0.337779i	−0.438356	+	0.0133311i
$643$			16.2352i			0.640254i	0.947375	+	0.320127i	$0.103726\pi$
$643$			16.2352i			0.640254i	−0.947375	+	0.320127i	$0.896274\pi$
$644$	7.83312	+	5.30417i	0.308668	+	0.209014i
$645$	28.8577	+	17.3294i	1.13627	+	0.682344i
$646$	−0.336834	+	0.216470i	−0.0132526	+	0.00851690i
$647$	−15.1224	−	2.17428i	−0.594524	−	0.0854797i	−0.161517	−	0.986870i	$-0.551639\pi$
$647$	−15.1224	−	2.17428i	−0.594524	−	0.0854797i	−0.433008	+	0.901390i	$0.642548\pi$
$648$	7.67268	−	4.70424i	0.301412	−	0.184800i
$649$	−4.01045	−	13.6583i	−0.157424	−	0.536136i
$650$	−6.05974	+	2.76739i	−0.237683	+	0.108546i
$651$	2.71057	+	15.4930i	0.106236	+	0.607218i
$652$	1.84534	+	12.8346i	0.0722690	+	0.502642i
$653$	−1.65285	+	5.62911i	−0.0646812	+	0.220284i	−0.985491	−	0.169728i	$-0.945711\pi$
$653$	−1.65285	+	5.62911i	−0.0646812	+	0.220284i	0.920810	+	0.390012i	$0.127529\pi$
$654$	8.02622	+	24.5482i	0.313850	+	0.959910i
$655$	−4.96980	+	7.73316i	−0.194186	+	0.302160i
$656$	−5.77438	+	8.98512i	−0.225452	+	0.350810i
$657$	−14.5171	−	3.31947i	−0.566365	−	0.129505i
$658$	−6.02100	+	20.5056i	−0.234723	+	0.799393i
$659$	−1.22033	−	8.48755i	−0.0475371	−	0.330628i	−0.999688	−	0.0249980i	$-0.992042\pi$
$659$	−1.22033	−	8.48755i	−0.0475371	−	0.330628i	0.952150	−	0.305630i	$-0.0988670\pi$
$660$	−7.06487	+	1.23603i	−0.275000	+	0.0481126i
$661$	35.9332	−	16.4101i	1.39764	−	0.638280i	0.432889	−	0.901447i	$-0.357494\pi$
$661$	35.9332	−	16.4101i	1.39764	−	0.638280i	0.964750	+	0.263167i	$0.0847670\pi$
$662$	−0.635773	−	2.16524i	−0.0247100	−	0.0841545i
$663$	−3.21249	−	4.67958i	−0.124763	−	0.181740i
$664$	10.9111	+	1.56878i	0.423433	+	0.0608805i
$665$	1.71755	−	1.10380i	0.0666038	−	0.0428037i
$666$	14.2316	+	26.7328i	0.551465	+	1.03588i
$667$	−4.41635	+	9.08627i	−0.171002	+	0.351822i
$668$			6.01351i			0.232670i
$669$	0.222847	+	7.32771i	0.00861576	+	0.283306i
$670$	1.69130	−	11.7633i	0.0653406	−	0.454454i
$671$	30.1827	+	13.7840i	1.16519	+	0.532125i
$672$	0.862463	−	3.30591i	0.0332702	−	0.127528i
$673$	−7.50779	−	16.4398i	−0.289404	−	0.633706i	0.707961	−	0.706251i	$-0.249615\pi$
$673$	−7.50779	−	16.4398i	−0.289404	−	0.633706i	−0.997365	+	0.0725452i	$0.976888\pi$
$674$	5.28967	+	6.10460i	0.203750	+	0.235140i
$675$	−0.698623	−	7.63854i	−0.0268900	−	0.294008i
$676$	7.06746	+	2.07519i	0.271826	+	0.0798152i
$677$	−11.0744	+	12.7806i	−0.425625	+	0.491198i	−0.927542	−	0.373718i	$-0.878083\pi$
$677$	−11.0744	+	12.7806i	−0.425625	+	0.491198i	0.501917	+	0.864916i	$0.332628\pi$
$678$	2.80558	+	5.67980i	0.107748	+	0.218132i
$679$	11.5268	+	7.40786i	0.442360	+	0.284287i
$680$	−1.03021	−	0.892684i	−0.0395068	−	0.0342329i
$681$	−31.3820	+	28.9089i	−1.20256	+	1.10779i
$682$	10.0516	−	1.44520i	0.384895	−	0.0553395i
$683$	−8.96738	+	7.77028i	−0.343127	+	0.297322i	−0.809327	−	0.587358i	$-0.800168\pi$
$683$	−8.96738	+	7.77028i	−0.343127	+	0.297322i	0.466200	+	0.884679i	$0.345623\pi$
$684$	1.31362	+	1.00526i	0.0502275	+	0.0384369i
$685$	−21.9316	+	6.43971i	−0.837965	+	0.246049i
$686$	−8.28363	+	18.1386i	−0.316270	+	0.692535i
$687$	6.09452	−	7.48137i	0.232520	−	0.285432i
$688$	5.59719	+	8.70940i	0.213391	+	0.332043i
$689$	13.6676			0.520693
$690$	−11.8493	−	10.1359i	−0.451097	−	0.385868i
$691$	49.8307			1.89565			0.947825	−	0.318792i	$-0.103277\pi$
$691$	49.8307			1.89565			0.947825	+	0.318792i	$0.103277\pi$
$692$	−1.30500	−	2.03062i	−0.0496088	−	0.0771928i
$693$	−4.43195	−	12.2783i	−0.168356	−	0.466414i
$694$	−9.22595	+	20.2020i	−0.350212	+	0.766858i
$695$	32.4269	−	9.52139i	1.23002	−	0.361167i
$696$	3.62564	+	0.409238i	0.137430	+	0.0155121i
$697$	−5.86160	+	5.07911i	−0.222024	+	0.192385i
$698$	−13.4116	+	1.92830i	−0.507638	+	0.0729873i
$699$	19.4689	+	21.1345i	0.736382	+	0.799380i
$700$	−2.20061	−	1.90684i	−0.0831753	−	0.0720718i
$701$	1.79941	+	1.15641i	0.0679628	+	0.0436770i	0.574181	−	0.818728i	$-0.305321\pi$
$701$	1.79941	+	1.15641i	0.0679628	+	0.0436770i	−0.506218	+	0.862405i	$0.668957\pi$
$702$	−13.6782	+	19.0469i	−0.516250	+	0.718879i
$703$	−3.64505	+	4.20661i	−0.137476	+	0.158655i
$704$	−2.11653	−	0.621471i	−0.0797699	−	0.0234226i
$705$	13.6529	−	32.4733i	0.514197	−	1.22302i
$706$	−23.6095	−	27.2468i	−0.888555	−	1.02545i
$707$	−14.7908	−	32.3873i	−0.556264	−	1.21805i
$708$	−10.8152	−	2.82153i	−0.406460	−	0.106039i
$709$	5.03891	+	2.30119i	0.189240	+	0.0864231i	0.507782	−	0.861486i	$-0.330466\pi$
$709$	5.03891	+	2.30119i	0.189240	+	0.0864231i	−0.318541	+	0.947909i	$0.603193\pi$
$710$	0.672491	−	4.67728i	0.0252381	−	0.175535i
$711$	−20.6045	+	36.8019i	−0.772729	+	1.38018i
$712$			2.74860i			0.103008i
$713$	16.3332	+	14.8546i	0.611685	+	0.556308i
$714$	1.27728	−	2.12698i	0.0478009	−	0.0796001i
$715$	15.7206	−	10.1030i	0.587917	−	0.377831i
$716$	−19.0441	−	2.73813i	−0.711711	−	0.102329i
$717$	11.0983	−	7.61884i	0.414472	−	0.284531i
$718$	3.04593	+	10.3735i	0.113673	+	0.387135i
$719$	−15.1259	+	6.90778i	−0.564102	+	0.257617i	−0.676991	−	0.735991i	$-0.736717\pi$
$719$	−15.1259	+	6.90778i	−0.564102	+	0.257617i	0.112890	+	0.993608i	$0.463989\pi$
$720$	−2.02382	+	5.25534i	−0.0754234	+	0.195855i
$721$	2.52286	+	17.5469i	0.0939561	+	0.653479i
$722$	5.26727	−	17.9387i	0.196027	−	0.667608i
$723$	−15.6601	+	5.12019i	−0.582405	+	0.190422i
$724$	−0.270095	+	0.420277i	−0.0100380	+	0.0156195i
$725$	1.68120	−	2.61600i	0.0624383	−	0.0971558i
$726$	10.0984	−	3.30176i	0.374788	−	0.122540i
$727$	−6.91197	+	23.5400i	−0.256351	+	0.873050i	0.726267	+	0.687412i	$0.241253\pi$
$727$	−6.91197	+	23.5400i	−0.256351	+	0.873050i	−0.982618	+	0.185638i	$0.940565\pi$
$728$	1.26686	+	8.81122i	0.0469530	+	0.326566i
$729$	−15.4854	−	22.1179i	−0.573533	−	0.819183i
$730$	8.47613	−	3.87092i	0.313716	−	0.143269i
$731$	2.11807	+	7.21347i	0.0783395	+	0.266800i
$732$	21.4795	−	14.7454i	0.793905	−	0.545007i
$733$	−6.33969	−	0.911510i	−0.234162	−	0.0336674i	0.0242348	−	0.999706i	$-0.492285\pi$
$733$	−6.33969	−	0.911510i	−0.234162	−	0.0336674i	−0.258397	+	0.966039i	$0.583194\pi$
$734$	−5.80790	+	3.73251i	−0.214373	+	0.137769i
$735$	5.20414	−	8.66616i	0.191958	−	0.319656i
$736$	−1.88689	−	4.40904i	−0.0695518	−	0.162519i
$737$		−	13.9652i		−	0.514414i
$738$	27.9582	+	15.6531i	1.02916	+	0.576200i
$739$	−2.18082	+	15.1679i	−0.0802226	+	0.557961i	0.909581	+	0.415526i	$0.136402\pi$
$739$	−2.18082	+	15.1679i	−0.0802226	+	0.557961i	−0.989804	+	0.142435i	$0.954507\pi$
$740$	−17.2377	−	7.87221i	−0.633671	−	0.289388i
$741$	−4.17024	−	1.08796i	−0.153198	−	0.0399670i
$742$	2.48171	+	5.43418i	0.0911063	+	0.199495i
$743$	−18.5414	−	21.3980i	−0.680219	−	0.785015i	0.305720	−	0.952122i	$-0.401103\pi$
$743$	−18.5414	−	21.3980i	−0.680219	−	0.785015i	−0.985939	+	0.167107i	$0.946558\pi$
$744$	3.09035	−	7.35037i	0.113298	−	0.269478i
$745$	0.884560	+	0.259730i	0.0324078	+	0.00951578i
$746$	−18.8193	+	21.7187i	−0.689024	+	0.795177i
$747$	2.70854	−	32.9588i	0.0991005	−	1.20590i
$748$	−1.34757	−	0.866032i	−0.0492721	−	0.0316653i
$749$	9.56403	+	8.28728i	0.349462	+	0.302810i
$750$	14.2664	+	15.4869i	0.520937	+	0.565503i
$751$	40.8972	−	5.88013i	1.49236	−	0.214569i	0.652673	−	0.757639i	$-0.273647\pi$
$751$	40.8972	−	5.88013i	1.49236	−	0.214569i	0.839687	+	0.543070i	$0.182738\pi$
$752$	8.18807	−	7.09500i	0.298588	−	0.258728i
$753$	−34.9008	−	3.93936i	−1.27185	−	0.143558i
$754$	−9.12150	+	2.67831i	−0.332185	+	0.0975384i
$755$	−10.7769	+	23.5981i	−0.392211	+	0.858823i
$756$	−10.0566	−	1.97994i	−0.365756	−	0.0720097i
$757$	−20.0019	−	31.1235i	−0.726980	−	1.13120i	−0.986228	−	0.165392i	$-0.947111\pi$
$757$	−20.0019	−	31.1235i	−0.726980	−	1.13120i	0.259248	−	0.965811i	$-0.416525\pi$
$758$	8.09716			0.294102
$759$	−15.4776	−	9.80791i	−0.561800	−	0.356004i
$760$	−1.03503			−0.0375446
$761$	4.00966	+	6.23915i	0.145350	+	0.226169i	0.906293	−	0.422649i	$-0.138900\pi$
$761$	4.00966	+	6.23915i	0.145350	+	0.226169i	−0.760943	+	0.648818i	$0.775263\pi$
$762$	7.50540	−	9.21331i	0.271892	−	0.333763i
$763$	12.2187	−	26.7551i	0.442345	−	0.968601i
$764$	10.3199	−	3.03019i	0.373360	−	0.109628i
$765$	−2.48529	+	3.24766i	−0.0898560	+	0.117419i
$766$	−9.71399	+	8.41722i	−0.350981	+	0.304127i
$767$	28.8257	−	4.14451i	1.04084	−	0.149650i
$768$	−1.27391	+	1.17352i	−0.0459684	+	0.0423457i
$769$	6.64976	+	5.76205i	0.239797	+	0.207785i	0.766465	−	0.642286i	$-0.222014\pi$
$769$	6.64976	+	5.76205i	0.239797	+	0.207785i	−0.526669	+	0.850071i	$0.676559\pi$
$770$	6.87141	+	4.41599i	0.247628	+	0.159141i
$771$	16.6294	+	33.6657i	0.598893	+	1.21244i
$772$	−5.72508	+	6.60709i	−0.206050	+	0.237794i
$773$	31.3272	+	9.19850i	1.12676	+	0.330847i	0.791434	−	0.611255i	$-0.209335\pi$
$773$	31.3272	+	9.19850i	1.12676	+	0.330847i	0.335328	+	0.942102i	$0.391153\pi$
$774$	25.0595	−	18.3483i	0.900746	−	0.659515i
$775$	−4.45021	−	5.13581i	−0.159856	−	0.184484i
$776$	−2.88561	−	6.31861i	−0.103587	−	0.226825i
$777$	8.70658	−	33.3732i	0.312347	−	1.19726i
$778$	−31.3497	−	14.3169i	−1.12394	−	0.513287i
$779$	−0.838098	+	5.82910i	−0.0300280	+	0.208849i
$780$	−0.446022	−	14.6662i	−0.0159702	−	0.525135i
$781$		−	5.55281i		−	0.198695i
$782$	−0.412678	−	3.45808i	−0.0147573	−	0.123661i
$783$	0.564488	−	10.9314i	0.0201732	−	0.390657i
$784$	2.61549	−	1.68088i	0.0934105	−	0.0600313i
$785$	5.49599	+	0.790205i	0.196160	+	0.0282036i
$786$	4.80034	+	6.99259i	0.171222	+	0.249417i
$787$	−9.70383	−	33.0482i	−0.345904	−	1.17804i	−0.930370	−	0.366623i	$-0.880514\pi$
$787$	−9.70383	−	33.0482i	−0.345904	−	1.17804i	0.584466	−	0.811419i	$-0.301304\pi$
$788$	0.769921	−	0.351611i	0.0274273	−	0.0125256i
$789$	3.28666	−	0.575016i	0.117008	−	0.0204711i
$790$	−3.75591	−	26.1229i	−0.133629	−	0.929411i
$791$	2.03258	−	6.92232i	0.0722701	−	0.246129i
$792$	−1.47512	+	6.45116i	−0.0524161	+	0.229232i
$793$	−36.7003	+	57.1067i	−1.30326	+	2.02792i
$794$	6.85193	−	10.6618i	0.243166	−	0.378373i
$795$	−3.06017	−	9.35952i	−0.108533	−	0.331948i
$796$	−3.29589	+	11.2248i	−0.116820	+	0.397852i
$797$	−4.64851	−	32.3311i	−0.164659	−	1.14523i	−0.889708	−	0.456530i	$-0.849092\pi$
$797$	−4.64851	−	32.3311i	−0.164659	−	1.14523i	0.725050	−	0.688697i	$-0.241817\pi$
$798$	−0.324650	−	1.85562i	−0.0114925	−	0.0656883i
$799$	7.15666	−	3.26834i	0.253185	−	0.115625i
$800$	0.415886	+	1.41638i	0.0147038	+	0.0500765i
$801$	8.23057	−	0.501072i	0.290813	−	0.0177045i
$802$	−2.69496	−	0.387477i	−0.0951623	−	0.0136823i
$803$	9.21160	−	5.91994i	0.325070	−	0.208910i
$804$	−9.40061	−	5.64519i	−0.331534	−	0.199090i
$805$	2.10429	+	17.6331i	0.0741664	+	0.621485i
$806$			20.7752i			0.731774i
$807$	−25.5315	+	0.776451i	−0.898750	+	0.0273324i
$808$	−2.56880	+	17.8664i	−0.0903702	+	0.628538i
$809$	−20.6777	−	9.44317i	−0.726988	−	0.332004i	0.0173118	−	0.999850i	$-0.494489\pi$
$809$	−20.6777	−	9.44317i	−0.726988	−	0.332004i	−0.744299	+	0.667846i	$0.767216\pi$
$810$	16.1058	+	5.10220i	0.565901	+	0.179273i
$811$	13.6884	+	29.9734i	0.480665	+	1.05251i	0.982280	+	0.187418i	$0.0600120\pi$
$811$	13.6884	+	29.9734i	0.480665	+	1.05251i	−0.501615	+	0.865091i	$0.667261\pi$
$812$	−2.72114	−	3.14036i	−0.0954932	−	0.110205i
$813$	−1.21849	−	0.512294i	−0.0427343	−	0.0179669i
$814$	−21.3664	−	6.27376i	−0.748894	−	0.219895i
$815$	−15.9398	+	18.3955i	−0.558346	+	0.644365i
$816$	−1.12770	+	0.557034i	−0.0394773	+	0.0195001i
$817$	4.80215	+	3.08615i	0.168006	+	0.107971i
$818$	−3.34154	−	2.89546i	−0.116834	−	0.101237i
$819$	26.1539	−	5.39985i	0.913890	−	0.188686i
$820$	−19.8454	+	2.85334i	−0.693033	+	0.0996431i
$821$	24.4505	−	21.1865i	0.853328	−	0.739413i	−0.113854	−	0.993498i	$-0.536320\pi$
$821$	24.4505	−	21.1865i	0.853328	−	0.739413i	0.967182	+	0.254084i	$0.0817741\pi$
$822$	−2.36551	+	20.9572i	−0.0825066	+	0.730967i
$823$	−1.63692	+	0.480642i	−0.0570593	+	0.0167541i	−0.310138	−	0.950692i	$-0.600375\pi$
$823$	−1.63692	+	0.480642i	−0.0570593	+	0.0167541i	0.253078	+	0.967446i	$0.418557\pi$
$824$	3.73333	−	8.17486i	0.130057	−	0.284785i
$825$	4.37275	+	3.56216i	0.152240	+	0.124019i
$826$	6.88191	+	10.7085i	0.239452	+	0.372595i
$827$	50.6354			1.76076			0.880382	−	0.474265i	$-0.157286\pi$
$827$	50.6354			1.76076			0.880382	+	0.474265i	$0.157286\pi$
$828$	−12.8587	+	6.45399i	−0.446871	+	0.224292i
$829$	−25.0320			−0.869398			−0.434699	−	0.900576i	$-0.643145\pi$
$829$	−25.0320			−0.869398			−0.434699	+	0.900576i	$0.643145\pi$
$830$	11.1874	+	17.4079i	0.388320	+	0.604237i
$831$	−21.3683	−	17.4072i	−0.741259	−	0.603849i
$832$	1.87471	−	4.10503i	0.0649938	−	0.142316i
$833$	2.16626	−	0.636070i	0.0750564	−	0.0220385i
$834$	3.49751	−	30.9862i	0.121109	−	1.07296i
$835$	−8.53126	+	7.39238i	−0.295236	+	0.255824i
$836$	−1.20389	+	0.173094i	−0.0416375	+	0.00598657i
$837$	−22.5737	−	7.91393i	−0.780263	−	0.273545i
$838$	−27.9656	−	24.2323i	−0.966054	−	0.837091i
$839$	3.32711	+	2.13820i	0.114865	+	0.0738190i	0.596812	−	0.802381i	$-0.296434\pi$
$839$	3.32711	+	2.13820i	0.114865	+	0.0738190i	−0.481947	+	0.876200i	$0.660070\pi$
$840$	5.75025	−	2.84038i	0.198403	−	0.0980023i
$841$	−16.0850	+	18.5630i	−0.554654	+	0.640105i
$842$	30.8720	+	9.06483i	1.06392	+	0.312395i
$843$	−18.9945	−	7.98593i	−0.654205	−	0.275050i
$844$	6.74901	+	7.78878i	0.232311	+	0.268101i
$845$	5.74396	+	12.5775i	0.197598	+	0.432680i
$846$	−22.7384	−	23.2254i	−0.781761	−	0.798505i
$847$	−11.0063	−	5.02641i	−0.378181	−	0.172710i
$848$	0.431013	−	2.99776i	0.0148010	−	0.102944i
$849$	14.0935	−	0.428604i	0.483686	−	0.0147096i
$850$			1.07196i			0.0367680i
$851$	−19.0482	−	44.5093i	−0.652964	−	1.52576i
$852$	−3.73785	−	2.24463i	−0.128057	−	0.0768997i
$853$	31.4646	−	20.2211i	1.07733	−	0.692357i	0.123389	−	0.992358i	$-0.460624\pi$
$853$	31.4646	−	20.2211i	1.07733	−	0.692357i	0.953939	+	0.300002i	$0.0969873\pi$
$854$	−29.3693	−	4.22267i	−1.00500	−	0.144497i
$855$	0.188687	+	3.09937i	0.00645297	+	0.105996i
$856$	−1.80747	−	6.15569i	−0.0617781	−	0.210397i
$857$	−18.4207	+	8.41246i	−0.629240	+	0.287364i	−0.704395	−	0.709808i	$-0.748782\pi$
$857$	−18.4207	+	8.41246i	−0.629240	+	0.287364i	0.0751559	+	0.997172i	$0.476055\pi$
$858$	−2.97149	−	16.9843i	−0.101445	−	0.579835i
$859$	2.28940	+	15.9231i	0.0781132	+	0.543289i	0.990874	+	0.134794i	$0.0430372\pi$
$859$	2.28940	+	15.9231i	0.0781132	+	0.543289i	−0.912761	+	0.408495i	$0.866054\pi$
$860$	−5.47527	+	18.6471i	−0.186705	+	0.635859i
$861$	−11.3403	−	34.6842i	−0.386475	−	1.18203i
$862$	−8.10674	+	12.6143i	−0.276117	+	0.429646i
$863$	−24.7373	+	38.4920i	−0.842067	+	1.31028i	0.106695	+	0.994292i	$0.465973\pi$
$863$	−24.7373	+	38.4920i	−0.842067	+	1.31028i	−0.948762	+	0.315991i	$0.897663\pi$
$864$	3.74628	+	3.60074i	0.127451	+	0.122500i
$865$	1.27658	−	4.34762i	0.0434049	−	0.147824i
$866$	1.58567	+	11.0285i	0.0538831	+	0.374765i
$867$	28.1046	−	4.91704i	0.954483	−	0.166991i
$868$	−8.26014	+	3.77228i	−0.280368	+	0.128040i
$869$	−8.73731	−	29.7566i	−0.296393	−	1.00942i
$870$	3.87641	+	5.64671i	0.131422	+	0.191441i
$871$	28.2795	+	4.06597i	0.958213	+	0.137770i
$872$	−12.5441	+	8.06161i	−0.424797	+	0.273001i
$873$	−18.3947	+	9.79272i	−0.622568	+	0.331433i
$874$	−1.95626	−	1.77916i	−0.0661714	−	0.0601809i
$875$		−	23.9803i		−	0.810681i
$876$	−0.261350	−	8.59379i	−0.00883021	−	0.290357i
$877$	3.44693	−	23.9739i	0.116395	−	0.809543i	−0.845078	−	0.534643i	$-0.820446\pi$
$877$	3.44693	−	23.9739i	0.116395	−	0.809543i	0.961473	−	0.274900i	$-0.0886447\pi$
$878$	13.1399	+	6.00078i	0.443449	+	0.202517i
$879$	12.7848	−	49.0054i	0.431220	−	1.65291i
$880$	−1.72018	−	3.76666i	−0.0579871	−	0.126974i
$881$	25.9870	+	29.9906i	0.875525	+	1.01041i	0.999835	+	0.0181666i	$0.00578294\pi$
$881$	25.9870	+	29.9906i	0.875525	+	1.01041i	−0.124310	+	0.992243i	$0.539672\pi$
$882$	−5.51011	−	7.52556i	−0.185535	−	0.253399i
$883$	−11.5686	−	3.39685i	−0.389315	−	0.114313i	0.0812162	−	0.996697i	$-0.474120\pi$
$883$	−11.5686	−	3.39685i	−0.389315	−	0.114313i	−0.470531	+	0.882383i	$0.655938\pi$
$884$	2.14606	−	2.47668i	0.0721797	−	0.0832999i
$885$	−9.29222	−	18.8118i	−0.312355	−	0.632353i
$886$	15.9212	+	10.2319i	0.534882	+	0.343748i
$887$	−9.06937	−	7.85865i	−0.304520	−	0.263868i	0.489173	−	0.872187i	$-0.337299\pi$
$887$	−9.06937	−	7.85865i	−0.304520	−	0.263868i	−0.793693	+	0.608319i	$0.791844\pi$
$888$	−12.8602	+	11.8467i	−0.431559	+	0.397549i
$889$	−13.3957	+	1.92602i	−0.449279	+	0.0645965i
$890$	−3.89939	+	3.37884i	−0.130708	+	0.113259i
$891$	19.5866	+	3.24113i	0.656177	+	0.108582i
$892$	−4.06116	+	1.19246i	−0.135978	+	0.0399267i
$893$	2.48161	−	5.43396i	0.0830439	−	0.181841i
$894$	0.537243	−	0.659496i	0.0179681	−	0.0220569i
$895$	−19.5263	−	30.3835i	−0.652691	−	1.01561i
$896$	1.97255			0.0658983
$897$	24.3673	−	28.4865i	0.813600	−	0.951135i
$898$	22.3941			0.747299
$899$	−5.24295	−	8.15819i	−0.174862	−	0.272091i
$900$	4.16547	−	1.50356i	0.138849	−	0.0501187i
$901$	0.913616	−	2.00054i	0.0304370	−	0.0666477i
$902$	−22.6059	+	6.63770i	−0.752695	+	0.221011i
$903$	−35.1480	−	3.96727i	−1.16965	−	0.132022i
$904$	−2.76414	+	2.39514i	−0.0919338	+	0.0796611i
$905$	−0.928266	+	0.133465i	−0.0308566	+	0.00443651i
$906$	16.2179	+	17.6053i	0.538803	+	0.584898i
$907$	40.3808	+	34.9902i	1.34082	+	1.16183i	0.972703	+	0.232052i	$0.0745441\pi$
$907$	40.3808	+	34.9902i	1.34082	+	1.16183i	0.368121	+	0.929778i	$0.380001\pi$
$908$	−20.7237	−	13.3183i	−0.687742	−	0.441985i
$909$	53.9685	+	4.43511i	1.79002	+	0.147103i
$910$	−10.9430	+	12.6289i	−0.362756	+	0.418643i
$911$	−36.6260	−	10.7543i	−1.21347	−	0.356308i	−0.388483	−	0.921456i	$-0.627001\pi$
$911$	−36.6260	−	10.7543i	−1.21347	−	0.356308i	−0.824989	+	0.565149i	$0.808819\pi$
$912$	−0.370136	+	0.880366i	−0.0122564	+	0.0291518i
$913$	15.9237	+	18.3770i	0.526999	+	0.608189i
$914$	−9.66008	−	21.1526i	−0.319527	−	0.699667i
$915$	47.3237	+	12.3461i	1.56447	+	0.408148i
$916$	5.06772	+	2.31435i	0.167442	+	0.0764683i
$917$	1.37468	−	9.56110i	0.0453959	−	0.315735i
$918$	1.87359	+	3.27530i	0.0618378	+	0.108101i
$919$		−	5.65476i		−	0.186533i	−0.995641	−	0.0932666i	$-0.970269\pi$
$919$		−	5.65476i		−	0.186533i	0.995641	−	0.0932666i	$-0.0297309\pi$
$920$	3.93548	−	8.09691i	0.129749	−	0.266947i
$921$	−3.86385	+	6.43424i	−0.127318	+	0.212016i
$922$	−21.7385	+	13.9705i	−0.715919	+	0.460093i
$923$	11.2444	+	1.61670i	0.370115	+	0.0532145i
$924$	6.21336	−	4.26541i	0.204405	−	0.140322i
$925$	4.19838	+	14.2984i	0.138042	+	0.470127i
$926$	14.2453	−	6.50559i	0.468128	−	0.213787i
$927$	−25.1598	−	9.68902i	−0.826358	−	0.318229i
$928$	0.299794	+	2.08512i	0.00984123	+	0.0684473i
$929$	−8.38515	+	28.5572i	−0.275108	+	0.936932i	0.699803	+	0.714336i	$0.253271\pi$
$929$	−8.38515	+	28.5572i	−0.275108	+	0.936932i	−0.974911	+	0.222596i	$0.928547\pi$
$930$	14.2268	−	4.65156i	0.466515	−	0.152531i
$931$	0.926794	−	1.44212i	0.0303744	−	0.0472636i
$932$	−8.96935	+	13.9566i	−0.293801	+	0.457163i
$933$	19.6320	−	6.41882i	0.642722	−	0.210143i
$934$	8.34333	−	28.4148i	0.273002	−	0.929760i
$935$	−0.427940	−	2.97638i	−0.0139951	−	0.0973382i
$936$	−12.6341	−	4.86538i	−0.412959	−	0.159030i
$937$	−32.5791	+	14.8784i	−1.06431	+	0.486055i	−0.869064	−	0.494699i	$-0.835278\pi$
$937$	−32.5791	+	14.8784i	−1.06431	+	0.486055i	−0.195248	+	0.980754i	$0.562551\pi$
$938$	3.51826	+	11.9821i	0.114875	+	0.391230i
$939$	−34.4688	+	23.6625i	−1.12485	+	0.772196i
$940$	20.1311	+	2.89442i	0.656604	+	0.0944054i
$941$	12.3544	−	7.93968i	0.402741	−	0.258826i	−0.323553	−	0.946210i	$-0.604877\pi$
$941$	12.3544	−	7.93968i	0.402741	−	0.258826i	0.726294	+	0.687384i	$0.241241\pi$
$942$	2.63753	−	4.39213i	0.0859354	−	0.143103i
$943$	−42.4134	−	28.7201i	−1.38117	−	0.935255i
$944$		−	6.45315i		−	0.210032i
$945$	−9.55366	−	16.7011i	−0.310780	−	0.543286i
$946$	−3.25009	+	22.6048i	−0.105669	+	0.734947i
$947$	9.02620	+	4.12213i	0.293312	+	0.133951i	0.556636	−	0.830756i	$-0.312092\pi$
$947$	9.02620	+	4.12213i	0.293312	+	0.133951i	−0.263324	+	0.964707i	$0.584819\pi$
$948$	−23.5624	−	6.14709i	−0.765272	−	0.199648i
$949$	9.30589	+	20.3771i	0.302082	+	0.661468i
$950$	0.533008	+	0.615125i	0.0172931	+	0.0199573i
$951$	9.98772	−	23.7557i	0.323874	−	0.770333i
$952$	1.37439	+	0.403559i	0.0445444	+	0.0130794i
$953$	26.5240	−	30.6104i	0.859197	−	0.991567i	−0.140801	−	0.990038i	$-0.544968\pi$
$953$	26.5240	−	30.6104i	0.859197	−	0.991567i	0.999999	−	0.00152885i	$-0.000486648\pi$
$954$	−9.05524	−	0.744156i	−0.293174	−	0.0240929i
$955$	16.9851	+	10.9156i	0.549624	+	0.353222i
$956$	5.87378	+	5.08966i	0.189972	+	0.164611i
$957$	5.45314	+	5.91966i	0.176275	+	0.191355i
$958$	17.7838	−	2.55693i	0.574570	−	0.0826106i
$959$	18.1522	−	15.7289i	0.586164	−	0.507914i
$960$	−3.23086	−	0.364678i	−0.104276	−	0.0117699i
$961$	9.40999	−	2.76302i	0.303548	−	0.0891297i
$962$	18.9252	−	41.4404i	0.610173	−	1.33609i
$963$	−18.1034	+	6.53458i	−0.583375	+	0.210574i
$964$	−5.14277	−	8.00230i	−0.165637	−	0.257737i
$965$	−16.4112			−0.528294
$966$	15.7506	+	4.51589i	0.506769	+	0.145296i
$967$	−33.1367			−1.06560			−0.532802	−	0.846240i	$-0.678861\pi$
$967$	−33.1367			−1.06560			−0.532802	+	0.846240i	$0.678861\pi$
$968$	3.31632	+	5.16030i	0.106591	+	0.165858i
$969$	−0.438008	+	0.537679i	−0.0140708	+	0.0172727i
$970$	5.41683	−	11.8612i	0.173924	−	0.380840i
$971$	33.5858	−	9.86169i	1.07782	−	0.316477i	0.305814	−	0.952091i	$-0.401071\pi$
$971$	33.5858	−	9.86169i	1.07782	−	0.316477i	0.772007	+	0.635614i	$0.219253\pi$
$972$	10.0993	−	11.8745i	0.323936	−	0.380875i
$973$	−26.8388	+	23.2559i	−0.860411	+	0.745550i
$974$	0.753545	−	0.108343i	0.0241451	−	0.00347154i
$975$	−8.48650	+	7.81769i	−0.271785	+	0.250366i
$976$	11.3681	+	9.85050i	0.363883	+	0.315307i
$977$	−6.01180	−	3.86355i	−0.192335	−	0.123606i	0.440929	−	0.897542i	$-0.354649\pi$
$977$	−6.01180	−	3.86355i	−0.192335	−	0.123606i	−0.633264	+	0.773936i	$0.718285\pi$
$978$	9.94641	+	20.1362i	0.318051	+	0.643885i
$979$	−3.97049	+	4.58219i	−0.126898	+	0.146448i
$980$	5.59984	+	1.64426i	0.178880	+	0.0525240i
$981$	26.4270	+	36.0932i	0.843748	+	1.15237i
$982$	22.8389	+	26.3575i	0.728818	+	0.841100i
$983$	16.9093	+	37.0263i	0.539324	+	1.18095i	0.961592	+	0.274483i	$0.0885067\pi$
$983$	16.9093	+	37.0263i	0.539324	+	1.18095i	−0.422268	+	0.906471i	$0.638766\pi$
$984$	−4.66992	+	17.9003i	−0.148871	+	0.570640i
$985$	1.44528	+	0.660039i	0.0460506	+	0.0210306i
$986$	−0.217703	+	1.51416i	−0.00693308	+	0.0482207i
$987$	1.12520	+	36.9991i	0.0358155	+	1.17770i
$988$		−	2.48828i		−	0.0791626i
$989$	−42.4016	+	25.8321i	−1.34829	+	0.821412i
$990$	−10.9655	+	5.83766i	−0.348507	+	0.185533i
$991$	−26.9519	+	17.3209i	−0.856156	+	0.550218i	−0.893489	−	0.449085i	$-0.851750\pi$
$991$	−26.9519	+	17.3209i	−0.856156	+	0.550218i	0.0373331	+	0.999303i	$0.488114\pi$
$992$	4.55670	+	0.655155i	0.144675	+	0.0208012i
$993$	−2.21214	−	3.22240i	−0.0702003	−	0.102260i
$994$	1.39893	+	4.76430i	0.0443712	+	0.151114i
$995$	−19.9760	+	9.12275i	−0.633283	+	0.289211i
$996$	18.8073	−	3.29042i	0.595931	−	0.104261i
$997$	4.09392	+	28.4738i	0.129656	+	0.901774i	0.945990	+	0.324195i	$0.105093\pi$
$997$	4.09392	+	28.4738i	0.129656	+	0.901774i	−0.816335	+	0.577579i	$0.803997\pi$
$998$	−0.354359	+	1.20684i	−0.0112170	+	0.0382017i
$999$	37.8188	+	36.3496i	1.19653	+	1.15005i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.2.f.a.11.8	yes	80
3.2	odd	2	inner	138.2.f.a.11.1	✓	80
23.21	odd	22	inner	138.2.f.a.113.1	yes	80
69.44	even	22	inner	138.2.f.a.113.8	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.f.a.11.1	✓	80	3.2	odd	2	inner
138.2.f.a.11.8	yes	80	1.1	even	1	trivial
138.2.f.a.113.1	yes	80	23.21	odd	22	inner
138.2.f.a.113.8	yes	80	69.44	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:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	138.f (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.540641 + 0.841254i) q^{2} +(1.34287 + 1.09394i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-1.80115 + 0.528864i) q^{5} +(-0.194269 + 1.72112i) q^{6} +(1.49075 - 1.29175i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(0.606601 + 2.93803i) q^{9} +O(q^{10})\)	\(q+(0.540641 + 0.841254i) q^{2} +(1.34287 + 1.09394i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-1.80115 + 0.528864i) q^{5} +(-0.194269 + 1.72112i) q^{6} +(1.49075 - 1.29175i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(0.606601 + 2.93803i) q^{9} +(-1.41868 - 1.22930i) q^{10} +(-1.85571 - 1.19259i) q^{11} +(-1.55293 + 0.767080i) q^{12} +(2.95529 - 3.41059i) q^{13} +(1.89265 + 0.555732i) q^{14} +(-2.99725 - 1.26015i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-0.301664 - 0.660552i) q^{17} +(-2.14368 + 2.09873i) q^{18} +(-0.501549 - 0.229050i) q^{19} +(0.267151 - 1.85808i) q^{20} +(3.41498 - 0.103855i) q^{21} -2.20589i q^{22} +(3.69884 - 3.05263i) q^{23} +(-1.48489 - 0.891693i) q^{24} +(-1.24184 + 0.798080i) q^{25} +(4.46692 + 0.642246i) q^{26} +(-2.39944 + 4.60898i) q^{27} +(0.555732 + 1.89265i) q^{28} +(-1.91619 + 0.875096i) q^{29} +(-0.560334 - 3.20273i) q^{30} +(0.655155 + 4.55670i) q^{31} +(0.281733 - 0.959493i) q^{32} +(-1.18736 - 3.63153i) q^{33} +(0.392600 - 0.610897i) q^{34} +(-2.00191 + 3.11503i) q^{35} +(-2.92452 - 0.668720i) q^{36} +(2.84409 - 9.68610i) q^{37} +(-0.0784689 - 0.545763i) q^{38} +(7.69954 - 1.34707i) q^{39} +(1.70755 - 0.779811i) q^{40} +(-3.00908 - 10.2480i) q^{41} +(1.93365 + 2.81672i) q^{42} +(-10.2475 - 1.47337i) q^{43} +(1.85571 - 1.19259i) q^{44} +(-2.64640 - 4.97102i) q^{45} +(4.56778 + 1.46129i) q^{46} +10.8344i q^{47} +(-0.0526500 - 1.73125i) q^{48} +(-0.442463 + 3.07740i) q^{49} +(-1.34277 - 0.613225i) q^{50} +(0.317507 - 1.21704i) q^{51} +(1.87471 + 4.10503i) q^{52} +(1.98330 + 2.28885i) q^{53} +(-5.17455 + 0.473266i) q^{54} +(3.97313 + 1.16662i) q^{55} +(-1.29175 + 1.49075i) q^{56} +(-0.422949 - 0.856247i) q^{57} +(-1.77215 - 1.13889i) q^{58} +(4.87697 + 4.22592i) q^{59} +(2.39137 - 2.20291i) q^{60} +(-14.8890 + 2.14072i) q^{61} +(-3.47914 + 3.01469i) q^{62} +(4.69948 + 3.59631i) q^{63} +(0.959493 - 0.281733i) q^{64} +(-3.51917 + 7.70591i) q^{65} +(2.41310 - 2.96222i) q^{66} +(3.42273 + 5.32586i) q^{67} +0.726175 q^{68} +(8.30645 - 0.0529805i) q^{69} -3.70284 q^{70} +(1.36094 + 2.11766i) q^{71} +(-1.01855 - 2.82180i) q^{72} +(-2.06209 + 4.51534i) q^{73} +(9.68610 - 2.84409i) q^{74} +(-2.54067 - 0.286774i) q^{75} +(0.416702 - 0.361074i) q^{76} +(-4.30694 + 0.619244i) q^{77} +(5.29591 + 5.74898i) q^{78} +(10.6252 + 9.20675i) q^{79} +(1.57919 + 1.01488i) q^{80} +(-8.26407 + 3.56442i) q^{81} +(6.99432 - 8.07188i) q^{82} +(-10.5768 - 3.10563i) q^{83} +(-1.32416 + 3.14952i) q^{84} +(0.892684 + 1.03021i) q^{85} +(-4.30074 - 9.41731i) q^{86} +(-3.53050 - 0.921055i) q^{87} +(2.00655 + 0.916359i) q^{88} +(0.391167 - 2.72063i) q^{89} +(2.75114 - 4.91383i) q^{90} -8.90183i q^{91} +(1.24021 + 4.63270i) q^{92} +(-4.10496 + 6.83576i) q^{93} +(-9.11445 + 5.85750i) q^{94} +(1.02450 + 0.147301i) q^{95} +(1.42796 - 0.980277i) q^{96} +(1.95701 + 6.66496i) q^{97} +(-2.82809 + 1.29154i) q^{98} +(2.37820 - 6.17557i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6}+O(q^{10}) \) 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6	\( 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6} - 4 q^{12} + 8 q^{13} - 22 q^{15} - 8 q^{16} - 28 q^{18} - 66 q^{21} - 4 q^{24} - 48 q^{25} - 38 q^{27} - 44 q^{30} - 16 q^{31} - 22 q^{33} - 44 q^{37} - 24 q^{39} - 44 q^{43} - 16 q^{46} + 4 q^{48} - 76 q^{49} - 8 q^{52} - 6 q^{54} + 64 q^{55} + 66 q^{57} + 36 q^{58} + 22 q^{60} + 88 q^{61} + 110 q^{63} + 8 q^{64} + 88 q^{66} + 44 q^{67} + 82 q^{69} + 112 q^{70} + 28 q^{72} + 52 q^{73} + 136 q^{75} + 82 q^{78} + 88 q^{79} + 36 q^{81} + 44 q^{82} + 22 q^{84} + 20 q^{85} - 10 q^{87} + 8 q^{93} - 56 q^{94} + 4 q^{96} - 132 q^{97} - 66 q^{99}+O(q^{100}) \) 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6 - 4 * q^12 + 8 * q^13 - 22 * q^15 - 8 * q^16 - 28 * q^18 - 66 * q^21 - 4 * q^24 - 48 * q^25 - 38 * q^27 - 44 * q^30 - 16 * q^31 - 22 * q^33 - 44 * q^37 - 24 * q^39 - 44 * q^43 - 16 * q^46 + 4 * q^48 - 76 * q^49 - 8 * q^52 - 6 * q^54 + 64 * q^55 + 66 * q^57 + 36 * q^58 + 22 * q^60 + 88 * q^61 + 110 * q^63 + 8 * q^64 + 88 * q^66 + 44 * q^67 + 82 * q^69 + 112 * q^70 + 28 * q^72 + 52 * q^73 + 136 * q^75 + 82 * q^78 + 88 * q^79 + 36 * q^81 + 44 * q^82 + 22 * q^84 + 20 * q^85 - 10 * q^87 + 8 * q^93 - 56 * q^94 + 4 * q^96 - 132 * q^97 - 66 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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