LMFDB - Embedded newform 138.2.f.a.113.1

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			113.1
Character	$\chi$	$=$	138.113
Dual form			138.2.f.a.11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.540641 + 0.841254i) q^{2} +(-1.59667 - 0.671295i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(1.80115 + 0.528864i) q^{5} +(1.42796 - 0.980277i) q^{6} +(1.49075 + 1.29175i) q^{7} +(0.989821 + 0.142315i) q^{8} +(2.09873 + 2.14368i) q^{9} +O(q^{10})$	\(q+(-0.540641 + 0.841254i) q^{2} +(-1.59667 - 0.671295i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(1.80115 + 0.528864i) q^{5} +(1.42796 - 0.980277i) q^{6} +(1.49075 + 1.29175i) q^{7} +(0.989821 + 0.142315i) q^{8} +(2.09873 + 2.14368i) q^{9} +(-1.41868 + 1.22930i) q^{10} +(1.85571 - 1.19259i) q^{11} +(0.0526500 + 1.73125i) q^{12} +(2.95529 + 3.41059i) q^{13} +(-1.89265 + 0.555732i) q^{14} +(-2.52082 - 2.05352i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(0.301664 - 0.660552i) q^{17} +(-2.93803 + 0.606601i) q^{18} +(-0.501549 + 0.229050i) q^{19} +(-0.267151 - 1.85808i) q^{20} +(-1.51310 - 3.06323i) 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} +(-1.91194 - 4.83161i) q^{27} +(0.555732 - 1.89265i) q^{28} +(1.91619 + 0.875096i) q^{29} +(3.09039 - 1.01043i) q^{30} +(0.655155 - 4.55670i) q^{31} +(-0.281733 - 0.959493i) q^{32} +(-3.76355 + 0.658450i) q^{33} +(0.392600 + 0.610897i) q^{34} +(2.00191 + 3.11503i) q^{35} +(1.07812 - 2.79958i) q^{36} +(2.84409 + 9.68610i) q^{37} +(0.0784689 - 0.545763i) q^{38} +(-2.42912 - 7.42946i) q^{39} +(1.70755 + 0.779811i) q^{40} +(3.00908 - 10.2480i) q^{41} +(3.39500 + 0.383205i) 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} +(1.55293 - 0.767080i) q^{48} +(-0.442463 - 3.07740i) q^{49} +(1.34277 - 0.613225i) q^{50} +(-0.925084 + 0.852180i) q^{51} +(1.87471 - 4.10503i) q^{52} +(-1.98330 + 2.28885i) q^{53} +(5.09828 + 1.00375i) q^{54} +(3.97313 - 1.16662i) q^{55} +(1.29175 + 1.49075i) q^{56} +(0.954569 - 0.0290299i) q^{57} +(-1.77215 + 1.13889i) q^{58} +(-4.87697 + 4.22592i) q^{59} +(-0.820766 + 3.14608i) q^{60} +(-14.8890 - 2.14072i) q^{61} +(3.47914 + 3.01469i) q^{62} +(0.359597 + 5.90672i) q^{63} +(0.959493 + 0.281733i) q^{64} +(3.51917 + 7.70591i) q^{65} +(1.48080 - 3.52208i) q^{66} +(3.42273 - 5.32586i) q^{67} -0.726175 q^{68} +(3.85663 + 7.35707i) q^{69} -3.70284 q^{70} +(-1.36094 + 2.11766i) q^{71} +(1.77229 + 2.42054i) q^{72} +(-2.06209 - 4.51534i) q^{73} +(-9.68610 - 2.84409i) q^{74} +(1.44706 + 2.10791i) q^{75} +(0.416702 + 0.361074i) q^{76} +(4.30694 + 0.619244i) q^{77} +(7.56334 + 1.97316i) q^{78} +(10.6252 - 9.20675i) q^{79} +(-1.57919 + 1.01488i) q^{80} +(-0.190705 + 8.99798i) q^{81} +(6.99432 + 8.07188i) q^{82} +(10.5768 - 3.10563i) q^{83} +(-2.15785 + 2.64888i) q^{84} +(0.892684 - 1.03021i) q^{85} +(4.30074 - 9.41731i) q^{86} +(-2.47208 - 2.68357i) q^{87} +(2.00655 - 0.916359i) q^{88} +(-0.391167 - 2.72063i) q^{89} +(-5.61264 - 0.461244i) 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} +(-0.194269 + 1.72112i) q^{96} +(1.95701 - 6.66496i) q^{97} +(2.82809 + 1.29154i) q^{98} +(6.45116 + 1.47512i) 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 $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$-1$	$e\left(\frac{13}{22}\right)$

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
$3$	−1.59667	−	0.671295i	−0.921839	−	0.387573i
$3$	−1.59667	−	0.671295i	−0.921839	−	0.387573i
$4$	−0.415415	−	0.909632i	−0.207708	−	0.454816i
$5$	1.80115	+	0.528864i	0.805497	+	0.236515i	0.658460	−	0.752616i	$-0.271208\pi$
$5$	1.80115	+	0.528864i	0.805497	+	0.236515i	0.147037	+	0.989131i	$0.453026\pi$
$6$	1.42796	−	0.980277i	0.582961	−	0.400196i
$7$	1.49075	+	1.29175i	0.563452	+	0.488234i	0.889385	−	0.457159i	$-0.151133\pi$
$7$	1.49075	+	1.29175i	0.563452	+	0.488234i	−0.325933	+	0.945393i	$0.605678\pi$
$8$	0.989821	+	0.142315i	0.349955	+	0.0503159i
$9$	2.09873	+	2.14368i	0.699575	+	0.714559i
$10$	−1.41868	+	1.22930i	−0.448627	+	0.388737i
$11$	1.85571	−	1.19259i	0.559518	−	0.359580i	−0.230112	−	0.973164i	$-0.573909\pi$
$11$	1.85571	−	1.19259i	0.559518	−	0.359580i	0.789630	+	0.613584i	$0.210273\pi$
$12$	0.0526500	+	1.73125i	0.0151987	+	0.499769i
$13$	2.95529	+	3.41059i	0.819650	+	0.945926i	0.999285	−	0.0378070i	$-0.0120372\pi$
$13$	2.95529	+	3.41059i	0.819650	+	0.945926i	−0.179635	+	0.983733i	$0.557492\pi$
$14$	−1.89265	+	0.555732i	−0.505832	+	0.148526i
$15$	−2.52082	−	2.05352i	−0.650872	−	0.530218i
$16$	−0.654861	+	0.755750i	−0.163715	+	0.188937i
$17$	0.301664	−	0.660552i	0.0731643	−	0.160207i	−0.869516	−	0.493905i	$-0.835569\pi$
$17$	0.301664	−	0.660552i	0.0731643	−	0.160207i	0.942680	+	0.333697i	$0.108296\pi$
$18$	−2.93803	+	0.606601i	−0.692501	+	0.142977i
$19$	−0.501549	+	0.229050i	−0.115063	+	0.0525476i	−0.472115	−	0.881537i	$-0.656509\pi$
$19$	−0.501549	+	0.229050i	−0.115063	+	0.0525476i	0.357052	+	0.934085i	$0.383782\pi$
$20$	−0.267151	−	1.85808i	−0.0597369	−	0.415479i
$21$	−1.51310	−	3.06323i	−0.330186	−	0.668452i
$22$			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
$27$	−1.91194	−	4.83161i	−0.367952	−	0.929845i
$28$	0.555732	−	1.89265i	0.105023	−	0.357677i
$29$	1.91619	+	0.875096i	0.355828	+	0.162501i	0.585306	−	0.810813i	$-0.300975\pi$
$29$	1.91619	+	0.875096i	0.355828	+	0.162501i	−0.229478	+	0.973314i	$0.573702\pi$
$30$	3.09039	−	1.01043i	0.564226	−	0.184478i
$31$	0.655155	−	4.55670i	0.117669	−	0.818408i	−0.842442	−	0.538788i	$-0.818882\pi$
$31$	0.655155	−	4.55670i	0.117669	−	0.818408i	0.960111	−	0.279620i	$-0.0902084\pi$
$32$	−0.281733	−	0.959493i	−0.0498038	−	0.169616i
$33$	−3.76355	+	0.658450i	−0.655149	+	0.114622i
$34$	0.392600	+	0.610897i	0.0673303	+	0.104768i
$35$	2.00191	+	3.11503i	0.338384	+	0.526536i
$36$	1.07812	−	2.79958i	0.179686	−	0.466597i
$37$	2.84409	+	9.68610i	0.467566	+	1.59238i	0.769231	+	0.638970i	$0.220639\pi$
$37$	2.84409	+	9.68610i	0.467566	+	1.59238i	−0.301665	+	0.953414i	$0.597542\pi$
$38$	0.0784689	−	0.545763i	0.0127293	−	0.0885345i
$39$	−2.42912	−	7.42946i	−0.388970	−	1.18967i
$40$	1.70755	+	0.779811i	0.269987	+	0.123299i
$41$	3.00908	−	10.2480i	0.469940	−	1.60047i	−0.294420	−	0.955676i	$-0.595126\pi$
$41$	3.00908	−	10.2480i	0.469940	−	1.60047i	0.764359	−	0.644791i	$-0.223055\pi$
$42$	3.39500	+	0.383205i	0.523860	+	0.0591297i
$43$	−10.2475	+	1.47337i	−1.56273	+	0.224687i	−0.868729	−	0.495288i	$-0.835063\pi$
$43$	−10.2475	+	1.47337i	−1.56273	+	0.224687i	−0.694000	+	0.719975i	$0.744153\pi$
$44$	−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	$0.709988\pi$
$48$	1.55293	−	0.767080i	0.224146	−	0.110718i
$49$	−0.442463	−	3.07740i	−0.0632090	−	0.439628i
$50$	1.34277	−	0.613225i	0.189897	−	0.0867231i
$51$	−0.925084	+	0.852180i	−0.129538	+	0.119329i
$52$	1.87471	−	4.10503i	0.259975	−	0.569266i
$53$	−1.98330	+	2.28885i	−0.272428	+	0.314398i	−0.875434	−	0.483338i	$-0.839424\pi$
$53$	−1.98330	+	2.28885i	−0.272428	+	0.314398i	0.603006	+	0.797737i	$0.293970\pi$
$54$	5.09828	+	1.00375i	0.693789	+	0.136592i
$55$	3.97313	−	1.16662i	0.535737	−	0.157306i
$56$	1.29175	+	1.49075i	0.172617	+	0.199210i
$57$	0.954569	−	0.0290299i	0.126436	−	0.00384511i
$58$	−1.77215	+	1.13889i	−0.232695	+	0.149544i
$59$	−4.87697	+	4.22592i	−0.634927	+	0.550168i	−0.911746	−	0.410755i	$-0.865265\pi$
$59$	−4.87697	+	4.22592i	−0.634927	+	0.550168i	0.276819	+	0.960922i	$0.410720\pi$
$60$	−0.820766	+	3.14608i	−0.105960	+	0.406157i
$61$	−14.8890	−	2.14072i	−1.90634	−	0.274091i	−0.914804	−	0.403898i	$-0.867655\pi$
$61$	−14.8890	−	2.14072i	−1.90634	−	0.274091i	−0.991539	+	0.129807i	$0.958564\pi$
$62$	3.47914	+	3.01469i	0.441851	+	0.382866i
$63$	0.359597	+	5.90672i	0.0453050	+	0.744176i
$64$	0.959493	+	0.281733i	0.119937	+	0.0352166i
$65$	3.51917	+	7.70591i	0.436500	+	0.955801i
$66$	1.48080	−	3.52208i	0.182274	−	0.433538i
$67$	3.42273	−	5.32586i	0.418152	−	0.650658i	−0.566726	−	0.823907i	$-0.691790\pi$
$67$	3.42273	−	5.32586i	0.418152	−	0.650658i	0.984878	+	0.173249i	$0.0554264\pi$
$68$	−0.726175			−0.0880617
$69$	3.85663	+	7.35707i	0.464283	+	0.885687i
$70$	−3.70284			−0.442575
$71$	−1.36094	+	2.11766i	−0.161514	+	0.251320i	−0.912572	−	0.408915i	$-0.865907\pi$
$71$	−1.36094	+	2.11766i	−0.161514	+	0.251320i	0.751059	+	0.660235i	$0.229543\pi$
$72$	1.77229	+	2.42054i	0.208866	+	0.285263i
$73$	−2.06209	−	4.51534i	−0.241349	−	0.528481i	0.749732	−	0.661742i	$-0.230182\pi$
$73$	−2.06209	−	4.51534i	−0.241349	−	0.528481i	−0.991081	+	0.133261i	$0.957455\pi$
$74$	−9.68610	−	2.84409i	−1.12599	−	0.330619i
$75$	1.44706	+	2.10791i	0.167092	+	0.243401i
$76$	0.416702	+	0.361074i	0.0477990	+	0.0414181i
$77$	4.30694	+	0.619244i	0.490821	+	0.0705694i
$78$	7.56334	+	1.97316i	0.856380	+	0.223417i
$79$	10.6252	−	9.20675i	1.19542	−	1.03584i	0.196961	−	0.980411i	$-0.436893\pi$
$79$	10.6252	−	9.20675i	1.19542	−	1.03584i	0.998463	−	0.0554287i	$-0.0176526\pi$
$80$	−1.57919	+	1.01488i	−0.176559	+	0.113467i
$81$	−0.190705	+	8.99798i	−0.0211894	+	0.999775i
$82$	6.99432	+	8.07188i	0.772394	+	0.891390i
$83$	10.5768	−	3.10563i	1.16095	−	0.340887i	0.356151	−	0.934428i	$-0.384089\pi$
$83$	10.5768	−	3.10563i	1.16095	−	0.340887i	0.804803	+	0.593542i	$0.202271\pi$
$84$	−2.15785	+	2.64888i	−0.235440	+	0.289016i
$85$	0.892684	−	1.03021i	0.0968251	−	0.111742i
$86$	4.30074	−	9.41731i	0.463761	−	1.01549i
$87$	−2.47208	−	2.68357i	−0.265035	−	0.287709i
$88$	2.00655	−	0.916359i	0.213899	−	0.0976842i
$89$	−0.391167	−	2.72063i	−0.0414636	−	0.288386i	−0.999994	−	0.00339624i	$-0.998919\pi$
$89$	−0.391167	−	2.72063i	−0.0414636	−	0.288386i	0.958531	−	0.284990i	$-0.0919901\pi$
$90$	−5.61264	−	0.461244i	−0.591624	−	0.0486194i
$91$			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
$96$	−0.194269	+	1.72112i	−0.0198274	+	0.175661i
$97$	1.95701	−	6.66496i	0.198704	−	0.676724i	−0.798500	−	0.601995i	$-0.794373\pi$
$97$	1.95701	−	6.66496i	0.198704	−	0.676724i	0.997204	−	0.0747288i	$-0.0238091\pi$
$98$	2.82809	+	1.29154i	0.285680	+	0.130466i
$99$	6.45116	+	1.47512i	0.648366	+	0.148255i
$100$	−0.210081	+	1.46115i	−0.0210081	+	0.146115i
$101$	−5.08531	−	17.3190i	−0.506008	−	1.72330i	−0.675121	−	0.737707i	$-0.735909\pi$
$101$	−5.08531	−	17.3190i	−0.506008	−	1.72330i	0.169114	−	0.985597i	$-0.445910\pi$
$102$	−0.216761	−	1.23895i	−0.0214625	−	0.122675i
$103$	−4.85874	−	7.56034i	−0.478745	−	0.744943i	0.514930	−	0.857232i	$-0.327818\pi$
$103$	−4.85874	−	7.56034i	−0.478745	−	0.744943i	−0.993676	+	0.112290i	$0.964182\pi$
$104$	2.43983	+	3.79645i	0.239245	+	0.372273i
$105$	−1.10529	−	6.31756i	−0.107865	−	0.616530i
$106$	−0.853252	−	2.90591i	−0.0828752	−	0.282247i
$107$	−0.913030	+	6.35026i	−0.0882659	+	0.613903i	0.896892	+	0.442250i	$0.145820\pi$
$107$	−0.913030	+	6.35026i	−0.0882659	+	0.613903i	−0.985158	+	0.171653i	$0.945089\pi$
$108$	−3.60074	+	3.74628i	−0.346482	+	0.360486i
$109$	13.5637	+	6.19435i	1.29917	+	0.593311i	0.940386	−	0.340110i	$-0.110464\pi$
$109$	13.5637	+	6.19435i	1.29917	+	0.593311i	0.358784	+	0.933421i	$0.383192\pi$
$110$	−1.16662	+	3.97313i	−0.111232	+	0.378823i
$111$	1.96114	−	17.3747i	0.186144	−	1.64914i
$112$	−1.95247	+	0.280723i	−0.184491	+	0.0265259i
$113$	−3.07687	−	1.97738i	−0.289447	−	0.186016i	0.387857	−	0.921720i	$-0.373215\pi$
$113$	−3.07687	−	1.97738i	−0.289447	−	0.186016i	−0.677304	+	0.735703i	$0.736852\pi$
$114$	−0.491658	+	0.818730i	−0.0460480	+	0.0766811i
$115$	−5.04773	−	7.45442i	−0.470704	−	0.695128i
$116$		−	2.10656i		−	0.195589i
$117$	−1.10885	+	13.4931i	−0.102514	+	1.24743i
$118$	−0.918379	−	6.38747i	−0.0845437	−	0.588014i
$119$	1.30297	−	0.595048i	0.119443	−	0.0545479i
$120$	−2.20291	−	2.39137i	−0.201097	−	0.218301i
$121$	−2.54818	+	5.57973i	−0.231653	+	0.507248i
$122$	9.85050	−	11.3681i	0.891822	−	1.02922i
$123$	−11.6839	+	14.3427i	−1.05351	+	1.29324i
$124$	−4.41708	+	1.29697i	−0.396666	+	0.116472i
$125$	−7.96113	−	9.18763i	−0.712065	−	0.821767i
$126$	−5.16346	−	2.89090i	−0.459997	−	0.257542i
$127$	−5.77176	+	3.70929i	−0.512161	+	0.329146i	−0.771064	−	0.636757i	$-0.780275\pi$
$127$	−5.77176	+	3.70929i	−0.512161	+	0.329146i	0.258903	+	0.965903i	$0.416639\pi$
$128$	−0.755750	+	0.654861i	−0.0667995	+	0.0578821i
$129$	17.3510	+	4.52661i	1.52767	+	0.398546i
$130$	−8.38523	−	1.20561i	−0.735434	−	0.105739i
$131$	−3.70085	−	3.20680i	−0.323344	−	0.280179i	0.478029	−	0.878344i	$-0.341351\pi$
$131$	−3.70085	−	3.20680i	−0.323344	−	0.280179i	−0.801373	+	0.598165i	$0.795897\pi$
$132$	2.16238	+	3.14991i	0.188211	+	0.274165i
$133$	−1.04356	−	0.306417i	−0.0904882	−	0.0265697i
$134$	2.62994	+	5.75876i	0.227192	+	0.497481i
$135$	−0.888408	−	9.71360i	−0.0764620	−	0.836014i
$136$	0.392600	−	0.610897i	0.0336652	−	0.0523840i
$137$	−12.1765			−1.04031			−0.520154	−	0.854073i	$-0.674125\pi$
$137$	−12.1765			−1.04031			−0.520154	+	0.854073i	$0.674125\pi$
$138$	−8.27421	−	0.733130i	−0.704347	−	0.0624082i
$139$	−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
$141$	7.27306	−	17.2989i	0.612502	−	1.45683i
$142$	−1.04571	−	2.28979i	−0.0877541	−	0.192155i
$143$	9.55161	+	2.80460i	0.798745	+	0.234533i
$144$	−2.99446	+	0.182301i	−0.249538	+	0.0151917i
$145$	2.98854	+	2.58958i	0.248184	+	0.215053i
$146$	4.91340	+	0.706440i	0.406635	+	0.0584654i
$147$	−1.35937	+	5.21062i	−0.112119	+	0.429765i
$148$	7.62930	−	6.61083i	0.627125	−	0.543407i
$149$	0.413148	−	0.265514i	0.0338464	−	0.0217517i	−0.523608	−	0.851959i	$-0.675414\pi$
$149$	0.413148	−	0.265514i	0.0338464	−	0.0217517i	0.557455	+	0.830207i	$0.311778\pi$
$150$	−2.55563	+	0.0777205i	−0.208666	+	0.00634585i
$151$	9.05009	+	10.4444i	0.736486	+	0.849950i	0.993186	−	0.116541i	$-0.0371806\pi$
$151$	9.05009	+	10.4444i	0.736486	+	0.849950i	−0.256700	+	0.966491i	$0.582635\pi$
$152$	−0.529041	+	0.155340i	−0.0429109	+	0.0125998i
$153$	2.04912	−	0.739647i	0.165662	−	0.0597969i
$154$	−2.84945	+	3.28844i	−0.229615	+	0.264990i
$155$	3.58991	−	7.86080i	0.288348	−	0.631394i
$156$	−5.74898	+	5.29591i	−0.460287	+	0.424012i
$157$	−2.69059	+	1.22875i	−0.214733	+	0.0980651i	−0.519877	−	0.854241i	$-0.674022\pi$
$157$	−2.69059	+	1.22875i	−0.214733	+	0.0980651i	0.305145	+	0.952306i	$0.401295\pi$
$158$	2.00082	+	13.9160i	0.159177	+	1.10710i
$159$	4.70318	−	2.32317i	0.372987	−	0.184239i
$160$		−	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	0.892943	−	0.450170i	$-0.148637\pi$
$163$	10.9082	+	7.01027i	0.854395	+	0.549087i	−0.0385473	+	0.999257i	$0.512273\pi$
$164$	−10.5719	+	1.52001i	−0.825528	+	0.118693i
$165$	−7.12693	−	0.804439i	−0.554831	−	0.0626255i
$166$	−3.10563	+	10.5768i	−0.241043	+	0.820919i
$167$	−5.47008	−	2.49810i	−0.423288	−	0.193309i	0.192370	−	0.981322i	$-0.438382\pi$
$167$	−5.47008	−	2.49810i	−0.423288	−	0.193309i	−0.615658	+	0.788013i	$0.711110\pi$
$168$	−1.06176	−	3.24739i	−0.0819165	−	0.250542i
$169$	−1.04827	+	7.29086i	−0.0806359	+	0.560835i
$170$	0.384048	+	1.30795i	0.0294551	+	0.100315i
$171$	−1.54362	−	0.594447i	−0.118044	−	0.0454585i
$172$	5.59719	+	8.70940i	0.426782	+	0.664085i
$173$	1.30500	+	2.03062i	0.0992176	+	0.154386i	0.887313	−	0.461167i	$-0.152569\pi$
$173$	1.30500	+	2.03062i	0.0992176	+	0.154386i	−0.788096	+	0.615553i	$0.788933\pi$
$174$	3.59407	−	0.628801i	0.272466	−	0.0476692i
$175$	−0.820357	−	2.79388i	−0.0620131	−	0.211197i
$176$	−0.313931	+	2.18344i	−0.0236634	+	0.164583i
$177$	10.6238	−	3.47352i	0.798531	−	0.261086i
$178$	2.50022	+	1.14181i	0.187399	+	0.0855824i
$179$	−5.42051	+	18.4606i	−0.405148	+	1.37981i	0.464254	+	0.885702i	$0.346322\pi$
$179$	−5.42051	+	18.4606i	−0.405148	+	1.37981i	−0.869402	+	0.494105i	$0.835496\pi$
$180$	3.42244	−	4.47228i	0.255094	−	0.333344i
$181$	0.494499	−	0.0710982i	0.0367558	−	0.00528469i	−0.123912	−	0.992293i	$-0.539544\pi$
$181$	0.494499	−	0.0710982i	0.0367558	−	0.00528469i	0.160668	+	0.987008i	$0.448635\pi$
$182$	−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
$186$	−3.53130	−	7.14900i	−0.258927	−	0.524190i
$187$	−0.227969	−	1.58556i	−0.0166707	−	0.115947i
$188$	9.85528	−	4.50076i	0.718770	−	0.328251i
$189$	3.39099	−	9.67249i	0.246658	−	0.703570i
$190$	0.429969	−	0.941501i	0.0311932	−	0.0683036i
$191$	7.04339	−	8.12851i	0.509642	−	0.588158i	−0.441365	−	0.897328i	$-0.645506\pi$
$191$	7.04339	−	8.12851i	0.509642	−	0.588158i	0.951007	+	0.309169i	$0.100051\pi$
$192$	−1.34287	−	1.09394i	−0.0969133	−	0.0789482i
$193$	8.38831	−	2.46303i	0.603803	−	0.177293i	0.0344787	−	0.999405i	$-0.489023\pi$
$193$	8.38831	−	2.46303i	0.603803	−	0.177293i	0.569325	+	0.822113i	$0.307205\pi$
$194$	4.54888	+	5.24969i	0.326591	+	0.376906i
$195$	−0.446022	−	14.6662i	−0.0319403	−	1.05027i
$196$	−2.61549	+	1.68088i	−0.186821	+	0.120063i
$197$	0.639673	−	0.554280i	0.0455748	−	0.0394908i	−0.631776	−	0.775151i	$-0.717674\pi$
$197$	0.639673	−	0.554280i	0.0455748	−	0.0394908i	0.677350	+	0.735661i	$0.263128\pi$
$198$	−4.72871	+	4.62955i	−0.336055	+	0.329008i
$199$	11.5796	+	1.66489i	0.820855	+	0.118021i	0.539932	−	0.841709i	$-0.318450\pi$
$199$	11.5796	+	1.66489i	0.820855	+	0.118021i	0.280924	+	0.959730i	$0.409359\pi$
$200$	−1.11562	−	0.966688i	−0.0788861	−	0.0683552i
$201$	−9.04020	+	6.20600i	−0.637646	+	0.437738i
$202$	17.3190	+	5.08531i	1.21856	+	0.357801i
$203$	1.72617	+	3.77979i	0.121153	+	0.265289i
$204$	1.15946	+	0.487478i	0.0811787	+	0.0341303i
$205$	10.8396	−	16.8667i	0.757070	−	1.17802i
$206$	8.98699			0.626154
$207$	−1.21900	−	14.3358i	−0.0847267	−	0.996404i
$208$	−4.51285			−0.312910
$209$	−0.657567	+	1.02319i	−0.0454849	+	0.0707758i
$210$	5.91223	+	2.48570i	0.407983	+	0.171530i
$211$	4.28128	+	9.37470i	0.294735	+	0.645381i	0.997839	−	0.0657069i	$-0.0209302\pi$
$211$	4.28128	+	9.37470i	0.294735	+	0.645381i	−0.703104	+	0.711088i	$0.748203\pi$
$212$	2.90591	+	0.853252i	0.199579	+	0.0586016i
$213$	3.59455	−	2.46762i	0.246294	−	0.169078i
$214$	−4.84856	−	4.20130i	−0.331441	−	0.287195i
$215$	−19.2365	−	2.76579i	−1.31192	−	0.188625i
$216$	−1.20486	−	5.05453i	−0.0819807	−	0.343917i
$217$	6.86277	−	5.94663i	0.465876	−	0.403683i
$218$	−12.5441	+	8.06161i	−0.849595	+	0.546001i
$219$	0.261350	+	8.59379i	0.0176604	+	0.580714i
$220$	−2.71169	−	3.12946i	−0.182822	−	0.210988i
$221$	3.14437	−	0.923272i	0.211514	−	0.0621060i
$222$	13.5563	+	11.0433i	0.909839	+	0.741179i
$223$	2.77177	−	3.19880i	0.185612	−	0.214207i	−0.655316	−	0.755355i	$-0.727465\pi$
$223$	2.77177	−	3.19880i	0.185612	−	0.214207i	0.840928	+	0.541148i	$0.182010\pi$
$224$	0.819427	−	1.79430i	0.0547503	−	0.119886i
$225$	−0.895448	−	4.33705i	−0.0596965	−	0.289136i
$226$	3.32696	−	1.51937i	0.221306	−	0.101067i
$227$	3.50584	+	24.3836i	0.232690	+	1.61840i	0.686383	+	0.727240i	$0.259197\pi$
$227$	3.50584	+	24.3836i	0.232690	+	1.61840i	−0.453693	+	0.891158i	$0.649894\pi$
$228$	−0.422949	−	0.856247i	−0.0280105	−	0.0567064i
$229$			5.57118i			0.368154i	0.982912	+	0.184077i	$0.0589295\pi$
$229$			5.57118i			0.368154i	−0.982912	+	0.184077i	$0.941070\pi$
$230$	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	$-0.728329\pi$
$233$	−16.4214	+	2.36103i	−1.07580	+	0.154676i	−0.418433	+	0.908248i	$0.637420\pi$
$234$	−10.7516	−	8.22773i	−0.702854	−	0.537864i
$235$	−5.72991	+	19.5143i	−0.373778	+	1.27297i
$236$	5.86999	+	2.68074i	0.382104	+	0.174501i
$237$	−23.1453	+	7.56754i	−1.50345	+	0.491565i
$238$	−0.203854	+	1.41784i	−0.0132139	+	0.0919047i
$239$	−2.18966	−	7.45730i	−0.141637	−	0.482373i	0.857866	−	0.513873i	$-0.171790\pi$
$239$	−2.18966	−	7.45730i	−0.141637	−	0.482373i	−0.999504	+	0.0315001i	$0.989972\pi$
$240$	3.20273	−	0.560334i	0.206736	−	0.0361694i
$241$	−5.14277	−	8.00230i	−0.331275	−	0.515474i	0.635162	−	0.772379i	$-0.280933\pi$
$241$	−5.14277	−	8.00230i	−0.331275	−	0.515474i	−0.966437	+	0.256905i	$0.917297\pi$
$242$	−3.31632	−	5.16030i	−0.213181	−	0.331716i
$243$	6.34479	−	14.2388i	0.407019	−	0.913420i
$244$	4.23786	+	14.4328i	0.271301	+	0.923966i
$245$	0.830585	−	5.77685i	0.0530641	−	0.369069i
$246$	−5.74903	−	17.5834i	−0.366545	−	1.12108i
$247$	−2.26342	−	1.03367i	−0.144018	−	0.0657707i
$248$	1.29697	−	4.41708i	0.0823578	−	0.280485i
$249$	−18.9725	−	2.14148i	−1.20233	−	0.135711i
$250$	12.0332	−	1.73012i	0.761049	−	0.109422i
$251$	17.0589	+	10.9631i	1.07675	+	0.691983i	0.953804	−	0.300431i	$-0.0971305\pi$
$251$	17.0589	+	10.9631i	1.07675	+	0.691983i	0.122943	+	0.992414i	$0.460767\pi$
$252$	5.22356	−	2.78084i	0.329053	−	0.175176i
$253$	−10.5045	−	1.25358i	−0.660414	−	0.0788121i
$254$		−	6.86091i		−	0.430492i
$255$	−2.11690	+	1.04566i	−0.132565	+	0.0654815i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	−19.7198	+	9.00572i	−1.23009	+	0.561761i	−0.921108	−	0.389308i	$-0.872714\pi$
$257$	−19.7198	+	9.00572i	−1.23009	+	0.561761i	−0.308978	+	0.951069i	$0.599987\pi$
$258$	−13.1887	+	12.1493i	−0.821091	+	0.756382i
$259$	−8.27213	+	18.1134i	−0.514005	+	1.12551i
$260$	5.54763	−	6.40230i	0.344049	−	0.397054i
$261$	2.14564	+	5.94428i	0.132812	+	0.367942i
$262$	4.69856	−	1.37962i	0.290278	−	0.0852333i
$263$	−1.26151	−	1.45586i	−0.0777878	−	0.0897719i	0.715522	−	0.698591i	$-0.246189\pi$
$263$	−1.26151	−	1.45586i	−0.0777878	−	0.0897719i	−0.793309	+	0.608819i	$0.791644\pi$
$264$	−3.81895	+	0.116140i	−0.235040	+	0.00714792i
$265$	−4.78271	+	3.07366i	−0.293800	+	0.188814i
$266$	0.821966	−	0.712237i	0.0503980	−	0.0436701i
$267$	−1.20178	+	4.60654i	−0.0735476	+	0.281916i
$268$	−6.26643	−	0.900976i	−0.382783	−	0.0550359i
$269$	11.1453	+	9.65750i	0.679544	+	0.588828i	0.924719	−	0.380651i	$-0.124300\pi$
$269$	11.1453	+	9.65750i	0.679544	+	0.588828i	−0.245175	+	0.969479i	$0.578845\pi$
$270$	8.65191	+	4.50419i	0.526539	+	0.274116i
$271$	−0.732230	−	0.215002i	−0.0444798	−	0.0130604i	0.259417	−	0.965765i	$-0.416470\pi$
$271$	−0.732230	−	0.215002i	−0.0444798	−	0.0130604i	−0.303897	+	0.952705i	$0.598288\pi$
$272$	0.301664	+	0.660552i	0.0182911	+	0.0400519i
$273$	5.97576	−	14.2133i	0.361669	−	0.860228i
$274$	6.58311	−	10.2435i	0.397700	−	0.618833i
$275$	−3.25628			−0.196361
$276$	5.09012	−	6.56435i	0.306389	−	0.395127i
$277$	−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
$279$	11.1431	−	8.15882i	0.667119	−	0.488456i
$280$	1.53822	+	3.36823i	0.0919260	+	0.201290i
$281$	11.4144	+	3.35157i	0.680927	+	0.199938i	0.603863	−	0.797088i	$-0.293627\pi$
$281$	11.4144	+	3.35157i	0.680927	+	0.199938i	0.0770637	+	0.997026i	$0.475446\pi$
$282$	10.6207	+	15.4710i	0.632452	+	0.921284i
$283$	6.15227	+	5.33097i	0.365715	+	0.316894i	0.818260	−	0.574848i	$-0.194939\pi$
$283$	6.15227	+	5.33097i	0.365715	+	0.316894i	−0.452546	+	0.891741i	$0.649484\pi$
$284$	2.49164	+	0.358244i	0.147852	+	0.0212579i
$285$	1.73467	+	0.452551i	0.102753	+	0.0268068i
$286$	−7.52337	+	6.51904i	−0.444866	+	0.385479i
$287$	17.7236	−	11.3903i	1.04619	−	0.672346i
$288$	1.46556	−	2.61766i	0.0863592	−	0.154247i
$289$	10.7873	+	12.4492i	0.634547	+	0.732307i
$290$	−3.79422	+	1.11408i	−0.222804	+	0.0654212i
$291$	−7.59885	+	9.32802i	−0.445453	+	0.546818i
$292$	−3.25068	+	3.75148i	−0.190231	+	0.219539i
$293$	12.1468	−	26.5979i	0.709626	−	1.55386i	−0.118269	−	0.992982i	$-0.537734\pi$
$293$	12.1468	−	26.5979i	0.709626	−	1.55386i	0.827895	−	0.560883i	$-0.189538\pi$
$294$	−3.64852	−	3.96065i	−0.212786	−	0.230990i
$295$	−11.0191	+	5.03224i	−0.641555	+	0.292988i
$296$	1.43667	+	9.99226i	0.0835048	+	0.580788i
$297$	−9.31015	−	6.68592i	−0.540230	−	0.387956i
$298$			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
$303$	−3.50658	+	31.0665i	−0.201447	+	1.78472i
$304$	0.155340	−	0.529041i	0.00890939	−	0.0303426i
$305$	−25.6852	−	11.7300i	−1.47073	−	0.671659i
$306$	−0.485608	+	2.12371i	−0.0277603	+	0.121405i
$307$	0.616673	−	4.28905i	0.0351954	−	0.244789i	−0.964627	−	0.263617i	$-0.915084\pi$
$307$	0.616673	−	4.28905i	0.0351954	−	0.244789i	0.999823	+	0.0188280i	$0.00599350\pi$
$308$	−1.22588	−	4.17497i	−0.0698511	−	0.237891i
$309$	2.68259	+	15.3330i	0.152607	+	0.872266i
$310$	4.67207	+	7.26989i	0.265356	+	0.412902i
$311$	−6.44713	−	10.0319i	−0.365583	−	0.568859i	0.608920	−	0.793232i	$-0.291603\pi$
$311$	−6.44713	−	10.0319i	−0.365583	−	0.568859i	−0.974503	+	0.224373i	$0.927967\pi$
$312$	−1.34707	−	7.69954i	−0.0762629	−	0.435901i
$313$	−6.80062	−	23.1608i	−0.384394	−	1.30913i	−0.893748	−	0.448569i	$-0.851934\pi$
$313$	−6.80062	−	23.1608i	−0.384394	−	1.30913i	0.509354	−	0.860557i	$-0.329884\pi$
$314$	0.420952	−	2.92778i	0.0237557	−	0.165224i
$315$	−2.47616	+	10.8290i	−0.139516	+	0.610147i
$316$	−12.7886	−	5.84036i	−0.719415	−	0.328546i
$317$	4.19170	−	14.2756i	0.235429	−	0.801798i	−0.754012	−	0.656861i	$-0.771884\pi$
$317$	4.19170	−	14.2756i	0.235429	−	0.801798i	0.989441	−	0.144937i	$-0.0462980\pi$
$318$	−0.588359	+	5.21257i	−0.0329936	+	0.292306i
$319$	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
$324$	8.26407	−	3.56442i	0.459115	−	0.198024i
$325$	−0.948066	−	6.59395i	−0.0525893	−	0.365766i
$326$	−11.7948	+	5.38652i	−0.653255	+	0.298332i
$327$	−17.4986	−	18.9956i	−0.967674	−	1.05046i
$328$	4.43689	−	9.71544i	0.244986	−	0.536446i
$329$	−13.9952	+	16.1514i	−0.771583	+	0.890454i
$330$	4.52985	−	5.56064i	0.249360	−	0.306103i
$331$	−2.16524	+	0.635773i	−0.119012	+	0.0349452i	−0.340696	−	0.940173i	$-0.610663\pi$
$331$	−2.16524	+	0.635773i	−0.119012	+	0.0349452i	0.221684	+	0.975119i	$0.428845\pi$
$332$	−7.21874	−	8.33087i	−0.396180	−	0.457216i
$333$	−14.7949	+	26.4253i	−0.810755	+	1.44810i
$334$	5.05889	−	3.25115i	0.276810	−	0.177895i
$335$	8.98149	−	7.78251i	0.490711	−	0.425204i
$336$	3.30591	+	0.862463i	0.180352	+	0.0470512i
$337$	7.99532	+	1.14955i	0.435533	+	0.0626202i	0.356594	−	0.934259i	$-0.383938\pi$
$337$	7.99532	+	1.14955i	0.435533	+	0.0626202i	0.0789386	+	0.996879i	$0.474847\pi$
$338$	−5.56672	−	4.82359i	−0.302790	−	0.262369i
$339$	3.58534	+	5.22272i	0.194729	+	0.283659i
$340$	−1.30795	−	0.384048i	−0.0709334	−	0.0208279i
$341$	−4.21851	−	9.23726i	−0.228445	−	0.500225i
$342$	1.33463	−	0.977196i	0.0721683	−	0.0528407i
$343$	10.7807	−	16.7751i	0.582103	−	0.905770i
$344$	−10.3529			−0.558190
$345$	3.05546	+	15.2908i	0.164500	+	0.823228i
$346$	−2.41381			−0.129767
$347$	−12.0071	+	18.6834i	−0.644574	+	1.00298i	0.353151	+	0.935566i	$0.385110\pi$
$347$	−12.0071	+	18.6834i	−0.644574	+	1.00298i	−0.997725	+	0.0674109i	$0.978526\pi$
$348$	−1.41412	+	3.36348i	−0.0758049	+	0.180302i
$349$	−5.62869	−	12.3251i	−0.301297	−	0.659748i	0.697062	−	0.717010i	$-0.254490\pi$
$349$	−5.62869	−	12.3251i	−0.301297	−	0.659748i	−0.998359	+	0.0572626i	$0.981763\pi$
$350$	2.79388	+	0.820357i	0.149339	+	0.0438499i
$351$	10.8283	−	20.7996i	0.577973	−	1.11020i
$352$	−1.66710	−	1.44455i	−0.0888567	−	0.0769948i
$353$	35.6857	+	5.13083i	1.89936	+	0.273087i	0.989798	−	0.142481i	$-0.0455080\pi$
$353$	35.6857	+	5.13083i	1.89936	+	0.273087i	0.909562	+	0.415568i	$0.136417\pi$
$354$	−2.82153	+	10.8152i	−0.149962	+	0.574821i
$355$	−3.57120	+	3.09446i	−0.189540	+	0.164237i
$356$	−2.31227	+	1.48601i	−0.122550	+	0.0787582i
$357$	−2.47987	+	0.0754168i	−0.131249	+	0.00399148i
$358$	−12.5995	−	14.5406i	−0.665902	−	0.768492i
$359$	−10.3735	+	3.04593i	−0.547492	+	0.160758i	−0.543769	−	0.839235i	$-0.683003\pi$
$359$	−10.3735	+	3.04593i	−0.547492	+	0.160758i	−0.00372270	+	0.999993i	$0.501185\pi$
$360$	1.91201	+	5.29704i	0.100772	+	0.279179i
$361$	−12.2433	+	14.1295i	−0.644382	+	0.743657i
$362$	−0.207535	+	0.454438i	−0.0109078	+	0.0238847i
$363$	7.81426	−	7.19843i	0.410142	−	0.377819i
$364$	8.09739	−	3.69795i	0.424418	−	0.193825i
$365$	−1.32612	−	9.22335i	−0.0694122	−	0.482772i
$366$	−23.3594	+	11.5385i	−1.22101	+	0.603127i
$367$		−	6.90386i		−	0.360379i	−0.983632	−	0.180189i	$-0.942329\pi$
$367$		−	6.90386i		−	0.360379i	0.983632	−	0.180189i	$-0.0576711\pi$
$368$	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
$372$	7.92328	+	0.894327i	0.410803	+	0.0463687i
$373$	8.09640	−	27.5738i	0.419216	−	1.42772i	−0.431510	−	0.902108i	$-0.642019\pi$
$373$	8.09640	−	27.5738i	0.419216	−	1.42772i	0.850726	−	0.525610i	$-0.176163\pi$
$374$	1.45710	+	0.665437i	0.0753451	+	0.0344089i
$375$	6.54370	+	20.0139i	0.337915	+	1.03351i
$376$	−1.54189	+	10.7241i	−0.0795169	+	0.553052i
$377$	2.67831	+	9.12150i	0.137940	+	0.469781i
$378$	6.30370	+	8.08203i	0.324228	+	0.415695i
$379$	4.37766	+	6.81177i	0.224865	+	0.349897i	0.935294	−	0.353872i	$-0.115135\pi$
$379$	4.37766	+	6.81177i	0.224865	+	0.349897i	−0.710429	+	0.703769i	$0.751499\pi$
$380$	0.559582	+	0.870726i	0.0287059	+	0.0446673i
$381$	11.7056	−	2.04796i	0.599698	−	0.104920i
$382$	3.03019	+	10.3199i	0.155038	+	0.528011i
$383$	−1.82924	+	12.7226i	−0.0934696	+	0.650096i	0.888193	+	0.459470i	$0.151961\pi$
$383$	−1.82924	+	12.7226i	−0.0934696	+	0.650096i	−0.981663	+	0.190625i	$0.938948\pi$
$384$	1.64629	−	0.538267i	0.0840119	−	0.0274683i
$385$	7.42993	+	3.39314i	0.378664	+	0.172930i
$386$	−2.46303	+	8.38831i	−0.125365	+	0.426954i
$387$	−24.6651	−	18.8751i	−1.25380	−	0.959477i
$388$	−6.87563	+	0.988566i	−0.349057	+	0.0501868i
$389$	28.9931	+	18.6327i	1.47001	+	0.944717i	0.998006	+	0.0631206i	$0.0201053\pi$
$389$	28.9931	+	18.6327i	1.47001	+	0.944717i	0.472003	+	0.881597i	$0.343531\pi$
$390$	12.5791	+	7.55394i	0.636970	+	0.382509i
$391$	−3.13223	+	1.52241i	−0.158404	+	0.0769916i
$392$		−	3.10904i		−	0.157030i
$393$	3.75633	+	7.60457i	0.189482	+	0.383600i
$394$	0.120457	+	0.837794i	0.00606852	+	0.0422074i
$395$	24.0066	−	10.9634i	1.20790	−	0.551630i
$396$	−1.33809	−	6.48097i	−0.0672417	−	0.325681i
$397$	−5.26485	+	11.5284i	−0.264235	+	0.578595i	−0.994520	−	0.104549i	$-0.966660\pi$
$397$	−5.26485	+	11.5284i	−0.264235	+	0.578595i	0.730285	+	0.683143i	$0.239387\pi$
$398$	−7.66100	+	8.84126i	−0.384011	+	0.443172i
$399$	1.46053	+	1.18978i	0.0731178	+	0.0595637i
$400$	1.41638	−	0.415886i	0.0708189	−	0.0207943i
$401$	1.78297	+	2.05766i	0.0890373	+	0.102755i	0.798520	−	0.601968i	$-0.205617\pi$
$401$	1.78297	+	2.05766i	0.0890373	+	0.102755i	−0.709483	+	0.704723i	$0.751071\pi$
$402$	−0.333320	−	10.9603i	−0.0166245	−	0.546651i
$403$	17.4772	−	11.2319i	0.870601	−	0.559501i
$404$	−13.6414	+	11.8203i	−0.678684	+	0.588083i
$405$	−5.10220	+	16.1058i	−0.253530	+	0.800305i
$406$	−4.11300	−	0.591360i	−0.204125	−	0.0293487i
$407$	16.8294	+	14.5828i	0.834202	+	0.722840i
$408$	−1.03695	+	0.711853i	−0.0513365	+	0.0352420i
$409$	−4.24238	−	1.24568i	−0.209772	−	0.0615947i	0.175158	−	0.984540i	$-0.443956\pi$
$409$	−4.24238	−	1.24568i	−0.209772	−	0.0615947i	−0.384930	+	0.922946i	$0.625775\pi$
$410$	8.32887	+	18.2377i	0.411334	+	0.900695i
$411$	19.4419	+	8.17402i	0.958996	+	0.403195i
$412$	−4.85874	+	7.56034i	−0.239373	+	0.372471i
$413$	−12.7292			−0.626362
$414$	12.7191	+	6.72501i	0.625107	+	0.330516i
$415$	20.6928			1.01577
$416$	2.43983	−	3.79645i	0.119623	−	0.186136i
$417$	28.7456	+	12.0856i	1.40768	+	0.591837i
$418$	−0.505258	−	1.10636i	−0.0247130	−	0.0541139i
$419$	35.5048	+	10.4252i	1.73452	+	0.509302i	0.987786	−	0.155816i	$-0.0498006\pi$
$419$	35.5048	+	10.4252i	1.73452	+	0.509302i	0.746738	+	0.665118i	$0.231619\pi$
$420$	−5.28750	+	3.62981i	−0.258003	+	0.177117i
$421$	24.3165	+	21.0704i	1.18511	+	1.02691i	0.999015	+	0.0443749i	$0.0141296\pi$
$421$	24.3165	+	21.0704i	1.18511	+	1.02691i	0.186098	+	0.982531i	$0.440416\pi$
$422$	−10.2011	−	1.46670i	−0.496583	−	0.0713979i
$423$	−23.2254	+	22.7384i	−1.12926	+	1.10558i
$424$	−2.28885	+	1.98330i	−0.111157	+	0.0963177i
$425$	−0.901791	+	0.579546i	−0.0437433	+	0.0281121i
$426$	0.132534	+	4.35802i	0.00642130	+	0.211147i
$427$	−19.4306	−	22.4241i	−0.940313	−	1.08518i
$428$	6.15569	−	1.80747i	0.297546	−	0.0873675i
$429$	−13.3681	−	10.8900i	−0.645416	−	0.525773i
$430$	12.7267	−	14.6874i	0.613738	−	0.708291i
$431$	−6.22902	+	13.6396i	−0.300041	+	0.656999i	−0.998265	−	0.0588809i	$-0.981247\pi$
$431$	−6.22902	+	13.6396i	−0.300041	+	0.656999i	0.698224	+	0.715880i	$0.253974\pi$
$432$	4.90354	+	1.71909i	0.235922	+	0.0827097i
$433$	10.1351	−	4.62854i	0.487061	−	0.222433i	−0.156720	−	0.987643i	$-0.550092\pi$
$433$	10.1351	−	4.62854i	0.487061	−	0.222433i	0.643781	+	0.765210i	$0.277365\pi$
$434$	1.29233	+	8.98832i	0.0620336	+	0.431453i
$435$	−3.03334	−	6.14090i	−0.145437	−	0.294434i
$436$		−	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	0.797498	−	0.603322i	$-0.206157\pi$
$439$	12.1521	+	7.80970i	0.579990	+	0.372737i	−0.217508	+	0.976058i	$0.569793\pi$
$440$	4.09871	−	0.589306i	0.195399	−	0.0280941i
$441$	5.66834	−	7.40711i	0.269921	−	0.352720i
$442$	−0.923272	+	3.14437i	−0.0439156	+	0.149563i
$443$	−17.2153	−	7.86195i	−0.817922	−	0.373532i	−0.0378976	−	0.999282i	$-0.512066\pi$
$443$	−17.2153	−	7.86195i	−0.817922	−	0.373532i	−0.780024	+	0.625749i	$0.784793\pi$
$444$	−16.6193	+	5.43381i	−0.788718	+	0.257877i
$445$	0.734293	−	5.10712i	0.0348088	−	0.242101i
$446$	1.19246	+	4.06116i	0.0564649	+	0.192302i
$447$	−0.837900	+	0.146595i	−0.0396313	+	0.00693369i
$448$	1.06644	+	1.65942i	0.0503846	+	0.0784000i
$449$	−12.1071	−	18.8391i	−0.571371	−	0.889071i	0.428524	−	0.903530i	$-0.359034\pi$
$449$	−12.1071	−	18.8391i	−0.571371	−	0.889071i	−0.999895	+	0.0144592i	$0.995397\pi$
$450$	4.13267	+	1.59149i	0.194816	+	0.0750234i
$451$	−6.63770	−	22.6059i	−0.312557	−	1.06447i
$452$	−0.520513	+	3.62025i	−0.0244829	+	0.170282i
$453$	−7.43878	−	22.7515i	−0.349504	−	1.06896i
$454$	−22.4082	−	10.2335i	−1.05167	−	0.480281i
$455$	−4.70786	+	16.0335i	−0.220708	+	0.751662i
$456$	0.948985	+	0.107115i	0.0444403	+	0.00501612i
$457$	−23.0174	+	3.30940i	−1.07671	+	0.154807i	−0.657778	−	0.753212i	$-0.728503\pi$
$457$	−23.0174	+	3.30940i	−1.07671	+	0.154807i	−0.418929	+	0.908019i	$0.637594\pi$
$458$	−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	$0.794467\pi$
$462$	6.75715	−	3.33774i	0.314371	−	0.155286i
$463$	2.22872	+	15.5011i	0.103577	+	0.720395i	0.973745	+	0.227640i	$0.0731010\pi$
$463$	2.22872	+	15.5011i	0.103577	+	0.720395i	−0.870168	+	0.492755i	$0.835990\pi$
$464$	−1.91619	+	0.875096i	−0.0889570	+	0.0406253i
$465$	−11.0088	+	10.1412i	−0.510522	+	0.470288i
$466$	6.89183	−	15.0910i	0.319258	−	0.699077i
$467$	19.3933	−	22.3810i	0.897414	−	1.03567i	−0.101751	−	0.994810i	$-0.532444\pi$
$467$	19.3933	−	22.3810i	0.897414	−	1.03567i	0.999165	−	0.0408613i	$-0.0130102\pi$
$468$	12.7344	−	4.59657i	0.588646	−	0.212477i
$469$	11.9821	−	3.51826i	0.553282	−	0.162458i
$470$	−13.3186	−	15.3705i	−0.614343	−	0.708989i
$471$	5.12085	−	0.155733i	0.235956	−	0.00717579i
$472$	−5.42874	+	3.48884i	−0.249878	+	0.160587i
$473$	−17.2593	+	14.9552i	−0.793582	+	0.687643i
$474$	6.14709	−	23.5624i	0.282345	−	1.08226i
$475$	0.805642	+	0.115834i	0.0369654	+	0.00531482i
$476$	−1.08255	−	0.938034i	−0.0496185	−	0.0429947i
$477$	−9.06897	+	0.552113i	−0.415240	+	0.0252795i
$478$	7.45730	+	2.18966i	0.341089	+	0.100153i
$479$	−7.46364	−	16.3431i	−0.341022	−	0.746735i	0.658963	−	0.752176i	$-0.270995\pi$
$479$	−7.46364	−	16.3431i	−0.341022	−	0.746735i	−0.999985	+	0.00544059i	$0.998268\pi$
$480$	−1.26015	+	2.99725i	−0.0575175	+	0.136805i
$481$	−24.6301	+	38.3252i	−1.12304	+	1.74748i
$482$	9.51236			0.433276
$483$	−3.75418	+	15.9494i	−0.170821	+	0.725721i
$484$	6.13406			0.278821
$485$	7.04972	−	10.9696i	0.320111	−	0.498103i
$486$	8.54819	+	13.0357i	0.387754	+	0.591310i
$487$	0.316253	+	0.692497i	0.0143308	+	0.0313800i	0.916662	−	0.399663i	$-0.130873\pi$
$487$	0.316253	+	0.692497i	0.0143308	+	0.0313800i	−0.902331	+	0.431043i	$0.858146\pi$
$488$	−14.4328	−	4.23786i	−0.653343	−	0.191839i
$489$	−12.7108	−	18.5157i	−0.574804	−	0.837310i
$490$	4.41075	+	3.82193i	0.199257	+	0.172657i
$491$	−34.5209	−	4.96336i	−1.55791	−	0.223993i	−0.691146	−	0.722715i	$-0.742894\pi$
$491$	−34.5209	−	4.96336i	−1.55791	−	0.223993i	−0.866762	+	0.498722i	$0.833803\pi$
$492$	17.9003	+	4.66992i	0.807006	+	0.210536i
$493$	1.15609	−	1.00176i	0.0520678	−	0.0451170i
$494$	2.09327	−	1.34526i	0.0941807	−	0.0605263i
$495$	10.8394	+	6.06870i	0.487193	+	0.272768i
$496$	3.01469	+	3.47914i	0.135364	+	0.156218i
$497$	−4.76430	+	1.39893i	−0.213708	+	0.0627504i
$498$	12.0588	−	14.8029i	0.540369	−	0.663333i
$499$	0.823674	−	0.950570i	0.0368727	−	0.0425534i	−0.737014	−	0.675878i	$-0.763765\pi$
$499$	0.823674	−	0.950570i	0.0368727	−	0.0425534i	0.773886	+	0.633324i	$0.218310\pi$
$500$	−5.05019	+	11.0584i	−0.225851	+	0.494546i
$501$	7.05696	+	7.66069i	0.315282	+	0.342254i
$502$	−18.4454	+	8.42375i	−0.823260	+	0.375970i
$503$	−0.121216	−	0.843078i	−0.00540477	−	0.0375910i	0.986941	−	0.161085i	$-0.0514992\pi$
$503$	−0.121216	−	0.843078i	−0.00540477	−	0.0375910i	−0.992345	+	0.123494i	$0.960590\pi$
$504$	−0.484676	+	5.89777i	−0.0215892	+	0.262708i
$505$		−	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	$-0.735494\pi$
$509$	−25.1088	+	3.61010i	−1.11293	+	0.160015i	−0.438767	+	0.898601i	$0.644585\pi$
$510$	0.264820	−	2.34617i	0.0117264	−	0.103890i
$511$	2.75861	−	9.39496i	0.122034	−	0.415608i
$512$	0.909632	+	0.415415i	0.0402004	+	0.0183589i
$513$	2.06561	+	1.98536i	0.0911989	+	0.0876559i
$514$	3.08522	−	21.4582i	0.136083	−	0.946480i
$515$	−4.75290	−	16.1869i	−0.209438	−	0.713280i
$516$	−3.09030	−	17.6634i	−0.136043	−	0.777589i
$517$	12.9210	+	20.1055i	0.568265	+	0.884237i
$518$	−10.7657	−	16.7518i	−0.473020	−	0.736033i
$519$	−0.720514	−	4.11829i	−0.0316270	−	0.180773i
$520$	2.38669	+	8.12831i	0.104663	+	0.356450i
$521$	2.84880	−	19.8138i	0.124808	−	0.868059i	−0.827183	−	0.561933i	$-0.810058\pi$
$521$	2.84880	−	19.8138i	0.124808	−	0.868059i	0.951991	−	0.306126i	$-0.0990330\pi$
$522$	−6.16067	−	1.40870i	−0.269645	−	0.0616570i
$523$	−26.7190	−	12.2021i	−1.16834	−	0.533563i	−0.265740	−	0.964045i	$-0.585616\pi$
$523$	−26.7190	−	12.2021i	−1.16834	−	0.533563i	−0.902599	+	0.430482i	$0.858344\pi$
$524$	−1.37962	+	4.69856i	−0.0602691	+	0.205258i
$525$	−0.565677	+	5.01161i	−0.0246881	+	0.218725i
$526$	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
$531$	−19.2944	−	1.58561i	−0.837306	−	0.0688095i
$532$	0.154784	+	1.07655i	0.00671074	+	0.0466742i
$533$	43.8444	−	20.0230i	1.89911	−	0.867294i
$534$	−3.22554	−	3.50148i	−0.139583	−	0.151524i
$535$	−5.00293	+	10.9549i	−0.216295	+	0.473621i
$536$	4.14584	−	4.78455i	0.179073	−	0.206661i
$537$	21.0473	−	25.8367i	0.908257	−	1.11494i
$538$	−14.1500	+	4.15482i	−0.610051	+	0.179127i
$539$	−4.49117	−	5.18308i	−0.193448	−	0.223251i
$540$	−8.46674	+	4.84330i	−0.364351	+	0.208422i
$541$	−14.6045	+	9.38573i	−0.627896	+	0.403524i	−0.815530	−	0.578715i	$-0.803554\pi$
$541$	−14.6045	+	9.38573i	−0.627896	+	0.403524i	0.187634	+	0.982239i	$0.439918\pi$
$542$	0.576745	−	0.499752i	0.0247733	−	0.0214662i
$543$	−0.837281	−	0.218434i	−0.0359312	−	0.00937391i
$544$	−0.718784	−	0.103346i	−0.0308176	−	0.00443090i
$545$	21.1543	+	18.3303i	0.906150	+	0.785183i
$546$	8.72626	+	12.7114i	0.373449	+	0.543998i
$547$	−11.0586	−	3.24711i	−0.472833	−	0.138836i	0.0366299	−	0.999329i	$-0.488338\pi$
$547$	−11.0586	−	3.24711i	−0.472833	−	0.138836i	−0.509463	+	0.860493i	$0.670156\pi$
$548$	5.05830	+	11.0761i	0.216080	+	0.473148i
$549$	−26.6589	−	36.4100i	−1.13778	−	1.55394i
$550$	1.76048	−	2.73935i	0.0750669	−	0.116806i
$551$	−1.16150			−0.0494818
$552$	2.77035	+	7.83104i	0.117914	+	0.333311i
$553$	27.7323			1.17930
$554$	8.60291	−	13.3864i	0.365503	−	0.568733i
$555$	12.7212	−	30.2573i	0.539985	−	1.28435i
$556$	7.47891	+	16.3765i	0.317176	+	0.694520i
$557$	17.4775	+	5.13187i	0.740547	+	0.217444i	0.630183	−	0.776447i	$-0.282980\pi$
$557$	17.4775	+	5.13187i	0.740547	+	0.217444i	0.110364	+	0.993891i	$0.464798\pi$
$558$	0.839232	+	13.7852i	0.0355275	+	0.583572i
$559$	−35.3094	−	30.5958i	−1.49343	−	1.29406i
$560$	−3.66515	−	0.526970i	−0.154881	−	0.0222685i
$561$	−0.700386	+	2.68465i	−0.0295703	+	0.113346i
$562$	−8.99062	+	7.79042i	−0.379247	+	0.328619i
$563$	2.07744	−	1.33509i	0.0875537	−	0.0562673i	−0.496131	−	0.868247i	$-0.665247\pi$
$563$	2.07744	−	1.33509i	0.0875537	−	0.0562673i	0.583685	+	0.811980i	$0.301610\pi$
$564$	−18.7570	+	0.570429i	−0.789812	+	0.0240194i
$565$	−4.49612	−	5.18880i	−0.189153	−	0.218294i
$566$	−7.81087	+	2.29348i	−0.328315	+	0.0964021i
$567$	−11.9074	+	13.1674i	−0.500064	+	0.552980i
$568$	−1.64846	+	1.90242i	−0.0691678	+	0.0798239i
$569$	−2.72157	+	5.95940i	−0.114094	+	0.249831i	−0.958061	−	0.286564i	$-0.907487\pi$
$569$	−2.72157	+	5.95940i	−0.114094	+	0.249831i	0.843967	+	0.536395i	$0.180214\pi$
$570$	−1.31854	+	1.21463i	−0.0552277	+	0.0508753i
$571$	29.2972	−	13.3796i	1.22605	−	0.559917i	0.306115	−	0.951994i	$-0.400971\pi$
$571$	29.2972	−	13.3796i	1.22605	−	0.559917i	0.919932	+	0.392077i	$0.128243\pi$
$572$	−1.41672	−	9.85352i	−0.0592361	−	0.411996i
$573$	−16.7026	+	8.25037i	−0.697762	+	0.344664i
$574$			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	0.847144	−	0.531363i	$-0.178320\pi$
$577$	17.1921	+	11.0487i	0.715716	+	0.459962i	−0.131429	+	0.991326i	$0.541956\pi$
$578$	−16.3050	+	2.34431i	−0.678199	+	0.0975102i
$579$	−15.0468	−	1.69838i	−0.625324	−	0.0705823i
$580$	1.11408	−	3.79422i	0.0462598	−	0.157546i
$581$	19.7791	+	9.03281i	0.820575	+	0.374744i
$582$	−3.73898	−	11.4357i	−0.154986	−	0.474024i
$583$	−0.950767	+	6.61273i	−0.0393767	+	0.273871i
$584$	−1.39850	−	4.76285i	−0.0578703	−	0.197088i
$585$	−9.13321	+	23.7166i	−0.377612	+	0.980559i
$586$	15.8085	+	24.5985i	0.653042	+	1.01615i
$587$	−11.7978	−	18.3578i	−0.486948	−	0.757706i	0.507644	−	0.861567i	$-0.330517\pi$
$587$	−11.7978	−	18.3578i	−0.486948	−	0.757706i	−0.994592	+	0.103861i	$0.966880\pi$
$588$	5.30445	−	0.928039i	0.218752	−	0.0382717i
$589$	0.715119	+	2.43547i	0.0294660	+	0.100352i
$590$	1.72397	−	11.9905i	0.0709747	−	0.493640i
$591$	−1.39343	+	0.455594i	−0.0573182	+	0.0187406i
$592$	−9.18275	−	4.19362i	−0.377409	−	0.172357i
$593$	2.22412	−	7.57465i	0.0913336	−	0.311054i	−0.901137	−	0.433534i	$-0.857267\pi$
$593$	2.22412	−	7.57465i	0.0913336	−	0.311054i	0.992471	+	0.122480i	$0.0390847\pi$
$594$	10.6580	−	4.21752i	0.437303	−	0.173047i
$595$	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	$-0.389367\pi$
$600$	1.13234	+	2.29239i	0.0462277	+	0.0935866i
$601$	6.54719	+	45.5367i	0.267065	+	1.85748i	0.475859	+	0.879522i	$0.342137\pi$
$601$	6.54719	+	45.5367i	0.267065	+	1.85748i	−0.208793	+	0.977960i	$0.566954\pi$
$602$	18.5761	−	8.48343i	0.757106	−	0.345759i
$603$	18.6003	−	3.84031i	0.757463	−	0.156389i
$604$	5.74098	−	12.5710i	0.233597	−	0.511507i
$605$	−7.54057	+	8.70228i	−0.306568	+	0.353798i
$606$	−24.2390	−	19.7457i	−0.984642	−	0.802116i
$607$	−20.0415	+	5.88471i	−0.813458	+	0.238853i	−0.661897	−	0.749595i	$-0.730248\pi$
$607$	−20.0415	+	5.88471i	−0.813458	+	0.238853i	−0.151561	+	0.988448i	$0.548430\pi$
$608$	0.361074	+	0.416702i	0.0146435	+	0.0168995i
$609$	−0.218776	−	7.19385i	−0.00886525	−	0.291510i
$610$	23.7544	−	15.2660i	0.961786	−	0.618102i
$611$	−36.9515	+	32.0187i	−1.49490	+	1.29534i
$612$	−1.52404	−	1.55669i	−0.0616058	−	0.0629253i
$613$	15.4837	+	2.22621i	0.625379	+	0.0899160i	0.447717	−	0.894175i	$-0.352237\pi$
$613$	15.4837	+	2.22621i	0.625379	+	0.0899160i	0.177663	+	0.984091i	$0.443146\pi$
$614$	3.27478	+	2.83762i	0.132159	+	0.114517i
$615$	−28.6298	+	19.6541i	−1.15447	+	0.792529i
$616$	4.17497	+	1.22588i	0.168214	+	0.0493922i
$617$	16.7198	+	36.6113i	0.673115	+	1.47392i	0.869777	+	0.493444i	$0.164262\pi$
$617$	16.7198	+	36.6113i	0.673115	+	1.47392i	−0.196663	+	0.980471i	$0.563010\pi$
$618$	−14.3493	−	6.03293i	−0.577213	−	0.242680i
$619$	−17.4352	+	27.1298i	−0.700782	+	1.09044i	0.290268	+	0.956945i	$0.406255\pi$
$619$	−17.4352	+	27.1298i	−0.700782	+	1.09044i	−0.991050	+	0.133492i	$0.957381\pi$
$620$	−8.64173			−0.347060
$621$	−7.67718	+	23.7078i	−0.308075	+	0.951362i
$622$	11.9250			0.478148
$623$	2.93122	−	4.56107i	0.117437	−	0.182736i
$624$	7.20555	+	3.02946i	0.288453	+	0.121275i
$625$	−6.41402	−	14.0448i	−0.256561	−	0.561790i
$626$	23.1608	+	6.80062i	0.925691	+	0.271808i
$627$	1.73678	−	1.19228i	0.0693605	−	0.0476152i
$628$	2.23543	+	1.93701i	0.0892032	+	0.0772950i
$629$	7.25613	+	1.04327i	0.289321	+	0.0415981i
$630$	−7.77125	−	7.93770i	−0.309614	−	0.316246i
$631$	−28.0739	+	24.3262i	−1.11760	+	0.968409i	−0.999697	−	0.0246152i	$-0.992164\pi$
$631$	−28.0739	+	24.3262i	−1.11760	+	0.968409i	−0.117907	+	0.993025i	$0.537619\pi$
$632$	11.8273	−	7.60092i	0.470463	−	0.302348i
$633$	−0.542612	−	17.8423i	−0.0215669	−	0.709169i
$634$	9.74320	+	11.2443i	0.386952	+	0.446566i
$635$	−12.3575	+	3.62849i	−0.490392	+	0.143992i
$636$	−4.06700	−	3.31309i	−0.161267	−	0.131372i
$637$	9.18812	−	10.6037i	0.364047	−	0.420132i
$638$	−1.93036	+	4.22691i	−0.0764238	+	0.167345i
$639$	−7.39581	+	1.52698i	−0.292574	+	0.0604062i
$640$	−1.70755	+	0.779811i	−0.0674968	+	0.0308247i
$641$	1.62988	+	11.3361i	0.0643763	+	0.447747i	0.996360	+	0.0852466i	$0.0271678\pi$
$641$	1.62988	+	11.3361i	0.0643763	+	0.447747i	−0.931984	+	0.362501i	$0.881923\pi$
$642$	4.92125	+	9.96291i	0.194226	+	0.393205i
$643$		−	16.2352i		−	0.640254i	−0.947375	−	0.320127i	$-0.896274\pi$
$643$		−	16.2352i		−	0.640254i	0.947375	−	0.320127i	$-0.103726\pi$
$644$	−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	$-0.448361\pi$
$647$	15.1224	−	2.17428i	0.594524	−	0.0854797i	0.433008	+	0.901390i	$0.357452\pi$
$648$	−1.46931	+	8.87925i	−0.0577199	+	0.348810i
$649$	−4.01045	+	13.6583i	−0.157424	+	0.536136i
$650$	6.05974	+	2.76739i	0.237683	+	0.108546i
$651$	−14.9495	+	4.88787i	−0.585919	+	0.191571i
$652$	1.84534	−	12.8346i	0.0722690	−	0.502642i
$653$	1.65285	+	5.62911i	0.0646812	+	0.220284i	0.985491	−	0.169728i	$-0.0542890\pi$
$653$	1.65285	+	5.62911i	0.0646812	+	0.220284i	−0.920810	+	0.390012i	$0.872471\pi$
$654$	25.4406	−	4.45095i	0.994805	−	0.174046i
$655$	−4.96980	−	7.73316i	−0.194186	−	0.302160i
$656$	5.77438	+	8.98512i	0.225452	+	0.350810i
$657$	5.35168	−	13.8969i	0.208789	−	0.542170i
$658$	−6.02100	−	20.5056i	−0.234723	−	0.799393i
$659$	1.22033	−	8.48755i	0.0475371	−	0.330628i	−0.952150	−	0.305630i	$-0.901133\pi$
$659$	1.22033	−	8.48755i	0.0475371	−	0.330628i	0.999688	−	0.0249980i	$-0.00795794\pi$
$660$	2.22889	+	6.81706i	0.0867594	+	0.265354i
$661$	35.9332	+	16.4101i	1.39764	+	0.638280i	0.964750	−	0.263167i	$-0.0847670\pi$
$661$	35.9332	+	16.4101i	1.39764	+	0.638280i	0.432889	+	0.901447i	$0.357494\pi$
$662$	0.635773	−	2.16524i	0.0247100	−	0.0841545i
$663$	−5.64032	−	0.636641i	−0.219052	−	0.0247251i
$664$	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
$669$	−6.57295	+	3.24675i	−0.254125	+	0.125527i
$670$	1.69130	+	11.7633i	0.0653406	+	0.454454i
$671$	−30.1827	+	13.7840i	−1.16519	+	0.532125i
$672$	−2.51286	+	2.31482i	−0.0969356	+	0.0892963i
$673$	−7.50779	+	16.4398i	−0.289404	+	0.633706i	−0.997365	−	0.0725452i	$-0.976888\pi$
$673$	−7.50779	+	16.4398i	−0.289404	+	0.633706i	0.707961	+	0.706251i	$0.249615\pi$
$674$	−5.28967	+	6.10460i	−0.203750	+	0.235140i
$675$	−1.48170	+	7.52595i	−0.0570307	+	0.289674i
$676$	7.06746	−	2.07519i	0.271826	−	0.0798152i
$677$	11.0744	+	12.7806i	0.425625	+	0.491198i	0.927542	−	0.373718i	$-0.121917\pi$
$677$	11.0744	+	12.7806i	0.425625	+	0.491198i	−0.501917	+	0.864916i	$0.667372\pi$
$678$	−6.33201	+	0.192566i	−0.243179	+	0.00739546i
$679$	11.5268	−	7.40786i	0.442360	−	0.284287i
$680$	1.03021	−	0.892684i	0.0395068	−	0.0342329i
$681$	10.7709	−	41.2861i	0.412743	−	1.58209i
$682$	10.0516	+	1.44520i	0.384895	+	0.0553395i
$683$	8.96738	+	7.77028i	0.343127	+	0.297322i	0.809327	−	0.587358i	$-0.199832\pi$
$683$	8.96738	+	7.77028i	0.343127	+	0.297322i	−0.466200	+	0.884679i	$0.654377\pi$
$684$	0.100516	+	1.65107i	0.00384333	+	0.0631302i
$685$	−21.9316	−	6.43971i	−0.837965	−	0.246049i
$686$	8.28363	+	18.1386i	0.316270	+	0.692535i
$687$	3.73991	−	8.89535i	0.142686	−	0.339379i
$688$	5.59719	−	8.70940i	0.213391	−	0.332043i
$689$	−13.6676			−0.520693
$690$	−14.5153	−	5.69641i	−0.552589	−	0.216859i
$691$	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
$693$	7.71162	+	10.5323i	0.292940	+	0.400089i
$694$	−9.22595	−	20.2020i	−0.350212	−	0.766858i
$695$	−32.4269	−	9.52139i	−1.23002	−	0.361167i
$696$	−2.06501	−	3.00807i	−0.0782740	−	0.114021i
$697$	−5.86160	−	5.07911i	−0.222024	−	0.192385i
$698$	13.4116	+	1.92830i	0.507638	+	0.0729873i
$699$	27.8045	+	7.25378i	1.05166	+	0.274363i
$700$	−2.20061	+	1.90684i	−0.0831753	+	0.0720718i
$701$	−1.79941	+	1.15641i	−0.0679628	+	0.0436770i	−0.574181	−	0.818728i	$-0.694679\pi$
$701$	−1.79941	+	1.15641i	−0.0679628	+	0.0436770i	0.506218	+	0.862405i	$0.331043\pi$
$702$	11.6435	+	20.3545i	0.439457	+	0.768231i
$703$	−3.64505	−	4.20661i	−0.137476	−	0.158655i
$704$	2.11653	−	0.621471i	0.0797699	−	0.0234226i
$705$	22.2486	−	27.3114i	0.837932	−	1.02861i
$706$	−23.6095	+	27.2468i	−0.888555	+	1.02545i
$707$	14.7908	−	32.3873i	0.556264	−	1.21805i
$708$	−7.57289	−	8.22076i	−0.284607	−	0.308955i
$709$	5.03891	−	2.30119i	0.189240	−	0.0864231i	−0.318541	−	0.947909i	$-0.603193\pi$
$709$	5.03891	−	2.30119i	0.189240	−	0.0864231i	0.507782	+	0.861486i	$0.330466\pi$
$710$	−0.672491	−	4.67728i	−0.0252381	−	0.175535i
$711$	42.0356	+	3.45447i	1.57646	+	0.129553i
$712$		−	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
$717$	−1.50988	+	13.3768i	−0.0563875	+	0.499565i
$718$	3.04593	−	10.3735i	0.113673	−	0.387135i
$719$	15.1259	+	6.90778i	0.564102	+	0.257617i	0.676991	−	0.735991i	$-0.263283\pi$
$719$	15.1259	+	6.90778i	0.564102	+	0.257617i	−0.112890	+	0.993608i	$0.536011\pi$
$720$	−5.48987	−	1.25531i	−0.204595	−	0.0467827i
$721$	2.52286	−	17.5469i	0.0939561	−	0.653479i
$722$	−5.26727	−	17.9387i	−0.196027	−	0.667608i
$723$	2.83941	+	16.2294i	0.105599	+	0.603577i
$724$	−0.270095	−	0.420277i	−0.0100380	−	0.0156195i
$725$	−1.68120	−	2.61600i	−0.0624383	−	0.0971558i
$726$	1.83100	+	10.4655i	0.0679546	+	0.388412i
$727$	−6.91197	−	23.5400i	−0.256351	−	0.873050i	−0.982618	−	0.185638i	$-0.940565\pi$
$727$	−6.91197	−	23.5400i	−0.256351	−	0.873050i	0.726267	−	0.687412i	$-0.241253\pi$
$728$	−1.26686	+	8.81122i	−0.0469530	+	0.326566i
$729$	−19.6890	+	18.4755i	−0.729222	+	0.684277i
$730$	8.47613	+	3.87092i	0.313716	+	0.143269i
$731$	−2.11807	+	7.21347i	−0.0783395	+	0.266800i
$732$	2.92221	−	25.8893i	0.108008	−	0.956897i
$733$	−6.33969	+	0.911510i	−0.234162	+	0.0336674i	−0.258397	−	0.966039i	$-0.583194\pi$
$733$	−6.33969	+	0.911510i	−0.234162	+	0.0336674i	0.0242348	+	0.999706i	$0.492285\pi$
$734$	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
$738$	−2.62434	+	31.9342i	−0.0966034	+	1.17552i
$739$	−2.18082	−	15.1679i	−0.0802226	−	0.557961i	−0.989804	−	0.142435i	$-0.954507\pi$
$739$	−2.18082	−	15.1679i	−0.0802226	−	0.557961i	0.909581	−	0.415526i	$-0.136402\pi$
$740$	17.2377	−	7.87221i	0.633671	−	0.289388i
$741$	2.92004	+	3.16985i	0.107270	+	0.116447i
$742$	2.48171	−	5.43418i	0.0911063	−	0.199495i
$743$	18.5414	−	21.3980i	0.680219	−	0.785015i	−0.305720	−	0.952122i	$-0.598897\pi$
$743$	18.5414	−	21.3980i	0.680219	−	0.785015i	0.985939	+	0.167107i	$0.0534425\pi$
$744$	−5.03601	+	6.18198i	−0.184629	+	0.226642i
$745$	0.884560	−	0.259730i	0.0324078	−	0.00951578i
$746$	18.8193	+	21.7187i	0.689024	+	0.795177i
$747$	28.8553	+	16.1554i	1.05576	+	0.591094i
$748$	−1.34757	+	0.866032i	−0.0492721	+	0.0316653i
$749$	−9.56403	+	8.28728i	−0.349462	+	0.302810i
$750$	−20.3746	−	5.31542i	−0.743974	−	0.194092i
$751$	40.8972	+	5.88013i	1.49236	+	0.214569i	0.839687	−	0.543070i	$-0.182738\pi$
$751$	40.8972	+	5.88013i	1.49236	+	0.214569i	0.652673	+	0.757639i	$0.273647\pi$
$752$	−8.18807	−	7.09500i	−0.298588	−	0.258728i
$753$	−19.8780	−	28.9560i	−0.724394	−	1.05521i
$754$	−9.12150	−	2.67831i	−0.332185	−	0.0975384i
$755$	10.7769	+	23.5981i	0.392211	+	0.858823i
$756$	−10.2071	+	0.933541i	−0.371228	+	0.0339526i
$757$	−20.0019	+	31.1235i	−0.726980	+	1.13120i	0.259248	+	0.965811i	$0.416525\pi$
$757$	−20.0019	+	31.1235i	−0.726980	+	1.13120i	−0.986228	+	0.165392i	$0.947111\pi$
$758$	−8.09716			−0.294102
$759$	15.9308	+	9.05321i	0.578251	+	0.328611i
$760$	−1.03503			−0.0375446
$761$	−4.00966	+	6.23915i	−0.145350	+	0.226169i	−0.906293	−	0.422649i	$-0.861100\pi$
$761$	−4.00966	+	6.23915i	−0.145350	+	0.226169i	0.760943	+	0.648818i	$0.224737\pi$
$762$	−4.60569	+	10.9546i	−0.166847	+	0.396844i
$763$	12.2187	+	26.7551i	0.442345	+	0.968601i
$764$	−10.3199	−	3.03019i	−0.373360	−	0.109628i
$765$	4.08194	−	0.248506i	0.147583	−	0.00898475i
$766$	−9.71399	−	8.41722i	−0.350981	−	0.304127i
$767$	−28.8257	−	4.14451i	−1.04084	−	0.149650i
$768$	−0.437232	+	1.67596i	−0.0157773	+	0.0604758i
$769$	6.64976	−	5.76205i	0.239797	−	0.207785i	−0.526669	−	0.850071i	$-0.676559\pi$
$769$	6.64976	−	5.76205i	0.239797	−	0.207785i	0.766465	+	0.642286i	$0.222014\pi$
$770$	−6.87141	+	4.41599i	−0.247628	+	0.159141i
$771$	37.5315	−	1.14139i	1.35166	−	0.0411062i
$772$	−5.72508	−	6.60709i	−0.206050	−	0.237794i
$773$	−31.3272	+	9.19850i	−1.12676	+	0.330847i	−0.791434	−	0.611255i	$-0.790665\pi$
$773$	−31.3272	+	9.19850i	−1.12676	+	0.330847i	−0.335328	+	0.942102i	$0.608847\pi$
$774$	29.2137	−	10.5449i	1.05007	−	0.379030i
$775$	−4.45021	+	5.13581i	−0.159856	+	0.184484i
$776$	2.88561	−	6.31861i	0.103587	−	0.226825i
$777$	25.3673	−	23.3682i	0.910049	−	0.838329i
$778$	−31.3497	+	14.3169i	−1.12394	+	0.513287i
$779$	0.838098	+	5.82910i	0.0300280	+	0.208849i
$780$	−13.1556	+	6.49828i	−0.471045	+	0.232676i
$781$			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
$786$	−8.42820	−	0.951317i	−0.300624	−	0.0339324i
$787$	−9.70383	+	33.0482i	−0.345904	+	1.17804i	0.584466	+	0.811419i	$0.301304\pi$
$787$	−9.70383	+	33.0482i	−0.345904	+	1.17804i	−0.930370	+	0.366623i	$0.880514\pi$
$788$	−0.769921	−	0.351611i	−0.0274273	−	0.0125256i
$789$	1.03690	+	3.17137i	0.0369147	+	0.112904i
$790$	−3.75591	+	26.1229i	−0.133629	+	0.929411i
$791$	−2.03258	−	6.92232i	−0.0722701	−	0.246129i
$792$	6.17557	+	2.37820i	0.219439	+	0.0845058i
$793$	−36.7003	−	57.1067i	−1.30326	−	2.02792i
$794$	−6.85193	−	10.6618i	−0.243166	−	0.378373i
$795$	9.69976	−	1.69702i	0.344015	−	0.0601871i
$796$	−3.29589	−	11.2248i	−0.116820	−	0.397852i
$797$	4.64851	−	32.3311i	0.164659	−	1.14523i	−0.725050	−	0.688697i	$-0.758183\pi$
$797$	4.64851	−	32.3311i	0.164659	−	1.14523i	0.889708	−	0.456530i	$-0.150908\pi$
$798$	−1.79053	+	0.585428i	−0.0633841	+	0.0207239i
$799$	7.15666	+	3.26834i	0.253185	+	0.115625i
$800$	−0.415886	+	1.41638i	−0.0147038	+	0.0500765i
$801$	5.01119	−	6.54838i	0.177062	−	0.231376i
$802$	−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
$807$	−11.3124	−	22.9017i	−0.398216	−	0.806177i
$808$	−2.56880	−	17.8664i	−0.0903702	−	0.628538i
$809$	20.6777	−	9.44317i	0.726988	−	0.332004i	−0.0173118	−	0.999850i	$-0.505511\pi$
$809$	20.6777	−	9.44317i	0.726988	−	0.332004i	0.744299	+	0.667846i	$0.232784\pi$
$810$	−10.7906	−	12.9997i	−0.379144	−	0.456763i
$811$	13.6884	−	29.9734i	0.480665	−	1.05251i	−0.501615	−	0.865091i	$-0.667261\pi$
$811$	13.6884	−	29.9734i	0.480665	−	1.05251i	0.982280	−	0.187418i	$-0.0600120\pi$
$812$	2.72114	−	3.14036i	0.0954932	−	0.110205i
$813$	1.02480	+	0.834830i	0.0359414	+	0.0292788i
$814$	−21.3664	+	6.27376i	−0.748894	+	0.219895i
$815$	15.9398	+	18.3955i	0.558346	+	0.644365i
$816$	−0.0382331	−	1.25719i	−0.00133843	−	0.0440105i
$817$	4.80215	−	3.08615i	0.168006	−	0.107971i
$818$	3.34154	−	2.89546i	0.116834	−	0.101237i
$819$	−19.0826	+	18.6825i	−0.666802	+	0.652819i
$820$	−19.8454	−	2.85334i	−0.693033	−	0.0996431i
$821$	−24.4505	−	21.1865i	−0.853328	−	0.739413i	0.113854	−	0.993498i	$-0.463680\pi$
$821$	−24.4505	−	21.1865i	−0.853328	−	0.739413i	−0.967182	+	0.254084i	$0.918226\pi$
$822$	−17.3875	+	11.9363i	−0.606458	+	0.416327i
$823$	−1.63692	−	0.480642i	−0.0570593	−	0.0167541i	0.253078	−	0.967446i	$-0.418557\pi$
$823$	−1.63692	−	0.480642i	−0.0570593	−	0.0167541i	−0.310138	+	0.950692i	$0.600375\pi$
$824$	−3.73333	−	8.17486i	−0.130057	−	0.284785i
$825$	5.19920	+	2.18592i	0.181013	+	0.0761040i
$826$	6.88191	−	10.7085i	0.239452	−	0.372595i
$827$	−50.6354			−1.76076			−0.880382	−	0.474265i	$-0.842714\pi$
$827$	−50.6354			−1.76076			−0.880382	+	0.474265i	$0.842714\pi$
$828$	−12.5339	+	7.06414i	−0.435582	+	0.245496i
$829$	−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
$831$	25.4069	+	10.6819i	0.881357	+	0.370552i
$832$	1.87471	+	4.10503i	0.0649938	+	0.142316i
$833$	−2.16626	−	0.636070i	−0.0750564	−	0.0220385i
$834$	−25.7082	+	17.6484i	−0.890201	+	0.611113i
$835$	−8.53126	−	7.39238i	−0.295236	−	0.255824i
$836$	1.20389	+	0.173094i	0.0416375	+	0.00598657i
$837$	−23.2688	+	5.54667i	−0.804289	+	0.191721i
$838$	−27.9656	+	24.2323i	−0.966054	+	0.837091i
$839$	−3.32711	+	2.13820i	−0.114865	+	0.0738190i	−0.596812	−	0.802381i	$-0.703566\pi$
$839$	−3.32711	+	2.13820i	−0.114865	+	0.0738190i	0.481947	+	0.876200i	$0.339930\pi$
$840$	−0.194955	−	6.41055i	−0.00672658	−	0.221185i
$841$	−16.0850	−	18.5630i	−0.554654	−	0.640105i
$842$	−30.8720	+	9.06483i	−1.06392	+	0.312395i
$843$	−15.9752	−	13.0138i	−0.550215	−	0.448219i
$844$	6.74901	−	7.78878i	0.232311	−	0.268101i
$845$	−5.74396	+	12.5775i	−0.197598	+	0.432680i
$846$	−6.57213	−	31.8317i	−0.225955	−	1.09440i
$847$	−11.0063	+	5.02641i	−0.378181	+	0.172710i
$848$	−0.431013	−	2.99776i	−0.0148010	−	0.102944i
$849$	−6.24450	−	12.6418i	−0.214311	−	0.433866i
$850$		−	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	0.953939	−	0.300002i	$-0.0969873\pi$
$853$	31.4646	+	20.2211i	1.07733	+	0.692357i	0.123389	+	0.992358i	$0.460624\pi$
$854$	29.3693	−	4.22267i	1.00500	−	0.144497i
$855$	−2.46591	−	1.88705i	−0.0843323	−	0.0645358i
$856$	−1.80747	+	6.15569i	−0.0617781	+	0.210397i
$857$	18.4207	+	8.41246i	0.629240	+	0.287364i	0.704395	−	0.709808i	$-0.251218\pi$
$857$	18.4207	+	8.41246i	0.629240	+	0.287364i	−0.0751559	+	0.997172i	$0.523945\pi$
$858$	16.3886	−	5.35837i	0.559496	−	0.182932i
$859$	2.28940	−	15.9231i	0.0781132	−	0.543289i	−0.912761	−	0.408495i	$-0.866054\pi$
$859$	2.28940	−	15.9231i	0.0781132	−	0.543289i	0.990874	−	0.134794i	$-0.0430372\pi$
$860$	5.47527	+	18.6471i	0.186705	+	0.635859i
$861$	−35.9450	+	6.28875i	−1.22500	+	0.214320i
$862$	−8.10674	−	12.6143i	−0.276117	−	0.429646i
$863$	24.7373	+	38.4920i	0.842067	+	1.31028i	0.948762	+	0.315991i	$0.102337\pi$
$863$	24.7373	+	38.4920i	0.842067	+	1.31028i	−0.106695	+	0.994292i	$0.534027\pi$
$864$	−4.09725	+	3.19571i	−0.139391	+	0.108720i
$865$	1.27658	+	4.34762i	0.0434049	+	0.147824i
$866$	−1.58567	+	11.0285i	−0.0538831	+	0.374765i
$867$	−8.86669	−	27.1188i	−0.301129	−	0.921002i
$868$	−8.26014	−	3.77228i	−0.280368	−	0.128040i
$869$	8.73731	−	29.7566i	0.296393	−	1.00942i
$870$	6.80600	+	0.768216i	0.230745	+	0.0260449i
$871$	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
$876$	7.70862	−	3.80772i	0.260450	−	0.128651i
$877$	3.44693	+	23.9739i	0.116395	+	0.809543i	0.961473	+	0.274900i	$0.0886447\pi$
$877$	3.44693	+	23.9739i	0.116395	+	0.809543i	−0.845078	+	0.534643i	$0.820446\pi$
$878$	−13.1399	+	6.00078i	−0.443449	+	0.202517i
$879$	−37.2496	+	34.3140i	−1.25640	+	1.15738i
$880$	−1.72018	+	3.76666i	−0.0579871	+	0.126974i
$881$	−25.9870	+	29.9906i	−0.875525	+	1.01041i	0.124310	+	0.992243i	$0.460328\pi$
$881$	−25.9870	+	29.9906i	−0.875525	+	1.01041i	−0.999835	+	0.0181666i	$0.994217\pi$
$882$	3.16672	+	8.77310i	0.106629	+	0.295406i
$883$	−11.5686	+	3.39685i	−0.389315	+	0.114313i	−0.470531	−	0.882383i	$-0.655938\pi$
$883$	−11.5686	+	3.39685i	−0.389315	+	0.114313i	0.0812162	+	0.996697i	$0.474120\pi$
$884$	−2.14606	−	2.47668i	−0.0721797	−	0.0832999i
$885$	20.9720	−	0.637790i	0.704965	−	0.0214391i
$886$	15.9212	−	10.2319i	0.534882	−	0.343748i
$887$	9.06937	−	7.85865i	0.304520	−	0.263868i	−0.489173	−	0.872187i	$-0.662701\pi$
$887$	9.06937	−	7.85865i	0.304520	−	0.263868i	0.793693	+	0.608319i	$0.208156\pi$
$888$	4.41387	−	16.9188i	0.148120	−	0.567758i
$889$	−13.3957	−	1.92602i	−0.449279	−	0.0645965i
$890$	3.89939	+	3.37884i	0.130708	+	0.113259i
$891$	10.3770	+	16.9251i	0.347644	+	0.567012i
$892$	−4.06116	−	1.19246i	−0.135978	−	0.0399267i
$893$	−2.48161	−	5.43396i	−0.0830439	−	0.181841i
$894$	0.329680	−	0.784141i	0.0110261	−	0.0262256i
$895$	−19.5263	+	30.3835i	−0.652691	+	1.01561i
$896$	−1.97255			−0.0658983
$897$	−13.6945	+	34.8956i	−0.457245	+	1.16513i
$898$	22.3941			0.747299
$899$	5.24295	−	8.15819i	0.174862	−	0.272091i
$900$	−3.57313	+	2.61620i	−0.119104	+	0.0872068i
$901$	0.913616	+	2.00054i	0.0304370	+	0.0666477i
$902$	22.6059	+	6.63770i	0.752695	+	0.221011i
$903$	20.0188	+	29.1611i	0.666184	+	0.970421i
$904$	−2.76414	−	2.39514i	−0.0919338	−	0.0796611i
$905$	0.928266	+	0.133465i	0.0308566	+	0.00443651i
$906$	23.1615	+	6.04250i	0.769489	+	0.200748i
$907$	40.3808	−	34.9902i	1.34082	−	1.16183i	0.368121	−	0.929778i	$-0.380001\pi$
$907$	40.3808	−	34.9902i	1.34082	−	1.16183i	0.972703	−	0.232052i	$-0.0745441\pi$
$908$	20.7237	−	13.3183i	0.687742	−	0.441985i
$909$	26.4536	−	47.2491i	0.877412	−	1.56715i
$910$	−10.9430	−	12.6289i	−0.362756	−	0.418643i
$911$	36.6260	−	10.7543i	1.21347	−	0.356308i	0.388483	−	0.921456i	$-0.372999\pi$
$911$	36.6260	−	10.7543i	1.21347	−	0.356308i	0.824989	+	0.565149i	$0.191181\pi$
$912$	−0.603171	+	0.740426i	−0.0199730	+	0.0245180i
$913$	15.9237	−	18.3770i	0.526999	−	0.608189i
$914$	9.66008	−	21.1526i	0.319527	−	0.699667i
$915$	33.1365	+	35.9713i	1.09546	+	1.18917i
$916$	5.06772	−	2.31435i	0.167442	−	0.0764683i
$917$	−1.37468	−	9.56110i	−0.0453959	−	0.315735i
$918$	2.20099	−	3.06489i	0.0726437	−	0.101156i
$919$			5.65476i			0.186533i	0.995641	+	0.0932666i	$0.0297309\pi$
$919$			5.65476i			0.186533i	−0.995641	+	0.0932666i	$0.970269\pi$
$920$	−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
$924$	−0.845307	+	7.48899i	−0.0278085	+	0.246370i
$925$	4.19838	−	14.2984i	0.138042	−	0.470127i
$926$	−14.2453	−	6.50559i	−0.468128	−	0.213787i
$927$	6.00978	−	26.2826i	0.197387	−	0.863235i
$928$	0.299794	−	2.08512i	0.00984123	−	0.0684473i
$929$	8.38515	+	28.5572i	0.275108	+	0.936932i	0.974911	+	0.222596i	$0.0714530\pi$
$929$	8.38515	+	28.5572i	0.275108	+	0.936932i	−0.699803	+	0.714336i	$0.746729\pi$
$930$	−2.57953	−	14.7440i	−0.0845861	−	0.483474i
$931$	0.926794	+	1.44212i	0.0303744	+	0.0472636i
$932$	8.96935	+	13.9566i	0.293801	+	0.457163i
$933$	3.55957	+	20.3456i	0.116535	+	0.666086i
$934$	8.34333	+	28.4148i	0.273002	+	0.929760i
$935$	0.427940	−	2.97638i	0.0139951	−	0.0973382i
$936$	−3.01783	+	13.1979i	−0.0986409	+	0.431388i
$937$	−32.5791	−	14.8784i	−1.06431	−	0.486055i	−0.195248	−	0.980754i	$-0.562551\pi$
$937$	−32.5791	−	14.8784i	−1.06431	−	0.486055i	−0.869064	+	0.494699i	$0.835278\pi$
$938$	−3.51826	+	11.9821i	−0.114875	+	0.391230i
$939$	−4.68937	+	41.5454i	−0.153032	+	1.35578i
$940$	20.1311	−	2.89442i	0.656604	−	0.0944054i
$941$	−12.3544	−	7.93968i	−0.402741	−	0.258826i	0.323553	−	0.946210i	$-0.395123\pi$
$941$	−12.3544	−	7.93968i	−0.402741	−	0.258826i	−0.726294	+	0.687384i	$0.758759\pi$
$942$	−2.63753	+	4.39213i	−0.0859354	+	0.143103i
$943$	−42.4134	+	28.7201i	−1.38117	+	0.935255i
$944$		−	6.45315i		−	0.210032i
$945$	11.2231	−	15.6282i	0.365088	−	0.508385i
$946$	−3.25009	−	22.6048i	−0.105669	−	0.734947i
$947$	−9.02620	+	4.12213i	−0.293312	+	0.133951i	−0.556636	−	0.830756i	$-0.687908\pi$
$947$	−9.02620	+	4.12213i	−0.293312	+	0.133951i	0.263324	+	0.964707i	$0.415181\pi$
$948$	16.4986	+	17.9101i	0.535850	+	0.581692i
$949$	9.30589	−	20.3771i	0.302082	−	0.661468i
$950$	−0.533008	+	0.615125i	−0.0172931	+	0.0199573i
$951$	−16.2759	+	19.9796i	−0.527783	+	0.647883i
$952$	1.37439	−	0.403559i	0.0445444	−	0.0130794i
$953$	−26.5240	−	30.6104i	−0.859197	−	0.991567i	−0.999999	−	0.00152885i	$-0.999513\pi$
$953$	−26.5240	−	30.6104i	−0.859197	−	0.991567i	0.140801	−	0.990038i	$-0.455032\pi$
$954$	4.43859	−	7.92780i	0.143705	−	0.256672i
$955$	16.9851	−	10.9156i	0.549624	−	0.353222i
$956$	−5.87378	+	5.08966i	−0.189972	+	0.164611i
$957$	−7.78788	−	2.03175i	−0.251747	−	0.0656770i
$958$	17.7838	+	2.55693i	0.574570	+	0.0826106i
$959$	−18.1522	−	15.7289i	−0.586164	−	0.507914i
$960$	−1.84016	−	2.68054i	−0.0593909	−	0.0865140i
$961$	9.40999	+	2.76302i	0.303548	+	0.0891297i
$962$	−18.9252	−	41.4404i	−0.610173	−	1.33609i
$963$	−15.5291	+	11.3702i	−0.500418	+	0.366400i
$964$	−5.14277	+	8.00230i	−0.165637	+	0.257737i
$965$	16.4112			0.528294
$966$	−11.3878	−	11.7811i	−0.366396	−	0.379050i
$967$	−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
$969$	0.268784	−	0.639300i	0.00863457	−	0.0205373i
$970$	5.41683	+	11.8612i	0.173924	+	0.380840i
$971$	−33.5858	−	9.86169i	−1.07782	−	0.316477i	−0.305814	−	0.952091i	$-0.598929\pi$
$971$	−33.5858	−	9.86169i	−1.07782	−	0.316477i	−0.772007	+	0.635614i	$0.780747\pi$
$972$	−15.5878	+	0.143586i	−0.499979	+	0.00460552i
$973$	−26.8388	−	23.2559i	−0.860411	−	0.745550i
$974$	−0.753545	−	0.108343i	−0.0241451	−	0.00347154i
$975$	−2.91273	+	11.1648i	−0.0932821	+	0.357560i
$976$	11.3681	−	9.85050i	0.363883	−	0.315307i
$977$	6.01180	−	3.86355i	0.192335	−	0.123606i	−0.440929	−	0.897542i	$-0.645351\pi$
$977$	6.01180	−	3.86355i	0.192335	−	0.123606i	0.633264	+	0.773936i	$0.281715\pi$
$978$	22.4484	−	0.682691i	0.717821	−	0.0218300i
$979$	−3.97049	−	4.58219i	−0.126898	−	0.146448i
$980$	−5.59984	+	1.64426i	−0.178880	+	0.0525240i
$981$	15.1879	+	42.0765i	0.484911	+	1.34340i
$982$	22.8389	−	26.3575i	0.728818	−	0.841100i
$983$	−16.9093	+	37.0263i	−0.539324	+	1.18095i	0.422268	+	0.906471i	$0.361234\pi$
$983$	−16.9093	+	37.0263i	−0.539324	+	1.18095i	−0.961592	+	0.274483i	$0.911493\pi$
$984$	−13.6062	+	12.5339i	−0.433750	+	0.399567i
$985$	1.44528	−	0.660039i	0.0460506	−	0.0210306i
$986$	0.217703	+	1.51416i	0.00693308	+	0.0482207i
$987$	33.1882	−	16.3935i	1.05639	−	0.521811i
$988$			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	0.0373331	−	0.999303i	$-0.488114\pi$
$991$	−26.9519	−	17.3209i	−0.856156	−	0.550218i	−0.893489	+	0.449085i	$0.851750\pi$
$992$	−4.55670	+	0.655155i	−0.144675	+	0.0208012i
$993$	3.88397	+	0.438397i	0.123254	+	0.0139121i
$994$	1.39893	−	4.76430i	0.0443712	−	0.151114i
$995$	19.9760	+	9.12275i	0.633283	+	0.289211i
$996$	5.93349	+	18.1476i	0.188010	+	0.575028i
$997$	4.09392	−	28.4738i	0.129656	−	0.901774i	−0.816335	−	0.577579i	$-0.803997\pi$
$997$	4.09392	−	28.4738i	0.129656	−	0.901774i	0.945990	−	0.324195i	$-0.105093\pi$
$998$	0.354359	+	1.20684i	0.0112170	+	0.0382017i
$999$	41.3618	−	32.2608i	1.30863	−	1.02069i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.f.a.11.1	✓	80	69.11	even	22	inner
138.2.f.a.11.8	yes	80	23.11	odd	22	inner
138.2.f.a.113.1	yes	80	1.1	even	1	trivial
138.2.f.a.113.8	yes	80	3.2	odd	2	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)

\(f(q)\)	\(=\)	\(q+(-0.540641 + 0.841254i) q^{2} +(-1.59667 - 0.671295i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(1.80115 + 0.528864i) q^{5} +(1.42796 - 0.980277i) q^{6} +(1.49075 + 1.29175i) q^{7} +(0.989821 + 0.142315i) q^{8} +(2.09873 + 2.14368i) q^{9} +O(q^{10})\)	\(q+(-0.540641 + 0.841254i) q^{2} +(-1.59667 - 0.671295i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(1.80115 + 0.528864i) q^{5} +(1.42796 - 0.980277i) q^{6} +(1.49075 + 1.29175i) q^{7} +(0.989821 + 0.142315i) q^{8} +(2.09873 + 2.14368i) q^{9} +(-1.41868 + 1.22930i) q^{10} +(1.85571 - 1.19259i) q^{11} +(0.0526500 + 1.73125i) q^{12} +(2.95529 + 3.41059i) q^{13} +(-1.89265 + 0.555732i) q^{14} +(-2.52082 - 2.05352i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(0.301664 - 0.660552i) q^{17} +(-2.93803 + 0.606601i) q^{18} +(-0.501549 + 0.229050i) q^{19} +(-0.267151 - 1.85808i) q^{20} +(-1.51310 - 3.06323i) 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} +(-1.91194 - 4.83161i) q^{27} +(0.555732 - 1.89265i) q^{28} +(1.91619 + 0.875096i) q^{29} +(3.09039 - 1.01043i) q^{30} +(0.655155 - 4.55670i) q^{31} +(-0.281733 - 0.959493i) q^{32} +(-3.76355 + 0.658450i) q^{33} +(0.392600 + 0.610897i) q^{34} +(2.00191 + 3.11503i) q^{35} +(1.07812 - 2.79958i) q^{36} +(2.84409 + 9.68610i) q^{37} +(0.0784689 - 0.545763i) q^{38} +(-2.42912 - 7.42946i) q^{39} +(1.70755 + 0.779811i) q^{40} +(3.00908 - 10.2480i) q^{41} +(3.39500 + 0.383205i) 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} +(1.55293 - 0.767080i) q^{48} +(-0.442463 - 3.07740i) q^{49} +(1.34277 - 0.613225i) q^{50} +(-0.925084 + 0.852180i) q^{51} +(1.87471 - 4.10503i) q^{52} +(-1.98330 + 2.28885i) q^{53} +(5.09828 + 1.00375i) q^{54} +(3.97313 - 1.16662i) q^{55} +(1.29175 + 1.49075i) q^{56} +(0.954569 - 0.0290299i) q^{57} +(-1.77215 + 1.13889i) q^{58} +(-4.87697 + 4.22592i) q^{59} +(-0.820766 + 3.14608i) q^{60} +(-14.8890 - 2.14072i) q^{61} +(3.47914 + 3.01469i) q^{62} +(0.359597 + 5.90672i) q^{63} +(0.959493 + 0.281733i) q^{64} +(3.51917 + 7.70591i) q^{65} +(1.48080 - 3.52208i) q^{66} +(3.42273 - 5.32586i) q^{67} -0.726175 q^{68} +(3.85663 + 7.35707i) q^{69} -3.70284 q^{70} +(-1.36094 + 2.11766i) q^{71} +(1.77229 + 2.42054i) q^{72} +(-2.06209 - 4.51534i) q^{73} +(-9.68610 - 2.84409i) q^{74} +(1.44706 + 2.10791i) q^{75} +(0.416702 + 0.361074i) q^{76} +(4.30694 + 0.619244i) q^{77} +(7.56334 + 1.97316i) q^{78} +(10.6252 - 9.20675i) q^{79} +(-1.57919 + 1.01488i) q^{80} +(-0.190705 + 8.99798i) q^{81} +(6.99432 + 8.07188i) q^{82} +(10.5768 - 3.10563i) q^{83} +(-2.15785 + 2.64888i) q^{84} +(0.892684 - 1.03021i) q^{85} +(4.30074 - 9.41731i) q^{86} +(-2.47208 - 2.68357i) q^{87} +(2.00655 - 0.916359i) q^{88} +(-0.391167 - 2.72063i) q^{89} +(-5.61264 - 0.461244i) 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} +(-0.194269 + 1.72112i) q^{96} +(1.95701 - 6.66496i) q^{97} +(2.82809 + 1.29154i) q^{98} +(6.45116 + 1.47512i) 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

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Database

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