LMFDB - Embedded newform 169.2.i.a.3.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,2,Mod(3,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([62]))

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

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

chi := DirichletCharacter("169.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	169.i (of order $39$, degree $24$, 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:	$1.34947179416$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$14$ over $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			3.12
Character	$\chi$	$=$	169.3
Dual form			169.2.i.a.113.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.43066 - 1.07507i) q^{2} +(-0.532083 + 2.60631i) q^{3} +(0.334579 - 1.15510i) q^{4} +(-0.657900 - 0.345292i) q^{5} +(2.04075 + 4.30078i) q^{6} +(2.44433 + 0.397242i) q^{7} +(0.506036 + 1.33431i) q^{8} +(-3.74982 - 1.59765i) q^{9} +(-1.31245 + 0.213294i) q^{10} +(0.986578 - 0.420341i) q^{11} +(2.83253 + 1.48663i) q^{12} +(-2.64177 - 2.45378i) q^{13} +(3.92407 - 2.05951i) q^{14} +(1.25000 - 1.53097i) q^{15} +(4.19126 + 2.65040i) q^{16} +(-0.931036 - 0.151308i) q^{17} +(-7.08231 + 1.74563i) q^{18} +(2.05942 - 3.56703i) q^{19} +(-0.618967 + 0.644413i) q^{20} +(-2.33592 + 6.15931i) q^{21} +(0.959562 - 1.66201i) q^{22} +(-3.92310 - 6.79501i) q^{23} +(-3.74687 + 0.608926i) q^{24} +(-2.52672 - 3.66058i) q^{25} +(-6.41748 - 0.670442i) q^{26} +(1.62590 - 2.35552i) q^{27} +(1.27667 - 2.69054i) q^{28} +(-1.29617 + 0.974010i) q^{29} +(0.142421 - 3.53414i) q^{30} +(-1.92189 + 2.78434i) q^{31} +(6.00083 - 0.484437i) q^{32} +(0.570600 + 2.79499i) q^{33} +(-1.49467 + 0.784462i) q^{34} +(-1.47096 - 1.10535i) q^{35} +(-3.10005 + 3.79688i) q^{36} +(5.74077 + 0.463443i) q^{37} +(-0.888475 - 7.31725i) q^{38} +(7.80097 - 5.57966i) q^{39} +(0.127805 - 1.05257i) q^{40} +(-0.352113 + 1.72476i) q^{41} +(3.27980 + 11.3232i) q^{42} +(9.84148 - 0.794487i) q^{43} +(-0.155449 - 1.28023i) q^{44} +(1.91535 + 2.34587i) q^{45} +(-12.9178 - 5.50375i) q^{46} +(-0.593493 - 0.146283i) q^{47} +(-9.13786 + 9.51352i) q^{48} +(-0.822826 - 0.274700i) q^{49} +(-7.55028 - 2.52065i) q^{50} +(0.889745 - 2.34606i) q^{51} +(-3.71825 + 2.23053i) q^{52} +(3.97684 + 10.4861i) q^{53} +(-0.206245 - 5.11793i) q^{54} +(-0.794210 - 0.0641152i) q^{55} +(0.706874 + 3.46250i) q^{56} +(8.20101 + 7.26546i) q^{57} +(-0.807253 + 2.78696i) q^{58} +(-10.7661 + 6.80809i) q^{59} +(-1.35020 - 1.95610i) q^{60} +(2.21118 + 2.70820i) q^{61} +(0.243792 + 6.04963i) q^{62} +(-8.53112 - 5.39475i) q^{63} +(0.640694 - 0.567606i) q^{64} +(0.890746 + 2.52653i) q^{65} +(3.82115 + 3.38525i) q^{66} +(-3.11774 - 10.7637i) q^{67} +(-0.486282 + 1.02482i) q^{68} +(19.7973 - 6.60932i) q^{69} -3.29278 q^{70} +(-4.59941 + 1.53551i) q^{71} +(0.234210 - 5.81187i) q^{72} +(-1.19674 + 9.85605i) q^{73} +(8.71135 - 5.50872i) q^{74} +(10.8850 - 4.63769i) q^{75} +(-3.43124 - 3.57230i) q^{76} +(2.57849 - 0.635542i) q^{77} +(5.16201 - 16.3692i) q^{78} +(7.82221 + 1.92800i) q^{79} +(-1.84227 - 3.19091i) q^{80} +(-3.19647 - 3.32787i) q^{81} +(1.35049 + 2.84610i) q^{82} +(-1.36646 + 1.21058i) q^{83} +(6.33308 + 4.75900i) q^{84} +(0.560283 + 0.421025i) q^{85} +(13.2257 - 11.7170i) q^{86} +(-1.84890 - 3.89648i) q^{87} +(1.06011 + 1.10369i) q^{88} +(-6.18653 - 10.7154i) q^{89} +(5.26220 + 1.29702i) q^{90} +(-5.48260 - 7.04727i) q^{91} +(-9.16151 + 2.25811i) q^{92} +(-6.23426 - 6.49055i) q^{93} +(-1.00635 + 0.428767i) q^{94} +(-2.58656 + 1.63564i) q^{95} +(-1.93034 + 15.8978i) q^{96} +(0.281016 - 6.97335i) q^{97} +(-1.47251 + 0.491596i) q^{98} -4.37104 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 26 q^{2} - 26 q^{3} - 12 q^{4} - 26 q^{5} - 26 q^{6} - 26 q^{7} - 26 q^{8} - 12 q^{9} - 22 q^{10} - 26 q^{11} - 34 q^{12} - 13 q^{13} - 30 q^{14} + 26 q^{15} - 8 q^{16} - 24 q^{17} - 104 q^{18}+ \cdots - 52 q^{99}+O(q^{100}) $ 336 * q - 26 * q^2 - 26 * q^3 - 12 * q^4 - 26 * q^5 - 26 * q^6 - 26 * q^7 - 26 * q^8 - 12 * q^9 - 22 * q^10 - 26 * q^11 - 34 * q^12 - 13 * q^13 - 30 * q^14 + 26 * q^15 - 8 * q^16 - 24 * q^17 - 104 * q^18 - 13 * q^19 - 26 * q^20 - 26 * q^21 + 19 * q^22 + 67 * q^23 + 52 * q^24 - 58 * q^25 - 26 * q^26 - 38 * q^27 - 26 * q^28 - 22 * q^29 - 120 * q^30 + 26 * q^31 + 117 * q^32 - 26 * q^33 + 39 * q^34 - 18 * q^35 - 2 * q^36 - 26 * q^37 + 41 * q^38 + 26 * q^39 + 67 * q^40 - 26 * q^41 - 270 * q^42 - 16 * q^43 + 39 * q^45 - 39 * q^47 + 31 * q^48 + 72 * q^49 - 26 * q^50 + 19 * q^51 + 39 * q^52 + 36 * q^53 - 182 * q^54 + 116 * q^55 - 10 * q^56 + 52 * q^57 + 26 * q^58 - 234 * q^59 + 78 * q^60 - 16 * q^61 + 53 * q^62 + 39 * q^63 - 82 * q^64 - 26 * q^65 - 135 * q^66 + 130 * q^67 + 51 * q^68 + 25 * q^69 + 156 * q^70 - 104 * q^71 + 143 * q^72 - 26 * q^73 + 79 * q^74 + 152 * q^75 - 104 * q^76 - 58 * q^77 + 104 * q^78 - 46 * q^79 - 13 * q^80 + 4 * q^81 + 118 * q^82 - 286 * q^83 + 221 * q^84 + 130 * q^85 + 52 * q^86 + 90 * q^87 - 204 * q^88 + 117 * q^89 - 86 * q^90 + 26 * q^91 - 22 * q^92 + 39 * q^93 + 126 * q^94 - 47 * q^95 + 143 * q^96 + 52 * q^97 - 26 * q^98 - 52 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{31}{39}\right)$

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 $

$2$	1.43066	−	1.07507i	1.01163	−	0.760192i	0.0406081	−	0.999175i	$-0.487070\pi$
$2$	1.43066	−	1.07507i	1.01163	−	0.760192i	0.971024	+	0.238983i	$0.0768141\pi$
$3$	−0.532083	+	2.60631i	−0.307198	+	1.50476i	0.474030	+	0.880509i	$0.342799\pi$
$3$	−0.532083	+	2.60631i	−0.307198	+	1.50476i	−0.781228	+	0.624246i	$0.785406\pi$
$4$	0.334579	−	1.15510i	0.167290	−	0.577551i
$5$	−0.657900	−	0.345292i	−0.294222	−	0.154419i	0.311154	−	0.950360i	$-0.399285\pi$
$5$	−0.657900	−	0.345292i	−0.294222	−	0.154419i	−0.605375	+	0.795940i	$0.706977\pi$
$6$	2.04075	+	4.30078i	0.833132	+	1.75579i
$7$	2.44433	+	0.397242i	0.923868	+	0.150143i	0.603695	−	0.797216i	$-0.293695\pi$
$7$	2.44433	+	0.397242i	0.923868	+	0.150143i	0.320174	+	0.947359i	$0.396259\pi$
$8$	0.506036	+	1.33431i	0.178911	+	0.471749i
$9$	−3.74982	−	1.59765i	−1.24994	−	0.532549i
$10$	−1.31245	+	0.213294i	−0.415032	+	0.0674493i
$11$	0.986578	−	0.420341i	0.297464	−	0.126738i	−0.238078	−	0.971246i	$-0.576517\pi$
$11$	0.986578	−	0.420341i	0.297464	−	0.126738i	0.535542	+	0.844508i	$0.320107\pi$
$12$	2.83253	+	1.48663i	0.817681	+	0.429152i
$13$	−2.64177	−	2.45378i	−0.732695	−	0.680557i
$13$	−2.64177	−	2.45378i	−0.732695	−	0.680557i
$14$	3.92407	−	2.05951i	1.04875	−	0.550428i
$15$	1.25000	−	1.53097i	0.322748	−	0.395294i
$16$	4.19126	+	2.65040i	1.04782	+	0.662599i
$17$	−0.931036	−	0.151308i	−0.225810	−	0.0366976i	0.0464536	−	0.998920i	$-0.485208\pi$
$17$	−0.931036	−	0.151308i	−0.225810	−	0.0366976i	−0.272263	+	0.962223i	$0.587772\pi$
$18$	−7.08231	+	1.74563i	−1.66932	+	0.411450i
$19$	2.05942	−	3.56703i	0.472464	−	0.818332i	−0.527039	−	0.849841i	$-0.676698\pi$
$19$	2.05942	−	3.56703i	0.472464	−	0.818332i	0.999503	+	0.0315087i	$0.0100312\pi$
$20$	−0.618967	+	0.644413i	−0.138405	+	0.144095i
$21$	−2.33592	+	6.15931i	−0.509739	+	1.34407i
$22$	0.959562	−	1.66201i	0.204579	−	0.354342i
$23$	−3.92310	−	6.79501i	−0.818023	−	1.41686i	−0.907137	−	0.420836i	$-0.861737\pi$
$23$	−3.92310	−	6.79501i	−0.818023	−	1.41686i	0.0891139	−	0.996021i	$-0.471596\pi$
$24$	−3.74687	+	0.608926i	−0.764827	+	0.124297i
$25$	−2.52672	−	3.66058i	−0.505344	−	0.732117i
$26$	−6.41748	−	0.670442i	−1.25857	−	0.131485i
$27$	1.62590	−	2.35552i	0.312905	−	0.453321i
$28$	1.27667	−	2.69054i	0.241269	−	0.508463i
$29$	−1.29617	+	0.974010i	−0.240693	+	0.180869i	−0.714243	−	0.699898i	$-0.753229\pi$
$29$	−1.29617	+	0.974010i	−0.240693	+	0.180869i	0.473550	+	0.880767i	$0.342972\pi$
$30$	0.142421	−	3.53414i	0.0260024	−	0.645243i
$31$	−1.92189	+	2.78434i	−0.345182	+	0.500082i	−0.956671	−	0.291170i	$-0.905955\pi$
$31$	−1.92189	+	2.78434i	−0.345182	+	0.500082i	0.611489	+	0.791253i	$0.290571\pi$
$32$	6.00083	−	0.484437i	1.06081	−	0.0856372i
$33$	0.570600	+	2.79499i	0.0993288	+	0.486545i
$34$	−1.49467	+	0.784462i	−0.256333	+	0.134534i
$35$	−1.47096	−	1.10535i	−0.248637	−	0.186839i
$36$	−3.10005	+	3.79688i	−0.516676	+	0.632813i
$37$	5.74077	+	0.463443i	0.943777	+	0.0761896i	0.542766	−	0.839884i	$-0.317377\pi$
$37$	5.74077	+	0.463443i	0.943777	+	0.0761896i	0.401011	+	0.916073i	$0.368659\pi$
$38$	−0.888475	−	7.31725i	−0.144130	−	1.18701i
$39$	7.80097	−	5.57966i	1.24915	−	0.893461i
$40$	0.127805	−	1.05257i	0.0202078	−	0.166426i
$41$	−0.352113	+	1.72476i	−0.0549907	+	0.269363i	−0.997985	−	0.0634457i	$-0.979791\pi$
$41$	−0.352113	+	1.72476i	−0.0549907	+	0.269363i	0.942995	+	0.332808i	$0.107996\pi$
$42$	3.27980	+	11.3232i	0.506084	+	1.74721i
$43$	9.84148	−	0.794487i	1.50081	−	0.121158i	0.697443	−	0.716640i	$-0.254321\pi$
$43$	9.84148	−	0.794487i	1.50081	−	0.121158i	0.803369	+	0.595482i	$0.203039\pi$
$44$	−0.155449	−	1.28023i	−0.0234348	−	0.193003i
$45$	1.91535	+	2.34587i	0.285523	+	0.349702i
$46$	−12.9178	−	5.50375i	−1.90462	−	0.811483i
$47$	−0.593493	−	0.146283i	−0.0865698	−	0.0213375i	0.195793	−	0.980645i	$-0.437272\pi$
$47$	−0.593493	−	0.146283i	−0.0865698	−	0.0213375i	−0.282363	+	0.959308i	$0.591118\pi$
$48$	−9.13786	+	9.51352i	−1.31894	+	1.37316i
$49$	−0.822826	−	0.274700i	−0.117547	−	0.0392428i
$50$	−7.55028	−	2.52065i	−1.06777	−	0.356474i
$51$	0.889745	−	2.34606i	0.124589	−	0.328515i
$52$	−3.71825	+	2.23053i	−0.515628	+	0.309318i
$53$	3.97684	+	10.4861i	0.546261	+	1.44037i	0.869442	+	0.494035i	$0.164478\pi$
$53$	3.97684	+	10.4861i	0.546261	+	1.44037i	−0.323181	+	0.946337i	$0.604752\pi$
$54$	−0.206245	−	5.11793i	−0.0280664	−	0.696461i
$55$	−0.794210	−	0.0641152i	−0.107091	−	0.00864530i
$56$	0.706874	+	3.46250i	0.0944600	+	0.462696i
$57$	8.20101	+	7.26546i	1.08625	+	0.962333i
$58$	−0.807253	+	2.78696i	−0.105998	+	0.365946i
$59$	−10.7661	+	6.80809i	−1.40163	+	0.886337i	−0.999571	−	0.0292763i	$-0.990680\pi$
$59$	−10.7661	+	6.80809i	−1.40163	+	0.886337i	−0.402059	+	0.915614i	$0.631705\pi$
$60$	−1.35020	−	1.95610i	−0.174310	−	0.252532i
$61$	2.21118	+	2.70820i	0.283112	+	0.346749i	0.896509	−	0.443025i	$-0.146095\pi$
$61$	2.21118	+	2.70820i	0.283112	+	0.346749i	−0.613397	+	0.789775i	$0.710197\pi$
$62$	0.243792	+	6.04963i	0.0309616	+	0.768304i
$63$	−8.53112	−	5.39475i	−1.07482	−	0.679675i
$64$	0.640694	−	0.567606i	0.0800868	−	0.0709507i
$65$	0.890746	+	2.52653i	0.110483	+	0.313377i
$66$	3.82115	+	3.38525i	0.470351	+	0.416695i
$67$	−3.11774	−	10.7637i	−0.380893	−	1.31500i	−0.890655	−	0.454680i	$-0.849754\pi$
$67$	−3.11774	−	10.7637i	−0.380893	−	1.31500i	0.509762	−	0.860315i	$-0.329733\pi$
$68$	−0.486282	+	1.02482i	−0.0589703	+	0.124277i
$69$	19.7973	−	6.60932i	2.38332	−	0.795669i
$70$	−3.29278			−0.393562
$71$	−4.59941	+	1.53551i	−0.545849	+	0.182231i	−0.576201	−	0.817308i	$-0.695465\pi$
$71$	−4.59941	+	1.53551i	−0.545849	+	0.182231i	0.0303517	+	0.999539i	$0.490337\pi$
$72$	0.234210	−	5.81187i	0.0276019	−	0.684935i
$73$	−1.19674	+	9.85605i	−0.140068	+	1.15356i	0.737923	+	0.674885i	$0.235807\pi$
$73$	−1.19674	+	9.85605i	−0.140068	+	1.15356i	−0.877991	+	0.478678i	$0.841116\pi$
$74$	8.71135	−	5.50872i	1.01267	−	0.640376i
$75$	10.8850	−	4.63769i	1.25690	−	0.535514i
$76$	−3.43124	−	3.57230i	−0.393590	−	0.409771i
$77$	2.57849	−	0.635542i	0.293847	−	0.0724267i
$78$	5.16201	−	16.3692i	0.584483	−	1.85345i
$79$	7.82221	+	1.92800i	0.880068	+	0.216917i	0.653362	−	0.757046i	$-0.273358\pi$
$79$	7.82221	+	1.92800i	0.880068	+	0.216917i	0.226706	+	0.973963i	$0.427204\pi$
$80$	−1.84227	−	3.19091i	−0.205972	−	0.356754i
$81$	−3.19647	−	3.32787i	−0.355163	−	0.369764i
$82$	1.35049	+	2.84610i	0.149137	+	0.314299i
$83$	−1.36646	+	1.21058i	−0.149988	+	0.132878i	−0.734780	−	0.678305i	$-0.762715\pi$
$83$	−1.36646	+	1.21058i	−0.149988	+	0.132878i	0.584792	+	0.811183i	$0.301176\pi$
$84$	6.33308	+	4.75900i	0.690996	+	0.519250i
$85$	0.560283	+	0.421025i	0.0607712	+	0.0456666i
$86$	13.2257	−	11.7170i	1.42617	−	1.26347i
$87$	−1.84890	−	3.89648i	−0.198223	−	0.417747i
$88$	1.06011	+	1.10369i	0.113008	+	0.117654i
$89$	−6.18653	−	10.7154i	−0.655770	−	1.13583i	−0.981700	−	0.190434i	$-0.939011\pi$
$89$	−6.18653	−	10.7154i	−0.655770	−	1.13583i	0.325930	−	0.945394i	$-0.394323\pi$
$90$	5.26220	+	1.29702i	0.554685	+	0.136718i
$91$	−5.48260	−	7.04727i	−0.574733	−	0.738755i
$92$	−9.16151	+	2.25811i	−0.955154	+	0.235424i
$93$	−6.23426	−	6.49055i	−0.646462	−	0.673039i
$94$	−1.00635	+	0.428767i	−0.103797	+	0.0442239i
$95$	−2.58656	+	1.63564i	−0.265376	+	0.167813i
$96$	−1.93034	+	15.8978i	−0.197015	+	1.62256i
$97$	0.281016	−	6.97335i	0.0285329	−	0.708036i	−0.920105	−	0.391672i	$-0.871897\pi$
$97$	0.281016	−	6.97335i	0.0285329	−	0.708036i	0.948638	−	0.316364i	$-0.102462\pi$
$98$	−1.47251	+	0.491596i	−0.148746	+	0.0496587i
$99$	−4.37104			−0.439306
$100$	−5.07373	+	1.69386i	−0.507373	+	0.169386i
$101$	−8.05077	+	16.9666i	−0.801082	+	1.68824i	−0.0785457	+	0.996911i	$0.525028\pi$
$101$	−8.05077	+	16.9666i	−0.801082	+	1.68824i	−0.722536	+	0.691333i	$0.757024\pi$
$102$	−1.24927	−	4.31297i	−0.123696	−	0.427048i
$103$	6.49381	+	5.75301i	0.639854	+	0.566861i	0.919426	−	0.393264i	$-0.128654\pi$
$103$	6.49381	+	5.75301i	0.639854	+	0.566861i	−0.279572	+	0.960125i	$0.590193\pi$
$104$	1.93727	−	4.76663i	0.189965	−	0.467407i
$105$	3.66356	−	3.24563i	0.357527	−	0.316742i
$106$	16.9628	+	10.7266i	1.64757	+	1.04186i
$107$	−0.564488	−	14.0076i	−0.0545711	−	1.35417i	−0.762089	−	0.647472i	$-0.775826\pi$
$107$	−0.564488	−	14.0076i	−0.0545711	−	1.35417i	0.707518	−	0.706695i	$-0.249815\pi$
$108$	−2.17688	−	2.66619i	−0.209470	−	0.256554i
$109$	6.29872	+	9.12528i	0.603308	+	0.874043i	0.999017	−	0.0443332i	$-0.0141163\pi$
$109$	6.29872	+	9.12528i	0.603308	+	0.874043i	−0.395709	+	0.918376i	$0.629501\pi$
$110$	−1.20518	+	0.762107i	−0.114909	+	0.0726640i
$111$	−4.26244	+	14.7157i	−0.404573	+	1.39675i
$112$	9.19197	+	8.14337i	0.868560	+	0.769477i
$113$	−3.21345	−	15.7405i	−0.302296	−	1.48075i	−0.792894	−	0.609360i	$-0.791427\pi$
$113$	−3.21345	−	15.7405i	−0.302296	−	1.48075i	0.490598	−	0.871386i	$-0.336779\pi$
$114$	19.5438	+	1.57774i	1.83044	+	0.147769i
$115$	0.234742	+	5.82505i	0.0218898	+	0.543189i
$116$	0.691408	+	1.82309i	0.0641957	+	0.169270i
$117$	5.98587	+	13.4219i	0.553393	+	1.24085i
$118$	−8.08351	+	21.3145i	−0.744147	+	1.96216i
$119$	−2.21565	−	0.739693i	−0.203108	−	0.0678075i
$120$	2.67532	+	0.893154i	0.244223	+	0.0815335i
$121$	−6.82332	+	7.10383i	−0.620302	+	0.645803i
$122$	6.07496	+	1.49734i	0.550001	+	0.135563i
$123$	−4.30791	−	1.83543i	−0.388432	−	0.165495i
$124$	2.57317	+	3.15156i	0.231078	+	0.283019i
$125$	0.846153	+	6.96870i	0.0756823	+	0.623299i
$126$	−18.0049	+	1.45351i	−1.60401	+	0.129489i
$127$	−4.50920	−	15.5675i	−0.400126	−	1.38140i	−0.867544	−	0.497360i	$-0.834303\pi$
$127$	−4.50920	−	15.5675i	−0.400126	−	1.38140i	0.467418	−	0.884037i	$-0.345184\pi$
$128$	−2.10205	+	10.2965i	−0.185797	+	0.910093i
$129$	−3.16580	+	26.0727i	−0.278733	+	2.29557i
$130$	3.99056	+	2.65699i	0.349995	+	0.233034i
$131$	−0.484839	−	3.99301i	−0.0423605	−	0.348870i	−0.998443	−	0.0557740i	$-0.982237\pi$
$131$	−0.484839	−	3.99301i	−0.0423605	−	0.348870i	0.956083	−	0.293096i	$-0.0946857\pi$
$132$	3.41940	+	0.276043i	0.297621	+	0.0240264i
$133$	6.45088	−	7.90089i	0.559362	−	0.685094i
$134$	−16.0322	−	12.0474i	−1.38497	−	1.04074i
$135$	−1.88302	+	0.988287i	−0.162065	+	0.0850582i
$136$	−0.269246	−	1.31886i	−0.0230877	−	0.113091i
$137$	−12.9976	+	1.04928i	−1.11046	+	0.0896456i	−0.622057	−	0.782972i	$-0.713703\pi$
$137$	−12.9976	+	1.04928i	−1.11046	+	0.0896456i	−0.488404	+	0.872618i	$0.662421\pi$
$138$	21.2178	−	30.7393i	1.80618	−	2.61670i
$139$	−0.465818	+	11.5592i	−0.0395102	+	0.980435i	0.850914	+	0.525304i	$0.176048\pi$
$139$	−0.465818	+	11.5592i	−0.0395102	+	0.980435i	−0.890425	+	0.455131i	$0.849593\pi$
$140$	−1.76895	+	1.32928i	−0.149503	+	0.112344i
$141$	0.697046	−	1.46899i	0.0587018	−	0.123712i
$142$	−4.92942	+	7.14150i	−0.413668	+	0.599301i
$143$	−3.63774	−	1.31040i	−0.304203	−	0.109581i
$144$	−11.4821	−	16.6347i	−0.956839	−	1.38622i
$145$	1.18907	−	0.193243i	0.0987469	−	0.0160479i
$146$	8.88384	+	15.3873i	0.735232	+	1.27346i
$147$	1.15376	−	1.99838i	0.0951609	−	0.164823i
$148$	2.45607	−	6.47611i	0.201887	−	0.532333i
$149$	3.81917	−	3.97618i	0.312879	−	0.325741i	−0.546132	−	0.837699i	$-0.683900\pi$
$149$	3.81917	−	3.97618i	0.312879	−	0.325741i	0.859010	+	0.511958i	$0.171080\pi$
$150$	10.5870	−	18.3372i	0.864424	−	1.49723i
$151$	−1.78649	+	0.440330i	−0.145382	+	0.0358336i	−0.311335	−	0.950300i	$-0.600776\pi$
$151$	−1.78649	+	0.440330i	−0.145382	+	0.0358336i	0.165953	+	0.986134i	$0.446930\pi$
$152$	5.80165	+	0.942860i	0.470576	+	0.0764760i
$153$	3.24948	+	2.05485i	0.262705	+	0.166124i
$154$	3.00570	−	3.68132i	0.242206	−	0.296649i
$155$	2.22582	−	1.16820i	0.178782	−	0.0938323i
$156$	−3.83503	−	10.8777i	−0.307048	−	0.870917i
$157$	−13.9445	−	7.31865i	−1.11289	−	0.584092i	−0.194954	−	0.980812i	$-0.562456\pi$
$157$	−13.9445	−	7.31865i	−1.11289	−	0.584092i	−0.917939	+	0.396721i	$0.870148\pi$
$158$	13.2637	−	5.65113i	1.05520	−	0.449580i
$159$	−29.4460	+	4.78544i	−2.33522	+	0.379510i
$160$	−4.11522	−	1.75333i	−0.325337	−	0.138613i
$161$	−6.89008	−	18.1676i	−0.543014	−	1.43181i
$162$	−8.15078	−	1.32463i	−0.640386	−	0.104073i
$163$	7.09054	+	14.9430i	0.555374	+	1.17043i	0.965981	+	0.258613i	$0.0832655\pi$
$163$	7.09054	+	14.9430i	0.555374	+	1.17043i	−0.410607	+	0.911812i	$0.634683\pi$
$164$	1.87446	+	0.983795i	0.146371	+	0.0768215i
$165$	0.589690	−	2.03584i	0.0459073	−	0.158490i
$166$	−0.653482	+	3.20097i	−0.0507201	+	0.248443i
$167$	0.513690	−	0.386013i	0.0397505	−	0.0298706i	−0.580681	−	0.814131i	$-0.697214\pi$
$167$	0.513690	−	0.386013i	0.0397505	−	0.0298706i	0.620432	+	0.784260i	$0.286957\pi$
$168$	−9.40047			−0.725262
$169$	0.957889	+	12.9647i	0.0736837	+	0.997282i
$170$	1.25421			0.0961935
$171$	−13.4213	+	10.0855i	−1.02635	+	0.771255i
$172$	2.37504	−	11.6337i	0.181095	−	0.887064i
$173$	0.599250	−	2.06885i	0.0455602	−	0.157292i	−0.934513	−	0.355929i	$-0.884164\pi$
$173$	0.599250	−	2.06885i	0.0455602	−	0.157292i	0.980073	+	0.198637i	$0.0636516\pi$
$174$	−6.83417	−	3.58685i	−0.518097	−	0.271918i
$175$	−4.72199	−	9.95138i	−0.356949	−	0.752254i
$176$	5.24908	+	0.853058i	0.395664	+	0.0643017i
$177$	−12.0155	−	31.6824i	−0.903143	−	2.38139i
$178$	−20.3707	−	8.67913i	−1.52685	−	0.650528i
$179$	25.6314	−	4.16551i	1.91578	−	0.311345i	0.919189	−	0.393817i	$-0.128846\pi$
$179$	25.6314	−	4.16551i	1.91578	−	0.311345i	0.996593	+	0.0824726i	$0.0262817\pi$
$180$	3.35056	−	1.42754i	0.249736	−	0.106402i
$181$	13.0249	+	6.83600i	0.968133	+	0.508116i	0.873197	−	0.487368i	$-0.162043\pi$
$181$	13.0249	+	6.83600i	0.968133	+	0.508116i	0.0949366	+	0.995483i	$0.469735\pi$
$182$	−15.4201	−	4.18807i	−1.14301	−	0.310440i
$183$	−8.23494	+	4.32203i	−0.608744	+	0.319494i
$184$	7.08140	−	8.67313i	0.522047	−	0.639392i
$185$	−3.61683	−	2.28714i	−0.265915	−	0.168154i
$186$	−15.8969	−	2.58350i	−1.16562	−	0.189432i
$187$	−0.982141	+	0.242076i	−0.0718213	+	0.0177023i
$188$	−0.367542	+	0.636601i	−0.0268057	+	0.0464289i
$189$	4.90994	−	5.11179i	0.357146	−	0.371828i
$190$	−1.94206	+	5.12080i	−0.140892	+	0.371502i
$191$	−2.01270	+	3.48610i	−0.145634	+	0.252245i	−0.929609	−	0.368547i	$-0.879855\pi$
$191$	−2.01270	+	3.48610i	−0.145634	+	0.252245i	0.783975	+	0.620792i	$0.213189\pi$
$192$	1.13846	+	1.97186i	0.0821610	+	0.142307i
$193$	19.0658	−	3.09850i	1.37239	−	0.223035i	0.570888	−	0.821028i	$-0.306599\pi$
$193$	19.0658	−	3.09850i	1.37239	−	0.223035i	0.801501	+	0.597993i	$0.204035\pi$
$194$	−7.09483	−	10.2786i	−0.509379	−	0.737963i
$195$	−7.05887	+	0.977242i	−0.505496	+	0.0699818i
$196$	−0.592606	+	0.858538i	−0.0423290	+	0.0613242i
$197$	−10.5112	+	22.1518i	−0.748890	+	1.57825i	0.0654434	+	0.997856i	$0.479154\pi$
$197$	−10.5112	+	22.1518i	−0.748890	+	1.57825i	−0.814334	+	0.580397i	$0.802897\pi$
$198$	−6.25349	+	4.69919i	−0.444416	+	0.333957i
$199$	−0.0284068	+	0.704908i	−0.00201371	+	0.0499696i	−0.999883	−	0.0152686i	$-0.995140\pi$
$199$	−0.0284068	+	0.704908i	−0.00201371	+	0.0499696i	0.997870	+	0.0652381i	$0.0207807\pi$
$200$	3.60573	−	5.22380i	0.254964	−	0.369379i
$201$	29.7125	−	2.39864i	2.09576	−	0.169187i
$202$	6.72245	+	32.9287i	0.472990	+	2.31686i
$203$	−3.55519	+	1.86591i	−0.249525	+	0.130961i
$204$	−2.41225	−	1.81269i	−0.168891	−	0.126914i
$205$	0.827202	−	1.01314i	0.0577743	−	0.0707607i
$206$	15.4754	+	1.24930i	1.07822	+	0.0870429i
$207$	3.85488	+	31.7478i	0.267932	+	2.20662i
$208$	−4.56886	−	17.2862i	−0.316793	−	1.19858i
$209$	0.532412	−	4.38481i	0.0368277	−	0.303304i
$210$	1.75203	−	8.58201i	0.120902	−	0.592215i
$211$	0.619875	+	2.14006i	0.0426740	+	0.147328i	0.979026	−	0.203734i	$-0.0653079\pi$
$211$	0.619875	+	2.14006i	0.0426740	+	0.147328i	−0.936352	+	0.351062i	$0.885821\pi$
$212$	13.4430	−	1.08523i	0.923271	−	0.0745342i
$213$	−1.55475	−	12.8045i	−0.106530	−	0.877351i
$214$	−15.8668	−	19.4333i	−1.08463	−	1.32843i
$215$	−6.74904	−	2.87550i	−0.460281	−	0.196107i
$216$	3.96575	+	0.977471i	0.269835	+	0.0665085i
$217$	−5.80379	+	6.04238i	−0.393987	+	0.410184i
$218$	18.8217	+	6.28361i	1.27477	+	0.425580i
$219$	−25.0512	−	8.36331i	−1.69280	−	0.565140i
$220$	−0.339786	+	0.895941i	−0.0229083	+	0.0604043i
$221$	2.08831	+	2.68428i	0.140475	+	0.180564i
$222$	9.72230	+	25.6356i	0.652518	+	1.72055i
$223$	0.208686	+	5.17850i	0.0139747	+	0.346778i	0.991017	+	0.133734i	$0.0426967\pi$
$223$	0.208686	+	5.17850i	0.0139747	+	0.346778i	−0.977043	+	0.213044i	$0.931662\pi$
$224$	14.8604	+	1.19966i	0.992904	+	0.0801555i
$225$	3.62641	+	17.7633i	0.241760	+	1.18422i
$226$	−21.5196	−	19.0647i	−1.43146	−	1.26817i
$227$	−0.588998	+	2.03346i	−0.0390932	+	0.134965i	−0.977691	−	0.210047i	$-0.932638\pi$
$227$	−0.588998	+	2.03346i	−0.0390932	+	0.134965i	0.938598	+	0.345013i	$0.112125\pi$
$228$	11.1362	−	7.04212i	0.737514	−	0.466376i
$229$	13.1300	+	19.0220i	0.867652	+	1.25701i	0.965129	+	0.261774i	$0.0843074\pi$
$229$	13.1300	+	19.0220i	0.867652	+	1.25701i	−0.0974769	+	0.995238i	$0.531077\pi$
$230$	6.59820	+	8.08132i	0.435072	+	0.532867i
$231$	0.284449	+	7.05852i	0.0187154	+	0.464417i
$232$	−1.95554	−	1.23661i	−0.128387	−	0.0811872i
$233$	1.06532	−	0.943787i	0.0697911	−	0.0618295i	−0.627506	−	0.778612i	$-0.715924\pi$
$233$	1.06532	−	0.943787i	0.0697911	−	0.0618295i	0.697297	+	0.716782i	$0.254386\pi$
$234$	22.9932	+	12.7669i	1.50312	+	0.834599i
$235$	0.339948	+	0.301168i	0.0221758	+	0.0196460i
$236$	4.26191	+	14.7138i	0.277427	+	0.957788i
$237$	−9.18704	+	19.3613i	−0.596762	+	1.25765i
$238$	−3.96508	+	1.32374i	−0.257018	+	0.0858051i
$239$	3.57767			0.231420			0.115710	−	0.993283i	$-0.463086\pi$
$239$	3.57767			0.231420			0.115710	+	0.993283i	$0.463086\pi$
$240$	9.29674	−	3.10371i	0.600102	−	0.200343i
$241$	0.425687	−	10.5633i	0.0274209	−	0.680443i	−0.925772	−	0.378081i	$-0.876584\pi$
$241$	0.425687	−	10.5633i	0.0274209	−	0.680443i	0.953193	−	0.302361i	$-0.0977750\pi$
$242$	−2.12473	+	17.4988i	−0.136583	+	1.12486i
$243$	17.6315	−	11.1495i	1.13106	−	0.715240i
$244$	3.86806	−	1.64803i	0.247627	−	0.105504i
$245$	0.446485	+	0.464840i	0.0285249	+	0.0296976i
$246$	−8.13640	+	2.00544i	−0.518758	+	0.127862i
$247$	−14.1932	+	4.36988i	−0.903094	+	0.278049i
$248$	−4.68771	−	1.15542i	−0.297670	−	0.0733690i
$249$	−2.42807	−	4.20554i	−0.153873	−	0.266515i
$250$	8.70243	+	9.06019i	0.550390	+	0.573017i
$251$	−0.574490	−	1.21071i	−0.0362615	−	0.0764195i	0.884511	−	0.466519i	$-0.154492\pi$
$251$	−0.574490	−	1.21071i	−0.0362615	−	0.0764195i	−0.920773	+	0.390099i	$0.872441\pi$
$252$	−9.08582	+	8.04934i	−0.572353	+	0.507060i
$253$	−6.72667	−	5.05476i	−0.422902	−	0.317790i
$254$	−23.1874	−	17.4242i	−1.45491	−	1.09329i
$255$	−1.39544	+	1.23625i	−0.0873859	+	0.0774171i
$256$	8.79609	+	18.5374i	0.549755	+	1.15858i
$257$	−9.21892	−	9.59791i	−0.575061	−	0.598701i	0.368612	−	0.929584i	$-0.379833\pi$
$257$	−9.21892	−	9.59791i	−0.575061	−	0.598701i	−0.943672	+	0.330882i	$0.892654\pi$
$258$	23.5009	+	40.7048i	1.46310	+	2.53417i
$259$	13.8482	+	3.41328i	0.860486	+	0.212091i
$260$	3.21642	−	0.183579i	0.199474	−	0.0113851i
$261$	6.41653	−	1.58153i	0.397173	−	0.0978944i
$262$	−4.98642	−	5.19141i	−0.308062	−	0.320726i
$263$	0.667754	−	0.284503i	0.0411755	−	0.0175432i	−0.371281	−	0.928521i	$-0.621081\pi$
$263$	0.667754	−	0.284503i	0.0411755	−	0.0175432i	0.412456	+	0.910977i	$0.364671\pi$
$264$	−3.44062	+	2.17572i	−0.211756	+	0.133906i
$265$	1.00440	−	8.27195i	0.0616996	−	0.508142i
$266$	0.734994	−	18.2387i	0.0450654	−	1.11829i
$267$	31.2194	−	10.4226i	1.91059	−	0.637850i
$268$	−13.4763			−0.823196
$269$	15.6040	−	5.20936i	0.951390	−	0.317621i	0.201728	−	0.979442i	$-0.435344\pi$
$269$	15.6040	−	5.20936i	0.951390	−	0.317621i	0.749662	+	0.661821i	$0.230216\pi$
$270$	−1.63149	+	3.43830i	−0.0992895	+	0.209248i
$271$	−5.95705	−	20.5661i	−0.361865	−	1.24930i	−0.910594	−	0.413302i	$-0.864375\pi$
$271$	−5.95705	−	20.5661i	−0.361865	−	1.24930i	0.548729	−	0.836000i	$-0.315112\pi$
$272$	−3.50119	−	3.10179i	−0.212291	−	0.188073i
$273$	21.2846	−	10.5396i	1.28820	−	0.637888i
$274$	−17.4671	+	15.4745i	−1.05523	+	0.934851i
$275$	−4.03150	−	2.54937i	−0.243109	−	0.153733i
$276$	−1.01066	−	25.0793i	−0.0608346	−	1.50959i
$277$	3.20196	+	3.92169i	0.192387	+	0.235632i	0.861786	−	0.507271i	$-0.169346\pi$
$277$	3.20196	+	3.92169i	0.192387	+	0.235632i	−0.669399	+	0.742903i	$0.733448\pi$
$278$	11.7605	+	17.0381i	0.705349	+	1.02187i
$279$	11.6551	−	7.37026i	0.697774	−	0.441246i
$280$	0.730522	−	2.52205i	0.0436570	−	0.150722i
$281$	17.3902	+	15.4063i	1.03741	+	0.919065i	0.996786	−	0.0801098i	$-0.0255271\pi$
$281$	17.3902	+	15.4063i	1.03741	+	0.919065i	0.0406236	+	0.999175i	$0.487066\pi$
$282$	−0.582038	−	2.85101i	−0.0346598	−	0.169775i
$283$	14.8875	+	1.20185i	0.884972	+	0.0714423i	0.514589	−	0.857437i	$-0.327944\pi$
$283$	14.8875	+	1.20185i	0.884972	+	0.0714423i	0.370383	+	0.928879i	$0.379226\pi$
$284$	0.234801	+	5.82653i	0.0139329	+	0.345741i
$285$	−2.88673	−	7.61169i	−0.170995	−	0.450877i
$286$	−6.61316	+	2.03609i	−0.391044	+	0.120397i
$287$	−1.54583	+	4.07601i	−0.0912472	+	0.240599i
$288$	−23.2760	−	7.77066i	−1.37155	−	0.457891i
$289$	−15.2812	−	5.10161i	−0.898893	−	0.300095i
$290$	1.49341	−	1.55480i	0.0876960	−	0.0913012i
$291$	18.0252	+	4.44281i	1.05666	+	0.260442i
$292$	10.9843	+	4.67998i	0.642809	+	0.273875i
$293$	−16.8291	−	20.6119i	−0.983166	−	1.20416i	−0.978936	−	0.204169i	$-0.934551\pi$
$293$	−16.8291	−	20.6119i	−0.983166	−	1.20416i	−0.00423077	−	0.999991i	$-0.501347\pi$
$294$	−0.497756	−	4.09939i	−0.0290297	−	0.239081i
$295$	9.43381	−	0.761576i	0.549258	−	0.0443407i
$296$	2.28666	+	7.89447i	0.132909	+	0.458857i
$297$	0.613953	−	3.00734i	0.0356252	−	0.174504i
$298$	1.18926	−	9.79447i	0.0688922	−	0.567378i
$299$	−6.30956	+	27.5773i	−0.364891	+	1.59484i
$300$	−1.71509	−	14.1250i	−0.0990206	−	0.815508i
$301$	24.3714	+	1.96746i	1.40474	+	0.113403i
$302$	−2.08248	+	2.55057i	−0.119833	+	0.146769i
$303$	−39.9367	−	30.0105i	−2.29430	−	1.72406i
$304$	18.0856	−	9.49207i	1.03728	−	0.544407i
$305$	−0.519612	−	2.54523i	−0.0297529	−	0.145739i
$306$	6.85802	−	0.553637i	0.392047	−	0.0316493i
$307$	19.4564	−	28.1875i	1.11044	−	1.60874i	0.381181	−	0.924500i	$-0.375517\pi$
$307$	19.4564	−	28.1875i	1.11044	−	1.60874i	0.729254	−	0.684243i	$-0.239867\pi$
$308$	0.128595	−	3.19106i	0.00732740	−	0.181828i
$309$	−18.4494	+	13.8638i	−1.04955	+	0.788685i
$310$	1.92850	−	4.06423i	0.109531	−	0.230833i
$311$	17.6707	−	25.6004i	1.00201	−	1.45167i	0.113103	−	0.993583i	$-0.463921\pi$
$311$	17.6707	−	25.6004i	1.00201	−	1.45167i	0.888910	−	0.458082i	$-0.151463\pi$
$312$	11.3925	+	7.58537i	0.644976	+	0.429437i
$313$	−14.3412	−	20.7768i	−0.810613	−	1.17438i	−0.981946	−	0.189162i	$-0.939423\pi$
$313$	−14.3412	−	20.7768i	−0.810613	−	1.17438i	0.171333	−	0.985213i	$-0.445193\pi$
$314$	−27.8180	+	4.52086i	−1.56986	+	0.255127i
$315$	3.74985	+	6.49494i	0.211280	+	0.365948i
$316$	4.84419	−	8.39038i	0.272507	−	0.471996i
$317$	−1.39661	+	3.68257i	−0.0784417	+	0.206834i	−0.968500	−	0.249012i	$-0.919894\pi$
$317$	−1.39661	+	3.68257i	−0.0784417	+	0.206834i	0.890059	+	0.455846i	$0.150663\pi$
$318$	−36.9826	+	38.5029i	−2.07388	+	2.15914i
$319$	−0.869358	+	1.50577i	−0.0486747	+	0.0843070i
$320$	−0.617503	+	0.152201i	−0.0345194	+	0.00850828i
$321$	36.8086	+	5.98198i	2.05446	+	0.333881i
$322$	−29.3889	−	18.5844i	−1.63778	−	1.03567i
$323$	−2.45712	+	3.00943i	−0.136718	+	0.167449i
$324$	−4.91350	+	2.57881i	−0.272972	+	0.143267i
$325$	−2.30727	+	15.8704i	−0.127985	+	0.880334i
$326$	26.2090	+	13.7555i	1.45158	+	0.761849i
$327$	−27.1348	+	11.5610i	−1.50056	+	0.639327i
$328$	−2.47954	+	0.402965i	−0.136910	+	0.0222500i
$329$	−1.39258	−	0.593323i	−0.0767754	−	0.0327109i
$330$	−1.34504	−	3.54657i	−0.0740418	−	0.195232i
$331$	−19.5488	−	3.17699i	−1.07450	−	0.174623i	−0.402682	−	0.915340i	$-0.631922\pi$
$331$	−19.5488	−	3.17699i	−1.07450	−	0.174623i	−0.671817	+	0.740717i	$0.734486\pi$
$332$	0.941149	+	1.98343i	0.0516523	+	0.108855i
$333$	−20.7864	−	10.9096i	−1.13909	−	0.597840i
$334$	0.319925	−	1.10451i	0.0175055	−	0.0604361i
$335$	−1.66546	+	8.15797i	−0.0909939	+	0.445717i
$336$	−26.1151	+	19.6242i	−1.42469	+	1.07059i
$337$	−17.4782			−0.952097			−0.476048	−	0.879419i	$-0.657931\pi$
$337$	−17.4782			−0.952097			−0.476048	+	0.879419i	$0.657931\pi$
$338$	15.3084	+	17.5183i	0.832666	+	0.952868i
$339$	42.7346			2.32102
$340$	0.673786	−	0.506317i	0.0365412	−	0.0274589i
$341$	−0.725721	+	3.55482i	−0.0393000	+	0.192504i
$342$	−8.35876	+	28.8578i	−0.451990	+	1.56045i
$343$	−17.2513	−	9.05418i	−0.931483	−	0.488880i
$344$	6.04023	+	12.7295i	0.325667	+	0.686330i
$345$	−15.3068	−	2.48760i	−0.824091	−	0.133928i
$346$	−1.36684	−	3.60407i	−0.0734820	−	0.193756i
$347$	8.50137	+	3.62209i	0.456377	+	0.194444i	0.607907	−	0.794009i	$-0.292010\pi$
$347$	8.50137	+	3.62209i	0.456377	+	0.194444i	−0.151529	+	0.988453i	$0.548420\pi$
$348$	−5.11944	+	0.831990i	−0.274431	+	0.0445993i
$349$	−8.76694	+	3.73525i	−0.469284	+	0.199943i	−0.613645	−	0.789582i	$-0.710297\pi$
$349$	−8.76694	+	3.73525i	−0.469284	+	0.199943i	0.144361	+	0.989525i	$0.453887\pi$
$350$	−17.4540	−	9.16059i	−0.932958	−	0.489654i
$351$	−10.0752	+	2.23314i	−0.537775	+	0.119196i
$352$	5.71666	−	3.00033i	0.304699	−	0.159918i
$353$	−4.48762	+	5.49634i	−0.238852	+	0.292541i	−0.880095	−	0.474797i	$-0.842521\pi$
$353$	−4.48762	+	5.49634i	−0.238852	+	0.292541i	0.641243	+	0.767338i	$0.278419\pi$
$354$	−51.2511	−	32.4092i	−2.72396	−	1.72253i
$355$	3.55615	+	0.577930i	0.188741	+	0.0306734i
$356$	−14.4472	+	3.56092i	−0.765702	+	0.188728i
$357$	3.10678	−	5.38110i	0.164428	−	0.284798i
$358$	32.1917	−	33.5151i	1.70138	−	1.77133i
$359$	−8.64168	+	22.7862i	−0.456091	+	1.20261i	0.487976	+	0.872857i	$0.337735\pi$
$359$	−8.64168	+	22.7862i	−0.456091	+	1.20261i	−0.944067	+	0.329755i	$0.893034\pi$
$360$	−2.16088	+	3.74276i	−0.113888	+	0.197261i
$361$	1.01754	+	1.76243i	0.0535548	+	0.0927597i
$362$	25.9835	−	4.22272i	1.36566	−	0.221941i
$363$	−14.8842	−	21.5635i	−0.781219	−	1.13179i
$364$	−9.97467	+	3.97509i	−0.522815	+	0.208351i
$365$	4.19055	−	6.07106i	0.219344	−	0.317774i
$366$	−7.13493	+	15.0365i	−0.372949	+	0.785973i
$367$	12.8602	−	9.66385i	0.671300	−	0.504449i	−0.209579	−	0.977792i	$-0.567209\pi$
$367$	12.8602	−	9.66385i	0.671300	−	0.504449i	0.880878	+	0.473343i	$0.156953\pi$
$368$	1.56671	−	38.8774i	0.0816703	−	2.02663i
$369$	4.07592	−	5.90499i	0.212184	−	0.307401i
$370$	−7.63331	+	0.616225i	−0.396837	+	0.0320360i
$371$	5.55519	+	27.2111i	0.288411	+	1.41273i
$372$	−9.58309	+	5.02960i	−0.496860	+	0.260772i
$373$	−4.56777	−	3.43245i	−0.236510	−	0.177726i	0.475879	−	0.879511i	$-0.342130\pi$
$373$	−4.56777	−	3.43245i	−0.236510	−	0.177726i	−0.712389	+	0.701785i	$0.752387\pi$
$374$	−1.14486	+	1.40220i	−0.0591995	+	0.0725062i
$375$	−18.6128	−	1.50258i	−0.961163	−	0.0775931i
$376$	−0.105142	−	0.865925i	−0.00542230	−	0.0446567i
$377$	5.81420	+	0.607416i	0.299446	+	0.0312835i
$378$	1.52892	−	12.5918i	0.0786393	−	0.647653i
$379$	7.48493	−	36.6636i	0.384475	−	1.88328i	−0.0785042	−	0.996914i	$-0.525014\pi$
$379$	7.48493	−	36.6636i	0.384475	−	1.88328i	0.462979	−	0.886369i	$-0.346780\pi$
$380$	1.02392	+	3.53499i	0.0525262	+	0.181341i
$381$	42.9732	−	3.46915i	2.20158	−	0.177730i
$382$	0.868317	+	7.15123i	0.0444270	+	0.365889i
$383$	22.9103	+	28.0600i	1.17066	+	1.43380i	0.878704	+	0.477368i	$0.158409\pi$
$383$	22.9103	+	28.0600i	1.17066	+	1.43380i	0.291957	+	0.956431i	$0.405694\pi$
$384$	−25.7175	−	10.9572i	−1.31239	−	0.559157i
$385$	−1.91584	−	0.472212i	−0.0976402	−	0.0240661i
$386$	23.9457	−	24.9301i	1.21880	−	1.26891i
$387$	−38.1731	−	12.7440i	−1.94045	−	0.647816i
$388$	−7.96090	−	2.65774i	−0.404154	−	0.134926i
$389$	1.21952	−	3.21560i	0.0618320	−	0.163038i	−0.900540	−	0.434773i	$-0.856828\pi$
$389$	1.21952	−	3.21560i	0.0618320	−	0.163038i	0.962372	+	0.271736i	$0.0875977\pi$
$390$	−9.04826	+	8.98691i	−0.458176	+	0.455070i
$391$	2.62441	+	6.92000i	0.132722	+	0.349959i
$392$	−0.0498457	−	1.23691i	−0.00251759	−	0.0624734i
$393$	10.6650	+	0.860967i	0.537978	+	0.0434301i
$394$	8.77690	+	42.9921i	0.442174	+	2.16591i
$395$	−4.48051	−	3.96938i	−0.225439	−	0.199721i
$396$	−1.46246	+	5.04900i	−0.0734913	+	0.253722i
$397$	15.3821	−	9.72703i	0.772004	−	0.488186i	−0.0894689	−	0.995990i	$-0.528517\pi$
$397$	15.3821	−	9.72703i	0.772004	−	0.488186i	0.861473	+	0.507804i	$0.169543\pi$
$398$	0.717187	+	1.03903i	0.0359494	+	0.0520816i
$399$	17.1598	+	21.0169i	0.859064	+	1.05216i
$400$	−0.888153	−	22.0393i	−0.0444076	−	1.10196i
$401$	9.81557	+	6.20699i	0.490166	+	0.309962i	0.756585	−	0.653895i	$-0.226866\pi$
$401$	9.81557	+	6.20699i	0.490166	+	0.309962i	−0.266419	+	0.963857i	$0.585841\pi$
$402$	39.9298	−	35.3747i	1.99152	−	1.76433i
$403$	11.9094	−	2.63968i	0.593248	−	0.131492i
$404$	16.9046	+	14.9761i	0.841034	+	0.745091i
$405$	0.953865	+	3.29312i	0.0473979	+	0.163637i
$406$	−3.08029	+	6.49157i	−0.152872	+	0.322171i
$407$	5.85852	−	1.95586i	0.290396	−	0.0969485i
$408$	3.58061			0.177267
$409$	−15.1982	+	5.07389i	−0.751500	+	0.250888i	−0.666512	−	0.745494i	$-0.732213\pi$
$409$	−15.1982	+	5.07389i	−0.751500	+	0.250888i	−0.0849883	+	0.996382i	$0.527085\pi$
$410$	0.0942489	−	2.33876i	0.00465462	−	0.115503i
$411$	4.18106	−	34.4341i	0.206236	−	1.69851i
$412$	8.81800	−	5.57617i	0.434432	−	0.274718i
$413$	−29.0204	+	12.3644i	−1.42800	+	0.608414i
$414$	39.6462	+	41.2761i	1.94850	+	2.02861i
$415$	1.31699	−	0.324610i	0.0646487	−	0.0159345i
$416$	−17.0415	−	13.4450i	−0.835529	−	0.659194i
$417$	−29.8789	−	7.36449i	−1.46318	−	0.360641i
$418$	−3.95229	−	6.84557i	−0.193313	−	0.334828i
$419$	−0.0678330	−	0.0706216i	−0.00331386	−	0.00345009i	0.719543	−	0.694447i	$-0.244351\pi$
$419$	−0.0678330	−	0.0706216i	−0.00331386	−	0.00345009i	−0.722857	+	0.690997i	$0.757172\pi$
$420$	−2.52328	−	5.31771i	−0.123124	−	0.259478i
$421$	−22.5534	+	19.9806i	−1.09919	+	0.973794i	−0.999774	−	0.0212519i	$-0.993235\pi$
$421$	−22.5534	+	19.9806i	−1.09919	+	0.973794i	−0.0994125	+	0.995046i	$0.531696\pi$
$422$	3.18755	+	2.39529i	0.155168	+	0.116601i
$423$	1.99178	+	1.49673i	0.0968436	+	0.0727733i
$424$	−11.9792	+	10.6126i	−0.581761	+	0.515396i
$425$	1.79859	+	3.79045i	0.0872445	+	0.183864i
$426$	−15.9901	−	16.6475i	−0.774724	−	0.806573i
$427$	4.32903	+	7.49809i	0.209496	+	0.362858i
$428$	−16.3691	−	4.03462i	−0.791230	−	0.195021i
$429$	5.35090	−	8.78384i	0.258344	−	0.424088i
$430$	−12.7470	+	3.14185i	−0.614714	+	0.151513i
$431$	8.69377	+	9.05117i	0.418764	+	0.435980i	0.896851	−	0.442333i	$-0.145849\pi$
$431$	8.69377	+	9.05117i	0.418764	+	0.435980i	−0.478087	+	0.878313i	$0.658670\pi$
$432$	13.0577	−	5.56334i	0.628237	−	0.267667i
$433$	9.82064	−	6.21020i	0.471950	−	0.298443i	−0.277237	−	0.960801i	$-0.589419\pi$
$433$	9.82064	−	6.21020i	0.471950	−	0.298443i	0.749187	+	0.662359i	$0.230444\pi$
$434$	−1.80726	+	14.8841i	−0.0867512	+	0.714460i
$435$	−0.129033	+	3.20191i	−0.00618664	+	0.153520i
$436$	12.6480	−	4.22254i	0.605731	−	0.202223i
$437$	−32.3173			−1.54595
$438$	−44.8310	+	14.9668i	−2.14211	+	0.715140i
$439$	9.99425	−	21.0624i	0.477000	−	1.00526i	−0.512225	−	0.858851i	$-0.671179\pi$
$439$	9.99425	−	21.0624i	0.477000	−	1.00526i	0.989225	−	0.146404i	$-0.0467700\pi$
$440$	−0.316349	−	1.09216i	−0.0150814	−	0.0520669i
$441$	2.64657	+	2.34466i	0.126027	+	0.111650i
$442$	5.87347	+	1.59522i	0.279372	+	0.0758770i
$443$	5.92760	−	5.25139i	0.281629	−	0.249501i	−0.510468	−	0.859897i	$-0.670528\pi$
$443$	5.92760	−	5.25139i	0.281629	−	0.249501i	0.792097	+	0.610395i	$0.208989\pi$
$444$	15.5719	+	9.84710i	0.739012	+	0.467323i
$445$	0.370175	+	9.18580i	0.0175480	+	0.435449i
$446$	5.86583	+	7.18433i	0.277755	+	0.340188i
$447$	8.33105	+	12.0696i	0.394045	+	0.570873i
$448$	1.79154	−	1.13290i	0.0846424	−	0.0535246i
$449$	−3.67452	+	12.6859i	−0.173411	+	0.598686i	0.825977	+	0.563704i	$0.190624\pi$
$449$	−3.67452	+	12.6859i	−0.173411	+	0.598686i	−0.999388	+	0.0349811i	$0.988863\pi$
$450$	24.2850	+	21.5147i	1.14481	+	1.01421i
$451$	0.377602	+	1.84962i	0.0177806	+	0.0870951i
$452$	−19.2571	−	1.55459i	−0.905777	−	0.0731219i
$453$	−0.197078	−	4.89044i	−0.00925954	−	0.229773i
$454$	1.34346	+	3.54241i	0.0630516	+	0.166254i
$455$	1.17363	+	6.52950i	0.0550207	+	0.306108i
$456$	−5.54434	+	14.6192i	−0.259638	+	0.684608i
$457$	20.8863	+	6.97288i	0.977021	+	0.326178i	0.759952	−	0.649979i	$-0.225222\pi$
$457$	20.8863	+	6.97288i	0.977021	+	0.326178i	0.217069	+	0.976156i	$0.430350\pi$
$458$	39.2346	+	13.0985i	1.83331	+	0.612050i
$459$	−1.87018	+	1.94707i	−0.0872927	+	0.0908813i
$460$	6.80706	+	1.67779i	0.317381	+	0.0782274i
$461$	−10.2784	−	4.37922i	−0.478714	−	0.203961i	0.139111	−	0.990277i	$-0.455576\pi$
$461$	−10.2784	−	4.37922i	−0.478714	−	0.203961i	−0.617824	+	0.786316i	$0.711986\pi$
$462$	7.99538	+	9.79257i	0.371979	+	0.455592i
$463$	2.51173	+	20.6859i	0.116730	+	0.961358i	0.926938	+	0.375215i	$0.122431\pi$
$463$	2.51173	+	20.6859i	0.116730	+	0.961358i	−0.810208	+	0.586143i	$0.800646\pi$
$464$	−8.01411	+	0.646966i	−0.372046	+	0.0300346i
$465$	1.86038	+	6.42277i	0.0862730	+	0.297849i
$466$	0.509467	−	2.49553i	0.0236006	−	0.115603i
$467$	−2.57704	+	21.2238i	−0.119251	+	0.982122i	0.803120	+	0.595817i	$0.203172\pi$
$467$	−2.57704	+	21.2238i	−0.119251	+	0.982122i	−0.922371	+	0.386305i	$0.873751\pi$
$468$	17.5063	−	2.42361i	0.809231	−	0.112031i
$469$	−3.34499	−	27.5485i	−0.154457	−	1.27207i
$470$	0.810129	+	0.0654004i	0.0373685	+	0.00301670i
$471$	26.4943	−	32.4496i	1.22079	−	1.49520i
$472$	−14.5321	−	10.9202i	−0.668895	−	0.502642i
$473$	9.37543	−	4.92061i	0.431083	−	0.226250i
$474$	7.67124	+	37.5762i	0.352352	+	1.72593i
$475$	−18.2610	+	1.47418i	−0.837872	+	0.0676400i
$476$	−1.59573	+	2.31182i	−0.0731402	+	0.105962i
$477$	1.84061	−	45.6744i	0.0842760	−	2.09129i
$478$	5.11844	−	3.84625i	0.234112	−	0.175924i
$479$	−4.15778	+	8.76233i	−0.189974	+	0.400361i	−0.975981	−	0.217856i	$-0.930094\pi$
$479$	−4.15778	+	8.76233i	−0.189974	+	0.400361i	0.786007	+	0.618217i	$0.212145\pi$
$480$	6.75936	−	9.79263i	0.308521	−	0.446970i
$481$	−14.0286	−	15.3109i	−0.639649	−	0.698118i
$482$	−10.7473	−	15.5702i	−0.489527	−	0.709203i
$483$	51.0166	−	8.29101i	2.32134	−	0.377254i
$484$	5.92270	+	10.2584i	0.269214	+	0.466292i
$485$	−2.59273	+	4.49073i	−0.117730	+	0.203914i
$486$	13.2382	−	34.9063i	0.600498	−	1.58338i
$487$	9.17143	−	9.54847i	0.415597	−	0.432683i	−0.480191	−	0.877164i	$-0.659433\pi$
$487$	9.17143	−	9.54847i	0.415597	−	0.432683i	0.895788	+	0.444481i	$0.146612\pi$
$488$	−2.49463	+	4.32083i	−0.112927	+	0.195595i
$489$	−42.7189	+	10.5293i	−1.93181	+	0.476149i
$490$	1.13851	+	0.185025i	0.0514325	+	0.00835860i
$491$	16.9426	+	10.7139i	0.764610	+	0.483510i	0.858969	−	0.512028i	$-0.171106\pi$
$491$	16.9426	+	10.7139i	0.764610	+	0.483510i	−0.0943585	+	0.995538i	$0.530080\pi$
$492$	−3.56145	+	4.36198i	−0.160562	+	0.196653i
$493$	1.35416	−	0.710718i	0.0609883	−	0.0320091i
$494$	−15.6078	+	21.5106i	−0.702228	+	0.967808i
$495$	2.87571	+	1.50929i	0.129253	+	0.0678374i
$496$	−15.4348	+	6.57614i	−0.693041	+	0.295277i
$497$	−11.8524	+	1.92621i	−0.531654	+	0.0864022i
$498$	−7.99502	−	3.40636i	−0.358265	−	0.152643i
$499$	−2.63204	−	6.94013i	−0.117827	−	0.310683i	0.863109	−	0.505018i	$-0.168514\pi$
$499$	−2.63204	−	6.94013i	−0.117827	−	0.310683i	−0.980935	+	0.194335i	$0.937745\pi$
$500$	8.33266	+	1.35419i	0.372648	+	0.0605612i
$501$	0.732745	+	1.54423i	0.0327366	+	0.0689910i
$502$	−2.12351	−	1.11450i	−0.0947768	−	0.0497427i
$503$	−0.116889	+	0.403546i	−0.00521181	+	0.0179932i	−0.963082	−	0.269209i	$-0.913238\pi$
$503$	−0.116889	+	0.403546i	−0.00521181	+	0.0179932i	0.957870	+	0.287202i	$0.0927251\pi$
$504$	2.88120	−	14.1131i	0.128339	−	0.628646i
$505$	11.1551	−	8.38248i	0.496393	−	0.373015i
$506$	−15.0578			−0.669403
$507$	−34.2996	−	4.40171i	−1.52330	−	0.195487i
$508$	−19.4908			−0.864763
$509$	−15.0918	+	11.3407i	−0.668932	+	0.502670i	−0.880105	−	0.474779i	$-0.842528\pi$
$509$	−15.0918	+	11.3407i	−0.668932	+	0.502670i	0.211173	+	0.977449i	$0.432272\pi$
$510$	−0.667343	+	3.26886i	−0.0295505	+	0.144748i
$511$	−6.84046	+	23.6160i	−0.302604	+	1.04471i
$512$	13.9029	+	7.29681i	0.614428	+	0.322477i
$513$	−5.05380	−	10.6507i	−0.223131	−	0.470238i
$514$	−23.5076	−	3.82036i	−1.03688	−	0.168509i
$515$	−2.28580	−	6.02717i	−0.100724	−	0.265589i
$516$	29.0574	+	12.3802i	1.27918	+	0.545008i
$517$	−0.647015	+	0.105150i	−0.0284557	+	0.00462450i
$518$	23.4817	−	10.0046i	1.03173	−	0.439577i
$519$	5.07323	+	2.66263i	0.222690	+	0.116877i
$520$	−2.92041	+	2.46704i	−0.128069	+	0.108187i
$521$	12.7827	−	6.70887i	0.560019	−	0.293921i	−0.160865	−	0.986976i	$-0.551428\pi$
$521$	12.7827	−	6.70887i	0.560019	−	0.293921i	0.720884	+	0.693056i	$0.243736\pi$
$522$	7.47963	−	9.16089i	0.327375	−	0.400961i
$523$	25.7360	+	16.2744i	1.12535	+	0.711631i	0.961487	−	0.274851i	$-0.0886285\pi$
$523$	25.7360	+	16.2744i	1.12535	+	0.711631i	0.163868	+	0.986482i	$0.447603\pi$
$524$	−4.77454	−	0.775939i	−0.208577	−	0.0338970i
$525$	28.4489	−	7.01202i	1.24161	−	0.306030i
$526$	0.649469	−	1.12491i	0.0283182	−	0.0490485i
$527$	2.21064	−	2.30152i	0.0962972	−	0.100256i
$528$	−5.01628	+	13.2268i	−0.218306	+	0.575624i
$529$	−19.2814	+	33.3964i	−0.838323	+	1.45202i
$530$	−7.45600	−	12.9142i	−0.323868	−	0.560956i
$531$	51.2479	−	8.32860i	2.22397	−	0.361430i
$532$	−6.96800	−	10.0949i	−0.302101	−	0.437669i
$533$	5.16239	−	3.69241i	0.223608	−	0.159936i
$534$	33.4594	−	48.4743i	1.44793	−	2.09769i
$535$	−4.46535	+	9.41052i	−0.193054	+	0.406852i
$536$	12.7844	−	9.60684i	0.552201	−	0.414952i
$537$	−2.78141	+	69.0199i	−0.120027	+	2.97843i
$538$	16.7236	−	24.2282i	0.721004	−	1.04455i
$539$	−0.927249	+	0.0748553i	−0.0399394	+	0.00322425i
$540$	0.511551	+	2.50574i	0.0220137	+	0.107830i
$541$	−20.4545	+	10.7354i	−0.879410	+	0.461550i	−0.843079	−	0.537790i	$-0.819259\pi$
$541$	−20.4545	+	10.7354i	−0.879410	+	0.461550i	−0.0363308	+	0.999340i	$0.511567\pi$
$542$	−30.6326	−	23.0189i	−1.31578	−	0.988747i
$543$	−24.7471	+	30.3097i	−1.06200	+	1.30071i
$544$	−5.66029	−	0.456946i	−0.242683	−	0.0195914i
$545$	−0.993040	−	8.17842i	−0.0425371	−	0.350325i
$546$	19.1202	−	37.9612i	0.818268	−	1.62459i
$547$	1.06447	−	8.76666i	0.0455132	−	0.374835i	−0.952100	−	0.305787i	$-0.901081\pi$
$547$	1.06447	−	8.76666i	0.0455132	−	0.374835i	0.997613	−	0.0690486i	$-0.0219964\pi$
$548$	−3.13671	+	15.3646i	−0.133994	+	0.656344i
$549$	−3.96476	−	13.6879i	−0.169212	−	0.584186i
$550$	−8.50847	+	0.686875i	−0.362803	+	0.0292885i
$551$	0.804953	+	6.62938i	0.0342921	+	0.282421i
$552$	18.8370	+	23.0712i	0.801757	+	0.981973i
$553$	18.3542	+	7.81998i	0.780498	+	0.332539i
$554$	8.79704	+	2.16827i	0.373750	+	0.0921212i
$555$	7.88546	−	8.20964i	0.334719	−	0.348480i
$556$	13.1961	+	4.40552i	0.559641	+	0.186836i
$557$	−16.4447	−	5.49006i	−0.696785	−	0.232621i	−0.0538584	−	0.998549i	$-0.517152\pi$
$557$	−16.4447	−	5.49006i	−0.696785	−	0.232621i	−0.642927	+	0.765927i	$0.722280\pi$
$558$	8.75100	−	23.0745i	0.370459	−	0.976821i
$559$	−27.9484	−	22.0500i	−1.18209	−	0.932617i
$560$	−3.23555	−	8.53144i	−0.136727	−	0.360519i
$561$	−0.108346	−	2.68857i	−0.00457436	−	0.113512i
$562$	41.4424	+	3.34558i	1.74814	+	0.141125i
$563$	−3.81516	−	18.6879i	−0.160790	−	0.787600i	−0.977563	−	0.210642i	$-0.932445\pi$
$563$	−3.81516	−	18.6879i	−0.160790	−	0.787600i	0.816774	−	0.576958i	$-0.195760\pi$
$564$	−1.46362	−	1.29665i	−0.0616295	−	0.0545989i
$565$	−3.32096	+	11.4653i	−0.139714	+	0.482348i
$566$	22.5911	−	14.2858i	0.949576	−	0.600475i
$567$	−6.49124	−	9.40418i	−0.272606	−	0.394938i
$568$	−4.37630	−	5.36000i	−0.183626	−	0.224901i
$569$	0.244956	+	6.07853i	0.0102691	+	0.254825i	0.996167	+	0.0874753i	$0.0278799\pi$
$569$	0.244956	+	6.07853i	0.0102691	+	0.254825i	−0.985898	+	0.167350i	$0.946479\pi$
$570$	−12.3131	−	7.78631i	−0.515738	−	0.326133i
$571$	−15.8080	+	14.0047i	−0.661544	+	0.586077i	−0.925633	−	0.378421i	$-0.876467\pi$
$571$	−15.8080	+	14.0047i	−0.661544	+	0.586077i	0.264089	+	0.964498i	$0.414929\pi$
$572$	−2.73076	+	3.76352i	−0.114179	+	0.157361i
$573$	−8.01494	−	7.10062i	−0.334829	−	0.296633i
$574$	2.17045	+	7.49327i	0.0905929	+	0.312763i
$575$	−14.9611	+	31.5299i	−0.623922	+	1.31489i
$576$	−3.30932	+	1.10481i	−0.137888	+	0.0460339i
$577$	−34.8469			−1.45069			−0.725347	−	0.688384i	$-0.758321\pi$
$577$	−34.8469			−1.45069			−0.725347	+	0.688384i	$0.758321\pi$
$578$	−27.3468	+	9.12972i	−1.13748	+	0.379746i
$579$	−2.06894	+	51.3402i	−0.0859821	+	2.13362i
$580$	0.174623	−	1.43815i	0.00725083	−	0.0597160i
$581$	−3.82096	+	2.41623i	−0.158520	+	0.100242i
$582$	30.5644	−	13.0223i	1.26693	−	0.539790i
$583$	8.33119	+	8.67368i	0.345043	+	0.359227i
$584$	−13.7566	+	3.39069i	−0.569251	+	0.140308i
$585$	0.696364	−	10.8971i	0.0287911	−	0.450540i
$586$	−46.2361	−	11.3962i	−1.91000	−	0.470772i
$587$	−0.208841	−	0.361724i	−0.00861981	−	0.0149299i	0.861683	−	0.507446i	$-0.169410\pi$
$587$	−0.208841	−	0.361724i	−0.00861981	−	0.0149299i	−0.870303	+	0.492516i	$0.836077\pi$
$588$	−1.92230	−	2.00133i	−0.0792745	−	0.0825335i
$589$	5.97383	+	12.5896i	0.246147	+	0.518745i
$590$	12.6779	−	11.2316i	0.521939	−	0.462398i
$591$	−52.1418	−	39.1820i	−2.14483	−	1.61173i
$592$	22.8328	+	17.1577i	0.938422	+	0.705178i
$593$	18.2958	−	16.2086i	0.751317	−	0.665609i	−0.197903	−	0.980222i	$-0.563413\pi$
$593$	18.2958	−	16.2086i	0.751317	−	0.665609i	0.949220	+	0.314613i	$0.101875\pi$
$594$	−2.35475	−	4.96254i	−0.0966167	−	0.203615i
$595$	1.20227	+	1.25169i	0.0492881	+	0.0513143i
$596$	−3.31507	−	5.74188i	−0.135791	−	0.235196i
$597$	−1.82210	−	0.449106i	−0.0745734	−	0.0183807i
$598$	20.6208	+	46.2371i	0.843246	+	1.89077i
$599$	43.0382	−	10.6080i	1.75849	−	0.433430i	0.777726	−	0.628604i	$-0.216373\pi$
$599$	43.0382	−	10.6080i	1.75849	−	0.433430i	0.980769	+	0.195174i	$0.0625271\pi$
$600$	11.6963	+	12.1772i	0.477500	+	0.497130i
$601$	1.18719	−	0.505816i	0.0484267	−	0.0206327i	−0.367617	−	0.929977i	$-0.619826\pi$
$601$	1.18719	−	0.505816i	0.0484267	−	0.0206327i	0.416044	+	0.909344i	$0.363416\pi$
$602$	36.9824	−	23.3863i	1.50729	−	0.953153i
$603$	−5.50563	+	45.3429i	−0.224207	+	1.84651i
$604$	−0.0890963	+	2.21090i	−0.00362528	+	0.0899603i
$605$	6.94196	−	2.31757i	0.282231	−	0.0942225i
$606$	−89.3994			−3.63160
$607$	−14.6111	+	4.87791i	−0.593047	+	0.197988i	−0.597321	−	0.802003i	$-0.703768\pi$
$607$	−14.6111	+	4.87791i	−0.593047	+	0.197988i	0.00427324	+	0.999991i	$0.498640\pi$
$608$	10.6303	−	22.4028i	0.431114	−	0.908553i
$609$	−2.97148	−	10.2587i	−0.120410	−	0.415705i
$610$	−3.47970	−	3.08274i	−0.140889	−	0.124817i
$611$	1.20892	+	1.84275i	0.0489078	+	0.0745496i
$612$	3.46076	−	3.06597i	0.139893	−	0.123934i
$613$	8.77238	+	5.54732i	0.354313	+	0.224054i	0.699750	−	0.714388i	$-0.253295\pi$
$613$	8.77238	+	5.54732i	0.354313	+	0.224054i	−0.345437	+	0.938442i	$0.612269\pi$
$614$	−2.46804	−	61.2438i	−0.0996021	−	2.47160i
$615$	2.20042	+	2.69502i	0.0887293	+	0.108674i
$616$	2.15282	+	3.11890i	0.0867395	+	0.125664i
$617$	1.07188	−	0.677817i	0.0431523	−	0.0272879i	−0.512715	−	0.858559i	$-0.671360\pi$
$617$	1.07188	−	0.677817i	0.0431523	−	0.0272879i	0.555868	+	0.831271i	$0.312386\pi$
$618$	−11.4902	+	39.6689i	−0.462205	+	1.59572i
$619$	0.713247	+	0.631881i	0.0286678	+	0.0253975i	0.677335	−	0.735675i	$-0.263135\pi$
$619$	0.713247	+	0.631881i	0.0286678	+	0.0253975i	−0.648667	+	0.761072i	$0.724673\pi$
$620$	−0.604678	−	2.96191i	−0.0242844	−	0.118953i
$621$	−22.3844	−	1.80705i	−0.898254	−	0.0725146i
$622$	−2.24152	−	55.6228i	−0.0898769	−	2.23027i
$623$	−10.8653	−	28.6494i	−0.435309	−	1.14781i
$624$	47.4842	−	2.71019i	1.90089	−	0.108494i
$625$	−6.03675	+	15.9176i	−0.241470	+	0.636704i
$626$	−42.8541	−	14.3068i	−1.71279	−	0.571814i
$627$	11.1449	+	3.72071i	0.445084	+	0.148591i
$628$	−13.1193	+	13.6587i	−0.523518	+	0.545040i
$629$	−5.27474	−	1.30011i	−0.210318	−	0.0518387i
$630$	12.3473	+	5.26070i	0.491929	+	0.209591i
$631$	23.4426	+	28.7120i	0.933237	+	1.14301i	0.989492	+	0.144591i	$0.0461866\pi$
$631$	23.4426	+	28.7120i	0.933237	+	1.14301i	−0.0562550	+	0.998416i	$0.517916\pi$
$632$	1.38577	+	11.4129i	0.0551231	+	0.453980i
$633$	−5.90748	+	0.476901i	−0.234801	+	0.0189551i
$634$	1.96095	+	6.76998i	0.0778792	+	0.268870i
$635$	−2.40876	+	11.7989i	−0.0955886	+	0.468224i
$636$	−4.32434	+	35.6142i	−0.171471	+	1.41219i
$637$	1.49966	+	2.74473i	0.0594188	+	0.108750i
$638$	0.375057	+	3.08888i	0.0148487	+	0.122290i
$639$	19.7001	+	1.59036i	0.779325	+	0.0629136i
$640$	4.93825	−	6.04826i	0.195202	−	0.239078i
$641$	9.96600	+	7.48897i	0.393633	+	0.295796i	0.779069	−	0.626939i	$-0.215692\pi$
$641$	9.96600	+	7.48897i	0.393633	+	0.295796i	−0.385435	+	0.922735i	$0.625949\pi$
$642$	59.0918	−	31.0138i	2.33217	−	1.22402i
$643$	−0.534084	−	2.61612i	−0.0210622	−	0.103170i	0.967901	−	0.251333i	$-0.0808689\pi$
$643$	−0.534084	−	2.61612i	−0.0210622	−	0.103170i	−0.988963	+	0.148164i	$0.952664\pi$
$644$	−23.2907	+	1.88022i	−0.917784	+	0.0740912i
$645$	11.0855	−	16.0601i	0.436491	−	0.632366i
$646$	−0.279957	+	6.94706i	−0.0110148	+	0.273328i
$647$	31.7679	−	23.8720i	1.24892	−	0.938505i	0.249370	−	0.968408i	$-0.419776\pi$
$647$	31.7679	−	23.8720i	1.24892	−	0.938505i	0.999553	+	0.0299032i	$0.00951991\pi$
$648$	2.82288	−	5.94909i	0.110893	−	0.233702i
$649$	−7.75990	+	11.2422i	−0.304603	+	0.441293i
$650$	13.7610	+	25.1857i	0.539749	+	0.987866i
$651$	−12.6602	−	18.3415i	−0.496194	−	0.718861i
$652$	19.6330	−	3.19068i	0.768888	−	0.124957i
$653$	−10.5727	−	18.3124i	−0.413740	−	0.716619i	0.581555	−	0.813507i	$-0.302445\pi$
$653$	−10.5727	−	18.3124i	−0.413740	−	0.716619i	−0.995295	+	0.0968878i	$0.969111\pi$
$654$	−26.3917	+	45.7118i	−1.03200	+	1.78747i
$655$	−1.05978	+	2.79441i	−0.0414090	+	0.109187i
$656$	−6.04710	+	6.29569i	−0.236099	+	0.245806i
$657$	20.2340	−	35.0464i	0.789405	−	1.36729i
$658$	−2.63018	+	0.648281i	−0.102535	+	0.0252726i
$659$	−0.995262	−	0.161746i	−0.0387699	−	0.00630072i	0.140995	−	0.990010i	$-0.454970\pi$
$659$	−0.995262	−	0.161746i	−0.0387699	−	0.00630072i	−0.179765	+	0.983710i	$0.557534\pi$
$660$	−2.15431	−	1.36230i	−0.0838564	−	0.0530275i
$661$	−3.66786	+	4.49232i	−0.142663	+	0.174731i	−0.840994	−	0.541044i	$-0.818029\pi$
$661$	−3.66786	+	4.49232i	−0.142663	+	0.174731i	0.698331	+	0.715775i	$0.253927\pi$
$662$	−31.3832	+	16.4712i	−1.21974	+	0.640171i
$663$	−8.10723	+	4.01452i	−0.314859	+	0.155911i
$664$	−2.30675	−	1.21068i	−0.0895194	−	0.0469834i
$665$	−6.97215	+	2.97055i	−0.270368	+	0.115193i
$666$	−41.4669	+	6.73903i	−1.60681	+	0.261132i
$667$	11.7034	+	4.98636i	0.453158	+	0.193073i
$668$	−0.274014	−	0.722516i	−0.0106019	−	0.0279550i
$669$	−13.6078	−	2.21149i	−0.526109	−	0.0855010i
$670$	6.38770	+	13.4618i	0.246779	+	0.520075i
$671$	3.31987	+	1.74240i	0.128162	+	0.0672646i
$672$	−11.0337	+	38.0926i	−0.425633	+	1.46945i
$673$	2.21321	−	10.8410i	0.0853130	−	0.417891i	−0.914596	−	0.404370i	$-0.867491\pi$
$673$	2.21321	−	10.8410i	0.0853130	−	0.417891i	0.999909	−	0.0135210i	$-0.00430400\pi$
$674$	−25.0054	+	18.7903i	−0.963171	+	0.723776i
$675$	−12.7308			−0.490008
$676$	15.2960	+	3.23125i	0.588307	+	0.124279i
$677$	−10.7526			−0.413256			−0.206628	−	0.978420i	$-0.566249\pi$
$677$	−10.7526			−0.413256			−0.206628	+	0.978420i	$0.566249\pi$
$678$	61.1388	−	45.9428i	2.34802	−	1.76442i
$679$	3.45700	−	16.9335i	0.132668	−	0.649848i
$680$	−0.278254	+	0.960643i	−0.0106705	+	0.0368390i
$681$	−4.98643	−	2.61708i	−0.191080	−	0.100287i
$682$	2.78343	+	5.86595i	0.106583	+	0.224619i
$683$	−19.2549	−	3.12922i	−0.736767	−	0.119736i	−0.219563	−	0.975598i	$-0.570463\pi$
$683$	−19.2549	−	3.12922i	−0.736767	−	0.119736i	−0.517204	+	0.855862i	$0.673027\pi$
$684$	7.15924	+	18.8774i	0.273740	+	0.721794i
$685$	8.91343	+	3.79766i	0.340565	+	0.145101i
$686$	−34.4147	+	5.59294i	−1.31396	+	0.213539i
$687$	−56.5636	+	24.0995i	−2.15804	+	0.919453i
$688$	43.3540	+	22.7539i	1.65285	+	0.867485i
$689$	15.2246	−	37.4601i	0.580013	−	1.42711i
$690$	−24.5732	+	12.8970i	−0.935487	+	0.490982i
$691$	−20.5159	+	25.1275i	−0.780463	+	0.955894i	−0.999805	−	0.0197544i	$-0.993712\pi$
$691$	−20.5159	+	25.1275i	−0.780463	+	0.955894i	0.219342	+	0.975648i	$0.429609\pi$
$692$	−2.18924	−	1.38439i	−0.0832223	−	0.0526266i
$693$	−10.6842	−	1.73636i	−0.405861	−	0.0659588i
$694$	16.0566	−	3.95760i	0.609501	−	0.150228i
$695$	4.29775	−	7.44392i	0.163023	−	0.282364i
$696$	4.26349	−	4.43877i	0.161607	−	0.168251i
$697$	0.588800	−	1.55254i	0.0223024	−	0.0588066i
$698$	−8.52688	+	14.7690i	−0.322747	+	0.559015i
$699$	1.89297	+	3.27872i	0.0715986	+	0.124012i
$700$	−13.0747	+	2.12485i	−0.494178	+	0.0803118i
$701$	−28.4251	−	41.1809i	−1.07360	−	1.55538i	−0.806058	−	0.591837i	$-0.798403\pi$
$701$	−28.4251	−	41.1809i	−1.07360	−	1.55538i	−0.267545	−	0.963545i	$-0.586212\pi$
$702$	−12.0134	+	14.0265i	−0.453418	+	0.529395i
$703$	13.4758	−	19.5231i	0.508249	−	0.736326i
$704$	0.393507	−	0.829298i	0.0148308	−	0.0312553i
$705$	−0.965818	+	0.725765i	−0.0363748	+	0.0273339i
$706$	−0.511306	+	12.6879i	−0.0192433	+	0.477517i
$707$	−26.4186	+	38.2739i	−0.993572	+	1.43944i
$708$	−40.6165	+	3.27890i	−1.52646	+	0.123229i
$709$	−6.90598	−	33.8277i	−0.259360	−	1.27043i	−0.875665	−	0.482920i	$-0.839576\pi$
$709$	−6.90598	−	33.8277i	−0.259360	−	1.27043i	0.616305	−	0.787508i	$-0.288629\pi$
$710$	5.70897	−	2.99630i	0.214254	−	0.112449i
$711$	−26.2516	−	19.7268i	−0.984511	−	0.739812i
$712$	11.1670	−	13.6771i	0.418501	−	0.512570i
$713$	26.4594	+	2.13602i	0.990912	+	0.0799947i
$714$	−1.34032	−	11.0386i	−0.0501604	−	0.413108i
$715$	1.94079	+	2.11820i	0.0725816	+	0.0792161i
$716$	3.76415	−	31.0006i	0.140673	−	1.15855i
$717$	−1.90361	+	9.32452i	−0.0710917	+	0.348230i
$718$	12.1336	+	41.8899i	0.452820	+	1.56332i
$719$	−17.9737	+	1.45099i	−0.670306	+	0.0541127i	−0.410934	−	0.911665i	$-0.634797\pi$
$719$	−17.9737	+	1.45099i	−0.670306	+	0.0541127i	−0.259372	+	0.965778i	$0.583515\pi$
$720$	1.81023	+	14.9086i	0.0674634	+	0.555611i
$721$	13.5876	+	16.6418i	0.506030	+	0.619775i
$722$	3.35051	+	1.42752i	0.124693	+	0.0531267i
$723$	27.3048	+	6.73003i	1.01548	+	0.250292i
$724$	12.2541	−	12.7579i	0.455421	−	0.474144i
$725$	6.84051	+	2.28370i	0.254050	+	0.0848144i
$726$	−44.4767	−	14.8485i	−1.65069	−	0.551080i
$727$	2.65683	−	7.00548i	0.0985363	−	0.259819i	−0.876679	−	0.481075i	$-0.840246\pi$
$727$	2.65683	−	7.00548i	0.0985363	−	0.259819i	0.975216	+	0.221256i	$0.0710157\pi$
$728$	6.62882	−	10.8816i	0.245681	−	0.403300i
$729$	14.7688	+	38.9422i	0.546994	+	1.44230i
$730$	−0.531571	−	13.1908i	−0.0196743	−	0.488214i
$731$	−9.28299	−	0.749401i	−0.343344	−	0.0277176i
$732$	2.23714	+	10.9583i	0.0826872	+	0.405029i
$733$	7.28926	+	6.45772i	0.269235	+	0.238521i	0.786928	−	0.617045i	$-0.211670\pi$
$733$	7.28926	+	6.45772i	0.269235	+	0.238521i	−0.517693	+	0.855567i	$0.673209\pi$
$734$	8.00934	−	27.6514i	0.295630	−	1.02063i
$735$	−1.44909	+	0.916346i	−0.0534503	+	0.0337999i
$736$	−26.8336	−	38.8752i	−0.989100	−	1.43296i
$737$	−7.60033	−	9.30871i	−0.279962	−	0.342891i
$738$	−0.517030	−	12.8300i	−0.0190321	−	0.472277i
$739$	−4.74035	−	2.99762i	−0.174377	−	0.110269i	0.444426	−	0.895816i	$-0.353408\pi$
$739$	−4.74035	−	2.99762i	−0.174377	−	0.110269i	−0.618803	+	0.785546i	$0.712382\pi$
$740$	−3.85200	+	3.41257i	−0.141602	+	0.125449i
$741$	−3.83730	−	39.3172i	−0.140967	−	1.44435i
$742$	37.2016	+	32.9577i	1.36571	+	1.20992i
$743$	2.50521	+	8.64899i	0.0919073	+	0.317301i	0.993279	−	0.115746i	$-0.0369258\pi$
$743$	2.50521	+	8.64899i	0.0919073	+	0.317301i	−0.901372	+	0.433046i	$0.857439\pi$
$744$	5.50562	−	11.6029i	0.201846	−	0.425381i
$745$	−3.88558	+	1.29720i	−0.142357	+	0.0475256i
$746$	−10.2251			−0.374367
$747$	7.05803	−	2.35632i	0.258240	−	0.0862131i
$748$	−0.0489816	+	1.21547i	−0.00179094	+	0.0444418i
$749$	4.18462	−	34.4634i	0.152903	−	1.25927i
$750$	−28.2441	+	17.8605i	−1.03133	+	0.652173i
$751$	−35.3339	+	15.0544i	−1.28935	+	0.549341i	−0.924307	−	0.381649i	$-0.875356\pi$
$751$	−35.3339	+	15.0544i	−1.28935	+	0.549341i	−0.365044	+	0.930990i	$0.618946\pi$
$752$	−2.09978	−	2.18610i	−0.0765710	−	0.0797189i
$753$	3.46117	−	0.853102i	0.126132	−	0.0310888i
$754$	8.97118	−	5.38168i	0.326711	−	0.195989i
$755$	1.32737	+	0.327168i	0.0483081	+	0.0119069i
$756$	−4.26187	−	7.38178i	−0.155003	−	0.268473i
$757$	−29.3794	−	30.5872i	−1.06781	−	1.11171i	−0.993426	−	0.114480i	$-0.963480\pi$
$757$	−29.3794	−	30.5872i	−1.06781	−	1.11171i	−0.0743860	−	0.997230i	$-0.523700\pi$
$758$	−28.7077	−	60.5001i	−1.04271	−	2.19746i
$759$	16.7534	−	14.8422i	0.608111	−	0.538739i
$760$	−3.49134	−	2.62357i	−0.126644	−	0.0951670i
$761$	−5.35190	−	4.02169i	−0.194006	−	0.145786i	0.499300	−	0.866429i	$-0.333590\pi$
$761$	−5.35190	−	4.02169i	−0.194006	−	0.145786i	−0.693307	+	0.720643i	$0.743847\pi$
$762$	57.7505	−	51.1625i	2.09208	−	1.85342i
$763$	11.7712	+	24.8073i	0.426146	+	0.898083i
$764$	3.35339	+	3.49125i	0.121321	+	0.126309i
$765$	−1.42831	−	2.47390i	−0.0516406	−	0.0894441i
$766$	62.9435	+	15.5142i	2.27424	+	0.560550i
$767$	45.1472	+	8.43236i	1.63017	+	0.304475i
$768$	−52.9944	+	13.0619i	−1.91227	+	0.471332i
$769$	4.96448	+	5.16858i	0.179024	+	0.186384i	0.804668	−	0.593725i	$-0.202343\pi$
$769$	4.96448	+	5.16858i	0.179024	+	0.186384i	−0.625644	+	0.780109i	$0.715164\pi$
$770$	−3.24858	+	1.38409i	−0.117071	+	0.0498792i
$771$	29.9204	−	18.9205i	1.07756	−	0.681406i
$772$	2.79995	−	23.0597i	0.100772	−	0.829935i
$773$	−1.17789	+	29.2290i	−0.0423658	+	1.05130i	0.828566	+	0.559891i	$0.189157\pi$
$773$	−1.17789	+	29.2290i	−0.0423658	+	1.05130i	−0.870932	+	0.491404i	$0.836484\pi$
$774$	−68.3136	+	22.8064i	−2.45548	+	0.819760i
$775$	15.0484			0.540554
$776$	9.44679	−	3.15380i	0.339120	−	0.113215i
$777$	−16.2645	+	34.2766i	−0.583485	+	1.22967i
$778$	−1.71229	−	5.91152i	−0.0613886	−	0.211938i
$779$	5.42712	+	4.80801i	0.194447	+	0.172265i
$780$	−1.23294	+	8.48067i	−0.0441462	+	0.303657i
$781$	−3.89224	+	3.44822i	−0.139275	+	0.123387i
$782$	11.1942	+	7.07875i	0.400302	+	0.253136i
$783$	0.186857	+	4.63681i	0.00667773	+	0.165706i
$784$	−2.72062	−	3.33215i	−0.0971649	−	0.119005i
$785$	6.64702	+	9.62987i	0.237242	+	0.343705i
$786$	16.1836	−	10.2339i	0.577251	−	0.365031i
$787$	11.7712	−	40.6391i	0.419600	−	1.44863i	−0.421045	−	0.907040i	$-0.638337\pi$
$787$	11.7712	−	40.6391i	0.419600	−	1.44863i	0.840645	−	0.541587i	$-0.182176\pi$
$788$	22.0708	+	19.5530i	0.786240	+	0.696547i
$789$	0.386204	+	1.89175i	0.0137492	+	0.0673482i
$790$	−10.6775	−	0.861975i	−0.379888	−	0.0306677i
$791$	−1.60193	−	39.7515i	−0.0569582	−	1.41340i
$792$	−2.21190	−	5.83231i	−0.0785965	−	0.207242i
$793$	0.803919	−	12.5802i	0.0285480	−	0.446736i
$794$	11.5493	−	30.4530i	0.409869	−	1.08073i
$795$	21.0249	+	7.01913i	0.745675	+	0.248943i
$796$	0.804736	+	0.268660i	0.0285231	+	0.00952241i
$797$	7.96313	−	8.29050i	0.282069	−	0.293665i	−0.565063	−	0.825048i	$-0.691148\pi$
$797$	7.96313	−	8.29050i	0.282069	−	0.293665i	0.847132	+	0.531383i	$0.178328\pi$
$798$	47.1446	+	11.6201i	1.66890	+	0.411347i
$799$	0.530430	+	0.225995i	0.0187652	+	0.00799512i
$800$	−16.9357	−	20.7425i	−0.598769	−	0.733359i
$801$	6.07894	+	50.0646i	0.214789	+	1.76894i
$802$	20.7157	−	1.67235i	0.731498	−	0.0590526i
$803$	2.96223	+	10.2268i	0.104535	+	0.360896i
$804$	7.17050	−	35.1234i	0.252884	−	1.23871i
$805$	−1.74017	+	14.3316i	−0.0613329	+	0.505122i
$806$	14.2004	−	16.5799i	0.500189	−	0.584003i
$807$	5.27464	+	43.4406i	0.185676	+	1.52918i
$808$	−26.7127	−	2.15647i	−0.939749	−	0.0758643i
$809$	31.9635	−	39.1482i	1.12378	−	1.37638i	0.206346	−	0.978479i	$-0.433843\pi$
$809$	31.9635	−	39.1482i	1.12378	−	1.37638i	0.917430	−	0.397897i	$-0.130260\pi$
$810$	4.90501	+	3.68588i	0.172344	+	0.129508i
$811$	−26.7927	+	14.0619i	−0.940818	+	0.493779i	−0.864126	−	0.503275i	$-0.832128\pi$
$811$	−26.7927	+	14.0619i	−0.940818	+	0.493779i	−0.0766919	+	0.997055i	$0.524436\pi$
$812$	0.965819	+	4.73089i	0.0338936	+	0.166022i
$813$	56.7714	−	4.58306i	1.99106	−	0.160735i
$814$	6.27888	−	9.09652i	0.220074	−	0.318833i
$815$	0.494839	−	12.2793i	0.0173334	−	0.430125i
$816$	9.94715	−	7.47480i	0.348220	−	0.261670i
$817$	17.4338	−	36.7410i	0.609933	−	1.28541i
$818$	−16.2886	+	23.5982i	−0.569519	+	0.825090i
$819$	9.29969	+	35.1852i	0.324957	+	1.22947i
$820$	−0.893513	−	1.29448i	−0.0312028	−	0.0452051i
$821$	26.9091	−	4.37315i	0.939134	−	0.152624i	0.328471	−	0.944514i	$-0.393467\pi$
$821$	26.9091	−	4.37315i	0.939134	−	0.152624i	0.610664	+	0.791890i	$0.290903\pi$
$822$	−31.0375	−	53.7586i	−1.08256	−	1.87505i
$823$	16.2153	−	28.0856i	0.565228	−	0.979004i	−0.431800	−	0.901969i	$-0.642121\pi$
$823$	16.2153	−	28.0856i	0.565228	−	0.979004i	0.997028	−	0.0770348i	$-0.0245452\pi$
$824$	−4.39018	+	11.5760i	−0.152939	+	0.403268i
$825$	8.78953	−	9.15087i	0.306012	−	0.318593i
$826$	−28.2257	+	48.8884i	−0.982099	+	1.70104i
$827$	0.281668	−	0.0694250i	0.00979457	−	0.00241414i	−0.234415	−	0.972137i	$-0.575318\pi$
$827$	0.281668	−	0.0694250i	0.00979457	−	0.00241414i	0.244210	+	0.969722i	$0.421471\pi$
$828$	37.9616	+	6.16937i	1.31926	+	0.214400i
$829$	35.5396	+	22.4739i	1.23434	+	0.780551i	0.982327	−	0.187172i	$-0.0599323\pi$
$829$	35.5396	+	22.4739i	1.23434	+	0.780551i	0.252015	+	0.967723i	$0.418907\pi$
$830$	1.53520	−	1.88027i	0.0532874	−	0.0652652i
$831$	−11.9249	+	6.25865i	−0.413669	+	0.217110i
$832$	−3.08535	−	0.0726424i	−0.106965	−	0.00251842i
$833$	0.724516	+	0.380256i	0.0251030	+	0.0131751i
$834$	−50.6641	+	21.5859i	−1.75435	+	0.747460i
$835$	−0.471244	+	0.0765846i	−0.0163081	+	0.00265032i
$836$	−4.88677	−	2.08206i	−0.169012	−	0.0720094i
$837$	3.43378	+	9.05412i	0.118689	+	0.312956i
$838$	−0.172970	−	0.0281103i	−0.00597513	−	0.000971054i
$839$	14.0457	+	29.6007i	0.484911	+	1.02193i	0.987532	+	0.157421i	$0.0503181\pi$
$839$	14.0457	+	29.6007i	0.484911	+	1.02193i	−0.502620	+	0.864507i	$0.667631\pi$
$840$	6.18457	+	3.24591i	0.213388	+	0.111995i
$841$	−7.33694	+	25.3301i	−0.252998	+	0.873450i
$842$	−10.7857	+	52.8321i	−0.371701	+	1.82071i
$843$	−49.4067	+	37.1267i	−1.70166	+	1.27871i
$844$	2.67938			0.0922281
$845$	3.84640	−	8.86020i	0.132320	−	0.304800i
$846$	4.45866			0.153292
$847$	−19.5004	+	14.6536i	−0.670040	+	0.503502i
$848$	−11.1242	+	54.4901i	−0.382007	+	1.87120i
$849$	−11.0538	+	38.1621i	−0.379365	+	1.30972i
$850$	6.64819	+	3.48924i	0.228031	+	0.119680i
$851$	−19.3725	−	40.8267i	−0.664082	−	1.39952i
$852$	−15.3107	−	2.48823i	−0.524536	−	0.0852454i
$853$	5.77904	+	15.2381i	0.197871	+	0.521742i	0.996823	−	0.0796526i	$-0.0253811\pi$
$853$	5.77904	+	15.2381i	0.197871	+	0.521742i	−0.798952	+	0.601395i	$0.794612\pi$
$854$	14.2544	+	6.07323i	0.487775	+	0.207822i
$855$	12.3123	−	2.00095i	0.421072	−	0.0684309i
$856$	18.4048	−	7.84155i	0.629063	−	0.268019i
$857$	4.46896	+	2.34549i	0.152657	+	0.0801205i	0.539322	−	0.842100i	$-0.318681\pi$
$857$	4.46896	+	2.34549i	0.152657	+	0.0801205i	−0.386665	+	0.922220i	$0.626373\pi$
$858$	−1.78794	−	18.3193i	−0.0610393	−	0.625411i
$859$	8.20267	−	4.30509i	0.279872	−	0.146888i	−0.318947	−	0.947772i	$-0.603329\pi$
$859$	8.20267	−	4.30509i	0.279872	−	0.146888i	0.598819	+	0.800885i	$0.295637\pi$
$860$	−5.57958	+	6.83374i	−0.190262	+	0.233029i
$861$	−9.80084	−	6.19768i	−0.334012	−	0.211216i
$862$	22.1685	+	3.60274i	0.755063	+	0.122710i
$863$	−29.8596	+	7.35974i	−1.01643	+	0.250528i	−0.712131	−	0.702047i	$-0.752270\pi$
$863$	−29.8596	+	7.35974i	−1.01643	+	0.250528i	−0.304303	+	0.952575i	$0.598423\pi$
$864$	8.61566	−	14.9228i	0.293111	−	0.507682i
$865$	−1.10861	+	1.15418i	−0.0376937	+	0.0392433i
$866$	7.37361	−	19.4426i	0.250565	−	0.660687i
$867$	21.4272	−	37.1131i	0.727707	−	1.26043i
$868$	5.03774	+	8.72562i	0.170992	+	0.296167i
$869$	8.52764	−	1.38588i	0.289280	−	0.0470126i
$870$	3.25769	+	4.71957i	0.110446	+	0.160009i
$871$	−18.1754	+	36.0855i	−0.615851	+	1.22271i
$872$	−8.98854	+	13.0221i	−0.304390	+	0.440985i
$873$	−12.1947	+	25.6998i	−0.412728	+	0.869807i
$874$	−46.2352	+	34.7435i	−1.56393	+	1.17522i
$875$	−0.699983	+	17.3699i	−0.0236638	+	0.587210i
$876$	−18.0421	+	26.1385i	−0.609585	+	0.883136i
$877$	−5.51633	+	0.445324i	−0.186273	+	0.0150375i	−0.173251	−	0.984878i	$-0.555427\pi$
$877$	−5.51633	+	0.445324i	−0.186273	+	0.0150375i	−0.0130220	+	0.999915i	$0.504145\pi$
$878$	−8.34527	−	40.8778i	−0.281639	−	1.37956i
$879$	62.6755	−	32.8947i	2.11399	−	1.10951i
$880$	−3.15881	−	2.37369i	−0.106484	−	0.0800172i
$881$	−2.55624	+	3.13083i	−0.0861220	+	0.105480i	−0.815868	−	0.578238i	$-0.803741\pi$
$881$	−2.55624	+	3.13083i	−0.0861220	+	0.105480i	0.729746	+	0.683718i	$0.239638\pi$
$882$	6.30703	+	0.509156i	0.212369	+	0.0171442i
$883$	−1.72218	−	14.1834i	−0.0579560	−	0.477310i	−0.992573	−	0.121654i	$-0.961180\pi$
$883$	−1.72218	−	14.1834i	−0.0579560	−	0.477310i	0.934617	−	0.355657i	$-0.115743\pi$
$884$	3.79932	−	1.51410i	0.127785	−	0.0509247i
$885$	−3.03466	+	24.9927i	−0.102009	+	0.840120i
$886$	2.83476	−	13.8856i	0.0952357	−	0.466495i
$887$	10.3958	+	35.8903i	0.349055	+	1.20508i	0.922552	+	0.385872i	$0.126099\pi$
$887$	10.3958	+	35.8903i	0.349055	+	1.20508i	−0.573497	+	0.819208i	$0.694414\pi$
$888$	−21.7921	+	1.75924i	−0.731296	+	0.0590363i
$889$	−4.83787	−	39.8434i	−0.162257	−	1.33630i
$890$	10.4050	+	12.7438i	0.348777	+	0.427174i
$891$	−4.55241	−	1.93960i	−0.152511	−	0.0649790i
$892$	6.05151	+	1.49156i	0.202620	+	0.0499412i
$893$	−1.74405	+	1.81575i	−0.0583623	+	0.0607616i
$894$	24.8947	+	8.31106i	0.832602	+	0.277963i
$895$	−18.3012	−	6.10985i	−0.611742	−	0.204230i
$896$	−9.22831	+	24.3330i	−0.308296	+	0.812910i
$897$	−68.5178	−	31.1181i	−2.28774	−	1.03900i
$898$	8.38130	+	22.0997i	0.279687	+	0.737475i
$899$	−0.220874	−	5.48093i	−0.00736655	−	0.182799i
$900$	21.7318	+	1.75437i	0.724392	+	0.0584789i
$901$	−2.11596	−	10.3646i	−0.0704927	−	0.345296i
$902$	2.52870	+	2.24023i	0.0841965	+	0.0745915i
$903$	−18.0954	+	62.4726i	−0.602178	+	2.07896i
$904$	19.3766	−	12.2530i	0.644456	−	0.407529i
$905$	−6.20866	−	8.99480i	−0.206383	−	0.298997i
$906$	−5.53954	−	6.78471i	−0.184039	−	0.225407i
$907$	0.00502262	+	0.124635i	0.000166773	+	0.00413844i	0.999270	−	0.0381966i	$-0.0121613\pi$
$907$	0.00502262	+	0.124635i	0.000166773	+	0.00413844i	−0.999103	+	0.0423351i	$0.986520\pi$
$908$	2.15178	+	1.36071i	0.0714094	+	0.0451566i
$909$	57.2956	−	50.7595i	1.90038	−	1.68359i
$910$	8.69876	+	8.07977i	0.288361	+	0.267842i
$911$	22.1989	+	19.6665i	0.735483	+	0.651581i	0.945316	−	0.326156i	$-0.105754\pi$
$911$	22.1989	+	19.6665i	0.735483	+	0.651581i	−0.209833	+	0.977737i	$0.567292\pi$
$912$	15.1163	+	52.1874i	0.500549	+	1.72810i
$913$	−0.839261	+	1.76870i	−0.0277755	+	0.0585356i
$914$	37.3777	−	12.4785i	1.23634	−	0.412752i
$915$	6.91013			0.228442
$916$	26.3654	−	8.80206i	0.871137	−	0.290828i
$917$	0.401084	−	9.95281i	0.0132450	−	0.328671i
$918$	−0.582362	+	4.79618i	−0.0192208	+	0.158298i
$919$	−31.5065	+	19.9235i	−1.03930	+	0.657217i	−0.941162	−	0.337956i	$-0.890265\pi$
$919$	−31.5065	+	19.9235i	−1.03930	+	0.657217i	−0.0981429	+	0.995172i	$0.531290\pi$
$920$	−7.65362	+	3.26090i	−0.252332	+	0.107509i
$921$	63.1129	+	65.7075i	2.07964	+	2.16514i
$922$	−19.4129	+	4.78486i	−0.639331	+	0.157581i
$923$	15.9184	+	7.22950i	0.523960	+	0.237962i
$924$	8.24848	+	2.03307i	0.271355	+	0.0668830i
$925$	−12.8088	−	22.1856i	−0.421152	−	0.729457i
$926$	25.8324	+	26.8943i	0.848904	+	0.883803i
$927$	−15.1593	−	31.9475i	−0.497897	−	1.04929i
$928$	−7.30627	+	6.47279i	−0.239840	+	0.212480i
$929$	11.1127	+	8.35064i	0.364595	+	0.273976i	0.767213	−	0.641393i	$-0.221643\pi$
$929$	11.1127	+	8.35064i	0.364595	+	0.273976i	−0.402617	+	0.915368i	$0.631899\pi$
$930$	9.56653	+	7.18878i	0.313699	+	0.235729i
$931$	−2.67441	+	2.36932i	−0.0876502	+	0.0776513i
$932$	−0.733737	−	1.54632i	−0.0240344	−	0.0506514i
$933$	57.3204	+	59.6768i	1.87659	+	1.95373i
$934$	19.1303	+	33.1347i	0.625963	+	1.08420i
$935$	0.729737	+	0.179864i	0.0238650	+	0.00588218i
$936$	−14.8798	+	14.7789i	−0.486361	+	0.483064i
$937$	23.1520	−	5.70646i	0.756344	−	0.186422i	0.157755	−	0.987478i	$-0.449574\pi$
$937$	23.1520	−	5.70646i	0.756344	−	0.186422i	0.598589	+	0.801056i	$0.295728\pi$
$938$	−34.4022	−	35.8165i	−1.12327	−	1.16945i
$939$	61.7816	−	26.3227i	2.01617	−	0.859008i
$940$	0.461619	−	0.291910i	0.0150564	−	0.00952106i
$941$	3.11786	−	25.6779i	0.101639	−	0.837076i	−0.849345	−	0.527838i	$-0.823003\pi$
$941$	3.11786	−	25.6779i	0.101639	−	0.837076i	0.950985	−	0.309238i	$-0.100074\pi$
$942$	3.01868	−	74.9079i	0.0983540	−	2.44063i
$943$	13.1011	−	4.37380i	0.426632	−	0.142431i
$944$	−63.1678			−2.05594
$945$	−4.99531	+	1.66768i	−0.162498	+	0.0542497i
$946$	8.12307	−	17.1190i	0.264104	−	0.556587i
$947$	6.58124	+	22.7211i	0.213862	+	0.738336i	0.993672	+	0.112320i	$0.0358282\pi$
$947$	6.58124	+	22.7211i	0.213862	+	0.738336i	−0.779810	+	0.626016i	$0.784685\pi$
$948$	19.2904	+	17.0898i	0.626525	+	0.555052i
$949$	27.3461	−	23.1009i	0.887693	−	0.749885i
$950$	−24.5405	+	21.7410i	−0.796198	+	0.705370i
$951$	−8.85481	−	5.59944i	−0.287137	−	0.181574i
$952$	−0.134221	−	3.33067i	−0.00435014	−	0.107948i
$953$	−29.3576	−	35.9565i	−0.950985	−	1.16475i	−0.986232	−	0.165367i	$-0.947119\pi$
$953$	−29.3576	−	35.9565i	−0.950985	−	1.16475i	0.0352467	−	0.999379i	$-0.488778\pi$
$954$	−46.4700	−	67.3235i	−1.50452	−	2.17968i
$955$	2.52788	−	1.59853i	0.0818002	−	0.0517273i
$956$	1.19701	−	4.13257i	0.0387141	−	0.133657i
$957$	−3.46194	−	3.06701i	−0.111909	−	0.0991424i
$958$	3.47177	+	17.0059i	0.112168	+	0.549434i
$959$	−32.1872	−	2.59842i	−1.03938	−	0.0839073i
$960$	−0.0681203	−	1.69039i	−0.00219857	−	0.0545570i
$961$	6.93387	+	18.2831i	0.223673	+	0.589778i
$962$	−36.5306	−	6.82299i	−1.17779	−	0.219982i
$963$	−20.2625	+	53.4278i	−0.652950	+	1.72169i
$964$	−12.0593	−	4.02598i	−0.388403	−	0.129668i
$965$	−13.6133	−	4.54479i	−0.438227	−	0.146302i
$966$	64.0742	−	66.7083i	2.06155	−	2.14630i
$967$	−20.3389	−	5.01308i	−0.654054	−	0.161210i	−0.101694	−	0.994816i	$-0.532426\pi$
$967$	−20.3389	−	5.01308i	−0.654054	−	0.161210i	−0.552360	+	0.833606i	$0.686273\pi$
$968$	−12.9315	−	5.50961i	−0.415635	−	0.177086i
$969$	−6.53611	−	8.00528i	−0.209970	−	0.257167i
$970$	1.11855	+	9.21210i	0.0359145	+	0.295783i
$971$	18.0689	−	1.45867i	0.579859	−	0.0468111i	0.212942	−	0.977065i	$-0.431695\pi$
$971$	18.0689	−	1.45867i	0.579859	−	0.0468111i	0.366917	+	0.930254i	$0.380413\pi$
$972$	−6.97966	−	24.0966i	−0.223873	−	0.772898i
$973$	−5.73039	+	28.0693i	−0.183708	+	0.899861i
$974$	2.85592	−	23.5206i	0.0915096	−	0.753649i
$975$	−40.1357	−	14.4579i	−1.28537	−	0.463022i
$976$	2.08983	+	17.2113i	0.0668937	+	0.550919i
$977$	−56.3146	−	4.54618i	−1.80166	−	0.145445i	−0.866389	−	0.499370i	$-0.833565\pi$
$977$	−56.3146	−	4.54618i	−1.80166	−	0.145445i	−0.935274	+	0.353924i	$0.884847\pi$
$978$	−49.7966	+	60.9897i	−1.59232	+	1.95024i
$979$	−10.6076	−	7.97110i	−0.339020	−	0.254757i
$980$	0.686322	−	0.360210i	0.0219238	−	0.0115065i
$981$	−9.04008	−	44.2812i	−0.288628	−	1.41379i
$982$	35.7574	−	2.88664i	1.14106	−	0.0921163i
$983$	−11.4094	+	16.5294i	−0.363903	+	0.527205i	−0.961577	−	0.274534i	$-0.911476\pi$
$983$	−11.4094	+	16.5294i	−0.363903	+	0.527205i	0.597674	+	0.801739i	$0.296092\pi$
$984$	0.269069	−	6.67687i	0.00857760	−	0.212851i
$985$	14.5642	−	10.9443i	0.464053	−	0.348713i
$986$	1.17327	−	2.47262i	0.0373646	−	0.0787442i
$987$	2.28735	−	3.31380i	0.0728072	−	0.105479i
$988$	0.298893	+	17.8567i	0.00950906	+	0.568097i
$989$	−44.0077	−	63.7561i	−1.39936	−	2.02733i
$990$	5.73676	−	0.932315i	0.182326	−	0.0296309i
$991$	−22.1392	−	38.3463i	−0.703276	−	1.21811i	−0.967310	−	0.253597i	$-0.918386\pi$
$991$	−22.1392	−	38.3463i	−0.703276	−	1.21811i	0.264034	−	0.964513i	$-0.414947\pi$
$992$	−10.1841	+	17.6394i	−0.323346	+	0.560051i
$993$	18.6818	−	49.2598i	0.592849	−	1.56321i
$994$	−14.8860	+	15.4980i	−0.472156	+	0.491566i
$995$	0.262088	−	0.453950i	0.00830875	−	0.0143912i
$996$	−5.67021	+	1.39758i	−0.179667	+	0.0442840i
$997$	−48.9446	−	7.95427i	−1.55009	−	0.251914i	−0.675714	−	0.737164i	$-0.736165\pi$
$997$	−48.9446	−	7.95427i	−1.55009	−	0.251914i	−0.874376	+	0.485250i	$0.838729\pi$
$998$	−11.2267	−	7.09935i	−0.355376	−	0.224726i
$999$	10.4256	−	12.7690i	0.329851	−	0.403994i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.2.i.a.3.12	✓	336
169.113	even	39	inner	169.2.i.a.113.12	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
169.2.i.a.3.12	✓	336	1.1	even	1	trivial
169.2.i.a.113.12	yes	336	169.113	even	39	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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	169.i (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(1.43066 - 1.07507i) q^{2} +(-0.532083 + 2.60631i) q^{3} +(0.334579 - 1.15510i) q^{4} +(-0.657900 - 0.345292i) q^{5} +(2.04075 + 4.30078i) q^{6} +(2.44433 + 0.397242i) q^{7} +(0.506036 + 1.33431i) q^{8} +(-3.74982 - 1.59765i) q^{9} +(-1.31245 + 0.213294i) q^{10} +(0.986578 - 0.420341i) q^{11} +(2.83253 + 1.48663i) q^{12} +(-2.64177 - 2.45378i) q^{13} +(3.92407 - 2.05951i) q^{14} +(1.25000 - 1.53097i) q^{15} +(4.19126 + 2.65040i) q^{16} +(-0.931036 - 0.151308i) q^{17} +(-7.08231 + 1.74563i) q^{18} +(2.05942 - 3.56703i) q^{19} +(-0.618967 + 0.644413i) q^{20} +(-2.33592 + 6.15931i) q^{21} +(0.959562 - 1.66201i) q^{22} +(-3.92310 - 6.79501i) q^{23} +(-3.74687 + 0.608926i) q^{24} +(-2.52672 - 3.66058i) q^{25} +(-6.41748 - 0.670442i) q^{26} +(1.62590 - 2.35552i) q^{27} +(1.27667 - 2.69054i) q^{28} +(-1.29617 + 0.974010i) q^{29} +(0.142421 - 3.53414i) q^{30} +(-1.92189 + 2.78434i) q^{31} +(6.00083 - 0.484437i) q^{32} +(0.570600 + 2.79499i) q^{33} +(-1.49467 + 0.784462i) q^{34} +(-1.47096 - 1.10535i) q^{35} +(-3.10005 + 3.79688i) q^{36} +(5.74077 + 0.463443i) q^{37} +(-0.888475 - 7.31725i) q^{38} +(7.80097 - 5.57966i) q^{39} +(0.127805 - 1.05257i) q^{40} +(-0.352113 + 1.72476i) q^{41} +(3.27980 + 11.3232i) q^{42} +(9.84148 - 0.794487i) q^{43} +(-0.155449 - 1.28023i) q^{44} +(1.91535 + 2.34587i) q^{45} +(-12.9178 - 5.50375i) q^{46} +(-0.593493 - 0.146283i) q^{47} +(-9.13786 + 9.51352i) q^{48} +(-0.822826 - 0.274700i) q^{49} +(-7.55028 - 2.52065i) q^{50} +(0.889745 - 2.34606i) q^{51} +(-3.71825 + 2.23053i) q^{52} +(3.97684 + 10.4861i) q^{53} +(-0.206245 - 5.11793i) q^{54} +(-0.794210 - 0.0641152i) q^{55} +(0.706874 + 3.46250i) q^{56} +(8.20101 + 7.26546i) q^{57} +(-0.807253 + 2.78696i) q^{58} +(-10.7661 + 6.80809i) q^{59} +(-1.35020 - 1.95610i) q^{60} +(2.21118 + 2.70820i) q^{61} +(0.243792 + 6.04963i) q^{62} +(-8.53112 - 5.39475i) q^{63} +(0.640694 - 0.567606i) q^{64} +(0.890746 + 2.52653i) q^{65} +(3.82115 + 3.38525i) q^{66} +(-3.11774 - 10.7637i) q^{67} +(-0.486282 + 1.02482i) q^{68} +(19.7973 - 6.60932i) q^{69} -3.29278 q^{70} +(-4.59941 + 1.53551i) q^{71} +(0.234210 - 5.81187i) q^{72} +(-1.19674 + 9.85605i) q^{73} +(8.71135 - 5.50872i) q^{74} +(10.8850 - 4.63769i) q^{75} +(-3.43124 - 3.57230i) q^{76} +(2.57849 - 0.635542i) q^{77} +(5.16201 - 16.3692i) q^{78} +(7.82221 + 1.92800i) q^{79} +(-1.84227 - 3.19091i) q^{80} +(-3.19647 - 3.32787i) q^{81} +(1.35049 + 2.84610i) q^{82} +(-1.36646 + 1.21058i) q^{83} +(6.33308 + 4.75900i) q^{84} +(0.560283 + 0.421025i) q^{85} +(13.2257 - 11.7170i) q^{86} +(-1.84890 - 3.89648i) q^{87} +(1.06011 + 1.10369i) q^{88} +(-6.18653 - 10.7154i) q^{89} +(5.26220 + 1.29702i) q^{90} +(-5.48260 - 7.04727i) q^{91} +(-9.16151 + 2.25811i) q^{92} +(-6.23426 - 6.49055i) q^{93} +(-1.00635 + 0.428767i) q^{94} +(-2.58656 + 1.63564i) q^{95} +(-1.93034 + 15.8978i) q^{96} +(0.281016 - 6.97335i) q^{97} +(-1.47251 + 0.491596i) q^{98} -4.37104 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 26 q^{2} - 26 q^{3} - 12 q^{4} - 26 q^{5} - 26 q^{6} - 26 q^{7} - 26 q^{8} - 12 q^{9} - 22 q^{10} - 26 q^{11} - 34 q^{12} - 13 q^{13} - 30 q^{14} + 26 q^{15} - 8 q^{16} - 24 q^{17} - 104 q^{18}+ \cdots - 52 q^{99}+O(q^{100}) \) 336 * q - 26 * q^2 - 26 * q^3 - 12 * q^4 - 26 * q^5 - 26 * q^6 - 26 * q^7 - 26 * q^8 - 12 * q^9 - 22 * q^10 - 26 * q^11 - 34 * q^12 - 13 * q^13 - 30 * q^14 + 26 * q^15 - 8 * q^16 - 24 * q^17 - 104 * q^18 - 13 * q^19 - 26 * q^20 - 26 * q^21 + 19 * q^22 + 67 * q^23 + 52 * q^24 - 58 * q^25 - 26 * q^26 - 38 * q^27 - 26 * q^28 - 22 * q^29 - 120 * q^30 + 26 * q^31 + 117 * q^32 - 26 * q^33 + 39 * q^34 - 18 * q^35 - 2 * q^36 - 26 * q^37 + 41 * q^38 + 26 * q^39 + 67 * q^40 - 26 * q^41 - 270 * q^42 - 16 * q^43 + 39 * q^45 - 39 * q^47 + 31 * q^48 + 72 * q^49 - 26 * q^50 + 19 * q^51 + 39 * q^52 + 36 * q^53 - 182 * q^54 + 116 * q^55 - 10 * q^56 + 52 * q^57 + 26 * q^58 - 234 * q^59 + 78 * q^60 - 16 * q^61 + 53 * q^62 + 39 * q^63 - 82 * q^64 - 26 * q^65 - 135 * q^66 + 130 * q^67 + 51 * q^68 + 25 * q^69 + 156 * q^70 - 104 * q^71 + 143 * q^72 - 26 * q^73 + 79 * q^74 + 152 * q^75 - 104 * q^76 - 58 * q^77 + 104 * q^78 - 46 * q^79 - 13 * q^80 + 4 * q^81 + 118 * q^82 - 286 * q^83 + 221 * q^84 + 130 * q^85 + 52 * q^86 + 90 * q^87 - 204 * q^88 + 117 * q^89 - 86 * q^90 + 26 * q^91 - 22 * q^92 + 39 * q^93 + 126 * q^94 - 47 * q^95 + 143 * q^96 + 52 * q^97 - 26 * q^98 - 52 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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