LMFDB - Embedded newform 138.2.f.a.65.2

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			65.2
Character	$\chi$	$=$	138.65
Dual form			138.2.f.a.17.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.909632 + 0.415415i) q^{2} +(-0.580581 - 1.63185i) q^{3} +(0.654861 - 0.755750i) q^{4} +(-1.63636 - 1.05163i) q^{5} +(1.20601 + 1.24320i) q^{6} +(-3.52778 + 0.507219i) q^{7} +(-0.281733 + 0.959493i) q^{8} +(-2.32585 + 1.89484i) q^{9} +O(q^{10})$	\(q+(-0.909632 + 0.415415i) q^{2} +(-0.580581 - 1.63185i) q^{3} +(0.654861 - 0.755750i) q^{4} +(-1.63636 - 1.05163i) q^{5} +(1.20601 + 1.24320i) q^{6} +(-3.52778 + 0.507219i) q^{7} +(-0.281733 + 0.959493i) q^{8} +(-2.32585 + 1.89484i) q^{9} +(1.92535 + 0.276823i) q^{10} +(-1.10493 + 2.41947i) q^{11} +(-1.61347 - 0.629859i) q^{12} +(0.977409 - 6.79803i) q^{13} +(2.99828 - 1.92688i) q^{14} +(-0.766051 + 3.28085i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(-3.22982 - 3.72741i) q^{17} +(1.32852 - 2.68980i) q^{18} +(1.19767 + 1.03779i) q^{19} +(-1.86635 + 0.548011i) q^{20} +(2.87587 + 5.46232i) q^{21} -2.65983i q^{22} +(4.79364 - 0.145045i) q^{23} +(1.72931 - 0.0973192i) q^{24} +(-0.505314 - 1.10648i) q^{25} +(1.93492 + 6.58974i) q^{26} +(4.44243 + 2.69532i) q^{27} +(-1.92688 + 2.99828i) q^{28} +(2.48747 - 2.15541i) q^{29} +(-0.666088 - 3.30259i) q^{30} +(-5.57827 - 1.63793i) q^{31} +(0.540641 + 0.841254i) q^{32} +(4.58970 + 0.398385i) q^{33} +(4.48636 + 2.04885i) q^{34} +(6.30613 + 2.87991i) q^{35} +(-0.0910837 + 2.99862i) q^{36} +(3.42164 + 5.32418i) q^{37} +(-1.52055 - 0.446473i) q^{38} +(-11.6608 + 2.35183i) q^{39} +(1.47004 - 1.27380i) q^{40} +(-0.280858 + 0.437024i) q^{41} +(-4.88511 - 3.77402i) q^{42} +(1.05153 + 3.58117i) q^{43} +(1.10493 + 2.41947i) q^{44} +(5.79859 - 0.654719i) q^{45} +(-4.30019 + 2.12329i) q^{46} -8.59526i q^{47} +(-1.53261 + 0.806908i) q^{48} +(5.47153 - 1.60658i) q^{49} +(0.919299 + 0.796577i) q^{50} +(-4.20739 + 7.43463i) q^{51} +(-4.49754 - 5.19044i) q^{52} +(-0.616803 - 4.28996i) q^{53} +(-5.16066 - 0.606299i) q^{54} +(4.35244 - 2.79714i) q^{55} +(0.507219 - 3.52778i) q^{56} +(0.998164 - 2.55693i) q^{57} +(-1.36730 + 2.99396i) q^{58} +(-7.37948 - 1.06101i) q^{59} +(1.97784 + 2.72744i) q^{60} +(2.50799 - 8.54143i) q^{61} +(5.75459 - 0.827385i) q^{62} +(7.24400 - 7.86430i) q^{63} +(-0.841254 - 0.540641i) q^{64} +(-8.74838 + 10.0962i) q^{65} +(-4.34043 + 1.54425i) q^{66} +(-7.78164 + 3.55375i) q^{67} -4.93207 q^{68} +(-3.01979 - 7.73827i) q^{69} -6.93262 q^{70} +(-3.61816 + 1.65236i) q^{71} +(-1.16282 - 2.76548i) q^{72} +(-0.420832 + 0.485666i) q^{73} +(-5.32418 - 3.42164i) q^{74} +(-1.51223 + 1.46700i) q^{75} +(1.56861 - 0.225532i) q^{76} +(2.67077 - 9.09579i) q^{77} +(9.63007 - 6.98338i) q^{78} +(9.47779 + 1.36270i) q^{79} +(-0.808043 + 1.76937i) q^{80} +(1.81916 - 8.81423i) q^{81} +(0.0739313 - 0.514203i) q^{82} +(4.85775 - 3.12189i) q^{83} +(6.01144 + 1.40362i) q^{84} +(1.36531 + 9.49594i) q^{85} +(-2.44417 - 2.82073i) q^{86} +(-4.96147 - 2.80779i) q^{87} +(-2.01016 - 1.74182i) q^{88} +(-4.12874 + 1.21231i) q^{89} +(-5.00261 + 3.00438i) q^{90} +24.4777i q^{91} +(3.02955 - 3.71777i) q^{92} +(0.565791 + 10.0538i) q^{93} +(3.57060 + 7.81853i) q^{94} +(-0.868456 - 2.95769i) q^{95} +(1.05891 - 1.37066i) q^{96} +(-2.18434 + 3.39889i) q^{97} +(-4.30968 + 3.73436i) q^{98} +(-2.01459 - 7.72099i) 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 $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$-1$	$e\left(\frac{15}{22}\right)$

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 $

$2$	−0.909632	+	0.415415i	−0.643207	+	0.293743i
$2$	−0.909632	+	0.415415i	−0.643207	+	0.293743i
$3$	−0.580581	−	1.63185i	−0.335199	−	0.942147i
$3$	−0.580581	−	1.63185i	−0.335199	−	0.942147i
$4$	0.654861	−	0.755750i	0.327430	−	0.377875i
$5$	−1.63636	−	1.05163i	−0.731803	−	0.470301i	0.120922	−	0.992662i	$-0.461415\pi$
$5$	−1.63636	−	1.05163i	−0.731803	−	0.470301i	−0.852725	+	0.522361i	$0.825051\pi$
$6$	1.20601	+	1.24320i	0.492351	+	0.507534i
$7$	−3.52778	+	0.507219i	−1.33338	+	0.191711i	−0.771880	−	0.635768i	$-0.780683\pi$
$7$	−3.52778	+	0.507219i	−1.33338	+	0.191711i	−0.561497	+	0.827479i	$0.689774\pi$
$8$	−0.281733	+	0.959493i	−0.0996075	+	0.339232i
$9$	−2.32585	+	1.89484i	−0.775284	+	0.631613i
$10$	1.92535	+	0.276823i	0.608848	+	0.0875392i
$11$	−1.10493	+	2.41947i	−0.333150	+	0.729496i	−0.999875	−	0.0158072i	$-0.994968\pi$
$11$	−1.10493	+	2.41947i	−0.333150	+	0.729496i	0.666725	+	0.745304i	$0.267695\pi$
$12$	−1.61347	−	0.629859i	−0.465768	−	0.181825i
$13$	0.977409	−	6.79803i	0.271085	−	1.88543i	−0.166170	−	0.986097i	$-0.553140\pi$
$13$	0.977409	−	6.79803i	0.271085	−	1.88543i	0.437255	−	0.899338i	$-0.355951\pi$
$14$	2.99828	−	1.92688i	0.801323	−	0.514979i
$15$	−0.766051	+	3.28085i	−0.197794	+	0.847111i
$16$	−0.142315	−	0.989821i	−0.0355787	−	0.247455i
$17$	−3.22982	−	3.72741i	−0.783345	−	0.904029i	0.214001	−	0.976833i	$-0.431350\pi$
$17$	−3.22982	−	3.72741i	−0.783345	−	0.904029i	−0.997346	+	0.0728046i	$0.976805\pi$
$18$	1.32852	−	2.68980i	0.313136	−	0.633992i
$19$	1.19767	+	1.03779i	0.274764	+	0.238084i	0.781332	−	0.624116i	$-0.214541\pi$
$19$	1.19767	+	1.03779i	0.274764	+	0.238084i	−0.506568	+	0.862200i	$0.669086\pi$
$20$	−1.86635	+	0.548011i	−0.417329	+	0.122539i
$21$	2.87587	+	5.46232i	0.627566	+	1.19198i
$22$		−	2.65983i		−	0.567078i
$23$	4.79364	−	0.145045i	0.999543	−	0.0302441i
$23$	4.79364	−	0.145045i	0.999543	−	0.0302441i
$24$	1.72931	−	0.0973192i	0.352995	−	0.0198652i
$25$	−0.505314	−	1.10648i	−0.101063	−	0.221296i
$26$	1.93492	+	6.58974i	0.379469	+	1.29235i
$27$	4.44243	+	2.69532i	0.854947	+	0.518715i
$28$	−1.92688	+	2.99828i	−0.364145	+	0.566621i
$29$	2.48747	−	2.15541i	0.461912	−	0.400249i	−0.392577	−	0.919719i	$-0.628416\pi$
$29$	2.48747	−	2.15541i	0.461912	−	0.400249i	0.854488	+	0.519470i	$0.173871\pi$
$30$	−0.666088	−	3.30259i	−0.121610	−	0.602968i
$31$	−5.57827	−	1.63793i	−1.00189	−	0.294180i	−0.260656	−	0.965432i	$-0.583939\pi$
$31$	−5.57827	−	1.63793i	−1.00189	−	0.294180i	−0.741230	+	0.671251i	$0.765757\pi$
$32$	0.540641	+	0.841254i	0.0955727	+	0.148714i
$33$	4.58970	+	0.398385i	0.798965	+	0.0693500i
$34$	4.48636	+	2.04885i	0.769405	+	0.351376i
$35$	6.30613	+	2.87991i	1.06593	+	0.486794i
$36$	−0.0910837	+	2.99862i	−0.0151806	+	0.499769i
$37$	3.42164	+	5.32418i	0.562514	+	0.875289i	0.999710	−	0.0240772i	$-0.00766476\pi$
$37$	3.42164	+	5.32418i	0.562514	+	0.875289i	−0.437196	+	0.899366i	$0.644028\pi$
$38$	−1.52055	−	0.446473i	−0.246666	−	0.0724276i
$39$	−11.6608	+	2.35183i	−1.86722	+	0.376594i
$40$	1.47004	−	1.27380i	0.232434	−	0.201405i
$41$	−0.280858	+	0.437024i	−0.0438627	+	0.0682516i	−0.862492	−	0.506070i	$-0.831098\pi$
$41$	−0.280858	+	0.437024i	−0.0438627	+	0.0682516i	0.818630	+	0.574322i	$0.194734\pi$
$42$	−4.88511	−	3.77402i	−0.753789	−	0.582344i
$43$	1.05153	+	3.58117i	0.160356	+	0.546123i	0.999996	+	0.00297888i	$0.000948207\pi$
$43$	1.05153	+	3.58117i	0.160356	+	0.546123i	−0.839639	+	0.543144i	$0.817234\pi$
$44$	1.10493	+	2.41947i	0.166575	+	0.364748i
$45$	5.79859	−	0.654719i	0.864403	−	0.0975997i
$46$	−4.30019	+	2.12329i	−0.634029	+	0.313062i
$47$		−	8.59526i		−	1.25375i	−0.779121	−	0.626874i	$-0.784334\pi$
$47$		−	8.59526i		−	1.25375i	0.779121	−	0.626874i	$-0.215666\pi$
$48$	−1.53261	+	0.806908i	−0.221213	+	0.116467i
$49$	5.47153	−	1.60658i	0.781647	−	0.229512i
$50$	0.919299	+	0.796577i	0.130008	+	0.112653i
$51$	−4.20739	+	7.43463i	−0.589152	+	1.04106i
$52$	−4.49754	−	5.19044i	−0.623697	−	0.719785i
$53$	−0.616803	−	4.28996i	−0.0847244	−	0.589271i	−0.987315	−	0.158772i	$-0.949247\pi$
$53$	−0.616803	−	4.28996i	−0.0847244	−	0.589271i	0.902591	−	0.430499i	$-0.141663\pi$
$54$	−5.16066	−	0.606299i	−0.702277	−	0.0825068i
$55$	4.35244	−	2.79714i	0.586883	−	0.377167i
$56$	0.507219	−	3.52778i	0.0677799	−	0.471420i
$57$	0.998164	−	2.55693i	0.132210	−	0.338674i
$58$	−1.36730	+	2.99396i	−0.179535	+	0.393126i
$59$	−7.37948	−	1.06101i	−0.960727	−	0.138132i	−0.355931	−	0.934512i	$-0.615836\pi$
$59$	−7.37948	−	1.06101i	−0.960727	−	0.138132i	−0.604796	+	0.796381i	$0.706745\pi$
$60$	1.97784	+	2.72744i	0.255338	+	0.352111i
$61$	2.50799	−	8.54143i	0.321115	−	1.09362i	−0.627876	−	0.778314i	$-0.716075\pi$
$61$	2.50799	−	8.54143i	0.321115	−	1.09362i	0.948991	−	0.315304i	$-0.102106\pi$
$62$	5.75459	−	0.827385i	0.730833	−	0.105078i
$63$	7.24400	−	7.86430i	0.912658	−	0.990808i
$64$	−0.841254	−	0.540641i	−0.105157	−	0.0675801i
$65$	−8.74838	+	10.0962i	−1.08510	+	1.25228i
$66$	−4.34043	+	1.54425i	−0.534271	+	0.190084i
$67$	−7.78164	+	3.55375i	−0.950678	+	0.434160i	−0.829522	−	0.558473i	$-0.811387\pi$
$67$	−7.78164	+	3.55375i	−0.950678	+	0.434160i	−0.121156	+	0.992634i	$0.538660\pi$
$68$	−4.93207			−0.598101
$69$	−3.01979	−	7.73827i	−0.363540	−	0.931579i
$70$	−6.93262			−0.828606
$71$	−3.61816	+	1.65236i	−0.429396	+	0.196099i	−0.618376	−	0.785882i	$-0.712209\pi$
$71$	−3.61816	+	1.65236i	−0.429396	+	0.196099i	0.188980	+	0.981981i	$0.439482\pi$
$72$	−1.16282	−	2.76548i	−0.137039	−	0.325914i
$73$	−0.420832	+	0.485666i	−0.0492547	+	0.0568429i	−0.779842	−	0.625976i	$-0.784701\pi$
$73$	−0.420832	+	0.485666i	−0.0492547	+	0.0568429i	0.730588	+	0.682819i	$0.239246\pi$
$74$	−5.32418	−	3.42164i	−0.618923	−	0.397758i
$75$	−1.51223	+	1.46700i	−0.174618	+	0.169394i
$76$	1.56861	−	0.225532i	0.179932	−	0.0258703i
$77$	2.67077	−	9.09579i	0.304362	−	1.03656i
$78$	9.63007	−	6.98338i	1.09039	−	0.790712i
$79$	9.47779	+	1.36270i	1.06633	+	0.153316i	0.653072	−	0.757296i	$-0.273480\pi$
$79$	9.47779	+	1.36270i	1.06633	+	0.153316i	0.413263	+	0.910612i	$0.364389\pi$
$80$	−0.808043	+	1.76937i	−0.0903419	+	0.197821i
$81$	1.81916	−	8.81423i	0.202129	−	0.979359i
$82$	0.0739313	−	0.514203i	0.00816434	−	0.0567843i
$83$	4.85775	−	3.12189i	0.533207	−	0.342672i	−0.246170	−	0.969227i	$-0.579172\pi$
$83$	4.85775	−	3.12189i	0.533207	−	0.342672i	0.779377	+	0.626555i	$0.215536\pi$
$84$	6.01144	+	1.40362i	0.655902	+	0.153148i
$85$	1.36531	+	9.49594i	0.148089	+	1.02998i
$86$	−2.44417	−	2.82073i	−0.263562	−	0.304167i
$87$	−4.96147	−	2.80779i	−0.531926	−	0.301026i
$88$	−2.01016	−	1.74182i	−0.214284	−	0.185678i
$89$	−4.12874	+	1.21231i	−0.437646	+	0.128504i	−0.493131	−	0.869955i	$-0.664148\pi$
$89$	−4.12874	+	1.21231i	−0.437646	+	0.128504i	0.0554850	+	0.998460i	$0.482330\pi$
$90$	−5.00261	+	3.00438i	−0.527321	+	0.316689i
$91$			24.4777i			2.56596i
$92$	3.02955	−	3.71777i	0.315852	−	0.387605i
$93$	0.565791	+	10.0538i	0.0586698	+	1.04253i
$94$	3.57060	+	7.81853i	0.368279	+	0.806420i
$95$	−0.868456	−	2.95769i	−0.0891017	−	0.303453i
$96$	1.05891	−	1.37066i	0.108075	−	0.139892i
$97$	−2.18434	+	3.39889i	−0.221786	+	0.345105i	−0.934260	−	0.356593i	$-0.883938\pi$
$97$	−2.18434	+	3.39889i	−0.221786	+	0.345105i	0.712474	+	0.701698i	$0.247575\pi$
$98$	−4.30968	+	3.73436i	−0.435343	+	0.377227i
$99$	−2.01459	−	7.72099i	−0.202474	−	0.775988i
$100$	−1.16713	−	0.342701i	−0.116713	−	0.0342701i
$101$	9.58063	+	14.9077i	0.953308	+	1.48338i	0.873651	+	0.486554i	$0.161746\pi$
$101$	9.58063	+	14.9077i	0.953308	+	1.48338i	0.0796572	+	0.996822i	$0.474617\pi$
$102$	0.738717	−	8.51059i	0.0731439	−	0.842674i
$103$	−13.7927	−	6.29890i	−1.35903	−	0.620649i	−0.403349	−	0.915046i	$-0.632154\pi$
$103$	−13.7927	−	6.29890i	−1.35903	−	0.620649i	−0.955683	+	0.294397i	$0.904881\pi$
$104$	6.24730	+	2.85304i	0.612598	+	0.279764i
$105$	1.03836	−	11.9627i	0.101333	−	1.16744i
$106$	2.34318	+	3.64605i	0.227589	+	0.354136i
$107$	−10.3695	−	3.04475i	−1.00245	−	0.294347i	−0.260991	−	0.965341i	$-0.584049\pi$
$107$	−10.3695	−	3.04475i	−1.00245	−	0.294347i	−0.741462	+	0.670994i	$0.765867\pi$
$108$	4.94617	−	1.59231i	0.475945	−	0.153220i
$109$	0.308110	−	0.266979i	0.0295116	−	0.0255720i	−0.639980	−	0.768391i	$-0.721057\pi$
$109$	0.308110	−	0.266979i	0.0295116	−	0.0255720i	0.669492	+	0.742820i	$0.266512\pi$
$110$	−2.79714	+	4.35244i	−0.266697	+	0.414989i
$111$	6.70170	−	8.67471i	0.636097	−	0.823367i
$112$	1.00411	+	3.41969i	0.0948796	+	0.323130i
$113$	−2.10451	−	4.60823i	−0.197976	−	0.433506i	0.784442	−	0.620202i	$-0.212949\pi$
$113$	−2.10451	−	4.60823i	−0.197976	−	0.433506i	−0.982418	+	0.186696i	$0.940222\pi$
$114$	0.154226	+	2.74052i	0.0144446	+	0.256673i
$115$	−7.99666	−	4.80376i	−0.745692	−	0.447953i
$116$		−	3.29140i		−	0.305599i
$117$	10.6079	+	17.6632i	0.980698	+	1.63297i
$118$	7.15337	−	2.10042i	0.658521	−	0.193359i
$119$	13.2847	+	11.5113i	1.21781	+	1.05524i
$120$	−2.93213	−	1.65934i	−0.267665	−	0.151476i
$121$	2.57053	+	2.96655i	0.233685	+	0.269686i
$122$	1.26689	+	8.81141i	0.114699	+	0.797748i
$123$	0.876217	+	0.204590i	0.0790058	+	0.0184472i
$124$	−4.89085	+	3.14316i	−0.439211	+	0.282264i
$125$	−1.72085	+	11.9687i	−0.153917	+	1.07052i
$126$	−3.32242	+	10.1629i	−0.295985	+	0.905381i
$127$	2.64549	−	5.79282i	0.234749	−	0.514030i	−0.755193	−	0.655503i	$-0.772457\pi$
$127$	2.64549	−	5.79282i	0.234749	−	0.514030i	0.989942	+	0.141473i	$0.0451839\pi$
$128$	0.989821	+	0.142315i	0.0874887	+	0.0125790i
$129$	5.23343	−	3.79509i	0.460777	−	0.334139i
$130$	3.76371	−	12.8180i	0.330099	−	1.12421i
$131$	−1.59559	+	0.229412i	−0.139408	+	0.0200438i	−0.211665	−	0.977342i	$-0.567889\pi$
$131$	−1.59559	+	0.229412i	−0.139408	+	0.0200438i	0.0722578	+	0.997386i	$0.476980\pi$
$132$	3.30670	−	3.20778i	0.287811	−	0.279201i
$133$	−4.75150	−	3.05360i	−0.412007	−	0.264781i
$134$	5.60214	−	6.46522i	0.483951	−	0.558510i
$135$	−4.43496	−	9.08230i	−0.381700	−	0.781680i
$136$	4.48636	−	2.04885i	0.384703	−	0.175688i
$137$	2.47440			0.211403			0.105701	−	0.994398i	$-0.466291\pi$
$137$	2.47440			0.211403			0.105701	+	0.994398i	$0.466291\pi$
$138$	5.96149	+	5.78452i	0.507476	+	0.492411i
$139$	12.3439			1.04699			0.523496	−	0.852028i	$-0.324627\pi$
$139$	12.3439			1.04699			0.523496	+	0.852028i	$0.324627\pi$
$140$	6.30613	−	2.87991i	0.532965	−	0.243397i
$141$	−14.0262	+	4.99025i	−1.18122	+	0.420255i
$142$	2.60478	−	3.00607i	0.218588	−	0.252264i
$143$	15.3676	+	9.87618i	1.28511	+	0.825888i
$144$	2.20656	+	2.03251i	0.183880	+	0.169376i
$145$	−6.33708	+	0.911135i	−0.526266	+	0.0756656i
$146$	0.181049	−	0.616597i	0.0149837	−	0.0510300i
$147$	−5.79837	−	7.99594i	−0.478241	−	0.659494i
$148$	6.26444	+	0.900691i	0.514934	+	0.0740363i
$149$	9.87803	−	21.6299i	0.809240	−	1.77199i	0.198599	−	0.980081i	$-0.436361\pi$
$149$	9.87803	−	21.6299i	0.809240	−	1.77199i	0.610641	−	0.791908i	$-0.290912\pi$
$150$	0.766164	−	1.96263i	0.0625570	−	0.160248i
$151$	2.74441	−	19.0878i	0.223337	−	1.55334i	−0.501952	−	0.864896i	$-0.667385\pi$
$151$	2.74441	−	19.0878i	0.223337	−	1.55334i	0.725289	−	0.688445i	$-0.241706\pi$
$152$	−1.33317	+	0.856776i	−0.108134	+	0.0694937i
$153$	14.5749	+	2.54941i	1.17831	+	0.206107i
$154$	1.34911	+	9.38330i	0.108715	+	0.756128i
$155$	7.40557	+	8.54648i	0.594830	+	0.686470i
$156$	−5.85882	+	10.3528i	−0.469081	+	0.828885i
$157$	−5.26294	−	4.56036i	−0.420028	−	0.363957i	0.419054	−	0.907961i	$-0.362362\pi$
$157$	−5.26294	−	4.56036i	−0.420028	−	0.363957i	−0.839082	+	0.544005i	$0.816907\pi$
$158$	−9.18739	+	2.69766i	−0.730909	+	0.214614i
$159$	−6.64245	+	3.49720i	−0.526781	+	0.277346i
$160$		−	1.94515i		−	0.153777i
$161$	−16.8373	+	2.94311i	−1.32697	+	0.231950i
$162$	2.00680	+	8.77341i	0.157669	+	0.689304i
$163$	4.37969	+	9.59019i	0.343044	+	0.751161i	0.999996	−	0.00277075i	$-0.000881957\pi$
$163$	4.37969	+	9.59019i	0.343044	+	0.751161i	−0.656952	+	0.753932i	$0.728155\pi$
$164$	0.146358	+	0.498448i	0.0114286	+	0.0389222i
$165$	−7.09146	−	5.47855i	−0.552069	−	0.426504i
$166$	−3.12189	+	4.85775i	−0.242305	+	0.377035i
$167$	−0.647431	+	0.561002i	−0.0500997	+	0.0434117i	−0.679551	−	0.733628i	$-0.737825\pi$
$167$	−0.647431	+	0.561002i	−0.0500997	+	0.0434117i	0.629451	+	0.777040i	$0.283280\pi$
$168$	−6.05128	+	1.22046i	−0.466867	+	0.0941606i
$169$	−32.7845	−	9.62640i	−2.52188	−	0.740492i
$170$	−5.18669	−	8.07064i	−0.397801	−	0.618990i
$171$	−4.75204	−	0.144344i	−0.363397	−	0.0110383i
$172$	3.39507	+	1.55048i	0.258872	+	0.118223i
$173$	−14.3184	−	6.53898i	−1.08861	−	0.497150i	−0.211466	−	0.977385i	$-0.567824\pi$
$173$	−14.3184	−	6.53898i	−1.08861	−	0.497150i	−0.877139	+	0.480236i	$0.840551\pi$
$174$	5.67951	+	0.492980i	0.430563	+	0.0373727i
$175$	2.34386	+	3.64712i	0.177180	+	0.275697i
$176$	2.55209	+	0.749360i	0.192371	+	0.0564852i
$177$	2.55298	+	12.6582i	0.191894	+	0.951448i
$178$	3.25203	−	2.81790i	0.243750	−	0.211210i
$179$	−0.697158	+	1.08480i	−0.0521080	+	0.0810817i	−0.866330	−	0.499472i	$-0.833527\pi$
$179$	−0.697158	+	1.08480i	−0.0521080	+	0.0810817i	0.814222	+	0.580554i	$0.197164\pi$
$180$	3.30247	−	4.81103i	0.246151	−	0.358593i
$181$	3.73429	+	12.7178i	0.277568	+	0.945309i	0.973784	+	0.227477i	$0.0730475\pi$
$181$	3.73429	+	12.7178i	0.277568	+	0.945309i	−0.696216	+	0.717833i	$0.745134\pi$
$182$	−10.1684	−	22.2657i	−0.753733	−	1.65045i
$183$	−15.3944	+	0.866338i	−1.13799	+	0.0640415i
$184$	−1.21135	+	4.64033i	−0.0893022	+	0.342089i
$185$		−	12.3106i		−	0.905090i
$186$	−4.69117	−	8.91024i	−0.343973	−	0.653331i
$187$	12.5871	−	3.69590i	0.920457	−	0.270271i
$188$	−6.49587	−	5.62870i	−0.473760	−	0.410515i
$189$	−17.0391	−	7.25523i	−1.23941	−	0.527740i
$190$	2.01864	+	2.32964i	0.146448	+	0.169010i
$191$	1.27266	+	8.85155i	0.0920865	+	0.640476i	0.982630	+	0.185577i	$0.0594154\pi$
$191$	1.27266	+	8.85155i	0.0920865	+	0.640476i	−0.890543	+	0.454899i	$0.849675\pi$
$192$	−0.393827	+	1.68668i	−0.0284220	+	0.121726i
$193$	−5.75760	+	3.70019i	−0.414441	+	0.266345i	−0.731203	−	0.682160i	$-0.761041\pi$
$193$	−5.75760	+	3.70019i	−0.414441	+	0.266345i	0.316762	+	0.948505i	$0.397404\pi$
$194$	0.574990	−	3.99915i	0.0412819	−	0.287122i
$195$	21.5545	+	8.41437i	1.54355	+	0.602566i
$196$	2.36891	−	5.18719i	0.169208	−	0.370514i
$197$	14.7138	+	2.11553i	1.04832	+	0.150725i	0.644882	−	0.764282i	$-0.276907\pi$
$197$	14.7138	+	2.11553i	1.04832	+	0.150725i	0.403436	+	0.915008i	$0.367816\pi$
$198$	5.03995	+	6.18637i	0.358174	+	0.439646i
$199$	1.62183	−	5.52343i	0.114968	−	0.391546i	−0.881824	−	0.471579i	$-0.843684\pi$
$199$	1.62183	−	5.52343i	0.114968	−	0.391546i	0.996792	+	0.0800329i	$0.0255025\pi$
$200$	1.20403	−	0.173113i	0.0851375	−	0.0122409i
$201$	10.3171	+	10.6352i	0.727709	+	0.750149i
$202$	−14.9077	−	9.58063i	−1.04891	−	0.674090i
$203$	−7.68200	+	8.86550i	−0.539170	+	0.622236i
$204$	2.86347	+	8.04838i	0.200483	+	0.563499i
$205$	0.919170	−	0.419771i	0.0641976	−	0.0293181i
$206$	15.1629			1.05645
$207$	−10.8744	+	9.42053i	−0.755826	+	0.654772i
$208$	−6.86794			−0.476206
$209$	−3.83423	+	1.75103i	−0.265219	+	0.121122i
$210$	4.02495	+	11.3130i	0.277748	+	0.780669i
$211$	11.6218	−	13.4123i	0.800080	−	0.923341i	−0.198306	−	0.980140i	$-0.563544\pi$
$211$	11.6218	−	13.4123i	0.800080	−	0.923341i	0.998386	+	0.0567990i	$0.0180894\pi$
$212$	−3.64605	−	2.34318i	−0.250412	−	0.160930i
$213$	4.79703	+	4.94495i	0.328687	+	0.338823i
$214$	10.6972	−	1.53803i	0.731247	−	0.105137i
$215$	2.04537	−	6.96590i	0.139493	−	0.475070i
$216$	−3.83772	+	3.50312i	−0.261124	+	0.238357i
$217$	20.5097	+	2.94885i	1.39229	+	0.200181i
$218$	−0.169360	+	0.370846i	−0.0114705	+	0.0251169i
$219$	1.03686	+	0.404765i	0.0700645	+	0.0273515i
$220$	0.736302	−	5.12110i	0.0496415	−	0.345264i
$221$	−28.4959	+	18.3132i	−1.91684	+	1.23188i
$222$	−2.49248	+	10.6748i	−0.167284	+	0.716444i
$223$	−1.96918	−	13.6959i	−0.131866	−	0.917148i	−0.943120	−	0.332454i	$-0.892124\pi$
$223$	−1.96918	−	13.6959i	−0.131866	−	0.917148i	0.811254	−	0.584694i	$-0.198786\pi$
$224$	−2.33396	−	2.69354i	−0.155944	−	0.179969i
$225$	3.27189	+	1.61602i	0.218126	+	0.107735i
$226$	3.82866	+	3.31755i	0.254679	+	0.220680i
$227$	18.5921	−	5.45913i	1.23400	−	0.362335i	0.401241	−	0.915972i	$-0.368579\pi$
$227$	18.5921	−	5.45913i	1.23400	−	0.362335i	0.832758	+	0.553637i	$0.186761\pi$
$228$	−1.27874	−	2.42880i	−0.0846867	−	0.160851i
$229$		−	22.5956i		−	1.49316i	−0.665296	−	0.746579i	$-0.731695\pi$
$229$		−	22.5956i		−	1.49316i	0.665296	−	0.746579i	$-0.268305\pi$
$230$	9.26957	+	1.04773i	0.611217	+	0.0690851i
$231$	−16.3935	+	0.922566i	−1.07862	+	0.0607004i
$232$	1.36730	+	2.99396i	0.0897674	+	0.196563i
$233$	−7.83566	−	26.6858i	−0.513331	−	1.74825i	−0.652312	−	0.757951i	$-0.726201\pi$
$233$	−7.83566	−	26.6858i	−0.513331	−	1.74825i	0.138981	−	0.990295i	$-0.455617\pi$
$234$	−16.9868	−	11.6604i	−1.11046	−	0.762263i
$235$	−9.03900	+	14.0650i	−0.589639	+	0.917497i
$236$	−5.63439	+	4.88223i	−0.366768	+	0.317806i
$237$	−3.27891	−	16.2575i	−0.212988	−	1.05604i
$238$	−16.8661	−	4.95234i	−1.09327	−	0.321013i
$239$	−0.694698	−	1.08097i	−0.0449363	−	0.0699222i	0.818059	−	0.575135i	$-0.195050\pi$
$239$	−0.694698	−	1.08097i	−0.0449363	−	0.0699222i	−0.862995	+	0.505213i	$0.831414\pi$
$240$	3.35647	+	0.291341i	0.216659	+	0.0188060i
$241$	23.9395	+	10.9328i	1.54208	+	0.704244i	0.991448	−	0.130505i	$-0.0416600\pi$
$241$	23.9395	+	10.9328i	1.54208	+	0.704244i	0.550631	+	0.834749i	$0.314387\pi$
$242$	−3.57059	−	1.63063i	−0.229526	−	0.104821i
$243$	−15.4396	+	2.14878i	−0.990454	+	0.137844i
$244$	−4.81280	−	7.48886i	−0.308108	−	0.479425i
$245$	−10.6429	−	3.12504i	−0.679951	−	0.199652i
$246$	−0.882024	+	0.177892i	−0.0562358	+	0.0113420i
$247$	8.22551	−	7.12745i	0.523377	−	0.453509i
$248$	3.14316	−	4.89085i	0.199591	−	0.310569i
$249$	−7.91476	−	6.11460i	−0.501578	−	0.387497i
$250$	−3.40666	−	11.6020i	−0.215456	−	0.733776i
$251$	7.25869	+	15.8943i	0.458164	+	1.00324i	0.987902	+	0.155079i	$0.0495631\pi$
$251$	7.25869	+	15.8943i	0.458164	+	1.00324i	−0.529738	+	0.848161i	$0.677710\pi$
$252$	−1.19963	−	10.6247i	−0.0755696	−	0.669291i
$253$	−4.94572	+	11.7583i	−0.310934	+	0.739238i
$254$			6.36831i			0.399583i
$255$	14.7032	−	7.74114i	0.920753	−	0.484769i
$256$	−0.959493	+	0.281733i	−0.0599683	+	0.0176083i
$257$	3.22526	+	2.79470i	0.201186	+	0.174329i	0.749627	−	0.661861i	$-0.230233\pi$
$257$	3.22526	+	2.79470i	0.201186	+	0.174329i	−0.548441	+	0.836189i	$0.684778\pi$
$258$	−3.18395	+	5.62618i	−0.198224	+	0.350271i
$259$	−14.7713	−	17.0470i	−0.917845	−	1.05925i
$260$	1.90120	+	13.2232i	0.117908	+	0.820066i
$261$	−1.70134	+	9.72652i	−0.105310	+	0.602056i
$262$	1.35610	−	0.871513i	0.0837802	−	0.0538423i
$263$	−1.18371	+	8.23292i	−0.0729910	+	0.507663i	0.920226	+	0.391387i	$0.128005\pi$
$263$	−1.18371	+	8.23292i	−0.0729910	+	0.507663i	−0.993217	+	0.116276i	$0.962904\pi$
$264$	−1.67532	+	4.29155i	−0.103109	+	0.264127i
$265$	−3.50212	+	7.66857i	−0.215133	+	0.471076i
$266$	5.59063	+	0.803811i	0.342783	+	0.0492848i
$267$	4.37537	+	6.03364i	0.267769	+	0.369253i
$268$	−2.41014	+	8.20818i	−0.147223	+	0.501395i
$269$	17.5668	−	2.52573i	1.07107	−	0.153996i	0.415848	−	0.909434i	$-0.363485\pi$
$269$	17.5668	−	2.52573i	1.07107	−	0.153996i	0.655220	+	0.755438i	$0.272576\pi$
$270$	7.80710	+	6.41920i	0.475125	+	0.390660i
$271$	−3.78240	−	2.43080i	−0.229764	−	0.147661i	0.420694	−	0.907203i	$-0.361787\pi$
$271$	−3.78240	−	2.43080i	−0.229764	−	0.147661i	−0.650458	+	0.759542i	$0.725423\pi$
$272$	−3.22982	+	3.72741i	−0.195836	+	0.226007i
$273$	39.9439	−	14.2113i	2.41752	−	0.860108i
$274$	−2.25080	+	1.02790i	−0.135976	+	0.0620980i
$275$	3.23543			0.195104
$276$	−7.82574	−	2.78529i	−0.471054	−	0.167655i
$277$	12.3707			0.743286			0.371643	−	0.928376i	$-0.378795\pi$
$277$	12.3707			0.743286			0.371643	+	0.928376i	$0.378795\pi$
$278$	−11.2284	+	5.12782i	−0.673433	+	0.307546i
$279$	16.0778	−	6.76035i	0.962554	−	0.404731i
$280$	−4.53990	+	5.23932i	−0.271311	+	0.313109i
$281$	14.5650	+	9.36036i	0.868876	+	0.558393i	0.897409	−	0.441200i	$-0.145447\pi$
$281$	14.5650	+	9.36036i	0.868876	+	0.558393i	−0.0285329	+	0.999593i	$0.509084\pi$
$282$	10.6856	−	10.3660i	0.636319	−	0.617284i
$283$	−10.2763	+	1.47751i	−0.610863	+	0.0878289i	−0.440802	−	0.897605i	$-0.645306\pi$
$283$	−10.2763	+	1.47751i	−0.610863	+	0.0878289i	−0.170062	+	0.985433i	$0.554397\pi$
$284$	−1.12062	+	3.81649i	−0.0664966	+	0.226467i
$285$	−4.32229	+	3.13437i	−0.256030	+	0.185664i
$286$	−18.0816	−	2.59974i	−1.06919	−	0.153726i
$287$	0.769140	−	1.68418i	0.0454009	−	0.0994140i
$288$	−2.85149	−	0.932202i	−0.168026	−	0.0549305i
$289$	−1.04249	+	7.25071i	−0.0613232	+	0.426512i
$290$	5.38591	−	3.46132i	0.316272	−	0.203256i
$291$	6.81466	+	1.59117i	0.399482	+	0.0932759i
$292$	0.0914556	+	0.636087i	0.00535203	+	0.0372242i
$293$	5.82879	+	6.72678i	0.340521	+	0.392983i	0.900020	−	0.435849i	$-0.143552\pi$
$293$	5.82879	+	6.72678i	0.340521	+	0.392983i	−0.559499	+	0.828831i	$0.689006\pi$
$294$	8.59601	+	4.86464i	0.501330	+	0.283711i
$295$	10.9597	+	9.49665i	0.638099	+	0.552916i
$296$	−6.07250	+	1.78305i	−0.352957	+	0.103637i
$297$	−11.4298	+	7.77017i	−0.663226	+	0.450871i
$298$			23.7787i			1.37746i
$299$	3.69932	−	32.7291i	0.213937	−	1.89277i
$300$	0.118380	+	2.10355i	0.00683466	+	0.121449i
$301$	−5.52599	−	12.1002i	−0.318513	−	0.697446i
$302$	5.43295	+	18.5029i	0.312631	+	1.06472i
$303$	18.7648	−	24.2893i	1.07801	−	1.39538i
$304$	0.856776	−	1.33317i	0.0491395	−	0.0764625i
$305$	−13.0864	+	11.3394i	−0.749323	+	0.649292i
$306$	−14.3169	+	3.73561i	−0.818441	+	0.213551i
$307$	21.4304	+	6.29254i	1.22310	+	0.359134i	0.828642	−	0.559780i	$-0.189114\pi$
$307$	21.4304	+	6.29254i	1.22310	+	0.359134i	0.394458	+	0.918914i	$0.370932\pi$
$308$	−5.12516	−	7.97491i	−0.292033	−	0.454412i
$309$	−2.27108	+	26.1646i	−0.129197	+	1.48845i
$310$	−10.2867	−	4.69777i	−0.584244	−	0.266815i
$311$	−6.80421	−	3.10738i	−0.385831	−	0.176203i	0.213050	−	0.977041i	$-0.431660\pi$
$311$	−6.80421	−	3.10738i	−0.385831	−	0.176203i	−0.598881	+	0.800838i	$0.704388\pi$
$312$	1.02867	−	11.8511i	0.0582369	−	0.670934i
$313$	−3.33547	−	5.19010i	−0.188532	−	0.293362i	0.734101	−	0.679040i	$-0.237604\pi$
$313$	−3.33547	−	5.19010i	−0.188532	−	0.293362i	−0.922633	+	0.385678i	$0.873967\pi$
$314$	6.68178	+	1.96195i	0.377075	+	0.110719i
$315$	−20.1241	+	5.25086i	−1.13386	+	0.295852i
$316$	7.23649	−	6.27046i	0.407085	−	0.352741i
$317$	−0.888919	+	1.38318i	−0.0499267	+	0.0776874i	−0.865320	−	0.501220i	$-0.832885\pi$
$317$	−0.888919	+	1.38318i	−0.0499267	+	0.0776874i	0.815393	+	0.578908i	$0.196521\pi$
$318$	4.58940	−	5.94054i	0.257361	−	0.333129i
$319$	2.46644	+	8.39993i	0.138094	+	0.470306i
$320$	0.808043	+	1.76937i	0.0451710	+	0.0989106i
$321$	1.05175	+	18.6891i	0.0587030	+	1.04312i
$322$	14.0932	−	9.67163i	0.785382	−	0.538979i
$323$		−	7.81605i		−	0.434897i
$324$	−5.47005	−	7.14692i	−0.303892	−	0.397051i
$325$	−8.01580	+	2.35365i	−0.444637	+	0.130557i
$326$	−7.96782	−	6.90415i	−0.441297	−	0.382386i
$327$	−0.614552	−	0.347786i	−0.0339848	−	0.0192326i
$328$	−0.340194	−	0.392605i	−0.0187841	−	0.0216780i
$329$	4.35968	+	30.3222i	0.240357	+	1.67172i
$330$	8.72649	+	2.03757i	0.480377	+	0.112164i
$331$	11.9212	−	7.66128i	0.655248	−	0.421102i	−0.170333	−	0.985387i	$-0.554484\pi$
$331$	11.9212	−	7.66128i	0.655248	−	0.421102i	0.825580	+	0.564285i	$0.190848\pi$
$332$	0.821785	−	5.71564i	0.0451013	−	0.313687i
$333$	−18.0467	−	5.89978i	−0.988952	−	0.323306i
$334$	0.355875	−	0.779258i	0.0194726	−	0.0426391i
$335$	16.4708	+	2.36814i	0.899895	+	0.129385i
$336$	4.99744	−	3.62396i	0.272633	−	0.197703i
$337$	−4.74687	+	16.1663i	−0.258578	+	0.880637i	0.723205	+	0.690633i	$0.242668\pi$
$337$	−4.74687	+	16.1663i	−0.258578	+	0.880637i	−0.981783	+	0.190004i	$0.939150\pi$
$338$	33.8208	−	4.86269i	1.83961	−	0.264496i
$339$	−6.29809	+	6.10969i	−0.342065	+	0.331833i
$340$	8.07064	+	5.18669i	0.437692	+	0.281288i
$341$	10.1265	−	11.6866i	0.548382	−	0.632866i
$342$	4.38257	−	1.84277i	0.236982	−	0.0996454i
$343$	4.20641	−	1.92100i	0.227125	−	0.103725i
$344$	−3.73236			−0.201235
$345$	−3.19630	+	15.8383i	−0.172083	+	0.852705i
$346$	15.7408			0.846233
$347$	−17.0652	+	7.79341i	−0.916108	+	0.418372i	−0.816956	−	0.576700i	$-0.804340\pi$
$347$	−17.0652	+	7.79341i	−0.916108	+	0.418372i	−0.0991518	+	0.995072i	$0.531613\pi$
$348$	−5.37106	+	1.91092i	−0.287919	+	0.102436i
$349$	−19.1868	+	22.1427i	−1.02704	+	1.18527i	−0.0445448	+	0.999007i	$0.514184\pi$
$349$	−19.1868	+	22.1427i	−1.02704	+	1.18527i	−0.982500	+	0.186265i	$0.940362\pi$
$350$	−3.64712	−	2.34386i	−0.194947	−	0.125285i
$351$	22.6650	−	27.5654i	1.20977	−	1.47133i
$352$	−2.63276	+	0.378533i	−0.140326	+	0.0201759i
$353$	−3.32205	+	11.3139i	−0.176815	+	0.602176i	0.822621	+	0.568590i	$0.192511\pi$
$353$	−3.32205	+	11.3139i	−0.176815	+	0.602176i	−0.999436	+	0.0335861i	$0.989307\pi$
$354$	−7.58068	−	10.4537i	−0.402909	−	0.555610i
$355$	7.65827	+	1.10109i	0.406459	+	0.0584400i
$356$	−1.78755	+	3.91419i	−0.0947400	+	0.207452i
$357$	11.0718	−	28.3618i	0.585980	−	1.50107i
$358$	0.183515	−	1.27638i	0.00969909	−	0.0674587i
$359$	−8.01984	+	5.15404i	−0.423271	+	0.272020i	−0.734889	−	0.678188i	$-0.762766\pi$
$359$	−8.01984	+	5.15404i	−0.423271	+	0.272020i	0.311618	+	0.950208i	$0.399129\pi$
$360$	−1.00545	+	5.74817i	−0.0529921	+	0.302955i
$361$	−2.34657	−	16.3208i	−0.123504	−	0.858987i
$362$	−8.68001	−	10.0173i	−0.456211	−	0.526496i
$363$	3.34855	−	5.91704i	0.175754	−	0.310564i
$364$	18.4990	+	16.0295i	0.969613	+	0.840175i
$365$	1.19937	−	0.352167i	0.0627780	−	0.0184333i
$366$	13.6433	−	7.18311i	0.713149	−	0.375467i
$367$			3.14905i			0.164379i	0.996617	+	0.0821896i	$0.0261913\pi$
$367$			3.14905i			0.164379i	−0.996617	+	0.0821896i	$0.973809\pi$
$368$	−0.825775	−	4.72420i	−0.0430465	−	0.246266i
$369$	−0.174856	−	1.54863i	−0.00910264	−	0.0806186i
$370$	5.11399	+	11.1981i	0.265864	+	0.582160i
$371$	4.35189	+	14.8212i	0.225939	+	0.769478i
$372$	7.96869	+	6.15626i	0.413157	+	0.319187i
$373$	2.69316	−	4.19063i	0.139446	−	0.216983i	−0.764505	−	0.644617i	$-0.777017\pi$
$373$	2.69316	−	4.19063i	0.139446	−	0.216983i	0.903952	+	0.427635i	$0.140653\pi$
$374$	−9.91426	+	8.59076i	−0.512654	+	0.444218i
$375$	20.5302	−	4.14067i	1.06018	−	0.213823i
$376$	8.24710	+	2.42157i	0.425311	+	0.124883i
$377$	−12.2212	−	19.0166i	−0.629426	−	0.979406i
$378$	18.5132	−	0.478691i	0.952217	−	0.0246212i
$379$	−26.1945	−	11.9626i	−1.34552	−	0.614479i	−0.393165	−	0.919468i	$-0.628620\pi$
$379$	−26.1945	−	11.9626i	−1.34552	−	0.614479i	−0.952356	+	0.304989i	$0.901347\pi$
$380$	−2.80399	−	1.28054i	−0.143842	−	0.0656903i
$381$	−10.9889	−	0.953836i	−0.562979	−	0.0488665i
$382$	−4.83472	−	7.52297i	−0.247366	−	0.384909i
$383$	−25.2459	−	7.41287i	−1.29001	−	0.378780i	−0.436426	−	0.899740i	$-0.643756\pi$
$383$	−25.2459	−	7.41287i	−1.29001	−	0.378780i	−0.853581	+	0.520960i	$0.825574\pi$
$384$	−0.342436	−	1.69786i	−0.0174749	−	0.0866437i
$385$	−13.9357	+	12.0754i	−0.710229	+	0.615417i
$386$	3.70019	−	5.75760i	0.188335	−	0.293054i
$387$	−9.23144	−	6.33679i	−0.469260	−	0.322117i
$388$	1.13828	+	3.87661i	0.0577872	+	0.196805i
$389$	−15.3834	−	33.6850i	−0.779971	−	1.70790i	−0.703356	−	0.710838i	$-0.748316\pi$
$389$	−15.3834	−	33.6850i	−0.779971	−	1.70790i	−0.0766148	−	0.997061i	$-0.524411\pi$
$390$	−23.1022	+	1.30010i	−1.16982	+	0.0658332i
$391$	−16.0232	−	17.3994i	−0.810329	−	0.879924i
$392$			5.70252i			0.288021i
$393$	1.30074	+	2.47057i	0.0656134	+	0.124624i
$394$	−14.2630	+	4.18800i	−0.718560	+	0.210988i
$395$	−14.0760	−	12.1970i	−0.708242	−	0.613695i
$396$	−7.15441	−	3.53364i	−0.359523	−	0.177572i
$397$	5.68271	+	6.55820i	0.285207	+	0.329146i	0.880217	−	0.474572i	$-0.157397\pi$
$397$	5.68271	+	6.55820i	0.285207	+	0.329146i	−0.595010	+	0.803719i	$0.702852\pi$
$398$	0.819252	+	5.69802i	0.0410654	+	0.285616i
$399$	−2.22438	+	9.52658i	−0.111358	+	0.476926i
$400$	−1.02331	+	0.657639i	−0.0511653	+	0.0328820i
$401$	0.773621	−	5.38065i	0.0386328	−	0.268697i	−0.961345	−	0.275346i	$-0.911207\pi$
$401$	0.773621	−	5.38065i	0.0386328	−	0.268697i	0.999978	+	0.00664939i	$0.00211658\pi$
$402$	−13.8027	−	5.38826i	−0.688418	−	0.268742i
$403$	−16.5869	+	36.3203i	−0.826254	+	1.80924i
$404$	17.5405	+	2.52194i	0.872672	+	0.125471i
$405$	−12.2461	+	12.5102i	−0.608512	+	0.621636i
$406$	3.30493	−	11.2556i	0.164021	−	0.558604i
$407$	−16.6623	+	2.39568i	−0.825922	+	0.118750i
$408$	−5.94812	−	6.13154i	−0.294476	−	0.303556i
$409$	11.6681	+	7.49865i	0.576952	+	0.370784i	0.796336	−	0.604854i	$-0.206769\pi$
$409$	11.6681	+	7.49865i	0.576952	+	0.370784i	−0.219385	+	0.975638i	$0.570405\pi$
$410$	−0.661728	+	0.763674i	−0.0326804	+	0.0377152i
$411$	−1.43659	−	4.03785i	−0.0708619	−	0.199172i
$412$	−13.7927	+	6.29890i	−0.679516	+	0.310325i
$413$	26.5714			1.30749
$414$	5.97832	−	13.0866i	0.293818	−	0.643173i
$415$	−11.2321			−0.551362
$416$	6.24730	−	2.85304i	0.306299	−	0.139882i
$417$	−7.16661	−	20.1433i	−0.350950	−	0.986421i
$418$	2.76033	−	3.18559i	0.135012	−	0.155812i
$419$	19.7827	+	12.7136i	0.966450	+	0.621100i	0.925776	−	0.378073i	$-0.123413\pi$
$419$	19.7827	+	12.7136i	0.966450	+	0.621100i	0.0406741	+	0.999172i	$0.487049\pi$
$420$	−8.36080	−	8.61862i	−0.407965	−	0.420545i
$421$	−1.89838	+	0.272946i	−0.0925216	+	0.0133026i	−0.188420	−	0.982089i	$-0.560337\pi$
$421$	−1.89838	+	0.272946i	−0.0925216	+	0.0133026i	0.0958985	+	0.995391i	$0.469428\pi$
$422$	−4.99991	+	17.0281i	−0.243392	+	0.828917i
$423$	16.2867	+	19.9913i	0.791884	+	0.972010i
$424$	4.28996	+	0.616803i	0.208339	+	0.0299546i
$425$	−2.49224	+	5.45724i	−0.120891	+	0.264715i
$426$	−6.41774	−	2.50533i	−0.310941	−	0.121384i
$427$	−4.51527	+	31.4044i	−0.218509	+	1.51976i
$428$	−9.09162	+	5.84283i	−0.439460	+	0.282424i
$429$	7.19425	−	30.8116i	0.347342	−	1.48760i
$430$	1.03320	+	7.18608i	0.0498255	+	0.346544i
$431$	−27.0851	−	31.2579i	−1.30464	−	1.50564i	−0.718812	−	0.695205i	$-0.755314\pi$
$431$	−27.0851	−	31.2579i	−1.30464	−	1.50564i	−0.585831	−	0.810433i	$-0.699232\pi$
$432$	2.03567	−	4.78080i	0.0979410	−	0.230016i
$433$	−13.7891	−	11.9483i	−0.662661	−	0.574199i	0.257241	−	0.966347i	$-0.417187\pi$
$433$	−13.7891	−	11.9483i	−0.662661	−	0.574199i	−0.919902	+	0.392148i	$0.871732\pi$
$434$	−19.8813	+	5.83767i	−0.954331	+	0.280217i
$435$	5.16602	+	9.81216i	0.247692	+	0.470457i
$436$		−	0.407688i		−	0.0195247i
$437$	5.89171	+	4.80105i	0.281839	+	0.229665i
$438$	−1.11131	+	0.0625401i	−0.0531003	+	0.00298828i
$439$	−4.36402	−	9.55587i	−0.208283	−	0.456077i	0.776443	−	0.630188i	$-0.217022\pi$
$439$	−4.36402	−	9.55587i	−0.208283	−	0.456077i	−0.984726	+	0.174111i	$0.944295\pi$
$440$	1.45762	+	4.96418i	0.0694891	+	0.236658i
$441$	−9.68173	+	14.1043i	−0.461035	+	0.671635i
$442$	18.3132	−	28.4959i	0.871070	−	1.35541i
$443$	2.88682	−	2.50145i	0.137157	−	0.118847i	−0.583580	−	0.812055i	$-0.698349\pi$
$443$	2.88682	−	2.50145i	0.137157	−	0.118847i	0.720738	+	0.693208i	$0.243803\pi$
$444$	−2.16723	−	10.7455i	−0.102852	−	0.509960i
$445$	8.03101	+	2.35812i	0.380706	+	0.111786i
$446$	7.48073	+	11.6402i	0.354223	+	0.551181i
$447$	−41.0317	−	3.56154i	−1.94073	−	0.168455i
$448$	3.24198	+	1.48056i	0.153169	+	0.0699501i
$449$	23.4815	+	10.7237i	1.10816	+	0.506081i	0.883535	−	0.468364i	$-0.155156\pi$
$449$	23.4815	+	10.7237i	1.10816	+	0.506081i	0.224627	+	0.974445i	$0.427884\pi$
$450$	−3.64754	−	0.110795i	−0.171947	−	0.00522292i
$451$	−0.747034	−	1.16241i	−0.0351765	−	0.0547357i
$452$	−4.86083	−	1.42727i	−0.228634	−	0.0671331i
$453$	−32.7417	+	6.60355i	−1.53834	+	0.310262i
$454$	−14.6441	+	12.6892i	−0.687284	+	0.595535i
$455$	25.7414	−	40.0544i	1.20678	−	1.87778i
$456$	2.17214	+	1.67810i	0.101720	+	0.0785843i
$457$	−0.383433	−	1.30585i	−0.0179362	−	0.0610852i	0.950039	−	0.312132i	$-0.101043\pi$
$457$	−0.383433	−	1.30585i	−0.0179362	−	0.0610852i	−0.967975	+	0.251047i	$0.919225\pi$
$458$	9.38655	+	20.5537i	0.438605	+	0.960410i
$459$	−4.30168	−	25.2642i	−0.200785	−	1.17923i
$460$	−8.86714	+	2.89767i	−0.413432	+	0.135105i
$461$		−	18.8146i		−	0.876283i	−0.898906	−	0.438142i	$-0.855637\pi$
$461$		−	18.8146i		−	0.876283i	0.898906	−	0.438142i	$-0.144363\pi$
$462$	14.5288	−	7.64932i	0.675943	−	0.355878i
$463$	−5.83743	+	1.71403i	−0.271289	+	0.0796575i	−0.414547	−	0.910028i	$-0.636060\pi$
$463$	−5.83743	+	1.71403i	−0.271289	+	0.0796575i	0.143259	+	0.989685i	$0.454242\pi$
$464$	−2.48747	−	2.15541i	−0.115478	−	0.100062i
$465$	9.64702	−	17.0467i	0.447370	−	0.790521i
$466$	18.2133	+	21.0192i	0.843713	+	0.973696i
$467$	−2.11053	−	14.6791i	−0.0976637	−	0.679266i	−0.978561	−	0.205958i	$-0.933969\pi$
$467$	−2.11053	−	14.6791i	−0.0976637	−	0.679266i	0.880897	−	0.473308i	$-0.156940\pi$
$468$	20.2957	+	3.55007i	0.938168	+	0.164102i
$469$	25.6494	−	16.4839i	1.18438	−	0.761154i
$470$	2.37937	−	16.5489i	0.109752	−	0.763342i
$471$	−4.38625	+	11.2360i	−0.202108	+	0.517727i
$472$	3.09707	−	6.78164i	0.142554	−	0.312150i
$473$	−9.82638	−	1.41282i	−0.451818	−	0.0649616i
$474$	9.73620	+	13.4262i	0.447198	+	0.616686i
$475$	0.543093	−	1.84961i	0.0249188	−	0.0848657i
$476$	17.3993	−	2.50163i	0.797493	−	0.114662i
$477$	9.56338	+	8.80906i	0.437877	+	0.403339i
$478$	1.08097	+	0.694698i	0.0494425	+	0.0317747i
$479$	−16.3955	+	18.9214i	−0.749129	+	0.864541i	−0.994484	−	0.104893i	$-0.966550\pi$
$479$	−16.3955	+	18.9214i	−0.749129	+	0.864541i	0.245355	+	0.969433i	$0.421096\pi$
$480$	−3.17418	+	1.12932i	−0.144881	+	0.0515460i
$481$	39.5383	−	18.0565i	1.80279	−	0.823306i
$482$	−26.3178			−1.19874
$483$	14.5782	+	25.7673i	0.663329	+	1.17245i
$484$	3.92531			0.178423
$485$	7.14872	−	3.26471i	0.324607	−	0.148243i
$486$	13.1518	−	8.36846i	0.596576	−	0.379601i
$487$	−21.5699	+	24.8930i	−0.977427	+	1.12801i	0.0143323	+	0.999897i	$0.495438\pi$
$487$	−21.5699	+	24.8930i	−0.977427	+	1.12801i	−0.991759	+	0.128114i	$0.959108\pi$
$488$	7.48886	+	4.81280i	0.339005	+	0.217865i
$489$	13.1070	−	12.7149i	0.592717	−	0.574986i
$490$	10.9793	−	1.57859i	0.495995	−	0.0713134i
$491$	9.11264	−	31.0348i	0.411248	−	1.40058i	−0.450287	−	0.892884i	$-0.648678\pi$
$491$	9.11264	−	31.0348i	0.411248	−	1.40058i	0.861535	−	0.507698i	$-0.169503\pi$
$492$	0.728419	−	0.528223i	0.0328396	−	0.0238141i
$493$	−16.0682	−	2.31025i	−0.723673	−	0.104048i
$494$	−4.52134	+	9.90035i	−0.203425	+	0.445438i
$495$	−4.82299	+	14.7529i	−0.216777	+	0.663094i
$496$	−0.827385	+	5.75459i	−0.0371507	+	0.258389i
$497$	11.9260	−	7.66435i	0.534953	−	0.343793i
$498$	9.73962	+	2.27412i	0.436443	+	0.101906i
$499$	2.44488	+	17.0045i	0.109448	+	0.761225i	0.968442	+	0.249240i	$0.0801808\pi$
$499$	2.44488	+	17.0045i	0.109448	+	0.761225i	−0.858994	+	0.511986i	$0.828910\pi$
$500$	7.91846	+	9.13839i	0.354124	+	0.408681i
$501$	1.29136	+	0.730801i	0.0576935	+	0.0326498i
$502$	−13.2055	−	11.4426i	−0.589389	−	0.510708i
$503$	−29.7485	+	8.73494i	−1.32642	+	0.389472i	−0.866805	−	0.498648i	$-0.833830\pi$
$503$	−29.7485	+	8.73494i	−1.32642	+	0.389472i	−0.459613	+	0.888119i	$0.652012\pi$
$504$	5.50487	+	9.16619i	0.245206	+	0.408295i
$505$		−	34.4697i		−	1.53388i
$506$	−0.385796	−	12.7503i	−0.0171507	−	0.566818i
$507$	3.32526	+	59.0882i	0.147680	+	2.62420i
$508$	−2.64549	−	5.79282i	−0.117375	−	0.257015i
$509$	−0.177037	−	0.602933i	−0.00784704	−	0.0267245i	0.955476	−	0.295068i	$-0.0953421\pi$
$509$	−0.177037	−	0.602933i	−0.00784704	−	0.0267245i	−0.963323	+	0.268343i	$0.913524\pi$
$510$	−10.1588	+	13.1495i	−0.449837	+	0.582271i
$511$	1.23827	−	1.92678i	0.0547776	−	0.0852356i
$512$	0.755750	−	0.654861i	0.0333997	−	0.0289410i
$513$	2.52340	+	7.83840i	0.111411	+	0.346074i
$514$	−4.09476	−	1.20233i	−0.180612	−	0.0530325i
$515$	15.9457	+	24.8120i	0.702652	+	1.09335i
$516$	0.559027	−	6.44041i	0.0246098	−	0.283523i
$517$	20.7959	+	9.49719i	0.914605	+	0.417686i
$518$	20.5181	+	9.37028i	0.901511	+	0.411706i
$519$	−2.35764	+	27.1618i	−0.103489	+	1.19227i
$520$	−7.22250	−	11.2384i	−0.316727	−	0.492838i
$521$	−8.03896	−	2.36045i	−0.352193	−	0.103413i	0.100850	−	0.994902i	$-0.467844\pi$
$521$	−8.03896	−	2.36045i	−0.352193	−	0.103413i	−0.453044	+	0.891488i	$0.649662\pi$
$522$	−2.49295	−	9.55431i	−0.109113	−	0.418181i
$523$	14.3775	−	12.4582i	0.628684	−	0.544758i	−0.281185	−	0.959654i	$-0.590727\pi$
$523$	14.3775	−	12.4582i	0.628684	−	0.544758i	0.909869	+	0.414896i	$0.136182\pi$
$524$	−0.871513	+	1.35610i	−0.0380722	+	0.0592415i
$525$	4.59075	−	5.94228i	0.200357	−	0.259342i
$526$	−2.34333	−	7.98066i	−0.102174	−	0.347973i
$527$	11.9116	+	26.0827i	0.518875	+	1.13618i
$528$	−0.258853	−	4.59968i	−0.0112651	−	0.200175i
$529$	22.9579	−	1.39059i	0.998171	−	0.0604605i
$530$		−	8.43041i		−	0.366193i
$531$	19.1740	−	11.5152i	0.832082	−	0.499717i
$532$	−5.41933	+	1.59126i	−0.234958	+	0.0689898i
$533$	2.69639	+	2.33643i	0.116794	+	0.101202i
$534$	−6.48644	−	3.67079i	−0.280696	−	0.158851i
$535$	13.7662	+	15.8871i	0.595167	+	0.686859i
$536$	−1.21746	−	8.46763i	−0.0525863	−	0.365746i
$537$	2.17498	+	0.507841i	0.0938575	+	0.0219150i
$538$	−14.9301	+	9.59500i	−0.643683	+	0.413670i
$539$	−2.15859	+	15.0133i	−0.0929771	+	0.646670i
$540$	−9.76822	−	2.59593i	−0.420357	−	0.111711i
$541$	−5.45778	+	11.9509i	−0.234648	+	0.513808i	−0.989924	−	0.141599i	$-0.954776\pi$
$541$	−5.45778	+	11.9509i	−0.234648	+	0.513808i	0.755276	+	0.655407i	$0.227503\pi$
$542$	4.45038	+	0.639868i	0.191160	+	0.0274847i
$543$	18.5855	−	13.4775i	0.797580	−	0.578376i
$544$	1.38952	−	4.73228i	0.0595753	−	0.202895i
$545$	−0.784942	+	0.112858i	−0.0336232	+	0.00483429i
$546$	−30.4307	+	29.5204i	−1.30231	+	1.26336i
$547$	0.0454444	+	0.0292053i	0.00194306	+	0.00124873i	0.541612	−	0.840629i	$-0.317814\pi$
$547$	0.0454444	+	0.0292053i	0.00194306	+	0.00124873i	−0.539669	+	0.841877i	$0.681451\pi$
$548$	1.62039	−	1.87003i	0.0692196	−	0.0798837i
$549$	10.3514	+	24.6183i	0.441788	+	1.05068i
$550$	−2.94305	+	1.34405i	−0.125492	+	0.0573104i
$551$	5.21602			0.222210
$552$	8.27559	−	0.717342i	0.352233	−	0.0305321i
$553$	−34.1268			−1.45122
$554$	−11.2528	+	5.13899i	−0.478087	+	0.218335i
$555$	−20.0889	+	7.14728i	−0.852728	+	0.303385i
$556$	8.08351	−	9.32886i	0.342817	−	0.395632i
$557$	24.8206	+	15.9512i	1.05168	+	0.675874i	0.947849	−	0.318721i	$-0.103253\pi$
$557$	24.8206	+	15.9512i	1.05168	+	0.675874i	0.103832	+	0.994595i	$0.466890\pi$
$558$	−11.8166	+	12.8284i	−0.500234	+	0.543069i
$559$	25.3727	−	3.64804i	1.07315	−	0.154296i
$560$	1.95314	−	6.65180i	0.0825354	−	0.281090i
$561$	−13.3389	−	18.3944i	−0.563171	−	0.776612i
$562$	−17.1372	−	2.46396i	−0.722891	−	0.103936i
$563$	−0.714815	+	1.56523i	−0.0301259	+	0.0659665i	−0.924097	−	0.382159i	$-0.875181\pi$
$563$	−0.714815	+	1.56523i	−0.0301259	+	0.0659665i	0.893971	+	0.448125i	$0.147908\pi$
$564$	−5.41380	+	13.8682i	−0.227962	+	0.583956i
$565$	−1.40240	+	9.75389i	−0.0589993	+	0.410349i
$566$	8.73388	−	5.61293i	0.367112	−	0.235929i
$567$	−1.94687	+	32.0174i	−0.0817608	+	1.34460i
$568$	−0.566072	−	3.93712i	−0.0237519	−	0.165198i
$569$	9.59261	+	11.0705i	0.402143	+	0.464098i	0.920315	−	0.391179i	$-0.127933\pi$
$569$	9.59261	+	11.0705i	0.402143	+	0.464098i	−0.518172	+	0.855277i	$0.673387\pi$
$570$	2.62963	−	4.64666i	0.110143	−	0.194627i
$571$	−6.32970	−	5.48471i	−0.264890	−	0.229528i	0.512281	−	0.858818i	$-0.328801\pi$
$571$	−6.32970	−	5.48471i	−0.264890	−	0.229528i	−0.777171	+	0.629290i	$0.783346\pi$
$572$	17.5276	−	5.14656i	0.732865	−	0.215189i
$573$	13.7055	−	7.21583i	0.572555	−	0.301446i
$574$			1.85150i			0.0772800i
$575$	−2.58278	−	5.23078i	−0.107709	−	0.218139i
$576$	2.98106	−	0.336591i	0.124211	−	0.0140246i
$577$	−12.2089	−	26.7338i	−0.508263	−	1.11294i	−0.973695	−	0.227857i	$-0.926828\pi$
$577$	−12.2089	−	26.7338i	−0.508263	−	1.11294i	0.465431	−	0.885084i	$-0.345899\pi$
$578$	−2.06377	−	7.02855i	−0.0858414	−	0.292349i
$579$	9.38089	+	7.24727i	0.389857	+	0.301186i
$580$	−3.46132	+	5.38591i	−0.143723	+	0.223638i
$581$	−15.5536	+	13.4773i	−0.645272	+	0.559132i
$582$	−6.85982	+	1.38353i	−0.284349	+	0.0573493i
$583$	11.0609	+	3.24778i	0.458097	+	0.134509i
$584$	−0.347431	−	0.540613i	−0.0143768	−	0.0223707i
$585$	1.21680	−	40.0589i	0.0503085	−	1.65623i
$586$	−8.09646	−	3.69753i	−0.334462	−	0.152743i
$587$	38.2153	+	17.4523i	1.57731	+	0.720334i	0.995657	−	0.0931008i	$-0.0296779\pi$
$587$	38.2153	+	17.4523i	1.57731	+	0.720334i	0.581656	+	0.813435i	$0.302405\pi$
$588$	−9.84005	−	0.854114i	−0.405797	−	0.0352231i
$589$	−4.98110	−	7.75074i	−0.205242	−	0.319364i
$590$	−13.9144	−	4.08562i	−0.572845	−	0.168202i
$591$	−5.09036	−	25.2390i	−0.209389	−	1.03819i
$592$	4.78303	−	4.14452i	0.196581	−	0.170339i
$593$	−23.6188	+	36.7515i	−0.969907	+	1.50921i	−0.113090	+	0.993585i	$0.536075\pi$
$593$	−23.6188	+	36.7515i	−0.969907	+	1.50921i	−0.856817	+	0.515620i	$0.827561\pi$
$594$	7.16910	−	11.8161i	0.294152	−	0.484821i
$595$	−9.63303	−	32.8071i	−0.394916	−	1.34496i
$596$	−9.87803	−	21.6299i	−0.404620	−	0.885994i
$597$	−9.95500	+	0.560229i	−0.407431	+	0.0229287i
$598$	10.2311	+	31.3082i	0.418382	+	1.28029i
$599$		−	1.50518i		−	0.0614999i	−0.999527	−	0.0307499i	$-0.990210\pi$
$599$		−	1.50518i		−	0.0614999i	0.999527	−	0.0307499i	$-0.00978956\pi$
$600$	−0.981528	−	1.86428i	−0.0400707	−	0.0761089i
$601$	27.0780	−	7.95081i	1.10453	−	0.324320i	0.321882	−	0.946780i	$-0.395685\pi$
$601$	27.0780	−	7.95081i	1.10453	−	0.324320i	0.782652	+	0.622460i	$0.213866\pi$
$602$	10.0532	+	8.71118i	0.409739	+	0.355041i
$603$	11.3651	−	23.0105i	0.462824	−	0.937058i
$604$	−12.6284	−	14.5739i	−0.513841	−	0.593004i
$605$	−1.08662	−	7.55758i	−0.0441772	−	0.307259i
$606$	−6.97896	+	29.8895i	−0.283501	+	1.21418i
$607$	−2.32503	+	1.49421i	−0.0943702	+	0.0606480i	−0.586975	−	0.809605i	$-0.699681\pi$
$607$	−2.32503	+	1.49421i	−0.0943702	+	0.0606480i	0.492605	+	0.870253i	$0.336045\pi$
$608$	−0.225532	+	1.56861i	−0.00914654	+	0.0636156i
$609$	18.9272	+	7.38870i	0.766967	+	0.299405i
$610$	7.19321	−	15.7509i	0.291245	−	0.637737i
$611$	−58.4309	−	8.40109i	−2.36386	−	0.339872i
$612$	11.4712	−	9.34548i	0.463698	−	0.377768i
$613$	−5.47446	+	18.6443i	−0.221111	+	0.753036i	0.771975	+	0.635652i	$0.219269\pi$
$613$	−5.47446	+	18.6443i	−0.221111	+	0.753036i	−0.993087	+	0.117383i	$0.962549\pi$
$614$	−22.1078	+	3.17863i	−0.892199	+	0.128279i
$615$	−1.21866	−	1.25623i	−0.0491409	−	0.0506563i
$616$	7.97491	+	5.12516i	0.321318	+	0.206499i
$617$	0.262825	−	0.303316i	0.0105809	−	0.0122110i	−0.750434	−	0.660945i	$-0.770156\pi$
$617$	0.262825	−	0.303316i	0.0105809	−	0.0122110i	0.761015	+	0.648734i	$0.224701\pi$
$618$	−8.80331	−	24.7436i	−0.354121	−	0.995332i
$619$	1.91437	−	0.874263i	0.0769450	−	0.0351396i	−0.376571	−	0.926388i	$-0.622897\pi$
$619$	1.91437	−	0.874263i	0.0769450	−	0.0351396i	0.453516	+	0.891248i	$0.350170\pi$
$620$	11.3086			0.454165
$621$	21.6864	+	12.2761i	0.870244	+	0.492621i
$622$	7.48018			0.299928
$623$	13.9504	−	6.37094i	0.558911	−	0.255246i
$624$	3.98740	+	11.2074i	0.159624	+	0.448656i
$625$	11.4197	−	13.1790i	0.456787	−	0.527160i
$626$	5.19010	+	3.33547i	0.207438	+	0.133312i
$627$	5.08350	+	5.24026i	0.203016	+	0.209276i
$628$	−6.89299	+	0.991062i	−0.275060	+	0.0395477i
$629$	8.79410	−	29.9499i	0.350644	−	1.19418i
$630$	16.1242	−	13.1362i	0.642405	−	0.523359i
$631$	−23.8344	−	3.42687i	−0.948833	−	0.136422i	−0.349513	−	0.936931i	$-0.613653\pi$
$631$	−23.8344	−	3.42687i	−0.948833	−	0.136422i	−0.599319	+	0.800510i	$0.704562\pi$
$632$	−3.97770	+	8.70996i	−0.158225	+	0.346463i
$633$	−28.6342	−	11.1781i	−1.13811	−	0.444290i
$634$	0.233993	−	1.62746i	0.00929306	−	0.0646347i
$635$	−10.4209	+	6.69708i	−0.413539	+	0.265765i
$636$	−1.70688	+	7.31021i	−0.0676820	+	0.289869i
$637$	−5.57369	−	38.7659i	−0.220838	−	1.53596i
$638$	−5.73301	−	6.61625i	−0.226972	−	0.261940i
$639$	5.28434	−	10.6990i	0.209045	−	0.423245i
$640$	−1.47004	−	1.27380i	−0.0581086	−	0.0503514i
$641$	3.31805	−	0.974269i	0.131055	−	0.0384813i	−0.215547	−	0.976493i	$-0.569153\pi$
$641$	3.31805	−	0.974269i	0.131055	−	0.0384813i	0.346602	+	0.938012i	$0.387335\pi$
$642$	−8.72044	−	16.5633i	−0.344168	−	0.653701i
$643$			1.57310i			0.0620370i	0.999519	+	0.0310185i	$0.00987508\pi$
$643$			1.57310i			0.0620370i	−0.999519	+	0.0310185i	$0.990125\pi$
$644$	−8.80186	+	14.6521i	−0.346842	+	0.577375i
$645$	−12.5548	+	0.706535i	−0.494344	+	0.0278198i
$646$	3.24691	+	7.10973i	0.127748	+	0.279729i
$647$	−4.76522	−	16.2288i	−0.187340	−	0.638022i	−0.998578	−	0.0533057i	$-0.983024\pi$
$647$	−4.76522	−	16.2288i	−0.187340	−	0.638022i	0.811238	−	0.584716i	$-0.198794\pi$
$648$	7.94467	+	4.22873i	0.312096	+	0.166120i
$649$	10.7209	−	16.6821i	0.420833	−	0.654828i
$650$	6.31369	−	5.47084i	0.247643	−	0.214584i
$651$	−7.09547	−	35.1807i	−0.278094	−	1.37884i
$652$	10.1159	+	2.97029i	0.396168	+	0.116325i
$653$	5.19435	+	8.08256i	0.203270	+	0.316295i	0.927890	−	0.372854i	$-0.121621\pi$
$653$	5.19435	+	8.08256i	0.203270	+	0.316295i	−0.724619	+	0.689149i	$0.757984\pi$
$654$	0.703492	+	0.0610629i	0.0275087	+	0.00238775i
$655$	2.85222	+	1.30257i	0.111445	+	0.0508954i
$656$	0.472546	+	0.215804i	0.0184498	+	0.00842575i
$657$	0.0585330	−	1.92700i	0.00228359	−	0.0751793i
$658$	−16.5620	−	25.7710i	−0.645654	−	1.00466i
$659$	−3.33308	−	0.978681i	−0.129838	−	0.0381240i	0.216168	−	0.976356i	$-0.430644\pi$
$659$	−3.33308	−	0.978681i	−0.129838	−	0.0381240i	−0.346006	+	0.938232i	$0.612462\pi$
$660$	−8.78433	+	1.77168i	−0.341930	+	0.0689625i
$661$	−30.0723	+	26.0578i	−1.16968	+	1.01353i	−0.170073	+	0.985432i	$0.554400\pi$
$661$	−30.0723	+	26.0578i	−1.16968	+	1.01353i	−0.999605	+	0.0281001i	$0.991054\pi$
$662$	−7.66128	+	11.9212i	−0.297764	+	0.463330i
$663$	46.4285	+	35.8686i	1.80313	+	1.39302i
$664$	1.62684	+	5.54051i	0.0631337	+	0.215014i
$665$	4.56392	+	9.99359i	0.176981	+	0.387535i
$666$	18.8667	−	2.13024i	0.731070	−	0.0825450i
$667$	11.6114	−	10.6930i	0.449595	−	0.414036i
$668$			0.856674i			0.0331457i
$669$	−21.2064	+	11.1650i	−0.819887	+	0.431664i
$670$	−15.9661	+	4.68807i	−0.616825	+	0.181116i
$671$	17.8945	+	15.5057i	0.690811	+	0.598591i
$672$	−3.04038	+	5.37249i	−0.117285	+	0.207248i
$673$	12.0600	+	13.9180i	0.464881	+	0.536501i	0.938981	−	0.343970i	$-0.111772\pi$
$673$	12.0600	+	13.9180i	0.464881	+	0.536501i	−0.474100	+	0.880471i	$0.657226\pi$
$674$	−2.39784	−	16.6773i	−0.0923613	−	0.642387i
$675$	0.737506	−	6.27746i	0.0283866	−	0.241620i
$676$	−28.7444	+	18.4729i	−1.10555	+	0.710497i
$677$	−5.82408	+	40.5074i	−0.223838	+	1.55683i	0.499489	+	0.866320i	$0.333521\pi$
$677$	−5.82408	+	40.5074i	−0.223838	+	1.55683i	−0.723327	+	0.690506i	$0.757388\pi$
$678$	3.19089	−	8.17389i	0.122545	−	0.313916i
$679$	5.98188	−	13.0985i	0.229563	−	0.502674i
$680$	−9.49594	−	1.36531i	−0.364153	−	0.0523572i
$681$	−19.7027	−	27.1700i	−0.755008	−	1.04116i
$682$	−4.35660	+	14.8372i	−0.166823	+	0.568147i
$683$	15.7474	−	2.26414i	0.602559	−	0.0866349i	0.165717	−	0.986173i	$-0.447006\pi$
$683$	15.7474	−	2.26414i	0.602559	−	0.0866349i	0.436842	+	0.899538i	$0.356097\pi$
$684$	−3.22101	+	3.49682i	−0.123158	+	0.133704i
$685$	−4.04902	−	2.60215i	−0.154705	−	0.0994229i
$686$	−3.02827	+	3.49481i	−0.115620	+	0.133433i
$687$	−36.8725	+	13.1186i	−1.40678	+	0.500505i
$688$	3.39507	−	1.55048i	0.129436	−	0.0591114i
$689$	−29.7661			−1.13400
$690$	−3.67201	−	15.7348i	−0.139791	−	0.599014i
$691$	26.0430			0.990723			0.495361	−	0.868687i	$-0.335036\pi$
$691$	26.0430			0.990723			0.495361	+	0.868687i	$0.335036\pi$
$692$	−14.3184	+	6.53898i	−0.544303	+	0.248575i
$693$	11.0233	+	26.2161i	0.418739	+	0.995868i
$694$	12.2855	−	14.1783i	0.466353	−	0.538200i
$695$	−20.1990	−	12.9811i	−0.766192	−	0.492402i
$696$	4.09186	−	3.96945i	0.155102	−	0.150462i
$697$	2.53608	−	0.364634i	0.0960611	−	0.0138115i
$698$	8.25449	−	28.1122i	0.312437	−	1.06406i
$699$	−38.9979	+	28.2799i	−1.47504	+	1.06964i
$700$	4.29122	+	0.616984i	0.162193	+	0.0233198i
$701$	9.63468	−	21.0970i	0.363897	−	0.796823i	−0.635792	−	0.771861i	$-0.719326\pi$
$701$	9.63468	−	21.0970i	0.363897	−	0.796823i	0.999688	−	0.0249619i	$-0.00794646\pi$
$702$	−9.16572	+	34.4897i	−0.345938	+	1.30173i
$703$	−1.42736	+	9.92752i	−0.0538340	+	0.374424i
$704$	2.23759	−	1.43801i	0.0843324	−	0.0541971i
$705$	28.1997	+	6.58441i	1.06206	+	0.247983i
$706$	−1.67811	−	11.6715i	−0.0631564	−	0.439262i
$707$	−41.3598	−	47.7318i	−1.55550	−	1.79514i
$708$	11.2383	+	6.35994i	0.422360	+	0.239021i
$709$	30.4072	+	26.3480i	1.14197	+	0.989520i	1.00000		0.000351106i	$-0.000111761\pi$
$709$	30.4072	+	26.3480i	1.14197	+	0.989520i	0.141967	+	0.989871i	$0.454657\pi$
$710$	−7.42362	+	2.17977i	−0.278604	+	0.0818054i
$711$	−24.6260	+	14.7895i	−0.923548	+	0.554648i
$712$		−	4.30305i		−	0.161264i
$713$	−26.9778	−	7.04252i	−1.01032	−	0.263745i
$714$	1.71069	+	30.3982i	0.0640211	+	1.13762i
$715$	−14.7610	−	32.3220i	−0.552028	−	1.20877i
$716$	0.363295	+	1.23727i	0.0135770	+	0.0462389i
$717$	−1.36065	+	1.76123i	−0.0508144	+	0.0657744i
$718$	5.15404	−	8.01984i	0.192347	−	0.299298i
$719$	9.14024	−	7.92006i	0.340873	−	0.295368i	−0.467554	−	0.883965i	$-0.654865\pi$
$719$	9.14024	−	7.92006i	0.340873	−	0.295368i	0.808427	+	0.588596i	$0.200319\pi$
$720$	−1.47328	−	5.64640i	−0.0549059	−	0.210429i
$721$	51.8525	+	15.2253i	1.93109	+	0.567018i
$722$	8.91441	+	13.8711i	0.331760	+	0.516228i
$723$	3.94184	−	45.4130i	0.146598	−	1.68893i
$724$	12.0569	+	5.50622i	0.448093	+	0.204637i
$725$	−3.64187	−	1.66319i	−0.135256	−	0.0617692i
$726$	−0.587927	+	6.77337i	−0.0218200	+	0.251383i
$727$	7.46309	+	11.6128i	0.276791	+	0.430695i	0.951619	−	0.307280i	$-0.0994188\pi$
$727$	7.46309	+	11.6128i	0.276791	+	0.430695i	−0.674828	+	0.737975i	$0.735782\pi$
$728$	−23.4862	−	6.89618i	−0.870457	−	0.255589i
$729$	12.4705	+	23.9476i	0.461869	+	0.886948i
$730$	−0.944692	+	0.818580i	−0.0349646	+	0.0302970i
$731$	9.95224	−	15.4860i	0.368097	−	0.572770i
$732$	−9.42645	+	12.2016i	−0.348412	+	0.450985i
$733$	−13.7465	−	46.8163i	−0.507739	−	1.72920i	−0.669914	−	0.742439i	$-0.733669\pi$
$733$	−13.7465	−	46.8163i	−0.507739	−	1.72920i	0.162174	−	0.986762i	$-0.448149\pi$
$734$	−1.30816	−	2.86448i	−0.0482852	−	0.105730i
$735$	1.07949	+	19.1820i	0.0398175	+	0.707537i
$736$	2.71366	+	3.95425i	0.100027	+	0.145755i
$737$		−	22.7541i		−	0.838157i
$738$	0.802380	+	1.33605i	0.0295360	+	0.0491806i
$739$	−21.9451	+	6.44365i	−0.807262	+	0.237033i	−0.659222	−	0.751948i	$-0.729114\pi$
$739$	−21.9451	+	6.44365i	−0.807262	+	0.237033i	−0.148039	+	0.988981i	$0.547296\pi$
$740$	−9.30370	−	8.06170i	−0.342011	−	0.296354i
$741$	−16.4065	−	9.28472i	−0.602707	−	0.341083i
$742$	−10.1156	−	11.6740i	−0.371354	−	0.428565i
$743$	0.339282	+	2.35976i	0.0124471	+	0.0865712i	0.995098	−	0.0988931i	$-0.0315302\pi$
$743$	0.339282	+	2.35976i	0.0124471	+	0.0865712i	−0.982651	+	0.185464i	$0.940621\pi$
$744$	−9.80598	−	2.28962i	−0.359505	−	0.0839415i
$745$	−38.9106	+	25.0063i	−1.42557	+	0.916160i
$746$	−0.708929	+	4.93071i	−0.0259557	+	0.180526i
$747$	−5.38293	+	16.4657i	−0.196951	+	0.602449i
$748$	5.44960	−	11.9330i	0.199257	−	0.436312i
$749$	38.1255	+	5.48162i	1.39308	+	0.200294i
$750$	−16.9549	+	12.2951i	−0.619104	+	0.448952i
$751$	−8.79675	+	29.9590i	−0.320998	+	1.09322i	0.628072	+	0.778155i	$0.283844\pi$
$751$	−8.79675	+	29.9590i	−0.320998	+	1.09322i	−0.949070	+	0.315064i	$0.897974\pi$
$752$	−8.50778	+	1.22323i	−0.310247	+	0.0446067i
$753$	21.7228	−	21.0730i	0.791624	−	0.767943i
$754$	19.0166	+	12.2212i	0.692545	+	0.445071i
$755$	−24.5640	+	28.3484i	−0.893976	+	1.03170i
$756$	−16.6414	+	8.12610i	−0.605240	+	0.295543i
$757$	5.26171	−	2.40294i	0.191240	−	0.0873365i	−0.317493	−	0.948261i	$-0.602841\pi$
$757$	5.26171	−	2.40294i	0.191240	−	0.0873365i	0.508734	+	0.860924i	$0.330114\pi$
$758$	28.7968			1.04595
$759$	22.0592	+	1.24400i	0.800696	+	0.0451543i
$760$	3.08256			0.111816
$761$	1.90441	−	0.869715i	0.0690348	−	0.0315271i	−0.380598	−	0.924740i	$-0.624282\pi$
$761$	1.90441	−	0.869715i	0.0690348	−	0.0315271i	0.449633	+	0.893213i	$0.351555\pi$
$762$	10.3921	−	3.69732i	0.376466	−	0.133940i
$763$	−0.951529	+	1.09812i	−0.0344477	+	0.0397547i
$764$	7.52297	+	4.83472i	0.272172	+	0.174914i
$765$	−21.1688	−	19.4991i	−0.765359	−	0.704991i
$766$	26.0439	−	3.74455i	0.941005	−	0.135296i
$767$	−14.4256	+	49.1289i	−0.520877	+	1.77394i
$768$	1.01681	+	1.40218i	0.0366909	+	0.0505967i
$769$	−19.5069	−	2.80467i	−0.703436	−	0.101139i	−0.218691	−	0.975794i	$-0.570179\pi$
$769$	−19.5069	−	2.80467i	−0.703436	−	0.101139i	−0.484745	+	0.874655i	$0.661088\pi$
$770$	7.66008	−	16.7732i	0.276050	−	0.604465i
$771$	2.68800	−	6.88569i	0.0968061	−	0.247982i
$772$	−0.974013	+	6.77441i	−0.0350555	+	0.243816i
$773$	43.1884	−	27.7555i	1.55338	−	0.998295i	0.568976	−	0.822354i	$-0.307340\pi$
$773$	43.1884	−	27.7555i	1.55338	−	0.998295i	0.984401	−	0.175941i	$-0.0562968\pi$
$774$	11.0296	+	1.92927i	0.396451	+	0.0693462i
$775$	1.00644	+	6.99992i	0.0361523	+	0.251445i
$776$	−2.64581	−	3.05343i	−0.0949792	−	0.109612i
$777$	−19.2422	+	34.0017i	−0.690309	+	1.21980i
$778$	27.9865	+	24.2505i	1.00337	+	0.869421i
$779$	−0.789912	+	0.231939i	−0.0283015	+	0.00831008i
$780$	20.4744	−	10.7796i	0.733100	−	0.385972i
$781$		−	10.5798i		−	0.378573i
$782$	21.8032	+	9.17074i	0.779680	+	0.327945i
$783$	16.8600	−	2.87071i	0.602525	−	0.102591i
$784$	−2.36891	−	5.18719i	−0.0846040	−	0.185257i
$785$	3.81628	+	12.9970i	0.136209	+	0.463884i
$786$	−2.20950	−	1.70697i	−0.0788104	−	0.0608854i
$787$	1.31275	−	2.04267i	0.0467943	−	0.0728134i	−0.817068	−	0.576541i	$-0.804402\pi$
$787$	1.31275	−	2.04267i	0.0467943	−	0.0728134i	0.863863	+	0.503728i	$0.168038\pi$
$788$	11.2343	−	9.73460i	0.400206	−	0.346781i
$789$	14.1221	−	2.84824i	0.502760	−	0.101400i
$790$	17.8708	+	5.24734i	0.635815	+	0.186692i
$791$	9.76163	+	15.1894i	0.347084	+	0.540073i
$792$	7.97581	+	0.242267i	0.283408	+	0.00860858i
$793$	−55.6136	−	25.3979i	−1.97490	−	0.901904i
$794$	−7.89355	−	3.60486i	−0.280131	−	0.127932i
$795$	14.5472	+	1.26269i	0.515936	+	0.0447831i
$796$	−3.11226	−	4.84277i	−0.110311	−	0.171648i
$797$	18.1475	+	5.32858i	0.642816	+	0.188748i	0.586864	−	0.809686i	$-0.300362\pi$
$797$	18.1475	+	5.32858i	0.642816	+	0.188748i	0.0559524	+	0.998433i	$0.482180\pi$
$798$	−1.93412	−	9.58972i	−0.0684670	−	0.339473i
$799$	−32.0380	+	27.7611i	−1.13342	+	0.982118i
$800$	0.657639	−	1.02331i	0.0232511	−	0.0361793i
$801$	7.30571	−	10.6430i	0.258135	−	0.376051i
$802$	1.53149	+	5.21579i	0.0540789	+	0.184176i
$803$	−0.710061	−	1.55482i	−0.0250575	−	0.0548683i
$804$	14.7938	−	0.832538i	0.521736	−	0.0293613i
$805$	30.6470	+	12.8906i	1.08017	+	0.454333i
$806$		−	39.9286i		−	1.40642i
$807$	−14.3206	−	27.2000i	−0.504108	−	0.957485i
$808$	−17.0030	+	4.99255i	−0.598165	+	0.175637i
$809$	13.0763	+	11.3307i	0.459738	+	0.398365i	0.853703	−	0.520760i	$-0.174351\pi$
$809$	13.0763	+	11.3307i	0.459738	+	0.398365i	−0.393965	+	0.919125i	$0.628897\pi$
$810$	5.94250	−	16.4669i	0.208798	−	0.578587i
$811$	−23.4341	−	27.0444i	−0.822883	−	0.949657i	0.176517	−	0.984298i	$-0.443517\pi$
$811$	−23.4341	−	27.0444i	−0.822883	−	0.949657i	−0.999400	+	0.0346405i	$0.988971\pi$
$812$	1.66946	+	11.6113i	0.0585865	+	0.407478i
$813$	−1.77070	+	7.58358i	−0.0621013	+	0.265968i
$814$	14.1614	−	9.10098i	0.496357	−	0.318989i
$815$	2.91853	−	20.2988i	0.102232	−	0.711036i
$816$	7.95773	+	3.10650i	0.278576	+	0.108749i
$817$	−2.45711	+	5.38031i	−0.0859633	+	0.188233i
$818$	−13.7287	−	1.97390i	−0.480014	−	0.0690157i
$819$	−46.3814	−	56.9316i	−1.62070	−	1.98935i
$820$	0.284687	−	0.969554i	0.00994169	−	0.0338583i
$821$	32.9287	−	4.73443i	1.14922	−	0.165233i	0.458730	−	0.888576i	$-0.348304\pi$
$821$	32.9287	−	4.73443i	1.14922	−	0.165233i	0.690489	+	0.723343i	$0.257395\pi$
$822$	2.98415	+	3.07617i	0.104084	+	0.107294i
$823$	23.5917	+	15.1615i	0.822355	+	0.528496i	0.882840	−	0.469673i	$-0.155628\pi$
$823$	23.5917	+	15.1615i	0.822355	+	0.528496i	−0.0604850	+	0.998169i	$0.519265\pi$
$824$	9.92960	−	11.4594i	0.345914	−	0.399206i
$825$	−1.87843	−	5.27973i	−0.0653986	−	0.183817i
$826$	−24.1702	+	11.0381i	−0.840988	+	0.384066i
$827$	6.32473			0.219933			0.109966	−	0.993935i	$-0.464926\pi$
$827$	6.32473			0.219933			0.109966	+	0.993935i	$0.464926\pi$
$828$	−0.00168640	+	14.3875i	−5.86063e−5	+	0.500000i
$829$	−5.82202			−0.202207			−0.101104	−	0.994876i	$-0.532237\pi$
$829$	−5.82202			−0.202207			−0.101104	+	0.994876i	$0.532237\pi$
$830$	10.2171	−	4.66598i	0.354640	−	0.161958i
$831$	−7.18222	−	20.1872i	−0.249149	−	0.700285i
$832$	−4.49754	+	5.19044i	−0.155924	+	0.179946i
$833$	−23.6604	−	15.2056i	−0.819785	−	0.526844i
$834$	14.8868	+	15.3459i	0.515488	+	0.531384i
$835$	1.64940	−	0.237147i	0.0570797	−	0.00820682i
$836$	−1.18754	+	4.04440i	−0.0410720	+	0.139879i
$837$	−20.3663	−	22.3116i	−0.703964	−	0.771202i
$838$	−23.2764	−	3.34665i	−0.804071	−	0.115608i
$839$	−6.98618	+	15.2976i	−0.241190	+	0.528132i	−0.991054	−	0.133459i	$-0.957391\pi$
$839$	−6.98618	+	15.2976i	−0.241190	+	0.528132i	0.749864	+	0.661591i	$0.230119\pi$
$840$	11.1856	+	4.36657i	0.385938	+	0.150661i
$841$	−2.58539	+	17.9818i	−0.0891514	+	0.620062i
$842$	1.61344	−	1.03690i	0.0556030	−	0.0357339i
$843$	6.81851	−	29.2023i	0.234842	−	1.00578i
$844$	−2.52566	−	17.5664i	−0.0869370	−	0.604660i
$845$	43.5239	+	50.2293i	1.49727	+	1.72794i
$846$	−23.1195	−	11.4190i	−0.794866	−	0.392594i
$847$	−10.5730	−	9.16152i	−0.363291	−	0.314794i
$848$	−4.15851	+	1.22105i	−0.142804	+	0.0419310i
$849$	8.37731	+	15.9116i	0.287508	+	0.546083i
$850$		−	5.99940i		−	0.205778i
$851$	17.1743	+	25.0259i	0.588729	+	0.857876i
$852$	6.87853	−	0.387098i	0.235655	−	0.0132617i
$853$	−2.73037	−	5.97869i	−0.0934862	−	0.204706i	0.857112	−	0.515130i	$-0.172256\pi$
$853$	−2.73037	−	5.97869i	−0.0934862	−	0.204706i	−0.950598	+	0.310424i	$0.899529\pi$
$854$	−8.93862	−	30.4421i	−0.305873	−	1.04171i
$855$	7.62425	+	5.23356i	0.260744	+	0.178984i
$856$	5.84283	−	9.09162i	0.199704	−	0.310745i
$857$	−32.8555	+	28.4694i	−1.12232	+	0.972497i	−0.999801	−	0.0199686i	$-0.993643\pi$
$857$	−32.8555	+	28.4694i	−1.12232	+	0.972497i	−0.122521	+	0.992466i	$0.539098\pi$
$858$	6.25546	+	31.0158i	0.213558	+	1.05886i
$859$	8.80144	+	2.58434i	0.300301	+	0.0881764i	0.428412	−	0.903583i	$-0.359073\pi$
$859$	8.80144	+	2.58434i	0.300301	+	0.0881764i	−0.128111	+	0.991760i	$0.540891\pi$
$860$	−3.92504	−	6.10748i	−0.133843	−	0.208263i
$861$	−3.19487	−	0.277314i	−0.108881	−	0.00945085i
$862$	37.6224	+	17.1816i	1.28143	+	0.585207i
$863$	0.712640	+	0.325452i	0.0242585	+	0.0110785i	0.427507	−	0.904012i	$-0.359392\pi$
$863$	0.712640	+	0.325452i	0.0242585	+	0.0110785i	−0.403249	+	0.915090i	$0.632119\pi$
$864$	0.134311	+	5.19442i	0.00456934	+	0.176718i
$865$	16.5535	+	25.7577i	0.562835	+	0.875788i
$866$	17.5065	+	5.14037i	0.594895	+	0.174677i
$867$	12.4373	−	2.50843i	0.422393	−	0.0851909i
$868$	15.6596	−	13.5691i	0.531521	−	0.460565i
$869$	−13.7693	+	21.4255i	−0.467093	+	0.726810i
$870$	−8.77530	−	6.77941i	−0.297511	−	0.229844i
$871$	16.5527	+	56.3733i	0.560866	+	1.91014i
$872$	0.169360	+	0.370846i	0.00573525	+	0.0125584i
$873$	−1.35992	−	12.0443i	−0.0460263	−	0.407637i
$874$	−7.35372	−	1.91968i	−0.248743	−	0.0649343i
$875$		−	43.0960i		−	1.45691i
$876$	0.984900	−	0.518542i	0.0332767	−	0.0175199i
$877$	−17.0805	+	5.01529i	−0.576768	+	0.169354i	−0.557090	−	0.830452i	$-0.688082\pi$
$877$	−17.0805	+	5.01529i	−0.576768	+	0.169354i	−0.0196776	+	0.999806i	$0.506264\pi$
$878$	7.93930	+	6.87944i	0.267938	+	0.232170i
$879$	7.59299	−	13.4171i	0.256105	−	0.452549i
$880$	−3.38809	−	3.91006i	−0.114212	−	0.131808i
$881$	7.38660	+	51.3749i	0.248861	+	1.73086i	0.604819	+	0.796363i	$0.293246\pi$
$881$	7.38660	+	51.3749i	0.248861	+	1.73086i	−0.355958	+	0.934502i	$0.615845\pi$
$882$	2.94766	−	16.8517i	0.0992527	−	0.567426i
$883$	30.9594	−	19.8964i	1.04187	−	0.669567i	0.0964192	−	0.995341i	$-0.469261\pi$
$883$	30.9594	−	19.8964i	1.04187	−	0.669567i	0.945448	+	0.325774i	$0.105625\pi$
$884$	−4.82065	+	33.5283i	−0.162136	+	1.12768i
$885$	9.13407	−	23.3982i	0.307038	−	0.786520i
$886$	−1.58681	+	3.47463i	−0.0533099	+	0.116732i
$887$	37.7792	+	5.43183i	1.26850	+	0.182383i	0.743511	−	0.668724i	$-0.233159\pi$
$887$	37.7792	+	5.43183i	1.26850	+	0.182383i	0.524992	+	0.851107i	$0.324068\pi$
$888$	6.43524	+	8.87418i	0.215952	+	0.297798i
$889$	−6.39450	+	21.7777i	−0.214464	+	0.730399i
$890$	−8.28486	+	1.19118i	−0.277709	+	0.0399286i
$891$	19.3157	+	14.1405i	0.647099	+	0.473726i
$892$	−11.6402	−	7.48073i	−0.389744	−	0.250473i
$893$	8.92004	−	10.2943i	0.298498	−	0.344485i
$894$	38.8032	−	13.8055i	1.29777	−	0.461724i
$895$	2.28160	−	1.04197i	0.0762656	−	0.0348293i
$896$	−3.56406			−0.119067
$897$	−55.5566	+	12.9652i	−1.85498	+	0.432894i
$898$	−25.8143			−0.861435
$899$	−17.4062	+	7.94913i	−0.580528	+	0.265118i
$900$	3.36394	−	1.41446i	0.112131	−	0.0471486i
$901$	−13.9983	+	16.1549i	−0.466350	+	0.538196i
$902$	1.16241	+	0.747034i	0.0387040	+	0.0248735i
$903$	−16.5374	+	16.0427i	−0.550332	+	0.533869i
$904$	5.01447	−	0.720973i	0.166779	−	0.0239792i
$905$	7.26375	−	24.7380i	0.241455	−	0.822320i
$906$	27.0397	−	19.6082i	0.898333	−	0.651438i
$907$	−23.5553	−	3.38674i	−0.782141	−	0.112455i	−0.260334	−	0.965519i	$-0.583833\pi$
$907$	−23.5553	−	3.38674i	−0.782141	−	0.112455i	−0.521807	+	0.853064i	$0.674742\pi$
$908$	8.04949	−	17.6259i	0.267132	−	0.584937i
$909$	−50.5309	−	16.5194i	−1.67600	−	0.547915i
$910$	−6.77600	+	47.1281i	−0.224622	+	1.56228i
$911$	15.7242	−	10.1054i	0.520967	−	0.334805i	−0.253587	−	0.967313i	$-0.581610\pi$
$911$	15.7242	−	10.1054i	0.520967	−	0.334805i	0.774555	+	0.632507i	$0.217974\pi$
$912$	−2.67296	−	0.624114i	−0.0885105	−	0.0206665i
$913$	2.18581	+	15.2026i	0.0723397	+	0.503134i
$914$	0.891254	+	1.02856i	0.0294801	+	0.0340218i
$915$	26.1018	+	14.7715i	0.862900	+	0.488331i
$916$	−17.0766	−	14.7970i	−0.564227	−	0.488905i
$917$	5.51254	−	1.61863i	0.182040	−	0.0534518i
$918$	14.4081	+	21.1941i	0.475537	+	0.699510i
$919$		−	39.0332i		−	1.28758i	−0.765200	−	0.643792i	$-0.777360\pi$
$919$		−	39.0332i		−	1.28758i	0.765200	−	0.643792i	$-0.222640\pi$
$920$	6.86210	−	6.31936i	0.226237	−	0.208343i
$921$	−2.17364	−	38.6245i	−0.0716239	−	1.27272i
$922$	7.81587	+	17.1144i	0.257402	+	0.563632i
$923$	7.69636	+	26.2114i	0.253329	+	0.862758i
$924$	−10.0383	+	12.9936i	−0.330234	+	0.427457i
$925$	4.16211	−	6.47636i	0.136849	−	0.212941i
$926$	4.59788	−	3.98409i	0.151096	−	0.130925i
$927$	44.0151	−	11.4846i	1.44565	−	0.377204i
$928$	3.15807	+	0.927294i	0.103669	+	0.0304399i
$929$	−6.93247	−	10.7871i	−0.227447	−	0.353914i	0.708708	−	0.705502i	$-0.249278\pi$
$929$	−6.93247	−	10.7871i	−0.227447	−	0.353914i	−0.936155	+	0.351588i	$0.885642\pi$
$930$	−1.69379	+	19.5137i	−0.0555415	+	0.639880i
$931$	8.22036	+	3.75411i	0.269412	+	0.123036i
$932$	−25.2991	−	11.5537i	−0.828698	−	0.378454i
$933$	−1.12037	+	12.9075i	−0.0366792	+	0.422573i
$934$	8.01771	+	12.4758i	0.262347	+	0.408220i
$935$	−24.4837	−	7.18906i	−0.800702	−	0.235107i
$936$	−19.9363	+	5.20187i	−0.651640	+	0.170028i
$937$	−10.3567	+	8.97416i	−0.338340	+	0.293173i	−0.807414	−	0.589986i	$-0.799133\pi$
$937$	−10.3567	+	8.97416i	−0.338340	+	0.293173i	0.469074	+	0.883159i	$0.344588\pi$
$938$	−16.4839	+	25.6494i	−0.538217	+	0.837482i
$939$	−6.53293	+	8.45626i	−0.213194	+	0.275960i
$940$	4.71030	+	16.0418i	0.153633	+	0.523226i
$941$	−9.67525	−	21.1858i	−0.315404	−	0.690639i	0.683835	−	0.729636i	$-0.260311\pi$
$941$	−9.67525	−	21.1858i	−0.315404	−	0.690639i	−0.999239	+	0.0389979i	$0.987583\pi$
$942$	−0.677718	−	12.0427i	−0.0220813	−	0.392373i
$943$	−1.28294	+	2.13567i	−0.0417784	+	0.0695470i
$944$			7.45537i			0.242652i
$945$	20.2523	+	29.7909i	0.658806	+	0.969098i
$946$	9.52530	−	2.79688i	0.309694	−	0.0909344i
$947$	−10.7597	−	9.32333i	−0.349643	−	0.302967i	0.462278	−	0.886735i	$-0.347032\pi$
$947$	−10.7597	−	9.32333i	−0.349643	−	0.302967i	−0.811921	+	0.583768i	$0.801578\pi$
$948$	−14.4338	−	8.16834i	−0.468788	−	0.265295i
$949$	2.89025	+	3.33552i	0.0938214	+	0.108276i
$950$	0.274339	+	1.90807i	0.00890073	+	0.0619060i
$951$	2.77324	+	0.647528i	0.0899283	+	0.0209975i
$952$	−14.7877	+	9.50348i	−0.479272	+	0.308009i
$953$	0.888810	−	6.18181i	0.0287914	−	0.200249i	−0.970349	−	0.241709i	$-0.922292\pi$
$953$	0.888810	−	6.18181i	0.0287914	−	0.200249i	0.999140	+	0.0414606i	$0.0132011\pi$
$954$	−12.3586	−	4.04023i	−0.400123	−	0.130807i
$955$	7.22598	−	15.8227i	0.233827	−	0.512010i
$956$	−1.27187	−	0.182868i	−0.0411353	−	0.00591437i
$957$	12.2754	−	8.90170i	0.396809	−	0.287751i
$958$	7.05363	−	24.0224i	0.227892	−	0.776130i
$959$	−8.72916	+	1.25506i	−0.281879	+	0.0405281i
$960$	2.41820	−	2.34586i	0.0780471	−	0.0757124i
$961$	2.35538	+	1.51371i	0.0759801	+	0.0488295i
$962$	−28.4643	+	32.8496i	−0.917726	+	1.05911i
$963$	29.8871	−	12.5668i	0.963099	−	0.404961i
$964$	23.9395	−	10.9328i	0.771039	−	0.352122i
$965$	13.3127			0.428552
$966$	−23.9649	−	17.3827i	−0.771057	−	0.559280i
$967$	−41.8472			−1.34572			−0.672858	−	0.739772i	$-0.734934\pi$
$967$	−41.8472			−1.34572			−0.672858	+	0.739772i	$0.734934\pi$
$968$	−3.57059	+	1.63063i	−0.114763	+	0.0524105i
$969$	−12.7546	+	4.53785i	−0.409737	+	0.145777i
$970$	−5.14650	+	5.93937i	−0.165244	+	0.190702i
$971$	−43.4191	−	27.9038i	−1.39339	−	0.895475i	−0.393669	−	0.919252i	$-0.628794\pi$
$971$	−43.4191	−	27.9038i	−1.39339	−	0.895475i	−0.999717	+	0.0237777i	$0.992431\pi$
$972$	−8.48688	+	13.0757i	−0.272217	+	0.419402i
$973$	−43.5464	+	6.26103i	−1.39603	+	0.200719i
$974$	9.27976	−	31.6040i	0.297343	−	1.01266i
$975$	8.49462	+	11.7141i	0.272046	+	0.375151i
$976$	−8.81141	−	1.26689i	−0.282046	−	0.0405521i
$977$	21.4070	−	46.8747i	0.684869	−	1.49965i	−0.172531	−	0.985004i	$-0.555195\pi$
$977$	21.4070	−	46.8747i	0.684869	−	1.49965i	0.857400	−	0.514650i	$-0.172078\pi$
$978$	−6.64056	+	17.0107i	−0.212342	+	0.543942i
$979$	1.62885	−	11.3289i	0.0520582	−	0.362072i
$980$	−9.33138	+	5.99691i	−0.298080	+	0.191564i
$981$	−0.210736	+	1.20477i	−0.00672828	+	0.0384654i
$982$	4.60318	+	32.0158i	0.146893	+	1.02167i
$983$	−7.79811	−	8.99950i	−0.248721	−	0.287040i	0.617636	−	0.786464i	$-0.288090\pi$
$983$	−7.79811	−	8.99950i	−0.248721	−	0.287040i	−0.866358	+	0.499424i	$0.833545\pi$
$984$	−0.443161	+	0.783084i	−0.0141275	+	0.0249638i
$985$	−21.8524	−	18.9352i	−0.696276	−	0.603326i
$986$	15.5758	−	4.57347i	0.496035	−	0.145649i
$987$	46.9501	−	24.7188i	1.49444	−	0.786809i
$988$		−	10.8839i		−	0.346263i
$989$	5.56007	+	17.0143i	0.176800	+	0.541024i
$990$	−1.74144	−	15.4233i	−0.0553466	−	0.490184i
$991$	18.5181	+	40.5490i	0.588247	+	1.28808i	0.936496	+	0.350679i	$0.114049\pi$
$991$	18.5181	+	40.5490i	0.588247	+	1.28808i	−0.348249	+	0.937402i	$0.613224\pi$
$992$	−1.63793	−	5.57827i	−0.0520042	−	0.177110i
$993$	−19.4233	−	15.0056i	−0.616378	−	0.476187i
$994$	−7.66435	+	11.9260i	−0.243099	+	0.378269i
$995$	−8.46247	+	7.33278i	−0.268278	+	0.232465i
$996$	−9.80417	+	1.97737i	−0.310657	+	0.0626553i
$997$	47.1673	+	13.8496i	1.49380	+	0.438621i	0.923753	−	0.382989i	$-0.125105\pi$
$997$	47.1673	+	13.8496i	1.49380	+	0.438621i	0.570051	+	0.821609i	$0.306923\pi$
$998$	−9.28786	−	14.4522i	−0.294002	−	0.457476i
$999$	0.850034	+	32.8747i	0.0268939	+	1.04011i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.2.f.a.65.2	yes	80
3.2	odd	2	inner	138.2.f.a.65.7	yes	80
23.17	odd	22	inner	138.2.f.a.17.7	yes	80
69.17	even	22	inner	138.2.f.a.17.2	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.f.a.17.2	✓	80	69.17	even	22	inner
138.2.f.a.17.7	yes	80	23.17	odd	22	inner
138.2.f.a.65.2	yes	80	1.1	even	1	trivial
138.2.f.a.65.7	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)

\(f(q)\)	\(=\)	\(q+(-0.909632 + 0.415415i) q^{2} +(-0.580581 - 1.63185i) q^{3} +(0.654861 - 0.755750i) q^{4} +(-1.63636 - 1.05163i) q^{5} +(1.20601 + 1.24320i) q^{6} +(-3.52778 + 0.507219i) q^{7} +(-0.281733 + 0.959493i) q^{8} +(-2.32585 + 1.89484i) q^{9} +O(q^{10})\)	\(q+(-0.909632 + 0.415415i) q^{2} +(-0.580581 - 1.63185i) q^{3} +(0.654861 - 0.755750i) q^{4} +(-1.63636 - 1.05163i) q^{5} +(1.20601 + 1.24320i) q^{6} +(-3.52778 + 0.507219i) q^{7} +(-0.281733 + 0.959493i) q^{8} +(-2.32585 + 1.89484i) q^{9} +(1.92535 + 0.276823i) q^{10} +(-1.10493 + 2.41947i) q^{11} +(-1.61347 - 0.629859i) q^{12} +(0.977409 - 6.79803i) q^{13} +(2.99828 - 1.92688i) q^{14} +(-0.766051 + 3.28085i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(-3.22982 - 3.72741i) q^{17} +(1.32852 - 2.68980i) q^{18} +(1.19767 + 1.03779i) q^{19} +(-1.86635 + 0.548011i) q^{20} +(2.87587 + 5.46232i) q^{21} -2.65983i q^{22} +(4.79364 - 0.145045i) q^{23} +(1.72931 - 0.0973192i) q^{24} +(-0.505314 - 1.10648i) q^{25} +(1.93492 + 6.58974i) q^{26} +(4.44243 + 2.69532i) q^{27} +(-1.92688 + 2.99828i) q^{28} +(2.48747 - 2.15541i) q^{29} +(-0.666088 - 3.30259i) q^{30} +(-5.57827 - 1.63793i) q^{31} +(0.540641 + 0.841254i) q^{32} +(4.58970 + 0.398385i) q^{33} +(4.48636 + 2.04885i) q^{34} +(6.30613 + 2.87991i) q^{35} +(-0.0910837 + 2.99862i) q^{36} +(3.42164 + 5.32418i) q^{37} +(-1.52055 - 0.446473i) q^{38} +(-11.6608 + 2.35183i) q^{39} +(1.47004 - 1.27380i) q^{40} +(-0.280858 + 0.437024i) q^{41} +(-4.88511 - 3.77402i) q^{42} +(1.05153 + 3.58117i) q^{43} +(1.10493 + 2.41947i) q^{44} +(5.79859 - 0.654719i) q^{45} +(-4.30019 + 2.12329i) q^{46} -8.59526i q^{47} +(-1.53261 + 0.806908i) q^{48} +(5.47153 - 1.60658i) q^{49} +(0.919299 + 0.796577i) q^{50} +(-4.20739 + 7.43463i) q^{51} +(-4.49754 - 5.19044i) q^{52} +(-0.616803 - 4.28996i) q^{53} +(-5.16066 - 0.606299i) q^{54} +(4.35244 - 2.79714i) q^{55} +(0.507219 - 3.52778i) q^{56} +(0.998164 - 2.55693i) q^{57} +(-1.36730 + 2.99396i) q^{58} +(-7.37948 - 1.06101i) q^{59} +(1.97784 + 2.72744i) q^{60} +(2.50799 - 8.54143i) q^{61} +(5.75459 - 0.827385i) q^{62} +(7.24400 - 7.86430i) q^{63} +(-0.841254 - 0.540641i) q^{64} +(-8.74838 + 10.0962i) q^{65} +(-4.34043 + 1.54425i) q^{66} +(-7.78164 + 3.55375i) q^{67} -4.93207 q^{68} +(-3.01979 - 7.73827i) q^{69} -6.93262 q^{70} +(-3.61816 + 1.65236i) q^{71} +(-1.16282 - 2.76548i) q^{72} +(-0.420832 + 0.485666i) q^{73} +(-5.32418 - 3.42164i) q^{74} +(-1.51223 + 1.46700i) q^{75} +(1.56861 - 0.225532i) q^{76} +(2.67077 - 9.09579i) q^{77} +(9.63007 - 6.98338i) q^{78} +(9.47779 + 1.36270i) q^{79} +(-0.808043 + 1.76937i) q^{80} +(1.81916 - 8.81423i) q^{81} +(0.0739313 - 0.514203i) q^{82} +(4.85775 - 3.12189i) q^{83} +(6.01144 + 1.40362i) q^{84} +(1.36531 + 9.49594i) q^{85} +(-2.44417 - 2.82073i) q^{86} +(-4.96147 - 2.80779i) q^{87} +(-2.01016 - 1.74182i) q^{88} +(-4.12874 + 1.21231i) q^{89} +(-5.00261 + 3.00438i) q^{90} +24.4777i q^{91} +(3.02955 - 3.71777i) q^{92} +(0.565791 + 10.0538i) q^{93} +(3.57060 + 7.81853i) q^{94} +(-0.868456 - 2.95769i) q^{95} +(1.05891 - 1.37066i) q^{96} +(-2.18434 + 3.39889i) q^{97} +(-4.30968 + 3.73436i) q^{98} +(-2.01459 - 7.72099i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6}+O(q^{10}) \) 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6	\( 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6} - 4 q^{12} + 8 q^{13} - 22 q^{15} - 8 q^{16} - 28 q^{18} - 66 q^{21} - 4 q^{24} - 48 q^{25} - 38 q^{27} - 44 q^{30} - 16 q^{31} - 22 q^{33} - 44 q^{37} - 24 q^{39} - 44 q^{43} - 16 q^{46} + 4 q^{48} - 76 q^{49} - 8 q^{52} - 6 q^{54} + 64 q^{55} + 66 q^{57} + 36 q^{58} + 22 q^{60} + 88 q^{61} + 110 q^{63} + 8 q^{64} + 88 q^{66} + 44 q^{67} + 82 q^{69} + 112 q^{70} + 28 q^{72} + 52 q^{73} + 136 q^{75} + 82 q^{78} + 88 q^{79} + 36 q^{81} + 44 q^{82} + 22 q^{84} + 20 q^{85} - 10 q^{87} + 8 q^{93} - 56 q^{94} + 4 q^{96} - 132 q^{97} - 66 q^{99}+O(q^{100}) \) 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6 - 4 * q^12 + 8 * q^13 - 22 * q^15 - 8 * q^16 - 28 * q^18 - 66 * q^21 - 4 * q^24 - 48 * q^25 - 38 * q^27 - 44 * q^30 - 16 * q^31 - 22 * q^33 - 44 * q^37 - 24 * q^39 - 44 * q^43 - 16 * q^46 + 4 * q^48 - 76 * q^49 - 8 * q^52 - 6 * q^54 + 64 * q^55 + 66 * q^57 + 36 * q^58 + 22 * q^60 + 88 * q^61 + 110 * q^63 + 8 * q^64 + 88 * q^66 + 44 * q^67 + 82 * q^69 + 112 * q^70 + 28 * q^72 + 52 * q^73 + 136 * q^75 + 82 * q^78 + 88 * q^79 + 36 * q^81 + 44 * q^82 + 22 * q^84 + 20 * q^85 - 10 * q^87 + 8 * q^93 - 56 * q^94 + 4 * q^96 - 132 * q^97 - 66 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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