LMFDB - Embedded newform 845.2.w.a.116.54

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(51,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([0, 19]))

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

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

chi := DirichletCharacter("845.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.w (of order $26$, degree $12$, 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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$744$
Relative dimension:	$62$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			116.54
Character	$\chi$	$=$	845.116
Dual form			845.2.w.a.51.54

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.42885 + 1.61284i) q^{2} +(-0.131195 - 0.345934i) q^{3} +(-0.318560 + 2.62358i) q^{4} +(0.239316 + 0.970942i) q^{5} +(0.370476 - 0.705884i) q^{6} +(1.02132 - 0.704963i) q^{7} +(-1.13997 + 0.786865i) q^{8} +(2.14307 - 1.89860i) q^{9} +O(q^{10})$	\(q+(1.42885 + 1.61284i) q^{2} +(-0.131195 - 0.345934i) q^{3} +(-0.318560 + 2.62358i) q^{4} +(0.239316 + 0.970942i) q^{5} +(0.370476 - 0.705884i) q^{6} +(1.02132 - 0.704963i) q^{7} +(-1.13997 + 0.786865i) q^{8} +(2.14307 - 1.89860i) q^{9} +(-1.22402 + 1.77331i) q^{10} +(-1.32030 + 1.49031i) q^{11} +(0.949379 - 0.234001i) q^{12} +(3.57593 - 0.461225i) q^{13} +(2.59630 + 0.639930i) q^{14} +(0.304484 - 0.210170i) q^{15} +(2.23418 + 0.550675i) q^{16} +(2.57165 + 3.72568i) q^{17} +(6.12426 + 0.743620i) q^{18} -0.246715i q^{19} +(-2.62358 + 0.318560i) q^{20} +(-0.377862 - 0.260820i) q^{21} -4.29012 q^{22} -5.57158 q^{23} +(0.421762 + 0.291121i) q^{24} +(-0.885456 + 0.464723i) q^{25} +(5.85334 + 5.10837i) q^{26} +(-1.92074 - 1.00808i) q^{27} +(1.52418 + 2.90408i) q^{28} +(-6.13663 + 5.43658i) q^{29} +(0.774033 + 0.190782i) q^{30} +(2.72358 - 5.18936i) q^{31} +(3.59159 + 6.84321i) q^{32} +(0.688763 + 0.261214i) q^{33} +(-2.33441 + 9.47108i) q^{34} +(0.928895 + 0.822929i) q^{35} +(4.29843 + 6.22735i) q^{36} +(-1.56356 + 2.97912i) q^{37} +(0.397912 - 0.352519i) q^{38} +(-0.628699 - 1.17652i) q^{39} +(-1.03681 - 0.918536i) q^{40} +(-1.19180 + 0.451990i) q^{41} +(-0.119249 - 0.982102i) q^{42} +(8.57132 - 4.49858i) q^{43} +(-3.48934 - 3.93865i) q^{44} +(2.35630 + 1.62644i) q^{45} +(-7.96094 - 8.98604i) q^{46} +(-6.01106 + 0.729875i) q^{47} +(-0.102617 - 0.845123i) q^{48} +(-1.93612 + 5.10513i) q^{49} +(-2.01471 - 0.764077i) q^{50} +(0.951449 - 1.37841i) q^{51} +(0.0709116 + 9.52867i) q^{52} +(-5.78836 - 8.38589i) q^{53} +(-1.11858 - 4.53824i) q^{54} +(-1.76297 - 0.925277i) q^{55} +(-0.609559 + 1.60728i) q^{56} +(-0.0853472 + 0.0323679i) q^{57} +(-17.5366 - 2.12933i) q^{58} +(-1.96525 - 7.97333i) q^{59} +(0.454402 + 0.865791i) q^{60} +(1.93209 - 2.79911i) q^{61} +(12.2612 - 3.02211i) q^{62} +(0.850313 - 3.44986i) q^{63} +(-4.27321 + 11.2675i) q^{64} +(1.30360 + 3.36164i) q^{65} +(0.562844 + 1.48410i) q^{66} +(8.93105 - 1.08443i) q^{67} +(-10.5938 + 5.56008i) q^{68} +(0.730965 + 1.92740i) q^{69} +2.67400i q^{70} +(4.84863 - 1.83884i) q^{71} +(-0.949102 + 3.85066i) q^{72} +(-2.39286 + 2.70098i) q^{73} +(-7.03893 + 1.73494i) q^{74} +(0.276931 + 0.245340i) q^{75} +(0.647278 + 0.0785938i) q^{76} +(-0.297828 + 2.45283i) q^{77} +(0.999226 - 2.69506i) q^{78} +(0.0260042 + 0.214164i) q^{79} +2.30104i q^{80} +(0.938595 - 7.73002i) q^{81} +(-2.43189 - 1.27635i) q^{82} +(-1.58599 - 0.601486i) q^{83} +(0.804653 - 0.908266i) q^{84} +(-3.00198 + 3.38854i) q^{85} +(19.5026 + 7.39636i) q^{86} +(2.68580 + 1.40961i) q^{87} +(0.332429 - 2.73780i) q^{88} -3.56097i q^{89} +(0.743620 + 6.12426i) q^{90} +(3.32701 - 2.99196i) q^{91} +(1.77488 - 14.6175i) q^{92} +(-2.15249 - 0.261360i) q^{93} +(-9.76606 - 8.65198i) q^{94} +(0.239546 - 0.0590428i) q^{95} +(1.89610 - 2.14025i) q^{96} +(-2.87816 + 11.6772i) q^{97} +(-11.0002 + 4.17181i) q^{98} +5.70055i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 744 q + 4 q^{3} + 66 q^{4} - 62 q^{9}+O(q^{10}) $ 744 * q + 4 * q^3 + 66 * q^4 - 62 * q^9	$ 744 q + 4 q^{3} + 66 q^{4} - 62 q^{9} - 2 q^{10} - 122 q^{13} - 4 q^{14} - 66 q^{16} - 12 q^{17} - 78 q^{18} - 24 q^{22} + 140 q^{23} + 156 q^{24} + 62 q^{25} - 14 q^{26} + 28 q^{27} + 8 q^{29} - 20 q^{30} - 52 q^{31} - 26 q^{32} - 130 q^{34} + 4 q^{35} + 70 q^{36} + 126 q^{38} + 16 q^{39} + 6 q^{40} - 24 q^{42} - 24 q^{43} - 78 q^{47} - 94 q^{48} - 32 q^{49} - 12 q^{51} + 110 q^{52} - 156 q^{54} + 16 q^{55} + 16 q^{56} - 78 q^{57} - 104 q^{58} - 104 q^{59} + 28 q^{61} + 106 q^{62} + 14 q^{64} - 2 q^{65} - 308 q^{66} - 104 q^{67} - 18 q^{68} + 20 q^{69} - 78 q^{71} - 338 q^{72} - 4 q^{75} - 286 q^{76} - 52 q^{77} + 312 q^{78} - 12 q^{79} - 78 q^{81} + 268 q^{82} + 12 q^{87} - 72 q^{88} + 26 q^{90} - 136 q^{91} + 52 q^{92} - 130 q^{93} + 124 q^{94} - 16 q^{95} + 338 q^{96}+O(q^{100}) $ 744 * q + 4 * q^3 + 66 * q^4 - 62 * q^9 - 2 * q^10 - 122 * q^13 - 4 * q^14 - 66 * q^16 - 12 * q^17 - 78 * q^18 - 24 * q^22 + 140 * q^23 + 156 * q^24 + 62 * q^25 - 14 * q^26 + 28 * q^27 + 8 * q^29 - 20 * q^30 - 52 * q^31 - 26 * q^32 - 130 * q^34 + 4 * q^35 + 70 * q^36 + 126 * q^38 + 16 * q^39 + 6 * q^40 - 24 * q^42 - 24 * q^43 - 78 * q^47 - 94 * q^48 - 32 * q^49 - 12 * q^51 + 110 * q^52 - 156 * q^54 + 16 * q^55 + 16 * q^56 - 78 * q^57 - 104 * q^58 - 104 * q^59 + 28 * q^61 + 106 * q^62 + 14 * q^64 - 2 * q^65 - 308 * q^66 - 104 * q^67 - 18 * q^68 + 20 * q^69 - 78 * q^71 - 338 * q^72 - 4 * q^75 - 286 * q^76 - 52 * q^77 + 312 * q^78 - 12 * q^79 - 78 * q^81 + 268 * q^82 + 12 * q^87 - 72 * q^88 + 26 * q^90 - 136 * q^91 + 52 * q^92 - 130 * q^93 + 124 * q^94 - 16 * q^95 + 338 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{7}{26}\right)$	$1$

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 $

$2$	1.42885	+	1.61284i	1.01035	+	1.14045i	0.990059	+	0.140654i	$0.0449204\pi$
$2$	1.42885	+	1.61284i	1.01035	+	1.14045i	0.0202897	+	0.999794i	$0.493541\pi$
$3$	−0.131195	−	0.345934i	−0.0757457	−	0.199725i	0.891795	−	0.452439i	$-0.149446\pi$
$3$	−0.131195	−	0.345934i	−0.0757457	−	0.199725i	−0.967541	+	0.252714i	$0.918677\pi$
$4$	−0.318560	+	2.62358i	−0.159280	+	1.31179i
$5$	0.239316	+	0.970942i	0.107025	+	0.434218i
$5$	0.239316	+	0.970942i	0.107025	+	0.434218i
$6$	0.370476	−	0.705884i	0.151246	−	0.288176i
$7$	1.02132	−	0.704963i	0.386021	−	0.266451i	−0.359211	−	0.933256i	$-0.616954\pi$
$7$	1.02132	−	0.704963i	0.386021	−	0.266451i	0.745232	+	0.666805i	$0.232339\pi$
$8$	−1.13997	+	0.786865i	−0.403041	+	0.278199i
$9$	2.14307	−	1.89860i	0.714358	−	0.632866i
$10$	−1.22402	+	1.77331i	−0.387071	+	0.560769i
$11$	−1.32030	+	1.49031i	−0.398084	+	0.449344i	−0.913038	−	0.407874i	$-0.866270\pi$
$11$	−1.32030	+	1.49031i	−0.398084	+	0.449344i	0.514954	+	0.857218i	$0.327809\pi$
$12$	0.949379	−	0.234001i	0.274062	−	0.0675502i
$13$	3.57593	−	0.461225i	0.991784	−	0.127921i
$13$	3.57593	−	0.461225i	0.991784	−	0.127921i
$14$	2.59630	+	0.639930i	0.693889	+	0.171028i
$15$	0.304484	−	0.210170i	0.0786175	−	0.0542658i
$16$	2.23418	+	0.550675i	0.558544	+	0.137669i
$17$	2.57165	+	3.72568i	0.623717	+	0.903610i	0.999735	−	0.0230022i	$-0.00732247\pi$
$17$	2.57165	+	3.72568i	0.623717	+	0.903610i	−0.376018	+	0.926612i	$0.622707\pi$
$18$	6.12426	+	0.743620i	1.44350	+	0.175273i
$19$		−	0.246715i		−	0.0566004i	−0.999599	−	0.0283002i	$-0.990991\pi$
$19$		−	0.246715i		−	0.0566004i	0.999599	−	0.0283002i	$-0.00900943\pi$
$20$	−2.62358	+	0.318560i	−0.586651	+	0.0712323i
$21$	−0.377862	−	0.260820i	−0.0824563	−	0.0569155i
$22$	−4.29012			−0.914657
$23$	−5.57158			−1.16175			−0.580877	−	0.813991i	$-0.697290\pi$
$23$	−5.57158			−1.16175			−0.580877	+	0.813991i	$0.697290\pi$
$24$	0.421762	+	0.291121i	0.0860918	+	0.0594249i
$25$	−0.885456	+	0.464723i	−0.177091	+	0.0929446i
$26$	5.85334	+	5.10837i	1.14793	+	1.00183i
$27$	−1.92074	−	1.00808i	−0.369647	−	0.194006i
$28$	1.52418	+	2.90408i	0.288043	+	0.548819i
$29$	−6.13663	+	5.43658i	−1.13954	+	1.00955i	−0.139732	+	0.990189i	$0.544624\pi$
$29$	−6.13663	+	5.43658i	−1.13954	+	1.00955i	−0.999813	+	0.0193588i	$0.993838\pi$
$30$	0.774033	+	0.190782i	0.141318	+	0.0348319i
$31$	2.72358	−	5.18936i	0.489170	−	0.932036i	−0.508316	−	0.861171i	$-0.669732\pi$
$31$	2.72358	−	5.18936i	0.489170	−	0.932036i	0.997486	−	0.0708651i	$-0.0225760\pi$
$32$	3.59159	+	6.84321i	0.634910	+	1.20972i
$33$	0.688763	+	0.261214i	0.119898	+	0.0454714i
$34$	−2.33441	+	9.47108i	−0.400348	+	1.62428i
$35$	0.928895	+	0.822929i	0.157012	+	0.139100i
$36$	4.29843	+	6.22735i	0.716405	+	1.03789i
$37$	−1.56356	+	2.97912i	−0.257048	+	0.489764i	−0.979444	−	0.201715i	$-0.935348\pi$
$37$	−1.56356	+	2.97912i	−0.257048	+	0.489764i	0.722396	+	0.691479i	$0.243041\pi$
$38$	0.397912	−	0.352519i	0.0645498	−	0.0571861i
$39$	−0.628699	−	1.17652i	−0.100672	−	0.188395i
$40$	−1.03681	−	0.918536i	−0.163935	−	0.145233i
$41$	−1.19180	+	0.451990i	−0.186128	+	0.0705890i	−0.445908	−	0.895079i	$-0.647119\pi$
$41$	−1.19180	+	0.451990i	−0.186128	+	0.0705890i	0.259780	+	0.965668i	$0.416350\pi$
$42$	−0.119249	−	0.982102i	−0.0184005	−	0.151542i
$43$	8.57132	−	4.49858i	1.30711	−	0.686026i	0.340013	−	0.940421i	$-0.389568\pi$
$43$	8.57132	−	4.49858i	1.30711	−	0.686026i	0.967101	+	0.254394i	$0.0818761\pi$
$44$	−3.48934	−	3.93865i	−0.526038	−	0.593775i
$45$	2.35630	+	1.62644i	0.351256	+	0.242455i
$46$	−7.96094	−	8.98604i	−1.17378	−	1.32492i
$47$	−6.01106	+	0.729875i	−0.876803	+	0.106463i	−0.546547	−	0.837428i	$-0.684058\pi$
$47$	−6.01106	+	0.729875i	−0.876803	+	0.106463i	−0.330256	+	0.943891i	$0.607135\pi$
$48$	−0.102617	−	0.845123i	−0.0148114	−	0.121983i
$49$	−1.93612	+	5.10513i	−0.276589	+	0.729305i
$50$	−2.01471	−	0.764077i	−0.284922	−	0.108057i
$51$	0.951449	−	1.37841i	0.133230	−	0.193016i
$52$	0.0709116	+	9.52867i	0.00983367	+	1.32139i
$53$	−5.78836	−	8.38589i	−0.795093	−	1.15189i	−0.985415	−	0.170169i	$-0.945569\pi$
$53$	−5.78836	−	8.38589i	−0.795093	−	1.15189i	0.190322	−	0.981722i	$-0.439047\pi$
$54$	−1.11858	−	4.53824i	−0.152219	−	0.617577i
$55$	−1.76297	−	0.925277i	−0.237718	−	0.124764i
$56$	−0.609559	+	1.60728i	−0.0814558	+	0.214781i
$57$	−0.0853472	+	0.0323679i	−0.0113045	+	0.00428723i
$58$	−17.5366	−	2.12933i	−2.30267	−	0.279595i
$59$	−1.96525	−	7.97333i	−0.255854	−	1.03804i	−0.948504	−	0.316765i	$-0.897403\pi$
$59$	−1.96525	−	7.97333i	−0.255854	−	1.03804i	0.692650	−	0.721273i	$-0.256443\pi$
$60$	0.454402	+	0.865791i	0.0586631	+	0.111773i
$61$	1.93209	−	2.79911i	0.247378	−	0.358390i	−0.679549	−	0.733630i	$-0.737825\pi$
$61$	1.93209	−	2.79911i	0.247378	−	0.358390i	0.926927	+	0.375241i	$0.122440\pi$
$62$	12.2612	−	3.02211i	1.55717	−	0.383808i
$63$	0.850313	−	3.44986i	0.107129	−	0.434641i
$64$	−4.27321	+	11.2675i	−0.534151	+	1.40844i
$65$	1.30360	+	3.36164i	0.161692	+	0.416960i
$66$	0.562844	+	1.48410i	0.0692813	+	0.182680i
$67$	8.93105	−	1.08443i	1.09110	−	0.132484i	0.444848	−	0.895606i	$-0.353258\pi$
$67$	8.93105	−	1.08443i	1.09110	−	0.132484i	0.646254	+	0.763123i	$0.276335\pi$
$68$	−10.5938	+	5.56008i	−1.28469	+	0.674259i
$69$	0.730965	+	1.92740i	0.0879978	+	0.232031i
$70$			2.67400i			0.319604i
$71$	4.84863	−	1.83884i	0.575427	−	0.218231i	−0.0496862	−	0.998765i	$-0.515822\pi$
$71$	4.84863	−	1.83884i	0.575427	−	0.218231i	0.625113	+	0.780534i	$0.285053\pi$
$72$	−0.949102	+	3.85066i	−0.111853	+	0.453804i
$73$	−2.39286	+	2.70098i	−0.280063	+	0.316126i	−0.871663	−	0.490106i	$-0.836958\pi$
$73$	−2.39286	+	2.70098i	−0.280063	+	0.316126i	0.591600	+	0.806232i	$0.298497\pi$
$74$	−7.03893	+	1.73494i	−0.818259	+	0.201683i
$75$	0.276931	+	0.245340i	0.0319772	+	0.0283294i
$76$	0.647278	+	0.0785938i	0.0742479	+	0.00901532i
$77$	−0.297828	+	2.45283i	−0.0339406	+	0.279526i
$78$	0.999226	−	2.69506i	0.113140	−	0.305156i
$79$	0.0260042	+	0.214164i	0.00292570	+	0.0240953i	0.994099	−	0.108480i	$-0.0345984\pi$
$79$	0.0260042	+	0.214164i	0.00292570	+	0.0240953i	−0.991173	+	0.132575i	$0.957675\pi$
$80$			2.30104i			0.257264i
$81$	0.938595	−	7.73002i	0.104288	−	0.858891i
$82$	−2.43189	−	1.27635i	−0.268557	−	0.140950i
$83$	−1.58599	−	0.601486i	−0.174085	−	0.0660216i	0.266023	−	0.963967i	$-0.414290\pi$
$83$	−1.58599	−	0.601486i	−0.174085	−	0.0660216i	−0.440107	+	0.897945i	$0.645060\pi$
$84$	0.804653	−	0.908266i	0.0877949	−	0.0990999i
$85$	−3.00198	+	3.38854i	−0.325611	+	0.367538i
$86$	19.5026	+	7.39636i	2.10302	+	0.797569i
$87$	2.68580	+	1.40961i	0.287947	+	0.151126i
$88$	0.332429	−	2.73780i	0.0354370	−	0.291850i
$89$		−	3.56097i		−	0.377462i	−0.982029	−	0.188731i	$-0.939563\pi$
$89$		−	3.56097i		−	0.377462i	0.982029	−	0.188731i	$-0.0604374\pi$
$90$	0.743620	+	6.12426i	0.0783844	+	0.645553i
$91$	3.32701	−	2.99196i	0.348765	−	0.313642i
$92$	1.77488	−	14.6175i	0.185044	−	1.52398i
$93$	−2.15249	−	0.261360i	−0.223203	−	0.0271018i
$94$	−9.76606	−	8.65198i	−1.00729	−	0.892383i
$95$	0.239546	−	0.0590428i	0.0245769	−	0.00605767i
$96$	1.89610	−	2.14025i	0.193519	−	0.218438i
$97$	−2.87816	+	11.6772i	−0.292233	+	1.18564i	0.622841	+	0.782349i	$0.285978\pi$
$97$	−2.87816	+	11.6772i	−0.292233	+	1.18564i	−0.915074	+	0.403287i	$0.867868\pi$
$98$	−11.0002	+	4.17181i	−1.11119	+	0.421417i
$99$			5.70055i			0.572926i
$100$	−0.937168	−	2.47111i	−0.0937168	−	0.247111i
$101$	−4.29095	+	2.25206i	−0.426966	+	0.224089i	−0.664497	−	0.747291i	$-0.731354\pi$
$101$	−4.29095	+	2.25206i	−0.426966	+	0.224089i	0.237531	+	0.971380i	$0.423662\pi$
$102$	3.58263	−	0.435010i	0.354733	−	0.0430724i
$103$	−1.64841	−	4.34651i	−0.162423	−	0.428274i	0.828954	−	0.559317i	$-0.188937\pi$
$103$	−1.64841	−	4.34651i	−0.162423	−	0.428274i	−0.991377	+	0.131043i	$0.958167\pi$
$104$	−3.71353	+	3.33956i	−0.364142	+	0.327471i
$105$	0.162812	−	0.429301i	0.0158888	−	0.0418955i
$106$	5.25438	−	21.3178i	0.510350	−	2.07057i
$107$	−8.19062	+	2.01881i	−0.791817	+	0.195165i	−0.614426	−	0.788975i	$-0.710612\pi$
$107$	−8.19062	+	2.01881i	−0.791817	+	0.195165i	−0.177392	+	0.984140i	$0.556766\pi$
$108$	3.25666	−	4.71809i	0.313373	−	0.453998i
$109$	1.22643	+	2.33676i	0.117471	+	0.223821i	0.937091	−	0.349086i	$-0.113508\pi$
$109$	1.22643	+	2.33676i	0.117471	+	0.223821i	−0.819620	+	0.572907i	$0.805816\pi$
$110$	−1.02669	−	4.16546i	−0.0978914	−	0.397161i
$111$	1.23571	+	0.150042i	0.117288	+	0.0142414i
$112$	2.67001	−	1.01260i	0.252292	−	0.0956817i
$113$	5.60916	−	14.7901i	0.527665	−	1.39134i	−0.360907	−	0.932602i	$-0.617533\pi$
$113$	5.60916	−	14.7901i	0.527665	−	1.39134i	0.888572	−	0.458737i	$-0.151698\pi$
$114$	−0.174152	−	0.0914022i	−0.0163109	−	0.00856060i
$115$	−1.33337	−	5.40968i	−0.124337	−	0.504455i
$116$	−12.3084	−	17.8318i	−1.14281	−	1.65564i
$117$	6.78780	−	7.77769i	0.627532	−	0.719048i
$118$	10.0516	−	14.5623i	0.925328	−	1.34057i
$119$	5.25293	+	1.99218i	0.481536	+	0.182622i
$120$	−0.181728	+	0.479176i	−0.0165894	+	0.0437426i
$121$	0.848073	+	6.98451i	0.0770976	+	0.634956i
$122$	7.27517	−	0.883366i	0.658663	−	0.0799762i
$123$	0.312717	+	0.352985i	0.0281968	+	0.0318276i
$124$	12.7471	+	8.79867i	1.14472	+	0.790144i
$125$	−0.663123	−	0.748511i	−0.0593115	−	0.0669488i
$126$	6.77903	−	3.55791i	0.603924	−	0.316964i
$127$	−2.02845	−	16.7058i	−0.179996	−	1.48240i	−0.750371	−	0.661017i	$-0.770125\pi$
$127$	−2.02845	−	16.7058i	−0.179996	−	1.48240i	0.570375	−	0.821385i	$-0.306798\pi$
$128$	−9.82600	+	3.72651i	−0.868504	+	0.329380i
$129$	−2.68073	−	2.37492i	−0.236025	−	0.209100i
$130$	−3.55913	+	6.90577i	−0.312157	+	0.605676i
$131$	−3.92153	+	3.47417i	−0.342626	+	0.303540i	−0.816834	−	0.576873i	$-0.804273\pi$
$131$	−3.92153	+	3.47417i	−0.342626	+	0.303540i	0.474208	+	0.880413i	$0.342734\pi$
$132$	−0.904728	+	1.72381i	−0.0787464	+	0.150039i
$133$	−0.173925	−	0.251974i	−0.0150812	−	0.0218489i
$134$	14.5101	+	12.8548i	1.25348	+	1.11049i
$135$	0.519127	−	2.10618i	0.0446793	−	0.181271i
$136$	−5.86321	−	2.22362i	−0.502766	−	0.190674i
$137$	−7.41097	−	14.1204i	−0.633162	−	1.20639i	−0.964800	−	0.262983i	$-0.915294\pi$
$137$	−7.41097	−	14.1204i	−0.633162	−	1.20639i	0.331638	−	0.943407i	$-0.392399\pi$
$138$	−2.06414	+	3.93288i	−0.175711	+	0.334789i
$139$	1.20772	+	0.297676i	0.102437	+	0.0252485i	0.290201	−	0.956966i	$-0.406278\pi$
$139$	1.20772	+	0.297676i	0.102437	+	0.0252485i	−0.187764	+	0.982214i	$0.560124\pi$
$140$	−2.45493	+	2.17488i	−0.207480	+	0.183811i
$141$	1.04111	+	1.98367i	0.0876774	+	0.167055i
$142$	9.89372	+	5.19262i	0.830262	+	0.435755i
$143$	−4.03392	+	5.93818i	−0.337333	+	0.496576i
$144$	5.83352	−	3.06167i	0.486127	−	0.255139i
$145$	−6.74720	−	4.65725i	−0.560324	−	0.386764i
$146$	−7.77527			−0.643486
$147$	2.02005			0.166611
$148$	−7.31787	−	5.05116i	−0.601525	−	0.415203i
$149$	−8.54129	+	1.03710i	−0.699730	+	0.0849626i	−0.462667	−	0.886532i	$-0.653108\pi$
$149$	−8.54129	+	1.03710i	−0.699730	+	0.0849626i	−0.237062	+	0.971494i	$0.576185\pi$
$150$			0.797198i			0.0650909i
$151$	−9.08435	−	1.10304i	−0.739274	−	0.0897641i	−0.257768	−	0.966207i	$-0.582987\pi$
$151$	−9.08435	−	1.10304i	−0.739274	−	0.0897641i	−0.481506	+	0.876443i	$0.659910\pi$
$152$	0.194132	+	0.281248i	0.0157462	+	0.0228123i
$153$	12.5848	+	3.10188i	1.01742	+	0.250772i
$154$	−4.38157	+	3.02438i	−0.353077	+	0.243711i
$155$	5.69036	+	1.40255i	0.457061	+	0.112655i
$156$	3.28698	−	1.27465i	0.263169	−	0.102053i
$157$	0.862372	−	0.212556i	0.0688248	−	0.0169638i	−0.204753	−	0.978814i	$-0.565639\pi$
$157$	0.862372	−	0.212556i	0.0688248	−	0.0169638i	0.273578	+	0.961850i	$0.411793\pi$
$158$	−0.308255	+	0.347948i	−0.0245235	+	0.0276813i
$159$	−2.14156	+	3.10258i	−0.169836	+	0.246050i
$160$	−5.78483	+	5.12491i	−0.457331	+	0.405160i
$161$	−5.69034	+	3.92776i	−0.448461	+	0.309551i
$162$	13.8084	−	9.53123i	1.08489	−	0.748844i
$163$	1.45801	−	2.77801i	0.114200	−	0.217591i	−0.821647	−	0.569997i	$-0.806944\pi$
$163$	1.45801	−	2.77801i	0.114200	−	0.217591i	0.935847	+	0.352406i	$0.114637\pi$
$164$	−0.806172	−	3.27077i	−0.0629515	−	0.255404i
$165$	−0.0887912	+	0.731262i	−0.00691239	+	0.0569286i
$166$	−1.29604	−	3.41737i	−0.100592	−	0.265239i
$167$	−15.2565	−	17.2210i	−1.18058	−	1.33260i	−0.931335	−	0.364163i	$-0.881355\pi$
$167$	−15.2565	−	17.2210i	−1.18058	−	1.33260i	−0.249248	−	0.968440i	$-0.580183\pi$
$168$	0.635982			0.0490671
$169$	12.5745	−	3.29862i	0.967273	−	0.253740i
$170$	−9.75453			−0.748139
$171$	−0.468413	−	0.528729i	−0.0358205	−	0.0404329i
$172$	9.07190	+	23.9206i	0.691726	+	1.82393i
$173$	−1.34217	+	11.0538i	−0.102044	+	0.840405i	0.848367	+	0.529408i	$0.177586\pi$
$173$	−1.34217	+	11.0538i	−0.102044	+	0.840405i	−0.950411	+	0.310997i	$0.899337\pi$
$174$	1.56412	+	6.34587i	0.118575	+	0.481079i
$175$	−0.576717	+	1.09884i	−0.0435957	+	0.0830647i
$176$	−3.77045	+	2.60255i	−0.284208	+	0.196175i
$177$	−2.50041	+	1.72591i	−0.187942	+	0.129727i
$178$	5.74326	−	5.08809i	0.430476	−	0.381368i
$179$	0.861805	−	1.24854i	0.0644144	−	0.0933203i	−0.789453	−	0.613811i	$-0.789636\pi$
$179$	0.861805	−	1.24854i	0.0644144	−	0.0933203i	0.853867	+	0.520491i	$0.174251\pi$
$180$	−5.01771	+	5.66383i	−0.373998	+	0.422157i
$181$	13.7971	−	3.40067i	1.02553	−	0.252770i	0.309542	−	0.950886i	$-0.399824\pi$
$181$	13.7971	−	3.40067i	1.02553	−	0.252770i	0.715985	+	0.698116i	$0.245978\pi$
$182$	9.57932	+	1.09087i	0.710067	+	0.0808604i
$183$	−1.22179	−	0.301144i	−0.0903172	−	0.0222612i
$184$	6.35143	−	4.38408i	0.468234	−	0.323199i
$185$	−3.26674	−	0.805178i	−0.240175	−	0.0591979i
$186$	−2.65406	−	3.84507i	−0.194605	−	0.281934i
$187$	−8.94774	−	1.08645i	−0.654323	−	0.0794493i
$188$		−	16.0030i		−	1.16714i
$189$	−2.67235	+	0.324482i	−0.194385	+	0.0236026i
$190$	0.437502	+	0.301986i	0.0317397	+	0.0219083i
$191$	25.3197			1.83207			0.916034	−	0.401101i	$-0.131372\pi$
$191$	25.3197			1.83207			0.916034	+	0.401101i	$0.131372\pi$
$192$	4.45844			0.321761
$193$	−8.16350	−	5.63486i	−0.587622	−	0.405606i	0.236819	−	0.971554i	$-0.423895\pi$
$193$	−8.16350	−	5.63486i	−0.587622	−	0.405606i	−0.824441	+	0.565948i	$0.808510\pi$
$194$	−22.9458	+	12.0429i	−1.64741	+	0.864629i
$195$	0.991879	−	0.891990i	0.0710299	−	0.0638768i
$196$	−12.7770	−	6.70587i	−0.912640	−	0.478990i
$197$	−8.46887	−	16.1361i	−0.603382	−	1.14965i	−0.975196	−	0.221341i	$-0.928957\pi$
$197$	−8.46887	−	16.1361i	−0.603382	−	1.14965i	0.371814	−	0.928307i	$-0.378736\pi$
$198$	−9.19405	+	8.14522i	−0.653393	+	0.578855i
$199$	−20.6695	−	5.09457i	−1.46522	−	0.361145i	−0.575557	−	0.817761i	$-0.695215\pi$
$199$	−20.6695	−	5.09457i	−1.46522	−	0.361145i	−0.889663	+	0.456617i	$0.849061\pi$
$200$	0.643720	−	1.22651i	0.0455179	−	0.0867270i
$201$	−1.54685	−	2.94728i	−0.109106	−	0.207885i
$202$	−9.76333	−	3.70274i	−0.686946	−	0.260524i
$203$	−2.43485	+	9.87857i	−0.170893	+	0.693340i
$204$	3.31328	+	2.93531i	0.231976	+	0.205513i
$205$	−0.724072	−	1.04900i	−0.0505714	−	0.0732653i
$206$	4.65488	−	8.86913i	0.324321	−	0.617941i
$207$	−11.9403	+	10.5782i	−0.829908	+	0.735235i
$208$	8.24325	+	0.938718i	0.571566	+	0.0650884i
$209$	0.367681	+	0.325737i	0.0254330	+	0.0225317i
$210$	0.925026	−	0.350816i	0.0638329	−	0.0242086i
$211$	1.99622	+	16.4404i	0.137426	+	1.13180i	0.884328	+	0.466867i	$0.154617\pi$
$211$	1.99622	+	16.4404i	0.137426	+	1.13180i	−0.746902	+	0.664934i	$0.768460\pi$
$212$	23.8450	−	12.5148i	1.63768	−	0.859522i
$213$	−1.27224	−	1.43606i	−0.0871722	−	0.0983970i
$214$	−14.9592	−	10.3256i	−1.02259	−	0.705841i
$215$	6.41911	+	7.24567i	0.437779	+	0.494151i
$216$	2.98282	−	0.362180i	0.202955	−	0.0246432i
$217$	−0.876667	−	7.22000i	−0.0595120	−	0.490125i
$218$	−2.01644	+	5.31691i	−0.136570	+	0.360107i
$219$	1.24829	+	0.473415i	0.0843518	+	0.0319904i
$220$	2.98915	−	4.33053i	0.201528	−	0.291964i
$221$	10.9144	+	12.1367i	0.734183	+	0.816400i
$222$	1.52365	+	2.20739i	0.102261	+	0.148150i
$223$	2.32405	+	9.42905i	0.155630	+	0.631416i	0.995996	+	0.0893965i	$0.0284938\pi$
$223$	2.32405	+	9.42905i	0.155630	+	0.631416i	−0.840366	+	0.542019i	$0.817660\pi$
$224$	8.49236	+	4.45713i	0.567420	+	0.297805i
$225$	−1.01528	+	2.67706i	−0.0676850	+	0.178471i
$226$	31.8687	−	12.0862i	2.11988	−	0.803963i
$227$	−23.8548	−	2.89650i	−1.58330	−	0.192247i	−0.718922	−	0.695090i	$-0.755364\pi$
$227$	−23.8548	−	2.89650i	−1.58330	−	0.192247i	−0.864378	+	0.502843i	$0.832287\pi$
$228$	−0.0577316	−	0.234226i	−0.00382337	−	0.0155120i
$229$	11.9933	+	22.8513i	0.792540	+	1.51006i	0.858832	+	0.512258i	$0.171191\pi$
$229$	11.9933	+	22.8513i	0.792540	+	1.51006i	−0.0662920	+	0.997800i	$0.521117\pi$
$230$	6.81975	−	9.88011i	0.449681	−	0.651475i
$231$	0.887591	−	0.218772i	0.0583992	−	0.0143941i
$232$	2.71773	−	11.0262i	0.178427	−	0.723909i
$233$	−9.08700	+	23.9604i	−0.595309	+	1.56970i	0.210543	+	0.977585i	$0.432477\pi$
$233$	−9.08700	+	23.9604i	−0.595309	+	1.56970i	−0.805852	+	0.592116i	$0.798293\pi$
$234$	22.2429	−	0.165530i	1.45406	−	0.0108210i
$235$	−2.14721	−	5.66172i	−0.140068	−	0.369330i
$236$	21.5447	−	2.61600i	1.40244	−	0.170287i
$237$	0.0706748	−	0.0370930i	0.00459082	−	0.00240945i
$238$	4.29259	+	11.3186i	0.278248	+	0.733679i
$239$		−	6.61983i		−	0.428201i	−0.976812	−	0.214101i	$-0.931318\pi$
$239$		−	6.61983i		−	0.428201i	0.976812	−	0.214101i	$-0.0686820\pi$
$240$	0.796008	−	0.301886i	0.0513821	−	0.0194867i
$241$	1.80508	−	7.32351i	0.116276	−	0.471749i	−0.883717	−	0.468021i	$-0.844967\pi$
$241$	1.80508	−	7.32351i	0.116276	−	0.471749i	0.999993	−	0.00372807i	$-0.00118669\pi$
$242$	−10.0531	+	11.3476i	−0.646238	+	0.729452i
$243$	−9.11575	+	2.24683i	−0.584776	+	0.144134i
$244$	6.72821	+	5.96068i	0.430730	+	0.381593i
$245$	−5.42013	−	0.658123i	−0.346280	−	0.0420459i
$246$	−0.122481	+	1.00872i	−0.00780912	+	0.0643139i
$247$	−0.113791	−	0.882237i	−0.00724037	−	0.0561354i
$248$	0.978517	+	8.05881i	0.0621359	+	0.511735i
$249$			0.627559i			0.0397699i
$250$	0.259724	−	2.13902i	0.0164264	−	0.135283i
$251$	9.77765	+	5.13171i	0.617160	+	0.323910i	0.744169	−	0.667991i	$-0.232846\pi$
$251$	9.77765	+	5.13171i	0.617160	+	0.323910i	−0.127010	+	0.991901i	$0.540538\pi$
$252$	8.78010	+	3.32985i	0.553095	+	0.209761i
$253$	7.35613	−	8.30335i	0.462476	−	0.522027i
$254$	24.0454	−	27.1417i	1.50874	−	1.70302i
$255$	1.56605	+	0.593926i	0.0980702	+	0.0371931i
$256$	1.29048	+	0.677294i	0.0806547	+	0.0423308i
$257$	2.17079	−	17.8780i	0.135410	−	1.11520i	−0.753606	−	0.657326i	$-0.771687\pi$
$257$	2.17079	−	17.8780i	0.135410	−	1.11520i	0.889016	−	0.457876i	$-0.151390\pi$
$258$		−	7.71697i		−	0.480437i
$259$	0.503279	+	4.14488i	0.0312722	+	0.257550i
$260$	−9.23481	+	2.34921i	−0.572719	+	0.145692i
$261$	−2.82938	+	23.3020i	−0.175134	+	1.44236i
$262$	−11.2065	−	1.36072i	−0.692343	−	0.0840656i
$263$	−13.4771	−	11.9396i	−0.831031	−	0.736229i	0.136049	−	0.990702i	$-0.456560\pi$
$263$	−13.4771	−	11.9396i	−0.831031	−	0.736229i	−0.967080	+	0.254473i	$0.918098\pi$
$264$	−0.990710	+	0.244188i	−0.0609740	+	0.0150287i
$265$	6.75696	−	7.62704i	0.415077	−	0.468525i
$266$	0.157880	−	0.640546i	0.00968027	−	0.0392744i
$267$	−1.23186	+	0.467183i	−0.0753886	+	0.0285911i
$268$			23.7768i			1.45240i
$269$	11.0675	+	29.1827i	0.674800	+	1.77930i	0.625110	+	0.780537i	$0.285054\pi$
$269$	11.0675	+	29.1827i	0.674800	+	1.77930i	0.0496900	+	0.998765i	$0.484177\pi$
$270$	4.13868	−	2.17215i	0.251872	−	0.132193i
$271$	−13.8074	+	1.67652i	−0.838739	+	0.101841i	−0.528622	−	0.848857i	$-0.677291\pi$
$271$	−13.8074	+	1.67652i	−0.838739	+	0.101841i	−0.310117	+	0.950698i	$0.600368\pi$
$272$	3.69388	+	9.73997i	0.223975	+	0.590573i
$273$	−1.47151	−	0.758393i	−0.0890596	−	0.0459000i
$274$	12.1848	−	32.1286i	0.736110	−	1.94096i
$275$	0.476484	−	1.93317i	0.0287331	−	0.116575i
$276$	−5.28954	+	1.30375i	−0.318393	+	0.0784767i
$277$	15.1318	−	21.9222i	0.909180	−	1.31717i	−0.0389332	−	0.999242i	$-0.512396\pi$
$277$	15.1318	−	21.9222i	0.909180	−	1.31717i	0.948113	−	0.317933i	$-0.102989\pi$
$278$	1.24554	+	2.37319i	0.0747028	+	0.142334i
$279$	−4.01566	−	16.2922i	−0.240411	−	0.975387i
$280$	−1.70645	−	0.207200i	−0.101980	−	0.0123826i
$281$	−10.6901	+	4.05421i	−0.637717	+	0.241854i	−0.652207	−	0.758041i	$-0.726157\pi$
$281$	−10.6901	+	4.05421i	−0.637717	+	0.241854i	0.0144903	+	0.999895i	$0.495387\pi$
$282$	−1.71175	+	4.51351i	−0.101933	+	0.268776i
$283$	12.9442	+	6.79366i	0.769455	+	0.403841i	0.803291	−	0.595586i	$-0.203080\pi$
$283$	12.9442	+	6.79366i	0.769455	+	0.403841i	−0.0338364	+	0.999427i	$0.510773\pi$
$284$	3.27977	+	13.3066i	0.194619	+	0.789599i
$285$	−0.0518523	−	0.0751210i	−0.00307146	−	0.00444978i
$286$	−15.3412	+	1.97871i	−0.907143	+	0.117004i
$287$	−0.898567	+	1.30180i	−0.0530408	+	0.0768428i
$288$	20.6895	+	7.84651i	1.21914	+	0.462360i
$289$	−1.23902	+	3.26702i	−0.0728833	+	0.192177i
$290$	−2.12933	−	17.5366i	−0.125039	−	1.02979i
$291$	4.41712	−	0.536336i	0.258936	−	0.0314406i
$292$	−6.32397	−	7.13829i	−0.370082	−	0.417737i
$293$	−12.6497	−	8.73148i	−0.739006	−	0.510099i	0.138087	−	0.990420i	$-0.455905\pi$
$293$	−12.6497	−	8.73148i	−0.739006	−	0.510099i	−0.877093	+	0.480321i	$0.840520\pi$
$294$	2.88634	+	3.25801i	0.168335	+	0.190011i
$295$	7.27132	−	3.81628i	0.423353	−	0.222193i
$296$	−0.561749	−	4.62642i	−0.0326510	−	0.268905i
$297$	4.03830	−	1.53153i	0.234326	−	0.0888681i
$298$	−13.8769	−	12.2938i	−0.803866	−	0.712163i
$299$	−19.9236	+	2.56975i	−1.15221	+	0.148612i
$300$	−0.731888	+	0.648396i	−0.0422555	+	0.0374351i
$301$	5.58269	−	10.6369i	0.321781	−	0.613103i
$302$	−11.2011	−	16.2277i	−0.644553	−	0.933797i
$303$	1.34202	+	1.18892i	0.0770969	+	0.0683019i
$304$	0.135860	−	0.551206i	0.00779211	−	0.0316138i
$305$	3.18015	+	1.20607i	0.182095	+	0.0690596i
$306$	12.9790	+	24.7293i	0.741958	+	1.41368i
$307$	−3.75432	+	7.15325i	−0.214270	+	0.408258i	−0.968740	−	0.248076i	$-0.920202\pi$
$307$	−3.75432	+	7.15325i	−0.214270	+	0.408258i	0.754470	+	0.656334i	$0.227894\pi$
$308$	−6.34033	−	1.56275i	−0.361274	−	0.0890460i
$309$	−1.28734	+	1.14048i	−0.0732342	+	0.0648798i
$310$	5.86858	+	11.1816i	0.333313	+	0.635075i
$311$	17.5043	+	9.18695i	0.992576	+	0.520944i	0.881154	−	0.472829i	$-0.156767\pi$
$311$	17.5043	+	9.18695i	0.992576	+	0.520944i	0.111422	+	0.993773i	$0.464459\pi$
$312$	1.64246	+	0.846502i	0.0929862	+	0.0479237i
$313$	−15.0067	+	7.87611i	−0.848227	+	0.445184i	−0.832060	−	0.554685i	$-0.812839\pi$
$313$	−15.0067	+	7.87611i	−0.848227	+	0.445184i	−0.0161669	+	0.999869i	$0.505146\pi$
$314$	1.57502	+	1.08716i	0.0888833	+	0.0613517i
$315$	3.55310			0.200195
$316$	−0.570160			−0.0320740
$317$	18.1576	+	12.5333i	1.01983	+	0.703938i	0.955802	−	0.294010i	$-0.0949899\pi$
$317$	18.1576	+	12.5333i	1.01983	+	0.703938i	0.0640279	+	0.997948i	$0.479605\pi$
$318$	−8.06391	+	0.979136i	−0.452202	+	0.0549072i
$319$		−	16.3234i		−	0.913932i
$320$	−11.9628	−	1.45254i	−0.668739	−	0.0811996i
$321$	1.77295	+	2.56855i	0.0989561	+	0.143363i
$322$	−14.4655	−	3.56542i	−0.806129	−	0.198693i
$323$	0.919182	−	0.634466i	0.0511447	−	0.0353026i
$324$	19.9813	+	4.92496i	1.11007	+	0.273609i
$325$	−2.95199	+	2.07021i	−0.163747	+	0.114835i
$326$	6.56376	−	1.61782i	0.363533	−	0.0896029i
$327$	0.647464	−	0.730835i	0.0358048	−	0.0404153i
$328$	1.00296	−	1.45304i	0.0553793	−	0.0802308i
$329$	−5.62465	+	4.98301i	−0.310097	+	0.274722i
$330$	−1.30627	+	0.901657i	−0.0719081	+	0.0496346i
$331$	16.5619	−	11.4318i	0.910322	−	0.628350i	−0.0181162	−	0.999836i	$-0.505767\pi$
$331$	16.5619	−	11.4318i	0.910322	−	0.628350i	0.928439	+	0.371486i	$0.121151\pi$
$332$	2.08328	−	3.96936i	0.114335	−	0.217847i
$333$	2.30532	+	9.35305i	0.126331	+	0.512544i
$334$	5.97548	−	49.2125i	0.326963	−	2.69279i
$335$	3.19025	+	8.41201i	0.174302	+	0.459597i
$336$	−0.700585	−	0.790797i	−0.0382200	−	0.0431415i
$337$	−12.9156			−0.703560			−0.351780	−	0.936083i	$-0.614423\pi$
$337$	−12.9156			−0.703560			−0.351780	+	0.936083i	$0.614423\pi$
$338$	23.2872	+	15.5675i	1.26666	+	0.846758i
$339$	−5.85230			−0.317853
$340$	−7.93379	−	8.95540i	−0.430270	−	0.485675i
$341$	4.13779	+	10.9105i	0.224074	+	0.590834i
$342$	0.183462	−	1.51095i	0.00992051	−	0.0817027i
$343$	3.70046	+	15.0134i	0.199806	+	0.810645i
$344$	−6.23128	+	11.8727i	−0.335968	+	0.640134i
$345$	−1.69646	+	1.17098i	−0.0913342	+	0.0630435i
$346$	−19.7457	+	13.6295i	−1.06154	+	0.732726i
$347$	3.59345	−	3.18352i	0.192907	−	0.170900i	−0.561141	−	0.827720i	$-0.689637\pi$
$347$	3.59345	−	3.18352i	0.192907	−	0.170900i	0.754047	+	0.656820i	$0.228099\pi$
$348$	−4.55382	+	6.59735i	−0.244111	+	0.353655i
$349$	−15.8264	+	17.8643i	−0.847167	+	0.956254i	−0.999485	−	0.0320772i	$-0.989788\pi$
$349$	−15.8264	+	17.8643i	−0.847167	+	0.956254i	0.152318	+	0.988332i	$0.451326\pi$
$350$	−2.59630	+	0.639930i	−0.138778	+	0.0342057i
$351$	−7.33340	−	2.71894i	−0.391428	−	0.145126i
$352$	−14.9404	−	3.68248i	−0.796328	−	0.196277i
$353$	−15.5217	+	10.7139i	−0.826139	+	0.570243i	−0.904398	−	0.426691i	$-0.859679\pi$
$353$	−15.5217	+	10.7139i	−0.826139	+	0.570243i	0.0782588	+	0.996933i	$0.475064\pi$
$354$	−6.35632	−	1.56669i	−0.337834	−	0.0832687i
$355$	2.94576	+	4.26768i	0.156345	+	0.226505i
$356$	9.34250	+	1.13438i	0.495151	+	0.0601223i
$357$		−	2.07853i		−	0.110008i
$358$	3.24508	−	0.394024i	0.171508	−	0.0208248i
$359$	10.8691	+	7.50238i	0.573648	+	0.395961i	0.819272	−	0.573404i	$-0.194378\pi$
$359$	10.8691	+	7.50238i	0.573648	+	0.395961i	−0.245624	+	0.969365i	$0.578993\pi$
$360$	−3.96590			−0.209021
$361$	18.9391			0.996796
$362$	25.1986	+	17.3934i	1.32441	+	0.914174i
$363$	2.30491	−	1.20971i	0.120977	−	0.0634934i
$364$	6.78979	+	9.68179i	0.355881	+	0.507464i
$365$	−3.19514	−	1.67694i	−0.167241	−	0.0877751i
$366$	−1.26005	−	2.40083i	−0.0658641	−	0.125494i
$367$	4.79258	−	4.24585i	0.250171	−	0.221632i	−0.528712	−	0.848801i	$-0.677325\pi$
$367$	4.79258	−	4.24585i	0.250171	−	0.221632i	0.778883	+	0.627169i	$0.215787\pi$
$368$	−12.4479	−	3.06813i	−0.648891	−	0.159937i
$369$	−1.69597	+	3.23140i	−0.0882886	+	0.168220i
$370$	−3.36905	−	6.41919i	−0.175149	−	0.333718i
$371$	−11.8235	−	4.48406i	−0.613845	−	0.232801i
$372$	1.37140	−	5.56399i	0.0711037	−	0.288479i
$373$	8.30883	+	7.36098i	0.430215	+	0.381137i	0.850257	−	0.526367i	$-0.176446\pi$
$373$	8.30883	+	7.36098i	0.430215	+	0.381137i	−0.420042	+	0.907504i	$0.637985\pi$
$374$	−11.0327	−	15.9836i	−0.570487	−	0.826493i
$375$	−0.171936	+	0.327598i	−0.00887876	+	0.0169171i
$376$	6.27812	−	5.56193i	0.323769	−	0.286835i
$377$	−19.4367	+	22.2712i	−1.00104	+	1.14703i
$378$	−4.34172	−	3.84642i	−0.223314	−	0.197839i
$379$	−20.8026	+	7.88937i	−1.06856	+	0.405250i	−0.825290	−	0.564709i	$-0.808988\pi$
$379$	−20.8026	+	7.88937i	−1.06856	+	0.405250i	−0.243267	+	0.969959i	$0.578219\pi$
$380$	0.0785938	+	0.647278i	0.00403177	+	0.0332046i
$381$	−5.51298	+	2.89344i	−0.282439	+	0.148235i
$382$	36.1780	+	40.8365i	1.85103	+	2.08938i
$383$	−23.1594	−	15.9858i	−1.18339	−	0.816834i	−0.196862	−	0.980431i	$-0.563075\pi$
$383$	−23.1594	−	15.9858i	−1.18339	−	0.816834i	−0.986527	+	0.163597i	$0.947690\pi$
$384$	2.57825	+	2.91024i	0.131571	+	0.148513i
$385$	−2.45283	+	0.297828i	−0.125008	+	0.0151787i
$386$	−2.57630	−	21.2178i	−0.131130	−	1.07996i
$387$	9.82799	−	25.9143i	0.499585	−	1.31730i
$388$	−29.7191	−	11.2710i	−1.50876	−	0.572197i
$389$	4.70266	−	6.81297i	0.238434	−	0.345431i	−0.685439	−	0.728130i	$-0.740390\pi$
$389$	4.70266	−	6.81297i	0.238434	−	0.345431i	0.923873	+	0.382698i	$0.125005\pi$
$390$	2.85588	+	0.325219i	0.144613	+	0.0164681i
$391$	−14.3281	−	20.7579i	−0.724606	−	1.04977i
$392$	−1.80993	−	7.34317i	−0.0914152	−	0.370886i
$393$	1.71632	+	0.900794i	0.0865769	+	0.0454391i
$394$	13.9241	−	36.7149i	0.701488	−	1.84967i
$395$	−0.201717	+	0.0765013i	−0.0101495	+	0.00384920i
$396$	−14.9558	−	1.81597i	−0.751559	−	0.0912558i
$397$	2.75421	+	11.1743i	0.138230	+	0.560821i	0.998684	+	0.0512924i	$0.0163340\pi$
$397$	2.75421	+	11.1743i	0.138230	+	0.560821i	−0.860454	+	0.509529i	$0.829820\pi$
$398$	−21.3169	−	40.6159i	−1.06852	−	2.03589i
$399$	−0.0643482	+	0.0932245i	−0.00322144	+	0.00466706i
$400$	−2.23418	+	0.550675i	−0.111709	+	0.0275338i
$401$	−5.41804	+	21.9819i	−0.270564	+	1.09772i	0.665642	+	0.746271i	$0.268158\pi$
$401$	−5.41804	+	21.9819i	−0.270564	+	1.09772i	−0.936206	+	0.351451i	$0.885688\pi$
$402$	2.54326	−	6.70603i	0.126846	−	0.334467i
$403$	7.34588	−	19.8130i	0.365925	−	0.986954i
$404$	−4.54155	−	11.9751i	−0.225950	−	0.595782i
$405$	7.73002	−	0.938595i	0.384108	−	0.0466391i
$406$	−19.4116	+	10.1880i	−0.963379	+	0.505620i
$407$	−2.37543	−	6.26350i	−0.117746	−	0.310470i
$408$			2.32001i			0.114858i
$409$	17.2410	−	6.53864i	0.852512	−	0.323315i	0.110643	−	0.993860i	$-0.464709\pi$
$409$	17.2410	−	6.53864i	0.852512	−	0.323315i	0.741869	+	0.670545i	$0.233940\pi$
$410$	0.657276	−	2.66667i	0.0324605	−	0.131698i
$411$	−3.91245	+	4.41624i	−0.192987	+	0.217837i
$412$	11.9285	−	2.94012i	0.587677	−	0.144849i
$413$	−7.62804	−	6.75785i	−0.375351	−	0.332532i
$414$	−34.1218	−	4.14313i	−1.67699	−	0.203624i
$415$	0.204456	−	1.68385i	0.0100363	−	0.0826568i
$416$	15.9995	+	22.8143i	0.784442	+	1.11856i
$417$	−0.0554709	−	0.456844i	−0.00271642	−	0.0223717i
$418$			1.05844i			0.0517699i
$419$	−1.51604	+	12.4857i	−0.0740632	+	0.609965i	0.907668	+	0.419690i	$0.137861\pi$
$419$	−1.51604	+	12.4857i	−0.0740632	+	0.609965i	−0.981731	+	0.190275i	$0.939062\pi$
$420$	1.07444	+	0.563909i	0.0524273	+	0.0275160i
$421$	−32.1969	−	12.2107i	−1.56918	−	0.595111i	−0.591703	−	0.806156i	$-0.701544\pi$
$421$	−32.1969	−	12.2107i	−1.56918	−	0.595111i	−0.977476	+	0.211044i	$0.932314\pi$
$422$	−23.6633	+	26.7104i	−1.15191	+	1.30024i
$423$	−11.4964	+	12.9768i	−0.558974	+	0.630952i
$424$	13.1971	+	5.00501i	0.640909	+	0.243065i
$425$	−4.00849	−	2.10382i	−0.194440	−	0.102050i
$426$	0.498294	−	4.10382i	0.0241424	−	0.198831i
$427$		−	4.22083i		−	0.204260i
$428$	−2.68730	−	22.1319i	−0.129895	−	1.06978i
$429$	2.58345	+	0.616406i	0.124730	+	0.0297604i
$430$	−2.51416	+	20.7059i	−0.121243	+	0.998529i
$431$	16.4997	+	2.00343i	0.794763	+	0.0965017i	0.507839	−	0.861452i	$-0.330444\pi$
$431$	16.4997	+	2.00343i	0.794763	+	0.0965017i	0.286924	+	0.957953i	$0.407367\pi$
$432$	−3.73615	−	3.30994i	−0.179756	−	0.159250i
$433$	−16.2341	+	4.00135i	−0.780161	+	0.192292i	−0.609233	−	0.792991i	$-0.708523\pi$
$433$	−16.2341	+	4.00135i	−0.780161	+	0.192292i	−0.170928	+	0.985284i	$0.554677\pi$
$434$	10.3921	−	11.7302i	0.498835	−	0.563068i
$435$	−0.725900	+	2.94509i	−0.0348043	+	0.141206i
$436$	−6.52138	+	2.47323i	−0.312318	+	0.118446i
$437$			1.37459i			0.0657557i
$438$	1.02008	+	2.68973i	0.0487413	+	0.128520i
$439$	1.36000	−	0.713780i	0.0649090	−	0.0340669i	−0.431956	−	0.901894i	$-0.642177\pi$
$439$	1.36000	−	0.713780i	0.0649090	−	0.0340669i	0.496865	+	0.867828i	$0.334484\pi$
$440$	2.73780	−	0.332429i	0.130519	−	0.0158479i
$441$	5.54334	+	14.6166i	0.263969	+	0.696028i
$442$	−3.97939	+	34.9446i	−0.189280	+	1.66215i
$443$	1.46040	−	3.85075i	0.0693855	−	0.182954i	−0.895838	−	0.444381i	$-0.853424\pi$
$443$	1.46040	−	3.85075i	0.0693855	−	0.182954i	0.965223	+	0.261426i	$0.0841929\pi$
$444$	−0.787296	+	3.19419i	−0.0373634	+	0.151589i
$445$	3.45750	−	0.852196i	0.163901	−	0.0403980i
$446$	−11.8868	+	17.2210i	−0.562856	+	0.815438i
$447$	1.47935	+	2.81866i	0.0699706	+	0.133318i
$448$	3.57890	+	14.5202i	0.169087	+	0.686013i
$449$	5.97078	+	0.724984i	0.281779	+	0.0342141i	0.260206	−	0.965553i	$-0.416210\pi$
$449$	5.97078	+	0.724984i	0.281779	+	0.0342141i	0.0215727	+	0.999767i	$0.493133\pi$
$450$	−5.76834	+	2.18764i	−0.271922	+	0.103126i
$451$	0.899925	−	2.37291i	0.0423758	−	0.111736i
$452$	37.0163	+	19.4276i	1.74110	+	0.913799i
$453$	0.810246	+	3.28730i	0.0380687	+	0.154451i
$454$	−29.4133	−	42.6126i	−1.38044	−	1.99991i
$455$	3.70122	+	2.51431i	0.173516	+	0.117873i
$456$	0.0718241	−	0.104055i	0.00336347	−	0.00487283i
$457$	−28.2226	−	10.7034i	−1.32020	−	0.500685i	−0.408955	−	0.912554i	$-0.634107\pi$
$457$	−28.2226	−	10.7034i	−1.32020	−	0.500685i	−0.911243	+	0.411869i	$0.864876\pi$
$458$	−19.7188	+	51.9943i	−0.921401	+	2.42954i
$459$	−1.18368	−	9.74851i	−0.0552496	−	0.455022i
$460$	14.6175	−	1.77488i	0.681544	−	0.0827544i
$461$	14.5429	+	16.4155i	0.677330	+	0.764548i	0.982198	−	0.187847i	$-0.0601509\pi$
$461$	14.5429	+	16.4155i	0.677330	+	0.764548i	−0.304868	+	0.952395i	$0.598612\pi$
$462$	1.62108	+	1.11895i	0.0754193	+	0.0520582i
$463$	1.97343	+	2.22755i	0.0917132	+	0.103523i	0.792576	−	0.609774i	$-0.208740\pi$
$463$	1.97343	+	2.22755i	0.0917132	+	0.103523i	−0.700862	+	0.713297i	$0.747201\pi$
$464$	−16.7041	+	8.76700i	−0.775469	+	0.406998i
$465$	−0.261360	−	2.15249i	−0.0121203	−	0.0998196i
$466$	−51.6282	+	19.5800i	−2.39163	+	0.907026i
$467$	20.1596	+	17.8598i	0.932873	+	0.826454i	0.985065	−	0.172183i	$-0.0550822\pi$
$467$	20.1596	+	17.8598i	0.932873	+	0.826454i	−0.0521915	+	0.998637i	$0.516621\pi$
$468$	18.2431	+	20.2860i	0.843287	+	0.937721i
$469$	8.35694	−	7.40360i	0.385888	−	0.341867i
$470$	6.06339	−	11.5528i	0.279683	−	0.532892i
$471$	−0.186669	−	0.270437i	−0.00860127	−	0.0124611i
$472$	8.51426	+	7.54297i	0.391900	+	0.347193i
$473$	−4.61242	+	18.7133i	−0.212079	+	0.860440i
$474$	0.160809	+	0.0609867i	0.00738618	+	0.00280121i
$475$	0.114654	+	0.218456i	0.00526070	+	0.0100234i
$476$	−6.90001	+	13.1469i	−0.316261	+	0.602586i
$477$	−28.3263	−	6.98181i	−1.29697	−	0.319675i
$478$	10.6767	−	9.45873i	0.488341	−	0.432632i
$479$	−16.4506	−	31.3440i	−0.751647	−	1.43214i	−0.896662	−	0.442715i	$-0.854015\pi$
$479$	−16.4506	−	31.3440i	−0.751647	−	1.43214i	0.145015	−	0.989429i	$-0.453677\pi$
$480$	2.53182	+	1.32880i	0.115561	+	0.0606513i
$481$	−4.21714	+	11.3743i	−0.192285	+	0.518622i
$482$	14.3908	−	7.55289i	0.655484	−	0.344025i
$483$	2.10529	+	1.45318i	0.0957940	+	0.0661218i
$484$	−18.5946			−0.845209
$485$	−12.0266			−0.546101
$486$	−16.6488	−	11.4918i	−0.755205	−	0.521280i
$487$	−4.80668	+	0.583637i	−0.217812	+	0.0264471i	−0.228715	−	0.973493i	$-0.573452\pi$
$487$	−4.80668	+	0.583637i	−0.217812	+	0.0264471i	0.0109033	+	0.999941i	$0.496529\pi$
$488$			4.71120i			0.213266i
$489$	−1.15229	−	0.139914i	−0.0521085	−	0.00632712i
$490$	−6.68310	−	9.68215i	−0.301912	−	0.437395i
$491$	−6.74678	−	1.66293i	−0.304478	−	0.0750471i	0.0841167	−	0.996456i	$-0.473193\pi$
$491$	−6.74678	−	1.66293i	−0.304478	−	0.0750471i	−0.388595	+	0.921409i	$0.627039\pi$
$492$	−1.02570	+	0.707992i	−0.0462423	+	0.0319187i
$493$	−36.0362	−	8.88214i	−1.62299	−	0.400031i
$494$	1.26031	−	1.44411i	0.0567042	−	0.0649736i
$495$	−5.53490	+	1.36423i	−0.248775	+	0.0613176i
$496$	8.94262	−	10.0941i	0.401536	−	0.453240i
$497$	3.65567	−	5.29615i	0.163979	−	0.237565i
$498$	−1.01215	+	0.896686i	−0.0453555	+	0.0401815i
$499$	13.2639	−	9.15539i	0.593773	−	0.409852i	−0.232928	−	0.972494i	$-0.574831\pi$
$499$	13.2639	−	9.15539i	0.593773	−	0.409852i	0.826700	+	0.562642i	$0.190215\pi$
$500$	2.17502	−	1.50131i	0.0972700	−	0.0671406i
$501$	−3.95575	+	7.53705i	−0.176730	+	0.336731i
$502$	5.69418	+	23.1022i	0.254144	+	1.03110i
$503$	−4.75277	+	39.1426i	−0.211916	+	1.74528i	0.367295	+	0.930105i	$0.380284\pi$
$503$	−4.75277	+	39.1426i	−0.211916	+	1.74528i	−0.579210	+	0.815178i	$0.696639\pi$
$504$	1.74524	+	4.60182i	0.0777391	+	0.204981i
$505$	−3.21352	−	3.62731i	−0.143000	−	0.161413i
$506$	23.9027			1.06261
$507$	−2.79082	−	3.91719i	−0.123945	−	0.173969i
$508$	44.4753			1.97327
$509$	15.8734	+	17.9174i	0.703577	+	0.794174i	0.986288	−	0.165031i	$-0.0527725\pi$
$509$	15.8734	+	17.9174i	0.703577	+	0.794174i	−0.282712	+	0.959205i	$0.591234\pi$
$510$	1.27975	+	3.37442i	0.0566683	+	0.149422i
$511$	−0.539773	+	4.44543i	−0.0238782	+	0.196654i
$512$	5.78142	+	23.4562i	0.255505	+	1.03663i
$513$	−0.248710	+	0.473877i	−0.0109808	+	0.0209222i
$514$	31.9361	−	22.0439i	1.40864	−	0.972315i
$515$	3.82572	−	2.64070i	0.168581	−	0.116363i
$516$	7.08476	−	6.27655i	0.311889	−	0.276310i
$517$	6.84864	−	9.92196i	0.301203	−	0.436367i
$518$	−5.96590	+	6.73411i	−0.262126	+	0.295880i
$519$	3.99997	−	0.985904i	0.175579	−	0.0432764i
$520$	−4.13122	−	2.80642i	−0.181166	−	0.123070i
$521$	9.52299	+	2.34721i	0.417210	+	0.102833i	0.442332	−	0.896851i	$-0.354151\pi$
$521$	9.52299	+	2.34721i	0.417210	+	0.102833i	−0.0251222	+	0.999684i	$0.507997\pi$
$522$	−41.6251	+	28.7317i	−1.82188	+	1.25755i
$523$	29.4020	+	7.24693i	1.28566	+	0.316886i	0.822183	−	0.569223i	$-0.192756\pi$
$523$	29.4020	+	7.24693i	1.28566	+	0.316886i	0.463475	+	0.886110i	$0.346602\pi$
$524$	−7.86553	−	11.3952i	−0.343607	−	0.497801i
$525$	0.455789	+	0.0553429i	0.0198923	+	0.00241536i
$526$		−	38.7962i		−	1.69160i
$527$	26.3380	−	3.19801i	1.14730	−	0.139308i
$528$	1.39498	+	0.962882i	0.0607085	+	0.0419041i
$529$	8.04246			0.349672
$530$	21.9558			0.953701
$531$	−19.3498	−	13.3562i	−0.839710	−	0.579610i
$532$	0.716481	−	0.376038i	0.0310634	−	0.0163033i
$533$	−4.05332	+	2.16597i	−0.175569	+	0.0938187i
$534$	−2.51363	−	1.31926i	−0.108775	−	0.0570898i
$535$	−3.92029	−	7.46949i	−0.169489	−	0.322934i
$536$	−9.32784	+	8.26374i	−0.402901	+	0.356939i
$537$	−0.544977	−	0.134325i	−0.0235175	−	0.00579654i
$538$	−31.2531	+	59.5478i	−1.34742	+	2.56729i
$539$	−5.05196	−	9.62570i	−0.217603	−	0.414608i
$540$	5.36036	+	2.03292i	0.230673	+	0.0874828i
$541$	6.07758	−	24.6577i	0.261296	−	1.06012i	−0.682842	−	0.730566i	$-0.739256\pi$
$541$	6.07758	−	24.6577i	0.261296	−	1.06012i	0.944137	−	0.329552i	$-0.106898\pi$
$542$	−22.4326	−	19.8736i	−0.963564	−	0.853643i
$543$	−2.98651	−	4.32671i	−0.128164	−	0.185677i
$544$	−16.2593	+	30.9795i	−0.697111	+	1.32823i
$545$	−1.97536	+	1.75001i	−0.0846150	+	0.0749624i
$546$	−0.879395	−	3.45693i	−0.0376346	−	0.147943i
$547$	13.9578	+	12.3655i	0.596793	+	0.528713i	0.906547	−	0.422104i	$-0.138708\pi$
$547$	13.9578	+	12.3655i	0.596793	+	0.528713i	−0.309754	+	0.950817i	$0.600247\pi$
$548$	39.4069	−	14.9451i	1.68338	−	0.638422i
$549$	−1.17378	−	9.66696i	−0.0500958	−	0.412576i
$550$	3.79871	−	1.99372i	0.161978	−	0.0850125i
$551$	1.34129	+	1.51400i	0.0571408	+	0.0644986i
$552$	−2.34988	−	1.62200i	−0.100017	−	0.0690371i
$553$	0.177536	+	0.200397i	0.00754960	+	0.00852174i
$554$	56.9779	−	6.91837i	2.42076	−	0.293933i
$555$	0.150042	+	1.23571i	0.00636894	+	0.0524530i
$556$	−1.16571	+	3.07372i	−0.0494370	+	0.130355i
$557$	8.78795	+	3.33283i	0.372357	+	0.141217i	0.533683	−	0.845685i	$-0.320808\pi$
$557$	8.78795	+	3.33283i	0.372357	+	0.141217i	−0.161325	+	0.986901i	$0.551577\pi$
$558$	20.5388	−	29.7556i	0.869478	−	1.25966i
$559$	28.5756	−	20.0399i	1.20862	−	0.847597i
$560$	1.62215	+	2.35009i	0.0685484	+	0.0993094i
$561$	0.798061	+	3.23786i	0.0336942	+	0.136703i
$562$	−21.8133	−	11.4485i	−0.920138	−	0.482926i
$563$	−0.576658	+	1.52052i	−0.0243033	+	0.0640824i	−0.946619	−	0.322355i	$-0.895525\pi$
$563$	−0.576658	+	1.52052i	−0.0243033	+	0.0640824i	0.922315	+	0.386438i	$0.126295\pi$
$564$	−5.53598	+	2.09952i	−0.233107	+	0.0884058i
$565$	15.7027	+	1.90666i	0.660618	+	0.0802136i
$566$	7.53829	+	30.5840i	0.316858	+	1.28554i
$567$	−4.49078	−	8.55647i	−0.188595	−	0.359338i
$568$	−4.08038	+	5.91145i	−0.171209	+	0.248039i
$569$	25.7889	−	6.35638i	1.08113	−	0.266474i	0.341766	−	0.939785i	$-0.388975\pi$
$569$	25.7889	−	6.35638i	1.08113	−	0.266474i	0.739359	+	0.673311i	$0.235129\pi$
$570$	0.0470688	−	0.190966i	0.00197150	−	0.00799867i
$571$	12.7442	−	33.6037i	0.533328	−	1.40627i	−0.349661	−	0.936876i	$-0.613703\pi$
$571$	12.7442	−	33.6037i	0.533328	−	1.40627i	0.882989	−	0.469394i	$-0.155528\pi$
$572$	−14.2943	−	12.4750i	−0.597673	−	0.521605i
$573$	−3.32182	−	8.75893i	−0.138771	−	0.365910i
$574$	−3.38351	+	0.410832i	−0.141225	+	0.0171478i
$575$	4.93339	−	2.58924i	0.205736	−	0.107979i
$576$	12.2347	+	32.2603i	0.509780	+	1.34418i
$577$			16.1044i			0.670437i	0.942140	+	0.335218i	$0.108810\pi$
$577$			16.1044i			0.670437i	−0.942140	+	0.335218i	$0.891190\pi$
$578$	−7.03953	+	2.66974i	−0.292806	+	0.111047i
$579$	−0.878274	+	3.56330i	−0.0364998	+	0.148086i
$580$	14.3681	−	16.2182i	0.596602	−	0.673424i
$581$	−2.04382	+	0.503756i	−0.0847919	+	0.0208993i
$582$	7.17642	+	6.35775i	0.297472	+	0.263537i
$583$	20.1399	+	2.44542i	0.834109	+	0.101279i
$584$	0.602483	−	4.96190i	0.0249309	−	0.205325i
$585$	9.17611	+	4.72924i	0.379386	+	0.195530i
$586$	−3.99210	−	32.8779i	−0.164912	−	1.35817i
$587$			29.3012i			1.20939i	0.796458	+	0.604694i	$0.206705\pi$
$587$			29.3012i			1.20939i	−0.796458	+	0.604694i	$0.793295\pi$
$588$	−0.643507	+	5.29976i	−0.0265378	+	0.218558i
$589$	−1.28029	−	0.671950i	−0.0527536	−	0.0276872i
$590$	16.5447	+	6.27456i	0.681133	+	0.258320i
$591$	−4.47094	+	5.04665i	−0.183910	+	0.207591i
$592$	−5.13380	+	5.79487i	−0.210998	+	0.238168i
$593$	20.4617	+	7.76010i	0.840262	+	0.318669i	0.736923	−	0.675977i	$-0.236278\pi$
$593$	20.4617	+	7.76010i	0.840262	+	0.318669i	0.103339	+	0.994646i	$0.467047\pi$
$594$	8.24022	+	4.32480i	0.338100	+	0.177449i
$595$	−0.677177	+	5.57705i	−0.0277615	+	0.228637i
$596$		−	22.7391i		−	0.931432i
$597$	0.949357	+	7.81865i	0.0388546	+	0.319996i
$598$	−32.6123	−	28.4617i	−1.33362	−	1.16388i
$599$	0.134441	−	1.10722i	0.00549312	−	0.0452399i	−0.989705	−	0.143125i	$-0.954285\pi$
$599$	0.134441	−	1.10722i	0.00549312	−	0.0452399i	0.995198	+	0.0978854i	$0.0312079\pi$
$600$	−0.508743	−	0.0617725i	−0.0207693	−	0.00252185i
$601$	33.2808	+	29.4842i	1.35755	+	1.20268i	0.958273	+	0.285855i	$0.0922774\pi$
$601$	33.2808	+	29.4842i	1.35755	+	1.20268i	0.399277	+	0.916830i	$0.369261\pi$
$602$	25.1325	−	6.19459i	1.02432	−	0.252473i
$603$	17.0810	−	19.2805i	0.695593	−	0.785162i
$604$	5.78783	−	23.4822i	0.235504	−	0.955475i
$605$	−6.57860	+	2.49493i	−0.267458	+	0.101433i
$606$			3.86325i			0.156934i
$607$	−10.8989	−	28.7381i	−0.442373	−	1.16644i	−0.952014	−	0.306055i	$-0.900991\pi$
$607$	−10.8989	−	28.7381i	−0.442373	−	1.16644i	0.509641	−	0.860387i	$-0.329778\pi$
$608$	1.68832	−	0.886101i	0.0684706	−	0.0359361i
$609$	3.73677	−	0.453726i	0.151422	−	0.0183859i
$610$	2.59876	+	6.85237i	0.105221	+	0.277444i
$611$	−21.1585	+	5.38243i	−0.855981	+	0.217750i
$612$	−12.1470	+	32.0291i	−0.491015	+	1.29470i
$613$	−8.38481	+	34.0185i	−0.338659	+	1.37399i	0.516792	+	0.856111i	$0.327126\pi$
$613$	−8.38481	+	34.0185i	−0.338659	+	1.37399i	−0.855451	+	0.517884i	$0.826720\pi$
$614$	−16.9014	+	4.16582i	−0.682084	+	0.168119i
$615$	−0.267890	+	0.388105i	−0.0108023	+	0.0156499i
$616$	−1.59053	−	3.03051i	−0.0640844	−	0.122103i
$617$	−5.55294	−	22.5292i	−0.223553	−	0.906990i	−0.970304	−	0.241887i	$-0.922234\pi$
$617$	−5.55294	−	22.5292i	−0.223553	−	0.906990i	0.746751	−	0.665103i	$-0.231612\pi$
$618$	−3.67883	−	0.446691i	−0.147984	−	0.0179685i
$619$	−22.4894	+	8.52909i	−0.903924	+	0.342813i	−0.762388	−	0.647120i	$-0.775973\pi$
$619$	−22.4894	+	8.52909i	−0.903924	+	0.342813i	−0.141536	+	0.989933i	$0.545204\pi$
$620$	−5.49242	+	14.4823i	−0.220581	+	0.581624i
$621$	10.7016	+	5.61662i	0.429439	+	0.225387i
$622$	10.1939	+	41.3583i	0.408738	+	1.65832i
$623$	−2.51035	−	3.63688i	−0.100575	−	0.145708i
$624$	−0.756742	−	2.97477i	−0.0302939	−	0.119086i
$625$	0.568065	−	0.822984i	0.0227226	−	0.0329194i
$626$	−34.1451	−	12.9495i	−1.36471	−	0.517568i
$627$	0.0644454	−	0.169929i	0.00257370	−	0.00678629i
$628$	0.282939	+	2.33021i	0.0112905	+	0.0929857i
$629$	−15.1202	+	1.83592i	−0.602881	+	0.0732030i
$630$	5.07685	+	5.73058i	0.202266	+	0.228312i
$631$	1.78568	+	1.23257i	0.0710868	+	0.0490677i	0.603078	−	0.797682i	$-0.293941\pi$
$631$	1.78568	+	1.23257i	0.0710868	+	0.0490677i	−0.531991	+	0.846750i	$0.678556\pi$
$632$	−0.198162	−	0.223679i	−0.00788246	−	0.00889746i
$633$	5.42538	−	2.84746i	0.215639	−	0.113176i
$634$	5.73031	+	47.1933i	0.227580	+	1.87429i
$635$	15.7349	−	5.96747i	0.624422	−	0.236812i
$636$	−7.45765	−	6.60690i	−0.295715	−	0.261981i
$637$	−4.56882	+	19.1486i	−0.181023	+	0.758695i
$638$	26.3269	−	23.3236i	1.04229	−	0.923390i
$639$	6.89975	−	13.1464i	0.272950	−	0.520063i
$640$	−5.96974	−	8.64867i	−0.235975	−	0.341869i
$641$	−0.970483	−	0.859773i	−0.0383318	−	0.0339590i	0.643739	−	0.765245i	$-0.277382\pi$
$641$	−0.970483	−	0.859773i	−0.0383318	−	0.0339590i	−0.682071	+	0.731286i	$0.738921\pi$
$642$	−1.60939	+	6.52955i	−0.0635175	+	0.257701i
$643$	28.5288	+	10.8195i	1.12506	+	0.426681i	0.845782	−	0.533529i	$-0.179134\pi$
$643$	28.5288	+	10.8195i	1.12506	+	0.426681i	0.279282	+	0.960209i	$0.409904\pi$
$644$	−8.49207	−	16.1803i	−0.334635	−	0.637593i
$645$	1.66437	−	3.17118i	0.0655343	−	0.124865i
$646$	2.33666	+	0.575935i	0.0919347	+	0.0226599i
$647$	22.0156	−	19.5041i	0.865521	−	0.766785i	−0.108296	−	0.994119i	$-0.534539\pi$
$647$	22.0156	−	19.5041i	0.865521	−	0.766785i	0.973817	+	0.227334i	$0.0730009\pi$
$648$	5.01251	+	9.55055i	0.196910	+	0.375181i
$649$	14.4774	+	7.59832i	0.568288	+	0.298260i
$650$	−7.55686	−	1.80305i	−0.296404	−	0.0707215i
$651$	−2.38263	+	1.25050i	−0.0933825	+	0.0490109i
$652$	6.82388	+	4.71018i	0.267244	+	0.184465i
$653$	22.6936			0.888068			0.444034	−	0.896010i	$-0.353547\pi$
$653$	22.6936			0.888068			0.444034	+	0.896010i	$0.353547\pi$
$654$	2.10385			0.0822669
$655$	−4.31170	−	2.97615i	−0.168472	−	0.116288i
$656$	−2.91159	+	0.353531i	−0.113679	+	0.0138031i
$657$			10.3315i			0.403069i
$658$	−16.0736	−	1.95168i	−0.626613	−	0.0760845i
$659$	27.7027	+	40.1343i	1.07914	+	1.56341i	0.796942	+	0.604056i	$0.206450\pi$
$659$	27.7027	+	40.1343i	1.07914	+	1.56341i	0.282202	+	0.959355i	$0.408935\pi$
$660$	−1.89024	−	0.465902i	−0.0735775	−	0.0181352i
$661$	−0.0649703	+	0.0448458i	−0.00252705	+	0.00174430i	−0.569328	−	0.822111i	$-0.692796\pi$
$661$	−0.0649703	+	0.0448458i	−0.00252705	+	0.00174430i	0.566801	+	0.823855i	$0.308181\pi$
$662$	42.1021	+	10.3772i	1.63634	+	0.403322i
$663$	2.76656	−	5.36794i	0.107444	−	0.208473i
$664$	2.28127	−	0.562282i	0.0885304	−	0.0218208i
$665$	0.203029	−	0.229173i	0.00787314	−	0.00888694i
$666$	−11.7910	+	17.0822i	−0.456892	+	0.661922i
$667$	34.1907	−	30.2903i	1.32387	−	1.17285i
$668$	50.0409	−	34.5407i	1.93614	−	1.33642i
$669$	2.95692	−	2.04101i	0.114321	−	0.0789102i
$670$	−9.00881	+	17.1648i	−0.348041	+	0.663136i
$671$	1.62061	+	6.57506i	0.0625628	+	0.253827i
$672$	0.427715	−	3.52255i	0.0164995	−	0.135885i
$673$	−12.9498	−	34.1458i	−0.499179	−	1.31623i	−0.913775	−	0.406220i	$-0.866847\pi$
$673$	−12.9498	−	34.1458i	−0.499179	−	1.31623i	0.414597	−	0.910005i	$-0.363923\pi$
$674$	−18.4545	−	20.8308i	−0.710841	−	0.802373i
$675$	2.16921			0.0834931
$676$	4.64844	+	34.0411i	0.178786	+	1.30927i
$677$	−12.6008			−0.484287			−0.242143	−	0.970240i	$-0.577850\pi$
$677$	−12.6008			−0.484287			−0.242143	+	0.970240i	$0.577850\pi$
$678$	−8.36205	−	9.43881i	−0.321143	−	0.362495i
$679$	5.29246	+	13.9551i	0.203106	+	0.535546i
$680$	0.755850	−	6.22499i	0.0289855	−	0.238717i
$681$	2.12764	+	8.63219i	0.0815315	+	0.330786i
$682$	−11.6845	+	22.2630i	−0.447423	+	0.852493i
$683$	32.8351	−	22.6644i	1.25640	−	0.867231i	0.261219	−	0.965279i	$-0.415875\pi$
$683$	32.8351	−	22.6644i	1.25640	−	0.867231i	0.995182	+	0.0980485i	$0.0312600\pi$
$684$	1.53638	−	1.06049i	0.0587450	−	0.0405488i
$685$	11.9366	−	10.5749i	0.456072	−	0.404045i
$686$	−18.9267	+	27.4201i	−0.722625	+	1.04690i
$687$	6.33158	−	7.14687i	0.241565	−	0.272670i
$688$	21.6271	−	5.33060i	0.824526	−	0.203227i
$689$	−24.5666	−	27.3176i	−0.935911	−	1.04072i
$690$	−4.31258	−	1.06296i	−0.164177	−	0.0404660i
$691$	−24.3225	+	16.7886i	−0.925272	+	0.638669i	−0.932448	−	0.361305i	$-0.882331\pi$
$691$	−24.3225	+	16.7886i	−0.925272	+	0.638669i	0.00717561	+	0.999974i	$0.497716\pi$
$692$	−28.5730	−	7.04261i	−1.08618	−	0.267720i
$693$	4.01868	+	5.82206i	0.152657	+	0.221162i
$694$	10.2690	+	1.24688i	0.389806	+	0.0473310i
$695$			1.24386i			0.0471824i
$696$	−4.17090	+	0.506439i	−0.158098	+	0.0191965i
$697$	−4.74886	−	3.27790i	−0.179876	−	0.124159i
$698$	−51.4257			−1.94649
$699$	9.48090			0.358600
$700$	−2.69918	−	1.86311i	−0.102020	−	0.0704190i
$701$	31.4500	−	16.5062i	1.18785	−	0.623431i	0.249249	−	0.968439i	$-0.419816\pi$
$701$	31.4500	−	16.5062i	1.18785	−	0.623431i	0.938600	+	0.345008i	$0.112124\pi$
$702$	−6.09310	−	15.7125i	−0.229969	−	0.593031i
$703$	0.734994	+	0.385755i	0.0277208	+	0.0145490i
$704$	−11.1502	−	21.2449i	−0.420238	−	0.800696i
$705$	−1.67688	+	1.48558i	−0.0631548	+	0.0559503i
$706$	−39.4580	−	9.72551i	−1.48502	−	0.366025i
$707$	−2.79479	+	5.32503i	−0.105109	+	0.200268i
$708$	−3.73153	−	7.10984i	−0.140239	−	0.267204i
$709$	−11.7170	−	4.44367i	−0.440041	−	0.166886i	0.124627	−	0.992204i	$-0.460227\pi$
$709$	−11.7170	−	4.44367i	−0.440041	−	0.166886i	−0.564668	+	0.825318i	$0.690996\pi$
$710$	−2.67401	+	10.8489i	−0.100354	+	0.407152i
$711$	0.462340	+	0.409597i	0.0173391	+	0.0153611i
$712$	2.80200	+	4.05940i	0.105010	+	0.152133i
$713$	−15.1747	+	28.9129i	−0.568295	+	1.08280i
$714$	3.35233	−	2.96991i	0.125458	−	0.111146i
$715$	−6.73101	−	2.49560i	−0.251725	−	0.0933301i
$716$	3.00111	+	2.65875i	0.112157	+	0.0993622i
$717$	−2.29002	+	0.868491i	−0.0855224	+	0.0324344i
$718$	3.43015	+	28.2498i	0.128012	+	1.05427i
$719$	−13.9877	+	7.34129i	−0.521651	+	0.273784i	−0.704930	−	0.709277i	$-0.749021\pi$
$719$	−13.9877	+	7.34129i	−0.521651	+	0.273784i	0.183278	+	0.983061i	$0.441329\pi$
$720$	4.36875	+	4.93130i	0.162814	+	0.183779i
$721$	−4.74768	−	3.27709i	−0.176813	−	0.122045i
$722$	27.0612	+	30.5457i	1.00711	+	1.13679i
$723$	−2.77027	+	0.336372i	−0.103027	+	0.0125098i
$724$	4.52673	+	37.2810i	0.168235	+	1.38554i
$725$	2.90721	−	7.66569i	0.107971	−	0.284697i
$726$	5.24444	+	1.98895i	0.194640	+	0.0738170i
$727$	1.99793	−	2.89450i	0.0740990	−	0.107351i	−0.784182	−	0.620531i	$-0.786917\pi$
$727$	1.99793	−	2.89450i	0.0740990	−	0.107351i	0.858281	+	0.513180i	$0.171533\pi$
$728$	−1.43842	+	6.02865i	−0.0533116	+	0.223437i
$729$	−11.2970	−	16.3665i	−0.418408	−	0.606168i
$730$	−1.86074	−	7.54934i	−0.0688693	−	0.279414i
$731$	38.8027	+	20.3652i	1.43517	+	0.753235i
$732$	1.17929	−	3.10953i	0.0435878	−	0.114931i
$733$	15.0637	−	5.71289i	0.556389	−	0.211010i	−0.0603515	−	0.998177i	$-0.519222\pi$
$733$	15.0637	−	5.71289i	0.556389	−	0.211010i	0.616740	+	0.787167i	$0.288453\pi$
$734$	13.6957	+	1.66296i	0.505519	+	0.0613811i
$735$	0.483429	+	1.96135i	0.0178316	+	0.0723454i
$736$	−20.0108	−	38.1274i	−0.737609	−	1.40540i
$737$	−10.1755	+	14.7418i	−0.374819	+	0.543019i
$738$	−7.63500	+	1.88186i	−0.281048	+	0.0692722i
$739$	2.24989	−	9.12817i	0.0827636	−	0.335785i	−0.914934	−	0.403603i	$-0.867758\pi$
$739$	2.24989	−	9.12817i	0.0827636	−	0.335785i	0.997698	+	0.0678181i	$0.0216037\pi$
$740$	3.15310	−	8.31405i	0.115910	−	0.305631i
$741$	−0.290267	+	0.155110i	−0.0106632	+	0.00569809i
$742$	−9.66192	−	25.4764i	−0.354700	−	0.935268i
$743$	38.9978	−	4.73519i	1.43069	−	0.173717i	0.631771	−	0.775155i	$-0.282328\pi$
$743$	38.9978	−	4.73519i	1.43069	−	0.173717i	0.798920	+	0.601438i	$0.205405\pi$
$744$	2.65944	−	1.39578i	0.0974997	−	0.0511718i
$745$	−3.05103	−	8.04490i	−0.111781	−	0.294742i
$746$			23.9185i			0.875719i
$747$	−4.54087	+	1.72212i	−0.166142	+	0.0630092i
$748$	5.70079	−	23.1290i	0.208442	−	0.845681i
$749$	−6.94203	+	7.83593i	−0.253656	+	0.286319i
$750$	−0.774033	+	0.190782i	−0.0282637	+	0.00696637i
$751$	−12.0271	−	10.6551i	−0.438874	−	0.388809i	0.414549	−	0.910027i	$-0.363939\pi$
$751$	−12.0271	−	10.6551i	−0.438874	−	0.388809i	−0.853423	+	0.521218i	$0.825478\pi$
$752$	−13.8317	−	1.67947i	−0.504390	−	0.0612440i
$753$	0.492448	−	4.05567i	0.0179458	−	0.147797i
$754$	−63.6919	+	0.473990i	−2.31952	+	0.0172617i
$755$	−1.10304	−	9.08435i	−0.0401437	−	0.330613i
$756$		−	7.11449i		−	0.258751i
$757$	5.03050	−	41.4299i	0.182837	−	1.50580i	−0.555587	−	0.831459i	$-0.687506\pi$
$757$	5.03050	−	41.4299i	0.182837	−	1.50580i	0.738424	−	0.674337i	$-0.235571\pi$
$758$	−42.4480	−	22.2784i	−1.54178	−	0.809189i
$759$	−3.83750	−	1.45537i	−0.139292	−	0.0528266i
$760$	−0.226617	+	0.255798i	−0.00822026	+	0.00927876i
$761$	−20.7530	+	23.4253i	−0.752297	+	0.849167i	−0.992587	−	0.121534i	$-0.961219\pi$
$761$	−20.7530	+	23.4253i	−0.752297	+	0.849167i	0.240291	+	0.970701i	$0.422757\pi$
$762$	−12.5439	−	4.75726i	−0.454416	−	0.172337i
$763$	2.89990	+	1.52199i	0.104984	+	0.0550996i
$764$	−8.06585	+	66.4283i	−0.291812	+	2.40329i
$765$			12.9614i			0.468622i
$766$	−7.30882	−	60.1935i	−0.264078	−	2.17488i
$767$	−10.7051	−	27.6056i	−0.386538	−	0.996781i
$768$	0.0649943	−	0.535277i	0.00234528	−	0.0193151i
$769$	11.5298	+	1.39997i	0.415773	+	0.0504840i	0.325751	−	0.945456i	$-0.394383\pi$
$769$	11.5298	+	1.39997i	0.415773	+	0.0504840i	0.0900227	+	0.995940i	$0.471306\pi$
$770$	−3.98507	−	3.53047i	−0.143612	−	0.127229i
$771$	−6.46942	+	1.59457i	−0.232990	+	0.0574270i
$772$	17.3841	−	19.6226i	0.625667	−	0.706232i
$773$	−7.06194	+	28.6514i	−0.254000	+	1.03052i	0.695943	+	0.718097i	$0.254987\pi$
$773$	−7.06194	+	28.6514i	−0.254000	+	1.03052i	−0.949943	+	0.312423i	$0.898859\pi$
$774$	55.8382	−	21.1766i	2.00706	−	0.761178i
$775$			5.86066i			0.210521i
$776$	−5.90733	−	15.5763i	−0.212061	−	0.559158i
$777$	1.36782	−	0.717889i	0.0490704	−	0.0257541i
$778$	17.7076	−	2.15009i	0.634848	−	0.0770845i
$779$	0.111513	+	0.294035i	0.00399536	+	0.0105349i
$780$	2.02424	+	2.88643i	0.0724793	+	0.103351i
$781$	−3.66119	+	9.65376i	−0.131008	+	0.345439i
$782$	13.0064	−	52.7689i	0.465106	−	1.88701i
$783$	17.2674	−	4.25604i	0.617088	−	0.152098i
$784$	−7.13691	+	10.3396i	−0.254890	+	0.369271i
$785$	0.412758	+	0.786445i	0.0147320	+	0.0280694i
$786$	0.999527	+	4.05524i	0.0356520	+	0.144646i
$787$	−42.2837	−	5.13417i	−1.50725	−	0.183013i	−0.675168	−	0.737664i	$-0.735929\pi$
$787$	−42.2837	−	5.13417i	−1.50725	−	0.183013i	−0.832084	+	0.554650i	$0.812852\pi$
$788$	45.0322	−	17.0785i	1.60420	−	0.608395i
$789$	−2.36219	+	6.22859i	−0.0840963	+	0.221744i
$790$	−0.411608	−	0.216028i	−0.0146443	−	0.00768594i
$791$	−4.69778	−	19.0596i	−0.167034	−	0.677683i
$792$	−4.48556	−	6.49846i	−0.159387	−	0.230913i
$793$	5.61799	−	10.9006i	0.199501	−	0.387090i
$794$	−14.0869	+	20.4084i	−0.499927	+	0.724269i
$795$	−3.52493	−	1.33683i	−0.125016	−	0.0474125i
$796$	19.9505	−	52.6051i	0.707127	−	1.86454i
$797$	−6.04374	−	49.7746i	−0.214080	−	1.76311i	−0.563475	−	0.826133i	$-0.690536\pi$
$797$	−6.04374	−	49.7746i	−0.214080	−	1.76311i	0.349395	−	0.936975i	$-0.386387\pi$
$798$	−0.242300	+	0.0294205i	−0.00857732	+	0.00104147i
$799$	−18.1776	−	20.5183i	−0.643078	−	0.725885i
$800$	−6.36039	−	4.39026i	−0.224874	−	0.155219i
$801$	−6.76085	−	7.63143i	−0.238883	−	0.269643i
$802$	−43.1947	+	22.6703i	−1.52526	+	0.800517i
$803$	−0.866004	−	7.13218i	−0.0305606	−	0.251689i
$804$	8.22519	−	3.11940i	0.290080	−	0.110013i
$805$	−5.17541	−	4.58501i	−0.182409	−	0.161600i
$806$	42.4512	−	16.4620i	1.49528	−	0.579849i
$807$	8.64327	−	7.65727i	0.304258	−	0.269549i
$808$	3.11949	−	5.94369i	0.109743	−	0.209098i
$809$	5.95035	+	8.62056i	0.209203	+	0.303083i	0.913513	−	0.406810i	$-0.133359\pi$
$809$	5.95035	+	8.62056i	0.209203	+	0.303083i	−0.704310	+	0.709893i	$0.748743\pi$
$810$	12.5588	+	11.1262i	0.441272	+	0.390933i
$811$	−5.40936	+	21.9466i	−0.189948	+	0.770651i	0.796234	+	0.604988i	$0.206822\pi$
$811$	−5.40936	+	21.9466i	−0.189948	+	0.770651i	−0.986183	+	0.165662i	$0.947024\pi$
$812$	−25.1416	−	9.53495i	−0.882297	−	0.334611i
$813$	2.39143	+	4.55649i	0.0838711	+	0.159803i
$814$	6.70787	−	12.7808i	0.235111	−	0.447966i
$815$	3.04622	+	0.750825i	0.106704	+	0.0263002i
$816$	2.88476	−	2.55568i	0.100987	−	0.0894666i
$817$	−1.10987	−	2.11468i	−0.0388294	−	0.0739832i
$818$	35.1805	+	18.4642i	1.23006	+	0.645584i
$819$	1.44950	−	12.7286i	0.0506496	−	0.444774i
$820$	2.98280	−	1.56549i	0.104164	−	0.0546694i
$821$	31.5641	+	21.7871i	1.10159	+	0.760376i	0.972881	−	0.231306i	$-0.0742999\pi$
$821$	31.5641	+	21.7871i	1.10159	+	0.760376i	0.128713	+	0.991682i	$0.458915\pi$
$822$	−12.7130			−0.443416
$823$	−20.2900			−0.707264			−0.353632	−	0.935385i	$-0.615053\pi$
$823$	−20.2900			−0.707264			−0.353632	+	0.935385i	$0.615053\pi$
$824$	5.29926	+	3.65782i	0.184608	+	0.127426i
$825$	−0.731262	+	0.0887912i	−0.0254593	+	0.00309131i
$826$		−	21.9587i		−	0.764042i
$827$	3.89823	+	0.473330i	0.135555	+	0.0164593i	0.188033	−	0.982163i	$-0.439789\pi$
$827$	3.89823	+	0.473330i	0.135555	+	0.0164593i	−0.0524781	+	0.998622i	$0.516712\pi$
$828$	−23.9490	−	34.6961i	−0.832286	−	1.20577i
$829$	−21.5114	−	5.30208i	−0.747122	−	0.184149i	−0.152666	−	0.988278i	$-0.548786\pi$
$829$	−21.5114	−	5.30208i	−0.747122	−	0.184149i	−0.594455	+	0.804129i	$0.702632\pi$
$830$	3.00791	−	2.07621i	0.104406	−	0.0720662i
$831$	−9.56883	−	2.35850i	−0.331939	−	0.0818156i
$832$	−10.0838	+	42.2628i	−0.349594	+	1.46520i
$833$	−23.9991	+	5.91525i	−0.831520	+	0.204951i
$834$	0.657555	−	0.742226i	0.0227693	−	0.0257012i
$835$	13.0695	−	18.9344i	0.452288	−	0.655253i
$836$	−0.971727	+	0.860875i	−0.0336079	+	0.0297740i
$837$	−10.4626	+	7.22182i	−0.361641	+	0.249623i
$838$	−22.3035	+	15.3950i	−0.770463	+	0.531812i
$839$	11.3325	−	21.5922i	0.391240	−	0.745445i	−0.607568	−	0.794268i	$-0.707855\pi$
$839$	11.3325	−	21.5922i	0.391240	−	0.745445i	0.998807	+	0.0488226i	$0.0155469\pi$
$840$	0.152200	+	0.617502i	0.00525141	+	0.0213058i
$841$	4.60627	−	37.9361i	0.158837	−	1.30814i
$842$	−26.3107	−	69.3755i	−0.906725	−	2.39084i
$843$	2.80498	+	3.16616i	0.0966085	+	0.109048i
$844$	−43.7685			−1.50658
$845$	6.21205	+	11.4197i	0.213701	+	0.392851i
$846$	−37.3560			−1.28433
$847$	5.78997	+	6.53553i	0.198946	+	0.224563i
$848$	−8.31432	−	21.9231i	−0.285515	−	0.752841i
$849$	0.651932	−	5.36914i	0.0223742	−	0.184269i
$850$	−2.33441	−	9.47108i	−0.0800697	−	0.324856i
$851$	8.71151	−	16.5984i	0.298627	−	0.568985i
$852$	4.17290	−	2.88034i	0.142961	−	0.0986789i
$853$	−24.4440	+	16.8724i	−0.836945	+	0.577702i	−0.907618	−	0.419798i	$-0.862101\pi$
$853$	−24.4440	+	16.8724i	−0.836945	+	0.577702i	0.0706723	+	0.997500i	$0.477486\pi$
$854$	6.80751	−	6.03092i	0.232948	−	0.206374i
$855$	0.401267	−	0.581335i	0.0137230	−	0.0198812i
$856$	7.74854	−	8.74630i	0.264840	−	0.298942i
$857$	−4.98098	+	1.22770i	−0.170147	+	0.0419375i	−0.323469	−	0.946239i	$-0.604849\pi$
$857$	−4.98098	+	1.22770i	−0.170147	+	0.0419375i	0.153322	+	0.988176i	$0.451003\pi$
$858$	2.69719	+	5.04743i	0.0920807	+	0.172316i
$859$	48.3986	+	11.9292i	1.65134	+	0.407018i	0.951590	−	0.307371i	$-0.0994492\pi$
$859$	48.3986	+	11.9292i	1.65134	+	0.407018i	0.699749	+	0.714389i	$0.253295\pi$
$860$	−21.0545	+	14.5329i	−0.717952	+	0.495566i
$861$	0.568224	+	0.140055i	0.0193650	+	0.00477305i
$862$	20.3444	+	29.4739i	0.692933	+	1.00389i
$863$	−10.0787	−	1.22378i	−0.343083	−	0.0416579i	−0.0528182	−	0.998604i	$-0.516820\pi$
$863$	−10.0787	−	1.22378i	−0.343083	−	0.0416579i	−0.290265	+	0.956946i	$0.593743\pi$
$864$		−	16.7647i		−	0.570346i
$865$	−11.0538	+	1.34217i	−0.375841	+	0.0456353i
$866$	−29.6496	−	20.4656i	−1.00753	−	0.695451i
$867$	1.29272			0.0439032
$868$	19.2215			0.652421
$869$	−0.353503	−	0.244005i	−0.0119918	−	0.00827731i
$870$	−5.78716	+	3.03733i	−0.196203	+	0.102975i
$871$	31.4366	−	7.99705i	1.06519	−	0.270970i
$872$	−3.23681	−	1.69881i	−0.109612	−	0.0575289i
$873$	16.0021	+	30.4895i	0.541589	+	1.03191i
$874$	−2.21699	+	1.96409i	−0.0749910	+	0.0664362i
$875$	−1.20493	−	0.296989i	−0.0407341	−	0.0100400i
$876$	−1.63970	+	3.12418i	−0.0554003	+	0.105556i
$877$	8.63464	+	16.4519i	0.291571	+	0.555542i	0.986544	−	0.163493i	$-0.0522762\pi$
$877$	8.63464	+	16.4519i	0.291571	+	0.555542i	−0.694973	+	0.719035i	$0.744584\pi$
$878$	3.09444	+	1.17357i	0.104432	+	0.0396059i
$879$	−1.36093	+	5.52150i	−0.0459030	+	0.186236i
$880$	−3.42926	−	3.03805i	−0.115600	−	0.102413i
$881$	20.5178	+	29.7252i	0.691262	+	1.00147i	0.998753	+	0.0499150i	$0.0158951\pi$
$881$	20.5178	+	29.7252i	0.691262	+	1.00147i	−0.307492	+	0.951551i	$0.599490\pi$
$882$	−15.6536	+	29.8254i	−0.527084	+	1.00427i
$883$	23.3337	−	20.6718i	0.785240	−	0.695662i	−0.171955	−	0.985105i	$-0.555008\pi$
$883$	23.3337	−	20.6718i	0.785240	−	0.695662i	0.957195	+	0.289443i	$0.0934700\pi$
$884$	−35.3184	+	24.7686i	−1.18789	+	0.833058i
$885$	−2.27414	−	2.01472i	−0.0764445	−	0.0677239i
$886$	8.29731	−	3.14675i	0.278754	−	0.105717i
$887$	−2.22513	−	18.3256i	−0.0747126	−	0.615314i	−0.981188	−	0.193055i	$-0.938160\pi$
$887$	−2.22513	−	18.3256i	−0.0747126	−	0.615314i	0.906475	−	0.422259i	$-0.138763\pi$
$888$	−1.52674	+	0.801293i	−0.0512339	+	0.0268896i
$889$	−13.8487	−	15.6319i	−0.464470	−	0.524278i
$890$	6.31469	+	4.35872i	0.211669	+	0.146105i
$891$	10.2809	+	11.6047i	0.344422	+	0.388772i
$892$	−25.4782	+	3.09362i	−0.853074	+	0.103582i
$893$	0.180071	+	1.48302i	0.00602586	+	0.0496274i
$894$	−2.43227	+	6.41338i	−0.0813474	+	0.214495i
$895$	1.41850	+	0.537968i	0.0474154	+	0.0179823i
$896$	−7.40840	+	10.7329i	−0.247497	+	0.358562i
$897$	3.50284	+	6.55509i	0.116956	+	0.218868i
$898$	7.36206	+	10.6658i	0.245675	+	0.355922i
$899$	11.4987	+	46.6522i	0.383504	+	1.55594i
$900$	−6.70006	−	3.51646i	−0.223335	−	0.117215i
$901$	16.3575	−	43.1312i	0.544947	−	1.43691i
$902$	5.11297	−	1.93909i	0.170243	−	0.0645647i
$903$	−4.41210	−	0.535725i	−0.146825	−	0.0178278i
$904$	5.24356	+	21.2740i	0.174398	+	0.707562i
$905$	6.60370	+	12.5823i	0.219514	+	0.418250i
$906$	−4.14416	+	6.00385i	−0.137680	+	0.199464i
$907$	−12.1215	+	2.98768i	−0.402487	+	0.0992042i	−0.435363	−	0.900255i	$-0.643380\pi$
$907$	−12.1215	+	2.98768i	−0.402487	+	0.0992042i	0.0328751	+	0.999459i	$0.489534\pi$
$908$	15.1984	−	61.6623i	0.504377	−	2.04634i
$909$	−4.92006	+	12.9731i	−0.163188	+	0.430292i
$910$	1.23331	+	9.56203i	0.0408840	+	0.316978i
$911$	1.12507	+	2.96656i	0.0372751	+	0.0982865i	0.952361	−	0.304972i	$-0.0986469\pi$
$911$	1.12507	+	2.96656i	0.0372751	+	0.0982865i	−0.915086	+	0.403258i	$0.867878\pi$
$912$	−0.208505	+	0.0253171i	−0.00690429	+	0.000838332i
$913$	2.99037	−	1.56947i	0.0989668	−	0.0519418i
$914$	−23.0630	−	60.8121i	−0.762855	−	2.01148i
$915$		−	1.25835i		−	0.0415999i
$916$	−63.7729	+	24.1859i	−2.10712	+	0.799124i
$917$	−1.55596	+	6.31276i	−0.0513822	+	0.208466i
$918$	14.0315	−	15.8382i	0.463107	−	0.522740i
$919$	−15.6308	+	3.85264i	−0.515611	+	0.127087i	−0.488531	−	0.872547i	$-0.662467\pi$
$919$	−15.6308	+	3.85264i	−0.515611	+	0.127087i	−0.0270802	+	0.999633i	$0.508621\pi$
$920$	5.77668	+	5.11769i	0.190452	+	0.168725i
$921$	2.96710	+	0.360271i	0.0977693	+	0.0118713i
$922$	−5.69598	+	46.9106i	−0.187587	+	1.54492i
$923$	16.4902	−	8.81189i	0.542783	−	0.290047i
$924$	0.291213	+	2.39836i	0.00958022	+	0.0789002i
$925$		−	3.36450i		−	0.110624i
$926$	−0.772930	+	6.36565i	−0.0254001	+	0.209188i
$927$	−11.7849	−	6.18522i	−0.387069	−	0.203149i
$928$	−59.2439	−	22.4683i	−1.94478	−	0.737557i
$929$	−3.38588	+	3.82187i	−0.111087	+	0.125392i	−0.801424	−	0.598097i	$-0.795924\pi$
$929$	−3.38588	+	3.82187i	−0.111087	+	0.125392i	0.690337	+	0.723488i	$0.257462\pi$
$930$	3.09818	−	3.49712i	0.101593	−	0.114675i
$931$	1.25951	+	0.477671i	0.0412789	+	0.0156550i
$932$	−59.9674	−	31.4733i	−1.96430	−	1.03094i
$933$	0.881597	−	7.26060i	0.0288622	−	0.237701i
$934$			58.0331i			1.89890i
$935$	−1.08645	−	8.94774i	−0.0355308	−	0.292622i
$936$	−1.61790	+	14.2074i	−0.0528828	+	0.464384i
$937$	−0.937367	+	7.71991i	−0.0306224	+	0.252199i	0.969356	+	0.245660i	$0.0790045\pi$
$937$	−0.937367	+	7.71991i	−0.0306224	+	0.252199i	−0.999979	+	0.00653900i	$0.997919\pi$
$938$	23.8816	+	2.89975i	0.779762	+	0.0946802i
$939$	4.69342	+	4.15800i	0.153164	+	0.135691i
$940$	15.5380	−	3.82977i	0.506793	−	0.124913i
$941$	3.92293	−	4.42807i	0.127884	−	0.144351i	−0.681081	−	0.732208i	$-0.738490\pi$
$941$	3.92293	−	4.42807i	0.127884	−	0.144351i	0.808965	+	0.587857i	$0.200028\pi$
$942$	0.169449	−	0.687481i	0.00552094	−	0.0223993i
$943$	6.64020	−	2.51830i	0.216235	−	0.0820070i
$944$		−	18.8960i		−	0.615014i
$945$	−0.954587	−	2.51704i	−0.0310527	−	0.0818793i
$946$	−36.7720	+	19.2994i	−1.19556	+	0.627479i
$947$	54.0935	−	6.56813i	1.75780	−	0.213436i	0.822861	−	0.568242i	$-0.192376\pi$
$947$	54.0935	−	6.56813i	1.75780	−	0.213436i	0.934940	+	0.354806i	$0.115453\pi$
$948$	0.0748023	+	0.197238i	0.00242947	+	0.00640598i
$949$	−7.31094	+	10.7622i	−0.237323	+	0.349355i
$950$	−0.188510	+	0.497059i	−0.00611606	+	0.0161267i
$951$	1.95349	−	7.92562i	0.0633462	−	0.257006i
$952$	−7.55577	+	1.86233i	−0.244884	+	0.0603584i
$953$	22.6168	−	32.7661i	0.732630	−	1.06140i	−0.262701	−	0.964877i	$-0.584613\pi$
$953$	22.6168	−	32.7661i	0.732630	−	1.06140i	0.995331	−	0.0965204i	$-0.0307713\pi$
$954$	−29.2135	−	55.6617i	−0.945822	−	1.80211i
$955$	6.05940	+	24.5839i	0.196077	+	0.795518i
$956$	17.3677	+	2.10882i	0.561710	+	0.0682040i
$957$	−5.64680	+	2.14155i	−0.182535	+	0.0692264i
$958$	27.0473	−	71.3180i	0.873860	−	2.30418i
$959$	−17.5233	−	9.19695i	−0.565858	−	0.296985i
$960$	1.06698	+	4.32889i	0.0344365	+	0.139714i
$961$	−1.90150	−	2.75480i	−0.0613388	−	0.0888645i
$962$	−24.3705	+	9.45055i	−0.785737	+	0.304698i
$963$	−13.7202	+	19.8772i	−0.442128	+	0.640532i
$964$	18.6388	+	7.06877i	0.600316	+	0.227670i
$965$	3.51747	−	9.27479i	0.113231	−	0.298566i
$966$	0.664404	+	5.47186i	0.0213768	+	0.176054i
$967$	−22.1560	+	2.69022i	−0.712488	+	0.0865117i	−0.468752	−	0.883330i	$-0.655296\pi$
$967$	−22.1560	+	2.69022i	−0.712488	+	0.0865117i	−0.243736	+	0.969842i	$0.578373\pi$
$968$	−6.46265	−	7.29482i	−0.207717	−	0.234464i
$969$	−0.340075	−	0.234737i	−0.0109248	−	0.00754084i
$970$	−17.1842	−	19.3970i	−0.551752	−	0.622800i
$971$	−47.3075	+	24.8289i	−1.51817	+	0.796797i	−0.998347	−	0.0574778i	$-0.981694\pi$
$971$	−47.3075	+	24.8289i	−1.51817	+	0.796797i	−0.519822	+	0.854274i	$0.674002\pi$
$972$	−2.99083	−	24.6317i	−0.0959308	−	0.790061i
$973$	1.44331	−	0.547376i	0.0462705	−	0.0175481i
$974$	−7.80933	−	6.91847i	−0.250227	−	0.221682i
$975$	1.10344	+	0.749589i	0.0353385	+	0.0240061i
$976$	5.85803	−	5.18976i	0.187511	−	0.166120i
$977$	16.5444	−	31.5228i	0.529304	−	1.00850i	−0.463196	−	0.886256i	$-0.653297\pi$
$977$	16.5444	−	31.5228i	0.529304	−	1.00850i	0.992500	−	0.122248i	$-0.0390104\pi$
$978$	−1.42079	−	2.05838i	−0.0454320	−	0.0658196i
$979$	5.30693	+	4.70153i	0.169610	+	0.150262i
$980$	3.45328	−	14.0105i	0.110311	−	0.447549i
$981$	7.06490	+	2.67936i	0.225565	+	0.0855455i
$982$	−6.95809	−	13.2575i	−0.222042	−	0.423065i
$983$	16.2126	−	30.8905i	0.517101	−	0.985253i	−0.477215	−	0.878786i	$-0.658354\pi$
$983$	16.2126	−	30.8905i	0.517101	−	0.985253i	0.994316	−	0.106467i	$-0.0339539\pi$
$984$	−0.634240	−	0.156326i	−0.0202188	−	0.00498349i
$985$	13.6405	−	12.0844i	0.434621	−	0.385041i
$986$	−37.1649	−	70.8118i	−1.18357	−	2.25511i
$987$	2.46172	+	1.29201i	0.0783574	+	0.0411251i
$988$	2.35087	−	0.0174950i	0.0747911	−	0.000556589i
$989$	−47.7558	+	25.0642i	−1.51854	+	0.796994i
$990$	−10.1088	−	6.97761i	−0.321279	−	0.221763i
$991$	7.93940			0.252203			0.126102	−	0.992017i	$-0.459753\pi$
$991$	7.93940			0.252203			0.126102	+	0.992017i	$0.459753\pi$
$992$	45.2938			1.43808
$993$	−6.12750	−	4.22950i	−0.194450	−	0.134219i
$994$	13.7652	−	1.67140i	0.436606	−	0.0530136i
$995$		−	21.2881i		−	0.674877i
$996$	−1.64645	−	0.199915i	−0.0521698	−	0.00633456i
$997$	12.3358	+	17.8714i	0.390677	+	0.565994i	0.968136	−	0.250426i	$-0.0805708\pi$
$997$	12.3358	+	17.8714i	0.390677	+	0.565994i	−0.577458	+	0.816420i	$0.695955\pi$
$998$	33.7182	+	8.31080i	1.06733	+	0.263074i
$999$	6.00640	−	4.14592i	0.190034	−	0.131171i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.w.a.116.54	yes	744
169.51	even	26	inner	845.2.w.a.51.54	✓	744

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
845.2.w.a.51.54	✓	744	169.51	even	26	inner
845.2.w.a.116.54	yes	744	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.w (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.42885 + 1.61284i) q^{2} +(-0.131195 - 0.345934i) q^{3} +(-0.318560 + 2.62358i) q^{4} +(0.239316 + 0.970942i) q^{5} +(0.370476 - 0.705884i) q^{6} +(1.02132 - 0.704963i) q^{7} +(-1.13997 + 0.786865i) q^{8} +(2.14307 - 1.89860i) q^{9} +O(q^{10})\)	\(q+(1.42885 + 1.61284i) q^{2} +(-0.131195 - 0.345934i) q^{3} +(-0.318560 + 2.62358i) q^{4} +(0.239316 + 0.970942i) q^{5} +(0.370476 - 0.705884i) q^{6} +(1.02132 - 0.704963i) q^{7} +(-1.13997 + 0.786865i) q^{8} +(2.14307 - 1.89860i) q^{9} +(-1.22402 + 1.77331i) q^{10} +(-1.32030 + 1.49031i) q^{11} +(0.949379 - 0.234001i) q^{12} +(3.57593 - 0.461225i) q^{13} +(2.59630 + 0.639930i) q^{14} +(0.304484 - 0.210170i) q^{15} +(2.23418 + 0.550675i) q^{16} +(2.57165 + 3.72568i) q^{17} +(6.12426 + 0.743620i) q^{18} -0.246715i q^{19} +(-2.62358 + 0.318560i) q^{20} +(-0.377862 - 0.260820i) q^{21} -4.29012 q^{22} -5.57158 q^{23} +(0.421762 + 0.291121i) q^{24} +(-0.885456 + 0.464723i) q^{25} +(5.85334 + 5.10837i) q^{26} +(-1.92074 - 1.00808i) q^{27} +(1.52418 + 2.90408i) q^{28} +(-6.13663 + 5.43658i) q^{29} +(0.774033 + 0.190782i) q^{30} +(2.72358 - 5.18936i) q^{31} +(3.59159 + 6.84321i) q^{32} +(0.688763 + 0.261214i) q^{33} +(-2.33441 + 9.47108i) q^{34} +(0.928895 + 0.822929i) q^{35} +(4.29843 + 6.22735i) q^{36} +(-1.56356 + 2.97912i) q^{37} +(0.397912 - 0.352519i) q^{38} +(-0.628699 - 1.17652i) q^{39} +(-1.03681 - 0.918536i) q^{40} +(-1.19180 + 0.451990i) q^{41} +(-0.119249 - 0.982102i) q^{42} +(8.57132 - 4.49858i) q^{43} +(-3.48934 - 3.93865i) q^{44} +(2.35630 + 1.62644i) q^{45} +(-7.96094 - 8.98604i) q^{46} +(-6.01106 + 0.729875i) q^{47} +(-0.102617 - 0.845123i) q^{48} +(-1.93612 + 5.10513i) q^{49} +(-2.01471 - 0.764077i) q^{50} +(0.951449 - 1.37841i) q^{51} +(0.0709116 + 9.52867i) q^{52} +(-5.78836 - 8.38589i) q^{53} +(-1.11858 - 4.53824i) q^{54} +(-1.76297 - 0.925277i) q^{55} +(-0.609559 + 1.60728i) q^{56} +(-0.0853472 + 0.0323679i) q^{57} +(-17.5366 - 2.12933i) q^{58} +(-1.96525 - 7.97333i) q^{59} +(0.454402 + 0.865791i) q^{60} +(1.93209 - 2.79911i) q^{61} +(12.2612 - 3.02211i) q^{62} +(0.850313 - 3.44986i) q^{63} +(-4.27321 + 11.2675i) q^{64} +(1.30360 + 3.36164i) q^{65} +(0.562844 + 1.48410i) q^{66} +(8.93105 - 1.08443i) q^{67} +(-10.5938 + 5.56008i) q^{68} +(0.730965 + 1.92740i) q^{69} +2.67400i q^{70} +(4.84863 - 1.83884i) q^{71} +(-0.949102 + 3.85066i) q^{72} +(-2.39286 + 2.70098i) q^{73} +(-7.03893 + 1.73494i) q^{74} +(0.276931 + 0.245340i) q^{75} +(0.647278 + 0.0785938i) q^{76} +(-0.297828 + 2.45283i) q^{77} +(0.999226 - 2.69506i) q^{78} +(0.0260042 + 0.214164i) q^{79} +2.30104i q^{80} +(0.938595 - 7.73002i) q^{81} +(-2.43189 - 1.27635i) q^{82} +(-1.58599 - 0.601486i) q^{83} +(0.804653 - 0.908266i) q^{84} +(-3.00198 + 3.38854i) q^{85} +(19.5026 + 7.39636i) q^{86} +(2.68580 + 1.40961i) q^{87} +(0.332429 - 2.73780i) q^{88} -3.56097i q^{89} +(0.743620 + 6.12426i) q^{90} +(3.32701 - 2.99196i) q^{91} +(1.77488 - 14.6175i) q^{92} +(-2.15249 - 0.261360i) q^{93} +(-9.76606 - 8.65198i) q^{94} +(0.239546 - 0.0590428i) q^{95} +(1.89610 - 2.14025i) q^{96} +(-2.87816 + 11.6772i) q^{97} +(-11.0002 + 4.17181i) q^{98} +5.70055i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 744 q + 4 q^{3} + 66 q^{4} - 62 q^{9}+O(q^{10}) \) 744 * q + 4 * q^3 + 66 * q^4 - 62 * q^9	\( 744 q + 4 q^{3} + 66 q^{4} - 62 q^{9} - 2 q^{10} - 122 q^{13} - 4 q^{14} - 66 q^{16} - 12 q^{17} - 78 q^{18} - 24 q^{22} + 140 q^{23} + 156 q^{24} + 62 q^{25} - 14 q^{26} + 28 q^{27} + 8 q^{29} - 20 q^{30} - 52 q^{31} - 26 q^{32} - 130 q^{34} + 4 q^{35} + 70 q^{36} + 126 q^{38} + 16 q^{39} + 6 q^{40} - 24 q^{42} - 24 q^{43} - 78 q^{47} - 94 q^{48} - 32 q^{49} - 12 q^{51} + 110 q^{52} - 156 q^{54} + 16 q^{55} + 16 q^{56} - 78 q^{57} - 104 q^{58} - 104 q^{59} + 28 q^{61} + 106 q^{62} + 14 q^{64} - 2 q^{65} - 308 q^{66} - 104 q^{67} - 18 q^{68} + 20 q^{69} - 78 q^{71} - 338 q^{72} - 4 q^{75} - 286 q^{76} - 52 q^{77} + 312 q^{78} - 12 q^{79} - 78 q^{81} + 268 q^{82} + 12 q^{87} - 72 q^{88} + 26 q^{90} - 136 q^{91} + 52 q^{92} - 130 q^{93} + 124 q^{94} - 16 q^{95} + 338 q^{96}+O(q^{100}) \) 744 * q + 4 * q^3 + 66 * q^4 - 62 * q^9 - 2 * q^10 - 122 * q^13 - 4 * q^14 - 66 * q^16 - 12 * q^17 - 78 * q^18 - 24 * q^22 + 140 * q^23 + 156 * q^24 + 62 * q^25 - 14 * q^26 + 28 * q^27 + 8 * q^29 - 20 * q^30 - 52 * q^31 - 26 * q^32 - 130 * q^34 + 4 * q^35 + 70 * q^36 + 126 * q^38 + 16 * q^39 + 6 * q^40 - 24 * q^42 - 24 * q^43 - 78 * q^47 - 94 * q^48 - 32 * q^49 - 12 * q^51 + 110 * q^52 - 156 * q^54 + 16 * q^55 + 16 * q^56 - 78 * q^57 - 104 * q^58 - 104 * q^59 + 28 * q^61 + 106 * q^62 + 14 * q^64 - 2 * q^65 - 308 * q^66 - 104 * q^67 - 18 * q^68 + 20 * q^69 - 78 * q^71 - 338 * q^72 - 4 * q^75 - 286 * q^76 - 52 * q^77 + 312 * q^78 - 12 * q^79 - 78 * q^81 + 268 * q^82 + 12 * q^87 - 72 * q^88 + 26 * q^90 - 136 * q^91 + 52 * q^92 - 130 * q^93 + 124 * q^94 - 16 * q^95 + 338 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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