LMFDB - Embedded newform 207.2.o.a.149.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [207,2,Mod(5,207)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("207.5"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(207, base_ring=CyclotomicField(66)) chi = DirichletCharacter(H, H._module([55, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	207.o (of order $66$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.65290332184$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			149.19
Character	$\chi$	$=$	207.149
Dual form			207.2.o.a.182.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.927335 - 1.79878i) q^{2} +(-0.342210 + 1.69791i) q^{3} +(-1.21554 - 1.70699i) q^{4} +(-0.509098 + 2.09853i) q^{5} +(2.73682 + 2.19009i) q^{6} +(4.00925 + 1.38762i) q^{7} +(-0.191421 + 0.0275221i) q^{8} +(-2.76579 - 1.16208i) q^{9} +(3.30269 + 2.86180i) q^{10} +(-0.142404 + 2.98944i) q^{11} +(3.31429 - 1.47973i) q^{12} +(-2.24641 - 6.49058i) q^{13} +(6.21393 - 5.92497i) q^{14} +(-3.38889 - 1.58254i) q^{15} +(1.24278 - 3.59077i) q^{16} +(0.615124 + 1.34693i) q^{17} +(-4.65514 + 3.89740i) q^{18} +(-5.21085 - 2.37972i) q^{19} +(4.20101 - 1.68183i) q^{20} +(-3.72805 + 6.33249i) q^{21} +(5.24528 + 3.02837i) q^{22} +(3.75563 + 2.98249i) q^{23} +(0.0187759 - 0.334433i) q^{24} +(0.299528 + 0.154417i) q^{25} +(-13.7583 - 1.97814i) q^{26} +(2.91958 - 4.29837i) q^{27} +(-2.50477 - 8.53047i) q^{28} +(0.707492 + 0.503803i) q^{29} +(-5.98928 + 4.62833i) q^{30} +(-1.63271 - 0.653639i) q^{31} +(-5.57343 - 5.84525i) q^{32} +(-5.02706 - 1.26480i) q^{33} +(2.99326 + 0.142587i) q^{34} +(-4.95305 + 7.70710i) q^{35} +(1.37827 + 6.13374i) q^{36} +(0.388365 - 1.32265i) q^{37} +(-9.11279 + 7.16638i) q^{38} +(11.7891 - 1.59306i) q^{39} +(0.0396958 - 0.415713i) q^{40} +(-11.4126 - 2.76867i) q^{41} +(7.93360 + 12.5783i) q^{42} +(-1.78680 - 4.46322i) q^{43} +(5.27605 - 3.39071i) q^{44} +(3.84672 - 5.21247i) q^{45} +(8.84758 - 3.98977i) q^{46} +(4.19556 - 2.42231i) q^{47} +(5.67150 + 3.33891i) q^{48} +(8.64625 + 6.79948i) q^{49} +(0.555525 - 0.395588i) q^{50} +(-2.49747 + 0.583490i) q^{51} +(-8.34876 + 11.7242i) q^{52} +(-4.97557 - 5.74212i) q^{53} +(-5.02440 - 9.23773i) q^{54} +(-6.20093 - 1.82076i) q^{55} +(-0.805643 - 0.155275i) q^{56} +(5.82374 - 8.03319i) q^{57} +(1.56231 - 0.805428i) q^{58} +(-0.0578431 + 0.0200197i) q^{59} +(1.41797 + 7.70846i) q^{60} +(4.21931 + 5.36529i) q^{61} +(-2.68982 + 2.33075i) q^{62} +(-9.47621 - 8.49692i) q^{63} +(-8.39109 + 2.46385i) q^{64} +(14.7643 - 1.40982i) q^{65} +(-6.93687 + 7.86967i) q^{66} +(1.08393 - 0.0516340i) q^{67} +(1.55149 - 2.68727i) q^{68} +(-6.34921 + 5.35607i) q^{69} +(9.27024 + 16.0565i) q^{70} +(-2.81387 - 4.37847i) q^{71} +(0.561411 + 0.146326i) q^{72} +(-5.08574 + 11.1362i) q^{73} +(-2.01901 - 1.92513i) q^{74} +(-0.364688 + 0.455728i) q^{75} +(2.27186 + 11.7875i) q^{76} +(-4.71912 + 11.7878i) q^{77} +(8.06693 - 22.6834i) q^{78} +(0.830849 - 4.31085i) q^{79} +(6.90264 + 4.43606i) q^{80} +(6.29914 + 6.42813i) q^{81} +(-15.5636 + 17.9613i) q^{82} +(-1.74448 - 7.19084i) q^{83} +(15.3411 - 1.33366i) q^{84} +(-3.13974 + 0.605135i) q^{85} +(-9.68531 - 0.924835i) q^{86} +(-1.09752 + 1.02885i) q^{87} +(-0.0550165 - 0.576159i) q^{88} +(-0.911221 + 6.33768i) q^{89} +(-5.80889 - 11.7531i) q^{90} -29.1395i q^{91} +(0.525968 - 10.0362i) q^{92} +(1.66855 - 2.54851i) q^{93} +(-0.466507 - 9.79319i) q^{94} +(7.64674 - 9.72362i) q^{95} +(11.8320 - 7.46288i) q^{96} +(3.28873 - 3.44912i) q^{97} +(20.2487 - 9.24729i) q^{98} +(3.86783 - 8.10266i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23}+ \cdots + 242 q^{99}+O(q^{100}) $ 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9 - 44 * q^10 - 33 * q^11 - 22 * q^12 - 9 * q^13 - 33 * q^14 + 3 * q^16 - 39 * q^18 - 44 * q^19 - 33 * q^20 - 55 * q^21 - 27 * q^23 + 52 * q^24 + 11 * q^25 - 79 * q^27 - 44 * q^28 + 27 * q^29 - 66 * q^30 - 3 * q^31 - 33 * q^32 - 11 * q^34 + 23 * q^36 - 44 * q^37 - 33 * q^38 - 40 * q^39 - 77 * q^40 + 9 * q^41 - 22 * q^42 - 11 * q^43 - 36 * q^46 - 120 * q^47 - 56 * q^48 + 35 * q^49 - 3 * q^50 - 22 * q^51 - 38 * q^52 + 42 * q^54 - 44 * q^55 + 165 * q^56 + 11 * q^57 - 10 * q^58 - 9 * q^59 + 88 * q^60 - 11 * q^61 + 33 * q^63 - 22 * q^64 + 198 * q^65 + 33 * q^66 - 11 * q^67 + 3 * q^69 - 70 * q^70 + 14 * q^72 - 36 * q^73 + 231 * q^74 - 13 * q^75 - 11 * q^76 + 39 * q^77 + 3 * q^78 - 11 * q^79 + 172 * q^81 - 10 * q^82 + 66 * q^83 - 110 * q^84 + q^85 - 33 * q^86 - 196 * q^87 - 99 * q^88 + 418 * q^90 + 63 * q^92 - 188 * q^93 - 42 * q^94 - 93 * q^95 - 82 * q^96 + 22 * q^97 + 242 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.927335	−	1.79878i	0.655725	−	1.27193i	−0.293086	−	0.956086i	$-0.594682\pi$
$2$	0.927335	−	1.79878i	0.655725	−	1.27193i	0.948811	−	0.315843i	$-0.102287\pi$
$3$	−0.342210	+	1.69791i	−0.197575	+	0.980288i
$3$	−0.342210	+	1.69791i	−0.197575	+	0.980288i
$4$	−1.21554	−	1.70699i	−0.607772	−	0.853496i
$5$	−0.509098	+	2.09853i	−0.227676	+	0.938491i	0.737177	+	0.675700i	$0.236158\pi$
$5$	−0.509098	+	2.09853i	−0.227676	+	0.938491i	−0.964853	+	0.262792i	$0.915357\pi$
$6$	2.73682	+	2.19009i	1.11730	+	0.894101i
$7$	4.00925	+	1.38762i	1.51535	+	0.524469i	0.953142	−	0.302524i	$-0.0978291\pi$
$7$	4.00925	+	1.38762i	1.51535	+	0.524469i	0.562213	+	0.826993i	$0.309950\pi$
$8$	−0.191421	+	0.0275221i	−0.0676774	+	0.00973054i
$9$	−2.76579	−	1.16208i	−0.921928	−	0.387360i
$10$	3.30269	+	2.86180i	1.04440	+	0.904980i
$11$	−0.142404	+	2.98944i	−0.0429366	+	0.901349i	0.869951	+	0.493138i	$0.164150\pi$
$11$	−0.142404	+	2.98944i	−0.0429366	+	0.901349i	−0.912888	+	0.408211i	$0.866153\pi$
$12$	3.31429	−	1.47973i	0.956752	−	0.427162i
$13$	−2.24641	−	6.49058i	−0.623042	−	1.80016i	−0.599411	−	0.800442i	$-0.704598\pi$
$13$	−2.24641	−	6.49058i	−0.623042	−	1.80016i	−0.0236316	−	0.999721i	$-0.507523\pi$
$14$	6.21393	−	5.92497i	1.66074	−	1.58352i
$15$	−3.38889	−	1.58254i	−0.875009	−	0.408610i
$16$	1.24278	−	3.59077i	0.310694	−	0.897691i
$17$	0.615124	+	1.34693i	0.149189	+	0.326679i	0.969441	−	0.245323i	$-0.0788941\pi$
$17$	0.615124	+	1.34693i	0.149189	+	0.326679i	−0.820252	+	0.572002i	$0.806167\pi$
$18$	−4.65514	+	3.89740i	−1.09723	+	0.918626i
$19$	−5.21085	−	2.37972i	−1.19545	−	0.545944i	−0.284587	−	0.958650i	$-0.591856\pi$
$19$	−5.21085	−	2.37972i	−1.19545	−	0.545944i	−0.910864	+	0.412706i	$0.864584\pi$
$20$	4.20101	−	1.68183i	0.939374	−	0.376069i
$21$	−3.72805	+	6.33249i	−0.813527	+	1.38186i
$22$	5.24528	+	3.02837i	1.11830	+	0.645650i
$23$	3.75563	+	2.98249i	0.783102	+	0.621893i
$23$	3.75563	+	2.98249i	0.783102	+	0.621893i
$24$	0.0187759	−	0.334433i	0.00383261	−	0.0682658i
$25$	0.299528	+	0.154417i	0.0599055	+	0.0308835i
$26$	−13.7583	−	1.97814i	−2.69822	−	0.387946i
$27$	2.91958	−	4.29837i	0.561874	−	0.827223i
$28$	−2.50477	−	8.53047i	−0.473357	−	1.61211i
$29$	0.707492	+	0.503803i	0.131378	+	0.0935538i	0.643857	−	0.765146i	$-0.277333\pi$
$29$	0.707492	+	0.503803i	0.131378	+	0.0935538i	−0.512479	+	0.858700i	$0.671273\pi$
$30$	−5.98928	+	4.62833i	−1.09349	+	0.845014i
$31$	−1.63271	−	0.653639i	−0.293244	−	0.117397i	0.220376	−	0.975415i	$-0.429272\pi$
$31$	−1.63271	−	0.653639i	−0.293244	−	0.117397i	−0.513620	+	0.858018i	$0.671696\pi$
$32$	−5.57343	−	5.84525i	−0.985253	−	1.03330i
$33$	−5.02706	−	1.26480i	−0.875099	−	0.220174i
$34$	2.99326	+	0.142587i	0.513340	+	0.0244534i
$35$	−4.95305	+	7.70710i	−0.837219	+	1.30274i
$36$	1.37827	+	6.13374i	0.229712	+	1.02229i
$37$	0.388365	−	1.32265i	0.0638469	−	0.217443i	−0.921390	−	0.388639i	$-0.872945\pi$
$37$	0.388365	−	1.32265i	0.0638469	−	0.217443i	0.985237	+	0.171197i	$0.0547634\pi$
$38$	−9.11279	+	7.16638i	−1.47829	+	1.16254i
$39$	11.7891	−	1.59306i	1.88777	−	0.255094i
$40$	0.0396958	−	0.415713i	0.00627646	−	0.0657300i
$41$	−11.4126	−	2.76867i	−1.78235	−	0.432394i	−0.797150	−	0.603782i	$-0.793660\pi$
$41$	−11.4126	−	2.76867i	−1.78235	−	0.432394i	−0.985204	+	0.171387i	$0.945175\pi$
$42$	7.93360	+	12.5783i	1.22418	+	1.94087i
$43$	−1.78680	−	4.46322i	−0.272485	−	0.680634i	0.727500	−	0.686108i	$-0.240682\pi$
$43$	−1.78680	−	4.46322i	−0.272485	−	0.680634i	−0.999985	+	0.00547325i	$0.998258\pi$
$44$	5.27605	−	3.39071i	0.795394	−	0.511169i
$45$	3.84672	−	5.21247i	0.573435	−	0.777029i
$46$	8.84758	−	3.98977i	1.30450	−	0.588260i
$47$	4.19556	−	2.42231i	0.611986	−	0.353330i	−0.161756	−	0.986831i	$-0.551716\pi$
$47$	4.19556	−	2.42231i	0.611986	−	0.353330i	0.773742	+	0.633501i	$0.218383\pi$
$48$	5.67150	+	3.33891i	0.818611	+	0.481931i
$49$	8.64625	+	6.79948i	1.23518	+	0.971355i
$50$	0.555525	−	0.395588i	0.0785632	−	0.0559446i
$51$	−2.49747	+	0.583490i	−0.349716	+	0.0817050i
$52$	−8.34876	+	11.7242i	−1.15776	+	1.62585i
$53$	−4.97557	−	5.74212i	−0.683447	−	0.788740i	0.302970	−	0.953000i	$-0.402022\pi$
$53$	−4.97557	−	5.74212i	−0.683447	−	0.788740i	−0.986417	+	0.164260i	$0.947476\pi$
$54$	−5.02440	−	9.23773i	−0.683734	−	1.25710i
$55$	−6.20093	−	1.82076i	−0.836133	−	0.245511i
$56$	−0.805643	−	0.155275i	−0.107659	−	0.0207495i
$57$	5.82374	−	8.03319i	0.771374	−	1.06402i
$58$	1.56231	−	0.805428i	0.205142	−	0.105758i
$59$	−0.0578431	+	0.0200197i	−0.00753054	+	0.00260634i	−0.330831	−	0.943690i	$-0.607329\pi$
$59$	−0.0578431	+	0.0200197i	−0.00753054	+	0.00260634i	0.323300	+	0.946296i	$0.395208\pi$
$60$	1.41797	+	7.70846i	0.183059	+	0.995158i
$61$	4.21931	+	5.36529i	0.540228	+	0.686955i	0.977152	−	0.212543i	$-0.0681745\pi$
$61$	4.21931	+	5.36529i	0.540228	+	0.686955i	−0.436924	+	0.899498i	$0.643932\pi$
$62$	−2.68982	+	2.33075i	−0.341608	+	0.296005i
$63$	−9.47621	−	8.49692i	−1.19389	−	1.07051i
$64$	−8.39109	+	2.46385i	−1.04889	+	0.307981i
$65$	14.7643	−	1.40982i	1.83129	−	0.174867i
$66$	−6.93687	+	7.86967i	−0.853870	+	0.968690i
$67$	1.08393	−	0.0516340i	0.132423	−	0.00630810i	0.0187344	−	0.999824i	$-0.494036\pi$
$67$	1.08393	−	0.0516340i	0.132423	−	0.00630810i	0.113689	+	0.993516i	$0.463733\pi$
$68$	1.55149	−	2.68727i	0.188146	−	0.325879i
$69$	−6.34921	+	5.35607i	−0.764355	+	0.644795i
$70$	9.27024	+	16.0565i	1.10801	+	1.91912i
$71$	−2.81387	−	4.37847i	−0.333945	−	0.519629i	0.633155	−	0.774025i	$-0.281760\pi$
$71$	−2.81387	−	4.37847i	−0.333945	−	0.519629i	−0.967100	+	0.254396i	$0.918123\pi$
$72$	0.561411	+	0.146326i	0.0661629	+	0.0172447i
$73$	−5.08574	+	11.1362i	−0.595240	+	1.30339i	0.336983	+	0.941511i	$0.390594\pi$
$73$	−5.08574	+	11.1362i	−0.595240	+	1.30339i	−0.932223	+	0.361884i	$0.882134\pi$
$74$	−2.01901	−	1.92513i	−0.234706	−	0.223791i
$75$	−0.364688	+	0.455728i	−0.0421105	+	0.0526229i
$76$	2.27186	+	11.7875i	0.260600	+	1.35212i
$77$	−4.71912	+	11.7878i	−0.537794	+	1.34334i
$78$	8.06693	−	22.6834i	0.913400	−	2.56839i
$79$	0.830849	−	4.31085i	0.0934778	−	0.485009i	−0.904773	−	0.425893i	$-0.859960\pi$
$79$	0.830849	−	4.31085i	0.0934778	−	0.485009i	0.998251	−	0.0591155i	$-0.0188280\pi$
$80$	6.90264	+	4.43606i	0.771738	+	0.495966i
$81$	6.29914	+	6.42813i	0.699904	+	0.714237i
$82$	−15.5636	+	17.9613i	−1.71871	+	1.98350i
$83$	−1.74448	−	7.19084i	−0.191481	−	0.789297i	−0.983812	−	0.179205i	$-0.942647\pi$
$83$	−1.74448	−	7.19084i	−0.191481	−	0.789297i	0.792330	−	0.610092i	$-0.208868\pi$
$84$	15.3411	−	1.33366i	1.67385	−	0.145515i
$85$	−3.13974	+	0.605135i	−0.340552	+	0.0656361i
$86$	−9.68531	−	0.924835i	−1.04439	−	0.0997275i
$87$	−1.09752	+	1.02885i	−0.117667	+	0.110304i
$88$	−0.0550165	−	0.576159i	−0.00586478	−	0.0614188i
$89$	−0.911221	+	6.33768i	−0.0965893	+	0.671793i	0.882791	+	0.469766i	$0.155662\pi$
$89$	−0.911221	+	6.33768i	−0.0965893	+	0.671793i	−0.979380	+	0.202027i	$0.935247\pi$
$90$	−5.80889	−	11.7531i	−0.612311	−	1.23889i
$91$		−	29.1395i		−	3.05465i
$92$	0.525968	−	10.0362i	0.0548359	−	1.04634i
$93$	1.66855	−	2.54851i	0.173020	−	0.264268i
$94$	−0.466507	−	9.79319i	−0.0481165	−	1.01009i
$95$	7.64674	−	9.72362i	0.784539	−	0.997623i
$96$	11.8320	−	7.46288i	1.20760	−	0.761677i
$97$	3.28873	−	3.44912i	0.333920	−	0.350205i	−0.535272	−	0.844679i	$-0.679791\pi$
$97$	3.28873	−	3.44912i	0.333920	−	0.350205i	0.869192	+	0.494475i	$0.164640\pi$
$98$	20.2487	−	9.24729i	2.04543	−	0.934117i
$99$	3.86783	−	8.10266i	0.388731	−	0.814348i
$100$	−0.100500	−	0.698993i	−0.0100500	−	0.0698993i
$101$	2.54146	−	0.616552i	0.252885	−	0.0613492i	−0.107313	−	0.994225i	$-0.534225\pi$
$101$	2.54146	−	0.616552i	0.252885	−	0.0613492i	0.360197	+	0.932876i	$0.382709\pi$
$102$	−1.26642	+	5.03349i	−0.125394	+	0.498390i
$103$	4.40556	+	8.54559i	0.434093	+	0.842022i	0.999848	+	0.0174490i	$0.00555449\pi$
$103$	4.40556	+	8.54559i	0.434093	+	0.842022i	−0.565755	+	0.824573i	$0.691415\pi$
$104$	0.608644	+	1.18060i	0.0596824	+	0.115768i
$105$	−11.3910	−	11.0473i	−1.11165	−	1.07810i
$106$	−14.9428	+	3.62509i	−1.45138	+	0.352100i
$107$	0.273332	+	1.90107i	0.0264240	+	0.183783i	0.998759	−	0.0498086i	$-0.0158611\pi$
$107$	0.273332	+	1.90107i	0.0264240	+	0.183783i	−0.972335	+	0.233592i	$0.924952\pi$
$108$	−10.8862	+	0.241154i	−1.04752	+	0.0232050i
$109$	8.24132	−	3.76368i	0.789375	−	0.360496i	0.0204145	−	0.999792i	$-0.493501\pi$
$109$	8.24132	−	3.76368i	0.789375	−	0.360496i	0.768961	+	0.639296i	$0.220774\pi$
$110$	−9.02548	+	9.46565i	−0.860546	+	0.902514i
$111$	2.11284	+	1.11203i	0.200542	+	0.105549i
$112$	9.96520	−	12.6718i	0.941623	−	1.19737i
$113$	0.421656	+	8.85164i	0.0396660	+	0.832692i	0.927793	+	0.373095i	$0.121703\pi$
$113$	0.421656	+	8.85164i	0.0396660	+	0.832692i	−0.888127	+	0.459598i	$0.847994\pi$
$114$	−9.04937	−	17.9251i	−0.847551	−	1.67884i
$115$	−8.17084	+	6.36291i	−0.761935	+	0.593345i
$116$		−	1.82008i		−	0.168990i
$117$	−1.32949	+	20.5621i	−0.122911	+	1.90096i
$118$	−0.0176290	+	0.122612i	−0.00162288	+	0.0112874i
$119$	0.597161	+	6.25375i	0.0547416	+	0.573280i
$120$	0.692259	+	0.209661i	0.0631943	+	0.0191393i
$121$	2.03373	+	0.194198i	0.184885	+	0.0176544i
$122$	13.5637	−	2.61419i	1.22800	−	0.236678i
$123$	8.60647	−	18.4301i	0.776019	−	1.66179i
$124$	0.868875	+	3.58155i	0.0780273	+	0.321633i
$125$	−7.54707	+	8.70979i	−0.675031	+	0.779027i
$126$	−24.0717	+	9.16611i	−2.14448	+	0.816582i
$127$	5.51842	+	3.54647i	0.489680	+	0.314698i	0.762077	−	0.647487i	$-0.224180\pi$
$127$	5.51842	+	3.54647i	0.489680	+	0.314698i	−0.272397	+	0.962185i	$0.587816\pi$
$128$	−0.292459	+	1.51742i	−0.0258499	+	0.134122i
$129$	8.18959	−	1.50647i	0.721054	−	0.132637i
$130$	11.1555	−	27.8651i	0.978404	−	2.44393i
$131$	0.293720	+	1.52396i	0.0256624	+	0.133149i	0.992500	−	0.122241i	$-0.0390081\pi$
$131$	0.293720	+	1.52396i	0.0256624	+	0.133149i	−0.966838	+	0.255390i	$0.917796\pi$
$132$	3.95160	+	10.1186i	0.343943	+	0.880709i
$133$	−17.5895	−	16.7715i	−1.52520	−	1.45428i
$134$	0.912290	−	1.99764i	0.0788098	−	0.172569i
$135$	7.53392	+	8.31513i	0.648416	+	0.715653i
$136$	−0.154818	−	0.240901i	−0.0132755	−	0.0206571i
$137$	1.92988	+	3.34266i	0.164881	+	0.285582i	0.936613	−	0.350366i	$-0.113943\pi$
$137$	1.92988	+	3.34266i	0.164881	+	0.285582i	−0.771732	+	0.635948i	$0.780609\pi$
$138$	3.74654	+	16.3877i	0.318927	+	1.39501i
$139$	0.118863	−	0.205877i	0.0100818	−	0.0174622i	−0.860940	−	0.508706i	$-0.830124\pi$
$139$	0.118863	−	0.205877i	0.0100818	−	0.0174622i	0.871022	+	0.491243i	$0.163457\pi$
$140$	19.1766	−	0.913495i	1.62072	−	0.0772044i
$141$	2.67710	+	7.95262i	0.225452	+	0.669731i
$142$	−10.4853	+	1.00123i	−0.879908	+	0.0840210i
$143$	19.7231	−	5.79122i	1.64933	−	0.484286i
$144$	−7.61001	+	8.48708i	−0.634168	+	0.707257i
$145$	−1.41743	+	1.22821i	−0.117711	+	0.101997i
$146$	15.3154	+	19.4751i	1.26751	+	1.61177i
$147$	−14.5037	+	12.3537i	−1.19625	+	1.01891i
$148$	−2.72983	+	0.944804i	−0.224391	+	0.0776624i
$149$	−7.71574	+	3.97774i	−0.632098	+	0.325869i	−0.744329	−	0.667813i	$-0.767231\pi$
$149$	−7.71574	+	3.97774i	−0.632098	+	0.325869i	0.112231	+	0.993682i	$0.464200\pi$
$150$	0.481566	+	1.07861i	0.0393197	+	0.0880677i
$151$	7.84027	+	1.51109i	0.638032	+	0.122971i	0.498001	−	0.867176i	$-0.334068\pi$
$151$	7.84027	+	1.51109i	0.638032	+	0.122971i	0.140031	+	0.990147i	$0.455280\pi$
$152$	1.06296	+	0.312113i	0.0862174	+	0.0253157i
$153$	−0.136055	−	4.44015i	−0.0109994	−	0.358965i
$154$	16.8274	+	19.4199i	1.35599	+	1.56490i
$155$	2.20289	−	3.09353i	0.176940	−	0.248478i
$156$	−17.0496	−	18.1876i	−1.36506	−	1.45617i
$157$	−8.58607	+	6.11411i	−0.685243	+	0.487959i	−0.868872	−	0.495036i	$-0.835155\pi$
$157$	−8.58607	+	6.11411i	−0.685243	+	0.487959i	0.183629	+	0.982996i	$0.441215\pi$
$158$	−6.98380	−	5.49212i	−0.555601	−	0.436930i
$159$	11.4523	−	6.48306i	0.908225	−	0.514140i
$160$	15.1039	−	8.72022i	1.19406	−	0.689394i
$161$	10.9187	+	17.1689i	0.860513	+	1.35310i
$162$	17.4042	−	5.36972i	1.36740	−	0.421885i
$163$	−2.89417	+	1.85997i	−0.226689	+	0.145684i	−0.649056	−	0.760741i	$-0.724836\pi$
$163$	−2.89417	+	1.85997i	−0.226689	+	0.145684i	0.422367	+	0.906425i	$0.361199\pi$
$164$	9.14645	+	22.8467i	0.714218	+	1.78403i
$165$	5.21349	−	9.90553i	0.405870	−	0.771144i
$166$	−14.5525	−	3.53039i	−1.12949	−	0.274011i
$167$	0.309990	−	3.24636i	0.0239877	−	0.251211i	−0.975522	−	0.219902i	$-0.929426\pi$
$167$	0.309990	−	3.24636i	0.0239877	−	0.251211i	0.999510	−	0.0313091i	$-0.00996761\pi$
$168$	0.539341	−	1.31477i	0.0416111	−	0.101437i
$169$	−26.8625	+	21.1249i	−2.06635	+	1.62500i
$170$	−1.82309	+	6.20886i	−0.139824	+	0.476198i
$171$	11.6467	+	12.6372i	0.890643	+	0.966392i
$172$	−5.44674	+	8.47530i	−0.415310	+	0.646235i
$173$	−19.1565	−	0.912537i	−1.45644	−	0.0693789i	−0.695653	−	0.718378i	$-0.744885\pi$
$173$	−19.1565	−	0.912537i	−1.45644	−	0.0693789i	−0.760789	+	0.648999i	$0.775188\pi$
$174$	0.832905	+	2.92829i	0.0631423	+	0.221993i
$175$	0.986610	+	1.03473i	0.0745807	+	0.0782180i
$176$	10.5574	+	4.22654i	0.795793	+	0.318588i
$177$	−0.0141972	−	0.105063i	−0.00106712	−	0.00789704i
$178$	10.5551	+	7.51625i	0.791137	+	0.563366i
$179$	−0.202571	−	0.689893i	−0.0151409	−	0.0515650i	0.951576	−	0.307413i	$-0.0994634\pi$
$179$	−0.202571	−	0.689893i	−0.0151409	−	0.0515650i	−0.966717	+	0.255848i	$0.917645\pi$
$180$	−13.5735	−	0.230330i	−1.01171	−	0.0171678i
$181$	13.1715	+	1.89378i	0.979030	+	0.140763i	0.613208	−	0.789922i	$-0.289879\pi$
$181$	13.1715	+	1.89378i	0.979030	+	0.140763i	0.365822	+	0.930685i	$0.380788\pi$
$182$	−52.4156	−	27.0221i	−3.88530	−	2.00301i
$183$	−10.5537	+	5.32795i	−0.780149	+	0.393854i
$184$	−0.800989	−	0.467548i	−0.0590497	−	0.0344681i
$185$	2.57791	+	1.48836i	0.189532	+	0.109426i
$186$	−3.03691	−	5.36468i	−0.222677	−	0.393357i
$187$	−4.11417	+	1.64706i	−0.300858	+	0.120445i
$188$	−9.23475	−	4.21737i	−0.673514	−	0.307583i
$189$	17.6698	−	13.1820i	1.28529	−	0.958850i
$190$	−10.3996	−	22.7719i	−0.754463	−	1.65204i
$191$	−0.122759	+	0.354689i	−0.00888253	+	0.0256644i	−0.949355	−	0.314206i	$-0.898262\pi$
$191$	−0.122759	+	0.354689i	−0.00888253	+	0.0256644i	0.940472	+	0.339870i	$0.110383\pi$
$192$	−1.31187	−	15.0905i	−0.0946764	−	1.08906i
$193$	−8.97561	+	8.55822i	−0.646078	+	0.616034i	−0.940562	−	0.339622i	$-0.889701\pi$
$193$	−8.97561	+	8.55822i	−0.646078	+	0.616034i	0.294484	+	0.955657i	$0.404852\pi$
$194$	−3.15445	−	9.11418i	−0.226476	−	0.654360i
$195$	−2.65874	+	25.5509i	−0.190397	+	1.82974i
$196$	1.09678	−	23.0241i	0.0783411	−	1.64458i
$197$	12.1590	+	10.5358i	0.866293	+	0.750647i	0.969779	−	0.243983i	$-0.0784543\pi$
$197$	12.1590	+	10.5358i	0.866293	+	0.750647i	−0.103486	+	0.994631i	$0.533000\pi$
$198$	−10.9881	−	14.4713i	−0.780892	−	1.02843i
$199$	−7.74040	+	1.11290i	−0.548702	+	0.0788915i	−0.411090	−	0.911595i	$-0.634852\pi$
$199$	−7.74040	+	1.11290i	−0.548702	+	0.0788915i	−0.137612	+	0.990486i	$0.543943\pi$
$200$	−0.0615857	−	0.0213150i	−0.00435476	−	0.00150720i
$201$	−0.283262	+	1.85809i	−0.0199797	+	0.131059i
$202$	1.24775	−	5.14328i	0.0877911	−	0.361880i
$203$	2.13743	+	3.00160i	0.150018	+	0.210671i
$204$	4.03180	+	3.55390i	0.282282	+	0.248823i
$205$	11.6203	−	22.5402i	0.811597	−	1.57428i
$206$	19.4571			1.35564
$207$	−6.92136	−	12.6133i	−0.481067	−	0.876684i
$208$	−26.0979			−1.80957
$209$	7.85606	−	15.2386i	0.543415	−	1.05408i
$210$	−30.4349	+	10.2453i	−2.10021	+	0.706994i
$211$	−6.28928	−	8.83206i	−0.432972	−	0.608024i	0.539233	−	0.842157i	$-0.318714\pi$
$211$	−6.28928	−	8.83206i	−0.432972	−	0.608024i	−0.972205	+	0.234133i	$0.924775\pi$
$212$	−3.75372	+	15.4731i	−0.257807	+	1.06269i
$213$	8.39718	−	3.27935i	0.575365	−	0.224697i
$214$	3.67307	+	1.27126i	0.251086	+	0.0869018i
$215$	10.2759	−	1.47744i	0.700808	−	0.100761i
$216$	−0.440568	+	0.903150i	−0.0299769	+	0.0614516i
$217$	−5.63895	−	4.88618i	−0.382797	−	0.331695i
$218$	0.872428	−	18.3145i	0.0590883	−	1.24042i
$219$	−17.1679	−	12.4460i	−1.16010	−	0.841025i
$220$	4.42948	+	12.7981i	0.298636	+	0.862851i
$221$	7.36055	−	7.01827i	0.495124	−	0.472100i
$222$	3.95961	−	2.76930i	0.265752	−	0.185863i
$223$	−5.39948	+	15.6008i	−0.361576	+	1.04470i	0.606724	+	0.794913i	$0.292483\pi$
$223$	−5.39948	+	15.6008i	−0.361576	+	1.04470i	−0.968300	+	0.249792i	$0.919638\pi$
$224$	−14.2343	−	31.1689i	−0.951072	−	2.08256i
$225$	−0.648984	−	0.775160i	−0.0432656	−	0.0516774i
$226$	16.3132	+	7.44997i	1.08514	+	0.495565i
$227$	−1.89690	+	0.759406i	−0.125902	+	0.0504036i	−0.433758	−	0.901029i	$-0.642813\pi$
$227$	−1.89690	+	0.759406i	−0.125902	+	0.0504036i	0.307856	+	0.951433i	$0.400388\pi$
$228$	−20.7916	−	0.176395i	−1.37696	−	0.0116820i
$229$	−21.6138	−	12.4788i	−1.42828	−	0.824620i	−0.431298	−	0.902210i	$-0.641944\pi$
$229$	−21.6138	−	12.4788i	−1.42828	−	0.824620i	−0.996985	+	0.0775900i	$0.975277\pi$
$230$	3.86837	+	20.5981i	0.255073	+	1.35820i
$231$	−18.3997	−	12.0465i	−1.21061	−	0.792604i
$232$	−0.149294	−	0.0769665i	−0.00980164	−	0.00505310i
$233$	3.28025	+	0.471628i	0.214896	+	0.0308974i	0.248922	−	0.968524i	$-0.419924\pi$
$233$	3.28025	+	0.471628i	0.214896	+	0.0308974i	−0.0340258	+	0.999421i	$0.510833\pi$
$234$	35.7537	+	21.4594i	2.33729	+	1.40284i
$235$	2.94734	+	10.0377i	0.192263	+	0.654788i
$236$	0.104484	+	0.0744030i	0.00680135	+	0.00484322i
$237$	7.03511	+	2.88592i	0.456979	+	0.187461i
$238$	11.8029	+	4.72516i	0.765067	+	0.306287i
$239$	4.44738	+	4.66428i	0.287677	+	0.301707i	0.851676	−	0.524068i	$-0.175586\pi$
$239$	4.44738	+	4.66428i	0.287677	+	0.301707i	−0.563999	+	0.825775i	$0.690738\pi$
$240$	−9.89416	+	10.2020i	−0.638665	+	0.658535i
$241$	20.9784	+	0.999325i	1.35134	+	0.0643722i	0.710714	−	0.703481i	$-0.248372\pi$
$241$	20.9784	+	0.999325i	1.35134	+	0.0643722i	0.640625	+	0.767854i	$0.278675\pi$
$242$	2.23527	−	3.47815i	0.143689	−	0.223584i
$243$	−13.0700	+	8.49559i	−0.838441	+	0.544992i
$244$	4.02976	−	13.7241i	0.257979	−	0.878595i
$245$	−18.6707	+	14.6828i	−1.19283	+	0.938050i
$246$	−25.1707	−	32.5721i	−1.60482	−	2.07672i
$247$	−3.74002	+	39.1673i	−0.237972	+	2.49215i
$248$	0.330524	+	0.0801843i	0.0209883	+	0.00509171i
$249$	12.8064	−	0.501191i	0.811571	−	0.0317617i
$250$	8.66832	+	21.6524i	0.548233	+	1.36942i
$251$	10.9766	−	7.05424i	0.692837	−	0.445260i	−0.146256	−	0.989247i	$-0.546722\pi$
$251$	10.9766	−	7.05424i	0.692837	−	0.445260i	0.839094	+	0.543987i	$0.183086\pi$
$252$	−2.98543	+	26.5042i	−0.188065	+	1.66961i
$253$	−9.45080	+	10.8025i	−0.594167	+	0.679147i
$254$	11.4967	−	6.63765i	0.721370	−	0.416483i
$255$	0.0469847	−	5.53807i	0.00294229	−	0.346807i
$256$	−11.2903	−	8.87880i	−0.705644	−	0.554925i
$257$	2.76448	−	1.96858i	0.172444	−	0.122797i	−0.490576	−	0.871398i	$-0.663214\pi$
$257$	2.76448	−	1.96858i	0.172444	−	0.122797i	0.663020	+	0.748602i	$0.269274\pi$
$258$	4.88469	−	16.1283i	0.304108	−	1.00410i
$259$	3.39239	−	4.76394i	0.210793	−	0.296017i
$260$	−20.3532	−	23.4889i	−1.26225	−	1.45672i
$261$	−1.37131	−	2.21557i	−0.0848820	−	0.137140i
$262$	3.01365	+	0.884887i	0.186184	+	0.0546685i
$263$	−0.180787	−	0.0348439i	−0.0111478	−	0.00214857i	0.183674	−	0.982987i	$-0.441201\pi$
$263$	−0.180787	−	0.0348439i	−0.0111478	−	0.00214857i	−0.194822	+	0.980839i	$0.562413\pi$
$264$	0.997092	+	0.103754i	0.0613668	+	0.00638562i
$265$	14.5831	−	7.51809i	0.895830	−	0.461833i
$266$	−46.4797	+	16.0868i	−2.84985	+	0.986343i
$267$	−10.4490	−	3.71599i	−0.639467	−	0.227415i
$268$	−1.40570	−	1.78750i	−0.0858671	−	0.109189i
$269$	−14.3250	+	12.4127i	−0.873409	+	0.756813i	−0.971168	−	0.238397i	$-0.923378\pi$
$269$	−14.3250	+	12.4127i	−0.873409	+	0.756813i	0.0977591	+	0.995210i	$0.468833\pi$
$270$	21.9436	−	5.84094i	1.33544	−	0.355468i
$271$	20.3982	−	5.98944i	1.23910	−	0.363833i	0.404423	−	0.914572i	$-0.367472\pi$
$271$	20.3982	−	5.98944i	1.23910	−	0.363833i	0.834677	+	0.550740i	$0.185654\pi$
$272$	5.60098	−	0.534829i	0.339609	−	0.0324288i
$273$	49.4762	+	9.97182i	2.99444	+	0.603522i
$274$	7.80235	−	0.371672i	0.471357	−	0.0224535i
$275$	−0.504275	+	0.873430i	−0.0304089	+	0.0526698i
$276$	16.8605	+	4.32752i	1.01488	+	0.260486i
$277$	4.12443	+	7.14372i	0.247813	+	0.429225i	0.962919	−	0.269792i	$-0.0869548\pi$
$277$	4.12443	+	7.14372i	0.247813	+	0.429225i	−0.715106	+	0.699016i	$0.753622\pi$
$278$	−0.260101	−	0.404725i	−0.0155998	−	0.0242738i
$279$	3.75615	+	3.70517i	0.224875	+	0.221823i
$280$	0.736001	−	1.61162i	0.0439845	−	0.0963125i
$281$	15.2064	+	14.4993i	0.907141	+	0.864957i	0.991317	−	0.131494i	$-0.0419774\pi$
$281$	15.2064	+	14.4993i	0.907141	+	0.864957i	−0.0841764	+	0.996451i	$0.526826\pi$
$282$	16.7876	+	2.55924i	0.999686	+	0.152400i
$283$	6.27065	+	32.5352i	0.372751	+	1.93402i	0.356900	+	0.934143i	$0.383834\pi$
$283$	6.27065	+	32.5352i	0.372751	+	1.93402i	0.0158512	+	0.999874i	$0.494954\pi$
$284$	−4.05364	+	10.1255i	−0.240539	+	0.600837i
$285$	13.8930	+	16.3110i	0.822952	+	0.966179i
$286$	7.87278	−	40.8479i	0.465527	−	2.41539i
$287$	−41.9142	−	26.9366i	−2.47412	−	1.59002i
$288$	8.62227	+	22.6435i	0.508072	+	1.33428i
$289$	9.69678	−	11.1907i	0.570399	−	0.658275i
$290$	0.894845	+	3.68860i	0.0525471	+	0.216602i
$291$	4.73085	+	6.76428i	0.277327	+	0.396529i
$292$	25.1914	−	4.85524i	1.47421	−	0.284131i
$293$	−19.8377	−	1.89427i	−1.15893	−	0.110664i	−0.502173	−	0.864767i	$-0.667466\pi$
$293$	−19.8377	−	1.89427i	−1.15893	−	0.110664i	−0.656756	+	0.754103i	$0.728072\pi$
$294$	8.77174	+	37.5450i	0.511578	+	2.18967i
$295$	−0.0125641	−	0.131578i	−0.000731512	−	0.00766074i
$296$	−0.0379390	+	0.263871i	−0.00220516	+	0.0153372i
$297$	12.4340	+	9.34002i	0.721492	+	0.541963i
$298$			17.5676i			1.01767i
$299$	10.9214	−	31.0761i	0.631603	−	1.79718i
$300$	1.22122	+	0.0685622i	0.0705070	+	0.00395844i
$301$	−0.970512	−	20.3736i	−0.0559394	−	1.17431i
$302$	9.98868	−	12.7016i	0.574784	−	0.730897i
$303$	0.177136	+	4.52616i	0.0101762	+	0.260021i
$304$	−15.0209	+	15.7535i	−0.861509	+	0.903525i
$305$	−13.4073	+	6.12290i	−0.767698	+	0.350596i
$306$	−8.11302	−	3.87278i	−0.463791	−	0.221392i
$307$	−2.10976	−	14.6737i	−0.120410	−	0.837471i	−0.957093	−	0.289782i	$-0.906417\pi$
$307$	−2.10976	−	14.6737i	−0.120410	−	0.837471i	0.836682	−	0.547688i	$-0.184492\pi$
$308$	25.8580	−	6.27308i	1.47340	−	0.357442i
$309$	−16.0173	+	4.55585i	−0.911190	+	0.259173i
$310$	−3.52176	−	6.83125i	−0.200022	−	0.387989i
$311$	−9.46165	−	18.3530i	−0.536521	−	1.04071i	−0.988858	−	0.148859i	$-0.952440\pi$
$311$	−9.46165	−	18.3530i	−0.536521	−	1.04071i	0.452337	−	0.891847i	$-0.350590\pi$
$312$	−2.21284	+	0.629407i	−0.125277	+	0.0356332i
$313$	−1.57445	+	0.381957i	−0.0889931	+	0.0215895i	−0.280008	−	0.959998i	$-0.590337\pi$
$313$	−1.57445	+	0.381957i	−0.0889931	+	0.0215895i	0.191015	+	0.981587i	$0.438822\pi$
$314$	3.03578	+	21.1143i	0.171319	+	1.19155i
$315$	22.6554	−	15.5603i	1.27649	−	0.876726i
$316$	−8.36853	+	3.82178i	−0.470766	+	0.214992i
$317$	−12.2898	+	12.8892i	−0.690264	+	0.723928i	−0.971848	−	0.235609i	$-0.924292\pi$
$317$	−12.2898	+	12.8892i	−0.690264	+	0.723928i	0.281584	+	0.959536i	$0.409140\pi$
$318$	−1.04149	−	26.6121i	−0.0584041	−	1.49233i
$319$	−1.60684	+	2.04326i	−0.0899656	+	0.114401i
$320$	−0.898570	−	18.8633i	−0.0502316	−	1.05449i
$321$	−3.32138	−	0.186470i	−0.185381	−	0.0104078i
$322$	41.0084	−	3.71896i	2.28531	−	0.207250i
$323$		−	8.48249i		−	0.471978i
$324$	3.31590	−	18.5663i	0.184216	−	1.03146i
$325$	0.329395	−	2.29099i	0.0182715	−	0.127081i
$326$	0.661809	+	6.93078i	0.0366542	+	0.383861i
$327$	3.57013	+	15.2810i	0.197429	+	0.845040i
$328$	2.26081	+	0.215881i	0.124832	+	0.0119201i
$329$	20.1823	−	3.88982i	1.11269	−	0.214453i
$330$	−12.9832	−	18.5637i	−0.714702	−	1.02190i
$331$	−5.89147	−	24.2850i	−0.323824	−	1.33482i	−0.868298	−	0.496044i	$-0.834786\pi$
$331$	−5.89147	−	24.2850i	−0.323824	−	1.33482i	0.544473	−	0.838778i	$-0.316730\pi$
$332$	−10.1542	+	11.7186i	−0.557285	+	0.643142i
$333$	−2.61116	+	3.20686i	−0.143091	+	0.175735i
$334$	−5.55202	−	3.56807i	−0.303793	−	0.195236i
$335$	−0.443472	+	2.30095i	−0.0242294	+	0.125714i
$336$	18.1053	+	21.2564i	0.987727	+	1.15963i
$337$	10.4521	−	26.1080i	0.569361	−	1.42219i	−0.312152	−	0.950032i	$-0.601050\pi$
$337$	10.4521	−	26.1080i	0.569361	−	1.42219i	0.881512	−	0.472161i	$-0.156526\pi$
$338$	13.0885	+	67.9097i	0.711922	+	3.69380i
$339$	−15.1736	−	2.31318i	−0.824115	−	0.125635i
$340$	4.84945	+	4.62394i	0.262998	+	0.250768i
$341$	2.18652	−	4.78781i	0.118407	−	0.259274i
$342$	33.5319	−	9.23087i	1.81320	−	0.499148i
$343$	9.17388	+	14.2748i	0.495343	+	0.770769i
$344$	0.464868	+	0.805175i	0.0250640	+	0.0434121i
$345$	−8.00751	−	16.0508i	−0.431110	−	0.864145i
$346$	−19.4060	+	33.6121i	−1.04327	+	1.80700i
$347$	0.622929	−	0.0296738i	0.0334406	−	0.00159297i	−0.0308550	−	0.999524i	$-0.509823\pi$
$347$	0.622929	−	0.0296738i	0.0334406	−	0.00159297i	0.0642955	+	0.997931i	$0.479520\pi$
$348$	3.09032	+	0.622848i	0.165659	+	0.0333881i
$349$	4.97750	−	0.475294i	0.266440	−	0.0254419i	0.0390188	−	0.999238i	$-0.487577\pi$
$349$	4.97750	−	0.475294i	0.266440	−	0.0254419i	0.227421	+	0.973797i	$0.426971\pi$
$350$	2.77616	−	0.815155i	0.148392	−	0.0435719i
$351$	−34.4575	−	9.29388i	−1.83921	−	0.496070i
$352$	18.2677	−	15.8290i	0.973671	−	0.843691i
$353$	−20.9496	−	26.6396i	−1.11504	−	1.41788i	−0.897048	−	0.441933i	$-0.854293\pi$
$353$	−20.9496	−	26.6396i	−1.11504	−	1.41788i	−0.217988	−	0.975951i	$-0.569950\pi$
$354$	−0.202151	−	0.0718914i	−0.0107442	−	0.00382098i
$355$	10.6209	−	3.67593i	0.563699	−	0.195098i
$356$	11.9260	−	6.14829i	0.632077	−	0.325858i
$357$	−10.8226	−	1.12617i	−0.572795	−	0.0596031i
$358$	−1.42882	−	0.275382i	−0.0755153	−	0.0145544i
$359$	−0.105422	−	0.0309547i	−0.00556396	−	0.00163373i	0.278949	−	0.960306i	$-0.410014\pi$
$359$	−0.105422	−	0.0309547i	−0.00556396	−	0.00163373i	−0.284513	+	0.958672i	$0.591832\pi$
$360$	−0.592883	+	1.10364i	−0.0312477	+	0.0581671i
$361$	9.04757	+	10.4415i	0.476188	+	0.549550i
$362$	15.6209	−	21.9365i	0.821016	−	1.15296i
$363$	−1.02569	+	3.38664i	−0.0538350	+	0.177752i
$364$	−49.7409	+	35.4204i	−2.60713	+	1.85653i
$365$	−20.7805	−	16.3420i	−1.08770	−	0.855379i
$366$	−0.202974	+	23.9245i	−0.0106096	+	1.25055i
$367$	−18.6924	+	10.7921i	−0.975735	+	0.563341i	−0.900980	−	0.433861i	$-0.857151\pi$
$367$	−18.6924	+	10.7921i	−0.975735	+	0.563341i	−0.0747554	+	0.997202i	$0.523818\pi$
$368$	15.3768	−	9.77900i	0.801573	−	0.509766i
$369$	28.3475	+	20.9200i	1.47571	+	1.08905i
$370$	5.06781	−	3.25688i	0.263463	−	0.169317i
$371$	−11.9805	−	29.9258i	−0.621995	−	1.55367i
$372$	−6.37849	+	0.249629i	−0.330709	+	0.0129427i
$373$	−4.53600	−	1.10042i	−0.234865	−	0.0569777i	0.116599	−	0.993179i	$-0.462801\pi$
$373$	−4.53600	−	1.10042i	−0.234865	−	0.0569777i	−0.351464	+	0.936201i	$0.614316\pi$
$374$	−0.852508	+	8.92786i	−0.0440821	+	0.461649i
$375$	−12.2057	−	15.7948i	−0.630302	−	0.815640i
$376$	−0.736450	+	0.579151i	−0.0379795	+	0.0298674i
$377$	1.68065	−	5.72378i	0.0865580	−	0.294790i
$378$	−7.32565	−	44.0083i	−0.376791	−	2.26354i
$379$	1.29489	−	2.01489i	0.0665141	−	0.103498i	−0.806403	−	0.591366i	$-0.798589\pi$
$379$	1.29489	−	2.01489i	0.0665141	−	0.103498i	0.872917	+	0.487868i	$0.162225\pi$
$380$	−25.8931	−	1.23344i	−1.32829	−	0.0632742i
$381$	−7.91004	+	8.15613i	−0.405243	+	0.417851i
$382$	0.524168	+	0.549732i	0.0268188	+	0.0281267i
$383$	−17.1153	−	6.85194i	−0.874552	−	0.350118i	−0.109423	−	0.993995i	$-0.534900\pi$
$383$	−17.1153	−	6.85194i	−0.874552	−	0.350118i	−0.765128	+	0.643878i	$0.777325\pi$
$384$	−2.47636	−	1.01584i	−0.126371	−	0.0518395i
$385$	−22.3346	−	15.9044i	−1.13827	−	0.810562i
$386$	7.07096	+	24.0815i	0.359902	+	1.22572i
$387$	−0.244707	+	14.4207i	−0.0124391	+	0.733046i
$388$	−9.88521	−	1.42128i	−0.501845	−	0.0721545i
$389$	20.0566	+	10.3399i	1.01691	+	0.524254i	0.884303	−	0.466914i	$-0.154634\pi$
$389$	20.0566	+	10.3399i	1.01691	+	0.524254i	0.132609	+	0.991168i	$0.457665\pi$
$390$	43.4949	+	28.4768i	2.20245	+	1.44198i
$391$	−1.70705	+	6.89318i	−0.0863290	+	0.348603i
$392$	−1.84221	−	1.06360i	−0.0930454	−	0.0537198i
$393$	−2.68806	−	0.0228054i	−0.135595	−	0.00115038i
$394$	30.2271	−	12.1011i	1.52282	−	0.609646i
$395$	8.62347	+	3.93821i	0.433894	+	0.198153i
$396$	−18.5327	+	3.24678i	−0.931303	+	0.163157i
$397$	13.4580	+	29.4688i	0.675436	+	1.47900i	0.867408	+	0.497598i	$0.165784\pi$
$397$	13.4580	+	29.4688i	0.675436	+	1.47900i	−0.191972	+	0.981400i	$0.561488\pi$
$398$	−5.17608	+	14.9553i	−0.259454	+	0.749642i
$399$	34.4958	−	24.1259i	1.72695	−	1.20781i
$400$	0.926722	−	0.883628i	0.0463361	−	0.0441814i
$401$	−11.2552	−	32.5197i	−0.562056	−	1.62395i	−0.764474	−	0.644655i	$-0.777001\pi$
$401$	−11.2552	−	32.5197i	−0.562056	−	1.62395i	0.202418	−	0.979299i	$-0.435120\pi$
$402$	3.07961	+	2.23259i	0.153597	+	0.111352i
$403$	−0.574754	+	12.0656i	−0.0286306	+	0.601029i
$404$	−4.14171	−	3.58881i	−0.206058	−	0.178550i
$405$	−16.6965	+	9.94638i	−0.829656	+	0.494240i
$406$	7.38132	−	1.06127i	0.366329	−	0.0526702i
$407$	3.89868	+	1.34935i	0.193250	+	0.0668846i
$408$	0.462008	−	0.180428i	0.0228728	−	0.00893250i
$409$	2.17258	−	8.95550i	0.107427	−	0.442821i	−0.892540	−	0.450969i	$-0.851078\pi$
$409$	2.17258	−	8.95550i	0.107427	−	0.442821i	0.999967	+	0.00814803i	$0.00259363\pi$
$410$	−29.7690	−	41.8047i	−1.47019	−	2.06459i
$411$	−6.33595	+	2.13288i	−0.312529	+	0.105207i
$412$	9.23211	−	17.9078i	0.454834	−	0.882254i
$413$	−0.259687			−0.0127784
$414$	−29.1069	+	0.753252i	−1.43053	+	0.0370203i
$415$	15.9783			0.784345
$416$	−25.4188	+	49.3056i	−1.24626	+	2.41741i
$417$	0.308884	+	0.272271i	0.0151261	+	0.0133332i
$418$	−20.1257	−	28.2626i	−0.984382	−	1.38237i
$419$	−4.73733	+	19.5275i	−0.231434	+	0.953982i	0.730981	+	0.682398i	$0.239063\pi$
$419$	−4.73733	+	19.5275i	−0.231434	+	0.953982i	−0.962415	+	0.271584i	$0.912452\pi$
$420$	−5.01139	+	32.8728i	−0.244531	+	1.60403i
$421$	−8.67009	−	3.00075i	−0.422554	−	0.146247i	0.107512	−	0.994204i	$-0.465712\pi$
$421$	−8.67009	−	3.00075i	−0.422554	−	0.146247i	−0.530066	+	0.847956i	$0.677833\pi$
$422$	−21.7192	+	3.12275i	−1.05727	+	0.152013i
$423$	−14.4189	+	1.82400i	−0.701073	+	0.0886861i
$424$	1.11046	+	0.962221i	0.0539288	+	0.0467296i
$425$	−0.0237431	+	0.498430i	−0.00115171	+	0.0241774i
$426$	1.88818	−	18.1457i	0.0914828	−	0.879164i
$427$	9.47132	+	27.3656i	0.458350	+	1.32431i
$428$	2.91286	−	2.77741i	0.140798	−	0.134251i
$429$	3.08353	+	35.4698i	0.148874	+	1.71250i
$430$	6.87157	−	19.8541i	0.331376	−	0.957449i
$431$	14.1326	+	30.9460i	0.680741	+	1.49062i	0.861856	+	0.507153i	$0.169302\pi$
$431$	14.1326	+	30.9460i	0.680741	+	1.49062i	−0.181115	+	0.983462i	$0.557970\pi$
$432$	−11.8061	−	15.8255i	−0.568020	−	0.761403i
$433$	−15.9313	−	7.27559i	−0.765610	−	0.349642i	−0.00596666	−	0.999982i	$-0.501899\pi$
$433$	−15.9313	−	7.27559i	−0.765610	−	0.349642i	−0.759643	+	0.650340i	$0.774627\pi$
$434$	−14.0184	+	5.61210i	−0.672903	+	0.269390i
$435$	−1.60033	−	2.82697i	−0.0767298	−	0.135543i
$436$	−16.4423	−	9.49295i	−0.787442	−	0.454630i
$437$	−12.4725	−	24.4787i	−0.596641	−	1.17097i
$438$	−38.3081	+	19.3396i	−1.83043	+	0.924081i
$439$	10.9324	+	5.63606i	0.521777	+	0.268995i	0.698932	−	0.715188i	$-0.253659\pi$
$439$	10.9324	+	5.63606i	0.521777	+	0.268995i	−0.177155	+	0.984183i	$0.556689\pi$
$440$	1.23710	+	0.177868i	0.0589762	+	0.00847950i
$441$	−16.0121	−	28.8535i	−0.762482	−	1.37398i
$442$	−5.79863	−	19.7483i	−0.275813	−	0.939331i
$443$	27.6316	+	19.6764i	1.31282	+	0.934852i	0.999889	−	0.0149245i	$-0.00475079\pi$
$443$	27.6316	+	19.6764i	1.31282	+	0.934852i	0.312928	+	0.949777i	$0.398690\pi$
$444$	−0.670016	−	4.95832i	−0.0317976	−	0.235312i
$445$	−12.8359	−	5.13873i	−0.608481	−	0.243599i
$446$	23.0552	+	24.1796i	1.09170	+	1.14494i
$447$	−4.11344	−	14.4618i	−0.194559	−	0.684022i
$448$	−37.0609	−	1.76543i	−1.75096	−	0.0834086i
$449$	1.09526	−	1.70426i	0.0516887	−	0.0804292i	−0.814447	−	0.580237i	$-0.802960\pi$
$449$	1.09526	−	1.70426i	0.0516887	−	0.0804292i	0.866136	+	0.499808i	$0.166596\pi$
$450$	−1.99617	+	0.448546i	−0.0941003	+	0.0211446i
$451$	9.90199	−	33.7231i	0.466266	−	1.58796i
$452$	14.5971	−	11.4793i	0.686592	−	0.539942i
$453$	−5.24871	+	12.7950i	−0.246606	+	0.601159i
$454$	−0.393063	+	4.11634i	−0.0184473	+	0.193189i
$455$	61.1502	+	14.8349i	2.86676	+	0.695469i
$456$	−0.893694	+	1.69800i	−0.0418510	+	0.0795161i
$457$	−12.7005	−	31.7243i	−0.594103	−	1.48400i	−0.854998	−	0.518631i	$-0.826442\pi$
$457$	−12.7005	−	31.7243i	−0.594103	−	1.48400i	0.260895	−	0.965367i	$-0.415982\pi$
$458$	−42.4898	+	27.3066i	−1.98542	+	1.27595i
$459$	7.58553	+	1.28845i	0.354062	+	0.0601398i
$460$	20.7935	+	6.21316i	0.969500	+	0.289690i
$461$	31.8368	−	18.3810i	1.48279	−	0.856089i	0.482980	−	0.875631i	$-0.339554\pi$
$461$	31.8368	−	18.3810i	1.48279	−	0.856089i	0.999809	+	0.0195427i	$0.00622103\pi$
$462$	−38.7317	+	21.9258i	−1.80196	+	1.02008i
$463$	−21.1398	−	16.6245i	−0.982448	−	0.772606i	−0.00863684	−	0.999963i	$-0.502749\pi$
$463$	−21.1398	−	16.6245i	−0.982448	−	0.772606i	−0.973812	+	0.227357i	$0.926992\pi$
$464$	2.68829	−	1.91432i	0.124801	−	0.0888702i
$465$	4.49868	+	4.79894i	0.208621	+	0.222546i
$466$	3.89024	−	5.46308i	0.180212	−	0.253072i
$467$	−26.1811	−	30.2146i	−1.21152	−	1.39816i	−0.892885	−	0.450285i	$-0.851322\pi$
$467$	−26.1811	−	30.2146i	−1.21152	−	1.39816i	−0.318632	−	0.947879i	$-0.603223\pi$
$468$	36.7153	−	22.7247i	1.69717	−	1.05045i
$469$	4.41740	+	1.29707i	0.203977	+	0.0598929i
$470$	20.7888	+	4.00671i	0.958916	+	0.184816i
$471$	−7.44297	−	16.6707i	−0.342954	−	0.768144i
$472$	0.0105214	−	0.00542415i	0.000484286	−	0.000249667i
$473$	13.5970	−	4.70595i	0.625189	−	0.216380i
$474$	11.7150	−	9.97840i	0.538090	−	0.458323i
$475$	−1.19333	−	1.51744i	−0.0547535	−	0.0696248i
$476$	9.94923	−	8.62105i	0.456022	−	0.395145i
$477$	7.08856	+	21.6635i	0.324563	+	0.991903i
$478$	12.5142	−	3.67451i	0.572387	−	0.168068i
$479$	4.63848	−	0.442921i	0.211938	−	0.0202376i	0.0114529	−	0.999934i	$-0.496354\pi$
$479$	4.63848	−	0.442921i	0.211938	−	0.0202376i	0.200485	+	0.979697i	$0.435748\pi$
$480$	9.63744	+	28.6291i	0.439887	+	1.30673i
$481$	−9.45720	+	0.450502i	−0.431211	+	0.0205411i
$482$	21.2516	−	36.8089i	0.967984	−	1.67660i
$483$	−32.8878	+	12.6636i	−1.49644	+	0.576212i
$484$	−2.14060	−	3.70763i	−0.0972999	−	0.168528i
$485$	5.56379	+	8.65743i	0.252639	+	0.393114i
$486$	3.16142	+	31.3883i	0.143405	+	1.42380i
$487$	−7.29368	+	15.9709i	−0.330508	+	0.723712i	−0.999814	−	0.0192747i	$-0.993864\pi$
$487$	−7.29368	+	15.9709i	−0.330508	+	0.723712i	0.669306	+	0.742987i	$0.266592\pi$
$488$	−0.955328	−	0.910903i	−0.0432456	−	0.0412346i
$489$	−2.16764	−	5.55053i	−0.0980242	−	0.251004i
$490$	9.09713	+	47.2004i	0.410966	+	2.13230i
$491$	−5.84146	+	14.5913i	−0.263621	+	0.658494i	−0.999833	−	0.0182567i	$-0.994188\pi$
$491$	−5.84146	+	14.5913i	−0.263621	+	0.658494i	0.736212	+	0.676751i	$0.236613\pi$
$492$	−41.9216	+	7.71146i	−1.88997	+	0.347660i
$493$	−0.243393	+	1.26284i	−0.0109619	+	0.0568757i
$494$	66.9850	+	43.0487i	3.01380	+	1.93685i
$495$	15.0346	+	12.2418i	0.675754	+	0.550228i
$496$	−4.37616	+	5.05036i	−0.196495	+	0.226768i
$497$	−5.20589	−	21.4590i	−0.233516	−	0.962567i
$498$	10.9743	−	23.5006i	0.491769	−	1.05309i
$499$	30.7434	−	5.92530i	1.37626	−	0.265253i	0.553127	−	0.833097i	$-0.313434\pi$
$499$	30.7434	−	5.92530i	1.37626	−	0.265253i	0.823136	+	0.567844i	$0.192222\pi$
$500$	24.0413	+	2.29567i	1.07516	+	0.102665i
$501$	5.40594	+	1.63727i	0.241520	+	0.0731478i
$502$	−2.51002	−	26.2861i	−0.112028	−	1.17321i
$503$	−1.00521	+	6.99136i	−0.0448199	+	0.311729i	0.955063	+	0.296404i	$0.0957875\pi$
$503$	−1.00521	+	6.99136i	−0.0448199	+	0.311729i	−0.999883	+	0.0153254i	$0.995122\pi$
$504$	2.04779	+	1.36568i	0.0912160	+	0.0608322i
$505$			5.64722i			0.251298i
$506$	10.6672	+	27.0174i	0.474217	+	1.20107i
$507$	−26.6756	−	52.8393i	−1.18470	−	2.34668i
$508$	−0.654078	−	13.7308i	−0.0290200	−	0.609205i
$509$	−8.64890	+	10.9980i	−0.383356	+	0.487477i	−0.938987	−	0.343952i	$-0.888234\pi$
$509$	−8.64890	+	10.9980i	−0.383356	+	0.487477i	0.555631	+	0.831429i	$0.312477\pi$
$510$	−9.91820	−	5.22016i	−0.439185	−	0.231153i
$511$	−35.8428	+	37.5908i	−1.58559	+	1.66292i
$512$	−29.2523	+	13.3591i	−1.29278	+	0.590393i
$513$	−25.4424	+	15.4504i	−1.12331	+	0.682152i
$514$	−0.977439	−	6.79823i	−0.0431130	−	0.299857i
$515$	−20.1761	+	4.89466i	−0.889063	+	0.215684i
$516$	−12.5263	−	12.1484i	−0.551442	−	0.534803i
$517$	6.64388	+	12.8873i	0.292197	+	0.566784i
$518$	−5.42340	−	10.5199i	−0.238290	−	0.462219i
$519$	8.10495	−	32.2137i	0.355768	−	1.41403i
$520$	−2.78739	+	0.676214i	−0.122235	+	0.0296540i
$521$	−1.29676	−	9.01919i	−0.0568122	−	0.395138i	−0.998310	−	0.0581178i	$-0.981490\pi$
$521$	−1.29676	−	9.01919i	−0.0568122	−	0.395138i	0.941497	−	0.337020i	$-0.109419\pi$
$522$	−5.25699	+	0.412108i	−0.230092	+	0.0180375i
$523$	29.2603	−	13.3627i	1.27946	−	0.584312i	0.344411	−	0.938819i	$-0.388079\pi$
$523$	29.2603	−	13.3627i	1.27946	−	0.584312i	0.935053	+	0.354507i	$0.115351\pi$
$524$	2.24436	−	2.35382i	0.0980455	−	0.102827i
$525$	−2.09450	+	1.32108i	−0.0914114	+	0.0576567i
$526$	−0.230327	+	0.292884i	−0.0100427	+	0.0127704i
$527$	−0.123911	−	2.60122i	−0.00539767	−	0.113311i
$528$	−10.7891	+	16.4791i	−0.469536	+	0.717162i
$529$	5.20945	+	22.4023i	0.226498	+	0.974012i
$530$		−	33.2035i		−	1.44227i
$531$	0.183246	+	0.0118482i	0.00795221	+	0.000514168i
$532$	−7.24810	+	50.4117i	−0.314245	+	2.18562i
$533$	7.66716	+	80.2941i	0.332102	+	3.47793i
$534$	−16.3739	+	15.3494i	−0.708570	+	0.664235i
$535$	−4.12860	−	0.394234i	−0.178495	−	0.0170442i
$536$	−0.206066	+	0.0397159i	−0.00890068	+	0.00171547i
$537$	1.24070	−	0.107859i	0.0535400	−	0.00465445i
$538$	9.04358	+	37.2782i	0.389897	+	1.60718i
$539$	−21.5579	+	24.8791i	−0.928564	+	1.07162i
$540$	5.03606	−	22.9677i	0.216718	−	0.988374i
$541$	−32.1857	−	20.6845i	−1.38377	−	0.889297i	−0.384347	−	0.923189i	$-0.625573\pi$
$541$	−32.1857	−	20.6845i	−1.38377	−	0.889297i	−0.999425	+	0.0338921i	$0.989210\pi$
$542$	8.14225	−	42.2460i	0.349740	−	1.81462i
$543$	−7.72287	+	21.7159i	−0.331420	+	0.931920i
$544$	4.44481	−	11.1026i	0.190570	−	0.476020i
$545$	3.70257	+	19.2107i	0.158601	+	0.822898i
$546$	63.8182	−	79.7496i	2.73116	−	3.41297i
$547$	6.33966	+	6.04485i	0.271064	+	0.258459i	0.813403	−	0.581701i	$-0.197613\pi$
$547$	6.33966	+	6.04485i	0.271064	+	0.258459i	−0.542339	+	0.840160i	$0.682461\pi$
$548$	3.36003	−	7.35744i	0.143533	−	0.314294i
$549$	−5.43481	−	19.7424i	−0.231952	−	0.842587i
$550$	1.10348	+	1.71704i	0.0470524	+	0.0732149i
$551$	−2.48773	−	4.30887i	−0.105981	−	0.183564i
$552$	1.06796	−	1.20001i	0.0454554	−	0.0510756i
$553$	9.31289	−	16.1304i	0.396024	−	0.685934i
$554$	16.6747	−	0.794314i	0.708440	−	0.0337472i
$555$	−3.40928	+	3.86772i	−0.144716	+	0.164176i
$556$	−0.495913	+	0.0473540i	−0.0210314	+	0.00200826i
$557$	15.4086	−	4.52438i	0.652884	−	0.191704i	0.0615165	−	0.998106i	$-0.480406\pi$
$557$	15.4086	−	4.52438i	0.652884	−	0.191704i	0.591368	+	0.806402i	$0.298588\pi$
$558$	10.1480	−	3.32055i	0.429599	−	0.140570i
$559$	−24.9550	+	21.6236i	−1.05548	+	0.914581i
$560$	21.5189	+	27.3635i	0.909338	+	1.15632i
$561$	−1.38866	−	7.54912i	−0.0586291	−	0.318724i
$562$	40.1826	−	13.9073i	1.69500	−	0.586645i
$563$	30.4479	−	15.6970i	1.28322	−	0.661548i	0.324500	−	0.945886i	$-0.394804\pi$
$563$	30.4479	−	15.6970i	1.28322	−	0.661548i	0.958724	+	0.284337i	$0.0917736\pi$
$564$	10.3209	−	14.2365i	0.434590	−	0.599467i
$565$	−18.7901	−	3.62150i	−0.790506	−	0.152357i
$566$	64.3387	+	18.8915i	2.70436	+	0.794070i
$567$	16.3350	+	34.5128i	0.686007	+	1.44940i
$568$	0.659138	+	0.760686i	0.0276568	+	0.0319177i
$569$	−21.9354	+	30.8039i	−0.919578	+	1.29137i	0.0368263	+	0.999322i	$0.488275\pi$
$569$	−21.9354	+	30.8039i	−0.919578	+	1.29137i	−0.956405	+	0.292045i	$0.905664\pi$
$570$	42.2234	−	9.86475i	1.76854	−	0.413189i
$571$	7.00613	−	4.98905i	0.293198	−	0.208785i	−0.423987	−	0.905668i	$-0.639370\pi$
$571$	7.00613	−	4.98905i	0.293198	−	0.208785i	0.717185	+	0.696883i	$0.245430\pi$
$572$	−33.8598	−	26.6277i	−1.41575	−	1.11336i
$573$	−0.560220	−	0.329811i	−0.0234035	−	0.0137781i
$574$	−87.3217	+	50.4152i	−3.64474	+	2.10429i
$575$	0.664365	+	1.47327i	0.0277060	+	0.0614397i
$576$	26.0712	+	2.93666i	1.08630	+	0.122361i
$577$	9.08795	−	5.84047i	0.378336	−	0.243142i	−0.337627	−	0.941280i	$-0.609624\pi$
$577$	9.08795	−	5.84047i	0.378336	−	0.243142i	0.715963	+	0.698138i	$0.245988\pi$
$578$	−11.1374	−	27.8199i	−0.463255	−	1.15715i
$579$	−11.4595	−	18.1685i	−0.476242	−	0.755056i
$580$	3.81949	+	0.926598i	0.158596	+	0.0384749i
$581$	2.98407	−	31.2506i	0.123800	−	1.29649i
$582$	16.5545	−	2.23701i	0.686207	−	0.0927269i
$583$	17.8742	−	14.0565i	0.740275	−	0.582159i
$584$	0.667022	−	2.27167i	0.0276016	−	0.0940024i
$585$	−42.4733	−	13.2581i	−1.75605	−	0.548154i
$586$	−21.8035	+	33.9270i	−0.900696	+	1.40151i
$587$	21.8920	+	1.04284i	0.903578	+	0.0430427i	0.494226	−	0.869334i	$-0.335452\pi$
$587$	21.8920	+	1.04284i	0.903578	+	0.0430427i	0.409352	+	0.912376i	$0.365755\pi$
$588$	38.7176	+	9.74131i	1.59669	+	0.401725i
$589$	6.95234	+	7.29140i	0.286466	+	0.300437i
$590$	−0.248330	−	0.0994164i	−0.0102236	−	0.00409291i
$591$	−22.0498	+	17.0394i	−0.907008	+	0.700908i
$592$	−4.26668	−	3.03829i	−0.175359	−	0.124873i
$593$	−4.31911	−	14.7095i	−0.177364	−	0.604048i	−0.999401	−	0.0346128i	$-0.988980\pi$
$593$	−4.31911	−	14.7095i	−0.177364	−	0.604048i	0.822036	−	0.569435i	$-0.192838\pi$
$594$	28.3311	−	13.7046i	1.16244	−	0.562307i
$595$	−13.4277	−	1.93061i	−0.550482	−	0.0791473i
$596$	16.1688	+	8.33560i	0.662300	+	0.341439i
$597$	0.759234	−	13.5233i	0.0310734	−	0.553473i
$598$	−45.7712	−	48.4632i	−1.87172	−	1.98181i
$599$	−24.7456	−	14.2869i	−1.01108	−	0.583746i	−0.0995713	−	0.995030i	$-0.531747\pi$
$599$	−24.7456	−	14.2869i	−1.01108	−	0.583746i	−0.911507	+	0.411284i	$0.865080\pi$
$600$	0.0572661	−	0.0972726i	0.00233788	−	0.00397114i
$601$	37.2952	−	14.9308i	1.52130	−	0.609038i	0.547577	−	0.836755i	$-0.315550\pi$
$601$	37.2952	−	14.9308i	1.52130	−	0.609038i	0.973727	+	0.227717i	$0.0731261\pi$
$602$	−37.5475	−	17.1474i	−1.53032	−	0.698875i
$603$	−3.05792	−	1.11681i	−0.124528	−	0.0454799i
$604$	−6.95078	−	15.2201i	−0.282823	−	0.619296i
$605$	−1.44290	+	4.16899i	−0.0586622	+	0.169493i
$606$	8.30582	+	3.87864i	0.337401	+	0.157559i
$607$	2.10759	−	2.00958i	0.0855444	−	0.0815664i	−0.646101	−	0.763252i	$-0.723601\pi$
$607$	2.10759	−	2.00958i	0.0855444	−	0.0815664i	0.731645	+	0.681686i	$0.238753\pi$
$608$	15.1323	+	43.7219i	0.613696	+	1.77316i
$609$	−5.82788	+	2.60198i	−0.236158	+	0.105438i
$610$	−1.41930	+	29.7947i	−0.0574657	+	1.20635i
$611$	−25.1471	−	21.7901i	−1.01734	−	0.881534i
$612$	−7.41392	+	5.62944i	−0.299690	+	0.227557i
$613$	9.88185	−	1.42079i	0.399124	−	0.0573854i	0.0601696	−	0.998188i	$-0.480836\pi$
$613$	9.88185	−	1.42079i	0.399124	−	0.0573854i	0.338954	+	0.940803i	$0.389927\pi$
$614$	−28.3512	−	9.81243i	−1.14416	−	0.395997i
$615$	34.2947	+	27.4437i	1.38289	+	1.10664i
$616$	0.578912	−	2.38631i	0.0233250	−	0.0961471i
$617$	−11.7109	−	16.4456i	−0.471462	−	0.662076i	0.508546	−	0.861035i	$-0.330183\pi$
$617$	−11.7109	−	16.4456i	−0.471462	−	0.662076i	−0.980008	+	0.198959i	$0.936244\pi$
$618$	−6.65840	+	33.0363i	−0.267840	+	1.32892i
$619$	6.07715	−	11.7880i	0.244261	−	0.473801i	−0.734553	−	0.678552i	$-0.762608\pi$
$619$	6.07715	−	11.7880i	0.244261	−	0.473801i	0.978814	+	0.204751i	$0.0656383\pi$
$620$	−7.95834			−0.319615
$621$	23.7847	−	7.43544i	0.954449	−	0.298374i
$622$	−41.7872			−1.67552
$623$	−12.4476	+	24.1449i	−0.498702	+	0.967347i
$624$	8.93096	−	44.3119i	0.357525	−	1.77390i
$625$	−13.4582	−	18.8994i	−0.538327	−	0.755975i
$626$	−0.772985	+	3.18629i	−0.0308947	+	0.127350i
$627$	23.1854	+	18.5537i	0.925935	+	0.740962i
$628$	20.8735	+	7.22439i	0.832943	+	0.288284i
$629$	2.02042	−	0.290492i	0.0805592	−	0.0115827i
$630$	−6.98051	−	55.1817i	−0.278110	−	2.19849i
$631$	16.6240	+	14.4048i	0.661791	+	0.573445i	0.919651	−	0.392737i	$-0.128472\pi$
$631$	16.6240	+	14.4048i	0.661791	+	0.573445i	−0.257860	+	0.966182i	$0.583017\pi$
$632$	−0.0403977	+	0.848053i	−0.00160694	+	0.0337337i
$633$	17.1483	−	7.65621i	0.681583	−	0.304307i
$634$	11.7880	+	34.0592i	0.468162	+	1.35266i
$635$	−10.2518	+	9.77506i	−0.406830	+	0.387912i
$636$	−24.9873	−	11.6685i	−0.990810	−	0.462686i
$637$	24.7096	−	71.3936i	0.979028	−	2.82872i
$638$	2.18530	+	4.78513i	0.0865167	+	0.189445i
$639$	2.69443	+	15.3799i	0.106590	+	0.608418i
$640$	−3.03546	−	1.38625i	−0.119987	−	0.0547963i
$641$	−7.88641	+	3.15724i	−0.311495	+	0.124704i	−0.522142	−	0.852858i	$-0.674867\pi$
$641$	−7.88641	+	3.15724i	−0.311495	+	0.124704i	0.210648	+	0.977562i	$0.432443\pi$
$642$	−3.41545	+	5.80150i	−0.134797	+	0.228967i
$643$	40.2666	+	23.2480i	1.58796	+	0.916810i	0.993643	+	0.112580i	$0.0359114\pi$
$643$	40.2666	+	23.2480i	1.58796	+	0.916810i	0.594318	+	0.804230i	$0.297422\pi$
$644$	16.0351	−	39.5077i	0.631871	−	1.55682i
$645$	−1.00793	+	17.9531i	−0.0396872	+	0.706901i
$646$	−15.2581	−	7.86611i	−0.600323	−	0.309488i
$647$	20.7578	+	2.98452i	0.816073	+	0.117334i	0.537697	−	0.843138i	$-0.319295\pi$
$647$	20.7578	+	2.98452i	0.816073	+	0.117334i	0.278377	+	0.960472i	$0.410204\pi$
$648$	−1.38270	−	1.05711i	−0.0543176	−	0.0415272i
$649$	−0.0516105	−	0.175769i	−0.00202589	−	0.00689955i
$650$	−3.81553	−	2.71703i	−0.149657	−	0.106571i
$651$	10.2260	−	7.90232i	0.400788	−	0.309716i
$652$	6.69294	+	2.67945i	0.262116	+	0.104935i
$653$	8.84696	+	9.27843i	0.346208	+	0.363093i	0.873698	−	0.486469i	$-0.161715\pi$
$653$	8.84696	+	9.27843i	0.346208	+	0.363093i	−0.527490	+	0.849561i	$0.676867\pi$
$654$	30.7978	+	7.74870i	1.20429	+	0.302998i
$655$	−3.34761	−	0.159467i	−0.130802	−	0.00623087i
$656$	−24.1250	+	37.5392i	−0.941923	+	1.46566i
$657$	27.0072	−	24.8903i	1.05365	−	0.971064i
$658$	11.7188	−	39.9107i	0.456848	−	1.55588i
$659$	22.5945	−	17.7685i	0.880156	−	0.692162i	−0.0721218	−	0.997396i	$-0.522977\pi$
$659$	22.5945	−	17.7685i	0.880156	−	0.692162i	0.952277	+	0.305234i	$0.0987346\pi$
$660$	−23.2459	+	3.14121i	−0.904845	+	0.122271i
$661$	−4.01760	+	42.0742i	−0.156266	+	1.63650i	0.488818	+	0.872386i	$0.337428\pi$
$661$	−4.01760	+	42.0742i	−0.156266	+	1.63650i	−0.645085	+	0.764111i	$0.723178\pi$
$662$	−49.1467	−	11.9228i	−1.91014	−	0.463395i
$663$	9.39753	+	14.8993i	0.364970	+	0.578639i
$664$	0.531836	+	1.32846i	0.0206393	+	0.0515544i
$665$	44.1504	−	28.3737i	1.71208	−	1.10029i
$666$	3.34701	+	7.67074i	0.129694	+	0.297235i
$667$	1.15449	+	4.00218i	0.0447019	+	0.154965i
$668$	−5.91832	+	3.41694i	−0.228987	+	0.132205i
$669$	−24.6409	−	14.5065i	−0.952673	−	0.560856i
$670$	3.72765	+	2.93146i	0.144012	+	0.113252i
$671$	−16.6401	+	11.8493i	−0.642382	+	0.457438i
$672$	57.7930	−	13.5023i	2.22941	−	0.520863i
$673$	−7.28640	+	10.2323i	−0.280870	+	0.394427i	−0.930777	−	0.365587i	$-0.880868\pi$
$673$	−7.28640	+	10.2323i	−0.280870	+	0.394427i	0.649907	+	0.760014i	$0.274808\pi$
$674$	−37.2700	−	43.0119i	−1.43559	−	1.65675i
$675$	1.53824	−	0.836648i	0.0592069	−	0.0322026i
$676$	68.7127	+	20.1759i	2.64280	+	0.775995i
$677$	−50.1811	−	9.67161i	−1.92862	−	0.371710i	−1.00000		0.000667756i	$-0.999787\pi$
$677$	−50.1811	−	9.67161i	−1.92862	−	0.371710i	−0.928616	−	0.371042i	$-0.879000\pi$
$678$	−18.2319	+	25.1488i	−0.700192	+	0.965834i
$679$	17.9714	−	9.26489i	0.689678	−	0.355554i
$680$	0.584356	−	0.202248i	0.0224090	−	0.00775584i
$681$	−0.640263	−	3.48065i	−0.0245349	−	0.133379i
$682$	−6.58457	−	8.37297i	−0.252136	−	0.320617i
$683$	11.2834	−	9.77713i	0.431747	−	0.374111i	−0.411703	−	0.911318i	$-0.635066\pi$
$683$	11.2834	−	9.77713i	0.431747	−	0.374111i	0.843451	+	0.537207i	$0.180520\pi$
$684$	7.41459	−	35.2419i	0.283504	−	1.34751i
$685$	−7.99717	+	2.34818i	−0.305556	+	0.0897193i
$686$	34.1846	−	3.26423i	1.30517	−	0.124629i
$687$	28.5843	−	32.4280i	1.09056	−	1.23720i
$688$	−18.2470	+	0.869210i	−0.695659	+	0.0331383i
$689$	−26.0925	+	45.1935i	−0.994044	+	1.72173i
$690$	−36.2975	−	0.480720i	−1.38182	−	0.0183007i
$691$	17.1247	+	29.6608i	0.651454	+	1.12835i	0.982770	+	0.184831i	$0.0591739\pi$
$691$	17.1247	+	29.6608i	0.651454	+	1.12835i	−0.331316	+	0.943520i	$0.607493\pi$
$692$	21.7279	+	33.8093i	0.825970	+	1.28523i
$693$	26.7505	−	27.1185i	1.01617	−	1.03015i
$694$	0.524288	−	1.14803i	0.0199017	−	0.0435786i
$695$	0.371526	+	0.354249i	0.0140928	+	0.0134374i
$696$	0.181772	−	0.227149i	0.00689005	−	0.00861007i
$697$	−3.29096	−	17.0751i	−0.124654	−	0.646767i
$698$	3.76087	−	9.39419i	0.142351	−	0.355575i
$699$	−1.92331	+	5.40816i	−0.0727464	+	0.204556i
$700$	0.567003	−	2.94189i	0.0214307	−	0.111193i
$701$	−18.1195	−	11.6447i	−0.684365	−	0.439815i	0.151713	−	0.988425i	$-0.451521\pi$
$701$	−18.1195	−	11.6447i	−0.684365	−	0.439815i	−0.836079	+	0.548610i	$0.815157\pi$
$702$	−48.6713	+	53.3630i	−1.83698	+	2.01405i
$703$	−5.17125	+	5.96794i	−0.195037	+	0.225085i
$704$	−6.17059	−	25.4355i	−0.232563	−	0.958637i
$705$	−18.0517	+	1.56931i	−0.679867	+	0.0591036i
$706$	−67.3462	+	12.9799i	−2.53461	+	0.488505i
$707$	11.0449	+	1.05466i	0.415386	+	0.0396645i
$708$	−0.162085	+	0.151943i	−0.00609153	+	0.00571038i
$709$	3.34406	+	35.0206i	0.125589	+	1.31523i	0.810130	+	0.586251i	$0.199397\pi$
$709$	3.34406	+	35.0206i	0.125589	+	1.31523i	−0.684541	+	0.728974i	$0.739997\pi$
$710$	3.23695	−	22.5135i	0.121481	−	0.844916i
$711$	−7.30751	+	10.9574i	−0.274053	+	0.410934i
$712$		−	1.23824i		−	0.0464051i
$713$	−4.18238	−	7.32438i	−0.156631	−	0.274300i
$714$	−12.0620	+	18.4232i	−0.451407	+	0.689472i
$715$	2.11207	+	44.3378i	0.0789869	+	1.65814i
$716$	−0.931408	+	1.18438i	−0.0348084	+	0.0442624i
$717$	−9.44145	+	5.95508i	−0.352597	+	0.222397i
$718$	−0.153442	+	0.160925i	−0.00572641	+	0.00600569i
$719$	30.4403	−	13.9016i	1.13523	−	0.518442i	0.243001	−	0.970026i	$-0.421868\pi$
$719$	30.4403	−	13.9016i	1.13523	−	0.518442i	0.892229	+	0.451584i	$0.149141\pi$
$720$	−13.9362	−	20.2906i	−0.519370	−	0.756186i
$721$	5.80500	+	40.3747i	0.216189	+	1.50363i
$722$	27.1720	−	6.59186i	1.01124	−	0.245324i
$723$	−8.87578	+	35.2775i	−0.330094	+	1.31198i
$724$	−12.7779	−	24.7856i	−0.474886	−	0.921151i
$725$	0.134118	+	0.260152i	0.00498100	+	0.00966179i
$726$	5.14065	+	4.98555i	0.190788	+	0.185031i
$727$	−8.51392	+	2.06545i	−0.315764	+	0.0766034i	−0.390509	−	0.920599i	$-0.627701\pi$
$727$	−8.51392	+	2.06545i	−0.315764	+	0.0766034i	0.0747450	+	0.997203i	$0.476186\pi$
$728$	0.801981	+	5.57790i	0.0297234	+	0.206731i
$729$	−9.95205	−	25.0989i	−0.368594	−	0.929590i
$730$	−48.6662	+	22.2251i	−1.80122	+	0.822588i
$731$	4.91255	−	5.15213i	0.181697	−	0.190559i
$732$	21.9232	+	11.5387i	0.810306	+	0.426481i
$733$	−2.80679	+	3.56912i	−0.103671	+	0.131829i	−0.835120	−	0.550068i	$-0.814602\pi$
$733$	−2.80679	+	3.56912i	−0.103671	+	0.131829i	0.731449	+	0.681896i	$0.238844\pi$
$734$	2.07842	+	43.6314i	0.0767158	+	1.61046i
$735$	−18.5408	−	36.7257i	−0.683887	−	1.35465i
$736$	−3.49831	−	38.5753i	−0.128949	−	1.42190i
$737$			3.24770i			0.119630i
$738$	63.9180	−	31.5910i	2.35285	−	1.16288i
$739$	−1.48672	+	10.3404i	−0.0546898	+	0.380376i	0.944033	+	0.329851i	$0.106999\pi$
$739$	−1.48672	+	10.3404i	−0.0546898	+	0.380376i	−0.998723	+	0.0505249i	$0.983911\pi$
$740$	−0.592948	−	6.20963i	−0.0217972	−	0.228271i
$741$	−65.2225	−	19.7536i	−2.39601	−	0.725667i
$742$	−64.9398	−	6.20100i	−2.38401	−	0.227646i
$743$	−38.1825	+	7.35908i	−1.40078	+	0.269978i	−0.833033	−	0.553224i	$-0.813397\pi$
$743$	−38.1825	+	7.35908i	−1.40078	+	0.269978i	−0.567748	+	0.823202i	$0.692185\pi$
$744$	−0.249254	+	0.533760i	−0.00913809	+	0.0195686i
$745$	−4.41934	−	18.2168i	−0.161912	−	0.667411i
$746$	−6.18582	+	7.13881i	−0.226479	+	0.261371i
$747$	−3.53148	+	21.9156i	−0.129210	+	0.801848i
$748$	7.81248	+	5.02078i	0.285653	+	0.183578i
$749$	−1.54209	+	8.00114i	−0.0563469	+	0.292355i
$750$	−39.7302	+	7.30835i	−1.45074	+	0.266863i
$751$	−7.46379	+	18.6437i	−0.272358	+	0.680317i	−0.999984	−	0.00565711i	$-0.998199\pi$
$751$	−7.46379	+	18.6437i	−0.272358	+	0.680317i	0.727626	+	0.685974i	$0.240624\pi$
$752$	−3.48380	−	18.0757i	−0.127041	−	0.659152i
$753$	8.22115	+	21.0513i	0.299595	+	0.767152i
$754$	−8.73729	−	8.33099i	−0.318193	−	0.303397i
$755$	−7.16253	+	15.6838i	−0.260671	+	0.570790i
$756$	−43.9800	−	14.1390i	−1.59954	−	0.514230i
$757$	23.4904	+	36.5518i	0.853774	+	1.32850i	0.943104	+	0.332497i	$0.107891\pi$
$757$	23.4904	+	36.5518i	0.853774	+	1.32850i	−0.0893298	+	0.996002i	$0.528473\pi$
$758$	−2.42355	−	4.19770i	−0.0880271	−	0.152467i
$759$	−15.1075	−	19.7433i	−0.548367	−	0.716637i
$760$	−1.19613	+	2.07176i	−0.0433881	+	0.0751505i
$761$	28.5600	−	1.36048i	1.03530	−	0.0493174i	0.476956	−	0.878927i	$-0.341740\pi$
$761$	28.5600	−	1.36048i	1.03530	−	0.0493174i	0.558343	+	0.829610i	$0.311437\pi$
$762$	7.33582	+	21.7919i	0.265749	+	0.789436i
$763$	38.2641	−	3.65377i	1.38525	−	0.132276i
$764$	0.754670	−	0.221591i	0.0273030	−	0.00801689i
$765$	9.38706	+	1.97496i	0.339390	+	0.0714047i
$766$	−28.1968	+	24.4326i	−1.01879	+	0.882787i
$767$	0.259879	+	0.330463i	0.00938368	+	0.0119323i
$768$	18.9390	−	16.1315i	0.683404	−	0.582095i
$769$	27.4499	−	9.50051i	0.989870	−	0.342597i	0.216313	−	0.976324i	$-0.430597\pi$
$769$	27.4499	−	9.50051i	0.989870	−	0.342597i	0.773557	+	0.633727i	$0.218476\pi$
$770$	−49.3201	+	25.4263i	−1.77737	+	0.916299i
$771$	2.39644	+	5.36751i	0.0863056	+	0.193306i
$772$	25.5191	+	4.91840i	0.918451	+	0.177017i
$773$	22.6223	+	6.64249i	0.813666	+	0.238914i	0.661986	−	0.749516i	$-0.269714\pi$
$773$	22.6223	+	6.64249i	0.813666	+	0.238914i	0.151680	+	0.988430i	$0.451532\pi$
$774$	25.7128	+	13.8130i	0.924226	+	0.496498i
$775$	−0.388109	−	0.447902i	−0.0139413	−	0.0160891i
$776$	−0.534603	+	0.750745i	−0.0191911	+	0.0269502i
$777$	6.92783	+	7.39023i	0.248534	+	0.265123i
$778$	37.1984	−	26.4889i	1.33363	−	0.949673i
$779$	52.8809	+	41.5860i	1.89465	+	1.48997i
$780$	46.8470	−	26.5198i	1.67739	−	0.949561i
$781$	13.4899	−	7.78839i	0.482706	−	0.278690i
$782$	10.8163	+	9.46289i	0.386790	+	0.338392i
$783$	4.23111	−	1.57017i	0.151208	−	0.0561133i
$784$	35.1607	−	22.5964i	1.25574	−	0.807015i
$785$	−8.45950	−	21.1308i	−0.301933	−	0.754191i
$786$	−2.53376	+	4.81408i	−0.0903761	+	0.171713i
$787$	33.5232	+	8.13264i	1.19497	+	0.289897i	0.783422	−	0.621490i	$-0.213472\pi$
$787$	33.5232	+	8.13264i	1.19497	+	0.289897i	0.411551	+	0.911387i	$0.364987\pi$
$788$	3.20479	−	33.5621i	0.114166	−	1.19560i
$789$	0.121029	−	0.295036i	0.00430874	−	0.0105036i
$790$	15.0808	−	11.8597i	0.536552	−	0.421949i
$791$	−10.5921	+	36.0735i	−0.376613	+	1.28263i
$792$	−0.517379	+	1.65747i	−0.0183843	+	0.0588955i
$793$	25.3455	−	39.4384i	0.900047	−	1.40050i
$794$	65.4880	+	3.11958i	2.32408	+	0.110710i
$795$	7.77457	+	27.3335i	0.275735	+	0.969418i
$796$	11.3085	+	11.8600i	0.400820	+	0.420367i
$797$	33.8819	+	13.5643i	1.20016	+	0.480471i	0.883664	−	0.468123i	$-0.155069\pi$
$797$	33.8819	+	13.5643i	1.20016	+	0.480471i	0.316496	+	0.948594i	$0.397494\pi$
$798$	−11.4081	−	84.4232i	−0.403841	−	2.98855i
$799$	5.84348	+	4.16112i	0.206727	+	0.147210i
$800$	−0.766791	−	2.61145i	−0.0271101	−	0.0923287i
$801$	9.88514	−	16.4698i	0.349274	−	0.581930i
$802$	−68.9330	−	9.91107i	−2.43411	−	0.349972i
$803$	−32.5668	−	16.7893i	−1.14926	−	0.592483i
$804$	3.51606	−	1.77506i	0.124002	−	0.0626015i
$805$	−41.5882	+	14.1725i	−1.46579	+	0.499516i
$806$	21.1703	+	12.2227i	0.745693	+	0.430526i
$807$	−16.1734	−	28.5702i	−0.569331	−	1.00572i
$808$	−0.469519	+	0.187967i	−0.0165176	+	0.00661266i
$809$	−6.95283	−	3.17525i	−0.244448	−	0.111636i	0.289424	−	0.957201i	$-0.406536\pi$
$809$	−6.95283	−	3.17525i	−0.244448	−	0.111636i	−0.533872	+	0.845565i	$0.679264\pi$
$810$	2.40809	+	39.2570i	0.0846115	+	1.37935i
$811$	−21.7655	−	47.6598i	−0.764290	−	1.67356i	−0.738836	−	0.673886i	$-0.764624\pi$
$811$	−21.7655	−	47.6598i	−0.764290	−	1.67356i	−0.0254543	−	0.999676i	$-0.508103\pi$
$812$	2.52557	−	7.29715i	0.0886300	−	0.256080i
$813$	3.18908	+	36.6838i	0.111846	+	1.28656i
$814$	6.04256	−	5.76157i	0.211792	−	0.201943i
$815$	−2.42978	−	7.02040i	−0.0851117	−	0.245914i
$816$	−1.00862	+	9.69298i	−0.0353087	+	0.339322i
$817$	−1.31043	+	27.5092i	−0.0458460	+	0.962427i
$818$	−14.0943	−	12.2127i	−0.492794	−	0.427009i
$819$	−33.8625	+	80.5936i	−1.18325	+	2.81617i
$820$	−52.6010	+	7.56288i	−1.83691	+	0.264107i
$821$	−11.4733	−	3.97094i	−0.400420	−	0.138587i	0.119433	−	0.992842i	$-0.461892\pi$
$821$	−11.4733	−	3.97094i	−0.400420	−	0.138587i	−0.519853	+	0.854256i	$0.674013\pi$
$822$	−2.03897	+	13.3749i	−0.0711174	+	0.466502i
$823$	6.95733	−	28.6785i	0.242517	−	0.999670i	−0.712158	−	0.702019i	$-0.752282\pi$
$823$	6.95733	−	28.6785i	0.242517	−	0.999670i	0.954675	−	0.297650i	$-0.0962029\pi$
$824$	−1.07851	−	1.51455i	−0.0375716	−	0.0527619i
$825$	−1.31044	−	1.15511i	−0.0456235	−	0.0402157i
$826$	−0.240817	+	0.467120i	−0.00837910	+	0.0162532i
$827$	10.8575			0.377552			0.188776	−	0.982020i	$-0.439548\pi$
$827$	10.8575			0.377552			0.188776	+	0.982020i	$0.439548\pi$
$828$	−13.1176	+	27.1467i	−0.455867	+	0.943413i
$829$	−10.9194			−0.379248			−0.189624	−	0.981857i	$-0.560727\pi$
$829$	−10.9194			−0.379248			−0.189624	+	0.981857i	$0.560727\pi$
$830$	14.8173	−	28.7415i	0.514314	−	0.997631i
$831$	−13.5408	+	4.55825i	−0.469725	+	0.158124i
$832$	34.8416	+	48.9282i	1.20792	+	1.69628i
$833$	−3.83994	+	15.8284i	−0.133046	+	0.548423i
$834$	0.776195	−	0.303127i	0.0268774	−	0.0104964i
$835$	6.65477	+	2.30324i	0.230298	+	0.0797068i
$836$	−35.5616	+	5.11299i	−1.22992	+	0.176836i
$837$	−7.57642	+	5.10965i	−0.261880	+	0.176615i
$838$	30.7326	+	26.6300i	1.06164	+	0.919917i
$839$	−0.983660	+	20.6496i	−0.0339597	+	0.712902i	0.916122	+	0.400900i	$0.131303\pi$
$839$	−0.983660	+	20.6496i	−0.0339597	+	0.712902i	−0.950081	+	0.312002i	$0.899000\pi$
$840$	2.48451	+	1.80117i	0.0857238	+	0.0621463i
$841$	−9.23824	−	26.6922i	−0.318560	−	0.920419i
$842$	−13.4378	+	12.8129i	−0.463096	+	0.441561i
$843$	−29.8223	+	20.8573i	−1.02713	+	0.718365i
$844$	−7.43137	+	21.4715i	−0.255798	+	0.739080i
$845$	−30.6557	−	67.1265i	−1.05459	−	2.30922i
$846$	−10.0902	+	27.6280i	−0.346909	+	0.949869i
$847$	7.88428	+	3.60063i	0.270907	+	0.123719i
$848$	−26.8021	+	10.7299i	−0.920389	+	0.368468i
$849$	−57.3877	−	0.486874i	−1.96954	−	0.0167095i
$850$	0.874547	+	0.504920i	0.0299967	+	0.0173186i
$851$	5.40336	−	3.80909i	0.185225	−	0.130574i
$852$	−15.8050	−	10.3477i	−0.541469	−	0.354508i
$853$	−21.2965	−	10.9791i	−0.729180	−	0.375918i	0.0533132	−	0.998578i	$-0.483022\pi$
$853$	−21.2965	−	10.9791i	−0.729180	−	0.375918i	−0.782493	+	0.622660i	$0.786052\pi$
$854$	58.0078	+	8.34026i	1.98499	+	0.285398i
$855$	−32.4489	+	18.0073i	−1.10973	+	0.615837i
$856$	−0.104643	−	0.356381i	−0.00357662	−	0.0121808i
$857$	0.580777	+	0.413569i	0.0198390	+	0.0141273i	0.589933	−	0.807452i	$-0.299154\pi$
$857$	0.580777	+	0.413569i	0.0198390	+	0.0141273i	−0.570094	+	0.821579i	$0.693093\pi$
$858$	66.6618	+	27.3458i	2.27580	+	0.933570i
$859$	−26.5061	−	10.6114i	−0.904375	−	0.362057i	−0.127593	−	0.991827i	$-0.540725\pi$
$859$	−26.5061	−	10.6114i	−0.904375	−	0.362057i	−0.776782	+	0.629769i	$0.783149\pi$
$860$	−15.0127	−	15.7449i	−0.511930	−	0.536897i
$861$	60.0794	−	61.9486i	2.04750	−	2.11120i
$862$	68.7706	+	3.27595i	2.34234	+	0.111579i
$863$	28.0881	−	43.7059i	0.956130	−	1.48777i	0.0851979	−	0.996364i	$-0.472848\pi$
$863$	28.0881	−	43.7059i	0.956130	−	1.48777i	0.870932	−	0.491403i	$-0.163516\pi$
$864$	−41.3972	+	6.89101i	−1.40836	+	0.234437i
$865$	11.6675	−	39.7360i	0.396708	−	1.35106i
$866$	−27.8609	+	21.9100i	−0.946750	+	0.744533i
$867$	15.6824	+	20.2938i	0.532603	+	0.689214i
$868$	−1.48628	+	15.5650i	−0.0504476	+	0.528311i
$869$	12.7687	+	3.09766i	0.433149	+	0.105081i
$870$	−6.56913	+	0.257090i	−0.222714	+	0.00871618i
$871$	−2.77009	−	6.91935i	−0.0938609	−	0.234453i
$872$	−1.47397	+	0.947265i	−0.0499150	+	0.0320784i
$873$	−13.1041	+	5.71775i	−0.443505	+	0.193517i
$874$	−55.5979	−	0.264615i	−1.88063	−	0.00895072i
$875$	−42.3439	+	24.4473i	−1.43149	+	0.826469i
$876$	−0.376977	+	44.4341i	−0.0127369	+	1.50129i
$877$	−12.0407	−	9.46888i	−0.406584	−	0.319741i	0.393836	−	0.919181i	$-0.371148\pi$
$877$	−12.0407	−	9.46888i	−0.406584	−	0.319741i	−0.800420	+	0.599439i	$0.795390\pi$
$878$	20.2761	−	14.4385i	0.684284	−	0.487277i
$879$	10.0049	−	33.0343i	0.337458	−	1.11422i
$880$	−14.2443	+	20.0033i	−0.480174	+	0.674311i
$881$	33.3778	+	38.5200i	1.12453	+	1.29777i	0.949696	+	0.313173i	$0.101392\pi$
$881$	33.3778	+	38.5200i	1.12453	+	1.29777i	0.174830	+	0.984599i	$0.444062\pi$
$882$	−66.7498	+	2.04535i	−2.24758	+	0.0688704i
$883$	−38.3402	−	11.2577i	−1.29025	−	0.378851i	−0.436580	−	0.899666i	$-0.643810\pi$
$883$	−38.3402	−	11.2577i	−1.29025	−	0.378851i	−0.853670	+	0.520814i	$0.825628\pi$
$884$	−20.9272	−	4.03339i	−0.703858	−	0.135658i
$885$	0.227706	+	0.0236944i	0.00765426	+	0.000796477i
$886$	61.0172	−	31.4566i	2.04991	−	1.05680i
$887$	29.4254	−	10.1842i	0.988007	−	0.341953i	0.215184	−	0.976574i	$-0.430965\pi$
$887$	29.4254	−	10.1842i	0.988007	−	0.341953i	0.772824	+	0.634621i	$0.218844\pi$
$888$	−0.435046	−	0.154716i	−0.0145992	−	0.00519193i
$889$	17.2036	+	21.8761i	0.576989	+	0.733702i
$890$	−21.1466	+	18.3237i	−0.708837	+	0.614211i
$891$	−20.1135	+	17.9155i	−0.673828	+	0.600191i
$892$	33.1937	−	9.74655i	1.11141	−	0.326339i
$893$	−27.6269	+	2.63805i	−0.924498	+	0.0882788i
$894$	−29.8282	−	6.01181i	−0.997605	−	0.201065i
$895$	1.55089	−	0.0738780i	0.0518405	−	0.00246947i
$896$	−3.27813	+	5.67790i	−0.109515	+	0.189685i
$897$	49.0269	+	29.1781i	1.63696	+	0.974229i
$898$	−2.04992	−	3.55056i	−0.0684067	−	0.118484i
$899$	−0.825825	−	1.28501i	−0.0275428	−	0.0428574i
$900$	−0.534325	+	2.05005i	−0.0178108	+	0.0683351i
$901$	4.67365	−	10.2339i	0.155702	−	0.340940i
$902$	−51.4779	−	49.0841i	−1.71403	−	1.63432i
$903$	34.9245	+	5.32418i	1.16222	+	0.177178i
$904$	−0.324329	−	1.68278i	−0.0107870	−	0.0559685i
$905$	−10.6797	+	26.6767i	−0.355006	+	0.886763i
$906$	18.1480	+	21.3065i	0.602927	+	0.707860i
$907$	−10.0156	+	51.9660i	−0.332563	+	1.72550i	0.302595	+	0.953119i	$0.402147\pi$
$907$	−10.0156	+	51.9660i	−0.332563	+	1.72550i	−0.635158	+	0.772382i	$0.719065\pi$
$908$	3.60207	+	2.31491i	0.119539	+	0.0768230i
$909$	−7.74562	−	1.24813i	−0.256906	−	0.0413980i
$910$	83.3914	−	96.2388i	2.76440	−	3.19028i
$911$	−2.34630	−	9.67158i	−0.0777364	−	0.320434i	0.919645	−	0.392750i	$-0.128476\pi$
$911$	−2.34630	−	9.67158i	−0.0777364	−	0.320434i	−0.997382	+	0.0723159i	$0.976961\pi$
$912$	−21.6077	−	30.8951i	−0.715502	−	1.02304i
$913$	21.7450	−	4.19100i	0.719654	−	0.138702i
$914$	−68.8426	−	6.57367i	−2.27711	−	0.217438i
$915$	−5.80802	−	24.8596i	−0.192007	−	0.821834i
$916$	4.97143	+	52.0632i	0.164261	+	1.72022i
$917$	−0.937078	+	6.51752i	−0.0309450	+	0.215227i
$918$	9.35197	−	12.4499i	0.308661	−	0.410907i
$919$		−	35.8737i		−	1.18336i	−0.806172	−	0.591682i	$-0.798464\pi$
$919$		−	35.8737i		−	1.18336i	0.806172	−	0.591682i	$-0.201536\pi$
$920$	1.38895	−	1.44287i	0.0457922	−	0.0475701i
$921$	25.6365	+	1.43930i	0.844752	+	0.0474265i
$922$	−3.53996	−	74.3128i	−0.116582	−	2.44736i
$923$	−22.0977	+	28.0995i	−0.727355	+	0.924907i
$924$	1.80227	+	46.0512i	0.0592902	+	1.51497i
$925$	0.320566	−	0.336200i	0.0105402	−	0.0110542i
$926$	−49.5075	+	22.6093i	−1.62692	+	0.742988i
$927$	−2.25416	−	28.7549i	−0.0740364	−	0.944435i
$928$	−0.998307	−	6.94338i	−0.0327710	−	0.227927i
$929$	−41.4490	+	10.0554i	−1.35990	+	0.329907i	−0.848390	−	0.529372i	$-0.822428\pi$
$929$	−41.4490	+	10.0554i	−1.35990	+	0.329907i	−0.511507	+	0.859279i	$0.670912\pi$
$930$	12.8040	−	3.64190i	0.419860	−	0.119423i
$931$	−28.8735	−	56.0067i	−0.946290	−	1.83555i
$932$	−3.18222	−	6.17264i	−0.104237	−	0.202192i
$933$	34.3997	−	9.78443i	1.12619	−	0.320328i
$934$	−78.6280	+	19.0750i	−2.57279	+	0.624152i
$935$	−1.36190	−	9.47223i	−0.0445389	−	0.309775i
$936$	−0.311420	−	3.97259i	−0.0101791	−	0.129848i
$937$	6.75275	−	3.08388i	0.220603	−	0.100746i	−0.302048	−	0.953293i	$-0.597670\pi$
$937$	6.75275	−	3.08388i	0.220603	−	0.100746i	0.522651	+	0.852547i	$0.324943\pi$
$938$	6.42955	−	6.74312i	0.209932	−	0.220171i
$939$	−0.109737	−	2.80398i	−0.00358112	−	0.0915044i
$940$	13.5517	−	17.2324i	0.442007	−	0.562058i
$941$	−1.48430	−	31.1592i	−0.0483867	−	1.01576i	−0.884306	−	0.466908i	$-0.845368\pi$
$941$	−1.48430	−	31.1592i	−0.0483867	−	1.01576i	0.835919	−	0.548853i	$-0.184935\pi$
$942$	−36.8890	−	2.07104i	−1.20191	−	0.0674781i
$943$	−34.6040	−	44.4362i	−1.12686	−	1.44704i
$944$			0.232581i			0.00756987i
$945$	18.6672	+	43.7916i	0.607243	+	1.42454i
$946$	4.14397	−	28.8219i	0.134732	−	0.937082i
$947$	−3.44419	−	36.0692i	−0.111921	−	1.17209i	−0.860644	−	0.509208i	$-0.829938\pi$
$947$	−3.44419	−	36.0692i	−0.111921	−	1.17209i	0.748722	−	0.662884i	$-0.230668\pi$
$948$	−3.62524	−	15.5168i	−0.117742	−	0.503964i
$949$	83.7051	+	7.99287i	2.71718	+	0.259459i
$950$	−3.83615	+	0.739357i	−0.124461	+	0.0239879i
$951$	−17.6789	−	25.2777i	−0.573279	−	0.819687i
$952$	−0.286425	−	1.18066i	−0.00928309	−	0.0382654i
$953$	−2.52669	+	2.91596i	−0.0818475	+	0.0944571i	−0.795196	−	0.606352i	$-0.792632\pi$
$953$	−2.52669	+	2.91596i	−0.0818475	+	0.0944571i	0.713349	+	0.700809i	$0.247178\pi$
$954$	45.5413	+	7.33855i	1.47445	+	0.237594i
$955$	−0.681829	−	0.438185i	−0.0220635	−	0.0141793i
$956$	2.55590	−	13.2613i	0.0826638	−	0.428900i
$957$	−2.91939	−	3.42748i	−0.0943705	−	0.110795i
$958$	3.50471	−	8.75434i	0.113232	−	0.282840i
$959$	3.09907	+	16.0795i	0.100074	+	0.519234i
$960$	32.3357	+	4.92951i	1.04363	+	0.159099i
$961$	−20.1973	−	19.2580i	−0.651524	−	0.621227i
$962$	−7.95964	+	17.4292i	−0.256629	+	0.561940i
$963$	1.45322	−	5.57558i	0.0468292	−	0.179671i
$964$	−23.7944	−	37.0247i	−0.766364	−	1.19249i
$965$	−13.3902	−	23.1926i	−0.431047	−	0.746595i
$966$	−7.71901	+	70.9012i	−0.248355	+	2.28121i
$967$	16.3061	−	28.2430i	0.524368	−	0.908232i	−0.475229	−	0.879862i	$-0.657635\pi$
$967$	16.3061	−	28.2430i	0.524368	−	0.908232i	0.999597	−	0.0283703i	$-0.00903177\pi$
$968$	−0.394643	+	0.0187992i	−0.0126843	+	0.000604228i
$969$	14.4025	+	2.90279i	0.462675	+	0.0932510i
$970$	20.7323	−	1.97970i	0.665675	−	0.0635642i
$971$	24.0840	−	7.07171i	0.772893	−	0.226942i	0.128575	−	0.991700i	$-0.458960\pi$
$971$	24.0840	−	7.07171i	0.772893	−	0.226942i	0.644318	+	0.764758i	$0.277141\pi$
$972$	30.3891	+	11.9836i	0.974730	+	0.384375i
$973$	0.762229	−	0.660475i	0.0244359	−	0.0211739i
$974$	21.9645	+	27.9301i	0.703788	+	0.894939i
$975$	3.77717	+	1.34328i	0.120966	+	0.0430195i
$976$	24.5092	−	8.48271i	0.784520	−	0.271525i
$977$	1.34777	−	0.694824i	0.0431190	−	0.0222294i	−0.436532	−	0.899689i	$-0.643794\pi$
$977$	1.34777	−	0.694824i	0.0431190	−	0.0222294i	0.479651	+	0.877459i	$0.340763\pi$
$978$	−11.9943	−	1.24809i	−0.383536	−	0.0399094i
$979$	−18.8163	−	3.62655i	−0.601373	−	0.115905i
$980$	47.7585	+	14.0232i	1.52559	+	0.447954i
$981$	−27.1674	+	0.832464i	−0.867389	+	0.0265785i
$982$	20.8295	+	24.0385i	0.664695	+	0.767099i
$983$	31.3607	−	44.0400i	1.00025	−	1.40466i	0.0874905	−	0.996165i	$-0.472115\pi$
$983$	31.3607	−	44.0400i	1.00025	−	1.40466i	0.912762	−	0.408492i	$-0.133945\pi$
$984$	−1.14022	+	3.76477i	−0.0363488	+	0.120017i
$985$	−28.2999	+	20.1523i	−0.901710	+	0.642105i
$986$	2.04587	+	1.60889i	0.0651539	+	0.0512376i
$987$	−0.302018	+	35.5988i	−0.00961335	+	1.13312i
$988$	71.4044	−	41.2253i	2.27168	−	1.31155i
$989$	6.60096	−	22.0913i	0.209898	−	0.702463i
$990$	35.9624	−	15.6916i	1.14296	−	0.498712i
$991$	−5.89497	+	3.78847i	−0.187260	+	0.120345i	−0.630912	−	0.775855i	$-0.717319\pi$
$991$	−5.89497	+	3.78847i	−0.187260	+	0.120345i	0.443652	+	0.896199i	$0.353683\pi$
$992$	5.27912	+	13.1866i	0.167612	+	0.418675i
$993$	43.2497	−	1.69263i	1.37249	−	0.0537139i
$994$	−43.4276	−	10.5354i	−1.37744	−	0.334163i
$995$	1.60516	−	16.8100i	0.0508871	−	0.532914i
$996$	−16.4222	−	21.2512i	−0.520358	−	0.673369i
$997$	20.6927	−	16.2729i	0.655344	−	0.515368i	−0.234217	−	0.972184i	$-0.575253\pi$
$997$	20.6927	−	16.2729i	0.655344	−	0.515368i	0.889561	+	0.456816i	$0.151010\pi$
$998$	17.8511	−	60.7953i	0.565067	−	1.92444i
$999$	−4.55139	−	5.53093i	−0.143999	−	0.174991i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.o.a.149.19	yes	440
3.2	odd	2		621.2.s.a.287.4		440
9.2	odd	6	inner	207.2.o.a.11.19	✓	440
9.7	even	3		621.2.s.a.494.4		440
23.21	odd	22	inner	207.2.o.a.113.19	yes	440
69.44	even	22		621.2.s.a.44.4		440
207.182	even	66	inner	207.2.o.a.182.19	yes	440
207.205	odd	66		621.2.s.a.251.4		440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.o.a.11.19	✓	440	9.2	odd	6	inner
207.2.o.a.113.19	yes	440	23.21	odd	22	inner
207.2.o.a.149.19	yes	440	1.1	even	1	trivial
207.2.o.a.182.19	yes	440	207.182	even	66	inner
621.2.s.a.44.4		440	69.44	even	22
621.2.s.a.251.4		440	207.205	odd	66
621.2.s.a.287.4		440	3.2	odd	2
621.2.s.a.494.4		440	9.7	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.o (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.927335 - 1.79878i) q^{2} +(-0.342210 + 1.69791i) q^{3} +(-1.21554 - 1.70699i) q^{4} +(-0.509098 + 2.09853i) q^{5} +(2.73682 + 2.19009i) q^{6} +(4.00925 + 1.38762i) q^{7} +(-0.191421 + 0.0275221i) q^{8} +(-2.76579 - 1.16208i) q^{9} +(3.30269 + 2.86180i) q^{10} +(-0.142404 + 2.98944i) q^{11} +(3.31429 - 1.47973i) q^{12} +(-2.24641 - 6.49058i) q^{13} +(6.21393 - 5.92497i) q^{14} +(-3.38889 - 1.58254i) q^{15} +(1.24278 - 3.59077i) q^{16} +(0.615124 + 1.34693i) q^{17} +(-4.65514 + 3.89740i) q^{18} +(-5.21085 - 2.37972i) q^{19} +(4.20101 - 1.68183i) q^{20} +(-3.72805 + 6.33249i) q^{21} +(5.24528 + 3.02837i) q^{22} +(3.75563 + 2.98249i) q^{23} +(0.0187759 - 0.334433i) q^{24} +(0.299528 + 0.154417i) q^{25} +(-13.7583 - 1.97814i) q^{26} +(2.91958 - 4.29837i) q^{27} +(-2.50477 - 8.53047i) q^{28} +(0.707492 + 0.503803i) q^{29} +(-5.98928 + 4.62833i) q^{30} +(-1.63271 - 0.653639i) q^{31} +(-5.57343 - 5.84525i) q^{32} +(-5.02706 - 1.26480i) q^{33} +(2.99326 + 0.142587i) q^{34} +(-4.95305 + 7.70710i) q^{35} +(1.37827 + 6.13374i) q^{36} +(0.388365 - 1.32265i) q^{37} +(-9.11279 + 7.16638i) q^{38} +(11.7891 - 1.59306i) q^{39} +(0.0396958 - 0.415713i) q^{40} +(-11.4126 - 2.76867i) q^{41} +(7.93360 + 12.5783i) q^{42} +(-1.78680 - 4.46322i) q^{43} +(5.27605 - 3.39071i) q^{44} +(3.84672 - 5.21247i) q^{45} +(8.84758 - 3.98977i) q^{46} +(4.19556 - 2.42231i) q^{47} +(5.67150 + 3.33891i) q^{48} +(8.64625 + 6.79948i) q^{49} +(0.555525 - 0.395588i) q^{50} +(-2.49747 + 0.583490i) q^{51} +(-8.34876 + 11.7242i) q^{52} +(-4.97557 - 5.74212i) q^{53} +(-5.02440 - 9.23773i) q^{54} +(-6.20093 - 1.82076i) q^{55} +(-0.805643 - 0.155275i) q^{56} +(5.82374 - 8.03319i) q^{57} +(1.56231 - 0.805428i) q^{58} +(-0.0578431 + 0.0200197i) q^{59} +(1.41797 + 7.70846i) q^{60} +(4.21931 + 5.36529i) q^{61} +(-2.68982 + 2.33075i) q^{62} +(-9.47621 - 8.49692i) q^{63} +(-8.39109 + 2.46385i) q^{64} +(14.7643 - 1.40982i) q^{65} +(-6.93687 + 7.86967i) q^{66} +(1.08393 - 0.0516340i) q^{67} +(1.55149 - 2.68727i) q^{68} +(-6.34921 + 5.35607i) q^{69} +(9.27024 + 16.0565i) q^{70} +(-2.81387 - 4.37847i) q^{71} +(0.561411 + 0.146326i) q^{72} +(-5.08574 + 11.1362i) q^{73} +(-2.01901 - 1.92513i) q^{74} +(-0.364688 + 0.455728i) q^{75} +(2.27186 + 11.7875i) q^{76} +(-4.71912 + 11.7878i) q^{77} +(8.06693 - 22.6834i) q^{78} +(0.830849 - 4.31085i) q^{79} +(6.90264 + 4.43606i) q^{80} +(6.29914 + 6.42813i) q^{81} +(-15.5636 + 17.9613i) q^{82} +(-1.74448 - 7.19084i) q^{83} +(15.3411 - 1.33366i) q^{84} +(-3.13974 + 0.605135i) q^{85} +(-9.68531 - 0.924835i) q^{86} +(-1.09752 + 1.02885i) q^{87} +(-0.0550165 - 0.576159i) q^{88} +(-0.911221 + 6.33768i) q^{89} +(-5.80889 - 11.7531i) q^{90} -29.1395i q^{91} +(0.525968 - 10.0362i) q^{92} +(1.66855 - 2.54851i) q^{93} +(-0.466507 - 9.79319i) q^{94} +(7.64674 - 9.72362i) q^{95} +(11.8320 - 7.46288i) q^{96} +(3.28873 - 3.44912i) q^{97} +(20.2487 - 9.24729i) q^{98} +(3.86783 - 8.10266i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23}+ \cdots + 242 q^{99}+O(q^{100}) \) 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9 - 44 * q^10 - 33 * q^11 - 22 * q^12 - 9 * q^13 - 33 * q^14 + 3 * q^16 - 39 * q^18 - 44 * q^19 - 33 * q^20 - 55 * q^21 - 27 * q^23 + 52 * q^24 + 11 * q^25 - 79 * q^27 - 44 * q^28 + 27 * q^29 - 66 * q^30 - 3 * q^31 - 33 * q^32 - 11 * q^34 + 23 * q^36 - 44 * q^37 - 33 * q^38 - 40 * q^39 - 77 * q^40 + 9 * q^41 - 22 * q^42 - 11 * q^43 - 36 * q^46 - 120 * q^47 - 56 * q^48 + 35 * q^49 - 3 * q^50 - 22 * q^51 - 38 * q^52 + 42 * q^54 - 44 * q^55 + 165 * q^56 + 11 * q^57 - 10 * q^58 - 9 * q^59 + 88 * q^60 - 11 * q^61 + 33 * q^63 - 22 * q^64 + 198 * q^65 + 33 * q^66 - 11 * q^67 + 3 * q^69 - 70 * q^70 + 14 * q^72 - 36 * q^73 + 231 * q^74 - 13 * q^75 - 11 * q^76 + 39 * q^77 + 3 * q^78 - 11 * q^79 + 172 * q^81 - 10 * q^82 + 66 * q^83 - 110 * q^84 + q^85 - 33 * q^86 - 196 * q^87 - 99 * q^88 + 418 * q^90 + 63 * q^92 - 188 * q^93 - 42 * q^94 - 93 * q^95 - 82 * q^96 + 22 * q^97 + 242 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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