LMFDB - Embedded newform 127.2.i.a.100.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [127,2,Mod(25,127)] 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("127.25"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(127, base_ring=CyclotomicField(42)) chi = DirichletCharacter(H, H._module([16])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	127.i (of order $21$, degree $12$, 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:	$1.01410010567$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$9$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			100.3
Character	$\chi$	$=$	127.100
Dual form			127.2.i.a.47.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.697360 + 0.874462i) q^{2} +(0.0224826 - 0.300009i) q^{3} +(0.166669 + 0.730226i) q^{4} +(0.675634 - 2.96015i) q^{5} +(0.246668 + 0.228874i) q^{6} +(3.35389 + 3.11196i) q^{7} +(-2.77021 - 1.33406i) q^{8} +(2.87699 + 0.433637i) q^{9} +(2.11738 + 2.65510i) q^{10} +(-1.59711 + 4.06938i) q^{11} +(0.222822 - 0.0335849i) q^{12} +(-2.81748 - 2.61424i) q^{13} +(-5.06016 + 0.762696i) q^{14} +(-0.872881 - 0.269248i) q^{15} +(1.74876 - 0.842160i) q^{16} +(2.16593 - 0.668100i) q^{17} +(-2.38550 + 2.21342i) q^{18} +1.78208 q^{19} +2.27418 q^{20} +(1.00902 - 0.936233i) q^{21} +(-2.44475 - 4.23443i) q^{22} +(-1.17123 - 2.98424i) q^{23} +(-0.462513 + 0.801096i) q^{24} +(-3.80114 - 1.83053i) q^{25} +(4.25086 - 0.640713i) q^{26} +(0.395614 - 1.73330i) q^{27} +(-1.71344 + 2.96777i) q^{28} +(-7.90140 - 5.38708i) q^{29} +(0.844159 - 0.575538i) q^{30} +(-3.87298 - 1.19466i) q^{31} +(0.885291 - 3.87871i) q^{32} +(1.18494 + 0.570638i) q^{33} +(-0.926203 + 2.35993i) q^{34} +(11.4779 - 7.82547i) q^{35} +(0.162854 + 2.17313i) q^{36} +(1.67288 + 2.89751i) q^{37} +(-1.24275 + 1.55836i) q^{38} +(-0.847641 + 0.786496i) q^{39} +(-5.82068 + 7.29890i) q^{40} +(-1.93625 + 0.597255i) q^{41} +(0.115050 + 1.53524i) q^{42} +(-8.79161 - 5.99402i) q^{43} +(-3.23775 - 0.488013i) q^{44} +(3.22742 - 8.22334i) q^{45} +(3.42637 + 1.05689i) q^{46} +(0.339189 + 1.48609i) q^{47} +(-0.213339 - 0.543579i) q^{48} +(1.04120 + 13.8939i) q^{49} +(4.25150 - 2.04741i) q^{50} +(-0.151740 - 0.664818i) q^{51} +(1.43940 - 2.49311i) q^{52} +(1.51007 + 0.227606i) q^{53} +(1.23982 + 1.55468i) q^{54} +(10.9669 + 7.47710i) q^{55} +(-5.13944 - 13.0951i) q^{56} +(0.0400656 - 0.534639i) q^{57} +(10.2209 - 3.15274i) q^{58} +(5.62629 + 9.74502i) q^{59} +(0.0511295 - 0.682276i) q^{60} +(-9.89436 + 4.76487i) q^{61} +(3.74554 - 2.55367i) q^{62} +(8.29966 + 10.4074i) q^{63} +(5.19478 + 6.51405i) q^{64} +(-9.64213 + 6.57389i) q^{65} +(-1.32533 + 0.638247i) q^{66} +(0.782148 - 10.4370i) q^{67} +(0.848858 + 1.47027i) q^{68} +(-0.921630 + 0.284285i) q^{69} +(-1.16112 + 15.4941i) q^{70} +(-0.600512 - 1.53008i) q^{71} +(-7.39138 - 5.03936i) q^{72} +(-0.788680 - 0.988974i) q^{73} +(-3.70036 - 0.557740i) q^{74} +(-0.634636 + 1.09922i) q^{75} +(0.297017 + 1.30132i) q^{76} +(-18.0203 + 8.67810i) q^{77} +(-0.0966497 - 1.28970i) q^{78} +(2.49578 + 6.35914i) q^{79} +(-1.31139 - 5.74559i) q^{80} +(7.82958 + 2.41510i) q^{81} +(0.827988 - 2.10968i) q^{82} +(3.17565 + 0.478652i) q^{83} +(0.851834 + 0.580771i) q^{84} +(-0.514300 - 6.86286i) q^{85} +(11.3725 - 3.50794i) q^{86} +(-1.79382 + 2.24938i) q^{87} +(9.85315 - 9.14239i) q^{88} +(3.84232 - 4.81812i) q^{89} +(4.94032 + 8.55689i) q^{90} +(-1.31412 - 17.5358i) q^{91} +(1.98396 - 1.35264i) q^{92} +(-0.445482 + 1.13507i) q^{93} +(-1.53606 - 0.739729i) q^{94} +(1.20403 - 5.27521i) q^{95} +(-1.14375 - 0.352799i) q^{96} +(14.0257 - 9.56258i) q^{97} +(-12.8758 - 8.77856i) q^{98} +(-6.35951 + 11.0150i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 5 q^{2} - 15 q^{3} - 17 q^{4} - 6 q^{5} + 7 q^{6} + 2 q^{7} - 22 q^{8} + 2 q^{9} - 10 q^{10} + 9 q^{12} - 14 q^{13} - 20 q^{14} + 4 q^{15} + 27 q^{16} - 8 q^{17} + 7 q^{18} - 16 q^{19} - 80 q^{20}+ \cdots - 24 q^{99}+O(q^{100}) $ 108 * q - 5 * q^2 - 15 * q^3 - 17 * q^4 - 6 * q^5 + 7 * q^6 + 2 * q^7 - 22 * q^8 + 2 * q^9 - 10 * q^10 + 9 * q^12 - 14 * q^13 - 20 * q^14 + 4 * q^15 + 27 * q^16 - 8 * q^17 + 7 * q^18 - 16 * q^19 - 80 * q^20 - 59 * q^21 - 13 * q^22 - 20 * q^23 + 41 * q^24 - 6 * q^25 - 56 * q^26 - 24 * q^27 - 19 * q^28 + 33 * q^29 + 23 * q^30 - 3 * q^31 + 39 * q^32 - 61 * q^33 + 16 * q^34 - 5 * q^35 + 48 * q^36 - 3 * q^37 + 3 * q^38 + 7 * q^39 - 6 * q^40 - 38 * q^41 + 14 * q^42 - 9 * q^43 + 134 * q^44 - 70 * q^45 - q^46 + 17 * q^47 - 76 * q^48 + 93 * q^49 + 24 * q^50 + 31 * q^51 - 54 * q^52 - 12 * q^53 - 44 * q^54 + 15 * q^55 + 30 * q^56 - 42 * q^57 - 52 * q^58 + 77 * q^59 + 36 * q^60 - 70 * q^61 + 41 * q^62 + 82 * q^63 - 6 * q^64 - 43 * q^65 + 160 * q^66 + 54 * q^67 + 6 * q^68 - 19 * q^69 + 49 * q^70 - 31 * q^71 + 11 * q^72 + 46 * q^73 - 111 * q^74 + 18 * q^75 - 19 * q^76 - 65 * q^77 + 27 * q^78 + 119 * q^79 + 114 * q^80 - 55 * q^81 - 44 * q^82 - 34 * q^83 + 34 * q^84 + 6 * q^85 + 89 * q^86 + 22 * q^87 - 118 * q^88 - 22 * q^89 + 121 * q^90 + 58 * q^91 + 115 * q^92 + 104 * q^93 + 62 * q^94 - 18 * q^95 + 31 * q^96 + 14 * q^97 + 87 * q^98 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/127\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{11}{21}\right)$

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 $

$2$	−0.697360	+	0.874462i	−0.493108	+	0.618338i	−0.964659	−	0.263501i	$-0.915123\pi$
$2$	−0.697360	+	0.874462i	−0.493108	+	0.618338i	0.471551	+	0.881839i	$0.343694\pi$
$3$	0.0224826	−	0.300009i	0.0129803	−	0.173210i	−0.986946	−	0.161053i	$-0.948511\pi$
$3$	0.0224826	−	0.300009i	0.0129803	−	0.173210i	0.999926	−	0.0121574i	$-0.00386992\pi$
$4$	0.166669	+	0.730226i	0.0833347	+	0.365113i
$5$	0.675634	−	2.96015i	0.302153	−	1.32382i	−0.564718	−	0.825284i	$-0.691015\pi$
$5$	0.675634	−	2.96015i	0.302153	−	1.32382i	0.866870	−	0.498534i	$-0.166128\pi$
$6$	0.246668	+	0.228874i	0.100702	+	0.0934376i
$7$	3.35389	+	3.11196i	1.26765	+	1.17621i	0.975539	+	0.219825i	$0.0705487\pi$
$7$	3.35389	+	3.11196i	1.26765	+	1.17621i	0.292113	+	0.956384i	$0.405642\pi$
$8$	−2.77021	−	1.33406i	−0.979418	−	0.471663i
$9$	2.87699	+	0.433637i	0.958998	+	0.144546i
$10$	2.11738	+	2.65510i	0.669573	+	0.839618i
$11$	−1.59711	+	4.06938i	−0.481547	+	1.22696i	0.459345	+	0.888258i	$0.348084\pi$
$11$	−1.59711	+	4.06938i	−0.481547	+	1.22696i	−0.940893	+	0.338705i	$0.890011\pi$
$12$	0.222822	−	0.0335849i	0.0643230	−	0.00969514i
$13$	−2.81748	−	2.61424i	−0.781429	−	0.725060i	0.184791	−	0.982778i	$-0.440839\pi$
$13$	−2.81748	−	2.61424i	−0.781429	−	0.725060i	−0.966220	+	0.257717i	$0.917030\pi$
$14$	−5.06016	+	0.762696i	−1.35238	+	0.203839i
$15$	−0.872881	−	0.269248i	−0.225377	−	0.0695195i
$16$	1.74876	−	0.842160i	0.437191	−	0.210540i
$17$	2.16593	−	0.668100i	0.525315	−	0.162038i	−0.0207444	−	0.999785i	$-0.506604\pi$
$17$	2.16593	−	0.668100i	0.525315	−	0.162038i	0.546059	+	0.837747i	$0.316127\pi$
$18$	−2.38550	+	2.21342i	−0.562267	+	0.521708i
$19$	1.78208			0.408836			0.204418	−	0.978884i	$-0.434470\pi$
$19$	1.78208			0.408836			0.204418	+	0.978884i	$0.434470\pi$
$20$	2.27418			0.508523
$21$	1.00902	−	0.936233i	0.220186	−	0.204303i
$22$	−2.44475	−	4.23443i	−0.521223	−	0.902784i
$23$	−1.17123	−	2.98424i	−0.244218	−	0.622257i	0.755231	−	0.655459i	$-0.227525\pi$
$23$	−1.17123	−	2.98424i	−0.244218	−	0.622257i	−0.999449	+	0.0332022i	$0.989429\pi$
$24$	−0.462513	+	0.801096i	−0.0944100	+	0.163523i
$25$	−3.80114	−	1.83053i	−0.760229	−	0.366107i
$26$	4.25086	−	0.640713i	0.833662	−	0.125654i
$27$	0.395614	−	1.73330i	0.0761359	−	0.333573i
$28$	−1.71344	+	2.96777i	−0.323810	+	0.560855i
$29$	−7.90140	−	5.38708i	−1.46725	−	1.00036i	−0.992762	−	0.120095i	$-0.961680\pi$
$29$	−7.90140	−	5.38708i	−1.46725	−	1.00036i	−0.474490	−	0.880261i	$-0.657368\pi$
$30$	0.844159	−	0.575538i	0.154122	−	0.105078i
$31$	−3.87298	−	1.19466i	−0.695608	−	0.214567i	−0.0732661	−	0.997312i	$-0.523342\pi$
$31$	−3.87298	−	1.19466i	−0.695608	−	0.214567i	−0.622341	+	0.782746i	$0.713818\pi$
$32$	0.885291	−	3.87871i	0.156499	−	0.685666i
$33$	1.18494	+	0.570638i	0.206272	+	0.0993353i
$34$	−0.926203	+	2.35993i	−0.158843	+	0.404724i
$35$	11.4779	−	7.82547i	1.94011	−	1.32275i
$36$	0.162854	+	2.17313i	0.0271423	+	0.362188i
$37$	1.67288	+	2.89751i	0.275020	+	0.476348i	0.970140	−	0.242545i	$-0.0779823\pi$
$37$	1.67288	+	2.89751i	0.275020	+	0.476348i	−0.695120	+	0.718893i	$0.744649\pi$
$38$	−1.24275	+	1.55836i	−0.201600	+	0.252799i
$39$	−0.847641	+	0.786496i	−0.135731	+	0.125940i
$40$	−5.82068	+	7.29890i	−0.920330	+	1.15406i
$41$	−1.93625	+	0.597255i	−0.302392	+	0.0932755i	−0.442238	−	0.896898i	$-0.645815\pi$
$41$	−1.93625	+	0.597255i	−0.302392	+	0.0932755i	0.139846	+	0.990173i	$0.455339\pi$
$42$	0.115050	+	1.53524i	0.0177527	+	0.236893i
$43$	−8.79161	−	5.99402i	−1.34071	−	0.914080i	−0.341046	−	0.940047i	$-0.610781\pi$
$43$	−8.79161	−	5.99402i	−1.34071	−	0.914080i	−0.999663	+	0.0259669i	$0.991734\pi$
$44$	−3.23775	−	0.488013i	−0.488110	−	0.0735707i
$45$	3.22742	−	8.22334i	0.481116	−	1.22586i
$46$	3.42637	+	1.05689i	0.505191	+	0.155831i
$47$	0.339189	+	1.48609i	0.0494759	+	0.216768i	0.993623	−	0.112758i	$-0.0359684\pi$
$47$	0.339189	+	1.48609i	0.0494759	+	0.216768i	−0.944147	+	0.329526i	$0.893111\pi$
$48$	−0.213339	−	0.543579i	−0.0307928	−	0.0784588i
$49$	1.04120	+	13.8939i	0.148744	+	1.98484i
$50$	4.25150	−	2.04741i	0.601253	−	0.289548i
$51$	−0.151740	−	0.664818i	−0.0212479	−	0.0930932i
$52$	1.43940	−	2.49311i	0.199609	−	0.345733i
$53$	1.51007	+	0.227606i	0.207424	+	0.0312641i	0.251932	−	0.967745i	$-0.418934\pi$
$53$	1.51007	+	0.227606i	0.207424	+	0.0312641i	−0.0445082	+	0.999009i	$0.514172\pi$
$54$	1.23982	+	1.55468i	0.168718	+	0.211565i
$55$	10.9669	+	7.47710i	1.47877	+	1.00821i
$56$	−5.13944	−	13.0951i	−0.686787	−	1.74990i
$57$	0.0400656	−	0.534639i	0.00530682	−	0.0708146i
$58$	10.2209	−	3.15274i	1.34207	−	0.413974i
$59$	5.62629	+	9.74502i	0.732480	+	1.26869i	0.955820	+	0.293953i	$0.0949708\pi$
$59$	5.62629	+	9.74502i	0.732480	+	1.26869i	−0.223340	+	0.974741i	$0.571696\pi$
$60$	0.0511295	−	0.682276i	0.00660079	−	0.0880814i
$61$	−9.89436	+	4.76487i	−1.26684	+	0.610079i	−0.941976	−	0.335680i	$-0.891034\pi$
$61$	−9.89436	+	4.76487i	−1.26684	+	0.610079i	−0.324867	+	0.945760i	$0.605319\pi$
$62$	3.74554	−	2.55367i	0.475684	−	0.324316i
$63$	8.29966	+	10.4074i	1.04566	+	1.31122i
$64$	5.19478	+	6.51405i	0.649348	+	0.814257i
$65$	−9.64213	+	6.57389i	−1.19596	+	0.815391i
$66$	−1.32533	+	0.638247i	−0.163137	+	0.0785627i
$67$	0.782148	−	10.4370i	0.0955545	−	1.27509i	−0.719004	−	0.695006i	$-0.755402\pi$
$67$	0.782148	−	10.4370i	0.0955545	−	1.27509i	0.814559	−	0.580081i	$-0.196979\pi$
$68$	0.848858	+	1.47027i	0.102939	+	0.178296i
$69$	−0.921630	+	0.284285i	−0.110951	+	0.0342239i
$70$	−1.16112	+	15.4941i	−0.138781	+	1.85190i
$71$	−0.600512	−	1.53008i	−0.0712677	−	0.181587i	0.890802	−	0.454393i	$-0.150144\pi$
$71$	−0.600512	−	1.53008i	−0.0712677	−	0.181587i	−0.962069	+	0.272806i	$0.912048\pi$
$72$	−7.39138	−	5.03936i	−0.871083	−	0.593894i
$73$	−0.788680	−	0.988974i	−0.0923080	−	0.115751i	0.733532	−	0.679654i	$-0.237870\pi$
$73$	−0.788680	−	0.988974i	−0.0923080	−	0.115751i	−0.825840	+	0.563904i	$0.809299\pi$
$74$	−3.70036	−	0.557740i	−0.430158	−	0.0648360i
$75$	−0.634636	+	1.09922i	−0.0732815	+	0.126927i
$76$	0.297017	+	1.30132i	0.0340702	+	0.149271i
$77$	−18.0203	+	8.67810i	−2.05360	+	0.988961i
$78$	−0.0966497	−	1.28970i	−0.0109434	−	0.146030i
$79$	2.49578	+	6.35914i	0.280797	+	0.715460i	0.999791	+	0.0204431i	$0.00650770\pi$
$79$	2.49578	+	6.35914i	0.280797	+	0.715460i	−0.718994	+	0.695016i	$0.755397\pi$
$80$	−1.31139	−	5.74559i	−0.146618	−	0.642376i
$81$	7.82958	+	2.41510i	0.869953	+	0.268345i
$82$	0.827988	−	2.10968i	0.0914360	−	0.232975i
$83$	3.17565	+	0.478652i	0.348573	+	0.0525389i	0.320995	−	0.947081i	$-0.395983\pi$
$83$	3.17565	+	0.478652i	0.348573	+	0.0525389i	0.0275775	+	0.999620i	$0.491221\pi$
$84$	0.851834	+	0.580771i	0.0929428	+	0.0633673i
$85$	−0.514300	−	6.86286i	−0.0557837	−	0.744381i
$86$	11.3725	−	3.50794i	1.22632	−	0.378271i
$87$	−1.79382	+	2.24938i	−0.192317	+	0.241158i
$88$	9.85315	−	9.14239i	1.05035	−	0.974582i
$89$	3.84232	−	4.81812i	0.407286	−	0.510720i	−0.535310	−	0.844655i	$-0.679805\pi$
$89$	3.84232	−	4.81812i	0.407286	−	0.510720i	0.942596	+	0.333935i	$0.108377\pi$
$90$	4.94032	+	8.55689i	0.520756	+	0.901975i
$91$	−1.31412	−	17.5358i	−0.137758	−	1.83825i
$92$	1.98396	−	1.35264i	0.206842	−	0.141023i
$93$	−0.445482	+	1.13507i	−0.0461943	+	0.117701i
$94$	−1.53606	−	0.739729i	−0.158433	−	0.0762972i
$95$	1.20403	−	5.27521i	0.123531	−	0.541225i
$96$	−1.14375	−	0.352799i	−0.116733	−	0.0360074i
$97$	14.0257	−	9.56258i	1.42410	−	0.970933i	0.426301	−	0.904581i	$-0.359816\pi$
$97$	14.0257	−	9.56258i	1.42410	−	0.970933i	0.997796	−	0.0663518i	$-0.0211359\pi$
$98$	−12.8758	−	8.77856i	−1.30065	−	0.886769i
$99$	−6.35951	+	11.0150i	−0.639155	+	1.10705i
$100$	0.703170	−	3.08079i	0.0703170	−	0.308079i
$101$	−2.29319	+	0.345643i	−0.228181	+	0.0343928i	−0.262138	−	0.965031i	$-0.584427\pi$
$101$	−2.29319	+	0.345643i	−0.228181	+	0.0343928i	0.0339563	+	0.999423i	$0.489189\pi$
$102$	0.687176	+	0.330927i	0.0680406	+	0.0327666i
$103$	4.64658	−	8.04811i	0.457841	−	0.793004i	−0.541005	−	0.841019i	$-0.681956\pi$
$103$	4.64658	−	8.04811i	0.457841	−	0.793004i	0.998847	+	0.0480149i	$0.0152895\pi$
$104$	4.31746	+	11.0007i	0.423362	+	1.07871i
$105$	−2.08966	−	3.61940i	−0.203930	−	0.353217i
$106$	−1.25210	+	1.16177i	−0.121614	+	0.112842i
$107$	−6.16595			−0.596085			−0.298042	−	0.954553i	$-0.596334\pi$
$107$	−6.16595			−0.596085			−0.298042	+	0.954553i	$0.596334\pi$
$108$	1.33163			0.128137
$109$	0.105113	−	0.0975308i	0.0100680	−	0.00934176i	−0.675123	−	0.737705i	$-0.735909\pi$
$109$	0.105113	−	0.0975308i	0.0100680	−	0.00934176i	0.685191	+	0.728364i	$0.259719\pi$
$110$	−14.1863	+	4.37590i	−1.35261	+	0.417225i
$111$	0.906890	−	0.436735i	0.0860782	−	0.0414531i
$112$	8.48593	+	2.61756i	0.801845	+	0.247336i
$113$	−18.0532	+	2.72108i	−1.69830	+	0.255977i	−0.925520	−	0.378698i	$-0.876372\pi$
$113$	−18.0532	+	2.72108i	−1.69830	+	0.255977i	−0.772779	+	0.634676i	$0.781134\pi$
$114$	0.439581	+	0.407872i	0.0411705	+	0.0382007i
$115$	−9.62510	+	1.45075i	−0.897546	+	0.135283i
$116$	2.61687	−	6.66767i	0.242970	−	0.619078i
$117$	−6.97225	−	8.74292i	−0.644584	−	0.808283i
$118$	−12.4452	−	1.87581i	−1.14567	−	0.172682i
$119$	9.34339	+	4.49954i	0.856507	+	0.412472i
$120$	2.05887	+	1.91035i	0.187948	+	0.174391i
$121$	−5.94548	−	5.51660i	−0.540498	−	0.501509i
$122$	2.73323	−	11.9751i	0.247455	−	1.08417i
$123$	0.135650	+	0.594321i	0.0122311	+	0.0535881i
$124$	0.226862	−	3.02726i	0.0203728	−	0.271856i
$125$	1.47859	−	1.85409i	0.132249	−	0.165835i
$126$	−14.8888			−1.32640
$127$	−7.47437	+	8.43408i	−0.663243	+	0.748404i
$127$	−7.47437	+	8.43408i	−0.663243	+	0.748404i
$128$	−1.36200			−0.120385
$129$	−1.99592	+	2.50280i	−0.175731	+	0.220359i
$130$	0.975418	−	13.0160i	0.0855498	−	1.14158i
$131$	4.41665	+	19.3506i	0.385884	+	1.69067i	0.678630	+	0.734480i	$0.262574\pi$
$131$	4.41665	+	19.3506i	0.385884	+	1.69067i	−0.292746	+	0.956190i	$0.594569\pi$
$132$	−0.219201	+	0.960384i	−0.0190790	+	0.0835907i
$133$	5.97689	+	5.54574i	0.518262	+	0.480877i
$134$	8.58135	+	7.96233i	0.741316	+	0.687841i
$135$	−4.86352	−	2.34215i	−0.418585	−	0.201580i
$136$	−6.89137	−	1.03871i	−0.590930	−	0.0890684i
$137$	9.27485	+	11.6303i	0.792404	+	0.993643i	0.999881	+	0.0154029i	$0.00490310\pi$
$137$	9.27485	+	11.6303i	0.792404	+	0.993643i	−0.207478	+	0.978240i	$0.566525\pi$
$138$	0.394112	−	1.00418i	0.0335490	−	0.0854815i
$139$	6.62937	−	0.999217i	0.562296	−	0.0847524i	0.138257	−	0.990396i	$-0.455850\pi$
$139$	6.62937	−	0.999217i	0.562296	−	0.0847524i	0.424039	+	0.905644i	$0.360612\pi$
$140$	7.62737	+	7.07716i	0.644630	+	0.598129i
$141$	0.453465	−	0.0683489i	0.0381886	−	0.00575601i
$142$	1.75677	+	0.541892i	0.147425	+	0.0454745i
$143$	15.1382	−	7.29016i	1.26592	−	0.609634i
$144$	5.39637	−	1.66456i	0.449698	−	0.138713i
$145$	−21.2850	+	19.7496i	−1.76762	+	1.64012i
$146$	1.41481			0.117091
$147$	4.19171			0.345726
$148$	−1.83702	+	1.70451i	−0.151002	+	0.140110i
$149$	−1.68276	−	2.91463i	−0.137857	−	0.238775i	0.788828	−	0.614614i	$-0.210688\pi$
$149$	−1.68276	−	2.91463i	−0.137857	−	0.238775i	−0.926685	+	0.375838i	$0.877355\pi$
$150$	−0.518658	−	1.32152i	−0.0423482	−	0.107902i
$151$	4.62405	−	8.00909i	0.376300	−	0.651770i	−0.614221	−	0.789134i	$-0.710530\pi$
$151$	4.62405	−	8.00909i	0.376300	−	0.651770i	0.990521	+	0.137364i	$0.0438630\pi$
$152$	−4.93673	−	2.37740i	−0.400422	−	0.192833i
$153$	6.52107	−	0.982893i	0.527197	−	0.0794622i
$154$	4.97794	−	21.8098i	0.401134	−	1.75748i
$155$	−6.15307	+	10.6574i	−0.494227	+	0.856026i
$156$	−0.715595	−	0.487885i	−0.0572935	−	0.0390620i
$157$	9.56653	−	6.52235i	0.763492	−	0.520540i	−0.117843	−	0.993032i	$-0.537598\pi$
$157$	9.56653	−	6.52235i	0.763492	−	0.520540i	0.881335	+	0.472492i	$0.156645\pi$
$158$	−7.30129	−	2.25215i	−0.580859	−	0.179171i
$159$	0.102234	−	0.447917i	0.00810770	−	0.0355221i
$160$	−10.8834	−	5.24118i	−0.860411	−	0.414352i
$161$	5.35865	−	13.6536i	0.422321	−	1.07606i
$162$	−7.57195	+	5.16247i	−0.594909	+	0.405602i
$163$	0.313822	+	4.18766i	0.0245804	+	0.328003i	0.995916	+	0.0902890i	$0.0287791\pi$
$163$	0.313822	+	4.18766i	0.0245804	+	0.328003i	−0.971335	+	0.237714i	$0.923602\pi$
$164$	−0.758845	−	1.31436i	−0.0592558	−	0.102634i
$165$	2.48976	−	3.12206i	0.193828	−	0.243052i
$166$	−2.63314	+	2.44319i	−0.204371	+	0.189629i
$167$	−2.79026	+	3.49887i	−0.215917	+	0.270751i	−0.877980	−	0.478697i	$-0.841109\pi$
$167$	−2.79026	+	3.49887i	−0.215917	+	0.270751i	0.662064	+	0.749448i	$0.269681\pi$
$168$	−4.04419	+	1.24747i	−0.312016	+	0.0962443i
$169$	0.132457	+	1.76752i	0.0101890	+	0.135963i
$170$	6.35996	+	4.33615i	0.487787	+	0.332567i
$171$	5.12702	+	0.772774i	0.392073	+	0.0590955i
$172$	2.91170	−	7.41889i	0.222015	−	0.565685i
$173$	2.15833	+	0.665758i	0.164095	+	0.0506166i	0.375714	−	0.926736i	$-0.377397\pi$
$173$	2.15833	+	0.665758i	0.164095	+	0.0506166i	−0.211619	+	0.977352i	$0.567874\pi$
$174$	−0.716057	−	3.13725i	−0.0542841	−	0.237834i
$175$	−7.05208	−	17.9684i	−0.533087	−	1.35828i
$176$	0.634094	+	8.46140i	0.0477966	+	0.637802i
$177$	3.05009	−	1.46884i	0.229259	−	0.110405i
$178$	1.53378	+	6.71993i	0.114962	+	0.503680i
$179$	−7.90966	+	13.6999i	−0.591196	+	1.02398i	0.402876	+	0.915255i	$0.368011\pi$
$179$	−7.90966	+	13.6999i	−0.591196	+	1.02398i	−0.994072	+	0.108727i	$0.965323\pi$
$180$	6.54281	+	0.986170i	0.487672	+	0.0735048i
$181$	10.4467	+	13.0997i	0.776496	+	0.973696i	0.999999	−	0.00100745i	$-0.000320681\pi$
$181$	10.4467	+	13.0997i	0.776496	+	0.973696i	−0.223503	+	0.974703i	$0.571749\pi$
$182$	16.2508	+	11.0796i	1.20459	+	0.821274i
$183$	1.20705	+	3.07552i	0.0892280	+	0.227349i
$184$	−0.736617	+	9.82947i	−0.0543041	+	0.724638i
$185$	9.70732	−	2.99431i	0.713696	−	0.220146i
$186$	−0.681914	−	1.18111i	−0.0500003	−	0.0866031i
$187$	−0.740479	+	9.88100i	−0.0541492	+	0.722571i
$188$	−1.02865	+	0.495370i	−0.0750217	+	0.0361286i
$189$	6.72079	−	4.58216i	0.488865	−	0.333303i
$190$	3.77332	+	4.73160i	0.273746	+	0.343266i
$191$	−2.35989	−	2.95920i	−0.170755	−	0.214121i	0.689089	−	0.724677i	$-0.258011\pi$
$191$	−2.35989	−	2.95920i	−0.170755	−	0.214121i	−0.859844	+	0.510556i	$0.829440\pi$
$192$	2.07107	−	1.41203i	0.149466	−	0.101904i
$193$	1.59135	−	0.766353i	0.114548	−	0.0551633i	−0.375732	−	0.926728i	$-0.622609\pi$
$193$	1.59135	−	0.766353i	0.114548	−	0.0551633i	0.490280	+	0.871565i	$0.336895\pi$
$194$	−1.41887	+	18.9335i	−0.101869	+	1.35935i
$195$	1.75545	+	3.04052i	0.125710	+	0.217736i
$196$	−9.97216	+	3.07600i	−0.712297	+	0.219715i
$197$	1.26915	−	16.9356i	0.0904231	−	1.20661i	−0.748789	−	0.662809i	$-0.769364\pi$
$197$	1.26915	−	16.9356i	0.0904231	−	1.20661i	0.839212	−	0.543804i	$-0.183017\pi$
$198$	−5.19733	−	13.2426i	−0.369358	−	0.941108i
$199$	12.9868	+	8.85428i	0.920613	+	0.627663i	0.928109	−	0.372309i	$-0.121434\pi$
$199$	12.9868	+	8.85428i	0.920613	+	0.627663i	−0.00749614	+	0.999972i	$0.502386\pi$
$200$	8.08793	+	10.1419i	0.571903	+	0.717143i
$201$	−3.11362	−	0.469303i	−0.219618	−	0.0331021i
$202$	1.29693	−	2.24635i	0.0912516	−	0.158052i
$203$	−9.73607	−	42.6565i	−0.683338	−	2.99390i
$204$	0.460177	−	0.221610i	0.0322189	−	0.0155158i
$205$	0.459763	+	6.13512i	0.0321113	+	0.428495i
$206$	3.79743	+	9.67569i	0.264579	+	0.674137i
$207$	−2.07554	−	9.09352i	−0.144260	−	0.632043i
$208$	−7.12872	−	2.19892i	−0.494288	−	0.152468i
$209$	−2.84618	+	7.25194i	−0.196874	+	0.501627i
$210$	4.62227	+	0.696695i	0.318967	+	0.0480765i
$211$	19.6174	+	13.3749i	1.35052	+	0.920767i	0.999876	−	0.0157436i	$-0.00501154\pi$
$211$	19.6174	+	13.3749i	1.35052	+	0.920767i	0.350640	+	0.936510i	$0.385964\pi$
$212$	0.0854782	+	1.14063i	0.00587067	+	0.0783386i
$213$	−0.472539	+	0.145759i	−0.0323778	+	0.00998724i
$214$	4.29989	−	5.39189i	0.293934	−	0.368582i
$215$	−23.6831	+	21.9747i	−1.61517	+	1.49866i
$216$	−3.40826	+	4.27383i	−0.231903	+	0.290797i
$217$	−9.27184	−	16.0593i	−0.629413	−	1.09018i
$218$	0.0119852	+	0.159932i	0.000811741	+	0.0108319i
$219$	−0.314433	+	0.214376i	−0.0212474	+	0.0144862i
$220$	−3.63213	+	9.25451i	−0.244878	+	0.623939i
$221$	−7.84904	−	3.77990i	−0.527984	−	0.254264i
$222$	−0.250521	+	1.09760i	−0.0168138	+	0.0736663i
$223$	−8.54961	−	2.63720i	−0.572524	−	0.176600i	−0.00504381	−	0.999987i	$-0.501606\pi$
$223$	−8.54961	−	2.63720i	−0.572524	−	0.176600i	−0.567480	+	0.823387i	$0.692082\pi$
$224$	15.0396	−	10.2538i	1.00487	−	0.685111i
$225$	−10.1421	−	6.91475i	−0.676138	−	0.460983i
$226$	10.2101	−	17.6844i	0.679164	−	1.17635i
$227$	−1.34116	+	5.87601i	−0.0890160	+	0.390004i	−0.999735	−	0.0230221i	$-0.992671\pi$
$227$	−1.34116	+	5.87601i	−0.0890160	+	0.390004i	0.910719	+	0.413027i	$0.135528\pi$
$228$	0.397085	−	0.0598509i	0.0262976	−	0.00396372i
$229$	−25.3548	−	12.2102i	−1.67549	−	0.806874i	−0.997413	−	0.0718827i	$-0.977099\pi$
$229$	−25.3548	−	12.2102i	−1.67549	−	0.806874i	−0.678077	−	0.734991i	$-0.737186\pi$
$230$	5.44354	−	9.42848i	0.358936	−	0.621696i
$231$	2.19837	+	5.60135i	0.144642	+	0.368542i
$232$	14.7018	+	25.4643i	0.965223	+	1.67182i
$233$	5.02293	−	4.66060i	0.329063	−	0.305326i	−0.498288	−	0.867012i	$-0.666038\pi$
$233$	5.02293	−	4.66060i	0.329063	−	0.305326i	0.827350	+	0.561686i	$0.189847\pi$
$234$	12.5075			0.817642
$235$	4.62820			0.301911
$236$	−6.17834	+	5.73266i	−0.402175	+	0.373164i
$237$	1.96391	−	0.605787i	0.127570	−	0.0393501i
$238$	−10.4504	+	5.03264i	−0.677397	+	0.326217i
$239$	−16.7410	−	5.16392i	−1.08289	−	0.334026i	−0.298570	−	0.954388i	$-0.596510\pi$
$239$	−16.7410	−	5.16392i	−1.08289	−	0.334026i	−0.784316	+	0.620362i	$0.786986\pi$
$240$	−1.75321	+	0.264254i	−0.113169	+	0.0170575i
$241$	5.11446	+	4.74553i	0.329451	+	0.305686i	0.827503	−	0.561461i	$-0.189761\pi$
$241$	5.11446	+	4.74553i	0.329451	+	0.305686i	−0.498052	+	0.867147i	$0.665951\pi$
$242$	8.97019	−	1.35204i	0.576626	−	0.0869124i
$243$	2.84917	−	7.25957i	0.182774	−	0.465701i
$244$	−5.12852	−	6.43096i	−0.328320	−	0.411700i
$245$	41.8315	+	6.30508i	2.67252	+	0.402817i
$246$	−0.614308	−	0.295835i	−0.0391668	−	0.0188618i
$247$	−5.02097	−	4.65878i	−0.319477	−	0.296431i
$248$	9.13523	+	8.47625i	0.580088	+	0.538243i
$249$	0.214997	−	0.941962i	0.0136249	−	0.0596944i
$250$	0.590225	+	2.58594i	0.0373291	+	0.163549i
$251$	−0.337416	+	4.50250i	−0.0212975	+	0.284195i	0.976379	+	0.216065i	$0.0693224\pi$
$251$	−0.337416	+	4.50250i	−0.0212975	+	0.284195i	−0.997676	+	0.0681302i	$0.978297\pi$
$252$	−6.21649	+	7.79523i	−0.391602	+	0.491054i
$253$	14.0146			0.881088
$254$	−2.16296	−	12.4176i	−0.135716	−	0.779152i
$255$	−2.07048			−0.129659
$256$	−9.43976	+	11.8371i	−0.589985	+	0.739818i
$257$	−2.04103	+	27.2356i	−0.127316	+	1.69891i	0.458684	+	0.888600i	$0.348321\pi$
$257$	−2.04103	+	27.2356i	−0.127316	+	1.69891i	−0.586000	+	0.810311i	$0.699298\pi$
$258$	−0.796732	−	3.49071i	−0.0496023	−	0.217322i
$259$	−3.40628	+	14.9239i	−0.211656	+	0.927324i
$260$	−6.40748	−	5.94527i	−0.397375	−	0.368710i
$261$	−20.3962	−	18.9249i	−1.26249	−	1.17142i
$262$	−20.0014	−	9.63215i	−1.23569	−	0.595076i
$263$	0.843239	+	0.127098i	0.0519963	+	0.00783718i	0.174989	−	0.984570i	$-0.444011\pi$
$263$	0.843239	+	0.127098i	0.0519963	+	0.00783718i	−0.122993	+	0.992408i	$0.539249\pi$
$264$	−2.52127	−	3.16158i	−0.155174	−	0.194582i
$265$	1.69400	−	4.31625i	0.104062	−	0.265145i
$266$	−9.01759	+	1.35918i	−0.552904	+	0.0833368i
$267$	−1.35910	−	1.26106i	−0.0831753	−	0.0771754i
$268$	7.75176	−	1.16839i	0.473514	−	0.0713707i
$269$	−7.60660	−	2.34633i	−0.463783	−	0.143058i	0.0540531	−	0.998538i	$-0.482786\pi$
$269$	−7.60660	−	2.34633i	−0.463783	−	0.143058i	−0.517836	+	0.855480i	$0.673262\pi$
$270$	5.43975	−	2.61964i	0.331052	−	0.159426i
$271$	11.3701	−	3.50721i	0.690685	−	0.213048i	0.0705092	−	0.997511i	$-0.477538\pi$
$271$	11.3701	−	3.50721i	0.690685	−	0.213048i	0.620175	+	0.784463i	$0.287061\pi$
$272$	3.22505	−	2.99241i	0.195547	−	0.181441i
$273$	−5.29044			−0.320192
$274$	−16.6382			−1.00515
$275$	13.5200	−	12.5447i	0.815286	−	0.756475i
$276$	−0.361200	−	0.625617i	−0.0217417	−	0.0376577i
$277$	1.81812	+	4.63250i	0.109240	+	0.278340i	0.975032	−	0.222065i	$-0.0712798\pi$
$277$	1.81812	+	4.63250i	0.109240	+	0.278340i	−0.865792	+	0.500405i	$0.833185\pi$
$278$	−3.74928	+	6.49394i	−0.224867	+	0.389481i
$279$	−10.6245	−	5.11648i	−0.636071	−	0.306316i
$280$	−42.2358	+	6.36602i	−2.52407	+	0.380442i
$281$	−0.175453	+	0.768711i	−0.0104667	+	0.0458575i	−0.979892	−	0.199531i	$-0.936058\pi$
$281$	−0.175453	+	0.768711i	−0.0104667	+	0.0458575i	0.969425	+	0.245388i	$0.0789154\pi$
$282$	−0.256460	+	0.444202i	−0.0152720	+	0.0264518i
$283$	1.72943	+	1.17911i	0.102804	+	0.0700906i	0.613631	−	0.789593i	$-0.289708\pi$
$283$	1.72943	+	1.17911i	0.102804	+	0.0700906i	−0.510827	+	0.859684i	$0.670661\pi$
$284$	1.01722	−	0.693527i	0.0603608	−	0.0411533i
$285$	−1.55554	−	0.479820i	−0.0921422	−	0.0284221i
$286$	−4.18179	+	18.3216i	−0.247274	+	1.08338i
$287$	−8.35261	−	4.02241i	−0.493039	−	0.237435i
$288$	4.22893	−	10.7751i	0.249192	−	0.634931i
$289$	−9.80117	+	6.68233i	−0.576540	+	0.393078i
$290$	−2.42696	−	32.3855i	−0.142516	−	1.90174i
$291$	−2.55353	−	4.42284i	−0.149690	−	0.259271i
$292$	0.590726	−	0.740746i	0.0345696	−	0.0433489i
$293$	3.44637	−	3.19776i	0.201339	−	0.186815i	−0.573059	−	0.819514i	$-0.694243\pi$
$293$	3.44637	−	3.19776i	0.201339	−	0.186815i	0.774398	+	0.632699i	$0.218053\pi$
$294$	−2.92313	+	3.66549i	−0.170480	+	0.213776i
$295$	32.6480	−	10.0706i	1.90084	−	0.586331i
$296$	−0.768765	−	10.2585i	−0.0446835	−	0.596260i
$297$	6.42159	+	4.37817i	0.372619	+	0.254047i
$298$	3.72222	+	0.561034i	0.215622	+	0.0324998i
$299$	−4.50161	+	11.4699i	−0.260335	+	0.663322i
$300$	−0.908455	−	0.280221i	−0.0524497	−	0.0161786i
$301$	−10.8330	−	47.4624i	−0.624403	−	2.73569i
$302$	3.77901	+	9.62877i	0.217458	+	0.554073i
$303$	0.0521392	+	0.695750i	0.00299532	+	0.0399698i
$304$	3.11643	−	1.50079i	0.178739	−	0.0860764i
$305$	7.41975	+	32.5081i	0.424854	+	1.86141i
$306$	−3.68803	+	6.38786i	−0.210831	+	0.365170i
$307$	−21.7229	−	3.27420i	−1.23979	−	0.186868i	−0.503776	−	0.863835i	$-0.668056\pi$
$307$	−21.7229	−	3.27420i	−1.23979	−	0.186868i	−0.736014	+	0.676966i	$0.763294\pi$
$308$	−9.34040	−	11.7125i	−0.532219	−	0.667381i
$309$	−2.31004	−	1.57496i	−0.131414	−	0.0895962i
$310$	−5.02861	−	12.8127i	−0.285606	−	0.727712i
$311$	1.70049	−	22.6915i	0.0964260	−	1.28672i	−0.713696	−	0.700455i	$-0.752980\pi$
$311$	1.70049	−	22.6915i	0.0964260	−	1.28672i	0.810122	−	0.586261i	$-0.199401\pi$
$312$	3.39738	−	1.04795i	0.192339	−	0.0593287i
$313$	−4.35566	−	7.54422i	−0.246196	−	0.426425i	0.716271	−	0.697822i	$-0.245848\pi$
$313$	−4.35566	−	7.54422i	−0.246196	−	0.426425i	−0.962467	+	0.271398i	$0.912514\pi$
$314$	−0.967770	+	12.9140i	−0.0546144	+	0.728779i
$315$	36.4151	−	17.5366i	2.05176	−	0.988075i
$316$	−4.22764	+	2.88236i	−0.237823	+	0.162145i
$317$	15.5202	+	19.4617i	0.871701	+	1.09308i	0.994917	+	0.100699i	$0.0321079\pi$
$317$	15.5202	+	19.4617i	0.871701	+	1.09308i	−0.123215	+	0.992380i	$0.539321\pi$
$318$	0.320392	+	0.401759i	0.0179667	+	0.0225296i
$319$	34.5415	−	23.5500i	1.93395	−	1.31855i
$320$	22.7923	−	10.9762i	1.27413	−	0.613589i
$321$	−0.138626	+	1.84984i	−0.00773737	+	0.103248i
$322$	8.20266	+	14.2074i	0.457116	+	0.791749i
$323$	3.85985	−	1.19061i	0.214768	−	0.0662471i
$324$	−0.458622	+	6.11988i	−0.0254790	+	0.339994i
$325$	5.92420	+	15.0946i	0.328615	+	0.837298i
$326$	−3.88080	−	2.64588i	−0.214938	−	0.146542i
$327$	−0.0268969	−	0.0337277i	−0.00148740	−	0.00186514i
$328$	6.16061	+	0.928562i	0.340163	+	0.0512713i
$329$	−3.48703	+	6.03971i	−0.192246	+	0.332980i
$330$	0.993863	+	4.35440i	0.0547104	+	0.239702i
$331$	2.39909	−	1.15534i	0.131866	−	0.0635033i	−0.366787	−	0.930305i	$-0.619542\pi$
$331$	2.39909	−	1.15534i	0.131866	−	0.0635033i	0.498653	+	0.866801i	$0.333828\pi$
$332$	0.179759	+	2.39872i	0.00986557	+	0.131647i
$333$	3.55639	+	9.06154i	0.194889	+	0.496569i
$334$	−1.11382	−	4.87995i	−0.0609453	−	0.267019i
$335$	−30.3667	−	9.36689i	−1.65911	−	0.511768i
$336$	0.976078	−	2.48701i	0.0532494	−	0.135677i
$337$	−27.2032	−	4.10022i	−1.48185	−	0.223353i	−0.642225	−	0.766516i	$-0.721989\pi$
$337$	−27.2032	−	4.10022i	−1.48185	−	0.223353i	−0.839627	+	0.543163i	$0.817227\pi$
$338$	−1.63800	−	1.11677i	−0.0890955	−	0.0607443i
$339$	0.410466	+	5.47729i	0.0222935	+	0.297486i
$340$	4.92572	−	1.51938i	0.267135	−	0.0824001i
$341$	11.0471	−	13.8526i	0.598233	−	0.750161i
$342$	−4.25114	+	3.94448i	−0.229875	+	0.213293i
$343$	−19.7768	+	24.7994i	−1.06785	+	1.33904i
$344$	16.3582	+	28.3333i	0.881977	+	1.52763i
$345$	0.218841	+	2.92023i	0.0117820	+	0.157220i
$346$	−2.08732	+	1.42311i	−0.112215	+	0.0765067i
$347$	−9.23774	+	23.5374i	−0.495908	+	1.26355i	0.435702	+	0.900091i	$0.356500\pi$
$347$	−9.23774	+	23.5374i	−0.495908	+	1.26355i	−0.931609	+	0.363461i	$0.881595\pi$
$348$	−1.94153	−	0.934990i	−0.104077	−	0.0501207i
$349$	6.79125	−	29.7544i	0.363527	−	1.59272i	−0.380640	−	0.924723i	$-0.624296\pi$
$349$	6.79125	−	29.7544i	0.363527	−	1.59272i	0.744167	−	0.667994i	$-0.232847\pi$
$350$	20.6305	+	6.36368i	1.10275	+	0.340153i
$351$	−5.64589	+	3.84930i	−0.301355	+	0.205461i
$352$	14.3700	+	9.79732i	0.765925	+	0.522199i
$353$	4.86857	−	8.43262i	0.259128	−	0.448823i	−0.706881	−	0.707333i	$-0.749898\pi$
$353$	4.86857	−	8.43262i	0.259128	−	0.448823i	0.966009	+	0.258510i	$0.0832315\pi$
$354$	−0.842560	+	3.69150i	−0.0447816	+	0.196201i
$355$	−4.93499	+	0.743830i	−0.261922	+	0.0394784i
$356$	4.15872	+	2.00273i	0.220412	+	0.106145i
$357$	1.55997	−	2.70194i	0.0825621	−	0.143002i
$358$	−6.46419	−	16.4705i	−0.341643	−	0.870492i
$359$	0.659539	+	1.14235i	0.0348091	+	0.0602912i	0.882905	−	0.469551i	$-0.155584\pi$
$359$	0.659539	+	1.14235i	0.0348091	+	0.0602912i	−0.848096	+	0.529843i	$0.822251\pi$
$360$	−19.9111	+	18.4748i	−1.04941	+	0.973708i
$361$	−15.8242			−0.832853
$362$	−18.7403			−0.984970
$363$	−1.78870	+	1.65967i	−0.0938823	+	0.0871101i
$364$	12.5861	−	3.88228i	0.659689	−	0.203487i
$365$	−3.46037	+	1.66642i	−0.181124	+	0.0872246i
$366$	−3.53118	−	1.08922i	−0.184578	−	0.0569347i
$367$	−1.42408	+	0.214646i	−0.0743364	+	0.0112044i	−0.186105	−	0.982530i	$-0.559587\pi$
$367$	−1.42408	+	0.214646i	−0.0743364	+	0.0112044i	0.111769	+	0.993734i	$0.464348\pi$
$368$	−4.56140	−	4.23236i	−0.237780	−	0.220627i
$369$	−5.82957	+	0.878667i	−0.303476	+	0.0457416i
$370$	−4.15108	+	10.5768i	−0.215805	+	0.549861i
$371$	4.35631	+	5.46264i	0.226168	+	0.283606i
$372$	−0.903106	−	0.136121i	−0.0468238	−	0.00705756i
$373$	25.3545	+	12.2101i	1.31280	+	0.632213i	0.953609	−	0.301049i	$-0.0973369\pi$
$373$	25.3545	+	12.2101i	1.31280	+	0.632213i	0.359195	+	0.933262i	$0.383051\pi$
$374$	−8.12418	−	7.53814i	−0.420091	−	0.389788i
$375$	−0.523003	−	0.485276i	−0.0270077	−	0.0250595i
$376$	1.04291	−	4.56927i	0.0537838	−	0.235642i
$377$	8.17892	+	35.8342i	0.421236	+	1.84555i
$378$	−0.679889	+	9.07249i	−0.0349697	+	0.466638i
$379$	7.23242	−	9.06917i	0.371504	−	0.465852i	−0.560576	−	0.828103i	$-0.689420\pi$
$379$	7.23242	−	9.06917i	0.371504	−	0.465852i	0.932081	+	0.362251i	$0.117992\pi$
$380$	4.05277			0.207903
$381$	2.36226	+	2.43200i	0.121022	+	0.124595i
$382$	4.23340			0.216600
$383$	2.55505	−	3.20394i	0.130557	−	0.163714i	−0.712256	−	0.701920i	$-0.752326\pi$
$383$	2.55505	−	3.20394i	0.130557	−	0.163714i	0.842813	+	0.538206i	$0.180898\pi$
$384$	−0.0306213	+	0.408613i	−0.00156264	+	0.0208519i
$385$	13.5133	+	59.2058i	0.688704	+	3.01741i
$386$	−0.439596	+	1.92600i	−0.0223749	+	0.0980306i
$387$	−22.6942	−	21.0571i	−1.15361	−	1.07039i
$388$	9.32051	+	8.64817i	0.473177	+	0.439044i
$389$	8.28598	+	3.99032i	0.420116	+	0.202317i	0.631985	−	0.774981i	$-0.282241\pi$
$389$	8.28598	+	3.99032i	0.420116	+	0.202317i	−0.211869	+	0.977298i	$0.567955\pi$
$390$	−3.88300	−	0.585268i	−0.196623	−	0.0296362i
$391$	−4.53056	−	5.68115i	−0.229120	−	0.287308i
$392$	15.6510	−	39.8781i	0.790495	−	2.01415i
$393$	5.90465	−	0.889983i	0.297850	−	0.0448937i
$394$	13.9245	+	12.9200i	0.701506	+	0.650903i
$395$	20.5102	−	3.09142i	1.03198	−	0.155546i
$396$	−9.10337	−	2.80802i	−0.457462	−	0.141108i
$397$	16.2582	−	7.82956i	0.815978	−	0.392954i	0.0211403	−	0.999777i	$-0.493270\pi$
$397$	16.2582	−	7.82956i	0.815978	−	0.392954i	0.794838	+	0.606822i	$0.207556\pi$
$398$	−16.7992	+	5.18188i	−0.842070	+	0.259744i
$399$	1.79815	−	1.66844i	0.0900200	−	0.0835264i
$400$	−8.18890			−0.409445
$401$	19.9149			0.994502			0.497251	−	0.867607i	$-0.334343\pi$
$401$	19.9149			0.994502			0.497251	+	0.867607i	$0.334343\pi$
$402$	2.58170	−	2.39547i	0.128764	−	0.119475i
$403$	7.78893	+	13.4908i	0.387994	+	0.672026i
$404$	−0.634603	−	1.61694i	−0.0315727	−	0.0804458i
$405$	12.4390	−	21.5450i	0.618099	−	1.07058i
$406$	44.0910	+	21.2331i	2.18820	+	1.05378i
$407$	−14.4628	+	2.17992i	−0.716896	+	0.108055i
$408$	−0.466557	+	2.04412i	−0.0230980	+	0.101199i
$409$	−2.42720	+	4.20404i	−0.120017	+	0.207876i	−0.919774	−	0.392448i	$-0.871628\pi$
$409$	−2.42720	+	4.20404i	−0.120017	+	0.207876i	0.799757	+	0.600324i	$0.204962\pi$
$410$	−5.68555	−	3.87634i	−0.280789	−	0.191439i
$411$	3.69771	−	2.52106i	0.182395	−	0.124355i
$412$	6.65139	+	2.05168i	0.327690	+	0.101079i
$413$	−11.4561	+	50.1925i	−0.563718	+	2.46981i
$414$	9.39933	+	4.52648i	0.461952	+	0.222464i
$415$	3.56246	−	9.07700i	0.174874	−	0.445572i
$416$	−12.6342	+	8.61385i	−0.619442	+	0.422329i
$417$	−0.150729	−	2.01134i	−0.00738122	−	0.0984955i
$418$	−4.35673	−	7.54608i	−0.213095	−	0.369091i
$419$	19.4123	−	24.3423i	0.948354	−	1.18920i	−0.0334761	−	0.999440i	$-0.510658\pi$
$419$	19.4123	−	24.3423i	0.948354	−	1.18920i	0.981831	−	0.189759i	$-0.0607708\pi$
$420$	2.29470	−	2.12917i	0.111970	−	0.103893i
$421$	8.90031	−	11.1606i	0.433774	−	0.543936i	−0.516116	−	0.856519i	$-0.672623\pi$
$421$	8.90031	−	11.1606i	0.433774	−	0.543936i	0.949891	+	0.312583i	$0.101194\pi$
$422$	−25.3762	+	7.82753i	−1.23530	+	0.381038i
$423$	0.331424	+	4.42254i	0.0161144	+	0.215031i
$424$	−3.87957	−	2.64505i	−0.188409	−	0.128455i
$425$	−9.45598	−	1.42526i	−0.458683	−	0.0691353i
$426$	0.202069	−	0.514864i	0.00979028	−	0.0249452i
$427$	−48.0127	−	14.8100i	−2.32350	−	0.716704i
$428$	−1.02767	−	4.50254i	−0.0496745	−	0.217638i
$429$	−1.84677	−	4.70549i	−0.0891628	−	0.227183i
$430$	−2.70039	−	36.0343i	−0.130225	−	1.73773i
$431$	4.20768	−	2.02631i	0.202677	−	0.0976039i	−0.329792	−	0.944054i	$-0.606979\pi$
$431$	4.20768	−	2.02631i	0.202677	−	0.0976039i	0.532469	+	0.846450i	$0.321264\pi$
$432$	−0.767878	−	3.36429i	−0.0369446	−	0.161865i
$433$	−3.35425	+	5.80973i	−0.161195	+	0.279198i	−0.935297	−	0.353862i	$-0.884868\pi$
$433$	−3.35425	+	5.80973i	−0.161195	+	0.279198i	0.774103	+	0.633060i	$0.218201\pi$
$434$	20.5090	+	3.09124i	0.984466	+	0.148384i
$435$	5.44652	+	6.82972i	0.261141	+	0.327460i
$436$	0.0887387	+	0.0605010i	0.00424981	+	0.00289747i
$437$	−2.08722	−	5.31814i	−0.0998451	−	0.254401i
$438$	0.0318086	−	0.424457i	0.00151988	−	0.0202813i
$439$	−23.9643	+	7.39199i	−1.14375	+	0.352801i	−0.808019	−	0.589157i	$-0.799460\pi$
$439$	−23.9643	+	7.39199i	−1.14375	+	0.352801i	−0.335733	+	0.941957i	$0.608984\pi$
$440$	−20.4057	−	35.3437i	−0.972803	−	1.68494i
$441$	−3.02937	+	40.4242i	−0.144256	+	1.92496i
$442$	8.77899	−	4.22774i	0.417574	−	0.201093i
$443$	−18.2709	+	12.4569i	−0.868078	+	0.591846i	−0.913371	−	0.407128i	$-0.866530\pi$
$443$	−18.2709	+	12.4569i	−0.868078	+	0.591846i	0.0452930	+	0.998974i	$0.485578\pi$
$444$	0.470066	+	0.589445i	0.0223084	+	0.0279738i
$445$	−11.6663	−	14.6291i	−0.553038	−	0.693488i
$446$	8.26829	−	5.63723i	0.391515	−	0.266930i
$447$	−0.912247	+	0.439315i	−0.0431478	+	0.0207789i
$448$	−2.84871	+	38.0134i	−0.134589	+	1.79596i
$449$	−6.40416	−	11.0923i	−0.302231	−	0.523479i	0.674410	−	0.738357i	$-0.264398\pi$
$449$	−6.40416	−	11.0923i	−0.302231	−	0.523479i	−0.976641	+	0.214878i	$0.931065\pi$
$450$	13.1194	−	4.04679i	0.618453	−	0.190767i
$451$	0.661958	−	8.83322i	0.0311704	−	0.415940i
$452$	−4.99591	−	12.7294i	−0.234988	−	0.598739i
$453$	−2.29884	−	1.56732i	−0.108009	−	0.0736391i
$454$	−4.20307	−	5.27049i	−0.197260	−	0.247356i
$455$	−52.7963	−	7.95777i	−2.47513	−	0.373066i
$456$	−0.824233	+	1.42761i	−0.0385982	+	0.0668541i
$457$	7.29264	+	31.9511i	0.341135	+	1.49461i	0.796682	+	0.604399i	$0.206587\pi$
$457$	7.29264	+	31.9511i	0.341135	+	1.49461i	−0.455547	+	0.890212i	$0.650556\pi$
$458$	28.3588	−	13.6569i	1.32512	−	0.638143i
$459$	−0.301145	−	4.01850i	−0.0140563	−	0.187568i
$460$	−2.66359	−	6.78671i	−0.124190	−	0.316432i
$461$	7.49955	+	32.8577i	0.349289	+	1.53033i	0.778799	+	0.627273i	$0.215829\pi$
$461$	7.49955	+	32.8577i	0.349289	+	1.53033i	−0.429511	+	0.903062i	$0.641314\pi$
$462$	−6.43122	−	1.98377i	−0.299207	−	0.0922932i
$463$	−5.56877	+	14.1890i	−0.258803	+	0.659418i	−0.999929	−	0.0119478i	$-0.996197\pi$
$463$	−5.56877	+	14.1890i	−0.258803	+	0.659418i	0.741126	+	0.671366i	$0.234292\pi$
$464$	−18.3545	−	2.76649i	−0.852084	−	0.128431i
$465$	3.05899	+	2.08558i	0.141857	+	0.0967166i
$466$	0.572724	+	7.64247i	0.0265309	+	0.354031i
$467$	−20.3778	+	6.28572i	−0.942972	+	0.290868i	−0.727864	−	0.685722i	$-0.759487\pi$
$467$	−20.3778	+	6.28572i	−0.942972	+	0.290868i	−0.215108	+	0.976590i	$0.569010\pi$
$468$	5.22225	−	6.54849i	0.241399	−	0.302704i
$469$	35.1028	−	32.5707i	1.62090	−	1.50397i
$470$	−3.22752	+	4.04719i	−0.148875	+	0.186683i
$471$	−1.74168	−	3.01669i	−0.0802526	−	0.139002i
$472$	−2.58554	−	34.5016i	−0.119009	−	1.58806i
$473$	38.4331	−	26.2033i	1.76716	−	1.20483i
$474$	−0.839817	+	2.13982i	−0.0385741	+	0.0982851i
$475$	−6.77393	−	3.26215i	−0.310809	−	0.149678i
$476$	−1.72842	+	7.57272i	−0.0792222	+	0.347095i
$477$	4.24576	+	1.30964i	0.194400	+	0.0599644i
$478$	16.1902	−	11.0383i	0.740521	−	0.504878i
$479$	−2.80634	−	1.91333i	−0.128225	−	0.0874224i	0.497509	−	0.867459i	$-0.334248\pi$
$479$	−2.80634	−	1.91333i	−0.128225	−	0.0874224i	−0.625734	+	0.780036i	$0.715201\pi$
$480$	−1.81709	+	3.14729i	−0.0829384	+	0.143654i
$481$	2.86149	−	12.5370i	0.130473	−	0.571638i
$482$	−7.71640	+	1.16306i	−0.351473	+	0.0529760i
$483$	−3.97573	−	1.91461i	−0.180902	−	0.0871179i
$484$	3.03743	−	5.26099i	0.138065	−	0.239136i
$485$	−18.8304	−	47.9790i	−0.855044	−	2.17862i
$486$	4.36132	+	7.55402i	0.197833	+	0.342657i
$487$	−7.40817	+	6.87378i	−0.335696	+	0.311481i	−0.829951	−	0.557837i	$-0.811632\pi$
$487$	−7.40817	+	6.87378i	−0.335696	+	0.311481i	0.494255	+	0.869317i	$0.335441\pi$
$488$	33.7661			1.52852
$489$	1.26339			0.0571326
$490$	−34.6852	+	32.1831i	−1.56692	+	1.45389i
$491$	16.0062	−	4.93726i	0.722350	−	0.222816i	0.0882852	−	0.996095i	$-0.471861\pi$
$491$	16.0062	−	4.93726i	0.722350	−	0.222816i	0.634065	+	0.773280i	$0.281385\pi$
$492$	−0.411380	+	0.198110i	−0.0185464	+	0.00893150i
$493$	−20.7130	−	6.38910i	−0.932865	−	0.287751i
$494$	7.57535	−	1.14180i	0.340831	−	0.0513720i
$495$	28.3093	+	26.2672i	1.27241	+	1.18062i
$496$	−7.77901	+	1.17250i	−0.349288	+	0.0526467i
$497$	2.74749	−	7.00049i	0.123242	−	0.314015i
$498$	0.673780	+	0.844893i	0.0301928	+	0.0378606i
$499$	18.9060	+	2.84962i	0.846349	+	0.127567i	0.557879	−	0.829922i	$-0.311615\pi$
$499$	18.9060	+	2.84962i	0.846349	+	0.127567i	0.288470	+	0.957489i	$0.406853\pi$
$500$	1.60034	+	0.770685i	0.0715696	+	0.0344661i
$501$	0.986961	+	0.915766i	0.0440942	+	0.0409134i
$502$	−3.70196	−	3.43492i	−0.165227	−	0.153308i
$503$	−4.24212	+	18.5859i	−0.189147	+	0.828706i	0.787921	+	0.615776i	$0.211158\pi$
$503$	−4.24212	+	18.5859i	−0.189147	+	0.828706i	−0.977068	+	0.212929i	$0.931700\pi$
$504$	−9.10763	−	39.9031i	−0.405686	−	1.77743i
$505$	−0.526205	+	7.02172i	−0.0234158	+	0.312462i
$506$	−9.77320	+	12.2552i	−0.434472	+	0.544810i
$507$	0.533251			0.0236825
$508$	−7.40454	−	4.05228i	−0.328523	−	0.179791i
$509$	22.7379			1.00784			0.503920	−	0.863750i	$-0.331891\pi$
$509$	22.7379			1.00784			0.503920	+	0.863750i	$0.331891\pi$
$510$	1.44387	−	1.81056i	0.0639357	−	0.0801728i
$511$	0.432495	−	5.77125i	0.0191325	−	0.255305i
$512$	−4.37432	−	19.1651i	−0.193319	−	0.846987i
$513$	0.705013	−	3.08887i	0.0311271	−	0.136377i
$514$	−22.3932	−	20.7778i	−0.987721	−	0.916471i
$515$	−20.6842	−	19.1921i	−0.911455	−	0.845707i
$516$	−2.16027	−	1.04033i	−0.0951006	−	0.0457980i
$517$	−6.58917	−	0.993157i	−0.289791	−	0.0436790i
$518$	−10.6750	−	13.3860i	−0.469031	−	0.588146i
$519$	0.248258	−	0.632552i	0.0108973	−	0.0277659i
$520$	35.4807	−	5.34786i	1.55593	−	0.234519i
$521$	−30.5638	−	28.3591i	−1.33902	−	1.24243i	−0.946505	−	0.322689i	$-0.895413\pi$
$521$	−30.5638	−	28.3591i	−1.33902	−	1.24243i	−0.392519	−	0.919744i	$-0.628396\pi$
$522$	30.7726	−	4.63823i	1.34688	−	0.203010i
$523$	−27.1680	−	8.38021i	−1.18797	−	0.366441i	−0.363095	−	0.931752i	$-0.618280\pi$
$523$	−27.1680	−	8.38021i	−1.18797	−	0.366441i	−0.824878	+	0.565311i	$0.808756\pi$
$524$	−13.3942	+	6.45030i	−0.585128	+	0.281783i
$525$	−5.54923	+	1.71171i	−0.242188	+	0.0747052i
$526$	−0.699183	+	0.648747i	−0.0304858	+	0.0282867i
$527$	−9.18674			−0.400181
$528$	2.55275			0.111094
$529$	9.32629	−	8.65353i	0.405491	−	0.376241i
$530$	2.59306	+	4.49132i	0.112636	+	0.195090i
$531$	11.9610	+	30.4761i	0.519063	+	1.32255i
$532$	−3.05348	+	5.28879i	−0.132385	+	0.229298i
$533$	7.01673	+	3.37908i	0.303928	+	0.146364i
$534$	2.05052	−	0.309067i	0.0887349	−	0.0133746i
$535$	−4.16593	+	18.2521i	−0.180109	+	0.789108i
$536$	−16.0904	+	27.8694i	−0.694999	+	1.20377i
$537$	3.93227	+	2.68098i	0.169690	+	0.115693i
$538$	7.35631	−	5.01545i	0.317153	−	0.216231i
$539$	−58.2025	−	17.9531i	−2.50696	−	0.773294i
$540$	0.899698	−	3.94183i	0.0387168	−	0.169630i
$541$	22.4531	+	10.8129i	0.965335	+	0.464881i	0.849037	−	0.528334i	$-0.177183\pi$
$541$	22.4531	+	10.8129i	0.965335	+	0.464881i	0.116298	+	0.993214i	$0.462897\pi$
$542$	−4.86213	+	12.3885i	−0.208847	+	0.532132i
$543$	4.16491	−	2.83959i	0.178733	−	0.121858i
$544$	−0.673893	−	8.99248i	−0.0288929	−	0.385549i
$545$	−0.217687	−	0.377046i	−0.00932471	−	0.0161509i
$546$	3.68934	−	4.62628i	0.157889	−	0.197987i
$547$	8.98557	−	8.33739i	0.384195	−	0.356481i	−0.464306	−	0.885675i	$-0.653696\pi$
$547$	8.98557	−	8.33739i	0.384195	−	0.356481i	0.848501	+	0.529194i	$0.177506\pi$
$548$	−6.94691	+	8.71115i	−0.296757	+	0.372122i
$549$	−30.5322	+	9.41794i	−1.30308	+	0.401948i
$550$	1.54158	+	20.5709i	0.0657330	+	0.877146i
$551$	−14.0809	−	9.60019i	−0.599866	−	0.408982i
$552$	2.93237	+	0.441983i	0.124810	+	0.0188121i
$553$	−11.4188	+	29.0946i	−0.485577	+	1.23723i
$554$	−5.31883	−	1.64064i	−0.225975	−	0.0697041i
$555$	−0.680075	−	2.97960i	−0.0288676	−	0.126477i
$556$	1.83457	+	4.67440i	0.0778030	+	0.198239i
$557$	−1.65898	−	22.1375i	−0.0702932	−	0.937998i	−0.915178	−	0.403050i	$-0.867950\pi$
$557$	−1.65898	−	22.1375i	−0.0702932	−	0.937998i	0.844885	−	0.534948i	$-0.179669\pi$
$558$	11.8833	−	5.72268i	0.503059	−	0.242260i
$559$	9.10040	+	39.8715i	0.384906	+	1.68638i
$560$	13.4818	−	23.3511i	0.569708	−	0.986763i
$561$	2.94774	+	0.444301i	0.124454	+	0.0187584i
$562$	−0.549855	−	0.689496i	−0.0231942	−	0.0290846i
$563$	28.5263	+	19.4489i	1.20224	+	0.819673i	0.987596	−	0.157019i	$-0.0501884\pi$
$563$	28.5263	+	19.4489i	1.20224	+	0.819673i	0.214644	+	0.976692i	$0.431141\pi$
$564$	0.125489	+	0.319740i	0.00528403	+	0.0134635i
$565$	−4.14255	+	55.2785i	−0.174278	+	2.32558i
$566$	−2.23712	+	0.690060i	−0.0940331	+	0.0290054i
$567$	18.7439	+	32.4653i	0.787168	+	1.36341i
$568$	−0.377678	+	5.03977i	−0.0158470	+	0.211464i
$569$	23.7982	−	11.4606i	0.997671	−	0.480453i	0.137524	−	0.990498i	$-0.456086\pi$
$569$	23.7982	−	11.4606i	0.997671	−	0.480453i	0.860147	+	0.510045i	$0.170371\pi$
$570$	1.50436	−	1.02565i	0.0630105	−	0.0429599i
$571$	−9.84350	−	12.3434i	−0.411938	−	0.516554i	0.531970	−	0.846763i	$-0.321452\pi$
$571$	−9.84350	−	12.3434i	−0.411938	−	0.516554i	−0.943908	+	0.330210i	$0.892881\pi$
$572$	7.84653	+	9.83924i	0.328080	+	0.411399i
$573$	−0.940844	+	0.641457i	−0.0393043	+	0.0267972i
$574$	9.34222	−	4.49898i	0.389937	−	0.187784i
$575$	−1.01075	+	13.4875i	−0.0421511	+	0.562467i
$576$	12.1206	+	20.9935i	0.505026	+	0.874731i
$577$	30.4930	−	9.40583i	1.26944	−	0.391570i	0.414381	−	0.910103i	$-0.363998\pi$
$577$	30.4930	−	9.40583i	1.26944	−	0.391570i	0.855057	+	0.518533i	$0.173522\pi$
$578$	0.991507	−	13.2307i	0.0412413	−	0.550326i
$579$	−0.194135	−	0.494648i	−0.00806798	−	0.0205569i
$580$	−17.9692	−	12.2512i	−0.746132	−	0.508704i
$581$	9.16124	+	11.4878i	0.380072	+	0.476596i
$582$	5.64833	+	0.851349i	0.234131	+	0.0352895i
$583$	−3.33797	+	5.78153i	−0.138244	+	0.239446i
$584$	0.865457	+	3.79182i	0.0358129	+	0.156906i
$585$	−30.5910	+	14.7319i	−1.26478	+	0.609087i
$586$	0.392962	+	5.24371i	0.0162331	+	0.216616i
$587$	2.69198	+	6.85906i	0.111110	+	0.283104i	0.975603	−	0.219541i	$-0.0704558\pi$
$587$	2.69198	+	6.85906i	0.111110	+	0.283104i	−0.864493	+	0.502644i	$0.832361\pi$
$588$	0.698629	+	3.06089i	0.0288110	+	0.126229i
$589$	−6.90194	−	2.12897i	−0.284390	−	0.0877226i
$590$	−13.9611	+	35.5722i	−0.574768	+	1.46449i
$591$	−5.05230	−	0.761512i	−0.207824	−	0.0313244i
$592$	5.36564	+	3.65823i	0.220526	+	0.150352i
$593$	−0.972397	−	12.9757i	−0.0399316	−	0.532850i	−0.980920	−	0.194411i	$-0.937720\pi$
$593$	−0.972397	−	12.9757i	−0.0399316	−	0.532850i	0.940989	−	0.338438i	$-0.109899\pi$
$594$	−8.30671	+	2.56228i	−0.340828	+	0.105132i
$595$	19.6320	−	24.6178i	0.804834	−	1.00923i
$596$	1.84787	−	1.71457i	0.0756918	−	0.0702317i
$597$	2.94834	−	3.69710i	0.120668	−	0.151312i
$598$	−6.89076	−	11.9351i	−0.281784	−	0.488064i
$599$	−1.22900	−	16.3999i	−0.0502158	−	0.670083i	−0.964343	−	0.264655i	$-0.914742\pi$
$599$	−1.22900	−	16.3999i	−0.0502158	−	0.670083i	0.914127	−	0.405427i	$-0.132877\pi$
$600$	3.22451	−	2.19843i	0.131640	−	0.0897507i
$601$	7.64864	−	19.4884i	0.311994	−	0.794949i	−0.685751	−	0.727836i	$-0.740526\pi$
$601$	7.64864	−	19.4884i	0.311994	−	0.794949i	0.997745	−	0.0671127i	$-0.0213787\pi$
$602$	49.0586	+	23.6254i	1.99948	+	0.962898i
$603$	6.77612	−	29.6881i	0.275945	−	1.20899i
$604$	6.61913	+	2.04173i	0.269329	+	0.0830769i
$605$	−20.3469	+	13.8723i	−0.827220	+	0.563989i
$606$	−0.644766	−	0.439594i	−0.0261918	−	0.0178573i
$607$	7.97685	−	13.8163i	0.323770	−	0.560787i	−0.657492	−	0.753461i	$-0.728383\pi$
$607$	7.97685	−	13.8163i	0.323770	−	0.560787i	0.981263	+	0.192674i	$0.0617161\pi$
$608$	1.57766	−	6.91216i	0.0639824	−	0.280325i
$609$	−13.0162	+	1.96188i	−0.527444	+	0.0794994i
$610$	−33.6013	−	16.1815i	−1.36048	−	0.655171i
$611$	2.92933	−	5.07375i	0.118508	−	0.205262i
$612$	1.80460	+	4.59804i	0.0729465	+	0.185865i
$613$	−9.14717	−	15.8434i	−0.369451	−	0.639907i	0.620029	−	0.784579i	$-0.287121\pi$
$613$	−9.14717	−	15.8434i	−0.369451	−	0.639907i	−0.989480	+	0.144672i	$0.953787\pi$
$614$	18.0118	−	16.7125i	0.726898	−	0.674463i
$615$	1.85093			0.0746366
$616$	61.4971			2.47779
$617$	−19.6057	+	18.1915i	−0.789298	+	0.732361i	−0.967839	−	0.251571i	$-0.919053\pi$
$617$	−19.6057	+	18.1915i	−0.789298	+	0.732361i	0.178541	+	0.983932i	$0.442862\pi$
$618$	2.98817	−	0.921728i	0.120202	−	0.0370774i
$619$	−39.6644	+	19.1014i	−1.59425	+	0.767749i	−0.999350	−	0.0360516i	$-0.988522\pi$
$619$	−39.6644	+	19.1014i	−1.59425	+	0.767749i	−0.594898	+	0.803801i	$0.702808\pi$
$620$	−8.80787	−	2.71687i	−0.353732	−	0.109112i
$621$	−5.63592	+	0.849479i	−0.226162	+	0.0340884i
$622$	18.6570	+	17.3112i	0.748077	+	0.694114i
$623$	27.8805	−	4.20231i	1.11701	−	0.168362i
$624$	−0.819968	+	2.08924i	−0.0328250	+	0.0836367i
$625$	−17.6418	−	22.1221i	−0.705671	−	0.884883i
$626$	9.63460	+	1.45218i	0.385076	+	0.0580409i
$627$	2.11166	+	1.01692i	0.0843314	+	0.0406119i
$628$	6.35724	+	5.89866i	0.253681	+	0.235382i
$629$	5.55916	+	5.15815i	0.221658	+	0.205669i
$630$	−10.0594	+	44.0729i	−0.400775	+	1.75591i
$631$	−0.573921	−	2.51451i	−0.0228474	−	0.100101i	0.962219	−	0.272278i	$-0.0877771\pi$
$631$	−0.573921	−	2.51451i	−0.0228474	−	0.100101i	−0.985066	+	0.172177i	$0.944920\pi$
$632$	1.56966	−	20.9457i	0.0624379	−	0.833176i
$633$	4.45364	−	5.58469i	0.177016	−	0.221972i
$634$	−27.8417			−1.10574
$635$	19.9162	+	27.8236i	0.790350	+	1.10415i
$636$	0.344120			0.0136453
$637$	33.3885	−	41.8678i	1.32290	−	1.65886i
$638$	−3.49429	+	46.6280i	−0.138340	+	1.84602i
$639$	−1.06417	−	4.66243i	−0.0420979	−	0.184443i
$640$	−0.920215	+	4.03173i	−0.0363747	+	0.159368i
$641$	−10.8944	−	10.1085i	−0.430302	−	0.399262i	0.435066	−	0.900398i	$-0.356725\pi$
$641$	−10.8944	−	10.1085i	−0.430302	−	0.399262i	−0.865368	+	0.501137i	$0.832915\pi$
$642$	−1.52094	−	1.41123i	−0.0600268	−	0.0556967i
$643$	16.0938	+	7.75038i	0.634678	+	0.305645i	0.723418	−	0.690410i	$-0.242570\pi$
$643$	16.0938	+	7.75038i	0.634678	+	0.305645i	−0.0887401	+	0.996055i	$0.528284\pi$
$644$	10.8634	+	1.63739i	0.428076	+	0.0645221i
$645$	6.06015	+	7.59919i	0.238618	+	0.299218i
$646$	−1.65056	+	4.20557i	−0.0649406	+	0.165466i
$647$	2.16766	−	0.326722i	0.0852194	−	0.0128448i	−0.106294	−	0.994335i	$-0.533899\pi$
$647$	2.16766	−	0.326722i	0.0852194	−	0.0128448i	0.191514	+	0.981490i	$0.438660\pi$
$648$	−18.4677	−	17.1355i	−0.725479	−	0.673146i
$649$	−48.6420	+	7.33159i	−1.90936	+	0.287790i
$650$	−17.3310	−	5.34589i	−0.679776	−	0.209683i
$651$	−5.02639	+	2.42058i	−0.197000	+	0.0948700i
$652$	−3.00564	+	0.927116i	−0.117710	+	0.0363087i
$653$	−0.557787	+	0.517551i	−0.0218279	+	0.0202533i	−0.691011	−	0.722844i	$-0.742835\pi$
$653$	−0.557787	+	0.517551i	−0.0218279	+	0.0202533i	0.669183	+	0.743097i	$0.266644\pi$
$654$	0.0482504			0.00188674
$655$	60.2647			2.35474
$656$	−2.88306	+	2.67509i	−0.112565	+	0.104445i
$657$	−1.84017	−	3.18727i	−0.0717919	−	0.124347i
$658$	−2.84978	−	7.26113i	−0.111096	−	0.283068i
$659$	−2.64695	+	4.58466i	−0.103111	+	0.178593i	−0.912965	−	0.408039i	$-0.866213\pi$
$659$	−2.64695	+	4.58466i	−0.103111	+	0.178593i	0.809854	+	0.586631i	$0.199546\pi$
$660$	2.69478	+	1.29774i	0.104894	+	0.0505143i
$661$	−6.43073	+	0.969277i	−0.250127	+	0.0377005i	−0.272909	−	0.962040i	$-0.587986\pi$
$661$	−6.43073	+	0.969277i	−0.250127	+	0.0377005i	0.0227821	+	0.999740i	$0.492748\pi$
$662$	−0.662728	+	2.90360i	−0.0257577	+	0.112852i
$663$	−1.31047	+	2.26980i	−0.0508945	+	0.0881518i
$664$	−8.15867	−	5.56249i	−0.316618	−	0.215866i
$665$	20.4544	−	13.9456i	0.793188	−	0.540786i
$666$	−10.4041	−	3.20923i	−0.403149	−	0.124355i
$667$	−6.82200	+	29.8891i	−0.264149	+	1.15731i
$668$	−3.02002	−	1.45436i	−0.116848	−	0.0562710i
$669$	−0.983402	+	2.50567i	−0.0380205	+	0.0968747i
$670$	29.3675	−	20.0224i	1.13457	−	0.773534i
$671$	−3.58765	−	47.8739i	−0.138500	−	1.84815i
$672$	−2.73810	−	4.74254i	−0.105625	−	0.182947i
$673$	−22.1442	+	27.7680i	−0.853597	+	1.07038i	0.143143	+	0.989702i	$0.454279\pi$
$673$	−22.1442	+	27.7680i	−0.853597	+	1.07038i	−0.996740	+	0.0806750i	$0.974292\pi$
$674$	22.5559	−	20.9288i	0.868821	−	0.806148i
$675$	−4.67664	+	5.86432i	−0.180004	+	0.225718i
$676$	−1.26861	+	0.391316i	−0.0487929	+	0.0150506i
$677$	−0.0242598	−	0.323725i	−0.000932381	−	0.0124418i	0.996718	−	0.0809495i	$-0.0257953\pi$
$677$	−0.0242598	−	0.323725i	−0.000932381	−	0.0124418i	−0.997651	+	0.0685078i	$0.978176\pi$
$678$	−5.07592	−	3.46071i	−0.194940	−	0.132908i
$679$	76.7991	+	11.5756i	2.94728	+	0.444231i
$680$	−7.73077	+	19.6977i	−0.296461	+	0.755371i
$681$	1.73270	+	0.534468i	0.0663973	+	0.0204809i
$682$	4.40978	+	19.3205i	0.168859	+	0.739821i
$683$	−6.03681	−	15.3815i	−0.230992	−	0.588559i	0.767638	−	0.640884i	$-0.221432\pi$
$683$	−6.03681	−	15.3815i	−0.230992	−	0.588559i	−0.998630	+	0.0523252i	$0.983337\pi$
$684$	0.290217	+	3.87268i	0.0110967	+	0.148076i
$685$	40.6938	−	19.5971i	1.55483	−	0.748766i
$686$	−7.89452	−	34.5882i	−0.301414	−	1.32058i
$687$	−4.23321	+	7.33214i	−0.161507	+	0.279739i
$688$	−20.4224	−	3.07818i	−0.778596	−	0.117354i
$689$	−3.65958	−	4.58896i	−0.139419	−	0.174826i
$690$	−2.70624	−	1.84509i	−0.103025	−	0.0702412i
$691$	14.2349	+	36.2699i	0.541520	+	1.37977i	0.895727	+	0.444604i	$0.146656\pi$
$691$	14.2349	+	36.2699i	0.541520	+	1.37977i	−0.354207	+	0.935167i	$0.615249\pi$
$692$	−0.126426	+	1.68703i	−0.00480598	+	0.0641314i
$693$	−55.6073	+	17.1526i	−2.11235	+	0.651573i
$694$	−14.1405	−	24.4921i	−0.536766	−	0.929706i
$695$	1.52120	−	20.2990i	0.0577024	−	0.769985i
$696$	7.97006	−	3.83818i	0.302105	−	0.145486i
$697$	−3.79476	+	2.58722i	−0.143737	+	0.0979980i
$698$	21.2832	+	26.6882i	0.805579	+	1.01016i
$699$	−1.28529	−	1.61171i	−0.0486142	−	0.0609603i
$700$	11.9456	−	8.14440i	0.451503	−	0.307829i
$701$	20.0121	−	9.63731i	0.755846	−	0.363996i	−0.0159448	−	0.999873i	$-0.505076\pi$
$701$	20.0121	−	9.63731i	0.755846	−	0.363996i	0.771791	+	0.635877i	$0.219361\pi$
$702$	0.571150	−	7.62147i	0.0215567	−	0.287654i
$703$	2.98120	+	5.16359i	0.112438	+	0.194748i
$704$	−34.8048	+	10.7359i	−1.31175	+	0.404623i
$705$	0.104054	−	1.38850i	0.00391889	−	0.0522940i
$706$	3.97885	+	10.1380i	0.149746	+	0.381547i
$707$	−8.76675	−	5.97707i	−0.329708	−	0.224791i
$708$	1.58094	+	1.98244i	0.0594155	+	0.0745047i
$709$	−32.2808	−	4.86555i	−1.21233	−	0.182730i	−0.488412	−	0.872613i	$-0.662424\pi$
$709$	−32.2808	−	4.86555i	−1.21233	−	0.182730i	−0.723921	+	0.689883i	$0.757662\pi$
$710$	2.79101	−	4.83418i	0.104745	−	0.181423i
$711$	4.42278	+	19.3775i	0.165867	+	0.726712i
$712$	−17.0717	+	8.22132i	−0.639791	+	0.308107i
$713$	0.971001	+	12.9571i	0.0363643	+	0.485247i
$714$	1.27489	+	3.24835i	0.0477114	+	0.121567i
$715$	−11.3521	−	49.7367i	−0.424544	−	1.86005i
$716$	−11.3223	−	3.49248i	−0.423136	−	0.130520i
$717$	−1.92560	+	4.90635i	−0.0719129	+	0.183231i
$718$	−1.45888	−	0.219891i	−0.0544450	−	0.00820626i
$719$	−8.42302	−	5.74272i	−0.314126	−	0.214167i	0.395986	−	0.918257i	$-0.370403\pi$
$719$	−8.42302	−	5.74272i	−0.314126	−	0.214167i	−0.710111	+	0.704090i	$0.751355\pi$
$720$	−1.28137	−	17.0987i	−0.0477538	−	0.637230i
$721$	40.6295	−	12.5325i	1.51312	−	0.466736i
$722$	11.0352	−	13.8377i	0.410686	−	0.514985i
$723$	1.53869	−	1.42769i	0.0572244	−	0.0530965i
$724$	−7.82463	+	9.81177i	−0.290800	+	0.364652i
$725$	20.1731	+	34.9409i	0.749211	+	1.29767i
$726$	−0.203951	−	2.72154i	−0.00756933	−	0.101006i
$727$	−7.78714	+	5.30918i	−0.288809	+	0.196907i	−0.699054	−	0.715069i	$-0.746395\pi$
$727$	−7.78714	+	5.30918i	−0.288809	+	0.196907i	0.410245	+	0.911975i	$0.365443\pi$
$728$	−19.7534	+	50.3310i	−0.732111	+	1.86539i
$729$	20.0326	+	9.64721i	0.741950	+	0.357304i
$730$	0.955897	−	4.18806i	0.0353793	−	0.155007i
$731$	−23.0466	−	7.10894i	−0.852410	−	0.262934i
$732$	−2.04465	+	1.39402i	−0.0755724	+	0.0515244i
$733$	−7.92261	−	5.40154i	−0.292628	−	0.199511i	0.408103	−	0.912936i	$-0.366190\pi$
$733$	−7.92261	−	5.40154i	−0.292628	−	0.199511i	−0.700731	+	0.713425i	$0.747143\pi$
$734$	0.805398	−	1.39499i	0.0297278	−	0.0514900i
$735$	2.83206	−	12.4081i	0.104462	−	0.457678i
$736$	−12.6119	+	1.90094i	−0.464880	+	0.0700694i
$737$	41.2230	+	19.8520i	1.51847	+	0.731257i
$738$	3.29695	−	5.71049i	0.121362	−	0.210206i
$739$	−6.55713	−	16.7073i	−0.241208	−	0.614588i	0.758086	−	0.652154i	$-0.226135\pi$
$739$	−6.55713	−	16.7073i	−0.241208	−	0.614588i	−0.999294	+	0.0375667i	$0.988039\pi$
$740$	3.80444	+	6.58948i	0.139854	+	0.242234i
$741$	−1.51056	+	1.40159i	−0.0554918	+	0.0514889i
$742$	−7.81478			−0.286890
$743$	7.62022			0.279559			0.139779	−	0.990183i	$-0.455361\pi$
$743$	7.62022			0.279559			0.139779	+	0.990183i	$0.455361\pi$
$744$	2.74834	−	2.55008i	0.100759	−	0.0934906i
$745$	−9.76465	+	3.01200i	−0.357749	+	0.110351i
$746$	−28.3584	+	13.6567i	−1.03828	+	0.500007i
$747$	8.92876	+	2.75416i	0.326686	+	0.100769i
$748$	−7.33878	+	1.10614i	−0.268332	+	0.0404446i
$749$	−20.6799	−	19.1882i	−0.755628	−	0.701120i
$750$	0.789076	−	0.118934i	0.0288130	−	0.00434286i
$751$	−6.48721	+	16.5291i	−0.236722	+	0.603157i	−0.999029	−	0.0440582i	$-0.985971\pi$
$751$	−6.48721	+	16.5291i	−0.236722	+	0.603157i	0.762307	+	0.647215i	$0.224067\pi$
$752$	1.84468	+	2.31316i	0.0672687	+	0.0843523i
$753$	1.34320	+	0.202456i	0.0489491	+	0.00737789i
$754$	−37.0393	−	17.8372i	−1.34889	−	0.649592i
$755$	−20.5839	−	19.0991i	−0.749125	−	0.695086i
$756$	4.46616	+	4.14399i	0.162433	+	0.150715i
$757$	3.71198	−	16.2632i	0.134914	−	0.591098i	−0.861594	−	0.507599i	$-0.830533\pi$
$757$	3.71198	−	16.2632i	0.134914	−	0.591098i	0.996508	−	0.0834990i	$-0.0266096\pi$
$758$	2.88704	+	12.6489i	0.104862	+	0.459430i
$759$	0.315083	−	4.20450i	0.0114368	−	0.152614i
$760$	−10.3729	+	13.0072i	−0.376264	+	0.471820i
$761$	30.5897			1.10888			0.554439	−	0.832225i	$-0.312933\pi$
$761$	30.5897			1.10888			0.554439	+	0.832225i	$0.312933\pi$
$762$	−3.77403	+	0.369726i	−0.136719	+	0.0133938i
$763$	0.656050			0.0237506
$764$	1.76757	−	2.21646i	0.0639484	−	0.0801887i
$765$	1.49635	−	19.9674i	0.0541006	−	0.721923i
$766$	1.01993	+	4.46860i	0.0368515	+	0.161457i
$767$	9.62387	−	42.1649i	0.347498	−	1.52249i
$768$	3.33900	+	3.09814i	0.120486	+	0.111795i
$769$	−10.1407	−	9.40921i	−0.365684	−	0.339305i	0.475833	−	0.879535i	$-0.342147\pi$
$769$	−10.1407	−	9.40921i	−0.365684	−	0.339305i	−0.841517	+	0.540231i	$0.818337\pi$
$770$	−61.1969	−	29.4709i	−2.20538	−	1.06206i
$771$	8.12504	+	1.22465i	0.292616	+	0.0441048i
$772$	0.824839	+	1.03432i	0.0296866	+	0.0372258i
$773$	8.70308	−	22.1751i	0.313028	−	0.797582i	−0.684611	−	0.728908i	$-0.740028\pi$
$773$	8.70308	−	22.1751i	0.313028	−	0.797582i	0.997639	−	0.0686739i	$-0.0218768\pi$
$774$	34.2397	−	5.16080i	1.23072	−	0.185501i
$775$	12.5349	+	11.6307i	0.450267	+	0.417786i
$776$	−51.6114	+	7.77916i	−1.85274	+	0.279256i
$777$	4.40071	+	1.35744i	0.157875	+	0.0486979i
$778$	−9.26769	+	4.46309i	−0.332263	+	0.160009i
$779$	−3.45055	+	1.06435i	−0.123629	+	0.0381344i
$780$	−1.92769	+	1.78864i	−0.0690224	+	0.0640434i
$781$	7.18556			0.257119
$782$	8.12738			0.290635
$783$	−12.4633	+	11.5643i	−0.445402	+	0.413273i
$784$	13.5217	+	23.4203i	0.482918	+	0.836439i
$785$	−12.8436	−	32.7251i	−0.458409	−	1.16801i
$786$	−3.33941	+	5.78403i	−0.119113	+	0.206310i
$787$	39.3971	+	18.9726i	1.40435	+	0.676301i	0.974039	−	0.226378i	$-0.0726886\pi$
$787$	39.3971	+	18.9726i	1.40435	+	0.676301i	0.430314	+	0.902679i	$0.358403\pi$
$788$	12.5784	−	1.89588i	0.448086	−	0.0675380i
$789$	0.0570886	−	0.250122i	0.00203241	−	0.00890457i
$790$	−11.5997	+	20.0913i	−0.412698	+	0.714815i
$791$	−69.0162	−	47.0545i	−2.45394	−	1.67306i
$792$	32.3119	−	22.0299i	1.14815	−	0.782798i
$793$	40.3337	+	12.4413i	1.43229	+	0.441804i
$794$	−4.49120	+	19.6772i	−0.159387	+	0.698319i
$795$	−1.25683	−	0.605256i	−0.0445751	−	0.0214662i
$796$	−4.30112	+	10.9591i	−0.152449	+	0.388434i
$797$	6.65836	−	4.53959i	0.235851	−	0.160801i	−0.439627	−	0.898180i	$-0.644889\pi$
$797$	6.65836	−	4.53959i	0.235851	−	0.160801i	0.675479	+	0.737380i	$0.263937\pi$
$798$	0.205028	+	2.73592i	0.00725793	+	0.0968503i
$799$	1.72751	+	2.99214i	0.0611151	+	0.105854i
$800$	−10.4652	+	13.1230i	−0.370002	+	0.463968i
$801$	13.1437	−	12.1955i	0.464408	−	0.430908i
$802$	−13.8879	+	17.4148i	−0.490397	+	0.614939i
$803$	5.28412	−	1.62993i	0.186472	−	0.0575191i
$804$	−0.176248	−	2.35187i	−0.00621578	−	0.0829439i
$805$	−36.7962	−	25.0872i	−1.29690	−	0.884209i
$806$	−17.2289	−	2.59684i	−0.606862	−	0.0914698i
$807$	−0.874935	+	2.22930i	−0.0307992	+	0.0784750i
$808$	6.81374	+	2.10176i	0.239707	+	0.0739397i
$809$	−0.0313708	−	0.137444i	−0.00110294	−	0.00483229i	0.974373	−	0.224936i	$-0.0722174\pi$
$809$	−0.0313708	−	0.137444i	−0.00110294	−	0.00483229i	−0.975476	+	0.220104i	$0.929360\pi$
$810$	10.1658	+	25.9020i	0.357190	+	0.910104i
$811$	2.70937	+	36.1540i	0.0951388	+	1.26954i	0.816649	+	0.577135i	$0.195829\pi$
$811$	2.70937	+	36.1540i	0.0951388	+	1.26954i	−0.721510	+	0.692404i	$0.756552\pi$
$812$	29.5262	−	14.2191i	1.03617	−	0.498991i
$813$	−0.796566	−	3.48999i	−0.0279368	−	0.122399i
$814$	8.17955	−	14.1674i	0.286693	−	0.496567i
$815$	12.6081	+	1.90037i	0.441643	+	0.0665670i
$816$	−0.825242	−	1.03482i	−0.0288892	−	0.0362260i
$817$	−15.6673	−	10.6818i	−0.548130	−	0.373709i
$818$	−1.98364	−	5.05422i	−0.0693562	−	0.176717i
$819$	3.82343	−	51.0201i	0.133602	−	1.78279i
$820$	−4.40339	+	1.35827i	−0.153773	+	0.0474327i
$821$	1.88932	+	3.27240i	0.0659377	+	0.114207i	0.897110	−	0.441808i	$-0.145663\pi$
$821$	1.88932	+	3.27240i	0.0659377	+	0.114207i	−0.831172	+	0.556016i	$0.812329\pi$
$822$	−0.374068	+	4.99160i	−0.0130471	+	0.174102i
$823$	−40.9446	+	19.7179i	−1.42724	+	0.687321i	−0.978482	−	0.206333i	$-0.933847\pi$
$823$	−40.9446	+	19.7179i	−1.42724	+	0.687321i	−0.448756	+	0.893654i	$0.648133\pi$
$824$	−23.6087	+	16.0961i	−0.822449	+	0.560736i
$825$	−3.45956	−	4.33815i	−0.120447	−	0.151035i
$826$	−35.9024	−	45.0202i	−1.24920	−	1.56645i
$827$	−39.9357	+	27.2277i	−1.38870	+	0.946800i	−0.389027	+	0.921226i	$0.627189\pi$
$827$	−39.9357	+	27.2277i	−1.38870	+	0.946800i	−0.999673	+	0.0255732i	$0.991859\pi$
$828$	6.29440	−	3.03122i	0.218745	−	0.105342i
$829$	−0.699887	+	9.33935i	−0.0243081	+	0.324369i	0.971773	+	0.235920i	$0.0758102\pi$
$829$	−0.699887	+	9.33935i	−0.0243081	+	0.324369i	−0.996081	+	0.0884494i	$0.971809\pi$
$830$	5.45317	+	9.44517i	0.189282	+	0.327847i
$831$	1.43067	−	0.441302i	0.0496293	−	0.0153086i
$832$	2.39310	−	31.9337i	0.0829657	−	1.10710i
$833$	11.5377	+	29.3976i	0.399758	+	1.01857i
$834$	1.86395	+	1.27082i	0.0645433	+	0.0440048i
$835$	8.47198	+	10.6235i	0.293185	+	0.367642i
$836$	−5.76992	−	0.869676i	−0.199557	−	0.0300784i
$837$	−3.60290	+	6.24040i	−0.124534	+	0.215700i
$838$	7.74902	+	33.9507i	0.267686	+	1.17281i
$839$	13.0465	−	6.28284i	0.450414	−	0.216908i	−0.194904	−	0.980822i	$-0.562439\pi$
$839$	13.0465	−	6.28284i	0.450414	−	0.216908i	0.645317	+	0.763915i	$0.276725\pi$
$840$	0.960294	+	12.8142i	0.0331333	+	0.442133i
$841$	22.8166	+	58.1356i	0.786778	+	2.00468i
$842$	3.55283	+	15.5660i	0.122439	+	0.536438i
$843$	0.226676	+	0.0699202i	0.00780712	+	0.00240818i
$844$	−6.49709	+	16.5543i	−0.223639	+	0.569823i
$845$	5.32162	+	0.802105i	0.183069	+	0.0275932i
$846$	−4.09847	−	2.79429i	−0.140908	−	0.0960696i
$847$	−2.77308	−	37.0041i	−0.0952841	−	1.27148i
$848$	2.83243	−	0.873690i	0.0972662	−	0.0300026i
$849$	0.392624	−	0.492335i	0.0134748	−	0.0168969i
$850$	7.84056	−	7.27498i	0.268929	−	0.249530i
$851$	6.68754	−	8.38591i	0.229246	−	0.287465i
$852$	−0.185195	−	0.320767i	−0.00634467	−	0.0109893i
$853$	0.757590	+	10.1093i	0.0259394	+	0.346137i	0.995040	+	0.0994725i	$0.0317155\pi$
$853$	0.757590	+	10.1093i	0.0259394	+	0.346137i	−0.969101	+	0.246665i	$0.920665\pi$
$854$	46.4329	−	31.6574i	1.58890	−	1.08329i
$855$	5.75151	−	14.6546i	0.196698	−	0.501177i
$856$	17.0810	+	8.22577i	0.583816	+	0.281151i
$857$	3.79600	−	16.6314i	0.129669	−	0.568117i	−0.867794	−	0.496925i	$-0.834463\pi$
$857$	3.79600	−	16.6314i	0.129669	−	0.568117i	0.997463	−	0.0711920i	$-0.0226803\pi$
$858$	5.40263	+	1.66649i	0.184443	+	0.0568931i
$859$	38.2738	−	26.0946i	1.30588	−	0.890337i	0.307754	−	0.951466i	$-0.400423\pi$
$859$	38.2738	−	26.0946i	1.30588	−	0.890337i	0.998130	+	0.0611292i	$0.0194702\pi$
$860$	−19.9938	−	13.6315i	−0.681781	−	0.464831i
$861$	−1.39455	+	2.41542i	−0.0475260	+	0.0823174i
$862$	−1.16233	+	5.09252i	−0.0395893	+	0.173452i
$863$	29.7715	−	4.48734i	1.01343	−	0.152751i	0.378731	−	0.925507i	$-0.376360\pi$
$863$	29.7715	−	4.48734i	1.01343	−	0.152751i	0.634703	+	0.772756i	$0.281122\pi$
$864$	−6.37273	−	3.06894i	−0.216805	−	0.104408i
$865$	3.42898	−	5.93918i	0.116589	−	0.201938i
$866$	−2.74127	−	6.98464i	−0.0931521	−	0.237348i
$867$	1.78440	+	3.09068i	0.0606015	+	0.104965i
$868$	10.1816	−	9.44713i	0.345585	−	0.320656i
$869$	−29.8638			−1.01306
$870$	−9.77051			−0.331251
$871$	−29.4886	+	27.3615i	−0.999184	+	0.927107i
$872$	−0.421298	+	0.129953i	−0.0142670	+	0.00440077i
$873$	44.4986	−	21.4294i	1.50605	−	0.725275i
$874$	6.10605	+	1.88347i	0.206540	+	0.0637092i
$875$	10.7289	−	1.61712i	0.362703	−	0.0546687i
$876$	−0.208950	−	0.193877i	−0.00705975	−	0.00655049i
$877$	−30.2224	+	4.55530i	−1.02054	+	0.153822i	−0.637934	−	0.770091i	$-0.720211\pi$
$877$	−30.2224	+	4.55530i	−1.02054	+	0.153822i	−0.382605	+	0.923912i	$0.624973\pi$
$878$	10.2477	−	26.1107i	0.345843	−	0.881194i
$879$	−0.881874	−	1.10584i	−0.0297449	−	0.0372989i
$880$	25.4754	+	3.83980i	0.858775	+	0.129440i
$881$	−8.23225	−	3.96444i	−0.277352	−	0.133565i	0.290038	−	0.957015i	$-0.406332\pi$
$881$	−8.23225	−	3.96444i	−0.277352	−	0.133565i	−0.567389	+	0.823450i	$0.692046\pi$
$882$	−33.2368	−	30.8393i	−1.11914	−	1.03841i
$883$	−40.3272	−	37.4182i	−1.35712	−	1.25922i	−0.935902	−	0.352261i	$-0.885413\pi$
$883$	−40.3272	−	37.4182i	−1.35712	−	1.25922i	−0.421216	−	0.906960i	$-0.638397\pi$
$884$	1.45199	−	6.36157i	0.0488356	−	0.213963i
$885$	−2.28725	−	10.0211i	−0.0768851	−	0.336856i
$886$	1.84833	−	24.6642i	0.0620957	−	0.828609i
$887$	−5.21684	+	6.54171i	−0.175164	+	0.219649i	−0.861662	−	0.507483i	$-0.830576\pi$
$887$	−5.21684	+	6.54171i	−0.175164	+	0.219649i	0.686497	+	0.727132i	$0.259147\pi$
$888$	−3.09491			−0.103858
$889$	−51.3147	+	5.02709i	−1.72104	+	0.168603i
$890$	20.9283			0.701517
$891$	−22.3327	+	28.0043i	−0.748173	+	0.938179i
$892$	0.500798	−	6.68269i	0.0167680	−	0.223753i
$893$	0.604461	+	2.64832i	0.0202275	+	0.0886226i
$894$	0.252000	−	1.10409i	0.00842815	−	0.0369262i
$895$	35.2098	+	32.6699i	1.17693	+	1.09203i
$896$	−4.56801	−	4.23849i	−0.152606	−	0.141598i
$897$	3.33987	+	1.60840i	0.111515	+	0.0537028i
$898$	14.1658	+	2.13515i	0.472719	+	0.0712510i
$899$	24.1662	+	30.3035i	0.805989	+	1.01068i
$900$	3.35896	−	8.55849i	0.111965	−	0.285283i
$901$	3.42276	−	0.515899i	0.114029	−	0.0171871i
$902$	7.26269	+	6.73879i	0.241821	+	0.224377i
$903$	−14.4827	+	2.18292i	−0.481954	+	0.0726429i
$904$	53.6412	+	16.5461i	1.78408	+	0.550316i
$905$	45.8353	−	22.0731i	1.52362	−	0.733735i
$906$	2.97368	−	0.917259i	0.0987939	−	0.0304739i
$907$	7.99651	−	7.41968i	0.265520	−	0.246366i	−0.536165	−	0.844113i	$-0.680128\pi$
$907$	7.99651	−	7.41968i	0.265520	−	0.246366i	0.801685	+	0.597747i	$0.203937\pi$
$908$	−4.51435			−0.149814
$909$	−6.74738			−0.223797
$910$	43.7768	−	40.6190i	1.45119	−	1.34651i
$911$	12.0842	+	20.9305i	0.400368	+	0.693457i	0.993770	−	0.111449i	$-0.0355491\pi$
$911$	12.0842	+	20.9305i	0.400368	+	0.693457i	−0.593402	+	0.804906i	$0.702216\pi$
$912$	−0.380186	−	0.968698i	−0.0125892	−	0.0320768i
$913$	−7.01969	+	12.1585i	−0.232318	+	0.402386i
$914$	−33.0256	−	15.9043i	−1.09239	−	0.526068i
$915$	9.91953	−	1.49513i	0.327929	−	0.0494274i
$916$	4.69035	−	20.5498i	0.154974	−	0.678984i
$917$	−45.4053	+	78.6443i	−1.49941	+	2.59706i
$918$	3.72404	+	2.53900i	0.122911	+	0.0837996i
$919$	−30.5698	+	20.8422i	−1.00841	+	0.687520i	−0.950475	−	0.310801i	$-0.899403\pi$
$919$	−30.5698	+	20.8422i	−1.00841	+	0.687520i	−0.0579311	+	0.998321i	$0.518450\pi$
$920$	28.5990	+	8.82162i	0.942880	+	0.290840i
$921$	−1.47067	+	6.44344i	−0.0484604	+	0.212319i
$922$	−33.9627	−	16.3556i	−1.11850	−	0.538642i
$923$	−2.30807	+	5.88086i	−0.0759710	+	0.193571i
$924$	−3.72385	+	2.53888i	−0.122506	+	0.0835229i
$925$	−1.05486	−	14.0761i	−0.0346836	−	0.462820i
$926$	−8.52429	−	14.7645i	−0.280126	−	0.485192i
$927$	16.8581	−	21.1394i	0.553694	−	0.694310i
$928$	−27.8900	+	25.8781i	−0.915534	+	0.849491i
$929$	15.8115	−	19.8270i	0.518758	−	0.650502i	−0.451587	−	0.892227i	$-0.649142\pi$
$929$	15.8115	−	19.8270i	0.518758	−	0.650502i	0.970345	+	0.241725i	$0.0777133\pi$
$930$	−3.95698	+	1.22057i	−0.129755	+	0.0400240i
$931$	1.85551	+	24.7600i	0.0608117	+	0.811476i
$932$	4.24046	+	2.89109i	0.138901	+	0.0947009i
$933$	−6.76942	−	1.02033i	−0.221621	−	0.0334040i
$934$	8.71404	−	22.2030i	0.285132	−	0.726505i
$935$	28.7489	+	8.86787i	0.940191	+	0.290010i
$936$	7.65099	+	33.5212i	0.250080	+	1.09567i
$937$	−9.96616	−	25.3934i	−0.325580	−	0.829565i	−0.996146	−	0.0877147i	$-0.972044\pi$
$937$	−9.96616	−	25.3934i	−0.325580	−	0.829565i	0.670565	−	0.741851i	$-0.266052\pi$
$938$	4.00250	+	53.4096i	0.130686	+	1.74389i
$939$	−2.36126	+	1.13712i	−0.0770569	+	0.0371086i
$940$	0.771379	+	3.37963i	0.0251596	+	0.110231i
$941$	−3.32072	+	5.75165i	−0.108252	+	0.187499i	−0.915062	−	0.403312i	$-0.867859\pi$
$941$	−3.32072	+	5.75165i	−0.108252	+	0.187499i	0.806810	+	0.590811i	$0.201192\pi$
$942$	3.85256	+	0.580680i	0.125523	+	0.0189196i
$943$	4.05014	+	5.07872i	0.131891	+	0.165386i
$944$	18.0459	+	12.3035i	0.587344	+	0.400445i
$945$	−9.02306	−	22.9904i	−0.293520	−	0.747877i
$946$	−3.88797	+	51.8814i	−0.126409	+	1.68681i
$947$	40.3018	−	12.4314i	1.30963	−	0.403968i	0.440146	−	0.897926i	$-0.354927\pi$
$947$	40.3018	−	12.4314i	1.30963	−	0.403968i	0.869485	+	0.493959i	$0.164451\pi$
$948$	0.769685	+	1.33313i	0.0249982	+	0.0432982i
$949$	−0.363324	+	4.84822i	−0.0117940	+	0.157380i
$950$	7.57649	−	3.64865i	0.245814	−	0.118378i
$951$	6.18763	−	4.21865i	0.200647	−	0.136799i
$952$	−19.8805	−	24.9294i	−0.644331	−	0.807965i
$953$	12.6937	+	15.9174i	0.411188	+	0.515614i	0.943697	−	0.330811i	$-0.107322\pi$
$953$	12.6937	+	15.9174i	0.411188	+	0.515614i	−0.532509	+	0.846424i	$0.678751\pi$
$954$	−4.10606	+	2.79946i	−0.132938	+	0.0906359i
$955$	−10.3541	+	4.98627i	−0.335051	+	0.161352i
$956$	0.980614	−	13.0854i	0.0317153	−	0.423212i
$957$	−6.28863	−	10.8922i	−0.203282	−	0.352095i
$958$	3.63017	−	1.11976i	0.117285	−	0.0361778i
$959$	−5.08613	+	67.8697i	−0.164240	+	2.19163i
$960$	−2.78053	−	7.08468i	−0.0897412	−	0.228657i
$961$	−12.0406	−	8.20917i	−0.388408	−	0.264812i
$962$	8.96764	+	11.2451i	0.289128	+	0.362556i
$963$	−17.7394	−	2.67378i	−0.571644	−	0.0861614i
$964$	−2.61288	+	4.52565i	−0.0841553	+	0.145761i
$965$	−1.19335	−	5.22840i	−0.0384152	−	0.168308i
$966$	4.44677	−	2.14145i	0.143073	−	0.0689001i
$967$	−4.21721	−	56.2748i	−0.135616	−	1.80967i	−0.486956	−	0.873426i	$-0.661893\pi$
$967$	−4.21721	−	56.2748i	−0.135616	−	1.80967i	0.351340	−	0.936248i	$-0.385726\pi$
$968$	9.11074	+	23.2138i	0.292830	+	0.746120i
$969$	−0.270413	−	1.18476i	−0.00868692	−	0.0380599i
$970$	55.0874	+	16.9922i	1.76875	+	0.545587i
$971$	9.53486	−	24.2944i	0.305988	−	0.779645i	−0.692325	−	0.721586i	$-0.743414\pi$
$971$	9.53486	−	24.2944i	0.305988	−	0.779645i	0.998313	−	0.0580593i	$-0.0184912\pi$
$972$	5.77599	+	0.870591i	0.185265	+	0.0279242i
$973$	25.3437	+	17.2790i	0.812482	+	0.553941i
$974$	−0.844694	−	11.2717i	−0.0270658	−	0.361167i
$975$	4.66171	−	1.43795i	0.149294	−	0.0460512i
$976$	−13.2901	+	16.6653i	−0.425406	+	0.533442i
$977$	0.464136	−	0.430655i	0.0148490	−	0.0137779i	−0.672713	−	0.739903i	$-0.734871\pi$
$977$	0.464136	−	0.430655i	0.0148490	−	0.0137779i	0.687562	+	0.726125i	$0.258681\pi$
$978$	−0.881039	+	1.10479i	−0.0281725	+	0.0353272i
$979$	13.4701	+	23.3309i	0.430507	+	0.745660i
$980$	2.36789	+	31.5973i	0.0756395	+	1.00934i
$981$	0.344703	−	0.235014i	0.0110055	−	0.00750343i
$982$	−6.84465	+	17.4399i	−0.218421	+	0.556529i
$983$	43.5511	+	20.9731i	1.38907	+	0.668939i	0.970912	−	0.239438i	$-0.0769631\pi$
$983$	43.5511	+	20.9731i	1.38907	+	0.668939i	0.418154	+	0.908376i	$0.362677\pi$
$984$	0.417083	−	1.82736i	0.0132961	−	0.0582541i
$985$	−49.2744	−	15.1992i	−1.57001	−	0.484285i
$986$	20.0314	−	13.6572i	0.637931	−	0.434934i
$987$	1.73357	+	1.18193i	0.0551802	+	0.0376212i
$988$	2.56512	−	4.44292i	0.0816074	−	0.141348i
$989$	−7.59061	+	33.2566i	−0.241367	+	1.05750i
$990$	−42.7114	+	6.43771i	−1.35746	+	0.204604i
$991$	0.209547	+	0.100913i	0.00665649	+	0.00320560i	0.437209	−	0.899360i	$-0.355967\pi$
$991$	0.209547	+	0.100913i	0.00665649	+	0.00320560i	−0.430553	+	0.902566i	$0.641681\pi$
$992$	−8.06244	+	13.9646i	−0.255983	+	0.443375i
$993$	−0.292675	−	0.745724i	−0.00928776	−	0.0236648i
$994$	4.20567	+	7.28444i	0.133396	+	0.231048i
$995$	34.9843	−	32.4607i	1.10908	−	1.02907i
$996$	0.723679			0.0229306
$997$	−50.4409			−1.59748			−0.798739	−	0.601677i	$-0.794499\pi$
$997$	−50.4409			−1.59748			−0.798739	+	0.601677i	$0.794499\pi$
$998$	−15.6762	+	14.5454i	−0.496221	+	0.460426i
$999$	5.68406	−	1.75330i	0.179836	−	0.0554720i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	127.2.i.a.100.3	yes	108
127.47	even	21	inner	127.2.i.a.47.3	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
127.2.i.a.47.3	✓	108	127.47	even	21	inner
127.2.i.a.100.3	yes	108	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	127.i (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.697360 + 0.874462i) q^{2} +(0.0224826 - 0.300009i) q^{3} +(0.166669 + 0.730226i) q^{4} +(0.675634 - 2.96015i) q^{5} +(0.246668 + 0.228874i) q^{6} +(3.35389 + 3.11196i) q^{7} +(-2.77021 - 1.33406i) q^{8} +(2.87699 + 0.433637i) q^{9} +(2.11738 + 2.65510i) q^{10} +(-1.59711 + 4.06938i) q^{11} +(0.222822 - 0.0335849i) q^{12} +(-2.81748 - 2.61424i) q^{13} +(-5.06016 + 0.762696i) q^{14} +(-0.872881 - 0.269248i) q^{15} +(1.74876 - 0.842160i) q^{16} +(2.16593 - 0.668100i) q^{17} +(-2.38550 + 2.21342i) q^{18} +1.78208 q^{19} +2.27418 q^{20} +(1.00902 - 0.936233i) q^{21} +(-2.44475 - 4.23443i) q^{22} +(-1.17123 - 2.98424i) q^{23} +(-0.462513 + 0.801096i) q^{24} +(-3.80114 - 1.83053i) q^{25} +(4.25086 - 0.640713i) q^{26} +(0.395614 - 1.73330i) q^{27} +(-1.71344 + 2.96777i) q^{28} +(-7.90140 - 5.38708i) q^{29} +(0.844159 - 0.575538i) q^{30} +(-3.87298 - 1.19466i) q^{31} +(0.885291 - 3.87871i) q^{32} +(1.18494 + 0.570638i) q^{33} +(-0.926203 + 2.35993i) q^{34} +(11.4779 - 7.82547i) q^{35} +(0.162854 + 2.17313i) q^{36} +(1.67288 + 2.89751i) q^{37} +(-1.24275 + 1.55836i) q^{38} +(-0.847641 + 0.786496i) q^{39} +(-5.82068 + 7.29890i) q^{40} +(-1.93625 + 0.597255i) q^{41} +(0.115050 + 1.53524i) q^{42} +(-8.79161 - 5.99402i) q^{43} +(-3.23775 - 0.488013i) q^{44} +(3.22742 - 8.22334i) q^{45} +(3.42637 + 1.05689i) q^{46} +(0.339189 + 1.48609i) q^{47} +(-0.213339 - 0.543579i) q^{48} +(1.04120 + 13.8939i) q^{49} +(4.25150 - 2.04741i) q^{50} +(-0.151740 - 0.664818i) q^{51} +(1.43940 - 2.49311i) q^{52} +(1.51007 + 0.227606i) q^{53} +(1.23982 + 1.55468i) q^{54} +(10.9669 + 7.47710i) q^{55} +(-5.13944 - 13.0951i) q^{56} +(0.0400656 - 0.534639i) q^{57} +(10.2209 - 3.15274i) q^{58} +(5.62629 + 9.74502i) q^{59} +(0.0511295 - 0.682276i) q^{60} +(-9.89436 + 4.76487i) q^{61} +(3.74554 - 2.55367i) q^{62} +(8.29966 + 10.4074i) q^{63} +(5.19478 + 6.51405i) q^{64} +(-9.64213 + 6.57389i) q^{65} +(-1.32533 + 0.638247i) q^{66} +(0.782148 - 10.4370i) q^{67} +(0.848858 + 1.47027i) q^{68} +(-0.921630 + 0.284285i) q^{69} +(-1.16112 + 15.4941i) q^{70} +(-0.600512 - 1.53008i) q^{71} +(-7.39138 - 5.03936i) q^{72} +(-0.788680 - 0.988974i) q^{73} +(-3.70036 - 0.557740i) q^{74} +(-0.634636 + 1.09922i) q^{75} +(0.297017 + 1.30132i) q^{76} +(-18.0203 + 8.67810i) q^{77} +(-0.0966497 - 1.28970i) q^{78} +(2.49578 + 6.35914i) q^{79} +(-1.31139 - 5.74559i) q^{80} +(7.82958 + 2.41510i) q^{81} +(0.827988 - 2.10968i) q^{82} +(3.17565 + 0.478652i) q^{83} +(0.851834 + 0.580771i) q^{84} +(-0.514300 - 6.86286i) q^{85} +(11.3725 - 3.50794i) q^{86} +(-1.79382 + 2.24938i) q^{87} +(9.85315 - 9.14239i) q^{88} +(3.84232 - 4.81812i) q^{89} +(4.94032 + 8.55689i) q^{90} +(-1.31412 - 17.5358i) q^{91} +(1.98396 - 1.35264i) q^{92} +(-0.445482 + 1.13507i) q^{93} +(-1.53606 - 0.739729i) q^{94} +(1.20403 - 5.27521i) q^{95} +(-1.14375 - 0.352799i) q^{96} +(14.0257 - 9.56258i) q^{97} +(-12.8758 - 8.77856i) q^{98} +(-6.35951 + 11.0150i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 5 q^{2} - 15 q^{3} - 17 q^{4} - 6 q^{5} + 7 q^{6} + 2 q^{7} - 22 q^{8} + 2 q^{9} - 10 q^{10} + 9 q^{12} - 14 q^{13} - 20 q^{14} + 4 q^{15} + 27 q^{16} - 8 q^{17} + 7 q^{18} - 16 q^{19} - 80 q^{20}+ \cdots - 24 q^{99}+O(q^{100}) \) 108 * q - 5 * q^2 - 15 * q^3 - 17 * q^4 - 6 * q^5 + 7 * q^6 + 2 * q^7 - 22 * q^8 + 2 * q^9 - 10 * q^10 + 9 * q^12 - 14 * q^13 - 20 * q^14 + 4 * q^15 + 27 * q^16 - 8 * q^17 + 7 * q^18 - 16 * q^19 - 80 * q^20 - 59 * q^21 - 13 * q^22 - 20 * q^23 + 41 * q^24 - 6 * q^25 - 56 * q^26 - 24 * q^27 - 19 * q^28 + 33 * q^29 + 23 * q^30 - 3 * q^31 + 39 * q^32 - 61 * q^33 + 16 * q^34 - 5 * q^35 + 48 * q^36 - 3 * q^37 + 3 * q^38 + 7 * q^39 - 6 * q^40 - 38 * q^41 + 14 * q^42 - 9 * q^43 + 134 * q^44 - 70 * q^45 - q^46 + 17 * q^47 - 76 * q^48 + 93 * q^49 + 24 * q^50 + 31 * q^51 - 54 * q^52 - 12 * q^53 - 44 * q^54 + 15 * q^55 + 30 * q^56 - 42 * q^57 - 52 * q^58 + 77 * q^59 + 36 * q^60 - 70 * q^61 + 41 * q^62 + 82 * q^63 - 6 * q^64 - 43 * q^65 + 160 * q^66 + 54 * q^67 + 6 * q^68 - 19 * q^69 + 49 * q^70 - 31 * q^71 + 11 * q^72 + 46 * q^73 - 111 * q^74 + 18 * q^75 - 19 * q^76 - 65 * q^77 + 27 * q^78 + 119 * q^79 + 114 * q^80 - 55 * q^81 - 44 * q^82 - 34 * q^83 + 34 * q^84 + 6 * q^85 + 89 * q^86 + 22 * q^87 - 118 * q^88 - 22 * q^89 + 121 * q^90 + 58 * q^91 + 115 * q^92 + 104 * q^93 + 62 * q^94 - 18 * q^95 + 31 * q^96 + 14 * q^97 + 87 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more