LMFDB - Embedded newform 112.2.v.a.19.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [112,2,Mod(3,112)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(112, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("112.3"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 112 = 2^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	112.v (of order $12$, degree $4$, 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:	$0.894324502638$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.8
Character	$\chi$	$=$	112.19
Dual form			112.2.v.a.59.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0679570 + 1.41258i) q^{2} +(-0.825526 + 3.08091i) q^{3} +(-1.99076 + 0.191990i) q^{4} +(1.86998 - 0.501060i) q^{5} +(-4.40813 - 0.956753i) q^{6} +(2.17953 - 1.49988i) q^{7} +(-0.406487 - 2.79907i) q^{8} +(-6.21241 - 3.58674i) q^{9} +(0.834865 + 2.60745i) q^{10} +(-0.944161 + 3.52366i) q^{11} +(1.05193 - 6.29185i) q^{12} +(0.372046 - 0.372046i) q^{13} +(2.26682 + 2.97683i) q^{14} +6.17487i q^{15} +(3.92628 - 0.764412i) q^{16} +(2.39966 - 1.38545i) q^{17} +(4.64438 - 9.01927i) q^{18} +(1.61000 - 0.431397i) q^{19} +(-3.62649 + 1.35651i) q^{20} +(2.82174 + 7.95312i) q^{21} +(-5.04161 - 1.09425i) q^{22} +(-1.27273 + 2.20444i) q^{23} +(8.95922 + 1.05835i) q^{24} +(-1.08436 + 0.626056i) q^{25} +(0.550828 + 0.500262i) q^{26} +(9.41278 - 9.41278i) q^{27} +(-4.05097 + 3.40436i) q^{28} +(2.14013 + 2.14013i) q^{29} +(-8.72250 + 0.419626i) q^{30} +(-2.74674 - 4.75749i) q^{31} +(1.34661 + 5.49424i) q^{32} +(-10.0766 - 5.81774i) q^{33} +(2.12013 + 3.29556i) q^{34} +(3.32415 - 3.89683i) q^{35} +(13.0561 + 5.94763i) q^{36} +(-1.21513 - 4.53493i) q^{37} +(0.718794 + 2.24493i) q^{38} +(0.839106 + 1.45337i) q^{39} +(-2.16262 - 5.03052i) q^{40} +3.95954 q^{41} +(-11.0427 + 4.52641i) q^{42} +(-4.29972 - 4.29972i) q^{43} +(1.20310 - 7.19604i) q^{44} +(-13.4143 - 3.59434i) q^{45} +(-3.20043 - 1.64803i) q^{46} +(1.85655 - 3.21563i) q^{47} +(-0.886167 + 12.7275i) q^{48} +(2.50070 - 6.53808i) q^{49} +(-0.958045 - 1.48920i) q^{50} +(2.28744 + 8.53685i) q^{51} +(-0.669227 + 0.812085i) q^{52} +(6.49892 + 1.74138i) q^{53} +(13.9360 + 12.6566i) q^{54} +7.06225i q^{55} +(-5.08422 - 5.49096i) q^{56} +5.31638i q^{57} +(-2.87767 + 3.16855i) q^{58} +(8.21574 + 2.20140i) q^{59} +(-1.18551 - 12.2927i) q^{60} +(0.101519 + 0.378874i) q^{61} +(6.53368 - 4.20330i) q^{62} +(-18.9198 + 1.50050i) q^{63} +(-7.66954 + 2.27557i) q^{64} +(0.509302 - 0.882137i) q^{65} +(7.53325 - 14.6294i) q^{66} +(-13.8977 - 3.72389i) q^{67} +(-4.51117 + 3.21880i) q^{68} +(-5.74099 - 5.74099i) q^{69} +(5.73048 + 4.43080i) q^{70} -8.98576 q^{71} +(-7.51425 + 18.8469i) q^{72} +(0.766294 + 1.32726i) q^{73} +(6.32337 - 2.02465i) q^{74} +(-1.03365 - 3.85764i) q^{75} +(-3.12230 + 1.16791i) q^{76} +(3.22725 + 9.09605i) q^{77} +(-1.99598 + 1.28407i) q^{78} +(3.47070 + 2.00381i) q^{79} +(6.95905 - 3.39674i) q^{80} +(10.4692 + 18.1331i) q^{81} +(0.269079 + 5.59317i) q^{82} +(-3.67570 - 3.67570i) q^{83} +(-7.14434 - 15.2910i) q^{84} +(3.79313 - 3.79313i) q^{85} +(5.78150 - 6.36589i) q^{86} +(-8.36028 + 4.82681i) q^{87} +(10.2467 + 1.21045i) q^{88} +(3.35201 - 5.80586i) q^{89} +(4.16570 - 19.1930i) q^{90} +(0.252860 - 1.36891i) q^{91} +(2.11048 - 4.63286i) q^{92} +(16.9249 - 4.53501i) q^{93} +(4.66851 + 2.40400i) q^{94} +(2.79451 - 1.61341i) q^{95} +(-18.0389 - 0.386856i) q^{96} -4.52980i q^{97} +(9.40550 + 3.08812i) q^{98} +(18.5040 - 18.5040i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{2} - 6 q^{3} - 4 q^{4} - 6 q^{5} - 8 q^{7} + 4 q^{8} - 24 q^{10} + 2 q^{11} - 6 q^{12} + 16 q^{14} + 8 q^{16} - 12 q^{17} - 30 q^{18} - 6 q^{19} - 10 q^{21} - 28 q^{22} - 12 q^{23} - 6 q^{24}+ \cdots - 16 q^{99}+O(q^{100}) $ 56 * q - 2 * q^2 - 6 * q^3 - 4 * q^4 - 6 * q^5 - 8 * q^7 + 4 * q^8 - 24 * q^10 + 2 * q^11 - 6 * q^12 + 16 * q^14 + 8 * q^16 - 12 * q^17 - 30 * q^18 - 6 * q^19 - 10 * q^21 - 28 * q^22 - 12 * q^23 - 6 * q^24 - 6 * q^26 + 26 * q^28 - 24 * q^29 - 18 * q^30 - 12 * q^32 - 12 * q^33 - 2 * q^35 + 16 * q^36 + 6 * q^37 - 6 * q^38 - 4 * q^39 - 66 * q^40 + 70 * q^42 + 26 * q^44 + 12 * q^45 + 16 * q^46 - 8 * q^49 - 34 * q^51 + 84 * q^52 + 6 * q^53 + 42 * q^54 + 16 * q^56 + 18 * q^58 + 42 * q^59 + 78 * q^60 - 6 * q^61 - 16 * q^64 - 4 * q^65 + 126 * q^66 + 6 * q^67 + 24 * q^68 - 80 * q^70 - 80 * q^71 - 4 * q^72 + 62 * q^74 + 24 * q^75 + 10 * q^77 + 4 * q^78 + 12 * q^80 - 8 * q^81 + 42 * q^82 - 152 * q^84 - 28 * q^85 - 12 * q^87 + 30 * q^88 + 16 * q^91 - 20 * q^92 + 10 * q^93 - 42 * q^94 + 36 * q^96 - 108 * q^98 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.0679570	+	1.41258i	0.0480529	+	0.998845i
$2$	0.0679570	+	1.41258i	0.0480529	+	0.998845i
$3$	−0.825526	+	3.08091i	−0.476618	+	1.77876i	0.138539	+	0.990357i	$0.455759\pi$
$3$	−0.825526	+	3.08091i	−0.476618	+	1.77876i	−0.615156	+	0.788405i	$0.710907\pi$
$4$	−1.99076	+	0.191990i	−0.995382	+	0.0959948i
$5$	1.86998	−	0.501060i	0.836281	−	0.224081i	0.184829	−	0.982771i	$-0.440827\pi$
$5$	1.86998	−	0.501060i	0.836281	−	0.224081i	0.651452	+	0.758690i	$0.274160\pi$
$6$	−4.40813	−	0.956753i	−1.79961	−	0.390593i
$7$	2.17953	−	1.49988i	0.823785	−	0.566903i
$7$	2.17953	−	1.49988i	0.823785	−	0.566903i
$8$	−0.406487	−	2.79907i	−0.143715	−	0.989619i
$9$	−6.21241	−	3.58674i	−2.07080	−	1.19558i
$10$	0.834865	+	2.60745i	0.264008	+	0.824547i
$11$	−0.944161	+	3.52366i	−0.284675	+	1.06242i	0.664401	+	0.747376i	$0.268687\pi$
$11$	−0.944161	+	3.52366i	−0.284675	+	1.06242i	−0.949076	+	0.315046i	$0.897980\pi$
$12$	1.05193	−	6.29185i	0.303665	−	1.81630i
$13$	0.372046	−	0.372046i	0.103187	−	0.103187i	−0.653628	−	0.756816i	$-0.726754\pi$
$13$	0.372046	−	0.372046i	0.103187	−	0.103187i	0.756816	+	0.653628i	$0.226754\pi$
$14$	2.26682	+	2.97683i	0.605833	+	0.795592i
$15$			6.17487i			1.59435i
$16$	3.92628	−	0.764412i	0.981570	−	0.191103i
$17$	2.39966	−	1.38545i	0.582003	−	0.336020i	−0.179926	−	0.983680i	$-0.557586\pi$
$17$	2.39966	−	1.38545i	0.582003	−	0.336020i	0.761929	+	0.647660i	$0.224252\pi$
$18$	4.64438	−	9.01927i	1.09469	−	2.12586i
$19$	1.61000	−	0.431397i	0.369358	−	0.0989693i	−0.0693652	−	0.997591i	$-0.522097\pi$
$19$	1.61000	−	0.431397i	0.369358	−	0.0989693i	0.438724	+	0.898622i	$0.355431\pi$
$20$	−3.62649	+	1.35651i	−0.810908	+	0.303324i
$21$	2.82174	+	7.95312i	0.615755	+	1.73551i
$22$	−5.04161	−	1.09425i	−1.07487	−	0.233294i
$23$	−1.27273	+	2.20444i	−0.265383	+	0.459657i	−0.967664	−	0.252243i	$-0.918832\pi$
$23$	−1.27273	+	2.20444i	−0.265383	+	0.459657i	0.702281	+	0.711900i	$0.252165\pi$
$24$	8.95922	+	1.05835i	1.82879	+	0.216036i
$25$	−1.08436	+	0.626056i	−0.216872	+	0.125211i
$26$	0.550828	+	0.500262i	0.108026	+	0.0981094i
$27$	9.41278	−	9.41278i	1.81149	−	1.81149i
$28$	−4.05097	+	3.40436i	−0.765561	+	0.643364i
$29$	2.14013	+	2.14013i	0.397413	+	0.397413i	0.877319	−	0.479907i	$-0.159330\pi$
$29$	2.14013	+	2.14013i	0.397413	+	0.397413i	−0.479907	+	0.877319i	$0.659330\pi$
$30$	−8.72250	+	0.419626i	−1.59250	+	0.0766129i
$31$	−2.74674	−	4.75749i	−0.493329	−	0.854471i	0.506641	−	0.862157i	$-0.330887\pi$
$31$	−2.74674	−	4.75749i	−0.493329	−	0.854471i	−0.999970	+	0.00768582i	$0.997554\pi$
$32$	1.34661	+	5.49424i	0.238049	+	0.971253i
$33$	−10.0766	−	5.81774i	−1.75412	−	1.01274i
$34$	2.12013	+	3.29556i	0.363599	+	0.565184i
$35$	3.32415	−	3.89683i	0.561883	−	0.658684i
$36$	13.0561	+	5.94763i	2.17601	+	0.991272i
$37$	−1.21513	−	4.53493i	−0.199766	−	0.745537i	−0.990981	−	0.134000i	$-0.957218\pi$
$37$	−1.21513	−	4.53493i	−0.199766	−	0.745537i	0.791215	−	0.611538i	$-0.209449\pi$
$38$	0.718794	+	2.24493i	0.116604	+	0.364176i
$39$	0.839106	+	1.45337i	0.134364	+	0.232726i
$40$	−2.16262	−	5.03052i	−0.341940	−	0.795396i
$41$	3.95954			0.618376			0.309188	−	0.951001i	$-0.399943\pi$
$41$	3.95954			0.618376			0.309188	+	0.951001i	$0.399943\pi$
$42$	−11.0427	+	4.52641i	−1.70392	+	0.698440i
$43$	−4.29972	−	4.29972i	−0.655701	−	0.655701i	0.298659	−	0.954360i	$-0.403461\pi$
$43$	−4.29972	−	4.29972i	−0.655701	−	0.655701i	−0.954360	+	0.298659i	$0.903461\pi$
$44$	1.20310	−	7.19604i	0.181374	−	1.08484i
$45$	−13.4143	−	3.59434i	−1.99968	−	0.535813i
$46$	−3.20043	−	1.64803i	−0.471878	−	0.242988i
$47$	1.85655	−	3.21563i	0.270805	−	0.469048i	−0.698263	−	0.715841i	$-0.746043\pi$
$47$	1.85655	−	3.21563i	0.270805	−	0.469048i	0.969068	+	0.246793i	$0.0793767\pi$
$48$	−0.886167	+	12.7275i	−0.127907	+	1.83706i
$49$	2.50070	−	6.53808i	0.357242	−	0.934012i
$50$	−0.958045	−	1.48920i	−0.135488	−	0.210605i
$51$	2.28744	+	8.53685i	0.320306	+	1.19540i
$52$	−0.669227	+	0.812085i	−0.0928051	+	0.112616i
$53$	6.49892	+	1.74138i	0.892696	+	0.239197i	0.675877	−	0.737015i	$-0.263765\pi$
$53$	6.49892	+	1.74138i	0.892696	+	0.239197i	0.216819	+	0.976212i	$0.430432\pi$
$54$	13.9360	+	12.6566i	1.89644	+	1.72235i
$55$			7.06225i			0.952274i
$56$	−5.08422	−	5.49096i	−0.679408	−	0.733761i
$57$			5.31638i			0.704171i
$58$	−2.87767	+	3.16855i	−0.377857	+	0.416050i
$59$	8.21574	+	2.20140i	1.06960	+	0.286598i	0.750328	−	0.661066i	$-0.229896\pi$
$59$	8.21574	+	2.20140i	1.06960	+	0.286598i	0.319270	+	0.947664i	$0.396562\pi$
$60$	−1.18551	−	12.2927i	−0.153049	−	1.58698i
$61$	0.101519	+	0.378874i	0.0129982	+	0.0485098i	0.972120	−	0.234483i	$-0.0753396\pi$
$61$	0.101519	+	0.378874i	0.0129982	+	0.0485098i	−0.959122	+	0.282992i	$0.908673\pi$
$62$	6.53368	−	4.20330i	0.829778	−	0.533819i
$63$	−18.9198	+	1.50050i	−2.38367	+	0.189045i
$64$	−7.66954	+	2.27557i	−0.958692	+	0.284446i
$65$	0.509302	−	0.882137i	0.0631711	−	0.109416i
$66$	7.53325	−	14.6294i	0.927279	−	1.80075i
$67$	−13.8977	−	3.72389i	−1.69788	−	0.454946i	−0.725476	−	0.688248i	$-0.758380\pi$
$67$	−13.8977	−	3.72389i	−1.69788	−	0.454946i	−0.972404	+	0.233302i	$0.925047\pi$
$68$	−4.51117	+	3.21880i	−0.547060	+	0.390337i
$69$	−5.74099	−	5.74099i	−0.691134	−	0.691134i
$70$	5.73048	+	4.43080i	0.684923	+	0.529582i
$71$	−8.98576			−1.06641			−0.533207	−	0.845985i	$-0.679013\pi$
$71$	−8.98576			−1.06641			−0.533207	+	0.845985i	$0.679013\pi$
$72$	−7.51425	+	18.8469i	−0.885563	+	2.22113i
$73$	0.766294	+	1.32726i	0.0896879	+	0.155344i	0.907379	−	0.420313i	$-0.138080\pi$
$73$	0.766294	+	1.32726i	0.0896879	+	0.155344i	−0.817691	+	0.575657i	$0.804746\pi$
$74$	6.32337	−	2.02465i	0.735077	−	0.235361i
$75$	−1.03365	−	3.85764i	−0.119356	−	0.445442i
$76$	−3.12230	+	1.16791i	−0.358152	+	0.133969i
$77$	3.22725	+	9.09605i	0.367779	+	1.03659i
$78$	−1.99598	+	1.28407i	−0.226001	+	0.145392i
$79$	3.47070	+	2.00381i	0.390484	+	0.225446i	0.682370	−	0.731007i	$-0.260949\pi$
$79$	3.47070	+	2.00381i	0.390484	+	0.225446i	−0.291886	+	0.956453i	$0.594283\pi$
$80$	6.95905	−	3.39674i	0.778046	−	0.379767i
$81$	10.4692	+	18.1331i	1.16324	+	2.01479i
$82$	0.269079	+	5.59317i	0.0297148	+	0.617662i
$83$	−3.67570	−	3.67570i	−0.403460	−	0.403460i	0.475990	−	0.879451i	$-0.342090\pi$
$83$	−3.67570	−	3.67570i	−0.403460	−	0.403460i	−0.879451	+	0.475990i	$0.842090\pi$
$84$	−7.14434	−	15.2910i	−0.779511	−	1.66839i
$85$	3.79313	−	3.79313i	0.411423	−	0.411423i
$86$	5.78150	−	6.36589i	0.623435	−	0.686451i
$87$	−8.36028	+	4.82681i	−0.896317	+	0.517489i
$88$	10.2467	+	1.21045i	1.09231	+	0.129034i
$89$	3.35201	−	5.80586i	0.355313	−	0.615420i	−0.631859	−	0.775084i	$-0.717708\pi$
$89$	3.35201	−	5.80586i	0.355313	−	0.615420i	0.987171	+	0.159664i	$0.0510410\pi$
$90$	4.16570	−	19.1930i	0.439103	−	2.02312i
$91$	0.252860	−	1.36891i	0.0265069	−	0.143501i
$92$	2.11048	−	4.63286i	0.220033	−	0.483009i
$93$	16.9249	−	4.53501i	1.75503	−	0.470259i
$94$	4.66851	+	2.40400i	0.481520	+	0.247953i
$95$	2.79451	−	1.61341i	0.286710	−	0.165532i
$96$	−18.0389	−	0.386856i	−1.84109	−	0.0394833i
$97$		−	4.52980i		−	0.459931i	−0.973199	−	0.229966i	$-0.926139\pi$
$97$		−	4.52980i		−	0.459931i	0.973199	−	0.229966i	$-0.0738613\pi$
$98$	9.40550	+	3.08812i	0.950099	+	0.311948i
$99$	18.5040	−	18.5040i	1.85972	−	1.85972i
$100$	2.03851	−	1.45452i	0.203851	−	0.145452i
$101$	−3.50302	+	13.0735i	−0.348564	+	1.30086i	0.539829	+	0.841775i	$0.318489\pi$
$101$	−3.50302	+	13.0735i	−0.348564	+	1.30086i	−0.888393	+	0.459084i	$0.848178\pi$
$102$	−11.9035	+	3.81134i	−1.17863	+	0.377378i
$103$	10.9548	+	6.32478i	1.07941	+	0.623200i	0.930738	−	0.365687i	$-0.119166\pi$
$103$	10.9548	+	6.32478i	1.07941	+	0.623200i	0.148675	+	0.988886i	$0.452499\pi$
$104$	−1.19261	−	0.890150i	−0.116945	−	0.0872864i
$105$	9.26159	+	13.4583i	0.903839	+	1.31340i
$106$	−2.01819	+	9.29859i	−0.196024	+	0.903158i
$107$	−3.48688	+	0.934307i	−0.337090	+	0.0903229i	−0.423393	−	0.905946i	$-0.639161\pi$
$107$	−3.48688	+	0.934307i	−0.337090	+	0.0903229i	0.0863036	+	0.996269i	$0.472494\pi$
$108$	−16.9315	+	20.5458i	−1.62923	+	1.97702i
$109$	2.63902	−	9.84896i	0.252772	−	0.943360i	−0.716544	−	0.697542i	$-0.754277\pi$
$109$	2.63902	−	9.84896i	0.252772	−	0.943360i	0.969316	−	0.245817i	$-0.0790564\pi$
$110$	−9.97599	+	0.479930i	−0.951174	+	0.0457595i
$111$	14.9748			1.42135
$112$	7.41091	−	7.55502i	0.700266	−	0.713882i
$113$	−18.4361			−1.73432			−0.867160	−	0.498030i	$-0.834057\pi$
$113$	−18.4361			−1.73432			−0.867160	+	0.498030i	$0.834057\pi$
$114$	−7.50981	+	0.361285i	−0.703358	+	0.0338375i
$115$	−1.27543	+	4.75997i	−0.118934	+	0.443869i
$116$	−4.67138	−	3.84962i	−0.433727	−	0.357428i
$117$	−3.64574	+	0.976873i	−0.337049	+	0.0903119i
$118$	−2.55134	+	11.7550i	−0.234869	+	1.08213i
$119$	3.15213	−	6.61883i	0.288955	−	0.606747i
$120$	17.2839	−	2.51000i	1.57779	−	0.229131i
$121$	−1.99844	−	1.15380i	−0.181676	−	0.104891i
$122$	−0.528291	+	0.169151i	−0.0478292	+	0.0153142i
$123$	−3.26871	+	12.1990i	−0.294729	+	1.09994i
$124$	6.38150	+	8.94370i	0.573076	+	0.803168i
$125$	−8.55865	+	8.55865i	−0.765509	+	0.765509i
$126$	−3.40531	−	26.6238i	−0.303369	−	2.37184i
$127$		−	20.5841i		−	1.82654i	−0.407350	−	0.913272i	$-0.633547\pi$
$127$		−	20.5841i		−	1.82654i	0.407350	−	0.913272i	$-0.366453\pi$
$128$	−3.73562	−	10.6792i	−0.330185	−	0.943916i
$129$	16.7966	−	9.69749i	1.47885	−	0.853817i
$130$	1.28070	+	0.659482i	0.112325	+	0.0578404i
$131$	−15.3810	+	4.12134i	−1.34385	+	0.360083i	−0.857860	−	0.513883i	$-0.828207\pi$
$131$	−15.3810	+	4.12134i	−1.34385	+	0.360083i	−0.485987	+	0.873966i	$0.661540\pi$
$132$	21.1771	+	9.64715i	1.84323	+	0.839676i
$133$	2.86199	−	3.35505i	0.248166	−	0.290920i
$134$	4.31584	−	19.8847i	0.372832	−	1.71778i
$135$	12.8853	−	22.3181i	1.10899	−	1.92083i
$136$	−4.85338	−	6.15365i	−0.416174	−	0.527671i
$137$	1.13536	−	0.655503i	0.0970008	−	0.0560034i	−0.450715	−	0.892668i	$-0.648831\pi$
$137$	1.13536	−	0.655503i	0.0970008	−	0.0560034i	0.547716	+	0.836665i	$0.315498\pi$
$138$	7.71946	−	8.49974i	0.657124	−	0.723546i
$139$	−15.6775	+	15.6775i	−1.32975	+	1.32975i	−0.424169	+	0.905583i	$0.639434\pi$
$139$	−15.6775	+	15.6775i	−1.32975	+	1.32975i	−0.905583	+	0.424169i	$0.860566\pi$
$140$	−5.86944	+	8.39586i	−0.496058	+	0.709580i
$141$	8.37444	+	8.37444i	0.705255	+	0.705255i
$142$	−0.610645	−	12.6931i	−0.0512442	−	1.06518i
$143$	0.959692	+	1.66224i	0.0802535	+	0.139003i
$144$	−27.1334	−	9.33370i	−2.26112	−	0.777808i
$145$	5.07434	+	2.92967i	0.421401	+	0.243296i
$146$	−1.82279	+	1.17265i	−0.150855	+	0.0970490i
$147$	18.0788	+	13.1018i	1.49112	+	1.08062i
$148$	3.28970	+	8.79468i	0.270411	+	0.722918i
$149$	3.24672	+	12.1169i	0.265981	+	0.992656i	0.961647	+	0.274290i	$0.0884428\pi$
$149$	3.24672	+	12.1169i	0.265981	+	0.992656i	−0.695666	+	0.718366i	$0.744891\pi$
$150$	5.37898	−	1.72227i	0.439192	−	0.140623i
$151$	4.56845	+	7.91278i	0.371775	+	0.643933i	0.989839	−	0.142195i	$-0.0454160\pi$
$151$	4.56845	+	7.91278i	0.371775	+	0.643933i	−0.618064	+	0.786128i	$0.712083\pi$
$152$	−1.86195	−	4.33113i	−0.151024	−	0.351301i
$153$	−19.8769			−1.60695
$154$	−12.6296	+	5.17689i	−1.01772	+	0.417166i
$155$	−7.52014	−	7.52014i	−0.604032	−	0.604032i
$156$	−1.94949	−	2.73222i	−0.156084	−	0.218753i
$157$	−12.7686	−	3.42134i	−1.01905	−	0.273053i	−0.289642	−	0.957135i	$-0.593536\pi$
$157$	−12.7686	−	3.42134i	−1.01905	−	0.273053i	−0.729405	+	0.684083i	$0.760203\pi$
$158$	−2.59468	+	5.03881i	−0.206422	+	0.400867i
$159$	−10.7301	+	18.5850i	−0.850949	+	1.47389i
$160$	5.27108	+	9.59938i	0.416715	+	0.758898i
$161$	0.532442	+	6.71358i	0.0419623	+	0.529104i
$162$	−24.9031	+	16.0208i	−1.95657	+	1.25871i
$163$	−0.102694	−	0.383258i	−0.00804358	−	0.0300191i	0.961787	−	0.273797i	$-0.0882798\pi$
$163$	−0.102694	−	0.383258i	−0.00804358	−	0.0300191i	−0.969831	+	0.243778i	$0.921613\pi$
$164$	−7.88251	+	0.760190i	−0.615521	+	0.0593609i
$165$	−21.7581	−	5.83007i	−1.69387	−	0.453871i
$166$	4.94243	−	5.44201i	0.383607	−	0.422382i
$167$		−	23.6587i		−	1.83076i	−0.402588	−	0.915381i	$-0.631889\pi$
$167$		−	23.6587i		−	1.83076i	0.402588	−	0.915381i	$-0.368111\pi$
$168$	21.1143	−	11.1311i	1.62900	−	0.858782i
$169$			12.7232i			0.978705i
$170$	5.61587	+	5.10033i	0.430717	+	0.391177i
$171$	−11.5493	−	3.09462i	−0.883195	−	0.236651i
$172$	9.38522	+	7.73422i	0.715616	+	0.589729i
$173$	3.98004	+	14.8537i	0.302597	+	1.12931i	0.934994	+	0.354662i	$0.115404\pi$
$173$	3.98004	+	14.8537i	0.302597	+	1.12931i	−0.632398	+	0.774644i	$0.717929\pi$
$174$	−7.38640	−	11.4816i	−0.559961	−	0.870414i
$175$	−1.42439	+	2.99092i	−0.107673	+	0.226093i
$176$	−1.01352	+	14.5566i	−0.0763967	+	1.09724i
$177$	−13.5646	+	23.4946i	−1.01958	+	1.76596i
$178$	8.42903	+	4.34044i	0.631783	+	0.325330i
$179$	0.555832	+	0.148935i	0.0415448	+	0.0111319i	0.279532	−	0.960136i	$-0.409821\pi$
$179$	0.555832	+	0.148935i	0.0415448	+	0.0111319i	−0.237987	+	0.971268i	$0.576487\pi$
$180$	27.3947	+	4.58008i	2.04188	+	0.341379i
$181$	0.240422	+	0.240422i	0.0178705	+	0.0178705i	0.715986	−	0.698115i	$-0.245978\pi$
$181$	0.240422	+	0.240422i	0.0178705	+	0.0178705i	−0.698115	+	0.715986i	$0.745978\pi$
$182$	1.95088	+	0.264157i	0.144609	+	0.0195806i
$183$	−1.25108			−0.0924826
$184$	6.68771	+	2.66638i	0.493024	+	0.196568i
$185$	−4.54454	−	7.87137i	−0.334121	−	0.578715i
$186$	7.55623	+	23.5996i	0.554050	+	1.73041i
$187$	2.61617	+	9.76367i	0.191313	+	0.713990i
$188$	−3.07858	+	6.75801i	−0.224528	+	0.492878i
$189$	6.39735	−	34.6335i	0.465339	−	2.51922i
$190$	2.46897	+	3.83782i	0.179118	+	0.278425i
$191$	4.57833	+	2.64330i	0.331277	+	0.191263i	0.656408	−	0.754406i	$-0.272075\pi$
$191$	4.57833	+	2.64330i	0.331277	+	0.191263i	−0.325131	+	0.945669i	$0.605408\pi$
$192$	−0.679405	−	25.5077i	−0.0490318	−	1.84086i
$193$	−8.43656	−	14.6125i	−0.607277	−	1.05183i	−0.991687	−	0.128672i	$-0.958929\pi$
$193$	−8.43656	−	14.6125i	−0.607277	−	1.05183i	0.384411	−	0.923162i	$-0.374405\pi$
$194$	6.39870	−	0.307832i	0.459400	−	0.0221010i
$195$	2.29734	+	2.29734i	0.164516	+	0.164516i
$196$	−3.72305	+	13.4959i	−0.265932	+	0.963992i
$197$	−1.81729	+	1.81729i	−0.129477	+	0.129477i	−0.768875	−	0.639399i	$-0.779183\pi$
$197$	−1.81729	+	1.81729i	−0.129477	+	0.129477i	0.639399	+	0.768875i	$0.279183\pi$
$198$	27.3958	+	24.8808i	1.94693	+	1.76820i
$199$	−0.631178	+	0.364411i	−0.0447430	+	0.0258324i	−0.522205	−	0.852820i	$-0.674890\pi$
$199$	−0.631178	+	0.364411i	−0.0447430	+	0.0258324i	0.477462	+	0.878653i	$0.341557\pi$
$200$	2.19315	+	2.78072i	0.155079	+	0.196626i
$201$	22.9459	−	39.7435i	1.61848	−	2.80329i
$202$	−18.7054	−	4.05987i	−1.31611	−	0.285651i
$203$	7.87443	+	1.45453i	0.552677	+	0.102088i
$204$	−6.19275	−	16.5557i	−0.433579	−	1.15913i
$205$	7.40426	−	1.98397i	0.517136	−	0.138566i
$206$	−8.18980	+	15.9044i	−0.570611	+	1.10811i
$207$	15.8135	−	9.12991i	1.09911	−	0.634573i
$208$	1.17636	−	1.74515i	0.0815660	−	0.121005i
$209$			6.08038i			0.420589i
$210$	−18.3816	+	13.9973i	−1.26845	+	0.965907i
$211$	−8.24367	+	8.24367i	−0.567518	+	0.567518i	−0.931432	−	0.363915i	$-0.881440\pi$
$211$	−8.24367	+	8.24367i	−0.567518	+	0.567518i	0.363915	+	0.931432i	$0.381440\pi$
$212$	−13.2721	−	2.21895i	−0.911535	−	0.152398i
$213$	7.41798	−	27.6843i	0.508272	−	1.89690i
$214$	−1.55674	−	4.86201i	−0.106417	−	0.332360i
$215$	−10.1948	−	5.88597i	−0.695280	−	0.401420i
$216$	−30.1732	−	22.5208i	−2.05302	−	1.53235i
$217$	−13.1223	−	6.24931i	−0.890799	−	0.424230i
$218$	14.0918	+	3.05852i	0.954416	+	0.207149i
$219$	−4.72176	+	1.26519i	−0.319067	+	0.0854937i
$220$	−1.35588	−	14.0593i	−0.0914133	−	0.947876i
$221$	0.377335	−	1.40824i	0.0253823	−	0.0947281i
$222$	1.01764	+	21.1531i	0.0682998	+	1.41970i
$223$	28.3640			1.89940			0.949698	−	0.313166i	$-0.101390\pi$
$223$	28.3640			1.89940			0.949698	+	0.313166i	$0.101390\pi$
$224$	11.1757	+	9.95509i	0.746708	+	0.665152i
$225$	8.98200			0.598800
$226$	−1.25286	−	26.0424i	−0.0833391	−	1.73232i
$227$	1.67563	−	6.25352i	0.111215	−	0.415061i	−0.887761	−	0.460305i	$-0.847740\pi$
$227$	1.67563	−	6.25352i	0.111215	−	0.415061i	0.998976	+	0.0452445i	$0.0144067\pi$
$228$	−1.02069	−	10.5837i	−0.0675968	−	0.700919i
$229$	7.68701	−	2.05973i	0.507972	−	0.136111i	0.00427468	−	0.999991i	$-0.498639\pi$
$229$	7.68701	−	2.05973i	0.507972	−	0.136111i	0.503697	+	0.863880i	$0.331973\pi$
$230$	−6.81051	−	1.47817i	−0.449071	−	0.0974678i
$231$	−30.6882	+	2.43383i	−2.01914	+	0.160134i
$232$	5.12044	−	6.86031i	0.336173	−	0.450401i
$233$	−0.159304	−	0.0919739i	−0.0104363	−	0.00602541i	0.494773	−	0.869022i	$-0.335251\pi$
$233$	−0.159304	−	0.0919739i	−0.0104363	−	0.00602541i	−0.505209	+	0.862997i	$0.668585\pi$
$234$	−1.62766	−	5.08351i	−0.106404	−	0.332320i
$235$	1.86048	−	6.94341i	0.121364	−	0.452938i
$236$	−16.7782	−	2.80513i	−1.09217	−	0.182599i
$237$	−9.03870	+	9.03870i	−0.587127	+	0.587127i
$238$	9.56384	+	4.00283i	0.619932	+	0.259465i
$239$			19.6670i			1.27215i	0.771626	+	0.636077i	$0.219444\pi$
$239$			19.6670i			1.27215i	−0.771626	+	0.636077i	$0.780556\pi$
$240$	4.72014	+	24.2443i	0.304684	+	1.56496i
$241$	−3.10397	+	1.79208i	−0.199944	+	0.115438i	−0.596630	−	0.802517i	$-0.703494\pi$
$241$	−3.10397	+	1.79208i	−0.199944	+	0.115438i	0.396685	+	0.917955i	$0.370160\pi$
$242$	1.49403	−	2.90137i	0.0960397	−	0.186507i
$243$	−25.9348	+	6.94921i	−1.66372	+	0.445792i
$244$	−0.274840	−	0.734758i	−0.0175948	−	0.0470381i
$245$	1.40028	−	13.4791i	0.0894608	−	0.861147i
$246$	−17.4542	−	3.78830i	−1.11284	−	0.241533i
$247$	0.438493	−	0.759493i	0.0279007	−	0.0483254i
$248$	−12.2000	+	9.62217i	−0.774702	+	0.611008i
$249$	14.3589	−	8.29010i	0.909957	−	0.525364i
$250$	−12.6714	−	11.5082i	−0.801409	−	0.727839i
$251$	11.1881	−	11.1881i	0.706184	−	0.706184i	−0.259547	−	0.965731i	$-0.583573\pi$
$251$	11.1881	−	11.1881i	0.706184	−	0.706184i	0.965731	+	0.259547i	$0.0835731\pi$
$252$	37.3768	−	6.61955i	2.35452	−	0.416992i
$253$	−6.56601	−	6.56601i	−0.412802	−	0.412802i
$254$	29.0767	−	1.39884i	1.82443	−	0.0877707i
$255$	8.55495	+	14.8176i	0.535732	+	0.927914i
$256$	14.8314	−	6.00259i	0.926959	−	0.375162i
$257$	7.97191	+	4.60259i	0.497274	+	0.287101i	0.727587	−	0.686015i	$-0.240642\pi$
$257$	7.97191	+	4.60259i	0.497274	+	0.287101i	−0.230313	+	0.973117i	$0.573975\pi$
$258$	14.8399	+	23.0675i	0.923894	+	1.43612i
$259$	−9.45028	−	8.06145i	−0.587212	−	0.500914i
$260$	−0.844539	+	1.85391i	−0.0523761	+	0.114974i
$261$	−5.61929	−	20.9715i	−0.347825	−	1.29810i
$262$	−6.86697	−	21.4469i	−0.424243	−	1.32499i
$263$	1.54283	+	2.67226i	0.0951349	+	0.164778i	0.909665	−	0.415343i	$-0.136338\pi$
$263$	1.54283	+	2.67226i	0.0951349	+	0.164778i	−0.814530	+	0.580121i	$0.803005\pi$
$264$	−12.1882	+	30.5700i	−0.750134	+	1.88145i
$265$	13.0254			0.800143
$266$	4.93377	+	3.81479i	0.302509	+	0.233900i
$267$	15.1201	+	15.1201i	0.925337	+	0.925337i
$268$	28.3821	+	4.74516i	1.73371	+	0.289857i
$269$	−23.3503	−	6.25670i	−1.42369	−	0.381478i	−0.536902	−	0.843645i	$-0.680405\pi$
$269$	−23.3503	−	6.25670i	−1.42369	−	0.381478i	−0.886793	+	0.462167i	$0.847072\pi$
$270$	32.4017	+	16.6849i	1.97191	+	1.01541i
$271$	5.80261	−	10.0504i	0.352484	−	0.610520i	−0.634200	−	0.773169i	$-0.718671\pi$
$271$	5.80261	−	10.0504i	0.352484	−	0.610520i	0.986684	+	0.162649i	$0.0520039\pi$
$272$	8.36269	−	7.27398i	0.507063	−	0.441050i
$273$	4.00875	+	1.90911i	0.242620	+	0.115545i
$274$	1.00311	+	1.55925i	0.0605999	+	0.0941976i
$275$	−1.18220	−	4.41202i	−0.0712891	−	0.266055i
$276$	12.5312	+	10.3267i	0.754287	+	0.621597i
$277$	−6.42687	−	1.72208i	−0.386153	−	0.103469i	0.0605191	−	0.998167i	$-0.480724\pi$
$277$	−6.42687	−	1.72208i	−0.386153	−	0.103469i	−0.446672	+	0.894698i	$0.647391\pi$
$278$	−23.2112	−	21.0804i	−1.39211	−	1.26432i
$279$			39.4074i			2.35926i
$280$	−12.2587	−	7.72049i	−0.732597	−	0.461388i
$281$			16.2605i			0.970022i	0.874508	+	0.485011i	$0.161184\pi$
$281$			16.2605i			0.970022i	−0.874508	+	0.485011i	$0.838816\pi$
$282$	−11.2605	+	12.3987i	−0.670551	+	0.738330i
$283$	23.1624	+	6.20636i	1.37686	+	0.368930i	0.869981	−	0.493085i	$-0.164131\pi$
$283$	23.1624	+	6.20636i	1.37686	+	0.368930i	0.506883	+	0.862015i	$0.330798\pi$
$284$	17.8885	−	1.72517i	1.06149	−	0.102370i
$285$	2.66382	+	9.94152i	0.157791	+	0.588885i
$286$	−2.28282	+	1.46860i	−0.134986	+	0.0868403i
$287$	8.62993	−	5.93885i	0.509409	−	0.350559i
$288$	11.3407	−	38.9624i	0.668257	−	2.29588i
$289$	−4.66108	+	8.07323i	−0.274181	+	0.474896i
$290$	−3.79356	+	7.36700i	−0.222765	+	0.432605i
$291$	13.9559	+	3.73947i	0.818108	+	0.219211i
$292$	−1.78033	−	2.49514i	−0.104186	−	0.146017i
$293$	−15.5002	−	15.5002i	−0.905534	−	0.905534i	0.0903743	−	0.995908i	$-0.471194\pi$
$293$	−15.5002	−	15.5002i	−0.905534	−	0.905534i	−0.995908	+	0.0903743i	$0.971194\pi$
$294$	−17.2787	+	26.4281i	−1.00771	+	1.54132i
$295$	16.4663			0.958705
$296$	−12.1996	+	5.24462i	−0.709089	+	0.304837i
$297$	24.2802	+	42.0546i	1.40888	+	2.44025i
$298$	−16.8955	+	5.40967i	−0.978728	+	0.313374i
$299$	0.346637	+	1.29367i	0.0200465	+	0.0748147i
$300$	2.79838	+	7.48120i	0.161565	+	0.431927i
$301$	−15.8204	−	2.92228i	−0.911875	−	0.168438i
$302$	−10.8670	+	6.99103i	−0.625324	+	0.402288i
$303$	−37.3863	−	21.5850i	−2.14779	−	1.24002i
$304$	5.99153	−	2.92449i	0.343638	−	0.167731i
$305$	0.379677	+	0.657620i	0.0217402	+	0.0376552i
$306$	−1.35078	−	28.0777i	−0.0772188	−	1.60510i
$307$	8.30421	+	8.30421i	0.473946	+	0.473946i	0.903189	−	0.429243i	$-0.141220\pi$
$307$	8.30421	+	8.30421i	0.473946	+	0.473946i	−0.429243	+	0.903189i	$0.641220\pi$
$308$	−8.17104	−	17.4885i	−0.465588	−	0.996499i
$309$	−28.5296	+	28.5296i	−1.62299	+	1.62299i
$310$	10.1117	−	11.1338i	0.574309	−	0.632360i
$311$	7.66004	−	4.42252i	0.434361	−	0.250778i	−0.266842	−	0.963740i	$-0.585980\pi$
$311$	7.66004	−	4.42252i	0.434361	−	0.250778i	0.701203	+	0.712962i	$0.252647\pi$
$312$	3.72700	−	2.93949i	0.211000	−	0.166416i
$313$	−12.5112	+	21.6700i	−0.707174	+	1.22486i	0.258727	+	0.965951i	$0.416697\pi$
$313$	−12.5112	+	21.6700i	−0.707174	+	1.22486i	−0.965901	+	0.258911i	$0.916636\pi$
$314$	3.96520	−	18.2692i	0.223769	−	1.03099i
$315$	−34.6279	+	12.2859i	−1.95106	+	0.692230i
$316$	−7.29405	−	3.32277i	−0.410323	−	0.186921i
$317$	−3.08904	+	0.827705i	−0.173498	+	0.0464885i	−0.344522	−	0.938778i	$-0.611959\pi$
$317$	−3.08904	+	0.827705i	−0.173498	+	0.0464885i	0.171024	+	0.985267i	$0.445292\pi$
$318$	−26.9820	−	13.8941i	−1.51308	−	0.779142i
$319$	−9.56172	+	5.52046i	−0.535354	+	0.309087i
$320$	−13.2017	+	8.09816i	−0.737997	+	0.452701i
$321$		−	11.5141i		−	0.642652i
$322$	−9.44729	+	1.20835i	−0.526477	+	0.0673388i
$323$	3.26577	−	3.26577i	0.181712	−	0.181712i
$324$	−24.3230	−	34.0888i	−1.35128	−	1.89382i
$325$	−0.170511	+	0.636355i	−0.00945823	+	0.0352986i
$326$	0.534403	−	0.171108i	0.0295979	−	0.00947679i
$327$	28.1652	+	16.2612i	1.55754	+	0.899244i
$328$	−1.60950	−	11.0830i	−0.0888699	−	0.611957i
$329$	−0.776679	−	9.79317i	−0.0428197	−	0.539915i
$330$	6.75683	−	31.1313i	0.371951	−	1.71372i
$331$	13.2504	−	3.55043i	0.728306	−	0.195149i	0.124431	−	0.992228i	$-0.460289\pi$
$331$	13.2504	−	3.55043i	0.728306	−	0.195149i	0.603875	+	0.797079i	$0.293623\pi$
$332$	8.02314	+	6.61175i	0.440327	+	0.362867i
$333$	−8.71671	+	32.5312i	−0.477673	+	1.78270i
$334$	33.4198	−	1.60777i	1.82865	−	0.0879734i
$335$	−27.8544			−1.52185
$336$	17.1584	+	29.0692i	0.936068	+	1.58585i
$337$	30.3580			1.65371			0.826854	−	0.562417i	$-0.190128\pi$
$337$	30.3580			1.65371			0.826854	+	0.562417i	$0.190128\pi$
$338$	−17.9725	+	0.864629i	−0.977574	+	0.0470296i
$339$	15.2195	−	56.7998i	0.826608	−	3.08494i
$340$	−6.82298	+	8.27947i	−0.370028	+	0.449017i
$341$	19.3571	−	5.18673i	1.04825	−	0.280877i
$342$	3.58654	−	16.5246i	0.193938	−	0.893546i
$343$	−4.35602	−	18.0007i	−0.235203	−	0.971946i
$344$	−10.2874	+	13.7830i	−0.554660	+	0.743128i
$345$	−13.6121	−	7.85895i	−0.732851	−	0.423112i
$346$	−20.7116	+	6.63154i	−1.11346	+	0.356514i
$347$	3.49811	−	13.0551i	0.187788	−	0.700836i	−0.806228	−	0.591605i	$-0.798494\pi$
$347$	3.49811	−	13.0551i	0.187788	−	0.700836i	0.994016	−	0.109231i	$-0.0348389\pi$
$348$	15.7167	−	11.2141i	0.842501	−	0.601140i
$349$	12.6593	−	12.6593i	0.677639	−	0.677639i	−0.281826	−	0.959465i	$-0.590940\pi$
$349$	12.6593	−	12.6593i	0.677639	−	0.677639i	0.959465	+	0.281826i	$0.0909402\pi$
$350$	−4.32172	−	1.80880i	−0.231005	−	0.0966846i
$351$		−	7.00398i		−	0.373845i
$352$	−20.6312	−	0.442450i	−1.09965	−	0.0235827i
$353$	−26.7828	+	15.4631i	−1.42550	+	0.823016i	−0.996762	−	0.0804108i	$-0.974377\pi$
$353$	−26.7828	+	15.4631i	−1.42550	+	0.823016i	−0.428743	+	0.903426i	$0.641043\pi$
$354$	−34.1098	−	17.5645i	−1.81292	−	0.933541i
$355$	−16.8032	+	4.50240i	−0.891821	+	0.238963i
$356$	−5.55840	+	12.2016i	−0.294595	+	0.646686i
$357$	17.7898	+	15.1754i	0.941538	+	0.803169i
$358$	−0.172609	+	0.795278i	−0.00912269	+	0.0420317i
$359$	−9.22928	+	15.9856i	−0.487103	+	0.843687i	−0.999890	−	0.0148287i	$-0.995280\pi$
$359$	−9.22928	+	15.9856i	−0.487103	+	0.843687i	0.512787	+	0.858516i	$0.328613\pi$
$360$	−4.60807	+	39.0084i	−0.242867	+	2.05593i
$361$	−14.0485	+	8.11090i	−0.739395	+	0.426890i
$362$	−0.323278	+	0.355954i	−0.0169911	+	0.0187085i
$363$	5.20452	−	5.20452i	0.273166	−	0.273166i
$364$	−0.240567	+	2.77373i	−0.0126091	+	0.145383i
$365$	2.09799	+	2.09799i	0.109814	+	0.109814i
$366$	−0.0850198	−	1.76725i	−0.00444406	−	0.0923758i
$367$	8.10460	+	14.0376i	0.423057	+	0.732756i	0.996237	−	0.0866738i	$-0.0276238\pi$
$367$	8.10460	+	14.0376i	0.423057	+	0.732756i	−0.573180	+	0.819429i	$0.694290\pi$
$368$	−3.31200	+	9.62812i	−0.172650	+	0.501901i
$369$	−24.5983	−	14.2018i	−1.28054	−	0.739318i
$370$	10.8101	−	6.95444i	0.561991	−	0.361544i
$371$	16.7765	−	5.95224i	0.870990	−	0.309025i
$372$	−32.8228	+	12.2775i	−1.70178	+	0.636561i
$373$	9.31929	+	34.7801i	0.482534	+	1.80084i	0.590915	+	0.806734i	$0.298767\pi$
$373$	9.31929	+	34.7801i	0.482534	+	1.80084i	−0.108381	+	0.994109i	$0.534567\pi$
$374$	−13.6142	+	4.35906i	−0.703972	+	0.225401i
$375$	−19.3030	−	33.4338i	−0.996803	−	1.72651i
$376$	−9.75543	−	3.88948i	−0.503098	−	0.200585i
$377$	1.59246			0.0820157
$378$	49.3573	+	6.68318i	2.53867	+	0.343746i
$379$	−18.9916	−	18.9916i	−0.975531	−	0.975531i	0.0241768	−	0.999708i	$-0.492304\pi$
$379$	−18.9916	−	18.9916i	−0.975531	−	0.975531i	−0.999708	+	0.0241768i	$0.992304\pi$
$380$	−5.25344	+	3.74843i	−0.269496	+	0.192290i
$381$	63.4177	+	16.9927i	3.24899	+	0.870564i
$382$	−3.42275	+	6.64689i	−0.175123	+	0.340085i
$383$	11.8784	−	20.5740i	0.606957	−	1.05128i	−0.384782	−	0.923007i	$-0.625723\pi$
$383$	11.8784	−	20.5740i	0.606957	−	1.05128i	0.991739	−	0.128273i	$-0.0409433\pi$
$384$	35.9854	−	2.69314i	1.83637	−	0.137434i
$385$	10.5926	+	15.3924i	0.539847	+	0.784468i
$386$	20.0681	−	12.9103i	1.02144	−	0.657119i
$387$	11.2897	+	42.1336i	0.573886	+	2.14177i
$388$	0.869673	+	9.01775i	0.0441510	+	0.457807i
$389$	13.0521	+	3.49731i	0.661770	+	0.177321i	0.574045	−	0.818824i	$-0.305374\pi$
$389$	13.0521	+	3.49731i	0.661770	+	0.177321i	0.0877254	+	0.996145i	$0.472040\pi$
$390$	−3.08905	+	3.40129i	−0.156420	+	0.172231i
$391$			7.05320i			0.356696i
$392$	−19.3170	−	4.34197i	−0.975657	−	0.219302i
$393$		−	50.7898i		−	2.56201i
$394$	−2.69056	−	2.44357i	−0.135549	−	0.123105i
$395$	7.49417	+	2.00806i	0.377073	+	0.101036i
$396$	−33.2844	+	40.3896i	−1.67261	+	2.02965i
$397$	−1.19554	−	4.46180i	−0.0600022	−	0.223931i	0.929413	−	0.369040i	$-0.120313\pi$
$397$	−1.19554	−	4.46180i	−0.0600022	−	0.223931i	−0.989416	+	0.145109i	$0.953647\pi$
$398$	−0.557652	−	0.866825i	−0.0279526	−	0.0434500i
$399$	7.97395	+	11.5872i	0.399197	+	0.580086i
$400$	−3.77894	+	3.28697i	−0.188947	+	0.164349i
$401$	11.1566	−	19.3238i	0.557135	−	0.964986i	−0.440599	−	0.897704i	$-0.645234\pi$
$401$	11.1566	−	19.3238i	0.557135	−	0.964986i	0.997734	−	0.0672821i	$-0.0214327\pi$
$402$	57.7002	+	29.7121i	2.87782	+	1.48190i
$403$	−2.79192	−	0.748093i	−0.139076	−	0.0372652i
$404$	4.46373	−	26.6987i	0.222079	−	1.32831i
$405$	28.6629	+	28.6629i	1.42427	+	1.42427i
$406$	−1.51952	+	11.2221i	−0.0754124	+	0.556944i
$407$	17.1268			0.848944
$408$	22.9654	−	9.87282i	1.13696	−	0.488778i
$409$	−2.83340	−	4.90759i	−0.140102	−	0.242665i	0.787433	−	0.616401i	$-0.211410\pi$
$409$	−2.83340	−	4.90759i	−0.140102	−	0.242665i	−0.927535	+	0.373736i	$0.878077\pi$
$410$	3.30568	+	10.3243i	0.163256	+	0.509880i
$411$	1.08227	+	4.03909i	0.0533845	+	0.199234i
$412$	−23.0228	−	10.4879i	−1.13425	−	0.516703i
$413$	21.2083	−	7.52464i	1.04359	−	0.370263i
$414$	13.9714	+	21.7173i	0.686655	+	1.06735i
$415$	−8.71523	−	5.03174i	−0.427814	−	0.246998i
$416$	2.54511	+	1.54311i	0.124784	+	0.0756571i
$417$	−35.3588	−	61.2433i	−1.73153	−	2.99910i
$418$	−8.58903	+	0.413205i	−0.420103	+	0.0202105i
$419$	2.67538	+	2.67538i	0.130701	+	0.130701i	0.769431	−	0.638730i	$-0.220540\pi$
$419$	2.67538	+	2.67538i	0.130701	+	0.130701i	−0.638730	+	0.769431i	$0.720540\pi$
$420$	−21.0215	−	25.0142i	−1.02574	−	1.22057i
$421$	17.2159	−	17.2159i	0.839052	−	0.839052i	−0.149682	−	0.988734i	$-0.547825\pi$
$421$	17.2159	−	17.2159i	0.839052	−	0.839052i	0.988734	+	0.149682i	$0.0478251\pi$
$422$	−12.2051	−	11.0846i	−0.594133	−	0.539591i
$423$	−23.0673	+	13.3179i	−1.12157	+	0.647538i
$424$	2.23251	−	18.8988i	0.108420	−	0.917805i
$425$	−1.73473	+	3.00465i	−0.0841470	+	0.145747i
$426$	39.6104	+	8.59715i	1.91913	+	0.416533i
$427$	0.789530	+	0.673500i	0.0382081	+	0.0325930i
$428$	6.76218	−	2.52943i	0.326862	−	0.122265i
$429$	−5.91344	+	1.58450i	−0.285504	+	0.0765005i
$430$	7.62159	−	14.8010i	0.367546	−	0.713766i
$431$	−27.7876	+	16.0432i	−1.33848	+	0.772774i	−0.986582	−	0.163264i	$-0.947798\pi$
$431$	−27.7876	+	16.0432i	−1.33848	+	0.772774i	−0.351901	+	0.936037i	$0.614465\pi$
$432$	29.7620	−	44.1524i	1.43192	−	2.12428i
$433$			15.7783i			0.758258i	0.925344	+	0.379129i	$0.123776\pi$
$433$			15.7783i			0.758258i	−0.925344	+	0.379129i	$0.876224\pi$
$434$	7.93589	−	18.9610i	0.380935	−	0.910156i
$435$	−13.2150	+	13.2150i	−0.633613	+	0.633613i
$436$	−3.36277	+	20.1136i	−0.161048	+	0.963268i
$437$	−1.09811	+	4.09819i	−0.0525295	+	0.196043i
$438$	−2.10806	−	6.58388i	−0.100727	−	0.314590i
$439$	1.89128	+	1.09193i	0.0902658	+	0.0521150i	0.544453	−	0.838791i	$-0.316737\pi$
$439$	1.89128	+	1.09193i	0.0902658	+	0.0521150i	−0.454188	+	0.890906i	$0.650070\pi$
$440$	19.7677	−	2.87071i	0.942388	−	0.136856i
$441$	−38.9857	+	31.6479i	−1.85646	+	1.50704i
$442$	2.01489	+	0.437317i	0.0958384	+	0.0208010i
$443$	−19.9847	+	5.35487i	−0.949500	+	0.254418i	−0.700150	−	0.713996i	$-0.746884\pi$
$443$	−19.9847	+	5.35487i	−0.949500	+	0.254418i	−0.249350	+	0.968413i	$0.580217\pi$
$444$	−29.8113	+	2.87501i	−1.41478	+	0.136442i
$445$	3.35912	−	12.5364i	0.159237	−	0.594282i
$446$	1.92754	+	40.0665i	0.0912715	+	1.89720i
$447$	−40.0113			−1.89247
$448$	−13.3029	+	16.4631i	−0.628503	+	0.777807i
$449$	31.8400			1.50262			0.751311	−	0.659949i	$-0.229422\pi$
$449$	31.8400			1.50262			0.751311	+	0.659949i	$0.229422\pi$
$450$	0.610390	+	12.6878i	0.0287741	+	0.598108i
$451$	−3.73844	+	13.9521i	−0.176036	+	0.656977i
$452$	36.7019	−	3.53953i	1.72631	−	0.166486i
$453$	−28.1499	+	7.54275i	−1.32260	+	0.354389i
$454$	8.94746	+	1.94198i	0.419925	+	0.0911418i
$455$	−0.213064	−	2.68654i	−0.00998861	−	0.125947i
$456$	14.8809	−	2.16104i	0.696862	−	0.101200i
$457$	−8.74709	−	5.05014i	−0.409172	−	0.236235i	0.281262	−	0.959631i	$-0.409247\pi$
$457$	−8.74709	−	5.05014i	−0.409172	−	0.236235i	−0.690434	+	0.723396i	$0.742580\pi$
$458$	3.43192	+	10.7185i	0.160363	+	0.500845i
$459$	9.54659	−	35.6284i	0.445597	−	1.66299i
$460$	1.62521	−	9.72084i	0.0757760	−	0.453236i
$461$	−14.0523	+	14.0523i	−0.654479	+	0.654479i	−0.954068	−	0.299589i	$-0.903150\pi$
$461$	−14.0523	+	14.0523i	−0.654479	+	0.654479i	0.299589	+	0.954068i	$0.403150\pi$
$462$	−5.52346	−	43.1842i	−0.256975	−	2.00911i
$463$		−	9.31917i		−	0.433099i	−0.976272	−	0.216549i	$-0.930520\pi$
$463$		−	9.31917i		−	0.433099i	0.976272	−	0.216549i	$-0.0694802\pi$
$464$	10.0387	+	6.76682i	0.466035	+	0.314142i
$465$	29.3769	−	16.9608i	1.36232	−	0.786537i
$466$	0.119095	−	0.231279i	0.00551696	−	0.0107138i
$467$	13.2103	−	3.53968i	0.611298	−	0.163797i	0.0601291	−	0.998191i	$-0.480849\pi$
$467$	13.2103	−	3.53968i	0.611298	−	0.163797i	0.551169	+	0.834394i	$0.314182\pi$
$468$	7.07025	−	2.64467i	0.326823	−	0.122250i
$469$	−35.8760	+	12.7287i	−1.65660	+	0.587756i
$470$	9.93456	+	2.15623i	0.458247	+	0.0994593i
$471$	21.0817	−	36.5145i	0.971391	−	1.68250i
$472$	2.82227	−	23.8912i	0.129906	−	1.09968i
$473$	19.2104	−	11.0911i	0.883293	−	0.509969i
$474$	−13.3821	−	12.1536i	−0.614662	−	0.558236i
$475$	−1.47574	+	1.47574i	−0.0677116	+	0.0677116i
$476$	−5.00439	+	13.7817i	−0.229376	+	0.631684i
$477$	−34.1281	−	34.1281i	−1.56262	−	1.56262i
$478$	−27.7812	+	1.33651i	−1.27068	+	0.0611307i
$479$	13.2090	+	22.8786i	0.603534	+	1.04535i	0.992281	+	0.124007i	$0.0395745\pi$
$479$	13.2090	+	22.8786i	0.603534	+	1.04535i	−0.388748	+	0.921344i	$0.627092\pi$
$480$	−33.9262	+	8.31515i	−1.54851	+	0.379533i
$481$	−2.13929	−	1.23512i	−0.0975431	−	0.0563165i
$482$	−2.74239	−	4.26282i	−0.124912	−	0.194166i
$483$	−21.1235	−	3.90183i	−0.961151	−	0.177540i
$484$	4.19994	+	1.91326i	0.190906	+	0.0869666i
$485$	−2.26970	−	8.47063i	−0.103062	−	0.384631i
$486$	−11.5788	−	36.1627i	−0.525223	−	1.64037i
$487$	16.0930	+	27.8738i	0.729242	+	1.26308i	0.957204	+	0.289414i	$0.0934604\pi$
$487$	16.0930	+	27.8738i	0.729242	+	1.26308i	−0.227962	+	0.973670i	$0.573206\pi$
$488$	1.01923	−	0.438166i	0.0461382	−	0.0198348i
$489$	1.26556			0.0572305
$490$	19.1354	+	1.06201i	0.864451	+	0.0479768i
$491$	−2.25713	−	2.25713i	−0.101863	−	0.101863i	0.654339	−	0.756202i	$-0.272947\pi$
$491$	−2.25713	−	2.25713i	−0.101863	−	0.101863i	−0.756202	+	0.654339i	$0.772947\pi$
$492$	4.16514	−	24.9128i	0.187779	−	1.12316i
$493$	8.10063	+	2.17056i	0.364834	+	0.0977570i
$494$	1.10264	+	0.567794i	0.0496103	+	0.0255463i
$495$	25.3304	−	43.8736i	1.13852	−	1.97197i
$496$	−14.4212	−	16.5796i	−0.647529	−	0.744447i
$497$	−19.5847	+	13.4776i	−0.878495	+	0.604553i
$498$	12.6862	+	19.7197i	0.568483	+	0.883660i
$499$	5.90659	+	22.0437i	0.264415	+	0.986811i	0.962607	+	0.270900i	$0.0873214\pi$
$499$	5.90659	+	22.0437i	0.264415	+	0.986811i	−0.698192	+	0.715910i	$0.746012\pi$
$500$	15.3951	−	18.6814i	0.688489	−	0.835458i
$501$	72.8901	+	19.5309i	3.25649	+	0.872574i
$502$	16.5643	+	15.0437i	0.739302	+	0.671434i
$503$		−	23.1194i		−	1.03084i	−0.856937	−	0.515422i	$-0.827635\pi$
$503$		−	23.1194i		−	1.03084i	0.856937	−	0.515422i	$-0.172365\pi$
$504$	11.8907	+	52.3479i	0.529652	+	2.33176i
$505$			26.2023i			1.16599i
$506$	8.82881	−	9.72122i	0.392488	−	0.432161i
$507$	−39.1989	−	10.5033i	−1.74088	−	0.466468i
$508$	3.95193	+	40.9781i	0.175339	+	1.81811i
$509$	2.84236	+	10.6078i	0.125986	+	0.470185i	0.999873	−	0.0159440i	$-0.00507533\pi$
$509$	2.84236	+	10.6078i	0.125986	+	0.470185i	−0.873887	+	0.486129i	$0.838409\pi$
$510$	−20.3497	+	13.0915i	−0.901099	+	0.579702i
$511$	3.66089	+	1.74345i	0.161948	+	0.0771257i
$512$	9.48703	+	20.5425i	0.419271	+	0.907861i
$513$	11.0939	−	19.2152i	0.489807	−	0.848371i
$514$	−5.95977	+	11.5737i	−0.262874	+	0.510496i
$515$	23.6544	+	6.33819i	1.04234	+	0.279294i
$516$	−31.5761	+	22.5302i	−1.39006	+	0.991836i
$517$	9.57791	+	9.57791i	0.421236	+	0.421236i
$518$	10.7452	−	13.8971i	0.472118	−	0.610604i
$519$	−49.0485			−2.15299
$520$	−2.67618	−	1.06699i	−0.117358	−	0.0467907i
$521$	−4.42108	−	7.65754i	−0.193691	−	0.335483i	0.752780	−	0.658273i	$-0.228713\pi$
$521$	−4.42108	−	7.65754i	−0.193691	−	0.335483i	−0.946471	+	0.322790i	$0.895379\pi$
$522$	29.2420	−	9.36286i	1.27989	−	0.409801i
$523$	−4.92948	−	18.3971i	−0.215551	−	0.804448i	−0.985972	−	0.166912i	$-0.946620\pi$
$523$	−4.92948	−	18.3971i	−0.215551	−	0.804448i	0.770420	−	0.637536i	$-0.220046\pi$
$524$	29.8288	−	11.1576i	1.30308	−	0.487422i
$525$	−8.03889	−	6.85749i	−0.350846	−	0.299285i
$526$	−3.66993	+	2.36097i	−0.160017	+	0.102943i
$527$	−13.1825	−	7.61092i	−0.574239	−	0.331537i
$528$	−44.0108	−	15.1394i	−1.91532	−	0.658858i
$529$	8.26031	+	14.3073i	0.359144	+	0.622055i
$530$	0.885167	+	18.3994i	0.0384492	+	0.799219i
$531$	−43.1437	−	43.1437i	−1.87228	−	1.87228i
$532$	−5.05341	+	7.22858i	−0.219093	+	0.313399i
$533$	1.47313	−	1.47313i	0.0638085	−	0.0638085i
$534$	−20.3309	+	22.3859i	−0.879803	+	0.968733i
$535$	−6.05226	+	3.49427i	−0.261662	+	0.151071i
$536$	−4.77416	+	40.4144i	−0.206212	+	1.74564i
$537$	−0.917707	+	1.58952i	−0.0396020	+	0.0685927i
$538$	7.25127	−	33.4094i	0.312624	−	1.44038i
$539$	20.6769	+	14.9846i	0.890617	+	0.645432i
$540$	−21.3668	+	46.9039i	−0.919482	+	2.01842i
$541$	−2.32628	+	0.623324i	−0.100014	+	0.0267988i	−0.308479	−	0.951231i	$-0.599820\pi$
$541$	−2.32628	+	0.623324i	−0.100014	+	0.0267988i	0.208465	+	0.978030i	$0.433153\pi$
$542$	14.5913	+	7.51366i	0.626752	+	0.322739i
$543$	−0.939194	+	0.542244i	−0.0403047	+	0.0232699i
$544$	10.8434	+	11.3187i	0.464906	+	0.485283i
$545$		−	19.7397i		−	0.845555i
$546$	−2.42435	+	5.79241i	−0.103752	+	0.247892i
$547$	−11.9972	+	11.9972i	−0.512962	+	0.512962i	−0.915433	−	0.402471i	$-0.868151\pi$
$547$	−11.9972	+	11.9972i	−0.512962	+	0.512962i	0.402471	+	0.915433i	$0.368151\pi$
$548$	−2.13439	+	1.52293i	−0.0911768	+	0.0650563i
$549$	0.728244	−	2.71784i	0.0310807	−	0.115995i
$550$	6.15199	−	1.96977i	0.262322	−	0.0839915i
$551$	4.36885	+	2.52236i	0.186119	+	0.107456i
$552$	−13.7358	+	18.4030i	−0.584633	+	0.783285i
$553$	10.5700	−	0.838286i	0.449481	−	0.0356475i
$554$	1.99582	−	9.19550i	0.0847942	−	0.390679i
$555$	28.0026	−	7.50327i	1.18864	−	0.318496i
$556$	28.2004	−	34.2202i	1.19596	−	1.45126i
$557$	5.28493	−	19.7236i	0.223930	−	0.835716i	−0.758901	−	0.651206i	$-0.774263\pi$
$557$	5.28493	−	19.7236i	0.223930	−	0.835716i	0.982831	−	0.184510i	$-0.0590699\pi$
$558$	−55.6660	+	2.67801i	−2.35653	+	0.113369i
$559$	−3.19939			−0.135320
$560$	10.0727	−	17.8411i	0.425651	−	0.753922i
$561$	−32.2407			−1.36120
$562$	−22.9693	+	1.10502i	−0.968901	+	0.0466124i
$563$	4.13466	−	15.4308i	0.174255	−	0.650330i	−0.822422	−	0.568878i	$-0.807378\pi$
$563$	4.13466	−	15.4308i	0.174255	−	0.650330i	0.996677	−	0.0814517i	$-0.0259556\pi$
$564$	−18.2793	−	15.0637i	−0.769699	−	0.634297i
$565$	−34.4751	+	9.23757i	−1.45038	+	0.388628i
$566$	−7.19292	+	33.1406i	−0.302341	+	1.39300i
$567$	50.0155	+	23.8192i	2.10045	+	1.00031i
$568$	3.65259	+	25.1517i	0.153259	+	1.05534i
$569$	−17.3910	−	10.0407i	−0.729068	−	0.420928i	0.0890129	−	0.996030i	$-0.471629\pi$
$569$	−17.3910	−	10.0407i	−0.729068	−	0.420928i	−0.818081	+	0.575103i	$0.804962\pi$
$570$	−13.8622	+	4.43846i	−0.580622	+	0.185907i
$571$	4.66153	−	17.3971i	0.195079	−	0.728045i	−0.797167	−	0.603758i	$-0.793669\pi$
$571$	4.66153	−	17.3971i	0.195079	−	0.728045i	0.992246	−	0.124286i	$-0.0396641\pi$
$572$	−2.22965	−	3.12487i	−0.0932264	−	0.130657i
$573$	−11.9233	+	11.9233i	−0.498103	+	0.498103i
$574$	8.97557	+	11.7869i	0.374633	+	0.491975i
$575$		−	3.18721i		−	0.132916i
$576$	55.8082	+	13.3719i	2.32534	+	0.557161i
$577$	−16.2314	+	9.37123i	−0.675724	+	0.390129i	−0.798242	−	0.602337i	$-0.794236\pi$
$577$	−16.2314	+	9.37123i	−0.675724	+	0.390129i	0.122518	+	0.992466i	$0.460903\pi$
$578$	−11.7208	−	6.03552i	−0.487523	−	0.251044i
$579$	51.9845	−	13.9292i	2.16040	−	0.578878i
$580$	−10.6643	−	4.85806i	−0.442810	−	0.201720i
$581$	−13.5244	−	2.49817i	−0.561087	−	0.103642i
$582$	−4.33389	+	19.9679i	−0.179646	+	0.827697i
$583$	−12.2721	+	21.2558i	−0.508257	+	0.880327i
$584$	3.40360	−	2.68442i	0.140842	−	0.111082i
$585$	−6.32799	+	3.65347i	−0.261630	+	0.151052i
$586$	20.8420	−	22.9487i	0.860974	−	0.948001i
$587$	−16.4500	+	16.4500i	−0.678963	+	0.678963i	−0.959766	−	0.280802i	$-0.909399\pi$
$587$	−16.4500	+	16.4500i	−0.678963	+	0.678963i	0.280802	+	0.959766i	$0.409399\pi$
$588$	−38.5061	−	22.6116i	−1.58796	−	0.932486i
$589$	−6.47461	−	6.47461i	−0.266782	−	0.266782i
$590$	1.11900	+	23.2600i	0.0460685	+	0.957597i
$591$	−4.09868	−	7.09912i	−0.168597	−	0.292019i
$592$	−8.23749	−	16.8765i	−0.338559	−	0.693621i
$593$	1.34548	+	0.776813i	0.0552522	+	0.0318999i	0.527372	−	0.849635i	$-0.323178\pi$
$593$	1.34548	+	0.776813i	0.0552522	+	0.0318999i	−0.472119	+	0.881535i	$0.656511\pi$
$594$	−57.7554	+	37.1557i	−2.36973	+	1.52452i
$595$	2.57798	−	13.9565i	0.105687	−	0.572160i
$596$	−8.78976	−	23.4986i	−0.360043	−	0.962539i
$597$	−0.601662	−	2.24543i	−0.0246244	−	0.0918994i
$598$	−1.80385	+	0.577566i	−0.0737650	+	0.0236184i
$599$	0.821999	+	1.42374i	0.0335860	+	0.0581726i	0.882330	−	0.470632i	$-0.155974\pi$
$599$	0.821999	+	1.42374i	0.0335860	+	0.0581726i	−0.848744	+	0.528804i	$0.822641\pi$
$600$	−10.3776	+	4.46134i	−0.423665	+	0.182133i
$601$	35.9484			1.46637			0.733183	−	0.680031i	$-0.238034\pi$
$601$	35.9484			1.46637			0.733183	+	0.680031i	$0.238034\pi$
$602$	3.05285	−	22.5462i	0.124425	−	0.918915i
$603$	72.9819	+	72.9819i	2.97205	+	2.97205i
$604$	−10.6139	−	14.8754i	−0.431872	−	0.605271i
$605$	−4.31517	−	1.15625i	−0.175437	−	0.0470081i
$606$	27.9498	−	54.2780i	1.13539	−	2.20489i
$607$	−12.3075	+	21.3172i	−0.499545	+	0.865237i	−1.00000		0.000525205i	$-0.999833\pi$
$607$	−12.3075	+	21.3172i	−0.499545	+	0.865237i	0.500455	+	0.865763i	$0.333166\pi$
$608$	4.53824	+	8.26478i	0.184050	+	0.335181i
$609$	−10.9818	+	23.0596i	−0.445006	+	0.934424i
$610$	−0.903139	+	0.581014i	−0.0365670	+	0.0235246i
$611$	−0.505643	−	1.88709i	−0.0204561	−	0.0763433i
$612$	39.5703	−	3.81616i	1.59953	−	0.154259i
$613$	−27.9559	−	7.49076i	−1.12913	−	0.302549i	−0.354556	−	0.935035i	$-0.615368\pi$
$613$	−27.9559	−	7.49076i	−1.12913	−	0.302549i	−0.774572	+	0.632485i	$0.782035\pi$
$614$	−11.1660	+	12.2947i	−0.450624	+	0.496173i
$615$			24.4497i			0.985905i
$616$	24.1486	−	12.7307i	0.972975	−	0.512935i
$617$			10.2299i			0.411839i	0.978569	+	0.205920i	$0.0660186\pi$
$617$			10.2299i			0.411839i	−0.978569	+	0.205920i	$0.933981\pi$
$618$	−42.2391	−	38.3615i	−1.69911	−	1.54313i
$619$	8.86168	+	2.37448i	0.356181	+	0.0954384i	0.432472	−	0.901647i	$-0.357641\pi$
$619$	8.86168	+	2.37448i	0.356181	+	0.0954384i	−0.0762915	+	0.997086i	$0.524308\pi$
$620$	16.4146	+	13.5270i	0.659226	+	0.543259i
$621$	8.76992	+	32.7298i	0.351925	+	1.31340i
$622$	6.76772	+	10.5199i	0.271361	+	0.421808i
$623$	−1.40230	−	17.6817i	−0.0561820	−	0.708401i
$624$	4.40554	+	5.06493i	0.176363	+	0.202759i
$625$	−8.58582	+	14.8711i	−0.343433	+	0.594843i
$626$	−31.4609	−	16.2004i	−1.25743	−	0.647499i
$627$	−18.7331	−	5.01952i	−0.748128	−	0.200460i
$628$	26.0762	+	4.35964i	1.04055	+	0.173969i
$629$	−9.19880	−	9.19880i	−0.366780	−	0.366780i
$630$	−19.7080	−	48.0797i	−0.785184	−	1.91554i
$631$	−2.48179			−0.0987983			−0.0493992	−	0.998779i	$-0.515731\pi$
$631$	−2.48179			−0.0987983			−0.0493992	+	0.998779i	$0.515731\pi$
$632$	4.19800	−	10.5292i	0.166987	−	0.418831i
$633$	−18.5926	−	32.2033i	−0.738990	−	1.27997i
$634$	−1.37912	−	4.30726i	−0.0547719	−	0.171063i
$635$	−10.3139	−	38.4919i	−0.409293	−	1.52750i
$636$	17.7929	−	39.0584i	0.705534	−	1.54877i
$637$	−1.50209	−	3.36284i	−0.0595152	−	0.133241i
$638$	−8.44788	−	13.1315i	−0.334455	−	0.519883i
$639$	55.8232	+	32.2296i	2.20833	+	1.27498i
$640$	−12.3364	−	18.0981i	−0.487641	−	0.715391i
$641$	7.96198	+	13.7906i	0.314479	+	0.544694i	0.979327	−	0.202285i	$-0.0648367\pi$
$641$	7.96198	+	13.7906i	0.314479	+	0.544694i	−0.664847	+	0.746979i	$0.731503\pi$
$642$	16.2645	−	0.782461i	0.641909	−	0.0308813i
$643$	7.66392	+	7.66392i	0.302236	+	0.302236i	0.841888	−	0.539652i	$-0.181444\pi$
$643$	7.66392	+	7.66392i	0.302236	+	0.302236i	−0.539652	+	0.841888i	$0.681444\pi$
$644$	−2.34890	−	13.2629i	−0.0925598	−	0.522633i
$645$	26.5502	−	26.5502i	1.04541	−	1.04541i
$646$	4.83509	+	4.39123i	0.190234	+	0.172771i
$647$	−7.28511	+	4.20606i	−0.286407	+	0.165357i	−0.636320	−	0.771425i	$-0.719544\pi$
$647$	−7.28511	+	4.20606i	−0.286407	+	0.165357i	0.349913	+	0.936782i	$0.386211\pi$
$648$	46.5003	−	36.6748i	1.82670	−	1.44072i
$649$	−15.5140	+	26.8710i	−0.608976	+	1.05478i
$650$	−0.910489	−	0.197615i	−0.0357123	−	0.00775111i
$651$	30.0863	−	35.2696i	1.17918	−	1.38232i
$652$	0.278020	+	0.743259i	0.0108881	+	0.0291083i
$653$	47.4173	−	12.7054i	1.85558	−	0.497201i	0.855783	−	0.517335i	$-0.173076\pi$
$653$	47.4173	−	12.7054i	1.85558	−	0.497201i	0.999797	+	0.0201333i	$0.00640906\pi$
$654$	−21.0562	+	40.8906i	−0.823361	+	1.59895i
$655$	−26.6972	+	15.4136i	−1.04315	+	0.602261i
$656$	15.5463	−	3.02672i	0.606980	−	0.118174i
$657$		−	10.9940i		−	0.428916i
$658$	13.7809	−	1.76264i	0.537234	−	0.0687147i
$659$	−4.57653	+	4.57653i	−0.178276	+	0.178276i	−0.790604	−	0.612328i	$-0.790233\pi$
$659$	−4.57653	+	4.57653i	−0.178276	+	0.178276i	0.612328	+	0.790604i	$0.290233\pi$
$660$	44.4346	+	7.42897i	1.72962	+	0.289172i
$661$	9.70671	−	36.2259i	0.377547	−	1.40903i	−0.472040	−	0.881577i	$-0.656482\pi$
$661$	9.70671	−	36.2259i	0.377547	−	1.40903i	0.849587	−	0.527448i	$-0.176851\pi$
$662$	5.91572	+	18.4759i	0.229921	+	0.718088i
$663$	4.02714	+	2.32507i	0.156401	+	0.0902983i
$664$	−8.79440	+	11.7826i	−0.341289	+	0.457255i
$665$	3.67078	−	7.70791i	0.142347	−	0.298900i
$666$	−46.5453	−	10.1023i	−1.80359	−	0.391457i
$667$	−7.44160	+	1.99397i	−0.288140	+	0.0772068i
$668$	4.54222	+	47.0988i	0.175744	+	1.82231i
$669$	−23.4153	+	87.3870i	−0.905286	+	3.37858i
$670$	−1.89290	−	39.3466i	−0.0731292	−	1.52009i
$671$	−1.43087			−0.0552382
$672$	−39.8965	+	26.2131i	−1.53904	+	1.01119i
$673$	1.25969			0.0485576			0.0242788	−	0.999705i	$-0.492271\pi$
$673$	1.25969			0.0485576			0.0242788	+	0.999705i	$0.492271\pi$
$674$	2.06304	+	42.8831i	0.0794654	+	1.65180i
$675$	−4.31392	+	16.0998i	−0.166043	+	0.619681i
$676$	−2.44271	−	25.3288i	−0.0939505	−	0.974185i
$677$	−10.2182	+	2.73796i	−0.392717	+	0.105228i	−0.449774	−	0.893143i	$-0.648495\pi$
$677$	−10.2182	+	2.73796i	−0.392717	+	0.105228i	0.0570560	+	0.998371i	$0.481829\pi$
$678$	81.2685	+	17.6388i	3.12110	+	0.677412i
$679$	−6.79417	−	9.87282i	−0.260736	−	0.378884i
$680$	−12.1591	−	9.07536i	−0.466279	−	0.348024i
$681$	17.8832	+	10.3249i	0.685287	+	0.395651i
$682$	8.64213	+	26.9910i	0.330924	+	1.03354i
$683$	−8.66885	+	32.3526i	−0.331705	+	1.23794i	0.575693	+	0.817666i	$0.304732\pi$
$683$	−8.66885	+	32.3526i	−0.331705	+	1.23794i	−0.907398	+	0.420272i	$0.861935\pi$
$684$	23.5860	+	3.94331i	0.901833	+	0.150776i
$685$	1.79466	−	1.79466i	0.0685706	−	0.0685706i
$686$	25.1314	−	7.37651i	0.959521	−	0.281636i
$687$			25.3833i			0.968434i
$688$	−20.1686	−	13.5951i	−0.768922	−	0.518310i
$689$	3.06577	−	1.77003i	0.116797	−	0.0674326i
$690$	10.1764	−	19.7623i	0.387407	−	0.752336i
$691$	−14.3264	+	3.83874i	−0.545001	+	0.146033i	−0.520807	−	0.853675i	$-0.674369\pi$
$691$	−14.3264	+	3.83874i	−0.545001	+	0.146033i	−0.0241943	+	0.999707i	$0.507702\pi$
$692$	−10.7751	−	28.8061i	−0.409607	−	1.09504i
$693$	12.5761	−	68.0837i	0.477728	−	2.58629i
$694$	18.6791	+	4.05417i	0.709050	+	0.153894i
$695$	−21.4613	+	37.1721i	−0.814074	+	1.41002i
$696$	16.9089	+	21.4389i	0.640931	+	0.812641i
$697$	9.50156	−	5.48573i	0.359897	−	0.207787i
$698$	18.7426	+	17.0220i	0.709419	+	0.644294i
$699$	0.414872	−	0.414872i	0.0156919	−	0.0156919i
$700$	2.26139	−	6.22769i	0.0854725	−	0.235385i
$701$	−14.0698	−	14.0698i	−0.531408	−	0.531408i	0.389583	−	0.920991i	$-0.372619\pi$
$701$	−14.0698	−	14.0698i	−0.531408	−	0.531408i	−0.920991	+	0.389583i	$0.872619\pi$
$702$	9.89368	−	0.475970i	0.373413	−	0.0179643i
$703$	−3.91271	−	6.77701i	−0.147571	−	0.255600i
$704$	−0.777041	−	29.1733i	−0.0292858	−	1.09951i
$705$	19.8561	+	11.4639i	0.747825	+	0.431757i
$706$	−23.6629	−	36.7820i	−0.890565	−	1.38431i
$707$	11.9737	+	33.7481i	0.450319	+	1.26923i
$708$	22.4932	−	49.3765i	0.845347	−	1.85568i
$709$	3.36966	+	12.5757i	0.126550	+	0.472291i	0.999890	−	0.0148195i	$-0.00471738\pi$
$709$	3.36966	+	12.5757i	0.126550	+	0.472291i	−0.873340	+	0.487111i	$0.838051\pi$
$710$	−7.50190	−	23.4299i	−0.281541	−	0.879308i
$711$	−14.3743	−	24.8970i	−0.539078	−	0.933710i
$712$	−17.6135	−	7.02250i	−0.660095	−	0.263179i
$713$	13.9835			0.523684
$714$	−20.2276	+	26.1608i	−0.756997	+	0.979045i
$715$	2.62748	+	2.62748i	0.0982623	+	0.0982623i
$716$	−1.13512	−	0.189780i	−0.0424215	−	0.00709240i
$717$	−60.5923	−	16.2356i	−2.26286	−	0.606331i
$718$	−23.2081	−	11.9508i	−0.866119	−	0.445999i
$719$	−10.1472	+	17.5754i	−0.378425	+	0.655452i	−0.990833	−	0.135090i	$-0.956868\pi$
$719$	−10.1472	+	17.5754i	−0.378425	+	0.655452i	0.612408	+	0.790542i	$0.290201\pi$
$720$	−55.4157	−	3.85837i	−2.06522	−	0.143793i
$721$	33.3629	−	2.64595i	1.24250	−	0.0985403i
$722$	−12.4120	−	19.2934i	−0.461927	−	0.718027i
$723$	−2.95882	−	11.0425i	−0.110040	−	0.410673i
$724$	−0.524783	−	0.432466i	−0.0195034	−	0.0160725i
$725$	−3.66052	−	0.980834i	−0.135948	−	0.0364272i
$726$	7.70548	+	6.99811i	0.285977	+	0.259724i
$727$		−	38.4308i		−	1.42532i	−0.701510	−	0.712660i	$-0.747490\pi$
$727$		−	38.4308i		−	1.42532i	0.701510	−	0.712660i	$-0.252510\pi$
$728$	−3.93446	−	0.151325i	−0.145821	−	0.00560850i
$729$		−	22.8244i		−	0.845348i
$730$	−2.82101	+	3.10615i	−0.104410	+	0.114964i
$731$	−16.2749	−	4.36084i	−0.601948	−	0.161292i
$732$	2.49061	−	0.240195i	0.0920555	−	0.00887785i
$733$	−12.9875	−	48.4699i	−0.479703	−	1.79028i	−0.602813	−	0.797882i	$-0.705954\pi$
$733$	−12.9875	−	48.4699i	−0.479703	−	1.79028i	0.123110	−	0.992393i	$-0.460713\pi$
$734$	−19.2784	+	12.4023i	−0.711580	+	0.457779i
$735$	40.3718	+	15.4415i	1.48914	+	0.569567i
$736$	−13.8256	−	4.02417i	−0.509617	−	0.148333i
$737$	26.2434	−	45.4549i	0.966689	−	1.67435i
$738$	18.3896	−	35.7122i	0.676931	−	1.31458i
$739$	−7.12602	−	1.90941i	−0.262135	−	0.0702388i	0.125358	−	0.992112i	$-0.459992\pi$
$739$	−7.12602	−	1.90941i	−0.262135	−	0.0702388i	−0.387493	+	0.921873i	$0.626659\pi$
$740$	10.5583	+	14.7975i	0.388132	+	0.543968i
$741$	1.97794	+	1.97794i	0.0726614	+	0.0726614i
$742$	9.54809	+	23.2936i	0.350521	+	0.855135i
$743$	13.2937			0.487698			0.243849	−	0.969813i	$-0.421590\pi$
$743$	13.2937			0.487698			0.243849	+	0.969813i	$0.421590\pi$
$744$	−19.5735	−	45.5305i	−0.717601	−	1.66923i
$745$	12.1426	+	21.0316i	0.444870	+	0.770537i
$746$	−48.4963	+	15.5278i	−1.77558	+	0.568513i
$747$	9.65119	+	36.0187i	0.353119	+	1.31786i
$748$	−7.08269	−	18.9349i	−0.258969	−	0.692328i
$749$	−6.19841	+	7.26627i	−0.226485	+	0.265504i
$750$	45.9161	−	29.5391i	1.67662	−	1.07861i
$751$	−10.6206	−	6.13182i	−0.387552	−	0.223753i	0.293547	−	0.955945i	$-0.405164\pi$
$751$	−10.6206	−	6.13182i	−0.387552	−	0.223753i	−0.681099	+	0.732191i	$0.738498\pi$
$752$	4.83126	−	14.0446i	0.176178	−	0.512156i
$753$	25.2333	+	43.7054i	0.919553	+	1.59271i
$754$	0.108219	+	2.24947i	0.00394109	+	0.0819210i
$755$	12.5077	+	12.5077i	0.455201	+	0.455201i
$756$	−6.08634	+	70.1753i	−0.221358	+	2.55225i
$757$	27.2609	−	27.2609i	0.990813	−	0.990813i	−0.00914525	−	0.999958i	$-0.502911\pi$
$757$	27.2609	−	27.2609i	0.990813	−	0.990813i	0.999958	+	0.00914525i	$0.00291107\pi$
$758$	25.5365	−	28.1177i	0.927527	−	1.02128i
$759$	25.6497	−	14.8089i	0.931025	−	0.537527i
$760$	−5.65197	−	7.16618i	−0.205018	−	0.259944i
$761$	10.1480	−	17.5769i	0.367867	−	0.637164i	−0.621365	−	0.783521i	$-0.713422\pi$
$761$	10.1480	−	17.5769i	0.367867	−	0.637164i	0.989232	+	0.146358i	$0.0467550\pi$
$762$	−19.6939	+	90.7373i	−0.713435	+	3.28707i
$763$	−9.02048	−	25.4243i	−0.326563	−	0.920423i
$764$	−9.62187	−	4.38320i	−0.348107	−	0.158579i
$765$	−37.1695	+	9.95952i	−1.34386	+	0.360087i
$766$	29.8696	+	15.3810i	1.07923	+	0.555739i
$767$	3.87566	−	2.23761i	0.139942	−	0.0807955i
$768$	6.24974	+	50.6493i	0.225518	+	1.82765i
$769$		−	19.6449i		−	0.708412i	−0.935167	−	0.354206i	$-0.884751\pi$
$769$		−	19.6449i		−	0.708412i	0.935167	−	0.354206i	$-0.115249\pi$
$770$	−21.0231	+	16.0089i	−0.757621	+	0.576919i
$771$	−20.7612	+	20.7612i	−0.747695	+	0.747695i
$772$	19.6006	+	27.4704i	0.705443	+	0.988681i
$773$	−12.6902	+	47.3606i	−0.456436	+	1.70344i	0.227397	+	0.973802i	$0.426979\pi$
$773$	−12.6902	+	47.3606i	−0.456436	+	1.70344i	−0.683832	+	0.729639i	$0.739688\pi$
$774$	−58.7498	+	18.8108i	−2.11172	+	0.676141i
$775$	5.95692	+	3.43923i	0.213979	+	0.123541i
$776$	−12.6792	+	1.84130i	−0.455157	+	0.0660989i
$777$	32.6380	−	22.4605i	1.17088	−	0.805765i
$778$	−4.05325	+	18.6749i	−0.145316	+	0.669526i
$779$	6.37485	−	1.70813i	0.228403	−	0.0612003i
$780$	−5.01452	−	4.13239i	−0.179549	−	0.147963i
$781$	8.48400	−	31.6627i	0.303581	−	1.13298i
$782$	−9.96321	+	0.479315i	−0.356284	+	0.0171403i
$783$	40.2892			1.43982
$784$	4.82065	−	27.5819i	0.172166	−	0.985068i
$785$	−25.5913			−0.913394
$786$	71.7447	−	3.45153i	2.55905	−	0.123112i
$787$	−0.740742	+	2.76449i	−0.0264046	+	0.0985433i	−0.977871	−	0.209210i	$-0.932911\pi$
$787$	−0.740742	+	2.76449i	−0.0264046	+	0.0985433i	0.951466	+	0.307754i	$0.0995773\pi$
$788$	3.26889	−	3.96669i	0.116450	−	0.141308i
$789$	−9.50662	+	2.54729i	−0.338445	+	0.0906860i
$790$	−2.32726	+	10.7226i	−0.0828001	+	0.381492i
$791$	−40.1820	+	27.6520i	−1.42871	+	0.983191i
$792$	−59.3154	−	44.2722i	−2.10768	−	1.57314i
$793$	0.178728	+	0.103189i	0.00634683	+	0.00366434i
$794$	6.22141	−	1.99200i	0.220789	−	0.0706935i
$795$	−10.7528	+	40.1300i	−0.381363	+	1.42326i
$796$	1.18656	−	0.846635i	0.0420566	−	0.0300082i
$797$	39.0301	−	39.0301i	1.38252	−	1.38252i	0.542386	−	0.840129i	$-0.317521\pi$
$797$	39.0301	−	39.0301i	1.38252	−	1.38252i	0.840129	−	0.542386i	$-0.182479\pi$
$798$	−15.8260	+	12.0513i	−0.560233	+	0.426610i
$799$		−	10.2886i		−	0.363984i
$800$	−4.89991	−	5.11468i	−0.173238	−	0.180831i
$801$	−41.6482	+	24.0456i	−1.47157	+	0.849609i
$802$	28.0546	+	14.4464i	0.990643	+	0.510121i
$803$	−5.40031	+	1.44701i	−0.190573	+	0.0510639i
$804$	−38.0496	+	83.5253i	−1.34190	+	2.94571i
$805$	4.35956	+	12.2875i	0.153654	+	0.433077i
$806$	0.867011	−	3.99465i	0.0305392	−	0.140706i
$807$	38.5526	−	66.7751i	1.35712	−	2.35059i
$808$	38.0174	+	4.49100i	1.33745	+	0.157993i
$809$	−36.0749	+	20.8279i	−1.26833	+	0.732269i	−0.974671	−	0.223642i	$-0.928205\pi$
$809$	−36.0749	+	20.8279i	−1.26833	+	0.732269i	−0.293656	+	0.955911i	$0.594872\pi$
$810$	−38.5408	+	42.4365i	−1.35419	+	1.49107i
$811$	−6.24833	+	6.24833i	−0.219409	+	0.219409i	−0.808249	−	0.588841i	$-0.799585\pi$
$811$	−6.24833	+	6.24833i	−0.219409	+	0.219409i	0.588841	+	0.808249i	$0.299585\pi$
$812$	−15.9554	−	1.38382i	−0.559924	−	0.0485625i
$813$	26.1742	+	26.1742i	0.917969	+	0.917969i
$814$	1.16389	+	24.1930i	0.0407942	+	0.847964i
$815$	−0.384070	−	0.665229i	−0.0134534	−	0.0233019i
$816$	15.5068	+	31.7695i	0.542847	+	1.11216i
$817$	−8.77741	−	5.06764i	−0.307083	−	0.177294i
$818$	6.73981	−	4.33591i	0.235652	−	0.151601i
$819$	−6.48080	+	7.59731i	−0.226457	+	0.265471i
$820$	−14.3592	+	5.37115i	−0.501446	+	0.187569i
$821$	−11.0196	−	41.1258i	−0.384588	−	1.43530i	−0.838816	−	0.544416i	$-0.816751\pi$
$821$	−11.0196	−	41.1258i	−0.384588	−	1.43530i	0.454228	−	0.890886i	$-0.349915\pi$
$822$	−5.63199	+	1.80328i	−0.196438	+	0.0628965i
$823$	0.688665	+	1.19280i	0.0240054	+	0.0415785i	0.877779	−	0.479067i	$-0.159025\pi$
$823$	0.688665	+	1.19280i	0.0240054	+	0.0415785i	−0.853773	+	0.520645i	$0.825691\pi$
$824$	13.2505	−	33.2343i	0.461602	−	1.15777i
$825$	14.5689			0.507225
$826$	12.0704	+	29.4470i	0.419983	+	1.02459i
$827$	−14.2870	−	14.2870i	−0.496807	−	0.496807i	0.413636	−	0.910443i	$-0.364259\pi$
$827$	−14.2870	−	14.2870i	−0.496807	−	0.496807i	−0.910443	+	0.413636i	$0.864259\pi$
$828$	−29.7280	+	21.2115i	−1.03312	+	0.737151i
$829$	20.0887	+	5.38274i	0.697708	+	0.186950i	0.590204	−	0.807254i	$-0.299047\pi$
$829$	20.0887	+	5.38274i	0.697708	+	0.186950i	0.107504	+	0.994205i	$0.465714\pi$
$830$	6.51547	−	12.6529i	0.226155	−	0.439189i
$831$	10.6111	−	18.3790i	0.368095	−	0.637560i
$832$	−2.00681	+	3.70004i	−0.0695735	+	0.128276i
$833$	−3.05733	−	19.1538i	−0.105930	−	0.663639i
$834$	84.1081	−	54.1091i	2.91243	−	1.87364i
$835$	−11.8544	−	44.2412i	−0.410239	−	1.53103i
$836$	−1.16737	−	12.1046i	−0.0403743	−	0.418647i
$837$	−70.6357	−	18.9268i	−2.44153	−	0.654205i
$838$	−3.59738	+	3.96100i	−0.124269	+	0.136831i
$839$			12.7357i			0.439684i	0.975535	+	0.219842i	$0.0705542\pi$
$839$			12.7357i			0.439684i	−0.975535	+	0.219842i	$0.929446\pi$
$840$	33.9060	−	31.3944i	1.16987	−	1.08321i
$841$		−	19.8397i		−	0.684126i
$842$	25.4888	+	23.1489i	0.878401	+	0.797764i
$843$	−50.0972	−	13.4235i	−1.72544	−	0.462330i
$844$	14.8285	−	17.9939i	0.510418	−	0.619375i
$845$	6.37506	+	23.7921i	0.219309	+	0.818472i
$846$	−20.3802	−	31.6793i	−0.700685	−	1.08916i
$847$	−6.08623	+	0.482688i	−0.209125	+	0.0165854i
$848$	26.8477	+	1.86930i	0.921954	+	0.0641920i
$849$	−38.2424	+	66.2378i	−1.31248	+	2.27328i
$850$	−4.36219	−	2.24626i	−0.149622	−	0.0770462i
$851$	11.5435	+	3.09307i	0.395706	+	0.106029i
$852$	−9.45235	+	56.5370i	−0.323832	+	1.93693i
$853$	17.4577	+	17.4577i	0.597741	+	0.597741i	0.939711	−	0.341970i	$-0.111094\pi$
$853$	17.4577	+	17.4577i	0.597741	+	0.597741i	−0.341970	+	0.939711i	$0.611094\pi$
$854$	−0.897719	+	1.16104i	−0.0307193	+	0.0397301i
$855$	−23.1475			−0.791628
$856$	4.03256	+	9.38023i	0.137830	+	0.320610i
$857$	−1.56865	−	2.71698i	−0.0535840	−	0.0928102i	0.837989	−	0.545687i	$-0.183731\pi$
$857$	−1.56865	−	2.71698i	−0.0535840	−	0.0928102i	−0.891573	+	0.452877i	$0.850398\pi$
$858$	−2.64010	−	8.24553i	−0.0901314	−	0.281498i
$859$	−0.462421	−	1.72578i	−0.0157776	−	0.0588828i	0.957588	−	0.288140i	$-0.0930369\pi$
$859$	−0.462421	−	1.72578i	−0.0157776	−	0.0588828i	−0.973366	+	0.229257i	$0.926370\pi$
$860$	21.4255	+	9.76028i	0.730603	+	0.332823i
$861$	11.1728	+	31.4907i	0.380768	+	1.07320i
$862$	−24.5507	−	38.1620i	−0.836199	−	1.29980i
$863$	−4.43745	−	2.56196i	−0.151052	−	0.0872101i	0.422569	−	0.906331i	$-0.361128\pi$
$863$	−4.43745	−	2.56196i	−0.151052	−	0.0872101i	−0.573621	+	0.819121i	$0.694462\pi$
$864$	64.3914	+	39.0407i	2.19064	+	1.32819i
$865$	14.8852	+	25.7819i	0.506112	+	0.876611i
$866$	−22.2882	+	1.07225i	−0.757382	+	0.0364365i
$867$	−21.0250	−	21.0250i	−0.714047	−	0.714047i
$868$	27.3232	+	9.92155i	0.927409	+	0.336759i
$869$	−10.3376	+	10.3376i	−0.350680	+	0.350680i
$870$	−19.5654	−	17.7693i	−0.663328	−	0.602434i
$871$	−6.55607	+	3.78515i	−0.222144	+	0.128255i
$872$	−28.6406	−	3.38332i	−0.969894	−	0.114574i
$873$	−16.2472	+	28.1410i	−0.549884	+	0.952427i
$874$	−5.86364	−	1.27266i	−0.198341	−	0.0430484i
$875$	−5.81684	+	31.4908i	−0.196645	+	1.06458i
$876$	9.15700	−	3.42522i	0.309386	−	0.115728i
$877$	4.01542	−	1.07593i	0.135591	−	0.0363316i	−0.190385	−	0.981709i	$-0.560974\pi$
$877$	4.01542	−	1.07593i	0.135591	−	0.0363316i	0.325976	+	0.945378i	$0.394307\pi$
$878$	−1.41391	+	2.74579i	−0.0477173	+	0.0926658i
$879$	60.5506	−	34.9589i	2.04232	−	1.17914i
$880$	5.39847	+	27.7284i	0.181982	+	0.934723i
$881$			27.5375i			0.927761i	0.885898	+	0.463880i	$0.153543\pi$
$881$			27.5375i			0.927761i	−0.885898	+	0.463880i	$0.846457\pi$
$882$	−47.3546	−	52.9198i	−1.59451	−	1.78190i
$883$	32.4922	−	32.4922i	1.09345	−	1.09345i	0.0982911	−	0.995158i	$-0.468662\pi$
$883$	32.4922	−	32.4922i	1.09345	−	1.09345i	0.995158	−	0.0982911i	$-0.0313376\pi$
$884$	−0.480819	+	2.87591i	−0.0161717	+	0.0967272i
$885$	−13.5934	+	50.7311i	−0.456936	+	1.70531i
$886$	−8.92229	−	27.8660i	−0.299750	−	0.936178i
$887$	−32.4376	−	18.7278i	−1.08915	−	0.628820i	−0.155798	−	0.987789i	$-0.549795\pi$
$887$	−32.4376	−	18.7278i	−1.08915	−	0.628820i	−0.933349	+	0.358969i	$0.883128\pi$
$888$	−6.08706	−	41.9155i	−0.204268	−	1.40659i
$889$	−30.8738	−	44.8637i	−1.03547	−	1.50468i
$890$	17.9369	+	3.89309i	0.601248	+	0.130497i
$891$	−73.7795	+	19.7692i	−2.47171	+	0.662292i
$892$	−56.4661	+	5.44560i	−1.89063	+	0.182332i
$893$	1.60182	−	5.97807i	0.0536028	−	0.200048i
$894$	−2.71905	−	56.5192i	−0.0909386	−	1.89028i
$895$	1.11402			0.0372376
$896$	−24.1594	−	17.6726i	−0.807110	−	0.590401i
$897$	−4.27183			−0.142632
$898$	2.16375	+	44.9765i	0.0722053	+	1.50089i
$899$	4.30328	−	16.0601i	0.143522	−	0.535633i
$900$	−17.8810	+	1.72445i	−0.596035	+	0.0574817i
$901$	18.0078	−	4.82518i	0.599927	−	0.160750i
$902$	−19.9625	−	4.33271i	−0.664677	−	0.144263i
$903$	22.0635	−	46.3289i	0.734226	−	1.54173i
$904$	7.49402	+	51.6038i	0.249247	+	1.71632i
$905$	0.570051	+	0.329119i	0.0189491	+	0.0109403i
$906$	−12.5677	−	39.2514i	−0.417534	−	1.30404i
$907$	−8.94245	+	33.3737i	−0.296929	+	1.10815i	0.642744	+	0.766081i	$0.277796\pi$
$907$	−8.94245	+	33.3737i	−0.296929	+	1.10815i	−0.939673	+	0.342074i	$0.888871\pi$
$908$	−2.13516	+	12.7710i	−0.0708579	+	0.423820i
$909$	68.6533	−	68.6533i	2.27709	−	2.27709i
$910$	3.78047	−	0.483540i	0.125321	−	0.0160292i
$911$			22.9373i			0.759946i	0.924998	+	0.379973i	$0.124067\pi$
$911$			22.9373i			0.759946i	−0.924998	+	0.379973i	$0.875933\pi$
$912$	4.06390	+	20.8736i	0.134569	+	0.691194i
$913$	16.4224	−	9.48145i	0.543501	−	0.313790i
$914$	6.53930	−	12.6992i	0.216301	−	0.420051i
$915$	−2.33950	+	0.626867i	−0.0773414	+	0.0207236i
$916$	−14.9076	+	5.57626i	−0.492560	+	0.184245i
$917$	−27.3419	+	32.0523i	−0.902909	+	1.05846i
$918$	50.9767	+	11.0641i	1.68248	+	0.365171i
$919$	13.8963	−	24.0691i	0.458396	−	0.793966i	−0.540480	−	0.841357i	$-0.681757\pi$
$919$	13.8963	−	24.0691i	0.458396	−	0.793966i	0.998876	+	0.0473912i	$0.0150907\pi$
$920$	13.8419	+	1.63515i	0.456354	+	0.0539092i
$921$	−32.4398	+	18.7291i	−1.06893	+	0.617146i
$922$	−20.8049	−	18.8950i	−0.685172	−	0.622273i
$923$	−3.34312	+	3.34312i	−0.110040	+	0.110040i
$924$	60.6258	−	10.7370i	1.99444	−	0.353221i
$925$	4.15676	+	4.15676i	0.136673	+	0.136673i
$926$	13.1641	−	0.633304i	0.432598	−	0.0208116i
$927$	−45.3707	−	78.5844i	−1.49017	−	2.58105i
$928$	−8.87647	+	14.6403i	−0.291384	+	0.480592i
$929$	13.2279	+	7.63716i	0.433995	+	0.250567i	0.701047	−	0.713115i	$-0.252716\pi$
$929$	13.2279	+	7.63716i	0.433995	+	0.250567i	−0.267052	+	0.963682i	$0.586050\pi$
$930$	25.9548	+	40.3446i	0.851092	+	1.32295i
$931$	1.20560	−	11.6051i	0.0395120	−	0.380341i
$932$	0.334794	+	0.152514i	0.0109665	+	0.00499575i
$933$	7.30182	+	27.2508i	0.239051	+	0.892150i
$934$	5.89781	+	18.4200i	0.192982	+	0.602721i
$935$	9.78436	+	16.9470i	0.319983	+	0.554227i
$936$	4.21628	+	9.80757i	0.137813	+	0.320571i
$937$	−18.1308			−0.592307			−0.296154	−	0.955140i	$-0.595704\pi$
$937$	−18.1308			−0.592307			−0.296154	+	0.955140i	$0.595704\pi$
$938$	−20.4183	−	49.8126i	−0.666681	−	1.62644i
$939$	−56.4350	−	56.4350i	−1.84169	−	1.84169i
$940$	−2.37072	+	14.1799i	−0.0773243	+	0.462497i
$941$	8.37369	+	2.24372i	0.272974	+	0.0731433i	0.392709	−	0.919663i	$-0.371538\pi$
$941$	8.37369	+	2.24372i	0.272974	+	0.0731433i	−0.119735	+	0.992806i	$0.538204\pi$
$942$	53.0123	+	27.2981i	1.72723	+	0.889420i
$943$	−5.03943	+	8.72855i	−0.164106	+	0.284241i
$944$	33.9401	+	2.36311i	1.10465	+	0.0769126i
$945$	−5.39053	−	67.9694i	−0.175354	−	2.21105i
$946$	16.9725	+	26.3824i	0.551825	+	0.857767i
$947$	3.98857	+	14.8856i	0.129611	+	0.483716i	0.999962	−	0.00871655i	$-0.00277460\pi$
$947$	3.98857	+	14.8856i	0.129611	+	0.483716i	−0.870351	+	0.492432i	$0.836108\pi$
$948$	16.2586	−	19.7293i	0.528054	−	0.640777i
$949$	0.778899	+	0.208705i	0.0252841	+	0.00677486i
$950$	−2.18489	−	1.98431i	−0.0708871	−	0.0643796i
$951$		−	10.2003i		−	0.330768i
$952$	−19.8078	−	6.13254i	−0.641976	−	0.198757i
$953$			14.4644i			0.468547i	0.972171	+	0.234273i	$0.0752711\pi$
$953$			14.4644i			0.468547i	−0.972171	+	0.234273i	$0.924729\pi$
$954$	45.8894	−	50.5279i	1.48573	−	1.63590i
$955$	9.88585	+	2.64890i	0.319899	+	0.0857165i
$956$	−3.77586	−	39.1524i	−0.122120	−	1.26628i
$957$	−9.11458	−	34.0161i	−0.294632	−	1.09958i
$958$	−31.4202	+	20.2135i	−1.01514	+	0.653069i
$959$	1.49138	−	3.13160i	0.0481592	−	0.101125i
$960$	−14.0513	−	47.3584i	−0.453505	−	1.52849i
$961$	0.410836	−	0.711589i	0.0132528	−	0.0229545i
$962$	1.59932	−	3.10585i	0.0515643	−	0.100137i
$963$	25.0131	+	6.70223i	0.806035	+	0.215976i
$964$	5.83521	−	4.16354i	0.187940	−	0.134098i
$965$	−23.0980	−	23.0980i	−0.743549	−	0.743549i
$966$	4.07616	−	30.1037i	0.131148	−	0.968572i
$967$	53.4246			1.71802			0.859010	−	0.511958i	$-0.171080\pi$
$967$	53.4246			1.71802			0.859010	+	0.511958i	$0.171080\pi$
$968$	−2.41722	+	6.06277i	−0.0776925	+	0.194865i
$969$	7.36555	+	12.7575i	0.236616	+	0.409830i
$970$	11.8112	−	3.78177i	0.379235	−	0.121425i
$971$	5.56119	+	20.7547i	0.178467	+	0.666048i	0.995935	+	0.0900743i	$0.0287105\pi$
$971$	5.56119	+	20.7547i	0.178467	+	0.666048i	−0.817468	+	0.575974i	$0.804623\pi$
$972$	50.2959	−	18.8134i	1.61324	−	0.603441i
$973$	−10.6552	+	57.6842i	−0.341589	+	1.84927i
$974$	−38.2804	+	24.6268i	−1.22658	+	0.789094i
$975$	−1.81979	−	1.05066i	−0.0582799	−	0.0336479i
$976$	0.688207	+	1.40996i	0.0220290	+	0.0451318i
$977$	−18.0960	−	31.3432i	−0.578942	−	1.00276i	−0.995601	−	0.0936944i	$-0.970132\pi$
$977$	−18.0960	−	31.3432i	−0.578942	−	1.00276i	0.416659	−	0.909063i	$-0.363201\pi$
$978$	0.0860035	+	1.78770i	0.00275009	+	0.0571644i
$979$	17.2930	+	17.2930i	0.552687	+	0.552687i
$980$	−0.199789	+	27.1025i	−0.00638202	+	0.865758i
$981$	−51.7204	+	51.7204i	−1.65130	+	1.65130i
$982$	3.03499	−	3.34177i	0.0968506	−	0.106640i
$983$	31.0312	−	17.9159i	0.989742	−	0.571428i	0.0845448	−	0.996420i	$-0.473056\pi$
$983$	31.0312	−	17.9159i	0.989742	−	0.571428i	0.905197	+	0.424992i	$0.139723\pi$
$984$	35.4744	+	4.19060i	1.13088	+	0.133591i
$985$	−2.48773	+	4.30887i	−0.0792655	+	0.137292i
$986$	−2.51559	+	11.5903i	−0.0801127	+	0.369110i
$987$	30.8130	+	5.69165i	0.980789	+	0.181167i
$988$	−0.727122	+	1.59616i	−0.0231328	+	0.0507805i
$989$	14.9508	−	4.00606i	0.475409	−	0.127385i
$990$	63.6964	+	32.7998i	2.02440	+	1.04244i
$991$	41.7865	−	24.1254i	1.32739	−	0.766370i	0.342496	−	0.939519i	$-0.388728\pi$
$991$	41.7865	−	24.1254i	1.32739	−	0.766370i	0.984896	+	0.173149i	$0.0553944\pi$
$992$	22.4400	−	21.4977i	0.712471	−	0.682554i
$993$			43.7541i			1.38850i
$994$	−20.3691	−	26.7491i	−0.646068	−	0.848429i
$995$	−0.997699	+	0.997699i	−0.0316292	+	0.0316292i
$996$	−26.9935	+	19.2604i	−0.855322	+	0.610288i
$997$	7.00832	−	26.1554i	0.221956	−	0.828351i	−0.761645	−	0.647994i	$-0.775608\pi$
$997$	7.00832	−	26.1554i	0.221956	−	0.828351i	0.983601	−	0.180357i	$-0.0577251\pi$
$998$	−30.7371	+	9.84155i	−0.972965	+	0.311529i
$999$	−54.1240	−	31.2485i	−1.71241	−	0.988659i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.2.v.a.19.8	yes	56
4.3	odd	2		448.2.z.a.47.14		56
7.2	even	3		784.2.j.a.195.23		56
7.3	odd	6	inner	112.2.v.a.3.2	✓	56
7.4	even	3		784.2.w.f.227.2		56
7.5	odd	6		784.2.j.a.195.24		56
7.6	odd	2		784.2.w.f.19.8		56
8.3	odd	2		896.2.z.a.607.1		56
8.5	even	2		896.2.z.b.607.14		56
16.3	odd	4		896.2.z.b.159.14		56
16.5	even	4		448.2.z.a.271.14		56
16.11	odd	4	inner	112.2.v.a.75.2	yes	56
16.13	even	4		896.2.z.a.159.1		56
28.3	even	6		448.2.z.a.367.14		56
56.3	even	6		896.2.z.a.479.1		56
56.45	odd	6		896.2.z.b.479.14		56
112.3	even	12		896.2.z.b.31.14		56
112.11	odd	12		784.2.w.f.619.8		56
112.27	even	4		784.2.w.f.411.2		56
112.45	odd	12		896.2.z.a.31.1		56
112.59	even	12	inner	112.2.v.a.59.8	yes	56
112.75	even	12		784.2.j.a.587.23		56
112.101	odd	12		448.2.z.a.143.14		56
112.107	odd	12		784.2.j.a.587.24		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.2	✓	56	7.3	odd	6	inner
112.2.v.a.19.8	yes	56	1.1	even	1	trivial
112.2.v.a.59.8	yes	56	112.59	even	12	inner
112.2.v.a.75.2	yes	56	16.11	odd	4	inner
448.2.z.a.47.14		56	4.3	odd	2
448.2.z.a.143.14		56	112.101	odd	12
448.2.z.a.271.14		56	16.5	even	4
448.2.z.a.367.14		56	28.3	even	6
784.2.j.a.195.23		56	7.2	even	3
784.2.j.a.195.24		56	7.5	odd	6
784.2.j.a.587.23		56	112.75	even	12
784.2.j.a.587.24		56	112.107	odd	12
784.2.w.f.19.8		56	7.6	odd	2
784.2.w.f.227.2		56	7.4	even	3
784.2.w.f.411.2		56	112.27	even	4
784.2.w.f.619.8		56	112.11	odd	12
896.2.z.a.31.1		56	112.45	odd	12
896.2.z.a.159.1		56	16.13	even	4
896.2.z.a.479.1		56	56.3	even	6
896.2.z.a.607.1		56	8.3	odd	2
896.2.z.b.31.14		56	112.3	even	12
896.2.z.b.159.14		56	16.3	odd	4
896.2.z.b.479.14		56	56.45	odd	6
896.2.z.b.607.14		56	8.5	even	2

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:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	112.v (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0679570 + 1.41258i) q^{2} +(-0.825526 + 3.08091i) q^{3} +(-1.99076 + 0.191990i) q^{4} +(1.86998 - 0.501060i) q^{5} +(-4.40813 - 0.956753i) q^{6} +(2.17953 - 1.49988i) q^{7} +(-0.406487 - 2.79907i) q^{8} +(-6.21241 - 3.58674i) q^{9} +(0.834865 + 2.60745i) q^{10} +(-0.944161 + 3.52366i) q^{11} +(1.05193 - 6.29185i) q^{12} +(0.372046 - 0.372046i) q^{13} +(2.26682 + 2.97683i) q^{14} +6.17487i q^{15} +(3.92628 - 0.764412i) q^{16} +(2.39966 - 1.38545i) q^{17} +(4.64438 - 9.01927i) q^{18} +(1.61000 - 0.431397i) q^{19} +(-3.62649 + 1.35651i) q^{20} +(2.82174 + 7.95312i) q^{21} +(-5.04161 - 1.09425i) q^{22} +(-1.27273 + 2.20444i) q^{23} +(8.95922 + 1.05835i) q^{24} +(-1.08436 + 0.626056i) q^{25} +(0.550828 + 0.500262i) q^{26} +(9.41278 - 9.41278i) q^{27} +(-4.05097 + 3.40436i) q^{28} +(2.14013 + 2.14013i) q^{29} +(-8.72250 + 0.419626i) q^{30} +(-2.74674 - 4.75749i) q^{31} +(1.34661 + 5.49424i) q^{32} +(-10.0766 - 5.81774i) q^{33} +(2.12013 + 3.29556i) q^{34} +(3.32415 - 3.89683i) q^{35} +(13.0561 + 5.94763i) q^{36} +(-1.21513 - 4.53493i) q^{37} +(0.718794 + 2.24493i) q^{38} +(0.839106 + 1.45337i) q^{39} +(-2.16262 - 5.03052i) q^{40} +3.95954 q^{41} +(-11.0427 + 4.52641i) q^{42} +(-4.29972 - 4.29972i) q^{43} +(1.20310 - 7.19604i) q^{44} +(-13.4143 - 3.59434i) q^{45} +(-3.20043 - 1.64803i) q^{46} +(1.85655 - 3.21563i) q^{47} +(-0.886167 + 12.7275i) q^{48} +(2.50070 - 6.53808i) q^{49} +(-0.958045 - 1.48920i) q^{50} +(2.28744 + 8.53685i) q^{51} +(-0.669227 + 0.812085i) q^{52} +(6.49892 + 1.74138i) q^{53} +(13.9360 + 12.6566i) q^{54} +7.06225i q^{55} +(-5.08422 - 5.49096i) q^{56} +5.31638i q^{57} +(-2.87767 + 3.16855i) q^{58} +(8.21574 + 2.20140i) q^{59} +(-1.18551 - 12.2927i) q^{60} +(0.101519 + 0.378874i) q^{61} +(6.53368 - 4.20330i) q^{62} +(-18.9198 + 1.50050i) q^{63} +(-7.66954 + 2.27557i) q^{64} +(0.509302 - 0.882137i) q^{65} +(7.53325 - 14.6294i) q^{66} +(-13.8977 - 3.72389i) q^{67} +(-4.51117 + 3.21880i) q^{68} +(-5.74099 - 5.74099i) q^{69} +(5.73048 + 4.43080i) q^{70} -8.98576 q^{71} +(-7.51425 + 18.8469i) q^{72} +(0.766294 + 1.32726i) q^{73} +(6.32337 - 2.02465i) q^{74} +(-1.03365 - 3.85764i) q^{75} +(-3.12230 + 1.16791i) q^{76} +(3.22725 + 9.09605i) q^{77} +(-1.99598 + 1.28407i) q^{78} +(3.47070 + 2.00381i) q^{79} +(6.95905 - 3.39674i) q^{80} +(10.4692 + 18.1331i) q^{81} +(0.269079 + 5.59317i) q^{82} +(-3.67570 - 3.67570i) q^{83} +(-7.14434 - 15.2910i) q^{84} +(3.79313 - 3.79313i) q^{85} +(5.78150 - 6.36589i) q^{86} +(-8.36028 + 4.82681i) q^{87} +(10.2467 + 1.21045i) q^{88} +(3.35201 - 5.80586i) q^{89} +(4.16570 - 19.1930i) q^{90} +(0.252860 - 1.36891i) q^{91} +(2.11048 - 4.63286i) q^{92} +(16.9249 - 4.53501i) q^{93} +(4.66851 + 2.40400i) q^{94} +(2.79451 - 1.61341i) q^{95} +(-18.0389 - 0.386856i) q^{96} -4.52980i q^{97} +(9.40550 + 3.08812i) q^{98} +(18.5040 - 18.5040i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{2} - 6 q^{3} - 4 q^{4} - 6 q^{5} - 8 q^{7} + 4 q^{8} - 24 q^{10} + 2 q^{11} - 6 q^{12} + 16 q^{14} + 8 q^{16} - 12 q^{17} - 30 q^{18} - 6 q^{19} - 10 q^{21} - 28 q^{22} - 12 q^{23} - 6 q^{24}+ \cdots - 16 q^{99}+O(q^{100}) \) 56 * q - 2 * q^2 - 6 * q^3 - 4 * q^4 - 6 * q^5 - 8 * q^7 + 4 * q^8 - 24 * q^10 + 2 * q^11 - 6 * q^12 + 16 * q^14 + 8 * q^16 - 12 * q^17 - 30 * q^18 - 6 * q^19 - 10 * q^21 - 28 * q^22 - 12 * q^23 - 6 * q^24 - 6 * q^26 + 26 * q^28 - 24 * q^29 - 18 * q^30 - 12 * q^32 - 12 * q^33 - 2 * q^35 + 16 * q^36 + 6 * q^37 - 6 * q^38 - 4 * q^39 - 66 * q^40 + 70 * q^42 + 26 * q^44 + 12 * q^45 + 16 * q^46 - 8 * q^49 - 34 * q^51 + 84 * q^52 + 6 * q^53 + 42 * q^54 + 16 * q^56 + 18 * q^58 + 42 * q^59 + 78 * q^60 - 6 * q^61 - 16 * q^64 - 4 * q^65 + 126 * q^66 + 6 * q^67 + 24 * q^68 - 80 * q^70 - 80 * q^71 - 4 * q^72 + 62 * q^74 + 24 * q^75 + 10 * q^77 + 4 * q^78 + 12 * q^80 - 8 * q^81 + 42 * q^82 - 152 * q^84 - 28 * q^85 - 12 * q^87 + 30 * q^88 + 16 * q^91 - 20 * q^92 + 10 * q^93 - 42 * q^94 + 36 * q^96 - 108 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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