LMFDB - Embedded newform 415.2.l.a.102.25

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [415,2,Mod(2,415)] 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("415.2"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(415, base_ring=CyclotomicField(164)) chi = DirichletCharacter(H, H._module([41, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 415 = 5 \cdot 83 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	415.l (of order $164$, degree $80$, 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:	$3.31379168388$
Analytic rank:	$0$
Dimension:	$3200$
Relative dimension:	$40$ over $\Q(\zeta_{164})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{164}]$

Embedding invariants

Embedding label			102.25
Character	$\chi$	$=$	415.102
Dual form			415.2.l.a.118.25

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.617386 - 0.383233i) q^{2} +(-2.29291 - 0.131914i) q^{3} +(-0.653141 + 1.31913i) q^{4} +(-2.12832 - 0.685745i) q^{5} +(-1.46616 + 0.797274i) q^{6} +(0.839813 - 0.477743i) q^{7} +(0.241278 + 2.51137i) q^{8} +(2.25981 + 0.260884i) q^{9} +(-1.57680 + 0.392273i) q^{10} +(2.76623 - 2.66223i) q^{11} +(1.67160 - 2.93847i) q^{12} +(3.65330 - 1.39168i) q^{13} +(0.335403 - 0.616795i) q^{14} +(4.78958 + 1.85310i) q^{15} +(-0.673286 - 0.883268i) q^{16} +(1.35005 + 2.60017i) q^{17} +(1.49516 - 0.704967i) q^{18} +(-1.18284 - 6.09904i) q^{19} +(2.29468 - 2.35964i) q^{20} +(-1.98863 + 0.984635i) q^{21} +(0.687580 - 2.70374i) q^{22} +(7.01042 + 3.30542i) q^{23} +(-0.221942 - 5.79017i) q^{24} +(4.05951 + 2.91897i) q^{25} +(1.72216 - 2.25927i) q^{26} +(1.64083 + 0.285723i) q^{27} +(0.0816863 + 1.41985i) q^{28} +(-3.33482 - 8.27424i) q^{29} +(3.66719 - 0.691443i) q^{30} +(-1.83338 + 1.51197i) q^{31} +(-5.46950 - 2.08353i) q^{32} +(-6.69390 + 5.73934i) q^{33} +(1.82997 + 1.08793i) q^{34} +(-2.11500 + 0.440892i) q^{35} +(-1.82011 + 2.81058i) q^{36} +(1.68637 - 2.12655i) q^{37} +(-3.06762 - 3.31216i) q^{38} +(-8.56026 + 2.70906i) q^{39} +(1.20864 - 5.51046i) q^{40} +(6.32192 - 1.47939i) q^{41} +(-0.850411 + 1.37001i) q^{42} +(1.92158 + 11.0351i) q^{43} +(1.70508 + 5.38782i) q^{44} +(-4.63071 - 2.10490i) q^{45} +(5.59488 - 0.645902i) q^{46} +(-2.38770 - 11.1631i) q^{47} +(1.42727 + 2.11407i) q^{48} +(-3.10008 + 5.21456i) q^{49} +(3.62493 + 0.246397i) q^{50} +(-2.75253 - 6.14004i) q^{51} +(-0.550325 + 5.72813i) q^{52} +(0.980057 - 4.58202i) q^{53} +(1.12252 - 0.452417i) q^{54} +(-7.71304 + 3.76916i) q^{55} +(1.40242 + 1.99381i) q^{56} +(1.90759 + 14.1406i) q^{57} +(-5.22983 - 3.83039i) q^{58} +(6.98350 - 0.267683i) q^{59} +(-5.57275 + 5.10773i) q^{60} +(-5.95237 + 3.53871i) q^{61} +(-0.552464 + 1.63608i) q^{62} +(2.02245 - 0.860514i) q^{63} +(-1.99467 + 0.386843i) q^{64} +(-8.72974 + 0.456702i) q^{65} +(-1.93322 + 6.10871i) q^{66} +(6.23504 + 0.841119i) q^{67} +(-4.31173 + 0.0826058i) q^{68} +(-15.6382 - 8.50379i) q^{69} +(-1.13681 + 1.08274i) q^{70} +(10.9028 - 2.99614i) q^{71} +(-0.109934 + 5.73817i) q^{72} +(-1.44053 - 1.96682i) q^{73} +(0.226177 - 1.95917i) q^{74} +(-8.92302 - 7.22843i) q^{75} +(8.81796 + 2.42322i) q^{76} +(1.05126 - 3.55732i) q^{77} +(-4.24679 + 4.95311i) q^{78} +(-0.950041 - 0.470395i) q^{79} +(0.827273 + 2.34158i) q^{80} +(-10.3695 - 2.42656i) q^{81} +(3.33612 - 3.33612i) q^{82} +(0.337788 - 9.10417i) q^{83} -3.26636i q^{84} +(-1.09028 - 6.45979i) q^{85} +(5.41537 + 6.07652i) q^{86} +(6.55493 + 19.4120i) q^{87} +(7.35328 + 6.30470i) q^{88} +(-7.22702 - 13.2903i) q^{89} +(-3.66560 + 0.475101i) q^{90} +(2.40323 - 2.91409i) q^{91} +(-8.93905 + 7.08873i) q^{92} +(4.40321 - 3.22497i) q^{93} +(-5.75221 - 5.97693i) q^{94} +(-1.66492 + 13.7918i) q^{95} +(12.2662 + 5.49885i) q^{96} +(-2.01113 - 6.80540i) q^{97} +(0.0844397 + 4.40745i) q^{98} +(6.94569 - 5.29447i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3200 q - 82 q^{2} - 78 q^{3} - 82 q^{5} - 164 q^{6} - 74 q^{7} - 82 q^{8} - 102 q^{10} - 164 q^{11} - 114 q^{12} - 82 q^{13} - 82 q^{15} - 96 q^{16} - 82 q^{17} - 82 q^{18} - 82 q^{20} - 148 q^{21} - 82 q^{22}+ \cdots + 246 q^{98}+O(q^{100}) $ 3200 * q - 82 * q^2 - 78 * q^3 - 82 * q^5 - 164 * q^6 - 74 * q^7 - 82 * q^8 - 102 * q^10 - 164 * q^11 - 114 * q^12 - 82 * q^13 - 82 * q^15 - 96 * q^16 - 82 * q^17 - 82 * q^18 - 82 * q^20 - 148 * q^21 - 82 * q^22 - 86 * q^23 - 74 * q^25 - 140 * q^26 - 90 * q^27 - 78 * q^28 - 114 * q^30 - 148 * q^31 - 82 * q^32 - 42 * q^33 - 82 * q^35 - 104 * q^36 - 66 * q^37 - 26 * q^38 - 130 * q^40 - 156 * q^41 - 82 * q^42 - 82 * q^43 - 82 * q^45 - 164 * q^46 - 82 * q^47 - 102 * q^48 - 82 * q^50 - 164 * q^51 - 82 * q^52 - 82 * q^53 - 82 * q^55 - 164 * q^56 - 82 * q^57 - 82 * q^58 - 82 * q^60 - 100 * q^61 - 82 * q^62 - 38 * q^63 - 134 * q^65 - 164 * q^66 - 82 * q^67 + 182 * q^68 - 138 * q^70 - 164 * q^71 - 82 * q^72 + 164 * q^73 - 138 * q^75 - 164 * q^76 - 106 * q^77 + 606 * q^78 - 82 * q^80 - 188 * q^81 + 192 * q^83 - 82 * q^85 - 84 * q^86 - 54 * q^87 + 738 * q^88 - 198 * q^90 - 164 * q^91 - 82 * q^92 + 576 * q^93 - 50 * q^95 - 164 * q^96 - 82 * q^97 + 246 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/415\mathbb{Z}\right)^\times$.

$n$	$167$	$251$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{47}{82}\right)$

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 $

$2$	0.617386	−	0.383233i	0.436558	−	0.270986i	−0.291409	−	0.956599i	$-0.594124\pi$
$2$	0.617386	−	0.383233i	0.436558	−	0.270986i	0.727967	+	0.685612i	$0.240465\pi$
$3$	−2.29291	−	0.131914i	−1.32381	−	0.0761608i	−0.618907	−	0.785464i	$-0.712424\pi$
$3$	−2.29291	−	0.131914i	−1.32381	−	0.0761608i	−0.704903	+	0.709304i	$0.749010\pi$
$4$	−0.653141	+	1.31913i	−0.326570	+	0.659563i
$5$	−2.12832	−	0.685745i	−0.951815	−	0.306674i
$5$	−2.12832	−	0.685745i	−0.951815	−	0.306674i
$6$	−1.46616	+	0.797274i	−0.598559	+	0.325486i
$7$	0.839813	−	0.477743i	0.317420	−	0.180570i	−0.327438	−	0.944873i	$-0.606185\pi$
$7$	0.839813	−	0.477743i	0.317420	−	0.180570i	0.644857	+	0.764303i	$0.276917\pi$
$8$	0.241278	+	2.51137i	0.0853047	+	0.887904i
$9$	2.25981	+	0.260884i	0.753270	+	0.0869614i
$10$	−1.57680	+	0.392273i	−0.498627	+	0.124048i
$11$	2.76623	−	2.66223i	0.834050	−	0.802693i	−0.148457	−	0.988919i	$-0.547431\pi$
$11$	2.76623	−	2.66223i	0.834050	−	0.802693i	0.982507	+	0.186226i	$0.0596257\pi$
$12$	1.67160	−	2.93847i	0.482550	−	0.848264i
$13$	3.65330	−	1.39168i	1.01324	−	0.385981i	0.207493	−	0.978236i	$-0.433470\pi$
$13$	3.65330	−	1.39168i	1.01324	−	0.385981i	0.805751	+	0.592255i	$0.201762\pi$
$14$	0.335403	−	0.616795i	0.0896402	−	0.164846i
$15$	4.78958	+	1.85310i	1.23666	+	0.478469i
$16$	−0.673286	−	0.883268i	−0.168322	−	0.220817i
$17$	1.35005	+	2.60017i	0.327435	+	0.630634i	0.993316	−	0.115423i	$-0.0368224\pi$
$17$	1.35005	+	2.60017i	0.327435	+	0.630634i	−0.665882	+	0.746058i	$0.731944\pi$
$18$	1.49516	−	0.704967i	0.352412	−	0.166162i
$19$	−1.18284	−	6.09904i	−0.271362	−	1.39922i	−0.824375	−	0.566044i	$-0.808473\pi$
$19$	−1.18284	−	6.09904i	−0.271362	−	1.39922i	0.553013	−	0.833172i	$-0.313478\pi$
$20$	2.29468	−	2.35964i	0.513106	−	0.527631i
$21$	−1.98863	+	0.984635i	−0.433955	+	0.214865i
$22$	0.687580	−	2.70374i	0.146593	−	0.576438i
$23$	7.01042	+	3.30542i	1.46177	+	0.689227i	0.982124	−	0.188233i	$-0.0602760\pi$
$23$	7.01042	+	3.30542i	1.46177	+	0.689227i	0.479649	+	0.877460i	$0.340764\pi$
$24$	−0.221942	−	5.79017i	−0.0453037	−	1.18191i
$25$	4.05951	+	2.91897i	0.811902	+	0.583794i
$26$	1.72216	−	2.25927i	0.337744	−	0.443079i
$27$	1.64083	+	0.285723i	0.315777	+	0.0549873i
$28$	0.0816863	+	1.41985i	0.0154373	+	0.268327i
$29$	−3.33482	−	8.27424i	−0.619260	−	1.53649i	−0.829305	−	0.558796i	$-0.811264\pi$
$29$	−3.33482	−	8.27424i	−0.619260	−	1.53649i	0.210045	−	0.977692i	$-0.432639\pi$
$30$	3.66719	−	0.691443i	0.669535	−	0.126240i
$31$	−1.83338	+	1.51197i	−0.329284	+	0.271559i	−0.786227	−	0.617937i	$-0.787969\pi$
$31$	−1.83338	+	1.51197i	−0.329284	+	0.271559i	0.456943	+	0.889496i	$0.348944\pi$
$32$	−5.46950	−	2.08353i	−0.966881	−	0.368320i
$33$	−6.69390	+	5.73934i	−1.16526	+	0.999091i
$34$	1.82997	+	1.08793i	0.313838	+	0.186578i
$35$	−2.11500	+	0.440892i	−0.357501	+	0.0745244i
$36$	−1.82011	+	2.81058i	−0.303352	+	0.468430i
$37$	1.68637	−	2.12655i	0.277237	−	0.349602i	−0.625169	−	0.780489i	$-0.714970\pi$
$37$	1.68637	−	2.12655i	0.277237	−	0.349602i	0.902406	+	0.430887i	$0.141799\pi$
$38$	−3.06762	−	3.31216i	−0.497634	−	0.537304i
$39$	−8.56026	+	2.70906i	−1.37074	+	0.433797i
$40$	1.20864	−	5.51046i	0.191103	−	0.871281i
$41$	6.32192	−	1.47939i	0.987318	−	0.231041i	0.297261	−	0.954796i	$-0.403927\pi$
$41$	6.32192	−	1.47939i	0.987318	−	0.231041i	0.690057	+	0.723755i	$0.257585\pi$
$42$	−0.850411	+	1.37001i	−0.131221	+	0.211397i
$43$	1.92158	+	11.0351i	0.293038	+	1.68284i	0.658948	+	0.752188i	$0.271002\pi$
$43$	1.92158	+	11.0351i	0.293038	+	1.68284i	−0.365910	+	0.930650i	$0.619242\pi$
$44$	1.70508	+	5.38782i	0.257050	+	0.812244i
$45$	−4.63071	−	2.10490i	−0.690305	−	0.313780i
$46$	5.59488	−	0.645902i	0.824920	−	0.0952330i
$47$	−2.38770	−	11.1631i	−0.348282	−	1.62831i	−0.715807	−	0.698298i	$-0.753941\pi$
$47$	−2.38770	−	11.1631i	−0.348282	−	1.62831i	0.367525	−	0.930014i	$-0.380205\pi$
$48$	1.42727	+	2.11407i	0.206008	+	0.305139i
$49$	−3.10008	+	5.21456i	−0.442869	+	0.744937i
$50$	3.62493	+	0.246397i	0.512643	+	0.0348458i
$51$	−2.75253	−	6.14004i	−0.385432	−	0.859778i
$52$	−0.550325	+	5.72813i	−0.0763164	+	0.794348i
$53$	0.980057	−	4.58202i	0.134621	−	0.629389i	−0.858551	−	0.512729i	$-0.828635\pi$
$53$	0.980057	−	4.58202i	0.134621	−	0.629389i	0.993172	−	0.116661i	$-0.0372190\pi$
$54$	1.12252	−	0.452417i	0.152756	−	0.0615662i
$55$	−7.71304	+	3.76916i	−1.04003	+	0.508233i
$56$	1.40242	+	1.99381i	0.187406	+	0.266435i
$57$	1.90759	+	14.1406i	0.252666	+	1.87296i
$58$	−5.22983	−	3.83039i	−0.686710	−	0.502955i
$59$	6.98350	−	0.267683i	0.909174	−	0.0348494i	0.420477	−	0.907303i	$-0.361863\pi$
$59$	6.98350	−	0.267683i	0.909174	−	0.0348494i	0.488697	+	0.872454i	$0.337472\pi$
$60$	−5.57275	+	5.10773i	−0.719439	+	0.659404i
$61$	−5.95237	+	3.53871i	−0.762122	+	0.453086i	−0.839121	−	0.543946i	$-0.816930\pi$
$61$	−5.95237	+	3.53871i	−0.762122	+	0.453086i	0.0769983	+	0.997031i	$0.475466\pi$
$62$	−0.552464	+	1.63608i	−0.0701630	+	0.207783i
$63$	2.02245	−	0.860514i	0.254805	−	0.108415i
$64$	−1.99467	+	0.386843i	−0.249333	+	0.0483553i
$65$	−8.72974	+	0.456702i	−1.08279	+	0.0566469i
$66$	−1.93322	+	6.10871i	−0.237963	+	0.751930i
$67$	6.23504	+	0.841119i	0.761732	+	0.102759i	0.504290	−	0.863535i	$-0.331754\pi$
$67$	6.23504	+	0.841119i	0.761732	+	0.102759i	0.257442	+	0.966294i	$0.417120\pi$
$68$	−4.31173	+	0.0826058i	−0.522874	+	0.0100174i
$69$	−15.6382	−	8.50379i	−1.88262	−	1.02374i
$70$	−1.13681	+	1.08274i	−0.135875	+	0.129412i
$71$	10.9028	−	2.99614i	1.29392	−	0.355576i	0.450476	−	0.892789i	$-0.351254\pi$
$71$	10.9028	−	2.99614i	1.29392	−	0.355576i	0.843447	+	0.537212i	$0.180523\pi$
$72$	−0.109934	+	5.73817i	−0.0129559	+	0.676250i
$73$	−1.44053	−	1.96682i	−0.168601	−	0.230199i	0.714206	−	0.699936i	$-0.246788\pi$
$73$	−1.44053	−	1.96682i	−0.168601	−	0.230199i	−0.882807	+	0.469736i	$0.844349\pi$
$74$	0.226177	−	1.95917i	0.0262925	−	0.227749i
$75$	−8.92302	−	7.22843i	−1.03034	−	0.834668i
$76$	8.81796	+	2.42322i	1.01149	+	0.277962i
$77$	1.05126	−	3.55732i	0.119802	−	0.405395i
$78$	−4.24679	+	4.95311i	−0.480854	+	0.560829i
$79$	−0.950041	−	0.470395i	−0.106888	−	0.0529236i	0.389486	−	0.921032i	$-0.372653\pi$
$79$	−0.950041	−	0.470395i	−0.106888	−	0.0529236i	−0.496374	+	0.868109i	$0.665336\pi$
$80$	0.827273	+	2.34158i	0.0924919	+	0.261797i
$81$	−10.3695	−	2.42656i	−1.15217	−	0.269618i
$82$	3.33612	−	3.33612i	0.368413	−	0.368413i
$83$	0.337788	−	9.10417i	0.0370771	−	0.999312i
$83$	0.337788	−	9.10417i	0.0370771	−	0.999312i
$84$		−	3.26636i		−	0.356390i
$85$	−1.09028	−	6.45979i	−0.118258	−	0.700663i
$86$	5.41537	+	6.07652i	0.583954	+	0.655248i
$87$	6.55493	+	19.4120i	0.702763	+	2.08118i
$88$	7.35328	+	6.30470i	0.783863	+	0.672083i
$89$	−7.22702	−	13.2903i	−0.766063	−	1.40877i	−0.908034	−	0.418896i	$-0.862417\pi$
$89$	−7.22702	−	13.2903i	−0.766063	−	1.40877i	0.141972	−	0.989871i	$-0.454656\pi$
$90$	−3.66560	+	0.475101i	−0.386388	+	0.0500801i
$91$	2.40323	−	2.91409i	0.251927	−	0.305479i
$92$	−8.93905	+	7.08873i	−0.931961	+	0.739051i
$93$	4.40321	−	3.22497i	0.456592	−	0.334413i
$94$	−5.75221	−	5.97693i	−0.593296	−	0.616473i
$95$	−1.66492	+	13.7918i	−0.170817	+	1.41501i
$96$	12.2662	+	5.49885i	1.25192	+	0.561224i
$97$	−2.01113	−	6.80540i	−0.204199	−	0.690984i	−0.996704	−	0.0811191i	$-0.974151\pi$
$97$	−2.01113	−	6.80540i	−0.204199	−	0.690984i	0.792505	−	0.609865i	$-0.208776\pi$
$98$	0.0844397	+	4.40745i	0.00852970	+	0.445220i
$99$	6.94569	−	5.29447i	0.698069	−	0.532115i
$100$	−6.50192	+	3.44850i	−0.650192	+	0.344850i
$101$	−2.04011	−	0.732719i	−0.202998	−	0.0729083i	0.234546	−	0.972105i	$-0.424640\pi$
$101$	−2.04011	−	0.732719i	−0.202998	−	0.0729083i	−0.437545	+	0.899197i	$0.644152\pi$
$102$	−4.05244	−	2.73592i	−0.401251	−	0.270896i
$103$	4.55168	+	10.6978i	0.448491	+	1.05408i	0.978529	+	0.206108i	$0.0660799\pi$
$103$	4.55168	+	10.6978i	0.448491	+	1.05408i	−0.530039	+	0.847974i	$0.677823\pi$
$104$	4.37648	+	8.83902i	0.429149	+	0.866737i
$105$	4.90766	−	0.731926i	0.478939	−	0.0714287i
$106$	−1.15091	−	3.20447i	−0.111786	−	0.311246i
$107$	9.44167	+	8.74458i	0.912761	+	0.845370i	0.988417	−	0.151764i	$-0.0484953\pi$
$107$	9.44167	+	8.74458i	0.912761	+	0.845370i	−0.0756560	+	0.997134i	$0.524105\pi$
$108$	−1.44860	+	1.97784i	−0.139391	+	0.190318i
$109$	14.2872	+	10.8906i	1.36846	+	1.04313i	0.993225	+	0.116203i	$0.0370724\pi$
$109$	14.2872	+	10.8906i	1.36846	+	1.04313i	0.375236	+	0.926929i	$0.377562\pi$
$110$	−3.31746	+	5.28291i	−0.316308	+	0.503706i
$111$	−4.14720	+	4.65352i	−0.393635	+	0.441693i
$112$	−0.987409	−	0.420123i	−0.0933014	−	0.0396979i
$113$	−12.2520	−	2.62060i	−1.15257	−	0.246525i	−0.407304	−	0.913293i	$-0.633531\pi$
$113$	−12.2520	−	2.62060i	−1.15257	−	0.246525i	−0.745266	+	0.666767i	$0.767677\pi$
$114$	6.59684	+	7.99914i	0.617851	+	0.749188i
$115$	−12.6538	−	11.8424i	−1.17997	−	1.10430i
$116$	13.0929	+	1.00520i	1.21564	+	0.0933304i
$117$	8.61884	−	2.19184i	0.796812	−	0.202635i
$118$	4.20893	−	2.84157i	0.387463	−	0.261587i
$119$	2.37600	+	1.53868i	0.217808	+	0.141051i
$120$	−3.49821	+	12.4755i	−0.319342	+	1.13886i
$121$	0.143233	−	3.73676i	0.0130212	−	0.339706i
$122$	−2.31876	+	4.46589i	−0.209931	+	0.404323i
$123$	−14.6907	+	2.55814i	−1.32462	+	0.230660i
$124$	−0.797031	−	3.40599i	−0.0715755	−	0.305867i
$125$	−6.63827	−	8.99630i	−0.593745	−	0.804653i
$126$	0.918859	−	1.30634i	0.0818585	−	0.116378i
$127$	5.08875	+	2.64215i	0.451553	+	0.234453i	0.671421	−	0.741076i	$-0.265684\pi$
$127$	5.08875	+	2.64215i	0.451553	+	0.234453i	−0.219867	+	0.975530i	$0.570562\pi$
$128$	7.50501	−	6.95090i	0.663355	−	0.614379i
$129$	−2.95031	−	25.5560i	−0.259760	−	2.25008i
$130$	−5.21460	+	3.62748i	−0.457351	+	0.318151i
$131$	2.03135	−	10.4742i	0.177480	−	0.915133i	−0.779813	−	0.626012i	$-0.784686\pi$
$131$	2.03135	−	10.4742i	0.177480	−	0.915133i	0.957293	−	0.289120i	$-0.0933628\pi$
$132$	−3.19886	−	12.5787i	−0.278425	−	1.09483i
$133$	−3.90714	−	4.55696i	−0.338792	−	0.395139i
$134$	4.17178	−	1.87018i	0.360386	−	0.161559i
$135$	−3.29628	−	1.73330i	−0.283698	−	0.149179i
$136$	−6.20426	+	4.01784i	−0.532011	+	0.344527i
$137$	−2.00351	+	4.70882i	−0.171171	+	0.402301i	−0.983502	−	0.180895i	$-0.942101\pi$
$137$	−2.00351	+	4.70882i	−0.171171	+	0.402301i	0.812331	+	0.583196i	$0.198198\pi$
$138$	−12.9137	+	0.742947i	−1.09929	+	0.0632439i
$139$	5.11714	−	3.59932i	0.434030	−	0.305290i	−0.337684	−	0.941260i	$-0.609643\pi$
$139$	5.11714	−	3.59932i	0.434030	−	0.305290i	0.771714	+	0.635969i	$0.219400\pi$
$140$	0.799802	−	3.07792i	0.0675956	−	0.260132i
$141$	4.00220	+	25.9110i	0.337046	+	2.18210i
$142$	5.58302	−	6.02808i	0.468516	−	0.505865i
$143$	6.40092	−	13.5756i	0.535272	−	1.13525i
$144$	−1.29107	−	2.17167i	−0.107589	−	0.180972i
$145$	1.42355	+	19.8971i	0.118219	+	1.65236i
$146$	−1.64311	−	0.662233i	−0.135985	−	0.0548068i
$147$	7.79607	−	11.5475i	0.643009	−	0.952426i
$148$	1.70375	+	3.61346i	0.140047	+	0.297025i
$149$	1.79661	+	0.568571i	0.147184	+	0.0465792i	0.374412	−	0.927262i	$-0.377844\pi$
$149$	1.79661	+	0.568571i	0.147184	+	0.0465792i	−0.227228	+	0.973841i	$0.572966\pi$
$150$	−8.27912	−	1.04315i	−0.675987	−	0.0851725i
$151$	−5.23600	−	5.03914i	−0.426100	−	0.410080i	0.449375	−	0.893343i	$-0.351647\pi$
$151$	−5.23600	−	5.03914i	−0.426100	−	0.410080i	−0.875475	+	0.483263i	$0.839451\pi$
$152$	15.0316	−	4.44211i	1.21922	−	0.360303i
$153$	2.37251	+	6.22810i	0.191806	+	0.503512i
$154$	−0.714250	−	2.59912i	−0.0575559	−	0.209443i
$155$	4.93884	−	1.96074i	0.396697	−	0.157490i
$156$	2.01747	−	13.0615i	0.161527	−	1.04575i
$157$	−6.19932	−	7.81749i	−0.494759	−	0.623903i	0.471378	−	0.881931i	$-0.343757\pi$
$157$	−6.19932	−	7.81749i	−0.494759	−	0.623903i	−0.966138	+	0.258028i	$0.916927\pi$
$158$	−0.766813	+	0.0736710i	−0.0610044	+	0.00586095i
$159$	−2.85161	+	10.3769i	−0.226148	+	0.822939i
$160$	10.2121	+	8.18511i	0.807337	+	0.647090i
$161$	7.46658	−	0.573243i	0.588449	−	0.0451779i
$162$	−7.33194	+	2.47581i	−0.576051	+	0.194518i
$163$	−0.0163250	+	0.283757i	−0.00127867	+	0.0222256i	−0.998927	−	0.0463202i	$-0.985251\pi$
$163$	−0.0163250	+	0.283757i	−0.00127867	+	0.0222256i	0.997648	+	0.0685458i	$0.0218359\pi$
$164$	−2.17761	+	9.30565i	−0.170043	+	0.726649i
$165$	18.1825	−	7.62486i	1.41550	−	0.593595i
$166$	−3.28047	−	5.75024i	−0.254614	−	0.446305i
$167$	4.83149	+	4.83149i	0.373872	+	0.373872i	0.868885	−	0.495013i	$-0.164837\pi$
$167$	4.83149	+	4.83149i	0.373872	+	0.373872i	−0.495013	+	0.868885i	$0.664837\pi$
$168$	−2.95260	−	4.75663i	−0.227798	−	0.366982i
$169$	1.70467	−	1.51919i	0.131128	−	0.116861i
$170$	−3.14873	−	3.57036i	−0.241496	−	0.273834i
$171$	−1.08185	−	14.0913i	−0.0827311	−	1.07759i
$172$	−15.8118	−	4.67268i	−1.20564	−	0.356288i
$173$	−2.44461	−	4.29733i	−0.185860	−	0.326720i	0.760781	−	0.649009i	$-0.224816\pi$
$173$	−2.44461	−	4.29733i	−0.185860	−	0.326720i	−0.946641	+	0.322289i	$0.895548\pi$
$174$	11.4862	+	9.47262i	0.870768	+	0.718117i
$175$	4.80375	+	0.511990i	0.363129	+	0.0387028i
$176$	−4.21393	−	0.650881i	−0.317637	−	0.0490620i
$177$	−16.0478	−	0.307450i	−1.20623	−	0.0231094i
$178$	−9.55513	−	5.43560i	−0.716187	−	0.407416i
$179$	0.507813	−	1.13277i	0.0379557	−	0.0846673i	−0.892543	−	0.450962i	$-0.851081\pi$
$179$	0.507813	−	1.13277i	0.0379557	−	0.0846673i	0.930499	+	0.366295i	$0.119374\pi$
$180$	5.80113	−	4.73369i	0.432391	−	0.352828i
$181$	3.74931	−	3.89578i	0.278684	−	0.289571i	−0.566483	−	0.824074i	$-0.691696\pi$
$181$	3.74931	−	3.89578i	0.278684	−	0.289571i	0.845167	+	0.534503i	$0.179501\pi$
$182$	0.366948	−	2.72011i	0.0272000	−	0.201628i
$183$	14.1150	−	7.32873i	1.04341	−	0.541756i
$184$	−6.60967	+	18.4033i	−0.487271	+	1.35671i
$185$	−5.04740	+	3.36956i	−0.371092	+	0.247735i
$186$	1.48257	−	3.67850i	0.108707	−	0.269721i
$187$	10.6568	+	3.59854i	0.779303	+	0.263151i
$188$	16.2851	+	4.14142i	1.18771	+	0.302044i
$189$	1.51449	−	0.543940i	0.110163	−	0.0395658i
$190$	4.25759	+	9.15295i	0.308878	+	0.664025i
$191$	−19.8460	+	3.06540i	−1.43600	+	0.221804i	−0.822894	−	0.568194i	$-0.807642\pi$
$191$	−19.8460	+	3.06540i	−1.43600	+	0.221804i	−0.613109	+	0.789999i	$0.710081\pi$
$192$	4.62461	−	0.623869i	0.333753	−	0.0450239i
$193$	−2.01091	+	11.5481i	−0.144748	+	0.831251i	0.820837	+	0.571163i	$0.193508\pi$
$193$	−2.01091	+	11.5481i	−0.144748	+	0.831251i	−0.965585	+	0.260088i	$0.916248\pi$
$194$	−3.84969	−	3.43083i	−0.276392	−	0.246320i
$195$	20.0767	+	0.104404i	1.43772	+	0.00747650i
$196$	−4.85387	−	7.49524i	−0.346705	−	0.535374i
$197$	−12.6529	−	1.21561i	−0.901478	−	0.0866089i	−0.365472	−	0.930822i	$-0.619092\pi$
$197$	−12.6529	−	1.21561i	−0.901478	−	0.0866089i	−0.536007	+	0.844214i	$0.680068\pi$
$198$	2.25916	−	5.93055i	0.160552	−	0.421466i
$199$	−0.825234	+	10.7488i	−0.0584993	+	0.761962i	0.892159	+	0.451722i	$0.149190\pi$
$199$	−0.825234	+	10.7488i	−0.0584993	+	0.761962i	−0.950658	+	0.310240i	$0.899590\pi$
$200$	−6.35115	+	10.8992i	−0.449094	+	0.770691i
$201$	−14.1854	−	2.75110i	−1.00056	−	0.194048i
$202$	−1.54034	+	0.329465i	−0.108378	+	0.0231811i
$203$	−6.75358	−	5.35563i	−0.474008	−	0.375892i
$204$	9.89728	+	0.379371i	0.692948	+	0.0265613i
$205$	−14.4696	−	1.18661i	−1.01060	−	0.0828766i
$206$	6.90988	+	4.86030i	0.481434	+	0.338633i
$207$	14.9799	+	9.29853i	1.04117	+	0.646292i
$208$	−3.68894	−	2.28985i	−0.255782	−	0.158773i
$209$	−19.5091	−	13.7224i	−1.34947	−	0.949196i
$210$	2.74943	−	2.33266i	0.189728	−	0.160969i
$211$	2.74521	+	0.105226i	0.188988	+	0.00724408i	0.132625	−	0.991166i	$-0.457659\pi$
$211$	2.74521	+	0.105226i	0.188988	+	0.00724408i	0.0563630	+	0.998410i	$0.482050\pi$
$212$	5.40415	+	4.28553i	0.371159	+	0.294331i
$213$	−25.3943	+	5.43163i	−1.73999	+	0.372169i
$214$	9.18037	+	1.78043i	0.627557	+	0.121707i
$215$	3.47753	−	24.8040i	0.237166	−	1.69162i
$216$	−0.321660	+	4.18967i	−0.0218862	+	0.285071i
$217$	−0.817359	+	2.14566i	−0.0554859	+	0.145657i
$218$	12.9943	+	1.24842i	0.880088	+	0.0845537i
$219$	3.04354	+	4.69976i	0.205663	+	0.317581i
$220$	0.0657115	−	12.6363i	0.00443027	−	0.851937i
$221$	8.55073	+	7.62038i	0.575185	+	0.512603i
$222$	−0.777045	+	4.46236i	−0.0521519	+	0.299494i
$223$	−4.37899	+	0.590734i	−0.293239	+	0.0395585i	−0.278839	−	0.960338i	$-0.589950\pi$
$223$	−4.37899	+	0.590734i	−0.293239	+	0.0395585i	−0.0143997	+	0.999896i	$0.504584\pi$
$224$	−5.58875	+	0.863236i	−0.373414	+	0.0576774i
$225$	8.41221	+	7.65538i	0.560814	+	0.510359i
$226$	−8.56851	+	3.07744i	−0.569969	+	0.204708i
$227$	4.93682	+	1.25547i	0.327668	+	0.0833285i	0.406750	−	0.913540i	$-0.366662\pi$
$227$	4.93682	+	1.25547i	0.327668	+	0.0833285i	−0.0790814	+	0.996868i	$0.525199\pi$
$228$	−19.8991	−	6.71943i	−1.31785	−	0.445005i
$229$	4.18839	−	10.3921i	0.276777	−	0.686729i	−0.723216	−	0.690622i	$-0.757337\pi$
$229$	4.18839	−	10.3921i	0.276777	−	0.686729i	0.999992	+	0.00389307i	$0.00123921\pi$
$230$	−12.3506	−	2.46197i	−0.814377	−	0.162338i
$231$	−2.87969	+	8.01793i	−0.189470	+	0.527541i
$232$	19.9751	−	10.3714i	1.31143	−	0.680913i
$233$	−0.709268	+	5.25766i	−0.0464657	+	0.344441i	0.952711	+	0.303877i	$0.0982812\pi$
$233$	−0.709268	+	5.25766i	−0.0464657	+	0.344441i	−0.999177	+	0.0405636i	$0.987085\pi$
$234$	4.48117	−	4.65623i	0.292943	−	0.304387i
$235$	−2.57326	+	25.3961i	−0.167861	+	1.65666i
$236$	−4.20810	+	9.38695i	−0.273924	+	0.611038i
$237$	2.11630	+	1.20390i	0.137469	+	0.0782015i
$238$	2.05658	+	0.0394009i	0.133309	+	0.00255398i
$239$	20.1796	+	3.11693i	1.30531	+	0.201617i	0.767282	−	0.641310i	$-0.221609\pi$
$239$	20.1796	+	3.11693i	1.30531	+	0.201617i	0.538027	+	0.842927i	$0.319170\pi$
$240$	−1.58797	−	5.47816i	−0.102503	−	0.353613i
$241$	6.58311	+	5.42905i	0.424055	+	0.349716i	0.823770	−	0.566924i	$-0.191867\pi$
$241$	6.58311	+	5.42905i	0.424055	+	0.349716i	−0.399715	+	0.916639i	$0.630891\pi$
$242$	−1.34362	−	2.36192i	−0.0863711	−	0.151830i
$243$	18.6645	+	5.51573i	1.19733	+	0.353834i
$244$	−0.780275	−	10.1632i	−0.0499520	−	0.650632i
$245$	10.1738	−	8.97239i	0.649982	−	0.573225i
$246$	−8.08949	+	7.20932i	−0.515767	+	0.459650i
$247$	−12.8092	−	20.6355i	−0.815027	−	1.31301i
$248$	−4.23948	−	4.23948i	−0.269207	−	0.269207i
$249$	−1.97549	+	20.8304i	−0.125191	+	1.32008i
$250$	−7.54605	−	3.01019i	−0.477254	−	0.190381i
$251$	−2.66266	+	11.3784i	−0.168066	+	0.718201i	0.821025	+	0.570892i	$0.193403\pi$
$251$	−2.66266	+	11.3784i	−0.168066	+	0.718201i	−0.989091	+	0.147309i	$0.952939\pi$
$252$	−0.185822	+	3.22991i	−0.0117057	+	0.203465i
$253$	28.1922	−	9.51981i	1.77243	−	0.598505i
$254$	4.15428	−	0.318943i	0.260663	−	0.0200123i
$255$	1.64778	+	14.9555i	0.103188	+	0.936551i
$256$	3.04647	−	11.0860i	0.190405	−	0.692872i
$257$	8.86059	−	0.851274i	0.552708	−	0.0531010i	0.184480	−	0.982836i	$-0.440940\pi$
$257$	8.86059	−	0.851274i	0.552708	−	0.0531010i	0.368229	+	0.929735i	$0.379964\pi$
$258$	−11.6154	−	14.6472i	−0.723140	−	0.911898i
$259$	0.400290	−	2.59155i	0.0248728	−	0.161031i
$260$	5.09930	−	11.8139i	0.316245	−	0.732668i
$261$	−5.37744	−	19.5682i	−0.332855	−	1.21124i
$262$	−2.75992	−	7.24509i	−0.170508	−	0.447603i
$263$	27.4775	−	8.12014i	1.69434	−	0.500709i	0.714354	−	0.699785i	$-0.246721\pi$
$263$	27.4775	−	8.12014i	1.69434	−	0.500709i	0.979984	+	0.199076i	$0.0637940\pi$
$264$	−16.0287	−	15.4261i	−0.986499	−	0.949410i
$265$	−5.22797	+	9.07995i	−0.321152	+	0.557777i
$266$	−4.15859	−	1.31607i	−0.254979	−	0.0806931i
$267$	14.8177	+	31.4267i	0.906829	+	1.92328i
$268$	−5.18190	+	7.67544i	−0.316535	+	0.468852i
$269$	4.46237	+	1.79850i	0.272075	+	0.109656i	0.505812	−	0.862644i	$-0.331193\pi$
$269$	4.46237	+	1.79850i	0.272075	+	0.109656i	−0.233737	+	0.972300i	$0.575095\pi$
$270$	−2.69933	+	0.193126i	−0.164276	+	0.0117533i
$271$	−12.7401	−	21.4297i	−0.773905	−	1.30176i	−0.948391	−	0.317103i	$-0.897290\pi$
$271$	−12.7401	−	21.4297i	−0.773905	−	1.30176i	0.174486	−	0.984660i	$-0.444174\pi$
$272$	1.38768	−	2.94311i	0.0841405	−	0.178453i
$273$	−5.89479	+	6.36470i	−0.356769	+	0.385209i
$274$	0.567634	+	3.67497i	0.0342920	+	0.222013i
$275$	19.0005	−	2.73280i	1.14577	−	0.164794i
$276$	21.4315	−	15.0746i	1.29003	−	0.907384i
$277$	−18.2991	+	1.05278i	−1.09949	+	0.0632552i	−0.597688	−	0.801728i	$-0.703914\pi$
$277$	−18.2991	+	1.05278i	−1.09949	+	0.0632552i	−0.501800	+	0.864984i	$0.667329\pi$
$278$	1.77988	−	4.18322i	0.106750	−	0.250893i
$279$	−4.53753	+	2.93848i	−0.271655	+	0.175922i
$280$	−1.61755	−	5.20518i	−0.0966670	−	0.311069i
$281$	−18.0405	+	8.08742i	−1.07621	+	0.482455i	−0.868476	−	0.495732i	$-0.834900\pi$
$281$	−18.0405	+	8.08742i	−1.07621	+	0.482455i	−0.207729	+	0.978186i	$0.566607\pi$
$282$	12.4008	+	14.4633i	0.738460	+	0.861279i
$283$	0.187027	+	0.735436i	0.0111176	+	0.0437171i	0.974465	−	0.224541i	$-0.0720884\pi$
$283$	0.187027	+	0.735436i	0.0111176	+	0.0437171i	−0.963347	+	0.268259i	$0.913552\pi$
$284$	−3.16877	+	16.3391i	−0.188032	+	0.969544i
$285$	5.63685	−	31.4038i	0.333898	−	1.86020i
$286$	−1.25078	−	10.8345i	−0.0739604	−	0.640655i
$287$	4.60246	−	4.26266i	0.271675	−	0.251617i
$288$	−11.8165	−	6.13530i	−0.696293	−	0.361526i
$289$	4.84216	−	6.88408i	0.284833	−	0.404946i
$290$	8.50409	+	11.7386i	0.499377	+	0.689316i
$291$	3.71359	+	15.8694i	0.217695	+	0.930283i
$292$	3.53535	−	0.615622i	0.206891	−	0.0360266i
$293$	−10.7923	+	20.7857i	−0.630491	+	1.21431i	0.332072	+	0.943254i	$0.392252\pi$
$293$	−10.7923	+	20.7857i	−0.630491	+	1.21431i	−0.962562	+	0.271060i	$0.912626\pi$
$294$	0.387794	−	10.1170i	0.0226166	−	0.590036i
$295$	−15.0467	−	4.21918i	−0.876052	−	0.245650i
$296$	5.74744	+	3.72200i	0.334063	+	0.216337i
$297$	5.29957	−	3.57789i	0.307512	−	0.207610i
$298$	1.32710	−	0.337491i	0.0768766	−	0.0195503i
$299$	30.2113	+	2.31946i	1.74716	+	0.134138i
$300$	15.3632	−	7.04940i	0.886995	−	0.406997i
$301$	6.88571	+	8.34941i	0.396886	+	0.481252i
$302$	−5.16380	−	1.10449i	−0.297143	−	0.0635565i
$303$	4.58112	+	1.94918i	0.263179	+	0.111977i
$304$	−4.59070	+	5.15116i	−0.263295	+	0.295439i
$305$	15.0952	−	3.44972i	0.864349	−	0.197530i
$306$	3.85157	+	2.93592i	0.220179	+	0.167836i
$307$	−11.2447	+	15.3529i	−0.641767	+	0.876237i	−0.998314	−	0.0580406i	$-0.981515\pi$
$307$	−11.2447	+	15.3529i	−0.641767	+	0.876237i	0.356548	+	0.934277i	$0.383954\pi$
$308$	4.00594	+	3.71017i	0.228260	+	0.211407i
$309$	−9.02539	−	25.1294i	−0.513437	−	1.42956i
$310$	2.29775	−	3.10326i	0.130504	−	0.176253i
$311$	10.5371	+	21.2814i	0.597503	+	1.20676i	0.961358	+	0.275300i	$0.0887773\pi$
$311$	10.5371	+	21.2814i	0.597503	+	1.20676i	−0.363855	+	0.931455i	$0.618540\pi$
$312$	−8.86886	−	20.8444i	−0.502100	−	1.18008i
$313$	4.60640	+	3.10991i	0.260369	+	0.175782i	0.682784	−	0.730620i	$-0.260769\pi$
$313$	4.60640	+	3.10991i	0.260369	+	0.175782i	−0.422415	+	0.906402i	$0.638818\pi$
$314$	−6.82329	−	2.45063i	−0.385061	−	0.138297i
$315$	−4.89453	+	0.444563i	−0.275775	+	0.0250483i
$316$	1.24102	−	0.945989i	0.0698129	−	0.0532161i
$317$	0.282184	+	14.7290i	0.0158490	+	0.827262i	0.918168	+	0.396192i	$0.129669\pi$
$317$	0.282184	+	14.7290i	0.0158490	+	0.827262i	−0.902319	+	0.431070i	$0.858136\pi$
$318$	2.21621	+	7.49937i	0.124279	+	0.420544i
$319$	−31.2528	−	14.0104i	−1.74982	−	0.784432i
$320$	4.51057	+	0.544506i	0.252148	+	0.0304388i
$321$	−20.4953	−	21.2960i	−1.14394	−	1.18863i
$322$	4.39008	−	3.21535i	0.244650	−	0.179184i
$323$	14.2617	−	11.3096i	0.793540	−	0.629282i
$324$	9.97370	−	12.0938i	0.554094	−	0.671879i
$325$	18.8929	+	5.01436i	1.04799	+	0.278147i
$326$	0.0986662	+	0.181444i	0.00546462	+	0.0100493i
$327$	−31.3225	−	26.8559i	−1.73214	−	1.48513i
$328$	5.24063	+	15.5197i	0.289365	+	0.856934i
$329$	−7.33833	−	8.23424i	−0.404575	−	0.453969i
$330$	8.30353	−	11.6756i	0.457094	−	0.642721i
$331$		−	18.5504i		−	1.01962i	−0.860286	−	0.509812i	$-0.829715\pi$
$331$		−	18.5504i		−	1.01962i	0.860286	−	0.509812i	$-0.170285\pi$
$332$	11.7889	+	6.39189i	0.647001	+	0.350801i
$333$	4.36565	−	4.36565i	0.239236	−	0.239236i
$334$	4.83448	+	1.13131i	0.264531	+	0.0619026i
$335$	−12.6934	−	6.06582i	−0.693514	−	0.331411i
$336$	2.20862	+	1.09356i	0.120490	+	0.0596584i
$337$	−23.0911	+	26.9316i	−1.25785	+	1.46706i	−0.433327	+	0.901237i	$0.642660\pi$
$337$	−23.0911	+	26.9316i	−1.25785	+	1.46706i	−0.824528	+	0.565821i	$0.808559\pi$
$338$	0.470233	−	1.59121i	0.0255773	−	0.0865505i
$339$	27.7470	+	7.62500i	1.50701	+	0.414133i
$340$	9.23339	+	2.78093i	0.500751	+	0.150817i
$341$	−1.04632	+	9.06334i	−0.0566613	+	0.490807i
$342$	−6.06815	−	8.28516i	−0.328128	−	0.448010i
$343$	−0.241825	+	12.6224i	−0.0130573	+	0.681545i
$344$	−27.2496	+	7.48833i	−1.46920	+	0.403744i
$345$	27.4517	+	28.8226i	1.47795	+	1.55176i
$346$	−3.15615	−	1.71626i	−0.169676	−	0.0922666i
$347$	−18.5376	+	0.355151i	−0.995150	+	0.0190655i	−0.514189	−	0.857677i	$-0.671907\pi$
$347$	−18.5376	+	0.355151i	−0.995150	+	0.0190655i	−0.480961	+	0.876742i	$0.659712\pi$
$348$	−29.8881	−	4.03196i	−1.60217	−	0.216136i
$349$	−5.99243	+	18.9353i	−0.320767	+	1.01358i	0.647161	+	0.762353i	$0.275956\pi$
$349$	−5.99243	+	18.9353i	−0.320767	+	1.01358i	−0.967928	+	0.251228i	$0.919166\pi$
$350$	3.16198	−	1.52486i	0.169015	−	0.0815070i
$351$	6.39207	−	1.23967i	0.341184	−	0.0661687i
$352$	−20.6768	+	8.79755i	−1.10208	+	0.468911i
$353$	3.02034	−	8.94452i	0.160756	−	0.476069i	−0.836675	−	0.547700i	$-0.815503\pi$
$353$	3.02034	−	8.94452i	0.160756	−	0.476069i	0.997431	+	0.0716315i	$0.0228205\pi$
$354$	−10.0255	+	5.96023i	−0.532851	+	0.316783i
$355$	−25.2592	−	1.09978i	−1.34062	−	0.0583703i
$356$	22.2518	−	0.852931i	1.17934	−	0.0452053i
$357$	−5.24497	−	3.84148i	−0.277593	−	0.203313i
$358$	−0.120598	−	0.893968i	−0.00637380	−	0.0472477i
$359$	−10.6044	−	15.0763i	−0.559680	−	0.795696i	0.434811	−	0.900522i	$-0.356815\pi$
$359$	−10.6044	−	15.0763i	−0.559680	−	0.795696i	−0.994491	+	0.104826i	$0.966571\pi$
$360$	4.16890	−	12.1373i	0.219720	−	0.639691i
$361$	−18.1766	+	7.32585i	−0.956666	+	0.385571i
$362$	0.821785	−	3.84206i	0.0431920	−	0.201934i
$363$	−0.821354	+	8.54916i	−0.0431099	+	0.448714i
$364$	2.27440	+	5.07347i	0.119211	+	0.265922i
$365$	1.71716	+	5.17386i	0.0898804	+	0.270812i
$366$	5.90581	−	9.93400i	0.308702	−	0.519258i
$367$	13.7734	+	20.4012i	0.718967	+	1.06493i	0.994611	+	0.103675i	$0.0330601\pi$
$367$	13.7734	+	20.4012i	0.718967	+	1.06493i	−0.275644	+	0.961260i	$0.588891\pi$
$368$	−1.80045	−	8.41757i	−0.0938549	−	0.438796i
$369$	14.6723	−	1.69384i	0.763809	−	0.0881780i
$370$	−1.82487	+	4.01465i	−0.0948704	+	0.208712i
$371$	−1.36596	−	4.31626i	−0.0709173	−	0.224089i
$372$	1.37822	+	7.91475i	0.0714574	+	0.410360i
$373$	−2.47963	+	3.99468i	−0.128390	+	0.206837i	−0.907501	−	0.420050i	$-0.862013\pi$
$373$	−2.47963	+	3.99468i	−0.128390	+	0.206837i	0.779111	+	0.626887i	$0.215671\pi$
$374$	7.95844	−	1.86235i	0.411521	−	0.0962997i
$375$	14.0342	+	21.5033i	0.724723	+	1.11043i
$376$	27.4587	−	8.68983i	1.41607	−	0.448144i
$377$	−23.6982	−	25.5873i	−1.22052	−	1.31781i
$378$	0.726571	−	0.916223i	0.0373708	−	0.0471254i
$379$	−1.86638	+	2.88203i	−0.0958697	+	0.148040i	−0.884030	−	0.467430i	$-0.845180\pi$
$379$	−1.86638	+	2.88203i	−0.0958697	+	0.148040i	0.788160	+	0.615470i	$0.211034\pi$
$380$	−17.1058	−	11.2043i	−0.877507	−	0.574767i
$381$	−11.3195	−	6.72949i	−0.579915	−	0.344762i
$382$	−11.0779	+	9.49815i	−0.566793	+	0.485968i
$383$	−2.05496	−	0.782807i	−0.105003	−	0.0399996i	0.302918	−	0.953017i	$-0.402039\pi$
$383$	−2.05496	−	0.782807i	−0.105003	−	0.0399996i	−0.407922	+	0.913017i	$0.633746\pi$
$384$	−18.1252	+	14.9477i	−0.924948	+	0.762799i
$385$	−4.67683	+	6.85023i	−0.238353	+	0.349120i
$386$	3.18410	+	7.90029i	0.162067	+	0.402114i
$387$	1.46352	+	25.4386i	0.0743949	+	1.29312i
$388$	10.2907	+	1.79196i	0.522433	+	0.0909729i
$389$	−1.64326	+	2.15576i	−0.0833166	+	0.109301i	−0.835071	−	0.550142i	$-0.814574\pi$
$389$	−1.64326	+	2.15576i	−0.0833166	+	0.109301i	0.751755	+	0.659443i	$0.229208\pi$
$390$	12.4351	−	7.62959i	0.629676	−	0.386340i
$391$	0.869757	+	22.6908i	0.0439855	+	1.14752i
$392$	−13.8437	−	6.52730i	−0.699211	−	0.329679i
$393$	−6.03938	+	23.7483i	−0.304646	+	1.19794i
$394$	−8.27756	+	4.09848i	−0.417018	+	0.206479i
$395$	1.69942	+	1.65264i	0.0855072	+	0.0831532i
$396$	2.44756	+	12.6203i	0.122994	+	0.634193i
$397$	9.04206	−	4.26333i	0.453808	−	0.213971i	−0.185931	−	0.982563i	$-0.559530\pi$
$397$	9.04206	−	4.26333i	0.453808	−	0.213971i	0.639739	+	0.768592i	$0.279042\pi$
$398$	3.60980	+	6.95242i	0.180943	+	0.348493i
$399$	8.35757	+	10.9641i	0.418402	+	0.548891i
$400$	−0.154977	−	5.55094i	−0.00774883	−	0.277547i
$401$	8.60550	−	15.8253i	0.429738	−	0.790275i	−0.569765	−	0.821808i	$-0.692966\pi$
$401$	8.60550	−	15.8253i	0.429738	−	0.790275i	0.999503	+	0.0315325i	$0.0100388\pi$
$402$	−9.81219	+	3.73782i	−0.489388	+	0.186426i
$403$	−4.59370	+	8.07516i	−0.228828	+	0.402253i
$404$	2.29903	−	2.21259i	0.114381	−	0.110081i
$405$	20.4057	+	12.2753i	1.01397	+	0.609967i
$406$	−6.22202	−	0.718302i	−0.308794	−	0.0356487i
$407$	−0.996484	−	10.3720i	−0.0493939	−	0.514122i
$408$	14.7558	−	8.39410i	0.730521	−	0.415570i
$409$	−27.1220	+	14.7485i	−1.34110	+	0.729266i	−0.979190	−	0.202948i	$-0.934948\pi$
$409$	−27.1220	+	14.7485i	−1.34110	+	0.729266i	−0.361908	+	0.932214i	$0.617875\pi$
$410$	−9.38806	+	4.81261i	−0.463643	+	0.237678i
$411$	5.21501	−	10.5326i	0.257238	−	0.519534i
$412$	−17.0846	−	0.982902i	−0.841697	−	0.0484241i
$413$	5.73695	−	3.56112i	0.282297	−	0.175231i
$414$	12.8119			0.629670
$415$	−6.96206	+	19.1450i	−0.341754	+	0.939789i
$416$	−22.8814			−1.12185
$417$	−12.2079	+	7.57787i	−0.597825	+	0.371090i
$418$	−17.3035	−	0.995496i	−0.846341	−	0.0486913i
$419$	−16.8415	+	34.0141i	−0.822760	+	1.66170i	−0.0755202	+	0.997144i	$0.524062\pi$
$419$	−16.8415	+	34.0141i	−0.822760	+	1.66170i	−0.747239	+	0.664555i	$0.768621\pi$
$420$	−2.23989	+	6.95187i	−0.109296	+	0.339217i
$421$	−10.7710	+	5.85711i	−0.524949	+	0.285458i	−0.718374	−	0.695657i	$-0.755113\pi$
$421$	−10.7710	+	5.85711i	−0.524949	+	0.285458i	0.193425	+	0.981115i	$0.438040\pi$
$422$	1.73518	−	0.987090i	0.0844674	−	0.0480508i
$423$	−2.48347	−	25.8495i	−0.120750	−	1.25685i
$424$	11.7436	+	1.35575i	0.570321	+	0.0658408i
$425$	−2.10929	+	14.4962i	−0.102316	+	0.703168i
$426$	−13.5965	+	13.0853i	−0.658754	+	0.633987i
$427$	−3.30828	+	5.81556i	−0.160099	+	0.281434i
$428$	−17.7019	+	6.74331i	−0.855655	+	0.325950i
$429$	−16.4675	+	30.2833i	−0.795060	+	1.46209i
$430$	−7.35871	−	16.6463i	−0.354869	−	0.802758i
$431$	9.27572	+	12.1686i	0.446796	+	0.586141i	0.962722	−	0.270492i	$-0.0871864\pi$
$431$	9.27572	+	12.1686i	0.446796	+	0.586141i	−0.515927	+	0.856633i	$0.672552\pi$
$432$	−0.852377	−	1.64166i	−0.0410100	−	0.0789846i
$433$	1.93349	−	0.911640i	0.0929174	−	0.0438106i	−0.379451	−	0.925212i	$-0.623887\pi$
$433$	1.93349	−	0.911640i	0.0929174	−	0.0438106i	0.472368	+	0.881401i	$0.343399\pi$
$434$	0.317659	+	1.63794i	0.0152481	+	0.0786235i
$435$	−0.639359	−	45.8099i	−0.0306549	−	2.19642i
$436$	−23.6976	+	11.7334i	−1.13491	+	0.561930i
$437$	11.8677	−	46.6666i	0.567708	−	2.23237i
$438$	3.68014	+	1.73519i	0.175844	+	0.0829105i
$439$	0.118590	+	3.09386i	0.00566000	+	0.147662i	0.999365	+	0.0356329i	$0.0113447\pi$
$439$	0.118590	+	3.09386i	0.00566000	+	0.147662i	−0.993705	+	0.112029i	$0.964265\pi$
$440$	−11.3267	−	18.4609i	−0.539981	−	0.880089i
$441$	−8.36600	+	10.9752i	−0.398381	+	0.522626i
$442$	8.19949	+	1.42780i	0.390010	+	0.0679136i
$443$	−0.430964	−	7.49092i	−0.0204757	−	0.355904i	−0.992599	−	0.121435i	$-0.961250\pi$
$443$	−0.430964	−	7.49092i	−0.0204757	−	0.355904i	0.972124	−	0.234469i	$-0.0753351\pi$
$444$	−3.42987	−	8.51009i	−0.162775	−	0.403871i
$445$	6.26769	+	33.2419i	0.297117	+	1.57582i
$446$	−2.47714	+	2.04288i	−0.117296	+	0.0967332i
$447$	−4.04445	−	1.54068i	−0.191296	−	0.0728716i
$448$	−1.49034	+	1.27781i	−0.0704117	+	0.0603710i
$449$	11.1527	+	6.63033i	0.526328	+	0.312905i	0.749644	−	0.661841i	$-0.230225\pi$
$449$	11.1527	+	6.63033i	0.526328	+	0.312905i	−0.223316	+	0.974746i	$0.571688\pi$
$450$	8.12738	+	1.50250i	0.383128	+	0.0708284i
$451$	13.5494	−	20.9227i	0.638017	−	0.985213i
$452$	11.4592	−	14.4503i	0.538994	−	0.679685i
$453$	11.3409	+	12.2450i	0.532843	+	0.575320i
$454$	3.52906	−	1.11684i	0.165627	−	0.0524159i
$455$	−7.11316	+	4.55411i	−0.333470	+	0.213500i
$456$	−35.0520	+	8.20247i	−1.64146	+	0.384116i
$457$	9.99593	−	16.1034i	0.467590	−	0.753286i	−0.527783	−	0.849380i	$-0.676976\pi$
$457$	9.99593	−	16.1034i	0.467590	−	0.753286i	0.995372	+	0.0960940i	$0.0306349\pi$
$458$	−1.39673	−	8.02107i	−0.0652651	−	0.374800i
$459$	1.47227	+	4.65217i	0.0687197	+	0.217145i
$460$	23.8862	−	8.95718i	1.11370	−	0.417631i
$461$	−15.8770	+	1.83292i	−0.739466	+	0.0853678i	−0.476177	−	0.879349i	$-0.657978\pi$
$461$	−15.8770	+	1.83292i	−0.739466	+	0.0853678i	−0.263289	+	0.964717i	$0.584807\pi$
$462$	1.29485	+	6.05375i	0.0602418	+	0.281646i
$463$	13.0612	+	19.3462i	0.607004	+	0.899095i	0.999789	−	0.0205355i	$-0.00653711\pi$
$463$	13.0612	+	19.3462i	0.607004	+	0.899095i	−0.392785	+	0.919630i	$0.628488\pi$
$464$	−5.06308	+	8.51647i	−0.235048	+	0.395367i
$465$	−11.5830	+	3.84429i	−0.537146	+	0.178275i
$466$	1.57701	+	3.51782i	0.0730537	+	0.162960i
$467$	−1.54440	+	16.0750i	−0.0714662	+	0.743864i	0.887587	+	0.460639i	$0.152380\pi$
$467$	−1.54440	+	16.0750i	−0.0714662	+	0.743864i	−0.959054	+	0.283225i	$0.908596\pi$
$468$	−2.73801	+	12.8009i	−0.126565	+	0.591722i
$469$	5.63811	−	2.27236i	0.260344	−	0.104928i
$470$	8.14392	+	16.6654i	0.375651	+	0.768716i
$471$	13.1832	+	18.7425i	0.607450	+	0.863611i
$472$	2.35722	+	17.4736i	0.108500	+	0.804286i
$473$	34.6935	+	25.4100i	1.59521	+	1.16835i
$474$	1.76795	−	0.0677670i	0.0812046	−	0.00311264i
$475$	13.0012	−	28.2118i	0.596535	−	1.29445i
$476$	−3.58158	+	2.12927i	−0.164161	+	0.0975949i
$477$	3.41012	−	10.0988i	0.156139	−	0.462394i
$478$	13.6531	−	5.80913i	0.624479	−	0.265703i
$479$	−7.40318	+	1.43576i	−0.338260	+	0.0656016i	−0.356674	−	0.934229i	$-0.616089\pi$
$479$	−7.40318	+	1.43576i	−0.338260	+	0.0656016i	0.0184144	+	0.999830i	$0.494138\pi$
$480$	−22.3356	−	20.1148i	−1.01948	−	0.918112i
$481$	3.20134	−	10.1158i	0.145968	−	0.461241i
$482$	6.14491	+	0.828960i	0.279893	+	0.0377581i
$483$	−17.1958	+	0.329444i	−0.782436	+	0.0149902i
$484$	4.83571	+	2.62958i	0.219805	+	0.119526i
$485$	−0.386444	+	15.8632i	−0.0175475	+	0.720311i
$486$	13.6370	−	3.74752i	0.618588	−	0.169991i
$487$	0.268264	−	14.0024i	0.0121562	−	0.634511i	−0.942068	−	0.335421i	$-0.891122\pi$
$487$	0.268264	−	14.0024i	0.0121562	−	0.634511i	0.954225	−	0.299091i	$-0.0966833\pi$
$488$	−10.3232	−	14.0948i	−0.467309	−	0.638041i
$489$	0.0748633	−	0.648476i	0.00338544	−	0.0293251i
$490$	2.84267	−	9.43838i	0.128419	−	0.426382i
$491$	−21.3710	−	5.87286i	−0.964461	−	0.265039i	−0.252766	−	0.967527i	$-0.581340\pi$
$491$	−21.3710	−	5.87286i	−0.964461	−	0.265039i	−0.711695	+	0.702489i	$0.752072\pi$
$492$	6.22060	−	21.0497i	0.280446	−	0.948995i
$493$	17.0123	−	19.8417i	0.766194	−	0.893626i
$494$	−15.8164	−	7.83120i	−0.711614	−	0.352342i
$495$	−18.4133	+	6.50537i	−0.827618	+	0.292395i
$496$	2.56986	+	0.601372i	0.115390	+	0.0270024i
$497$	7.72492	−	7.72492i	0.346510	−	0.346510i
$498$	6.76327	+	13.6175i	0.303069	+	0.610215i
$499$		−	22.9807i		−	1.02876i	−0.857563	−	0.514379i	$-0.828022\pi$
$499$		−	22.9807i		−	1.02876i	0.857563	−	0.514379i	$-0.171978\pi$
$500$	16.2030	−	2.88087i	0.724619	−	0.128836i
$501$	−10.4408	−	11.7155i	−0.466461	−	0.523410i
$502$	2.71670	+	8.04532i	0.121252	+	0.359080i
$503$	−30.5726	−	26.2129i	−1.36317	−	1.16878i	−0.968228	−	0.250070i	$-0.919546\pi$
$503$	−30.5726	−	26.2129i	−1.36317	−	1.16878i	−0.394938	−	0.918708i	$-0.629234\pi$
$504$	2.64904	+	4.87151i	0.117998	+	0.216994i
$505$	3.83955	+	2.95846i	0.170858	+	0.131650i
$506$	13.7572	−	16.6816i	0.611582	−	0.741587i
$507$	−4.10904	+	3.25850i	−0.182489	+	0.144715i
$508$	−6.80900	+	4.98700i	−0.302101	+	0.221262i
$509$	−20.8794	−	21.6950i	−0.925462	−	0.961615i	0.0739022	−	0.997265i	$-0.476455\pi$
$509$	−20.8794	−	21.6950i	−0.925462	−	0.961615i	−0.999364	+	0.0356500i	$0.988650\pi$
$510$	6.74876	+	8.60185i	0.298840	+	0.380896i
$511$	−2.14941	−	0.963563i	−0.0950841	−	0.0426255i
$512$	3.43043	+	11.6081i	0.151605	+	0.513012i
$513$	−0.198202	−	10.3454i	−0.00875083	−	0.456762i
$514$	5.14417	−	3.92123i	0.226900	−	0.172958i
$515$	−2.35151	−	25.8896i	−0.103620	−	1.14083i
$516$	35.6385	+	12.7998i	1.56890	+	0.563480i
$517$	−36.3238	−	24.5232i	−1.59752	−	1.07853i
$518$	−0.746034	−	1.75339i	−0.0327788	−	0.0770397i
$519$	5.03839	+	10.1759i	0.221161	+	0.446671i
$520$	−3.25324	−	21.8134i	−0.142664	−	0.956582i
$521$	7.75297	+	21.5866i	0.339664	+	0.945726i	0.983555	+	0.180609i	$0.0578068\pi$
$521$	7.75297	+	21.5866i	0.339664	+	0.945726i	−0.643891	+	0.765117i	$0.722681\pi$
$522$	−10.8191	−	10.0203i	−0.473541	−	0.438578i
$523$	8.77312	−	11.9784i	0.383622	−	0.523778i	−0.571258	−	0.820770i	$-0.693545\pi$
$523$	8.77312	−	11.9784i	0.383622	−	0.523778i	0.954880	+	0.296992i	$0.0959836\pi$
$524$	12.4900	+	9.52071i	0.545628	+	0.415914i
$525$	−10.9470	−	1.80763i	−0.477766	−	0.0788914i
$526$	13.8524	−	15.5435i	0.603992	−	0.677731i
$527$	−6.40654	−	2.72585i	−0.279073	−	0.118740i
$528$	9.57628	+	2.04829i	0.416754	+	0.0891403i
$529$	23.5866	+	28.6005i	1.02551	+	1.24350i
$530$	0.252053	+	7.60937i	0.0109485	+	0.330530i
$531$	15.8512	+	1.21697i	0.687884	+	0.0528120i
$532$	8.56312	−	2.17767i	0.371258	−	0.0944138i
$533$	21.0371	−	14.2027i	0.911216	−	0.615187i
$534$	21.1920	+	13.7238i	0.917067	+	0.593886i
$535$	−14.0984	−	25.0858i	−0.609526	−	1.08456i
$536$	−0.607983	+	15.8615i	−0.0262609	+	0.685111i
$537$	−1.31380	+	2.53035i	−0.0566945	+	0.109193i
$538$	3.44425	−	0.599758i	0.148492	−	0.0258574i
$539$	5.30681	+	22.6778i	0.228581	+	0.976802i
$540$	4.43937	−	3.21612i	0.191040	−	0.138400i
$541$	18.9263	−	26.9075i	0.813705	−	1.15684i	−0.171453	−	0.985192i	$-0.554846\pi$
$541$	18.9263	−	26.9075i	0.813705	−	1.15684i	0.985158	−	0.171651i	$-0.0549100\pi$
$542$	−16.0781	−	8.34801i	−0.690615	−	0.358578i
$543$	−9.11073	+	8.43807i	−0.390979	+	0.362112i
$544$	−1.96655	−	17.0345i	−0.0843152	−	0.730349i
$545$	−22.9395	−	32.9761i	−0.982619	−	1.41254i
$546$	−1.20020	+	6.18856i	−0.0513638	+	0.264846i
$547$	−3.84419	−	15.1163i	−0.164366	−	0.646326i	−0.995869	−	0.0908058i	$-0.971056\pi$
$547$	−3.84419	−	15.1163i	−0.164366	−	0.646326i	0.831503	−	0.555520i	$-0.187481\pi$
$548$	−4.90295	−	5.71840i	−0.209444	−	0.244278i
$549$	−14.3744	+	6.44394i	−0.613485	+	0.275021i
$550$	10.6834	−	8.96881i	0.455540	−	0.382431i
$551$	−46.5204	+	30.1263i	−1.98183	+	1.28342i
$552$	17.5830	−	41.3251i	0.748383	−	1.75891i
$553$	−1.02258	+	0.0588308i	−0.0434847	+	0.00250174i
$554$	−10.8942	+	7.66279i	−0.462849	+	0.325561i
$555$	12.0177	−	7.06027i	0.510123	−	0.299692i
$556$	1.40574	+	9.10102i	0.0596166	+	0.385969i
$557$	24.0919	−	26.0125i	1.02081	−	1.10218i	0.0260775	−	0.999660i	$-0.491698\pi$
$557$	24.0919	−	26.0125i	1.02081	−	1.10218i	0.994731	−	0.102524i	$-0.0326919\pi$
$558$	−1.67529	+	3.55311i	−0.0709207	+	0.150415i
$559$	22.3774	+	37.6404i	0.946463	+	1.59202i
$560$	1.81343	+	1.57127i	0.0766313	+	0.0663982i
$561$	−23.9604	−	9.65689i	−1.01161	−	0.407714i
$562$	−8.03859	+	11.9068i	−0.339087	+	0.502256i
$563$	−15.5387	−	32.9559i	−0.654879	−	1.38893i	−0.906959	−	0.421219i	$-0.861602\pi$
$563$	−15.5387	−	32.9559i	−0.654879	−	1.38893i	0.252080	−	0.967706i	$-0.418885\pi$
$564$	−36.7939	−	11.6441i	−1.54930	−	0.490306i
$565$	24.2791	+	13.9792i	1.02143	+	0.588110i
$566$	0.397311	+	0.382373i	0.0167002	+	0.0160724i
$567$	−9.86773	+	2.91610i	−0.414406	+	0.122465i
$568$	10.1550	+	26.6581i	0.426095	+	1.11855i
$569$	4.30612	+	15.6698i	0.180522	+	0.656910i	0.996849	+	0.0793203i	$0.0252750\pi$
$569$	4.30612	+	15.6698i	0.180522	+	0.656910i	−0.816327	+	0.577590i	$0.803993\pi$
$570$	−8.55484	−	21.5485i	−0.358323	−	0.902567i
$571$	−1.05504	+	6.83053i	−0.0441520	+	0.285849i	−0.999967	−	0.00812021i	$-0.997415\pi$
$571$	−1.05504	+	6.83053i	−0.0441520	+	0.285849i	0.955815	+	0.293969i	$0.0949762\pi$
$572$	13.7273	+	17.3104i	0.573966	+	0.723785i
$573$	45.9093	−	4.41070i	1.91789	−	0.184260i
$574$	1.20791	−	4.39552i	0.0504172	−	0.183465i
$575$	18.8104	+	33.8816i	0.784450	+	1.41296i
$576$	−4.60849	+	0.353815i	−0.192020	+	0.0147423i
$577$	−21.0967	+	7.12382i	−0.878267	+	0.296569i	−0.722621	−	0.691244i	$-0.757063\pi$
$577$	−21.0967	+	7.12382i	−0.878267	+	0.296569i	−0.155646	+	0.987813i	$0.549746\pi$
$578$	0.351276	−	6.10581i	0.0146112	−	0.253968i
$579$	6.13419	−	26.2135i	0.254928	−	1.08939i
$580$	−27.1765	−	11.1178i	−1.12844	−	0.461639i
$581$	−4.06577	−	7.80718i	−0.168677	−	0.323896i
$582$	8.37441	+	8.37441i	0.347130	+	0.347130i
$583$	−9.48734	−	15.2841i	−0.392926	−	0.633002i
$584$	4.59185	−	4.09225i	0.190012	−	0.169338i
$585$	−19.8467	−	1.24539i	−0.820560	−	0.0514906i
$586$	1.30277	+	16.9688i	0.0538169	+	0.700973i
$587$	45.8306	+	13.5438i	1.89163	+	0.559013i	0.992649	+	0.121028i	$0.0386189\pi$
$587$	45.8306	+	13.5438i	1.89163	+	0.559013i	0.898982	+	0.437986i	$0.144308\pi$
$588$	10.1407	+	17.8262i	0.418197	+	0.735139i
$589$	11.3902	+	9.39341i	0.469324	+	0.387049i
$590$	−10.9065	+	3.16152i	−0.449016	+	0.130158i
$591$	28.8514	+	4.45638i	1.18679	+	0.183311i
$592$	−3.01372	−	0.0577380i	−0.123863	−	0.00237302i
$593$	15.2681	+	8.68552i	0.626985	+	0.356671i	0.774672	−	0.632363i	$-0.217915\pi$
$593$	15.2681	+	8.68552i	0.626985	+	0.356671i	−0.147688	+	0.989034i	$0.547183\pi$
$594$	1.90072	−	4.23991i	0.0779874	−	0.173965i
$595$	−4.00175	−	4.90414i	−0.164056	−	0.201050i
$596$	−1.92346	+	1.99860i	−0.0787878	+	0.0818657i
$597$	3.31010	−	24.5371i	0.135474	−	1.00424i
$598$	19.5409	−	10.1459i	0.799087	−	0.414898i
$599$	8.78730	−	24.4665i	0.359039	−	0.999673i	−0.617919	−	0.786242i	$-0.712024\pi$
$599$	8.78730	−	24.4665i	0.359039	−	0.999673i	0.976958	−	0.213431i	$-0.0684638\pi$
$600$	16.0004	−	24.1531i	0.653212	−	0.986045i
$601$	1.47283	−	3.65435i	0.0600782	−	0.149064i	−0.894464	−	0.447140i	$-0.852443\pi$
$601$	1.47283	−	3.65435i	0.0600782	−	0.149064i	0.954542	+	0.298076i	$0.0963450\pi$
$602$	7.45091	+	2.51599i	0.303676	+	0.102544i
$603$	13.8706	+	3.52739i	0.564854	+	0.143647i
$604$	10.0671	−	3.61567i	0.409625	−	0.147120i
$605$	−2.86731	+	7.85482i	−0.116573	+	0.319344i
$606$	3.57531	−	0.552240i	0.145237	−	0.0224332i
$607$	−2.02624	+	0.273344i	−0.0822426	+	0.0110947i	−0.174697	−	0.984622i	$-0.555895\pi$
$607$	−2.02624	+	0.273344i	−0.0822426	+	0.0110947i	0.0924544	+	0.995717i	$0.470529\pi$
$608$	−6.23801	+	35.8232i	−0.252985	+	1.45282i
$609$	14.7788	+	13.1709i	0.598869	+	0.533710i
$610$	7.99753	−	7.91478i	0.323810	−	0.320460i
$611$	−24.2585	−	37.4594i	−0.981393	−	1.51545i
$612$	−9.76524	−	0.938188i	−0.394736	−	0.0379240i
$613$	5.58036	−	14.6491i	0.225389	−	0.591670i	−0.773736	−	0.633509i	$-0.781614\pi$
$613$	5.58036	−	14.6491i	0.225389	−	0.591670i	0.999124	+	0.0418384i	$0.0133215\pi$
$614$	−1.05857	+	13.7880i	−0.0427203	+	0.556438i
$615$	33.0208	+	4.62953i	1.33153	+	0.186681i
$616$	9.18741	+	1.78179i	0.370171	+	0.0717905i
$617$	7.98101	−	1.70707i	0.321303	−	0.0687241i	−0.0456671	−	0.998957i	$-0.514541\pi$
$617$	7.98101	−	1.70707i	0.321303	−	0.0687241i	0.366970	+	0.930233i	$0.380395\pi$
$618$	−15.2026	−	12.0557i	−0.611537	−	0.484952i
$619$	30.5832	+	1.17228i	1.22924	+	0.0471180i	0.644822	−	0.764332i	$-0.276931\pi$
$619$	30.5832	+	1.17228i	1.22924	+	0.0471180i	0.584421	+	0.811450i	$0.301322\pi$
$620$	−0.639297	+	7.79559i	−0.0256748	+	0.313079i
$621$	10.5585	+	7.42666i	0.423696	+	0.298021i
$622$	14.6612	+	9.10068i	0.587859	+	0.364904i
$623$	−12.4187	−	7.70869i	−0.497544	−	0.308842i
$624$	8.15633	+	5.73703i	0.326515	+	0.229665i
$625$	7.95922	+	23.6992i	0.318369	+	0.947967i
$626$	4.03575	+	0.154694i	0.161301	+	0.00618280i
$627$	42.9223	+	34.0376i	1.71415	+	1.35933i
$628$	14.3613	−	3.07176i	0.573077	−	0.122577i
$629$	7.80607	+	1.51390i	0.311248	+	0.0603630i
$630$	−2.85144	+	2.15021i	−0.113604	+	0.0856664i
$631$	2.51273	−	32.7287i	0.100030	−	1.30291i	−0.704800	−	0.709406i	$-0.748963\pi$
$631$	2.51273	−	32.7287i	0.100030	−	1.30291i	0.804830	−	0.593505i	$-0.202256\pi$
$632$	0.952113	−	2.49940i	0.0378730	−	0.0994209i
$633$	−6.28064	−	0.603407i	−0.249633	−	0.0239833i
$634$	5.81884	+	8.98533i	0.231096	+	0.356853i
$635$	−9.01865	−	9.11294i	−0.357894	−	0.361636i
$636$	−11.8259	−	10.5392i	−0.468927	−	0.417906i
$637$	−4.06856	+	23.3647i	−0.161202	+	0.925742i
$638$	−24.6643	+	3.32726i	−0.976469	+	0.131728i
$639$	25.4199	−	3.92634i	1.00560	−	0.155324i
$640$	−20.7396	+	9.64724i	−0.819805	+	0.381340i
$641$	−8.27701	+	2.97274i	−0.326922	+	0.117416i	−0.496341	−	0.868128i	$-0.665323\pi$
$641$	−8.27701	+	2.97274i	−0.326922	+	0.117416i	0.169418	+	0.985544i	$0.445811\pi$
$642$	−20.8149	−	5.29337i	−0.821497	−	0.208913i
$643$	−34.4117	−	11.6200i	−1.35706	−	0.458246i	−0.455247	−	0.890365i	$-0.650449\pi$
$643$	−34.4117	−	11.6200i	−1.35706	−	0.458246i	−0.901816	+	0.432119i	$0.857766\pi$
$644$	−4.12055	+	10.2238i	−0.162372	+	0.402873i
$645$	−11.2456	+	56.4145i	−0.442797	+	2.22132i
$646$	4.47076	−	12.4479i	0.175900	−	0.489757i
$647$	−5.07881	+	2.63699i	−0.199669	+	0.103671i	−0.557714	−	0.830033i	$-0.688321\pi$
$647$	−5.07881	+	2.63699i	−0.199669	+	0.103671i	0.358045	+	0.933704i	$0.383443\pi$
$648$	3.59206	−	26.6272i	0.141109	−	1.04602i
$649$	18.6053	−	19.3322i	0.730323	−	0.758853i
$650$	13.5859	−	4.14456i	0.532882	−	0.162563i
$651$	2.15717	−	4.81197i	0.0845462	−	0.188596i
$652$	−0.363649	−	0.206868i	−0.0142416	−	0.00810159i
$653$	0.176273	+	0.00337711i	0.00689810	+	0.000132156i	0.0226038	−	0.999745i	$-0.492804\pi$
$653$	0.176273	+	0.00337711i	0.00689810	+	0.000132156i	−0.0157057	+	0.999877i	$0.504999\pi$
$654$	−29.6301	−	4.57665i	−1.15863	−	0.178961i
$655$	−11.5060	+	20.8994i	−0.449575	+	0.816608i
$656$	−5.56315	−	4.58790i	−0.217205	−	0.179127i
$657$	−2.74220	−	4.82046i	−0.106983	−	0.188064i
$658$	−7.68622	−	2.27142i	−0.299640	−	0.0885493i
$659$	−0.510781	−	6.65300i	−0.0198972	−	0.259164i	−0.998558	−	0.0536820i	$-0.982904\pi$
$659$	−0.510781	−	6.65300i	−0.0198972	−	0.259164i	0.978661	−	0.205482i	$-0.0658762\pi$
$660$	−1.81757	+	28.9651i	−0.0707490	+	1.12746i
$661$	37.2976	−	33.2395i	1.45071	−	1.29287i	0.567927	−	0.823079i	$-0.307746\pi$
$661$	37.2976	−	33.2395i	1.45071	−	1.29287i	0.882780	−	0.469786i	$-0.155669\pi$
$662$	−7.10912	−	11.4528i	−0.276304	−	0.445125i
$663$	−18.6008	−	18.6008i	−0.722395	−	0.722395i
$664$	22.9455	−	1.34833i	0.890456	−	0.0523252i
$665$	5.19073	+	12.3780i	0.201288	+	0.479997i
$666$	1.02223	−	4.36835i	0.0396108	−	0.169270i
$667$	3.97133	−	69.0289i	0.153771	−	2.67281i
$668$	−9.52898	+	3.21770i	−0.368687	+	0.124497i
$669$	10.1185	−	0.776846i	0.391205	−	0.0300346i
$670$	−10.1613	+	1.11956i	−0.392567	+	0.0432525i
$671$	−7.04475	+	25.6355i	−0.271960	+	0.989646i
$672$	12.9284	−	1.24208i	0.498722	−	0.0479144i
$673$	15.1369	+	19.0880i	0.583486	+	0.735790i	0.983538	−	0.180703i	$-0.0578372\pi$
$673$	15.1369	+	19.0880i	0.583486	+	0.735790i	−0.400052	+	0.916492i	$0.631008\pi$
$674$	−3.93508	+	25.4765i	−0.151574	+	0.981318i
$675$	5.82694	+	5.94942i	0.224279	+	0.228993i
$676$	0.890619	+	3.24092i	0.0342546	+	0.124651i
$677$	11.0206	+	28.9302i	0.423554	+	1.11188i	0.962916	+	0.269803i	$0.0869584\pi$
$677$	11.0206	+	28.9302i	0.423554	+	1.11188i	−0.539361	+	0.842074i	$0.681334\pi$
$678$	20.0527	−	5.92597i	0.770121	−	0.227585i
$679$	−4.94020	−	4.75447i	−0.189587	−	0.182460i
$680$	15.9599	−	4.29672i	0.612033	−	0.164772i
$681$	−11.1541	−	3.52991i	−0.427424	−	0.135267i
$682$	2.82738	+	5.99657i	0.108266	+	0.229620i
$683$	−18.1315	+	26.8565i	−0.693784	+	1.02763i	0.303416	+	0.952858i	$0.401873\pi$
$683$	−18.1315	+	26.8565i	−0.693784	+	1.02763i	−0.997200	+	0.0747756i	$0.976176\pi$
$684$	19.2948	+	7.77648i	0.737753	+	0.297341i
$685$	7.49315	−	8.64798i	0.286299	−	0.330422i
$686$	4.68801	+	7.88557i	0.178989	+	0.301072i
$687$	−10.9745	+	23.2756i	−0.418702	+	0.888019i
$688$	8.45319	−	9.12705i	0.322275	−	0.347966i
$689$	−2.79625	−	18.1034i	−0.106529	−	0.689686i
$690$	27.9941	+	7.27430i	1.06572	+	0.276928i
$691$	−27.9323	+	19.6471i	−1.06259	+	0.747411i	−0.968716	−	0.248172i	$-0.920170\pi$
$691$	−27.9323	+	19.6471i	−1.06259	+	0.747411i	−0.0938775	+	0.995584i	$0.529926\pi$
$692$	7.26540	−	0.417989i	0.276189	−	0.0158896i
$693$	3.30369	−	7.76462i	0.125497	−	0.294954i
$694$	−11.3088	+	7.32347i	−0.429274	+	0.277995i
$695$	−13.3591	+	4.15145i	−0.506741	+	0.157474i
$696$	−47.1691	+	21.1456i	−1.78794	+	0.801520i
$697$	12.3816	+	14.4408i	0.468985	+	0.546985i
$698$	3.55696	+	13.9869i	0.134633	+	0.529411i
$699$	2.31985	−	11.9618i	0.0877446	−	0.452435i
$700$	−3.81290	+	6.00234i	−0.144114	+	0.226867i
$701$	−1.93134	−	16.7295i	−0.0729457	−	0.631865i	−0.978298	−	0.207203i	$-0.933564\pi$
$701$	−1.93134	−	16.7295i	−0.0729457	−	0.631865i	0.905352	−	0.424661i	$-0.139607\pi$
$702$	3.47130	−	3.21501i	0.131016	−	0.121343i
$703$	−14.9646	−	7.76985i	−0.564401	−	0.293045i
$704$	−4.48784	+	6.38036i	−0.169142	+	0.240469i
$705$	9.25036	−	57.8914i	0.348389	−	2.18032i
$706$	−1.56311	−	6.67972i	−0.0588286	−	0.251394i
$707$	−2.06336	+	0.359300i	−0.0776007	+	0.0135129i
$708$	10.8870	−	20.9683i	0.409160	−	0.788036i
$709$	1.77812	−	46.3888i	0.0667788	−	1.74217i	−0.456248	−	0.889852i	$-0.650807\pi$
$709$	1.77812	−	46.3888i	0.0667788	−	1.74217i	0.523027	−	0.852316i	$-0.324803\pi$
$710$	−16.0162	+	9.00117i	−0.601076	+	0.337808i
$711$	−2.02419	−	1.31085i	−0.0759132	−	0.0491609i
$712$	31.6331	−	21.3564i	1.18550	−	0.800365i
$713$	−17.8504	+	4.53950i	−0.668504	+	0.170006i
$714$	−4.71036	−	0.361635i	−0.176281	−	0.0135339i
$715$	−22.9326	+	24.5039i	−0.857632	+	0.916395i
$716$	1.16259	+	1.40973i	0.0434482	+	0.0526840i
$717$	−45.8587	−	9.80880i	−1.71263	−	0.366317i
$718$	−12.3247	−	5.24393i	−0.459955	−	0.195702i
$719$	−16.1777	+	18.1528i	−0.603327	+	0.676986i	−0.967069	−	0.254514i	$-0.918084\pi$
$719$	−16.1777	+	18.1528i	−0.603327	+	0.676986i	0.363742	+	0.931500i	$0.381499\pi$
$720$	1.25860	+	5.50735i	0.0469052	+	0.205247i
$721$	8.93334	+	6.80959i	0.332695	+	0.253602i
$722$	−8.41451	+	11.4888i	−0.313156	+	0.427567i
$723$	−14.3783	−	13.3167i	−0.534734	−	0.495254i
$724$	2.69020	+	7.49031i	0.0999803	+	0.278375i
$725$	10.6145	−	43.3236i	0.394214	−	1.60900i
$726$	2.76922	+	5.59290i	0.102775	+	0.207572i
$727$	0.569077	+	1.33750i	0.0211059	+	0.0496049i	0.930390	−	0.366570i	$-0.119468\pi$
$727$	0.569077	+	1.33750i	0.0211059	+	0.0496049i	−0.909285	+	0.416175i	$0.863370\pi$
$728$	7.89820	+	5.33230i	0.292727	+	0.197628i
$729$	−12.0000	−	4.30987i	−0.444443	−	0.159625i
$730$	3.04295	+	2.53620i	0.112624	+	0.0938690i
$731$	−26.0990	+	19.8944i	−0.965305	+	0.735820i
$732$	0.448425	+	23.4062i	0.0165743	+	0.865118i
$733$	−10.9914	−	37.1937i	−0.405978	−	1.37378i	−0.872217	−	0.489120i	$-0.837318\pi$
$733$	−10.9914	−	37.1937i	−0.405978	−	1.37378i	0.466239	−	0.884659i	$-0.345609\pi$
$734$	16.3219	+	7.31700i	0.602454	+	0.270076i
$735$	−24.5112	+	19.2308i	−0.904110	+	0.709338i
$736$	−31.4566	−	32.6854i	−1.15951	−	1.20480i
$737$	19.4868	−	14.2724i	0.717806	−	0.525730i
$738$	8.40933	−	6.66865i	0.309552	−	0.245477i
$739$	−15.8742	+	19.2485i	−0.583940	+	0.708069i	−0.977430	−	0.211260i	$-0.932243\pi$
$739$	−15.8742	+	19.2485i	−0.583940	+	0.708069i	0.393490	+	0.919329i	$0.371268\pi$
$740$	−1.14822	−	8.85895i	−0.0422092	−	0.325662i
$741$	26.6481	+	49.0050i	0.978942	+	1.80024i
$742$	−2.49746	−	2.14132i	−0.0916846	−	0.0786103i
$743$	1.75695	+	5.20308i	0.0644562	+	0.190882i	0.974851	−	0.222859i	$-0.0715389\pi$
$743$	1.75695	+	5.20308i	0.0644562	+	0.190882i	−0.910395	+	0.413741i	$0.864222\pi$
$744$	9.16149	+	10.2800i	0.335876	+	0.376882i
$745$	−3.43387	−	2.44212i	−0.125807	−	0.0894723i
$746$			3.41654i			0.125088i
$747$	3.13847	−	20.4856i	0.114831	−	0.749528i
$748$	−11.7073	+	11.7073i	−0.428062	+	0.428062i
$749$	12.1069	+	2.83312i	0.442376	+	0.103520i
$750$	16.9053	+	7.89751i	0.617294	+	0.288376i
$751$	31.9897	+	15.8391i	1.16732	+	0.577977i	0.920369	−	0.391051i	$-0.127888\pi$
$751$	31.9897	+	15.8391i	1.16732	+	0.577977i	0.246951	+	0.969028i	$0.420571\pi$
$752$	−8.25244	+	9.62497i	−0.300935	+	0.350986i
$753$	7.60621	−	25.7385i	0.277186	−	0.937962i
$754$	−24.4368	−	6.71535i	−0.889936	−	0.244559i
$755$	7.68833	+	14.3155i	0.279807	+	0.520994i
$756$	−0.271651	+	2.35307i	−0.00987984	+	0.0855804i
$757$	2.64431	+	3.61041i	0.0961090	+	0.131223i	0.852141	−	0.523312i	$-0.175304\pi$
$757$	2.64431	+	3.61041i	0.0961090	+	0.131223i	−0.756032	+	0.654534i	$0.772865\pi$
$758$	−0.0477922	+	2.49458i	−0.00173589	+	0.0906074i
$759$	−65.8979	+	18.1091i	−2.39194	+	0.657318i
$760$	−35.0382	−	0.853567i	−1.27097	−	0.0309621i
$761$	−12.7673	−	6.94262i	−0.462813	−	0.251670i	0.229442	−	0.973322i	$-0.426310\pi$
$761$	−12.7673	−	6.94262i	−0.462813	−	0.251670i	−0.692256	+	0.721652i	$0.743383\pi$
$762$	−9.56745	+	0.183297i	−0.346592	+	0.00664015i
$763$	17.2015	+	2.32051i	0.622735	+	0.0840081i
$764$	8.91856	−	28.1815i	0.322662	−	1.01957i
$765$	−0.778579	−	14.8823i	−0.0281496	−	0.538072i
$766$	−1.56870	+	0.304231i	−0.0566794	+	0.0109923i
$767$	25.1403	−	10.6967i	0.907763	−	0.386235i
$768$	−8.44768	+	25.0172i	−0.304829	+	0.902730i
$769$	11.5222	−	6.85001i	0.415501	−	0.247018i	−0.288118	−	0.957595i	$-0.593030\pi$
$769$	11.5222	−	6.85001i	0.415501	−	0.247018i	0.703619	+	0.710577i	$0.251566\pi$
$770$	−0.262177	+	6.02155i	−0.00944821	+	0.217002i
$771$	−20.4288	+	0.783053i	−0.735725	+	0.0282010i
$772$	−13.9200	−	10.1952i	−0.500992	−	0.366933i
$773$	−4.39938	−	32.6117i	−0.158235	−	1.17296i	−0.877971	−	0.478714i	$-0.841103\pi$
$773$	−4.39938	−	32.6117i	−0.158235	−	1.17296i	0.719736	−	0.694248i	$-0.244263\pi$
$774$	10.6524	+	15.1446i	0.382894	+	0.544360i
$775$	−11.8560	+	0.786300i	−0.425881	+	0.0282447i
$776$	16.6057	−	6.69268i	0.596108	−	0.240253i
$777$	−1.25969	+	5.88938i	−0.0451911	+	0.211280i
$778$	−0.188371	+	1.96069i	−0.00675344	+	0.0702940i
$779$	−16.5006	−	36.8078i	−0.591197	−	1.31877i
$780$	−13.2506	+	26.4155i	−0.474449	+	0.945828i
$781$	22.1832	−	37.3138i	0.793778	−	1.33519i
$782$	9.23282	+	13.6757i	0.330165	+	0.489040i
$783$	−3.10773	−	14.5294i	−0.111061	−	0.519240i
$784$	6.69310	−	0.772685i	0.239039	−	0.0275959i
$785$	7.83334	+	20.8893i	0.279584	+	0.745570i
$786$	5.37250	+	16.9764i	0.191631	+	0.605528i
$787$	2.47963	+	14.2399i	0.0883894	+	0.507597i	0.996117	+	0.0880370i	$0.0280594\pi$
$787$	2.47963	+	14.2399i	0.0883894	+	0.507597i	−0.907728	+	0.419560i	$0.862185\pi$
$788$	9.86764	−	15.8967i	0.351520	−	0.566298i
$789$	−64.0746	+	14.9940i	−2.28112	+	0.533802i
$790$	1.68254	+	0.369042i	0.0598623	+	0.0131299i
$791$	−11.5414	+	3.65248i	−0.410363	+	0.129867i
$792$	14.9722	+	16.1658i	0.532015	+	0.574426i
$793$	−16.8210	+	21.2118i	−0.597333	+	0.753251i
$794$	3.94859	−	6.09734i	0.140130	−	0.216386i
$795$	13.1850	−	20.1298i	0.467625	−	0.713932i
$796$	−13.6400	−	8.10907i	−0.483458	−	0.287418i
$797$	−24.1319	+	20.6906i	−0.854794	+	0.732900i	−0.965347	−	0.260971i	$-0.915957\pi$
$797$	−24.1319	+	20.6906i	−0.854794	+	0.732900i	0.110553	+	0.993870i	$0.464738\pi$
$798$	9.36165	+	3.56619i	0.331399	+	0.126242i
$799$	25.8026	−	21.2792i	0.912829	−	0.752805i
$800$	−16.1217	−	24.4234i	−0.569989	−	0.863499i
$801$	−12.8645	−	31.9189i	−0.454544	−	1.12780i
$802$	−0.751834	−	13.0682i	−0.0265482	−	0.461454i
$803$	−9.22096	−	1.60568i	−0.325401	−	0.0566630i
$804$	12.8941	−	16.9155i	0.454741	−	0.596563i
$805$	−16.2844	−	3.90012i	−0.573949	−	0.137461i
$806$	0.258578	+	6.74595i	0.00910803	+	0.237616i
$807$	−9.99455	−	4.71243i	−0.351825	−	0.165886i
$808$	1.34790	−	5.30026i	0.0474188	−	0.186463i
$809$	34.3934	−	17.0293i	1.20921	−	0.598718i	0.277081	−	0.960846i	$-0.410633\pi$
$809$	34.3934	−	17.0293i	1.20921	−	0.598718i	0.932128	+	0.362129i	$0.117950\pi$
$810$	17.3025	−	0.241487i	0.607948	−	0.00848499i
$811$	8.49343	+	43.7945i	0.298245	+	1.53783i	0.759466	+	0.650546i	$0.225460\pi$
$811$	8.49343	+	43.7945i	0.298245	+	1.53783i	−0.461222	+	0.887285i	$0.652589\pi$
$812$	11.4758	−	5.41084i	0.402721	−	0.189883i
$813$	26.3849	+	50.8169i	0.925360	+	1.78223i
$814$	−4.59011	−	6.02166i	−0.160883	−	0.211059i
$815$	0.229330	−	0.592732i	0.00803308	−	0.0207625i
$816$	−3.57006	+	6.56523i	−0.124977	+	0.229829i
$817$	65.0307	−	24.7725i	2.27514	−	0.866682i
$818$	−11.0927	+	19.4996i	−0.387846	+	0.681786i
$819$	6.19108	−	5.95832i	0.216334	−	0.208200i
$820$	11.0159	−	18.3121i	0.384694	−	0.639488i
$821$	34.0898	+	3.93550i	1.18974	+	0.137350i	0.686719	−	0.726923i	$-0.259050\pi$
$821$	34.0898	+	3.93550i	1.18974	+	0.137350i	0.503023	+	0.864273i	$0.332221\pi$
$822$	−0.816750	−	8.50124i	−0.0284874	−	0.296515i
$823$	13.6142	−	7.74469i	0.474562	−	0.269963i	−0.238398	−	0.971168i	$-0.576622\pi$
$823$	13.6142	−	7.74469i	0.474562	−	0.269963i	0.712960	+	0.701204i	$0.247354\pi$
$824$	−25.7678	+	14.0121i	−0.897665	+	0.488135i
$825$	−43.9269	+	3.75961i	−1.52934	+	0.130893i
$826$	2.17718	−	4.39717i	0.0757537	−	0.152997i
$827$	−30.6200	−	1.76161i	−1.06476	−	0.0612573i	−0.483792	−	0.875183i	$-0.660741\pi$
$827$	−30.6200	−	1.76161i	−1.06476	−	0.0612573i	−0.580969	+	0.813926i	$0.697326\pi$
$828$	−22.0499	+	13.6871i	−0.766287	+	0.475660i
$829$	−1.60012			−0.0555744			−0.0277872	−	0.999614i	$-0.508846\pi$
$829$	−1.60012			−0.0555744			−0.0277872	+	0.999614i	$0.508846\pi$
$830$	3.03869	+	14.4879i	0.105475	+	0.502883i
$831$	42.0971			1.46033
$832$	−6.74876	+	4.18918i	−0.233971	+	0.145234i
$833$	−17.7440	−	1.02084i	−0.614794	−	0.0353700i
$834$	−4.63292	+	9.35695i	−0.160425	+	0.324005i
$835$	−6.96980	−	13.5961i	−0.241200	−	0.470513i
$836$	30.8437	−	16.7723i	1.06675	−	0.580081i
$837$	−3.44026	+	1.95705i	−0.118913	+	0.0676456i
$838$	2.63763	+	27.4541i	0.0911154	+	0.948385i
$839$	49.4018	+	5.70319i	1.70554	+	0.196896i	0.911593	−	0.411093i	$-0.134853\pi$
$839$	49.4018	+	5.70319i	1.70554	+	0.196896i	0.793945	+	0.607989i	$0.208024\pi$
$840$	3.02225	+	12.1484i	0.104278	+	0.419158i
$841$	−36.4469	+	35.0766i	−1.25679	+	1.20954i
$842$	−4.40526	+	7.74392i	−0.151815	+	0.266873i
$843$	42.4320	−	16.1639i	1.46144	−	0.556714i
$844$	−1.93182	+	3.55255i	−0.0664959	+	0.122284i
$845$	−4.66986	+	2.06436i	−0.160648	+	0.0710163i
$846$	−11.4396	−	15.0074i	−0.393303	−	0.515964i
$847$	−1.66492	−	3.20661i	−0.0572074	−	0.110181i
$848$	−4.70701	+	2.21936i	−0.161640	+	0.0762131i
$849$	−0.331821	−	1.71096i	−0.0113881	−	0.0587199i
$850$	4.25316	+	9.75809i	0.145882	+	0.334700i
$851$	18.8513	−	9.33386i	0.646213	−	0.319960i
$852$	9.42105	−	37.0459i	0.322760	−	1.26917i
$853$	12.7003	+	5.98822i	0.434851	+	0.205033i	0.631393	−	0.775463i	$-0.282483\pi$
$853$	12.7003	+	5.98822i	0.434851	+	0.205033i	−0.196542	+	0.980495i	$0.562971\pi$
$854$	0.186222	+	4.85829i	0.00637240	+	0.166247i
$855$	−7.36048	+	30.7326i	−0.251723	+	1.05103i
$856$	−19.6828	+	25.8214i	−0.672745	+	0.882558i
$857$	20.7345	+	3.61057i	0.708279	+	0.123335i	0.514224	−	0.857656i	$-0.328080\pi$
$857$	20.7345	+	3.61057i	0.708279	+	0.123335i	0.194055	+	0.980991i	$0.437836\pi$
$858$	1.43871	+	25.0074i	0.0491168	+	0.853738i
$859$	−8.96403	−	22.2413i	−0.305849	−	0.758862i	−0.999265	−	0.0383249i	$-0.987798\pi$
$859$	−8.96403	−	22.2413i	−0.305849	−	0.758862i	0.693417	−	0.720537i	$-0.256105\pi$
$860$	30.4483	+	20.7878i	1.03828	+	0.708858i
$861$	−11.1153	+	9.16674i	−0.378809	+	0.312402i
$862$	10.3901	+	3.95797i	0.353888	+	0.134809i
$863$	−2.24604	+	1.92575i	−0.0764562	+	0.0655534i	−0.688306	−	0.725421i	$-0.741645\pi$
$863$	−2.24604	+	1.92575i	−0.0764562	+	0.0655534i	0.611850	+	0.790974i	$0.290426\pi$
$864$	−8.37920	−	4.98148i	−0.285066	−	0.169473i
$865$	2.25605	+	10.8225i	0.0767080	+	0.367976i
$866$	0.844338	−	1.30381i	0.0286918	−	0.0443052i
$867$	−12.0107	+	15.1458i	−0.407905	+	0.514378i
$868$	−2.29654	−	2.47962i	−0.0779497	−	0.0841636i
$869$	−3.88033	+	1.22801i	−0.131631	+	0.0416573i
$870$	−17.9506	−	28.0374i	−0.608582	−	0.950557i
$871$	23.9491	−	5.60430i	0.811483	−	0.189894i
$872$	−23.9032	+	38.5080i	−0.809466	+	1.30405i
$873$	−2.76934	−	15.9036i	−0.0937281	−	0.538255i
$874$	−10.5572	−	33.3594i	−0.357104	−	1.12840i
$875$	−9.87282	−	4.38382i	−0.333762	−	0.148200i
$876$	−8.18744	+	0.945200i	−0.276628	+	0.0319353i
$877$	2.51966	+	11.7801i	0.0850829	+	0.397785i	0.999983	−	0.00589634i	$-0.00187688\pi$
$877$	2.51966	+	11.7801i	0.0850829	+	0.397785i	−0.914900	+	0.403681i	$0.867731\pi$
$878$	1.25888	+	1.86466i	0.0424853	+	0.0629292i
$879$	27.4876	−	46.2360i	0.927133	−	1.55950i
$880$	8.52226	+	4.27496i	0.287285	+	0.144109i
$881$	8.72810	+	19.4696i	0.294057	+	0.655949i	0.998554	−	0.0537580i	$-0.0171200\pi$
$881$	8.72810	+	19.4696i	0.294057	+	0.655949i	−0.704497	+	0.709707i	$0.748827\pi$
$882$	−0.959016	+	9.98203i	−0.0322918	+	0.336113i
$883$	−0.250050	+	1.16905i	−0.00841486	+	0.0393417i	−0.981891	−	0.189448i	$-0.939330\pi$
$883$	−0.250050	+	1.16905i	−0.00841486	+	0.0393417i	0.973476	+	0.228789i	$0.0734767\pi$
$884$	−15.6371	+	6.30231i	−0.525932	+	0.211970i
$885$	33.9441	+	11.6591i	1.14102	+	0.391915i
$886$	−3.13684	−	4.45963i	−0.105384	−	0.149824i
$887$	4.62466	+	34.2817i	0.155281	+	1.15107i	0.884417	+	0.466697i	$0.154556\pi$
$887$	4.62466	+	34.2817i	0.155281	+	1.15107i	−0.729136	+	0.684368i	$0.760078\pi$
$888$	−12.6873	−	9.29237i	−0.425760	−	0.311832i
$889$	5.53587	−	0.212194i	0.185667	−	0.00711677i
$890$	16.6090	+	18.1211i	0.556734	+	0.607421i
$891$	−35.1446	+	20.8936i	−1.17739	+	0.699963i
$892$	2.08084	−	6.16227i	0.0696718	−	0.206328i
$893$	−65.2602	+	27.7669i	−2.18385	+	0.929184i
$894$	−3.08743	+	0.598771i	−0.103259	+	0.0200259i
$895$	−1.85758	+	2.06267i	−0.0620921	+	0.0689475i
$896$	2.98206	−	9.42292i	0.0996238	−	0.314798i
$897$	−68.9656	−	9.30359i	−2.30269	−	0.310638i
$898$	9.42648	−	0.180596i	0.314566	−	0.00602657i
$899$	18.6244	+	10.1276i	0.621159	+	0.337775i
$900$	−15.5928	+	6.09672i	−0.519759	+	0.203224i
$901$	13.2372	−	3.63764i	0.440994	−	0.121187i
$902$	0.346958	−	18.1100i	0.0115524	−	0.602997i
$903$	−14.6869	−	20.0527i	−0.488749	−	0.667313i
$904$	3.62516	−	31.4016i	0.120571	−	1.04440i
$905$	−10.6513	+	5.72040i	−0.354060	+	0.190153i
$906$	11.6944	+	3.21368i	0.388521	+	0.106767i
$907$	−12.4513	+	42.1338i	−0.413440	+	1.39903i	0.449299	+	0.893381i	$0.351674\pi$
$907$	−12.4513	+	42.1338i	−0.413440	+	1.39903i	−0.862739	+	0.505649i	$0.831253\pi$
$908$	−4.88056	+	5.69229i	−0.161967	+	0.188905i
$909$	−4.41911	−	2.18804i	−0.146572	−	0.0725727i
$910$	−2.64629	+	5.53764i	−0.0877235	+	0.183571i
$911$	−37.4566	−	8.76519i	−1.24099	−	0.290404i	−0.444902	−	0.895579i	$-0.646761\pi$
$911$	−37.4566	−	8.76519i	−1.24099	−	0.290404i	−0.796092	+	0.605176i	$0.793103\pi$
$912$	11.2056	−	11.2056i	0.371053	−	0.371053i
$913$	−23.3030	−	26.0835i	−0.771217	−	0.863238i
$914$		−	13.7728i		−	0.455563i
$915$	−35.0670	+	5.91860i	−1.15928	+	0.195663i
$916$	10.9729	+	12.3125i	0.362554	+	0.406817i
$917$	−3.29801	−	9.76681i	−0.108910	−	0.322528i
$918$	2.69182	+	2.30797i	0.0888434	+	0.0761743i
$919$	−18.5955	−	34.1965i	−0.613408	−	1.12804i	−0.980251	−	0.197757i	$-0.936634\pi$
$919$	−18.5955	−	34.1965i	−0.613408	−	1.12804i	0.366843	−	0.930283i	$-0.380439\pi$
$920$	26.6875	−	34.6356i	0.879860	−	1.14190i
$921$	27.8082	−	33.7194i	0.916312	−	1.11109i
$922$	−9.09982	+	7.21621i	−0.299687	+	0.237653i
$923$	35.6615	−	26.1189i	1.17381	−	0.859716i
$924$	−8.69581	−	9.03552i	−0.286071	−	0.297247i
$925$	13.0532	−	3.71029i	0.429185	−	0.121994i
$926$	15.4779	+	6.93862i	0.508635	+	0.228017i
$927$	7.49507	+	25.3624i	0.246170	+	0.833010i
$928$	1.00015	+	52.2042i	0.0328315	+	1.71369i
$929$	−40.1787	+	30.6269i	−1.31822	+	1.00484i	−0.319867	+	0.947462i	$0.603638\pi$
$929$	−40.1787	+	30.6269i	−1.31822	+	1.00484i	−0.998353	+	0.0573732i	$0.981728\pi$
$930$	−5.67790	+	6.81237i	−0.186186	+	0.223387i
$931$	35.4707	+	12.7395i	1.16251	+	0.417522i
$932$	−6.47226	−	4.36960i	−0.212006	−	0.143131i
$933$	−21.3532	−	50.1862i	−0.699073	−	1.64302i
$934$	5.20699	+	10.5164i	0.170378	+	0.344106i
$935$	−20.2134	−	14.9667i	−0.661050	−	0.489463i
$936$	7.58405	+	21.1163i	0.247893	+	0.690207i
$937$	−3.44375	−	3.18950i	−0.112503	−	0.104196i	0.621252	−	0.783611i	$-0.286624\pi$
$937$	−3.44375	−	3.18950i	−0.112503	−	0.104196i	−0.733755	+	0.679414i	$0.762234\pi$
$938$	2.61005	−	3.56363i	0.0852211	−	0.116357i
$939$	−10.1518	−	7.73838i	−0.331291	−	0.252532i
$940$	−31.8200	−	19.9817i	−1.03785	−	0.651731i
$941$	−15.4534	+	17.3400i	−0.503766	+	0.565269i	−0.942867	−	0.333168i	$-0.891882\pi$
$941$	−15.4534	+	17.3400i	−0.503766	+	0.565269i	0.439101	+	0.898437i	$0.355297\pi$
$942$	15.3219	+	6.51916i	0.499214	+	0.212406i
$943$	49.2093	+	10.5255i	1.60247	+	0.342756i
$944$	−4.93833	−	5.98807i	−0.160729	−	0.194895i
$945$	−3.59633	+	0.119125i	−0.116989	+	0.00387513i
$946$	31.1573	+	2.39208i	1.01301	+	0.0777733i
$947$	−37.9040	+	9.63926i	−1.23171	+	0.313234i	−0.806159	−	0.591699i	$-0.798457\pi$
$947$	−37.9040	+	9.63926i	−1.23171	+	0.313234i	−0.425554	+	0.904933i	$0.639921\pi$
$948$	−2.97033	+	2.00536i	−0.0964720	+	0.0651309i
$949$	−7.99985	−	5.18065i	−0.259686	−	0.168171i
$950$	−2.78492	−	22.4000i	−0.0903549	−	0.726753i
$951$	1.29594	−	33.8094i	0.0420238	−	1.09634i
$952$	−3.29093	+	6.33827i	−0.106660	+	0.205425i
$953$	−39.9034	+	6.94851i	−1.29260	+	0.225084i	−0.775776	−	0.631008i	$-0.782641\pi$
$953$	−39.9034	+	6.94851i	−1.29260	+	0.225084i	−0.516823	+	0.856093i	$0.672885\pi$
$954$	−1.76484	−	7.54175i	−0.0571387	−	0.244173i
$955$	44.3407	+	7.08511i	1.43483	+	0.229269i
$956$	−17.2917	+	24.5836i	−0.559255	+	0.795091i
$957$	69.8116	+	36.2472i	2.25669	+	1.17171i
$958$	−4.02039	+	3.72356i	−0.129893	+	0.120303i
$959$	0.567030	+	4.91169i	0.0183104	+	0.158607i
$960$	−10.2705	−	1.84351i	−0.331478	−	0.0594990i
$961$	−4.82692	+	24.8889i	−0.155707	+	0.802869i
$962$	−1.90024	−	7.47221i	−0.0612662	−	0.240914i
$963$	19.0551	+	22.2243i	0.614041	+	0.716167i
$964$	−11.4613	+	5.13802i	−0.369144	+	0.165484i
$965$	12.1989	−	23.1991i	0.392697	−	0.746806i
$966$	−10.4902	+	6.79338i	−0.337516	+	0.218573i
$967$	−12.3733	+	29.0809i	−0.397899	+	0.935177i	0.593564	+	0.804787i	$0.297721\pi$
$967$	−12.3733	+	29.0809i	−0.397899	+	0.935177i	−0.991463	+	0.130390i	$0.958377\pi$
$968$	9.41897	−	0.541887i	0.302737	−	0.0174169i
$969$	−34.1926	+	24.0505i	−1.09842	+	0.772614i
$970$	5.84071	+	9.94183i	0.187534	+	0.319213i
$971$	−3.46693	−	22.4456i	−0.111259	−	0.720312i	−0.975948	−	0.218004i	$-0.930045\pi$
$971$	−3.46693	−	22.4456i	−0.111259	−	0.720312i	0.864689	−	0.502308i	$-0.167516\pi$
$972$	−19.4665	+	21.0183i	−0.624388	+	0.674163i
$973$	2.57790	−	5.46743i	0.0826436	−	0.175278i
$974$	−5.20057	−	8.74773i	−0.166637	−	0.280295i
$975$	−42.6581	−	13.9897i	−1.36615	−	0.448029i
$976$	7.13328	+	2.87497i	0.228331	+	0.0920255i
$977$	11.2588	−	16.6765i	0.360201	−	0.533529i	−0.604594	−	0.796534i	$-0.706665\pi$
$977$	11.2588	−	16.6765i	0.360201	−	0.533529i	0.964795	+	0.263004i	$0.0847134\pi$
$978$	−0.202297	−	0.429050i	−0.00646875	−	0.0137195i
$979$	−55.3734	−	17.5240i	−1.76974	−	0.560069i
$980$	5.19077	+	19.2808i	0.165813	+	0.615903i
$981$	29.4451	+	28.3380i	0.940109	+	0.904764i
$982$	−15.4449	+	4.56425i	−0.492865	+	0.145651i
$983$	14.8033	+	38.8602i	0.472151	+	1.23945i	0.935517	+	0.353281i	$0.114934\pi$
$983$	14.8033	+	38.8602i	0.472151	+	1.23945i	−0.463366	+	0.886167i	$0.653359\pi$
$984$	−9.96899	−	36.2766i	−0.317800	−	1.15646i
$985$	26.0957	+	11.2638i	0.831480	+	0.358896i
$986$	2.89915	−	18.7697i	0.0923278	−	0.597748i
$987$	15.7399	+	19.8484i	0.501006	+	0.631781i
$988$	35.5870	−	3.41900i	1.13217	−	0.108773i
$989$	−23.0046	+	83.7124i	−0.731503	+	2.66190i
$990$	−8.87507	+	11.0729i	−0.282068	+	0.351920i
$991$	−11.0680	+	0.849740i	−0.351586	+	0.0269929i	−0.251143	−	0.967950i	$-0.580807\pi$
$991$	−11.0680	+	0.849740i	−0.351586	+	0.0269929i	−0.100443	+	0.994943i	$0.532026\pi$
$992$	13.1779	−	4.44985i	0.418399	−	0.141283i
$993$	−2.44707	+	42.5344i	−0.0776553	+	1.34979i
$994$	1.80882	−	7.72970i	0.0573723	−	0.245171i
$995$	9.12729	−	22.3110i	0.289355	−	0.707306i
$996$	−26.1877	−	16.2111i	−0.829789	−	0.513669i
$997$	−8.23414	−	8.23414i	−0.260778	−	0.260778i	0.564592	−	0.825370i	$-0.309033\pi$
$997$	−8.23414	−	8.23414i	−0.260778	−	0.260778i	−0.825370	+	0.564592i	$0.809033\pi$
$998$	−8.80696	−	14.1880i	−0.278780	−	0.449113i
$999$	3.37464	−	3.00747i	0.106769	−	0.0951520i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	415.2.l.a.102.25	✓	3200
5.3	odd	4	inner	415.2.l.a.268.16	yes	3200
83.35	odd	82	inner	415.2.l.a.367.16	yes	3200
415.118	even	164	inner	415.2.l.a.118.25	yes	3200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
415.2.l.a.102.25	✓	3200	1.1	even	1	trivial
415.2.l.a.118.25	yes	3200	415.118	even	164	inner
415.2.l.a.268.16	yes	3200	5.3	odd	4	inner
415.2.l.a.367.16	yes	3200	83.35	odd	82	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 415 = 5 \cdot 83 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	415.l (of order \(164\), degree \(80\), minimal)

\(f(q)\)	\(=\)	\(q+(0.617386 - 0.383233i) q^{2} +(-2.29291 - 0.131914i) q^{3} +(-0.653141 + 1.31913i) q^{4} +(-2.12832 - 0.685745i) q^{5} +(-1.46616 + 0.797274i) q^{6} +(0.839813 - 0.477743i) q^{7} +(0.241278 + 2.51137i) q^{8} +(2.25981 + 0.260884i) q^{9} +(-1.57680 + 0.392273i) q^{10} +(2.76623 - 2.66223i) q^{11} +(1.67160 - 2.93847i) q^{12} +(3.65330 - 1.39168i) q^{13} +(0.335403 - 0.616795i) q^{14} +(4.78958 + 1.85310i) q^{15} +(-0.673286 - 0.883268i) q^{16} +(1.35005 + 2.60017i) q^{17} +(1.49516 - 0.704967i) q^{18} +(-1.18284 - 6.09904i) q^{19} +(2.29468 - 2.35964i) q^{20} +(-1.98863 + 0.984635i) q^{21} +(0.687580 - 2.70374i) q^{22} +(7.01042 + 3.30542i) q^{23} +(-0.221942 - 5.79017i) q^{24} +(4.05951 + 2.91897i) q^{25} +(1.72216 - 2.25927i) q^{26} +(1.64083 + 0.285723i) q^{27} +(0.0816863 + 1.41985i) q^{28} +(-3.33482 - 8.27424i) q^{29} +(3.66719 - 0.691443i) q^{30} +(-1.83338 + 1.51197i) q^{31} +(-5.46950 - 2.08353i) q^{32} +(-6.69390 + 5.73934i) q^{33} +(1.82997 + 1.08793i) q^{34} +(-2.11500 + 0.440892i) q^{35} +(-1.82011 + 2.81058i) q^{36} +(1.68637 - 2.12655i) q^{37} +(-3.06762 - 3.31216i) q^{38} +(-8.56026 + 2.70906i) q^{39} +(1.20864 - 5.51046i) q^{40} +(6.32192 - 1.47939i) q^{41} +(-0.850411 + 1.37001i) q^{42} +(1.92158 + 11.0351i) q^{43} +(1.70508 + 5.38782i) q^{44} +(-4.63071 - 2.10490i) q^{45} +(5.59488 - 0.645902i) q^{46} +(-2.38770 - 11.1631i) q^{47} +(1.42727 + 2.11407i) q^{48} +(-3.10008 + 5.21456i) q^{49} +(3.62493 + 0.246397i) q^{50} +(-2.75253 - 6.14004i) q^{51} +(-0.550325 + 5.72813i) q^{52} +(0.980057 - 4.58202i) q^{53} +(1.12252 - 0.452417i) q^{54} +(-7.71304 + 3.76916i) q^{55} +(1.40242 + 1.99381i) q^{56} +(1.90759 + 14.1406i) q^{57} +(-5.22983 - 3.83039i) q^{58} +(6.98350 - 0.267683i) q^{59} +(-5.57275 + 5.10773i) q^{60} +(-5.95237 + 3.53871i) q^{61} +(-0.552464 + 1.63608i) q^{62} +(2.02245 - 0.860514i) q^{63} +(-1.99467 + 0.386843i) q^{64} +(-8.72974 + 0.456702i) q^{65} +(-1.93322 + 6.10871i) q^{66} +(6.23504 + 0.841119i) q^{67} +(-4.31173 + 0.0826058i) q^{68} +(-15.6382 - 8.50379i) q^{69} +(-1.13681 + 1.08274i) q^{70} +(10.9028 - 2.99614i) q^{71} +(-0.109934 + 5.73817i) q^{72} +(-1.44053 - 1.96682i) q^{73} +(0.226177 - 1.95917i) q^{74} +(-8.92302 - 7.22843i) q^{75} +(8.81796 + 2.42322i) q^{76} +(1.05126 - 3.55732i) q^{77} +(-4.24679 + 4.95311i) q^{78} +(-0.950041 - 0.470395i) q^{79} +(0.827273 + 2.34158i) q^{80} +(-10.3695 - 2.42656i) q^{81} +(3.33612 - 3.33612i) q^{82} +(0.337788 - 9.10417i) q^{83} -3.26636i q^{84} +(-1.09028 - 6.45979i) q^{85} +(5.41537 + 6.07652i) q^{86} +(6.55493 + 19.4120i) q^{87} +(7.35328 + 6.30470i) q^{88} +(-7.22702 - 13.2903i) q^{89} +(-3.66560 + 0.475101i) q^{90} +(2.40323 - 2.91409i) q^{91} +(-8.93905 + 7.08873i) q^{92} +(4.40321 - 3.22497i) q^{93} +(-5.75221 - 5.97693i) q^{94} +(-1.66492 + 13.7918i) q^{95} +(12.2662 + 5.49885i) q^{96} +(-2.01113 - 6.80540i) q^{97} +(0.0844397 + 4.40745i) q^{98} +(6.94569 - 5.29447i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3200 q - 82 q^{2} - 78 q^{3} - 82 q^{5} - 164 q^{6} - 74 q^{7} - 82 q^{8} - 102 q^{10} - 164 q^{11} - 114 q^{12} - 82 q^{13} - 82 q^{15} - 96 q^{16} - 82 q^{17} - 82 q^{18} - 82 q^{20} - 148 q^{21} - 82 q^{22}+ \cdots + 246 q^{98}+O(q^{100}) \) 3200 * q - 82 * q^2 - 78 * q^3 - 82 * q^5 - 164 * q^6 - 74 * q^7 - 82 * q^8 - 102 * q^10 - 164 * q^11 - 114 * q^12 - 82 * q^13 - 82 * q^15 - 96 * q^16 - 82 * q^17 - 82 * q^18 - 82 * q^20 - 148 * q^21 - 82 * q^22 - 86 * q^23 - 74 * q^25 - 140 * q^26 - 90 * q^27 - 78 * q^28 - 114 * q^30 - 148 * q^31 - 82 * q^32 - 42 * q^33 - 82 * q^35 - 104 * q^36 - 66 * q^37 - 26 * q^38 - 130 * q^40 - 156 * q^41 - 82 * q^42 - 82 * q^43 - 82 * q^45 - 164 * q^46 - 82 * q^47 - 102 * q^48 - 82 * q^50 - 164 * q^51 - 82 * q^52 - 82 * q^53 - 82 * q^55 - 164 * q^56 - 82 * q^57 - 82 * q^58 - 82 * q^60 - 100 * q^61 - 82 * q^62 - 38 * q^63 - 134 * q^65 - 164 * q^66 - 82 * q^67 + 182 * q^68 - 138 * q^70 - 164 * q^71 - 82 * q^72 + 164 * q^73 - 138 * q^75 - 164 * q^76 - 106 * q^77 + 606 * q^78 - 82 * q^80 - 188 * q^81 + 192 * q^83 - 82 * q^85 - 84 * q^86 - 54 * q^87 + 738 * q^88 - 198 * q^90 - 164 * q^91 - 82 * q^92 + 576 * q^93 - 50 * q^95 - 164 * q^96 - 82 * q^97 + 246 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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