LMFDB - Embedded newform 415.2.l.a.102.3

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			102.3
Character	$\chi$	$=$	415.102
Dual form			415.2.l.a.118.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.19559 + 1.36288i) q^{2} +(-1.50039 - 0.0863199i) q^{3} +(2.07574 - 4.19230i) q^{4} +(-1.48666 + 1.67028i) q^{5} +(3.41189 - 1.85533i) q^{6} +(-0.800461 + 0.455356i) q^{7} +(0.661841 + 6.88885i) q^{8} +(-0.736477 - 0.0850227i) q^{9} +(0.987722 - 5.69338i) q^{10} +(-0.559563 + 0.538525i) q^{11} +(-3.47631 + 6.11092i) q^{12} +(-3.85043 + 1.46677i) q^{13} +(1.13689 - 2.09070i) q^{14} +(2.37476 - 2.37775i) q^{15} +(-5.16989 - 6.78226i) q^{16} +(-0.424452 - 0.817487i) q^{17} +(1.73288 - 0.817052i) q^{18} +(-0.933294 - 4.81232i) q^{19} +(3.91638 + 9.69961i) q^{20} +(1.24031 - 0.614118i) q^{21} +(0.494627 - 1.94499i) q^{22} +(0.438268 + 0.206643i) q^{23} +(-0.398377 - 10.3931i) q^{24} +(-0.579657 - 4.96629i) q^{25} +(6.45493 - 8.46807i) q^{26} +(5.53945 + 0.964602i) q^{27} +(0.247441 + 4.30097i) q^{28} +(2.48887 + 6.17530i) q^{29} +(-1.97342 + 8.45705i) q^{30} +(1.53623 - 1.26692i) q^{31} +(7.65988 + 2.91793i) q^{32} +(0.886050 - 0.759698i) q^{33} +(2.04606 + 1.21639i) q^{34} +(0.429445 - 2.01395i) q^{35} +(-1.88518 + 2.91105i) q^{36} +(4.24852 - 5.35748i) q^{37} +(8.60772 + 9.29390i) q^{38} +(5.90377 - 1.86836i) q^{39} +(-12.4902 - 9.13596i) q^{40} +(3.56207 - 0.833557i) q^{41} +(-1.88625 + 3.03874i) q^{42} +(0.148565 + 0.853167i) q^{43} +(1.09615 + 3.46369i) q^{44} +(1.23691 - 1.10372i) q^{45} +(-1.24389 + 0.143600i) q^{46} +(0.922939 + 4.31498i) q^{47} +(7.17142 + 10.6223i) q^{48} +(-3.14374 + 5.28800i) q^{49} +(8.04112 + 10.1139i) q^{50} +(0.566279 + 1.26319i) q^{51} +(-1.84335 + 19.1868i) q^{52} +(1.07627 - 5.03186i) q^{53} +(-13.4770 + 5.43171i) q^{54} +(-0.0676046 - 1.73523i) q^{55} +(-3.66666 - 5.21288i) q^{56} +(0.984909 + 7.30093i) q^{57} +(-13.8807 - 10.1664i) q^{58} +(10.5146 - 0.403033i) q^{59} +(-5.03884 - 14.8913i) q^{60} +(9.22318 - 5.48323i) q^{61} +(-1.64628 + 4.87534i) q^{62} +(0.628237 - 0.267302i) q^{63} +(-4.05070 + 0.785587i) q^{64} +(3.27438 - 8.61188i) q^{65} +(-0.910026 + 2.87556i) q^{66} +(11.9572 + 1.61305i) q^{67} +(-4.30820 + 0.0825383i) q^{68} +(-0.639736 - 0.347878i) q^{69} +(1.80188 + 5.00710i) q^{70} +(-8.27918 + 2.27516i) q^{71} +(0.0982779 - 5.12976i) q^{72} +(-8.15628 - 11.1362i) q^{73} +(-2.02641 + 17.5530i) q^{74} +(0.441025 + 7.50142i) q^{75} +(-22.1120 - 6.07647i) q^{76} +(0.202687 - 0.685869i) q^{77} +(-10.4159 + 12.1483i) q^{78} +(-4.39159 - 2.17441i) q^{79} +(19.0141 + 1.44779i) q^{80} +(-6.06249 - 1.41868i) q^{81} +(-6.68482 + 6.68482i) q^{82} +(4.21782 - 8.07527i) q^{83} -6.47451i q^{84} +(1.99645 + 0.506377i) q^{85} +(-1.48895 - 1.67073i) q^{86} +(-3.20123 - 9.48022i) q^{87} +(-4.08016 - 3.49833i) q^{88} +(-6.06388 - 11.1513i) q^{89} +(-1.21150 + 4.10907i) q^{90} +(2.41421 - 2.92741i) q^{91} +(1.77604 - 1.40841i) q^{92} +(-2.41432 + 1.76828i) q^{93} +(-7.90718 - 8.21608i) q^{94} +(9.42540 + 5.59544i) q^{95} +(-11.2410 - 5.03924i) q^{96} +(-4.51312 - 15.2718i) q^{97} +(-0.304519 - 15.8948i) q^{98} +(0.457892 - 0.349036i) 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 $

$2$	−2.19559	+	1.36288i	−1.55252	+	0.963699i	−0.561872	+	0.827224i	$0.689919\pi$
$2$	−2.19559	+	1.36288i	−1.55252	+	0.963699i	−0.990644	+	0.136475i	$0.956423\pi$
$3$	−1.50039	−	0.0863199i	−0.866252	−	0.0498368i	−0.381377	−	0.924420i	$-0.624550\pi$
$3$	−1.50039	−	0.0863199i	−0.866252	−	0.0498368i	−0.484876	+	0.874583i	$0.661135\pi$
$4$	2.07574	−	4.19230i	1.03787	−	2.09615i
$5$	−1.48666	+	1.67028i	−0.664857	+	0.746971i
$5$	−1.48666	+	1.67028i	−0.664857	+	0.746971i
$6$	3.41189	−	1.85533i	1.39290	−	0.757434i
$7$	−0.800461	+	0.455356i	−0.302546	+	0.172108i	−0.638187	−	0.769881i	$-0.720315\pi$
$7$	−0.800461	+	0.455356i	−0.302546	+	0.172108i	0.335641	+	0.941990i	$0.391047\pi$
$8$	0.661841	+	6.88885i	0.233996	+	2.43558i
$9$	−0.736477	−	0.0850227i	−0.245492	−	0.0283409i
$10$	0.987722	−	5.69338i	0.312345	−	1.80041i
$11$	−0.559563	+	0.538525i	−0.168715	+	0.162371i	−0.773021	−	0.634381i	$-0.781255\pi$
$11$	−0.559563	+	0.538525i	−0.168715	+	0.162371i	0.604306	+	0.796752i	$0.293450\pi$
$12$	−3.47631	+	6.11092i	−1.00352	+	1.76407i
$13$	−3.85043	+	1.46677i	−1.06792	+	0.406808i	−0.826106	−	0.563515i	$-0.809449\pi$
$13$	−3.85043	+	1.46677i	−1.06792	+	0.406808i	−0.241811	+	0.970323i	$0.577741\pi$
$14$	1.13689	−	2.09070i	0.303846	−	0.558764i
$15$	2.37476	−	2.37775i	0.613160	−	0.613931i
$16$	−5.16989	−	6.78226i	−1.29247	−	1.69556i
$17$	−0.424452	−	0.817487i	−0.102945	−	0.198270i	0.830475	−	0.557055i	$-0.188069\pi$
$17$	−0.424452	−	0.817487i	−0.102945	−	0.198270i	−0.933420	+	0.358786i	$0.883191\pi$
$18$	1.73288	−	0.817052i	0.408443	−	0.192581i
$19$	−0.933294	−	4.81232i	−0.214112	−	1.10402i	−0.918866	−	0.394569i	$-0.870894\pi$
$19$	−0.933294	−	4.81232i	−0.214112	−	1.10402i	0.704754	−	0.709452i	$-0.251057\pi$
$20$	3.91638	+	9.69961i	0.875729	+	2.16890i
$21$	1.24031	−	0.614118i	0.270658	−	0.134011i
$22$	0.494627	−	1.94499i	0.105455	−	0.414674i
$23$	0.438268	+	0.206643i	0.0913851	+	0.0430881i	0.471621	−	0.881802i	$-0.343669\pi$
$23$	0.438268	+	0.206643i	0.0913851	+	0.0430881i	−0.380235	+	0.924890i	$0.624157\pi$
$24$	−0.398377	−	10.3931i	−0.0813184	−	2.12149i
$25$	−0.579657	−	4.96629i	−0.115931	−	0.993257i
$26$	6.45493	−	8.46807i	1.26592	−	1.66073i
$27$	5.53945	+	0.964602i	1.06607	+	0.185638i
$28$	0.247441	+	4.30097i	0.0467620	+	0.812807i
$29$	2.48887	+	6.17530i	0.462172	+	1.14672i	0.960138	+	0.279528i	$0.0901780\pi$
$29$	2.48887	+	6.17530i	0.462172	+	1.14672i	−0.497966	+	0.867197i	$0.665920\pi$
$30$	−1.97342	+	8.45705i	−0.360296	+	1.54404i
$31$	1.53623	−	1.26692i	0.275916	−	0.227546i	−0.488029	−	0.872827i	$-0.662284\pi$
$31$	1.53623	−	1.26692i	0.275916	−	0.227546i	0.763945	+	0.645281i	$0.223260\pi$
$32$	7.65988	+	2.91793i	1.35409	+	0.515821i
$33$	0.886050	−	0.759698i	0.154241	−	0.132246i
$34$	2.04606	+	1.21639i	0.350896	+	0.208609i
$35$	0.429445	−	2.01395i	0.0725895	−	0.340420i
$36$	−1.88518	+	2.91105i	−0.314196	+	0.485175i
$37$	4.24852	−	5.35748i	0.698452	−	0.880765i	−0.298840	−	0.954303i	$-0.596600\pi$
$37$	4.24852	−	5.35748i	0.698452	−	0.880765i	0.997292	+	0.0735383i	$0.0234291\pi$
$38$	8.60772	+	9.29390i	1.39636	+	1.50767i
$39$	5.90377	−	1.86836i	0.945359	−	0.299177i
$40$	−12.4902	−	9.13596i	−1.97488	−	1.44452i
$41$	3.56207	−	0.833557i	0.556302	−	0.130180i	0.0597925	−	0.998211i	$-0.480956\pi$
$41$	3.56207	−	0.833557i	0.556302	−	0.130180i	0.496510	+	0.868031i	$0.334615\pi$
$42$	−1.88625	+	3.03874i	−0.291055	+	0.468888i
$43$	0.148565	+	0.853167i	0.0226559	+	0.130107i	0.994353	−	0.106124i	$-0.0338440\pi$
$43$	0.148565	+	0.853167i	0.0226559	+	0.130107i	−0.971697	+	0.236231i	$0.924088\pi$
$44$	1.09615	+	3.46369i	0.165251	+	0.522171i
$45$	1.23691	−	1.10372i	0.184387	−	0.164533i
$46$	−1.24389	+	0.143600i	−0.183401	+	0.0211727i
$47$	0.922939	+	4.31498i	0.134624	+	0.629405i	0.993171	+	0.116669i	$0.0372217\pi$
$47$	0.922939	+	4.31498i	0.134624	+	0.629405i	−0.858546	+	0.512736i	$0.828632\pi$
$48$	7.17142	+	10.6223i	1.03511	+	1.53320i
$49$	−3.14374	+	5.28800i	−0.449106	+	0.755428i
$50$	8.04112	+	10.1139i	1.13719	+	1.43032i
$51$	0.566279	+	1.26319i	0.0792949	+	0.176882i
$52$	−1.84335	+	19.1868i	−0.255627	+	2.66073i
$53$	1.07627	−	5.03186i	0.147837	−	0.691179i	−0.840860	−	0.541253i	$-0.817950\pi$
$53$	1.07627	−	5.03186i	0.147837	−	0.691179i	0.988697	−	0.149926i	$-0.0479035\pi$
$54$	−13.4770	+	5.43171i	−1.83399	+	0.739163i
$55$	−0.0676046	−	1.73523i	−0.00911581	−	0.233979i
$56$	−3.66666	−	5.21288i	−0.489978	−	0.696601i
$57$	0.984909	+	7.30093i	0.130454	+	0.967032i
$58$	−13.8807	−	10.1664i	−1.82263	−	1.33491i
$59$	10.5146	−	0.403033i	1.36888	−	0.0524704i	0.656533	−	0.754297i	$-0.272022\pi$
$59$	10.5146	−	0.403033i	1.36888	−	0.0524704i	0.712348	+	0.701827i	$0.247632\pi$
$60$	−5.03884	−	14.8913i	−0.650511	−	1.92246i
$61$	9.22318	−	5.48323i	1.18091	−	0.702056i	0.219078	−	0.975707i	$-0.429695\pi$
$61$	9.22318	−	5.48323i	1.18091	−	0.702056i	0.961829	+	0.273652i	$0.0882316\pi$
$62$	−1.64628	+	4.87534i	−0.209078	+	0.619169i
$63$	0.628237	−	0.267302i	0.0791504	−	0.0336769i
$64$	−4.05070	+	0.785587i	−0.506337	+	0.0981983i
$65$	3.27438	−	8.61188i	0.406137	−	1.06817i
$66$	−0.910026	+	2.87556i	−0.112017	+	0.353957i
$67$	11.9572	+	1.61305i	1.46081	+	0.197066i	0.820762	−	0.571271i	$-0.193549\pi$
$67$	11.9572	+	1.61305i	1.46081	+	0.197066i	0.640046	+	0.768337i	$0.278915\pi$
$68$	−4.30820	+	0.0825383i	−0.522446	+	0.0100092i
$69$	−0.639736	−	0.347878i	−0.0770152	−	0.0418796i
$70$	1.80188	+	5.00710i	0.215366	+	0.598462i
$71$	−8.27918	+	2.27516i	−0.982557	+	0.270011i	−0.719289	−	0.694711i	$-0.755532\pi$
$71$	−8.27918	+	2.27516i	−0.982557	+	0.270011i	−0.263268	+	0.964723i	$0.584801\pi$
$72$	0.0982779	−	5.12976i	0.0115822	−	0.604548i
$73$	−8.15628	−	11.1362i	−0.954620	−	1.30339i	−0.952866	−	0.303393i	$-0.901881\pi$
$73$	−8.15628	−	11.1362i	−0.954620	−	1.30339i	−0.00175460	−	0.999998i	$-0.500559\pi$
$74$	−2.02641	+	17.5530i	−0.235566	+	2.04050i
$75$	0.441025	+	7.50142i	0.0509251	+	0.866189i
$76$	−22.1120	−	6.07647i	−2.53641	−	0.697019i
$77$	0.202687	−	0.685869i	0.0230984	−	0.0781620i
$78$	−10.4159	+	12.1483i	−1.17937	+	1.37552i
$79$	−4.39159	−	2.17441i	−0.494092	−	0.244641i	0.179481	−	0.983761i	$-0.442558\pi$
$79$	−4.39159	−	2.17441i	−0.494092	−	0.244641i	−0.673573	+	0.739121i	$0.735241\pi$
$80$	19.0141	+	1.44779i	2.12585	+	0.161868i
$81$	−6.06249	−	1.41868i	−0.673610	−	0.157631i
$82$	−6.68482	+	6.68482i	−0.738214	+	0.738214i
$83$	4.21782	−	8.07527i	0.462966	−	0.886376i
$83$	4.21782	−	8.07527i	0.462966	−	0.886376i
$84$		−	6.47451i		−	0.706427i
$85$	1.99645	+	0.506377i	0.216545	+	0.0549243i
$86$	−1.48895	−	1.67073i	−0.160557	−	0.180159i
$87$	−3.20123	−	9.48022i	−0.343208	−	1.01639i
$88$	−4.08016	−	3.49833i	−0.434947	−	0.372923i
$89$	−6.06388	−	11.1513i	−0.642770	−	1.18204i	−0.971371	−	0.237566i	$-0.923650\pi$
$89$	−6.06388	−	11.1513i	−0.642770	−	1.18204i	0.328601	−	0.944469i	$-0.393423\pi$
$90$	−1.21150	+	4.10907i	−0.127704	+	0.433134i
$91$	2.41421	−	2.92741i	0.253078	−	0.306875i
$92$	1.77604	−	1.40841i	0.185165	−	0.146837i
$93$	−2.41432	+	1.76828i	−0.250353	+	0.183362i
$94$	−7.90718	−	8.21608i	−0.815564	−	0.847424i
$95$	9.42540	+	5.59544i	0.967026	+	0.574080i
$96$	−11.2410	−	5.03924i	−1.14727	−	0.514315i
$97$	−4.51312	−	15.2718i	−0.458237	−	1.55062i	−0.793546	−	0.608511i	$-0.791767\pi$
$97$	−4.51312	−	15.2718i	−0.458237	−	1.55062i	0.335308	−	0.942108i	$-0.391160\pi$
$98$	−0.304519	−	15.8948i	−0.0307611	−	1.60562i
$99$	0.457892	−	0.349036i	0.0460199	−	0.0350794i
$100$	−22.0234	−	7.87862i	−2.20234	−	0.787862i
$101$	−8.07639	−	2.90069i	−0.803631	−	0.288629i	−0.0961543	−	0.995366i	$-0.530654\pi$
$101$	−8.07639	−	2.90069i	−0.803631	−	0.288629i	−0.707476	+	0.706737i	$0.750166\pi$
$102$	−2.96489	−	2.00168i	−0.293568	−	0.198196i
$103$	3.71194	+	8.72413i	0.365748	+	0.859614i	0.996497	+	0.0836266i	$0.0266503\pi$
$103$	3.71194	+	8.72413i	0.365748	+	0.859614i	−0.630749	+	0.775987i	$0.717252\pi$
$104$	−12.6527	−	25.5543i	−1.24070	−	2.50580i
$105$	−0.818181	+	2.98465i	−0.0798463	+	0.291272i
$106$	4.49475	+	12.5147i	0.436568	+	1.21554i
$107$	−8.01889	−	7.42685i	−0.775216	−	0.717980i	0.189325	−	0.981914i	$-0.439370\pi$
$107$	−8.01889	−	7.42685i	−0.775216	−	0.717980i	−0.964541	+	0.263934i	$0.914980\pi$
$108$	15.5424	−	21.2208i	1.49556	−	2.04197i
$109$	6.64373	+	5.06429i	0.636354	+	0.485071i	0.873772	−	0.486336i	$-0.161667\pi$
$109$	6.64373	+	5.06429i	0.636354	+	0.485071i	−0.237418	+	0.971408i	$0.576301\pi$
$110$	2.51334	+	3.71772i	0.239637	+	0.354471i
$111$	−6.83690	+	7.67160i	−0.648930	+	0.728156i
$112$	7.22664	+	3.07479i	0.682853	+	0.290540i
$113$	−13.0269	−	2.78635i	−1.22547	−	0.262118i	−0.449726	−	0.893167i	$-0.648478\pi$
$113$	−13.0269	−	2.78635i	−1.22547	−	0.262118i	−0.775743	+	0.631049i	$0.782625\pi$
$114$	−12.1127	−	14.6875i	−1.13446	−	1.37561i
$115$	−0.996709	+	0.424819i	−0.0929436	+	0.0396146i
$116$	31.0550	+	2.38423i	2.88338	+	0.221370i
$117$	2.96046	−	0.752867i	0.273695	−	0.0696026i
$118$	−22.5364	+	15.2150i	−2.07464	+	1.40065i
$119$	0.712005	+	0.461090i	0.0652694	+	0.0422680i
$120$	17.9517	+	14.7857i	1.63875	+	1.34974i
$121$	−0.398229	+	10.3893i	−0.0362026	+	0.944477i
$122$	−12.7774	+	24.6090i	−1.15681	+	2.22799i
$123$	−5.41646	+	0.943186i	−0.488386	+	0.0850442i
$124$	−2.12250	−	9.07016i	−0.190606	−	0.814524i
$125$	9.15683	+	6.41501i	0.819012	+	0.573776i
$126$	−1.01505	+	1.44309i	−0.0904278	+	0.128561i
$127$	6.84258	+	3.55277i	0.607180	+	0.315257i	0.736596	−	0.676333i	$-0.236432\pi$
$127$	6.84258	+	3.55277i	0.607180	+	0.315257i	−0.129415	+	0.991590i	$0.541310\pi$
$128$	−4.20455	+	3.89413i	−0.371634	+	0.344195i
$129$	−0.149260	−	1.29291i	−0.0131416	−	0.113834i
$130$	4.54772	+	23.3707i	0.398861	+	2.04975i
$131$	−3.71383	+	19.1495i	−0.324479	+	1.67310i	0.351505	+	0.936186i	$0.385670\pi$
$131$	−3.71383	+	19.1495i	−0.324479	+	1.67310i	−0.675984	+	0.736916i	$0.736281\pi$
$132$	−1.34567	−	5.29152i	−0.117126	−	0.460568i
$133$	2.93838	+	3.42709i	0.254790	+	0.297166i
$134$	−28.4515	+	12.7546i	−2.45784	+	1.10183i
$135$	−9.84646	+	7.81838i	−0.847448	+	0.672899i
$136$	5.35063	−	3.46503i	0.458813	−	0.297124i
$137$	4.93244	−	11.5926i	0.421407	−	0.990427i	−0.564848	−	0.825195i	$-0.691065\pi$
$137$	4.93244	−	11.5926i	0.421407	−	0.990427i	0.986255	−	0.165232i	$-0.0528372\pi$
$138$	1.87871	−	0.108085i	0.159927	−	0.00920082i
$139$	18.3912	−	12.9361i	1.55992	−	1.09722i	0.606703	−	0.794929i	$-0.292492\pi$
$139$	18.3912	−	12.9361i	1.55992	−	1.09722i	0.953215	−	0.302293i	$-0.0977520\pi$
$140$	−7.55168	−	5.98081i	−0.638234	−	0.505471i
$141$	−1.01230	−	6.55384i	−0.0852513	−	0.551933i
$142$	15.0769	−	16.2788i	1.26523	−	1.36609i
$143$	1.36466	−	2.89430i	0.114119	−	0.242034i
$144$	3.23086	+	5.43454i	0.269238	+	0.452878i
$145$	−14.0146	−	5.02350i	−1.16385	−	0.417179i
$146$	33.0851	+	13.3345i	2.73814	+	1.10357i
$147$	5.17331	−	7.66271i	0.426687	−	0.632010i
$148$	−13.6414	−	28.9318i	−1.12131	−	2.37818i
$149$	−14.0127	−	4.43458i	−1.14796	−	0.363295i	−0.333068	−	0.942903i	$-0.608084\pi$
$149$	−14.0127	−	4.43458i	−1.14796	−	0.363295i	−0.814896	+	0.579608i	$0.803206\pi$
$150$	−11.1918	−	15.8690i	−0.913808	−	1.29570i
$151$	6.21572	+	5.98203i	0.505828	+	0.486810i	0.902223	−	0.431269i	$-0.141934\pi$
$151$	6.21572	+	5.98203i	0.505828	+	0.486810i	−0.396395	+	0.918080i	$0.629739\pi$
$152$	32.5336	−	9.61431i	2.63883	−	0.779824i
$153$	0.243094	+	0.638149i	0.0196530	+	0.0515913i
$154$	0.489736	+	1.78212i	0.0394641	+	0.143608i
$155$	−0.167751	+	4.44943i	−0.0134741	+	0.357387i
$156$	4.42196	−	28.6286i	0.354040	−	2.29212i
$157$	5.78255	+	7.29193i	0.461498	+	0.581960i	0.958250	−	0.285933i	$-0.0923034\pi$
$157$	5.78255	+	7.29193i	0.461498	+	0.581960i	−0.496752	+	0.867892i	$0.665474\pi$
$158$	12.6056	−	1.21107i	1.00285	−	0.0963476i
$159$	−2.04918	+	7.45686i	−0.162511	+	0.591368i
$160$	−16.2614	+	8.45615i	−1.28558	+	0.668517i
$161$	−0.444912	+	0.0341579i	−0.0350640	+	0.00269202i
$162$	15.2442	−	5.14759i	1.19770	−	0.404433i
$163$	−1.05792	+	18.3885i	−0.0828626	+	1.44030i	0.650005	+	0.759930i	$0.274767\pi$
$163$	−1.05792	+	18.3885i	−0.0828626	+	1.44030i	−0.732868	+	0.680371i	$0.761819\pi$
$164$	3.89942	−	16.6635i	0.304493	−	1.30120i
$165$	−0.0483515	+	2.60937i	−0.00376416	+	0.203139i
$166$	1.74500	+	23.4783i	0.135438	+	1.82227i
$167$	−10.6189	−	10.6189i	−0.821718	−	0.821718i	0.164637	−	0.986354i	$-0.447355\pi$
$167$	−10.6189	−	10.6189i	−0.821718	−	0.821718i	−0.986354	+	0.164637i	$0.947355\pi$
$168$	5.05146	+	8.13788i	0.389728	+	0.627851i
$169$	2.96919	−	2.64613i	0.228399	−	0.203549i
$170$	−5.07351	+	1.60912i	−0.389120	+	0.123414i
$171$	0.278193	+	3.62351i	0.0212740	+	0.277097i
$172$	3.88511	+	1.14813i	0.296237	+	0.0875437i
$173$	−8.15096	−	14.3284i	−0.619706	−	1.08937i	−0.987222	−	0.159350i	$-0.949060\pi$
$173$	−8.15096	−	14.3284i	−0.619706	−	1.08937i	0.367516	−	0.930017i	$-0.380208\pi$
$174$	19.9490	+	16.4518i	1.51233	+	1.24721i
$175$	2.72542	+	3.71137i	0.206023	+	0.280553i
$176$	6.54529	+	1.01098i	0.493370	+	0.0762057i
$177$	−15.8108	−	0.302909i	−1.18841	−	0.0227681i
$178$	28.5116	+	16.2193i	2.13704	+	1.21569i
$179$	0.348700	−	0.777840i	0.0260630	−	0.0581385i	−0.899009	−	0.437930i	$-0.855712\pi$
$179$	0.348700	−	0.777840i	0.0260630	−	0.0581385i	0.925072	+	0.379792i	$0.124004\pi$
$180$	−2.05964	−	7.47652i	−0.153516	−	0.557267i
$181$	−10.4507	+	10.8589i	−0.776792	+	0.807138i	−0.985291	−	0.170885i	$-0.945337\pi$
$181$	−10.4507	+	10.8589i	−0.776792	+	0.807138i	0.208499	+	0.978023i	$0.433142\pi$
$182$	−1.31093	+	9.71765i	−0.0971726	+	0.720320i
$183$	−14.3117	+	7.43086i	−1.05795	+	0.549305i
$184$	−1.13347	+	3.15593i	−0.0835607	+	0.232658i
$185$	2.63237	+	15.0610i	0.193535	+	1.10731i
$186$	2.89091	−	7.17282i	0.211972	−	0.525937i
$187$	0.677745	+	0.228857i	0.0495616	+	0.0167357i
$188$	20.0055	+	5.08755i	1.45905	+	0.371047i
$189$	−4.87335	+	1.75030i	−0.354484	+	0.127315i
$190$	−28.3202	+	0.560367i	−2.05456	+	0.0406533i
$191$	18.3114	−	2.82838i	1.32497	−	0.204654i	0.549211	−	0.835684i	$-0.314928\pi$
$191$	18.3114	−	2.82838i	1.32497	−	0.204654i	0.775759	+	0.631030i	$0.217367\pi$
$192$	6.14545	−	0.829033i	0.443510	−	0.0598303i
$193$	0.639080	−	3.67006i	0.0460020	−	0.264177i	−0.953279	−	0.302091i	$-0.902315\pi$
$193$	0.639080	−	3.67006i	0.0460020	−	0.264177i	0.999281	+	0.0379142i	$0.0120714\pi$
$194$	30.7226	+	27.3798i	2.20575	+	1.96576i
$195$	−5.65624	+	12.6386i	−0.405052	+	0.905066i
$196$	15.6433	+	24.1560i	1.11738	+	1.72543i
$197$	4.76586	+	0.457876i	0.339553	+	0.0326223i	0.264009	−	0.964520i	$-0.414955\pi$
$197$	4.76586	+	0.457876i	0.339553	+	0.0326223i	0.0755441	+	0.997142i	$0.475931\pi$
$198$	−0.529650	+	1.39039i	−0.0376406	+	0.0988107i
$199$	0.928642	−	12.0957i	0.0658297	−	0.857442i	−0.867273	−	0.497833i	$-0.834129\pi$
$199$	0.928642	−	12.0957i	0.0658297	−	0.857442i	0.933103	−	0.359610i	$-0.117090\pi$
$200$	33.8284	−	7.28007i	2.39203	−	0.514779i
$201$	−17.8013	−	3.45236i	−1.25561	−	0.243511i
$202$	21.6857	−	4.63839i	1.52580	−	0.326356i
$203$	−4.80420	−	3.80976i	−0.337189	−	0.267393i
$204$	6.47112	+	0.248044i	0.453069	+	0.0173665i
$205$	−3.90334	+	7.18887i	−0.272621	+	0.502093i
$206$	−20.0398	−	14.0957i	−1.39624	−	0.982093i
$207$	−0.305205	−	0.189451i	−0.0212132	−	0.0131677i
$208$	29.8543	+	18.5316i	2.07002	+	1.28493i
$209$	3.11379	+	2.19019i	0.215385	+	0.151499i
$210$	−2.27132	−	7.66815i	−0.156736	−	0.529153i
$211$	−17.9693	−	0.688779i	−1.23706	−	0.0474175i	−0.588446	−	0.808537i	$-0.700260\pi$
$211$	−17.9693	−	0.688779i	−1.23706	−	0.0474175i	−0.648612	+	0.761119i	$0.724650\pi$
$212$	−18.8610	−	14.9569i	−1.29538	−	1.02724i
$213$	12.6184	−	2.69897i	0.864599	−	0.184931i
$214$	27.7281	+	5.37754i	1.89545	+	0.367601i
$215$	−1.64589	−	1.02023i	−0.112249	−	0.0695790i
$216$	−2.97876	+	38.7989i	−0.202679	+	2.63993i
$217$	−0.652794	+	1.71366i	−0.0443145	+	0.116331i
$218$	−21.4889	−	2.06453i	−1.45541	−	0.139828i
$219$	11.2764	+	17.4127i	0.761985	+	1.17664i
$220$	−7.41494	−	3.31847i	−0.499915	−	0.223731i
$221$	2.83338	+	2.52510i	0.190594	+	0.169857i
$222$	4.55559	−	26.1615i	0.305751	−	1.75585i
$223$	6.17548	−	0.833084i	0.413541	−	0.0557875i	0.0760219	−	0.997106i	$-0.475778\pi$
$223$	6.17548	−	0.833084i	0.413541	−	0.0557875i	0.337519	+	0.941319i	$0.390412\pi$
$224$	−7.46013	+	1.15229i	−0.498451	+	0.0769904i
$225$	0.00465728	+	3.70684i	0.000310486	+	0.247123i
$226$	32.3992	−	11.6364i	2.15516	−	0.774041i
$227$	6.24534	+	1.58824i	0.414518	+	0.105415i	0.448020	−	0.894024i	$-0.352129\pi$
$227$	6.24534	+	1.58824i	0.414518	+	0.105415i	−0.0335020	+	0.999439i	$0.510666\pi$
$228$	32.6521	+	11.0258i	2.16244	+	0.730201i
$229$	8.03631	−	19.9394i	0.531054	−	1.31763i	−0.387329	−	0.921942i	$-0.626602\pi$
$229$	8.03631	−	19.9394i	0.531054	−	1.31763i	0.918383	−	0.395693i	$-0.129495\pi$
$230$	1.60939	−	2.29112i	0.106120	−	0.151072i
$231$	−0.363315	+	1.01158i	−0.0239043	+	0.0665569i
$232$	−40.8935	+	21.2325i	−2.68479	+	1.39398i
$233$	−1.96138	+	14.5393i	−0.128494	+	0.952500i	0.804840	+	0.593491i	$0.202251\pi$
$233$	−1.96138	+	14.5393i	−0.128494	+	0.952500i	−0.933334	+	0.359008i	$0.883115\pi$
$234$	−5.47389	+	5.68773i	−0.357839	+	0.371818i
$235$	−8.57932	−	4.87337i	−0.559653	−	0.317903i
$236$	20.1359	−	44.9168i	1.31073	−	2.92384i
$237$	6.40141	+	3.64156i	0.415816	+	0.236544i
$238$	−2.19168	−	0.0419890i	−0.142065	−	0.00272174i
$239$	−4.10434	−	0.633955i	−0.265488	−	0.0410071i	0.0185220	−	0.999828i	$-0.494104\pi$
$239$	−4.10434	−	0.633955i	−0.265488	−	0.0410071i	−0.284010	+	0.958821i	$0.591665\pi$
$240$	−28.4037	−	3.81355i	−1.83345	−	0.246164i
$241$	−19.5566	−	16.1282i	−1.25975	−	1.03891i	−0.997260	−	0.0739726i	$-0.976432\pi$
$241$	−19.5566	−	16.1282i	−1.25975	−	1.03891i	−0.262489	−	0.964935i	$-0.584543\pi$
$242$	−13.2849	−	23.3533i	−0.853987	−	1.50120i
$243$	−7.20318	−	2.12868i	−0.462084	−	0.136555i
$244$	−3.84242	−	50.0481i	−0.245986	−	3.20400i
$245$	−4.15874	−	13.1124i	−0.265692	−	0.837721i
$246$	10.6069	−	9.45282i	0.676270	−	0.602690i
$247$	10.6521	+	17.1605i	0.677779	+	1.09190i
$248$	9.74439	+	9.74439i	0.618769	+	0.618769i
$249$	−7.02544	+	11.7520i	−0.445219	+	0.744753i
$250$	−28.8475	−	1.60510i	−1.82448	−	0.101515i
$251$	2.30570	−	9.85303i	0.145534	−	0.621918i	−0.849939	−	0.526880i	$-0.823362\pi$
$251$	2.30570	−	9.85303i	0.145534	−	0.621918i	0.995474	−	0.0950371i	$-0.0302970\pi$
$252$	0.183445	−	3.18861i	0.0115560	−	0.200863i
$253$	−0.356521	+	0.120388i	−0.0224143	+	0.00756874i
$254$	−19.8655	+	1.52516i	−1.24647	+	0.0956972i
$255$	−2.95175	−	0.932097i	−0.184846	−	0.0583702i
$256$	6.11098	−	22.2375i	0.381936	−	1.38985i
$257$	−12.3524	+	1.18675i	−0.770524	+	0.0740275i	−0.473443	−	0.880825i	$-0.656989\pi$
$257$	−12.3524	+	1.18675i	−0.770524	+	0.0740275i	−0.297081	+	0.954852i	$0.596013\pi$
$258$	2.08979	+	2.63528i	0.130105	+	0.164065i
$259$	−0.961208	+	6.22304i	−0.0597266	+	0.386681i
$260$	−29.3068	−	31.6032i	−1.81753	−	1.95995i
$261$	−1.30796	−	4.75958i	−0.0809604	−	0.294611i
$262$	−17.9444	−	47.1060i	−1.10861	−	2.91022i
$263$	11.6118	−	3.43151i	0.716015	−	0.211596i	0.0950929	−	0.995468i	$-0.469685\pi$
$263$	11.6118	−	3.43151i	0.716015	−	0.211596i	0.620922	+	0.783872i	$0.286758\pi$
$264$	5.81987	+	5.60107i	0.358188	+	0.344722i
$265$	6.80455	+	9.27836i	0.418000	+	0.569965i
$266$	−11.1222	−	3.51983i	−0.681944	−	0.215814i
$267$	8.13563	+	17.2548i	0.497893	+	1.05597i
$268$	31.5825	−	46.7800i	1.92921	−	2.85754i
$269$	−3.52166	−	1.41936i	−0.214720	−	0.0865398i	0.263945	−	0.964538i	$-0.414976\pi$
$269$	−3.52166	−	1.41936i	−0.214720	−	0.0865398i	−0.478664	+	0.877998i	$0.658879\pi$
$270$	10.9633	−	30.5855i	0.667204	−	1.86137i
$271$	−11.9265	−	20.0612i	−0.724483	−	1.21863i	−0.968537	−	0.248869i	$-0.919941\pi$
$271$	−11.9265	−	20.0612i	−0.724483	−	1.21863i	0.244054	−	0.969762i	$-0.421522\pi$
$272$	−3.35004	+	7.10506i	−0.203126	+	0.430807i
$273$	−3.87496	+	4.18387i	−0.234523	+	0.253219i
$274$	4.96973	+	32.1750i	0.300233	+	1.94376i
$275$	2.99882	+	2.46679i	0.180836	+	0.148753i
$276$	−2.78633	+	1.95986i	−0.167718	+	0.117970i
$277$	10.5019	−	0.604192i	0.631000	−	0.0363024i	0.261007	−	0.965337i	$-0.415945\pi$
$277$	10.5019	−	0.604192i	0.631000	−	0.0363024i	0.369993	+	0.929035i	$0.379360\pi$
$278$	−22.7492	+	53.4671i	−1.36441	+	3.20675i
$279$	−1.23912	+	0.802445i	−0.0741841	+	0.0480411i
$280$	14.1581	+	1.62547i	0.846106	+	0.0971402i
$281$	7.24858	−	3.24948i	0.432414	−	0.193848i	−0.181213	−	0.983444i	$-0.558002\pi$
$281$	7.24858	−	3.24948i	0.432414	−	0.193848i	0.613627	+	0.789596i	$0.289710\pi$
$282$	11.1547	+	13.0099i	0.664251	+	0.774728i
$283$	−4.68756	−	18.4326i	−0.278646	−	1.09571i	−0.938769	−	0.344548i	$-0.888032\pi$
$283$	−4.68756	−	18.4326i	−0.278646	−	1.09571i	0.660122	−	0.751158i	$-0.270505\pi$
$284$	−7.64728	+	39.4314i	−0.453782	+	2.33982i
$285$	−13.6588	−	9.20896i	−0.809078	−	0.545492i
$286$	0.948331	+	8.21456i	0.0560760	+	0.485737i
$287$	−2.47173	+	2.28924i	−0.145902	+	0.135130i
$288$	−5.39324	−	2.80025i	−0.317799	−	0.165006i
$289$	9.29229	−	13.2108i	0.546605	−	0.777108i
$290$	37.6167	−	8.07061i	2.20893	−	0.473922i
$291$	5.45319	+	23.3033i	0.319671	+	1.36606i
$292$	−63.6165	+	11.0777i	−3.72288	+	0.648276i
$293$	14.9392	−	28.7726i	0.872757	−	1.68092i	0.151264	−	0.988493i	$-0.451666\pi$
$293$	14.9392	−	28.7726i	0.872757	−	1.68092i	0.721492	−	0.692422i	$-0.243456\pi$
$294$	−0.915139	+	23.8747i	−0.0533720	+	1.39240i
$295$	−14.9585	+	18.1614i	−0.870915	+	1.05740i
$296$	39.7188	+	25.7216i	2.30861	+	1.49504i
$297$	−3.61913	+	2.44338i	−0.210003	+	0.141779i
$298$	36.8099	−	9.36103i	2.13234	−	0.542270i
$299$	−1.99062	−	0.152829i	−0.115120	−	0.00883830i
$300$	32.3637	+	13.7221i	1.86852	+	0.792245i
$301$	−0.507415	−	0.615277i	−0.0292469	−	0.0354640i
$302$	−21.7999	−	4.66282i	−1.25444	−	0.268315i
$303$	11.8674	+	5.04933i	0.681763	+	0.290076i
$304$	−27.8133	+	31.2090i	−1.59520	+	1.78996i
$305$	−4.55326	+	23.5570i	−0.260719	+	1.34887i
$306$	−1.40345	−	1.06981i	−0.0802300	−	0.0611567i
$307$	12.8007	−	17.4774i	0.730573	−	0.997488i	−0.268839	−	0.963185i	$-0.586640\pi$
$307$	12.8007	−	17.4774i	0.730573	−	0.997488i	0.999411	−	0.0343031i	$-0.0109212\pi$
$308$	−2.45464	−	2.27341i	−0.139866	−	0.129540i
$309$	−4.81631	−	13.4100i	−0.273990	−	0.762870i
$310$	−5.69571	−	9.99774i	−0.323494	−	0.567833i
$311$	14.1287	+	28.5353i	0.801167	+	1.61809i	0.786018	+	0.618204i	$0.212139\pi$
$311$	14.1287	+	28.5353i	0.801167	+	1.61809i	0.0151493	+	0.999885i	$0.495178\pi$
$312$	16.7782	+	39.4336i	0.949879	+	2.23249i
$313$	14.0120	+	9.45990i	0.792005	+	0.534705i	0.887545	−	0.460720i	$-0.152409\pi$
$313$	14.0120	+	9.45990i	0.792005	+	0.534705i	−0.0955398	+	0.995426i	$0.530458\pi$
$314$	−22.6341	−	8.12919i	−1.27732	−	0.458757i
$315$	−0.487508	+	1.44672i	−0.0274680	+	0.0815134i
$316$	−18.2316	+	13.8973i	−1.02561	+	0.781786i
$317$	0.171218	+	8.93697i	0.00961657	+	0.501950i	0.972612	+	0.232434i	$0.0746689\pi$
$317$	0.171218	+	8.93697i	0.00961657	+	0.501950i	−0.962996	+	0.269517i	$0.913136\pi$
$318$	−5.66362	−	19.1650i	−0.317600	−	1.07472i
$319$	−4.71823	−	2.11515i	−0.264170	−	0.118426i
$320$	4.70988	−	7.93370i	0.263290	−	0.443507i
$321$	11.3904	+	11.8354i	0.635751	+	0.660586i
$322$	0.930292	−	0.681357i	0.0518431	−	0.0379706i
$323$	−3.53787	+	2.80555i	−0.196852	+	0.156105i
$324$	−18.5317	+	22.4710i	−1.02954	+	1.24839i
$325$	9.51632	+	18.2721i	0.527870	+	1.01355i
$326$	−22.7385	−	41.8155i	−1.25937	−	2.31594i
$327$	−9.53105	−	8.17192i	−0.527068	−	0.451908i
$328$	8.09978	+	23.9869i	0.447236	+	1.32446i
$329$	−2.70363	−	3.03371i	−0.149056	−	0.167254i
$330$	−3.45008	−	5.79499i	−0.189921	−	0.319004i
$331$			12.3064i			0.676421i	0.941070	+	0.338211i	$0.109822\pi$
$331$			12.3064i			0.676421i	−0.941070	+	0.338211i	$0.890178\pi$
$332$	−25.0989	−	34.4445i	−1.37748	−	1.89039i
$333$	−3.58444	+	3.58444i	−0.196426	+	0.196426i
$334$	37.7871	+	8.84252i	2.06762	+	0.483841i
$335$	−20.4706	+	17.5738i	−1.11843	+	0.960161i
$336$	−10.5774	−	5.23719i	−0.577043	−	0.285712i
$337$	4.60817	−	5.37459i	0.251023	−	0.292773i	−0.619402	−	0.785074i	$-0.712625\pi$
$337$	4.60817	−	5.37459i	0.251023	−	0.292773i	0.870425	+	0.492302i	$0.163844\pi$
$338$	−2.91277	+	9.85645i	−0.158434	+	0.536120i
$339$	19.3050	+	5.30510i	1.04850	+	0.288134i
$340$	6.26699	−	7.31860i	0.339875	−	0.396907i
$341$	−0.177350	+	1.53622i	−0.00960402	+	0.0831912i
$342$	−5.54920	−	7.57660i	−0.300066	−	0.409696i
$343$	0.232000	−	12.1096i	0.0125268	−	0.653856i
$344$	−5.77902	+	1.58810i	−0.311584	+	0.0856247i
$345$	1.53213	−	0.551360i	0.0824869	−	0.0296842i
$346$	37.4240	+	20.3505i	2.01193	+	1.09405i
$347$	8.21483	−	0.157383i	0.440995	−	0.00844877i	0.201814	−	0.979424i	$-0.435316\pi$
$347$	8.21483	−	0.157383i	0.440995	−	0.00844877i	0.239181	+	0.970975i	$0.423121\pi$
$348$	−46.3889	−	6.25794i	−2.48670	−	0.335461i
$349$	−2.35325	+	7.43596i	−0.125967	+	0.398038i	−0.995376	−	0.0960548i	$-0.969378\pi$
$349$	−2.35325	+	7.43596i	−0.125967	+	0.398038i	0.869409	+	0.494092i	$0.164500\pi$
$350$	−11.0420	−	4.43422i	−0.590222	−	0.237019i
$351$	−22.7441	+	4.41096i	−1.21399	+	0.235439i
$352$	−5.85756	+	2.49227i	−0.312209	+	0.132839i
$353$	−0.248901	+	0.737102i	−0.0132477	+	0.0392320i	−0.953863	−	0.300243i	$-0.902932\pi$
$353$	−0.248901	+	0.737102i	−0.0132477	+	0.0392320i	0.940615	+	0.339475i	$0.110249\pi$
$354$	35.1268	−	20.8831i	1.86697	−	1.10992i
$355$	8.50821	−	17.2109i	0.451569	−	0.913461i
$356$	−59.3366	+	2.27442i	−3.14484	+	0.120544i
$357$	−1.02849	−	0.753276i	−0.0544332	−	0.0398676i
$358$	0.294498	+	2.18305i	0.0155647	+	0.115378i
$359$	−3.67179	−	5.22017i	−0.193789	−	0.275510i	0.709351	−	0.704856i	$-0.248988\pi$
$359$	−3.67179	−	5.22017i	−0.193789	−	0.275510i	−0.903140	+	0.429345i	$0.858744\pi$
$360$	8.42201	+	7.79038i	0.443879	+	0.410589i
$361$	−4.66480	+	1.88008i	−0.245516	+	0.0989518i
$362$	8.14600	−	38.0847i	0.428144	−	2.00169i
$363$	1.49430	−	15.5536i	0.0784304	−	0.816352i
$364$	−7.26128	−	16.1976i	−0.380595	−	0.848987i
$365$	30.7262	+	2.93251i	1.60828	+	0.153495i
$366$	21.2953	−	35.8202i	1.11312	−	1.87235i
$367$	14.4627	+	21.4222i	0.754948	+	1.11823i	0.989274	+	0.146071i	$0.0466629\pi$
$367$	14.4627	+	21.4222i	0.754948	+	1.11823i	−0.234326	+	0.972158i	$0.575288\pi$
$368$	−0.864287	−	4.04077i	−0.0450541	−	0.210640i
$369$	−2.69426	+	0.311039i	−0.140257	+	0.0161920i
$370$	−26.3059	−	29.4801i	−1.36758	−	1.53260i
$371$	1.42977	+	4.51789i	0.0742302	+	0.234557i
$372$	2.40165	+	13.7920i	0.124520	+	0.715083i
$373$	−10.2308	+	16.4818i	−0.529731	+	0.853394i	−0.999569	−	0.0293583i	$-0.990654\pi$
$373$	−10.2308	+	16.4818i	−0.529731	+	0.853394i	0.469838	+	0.882752i	$0.344312\pi$
$374$	−1.79995	+	0.421205i	−0.0930734	+	0.0217800i
$375$	−13.1851	−	10.4155i	−0.680876	−	0.537852i
$376$	−29.1144	+	9.21383i	−1.50146	+	0.475167i
$377$	−18.6409	−	20.1270i	−0.960058	−	1.03659i
$378$	8.31443	−	10.4847i	0.427648	−	0.539275i
$379$	8.21632	−	12.6875i	0.422044	−	0.651712i	−0.562510	−	0.826790i	$-0.690164\pi$
$379$	8.21632	−	12.6875i	0.422044	−	0.651712i	0.984554	+	0.175079i	$0.0560180\pi$
$380$	43.0224	−	27.8994i	2.20701	−	1.43121i
$381$	−9.95988	−	5.92120i	−0.510260	−	0.303352i
$382$	−36.3497	+	31.1662i	−1.85981	+	1.59460i
$383$	0.119452	+	0.0455035i	0.00610370	+	0.00232512i	0.359032	−	0.933325i	$-0.383107\pi$
$383$	0.119452	+	0.0455035i	0.00610370	+	0.00232512i	−0.352929	+	0.935650i	$0.614814\pi$
$384$	6.64463	−	5.47978i	0.339082	−	0.279639i
$385$	0.844263	+	1.35820i	0.0430276	+	0.0692203i
$386$	3.59869	+	8.92894i	0.183168	+	0.454471i
$387$	−0.0368759	−	0.640969i	−0.00187451	−	0.0325823i
$388$	−73.3921	−	12.7800i	−3.72592	−	0.648807i
$389$	7.27001	−	9.53736i	0.368604	−	0.483563i	−0.573347	−	0.819313i	$-0.694355\pi$
$389$	7.27001	−	9.53736i	0.368604	−	0.483563i	0.941951	+	0.335749i	$0.108989\pi$
$390$	−4.80601	−	35.4578i	−0.243362	−	1.79548i
$391$	−0.0170951	−	0.445988i	−0.000864537	−	0.0225546i
$392$	−38.5089	−	18.1570i	−1.94499	−	0.917065i
$393$	7.22520	−	28.4113i	0.364463	−	1.43316i
$394$	−11.0879	+	5.48997i	−0.558600	+	0.276581i
$395$	10.1607	−	4.10255i	0.511240	−	0.206422i
$396$	−0.512799	−	2.64413i	−0.0257691	−	0.132873i
$397$	−6.46451	+	3.04802i	−0.324444	+	0.152976i	−0.581780	−	0.813347i	$-0.697643\pi$
$397$	−6.46451	+	3.04802i	−0.324444	+	0.152976i	0.257335	+	0.966322i	$0.417156\pi$
$398$	14.4460	+	27.8228i	0.724114	+	1.39463i
$399$	−4.11290	−	5.39562i	−0.205903	−	0.270119i
$400$	−30.6859	+	29.6065i	−1.53429	+	1.48033i
$401$	13.0597	−	24.0163i	0.652169	−	1.19932i	−0.315938	−	0.948780i	$-0.602319\pi$
$401$	13.0597	−	24.0163i	0.652169	−	1.19932i	0.968107	−	0.250539i	$-0.0806077\pi$
$402$	43.7895	−	16.6810i	2.18402	−	0.831973i
$403$	−4.05688	+	7.13149i	−0.202087	+	0.355245i
$404$	−28.9251	+	27.8376i	−1.43908	+	1.38497i
$405$	11.3825	−	8.01694i	0.565599	−	0.398365i
$406$	15.7403	+	1.81714i	0.781178	+	0.0901831i
$407$	0.507827	+	5.28578i	0.0251721	+	0.262006i
$408$	−8.32715	+	4.73705i	−0.412255	+	0.234519i
$409$	0.495699	−	0.269553i	0.0245108	−	0.0133285i	−0.465418	−	0.885091i	$-0.654096\pi$
$409$	0.495699	−	0.269553i	0.0245108	−	0.0133285i	0.489929	+	0.871762i	$0.337023\pi$
$410$	−1.22742	−	21.1036i	−0.0606181	−	1.04223i
$411$	−8.40128	+	16.9678i	−0.414404	+	0.836958i
$412$	44.2792	+	2.54745i	2.18148	+	0.125504i
$413$	−8.23298	+	5.11049i	−0.405118	+	0.251471i
$414$	0.928303			0.0456236
$415$	7.21747	+	19.0501i	0.354292	+	0.935135i
$416$	−33.7737			−1.65589
$417$	−28.7106	+	17.8216i	−1.40596	+	0.872730i
$418$	−9.82156	−	0.565049i	−0.480388	−	0.0276375i
$419$	8.27222	−	16.7071i	0.404124	−	0.816196i	−0.595791	−	0.803140i	$-0.703161\pi$
$419$	8.27222	−	16.7071i	0.404124	−	0.816196i	0.999915	−	0.0130557i	$-0.00415589\pi$
$420$	10.8142	+	9.62542i	0.527680	+	0.469673i
$421$	12.0504	−	6.55281i	0.587302	−	0.319365i	−0.156591	−	0.987664i	$-0.550050\pi$
$421$	12.0504	−	6.55281i	0.587302	−	0.319365i	0.743893	+	0.668299i	$0.232977\pi$
$422$	40.3919	−	22.9776i	1.96625	−	1.11853i
$423$	−0.312852	−	3.25636i	−0.0152114	−	0.158330i
$424$	35.3761	+	4.08399i	1.71801	+	0.198336i
$425$	−3.81384	+	2.58181i	−0.184998	+	0.125236i
$426$	−24.0265	+	23.1232i	−1.16409	+	1.12032i
$427$	−4.88597	+	8.58894i	−0.236449	+	0.415648i
$428$	−47.7807	+	18.2014i	−2.30957	+	0.879798i
$429$	−2.29737	+	4.22479i	−0.110918	+	0.203975i
$430$	5.00415	−	0.00314361i	0.241321	−	0.000151598i
$431$	−2.15932	−	2.83276i	−0.104011	−	0.136449i	0.740356	−	0.672215i	$-0.234657\pi$
$431$	−2.15932	−	2.83276i	−0.104011	−	0.136449i	−0.844366	+	0.535766i	$0.820023\pi$
$432$	−22.0962	−	42.5569i	−1.06310	−	2.04752i
$433$	18.0516	−	8.51132i	0.867503	−	0.409028i	0.0595151	−	0.998227i	$-0.481045\pi$
$433$	18.0516	−	8.51132i	0.867503	−	0.409028i	0.807988	+	0.589199i	$0.200557\pi$
$434$	−0.902233	−	4.65216i	−0.0433086	−	0.223311i
$435$	20.5938	+	8.74696i	0.987395	+	0.419385i
$436$	35.0217	−	17.3403i	1.67723	−	0.830452i
$437$	0.585401	−	2.30194i	0.0280035	−	0.110117i
$438$	−48.4896	−	22.8629i	−2.31692	−	1.09243i
$439$	0.838431	+	21.8735i	0.0400161	+	1.04397i	0.872103	+	0.489322i	$0.162756\pi$
$439$	0.838431	+	21.8735i	0.0400161	+	1.04397i	−0.832087	+	0.554645i	$0.812854\pi$
$440$	11.9090	−	1.61417i	0.567740	−	0.0769524i
$441$	2.76490	−	3.62720i	0.131662	−	0.172724i
$442$	−9.66235	−	1.68254i	−0.459591	−	0.0800300i
$443$	1.30820	+	22.7389i	0.0621545	+	1.08036i	0.870666	+	0.491875i	$0.163688\pi$
$443$	1.30820	+	22.7389i	0.0621545	+	1.08036i	−0.808511	+	0.588481i	$0.799726\pi$
$444$	17.9700	+	44.5866i	0.852819	+	2.11599i
$445$	27.6407	+	6.44987i	1.31030	+	0.305753i
$446$	−12.4234	+	10.2455i	−0.588267	+	0.485140i
$447$	20.6417	+	7.86319i	0.976321	+	0.371916i
$448$	2.88470	−	2.47334i	0.136289	−	0.116854i
$449$	−18.1730	−	10.8040i	−0.857639	−	0.509871i	0.0140666	−	0.999901i	$-0.495522\pi$
$449$	−18.1730	−	10.8040i	−0.857639	−	0.509871i	−0.871705	+	0.490030i	$0.836986\pi$
$450$	−5.06219	−	8.13235i	−0.238634	−	0.383363i
$451$	−1.54431	+	2.38469i	−0.0727188	+	0.112291i
$452$	−38.7217	+	48.8290i	−1.82132	+	2.29672i
$453$	−8.80965	−	9.51193i	−0.413914	−	0.446910i
$454$	−15.8768	+	5.02451i	−0.745134	+	0.235812i
$455$	1.30046	+	8.38448i	0.0609663	+	0.393070i
$456$	−49.6432	+	11.6170i	−2.32475	+	0.544014i
$457$	−9.22453	+	14.8607i	−0.431505	+	0.695153i	−0.991027	−	0.133662i	$-0.957326\pi$
$457$	−9.22453	+	14.8607i	−0.431505	+	0.695153i	0.559522	+	0.828816i	$0.310985\pi$
$458$	9.53053	+	54.7313i	0.445333	+	2.55742i
$459$	−1.56268	−	4.93786i	−0.0729396	−	0.230479i
$460$	−0.287938	+	5.06032i	−0.0134252	+	0.235939i
$461$	5.82855	−	0.672878i	0.271463	−	0.0313391i	0.0221235	−	0.999755i	$-0.492957\pi$
$461$	5.82855	−	0.672878i	0.271463	−	0.0313391i	0.249339	+	0.968416i	$0.419787\pi$
$462$	−0.580964	−	2.71616i	−0.0270289	−	0.126367i
$463$	−12.8229	−	18.9933i	−0.595930	−	0.882692i	0.403549	−	0.914958i	$-0.367776\pi$
$463$	−12.8229	−	18.9933i	−0.595930	−	0.882692i	−0.999479	+	0.0322659i	$0.989728\pi$
$464$	29.0153	−	48.8058i	1.34700	−	2.26575i
$465$	0.635767	−	6.66141i	0.0294830	−	0.308916i
$466$	−15.5089	−	34.5954i	−0.718434	−	1.60260i
$467$	−0.152442	+	1.58671i	−0.00705416	+	0.0734241i	−0.998266	−	0.0588568i	$-0.981254\pi$
$467$	−0.152442	+	1.58671i	−0.00705416	+	0.0734241i	0.991212	+	0.132281i	$0.0422301\pi$
$468$	2.98890	−	13.9739i	0.138162	−	0.645944i
$469$	−10.3058	+	4.15361i	−0.475878	+	0.191796i
$470$	25.4785	−	0.992641i	1.17523	−	0.0457871i
$471$	−8.04666	−	11.4399i	−0.370770	−	0.527124i
$472$	9.73541	+	72.1666i	0.448109	+	3.32174i
$473$	−0.542583	−	0.397395i	−0.0249480	−	0.0182722i
$474$	−19.0179	+	0.728971i	−0.873519	+	0.0334827i
$475$	−23.3583	+	7.42450i	−1.07175	+	0.340659i
$476$	3.41096	−	2.02784i	0.156341	−	0.0929457i
$477$	−1.22047	+	3.61434i	−0.0558816	+	0.165489i
$478$	9.87545	−	4.20181i	0.451693	−	0.192186i
$479$	−26.8784	+	5.21277i	−1.22811	+	0.238177i	−0.762602	−	0.646868i	$-0.776079\pi$
$479$	−26.8784	+	5.21277i	−1.22811	+	0.238177i	−0.465505	+	0.885045i	$0.654127\pi$
$480$	25.1285	−	11.2839i	1.14695	−	0.515036i
$481$	−8.50042	+	26.8602i	−0.387586	+	1.22472i
$482$	64.9189	+	8.75768i	2.95698	+	0.398902i
$483$	0.670492	−	0.0128456i	0.0305084	−	0.000584493i
$484$	42.7282	+	23.2349i	1.94219	+	1.05613i
$485$	32.2177	+	15.1659i	1.46293	+	0.688649i
$486$	18.7163	−	5.14334i	0.848990	−	0.233307i
$487$	0.607310	−	31.6994i	0.0275199	−	1.43644i	−0.681793	−	0.731545i	$-0.738800\pi$
$487$	0.607310	−	31.6994i	0.0275199	−	1.43644i	0.709313	−	0.704893i	$-0.249005\pi$
$488$	43.8774	+	59.9081i	1.98624	+	2.71191i
$489$	3.17459	−	27.4987i	0.143560	−	1.24353i
$490$	27.0015	+	23.1216i	1.21980	+	1.04453i
$491$	−11.2226	−	3.08403i	−0.506470	−	0.139180i	0.00244531	−	0.999997i	$-0.499222\pi$
$491$	−11.2226	−	3.08403i	−0.506470	−	0.139180i	−0.508915	+	0.860817i	$0.669953\pi$
$492$	−7.28905	+	24.6653i	−0.328616	+	1.11200i
$493$	3.99182	−	4.65574i	0.179783	−	0.209684i
$494$	−46.7754	−	23.1600i	−2.10452	−	1.04202i
$495$	−0.0977448	+	1.28371i	−0.00439330	+	0.0576983i
$496$	−16.5348	−	3.86928i	−0.742433	−	0.173736i
$497$	5.59115	−	5.59115i	0.250797	−	0.250797i
$498$	−0.591542	−	35.3774i	−0.0265076	−	1.58530i
$499$			10.5825i			0.473736i	0.971542	+	0.236868i	$0.0761208\pi$
$499$			10.5825i			0.473736i	−0.971542	+	0.236868i	$0.923879\pi$
$500$	45.9009	−	25.0723i	2.05275	−	1.12127i
$501$	15.0159	+	16.8492i	0.670863	+	0.752767i
$502$	8.36609	+	24.7756i	0.373397	+	1.10579i
$503$	14.2597	+	12.2263i	0.635809	+	0.545142i	0.908989	−	0.416821i	$-0.136856\pi$
$503$	14.2597	+	12.2263i	0.635809	+	0.545142i	−0.273179	+	0.961963i	$0.588075\pi$
$504$	2.25720	+	4.15092i	0.100544	+	0.184897i
$505$	16.8518	−	9.17746i	0.749897	−	0.408392i
$506$	0.618699	−	0.750217i	0.0275045	−	0.0333512i
$507$	−4.68336	+	3.71394i	−0.207996	+	0.164942i
$508$	29.0977	−	21.3115i	1.29100	−	0.945545i
$509$	4.30301	+	4.47111i	0.190728	+	0.198178i	0.809039	−	0.587755i	$-0.199988\pi$
$509$	4.30301	+	4.47111i	0.190728	+	0.198178i	−0.618312	+	0.785933i	$0.712183\pi$
$510$	7.75116	−	1.97636i	0.343227	−	0.0875148i
$511$	11.5997	+	5.20006i	0.513141	+	0.230037i
$512$	13.6415	+	46.1613i	0.602876	+	2.04006i
$513$	−0.527964	−	27.5578i	−0.0233102	−	1.21671i
$514$	25.5035	−	19.4405i	1.12491	−	0.857482i
$515$	−20.0901	−	6.76988i	−0.885277	−	0.298316i
$516$	−5.73009	−	2.05800i	−0.252253	−	0.0905985i
$517$	−2.84017	−	1.91748i	−0.124910	−	0.0843306i
$518$	−6.37082	−	14.9733i	−0.279918	−	0.657887i
$519$	10.9928	+	22.2018i	0.482531	+	0.974552i
$520$	61.4931	+	16.8571i	2.69665	+	0.739231i
$521$	−8.17130	−	22.7513i	−0.357991	−	0.996754i	−0.977347	−	0.211644i	$-0.932118\pi$
$521$	−8.17130	−	22.7513i	−0.357991	−	0.996754i	0.619356	−	0.785110i	$-0.287394\pi$
$522$	9.35845	+	8.66750i	0.409608	+	0.379366i
$523$	12.1880	−	16.6410i	0.532946	−	0.727658i	−0.453589	−	0.891211i	$-0.649856\pi$
$523$	12.1880	−	16.6410i	0.532946	−	0.727658i	0.986535	+	0.163553i	$0.0522955\pi$
$524$	72.5717	+	55.3190i	3.17031	+	2.41662i
$525$	−3.76884	−	5.80377i	−0.164486	−	0.253297i
$526$	−20.8180	+	23.3596i	−0.907710	+	1.01853i
$527$	−1.68775	−	0.718104i	−0.0735196	−	0.0312811i
$528$	−9.73325	−	2.08186i	−0.423585	−	0.0906014i
$529$	−14.4842	−	17.5631i	−0.629748	−	0.763614i
$530$	−27.5852	−	11.0977i	−1.19823	−	0.482054i
$531$	−7.77801	−	0.597153i	−0.337537	−	0.0259142i
$532$	20.4667	−	5.20484i	0.887344	−	0.225658i
$533$	−12.4929	+	8.43429i	−0.541126	+	0.365330i
$534$	−41.3786	−	26.7965i	−1.79063	−	1.15960i
$535$	24.3263	−	2.35255i	1.05172	−	0.101710i
$536$	−3.19830	+	83.4392i	−0.138145	+	3.60402i
$537$	−0.590330	+	1.13697i	−0.0254746	+	0.0490637i
$538$	9.66654	−	1.68326i	0.416754	−	0.0725707i
$539$	−1.08860	−	4.65195i	−0.0468893	−	0.200374i
$540$	12.3383	+	57.5082i	0.530957	+	2.47476i
$541$	5.49480	−	7.81195i	0.236240	−	0.335862i	−0.682385	−	0.730993i	$-0.739057\pi$
$541$	5.49480	−	7.81195i	0.236240	−	0.335862i	0.918625	+	0.395131i	$0.129301\pi$
$542$	53.5266	+	27.7918i	2.29916	+	1.19376i
$543$	16.6175	−	15.3906i	0.713123	−	0.660472i
$544$	−0.865881	−	7.50037i	−0.0371243	−	0.321576i
$545$	−18.3358	+	3.56797i	−0.785418	+	0.152835i
$546$	2.80574	−	14.4671i	0.120074	−	0.619137i
$547$	5.92388	+	23.2942i	0.253287	+	0.995986i	0.958063	+	0.286557i	$0.0925107\pi$
$547$	5.92388	+	23.2942i	0.253287	+	0.995986i	−0.704776	+	0.709429i	$0.748953\pi$
$548$	−38.3614	−	44.7416i	−1.63872	−	1.91127i
$549$	−7.25886	+	3.25409i	−0.309801	+	0.138881i
$550$	−9.94611	−	1.32903i	−0.424104	−	0.0566699i
$551$	27.3947	−	17.7406i	1.16705	−	0.755775i
$552$	1.97307	−	4.63729i	0.0839796	−	0.197376i
$553$	4.50542	−	0.259204i	0.191590	−	0.0110225i
$554$	−22.2345	+	15.6394i	−0.944653	+	0.664454i
$555$	−2.64952	−	22.8246i	−0.112466	−	0.968851i
$556$	−16.0566	−	103.953i	−0.680949	−	4.40860i
$557$	−19.1865	+	20.7160i	−0.812959	+	0.877766i	−0.994405	−	0.105635i	$-0.966312\pi$
$557$	−19.1865	+	20.7160i	−0.812959	+	0.877766i	0.181446	+	0.983401i	$0.441922\pi$
$558$	1.62696	−	3.45061i	0.0688748	−	0.146076i
$559$	−1.82344	−	3.06715i	−0.0771231	−	0.129727i
$560$	−15.8793	+	7.49931i	−0.671024	+	0.316904i
$561$	−0.997129	−	0.401879i	−0.0420988	−	0.0169673i
$562$	−11.4863	+	17.0134i	−0.484518	+	0.717669i
$563$	1.38775	+	2.94326i	0.0584865	+	0.124043i	0.931615	−	0.363447i	$-0.118400\pi$
$563$	1.38775	+	2.94326i	0.0584865	+	0.124043i	−0.873128	+	0.487490i	$0.837912\pi$
$564$	−29.5769	−	9.36019i	−1.24541	−	0.394135i
$565$	24.0206	−	17.6162i	1.01056	−	0.741119i
$566$	35.4134	+	34.0819i	1.48853	+	1.43257i
$567$	5.49879	−	1.62500i	0.230927	−	0.0682434i
$568$	−21.1527	−	55.5282i	−0.887549	−	2.32991i
$569$	4.03822	+	14.6949i	0.169291	+	0.616040i	0.998379	+	0.0569219i	$0.0181286\pi$
$569$	4.03822	+	14.6949i	0.169291	+	0.616040i	−0.829088	+	0.559118i	$0.811140\pi$
$570$	42.5398	+	1.60383i	1.78180	+	0.0671768i
$571$	4.94705	−	32.0282i	0.207028	−	1.34034i	−0.622828	−	0.782359i	$-0.714016\pi$
$571$	4.94705	−	32.0282i	0.207028	−	1.34034i	0.829856	−	0.557978i	$-0.188423\pi$
$572$	−9.30109	−	11.7289i	−0.388898	−	0.490410i
$573$	−27.7185	+	2.66304i	−1.15796	+	0.111250i
$574$	2.30696	−	8.39490i	0.0962906	−	0.350396i
$575$	0.772205	−	2.29635i	0.0322032	−	0.0957642i
$576$	3.05004	−	0.234165i	0.127085	−	0.00975689i
$577$	25.6954	−	8.67670i	1.06971	−	0.361216i	0.270785	−	0.962640i	$-0.412717\pi$
$577$	25.6954	−	8.67670i	1.06971	−	0.361216i	0.798930	+	0.601424i	$0.205400\pi$
$578$	−2.39733	+	41.6698i	−0.0997156	+	1.73324i
$579$	−1.27567	+	5.45137i	−0.0530151	+	0.226551i
$580$	−50.1506	+	48.3259i	−2.08239	+	2.00662i
$581$	0.300928	+	8.38455i	0.0124846	+	0.347850i
$582$	−43.7325	−	43.7325i	−1.81277	−	1.81277i
$583$	2.10754	+	3.39524i	0.0872854	+	0.140616i
$584$	71.3174	−	63.5578i	2.95113	−	2.63004i
$585$	−3.14371	+	6.06405i	−0.129977	+	0.250718i
$586$	6.41322	+	83.5332i	0.264928	+	3.45072i
$587$	33.9683	+	10.0383i	1.40202	+	0.414325i	0.894405	−	0.447257i	$-0.147599\pi$
$587$	33.9683	+	10.0383i	1.40202	+	0.414325i	0.507618	+	0.861582i	$0.330526\pi$
$588$	−21.3859	−	37.5939i	−0.881941	−	1.55034i
$589$	−7.53059	−	6.21043i	−0.310293	−	0.255896i
$590$	8.09086	−	60.2616i	0.333095	−	2.48093i
$591$	−7.11114	−	1.09838i	−0.292513	−	0.0451814i
$592$	−58.3002	−	1.11694i	−2.39612	−	0.0459059i
$593$	−4.65090	−	2.64575i	−0.190990	−	0.108648i	0.395972	−	0.918263i	$-0.370408\pi$
$593$	−4.65090	−	2.64575i	−0.190990	−	0.108648i	−0.586962	+	0.809615i	$0.699676\pi$
$594$	4.61611	−	10.2971i	0.189401	−	0.422494i
$595$	−1.82866	+	0.503760i	−0.0749677	+	0.0206522i
$596$	−47.6778	+	49.5403i	−1.95296	+	2.02925i
$597$	−2.43743	+	18.0682i	−0.0997573	+	0.739481i
$598$	4.57886	−	2.37741i	0.187244	−	0.0972197i
$599$	11.1975	−	31.1771i	0.457515	−	1.27386i	−0.464109	−	0.885778i	$-0.653626\pi$
$599$	11.1975	−	31.1771i	0.457515	−	1.27386i	0.921625	−	0.388082i	$-0.126862\pi$
$600$	−51.3843	+	8.00290i	−2.09775	+	0.326717i
$601$	−10.7526	+	26.6790i	−0.438607	+	1.08826i	0.531818	+	0.846859i	$0.321509\pi$
$601$	−10.7526	+	26.6790i	−0.438607	+	1.08826i	−0.970426	+	0.241400i	$0.922393\pi$
$602$	1.95262	+	0.659351i	0.0795829	+	0.0268731i
$603$	−8.66908	−	2.20461i	−0.353032	−	0.0897787i
$604$	37.9807	−	13.6410i	1.54541	−	0.555045i
$605$	−16.7609	−	16.1105i	−0.681428	−	0.654984i
$606$	−32.9375	+	5.08751i	−1.33799	+	0.206666i
$607$	−3.27901	+	0.442344i	−0.133091	+	0.0179542i	−0.199935	−	0.979809i	$-0.564073\pi$
$607$	−3.27901	+	0.442344i	−0.133091	+	0.0179542i	0.0668437	+	0.997763i	$0.478707\pi$
$608$	6.89307	−	39.5850i	0.279551	−	1.60538i
$609$	6.87934	+	6.13084i	0.278765	+	0.248434i
$610$	−22.1082	−	57.9270i	−0.895134	−	2.34540i
$611$	−9.88279	−	15.2608i	−0.399815	−	0.617385i
$612$	3.17991	+	0.305508i	0.128540	+	0.0123494i
$613$	−12.2207	+	32.0806i	−0.493588	+	1.29572i	0.426670	+	0.904408i	$0.359687\pi$
$613$	−12.2207	+	32.0806i	−0.493588	+	1.29572i	−0.920257	+	0.391314i	$0.872021\pi$
$614$	−4.28547	+	55.8189i	−0.172948	+	2.25267i
$615$	6.47708	−	10.4492i	0.261181	−	0.421353i
$616$	4.85899	+	0.942347i	0.195774	+	0.0379682i
$617$	−15.4730	+	3.30955i	−0.622920	+	0.133237i	−0.509728	−	0.860336i	$-0.670254\pi$
$617$	−15.4730	+	3.30955i	−0.622920	+	0.133237i	−0.113192	+	0.993573i	$0.536108\pi$
$618$	28.8508	+	22.8789i	1.16055	+	0.920324i
$619$	9.60743	+	0.368261i	0.386155	+	0.0148017i	0.230659	−	0.973035i	$-0.425912\pi$
$619$	9.60743	+	0.368261i	0.386155	+	0.0148017i	0.155497	+	0.987836i	$0.450302\pi$
$620$	18.3051	+	9.93912i	0.735152	+	0.399165i
$621$	2.22843	+	1.56744i	0.0894239	+	0.0628994i
$622$	−69.9110	−	43.3961i	−2.80318	−	1.74003i
$623$	9.93171	+	6.16495i	0.397906	+	0.246993i
$624$	−43.1935	−	30.3816i	−1.72912	−	1.21624i
$625$	−24.3280	+	5.75749i	−0.973120	+	0.230299i
$626$	−43.6573	−	1.67342i	−1.74490	−	0.0668834i
$627$	−4.48285	−	3.55493i	−0.179028	−	0.141970i
$628$	42.5730	−	9.10602i	1.69885	−	0.363370i
$629$	−6.18296	−	1.19912i	−0.246531	−	0.0478119i
$630$	−0.901330	−	3.84081i	−0.0359099	−	0.153022i
$631$	1.75876	−	22.9081i	0.0700150	−	0.911956i	−0.851685	−	0.524053i	$-0.824419\pi$
$631$	1.75876	−	22.9081i	0.0700150	−	0.911956i	0.921700	−	0.387902i	$-0.126800\pi$
$632$	12.0727	−	31.6921i	0.480225	−	1.26064i
$633$	26.9016	+	2.58455i	1.06924	+	0.102726i
$634$	−12.5559	−	19.3886i	−0.498659	−	0.770019i
$635$	−16.1067	+	6.14723i	−0.639176	+	0.243945i
$636$	27.0078	+	24.0693i	1.07093	+	0.954410i
$637$	4.34849	−	24.9722i	0.172293	−	0.989434i
$638$	13.2420	−	1.78637i	0.524255	−	0.0707230i
$639$	6.29086	−	0.971684i	0.248863	−	0.0384392i
$640$	−0.253510	−	12.8120i	−0.0100208	−	0.506440i
$641$	−28.9762	+	10.4070i	−1.14449	+	0.411052i	−0.840601	−	0.541654i	$-0.817798\pi$
$641$	−28.9762	+	10.4070i	−1.14449	+	0.411052i	−0.303891	+	0.952707i	$0.598286\pi$
$642$	−41.1388	−	10.4619i	−1.62362	−	0.412899i
$643$	−3.27429	−	1.10565i	−0.129126	−	0.0436025i	0.254621	−	0.967041i	$-0.418049\pi$
$643$	−3.27429	−	1.10565i	−0.129126	−	0.0436025i	−0.383747	+	0.923438i	$0.625366\pi$
$644$	−0.780322	+	1.93611i	−0.0307490	+	0.0762934i
$645$	2.38142	+	1.67282i	0.0937683	+	0.0658671i
$646$	3.94409	−	10.9815i	0.155178	−	0.432062i
$647$	−20.0285	+	10.3991i	−0.787400	+	0.408830i	−0.806683	−	0.590984i	$-0.798740\pi$
$647$	−20.0285	+	10.3991i	−0.787400	+	0.408830i	0.0192834	+	0.999814i	$0.493862\pi$
$648$	5.76065	−	42.7025i	0.226300	−	1.67751i
$649$	−5.66652	+	5.88788i	−0.222430	+	0.231120i
$650$	−45.7965	−	27.1485i	−1.79629	−	1.06485i
$651$	1.12737	−	2.51481i	0.0441851	−	0.0985631i
$652$	74.8942	+	42.6049i	2.93309	+	1.66854i
$653$	40.3615	+	0.773262i	1.57947	+	0.0302601i	0.801481	−	0.598021i	$-0.204046\pi$
$653$	40.3615	+	0.773262i	1.57947	+	0.0302601i	0.777987	+	0.628281i	$0.216241\pi$
$654$	32.0636	+	4.95252i	1.25379	+	0.193659i
$655$	−26.4638	−	34.6721i	−1.03403	−	1.35475i
$656$	−24.0689	−	19.8495i	−0.939734	−	0.774993i
$657$	5.06009	+	8.89501i	0.197413	+	0.347028i
$658$	10.0706	+	2.97606i	0.392594	+	0.116019i
$659$	−1.71267	−	22.3078i	−0.0667161	−	0.868987i	−0.930774	−	0.365595i	$-0.880866\pi$
$659$	−1.71267	−	22.3078i	−0.0667161	−	0.868987i	0.864058	−	0.503392i	$-0.167915\pi$
$660$	10.8389	+	5.61907i	0.421903	+	0.218722i
$661$	23.2949	−	20.7604i	0.906068	−	0.807485i	−0.0757859	−	0.997124i	$-0.524147\pi$
$661$	23.2949	−	20.7604i	0.906068	−	0.807485i	0.981854	+	0.189640i	$0.0607319\pi$
$662$	−16.7721	−	27.0198i	−0.651866	−	1.05015i
$663$	−4.03322	−	4.03322i	−0.156637	−	0.156637i
$664$	58.4209	+	23.7114i	2.26717	+	0.920180i
$665$	−10.0926	−	0.187015i	−0.391373	−	0.00725214i
$666$	2.98481	−	12.7551i	0.115659	−	0.494251i
$667$	−0.185294	+	3.22074i	−0.00717462	+	0.124708i
$668$	−66.5599	+	22.4756i	−2.57528	+	0.869607i
$669$	−9.33757	+	0.716887i	−0.361011	+	0.0277165i
$670$	20.9941	−	66.4838i	0.811075	−	2.56849i
$671$	−2.20809	+	8.03512i	−0.0852424	+	0.310193i
$672$	11.2926	−	1.08493i	0.435621	−	0.0418520i
$673$	15.5255	+	19.5780i	0.598463	+	0.754676i	0.985921	−	0.167211i	$-0.0534761\pi$
$673$	15.5255	+	19.5780i	0.598463	+	0.754676i	−0.387458	+	0.921887i	$0.626647\pi$
$674$	−2.79275	+	18.0808i	−0.107573	+	0.696445i
$675$	1.57951	−	28.0696i	0.0607953	−	1.08040i
$676$	−4.93011	−	17.9404i	−0.189620	−	0.690016i
$677$	−11.5823	−	30.4049i	−0.445146	−	1.16856i	−0.951885	−	0.306457i	$-0.900857\pi$
$677$	−11.5823	−	30.4049i	−0.445146	−	1.16856i	0.506739	−	0.862099i	$-0.330851\pi$
$678$	−49.6160	+	14.6625i	−1.90549	+	0.563109i
$679$	10.5667	+	10.1694i	0.405512	+	0.390267i
$680$	−2.16702	+	14.0884i	−0.0831015	+	0.540265i
$681$	−9.23337	−	2.92208i	−0.353823	−	0.111974i
$682$	−1.70430	−	3.61462i	−0.0652609	−	0.138411i
$683$	6.46396	−	9.57442i	0.247337	−	0.366355i	−0.684635	−	0.728886i	$-0.740038\pi$
$683$	6.46396	−	9.57442i	0.247337	−	0.366355i	0.931972	+	0.362531i	$0.118087\pi$
$684$	15.7683	+	6.35520i	0.602916	+	0.242997i
$685$	12.0301	+	25.4729i	0.459645	+	0.973270i
$686$	15.9945	+	26.9039i	0.610672	+	1.02719i
$687$	−13.7788	+	29.2233i	−0.525694	+	1.11494i
$688$	5.01833	−	5.41838i	0.191322	−	0.206574i
$689$	3.23646	+	20.9534i	0.123299	+	0.798263i
$690$	−2.61248	+	3.29866i	−0.0994555	+	0.125578i
$691$	−10.6122	+	7.46444i	−0.403706	+	0.283961i	−0.759377	−	0.650651i	$-0.774496\pi$
$691$	−10.6122	+	7.46444i	−0.403706	+	0.283961i	0.355671	+	0.934611i	$0.384252\pi$
$692$	−76.9882	+	4.42925i	−2.92665	+	0.168375i
$693$	−0.207589	+	0.487894i	−0.00788565	+	0.0185335i
$694$	−17.8219	+	11.5414i	−0.676510	+	0.438104i
$695$	−5.73468	+	49.9499i	−0.217529	+	1.89471i
$696$	63.1891	−	28.3272i	2.39518	−	1.07374i
$697$	−2.19335	−	2.55814i	−0.0830791	−	0.0968966i
$698$	−4.96752	−	19.5335i	−0.188023	−	0.739354i
$699$	4.19786	−	21.6453i	0.158778	−	0.818702i
$700$	21.2164	−	3.72196i	0.801906	−	0.140677i
$701$	−0.997846	−	8.64347i	−0.0376881	−	0.326459i	−0.998744	−	0.0501049i	$-0.984044\pi$
$701$	−0.997846	−	8.64347i	−0.0376881	−	0.326459i	0.961056	−	0.276354i	$-0.0891263\pi$
$702$	43.9251	−	40.6820i	1.65785	−	1.53544i
$703$	−29.7470	−	15.4451i	−1.12193	−	0.582523i
$704$	1.84356	−	2.62099i	0.0694819	−	0.0987822i
$705$	12.4517	+	8.05253i	0.468958	+	0.303276i
$706$	−0.458095	−	1.95759i	−0.0172406	−	0.0736751i
$707$	7.78568	−	1.35574i	0.292811	−	0.0509880i
$708$	−34.0890	+	65.6548i	−1.28114	+	2.46746i
$709$	−1.30859	+	34.1394i	−0.0491452	+	1.28213i	0.741957	+	0.670447i	$0.233898\pi$
$709$	−1.30859	+	34.1394i	−0.0491452	+	1.28213i	−0.791103	+	0.611683i	$0.790493\pi$
$710$	4.77582	+	49.3837i	0.179233	+	1.85334i
$711$	3.04943	+	1.97479i	0.114363	+	0.0740604i
$712$	72.8063	−	49.1536i	2.72853	−	1.84211i
$713$	0.935083	−	0.237799i	0.0350191	−	0.00890563i
$714$	3.28475	+	0.252185i	0.122929	+	0.00943780i
$715$	2.80549	+	6.58222i	0.104919	+	0.246161i
$716$	−2.53713	−	3.07645i	−0.0948169	−	0.114972i
$717$	6.10341	+	1.30547i	0.227936	+	0.0487536i
$718$	15.1762	+	6.45716i	0.566370	+	0.240979i
$719$	−2.38840	+	2.67999i	−0.0890724	+	0.0999469i	−0.789415	−	0.613860i	$-0.789616\pi$
$719$	−2.38840	+	2.67999i	−0.0890724	+	0.0999469i	0.700343	+	0.713807i	$0.253031\pi$
$720$	−13.8804	−	2.68290i	−0.517292	−	0.0999857i
$721$	−6.94385	−	5.29306i	−0.258602	−	0.197124i
$722$	7.67966	−	10.4854i	0.285808	−	0.390228i
$723$	27.9504	+	25.8867i	1.03949	+	0.962738i
$724$	23.8310	+	66.3527i	0.885673	+	2.46598i
$725$	29.2256	−	15.9400i	1.08541	−	0.591997i
$726$	17.9167	+	36.1858i	0.664953	+	1.34298i
$727$	−10.0575	−	23.6379i	−0.373011	−	0.876683i	−0.995562	−	0.0941039i	$-0.970001\pi$
$727$	−10.0575	−	23.6379i	−0.373011	−	0.876683i	0.622551	−	0.782579i	$-0.286096\pi$
$728$	21.7643	+	14.6937i	0.806638	+	0.544584i
$729$	28.2032	+	10.1294i	1.04456	+	0.375162i
$730$	−71.4587	+	35.4374i	−2.64480	+	1.31160i
$731$	0.634394	−	0.483578i	0.0234639	−	0.0178858i
$732$	1.44499	+	75.4235i	0.0534085	+	2.78773i
$733$	10.6311	+	35.9742i	0.392667	+	1.32874i	0.887924	+	0.459991i	$0.152147\pi$
$733$	10.6311	+	35.9742i	0.392667	+	1.32874i	−0.495256	+	0.868747i	$0.664926\pi$
$734$	−60.9500	−	27.3234i	−2.24971	−	1.00853i
$735$	5.10788	+	20.0327i	0.188407	+	0.738919i
$736$	2.75411	+	2.86170i	0.101518	+	0.105484i
$737$	−7.55949	+	5.53666i	−0.278457	+	0.203946i
$738$	5.49158	−	4.35485i	0.202148	−	0.160304i
$739$	1.17274	−	1.42203i	0.0431399	−	0.0523102i	−0.749476	−	0.662032i	$-0.769694\pi$
$739$	1.17274	−	1.42203i	0.0431399	−	0.0523102i	0.792616	+	0.609722i	$0.208719\pi$
$740$	68.6043	+	20.2270i	2.52194	+	0.743560i
$741$	−14.5011	−	26.6671i	−0.532711	−	0.979639i
$742$	−9.29652	−	7.97083i	−0.341286	−	0.292618i
$743$	−14.5552	−	43.1041i	−0.533978	−	1.58134i	−0.788994	−	0.614401i	$-0.789398\pi$
$743$	−14.5552	−	43.1041i	−0.533978	−	1.58134i	0.255016	−	0.966937i	$-0.417919\pi$
$744$	−13.7793	−	15.4616i	−0.505173	−	0.566848i
$745$	28.2391	−	16.8123i	1.03460	−	0.615956i
$746$		−	50.1305i		−	1.83541i
$747$	−3.79291	+	5.58864i	−0.138775	+	0.204478i
$748$	2.36626	−	2.36626i	0.0865191	−	0.0865191i
$749$	9.80067	+	2.29344i	0.358109	+	0.0838006i
$750$	43.1441	+	4.89840i	1.57540	+	0.178864i
$751$	1.84779	+	0.914901i	0.0674269	+	0.0333852i	0.477119	−	0.878839i	$-0.341681\pi$
$751$	1.84779	+	0.914901i	0.0674269	+	0.0333852i	−0.409692	+	0.912224i	$0.634364\pi$
$752$	24.4938	−	28.5676i	0.893198	−	1.04175i
$753$	−4.30996	+	14.5844i	−0.157064	+	0.531485i
$754$	68.3584	+	18.7852i	2.48947	+	0.684117i
$755$	−19.2323	+	1.48871i	−0.699936	+	0.0541796i
$756$	−2.77804	+	24.0637i	−0.101036	+	0.875189i
$757$	−4.31801	−	5.89560i	−0.156941	−	0.214279i	0.721143	−	0.692786i	$-0.243617\pi$
$757$	−4.31801	−	5.89560i	−0.156941	−	0.214279i	−0.878084	+	0.478507i	$0.841178\pi$
$758$	−0.748218	+	39.0543i	−0.0271765	+	1.41852i
$759$	0.545314	−	0.149855i	0.0197936	−	0.00543938i
$760$	−32.3080	+	68.6335i	−1.17194	+	2.48960i
$761$	29.8227	+	16.2171i	1.08107	+	0.587868i	0.917125	−	0.398601i	$-0.130504\pi$
$761$	29.8227	+	16.2171i	1.08107	+	0.587868i	0.163947	+	0.986469i	$0.447577\pi$
$762$	29.9377	−	0.573558i	1.08453	−	0.0207778i
$763$	−7.62410	−	1.02851i	−0.276011	−	0.0372344i
$764$	26.1524	−	82.6381i	0.946161	−	2.98974i
$765$	−1.42729	−	0.542678i	−0.0516036	−	0.0196206i
$766$	−0.324282	+	0.0628909i	−0.0117168	+	0.00227234i
$767$	−39.8944	+	16.9743i	−1.44050	+	0.612906i
$768$	−11.0884	+	32.8376i	−0.400119	+	1.18492i
$769$	−47.3419	+	28.1450i	−1.70719	+	1.01493i	−0.793452	+	0.608632i	$0.791718\pi$
$769$	−47.3419	+	28.1450i	−1.70719	+	1.01493i	−0.913739	+	0.406302i	$0.866818\pi$
$770$	−3.70471	−	1.83142i	−0.133509	−	0.0659999i
$771$	18.6360	−	0.714332i	0.671157	−	0.0257260i
$772$	−14.0594	−	10.2973i	−0.506011	−	0.370608i
$773$	−3.50044	−	25.9481i	−0.125902	−	0.933288i	−0.937234	−	0.348701i	$-0.886623\pi$
$773$	−3.50044	−	25.9481i	−0.125902	−	0.933288i	0.811332	−	0.584586i	$-0.198743\pi$
$774$	0.954526	+	1.35705i	0.0343097	+	0.0487781i
$775$	−7.18239	−	6.89500i	−0.257999	−	0.247676i
$776$	102.218	−	41.1977i	3.66943	−	1.47891i
$777$	1.97936	−	9.25404i	0.0710092	−	0.331987i
$778$	−2.96372	+	30.8483i	−0.106255	+	1.10596i
$779$	−7.33580	−	16.3639i	−0.262832	−	0.586297i
$780$	41.2437	+	49.9470i	1.47676	+	1.78839i
$781$	3.40749	−	5.73164i	0.121930	−	0.205094i
$782$	0.645361	+	0.955909i	0.0230781	+	0.0341832i
$783$	7.83026	+	36.6085i	0.279831	+	1.30828i
$784$	52.1174	−	6.01669i	1.86133	−	0.214882i
$785$	−20.7763	−	1.18220i	−0.741537	−	0.0421944i
$786$	22.8575	+	72.2265i	0.815299	+	2.57623i
$787$	0.781410	+	4.48743i	0.0278543	+	0.159960i	0.995850	−	0.0910056i	$-0.0290081\pi$
$787$	0.781410	+	4.48743i	0.0278543	+	0.159960i	−0.967996	+	0.250965i	$0.919252\pi$
$788$	11.8122	−	19.0295i	0.420794	−	0.677897i
$789$	−17.7185	+	4.14629i	−0.630795	+	0.147612i
$790$	−16.7174	+	22.8553i	−0.594780	+	0.813154i
$791$	11.6963	−	3.70152i	0.415873	−	0.131611i
$792$	2.70751	+	2.92335i	0.0962072	+	0.103877i
$793$	−27.4706	+	34.6410i	−0.975508	+	1.23014i
$794$	10.0393	−	15.5025i	0.356283	−	0.550164i
$795$	−9.40859	−	14.5086i	−0.333688	−	0.514566i
$796$	−48.7812	−	29.0007i	−1.72900	−	1.02790i
$797$	23.6780	−	20.3015i	0.838718	−	0.719116i	−0.123221	−	0.992379i	$-0.539323\pi$
$797$	23.6780	−	20.3015i	0.838718	−	0.719116i	0.961939	+	0.273263i	$0.0881030\pi$
$798$	16.3838	+	6.24119i	0.579981	+	0.220936i
$799$	3.13570	−	2.58599i	0.110933	−	0.0914858i
$800$	10.0512	−	39.7325i	0.355362	−	1.40476i
$801$	3.51780	+	8.72825i	0.124295	+	0.308397i
$802$	4.05762	+	70.5287i	0.143280	+	2.49046i
$803$	10.5611	+	1.83903i	0.372692	+	0.0648980i
$804$	−51.4242	+	67.4622i	−1.81359	+	2.37921i
$805$	0.604382	−	0.793909i	0.0213017	−	0.0279816i
$806$	−0.812110	−	21.1868i	−0.0286054	−	0.746275i
$807$	5.16136	+	2.43359i	0.181689	+	0.0856663i
$808$	14.6371	−	57.5569i	0.514933	−	2.02484i
$809$	−24.2454	+	12.0047i	−0.852423	+	0.422062i	−0.816536	−	0.577294i	$-0.804109\pi$
$809$	−24.2454	+	12.0047i	−0.852423	+	0.422062i	−0.0358871	+	0.999356i	$0.511426\pi$
$810$	−14.0651	+	33.1148i	−0.494198	+	1.16354i
$811$	−10.1179	−	52.1708i	−0.355288	−	1.83196i	−0.530814	−	0.847489i	$-0.678114\pi$
$811$	−10.1179	−	52.1708i	−0.355288	−	1.83196i	0.175525	−	0.984475i	$-0.443838\pi$
$812$	−25.9440	+	12.2326i	−0.910454	+	0.429280i
$813$	16.1627	+	31.1292i	0.566852	+	1.09175i
$814$	−8.31885	−	10.9133i	−0.291575	−	0.382511i
$815$	−29.1412	−	29.1046i	−1.02077	−	1.01949i
$816$	5.63968	−	10.3712i	0.197428	−	0.363065i
$817$	3.96705	−	1.51120i	0.138790	−	0.0528700i
$818$	−0.720985	+	1.26740i	−0.0252087	+	0.0443138i
$819$	−2.02691	+	1.95070i	−0.0708259	+	0.0681631i
$820$	22.0356	+	31.2862i	0.769517	+	1.09256i
$821$	15.3066	+	1.76708i	0.534205	+	0.0616714i	0.377563	−	0.925984i	$-0.376762\pi$
$821$	15.3066	+	1.76708i	0.534205	+	0.0616714i	0.156642	+	0.987655i	$0.449933\pi$
$822$	−4.67921	−	48.7041i	−0.163206	−	1.69875i
$823$	24.3770	−	13.8673i	0.849729	−	0.483383i	−0.00650072	−	0.999979i	$-0.502069\pi$
$823$	24.3770	−	13.8673i	0.849729	−	0.483383i	0.856229	+	0.516596i	$0.172801\pi$
$824$	−57.6425	+	31.3450i	−2.00807	+	1.09196i
$825$	−4.28648	−	3.96001i	−0.149236	−	0.137870i
$826$	11.1113	−	22.4411i	0.386611	−	0.780824i
$827$	1.47691	+	0.0849688i	0.0513572	+	0.00295466i	0.0830961	−	0.996542i	$-0.473519\pi$
$827$	1.47691	+	0.0849688i	0.0513572	+	0.00295466i	−0.0317389	+	0.999496i	$0.510105\pi$
$828$	−1.42776	+	0.886259i	−0.0496181	+	0.0307996i
$829$	−14.5649			−0.505860			−0.252930	−	0.967485i	$-0.581394\pi$
$829$	−14.5649			−0.505860			−0.252930	+	0.967485i	$0.581394\pi$
$830$	−41.8096	−	31.9898i	−1.45123	−	1.11038i
$831$	−15.8092			−0.548414
$832$	14.4446	−	8.96628i	0.500778	−	0.310850i
$833$	5.65724	+	0.325469i	0.196012	+	0.0112768i
$834$	38.7480	−	78.2580i	1.34173	−	2.70985i
$835$	33.5234	−	1.94978i	1.16012	−	0.0674749i
$836$	15.6454	−	8.50768i	0.541106	−	0.294244i
$837$	9.73197	−	5.53620i	0.336386	−	0.191359i
$838$	4.60733	+	47.9559i	0.159158	+	1.65661i
$839$	40.2540	+	4.64713i	1.38972	+	0.160437i	0.776820	−	0.629723i	$-0.216831\pi$
$839$	40.2540	+	4.64713i	1.38972	+	0.160437i	0.612902	+	0.790159i	$0.290002\pi$
$840$	−21.1023	−	3.66096i	−0.728100	−	0.126315i
$841$	−11.0447	+	10.6295i	−0.380853	+	0.366535i
$842$	−17.5271	+	30.8105i	−0.604024	+	1.06180i
$843$	−11.1562	+	4.24981i	−0.384240	+	0.146371i
$844$	−40.1872	+	73.9030i	−1.38330	+	2.54385i
$845$	0.00558677	+	8.89328i	0.000192191	+	0.305938i
$846$	5.12491	+	6.72324i	0.176198	+	0.231150i
$847$	−4.41204	−	8.49752i	−0.151600	−	0.291978i
$848$	−39.6916	+	18.7146i	−1.36301	+	0.642662i
$849$	5.44208	+	28.0608i	0.186772	+	0.963045i
$850$	4.85493	−	10.8664i	0.166523	−	0.372714i
$851$	2.96908	−	1.47008i	0.101779	−	0.0503938i
$852$	14.8776	−	58.5025i	0.509699	−	2.00426i
$853$	−37.1626	−	17.5222i	−1.27242	−	0.599949i	−0.333072	−	0.942902i	$-0.608085\pi$
$853$	−37.1626	−	17.5222i	−1.27242	−	0.599949i	−0.939353	+	0.342953i	$0.888573\pi$
$854$	−0.978079	−	25.5168i	−0.0334692	−	0.873165i
$855$	−6.46585	−	4.92229i	−0.221128	−	0.168339i
$856$	45.8552	−	60.1564i	1.56730	−	2.05610i
$857$	−50.5292	−	8.79881i	−1.72605	−	0.300562i	−0.780284	−	0.625425i	$-0.784926\pi$
$857$	−50.5292	−	8.79881i	−1.72605	−	0.300562i	−0.945761	+	0.324863i	$0.894682\pi$
$858$	−0.713790	−	12.4069i	−0.0243684	−	0.423566i
$859$	6.93419	+	17.2049i	0.236591	+	0.587023i	0.998132	−	0.0610945i	$-0.0194591\pi$
$859$	6.93419	+	17.2049i	0.236591	+	0.587023i	−0.761541	+	0.648117i	$0.775557\pi$
$860$	−7.69355	+	4.78234i	−0.262348	+	0.163077i
$861$	3.90618	−	3.22140i	0.133122	−	0.109785i
$862$	8.60167	+	3.27669i	0.292974	+	0.111604i
$863$	−36.6466	+	31.4207i	−1.24746	+	1.06957i	−0.252682	+	0.967549i	$0.581313\pi$
$863$	−36.6466	+	31.4207i	−1.24746	+	1.06957i	−0.994782	+	0.102025i	$0.967468\pi$
$864$	39.6169	+	23.5524i	1.34779	+	0.801270i
$865$	36.0501	+	7.68715i	1.22574	+	0.261371i
$866$	−28.0339	+	43.2894i	−0.952632	+	1.47103i
$867$	−15.0824	+	19.0193i	−0.512227	+	0.645930i
$868$	5.82913	+	6.29381i	0.197854	+	0.213626i
$869$	3.62834	−	1.14826i	0.123083	−	0.0389520i
$870$	−57.1365	+	8.86202i	−1.93711	+	0.300451i
$871$	−48.4064	+	11.3275i	−1.64019	+	0.383819i
$872$	−30.4901	+	49.1194i	−1.03252	+	1.66339i
$873$	2.02536	+	11.6311i	0.0685479	+	0.393652i
$874$	1.85196	+	5.85195i	0.0626435	+	0.197945i
$875$	−10.2508	−	0.965344i	−0.346540	−	0.0326346i
$876$	96.4061	−	11.1296i	3.25726	−	0.376035i
$877$	0.126262	+	0.590306i	0.00426355	+	0.0199332i	0.979962	−	0.199183i	$-0.0638289\pi$
$877$	0.126262	+	0.590306i	0.00426355	+	0.0199332i	−0.975699	+	0.219116i	$0.929683\pi$
$878$	−31.6518	−	46.8826i	−1.06820	−	1.58221i
$879$	−24.8983	+	41.8807i	−0.839799	+	1.41260i
$880$	−11.4193	+	9.42947i	−0.384944	+	0.317867i
$881$	−11.5649	−	25.7978i	−0.389633	−	0.869148i	−0.997193	−	0.0748747i	$-0.976144\pi$
$881$	−11.5649	−	25.7978i	−0.389633	−	0.869148i	0.607560	−	0.794274i	$-0.292148\pi$
$882$	−1.12715	+	11.7321i	−0.0379530	+	0.395039i
$883$	−5.17925	+	24.2143i	−0.174296	+	0.814877i	0.801810	+	0.597579i	$0.203871\pi$
$883$	−5.17925	+	24.2143i	−0.174296	+	0.814877i	−0.976105	+	0.217298i	$0.930276\pi$
$884$	16.4674	−	6.63694i	0.553857	−	0.223224i
$885$	24.0113	−	25.9581i	0.807130	−	0.872571i
$886$	−33.8625	−	48.1423i	−1.13763	−	1.61737i
$887$	5.14137	+	38.1119i	0.172630	+	1.27967i	0.843108	+	0.537744i	$0.180723\pi$
$887$	5.14137	+	38.1119i	0.172630	+	1.27967i	−0.670478	+	0.741929i	$0.733911\pi$
$888$	−57.3735	−	42.0211i	−1.92533	−	1.41013i
$889$	−7.09499	+	0.271957i	−0.237958	+	0.00912114i
$890$	−69.4781	+	23.5096i	−2.32891	+	0.788045i
$891$	4.15633	−	2.47096i	0.139242	−	0.0827804i
$892$	9.32616	−	27.6188i	0.312263	−	0.924744i
$893$	19.9037	−	8.46862i	0.666052	−	0.283392i
$894$	−56.0373	+	10.8678i	−1.87417	+	0.363474i
$895$	0.780809	+	1.73881i	0.0260996	+	0.0581221i
$896$	1.59237	−	5.03166i	0.0531972	−	0.168096i
$897$	2.97351	+	0.401133i	0.0992828	+	0.0133934i
$898$	54.6250	−	1.04653i	1.82286	−	0.0349231i
$899$	11.6471	+	6.33350i	0.388453	+	0.211234i
$900$	15.5499	+	7.67491i	0.518329	+	0.255830i
$901$	−4.57031	+	1.25594i	−0.152259	+	0.0418415i
$902$	0.140632	−	7.34051i	0.00468255	−	0.244412i
$903$	0.708211	+	0.966957i	0.0235678	+	0.0321783i
$904$	10.5730	−	91.5846i	0.351653	−	3.04606i
$905$	−2.60079	−	33.5991i	−0.0864531	−	1.11687i
$906$	32.3060	+	8.87783i	1.07329	+	0.294946i
$907$	2.40113	−	8.12514i	0.0797283	−	0.269791i	−0.909602	−	0.415481i	$-0.863613\pi$
$907$	2.40113	−	8.12514i	0.0797283	−	0.269791i	0.989330	+	0.145690i	$0.0465402\pi$
$908$	19.6221	−	22.8856i	0.651181	−	0.759484i
$909$	5.70145	+	2.82297i	0.189105	+	0.0936320i
$910$	−14.2823	−	16.6365i	−0.473453	−	0.551495i
$911$	3.18998	+	0.746483i	0.105689	+	0.0247321i	0.280362	−	0.959894i	$-0.409545\pi$
$911$	3.18998	+	0.746483i	0.105689	+	0.0247321i	−0.174673	+	0.984626i	$0.555887\pi$
$912$	44.4249	−	44.4249i	1.47106	−	1.47106i
$913$	1.98860	+	6.79002i	0.0658132	+	0.224717i
$914$		−	45.1998i		−	1.49508i
$915$	8.86511	−	34.9517i	0.293072	−	1.15547i
$916$	−66.9108	−	75.0797i	−2.21079	−	2.48070i
$917$	−5.74708	−	17.0196i	−0.189785	−	0.562036i
$918$	10.1607	+	8.71176i	0.335353	+	0.287531i
$919$	−17.5830	−	32.3347i	−0.580011	−	1.06662i	−0.988119	−	0.153689i	$-0.950885\pi$
$919$	−17.5830	−	32.3347i	−0.580011	−	1.06662i	0.408109	−	0.912933i	$-0.366188\pi$
$920$	−3.58618	−	6.58502i	−0.118233	−	0.217102i
$921$	−20.7147	+	25.1180i	−0.682572	+	0.827667i
$922$	−11.8801	+	9.42096i	−0.391249	+	0.310263i
$923$	28.5412	−	20.9040i	0.939446	−	0.688062i
$924$	3.48669	+	3.62289i	0.114704	+	0.119184i
$925$	−29.0695	−	17.9938i	−0.955799	−	0.591634i
$926$	54.0393	+	24.2254i	1.77584	+	0.796096i
$927$	−1.99201	−	6.74072i	−0.0654262	−	0.221394i
$928$	1.04537	+	54.5644i	0.0343158	+	1.79116i
$929$	14.7618	−	11.2524i	0.484318	−	0.369180i	−0.335280	−	0.942119i	$-0.608831\pi$
$929$	14.7618	−	11.2524i	0.484318	−	0.369180i	0.819598	+	0.572939i	$0.194197\pi$
$930$	7.68280	+	15.4922i	0.251929	+	0.508009i
$931$	28.3816	+	10.1934i	0.930168	+	0.334076i
$932$	56.8817	+	38.4024i	1.86322	+	1.25791i
$933$	−18.7355	−	44.0338i	−0.613373	−	1.44160i
$934$	−1.82779	−	3.69152i	−0.0598070	−	0.120790i
$935$	−1.38983	+	0.791788i	−0.0454524	+	0.0258942i
$936$	7.14575	+	19.8959i	0.233566	+	0.650318i
$937$	−28.3856	−	26.2898i	−0.927316	−	0.858851i	0.0629530	−	0.998016i	$-0.479948\pi$
$937$	−28.3856	−	26.2898i	−0.927316	−	0.858851i	−0.990269	+	0.139166i	$0.955558\pi$
$938$	16.9664	−	23.1652i	0.553974	−	0.756369i
$939$	−20.2069	−	15.4031i	−0.659429	−	0.502661i
$940$	−38.2391	+	25.8513i	−1.24722	+	0.843175i
$941$	−0.908828	+	1.01978i	−0.0296269	+	0.0332440i	−0.761182	−	0.648539i	$-0.775380\pi$
$941$	−0.908828	+	1.01978i	−0.0296269	+	0.0332440i	0.731555	+	0.681783i	$0.238795\pi$
$942$	33.2583	+	14.1508i	1.08362	+	0.461057i
$943$	1.73339	+	0.370758i	0.0564470	+	0.0120735i
$944$	−57.0926	−	69.2289i	−1.85821	−	2.25321i
$945$	4.32155	−	10.7420i	0.140580	−	0.349436i
$946$	1.73289	+	0.133042i	0.0563411	+	0.00432556i
$947$	8.10738	−	2.06177i	0.263454	−	0.0669985i	−0.112448	−	0.993658i	$-0.535869\pi$
$947$	8.10738	−	2.06177i	0.263454	−	0.0669985i	0.375903	+	0.926659i	$0.377333\pi$
$948$	28.5542	−	19.2777i	0.927396	−	0.626111i
$949$	47.7393	+	30.9157i	1.54968	+	1.00357i
$950$	41.1667	−	48.1357i	1.33562	−	1.56173i
$951$	0.514544	−	13.4238i	0.0166852	−	0.435295i
$952$	−2.70514	+	5.21006i	−0.0876742	+	0.168859i
$953$	−5.69730	+	0.992089i	−0.184554	+	0.0321369i	−0.263074	−	0.964776i	$-0.584736\pi$
$953$	−5.69730	+	0.992089i	−0.184554	+	0.0321369i	0.0785207	+	0.996912i	$0.474980\pi$
$954$	−2.24624	−	9.59896i	−0.0727248	−	0.310778i
$955$	−22.4988	+	34.7901i	−0.728044	+	1.12578i
$956$	−11.1773	+	15.8907i	−0.361499	+	0.513943i
$957$	6.89663	+	3.58083i	0.222936	+	0.115752i
$958$	51.9097	−	48.0771i	1.67712	−	1.55330i
$959$	1.33056	+	11.5255i	0.0429660	+	0.372177i
$960$	−7.75151	+	11.4971i	−0.250179	+	0.371068i
$961$	−5.14720	+	26.5404i	−0.166039	+	0.856141i
$962$	−17.9437	−	70.5590i	−0.578527	−	2.27491i
$963$	5.27428	+	6.15149i	0.169961	+	0.198229i
$964$	−108.209	+	48.5091i	−3.48516	+	1.56237i
$965$	5.17993	+	6.52360i	0.166748	+	0.210002i
$966$	−1.45462	+	0.942001i	−0.0468016	+	0.0303084i
$967$	10.2689	−	24.1349i	0.330226	−	0.776126i	−0.669227	−	0.743058i	$-0.733375\pi$
$967$	10.2689	−	24.1349i	0.330226	−	0.776126i	0.999453	−	0.0330677i	$-0.0105277\pi$
$968$	−71.8336	+	4.13269i	−2.30882	+	0.132830i
$969$	5.55037	−	3.90404i	0.178304	−	0.125416i
$970$	−91.4061	+	10.6106i	−2.93487	+	0.340685i
$971$	2.58040	+	16.7060i	0.0828088	+	0.536120i	0.992636	+	0.121133i	$0.0386528\pi$
$971$	2.58040	+	16.7060i	0.0828088	+	0.536120i	−0.909827	+	0.414987i	$0.863786\pi$
$972$	−23.8760	+	25.7793i	−0.765822	+	0.826872i
$973$	−8.83089	+	18.7293i	−0.283105	+	0.600435i
$974$	41.8690	+	70.4266i	1.34157	+	2.25661i
$975$	−12.7010	−	28.2368i	−0.406757	−	0.904301i
$976$	−84.8715	−	34.2063i	−2.71667	−	1.09492i
$977$	11.8827	−	17.6007i	0.380163	−	0.563097i	−0.589431	−	0.807819i	$-0.700648\pi$
$977$	11.8827	−	17.6007i	0.380163	−	0.563097i	0.969593	+	0.244722i	$0.0786967\pi$
$978$	30.5072	+	64.7024i	0.975513	+	2.06895i
$979$	9.39838	+	2.97430i	0.300373	+	0.0950590i
$980$	−63.6036	−	9.78327i	−2.03174	−	0.312515i
$981$	−4.46237	−	4.29460i	−0.142473	−	0.137116i
$982$	28.8434	−	8.52378i	0.920431	−	0.272005i
$983$	2.10676	+	5.53048i	0.0671952	+	0.176395i	0.963919	−	0.266196i	$-0.0857668\pi$
$983$	2.10676	+	5.53048i	0.0671952	+	0.176395i	−0.896724	+	0.442591i	$0.854059\pi$
$984$	−10.0823	−	36.6890i	−0.321412	−	1.16960i
$985$	−7.85002	+	7.27960i	−0.250122	+	0.231947i
$986$	−2.41921	+	15.6624i	−0.0770434	+	0.498794i
$987$	3.79464	+	4.78513i	0.120785	+	0.152312i
$988$	94.0532	−	9.03609i	2.99223	−	0.287476i
$989$	−0.111190	+	0.404615i	−0.00353564	+	0.0128660i
$990$	−1.53493	−	2.95171i	−0.0487831	−	0.0938114i
$991$	−26.7835	+	2.05629i	−0.850806	+	0.0653203i	−0.494635	−	0.869101i	$-0.664698\pi$
$991$	−26.7835	+	2.05629i	−0.850806	+	0.0653203i	−0.356171	+	0.934421i	$0.615918\pi$
$992$	15.4642	−	5.22186i	0.490987	−	0.165794i
$993$	1.06229	−	18.4644i	0.0337107	−	0.585951i
$994$	−4.65582	+	19.8959i	−0.147674	+	0.631060i
$995$	18.8226	+	19.5334i	0.596717	+	0.619249i
$996$	34.6849	+	53.8469i	1.09903	+	1.70620i
$997$	36.1596	+	36.1596i	1.14519	+	1.14519i	0.987487	+	0.157699i	$0.0504075\pi$
$997$	36.1596	+	36.1596i	1.14519	+	1.14519i	0.157699	+	0.987487i	$0.449593\pi$
$998$	−14.4226	−	23.2347i	−0.456539	−	0.735482i
$999$	28.7023	−	25.5794i	0.908100	−	0.809296i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	415.2.l.a.102.3	✓	3200
5.3	odd	4	inner	415.2.l.a.268.38	yes	3200
83.35	odd	82	inner	415.2.l.a.367.38	yes	3200
415.118	even	164	inner	415.2.l.a.118.3	yes	3200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
415.2.l.a.102.3	✓	3200	1.1	even	1	trivial
415.2.l.a.118.3	yes	3200	415.118	even	164	inner
415.2.l.a.268.38	yes	3200	5.3	odd	4	inner
415.2.l.a.367.38	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+(-2.19559 + 1.36288i) q^{2} +(-1.50039 - 0.0863199i) q^{3} +(2.07574 - 4.19230i) q^{4} +(-1.48666 + 1.67028i) q^{5} +(3.41189 - 1.85533i) q^{6} +(-0.800461 + 0.455356i) q^{7} +(0.661841 + 6.88885i) q^{8} +(-0.736477 - 0.0850227i) q^{9} +(0.987722 - 5.69338i) q^{10} +(-0.559563 + 0.538525i) q^{11} +(-3.47631 + 6.11092i) q^{12} +(-3.85043 + 1.46677i) q^{13} +(1.13689 - 2.09070i) q^{14} +(2.37476 - 2.37775i) q^{15} +(-5.16989 - 6.78226i) q^{16} +(-0.424452 - 0.817487i) q^{17} +(1.73288 - 0.817052i) q^{18} +(-0.933294 - 4.81232i) q^{19} +(3.91638 + 9.69961i) q^{20} +(1.24031 - 0.614118i) q^{21} +(0.494627 - 1.94499i) q^{22} +(0.438268 + 0.206643i) q^{23} +(-0.398377 - 10.3931i) q^{24} +(-0.579657 - 4.96629i) q^{25} +(6.45493 - 8.46807i) q^{26} +(5.53945 + 0.964602i) q^{27} +(0.247441 + 4.30097i) q^{28} +(2.48887 + 6.17530i) q^{29} +(-1.97342 + 8.45705i) q^{30} +(1.53623 - 1.26692i) q^{31} +(7.65988 + 2.91793i) q^{32} +(0.886050 - 0.759698i) q^{33} +(2.04606 + 1.21639i) q^{34} +(0.429445 - 2.01395i) q^{35} +(-1.88518 + 2.91105i) q^{36} +(4.24852 - 5.35748i) q^{37} +(8.60772 + 9.29390i) q^{38} +(5.90377 - 1.86836i) q^{39} +(-12.4902 - 9.13596i) q^{40} +(3.56207 - 0.833557i) q^{41} +(-1.88625 + 3.03874i) q^{42} +(0.148565 + 0.853167i) q^{43} +(1.09615 + 3.46369i) q^{44} +(1.23691 - 1.10372i) q^{45} +(-1.24389 + 0.143600i) q^{46} +(0.922939 + 4.31498i) q^{47} +(7.17142 + 10.6223i) q^{48} +(-3.14374 + 5.28800i) q^{49} +(8.04112 + 10.1139i) q^{50} +(0.566279 + 1.26319i) q^{51} +(-1.84335 + 19.1868i) q^{52} +(1.07627 - 5.03186i) q^{53} +(-13.4770 + 5.43171i) q^{54} +(-0.0676046 - 1.73523i) q^{55} +(-3.66666 - 5.21288i) q^{56} +(0.984909 + 7.30093i) q^{57} +(-13.8807 - 10.1664i) q^{58} +(10.5146 - 0.403033i) q^{59} +(-5.03884 - 14.8913i) q^{60} +(9.22318 - 5.48323i) q^{61} +(-1.64628 + 4.87534i) q^{62} +(0.628237 - 0.267302i) q^{63} +(-4.05070 + 0.785587i) q^{64} +(3.27438 - 8.61188i) q^{65} +(-0.910026 + 2.87556i) q^{66} +(11.9572 + 1.61305i) q^{67} +(-4.30820 + 0.0825383i) q^{68} +(-0.639736 - 0.347878i) q^{69} +(1.80188 + 5.00710i) q^{70} +(-8.27918 + 2.27516i) q^{71} +(0.0982779 - 5.12976i) q^{72} +(-8.15628 - 11.1362i) q^{73} +(-2.02641 + 17.5530i) q^{74} +(0.441025 + 7.50142i) q^{75} +(-22.1120 - 6.07647i) q^{76} +(0.202687 - 0.685869i) q^{77} +(-10.4159 + 12.1483i) q^{78} +(-4.39159 - 2.17441i) q^{79} +(19.0141 + 1.44779i) q^{80} +(-6.06249 - 1.41868i) q^{81} +(-6.68482 + 6.68482i) q^{82} +(4.21782 - 8.07527i) q^{83} -6.47451i q^{84} +(1.99645 + 0.506377i) q^{85} +(-1.48895 - 1.67073i) q^{86} +(-3.20123 - 9.48022i) q^{87} +(-4.08016 - 3.49833i) q^{88} +(-6.06388 - 11.1513i) q^{89} +(-1.21150 + 4.10907i) q^{90} +(2.41421 - 2.92741i) q^{91} +(1.77604 - 1.40841i) q^{92} +(-2.41432 + 1.76828i) q^{93} +(-7.90718 - 8.21608i) q^{94} +(9.42540 + 5.59544i) q^{95} +(-11.2410 - 5.03924i) q^{96} +(-4.51312 - 15.2718i) q^{97} +(-0.304519 - 15.8948i) q^{98} +(0.457892 - 0.349036i) 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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