LMFDB - Embedded newform 216.2.t.a.133.29

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [216,2,Mod(13,216)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(216, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("216.13"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.t (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			133.29
Character	$\chi$	$=$	216.133
Dual form			216.2.t.a.13.29

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.15171 + 0.820715i) q^{2} +(-0.411299 - 1.68251i) q^{3} +(0.652854 + 1.89044i) q^{4} +(2.15975 + 2.57389i) q^{5} +(0.907164 - 2.27531i) q^{6} +(-1.78453 + 0.649515i) q^{7} +(-0.799620 + 2.71304i) q^{8} +(-2.66167 + 1.38403i) q^{9} +(0.374968 + 4.73691i) q^{10} +(3.21944 - 3.83678i) q^{11} +(2.91217 - 1.87597i) q^{12} +(3.61424 - 0.637289i) q^{13} +(-2.58832 - 0.716539i) q^{14} +(3.44229 - 4.69244i) q^{15} +(-3.14756 + 2.46837i) q^{16} +(-1.74380 - 3.02034i) q^{17} +(-4.20135 - 0.590478i) q^{18} +(-2.73085 - 1.57666i) q^{19} +(-3.45580 + 5.76327i) q^{20} +(1.82679 + 2.73534i) q^{21} +(6.85676 - 1.77660i) q^{22} +(-2.93428 - 1.06799i) q^{23} +(4.89360 + 0.229496i) q^{24} +(-1.09215 + 6.19390i) q^{25} +(4.68558 + 2.23229i) q^{26} +(3.42338 + 3.90903i) q^{27} +(-2.39291 - 2.94951i) q^{28} +(-6.61611 - 1.16660i) q^{29} +(7.81566 - 2.57917i) q^{30} +(0.842639 + 0.306695i) q^{31} +(-5.65090 + 0.259585i) q^{32} +(-7.77957 - 3.83868i) q^{33} +(0.470500 - 4.90971i) q^{34} +(-5.52592 - 3.19039i) q^{35} +(-4.35411 - 4.12817i) q^{36} +(6.21485 - 3.58815i) q^{37} +(-1.85115 - 4.05710i) q^{38} +(-2.55878 - 5.81888i) q^{39} +(-8.71007 + 3.80137i) q^{40} +(-0.341649 - 1.93759i) q^{41} +(-0.141009 + 4.64958i) q^{42} +(-5.36405 + 6.39263i) q^{43} +(9.35505 + 3.58132i) q^{44} +(-9.31088 - 3.86169i) q^{45} +(-2.50291 - 3.63822i) q^{46} +(2.63733 - 0.959909i) q^{47} +(5.44764 + 4.28056i) q^{48} +(-2.59964 + 2.18135i) q^{49} +(-6.34127 + 6.23721i) q^{50} +(-4.36453 + 4.17621i) q^{51} +(3.56433 + 6.41647i) q^{52} -9.52536i q^{53} +(0.734526 + 7.31167i) q^{54} +16.8287 q^{55} +(-0.335219 - 5.36087i) q^{56} +(-1.52954 + 5.24316i) q^{57} +(-6.66237 - 6.77352i) q^{58} +(-6.13695 - 7.31373i) q^{59} +(11.1181 + 3.44398i) q^{60} +(2.92540 + 8.03747i) q^{61} +(0.718763 + 1.04479i) q^{62} +(3.85088 - 4.19863i) q^{63} +(-6.72122 - 4.33881i) q^{64} +(9.44618 + 7.92629i) q^{65} +(-5.80932 - 10.8058i) q^{66} +(13.7512 - 2.42470i) q^{67} +(4.57135 - 5.26839i) q^{68} +(-0.590037 + 5.37621i) q^{69} +(-3.74584 - 8.20960i) q^{70} +(1.50109 + 2.59997i) q^{71} +(-1.62660 - 8.32791i) q^{72} +(0.472663 - 0.818676i) q^{73} +(10.1025 + 0.968131i) q^{74} +(10.8705 - 0.709989i) q^{75} +(1.19774 - 6.19185i) q^{76} +(-3.25314 + 8.93793i) q^{77} +(1.82868 - 8.80166i) q^{78} +(-0.803209 + 4.55523i) q^{79} +(-13.1513 - 2.77042i) q^{80} +(5.16894 - 7.36764i) q^{81} +(1.19673 - 2.51193i) q^{82} +(2.12803 + 0.375229i) q^{83} +(-3.97838 + 5.23922i) q^{84} +(4.00787 - 11.0115i) q^{85} +(-11.4243 + 2.96007i) q^{86} +(0.758385 + 11.6115i) q^{87} +(7.83503 + 11.8025i) q^{88} +(-7.83712 + 13.5743i) q^{89} +(-7.55405 - 12.0891i) q^{90} +(-6.03579 + 3.48477i) q^{91} +(0.103320 - 6.24433i) q^{92} +(0.169441 - 1.54389i) q^{93} +(3.82524 + 1.05896i) q^{94} +(-1.83982 - 10.4341i) q^{95} +(2.76096 + 9.40091i) q^{96} +(1.68619 + 1.41488i) q^{97} +(-4.78429 + 0.378719i) q^{98} +(-3.25888 + 14.6680i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26}+ \cdots + 54 q^{98}+O(q^{100}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{9}\right)$

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 $

$2$	1.15171	+	0.820715i	0.814379	+	0.580333i
$2$	1.15171	+	0.820715i	0.814379	+	0.580333i
$3$	−0.411299	−	1.68251i	−0.237463	−	0.971396i
$3$	−0.411299	−	1.68251i	−0.237463	−	0.971396i
$4$	0.652854	+	1.89044i	0.326427	+	0.945222i
$5$	2.15975	+	2.57389i	0.965871	+	1.15108i	0.988482	+	0.151335i	$0.0483574\pi$
$5$	2.15975	+	2.57389i	0.965871	+	1.15108i	−0.0226118	+	0.999744i	$0.507198\pi$
$6$	0.907164	−	2.27531i	0.370348	−	0.928893i
$7$	−1.78453	+	0.649515i	−0.674489	+	0.245494i	−0.656479	−	0.754344i	$-0.727955\pi$
$7$	−1.78453	+	0.649515i	−0.674489	+	0.245494i	−0.0180093	+	0.999838i	$0.505733\pi$
$8$	−0.799620	+	2.71304i	−0.282708	+	0.959206i
$9$	−2.66167	+	1.38403i	−0.887222	+	0.461342i
$10$	0.374968	+	4.73691i	0.118575	+	1.49794i
$11$	3.21944	−	3.83678i	0.970699	−	1.15683i	−0.0169036	−	0.999857i	$-0.505381\pi$
$11$	3.21944	−	3.83678i	0.970699	−	1.15683i	0.987602	−	0.156977i	$-0.0501747\pi$
$12$	2.91217	−	1.87597i	0.840671	−	0.541546i
$13$	3.61424	−	0.637289i	1.00241	−	0.176752i	0.351728	−	0.936102i	$-0.385594\pi$
$13$	3.61424	−	0.637289i	1.00241	−	0.176752i	0.650682	+	0.759350i	$0.274483\pi$
$14$	−2.58832	−	0.716539i	−0.691758	−	0.191503i
$15$	3.44229	−	4.69244i	0.888796	−	1.21158i
$16$	−3.14756	+	2.46837i	−0.786891	+	0.617092i
$17$	−1.74380	−	3.02034i	−0.422932	−	0.732541i	0.573292	−	0.819351i	$-0.305666\pi$
$17$	−1.74380	−	3.02034i	−0.422932	−	0.732541i	−0.996225	+	0.0868103i	$0.972333\pi$
$18$	−4.20135	−	0.590478i	−0.990268	−	0.139177i
$19$	−2.73085	−	1.57666i	−0.626501	−	0.361710i	0.152895	−	0.988242i	$-0.451140\pi$
$19$	−2.73085	−	1.57666i	−0.626501	−	0.361710i	−0.779396	+	0.626532i	$0.784474\pi$
$20$	−3.45580	+	5.76327i	−0.772740	+	1.28871i
$21$	1.82679	+	2.73534i	0.398638	+	0.596900i
$22$	6.85676	−	1.77660i	1.46187	−	0.378773i
$23$	−2.93428	−	1.06799i	−0.611839	−	0.222691i	0.0174685	−	0.999847i	$-0.494439\pi$
$23$	−2.93428	−	1.06799i	−0.611839	−	0.222691i	−0.629308	+	0.777156i	$0.716662\pi$
$24$	4.89360	+	0.229496i	0.998902	+	0.0468456i
$25$	−1.09215	+	6.19390i	−0.218430	+	1.23878i
$26$	4.68558	+	2.23229i	0.918918	+	0.437789i
$27$	3.42338	+	3.90903i	0.658829	+	0.752293i
$28$	−2.39291	−	2.94951i	−0.452218	−	0.557406i
$29$	−6.61611	−	1.16660i	−1.22858	−	0.216632i	−0.478565	−	0.878052i	$-0.658843\pi$
$29$	−6.61611	−	1.16660i	−1.22858	−	0.216632i	−0.750015	+	0.661420i	$0.769954\pi$
$30$	7.81566	−	2.57917i	1.42694	−	0.470890i
$31$	0.842639	+	0.306695i	0.151342	+	0.0550841i	0.416581	−	0.909099i	$-0.363228\pi$
$31$	0.842639	+	0.306695i	0.151342	+	0.0550841i	−0.265238	+	0.964183i	$0.585451\pi$
$32$	−5.65090	+	0.259585i	−0.998947	+	0.0458885i
$33$	−7.77957	−	3.83868i	−1.35425	−	0.668228i
$34$	0.470500	−	4.90971i	0.0806901	−	0.842008i
$35$	−5.52592	−	3.19039i	−0.934052	−	0.539275i
$36$	−4.35411	−	4.12817i	−0.725684	−	0.688028i
$37$	6.21485	−	3.58815i	1.02172	−	0.589887i	0.107115	−	0.994247i	$-0.465839\pi$
$37$	6.21485	−	3.58815i	1.02172	−	0.589887i	0.914600	+	0.404359i	$0.132505\pi$
$38$	−1.85115	−	4.05710i	−0.300297	−	0.658148i
$39$	−2.55878	−	5.81888i	−0.409732	−	0.931766i
$40$	−8.71007	+	3.80137i	−1.37718	+	0.601049i
$41$	−0.341649	−	1.93759i	−0.0533567	−	0.302601i	0.946438	−	0.322887i	$-0.104653\pi$
$41$	−0.341649	−	1.93759i	−0.0533567	−	0.302601i	−0.999794	+	0.0202862i	$0.993542\pi$
$42$	−0.141009	+	4.64958i	−0.0217582	+	0.717446i
$43$	−5.36405	+	6.39263i	−0.818010	+	0.974867i	−0.999964	−	0.00844018i	$-0.997313\pi$
$43$	−5.36405	+	6.39263i	−0.818010	+	0.974867i	0.181954	+	0.983307i	$0.441758\pi$
$44$	9.35505	+	3.58132i	1.41033	+	0.539904i
$45$	−9.31088	−	3.86169i	−1.38798	−	0.575667i
$46$	−2.50291	−	3.63822i	−0.369034	−	0.536426i
$47$	2.63733	−	0.959909i	0.384694	−	0.140017i	−0.142432	−	0.989805i	$-0.545492\pi$
$47$	2.63733	−	0.959909i	0.384694	−	0.140017i	0.527125	+	0.849788i	$0.323270\pi$
$48$	5.44764	+	4.28056i	0.786299	+	0.617846i
$49$	−2.59964	+	2.18135i	−0.371377	+	0.311622i
$50$	−6.34127	+	6.23721i	−0.896791	+	0.882075i
$51$	−4.36453	+	4.17621i	−0.611156	+	0.584787i
$52$	3.56433	+	6.41647i	0.494284	+	0.889804i
$53$		−	9.52536i		−	1.30841i	−0.756318	−	0.654205i	$-0.773004\pi$
$53$		−	9.52536i		−	1.30841i	0.756318	−	0.654205i	$-0.226996\pi$
$54$	0.734526	+	7.31167i	0.0999563	+	0.994992i
$55$	16.8287			2.26918
$56$	−0.335219	−	5.36087i	−0.0447955	−	0.716377i
$57$	−1.52954	+	5.24316i	−0.202593	+	0.694473i
$58$	−6.66237	−	6.77352i	−0.874812	−	0.889406i
$59$	−6.13695	−	7.31373i	−0.798963	−	0.952167i	0.200659	−	0.979661i	$-0.435692\pi$
$59$	−6.13695	−	7.31373i	−0.798963	−	0.952167i	−0.999622	+	0.0274946i	$0.991247\pi$
$60$	11.1181	+	3.44398i	1.43534	+	0.444616i
$61$	2.92540	+	8.03747i	0.374559	+	1.02909i	0.973577	+	0.228358i	$0.0733355\pi$
$61$	2.92540	+	8.03747i	0.374559	+	1.02909i	−0.599018	+	0.800735i	$0.704442\pi$
$62$	0.718763	+	1.04479i	0.0912830	+	0.132688i
$63$	3.85088	−	4.19863i	0.485165	−	0.528978i
$64$	−6.72122	−	4.33881i	−0.840152	−	0.542351i
$65$	9.44618	+	7.92629i	1.17165	+	0.983135i
$66$	−5.80932	−	10.8058i	−0.715078	−	1.33011i
$67$	13.7512	−	2.42470i	1.67997	−	0.296224i	0.749341	−	0.662184i	$-0.230370\pi$
$67$	13.7512	−	2.42470i	1.67997	−	0.296224i	0.930631	+	0.365960i	$0.119259\pi$
$68$	4.57135	−	5.26839i	0.554357	−	0.638886i
$69$	−0.590037	+	5.37621i	−0.0710321	+	0.647220i
$70$	−3.74584	−	8.20960i	−0.447713	−	0.981235i
$71$	1.50109	+	2.59997i	0.178147	+	0.308560i	0.941246	−	0.337722i	$-0.109656\pi$
$71$	1.50109	+	2.59997i	0.178147	+	0.308560i	−0.763099	+	0.646282i	$0.776323\pi$
$72$	−1.62660	−	8.32791i	−0.191697	−	0.981454i
$73$	0.472663	−	0.818676i	0.0553210	−	0.0958187i	−0.837039	−	0.547144i	$-0.815715\pi$
$73$	0.472663	−	0.818676i	0.0553210	−	0.0958187i	0.892360	+	0.451325i	$0.149048\pi$
$74$	10.1025	+	0.968131i	1.17439	+	0.112543i
$75$	10.8705	−	0.709989i	1.25522	−	0.0819825i
$76$	1.19774	−	6.19185i	0.137390	−	0.710254i
$77$	−3.25314	+	8.93793i	−0.370730	+	1.01857i
$78$	1.82868	−	8.80166i	0.207057	−	0.996592i
$79$	−0.803209	+	4.55523i	−0.0903681	+	0.512503i	0.905701	+	0.423918i	$0.139346\pi$
$79$	−0.803209	+	4.55523i	−0.0903681	+	0.512503i	−0.996069	+	0.0885849i	$0.971766\pi$
$80$	−13.1513	−	2.77042i	−1.47036	−	0.309743i
$81$	5.16894	−	7.36764i	0.574327	−	0.818626i
$82$	1.19673	−	2.51193i	0.132157	−	0.277396i
$83$	2.12803	+	0.375229i	0.233582	+	0.0411868i	0.289214	−	0.957265i	$-0.406606\pi$
$83$	2.12803	+	0.375229i	0.233582	+	0.0411868i	−0.0556319	+	0.998451i	$0.517717\pi$
$84$	−3.97838	+	5.23922i	−0.434077	+	0.571646i
$85$	4.00787	−	11.0115i	0.434715	−	1.19437i
$86$	−11.4243	+	2.96007i	−1.23192	+	0.319193i
$87$	0.758385	+	11.6115i	0.0813074	+	1.24488i
$88$	7.83503	+	11.8025i	0.835217	+	1.25815i
$89$	−7.83712	+	13.5743i	−0.830733	+	1.43887i	0.0667245	+	0.997771i	$0.478745\pi$
$89$	−7.83712	+	13.5743i	−0.830733	+	1.43887i	−0.897458	+	0.441101i	$0.854588\pi$
$90$	−7.55405	−	12.0891i	−0.796267	−	1.27430i
$91$	−6.03579	+	3.48477i	−0.632723	+	0.365303i
$92$	0.103320	−	6.24433i	0.0107719	−	0.651017i
$93$	0.169441	−	1.54389i	0.0175703	−	0.160094i
$94$	3.82524	+	1.05896i	0.394543	+	0.109223i
$95$	−1.83982	−	10.4341i	−0.188761	−	1.07052i
$96$	2.76096	+	9.40091i	0.281789	+	0.959476i
$97$	1.68619	+	1.41488i	0.171207	+	0.143659i	0.724365	−	0.689417i	$-0.242133\pi$
$97$	1.68619	+	1.41488i	0.171207	+	0.143659i	−0.553158	+	0.833076i	$0.686578\pi$
$98$	−4.78429	+	0.378719i	−0.483286	+	0.0382564i
$99$	−3.25888	+	14.6680i	−0.327529	+	1.47419i
$100$	−12.4222	+	1.97906i	−1.24222	+	0.197906i
$101$	6.12830	+	16.8374i	0.609789	+	1.67538i	0.730684	+	0.682716i	$0.239201\pi$
$101$	6.12830	+	16.8374i	0.609789	+	1.67538i	−0.120895	+	0.992665i	$0.538576\pi$
$102$	−8.45413	+	1.22774i	−0.837084	+	0.121564i
$103$	−10.6973	+	8.97613i	−1.05404	+	0.884444i	−0.993513	−	0.113723i	$-0.963723\pi$
$103$	−10.6973	+	8.97613i	−1.05404	+	0.884444i	−0.0605268	+	0.998167i	$0.519278\pi$
$104$	−1.16103	+	10.3152i	−0.113848	+	1.01149i
$105$	−3.09506	+	10.6096i	−0.302047	+	1.03539i
$106$	7.81761	−	10.9704i	0.759313	−	1.06554i
$107$		−	12.3518i		−	1.19409i	−0.802207	−	0.597046i	$-0.796341\pi$
$107$		−	12.3518i		−	1.19409i	0.802207	−	0.597046i	$-0.203659\pi$
$108$	−5.15484	+	9.02373i	−0.496024	+	0.868309i
$109$			2.18468i			0.209255i	0.994511	+	0.104627i	$0.0333650\pi$
$109$			2.18468i			0.209255i	−0.994511	+	0.104627i	$0.966635\pi$
$110$	19.3817	+	13.8115i	1.84797	+	1.31688i
$111$	−8.59324	−	8.98074i	−0.815634	−	0.852414i
$112$	4.01367	−	6.44927i	0.379256	−	0.609399i
$113$	12.1210	−	10.1708i	1.14025	−	0.956785i	0.140805	−	0.990037i	$-0.455031\pi$
$113$	12.1210	−	10.1708i	1.14025	−	0.956785i	0.999447	+	0.0332523i	$0.0105865\pi$
$114$	−6.06472	+	4.78326i	−0.568014	+	0.447993i
$115$	−3.58842	−	9.85911i	−0.334622	−	0.919367i
$116$	−2.11396	−	13.2690i	−0.196277	−	1.23200i
$117$	−8.73789	+	6.69846i	−0.807818	+	0.619273i
$118$	−1.06547	−	13.4600i	−0.0980848	−	1.23909i
$119$	5.07361	+	4.25727i	0.465097	+	0.390263i
$120$	9.97827	+	13.0913i	0.910887	+	1.19506i
$121$	−2.44596	−	13.8717i	−0.222360	−	1.26107i
$122$	−3.22727	+	11.6577i	−0.292183	+	1.05544i
$123$	−3.11949	+	1.37176i	−0.281275	+	0.123687i
$124$	−0.0296705	+	1.79319i	−0.00266449	+	0.161033i
$125$	−3.75209	+	2.16627i	−0.335597	+	0.193757i
$126$	7.88095	−	1.67512i	0.702091	−	0.149231i
$127$	−5.17381	+	8.96131i	−0.459102	+	0.795187i	−0.998914	−	0.0465982i	$-0.985162\pi$
$127$	−5.17381	+	8.96131i	−0.459102	+	0.795187i	0.539812	+	0.841786i	$0.318495\pi$
$128$	−4.17994	−	10.5132i	−0.369458	−	0.929247i
$129$	12.9619	+	6.39578i	1.14123	+	0.563117i
$130$	4.37400	+	16.8814i	0.383626	+	1.48059i
$131$	−3.07414	+	8.44614i	−0.268589	+	0.737942i	0.729929	+	0.683523i	$0.239553\pi$
$131$	−3.07414	+	8.44614i	−0.268589	+	0.737942i	−0.998518	+	0.0544195i	$0.982669\pi$
$132$	2.17788	−	17.2129i	0.189560	−	1.49819i
$133$	5.89735	+	1.03986i	0.511365	+	0.0901675i
$134$	17.8273	+	8.49324i	1.54004	+	0.733704i
$135$	−2.66777	+	17.2539i	−0.229605	+	1.48498i
$136$	9.58869	−	2.31587i	0.822224	−	0.198584i
$137$	2.92683	−	16.5989i	0.250056	−	1.41814i	−0.558395	−	0.829575i	$-0.688583\pi$
$137$	2.92683	−	16.5989i	0.250056	−	1.41814i	0.808451	−	0.588563i	$-0.200306\pi$
$138$	−5.09188	+	5.70756i	−0.433450	+	0.485860i
$139$	−3.76833	+	10.3534i	−0.319626	+	0.878164i	0.670988	+	0.741469i	$0.265870\pi$
$139$	−3.76833	+	10.3534i	−0.319626	+	0.878164i	−0.990613	+	0.136695i	$0.956352\pi$
$140$	2.42364	−	12.5293i	0.204835	−	1.05892i
$141$	−2.69978	−	4.04252i	−0.227363	−	0.340441i
$142$	−0.405016	+	4.22637i	−0.0339882	+	0.354669i
$143$	9.19071	−	15.9188i	0.768566	−	1.33120i
$144$	4.96147	−	10.9263i	0.413456	−	0.910524i
$145$	−11.2865	−	19.5487i	−0.937289	−	1.62343i
$146$	1.21627	−	0.554953i	0.100659	−	0.0459282i
$147$	4.73937	+	3.47672i	0.390897	+	0.286755i
$148$	10.8406	+	9.40629i	0.891090	+	0.773193i
$149$	10.6491	−	1.87772i	0.872406	−	0.153829i	0.280518	−	0.959849i	$-0.409494\pi$
$149$	10.6491	−	1.87772i	0.872406	−	0.153829i	0.591888	+	0.806020i	$0.298383\pi$
$150$	13.1023	+	8.10388i	1.06980	+	0.661679i
$151$	−0.489785	−	0.410979i	−0.0398582	−	0.0334450i	0.622641	−	0.782508i	$-0.286060\pi$
$151$	−0.489785	−	0.410979i	−0.0398582	−	0.0334450i	−0.662499	+	0.749063i	$0.730504\pi$
$152$	6.46119	−	6.14820i	0.524072	−	0.498685i
$153$	8.82164	+	5.62569i	0.713187	+	0.454810i
$154$	−11.0822	+	7.62397i	−0.893025	+	0.614357i
$155$	1.03049	+	2.83125i	0.0827709	+	0.227411i
$156$	9.32976	−	8.63610i	0.746979	−	0.691442i
$157$	−5.93021	−	7.06735i	−0.473282	−	0.564036i	0.475602	−	0.879661i	$-0.342230\pi$
$157$	−5.93021	−	7.06735i	−0.473282	−	0.564036i	−0.948884	+	0.315625i	$0.897786\pi$
$158$	−4.66360	+	4.58708i	−0.371016	+	0.364928i
$159$	−16.0265	+	3.91777i	−1.27098	+	0.310699i
$160$	−12.8727	−	13.9842i	−1.01767	−	1.10554i
$161$	5.92998			0.467348
$162$	11.9998	−	4.24312i	0.942796	−	0.333371i
$163$			8.36032i			0.654831i	0.944881	+	0.327415i	$0.106178\pi$
$163$			8.36032i			0.654831i	−0.944881	+	0.327415i	$0.893822\pi$
$164$	3.43986	−	1.91083i	0.268608	−	0.149211i
$165$	−6.92161	−	28.3144i	−0.538847	−	2.20427i
$166$	2.14291	+	2.17866i	0.166322	+	0.169097i
$167$	−4.77570	+	4.00729i	−0.369555	+	0.310094i	−0.808586	−	0.588379i	$-0.799766\pi$
$167$	−4.77570	+	4.00729i	−0.369555	+	0.310094i	0.439030	+	0.898472i	$0.355322\pi$
$168$	−8.88183	+	2.76893i	−0.685248	+	0.213627i
$169$	0.440614	−	0.160370i	0.0338934	−	0.0123362i
$170$	13.6532	−	9.39273i	1.04715	−	0.720390i
$171$	9.45076	+	0.416967i	0.722717	+	0.0318863i
$172$	−15.5869	−	5.96699i	−1.18849	−	0.454979i
$173$	−5.72780	+	6.82613i	−0.435477	+	0.518981i	−0.938494	−	0.345295i	$-0.887779\pi$
$173$	−5.72780	+	6.82613i	−0.435477	+	0.518981i	0.503017	+	0.864276i	$0.332223\pi$
$174$	−8.65627	+	13.9954i	−0.656230	+	1.06099i
$175$	−2.07406	−	11.7626i	−0.156784	−	0.889167i
$176$	−0.662802	+	20.0233i	−0.0499605	+	1.50931i
$177$	−9.78129	+	13.3336i	−0.735207	+	1.00221i
$178$	−20.1667	+	9.20155i	−1.51156	+	0.689686i
$179$	12.5035	−	7.21893i	0.934559	−	0.539568i	0.0463085	−	0.998927i	$-0.485254\pi$
$179$	12.5035	−	7.21893i	0.934559	−	0.539568i	0.888251	+	0.459359i	$0.151921\pi$
$180$	1.22167	−	20.1228i	0.0910577	−	1.49987i
$181$	4.19806	+	2.42375i	0.312039	+	0.180156i	0.647839	−	0.761778i	$-0.275673\pi$
$181$	4.19806	+	2.42375i	0.312039	+	0.180156i	−0.335799	+	0.941934i	$0.609006\pi$
$182$	−9.81146	−	0.940238i	−0.727274	−	0.0696951i
$183$	12.3199	−	8.22781i	0.910713	−	0.608217i
$184$	5.24381	−	7.10684i	0.386579	−	0.523923i
$185$	22.6580	+	8.24685i	1.66585	+	0.606321i
$186$	1.46224	−	1.63904i	0.107217	−	0.120181i
$187$	−17.2024	−	3.03326i	−1.25797	−	0.221814i
$188$	3.53644	+	4.35904i	0.257922	+	0.317916i
$189$	−8.64809	−	4.75224i	−0.629056	−	0.345674i
$190$	6.44451	−	13.5270i	0.467534	−	0.981352i
$191$	−4.56335	+	25.8800i	−0.330192	+	1.87261i	0.140153	+	0.990130i	$0.455241\pi$
$191$	−4.56335	+	25.8800i	−0.330192	+	1.87261i	−0.470345	+	0.882483i	$0.655871\pi$
$192$	−4.53565	+	13.0930i	−0.327333	+	0.944909i
$193$	3.82953	+	1.39383i	0.275655	+	0.100330i	0.476149	−	0.879365i	$-0.342032\pi$
$193$	3.82953	+	1.39383i	0.275655	+	0.100330i	−0.200494	+	0.979695i	$0.564255\pi$
$194$	0.780781	+	3.01341i	0.0560568	+	0.216350i
$195$	9.45084	−	19.1534i	0.676789	−	1.37160i
$196$	−5.82091	−	3.49036i	−0.415780	−	0.249312i
$197$	8.91014	+	5.14427i	0.634821	+	0.366514i	0.782617	−	0.622504i	$-0.213884\pi$
$197$	8.91014	+	5.14427i	0.634821	+	0.366514i	−0.147796	+	0.989018i	$0.547218\pi$
$198$	−15.7915	+	14.2187i	−1.12226	+	1.01048i
$199$	0.690545	+	1.19606i	0.0489514	+	0.0847864i	0.889463	−	0.457007i	$-0.151079\pi$
$199$	0.690545	+	1.19606i	0.0489514	+	0.0847864i	−0.840511	+	0.541794i	$0.817745\pi$
$200$	−15.9310	−	7.91583i	−1.12649	−	0.559733i
$201$	−9.73541	−	22.1392i	−0.686683	−	1.56158i
$202$	−6.76068	+	24.4213i	−0.475680	+	1.71828i
$203$	12.5644	−	2.21544i	0.881845	−	0.155493i
$204$	−10.7443	−	5.52444i	−0.752251	−	0.386788i
$205$	4.24927	−	5.06408i	0.296782	−	0.353691i
$206$	−19.6870	+	1.55840i	−1.37166	+	0.108579i
$207$	9.28820	−	1.21849i	0.645574	−	0.0846906i
$208$	−9.80299	+	10.9272i	−0.679715	+	0.757665i
$209$	−14.8411	+	5.40173i	−1.02658	+	0.373645i
$210$	−12.2721	+	9.67900i	−0.846853	+	0.667915i
$211$	−7.42731	−	8.85152i	−0.511317	−	0.609364i	0.447188	−	0.894440i	$-0.352426\pi$
$211$	−7.42731	−	8.85152i	−0.511317	−	0.609364i	−0.958505	+	0.285076i	$0.907981\pi$
$212$	18.0072	−	6.21867i	1.23674	−	0.427100i
$213$	3.75707	−	3.59497i	0.257430	−	0.246323i
$214$	10.1373	−	14.2256i	0.692971	−	0.972444i
$215$	−28.0390			−1.91224
$216$	−13.3428	+	6.16203i	−0.907860	+	0.419273i
$217$	−1.70292			−0.115602
$218$	−1.79300	+	2.51611i	−0.121437	+	0.170413i
$219$	−1.57183	−	0.458539i	−0.106215	−	0.0309852i
$220$	10.9867	+	31.8137i	0.740721	+	2.14488i
$221$	−8.22733	−	9.80495i	−0.553430	−	0.659552i
$222$	−2.52627	−	17.3958i	−0.169552	−	1.16753i
$223$	2.85912	−	1.04063i	0.191461	−	0.0696860i	−0.244510	−	0.969647i	$-0.578627\pi$
$223$	2.85912	−	1.04063i	0.191461	−	0.0696860i	0.435971	+	0.899961i	$0.356405\pi$
$224$	9.91558	−	4.13358i	0.662513	−	0.276186i
$225$	−5.66558	−	17.9977i	−0.377705	−	1.19984i
$226$	22.3072	−	1.76581i	1.48385	−	0.117460i
$227$	0.641654	−	0.764693i	0.0425881	−	0.0507545i	−0.744330	−	0.667812i	$-0.767231\pi$
$227$	0.641654	−	0.764693i	0.0425881	−	0.0507545i	0.786918	+	0.617058i	$0.211675\pi$
$228$	−10.9105	+	0.531499i	−0.722564	+	0.0351994i
$229$	0.846018	−	0.149176i	0.0559064	−	0.00985781i	−0.145625	−	0.989340i	$-0.546519\pi$
$229$	0.846018	−	0.149176i	0.0559064	−	0.00985781i	0.201531	+	0.979482i	$0.435408\pi$
$230$	3.95871	−	14.2999i	0.261030	−	0.942906i
$231$	16.3762	+	1.79728i	1.07747	+	0.118252i
$232$	8.45541	−	17.0170i	0.555125	−	1.11722i
$233$	−5.17379	−	8.96127i	−0.338946	−	0.587072i	0.645288	−	0.763939i	$-0.276737\pi$
$233$	−5.17379	−	8.96127i	−0.338946	−	0.587072i	−0.984235	+	0.176867i	$0.943404\pi$
$234$	−15.5610	+	0.543342i	−1.01725	+	0.0355194i
$235$	8.16668	+	4.71503i	0.532735	+	0.307575i
$236$	9.81967	−	16.3764i	0.639206	−	1.06601i
$237$	7.99456	−	0.522152i	0.519303	−	0.0339174i
$238$	2.34931	+	9.06711i	0.152283	+	0.587733i
$239$	−11.5092	−	4.18901i	−0.744469	−	0.270965i	−0.0581928	−	0.998305i	$-0.518534\pi$
$239$	−11.5092	−	4.18901i	−0.744469	−	0.270965i	−0.686277	+	0.727341i	$0.740756\pi$
$240$	0.747844	+	23.2666i	0.0482731	+	1.50185i
$241$	−2.60278	+	14.7611i	−0.167660	+	0.950846i	0.778620	+	0.627496i	$0.215920\pi$
$241$	−2.60278	+	14.7611i	−0.167660	+	0.950846i	−0.946279	+	0.323350i	$0.895191\pi$
$242$	8.56771	−	17.9836i	0.550753	−	1.15603i
$243$	−14.5221	−	5.66649i	−0.931592	−	0.363505i
$244$	−13.2845	+	10.7776i	−0.850455	+	0.689966i
$245$	−11.2291	−	1.98000i	−0.717404	−	0.126498i
$246$	−4.71856	−	0.980353i	−0.300844	−	0.0625050i
$247$	−10.8748	−	3.95809i	−0.691944	−	0.251847i
$248$	−1.50587	+	2.04088i	−0.0956228	+	0.129596i
$249$	−0.243930	−	3.73476i	−0.0154584	−	0.236681i
$250$	−6.09919	−	0.584489i	−0.385747	−	0.0369663i
$251$	−13.8356	−	7.98801i	−0.873298	−	0.504199i	−0.00485525	−	0.999988i	$-0.501545\pi$
$251$	−13.8356	−	7.98801i	−0.873298	−	0.504199i	−0.868443	+	0.495789i	$0.834879\pi$
$252$	10.4513	+	4.53877i	0.658372	+	0.285916i
$253$	−13.5444	+	7.81986i	−0.851528	+	0.491630i
$254$	−13.3134	+	6.07457i	−0.835356	+	0.381152i
$255$	−20.1754	−	2.21425i	−1.26343	−	0.138661i
$256$	3.81430	−	15.5387i	0.238394	−	0.971169i
$257$	−1.36142	−	7.72098i	−0.0849229	−	0.481622i	−0.997373	−	0.0724341i	$-0.976923\pi$
$257$	−1.36142	−	7.72098i	−0.0849229	−	0.481622i	0.912450	−	0.409187i	$-0.134188\pi$
$258$	9.67916	+	18.0041i	0.602598	+	1.12088i
$259$	−8.76002	+	10.4398i	−0.544321	+	0.648697i
$260$	−8.81723	+	23.0322i	−0.546821	+	1.42840i
$261$	19.2245	−	6.05177i	1.18997	−	0.374595i
$262$	−10.4724	+	7.20447i	−0.646986	+	0.445094i
$263$	−19.3707	+	7.05037i	−1.19445	+	0.434744i	−0.861284	−	0.508124i	$-0.830339\pi$
$263$	−19.3707	+	7.05037i	−1.19445	+	0.434744i	−0.333166	+	0.942868i	$0.608117\pi$
$264$	16.6352	−	18.0368i	1.02383	−	1.11009i
$265$	24.5173	−	20.5724i	1.50608	−	1.26375i
$266$	5.93858	+	6.03766i	0.364118	+	0.370193i
$267$	26.0623	+	7.60293i	1.59498	+	0.465292i
$268$	13.5613	+	24.4128i	0.828386	+	1.49125i
$269$			15.9724i			0.973852i	0.873443	+	0.486926i	$0.161882\pi$
$269$			15.9724i			0.973852i	−0.873443	+	0.486926i	$0.838118\pi$
$270$	−17.2331	+	17.6820i	−1.04877	+	1.07609i
$271$	7.19443			0.437031			0.218515	−	0.975834i	$-0.429879\pi$
$271$	7.19443			0.437031			0.218515	+	0.975834i	$0.429879\pi$
$272$	12.9440	+	5.20239i	0.784847	+	0.315441i
$273$	8.34566	+	8.72199i	0.505102	+	0.527879i
$274$	16.9938	−	16.7149i	1.02663	−	1.00979i
$275$	20.2485	+	24.1313i	1.22103	+	1.45517i
$276$	−10.5486	+	2.39445i	−0.634953	+	0.144129i
$277$	−6.45750	−	17.7418i	−0.387993	−	1.06600i	−0.967903	−	0.251322i	$-0.919135\pi$
$277$	−6.45750	−	17.7418i	−0.387993	−	1.06600i	0.579910	−	0.814680i	$-0.303088\pi$
$278$	−12.8372	+	8.83135i	−0.769924	+	0.529669i
$279$	−2.66730	+	0.349913i	−0.159687	+	0.0209488i
$280$	13.0743	−	12.4410i	0.781340	−	0.743490i
$281$	−14.1133	−	11.8425i	−0.841932	−	0.706465i	0.116066	−	0.993242i	$-0.462972\pi$
$281$	−14.1133	−	11.8425i	−0.841932	−	0.706465i	−0.957997	+	0.286777i	$0.907416\pi$
$282$	0.208396	−	6.87154i	0.0124098	−	0.409194i
$283$	−8.62324	+	1.52051i	−0.512599	+	0.0903850i	−0.423964	−	0.905679i	$-0.639362\pi$
$283$	−8.62324	+	1.52051i	−0.512599	+	0.0903850i	−0.0886349	+	0.996064i	$0.528250\pi$
$284$	−3.93511	+	4.53514i	−0.233506	+	0.269111i
$285$	−16.7988	+	7.38704i	−0.995073	+	0.437571i
$286$	23.6498	−	10.7908i	1.39844	−	0.638074i
$287$	1.86818	+	3.23578i	0.110275	+	0.191002i
$288$	14.6815	−	8.51192i	0.865117	−	0.501570i
$289$	2.41836	−	4.18872i	0.142256	−	0.246395i
$290$	3.04524	−	31.7773i	0.178823	−	1.86603i
$291$	1.68702	−	3.41897i	0.0988950	−	0.200423i
$292$	1.85624	+	0.359067i	0.108628	+	0.0210128i
$293$	4.67724	−	12.8506i	0.273247	−	0.750741i	−0.724840	−	0.688918i	$-0.758086\pi$
$293$	4.67724	−	12.8506i	0.273247	−	0.750741i	0.998087	−	0.0618236i	$-0.0196916\pi$
$294$	2.60497	+	7.89384i	0.151925	+	0.460378i
$295$	5.57047	−	31.5917i	0.324325	−	1.83934i
$296$	4.76528	+	19.7303i	0.276976	+	1.14680i
$297$	26.0195	−	0.549857i	1.50980	−	0.0319060i
$298$	13.8057	+	6.57727i	0.799742	+	0.381011i
$299$	−11.2858	−	1.98999i	−0.652675	−	0.115084i
$300$	8.43904	+	20.0865i	0.487228	+	1.15970i
$301$	5.42020	−	14.8919i	0.312415	−	0.858353i
$302$	−0.226792	−	0.875301i	−0.0130504	−	0.0503679i
$303$	25.8085	−	17.2361i	1.48266	−	0.990188i
$304$	12.4873	−	1.77812i	0.716196	−	0.101982i
$305$	−14.3695	+	24.8886i	−0.822792	+	1.42512i
$306$	5.54285	+	13.7192i	0.316864	+	0.784274i
$307$	21.3532	−	12.3283i	1.21869	−	0.703612i	0.254053	−	0.967190i	$-0.418236\pi$
$307$	21.3532	−	12.3283i	1.21869	−	0.703612i	0.964638	+	0.263578i	$0.0849028\pi$
$308$	−19.0205	−	0.314717i	−1.08379	−	0.0179327i
$309$	19.5022	+	14.3065i	1.10944	+	0.813867i
$310$	−1.13683	+	4.10650i	−0.0645674	+	0.233234i
$311$	0.221479	+	1.25607i	0.0125589	+	0.0712250i	0.990443	−	0.137922i	$-0.0440424\pi$
$311$	0.221479	+	1.25607i	0.0125589	+	0.0712250i	−0.977884	+	0.209147i	$0.932931\pi$
$312$	17.8329	−	2.28918i	1.00959	−	0.129599i
$313$	15.3438	+	12.8749i	0.867280	+	0.727735i	0.963524	−	0.267623i	$-0.0862382\pi$
$313$	15.3438	+	12.8749i	0.867280	+	0.727735i	−0.0962433	+	0.995358i	$0.530683\pi$
$314$	−1.02958	−	13.0065i	−0.0581026	−	0.734001i
$315$	19.1238	+	0.843740i	1.07750	+	0.0475393i
$316$	−9.13578	+	1.45548i	−0.513928	+	0.0818769i
$317$	−2.05364	−	5.64232i	−0.115344	−	0.316904i	0.868565	−	0.495575i	$-0.165043\pi$
$317$	−2.05364	−	5.64232i	−0.115344	−	0.316904i	−0.983909	+	0.178671i	$0.942820\pi$
$318$	−21.6732	−	8.64107i	−1.21537	−	0.484567i
$319$	−25.7762	+	21.6288i	−1.44319	+	1.21098i
$320$	−3.34853	−	26.6704i	−0.187189	−	1.49092i
$321$	−20.7820	+	5.08027i	−1.15994	+	0.283553i
$322$	6.82960	+	4.86682i	0.380598	+	0.271217i
$323$			10.9975i			0.611916i
$324$	17.3027	+	4.96161i	0.961260	+	0.275645i
$325$			23.0823i			1.28038i
$326$	−6.86144	+	9.62863i	−0.380020	+	0.533280i
$327$	3.67575	−	0.898558i	0.203269	−	0.0496904i
$328$	5.52996	+	0.622426i	0.305341	+	0.0343677i
$329$	−4.08291	+	3.42597i	−0.225098	+	0.188880i
$330$	15.2664	−	38.2905i	0.840386	−	2.10782i
$331$	6.69009	+	18.3809i	0.367721	+	1.01030i	0.976226	+	0.216755i	$0.0695472\pi$
$331$	6.69009	+	18.3809i	0.367721	+	1.01030i	−0.608505	+	0.793550i	$0.708231\pi$
$332$	0.679944	+	4.26790i	0.0373168	+	0.234231i
$333$	−11.5758	+	18.1520i	−0.634348	+	0.994722i
$334$	−8.78905	+	0.695731i	−0.480916	+	0.0380687i
$335$	35.9400	+	30.1573i	1.96361	+	1.64767i
$336$	−12.5018	−	4.10046i	−0.682027	−	0.223699i
$337$	3.82769	+	21.7079i	0.208508	+	1.18251i	0.891824	+	0.452383i	$0.149426\pi$
$337$	3.82769	+	21.7079i	0.208508	+	1.18251i	−0.683316	+	0.730123i	$0.739463\pi$
$338$	0.639077	+	0.176919i	0.0347612	+	0.00962313i
$339$	−22.0978	−	16.2105i	−1.20019	−	0.880435i
$340$	23.4332	+	0.387732i	1.27085	+	0.0210277i
$341$	3.88955	−	2.24563i	0.210631	−	0.121608i
$342$	10.5423	+	8.23660i	0.570061	+	0.445384i
$343$	9.86900	−	17.0936i	0.532876	−	0.922968i
$344$	−13.0543	−	19.6646i	−0.703840	−	1.06024i
$345$	−15.1121	+	10.0926i	−0.813609	+	0.543367i
$346$	−12.1990	+	3.16080i	−0.655825	+	0.169926i
$347$	0.0110975	−	0.0304900i	0.000595743	−	0.00163679i	−0.939394	−	0.342838i	$-0.888612\pi$
$347$	0.0110975	−	0.0304900i	0.000595743	−	0.00163679i	0.939990	+	0.341202i	$0.110834\pi$
$348$	−21.4557	+	9.01429i	−1.15015	+	0.483216i
$349$	−32.0493	−	5.65116i	−1.71556	−	0.302500i	−0.772474	−	0.635046i	$-0.780981\pi$
$349$	−32.0493	−	5.65116i	−1.71556	−	0.302500i	−0.943087	+	0.332546i	$0.892092\pi$
$350$	7.26501	−	15.2492i	0.388331	−	0.815106i
$351$	14.8641	+	11.9465i	0.793387	+	0.637657i
$352$	−17.1968	+	22.5170i	−0.916591	+	1.20016i
$353$	−0.185474	+	1.05188i	−0.00987180	+	0.0559857i	−0.989346	−	0.145585i	$-0.953494\pi$
$353$	−0.185474	+	1.05188i	−0.00987180	+	0.0559857i	0.979474	+	0.201571i	$0.0646046\pi$
$354$	−22.2082	+	7.32873i	−1.18036	+	0.389518i
$355$	−3.45005	+	9.47895i	−0.183110	+	0.503090i
$356$	−30.7779	−	5.95361i	−1.63123	−	0.315541i
$357$	5.07612	−	10.2874i	0.268656	−	0.544467i
$358$	20.3251	+	1.94777i	1.07421	+	0.102943i
$359$	5.68242	−	9.84224i	0.299907	−	0.519453i	−0.676208	−	0.736711i	$-0.736378\pi$
$359$	5.68242	−	9.84224i	0.299907	−	0.519453i	0.976114	+	0.217258i	$0.0697111\pi$
$360$	17.9221	−	22.1729i	0.944578	−	1.16862i
$361$	−4.52830	−	7.84324i	−0.238331	−	0.412802i
$362$	2.84572	+	6.23686i	0.149568	+	0.327802i
$363$	−22.3333	+	9.82077i	−1.17219	+	0.515457i
$364$	−10.5283	−	9.13529i	−0.551830	−	0.478819i
$365$	3.12802	−	0.551554i	0.163728	−	0.0288697i
$366$	20.9416	+	0.635103i	1.09463	+	0.0331974i
$367$	6.59453	+	5.53346i	0.344231	+	0.288844i	0.798469	−	0.602036i	$-0.205644\pi$
$367$	6.59453	+	5.53346i	0.344231	+	0.288844i	−0.454237	+	0.890881i	$0.650088\pi$
$368$	11.8720	−	3.88132i	0.618872	−	0.202328i
$369$	3.59103	+	4.68437i	0.186942	+	0.243858i
$370$	19.3271	+	28.0937i	1.00477	+	1.46052i
$371$	6.18687	+	16.9983i	0.321206	+	0.882507i
$372$	3.02926	−	0.687615i	0.157060	−	0.0356512i
$373$	24.5912	+	29.3067i	1.27328	+	1.51744i	0.742318	+	0.670048i	$0.233726\pi$
$373$	24.5912	+	29.3067i	1.27328	+	1.51744i	0.530966	+	0.847393i	$0.321829\pi$
$374$	−17.3227	−	17.6117i	−0.895737	−	0.910681i
$375$	5.18799	+	5.42193i	0.267907	+	0.279988i
$376$	0.495415	+	7.92275i	0.0255491	+	0.408584i
$377$	−24.6557			−1.26983
$378$	−6.05982	−	12.5708i	−0.311684	−	0.646572i
$379$		−	22.1132i		−	1.13588i	−0.823071	−	0.567939i	$-0.807741\pi$
$379$		−	22.1132i		−	1.13588i	0.823071	−	0.567939i	$-0.192259\pi$
$380$	18.5240	−	10.2900i	0.950260	−	0.527867i
$381$	17.2055	+	5.01921i	0.881462	+	0.257142i
$382$	−26.4958	+	26.0610i	−1.35564	+	1.33340i
$383$	−1.25391	+	1.05215i	−0.0640717	+	0.0537626i	−0.674261	−	0.738493i	$-0.735538\pi$
$383$	−1.25391	+	1.05215i	−0.0640717	+	0.0537626i	0.610189	+	0.792256i	$0.291093\pi$
$384$	−15.9694	+	11.3569i	−0.814935	+	0.579553i
$385$	−30.0312	+	10.9305i	−1.53053	+	0.557069i
$386$	3.26655	+	4.74824i	0.166263	+	0.241679i
$387$	5.42975	−	24.4390i	0.276010	−	1.24231i
$388$	−1.57392	+	4.11136i	−0.0799036	+	0.208723i
$389$	7.37158	−	8.78511i	0.373754	−	0.445423i	−0.546079	−	0.837734i	$-0.683880\pi$
$389$	7.37158	−	8.78511i	0.373754	−	0.445423i	0.919832	+	0.392311i	$0.128324\pi$
$390$	26.6040	−	14.3026i	1.34715	−	0.724240i
$391$	1.89109	+	10.7249i	0.0956363	+	0.542380i
$392$	−3.83939	−	8.79719i	−0.193918	−	0.444325i
$393$	15.4751	+	1.69838i	0.780615	+	0.0856722i
$394$	6.03988	+	13.2374i	0.304285	+	0.666889i
$395$	−13.4594	+	7.77079i	−0.677216	+	0.390991i
$396$	−29.8567	+	3.41536i	−1.50035	+	0.171628i
$397$	−2.58188	−	1.49065i	−0.129581	−	0.0748137i	0.433808	−	0.901005i	$-0.357170\pi$
$397$	−2.58188	−	1.49065i	−0.129581	−	0.0748137i	−0.563389	+	0.826192i	$0.690503\pi$
$398$	−0.186319	+	1.94425i	−0.00933930	+	0.0974564i
$399$	−0.675996	−	10.3500i	−0.0338421	−	0.518150i
$400$	−11.8512	−	22.1915i	−0.592561	−	1.10958i
$401$	−8.85877	−	3.22433i	−0.442386	−	0.161015i	0.111217	−	0.993796i	$-0.464525\pi$
$401$	−8.85877	−	3.22433i	−0.442386	−	0.161015i	−0.553603	+	0.832781i	$0.686747\pi$
$402$	6.95761	−	33.4878i	0.347014	−	1.67022i
$403$	3.24096	+	0.571468i	0.161443	+	0.0284668i
$404$	−27.8292	+	22.5776i	−1.38456	+	1.12328i
$405$	30.1271	−	2.60797i	1.49703	−	0.129591i
$406$	16.2887	+	7.76023i	0.808394	+	0.385134i
$407$	6.24142	−	35.3969i	0.309376	−	1.75456i
$408$	−7.84028	−	15.1805i	−0.388152	−	0.751549i
$409$	−24.0695	−	8.76058i	−1.19016	−	0.433183i	−0.330380	−	0.943848i	$-0.607177\pi$
$409$	−24.0695	−	8.76058i	−1.19016	−	0.433183i	−0.859779	+	0.510665i	$0.829399\pi$
$410$	9.05008	−	2.34490i	0.446952	−	0.115806i
$411$	−29.1316	+	1.90268i	−1.43695	+	0.0938523i
$412$	−23.9527	−	14.3626i	−1.18006	−	0.707595i
$413$	15.7019	+	9.06552i	0.772642	+	0.446085i
$414$	11.6973	+	6.21962i	0.574891	+	0.305678i
$415$	3.63022	+	6.28773i	0.178201	+	0.308652i
$416$	−20.2583	+	4.53945i	−0.993244	+	0.222565i
$417$	18.9696	+	2.08191i	0.928945	+	0.101951i
$418$	−21.5259	−	5.95913i	−1.05287	−	0.291470i
$419$	−2.41298	+	0.425474i	−0.117882	+	0.0207858i	−0.232278	−	0.972649i	$-0.574618\pi$
$419$	−2.41298	+	0.425474i	−0.117882	+	0.0207858i	0.114396	+	0.993435i	$0.463507\pi$
$420$	−22.0775	+	1.07550i	−1.07727	+	0.0524788i
$421$	8.35420	−	9.95615i	0.407159	−	0.485233i	−0.523030	−	0.852314i	$-0.675198\pi$
$421$	8.35420	−	9.95615i	0.407159	−	0.485233i	0.930189	+	0.367081i	$0.119643\pi$
$422$	−1.28950	−	16.2901i	−0.0627720	−	0.792988i
$423$	−5.69115	+	6.20509i	−0.276713	+	0.301702i
$424$	25.8427	+	7.61667i	1.25503	+	0.369898i
$425$	20.6122	−	7.50223i	0.999838	−	0.363911i
$426$	7.27749	−	1.05686i	0.352595	−	0.0512050i
$427$	−10.4409	−	12.4430i	−0.505272	−	0.602160i
$428$	23.3504	−	8.06391i	1.12868	−	0.389784i
$429$	−30.5636	−	8.91608i	−1.47562	−	0.430472i
$430$	−32.2927	−	23.0120i	−1.55729	−	1.10974i
$431$	26.6357			1.28300			0.641499	−	0.767124i	$-0.278313\pi$
$431$	26.6357			1.28300			0.641499	+	0.767124i	$0.278313\pi$
$432$	−20.4242	−	3.85375i	−0.982661	−	0.185414i
$433$	27.8356			1.33769			0.668846	−	0.743401i	$-0.266788\pi$
$433$	27.8356			1.33769			0.668846	+	0.743401i	$0.266788\pi$
$434$	−1.96126	−	1.39761i	−0.0941435	−	0.0670874i
$435$	−28.2488	+	27.0299i	−1.35442	+	1.29599i
$436$	−4.13003	+	1.42628i	−0.197792	+	0.0683064i
$437$	6.32923	+	7.54288i	0.302768	+	0.360825i
$438$	−1.43396	−	1.81813i	−0.0685173	−	0.0868736i
$439$	15.2198	−	5.53956i	0.726402	−	0.264389i	0.0477612	−	0.998859i	$-0.484791\pi$
$439$	15.2198	−	5.53956i	0.726402	−	0.264389i	0.678641	+	0.734470i	$0.262569\pi$
$440$	−13.4565	+	45.6569i	−0.641515	+	2.17661i
$441$	3.90032	−	9.40401i	0.185729	−	0.447810i
$442$	−1.42840	−	18.0447i	−0.0679420	−	0.858300i
$443$	11.8910	−	14.1711i	0.564957	−	0.673290i	−0.405631	−	0.914037i	$-0.632948\pi$
$443$	11.8910	−	14.1711i	0.564957	−	0.673290i	0.970588	+	0.240747i	$0.0773925\pi$
$444$	11.3675	−	22.1082i	0.539475	−	1.04921i
$445$	−51.8650	+	9.14520i	−2.45864	+	0.433524i
$446$	4.14693	+	1.14802i	0.196363	+	0.0543601i
$447$	−7.53923	−	17.1449i	−0.356593	−	0.810924i
$448$	14.8123	+	3.37720i	0.699817	+	0.159558i
$449$	3.76662	+	6.52398i	0.177758	+	0.307886i	0.941112	−	0.338094i	$-0.109782\pi$
$449$	3.76662	+	6.52398i	0.177758	+	0.307886i	−0.763354	+	0.645980i	$0.776449\pi$
$450$	8.24587	−	25.3779i	0.388714	−	1.19632i
$451$	−8.53403	−	4.92713i	−0.401852	−	0.232009i
$452$	27.1405	+	16.2741i	1.27658	+	0.765471i
$453$	−0.490027	+	0.993103i	−0.0230235	+	0.0466600i
$454$	1.36659	−	0.354087i	0.0641373	−	0.0166181i
$455$	−22.0052	−	8.00925i	−1.03162	−	0.375479i
$456$	−13.0019	−	8.34226i	−0.608868	−	0.390662i
$457$	−2.46966	+	14.0062i	−0.115526	+	0.655180i	0.870962	+	0.491350i	$0.163496\pi$
$457$	−2.46966	+	14.0062i	−0.115526	+	0.655180i	−0.986488	+	0.163831i	$0.947615\pi$
$458$	1.09679	+	0.522533i	0.0512499	+	0.0244164i
$459$	5.83693	−	17.1563i	0.272445	−	0.800788i
$460$	16.2954	−	13.2203i	0.759776	−	0.616399i
$461$	−12.3225	−	2.17278i	−0.573914	−	0.101197i	−0.120844	−	0.992672i	$-0.538560\pi$
$461$	−12.3225	−	2.17278i	−0.573914	−	0.101197i	−0.453070	+	0.891475i	$0.649671\pi$
$462$	17.3855	+	15.5101i	0.808845	+	0.721594i
$463$	−5.11858	−	1.86301i	−0.237881	−	0.0865815i	0.220329	−	0.975426i	$-0.429287\pi$
$463$	−5.11858	−	1.86301i	−0.237881	−	0.0865815i	−0.458210	+	0.888844i	$0.651509\pi$
$464$	23.7042	−	12.6591i	1.10044	−	0.587682i
$465$	4.33976	−	2.89830i	0.201251	−	0.134405i
$466$	1.39596	−	14.5670i	0.0646666	−	0.674801i
$467$	−6.32947	−	3.65432i	−0.292893	−	0.169102i	0.346353	−	0.938104i	$-0.387420\pi$
$467$	−6.32947	−	3.65432i	−0.292893	−	0.169102i	−0.639246	+	0.769003i	$0.720753\pi$
$468$	−18.3676	−	12.1454i	−0.849044	−	0.561420i
$469$	−22.9645	+	13.2585i	−1.06040	+	0.612222i
$470$	5.53591	+	12.1328i	0.255353	+	0.559646i
$471$	−9.45179	+	12.8844i	−0.435515	+	0.593683i
$472$	24.7497	−	10.8016i	1.13920	−	0.497184i
$473$	7.25787	+	41.1614i	0.333717	+	1.89260i
$474$	9.63593	+	5.95989i	0.442593	+	0.273747i
$475$	12.7482	−	15.1927i	0.584926	−	0.697088i
$476$	−4.73580	+	12.3708i	−0.217065	+	0.567013i
$477$	13.1834	+	25.3533i	0.603624	+	1.16085i
$478$	−9.81725	−	14.2703i	−0.449031	−	0.652708i
$479$	6.51285	−	2.37048i	0.297580	−	0.108310i	−0.188916	−	0.981993i	$-0.560497\pi$
$479$	6.51285	−	2.37048i	0.297580	−	0.108310i	0.486495	+	0.873683i	$0.338275\pi$
$480$	−18.2339	+	27.4100i	−0.832262	+	1.25109i
$481$	20.1753	−	16.9291i	0.919914	−	0.771900i
$482$	−15.1123	+	14.8643i	−0.688346	+	0.677051i
$483$	−2.43899	−	9.97724i	−0.110978	−	0.453980i
$484$	24.6269	−	13.6802i	1.11940	−	0.621826i
$485$			7.39586i			0.335829i
$486$	−12.0746	−	18.4446i	−0.547715	−	0.836665i
$487$	29.6823			1.34503			0.672517	−	0.740081i	$-0.265213\pi$
$487$	29.6823			1.34503			0.672517	+	0.740081i	$0.265213\pi$
$488$	−24.1452	+	1.50982i	−1.09300	+	0.0683462i
$489$	14.0663	−	3.43859i	0.636100	−	0.155498i
$490$	−11.3077	−	11.4963i	−0.510828	−	0.519350i
$491$	5.65695	+	6.74169i	0.255295	+	0.304248i	0.878435	−	0.477862i	$-0.158588\pi$
$491$	5.65695	+	6.74169i	0.255295	+	0.304248i	−0.623140	+	0.782110i	$0.714144\pi$
$492$	−4.62980	−	5.00167i	−0.208728	−	0.225493i
$493$	8.01361	+	22.0172i	0.360915	+	0.991606i
$494$	−9.27606	−	13.4836i	−0.417350	−	0.606657i
$495$	−44.7923	+	23.2913i	−2.01326	+	1.04687i
$496$	−3.40930	+	1.11460i	−0.153082	+	0.0500471i
$497$	−4.36747	−	3.66474i	−0.195908	−	0.164386i
$498$	2.78424	−	4.50154i	0.124765	−	0.201719i
$499$	14.6580	−	2.58460i	0.656181	−	0.115702i	0.164362	−	0.986400i	$-0.447443\pi$
$499$	14.6580	−	2.58460i	0.656181	−	0.115702i	0.491819	+	0.870698i	$0.336332\pi$
$500$	−6.54478	−	5.67886i	−0.292691	−	0.253966i
$501$	8.70654	+	6.38697i	0.388980	+	0.285349i
$502$	−9.37872	−	20.5550i	−0.418593	−	0.917413i
$503$	−5.25851	−	9.10801i	−0.234465	−	0.406106i	0.724652	−	0.689115i	$-0.242001\pi$
$503$	−5.25851	−	9.10801i	−0.234465	−	0.406106i	−0.959117	+	0.283009i	$0.908667\pi$
$504$	8.31183	+	13.8049i	0.370238	+	0.614919i
$505$	−30.1020	+	52.1381i	−1.33952	+	2.32012i
$506$	−22.0170	−	2.10990i	−0.978776	−	0.0937967i
$507$	−0.451049	−	0.675377i	−0.0200318	−	0.0299945i
$508$	−20.3186	−	3.93038i	−0.901492	−	0.174382i
$509$	8.68462	−	23.8608i	0.384939	−	1.05761i	−0.584310	−	0.811531i	$-0.698635\pi$
$509$	8.68462	−	23.8608i	0.384939	−	1.05761i	0.969249	−	0.246081i	$-0.0791430\pi$
$510$	−21.4189	−	19.1084i	−0.948445	−	0.846136i
$511$	−0.311738	+	1.76795i	−0.0137905	+	0.0782096i
$512$	17.1458	−	14.7656i	0.757744	−	0.652552i
$513$	−3.18553	−	16.0725i	−0.140645	−	0.709617i
$514$	4.76877	−	10.0096i	0.210341	−	0.441506i
$515$	−46.2072	−	8.14757i	−2.03613	−	0.359025i
$516$	−3.62866	+	28.6792i	−0.159743	+	1.26253i
$517$	4.80776	−	13.2092i	0.211445	−	0.580941i
$518$	−18.6571	+	4.83409i	−0.819744	+	0.212398i
$519$	13.8409	+	6.82949i	0.607546	+	0.299782i
$520$	−29.0577	+	19.2899i	−1.27427	+	0.845918i
$521$	−5.54892	+	9.61101i	−0.243103	+	0.421066i	−0.961596	−	0.274467i	$-0.911498\pi$
$521$	−5.54892	+	9.61101i	−0.243103	+	0.421066i	0.718494	+	0.695533i	$0.244832\pi$
$522$	27.1077	+	8.80795i	1.18647	+	0.385514i
$523$	21.2339	−	12.2594i	0.928493	−	0.536066i	0.0421586	−	0.999111i	$-0.486577\pi$
$523$	21.2339	−	12.2594i	0.928493	−	0.536066i	0.886335	+	0.463045i	$0.153243\pi$
$524$	−17.9739	−	0.297401i	−0.785194	−	0.0129920i
$525$	−18.9376	+	8.32755i	−0.826503	+	0.363444i
$526$	−28.0957	−	7.77789i	−1.22503	−	0.339132i
$527$	−0.543064	−	3.07987i	−0.0236563	−	0.134161i
$528$	33.9620	−	7.12038i	1.47800	−	0.309875i
$529$	−10.1496	−	8.51656i	−0.441289	−	0.370285i
$530$	45.1208	−	3.57171i	1.95992	−	0.155145i
$531$	26.4569	+	10.9730i	1.14813	+	0.476188i
$532$	1.88431	+	11.8275i	0.0816951	+	0.512787i
$533$	−2.46961	−	6.78519i	−0.106971	−	0.293899i
$534$	23.7762	+	30.1460i	1.02890	+	1.30455i
$535$	31.7922	−	26.6768i	1.37450	−	1.15334i
$536$	−4.41738	+	39.2463i	−0.190802	+	1.69518i
$537$	−17.2886	−	18.0682i	−0.746058	−	0.779700i
$538$	−13.1088	+	18.3955i	−0.565158	+	0.793085i
$539$			16.9970i			0.732112i
$540$	−34.3593	+	6.22102i	−1.47859	+	0.267710i
$541$			10.1117i			0.434737i	0.976090	+	0.217369i	$0.0697474\pi$
$541$			10.1117i			0.434737i	−0.976090	+	0.217369i	$0.930253\pi$
$542$	8.28587	+	5.90458i	0.355909	+	0.253623i
$543$	2.35132	−	8.06015i	0.100905	−	0.345894i
$544$	10.6380	+	16.6150i	0.456102	+	0.712361i
$545$	−5.62314	+	4.71838i	−0.240869	+	0.202113i
$546$	2.45348	+	16.8946i	0.104999	+	0.723021i
$547$	−9.82775	−	27.0015i	−0.420204	−	1.15450i	−0.951590	−	0.307371i	$-0.900551\pi$
$547$	−9.82775	−	27.0015i	−0.420204	−	1.15450i	0.531386	−	0.847130i	$-0.321672\pi$
$548$	33.2901	−	5.30364i	1.42208	−	0.226560i
$549$	−18.9105	−	17.3442i	−0.807081	−	0.740234i
$550$	3.51548	+	44.4104i	0.149900	+	1.89367i
$551$	16.2283	+	13.6172i	0.691348	+	0.580110i
$552$	−14.1141	−	5.89972i	−0.600735	−	0.251109i
$553$	−1.52534	−	8.65063i	−0.0648640	−	0.367862i
$554$	7.12384	−	25.7331i	0.302663	−	1.09330i
$555$	4.55617	−	41.5143i	0.193399	−	1.76218i
$556$	−22.0327	−	0.364558i	−0.934395	−	0.0154607i
$557$	−10.4290	+	6.02119i	−0.441891	+	0.255126i	−0.704400	−	0.709804i	$-0.748784\pi$
$557$	−10.4290	+	6.02119i	−0.441891	+	0.255126i	0.262508	+	0.964930i	$0.415450\pi$
$558$	−3.35912	−	1.78609i	−0.142203	−	0.0756114i
$559$	−15.3130	+	26.5230i	−0.647673	+	1.12180i
$560$	25.2683	−	3.59806i	1.06778	−	0.152046i
$561$	1.97187	+	30.1908i	0.0832523	+	1.27466i
$562$	−6.53511	−	25.2221i	−0.275667	−	1.06393i
$563$	1.52700	−	4.19539i	0.0643553	−	0.176815i	−0.903347	−	0.428910i	$-0.858898\pi$
$563$	1.52700	−	4.19539i	0.0643553	−	0.176815i	0.967702	+	0.252096i	$0.0811198\pi$
$564$	5.87959	−	7.74296i	0.247575	−	0.326038i
$565$	52.3569	+	9.23194i	2.20267	+	0.388390i
$566$	−11.1793	−	5.32604i	−0.469903	−	0.223870i
$567$	−4.43873	+	16.5051i	−0.186409	+	0.693148i
$568$	−8.25414	+	1.99354i	−0.346336	+	0.0836473i
$569$	5.31792	−	30.1594i	0.222939	−	1.26435i	−0.643648	−	0.765322i	$-0.722580\pi$
$569$	5.31792	−	30.1594i	0.222939	−	1.26435i	0.866586	−	0.499027i	$-0.166309\pi$
$570$	−25.4099	−	5.27930i	−1.06430	−	0.221125i
$571$	−4.43557	+	12.1866i	−0.185623	+	0.509994i	−0.997244	−	0.0741895i	$-0.976363\pi$
$571$	−4.43557	+	12.1866i	−0.185623	+	0.509994i	0.811621	+	0.584184i	$0.198585\pi$
$572$	36.0938	+	6.98189i	1.50916	+	0.291928i
$573$	45.4202	−	2.96655i	1.89746	−	0.123929i
$574$	−0.504060	+	5.25991i	−0.0210391	+	0.219544i
$575$	9.81971	−	17.0082i	0.409510	−	0.709292i
$576$	23.8947	+	2.24612i	0.995611	+	0.0935884i
$577$	−9.34815	−	16.1915i	−0.389169	−	0.674060i	0.603169	−	0.797613i	$-0.293904\pi$
$577$	−9.34815	−	16.1915i	−0.389169	−	0.674060i	−0.992338	+	0.123553i	$0.960571\pi$
$578$	6.22298	−	2.83939i	0.258842	−	0.118103i
$579$	0.770057	−	7.01649i	0.0320025	−	0.291595i
$580$	29.5874	−	34.0989i	1.22855	−	1.41588i
$581$	−4.04125	+	0.712582i	−0.167659	+	0.0295629i
$582$	4.74895	−	2.55308i	0.196850	−	0.105829i
$583$	−36.5468	−	30.6664i	−1.51361	−	1.27007i
$584$	1.84315	+	1.93698i	0.0762702	+	0.0801530i
$585$	−36.1128	−	8.02337i	−1.49308	−	0.331726i
$586$	15.9335	−	10.9615i	0.658207	−	0.452814i
$587$	9.91990	+	27.2547i	0.409438	+	1.12492i	0.957487	+	0.288475i	$0.0931484\pi$
$587$	9.91990	+	27.2547i	0.409438	+	1.12492i	−0.548049	+	0.836446i	$0.684629\pi$
$588$	−3.47843	+	11.2293i	−0.143448	+	0.463089i
$589$	−1.81757	−	2.16609i	−0.0748916	−	0.0892523i
$590$	32.3433	−	31.8126i	1.33155	−	1.30970i
$591$	4.99055	−	17.1072i	0.205284	−	0.703697i
$592$	−10.7048	+	26.6345i	−0.439963	+	1.09467i
$593$	12.4895			0.512883			0.256441	−	0.966560i	$-0.417450\pi$
$593$	12.4895			0.512883			0.256441	+	0.966560i	$0.417450\pi$
$594$	30.4180	+	20.7213i	1.24807	+	0.850204i
$595$			22.2536i			0.912308i
$596$	10.5020	+	18.9056i	0.430179	+	0.774404i
$597$	1.72836	−	1.65379i	0.0707370	−	0.0676849i
$598$	−11.3647	−	11.5543i	−0.464738	−	0.472491i
$599$	7.49705	−	6.29078i	0.306321	−	0.257034i	−0.476648	−	0.879094i	$-0.658148\pi$
$599$	7.49705	−	6.29078i	0.306321	−	0.257034i	0.782970	+	0.622060i	$0.213704\pi$
$600$	−6.76603	+	30.0598i	−0.276222	+	1.22719i
$601$	27.8247	−	10.1274i	1.13499	−	0.413103i	0.294890	−	0.955531i	$-0.404717\pi$
$601$	27.8247	−	10.1274i	1.13499	−	0.413103i	0.840102	+	0.542428i	$0.182495\pi$
$602$	18.4645	−	12.7026i	0.752555	−	0.517720i
$603$	−33.2452	+	25.4857i	−1.35385	+	1.03786i
$604$	0.457174	−	1.19422i	0.0186022	−	0.0485922i
$605$	30.4217	−	36.2551i	1.23682	−	1.47398i
$606$	43.8697	+	1.33045i	1.78208	+	0.0540459i
$607$	1.41051	+	7.99939i	0.0572507	+	0.324685i	0.999960	−	0.00892998i	$-0.00284254\pi$
$607$	1.41051	+	7.99939i	0.0572507	+	0.324685i	−0.942709	+	0.333615i	$0.891731\pi$
$608$	15.8410	+	8.20064i	0.642439	+	0.332580i
$609$	−8.89519	−	20.2284i	−0.360451	−	0.819698i
$610$	−36.9758	+	16.8712i	−1.49711	+	0.683093i
$611$	8.92020	−	5.15008i	0.360873	−	0.208350i
$612$	−4.87581	+	20.3496i	−0.197093	+	0.822583i
$613$	−10.1533	−	5.86202i	−0.410088	−	0.236765i	0.280739	−	0.959784i	$-0.409420\pi$
$613$	−10.1533	−	5.86202i	−0.410088	−	0.236765i	−0.690828	+	0.723019i	$0.742754\pi$
$614$	34.7106	+	3.32634i	1.40081	+	0.134240i
$615$	−10.2681	−	5.06658i	−0.414049	−	0.204304i
$616$	−21.6477	−	15.9729i	−0.872212	−	0.643565i
$617$	−1.24227	−	0.452149i	−0.0500118	−	0.0182028i	0.316893	−	0.948461i	$-0.397360\pi$
$617$	−1.24227	−	0.452149i	−0.0500118	−	0.0182028i	−0.366905	+	0.930258i	$0.619583\pi$
$618$	10.7193	+	32.4826i	0.431192	+	1.30664i
$619$	25.4782	+	4.49249i	1.02405	+	0.180568i	0.660359	−	0.750950i	$-0.270404\pi$
$619$	25.4782	+	4.49249i	1.02405	+	0.180568i	0.363695	+	0.931518i	$0.381515\pi$
$620$	−4.67956	+	3.79648i	−0.187936	+	0.152470i
$621$	−5.87033	−	15.1263i	−0.235568	−	0.606998i
$622$	−0.775795	+	1.62839i	−0.0311065	+	0.0652925i
$623$	5.16886	−	29.3141i	0.207086	−	1.17444i
$624$	22.4171	+	11.9993i	0.897400	+	0.480356i
$625$	15.8714	+	5.77673i	0.634858	+	0.231069i
$626$	7.10484	+	27.4210i	0.283967	+	1.09596i
$627$	15.1926	+	22.7486i	0.606733	+	0.908491i
$628$	9.48887	−	15.8247i	0.378647	−	0.631474i
$629$	−21.6749	−	12.5140i	−0.864233	−	0.498965i
$630$	21.3325	+	16.6669i	0.849906	+	0.664025i
$631$	−6.70635	−	11.6157i	−0.266976	−	0.462415i	0.701104	−	0.713059i	$-0.252691\pi$
$631$	−6.70635	−	11.6157i	−0.266976	−	0.462415i	−0.968079	+	0.250644i	$0.919358\pi$
$632$	−11.7163	−	5.82159i	−0.466048	−	0.231571i
$633$	−11.8379	+	16.1371i	−0.470515	+	0.641393i
$634$	2.26555	−	8.18375i	0.0899765	−	0.325018i
$635$	−34.2396	+	6.03736i	−1.35876	+	0.239585i
$636$	−17.8693	−	27.7395i	−0.708564	−	1.09994i
$637$	−8.00557	+	9.54067i	−0.317192	+	0.378015i
$638$	−47.4376	+	3.75511i	−1.87807	+	0.148666i
$639$	−7.59384	−	4.84270i	−0.300408	−	0.191574i
$640$	18.0323	−	33.4647i	0.712789	−	1.32281i
$641$	−30.4904	+	11.0976i	−1.20430	+	0.438328i	−0.864722	−	0.502251i	$-0.832505\pi$
$641$	−30.4904	+	11.0976i	−1.20430	+	0.438328i	−0.339575	+	0.940579i	$0.610283\pi$
$642$	−28.1042	−	11.2051i	−1.10918	−	0.442230i
$643$	17.3052	+	20.6235i	0.682449	+	0.813312i	0.990420	−	0.138084i	$-0.0440944\pi$
$643$	17.3052	+	20.6235i	0.682449	+	0.813312i	−0.307971	+	0.951396i	$0.599650\pi$
$644$	3.87141	+	11.2103i	0.152555	+	0.441748i
$645$	11.5324	+	47.1758i	0.454087	+	1.85755i
$646$	−9.02579	+	12.6659i	−0.355115	+	0.498332i
$647$	25.1491			0.988713			0.494356	−	0.869259i	$-0.335404\pi$
$647$	25.1491			0.988713			0.494356	+	0.869259i	$0.335404\pi$
$648$	15.8555	+	19.9149i	0.622864	+	0.782330i
$649$	−47.8188			−1.87705
$650$	−18.9440	+	26.5840i	−0.743044	+	1.04271i
$651$	0.700407	+	2.86517i	0.0274511	+	0.112295i
$652$	−15.8047	+	5.45807i	−0.618960	+	0.213754i
$653$	−13.3995	−	15.9689i	−0.524363	−	0.624912i	0.437243	−	0.899343i	$-0.355955\pi$
$653$	−13.3995	−	15.9689i	−0.524363	−	0.624912i	−0.961607	+	0.274431i	$0.911510\pi$
$654$	4.97084	+	1.98187i	0.194375	+	0.0774972i
$655$	−28.3788	+	10.3291i	−1.10885	+	0.403589i
$656$	5.85805	+	5.25537i	0.228718	+	0.205188i
$657$	−0.125002	+	2.83322i	−0.00487678	+	0.110534i
$658$	−7.51406	+	0.594804i	−0.292929	+	0.0231879i
$659$	18.1622	−	21.6448i	0.707497	−	0.843162i	−0.285856	−	0.958273i	$-0.592278\pi$
$659$	18.1622	−	21.6448i	0.707497	−	0.843162i	0.993353	+	0.115110i	$0.0367222\pi$
$660$	49.0080	−	31.5701i	1.90763	−	1.22886i
$661$	−37.0880	+	6.53962i	−1.44256	+	0.254362i	−0.839510	−	0.543344i	$-0.817158\pi$
$661$	−37.0880	+	6.53962i	−1.44256	+	0.254362i	−0.603046	+	0.797706i	$0.706047\pi$
$662$	−7.38044	+	26.6600i	−0.286849	+	1.03617i
$663$	−13.1130	+	17.8753i	−0.509267	+	0.694220i
$664$	−2.71963	+	5.47340i	−0.105542	+	0.212409i
$665$	10.0603	+	17.4250i	0.390123	+	0.675712i
$666$	−28.2295	+	11.4053i	−1.09387	+	0.441947i
$667$	18.1676	+	10.4891i	0.703452	+	0.406138i
$668$	−10.6934	−	6.41203i	−0.413740	−	0.248089i
$669$	−2.92682	−	4.38248i	−0.113158	−	0.169436i
$670$	16.6418	+	64.2288i	0.642930	+	2.48138i
$671$	40.2562	+	14.6521i	1.55407	+	0.565636i
$672$	−11.0330	−	14.9829i	−0.425609	−	0.577978i
$673$	0.887037	−	5.03064i	0.0341928	−	0.193917i	−0.962927	−	0.269763i	$-0.913055\pi$
$673$	0.887037	−	5.03064i	0.0341928	−	0.193917i	0.997120	+	0.0758462i	$0.0241658\pi$
$674$	−13.4076	+	28.1426i	−0.516443	+	1.08401i
$675$	−27.9510	+	16.9348i	−1.07583	+	0.651821i
$676$	0.590828	+	0.728258i	0.0227242	+	0.0280099i
$677$	−29.3482	−	5.17487i	−1.12794	−	0.198887i	−0.421617	−	0.906774i	$-0.638537\pi$
$677$	−29.3482	−	5.17487i	−1.12794	−	0.198887i	−0.706325	+	0.707888i	$0.749648\pi$
$678$	−12.1459	−	36.8057i	−0.466461	−	1.41352i
$679$	−3.92804	−	1.42969i	−0.150744	−	0.0548665i
$680$	26.6700	+	19.6786i	1.02275	+	0.754639i
$681$	−1.55051	−	0.765070i	−0.0594158	−	0.0293176i
$682$	6.32265	+	0.605903i	0.242107	+	0.0232012i
$683$	41.0964	+	23.7270i	1.57251	+	0.907889i	0.995860	+	0.0908981i	$0.0289738\pi$
$683$	41.0964	+	23.7270i	1.57251	+	0.907889i	0.576650	+	0.816991i	$0.304360\pi$
$684$	5.38171	+	18.1384i	0.205775	+	0.693537i
$685$	49.0450	−	28.3161i	1.87391	−	1.08190i
$686$	25.3952	−	11.5872i	0.969592	−	0.442401i
$687$	−0.598956	−	1.36208i	−0.0228516	−	0.0519664i
$688$	1.10432	−	33.3617i	0.0421019	−	1.27190i
$689$	−6.07041	−	34.4270i	−0.231264	−	1.31156i
$690$	−25.6879	−	0.779045i	−0.977920	−	0.0296577i
$691$	19.5742	−	23.3276i	0.744637	−	0.887424i	−0.252136	−	0.967692i	$-0.581133\pi$
$691$	19.5742	−	23.3276i	0.744637	−	0.887424i	0.996773	+	0.0802677i	$0.0255775\pi$
$692$	−16.6438	−	6.37163i	−0.632704	−	0.242213i
$693$	−3.71156	−	28.2922i	−0.140990	−	1.07473i
$694$	0.0378046	−	0.0260077i	0.00143504	−	0.000987239i
$695$	−34.7872	+	12.6615i	−1.31955	+	0.480278i
$696$	−32.1089	−	7.22724i	−1.21708	−	0.273948i
$697$	−5.25642	+	4.41066i	−0.199101	+	0.167066i
$698$	−32.2734	−	32.8118i	−1.22157	−	1.24195i
$699$	−12.9494	+	12.3907i	−0.489793	+	0.468659i
$700$	20.8824	−	11.6001i	0.789282	−	0.438444i
$701$		−	22.9653i		−	0.867386i	−0.901061	−	0.433693i	$-0.857210\pi$
$701$		−	22.9653i		−	0.867386i	0.901061	−	0.433693i	$-0.142790\pi$
$702$	7.31440	+	25.9580i	0.276064	+	0.979723i
$703$	−22.6291			−0.853473
$704$	−38.2856	+	11.8193i	−1.44294	+	0.445457i
$705$	4.57414	−	15.6798i	0.172272	−	0.590535i
$706$	−1.07690	+	1.05923i	−0.0405298	+	0.0398647i
$707$	−21.8723	−	26.0664i	−0.822591	−	0.980326i
$708$	−31.5922	−	9.78610i	−1.18731	−	0.367784i
$709$	−12.4178	−	34.1176i	−0.466361	−	1.28132i	−0.920625	−	0.390448i	$-0.872320\pi$
$709$	−12.4178	−	34.1176i	−0.466361	−	1.28132i	0.454264	−	0.890867i	$-0.349902\pi$
$710$	−11.7530	+	8.08545i	−0.441081	+	0.303442i
$711$	−4.16668	−	13.2362i	−0.156263	−	0.496395i
$712$	−30.5609	−	32.1167i	−1.14532	−	1.20363i
$713$	−2.14499	−	1.79986i	−0.0803305	−	0.0674053i
$714$	14.2892	−	7.68202i	0.534760	−	0.287492i
$715$	60.8229	−	10.7247i	2.27465	−	0.401082i
$716$	21.8100	+	18.9244i	0.815077	+	0.707237i
$717$	−2.31432	+	21.0873i	−0.0864299	+	0.787519i
$718$	14.6221	−	6.67172i	0.545694	−	0.248986i
$719$	13.7419	+	23.8016i	0.512485	+	0.887651i	0.999895	+	0.0144775i	$0.00460849\pi$
$719$	13.7419	+	23.8016i	0.512485	+	0.887651i	−0.487410	+	0.873173i	$0.662058\pi$
$720$	38.8386	−	10.8278i	1.44743	−	0.403527i
$721$	13.2596	−	22.9662i	0.493812	−	0.855308i
$722$	1.22180	−	12.7495i	0.0454706	−	0.474489i
$723$	25.9062	−	1.69202i	0.963462	−	0.0629270i
$724$	−1.84125	+	9.51855i	−0.0684294	+	0.353754i
$725$	14.4516	−	39.7054i	0.536719	−	1.47462i
$726$	−33.7814	−	7.01861i	−1.25375	−	0.260485i
$727$	−0.612001	+	3.47083i	−0.0226979	+	0.128726i	−0.994051	−	0.108914i	$-0.965263\pi$
$727$	−0.612001	+	3.47083i	−0.0226979	+	0.128726i	0.971353	+	0.237640i	$0.0763738\pi$
$728$	−4.62799	−	19.1619i	−0.171525	−	0.710186i
$729$	−3.56100	+	26.7641i	−0.131889	+	0.991265i
$730$	4.05523	+	1.93198i	0.150091	+	0.0715059i
$731$	28.6617	+	5.05384i	1.06009	+	0.186923i
$732$	23.5973	+	17.9185i	0.872182	+	0.662288i
$733$	4.83027	−	13.2711i	0.178410	−	0.490178i	−0.817963	−	0.575271i	$-0.804897\pi$
$733$	4.83027	−	13.2711i	0.178410	−	0.490178i	0.996373	+	0.0850933i	$0.0271188\pi$
$734$	3.05356	+	11.7851i	0.112709	+	0.434998i
$735$	1.28716	+	19.7075i	0.0474778	+	0.726922i
$736$	16.8585	+	5.27341i	0.621414	+	0.194380i
$737$	34.9680	−	60.5664i	1.28806	−	2.23099i
$738$	0.291285	+	8.34223i	0.0107223	+	0.307082i
$739$	−2.52352	+	1.45695i	−0.0928291	+	0.0535949i	−0.545696	−	0.837983i	$-0.683735\pi$
$739$	−2.52352	+	1.45695i	−0.0928291	+	0.0535949i	0.452867	+	0.891578i	$0.350401\pi$
$740$	−0.797822	+	48.2178i	−0.0293285	+	1.77252i
$741$	−2.18674	+	19.9248i	−0.0803319	+	0.731956i
$742$	−6.82529	+	24.6547i	−0.250564	+	0.905102i
$743$	0.918280	+	5.20783i	0.0336884	+	0.191057i	0.997008	−	0.0773010i	$-0.0246302\pi$
$743$	0.918280	+	5.20783i	0.0336884	+	0.191057i	−0.963319	+	0.268358i	$0.913519\pi$
$744$	4.05315	+	1.69423i	0.148596	+	0.0621134i
$745$	27.8324	+	23.3542i	1.01970	+	0.855631i
$746$	4.26943	+	53.9350i	0.156315	+	1.97470i
$747$	−6.18344	+	1.94652i	−0.226240	+	0.0712193i
$748$	−5.49649	−	34.5006i	−0.200971	−	1.26147i
$749$	8.02267	+	22.0421i	0.293142	+	0.805401i
$750$	1.52518	+	10.5023i	0.0556918	+	0.383491i
$751$	−27.0071	+	22.6616i	−0.985502	+	0.826935i	−0.984910	−	0.173065i	$-0.944633\pi$
$751$	−27.0071	+	22.6616i	−0.985502	+	0.826935i	−0.000591865		1.00000i	$0.500188\pi$
$752$	−5.93174	+	9.53127i	−0.216308	+	0.347570i
$753$	−7.74931	+	26.5640i	−0.282401	+	0.968047i
$754$	−28.3961	−	20.2353i	−1.03413	−	0.736926i
$755$		−	2.14827i		−	0.0781834i
$756$	3.33790	−	19.4513i	0.121398	−	0.707435i
$757$		−	38.9874i		−	1.41702i	−0.705700	−	0.708511i	$-0.749367\pi$
$757$		−	38.9874i		−	1.41702i	0.705700	−	0.708511i	$-0.250633\pi$
$758$	18.1486	−	25.4679i	0.659187	−	0.925035i
$759$	18.7278	+	19.5722i	0.679775	+	0.710428i
$760$	29.7794	+	3.35182i	1.08021	+	0.121583i
$761$	31.7399	−	26.6329i	1.15057	−	0.965443i	0.150837	−	0.988559i	$-0.451803\pi$
$761$	31.7399	−	26.6329i	1.15057	−	0.965443i	0.999733	+	0.0231155i	$0.00735856\pi$
$762$	15.6963	+	19.9014i	0.568616	+	0.720952i
$763$	−1.41899	−	3.89863i	−0.0513708	−	0.141140i
$764$	−51.9039	+	8.26913i	−1.87782	+	0.299166i
$765$	4.57264	+	34.8560i	0.165324	+	1.26022i
$766$	−2.30765	+	0.182671i	−0.0833789	+	0.00660017i
$767$	−26.8414	−	22.5226i	−0.969186	−	0.813244i
$768$	−27.7128	−	0.0265521i	−1.00000	−	0.000958117i
$769$	8.75977	+	49.6791i	0.315886	+	1.79148i	0.567210	+	0.823573i	$0.308023\pi$
$769$	8.75977	+	49.6791i	0.315886	+	1.79148i	−0.251325	+	0.967903i	$0.580866\pi$
$770$	−43.5580	−	12.0584i	−1.56972	−	0.434554i
$771$	−12.4307	+	5.46622i	−0.447679	+	0.196861i
$772$	−0.134843	+	8.14948i	−0.00485311	+	0.293306i
$773$	26.2565	−	15.1592i	0.944379	−	0.545238i	0.0530488	−	0.998592i	$-0.483106\pi$
$773$	26.2565	−	15.1592i	0.944379	−	0.545238i	0.891330	+	0.453354i	$0.149773\pi$
$774$	26.3110	−	23.6903i	0.945728	−	0.851531i
$775$	−2.81993	+	4.88427i	−0.101295	+	0.175448i
$776$	−5.18695	+	3.44334i	−0.186201	+	0.123609i
$777$	21.1680	+	10.4449i	0.759398	+	0.374710i
$778$	15.7000	−	4.06790i	0.562871	−	0.145841i
$779$	−2.12192	+	5.82994i	−0.0760258	+	0.208879i
$780$	42.3784	+	5.36195i	1.51739	+	0.191989i
$781$	14.8082	+	2.61109i	0.529879	+	0.0934320i
$782$	−6.62409	+	13.9040i	−0.236877	+	0.497204i
$783$	−18.0892	−	29.8563i	−0.646454	−	1.06698i
$784$	2.79813	−	13.2828i	0.0999333	−	0.474386i
$785$	5.38281	−	30.5275i	0.192121	−	1.08957i
$786$	16.4289	+	14.6567i	0.585998	+	0.522786i
$787$	−9.23473	+	25.3722i	−0.329182	+	0.904421i	0.659137	+	0.752023i	$0.270922\pi$
$787$	−9.23473	+	25.3722i	−0.329182	+	0.904421i	−0.988319	+	0.152398i	$0.951300\pi$
$788$	−3.90794	+	20.2026i	−0.139215	+	0.719687i
$789$	19.8295	+	29.6916i	0.705947	+	1.05705i
$790$	−21.8789	−	2.09666i	−0.778415	−	0.0745960i
$791$	−15.0243	+	26.0228i	−0.534202	+	0.925265i
$792$	−37.1892	−	20.5703i	−1.32146	−	0.730935i
$793$	15.6953	+	27.1851i	0.557356	+	0.965370i
$794$	−1.75017	−	3.83578i	−0.0621113	−	0.136127i
$795$	−44.6972	−	32.7891i	−1.58525	−	1.16291i
$796$	−1.81026	+	2.08629i	−0.0641629	+	0.0739466i
$797$	−52.0759	+	9.18239i	−1.84462	+	0.325257i	−0.983186	−	0.182608i	$-0.941546\pi$
$797$	−52.0759	+	9.18239i	−1.84462	+	0.325257i	−0.861437	+	0.507864i	$0.830435\pi$
$798$	7.71588	−	12.4750i	0.273139	−	0.441610i
$799$	−7.49821	−	6.29175i	−0.265268	−	0.222586i
$800$	4.56380	−	35.2846i	0.161355	−	1.24750i
$801$	2.07262	−	46.9770i	0.0732326	−	1.65985i
$802$	−7.55644	−	10.9840i	−0.266827	−	0.387858i
$803$	−1.61937	−	4.44918i	−0.0571463	−	0.157008i
$804$	35.4971	−	32.8579i	1.25188	−	1.15881i
$805$	12.8073	+	15.2631i	0.451398	+	0.537955i
$806$	3.26362	+	3.31806i	0.114956	+	0.116874i
$807$	26.8736	−	6.56941i	0.945996	−	0.231254i
$808$	−50.5808	+	3.16286i	−1.77943	+	0.111269i
$809$	−18.3017			−0.643453			−0.321727	−	0.946833i	$-0.604263\pi$
$809$	−18.3017			−0.643453			−0.321727	+	0.946833i	$0.604263\pi$
$810$	36.8380	+	21.7222i	1.29436	+	0.763239i
$811$		−	34.2759i		−	1.20359i	−0.798650	−	0.601795i	$-0.794452\pi$
$811$		−	34.2759i		−	1.20359i	0.798650	−	0.601795i	$-0.205548\pi$
$812$	12.3909	+	22.3059i	0.434834	+	0.782783i
$813$	−2.95906	−	12.1047i	−0.103779	−	0.424530i
$814$	36.2390	−	35.6444i	1.27018	−	1.24933i
$815$	−21.5186	+	18.0562i	−0.753762	+	0.632482i
$816$	3.42920	−	23.9182i	0.120046	−	0.837303i
$817$	24.7274	−	9.00005i	0.865103	−	0.314872i
$818$	−20.5310	−	29.8438i	−0.717851	−	1.04346i
$819$	11.2423	−	17.6290i	0.392836	−	0.616007i
$820$	12.3475	+	4.72690i	0.431194	+	0.165071i
$821$	−16.1380	+	19.2325i	−0.563221	+	0.671220i	−0.970225	−	0.242206i	$-0.922129\pi$
$821$	−16.1380	+	19.2325i	−0.563221	+	0.671220i	0.407004	+	0.913426i	$0.366573\pi$
$822$	−35.1125	−	21.7174i	−1.22469	−	0.757480i
$823$	−5.65012	−	32.0434i	−0.196951	−	1.11696i	−0.909613	−	0.415456i	$-0.863622\pi$
$823$	−5.65012	−	32.0434i	−0.196951	−	1.11696i	0.712662	−	0.701507i	$-0.247489\pi$
$824$	−15.7988	−	36.1998i	−0.550378	−	1.26108i
$825$	32.2729	−	43.9935i	1.12360	−	1.53166i
$826$	10.6438	+	23.3276i	0.370346	+	0.811672i
$827$	−39.6695	+	22.9032i	−1.37944	+	0.796423i	−0.992092	−	0.125509i	$-0.959944\pi$
$827$	−39.6695	+	22.9032i	−1.37944	+	0.796423i	−0.387352	+	0.921932i	$0.626610\pi$
$828$	8.36732	+	16.7633i	0.290784	+	0.582566i
$829$	17.0001	+	9.81500i	0.590437	+	0.340889i	0.765270	−	0.643709i	$-0.222605\pi$
$829$	17.0001	+	9.81500i	0.590437	+	0.340889i	−0.174833	+	0.984598i	$0.555939\pi$
$830$	−0.979483	+	10.2210i	−0.0339984	+	0.354776i
$831$	−27.1948	+	18.1620i	−0.943377	+	0.630032i
$832$	−27.0572	−	11.3982i	−0.938039	−	0.395160i
$833$	11.1217	+	4.04796i	0.385343	+	0.140253i
$834$	20.1387	+	17.9664i	0.697348	+	0.622124i
$835$	−20.6287	−	3.63739i	−0.713885	−	0.125877i
$836$	−19.9008	−	24.5298i	−0.688282	−	0.848380i
$837$	1.68579	+	4.34383i	0.0582694	+	0.150145i
$838$	−3.12824	−	1.49035i	−0.108063	−	0.0514833i
$839$	−8.40287	+	47.6550i	−0.290099	+	1.64523i	0.396381	+	0.918086i	$0.370266\pi$
$839$	−8.40287	+	47.6550i	−0.290099	+	1.64523i	−0.686480	+	0.727149i	$0.740845\pi$
$840$	−26.3095	−	16.8807i	−0.907764	−	0.582439i
$841$	15.1609	+	5.51810i	0.522788	+	0.190279i
$842$	17.7928	−	4.61014i	0.613179	−	0.158876i
$843$	−14.1203	+	28.6166i	−0.486329	+	0.985609i
$844$	11.8844	−	19.8197i	0.409077	−	0.682221i
$845$	1.36439	+	0.787733i	0.0469366	+	0.0270989i
$846$	−11.6471	+	2.47563i	−0.400437	+	0.0851139i
$847$	13.3748	+	23.1658i	0.459563	+	0.795987i
$848$	23.5121	+	29.9817i	0.807409	+	1.02958i
$849$	6.10500	+	13.8833i	0.209523	+	0.476473i
$850$	29.8964	+	8.27638i	1.02544	+	0.283877i
$851$	−22.0682	+	3.89122i	−0.756488	+	0.133389i
$852$	9.24891	+	4.75555i	0.316862	+	0.162922i
$853$	−30.1220	+	35.8980i	−1.03136	+	1.22912i	−0.0583624	+	0.998295i	$0.518588\pi$
$853$	−30.1220	+	35.8980i	−1.03136	+	1.22912i	−0.972995	+	0.230828i	$0.925857\pi$
$854$	−1.81271	−	22.8997i	−0.0620298	−	0.783612i
$855$	19.3381	+	25.2258i	0.661348	+	0.862703i
$856$	33.5109	+	9.87673i	1.14538	+	0.337580i
$857$	−5.93538	+	2.16030i	−0.202749	+	0.0737946i	−0.441399	−	0.897311i	$-0.645517\pi$
$857$	−5.93538	+	2.16030i	−0.202749	+	0.0737946i	0.238650	+	0.971106i	$0.423295\pi$
$858$	−27.8827	−	35.3527i	−0.951901	−	1.20692i
$859$	−19.3877	−	23.1054i	−0.661501	−	0.788346i	0.326100	−	0.945335i	$-0.394266\pi$
$859$	−19.3877	−	23.1054i	−0.661501	−	0.788346i	−0.987600	+	0.156990i	$0.949821\pi$
$860$	−18.3054	−	53.0061i	−0.624208	−	1.80749i
$861$	4.67584	−	4.47410i	0.159352	−	0.152477i
$862$	30.6765	+	21.8603i	1.04485	+	0.744566i
$863$	48.6885			1.65737			0.828687	−	0.559712i	$-0.189088\pi$
$863$	48.6885			1.65737			0.828687	+	0.559712i	$0.189088\pi$
$864$	−20.3599	−	21.2008i	−0.692657	−	0.721268i
$865$	−29.9404			−1.01800
$866$	32.0584	+	22.8451i	1.08939	+	0.776307i
$867$	−8.04221	−	2.34609i	−0.273128	−	0.0796774i
$868$	−1.11176	−	3.21927i	−0.0377355	−	0.109269i
$869$	14.8915	+	17.7470i	0.505161	+	0.602027i
$870$	−54.7181	+	7.94633i	−1.85512	+	0.269406i
$871$	48.1548	−	17.5269i	1.63166	−	0.593877i
$872$	−5.92715	−	1.74692i	−0.200718	−	0.0591581i
$873$	−6.44631	−	1.43221i	−0.218174	−	0.0484730i
$874$	1.09886	+	13.8817i	0.0371694	+	0.469554i
$875$	5.28869	−	6.30281i	0.178790	−	0.213074i
$876$	−0.159337	−	3.27082i	−0.00538349	−	0.110511i
$877$	−34.7601	+	6.12915i	−1.17377	+	0.206967i	−0.726328	−	0.687348i	$-0.758775\pi$
$877$	−34.7601	+	6.12915i	−1.17377	+	0.206967i	−0.447438	+	0.894315i	$0.647664\pi$
$878$	22.0752	+	6.11119i	0.745001	+	0.206243i
$879$	−23.5450	−	2.58406i	−0.794154	−	0.0871581i
$880$	−52.9693	+	41.5394i	−1.78559	+	1.40029i
$881$	7.22906	+	12.5211i	0.243553	+	0.421847i	0.961724	−	0.274020i	$-0.0883536\pi$
$881$	7.22906	+	12.5211i	0.243553	+	0.421847i	−0.718171	+	0.695867i	$0.755020\pi$
$882$	12.2100	−	7.62961i	0.411133	−	0.256902i
$883$	−30.6193	−	17.6781i	−1.03042	−	0.594915i	−0.113317	−	0.993559i	$-0.536148\pi$
$883$	−30.6193	−	17.6781i	−1.03042	−	0.594915i	−0.917106	+	0.398644i	$0.869481\pi$
$884$	13.1645	−	21.9545i	0.442769	−	0.738410i
$885$	−55.4444	+	3.62126i	−1.86374	+	0.121727i
$886$	25.3253	−	6.56186i	0.850822	−	0.220450i
$887$	−33.6657	−	12.2533i	−1.13038	−	0.411426i	−0.291952	−	0.956433i	$-0.594305\pi$
$887$	−33.6657	−	12.2533i	−1.13038	−	0.411426i	−0.838432	+	0.545007i	$0.816527\pi$
$888$	31.2365	−	16.1327i	1.04823	−	0.541377i
$889$	3.41231	−	19.3522i	0.114445	−	0.649051i
$890$	−67.2389	−	32.0338i	−2.25385	−	1.07378i
$891$	−11.6269	−	43.5518i	−0.389516	−	1.45904i
$892$	3.83385	+	4.72562i	0.128367	+	0.158225i
$893$	−8.71560	−	1.53680i	−0.291656	−	0.0514269i
$894$	5.38806	−	25.9334i	0.180204	−	0.867342i
$895$	45.5853	+	16.5917i	1.52375	+	0.554599i
$896$	14.2877	+	16.0462i	0.477320	+	0.536067i
$897$	1.29366	+	19.8070i	0.0431940	+	0.661335i
$898$	−1.01629	+	10.6050i	−0.0339139	+	0.353894i
$899$	−5.21720	−	3.01215i	−0.174003	−	0.100461i
$900$	30.3248	−	22.4603i	1.01083	−	0.748678i
$901$	−28.7699	+	16.6103i	−0.958463	+	0.553369i
$902$	−5.78493	−	12.6786i	−0.192617	−	0.422151i
$903$	−27.2850	−	2.99452i	−0.907988	−	0.0996514i
$904$	17.9015	+	41.0177i	0.595395	+	1.36423i
$905$	2.82829	+	16.0401i	0.0940157	+	0.533189i
$906$	−1.37942	+	0.741590i	−0.0458282	+	0.0246377i
$907$	5.65021	−	6.73365i	0.187612	−	0.223587i	−0.664037	−	0.747700i	$-0.731158\pi$
$907$	5.65021	−	6.73365i	0.187612	−	0.223587i	0.851649	+	0.524112i	$0.175603\pi$
$908$	1.86452	+	0.713778i	0.0618762	+	0.0236876i
$909$	−39.6149	−	36.3337i	−1.31394	−	1.20511i
$910$	−18.7703	−	27.2843i	−0.622228	−	0.904467i
$911$	13.4129	−	4.88190i	0.444389	−	0.161744i	−0.110127	−	0.993918i	$-0.535126\pi$
$911$	13.4129	−	4.88190i	0.444389	−	0.161744i	0.554516	+	0.832173i	$0.312903\pi$
$912$	−8.12772	−	20.2787i	−0.269136	−	0.671493i
$913$	8.29075	−	6.95676i	0.274384	−	0.230235i
$914$	−14.3394	+	14.1041i	−0.474305	+	0.466522i
$915$	47.7854	+	13.9401i	1.57974	+	0.460844i
$916$	0.834335	+	1.50196i	0.0275672	+	0.0496262i
$917$		−	17.0691i		−	0.563671i
$918$	20.8029	−	14.9686i	0.686597	−	0.494036i
$919$	−54.9336			−1.81209			−0.906046	−	0.423179i	$-0.860914\pi$
$919$	−54.9336			−1.81209			−0.906046	+	0.423179i	$0.860914\pi$
$920$	29.6176	−	1.85201i	0.976463	−	0.0610589i
$921$	−29.5250	−	30.8563i	−0.972881	−	1.01675i
$922$	−12.4086	−	12.6156i	−0.408656	−	0.415474i
$923$	7.08225	+	8.44030i	0.233115	+	0.277816i
$924$	7.29359	+	32.1316i	0.239941	+	1.05705i
$925$	15.4371	+	42.4130i	0.507567	+	1.39453i
$926$	−4.36610	−	6.34654i	−0.143479	−	0.208560i
$927$	16.0495	−	38.6968i	0.527136	−	1.27097i
$928$	37.6898	+	4.87488i	1.23723	+	0.160026i
$929$	20.0336	+	16.8102i	0.657282	+	0.551525i	0.909271	−	0.416205i	$-0.136640\pi$
$929$	20.0336	+	16.8102i	0.657282	+	0.551525i	−0.251989	+	0.967730i	$0.581085\pi$
$930$	7.37680	+	0.223719i	0.241895	+	0.00733603i
$931$	10.5385	−	1.85822i	0.345385	−	0.0609006i
$932$	13.5631	−	15.6312i	0.444273	−	0.512016i
$933$	2.02225	−	0.889258i	0.0662055	−	0.0291130i
$934$	−4.29053	−	9.40339i	−0.140390	−	0.307688i
$935$	−29.3458	−	50.8283i	−0.959709	−	1.66226i
$936$	−11.1862	−	29.0625i	−0.365633	−	0.949937i
$937$	30.0604	−	52.0662i	0.982031	−	1.70093i	0.327580	−	0.944823i	$-0.393767\pi$
$937$	30.0604	−	52.0662i	0.982031	−	1.70093i	0.654451	−	0.756105i	$-0.272900\pi$
$938$	−37.3298	−	3.57734i	−1.21886	−	0.116804i
$939$	15.3513	−	31.1114i	0.500972	−	1.01528i
$940$	−3.58186	+	18.5169i	−0.116827	+	0.603954i
$941$	−19.3533	+	53.1728i	−0.630900	+	1.73338i	0.0476846	+	0.998862i	$0.484816\pi$
$941$	−19.3533	+	53.1728i	−0.630900	+	1.73338i	−0.678585	+	0.734522i	$0.737406\pi$
$942$	−21.4601	+	7.08184i	−0.699208	+	0.230739i
$943$	−1.06683	+	6.05031i	−0.0347408	+	0.197025i
$944$	37.3694	+	7.87217i	1.21627	+	0.256217i
$945$	−6.44598	−	32.5229i	−0.209688	−	1.05797i
$946$	−25.4229	+	53.3625i	−0.826568	+	1.73496i
$947$	45.6408	+	8.04770i	1.48313	+	0.261515i	0.855826	−	0.517263i	$-0.173049\pi$
$947$	45.6408	+	8.04770i	1.48313	+	0.261515i	0.627299	+	0.778778i	$0.284160\pi$
$948$	6.20638	+	14.7724i	0.201574	+	0.479785i
$949$	1.18659	−	3.26012i	0.0385182	−	0.105828i
$950$	27.1510	−	7.03489i	0.880895	−	0.228242i
$951$	−8.64859	+	5.77594i	−0.280450	+	0.187298i
$952$	−15.6071	+	10.3607i	−0.505829	+	0.335793i
$953$	−2.93376	+	5.08142i	−0.0950338	+	0.164603i	−0.909623	−	0.415435i	$-0.863629\pi$
$953$	−2.93376	+	5.08142i	−0.0950338	+	0.164603i	0.814589	+	0.580039i	$0.196963\pi$
$954$	−5.62451	+	40.0194i	−0.182100	+	1.29568i
$955$	−76.4681	+	44.1489i	−2.47445	+	1.42862i
$956$	0.405256	−	24.4924i	0.0131069	−	0.792139i
$957$	46.9923	+	34.4727i	1.51905	+	1.11435i
$958$	9.44638	+	2.61509i	0.305199	+	0.0844898i
$959$	5.55822	+	31.5222i	0.179484	+	1.01791i
$960$	−43.4960	+	16.6035i	−1.40383	+	0.535874i
$961$	−23.1314	−	19.4095i	−0.746174	−	0.626114i
$962$	37.1300	−	2.93916i	1.19712	−	0.0947625i
$963$	17.0952	+	32.8763i	0.550885	+	1.05943i
$964$	−29.6043	+	4.71643i	−0.953490	+	0.151906i
$965$	4.68325	+	12.8671i	0.150759	+	0.414207i
$966$	5.37947	−	13.4926i	0.173082	−	0.434116i
$967$	−17.2553	+	14.4789i	−0.554893	+	0.465610i	−0.876594	−	0.481231i	$-0.840190\pi$
$967$	−17.2553	+	14.4789i	−0.554893	+	0.465610i	0.321701	+	0.946841i	$0.395745\pi$
$968$	39.5904	+	4.45611i	1.27249	+	0.143225i
$969$	18.5033	−	4.52325i	0.594413	−	0.145308i
$970$	−6.06990	+	8.51786i	−0.194893	+	0.273492i
$971$		−	21.9521i		−	0.704475i	−0.935911	−	0.352238i	$-0.885421\pi$
$971$		−	21.9521i		−	0.704475i	0.935911	−	0.352238i	$-0.114579\pi$
$972$	1.23138	−	31.1526i	0.0394964	−	0.999220i
$973$		−	20.9235i		−	0.670778i
$974$	34.1853	+	24.3607i	1.09537	+	0.780568i
$975$	38.8361	−	9.49371i	1.24375	−	0.304042i
$976$	−29.0473	−	18.0775i	−0.929783	−	0.578646i
$977$	−36.9729	+	31.0239i	−1.18287	+	0.992543i	−0.182911	+	0.983129i	$0.558552\pi$
$977$	−36.9729	+	31.0239i	−1.18287	+	0.992543i	−0.999956	+	0.00941403i	$0.997003\pi$
$978$	19.0223	+	7.58418i	0.608267	+	0.242515i
$979$	26.8504	+	73.7710i	0.858144	+	2.35773i
$980$	−3.58791	−	22.5207i	−0.114612	−	0.719398i
$981$	−3.02366	−	5.81490i	−0.0965381	−	0.185656i
$982$	0.982139	+	12.4072i	0.0313413	+	0.395929i
$983$	−35.0417	−	29.4034i	−1.11766	−	0.937824i	−0.119172	−	0.992874i	$-0.538024\pi$
$983$	−35.0417	−	29.4034i	−1.11766	−	0.937824i	−0.998484	+	0.0550493i	$0.982468\pi$
$984$	−1.22723	−	9.56020i	−0.0391226	−	0.304768i
$985$	6.00289	+	34.0441i	0.191268	+	1.08474i
$986$	−8.84053	+	31.9343i	−0.281540	+	1.01699i
$987$	7.44352	+	5.46044i	0.236930	+	0.173808i
$988$	0.382916	−	23.1422i	0.0121822	−	0.736251i
$989$	22.5669	−	13.0290i	0.717585	−	0.414298i
$990$	−70.7031	−	9.93695i	−2.24709	−	0.315817i
$991$	6.44420	−	11.1617i	0.204707	−	0.354562i	−0.745333	−	0.666693i	$-0.767709\pi$
$991$	6.44420	−	11.1617i	0.204707	−	0.354562i	0.950039	+	0.312130i	$0.101043\pi$
$992$	−4.84128	−	1.51437i	−0.153711	−	0.0480812i
$993$	28.1744	−	18.8162i	0.894086	−	0.597113i
$994$	−2.02233	−	7.80515i	−0.0641445	−	0.247564i
$995$	−1.58712	+	4.36058i	−0.0503151	+	0.138240i
$996$	6.90111	−	2.89939i	0.218670	−	0.0918707i
$997$	−4.83400	−	0.852365i	−0.153094	−	0.0269947i	0.0965756	−	0.995326i	$-0.469211\pi$
$997$	−4.83400	−	0.852365i	−0.153094	−	0.0269947i	−0.249670	+	0.968331i	$0.580322\pi$
$998$	19.0029	+	9.05332i	0.601526	+	0.286578i
$999$	35.3019	+	12.0105i	1.11690	+	0.379994i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.t.a.133.29	yes	204
3.2	odd	2		648.2.t.a.397.6		204
4.3	odd	2		864.2.bf.a.241.20		204
8.3	odd	2		864.2.bf.a.241.15		204
8.5	even	2	inner	216.2.t.a.133.3	yes	204
24.5	odd	2		648.2.t.a.397.32		204
27.13	even	9	inner	216.2.t.a.13.3	✓	204
27.14	odd	18		648.2.t.a.253.32		204
108.67	odd	18		864.2.bf.a.337.15		204
216.13	even	18	inner	216.2.t.a.13.29	yes	204
216.67	odd	18		864.2.bf.a.337.20		204
216.149	odd	18		648.2.t.a.253.6		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.13.3	✓	204	27.13	even	9	inner
216.2.t.a.13.29	yes	204	216.13	even	18	inner
216.2.t.a.133.3	yes	204	8.5	even	2	inner
216.2.t.a.133.29	yes	204	1.1	even	1	trivial
648.2.t.a.253.6		204	216.149	odd	18
648.2.t.a.253.32		204	27.14	odd	18
648.2.t.a.397.6		204	3.2	odd	2
648.2.t.a.397.32		204	24.5	odd	2
864.2.bf.a.241.15		204	8.3	odd	2
864.2.bf.a.241.20		204	4.3	odd	2
864.2.bf.a.337.15		204	108.67	odd	18
864.2.bf.a.337.20		204	216.67	odd	18

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.t (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.15171 + 0.820715i) q^{2} +(-0.411299 - 1.68251i) q^{3} +(0.652854 + 1.89044i) q^{4} +(2.15975 + 2.57389i) q^{5} +(0.907164 - 2.27531i) q^{6} +(-1.78453 + 0.649515i) q^{7} +(-0.799620 + 2.71304i) q^{8} +(-2.66167 + 1.38403i) q^{9} +(0.374968 + 4.73691i) q^{10} +(3.21944 - 3.83678i) q^{11} +(2.91217 - 1.87597i) q^{12} +(3.61424 - 0.637289i) q^{13} +(-2.58832 - 0.716539i) q^{14} +(3.44229 - 4.69244i) q^{15} +(-3.14756 + 2.46837i) q^{16} +(-1.74380 - 3.02034i) q^{17} +(-4.20135 - 0.590478i) q^{18} +(-2.73085 - 1.57666i) q^{19} +(-3.45580 + 5.76327i) q^{20} +(1.82679 + 2.73534i) q^{21} +(6.85676 - 1.77660i) q^{22} +(-2.93428 - 1.06799i) q^{23} +(4.89360 + 0.229496i) q^{24} +(-1.09215 + 6.19390i) q^{25} +(4.68558 + 2.23229i) q^{26} +(3.42338 + 3.90903i) q^{27} +(-2.39291 - 2.94951i) q^{28} +(-6.61611 - 1.16660i) q^{29} +(7.81566 - 2.57917i) q^{30} +(0.842639 + 0.306695i) q^{31} +(-5.65090 + 0.259585i) q^{32} +(-7.77957 - 3.83868i) q^{33} +(0.470500 - 4.90971i) q^{34} +(-5.52592 - 3.19039i) q^{35} +(-4.35411 - 4.12817i) q^{36} +(6.21485 - 3.58815i) q^{37} +(-1.85115 - 4.05710i) q^{38} +(-2.55878 - 5.81888i) q^{39} +(-8.71007 + 3.80137i) q^{40} +(-0.341649 - 1.93759i) q^{41} +(-0.141009 + 4.64958i) q^{42} +(-5.36405 + 6.39263i) q^{43} +(9.35505 + 3.58132i) q^{44} +(-9.31088 - 3.86169i) q^{45} +(-2.50291 - 3.63822i) q^{46} +(2.63733 - 0.959909i) q^{47} +(5.44764 + 4.28056i) q^{48} +(-2.59964 + 2.18135i) q^{49} +(-6.34127 + 6.23721i) q^{50} +(-4.36453 + 4.17621i) q^{51} +(3.56433 + 6.41647i) q^{52} -9.52536i q^{53} +(0.734526 + 7.31167i) q^{54} +16.8287 q^{55} +(-0.335219 - 5.36087i) q^{56} +(-1.52954 + 5.24316i) q^{57} +(-6.66237 - 6.77352i) q^{58} +(-6.13695 - 7.31373i) q^{59} +(11.1181 + 3.44398i) q^{60} +(2.92540 + 8.03747i) q^{61} +(0.718763 + 1.04479i) q^{62} +(3.85088 - 4.19863i) q^{63} +(-6.72122 - 4.33881i) q^{64} +(9.44618 + 7.92629i) q^{65} +(-5.80932 - 10.8058i) q^{66} +(13.7512 - 2.42470i) q^{67} +(4.57135 - 5.26839i) q^{68} +(-0.590037 + 5.37621i) q^{69} +(-3.74584 - 8.20960i) q^{70} +(1.50109 + 2.59997i) q^{71} +(-1.62660 - 8.32791i) q^{72} +(0.472663 - 0.818676i) q^{73} +(10.1025 + 0.968131i) q^{74} +(10.8705 - 0.709989i) q^{75} +(1.19774 - 6.19185i) q^{76} +(-3.25314 + 8.93793i) q^{77} +(1.82868 - 8.80166i) q^{78} +(-0.803209 + 4.55523i) q^{79} +(-13.1513 - 2.77042i) q^{80} +(5.16894 - 7.36764i) q^{81} +(1.19673 - 2.51193i) q^{82} +(2.12803 + 0.375229i) q^{83} +(-3.97838 + 5.23922i) q^{84} +(4.00787 - 11.0115i) q^{85} +(-11.4243 + 2.96007i) q^{86} +(0.758385 + 11.6115i) q^{87} +(7.83503 + 11.8025i) q^{88} +(-7.83712 + 13.5743i) q^{89} +(-7.55405 - 12.0891i) q^{90} +(-6.03579 + 3.48477i) q^{91} +(0.103320 - 6.24433i) q^{92} +(0.169441 - 1.54389i) q^{93} +(3.82524 + 1.05896i) q^{94} +(-1.83982 - 10.4341i) q^{95} +(2.76096 + 9.40091i) q^{96} +(1.68619 + 1.41488i) q^{97} +(-4.78429 + 0.378719i) q^{98} +(-3.25888 + 14.6680i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26}+ \cdots + 54 q^{98}+O(q^{100}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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