LMFDB - Embedded newform 216.2.t.a.205.12

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)

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);

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")

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			205.12
Character	$\chi$	$=$	216.205
Dual form			216.2.t.a.157.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.654194 + 1.25381i) q^{2} +(-0.684682 + 1.59098i) q^{3} +(-1.14406 - 1.64047i) q^{4} +(1.15428 - 3.17134i) q^{5} +(-1.54686 - 1.89927i) q^{6} +(0.593321 - 3.36489i) q^{7} +(2.80526 - 0.361244i) q^{8} +(-2.06242 - 2.17863i) q^{9} +(3.22113 + 3.52191i) q^{10} +(0.197048 + 0.541384i) q^{11} +(3.39326 - 0.696975i) q^{12} +(-4.30199 - 5.12691i) q^{13} +(3.83077 + 2.94520i) q^{14} +(4.25523 + 4.00779i) q^{15} +(-1.38226 + 3.75358i) q^{16} +(1.15893 + 2.00733i) q^{17} +(4.08080 - 1.16063i) q^{18} +(0.353289 + 0.203971i) q^{19} +(-6.52304 + 1.73466i) q^{20} +(4.94723 + 3.24784i) q^{21} +(-0.807698 - 0.107111i) q^{22} +(1.15186 + 6.53250i) q^{23} +(-1.34598 + 4.71045i) q^{24} +(-4.89486 - 4.10727i) q^{25} +(9.24249 - 2.03986i) q^{26} +(4.87825 - 1.78960i) q^{27} +(-6.19878 + 2.87631i) q^{28} +(2.24644 - 2.67721i) q^{29} +(-7.80874 + 2.71336i) q^{30} +(-0.382945 - 2.17179i) q^{31} +(-3.80200 - 4.18865i) q^{32} +(-0.996245 - 0.0571774i) q^{33} +(-3.27497 + 0.139892i) q^{34} +(-9.98637 - 5.76564i) q^{35} +(-1.21443 + 5.87581i) q^{36} +(1.05249 - 0.607656i) q^{37} +(-0.486860 + 0.309519i) q^{38} +(11.1023 - 3.33407i) q^{39} +(2.09242 - 9.31343i) q^{40} +(5.09057 - 4.27150i) q^{41} +(-7.30861 + 4.07815i) q^{42} +(-0.442145 - 1.21478i) q^{43} +(0.662688 - 0.942626i) q^{44} +(-9.28978 + 4.02591i) q^{45} +(-8.94402 - 2.82932i) q^{46} +(-0.547022 + 3.10232i) q^{47} +(-5.02546 - 4.76915i) q^{48} +(-4.39261 - 1.59878i) q^{49} +(8.35191 - 3.45024i) q^{50} +(-3.98712 + 0.469453i) q^{51} +(-3.48879 + 12.9228i) q^{52} +9.35460i q^{53} +(-0.947515 + 7.28713i) q^{54} +1.94436 q^{55} +(0.448874 - 9.65374i) q^{56} +(-0.566405 + 0.422419i) q^{57} +(1.88709 + 4.56802i) q^{58} +(3.00302 - 8.25072i) q^{59} +(1.70641 - 11.5657i) q^{60} +(4.67459 + 0.824257i) q^{61} +(2.97352 + 0.940634i) q^{62} +(-8.55452 + 5.64720i) q^{63} +(7.73901 - 2.02677i) q^{64} +(-21.2249 + 7.72523i) q^{65} +(0.723428 - 1.21169i) q^{66} +(9.67062 + 11.5250i) q^{67} +(1.96707 - 4.19769i) q^{68} +(-11.1817 - 2.64011i) q^{69} +(13.7620 - 8.74913i) q^{70} +(-3.92323 - 6.79524i) q^{71} +(-6.57265 - 5.36659i) q^{72} +(0.641809 - 1.11165i) q^{73} +(0.0733489 + 1.71715i) q^{74} +(9.88600 - 4.97543i) q^{75} +(-0.0695752 - 0.812914i) q^{76} +(1.93861 - 0.341829i) q^{77} +(-3.08279 + 16.1013i) q^{78} +(3.84081 + 3.22282i) q^{79} +(10.3084 + 8.71628i) q^{80} +(-0.492839 + 8.98650i) q^{81} +(2.02541 + 9.17698i) q^{82} +(-6.67152 + 7.95081i) q^{83} +(-0.331952 - 11.8315i) q^{84} +(7.70366 - 1.35836i) q^{85} +(1.81235 + 0.240341i) q^{86} +(2.72128 + 5.40708i) q^{87} +(0.748343 + 1.44754i) q^{88} +(-2.86501 + 4.96234i) q^{89} +(1.02961 - 14.2813i) q^{90} +(-19.8040 + 11.4338i) q^{91} +(9.39855 - 9.36314i) q^{92} +(3.71746 + 0.877728i) q^{93} +(-3.53185 - 2.71538i) q^{94} +(1.05466 - 0.884962i) q^{95} +(9.26721 - 3.18100i) q^{96} +(10.5548 - 3.84165i) q^{97} +(4.87818 - 4.46157i) q^{98} +(0.773079 - 1.54586i) 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 $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{9}\right)$

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 $

$2$	−0.654194	+	1.25381i	−0.462585	+	0.886575i
$2$	−0.654194	+	1.25381i	−0.462585	+	0.886575i
$3$	−0.684682	+	1.59098i	−0.395301	+	0.918551i
$3$	−0.684682	+	1.59098i	−0.395301	+	0.918551i
$4$	−1.14406	−	1.64047i	−0.572030	−	0.820233i
$5$	1.15428	−	3.17134i	0.516208	−	1.41827i	−0.358460	−	0.933545i	$-0.616698\pi$
$5$	1.15428	−	3.17134i	0.516208	−	1.41827i	0.874667	−	0.484723i	$-0.161080\pi$
$6$	−1.54686	−	1.89927i	−0.631504	−	0.775373i
$7$	0.593321	−	3.36489i	0.224254	−	1.27181i	−0.639851	−	0.768499i	$-0.721004\pi$
$7$	0.593321	−	3.36489i	0.224254	−	1.27181i	0.864106	−	0.503311i	$-0.167885\pi$
$8$	2.80526	−	0.361244i	0.991810	−	0.127719i
$9$	−2.06242	−	2.17863i	−0.687474	−	0.726209i
$10$	3.22113	+	3.52191i	1.01861	+	1.11373i
$11$	0.197048	+	0.541384i	0.0594121	+	0.163233i	0.965848	−	0.259111i	$-0.0834295\pi$
$11$	0.197048	+	0.541384i	0.0594121	+	0.163233i	−0.906435	+	0.422344i	$0.861207\pi$
$12$	3.39326	−	0.696975i	0.979550	−	0.201199i
$13$	−4.30199	−	5.12691i	−1.19316	−	1.42195i	−0.881779	−	0.471664i	$-0.843654\pi$
$13$	−4.30199	−	5.12691i	−1.19316	−	1.42195i	−0.311379	−	0.950286i	$-0.600791\pi$
$14$	3.83077	+	2.94520i	1.02382	+	0.787139i
$15$	4.25523	+	4.00779i	1.09870	+	1.03481i
$16$	−1.38226	+	3.75358i	−0.345564	+	0.938395i
$17$	1.15893	+	2.00733i	0.281082	+	0.486849i	0.971652	−	0.236417i	$-0.0759732\pi$
$17$	1.15893	+	2.00733i	0.281082	+	0.486849i	−0.690569	+	0.723266i	$0.742640\pi$
$18$	4.08080	−	1.16063i	0.961854	−	0.273563i
$19$	0.353289	+	0.203971i	0.0810500	+	0.0467943i	0.539977	−	0.841680i	$-0.318433\pi$
$19$	0.353289	+	0.203971i	0.0810500	+	0.0467943i	−0.458927	+	0.888474i	$0.651766\pi$
$20$	−6.52304	+	1.73466i	−1.45860	+	0.387881i
$21$	4.94723	+	3.24784i	1.07957	+	0.708737i
$22$	−0.807698	−	0.107111i	−0.172202	−	0.0228361i
$23$	1.15186	+	6.53250i	0.240178	+	1.36212i	0.831429	+	0.555631i	$0.187523\pi$
$23$	1.15186	+	6.53250i	0.240178	+	1.36212i	−0.591250	+	0.806488i	$0.701365\pi$
$24$	−1.34598	+	4.71045i	−0.274747	+	0.961516i
$25$	−4.89486	−	4.10727i	−0.978971	−	0.821454i
$26$	9.24249	−	2.03986i	1.81260	−	0.400050i
$27$	4.87825	−	1.78960i	0.938820	−	0.344408i
$28$	−6.19878	+	2.87631i	−1.17146	+	0.543572i
$29$	2.24644	−	2.67721i	0.417154	−	0.497145i	−0.516016	−	0.856579i	$-0.672586\pi$
$29$	2.24644	−	2.67721i	0.417154	−	0.497145i	0.933171	+	0.359434i	$0.117030\pi$
$30$	−7.80874	+	2.71336i	−1.42567	+	0.495389i
$31$	−0.382945	−	2.17179i	−0.0687790	−	0.390065i	−0.999692	−	0.0248236i	$-0.992098\pi$
$31$	−0.382945	−	2.17179i	−0.0687790	−	0.390065i	0.930913	−	0.365241i	$-0.119014\pi$
$32$	−3.80200	−	4.18865i	−0.672104	−	0.740456i
$33$	−0.996245	−	0.0571774i	−0.173424	−	0.00995332i
$34$	−3.27497	+	0.139892i	−0.561653	+	0.0239913i
$35$	−9.98637	−	5.76564i	−1.68801	−	0.974570i
$36$	−1.21443	+	5.87581i	−0.202406	+	0.979302i
$37$	1.05249	−	0.607656i	0.173028	−	0.0998980i	−0.410985	−	0.911642i	$-0.634815\pi$
$37$	1.05249	−	0.607656i	0.173028	−	0.0998980i	0.584013	+	0.811744i	$0.301482\pi$
$38$	−0.486860	+	0.309519i	−0.0789792	+	0.0502106i
$39$	11.1023	−	3.33407i	1.77779	−	0.533878i
$40$	2.09242	−	9.31343i	0.330840	−	1.47258i
$41$	5.09057	−	4.27150i	0.795014	−	0.667096i	−0.151967	−	0.988386i	$-0.548561\pi$
$41$	5.09057	−	4.27150i	0.795014	−	0.667096i	0.946981	+	0.321290i	$0.104116\pi$
$42$	−7.30861	+	4.07815i	−1.12774	+	0.629272i
$43$	−0.442145	−	1.21478i	−0.0674265	−	0.185253i	0.901403	−	0.432981i	$-0.142538\pi$
$43$	−0.442145	−	1.21478i	−0.0674265	−	0.185253i	−0.968830	+	0.247728i	$0.920316\pi$
$44$	0.662688	−	0.942626i	0.0999040	−	0.142106i
$45$	−9.28978	+	4.02591i	−1.38484	+	0.600148i
$46$	−8.94402	−	2.82932i	−1.31872	−	0.417160i
$47$	−0.547022	+	3.10232i	−0.0797914	+	0.452520i	0.918568	+	0.395263i	$0.129346\pi$
$47$	−0.547022	+	3.10232i	−0.0797914	+	0.452520i	−0.998359	+	0.0572567i	$0.981765\pi$
$48$	−5.02546	−	4.76915i	−0.725362	−	0.688368i
$49$	−4.39261	−	1.59878i	−0.627516	−	0.228397i
$50$	8.35191	−	3.45024i	1.18114	−	0.487938i
$51$	−3.98712	+	0.469453i	−0.558308	+	0.0657366i
$52$	−3.48879	+	12.9228i	−0.483809	+	1.79206i
$53$			9.35460i			1.28495i	0.766305	+	0.642477i	$0.222093\pi$
$53$			9.35460i			1.28495i	−0.766305	+	0.642477i	$0.777907\pi$
$54$	−0.947515	+	7.28713i	−0.128941	+	0.991652i
$55$	1.94436			0.262178
$56$	0.448874	−	9.65374i	0.0599833	−	1.29004i
$57$	−0.566405	+	0.422419i	−0.0750221	+	0.0559508i
$58$	1.88709	+	4.56802i	0.247787	+	0.599810i
$59$	3.00302	−	8.25072i	0.390959	−	1.07415i	−0.575605	−	0.817728i	$-0.695233\pi$
$59$	3.00302	−	8.25072i	0.390959	−	1.07415i	0.966564	−	0.256424i	$-0.0825444\pi$
$60$	1.70641	−	11.5657i	0.220296	−	1.49313i
$61$	4.67459	+	0.824257i	0.598520	+	0.105535i	0.464697	−	0.885470i	$-0.346163\pi$
$61$	4.67459	+	0.824257i	0.598520	+	0.105535i	0.133824	+	0.991005i	$0.457274\pi$
$62$	2.97352	+	0.940634i	0.377638	+	0.119461i
$63$	−8.55452	+	5.64720i	−1.07777	+	0.711480i
$64$	7.73901	−	2.02677i	0.967376	−	0.253346i
$65$	−21.2249	+	7.72523i	−2.63262	+	0.958196i
$66$	0.723428	−	1.21169i	0.0890478	−	0.149149i
$67$	9.67062	+	11.5250i	1.18145	+	1.40800i	0.892731	+	0.450589i	$0.148786\pi$
$67$	9.67062	+	11.5250i	1.18145	+	1.40800i	0.288723	+	0.957413i	$0.406769\pi$
$68$	1.96707	−	4.19769i	0.238542	−	0.509045i
$69$	−11.1817	−	2.64011i	−1.34612	−	0.317831i
$70$	13.7620	−	8.74913i	1.64488	−	1.04572i
$71$	−3.92323	−	6.79524i	−0.465602	−	0.806446i	0.533627	−	0.845720i	$-0.320829\pi$
$71$	−3.92323	−	6.79524i	−0.465602	−	0.806446i	−0.999228	+	0.0392740i	$0.987495\pi$
$72$	−6.57265	−	5.36659i	−0.774594	−	0.632458i
$73$	0.641809	−	1.11165i	0.0751180	−	0.130108i	−0.826020	−	0.563641i	$-0.809400\pi$
$73$	0.641809	−	1.11165i	0.0751180	−	0.130108i	0.901138	+	0.433533i	$0.142733\pi$
$74$	0.0733489	+	1.71715i	0.00852664	+	0.199614i
$75$	9.88600	−	4.97543i	1.14154	−	0.574513i
$76$	−0.0695752	−	0.812914i	−0.00798082	−	0.0932476i
$77$	1.93861	−	0.341829i	0.220925	−	0.0389551i
$78$	−3.08279	+	16.1013i	−0.349057	+	1.82311i
$79$	3.84081	+	3.22282i	0.432125	+	0.362596i	0.832753	−	0.553645i	$-0.186764\pi$
$79$	3.84081	+	3.22282i	0.432125	+	0.362596i	−0.400628	+	0.916241i	$0.631208\pi$
$80$	10.3084	+	8.71628i	1.15251	+	0.974510i
$81$	−0.492839	+	8.98650i	−0.0547599	+	0.998500i
$82$	2.02541	+	9.17698i	0.223669	+	1.01343i
$83$	−6.67152	+	7.95081i	−0.732295	+	0.872715i	−0.995763	−	0.0919529i	$-0.970689\pi$
$83$	−6.67152	+	7.95081i	−0.732295	+	0.872715i	0.263468	+	0.964668i	$0.415134\pi$
$84$	−0.331952	−	11.8315i	−0.0362189	−	1.29092i
$85$	7.70366	−	1.35836i	0.835580	−	0.147335i
$86$	1.81235	+	0.240341i	0.195431	+	0.0259166i
$87$	2.72128	+	5.40708i	0.291752	+	0.579700i
$88$	0.748343	+	1.44754i	0.0797736	+	0.154309i
$89$	−2.86501	+	4.96234i	−0.303690	+	0.526007i	−0.976969	−	0.213382i	$-0.931552\pi$
$89$	−2.86501	+	4.96234i	−0.303690	+	0.526007i	0.673278	+	0.739389i	$0.264886\pi$
$90$	1.02961	−	14.2813i	0.108531	−	1.50538i
$91$	−19.8040	+	11.4338i	−2.07602	+	1.19859i
$92$	9.39855	−	9.36314i	0.979866	−	0.976175i
$93$	3.71746	+	0.877728i	0.385483	+	0.0910161i
$94$	−3.53185	−	2.71538i	−0.364282	−	0.280070i
$95$	1.05466	−	0.884962i	0.108205	−	0.0907952i
$96$	9.26721	−	3.18100i	0.945831	−	0.324659i
$97$	10.5548	−	3.84165i	1.07168	−	0.390061i	0.254877	−	0.966974i	$-0.417965\pi$
$97$	10.5548	−	3.84165i	1.07168	−	0.390061i	0.816806	+	0.576913i	$0.195743\pi$
$98$	4.87818	−	4.46157i	0.492771	−	0.450687i
$99$	0.773079	−	1.54586i	0.0776974	−	0.155364i
$100$	−1.13784	+	12.7288i	−0.113784	+	1.27288i
$101$	12.2411	+	2.15844i	1.21804	+	0.214773i	0.745481	−	0.666527i	$-0.232220\pi$
$101$	12.2411	+	2.15844i	1.21804	+	0.214773i	0.472557	+	0.881300i	$0.343331\pi$
$102$	2.01975	−	5.30619i	0.199985	−	0.525391i
$103$	−14.8537	−	5.40632i	−1.46358	−	0.532701i	−0.517233	−	0.855844i	$-0.673038\pi$
$103$	−14.8537	−	5.40632i	−1.46358	−	0.532701i	−0.946350	+	0.323144i	$0.895260\pi$
$104$	−13.9203	−	12.8283i	−1.36500	−	1.25792i
$105$	16.0105	−	11.9405i	1.56246	−	1.16527i
$106$	−11.7289	−	6.11973i	−1.13921	−	0.594401i
$107$			2.44491i			0.236359i	0.992992	+	0.118179i	$0.0377058\pi$
$107$			2.44491i			0.236359i	−0.992992	+	0.118179i	$0.962294\pi$
$108$	−8.51678	−	5.95520i	−0.819528	−	0.573039i
$109$		−	16.2522i		−	1.55668i	−0.627843	−	0.778340i	$-0.716062\pi$
$109$		−	16.2522i		−	1.55668i	0.627843	−	0.778340i	$-0.283938\pi$
$110$	−1.27199	+	2.43785i	−0.121280	+	0.232440i
$111$	0.246146	+	2.09054i	0.0233631	+	0.198425i
$112$	11.8103	+	6.87822i	1.11597	+	0.649931i
$113$	−11.4376	−	4.16294i	−1.07596	−	0.391617i	−0.257556	−	0.966263i	$-0.582917\pi$
$113$	−11.4376	−	4.16294i	−1.07596	−	0.391617i	−0.818402	+	0.574646i	$0.805140\pi$
$114$	−0.159093	−	0.986506i	−0.0149004	−	0.0923948i
$115$	22.0464	+	3.88737i	2.05583	+	0.362499i
$116$	−6.96193	−	0.622331i	−0.646399	−	0.0577820i
$117$	−2.29712	+	19.9463i	−0.212369	+	1.84403i
$118$	8.38025	+	9.16278i	0.771464	+	0.843502i
$119$	7.44207	−	2.70869i	0.682213	−	0.248305i
$120$	13.3848	+	9.70573i	1.22186	+	0.886008i
$121$	8.17222	−	6.85731i	0.742929	−	0.623392i
$122$	−4.09155	+	5.32181i	−0.370432	+	0.481814i
$123$	3.31044	+	11.0236i	0.298492	+	0.993965i
$124$	−3.12463	+	3.11286i	−0.280600	+	0.279543i
$125$	−4.06195	+	2.34517i	−0.363312	+	0.209758i
$126$	−1.48417	−	14.4201i	−0.132220	−	1.28464i
$127$	−4.79341	+	8.30243i	−0.425346	+	0.736722i	−0.996453	−	0.0841546i	$-0.973181\pi$
$127$	−4.79341	+	8.30243i	−0.425346	+	0.736722i	0.571106	+	0.820876i	$0.306514\pi$
$128$	−2.52164	+	11.0291i	−0.222883	+	0.974845i
$129$	2.23542	+	0.128297i	0.196818	+	0.0112960i
$130$	4.19927	−	31.6657i	0.368300	−	2.77726i
$131$	−0.406480	+	0.0716734i	−0.0355143	+	0.00626213i	−0.191377	−	0.981517i	$-0.561295\pi$
$131$	−0.406480	+	0.0716734i	−0.0355143	+	0.00626213i	0.155863	+	0.987779i	$0.450184\pi$
$132$	1.04597	+	1.69972i	0.0910396	+	0.147942i
$133$	0.895956	−	1.06776i	0.0776892	−	0.0925864i
$134$	−20.7766	+	4.58549i	−1.79482	+	0.396126i
$135$	−0.0445910	−	17.5363i	−0.00383778	−	1.50928i
$136$	3.97625	+	5.21243i	0.340960	+	0.446962i
$137$	12.0727	+	10.1302i	1.03144	+	0.865480i	0.991021	−	0.133703i	$-0.0426867\pi$
$137$	12.0727	+	10.1302i	1.03144	+	0.865480i	0.0404177	+	0.999183i	$0.487131\pi$
$138$	10.6252	−	12.2926i	0.904477	−	1.04641i
$139$	−2.17442	+	0.383409i	−0.184432	+	0.0325204i	−0.265101	−	0.964221i	$-0.585405\pi$
$139$	−2.17442	+	0.383409i	−0.184432	+	0.0325204i	0.0806691	+	0.996741i	$0.474294\pi$
$140$	1.96667	+	22.9785i	0.166214	+	1.94204i
$141$	−4.56118	−	2.99440i	−0.384121	−	0.252174i
$142$	11.0865	−	0.473565i	0.930356	−	0.0397407i
$143$	1.92793	−	3.33928i	0.161222	−	0.279244i
$144$	11.0285	−	4.73004i	0.919038	−	0.394170i
$145$	−5.89733	−	10.2145i	−0.489747	−	0.848267i
$146$	0.973920	+	1.53194i	0.0806022	+	0.126784i
$147$	5.55117	−	5.89389i	0.457853	−	0.486120i
$148$	−2.20095	−	1.03138i	−0.180917	−	0.0847790i
$149$	4.40044	+	5.24424i	0.360498	+	0.429625i	0.915558	−	0.402186i	$-0.131749\pi$
$149$	4.40044	+	5.24424i	0.360498	+	0.429625i	−0.555060	+	0.831810i	$0.687305\pi$
$150$	−0.229139	+	15.6500i	−0.0187091	+	1.27782i
$151$	11.0866	−	4.03519i	0.902213	−	0.328379i	0.151074	−	0.988522i	$-0.451727\pi$
$151$	11.0866	−	4.03519i	0.902213	−	0.328379i	0.751139	+	0.660144i	$0.229505\pi$
$152$	1.06475	+	0.444570i	0.0863628	+	0.0360594i
$153$	1.98302	−	6.66484i	0.160318	−	0.538821i
$154$	−0.839641	+	2.65427i	−0.0676602	+	0.213887i
$155$	−7.32952	−	1.29239i	−0.588721	−	0.103807i
$156$	−18.1711	−	14.3986i	−1.45485	−	1.15281i
$157$	−4.12184	+	11.3247i	−0.328959	+	0.903808i	0.659417	+	0.751778i	$0.270803\pi$
$157$	−4.12184	+	11.3247i	−0.328959	+	0.903808i	−0.988376	+	0.152030i	$0.951419\pi$
$158$	−6.55343	+	2.70728i	−0.521363	+	0.215380i
$159$	−14.8830	−	6.40493i	−1.18030	−	0.507944i
$160$	−17.6722	+	7.22258i	−1.39711	+	0.570995i
$161$	22.6646			1.78622
$162$	−10.9449	−	6.49684i	−0.859913	−	0.510440i
$163$		−	13.3972i		−	1.04935i	−0.851303	−	0.524675i	$-0.824187\pi$
$163$		−	13.3972i		−	1.04935i	0.851303	−	0.524675i	$-0.175813\pi$
$164$	−12.8312	−	3.46407i	−1.00195	−	0.270498i
$165$	−1.33127	+	3.09344i	−0.103639	+	0.240824i
$166$	−5.60430	−	13.5662i	−0.434978	−	1.05294i
$167$	−6.36473	−	2.31657i	−0.492517	−	0.179262i	0.0838081	−	0.996482i	$-0.473292\pi$
$167$	−6.36473	−	2.31657i	−0.492517	−	0.179262i	−0.576325	+	0.817220i	$0.695514\pi$
$168$	15.0515	+	7.32389i	1.16125	+	0.565050i
$169$	−5.52068	+	31.3093i	−0.424668	+	2.40841i
$170$	−3.33657	+	10.5475i	−0.255903	+	0.808959i
$171$	−0.284253	−	1.19036i	−0.0217373	−	0.0910291i
$172$	−1.48697	+	2.11511i	−0.113380	+	0.161275i
$173$	−0.576454	−	1.58380i	−0.0438270	−	0.120414i	0.915848	−	0.401524i	$-0.131519\pi$
$173$	−0.576454	−	1.58380i	−0.0438270	−	0.120414i	−0.959675	+	0.281111i	$0.909297\pi$
$174$	−8.55967	−	0.125326i	−0.648907	−	0.00950093i
$175$	−16.7247	+	14.0337i	−1.26427	+	1.06085i
$176$	−2.30450	−	0.00869789i	−0.173708	−	0.000655628i
$177$	11.0706	+	10.4269i	0.832117	+	0.783730i
$178$	−4.34754	−	6.83850i	−0.325862	−	0.512568i
$179$	−10.3190	+	5.95768i	−0.771279	+	0.445298i	−0.833331	−	0.552775i	$-0.813569\pi$
$179$	−10.3190	+	5.95768i	−0.771279	+	0.445298i	0.0620517	+	0.998073i	$0.480236\pi$
$180$	17.2324	+	10.6337i	1.28443	+	0.792588i
$181$	−14.3027	−	8.25769i	−1.06311	−	0.613789i	−0.136822	−	0.990596i	$-0.543689\pi$
$181$	−14.3027	−	8.25769i	−1.06311	−	0.613789i	−0.926292	+	0.376806i	$0.877022\pi$
$182$	−1.38015	−	32.3103i	−0.102304	−	2.39500i
$183$	−4.51198	+	6.87282i	−0.333536	+	0.508054i
$184$	5.59109	+	17.9093i	0.412180	+	1.32029i
$185$	−0.712223	−	4.03922i	−0.0523636	−	0.296969i
$186$	−3.53245	+	4.08677i	−0.259011	+	0.299657i
$187$	−0.858372	+	1.02297i	−0.0627703	+	0.0748068i
$188$	5.71507	−	2.65186i	0.416815	−	0.193407i
$189$	−3.12744	−	17.4766i	−0.227487	−	1.27123i
$190$	0.419620	+	1.90127i	0.0304424	+	0.137933i
$191$	−10.1267	−	8.49734i	−0.732745	−	0.614846i	0.198134	−	0.980175i	$-0.436512\pi$
$191$	−10.1267	−	8.49734i	−0.732745	−	0.614846i	−0.930878	+	0.365329i	$0.880956\pi$
$192$	−2.07421	+	13.7003i	−0.149693	+	0.988732i
$193$	−0.0307325	−	0.174293i	−0.00221218	−	0.0125459i	0.983682	−	0.179918i	$-0.0575831\pi$
$193$	−0.0307325	−	0.174293i	−0.00221218	−	0.0125459i	−0.985894	+	0.167372i	$0.946472\pi$
$194$	−2.08824	+	15.7469i	−0.149927	+	1.13056i
$195$	2.24163	−	39.0576i	0.160527	−	2.79698i
$196$	2.40266	+	9.03503i	0.171619	+	0.645359i
$197$	0.841221	+	0.485679i	0.0599345	+	0.0346032i	0.529668	−	0.848205i	$-0.322317\pi$
$197$	0.841221	+	0.485679i	0.0599345	+	0.0346032i	−0.469733	+	0.882808i	$0.655650\pi$
$198$	1.43246	+	1.98058i	0.101800	+	0.140754i
$199$	2.04926	+	3.54942i	0.145268	+	0.251612i	0.929473	−	0.368890i	$-0.120262\pi$
$199$	2.04926	+	3.54942i	0.145268	+	0.251612i	−0.784205	+	0.620502i	$0.786929\pi$
$200$	−15.2151	−	9.75374i	−1.07587	−	0.689693i
$201$	−24.9573	+	7.49478i	−1.76035	+	0.528641i
$202$	−10.7143	+	13.9360i	−0.753858	+	0.980530i
$203$	−7.67565	−	9.14748i	−0.538725	−	0.642027i
$204$	5.33162	+	6.00365i	0.373288	+	0.420340i
$205$	−7.67047	−	21.0745i	−0.535729	−	1.47190i
$206$	16.4957	−	15.0869i	1.14931	−	1.05116i
$207$	11.8563	−	15.9822i	0.824068	−	1.11084i
$208$	25.1907	−	9.06115i	1.74666	−	0.628278i
$209$	−0.0408121	+	0.231457i	−0.00282303	+	0.0160102i
$210$	4.49706	+	27.8854i	0.310327	+	1.92428i
$211$	−1.28341	+	3.52613i	−0.0883534	+	0.242749i	−0.975998	−	0.217781i	$-0.930118\pi$
$211$	−1.28341	+	3.52613i	−0.0883534	+	0.242749i	0.887644	+	0.460530i	$0.152340\pi$
$212$	15.3459	−	10.7022i	1.05396	−	0.735031i
$213$	13.4972	−	1.58920i	0.924815	−	0.108890i
$214$	−3.06545	−	1.59945i	−0.209550	−	0.109336i
$215$	−4.36285			−0.297544
$216$	13.0383	−	6.78254i	0.887144	−	0.461493i
$217$	−7.53504			−0.511512
$218$	20.3771	+	10.6321i	1.38011	+	0.720097i
$219$	1.32917	+	1.78223i	0.0898169	+	0.120432i
$220$	−2.22447	−	3.18966i	−0.149973	−	0.215047i
$221$	5.30569	−	14.5773i	0.356899	−	0.980572i
$222$	−2.78216	−	1.05900i	−0.186726	−	0.0710756i
$223$	0.680991	−	3.86209i	0.0456025	−	0.258625i	−0.953480	−	0.301457i	$-0.902527\pi$
$223$	0.680991	−	3.86209i	0.0456025	−	0.258625i	0.999082	+	0.0428323i	$0.0136381\pi$
$224$	−16.3502	+	10.3081i	−1.09244	+	0.688738i
$225$	1.14704	+	19.1350i	0.0764691	+	1.27567i
$226$	12.7019	−	11.6171i	0.844920	−	0.772761i
$227$	4.04735	+	11.1200i	0.268632	+	0.738061i	0.998514	+	0.0544879i	$0.0173526\pi$
$227$	4.04735	+	11.1200i	0.268632	+	0.738061i	−0.729882	+	0.683573i	$0.760425\pi$
$228$	1.34097	+	0.445895i	0.0888076	+	0.0295301i
$229$	6.81207	+	8.11831i	0.450154	+	0.536473i	0.942624	−	0.333857i	$-0.108350\pi$
$229$	6.81207	+	8.11831i	0.450154	+	0.536473i	−0.492470	+	0.870330i	$0.663906\pi$
$230$	−19.2966	+	25.0988i	−1.27238	+	1.65496i
$231$	−0.783489	+	3.31833i	−0.0515498	+	0.218330i
$232$	5.33474	−	8.32179i	0.350243	−	0.546352i
$233$	−0.565006	−	0.978619i	−0.0370148	−	0.0641115i	0.846925	−	0.531713i	$-0.178452\pi$
$233$	−0.565006	−	0.978619i	−0.0370148	−	0.0641115i	−0.883939	+	0.467602i	$0.845118\pi$
$234$	−23.5060	−	15.9289i	−1.53664	−	1.04130i
$235$	9.20711	+	5.31572i	0.600605	+	0.346760i
$236$	−16.9707	+	4.51296i	−1.10470	+	0.293769i
$237$	−7.75717	+	3.90404i	−0.503883	+	0.253594i
$238$	−1.47239	+	11.1029i	−0.0954406	+	0.719695i
$239$	1.00787	+	5.71591i	0.0651936	+	0.369731i	0.999898	+	0.0143045i	$0.00455341\pi$
$239$	1.00787	+	5.71591i	0.0651936	+	0.369731i	−0.934704	+	0.355427i	$0.884335\pi$
$240$	−20.9254	+	10.4325i	−1.35073	+	0.673418i
$241$	22.5974	+	18.9615i	1.45563	+	1.22142i	0.928342	+	0.371728i	$0.121235\pi$
$241$	22.5974	+	18.9615i	1.45563	+	1.22142i	0.527286	+	0.849688i	$0.323210\pi$
$242$	3.25151	+	14.7324i	0.209015	+	0.947034i
$243$	−13.9599	−	6.93699i	−0.895527	−	0.445008i
$244$	−3.99585	−	8.61151i	−0.255808	−	0.551295i
$245$	−10.1406	+	12.0851i	−0.647857	+	0.772086i
$246$	−15.9871	−	3.06094i	−1.01930	−	0.195158i
$247$	−0.474102	−	2.68876i	−0.0301664	−	0.171082i
$248$	−1.85881	−	5.95410i	−0.118034	−	0.378086i
$249$	−8.08169	−	16.0580i	−0.512157	−	1.01764i
$250$	−0.283080	−	6.62709i	−0.0179036	−	0.419134i
$251$	5.20730	+	3.00644i	0.328682	+	0.189765i	0.655256	−	0.755407i	$-0.272561\pi$
$251$	5.20730	+	3.00644i	0.328682	+	0.189765i	−0.326574	+	0.945172i	$0.605894\pi$
$252$	19.0509	+	7.57268i	1.20009	+	0.477034i
$253$	−3.30962	+	1.91081i	−0.208074	+	0.120132i
$254$	−7.27381	−	11.4414i	−0.456400	−	0.717898i
$255$	−3.11343	+	13.1864i	−0.194971	+	0.825765i
$256$	−12.1787	−	10.3768i	−0.761171	−	0.648552i
$257$	19.8936	−	16.6927i	1.24093	−	1.04126i	0.243480	−	0.969906i	$-0.421711\pi$
$257$	19.8936	−	16.6927i	1.24093	−	1.04126i	0.997451	−	0.0713589i	$-0.0227336\pi$
$258$	−1.62326	+	2.71885i	−0.101060	+	0.169268i
$259$	−1.42023	−	3.90205i	−0.0882489	−	0.242462i
$260$	36.9555	+	25.9806i	2.29188	+	1.61125i
$261$	−10.4658	+	0.627364i	−0.647814	+	0.0388329i
$262$	0.176052	−	0.556535i	0.0108766	−	0.0343829i
$263$	−2.41565	+	13.6998i	−0.148956	+	0.844769i	0.815150	+	0.579250i	$0.196654\pi$
$263$	−2.41565	+	13.6998i	−0.148956	+	0.844769i	−0.964106	+	0.265519i	$0.914457\pi$
$264$	−2.81539	+	0.199490i	−0.173275	+	0.0122778i
$265$	29.6667	+	10.7978i	1.82241	+	0.663303i
$266$	0.752633	+	1.82188i	0.0461469	+	0.111706i
$267$	−5.93336	−	7.95579i	−0.363115	−	0.486887i
$268$	7.84260	−	29.0496i	0.479063	−	1.77449i
$269$			3.89404i			0.237424i	0.992929	+	0.118712i	$0.0378765\pi$
$269$			3.89404i			0.237424i	−0.992929	+	0.118712i	$0.962123\pi$
$270$	22.0163	+	11.4162i	1.33987	+	0.694771i
$271$	27.1005			1.64624			0.823119	−	0.567869i	$-0.192232\pi$
$271$	27.1005			1.64624			0.823119	+	0.567869i	$0.192232\pi$
$272$	−9.13662	+	1.57550i	−0.553989	+	0.0955287i
$273$	−4.63154	−	39.3362i	−0.280314	−	2.38073i
$274$	−20.5992	+	8.50969i	−1.24444	+	0.514089i
$275$	1.25909	−	3.45933i	0.0759261	−	0.208605i
$276$	8.46153	+	21.3637i	0.509324	+	1.28594i
$277$	7.05421	+	1.24385i	0.423847	+	0.0747356i	0.381503	−	0.924368i	$-0.375407\pi$
$277$	7.05421	+	1.24385i	0.423847	+	0.0747356i	0.0423435	+	0.999103i	$0.486518\pi$
$278$	0.941775	−	2.97713i	0.0564839	−	0.178556i
$279$	−3.94173	+	5.31344i	−0.235985	+	0.318107i
$280$	−30.0972	−	12.5666i	−1.79865	−	0.750998i
$281$	−0.728892	+	0.265295i	−0.0434820	+	0.0158262i	−0.363670	−	0.931528i	$-0.618476\pi$
$281$	−0.728892	+	0.265295i	−0.0434820	+	0.0158262i	0.320188	+	0.947354i	$0.396254\pi$
$282$	6.73830	−	3.75992i	0.401260	−	0.223900i
$283$	−0.982704	−	1.17114i	−0.0584157	−	0.0696171i	0.736045	−	0.676932i	$-0.236691\pi$
$283$	−0.982704	−	1.17114i	−0.0584157	−	0.0696171i	−0.794461	+	0.607315i	$0.792247\pi$
$284$	−6.65895	+	14.2101i	−0.395136	+	0.843213i
$285$	0.685850	+	2.28385i	0.0406263	+	0.135284i
$286$	2.92556	+	4.60179i	0.172992	+	0.272109i
$287$	−11.3528	−	19.6636i	−0.670134	−	1.16071i
$288$	−1.28420	+	16.9219i	−0.0756723	+	0.997133i
$289$	5.81375	−	10.0697i	0.341985	−	0.592336i
$290$	16.6650	−	0.711855i	0.978601	−	0.0418016i
$291$	−1.11473	+	19.4228i	−0.0653469	+	1.13859i
$292$	−2.55788	+	0.218923i	−0.149689	+	0.0128115i
$293$	15.6621	−	2.76164i	0.914987	−	0.161337i	0.303720	−	0.952761i	$-0.401771\pi$
$293$	15.6621	−	2.76164i	0.914987	−	0.161337i	0.611267	+	0.791424i	$0.290660\pi$
$294$	3.75826	+	10.8158i	0.219186	+	0.630793i
$295$	−22.6996	−	19.0472i	−1.32162	−	1.10897i
$296$	2.73300	−	2.08484i	0.158853	−	0.121179i
$297$	1.93011	+	2.28837i	0.111996	+	0.132785i
$298$	−9.45399	+	2.08654i	−0.547655	+	0.120870i
$299$	28.5363	−	34.0082i	1.65029	−	1.96674i
$300$	−19.4722	−	10.5255i	−1.12423	−	0.607687i
$301$	−4.34995	+	0.767013i	−0.250727	+	0.0442099i
$302$	−2.19344	+	16.5402i	−0.126218	+	0.951783i
$303$	−11.8153	+	17.9975i	−0.678772	+	1.03393i
$304$	−1.25396	+	1.04416i	−0.0719195	+	0.0598865i
$305$	8.00977	−	13.8733i	0.458638	−	0.794385i
$306$	7.05914	+	6.84642i	0.403544	+	0.391384i
$307$	−0.370582	+	0.213955i	−0.0211502	+	0.0122111i	−0.510538	−	0.859855i	$-0.670554\pi$
$307$	−0.370582	+	0.213955i	−0.0211502	+	0.0122111i	0.489388	+	0.872066i	$0.337220\pi$
$308$	−2.77865	−	2.78915i	−0.158328	−	0.158927i
$309$	18.7714	−	19.9304i	1.06787	−	1.13380i
$310$	6.41534	−	8.34432i	0.364367	−	0.473925i
$311$	8.46179	−	7.10028i	0.479824	−	0.402620i	−0.370539	−	0.928817i	$-0.620827\pi$
$311$	8.46179	−	7.10028i	0.479824	−	0.402620i	0.850363	+	0.526197i	$0.176383\pi$
$312$	29.9405	−	13.3636i	1.69504	−	0.756564i
$313$	−26.1193	+	9.50664i	−1.47635	+	0.537347i	−0.949817	−	0.312807i	$-0.898731\pi$
$313$	−26.1193	+	9.50664i	−1.47635	+	0.537347i	−0.526533	+	0.850155i	$0.676508\pi$
$314$	−11.5025	−	12.5765i	−0.649121	−	0.709735i
$315$	8.03493	+	33.6478i	0.452717	+	1.89584i
$316$	0.892817	−	9.98782i	0.0502249	−	0.561859i
$317$	3.46040	+	0.610163i	0.194356	+	0.0342701i	0.269979	−	0.962866i	$-0.412983\pi$
$317$	3.46040	+	0.610163i	0.194356	+	0.0342701i	−0.0756229	+	0.997136i	$0.524095\pi$
$318$	17.7669	−	14.4703i	0.996318	−	0.811453i
$319$	1.89205	+	0.688651i	0.105935	+	0.0385571i
$320$	2.50535	−	26.8825i	0.140053	−	1.50278i
$321$	−3.88980	−	1.67399i	−0.217108	−	0.0934329i
$322$	−14.8270	+	28.4170i	−0.826278	+	1.58362i
$323$			0.945557i			0.0526122i
$324$	15.3059	−	9.47260i	0.850327	−	0.526255i
$325$			42.7649i			2.37217i
$326$	16.7975	+	8.76438i	0.930327	+	0.485414i
$327$	25.8569	+	11.1276i	1.42989	+	0.615358i
$328$	12.7373	−	13.8216i	0.703302	−	0.763171i
$329$	10.1144	+	3.68134i	0.557625	+	0.202959i
$330$	−3.00766	−	3.69287i	−0.165566	−	0.203286i
$331$	−17.1533	−	3.02459i	−0.942832	−	0.166247i	−0.318956	−	0.947770i	$-0.603332\pi$
$331$	−17.1533	−	3.02459i	−0.942832	−	0.166247i	−0.623876	+	0.781523i	$0.714443\pi$
$332$	20.6757	+	1.84821i	1.13472	+	0.101434i
$333$	−3.49454	−	1.03974i	−0.191499	−	0.0569776i
$334$	7.06830	−	6.46465i	0.386760	−	0.353730i
$335$	47.7123	−	17.3659i	2.60680	−	0.948798i
$336$	−19.0294	+	14.0805i	−1.03814	+	0.768153i
$337$	−2.18023	+	1.82943i	−0.118765	+	0.0996554i	−0.700236	−	0.713912i	$-0.746922\pi$
$337$	−2.18023	+	1.82943i	−0.118765	+	0.0996554i	0.581471	+	0.813567i	$0.302477\pi$
$338$	−35.6442	−	27.4043i	−1.93879	−	1.49060i
$339$	14.4543	−	15.3467i	0.785048	−	0.833516i
$340$	−11.0418	−	11.0835i	−0.598825	−	0.601090i
$341$	1.10031	−	0.635266i	0.0595853	−	0.0344016i
$342$	1.67844	+	0.422329i	0.0907595	+	0.0228370i
$343$	3.97285	−	6.88117i	0.214514	−	0.371548i
$344$	−1.67917	−	3.24806i	−0.0905346	−	0.175124i
$345$	−21.2795	+	32.4137i	−1.14565	+	1.74509i
$346$	2.36289	+	0.313348i	0.127029	+	0.0168457i
$347$	−25.7859	+	4.54675i	−1.38426	+	0.244082i	−0.815659	−	0.578533i	$-0.803626\pi$
$347$	−25.7859	+	4.54675i	−1.38426	+	0.244082i	−0.568599	+	0.822615i	$0.692514\pi$
$348$	5.75682	−	10.6502i	0.308598	−	0.570910i
$349$	3.27963	−	3.90851i	0.175555	−	0.209218i	−0.671091	−	0.741375i	$-0.734174\pi$
$349$	3.27963	−	3.90851i	0.175555	−	0.209218i	0.846646	+	0.532157i	$0.178618\pi$
$350$	−6.65433	−	30.1504i	−0.355689	−	1.61160i
$351$	−30.1613	−	17.3115i	−1.60989	−	0.924021i
$352$	1.51850	−	2.88371i	0.0809361	−	0.153702i
$353$	−11.4022	−	9.56754i	−0.606875	−	0.509229i	0.286772	−	0.957999i	$-0.407418\pi$
$353$	−11.4022	−	9.56754i	−0.606875	−	0.509229i	−0.893647	+	0.448770i	$0.851862\pi$
$354$	−20.3156	+	7.05920i	−1.07976	+	0.375192i
$355$	−26.0785	+	4.59835i	−1.38410	+	0.244055i
$356$	11.4183	−	0.977262i	0.605168	−	0.0517948i
$357$	−0.785982	+	13.6948i	−0.0415986	+	0.724803i
$358$	−0.719139	−	16.8355i	−0.0380077	−	0.889785i
$359$	−7.74329	+	13.4118i	−0.408675	+	0.707846i	−0.994742	−	0.102417i	$-0.967342\pi$
$359$	−7.74329	+	13.4118i	−0.408675	+	0.707846i	0.586066	+	0.810263i	$0.300676\pi$
$360$	−24.6059	+	14.6496i	−1.29685	+	0.772103i
$361$	−9.41679	−	16.3104i	−0.495621	−	0.858440i
$362$	19.7103	−	12.5307i	1.03595	−	0.658600i
$363$	5.31445	+	17.6969i	0.278936	+	0.928846i
$364$	41.4137	+	19.4068i	2.17067	+	1.01719i
$365$	−2.78459	−	3.31854i	−0.145752	−	0.173700i
$366$	−5.66547	−	10.1533i	−0.296139	−	0.530722i
$367$	24.0744	−	8.76237i	1.25667	−	0.457392i	0.374023	−	0.927419i	$-0.377978\pi$
$367$	24.0744	−	8.76237i	1.25667	−	0.457392i	0.882652	+	0.470027i	$0.155756\pi$
$368$	−26.1124	−	4.70601i	−1.36120	−	0.245318i
$369$	−19.8049	−	2.28084i	−1.03100	−	0.118736i
$370$	5.53032	+	1.74944i	0.287508	+	0.0909492i
$371$	31.4772	+	5.55028i	1.63422	+	0.288156i
$372$	−2.81312	−	7.10255i	−0.145853	−	0.368250i
$373$	−4.86012	+	13.3531i	−0.251648	+	0.691396i	0.747970	+	0.663733i	$0.231029\pi$
$373$	−4.86012	+	13.3531i	−0.251648	+	0.691396i	−0.999617	+	0.0276634i	$0.991193\pi$
$374$	−0.721061	−	1.74545i	−0.0372852	−	0.0902551i
$375$	−0.949965	−	8.06816i	−0.0490560	−	0.416638i
$376$	−0.413847	+	8.90043i	−0.0213425	+	0.459004i
$377$	−23.3900			−1.20465
$378$	23.9582	+	7.51189i	1.23228	+	0.386370i
$379$		−	1.93137i		−	0.0992080i	−0.998769	−	0.0496040i	$-0.984204\pi$
$379$		−	1.93137i		−	0.0992080i	0.998769	−	0.0496040i	$-0.0157959\pi$
$380$	−2.65834	−	0.717680i	−0.136370	−	0.0368162i
$381$	−9.92702	−	13.3107i	−0.508577	−	0.681930i
$382$	17.2789	−	7.13805i	0.884064	−	0.365214i
$383$	12.4377	+	4.52695i	0.635537	+	0.231317i	0.639639	−	0.768675i	$-0.279084\pi$
$383$	12.4377	+	4.52695i	0.635537	+	0.231317i	−0.00410258	+	0.999992i	$0.501306\pi$
$384$	−15.8206	−	11.5633i	−0.807339	−	0.590087i
$385$	1.15363	−	6.54257i	0.0587945	−	0.333440i
$386$	0.238634	+	0.0754888i	0.0121462	+	0.00384228i
$387$	−1.73467	+	3.46866i	−0.0881783	+	0.176322i
$388$	−18.3775	−	12.9198i	−0.932975	−	0.655903i
$389$	8.22522	+	22.5986i	0.417035	+	1.14579i	0.953374	+	0.301792i	$0.0975848\pi$
$389$	8.22522	+	22.5986i	0.417035	+	1.14579i	−0.536339	+	0.844003i	$0.680193\pi$
$390$	47.5042	+	28.3619i	2.40547	+	1.43616i
$391$	−11.7780	+	9.88288i	−0.595637	+	0.499799i
$392$	−12.9000	−	2.89819i	−0.651548	−	0.146381i
$393$	0.164279	−	0.695774i	0.00828677	−	0.0350972i
$394$	−1.15927	+	0.736999i	−0.0584032	+	0.0371295i
$395$	14.6540	−	8.46051i	0.737325	−	0.425695i
$396$	−3.42037	+	0.500340i	−0.171880	+	0.0251430i
$397$	−28.6833	−	16.5603i	−1.43957	−	0.831137i	−0.441752	−	0.897137i	$-0.645643\pi$
$397$	−28.6833	−	16.5603i	−1.43957	−	0.831137i	−0.997820	+	0.0659997i	$0.978976\pi$
$398$	−5.79090	+	0.247362i	−0.290272	+	0.0123991i
$399$	1.08534	+	2.15652i	0.0543347	+	0.107961i
$400$	22.1829	−	12.6959i	1.10915	−	0.634796i
$401$	1.94567	+	11.0344i	0.0971620	+	0.551033i	0.994063	+	0.108802i	$0.0347016\pi$
$401$	1.94567	+	11.0344i	0.0971620	+	0.551033i	−0.896901	+	0.442231i	$0.854187\pi$
$402$	6.92993	−	36.1947i	0.345633	−	1.80523i
$403$	−9.48715	+	11.3063i	−0.472588	+	0.563209i
$404$	−10.4637	−	22.5505i	−0.520590	−	1.12193i
$405$	27.9304	+	11.9359i	1.38787	+	0.593097i
$406$	16.4905	−	3.63954i	0.818412	−	0.180627i
$407$	0.536366	+	0.450065i	0.0265867	+	0.0223089i
$408$	−11.0153	+	2.75726i	−0.545340	+	0.136505i
$409$	1.95004	+	11.0592i	0.0964233	+	0.546844i	0.994302	+	0.106601i	$0.0339966\pi$
$409$	1.95004	+	11.0592i	0.0964233	+	0.546844i	−0.897879	+	0.440243i	$0.854892\pi$
$410$	31.4413	+	4.16950i	1.55277	+	0.205917i
$411$	−24.3829	+	12.2714i	−1.20272	+	0.605305i
$412$	8.12468	+	30.5522i	0.400274	+	1.50520i
$413$	−25.9810	−	15.0001i	−1.27844	−	0.738109i
$414$	12.2823	+	25.3209i	0.603642	+	1.24446i
$415$	17.5140	+	30.3351i	0.859728	+	1.48909i
$416$	−5.11871	+	37.5120i	−0.250966	+	1.83918i
$417$	0.878792	−	3.72197i	0.0430347	−	0.182266i
$418$	−0.263503	−	0.202589i	−0.0128884	−	0.00990893i
$419$	8.95678	+	10.6743i	0.437567	+	0.521472i	0.939090	−	0.343672i	$-0.111671\pi$
$419$	8.95678	+	10.6743i	0.437567	+	0.521472i	−0.501522	+	0.865145i	$0.667226\pi$
$420$	−37.9049	−	12.6041i	−1.84957	−	0.615015i
$421$	−4.06687	−	11.1736i	−0.198207	−	0.544570i	0.800276	−	0.599632i	$-0.204686\pi$
$421$	−4.06687	−	11.1736i	−0.198207	−	0.544570i	−0.998483	+	0.0550623i	$0.982464\pi$
$422$	−3.58149	−	3.91592i	−0.174344	−	0.190624i
$423$	7.88699	−	5.20653i	0.383478	−	0.253150i
$424$	3.37930	+	26.2421i	0.164113	+	1.27443i
$425$	2.57184	−	14.5856i	0.124753	−	0.707507i
$426$	−6.83727	+	17.9626i	−0.331267	+	0.870289i
$427$	5.54707	−	15.2404i	0.268442	−	0.737537i
$428$	4.01080	−	2.79713i	0.193869	−	0.135204i
$429$	3.99269	+	5.35364i	0.192769	+	0.258476i
$430$	2.85415	−	5.47017i	0.137640	−	0.263795i
$431$	−28.2506			−1.36079			−0.680393	−	0.732848i	$-0.738191\pi$
$431$	−28.2506			−1.36079			−0.680393	+	0.732848i	$0.738191\pi$
$432$	−0.0255966	+	20.7846i	−0.00123152	+	0.999999i
$433$	−27.8524			−1.33850			−0.669251	−	0.743036i	$-0.733385\pi$
$433$	−27.8524			−1.33850			−0.669251	+	0.743036i	$0.733385\pi$
$434$	4.92938	−	9.44748i	0.236618	−	0.453494i
$435$	20.2888	−	2.38886i	0.972774	−	0.114537i
$436$	−26.6612	+	18.5935i	−1.27684	+	0.890467i
$437$	−0.925505	+	2.54280i	−0.0442729	+	0.121639i
$438$	−3.10410	+	0.500596i	−0.148320	+	0.0239194i
$439$	−2.13242	+	12.0935i	−0.101775	+	0.577193i	0.890685	+	0.454621i	$0.150225\pi$
$439$	−2.13242	+	12.0935i	−0.101775	+	0.577193i	−0.992460	+	0.122572i	$0.960886\pi$
$440$	5.45445	−	0.702390i	0.260031	−	0.0334851i
$441$	5.57627	+	12.8672i	0.265537	+	0.612725i
$442$	14.8061	+	16.1887i	0.704254	+	0.770016i
$443$	7.22670	+	19.8552i	0.343351	+	0.943348i	0.984415	+	0.175861i	$0.0562710\pi$
$443$	7.22670	+	19.8552i	0.343351	+	0.943348i	−0.641064	+	0.767487i	$0.721507\pi$
$444$	3.14786	−	2.79550i	0.149391	−	0.132668i
$445$	12.4303	+	14.8138i	0.589252	+	0.702243i
$446$	4.39681	+	3.38039i	0.208195	+	0.160066i
$447$	−11.3564	+	3.41036i	−0.537137	+	0.161305i
$448$	−2.22815	−	27.2434i	−0.105270	−	1.28713i
$449$	13.8708	+	24.0249i	0.654604	+	1.13381i	0.981993	+	0.188917i	$0.0604978\pi$
$449$	13.8708	+	24.0249i	0.654604	+	1.13381i	−0.327389	+	0.944890i	$0.606169\pi$
$450$	−24.7420	−	11.0798i	−1.16635	−	0.522309i
$451$	3.31561	+	1.91427i	0.156126	+	0.0901393i
$452$	6.25612	+	23.5256i	0.294263	+	1.10655i
$453$	−1.17089	+	20.4013i	−0.0550133	+	0.958538i
$454$	−16.5901	−	2.20005i	−0.778611	−	0.103254i
$455$	13.4014	+	76.0030i	0.628266	+	3.56307i
$456$	−1.43632	+	1.38961i	−0.0672617	+	0.0650744i
$457$	−26.0906	−	21.8926i	−1.22047	−	1.02409i	−0.998800	−	0.0489720i	$-0.984405\pi$
$457$	−26.0906	−	21.8926i	−1.22047	−	1.02409i	−0.221668	−	0.975122i	$-0.571150\pi$
$458$	−14.6352	+	3.23006i	−0.683858	+	0.150931i
$459$	9.24588	+	7.71824i	0.431561	+	0.360256i
$460$	−18.8452	−	40.6137i	−0.878664	−	1.89362i
$461$	8.93591	−	10.6494i	0.416187	−	0.495992i	−0.516698	−	0.856168i	$-0.672839\pi$
$461$	8.93591	−	10.6494i	0.416187	−	0.495992i	0.932884	+	0.360176i	$0.117283\pi$
$462$	−3.64799	−	3.15318i	−0.169720	−	0.146699i
$463$	3.22751	+	18.3041i	0.149995	+	0.850665i	0.963220	+	0.268715i	$0.0865991\pi$
$463$	3.22751	+	18.3041i	0.149995	+	0.850665i	−0.813224	+	0.581950i	$0.802290\pi$
$464$	6.94395	+	12.1328i	0.322365	+	0.563251i
$465$	7.07455	−	10.7762i	0.328075	−	0.499735i
$466$	1.59662	−	0.0682007i	0.0739621	−	0.00315934i
$467$	8.34116	+	4.81577i	0.385983	+	0.222847i	0.680418	−	0.732824i	$-0.261798\pi$
$467$	8.34116	+	4.81577i	0.385983	+	0.222847i	−0.294435	+	0.955671i	$0.595132\pi$
$468$	35.3492	−	19.0514i	1.63402	−	0.880651i
$469$	44.5181	−	25.7026i	2.05566	−	1.18683i
$470$	−12.6881	+	8.06641i	−0.585260	+	0.372076i
$471$	−15.1952	−	14.3116i	−0.700156	−	0.659442i
$472$	5.44373	−	24.2303i	0.250568	−	1.11529i
$473$	0.570541	−	0.478741i	0.0262335	−	0.0220125i
$474$	0.179797	−	12.2800i	0.00825834	−	0.564039i
$475$	−0.891532	−	2.44946i	−0.0409063	−	0.112389i
$476$	−12.9577	−	9.10955i	−0.593914	−	0.417536i
$477$	20.3802	−	19.2931i	0.933145	−	0.883372i
$478$	−7.82598	−	2.47564i	−0.357952	−	0.113233i
$479$	5.05443	−	28.6651i	0.230943	−	1.30974i	−0.620049	−	0.784563i	$-0.712887\pi$
$479$	5.05443	−	28.6651i	0.230943	−	1.30974i	0.850992	−	0.525179i	$-0.176002\pi$
$480$	0.608882	−	33.0613i	0.0277915	−	1.50903i
$481$	−7.64321	−	2.78190i	−0.348500	−	0.126844i
$482$	−38.5571	+	15.9283i	−1.75623	+	0.725513i
$483$	−15.5180	+	36.0588i	−0.706094	+	1.64073i
$484$	−20.5987	−	5.56108i	−0.936304	−	0.252777i
$485$		−	37.9074i		−	1.72129i
$486$	17.8301	−	12.9648i	0.808790	−	0.588097i
$487$	−13.1429			−0.595563			−0.297782	−	0.954634i	$-0.596247\pi$
$487$	−13.1429			−0.595563			−0.297782	+	0.954634i	$0.596247\pi$
$488$	13.4112	+	0.623587i	0.607098	+	0.0282285i
$489$	21.3147	+	9.17282i	0.963882	+	0.414809i
$490$	−8.51842	−	20.6203i	−0.384823	−	0.931530i
$491$	−4.01945	+	11.0433i	−0.181395	+	0.498379i	−0.996748	−	0.0805856i	$-0.974321\pi$
$491$	−4.01945	+	11.0433i	−0.181395	+	0.498379i	0.815352	+	0.578965i	$0.196543\pi$
$492$	14.2965	−	18.0423i	0.644537	−	0.813411i
$493$	7.97752	+	1.40665i	0.359289	+	0.0633524i
$494$	3.68134	+	1.16454i	0.165631	+	0.0523953i
$495$	−4.01010	−	4.23604i	−0.180240	−	0.190396i
$496$	8.68131	+	1.56456i	0.389802	+	0.0702507i
$497$	−25.1930	+	9.16949i	−1.13006	+	0.411308i
$498$	25.4206	+	0.372195i	1.13913	+	0.0166785i
$499$	−23.2598	−	27.7199i	−1.04125	−	1.24091i	−0.969911	−	0.243461i	$-0.921717\pi$
$499$	−23.2598	−	27.7199i	−1.04125	−	1.24091i	−0.0713387	−	0.997452i	$-0.522727\pi$
$500$	8.49427	+	3.98048i	0.379875	+	0.178012i
$501$	8.04343	−	8.54003i	0.359354	−	0.381540i
$502$	−7.17608	+	4.56215i	−0.320284	+	0.203619i
$503$	1.18773	+	2.05720i	0.0529581	+	0.0917261i	0.891289	−	0.453435i	$-0.149802\pi$
$503$	1.18773	+	2.05720i	0.0529581	+	0.0917261i	−0.838331	+	0.545161i	$0.816468\pi$
$504$	−21.9577	+	18.9321i	−0.978072	+	0.843305i
$505$	20.9748	−	36.3294i	0.933366	−	1.61664i
$506$	−0.230650	−	5.39966i	−0.0102536	−	0.240044i
$507$	−46.0326	−	30.2202i	−2.04438	−	1.34213i
$508$	19.1038	−	1.63504i	0.847594	−	0.0725434i
$509$	−40.5051	+	7.14215i	−1.79536	+	0.316570i	−0.969090	−	0.246706i	$-0.920652\pi$
$509$	−40.5051	+	7.14215i	−1.79536	+	0.316570i	−0.826269	+	0.563276i	$0.809541\pi$
$510$	−14.4964	−	12.5301i	−0.641911	−	0.554843i
$511$	−3.35977	−	2.81918i	−0.148627	−	0.124713i
$512$	20.9778	−	8.48130i	0.927096	−	0.374824i
$513$	2.08846	+	0.362779i	0.0922077	+	0.0160171i
$514$	7.91515	+	35.8631i	0.349123	+	1.58185i
$515$	−34.2906	+	40.8660i	−1.51103	+	1.80077i
$516$	−2.34699	−	3.81391i	−0.103320	−	0.167898i
$517$	−1.78734	+	0.315155i	−0.0786069	+	0.0138605i
$518$	5.82153	+	0.772007i	0.255783	+	0.0339201i
$519$	2.91447	+	0.167270i	0.127931	+	0.00734234i
$520$	−56.7507	+	29.3387i	−2.48868	+	1.28659i
$521$	−5.21530	+	9.03316i	−0.228486	+	0.395750i	−0.957360	−	0.288899i	$-0.906711\pi$
$521$	−5.21530	+	9.03316i	−0.228486	+	0.395750i	0.728873	+	0.684649i	$0.240044\pi$
$522$	6.06004	−	13.5324i	0.265241	−	0.592299i
$523$	14.6626	−	8.46543i	0.641149	−	0.370167i	−0.143908	−	0.989591i	$-0.545967\pi$
$523$	14.6626	−	8.46543i	0.641149	−	0.370167i	0.785057	+	0.619424i	$0.212634\pi$
$524$	0.582615	+	0.584818i	0.0254516	+	0.0255479i
$525$	−10.8762	−	36.2173i	−0.474677	−	1.58065i
$526$	−15.5966	−	11.9911i	−0.680046	−	0.522838i
$527$	3.91569	−	3.28565i	0.170570	−	0.143125i
$528$	1.59169	−	3.66045i	0.0692693	−	0.159301i
$529$	−19.7338	+	7.18252i	−0.857992	+	0.312283i
$530$	−32.9461	+	30.1324i	−1.43109	+	1.30887i
$531$	−24.1687	+	10.4740i	−1.04883	+	0.454533i
$532$	−2.77665	−	0.248206i	−0.120383	−	0.0107611i
$533$	−43.7992	−	7.72298i	−1.89715	−	0.334519i
$534$	13.8566	−	2.23464i	0.599633	−	0.0967024i
$535$	7.75366	+	2.82210i	0.335220	+	0.122010i
$536$	31.2920	+	28.8372i	1.35161	+	1.24558i
$537$	−2.41330	−	20.4964i	−0.104142	−	0.884486i
$538$	−4.88238	−	2.54746i	−0.210494	−	0.109829i
$539$		−	2.69313i		−	0.116001i
$540$	−28.7167	+	20.1357i	−1.23577	+	0.866504i
$541$			29.4745i			1.26721i	0.773658	+	0.633603i	$0.218425\pi$
$541$			29.4745i			1.26721i	−0.773658	+	0.633603i	$0.781575\pi$
$542$	−17.7290	+	33.9788i	−0.761526	+	1.45951i
$543$	22.9306	−	17.1015i	0.984048	−	0.733894i
$544$	4.00175	−	12.4862i	0.171574	−	0.535343i
$545$	−51.5414	−	18.7595i	−2.20779	−	0.803570i
$546$	52.3499	+	19.9265i	2.24037	+	0.852774i
$547$	31.4846	+	5.55158i	1.34618	+	0.237369i	0.799850	−	0.600199i	$-0.204912\pi$
$547$	31.4846	+	5.55158i	1.34618	+	0.237369i	0.546333	+	0.837568i	$0.316023\pi$
$548$	2.80636	−	31.3944i	0.119882	−	1.34110i
$549$	−7.84523	−	11.8842i	−0.334826	−	0.507204i
$550$	3.51363	+	3.84173i	0.149822	+	0.163812i
$551$	1.33972	−	0.487617i	0.0570739	−	0.0207732i
$552$	−32.3214	−	3.36686i	−1.37569	−	0.143303i
$553$	13.1233	−	11.0117i	0.558059	−	0.468267i
$554$	−6.17437	+	8.03090i	−0.262324	+	0.341200i
$555$	6.91395	+	1.63245i	0.293481	+	0.0692935i
$556$	3.11664	+	3.12842i	0.132175	+	0.132675i
$557$	−7.19468	+	4.15385i	−0.304849	+	0.176004i	−0.644619	−	0.764504i	$-0.722984\pi$
$557$	−7.19468	+	4.15385i	−0.304849	+	0.176004i	0.339770	+	0.940508i	$0.389651\pi$
$558$	−4.08337	−	8.41818i	−0.172863	−	0.356370i
$559$	−4.32598	+	7.49282i	−0.182970	+	0.316913i
$560$	35.4455	−	29.5151i	1.49785	−	1.24724i
$561$	−1.03981	−	2.06606i	−0.0439007	−	0.0872290i
$562$	0.144209	−	1.08744i	0.00608307	−	0.0458710i
$563$	6.57453	−	1.15927i	0.277083	−	0.0488573i	−0.0333796	−	0.999443i	$-0.510627\pi$
$563$	6.57453	−	1.15927i	0.277083	−	0.0488573i	0.310463	+	0.950585i	$0.399516\pi$
$564$	0.306048	+	10.9082i	0.0128870	+	0.459320i
$565$	−26.4043	+	31.4674i	−1.11084	+	1.32384i
$566$	2.11126	−	0.465966i	0.0887430	−	0.0195860i
$567$	29.9462	+	6.99023i	1.25762	+	0.293562i
$568$	−13.4604	−	17.6452i	−0.564787	−	0.740375i
$569$	−24.2709	−	20.3657i	−1.01749	−	0.853775i	−0.0281798	−	0.999603i	$-0.508971\pi$
$569$	−24.2709	−	20.3657i	−1.01749	−	0.853775i	−0.989310	+	0.145827i	$0.953416\pi$
$570$	−3.31219	−	0.634161i	−0.138732	−	0.0265621i
$571$	32.6020	−	5.74861i	1.36435	−	0.240572i	0.556936	−	0.830555i	$-0.311977\pi$
$571$	32.6020	−	5.74861i	1.36435	−	0.240572i	0.807416	+	0.589983i	$0.200866\pi$
$572$	−7.68363	+	0.657622i	−0.321269	+	0.0274966i
$573$	20.4527	−	10.2934i	0.854423	−	0.430014i
$574$	32.0813	−	1.37037i	1.33905	−	0.0571982i
$575$	21.1926	−	36.7066i	0.883791	−	1.53077i
$576$	−20.3767	−	12.6804i	−0.849028	−	0.528348i
$577$	15.0611	+	26.0866i	0.627001	+	1.08600i	0.988150	+	0.153490i	$0.0490512\pi$
$577$	15.0611	+	26.0866i	0.627001	+	1.08600i	−0.361149	+	0.932508i	$0.617615\pi$
$578$	8.82214	+	13.8769i	0.366953	+	0.577202i
$579$	0.298338	+	0.0704404i	0.0123985	+	0.00292740i
$580$	−10.0096	+	21.3603i	−0.415627	+	0.886940i
$581$	22.7953	+	27.1663i	0.945707	+	1.12705i
$582$	−23.6232	−	14.1040i	−0.979214	−	0.584629i
$583$	−5.06443	+	1.84330i	−0.209747	+	0.0763418i
$584$	1.39887	−	3.35031i	0.0578855	−	0.138637i
$585$	60.6050	+	30.3085i	2.50571	+	1.25310i
$586$	−6.78347	+	21.4438i	−0.280222	+	0.885837i
$587$	−15.0318	−	2.65051i	−0.620427	−	0.109398i	−0.145406	−	0.989372i	$-0.546449\pi$
$587$	−15.0318	−	2.65051i	−0.620427	−	0.109398i	−0.475022	+	0.879974i	$0.657560\pi$
$588$	−16.0196	−	2.36354i	−0.660637	−	0.0974707i
$589$	0.307693	−	0.845379i	0.0126783	−	0.0348332i
$590$	38.7314	−	16.0003i	1.59455	−	0.658721i
$591$	−1.34867	+	1.00583i	−0.0554770	+	0.0413743i
$592$	0.826072	+	4.79055i	0.0339513	+	0.196890i
$593$	27.1813			1.11620			0.558101	−	0.829773i	$-0.311530\pi$
$593$	27.1813			1.11620			0.558101	+	0.829773i	$0.311530\pi$
$594$	−4.13184	+	0.922942i	−0.169531	+	0.0378688i
$595$		−	26.7279i		−	1.09574i
$596$	3.56863	−	13.2185i	0.146177	−	0.541450i
$597$	−7.05014	+	0.830102i	−0.288543	+	0.0339738i
$598$	23.9714	+	58.0269i	0.980264	+	2.37290i
$599$	−39.7660	−	14.4737i	−1.62480	−	0.591378i	−0.640509	−	0.767951i	$-0.721277\pi$
$599$	−39.7660	−	14.4737i	−1.62480	−	0.591378i	−0.984288	+	0.176573i	$0.943499\pi$
$600$	25.9355	−	17.5287i	1.05881	−	0.715604i
$601$	−0.648834	+	3.67972i	−0.0264665	+	0.150099i	−0.995177	−	0.0980937i	$-0.968726\pi$
$601$	−0.648834	+	3.67972i	−0.0264665	+	0.150099i	0.968711	+	0.248193i	$0.0798366\pi$
$602$	1.88403	−	5.95577i	0.0767872	−	0.242739i
$603$	5.16379	−	44.8381i	0.210286	−	1.82595i
$604$	−19.3033	−	13.5707i	−0.785440	−	0.552183i
$605$	−12.3139	−	33.8321i	−0.500631	−	1.37547i
$606$	−14.8359	−	26.5880i	−0.602666	−	1.08006i
$607$	35.5497	−	29.8298i	1.44292	−	1.21075i	0.505370	−	0.862903i	$-0.331356\pi$
$607$	35.5497	−	29.8298i	1.44292	−	1.21075i	0.937550	−	0.347850i	$-0.113088\pi$
$608$	−0.488837	−	2.25530i	−0.0198250	−	0.0914647i
$609$	19.8088	−	5.94867i	0.802694	−	0.241052i
$610$	12.1545	+	19.1186i	0.492122	+	0.774088i
$611$	18.2586	−	10.5416i	0.738664	−	0.426468i
$612$	−13.2021	+	4.37190i	−0.533665	+	0.176724i
$613$	21.9670	+	12.6827i	0.887239	+	0.512248i	0.873038	−	0.487652i	$-0.162146\pi$
$613$	21.9670	+	12.6827i	0.887239	+	0.512248i	0.0142005	+	0.999899i	$0.495480\pi$
$614$	−0.0258261	−	0.604606i	−0.00104226	−	0.0243999i
$615$	38.7808	+	2.22575i	1.56379	+	0.0897507i
$616$	5.31483	−	1.65923i	0.214141	−	0.0668524i
$617$	1.23909	+	7.02722i	0.0498838	+	0.282905i	0.999538	−	0.0303950i	$-0.00967653\pi$
$617$	1.23909	+	7.02722i	0.0498838	+	0.282905i	−0.949654	+	0.313300i	$0.898565\pi$
$618$	12.7087	+	36.5741i	0.511217	+	1.47123i
$619$	17.2889	−	20.6041i	0.694900	−	0.828149i	−0.297039	−	0.954865i	$-0.595999\pi$
$619$	17.2889	−	20.6041i	0.694900	−	0.828149i	0.991939	+	0.126716i	$0.0404437\pi$
$620$	6.26528	+	13.5024i	0.251620	+	0.542269i
$621$	17.3096	+	29.8058i	0.694610	+	1.19607i
$622$	3.36672	+	15.2544i	0.134993	+	0.611646i
$623$	14.9979	+	12.5847i	0.600877	+	0.504196i
$624$	−2.83155	+	46.2819i	−0.113353	+	1.85276i
$625$	−2.79914	−	15.8747i	−0.111966	−	0.634989i
$626$	5.16761	−	38.9677i	0.206539	−	1.55746i
$627$	−0.340300	−	0.223406i	−0.0135903	−	0.00892197i
$628$	23.2934	−	6.19435i	0.929507	−	0.247182i
$629$	2.43953	+	1.40846i	0.0972705	+	0.0561592i
$630$	−47.4442	−	11.9379i	−1.89022	−	0.475619i
$631$	−11.7466	−	20.3457i	−0.467624	−	0.809949i	0.531691	−	0.846938i	$-0.321557\pi$
$631$	−11.7466	−	20.3457i	−0.467624	−	0.809949i	−0.999316	+	0.0369893i	$0.988223\pi$
$632$	11.9387	+	7.65340i	0.474897	+	0.304436i
$633$	−4.73127	−	4.45615i	−0.188051	−	0.177116i
$634$	−3.02880	+	3.93951i	−0.120289	+	0.156458i
$635$	20.7970	+	24.7848i	0.825302	+	0.983557i
$636$	6.51993	+	31.7426i	0.258532	+	1.25868i
$637$	10.7002	+	29.3985i	0.423956	+	1.16481i
$638$	−2.10121	+	1.92176i	−0.0831876	+	0.0760831i
$639$	−6.71294	+	22.5619i	−0.265560	+	0.892535i
$640$	32.0665	+	20.7276i	1.26754	+	0.819331i
$641$	−7.57282	+	42.9476i	−0.299108	+	1.69633i	0.350911	+	0.936409i	$0.385872\pi$
$641$	−7.57282	+	42.9476i	−0.299108	+	1.69633i	−0.650019	+	0.759918i	$0.725239\pi$
$642$	4.64355	−	3.78195i	0.183266	−	0.149261i
$643$	0.120739	−	0.331727i	0.00476148	−	0.0130820i	−0.937289	−	0.348553i	$-0.886673\pi$
$643$	0.120739	−	0.331727i	0.00476148	−	0.0130820i	0.942051	+	0.335471i	$0.108895\pi$
$644$	−25.9296	−	37.1804i	−1.02177	−	1.46511i
$645$	2.98717	−	6.94120i	0.117620	−	0.273310i
$646$	−1.18554	−	0.618578i	−0.0466446	−	0.0243376i
$647$	−26.0967			−1.02597			−0.512984	−	0.858398i	$-0.671460\pi$
$647$	−26.0967			−1.02597			−0.512984	+	0.858398i	$0.671460\pi$
$648$	1.86378	+	25.3875i	0.0732161	+	0.997316i
$649$	5.05855			0.198565
$650$	−53.6189	−	27.9766i	−2.10311	−	1.09733i
$651$	5.15911	−	11.9881i	0.202201	−	0.469850i
$652$	−21.9777	+	15.3272i	−0.860711	+	0.600259i
$653$	−0.281991	+	0.774764i	−0.0110352	+	0.0303189i	−0.945088	−	0.326816i	$-0.894024\pi$
$653$	−0.281991	+	0.774764i	−0.0110352	+	0.0303189i	0.934053	+	0.357135i	$0.116246\pi$
$654$	−30.8673	+	25.1399i	−1.20701	+	0.983050i
$655$	−0.241889	+	1.37182i	−0.00945137	+	0.0536014i
$656$	8.99693	+	25.0122i	0.351271	+	0.976562i
$657$	−3.74554	+	0.894418i	−0.146127	+	0.0348946i
$658$	−11.2325	+	10.2732i	−0.437887	+	0.400490i
$659$	−14.2971	−	39.2809i	−0.556935	−	1.53017i	−0.824058	−	0.566505i	$-0.808295\pi$
$659$	−14.2971	−	39.2809i	−0.556935	−	1.53017i	0.267123	−	0.963662i	$-0.413927\pi$
$660$	6.59773	−	1.35517i	0.256816	−	0.0527500i
$661$	−1.06741	−	1.27208i	−0.0415173	−	0.0494784i	0.744886	−	0.667192i	$-0.232504\pi$
$661$	−1.06741	−	1.27208i	−0.0415173	−	0.0494784i	−0.786404	+	0.617713i	$0.788059\pi$
$662$	15.0139	−	19.5283i	0.583530	−	0.758988i
$663$	19.5594	+	18.4220i	0.759624	+	0.715452i
$664$	−15.8432	+	24.7142i	−0.614835	+	0.959096i
$665$	−2.35205	−	4.07387i	−0.0912086	−	0.157978i
$666$	3.58974	−	3.70128i	0.139100	−	0.143422i
$667$	20.0764	+	11.5911i	0.777362	+	0.448810i
$668$	3.48137	+	13.0914i	0.134698	+	0.506522i
$669$	5.67824	+	3.72775i	0.219533	+	0.144123i
$670$	−9.43970	+	71.1826i	−0.364688	+	2.75002i
$671$	0.474878	+	2.69317i	0.0183325	+	0.103969i
$672$	−5.20527	−	33.0705i	−0.200798	−	1.27572i
$673$	−4.23311	−	3.55200i	−0.163175	−	0.136920i	0.557544	−	0.830147i	$-0.311744\pi$
$673$	−4.23311	−	3.55200i	−0.163175	−	0.136920i	−0.720719	+	0.693227i	$0.756188\pi$
$674$	−0.867456	−	3.93039i	−0.0334132	−	0.151393i
$675$	−31.2287	−	11.2765i	−1.20199	−	0.434032i
$676$	57.6779	−	26.7632i	2.21838	−	1.02936i
$677$	2.08429	−	2.48396i	0.0801056	−	0.0954662i	−0.724503	−	0.689272i	$-0.757931\pi$
$677$	2.08429	−	2.48396i	0.0801056	−	0.0954662i	0.804609	+	0.593805i	$0.202375\pi$
$678$	9.78584	+	28.1625i	0.375823	+	1.08158i
$679$	−6.66432	−	37.7952i	−0.255753	−	1.45045i
$680$	21.1201	−	6.59347i	0.809919	−	0.252848i
$681$	−20.4628	−	1.17442i	−0.784137	−	0.0450040i
$682$	0.0766817	+	1.79517i	0.00293629	+	0.0687405i
$683$	22.4547	+	12.9642i	0.859206	+	0.496063i	0.863746	−	0.503927i	$-0.168112\pi$
$683$	22.4547	+	12.9642i	0.859206	+	0.496063i	−0.00454025	+	0.999990i	$0.501445\pi$
$684$	−1.62754	+	1.82815i	−0.0622307	+	0.0699010i
$685$	46.0615	−	26.5936i	1.75992	−	1.01609i
$686$	6.02864	+	9.48281i	0.230175	+	0.362055i
$687$	−17.5801	+	5.27939i	−0.670724	+	0.201421i
$688$	5.17094	+	0.0195167i	0.197140	+	0.000744069i
$689$	47.9602	−	40.2434i	1.82714	−	1.53315i
$690$	−26.7195	−	47.8851i	−1.01720	−	1.82296i
$691$	−10.2247	−	28.0920i	−0.388964	−	1.06867i	−0.967469	−	0.252991i	$-0.918586\pi$
$691$	−10.2247	−	28.0920i	−0.388964	−	1.06867i	0.578504	−	0.815679i	$-0.303637\pi$
$692$	−1.93866	+	2.75761i	−0.0736970	+	0.104829i
$693$	−4.74295	−	3.51852i	−0.180170	−	0.133657i
$694$	11.1682	−	35.3049i	0.423941	−	1.34016i
$695$	−1.29396	+	7.33841i	−0.0490827	+	0.278362i
$696$	9.58718	+	14.1852i	0.363401	+	0.537690i
$697$	14.4739	+	5.26808i	0.548240	+	0.199543i
$698$	2.75500	+	6.66895i	0.104278	+	0.252423i
$699$	1.94381	−	0.228869i	0.0735217	−	0.00865663i
$700$	42.1559	+	11.3810i	1.59334	+	0.430160i
$701$			24.6223i			0.929973i	0.885318	+	0.464987i	$0.153941\pi$
$701$			24.6223i			0.929973i	−0.885318	+	0.464987i	$0.846059\pi$
$702$	41.4367	−	26.4913i	1.56393	−	0.999850i
$703$	0.495778			0.0186986
$704$	2.62221	+	3.79040i	0.0988284	+	0.142856i
$705$	−14.7611	+	11.0087i	−0.555937	+	0.414612i
$706$	19.4551	−	8.03705i	0.732201	−	0.302479i
$707$	14.5258	−	39.9094i	0.546300	−	1.50095i
$708$	4.43947	−	30.0899i	0.166846	−	1.13085i
$709$	−26.4148	−	4.65765i	−0.992030	−	0.174922i	−0.346001	−	0.938234i	$-0.612460\pi$
$709$	−26.4148	−	4.65765i	−0.992030	−	0.174922i	−0.646029	+	0.763313i	$0.723572\pi$
$710$	11.2950	−	35.7056i	0.423894	−	1.34001i
$711$	−0.900037	−	15.0145i	−0.0337540	−	0.563088i
$712$	−6.24449	+	14.9556i	−0.234022	+	0.560487i
$713$	13.7461	−	5.00317i	0.514796	−	0.187370i
$714$	−16.6564	−	9.94450i	−0.623349	−	0.372164i
$715$	−8.36463	−	9.96858i	−0.312819	−	0.372804i
$716$	21.5789	+	10.1120i	0.806443	+	0.377905i
$717$	−9.78395	−	2.31008i	−0.365388	−	0.0862716i
$718$	−11.7501	−	18.4825i	−0.438512	−	0.689761i
$719$	9.26666	+	16.0503i	0.345588	+	0.598576i	0.985460	−	0.169905i	$-0.0543462\pi$
$719$	9.26666	+	16.0503i	0.345588	+	0.598576i	−0.639872	+	0.768481i	$0.721013\pi$
$720$	−2.27071	−	40.4348i	−0.0846245	−	1.50692i
$721$	−27.0047	+	46.7736i	−1.00571	+	1.74194i
$722$	26.6104	−	1.13668i	0.990338	−	0.0423029i
$723$	−45.6393	+	22.9694i	−1.69735	+	0.854241i
$724$	2.81672	+	32.9105i	0.104683	+	1.22311i
$725$	−21.9920	+	3.87779i	−0.816764	+	0.144017i
$726$	−25.6652	−	4.91392i	−0.952523	−	0.182373i
$727$	4.82234	+	4.04643i	0.178851	+	0.150074i	0.727818	−	0.685770i	$-0.240534\pi$
$727$	4.82234	+	4.04643i	0.178851	+	0.150074i	−0.548967	+	0.835844i	$0.684979\pi$
$728$	−51.4249	+	39.2290i	−1.90593	+	1.45392i
$729$	20.5947	−	17.4602i	0.762766	−	0.646675i
$730$	5.98247	−	1.32036i	0.221421	−	0.0488687i
$731$	1.92605	−	2.29538i	0.0712377	−	0.0848978i
$732$	16.4366	−	0.461156i	0.607514	−	0.0170448i
$733$	−22.4113	+	3.95172i	−0.827781	+	0.145960i	−0.571458	−	0.820631i	$-0.693622\pi$
$733$	−22.4113	+	3.95172i	−0.827781	+	0.145960i	−0.256323	+	0.966591i	$0.582511\pi$
$734$	−4.76304	+	35.9170i	−0.175807	+	1.32572i
$735$	−12.2840	−	24.4078i	−0.453102	−	0.900297i
$736$	22.9830	−	29.6612i	0.847165	−	1.09333i
$737$	−4.33388	+	7.50649i	−0.159640	+	0.276505i
$738$	15.8160	−	23.3394i	0.582195	−	0.859136i
$739$	−37.2940	+	21.5317i	−1.37188	+	0.792056i	−0.991165	−	0.132636i	$-0.957656\pi$
$739$	−37.2940	+	21.5317i	−1.37188	+	0.792056i	−0.380717	+	0.924692i	$0.624323\pi$
$740$	−5.81137	+	5.78948i	−0.213630	+	0.212825i
$741$	4.60237	+	1.08666i	0.169072	+	0.0399196i
$742$	−27.5512	+	35.8354i	−1.01144	+	1.31556i
$743$	−27.0616	+	22.7074i	−0.992794	+	0.833053i	−0.985970	−	0.166924i	$-0.946617\pi$
$743$	−27.0616	+	22.7074i	−0.992794	+	0.833053i	−0.00682406	+	0.999977i	$0.502172\pi$
$744$	10.7455	+	1.11935i	0.393951	+	0.0410372i
$745$	21.7106	−	7.90201i	0.795415	−	0.289507i
$746$	−13.5627	−	14.8292i	−0.496566	−	0.542934i
$747$	31.0814	−	1.86316i	1.13721	−	0.0681693i
$748$	2.66017	+	0.237794i	0.0972655	+	0.00869462i
$749$	8.22687	+	1.45062i	0.300603	+	0.0530045i
$750$	10.7374	+	4.08707i	0.392073	+	0.149239i
$751$	−23.5008	−	8.55359i	−0.857557	−	0.312125i	−0.124439	−	0.992227i	$-0.539713\pi$
$751$	−23.5008	−	8.55359i	−0.857557	−	0.312125i	−0.733117	+	0.680102i	$0.761935\pi$
$752$	−10.8887	−	6.34149i	−0.397069	−	0.231250i
$753$	−8.34852	+	6.22625i	−0.304237	+	0.226897i
$754$	15.3016	−	29.3265i	0.557251	−	1.06801i
$755$		−	39.8171i		−	1.44909i
$756$	−25.0918	+	25.1247i	−0.912579	+	0.913777i
$757$			31.3025i			1.13771i	0.822439	+	0.568853i	$0.192613\pi$
$757$			31.3025i			1.13771i	−0.822439	+	0.568853i	$0.807387\pi$
$758$	2.42157	+	1.26349i	0.0879553	+	0.0458922i
$759$	−0.774019	−	6.57383i	−0.0280951	−	0.238615i
$760$	2.63890	−	2.86354i	0.0957230	−	0.103872i
$761$	−2.59308	−	0.943805i	−0.0939992	−	0.0342129i	0.294592	−	0.955623i	$-0.404816\pi$
$761$	−2.59308	−	0.943805i	−0.0939992	−	0.0342129i	−0.388592	+	0.921410i	$0.627038\pi$
$762$	23.1833	−	3.73875i	0.839842	−	0.135441i
$763$	−54.6869	−	9.64278i	−1.97980	−	0.349092i
$764$	−2.35401	+	26.3340i	−0.0851652	+	0.952732i
$765$	−18.8476	−	13.9819i	−0.681435	−	0.505517i
$766$	−13.8126	+	12.6330i	−0.499069	+	0.456447i
$767$	−55.2197	+	20.0983i	−1.99387	+	0.725708i
$768$	24.8479	−	12.2713i	0.896620	−	0.442801i
$769$	3.61913	−	3.03681i	0.130509	−	0.109510i	−0.575197	−	0.818015i	$-0.695074\pi$
$769$	3.61913	−	3.03681i	0.130509	−	0.109510i	0.705706	+	0.708505i	$0.250630\pi$
$770$	7.44841	+	5.72654i	0.268422	+	0.206370i
$771$	12.9370	+	43.0796i	0.465914	+	1.55147i
$772$	−0.250762	+	0.249817i	−0.00902511	+	0.00899111i
$773$	−17.3435	+	10.0133i	−0.623803	+	0.360153i	−0.778348	−	0.627833i	$-0.783942\pi$
$773$	−17.3435	+	10.0133i	−0.623803	+	0.360153i	0.154545	+	0.987986i	$0.450609\pi$
$774$	−3.21422	−	4.44412i	−0.115533	−	0.159741i
$775$	−7.04567	+	12.2035i	−0.253088	+	0.438361i
$776$	28.2214	−	14.5897i	1.01309	−	0.523741i
$777$	7.18049	+	0.412109i	0.257599	+	0.0147843i
$778$	−33.7152	−	4.47105i	−1.20875	−	0.160295i
$779$	2.66971	−	0.470742i	0.0956522	−	0.0168661i
$780$	−66.6373	+	41.0069i	−2.38600	+	1.46828i
$781$	2.90577	−	3.46296i	0.103977	−	0.123914i
$782$	−4.68614	−	21.2326i	−0.167576	−	0.759276i
$783$	6.16759	−	17.0803i	0.220412	−	0.610401i
$784$	12.0729	−	14.2781i	0.431174	−	0.509932i
$785$	31.1567	+	26.1436i	1.11203	+	0.933105i
$786$	0.764895	+	0.661145i	0.0272829	+	0.0235823i
$787$	41.5062	−	7.31867i	1.47954	−	0.260882i	0.625144	−	0.780510i	$-0.285040\pi$
$787$	41.5062	−	7.31867i	1.47954	−	0.260882i	0.854393	+	0.519627i	$0.173929\pi$
$788$	−0.165666	−	1.93564i	−0.00590162	−	0.0689543i
$789$	−20.1422	−	13.2233i	−0.717081	−	0.470762i
$790$	1.02125	+	23.9081i	0.0363345	+	0.850613i
$791$	−20.7940	+	36.0163i	−0.739350	+	1.28059i
$792$	1.61026	−	4.61580i	0.0572181	−	0.164015i
$793$	−15.8842	−	27.5122i	−0.564063	−	0.976986i
$794$	39.5278	−	25.1296i	1.40279	−	0.891816i
$795$	−37.4913	+	39.8060i	−1.32968	+	1.41177i
$796$	3.47823	−	7.42249i	0.123283	−	0.263083i
$797$	−32.1711	−	38.3400i	−1.13956	−	1.35807i	−0.924369	−	0.381500i	$-0.875408\pi$
$797$	−32.1711	−	38.3400i	−1.13956	−	1.35807i	−0.215189	−	0.976572i	$-0.569037\pi$
$798$	−3.41388	−	0.0499841i	−0.120850	−	0.00176942i
$799$	−6.86134	+	2.49732i	−0.242737	+	0.0883489i
$800$	1.40628	+	36.1187i	0.0497196	+	1.27699i
$801$	16.7200	−	3.99265i	0.590771	−	0.141073i
$802$	−15.1079	−	4.77917i	−0.533478	−	0.168758i
$803$	0.728294	+	0.128418i	0.0257009	+	0.00453177i
$804$	40.8476	+	32.3671i	1.44058	+	1.14150i
$805$	26.1611	−	71.8771i	0.922059	−	2.53334i
$806$	−7.96952	−	19.2916i	−0.280714	−	0.679517i
$807$	−6.19534	−	2.66618i	−0.218086	−	0.0938541i
$808$	35.1193	+	1.63296i	1.23549	+	0.0574472i
$809$	7.89082			0.277426			0.138713	−	0.990333i	$-0.455703\pi$
$809$	7.89082			0.277426			0.138713	+	0.990333i	$0.455703\pi$
$810$	−33.2372	+	27.2109i	−1.16783	+	0.956095i
$811$		−	16.9433i		−	0.594960i	−0.954728	−	0.297480i	$-0.903854\pi$
$811$		−	16.9433i		−	0.594960i	0.954728	−	0.297480i	$-0.0961461\pi$
$812$	−6.22474	+	23.0569i	−0.218445	+	0.809139i
$813$	−18.5552	+	43.1163i	−0.650760	+	1.51215i
$814$	−0.915182	+	0.378069i	−0.0320771	+	0.0132513i
$815$	−42.4871	−	15.4641i	−1.48826	−	0.541682i
$816$	3.74909	−	15.6149i	0.131245	−	0.546630i
$817$	0.0915762	−	0.519355i	0.00320385	−	0.0181699i
$818$	−15.1418	−	4.78992i	−0.529422	−	0.167475i
$819$	65.7541	+	19.5641i	2.29764	+	0.683625i
$820$	−25.7964	+	36.6936i	−0.900851	+	1.28140i
$821$	−16.2209	−	44.5665i	−0.566112	−	1.55538i	−0.810522	−	0.585708i	$-0.800816\pi$
$821$	−16.2209	−	44.5665i	−0.566112	−	1.55538i	0.244410	−	0.969672i	$-0.421406\pi$
$822$	0.565149	−	38.5993i	0.0197118	−	1.34630i
$823$	−3.65996	+	3.07107i	−0.127578	+	0.107051i	−0.704344	−	0.709858i	$-0.748759\pi$
$823$	−3.65996	+	3.07107i	−0.127578	+	0.107051i	0.576766	+	0.816909i	$0.304314\pi$
$824$	−43.6217	−	9.80032i	−1.51963	−	0.341410i
$825$	4.64163	+	4.37172i	0.161601	+	0.152204i
$826$	35.8039	−	22.7621i	1.24578	−	0.791996i
$827$	−25.0451	+	14.4598i	−0.870903	+	0.502816i	−0.867648	−	0.497179i	$-0.834369\pi$
$827$	−25.0451	+	14.4598i	−0.870903	+	0.502816i	−0.00325451	+	0.999995i	$0.501036\pi$
$828$	−39.7826	−	1.16520i	−1.38254	−	0.0404934i
$829$	−17.1833	−	9.92077i	−0.596800	−	0.344563i	0.170982	−	0.985274i	$-0.445306\pi$
$829$	−17.1833	−	9.92077i	−0.596800	−	0.344563i	−0.767782	+	0.640711i	$0.778639\pi$
$830$	−49.4919	+	2.11408i	−1.71789	+	0.0733807i
$831$	−6.80883	+	10.3715i	−0.236196	+	0.359782i
$832$	−43.6842	−	30.9580i	−1.51448	−	1.07328i
$833$	−1.88146	−	10.6703i	−0.0651888	−	0.369704i
$834$	4.09173	+	3.53673i	0.141685	+	0.122467i
$835$	−14.6933	+	17.5108i	−0.508482	+	0.605986i
$836$	0.426389	−	0.197850i	0.0147470	−	0.00684278i
$837$	−5.75473	−	9.90922i	−0.198913	−	0.342513i
$838$	−19.2429	+	4.24701i	−0.664737	+	0.146711i
$839$	26.2638	+	22.0379i	0.906725	+	0.760833i	0.971493	−	0.237067i	$-0.0761862\pi$
$839$	26.2638	+	22.0379i	0.906725	+	0.760833i	−0.0647677	+	0.997900i	$0.520631\pi$
$840$	40.6002	−	39.2799i	1.40084	−	1.35528i
$841$	2.91487	+	16.5310i	0.100513	+	0.570036i
$842$	16.6701	+	2.21066i	0.574490	+	0.0761845i
$843$	0.0769808	−	1.34129i	0.00265136	−	0.0461966i
$844$	7.25279	−	1.92872i	0.249651	−	0.0663892i
$845$	92.9203	+	53.6476i	3.19656	+	1.84553i
$846$	1.36835	+	13.2948i	0.0470449	+	0.457086i
$847$	−18.2253	−	31.5672i	−0.626230	−	1.08466i
$848$	−35.1133	−	12.9305i	−1.20579	−	0.444034i
$849$	2.53610	−	0.761601i	0.0870387	−	0.0261381i
$850$	16.6051	+	12.7664i	0.569549	+	0.437885i
$851$	5.18183	+	6.17546i	0.177631	+	0.211692i
$852$	−18.0487	−	20.3236i	−0.618337	−	0.696276i
$853$	11.5939	+	31.8539i	0.396967	+	1.09066i	0.963754	+	0.266793i	$0.0859641\pi$
$853$	11.5939	+	31.8539i	0.396967	+	1.09066i	−0.566787	+	0.823865i	$0.691814\pi$
$854$	15.4797	+	16.9252i	0.529705	+	0.579167i
$855$	−4.10315	−	0.472540i	−0.140325	−	0.0161605i
$856$	0.883211	+	6.85863i	0.0301875	+	0.234423i
$857$	0.670084	−	3.80024i	0.0228896	−	0.129814i	−0.971222	−	0.238177i	$-0.923450\pi$
$857$	0.670084	−	3.80024i	0.0228896	−	0.129814i	0.994111	+	0.108364i	$0.0345611\pi$
$858$	−9.32442	+	1.50374i	−0.318330	+	0.0513369i
$859$	−7.37600	+	20.2654i	−0.251666	+	0.691446i	0.747951	+	0.663754i	$0.231038\pi$
$859$	−7.37600	+	20.2654i	−0.251666	+	0.691446i	−0.999617	+	0.0276917i	$0.991184\pi$
$860$	4.99136	+	7.15711i	0.170204	+	0.244056i
$861$	39.0574	−	4.59872i	1.33107	−	0.156724i
$862$	18.4814	−	35.4208i	0.629480	−	1.20644i
$863$	30.2497			1.02971			0.514857	−	0.857276i	$-0.327845\pi$
$863$	30.2497			1.02971			0.514857	+	0.857276i	$0.327845\pi$
$864$	−26.0431	−	13.6293i	−0.886004	−	0.463677i
$865$	−5.68815			−0.193403
$866$	18.2209	−	34.9216i	0.619172	−	1.18668i
$867$	12.0401	+	16.1441i	0.408904	+	0.548282i
$868$	8.62053	+	12.3610i	0.292600	+	0.419559i
$869$	−0.987962	+	2.71440i	−0.0335143	+	0.0920799i
$870$	−10.2777	+	27.0010i	−0.348446	+	0.915420i
$871$	17.4847	−	99.1608i	0.592447	−	3.35994i
$872$	−5.87102	−	45.5917i	−0.198818	−	1.54393i
$873$	−30.1381	−	15.0720i	−1.02002	−	0.510109i
$874$	−2.58272	−	2.82389i	−0.0873619	−	0.0955196i
$875$	5.48119	+	15.0594i	0.185298	+	0.509102i
$876$	1.40304	−	4.21943i	0.0474042	−	0.142561i
$877$	−10.0265	−	11.9491i	−0.338571	−	0.403493i	0.569715	−	0.821842i	$-0.307053\pi$
$877$	−10.0265	−	11.9491i	−0.338571	−	0.403493i	−0.908286	+	0.418349i	$0.862609\pi$
$878$	−13.7679	−	10.5852i	−0.464645	−	0.357232i
$879$	−6.32982	+	26.8088i	−0.213499	+	0.904239i
$880$	−2.68761	+	7.29832i	−0.0905993	+	0.246026i
$881$	18.2832	+	31.6674i	0.615977	+	1.06690i	0.990212	+	0.139569i	$0.0445719\pi$
$881$	18.2832	+	31.6674i	0.615977	+	1.06690i	−0.374235	+	0.927334i	$0.622095\pi$
$882$	−19.7810	−	1.42611i	−0.666060	−	0.0480196i
$883$	26.1355	+	15.0893i	0.879529	+	0.507796i	0.870503	−	0.492163i	$-0.163794\pi$
$883$	26.1355	+	15.0893i	0.879529	+	0.507796i	0.00902592	+	0.999959i	$0.497127\pi$
$884$	−29.9835	+	7.97344i	−1.00845	+	0.268176i
$885$	45.8457	−	23.0732i	1.54109	−	0.775598i
$886$	−29.6222	−	3.92828i	−0.995178	−	0.131973i
$887$	−7.16882	−	40.6564i	−0.240705	−	1.36511i	−0.830258	−	0.557379i	$-0.811807\pi$
$887$	−7.16882	−	40.6564i	−0.240705	−	1.36511i	0.589553	−	0.807730i	$-0.299304\pi$
$888$	1.44570	+	5.77560i	0.0485145	+	0.193816i
$889$	25.0927	+	21.0553i	0.841584	+	0.706172i
$890$	−26.7055	+	5.89404i	−0.895171	+	0.197569i
$891$	−4.96226	+	1.50395i	−0.166242	+	0.0503843i
$892$	−7.11472	+	3.30132i	−0.238219	+	0.110536i
$893$	−0.826041	+	0.984438i	−0.0276424	+	0.0329430i
$894$	3.15334	−	16.4697i	0.105463	−	0.550830i
$895$	6.98289	+	39.6019i	0.233412	+	1.32375i
$896$	35.6156	+	15.0288i	1.18983	+	0.502078i
$897$	34.5680	+	68.6854i	1.15419	+	2.29334i
$898$	−39.1968	+	1.67432i	−1.30801	+	0.0558726i
$899$	−6.67459	−	3.85358i	−0.222610	−	0.128524i
$900$	30.0780	−	23.7732i	1.00260	−	0.792441i
$901$	−18.7778	+	10.8414i	−0.625578	+	0.361178i
$902$	−4.56917	+	2.90483i	−0.152137	+	0.0967201i
$903$	1.75803	−	7.44583i	0.0585036	−	0.247782i
$904$	−33.5893	−	7.54639i	−1.11716	−	0.250989i
$905$	−42.6973	+	35.8273i	−1.41931	+	1.19094i
$906$	−24.8133	−	14.8145i	−0.824367	−	0.492179i
$907$	13.9229	+	38.2529i	0.462303	+	1.27017i	0.923749	+	0.382999i	$0.125109\pi$
$907$	13.9229	+	38.2529i	0.462303	+	1.27017i	−0.461446	+	0.887168i	$0.652669\pi$
$908$	13.6116	−	19.3615i	0.451716	−	0.642533i
$909$	−20.5439	−	31.1205i	−0.681399	−	1.03220i
$910$	−104.060	−	32.9180i	−3.44956	−	1.09122i
$911$	7.42318	−	42.0989i	0.245941	−	1.39480i	−0.572357	−	0.820005i	$-0.693971\pi$
$911$	7.42318	−	42.0989i	0.245941	−	1.39480i	0.818298	−	0.574795i	$-0.194918\pi$
$912$	−0.802668	−	2.70994i	−0.0265790	−	0.0897350i
$913$	−5.61905	−	2.04517i	−0.185963	−	0.0676852i
$914$	44.5175	−	18.3905i	1.47251	−	0.608305i
$915$	16.5880	+	22.2422i	0.548383	+	0.735304i
$916$	5.52440	−	20.4628i	0.182531	−	0.676110i
$917$			1.41029i			0.0465717i
$918$	−15.7258	+	6.54331i	−0.519028	+	0.215961i
$919$	−4.00742			−0.132193			−0.0660963	−	0.997813i	$-0.521054\pi$
$919$	−4.00742			−0.132193			−0.0660963	+	0.997813i	$0.521054\pi$
$920$	63.2501	+	2.94097i	2.08529	+	0.0969608i
$921$	−0.0866677	−	0.736078i	−0.00285580	−	0.0242546i
$922$	7.50646	+	18.1707i	0.247212	+	0.598419i
$923$	−17.9609	+	49.3471i	−0.591189	+	1.62428i
$924$	6.33997	−	2.51108i	0.208570	−	0.0826085i
$925$	−7.64760	−	1.34848i	−0.251452	−	0.0443377i
$926$	−25.0613	−	7.92779i	−0.823564	−	0.260523i
$927$	18.8563	+	43.5109i	0.619323	+	1.42909i
$928$	−19.7549	+	0.769156i	−0.648485	+	0.0252488i
$929$	46.5451	−	16.9410i	1.52710	−	0.555818i	0.564188	−	0.825646i	$-0.309189\pi$
$929$	46.5451	−	16.9410i	1.52710	−	0.555818i	0.962908	+	0.269829i	$0.0869671\pi$
$930$	8.88316	+	15.9199i	0.291290	+	0.522033i
$931$	−1.22576	−	1.46080i	−0.0401725	−	0.0478758i
$932$	−0.958991	+	2.04647i	−0.0314128	+	0.0670344i
$933$	5.50276	+	18.3239i	0.180152	+	0.599899i
$934$	−11.4948	+	7.30774i	−0.376121	+	0.239117i
$935$	2.25339	+	3.90298i	0.0736936	+	0.127641i
$936$	0.761461	+	56.7844i	0.0248891	+	1.85606i
$937$	4.84280	−	8.38798i	0.158207	−	0.274023i	−0.776015	−	0.630715i	$-0.782762\pi$
$937$	4.84280	−	8.38798i	0.158207	−	0.274023i	0.934222	+	0.356691i	$0.116095\pi$
$938$	3.10250	+	72.6316i	0.101300	+	2.37150i
$939$	2.75855	−	48.0642i	0.0900218	−	1.56852i
$940$	−1.81321	−	21.1854i	−0.0591403	−	0.690993i
$941$	−5.10500	+	0.900150i	−0.166418	+	0.0293440i	−0.256236	−	0.966614i	$-0.582483\pi$
$941$	−5.10500	+	0.900150i	−0.166418	+	0.0293440i	0.0898181	+	0.995958i	$0.471371\pi$
$942$	27.8845	−	9.68923i	0.908527	−	0.315692i
$943$	33.7672	+	28.3340i	1.09961	+	0.922682i
$944$	26.8188	+	22.6767i	0.872877	+	0.738063i
$945$	−59.0342	−	10.2546i	−1.92038	−	0.333583i
$946$	0.227003	+	1.02854i	0.00738051	+	0.0334406i
$947$	19.6357	−	23.4009i	0.638075	−	0.760428i	−0.345990	−	0.938238i	$-0.612457\pi$
$947$	19.6357	−	23.4009i	0.638075	−	0.760428i	0.984065	+	0.177811i	$0.0569014\pi$
$948$	15.2791	+	8.25893i	0.496242	+	0.268238i
$949$	−8.46036	+	1.49179i	−0.274635	+	0.0484256i
$950$	3.65439	+	0.484618i	0.118564	+	0.0157231i
$951$	−3.34003	+	5.08766i	−0.108308	+	0.164979i
$952$	19.8985	−	10.2870i	0.644913	−	0.333403i
$953$	8.71927	−	15.1022i	0.282445	−	0.489209i	−0.689542	−	0.724246i	$-0.742188\pi$
$953$	8.71927	−	15.1022i	0.282445	−	0.489209i	0.971986	+	0.235037i	$0.0755213\pi$
$954$	10.8572	+	38.1743i	0.351516	+	1.23594i
$955$	−38.6370	+	22.3071i	−1.25027	+	0.721841i
$956$	8.22369	−	8.19271i	0.265973	−	0.264971i
$957$	−2.39108	+	2.53871i	−0.0772928	+	0.0820648i
$958$	32.6339	+	25.0898i	1.05435	+	0.810616i
$959$	41.2500	−	34.6128i	1.33203	−	1.11771i
$960$	41.0541	+	22.3919i	1.32502	+	0.722696i
$961$	24.5605	−	8.93927i	0.792273	−	0.288364i
$962$	8.48811	−	7.76319i	0.273667	−	0.250295i
$963$	5.32656	−	5.04244i	0.171646	−	0.162490i
$964$	5.25289	−	58.7633i	0.169184	−	1.89264i
$965$	−0.588217	−	0.103718i	−0.0189354	−	0.00333882i
$966$	−35.0590	−	43.0461i	−1.12800	−	1.38498i
$967$	−46.2859	−	16.8467i	−1.48845	−	0.541752i	−0.535411	−	0.844592i	$-0.679843\pi$
$967$	−46.2859	−	16.8467i	−1.48845	−	0.541752i	−0.953042	+	0.302839i	$0.902065\pi$
$968$	20.4481	−	22.1887i	0.657226	−	0.713172i
$969$	−1.50436	−	0.647406i	−0.0483270	−	0.0207977i
$970$	47.5285	+	24.7988i	1.52605	+	0.796242i
$971$			13.2201i			0.424253i	0.977242	+	0.212126i	$0.0680388\pi$
$971$			13.2201i			0.424253i	−0.977242	+	0.212126i	$0.931961\pi$
$972$	4.59103	+	30.8370i	0.147257	+	0.989098i
$973$			7.54418i			0.241855i
$974$	8.59804	−	16.4787i	0.275499	−	0.528011i
$975$	−68.0381	−	29.2804i	−2.17896	−	0.937723i
$976$	−9.55541	+	16.4071i	−0.305861	+	0.525179i
$977$	−22.1311	−	8.05506i	−0.708037	−	0.257704i	−0.0371983	−	0.999308i	$-0.511843\pi$
$977$	−22.1311	−	8.05506i	−0.708037	−	0.257704i	−0.670838	+	0.741604i	$0.734066\pi$
$978$	−25.4449	+	20.7236i	−0.813637	+	0.662669i
$979$	−3.25108	−	0.573253i	−0.103905	−	0.0183212i
$980$	31.4265	+	2.80924i	1.00388	+	0.0897378i
$981$	−35.4075	+	33.5189i	−1.13048	+	1.07018i
$982$	−11.2167	−	12.2641i	−0.357940	−	0.391363i
$983$	−44.1620	+	16.0737i	−1.40855	+	0.512670i	−0.930704	−	0.365773i	$-0.880805\pi$
$983$	−44.1620	+	16.0737i	−1.40855	+	0.512670i	−0.477846	+	0.878444i	$0.658582\pi$
$984$	13.2689	+	29.7283i	0.422996	+	0.947702i
$985$	2.51126	−	2.10719i	0.0800153	−	0.0671408i
$986$	−6.98251	+	9.08203i	−0.222369	+	0.289231i
$987$	−12.7821	+	13.5712i	−0.406858	+	0.431977i
$988$	−3.86843	+	3.85385i	−0.123071	+	0.122607i
$989$	7.42628	−	4.28756i	0.236142	−	0.136337i
$990$	7.93456	−	2.25669i	0.252177	−	0.0717222i
$991$	−10.5119	+	18.2072i	−0.333922	+	0.578370i	−0.983277	−	0.182115i	$-0.941706\pi$
$991$	−10.5119	+	18.2072i	−0.333922	+	0.578370i	0.649355	+	0.760486i	$0.275039\pi$
$992$	−7.64092	+	9.86116i	−0.242599	+	0.313092i
$993$	16.5566	−	25.2197i	0.525409	−	0.800322i
$994$	4.98434	−	37.5857i	0.158094	−	1.19215i
$995$	13.6219	−	2.40190i	0.431842	−	0.0761454i
$996$	−17.0967	+	31.6291i	−0.541730	+	1.00221i
$997$	1.15413	−	1.37543i	0.0365515	−	0.0435604i	−0.747459	−	0.664308i	$-0.768726\pi$
$997$	1.15413	−	1.37543i	0.0365515	−	0.0435604i	0.784011	+	0.620748i	$0.213171\pi$
$998$	49.9718	−	11.0290i	1.58183	−	0.349117i
$999$	4.04686	−	4.84784i	0.128037	−	0.153379i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.t.a.205.12	yes	204
3.2	odd	2		648.2.t.a.613.23		204
4.3	odd	2		864.2.bf.a.529.22		204
8.3	odd	2		864.2.bf.a.529.13		204
8.5	even	2	inner	216.2.t.a.205.27	yes	204
24.5	odd	2		648.2.t.a.613.8		204
27.5	odd	18		648.2.t.a.37.8		204
27.22	even	9	inner	216.2.t.a.157.27	yes	204
108.103	odd	18		864.2.bf.a.49.13		204
216.5	odd	18		648.2.t.a.37.23		204
216.157	even	18	inner	216.2.t.a.157.12	✓	204
216.211	odd	18		864.2.bf.a.49.22		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.157.12	✓	204	216.157	even	18	inner
216.2.t.a.157.27	yes	204	27.22	even	9	inner
216.2.t.a.205.12	yes	204	1.1	even	1	trivial
216.2.t.a.205.27	yes	204	8.5	even	2	inner
648.2.t.a.37.8		204	27.5	odd	18
648.2.t.a.37.23		204	216.5	odd	18
648.2.t.a.613.8		204	24.5	odd	2
648.2.t.a.613.23		204	3.2	odd	2
864.2.bf.a.49.13		204	108.103	odd	18
864.2.bf.a.49.22		204	216.211	odd	18
864.2.bf.a.529.13		204	8.3	odd	2
864.2.bf.a.529.22		204	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.654194 + 1.25381i) q^{2} +(-0.684682 + 1.59098i) q^{3} +(-1.14406 - 1.64047i) q^{4} +(1.15428 - 3.17134i) q^{5} +(-1.54686 - 1.89927i) q^{6} +(0.593321 - 3.36489i) q^{7} +(2.80526 - 0.361244i) q^{8} +(-2.06242 - 2.17863i) q^{9} +(3.22113 + 3.52191i) q^{10} +(0.197048 + 0.541384i) q^{11} +(3.39326 - 0.696975i) q^{12} +(-4.30199 - 5.12691i) q^{13} +(3.83077 + 2.94520i) q^{14} +(4.25523 + 4.00779i) q^{15} +(-1.38226 + 3.75358i) q^{16} +(1.15893 + 2.00733i) q^{17} +(4.08080 - 1.16063i) q^{18} +(0.353289 + 0.203971i) q^{19} +(-6.52304 + 1.73466i) q^{20} +(4.94723 + 3.24784i) q^{21} +(-0.807698 - 0.107111i) q^{22} +(1.15186 + 6.53250i) q^{23} +(-1.34598 + 4.71045i) q^{24} +(-4.89486 - 4.10727i) q^{25} +(9.24249 - 2.03986i) q^{26} +(4.87825 - 1.78960i) q^{27} +(-6.19878 + 2.87631i) q^{28} +(2.24644 - 2.67721i) q^{29} +(-7.80874 + 2.71336i) q^{30} +(-0.382945 - 2.17179i) q^{31} +(-3.80200 - 4.18865i) q^{32} +(-0.996245 - 0.0571774i) q^{33} +(-3.27497 + 0.139892i) q^{34} +(-9.98637 - 5.76564i) q^{35} +(-1.21443 + 5.87581i) q^{36} +(1.05249 - 0.607656i) q^{37} +(-0.486860 + 0.309519i) q^{38} +(11.1023 - 3.33407i) q^{39} +(2.09242 - 9.31343i) q^{40} +(5.09057 - 4.27150i) q^{41} +(-7.30861 + 4.07815i) q^{42} +(-0.442145 - 1.21478i) q^{43} +(0.662688 - 0.942626i) q^{44} +(-9.28978 + 4.02591i) q^{45} +(-8.94402 - 2.82932i) q^{46} +(-0.547022 + 3.10232i) q^{47} +(-5.02546 - 4.76915i) q^{48} +(-4.39261 - 1.59878i) q^{49} +(8.35191 - 3.45024i) q^{50} +(-3.98712 + 0.469453i) q^{51} +(-3.48879 + 12.9228i) q^{52} +9.35460i q^{53} +(-0.947515 + 7.28713i) q^{54} +1.94436 q^{55} +(0.448874 - 9.65374i) q^{56} +(-0.566405 + 0.422419i) q^{57} +(1.88709 + 4.56802i) q^{58} +(3.00302 - 8.25072i) q^{59} +(1.70641 - 11.5657i) q^{60} +(4.67459 + 0.824257i) q^{61} +(2.97352 + 0.940634i) q^{62} +(-8.55452 + 5.64720i) q^{63} +(7.73901 - 2.02677i) q^{64} +(-21.2249 + 7.72523i) q^{65} +(0.723428 - 1.21169i) q^{66} +(9.67062 + 11.5250i) q^{67} +(1.96707 - 4.19769i) q^{68} +(-11.1817 - 2.64011i) q^{69} +(13.7620 - 8.74913i) q^{70} +(-3.92323 - 6.79524i) q^{71} +(-6.57265 - 5.36659i) q^{72} +(0.641809 - 1.11165i) q^{73} +(0.0733489 + 1.71715i) q^{74} +(9.88600 - 4.97543i) q^{75} +(-0.0695752 - 0.812914i) q^{76} +(1.93861 - 0.341829i) q^{77} +(-3.08279 + 16.1013i) q^{78} +(3.84081 + 3.22282i) q^{79} +(10.3084 + 8.71628i) q^{80} +(-0.492839 + 8.98650i) q^{81} +(2.02541 + 9.17698i) q^{82} +(-6.67152 + 7.95081i) q^{83} +(-0.331952 - 11.8315i) q^{84} +(7.70366 - 1.35836i) q^{85} +(1.81235 + 0.240341i) q^{86} +(2.72128 + 5.40708i) q^{87} +(0.748343 + 1.44754i) q^{88} +(-2.86501 + 4.96234i) q^{89} +(1.02961 - 14.2813i) q^{90} +(-19.8040 + 11.4338i) q^{91} +(9.39855 - 9.36314i) q^{92} +(3.71746 + 0.877728i) q^{93} +(-3.53185 - 2.71538i) q^{94} +(1.05466 - 0.884962i) q^{95} +(9.26721 - 3.18100i) q^{96} +(10.5548 - 3.84165i) q^{97} +(4.87818 - 4.46157i) q^{98} +(0.773079 - 1.54586i) 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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