LMFDB - Embedded newform 669.2.i.b.4.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [669,2,Mod(4,669)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(669, base_ring=CyclotomicField(74)) chi = DirichletCharacter(H, H._module([0, 46])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("669.4"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 669 = 3 \cdot 223 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	669.i (of order $37$, degree $36$, minimal)

Newform invariants

comment:select newform

sage:traces = [720] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.34199189522$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$20$ over $\Q(\zeta_{37})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{37}]$

Embedding invariants

Embedding label			4.7
Character	$\chi$	$=$	669.4
Dual form			669.2.i.b.502.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.17140 + 0.413884i) q^{2} +(0.372856 - 0.927889i) q^{3} +(-0.355182 + 0.286790i) q^{4} +(0.695338 + 1.12930i) q^{5} +(-0.0527278 + 1.24125i) q^{6} +(-0.102959 + 0.804025i) q^{7} +(1.60013 - 2.59878i) q^{8} +(-0.721956 - 0.691939i) q^{9} +(-1.28192 - 1.03508i) q^{10} +(0.0622231 - 1.46478i) q^{11} +(0.133677 + 0.436501i) q^{12} +(-1.86987 - 4.65335i) q^{13} +(-0.212166 - 0.984452i) q^{14} +(1.30713 - 0.224130i) q^{15} +(-0.606456 + 2.81397i) q^{16} +(0.0171092 - 0.402764i) q^{17} +(1.13208 + 0.511735i) q^{18} +(1.69986 - 0.442609i) q^{19} +(-0.570844 - 0.201692i) q^{20} +(0.707657 + 0.395321i) q^{21} +(0.533360 + 1.74160i) q^{22} +(0.937149 + 1.52203i) q^{23} +(-1.81476 - 2.45372i) q^{24} +(1.45919 - 2.89414i) q^{25} +(4.11632 + 4.67705i) q^{26} +(-0.911228 + 0.411901i) q^{27} +(-0.194017 - 0.315103i) q^{28} +(-1.60803 + 7.46127i) q^{29} +(-1.43841 + 0.803545i) q^{30} +(9.00572 - 0.766500i) q^{31} +(0.321043 + 2.50707i) q^{32} +(-1.33595 - 0.603889i) q^{33} +(0.146656 + 0.478881i) q^{34} +(-0.979578 + 0.442797i) q^{35} +(0.454867 + 0.0387149i) q^{36} +(-0.351548 - 8.27572i) q^{37} +(-1.80804 + 1.22202i) q^{38} -5.01499 q^{39} +4.04744 q^{40} +(9.04574 - 6.11385i) q^{41} +(-0.992570 - 0.170193i) q^{42} +(-4.65030 - 9.22332i) q^{43} +(0.397983 + 0.538109i) q^{44} +(0.279404 - 1.29644i) q^{45} +(-1.72772 - 1.39504i) q^{46} +(6.77963 + 1.76528i) q^{47} +(2.38493 + 1.61193i) q^{48} +(6.13827 + 1.59828i) q^{49} +(-0.511470 + 3.99414i) q^{50} +(-0.367341 - 0.166049i) q^{51} +(1.99868 + 1.11653i) q^{52} +(-6.91558 + 7.85763i) q^{53} +(0.896938 - 0.859646i) q^{54} +(1.69744 - 0.948249i) q^{55} +(1.92474 + 1.55412i) q^{56} +(0.223112 - 1.74231i) q^{57} +(-1.20445 - 9.40570i) q^{58} +(3.64496 - 11.9020i) q^{59} +(-0.399991 + 0.454478i) q^{60} +(-4.75413 - 11.8311i) q^{61} +(-10.2321 + 4.62520i) q^{62} +(0.630669 - 0.509229i) q^{63} +(-4.00560 - 7.94463i) q^{64} +(3.95484 - 5.34730i) q^{65} +(1.81488 + 0.154469i) q^{66} +(-3.54710 + 2.86409i) q^{67} +(0.109432 + 0.147961i) q^{68} +(1.76169 - 0.302073i) q^{69} +(0.964216 - 0.924126i) q^{70} +(2.87674 - 9.39353i) q^{71} +(-2.95343 + 0.769012i) q^{72} +(9.40053 + 5.25145i) q^{73} +(3.83699 + 9.54872i) q^{74} +(-2.14137 - 2.43307i) q^{75} +(-0.476825 + 0.644710i) q^{76} +(1.17131 + 0.200842i) q^{77} +(5.87458 - 2.07562i) q^{78} +(-3.13880 + 2.12146i) q^{79} +(-3.59951 + 1.27179i) q^{80} +(0.0424412 + 0.999099i) q^{81} +(-8.06580 + 10.9057i) q^{82} +(-3.00868 + 5.96736i) q^{83} +(-0.364721 + 0.0625377i) q^{84} +(0.466739 - 0.260736i) q^{85} +(9.26476 + 8.87955i) q^{86} +(6.32366 + 4.27405i) q^{87} +(-3.70708 - 2.50555i) q^{88} +(-5.00072 + 8.12168i) q^{89} +(0.209279 + 1.63429i) q^{90} +(3.93393 - 1.02432i) q^{91} +(-0.769360 - 0.271832i) q^{92} +(2.64662 - 8.64211i) q^{93} +(-8.67231 + 0.738122i) q^{94} +(1.68182 + 1.61189i) q^{95} +(2.44599 + 0.636885i) q^{96} +(7.95072 - 12.9128i) q^{97} +(-7.85191 + 0.668296i) q^{98} +(-1.05846 + 1.01445i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q - q^{2} - 20 q^{3} - 23 q^{4} - 4 q^{5} - q^{6} - 12 q^{7} - 9 q^{8} - 20 q^{9} - 16 q^{10} - 14 q^{11} - 23 q^{12} - 14 q^{13} - 28 q^{14} - 4 q^{15} - 37 q^{16} - 20 q^{17} - q^{18} + 42 q^{19}+ \cdots - 14 q^{99}+O(q^{100}) $ 720 * q - q^2 - 20 * q^3 - 23 * q^4 - 4 * q^5 - q^6 - 12 * q^7 - 9 * q^8 - 20 * q^9 - 16 * q^10 - 14 * q^11 - 23 * q^12 - 14 * q^13 - 28 * q^14 - 4 * q^15 - 37 * q^16 - 20 * q^17 - q^18 + 42 * q^19 - 34 * q^20 - 12 * q^21 - 32 * q^22 - 18 * q^23 - 9 * q^24 - 48 * q^25 - 48 * q^26 - 20 * q^27 - 80 * q^28 + 7 * q^29 - 16 * q^30 - 40 * q^31 - 59 * q^32 - 14 * q^33 + 22 * q^34 - 32 * q^35 - 23 * q^36 - 44 * q^37 - 36 * q^38 + 60 * q^39 + 124 * q^40 + 176 * q^41 + 46 * q^42 - 42 * q^43 + 76 * q^44 - 4 * q^45 - 88 * q^46 - 26 * q^47 - 37 * q^48 - 94 * q^49 - 87 * q^50 + 54 * q^51 + 206 * q^52 - 54 * q^53 - q^54 - 74 * q^55 - 107 * q^56 - 32 * q^57 + 13 * q^58 - 50 * q^59 - 34 * q^60 - 86 * q^61 - 83 * q^62 - 12 * q^63 + 99 * q^64 + 52 * q^65 + 42 * q^66 - 68 * q^67 + 63 * q^68 - 18 * q^69 - 62 * q^70 - 68 * q^71 - 9 * q^72 - 58 * q^73 - 82 * q^74 - 48 * q^75 - 145 * q^76 + 40 * q^77 + 26 * q^78 - 90 * q^79 + 325 * q^80 - 20 * q^81 + 62 * q^82 + 58 * q^83 - 80 * q^84 - 14 * q^85 - 153 * q^86 - 30 * q^87 - 152 * q^88 - 110 * q^89 - 16 * q^90 - 114 * q^91 - 110 * q^92 - 40 * q^93 + 102 * q^94 - 118 * q^95 - 59 * q^96 - 110 * q^97 - 154 * q^98 - 14 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/669\mathbb{Z}\right)^\times$.

$n$	$224$	$226$
$\chi(n)$	$1$	$e\left(\frac{23}{37}\right)$

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 $

$2$	−1.17140	+	0.413884i	−0.828308	+	0.292660i	−0.713436	−	0.700720i	$-0.752862\pi$
$2$	−1.17140	+	0.413884i	−0.828308	+	0.292660i	−0.114872	+	0.993380i	$0.536646\pi$
$3$	0.372856	−	0.927889i	0.215269	−	0.535717i
$3$	0.372856	−	0.927889i	0.215269	−	0.535717i
$4$	−0.355182	+	0.286790i	−0.177591	+	0.143395i
$5$	0.695338	+	1.12930i	0.310965	+	0.505039i	0.968708	−	0.248203i	$-0.0798401\pi$
$5$	0.695338	+	1.12930i	0.310965	+	0.505039i	−0.657743	+	0.753242i	$0.728489\pi$
$6$	−0.0527278	+	1.24125i	−0.0215260	+	0.506739i
$7$	−0.102959	+	0.804025i	−0.0389150	+	0.303893i	0.960736	+	0.277465i	$0.0894943\pi$
$7$	−0.102959	+	0.804025i	−0.0389150	+	0.303893i	−0.999651	+	0.0264278i	$0.991587\pi$
$8$	1.60013	−	2.59878i	0.565733	−	0.918809i
$9$	−0.721956	−	0.691939i	−0.240652	−	0.230646i
$10$	−1.28192	−	1.03508i	−0.405379	−	0.327321i
$11$	0.0622231	−	1.46478i	0.0187610	−	0.441648i	−0.965009	−	0.262215i	$-0.915547\pi$
$11$	0.0622231	−	1.46478i	0.0187610	−	0.441648i	0.983770	−	0.179432i	$-0.0574261\pi$
$12$	0.133677	+	0.436501i	0.0385892	+	0.126007i
$13$	−1.86987	−	4.65335i	−0.518609	−	1.29061i	−0.926058	−	0.377380i	$-0.876825\pi$
$13$	−1.86987	−	4.65335i	−0.518609	−	1.29061i	0.407449	−	0.913228i	$-0.366418\pi$
$14$	−0.212166	−	0.984452i	−0.0567037	−	0.263106i
$15$	1.30713	−	0.224130i	0.337499	−	0.0578700i
$16$	−0.606456	+	2.81397i	−0.151614	+	0.703491i
$17$	0.0171092	−	0.402764i	0.00414959	−	0.0976846i	−0.995830	−	0.0912328i	$-0.970919\pi$
$17$	0.0171092	−	0.402764i	0.00414959	−	0.0976846i	0.999979	−	0.00645186i	$-0.00205370\pi$
$18$	1.13208	+	0.511735i	0.266835	+	0.120617i
$19$	1.69986	−	0.442609i	0.389975	−	0.101542i	−0.0518227	−	0.998656i	$-0.516503\pi$
$19$	1.69986	−	0.442609i	0.389975	−	0.101542i	0.441798	+	0.897115i	$0.354341\pi$
$20$	−0.570844	−	0.201692i	−0.127645	−	0.0450997i
$21$	0.707657	+	0.395321i	0.154423	+	0.0862661i
$22$	0.533360	+	1.74160i	0.113713	+	0.371311i
$23$	0.937149	+	1.52203i	0.195409	+	0.317365i	0.934318	−	0.356441i	$-0.116010\pi$
$23$	0.937149	+	1.52203i	0.195409	+	0.317365i	−0.738909	+	0.673806i	$0.764659\pi$
$24$	−1.81476	−	2.45372i	−0.370437	−	0.500863i
$25$	1.45919	−	2.89414i	0.291839	−	0.578827i
$26$	4.11632	+	4.67705i	0.807277	+	0.917245i
$27$	−0.911228	+	0.411901i	−0.175366	+	0.0792704i
$28$	−0.194017	−	0.315103i	−0.0366657	−	0.0595489i
$29$	−1.60803	+	7.46127i	−0.298603	+	1.38552i	0.540406	+	0.841405i	$0.318271\pi$
$29$	−1.60803	+	7.46127i	−0.298603	+	1.38552i	−0.839009	+	0.544118i	$0.816864\pi$
$30$	−1.43841	+	0.803545i	−0.262617	+	0.146707i
$31$	9.00572	−	0.766500i	1.61748	−	0.137667i	0.759200	−	0.650857i	$-0.225590\pi$
$31$	9.00572	−	0.766500i	1.61748	−	0.137667i	0.858275	+	0.513189i	$0.171536\pi$
$32$	0.321043	+	2.50707i	0.0567529	+	0.443192i
$33$	−1.33595	−	0.603889i	−0.232559	−	0.105124i
$34$	0.146656	+	0.478881i	0.0251512	+	0.0821274i
$35$	−0.979578	+	0.442797i	−0.165579	+	0.0748464i
$36$	0.454867	+	0.0387149i	0.0758112	+	0.00645248i
$37$	−0.351548	−	8.27572i	−0.0577942	−	1.36052i	−0.760638	−	0.649176i	$-0.775114\pi$
$37$	−0.351548	−	8.27572i	−0.0577942	−	1.36052i	0.702844	−	0.711344i	$-0.251913\pi$
$38$	−1.80804	+	1.22202i	−0.293302	+	0.198238i
$39$	−5.01499			−0.803041
$40$	4.04744			0.639957
$41$	9.04574	−	6.11385i	1.41271	−	0.954823i	0.413694	−	0.910416i	$-0.364238\pi$
$41$	9.04574	−	6.11385i	1.41271	−	0.954823i	0.999014	−	0.0444073i	$-0.0141399\pi$
$42$	−0.992570	−	0.170193i	−0.153157	−	0.0262614i
$43$	−4.65030	−	9.22332i	−0.709164	−	1.40654i	−0.904787	−	0.425864i	$-0.859970\pi$
$43$	−4.65030	−	9.22332i	−0.709164	−	1.40654i	0.195623	−	0.980679i	$-0.437327\pi$
$44$	0.397983	+	0.538109i	0.0599982	+	0.0811229i
$45$	0.279404	−	1.29644i	0.0416510	−	0.193262i
$46$	−1.72772	−	1.39504i	−0.254739	−	0.205687i
$47$	6.77963	+	1.76528i	0.988911	+	0.257492i	0.711060	−	0.703132i	$-0.248216\pi$
$47$	6.77963	+	1.76528i	0.988911	+	0.257492i	0.277851	+	0.960624i	$0.410378\pi$
$48$	2.38493	+	1.61193i	0.344234	+	0.232662i
$49$	6.13827	+	1.59828i	0.876896	+	0.228326i
$50$	−0.511470	+	3.99414i	−0.0723327	+	0.564857i
$51$	−0.367341	−	0.166049i	−0.0514380	−	0.0232515i
$52$	1.99868	+	1.11653i	0.277167	+	0.154835i
$53$	−6.91558	+	7.85763i	−0.949929	+	1.07933i	0.0468320	+	0.998903i	$0.485087\pi$
$53$	−6.91558	+	7.85763i	−0.949929	+	1.07933i	−0.996761	+	0.0804258i	$0.974372\pi$
$54$	0.896938	−	0.859646i	0.122058	−	0.116983i
$55$	1.69744	−	0.948249i	0.228883	−	0.127862i
$56$	1.92474	+	1.55412i	0.257204	+	0.207678i
$57$	0.223112	−	1.74231i	0.0295519	−	0.230775i
$58$	−1.20445	−	9.40570i	−0.158152	−	1.23503i
$59$	3.64496	−	11.9020i	0.474533	−	1.54951i	−0.323097	−	0.946366i	$-0.604724\pi$
$59$	3.64496	−	11.9020i	0.474533	−	1.54951i	0.797630	−	0.603147i	$-0.206087\pi$
$60$	−0.399991	+	0.454478i	−0.0516386	+	0.0586728i
$61$	−4.75413	−	11.8311i	−0.608704	−	1.51482i	−0.840364	−	0.542022i	$-0.817659\pi$
$61$	−4.75413	−	11.8311i	−0.608704	−	1.51482i	0.231660	−	0.972797i	$-0.425584\pi$
$62$	−10.2321	+	4.62520i	−1.29948	+	0.587401i
$63$	0.630669	−	0.509229i	0.0794568	−	0.0641569i
$64$	−4.00560	−	7.94463i	−0.500700	−	0.993078i
$65$	3.95484	−	5.34730i	0.490538	−	0.663251i
$66$	1.81488	+	0.154469i	0.223396	+	0.0190138i
$67$	−3.54710	+	2.86409i	−0.433348	+	0.349904i	−0.820041	−	0.572304i	$-0.806050\pi$
$67$	−3.54710	+	2.86409i	−0.433348	+	0.349904i	0.386693	+	0.922208i	$0.373617\pi$
$68$	0.109432	+	0.147961i	0.0132705	+	0.0179430i
$69$	1.76169	−	0.302073i	0.212083	−	0.0363653i
$70$	0.964216	−	0.924126i	0.115246	−	0.110454i
$71$	2.87674	−	9.39353i	0.341406	−	1.11481i	−0.606186	−	0.795323i	$-0.707301\pi$
$71$	2.87674	−	9.39353i	0.341406	−	1.11481i	0.947592	−	0.319484i	$-0.103510\pi$
$72$	−2.95343	+	0.769012i	−0.348065	+	0.0906290i
$73$	9.40053	+	5.25145i	1.10025	+	0.614636i	0.928809	−	0.370559i	$-0.120834\pi$
$73$	9.40053	+	5.25145i	1.10025	+	0.614636i	0.171440	+	0.985195i	$0.445158\pi$
$74$	3.83699	+	9.54872i	0.446041	+	1.11002i
$75$	−2.14137	−	2.43307i	−0.247264	−	0.280946i
$76$	−0.476825	+	0.644710i	−0.0546956	+	0.0739533i
$77$	1.17131	+	0.200842i	0.133484	+	0.0228880i
$78$	5.87458	−	2.07562i	0.665165	−	0.235018i
$79$	−3.13880	+	2.12146i	−0.353143	+	0.238683i	−0.723682	−	0.690134i	$-0.757552\pi$
$79$	−3.13880	+	2.12146i	−0.353143	+	0.238683i	0.370539	+	0.928817i	$0.379173\pi$
$80$	−3.59951	+	1.27179i	−0.402437	+	0.142190i
$81$	0.0424412	+	0.999099i	0.00471569	+	0.111011i
$82$	−8.06580	+	10.9057i	−0.890718	+	1.20433i
$83$	−3.00868	+	5.96736i	−0.330246	+	0.655003i	−0.995821	−	0.0913276i	$-0.970889\pi$
$83$	−3.00868	+	5.96736i	−0.330246	+	0.655003i	0.665575	+	0.746331i	$0.268186\pi$
$84$	−0.364721	+	0.0625377i	−0.0397944	+	0.00682343i
$85$	0.466739	−	0.260736i	0.0506249	−	0.0282808i
$86$	9.26476	+	8.87955i	0.999045	+	0.957507i
$87$	6.32366	+	4.27405i	0.677968	+	0.458226i
$88$	−3.70708	−	2.50555i	−0.395176	−	0.267092i
$89$	−5.00072	+	8.12168i	−0.530075	+	0.860896i	−0.999759	−	0.0219382i	$-0.993016\pi$
$89$	−5.00072	+	8.12168i	−0.530075	+	0.860896i	0.469685	+	0.882834i	$0.344368\pi$
$90$	0.209279	+	1.63429i	0.0220600	+	0.172270i
$91$	3.93393	−	1.02432i	0.412388	−	0.107378i
$92$	−0.769360	−	0.271832i	−0.0802114	−	0.0283405i
$93$	2.64662	−	8.64211i	0.274441	−	0.896145i
$94$	−8.67231	+	0.738122i	−0.894481	+	0.0761315i
$95$	1.68182	+	1.61189i	0.172551	+	0.165377i
$96$	2.44599	+	0.636885i	0.249642	+	0.0650018i
$97$	7.95072	−	12.9128i	0.807273	−	1.31110i	−0.139833	−	0.990175i	$-0.544657\pi$
$97$	7.95072	−	12.9128i	0.807273	−	1.31110i	0.947106	−	0.320920i	$-0.103992\pi$
$98$	−7.85191	+	0.668296i	−0.793162	+	0.0675081i
$99$	−1.05846	+	1.01445i	−0.106379	+	0.101956i
$100$	0.311729	+	1.44643i	0.0311729	+	0.144643i
$101$	6.74907	+	7.66844i	0.671558	+	0.763038i	0.982271	−	0.187466i	$-0.0600273\pi$
$101$	6.74907	+	7.66844i	0.671558	+	0.763038i	−0.310713	+	0.950504i	$0.600568\pi$
$102$	0.499030	+	0.0424737i	0.0494113	+	0.00420552i
$103$	1.30667	−	3.25177i	0.128750	−	0.320406i	−0.849580	−	0.527460i	$-0.823144\pi$
$103$	1.30667	−	3.25177i	0.128750	−	0.320406i	0.978329	+	0.207054i	$0.0663876\pi$
$104$	−15.0851	−	2.58660i	−1.47922	−	0.253637i
$105$	0.0456247	+	1.07404i	0.00445251	+	0.104816i
$106$	4.84880	−	12.0667i	0.470957	−	1.17202i
$107$	2.13078	+	4.22615i	0.205990	+	0.408557i	0.972240	−	0.233986i	$-0.0751768\pi$
$107$	2.13078	+	4.22615i	0.205990	+	0.408557i	−0.766250	+	0.642543i	$0.777880\pi$
$108$	0.205523	−	0.407631i	0.0197765	−	0.0392243i
$109$	3.79580	+	17.6126i	0.363571	+	1.68698i	0.675892	+	0.737000i	$0.263758\pi$
$109$	3.79580	+	17.6126i	0.363571	+	1.68698i	−0.312321	+	0.949977i	$0.601106\pi$
$110$	−1.59593	+	1.81333i	−0.152166	+	0.172894i
$111$	−7.81003	−	2.75946i	−0.741295	−	0.261916i
$112$	−2.20006	−	0.777330i	−0.207886	−	0.0734508i
$113$	−0.545040	+	0.619285i	−0.0512730	+	0.0582575i	−0.775743	−	0.631048i	$-0.782625\pi$
$113$	−0.545040	+	0.619285i	−0.0512730	+	0.0582575i	0.724470	+	0.689306i	$0.242084\pi$
$114$	0.459760	+	2.13330i	0.0430605	+	0.199801i
$115$	−1.06719	+	2.11665i	−0.0995161	+	0.197378i
$116$	−1.56867	−	3.11128i	−0.145648	−	0.288875i
$117$	−1.86987	+	4.65335i	−0.172870	+	0.430203i
$118$	0.656337	+	15.4507i	0.0604207	+	1.42235i
$119$	0.322071	+	0.0552246i	0.0295242	+	0.00506243i
$120$	1.50912	−	3.75558i	0.137763	−	0.342836i
$121$	8.81867	+	0.750579i	0.801697	+	0.0682345i
$122$	10.4657	+	11.8914i	0.947521	+	1.07659i
$123$	−2.30021	−	10.6730i	−0.207403	−	0.962355i
$124$	−2.97885	+	2.85500i	−0.267509	+	0.256386i
$125$	10.8901	−	0.926885i	0.974042	−	0.0829032i
$126$	−0.528006	+	0.857537i	−0.0470385	+	0.0763955i
$127$	−16.6658	−	4.33945i	−1.47885	−	0.385064i	−0.576871	−	0.816835i	$-0.695726\pi$
$127$	−16.6658	−	4.33945i	−1.47885	−	0.385064i	−0.901983	+	0.431772i	$0.857889\pi$
$128$	4.33077	+	4.15071i	0.382790	+	0.366875i
$129$	−10.2921	+	0.875988i	−0.906170	+	0.0771264i
$130$	−2.41956	+	7.90070i	−0.212210	+	0.692937i
$131$	−3.31679	−	1.17190i	−0.289789	−	0.102389i	0.184288	−	0.982872i	$-0.441002\pi$
$131$	−3.31679	−	1.17190i	−0.289789	−	0.102389i	−0.474077	+	0.880483i	$0.657218\pi$
$132$	0.647696	−	0.168647i	0.0563747	−	0.0146788i
$133$	0.180852	+	1.41230i	0.0156819	+	0.122462i
$134$	2.96970	−	4.82309i	0.256543	−	0.416652i
$135$	−1.09877	−	0.742641i	−0.0945673	−	0.0639163i
$136$	−1.01932	−	0.688940i	−0.0874059	−	0.0590761i
$137$	−3.62519	−	3.47446i	−0.309721	−	0.296843i	0.520973	−	0.853573i	$-0.325569\pi$
$137$	−3.62519	−	3.47446i	−0.309721	−	0.296843i	−0.830693	+	0.556730i	$0.812056\pi$
$138$	−1.93863	+	1.08299i	−0.165027	+	0.0921899i
$139$	−6.21941	+	1.06643i	−0.527524	+	0.0904530i	−0.426599	−	0.904441i	$-0.640288\pi$
$139$	−6.21941	+	1.06643i	−0.527524	+	0.0904530i	−0.100925	+	0.994894i	$0.532180\pi$
$140$	0.220939	−	0.438207i	0.0186728	−	0.0370352i
$141$	4.16581	−	5.63255i	0.350825	−	0.474346i
$142$	0.518006	+	12.1943i	0.0434701	+	1.02332i
$143$	−6.93249	+	2.44940i	−0.579724	+	0.204829i
$144$	2.38493	−	1.61193i	0.198744	−	0.134327i
$145$	−9.54414	+	3.37216i	−0.792598	+	0.280043i
$146$	−13.1853	−	2.26085i	−1.09122	−	0.187109i
$147$	3.77172	−	5.09971i	0.311087	−	0.420617i
$148$	2.49826	+	2.83857i	0.205355	+	0.233329i
$149$	5.89031	+	14.6586i	0.482553	+	1.20088i	0.948702	+	0.316173i	$0.102398\pi$
$149$	5.89031	+	14.6586i	0.482553	+	1.20088i	−0.466149	+	0.884706i	$0.654359\pi$
$150$	3.51541	+	1.96383i	0.287032	+	0.160346i
$151$	−13.0692	+	3.40296i	−1.06356	+	0.276929i	−0.742303	−	0.670064i	$-0.766267\pi$
$151$	−13.0692	+	3.40296i	−1.06356	+	0.276929i	−0.321254	+	0.946993i	$0.604104\pi$
$152$	1.56976	−	5.12580i	0.127324	−	0.415758i
$153$	−0.291040	+	0.278939i	−0.0235292	+	0.0225509i
$154$	−1.45521	+	0.249520i	−0.117264	+	0.0201069i
$155$	7.12764	+	9.63720i	0.572505	+	0.774078i
$156$	1.78124	−	1.43825i	0.142613	−	0.115152i
$157$	−6.18867	−	0.526733i	−0.493910	−	0.0420379i	−0.164795	−	0.986328i	$-0.552696\pi$
$157$	−6.18867	−	0.526733i	−0.493910	−	0.0420379i	−0.329115	+	0.944290i	$0.606750\pi$
$158$	2.79877	−	3.78419i	0.222658	−	0.301054i
$159$	4.71249	+	9.34666i	0.373725	+	0.741239i
$160$	−2.60800	+	2.10582i	−0.206181	+	0.166479i
$161$	−1.32024	+	0.596784i	−0.104049	+	0.0470332i
$162$	−0.463226	−	1.15278i	−0.0363945	−	0.0905712i
$163$	2.05202	−	2.33155i	0.160727	−	0.182621i	−0.664735	−	0.747079i	$-0.731456\pi$
$163$	2.05202	−	2.33155i	0.160727	−	0.182621i	0.825461	+	0.564458i	$0.190915\pi$
$164$	−1.45950	+	4.76576i	−0.113968	+	0.372143i
$165$	−0.246967	−	1.92860i	−0.0192263	−	0.150141i
$166$	1.05459	−	8.23544i	0.0818520	−	0.639194i
$167$	−18.9491	−	15.3003i	−1.46632	−	1.18397i	−0.943428	−	0.331578i	$-0.892419\pi$
$167$	−18.9491	−	15.3003i	−1.46632	−	1.18397i	−0.522897	−	0.852396i	$-0.675149\pi$
$168$	2.15970	−	1.20648i	0.166624	−	0.0930820i
$169$	−8.77185	+	8.40714i	−0.674758	+	0.646703i
$170$	−0.438826	+	0.498603i	−0.0336564	+	0.0382411i
$171$	−1.53348	−	0.856655i	−0.117268	−	0.0655101i
$172$	4.29686	+	1.94230i	0.327632	+	0.148099i
$173$	−0.545562	+	4.26037i	−0.0414783	+	0.323910i	0.957850	+	0.287268i	$0.0927471\pi$
$173$	−0.545562	+	4.26037i	−0.0414783	+	0.323910i	−0.999328	+	0.0366418i	$0.988334\pi$
$174$	−9.17653	−	2.38938i	−0.695671	−	0.181139i
$175$	2.17672	+	1.47121i	0.164545	+	0.111213i
$176$	4.08410	+	1.06342i	0.307851	+	0.0801581i
$177$	−9.68472	−	7.81987i	−0.727948	−	0.587777i
$178$	2.49643	−	11.5835i	0.187115	−	0.868219i
$179$	−8.60268	−	11.6316i	−0.642995	−	0.869386i	0.354856	−	0.934921i	$-0.384530\pi$
$179$	−8.60268	−	11.6316i	−0.642995	−	0.869386i	−0.997850	+	0.0655350i	$0.979125\pi$
$180$	0.272566	+	0.540602i	0.0203158	+	0.0402941i
$181$	−25.5745	−	4.38520i	−1.90094	−	0.325949i	−0.905742	−	0.423829i	$-0.860686\pi$
$181$	−25.5745	−	4.38520i	−1.90094	−	0.325949i	−0.995198	+	0.0978795i	$0.968794\pi$
$182$	−4.18428	+	2.82808i	−0.310160	+	0.209631i
$183$	−12.7506			−0.942549
$184$	5.45498			0.402147
$185$	9.10134	−	6.15143i	0.669144	−	0.452262i
$186$	0.476569	+	11.2188i	0.0349437	+	0.822602i
$187$	−0.588896	−	0.0501224i	−0.0430643	−	0.00366532i
$188$	−2.91427	+	1.31733i	−0.212545	+	0.0960764i
$189$	−0.237359	−	0.775060i	−0.0172654	−	0.0563773i
$190$	−2.63723	−	1.19210i	−0.191324	−	0.0864841i
$191$	0.548776	+	4.28547i	0.0397081	+	0.310086i	0.999562	+	0.0295864i	$0.00941903\pi$
$191$	0.548776	+	4.28547i	0.0397081	+	0.310086i	−0.959854	+	0.280500i	$0.909500\pi$
$192$	−8.86524	+	0.754543i	−0.639794	+	0.0544545i
$193$	8.47293	−	4.73326i	0.609895	−	0.340708i	−0.152027	−	0.988376i	$-0.548580\pi$
$193$	8.47293	−	4.73326i	0.609895	−	0.340708i	0.761922	+	0.647669i	$0.224256\pi$
$194$	−3.96912	+	18.4168i	−0.284966	+	1.32225i
$195$	−3.48711	−	5.66343i	−0.249717	−	0.405567i
$196$	−2.63858	+	1.19271i	−0.188470	+	0.0851937i
$197$	10.3193	+	11.7250i	0.735218	+	0.835370i	0.991346	−	0.131273i	$-0.0419065\pi$
$197$	10.3193	+	11.7250i	0.735218	+	0.835370i	−0.256129	+	0.966643i	$0.582447\pi$
$198$	0.820020	−	1.62641i	0.0582763	−	0.115584i
$199$	−5.09540	−	6.88944i	−0.361204	−	0.488380i	0.585416	−	0.810733i	$-0.300931\pi$
$199$	−5.09540	−	6.88944i	−0.361204	−	0.488380i	−0.946619	+	0.322354i	$0.895526\pi$
$200$	−5.18633	−	8.42313i	−0.366729	−	0.595605i
$201$	1.33499	+	4.35921i	0.0941632	+	0.307475i
$202$	−11.0797	−	6.18951i	−0.779568	−	0.435493i
$203$	−5.83349	−	2.06110i	−0.409430	−	0.144661i
$204$	0.178094	−	0.0463721i	0.0124691	−	0.00324670i
$205$	13.1942	+	5.96417i	0.921525	+	0.416556i
$206$	−0.184783	+	4.34994i	−0.0128745	+	0.303075i
$207$	0.376569	−	1.74729i	0.0261734	−	0.121445i
$208$	14.2284	−	2.43970i	0.986560	−	0.169163i
$209$	−0.542555	−	2.51746i	−0.0375293	−	0.174136i
$210$	−0.497972	−	1.23925i	−0.0343634	−	0.0855165i
$211$	5.95054	+	19.4306i	0.409652	+	1.33766i	0.888145	+	0.459564i	$0.151994\pi$
$211$	5.95054	+	19.4306i	0.409652	+	1.33766i	−0.478493	+	0.878092i	$0.658817\pi$
$212$	0.202806	−	4.77421i	0.0139288	−	0.327894i
$213$	−7.64355	−	6.17173i	−0.523727	−	0.422880i
$214$	−4.24514	−	4.06863i	−0.290192	−	0.278126i
$215$	7.18237	−	11.6649i	0.489834	−	0.795541i
$216$	−0.387646	+	3.02718i	−0.0263760	+	0.205974i
$217$	−0.310939	+	7.31975i	−0.0211079	+	0.496897i
$218$	−11.7360	−	19.0604i	−0.794860	−	1.29093i
$219$	8.37781	−	6.76461i	0.566120	−	0.457110i
$220$	−0.330954	+	0.823610i	−0.0223129	+	0.0555278i
$221$	−1.90620	+	0.673502i	−0.128225	+	0.0453046i
$222$	10.2908			0.690673
$223$	0.116281	+	14.9327i	0.00778672	+	0.999970i
$223$	0.116281	+	14.9327i	0.00778672	+	0.999970i
$224$	−2.04880			−0.136891
$225$	−3.05604	+	1.07977i	−0.203736	+	0.0719845i
$226$	0.382150	−	0.951017i	0.0254202	−	0.0632607i
$227$	−19.5452	+	15.7816i	−1.29726	+	1.04746i	−0.301691	+	0.953406i	$0.597551\pi$
$227$	−19.5452	+	15.7816i	−1.29726	+	1.04746i	−0.995567	+	0.0940569i	$0.970016\pi$
$228$	0.420432	+	0.682825i	0.0278438	+	0.0452212i
$229$	0.596855	−	14.0504i	0.0394413	−	0.928479i	−0.864972	−	0.501821i	$-0.832664\pi$
$229$	0.596855	−	14.0504i	0.0394413	−	0.928479i	0.904413	−	0.426658i	$-0.140309\pi$
$230$	0.374067	−	2.92114i	0.0246653	−	0.192615i
$231$	0.623091	−	1.01196i	0.0409964	−	0.0665823i
$232$	16.8172	+	16.1179i	1.10410	+	1.05819i
$233$	−23.2422	−	18.7668i	−1.52265	−	1.22945i	−0.890834	−	0.454329i	$-0.849879\pi$
$233$	−23.2422	−	18.7668i	−1.52265	−	1.22945i	−0.631812	−	0.775122i	$-0.717688\pi$
$234$	0.264429	−	6.22487i	0.0172863	−	0.406932i
$235$	2.72061	+	8.88371i	0.177473	+	0.579510i
$236$	2.11876	+	5.27273i	0.137919	+	0.343225i
$237$	0.798157	+	3.70346i	0.0518459	+	0.240566i
$238$	−0.400132	+	0.0686095i	−0.0259367	+	0.00444729i
$239$	3.92031	−	18.1903i	0.253584	−	1.17663i	−0.653911	−	0.756571i	$-0.726873\pi$
$239$	3.92031	−	18.1903i	0.253584	−	1.17663i	0.907495	−	0.420062i	$-0.137992\pi$
$240$	−0.162023	+	3.81414i	−0.0104585	+	0.246201i
$241$	19.0538	+	8.61286i	1.22736	+	0.554803i	0.918166	−	0.396195i	$-0.129670\pi$
$241$	19.0538	+	8.61286i	1.22736	+	0.554803i	0.309196	+	0.950998i	$0.399940\pi$
$242$	−10.6409	+	2.77067i	−0.684022	+	0.178105i
$243$	0.942877	+	0.333140i	0.0604856	+	0.0213709i
$244$	5.08163	+	2.83877i	0.325318	+	0.181733i
$245$	2.46324	+	8.04331i	0.157370	+	0.513868i
$246$	7.11187	+	11.5504i	0.453437	+	0.736428i
$247$	−5.23814	−	7.08243i	−0.333295	−	0.450644i
$248$	12.4184	−	24.6304i	0.788569	−	1.56403i
$249$	4.41524	+	5.01669i	0.279805	+	0.317920i
$250$	−12.3731	+	5.59300i	−0.782544	+	0.353732i
$251$	−1.11857	−	1.81667i	−0.0706035	−	0.114667i	0.814295	−	0.580451i	$-0.197124\pi$
$251$	−1.11857	−	1.81667i	−0.0706035	−	0.114667i	−0.884899	+	0.465784i	$0.845772\pi$
$252$	−0.0779606	+	0.361738i	−0.00491106	+	0.0227874i
$253$	2.28775	−	1.27801i	0.143829	−	0.0803479i
$254$	21.3185	−	1.81447i	1.33764	−	0.113850i
$255$	−0.0679074	−	0.530299i	−0.00425253	−	0.0332086i
$256$	9.42394	+	4.25989i	0.588996	+	0.266243i
$257$	2.81316	+	9.18592i	0.175480	+	0.573002i	0.999975	+	0.00713216i	$0.00227026\pi$
$257$	2.81316	+	9.18592i	0.175480	+	0.573002i	−0.824495	+	0.565870i	$0.808541\pi$
$258$	11.6937	−	5.28587i	0.728016	−	0.329084i
$259$	6.69009	+	0.569410i	0.415702	+	0.0353814i
$260$	0.128860	+	3.03348i	0.00799159	+	0.188128i
$261$	6.32366	−	4.27405i	0.391425	−	0.264557i
$262$	4.37033			0.270000
$263$	−19.7631			−1.21864			−0.609321	−	0.792923i	$-0.708558\pi$
$263$	−19.7631			−1.21864			−0.609321	+	0.792923i	$0.708558\pi$
$264$	−3.70708	+	2.50555i	−0.228155	+	0.154206i
$265$	−13.6823	−	2.34607i	−0.840497	−	0.144118i
$266$	−0.796380	−	1.57953i	−0.0488292	−	0.0968469i
$267$	5.67147	+	7.66833i	0.347088	+	0.469294i
$268$	0.438478	−	2.03455i	0.0267843	−	0.124280i
$269$	19.4391	+	15.6960i	1.18522	+	0.957002i	0.999671	−	0.0256324i	$-0.00815994\pi$
$269$	19.4391	+	15.6960i	1.18522	+	0.957002i	0.185553	+	0.982634i	$0.440592\pi$
$270$	1.59447	+	0.415169i	0.0970366	+	0.0252664i
$271$	1.28668	+	0.869645i	0.0781604	+	0.0528272i	0.598432	−	0.801174i	$-0.295791\pi$
$271$	1.28668	+	0.869645i	0.0781604	+	0.0528272i	−0.520271	+	0.854001i	$0.674169\pi$
$272$	1.12299	+	0.292403i	0.0680912	+	0.0177296i
$273$	0.516341	−	4.03218i	0.0312504	−	0.244039i
$274$	5.68458	+	2.56959i	0.343418	+	0.155235i
$275$	−4.14848	−	2.31748i	−0.250162	−	0.139749i
$276$	−0.539091	+	0.612527i	−0.0324495	+	0.0368698i
$277$	3.18977	−	3.05714i	0.191654	−	0.183686i	−0.589989	−	0.807411i	$-0.700868\pi$
$277$	3.18977	−	3.05714i	0.191654	−	0.183686i	0.781644	+	0.623725i	$0.214382\pi$
$278$	6.84407	−	3.82333i	0.410480	−	0.229308i
$279$	−7.03211	−	5.67803i	−0.421001	−	0.339935i
$280$	−0.416723	+	3.25425i	−0.0249039	+	0.194478i
$281$	0.729561	+	5.69725i	0.0435220	+	0.339869i	0.998996	+	0.0447948i	$0.0142634\pi$
$281$	0.729561	+	5.69725i	0.0435220	+	0.339869i	−0.955474	+	0.295074i	$0.904656\pi$
$282$	−2.54863	+	8.32216i	−0.151769	+	0.495577i
$283$	5.80894	−	6.60023i	0.345305	−	0.392343i	−0.551934	−	0.833888i	$-0.686110\pi$
$283$	5.80894	−	6.60023i	0.345305	−	0.392343i	0.897239	+	0.441545i	$0.145569\pi$
$284$	1.67220	+	4.16144i	0.0992269	+	0.246936i
$285$	2.12273	−	0.959536i	0.125740	−	0.0568380i
$286$	7.10698	−	5.73848i	0.420244	−	0.339324i
$287$	3.98435	+	7.90248i	0.235189	+	0.466469i
$288$	1.50296	−	2.03214i	0.0885628	−	0.119745i
$289$	16.7768	+	1.42792i	0.986872	+	0.0839952i
$290$	9.78437	−	7.90033i	0.574558	−	0.463923i
$291$	−9.01716	−	12.1920i	−0.528595	−	0.714708i
$292$	−4.84496	+	0.830753i	−0.283530	+	0.0486161i
$293$	14.6362	−	14.0277i	0.855058	−	0.819507i	−0.130038	−	0.991509i	$-0.541510\pi$
$293$	14.6362	−	14.0277i	0.855058	−	0.819507i	0.985097	+	0.172002i	$0.0550235\pi$
$294$	−2.30753	+	7.53488i	−0.134578	+	0.439443i
$295$	15.9755	−	4.15969i	0.930128	−	0.242186i
$296$	−22.0693	−	12.3287i	−1.28275	−	0.716589i
$297$	0.546645	+	1.36038i	0.0317196	+	0.0789372i
$298$	−12.9669	−	14.7332i	−0.751152	−	0.853474i
$299$	5.33018	−	7.20688i	0.308252	−	0.416785i
$300$	1.45835	+	0.250060i	0.0841981	+	0.0144372i
$301$	7.89457	−	2.78933i	0.455036	−	0.160774i
$302$	13.9009	−	9.39537i	0.799907	−	0.540643i
$303$	9.63189	−	3.40316i	0.553338	−	0.195507i
$304$	0.214597	+	5.05177i	0.0123080	+	0.289739i
$305$	10.0552	−	13.5955i	0.575757	−	0.778475i
$306$	0.225477	−	0.447208i	0.0128897	−	0.0255652i
$307$	−24.7642	+	4.24624i	−1.41337	+	0.242346i	−0.824489	−	0.565878i	$-0.808537\pi$
$307$	−24.7642	+	4.24624i	−1.41337	+	0.242346i	−0.588876	+	0.808223i	$0.700429\pi$
$308$	−0.473629	+	0.264585i	−0.0269875	+	0.0150761i
$309$	−2.53008	−	2.42488i	−0.143931	−	0.137947i
$310$	−12.3380	−	8.33905i	−0.700753	−	0.473626i
$311$	16.5525	+	11.1876i	0.938609	+	0.634389i	0.930780	−	0.365581i	$-0.119130\pi$
$311$	16.5525	+	11.1876i	0.938609	+	0.634389i	0.00782887	+	0.999969i	$0.497508\pi$
$312$	−8.02466	+	13.0329i	−0.454307	+	0.737841i
$313$	0.745482	+	5.82158i	0.0421372	+	0.329055i	0.999229	+	0.0392693i	$0.0125030\pi$
$313$	0.745482	+	5.82158i	0.0421372	+	0.329055i	−0.957092	+	0.289786i	$0.906416\pi$
$314$	7.46744	−	1.94437i	0.421412	−	0.109727i
$315$	1.01360	+	0.358128i	0.0571100	+	0.0201782i
$316$	0.506434	−	1.65368i	0.0284892	−	0.0930269i
$317$	−1.99113	+	0.169470i	−0.111833	+	0.00951841i	−0.140589	−	0.990068i	$-0.544900\pi$
$317$	−1.99113	+	0.169470i	−0.111833	+	0.00951841i	0.0287557	+	0.999586i	$0.490846\pi$
$318$	−9.38866	−	8.99830i	−0.526490	−	0.504600i
$319$	10.8291	+	2.81967i	0.606311	+	0.157871i
$320$	6.18663	−	10.0477i	0.345843	−	0.561685i
$321$	4.71587	−	0.401380i	0.263214	−	0.0224028i
$322$	1.29953	−	1.24550i	0.0724201	−	0.0694090i
$323$	−0.149184	−	0.692216i	−0.00830081	−	0.0385159i
$324$	−0.301606	−	0.342691i	−0.0167559	−	0.0190384i
$325$	−16.1959	−	1.37848i	−0.898389	−	0.0764642i
$326$	−1.43876	+	3.58048i	−0.0796853	+	0.198305i
$327$	17.7578	+	3.04488i	0.982008	+	0.168382i
$328$	−1.41418	−	33.2909i	−0.0780850	−	1.83818i
$329$	−2.11736	+	5.26924i	−0.116734	+	0.290503i
$330$	1.08751	+	2.15696i	0.0598657	+	0.118736i
$331$	−2.92709	+	5.80554i	−0.160887	+	0.319101i	−0.958999	−	0.283408i	$-0.908535\pi$
$331$	−2.92709	+	5.80554i	−0.160887	+	0.319101i	0.798112	+	0.602509i	$0.205832\pi$
$332$	−0.642748	−	2.98236i	−0.0352754	−	0.163678i
$333$	−5.47249	+	6.21796i	−0.299891	+	0.340742i
$334$	28.5296	+	10.0801i	1.56107	+	0.551561i
$335$	−5.70086	−	2.01424i	−0.311471	−	0.110050i
$336$	−1.54158	+	1.75158i	−0.0841002	+	0.0955564i
$337$	1.18028	+	5.47654i	0.0642942	+	0.298326i	0.998255	−	0.0590492i	$-0.0188069\pi$
$337$	1.18028	+	5.47654i	0.0642942	+	0.298326i	−0.933961	+	0.357375i	$0.883672\pi$
$338$	6.79581	−	13.4787i	0.369643	−	0.733144i
$339$	0.371407	+	0.736641i	0.0201720	+	0.0400088i
$340$	−0.0910010	+	0.226465i	−0.00493522	+	0.0122818i
$341$	−0.562390	−	13.2391i	−0.0304551	−	0.716937i
$342$	2.15089	+	0.368806i	0.116307	+	0.0199428i
$343$	−4.03269	+	10.0357i	−0.217745	+	0.541879i
$344$	−31.4105	−	2.67343i	−1.69354	−	0.144142i
$345$	1.56610	+	1.77944i	0.0843162	+	0.0958019i
$346$	−1.12422	−	5.21642i	−0.0604387	−	0.280436i
$347$	12.0546	−	11.5534i	0.647125	−	0.620219i	−0.294994	−	0.955499i	$-0.595318\pi$
$347$	12.0546	−	11.5534i	0.647125	−	0.620219i	0.942118	+	0.335280i	$0.108831\pi$
$348$	−3.47181	+	0.295494i	−0.186108	+	0.0158402i
$349$	−14.8894	+	24.1819i	−0.797009	+	1.29442i	0.154865	+	0.987936i	$0.450506\pi$
$349$	−14.8894	+	24.1819i	−0.797009	+	1.29442i	−0.951874	+	0.306489i	$0.900846\pi$
$350$	−3.15873	−	0.822469i	−0.168841	−	0.0439628i
$351$	3.62060	+	3.47007i	0.193253	+	0.185218i
$352$	3.69228	−	0.314260i	0.196799	−	0.0167501i
$353$	2.89215	−	9.44385i	0.153933	−	0.502645i	−0.845580	−	0.533849i	$-0.820745\pi$
$353$	2.89215	−	9.44385i	0.153933	−	0.502645i	0.999513	+	0.0312041i	$0.00993417\pi$
$354$	14.5812	+	5.15188i	0.774984	+	0.273819i
$355$	12.6084	−	3.28298i	0.669186	−	0.174243i
$356$	−0.553048	−	4.31883i	−0.0293115	−	0.228898i
$357$	0.171329	−	0.278255i	0.00906767	−	0.0147268i
$358$	14.8913	+	10.0648i	0.787032	+	0.531941i
$359$	9.61712	+	6.50004i	0.507572	+	0.343059i	0.786843	−	0.617154i	$-0.211714\pi$
$359$	9.61712	+	6.50004i	0.507572	+	0.343059i	−0.279271	+	0.960212i	$0.590093\pi$
$360$	−2.92208	−	2.80058i	−0.154007	−	0.147604i
$361$	−13.8936	+	7.76145i	−0.731244	+	0.408498i
$362$	31.7731	−	5.44804i	1.66996	−	0.286343i
$363$	3.98455	−	7.90288i	0.209135	−	0.414794i
$364$	−1.10350	+	1.49203i	−0.0578391	+	0.0782037i
$365$	0.606079	+	14.2676i	0.0317236	+	0.746799i
$366$	14.9361	−	5.27725i	0.780721	−	0.275846i
$367$	24.0437	−	16.2507i	1.25507	−	0.848278i	0.261915	−	0.965091i	$-0.415646\pi$
$367$	24.0437	−	16.2507i	1.25507	−	0.848278i	0.993154	+	0.116813i	$0.0372677\pi$
$368$	−4.85127	+	1.71406i	−0.252890	+	0.0893517i
$369$	−10.7610	−	1.84517i	−0.560197	−	0.0960555i
$370$	−8.11537	+	10.9727i	−0.421898	+	0.570444i
$371$	−5.60571	−	6.36932i	−0.291034	−	0.330679i
$372$	1.53844	+	3.82855i	0.0797642	+	0.198501i
$373$	21.7040	+	12.1246i	1.12379	+	0.627788i	0.935148	−	0.354258i	$-0.115266\pi$
$373$	21.7040	+	12.1246i	1.12379	+	0.627788i	0.188644	+	0.982045i	$0.439591\pi$
$374$	0.710580	−	0.185021i	0.0367432	−	0.00956719i
$375$	3.20040	−	10.4504i	0.165268	−	0.539657i
$376$	15.4359	−	14.7941i	0.796046	−	0.762948i
$377$	37.7267	−	6.46889i	1.94302	−	0.333165i
$378$	0.598828	+	0.809670i	0.0308004	+	0.0416449i
$379$	−6.55016	+	5.28888i	−0.336459	+	0.271672i	−0.781588	−	0.623795i	$-0.785590\pi$
$379$	−6.55016	+	5.28888i	−0.336459	+	0.271672i	0.445129	+	0.895466i	$0.353158\pi$
$380$	−1.05963	−	0.0901875i	−0.0543577	−	0.00462652i
$381$	−10.2405	+	13.8461i	−0.524636	+	0.709355i
$382$	−2.41653	−	4.79289i	−0.123640	−	0.245226i
$383$	20.2736	−	16.3698i	1.03593	−	0.836459i	0.0491982	−	0.998789i	$-0.484333\pi$
$383$	20.2736	−	16.3698i	1.03593	−	0.836459i	0.986737	+	0.162330i	$0.0519010\pi$
$384$	5.46616	−	2.47086i	0.278944	−	0.126090i
$385$	0.587648	+	1.46242i	0.0299493	+	0.0745317i
$386$	−7.96621	+	9.05137i	−0.405469	+	0.460703i
$387$	−3.02466	+	9.87655i	−0.153752	+	0.502053i
$388$	0.879300	+	6.86658i	0.0446397	+	0.348598i
$389$	−3.20456	+	25.0248i	−0.162477	+	1.26881i	0.681255	+	0.732046i	$0.261434\pi$
$389$	−3.20456	+	25.0248i	−0.162477	+	1.26881i	−0.843733	+	0.536764i	$0.819647\pi$
$390$	6.42882	+	5.19091i	0.325536	+	0.262852i
$391$	0.629052	−	0.351409i	0.0318125	−	0.0177715i
$392$	13.9757	−	13.3946i	0.705877	−	0.676528i
$393$	−2.32407	+	2.64066i	−0.117234	+	0.133204i
$394$	−16.9408	−	9.46371i	−0.853466	−	0.476775i
$395$	−4.57830	−	2.06952i	−0.230359	−	0.104129i
$396$	0.0850120	−	0.663871i	0.00427201	−	0.0333608i
$397$	−2.29060	−	0.596427i	−0.114962	−	0.0299338i	0.194052	−	0.980991i	$-0.437837\pi$
$397$	−2.29060	−	0.596427i	−0.114962	−	0.0299338i	−0.309014	+	0.951057i	$0.599999\pi$
$398$	8.82021	+	5.96142i	0.442117	+	0.298819i
$399$	1.37789	+	0.358775i	0.0689809	+	0.0179612i
$400$	7.25906	+	5.86128i	0.362953	+	0.293064i
$401$	3.56678	−	16.5499i	0.178117	−	0.826464i	−0.796861	−	0.604162i	$-0.793508\pi$
$401$	3.56678	−	16.5499i	0.178117	−	0.826464i	0.974978	−	0.222302i	$-0.0713571\pi$
$402$	−3.36802	−	4.55387i	−0.167982	−	0.227126i
$403$	−20.4063	−	40.4736i	−1.01651	−	2.01613i
$404$	−4.59638	−	0.788129i	−0.228678	−	0.0392109i
$405$	−1.09877	+	0.742641i	−0.0545985	+	0.0369021i
$406$	7.68643			0.381471
$407$	−12.1440			−0.601955
$408$	−1.01932	+	0.688940i	−0.0504638	+	0.0341076i
$409$	0.0774743	+	1.82381i	0.00383086	+	0.0901814i	0.999996	+	0.00269274i	$0.000857128\pi$
$409$	0.0774743	+	1.82381i	0.00383086	+	0.0901814i	−0.996166	+	0.0874887i	$0.972116\pi$
$410$	−17.9243	−	1.52558i	−0.885216	−	0.0753430i
$411$	−4.57559	+	2.06830i	−0.225697	+	0.102022i
$412$	0.468468	+	1.52971i	0.0230798	+	0.0753633i
$413$	9.19426	+	4.15607i	0.452420	+	0.204507i
$414$	0.282058	+	2.20264i	0.0138624	+	0.108254i
$415$	−8.83100	+	0.751629i	−0.433497	+	0.0368960i
$416$	11.0660	−	6.18183i	0.542554	−	0.303089i
$417$	−1.32942	+	6.16855i	−0.0651022	+	0.302075i
$418$	1.67749	+	2.72441i	0.0820486	+	0.133255i
$419$	−11.8645	+	5.36307i	−0.579617	+	0.262003i	−0.680322	−	0.732913i	$-0.738160\pi$
$419$	−11.8645	+	5.36307i	−0.579617	+	0.262003i	0.100706	+	0.994916i	$0.467890\pi$
$420$	−0.324229	−	0.368395i	−0.0158207	−	0.0179759i
$421$	−4.74193	+	9.40506i	−0.231108	+	0.458374i	−0.978566	−	0.205934i	$-0.933977\pi$
$421$	−4.74193	+	9.40506i	−0.231108	+	0.458374i	0.747458	+	0.664309i	$0.231274\pi$
$422$	−15.0125	−	20.2982i	−0.730796	−	0.988102i
$423$	−3.67313	−	5.96554i	−0.178594	−	0.290055i
$424$	9.35441	+	30.5454i	0.454290	+	1.48341i
$425$	−1.14069	−	0.637227i	−0.0553315	−	0.0309100i
$426$	11.5081	+	4.06606i	0.557567	+	0.197001i
$427$	10.0020	−	2.60432i	0.484031	−	0.126032i
$428$	−1.96883	−	0.889967i	−0.0951670	−	0.0430182i
$429$	−0.312048	+	7.34585i	−0.0150658	+	0.354661i
$430$	−3.58555	+	16.6370i	−0.172910	+	0.802307i
$431$	−16.9951	+	2.91410i	−0.818624	+	0.140367i	−0.563051	−	0.826422i	$-0.690372\pi$
$431$	−16.9951	+	2.91410i	−0.818624	+	0.140367i	−0.255574	+	0.966790i	$0.582264\pi$
$432$	−0.606456	−	2.81397i	−0.0291781	−	0.135387i
$433$	−8.79896	−	21.8970i	−0.422851	−	1.05230i	−0.975717	−	0.219035i	$-0.929709\pi$
$433$	−8.79896	−	21.8970i	−0.422851	−	1.05230i	0.552866	−	0.833270i	$-0.313534\pi$
$434$	−2.66529	−	8.70308i	−0.127938	−	0.417761i
$435$	−0.429605	+	10.1132i	−0.0205980	+	0.484892i
$436$	−6.39930	−	5.16707i	−0.306471	−	0.247458i
$437$	2.26669	+	2.17244i	0.108430	+	0.103922i
$438$	−7.01405	+	11.3915i	−0.335144	+	0.544309i
$439$	1.15082	−	8.98693i	0.0549257	−	0.428923i	−0.940975	−	0.338475i	$-0.890089\pi$
$439$	1.15082	−	8.98693i	0.0549257	−	0.428923i	0.995901	−	0.0904480i	$-0.0288299\pi$
$440$	0.251844	−	5.92861i	0.0120062	−	0.282635i
$441$	−3.32565	−	5.40120i	−0.158364	−	0.257200i
$442$	1.95417	−	1.57789i	0.0929506	−	0.0750524i
$443$	3.45472	−	8.59741i	0.164139	−	0.408475i	−0.823063	−	0.567950i	$-0.807737\pi$
$443$	3.45472	−	8.59741i	0.164139	−	0.408475i	0.987202	+	0.159474i	$0.0509800\pi$
$444$	3.56537	−	1.25972i	0.169205	−	0.0597839i
$445$	−12.6490			−0.599621
$446$	−6.31662	−	17.4441i	−0.299101	−	0.826004i
$447$	15.7978			0.747210
$448$	6.80009	−	2.40263i	0.321274	−	0.113513i
$449$	−0.163176	+	0.406079i	−0.00770075	+	0.0191641i	−0.931690	−	0.363255i	$-0.881666\pi$
$449$	−0.163176	+	0.406079i	−0.00770075	+	0.0191641i	0.923989	+	0.382419i	$0.124909\pi$
$450$	3.13296	−	2.52969i	0.147689	−	0.119251i
$451$	−8.39259	−	13.6304i	−0.395192	−	0.641832i
$452$	0.0159838	−	0.376271i	0.000751815	−	0.0176983i
$453$	−1.71537	+	13.3956i	−0.0805953	+	0.629380i
$454$	16.3635	−	26.5761i	0.767979	−	1.24728i
$455$	3.89218	+	3.73035i	0.182468	+	0.174882i
$456$	−4.17088	−	3.36775i	−0.195319	−	0.157709i
$457$	−0.00871659	+	0.205195i	−0.000407745	+	0.00959864i	−0.999291	−	0.0376414i	$-0.988016\pi$
$457$	−0.00871659	+	0.205195i	−0.000407745	+	0.00959864i	0.998884	+	0.0472400i	$0.0150426\pi$
$458$	5.11609	+	16.7058i	0.239059	+	0.780610i
$459$	0.150309	+	0.374057i	0.00701581	+	0.0174595i
$460$	−0.227985	−	1.05786i	−0.0106299	−	0.0493228i
$461$	−3.67728	+	0.630532i	−0.171268	+	0.0293668i	−0.253996	−	0.967205i	$-0.581745\pi$
$461$	−3.67728	+	0.630532i	−0.171268	+	0.0293668i	0.0827278	+	0.996572i	$0.473637\pi$
$462$	−0.311056	+	1.44331i	−0.0144716	+	0.0671487i
$463$	0.780004	−	18.3619i	0.0362499	−	0.853350i	−0.885284	−	0.465052i	$-0.846036\pi$
$463$	0.780004	−	18.3619i	0.0362499	−	0.853350i	0.921533	−	0.388299i	$-0.126937\pi$
$464$	−20.0205	−	9.04986i	−0.929431	−	0.420129i
$465$	11.5998	−	3.02036i	0.537930	−	0.140066i
$466$	34.9932	+	12.3639i	1.62103	+	0.572747i
$467$	11.6595	+	6.51338i	0.539536	+	0.301403i	0.733595	−	0.679587i	$-0.237841\pi$
$467$	11.6595	+	6.51338i	0.539536	+	0.301403i	−0.194059	+	0.980990i	$0.562165\pi$
$468$	−0.670389	−	2.18905i	−0.0309887	−	0.101189i
$469$	−1.93759	−	3.14685i	−0.0894696	−	0.145308i
$470$	−6.86375	−	9.28041i	−0.316601	−	0.428073i
$471$	−2.79624	+	5.54600i	−0.128844	+	0.255546i
$472$	−25.0984	−	28.5173i	−1.15525	−	1.31262i
$473$	−13.7995	+	6.23776i	−0.634501	+	0.286812i
$474$	−2.46777	−	4.00791i	−0.113348	−	0.184089i
$475$	1.19945	−	5.56548i	0.0550347	−	0.255362i
$476$	−0.130232	+	0.0727518i	−0.00596916	+	0.00333457i
$477$	10.4297	−	0.887702i	0.477545	−	0.0406451i
$478$	2.93640	+	22.9308i	0.134308	+	1.04883i
$479$	2.72459	+	1.23159i	0.124490	+	0.0562728i	0.473184	−	0.880964i	$-0.343105\pi$
$479$	2.72459	+	1.23159i	0.124490	+	0.0562728i	−0.348694	+	0.937236i	$0.613375\pi$
$480$	0.981553	+	3.20511i	0.0448016	+	0.146292i
$481$	−37.8525	+	17.1104i	−1.72593	+	0.780168i
$482$	−25.8844	−	2.20309i	−1.17900	−	0.100348i
$483$	0.0614911	+	1.44755i	0.00279794	+	0.0658657i
$484$	−3.34749	+	2.26251i	−0.152159	+	0.102841i
$485$	20.1109			0.913188
$486$	−1.24237			−0.0563551
$487$	−16.0507	+	10.8484i	−0.727327	+	0.491587i	−0.866811	−	0.498637i	$-0.833834\pi$
$487$	−16.0507	+	10.8484i	−0.727327	+	0.491587i	0.139484	+	0.990224i	$0.455456\pi$
$488$	−38.3537	−	6.57641i	−1.73619	−	0.297700i
$489$	−1.39831	−	2.77338i	−0.0632337	−	0.125417i
$490$	−6.21444	−	8.40248i	−0.280740	−	0.379585i
$491$	−2.71038	+	12.5762i	−0.122318	+	0.567556i	0.874301	+	0.485385i	$0.161321\pi$
$491$	−2.71038	+	12.5762i	−0.122318	+	0.567556i	−0.996618	+	0.0821710i	$0.973815\pi$
$492$	3.87791	+	3.13119i	0.174830	+	0.141165i
$493$	2.97762	+	0.775311i	0.134105	+	0.0349183i
$494$	9.06728	+	6.12841i	0.407956	+	0.275730i
$495$	−1.88161	−	0.489933i	−0.0845721	−	0.0220209i
$496$	−3.30467	+	25.8066i	−0.148384	+	1.15875i
$497$	7.25645	+	3.28012i	0.325496	+	0.147134i
$498$	−7.24836	−	4.04918i	−0.324807	−	0.181448i
$499$	−11.0516	+	12.5570i	−0.494736	+	0.562129i	−0.943437	−	0.331553i	$-0.892427\pi$
$499$	−11.0516	+	12.5570i	−0.494736	+	0.562129i	0.448701	+	0.893682i	$0.351887\pi$
$500$	−3.60216	+	3.45239i	−0.161093	+	0.154395i
$501$	−21.2623	+	11.8778i	−0.949929	+	0.530662i
$502$	2.06219	+	1.66510i	0.0920399	+	0.0743171i
$503$	−4.74964	+	37.0906i	−0.211776	+	1.65379i	0.441936	+	0.897047i	$0.354292\pi$
$503$	−4.74964	+	37.0906i	−0.211776	+	1.65379i	−0.653712	+	0.756744i	$0.726789\pi$
$504$	−0.314222	−	2.45381i	−0.0139966	−	0.109301i
$505$	−3.96709	+	12.9539i	−0.176533	+	0.576441i
$506$	−2.15093	+	2.44393i	−0.0956204	+	0.108646i
$507$	4.53025	+	11.2740i	0.201195	+	0.500694i
$508$	7.16392	−	3.23829i	0.317847	−	0.143676i
$509$	−19.2257	+	15.5237i	−0.852164	+	0.688075i	−0.951723	−	0.306957i	$-0.900689\pi$
$509$	−19.2257	+	15.5237i	−0.852164	+	0.688075i	0.0995590	+	0.995032i	$0.468257\pi$
$510$	0.299029	+	0.593089i	0.0132412	+	0.0262624i
$511$	−5.19017	+	7.01758i	−0.229600	+	0.310439i
$512$	−24.7565	−	2.10709i	−1.09409	−	0.0931209i
$513$	−1.36665	+	1.10349i	−0.0603391	+	0.0487204i
$514$	−7.09724	−	9.59611i	−0.313046	−	0.423266i
$515$	4.58080	−	0.785457i	0.201854	−	0.0346114i
$516$	3.40435	−	3.26281i	0.149868	−	0.143637i
$517$	3.00759	−	9.82082i	0.132274	−	0.431919i
$518$	−8.07247	+	2.10191i	−0.354684	+	0.0923525i
$519$	3.74974	+	2.09473i	0.164595	+	0.0919484i
$520$	−7.56820	−	18.8342i	−0.331887	−	0.825934i
$521$	4.34918	+	4.94162i	0.190541	+	0.216496i	0.838097	−	0.545521i	$-0.183668\pi$
$521$	4.34918	+	4.94162i	0.190541	+	0.216496i	−0.647556	+	0.762018i	$0.724209\pi$
$522$	−5.63861	+	7.62390i	−0.246795	+	0.333689i
$523$	33.2943	+	5.70889i	1.45586	+	0.249632i	0.841869	−	0.539681i	$-0.181455\pi$
$523$	33.2943	+	5.70889i	1.45586	+	0.249632i	0.613990	+	0.789313i	$0.289563\pi$
$524$	1.51415	−	0.534984i	0.0661460	−	0.0233709i
$525$	2.17672	−	1.47121i	0.0949999	−	0.0642087i
$526$	23.1505	−	8.17961i	1.00941	−	0.356648i
$527$	−0.154638	−	3.64030i	−0.00673613	−	0.158574i
$528$	2.50952	−	3.39309i	0.109213	−	0.147665i
$529$	8.91637	−	17.6846i	0.387668	−	0.768894i
$530$	16.9985	−	2.91469i	0.738368	−	0.126606i
$531$	−10.8670	+	6.07066i	−0.471587	+	0.263444i
$532$	−0.469269	−	0.449758i	−0.0203454	−	0.0194995i
$533$	−45.3643	−	30.6609i	−1.96495	−	1.32807i
$534$	−9.81738	−	6.63539i	−0.424840	−	0.287141i
$535$	−3.29098	+	5.34489i	−0.142282	+	0.231080i
$536$	1.76730	+	13.8011i	0.0763356	+	0.596116i
$537$	−14.0004	+	3.64542i	−0.604162	+	0.157311i
$538$	−29.2674	−	10.3408i	−1.26181	−	0.445825i
$539$	2.72307	−	8.89177i	0.117291	−	0.382996i
$540$	0.603246	−	0.0513438i	0.0259596	−	0.00220949i
$541$	16.3447	+	15.6651i	0.702713	+	0.673496i	0.955823	−	0.293941i	$-0.0949670\pi$
$541$	16.3447	+	15.6651i	0.702713	+	0.673496i	−0.253110	+	0.967437i	$0.581454\pi$
$542$	−1.86716	−	0.486170i	−0.0802013	−	0.0208828i
$543$	−13.6046	+	22.0953i	−0.583830	+	0.948200i
$544$	1.01525	−	0.0864106i	0.0435285	−	0.00370482i
$545$	−17.2505	+	16.5333i	−0.738931	+	0.708208i
$546$	1.06401	+	4.93702i	0.0455354	+	0.211285i
$547$	−22.2994	−	25.3371i	−0.953455	−	1.08334i	−0.996444	−	0.0842595i	$-0.973148\pi$
$547$	−22.2994	−	25.3371i	−0.953455	−	1.08334i	0.0429891	−	0.999076i	$-0.486312\pi$
$548$	2.28404	+	0.194401i	0.0975694	+	0.00830438i
$549$	−4.75413	+	11.8311i	−0.202901	+	0.504940i
$550$	5.81871	+	0.997718i	0.248111	+	0.0425428i
$551$	0.569006	+	13.3948i	0.0242405	+	0.570640i
$552$	2.03393	−	5.06162i	0.0865696	−	0.215437i
$553$	−1.38254	−	2.74210i	−0.0587915	−	0.116606i
$554$	−2.47120	+	4.90134i	−0.104991	+	0.208238i
$555$	−2.31435	−	10.7386i	−0.0982388	−	0.455830i
$556$	1.90319	−	2.16244i	0.0807130	−	0.0917078i
$557$	−19.1486	−	6.76564i	−0.811353	−	0.286669i	−0.104949	−	0.994478i	$-0.533468\pi$
$557$	−19.1486	−	6.76564i	−0.811353	−	0.286669i	−0.706405	+	0.707808i	$0.749684\pi$
$558$	10.5875	+	3.74080i	0.448204	+	0.158361i
$559$	−34.2239	+	38.8859i	−1.44752	+	1.64470i
$560$	−0.651945	−	3.02504i	−0.0275497	−	0.127831i
$561$	−0.266082	+	0.527742i	−0.0112340	+	0.0222813i
$562$	−3.21261	−	6.37183i	−0.135516	−	0.268779i
$563$	10.0673	−	25.0533i	0.424284	−	1.05587i	−0.550919	−	0.834559i	$-0.685723\pi$
$563$	10.0673	−	25.0533i	0.424284	−	1.05587i	0.975203	−	0.221313i	$-0.0710342\pi$
$564$	0.135734	+	3.19529i	0.00571545	+	0.134546i
$565$	−1.07835	−	0.184901i	−0.0453664	−	0.00777885i
$566$	−4.07289	+	10.1358i	−0.171196	+	0.426038i
$567$	−0.807671	−	0.0687429i	−0.0339190	−	0.00288693i
$568$	−19.8086	−	22.5069i	−0.831150	−	0.944370i
$569$	0.774165	+	3.59214i	0.0324547	+	0.150590i	0.990879	−	0.134758i	$-0.0430258\pi$
$569$	0.774165	+	3.59214i	0.0324547	+	0.150590i	−0.958424	+	0.285349i	$0.907891\pi$
$570$	−2.08944	+	2.00257i	−0.0875172	+	0.0838784i
$571$	29.6745	−	2.52568i	1.24184	−	0.105696i	0.554594	−	0.832121i	$-0.312873\pi$
$571$	29.6745	−	2.52568i	1.24184	−	0.105696i	0.687246	+	0.726425i	$0.258819\pi$
$572$	1.75983	−	2.85815i	0.0735823	−	0.119505i
$573$	4.18106	+	1.08866i	0.174666	+	0.0454795i
$574$	−7.93799	−	7.60795i	−0.331325	−	0.317550i
$575$	5.77243	−	0.491307i	0.240727	−	0.0204889i
$576$	−2.60533	+	8.50730i	−0.108555	+	0.354471i
$577$	2.22725	+	0.786938i	0.0927217	+	0.0327606i	0.379098	−	0.925357i	$-0.376234\pi$
$577$	2.22725	+	0.786938i	0.0927217	+	0.0327606i	−0.286376	+	0.958117i	$0.592451\pi$
$578$	−20.2434	+	5.27098i	−0.842017	+	0.219244i
$579$	−1.23276	−	9.62677i	−0.0512316	−	0.400075i
$580$	2.42281	−	3.93489i	0.100602	−	0.163388i
$581$	−4.48814	−	3.03345i	−0.186199	−	0.125849i
$582$	15.6088	+	10.5497i	0.647006	+	0.437300i
$583$	11.0794	+	10.6187i	0.458861	+	0.439783i
$584$	28.6895	−	16.0269i	1.18718	−	0.663198i
$585$	−6.55523	+	1.12401i	−0.271025	+	0.0464720i
$586$	−11.3391	+	22.4898i	−0.468415	+	0.929046i
$587$	−23.1943	+	31.3607i	−0.957330	+	1.29440i	−0.00164668	+	0.999999i	$0.500524\pi$
$587$	−23.1943	+	31.3607i	−0.957330	+	1.29440i	−0.955683	+	0.294397i	$0.904881\pi$
$588$	0.122894	+	2.89302i	0.00506806	+	0.119306i
$589$	14.9692	−	5.28896i	0.616796	−	0.217928i
$590$	−16.9921	+	11.4847i	−0.699554	+	0.472816i
$591$	14.7271	−	5.20341i	0.605791	−	0.214040i
$592$	23.5008	+	4.02962i	0.965877	+	0.165616i
$593$	17.3830	−	23.5034i	0.713834	−	0.965168i	−0.286141	−	0.958187i	$-0.592373\pi$
$593$	17.3830	−	23.5034i	0.713834	−	0.965168i	0.999976	−	0.00698016i	$-0.00222187\pi$
$594$	−1.20338	−	1.36731i	−0.0493753	−	0.0561013i
$595$	0.161583	+	0.402115i	0.00662426	+	0.0164851i
$596$	−6.29607	−	3.51720i	−0.257897	−	0.144070i
$597$	−8.29249	+	2.15920i	−0.339389	+	0.0883700i
$598$	−3.26099	+	10.6482i	−0.133352	+	0.435439i
$599$	0.277136	−	0.265613i	0.0113235	−	0.0108527i	−0.686256	−	0.727360i	$-0.740747\pi$
$599$	0.277136	−	0.265613i	0.0113235	−	0.0108527i	0.697579	+	0.716508i	$0.254260\pi$
$600$	−9.74949	+	1.67172i	−0.398021	+	0.0682476i
$601$	−3.07692	−	4.16027i	−0.125510	−	0.169701i	0.736752	−	0.676163i	$-0.236358\pi$
$601$	−3.07692	−	4.16027i	−0.125510	−	0.169701i	−0.862262	+	0.506462i	$0.830953\pi$
$602$	−8.09328	+	6.53487i	−0.329857	+	0.266341i
$603$	4.54263	+	0.386635i	0.184990	+	0.0157450i
$604$	3.66602	−	4.95679i	0.149168	−	0.201689i
$605$	5.28433	+	10.4808i	0.214838	+	0.426107i
$606$	−9.87433	+	7.97297i	−0.401117	+	0.323880i
$607$	26.1266	−	11.8100i	1.06045	−	0.479352i	0.195234	−	0.980757i	$-0.437453\pi$
$607$	26.1266	−	11.8100i	1.06045	−	0.479352i	0.865213	+	0.501404i	$0.167183\pi$
$608$	1.65538	+	4.11958i	0.0671346	+	0.167071i
$609$	−4.08753	+	4.64433i	−0.165635	+	0.188198i
$610$	−6.15172	+	20.0875i	−0.249076	+	0.813318i
$611$	−4.46257	−	34.8489i	−0.180536	−	1.40983i
$612$	0.0233754	−	0.182542i	0.000944894	−	0.00737881i
$613$	33.9152	+	27.3846i	1.36982	+	1.10605i	0.982941	+	0.183922i	$0.0588795\pi$
$613$	33.9152	+	27.3846i	1.36982	+	1.10605i	0.386879	+	0.922130i	$0.373553\pi$
$614$	27.2514	−	15.2235i	1.09978	−	0.614372i
$615$	10.4536	−	10.0190i	0.421532	−	0.404005i
$616$	2.39620	−	2.72261i	0.0965458	−	0.109697i
$617$	36.2888	+	20.2721i	1.46093	+	0.816125i	0.997545	−	0.0700315i	$-0.0223100\pi$
$617$	36.2888	+	20.2721i	1.46093	+	0.816125i	0.463386	+	0.886156i	$0.346634\pi$
$618$	3.96737	+	1.79336i	0.159591	+	0.0721396i
$619$	−2.97230	+	23.2111i	−0.119467	+	0.932933i	0.815638	+	0.578562i	$0.196386\pi$
$619$	−2.97230	+	23.2111i	−0.119467	+	0.932933i	−0.935105	+	0.354371i	$0.884695\pi$
$620$	−5.29546	−	1.37883i	−0.212671	−	0.0553752i
$621$	−1.48088	−	1.00090i	−0.0594257	−	0.0401648i
$622$	−24.0201	−	6.25434i	−0.963117	−	0.250776i
$623$	−6.01516	−	4.85691i	−0.240992	−	0.194588i
$624$	3.04137	−	14.1120i	0.121752	−	0.564932i
$625$	−1.01753	−	1.37579i	−0.0407010	−	0.0550314i
$626$	−3.28272	−	6.51088i	−0.131204	−	0.260227i
$627$	−2.53822	−	0.435222i	−0.101367	−	0.0173811i
$628$	2.34917	−	1.58776i	0.0937420	−	0.0633585i
$629$	−3.33918			−0.133142
$630$	−1.33556			−0.0532100
$631$	4.02495	−	2.72039i	0.160231	−	0.108297i	−0.477235	−	0.878776i	$-0.658361\pi$
$631$	4.02495	−	2.72039i	0.160231	−	0.108297i	0.637466	+	0.770479i	$0.279983\pi$
$632$	0.490710	+	11.5517i	0.0195194	+	0.459502i
$633$	20.2481	+	1.72337i	0.804790	+	0.0684977i
$634$	2.26228	−	1.02262i	0.0898467	−	0.0406133i
$635$	−6.68785	−	21.8381i	−0.265399	−	0.866620i
$636$	−4.35432	−	1.96828i	−0.172660	−	0.0780472i
$637$	−4.04041	−	31.5521i	−0.160087	−	1.25014i
$638$	−13.8522	+	1.17900i	−0.548415	+	0.0466770i
$639$	−8.57663	+	4.79119i	−0.339286	+	0.189537i
$640$	−1.67605	+	7.77690i	−0.0662517	+	0.307409i
$641$	7.45754	+	12.1118i	0.294555	+	0.478388i	0.964522	−	0.264003i	$-0.0850430\pi$
$641$	7.45754	+	12.1118i	0.294555	+	0.478388i	−0.669967	+	0.742391i	$0.733692\pi$
$642$	−5.35807	+	2.42200i	−0.211466	+	0.0955887i
$643$	−1.56271	−	1.77558i	−0.0616273	−	0.0700222i	0.719042	−	0.694967i	$-0.244581\pi$
$643$	−1.56271	−	1.77558i	−0.0616273	−	0.0700222i	−0.780669	+	0.624945i	$0.785122\pi$
$644$	0.297773	−	0.590598i	0.0117339	−	0.0232728i
$645$	−8.14575	−	11.0138i	−0.320739	−	0.433667i
$646$	0.461251	+	0.749120i	0.0181477	+	0.0294737i
$647$	9.46418	+	30.9038i	0.372075	+	1.21495i	0.924433	+	0.381346i	$0.124539\pi$
$647$	9.46418	+	30.9038i	0.372075	+	1.21495i	−0.552357	+	0.833607i	$0.686272\pi$
$648$	2.66435	+	1.48840i	0.104666	+	0.0584698i
$649$	−17.2071	−	6.07964i	−0.675436	−	0.238647i
$650$	19.5425	−	5.08848i	0.766521	−	0.199587i
$651$	6.67598	+	3.01773i	0.261652	+	0.118274i
$652$	−0.0601774	+	1.41662i	−0.00235673	+	0.0554792i
$653$	8.41625	−	39.0515i	0.329353	−	1.52821i	−0.445046	−	0.895508i	$-0.646813\pi$
$653$	8.41625	−	39.0515i	0.329353	−	1.52821i	0.774399	−	0.632697i	$-0.218052\pi$
$654$	−22.0618	+	3.78287i	−0.862684	+	0.147922i
$655$	−0.982866	−	4.56051i	−0.0384038	−	0.178194i
$656$	11.7183	+	29.1622i	0.457524	+	1.13859i
$657$	−3.15309	−	10.2959i	−0.123014	−	0.401682i
$658$	0.299427	−	7.04875i	0.0116729	−	0.274789i
$659$	19.8321	+	16.0133i	0.772550	+	0.623791i	0.931602	−	0.363479i	$-0.118411\pi$
$659$	19.8321	+	16.0133i	0.772550	+	0.623791i	−0.159052	+	0.987270i	$0.550844\pi$
$660$	0.640821	+	0.614177i	0.0249439	+	0.0239068i
$661$	−16.2146	+	26.3341i	−0.630674	+	1.02428i	0.364968	+	0.931020i	$0.381080\pi$
$661$	−16.2146	+	26.3341i	−0.630674	+	1.02428i	−0.995642	+	0.0932593i	$0.970271\pi$
$662$	1.02599	−	8.01211i	0.0398762	−	0.311399i
$663$	−0.0858025	+	2.01986i	−0.00333229	+	0.0784448i
$664$	10.6936	+	17.3675i	0.414992	+	0.673989i
$665$	−1.46916	+	1.18626i	−0.0569716	+	0.0460014i
$666$	3.83699	−	9.54872i	0.148680	−	0.370005i
$667$	−12.8632	+	4.54486i	−0.498065	+	0.175978i
$668$	11.1184			0.430182
$669$	13.8993	+	5.45987i	0.537377	+	0.211091i
$670$	7.51167			0.290201
$671$	−17.6258	+	6.22759i	−0.680436	+	0.240413i
$672$	−0.763909	+	1.90106i	−0.0294684	+	0.0733350i
$673$	−15.8418	+	12.7914i	−0.610657	+	0.493071i	−0.883153	−	0.469086i	$-0.844584\pi$
$673$	−15.8418	+	12.7914i	−0.610657	+	0.493071i	0.272495	+	0.962157i	$0.412151\pi$
$674$	−3.64924	−	5.92674i	−0.140563	−	0.228290i
$675$	−0.137560	+	3.23826i	−0.00529468	+	0.124641i
$676$	0.704526	−	5.50174i	0.0270971	−	0.211605i
$677$	−21.1284	+	34.3147i	−0.812030	+	1.31882i	0.132761	+	0.991148i	$0.457616\pi$
$677$	−21.1284	+	34.3147i	−0.812030	+	1.31882i	−0.944791	+	0.327673i	$0.893736\pi$
$678$	−0.739951	−	0.709186i	−0.0284176	−	0.0272361i
$679$	9.56361	+	7.72207i	0.367018	+	0.296346i
$680$	0.0692486	−	1.63016i	0.00265556	−	0.0625140i
$681$	7.35605	+	24.0200i	0.281884	+	0.920449i
$682$	6.13823	+	15.2756i	0.235045	+	0.584932i
$683$	−6.37909	−	29.5991i	−0.244089	−	1.13258i	−0.918870	−	0.394559i	$-0.870897\pi$
$683$	−6.37909	−	29.5991i	−0.244089	−	1.13258i	0.674781	−	0.738018i	$-0.264238\pi$
$684$	0.790346	−	0.135518i	0.0302196	−	0.00518168i
$685$	1.40298	−	6.50985i	0.0536051	−	0.248729i
$686$	0.570286	−	13.4250i	0.0217736	−	0.512568i
$687$	−12.8147	−	5.79261i	−0.488912	−	0.221002i
$688$	28.7743	−	7.49224i	1.09701	−	0.285639i
$689$	49.4956	+	17.4879i	1.88563	+	0.666236i
$690$	−2.57102	−	1.43626i	−0.0978772	−	0.0546775i
$691$	−11.3733	−	37.1378i	−0.432662	−	1.41279i	−0.860739	−	0.509047i	$-0.829998\pi$
$691$	−11.3733	−	37.1378i	−0.432662	−	1.41279i	0.428077	−	0.903742i	$-0.359191\pi$
$692$	−1.02806	−	1.66967i	−0.0390809	−	0.0634713i
$693$	−0.706666	−	0.955476i	−0.0268440	−	0.0362955i
$694$	−9.33905	+	18.5229i	−0.354506	+	0.703120i
$695$	−5.52891	−	6.28206i	−0.209724	−	0.238292i
$696$	21.2260	−	9.59478i	0.804571	−	0.363689i
$697$	−2.30767	−	3.74790i	−0.0874094	−	0.141962i
$698$	7.43299	−	34.4892i	0.281343	−	1.30544i
$699$	−26.0795	+	14.5689i	−0.986416	+	0.551045i
$700$	−1.19506	+	0.101715i	−0.0451690	+	0.00384445i
$701$	4.60656	+	35.9733i	0.173987	+	1.35869i	0.809736	+	0.586795i	$0.199610\pi$
$701$	4.60656	+	35.9733i	0.173987	+	1.35869i	−0.635749	+	0.771896i	$0.719308\pi$
$702$	−5.67739	−	2.56634i	−0.214279	−	0.0968604i
$703$	−4.26050	−	13.9120i	−0.160688	−	0.524700i
$704$	−11.8864	+	5.37298i	−0.447984	+	0.202502i
$705$	9.25750	+	0.787929i	0.348657	+	0.0296751i
$706$	0.520780	+	12.2596i	0.0195998	+	0.461395i
$707$	−6.86050	+	4.63689i	−0.258016	+	0.174388i
$708$	5.68250			0.213561
$709$	13.9093			0.522375			0.261187	−	0.965288i	$-0.415886\pi$
$709$	13.9093			0.522375			0.261187	+	0.965288i	$0.415886\pi$
$710$	−13.4108	+	9.06412i	−0.503299	+	0.340170i
$711$	3.73400	+	0.640259i	0.140036	+	0.0240116i
$712$	13.1047	+	25.9915i	0.491118	+	0.974074i
$713$	9.60634	+	12.9886i	0.359760	+	0.486428i
$714$	−0.0855298	+	0.396860i	−0.00320087	+	0.0148521i
$715$	−7.58654	−	6.12570i	−0.283720	−	0.229088i
$716$	6.39134	+	1.66418i	0.238856	+	0.0621932i
$717$	−15.4169	−	10.4200i	−0.575754	−	0.389142i
$718$	−13.9558	−	3.63381i	−0.520826	−	0.135612i
$719$	−1.05065	+	8.20471i	−0.0391828	+	0.305984i	0.960439	+	0.278490i	$0.0898339\pi$
$719$	−1.05065	+	8.20471i	−0.0391828	+	0.305984i	−0.999622	+	0.0274942i	$0.991247\pi$
$720$	3.47868	+	1.57246i	0.129643	+	0.0586023i
$721$	2.47997	+	1.38539i	0.0923588	+	0.0515947i
$722$	13.0627	−	14.8422i	0.486145	−	0.552368i
$723$	15.0961	−	14.4684i	0.561430	−	0.538087i
$724$	10.3413	−	5.77697i	0.384330	−	0.214699i
$725$	19.2475	+	15.5413i	0.714834	+	0.577188i
$726$	−1.39665	+	10.9066i	−0.0518344	+	0.404782i
$727$	−1.41692	−	11.0649i	−0.0525506	−	0.410376i	−0.996721	−	0.0809174i	$-0.974215\pi$
$727$	−1.41692	−	11.0649i	−0.0525506	−	0.410376i	0.944170	−	0.329458i	$-0.106866\pi$
$728$	3.63285	−	11.8625i	0.134642	−	0.439653i
$729$	0.660675	−	0.750672i	0.0244694	−	0.0278027i
$730$	−6.61507	−	16.4622i	−0.244835	−	0.609295i
$731$	−3.79438	+	1.71517i	−0.140340	+	0.0634378i
$732$	4.52878	−	3.65673i	0.167388	−	0.135157i
$733$	−4.06757	−	8.06754i	−0.150239	−	0.297982i	0.805288	−	0.592883i	$-0.202010\pi$
$733$	−4.06757	−	8.06754i	−0.150239	−	0.297982i	−0.955528	+	0.294902i	$0.904713\pi$
$734$	−21.4390	+	28.9874i	−0.791327	+	1.06994i
$735$	8.38173	+	0.713390i	0.309165	+	0.0263138i
$736$	−3.51496	+	2.83814i	−0.129563	+	0.104615i
$737$	3.97454	+	5.37394i	0.146404	+	0.197952i
$738$	13.3692	−	2.29238i	0.492128	−	0.0843838i
$739$	27.1069	−	25.9799i	0.997144	−	0.955685i	−0.00187408	−	0.999998i	$-0.500597\pi$
$739$	27.1069	−	25.9799i	0.997144	−	0.955685i	0.999018	+	0.0443135i	$0.0141101\pi$
$740$	−1.46847	+	4.79505i	−0.0539819	+	0.176270i
$741$	−8.52479	+	2.21968i	−0.313166	+	0.0815420i
$742$	9.20271	+	5.14094i	0.337842	+	0.188730i
$743$	−4.94452	−	12.3049i	−0.181397	−	0.451423i	0.809320	−	0.587369i	$-0.199836\pi$
$743$	−4.94452	−	12.3049i	−0.181397	−	0.451423i	−0.990716	+	0.135945i	$0.956593\pi$
$744$	−18.2240	−	20.7065i	−0.668125	−	0.759137i
$745$	−12.4582	+	16.8446i	−0.456434	+	0.617139i
$746$	−30.4424	−	5.21987i	−1.11457	−	0.191113i
$747$	6.30119	−	2.22635i	0.230548	−	0.0814579i
$748$	0.223540	−	0.151087i	0.00817343	−	0.00552428i
$749$	−3.61731	+	1.27808i	−0.132174	+	0.0467000i
$750$	0.576288	+	13.5663i	0.0210430	+	0.495370i
$751$	7.36088	−	9.95257i	0.268602	−	0.363175i	−0.648921	−	0.760856i	$-0.724780\pi$
$751$	7.36088	−	9.95257i	0.268602	−	0.363175i	0.917524	+	0.397681i	$0.130185\pi$
$752$	−9.07898	+	18.0071i	−0.331076	+	0.656651i
$753$	−2.10274	+	0.360550i	−0.0766279	+	0.0131392i
$754$	−41.5159	+	23.1922i	−1.51192	+	0.844609i
$755$	−12.9305	−	12.3929i	−0.470589	−	0.451023i
$756$	0.306585	+	0.207215i	0.0111504	+	0.00753635i
$757$	23.5924	+	15.9457i	0.857482	+	0.579556i	0.907907	−	0.419171i	$-0.137679\pi$
$757$	23.5924	+	15.9457i	0.857482	+	0.579556i	−0.0504255	+	0.998728i	$0.516058\pi$
$758$	5.48390	−	8.90643i	0.199184	−	0.323496i
$759$	−0.332852	−	2.59929i	−0.0120818	−	0.0943482i
$760$	6.88009	−	1.79144i	0.249567	−	0.0649822i
$761$	8.99950	+	3.17973i	0.326232	+	0.115265i	0.491233	−	0.871028i	$-0.336546\pi$
$761$	8.99950	+	3.17973i	0.326232	+	0.115265i	−0.165001	+	0.986293i	$0.552763\pi$
$762$	6.26510	−	20.4577i	0.226961	−	0.741104i
$763$	−14.5518	+	1.23854i	−0.526809	+	0.0448380i
$764$	−1.42395	−	1.36474i	−0.0515165	−	0.0493746i
$765$	−0.517378	−	0.134715i	−0.0187058	−	0.00487062i
$766$	−16.9734	+	27.5666i	−0.613275	+	0.996022i
$767$	−62.2000	+	5.29400i	−2.24591	+	0.191155i
$768$	7.46648	−	7.15604i	0.269423	−	0.258221i
$769$	2.84306	+	13.1919i	0.102524	+	0.475711i	0.999438	+	0.0335077i	$0.0106678\pi$
$769$	2.84306	+	13.1919i	0.102524	+	0.475711i	−0.896915	+	0.442203i	$0.854197\pi$
$770$	−1.29364	−	1.46987i	−0.0466197	−	0.0529703i
$771$	9.57241	+	0.814733i	0.344742	+	0.0293419i
$772$	−1.65198	+	4.11112i	−0.0594562	+	0.147962i
$773$	18.4672	+	3.16652i	0.664220	+	0.113892i	0.491228	−	0.871031i	$-0.336548\pi$
$773$	18.4672	+	3.16652i	0.664220	+	0.113892i	0.172992	+	0.984923i	$0.444656\pi$
$774$	−0.544642	−	12.8213i	−0.0195768	−	0.460852i
$775$	10.9227	−	27.1823i	0.392356	−	0.976416i
$776$	−20.8353	−	41.3244i	−0.747944	−	1.48346i
$777$	3.02279	−	5.99535i	0.108442	−	0.215082i
$778$	−6.60354	−	30.6405i	−0.236748	−	1.09852i
$779$	12.6705	−	14.3964i	0.453966	−	0.515806i
$780$	2.86278	+	1.01148i	0.102504	+	0.0362169i
$781$	−13.5805	−	4.79828i	−0.485947	−	0.171696i
$782$	−0.591431	+	0.671997i	−0.0211495	+	0.0240306i
$783$	−1.60803	−	7.46127i	−0.0574662	−	0.266644i
$784$	−8.22010	+	16.3036i	−0.293575	+	0.582272i
$785$	−3.70838	−	7.35513i	−0.132358	−	0.262516i
$786$	1.62950	−	4.05518i	0.0581225	−	0.144643i
$787$	−0.509431	−	11.9924i	−0.0181592	−	0.427483i	−0.985048	−	0.172283i	$-0.944886\pi$
$787$	−0.509431	−	11.9924i	−0.0181592	−	0.427483i	0.966888	−	0.255200i	$-0.0821413\pi$
$788$	−7.02782	−	1.20504i	−0.250356	−	0.0429278i
$789$	−7.36879	+	18.3379i	−0.262336	+	0.652848i
$790$	6.21958	+	0.529364i	0.221283	+	0.0188339i
$791$	−0.441804	−	0.501987i	−0.0157087	−	0.0178486i
$792$	0.942662	+	4.37397i	0.0334960	+	0.155422i
$793$	−46.1647	+	44.2453i	−1.63936	+	1.57120i
$794$	2.93007	−	0.249386i	0.103984	−	0.00885038i
$795$	−7.27843	+	11.8209i	−0.258139	+	0.419245i
$796$	3.78562	+	0.985698i	0.134178	+	0.0349371i
$797$	9.97161	+	9.55701i	0.353212	+	0.338527i	0.847523	−	0.530759i	$-0.178093\pi$
$797$	9.97161	+	9.55701i	0.353212	+	0.338527i	−0.494311	+	0.869285i	$0.664579\pi$
$798$	−1.76256	+	0.150016i	−0.0623939	+	0.00531051i
$799$	0.826985	−	2.70039i	0.0292566	−	0.0955329i
$800$	7.72427	+	2.72916i	0.273094	+	0.0964903i
$801$	9.23000	−	2.40331i	0.326126	−	0.0849166i
$802$	2.67160	+	20.8629i	0.0943375	+	0.736695i
$803$	8.27715	−	13.4429i	0.292094	−	0.474391i
$804$	−1.72434	−	1.16545i	−0.0608129	−	0.0411024i
$805$	−1.59196	−	1.07598i	−0.0561092	−	0.0379232i
$806$	40.6554	+	38.9651i	1.43203	+	1.37249i
$807$	21.8121	−	12.1850i	0.767824	−	0.428932i
$808$	30.7280	−	5.26885i	1.08101	−	0.185357i
$809$	6.61681	−	13.1237i	0.232635	−	0.461404i	−0.746291	−	0.665620i	$-0.768167\pi$
$809$	6.61681	−	13.1237i	0.232635	−	0.461404i	0.978926	+	0.204216i	$0.0654646\pi$
$810$	0.979741	−	1.32470i	0.0344246	−	0.0465451i
$811$	0.634968	+	14.9476i	0.0222967	+	0.524883i	0.975163	+	0.221490i	$0.0710922\pi$
$811$	0.634968	+	14.9476i	0.0222967	+	0.524883i	−0.952866	+	0.303392i	$0.901881\pi$
$812$	2.66305	−	0.940917i	0.0934549	−	0.0330197i
$813$	1.28668	−	0.869645i	0.0451259	−	0.0304998i
$814$	14.2255	−	5.02620i	0.498604	−	0.176168i
$815$	4.05987	+	0.696134i	0.142211	+	0.0243845i
$816$	0.690031	−	0.932984i	0.0241559	−	0.0326610i
$817$	−11.9872	−	13.6201i	−0.419379	−	0.476507i
$818$	−0.845597	−	2.10435i	−0.0295656	−	0.0735769i
$819$	−3.54889	−	1.98253i	−0.124008	−	0.0692752i
$820$	−6.39682	+	1.66560i	−0.223387	+	0.0581654i
$821$	−2.70219	+	8.82358i	−0.0943071	+	0.307945i	−0.990842	−	0.135029i	$-0.956887\pi$
$821$	−2.70219	+	8.82358i	−0.0943071	+	0.307945i	0.896535	+	0.442974i	$0.146077\pi$
$822$	4.50383	−	4.31657i	0.157089	−	0.150558i
$823$	25.1574	−	4.31368i	0.876933	−	0.150365i	0.287110	−	0.957898i	$-0.407306\pi$
$823$	25.1574	−	4.31368i	0.876933	−	0.150365i	0.589823	+	0.807532i	$0.299197\pi$
$824$	−6.35979	−	8.59901i	−0.221554	−	0.299561i
$825$	−3.69715	+	2.98524i	−0.128718	+	0.103933i
$826$	−12.4903	−	1.06308i	−0.434594	−	0.0369894i
$827$	13.6188	−	18.4138i	0.473572	−	0.640312i	−0.500717	−	0.865611i	$-0.666930\pi$
$827$	13.6188	−	18.4138i	0.473572	−	0.640312i	0.974290	+	0.225299i	$0.0723358\pi$
$828$	0.367353	+	0.728601i	0.0127664	+	0.0253206i
$829$	30.8431	−	24.9041i	1.07123	−	0.864954i	0.0799554	−	0.996798i	$-0.474522\pi$
$829$	30.8431	−	24.9041i	1.07123	−	0.864954i	0.991270	+	0.131844i	$0.0420898\pi$
$830$	10.0336	−	4.53547i	0.348271	−	0.157428i
$831$	−1.64736	−	4.09962i	−0.0571464	−	0.142214i
$832$	−29.4792	+	33.4949i	−1.02201	+	1.16123i
$833$	0.748752	−	2.44493i	0.0259427	−	0.0847118i
$834$	−0.995768	−	7.77609i	−0.0344806	−	0.269264i
$835$	4.10264	−	32.0381i	0.141978	−	1.10873i
$836$	0.914688	+	0.738559i	0.0316351	+	0.0255436i
$837$	−7.89055	+	4.40793i	−0.272737	+	0.152360i
$838$	11.6784	−	11.1928i	0.403424	−	0.386650i
$839$	28.9199	−	32.8594i	0.998425	−	1.13443i	0.00750572	−	0.999972i	$-0.497611\pi$
$839$	28.9199	−	32.8594i	0.998425	−	1.13443i	0.990919	−	0.134459i	$-0.0429297\pi$
$840$	2.86420	+	1.60004i	0.0988244	+	0.0552066i
$841$	−26.6591	−	12.0507i	−0.919280	−	0.415541i
$842$	1.66212	−	12.9797i	0.0572804	−	0.447311i
$843$	5.55843	+	1.44730i	0.191443	+	0.0498478i
$844$	−7.68601	−	5.19484i	−0.264563	−	0.178814i
$845$	−15.5936	−	4.06026i	−0.536436	−	0.139677i
$846$	6.77176	+	5.46782i	0.232818	+	0.187987i
$847$	−1.51145	+	7.01315i	−0.0519340	+	0.240975i
$848$	−17.9171	−	24.2255i	−0.615276	−	0.831908i
$849$	−3.95839	−	7.85099i	−0.135851	−	0.269445i
$850$	1.59995	+	0.274338i	0.0548777	+	0.00940972i
$851$	12.2664	−	8.29065i	0.420487	−	0.284200i
$852$	4.48484			0.153648
$853$	3.93840			0.134848			0.0674241	−	0.997724i	$-0.478522\pi$
$853$	3.93840			0.134848			0.0674241	+	0.997724i	$0.478522\pi$
$854$	−10.6385	+	7.19037i	−0.364042	+	0.246049i
$855$	−0.0988680	−	2.32743i	−0.00338122	−	0.0795965i
$856$	14.3924	+	1.22497i	0.491921	+	0.0418687i
$857$	−7.96276	+	3.59939i	−0.272003	+	0.122953i	−0.543289	−	0.839546i	$-0.682821\pi$
$857$	−7.96276	+	3.59939i	−0.272003	+	0.122953i	0.271286	+	0.962499i	$0.412551\pi$
$858$	−2.67479	−	8.73412i	−0.0913159	−	0.298178i
$859$	14.3079	+	6.46758i	0.488179	+	0.220671i	0.640938	−	0.767593i	$-0.278546\pi$
$859$	14.3079	+	6.46758i	0.488179	+	0.220671i	−0.152759	+	0.988263i	$0.548816\pi$
$860$	0.794325	+	6.20300i	0.0270863	+	0.211521i
$861$	8.81822	−	0.750541i	0.300524	−	0.0255784i
$862$	18.7020	−	10.4476i	0.636993	−	0.355846i
$863$	−7.80933	+	36.2354i	−0.265833	+	1.23347i	0.625538	+	0.780194i	$0.284879\pi$
$863$	−7.80933	+	36.2354i	−0.265833	+	1.23347i	−0.891371	+	0.453275i	$0.850256\pi$
$864$	−1.32521	−	2.15228i	−0.0450845	−	0.0732219i
$865$	−5.19059	+	2.34630i	−0.176485	+	0.0797765i
$866$	19.3700	+	22.0086i	0.658218	+	0.747881i
$867$	7.58030	−	15.0346i	0.257440	−	0.510603i
$868$	−1.98879	−	2.68902i	−0.0675039	−	0.0912713i
$869$	2.91217	+	4.72966i	0.0987885	+	0.160443i
$870$	−3.68246	−	12.0245i	−0.124847	−	0.407669i
$871$	19.9602	+	11.1505i	0.676327	+	0.377819i
$872$	51.8450	+	18.3180i	1.75569	+	0.620326i
$873$	−14.6749	+	3.82106i	−0.496671	+	0.129323i
$874$	−3.55435	−	1.60667i	−0.120228	−	0.0543463i
$875$	−0.376001	+	8.85136i	−0.0127112	+	0.299231i
$876$	−1.03563	+	4.80534i	−0.0349907	+	0.162357i
$877$	−42.0519	+	7.21052i	−1.41999	+	0.243482i	−0.827215	−	0.561885i	$-0.810076\pi$
$877$	−42.0519	+	7.21052i	−1.41999	+	0.243482i	−0.592776	+	0.805367i	$0.701968\pi$
$878$	2.37147	+	11.0036i	0.0800331	+	0.371355i
$879$	−7.55893	−	18.8111i	−0.254957	−	0.634484i
$880$	1.63891	+	5.35162i	0.0552478	+	0.180403i
$881$	−1.09300	+	25.7300i	−0.0368239	+	0.866864i	0.881774	+	0.471672i	$0.156349\pi$
$881$	−1.09300	+	25.7300i	−0.0368239	+	0.866864i	−0.918598	+	0.395193i	$0.870678\pi$
$882$	6.13115	+	4.95056i	0.206447	+	0.166694i
$883$	−3.40269	−	3.26121i	−0.114510	−	0.109749i	0.632505	−	0.774556i	$-0.282027\pi$
$883$	−3.40269	−	3.26121i	−0.114510	−	0.109749i	−0.747014	+	0.664808i	$0.768513\pi$
$884$	0.483894	−	0.785893i	0.0162751	−	0.0264324i
$885$	2.09683	−	16.3744i	0.0704841	−	0.550420i
$886$	−0.488552	+	11.5009i	−0.0164132	+	0.386380i
$887$	5.06762	+	8.23034i	0.170154	+	0.276348i	0.925321	−	0.379185i	$-0.123796\pi$
$887$	5.06762	+	8.23034i	0.170154	+	0.276348i	−0.755167	+	0.655533i	$0.772444\pi$
$888$	−19.6683	+	15.8811i	−0.660026	+	0.532934i
$889$	5.20493	−	12.9530i	0.174568	−	0.434428i
$890$	14.8171	−	5.23522i	0.496671	−	0.175485i
$891$	1.46610			0.0491162
$892$	−4.32385	−	5.27049i	−0.144773	−	0.176469i
$893$	12.3058			0.411797
$894$	−18.5056	+	6.53845i	−0.618920	+	0.218678i
$895$	7.15380	−	17.8029i	0.239125	−	0.595086i
$896$	−3.78317	+	3.05470i	−0.126387	+	0.102050i
$897$	−4.69979	−	7.63295i	−0.156922	−	0.254857i
$898$	0.0230757	−	0.543219i	0.000770044	−	0.0181274i
$899$	−8.76238	+	68.4267i	−0.292242	+	2.28216i
$900$	0.775785	−	1.25995i	0.0258595	−	0.0419985i
$901$	3.04645	+	2.91979i	0.101492	+	0.0972722i
$902$	15.4725	+	12.4932i	0.515179	+	0.415978i
$903$	0.355354	−	8.36531i	0.0118254	−	0.278380i
$904$	0.737252	+	2.40738i	0.0245206	+	0.0800683i
$905$	−12.8308	−	31.9306i	−0.426509	−	1.06141i
$906$	−3.53482	−	16.4016i	−0.117437	−	0.544908i
$907$	−39.5915	+	6.78864i	−1.31461	+	0.225413i	−0.783237	−	0.621723i	$-0.786433\pi$
$907$	−39.5915	+	6.78864i	−1.31461	+	0.225413i	−0.531376	+	0.847136i	$0.678325\pi$
$908$	2.41609	−	11.2107i	0.0801808	−	0.372040i
$909$	0.433555	−	10.2062i	0.0143801	−	0.338519i
$910$	−6.10325	−	2.75884i	−0.202321	−	0.0914547i
$911$	4.21294	−	1.09696i	0.139581	−	0.0363440i	−0.181532	−	0.983385i	$-0.558105\pi$
$911$	4.21294	−	1.09696i	0.139581	−	0.0363440i	0.321112	+	0.947041i	$0.395943\pi$
$912$	4.76750	+	1.68446i	0.157868	+	0.0557782i
$913$	8.55366	+	4.77836i	0.283085	+	0.158141i
$914$	−0.0747163	−	0.243974i	−0.00247140	−	0.00806996i
$915$	−8.86596	−	14.3992i	−0.293100	−	0.476024i
$916$	3.81753	+	5.16164i	0.126135	+	0.170545i
$917$	1.28373	−	2.54612i	0.0423924	−	0.0840804i
$918$	−0.330888	−	0.375962i	−0.0109209	−	0.0124086i
$919$	−52.9945	+	23.9550i	−1.74813	+	0.790203i	−0.757626	+	0.652689i	$0.773641\pi$
$919$	−52.9945	+	23.9550i	−1.74813	+	0.790203i	−0.990500	+	0.137514i	$0.956089\pi$
$920$	3.79306	+	6.16032i	0.125053	+	0.203100i
$921$	−5.29344	+	24.5616i	−0.174425	+	0.809333i
$922$	4.04661	−	2.26057i	0.133268	−	0.0744480i
$923$	−49.0906	+	4.17822i	−1.61584	+	0.137528i
$924$	0.0689099	+	0.538128i	0.00226697	+	0.0177031i
$925$	−24.4640	−	11.0584i	−0.804373	−	0.363599i
$926$	6.68599	+	21.8321i	0.219715	+	0.717446i
$927$	−3.19338	+	1.44350i	−0.104884	+	0.0474107i
$928$	−19.2222	−	1.63605i	−0.630999	−	0.0537059i
$929$	0.602129	+	14.1746i	0.0197552	+	0.465053i	0.981541	+	0.191251i	$0.0612543\pi$
$929$	0.602129	+	14.1746i	0.0197552	+	0.465053i	−0.961786	+	0.273802i	$0.911719\pi$
$930$	−12.3380	+	8.33905i	−0.404580	+	0.273448i
$931$	11.1416			0.365152
$932$	13.6373			0.446705
$933$	16.5525	−	11.1876i	0.541906	−	0.366264i
$934$	−16.3537	−	2.80413i	−0.535111	−	0.0917540i
$935$	−0.352879	−	0.699893i	−0.0115404	−	0.0228889i
$936$	9.10101	+	12.3054i	0.297476	+	0.402214i
$937$	−7.52827	+	34.9313i	−0.245938	+	1.14116i	0.670791	+	0.741646i	$0.265955\pi$
$937$	−7.52827	+	34.9313i	−0.245938	+	1.14116i	−0.916729	+	0.399510i	$0.869180\pi$
$938$	3.57213	+	2.88429i	0.116634	+	0.0941755i
$939$	5.67974	+	1.47889i	0.185351	+	0.0482617i
$940$	−3.51407	−	2.37510i	−0.114616	−	0.0774671i
$941$	−27.8401	−	7.24900i	−0.907562	−	0.236311i	−0.231222	−	0.972901i	$-0.574273\pi$
$941$	−27.8401	−	7.24900i	−0.907562	−	0.236311i	−0.676339	+	0.736590i	$0.736435\pi$
$942$	0.980124	−	7.65393i	0.0319342	−	0.249379i
$943$	17.7827	+	8.03827i	0.579083	+	0.261762i
$944$	31.2814	+	17.4748i	1.01812	+	0.568758i
$945$	0.710231	−	0.806979i	0.0231038	−	0.0262510i
$946$	13.5831	−	13.0183i	0.441624	−	0.423262i
$947$	44.6546	−	24.9455i	1.45108	−	0.810621i	0.454302	−	0.890848i	$-0.349889\pi$
$947$	44.6546	−	24.9455i	1.45108	−	0.810621i	0.996777	+	0.0802262i	$0.0255643\pi$
$948$	−1.34561	−	1.08650i	−0.0437033	−	0.0352879i
$949$	6.85908	−	53.5635i	0.222655	−	1.73875i
$950$	0.898417	+	7.01587i	0.0291485	+	0.227625i
$951$	−0.585157	+	1.91074i	−0.0189750	+	0.0619599i
$952$	0.658873	−	0.748626i	0.0213542	−	0.0242631i
$953$	−20.3450	−	50.6305i	−0.659039	−	1.64008i	−0.763698	−	0.645573i	$-0.776618\pi$
$953$	−20.3450	−	50.6305i	−0.659039	−	1.64008i	0.104659	−	0.994508i	$-0.466625\pi$
$954$	−11.8501	+	5.35656i	−0.383660	+	0.173425i
$955$	−4.45801	+	3.59959i	−0.144258	+	0.116480i
$956$	3.82437	+	7.58518i	0.123689	+	0.245322i
$957$	6.65402	−	8.99683i	0.215094	−	0.290826i
$958$	−3.70133	−	0.315030i	−0.119585	−	0.0101781i
$959$	3.16680	−	2.55701i	0.102261	−	0.0825703i
$960$	−7.01645	−	9.48687i	−0.226455	−	0.306187i
$961$	49.9614	−	8.56675i	1.61166	−	0.276347i
$962$	37.2589	−	35.7098i	1.20127	−	1.15133i
$963$	1.38591	−	4.52546i	0.0446602	−	0.145831i
$964$	−9.23765	+	2.40530i	−0.297525	+	0.0774694i
$965$	11.2368	+	6.27727i	0.361726	+	0.202073i
$966$	−0.671147	−	1.67021i	−0.0215938	−	0.0537383i
$967$	−0.289843	−	0.329325i	−0.00932072	−	0.0105904i	0.745993	−	0.665953i	$-0.231975\pi$
$967$	−0.289843	−	0.329325i	−0.00932072	−	0.0105904i	−0.755314	+	0.655363i	$0.772516\pi$
$968$	16.0616	−	21.7168i	0.516241	−	0.698003i
$969$	−0.697924	−	0.119671i	−0.0224205	−	0.00384439i
$970$	−23.5580	+	8.32356i	−0.756401	+	0.267253i
$971$	−22.7024	+	15.3441i	−0.728554	+	0.492416i	−0.867221	−	0.497923i	$-0.834096\pi$
$971$	−22.7024	+	15.3441i	−0.728554	+	0.492416i	0.138668	+	0.990339i	$0.455718\pi$
$972$	−0.430434	+	0.152082i	−0.0138062	+	0.00487804i
$973$	−0.217086	−	5.11036i	−0.00695944	−	0.163831i
$974$	14.3119	−	19.3510i	0.458583	−	0.620045i
$975$	−7.31784	+	14.5141i	−0.234358	+	0.464822i
$976$	36.1755	−	6.20291i	1.15795	−	0.198550i
$977$	−3.43418	+	1.91845i	−0.109869	+	0.0613765i	−0.541663	−	0.840596i	$-0.682205\pi$
$977$	−3.43418	+	1.91845i	−0.109869	+	0.0613765i	0.431794	+	0.901972i	$0.357881\pi$
$978$	2.78584	+	2.67001i	0.0890814	+	0.0853776i
$979$	11.5853	+	7.83030i	0.370268	+	0.250257i
$980$	−3.18164	−	2.15041i	−0.101634	−	0.0686923i
$981$	9.44642	−	15.3420i	0.301601	−	0.489831i
$982$	−2.03013	−	15.8536i	−0.0647841	−	0.505909i
$983$	−15.0641	+	3.92237i	−0.480469	+	0.125104i	−0.484325	−	0.874888i	$-0.660935\pi$
$983$	−15.0641	+	3.92237i	−0.480469	+	0.125104i	0.00385616	+	0.999993i	$0.498773\pi$
$984$	−31.4175	−	11.1005i	−1.00155	−	0.353872i
$985$	−6.06564	+	19.8064i	−0.193267	+	0.631084i
$986$	−3.80888	+	0.324184i	−0.121300	+	0.0103241i
$987$	4.09980	+	3.92934i	0.130498	+	0.125072i
$988$	3.89166	+	1.01331i	0.123810	+	0.0322377i
$989$	9.68011	−	15.7215i	0.307810	−	0.499915i
$990$	2.40690	−	0.204858i	0.0764964	−	0.00651080i
$991$	26.1814	−	25.0928i	0.831680	−	0.797100i	−0.149790	−	0.988718i	$-0.547860\pi$
$991$	26.1814	−	25.0928i	0.831680	−	0.797100i	0.981470	+	0.191617i	$0.0613733\pi$
$992$	4.81289	+	22.3319i	0.152810	+	0.709039i
$993$	4.29551	+	4.88065i	0.136314	+	0.154883i
$994$	−9.85783	−	0.839025i	−0.312671	−	0.0266123i
$995$	4.23722	−	10.5447i	0.134329	−	0.334291i
$996$	−3.00695	−	0.515594i	−0.0952789	−	0.0163372i
$997$	0.517150	+	12.1741i	0.0163783	+	0.385558i	0.988513	+	0.151135i	$0.0482929\pi$
$997$	0.517150	+	12.1741i	0.0163783	+	0.385558i	−0.972135	+	0.234423i	$0.924680\pi$
$998$	7.74871	−	19.2834i	0.245281	−	0.610405i
$999$	3.72912	+	7.39627i	0.117984	+	0.234008i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	669.2.i.b.4.7	✓	720
223.56	even	37	inner	669.2.i.b.502.7	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
669.2.i.b.4.7	✓	720	1.1	even	1	trivial
669.2.i.b.502.7	yes	720	223.56	even	37	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 669 = 3 \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	669.i (of order \(37\), degree \(36\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17140 + 0.413884i) q^{2} +(0.372856 - 0.927889i) q^{3} +(-0.355182 + 0.286790i) q^{4} +(0.695338 + 1.12930i) q^{5} +(-0.0527278 + 1.24125i) q^{6} +(-0.102959 + 0.804025i) q^{7} +(1.60013 - 2.59878i) q^{8} +(-0.721956 - 0.691939i) q^{9} +(-1.28192 - 1.03508i) q^{10} +(0.0622231 - 1.46478i) q^{11} +(0.133677 + 0.436501i) q^{12} +(-1.86987 - 4.65335i) q^{13} +(-0.212166 - 0.984452i) q^{14} +(1.30713 - 0.224130i) q^{15} +(-0.606456 + 2.81397i) q^{16} +(0.0171092 - 0.402764i) q^{17} +(1.13208 + 0.511735i) q^{18} +(1.69986 - 0.442609i) q^{19} +(-0.570844 - 0.201692i) q^{20} +(0.707657 + 0.395321i) q^{21} +(0.533360 + 1.74160i) q^{22} +(0.937149 + 1.52203i) q^{23} +(-1.81476 - 2.45372i) q^{24} +(1.45919 - 2.89414i) q^{25} +(4.11632 + 4.67705i) q^{26} +(-0.911228 + 0.411901i) q^{27} +(-0.194017 - 0.315103i) q^{28} +(-1.60803 + 7.46127i) q^{29} +(-1.43841 + 0.803545i) q^{30} +(9.00572 - 0.766500i) q^{31} +(0.321043 + 2.50707i) q^{32} +(-1.33595 - 0.603889i) q^{33} +(0.146656 + 0.478881i) q^{34} +(-0.979578 + 0.442797i) q^{35} +(0.454867 + 0.0387149i) q^{36} +(-0.351548 - 8.27572i) q^{37} +(-1.80804 + 1.22202i) q^{38} -5.01499 q^{39} +4.04744 q^{40} +(9.04574 - 6.11385i) q^{41} +(-0.992570 - 0.170193i) q^{42} +(-4.65030 - 9.22332i) q^{43} +(0.397983 + 0.538109i) q^{44} +(0.279404 - 1.29644i) q^{45} +(-1.72772 - 1.39504i) q^{46} +(6.77963 + 1.76528i) q^{47} +(2.38493 + 1.61193i) q^{48} +(6.13827 + 1.59828i) q^{49} +(-0.511470 + 3.99414i) q^{50} +(-0.367341 - 0.166049i) q^{51} +(1.99868 + 1.11653i) q^{52} +(-6.91558 + 7.85763i) q^{53} +(0.896938 - 0.859646i) q^{54} +(1.69744 - 0.948249i) q^{55} +(1.92474 + 1.55412i) q^{56} +(0.223112 - 1.74231i) q^{57} +(-1.20445 - 9.40570i) q^{58} +(3.64496 - 11.9020i) q^{59} +(-0.399991 + 0.454478i) q^{60} +(-4.75413 - 11.8311i) q^{61} +(-10.2321 + 4.62520i) q^{62} +(0.630669 - 0.509229i) q^{63} +(-4.00560 - 7.94463i) q^{64} +(3.95484 - 5.34730i) q^{65} +(1.81488 + 0.154469i) q^{66} +(-3.54710 + 2.86409i) q^{67} +(0.109432 + 0.147961i) q^{68} +(1.76169 - 0.302073i) q^{69} +(0.964216 - 0.924126i) q^{70} +(2.87674 - 9.39353i) q^{71} +(-2.95343 + 0.769012i) q^{72} +(9.40053 + 5.25145i) q^{73} +(3.83699 + 9.54872i) q^{74} +(-2.14137 - 2.43307i) q^{75} +(-0.476825 + 0.644710i) q^{76} +(1.17131 + 0.200842i) q^{77} +(5.87458 - 2.07562i) q^{78} +(-3.13880 + 2.12146i) q^{79} +(-3.59951 + 1.27179i) q^{80} +(0.0424412 + 0.999099i) q^{81} +(-8.06580 + 10.9057i) q^{82} +(-3.00868 + 5.96736i) q^{83} +(-0.364721 + 0.0625377i) q^{84} +(0.466739 - 0.260736i) q^{85} +(9.26476 + 8.87955i) q^{86} +(6.32366 + 4.27405i) q^{87} +(-3.70708 - 2.50555i) q^{88} +(-5.00072 + 8.12168i) q^{89} +(0.209279 + 1.63429i) q^{90} +(3.93393 - 1.02432i) q^{91} +(-0.769360 - 0.271832i) q^{92} +(2.64662 - 8.64211i) q^{93} +(-8.67231 + 0.738122i) q^{94} +(1.68182 + 1.61189i) q^{95} +(2.44599 + 0.636885i) q^{96} +(7.95072 - 12.9128i) q^{97} +(-7.85191 + 0.668296i) q^{98} +(-1.05846 + 1.01445i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q - q^{2} - 20 q^{3} - 23 q^{4} - 4 q^{5} - q^{6} - 12 q^{7} - 9 q^{8} - 20 q^{9} - 16 q^{10} - 14 q^{11} - 23 q^{12} - 14 q^{13} - 28 q^{14} - 4 q^{15} - 37 q^{16} - 20 q^{17} - q^{18} + 42 q^{19}+ \cdots - 14 q^{99}+O(q^{100}) \) 720 * q - q^2 - 20 * q^3 - 23 * q^4 - 4 * q^5 - q^6 - 12 * q^7 - 9 * q^8 - 20 * q^9 - 16 * q^10 - 14 * q^11 - 23 * q^12 - 14 * q^13 - 28 * q^14 - 4 * q^15 - 37 * q^16 - 20 * q^17 - q^18 + 42 * q^19 - 34 * q^20 - 12 * q^21 - 32 * q^22 - 18 * q^23 - 9 * q^24 - 48 * q^25 - 48 * q^26 - 20 * q^27 - 80 * q^28 + 7 * q^29 - 16 * q^30 - 40 * q^31 - 59 * q^32 - 14 * q^33 + 22 * q^34 - 32 * q^35 - 23 * q^36 - 44 * q^37 - 36 * q^38 + 60 * q^39 + 124 * q^40 + 176 * q^41 + 46 * q^42 - 42 * q^43 + 76 * q^44 - 4 * q^45 - 88 * q^46 - 26 * q^47 - 37 * q^48 - 94 * q^49 - 87 * q^50 + 54 * q^51 + 206 * q^52 - 54 * q^53 - q^54 - 74 * q^55 - 107 * q^56 - 32 * q^57 + 13 * q^58 - 50 * q^59 - 34 * q^60 - 86 * q^61 - 83 * q^62 - 12 * q^63 + 99 * q^64 + 52 * q^65 + 42 * q^66 - 68 * q^67 + 63 * q^68 - 18 * q^69 - 62 * q^70 - 68 * q^71 - 9 * q^72 - 58 * q^73 - 82 * q^74 - 48 * q^75 - 145 * q^76 + 40 * q^77 + 26 * q^78 - 90 * q^79 + 325 * q^80 - 20 * q^81 + 62 * q^82 + 58 * q^83 - 80 * q^84 - 14 * q^85 - 153 * q^86 - 30 * q^87 - 152 * q^88 - 110 * q^89 - 16 * q^90 - 114 * q^91 - 110 * q^92 - 40 * q^93 + 102 * q^94 - 118 * q^95 - 59 * q^96 - 110 * q^97 - 154 * q^98 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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