LMFDB - Embedded newform 669.2.i.a.4.1

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 = [648] 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:	$648$
Relative dimension:	$18$ over $\Q(\zeta_{37})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{37}]$

Embedding invariants

Embedding label			4.1
Character	$\chi$	$=$	669.4
Dual form			669.2.i.a.502.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.51246 + 0.887710i) q^{2} +(-0.372856 + 0.927889i) q^{3} +(3.96837 - 3.20424i) q^{4} +(-2.24573 - 3.64729i) q^{5} +(0.113092 - 2.66228i) q^{6} +(0.412183 - 3.21880i) q^{7} +(-4.33174 + 7.03519i) q^{8} +(-0.721956 - 0.691939i) q^{9} +(8.88004 + 7.17013i) q^{10} +(0.0936929 - 2.20560i) q^{11} +(1.49354 + 4.87693i) q^{12} +(-1.85168 - 4.60807i) q^{13} +(1.82176 + 8.45301i) q^{14} +(4.22161 - 0.723869i) q^{15} +(2.48899 - 11.5490i) q^{16} +(0.187403 - 4.41161i) q^{17} +(2.42813 + 1.09758i) q^{18} +(4.32634 - 1.12649i) q^{19} +(-20.5987 - 7.27797i) q^{20} +(2.83300 + 1.58261i) q^{21} +(1.72254 + 5.62467i) q^{22} +(0.0604044 + 0.0981031i) q^{23} +(-4.91276 - 6.64249i) q^{24} +(-6.00843 + 11.9170i) q^{25} +(8.74290 + 9.93386i) q^{26} +(0.911228 - 0.411901i) q^{27} +(-8.67809 - 14.0941i) q^{28} +(-1.60135 + 7.43028i) q^{29} +(-9.96407 + 5.56626i) q^{30} +(-6.61917 + 0.563374i) q^{31} +(1.89982 + 14.8360i) q^{32} +(2.01162 + 0.909310i) q^{33} +(3.44538 + 11.2504i) q^{34} +(-12.6655 + 5.72518i) q^{35} +(-5.08213 - 0.432553i) q^{36} +(0.240678 + 5.66574i) q^{37} +(-9.86978 + 6.67080i) q^{38} +4.96619 q^{39} +35.3873 q^{40} +(9.50297 - 6.42289i) q^{41} +(-8.52271 - 1.46137i) q^{42} +(-2.86877 - 5.68986i) q^{43} +(-6.69547 - 9.05287i) q^{44} +(-0.902387 + 4.18709i) q^{45} +(-0.238851 - 0.192859i) q^{46} +(-3.16295 - 0.823569i) q^{47} +(9.78811 + 6.61561i) q^{48} +(-3.41663 - 0.889620i) q^{49} +(4.51711 - 35.2748i) q^{50} +(4.02361 + 1.81878i) q^{51} +(-22.1135 - 12.3533i) q^{52} +(0.675944 - 0.768022i) q^{53} +(-1.92378 + 1.84379i) q^{54} +(-8.25489 + 4.61146i) q^{55} +(20.8594 + 16.8428i) q^{56} +(-0.567845 + 4.43438i) q^{57} +(-2.57260 - 20.0898i) q^{58} +(0.281318 - 0.918598i) q^{59} +(14.4335 - 16.3996i) q^{60} +(4.52335 + 11.2568i) q^{61} +(16.1303 - 7.29136i) q^{62} +(-2.52479 + 2.03862i) q^{63} +(-7.30576 - 14.4901i) q^{64} +(-12.6486 + 17.1021i) q^{65} +(-5.86133 - 0.498873i) q^{66} +(7.76375 - 6.26879i) q^{67} +(-13.3921 - 18.1074i) q^{68} +(-0.113551 + 0.0194703i) q^{69} +(26.7394 - 25.6276i) q^{70} +(-0.125792 + 0.410753i) q^{71} +(7.99525 - 2.08180i) q^{72} +(-8.51105 - 4.75456i) q^{73} +(-5.63422 - 14.0213i) q^{74} +(-8.81738 - 10.0185i) q^{75} +(13.5590 - 18.3330i) q^{76} +(-7.06077 - 1.21069i) q^{77} +(-12.4774 + 4.40853i) q^{78} +(6.06539 - 4.09949i) q^{79} +(-47.7120 + 16.8577i) q^{80} +(0.0424412 + 0.999099i) q^{81} +(-18.1742 + 24.5732i) q^{82} +(-0.529479 + 1.05016i) q^{83} +(16.3135 - 2.79722i) q^{84} +(-16.5113 + 9.22375i) q^{85} +(12.2586 + 11.7489i) q^{86} +(-6.29740 - 4.25630i) q^{87} +(15.1110 + 10.2132i) q^{88} +(6.52918 - 10.6041i) q^{89} +(-1.44971 - 11.3210i) q^{90} +(-15.5957 + 4.06080i) q^{91} +(0.554053 + 0.195759i) q^{92} +(1.94525 - 6.35191i) q^{93} +(8.67789 - 0.738597i) q^{94} +(-13.8244 - 13.2496i) q^{95} +(-14.4745 - 3.76887i) q^{96} +(-0.0974213 + 0.158222i) q^{97} +(9.37388 - 0.797834i) q^{98} +(-1.59378 + 1.52752i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q + q^{2} + 18 q^{3} - 17 q^{4} + 4 q^{5} - q^{6} + 4 q^{7} + 9 q^{8} - 18 q^{9} + 8 q^{10} + 6 q^{11} + 17 q^{12} - 2 q^{13} + 12 q^{14} - 4 q^{15} - 7 q^{16} + 8 q^{17} + q^{18} - 66 q^{19} + 14 q^{20}+ \cdots + 6 q^{99}+O(q^{100}) $ 648 * q + q^2 + 18 * q^3 - 17 * q^4 + 4 * q^5 - q^6 + 4 * q^7 + 9 * q^8 - 18 * q^9 + 8 * q^10 + 6 * q^11 + 17 * q^12 - 2 * q^13 + 12 * q^14 - 4 * q^15 - 7 * q^16 + 8 * q^17 + q^18 - 66 * q^19 + 14 * q^20 - 4 * q^21 - 24 * q^22 - 2 * q^23 - 9 * q^24 - 26 * q^25 - 8 * q^26 + 18 * q^27 + 8 * q^28 - 27 * q^29 - 8 * q^30 + 16 * q^31 + 19 * q^32 - 6 * q^33 - 50 * q^34 + 16 * q^35 - 17 * q^36 + 16 * q^37 - 28 * q^38 - 72 * q^39 + 212 * q^40 + 240 * q^41 - 86 * q^42 + 6 * q^43 - 128 * q^44 + 4 * q^45 + 16 * q^46 - 14 * q^47 + 7 * q^48 - 28 * q^49 + 23 * q^50 + 66 * q^51 - 286 * q^52 + 10 * q^53 - q^54 + 14 * q^55 + 25 * q^56 - 8 * q^57 + 49 * q^58 + 22 * q^59 - 14 * q^60 - 2 * q^61 - 23 * q^62 + 4 * q^63 + 257 * q^64 - 116 * q^65 - 50 * q^66 + 8 * q^67 + 211 * q^68 + 2 * q^69 + 82 * q^70 + 9 * q^72 + 10 * q^73 - 10 * q^74 + 26 * q^75 + 7 * q^76 - 116 * q^77 - 66 * q^78 - 14 * q^79 - 477 * q^80 - 18 * q^81 - 234 * q^82 - 142 * q^83 - 8 * q^84 + 98 * q^85 + 35 * q^86 - 10 * q^87 - 72 * q^88 + 2 * q^89 + 8 * q^90 + 6 * q^91 - 46 * q^92 - 16 * q^93 - 206 * q^94 - 6 * q^95 - 19 * q^96 - 34 * q^97 + 4 * q^98 + 6 * 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 $

$2$	−2.51246	+	0.887710i	−1.77658	+	0.627706i	−0.999997	−	0.00230969i	$-0.999265\pi$
$2$	−2.51246	+	0.887710i	−1.77658	+	0.627706i	−0.776583	+	0.630015i	$0.783049\pi$
$3$	−0.372856	+	0.927889i	−0.215269	+	0.535717i
$3$	−0.372856	+	0.927889i	−0.215269	+	0.535717i
$4$	3.96837	−	3.20424i	1.98419	−	1.60212i
$5$	−2.24573	−	3.64729i	−1.00432	−	1.63112i	−0.747038	−	0.664782i	$-0.768525\pi$
$5$	−2.24573	−	3.64729i	−1.00432	−	1.63112i	−0.257282	−	0.966336i	$-0.582827\pi$
$6$	0.113092	−	2.66228i	0.0461697	−	1.08687i
$7$	0.412183	−	3.21880i	0.155791	−	1.21659i	−0.705586	−	0.708624i	$-0.749316\pi$
$7$	0.412183	−	3.21880i	0.155791	−	1.21659i	0.861377	−	0.507967i	$-0.169603\pi$
$8$	−4.33174	+	7.03519i	−1.53150	+	2.48732i
$9$	−0.721956	−	0.691939i	−0.240652	−	0.230646i
$10$	8.88004	+	7.17013i	2.80812	+	2.26740i
$11$	0.0936929	−	2.20560i	0.0282495	−	0.665014i	−0.928021	−	0.372529i	$-0.878491\pi$
$11$	0.0936929	−	2.20560i	0.0282495	−	0.665014i	0.956270	−	0.292485i	$-0.0944823\pi$
$12$	1.49354	+	4.87693i	0.431149	+	1.40785i
$13$	−1.85168	−	4.60807i	−0.513562	−	1.27805i	−0.929556	−	0.368682i	$-0.879809\pi$
$13$	−1.85168	−	4.60807i	−0.513562	−	1.27805i	0.415993	−	0.909368i	$-0.363434\pi$
$14$	1.82176	+	8.45301i	0.486887	+	2.25916i
$15$	4.22161	−	0.723869i	1.09002	−	0.186902i
$16$	2.48899	−	11.5490i	0.622247	−	2.88724i
$17$	0.187403	−	4.41161i	0.0454518	−	1.06997i	−0.821068	−	0.570830i	$-0.806622\pi$
$17$	0.187403	−	4.41161i	0.0454518	−	1.06997i	0.866520	−	0.499142i	$-0.166351\pi$
$18$	2.42813	+	1.09758i	0.572316	+	0.258703i
$19$	4.32634	−	1.12649i	0.992531	−	0.258435i	0.279942	−	0.960017i	$-0.409685\pi$
$19$	4.32634	−	1.12649i	0.992531	−	0.258435i	0.712589	+	0.701582i	$0.247523\pi$
$20$	−20.5987	−	7.27797i	−4.60600	−	1.62740i
$21$	2.83300	+	1.58261i	0.618212	+	0.345354i
$22$	1.72254	+	5.62467i	0.367246	+	1.19918i
$23$	0.0604044	+	0.0981031i	0.0125952	+	0.0204559i	0.857765	−	0.514042i	$-0.171852\pi$
$23$	0.0604044	+	0.0981031i	0.0125952	+	0.0204559i	−0.845170	+	0.534497i	$0.820501\pi$
$24$	−4.91276	−	6.64249i	−1.00281	−	1.35589i
$25$	−6.00843	+	11.9170i	−1.20169	+	2.38340i
$26$	8.74290	+	9.93386i	1.71462	+	1.94819i
$27$	0.911228	−	0.411901i	0.175366	−	0.0792704i
$28$	−8.67809	−	14.0941i	−1.64001	−	2.66354i
$29$	−1.60135	+	7.43028i	−0.297363	+	1.37977i	0.543904	+	0.839147i	$0.316946\pi$
$29$	−1.60135	+	7.43028i	−0.297363	+	1.37977i	−0.841267	+	0.540620i	$0.818190\pi$
$30$	−9.96407	+	5.56626i	−1.81918	+	1.01626i
$31$	−6.61917	+	0.563374i	−1.18884	+	0.101185i	−0.662481	−	0.749079i	$-0.730496\pi$
$31$	−6.61917	+	0.563374i	−1.18884	+	0.101185i	−0.526357	+	0.850264i	$0.676442\pi$
$32$	1.89982	+	14.8360i	0.335844	+	2.62266i
$33$	2.01162	+	0.909310i	0.350178	+	0.158291i
$34$	3.44538	+	11.2504i	0.590878	+	1.92942i
$35$	−12.6655	+	5.72518i	−2.14087	+	0.967733i
$36$	−5.08213	−	0.432553i	−0.847021	−	0.0720921i
$37$	0.240678	+	5.66574i	0.0395671	+	0.931441i	0.903697	+	0.428172i	$0.140842\pi$
$37$	0.240678	+	5.66574i	0.0395671	+	0.931441i	−0.864130	+	0.503269i	$0.832131\pi$
$38$	−9.86978	+	6.67080i	−1.60109	+	1.08215i
$39$	4.96619			0.795227
$40$	35.3873			5.59522
$41$	9.50297	−	6.42289i	1.48412	−	1.00309i	0.493007	−	0.870025i	$-0.335898\pi$
$41$	9.50297	−	6.42289i	1.48412	−	1.00309i	0.991108	−	0.133062i	$-0.0424808\pi$
$42$	−8.52271	−	1.46137i	−1.31508	−	0.225494i
$43$	−2.86877	−	5.68986i	−0.437483	−	0.867696i	−0.999185	−	0.0403565i	$-0.987151\pi$
$43$	−2.86877	−	5.68986i	−0.437483	−	0.867696i	0.561702	−	0.827339i	$-0.310147\pi$
$44$	−6.69547	−	9.05287i	−1.00938	−	1.36477i
$45$	−0.902387	+	4.18709i	−0.134520	+	0.624174i
$46$	−0.238851	−	0.192859i	−0.0352167	−	0.0284355i
$47$	−3.16295	−	0.823569i	−0.461364	−	0.120130i	0.0140325	−	0.999902i	$-0.495533\pi$
$47$	−3.16295	−	0.823569i	−0.461364	−	0.120130i	−0.475396	+	0.879772i	$0.657695\pi$
$48$	9.78811	+	6.61561i	1.41279	+	0.954881i
$49$	−3.41663	−	0.889620i	−0.488090	−	0.127089i
$50$	4.51711	−	35.2748i	0.638816	−	4.98861i
$51$	4.02361	+	1.81878i	0.563418	+	0.254681i
$52$	−22.1135	−	12.3533i	−3.06659	−	1.71310i
$53$	0.675944	−	0.768022i	0.0928481	−	0.105496i	−0.702393	−	0.711790i	$-0.747885\pi$
$53$	0.675944	−	0.768022i	0.0928481	−	0.105496i	0.795241	+	0.606294i	$0.207344\pi$
$54$	−1.92378	+	1.84379i	−0.261793	+	0.250908i
$55$	−8.25489	+	4.61146i	−1.11309	+	0.621809i
$56$	20.8594	+	16.8428i	2.78745	+	2.25071i
$57$	−0.567845	+	4.43438i	−0.0752129	+	0.587349i
$58$	−2.57260	−	20.0898i	−0.337799	−	2.63792i
$59$	0.281318	−	0.918598i	0.0366244	−	0.119591i	−0.935983	−	0.352045i	$-0.885486\pi$
$59$	0.281318	−	0.918598i	0.0366244	−	0.119591i	0.972607	+	0.232454i	$0.0746755\pi$
$60$	14.4335	−	16.3996i	1.86336	−	2.11718i
$61$	4.52335	+	11.2568i	0.579156	+	1.44129i	0.874088	+	0.485767i	$0.161460\pi$
$61$	4.52335	+	11.2568i	0.579156	+	1.44129i	−0.294932	+	0.955518i	$0.595297\pi$
$62$	16.1303	−	7.29136i	2.04855	−	0.926003i
$63$	−2.52479	+	2.03862i	−0.318093	+	0.256843i
$64$	−7.30576	−	14.4901i	−0.913220	−	1.81126i
$65$	−12.6486	+	17.1021i	−1.56887	+	2.12125i
$66$	−5.86133	−	0.498873i	−0.721480	−	0.0614070i
$67$	7.76375	−	6.26879i	0.948493	−	0.765854i	−0.0237769	−	0.999717i	$-0.507569\pi$
$67$	7.76375	−	6.26879i	0.948493	−	0.765854i	0.972270	+	0.233863i	$0.0751367\pi$
$68$	−13.3921	−	18.1074i	−1.62404	−	2.19584i
$69$	−0.113551	+	0.0194703i	−0.0136699	+	0.00234394i
$70$	26.7394	−	25.6276i	3.19597	−	3.06309i
$71$	−0.125792	+	0.410753i	−0.0149287	+	0.0487474i	−0.963320	−	0.268354i	$-0.913520\pi$
$71$	−0.125792	+	0.410753i	−0.0149287	+	0.0487474i	0.948392	+	0.317101i	$0.102710\pi$
$72$	7.99525	−	2.08180i	0.942249	−	0.245343i
$73$	−8.51105	−	4.75456i	−0.996143	−	0.556479i	−0.0975354	−	0.995232i	$-0.531096\pi$
$73$	−8.51105	−	4.75456i	−0.996143	−	0.556479i	−0.898608	+	0.438753i	$0.855420\pi$
$74$	−5.63422	−	14.0213i	−0.654965	−	1.62994i
$75$	−8.81738	−	10.0185i	−1.01814	−	1.15684i
$76$	13.5590	−	18.3330i	1.55532	−	2.10293i
$77$	−7.06077	−	1.21069i	−0.804649	−	0.137971i
$78$	−12.4774	+	4.40853i	−1.41278	+	0.499168i
$79$	6.06539	−	4.09949i	0.682410	−	0.461229i	−0.169078	−	0.985603i	$-0.554079\pi$
$79$	6.06539	−	4.09949i	0.682410	−	0.461229i	0.851488	+	0.524374i	$0.175701\pi$
$80$	−47.7120	+	16.8577i	−5.33436	+	1.88475i
$81$	0.0424412	+	0.999099i	0.00471569	+	0.111011i
$82$	−18.1742	+	24.5732i	−2.00701	+	2.71365i
$83$	−0.529479	+	1.05016i	−0.0581179	+	0.115270i	−0.920123	−	0.391630i	$-0.871911\pi$
$83$	−0.529479	+	1.05016i	−0.0581179	+	0.115270i	0.862005	+	0.506900i	$0.169209\pi$
$84$	16.3135	−	2.79722i	1.77994	−	0.305202i
$85$	−16.5113	+	9.22375i	−1.79090	+	1.00046i
$86$	12.2586	+	11.7489i	1.32188	+	1.26692i
$87$	−6.29740	−	4.25630i	−0.675152	−	0.456323i
$88$	15.1110	+	10.2132i	1.61084	+	1.08874i
$89$	6.52918	−	10.6041i	0.692092	−	1.12403i	−0.293674	−	0.955906i	$-0.594878\pi$
$89$	6.52918	−	10.6041i	0.692092	−	1.12403i	0.985766	−	0.168123i	$-0.0537705\pi$
$90$	−1.44971	−	11.3210i	−0.152812	−	1.19333i
$91$	−15.5957	+	4.06080i	−1.63487	+	0.425687i
$92$	0.554053	+	0.195759i	0.0577640	+	0.0204093i
$93$	1.94525	−	6.35191i	0.201713	−	0.658662i
$94$	8.67789	−	0.738597i	0.895056	−	0.0761805i
$95$	−13.8244	−	13.2496i	−1.41836	−	1.35938i
$96$	−14.4745	−	3.76887i	−1.47730	−	0.384659i
$97$	−0.0974213	+	0.158222i	−0.00989164	+	0.0160650i	−0.856437	−	0.516251i	$-0.827327\pi$
$97$	−0.0974213	+	0.158222i	−0.00989164	+	0.0160650i	0.846545	+	0.532316i	$0.178678\pi$
$98$	9.37388	−	0.797834i	0.946904	−	0.0805934i
$99$	−1.59378	+	1.52752i	−0.160181	+	0.153521i
$100$	14.3412	+	66.5435i	1.43412	+	6.65435i
$101$	−4.12979	−	4.69236i	−0.410930	−	0.466907i	0.507983	−	0.861367i	$-0.330391\pi$
$101$	−4.12979	−	4.69236i	−0.410930	−	0.466907i	−0.918913	+	0.394460i	$0.870932\pi$
$102$	−11.7237	−	0.997835i	−1.16082	−	0.0988004i
$103$	−0.646954	+	1.61001i	−0.0637463	+	0.158639i	−0.956366	−	0.292172i	$-0.905622\pi$
$103$	−0.646954	+	1.61001i	−0.0637463	+	0.158639i	0.892619	+	0.450811i	$0.148865\pi$
$104$	40.4397	+	6.93408i	3.96543	+	0.679942i
$105$	−0.589908	−	13.8869i	−0.0575691	−	1.35522i
$106$	−1.01650	+	2.52967i	−0.0987316	+	0.245703i
$107$	4.89675	+	9.71212i	0.473386	+	0.938906i	0.996253	+	0.0864912i	$0.0275654\pi$
$107$	4.89675	+	9.71212i	0.473386	+	0.938906i	−0.522866	+	0.852415i	$0.675137\pi$
$108$	2.29627	−	4.55437i	0.220958	−	0.438244i
$109$	−0.588997	−	2.73296i	−0.0564157	−	0.261770i	0.940546	−	0.339667i	$-0.110314\pi$
$109$	−0.588997	−	2.73296i	−0.0564157	−	0.261770i	−0.996961	+	0.0778975i	$0.975179\pi$
$110$	16.6465	−	18.9141i	1.58718	−	1.80338i
$111$	−5.34691	−	1.88918i	−0.507506	−	0.179313i
$112$	−36.1478	−	12.7718i	−3.41565	−	1.20682i
$113$	−1.23253	+	1.40042i	−0.115946	+	0.131741i	−0.805750	−	0.592256i	$-0.798237\pi$
$113$	−1.23253	+	1.40042i	−0.115946	+	0.131741i	0.689803	+	0.723997i	$0.257697\pi$
$114$	−2.50976	−	11.6453i	−0.235060	−	1.09068i
$115$	0.222159	−	0.440625i	0.0207164	−	0.0410885i
$116$	17.4536	+	34.6172i	1.62053	+	3.21413i
$117$	−1.85168	+	4.60807i	−0.171187	+	0.426016i
$118$	0.108649	+	2.55767i	0.0100019	+	0.235453i
$119$	−14.1228	−	2.42160i	−1.29464	−	0.221988i
$120$	−13.1944	+	32.8355i	−1.20448	+	2.99746i
$121$	6.10447	+	0.519567i	0.554951	+	0.0472333i
$122$	−21.3575	−	24.2669i	−1.93362	−	2.19702i
$123$	2.41648	+	11.2125i	0.217887	+	1.01100i
$124$	−24.4621	+	23.4451i	−2.19677	+	2.10543i
$125$	35.6191	−	3.03163i	3.18587	−	0.271157i
$126$	4.53373	−	7.36325i	0.403897	−	0.655970i
$127$	−4.90123	−	1.27618i	−0.434914	−	0.113243i	0.0280770	−	0.999606i	$-0.491062\pi$
$127$	−4.90123	−	1.27618i	−0.434914	−	0.113243i	−0.462991	+	0.886363i	$0.653224\pi$
$128$	9.62170	+	9.22165i	0.850446	+	0.815087i
$129$	6.34920	−	0.540397i	0.559016	−	0.0475793i
$130$	16.5975	−	54.1966i	1.45570	−	4.75336i
$131$	12.3433	+	4.36117i	1.07844	+	0.381037i	0.812505	−	0.582954i	$-0.198103\pi$
$131$	12.3433	+	4.36117i	1.07844	+	0.381037i	0.265934	+	0.963991i	$0.414320\pi$
$132$	10.8965	−	2.83723i	0.948419	−	0.246949i
$133$	−1.84270	−	14.3899i	−0.159783	−	1.24777i
$134$	−13.9413	+	22.6421i	−1.20434	+	1.95598i
$135$	−3.54869	−	2.39850i	−0.305423	−	0.206430i
$136$	30.2247	+	20.4283i	2.59175	+	1.75172i
$137$	−3.03566	−	2.90944i	−0.259354	−	0.248570i	0.551009	−	0.834500i	$-0.314243\pi$
$137$	−3.03566	−	2.90944i	−0.259354	−	0.248570i	−0.810362	+	0.585929i	$0.800730\pi$
$138$	0.268009	−	0.149719i	0.0228144	−	0.0127449i
$139$	−3.84838	+	0.659872i	−0.326416	+	0.0559696i	−0.329876	−	0.944024i	$-0.607007\pi$
$139$	−3.84838	+	0.659872i	−0.326416	+	0.0559696i	0.00345984	+	0.999994i	$0.498899\pi$
$140$	−31.9167	+	63.3031i	−2.69746	+	5.35008i
$141$	1.94351	−	2.62780i	0.163673	−	0.221300i
$142$	−0.0485825	−	1.14367i	−0.00407695	−	0.0959746i
$143$	−10.3371	+	3.65232i	−0.864429	+	0.305422i
$144$	−9.78811	+	6.61561i	−0.815676	+	0.551301i
$145$	30.6966	−	10.8458i	2.54921	−	0.900694i
$146$	25.6044	+	4.39031i	2.11903	+	0.363345i
$147$	2.09938	−	2.83855i	0.173154	−	0.234120i
$148$	19.1095	+	21.7126i	1.57079	+	1.78476i
$149$	8.59936	+	21.4003i	0.704487	+	1.75318i	0.656489	+	0.754336i	$0.272041\pi$
$149$	8.59936	+	21.4003i	0.704487	+	1.75318i	0.0479984	+	0.998847i	$0.484716\pi$
$150$	31.0468	+	17.3438i	2.53496	+	1.41612i
$151$	−15.7522	+	4.10154i	−1.28189	+	0.333779i	−0.829734	−	0.558159i	$-0.811508\pi$
$151$	−15.7522	+	4.10154i	−1.28189	+	0.333779i	−0.452158	+	0.891938i	$0.649346\pi$
$152$	−10.8155	+	35.3163i	−0.877253	+	2.86453i
$153$	−3.18786	+	3.05531i	−0.257723	+	0.247008i
$154$	18.8147	−	3.22610i	1.51613	−	0.259966i
$155$	16.9196	+	22.8768i	1.35902	+	1.83751i
$156$	19.7077	−	15.9128i	1.57788	−	1.27405i
$157$	−8.76127	−	0.745694i	−0.699225	−	0.0595129i	−0.270199	−	0.962805i	$-0.587089\pi$
$157$	−8.76127	−	0.745694i	−0.699225	−	0.0595129i	−0.429027	+	0.903292i	$0.641143\pi$
$158$	−11.5999	+	15.6841i	−0.922840	+	1.24776i
$159$	0.460609	+	0.913563i	0.0365286	+	0.0724502i
$160$	49.8447	−	40.2468i	3.94057	−	3.18179i
$161$	0.340671	−	0.153993i	0.0268487	−	0.0121364i
$162$	−0.993542	−	2.47252i	−0.0780600	−	0.194260i
$163$	−6.77222	+	7.69474i	−0.530441	+	0.602698i	−0.952751	−	0.303753i	$-0.901760\pi$
$163$	−6.77222	+	7.69474i	−0.530441	+	0.602698i	0.422309	+	0.906452i	$0.361220\pi$
$164$	17.1309	−	55.9382i	1.33770	−	4.36804i
$165$	−1.20103	−	9.37903i	−0.0935002	−	0.730156i
$166$	0.398060	−	3.10851i	0.0308955	−	0.241267i
$167$	−3.42209	−	2.76314i	−0.264809	−	0.213818i	0.486652	−	0.873596i	$-0.338218\pi$
$167$	−3.42209	−	2.76314i	−0.264809	−	0.213818i	−0.751461	+	0.659778i	$0.770650\pi$
$168$	−23.4058	+	13.0753i	−1.80580	+	1.00878i
$169$	−8.42020	+	8.07011i	−0.647707	+	0.620777i
$170$	33.2959	−	37.8315i	2.55368	−	2.90155i
$171$	−3.90289	−	2.18029i	−0.298462	−	0.166731i
$172$	−29.6160	−	13.3873i	−2.25820	−	1.02077i
$173$	−0.0260892	+	0.203735i	−0.00198353	+	0.0154897i	−0.992862	−	0.119269i	$-0.961945\pi$
$173$	−0.0260892	+	0.203735i	−0.00198353	+	0.0154897i	0.990878	+	0.134759i	$0.0430260\pi$
$174$	19.6003	+	5.10353i	1.48590	+	0.386898i
$175$	35.8818	+	24.2519i	2.71241	+	1.83327i
$176$	−25.2392	−	6.57178i	−1.90248	−	0.495366i
$177$	0.747466	+	0.603537i	0.0561830	+	0.0453646i
$178$	−6.99100	+	32.4383i	−0.523997	+	2.43136i
$179$	−9.19166	−	12.4279i	−0.687017	−	0.928908i	0.312764	−	0.949831i	$-0.398745\pi$
$179$	−9.19166	−	12.4279i	−0.687017	−	0.928908i	−0.999781	+	0.0209226i	$0.993340\pi$
$180$	9.83542	+	19.5074i	0.733089	+	1.45400i
$181$	−8.10575	−	1.38987i	−0.602496	−	0.103308i	−0.140334	−	0.990104i	$-0.544818\pi$
$181$	−8.10575	−	1.38987i	−0.602496	−	0.103308i	−0.462161	+	0.886796i	$0.652926\pi$
$182$	35.5788	−	24.0470i	2.63727	−	1.78249i
$183$	−12.1316			−0.896795
$184$	−0.951830			−0.0701699
$185$	20.1241	−	13.6015i	1.47955	−	1.00000i
$186$	0.751282	+	17.6858i	0.0550867	+	1.29678i
$187$	−9.71269	−	0.826672i	−0.710262	−	0.0604522i
$188$	−15.1907	+	6.86662i	−1.10789	+	0.500800i
$189$	−0.950233	−	3.10284i	−0.0691193	−	0.225698i
$190$	46.4952	+	21.0171i	3.37312	+	1.52474i
$191$	−0.500744	−	3.91038i	−0.0362325	−	0.282945i	−0.999876	−	0.0157533i	$-0.994985\pi$
$191$	−0.500744	−	3.91038i	−0.0362325	−	0.282945i	0.963643	−	0.267192i	$-0.0860957\pi$
$192$	16.1692	−	1.37620i	1.16691	−	0.0993189i
$193$	4.77721	−	2.66871i	0.343871	−	0.192098i	−0.306208	−	0.951965i	$-0.599060\pi$
$193$	4.77721	−	2.66871i	0.343871	−	0.192098i	0.650079	+	0.759867i	$0.274736\pi$
$194$	0.104312	−	0.484010i	0.00748917	−	0.0347499i
$195$	−11.1527	−	18.1131i	−0.798661	−	1.29711i
$196$	−16.4090	+	7.41734i	−1.17207	+	0.529810i
$197$	2.57030	+	2.92042i	0.183126	+	0.208072i	0.834991	−	0.550263i	$-0.185473\pi$
$197$	2.57030	+	2.92042i	0.183126	+	0.208072i	−0.651865	+	0.758335i	$0.726013\pi$
$198$	2.64833	−	5.25265i	0.188209	−	0.373290i
$199$	−6.72703	−	9.09554i	−0.476866	−	0.644766i	0.498100	−	0.867120i	$-0.334031\pi$
$199$	−6.72703	−	9.09554i	−0.476866	−	0.644766i	−0.974966	+	0.222354i	$0.928626\pi$
$200$	−57.8115	−	93.8918i	−4.08789	−	6.63915i
$201$	2.92198	+	9.54125i	0.206100	+	0.672988i
$202$	14.5414	+	8.12332i	1.02313	+	0.571555i
$203$	23.2565	+	8.21704i	1.63229	+	0.576723i
$204$	21.7950	−	5.67497i	1.52595	−	0.397328i
$205$	−44.7672	−	20.2361i	−3.12668	−	1.41335i
$206$	0.196229	−	4.61939i	0.0136720	−	0.321848i
$207$	0.0242720	−	0.112622i	0.00168702	−	0.00782779i
$208$	−57.8272	+	9.91547i	−4.00959	+	0.687514i
$209$	−2.07925	−	9.64774i	−0.143824	−	0.667348i
$210$	13.8096	+	34.3666i	0.952956	+	2.37152i
$211$	5.86666	+	19.1566i	0.403877	+	1.31880i	0.894360	+	0.447347i	$0.147631\pi$
$211$	5.86666	+	19.1566i	0.403877	+	1.31880i	−0.490483	+	0.871451i	$0.663180\pi$
$212$	0.221474	−	5.21368i	0.0152109	−	0.358077i
$213$	−0.334231	−	0.269873i	−0.0229011	−	0.0184914i
$214$	−20.9244	−	20.0545i	−1.43037	−	1.37089i
$215$	−14.3101	+	23.2411i	−0.975942	+	1.58503i
$216$	−1.04940	+	8.19492i	−0.0714026	+	0.557594i
$217$	−0.914922	+	21.5380i	−0.0621089	+	1.46209i
$218$	3.90591	+	6.34359i	0.264541	+	0.429642i
$219$	7.58510	−	6.12454i	0.512554	−	0.413858i
$220$	−17.9823	+	44.7506i	−1.21236	+	3.01708i
$221$	−20.6760	+	7.30530i	−1.39082	+	0.491407i
$222$	15.1110			1.01418
$223$	12.8296	+	7.64201i	0.859136	+	0.511747i
$223$	12.8296	+	7.64201i	0.859136	+	0.511747i
$224$	48.5371			3.24302
$225$	12.5837	−	4.44609i	0.838911	−	0.296406i
$226$	1.85351	−	4.61264i	0.123294	−	0.306828i
$227$	3.51339	−	2.83686i	0.233192	−	0.188289i	−0.504530	−	0.863394i	$-0.668334\pi$
$227$	3.51339	−	2.83686i	0.233192	−	0.188289i	0.737722	+	0.675105i	$0.235902\pi$
$228$	11.9554	+	19.4168i	0.791766	+	1.28591i
$229$	0.902887	−	21.2547i	0.0596645	−	1.40455i	−0.680808	−	0.732462i	$-0.738371\pi$
$229$	0.902887	−	21.2547i	0.0596645	−	1.40455i	0.740473	−	0.672086i	$-0.234602\pi$
$230$	−0.167018	+	1.30427i	−0.0110128	+	0.0860008i
$231$	3.75604	−	6.10020i	0.247129	−	0.401363i
$232$	−45.3368	−	43.4518i	−2.97651	−	2.85275i
$233$	−7.19538	−	5.80986i	−0.471385	−	0.380617i	0.363009	−	0.931786i	$-0.381750\pi$
$233$	−7.19538	−	5.80986i	−0.471385	−	0.380617i	−0.834394	+	0.551169i	$0.814182\pi$
$234$	0.561637	−	13.2214i	0.0367153	−	0.864308i
$235$	4.09933	+	13.3857i	0.267411	+	0.873188i
$236$	−1.82703	−	4.54675i	−0.118930	−	0.295968i
$237$	1.54235	+	7.15653i	0.100186	+	0.464867i
$238$	37.6327	−	6.45278i	2.43937	−	0.418272i
$239$	−2.49172	+	11.5616i	−0.161176	+	0.747859i	0.822623	+	0.568587i	$0.192510\pi$
$239$	−2.49172	+	11.5616i	−0.161176	+	0.747859i	−0.983799	+	0.179273i	$0.942626\pi$
$240$	2.14763	−	50.5569i	0.138629	−	3.26344i
$241$	6.85677	+	3.09945i	0.441683	+	0.199653i	0.620463	−	0.784236i	$-0.286945\pi$
$241$	6.85677	+	3.09945i	0.441683	+	0.199653i	−0.178780	+	0.983889i	$0.557215\pi$
$242$	−15.7985	+	4.11360i	−1.01556	+	0.264432i
$243$	−0.942877	−	0.333140i	−0.0604856	−	0.0213709i
$244$	54.0198	+	30.1773i	3.45826	+	1.93190i
$245$	4.42810	+	14.4593i	0.282901	+	0.923769i
$246$	−16.0248	−	26.0259i	−1.02170	−	1.65935i
$247$	−13.2019	−	17.8502i	−0.840019	−	1.13578i
$248$	24.7091	−	49.0075i	1.56903	−	3.11198i
$249$	−0.777011	−	0.882856i	−0.0492411	−	0.0559487i
$250$	−86.8005	+	39.2363i	−5.48974	+	2.48152i
$251$	−6.87680	−	11.1686i	−0.434060	−	0.704958i	0.558122	−	0.829759i	$-0.311522\pi$
$251$	−6.87680	−	11.1686i	−0.434060	−	0.704958i	−0.992182	+	0.124801i	$0.960171\pi$
$252$	−3.48707	+	16.1800i	−0.219665	+	1.01925i
$253$	0.222036	−	0.124037i	0.0139593	−	0.00779812i
$254$	13.4470	−	1.14451i	0.843743	−	0.0718131i
$255$	−2.40228	−	18.7598i	−0.150437	−	1.17478i
$256$	−2.78607	−	1.25938i	−0.174130	−	0.0787115i
$257$	1.42634	+	4.65748i	0.0889724	+	0.290525i	0.989554	−	0.144161i	$-0.0460484\pi$
$257$	1.42634	+	4.65748i	0.0889724	+	0.290525i	−0.900582	+	0.434687i	$0.856859\pi$
$258$	−15.4724	+	6.99397i	−0.963271	+	0.435426i
$259$	18.3361	+	1.56063i	1.13935	+	0.0969727i
$260$	4.60463	+	108.397i	0.285567	+	6.72247i
$261$	6.29740	−	4.25630i	0.389799	−	0.263458i
$262$	−34.8836			−2.15511
$263$	6.18186			0.381190			0.190595	−	0.981669i	$-0.438958\pi$
$263$	6.18186			0.381190			0.190595	+	0.981669i	$0.438958\pi$
$264$	−15.1110	+	10.2132i	−0.930017	+	0.628582i
$265$	−4.31918	−	0.740598i	−0.265325	−	0.0454946i
$266$	17.4038	+	34.5184i	1.06710	+	2.11646i
$267$	7.40495	+	10.0121i	0.453175	+	0.612733i
$268$	10.7228	−	49.7538i	0.654997	−	3.03920i
$269$	7.82342	+	6.31697i	0.477003	+	0.385153i	0.836477	−	0.548002i	$-0.184612\pi$
$269$	7.82342	+	6.31697i	0.477003	+	0.385153i	−0.359474	+	0.933155i	$0.617044\pi$
$270$	11.0451	+	2.87593i	0.672185	+	0.175023i
$271$	−6.51754	−	4.40509i	−0.395913	−	0.267590i	0.345800	−	0.938308i	$-0.387608\pi$
$271$	−6.51754	−	4.40509i	−0.395913	−	0.267590i	−0.741712	+	0.670718i	$0.765986\pi$
$272$	−50.4830	−	13.1447i	−3.06098	−	0.797017i
$273$	2.04698	−	15.9852i	0.123889	−	0.967465i
$274$	10.2097	+	4.61508i	0.616791	+	0.278807i
$275$	25.7212	+	14.3687i	1.55105	+	0.866468i
$276$	−0.388225	+	0.441109i	−0.0233684	+	0.0265517i
$277$	0.0947438	−	0.0908046i	0.00569261	−	0.00545592i	−0.689087	−	0.724678i	$-0.741988\pi$
$277$	0.0947438	−	0.0908046i	0.00569261	−	0.00545592i	0.694780	+	0.719223i	$0.255502\pi$
$278$	9.08315	−	5.07415i	0.544771	−	0.304327i
$279$	5.16857	+	4.17333i	0.309434	+	0.249851i
$280$	14.5860	−	113.905i	0.871683	−	6.80710i
$281$	2.01066	+	15.7015i	0.119946	+	0.936675i	0.934345	+	0.356370i	$0.115986\pi$
$281$	2.01066	+	15.7015i	0.119946	+	0.936675i	−0.814399	+	0.580305i	$0.802933\pi$
$282$	−2.55027	+	8.32751i	−0.151866	+	0.495896i
$283$	−18.6099	+	21.1449i	−1.10624	+	1.25694i	−0.142589	+	0.989782i	$0.545543\pi$
$283$	−18.6099	+	21.1449i	−1.10624	+	1.25694i	−0.963654	+	0.267154i	$0.913917\pi$
$284$	0.816962	+	2.03309i	0.0484778	+	0.120642i
$285$	17.4487	−	7.88732i	1.03357	−	0.467204i
$286$	22.7293	−	18.3526i	1.34401	−	1.08521i
$287$	−16.7570	−	33.2355i	−0.989135	−	1.96183i
$288$	8.89400	−	12.0255i	0.524084	−	0.708609i
$289$	−2.48839	−	0.211793i	−0.146376	−	0.0124584i
$290$	−67.4961	+	54.4993i	−3.96351	+	3.20031i
$291$	−0.110489	−	0.149390i	−0.00647695	−	0.00875742i
$292$	−49.0097	+	8.40357i	−2.86808	+	0.491781i
$293$	−9.14214	+	8.76204i	−0.534090	+	0.511884i	−0.909908	−	0.414810i	$-0.863848\pi$
$293$	−9.14214	+	8.76204i	−0.534090	+	0.511884i	0.375818	+	0.926693i	$0.377362\pi$
$294$	−2.75481	+	8.99539i	−0.160664	+	0.524622i
$295$	−3.98216	+	1.03687i	−0.231850	+	0.0603691i
$296$	−40.9021	−	22.8493i	−2.37739	−	1.32809i
$297$	−0.823115	−	2.04840i	−0.0477620	−	0.118860i
$298$	−40.6029	−	46.1338i	−2.35206	−	2.67246i
$299$	0.340217	−	0.460003i	0.0196752	−	0.0266027i
$300$	−67.0922	−	11.5041i	−3.87357	−	0.664191i
$301$	−19.4970	+	6.88872i	−1.12379	+	0.397059i
$302$	35.9357	−	24.2883i	2.06787	−	1.39764i
$303$	5.89381	−	2.08241i	0.338590	−	0.119632i
$304$	−2.24158	−	52.7685i	−0.128563	−	3.02648i
$305$	30.8986	−	41.7777i	1.76925	−	2.39218i
$306$	5.29714	−	10.5063i	0.302818	−	0.600603i
$307$	23.3449	−	4.00288i	1.33236	−	0.228457i	0.541629	−	0.840617i	$-0.317808\pi$
$307$	23.3449	−	4.00288i	1.33236	−	0.228457i	0.790733	+	0.612161i	$0.209700\pi$
$308$	−31.8991	+	17.8199i	−1.81762	+	1.01538i
$309$	−1.25269	−	1.20060i	−0.0712629	−	0.0683000i
$310$	−62.8180	−	42.4575i	−3.56782	−	2.41143i
$311$	−26.4261	−	17.8609i	−1.49849	−	1.01280i	−0.988264	−	0.152758i	$-0.951185\pi$
$311$	−26.4261	−	17.8609i	−1.49849	−	1.01280i	−0.510223	−	0.860042i	$-0.670437\pi$
$312$	−21.5122	+	34.9381i	−1.21789	+	1.97798i
$313$	−0.577341	−	4.50854i	−0.0326333	−	0.254838i	−0.999999	−	0.00145348i	$-0.999537\pi$
$313$	−0.577341	−	4.50854i	−0.0326333	−	0.254838i	0.967366	−	0.253384i	$-0.0815437\pi$
$314$	22.6743	−	5.90394i	1.27959	−	0.333178i
$315$	13.1054	+	4.63045i	0.738408	+	0.260896i
$316$	10.9340	−	35.7033i	0.615086	−	2.00847i
$317$	17.8477	−	1.51907i	1.00243	−	0.0853192i	0.427919	−	0.903817i	$-0.359247\pi$
$317$	17.8477	−	1.51907i	1.00243	−	0.0853192i	0.574509	+	0.818498i	$0.305193\pi$
$318$	−1.96824	−	1.88641i	−0.110373	−	0.105784i
$319$	16.2382	+	4.22810i	0.909165	+	0.236728i
$320$	−36.4429	+	59.1871i	−2.03722	+	3.30866i
$321$	−10.8376	+	0.922412i	−0.604893	+	0.0514840i
$322$	−0.719223	+	0.689320i	−0.0400808	+	0.0384143i
$323$	−4.15887	−	19.2972i	−0.231406	−	1.07373i
$324$	3.36977	+	3.82881i	0.187210	+	0.212711i
$325$	66.0401	+	5.62084i	3.66324	+	0.311788i
$326$	10.1843	−	25.3445i	0.564054	−	1.40370i
$327$	2.75549	+	0.472476i	0.152379	+	0.0261280i
$328$	4.02185	+	94.6775i	0.222070	+	5.22769i
$329$	−3.95461	+	9.84144i	−0.218025	+	0.542576i
$330$	11.3434	+	22.4983i	0.624434	+	1.23849i
$331$	−3.42632	+	6.79569i	−0.188327	+	0.373525i	−0.967340	−	0.253484i	$-0.918424\pi$
$331$	−3.42632	+	6.79569i	−0.188327	+	0.373525i	0.779012	+	0.627009i	$0.215721\pi$
$332$	1.26379	+	5.86400i	0.0693594	+	0.321829i
$333$	3.74658	−	4.25695i	0.205312	−	0.233279i
$334$	11.0507	+	3.90447i	0.604669	+	0.213643i
$335$	−40.2993	−	14.2387i	−2.20179	−	0.777941i
$336$	25.3288	−	28.7791i	1.38180	−	1.57003i
$337$	−2.77431	−	12.8728i	−0.151126	−	0.701229i	−0.988078	−	0.153952i	$-0.950800\pi$
$337$	−2.77431	−	12.8728i	−0.151126	−	0.701229i	0.836952	−	0.547276i	$-0.184335\pi$
$338$	13.9915	−	27.7505i	0.761039	−	1.50943i
$339$	−0.839882	−	1.66581i	−0.0456161	−	0.0904742i
$340$	−35.9678	+	89.5093i	−1.95063	+	4.85432i
$341$	0.622411	+	14.6520i	0.0337054	+	0.793452i
$342$	11.7413	+	2.01325i	0.634899	+	0.108864i
$343$	4.19786	−	10.4468i	0.226663	−	0.564073i
$344$	52.4560	+	4.46467i	2.82824	+	0.240719i
$345$	0.326018	+	0.370428i	0.0175522	+	0.0199432i
$346$	−0.115309	−	0.535035i	−0.00619905	−	0.0287637i
$347$	−4.30162	+	4.12277i	−0.230923	+	0.221322i	−0.798494	−	0.602002i	$-0.794370\pi$
$347$	−4.30162	+	4.12277i	−0.230923	+	0.221322i	0.567571	+	0.823324i	$0.307883\pi$
$348$	−38.6286	+	3.28778i	−2.07071	+	0.176244i
$349$	10.9117	−	17.7217i	0.584089	−	0.948621i	−0.415155	−	0.909750i	$-0.636273\pi$
$349$	10.9117	−	17.7217i	0.584089	−	0.948621i	0.999244	−	0.0388700i	$-0.0123758\pi$
$350$	−111.680	−	29.0793i	−5.96957	−	1.55436i
$351$	−3.58537	−	3.43630i	−0.191373	−	0.183416i
$352$	32.9003	−	2.80023i	1.75359	−	0.149253i
$353$	1.16426	−	3.80169i	0.0619671	−	0.202344i	−0.919816	−	0.392351i	$-0.871662\pi$
$353$	1.16426	−	3.80169i	0.0619671	−	0.202344i	0.981783	+	0.190007i	$0.0608511\pi$
$354$	−2.41375	−	0.852831i	−0.128289	−	0.0453275i
$355$	1.78063	−	0.463640i	0.0945061	−	0.0246075i
$356$	−8.06771	−	63.0019i	−0.427588	−	3.33909i
$357$	7.51276	−	12.2015i	0.397617	−	0.645772i
$358$	34.1261	+	23.0652i	1.80362	+	1.21904i
$359$	12.1187	+	8.19081i	0.639600	+	0.432294i	0.836377	−	0.548154i	$-0.184669\pi$
$359$	12.1187	+	8.19081i	0.639600	+	0.432294i	−0.196777	+	0.980448i	$0.563048\pi$
$360$	−25.5481	−	24.4858i	−1.34650	−	1.29052i
$361$	0.860976	−	0.480970i	0.0453145	−	0.0253142i
$362$	21.5992	−	3.70355i	1.13523	−	0.194655i
$363$	−2.75819	+	5.47054i	−0.144767	+	0.287129i
$364$	−48.8777	+	66.0870i	−2.56189	+	3.46390i
$365$	1.77223	+	41.7197i	0.0927628	+	2.18371i
$366$	30.4803	−	10.7694i	1.59323	−	0.562924i
$367$	9.95198	−	6.72636i	0.519489	−	0.351113i	−0.271999	−	0.962297i	$-0.587685\pi$
$367$	9.95198	−	6.72636i	0.519489	−	0.351113i	0.791489	+	0.611184i	$0.209306\pi$
$368$	1.28333	−	0.453431i	0.0668984	−	0.0236367i
$369$	−11.3050	−	1.93843i	−0.588514	−	0.100911i
$370$	−38.4869	+	52.0377i	−2.00084	+	2.70531i
$371$	−2.19349	−	2.49229i	−0.113880	−	0.129393i
$372$	−12.6335	−	31.4398i	−0.655019	−	1.63008i
$373$	−0.218200	−	0.121894i	−0.0112980	−	0.00631142i	0.482036	−	0.876152i	$-0.339898\pi$
$373$	−0.218200	−	0.121894i	−0.0112980	−	0.00631142i	−0.493334	+	0.869840i	$0.664222\pi$
$374$	25.1366	−	6.54507i	1.29978	−	0.338437i
$375$	−10.4678	+	34.1809i	−0.540554	+	1.76510i
$376$	19.4950	−	18.6845i	1.00538	−	0.963579i
$377$	37.2044	−	6.37934i	1.91613	−	0.328553i
$378$	5.14185	+	6.95224i	0.264468	+	0.357584i
$379$	−5.19132	+	4.19170i	−0.266660	+	0.215313i	−0.752257	−	0.658870i	$-0.771035\pi$
$379$	−5.19132	+	4.19170i	−0.266660	+	0.215313i	0.485597	+	0.874183i	$0.338602\pi$
$380$	−97.3154	−	8.28276i	−4.99218	−	0.424897i
$381$	3.01161	−	4.07197i	0.154289	−	0.208613i
$382$	4.72938	+	9.38017i	0.241976	+	0.479931i
$383$	−6.14541	+	4.96207i	−0.314016	+	0.253550i	−0.772303	−	0.635254i	$-0.780895\pi$
$383$	−6.14541	+	4.96207i	−0.314016	+	0.253550i	0.458288	+	0.888804i	$0.348463\pi$
$384$	−12.1442	+	5.48952i	−0.619730	+	0.280136i
$385$	11.4408	+	28.4716i	0.583078	+	1.45105i
$386$	−9.63352	+	10.9458i	−0.490333	+	0.557127i
$387$	−1.86591	+	6.09284i	−0.0948497	+	0.309717i
$388$	0.120378	+	0.940046i	0.00611125	+	0.0477236i
$389$	2.37153	−	18.5196i	0.120242	−	0.938983i	−0.813632	−	0.581380i	$-0.802513\pi$
$389$	2.37153	−	18.5196i	0.120242	−	0.938983i	0.933874	−	0.357603i	$-0.116406\pi$
$390$	44.1000	+	35.6082i	2.23309	+	1.80309i
$391$	0.444112	−	0.248096i	0.0224597	−	0.0125467i
$392$	21.0586	−	20.1830i	1.06362	−	1.01940i
$393$	−8.64896	+	9.82713i	−0.436282	+	0.495713i
$394$	−9.05026	−	5.05578i	−0.455946	−	0.254707i
$395$	−28.5733	−	12.9159i	−1.43768	−	0.649871i
$396$	−1.43020	+	11.1686i	−0.0718702	+	0.561245i
$397$	32.3580	+	8.42538i	1.62400	+	0.422858i	0.949081	−	0.315031i	$-0.102015\pi$
$397$	32.3580	+	8.42538i	1.62400	+	0.422858i	0.674923	+	0.737889i	$0.264177\pi$
$398$	24.9756	+	16.8806i	1.25191	+	0.846146i
$399$	14.0393	+	3.65556i	0.702845	+	0.183007i
$400$	122.674	+	99.0523i	6.13370	+	4.95262i
$401$	7.11301	−	33.0045i	0.355207	−	1.64817i	−0.348231	−	0.937409i	$-0.613218\pi$
$401$	7.11301	−	33.0045i	0.355207	−	1.64817i	0.703438	−	0.710757i	$-0.251647\pi$
$402$	−15.8112	−	21.3782i	−0.788592	−	1.06625i
$403$	14.8526	+	29.4584i	0.739862	+	1.46743i
$404$	−31.4240	−	5.38818i	−1.56340	−	0.268072i
$405$	3.54869	−	2.39850i	0.176336	−	0.119182i
$406$	−65.7255			−3.26190
$407$	12.5189			0.620540
$408$	−30.2247	+	20.4283i	−1.49635	+	1.01135i
$409$	0.536590	+	12.6317i	0.0265327	+	0.624600i	0.962301	+	0.271985i	$0.0876802\pi$
$409$	0.536590	+	12.6317i	0.0265327	+	0.624600i	−0.935769	+	0.352614i	$0.885293\pi$
$410$	130.440	+	11.1021i	6.44196	+	0.548292i
$411$	3.83150	−	1.73195i	0.188994	−	0.0854307i
$412$	2.59149	+	8.46211i	0.127674	+	0.416898i
$413$	−2.84083	−	1.28413i	−0.139788	−	0.0631881i
$414$	0.0389935	+	0.304506i	0.00191643	+	0.0149656i
$415$	5.01930	−	0.427205i	0.246388	−	0.0209707i
$416$	64.8474	−	36.2259i	3.17941	−	1.77612i
$417$	0.822607	−	3.81691i	0.0402833	−	0.186915i
$418$	13.7884	+	22.3938i	0.674414	+	1.09532i
$419$	14.2905	−	6.45971i	0.698137	−	0.315578i	−0.0314121	−	0.999507i	$-0.510000\pi$
$419$	14.2905	−	6.45971i	0.698137	−	0.315578i	0.729549	+	0.683929i	$0.239730\pi$
$420$	−46.8379	−	53.2181i	−2.28545	−	2.59678i
$421$	5.41192	−	10.7339i	0.263761	−	0.523138i	−0.721875	−	0.692023i	$-0.756719\pi$
$421$	5.41192	−	10.7339i	0.263761	−	0.523138i	0.985636	+	0.168885i	$0.0540168\pi$
$422$	−31.7453	−	42.9225i	−1.54534	−	2.08943i
$423$	1.71365	+	2.78315i	0.0833207	+	0.135321i
$424$	2.47517	+	8.08227i	0.120205	+	0.392510i
$425$	51.4471	+	28.7401i	2.49555	+	1.39410i
$426$	1.07931	+	0.381345i	0.0522929	+	0.0184762i
$427$	38.0978	−	9.91990i	1.84368	−	0.480057i
$428$	50.5521	+	22.8510i	2.44353	+	1.10454i
$429$	0.465296	−	10.9534i	0.0224647	−	0.528837i
$430$	15.3223	−	71.0957i	0.738906	−	3.42854i
$431$	−30.5372	+	5.23613i	−1.47093	+	0.252216i	−0.847972	−	0.530042i	$-0.822176\pi$
$431$	−30.5372	+	5.23613i	−1.47093	+	0.252216i	−0.622955	+	0.782257i	$0.714068\pi$
$432$	−2.48899	−	11.5490i	−0.119752	−	0.555649i
$433$	−10.1704	−	25.3101i	−0.488760	−	1.21633i	−0.945177	−	0.326560i	$-0.894111\pi$
$433$	−10.1704	−	25.3101i	−0.488760	−	1.21633i	0.456416	−	0.889766i	$-0.349133\pi$
$434$	−16.8208	−	54.9255i	−0.807422	−	2.63651i
$435$	−1.38173	+	32.5269i	−0.0662487	+	1.55955i
$436$	−11.0944	−	8.95810i	−0.531325	−	0.429015i
$437$	0.371843	+	0.356382i	0.0177876	+	0.0170481i
$438$	−13.6205	+	22.1211i	−0.650811	+	1.05699i
$439$	1.28484	−	10.0335i	0.0613221	−	0.478873i	−0.931907	−	0.362698i	$-0.881856\pi$
$439$	1.28484	−	10.0335i	0.0613221	−	0.478873i	0.993229	−	0.116175i	$-0.0370633\pi$
$440$	3.31554	−	78.0503i	0.158062	−	3.72090i
$441$	1.85109	+	3.00636i	0.0881472	+	0.143160i
$442$	45.4627	−	36.7086i	2.16244	−	1.74605i
$443$	−8.08249	+	20.1141i	−0.384011	+	0.955648i	0.603395	+	0.797442i	$0.293814\pi$
$443$	−8.08249	+	20.1141i	−0.384011	+	0.955648i	−0.987406	+	0.158206i	$0.949429\pi$
$444$	−27.2719	+	9.63579i	−1.29427	+	0.457294i
$445$	−53.3388			−2.52850
$446$	−39.0179	−	7.81128i	−1.84755	−	0.369875i
$447$	−23.0635			−1.09086
$448$	−49.6520	+	17.5432i	−2.34584	+	0.828838i
$449$	14.2271	−	35.4055i	0.671418	−	1.67089i	−0.0680363	−	0.997683i	$-0.521673\pi$
$449$	14.2271	−	35.4055i	0.671418	−	1.67089i	0.739455	−	0.673206i	$-0.235083\pi$
$450$	−27.6691	+	22.3413i	−1.30434	+	1.05318i
$451$	−13.2760	−	21.5616i	−0.625142	−	1.01529i
$452$	−0.403840	+	9.50671i	−0.0189950	+	0.447158i
$453$	2.06752	−	16.1455i	0.0971404	−	0.758583i
$454$	−6.30895	+	10.2464i	−0.296094	+	0.480887i
$455$	49.8345	+	47.7625i	2.33628	+	2.23914i
$456$	−28.7370	−	23.2035i	−1.34573	−	1.08660i
$457$	−1.33220	+	31.3611i	−0.0623178	+	1.46701i	0.647200	+	0.762321i	$0.275940\pi$
$457$	−1.33220	+	31.3611i	−0.0623178	+	1.46701i	−0.709517	+	0.704688i	$0.751087\pi$
$458$	16.5995	+	54.2031i	0.775644	+	2.53274i
$459$	−1.64638	−	4.09717i	−0.0768464	−	0.191240i
$460$	−0.530260	−	2.46041i	−0.0247235	−	0.114717i
$461$	−34.4222	+	5.90228i	−1.60320	+	0.274897i	−0.899934	−	0.436027i	$-0.856385\pi$
$461$	−34.4222	+	5.90228i	−1.60320	+	0.274897i	−0.703269	+	0.710923i	$0.748277\pi$
$462$	−4.02171	+	18.6608i	−0.187107	+	0.868179i
$463$	0.972245	−	22.8874i	0.0451841	−	1.06367i	−0.823192	−	0.567763i	$-0.807809\pi$
$463$	0.972245	−	22.8874i	0.0451841	−	1.06367i	0.868376	−	0.495906i	$-0.165164\pi$
$464$	81.8262	+	36.9878i	3.79868	+	1.71711i
$465$	−27.5358	+	7.16976i	−1.27694	+	0.332489i
$466$	23.2356	+	8.20966i	1.07637	+	0.380305i
$467$	−23.5338	−	13.1468i	−1.08901	−	0.608359i	−0.163296	−	0.986577i	$-0.552213\pi$
$467$	−23.5338	−	13.1468i	−1.08901	−	0.608359i	−0.925717	+	0.378218i	$0.876537\pi$
$468$	7.41722	+	24.2198i	0.342861	+	1.11956i
$469$	−16.9779	−	27.5738i	−0.783965	−	1.27324i
$470$	−22.1820	−	29.9921i	−1.02318	−	1.38343i
$471$	3.95862	−	7.85145i	0.182403	−	0.361776i
$472$	5.24392	+	5.95825i	0.241371	+	0.274251i
$473$	−12.8184	+	5.79427i	−0.589389	+	0.266421i
$474$	−10.2280	−	16.6114i	−0.469789	−	0.762986i
$475$	−12.5701	+	58.3255i	−0.576756	+	2.67616i
$476$	−63.8040	+	35.6430i	−2.92445	+	1.63370i
$477$	−1.01943	+	0.0867659i	−0.0466763	+	0.00397274i
$478$	−4.00301	−	31.2601i	−0.183093	−	1.42980i
$479$	−28.3545	−	12.8170i	−1.29555	−	0.585625i	−0.358079	−	0.933691i	$-0.616568\pi$
$479$	−28.3545	−	12.8170i	−1.29555	−	0.585625i	−0.937470	+	0.348067i	$0.886838\pi$
$480$	18.7596	+	61.2566i	0.856255	+	2.79597i
$481$	25.6625	−	11.6002i	1.17011	−	0.528922i
$482$	−19.9788	−	1.70045i	−0.910009	−	0.0774532i
$483$	0.0158671	+	0.373523i	0.000721976	+	0.0169959i
$484$	25.8896	−	17.4983i	1.17680	−	0.795378i
$485$	0.795864			0.0361383
$486$	2.66468			0.120872
$487$	−0.200982	+	0.135840i	−0.00910737	+	0.00615551i	−0.564520	−	0.825419i	$-0.690939\pi$
$487$	−0.200982	+	0.135840i	−0.00910737	+	0.00615551i	0.555413	+	0.831575i	$0.312560\pi$
$488$	−98.7878	−	16.9389i	−4.47191	−	0.766786i
$489$	−4.61480	−	9.15290i	−0.208688	−	0.413909i
$490$	−23.9611	−	32.3975i	−1.08245	−	1.46357i
$491$	−6.48855	+	30.1070i	−0.292824	+	1.35871i	0.556504	+	0.830845i	$0.312142\pi$
$491$	−6.48855	+	30.1070i	−0.292824	+	1.35871i	−0.849329	+	0.527864i	$0.822993\pi$
$492$	45.5171	+	36.7525i	2.05207	+	1.65693i
$493$	32.4794	+	8.45697i	1.46280	+	0.380883i
$494$	49.0152	+	33.1285i	2.20530	+	1.49052i
$495$	9.15051	+	2.38261i	0.411285	+	0.107090i
$496$	−9.96866	+	77.8467i	−0.447606	+	3.49542i
$497$	1.27028	+	0.574204i	0.0569799	+	0.0257566i
$498$	2.73593	+	1.52838i	0.122600	+	0.0684885i
$499$	22.5752	−	25.6504i	1.01061	−	1.14827i	0.0216950	−	0.999765i	$-0.493094\pi$
$499$	22.5752	−	25.6504i	1.01061	−	1.14827i	0.988911	−	0.148507i	$-0.0474468\pi$
$500$	131.636	−	126.163i	5.88693	−	5.64217i
$501$	3.83984	−	2.14506i	0.171551	−	0.0958342i
$502$	27.1922	+	21.9562i	1.21365	+	0.979952i
$503$	4.09928	−	32.0119i	0.182778	−	1.42734i	−0.597481	−	0.801883i	$-0.703832\pi$
$503$	4.09928	−	32.0119i	0.182778	−	1.42734i	0.780259	−	0.625456i	$-0.215087\pi$
$504$	−3.40539	−	26.5932i	−0.151688	−	1.18455i
$505$	−7.84001	+	25.6003i	−0.348876	+	1.13920i
$506$	−0.447748	+	0.508741i	−0.0199048	+	0.0226163i
$507$	−4.34864	−	10.8220i	−0.193130	−	0.480622i
$508$	−23.5391	+	10.6403i	−1.04438	+	0.472089i
$509$	19.9650	−	16.1206i	0.884934	−	0.714534i	−0.0742735	−	0.997238i	$-0.523664\pi$
$509$	19.9650	−	16.1206i	0.884934	−	0.714534i	0.959207	+	0.282704i	$0.0912314\pi$
$510$	22.6889	+	45.0007i	1.00468	+	1.99266i
$511$	−18.8121	+	25.4356i	−0.832197	+	1.12520i
$512$	−18.4406	−	1.56953i	−0.814969	−	0.0693640i
$513$	3.47828	−	2.80852i	0.153570	−	0.123999i
$514$	−7.71810	−	10.4356i	−0.340431	−	0.460293i
$515$	7.32505	−	1.25601i	0.322780	−	0.0553462i
$516$	23.4644	−	22.4888i	1.03296	−	0.990016i
$517$	−2.11281	+	6.89905i	−0.0929213	+	0.303420i
$518$	−47.4541	+	12.3561i	−2.08501	+	0.542895i
$519$	−0.179316	−	0.100172i	−0.00787108	−	0.00439705i
$520$	−65.5258	−	163.067i	−2.87350	−	7.15097i
$521$	5.01065	+	5.69320i	0.219521	+	0.249424i	0.850001	−	0.526782i	$-0.176601\pi$
$521$	5.01065	+	5.69320i	0.219521	+	0.249424i	−0.630480	+	0.776205i	$0.717142\pi$
$522$	−12.0436	+	16.2841i	−0.527135	+	0.712734i
$523$	19.7858	+	3.39261i	0.865171	+	0.148348i	0.584439	−	0.811438i	$-0.301315\pi$
$523$	19.7858	+	3.39261i	0.865171	+	0.148348i	0.280732	+	0.959786i	$0.409423\pi$
$524$	62.9570	−	22.2441i	2.75029	−	0.971740i
$525$	−35.8818	+	24.2519i	−1.56601	+	1.05844i
$526$	−15.5317	+	5.48770i	−0.677214	+	0.239275i
$527$	1.24493	+	29.3067i	0.0542302	+	1.27662i
$528$	15.5085	−	20.9688i	0.674920	−	0.912552i
$529$	10.3487	−	20.5254i	0.449944	−	0.892411i
$530$	11.5092	−	1.97346i	0.499929	−	0.0857214i
$531$	−0.838713	+	0.468533i	−0.0363970	+	0.0203326i
$532$	−53.4213	−	51.2002i	−2.31611	−	2.21981i
$533$	−47.1936	−	31.8973i	−2.04418	−	1.38162i
$534$	−27.4925	−	18.5817i	−1.18972	−	0.804109i
$535$	24.4262	−	39.6706i	1.05604	−	1.71511i
$536$	10.4716	+	81.7742i	0.452304	+	3.53211i
$537$	14.9589	−	3.89500i	0.645525	−	0.168082i
$538$	−25.2637	−	8.92624i	−1.08920	−	0.384837i
$539$	−2.28226	+	7.45237i	−0.0983040	+	0.320996i
$540$	−21.7679	+	1.85272i	−0.936741	+	0.0797284i
$541$	−12.9843	−	12.4444i	−0.558237	−	0.535026i	0.359017	−	0.933331i	$-0.383112\pi$
$541$	−12.9843	−	12.4444i	−0.558237	−	0.535026i	−0.917253	+	0.398305i	$0.869599\pi$
$542$	20.2855	+	5.28194i	0.871338	+	0.226879i
$543$	4.31193	−	7.00301i	0.185042	−	0.300528i
$544$	65.8065	−	5.60096i	2.82143	−	0.240139i
$545$	−8.64516	+	8.28571i	−0.370318	+	0.354921i
$546$	9.04722	+	41.9792i	0.387185	+	1.79655i
$547$	−7.40224	−	8.41057i	−0.316497	−	0.359610i	0.570572	−	0.821248i	$-0.306722\pi$
$547$	−7.40224	−	8.41057i	−0.316497	−	0.359610i	−0.887069	+	0.461637i	$0.847262\pi$
$548$	−21.3692	−	1.81878i	−0.912845	−	0.0776945i
$549$	4.52335	−	11.2568i	0.193052	−	0.480429i
$550$	−77.3789	−	13.2680i	−3.29945	−	0.565747i
$551$	1.44217	+	33.9498i	0.0614385	+	1.44631i
$552$	0.354896	−	0.883193i	0.0151054	−	0.0375912i
$553$	−10.6954	−	21.2130i	−0.454814	−	0.902069i
$554$	−0.157432	+	0.312248i	−0.00668866	+	0.0132662i
$555$	5.11730	+	23.7443i	0.217217	+	1.00789i
$556$	−13.1574	+	14.9498i	−0.558000	+	0.634011i
$557$	−0.398190	−	0.140690i	−0.0168719	−	0.00596121i	0.324691	−	0.945820i	$-0.394740\pi$
$557$	−0.398190	−	0.140690i	−0.0168719	−	0.00596121i	−0.341562	+	0.939859i	$0.610956\pi$
$558$	−16.6905	−	5.89714i	−0.706567	−	0.249646i
$559$	−20.9073	+	23.7553i	−0.884283	+	1.00474i
$560$	34.5955	+	160.524i	1.46193	+	6.78336i
$561$	4.38850	−	8.70407i	0.185283	−	0.367486i
$562$	−18.9901	−	37.6646i	−0.801050	−	1.58879i
$563$	−14.0880	+	35.0594i	−0.593740	+	1.47758i	0.264528	+	0.964378i	$0.414784\pi$
$563$	−14.0880	+	35.0594i	−0.593740	+	1.47758i	−0.858268	+	0.513201i	$0.828459\pi$
$564$	−0.707518	−	16.6555i	−0.0297919	−	0.701324i
$565$	7.87567	+	1.35042i	0.331332	+	0.0568126i
$566$	27.9861	−	69.6461i	1.17634	−	2.92744i
$567$	3.23339	+	0.275202i	0.135790	+	0.0115574i
$568$	−2.34483	−	2.66425i	−0.0983869	−	0.111789i
$569$	−3.03402	−	14.0779i	−0.127193	−	0.590176i	−0.995550	−	0.0942368i	$-0.969959\pi$
$569$	−3.03402	−	14.0779i	−0.127193	−	0.590176i	0.868357	−	0.495939i	$-0.165176\pi$
$570$	−36.8376	+	35.3060i	−1.54296	+	1.47881i
$571$	8.11447	−	0.690643i	0.339580	−	0.0289025i	0.0862245	−	0.996276i	$-0.472520\pi$
$571$	8.11447	−	0.690643i	0.339580	−	0.0289025i	0.253356	+	0.967373i	$0.418466\pi$
$572$	−29.3184	+	47.6162i	−1.22587	+	1.99093i
$573$	3.81510	+	0.993376i	0.159378	+	0.0414989i
$574$	71.6049	+	68.6277i	2.98873	+	2.86447i
$575$	−1.53203	+	0.130395i	−0.0638901	+	0.00543785i
$576$	−4.75183	+	15.5164i	−0.197993	+	0.646515i
$577$	30.9082	+	10.9206i	1.28673	+	0.454629i	0.886900	−	0.461962i	$-0.152854\pi$
$577$	30.9082	+	10.9206i	1.28673	+	0.454629i	0.399826	+	0.916591i	$0.369070\pi$
$578$	6.43999	−	1.67684i	0.267868	−	0.0697475i
$579$	0.695052	+	5.42776i	0.0288854	+	0.225570i
$580$	87.0629	−	141.399i	3.61509	−	5.87128i
$581$	3.16201	+	2.13714i	0.131182	+	0.0886636i
$582$	0.410214	+	0.277256i	0.0170039	+	0.0114926i
$583$	−1.63062	−	1.56282i	−0.0675334	−	0.0647255i
$584$	70.3169	−	39.2814i	2.90973	−	1.62547i
$585$	20.9653	−	3.59487i	0.866810	−	0.148630i
$586$	15.1912	−	30.1299i	0.627541	−	1.24465i
$587$	−4.34404	+	5.87353i	−0.179298	+	0.242427i	−0.884456	−	0.466623i	$-0.845470\pi$
$587$	−4.34404	+	5.87353i	−0.179298	+	0.242427i	0.705158	+	0.709050i	$0.250876\pi$
$588$	−0.764263	−	17.9913i	−0.0315177	−	0.741950i
$589$	−28.0021	+	9.89379i	−1.15381	+	0.407666i
$590$	9.08458	−	6.14011i	0.374006	−	0.252784i
$591$	−3.66818	+	1.29605i	−0.150889	+	0.0533124i
$592$	66.0323	+	11.3224i	2.71391	+	0.465347i
$593$	15.4633	−	20.9078i	0.635003	−	0.858581i	−0.362293	−	0.932064i	$-0.618006\pi$
$593$	15.4633	−	20.9078i	0.635003	−	0.858581i	0.997296	+	0.0734834i	$0.0234116\pi$
$594$	3.88643	+	4.41584i	0.159462	+	0.181184i
$595$	22.8837	+	56.9483i	0.938140	+	2.33465i
$596$	102.697	+	57.3701i	4.20664	+	2.34997i
$597$	10.9479	−	2.85060i	0.448066	−	0.116667i
$598$	−0.446432	+	1.45775i	−0.0182560	+	0.0596120i
$599$	1.56696	−	1.50181i	0.0640244	−	0.0613624i	−0.659246	−	0.751927i	$-0.729124\pi$
$599$	1.56696	−	1.50181i	0.0640244	−	0.0613624i	0.723271	+	0.690565i	$0.242638\pi$
$600$	108.677	−	18.6345i	4.43670	−	0.760749i
$601$	−25.9242	−	35.0518i	−1.05747	−	1.42979i	−0.896613	−	0.442815i	$-0.853980\pi$
$601$	−25.9242	−	35.0518i	−1.05747	−	1.42979i	−0.160856	−	0.986978i	$-0.551425\pi$
$602$	42.8702	−	34.6153i	1.74726	−	1.41081i
$603$	−9.94270	−	0.846249i	−0.404898	−	0.0344619i
$604$	−49.3681	+	66.7501i	−2.00876	+	2.71602i
$605$	−11.8139	−	23.4316i	−0.480305	−	0.952629i
$606$	−12.9594	+	10.4640i	−0.526439	+	0.425070i
$607$	28.8622	−	13.0465i	1.17148	−	0.529543i	0.270211	−	0.962801i	$-0.412906\pi$
$607$	28.8622	−	13.0465i	1.17148	−	0.529543i	0.901270	+	0.433258i	$0.142636\pi$
$608$	24.9319	+	62.0454i	1.01112	+	2.51627i
$609$	−16.2958	+	18.5157i	−0.660341	+	0.750293i
$610$	−40.5452	+	132.394i	−1.64163	+	5.36047i
$611$	2.06170	+	16.1001i	0.0834073	+	0.651340i
$612$	−2.86066	+	22.3393i	−0.115635	+	0.903012i
$613$	−17.3919	−	14.0430i	−0.702451	−	0.567190i	0.209341	−	0.977843i	$-0.432868\pi$
$613$	−17.3919	−	14.0430i	−0.702451	−	0.567190i	−0.911792	+	0.410653i	$0.865301\pi$
$614$	−55.0998	+	30.7806i	−2.22365	+	1.24220i
$615$	35.4686	−	33.9939i	1.43023	−	1.37077i
$616$	39.1029	−	44.4295i	1.57550	−	1.79011i
$617$	7.29929	+	4.07763i	0.293858	+	0.164159i	0.627667	−	0.778482i	$-0.284010\pi$
$617$	7.29929	+	4.07763i	0.293858	+	0.164159i	−0.333809	+	0.942641i	$0.608334\pi$
$618$	4.21312	+	1.90445i	0.169477	+	0.0766082i
$619$	−5.46668	+	42.6901i	−0.219724	+	1.71586i	0.387956	+	0.921678i	$0.373181\pi$
$619$	−5.46668	+	42.6901i	−0.219724	+	1.71586i	−0.607680	+	0.794182i	$0.707900\pi$
$620$	140.446	+	36.5694i	5.64046	+	1.46866i
$621$	0.0954510	+	0.0645136i	0.00383032	+	0.00258884i
$622$	82.2499	+	21.4162i	3.29792	+	0.858712i
$623$	−31.4411	−	25.3869i	−1.25966	−	1.01711i
$624$	12.3608	−	57.3543i	0.494828	−	2.29601i
$625$	−51.3680	−	69.4542i	−2.05472	−	2.77817i
$626$	5.45283	+	10.8150i	0.217939	+	0.432256i
$627$	9.72729	+	1.66791i	0.388470	+	0.0666100i
$628$	−37.1574	+	25.1140i	−1.48274	+	1.00216i
$629$	25.0401			0.998414
$630$	−37.0374			−1.47561
$631$	−33.4981	+	22.6408i	−1.33354	+	0.901314i	−0.999154	−	0.0411228i	$-0.986906\pi$
$631$	−33.4981	+	22.6408i	−1.33354	+	0.901314i	−0.334384	+	0.942437i	$0.608528\pi$
$632$	2.56700	+	60.4292i	0.102110	+	2.40374i
$633$	−19.9627	−	1.69907i	−0.793445	−	0.0675321i
$634$	−43.4933	+	19.6602i	−1.72734	+	0.780806i
$635$	6.35222	+	20.7422i	0.252080	+	0.823128i
$636$	4.75514	+	2.14946i	0.188554	+	0.0852316i
$637$	2.22705	+	17.3914i	0.0882389	+	0.689070i
$638$	−44.5512	+	3.79187i	−1.76380	+	0.150121i
$639$	0.375032	−	0.209506i	0.0148360	−	0.00828791i
$640$	12.0263	−	55.8024i	0.475383	−	2.20579i
$641$	17.5645	+	28.5266i	0.693756	+	1.12673i	0.985408	+	0.170207i	$0.0544438\pi$
$641$	17.5645	+	28.5266i	0.693756	+	1.12673i	−0.291652	+	0.956525i	$0.594205\pi$
$642$	26.4101	−	11.9381i	1.04232	−	0.471160i
$643$	15.1853	+	17.2539i	0.598851	+	0.680427i	0.968577	−	0.248714i	$-0.0800078\pi$
$643$	15.1853	+	17.2539i	0.598851	+	0.680427i	−0.369726	+	0.929141i	$0.620548\pi$
$644$	0.858481	−	1.70269i	0.0338289	−	0.0670956i
$645$	−16.2295	−	21.9438i	−0.639038	−	0.864036i
$646$	27.5793	+	44.7917i	1.08509	+	1.76231i
$647$	10.3241	+	33.7117i	0.405882	+	1.32534i	0.892231	+	0.451579i	$0.149139\pi$
$647$	10.3241	+	33.7117i	0.405882	+	1.32534i	−0.486349	+	0.873765i	$0.661672\pi$
$648$	−7.21270	−	4.02926i	−0.283342	−	0.158284i
$649$	−1.99971	−	0.706541i	−0.0784953	−	0.0277342i
$650$	−170.913	+	44.5023i	−6.70376	+	1.74552i
$651$	−19.6437	−	8.87952i	−0.769898	−	0.348016i
$652$	−2.21893	+	52.2354i	−0.0869001	+	2.04570i
$653$	−7.17774	+	33.3048i	−0.280887	+	1.30332i	0.588223	+	0.808699i	$0.299828\pi$
$653$	−7.17774	+	33.3048i	−0.280887	+	1.30332i	−0.869110	+	0.494620i	$0.835307\pi$
$654$	−7.34249	+	1.25900i	−0.287114	+	0.0492307i
$655$	−11.8132	−	54.8136i	−0.461581	−	2.14174i
$656$	−50.5248	−	125.736i	−1.97266	−	4.90916i
$657$	2.85474	+	9.32171i	0.111374	+	0.363674i
$658$	1.19948	−	28.2368i	0.0467608	−	1.10079i
$659$	−20.3896	−	16.4635i	−0.794266	−	0.641325i	0.143085	−	0.989710i	$-0.454298\pi$
$659$	−20.3896	−	16.4635i	−0.794266	−	0.641325i	−0.937351	+	0.348385i	$0.886730\pi$
$660$	−34.8188	−	33.3711i	−1.35532	−	1.29897i
$661$	−3.31227	+	5.37946i	−0.128832	+	0.209237i	−0.909494	−	0.415717i	$-0.863531\pi$
$661$	−3.31227	+	5.37946i	−0.128832	+	0.209237i	0.780662	+	0.624954i	$0.214882\pi$
$662$	2.57589	−	20.1155i	0.100115	−	0.781811i
$663$	0.930677	−	21.9089i	0.0361445	−	0.850870i
$664$	−5.09451	−	8.27400i	−0.197705	−	0.321094i
$665$	−48.3461	+	39.0367i	−1.87478	+	1.51378i
$666$	−5.63422	+	14.0213i	−0.218322	+	0.543314i
$667$	−0.825661	+	0.291725i	−0.0319697	+	0.0112956i
$668$	−22.4339			−0.867993
$669$	−11.8746	+	9.05511i	−0.459097	+	0.350091i
$670$	113.890			4.39997
$671$	25.2518	−	8.92204i	0.974837	−	0.344432i
$672$	−18.0974	+	45.0370i	−0.698121	+	1.73734i
$673$	25.6923	−	20.7451i	0.990365	−	0.799664i	0.0106259	−	0.999944i	$-0.496618\pi$
$673$	25.6923	−	20.7451i	0.990365	−	0.799664i	0.979739	+	0.200280i	$0.0641852\pi$
$674$	18.3977	+	29.8798i	0.708653	+	1.15093i
$675$	−0.566421	+	13.3340i	−0.0218016	+	0.513226i
$676$	−7.55595	+	59.0055i	−0.290613	+	2.26944i
$677$	−25.9151	+	42.0888i	−0.995999	+	1.61761i	−0.231654	+	0.972798i	$0.574414\pi$
$677$	−25.9151	+	42.0888i	−0.995999	+	1.61761i	−0.764345	+	0.644807i	$0.776938\pi$
$678$	3.58892	+	3.43971i	0.137832	+	0.132101i
$679$	0.469130	+	0.378796i	0.0180036	+	0.0145369i
$680$	6.63168	−	156.115i	0.254313	−	5.98673i
$681$	1.32230	+	4.31778i	0.0506708	+	0.165458i
$682$	−14.5705	−	36.2602i	−0.557935	−	1.38847i
$683$	−9.30813	−	43.1899i	−0.356166	−	1.65261i	−0.700415	−	0.713736i	$-0.747002\pi$
$683$	−9.30813	−	43.1899i	−0.356166	−	1.65261i	0.344250	−	0.938878i	$-0.388133\pi$
$684$	−22.4743	+	3.85360i	−0.859326	+	0.147346i
$685$	−3.79432	+	17.6057i	−0.144974	+	0.672680i
$686$	−1.27326	+	29.9736i	−0.0486135	+	1.14440i
$687$	19.3853	+	8.76272i	0.739596	+	0.334319i
$688$	−72.8523	+	18.9693i	−2.77747	+	0.723196i
$689$	−4.79073	−	1.69267i	−0.182512	−	0.0644857i
$690$	−1.14794	−	0.641279i	−0.0437014	−	0.0244131i
$691$	−7.58923	−	24.7814i	−0.288708	−	0.942730i	−0.976261	−	0.216596i	$-0.930504\pi$
$691$	−7.58923	−	24.7814i	−0.288708	−	0.942730i	0.687553	−	0.726134i	$-0.258685\pi$
$692$	0.549282	+	0.892091i	0.0208806	+	0.0339122i
$693$	4.25984	+	5.75969i	0.161818	+	0.218792i
$694$	7.14785	−	14.1769i	0.271329	−	0.538148i
$695$	11.0492	+	12.5543i	0.419119	+	0.476211i
$696$	57.2226	−	25.8662i	2.16902	−	0.980457i
$697$	−26.5544	−	43.1270i	−1.00582	−	1.63355i
$698$	−11.6835	+	54.2115i	−0.442226	+	2.05194i
$699$	8.07375	−	4.51027i	0.305377	−	0.170594i
$700$	220.101	−	18.7334i	8.31905	−	0.708055i
$701$	5.37277	+	41.9568i	0.202927	+	1.58469i	0.698171	+	0.715931i	$0.253998\pi$
$701$	5.37277	+	41.9568i	0.202927	+	1.58469i	−0.495244	+	0.868754i	$0.664921\pi$
$702$	12.0585	+	5.45081i	0.455121	+	0.205727i
$703$	7.42366	+	24.2408i	0.279989	+	0.914259i
$704$	−32.6439	+	14.7560i	−1.23031	+	0.556137i
$705$	−13.9489	−	1.18723i	−0.525347	−	0.0447136i
$706$	0.449651	+	10.5851i	0.0169228	+	0.398377i
$707$	−16.8060	+	11.3589i	−0.632054	+	0.427194i
$708$	4.90010			0.184157
$709$	−46.0452			−1.72926			−0.864631	−	0.502407i	$-0.832448\pi$
$709$	−46.0452			−1.72926			−0.864631	+	0.502407i	$0.832448\pi$
$710$	−4.06219	+	2.74556i	−0.152451	+	0.103039i
$711$	−7.21555	−	1.23723i	−0.270604	−	0.0463997i
$712$	46.3189	+	91.8681i	1.73587	+	3.44290i
$713$	−0.455096	−	0.615330i	−0.0170435	−	0.0230443i
$714$	−8.04415	+	37.3250i	−0.301045	+	1.39685i
$715$	36.5353	+	29.5002i	1.36634	+	1.10324i
$716$	−76.2980	−	19.8665i	−2.85139	−	0.742444i
$717$	−9.79885	−	6.62287i	−0.365945	−	0.247336i
$718$	−37.7188	−	9.82122i	−1.40765	−	0.366525i
$719$	0.476971	−	3.72473i	0.0177880	−	0.138909i	−0.980572	−	0.196161i	$-0.937153\pi$
$719$	0.476971	−	3.72473i	0.0177880	−	0.138909i	0.998360	+	0.0572515i	$0.0182337\pi$
$720$	46.1105	+	20.8432i	1.71844	+	0.776782i
$721$	4.91563	+	2.74603i	0.183067	+	0.102268i
$722$	−1.73621	+	1.97272i	−0.0646150	+	0.0734169i
$723$	−5.43254	+	5.20667i	−0.202038	+	0.193638i
$724$	−36.6201	+	20.4572i	−1.36098	+	0.760287i
$725$	−78.9251	−	63.7275i	−2.93120	−	2.36678i
$726$	2.07360	−	16.1930i	0.0769584	−	0.600979i
$727$	−1.33975	−	10.4623i	−0.0496884	−	0.388024i	−0.997586	−	0.0694475i	$-0.977876\pi$
$727$	−1.33975	−	10.4623i	−0.0496884	−	0.388024i	0.947897	−	0.318576i	$-0.103205\pi$
$728$	38.9879	−	127.309i	1.44499	−	4.71838i
$729$	0.660675	−	0.750672i	0.0244694	−	0.0278027i
$730$	−41.4877	−	103.246i	−1.53553	−	3.82131i
$731$	−25.6390	+	11.5896i	−0.948294	+	0.428656i
$732$	−48.1428	+	38.8726i	−1.77941	+	1.43677i
$733$	4.00712	+	7.94765i	0.148006	+	0.293553i	0.954783	−	0.297303i	$-0.0960872\pi$
$733$	4.00712	+	7.94765i	0.148006	+	0.293553i	−0.806777	+	0.590856i	$0.798790\pi$
$734$	−19.0329	+	25.7342i	−0.702518	+	0.949867i
$735$	−15.0677	−	1.28245i	−0.555779	−	0.0473037i
$736$	−1.34070	+	1.08254i	−0.0494188	+	0.0399029i
$737$	−13.0990	−	17.7111i	−0.482510	−	0.652396i
$738$	30.1241	−	5.16530i	1.10888	−	0.190137i
$739$	17.6284	−	16.8954i	0.648471	−	0.621509i	−0.293997	−	0.955806i	$-0.594985\pi$
$739$	17.6284	−	16.8954i	0.648471	−	0.621509i	0.942468	+	0.334297i	$0.108499\pi$
$740$	36.2774	−	118.458i	1.33358	−	4.35461i
$741$	21.4854	−	5.59437i	0.789287	−	0.205514i
$742$	7.72350	+	4.31461i	0.283539	+	0.158394i
$743$	−9.51155	−	23.6704i	−0.348945	−	0.868383i	−0.994507	−	0.104675i	$-0.966620\pi$
$743$	−9.51155	−	23.6704i	−0.348945	−	0.868383i	0.645562	−	0.763708i	$-0.276623\pi$
$744$	36.2606	+	41.2000i	1.32938	+	1.51047i
$745$	58.7414	−	79.4236i	2.15212	−	2.90986i
$746$	0.656425	+	0.112555i	0.0240334	+	0.00412095i
$747$	1.10891	−	0.391802i	0.0405728	−	0.0143353i
$748$	−41.1924	+	27.8412i	−1.50614	+	1.01798i
$749$	33.2797	−	11.7585i	1.21601	−	0.429645i
$750$	−4.04280	−	95.1707i	−0.147622	−	3.47514i
$751$	22.6602	−	30.6385i	0.826881	−	1.11802i	−0.164419	−	0.986391i	$-0.552575\pi$
$751$	22.6602	−	30.6385i	0.826881	−	1.11802i	0.991299	−	0.131626i	$-0.0420198\pi$
$752$	−17.3839	+	34.4789i	−0.633926	+	1.25732i
$753$	12.9273	−	2.21661i	0.471097	−	0.0807777i
$754$	−87.8118	+	49.0546i	−3.19792	+	1.78646i
$755$	50.3345	+	48.2417i	1.83186	+	1.75570i
$756$	−13.7131	−	9.26844i	−0.498741	−	0.337090i
$757$	−14.2608	−	9.63860i	−0.518316	−	0.350321i	0.272716	−	0.962094i	$-0.412078\pi$
$757$	−14.2608	−	9.63860i	−0.518316	−	0.350321i	−0.791033	+	0.611774i	$0.790456\pi$
$758$	9.32200	−	15.1399i	0.338590	−	0.549905i
$759$	0.0323048	+	0.252273i	0.00117259	+	0.00915691i
$760$	153.098	−	39.8635i	5.55343	−	1.44600i
$761$	18.3183	+	6.47226i	0.664037	+	0.234619i	0.643821	−	0.765176i	$-0.277348\pi$
$761$	18.3183	+	6.47226i	0.664037	+	0.234619i	0.0202164	+	0.999796i	$0.493564\pi$
$762$	−3.95184	+	12.9041i	−0.143160	+	0.467466i
$763$	−9.03960	+	0.769384i	−0.327256	+	0.0278536i
$764$	−14.5169	−	13.9133i	−0.525204	−	0.503367i
$765$	18.3027	+	4.76565i	0.661735	+	0.172302i
$766$	11.0352	−	17.9224i	0.398719	−	0.647561i
$767$	−4.75388	+	0.404614i	−0.171653	+	0.0146098i
$768$	2.20737	−	2.11560i	0.0796517	−	0.0763400i
$769$	4.28107	+	19.8642i	0.154379	+	0.716322i	0.986769	+	0.162132i	$0.0518369\pi$
$769$	4.28107	+	19.8642i	0.154379	+	0.716322i	−0.832390	+	0.554190i	$0.813028\pi$
$770$	−54.0191	−	61.3776i	−1.94671	−	2.21190i
$771$	−4.85344	−	0.413089i	−0.174792	−	0.0148770i
$772$	10.4066	−	25.8977i	0.374540	−	0.932080i
$773$	−6.51709	−	1.11747i	−0.234404	−	0.0401925i	0.0505999	−	0.998719i	$-0.483887\pi$
$773$	−6.51709	−	1.11747i	−0.234404	−	0.0401925i	−0.285003	+	0.958526i	$0.591995\pi$
$774$	−0.720640	−	16.9644i	−0.0259029	−	0.609774i
$775$	33.0571	−	82.2656i	1.18744	−	2.95507i
$776$	−0.691120	−	1.37076i	−0.0248098	−	0.0492073i
$777$	−8.28481	+	16.4319i	−0.297216	+	0.589492i
$778$	10.4817	+	48.6352i	0.375787	+	1.74366i
$779$	33.8778	−	38.4926i	1.21380	−	1.37914i
$780$	−102.297	−	36.1438i	−3.66282	−	1.29415i
$781$	0.894173	+	0.315931i	0.0319960	+	0.0113049i
$782$	−0.895578	+	1.01757i	−0.0320258	+	0.0363884i
$783$	1.60135	+	7.43028i	0.0572275	+	0.265536i
$784$	−18.7781	+	37.2442i	−0.670648	+	1.33015i
$785$	16.9557	+	33.6295i	0.605173	+	1.20029i
$786$	13.0066	−	32.3681i	0.463929	−	1.15453i
$787$	−0.324592	−	7.64115i	−0.0115705	−	0.272378i	−0.995559	−	0.0941438i	$-0.969989\pi$
$787$	−0.324592	−	7.64115i	−0.0115705	−	0.272378i	0.983988	−	0.178234i	$-0.0570384\pi$
$788$	19.5576	+	3.35349i	0.696712	+	0.119463i
$789$	−2.30495	+	5.73608i	−0.0820583	+	0.204210i
$790$	83.2548	+	7.08603i	2.96207	+	0.252110i
$791$	3.99965	+	4.54449i	0.142211	+	0.161583i
$792$	−3.84253	−	17.8294i	−0.136538	−	0.633540i
$793$	43.4964	−	41.6879i	1.54460	−	1.48038i
$794$	−88.7777	+	7.55610i	−3.15060	+	0.268156i
$795$	2.29763	−	3.73159i	0.0814885	−	0.132346i
$796$	−55.8396	−	14.5395i	−1.97918	−	0.515339i
$797$	6.65392	+	6.37726i	0.235694	+	0.225894i	0.800505	−	0.599326i	$-0.204565\pi$
$797$	6.65392	+	6.37726i	0.235694	+	0.225894i	−0.564811	+	0.825220i	$0.691051\pi$
$798$	−38.5184	+	3.27840i	−1.36354	+	0.116054i
$799$	−4.22601	+	13.7994i	−0.149505	+	0.488186i
$800$	−188.215	−	66.5007i	−6.65442	−	2.35116i
$801$	−12.0511	+	3.13787i	−0.425806	+	0.110871i
$802$	11.4272	+	89.2368i	0.403509	+	3.15106i
$803$	−11.2841	+	18.3265i	−0.398207	+	0.646729i
$804$	42.1679	+	28.5005i	1.48715	+	1.00514i
$805$	−1.32671	−	0.896701i	−0.0467605	−	0.0316046i
$806$	−63.4672	−	60.8284i	−2.23554	−	2.14259i
$807$	−8.77846	+	4.90394i	−0.309017	+	0.172627i
$808$	50.9008	−	8.72783i	1.79069	−	0.307044i
$809$	19.3631	−	38.4045i	0.680771	−	1.35023i	−0.244026	−	0.969769i	$-0.578468\pi$
$809$	19.3631	−	38.4045i	0.680771	−	1.35023i	0.924797	−	0.380460i	$-0.124234\pi$
$810$	−6.78679	+	9.17635i	−0.238464	+	0.322424i
$811$	1.92422	+	45.2977i	0.0675685	+	1.59062i	0.638502	+	0.769620i	$0.279554\pi$
$811$	1.92422	+	45.2977i	0.0675685	+	1.59062i	−0.570934	+	0.820996i	$0.693419\pi$
$812$	118.620	−	41.9111i	4.16274	−	1.47079i
$813$	6.51754	−	4.40509i	0.228580	−	0.154493i
$814$	−31.4533	+	11.1132i	−1.10244	+	0.389516i
$815$	43.2735	+	7.41999i	1.51580	+	0.259911i
$816$	31.0198	−	41.9415i	1.08591	−	1.46825i
$817$	−18.8209	−	21.3846i	−0.658458	−	0.748154i
$818$	−12.5615	−	31.2605i	−0.439202	−	1.09300i
$819$	14.0692	+	7.85954i	0.491618	+	0.274634i
$820$	−242.494	+	63.1406i	−8.46826	+	2.20496i
$821$	7.46528	−	24.3767i	0.260540	−	0.850753i	−0.726065	−	0.687626i	$-0.758653\pi$
$821$	7.46528	−	24.3767i	0.260540	−	0.850753i	0.986605	−	0.163127i	$-0.0521579\pi$
$822$	−8.08904	+	7.75272i	−0.282138	+	0.270407i
$823$	−8.60216	+	1.47499i	−0.299852	+	0.0514149i	−0.316960	−	0.948439i	$-0.602662\pi$
$823$	−8.60216	+	1.47499i	−0.299852	+	0.0514149i	0.0171079	+	0.999854i	$0.494554\pi$
$824$	−8.52428	−	11.5256i	−0.296957	−	0.401513i
$825$	−22.9229	+	18.5090i	−0.798074	+	0.644400i
$826$	8.27741	+	0.704512i	0.288008	+	0.0245131i
$827$	−2.31492	+	3.12998i	−0.0804976	+	0.108840i	−0.842402	−	0.538849i	$-0.818859\pi$
$827$	−2.31492	+	3.12998i	−0.0804976	+	0.108840i	0.761904	+	0.647689i	$0.224265\pi$
$828$	−0.264548	−	0.524700i	−0.00919369	−	0.0182346i
$829$	28.2341	−	22.7975i	0.980612	−	0.791789i	0.00252722	−	0.999997i	$-0.499196\pi$
$829$	28.2341	−	22.7975i	0.980612	−	0.791789i	0.978085	+	0.208208i	$0.0667631\pi$
$830$	−12.2316	+	5.52902i	−0.424564	+	0.191915i
$831$	0.0489308	+	0.121769i	0.00169739	+	0.00422412i
$832$	−53.2436	+	60.4965i	−1.84589	+	2.09734i
$833$	−4.56494	+	14.9061i	−0.158166	+	0.516466i
$834$	1.32154	+	10.3201i	0.0457612	+	0.357355i
$835$	−2.39291	+	18.6866i	−0.0828102	+	0.646677i
$836$	−39.1649	−	31.6234i	−1.35454	−	1.09372i
$837$	−5.79952	+	3.23981i	−0.200461	+	0.111984i
$838$	−30.1700	+	28.9156i	−1.04221	+	0.998873i
$839$	−29.8869	+	33.9581i	−1.03181	+	1.17237i	−0.0469721	+	0.998896i	$0.514957\pi$
$839$	−29.8869	+	33.9581i	−1.03181	+	1.17237i	−0.984839	+	0.173469i	$0.944502\pi$
$840$	100.252	+	56.0043i	3.45903	+	1.93233i
$841$	−26.2191	−	11.8518i	−0.904106	−	0.408682i
$842$	−4.06866	+	31.7727i	−0.140215	+	1.09496i
$843$	−15.3190	−	3.98875i	−0.527613	−	0.137380i
$844$	84.6635	+	57.2226i	2.91424	+	1.96968i
$845$	48.3435	+	12.5877i	1.66307	+	0.433029i
$846$	−6.77612	−	5.47133i	−0.232968	−	0.188108i
$847$	4.18854	−	19.4349i	0.143920	−	0.667790i
$848$	−7.18743	−	9.71804i	−0.246817	−	0.333719i
$849$	−12.6813	−	25.1519i	−0.435223	−	0.863212i
$850$	−154.772	−	26.5383i	−5.30863	−	0.910256i
$851$	−0.541288	+	0.365847i	−0.0185551	+	0.0125411i
$852$	−2.19109			−0.0750655
$853$	20.3605			0.697129			0.348564	−	0.937285i	$-0.386669\pi$
$853$	20.3605			0.697129			0.348564	+	0.937285i	$0.386669\pi$
$854$	−86.9134	+	58.7432i	−2.97411	+	2.01015i
$855$	0.812688	+	19.1313i	0.0277933	+	0.654277i
$856$	−89.5381	−	7.62081i	−3.06035	−	0.260474i
$857$	−3.01089	+	1.36101i	−0.102850	+	0.0464912i	−0.462670	−	0.886531i	$-0.653108\pi$
$857$	−3.01089	+	1.36101i	−0.102850	+	0.0464912i	0.359820	+	0.933022i	$0.382838\pi$
$858$	8.55444	+	27.9332i	0.292044	+	0.953623i
$859$	−48.6813	−	22.0053i	−1.66098	−	0.750812i	−1.00000		0.000412890i	$-0.999869\pi$
$859$	−48.6813	−	22.0053i	−1.66098	−	0.750812i	−0.660985	−	0.750399i	$-0.729861\pi$
$860$	17.6821	+	138.082i	0.602956	+	4.70857i
$861$	37.0869	−	3.15656i	1.26392	−	0.107575i
$862$	72.0755	−	40.2638i	2.45490	−	1.37139i
$863$	−6.79291	+	31.5192i	−0.231233	+	1.07293i	0.701586	+	0.712584i	$0.252475\pi$
$863$	−6.79291	+	31.5192i	−0.231233	+	1.07293i	−0.932820	+	0.360343i	$0.882660\pi$
$864$	7.84213	+	12.7364i	0.266795	+	0.433302i
$865$	0.801669	−	0.362377i	0.0272576	−	0.0123212i
$866$	48.0209	+	54.5623i	1.63182	+	1.85410i
$867$	1.12433	−	2.22998i	0.0381843	−	0.0757340i
$868$	65.3820	+	88.4023i	2.21921	+	3.00057i
$869$	−8.47357	−	13.7619i	−0.287446	−	0.466842i
$870$	−25.4029	−	82.9493i	−0.861240	−	2.81224i
$871$	−43.2630	−	24.1681i	−1.46591	−	0.818906i
$872$	21.7783	+	7.69475i	0.737505	+	0.260577i
$873$	0.179814	−	0.0468199i	0.00608578	−	0.00158461i
$874$	−1.25060	−	0.565309i	−0.0423023	−	0.0191219i
$875$	4.92338	−	115.900i	0.166441	−	3.91814i
$876$	10.4760	−	48.6089i	0.353952	−	1.64234i
$877$	3.30270	−	0.566305i	0.111524	−	0.0191227i	−0.112968	−	0.993599i	$-0.536036\pi$
$877$	3.30270	−	0.566305i	0.111524	−	0.0191227i	0.224492	+	0.974476i	$0.427928\pi$
$878$	5.67872	+	26.3494i	0.191648	+	0.889248i
$879$	−4.72149	−	11.7499i	−0.159252	−	0.396314i
$880$	32.7112	+	106.813i	1.10269	+	3.60067i
$881$	−0.161486	+	3.80151i	−0.00544061	+	0.128076i	0.994324	+	0.106392i	$0.0339298\pi$
$881$	−0.161486	+	3.80151i	−0.00544061	+	0.128076i	−0.999765	+	0.0216841i	$0.993097\pi$
$882$	−7.31958	−	5.91015i	−0.246463	−	0.199005i
$883$	−28.8840	−	27.6830i	−0.972023	−	0.931608i	0.0256583	−	0.999671i	$-0.491832\pi$
$883$	−28.8840	−	27.6830i	−0.972023	−	0.931608i	−0.997681	+	0.0680624i	$0.978318\pi$
$884$	−58.6422	+	95.2410i	−1.97235	+	3.20330i
$885$	0.522670	−	4.08160i	0.0175694	−	0.137202i
$886$	2.45152	−	57.7108i	0.0823605	−	1.93883i
$887$	−16.2385	−	26.3730i	−0.545235	−	0.885518i	0.454752	−	0.890618i	$-0.349728\pi$
$887$	−16.2385	−	26.3730i	−0.545235	−	0.885518i	−0.999987	+	0.00510014i	$0.998377\pi$
$888$	36.4522	−	29.4331i	1.22326	−	0.987710i
$889$	−6.12797	+	15.2500i	−0.205526	+	0.511470i
$890$	134.012	−	47.3494i	4.49209	−	1.58716i
$891$	2.20759			0.0739571
$892$	75.3996	−	10.7828i	2.52457	−	0.361036i
$893$	−14.6118			−0.488964
$894$	57.9461	−	20.4737i	1.93801	−	0.684742i
$895$	−24.6864	+	61.4344i	−0.825175	+	2.05353i
$896$	33.6485	−	27.1693i	1.12412	−	0.907662i
$897$	0.299980	+	0.487198i	0.0100160	+	0.0162671i
$898$	−4.31526	+	101.585i	−0.144002	+	3.38992i
$899$	6.41356	−	50.0844i	0.213904	−	1.67041i
$900$	35.6903	−	57.9648i	1.18968	−	1.93216i
$901$	−3.26153	−	3.12593i	−0.108657	−	0.104140i
$902$	52.4958	+	42.3874i	1.74792	+	1.41135i
$903$	0.877606	−	20.6595i	0.0292049	−	0.687506i
$904$	−4.51326	−	14.7373i	−0.150109	−	0.490157i
$905$	13.1340	+	32.6853i	0.436590	+	1.08650i
$906$	9.13799	+	42.4004i	0.303589	+	1.40866i
$907$	8.38312	−	1.43743i	0.278357	−	0.0477291i	−0.0281289	−	0.999604i	$-0.508955\pi$
$907$	8.38312	−	1.43743i	0.278357	−	0.0477291i	0.306486	+	0.951875i	$0.400847\pi$
$908$	4.85245	−	22.5155i	0.161034	−	0.747202i
$909$	−0.265295	+	6.24524i	−0.00879927	+	0.207142i
$910$	−167.607	−	75.7630i	−5.55611	−	2.51152i
$911$	−1.84987	+	0.481669i	−0.0612889	+	0.0159584i	−0.282496	−	0.959268i	$-0.591162\pi$
$911$	−1.84987	+	0.481669i	−0.0612889	+	0.0159584i	0.221207	+	0.975227i	$0.429000\pi$
$912$	49.7991	+	17.5951i	1.64901	+	0.582634i
$913$	2.26663	+	1.26621i	0.0750144	+	0.0419055i
$914$	−24.4924	−	79.9761i	−0.810137	−	2.64538i
$915$	27.2443	+	44.2476i	0.900669	+	1.46278i
$916$	−64.5220	−	87.2395i	−2.13187	−	2.88248i
$917$	19.1254	−	37.9330i	0.631577	−	1.25266i
$918$	7.77357	+	8.83249i	0.256566	+	0.291516i
$919$	−31.6983	+	14.3285i	−1.04563	+	0.472654i	−0.860175	−	0.509998i	$-0.829646\pi$
$919$	−31.6983	+	14.3285i	−1.04563	+	0.472654i	−0.185454	+	0.982653i	$0.559376\pi$
$920$	2.13755	+	3.47160i	0.0704729	+	0.114455i
$921$	−4.99006	+	23.1540i	−0.164428	+	0.762949i
$922$	81.2451	−	45.3862i	2.67566	−	1.49472i
$923$	2.12571	−	0.180924i	0.0699685	−	0.00595520i
$924$	−4.64111	−	36.2431i	−0.152681	−	1.19231i
$925$	−68.9647	−	31.1740i	−2.26755	−	1.02500i
$926$	17.8746	+	58.3669i	0.587397	+	1.91805i
$927$	1.58110	−	0.714702i	0.0519301	−	0.0234739i
$928$	−113.278	−	9.64135i	−3.71852	−	0.316493i
$929$	0.871623	+	20.5187i	0.0285970	+	0.673196i	0.954990	+	0.296638i	$0.0958655\pi$
$929$	0.871623	+	20.5187i	0.0285970	+	0.673196i	−0.926393	+	0.376558i	$0.877107\pi$
$930$	62.8180	−	42.4575i	2.05988	−	1.39224i
$931$	−15.7836			−0.517288
$932$	−47.1701			−1.54511
$933$	26.4261	−	17.8609i	0.865151	−	0.584740i
$934$	70.7982	+	12.1396i	2.31659	+	0.397219i
$935$	18.7969	+	37.2815i	0.614725	+	1.21924i
$936$	−24.3977	−	32.9879i	−0.797464	−	1.07824i
$937$	−1.33648	+	6.20131i	−0.0436611	+	0.202588i	−0.994124	−	0.108251i	$-0.965475\pi$
$937$	−1.33648	+	6.20131i	−0.0436611	+	0.202588i	0.950463	+	0.310839i	$0.100610\pi$
$938$	67.1338	+	54.2068i	2.19200	+	1.76991i
$939$	4.39869	+	1.14533i	0.143546	+	0.0373764i
$940$	59.1587	+	39.9843i	1.92954	+	1.30414i
$941$	15.2364	+	3.96724i	0.496691	+	0.129328i	0.491885	−	0.870660i	$-0.336308\pi$
$941$	15.2364	+	3.96724i	0.496691	+	0.129328i	0.00480593	+	0.999988i	$0.498470\pi$
$942$	−2.97607	+	23.2406i	−0.0969657	+	0.757219i
$943$	1.20413	+	0.544300i	0.0392118	+	0.0177248i
$944$	−9.90865	−	5.53530i	−0.322499	−	0.180159i
$945$	−9.18299	+	10.4339i	−0.298723	+	0.339415i
$946$	27.0620	−	25.9369i	0.879863	−	0.843280i
$947$	33.5641	−	18.7501i	1.09069	−	0.609295i	0.164508	−	0.986376i	$-0.447396\pi$
$947$	33.5641	−	18.7501i	1.09069	−	0.609295i	0.926180	+	0.377081i	$0.123072\pi$
$948$	29.0519	+	23.4577i	0.943561	+	0.761872i
$949$	−6.14964	+	48.0234i	−0.199626	+	1.55891i
$950$	−20.1942	−	157.699i	−0.655186	−	5.11644i
$951$	−5.24512	+	17.1271i	−0.170085	+	0.555384i
$952$	78.2128	−	88.8670i	2.53489	−	2.88020i
$953$	8.19735	+	20.3999i	0.265538	+	0.660817i	0.999838	−	0.0180084i	$-0.00573255\pi$
$953$	8.19735	+	20.3999i	0.265538	+	0.660817i	−0.734300	+	0.678825i	$0.762489\pi$
$954$	2.48425	−	1.12295i	0.0804305	−	0.0363569i
$955$	−13.1378	+	10.6080i	−0.425128	+	0.343267i
$956$	27.1581	+	53.8649i	0.878356	+	1.74212i
$957$	−9.97773	+	13.4908i	−0.322534	+	0.436095i
$958$	82.6173	+	7.03177i	2.66925	+	0.227186i
$959$	−10.6161	+	8.57194i	−0.342813	+	0.276802i
$960$	−41.3311	−	55.8833i	−1.33395	−	1.80362i
$961$	12.9419	−	2.21911i	0.417481	−	0.0715842i
$962$	−54.1784	+	51.9258i	−1.74678	+	1.67416i
$963$	3.18496	−	10.4000i	0.102634	−	0.335134i
$964$	37.1416	−	9.67092i	1.19625	−	0.311479i
$965$	−20.4619	−	11.4307i	−0.658690	−	0.367966i
$966$	−0.371445	−	0.924377i	−0.0119511	−	0.0297413i
$967$	−10.6067	−	12.0515i	−0.341088	−	0.387551i	0.554687	−	0.832059i	$-0.312838\pi$
$967$	−10.6067	−	12.0515i	−0.341088	−	0.387551i	−0.895775	+	0.444508i	$0.853378\pi$
$968$	−30.0982	+	40.6955i	−0.967393	+	1.30800i
$969$	19.4563	+	3.33612i	0.625028	+	0.107172i
$970$	−1.99958	+	0.706497i	−0.0642026	+	0.0226842i
$971$	−11.6210	+	7.85441i	−0.372935	+	0.252060i	−0.732075	−	0.681224i	$-0.761448\pi$
$971$	−11.6210	+	7.85441i	−0.372935	+	0.252060i	0.359141	+	0.933283i	$0.383070\pi$
$972$	−4.80915	+	1.69918i	−0.154253	+	0.0545012i
$973$	0.537754	+	12.6592i	0.0172396	+	0.405834i
$974$	0.384374	−	0.519708i	0.0123161	−	0.0166525i
$975$	−29.8390	+	59.1821i	−0.955612	+	1.89534i
$976$	141.263	−	24.2219i	4.52171	−	0.775326i
$977$	−27.4118	+	15.3131i	−0.876980	+	0.489910i	−0.860205	−	0.509949i	$-0.829664\pi$
$977$	−27.4118	+	15.3131i	−0.876980	+	0.489910i	−0.0167753	+	0.999859i	$0.505340\pi$
$978$	19.7196	+	18.8997i	0.630564	+	0.604347i
$979$	−22.7766	−	15.3943i	−0.727944	−	0.492004i
$980$	63.9033	+	43.1911i	2.04132	+	1.37969i
$981$	−1.46581	+	2.38062i	−0.0467997	+	0.0760075i
$982$	−10.4240	−	81.4026i	−0.332644	−	2.59766i
$983$	0.592519	−	0.154280i	0.0188984	−	0.00492077i	−0.242517	−	0.970147i	$-0.577973\pi$
$983$	0.592519	−	0.154280i	0.0188984	−	0.00492077i	0.261415	+	0.965226i	$0.415811\pi$
$984$	−89.3498	−	31.5693i	−2.84837	−	1.00639i
$985$	4.87945	−	15.9331i	0.155472	−	0.507670i
$986$	−89.1105	+	7.58442i	−2.83786	+	0.241537i
$987$	−7.65726	−	7.33889i	−0.243733	−	0.233599i
$988$	−109.586	−	28.5341i	−3.48641	−	0.907791i
$989$	0.384907	−	0.625128i	0.0122393	−	0.0198779i
$990$	−25.1054	+	2.13678i	−0.797902	+	0.0679114i
$991$	−5.72276	+	5.48482i	−0.181790	+	0.174231i	−0.777328	−	0.629096i	$-0.783425\pi$
$991$	−5.72276	+	5.48482i	−0.181790	+	0.174231i	0.595538	+	0.803327i	$0.296939\pi$
$992$	−20.9334	−	97.1315i	−0.664638	−	3.08393i
$993$	−5.02812	−	5.71306i	−0.159563	−	0.181298i
$994$	−3.70126	−	0.315024i	−0.117397	−	0.00999195i
$995$	−18.0670	+	44.9615i	−0.572763	+	1.42538i
$996$	−5.91235	−	1.01377i	−0.187340	−	0.0321227i
$997$	−1.46766	−	34.5498i	−0.0464812	−	1.09420i	−0.859230	−	0.511589i	$-0.829057\pi$
$997$	−1.46766	−	34.5498i	−0.0464812	−	1.09420i	0.812749	−	0.582614i	$-0.197970\pi$
$998$	−33.9493	+	84.4861i	−1.07465	+	2.67436i
$999$	2.55304	+	5.06364i	0.0807745	+	0.160207i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	669.2.i.a.4.1	✓	648
223.56	even	37	inner	669.2.i.a.502.1	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
669.2.i.a.4.1	✓	648	1.1	even	1	trivial
669.2.i.a.502.1	yes	648	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+(-2.51246 + 0.887710i) q^{2} +(-0.372856 + 0.927889i) q^{3} +(3.96837 - 3.20424i) q^{4} +(-2.24573 - 3.64729i) q^{5} +(0.113092 - 2.66228i) q^{6} +(0.412183 - 3.21880i) q^{7} +(-4.33174 + 7.03519i) q^{8} +(-0.721956 - 0.691939i) q^{9} +(8.88004 + 7.17013i) q^{10} +(0.0936929 - 2.20560i) q^{11} +(1.49354 + 4.87693i) q^{12} +(-1.85168 - 4.60807i) q^{13} +(1.82176 + 8.45301i) q^{14} +(4.22161 - 0.723869i) q^{15} +(2.48899 - 11.5490i) q^{16} +(0.187403 - 4.41161i) q^{17} +(2.42813 + 1.09758i) q^{18} +(4.32634 - 1.12649i) q^{19} +(-20.5987 - 7.27797i) q^{20} +(2.83300 + 1.58261i) q^{21} +(1.72254 + 5.62467i) q^{22} +(0.0604044 + 0.0981031i) q^{23} +(-4.91276 - 6.64249i) q^{24} +(-6.00843 + 11.9170i) q^{25} +(8.74290 + 9.93386i) q^{26} +(0.911228 - 0.411901i) q^{27} +(-8.67809 - 14.0941i) q^{28} +(-1.60135 + 7.43028i) q^{29} +(-9.96407 + 5.56626i) q^{30} +(-6.61917 + 0.563374i) q^{31} +(1.89982 + 14.8360i) q^{32} +(2.01162 + 0.909310i) q^{33} +(3.44538 + 11.2504i) q^{34} +(-12.6655 + 5.72518i) q^{35} +(-5.08213 - 0.432553i) q^{36} +(0.240678 + 5.66574i) q^{37} +(-9.86978 + 6.67080i) q^{38} +4.96619 q^{39} +35.3873 q^{40} +(9.50297 - 6.42289i) q^{41} +(-8.52271 - 1.46137i) q^{42} +(-2.86877 - 5.68986i) q^{43} +(-6.69547 - 9.05287i) q^{44} +(-0.902387 + 4.18709i) q^{45} +(-0.238851 - 0.192859i) q^{46} +(-3.16295 - 0.823569i) q^{47} +(9.78811 + 6.61561i) q^{48} +(-3.41663 - 0.889620i) q^{49} +(4.51711 - 35.2748i) q^{50} +(4.02361 + 1.81878i) q^{51} +(-22.1135 - 12.3533i) q^{52} +(0.675944 - 0.768022i) q^{53} +(-1.92378 + 1.84379i) q^{54} +(-8.25489 + 4.61146i) q^{55} +(20.8594 + 16.8428i) q^{56} +(-0.567845 + 4.43438i) q^{57} +(-2.57260 - 20.0898i) q^{58} +(0.281318 - 0.918598i) q^{59} +(14.4335 - 16.3996i) q^{60} +(4.52335 + 11.2568i) q^{61} +(16.1303 - 7.29136i) q^{62} +(-2.52479 + 2.03862i) q^{63} +(-7.30576 - 14.4901i) q^{64} +(-12.6486 + 17.1021i) q^{65} +(-5.86133 - 0.498873i) q^{66} +(7.76375 - 6.26879i) q^{67} +(-13.3921 - 18.1074i) q^{68} +(-0.113551 + 0.0194703i) q^{69} +(26.7394 - 25.6276i) q^{70} +(-0.125792 + 0.410753i) q^{71} +(7.99525 - 2.08180i) q^{72} +(-8.51105 - 4.75456i) q^{73} +(-5.63422 - 14.0213i) q^{74} +(-8.81738 - 10.0185i) q^{75} +(13.5590 - 18.3330i) q^{76} +(-7.06077 - 1.21069i) q^{77} +(-12.4774 + 4.40853i) q^{78} +(6.06539 - 4.09949i) q^{79} +(-47.7120 + 16.8577i) q^{80} +(0.0424412 + 0.999099i) q^{81} +(-18.1742 + 24.5732i) q^{82} +(-0.529479 + 1.05016i) q^{83} +(16.3135 - 2.79722i) q^{84} +(-16.5113 + 9.22375i) q^{85} +(12.2586 + 11.7489i) q^{86} +(-6.29740 - 4.25630i) q^{87} +(15.1110 + 10.2132i) q^{88} +(6.52918 - 10.6041i) q^{89} +(-1.44971 - 11.3210i) q^{90} +(-15.5957 + 4.06080i) q^{91} +(0.554053 + 0.195759i) q^{92} +(1.94525 - 6.35191i) q^{93} +(8.67789 - 0.738597i) q^{94} +(-13.8244 - 13.2496i) q^{95} +(-14.4745 - 3.76887i) q^{96} +(-0.0974213 + 0.158222i) q^{97} +(9.37388 - 0.797834i) q^{98} +(-1.59378 + 1.52752i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q + q^{2} + 18 q^{3} - 17 q^{4} + 4 q^{5} - q^{6} + 4 q^{7} + 9 q^{8} - 18 q^{9} + 8 q^{10} + 6 q^{11} + 17 q^{12} - 2 q^{13} + 12 q^{14} - 4 q^{15} - 7 q^{16} + 8 q^{17} + q^{18} - 66 q^{19} + 14 q^{20}+ \cdots + 6 q^{99}+O(q^{100}) \) 648 * q + q^2 + 18 * q^3 - 17 * q^4 + 4 * q^5 - q^6 + 4 * q^7 + 9 * q^8 - 18 * q^9 + 8 * q^10 + 6 * q^11 + 17 * q^12 - 2 * q^13 + 12 * q^14 - 4 * q^15 - 7 * q^16 + 8 * q^17 + q^18 - 66 * q^19 + 14 * q^20 - 4 * q^21 - 24 * q^22 - 2 * q^23 - 9 * q^24 - 26 * q^25 - 8 * q^26 + 18 * q^27 + 8 * q^28 - 27 * q^29 - 8 * q^30 + 16 * q^31 + 19 * q^32 - 6 * q^33 - 50 * q^34 + 16 * q^35 - 17 * q^36 + 16 * q^37 - 28 * q^38 - 72 * q^39 + 212 * q^40 + 240 * q^41 - 86 * q^42 + 6 * q^43 - 128 * q^44 + 4 * q^45 + 16 * q^46 - 14 * q^47 + 7 * q^48 - 28 * q^49 + 23 * q^50 + 66 * q^51 - 286 * q^52 + 10 * q^53 - q^54 + 14 * q^55 + 25 * q^56 - 8 * q^57 + 49 * q^58 + 22 * q^59 - 14 * q^60 - 2 * q^61 - 23 * q^62 + 4 * q^63 + 257 * q^64 - 116 * q^65 - 50 * q^66 + 8 * q^67 + 211 * q^68 + 2 * q^69 + 82 * q^70 + 9 * q^72 + 10 * q^73 - 10 * q^74 + 26 * q^75 + 7 * q^76 - 116 * q^77 - 66 * q^78 - 14 * q^79 - 477 * q^80 - 18 * q^81 - 234 * q^82 - 142 * q^83 - 8 * q^84 + 98 * q^85 + 35 * q^86 - 10 * q^87 - 72 * q^88 + 2 * q^89 + 8 * q^90 + 6 * q^91 - 46 * q^92 - 16 * q^93 - 206 * q^94 - 6 * q^95 - 19 * q^96 - 34 * q^97 + 4 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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