LMFDB - Embedded newform 220.2.r.d.151.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [220,2,Mod(51,220)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("220.51"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(220, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 0, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	220.r (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			151.6
Character	$\chi$	$=$	220.151
Dual form			220.2.r.d.51.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.385414 + 1.36068i) q^{2} +(-1.51690 + 0.492870i) q^{3} +(-1.70291 - 1.04885i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-0.0860056 - 2.25398i) q^{6} +(1.09672 - 3.37535i) q^{7} +(2.08348 - 1.91288i) q^{8} +(-0.368991 + 0.268088i) q^{9} +(1.11160 - 0.874274i) q^{10} +(3.10782 + 1.15820i) q^{11} +(3.10009 + 0.751688i) q^{12} +(-3.19085 - 4.39182i) q^{13} +(4.17008 + 2.79319i) q^{14} +(1.51690 + 0.492870i) q^{15} +(1.79982 + 3.57221i) q^{16} +(2.95060 - 4.06116i) q^{17} +(-0.222568 - 0.605404i) q^{18} +(0.549856 + 1.69228i) q^{19} +(0.761185 + 1.84949i) q^{20} +5.66060i q^{21} +(-2.77374 + 3.78238i) q^{22} -2.09462i q^{23} +(-2.21763 + 3.92853i) q^{24} +(0.309017 + 0.951057i) q^{25} +(7.20567 - 2.64906i) q^{26} +(3.24007 - 4.45958i) q^{27} +(-5.40785 + 4.59762i) q^{28} +(-5.55889 - 1.80619i) q^{29} +(-1.25527 + 1.87406i) q^{30} +(-6.31471 - 8.69146i) q^{31} +(-5.55431 + 1.07220i) q^{32} +(-5.28510 - 0.225117i) q^{33} +(4.38874 + 5.58006i) q^{34} +(-2.87124 + 2.08608i) q^{35} +(0.909544 - 0.0695126i) q^{36} +(-0.865827 + 2.66474i) q^{37} +(-2.51458 + 0.0959496i) q^{38} +(7.00479 + 5.08928i) q^{39} +(-2.80993 + 0.322913i) q^{40} +(10.7498 - 3.49283i) q^{41} +(-7.70227 - 2.18167i) q^{42} -0.538324 q^{43} +(-4.07757 - 5.23196i) q^{44} +0.456098 q^{45} +(2.85011 + 0.807294i) q^{46} +(-1.62957 + 0.529478i) q^{47} +(-4.49077 - 4.53160i) q^{48} +(-4.52706 - 3.28910i) q^{49} +(-1.41319 + 0.0539233i) q^{50} +(-2.47414 + 7.61463i) q^{51} +(0.827357 + 10.8256i) q^{52} +(-2.32319 + 1.68789i) q^{53} +(4.81930 + 6.12750i) q^{54} +(-1.83351 - 2.76374i) q^{55} +(-4.17164 - 9.13036i) q^{56} +(-1.66815 - 2.29601i) q^{57} +(4.60013 - 6.86775i) q^{58} +(-2.45058 - 0.796242i) q^{59} +(-2.06620 - 2.43032i) q^{60} +(-4.54316 + 6.25312i) q^{61} +(14.2601 - 5.24251i) q^{62} +(0.500210 + 1.53949i) q^{63} +(0.681785 - 7.97090i) q^{64} +5.42859i q^{65} +(2.34326 - 7.10457i) q^{66} +4.39227i q^{67} +(-9.28417 + 3.82105i) q^{68} +(1.03237 + 3.17732i) q^{69} +(-1.73187 - 4.71085i) q^{70} +(-2.37159 + 3.26421i) q^{71} +(-0.255966 + 1.26439i) q^{72} +(-6.38412 - 2.07433i) q^{73} +(-3.29217 - 2.20515i) q^{74} +(-0.937495 - 1.29035i) q^{75} +(0.838598 - 3.45853i) q^{76} +(7.31773 - 9.21977i) q^{77} +(-9.62464 + 7.56981i) q^{78} +(3.08285 - 2.23982i) q^{79} +(0.643607 - 3.94788i) q^{80} +(-2.29404 + 7.06034i) q^{81} +(0.609497 + 15.9733i) q^{82} +(7.74593 + 5.62775i) q^{83} +(5.93713 - 9.63950i) q^{84} +(-4.77418 + 1.55122i) q^{85} +(0.207478 - 0.732488i) q^{86} +9.32249 q^{87} +(8.69059 - 3.53181i) q^{88} +18.4768 q^{89} +(-0.175787 + 0.620604i) q^{90} +(-18.3234 + 5.95363i) q^{91} +(-2.19694 + 3.56695i) q^{92} +(13.8625 + 10.0717i) q^{93} +(-0.0923936 - 2.42139i) q^{94} +(0.549856 - 1.69228i) q^{95} +(7.89687 - 4.36398i) q^{96} +(-3.54048 + 2.57231i) q^{97} +(6.22021 - 4.89222i) q^{98} +(-1.45726 + 0.405804i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 12 q^{5} + 20 q^{6} + 16 q^{9} + 14 q^{12} - 10 q^{13} - 21 q^{14} - 4 q^{16} - 25 q^{18} + 5 q^{20} + 15 q^{22} - 30 q^{24} - 12 q^{25} - 4 q^{26} - 60 q^{28} + 20 q^{29} - 10 q^{33} - 18 q^{34}+ \cdots + 38 q^{97}+O(q^{100}) $ 48 * q - 12 * q^5 + 20 * q^6 + 16 * q^9 + 14 * q^12 - 10 * q^13 - 21 * q^14 - 4 * q^16 - 25 * q^18 + 5 * q^20 + 15 * q^22 - 30 * q^24 - 12 * q^25 - 4 * q^26 - 60 * q^28 + 20 * q^29 - 10 * q^33 - 18 * q^34 + 66 * q^36 - 44 * q^37 + 11 * q^38 - 10 * q^41 + 19 * q^42 - 35 * q^44 - 44 * q^45 + 5 * q^46 + 41 * q^48 - 2 * q^49 + 50 * q^52 - 36 * q^53 - 28 * q^56 + 30 * q^57 - 38 * q^58 - 21 * q^60 + 36 * q^64 + 43 * q^66 - 65 * q^68 + 24 * q^69 - 21 * q^70 - 60 * q^72 - 20 * q^73 - 70 * q^74 + 16 * q^77 - 56 * q^78 + q^80 + 50 * q^81 + 35 * q^82 + 60 * q^84 + 10 * q^85 + 38 * q^86 - 101 * q^88 + 64 * q^89 + 70 * q^92 - 28 * q^93 + 130 * q^94 + 105 * q^96 + 38 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.385414	+	1.36068i	−0.272529	+	0.962148i
$2$	−0.385414	+	1.36068i	−0.272529	+	0.962148i
$3$	−1.51690	+	0.492870i	−0.875782	+	0.284559i	−0.712205	−	0.701972i	$-0.752303\pi$
$3$	−1.51690	+	0.492870i	−0.875782	+	0.284559i	−0.163577	+	0.986531i	$0.552303\pi$
$4$	−1.70291	−	1.04885i	−0.851456	−	0.524426i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$	−0.0860056	−	2.25398i	−0.0351116	−	0.920182i
$7$	1.09672	−	3.37535i	0.414520	−	1.27576i	−0.498160	−	0.867085i	$-0.665991\pi$
$7$	1.09672	−	3.37535i	0.414520	−	1.27576i	0.912680	−	0.408676i	$-0.134009\pi$
$8$	2.08348	−	1.91288i	0.736622	−	0.676305i
$9$	−0.368991	+	0.268088i	−0.122997	+	0.0893626i
$10$	1.11160	−	0.874274i	0.351517	−	0.276470i
$11$	3.10782	+	1.15820i	0.937044	+	0.349210i
$11$	3.10782	+	1.15820i	0.937044	+	0.349210i
$12$	3.10009	+	0.751688i	0.894920	+	0.216994i
$13$	−3.19085	−	4.39182i	−0.884982	−	1.21807i	−0.975016	−	0.222134i	$-0.928698\pi$
$13$	−3.19085	−	4.39182i	−0.884982	−	1.21807i	0.0900343	−	0.995939i	$-0.471302\pi$
$14$	4.17008	+	2.79319i	1.11450	+	0.746511i
$15$	1.51690	+	0.492870i	0.391662	+	0.127259i
$16$	1.79982	+	3.57221i	0.449954	+	0.893051i
$17$	2.95060	−	4.06116i	0.715626	−	0.984975i	−0.284031	−	0.958815i	$-0.591672\pi$
$17$	2.95060	−	4.06116i	0.715626	−	0.984975i	0.999658	−	0.0261602i	$-0.00832799\pi$
$18$	−0.222568	−	0.605404i	−0.0524597	−	0.142695i
$19$	0.549856	+	1.69228i	0.126146	+	0.388236i	0.994108	−	0.108394i	$-0.0345707\pi$
$19$	0.549856	+	1.69228i	0.126146	+	0.388236i	−0.867962	+	0.496630i	$0.834571\pi$
$20$	0.761185	+	1.84949i	0.170206	+	0.413558i
$21$			5.66060i			1.23524i
$22$	−2.77374	+	3.78238i	−0.591364	+	0.806405i
$23$		−	2.09462i		−	0.436758i	−0.975864	−	0.218379i	$-0.929923\pi$
$23$		−	2.09462i		−	0.436758i	0.975864	−	0.218379i	$-0.0700768\pi$
$24$	−2.21763	+	3.92853i	−0.452671	+	0.801908i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	7.20567	−	2.64906i	1.41315	−	0.519523i
$27$	3.24007	−	4.45958i	0.623553	−	0.858246i
$28$	−5.40785	+	4.59762i	−1.02199	+	0.868869i
$29$	−5.55889	−	1.80619i	−1.03226	−	0.335402i	−0.256577	−	0.966524i	$-0.582595\pi$
$29$	−5.55889	−	1.80619i	−1.03226	−	0.335402i	−0.775683	+	0.631122i	$0.782595\pi$
$30$	−1.25527	+	1.87406i	−0.229181	+	0.342155i
$31$	−6.31471	−	8.69146i	−1.13416	−	1.56103i	−0.779924	−	0.625875i	$-0.784742\pi$
$31$	−6.31471	−	8.69146i	−1.13416	−	1.56103i	−0.354233	−	0.935157i	$-0.615258\pi$
$32$	−5.55431	+	1.07220i	−0.981873	+	0.189540i
$33$	−5.28510	−	0.225117i	−0.920017	−	0.0391878i
$34$	4.38874	+	5.58006i	0.752663	+	0.956972i
$35$	−2.87124	+	2.08608i	−0.485328	+	0.352612i
$36$	0.909544	−	0.0695126i	0.151591	−	0.0115854i
$37$	−0.865827	+	2.66474i	−0.142341	+	0.438081i	−0.996660	−	0.0816691i	$-0.973975\pi$
$37$	−0.865827	+	2.66474i	−0.142341	+	0.438081i	0.854318	+	0.519750i	$0.173975\pi$
$38$	−2.51458	+	0.0959496i	−0.407919	+	0.0155651i
$39$	7.00479	+	5.08928i	1.12166	+	0.814937i
$40$	−2.80993	+	0.322913i	−0.444290	+	0.0510570i
$41$	10.7498	−	3.49283i	1.67884	−	0.545488i	0.694154	−	0.719826i	$-0.255778\pi$
$41$	10.7498	−	3.49283i	1.67884	−	0.545488i	0.984686	+	0.174338i	$0.0557785\pi$
$42$	−7.70227	−	2.18167i	−1.18849	−	0.336640i
$43$	−0.538324			−0.0820937			−0.0410468	−	0.999157i	$-0.513069\pi$
$43$	−0.538324			−0.0820937			−0.0410468	+	0.999157i	$0.513069\pi$
$44$	−4.07757	−	5.23196i	−0.614717	−	0.788748i
$45$	0.456098			0.0679911
$46$	2.85011	+	0.807294i	0.420225	+	0.119029i
$47$	−1.62957	+	0.529478i	−0.237697	+	0.0772323i	−0.425443	−	0.904985i	$-0.639882\pi$
$47$	−1.62957	+	0.529478i	−0.237697	+	0.0772323i	0.187746	+	0.982218i	$0.439882\pi$
$48$	−4.49077	−	4.53160i	−0.648188	−	0.654080i
$49$	−4.52706	−	3.28910i	−0.646722	−	0.469871i
$50$	−1.41319	+	0.0539233i	−0.199855	+	0.00762591i
$51$	−2.47414	+	7.61463i	−0.346449	+	1.06626i
$52$	0.827357	+	10.8256i	0.114734	+	1.50124i
$53$	−2.32319	+	1.68789i	−0.319114	+	0.231850i	−0.735797	−	0.677202i	$-0.763192\pi$
$53$	−2.32319	+	1.68789i	−0.319114	+	0.231850i	0.416683	+	0.909052i	$0.363192\pi$
$54$	4.81930	+	6.12750i	0.655824	+	0.833847i
$55$	−1.83351	−	2.76374i	−0.247230	−	0.372662i
$56$	−4.17164	−	9.13036i	−0.557459	−	1.22010i
$57$	−1.66815	−	2.29601i	−0.220952	−	0.304114i
$58$	4.60013	−	6.86775i	0.604027	−	0.901780i
$59$	−2.45058	−	0.796242i	−0.319038	−	0.103662i	0.145120	−	0.989414i	$-0.453643\pi$
$59$	−2.45058	−	0.796242i	−0.319038	−	0.103662i	−0.464158	+	0.885752i	$0.653643\pi$
$60$	−2.06620	−	2.43032i	−0.266745	−	0.313753i
$61$	−4.54316	+	6.25312i	−0.581692	+	0.800630i	−0.993880	−	0.110469i	$-0.964765\pi$
$61$	−4.54316	+	6.25312i	−0.581692	+	0.800630i	0.412188	+	0.911099i	$0.364765\pi$
$62$	14.2601	−	5.24251i	1.81103	−	0.665799i
$63$	0.500210	+	1.53949i	0.0630206	+	0.193957i
$64$	0.681785	−	7.97090i	0.0852231	−	0.996362i
$65$			5.42859i			0.673334i
$66$	2.34326	−	7.10457i	0.288436	−	0.874513i
$67$			4.39227i			0.536601i	0.963335	+	0.268301i	$0.0864620\pi$
$67$			4.39227i			0.536601i	−0.963335	+	0.268301i	$0.913538\pi$
$68$	−9.28417	+	3.82105i	−1.12587	+	0.463370i
$69$	1.03237	+	3.17732i	0.124283	+	0.382504i
$70$	−1.73187	−	4.71085i	−0.206998	−	0.563054i
$71$	−2.37159	+	3.26421i	−0.281455	+	0.387390i	−0.926215	−	0.376995i	$-0.876957\pi$
$71$	−2.37159	+	3.26421i	−0.281455	+	0.387390i	0.644760	+	0.764385i	$0.276957\pi$
$72$	−0.255966	+	1.26439i	−0.0301659	+	0.149010i
$73$	−6.38412	−	2.07433i	−0.747204	−	0.242781i	−0.0894266	−	0.995993i	$-0.528503\pi$
$73$	−6.38412	−	2.07433i	−0.747204	−	0.242781i	−0.657778	+	0.753212i	$0.728503\pi$
$74$	−3.29217	−	2.20515i	−0.382706	−	0.256343i
$75$	−0.937495	−	1.29035i	−0.108253	−	0.148997i
$76$	0.838598	−	3.45853i	0.0961938	−	0.396720i
$77$	7.31773	−	9.21977i	0.833932	−	1.05069i
$78$	−9.62464	+	7.56981i	−1.08978	+	0.857113i
$79$	3.08285	−	2.23982i	0.346848	−	0.252000i	−0.400698	−	0.916210i	$-0.631232\pi$
$79$	3.08285	−	2.23982i	0.346848	−	0.252000i	0.747545	+	0.664211i	$0.231232\pi$
$80$	0.643607	−	3.94788i	0.0719574	−	0.441387i
$81$	−2.29404	+	7.06034i	−0.254894	+	0.784482i
$82$	0.609497	+	15.9733i	0.0673077	+	1.76395i
$83$	7.74593	+	5.62775i	0.850226	+	0.617726i	0.925208	−	0.379459i	$-0.123890\pi$
$83$	7.74593	+	5.62775i	0.850226	+	0.617726i	−0.0749821	+	0.997185i	$0.523890\pi$
$84$	5.93713	−	9.63950i	0.647794	−	1.05176i
$85$	−4.77418	+	1.55122i	−0.517832	+	0.168254i
$86$	0.207478	−	0.732488i	0.0223729	−	0.0789862i
$87$	9.32249			0.999476
$88$	8.69059	−	3.53181i	0.926420	−	0.376492i
$89$	18.4768			1.95854			0.979270	−	0.202559i	$-0.0649257\pi$
$89$	18.4768			1.95854			0.979270	+	0.202559i	$0.0649257\pi$
$90$	−0.175787	+	0.620604i	−0.0185295	+	0.0654175i
$91$	−18.3234	+	5.95363i	−1.92081	+	0.624110i
$92$	−2.19694	+	3.56695i	−0.229047	+	0.371880i
$93$	13.8625	+	10.0717i	1.43748	+	1.04439i
$94$	−0.0923936	−	2.42139i	−0.00952967	−	0.249747i
$95$	0.549856	−	1.69228i	0.0564140	−	0.173625i
$96$	7.89687	−	4.36398i	0.805971	−	0.445396i
$97$	−3.54048	+	2.57231i	−0.359481	+	0.261179i	−0.752836	−	0.658208i	$-0.771315\pi$
$97$	−3.54048	+	2.57231i	−0.359481	+	0.261179i	0.393354	+	0.919387i	$0.371315\pi$
$98$	6.22021	−	4.89222i	0.628336	−	0.494189i
$99$	−1.45726	+	0.405804i	−0.146460	+	0.0407849i
$100$	0.471289	−	1.94368i	0.0471289	−	0.194368i
$101$	9.87151	+	13.5870i	0.982252	+	1.35195i	0.935607	+	0.353042i	$0.114853\pi$
$101$	9.87151	+	13.5870i	0.982252	+	1.35195i	0.0466447	+	0.998912i	$0.485147\pi$
$102$	−9.40752	−	6.30131i	−0.931483	−	0.623922i
$103$	9.79401	+	3.18227i	0.965032	+	0.313558i	0.748809	−	0.662786i	$-0.230626\pi$
$103$	9.79401	+	3.18227i	0.965032	+	0.313558i	0.216223	+	0.976344i	$0.430626\pi$
$104$	−15.0491	−	3.04658i	−1.47569	−	0.298741i
$105$	3.32722	−	4.57952i	0.324703	−	0.446915i
$106$	−1.40130	−	3.81166i	−0.136106	−	0.370221i
$107$	0.00970105	+	0.0298568i	0.000937836	+	0.00288636i	0.951524	−	0.307573i	$-0.0995170\pi$
$107$	0.00970105	+	0.0298568i	0.000937836	+	0.00288636i	−0.950587	+	0.310460i	$0.899517\pi$
$108$	−10.1950	+	4.19591i	−0.981014	+	0.403752i
$109$		−	7.63015i		−	0.730836i	−0.930844	−	0.365418i	$-0.880926\pi$
$109$		−	7.63015i		−	0.730836i	0.930844	−	0.365418i	$-0.119074\pi$
$110$	4.46723	−	1.42964i	0.425933	−	0.136311i
$111$		−	4.46888i		−	0.424168i
$112$	14.0313	−	2.15731i	1.32584	−	0.203847i
$113$	−3.81654	−	11.7461i	−0.359030	−	1.10498i	−0.953636	−	0.300963i	$-0.902692\pi$
$113$	−3.81654	−	11.7461i	−0.359030	−	1.10498i	0.594606	−	0.804017i	$-0.297308\pi$
$114$	3.76707	−	1.38491i	0.352819	−	0.129708i
$115$	−1.23118	+	1.69458i	−0.114809	+	0.158020i
$116$	7.57187	+	8.90624i	0.703031	+	0.826924i
$117$	2.35479	+	0.765117i	0.217700	+	0.0707351i
$118$	2.02792	−	3.02758i	0.186685	−	0.278711i
$119$	−10.4718	−	14.4132i	−0.959951	−	1.32126i
$120$	4.10323	−	1.87476i	0.374572	−	0.171141i
$121$	8.31715	+	7.19896i	0.756104	+	0.654451i
$122$	−6.75751	−	8.59184i	−0.611796	−	0.777868i
$123$	−14.5849	+	10.5965i	−1.31507	+	0.955457i
$124$	1.63735	+	21.4240i	0.147038	+	1.92393i
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$	−2.28754	+	0.0872864i	−0.203791	+	0.00777609i
$127$	2.24495	+	1.63105i	0.199207	+	0.144732i	0.682917	−	0.730496i	$-0.260711\pi$
$127$	2.24495	+	1.63105i	0.199207	+	0.144732i	−0.483710	+	0.875228i	$0.660711\pi$
$128$	10.5831	+	3.99979i	0.935421	+	0.353535i
$129$	0.816583	−	0.265324i	0.0718961	−	0.0233605i
$130$	−7.38659	−	2.09226i	−0.647847	−	0.183503i
$131$	9.29212			0.811856			0.405928	−	0.913905i	$-0.366948\pi$
$131$	9.29212			0.811856			0.405928	+	0.913905i	$0.366948\pi$
$132$	8.76394	+	5.92664i	0.762803	+	0.515848i
$133$	6.31507			0.547586
$134$	−5.97648	−	1.69284i	−0.516289	−	0.146239i
$135$	−5.24255	+	1.70341i	−0.451207	+	0.146606i
$136$	−1.62098	−	14.1055i	−0.138998	−	1.20954i
$137$	−10.1840	−	7.39910i	−0.870077	−	0.632148i	0.0605305	−	0.998166i	$-0.480721\pi$
$137$	−10.1840	−	7.39910i	−0.870077	−	0.632148i	−0.930608	+	0.366018i	$0.880721\pi$
$138$	−4.72121	+	0.180149i	−0.401896	+	0.0153353i
$139$	−0.125020	+	0.384773i	−0.0106041	+	0.0326360i	−0.956219	−	0.292654i	$-0.905462\pi$
$139$	−0.125020	+	0.384773i	−0.0106041	+	0.0326360i	0.945614	+	0.325290i	$0.105462\pi$
$140$	7.07746	−	0.540901i	0.598154	−	0.0457145i
$141$	2.21092	−	1.60633i	0.186193	−	0.135277i
$142$	−3.52751	−	4.48505i	−0.296022	−	0.376377i
$143$	−4.82998	−	17.3447i	−0.403904	−	1.45043i
$144$	−1.62178	−	0.835603i	−0.135148	−	0.0696336i
$145$	3.43558	+	4.72867i	0.285310	+	0.392695i
$146$	5.28303	−	7.88728i	0.437226	−	0.652756i
$147$	8.48818	+	2.75798i	0.700094	+	0.227474i
$148$	4.26935	−	3.62970i	0.350938	−	0.298359i
$149$	4.65036	−	6.40067i	0.380972	−	0.524363i	−0.574870	−	0.818245i	$-0.694947\pi$
$149$	4.65036	−	6.40067i	0.380972	−	0.524363i	0.955842	+	0.293882i	$0.0949472\pi$
$150$	2.11708	−	0.778313i	0.172859	−	0.0635490i
$151$	0.801162	+	2.46572i	0.0651976	+	0.200658i	0.978349	−	0.206964i	$-0.0663583\pi$
$151$	0.801162	+	2.46572i	0.0651976	+	0.200658i	−0.913151	+	0.407622i	$0.866358\pi$
$152$	4.38275	+	2.47403i	0.355488	+	0.200670i
$153$			2.28955i			0.185099i
$154$	9.72482	+	13.5105i	0.783648	+	1.08871i
$155$			10.7432i			0.862917i
$156$	−6.59064	−	16.0136i	−0.527674	−	1.28211i
$157$	−3.69882	−	11.3838i	−0.295198	−	0.908527i	−0.983155	−	0.182775i	$-0.941492\pi$
$157$	−3.69882	−	11.3838i	−0.295198	−	0.908527i	0.687956	−	0.725752i	$-0.258508\pi$
$158$	1.85951	+	5.05804i	0.147935	+	0.402396i
$159$	2.69213	−	3.70539i	0.213500	−	0.293857i
$160$	5.12376	+	2.39731i	0.405069	+	0.189524i
$161$	−7.07005	−	2.29720i	−0.557198	−	0.181045i
$162$	−8.72272	−	5.84262i	−0.685322	−	0.459039i
$163$	−2.06262	−	2.83895i	−0.161557	−	0.222364i	0.720562	−	0.693390i	$-0.243884\pi$
$163$	−2.06262	−	2.83895i	−0.161557	−	0.222364i	−0.882119	+	0.471026i	$0.843884\pi$
$164$	−21.9695	−	5.32700i	−1.71553	−	0.415968i
$165$	4.14341	+	3.28863i	0.322564	+	0.256019i
$166$	−10.6430	+	8.37074i	−0.826054	+	0.649695i
$167$	−11.6837	+	8.48868i	−0.904109	+	0.656874i	−0.939518	−	0.342499i	$-0.888727\pi$
$167$	−11.6837	+	8.48868i	−0.904109	+	0.656874i	0.0354088	+	0.999373i	$0.488727\pi$
$168$	10.8280	+	11.7937i	0.835401	+	0.909907i
$169$	−5.08939	+	15.6635i	−0.391492	+	1.20489i
$170$	−0.270688	−	7.09400i	−0.0207608	−	0.544085i
$171$	−0.656572	−	0.477027i	−0.0502093	−	0.0364792i
$172$	0.916718	+	0.564622i	0.0698991	+	0.0430521i
$173$	0.416466	−	0.135318i	0.0316633	−	0.0102880i	−0.293143	−	0.956069i	$-0.594701\pi$
$173$	0.416466	−	0.135318i	0.0316633	−	0.0102880i	0.324806	+	0.945781i	$0.394701\pi$
$174$	−3.59302	+	12.6849i	−0.272386	+	0.961643i
$175$	3.54905			0.268283
$176$	1.45619	+	13.1863i	0.109765	+	0.993958i
$177$	4.10973			0.308906
$178$	−7.12123	+	25.1411i	−0.533759	+	1.88440i
$179$	−1.88812	+	0.613487i	−0.141125	+	0.0458542i	−0.378728	−	0.925508i	$-0.623638\pi$
$179$	−1.88812	+	0.613487i	−0.141125	+	0.0458542i	0.237603	+	0.971362i	$0.423638\pi$
$180$	−0.776695	−	0.478379i	−0.0578914	−	0.0356563i
$181$	−8.13811	−	5.91268i	−0.604901	−	0.439486i	0.242714	−	0.970098i	$-0.421962\pi$
$181$	−8.13811	−	5.91268i	−0.604901	−	0.439486i	−0.847615	+	0.530612i	$0.821962\pi$
$182$	−1.03890	−	27.2269i	−0.0770088	−	2.01819i
$183$	3.80953	−	11.7245i	0.281609	−	0.866703i
$184$	−4.00675	−	4.36409i	−0.295381	−	0.321725i
$185$	2.26677	−	1.64690i	0.166656	−	0.121083i
$186$	−19.0472	+	14.9807i	−1.39661	+	1.09844i
$187$	13.8736	−	9.20398i	1.01454	−	0.673061i
$188$	3.33035	+	0.807519i	0.242891	+	0.0588944i
$189$	−11.4992	−	15.8273i	−0.836442	−	1.15126i
$190$	2.09074	+	1.40041i	0.151678	+	0.101596i
$191$	1.59439	+	0.518049i	0.115366	+	0.0374847i	0.366131	−	0.930563i	$-0.380682\pi$
$191$	1.59439	+	0.518049i	0.115366	+	0.0374847i	−0.250765	+	0.968048i	$0.580682\pi$
$192$	2.89442	+	12.4271i	0.208887	+	0.896847i
$193$	−6.97629	+	9.60204i	−0.502164	+	0.691170i	−0.982573	−	0.185875i	$-0.940488\pi$
$193$	−6.97629	+	9.60204i	−0.502164	+	0.691170i	0.480409	+	0.877044i	$0.340488\pi$
$194$	−2.13555	−	5.80888i	−0.153323	−	0.417053i
$195$	−2.67559	−	8.23462i	−0.191603	−	0.589694i
$196$	4.25940	+	10.3493i	0.304243	+	0.739233i
$197$			2.10498i			0.149974i	0.997185	+	0.0749868i	$0.0238915\pi$
$197$			2.10498i			0.149974i	−0.997185	+	0.0749868i	$0.976109\pi$
$198$	0.00947739	−	2.13927i	0.000673529	−	0.152031i
$199$		−	18.7018i		−	1.32573i	−0.748737	−	0.662867i	$-0.769340\pi$
$199$		−	18.7018i		−	1.32573i	0.748737	−	0.662867i	$-0.230660\pi$
$200$	2.46309	+	1.39040i	0.174167	+	0.0983158i
$201$	−2.16482	−	6.66263i	−0.152695	−	0.469945i
$202$	−22.2922	+	8.19538i	−1.56847	+	0.576625i
$203$	−12.1931	+	16.7823i	−0.855784	+	1.17789i
$204$	12.1999	−	10.3720i	0.854161	−	0.726187i
$205$	−10.7498	−	3.49283i	−0.750800	−	0.243950i
$206$	−8.10480	+	12.1000i	−0.564688	+	0.843050i
$207$	0.561541	+	0.772894i	0.0390298	+	0.0537199i
$208$	9.94556	−	19.3028i	0.689600	−	1.33841i
$209$	−0.251145	+	5.89616i	−0.0173721	+	0.407846i
$210$	4.94891	+	6.29229i	0.341507	+	0.434209i
$211$	16.0143	−	11.6351i	1.10247	−	0.800994i	0.121011	−	0.992651i	$-0.461386\pi$
$211$	16.0143	−	11.6351i	1.10247	−	0.800994i	0.981462	+	0.191657i	$0.0613863\pi$
$212$	5.72653	−	0.437655i	0.393300	−	0.0300583i
$213$	1.98862	−	6.12035i	0.136258	−	0.419360i
$214$	−0.0443645	+	0.00169283i	−0.00303270	+	0.000115719i
$215$	0.435513	+	0.316419i	0.0297018	+	0.0215796i
$216$	−1.78001	−	15.4893i	−0.121114	−	1.05391i
$217$	−36.2621	+	11.7823i	−2.46163	+	0.799833i
$218$	10.3822	+	2.94077i	0.703172	+	0.199174i
$219$	10.7064			0.723474
$220$	0.223555	+	6.62948i	0.0150721	+	0.446960i
$221$	−27.2508			−1.83309
$222$	6.08073	+	1.72237i	0.408112	+	0.115598i
$223$	15.7095	−	5.10434i	1.05199	−	0.341812i	0.268540	−	0.963268i	$-0.413459\pi$
$223$	15.7095	−	5.10434i	1.05199	−	0.341812i	0.783449	+	0.621456i	$0.213459\pi$
$224$	−2.47245	+	19.9236i	−0.165198	+	1.33120i
$225$	−0.368991	−	0.268088i	−0.0245994	−	0.0178725i
$226$	17.4537	−	0.665984i	1.16100	−	0.0443006i
$227$	−4.27781	+	13.1657i	−0.283928	+	0.873840i	0.702790	+	0.711397i	$0.251937\pi$
$227$	−4.27781	+	13.1657i	−0.283928	+	0.873840i	−0.986718	+	0.162443i	$0.948063\pi$
$228$	0.432536	+	5.65955i	0.0286454	+	0.374813i
$229$	−1.02986	+	0.748240i	−0.0680553	+	0.0494451i	−0.621293	−	0.783579i	$-0.713392\pi$
$229$	−1.02986	+	0.748240i	−0.0680553	+	0.0494451i	0.553237	+	0.833024i	$0.313392\pi$
$230$	−1.83127	−	2.32837i	−0.120750	−	0.153528i
$231$	−6.55610	+	17.5921i	−0.431360	+	1.15748i
$232$	−15.0369	+	6.87032i	−0.987219	+	0.451058i
$233$	8.17688	+	11.2545i	0.535685	+	0.737307i	0.987983	−	0.154559i	$-0.0493958\pi$
$233$	8.17688	+	11.2545i	0.535685	+	0.737307i	−0.452298	+	0.891867i	$0.649396\pi$
$234$	−1.94865	+	2.90923i	−0.127387	+	0.190182i
$235$	1.62957	+	0.529478i	0.106301	+	0.0345393i
$236$	3.33798	+	3.92623i	0.217284	+	0.255576i
$237$	−3.57243	+	4.91703i	−0.232054	+	0.319395i
$238$	23.6478	−	8.69377i	1.53286	−	0.563533i
$239$	7.51220	+	23.1202i	0.485924	+	1.49552i	0.830638	+	0.556812i	$0.187976\pi$
$239$	7.51220	+	23.1202i	0.485924	+	1.49552i	−0.344715	+	0.938708i	$0.612024\pi$
$240$	0.969507	+	6.30575i	0.0625814	+	0.407034i
$241$		−	10.6288i		−	0.684662i	−0.939579	−	0.342331i	$-0.888784\pi$
$241$		−	10.6288i		−	0.684662i	0.939579	−	0.342331i	$-0.111216\pi$
$242$	−13.0010	+	8.54241i	−0.835739	+	0.549127i
$243$			4.69654i			0.301284i
$244$	14.2952	−	5.88341i	0.915156	−	0.376647i
$245$	1.72918	+	5.32187i	0.110473	+	0.340002i
$246$	−8.79730	−	23.9294i	−0.560895	−	1.52569i
$247$	5.67770	−	7.81468i	0.361263	−	0.497236i
$248$	−29.7823	−	6.02920i	−1.89118	−	0.382855i
$249$	−14.5235	−	4.71898i	−0.920392	−	0.299053i
$250$	1.17499	+	0.787025i	0.0743126	+	0.0497758i
$251$	−6.99220	−	9.62393i	−0.441344	−	0.607457i	0.529166	−	0.848518i	$-0.322505\pi$
$251$	−6.99220	−	9.62393i	−0.441344	−	0.607457i	−0.970510	+	0.241061i	$0.922505\pi$
$252$	0.762882	−	3.14626i	0.0480571	−	0.198196i
$253$	2.42598	−	6.50970i	0.152520	−	0.409261i
$254$	−3.08458	+	2.42603i	−0.193544	+	0.152223i
$255$	6.47739	−	4.70610i	0.405630	−	0.294707i
$256$	−9.52131	+	12.8586i	−0.595082	+	0.803665i
$257$	1.79040	−	5.51028i	0.111682	−	0.343722i	−0.879559	−	0.475791i	$-0.842162\pi$
$257$	1.79040	−	5.51028i	0.111682	−	0.343722i	0.991241	+	0.132069i	$0.0421620\pi$
$258$	0.0462989	+	1.21337i	0.00288244	+	0.0755411i
$259$	8.04486	+	5.84493i	0.499883	+	0.363187i
$260$	5.69379	−	9.24442i	0.353114	−	0.573314i
$261$	2.53540	−	0.823801i	0.156937	−	0.0509920i
$262$	−3.58131	+	12.6436i	−0.221254	+	0.781125i
$263$	30.3637			1.87231			0.936154	−	0.351591i	$-0.114359\pi$
$263$	30.3637			1.87231			0.936154	+	0.351591i	$0.114359\pi$
$264$	−11.4420	+	9.64073i	−0.704208	+	0.593346i
$265$	2.87162			0.176402
$266$	−2.43392	+	8.59281i	−0.149233	+	0.526859i
$267$	−28.0275	+	9.10668i	−1.71525	+	0.557320i
$268$	4.60684	−	7.47965i	0.281408	−	0.456892i
$269$	13.6548	+	9.92082i	0.832550	+	0.604883i	0.920280	−	0.391261i	$-0.127961\pi$
$269$	13.6548	+	9.92082i	0.832550	+	0.604883i	−0.0877298	+	0.996144i	$0.527961\pi$
$270$	−0.297244	−	7.78996i	−0.0180897	−	0.474082i
$271$	−5.16893	+	15.9083i	−0.313990	+	0.966362i	0.662178	+	0.749347i	$0.269632\pi$
$271$	−5.16893	+	15.9083i	−0.313990	+	0.966362i	−0.976168	+	0.217016i	$0.930368\pi$
$272$	19.8178	+	3.23082i	1.20163	+	0.195897i
$273$	24.8603	−	18.0621i	1.50462	−	1.09317i
$274$	13.9929	−	11.0055i	0.845341	−	0.664864i
$275$	−0.141143	+	3.31362i	−0.00851122	+	0.199819i
$276$	1.57450	−	6.49350i	0.0947736	−	0.390863i
$277$	−2.41925	−	3.32981i	−0.145359	−	0.200069i	0.730129	−	0.683309i	$-0.239460\pi$
$277$	−2.41925	−	3.32981i	−0.145359	−	0.200069i	−0.875488	+	0.483240i	$0.839460\pi$
$278$	−0.475369	−	0.318410i	−0.0285107	−	0.0190969i
$279$	4.66015	+	1.51417i	0.278996	+	0.0906512i
$280$	−1.99176	+	9.83864i	−0.119030	+	0.587971i
$281$	−3.33630	+	4.59202i	−0.199027	+	0.273937i	−0.896852	−	0.442331i	$-0.854151\pi$
$281$	−3.33630	+	4.59202i	−0.199027	+	0.273937i	0.697825	+	0.716269i	$0.254151\pi$
$282$	1.33358	+	3.62746i	0.0794137	+	0.216012i
$283$	−8.65086	−	26.6246i	−0.514241	−	1.58267i	−0.784660	−	0.619927i	$-0.787162\pi$
$283$	−8.65086	−	26.6246i	−0.514241	−	1.58267i	0.270419	−	0.962743i	$-0.412838\pi$
$284$	7.46227	−	3.07121i	0.442804	−	0.182243i
$285$			2.83803i			0.168110i
$286$	25.4621	+	0.112802i	1.50561	+	0.00667014i
$287$		−	40.1150i		−	2.36791i
$288$	1.76205	−	1.88468i	0.103830	−	0.111056i
$289$	−2.53365	−	7.79776i	−0.149038	−	0.458692i
$290$	−7.75834	+	2.85224i	−0.455586	+	0.167489i
$291$	4.10274	−	5.64693i	0.240507	−	0.331029i
$292$	8.69593	+	10.2284i	0.508891	+	0.598571i
$293$	1.24924	+	0.405903i	0.0729815	+	0.0237131i	0.345280	−	0.938500i	$-0.387784\pi$
$293$	1.24924	+	0.405903i	0.0729815	+	0.0237131i	−0.272299	+	0.962213i	$0.587784\pi$
$294$	−7.02420	+	10.4868i	−0.409659	+	0.611600i
$295$	1.51454	+	2.08459i	0.0881801	+	0.121369i
$296$	3.29340	+	7.20816i	0.191425	+	0.418966i
$297$	15.2347	−	10.1069i	0.884005	−	0.586464i
$298$	6.91696	+	8.79457i	0.400689	+	0.509456i
$299$	−9.19918	+	6.68360i	−0.532003	+	0.386522i
$300$	0.243084	+	3.18065i	0.0140344	+	0.183635i
$301$	−0.590389	+	1.81703i	−0.0340294	+	0.104732i
$302$	−3.66384	+	0.139802i	−0.210831	+	0.00804472i
$303$	−21.6707	−	15.7447i	−1.24495	−	0.904508i
$304$	−5.05554	+	5.01000i	−0.289955	+	0.287343i
$305$	7.35098	−	2.38848i	0.420916	−	0.136764i
$306$	−3.11535	−	0.882425i	−0.178093	−	0.0504449i
$307$	−11.8621			−0.677004			−0.338502	−	0.940966i	$-0.609920\pi$
$307$	−11.8621			−0.677004			−0.338502	+	0.940966i	$0.609920\pi$
$308$	−22.1316	+	8.02524i	−1.26107	+	0.457280i
$309$	−16.4250			−0.934383
$310$	−14.6181	−	4.14059i	−0.830254	−	0.235170i
$311$	8.14461	−	2.64634i	0.461838	−	0.150060i	−0.0688507	−	0.997627i	$-0.521933\pi$
$311$	8.14461	−	2.64634i	0.461838	−	0.150060i	0.530689	+	0.847567i	$0.321933\pi$
$312$	24.3295	−	2.79591i	1.37739	−	0.158287i
$313$	24.2701	+	17.6333i	1.37183	+	0.996691i	0.997592	+	0.0693576i	$0.0220950\pi$
$313$	24.2701	+	17.6333i	1.37183	+	0.996691i	0.374236	+	0.927334i	$0.377905\pi$
$314$	16.9153	−	0.645443i	0.954587	−	0.0364245i
$315$	0.500210	−	1.53949i	0.0281837	−	0.0867404i
$316$	−7.59907	+	0.580765i	−0.427481	+	0.0326706i
$317$	9.86035	−	7.16396i	0.553812	−	0.402368i	−0.275377	−	0.961336i	$-0.588803\pi$
$317$	9.86035	−	7.16396i	0.553812	−	0.402368i	0.829189	+	0.558968i	$0.188803\pi$
$318$	4.00428	+	5.09124i	0.224549	+	0.285503i
$319$	−15.1841	−	12.0516i	−0.850148	−	0.674762i
$320$	−5.23675	+	6.04785i	−0.292743	+	0.338085i
$321$	−0.0294310	−	0.0405083i	−0.00164268	−	0.00226095i
$322$	5.85066	−	8.73472i	0.326044	−	0.486767i
$323$	8.49503	+	2.76020i	0.472676	+	0.153582i
$324$	11.3118	−	9.61702i	0.628434	−	0.534279i
$325$	3.19085	−	4.39182i	0.176996	−	0.243615i
$326$	4.65787	−	1.71240i	0.257976	−	0.0948408i
$327$	3.76067	+	11.5742i	0.207966	+	0.640053i
$328$	15.7157	−	27.8404i	0.867754	−	1.53723i
$329$			6.08103i			0.335258i
$330$	−6.07170	+	4.37038i	−0.334236	+	0.240582i
$331$		−	20.5092i		−	1.12729i	−0.826018	−	0.563643i	$-0.809399\pi$
$331$		−	20.5092i		−	1.12729i	0.826018	−	0.563643i	$-0.190601\pi$
$332$	−7.28796	−	17.7079i	−0.399979	−	0.971847i
$333$	−0.394902	−	1.21538i	−0.0216405	−	0.0666026i
$334$	−7.04735	−	19.1694i	−0.385614	−	1.04890i
$335$	2.58171	−	3.55342i	0.141054	−	0.194144i
$336$	−20.2208	+	10.1880i	−1.10314	+	0.555803i
$337$	5.43161	+	1.76484i	0.295878	+	0.0961367i	0.453195	−	0.891412i	$-0.350284\pi$
$337$	5.43161	+	1.76484i	0.295878	+	0.0961367i	−0.157316	+	0.987548i	$0.550284\pi$
$338$	−19.3516	−	12.9620i	−1.05259	−	0.705040i
$339$	11.5786	+	15.9366i	0.628864	+	0.865557i
$340$	9.75701	+	2.36581i	0.529148	+	0.128304i
$341$	−9.55858	−	34.3252i	−0.517626	−	1.85882i
$342$	0.902135	−	0.709533i	0.0487819	−	0.0383671i
$343$	4.03194	−	2.92938i	0.217705	−	0.158172i
$344$	−1.12159	+	1.02975i	−0.0604720	+	0.0555203i
$345$	1.03237	−	3.17732i	0.0555811	−	0.171061i
$346$	0.0236129	+	0.618831i	0.00126944	+	0.0332686i
$347$	11.1719	+	8.11689i	0.599741	+	0.435738i	0.845787	−	0.533521i	$-0.179131\pi$
$347$	11.1719	+	8.11689i	0.599741	+	0.435738i	−0.246046	+	0.969258i	$0.579131\pi$
$348$	−15.8754	−	9.77791i	−0.851010	−	0.524151i
$349$	30.8726	−	10.0311i	1.65257	−	0.536953i	0.673276	−	0.739391i	$-0.264886\pi$
$349$	30.8726	−	10.0311i	1.65257	−	0.536953i	0.979295	+	0.202438i	$0.0648864\pi$
$350$	−1.36785	+	4.82913i	−0.0731148	+	0.258128i
$351$	−29.9243			−1.59724
$352$	−18.5037	−	3.10079i	−0.986248	−	0.165273i
$353$	−20.4320			−1.08749			−0.543744	−	0.839251i	$-0.682994\pi$
$353$	−20.4320			−1.08749			−0.543744	+	0.839251i	$0.682994\pi$
$354$	−1.58395	+	5.59203i	−0.0841858	+	0.297213i
$355$	3.83731	−	1.24682i	0.203663	−	0.0661741i
$356$	−31.4644	−	19.3795i	−1.66761	−	1.02711i
$357$	22.9886	+	16.7022i	1.21668	+	0.883973i
$358$	−0.107053	−	2.80558i	−0.00565793	−	0.148279i
$359$	−5.92074	+	18.2222i	−0.312485	+	0.961729i	0.664293	+	0.747472i	$0.268733\pi$
$359$	−5.92074	+	18.2222i	−0.312485	+	0.961729i	−0.976777	+	0.214256i	$0.931267\pi$
$360$	0.950271	−	0.872461i	0.0500837	−	0.0459827i
$361$	12.8098	−	9.30690i	0.674202	−	0.489837i
$362$	11.1818	−	8.79455i	0.587704	−	0.462231i
$363$	−16.1644	−	6.82082i	−0.848412	−	0.358000i
$364$	37.4476	+	9.08002i	1.96279	+	0.475922i
$365$	3.94560	+	5.43066i	0.206522	+	0.284253i
$366$	14.4851	+	9.70237i	0.757149	+	0.507151i
$367$	−9.22840	−	2.99849i	−0.481718	−	0.156520i	0.0580838	−	0.998312i	$-0.481501\pi$
$367$	−9.22840	−	2.99849i	−0.481718	−	0.156520i	−0.539802	+	0.841792i	$0.681501\pi$
$368$	7.48240	−	3.76993i	0.390047	−	0.196521i
$369$	−3.03020	+	4.17072i	−0.157746	+	0.217119i
$370$	1.36727	+	3.71909i	0.0710808	+	0.193346i
$371$	3.14935	+	9.69270i	0.163506	+	0.503220i
$372$	−13.0429	−	31.6910i	−0.676245	−	1.64310i
$373$			13.7667i			0.712815i	0.934331	+	0.356407i	$0.115998\pi$
$373$			13.7667i			0.712815i	−0.934331	+	0.356407i	$0.884002\pi$
$374$	7.17661	+	22.4249i	0.371094	+	1.15956i
$375$			1.59496i			0.0823635i
$376$	−2.38234	+	4.22032i	−0.122860	+	0.217646i
$377$	9.80509	+	30.1770i	0.504988	+	1.55419i
$378$	25.9678	−	9.54668i	1.33564	−	0.491028i
$379$	−0.177637	+	0.244497i	−0.00912462	+	0.0125590i	−0.813555	−	0.581488i	$-0.802471\pi$
$379$	−0.177637	+	0.244497i	−0.00912462	+	0.0125590i	0.804430	+	0.594047i	$0.202471\pi$
$380$	−2.71131	+	2.30509i	−0.139087	+	0.118249i
$381$	−4.20926	−	1.36767i	−0.215647	−	0.0700679i
$382$	−1.31940	+	1.96979i	−0.0675064	+	0.100783i
$383$	−0.898317	−	1.23643i	−0.0459018	−	0.0631785i	0.785449	−	0.618926i	$-0.212432\pi$
$383$	−0.898317	−	1.23643i	−0.0459018	−	0.0631785i	−0.831351	+	0.555748i	$0.812432\pi$
$384$	−18.0248	−	0.851185i	−0.919826	−	0.0434368i
$385$	−11.3394	+	3.15770i	−0.577910	+	0.160931i
$386$	−10.3766	−	13.1933i	−0.528153	−	0.671520i
$387$	0.198637	−	0.144318i	0.0100973	−	0.00733610i
$388$	8.72710	−	0.666976i	0.443052	−	0.0338606i
$389$	−8.69823	+	26.7704i	−0.441018	+	1.35731i	0.445775	+	0.895145i	$0.352928\pi$
$389$	−8.69823	+	26.7704i	−0.441018	+	1.35731i	−0.886793	+	0.462167i	$0.847072\pi$
$390$	12.2359	−	0.466889i	0.619590	−	0.0236419i
$391$	−8.50656	−	6.18038i	−0.430195	−	0.312555i
$392$	−15.7237	+	1.80694i	−0.794166	+	0.0912642i
$393$	−14.0952	+	4.57981i	−0.711009	+	0.231021i
$394$	−2.86421	−	0.811289i	−0.144297	−	0.0408722i
$395$	−3.81061			−0.191733
$396$	2.90721	+	0.837400i	0.146093	+	0.0420809i
$397$	20.1995			1.01378			0.506891	−	0.862010i	$-0.330795\pi$
$397$	20.1995			1.01378			0.506891	+	0.862010i	$0.330795\pi$
$398$	25.4472	+	7.20793i	1.27555	+	0.361301i
$399$	−9.57933	+	3.11251i	−0.479566	+	0.155821i
$400$	−2.84120	+	2.81560i	−0.142060	+	0.140780i
$401$	3.74014	+	2.71737i	0.186774	+	0.135699i	0.677243	−	0.735760i	$-0.263175\pi$
$401$	3.74014	+	2.71737i	0.186774	+	0.135699i	−0.490469	+	0.871458i	$0.663175\pi$
$402$	9.90007	−	0.377760i	0.493771	−	0.0188409i
$403$	−18.0221	+	55.4662i	−0.897743	+	2.76297i
$404$	−2.55959	−	33.4912i	−0.127344	−	1.66625i
$405$	6.00588	−	4.36353i	0.298435	−	0.216826i
$406$	−18.1360	−	23.0590i	−0.900074	−	1.14440i
$407$	−5.77714	+	7.27875i	−0.286362	+	0.360794i
$408$	9.41103	+	20.5977i	0.465916	+	1.01974i
$409$	−16.3725	−	22.5348i	−0.809566	−	1.11427i	−0.991390	−	0.130941i	$-0.958200\pi$
$409$	−16.3725	−	22.5348i	−0.809566	−	1.11427i	0.181824	−	0.983331i	$-0.441800\pi$
$410$	8.89576	−	13.2809i	0.439330	−	0.655897i
$411$	19.0949	+	6.20430i	0.941881	+	0.306036i
$412$	−13.3406	−	15.6916i	−0.657244	−	0.773069i
$413$	−5.37518	+	7.39831i	−0.264496	+	0.364047i
$414$	−1.26809	+	0.466194i	−0.0623232	+	0.0229122i
$415$	−2.95868	−	9.10589i	−0.145236	−	0.446990i
$416$	22.4319	+	20.9723i	1.09981	+	1.02825i
$417$		−	0.645280i		−	0.0315995i
$418$	−7.92600	−	2.61419i	−0.387674	−	0.127864i
$419$			21.0186i			1.02683i	0.858141	+	0.513414i	$0.171619\pi$
$419$			21.0186i			1.02683i	−0.858141	+	0.513414i	$0.828381\pi$
$420$	−10.4692	+	4.30876i	−0.510844	+	0.210246i
$421$	−3.00740	−	9.25581i	−0.146572	−	0.451101i	0.850638	−	0.525751i	$-0.176216\pi$
$421$	−3.00740	−	9.25581i	−0.146572	−	0.451101i	−0.997210	+	0.0746507i	$0.976216\pi$
$422$	9.65952	+	26.2748i	0.470218	+	1.27904i
$423$	0.459349	−	0.632239i	0.0223343	−	0.0307405i
$424$	−1.61158	+	7.96067i	−0.0782651	+	0.386604i
$425$	4.77418	+	1.55122i	0.231582	+	0.0752454i
$426$	7.56141	+	5.06476i	0.366352	+	0.245388i
$427$	16.1239	+	22.1926i	0.780290	+	1.07398i
$428$	0.0147953	−	0.0610184i	0.000715158	−	0.00294944i
$429$	15.8753	+	23.9295i	0.766465	+	1.15533i
$430$	−0.598399	+	0.470643i	−0.0288573	+	0.0226964i
$431$	26.2798	−	19.0934i	1.26585	−	0.919697i	0.266825	−	0.963745i	$-0.414025\pi$
$431$	26.2798	−	19.0934i	1.26585	−	0.919697i	0.999029	+	0.0440477i	$0.0140254\pi$
$432$	21.7621	+	3.54778i	1.04703	+	0.170693i
$433$	3.35754	−	10.3334i	0.161353	−	0.496594i	−0.837396	−	0.546597i	$-0.815923\pi$
$433$	3.35754	−	10.3334i	0.161353	−	0.496594i	0.998749	+	0.0500029i	$0.0159231\pi$
$434$	−2.05600	−	53.8823i	−0.0986913	−	2.58643i
$435$	−7.54205	−	5.47962i	−0.361614	−	0.262728i
$436$	−8.00290	+	12.9935i	−0.383269	+	0.622275i
$437$	3.54468	−	1.15174i	0.169565	−	0.0550950i
$438$	−4.12641	+	14.5681i	−0.197167	+	0.696088i
$439$	0.976563			0.0466088			0.0233044	−	0.999728i	$-0.492581\pi$
$439$	0.976563			0.0466088			0.0233044	+	0.999728i	$0.492581\pi$
$440$	−9.10678	−	2.25091i	−0.434149	−	0.107308i
$441$	2.55221			0.121534
$442$	10.5028	−	37.0797i	0.499569	−	1.76370i
$443$	2.87224	−	0.933246i	0.136464	−	0.0443399i	−0.239989	−	0.970776i	$-0.577144\pi$
$443$	2.87224	−	0.933246i	0.136464	−	0.0443399i	0.376453	+	0.926436i	$0.377144\pi$
$444$	−4.68720	+	7.61012i	−0.222445	+	0.361160i
$445$	−14.9481	−	10.8604i	−0.708607	−	0.514833i
$446$	0.890705	+	23.3430i	0.0421761	+	1.10532i
$447$	−3.89942	+	12.0012i	−0.184436	+	0.567637i
$448$	−26.1568	−	11.0431i	−1.23579	−	0.521736i
$449$	−20.0226	+	14.5473i	−0.944926	+	0.686529i	−0.949601	−	0.313460i	$-0.898512\pi$
$449$	−20.0226	+	14.5473i	−0.944926	+	0.686529i	0.00467526	+	0.999989i	$0.498512\pi$
$450$	0.506996	−	0.398755i	0.0239000	−	0.0187975i
$451$	37.4540	+	1.59534i	1.76364	+	0.0751216i
$452$	−5.82070	+	24.0056i	−0.273782	+	1.12913i
$453$	−2.43056	−	3.34538i	−0.114198	−	0.157180i
$454$	−16.2657	−	10.8950i	−0.763385	−	0.511327i
$455$	18.3234	+	5.95363i	0.859013	+	0.279110i
$456$	−7.86756	−	1.59273i	−0.368432	−	0.0745863i
$457$	−23.9067	+	32.9048i	−1.11831	+	1.53922i	−0.309737	+	0.950822i	$0.600241\pi$
$457$	−23.9067	+	32.9048i	−1.11831	+	1.53922i	−0.808572	+	0.588398i	$0.799759\pi$
$458$	−0.621193	−	1.68970i	−0.0290264	−	0.0789545i
$459$	−8.55088	−	26.3169i	−0.399121	−	1.22837i
$460$	3.87396	−	1.59439i	0.180624	−	0.0743388i
$461$			30.5966i			1.42502i	0.701660	+	0.712512i	$0.252443\pi$
$461$			30.5966i			1.42502i	−0.701660	+	0.712512i	$0.747557\pi$
$462$	−21.4105	−	15.7010i	−0.996107	−	0.730478i
$463$			37.7916i			1.75633i	0.478361	+	0.878163i	$0.341231\pi$
$463$			37.7916i			1.75633i	−0.478361	+	0.878163i	$0.658769\pi$
$464$	−3.55290	−	23.1083i	−0.164939	−	1.07278i
$465$	−5.29502	−	16.2964i	−0.245551	−	0.755727i
$466$	−18.4653	+	6.78849i	−0.855388	+	0.314470i
$467$	18.8449	−	25.9378i	0.872038	−	1.20026i	−0.106526	−	0.994310i	$-0.533973\pi$
$467$	18.8449	−	25.9378i	0.872038	−	1.20026i	0.978563	−	0.205947i	$-0.0660274\pi$
$468$	−3.20750	−	3.77275i	−0.148267	−	0.174396i
$469$	14.8254	+	4.81707i	0.684575	+	0.222432i
$470$	−1.34851	+	2.01325i	−0.0622021	+	0.0928644i
$471$	11.2215	+	15.4450i	0.517059	+	0.711670i
$472$	−6.62885	+	3.02871i	−0.305118	+	0.139408i
$473$	−1.67302	−	0.623487i	−0.0769254	−	0.0286679i
$474$	−5.31365	−	6.75603i	−0.244064	−	0.310315i
$475$	−1.43954	+	1.04589i	−0.0660507	+	0.0479886i
$476$	2.71525	+	35.5279i	0.124453	+	1.62842i
$477$	0.404732	−	1.24564i	0.0185314	−	0.0570337i
$478$	−34.3545	+	1.31088i	−1.57134	+	0.0599580i
$479$	−1.59117	−	1.15605i	−0.0727025	−	0.0528214i	0.550840	−	0.834611i	$-0.314307\pi$
$479$	−1.59117	−	1.15605i	−0.0727025	−	0.0528214i	−0.623543	+	0.781789i	$0.714307\pi$
$480$	−8.95378	−	1.11113i	−0.408682	−	0.0507161i
$481$	14.4658	−	4.70022i	0.659584	−	0.214312i
$482$	14.4624	+	4.09650i	0.658746	+	0.186590i
$483$	11.8568			0.539502
$484$	−6.61272	−	20.9827i	−0.300578	−	0.953757i
$485$	4.37628			0.198716
$486$	−6.39051	−	1.81011i	−0.289879	−	0.0821085i
$487$	−9.22195	+	2.99639i	−0.417887	+	0.135780i	−0.510410	−	0.859931i	$-0.670507\pi$
$487$	−9.22195	+	2.99639i	−0.417887	+	0.135780i	0.0925240	+	0.995710i	$0.470507\pi$
$488$	2.49588	+	21.7188i	0.112983	+	0.983163i
$489$	4.52802	+	3.28980i	0.204764	+	0.148770i
$490$	−7.90783	+	0.301741i	−0.357239	+	0.0136313i
$491$	2.56307	−	7.88831i	0.115670	−	0.355994i	−0.876416	−	0.481554i	$-0.840073\pi$
$491$	2.56307	−	7.88831i	0.115670	−	0.355994i	0.992086	+	0.125559i	$0.0400726\pi$
$492$	35.9510	−	2.74758i	1.62079	−	0.123871i
$493$	−23.7373	+	17.2462i	−1.06907	+	0.776728i
$494$	8.44504	+	10.7374i	0.379960	+	0.483100i
$495$	1.41747	+	0.528253i	0.0637107	+	0.0237432i
$496$	19.6823	−	38.2005i	0.883763	−	1.71525i
$497$	8.41687	+	11.5848i	0.377548	+	0.519651i
$498$	12.0186	−	17.9432i	0.538567	−	0.804052i
$499$	−33.5064	−	10.8869i	−1.49995	−	0.487364i	−0.559948	−	0.828528i	$-0.689179\pi$
$499$	−33.5064	−	10.8869i	−1.49995	−	0.487364i	−0.940004	+	0.341164i	$0.889179\pi$
$500$	−1.52375	+	1.29545i	−0.0681440	+	0.0579344i
$501$	13.5391	−	18.6350i	0.604883	−	0.832550i
$502$	15.7900	−	5.80496i	0.704742	−	0.259088i
$503$	3.81847	+	11.7520i	0.170257	+	0.523997i	0.999385	−	0.0350614i	$-0.0111627\pi$
$503$	3.81847	+	11.7520i	0.170257	+	0.523997i	−0.829128	+	0.559059i	$0.811163\pi$
$504$	3.98703	+	2.25065i	0.177597	+	0.100252i
$505$		−	16.7944i		−	0.747342i
$506$	7.92262	+	5.80992i	0.352204	+	0.258282i
$507$		−	26.2684i		−	1.16662i
$508$	−2.11222	−	5.13216i	−0.0937146	−	0.227703i
$509$	−0.232557	−	0.715736i	−0.0103079	−	0.0317244i	0.945770	−	0.324836i	$-0.105309\pi$
$509$	−0.232557	−	0.715736i	−0.0103079	−	0.0317244i	−0.956078	+	0.293112i	$0.905309\pi$
$510$	3.90703	+	10.6275i	0.173006	+	0.470592i
$511$	−14.0031	+	19.2737i	−0.619462	+	0.852617i
$512$	−13.8269	−	17.9114i	−0.611067	−	0.791579i
$513$	9.32844	+	3.03099i	0.411861	+	0.133822i
$514$	6.80769	+	4.55990i	0.300274	+	0.201129i
$515$	−6.05303	−	8.33128i	−0.266728	−	0.367120i
$516$	−1.66885	−	0.404652i	−0.0734672	−	0.0178138i
$517$	−5.67764	−	0.241837i	−0.249703	−	0.0106360i
$518$	−11.0537	+	8.69378i	−0.485672	+	0.381983i
$519$	−0.565042	+	0.410527i	−0.0248026	+	0.0180201i
$520$	10.3842	+	11.3104i	0.455379	+	0.495993i
$521$	0.145391	−	0.447468i	0.00636971	−	0.0196039i	−0.947821	−	0.318803i	$-0.896719\pi$
$521$	0.145391	−	0.447468i	0.00636971	−	0.0196039i	0.954191	+	0.299199i	$0.0967193\pi$
$522$	0.143753	+	3.76738i	0.00629189	+	0.164894i
$523$	−19.4805	−	14.1534i	−0.851824	−	0.618886i	0.0738244	−	0.997271i	$-0.476480\pi$
$523$	−19.4805	−	14.1534i	−0.851824	−	0.618886i	−0.925648	+	0.378385i	$0.876480\pi$
$524$	−15.8237	−	9.74606i	−0.691260	−	0.425758i
$525$	−5.38355	+	1.74922i	−0.234957	+	0.0763422i
$526$	−11.7026	+	41.3154i	−0.510258	+	1.80144i
$527$	−53.9296			−2.34921
$528$	−8.70805	−	19.2846i	−0.378969	−	0.839255i
$529$	18.6126			0.809243
$530$	−1.10676	+	3.90736i	−0.0480747	+	0.169725i
$531$	1.11771	−	0.363164i	0.0485043	−	0.0157600i
$532$	−10.7540	−	6.62358i	−0.466246	−	0.287169i
$533$	−49.6409	−	36.0662i	−2.15019	−	1.56220i
$534$	−1.58911	−	41.6463i	−0.0687676	−	1.80221i
$535$	0.00970105	−	0.0298568i	0.000419413	−	0.00129082i
$536$	8.40188	+	9.15121i	0.362906	+	0.395272i
$537$	2.56171	−	1.86119i	0.110546	−	0.0803165i
$538$	−18.7618	+	14.7563i	−0.808880	+	0.636188i
$539$	−10.2599	−	15.4652i	−0.441924	−	0.666132i
$540$	10.7142	+	2.59791i	0.461067	+	0.111796i
$541$	−4.36972	−	6.01441i	−0.187869	−	0.258580i	0.704685	−	0.709521i	$-0.251088\pi$
$541$	−4.36972	−	6.01441i	−0.187869	−	0.258580i	−0.892554	+	0.450941i	$0.851088\pi$
$542$	−19.6540	−	13.1646i	−0.844212	−	0.565466i
$543$	15.2589	+	4.95791i	0.654821	+	0.212764i
$544$	−12.0342	+	25.7206i	−0.515962	+	1.10276i
$545$	−4.48489	+	6.17292i	−0.192112	+	0.264419i
$546$	14.9952	+	40.7884i	0.641737	+	1.74558i
$547$	−6.99424	−	21.5261i	−0.299052	−	0.920388i	−0.981830	−	0.189762i	$-0.939228\pi$
$547$	−6.99424	−	21.5261i	−0.299052	−	0.920388i	0.682778	−	0.730626i	$-0.260772\pi$
$548$	9.58188	+	23.2815i	0.409317	+	0.994537i
$549$		−	3.52531i		−	0.150457i
$550$	−4.45439	−	1.46917i	−0.189936	−	0.0626455i
$551$		−	10.4004i		−	0.443070i
$552$	8.22876	+	4.64508i	0.350239	+	0.197708i
$553$	−4.17916	−	12.8621i	−0.177716	−	0.546954i
$554$	5.46323	−	2.00847i	0.232110	−	0.0853319i
$555$	−2.62674	+	3.61540i	−0.111499	+	0.153465i
$556$	0.616468	−	0.524106i	0.0261441	−	0.0222271i
$557$	−14.7749	−	4.80065i	−0.626031	−	0.203410i	−0.0212150	−	0.999775i	$-0.506753\pi$
$557$	−14.7749	−	4.80065i	−0.626031	−	0.203410i	−0.604816	+	0.796365i	$0.706753\pi$
$558$	−3.85639	+	5.75739i	−0.163254	+	0.243730i
$559$	1.71771	+	2.36422i	0.0726514	+	0.0999961i
$560$	−12.6196	−	6.50210i	−0.533276	−	0.274764i
$561$	−16.5085	+	20.7994i	−0.696988	+	0.878150i
$562$	−4.96243	−	6.30948i	−0.209327	−	0.266149i
$563$	−15.0239	+	10.9155i	−0.633180	+	0.460033i	−0.857501	−	0.514483i	$-0.827984\pi$
$563$	−15.0239	+	10.9155i	−0.633180	+	0.460033i	0.224320	+	0.974516i	$0.427984\pi$
$564$	−5.44981	+	0.416506i	−0.229478	+	0.0175381i
$565$	−3.81654	+	11.7461i	−0.160563	+	0.494162i
$566$	39.5618	−	1.50957i	1.66291	−	0.0634520i
$567$	21.3152	+	15.4864i	0.895153	+	0.650367i
$568$	1.30288	+	11.3375i	0.0546677	+	0.475710i
$569$	−2.09223	+	0.679807i	−0.0877108	+	0.0284990i	−0.352544	−	0.935795i	$-0.614683\pi$
$569$	−2.09223	+	0.679807i	−0.0877108	+	0.0284990i	0.264833	+	0.964294i	$0.414683\pi$
$570$	−3.86165	−	1.09382i	−0.161747	−	0.0458149i
$571$	13.5505			0.567070			0.283535	−	0.958962i	$-0.408493\pi$
$571$	13.5505			0.567070			0.283535	+	0.958962i	$0.408493\pi$
$572$	−9.96694	+	34.6024i	−0.416739	+	1.44680i
$573$	−2.67386			−0.111702
$574$	54.5838	+	15.4609i	2.27828	+	0.645325i
$575$	1.99210	−	0.647272i	0.0830762	−	0.0269931i
$576$	1.88533	+	3.12397i	0.0785553	+	0.130165i
$577$	−11.8260	−	8.59209i	−0.492322	−	0.357693i	0.313754	−	0.949504i	$-0.398413\pi$
$577$	−11.8260	−	8.59209i	−0.492322	−	0.357693i	−0.806077	+	0.591811i	$0.798413\pi$
$578$	11.5868	−	0.442120i	0.481946	−	0.0183898i
$579$	5.84976	−	18.0037i	0.243108	−	0.748209i
$580$	−0.890815	−	11.6559i	−0.0369891	−	0.483986i
$581$	27.4907	−	19.9732i	1.14051	−	0.828626i
$582$	6.10243	+	7.75893i	0.252954	+	0.321618i
$583$	−9.17498	+	2.55497i	−0.379989	+	0.105816i
$584$	−17.2691	+	7.89023i	−0.714601	+	0.326500i
$585$	−1.45534	−	2.00310i	−0.0601709	−	0.0828181i
$586$	−1.03378	+	1.54338i	−0.0427051	+	0.0637565i
$587$	−32.9192	−	10.6961i	−1.35872	−	0.441475i	−0.463104	−	0.886304i	$-0.653264\pi$
$587$	−32.9192	−	10.6961i	−1.35872	−	0.441475i	−0.895615	+	0.444829i	$0.853264\pi$
$588$	−11.5619	−	13.5994i	−0.476805	−	0.560832i
$589$	11.2362	−	15.4653i	0.462980	−	0.637238i
$590$	−3.42019	+	1.25738i	−0.140807	+	0.0517655i
$591$	−1.03748	−	3.19304i	−0.0426763	−	0.131344i
$592$	−11.0773	+	1.70314i	−0.455276	+	0.0699985i
$593$		−	34.6751i		−	1.42393i	−0.702213	−	0.711967i	$-0.747805\pi$
$593$		−	34.6751i		−	1.42393i	0.702213	−	0.711967i	$-0.252195\pi$
$594$	7.88068	+	24.6249i	0.323348	+	1.01037i
$595$			17.8157i			0.730375i
$596$	−14.6325	+	6.02224i	−0.599371	+	0.246680i
$597$	9.21755	+	28.3687i	0.377249	+	1.16105i
$598$	−5.54876	−	15.0931i	−0.226906	−	0.617204i
$599$	0.488852	−	0.672847i	0.0199740	−	0.0274918i	−0.798913	−	0.601446i	$-0.794591\pi$
$599$	0.488852	−	0.672847i	0.0199740	−	0.0274918i	0.818887	+	0.573955i	$0.194591\pi$
$600$	−4.42154	−	0.895107i	−0.180509	−	0.0365426i
$601$	21.1405	+	6.86896i	0.862338	+	0.280191i	0.706605	−	0.707608i	$-0.250226\pi$
$601$	21.1405	+	6.86896i	0.862338	+	0.280191i	0.155733	+	0.987799i	$0.450226\pi$
$602$	−2.24486	−	1.50364i	−0.0914935	−	0.0612838i
$603$	−1.17751	−	1.62071i	−0.0479520	−	0.0660003i
$604$	1.22187	−	5.03921i	0.0497172	−	0.205042i
$605$	−2.49727	−	10.7128i	−0.101528	−	0.435536i
$606$	29.7757	−	23.4187i	1.20955	−	0.951320i
$607$	−30.1752	+	21.9236i	−1.22477	+	0.889851i	−0.996487	−	0.0837427i	$-0.973313\pi$
$607$	−30.1752	+	21.9236i	−1.22477	+	0.889851i	−0.228287	+	0.973594i	$0.573313\pi$
$608$	−4.86854	−	8.80991i	−0.197445	−	0.357289i
$609$	10.2241	−	31.4666i	0.414303	−	1.27509i
$610$	0.416788	+	10.9229i	0.0168753	+	0.442256i
$611$	7.52507	+	5.46728i	0.304432	+	0.221183i
$612$	2.40140	−	3.89890i	0.0970709	−	0.157604i
$613$	29.2699	−	9.51038i	1.18220	−	0.384120i	0.349017	−	0.937116i	$-0.386515\pi$
$613$	29.2699	−	9.51038i	1.18220	−	0.384120i	0.833184	+	0.552996i	$0.186515\pi$
$614$	4.57181	−	16.1405i	0.184503	−	0.651378i
$615$	18.0279			0.726955
$616$	−2.38996	−	33.2071i	−0.0962942	−	1.33795i
$617$	33.0119			1.32901			0.664505	−	0.747284i	$-0.268642\pi$
$617$	33.0119			1.32901			0.664505	+	0.747284i	$0.268642\pi$
$618$	6.33041	−	22.3491i	0.254646	−	0.899015i
$619$	40.4049	−	13.1283i	1.62401	−	0.527673i	0.651126	−	0.758970i	$-0.274297\pi$
$619$	40.4049	−	13.1283i	1.62401	−	0.527673i	0.972883	+	0.231297i	$0.0742970\pi$
$620$	11.2681	−	18.2948i	0.452536	−	0.734736i
$621$	−9.34110	−	6.78671i	−0.374846	−	0.272341i
$622$	0.461786	+	12.1022i	0.0185159	+	0.485252i
$623$	20.2638	−	62.3657i	0.811854	−	2.49863i
$624$	−5.57260	+	34.1823i	−0.223083	+	1.36839i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	−33.3473	+	26.2278i	−1.33283	+	1.04827i
$627$	−2.52508	−	9.06766i	−0.100842	−	0.362127i
$628$	−5.64116	+	23.2651i	−0.225107	+	0.928380i
$629$	8.26722	+	11.3789i	0.329636	+	0.453705i
$630$	1.90197	+	1.27397i	0.0757762	+	0.0507561i
$631$	16.4737	+	5.35264i	0.655809	+	0.213085i	0.617974	−	0.786199i	$-0.287954\pi$
$631$	16.4737	+	5.35264i	0.655809	+	0.213085i	0.0378355	+	0.999284i	$0.487954\pi$
$632$	2.13855	−	10.5637i	0.0850670	−	0.420203i
$633$	−18.5575	+	25.5423i	−0.737596	+	1.01521i
$634$	5.94756	+	16.1779i	0.236208	+	0.642506i
$635$	−0.857494	−	2.63910i	−0.0340286	−	0.104729i
$636$	−8.47086	+	3.48632i	−0.335892	+	0.138241i
$637$			30.3770i			1.20358i
$638$	22.2506	−	16.0159i	0.880910	−	0.634075i
$639$		−	1.84026i		−	0.0727994i
$640$	−6.21088	−	9.45648i	−0.245507	−	0.373800i
$641$	−11.0235	−	33.9270i	−0.435403	−	1.34003i	−0.892673	−	0.450706i	$-0.851172\pi$
$641$	−11.0235	−	33.9270i	−0.435403	−	1.34003i	0.457269	−	0.889328i	$-0.348828\pi$
$642$	0.0664621	−	0.0244338i	0.00262305	−	0.000964325i
$643$	17.1452	−	23.5984i	0.676143	−	0.930630i	−0.323737	−	0.946147i	$-0.604939\pi$
$643$	17.1452	−	23.5984i	0.676143	−	0.930630i	0.999880	+	0.0155166i	$0.00493929\pi$
$644$	9.63025	+	11.3274i	0.379485	+	0.446361i
$645$	−0.816583	−	0.265324i	−0.0321529	−	0.0104471i
$646$	−7.02986	+	10.4952i	−0.276586	+	0.412929i
$647$	20.5788	+	28.3243i	0.809036	+	1.11354i	0.991471	+	0.130325i	$0.0416019\pi$
$647$	20.5788	+	28.3243i	0.809036	+	1.11354i	−0.182435	+	0.983218i	$0.558398\pi$
$648$	8.72598	+	19.0983i	0.342789	+	0.750253i
$649$	−6.69377	−	5.31284i	−0.262753	−	0.208547i
$650$	4.74608	+	6.03440i	0.186157	+	0.236689i
$651$	49.1988	−	35.7450i	1.92825	−	1.40096i
$652$	0.534818	+	6.99786i	0.0209451	+	0.274057i
$653$	−8.34976	+	25.6979i	−0.326752	+	1.00564i	0.643892	+	0.765116i	$0.277318\pi$
$653$	−8.34976	+	25.6979i	−0.326752	+	1.00564i	−0.970644	+	0.240522i	$0.922682\pi$
$654$	−17.1982	+	0.656236i	−0.672502	+	0.0256608i
$655$	−7.51748	−	5.46177i	−0.293732	−	0.213409i
$656$	31.8248	+	32.1141i	1.24255	+	1.25385i
$657$	2.91178	−	0.946096i	0.113599	−	0.0369107i
$658$	−8.27436	−	2.34372i	−0.322568	−	0.0913676i
$659$	−19.9516			−0.777204			−0.388602	−	0.921406i	$-0.627042\pi$
$659$	−19.9516			−0.777204			−0.388602	+	0.921406i	$0.627042\pi$
$660$	−3.60658	−	9.94607i	−0.140386	−	0.387150i
$661$	−9.89736			−0.384963			−0.192481	−	0.981301i	$-0.561653\pi$
$661$	−9.89736			−0.384963			−0.192481	+	0.981301i	$0.561653\pi$
$662$	27.9065	+	7.90453i	1.08462	+	0.307218i
$663$	41.3367	−	13.4311i	1.60538	−	0.521621i
$664$	26.9037	−	3.09173i	1.04407	−	0.119982i
$665$	−5.10900	−	3.71191i	−0.198119	−	0.143942i
$666$	1.80595	−	0.0689102i	0.0699792	−	0.00267022i
$667$	−3.78328	+	11.6437i	−0.146489	+	0.450847i
$668$	28.7996	−	2.20104i	1.11429	−	0.0851606i
$669$	−21.3140	+	15.4855i	−0.824047	+	0.598705i
$670$	3.84005	+	4.88243i	0.148354	+	0.188625i
$671$	−21.3617	+	14.1717i	−0.824659	+	0.547093i
$672$	−6.06930	−	31.4407i	−0.234128	−	1.21285i
$673$	4.42290	+	6.08760i	0.170490	+	0.234660i	0.885709	−	0.464241i	$-0.153673\pi$
$673$	4.42290	+	6.08760i	0.170490	+	0.234660i	−0.715219	+	0.698901i	$0.753673\pi$
$674$	−4.49480	+	6.71050i	−0.173133	+	0.258479i
$675$	5.24255	+	1.70341i	0.201786	+	0.0655642i
$676$	25.0955	−	21.3356i	0.965213	−	0.820601i
$677$	5.07657	−	6.98730i	0.195108	−	0.268544i	−0.700242	−	0.713905i	$-0.746925\pi$
$677$	5.07657	−	6.98730i	0.195108	−	0.268544i	0.895351	+	0.445361i	$0.146925\pi$
$678$	−26.1472	+	9.61262i	−1.00418	+	0.369171i
$679$	4.79953	+	14.7714i	0.184189	+	0.566876i
$680$	−6.97960	+	12.3644i	−0.267655	+	0.474152i
$681$		−	22.0795i		−	0.846088i
$682$	50.3897	+	0.223237i	1.92952	+	0.00854817i
$683$			18.3744i			0.703078i	0.936173	+	0.351539i	$0.114342\pi$
$683$			18.3744i			0.703078i	−0.936173	+	0.351539i	$0.885658\pi$
$684$	0.617753	+	1.50098i	0.0236204	+	0.0573915i
$685$	3.88994	+	11.9720i	0.148627	+	0.457427i
$686$	2.43199	+	6.61522i	0.0928536	+	0.252570i
$687$	1.19341	−	1.64259i	0.0455316	−	0.0626689i
$688$	−0.968885	−	1.92300i	−0.0369384	−	0.0733139i
$689$	14.8259	+	4.81722i	0.564821	+	0.183521i
$690$	3.92543	+	2.62932i	0.149439	+	0.100096i
$691$	−18.7009	−	25.7395i	−0.711415	−	0.979178i	−0.999766	−	0.0216536i	$-0.993107\pi$
$691$	−18.7009	−	25.7395i	−0.711415	−	0.979178i	0.288351	−	0.957525i	$-0.406893\pi$
$692$	−0.851133	−	0.206377i	−0.0323552	−	0.00784526i
$693$	−0.228470	+	5.36380i	−0.00867884	+	0.203754i
$694$	−15.3503	+	12.0731i	−0.582691	+	0.458289i
$695$	0.327307	−	0.237803i	0.0124155	−	0.00902037i
$696$	19.4232	−	17.8328i	0.736236	−	0.675951i
$697$	17.5335	−	53.9627i	0.664130	−	2.04398i
$698$	1.75042	+	45.8739i	0.0662545	+	1.73635i
$699$	−17.9505	−	13.0418i	−0.678950	−	0.493286i
$700$	−6.04372	−	3.72243i	−0.228431	−	0.140695i
$701$	−26.7636	+	8.69602i	−1.01085	+	0.328444i	−0.767192	−	0.641418i	$-0.778346\pi$
$701$	−26.7636	+	8.69602i	−1.01085	+	0.328444i	−0.243655	+	0.969862i	$0.578346\pi$
$702$	11.5332	−	40.7174i	0.435294	−	1.53678i
$703$	−4.98558			−0.188035
$704$	11.3508	−	23.9825i	0.427798	−	0.903875i
$705$	−2.73285			−0.102925
$706$	7.87479	−	27.8015i	0.296372	−	1.04632i
$707$	56.6870	−	18.4187i	2.13193	−	0.692707i
$708$	−6.99850	−	4.31050i	−0.263020	−	0.161998i
$709$	5.61836	+	4.08198i	0.211002	+	0.153302i	0.688267	−	0.725458i	$-0.258372\pi$
$709$	5.61836	+	4.08198i	0.211002	+	0.153302i	−0.477265	+	0.878759i	$0.658372\pi$
$710$	0.217569	+	5.70189i	0.00816521	+	0.213988i
$711$	−0.537076	+	1.65295i	−0.0201419	+	0.0619904i
$712$	38.4961	−	35.3440i	1.44270	−	1.32457i
$713$	−18.2053	+	13.2269i	−0.681793	+	0.495351i
$714$	−31.5865	+	24.8429i	−1.18209	+	0.929721i
$715$	−6.28739	+	16.8711i	−0.235135	+	0.630944i
$716$	3.85876	+	0.935643i	0.144208	+	0.0349666i
$717$	−22.7905	−	31.3684i	−0.851126	−	1.17148i
$718$	−22.5126	−	15.0793i	−0.840164	−	0.562755i
$719$	14.4050	+	4.68047i	0.537216	+	0.174552i	0.565044	−	0.825061i	$-0.308859\pi$
$719$	14.4050	+	4.68047i	0.537216	+	0.174552i	−0.0278281	+	0.999613i	$0.508859\pi$
$720$	0.820893	+	1.62928i	0.0305929	+	0.0607195i
$721$	21.4825	−	29.5681i	0.800050	−	1.10117i
$722$	7.72663	+	21.0171i	0.287556	+	0.782177i
$723$	5.23863	+	16.1228i	0.194827	+	0.599615i
$724$	7.65695	+	18.6045i	0.284568	+	0.691429i
$725$		−	5.84496i		−	0.217076i
$726$	15.5110	−	19.3658i	0.575666	−	0.718732i
$727$			51.9972i			1.92847i	0.265048	+	0.964235i	$0.414612\pi$
$727$			51.9972i			1.92847i	−0.265048	+	0.964235i	$0.585388\pi$
$728$	−26.7878	+	47.4547i	−0.992824	+	1.75879i
$729$	−9.19692	−	28.3052i	−0.340627	−	1.04834i
$730$	−8.91009	+	3.27566i	−0.329777	+	0.121238i
$731$	−1.58838	+	2.18622i	−0.0587484	+	0.0808602i
$732$	−18.7846	+	15.9702i	−0.694299	+	0.590276i
$733$	14.3745	+	4.67057i	0.530936	+	0.172512i	0.562203	−	0.826999i	$-0.309954\pi$
$733$	14.3745	+	4.67057i	0.530936	+	0.172512i	−0.0312666	+	0.999511i	$0.509954\pi$
$734$	7.63674	−	11.4013i	0.281877	−	0.420828i
$735$	−5.24599	−	7.22048i	−0.193501	−	0.266331i
$736$	2.24585	+	11.6341i	0.0827831	+	0.428840i
$737$	−5.08712	+	13.6504i	−0.187387	+	0.502819i
$738$	−4.50714	−	5.73060i	−0.165910	−	0.210946i
$739$	30.6253	−	22.2506i	1.12657	−	0.818502i	0.141379	−	0.989956i	$-0.454846\pi$
$739$	30.6253	−	22.2506i	1.12657	−	0.818502i	0.985192	+	0.171454i	$0.0548465\pi$
$740$	−5.58746	+	0.427026i	−0.205399	+	0.0156978i
$741$	−4.76087	+	14.6525i	−0.174895	+	0.538271i
$742$	−14.4025	+	0.549560i	−0.528732	+	0.0201750i
$743$	−15.1756	−	11.0257i	−0.556738	−	0.404494i	0.273525	−	0.961865i	$-0.411810\pi$
$743$	−15.1756	−	11.0257i	−0.556738	−	0.404494i	−0.830264	+	0.557371i	$0.811810\pi$
$744$	48.1483	−	5.53312i	1.76520	−	0.202854i
$745$	−7.52444	+	2.44484i	−0.275674	+	0.0895719i
$746$	−18.7322	−	5.30590i	−0.685833	−	0.194263i
$747$	−4.36691			−0.159777
$748$	−33.2791	+	1.12222i	−1.21680	+	0.0410323i
$749$	0.111416			0.00407106
$750$	−2.17024	−	0.614721i	−0.0792458	−	0.0224464i
$751$	−45.1973	+	14.6855i	−1.64927	+	0.535882i	−0.978583	−	0.205855i	$-0.934003\pi$
$751$	−45.1973	+	14.6855i	−1.64927	+	0.535882i	−0.670692	+	0.741736i	$0.734003\pi$
$752$	−4.82433	−	4.86818i	−0.175925	−	0.177524i
$753$	15.3498	+	11.1523i	0.559378	+	0.406412i
$754$	−44.8403	+	1.71098i	−1.63299	+	0.0623103i
$755$	0.801162	−	2.46572i	0.0291573	−	0.0897368i
$756$	2.98163	+	39.0134i	0.108441	+	1.41890i
$757$	−39.6011	+	28.7719i	−1.43933	+	1.04573i	−0.451144	+	0.892451i	$0.648984\pi$
$757$	−39.6011	+	28.7719i	−1.43933	+	1.04573i	−0.988183	+	0.153281i	$0.951016\pi$
$758$	−0.264219	−	0.335940i	−0.00959685	−	0.0122019i
$759$	−0.471534	+	11.0702i	−0.0171156	+	0.401824i
$760$	−2.09152	−	4.57765i	−0.0758673	−	0.166049i
$761$	10.8718	+	14.9637i	0.394102	+	0.542434i	0.959251	−	0.282554i	$-0.0911816\pi$
$761$	10.8718	+	14.9637i	0.394102	+	0.542434i	−0.565150	+	0.824988i	$0.691182\pi$
$762$	3.48327	−	5.20034i	0.126186	−	0.188388i
$763$	−25.7544	−	8.36811i	−0.932372	−	0.302946i
$764$	−2.17175	−	2.55447i	−0.0785711	−	0.0924175i
$765$	1.34576	−	1.85229i	0.0486562	−	0.0669695i
$766$	2.02861	−	0.745787i	0.0732966	−	0.0269464i
$767$	4.32247	+	13.3032i	0.156075	+	0.480351i
$768$	8.10522	−	24.1980i	0.292472	−	0.873171i
$769$			29.8320i			1.07577i	0.843019	+	0.537884i	$0.180776\pi$
$769$			29.8320i			1.07577i	−0.843019	+	0.537884i	$0.819224\pi$
$770$	0.0737467	−	16.6464i	0.00265765	−	0.599893i
$771$			9.24097i			0.332805i
$772$	21.9511	−	9.03433i	0.790038	−	0.325153i
$773$	−5.63684	−	17.3484i	−0.202743	−	0.623979i	−0.999799	−	0.0200726i	$-0.993610\pi$
$773$	−5.63684	−	17.3484i	−0.202743	−	0.623979i	0.797056	−	0.603906i	$-0.206390\pi$
$774$	0.119814	+	0.325904i	0.00430661	+	0.0117144i
$775$	6.31471	−	8.69146i	0.226831	−	0.312206i
$776$	−2.45601	+	12.1319i	−0.0881655	+	0.435509i
$777$	−15.0840	−	4.90110i	−0.541137	−	0.175826i
$778$	−33.0736	−	22.1532i	−1.18574	−	0.794231i
$779$	11.8217	+	16.2712i	0.423557	+	0.582976i
$780$	−4.08061	+	16.8291i	−0.146109	+	0.602580i
$781$	−11.1511	+	7.39781i	−0.399017	+	0.264715i
$782$	11.6881	−	9.19272i	0.417965	−	0.328731i
$783$	−26.0661	+	18.9381i	−0.931525	+	0.676793i
$784$	3.60146	−	22.0914i	0.128624	−	0.788977i
$785$	−3.69882	+	11.3838i	−0.132017	+	0.406306i
$786$	−0.799174	−	20.9442i	−0.0285056	−	0.747055i
$787$	0.451324	+	0.327906i	0.0160880	+	0.0116886i	0.595800	−	0.803133i	$-0.296835\pi$
$787$	0.451324	+	0.327906i	0.0160880	+	0.0116886i	−0.579712	+	0.814821i	$0.696835\pi$
$788$	2.20781	−	3.58460i	0.0786501	−	0.127696i
$789$	−46.0587	+	14.9654i	−1.63973	+	0.532781i
$790$	1.46866	−	5.18503i	0.0522527	−	0.184475i
$791$	−43.8328			−1.55852
$792$	−2.25992	+	3.63305i	−0.0803026	+	0.129095i
$793$	41.9591			1.49001
$794$	−7.78516	+	27.4851i	−0.276285	+	0.975408i
$795$	−4.35595	+	1.41533i	−0.154490	+	0.0501967i
$796$	−19.6154	+	31.8475i	−0.695249	+	1.12880i
$797$	−6.12390	−	4.44928i	−0.216920	−	0.157601i	0.474019	−	0.880514i	$-0.342803\pi$
$797$	−6.12390	−	4.44928i	−0.216920	−	0.157601i	−0.690939	+	0.722913i	$0.742803\pi$
$798$	−0.543132	−	14.2340i	−0.0192267	−	0.503879i
$799$	−2.65791	+	8.18020i	−0.0940300	+	0.289395i
$800$	−2.73610	−	4.95114i	−0.0967358	−	0.175049i
$801$	−6.81779	+	4.95341i	−0.240895	+	0.175020i
$802$	−5.13898	+	4.04183i	−0.181464	+	0.142722i
$803$	−17.4382	−	13.8407i	−0.615382	−	0.488428i
$804$	−3.30162	+	13.6164i	−0.116439	+	0.480215i
$805$	4.36953	+	6.01415i	0.154006	+	0.211971i
$806$	−68.5260	−	45.8998i	−2.41372	−	1.61675i
$807$	−25.6027	−	8.31881i	−0.901257	−	0.292836i
$808$	46.5573	+	9.42518i	1.63788	+	0.331577i
$809$	−2.96962	+	4.08734i	−0.104406	+	0.143703i	−0.858023	−	0.513611i	$-0.828307\pi$
$809$	−2.96962	+	4.08734i	−0.104406	+	0.143703i	0.753617	+	0.657314i	$0.228307\pi$
$810$	3.62262	+	9.85386i	0.127286	+	0.346230i
$811$	−11.7273	−	36.0930i	−0.411802	−	1.26740i	−0.915080	−	0.403272i	$-0.867873\pi$
$811$	−11.7273	−	36.0930i	−0.411802	−	1.26740i	0.503278	−	0.864125i	$-0.332127\pi$
$812$	38.3658	−	15.7901i	1.34638	−	0.554123i
$813$		−	26.6789i		−	0.935671i
$814$	−7.67748	−	10.6662i	−0.269095	−	0.373850i
$815$			3.50914i			0.122920i
$816$	−31.6540	+	4.86680i	−1.10811	+	0.170372i
$817$	−0.296001	−	0.910996i	−0.0103558	−	0.0318717i
$818$	36.9728	−	13.5925i	1.29272	−	0.475251i
$819$	5.16507	−	7.10911i	0.180482	−	0.248412i
$820$	14.6425	+	17.2230i	0.511340	+	0.601452i
$821$	8.33963	+	2.70971i	0.291055	+	0.0945695i	0.450905	−	0.892572i	$-0.351101\pi$
$821$	8.33963	+	2.70971i	0.291055	+	0.0945695i	−0.159850	+	0.987141i	$0.551101\pi$
$822$	−15.8015	+	23.5908i	−0.551141	+	0.822825i
$823$	20.9881	+	28.8876i	0.731599	+	1.00696i	0.999058	+	0.0433905i	$0.0138160\pi$
$823$	20.9881	+	28.8876i	0.731599	+	1.00696i	−0.267459	+	0.963569i	$0.586184\pi$
$824$	26.4929	−	12.1046i	0.922925	−	0.421683i
$825$	−1.41909	−	5.09599i	−0.0494062	−	0.177420i
$826$	−7.99507	−	10.1653i	−0.278184	−	0.353697i
$827$	25.9453	−	18.8504i	0.902207	−	0.655492i	−0.0368250	−	0.999322i	$-0.511724\pi$
$827$	25.9453	−	18.8504i	0.902207	−	0.655492i	0.939032	+	0.343830i	$0.111724\pi$
$828$	−0.145602	−	1.90514i	−0.00506003	−	0.0662083i
$829$	12.8974	−	39.6940i	0.447944	−	1.37863i	−0.431280	−	0.902218i	$-0.641938\pi$
$829$	12.8974	−	39.6940i	0.447944	−	1.37863i	0.879223	−	0.476410i	$-0.158062\pi$
$830$	13.5305	−	0.516288i	0.469652	−	0.0179206i
$831$	5.31092	+	3.85861i	0.184234	+	0.133854i
$832$	−37.1822	+	22.4396i	−1.28906	+	0.777954i
$833$	−26.7151	+	8.68026i	−0.925623	+	0.300753i
$834$	0.878021	+	0.248700i	0.0304034	+	0.00861178i
$835$	14.4418			0.499779
$836$	6.61188	−	9.77723i	0.228677	−	0.338152i
$837$	−59.2204			−2.04696
$838$	−28.5997	−	8.10088i	−0.987960	−	0.279840i
$839$	−31.6422	+	10.2812i	−1.09241	+	0.354945i	−0.799177	−	0.601096i	$-0.794731\pi$
$839$	−31.6422	+	10.2812i	−1.09241	+	0.354945i	−0.293233	+	0.956041i	$0.594731\pi$
$840$	−1.82788	−	15.9059i	−0.0630678	−	0.548806i
$841$	4.17743	+	3.03508i	0.144049	+	0.104658i
$842$	13.7533	−	0.524789i	0.473971	−	0.0180854i
$843$	2.79756	−	8.61000i	0.0963530	−	0.296544i
$844$	−39.4745	+	3.01687i	−1.35877	+	0.103845i
$845$	13.3242	−	9.68060i	0.458367	−	0.333023i
$846$	0.683237	+	0.868701i	0.0234902	+	0.0298666i
$847$	33.4205	−	20.1780i	1.14834	−	0.693325i
$848$	−10.2108	−	5.26100i	−0.350641	−	0.180664i
$849$	26.2450	+	36.1231i	0.900725	+	1.23974i
$850$	−3.95076	+	5.89827i	−0.135510	+	0.202309i
$851$	5.58161	+	1.81358i	0.191335	+	0.0621686i
$852$	−9.80580	+	8.33665i	−0.335941	+	0.285609i
$853$	27.2406	−	37.4934i	0.932699	−	1.28375i	−0.0260981	−	0.999659i	$-0.508308\pi$
$853$	27.2406	−	37.4934i	0.932699	−	1.28375i	0.958797	−	0.284091i	$-0.0916918\pi$
$854$	−36.4115	+	13.3861i	−1.24598	+	0.458064i
$855$	0.250788	+	0.771847i	0.00857677	+	0.0263966i
$856$	0.0773244	+	0.0436491i	0.00264289	+	0.00149189i
$857$			10.1071i			0.345252i	0.984987	+	0.172626i	$0.0552252\pi$
$857$			10.1071i			0.345252i	−0.984987	+	0.172626i	$0.944775\pi$
$858$	−38.6790	+	12.3784i	−1.32048	+	0.422592i
$859$		−	19.7240i		−	0.672975i	−0.941688	−	0.336488i	$-0.890761\pi$
$859$		−	19.7240i		−	0.672975i	0.941688	−	0.336488i	$-0.109239\pi$
$860$	−0.409764	−	0.995623i	−0.0139728	−	0.0339505i
$861$	19.7715	+	60.8504i	0.673811	+	2.07378i
$862$	15.8514	+	43.1174i	0.539902	+	1.46858i
$863$	12.3444	−	16.9906i	0.420208	−	0.578367i	−0.545463	−	0.838135i	$-0.683646\pi$
$863$	12.3444	−	16.9906i	0.420208	−	0.578367i	0.965671	+	0.259768i	$0.0836460\pi$
$864$	−13.2148	+	28.2439i	−0.449577	+	0.960877i
$865$	−0.416466	−	0.135318i	−0.0141603	−	0.00460095i
$866$	12.7665	+	8.55120i	0.433823	+	0.290582i
$867$	7.68657	+	10.5797i	0.261050	+	0.359304i
$868$	74.1091	+	17.9694i	2.51543	+	0.609922i
$869$	12.1751	−	3.39042i	0.413013	−	0.115012i
$870$	10.3628	−	8.15041i	0.351333	−	0.276325i
$871$	19.2901	−	14.0151i	0.653619	−	0.474882i
$872$	−14.5956	−	15.8973i	−0.494268	−	0.538350i
$873$	0.616801	−	1.89832i	0.0208756	−	0.0642484i
$874$	0.200977	+	5.26708i	0.00679816	+	0.178162i
$875$	−2.87124	−	2.08608i	−0.0970657	−	0.0705223i
$876$	−18.2321	−	11.2295i	−0.616006	−	0.379408i
$877$	38.4709	−	12.4999i	1.29907	−	0.422093i	0.423812	−	0.905750i	$-0.360692\pi$
$877$	38.4709	−	12.4999i	1.29907	−	0.422093i	0.875258	+	0.483657i	$0.160692\pi$
$878$	−0.376381	+	1.32879i	−0.0127023	+	0.0448446i
$879$	−2.09503			−0.0706636
$880$	6.57265	−	11.5239i	0.221564	−	0.388471i
$881$	−13.8272			−0.465851			−0.232925	−	0.972495i	$-0.574830\pi$
$881$	−13.8272			−0.465851			−0.232925	+	0.972495i	$0.574830\pi$
$882$	−0.983658	+	3.47275i	−0.0331215	+	0.116933i
$883$	−34.0414	+	11.0607i	−1.14558	+	0.372222i	−0.819478	−	0.573111i	$-0.805736\pi$
$883$	−34.0414	+	11.0607i	−1.14558	+	0.372222i	−0.326105	+	0.945333i	$0.605736\pi$
$884$	46.4057	+	28.5821i	1.56079	+	0.961319i
$885$	−3.32484	−	2.41564i	−0.111763	−	0.0812007i
$886$	0.162851	+	4.26789i	0.00547108	+	0.143382i
$887$	7.19100	−	22.1316i	0.241450	−	0.743107i	−0.754750	−	0.656012i	$-0.772242\pi$
$887$	7.19100	−	22.1316i	0.241450	−	0.743107i	0.996200	−	0.0870942i	$-0.0277581\pi$
$888$	−8.54844	−	9.31084i	−0.286867	−	0.312451i
$889$	7.96743	−	5.78868i	0.267219	−	0.194146i
$890$	20.5388	−	16.1538i	0.688461	−	0.541477i
$891$	−15.3068	+	19.2853i	−0.512796	+	0.646083i
$892$	−32.1057	−	7.78475i	−1.07498	−	0.260653i
$893$	−1.79205	−	2.46655i	−0.0599687	−	0.0825399i
$894$	−14.8269	−	9.93130i	−0.495886	−	0.332152i
$895$	1.88812	+	0.613487i	0.0631128	+	0.0205066i
$896$	25.1073	−	31.3349i	0.838776	−	1.04683i
$897$	10.6601	−	14.6723i	0.355930	−	0.489895i
$898$	−12.0772	−	32.8512i	−0.403023	−	1.09626i
$899$	19.4044	+	59.7205i	0.647171	+	1.99179i
$900$	0.347175	+	0.843547i	0.0115725	+	0.0281182i
$901$			14.4151i			0.480238i
$902$	−16.6060	+	50.3481i	−0.552920	+	1.67641i
$903$		−	3.04724i		−	0.101406i
$904$	−30.4206	−	17.1722i	−1.01177	−	0.571139i
$905$	3.10848	+	9.56692i	0.103329	+	0.318015i
$906$	5.48877	−	2.01787i	0.182352	−	0.0670391i
$907$	−14.5155	+	19.9789i	−0.481979	+	0.663387i	−0.978884	−	0.204418i	$-0.934470\pi$
$907$	−14.5155	+	19.9789i	−0.481979	+	0.663387i	0.496905	+	0.867805i	$0.334470\pi$
$908$	21.0936	−	17.9333i	0.700017	−	0.595137i
$909$	−7.28500	−	2.36704i	−0.241628	−	0.0785097i
$910$	−15.1631	+	22.6377i	−0.502651	+	0.750432i
$911$	−11.8954	−	16.3726i	−0.394112	−	0.542449i	0.565142	−	0.824994i	$-0.308821\pi$
$911$	−11.8954	−	16.3726i	−0.394112	−	0.542449i	−0.959254	+	0.282545i	$0.908821\pi$
$912$	5.19946	−	10.0914i	0.172171	−	0.334159i
$913$	17.5549	+	26.4614i	0.580984	+	0.875744i
$914$	−35.5589	−	45.2114i	−1.17619	−	1.49546i
$915$	−9.97349	+	7.24616i	−0.329713	+	0.239551i
$916$	2.53856	−	0.194012i	0.0838764	−	0.00641033i
$917$	10.1908	−	31.3641i	0.336530	−	1.03573i
$918$	39.1046	−	1.49212i	1.29064	−	0.0492474i
$919$	22.5099	+	16.3544i	0.742532	+	0.539481i	0.893503	−	0.449057i	$-0.148240\pi$
$919$	22.5099	+	16.3544i	0.742532	+	0.539481i	−0.150971	+	0.988538i	$0.548240\pi$
$920$	0.676378	+	5.88573i	0.0222995	+	0.194047i
$921$	17.9935	−	5.84646i	0.592908	−	0.192647i
$922$	−41.6322	−	11.7924i	−1.37108	−	0.388360i
$923$	21.9032			0.720952
$924$	29.6160	−	23.0815i	0.974295	−	0.759325i
$925$	−2.80188			−0.0921251
$926$	−51.4224	−	14.5654i	−1.68985	−	0.478650i
$927$	−4.46703	+	1.45143i	−0.146716	+	0.0476711i
$928$	32.8124	+	4.07191i	1.07712	+	0.133667i
$929$	−22.4429	−	16.3057i	−0.736327	−	0.534973i	0.155231	−	0.987878i	$-0.450388\pi$
$929$	−22.4429	−	16.3057i	−0.736327	−	0.534973i	−0.891559	+	0.452905i	$0.850388\pi$
$930$	24.2150	−	0.923978i	0.794041	−	0.0302984i
$931$	3.07686	−	9.46959i	0.100840	−	0.310353i
$932$	−2.12019	−	27.7418i	−0.0694491	−	0.908712i
$933$	−11.0502	+	8.02847i	−0.361769	+	0.262840i
$934$	28.0300	+	35.6387i	0.917169	+	1.16613i
$935$	−16.6339	−	0.708517i	−0.543988	−	0.0231710i
$936$	6.36973	−	2.91032i	0.208201	−	0.0951268i
$937$	−5.20146	−	7.15920i	−0.169924	−	0.233881i	0.715559	−	0.698553i	$-0.246172\pi$
$937$	−5.20146	−	7.15920i	−0.169924	−	0.233881i	−0.885483	+	0.464672i	$0.846172\pi$
$938$	−12.2684	+	18.3161i	−0.400579	+	0.598043i
$939$	−45.5062	−	14.7859i	−1.48504	−	0.482518i
$940$	−2.21966	−	2.61083i	−0.0723974	−	0.0851558i
$941$	30.0710	−	41.3892i	0.980286	−	1.34925i	0.0436112	−	0.999049i	$-0.486114\pi$
$941$	30.0710	−	41.3892i	0.980286	−	1.34925i	0.936675	−	0.350200i	$-0.113886\pi$
$942$	−25.3407	+	9.31613i	−0.825645	+	0.303536i
$943$	−7.31613	−	22.5167i	−0.238246	−	0.733246i
$944$	−1.56626	−	10.1871i	−0.0509774	−	0.331561i
$945$			19.5636i			0.636403i
$946$	1.49317	−	2.03614i	0.0485472	−	0.0662007i
$947$		−	9.07490i		−	0.294895i	−0.989070	−	0.147447i	$-0.952894\pi$
$947$		−	9.07490i		−	0.294895i	0.989070	−	0.147447i	$-0.0471057\pi$
$948$	11.2408	−	4.62631i	0.365083	−	0.150256i
$949$	11.2607	+	34.6568i	0.365537	+	1.12501i
$950$	−0.868302	−	2.36186i	−0.0281714	−	0.0766288i
$951$	−11.4262	+	15.7269i	−0.370521	+	0.509979i
$952$	−49.3887	−	9.99836i	−1.60070	−	0.324049i
$953$	−0.425212	−	0.138160i	−0.0137740	−	0.00447543i	0.302122	−	0.953269i	$-0.402305\pi$
$953$	−0.425212	−	0.138160i	−0.0137740	−	0.00447543i	−0.315896	+	0.948794i	$0.602305\pi$
$954$	1.53893	+	1.03080i	0.0498245	+	0.0333733i
$955$	−0.985387	−	1.35627i	−0.0318864	−	0.0438878i
$956$	11.4570	−	47.2508i	0.370547	−	1.52820i
$957$	28.9727	+	10.7973i	0.936553	+	0.349027i
$958$	2.18628	−	1.71952i	0.0706355	−	0.0555551i
$959$	−36.1435	+	26.2598i	−1.16713	+	0.847973i
$960$	4.96281	−	11.7550i	0.160174	−	0.379391i
$961$	−26.0863	+	80.2854i	−0.841494	+	2.58985i
$962$	0.820187	+	21.4949i	0.0264439	+	0.693023i
$963$	−0.0115838	−	0.00841615i	−0.000373284	−	0.000271207i
$964$	−11.1481	+	18.0999i	−0.359055	+	0.582960i
$965$	11.2879	−	3.66765i	0.363369	−	0.118066i
$966$	−4.56977	+	16.1333i	−0.147030	+	0.519080i
$967$	38.4092			1.23516			0.617579	−	0.786509i	$-0.288114\pi$
$967$	38.4092			1.23516			0.617579	+	0.786509i	$0.288114\pi$
$968$	31.0994	−	0.910801i	0.999571	−	0.0292743i
$969$	−14.2465			−0.457664
$970$	−1.68668	+	5.95472i	−0.0541560	+	0.191195i
$971$	−5.33951	+	1.73491i	−0.171353	+	0.0556760i	−0.393437	−	0.919352i	$-0.628714\pi$
$971$	−5.33951	+	1.73491i	−0.171353	+	0.0556760i	0.222084	+	0.975028i	$0.428714\pi$
$972$	4.92598	−	7.99780i	0.158001	−	0.256530i
$973$	1.16163	+	0.843973i	0.0372401	+	0.0270565i
$974$	−0.522869	−	13.7030i	−0.0167538	−	0.439072i
$975$	−2.67559	+	8.23462i	−0.0856875	+	0.263719i
$976$	−30.5143	−	4.97462i	−0.976739	−	0.159234i
$977$	14.1464	−	10.2780i	0.452584	−	0.328822i	−0.338031	−	0.941135i	$-0.609761\pi$
$977$	14.1464	−	10.2780i	0.452584	−	0.328822i	0.790615	+	0.612313i	$0.209761\pi$
$978$	−6.22153	+	4.89326i	−0.198943	+	0.156469i
$979$	57.4228	+	21.3999i	1.83524	+	0.683942i
$980$	2.63721	−	10.8763i	0.0842427	−	0.347432i
$981$	2.04555	+	2.81546i	0.0653094	+	0.0898906i
$982$	9.74564	+	6.52779i	0.310996	+	0.208310i
$983$	−31.3756	−	10.1945i	−1.00073	−	0.325156i	−0.237570	−	0.971370i	$-0.576351\pi$
$983$	−31.3756	−	10.1945i	−1.00073	−	0.325156i	−0.763156	+	0.646215i	$0.776351\pi$
$984$	−10.1174	+	49.9768i	−0.322532	+	1.59320i
$985$	1.23728	−	1.70297i	0.0394229	−	0.0542610i
$986$	−14.3179	−	38.9458i	−0.455973	−	1.24029i
$987$	−2.99716	−	9.22431i	−0.0954007	−	0.293613i
$988$	−17.8651	+	7.35265i	−0.568364	+	0.233919i
$989$			1.12758i			0.0358550i
$990$	−1.26510	+	1.72513i	−0.0402074	+	0.0548284i
$991$			55.3149i			1.75714i	0.477616	+	0.878569i	$0.341501\pi$
$991$			55.3149i			1.75714i	−0.477616	+	0.878569i	$0.658499\pi$
$992$	44.3929	+	41.5044i	1.40948	+	1.31777i
$993$	10.1084	+	31.1103i	0.320779	+	0.987257i
$994$	−19.0073	+	6.98773i	−0.602873	+	0.221637i
$995$	−10.9926	+	15.1301i	−0.348490	+	0.479655i
$996$	19.7828	+	23.2691i	0.626842	+	0.737308i
$997$	19.1254	+	6.21423i	0.605709	+	0.196807i	0.595785	−	0.803144i	$-0.296841\pi$
$997$	19.1254	+	6.21423i	0.605709	+	0.196807i	0.00992390	+	0.999951i	$0.496841\pi$
$998$	27.7274	−	41.3956i	0.877696	−	1.31035i
$999$	9.07829	+	12.4952i	0.287224	+	0.395330i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.r.d.151.6	yes	48
4.3	odd	2	inner	220.2.r.d.151.12	yes	48
11.7	odd	10	inner	220.2.r.d.51.12	yes	48
44.7	even	10	inner	220.2.r.d.51.6	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.r.d.51.6	✓	48	44.7	even	10	inner
220.2.r.d.51.12	yes	48	11.7	odd	10	inner
220.2.r.d.151.6	yes	48	1.1	even	1	trivial
220.2.r.d.151.12	yes	48	4.3	odd	2	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:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.385414 + 1.36068i) q^{2} +(-1.51690 + 0.492870i) q^{3} +(-1.70291 - 1.04885i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-0.0860056 - 2.25398i) q^{6} +(1.09672 - 3.37535i) q^{7} +(2.08348 - 1.91288i) q^{8} +(-0.368991 + 0.268088i) q^{9} +(1.11160 - 0.874274i) q^{10} +(3.10782 + 1.15820i) q^{11} +(3.10009 + 0.751688i) q^{12} +(-3.19085 - 4.39182i) q^{13} +(4.17008 + 2.79319i) q^{14} +(1.51690 + 0.492870i) q^{15} +(1.79982 + 3.57221i) q^{16} +(2.95060 - 4.06116i) q^{17} +(-0.222568 - 0.605404i) q^{18} +(0.549856 + 1.69228i) q^{19} +(0.761185 + 1.84949i) q^{20} +5.66060i q^{21} +(-2.77374 + 3.78238i) q^{22} -2.09462i q^{23} +(-2.21763 + 3.92853i) q^{24} +(0.309017 + 0.951057i) q^{25} +(7.20567 - 2.64906i) q^{26} +(3.24007 - 4.45958i) q^{27} +(-5.40785 + 4.59762i) q^{28} +(-5.55889 - 1.80619i) q^{29} +(-1.25527 + 1.87406i) q^{30} +(-6.31471 - 8.69146i) q^{31} +(-5.55431 + 1.07220i) q^{32} +(-5.28510 - 0.225117i) q^{33} +(4.38874 + 5.58006i) q^{34} +(-2.87124 + 2.08608i) q^{35} +(0.909544 - 0.0695126i) q^{36} +(-0.865827 + 2.66474i) q^{37} +(-2.51458 + 0.0959496i) q^{38} +(7.00479 + 5.08928i) q^{39} +(-2.80993 + 0.322913i) q^{40} +(10.7498 - 3.49283i) q^{41} +(-7.70227 - 2.18167i) q^{42} -0.538324 q^{43} +(-4.07757 - 5.23196i) q^{44} +0.456098 q^{45} +(2.85011 + 0.807294i) q^{46} +(-1.62957 + 0.529478i) q^{47} +(-4.49077 - 4.53160i) q^{48} +(-4.52706 - 3.28910i) q^{49} +(-1.41319 + 0.0539233i) q^{50} +(-2.47414 + 7.61463i) q^{51} +(0.827357 + 10.8256i) q^{52} +(-2.32319 + 1.68789i) q^{53} +(4.81930 + 6.12750i) q^{54} +(-1.83351 - 2.76374i) q^{55} +(-4.17164 - 9.13036i) q^{56} +(-1.66815 - 2.29601i) q^{57} +(4.60013 - 6.86775i) q^{58} +(-2.45058 - 0.796242i) q^{59} +(-2.06620 - 2.43032i) q^{60} +(-4.54316 + 6.25312i) q^{61} +(14.2601 - 5.24251i) q^{62} +(0.500210 + 1.53949i) q^{63} +(0.681785 - 7.97090i) q^{64} +5.42859i q^{65} +(2.34326 - 7.10457i) q^{66} +4.39227i q^{67} +(-9.28417 + 3.82105i) q^{68} +(1.03237 + 3.17732i) q^{69} +(-1.73187 - 4.71085i) q^{70} +(-2.37159 + 3.26421i) q^{71} +(-0.255966 + 1.26439i) q^{72} +(-6.38412 - 2.07433i) q^{73} +(-3.29217 - 2.20515i) q^{74} +(-0.937495 - 1.29035i) q^{75} +(0.838598 - 3.45853i) q^{76} +(7.31773 - 9.21977i) q^{77} +(-9.62464 + 7.56981i) q^{78} +(3.08285 - 2.23982i) q^{79} +(0.643607 - 3.94788i) q^{80} +(-2.29404 + 7.06034i) q^{81} +(0.609497 + 15.9733i) q^{82} +(7.74593 + 5.62775i) q^{83} +(5.93713 - 9.63950i) q^{84} +(-4.77418 + 1.55122i) q^{85} +(0.207478 - 0.732488i) q^{86} +9.32249 q^{87} +(8.69059 - 3.53181i) q^{88} +18.4768 q^{89} +(-0.175787 + 0.620604i) q^{90} +(-18.3234 + 5.95363i) q^{91} +(-2.19694 + 3.56695i) q^{92} +(13.8625 + 10.0717i) q^{93} +(-0.0923936 - 2.42139i) q^{94} +(0.549856 - 1.69228i) q^{95} +(7.89687 - 4.36398i) q^{96} +(-3.54048 + 2.57231i) q^{97} +(6.22021 - 4.89222i) q^{98} +(-1.45726 + 0.405804i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{5} + 20 q^{6} + 16 q^{9} + 14 q^{12} - 10 q^{13} - 21 q^{14} - 4 q^{16} - 25 q^{18} + 5 q^{20} + 15 q^{22} - 30 q^{24} - 12 q^{25} - 4 q^{26} - 60 q^{28} + 20 q^{29} - 10 q^{33} - 18 q^{34}+ \cdots + 38 q^{97}+O(q^{100}) \) 48 * q - 12 * q^5 + 20 * q^6 + 16 * q^9 + 14 * q^12 - 10 * q^13 - 21 * q^14 - 4 * q^16 - 25 * q^18 + 5 * q^20 + 15 * q^22 - 30 * q^24 - 12 * q^25 - 4 * q^26 - 60 * q^28 + 20 * q^29 - 10 * q^33 - 18 * q^34 + 66 * q^36 - 44 * q^37 + 11 * q^38 - 10 * q^41 + 19 * q^42 - 35 * q^44 - 44 * q^45 + 5 * q^46 + 41 * q^48 - 2 * q^49 + 50 * q^52 - 36 * q^53 - 28 * q^56 + 30 * q^57 - 38 * q^58 - 21 * q^60 + 36 * q^64 + 43 * q^66 - 65 * q^68 + 24 * q^69 - 21 * q^70 - 60 * q^72 - 20 * q^73 - 70 * q^74 + 16 * q^77 - 56 * q^78 + q^80 + 50 * q^81 + 35 * q^82 + 60 * q^84 + 10 * q^85 + 38 * q^86 - 101 * q^88 + 64 * q^89 + 70 * q^92 - 28 * q^93 + 130 * q^94 + 105 * q^96 + 38 * q^97

Introduction

L-functions

Modular forms

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Database

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