LMFDB - Embedded newform 620.2.k.c.63.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [620,2,Mod(63,620)] 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("620.63"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(620, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 620 = 2^{2} \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	620.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [88,2,-2] 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:	$4.95072492532$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			63.14
Character	$\chi$	$=$	620.63
Dual form			620.2.k.c.187.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.752899 + 1.19714i) q^{2} +(2.32623 - 2.32623i) q^{3} +(-0.866287 - 1.80265i) q^{4} +(2.15511 + 0.596241i) q^{5} +(1.03341 + 4.53624i) q^{6} +(0.483723 + 0.483723i) q^{7} +(2.81025 + 0.320145i) q^{8} -7.82269i q^{9} +(-2.33636 + 2.13106i) q^{10} -0.611810i q^{11} +(-6.20856 - 2.17819i) q^{12} +(3.25195 + 3.25195i) q^{13} +(-0.943279 + 0.214890i) q^{14} +(6.40027 - 3.62629i) q^{15} +(-2.49909 + 3.12323i) q^{16} +(3.15741 - 3.15741i) q^{17} +(9.36485 + 5.88969i) q^{18} -5.82338 q^{19} +(-0.792131 - 4.40142i) q^{20} +2.25050 q^{21} +(0.732422 + 0.460631i) q^{22} +(-5.77417 + 5.77417i) q^{23} +(7.28202 - 5.79256i) q^{24} +(4.28899 + 2.56993i) q^{25} +(-6.34143 + 1.44465i) q^{26} +(-11.2187 - 11.2187i) q^{27} +(0.452940 - 1.29103i) q^{28} +1.88211i q^{29} +(-0.477585 + 10.3922i) q^{30} -1.00000i q^{31} +(-1.85737 - 5.34323i) q^{32} +(-1.42321 - 1.42321i) q^{33} +(1.40265 + 6.15707i) q^{34} +(0.754061 + 1.33089i) q^{35} +(-14.1016 + 6.77670i) q^{36} +(-5.83854 + 5.83854i) q^{37} +(4.38441 - 6.97140i) q^{38} +15.1296 q^{39} +(5.86551 + 2.36553i) q^{40} -1.16432 q^{41} +(-1.69440 + 2.69417i) q^{42} +(7.31547 - 7.31547i) q^{43} +(-1.10288 + 0.530003i) q^{44} +(4.66421 - 16.8587i) q^{45} +(-2.56512 - 11.2599i) q^{46} +(1.53702 + 1.53702i) q^{47} +(1.45188 + 13.0788i) q^{48} -6.53202i q^{49} +(-6.30574 + 3.19963i) q^{50} -14.6897i q^{51} +(3.04501 - 8.67926i) q^{52} +(-6.12008 - 6.12008i) q^{53} +(21.8769 - 4.98380i) q^{54} +(0.364786 - 1.31852i) q^{55} +(1.20452 + 1.51425i) q^{56} +(-13.5465 + 13.5465i) q^{57} +(-2.25315 - 1.41704i) q^{58} -4.45477 q^{59} +(-12.0814 - 8.39604i) q^{60} +8.28126 q^{61} +(1.19714 + 0.752899i) q^{62} +(3.78402 - 3.78402i) q^{63} +(7.79501 + 1.79938i) q^{64} +(5.06937 + 8.94726i) q^{65} +(2.77531 - 0.632249i) q^{66} +(0.0933865 + 0.0933865i) q^{67} +(-8.42693 - 2.95648i) q^{68} +26.8641i q^{69} +(-2.16100 - 0.0993105i) q^{70} +4.88336i q^{71} +(2.50440 - 21.9837i) q^{72} +(3.57550 + 3.57550i) q^{73} +(-2.59372 - 11.3854i) q^{74} +(15.9554 - 3.99894i) q^{75} +(5.04472 + 10.4975i) q^{76} +(0.295947 - 0.295947i) q^{77} +(-11.3910 + 18.1122i) q^{78} -5.60298 q^{79} +(-7.24801 + 5.24083i) q^{80} -28.7264 q^{81} +(0.876612 - 1.39385i) q^{82} +(-1.46421 + 1.46421i) q^{83} +(-1.94958 - 4.05687i) q^{84} +(8.68714 - 4.92199i) q^{85} +(3.24983 + 14.2654i) q^{86} +(4.37822 + 4.37822i) q^{87} +(0.195868 - 1.71934i) q^{88} +16.9786i q^{89} +(16.6706 + 18.2766i) q^{90} +3.14609i q^{91} +(15.4109 + 5.40672i) q^{92} +(-2.32623 - 2.32623i) q^{93} +(-2.99725 + 0.682808i) q^{94} +(-12.5500 - 3.47214i) q^{95} +(-16.7503 - 8.10891i) q^{96} +(-4.67352 + 4.67352i) q^{97} +(7.81975 + 4.91795i) q^{98} -4.78600 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 2 q^{2} - 2 q^{3} - 2 q^{5} - 4 q^{7} - 10 q^{8} - 10 q^{10} - 4 q^{12} - 6 q^{13} - 22 q^{14} + 2 q^{15} + 8 q^{16} - 2 q^{17} + 56 q^{18} - 8 q^{19} + 8 q^{20} - 16 q^{21} - 10 q^{23} + 44 q^{24}+ \cdots + 8 q^{99}+O(q^{100}) $ 88 * q + 2 * q^2 - 2 * q^3 - 2 * q^5 - 4 * q^7 - 10 * q^8 - 10 * q^10 - 4 * q^12 - 6 * q^13 - 22 * q^14 + 2 * q^15 + 8 * q^16 - 2 * q^17 + 56 * q^18 - 8 * q^19 + 8 * q^20 - 16 * q^21 - 10 * q^23 + 44 * q^24 - 4 * q^25 - 8 * q^26 - 8 * q^27 - 72 * q^28 - 8 * q^32 - 8 * q^33 - 40 * q^34 + 12 * q^35 - 20 * q^36 + 10 * q^37 + 30 * q^38 - 8 * q^39 + 8 * q^41 + 28 * q^42 - 10 * q^43 + 16 * q^44 + 6 * q^45 - 24 * q^46 + 64 * q^47 - 80 * q^48 - 14 * q^50 + 20 * q^52 + 18 * q^53 - 36 * q^54 - 40 * q^55 - 24 * q^56 - 24 * q^57 + 76 * q^58 - 8 * q^60 + 20 * q^61 - 2 * q^62 + 4 * q^63 + 150 * q^64 - 18 * q^65 + 8 * q^66 - 116 * q^67 - 48 * q^68 + 16 * q^70 + 4 * q^72 + 38 * q^73 - 36 * q^74 + 70 * q^75 - 8 * q^76 + 40 * q^77 + 128 * q^78 - 32 * q^79 - 12 * q^80 - 60 * q^81 - 28 * q^82 + 14 * q^83 + 120 * q^84 + 6 * q^85 + 4 * q^86 + 44 * q^87 - 68 * q^88 + 34 * q^90 + 56 * q^92 + 2 * q^93 - 112 * q^94 - 104 * q^95 - 20 * q^96 + 16 * q^97 + 52 * q^98 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/620\mathbb{Z}\right)^\times$.

$n$	$311$	$497$	$561$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−0.752899	+	1.19714i	−0.532380	+	0.846506i
$2$	−0.752899	+	1.19714i	−0.532380	+	0.846506i
$3$	2.32623	−	2.32623i	1.34305	−	1.34305i	0.450042	−	0.893008i	$-0.351409\pi$
$3$	2.32623	−	2.32623i	1.34305	−	1.34305i	0.893008	−	0.450042i	$-0.148591\pi$
$4$	−0.866287	−	1.80265i	−0.433144	−	0.901325i
$5$	2.15511	+	0.596241i	0.963794	+	0.266647i
$5$	2.15511	+	0.596241i	0.963794	+	0.266647i
$6$	1.03341	+	4.53624i	0.421887	+	1.85191i
$7$	0.483723	+	0.483723i	0.182830	+	0.182830i	0.792588	−	0.609758i	$-0.208733\pi$
$7$	0.483723	+	0.483723i	0.182830	+	0.182830i	−0.609758	+	0.792588i	$0.708733\pi$
$8$	2.81025	+	0.320145i	0.993574	+	0.113188i
$9$		−	7.82269i		−	2.60756i
$10$	−2.33636	+	2.13106i	−0.738823	+	0.673900i
$11$		−	0.611810i		−	0.184468i	−0.995737	−	0.0922338i	$-0.970599\pi$
$11$		−	0.611810i		−	0.184468i	0.995737	−	0.0922338i	$-0.0294007\pi$
$12$	−6.20856	−	2.17819i	−1.79226	−	0.628790i
$13$	3.25195	+	3.25195i	0.901929	+	0.901929i	0.995603	−	0.0936737i	$-0.0298611\pi$
$13$	3.25195	+	3.25195i	0.901929	+	0.901929i	−0.0936737	+	0.995603i	$0.529861\pi$
$14$	−0.943279	+	0.214890i	−0.252102	+	0.0574317i
$15$	6.40027	−	3.62629i	1.65254	−	0.936303i
$16$	−2.49909	+	3.12323i	−0.624773	+	0.780806i
$17$	3.15741	−	3.15741i	0.765784	−	0.765784i	−0.211577	−	0.977361i	$-0.567860\pi$
$17$	3.15741	−	3.15741i	0.765784	−	0.765784i	0.977361	+	0.211577i	$0.0678599\pi$
$18$	9.36485	+	5.88969i	2.20732	+	1.38821i
$19$	−5.82338			−1.33597			−0.667987	−	0.744173i	$-0.732844\pi$
$19$	−5.82338			−1.33597			−0.667987	+	0.744173i	$0.732844\pi$
$20$	−0.792131	−	4.40142i	−0.177126	−	0.984188i
$21$	2.25050			0.491100
$22$	0.732422	+	0.460631i	0.156153	+	0.0982068i
$23$	−5.77417	+	5.77417i	−1.20400	+	1.20400i	−0.231058	+	0.972940i	$0.574219\pi$
$23$	−5.77417	+	5.77417i	−1.20400	+	1.20400i	−0.972940	+	0.231058i	$0.925781\pi$
$24$	7.28202	−	5.79256i	1.48644	−	1.18240i
$25$	4.28899	+	2.56993i	0.857799	+	0.513986i
$26$	−6.34143	+	1.44465i	−1.24366	+	0.283319i
$27$	−11.2187	−	11.2187i	−2.15904	−	2.15904i
$28$	0.452940	−	1.29103i	0.0855977	−	0.243981i
$29$			1.88211i			0.349499i	0.984613	+	0.174749i	$0.0559115\pi$
$29$			1.88211i			0.349499i	−0.984613	+	0.174749i	$0.944088\pi$
$30$	−0.477585	+	10.3922i	−0.0871947	+	1.89736i
$31$		−	1.00000i		−	0.179605i
$31$		−	1.00000i		−	0.179605i
$32$	−1.85737	−	5.34323i	−0.328341	−	0.944559i
$33$	−1.42321	−	1.42321i	−0.247749	−	0.247749i
$34$	1.40265	+	6.15707i	0.240553	+	1.05593i
$35$	0.754061	+	1.33089i	0.127460	+	0.224962i
$36$	−14.1016	+	6.77670i	−2.35026	+	1.12945i
$37$	−5.83854	+	5.83854i	−0.959851	+	0.959851i	−0.999225	−	0.0393740i	$-0.987464\pi$
$37$	−5.83854	+	5.83854i	−0.959851	+	0.959851i	0.0393740	+	0.999225i	$0.487464\pi$
$38$	4.38441	−	6.97140i	0.711246	−	1.13091i
$39$	15.1296			2.42267
$40$	5.86551	+	2.36553i	0.927419	+	0.374024i
$41$	−1.16432			−0.181836			−0.0909179	−	0.995858i	$-0.528980\pi$
$41$	−1.16432			−0.181836			−0.0909179	+	0.995858i	$0.528980\pi$
$42$	−1.69440	+	2.69417i	−0.261452	+	0.415719i
$43$	7.31547	−	7.31547i	1.11560	−	1.11560i	0.123218	−	0.992380i	$-0.460678\pi$
$43$	7.31547	−	7.31547i	1.11560	−	1.11560i	0.992380	−	0.123218i	$-0.0393216\pi$
$44$	−1.10288	+	0.530003i	−0.166265	+	0.0799010i
$45$	4.66421	−	16.8587i	0.695299	−	2.51315i
$46$	−2.56512	−	11.2599i	−0.378207	−	1.66018i
$47$	1.53702	+	1.53702i	0.224197	+	0.224197i	0.810263	−	0.586066i	$-0.199324\pi$
$47$	1.53702	+	1.53702i	0.224197	+	0.224197i	−0.586066	+	0.810263i	$0.699324\pi$
$48$	1.45188	+	13.0788i	0.209560	+	1.88776i
$49$		−	6.53202i		−	0.933146i
$50$	−6.30574	+	3.19963i	−0.891766	+	0.452496i
$51$		−	14.6897i		−	2.05697i
$52$	3.04501	−	8.67926i	0.422266	−	1.20360i
$53$	−6.12008	−	6.12008i	−0.840658	−	0.840658i	0.148287	−	0.988944i	$-0.452624\pi$
$53$	−6.12008	−	6.12008i	−0.840658	−	0.840658i	−0.988944	+	0.148287i	$0.952624\pi$
$54$	21.8769	−	4.98380i	2.97706	−	0.678209i
$55$	0.364786	−	1.31852i	0.0491877	−	0.177789i
$56$	1.20452	+	1.51425i	0.160961	+	0.202350i
$57$	−13.5465	+	13.5465i	−1.79428	+	1.79428i
$58$	−2.25315	−	1.41704i	−0.295853	−	0.186066i
$59$	−4.45477			−0.579961			−0.289981	−	0.957032i	$-0.593649\pi$
$59$	−4.45477			−0.579961			−0.289981	+	0.957032i	$0.593649\pi$
$60$	−12.0814	−	8.39604i	−1.55970	−	1.08392i
$61$	8.28126			1.06031			0.530154	−	0.847902i	$-0.322134\pi$
$61$	8.28126			1.06031			0.530154	+	0.847902i	$0.322134\pi$
$62$	1.19714	+	0.752899i	0.152037	+	0.0956182i
$63$	3.78402	−	3.78402i	0.476741	−	0.476741i
$64$	7.79501	+	1.79938i	0.974377	+	0.224922i
$65$	5.06937	+	8.94726i	0.628777	+	1.10977i
$66$	2.77531	−	0.632249i	0.341618	−	0.0778244i
$67$	0.0933865	+	0.0933865i	0.0114090	+	0.0114090i	0.712788	−	0.701379i	$-0.247432\pi$
$67$	0.0933865	+	0.0933865i	0.0114090	+	0.0114090i	−0.701379	+	0.712788i	$0.747432\pi$
$68$	−8.42693	−	2.95648i	−1.02192	−	0.358526i
$69$			26.8641i			3.23406i
$70$	−2.16100	−	0.0993105i	−0.258288	−	0.0118699i
$71$			4.88336i			0.579548i	0.957095	+	0.289774i	$0.0935802\pi$
$71$			4.88336i			0.579548i	−0.957095	+	0.289774i	$0.906420\pi$
$72$	2.50440	−	21.9837i	0.295146	−	2.59081i
$73$	3.57550	+	3.57550i	0.418481	+	0.418481i	0.884680	−	0.466199i	$-0.154377\pi$
$73$	3.57550	+	3.57550i	0.418481	+	0.418481i	−0.466199	+	0.884680i	$0.654377\pi$
$74$	−2.59372	−	11.3854i	−0.301514	−	1.32352i
$75$	15.9554	−	3.99894i	1.84237	−	0.461758i
$76$	5.04472	+	10.4975i	0.578669	+	1.20415i
$77$	0.295947	−	0.295947i	0.0337263	−	0.0337263i
$78$	−11.3910	+	18.1122i	−1.28978	+	2.05080i
$79$	−5.60298			−0.630384			−0.315192	−	0.949028i	$-0.602069\pi$
$79$	−5.60298			−0.630384			−0.315192	+	0.949028i	$0.602069\pi$
$80$	−7.24801	+	5.24083i	−0.810352	+	0.585943i
$81$	−28.7264			−3.19182
$82$	0.876612	−	1.39385i	0.0968056	−	0.153925i
$83$	−1.46421	+	1.46421i	−0.160718	+	0.160718i	−0.782885	−	0.622167i	$-0.786253\pi$
$83$	−1.46421	+	1.46421i	−0.160718	+	0.160718i	0.622167	+	0.782885i	$0.286253\pi$
$84$	−1.94958	−	4.05687i	−0.212717	−	0.442641i
$85$	8.68714	−	4.92199i	0.942253	−	0.533864i
$86$	3.24983	+	14.2654i	0.350438	+	1.53828i
$87$	4.37822	+	4.37822i	0.469394	+	0.469394i
$88$	0.195868	−	1.71934i	0.0208796	−	0.183282i
$89$			16.9786i			1.79973i	0.436172	+	0.899863i	$0.356334\pi$
$89$			16.9786i			1.79973i	−0.436172	+	0.899863i	$0.643666\pi$
$90$	16.6706	+	18.2766i	1.75724	+	1.92653i
$91$			3.14609i			0.329800i
$92$	15.4109	+	5.40672i	1.60670	+	0.563689i
$93$	−2.32623	−	2.32623i	−0.241219	−	0.241219i
$94$	−2.99725	+	0.682808i	−0.309143	+	0.0704263i
$95$	−12.5500	−	3.47214i	−1.28760	−	0.356234i
$96$	−16.7503	−	8.10891i	−1.70957	−	0.827612i
$97$	−4.67352	+	4.67352i	−0.474524	+	0.474524i	−0.903375	−	0.428851i	$-0.858918\pi$
$97$	−4.67352	+	4.67352i	−0.474524	+	0.474524i	0.428851	+	0.903375i	$0.358918\pi$
$98$	7.81975	+	4.91795i	0.789914	+	0.496788i
$99$	−4.78600			−0.481011
$100$	0.917181	−	9.95785i	0.0917181	−	0.995785i
$101$	−5.61619			−0.558832			−0.279416	−	0.960170i	$-0.590141\pi$
$101$	−5.61619			−0.558832			−0.279416	+	0.960170i	$0.590141\pi$
$102$	17.5856	+	11.0599i	1.74124	+	1.09509i
$103$	6.83814	−	6.83814i	0.673782	−	0.673782i	−0.284804	−	0.958586i	$-0.591928\pi$
$103$	6.83814	−	6.83814i	0.673782	−	0.673782i	0.958586	+	0.284804i	$0.0919284\pi$
$104$	8.09770	+	10.1799i	0.794045	+	0.998221i
$105$	4.85008	+	1.34184i	0.473319	+	0.130950i
$106$	11.9344	−	2.71879i	1.15917	−	0.264072i
$107$	2.83502	+	2.83502i	0.274072	+	0.274072i	0.830737	−	0.556665i	$-0.187919\pi$
$107$	2.83502	+	2.83502i	0.274072	+	0.274072i	−0.556665	+	0.830737i	$0.687919\pi$
$108$	−10.5047	+	29.9419i	−1.01082	+	2.88117i
$109$			6.77612i			0.649034i	0.945880	+	0.324517i	$0.105202\pi$
$109$			6.77612i			0.649034i	−0.945880	+	0.324517i	$0.894798\pi$
$110$	1.30380	+	1.42941i	0.124313	+	0.136289i
$111$			27.1636i			2.57825i
$112$	−2.71965	+	0.301908i	−0.256982	+	0.0285276i
$113$	−5.66216	−	5.66216i	−0.532651	−	0.532651i	0.388709	−	0.921361i	$-0.372921\pi$
$113$	−5.66216	−	5.66216i	−0.532651	−	0.532651i	−0.921361	+	0.388709i	$0.872921\pi$
$114$	−6.01792	−	26.4162i	−0.563630	−	2.47411i
$115$	−15.8868	+	9.00117i	−1.48145	+	0.839364i
$116$	3.39278	−	1.63045i	0.315012	−	0.151383i
$117$	25.4390	−	25.4390i	2.35184	−	2.35184i
$118$	3.35399	−	5.33298i	0.308760	−	0.490941i
$119$	3.05463			0.280017
$120$	19.1473	−	8.14175i	1.74790	−	0.743237i
$121$	10.6257			0.965972
$122$	−6.23495	+	9.91383i	−0.564486	+	0.897556i
$123$	−2.70847	+	2.70847i	−0.244214	+	0.244214i
$124$	−1.80265	+	0.866287i	−0.161883	+	0.0777949i
$125$	7.71095	+	8.09575i	0.689689	+	0.724106i
$126$	1.68102	+	7.37898i	0.149757	+	0.657372i
$127$	−10.9103	−	10.9103i	−0.968129	−	0.968129i	0.0313784	−	0.999508i	$-0.490010\pi$
$127$	−10.9103	−	10.9103i	−0.968129	−	0.968129i	−0.999508	+	0.0313784i	$0.990010\pi$
$128$	−8.02296	+	7.97697i	−0.709136	+	0.705071i
$129$		−	34.0349i		−	2.99661i
$130$	−14.5278	−	0.667640i	−1.27418	−	0.0585559i
$131$			12.9615i			1.13245i	0.824251	+	0.566224i	$0.191596\pi$
$131$			12.9615i			1.13245i	−0.824251	+	0.566224i	$0.808404\pi$
$132$	−1.33264	+	3.79846i	−0.115991	+	0.330613i
$133$	−2.81690	−	2.81690i	−0.244257	−	0.244257i
$134$	−0.182107	+	0.0414861i	−0.0157317	+	0.00358386i
$135$	−17.4884	−	30.8665i	−1.50517	−	2.65657i
$136$	9.88394	−	7.86228i	0.847541	−	0.674185i
$137$	−4.73775	+	4.73775i	−0.404774	+	0.404774i	−0.879911	−	0.475138i	$-0.842398\pi$
$137$	−4.73775	+	4.73775i	−0.404774	+	0.404774i	0.475138	+	0.879911i	$0.342398\pi$
$138$	−32.1601	−	20.2259i	−2.73765	−	1.72175i
$139$	−8.88843			−0.753906			−0.376953	−	0.926232i	$-0.623028\pi$
$139$	−8.88843			−0.753906			−0.376953	+	0.926232i	$0.623028\pi$
$140$	1.74590	−	2.51224i	0.147555	−	0.212323i
$141$	7.15093			0.602217
$142$	−5.84606	−	3.67667i	−0.490591	−	0.308540i
$143$	1.98958	−	1.98958i	0.166377	−	0.166377i
$144$	24.4320	+	19.5496i	2.03600	+	1.62913i
$145$	−1.12219	+	4.05615i	−0.0931928	+	0.336845i
$146$	−6.97237	+	1.58839i	−0.577037	+	0.131456i
$147$	−15.1950	−	15.1950i	−1.25326	−	1.25326i
$148$	15.5827	+	5.46699i	1.28089	+	0.449384i
$149$			12.2725i			1.00540i	0.864461	+	0.502700i	$0.167660\pi$
$149$			12.2725i			1.00540i	−0.864461	+	0.502700i	$0.832340\pi$
$150$	−7.22553	+	22.1117i	−0.589962	+	1.80541i
$151$		−	2.57347i		−	0.209426i	−0.994502	−	0.104713i	$-0.966608\pi$
$151$		−	2.57347i		−	0.209426i	0.994502	−	0.104713i	$-0.0333924\pi$
$152$	−16.3652	−	1.86433i	−1.32739	−	0.151217i
$153$	−24.6994	−	24.6994i	−1.99683	−	1.99683i
$154$	0.131472	+	0.577107i	0.0105943	+	0.0465046i
$155$	0.596241	−	2.15511i	0.0478912	−	0.173103i
$156$	−13.1066	−	27.2733i	−1.04936	−	2.18361i
$157$	8.57036	−	8.57036i	0.683989	−	0.683989i	−0.276907	−	0.960897i	$-0.589310\pi$
$157$	8.57036	−	8.57036i	0.683989	−	0.683989i	0.960897	+	0.276907i	$0.0893095\pi$
$158$	4.21847	−	6.70755i	0.335604	−	0.533624i
$159$	−28.4734			−2.25809
$160$	−0.816990	−	12.6227i	−0.0645887	−	0.997912i
$161$	−5.58620			−0.440254
$162$	21.6280	−	34.3895i	1.69926	−	2.70189i
$163$	2.09145	−	2.09145i	0.163815	−	0.163815i	−0.620439	−	0.784254i	$-0.713046\pi$
$163$	2.09145	−	2.09145i	0.163815	−	0.163815i	0.784254	+	0.620439i	$0.213046\pi$
$164$	1.00863	+	2.09886i	0.0787610	+	0.163893i
$165$	−2.21860	−	3.91575i	−0.172718	−	0.304841i
$166$	−0.650464	−	2.85527i	−0.0504858	−	0.221612i
$167$	−3.19551	−	3.19551i	−0.247276	−	0.247276i	0.572576	−	0.819852i	$-0.305944\pi$
$167$	−3.19551	−	3.19551i	−0.247276	−	0.247276i	−0.819852	+	0.572576i	$0.805944\pi$
$168$	6.32448	+	0.720488i	0.487944	+	0.0555869i
$169$			8.15038i			0.626953i
$170$	−0.648230	+	14.1055i	−0.0497169	+	1.08184i
$171$			45.5545i			3.48364i
$172$	−19.5245	−	6.84993i	−1.48873	−	0.522302i
$173$	−8.10812	−	8.10812i	−0.616449	−	0.616449i	0.328170	−	0.944619i	$-0.393568\pi$
$173$	−8.10812	−	8.10812i	−0.616449	−	0.616449i	−0.944619	+	0.328170i	$0.893568\pi$
$174$	−8.53769	+	1.94498i	−0.647240	+	0.147449i
$175$	0.831552	+	3.31782i	0.0628594	+	0.250804i
$176$	1.91082	+	1.52897i	0.144033	+	0.115250i
$177$	−10.3628	+	10.3628i	−0.778917	+	0.778917i
$178$	−20.3257	−	12.7832i	−1.52348	−	0.958138i
$179$	4.03738			0.301768			0.150884	−	0.988551i	$-0.451788\pi$
$179$	4.03738			0.301768			0.150884	+	0.988551i	$0.451788\pi$
$180$	−34.4310	+	6.19659i	−2.56633	+	0.461867i
$181$	7.41836			0.551402			0.275701	−	0.961243i	$-0.411090\pi$
$181$	7.41836			0.551402			0.275701	+	0.961243i	$0.411090\pi$
$182$	−3.76631	−	2.36869i	−0.279177	−	0.175579i
$183$	19.2641	−	19.2641i	1.42404	−	1.42404i
$184$	−18.0754	+	14.3783i	−1.33254	+	1.05998i
$185$	−16.0639	+	9.10152i	−1.18104	+	0.669157i
$186$	4.53624	−	1.03341i	0.332613	−	0.0757731i
$187$	−1.93173	−	1.93173i	−0.141262	−	0.141262i
$188$	1.43921	−	4.10221i	0.104965	−	0.299185i
$189$		−	10.8535i		−	0.789474i
$190$	13.6055	−	12.4100i	0.987049	−	0.900313i
$191$			4.29702i			0.310922i	0.987842	+	0.155461i	$0.0496862\pi$
$191$			4.29702i			0.310922i	−0.987842	+	0.155461i	$0.950314\pi$
$192$	22.3188	−	13.9472i	1.61072	−	1.00655i
$193$	−1.10335	−	1.10335i	−0.0794207	−	0.0794207i	0.666280	−	0.745701i	$-0.267885\pi$
$193$	−1.10335	−	1.10335i	−0.0794207	−	0.0794207i	−0.745701	+	0.666280i	$0.767885\pi$
$194$	−2.07617	−	9.11354i	−0.149060	−	0.654314i
$195$	32.6059	+	9.02087i	2.33496	+	0.645998i
$196$	−11.7750	+	5.65861i	−0.841068	+	0.404186i
$197$	4.77507	−	4.77507i	0.340210	−	0.340210i	−0.516237	−	0.856446i	$-0.672667\pi$
$197$	4.77507	−	4.77507i	0.340210	−	0.340210i	0.856446	+	0.516237i	$0.172667\pi$
$198$	3.60337	−	5.72951i	0.256080	−	0.407178i
$199$	9.77288			0.692781			0.346390	−	0.938090i	$-0.387407\pi$
$199$	9.77288			0.692781			0.346390	+	0.938090i	$0.387407\pi$
$200$	11.2304	+	8.59524i	0.794109	+	0.607776i
$201$	0.434477			0.0306456
$202$	4.22842	−	6.72337i	0.297511	−	0.473055i
$203$	−0.910420	+	0.910420i	−0.0638989	+	0.0638989i
$204$	−26.4804	+	12.7255i	−1.85400	+	0.890965i
$205$	−2.50923	−	0.694213i	−0.175252	−	0.0484860i
$206$	3.03779	+	13.3346i	0.211653	+	0.929069i
$207$	45.1695	+	45.1695i	3.13950	+	3.13950i
$208$	−18.2835	+	2.02965i	−1.26773	+	0.140731i
$209$			3.56280i			0.246444i
$210$	−5.25799	+	4.79595i	−0.362836	+	0.330952i
$211$			10.6928i			0.736125i	0.929801	+	0.368062i	$0.119979\pi$
$211$			10.6928i			0.736125i	−0.929801	+	0.368062i	$0.880021\pi$
$212$	−5.73061	+	16.3341i	−0.393580	+	1.12183i
$213$	11.3598	+	11.3598i	0.778362	+	0.778362i
$214$	−5.52840	+	1.25943i	−0.377914	+	0.0860931i
$215$	20.1274	−	11.4038i	1.37268	−	0.777736i
$216$	−27.9357	−	35.1189i	−1.90078	−	2.38954i
$217$	0.483723	−	0.483723i	0.0328373	−	0.0328373i
$218$	−8.11196	−	5.10173i	−0.549411	−	0.345533i
$219$	16.6349			1.12408
$220$	−2.69283	+	0.484633i	−0.181551	+	0.0326740i
$221$	20.5355			1.38137
$222$	−32.5186	−	20.4514i	−2.18251	−	1.37261i
$223$	−18.1948	+	18.1948i	−1.21841	+	1.21841i	−0.250227	+	0.968187i	$0.580505\pi$
$223$	−18.1948	+	18.1948i	−1.21841	+	1.21841i	−0.968187	+	0.250227i	$0.919495\pi$
$224$	1.68619	−	3.48310i	0.112663	−	0.232725i
$225$	20.1038	−	33.5515i	1.34025	−	2.23676i
$226$	11.0414	−	2.51537i	0.734465	−	0.167320i
$227$	−6.13354	−	6.13354i	−0.407098	−	0.407098i	0.473628	−	0.880725i	$-0.342944\pi$
$227$	−6.13354	−	6.13354i	−0.407098	−	0.407098i	−0.880725	+	0.473628i	$0.842944\pi$
$228$	36.1548	+	12.6844i	2.39441	+	0.840048i
$229$			15.9643i			1.05495i	0.849571	+	0.527474i	$0.176861\pi$
$229$			15.9643i			1.05495i	−0.849571	+	0.527474i	$0.823139\pi$
$230$	1.18546	−	25.7957i	0.0781671	−	1.70092i
$231$		−	1.37688i		−	0.0905920i
$232$	−0.602548	+	5.28920i	−0.0395592	+	0.347253i
$233$	12.9449	+	12.9449i	0.848051	+	0.848051i	0.989890	−	0.141839i	$-0.0453014\pi$
$233$	12.9449	+	12.9449i	0.848051	+	0.848051i	−0.141839	+	0.989890i	$0.545301\pi$
$234$	11.3011	+	49.6070i	0.738773	+	3.24291i
$235$	2.39601	+	4.22888i	0.156299	+	0.275862i
$236$	3.85911	+	8.03039i	0.251207	+	0.522734i
$237$	−13.0338	+	13.0338i	−0.846637	+	0.846637i
$238$	−2.29982	+	3.65681i	−0.149075	+	0.237036i
$239$	−2.96454			−0.191760			−0.0958800	−	0.995393i	$-0.530567\pi$
$239$	−2.96454			−0.191760			−0.0958800	+	0.995393i	$0.530567\pi$
$240$	−4.66916	+	29.0519i	−0.301393	+	1.87529i
$241$	−23.9141			−1.54044			−0.770221	−	0.637777i	$-0.779854\pi$
$241$	−23.9141			−1.54044			−0.770221	+	0.637777i	$0.779854\pi$
$242$	−8.00007	+	12.7204i	−0.514264	+	0.817701i
$243$	−33.1681	+	33.1681i	−2.12774	+	2.12774i
$244$	−7.17395	−	14.9282i	−0.459265	−	0.955681i
$245$	3.89466	−	14.0772i	0.248821	−	0.899361i
$246$	−1.20321	−	5.28162i	−0.0767141	−	0.336744i
$247$	−18.9374	−	18.9374i	−1.20495	−	1.20495i
$248$	0.320145	−	2.81025i	0.0203293	−	0.178451i
$249$			6.81219i			0.431705i
$250$	−15.4973	+	3.13581i	−0.980136	+	0.198326i
$251$			9.91181i			0.625628i	0.949814	+	0.312814i	$0.101272\pi$
$251$			9.91181i			0.625628i	−0.949814	+	0.312814i	$0.898728\pi$
$252$	−10.0993	−	3.54321i	−0.636196	−	0.223201i
$253$	3.53270	+	3.53270i	0.222099	+	0.222099i
$254$	21.2754	−	4.84679i	1.33494	−	0.304115i
$255$	8.75861	−	31.6580i	0.548486	−	1.98250i
$256$	−3.50908	−	15.6105i	−0.219317	−	0.975654i
$257$	10.0498	−	10.0498i	0.626887	−	0.626887i	−0.320396	−	0.947284i	$-0.603816\pi$
$257$	10.0498	−	10.0498i	0.626887	−	0.626887i	0.947284	+	0.320396i	$0.103816\pi$
$258$	40.7445	+	25.6248i	2.53664	+	1.59533i
$259$	−5.64848			−0.350979
$260$	11.7372	−	16.8892i	0.727913	−	1.04742i
$261$	14.7231			0.911340
$262$	−15.5167	−	9.75866i	−0.958624	−	0.602892i
$263$	−6.07934	+	6.07934i	−0.374868	+	0.374868i	−0.869247	−	0.494378i	$-0.835396\pi$
$263$	−6.07934	+	6.07934i	−0.374868	+	0.374868i	0.494378	+	0.869247i	$0.335396\pi$
$264$	−3.54394	−	4.45521i	−0.218115	−	0.274199i
$265$	−9.54040	−	16.8385i	−0.586062	−	1.03438i
$266$	5.49307	−	1.25139i	0.336802	−	0.0767273i
$267$	39.4961	+	39.4961i	2.41712	+	2.41712i
$268$	0.0874436	−	0.249243i	0.00534147	−	0.0152249i
$269$		−	5.71293i		−	0.348324i	−0.984717	−	0.174162i	$-0.944278\pi$
$269$		−	5.71293i		−	0.348324i	0.984717	−	0.174162i	$-0.0557216\pi$
$270$	50.1186	+	2.30324i	3.05012	+	0.140171i
$271$		−	28.9050i		−	1.75585i	−0.478796	−	0.877926i	$-0.658927\pi$
$271$		−	28.9050i		−	1.75585i	0.478796	−	0.877926i	$-0.341073\pi$
$272$	1.97064	+	17.7520i	0.119488	+	1.07637i
$273$	7.31853	+	7.31853i	0.442937	+	0.442937i
$274$	−2.10471	−	9.23880i	−0.127150	−	0.558136i
$275$	1.57231	−	2.62405i	0.0948137	−	0.158236i
$276$	48.4266	−	23.2720i	2.91494	−	1.40081i
$277$	13.3417	−	13.3417i	0.801626	−	0.801626i	−0.181724	−	0.983350i	$-0.558168\pi$
$277$	13.3417	−	13.3417i	0.801626	−	0.801626i	0.983350	+	0.181724i	$0.0581677\pi$
$278$	6.69208	−	10.6407i	0.401364	−	0.638186i
$279$	−7.82269			−0.468332
$280$	1.69302	+	3.98155i	0.101177	+	0.237943i
$281$	−1.56039			−0.0930850			−0.0465425	−	0.998916i	$-0.514820\pi$
$281$	−1.56039			−0.0930850			−0.0465425	+	0.998916i	$0.514820\pi$
$282$	−5.38392	+	8.56066i	−0.320608	+	0.509780i
$283$	16.9925	−	16.9925i	1.01010	−	1.01010i	0.0101511	−	0.999948i	$-0.496769\pi$
$283$	16.9925	−	16.9925i	1.01010	−	1.01010i	0.999948	−	0.0101511i	$-0.00323126\pi$
$284$	8.80299	−	4.23039i	0.522361	−	0.251028i
$285$	−37.2712	+	21.1172i	−2.20776	+	1.25088i
$286$	0.883852	+	3.87975i	0.0522633	+	0.229414i
$287$	−0.563207	−	0.563207i	−0.0332451	−	0.0332451i
$288$	−41.7985	+	14.5297i	−2.46300	+	0.856168i
$289$		−	2.93847i		−	0.172851i
$290$	−4.01088	−	4.39729i	−0.235527	−	0.258218i
$291$			21.7433i			1.27462i
$292$	3.34797	−	9.54279i	0.195925	−	0.558450i
$293$	−21.7795	−	21.7795i	−1.27237	−	1.27237i	−0.944841	−	0.327530i	$-0.893784\pi$
$293$	−21.7795	−	21.7795i	−1.27237	−	1.27237i	−0.327530	−	0.944841i	$-0.606216\pi$
$294$	29.6308	−	6.75024i	1.72810	−	0.393682i
$295$	−9.60051	−	2.65611i	−0.558963	−	0.154645i
$296$	−18.2769	+	14.5386i	−1.06233	+	0.845038i
$297$	−6.86370	+	6.86370i	−0.398272	+	0.398272i
$298$	−14.6919	−	9.23993i	−0.851077	−	0.535255i
$299$	−37.5547			−2.17184
$300$	−21.0307	−	25.2978i	−1.21421	−	1.46057i
$301$	7.07732			0.407930
$302$	3.08080	+	1.93756i	0.177280	+	0.111494i
$303$	−13.0646	+	13.0646i	−0.750539	+	0.750539i
$304$	14.5532	−	18.1877i	0.834681	−	1.04314i
$305$	17.8470	+	4.93763i	1.02192	+	0.282728i
$306$	48.1648	−	10.9725i	2.75340	−	0.627256i
$307$	17.8116	+	17.8116i	1.01656	+	1.01656i	0.999861	+	0.0166989i	$0.00531567\pi$
$307$	17.8116	+	17.8116i	1.01656	+	1.01656i	0.0166989	+	0.999861i	$0.494684\pi$
$308$	−0.789863	−	0.277113i	−0.0450066	−	0.0157900i
$309$		−	31.8142i		−	1.80985i
$310$	2.13106	+	2.33636i	0.121036	+	0.132696i
$311$			6.17773i			0.350307i	0.984541	+	0.175153i	$0.0560421\pi$
$311$			6.17773i			0.350307i	−0.984541	+	0.175153i	$0.943958\pi$
$312$	42.5179	+	4.84366i	2.40710	+	0.274218i
$313$	−3.23247	−	3.23247i	−0.182710	−	0.182710i	0.609826	−	0.792536i	$-0.291239\pi$
$313$	−3.23247	−	3.23247i	−0.182710	−	0.182710i	−0.792536	+	0.609826i	$0.791239\pi$
$314$	3.80731	+	16.7125i	0.214859	+	0.943143i
$315$	10.4112	−	5.89878i	0.586602	−	0.332359i
$316$	4.85379	+	10.1002i	0.273047	+	0.568181i
$317$	−18.1714	+	18.1714i	−1.02061	+	1.02061i	−0.0208254	+	0.999783i	$0.506629\pi$
$317$	−18.1714	+	18.1714i	−1.02061	+	1.02061i	−0.999783	+	0.0208254i	$0.993371\pi$
$318$	21.4376	−	34.0867i	1.20216	−	1.91149i
$319$	1.15149			0.0644712
$320$	15.7262	+	8.52556i	0.879124	+	0.476593i
$321$	13.1898			0.736184
$322$	4.20584	−	6.68747i	0.234383	−	0.372678i
$323$	−18.3868	+	18.3868i	−1.02307	+	1.02307i
$324$	24.8853	+	51.7836i	1.38252	+	2.87687i
$325$	5.59032	+	22.3049i	0.310095	+	1.23725i
$326$	0.929109	+	4.07841i	0.0514586	+	0.225882i
$327$	15.7628	+	15.7628i	0.871685	+	0.871685i
$328$	−3.27202	−	0.372751i	−0.180667	−	0.0205817i
$329$			1.48699i			0.0819802i
$330$	6.35808	+	0.292191i	0.350001	+	0.0160846i
$331$		−	30.0986i		−	1.65437i	−0.561929	−	0.827185i	$-0.689941\pi$
$331$		−	30.0986i		−	1.65437i	0.561929	−	0.827185i	$-0.310059\pi$
$332$	3.90789	+	1.37103i	0.214474	+	0.0752453i
$333$	45.6731	+	45.6731i	2.50287	+	2.50287i
$334$	6.23137	−	1.41958i	0.340965	−	0.0776758i
$335$	0.145577	+	0.256939i	0.00795374	+	0.0140381i
$336$	−5.62421	+	7.02883i	−0.306826	+	0.383454i
$337$	11.6917	−	11.6917i	0.636888	−	0.636888i	−0.312898	−	0.949787i	$-0.601300\pi$
$337$	11.6917	−	11.6917i	0.636888	−	0.636888i	0.949787	+	0.312898i	$0.101300\pi$
$338$	−9.75715	−	6.13641i	−0.530719	−	0.333777i
$339$	−26.3430			−1.43075
$340$	−16.3982	−	11.3960i	−0.889316	−	0.618036i
$341$	−0.611810			−0.0331314
$342$	−54.5351	−	34.2979i	−2.94892	−	1.85462i
$343$	6.54576	−	6.54576i	0.353438	−	0.353438i
$344$	22.9003	−	18.2163i	1.23470	−	0.982156i
$345$	−16.0175	+	57.8951i	−0.862352	+	3.11697i
$346$	15.8111	−	3.60196i	0.850012	−	0.193643i
$347$	16.0495	+	16.0495i	0.861582	+	0.861582i	0.991522	−	0.129940i	$-0.0414784\pi$
$347$	16.0495	+	16.0495i	0.861582	+	0.861582i	−0.129940	+	0.991522i	$0.541478\pi$
$348$	4.09960	−	11.6852i	0.219761	−	0.626392i
$349$		−	3.30057i		−	0.176675i	−0.996091	−	0.0883376i	$-0.971845\pi$
$349$		−	3.30057i		−	0.176675i	0.996091	−	0.0883376i	$-0.0281554\pi$
$350$	−4.59797	−	1.50250i	−0.245772	−	0.0803119i
$351$		−	72.9652i		−	3.89459i
$352$	−3.26904	+	1.13636i	−0.174241	+	0.0605682i
$353$	−5.98766	−	5.98766i	−0.318691	−	0.318691i	0.529573	−	0.848264i	$-0.322352\pi$
$353$	−5.98766	−	5.98766i	−0.318691	−	0.318691i	−0.848264	+	0.529573i	$0.822352\pi$
$354$	−4.60359	−	20.2079i	−0.244678	−	1.07404i
$355$	−2.91166	+	10.5242i	−0.154535	+	0.558565i
$356$	30.6064	−	14.7083i	1.62214	−	0.779540i
$357$	7.10576	−	7.10576i	0.376077	−	0.376077i
$358$	−3.03974	+	4.83330i	−0.160655	+	0.255448i
$359$	29.2698			1.54480			0.772402	−	0.635134i	$-0.219055\pi$
$359$	29.2698			1.54480			0.772402	+	0.635134i	$0.219055\pi$
$360$	18.5048	−	45.8841i	0.975291	−	2.41830i
$361$	14.9118			0.784829
$362$	−5.58527	+	8.88081i	−0.293555	+	0.466765i
$363$	24.7178	−	24.7178i	1.29735	−	1.29735i
$364$	5.67130	−	2.72542i	0.297257	−	0.142851i
$365$	5.57374	+	9.83746i	0.291743	+	0.514916i
$366$	8.55792	+	37.5658i	0.447329	+	1.96359i
$367$	6.84449	+	6.84449i	0.357279	+	0.357279i	0.862809	−	0.505530i	$-0.168703\pi$
$367$	6.84449	+	6.84449i	0.357279	+	0.357279i	−0.505530	+	0.862809i	$0.668703\pi$
$368$	−3.60385	−	32.4642i	−0.187864	−	1.69231i
$369$			9.10808i			0.474148i
$370$	1.19868	−	26.0832i	0.0623163	−	1.35600i
$371$		−	5.92085i		−	0.307395i
$372$	−2.17819	+	6.20856i	−0.112934	+	0.321899i
$373$	−15.5005	−	15.5005i	−0.802586	−	0.802586i	0.180913	−	0.983499i	$-0.442095\pi$
$373$	−15.5005	−	15.5005i	−0.802586	−	0.802586i	−0.983499	+	0.180913i	$0.942095\pi$
$374$	3.76696	−	0.858156i	0.194785	−	0.0443742i
$375$	36.7700	+	0.895127i	1.89880	+	0.0462242i
$376$	3.82734	+	4.81148i	0.197380	+	0.248133i
$377$	−6.12053	+	6.12053i	−0.315223	+	0.315223i
$378$	12.9931	+	8.17156i	0.668294	+	0.420300i
$379$	24.6318			1.26525			0.632625	−	0.774458i	$-0.281977\pi$
$379$	24.6318			1.26525			0.632625	+	0.774458i	$0.281977\pi$
$380$	4.61288	+	25.6312i	0.236636	+	1.31485i
$381$	−50.7595			−2.60049
$382$	−5.14414	−	3.23522i	−0.263197	−	0.165528i
$383$	−1.55916	+	1.55916i	−0.0796696	+	0.0796696i	−0.745819	−	0.666149i	$-0.767941\pi$
$383$	−1.55916	+	1.55916i	−0.0796696	+	0.0796696i	0.666149	+	0.745819i	$0.267941\pi$
$384$	−0.106979	+	37.2195i	−0.00545927	+	1.89935i
$385$	0.814253	−	0.461342i	0.0414982	−	0.0235122i
$386$	2.15157	−	0.490153i	0.109512	−	0.0249481i
$387$	−57.2266	−	57.2266i	−2.90899	−	2.90899i
$388$	12.4733	+	4.37611i	0.633237	+	0.222163i
$389$			2.26974i			0.115080i	0.998343	+	0.0575401i	$0.0183257\pi$
$389$			2.26974i			0.115080i	−0.998343	+	0.0575401i	$0.981674\pi$
$390$	−35.3482	+	32.2420i	−1.78992	+	1.63264i
$391$			36.4629i			1.84401i
$392$	2.09120	−	18.3566i	0.105621	−	0.927149i
$393$	30.1513	+	30.1513i	1.52093	+	1.52093i
$394$	2.12128	+	9.31157i	0.106869	+	0.469110i
$395$	−12.0750	−	3.34072i	−0.607561	−	0.168090i
$396$	4.14605	+	8.62748i	0.208347	+	0.433547i
$397$	−2.42350	+	2.42350i	−0.121632	+	0.121632i	−0.765303	−	0.643671i	$-0.777411\pi$
$397$	−2.42350	+	2.42350i	−0.121632	+	0.121632i	0.643671	+	0.765303i	$0.277411\pi$
$398$	−7.35799	+	11.6995i	−0.368822	+	0.586443i
$399$	−13.1055			−0.656097
$400$	−18.7451	+	6.97300i	−0.937253	+	0.348650i
$401$	32.2602			1.61100			0.805498	−	0.592598i	$-0.201898\pi$
$401$	32.2602			1.61100			0.805498	+	0.592598i	$0.201898\pi$
$402$	−0.327117	+	0.520129i	−0.0163151	+	0.0259417i
$403$	3.25195	−	3.25195i	0.161991	−	0.161991i
$404$	4.86524	+	10.1240i	0.242055	+	0.503689i
$405$	−61.9085	−	17.1278i	−3.07626	−	0.851089i
$406$	−0.404446	−	1.77535i	−0.0200723	−	0.0881093i
$407$	3.57208	+	3.57208i	0.177061	+	0.177061i
$408$	4.70285	−	41.2818i	0.232826	−	2.04375i
$409$		−	3.76269i		−	0.186053i	−0.995664	−	0.0930265i	$-0.970346\pi$
$409$		−	3.76269i		−	0.186053i	0.995664	−	0.0930265i	$-0.0296541\pi$
$410$	2.72027	−	2.48123i	0.134344	−	0.122539i
$411$			22.0422i			1.08726i
$412$	−18.2506	−	6.40298i	−0.899141	−	0.315452i
$413$	−2.15488	−	2.15488i	−0.106034	−	0.106034i
$414$	−88.0823	+	20.0662i	−4.32901	+	0.986198i
$415$	−4.02856	+	2.28252i	−0.197754	+	0.112044i
$416$	11.3359	−	23.4160i	0.555786	−	1.14807i
$417$	−20.6765	+	20.6765i	−1.01253	+	1.01253i
$418$	−4.26517	−	2.68243i	−0.208616	−	0.131202i
$419$	−23.7514			−1.16033			−0.580166	−	0.814499i	$-0.697012\pi$
$419$	−23.7514			−1.16033			−0.580166	+	0.814499i	$0.697012\pi$
$420$	−1.78269	−	9.90542i	−0.0869865	−	0.483335i
$421$	−5.18656			−0.252777			−0.126389	−	0.991981i	$-0.540339\pi$
$421$	−5.18656			−0.252777			−0.126389	+	0.991981i	$0.540339\pi$
$422$	−12.8008	−	8.05061i	−0.623134	−	0.391898i
$423$	12.0236	−	12.0236i	0.584609	−	0.584609i
$424$	−15.2396	−	19.1583i	−0.740103	−	0.930408i
$425$	21.6564	−	5.42779i	1.05049	−	0.263287i
$426$	−22.1521	+	5.04650i	−1.07327	+	0.244504i
$427$	4.00584	+	4.00584i	0.193856	+	0.193856i
$428$	2.65461	−	7.56650i	0.128315	−	0.365740i
$429$		−	9.25642i		−	0.446904i
$430$	−1.50190	+	32.6813i	−0.0724279	+	1.57603i
$431$		−	14.9928i		−	0.722176i	−0.932532	−	0.361088i	$-0.882405\pi$
$431$		−	14.9928i		−	0.722176i	0.932532	−	0.361088i	$-0.117595\pi$
$432$	63.0750	−	7.00195i	3.03470	−	0.336881i
$433$	2.12930	+	2.12930i	0.102328	+	0.102328i	0.756417	−	0.654090i	$-0.226948\pi$
$433$	2.12930	+	2.12930i	0.102328	+	0.102328i	−0.654090	+	0.756417i	$0.726948\pi$
$434$	0.214890	+	0.943279i	0.0103150	+	0.0452788i
$435$	6.82506	+	12.0460i	0.327237	+	0.577562i
$436$	12.2150	−	5.87006i	0.584991	−	0.281125i
$437$	33.6252	−	33.6252i	1.60851	−	1.60851i
$438$	−12.5244	+	19.9143i	−0.598438	+	0.951541i
$439$	15.8994			0.758839			0.379419	−	0.925225i	$-0.376124\pi$
$439$	15.8994			0.758839			0.379419	+	0.925225i	$0.376124\pi$
$440$	1.44726	−	3.58858i	0.0689953	−	0.171079i
$441$	−51.0980			−2.43324
$442$	−15.4611	+	24.5839i	−0.735412	+	1.16933i
$443$	−7.03278	+	7.03278i	−0.334138	+	0.334138i	−0.854155	−	0.520018i	$-0.825925\pi$
$443$	−7.03278	+	7.03278i	−0.334138	+	0.334138i	0.520018	+	0.854155i	$0.325925\pi$
$444$	48.9664	−	23.5315i	2.32384	−	1.11675i
$445$	−10.1233	+	36.5907i	−0.479892	+	1.73457i
$446$	−8.08288	−	35.4806i	−0.382736	−	1.68005i
$447$	28.5486	+	28.5486i	1.35030	+	1.35030i
$448$	2.90023	+	4.64103i	0.137023	+	0.219268i
$449$		−	35.6653i		−	1.68315i	−0.540141	−	0.841575i	$-0.681629\pi$
$449$		−	35.6653i		−	1.68315i	0.540141	−	0.841575i	$-0.318371\pi$
$450$	25.0297	+	49.3278i	1.17991	+	2.32534i
$451$			0.712340i			0.0335428i
$452$	−5.30184	+	15.1120i	−0.249377	+	0.710807i
$453$	−5.98647	−	5.98647i	−0.281269	−	0.281269i
$454$	11.9606	−	2.72477i	0.561341	−	0.127880i
$455$	−1.87583	+	6.78017i	−0.0879402	+	0.317859i
$456$	−42.4060	+	33.7323i	−1.98584	+	1.57966i
$457$	22.4233	−	22.4233i	1.04892	−	1.04892i	0.0501755	−	0.998740i	$-0.484022\pi$
$457$	22.4233	−	22.4233i	1.04892	−	1.04892i	0.998740	−	0.0501755i	$-0.0159781\pi$
$458$	−19.1115	−	12.0195i	−0.893020	−	0.561633i
$459$	−70.8439			−3.30671
$460$	29.9885	+	20.8407i	1.39822	+	0.971702i
$461$	−0.384645			−0.0179147			−0.00895736	−	0.999960i	$-0.502851\pi$
$461$	−0.384645			−0.0179147			−0.00895736	+	0.999960i	$0.502851\pi$
$462$	1.64832	+	1.03665i	0.0766867	+	0.0482294i
$463$	21.8350	−	21.8350i	1.01476	−	1.01476i	0.0148674	−	0.999889i	$-0.495267\pi$
$463$	21.8350	−	21.8350i	1.01476	−	1.01476i	0.999889	−	0.0148674i	$-0.00473262\pi$
$464$	−5.87825	−	4.70356i	−0.272891	−	0.218357i
$465$	−3.62629	−	6.40027i	−0.168165	−	0.296806i
$466$	−25.2431	+	5.75068i	−1.16937	+	0.266395i
$467$	−16.9566	−	16.9566i	−0.784656	−	0.784656i	0.195956	−	0.980613i	$-0.437219\pi$
$467$	−16.9566	−	16.9566i	−0.784656	−	0.784656i	−0.980613	+	0.195956i	$0.937219\pi$
$468$	−67.8951	−	23.8201i	−3.13845	−	1.10109i
$469$			0.0903464i			0.00417181i
$470$	−6.86652	−	0.315557i	−0.316729	−	0.0145556i
$471$		−	39.8733i		−	1.83726i
$472$	−12.5190	−	1.42617i	−0.576234	−	0.0656449i
$473$	−4.47567	−	4.47567i	−0.205792	−	0.205792i
$474$	−5.79016	−	25.4164i	−0.265951	−	1.16742i
$475$	−24.9764	−	14.9657i	−1.14600	−	0.686672i
$476$	−2.64618	−	5.50642i	−0.121288	−	0.252386i
$477$	−47.8755	+	47.8755i	−2.19207	+	2.19207i
$478$	2.23200	−	3.54897i	0.102089	−	0.162326i
$479$	−5.48247			−0.250501			−0.125250	−	0.992125i	$-0.539973\pi$
$479$	−5.48247			−0.250501			−0.125250	+	0.992125i	$0.539973\pi$
$480$	−31.2638	−	27.4628i	−1.42699	−	1.25350i
$481$	−37.9733			−1.73143
$482$	18.0049	−	28.6285i	0.820100	−	1.30399i
$483$	−12.9948	+	12.9948i	−0.591283	+	0.591283i
$484$	−9.20490	−	19.1544i	−0.418405	−	0.870654i
$485$	−12.8585	+	7.28540i	−0.583874	+	0.330813i
$486$	−14.7346	−	64.6791i	−0.668377	−	2.93390i
$487$	14.7941	+	14.7941i	0.670385	+	0.670385i	0.957805	−	0.287420i	$-0.0927976\pi$
$487$	14.7941	+	14.7941i	0.670385	+	0.670385i	−0.287420	+	0.957805i	$0.592798\pi$
$488$	23.2724	+	2.65121i	1.05349	+	0.120015i
$489$		−	9.73040i		−	0.440024i
$490$	13.9201	+	15.2612i	0.628847	+	0.689430i
$491$		−	3.83185i		−	0.172929i	−0.996255	−	0.0864645i	$-0.972443\pi$
$491$		−	3.83185i		−	0.172929i	0.996255	−	0.0864645i	$-0.0275569\pi$
$492$	7.22873	+	2.53611i	0.325896	+	0.114337i
$493$	5.94259	+	5.94259i	0.267641	+	0.267641i
$494$	36.9286	−	8.41275i	1.66149	−	0.378508i
$495$	−10.3143	−	2.85361i	−0.463595	−	0.128260i
$496$	3.12323	+	2.49909i	0.140237	+	0.112213i
$497$	−2.36220	+	2.36220i	−0.105959	+	0.105959i
$498$	−8.15515	−	5.12889i	−0.365441	−	0.229831i
$499$	3.54089			0.158512			0.0792561	−	0.996854i	$-0.474746\pi$
$499$	3.54089			0.158512			0.0792561	+	0.996854i	$0.474746\pi$
$500$	7.91390	−	20.9134i	0.353920	−	0.935276i
$501$	−14.8670			−0.664208
$502$	−11.8658	−	7.46259i	−0.529598	−	0.333072i
$503$	−25.8928	+	25.8928i	−1.15450	+	1.15450i	−0.168865	+	0.985639i	$0.554010\pi$
$503$	−25.8928	+	25.8928i	−1.15450	+	1.15450i	−0.985639	+	0.168865i	$0.945990\pi$
$504$	11.8455	−	9.42260i	0.527639	−	0.419716i
$505$	−12.1035	−	3.34860i	−0.538599	−	0.149011i
$506$	−6.88889	+	1.56937i	−0.306249	+	0.0697670i
$507$	18.9597	+	18.9597i	0.842028	+	0.842028i
$508$	−10.2160	+	29.1188i	−0.453260	+	1.29194i
$509$		−	20.2711i		−	0.898503i	−0.893405	−	0.449251i	$-0.851691\pi$
$509$		−	20.2711i		−	0.898503i	0.893405	−	0.449251i	$-0.148309\pi$
$510$	31.3046	+	34.3205i	1.38619	+	1.51974i
$511$			3.45911i			0.153022i
$512$	21.3299	+	7.55224i	0.942656	+	0.333765i
$513$	65.3306	+	65.3306i	2.88442	+	2.88442i
$514$	4.46452	+	19.5974i	0.196922	+	0.864406i
$515$	18.8141	−	10.6598i	0.829050	−	0.469725i
$516$	−61.3530	+	29.4840i	−2.70092	+	1.29796i
$517$	0.940364	−	0.940364i	0.0413572	−	0.0413572i
$518$	4.25273	−	6.76202i	0.186854	−	0.297106i
$519$	−37.7227			−1.65584
$520$	11.3818	+	26.7670i	0.499123	+	1.17381i
$521$	−20.4136			−0.894335			−0.447168	−	0.894450i	$-0.647567\pi$
$521$	−20.4136			−0.894335			−0.447168	+	0.894450i	$0.647567\pi$
$522$	−11.0850	+	17.6257i	−0.485179	+	0.771454i
$523$	16.1058	−	16.1058i	0.704258	−	0.704258i	−0.261063	−	0.965322i	$-0.584073\pi$
$523$	16.1058	−	16.1058i	0.704258	−	0.704258i	0.965322	+	0.261063i	$0.0840731\pi$
$524$	23.3650	−	11.2283i	1.02070	−	0.490513i
$525$	9.65239	+	5.78363i	0.421265	+	0.252418i
$526$	−2.70069	−	11.8550i	−0.117756	−	0.516900i
$527$	−3.15741	−	3.15741i	−0.137539	−	0.137539i
$528$	8.00174	−	0.888273i	0.348231	−	0.0386571i
$529$		−	43.6821i		−	1.89922i
$530$	27.3410	+	1.25648i	1.18762	+	0.0545780i
$531$			34.8483i			1.51229i
$532$	−2.63764	+	7.51814i	−0.114356	+	0.325953i
$533$	−3.78630	−	3.78630i	−0.164003	−	0.164003i
$534$	−77.0189	+	17.5458i	−3.33293	+	0.759281i
$535$	4.41943	+	7.80014i	0.191068	+	0.337229i
$536$	0.232542	+	0.292337i	0.0100443	+	0.0126270i
$537$	9.39186	−	9.39186i	0.405289	−	0.405289i
$538$	6.83918	+	4.30126i	0.294858	+	0.185440i
$539$	−3.99636			−0.172135
$540$	−40.4915	+	58.2648i	−1.74248	+	2.50732i
$541$	25.3352			1.08924			0.544622	−	0.838682i	$-0.316673\pi$
$541$	25.3352			1.08924			0.544622	+	0.838682i	$0.316673\pi$
$542$	34.6033	+	21.7625i	1.48634	+	0.934780i
$543$	17.2568	−	17.2568i	0.740560	−	0.740560i
$544$	−22.7353	−	11.0063i	−0.974767	−	0.471891i
$545$	−4.04020	+	14.6033i	−0.173063	+	0.625535i
$546$	−14.2714	+	3.25119i	−0.610760	+	0.139138i
$547$	−25.8545	−	25.8545i	−1.10546	−	1.10546i	−0.993740	−	0.111721i	$-0.964364\pi$
$547$	−25.8545	−	25.8545i	−1.10546	−	1.10546i	−0.111721	−	0.993740i	$-0.535636\pi$
$548$	12.6448	+	4.43625i	0.540158	+	0.189507i
$549$		−	64.7817i		−	2.76482i
$550$	1.95756	+	3.85791i	0.0834708	+	0.164502i
$551$		−	10.9602i		−	0.466922i
$552$	−8.60042	+	75.4948i	−0.366058	+	3.21327i
$553$	−2.71029	−	2.71029i	−0.115253	−	0.115253i
$554$	5.92694	+	26.0168i	0.251811	+	1.10535i
$555$	−16.1960	+	58.5405i	−0.687484	+	2.48491i
$556$	7.69993	+	16.0227i	0.326550	+	0.679515i
$557$	−0.127023	+	0.127023i	−0.00538215	+	0.00538215i	−0.709793	−	0.704411i	$-0.751211\pi$
$557$	−0.127023	+	0.127023i	−0.00538215	+	0.00538215i	0.704411	+	0.709793i	$0.251211\pi$
$558$	5.88969	−	9.36485i	0.249330	−	0.396446i
$559$	47.5791			2.01238
$560$	−6.04115	−	0.970920i	−0.255285	−	0.0410289i
$561$	−8.98732			−0.379445
$562$	1.17481	−	1.86800i	0.0495566	−	0.0787970i
$563$	17.4490	−	17.4490i	0.735388	−	0.735388i	−0.236294	−	0.971682i	$-0.575933\pi$
$563$	17.4490	−	17.4490i	0.735388	−	0.735388i	0.971682	+	0.236294i	$0.0759327\pi$
$564$	−6.19476	−	12.8906i	−0.260846	−	0.542793i
$565$	−8.82657	−	15.5786i	−0.371337	−	0.655396i
$566$	7.54877	+	33.1360i	0.317299	+	1.39281i
$567$	−13.8956	−	13.8956i	−0.583561	−	0.583561i
$568$	−1.56339	+	13.7235i	−0.0655982	+	0.575824i
$569$		−	43.3422i		−	1.81700i	−0.417884	−	0.908501i	$-0.637228\pi$
$569$		−	43.3422i		−	1.81700i	0.417884	−	0.908501i	$-0.362772\pi$
$570$	2.78116	−	60.5180i	0.116490	−	2.53482i
$571$			31.1653i			1.30423i	0.758121	+	0.652114i	$0.226118\pi$
$571$			31.1653i			1.30423i	−0.758121	+	0.652114i	$0.773882\pi$
$572$	−5.31005	−	1.86296i	−0.222025	−	0.0778945i
$573$	9.99586	+	9.99586i	0.417583	+	0.417583i
$574$	1.09828	−	0.250200i	0.0458411	−	0.0104431i
$575$	−39.6046	+	9.92617i	−1.65163	+	0.413950i
$576$	14.0760	−	60.9780i	0.586499	−	2.54075i
$577$	−6.05746	+	6.05746i	−0.252175	+	0.252175i	−0.821862	−	0.569687i	$-0.807065\pi$
$577$	−6.05746	+	6.05746i	−0.252175	+	0.252175i	0.569687	+	0.821862i	$0.307065\pi$
$578$	3.51776	+	2.21237i	0.146320	+	0.0920225i
$579$	−5.13328			−0.213332
$580$	8.28396	−	1.49088i	0.343973	−	0.0619052i
$581$	−1.41655			−0.0587683
$582$	−26.0298	−	16.3705i	−1.07897	−	0.678581i
$583$	−3.74433	+	3.74433i	−0.155074	+	0.155074i
$584$	8.90338	+	11.1927i	0.368424	+	0.463159i
$585$	69.9916	−	39.6561i	2.89380	−	1.63958i
$586$	42.4708	−	9.67534i	1.75445	−	0.399685i
$587$	−19.1182	−	19.1182i	−0.789091	−	0.789091i	0.192254	−	0.981345i	$-0.438420\pi$
$587$	−19.1182	−	19.1182i	−0.789091	−	0.789091i	−0.981345	+	0.192254i	$0.938420\pi$
$588$	−14.2280	+	40.5545i	−0.586753	+	1.67244i
$589$			5.82338i			0.239948i
$590$	10.4080	−	9.49337i	0.428489	−	0.390836i
$591$		−	22.2158i		−	0.913836i
$592$	−3.64403	−	32.8261i	−0.149769	−	1.34915i
$593$	−24.5379	−	24.5379i	−1.00765	−	1.00765i	−0.999971	−	0.00767892i	$-0.997556\pi$
$593$	−24.5379	−	24.5379i	−1.00765	−	1.00765i	−0.00767892	−	0.999971i	$-0.502444\pi$
$594$	−3.04914	−	13.3845i	−0.125108	−	0.549172i
$595$	6.58305	+	1.82129i	0.269879	+	0.0746657i
$596$	22.1230	−	10.6315i	0.906192	−	0.435483i
$597$	22.7340	−	22.7340i	0.930439	−	0.930439i
$598$	28.2749	−	44.9582i	1.15624	−	1.83848i
$599$	−23.1146			−0.944437			−0.472218	−	0.881482i	$-0.656547\pi$
$599$	−23.1146			−0.944437			−0.472218	+	0.881482i	$0.656547\pi$
$600$	46.1190	−	6.12996i	1.88280	−	0.250255i
$601$	28.3137			1.15494			0.577469	−	0.816412i	$-0.304040\pi$
$601$	28.3137			1.15494			0.577469	+	0.816412i	$0.304040\pi$
$602$	−5.32851	+	8.47254i	−0.217174	+	0.345315i
$603$	0.730533	−	0.730533i	0.0297496	−	0.0297496i
$604$	−4.63906	+	2.22936i	−0.188761	+	0.0907114i
$605$	22.8995	+	6.33547i	0.930998	+	0.257573i
$606$	−5.80381	−	25.4764i	−0.235764	−	1.03491i
$607$	10.1476	+	10.1476i	0.411878	+	0.411878i	0.882392	−	0.470514i	$-0.155932\pi$
$607$	10.1476	+	10.1476i	0.411878	+	0.411878i	−0.470514	+	0.882392i	$0.655932\pi$
$608$	10.8162	+	31.1157i	0.438655	+	1.26191i
$609$			4.23569i			0.171639i
$610$	−19.3480	+	17.6479i	−0.783379	+	0.714541i
$611$			9.99663i			0.404421i
$612$	−23.1276	+	65.9212i	−0.934878	+	2.66471i
$613$	−0.0298204	−	0.0298204i	−0.00120444	−	0.00120444i	0.706504	−	0.707709i	$-0.250271\pi$
$613$	−0.0298204	−	0.0298204i	−0.00120444	−	0.00120444i	−0.707709	+	0.706504i	$0.750271\pi$
$614$	−34.7332	+	7.91263i	−1.40172	+	0.319328i
$615$	−7.45194	+	4.22215i	−0.300491	+	0.170253i
$616$	0.926430	−	0.736938i	0.0373269	−	0.0296921i
$617$	−10.5401	+	10.5401i	−0.424329	+	0.424329i	−0.886691	−	0.462362i	$-0.847002\pi$
$617$	−10.5401	+	10.5401i	−0.424329	+	0.424329i	0.462362	+	0.886691i	$0.347002\pi$
$618$	38.0860	+	23.9529i	1.53204	+	0.963525i
$619$	47.0803			1.89232			0.946159	−	0.323701i	$-0.104927\pi$
$619$	47.0803			1.89232			0.946159	+	0.323701i	$0.104927\pi$
$620$	−4.40142	+	0.792131i	−0.176765	+	0.0318127i
$621$	129.557			5.19895
$622$	−7.39560	−	4.65120i	−0.296537	−	0.186496i
$623$	−8.21294	+	8.21294i	−0.329044	+	0.329044i
$624$	−37.8102	+	47.2531i	−1.51362	+	1.89164i
$625$	11.7909	+	22.0448i	0.471637	+	0.881793i
$626$	6.30344	−	1.43600i	0.251936	−	0.0573939i
$627$	8.28789	+	8.28789i	0.330987	+	0.330987i
$628$	−22.8738	−	8.02496i	−0.912762	−	0.320231i
$629$			36.8693i			1.47008i
$630$	−0.776875	+	16.9048i	−0.0309514	+	0.673503i
$631$		−	27.3050i		−	1.08700i	−0.839410	−	0.543498i	$-0.817099\pi$
$631$		−	27.3050i		−	1.08700i	0.839410	−	0.543498i	$-0.182901\pi$
$632$	−15.7458	−	1.79377i	−0.626333	−	0.0713522i
$633$	24.8740	+	24.8740i	0.988652	+	0.988652i
$634$	−8.07249	−	35.4350i	−0.320600	−	1.40730i
$635$	−17.0077	−	30.0180i	−0.674929	−	1.19123i
$636$	24.6662	+	51.3276i	0.978077	+	2.03527i
$637$	21.2418	−	21.2418i	0.841632	−	0.841632i
$638$	−0.866957	+	1.37850i	−0.0343232	+	0.0545752i
$639$	38.2010			1.51121
$640$	−22.0466	+	12.4076i	−0.871467	+	0.490455i
$641$	−8.08131			−0.319193			−0.159596	−	0.987182i	$-0.551019\pi$
$641$	−8.08131			−0.319193			−0.159596	+	0.987182i	$0.551019\pi$
$642$	−9.93060	+	15.7901i	−0.391929	+	0.623184i
$643$	0.269257	−	0.269257i	0.0106185	−	0.0106185i	−0.701778	−	0.712396i	$-0.747610\pi$
$643$	0.269257	−	0.269257i	0.0106185	−	0.0106185i	0.712396	+	0.701778i	$0.247610\pi$
$644$	4.83926	+	10.0700i	0.190693	+	0.396812i
$645$	20.2930	−	73.3489i	0.799036	−	2.88811i
$646$	−8.16817	−	35.8550i	−0.321372	−	1.41069i
$647$	10.5537	+	10.5537i	0.414907	+	0.414907i	0.883444	−	0.468537i	$-0.155219\pi$
$647$	10.5537	+	10.5537i	0.414907	+	0.414907i	−0.468537	+	0.883444i	$0.655219\pi$
$648$	−80.7283	−	9.19662i	−3.17131	−	0.361277i
$649$			2.72547i			0.106984i
$650$	−30.9110	−	10.1009i	−1.21243	−	0.396191i
$651$		−	2.25050i		−	0.0882042i
$652$	−5.58196	−	1.95836i	−0.218606	−	0.0766952i
$653$	22.2631	+	22.2631i	0.871221	+	0.871221i	0.992606	−	0.121385i	$-0.0387334\pi$
$653$	22.2631	+	22.2631i	0.871221	+	0.871221i	−0.121385	+	0.992606i	$0.538733\pi$
$654$	−30.7381	+	7.00249i	−1.20195	+	0.273819i
$655$	−7.72815	+	27.9334i	−0.301964	+	1.09145i
$656$	2.90973	−	3.63642i	0.113606	−	0.141978i
$657$	27.9700	−	27.9700i	1.09122	−	1.09122i
$658$	−1.78013	−	1.11955i	−0.0693967	−	0.0436446i
$659$	−9.75764			−0.380104			−0.190052	−	0.981774i	$-0.560866\pi$
$659$	−9.75764			−0.380104			−0.190052	+	0.981774i	$0.560866\pi$
$660$	−5.13678	+	7.39152i	−0.199949	+	0.287714i
$661$	−28.0256			−1.09007			−0.545034	−	0.838414i	$-0.683483\pi$
$661$	−28.0256			−1.09007			−0.545034	+	0.838414i	$0.683483\pi$
$662$	36.0323	+	22.6612i	1.40043	+	0.880753i
$663$	47.7703	−	47.7703i	1.85524	−	1.85524i
$664$	−4.58357	+	3.64605i	−0.177877	+	0.141494i
$665$	−4.39118	−	7.75029i	−0.170283	−	0.300543i
$666$	−89.0643	+	20.2899i	−3.45117	+	0.786217i
$667$	−10.8676	−	10.8676i	−0.420796	−	0.420796i
$668$	−2.99216	+	8.52862i	−0.115770	+	0.329982i
$669$			84.6506i			3.27278i
$670$	−0.417197	−	0.0191726i	−0.0161177	−	0.000740704i
$671$		−	5.06656i		−	0.195592i
$672$	−4.18003	−	12.0250i	−0.161248	−	0.463873i
$673$	−31.0977	−	31.0977i	−1.19873	−	1.19873i	−0.974547	−	0.224183i	$-0.928029\pi$
$673$	−31.0977	−	31.0977i	−1.19873	−	1.19873i	−0.224183	−	0.974547i	$-0.571971\pi$
$674$	5.19394	+	22.7993i	0.200063	+	0.878196i
$675$	−19.2856	−	76.9480i	−0.742304	−	2.96173i
$676$	14.6923	−	7.06057i	0.565088	−	0.271561i
$677$	−5.38942	+	5.38942i	−0.207132	+	0.207132i	−0.803047	−	0.595915i	$-0.796789\pi$
$677$	−5.38942	+	5.38942i	−0.207132	+	0.207132i	0.595915	+	0.803047i	$0.296789\pi$
$678$	19.8336	−	31.5362i	0.761705	−	1.21114i
$679$	−4.52138			−0.173515
$680$	25.9888	−	11.0509i	0.996625	−	0.423781i
$681$	−28.5361			−1.09350
$682$	0.460631	−	0.732422i	0.0176385	−	0.0280459i
$683$	−29.3998	+	29.3998i	−1.12495	+	1.12495i	−0.133968	+	0.990986i	$0.542772\pi$
$683$	−29.3998	+	29.3998i	−1.12495	+	1.12495i	−0.990986	+	0.133968i	$0.957228\pi$
$684$	82.1188	−	39.4633i	3.13989	−	1.50892i
$685$	−13.0352	+	7.38553i	−0.498050	+	0.282187i
$686$	2.90789	+	12.7645i	0.111024	+	0.487350i
$687$	37.1366	+	37.1366i	1.41685	+	1.41685i
$688$	4.56582	+	41.1299i	0.174070	+	1.56806i
$689$		−	39.8044i		−	1.51643i
$690$	−57.2490	−	62.7643i	−2.17943	−	2.38940i
$691$			45.9853i			1.74936i	0.484697	+	0.874682i	$0.338930\pi$
$691$			45.9853i			1.74936i	−0.484697	+	0.874682i	$0.661070\pi$
$692$	−7.59213	+	21.6401i	−0.288610	+	0.822631i
$693$	−2.31510	−	2.31510i	−0.0879433	−	0.0879433i
$694$	−31.2971	+	7.12985i	−1.18802	+	0.270645i
$695$	−19.1555	−	5.29964i	−0.726611	−	0.201027i
$696$	10.9022	+	13.7055i	0.413247	+	0.519507i
$697$	−3.67622	+	3.67622i	−0.139247	+	0.139247i
$698$	3.95124	+	2.48499i	0.149557	+	0.0940583i
$699$	60.2258			2.27795
$700$	5.26051	−	4.37318i	0.198828	−	0.165291i
$701$	−42.5404			−1.60673			−0.803364	−	0.595488i	$-0.796959\pi$
$701$	−42.5404			−1.60673			−0.803364	+	0.595488i	$0.796959\pi$
$702$	87.3495	+	54.9354i	3.29680	+	2.07340i
$703$	34.0001	−	34.0001i	1.28234	−	1.28234i
$704$	1.10088	−	4.76907i	0.0414909	−	0.179741i
$705$	15.4110	+	4.26367i	0.580413	+	0.160579i
$706$	11.6762	−	2.65997i	0.439439	−	0.100109i
$707$	−2.71668	−	2.71668i	−0.102171	−	0.102171i
$708$	27.6577	+	9.70335i	1.03944	+	0.364674i
$709$			24.0334i			0.902593i	0.892374	+	0.451296i	$0.149038\pi$
$709$			24.0334i			0.902593i	−0.892374	+	0.451296i	$0.850962\pi$
$710$	−10.4067	−	11.4093i	−0.390557	−	0.428183i
$711$			43.8303i			1.64377i
$712$	−5.43562	+	47.7141i	−0.203708	+	1.78816i
$713$	5.77417	+	5.77417i	0.216244	+	0.216244i
$714$	3.15667	+	13.8565i	0.118135	+	0.518567i
$715$	5.47402	−	3.10149i	0.204717	−	0.115989i
$716$	−3.49753	−	7.27798i	−0.130709	−	0.271991i
$717$	−6.89620	+	6.89620i	−0.257543	+	0.257543i
$718$	−22.0372	+	35.0401i	−0.822422	+	1.30768i
$719$	42.9756			1.60272			0.801360	−	0.598183i	$-0.204110\pi$
$719$	42.9756			1.60272			0.801360	+	0.598183i	$0.204110\pi$
$720$	40.9974	+	56.6989i	1.52788	+	2.11304i
$721$	6.61554			0.246376
$722$	−11.2270	+	17.8515i	−0.417827	+	0.664362i
$723$	−55.6297	+	55.6297i	−2.06889	+	2.06889i
$724$	−6.42643	−	13.3727i	−0.238836	−	0.496993i
$725$	−4.83688	+	8.07235i	−0.179637	+	0.299800i
$726$	10.9807	+	48.2006i	0.407531	+	1.78889i
$727$	−32.3424	−	32.3424i	−1.19951	−	1.19951i	−0.974312	−	0.225202i	$-0.927696\pi$
$727$	−32.3424	−	32.3424i	−1.19951	−	1.19951i	−0.225202	−	0.974312i	$-0.572304\pi$
$728$	−1.00721	+	8.84130i	−0.0373295	+	0.327680i
$729$			68.1341i			2.52349i
$730$	−15.9733	−	0.734066i	−0.591197	−	0.0271690i
$731$		−	46.1958i		−	1.70861i
$732$	−51.4147	−	18.0382i	−1.90034	−	0.666711i
$733$	−25.7092	−	25.7092i	−0.949590	−	0.949590i	0.0491985	−	0.998789i	$-0.484333\pi$
$733$	−25.7092	−	25.7092i	−0.949590	−	0.949590i	−0.998789	+	0.0491985i	$0.984333\pi$
$734$	−13.3470	+	3.04060i	−0.492647	+	0.112231i
$735$	−23.6870	−	41.8067i	−0.873708	−	1.54206i
$736$	41.5776	+	20.1280i	1.53257	+	0.741926i
$737$	0.0571348	−	0.0571348i	0.00210459	−	0.00210459i
$738$	−10.9037	−	6.85746i	−0.401369	−	0.252427i
$739$	6.20498			0.228254			0.114127	−	0.993466i	$-0.463593\pi$
$739$	6.20498			0.228254			0.114127	+	0.993466i	$0.463593\pi$
$740$	30.3228	+	21.0730i	1.11469	+	0.774659i
$741$	−88.1053			−3.23663
$742$	7.08809	+	4.45780i	0.260212	+	0.163651i
$743$	30.8065	−	30.8065i	1.13018	−	1.13018i	0.140034	−	0.990147i	$-0.455279\pi$
$743$	30.8065	−	30.8065i	1.13018	−	1.13018i	0.990147	−	0.140034i	$-0.0447212\pi$
$744$	−5.79256	−	7.28202i	−0.212365	−	0.266972i
$745$	−7.31735	+	26.4485i	−0.268087	+	0.968999i
$746$	30.2266	−	6.88596i	1.10667	−	0.252113i
$747$	11.4541	+	11.4541i	0.419083	+	0.419083i
$748$	−1.80880	+	5.15568i	−0.0661364	+	0.188510i
$749$			2.74273i			0.100217i
$750$	−28.7557	+	43.3449i	−1.05001	+	1.58273i
$751$			2.69103i			0.0981972i	0.998794	+	0.0490986i	$0.0156349\pi$
$751$			2.69103i			0.0981972i	−0.998794	+	0.0490986i	$0.984365\pi$
$752$	−8.64162	+	0.959306i	−0.315127	+	0.0349823i
$753$	23.0572	+	23.0572i	0.840249	+	0.840249i
$754$	−2.71899	−	11.9353i	−0.0990198	−	0.434657i
$755$	1.53441	−	5.54610i	0.0558428	−	0.201843i
$756$	−19.5650	+	9.40223i	−0.711573	+	0.341956i
$757$	−7.83670	+	7.83670i	−0.284830	+	0.284830i	−0.835032	−	0.550202i	$-0.814551\pi$
$757$	−7.83670	+	7.83670i	−0.284830	+	0.284830i	0.550202	+	0.835032i	$0.314551\pi$
$758$	−18.5452	+	29.4877i	−0.673593	+	1.07104i
$759$	16.4357			0.596579
$760$	−34.1571	−	13.7754i	−1.23901	−	0.499686i
$761$	−15.4454			−0.559894			−0.279947	−	0.960015i	$-0.590317\pi$
$761$	−15.4454			−0.559894			−0.279947	+	0.960015i	$0.590317\pi$
$762$	38.2168	−	60.7663i	1.38445	−	2.20133i
$763$	−3.27777	+	3.27777i	−0.118663	+	0.118663i
$764$	7.74603	−	3.72246i	0.280241	−	0.134674i
$765$	−38.5032	−	67.9568i	−1.39208	−	2.45698i
$766$	−0.692645	−	3.04043i	−0.0250263	−	0.109855i
$767$	−14.4867	−	14.4867i	−0.523084	−	0.523084i
$768$	−44.4764	−	28.1506i	−1.60490	−	1.01580i
$769$			4.01035i			0.144617i	0.997382	+	0.0723084i	$0.0230366\pi$
$769$			4.01035i			0.144617i	−0.997382	+	0.0723084i	$0.976963\pi$
$770$	−0.0607591	+	1.32212i	−0.00218961	+	0.0476458i
$771$		−	46.7561i		−	1.68388i
$772$	−1.03313	+	2.94477i	−0.0371833	+	0.105984i
$773$	−5.08140	−	5.08140i	−0.182765	−	0.182765i	0.609794	−	0.792560i	$-0.291252\pi$
$773$	−5.08140	−	5.08140i	−0.182765	−	0.182765i	−0.792560	+	0.609794i	$0.791252\pi$
$774$	111.594	−	25.4224i	4.01117	−	0.913790i
$775$	2.56993	−	4.28899i	0.0923146	−	0.154065i
$776$	−14.6300	+	11.6375i	−0.525185	+	0.417764i
$777$	−13.1397	+	13.1397i	−0.471383	+	0.471383i
$778$	−2.71719	−	1.70888i	−0.0974161	−	0.0612664i
$779$	6.78026			0.242928
$780$	−11.9846	−	66.5917i	−0.429117	−	2.38436i
$781$	2.98769			0.106908
$782$	−43.6511	−	27.4528i	−1.56096	−	0.981711i
$783$	21.1148	−	21.1148i	0.754580	−	0.754580i
$784$	20.4010	+	16.3241i	0.728607	+	0.583005i
$785$	23.5801	−	13.3601i	0.841609	−	0.476841i
$786$	−58.7963	+	13.3945i	−2.09719	+	0.477765i
$787$	3.04645	+	3.04645i	0.108594	+	0.108594i	0.759316	−	0.650722i	$-0.225534\pi$
$787$	3.04645	+	3.04645i	0.108594	+	0.108594i	−0.650722	+	0.759316i	$0.725534\pi$
$788$	−12.7444	−	4.47119i	−0.453999	−	0.159280i
$789$			28.2839i			1.00693i
$790$	13.0906	−	11.9403i	0.465742	−	0.424816i
$791$		−	5.47784i		−	0.194770i
$792$	−13.4499	−	1.53221i	−0.477920	−	0.0544449i
$793$	26.9303	+	26.9303i	0.956322	+	0.956322i
$794$	−1.07662	−	4.72591i	−0.0382077	−	0.167716i
$795$	−61.3634	−	16.9770i	−2.17633	−	0.602113i
$796$	−8.46612	−	17.6171i	−0.300074	−	0.624421i
$797$	−11.0518	+	11.0518i	−0.391476	+	0.391476i	−0.875213	−	0.483737i	$-0.839279\pi$
$797$	−11.0518	+	11.0518i	−0.391476	+	0.391476i	0.483737	+	0.875213i	$0.339279\pi$
$798$	9.86714	−	15.6892i	0.349293	−	0.555390i
$799$	9.70601			0.343374
$800$	5.76547	−	27.6904i	0.203840	−	0.979004i
$801$	132.818			4.69290
$802$	−24.2887	+	38.6200i	−0.857662	+	1.36372i
$803$	2.18753	−	2.18753i	0.0771962	−	0.0771962i
$804$	−0.376382	−	0.783209i	−0.0132740	−	0.0276217i
$805$	−12.0389	−	3.33072i	−0.424315	−	0.117393i
$806$	1.44465	+	6.34143i	0.0508857	+	0.223367i
$807$	−13.2896	−	13.2896i	−0.467816	−	0.467816i
$808$	−15.7829	−	1.79800i	−0.555241	−	0.0632534i
$809$			2.12723i			0.0747896i	0.999301	+	0.0373948i	$0.0119059\pi$
$809$			2.12723i			0.0747896i	−0.999301	+	0.0373948i	$0.988094\pi$
$810$	67.1152	−	61.2176i	2.35819	−	2.15097i
$811$		−	0.160251i		−	0.00562717i	−0.999996	−	0.00281359i	$-0.999104\pi$
$811$		−	0.160251i		−	0.00562717i	0.999996	−	0.00281359i	$-0.000895594\pi$
$812$	2.42985	+	0.852483i	0.0852711	+	0.0299163i
$813$	−67.2396	−	67.2396i	−2.35820	−	2.35820i
$814$	−6.96569	+	1.58686i	−0.244147	+	0.0556196i
$815$	5.75432	−	3.26030i	0.201565	−	0.114203i
$816$	45.8793	+	36.7110i	1.60610	+	1.28514i
$817$	−42.6007	+	42.6007i	−1.49041	+	1.49041i
$818$	4.50447	+	2.83292i	0.157495	+	0.0990508i
$819$	24.6109			0.859974
$820$	0.922291	+	5.12465i	0.0322078	+	0.178961i
$821$	−12.7604			−0.445342			−0.222671	−	0.974894i	$-0.571477\pi$
$821$	−12.7604			−0.445342			−0.222671	+	0.974894i	$0.571477\pi$
$822$	−26.3876	−	16.5955i	−0.920373	−	0.578836i
$823$	−30.4438	+	30.4438i	−1.06120	+	1.06120i	−0.0632023	+	0.998001i	$0.520131\pi$
$823$	−30.4438	+	30.4438i	−1.06120	+	1.06120i	−0.998001	+	0.0632023i	$0.979869\pi$
$824$	21.4061	−	17.0277i	0.745717	−	0.593188i
$825$	−2.44659	−	9.76169i	−0.0851793	−	0.339858i
$826$	4.20209	−	0.957284i	0.146209	−	0.0333082i
$827$	32.1973	+	32.1973i	1.11961	+	1.11961i	0.991799	+	0.127810i	$0.0407948\pi$
$827$	32.1973	+	32.1973i	1.11961	+	1.11961i	0.127810	+	0.991799i	$0.459205\pi$
$828$	42.2951	−	120.555i	1.46985	−	4.18956i
$829$			1.34701i			0.0467836i	0.999726	+	0.0233918i	$0.00744652\pi$
$829$			1.34701i			0.0467836i	−0.999726	+	0.0233918i	$0.992553\pi$
$830$	0.300609	−	6.54126i	0.0104343	−	0.227050i
$831$		−	62.0718i		−	2.15325i
$832$	19.4975	+	31.2005i	0.675955	+	1.08168i
$833$	−20.6243	−	20.6243i	−0.714589	−	0.714589i
$834$	−9.18536	−	40.3200i	−0.318063	−	1.39617i
$835$	−4.98138	−	8.79197i	−0.172388	−	0.304259i
$836$	6.42248	−	3.08641i	0.222126	−	0.106746i
$837$	−11.2187	+	11.2187i	−0.387774	+	0.387774i
$838$	17.8824	−	28.4337i	0.617737	−	0.982227i
$839$	−39.0608			−1.34853			−0.674265	−	0.738490i	$-0.735539\pi$
$839$	−39.0608			−1.34853			−0.674265	+	0.738490i	$0.735539\pi$
$840$	13.2004	+	5.32364i	0.455456	+	0.183683i
$841$	25.4577			0.877851
$842$	3.90495	−	6.20904i	0.134574	−	0.213978i
$843$	−3.62982	+	3.62982i	−0.125018	+	0.125018i
$844$	19.2754	−	9.26306i	0.663487	−	0.318848i
$845$	−4.85959	+	17.5650i	−0.167175	+	0.604253i
$846$	5.34139	+	23.4465i	0.183641	+	0.806109i
$847$	5.13989	+	5.13989i	0.176609	+	0.176609i
$848$	34.4090	−	3.81975i	1.18161	−	0.131171i
$849$		−	79.0569i		−	2.71323i
$850$	−9.80727	+	30.0123i	−0.336387	+	1.02942i
$851$		−	67.4255i		−	2.31132i
$852$	10.6369	−	30.3186i	0.364414	−	1.03870i
$853$	10.4050	+	10.4050i	0.356260	+	0.356260i	0.862432	−	0.506172i	$-0.168940\pi$
$853$	10.4050	+	10.4050i	0.356260	+	0.356260i	−0.506172	+	0.862432i	$0.668940\pi$
$854$	−7.81154	+	1.77956i	−0.267305	+	0.0608953i
$855$	−27.1614	+	98.1749i	−0.928902	+	3.35751i
$856$	7.05950	+	8.87474i	0.241289	+	0.303332i
$857$	31.2295	−	31.2295i	1.06678	−	1.06678i	0.0691744	−	0.997605i	$-0.477963\pi$
$857$	31.2295	−	31.2295i	1.06678	−	1.06678i	0.997605	−	0.0691744i	$-0.0220365\pi$
$858$	11.0812	+	6.96915i	0.378307	+	0.237923i
$859$	−21.2826			−0.726151			−0.363076	−	0.931760i	$-0.618273\pi$
$859$	−21.2826			−0.726151			−0.363076	+	0.931760i	$0.618273\pi$
$860$	−37.9933	−	26.4037i	−1.29556	−	0.900357i
$861$	−2.62030			−0.0892995
$862$	17.9484	+	11.2880i	0.611326	+	0.384472i
$863$	10.1839	−	10.1839i	0.346664	−	0.346664i	−0.512202	−	0.858865i	$-0.671170\pi$
$863$	10.1839	−	10.1839i	0.346664	−	0.346664i	0.858865	+	0.512202i	$0.171170\pi$
$864$	−39.1067	+	80.7813i	−1.33044	+	2.74824i
$865$	−12.6395	−	22.3083i	−0.429755	−	0.758504i
$866$	−4.15221	+	0.945922i	−0.141098	+	0.0321437i
$867$	−6.83556	−	6.83556i	−0.232148	−	0.232148i
$868$	−1.29103	−	0.452940i	−0.0438203	−	0.0153738i
$869$			3.42796i			0.116285i
$870$	−19.5593	−	0.898866i	−0.663123	−	0.0304744i
$871$			0.607377i			0.0205802i
$872$	−2.16934	+	19.0426i	−0.0734632	+	0.644863i
$873$	36.5595	+	36.5595i	1.23735	+	1.23735i
$874$	14.9377	+	65.5704i	0.505275	+	2.21795i
$875$	−0.186136	+	7.64607i	−0.00629253	+	0.258484i
$876$	−14.4106	−	29.9869i	−0.486889	−	1.01316i
$877$	9.79862	−	9.79862i	0.330876	−	0.330876i	−0.522043	−	0.852919i	$-0.674830\pi$
$877$	9.79862	−	9.79862i	0.330876	−	0.330876i	0.852919	+	0.522043i	$0.174830\pi$
$878$	−11.9707	+	19.0339i	−0.403990	+	0.642361i
$879$	−101.328			−3.41771
$880$	3.20639	+	4.43441i	0.108087	+	0.149484i
$881$	−37.1204			−1.25062			−0.625309	−	0.780377i	$-0.715027\pi$
$881$	−37.1204			−1.25062			−0.625309	+	0.780377i	$0.715027\pi$
$882$	38.4716	−	61.1714i	1.29541	−	2.05975i
$883$	13.7690	−	13.7690i	0.463364	−	0.463364i	−0.436392	−	0.899757i	$-0.643744\pi$
$883$	13.7690	−	13.7690i	0.463364	−	0.463364i	0.899757	+	0.436392i	$0.143744\pi$
$884$	−17.7896	−	37.0183i	−0.598330	−	1.24506i
$885$	−28.5117	+	16.1543i	−0.958411	+	0.543020i
$886$	−3.12425	−	13.7142i	−0.104961	−	0.460737i
$887$	−11.8585	−	11.8585i	−0.398168	−	0.398168i	0.479419	−	0.877586i	$-0.340848\pi$
$887$	−11.8585	−	11.8585i	−0.398168	−	0.398168i	−0.877586	+	0.479419i	$0.840848\pi$
$888$	−8.69629	+	76.3365i	−0.291829	+	2.56168i
$889$		−	10.5551i		−	0.354007i
$890$	−36.1824	−	39.6681i	−1.21284	−	1.32968i
$891$			17.5751i			0.588787i
$892$	48.5608	+	17.0369i	1.62594	+	0.570439i
$893$	−8.95065	−	8.95065i	−0.299522	−	0.299522i
$894$	−55.6708	+	12.6825i	−1.86191	+	0.424165i
$895$	8.70099	+	2.40725i	0.290842	+	0.0804655i
$896$	−7.73954	−	0.0222456i	−0.258560	−	0.000743174i
$897$	−87.3608	+	87.3608i	−2.91689	+	2.91689i
$898$	42.6963	+	26.8523i	1.42480	+	0.896074i
$899$	1.88211			0.0627718
$900$	−77.8971	−	7.17482i	−2.59657	−	0.239161i
$901$	−38.6472			−1.28753
$902$	−0.852771	−	0.536320i	−0.0283942	−	0.0178575i
$903$	16.4635	−	16.4635i	0.547870	−	0.547870i
$904$	−14.0994	−	17.7248i	−0.468938	−	0.589518i
$905$	15.9874	+	4.42313i	0.531438	+	0.147030i
$906$	11.6739	−	2.65944i	0.387838	−	0.0883539i
$907$	35.9185	+	35.9185i	1.19265	+	1.19265i	0.976319	+	0.216334i	$0.0694100\pi$
$907$	35.9185	+	35.9185i	1.19265	+	1.19265i	0.216334	+	0.976319i	$0.430590\pi$
$908$	−5.74322	+	16.3700i	−0.190595	+	0.543259i
$909$			43.9337i			1.45719i
$910$	−6.70450	−	7.35041i	−0.222252	−	0.243664i
$911$			37.5263i			1.24330i	0.783294	+	0.621651i	$0.213538\pi$
$911$			37.5263i			1.24330i	−0.783294	+	0.621651i	$0.786462\pi$
$912$	−8.45483	−	76.1628i	−0.279967	−	2.52200i
$913$	0.895820	+	0.895820i	0.0296473	+	0.0296473i
$914$	9.96134	+	43.7262i	0.329492	+	1.44633i
$915$	53.0023	−	30.0302i	1.75220	−	0.992769i
$916$	28.7780	−	13.8296i	0.950852	−	0.456944i
$917$	−6.26976	+	6.26976i	−0.207046	+	0.207046i
$918$	53.3383	−	84.8101i	1.76043	−	2.79915i
$919$	−16.1593			−0.533045			−0.266522	−	0.963829i	$-0.585875\pi$
$919$	−16.1593			−0.533045			−0.266522	+	0.963829i	$0.585875\pi$
$920$	−47.5275	+	20.2095i	−1.56693	+	0.666287i
$921$	82.8676			2.73058
$922$	0.289599	−	0.460474i	0.00953744	−	0.0151649i
$923$	−15.8805	+	15.8805i	−0.522711	+	0.522711i
$924$	−2.48203	+	1.19277i	−0.0816529	+	0.0392394i
$925$	−40.0461	+	10.0368i	−1.31671	+	0.330009i
$926$	9.69999	+	42.5790i	0.318761	+	1.39923i
$927$	−53.4927	−	53.4927i	−1.75693	−	1.75693i
$928$	10.0565	−	3.49578i	0.330122	−	0.114755i
$929$		−	22.1903i		−	0.728042i	−0.931391	−	0.364021i	$-0.881404\pi$
$929$		−	22.1903i		−	0.728042i	0.931391	−	0.364021i	$-0.118596\pi$
$930$	10.3922	+	0.477585i	0.340775	+	0.0156606i
$931$			38.0385i			1.24666i
$932$	12.1212	−	34.5492i	0.397042	−	1.13170i
$933$	14.3708	+	14.3708i	0.470479	+	0.470479i
$934$	33.0659	−	7.53280i	1.08195	−	0.246481i
$935$	−3.01132	−	5.31488i	−0.0984807	−	0.173815i
$936$	79.6341	−	63.3458i	2.60292	−	2.07052i
$937$	23.9342	−	23.9342i	0.781898	−	0.781898i	−0.198253	−	0.980151i	$-0.563527\pi$
$937$	23.9342	−	23.9342i	0.781898	−	0.781898i	0.980151	+	0.198253i	$0.0635268\pi$
$938$	−0.108157	−	0.0680217i	−0.00353146	−	0.00222099i
$939$	−15.0389			−0.490777
$940$	5.54756	−	7.98260i	0.180941	−	0.260364i
$941$	37.7635			1.23106			0.615528	−	0.788115i	$-0.288943\pi$
$941$	37.7635			1.23106			0.615528	+	0.788115i	$0.288943\pi$
$942$	47.7339	+	30.0205i	1.55525	+	0.978121i
$943$	6.72296	−	6.72296i	0.218930	−	0.218930i
$944$	11.1329	−	13.9132i	0.362344	−	0.452838i
$945$	6.47128	−	23.3904i	0.210511	−	0.760890i
$946$	8.72774	−	1.98828i	0.283763	−	0.0646445i
$947$	−21.6518	−	21.6518i	−0.703590	−	0.703590i	0.261590	−	0.965179i	$-0.415753\pi$
$947$	−21.6518	−	21.6518i	−0.703590	−	0.703590i	−0.965179	+	0.261590i	$0.915753\pi$
$948$	34.7864	+	12.2044i	1.12981	+	0.396379i
$949$			23.2547i			0.754880i
$950$	36.7207	−	18.6327i	1.19138	−	0.604523i
$951$			84.5418i			2.74145i
$952$	8.58426	+	0.977924i	0.278218	+	0.0316947i
$953$	3.23123	+	3.23123i	0.104670	+	0.104670i	0.757502	−	0.652833i	$-0.226419\pi$
$953$	3.23123	+	3.23123i	0.104670	+	0.104670i	−0.652833	+	0.757502i	$0.726419\pi$
$954$	−21.2683	−	93.3590i	−0.688585	−	3.02261i
$955$	−2.56206	+	9.26055i	−0.0829063	+	0.299664i
$956$	2.56814	+	5.34402i	0.0830596	+	0.172838i
$957$	2.67864	−	2.67864i	0.0865880	−	0.0865880i
$958$	4.12775	−	6.56329i	0.133361	−	0.212050i
$959$	−4.58352			−0.148010
$960$	56.4153	−	16.7504i	1.82079	−	0.540618i
$961$	−1.00000			−0.0322581
$962$	28.5901	−	45.4594i	0.921781	−	1.46567i
$963$	22.1775	−	22.1775i	0.714660	−	0.714660i
$964$	20.7165	+	43.1087i	0.667233	+	1.38844i
$965$	−1.71997	−	3.03570i	−0.0553679	−	0.0977225i
$966$	−5.77282	−	25.3403i	−0.185737	−	0.815312i
$967$	−0.111476	−	0.111476i	−0.00358482	−	0.00358482i	0.705312	−	0.708897i	$-0.250807\pi$
$967$	−0.111476	−	0.111476i	−0.00358482	−	0.00358482i	−0.708897	+	0.705312i	$0.750807\pi$
$968$	29.8608	+	3.40176i	0.959764	+	0.109337i
$969$			85.5438i			2.74806i
$970$	0.959493	−	20.8786i	0.0308075	−	0.670370i
$971$			14.8876i			0.477766i	0.971048	+	0.238883i	$0.0767813\pi$
$971$			14.8876i			0.477766i	−0.971048	+	0.238883i	$0.923219\pi$
$972$	88.5236	+	31.0574i	2.83940	+	0.996166i
$973$	−4.29954	−	4.29954i	−0.137837	−	0.137837i
$974$	−28.8491	+	6.57215i	−0.924383	+	0.210585i
$975$	64.8906	+	38.8819i	2.07816	+	1.24522i
$976$	−20.6956	+	25.8643i	−0.662451	+	0.827895i
$977$	7.60231	−	7.60231i	0.243220	−	0.243220i	−0.574961	−	0.818181i	$-0.694983\pi$
$977$	7.60231	−	7.60231i	0.243220	−	0.243220i	0.818181	+	0.574961i	$0.194983\pi$
$978$	11.6486	+	7.32600i	0.372483	+	0.234260i
$979$	10.3877			0.331991
$980$	−28.7502	+	5.17422i	−0.918392	+	0.165284i
$981$	53.0074			1.69240
$982$	4.58726	+	2.88500i	0.146385	+	0.0920639i
$983$	−3.81760	+	3.81760i	−0.121762	+	0.121762i	−0.765362	−	0.643600i	$-0.777440\pi$
$983$	−3.81760	+	3.81760i	−0.121762	+	0.121762i	0.643600	+	0.765362i	$0.277440\pi$
$984$	−8.47858	+	6.74437i	−0.270287	+	0.215003i
$985$	13.1379	−	7.44370i	0.418608	−	0.237176i
$986$	−11.5883	+	2.63994i	−0.369046	+	0.0840729i
$987$	3.45907	+	3.45907i	0.110103	+	0.110103i
$988$	−17.7322	+	50.5426i	−0.564137	+	1.60797i
$989$			84.4815i			2.68636i
$990$	11.1818	−	10.1992i	0.355382	−	0.324153i
$991$		−	48.7811i		−	1.54958i	−0.632218	−	0.774791i	$-0.717855\pi$
$991$		−	48.7811i		−	1.54958i	0.632218	−	0.774791i	$-0.282145\pi$
$992$	−5.34323	+	1.85737i	−0.169648	+	0.0589717i
$993$	−70.0163	−	70.0163i	−2.22190	−	2.22190i
$994$	−1.04938	−	4.60637i	−0.0332845	−	0.146105i
$995$	21.0616	+	5.82699i	0.667698	+	0.184728i
$996$	12.2800	−	5.90132i	0.389107	−	0.186990i
$997$	10.0739	−	10.0739i	0.319044	−	0.319044i	−0.529356	−	0.848400i	$-0.677566\pi$
$997$	10.0739	−	10.0739i	0.319044	−	0.319044i	0.848400	+	0.529356i	$0.177566\pi$
$998$	−2.66593	+	4.23895i	−0.0843887	+	0.134181i
$999$	131.001			4.14470

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	620.2.k.c.63.14	✓	88
4.3	odd	2		620.2.k.d.63.9	yes	88
5.2	odd	4		620.2.k.d.187.9	yes	88
20.7	even	4	inner	620.2.k.c.187.14	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
620.2.k.c.63.14	✓	88	1.1	even	1	trivial
620.2.k.c.187.14	yes	88	20.7	even	4	inner
620.2.k.d.63.9	yes	88	4.3	odd	2
620.2.k.d.187.9	yes	88	5.2	odd	4

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:	\( N \)	\(=\)	\( 620 = 2^{2} \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	620.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.752899 + 1.19714i) q^{2} +(2.32623 - 2.32623i) q^{3} +(-0.866287 - 1.80265i) q^{4} +(2.15511 + 0.596241i) q^{5} +(1.03341 + 4.53624i) q^{6} +(0.483723 + 0.483723i) q^{7} +(2.81025 + 0.320145i) q^{8} -7.82269i q^{9} +(-2.33636 + 2.13106i) q^{10} -0.611810i q^{11} +(-6.20856 - 2.17819i) q^{12} +(3.25195 + 3.25195i) q^{13} +(-0.943279 + 0.214890i) q^{14} +(6.40027 - 3.62629i) q^{15} +(-2.49909 + 3.12323i) q^{16} +(3.15741 - 3.15741i) q^{17} +(9.36485 + 5.88969i) q^{18} -5.82338 q^{19} +(-0.792131 - 4.40142i) q^{20} +2.25050 q^{21} +(0.732422 + 0.460631i) q^{22} +(-5.77417 + 5.77417i) q^{23} +(7.28202 - 5.79256i) q^{24} +(4.28899 + 2.56993i) q^{25} +(-6.34143 + 1.44465i) q^{26} +(-11.2187 - 11.2187i) q^{27} +(0.452940 - 1.29103i) q^{28} +1.88211i q^{29} +(-0.477585 + 10.3922i) q^{30} -1.00000i q^{31} +(-1.85737 - 5.34323i) q^{32} +(-1.42321 - 1.42321i) q^{33} +(1.40265 + 6.15707i) q^{34} +(0.754061 + 1.33089i) q^{35} +(-14.1016 + 6.77670i) q^{36} +(-5.83854 + 5.83854i) q^{37} +(4.38441 - 6.97140i) q^{38} +15.1296 q^{39} +(5.86551 + 2.36553i) q^{40} -1.16432 q^{41} +(-1.69440 + 2.69417i) q^{42} +(7.31547 - 7.31547i) q^{43} +(-1.10288 + 0.530003i) q^{44} +(4.66421 - 16.8587i) q^{45} +(-2.56512 - 11.2599i) q^{46} +(1.53702 + 1.53702i) q^{47} +(1.45188 + 13.0788i) q^{48} -6.53202i q^{49} +(-6.30574 + 3.19963i) q^{50} -14.6897i q^{51} +(3.04501 - 8.67926i) q^{52} +(-6.12008 - 6.12008i) q^{53} +(21.8769 - 4.98380i) q^{54} +(0.364786 - 1.31852i) q^{55} +(1.20452 + 1.51425i) q^{56} +(-13.5465 + 13.5465i) q^{57} +(-2.25315 - 1.41704i) q^{58} -4.45477 q^{59} +(-12.0814 - 8.39604i) q^{60} +8.28126 q^{61} +(1.19714 + 0.752899i) q^{62} +(3.78402 - 3.78402i) q^{63} +(7.79501 + 1.79938i) q^{64} +(5.06937 + 8.94726i) q^{65} +(2.77531 - 0.632249i) q^{66} +(0.0933865 + 0.0933865i) q^{67} +(-8.42693 - 2.95648i) q^{68} +26.8641i q^{69} +(-2.16100 - 0.0993105i) q^{70} +4.88336i q^{71} +(2.50440 - 21.9837i) q^{72} +(3.57550 + 3.57550i) q^{73} +(-2.59372 - 11.3854i) q^{74} +(15.9554 - 3.99894i) q^{75} +(5.04472 + 10.4975i) q^{76} +(0.295947 - 0.295947i) q^{77} +(-11.3910 + 18.1122i) q^{78} -5.60298 q^{79} +(-7.24801 + 5.24083i) q^{80} -28.7264 q^{81} +(0.876612 - 1.39385i) q^{82} +(-1.46421 + 1.46421i) q^{83} +(-1.94958 - 4.05687i) q^{84} +(8.68714 - 4.92199i) q^{85} +(3.24983 + 14.2654i) q^{86} +(4.37822 + 4.37822i) q^{87} +(0.195868 - 1.71934i) q^{88} +16.9786i q^{89} +(16.6706 + 18.2766i) q^{90} +3.14609i q^{91} +(15.4109 + 5.40672i) q^{92} +(-2.32623 - 2.32623i) q^{93} +(-2.99725 + 0.682808i) q^{94} +(-12.5500 - 3.47214i) q^{95} +(-16.7503 - 8.10891i) q^{96} +(-4.67352 + 4.67352i) q^{97} +(7.81975 + 4.91795i) q^{98} -4.78600 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 2 q^{2} - 2 q^{3} - 2 q^{5} - 4 q^{7} - 10 q^{8} - 10 q^{10} - 4 q^{12} - 6 q^{13} - 22 q^{14} + 2 q^{15} + 8 q^{16} - 2 q^{17} + 56 q^{18} - 8 q^{19} + 8 q^{20} - 16 q^{21} - 10 q^{23} + 44 q^{24}+ \cdots + 8 q^{99}+O(q^{100}) \) 88 * q + 2 * q^2 - 2 * q^3 - 2 * q^5 - 4 * q^7 - 10 * q^8 - 10 * q^10 - 4 * q^12 - 6 * q^13 - 22 * q^14 + 2 * q^15 + 8 * q^16 - 2 * q^17 + 56 * q^18 - 8 * q^19 + 8 * q^20 - 16 * q^21 - 10 * q^23 + 44 * q^24 - 4 * q^25 - 8 * q^26 - 8 * q^27 - 72 * q^28 - 8 * q^32 - 8 * q^33 - 40 * q^34 + 12 * q^35 - 20 * q^36 + 10 * q^37 + 30 * q^38 - 8 * q^39 + 8 * q^41 + 28 * q^42 - 10 * q^43 + 16 * q^44 + 6 * q^45 - 24 * q^46 + 64 * q^47 - 80 * q^48 - 14 * q^50 + 20 * q^52 + 18 * q^53 - 36 * q^54 - 40 * q^55 - 24 * q^56 - 24 * q^57 + 76 * q^58 - 8 * q^60 + 20 * q^61 - 2 * q^62 + 4 * q^63 + 150 * q^64 - 18 * q^65 + 8 * q^66 - 116 * q^67 - 48 * q^68 + 16 * q^70 + 4 * q^72 + 38 * q^73 - 36 * q^74 + 70 * q^75 - 8 * q^76 + 40 * q^77 + 128 * q^78 - 32 * q^79 - 12 * q^80 - 60 * q^81 - 28 * q^82 + 14 * q^83 + 120 * q^84 + 6 * q^85 + 4 * q^86 + 44 * q^87 - 68 * q^88 + 34 * q^90 + 56 * q^92 + 2 * q^93 - 112 * q^94 - 104 * q^95 - 20 * q^96 + 16 * q^97 + 52 * q^98 + 8 * q^99

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