LMFDB - Embedded newform 650.2.bd.a.47.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [650,2,Mod(47,650)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(650, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([17, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("650.47"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.bd (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [136] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$17$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			47.7
Character	$\chi$	$=$	650.47
Dual form			650.2.bd.a.83.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.951057 + 0.309017i) q^{2} +(-0.903505 + 0.143101i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.399063 - 2.20017i) q^{5} +(-0.903505 - 0.143101i) q^{6} -2.83760 q^{7} +(0.587785 + 0.809017i) q^{8} +(-2.05733 + 0.668466i) q^{9} +(1.05942 - 1.96917i) q^{10} +(-1.30398 - 2.55921i) q^{11} +(-0.815064 - 0.415296i) q^{12} +(2.98512 - 2.02215i) q^{13} +(-2.69872 - 0.876868i) q^{14} +(-0.0457083 + 2.04497i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.858770 - 5.42206i) q^{17} -2.16320 q^{18} +(0.705437 - 4.45396i) q^{19} +(1.61608 - 1.54541i) q^{20} +(2.56379 - 0.406064i) q^{21} +(-0.449322 - 2.83691i) q^{22} +(-1.72566 + 0.879268i) q^{23} +(-0.646838 - 0.646838i) q^{24} +(-4.68150 - 1.75601i) q^{25} +(3.46389 - 1.00072i) q^{26} +(4.20834 - 2.14426i) q^{27} +(-2.29567 - 1.66790i) q^{28} +(-2.09520 + 2.88380i) q^{29} +(-0.675402 + 1.93076i) q^{30} +(-7.90532 - 1.25208i) q^{31} +1.00000i q^{32} +(1.54438 + 2.12566i) q^{33} +(2.49225 - 4.89131i) q^{34} +(-1.13238 + 6.24321i) q^{35} +(-2.05733 - 0.668466i) q^{36} +(2.69068 + 8.28106i) q^{37} +(2.04726 - 4.01797i) q^{38} +(-2.40770 + 2.25419i) q^{39} +(2.01454 - 0.970379i) q^{40} +(4.89828 - 9.61342i) q^{41} +(2.56379 + 0.406064i) q^{42} +(-6.11638 - 6.11638i) q^{43} +(0.449322 - 2.83691i) q^{44} +(0.649736 + 4.79323i) q^{45} +(-1.91291 + 0.302975i) q^{46} +(5.32086 + 3.86583i) q^{47} +(-0.415296 - 0.815064i) q^{48} +1.05199 q^{49} +(-3.90973 - 3.11673i) q^{50} +5.02175i q^{51} +(3.60360 + 0.118658i) q^{52} +(7.67994 - 1.21638i) q^{53} +(4.66498 - 0.738860i) q^{54} +(-6.15107 + 1.84770i) q^{55} +(-1.66790 - 2.29567i) q^{56} +4.12512i q^{57} +(-2.88380 + 2.09520i) q^{58} +(-5.27006 + 10.3431i) q^{59} +(-1.23898 + 1.62755i) q^{60} +(2.33193 - 7.17695i) q^{61} +(-7.13150 - 3.63368i) q^{62} +(5.83787 - 1.89684i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-3.25782 - 7.37473i) q^{65} +(0.811929 + 2.49886i) q^{66} +(1.69387 + 2.33142i) q^{67} +(3.88177 - 3.88177i) q^{68} +(1.43332 - 1.04137i) q^{69} +(-3.00622 + 5.58772i) q^{70} +(-0.678988 - 4.28696i) q^{71} +(-1.75007 - 1.27150i) q^{72} +(10.4829 + 3.40609i) q^{73} +8.70722i q^{74} +(4.48104 + 0.916638i) q^{75} +(3.18868 - 3.18868i) q^{76} +(3.70018 + 7.26202i) q^{77} +(-2.98644 + 1.39985i) q^{78} +(-3.03466 + 4.17686i) q^{79} +(2.21580 - 0.300359i) q^{80} +(1.75479 - 1.27493i) q^{81} +(7.62925 - 7.62925i) q^{82} +(9.68080 - 7.03351i) q^{83} +(2.31283 + 1.17844i) q^{84} +(-11.5868 - 4.05318i) q^{85} +(-3.92696 - 7.70709i) q^{86} +(1.48035 - 2.90535i) q^{87} +(1.30398 - 2.55921i) q^{88} +(-6.42119 + 3.27176i) q^{89} +(-0.863253 + 4.75941i) q^{90} +(-8.47058 + 5.73805i) q^{91} +(-1.91291 - 0.302975i) q^{92} +7.32168 q^{93} +(3.86583 + 5.32086i) q^{94} +(-9.51795 - 3.32949i) q^{95} +(-0.143101 - 0.903505i) q^{96} +(-4.42953 + 6.09672i) q^{97} +(1.00050 + 0.325083i) q^{98} +(4.39346 + 4.39346i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q + 34 q^{4} + 20 q^{9} + 2 q^{13} - 14 q^{15} - 34 q^{16} - 4 q^{17} + 128 q^{18} - 20 q^{19} + 6 q^{21} - 12 q^{23} - 14 q^{26} + 36 q^{27} + 20 q^{29} - 12 q^{30} + 6 q^{31} + 30 q^{33} + 16 q^{34}+ \cdots + 40 q^{99}+O(q^{100}) $ 136 * q + 34 * q^4 + 20 * q^9 + 2 * q^13 - 14 * q^15 - 34 * q^16 - 4 * q^17 + 128 * q^18 - 20 * q^19 + 6 * q^21 - 12 * q^23 - 14 * q^26 + 36 * q^27 + 20 * q^29 - 12 * q^30 + 6 * q^31 + 30 * q^33 + 16 * q^34 - 52 * q^35 + 20 * q^36 - 6 * q^37 - 20 * q^39 - 42 * q^41 + 6 * q^42 + 12 * q^43 - 18 * q^45 + 12 * q^46 - 18 * q^47 + 120 * q^49 - 2 * q^52 - 50 * q^53 - 6 * q^54 + 24 * q^55 - 4 * q^58 - 16 * q^59 - 6 * q^60 - 12 * q^61 - 6 * q^62 - 100 * q^63 + 34 * q^64 - 56 * q^65 + 16 * q^66 + 4 * q^68 + 26 * q^69 + 34 * q^70 - 12 * q^71 + 22 * q^72 + 40 * q^73 - 192 * q^75 - 64 * q^77 - 84 * q^78 + 20 * q^79 - 54 * q^81 + 12 * q^82 + 74 * q^83 + 24 * q^84 - 12 * q^85 - 12 * q^86 + 8 * q^87 - 52 * q^89 - 44 * q^90 + 136 * q^91 + 12 * q^92 - 16 * q^93 - 50 * q^94 - 110 * q^95 - 40 * q^98 + 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.951057	+	0.309017i	0.672499	+	0.218508i
$2$	0.951057	+	0.309017i	0.672499	+	0.218508i
$3$	−0.903505	+	0.143101i	−0.521639	+	0.0826195i	−0.411701	−	0.911319i	$-0.635065\pi$
$3$	−0.903505	+	0.143101i	−0.521639	+	0.0826195i	−0.109938	+	0.993938i	$0.535065\pi$
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	0.399063	−	2.20017i	0.178466	−	0.983946i
$5$	0.399063	−	2.20017i	0.178466	−	0.983946i
$6$	−0.903505	−	0.143101i	−0.368854	−	0.0584208i
$7$	−2.83760			−1.07251			−0.536257	−	0.844055i	$-0.680162\pi$
$7$	−2.83760			−1.07251			−0.536257	+	0.844055i	$0.680162\pi$
$8$	0.587785	+	0.809017i	0.207813	+	0.286031i
$9$	−2.05733	+	0.668466i	−0.685775	+	0.222822i
$10$	1.05942	−	1.96917i	0.335018	−	0.622706i
$11$	−1.30398	−	2.55921i	−0.393165	−	0.771631i	0.606561	−	0.795037i	$-0.292549\pi$
$11$	−1.30398	−	2.55921i	−0.393165	−	0.771631i	−0.999726	+	0.0234066i	$0.992549\pi$
$12$	−0.815064	−	0.415296i	−0.235289	−	0.119886i
$13$	2.98512	−	2.02215i	0.827923	−	0.560842i
$13$	2.98512	−	2.02215i	0.827923	−	0.560842i
$14$	−2.69872	−	0.876868i	−0.721263	−	0.234353i
$15$	−0.0457083	+	2.04497i	−0.0118018	+	0.528009i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	0.858770	−	5.42206i	0.208282	−	1.31504i	−0.632875	−	0.774254i	$-0.718125\pi$
$17$	0.858770	−	5.42206i	0.208282	−	1.31504i	0.841158	−	0.540790i	$-0.181875\pi$
$18$	−2.16320			−0.509871
$19$	0.705437	−	4.45396i	0.161838	−	1.02181i	−0.764365	−	0.644784i	$-0.776947\pi$
$19$	0.705437	−	4.45396i	0.161838	−	1.02181i	0.926203	−	0.377024i	$-0.123053\pi$
$20$	1.61608	−	1.54541i	0.361366	−	0.345565i
$21$	2.56379	−	0.406064i	0.559465	−	0.0886105i
$22$	−0.449322	−	2.83691i	−0.0957957	−	0.604830i
$23$	−1.72566	+	0.879268i	−0.359825	+	0.183340i	−0.624552	−	0.780983i	$-0.714718\pi$
$23$	−1.72566	+	0.879268i	−0.359825	+	0.183340i	0.264727	+	0.964324i	$0.414718\pi$
$24$	−0.646838	−	0.646838i	−0.132035	−	0.132035i
$25$	−4.68150	−	1.75601i	−0.936300	−	0.351202i
$26$	3.46389	−	1.00072i	0.679325	−	0.196258i
$27$	4.20834	−	2.14426i	0.809895	−	0.412662i
$28$	−2.29567	−	1.66790i	−0.433841	−	0.315204i
$29$	−2.09520	+	2.88380i	−0.389069	+	0.535508i	−0.957959	−	0.286906i	$-0.907373\pi$
$29$	−2.09520	+	2.88380i	−0.389069	+	0.535508i	0.568890	+	0.822414i	$0.307373\pi$
$30$	−0.675402	+	1.93076i	−0.123311	+	0.352507i
$31$	−7.90532	−	1.25208i	−1.41984	−	0.224880i	−0.601158	−	0.799130i	$-0.705294\pi$
$31$	−7.90532	−	1.25208i	−1.41984	−	0.224880i	−0.818680	+	0.574250i	$0.805294\pi$
$32$			1.00000i			0.176777i
$33$	1.54438	+	2.12566i	0.268842	+	0.370029i
$34$	2.49225	−	4.89131i	0.427417	−	0.838853i
$35$	−1.13238	+	6.24321i	−0.191407	+	1.05530i
$36$	−2.05733	−	0.668466i	−0.342888	−	0.111411i
$37$	2.69068	+	8.28106i	0.442345	+	1.36140i	0.885369	+	0.464888i	$0.153905\pi$
$37$	2.69068	+	8.28106i	0.442345	+	1.36140i	−0.443024	+	0.896510i	$0.646095\pi$
$38$	2.04726	−	4.01797i	0.332109	−	0.651801i
$39$	−2.40770	+	2.25419i	−0.385540	+	0.360960i
$40$	2.01454	−	0.970379i	0.318526	−	0.153430i
$41$	4.89828	−	9.61342i	0.764983	−	1.50136i	−0.0974770	−	0.995238i	$-0.531077\pi$
$41$	4.89828	−	9.61342i	0.764983	−	1.50136i	0.862460	−	0.506126i	$-0.168923\pi$
$42$	2.56379	+	0.406064i	0.395601	+	0.0626571i
$43$	−6.11638	−	6.11638i	−0.932740	−	0.932740i	0.0651365	−	0.997876i	$-0.479252\pi$
$43$	−6.11638	−	6.11638i	−0.932740	−	0.932740i	−0.997876	+	0.0651365i	$0.979252\pi$
$44$	0.449322	−	2.83691i	0.0677378	−	0.427680i
$45$	0.649736	+	4.79323i	0.0968570	+	0.714532i
$46$	−1.91291	+	0.302975i	−0.282043	+	0.0446713i
$47$	5.32086	+	3.86583i	0.776127	+	0.563889i	0.903814	−	0.427926i	$-0.140755\pi$
$47$	5.32086	+	3.86583i	0.776127	+	0.563889i	−0.127687	+	0.991814i	$0.540755\pi$
$48$	−0.415296	−	0.815064i	−0.0599428	−	0.117644i
$49$	1.05199			0.150284
$50$	−3.90973	−	3.11673i	−0.552920	−	0.440772i
$51$			5.02175i			0.703186i
$52$	3.60360	+	0.118658i	0.499729	+	0.0164549i
$53$	7.67994	−	1.21638i	1.05492	−	0.167083i	0.395201	−	0.918595i	$-0.370675\pi$
$53$	7.67994	−	1.21638i	1.05492	−	0.167083i	0.659720	+	0.751512i	$0.270675\pi$
$54$	4.66498	−	0.738860i	0.634823	−	0.100546i
$55$	−6.15107	+	1.84770i	−0.829410	+	0.249144i
$56$	−1.66790	−	2.29567i	−0.222883	−	0.306772i
$57$			4.12512i			0.546386i
$58$	−2.88380	+	2.09520i	−0.378661	+	0.275113i
$59$	−5.27006	+	10.3431i	−0.686104	+	1.34655i	0.240549	+	0.970637i	$0.422672\pi$
$59$	−5.27006	+	10.3431i	−0.686104	+	1.34655i	−0.926653	+	0.375918i	$0.877328\pi$
$60$	−1.23898	+	1.62755i	−0.159952	+	0.210116i
$61$	2.33193	−	7.17695i	0.298573	−	0.918915i	−0.683424	−	0.730021i	$-0.739510\pi$
$61$	2.33193	−	7.17695i	0.298573	−	0.918915i	0.981998	−	0.188893i	$-0.0604900\pi$
$62$	−7.13150	−	3.63368i	−0.905701	−	0.461478i
$63$	5.83787	−	1.89684i	0.735503	−	0.238979i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	−3.25782	−	7.37473i	−0.404082	−	0.914723i
$66$	0.811929	+	2.49886i	0.0999415	+	0.307588i
$67$	1.69387	+	2.33142i	0.206939	+	0.284828i	0.899853	−	0.436193i	$-0.143673\pi$
$67$	1.69387	+	2.33142i	0.206939	+	0.284828i	−0.692914	+	0.721020i	$0.743673\pi$
$68$	3.88177	−	3.88177i	0.470734	−	0.470734i
$69$	1.43332	−	1.04137i	0.172551	−	0.125366i
$70$	−3.00622	+	5.58772i	−0.359312	+	0.667860i
$71$	−0.678988	−	4.28696i	−0.0805811	−	0.508769i	−0.994658	−	0.103228i	$-0.967083\pi$
$71$	−0.678988	−	4.28696i	−0.0805811	−	0.508769i	0.914077	−	0.405541i	$-0.132917\pi$
$72$	−1.75007	−	1.27150i	−0.206247	−	0.149847i
$73$	10.4829	+	3.40609i	1.22693	+	0.398652i	0.849600	−	0.527428i	$-0.176844\pi$
$73$	10.4829	+	3.40609i	1.22693	+	0.398652i	0.377326	+	0.926080i	$0.376844\pi$
$74$			8.70722i			1.01219i
$75$	4.48104	+	0.916638i	0.517426	+	0.105844i
$76$	3.18868	−	3.18868i	0.365767	−	0.365767i
$77$	3.70018	+	7.26202i	0.421675	+	0.827584i
$78$	−2.98644	+	1.39985i	−0.338148	+	0.158501i
$79$	−3.03466	+	4.17686i	−0.341426	+	0.469933i	−0.944857	−	0.327482i	$-0.893800\pi$
$79$	−3.03466	+	4.17686i	−0.341426	+	0.469933i	0.603431	+	0.797415i	$0.293800\pi$
$80$	2.21580	−	0.300359i	0.247734	−	0.0335811i
$81$	1.75479	−	1.27493i	0.194976	−	0.141659i
$82$	7.62925	−	7.62925i	0.842510	−	0.842510i
$83$	9.68080	−	7.03351i	1.06261	−	0.772028i	0.0880373	−	0.996117i	$-0.471941\pi$
$83$	9.68080	−	7.03351i	1.06261	−	0.772028i	0.974569	+	0.224089i	$0.0719405\pi$
$84$	2.31283	+	1.17844i	0.252350	+	0.128579i
$85$	−11.5868	−	4.05318i	−1.25676	−	0.439629i
$86$	−3.92696	−	7.70709i	−0.423455	−	0.831077i
$87$	1.48035	−	2.90535i	0.158710	−	0.311486i
$88$	1.30398	−	2.55921i	0.139005	−	0.272813i
$89$	−6.42119	+	3.27176i	−0.680644	+	0.346806i	−0.759892	−	0.650049i	$-0.774748\pi$
$89$	−6.42119	+	3.27176i	−0.680644	+	0.346806i	0.0792477	+	0.996855i	$0.474748\pi$
$90$	−0.863253	+	4.75941i	−0.0909948	+	0.501686i
$91$	−8.47058	+	5.73805i	−0.887958	+	0.601511i
$92$	−1.91291	−	0.302975i	−0.199435	−	0.0315873i
$93$	7.32168			0.759222
$94$	3.86583	+	5.32086i	0.398730	+	0.548804i
$95$	−9.51795	−	3.32949i	−0.976521	−	0.341599i
$96$	−0.143101	−	0.903505i	−0.0146052	−	0.0922136i
$97$	−4.42953	+	6.09672i	−0.449751	+	0.619029i	−0.972344	−	0.233554i	$-0.924965\pi$
$97$	−4.42953	+	6.09672i	−0.449751	+	0.619029i	0.522593	+	0.852582i	$0.324965\pi$
$98$	1.00050	+	0.325083i	0.101066	+	0.0328383i
$99$	4.39346	+	4.39346i	0.441559	+	0.441559i
$100$	−2.75525	−	4.17236i	−0.275525	−	0.417236i
$101$		−	1.98042i		−	0.197059i	−0.995134	−	0.0985295i	$-0.968586\pi$
$101$		−	1.98042i		−	0.197059i	0.995134	−	0.0985295i	$-0.0314139\pi$
$102$	−1.55181	+	4.77597i	−0.153652	+	0.472892i
$103$	1.86198	+	11.7561i	0.183467	+	1.15836i	0.891781	+	0.452466i	$0.149456\pi$
$103$	1.86198	+	11.7561i	0.183467	+	1.15836i	−0.708315	+	0.705897i	$0.750544\pi$
$104$	3.39056	+	1.22642i	0.332472	+	0.120261i
$105$	0.129702	−	5.80282i	0.0126576	−	0.566297i
$106$	7.67994	+	1.21638i	0.745941	+	0.118146i
$107$	9.39439	+	9.39439i	0.908189	+	0.908189i	0.996126	−	0.0879366i	$-0.0280273\pi$
$107$	9.39439	+	9.39439i	0.908189	+	0.908189i	−0.0879366	+	0.996126i	$0.528027\pi$
$108$	4.66498	+	0.738860i	0.448888	+	0.0710968i
$109$	12.4278	+	6.33228i	1.19037	+	0.606522i	0.933030	−	0.359799i	$-0.117155\pi$
$109$	12.4278	+	6.33228i	1.19037	+	0.606522i	0.257337	+	0.966322i	$0.417155\pi$
$110$	−6.42098	−	0.143519i	−0.612217	−	0.0136840i
$111$	−3.61607	−	7.09694i	−0.343222	−	0.673612i
$112$	−0.876868	−	2.69872i	−0.0828562	−	0.255005i
$113$	−16.9049	−	8.61350i	−1.59028	−	0.810290i	−0.999995	−	0.00309722i	$-0.999014\pi$
$113$	−16.9049	−	8.61350i	−1.59028	−	0.810290i	−0.590288	−	0.807193i	$-0.700986\pi$
$114$	−1.27473	+	3.92322i	−0.119390	+	0.367444i
$115$	1.24589	+	4.14763i	0.116180	+	0.386769i
$116$	−3.39011	+	1.10151i	−0.314763	+	0.102273i
$117$	−4.78963	+	6.15566i	−0.442801	+	0.569091i
$118$	−8.20832	+	8.20832i	−0.755637	+	0.755637i
$119$	−2.43685	+	15.3857i	−0.223386	+	1.41040i
$120$	−1.68128	+	1.16503i	−0.153479	+	0.106352i
$121$	1.61646	−	2.22486i	0.146951	−	0.202260i
$122$	4.43560	−	6.10508i	0.401580	−	0.552728i
$123$	−3.04993	+	9.38672i	−0.275003	+	0.846372i
$124$	−5.65959	−	5.65959i	−0.508246	−	0.508246i
$125$	−5.73174	+	9.59933i	−0.512662	+	0.858591i
$126$	6.13830			0.546844
$127$	−6.27380	−	12.3130i	−0.556710	−	1.09260i	−0.982235	−	0.187657i	$-0.939911\pi$
$127$	−6.27380	−	12.3130i	−0.556710	−	1.09260i	0.425525	−	0.904947i	$-0.360089\pi$
$128$	−0.587785	+	0.809017i	−0.0519534	+	0.0715077i
$129$	6.40145	+	4.65092i	0.563616	+	0.409491i
$130$	−0.819449	−	8.02051i	−0.0718705	−	0.703445i
$131$	−8.87715	+	6.44963i	−0.775600	+	0.563506i	−0.903655	−	0.428261i	$-0.859127\pi$
$131$	−8.87715	+	6.44963i	−0.775600	+	0.563506i	0.128055	+	0.991767i	$0.459127\pi$
$132$			2.62746i			0.228691i
$133$	−2.00175	+	12.6386i	−0.173574	+	1.09590i
$134$	0.890521	+	2.74074i	0.0769293	+	0.236764i
$135$	−3.03834	−	10.1148i	−0.261498	−	0.870539i
$136$	4.89131	−	2.49225i	0.419427	−	0.213709i
$137$	5.65422	+	17.4019i	0.483073	+	1.48675i	0.834752	+	0.550625i	$0.185611\pi$
$137$	5.65422	+	17.4019i	0.483073	+	1.48675i	−0.351679	+	0.936120i	$0.614389\pi$
$138$	1.68497	−	0.547479i	0.143434	−	0.0466045i
$139$	−11.0244	−	3.58203i	−0.935074	−	0.303824i	−0.198438	−	0.980113i	$-0.563587\pi$
$139$	−11.0244	−	3.58203i	−0.935074	−	0.303824i	−0.736636	+	0.676289i	$0.763587\pi$
$140$	−4.58578	+	4.38527i	−0.387569	+	0.370623i
$141$	−5.36062	−	2.73137i	−0.451446	−	0.230023i
$142$	0.678988	−	4.28696i	0.0569794	−	0.359754i
$143$	−9.06763	−	5.00270i	−0.758274	−	0.418347i
$144$	−1.27150	−	1.75007i	−0.105958	−	0.145839i
$145$	5.50873	+	5.76061i	0.457475	+	0.478393i
$146$	8.91725	+	6.47876i	0.737997	+	0.536186i
$147$	−0.950479	+	0.150541i	−0.0783942	+	0.0124164i
$148$	−2.69068	+	8.28106i	−0.221172	+	0.680699i
$149$	5.14808	−	5.14808i	0.421747	−	0.421747i	−0.464058	−	0.885805i	$-0.653607\pi$
$149$	5.14808	−	5.14808i	0.421747	−	0.421747i	0.885805	+	0.464058i	$0.153607\pi$
$150$	3.97847	+	2.25649i	0.324841	+	0.184242i
$151$	5.18157	−	5.18157i	0.421670	−	0.421670i	−0.464108	−	0.885779i	$-0.653625\pi$
$151$	5.18157	−	5.18157i	0.421670	−	0.421670i	0.885779	+	0.464108i	$0.153625\pi$
$152$	4.01797	−	2.04726i	0.325901	−	0.166055i
$153$	1.85769	+	11.7290i	0.150186	+	0.948234i
$154$	1.27500	+	8.05001i	0.102742	+	0.648688i
$155$	−5.90951	+	16.8934i	−0.474663	+	1.35691i
$156$	−3.27285	+	0.408471i	−0.262038	+	0.0327038i
$157$	−5.00053	−	5.00053i	−0.399086	−	0.399086i	0.478825	−	0.877910i	$-0.341063\pi$
$157$	−5.00053	−	5.00053i	−0.399086	−	0.399086i	−0.877910	+	0.478825i	$0.841063\pi$
$158$	−4.17686	+	3.03466i	−0.332293	+	0.241425i
$159$	−6.76480	+	2.19802i	−0.536483	+	0.174314i
$160$	2.20017	+	0.399063i	0.173939	+	0.0315487i
$161$	4.89674	−	2.49501i	0.385917	−	0.196635i
$162$	2.06288	−	0.670269i	0.162075	−	0.0526613i
$163$	−2.62557	+	0.853099i	−0.205650	+	0.0668198i	−0.410031	−	0.912072i	$-0.634482\pi$
$163$	−2.62557	+	0.853099i	−0.205650	+	0.0668198i	0.204380	+	0.978892i	$0.434482\pi$
$164$	9.61342	−	4.89828i	0.750682	−	0.382491i
$165$	5.29311	−	2.54963i	0.412068	−	0.198488i
$166$	11.3805	−	3.69774i	0.883295	−	0.287000i
$167$	19.2308	−	13.9720i	1.48813	−	1.08119i	0.513305	−	0.858206i	$-0.328421\pi$
$167$	19.2308	−	13.9720i	1.48813	−	1.08119i	0.974823	−	0.222982i	$-0.0715791\pi$
$168$	1.83547	+	1.83547i	0.141610	+	0.141610i
$169$	4.82186	−	12.0727i	0.370912	−	0.928668i
$170$	−9.76716	−	7.43531i	−0.749107	−	0.570262i
$171$	1.52600	+	9.63480i	0.116696	+	0.736792i
$172$	−1.35314	−	8.54338i	−0.103176	−	0.651427i
$173$	17.7963	−	9.06764i	1.35302	−	0.689400i	0.381065	−	0.924548i	$-0.375558\pi$
$173$	17.7963	−	9.06764i	1.35302	−	0.689400i	0.971960	+	0.235148i	$0.0755576\pi$
$174$	2.30570	−	2.30570i	0.174795	−	0.174795i
$175$	13.2842	+	4.98286i	1.00419	+	0.376669i
$176$	2.03100	−	2.03100i	0.153092	−	0.153092i
$177$	3.28142	−	10.0992i	0.246647	−	0.759101i
$178$	−7.11794	+	1.12737i	−0.533512	+	0.0845000i
$179$	7.35421	+	5.34315i	0.549680	+	0.399366i	0.827667	−	0.561219i	$-0.189667\pi$
$179$	7.35421	+	5.34315i	0.549680	+	0.399366i	−0.277988	+	0.960585i	$0.589667\pi$
$180$	−2.29174	+	4.25971i	−0.170816	+	0.317500i
$181$	−9.25060	−	12.7324i	−0.687592	−	0.946389i	0.312402	−	0.949950i	$-0.398867\pi$
$181$	−9.25060	−	12.7324i	−0.687592	−	0.946389i	−0.999994	+	0.00356093i	$0.998867\pi$
$182$	−9.82915	+	2.83965i	−0.728585	+	0.210489i
$183$	−1.07988	+	6.81812i	−0.0798273	+	0.504010i
$184$	−1.72566	−	0.879268i	−0.127217	−	0.0648205i
$185$	19.2935	−	2.61529i	1.41849	−	0.192280i
$186$	6.96333	+	2.26252i	0.510576	+	0.165896i
$187$	−14.9960	+	4.87250i	−1.09662	+	0.356312i
$188$	2.03239	+	6.25504i	0.148227	+	0.456196i
$189$	−11.9416	+	6.08454i	−0.868623	+	0.442586i
$190$	−8.02324	−	6.10774i	−0.582067	−	0.443102i
$191$	−1.78429	−	5.49149i	−0.129107	−	0.397350i	0.865520	−	0.500874i	$-0.166988\pi$
$191$	−1.78429	−	5.49149i	−0.129107	−	0.397350i	−0.994627	+	0.103524i	$0.966988\pi$
$192$	0.143101	−	0.903505i	0.0103274	−	0.0652049i
$193$		−	12.3425i		−	0.888434i	−0.895919	−	0.444217i	$-0.853482\pi$
$193$		−	12.3425i		−	0.888434i	0.895919	−	0.444217i	$-0.146518\pi$
$194$	−6.09672	+	4.42953i	−0.437719	+	0.318022i
$195$	3.99879	+	6.19691i	0.286359	+	0.443770i
$196$	0.851078	+	0.618344i	0.0607913	+	0.0441675i
$197$	2.94820	−	4.05785i	0.210050	−	0.289110i	−0.690973	−	0.722881i	$-0.742817\pi$
$197$	2.94820	−	4.05785i	0.210050	−	0.289110i	0.901023	+	0.433771i	$0.142817\pi$
$198$	2.82077	+	5.53608i	0.200464	+	0.393432i
$199$	5.74963			0.407580			0.203790	−	0.979015i	$-0.434674\pi$
$199$	5.74963			0.407580			0.203790	+	0.979015i	$0.434674\pi$
$200$	−1.33107	−	4.81957i	−0.0941210	−	0.340795i
$201$	−1.86405	−	1.86405i	−0.131480	−	0.131480i
$202$	0.611983	−	1.88349i	0.0430590	−	0.132522i
$203$	5.94535	−	8.18307i	0.417282	−	0.574339i
$204$	−2.95171	+	4.06268i	−0.206661	+	0.284445i
$205$	−19.1964	−	14.6134i	−1.34074	−	1.02064i
$206$	−1.86198	+	11.7561i	−0.129731	+	0.819086i
$207$	2.96249	−	2.96249i	0.205907	−	0.205907i
$208$	2.84563	+	2.21414i	0.197309	+	0.153523i
$209$	−12.3185	+	4.00252i	−0.852087	+	0.276860i
$210$	1.91652	−	5.47873i	0.132253	−	0.378068i
$211$	4.34773	−	13.3809i	0.299310	−	0.921182i	−0.682429	−	0.730952i	$-0.739076\pi$
$211$	4.34773	−	13.3809i	0.299310	−	0.921182i	0.981739	−	0.190231i	$-0.0609236\pi$
$212$	6.92817	+	3.53008i	0.475829	+	0.242447i
$213$	1.22694	+	3.77613i	0.0840685	+	0.258736i
$214$	6.03157	+	11.8376i	0.412309	+	0.809203i
$215$	−15.8979	+	11.0163i	−1.08423	+	0.751303i
$216$	4.20834	+	2.14426i	0.286341	+	0.145898i
$217$	22.4322	+	3.55291i	1.52280	+	0.241187i
$218$	9.86275	+	9.86275i	0.667990	+	0.667990i
$219$	−9.95873	−	1.57731i	−0.672949	−	0.106585i
$220$	−6.06237	−	2.12069i	−0.408725	−	0.142977i
$221$	−8.40067	−	17.9221i	−0.565090	−	1.20557i
$222$	−1.24601	−	7.86702i	−0.0836269	−	0.528000i
$223$	2.54063	−	7.81926i	0.170133	−	0.523617i	−0.829244	−	0.558886i	$-0.811229\pi$
$223$	2.54063	−	7.81926i	0.170133	−	0.523617i	0.999378	+	0.0352694i	$0.0112289\pi$
$224$		−	2.83760i		−	0.189595i
$225$	10.8052	+	0.483267i	0.720347	+	0.0322178i
$226$	−13.4158	−	13.4158i	−0.892408	−	0.892408i
$227$	−9.32104	−	3.02859i	−0.618659	−	0.201015i	−0.0171144	−	0.999854i	$-0.505448\pi$
$227$	−9.32104	−	3.02859i	−0.618659	−	0.201015i	−0.601545	+	0.798839i	$0.705448\pi$
$228$	−2.42469	+	3.33729i	−0.160579	+	0.221018i
$229$	−2.38677	−	15.0695i	−0.157722	−	0.995820i	−0.931864	−	0.362808i	$-0.881818\pi$
$229$	−2.38677	−	15.0695i	−0.157722	−	0.995820i	0.774142	−	0.633013i	$-0.218182\pi$
$230$	−0.0967740	+	4.32963i	−0.00638109	+	0.285488i
$231$	−4.38234	−	6.03177i	−0.288337	−	0.396861i
$232$	−3.56457			−0.234025
$233$	8.82787	+	1.39820i	0.578333	+	0.0915990i	0.438746	−	0.898611i	$-0.355423\pi$
$233$	8.82787	+	1.39820i	0.578333	+	0.0915990i	0.139587	+	0.990210i	$0.455423\pi$
$234$	−6.45741	+	4.37431i	−0.422134	+	0.285957i
$235$	10.6288	−	10.1641i	0.693349	−	0.663031i
$236$	−10.3431	+	5.27006i	−0.673277	+	0.343052i
$237$	2.14412	−	4.20807i	0.139276	−	0.273344i
$238$	−7.07201	+	13.8796i	−0.458410	+	0.899681i
$239$	−3.25586	−	6.38998i	−0.210604	−	0.413334i	0.761405	−	0.648276i	$-0.224510\pi$
$239$	−3.25586	−	6.38998i	−0.210604	−	0.413334i	−0.972009	+	0.234943i	$0.924510\pi$
$240$	−1.95901	+	0.588460i	−0.126453	+	0.0379849i
$241$	−11.2733	−	5.74402i	−0.726175	−	0.370005i	0.0514983	−	0.998673i	$-0.483600\pi$
$241$	−11.2733	−	5.74402i	−0.726175	−	0.370005i	−0.777674	+	0.628668i	$0.783600\pi$
$242$	2.22486	−	1.61646i	0.143019	−	0.103910i
$243$	−11.4223	+	11.4223i	−0.732740	+	0.732740i
$244$	6.10508	−	4.43560i	0.390838	−	0.283960i
$245$	0.419810	−	2.31456i	0.0268207	−	0.147872i
$246$	−5.80131	+	7.98482i	−0.369878	+	0.509094i
$247$	−6.90073	−	14.7221i	−0.439083	−	0.936744i
$248$	−3.63368	−	7.13150i	−0.230739	−	0.452850i
$249$	−7.74015	+	7.74015i	−0.490512	+	0.490512i
$250$	−8.41756	+	7.35831i	−0.532373	+	0.465380i
$251$			16.5410i			1.04406i	0.852927	+	0.522030i	$0.174825\pi$
$251$			16.5410i			1.04406i	−0.852927	+	0.522030i	$0.825175\pi$
$252$	5.83787	+	1.89684i	0.367751	+	0.119490i
$253$	4.50046	+	3.26978i	0.282942	+	0.205569i
$254$	−2.16180	−	13.6491i	−0.135644	−	0.856420i
$255$	11.0487	+	2.00399i	0.691897	+	0.125495i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	3.51942	−	3.51942i	0.219535	−	0.219535i	−0.588767	−	0.808303i	$-0.700387\pi$
$257$	3.51942	−	3.51942i	0.219535	−	0.219535i	0.808303	+	0.588767i	$0.200387\pi$
$258$	4.65092	+	6.40145i	0.289554	+	0.398537i
$259$	−7.63508	−	23.4984i	−0.474421	−	1.46012i
$260$	1.69913	−	7.88118i	0.105376	−	0.488770i
$261$	2.38279	−	7.33348i	0.147491	−	0.453931i
$262$	−10.4357	+	3.39077i	−0.644721	+	0.209482i
$263$	26.3992	+	13.4511i	1.62785	+	0.829429i	0.998637	+	0.0521928i	$0.0166210\pi$
$263$	26.3992	+	13.4511i	1.62785	+	0.829429i	0.629209	+	0.777236i	$0.283379\pi$
$264$	−0.811929	+	2.49886i	−0.0499708	+	0.153794i
$265$	0.388528	−	17.3826i	0.0238671	−	1.06780i
$266$	−5.80931	+	11.4014i	−0.356192	+	0.699065i
$267$	5.33338	−	3.87493i	0.326398	−	0.237142i
$268$			2.88179i			0.176033i
$269$	7.53783	+	10.3749i	0.459590	+	0.632571i	0.974424	−	0.224719i	$-0.0721464\pi$
$269$	7.53783	+	10.3749i	0.459590	+	0.632571i	−0.514834	+	0.857290i	$0.672146\pi$
$270$	0.236001	−	10.5586i	0.0143626	−	0.642576i
$271$	17.7394	−	2.80964i	1.07759	−	0.170673i	0.407686	−	0.913122i	$-0.366336\pi$
$271$	17.7394	−	2.80964i	1.07759	−	0.170673i	0.669903	+	0.742449i	$0.266336\pi$
$272$	5.42206	−	0.858770i	0.328761	−	0.0520706i
$273$	6.83209	−	6.39650i	0.413497	−	0.387134i
$274$			18.2975i			1.10539i
$275$	1.61059	+	14.2707i	0.0971222	+	0.860558i
$276$	1.77168			0.106643
$277$	−12.0736	−	23.6959i	−0.725435	−	1.42375i	−0.898562	−	0.438847i	$-0.855387\pi$
$277$	−12.0736	−	23.6959i	−0.725435	−	1.42375i	0.173127	−	0.984900i	$-0.444613\pi$
$278$	−9.37788	−	6.81343i	−0.562448	−	0.408642i
$279$	17.1008	−	2.70850i	1.02380	−	0.162154i
$280$	−5.71646	+	2.75355i	−0.341624	+	0.164556i
$281$	−4.73599	+	29.9019i	−0.282526	+	1.78380i	0.283055	+	0.959104i	$0.408652\pi$
$281$	−4.73599	+	29.9019i	−0.282526	+	1.78380i	−0.565580	+	0.824693i	$0.691348\pi$
$282$	−4.25422	−	4.25422i	−0.253335	−	0.253335i
$283$	−0.639252	−	0.101248i	−0.0379996	−	0.00601854i	0.137406	−	0.990515i	$-0.456124\pi$
$283$	−0.639252	−	0.101248i	−0.0379996	−	0.00601854i	−0.175405	+	0.984496i	$0.556124\pi$
$284$	1.97050	−	3.86733i	0.116928	−	0.229484i
$285$	9.07597	+	1.64618i	0.537614	+	0.0975114i
$286$	−7.07791	−	7.55990i	−0.418526	−	0.447026i
$287$	−13.8994	+	27.2791i	−0.820454	+	1.61023i
$288$	−0.668466	−	2.05733i	−0.0393897	−	0.121229i
$289$	−12.4933	−	4.05932i	−0.734901	−	0.238784i
$290$	3.45898	+	7.18096i	0.203118	+	0.421681i
$291$	3.12965	−	6.14229i	0.183464	−	0.360068i
$292$	6.47876	+	8.91725i	0.379141	+	0.521843i
$293$		−	4.40707i		−	0.257464i	−0.991679	−	0.128732i	$-0.958909\pi$
$293$		−	4.40707i		−	0.257464i	0.991679	−	0.128732i	$-0.0410907\pi$
$294$	−0.950479	−	0.150541i	−0.0554330	−	0.00877973i
$295$	20.6535	+	15.7226i	1.20249	+	0.915404i
$296$	−5.11798	+	7.04429i	−0.297476	+	0.409441i
$297$	−10.9752	−	7.97395i	−0.636845	−	0.462695i
$298$	6.48696	−	3.30527i	0.375780	−	0.191469i
$299$	−3.37329	+	6.11426i	−0.195083	+	0.353597i
$300$	3.08646	+	3.37547i	0.178197	+	0.194883i
$301$	17.3559	+	17.3559i	1.00038	+	1.00038i
$302$	6.52916	−	3.32677i	0.375711	−	0.191434i
$303$	0.283400	+	1.78932i	0.0162809	+	0.102794i
$304$	4.45396	−	0.705437i	0.255452	−	0.0404596i
$305$	−14.8599	−	7.99470i	−0.850877	−	0.457775i
$306$	−1.85769	+	11.7290i	−0.106197	+	0.670503i
$307$	1.30099			0.0742512			0.0371256	−	0.999311i	$-0.488180\pi$
$307$	1.30099			0.0742512			0.0371256	+	0.999311i	$0.488180\pi$
$308$	−1.27500	+	8.05001i	−0.0726497	+	0.458692i
$309$	−3.36462	−	10.3552i	−0.191407	−	0.589089i
$310$	−10.8406	+	14.2404i	−0.615706	+	0.808803i
$311$	−23.1698	−	7.52832i	−1.31384	−	0.426892i	−0.433464	−	0.901171i	$-0.642709\pi$
$311$	−23.1698	−	7.52832i	−1.31384	−	0.426892i	−0.880375	+	0.474279i	$0.842709\pi$
$312$	−3.23889	−	0.622887i	−0.183366	−	0.0352641i
$313$	8.64331	+	4.40398i	0.488549	+	0.248928i	0.680870	−	0.732404i	$-0.261602\pi$
$313$	8.64331	+	4.40398i	0.488549	+	0.248928i	−0.192322	+	0.981332i	$0.561602\pi$
$314$	−3.21054	−	6.30103i	−0.181181	−	0.355588i
$315$	−1.84369	−	13.6013i	−0.103880	−	0.766345i
$316$	−4.91019	+	1.59542i	−0.276220	+	0.0897492i
$317$	3.44610	+	4.74315i	0.193552	+	0.266402i	0.894752	−	0.446563i	$-0.147352\pi$
$317$	3.44610	+	4.74315i	0.193552	+	0.266402i	−0.701200	+	0.712964i	$0.747352\pi$
$318$	−7.11293			−0.398873
$319$	10.1123	+	1.60164i	0.566183	+	0.0896745i
$320$	1.96917	+	1.05942i	0.110080	+	0.0592234i
$321$	−9.83222	−	7.14353i	−0.548781	−	0.398713i
$322$	5.42808	−	0.859723i	0.302495	−	0.0479105i
$323$	−23.5438	−	7.64985i	−1.31001	−	0.425649i
$324$	2.16904			0.120502
$325$	−17.5257	+	4.22477i	−0.972153	+	0.234348i
$326$	−2.76069			−0.152900
$327$	−12.1347	−	3.94281i	−0.671052	−	0.218038i
$328$	10.6566	−	1.68783i	0.588410	−	0.0931949i
$329$	−15.0985	−	10.9697i	−0.832406	−	0.604778i
$330$	5.82193	−	0.789180i	0.320487	−	0.0434429i
$331$	15.0419	+	2.38240i	0.826775	+	0.130948i	0.555461	−	0.831543i	$-0.312542\pi$
$331$	15.0419	+	2.38240i	0.826775	+	0.130948i	0.271314	+	0.962491i	$0.412542\pi$
$332$	11.9661			0.656727
$333$	−11.0712	−	15.2382i	−0.606698	−	0.835049i
$334$	22.6072	−	7.34553i	1.23701	−	0.401930i
$335$	5.80547	−	2.79643i	0.317187	−	0.152785i
$336$	1.17844	+	2.31283i	0.0642894	+	0.126175i
$337$	−3.76379	−	1.91775i	−0.205027	−	0.104466i	0.348462	−	0.937323i	$-0.386704\pi$
$337$	−3.76379	−	1.91775i	−0.205027	−	0.104466i	−0.553489	+	0.832856i	$0.686704\pi$
$338$	8.31652	−	9.99177i	0.452359	−	0.543481i
$339$	16.5063	+	5.36322i	0.896499	+	0.291290i
$340$	−6.99148	−	10.0896i	−0.379166	−	0.547186i
$341$	7.10407	+	21.8641i	0.384707	+	1.18401i
$342$	−1.52600	+	9.63480i	−0.0825168	+	0.520990i
$343$	16.8781			0.911331
$344$	1.35314	−	8.54338i	0.0729563	−	0.460628i
$345$	−1.71920	−	3.56912i	−0.0925587	−	0.192155i
$346$	19.7273	−	3.12450i	1.06055	−	0.167974i
$347$	−3.14858	−	19.8794i	−0.169025	−	1.06718i	−0.915662	−	0.401949i	$-0.868333\pi$
$347$	−3.14858	−	19.8794i	−0.169025	−	1.06718i	0.746638	−	0.665231i	$-0.231667\pi$
$348$	2.90535	−	1.48035i	0.155743	−	0.0793551i
$349$	7.27420	+	7.27420i	0.389379	+	0.389379i	0.874466	−	0.485087i	$-0.161212\pi$
$349$	7.27420	+	7.27420i	0.389379	+	0.389379i	−0.485087	+	0.874466i	$0.661212\pi$
$350$	11.0943	+	8.84404i	0.593013	+	0.472734i
$351$	8.22639	−	14.9107i	0.439092	−	0.795876i
$352$	2.55921	−	1.30398i	0.136406	−	0.0695025i
$353$	6.47124	+	4.70163i	0.344429	+	0.250242i	0.746528	−	0.665354i	$-0.231719\pi$
$353$	6.47124	+	4.70163i	0.344429	+	0.250242i	−0.402099	+	0.915596i	$0.631719\pi$
$354$	6.24164	−	8.59088i	0.331739	−	0.456600i
$355$	−9.70301	−	0.216877i	−0.514982	−	0.0115107i
$356$	−7.11794	−	1.12737i	−0.377250	−	0.0597505i
$357$		−	14.2497i		−	0.754176i
$358$	5.34315	+	7.35421i	0.282394	+	0.388682i
$359$	−5.92182	+	11.6222i	−0.312542	+	0.613397i	−0.992828	−	0.119549i	$-0.961855\pi$
$359$	−5.92182	+	11.6222i	−0.312542	+	0.613397i	0.680287	+	0.732946i	$0.261855\pi$
$360$	−3.49590	+	3.34304i	−0.184250	+	0.176193i
$361$	−1.27002	−	0.412653i	−0.0668430	−	0.0217186i
$362$	−4.86333	−	14.9678i	−0.255611	−	0.786690i
$363$	−1.14210	+	2.24149i	−0.0599445	+	0.117648i
$364$	−10.2256	−	0.336705i	−0.535966	−	0.0176481i
$365$	11.6773	−	21.7048i	0.611217	−	1.13608i
$366$	−3.13394	+	6.15071i	−0.163814	+	0.321503i
$367$	16.4875	+	2.61137i	0.860643	+	0.136312i	0.571128	−	0.820861i	$-0.306506\pi$
$367$	16.4875	+	2.61137i	0.860643	+	0.136312i	0.289515	+	0.957174i	$0.406506\pi$
$368$	−1.36949	−	1.36949i	−0.0713897	−	0.0713897i
$369$	−3.65112	+	23.0523i	−0.190070	+	1.20005i
$370$	19.1574	+	3.47473i	0.995944	+	0.180642i
$371$	−21.7926	+	3.45161i	−1.13142	+	0.179199i
$372$	5.92336	+	4.30357i	0.307112	+	0.223130i
$373$	−11.3932	−	22.3604i	−0.589918	−	1.15778i	−0.972292	−	0.233771i	$-0.924893\pi$
$373$	−11.3932	−	22.3604i	−0.589918	−	1.15778i	0.382374	−	0.924008i	$-0.375107\pi$
$374$	−15.7677			−0.815330
$375$	3.80498	−	9.49327i	0.196488	−	0.490230i
$376$			6.57694i			0.339180i
$377$	−0.422965	+	12.8453i	−0.0217838	+	0.661565i
$378$	−13.2374	+	2.09659i	−0.680856	+	0.107837i
$379$	−27.8728	+	4.41462i	−1.43173	+	0.226764i	−0.823644	−	0.567107i	$-0.808062\pi$
$379$	−27.8728	+	4.41462i	−1.43173	+	0.226764i	−0.608086	+	0.793871i	$0.708062\pi$
$380$	−5.74316	−	8.28812i	−0.294618	−	0.425172i
$381$	7.43042	+	10.2271i	0.380672	+	0.523950i
$382$		−	5.77410i		−	0.295428i
$383$	−13.6814	+	9.94009i	−0.699085	+	0.507915i	−0.879634	−	0.475651i	$-0.842212\pi$
$383$	−13.6814	+	9.94009i	−0.699085	+	0.507915i	0.180549	+	0.983566i	$0.442212\pi$
$384$	0.415296	−	0.815064i	0.0211930	−	0.0415935i
$385$	17.4543	−	5.24303i	0.889553	−	0.267210i
$386$	3.81405	−	11.7384i	0.194130	−	0.597470i
$387$	16.6720	+	8.49480i	0.847485	+	0.431815i
$388$	−7.16713	+	2.32874i	−0.363856	+	0.118224i
$389$	−2.81514	+	8.66410i	−0.142733	+	0.439287i	−0.996713	−	0.0810195i	$-0.974182\pi$
$389$	−2.81514	+	8.66410i	−0.142733	+	0.439287i	0.853979	+	0.520307i	$0.174182\pi$
$390$	1.88812	+	7.12930i	0.0956087	+	0.361006i
$391$	3.28550	+	10.1117i	0.166155	+	0.511372i
$392$	0.618344	+	0.851078i	0.0312311	+	0.0429859i
$393$	7.09760	−	7.09760i	0.358027	−	0.358027i
$394$	4.05785	−	2.94820i	0.204431	−	0.148528i
$395$	7.97877	+	8.34360i	0.401456	+	0.419812i
$396$	0.971973	+	6.13679i	0.0488435	+	0.308386i
$397$	2.49298	+	1.81126i	0.125119	+	0.0909043i	0.648585	−	0.761142i	$-0.275361\pi$
$397$	2.49298	+	1.81126i	0.125119	+	0.0909043i	−0.523466	+	0.852047i	$0.675361\pi$
$398$	5.46822	+	1.77673i	0.274097	+	0.0890596i
$399$		−	11.7055i		−	0.586006i
$400$	0.223404	−	4.99501i	0.0111702	−	0.249750i
$401$	22.3462	−	22.3462i	1.11592	−	1.11592i	0.123584	−	0.992334i	$-0.460561\pi$
$401$	22.3462	−	22.3462i	1.11592	−	1.11592i	0.992334	−	0.123584i	$-0.0394388\pi$
$402$	−1.19679	−	2.34884i	−0.0596907	−	0.117150i
$403$	−26.1302	+	12.2481i	−1.30164	+	0.610122i
$404$	1.16406	−	1.60219i	0.0579142	−	0.0797121i
$405$	−2.10479	−	4.36961i	−0.104588	−	0.217128i
$406$	8.18307	−	5.94535i	0.406119	−	0.295063i
$407$	17.6844	−	17.6844i	0.876581	−	0.876581i
$408$	−4.06268	+	2.95171i	−0.201133	+	0.146132i
$409$	−16.7426	−	8.53076i	−0.827866	−	0.421819i	−0.0119074	−	0.999929i	$-0.503790\pi$
$409$	−16.7426	−	8.53076i	−0.827866	−	0.421819i	−0.815959	+	0.578110i	$0.803790\pi$
$410$	−13.7411	−	19.8302i	−0.678625	−	0.979344i
$411$	−7.59886	−	14.9136i	−0.374824	−	0.735633i
$412$	−5.40369	+	10.6053i	−0.266221	+	0.522487i
$413$	14.9543	−	29.3496i	0.735855	−	1.44420i
$414$	3.73295	−	1.90203i	0.183465	−	0.0934798i
$415$	−11.6117	−	24.1062i	−0.569995	−	1.18333i
$416$	2.02215	+	2.98512i	0.0991438	+	0.146357i
$417$	10.4732	+	1.65879i	0.512873	+	0.0812311i
$418$	−12.9524			−0.633524
$419$	−4.48051	−	6.16690i	−0.218887	−	0.301273i	0.685426	−	0.728143i	$-0.259616\pi$
$419$	−4.48051	−	6.16690i	−0.218887	−	0.301273i	−0.904313	+	0.426870i	$0.859616\pi$
$420$	3.51574	−	4.61834i	0.171551	−	0.225352i
$421$	−3.32087	−	20.9672i	−0.161849	−	1.02188i	−0.926188	−	0.377062i	$-0.876934\pi$
$421$	−3.32087	−	20.9672i	−0.161849	−	1.02188i	0.764339	−	0.644815i	$-0.223066\pi$
$422$	8.26988	−	11.3825i	0.402571	−	0.554092i
$423$	−13.5309	−	4.39646i	−0.657895	−	0.213763i
$424$	5.49823	+	5.49823i	0.267018	+	0.267018i
$425$	−13.5415	+	23.8754i	−0.656861	+	1.15813i
$426$			3.97046i			0.192369i
$427$	−6.61710	+	20.3653i	−0.320224	+	0.985548i
$428$	2.07834	+	13.1221i	0.100460	+	0.634281i
$429$	8.90855	+	3.22238i	0.430109	+	0.155578i
$430$	−18.5240	+	5.56437i	−0.893308	+	0.268338i
$431$	−3.17324	−	0.502591i	−0.152849	−	0.0242090i	0.0795407	−	0.996832i	$-0.474655\pi$
$431$	−3.17324	−	0.502591i	−0.152849	−	0.0242090i	−0.232390	+	0.972623i	$0.574655\pi$
$432$	3.33976	+	3.33976i	0.160684	+	0.160684i
$433$	23.6401	+	3.74422i	1.13607	+	0.179936i	0.696009	−	0.718033i	$-0.254957\pi$
$433$	23.6401	+	3.74422i	1.13607	+	0.179936i	0.440059	+	0.897969i	$0.354957\pi$
$434$	20.2364	+	10.3109i	0.971376	+	0.494941i
$435$	−5.80151	−	4.41644i	−0.278161	−	0.211752i
$436$	6.33228	+	12.4278i	0.303261	+	0.595183i
$437$	2.69888	+	8.30629i	0.129105	+	0.397344i
$438$	−8.98390	−	4.57753i	−0.429267	−	0.218723i
$439$	10.8201	−	33.3009i	0.516415	−	1.58936i	−0.264277	−	0.964447i	$-0.585133\pi$
$439$	10.8201	−	33.3009i	0.516415	−	1.58936i	0.780692	−	0.624916i	$-0.214867\pi$
$440$	−5.11033	−	3.89027i	−0.243625	−	0.185461i
$441$	−2.16429	+	0.703219i	−0.103061	+	0.0334866i
$442$	−2.45129	−	19.6408i	−0.116596	−	0.934219i
$443$	10.5276	−	10.5276i	0.500180	−	0.500180i	−0.411314	−	0.911494i	$-0.634930\pi$
$443$	10.5276	−	10.5276i	0.500180	−	0.500180i	0.911494	+	0.411314i	$0.134930\pi$
$444$	1.24601	−	7.86702i	0.0591332	−	0.373352i
$445$	4.63597	+	15.4333i	0.219766	+	0.731610i
$446$	4.83257	−	6.65146i	0.228829	−	0.314956i
$447$	−3.91462	+	5.38802i	−0.185155	+	0.254844i
$448$	0.876868	−	2.69872i	0.0414281	−	0.127503i
$449$	−18.0575	−	18.0575i	−0.852186	−	0.852186i	0.138216	−	0.990402i	$-0.455863\pi$
$449$	−18.0575	−	18.0575i	−0.852186	−	0.852186i	−0.990402	+	0.138216i	$0.955863\pi$
$450$	10.1270	+	3.79861i	0.477392	+	0.179068i
$451$	−30.9900			−1.45926
$452$	−8.61350	−	16.9049i	−0.405145	−	0.795142i
$453$	−3.94009	+	5.42307i	−0.185122	+	0.254798i
$454$	−7.92895	−	5.76072i	−0.372124	−	0.270364i
$455$	9.24439	+	20.9266i	0.433383	+	0.981052i
$456$	−3.33729	+	2.42469i	−0.156283	+	0.113546i
$457$			16.0727i			0.751849i	0.926650	+	0.375924i	$0.122675\pi$
$457$			16.0727i			0.751849i	−0.926650	+	0.375924i	$0.877325\pi$
$458$	2.38677	−	15.0695i	0.111527	−	0.704151i
$459$	−8.01229	−	24.6593i	−0.373982	−	1.15100i
$460$	−1.42997	+	4.08782i	−0.0666726	+	0.190596i
$461$	12.3028	−	6.26860i	0.572999	−	0.291958i	−0.143381	−	0.989668i	$-0.545797\pi$
$461$	12.3028	−	6.26860i	0.572999	−	0.291958i	0.716381	+	0.697710i	$0.245797\pi$
$462$	−2.30393	−	7.09077i	−0.107189	−	0.329893i
$463$	10.1355	−	3.29321i	0.471034	−	0.153048i	−0.0638748	−	0.997958i	$-0.520346\pi$
$463$	10.1355	−	3.29321i	0.471034	−	0.153048i	0.534909	+	0.844910i	$0.320346\pi$
$464$	−3.39011	−	1.10151i	−0.157382	−	0.0511364i
$465$	2.92181	−	16.1089i	0.135496	−	0.747034i
$466$	7.96374	+	4.05773i	0.368913	+	0.187971i
$467$	−3.06426	+	19.3470i	−0.141797	+	0.895271i	0.809528	+	0.587081i	$0.199723\pi$
$467$	−3.06426	+	19.3470i	−0.141797	+	0.895271i	−0.951325	+	0.308190i	$0.900277\pi$
$468$	−7.49309	+	2.16476i	−0.346368	+	0.100066i
$469$	−4.80654	−	6.61563i	−0.221945	−	0.305481i
$470$	13.2495	−	6.38212i	0.611154	−	0.294385i
$471$	5.23359	+	3.80242i	0.241151	+	0.175206i
$472$	−11.4654	+	1.81594i	−0.527738	+	0.0835854i
$473$	−7.67745	+	23.6288i	−0.353010	+	1.08645i
$474$	3.33955	−	3.33955i	0.153390	−	0.153390i
$475$	−11.1237	+	19.6124i	−0.510391	+	0.899880i
$476$	−11.0149	+	11.0149i	−0.504868	+	0.504868i
$477$	−14.9870	+	7.63627i	−0.686209	+	0.349641i
$478$	−1.12189	−	7.08335i	−0.0513142	−	0.323985i
$479$	2.29777	+	14.5076i	0.104988	+	0.662867i	0.982913	+	0.184070i	$0.0589272\pi$
$479$	2.29777	+	14.5076i	0.104988	+	0.662867i	−0.877925	+	0.478798i	$0.841073\pi$
$480$	−2.04497	−	0.0457083i	−0.0933398	−	0.00208629i
$481$	24.7775	+	19.2790i	1.12976	+	0.879046i
$482$	−8.94652	−	8.94652i	−0.407503	−	0.407503i
$483$	−4.06719	+	2.95499i	−0.185064	+	0.134457i
$484$	2.61548	−	0.849821i	0.118885	−	0.0386282i
$485$	11.6462	+	12.1787i	0.528825	+	0.553006i
$486$	−14.3929	+	7.33356i	−0.652876	+	0.332657i
$487$	−12.2867	+	3.99219i	−0.556763	+	0.180903i	−0.573864	−	0.818950i	$-0.694556\pi$
$487$	−12.2867	+	3.99219i	−0.556763	+	0.180903i	0.0171009	+	0.999854i	$0.494556\pi$
$488$	7.17695	−	2.33193i	0.324885	−	0.105562i
$489$	2.25013	−	1.14650i	0.101755	−	0.0518466i
$490$	1.11450	−	2.07155i	0.0503480	−	0.0935829i
$491$	−13.3100	+	4.32467i	−0.600671	+	0.195170i	−0.593540	−	0.804805i	$-0.702270\pi$
$491$	−13.3100	+	4.32467i	−0.600671	+	0.195170i	−0.00713127	+	0.999975i	$0.502270\pi$
$492$	−7.98482	+	5.80131i	−0.359984	+	0.261543i
$493$	13.8368	+	13.8368i	0.623179	+	0.623179i
$494$	−2.01361	−	16.1340i	−0.0905968	−	0.725902i
$495$	11.4196	−	7.91309i	0.513274	−	0.355667i
$496$	−1.25208	−	7.90532i	−0.0562201	−	0.354960i
$497$	1.92670	+	12.1647i	0.0864243	+	0.545661i
$498$	−9.75316	+	4.96948i	−0.437049	+	0.222688i
$499$	3.29103	−	3.29103i	0.147327	−	0.147327i	−0.629596	−	0.776923i	$-0.716780\pi$
$499$	3.29103	−	3.29103i	0.147327	−	0.147327i	0.776923	+	0.629596i	$0.216780\pi$
$500$	−10.2794	+	4.39699i	−0.459710	+	0.196640i
$501$	−15.3758	+	15.3758i	−0.686938	+	0.686938i
$502$	−5.11146	+	15.7315i	−0.228136	+	0.702129i
$503$	11.5314	−	1.82639i	0.514159	−	0.0814348i	0.106037	−	0.994362i	$-0.466184\pi$
$503$	11.5314	−	1.82639i	0.514159	−	0.0814348i	0.408122	+	0.912927i	$0.366184\pi$
$504$	4.96599	+	3.60800i	0.221203	+	0.160713i
$505$	−4.35726	−	0.790311i	−0.193895	−	0.0351684i
$506$	3.26978	+	4.50046i	0.145359	+	0.200070i
$507$	−2.62896	+	11.5977i	−0.116756	+	0.515074i
$508$	2.16180	−	13.6491i	0.0959145	−	0.605580i
$509$	27.3928	+	13.9573i	1.21416	+	0.618647i	0.939386	−	0.342861i	$-0.111396\pi$
$509$	27.3928	+	13.9573i	1.21416	+	0.618647i	0.274777	+	0.961508i	$0.411396\pi$
$510$	9.88868	+	5.32015i	0.437878	+	0.235580i
$511$	−29.7462	−	9.66512i	−1.31589	−	0.427560i
$512$	−0.951057	+	0.309017i	−0.0420312	+	0.0136568i
$513$	−6.58170	−	20.2564i	−0.290589	−	0.894342i
$514$	4.43473	−	2.25961i	0.195607	−	0.0996670i
$515$	26.6085	+	0.594740i	1.17251	+	0.0262074i
$516$	2.44514	+	7.52535i	0.107641	+	0.331285i
$517$	2.95516	−	18.6582i	0.129968	−	0.820585i
$518$		−	24.7076i		−	1.08559i
$519$	−14.7814	+	10.7393i	−0.648832	+	0.471404i
$520$	4.05139	−	6.97039i	0.177665	−	0.305672i
$521$	0.430419	+	0.312718i	0.0188570	+	0.0137004i	0.597174	−	0.802112i	$-0.296290\pi$
$521$	0.430419	+	0.312718i	0.0188570	+	0.0137004i	−0.578317	+	0.815812i	$0.696290\pi$
$522$	4.53234	−	6.23823i	0.198375	−	0.273040i
$523$	−17.2262	−	33.8082i	−0.753247	−	1.47833i	−0.874144	−	0.485666i	$-0.838577\pi$
$523$	−17.2262	−	33.8082i	−0.753247	−	1.47833i	0.120897	−	0.992665i	$-0.461423\pi$
$524$	−10.9728			−0.479347
$525$	−12.7154	−	2.60105i	−0.554947	−	0.113519i
$526$	20.9505	+	20.9505i	0.913487	+	0.913487i
$527$	−13.5777	+	41.7879i	−0.591455	+	1.82031i
$528$	−1.54438	+	2.12566i	−0.0672105	+	0.0925074i
$529$	−11.3143	+	15.5728i	−0.491925	+	0.677076i
$530$	5.74102	−	16.4118i	0.249374	−	0.712881i
$531$	3.92824	−	24.8019i	0.170471	−	1.07631i
$532$	−9.04821	+	9.04821i	−0.392290	+	0.392290i
$533$	−4.81778	−	38.6022i	−0.208681	−	1.67205i
$534$	6.26977	−	2.03717i	0.271319	−	0.0881570i
$535$	24.4182	−	16.9203i	1.05569	−	0.731528i
$536$	−0.890521	+	2.74074i	−0.0384647	+	0.118382i
$537$	−7.40918	−	3.77517i	−0.319730	−	0.162910i
$538$	3.96287	+	12.1965i	0.170852	+	0.525827i
$539$	−1.37178	−	2.69226i	−0.0590866	−	0.115964i
$540$	3.48724	−	9.96889i	0.150067	−	0.428993i
$541$	−4.83723	−	2.46469i	−0.207969	−	0.105965i	0.346904	−	0.937901i	$-0.387233\pi$
$541$	−4.83723	−	2.46469i	−0.207969	−	0.105965i	−0.554873	+	0.831935i	$0.687233\pi$
$542$	17.7394	+	2.80964i	0.761971	+	0.120684i
$543$	10.1800	+	10.1800i	0.436865	+	0.436865i
$544$	5.42206	+	0.858770i	0.232469	+	0.0368195i
$545$	18.8916	−	24.8163i	0.809226	−	1.06301i
$546$	8.47433	−	3.97220i	0.362668	−	0.169995i
$547$	−3.68473	−	23.2645i	−0.157548	−	0.994717i	−0.932098	−	0.362205i	$-0.882024\pi$
$547$	−3.68473	−	23.2645i	−0.157548	−	0.994717i	0.774551	−	0.632512i	$-0.217976\pi$
$548$	−5.65422	+	17.4019i	−0.241537	+	0.743373i
$549$			16.3241i			0.696698i
$550$	−2.87814	+	14.0700i	−0.122724	+	0.599946i
$551$	11.3663	+	11.3663i	0.484220	+	0.484220i
$552$	1.68497	+	0.547479i	0.0717170	+	0.0233023i
$553$	8.61117	−	11.8523i	0.366184	−	0.504009i
$554$	−4.16029	−	26.2671i	−0.176754	−	1.11598i
$555$	−17.0575	+	5.12385i	−0.724051	+	0.217495i
$556$	−6.81343	−	9.37788i	−0.288954	−	0.397711i
$557$	−21.3277			−0.903685			−0.451842	−	0.892098i	$-0.649233\pi$
$557$	−21.3277			−0.903685			−0.451842	+	0.892098i	$0.649233\pi$
$558$	17.1008	+	2.70850i	0.723935	+	0.114660i
$559$	−30.6263	−	5.88991i	−1.29536	−	0.249117i
$560$	−6.28757	+	0.852299i	−0.265698	+	0.0360162i
$561$	12.8517	−	6.54828i	0.542600	−	0.276468i
$562$	−13.7444	+	26.9749i	−0.579772	+	1.13787i
$563$	−17.4833	+	34.3129i	−0.736833	+	1.44612i	0.152237	+	0.988344i	$0.451352\pi$
$563$	−17.4833	+	34.3129i	−0.736833	+	1.44612i	−0.889070	+	0.457772i	$0.848648\pi$
$564$	−2.73137	−	5.36062i	−0.115012	−	0.225723i
$565$	−25.6973	+	33.7564i	−1.08109	+	1.42014i
$566$	−0.576677	−	0.293832i	−0.0242396	−	0.0123507i
$567$	−4.97939	+	3.61774i	−0.209115	+	0.151931i
$568$	3.06913	−	3.06913i	0.128778	−	0.128778i
$569$	−15.2310	+	11.0660i	−0.638518	+	0.463910i	−0.859341	−	0.511404i	$-0.829126\pi$
$569$	−15.2310	+	11.0660i	−0.638518	+	0.463910i	0.220823	+	0.975314i	$0.429126\pi$
$570$	8.12306	+	4.37024i	0.340238	+	0.183049i
$571$	18.4114	−	25.3411i	0.770492	−	1.06049i	−0.225776	−	0.974179i	$-0.572492\pi$
$571$	18.4114	−	25.3411i	0.770492	−	1.06049i	0.996268	−	0.0863118i	$-0.0275081\pi$
$572$	−4.39536	−	9.37709i	−0.183779	−	0.392076i
$573$	2.39796	+	4.70626i	0.100176	+	0.196607i
$574$	−21.6488	+	21.6488i	−0.903603	+	0.903603i
$575$	9.62268	−	1.08601i	0.401294	−	0.0452898i
$576$		−	2.16320i		−	0.0901334i
$577$	23.4669	+	7.62487i	0.976941	+	0.317427i	0.753615	−	0.657316i	$-0.228308\pi$
$577$	23.4669	+	7.62487i	0.976941	+	0.317427i	0.223326	+	0.974744i	$0.428308\pi$
$578$	−10.6274	−	7.72129i	−0.442044	−	0.321163i
$579$	1.76623	+	11.1515i	0.0734020	+	0.463442i
$580$	1.07065	+	7.89838i	0.0444563	+	0.327963i
$581$	−27.4703	+	19.9583i	−1.13966	+	0.828011i
$582$	4.87455	−	4.87455i	0.202057	−	0.202057i
$583$	−13.1275	−	18.0684i	−0.543685	−	0.748318i
$584$	3.40609	+	10.4829i	0.140945	+	0.433784i
$585$	11.6321	+	12.9945i	0.480930	+	0.537256i
$586$	1.36186	−	4.19137i	0.0562579	−	0.173144i
$587$	12.0870	−	3.92731i	0.498885	−	0.162097i	−0.0487566	−	0.998811i	$-0.515526\pi$
$587$	12.0870	−	3.92731i	0.498885	−	0.162097i	0.547641	+	0.836713i	$0.315526\pi$
$588$	−0.857439	−	0.436887i	−0.0353602	−	0.0180169i
$589$	−11.1534	+	34.3267i	−0.459569	+	1.41441i
$590$	14.7841	+	21.3353i	0.608650	+	0.878361i
$591$	−2.08303	+	4.08818i	−0.0856844	+	0.168165i
$592$	−7.04429	+	5.11798i	−0.289519	+	0.210348i
$593$			1.92359i			0.0789924i	0.999220	+	0.0394962i	$0.0125753\pi$
$593$			1.92359i			0.0789924i	−0.999220	+	0.0394962i	$0.987425\pi$
$594$	−7.97395	−	10.9752i	−0.327175	−	0.450318i
$595$	32.8786	+	11.5013i	1.34789	+	0.471508i
$596$	7.19085	−	1.13892i	0.294549	−	0.0466520i
$597$	−5.19482	+	0.822779i	−0.212610	+	0.0336741i
$598$	−5.09760	+	4.77260i	−0.208456	+	0.195166i
$599$			5.17836i			0.211582i	0.994388	+	0.105791i	$0.0337375\pi$
$599$			5.17836i			0.211582i	−0.994388	+	0.105791i	$0.966263\pi$
$600$	1.89232	+	4.16403i	0.0772535	+	0.169996i
$601$	11.2655			0.459528			0.229764	−	0.973246i	$-0.426205\pi$
$601$	11.2655			0.459528			0.229764	+	0.973246i	$0.426205\pi$
$602$	11.1432	+	21.8697i	0.454161	+	0.891341i
$603$	−5.04332	−	3.66419i	−0.205380	−	0.149217i
$604$	7.23763	−	1.14633i	0.294495	−	0.0466434i
$605$	−4.25000	−	4.44434i	−0.172787	−	0.180688i
$606$	−0.283400	+	1.78932i	−0.0115123	+	0.0726861i
$607$	−17.7900	−	17.7900i	−0.722072	−	0.722072i	0.246955	−	0.969027i	$-0.420570\pi$
$607$	−17.7900	−	17.7900i	−0.722072	−	0.722072i	−0.969027	+	0.246955i	$0.920570\pi$
$608$	4.45396	+	0.705437i	0.180632	+	0.0286093i
$609$	−4.20065	+	8.24423i	−0.170219	+	0.334073i
$610$	−11.6621	−	12.1954i	−0.472186	−	0.493777i
$611$	23.7006	+	0.780407i	0.958826	+	0.0315719i
$612$	−5.39123	+	10.5809i	−0.217928	+	0.427707i
$613$	7.36955	+	22.6811i	0.297653	+	0.916083i	0.982317	+	0.187224i	$0.0599490\pi$
$613$	7.36955	+	22.6811i	0.297653	+	0.916083i	−0.684664	+	0.728859i	$0.740051\pi$
$614$	1.23731	+	0.402027i	0.0499338	+	0.0162245i
$615$	19.4353	+	10.4563i	0.783706	+	0.421637i
$616$	−3.70018	+	7.26202i	−0.149085	+	0.292595i
$617$	14.4315	+	19.8633i	0.580991	+	0.799666i	0.993804	−	0.111150i	$-0.0354535\pi$
$617$	14.4315	+	19.8633i	0.580991	+	0.799666i	−0.412812	+	0.910816i	$0.635454\pi$
$618$		−	10.8882i		−	0.437986i
$619$	6.01060	+	0.951986i	0.241586	+	0.0382635i	0.276053	−	0.961142i	$-0.410973\pi$
$619$	6.01060	+	0.951986i	0.241586	+	0.0382635i	−0.0344669	+	0.999406i	$0.510973\pi$
$620$	−14.7106	+	10.1935i	−0.590791	+	0.409382i
$621$	−5.37679	+	7.40052i	−0.215763	+	0.296972i
$622$	−19.7094	−	14.3197i	−0.790275	−	0.574168i
$623$	18.2208	−	9.28395i	0.730000	−	0.371954i
$624$	−2.88788	−	1.59327i	−0.115608	−	0.0637820i
$625$	18.8328	+	16.4415i	0.753314	+	0.657661i
$626$	6.85937	+	6.85937i	0.274155	+	0.274155i
$627$	10.5571	−	5.37909i	0.421608	−	0.214820i
$628$	−1.10628	−	6.98475i	−0.0441452	−	0.278722i
$629$	47.2111	−	7.47750i	1.88243	−	0.298148i
$630$	2.44957	−	13.5053i	0.0975931	−	0.538065i
$631$	−5.35506	+	33.8105i	−0.213181	+	1.34597i	0.616332	+	0.787487i	$0.288618\pi$
$631$	−5.35506	+	33.8105i	−0.213181	+	1.34597i	−0.829513	+	0.558488i	$0.811382\pi$
$632$	−5.16288			−0.205368
$633$	−2.01337	+	12.7119i	−0.0800243	+	0.505254i
$634$	1.81172	+	5.57590i	0.0719526	+	0.221447i
$635$	−29.5944	+	8.88976i	−1.17442	+	0.352779i
$636$	−6.76480	−	2.19802i	−0.268242	−	0.0871570i
$637$	3.14032	−	2.12728i	0.124424	−	0.0842858i
$638$	9.12248	+	4.64813i	0.361162	+	0.184021i
$639$	4.26259	+	8.36580i	0.168625	+	0.330946i
$640$	1.54541	+	1.61608i	0.0610878	+	0.0638810i
$641$	25.0372	−	8.13508i	0.988910	−	0.321316i	0.230484	−	0.973076i	$-0.425969\pi$
$641$	25.0372	−	8.13508i	0.988910	−	0.321316i	0.758425	+	0.651760i	$0.225969\pi$
$642$	−7.14353	−	9.83222i	−0.281933	−	0.388047i
$643$	−11.6395			−0.459018			−0.229509	−	0.973307i	$-0.573712\pi$
$643$	−11.6395			−0.459018			−0.229509	+	0.973307i	$0.573712\pi$
$644$	5.42808	+	0.859723i	0.213896	+	0.0338778i
$645$	12.7874	−	12.2283i	0.503503	−	0.481487i
$646$	−20.0276	−	14.5509i	−0.787974	−	0.572497i
$647$	42.5050	−	6.73213i	1.67104	−	0.264667i	0.752098	−	0.659051i	$-0.229042\pi$
$647$	42.5050	−	6.73213i	1.67104	−	0.264667i	0.918946	+	0.394384i	$0.129042\pi$
$648$	2.06288	+	0.670269i	0.0810375	+	0.0263307i
$649$	33.3422			1.30880
$650$	−17.9735	−	1.39776i	−0.704978	−	0.0548245i
$651$	−20.7760			−0.814276
$652$	−2.62557	−	0.853099i	−0.102825	−	0.0334099i
$653$	−41.6619	+	6.59860i	−1.63036	+	0.258223i	−0.903507	−	0.428574i	$-0.859016\pi$
$653$	−41.6619	+	6.59860i	−1.63036	+	0.258223i	−0.726850	+	0.686797i	$0.759016\pi$
$654$	−10.3224	−	7.49968i	−0.403639	−	0.293261i
$655$	10.6477	+	22.1050i	0.416041	+	0.863715i
$656$	10.6566	+	1.68783i	0.416069	+	0.0658988i
$657$	−23.8435			−0.930224
$658$	−10.9697	−	15.0985i	−0.427643	−	0.588600i
$659$	48.6915	−	15.8208i	1.89675	−	0.616292i	0.925192	−	0.379501i	$-0.123904\pi$
$659$	48.6915	−	15.8208i	1.89675	−	0.616292i	0.971560	−	0.236792i	$-0.0760958\pi$
$660$	5.78085	+	1.04852i	0.225019	+	0.0408136i
$661$	15.2421	+	29.9144i	0.592851	+	1.16354i	0.971288	+	0.237908i	$0.0764617\pi$
$661$	15.2421	+	29.9144i	0.592851	+	1.16354i	−0.378437	+	0.925627i	$0.623538\pi$
$662$	13.5695	+	6.91398i	0.527392	+	0.268719i
$663$	10.1547	+	14.9905i	0.394376	+	0.582184i
$664$	11.3805	+	3.69774i	0.441648	+	0.143500i
$665$	27.0082	+	9.44777i	1.04733	+	0.366369i
$666$	−5.82048	−	17.9136i	−0.225539	−	0.694138i
$667$	1.07998	−	6.81870i	0.0418168	−	0.264021i
$668$	23.7706			0.919714
$669$	−1.17653	+	7.42831i	−0.0454873	+	0.287195i
$670$	6.38547	−	0.865570i	0.246692	−	0.0334399i
$671$	−21.4081	+	3.39071i	−0.826451	+	0.130897i
$672$	0.406064	+	2.56379i	0.0156643	+	0.0989003i
$673$	−33.7255	+	17.1840i	−1.30002	+	0.662395i	−0.960520	−	0.278210i	$-0.910259\pi$
$673$	−33.7255	+	17.1840i	−1.30002	+	0.662395i	−0.339503	+	0.940605i	$0.610259\pi$
$674$	−2.98696	−	2.98696i	−0.115054	−	0.115054i
$675$	−23.4667	+	2.64844i	−0.903232	+	0.101938i
$676$	10.9971	−	6.93279i	0.422966	−	0.266646i
$677$	−34.6483	+	17.6542i	−1.33164	+	0.678505i	−0.967508	−	0.252842i	$-0.918635\pi$
$677$	−34.6483	+	17.6542i	−1.33164	+	0.678505i	−0.364133	+	0.931347i	$0.618635\pi$
$678$	14.0411	+	10.2015i	0.539245	+	0.391785i
$679$	12.5692	−	17.3001i	0.482363	−	0.663916i
$680$	−3.53143	−	11.7563i	−0.135424	−	0.450833i
$681$	8.85501	+	1.40250i	0.339325	+	0.0537437i
$682$			22.9892i			0.880304i
$683$	12.4996	+	17.2043i	0.478286	+	0.658304i	0.978174	−	0.207786i	$-0.0666257\pi$
$683$	12.4996	+	17.2043i	0.478286	+	0.658304i	−0.499889	+	0.866090i	$0.666626\pi$
$684$	−4.42863	+	8.69168i	−0.169333	+	0.332335i
$685$	40.5436	−	5.49580i	1.54909	−	0.209984i
$686$	16.0520	+	5.21562i	0.612869	+	0.199133i
$687$	4.31292	+	13.2738i	0.164548	+	0.506428i
$688$	3.92696	−	7.70709i	0.149714	−	0.293830i
$689$	20.4658	−	19.1610i	0.779685	−	0.729976i
$690$	−0.532140	−	3.92569i	−0.0202582	−	0.149449i
$691$	−16.0739	+	31.5467i	−0.611479	+	1.20009i	0.352923	+	0.935652i	$0.385188\pi$
$691$	−16.0739	+	31.5467i	−0.611479	+	1.20009i	−0.964402	+	0.264442i	$0.914812\pi$
$692$	19.7273	+	3.12450i	0.749919	+	0.118776i
$693$	−12.4669	−	12.4669i	−0.473578	−	0.473578i
$694$	3.14858	−	19.8794i	0.119518	−	0.754610i
$695$	−12.2805	+	22.8260i	−0.465826	+	0.865840i
$696$	3.22061	−	0.510094i	0.122077	−	0.0193351i
$697$	−47.9180	−	34.8145i	−1.81503	−	1.31869i
$698$	4.67032	+	9.16602i	0.176774	+	0.346939i
$699$	−8.17611			−0.309249
$700$	7.81832	+	11.8395i	0.295505	+	0.447491i
$701$			27.8404i			1.05152i	0.850634	+	0.525758i	$0.176218\pi$
$701$			27.8404i			1.05152i	−0.850634	+	0.525758i	$0.823782\pi$
$702$	12.4314	−	11.6388i	0.469194	−	0.439280i
$703$	38.7816	−	6.14240i	1.46268	−	0.231665i
$704$	2.83691	−	0.449322i	0.106920	−	0.0169344i
$705$	−8.14871	+	10.7043i	−0.306898	+	0.403147i
$706$	4.70163	+	6.47124i	0.176948	+	0.243548i
$707$			5.61964i			0.211348i
$708$	8.59088	−	6.24164i	0.322865	−	0.234575i
$709$	−10.1910	+	20.0010i	−0.382732	+	0.751154i	−0.999348	−	0.0361101i	$-0.988503\pi$
$709$	−10.1910	+	20.0010i	−0.382732	+	0.751154i	0.616616	+	0.787264i	$0.288503\pi$
$710$	−9.16109	−	3.20466i	−0.343810	−	0.120269i
$711$	3.45121	−	10.6217i	0.129430	−	0.398346i
$712$	−6.42119	−	3.27176i	−0.240644	−	0.122614i
$713$	14.7428	−	4.79023i	0.552123	−	0.179396i
$714$	4.40341	−	13.5523i	0.164794	−	0.507182i
$715$	−14.6253	+	17.9539i	−0.546957	+	0.671440i
$716$	2.80906	+	8.64539i	0.104979	+	0.323094i
$717$	3.85610	+	5.30747i	0.144009	+	0.198211i
$718$	−9.22345	+	9.22345i	−0.344216	+	0.344216i
$719$	1.96053	−	1.42441i	0.0731154	−	0.0531214i	−0.550627	−	0.834751i	$-0.685611\pi$
$719$	1.96053	−	1.42441i	0.0731154	−	0.0531214i	0.623743	+	0.781630i	$0.285611\pi$
$720$	−4.35785	+	2.09912i	−0.162407	+	0.0782298i
$721$	−5.28357	−	33.3591i	−0.196770	−	1.24236i
$722$	−1.08034	−	0.784914i	−0.0402061	−	0.0292115i
$723$	11.0074	+	3.57653i	0.409371	+	0.133013i
$724$		−	15.7381i		−	0.584901i
$725$	14.8727	−	9.82129i	0.552357	−	0.364754i
$726$	−1.77886	+	1.77886i	−0.0660195	+	0.0660195i
$727$	2.17049	+	4.25982i	0.0804988	+	0.157988i	0.927747	−	0.373209i	$-0.121743\pi$
$727$	2.17049	+	4.25982i	0.0804988	+	0.157988i	−0.847249	+	0.531197i	$0.821743\pi$
$728$	−9.62106	−	3.48010i	−0.356580	−	0.128981i
$729$	4.86077	−	6.69027i	0.180028	−	0.247788i
$730$	17.8129	−	17.0340i	0.659286	−	0.630458i
$731$	−38.4160	+	27.9108i	−1.42087	+	1.03232i
$732$	−4.88123	+	4.88123i	−0.180416	+	0.180416i
$733$	−37.5054	+	27.2492i	−1.38529	+	1.00647i	−0.388929	+	0.921268i	$0.627155\pi$
$733$	−37.5054	+	27.2492i	−1.38529	+	1.00647i	−0.996363	+	0.0852062i	$0.972845\pi$
$734$	14.8736	+	7.57849i	0.548995	+	0.279727i
$735$	−0.0480847	+	2.15129i	−0.00177363	+	0.0793515i
$736$	−0.879268	−	1.72566i	−0.0324103	−	0.0636087i
$737$	3.75780	−	7.37510i	0.138420	−	0.271665i
$738$	−10.5960	+	20.7957i	−0.390043	+	0.765502i
$739$	4.65339	−	2.37102i	0.171178	−	0.0872194i	−0.366302	−	0.930496i	$-0.619376\pi$
$739$	4.65339	−	2.37102i	0.171178	−	0.0872194i	0.537480	+	0.843276i	$0.319376\pi$
$740$	17.1460	+	9.22461i	0.630299	+	0.339104i
$741$	8.34160	+	12.3140i	0.306436	+	0.452365i
$742$	−21.7926	−	3.45161i	−0.800032	−	0.126713i
$743$	−2.97827			−0.109262			−0.0546310	−	0.998507i	$-0.517398\pi$
$743$	−2.97827			−0.109262			−0.0546310	+	0.998507i	$0.517398\pi$
$744$	4.30357	+	5.92336i	0.157777	+	0.217161i
$745$	−9.27225	−	13.3811i	−0.339709	−	0.490244i
$746$	−3.92583	−	24.7867i	−0.143735	−	0.907506i
$747$	−15.2149	+	20.9415i	−0.556684	+	0.766210i
$748$	−14.9960	−	4.87250i	−0.548309	−	0.178156i
$749$	−26.6575	−	26.6575i	−0.974045	−	0.974045i
$750$	6.55233	−	7.85283i	0.239257	−	0.286745i
$751$		−	8.11779i		−	0.296222i	−0.988971	−	0.148111i	$-0.952681\pi$
$751$		−	8.11779i		−	0.296222i	0.988971	−	0.148111i	$-0.0473194\pi$
$752$	−2.03239	+	6.25504i	−0.0741135	+	0.228098i
$753$	−2.36704	−	14.9449i	−0.0862598	−	0.544623i
$754$	−4.37167	+	12.0859i	−0.159207	+	0.440142i
$755$	−9.33257	−	13.4681i	−0.339647	−	0.490155i
$756$	−13.2374	−	2.09659i	−0.481438	−	0.0762523i
$757$	−19.2610	−	19.2610i	−0.700052	−	0.700052i	0.264370	−	0.964421i	$-0.414836\pi$
$757$	−19.2610	−	19.2610i	−0.700052	−	0.700052i	−0.964421	+	0.264370i	$0.914836\pi$
$758$	−27.8728	−	4.41462i	−1.01239	−	0.160346i
$759$	−4.53410	−	2.31024i	−0.164577	−	0.0838564i
$760$	−2.90090	−	9.65721i	−0.105227	−	0.350304i
$761$	8.48354	+	16.6499i	0.307528	+	0.603558i	0.992109	−	0.125379i	$-0.0400148\pi$
$761$	8.48354	+	16.6499i	0.307528	+	0.603558i	−0.684581	+	0.728937i	$0.740015\pi$
$762$	3.90640	+	12.0227i	0.141514	+	0.435535i
$763$	−35.2652	−	17.9685i	−1.27668	−	0.650503i
$764$	1.78429	−	5.49149i	0.0645535	−	0.198675i
$765$	26.5471	+	0.593370i	0.959814	+	0.0214533i
$766$	−16.0834	+	5.22581i	−0.581117	+	0.188816i
$767$	5.18346	+	41.5322i	0.187164	+	1.49964i
$768$	0.646838	−	0.646838i	0.0233408	−	0.0233408i
$769$	−0.842276	+	5.31792i	−0.0303733	+	0.191769i	−0.998210	−	0.0598110i	$-0.980950\pi$
$769$	−0.842276	+	5.31792i	−0.0303733	+	0.191769i	0.967836	+	0.251580i	$0.0809502\pi$
$770$	18.2202	+	0.407250i	0.656610	+	0.0146763i
$771$	−2.67618	+	3.68345i	−0.0963803	+	0.132656i
$772$	7.25475	−	9.98531i	0.261104	−	0.359379i
$773$	−10.3093	+	31.7286i	−0.370798	+	1.14120i	0.575472	+	0.817821i	$0.304818\pi$
$773$	−10.3093	+	31.7286i	−0.370798	+	1.14120i	−0.946270	+	0.323377i	$0.895182\pi$
$774$	13.2310	+	13.2310i	0.475577	+	0.475577i
$775$	34.8101	+	19.7435i	1.25042	+	0.709206i
$776$	−7.53597			−0.270525
$777$	10.2610	+	20.1383i	0.368110	+	0.722457i
$778$	−5.35471	+	7.37012i	−0.191976	+	0.264232i
$779$	−39.3623	−	28.5984i	−1.41030	−	1.02464i
$780$	−0.407367	+	7.36383i	−0.0145861	+	0.263667i
$781$	−10.0858	+	7.32780i	−0.360900	+	0.262209i
$782$			10.6321i			0.380203i
$783$	−2.63372	+	16.6286i	−0.0941214	+	0.594259i
$784$	0.325083	+	1.00050i	0.0116101	+	0.0357322i
$785$	−12.9975	+	9.00649i	−0.463902	+	0.321455i
$786$	8.94350	−	4.55694i	0.319004	−	0.162541i
$787$	2.95133	+	9.08325i	0.105203	+	0.323783i	0.989778	−	0.142616i	$-0.0455513\pi$
$787$	2.95133	+	9.08325i	0.105203	+	0.323783i	−0.884575	+	0.466399i	$0.845551\pi$
$788$	4.77028	−	1.54996i	0.169934	−	0.0552150i
$789$	−25.7767	−	8.37536i	−0.917675	−	0.298171i
$790$	5.00995	+	10.4008i	0.178246	+	0.370044i
$791$	47.9695	+	24.4417i	1.70560	+	0.869046i
$792$	−0.971973	+	6.13679i	−0.0345376	+	0.218062i
$793$	−7.55175	−	26.1396i	−0.268170	−	0.928243i
$794$	1.81126	+	2.49298i	0.0642790	+	0.0884725i
$795$	2.13643	+	15.7609i	0.0757714	+	0.558980i
$796$	4.65155	+	3.37955i	0.164870	+	0.119785i
$797$	2.83024	−	0.448267i	0.100252	−	0.0158784i	−0.106107	−	0.994355i	$-0.533839\pi$
$797$	2.83024	−	0.448267i	0.100252	−	0.0158784i	0.206359	+	0.978476i	$0.433839\pi$
$798$	3.61719	−	11.1326i	0.128047	−	0.394088i
$799$	25.5302	−	25.5302i	0.903192	−	0.903192i
$800$	1.75601	−	4.68150i	0.0620844	−	0.165516i
$801$	11.0234	−	11.0234i	0.389493	−	0.389493i
$802$	28.1579	−	14.3472i	0.994290	−	0.506616i
$803$	−4.95257	−	31.2693i	−0.174772	−	1.10347i
$804$	−0.412387	−	2.60371i	−0.0145438	−	0.0918258i
$805$	−3.53535	−	11.7693i	−0.124605	−	0.414814i
$806$	−28.6362	+	3.57396i	−1.00867	+	0.125887i
$807$	−8.29513	−	8.29513i	−0.292003	−	0.292003i
$808$	1.60219	−	1.16406i	0.0563649	−	0.0409515i
$809$	−26.9681	+	8.76246i	−0.948147	+	0.308072i	−0.741962	−	0.670442i	$-0.766105\pi$
$809$	−26.9681	+	8.76246i	−0.948147	+	0.308072i	−0.206184	+	0.978513i	$0.566105\pi$
$810$	−0.651490	−	4.80616i	−0.0228910	−	0.168871i
$811$	8.26370	−	4.21057i	0.290178	−	0.147853i	−0.302842	−	0.953041i	$-0.597935\pi$
$811$	8.26370	−	4.21057i	0.290178	−	0.147853i	0.593020	+	0.805188i	$0.297935\pi$
$812$	9.61978	−	3.12565i	0.337588	−	0.109689i
$813$	−15.6255	+	5.07704i	−0.548012	+	0.178060i
$814$	22.2836	−	11.3541i	0.781040	−	0.397960i
$815$	0.829196	+	6.11714i	0.0290455	+	0.214274i
$816$	−4.77597	+	1.55181i	−0.167192	+	0.0543241i
$817$	−31.5568	+	22.9274i	−1.10403	+	0.802128i
$818$	−13.2870	−	13.2870i	−0.464568	−	0.464568i
$819$	13.5911	−	17.4673i	0.474910	−	0.610358i
$820$	−6.94069	−	23.1059i	−0.242380	−	0.806892i
$821$	3.29860	+	20.8265i	0.115122	+	0.726851i	0.975956	+	0.217966i	$0.0699421\pi$
$821$	3.29860	+	20.8265i	0.115122	+	0.726851i	−0.860835	+	0.508885i	$0.830058\pi$
$822$	−2.61839	−	16.5318i	−0.0913267	−	0.576614i
$823$	−3.49239	+	1.77946i	−0.121737	+	0.0620281i	−0.513798	−	0.857911i	$-0.671762\pi$
$823$	−3.49239	+	1.77946i	−0.121737	+	0.0620281i	0.392061	+	0.919939i	$0.371762\pi$
$824$	−8.41644	+	8.41644i	−0.293201	+	0.293201i
$825$	−3.49734	−	12.6632i	−0.121762	−	0.440876i
$826$	23.2919	−	23.2919i	0.810430	−	0.810430i
$827$	0.651560	−	2.00529i	0.0226569	−	0.0697309i	−0.939089	−	0.343675i	$-0.888328\pi$
$827$	0.651560	−	2.00529i	0.0226569	−	0.0697309i	0.961746	+	0.273944i	$0.0883282\pi$
$828$	4.13801	−	0.655396i	0.143806	−	0.0227766i
$829$	−22.3922	−	16.2689i	−0.777712	−	0.565041i	0.126579	−	0.991956i	$-0.459600\pi$
$829$	−22.3922	−	16.2689i	−0.777712	−	0.565041i	−0.904291	+	0.426916i	$0.859600\pi$
$830$	−3.59413	−	26.5146i	−0.124754	−	0.920335i
$831$	14.2995	+	19.6816i	0.496044	+	0.682746i
$832$	1.00072	+	3.46389i	0.0346938	+	0.120089i
$833$	0.903418	−	5.70396i	0.0313016	−	0.197630i
$834$	9.44798	+	4.81398i	0.327157	+	0.166695i
$835$	−23.0665	−	47.8869i	−0.798250	−	1.65719i
$836$	−12.3185	−	4.00252i	−0.426044	−	0.138430i
$837$	−35.9531	+	11.6819i	−1.24272	+	0.403784i
$838$	−2.35554	−	7.24962i	−0.0813709	−	0.250434i
$839$	37.4509	−	19.0822i	1.29295	−	0.658791i	0.334055	−	0.942554i	$-0.391583\pi$
$839$	37.4509	−	19.0822i	1.29295	−	0.658791i	0.958894	+	0.283763i	$0.0915828\pi$
$840$	4.77081	−	3.30588i	0.164609	−	0.114064i
$841$	5.03508	+	15.4964i	0.173623	+	0.534358i
$842$	3.32087	−	20.9672i	0.114445	−	0.722576i
$843$		−	27.6942i		−	0.953840i
$844$	11.3825	−	8.26988i	0.391802	−	0.284661i
$845$	−24.6377	−	15.4267i	−0.847564	−	0.530693i
$846$	−11.5101	−	8.36256i	−0.395725	−	0.287511i
$847$	−4.58686	+	6.31327i	−0.157606	+	0.216927i
$848$	3.53008	+	6.92817i	0.121223	+	0.237914i
$849$	0.592056			0.0203193
$850$	−20.2567	+	18.5223i	−0.694798	+	0.635308i
$851$	−11.9245	−	11.9245i	−0.408766	−	0.408766i
$852$	−1.22694	+	3.77613i	−0.0420342	+	0.129368i
$853$	−17.8452	+	24.5618i	−0.611008	+	0.840980i	−0.996660	−	0.0816642i	$-0.973977\pi$
$853$	−17.8452	+	24.5618i	−0.611008	+	0.840980i	0.385652	+	0.922644i	$0.373977\pi$
$854$	−12.5865	+	17.3238i	−0.430700	+	0.592808i
$855$	21.8072	+	0.487424i	0.745790	+	0.0166696i
$856$	−2.07834	+	13.1221i	−0.0710361	+	0.448504i
$857$	4.28926	−	4.28926i	0.146518	−	0.146518i	−0.630042	−	0.776561i	$-0.716962\pi$
$857$	4.28926	−	4.28926i	0.146518	−	0.146518i	0.776561	+	0.630042i	$0.216962\pi$
$858$	7.47676	+	5.81755i	0.255252	+	0.198608i
$859$	28.8121	−	9.36162i	0.983056	−	0.319414i	0.226981	−	0.973899i	$-0.427114\pi$
$859$	28.8121	−	9.36162i	0.983056	−	0.319414i	0.756075	+	0.654485i	$0.227114\pi$
$860$	−19.3369	−	0.432209i	−0.659382	−	0.0147382i
$861$	8.65449	−	26.6358i	0.294944	−	0.907745i
$862$	−2.86262	−	1.45858i	−0.0975012	−	0.0496793i
$863$	−3.93140	−	12.0996i	−0.133826	−	0.411876i	0.861579	−	0.507623i	$-0.169476\pi$
$863$	−3.93140	−	12.0996i	−0.133826	−	0.411876i	−0.995406	+	0.0957477i	$0.969476\pi$
$864$	2.14426	+	4.20834i	0.0729490	+	0.143171i
$865$	−12.8485	−	42.7733i	−0.436863	−	1.45434i
$866$	21.3260	+	10.8661i	0.724687	+	0.369246i
$867$	11.8687	+	1.87981i	0.403081	+	0.0638418i
$868$	16.0597	+	16.0597i	0.545100	+	0.545100i
$869$	14.6466	+	2.31979i	0.496852	+	0.0786936i
$870$	−4.15281	−	5.99305i	−0.140794	−	0.203183i
$871$	9.77087	+	3.53429i	0.331073	+	0.119755i
$872$	2.18195	+	13.7763i	0.0738903	+	0.466525i
$873$	5.03753	−	15.5039i	0.170495	−	0.524729i
$874$			8.73375i			0.295423i
$875$	16.2644	−	27.2391i	0.549837	−	0.920850i
$876$	−7.12967	−	7.12967i	−0.240889	−	0.240889i
$877$	10.3321	+	3.35711i	0.348890	+	0.113361i	0.478219	−	0.878240i	$-0.341282\pi$
$877$	10.3321	+	3.35711i	0.348890	+	0.113361i	−0.129329	+	0.991602i	$0.541282\pi$
$878$	20.5811	−	28.3274i	0.694577	−	0.956003i
$879$	0.630657	+	3.98181i	0.0212715	+	0.134303i
$880$	−3.65805	−	5.27904i	−0.123313	−	0.177956i
$881$	−1.04310	−	1.43571i	−0.0351431	−	0.0483703i	0.791084	−	0.611708i	$-0.209517\pi$
$881$	−1.04310	−	1.43571i	−0.0351431	−	0.0483703i	−0.826227	+	0.563337i	$0.809517\pi$
$882$	−2.27567			−0.0766257
$883$	−16.1476	−	2.55753i	−0.543410	−	0.0860678i	−0.121306	−	0.992615i	$-0.538708\pi$
$883$	−16.1476	−	2.55753i	−0.543410	−	0.0860678i	−0.422104	+	0.906547i	$0.638708\pi$
$884$	3.73804	−	19.4370i	0.125724	−	0.653738i
$885$	−20.9104	−	11.2499i	−0.702896	−	0.378161i
$886$	13.2655	−	6.75912i	0.445664	−	0.227077i
$887$	−11.2266	+	22.0335i	−0.376953	+	0.739811i	−0.999070	−	0.0431127i	$-0.986273\pi$
$887$	−11.2266	+	22.0335i	−0.376953	+	0.739811i	0.622118	+	0.782924i	$0.286273\pi$
$888$	3.61607	−	7.09694i	0.121347	−	0.238158i
$889$	17.8025	+	34.9395i	0.597078	+	1.17183i
$890$	−0.360096	+	16.1106i	−0.0120704	+	0.540028i
$891$	−5.55102	−	2.82839i	−0.185966	−	0.0947545i
$892$	6.65146	−	4.83257i	0.222707	−	0.161806i
$893$	20.9718	−	20.9718i	0.701793	−	0.701793i
$894$	−5.38802	+	3.91462i	−0.180202	+	0.130925i
$895$	14.6906	−	14.0483i	0.491053	−	0.469582i
$896$	1.66790	−	2.29567i	0.0557207	−	0.0766929i
$897$	2.17283	−	6.00698i	0.0725487	−	0.200567i
$898$	−11.5936	−	22.7538i	−0.386884	−	0.759303i
$899$	20.1740	−	20.1740i	0.672840	−	0.672840i
$900$	8.45753	+	6.74211i	0.281918	+	0.224737i
$901$		−	42.6857i		−	1.42207i
$902$	−29.4733	−	9.57644i	−0.981352	−	0.318861i
$903$	−18.1648	−	13.1975i	−0.604486	−	0.439184i
$904$	−2.96801	−	18.7393i	−0.0987145	−	0.623259i
$905$	−31.7049	+	15.2719i	−1.05391	+	0.507655i
$906$	−5.42307	+	3.94009i	−0.180169	+	0.130901i
$907$	18.7108	−	18.7108i	0.621283	−	0.621283i	−0.324577	−	0.945859i	$-0.605222\pi$
$907$	18.7108	−	18.7108i	0.621283	−	0.621283i	0.945859	+	0.324577i	$0.105222\pi$
$908$	−5.76072	−	7.92895i	−0.191176	−	0.263132i
$909$	1.32384	+	4.07437i	0.0439091	+	0.135138i
$910$	2.32527	+	22.7590i	0.0770820	+	0.754454i
$911$	11.6896	−	35.9767i	0.387292	−	1.19196i	−0.547512	−	0.836798i	$-0.684425\pi$
$911$	11.6896	−	35.9767i	0.387292	−	1.19196i	0.934804	−	0.355165i	$-0.115575\pi$
$912$	−3.92322	+	1.27473i	−0.129911	+	0.0422106i
$913$	−30.6238	−	15.6036i	−1.01350	−	0.516404i
$914$	−4.96673	+	15.2860i	−0.164285	+	0.505617i
$915$	14.5701	+	5.09678i	0.481672	+	0.168494i
$916$	6.92669	−	13.5944i	0.228864	−	0.449171i
$917$	25.1898	−	18.3015i	0.831841	−	0.604368i
$918$		−	25.9283i		−	0.855762i
$919$	−13.4237	−	18.4761i	−0.442805	−	0.609469i	0.528027	−	0.849227i	$-0.322932\pi$
$919$	−13.4237	−	18.4761i	−0.442805	−	0.609469i	−0.970833	+	0.239758i	$0.922932\pi$
$920$	−2.62319	+	3.44586i	−0.0864839	+	0.113607i
$921$	−1.17545	+	0.186173i	−0.0387323	+	0.00613460i
$922$	13.6378	−	2.16001i	0.449136	−	0.0711362i
$923$	−10.6957	−	11.4241i	−0.352054	−	0.376028i
$924$		−	7.45568i		−	0.245274i
$925$	1.94523	−	43.4926i	0.0639587	−	1.43003i
$926$	10.6570			0.350212
$927$	−11.6893	−	22.9415i	−0.383926	−	0.753496i
$928$	−2.88380	−	2.09520i	−0.0946653	−	0.0687783i
$929$	−0.558310	+	0.0884277i	−0.0183176	+	0.00290122i	−0.165587	−	0.986195i	$-0.552952\pi$
$929$	−0.558310	+	0.0884277i	−0.0183176	+	0.00290122i	0.147269	+	0.989096i	$0.452952\pi$
$930$	7.75674	−	14.4176i	0.254353	−	0.472772i
$931$	0.742113	−	4.68552i	0.0243218	−	0.153562i
$932$	6.32006	+	6.32006i	0.207020	+	0.207020i
$933$	22.0113	+	3.48625i	0.720619	+	0.114135i
$934$	−8.89283	+	17.4532i	−0.290982	+	0.571085i
$935$	4.73598	+	34.9382i	0.154883	+	1.14260i
$936$	−7.79531	−	0.256681i	−0.254798	−	0.00838989i
$937$	−14.0997	+	27.6723i	−0.460618	+	0.904013i	0.537534	+	0.843242i	$0.319356\pi$
$937$	−14.0997	+	27.6723i	−0.460618	+	0.904013i	−0.998152	+	0.0607711i	$0.980644\pi$
$938$	−2.52695	−	7.77714i	−0.0825077	−	0.253933i
$939$	−8.43949	−	2.74216i	−0.275412	−	0.0894869i
$940$	14.5732	−	1.97544i	0.475326	−	0.0644318i
$941$	2.11837	−	4.15754i	0.0690569	−	0.135532i	−0.853897	−	0.520441i	$-0.825767\pi$
$941$	2.11837	−	4.15754i	0.0690569	−	0.135532i	0.922954	+	0.384910i	$0.125767\pi$
$942$	3.80242	+	5.23359i	0.123890	+	0.170519i
$943$			20.8964i			0.680480i
$944$	−11.4654	−	1.81594i	−0.373167	−	0.0591038i
$945$	8.62159	+	28.7016i	0.280460	+	0.933665i
$946$	−14.6034	+	20.0998i	−0.474797	+	0.653502i
$947$	−8.66563	−	6.29595i	−0.281595	−	0.204591i	0.438018	−	0.898966i	$-0.355681\pi$
$947$	−8.66563	−	6.29595i	−0.281595	−	0.204591i	−0.719613	+	0.694375i	$0.755681\pi$
$948$	4.20807	−	2.14412i	0.136672	−	0.0696378i
$949$	38.1802	−	11.0303i	1.23938	−	0.358058i
$950$	−16.6398	+	15.2151i	−0.539868	+	0.493644i
$951$	−3.79232	−	3.79232i	−0.122974	−	0.122974i
$952$	−13.8796	+	7.07201i	−0.449841	+	0.229205i
$953$	−1.83571	−	11.5902i	−0.0594644	−	0.375444i	−0.999417	−	0.0341388i	$-0.989131\pi$
$953$	−1.83571	−	11.5902i	−0.0594644	−	0.375444i	0.939953	−	0.341305i	$-0.110869\pi$
$954$	−16.6132	+	2.63128i	−0.537874	+	0.0851908i
$955$	−12.7943	+	1.73430i	−0.414013	+	0.0561207i
$956$	1.12189	−	7.08335i	0.0362846	−	0.229092i
$957$	−9.36575			−0.302752
$958$	−2.29777	+	14.5076i	−0.0742376	+	0.468718i
$959$	−16.0444	−	49.3797i	−0.518102	−	1.59455i
$960$	−1.93076	−	0.675402i	−0.0623150	−	0.0217985i
$961$	31.4437	+	10.2167i	1.01431	+	0.329570i
$962$	17.6073	+	25.9921i	0.567681	+	0.838018i
$963$	−25.6071	−	13.0475i	−0.825178	−	0.420449i
$964$	−5.74402	−	11.2733i	−0.185002	−	0.363088i
$965$	−27.1556	−	4.92544i	−0.874171	−	0.158555i
$966$	−4.78127	+	1.55353i	−0.153835	+	0.0499840i
$967$	10.8210	+	14.8938i	0.347980	+	0.478954i	0.946751	−	0.321967i	$-0.104344\pi$
$967$	10.8210	+	14.8938i	0.347980	+	0.478954i	−0.598771	+	0.800920i	$0.704344\pi$
$968$	2.75008			0.0883909
$969$	22.3667	+	3.54253i	0.718521	+	0.113803i
$970$	7.31274	+	15.1815i	0.234798	+	0.487448i
$971$	12.9322	+	9.39582i	0.415015	+	0.301526i	0.775629	−	0.631189i	$-0.217433\pi$
$971$	12.9322	+	9.39582i	0.415015	+	0.301526i	−0.360614	+	0.932715i	$0.617433\pi$
$972$	−15.9547	+	2.52697i	−0.511746	+	0.0810527i
$973$	31.2828	+	10.1644i	1.00288	+	0.325855i
$974$	−12.9190			−0.413951
$975$	15.2300	−	6.32505i	0.487751	−	0.202564i
$976$	7.54629			0.241551
$977$	−45.3422	−	14.7326i	−1.45063	−	0.471337i	−0.525433	−	0.850835i	$-0.676097\pi$
$977$	−45.3422	−	14.7326i	−1.45063	−	0.471337i	−0.925193	+	0.379498i	$0.876097\pi$
$978$	2.49429	−	0.395057i	0.0797587	−	0.0126325i
$979$	16.7462	+	12.1668i	0.535212	+	0.388854i
$980$	1.70010	−	1.62576i	0.0543076	−	0.0519329i
$981$	−29.8009	−	4.72000i	−0.951471	−	0.150698i
$982$	−13.9949			−0.446596
$983$	−17.9607	−	24.7208i	−0.572857	−	0.788470i	0.420032	−	0.907509i	$-0.362019\pi$
$983$	−17.9607	−	24.7208i	−0.572857	−	0.788470i	−0.992890	+	0.119039i	$0.962019\pi$
$984$	−9.38672	+	3.04993i	−0.299238	+	0.0972282i
$985$	−7.75144	−	8.10587i	−0.246981	−	0.258275i
$986$	8.88379	+	17.4354i	0.282918	+	0.555257i
$987$	15.2113	+	7.75056i	0.484182	+	0.246703i
$988$	3.07061	−	15.9666i	0.0976892	−	0.507964i
$989$	15.9327	+	5.17686i	0.506632	+	0.164615i
$990$	13.3060	−	3.99694i	0.422892	−	0.127031i
$991$	1.99750	+	6.14766i	0.0634526	+	0.195287i	0.977757	−	0.209741i	$-0.0672619\pi$
$991$	1.99750	+	6.14766i	0.0634526	+	0.195287i	−0.914305	+	0.405027i	$0.867262\pi$
$992$	1.25208	−	7.90532i	0.0397536	−	0.250994i
$993$	−13.9313			−0.442097
$994$	−1.92670	+	12.1647i	−0.0611112	+	0.385841i
$995$	2.29446	−	12.6502i	0.0727393	−	0.401037i
$996$	−10.8115	+	1.71237i	−0.342574	+	0.0542584i
$997$	6.02660	+	38.0504i	0.190864	+	1.20507i	0.878043	+	0.478581i	$0.158849\pi$
$997$	6.02660	+	38.0504i	0.190864	+	1.20507i	−0.687179	+	0.726488i	$0.741151\pi$
$998$	4.14695	−	2.11297i	0.131269	−	0.0668850i
$999$	29.0800	+	29.0800i	0.920050	+	0.920050i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.bd.a.47.7	yes	136
13.5	odd	4		650.2.ba.a.447.7	yes	136
25.8	odd	20		650.2.ba.a.333.7	✓	136
325.83	even	20	inner	650.2.bd.a.83.7	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.ba.a.333.7	✓	136	25.8	odd	20
650.2.ba.a.447.7	yes	136	13.5	odd	4
650.2.bd.a.47.7	yes	136	1.1	even	1	trivial
650.2.bd.a.83.7	yes	136	325.83	even	20	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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.bd (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 + 0.309017i) q^{2} +(-0.903505 + 0.143101i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.399063 - 2.20017i) q^{5} +(-0.903505 - 0.143101i) q^{6} -2.83760 q^{7} +(0.587785 + 0.809017i) q^{8} +(-2.05733 + 0.668466i) q^{9} +(1.05942 - 1.96917i) q^{10} +(-1.30398 - 2.55921i) q^{11} +(-0.815064 - 0.415296i) q^{12} +(2.98512 - 2.02215i) q^{13} +(-2.69872 - 0.876868i) q^{14} +(-0.0457083 + 2.04497i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.858770 - 5.42206i) q^{17} -2.16320 q^{18} +(0.705437 - 4.45396i) q^{19} +(1.61608 - 1.54541i) q^{20} +(2.56379 - 0.406064i) q^{21} +(-0.449322 - 2.83691i) q^{22} +(-1.72566 + 0.879268i) q^{23} +(-0.646838 - 0.646838i) q^{24} +(-4.68150 - 1.75601i) q^{25} +(3.46389 - 1.00072i) q^{26} +(4.20834 - 2.14426i) q^{27} +(-2.29567 - 1.66790i) q^{28} +(-2.09520 + 2.88380i) q^{29} +(-0.675402 + 1.93076i) q^{30} +(-7.90532 - 1.25208i) q^{31} +1.00000i q^{32} +(1.54438 + 2.12566i) q^{33} +(2.49225 - 4.89131i) q^{34} +(-1.13238 + 6.24321i) q^{35} +(-2.05733 - 0.668466i) q^{36} +(2.69068 + 8.28106i) q^{37} +(2.04726 - 4.01797i) q^{38} +(-2.40770 + 2.25419i) q^{39} +(2.01454 - 0.970379i) q^{40} +(4.89828 - 9.61342i) q^{41} +(2.56379 + 0.406064i) q^{42} +(-6.11638 - 6.11638i) q^{43} +(0.449322 - 2.83691i) q^{44} +(0.649736 + 4.79323i) q^{45} +(-1.91291 + 0.302975i) q^{46} +(5.32086 + 3.86583i) q^{47} +(-0.415296 - 0.815064i) q^{48} +1.05199 q^{49} +(-3.90973 - 3.11673i) q^{50} +5.02175i q^{51} +(3.60360 + 0.118658i) q^{52} +(7.67994 - 1.21638i) q^{53} +(4.66498 - 0.738860i) q^{54} +(-6.15107 + 1.84770i) q^{55} +(-1.66790 - 2.29567i) q^{56} +4.12512i q^{57} +(-2.88380 + 2.09520i) q^{58} +(-5.27006 + 10.3431i) q^{59} +(-1.23898 + 1.62755i) q^{60} +(2.33193 - 7.17695i) q^{61} +(-7.13150 - 3.63368i) q^{62} +(5.83787 - 1.89684i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-3.25782 - 7.37473i) q^{65} +(0.811929 + 2.49886i) q^{66} +(1.69387 + 2.33142i) q^{67} +(3.88177 - 3.88177i) q^{68} +(1.43332 - 1.04137i) q^{69} +(-3.00622 + 5.58772i) q^{70} +(-0.678988 - 4.28696i) q^{71} +(-1.75007 - 1.27150i) q^{72} +(10.4829 + 3.40609i) q^{73} +8.70722i q^{74} +(4.48104 + 0.916638i) q^{75} +(3.18868 - 3.18868i) q^{76} +(3.70018 + 7.26202i) q^{77} +(-2.98644 + 1.39985i) q^{78} +(-3.03466 + 4.17686i) q^{79} +(2.21580 - 0.300359i) q^{80} +(1.75479 - 1.27493i) q^{81} +(7.62925 - 7.62925i) q^{82} +(9.68080 - 7.03351i) q^{83} +(2.31283 + 1.17844i) q^{84} +(-11.5868 - 4.05318i) q^{85} +(-3.92696 - 7.70709i) q^{86} +(1.48035 - 2.90535i) q^{87} +(1.30398 - 2.55921i) q^{88} +(-6.42119 + 3.27176i) q^{89} +(-0.863253 + 4.75941i) q^{90} +(-8.47058 + 5.73805i) q^{91} +(-1.91291 - 0.302975i) q^{92} +7.32168 q^{93} +(3.86583 + 5.32086i) q^{94} +(-9.51795 - 3.32949i) q^{95} +(-0.143101 - 0.903505i) q^{96} +(-4.42953 + 6.09672i) q^{97} +(1.00050 + 0.325083i) q^{98} +(4.39346 + 4.39346i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q + 34 q^{4} + 20 q^{9} + 2 q^{13} - 14 q^{15} - 34 q^{16} - 4 q^{17} + 128 q^{18} - 20 q^{19} + 6 q^{21} - 12 q^{23} - 14 q^{26} + 36 q^{27} + 20 q^{29} - 12 q^{30} + 6 q^{31} + 30 q^{33} + 16 q^{34}+ \cdots + 40 q^{99}+O(q^{100}) \) 136 * q + 34 * q^4 + 20 * q^9 + 2 * q^13 - 14 * q^15 - 34 * q^16 - 4 * q^17 + 128 * q^18 - 20 * q^19 + 6 * q^21 - 12 * q^23 - 14 * q^26 + 36 * q^27 + 20 * q^29 - 12 * q^30 + 6 * q^31 + 30 * q^33 + 16 * q^34 - 52 * q^35 + 20 * q^36 - 6 * q^37 - 20 * q^39 - 42 * q^41 + 6 * q^42 + 12 * q^43 - 18 * q^45 + 12 * q^46 - 18 * q^47 + 120 * q^49 - 2 * q^52 - 50 * q^53 - 6 * q^54 + 24 * q^55 - 4 * q^58 - 16 * q^59 - 6 * q^60 - 12 * q^61 - 6 * q^62 - 100 * q^63 + 34 * q^64 - 56 * q^65 + 16 * q^66 + 4 * q^68 + 26 * q^69 + 34 * q^70 - 12 * q^71 + 22 * q^72 + 40 * q^73 - 192 * q^75 - 64 * q^77 - 84 * q^78 + 20 * q^79 - 54 * q^81 + 12 * q^82 + 74 * q^83 + 24 * q^84 - 12 * q^85 - 12 * q^86 + 8 * q^87 - 52 * q^89 - 44 * q^90 + 136 * q^91 + 12 * q^92 - 16 * q^93 - 50 * q^94 - 110 * q^95 - 40 * q^98 + 40 * q^99

Introduction

L-functions

Modular forms

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