LMFDB - Embedded newform 560.2.cp.a.261.38

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [560,2,Mod(221,560)] 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("560.221"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(560, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 9, 0, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.cp (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$64$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			261.38
Character	$\chi$	$=$	560.261
Dual form			560.2.cp.a.221.38

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.313410 - 1.37905i) q^{2} +(0.215633 + 0.0577786i) q^{3} +(-1.80355 - 0.864415i) q^{4} +(0.965926 - 0.258819i) q^{5} +(0.147261 - 0.279259i) q^{6} +(0.618432 + 2.57246i) q^{7} +(-1.75732 + 2.21626i) q^{8} +(-2.55492 - 1.47508i) q^{9} +(-0.0541931 - 1.41317i) q^{10} +(1.49102 - 5.56455i) q^{11} +(-0.338959 - 0.290603i) q^{12} +(2.05264 - 2.05264i) q^{13} +(3.74137 - 0.0466135i) q^{14} +0.223239 q^{15} +(2.50557 + 3.11803i) q^{16} +(-2.61892 - 4.53611i) q^{17} +(-2.83495 + 3.06105i) q^{18} +(-1.69724 - 6.33419i) q^{19} +(-1.96582 - 0.368168i) q^{20} +(-0.0152789 + 0.590438i) q^{21} +(-7.20649 - 3.80017i) q^{22} +(3.67258 + 2.12037i) q^{23} +(-0.506988 + 0.376363i) q^{24} +(0.866025 - 0.500000i) q^{25} +(-2.18737 - 3.47401i) q^{26} +(-0.939257 - 0.939257i) q^{27} +(1.10830 - 5.17413i) q^{28} +(3.61371 - 3.61371i) q^{29} +(0.0699654 - 0.307858i) q^{30} +(0.973069 + 1.68540i) q^{31} +(5.08518 - 2.47808i) q^{32} +(0.643024 - 1.11375i) q^{33} +(-7.07631 + 2.18996i) q^{34} +(1.26316 + 2.32474i) q^{35} +(3.33283 + 4.86889i) q^{36} +(-8.57181 + 2.29681i) q^{37} +(-9.26708 + 0.355378i) q^{38} +(0.561215 - 0.324018i) q^{39} +(-1.12383 + 2.59557i) q^{40} +8.93557i q^{41} +(0.809454 + 0.206120i) q^{42} +(8.54067 + 8.54067i) q^{43} +(-7.49921 + 8.74708i) q^{44} +(-2.84964 - 0.763559i) q^{45} +(4.07511 - 4.40012i) q^{46} +(3.31009 - 5.73324i) q^{47} +(0.360128 + 0.817117i) q^{48} +(-6.23508 + 3.18178i) q^{49} +(-0.418103 - 1.35100i) q^{50} +(-0.302635 - 1.12945i) q^{51} +(-5.47637 + 1.92770i) q^{52} +(0.272283 - 1.01618i) q^{53} +(-1.58965 + 1.00091i) q^{54} -5.76085i q^{55} +(-6.78803 - 3.15002i) q^{56} -1.46392i q^{57} +(-3.85091 - 6.11606i) q^{58} +(-1.53126 + 5.71473i) q^{59} +(-0.402623 - 0.192971i) q^{60} +(0.386082 + 1.44088i) q^{61} +(2.62922 - 0.813686i) q^{62} +(2.21454 - 7.48466i) q^{63} +(-1.82365 - 7.78937i) q^{64} +(1.45144 - 2.51396i) q^{65} +(-1.33439 - 1.23582i) q^{66} +(4.05630 + 1.08688i) q^{67} +(0.802274 + 10.4449i) q^{68} +(0.669417 + 0.669417i) q^{69} +(3.60182 - 1.01336i) q^{70} -9.42423i q^{71} +(7.75898 - 3.07018i) q^{72} +(-5.96549 + 3.44417i) q^{73} +(0.480920 + 12.5408i) q^{74} +(0.215633 - 0.0577786i) q^{75} +(-2.41431 + 12.8911i) q^{76} +(15.2367 + 0.394282i) q^{77} +(-0.270946 - 0.875493i) q^{78} +(-1.83175 + 3.17269i) q^{79} +(3.22720 + 2.36329i) q^{80} +(4.27698 + 7.40795i) q^{81} +(12.3226 + 2.80050i) q^{82} +(5.98035 - 5.98035i) q^{83} +(0.537940 - 1.05168i) q^{84} +(-3.70372 - 3.70372i) q^{85} +(14.4547 - 9.10126i) q^{86} +(0.988029 - 0.570439i) q^{87} +(9.71232 + 13.0832i) q^{88} +(-9.34268 - 5.39400i) q^{89} +(-1.94609 + 3.69048i) q^{90} +(6.54975 + 4.01091i) q^{91} +(-4.79080 - 6.99882i) q^{92} +(0.112445 + 0.419651i) q^{93} +(-6.86900 - 6.36163i) q^{94} +(-3.27882 - 5.67908i) q^{95} +(1.23971 - 0.240541i) q^{96} +6.65912 q^{97} +(2.43369 + 9.59568i) q^{98} +(-12.0176 + 12.0176i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 4 q^{4} + 8 q^{11} + 16 q^{14} - 20 q^{16} - 40 q^{18} - 16 q^{20} + 56 q^{22} - 40 q^{24} + 4 q^{28} - 32 q^{29} - 20 q^{32} + 16 q^{37} - 40 q^{38} - 60 q^{42} + 16 q^{43} + 32 q^{44} - 20 q^{46}+ \cdots - 80 q^{99}+O(q^{100}) $ 256 * q + 4 * q^4 + 8 * q^11 + 16 * q^14 - 20 * q^16 - 40 * q^18 - 16 * q^20 + 56 * q^22 - 40 * q^24 + 4 * q^28 - 32 * q^29 - 20 * q^32 + 16 * q^37 - 40 * q^38 - 60 * q^42 + 16 * q^43 + 32 * q^44 - 20 * q^46 + 80 * q^47 - 160 * q^48 - 8 * q^50 - 40 * q^51 + 24 * q^52 - 16 * q^53 - 116 * q^54 - 96 * q^56 - 8 * q^58 + 16 * q^59 - 28 * q^60 + 88 * q^62 - 56 * q^64 - 16 * q^66 - 40 * q^67 - 20 * q^68 - 16 * q^70 + 76 * q^72 + 52 * q^74 - 48 * q^78 + 128 * q^81 - 80 * q^83 - 68 * q^84 + 52 * q^86 + 20 * q^88 - 72 * q^90 - 32 * q^91 - 112 * q^92 + 120 * q^94 + 140 * q^96 + 24 * q^98 - 80 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.313410	−	1.37905i	0.221614	−	0.975134i
$2$	0.313410	−	1.37905i	0.221614	−	0.975134i
$3$	0.215633	+	0.0577786i	0.124496	+	0.0333585i	0.320529	−	0.947239i	$-0.396139\pi$
$3$	0.215633	+	0.0577786i	0.124496	+	0.0333585i	−0.196033	+	0.980597i	$0.562806\pi$
$4$	−1.80355	−	0.864415i	−0.901774	−	0.432208i
$5$	0.965926	−	0.258819i	0.431975	−	0.115747i
$5$	0.965926	−	0.258819i	0.431975	−	0.115747i
$6$	0.147261	−	0.279259i	0.0601190	−	0.114007i
$7$	0.618432	+	2.57246i	0.233745	+	0.972298i
$7$	0.618432	+	2.57246i	0.233745	+	0.972298i
$8$	−1.75732	+	2.21626i	−0.621307	+	0.783568i
$9$	−2.55492	−	1.47508i	−0.851639	−	0.491694i
$10$	−0.0541931	−	1.41317i	−0.0171374	−	0.446885i
$11$	1.49102	−	5.56455i	0.449559	−	1.67778i	−0.254052	−	0.967191i	$-0.581763\pi$
$11$	1.49102	−	5.56455i	0.449559	−	1.67778i	0.703611	−	0.710586i	$-0.251570\pi$
$12$	−0.338959	−	0.290603i	−0.0978491	−	0.0838897i
$13$	2.05264	−	2.05264i	0.569300	−	0.569300i	−0.362632	−	0.931932i	$-0.618122\pi$
$13$	2.05264	−	2.05264i	0.569300	−	0.569300i	0.931932	+	0.362632i	$0.118122\pi$
$14$	3.74137	−	0.0466135i	0.999922	−	0.0124580i
$15$	0.223239			0.0576401
$16$	2.50557	+	3.11803i	0.626393	+	0.779507i
$17$	−2.61892	−	4.53611i	−0.635182	−	1.10017i	−0.986477	−	0.163902i	$-0.947592\pi$
$17$	−2.61892	−	4.53611i	−0.635182	−	1.10017i	0.351295	−	0.936265i	$-0.385742\pi$
$18$	−2.83495	+	3.06105i	−0.668203	+	0.721496i
$19$	−1.69724	−	6.33419i	−0.389374	−	1.45316i	−0.831156	−	0.556040i	$-0.812320\pi$
$19$	−1.69724	−	6.33419i	−0.389374	−	1.45316i	0.441782	−	0.897122i	$-0.354346\pi$
$20$	−1.96582	−	0.368168i	−0.439571	−	0.0823249i
$21$	−0.0152789	+	0.590438i	−0.00333412	+	0.128844i
$22$	−7.20649	−	3.80017i	−1.53643	−	0.810200i
$23$	3.67258	+	2.12037i	0.765786	+	0.442127i	0.831369	−	0.555720i	$-0.187557\pi$
$23$	3.67258	+	2.12037i	0.765786	+	0.442127i	−0.0655831	+	0.997847i	$0.520891\pi$
$24$	−0.506988	+	0.376363i	−0.103489	+	0.0768248i
$25$	0.866025	−	0.500000i	0.173205	−	0.100000i
$26$	−2.18737	−	3.47401i	−0.428979	−	0.681309i
$27$	−0.939257	−	0.939257i	−0.180760	−	0.180760i
$28$	1.10830	−	5.17413i	0.209449	−	0.977820i
$29$	3.61371	−	3.61371i	0.671049	−	0.671049i	−0.286909	−	0.957958i	$-0.592628\pi$
$29$	3.61371	−	3.61371i	0.671049	−	0.671049i	0.957958	+	0.286909i	$0.0926276\pi$
$30$	0.0699654	−	0.307858i	0.0127739	−	0.0562069i
$31$	0.973069	+	1.68540i	0.174768	+	0.302708i	0.940081	−	0.340951i	$-0.110749\pi$
$31$	0.973069	+	1.68540i	0.174768	+	0.302708i	−0.765313	+	0.643659i	$0.777416\pi$
$32$	5.08518	−	2.47808i	0.898942	−	0.438068i
$33$	0.643024	−	1.11375i	0.111936	−	0.193879i
$34$	−7.07631	+	2.18996i	−1.21358	+	0.375575i
$35$	1.26316	+	2.32474i	0.213513	+	0.392953i
$36$	3.33283	+	4.86889i	0.555472	+	0.811482i
$37$	−8.57181	+	2.29681i	−1.40920	+	0.377593i	−0.881639	−	0.471925i	$-0.843559\pi$
$37$	−8.57181	+	2.29681i	−1.40920	+	0.377593i	−0.527559	+	0.849518i	$0.676893\pi$
$38$	−9.26708	+	0.355378i	−1.50332	+	0.0576500i
$39$	0.561215	−	0.324018i	0.0898663	−	0.0518844i
$40$	−1.12383	+	2.59557i	−0.177693	+	0.410396i
$41$			8.93557i			1.39550i	0.716341	+	0.697751i	$0.245816\pi$
$41$			8.93557i			1.39550i	−0.716341	+	0.697751i	$0.754184\pi$
$42$	0.809454	+	0.206120i	0.124901	+	0.0318049i
$43$	8.54067	+	8.54067i	1.30244	+	1.30244i	0.926742	+	0.375697i	$0.122597\pi$
$43$	8.54067	+	8.54067i	1.30244	+	1.30244i	0.375697	+	0.926742i	$0.377403\pi$
$44$	−7.49921	+	8.74708i	−1.13055	+	1.31867i
$45$	−2.84964	−	0.763559i	−0.424799	−	0.113825i
$46$	4.07511	−	4.40012i	0.600842	−	0.648763i
$47$	3.31009	−	5.73324i	0.482826	−	0.836279i	−0.516979	−	0.855998i	$-0.672944\pi$
$47$	3.31009	−	5.73324i	0.482826	−	0.836279i	0.999806	+	0.0197184i	$0.00627696\pi$
$48$	0.360128	+	0.817117i	0.0519800	+	0.117941i
$49$	−6.23508	+	3.18178i	−0.890726	+	0.454540i
$50$	−0.418103	−	1.35100i	−0.0591287	−	0.191060i
$51$	−0.302635	−	1.12945i	−0.0423774	−	0.158155i
$52$	−5.47637	+	1.92770i	−0.759436	+	0.267324i
$53$	0.272283	−	1.01618i	0.0374010	−	0.139582i	−0.944701	−	0.327934i	$-0.893648\pi$
$53$	0.272283	−	1.01618i	0.0374010	−	0.139582i	0.982102	+	0.188351i	$0.0603144\pi$
$54$	−1.58965	+	1.00091i	−0.216325	+	0.136206i
$55$		−	5.76085i		−	0.776793i
$56$	−6.78803	−	3.15002i	−0.907089	−	0.420940i
$57$		−	1.46392i		−	0.193901i
$58$	−3.85091	−	6.11606i	−0.505649	−	0.803078i
$59$	−1.53126	+	5.71473i	−0.199353	+	0.743995i	0.791744	+	0.610853i	$0.209173\pi$
$59$	−1.53126	+	5.71473i	−0.199353	+	0.743995i	−0.991097	+	0.133142i	$0.957493\pi$
$60$	−0.402623	−	0.192971i	−0.0519784	−	0.0249125i
$61$	0.386082	+	1.44088i	0.0494327	+	0.184485i	0.986228	−	0.165394i	$-0.0528894\pi$
$61$	0.386082	+	1.44088i	0.0494327	+	0.184485i	−0.936795	+	0.349879i	$0.886223\pi$
$62$	2.62922	−	0.813686i	0.333912	−	0.103338i
$63$	2.21454	−	7.48466i	0.279006	−	0.942978i
$64$	−1.82365	−	7.78937i	−0.227956	−	0.973671i
$65$	1.45144	−	2.51396i	0.180029	−	0.311819i
$66$	−1.33439	−	1.23582i	−0.164251	−	0.152119i
$67$	4.05630	+	1.08688i	0.495556	+	0.132784i	0.497937	−	0.867213i	$-0.334091\pi$
$67$	4.05630	+	1.08688i	0.495556	+	0.132784i	−0.00238094	+	0.999997i	$0.500758\pi$
$68$	0.802274	+	10.4449i	0.0972900	+	1.26663i
$69$	0.669417	+	0.669417i	0.0805883	+	0.0805883i
$70$	3.60182	−	1.01336i	0.430500	−	0.121120i
$71$		−	9.42423i		−	1.11845i	−0.829016	−	0.559225i	$-0.811099\pi$
$71$		−	9.42423i		−	1.11845i	0.829016	−	0.559225i	$-0.188901\pi$
$72$	7.75898	−	3.07018i	0.914404	−	0.361824i
$73$	−5.96549	+	3.44417i	−0.698207	+	0.403110i	−0.806679	−	0.590989i	$-0.798738\pi$
$73$	−5.96549	+	3.44417i	−0.698207	+	0.403110i	0.108472	+	0.994099i	$0.465404\pi$
$74$	0.480920	+	12.5408i	0.0559058	+	1.45784i
$75$	0.215633	−	0.0577786i	0.0248991	−	0.00667170i
$76$	−2.41431	+	12.8911i	−0.276941	+	1.47871i
$77$	15.2367	+	0.394282i	1.73638	+	0.0449326i
$78$	−0.270946	−	0.875493i	−0.0306785	−	0.0991301i
$79$	−1.83175	+	3.17269i	−0.206088	+	0.356955i	−0.950479	−	0.310789i	$-0.899407\pi$
$79$	−1.83175	+	3.17269i	−0.206088	+	0.356955i	0.744391	+	0.667744i	$0.232740\pi$
$80$	3.22720	+	2.36329i	0.360812	+	0.264224i
$81$	4.27698	+	7.40795i	0.475220	+	0.823105i
$82$	12.3226	+	2.80050i	1.36080	+	0.309263i
$83$	5.98035	−	5.98035i	0.656429	−	0.656429i	−0.298104	−	0.954533i	$-0.596354\pi$
$83$	5.98035	−	5.98035i	0.656429	−	0.656429i	0.954533	+	0.298104i	$0.0963543\pi$
$84$	0.537940	−	1.05168i	0.0586940	−	0.114747i
$85$	−3.70372	−	3.70372i	−0.401724	−	0.401724i
$86$	14.4547	−	9.10126i	1.55869	−	0.981414i
$87$	0.988029	−	0.570439i	0.105928	−	0.0611575i
$88$	9.71232	+	13.0832i	1.03534	+	1.39467i
$89$	−9.34268	−	5.39400i	−0.990322	−	0.571763i	−0.0849517	−	0.996385i	$-0.527074\pi$
$89$	−9.34268	−	5.39400i	−0.990322	−	0.571763i	−0.905371	+	0.424622i	$0.860407\pi$
$90$	−1.94609	+	3.69048i	−0.205136	+	0.389011i
$91$	6.54975	+	4.01091i	0.686601	+	0.420458i
$92$	−4.79080	−	6.99882i	−0.499476	−	0.729677i
$93$	0.112445	+	0.419651i	0.0116600	+	0.0435158i
$94$	−6.86900	−	6.36163i	−0.708484	−	0.656152i
$95$	−3.27882	−	5.67908i	−0.336399	−	0.582661i
$96$	1.23971	−	0.240541i	0.126528	−	0.0245501i
$97$	6.65912			0.676131			0.338066	−	0.941123i	$-0.390227\pi$
$97$	6.65912			0.676131			0.338066	+	0.941123i	$0.390227\pi$
$98$	2.43369	+	9.59568i	0.245840	+	0.969310i
$99$	−12.0176	+	12.0176i	−1.20781	+	1.20781i
$100$	−1.99413	+	0.153169i	−0.199413	+	0.0153169i
$101$	−4.65168	+	17.3603i	−0.462860	+	1.72742i	0.201029	+	0.979585i	$0.435571\pi$
$101$	−4.65168	+	17.3603i	−0.462860	+	1.72742i	−0.663889	+	0.747831i	$0.731095\pi$
$102$	−1.65242	+	0.0633676i	−0.163613	+	0.00627433i
$103$	6.62485	+	3.82486i	0.652766	+	0.376875i	0.789515	−	0.613731i	$-0.210332\pi$
$103$	6.62485	+	3.82486i	0.652766	+	0.376875i	−0.136749	+	0.990606i	$0.543665\pi$
$104$	0.942046	+	8.15634i	0.0923752	+	0.799795i
$105$	0.138058	+	0.574274i	0.0134731	+	0.0560434i
$106$	−1.31602	−	0.693972i	−0.127823	−	0.0674045i
$107$	8.35034	−	2.23747i	0.807258	−	0.216304i	0.168490	−	0.985703i	$-0.446111\pi$
$107$	8.35034	−	2.23747i	0.807258	−	0.216304i	0.638768	+	0.769399i	$0.279444\pi$
$108$	0.882088	+	2.50590i	0.0848789	+	0.241131i
$109$	2.86036	+	0.766432i	0.273973	+	0.0734108i	0.393190	−	0.919457i	$-0.371372\pi$
$109$	2.86036	+	0.766432i	0.273973	+	0.0734108i	−0.119217	+	0.992868i	$0.538038\pi$
$110$	−7.94449	−	1.80551i	−0.757477	−	0.172148i
$111$	−1.98107			−0.188035
$112$	−6.47147	+	8.37377i	−0.611497	+	0.791247i
$113$	1.53887			0.144764			0.0723822	−	0.997377i	$-0.476940\pi$
$113$	1.53887			0.144764			0.0723822	+	0.997377i	$0.476940\pi$
$114$	−2.01882	−	0.458808i	−0.189080	−	0.0429713i
$115$	4.09623	+	1.09758i	0.381976	+	0.102350i
$116$	−9.64125	+	3.39376i	−0.895168	+	0.315102i
$117$	−8.27214	+	2.21651i	−0.764760	+	0.204917i
$118$	7.40098	+	3.90273i	0.681315	+	0.359276i
$119$	10.0493	−	9.54234i	0.921220	−	0.874745i
$120$	−0.392303	+	0.494757i	−0.0358122	+	0.0451649i
$121$	−19.2148	−	11.0937i	−1.74680	−	1.00852i
$122$	2.10804	−	0.0808401i	0.190853	−	0.00731892i
$123$	−0.516285	+	1.92680i	−0.0465518	+	0.173734i
$124$	−0.298087	−	3.88084i	−0.0267690	−	0.348510i
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$	−9.62764	−	5.39973i	−0.857698	−	0.481046i
$127$	−1.77329			−0.157354			−0.0786771	−	0.996900i	$-0.525070\pi$
$127$	−1.77329			−0.157354			−0.0786771	+	0.996900i	$0.525070\pi$
$128$	−11.3135	+	0.0736344i	−0.999979	+	0.00650842i
$129$	1.34818	+	2.33511i	0.118701	+	0.205595i
$130$	−3.01198	−	2.78950i	−0.264168	−	0.244655i
$131$	2.56080	+	9.55702i	0.223738	+	0.835001i	0.982906	+	0.184107i	$0.0589392\pi$
$131$	2.56080	+	9.55702i	0.223738	+	0.835001i	−0.759168	+	0.650894i	$0.774394\pi$
$132$	−2.12247	+	1.45286i	−0.184737	+	0.126455i
$133$	15.2448	−	8.28334i	1.32189	−	0.718257i
$134$	2.77015	−	5.25319i	0.239304	−	0.453807i
$135$	−1.15035	−	0.664155i	−0.0990064	−	0.0571614i
$136$	14.6555	+	2.16717i	1.25670	+	0.185833i
$137$	7.30436	−	4.21717i	0.624054	−	0.360298i	−0.154392	−	0.988010i	$-0.549342\pi$
$137$	7.30436	−	4.21717i	0.624054	−	0.360298i	0.778446	+	0.627712i	$0.216008\pi$
$138$	1.13296	−	0.713356i	0.0964440	−	0.0607249i
$139$	−0.699743	−	0.699743i	−0.0593515	−	0.0593515i	0.676808	−	0.736160i	$-0.263363\pi$
$139$	−0.699743	−	0.699743i	−0.0593515	−	0.0593515i	−0.736160	+	0.676808i	$0.763363\pi$
$140$	−0.268629	−	5.28468i	−0.0227033	−	0.446637i
$141$	1.04502	−	1.04502i	0.0880067	−	0.0880067i
$142$	−12.9965	−	2.95365i	−1.09064	−	0.247865i
$143$	−8.36151	−	14.4826i	−0.699224	−	1.21109i
$144$	−1.80218	−	11.6622i	−0.150182	−	0.971853i
$145$	2.55528	−	4.42587i	0.212204	−	0.367549i
$146$	2.88004	+	9.30613i	0.238354	+	0.770181i
$147$	−1.52833	+	0.325842i	−0.126054	+	0.0268750i
$148$	17.4451	+	3.26720i	1.43398	+	0.268562i
$149$	8.98357	−	2.40714i	0.735963	−	0.197201i	0.128680	−	0.991686i	$-0.458926\pi$
$149$	8.98357	−	2.40714i	0.735963	−	0.197201i	0.607283	+	0.794486i	$0.292259\pi$
$150$	−0.0120980	−	0.315476i	−0.000987800	−	0.0257585i
$151$	14.0703	−	8.12347i	1.14502	−	0.661079i	0.197352	−	0.980333i	$-0.436766\pi$
$151$	14.0703	−	8.12347i	1.14502	−	0.661079i	0.947669	+	0.319254i	$0.103432\pi$
$152$	17.0208	+	7.36966i	1.38057	+	0.597759i
$153$			15.4525i			1.24926i
$154$	5.31906	−	20.8885i	0.428622	−	1.68325i
$155$	1.37613	+	1.37613i	0.110533	+	0.110533i
$156$	−1.29226	+	0.0992587i	−0.103464	+	0.00794706i
$157$	−2.07495	−	0.555981i	−0.165599	−	0.0443721i	0.175067	−	0.984557i	$-0.443986\pi$
$157$	−2.07495	−	0.555981i	−0.165599	−	0.0443721i	−0.340666	+	0.940184i	$0.610652\pi$
$158$	3.80120	+	3.52042i	0.302407	+	0.280070i
$159$	0.117426	−	0.203388i	0.00931252	−	0.0161298i
$160$	4.27054	−	3.70979i	0.337615	−	0.293285i
$161$	−3.18331	+	10.7589i	−0.250880	+	0.847917i
$162$	11.5564	−	3.57644i	0.907954	−	0.280991i
$163$	−1.51942	−	5.67057i	−0.119010	−	0.444153i	0.880545	−	0.473962i	$-0.157177\pi$
$163$	−1.51942	−	5.67057i	−0.119010	−	0.444153i	−0.999556	+	0.0298091i	$0.990510\pi$
$164$	7.72404	−	16.1157i	0.603146	−	1.25843i
$165$	0.332854	−	1.24223i	0.0259126	−	0.0967073i
$166$	−6.37289	−	10.1215i	−0.494633	−	0.785581i
$167$			24.2941i			1.87993i	0.341264	+	0.939967i	$0.389145\pi$
$167$			24.2941i			1.87993i	−0.341264	+	0.939967i	$0.610855\pi$
$168$	−1.28172	−	1.07145i	−0.0988866	−	0.0826642i
$169$			4.57333i			0.351795i
$170$	−6.26838	+	3.94682i	−0.480763	+	0.302707i
$171$	−5.00714	+	18.6869i	−0.382905	+	1.42902i
$172$	−8.02083	−	22.7862i	−0.611582	−	1.73743i
$173$	0.227716	+	0.849846i	0.0173129	+	0.0646126i	0.974042	−	0.226368i	$-0.0726852\pi$
$173$	0.227716	+	0.849846i	0.0173129	+	0.0646126i	−0.956729	+	0.290981i	$0.906019\pi$
$174$	−0.477005	−	1.54132i	−0.0361616	−	0.116847i
$175$	1.82181	+	1.91860i	0.137716	+	0.145032i
$176$	21.0863	−	9.29336i	1.58944	−	0.700513i
$177$	−0.660378	+	1.14381i	−0.0496371	+	0.0859739i
$178$	−10.3667	+	11.1935i	−0.777015	+	0.838987i
$179$	19.7774	+	5.29935i	1.47823	+	0.396092i	0.905746	−	0.423821i	$-0.139311\pi$
$179$	19.7774	+	5.29935i	1.47823	+	0.396092i	0.572489	+	0.819913i	$0.305978\pi$
$180$	4.47943	+	3.84039i	0.333877	+	0.286246i
$181$	−11.3395	−	11.3395i	−0.842855	−	0.842855i	0.146374	−	0.989229i	$-0.453240\pi$
$181$	−11.3395	−	11.3395i	−0.842855	−	0.842855i	−0.989229	+	0.146374i	$0.953240\pi$
$182$	7.58400	−	7.77536i	0.562164	−	0.576348i
$183$			0.333007i			0.0246166i
$184$	−11.1532	+	4.41325i	−0.822224	+	0.325349i
$185$	−7.68528	+	4.43710i	−0.565033	+	0.326222i
$186$	0.613960	−	0.0235444i	0.0450177	−	0.00172636i
$187$	−29.1463	+	7.80972i	−2.13139	+	0.571103i
$188$	−10.9258	+	7.47889i	−0.796846	+	0.545454i
$189$	1.83533	−	2.99707i	0.133501	−	0.218005i
$190$	−8.85933	+	2.74177i	−0.642724	+	0.198909i
$191$	4.19425	−	7.26466i	0.303486	−	0.525652i	−0.673437	−	0.739244i	$-0.735183\pi$
$191$	4.19425	−	7.26466i	0.303486	−	0.525652i	0.976923	+	0.213592i	$0.0685162\pi$
$192$	0.0568204	−	1.78501i	0.00410066	−	0.128822i
$193$	−6.89003	−	11.9339i	−0.495955	−	0.859020i	0.504034	−	0.863684i	$-0.331849\pi$
$193$	−6.89003	−	11.9339i	−0.495955	−	0.859020i	−0.999989	+	0.00466400i	$0.998515\pi$
$194$	2.08704	−	9.18325i	0.149840	−	0.659319i
$195$	0.458230	−	0.458230i	0.0328145	−	0.0328145i
$196$	13.9957	−	0.348796i	0.999690	−	0.0249140i
$197$	6.48216	+	6.48216i	0.461835	+	0.461835i	0.899256	−	0.437422i	$-0.144108\pi$
$197$	6.48216	+	6.48216i	0.461835	+	0.461835i	−0.437422	+	0.899256i	$0.644108\pi$
$198$	12.8064	+	20.3393i	0.910112	+	1.44545i
$199$	−6.83270	+	3.94486i	−0.484357	+	0.279644i	−0.722231	−	0.691652i	$-0.756883\pi$
$199$	−6.83270	+	3.94486i	−0.484357	+	0.279644i	0.237873	+	0.971296i	$0.423550\pi$
$200$	−0.413752	+	2.79800i	−0.0292567	+	0.197849i
$201$	0.811872	+	0.468734i	0.0572650	+	0.0330620i
$202$	22.4828	+	11.8558i	1.58189	+	0.834171i
$203$	11.5310	+	7.06129i	0.809315	+	0.495605i
$204$	−0.430497	+	2.29862i	−0.0301408	+	0.160936i
$205$	2.31270	+	8.63110i	0.161526	+	0.602822i
$206$	7.35097	−	7.93724i	0.512166	−	0.553014i
$207$	−6.25543	−	10.8347i	−0.434782	−	0.753065i
$208$	11.5432	+	1.25715i	0.800379	+	0.0871679i
$209$	−37.7775			−2.61313
$210$	0.835220	−	0.0104060i	0.0576357	−	0.000718079i
$211$	−0.0206278	+	0.0206278i	−0.00142008	+	0.00142008i	−0.707816	−	0.706396i	$-0.750320\pi$
$211$	−0.0206278	+	0.0206278i	−0.00142008	+	0.00142008i	0.706396	+	0.707816i	$0.250320\pi$
$212$	−1.36947	+	1.59736i	−0.0940558	+	0.109707i
$213$	0.544519	−	2.03217i	0.0373098	−	0.139242i
$214$	−0.468495	−	12.2168i	−0.0320256	−	0.835121i
$215$	10.4601	+	6.03916i	0.713376	+	0.411868i
$216$	3.73222	−	0.431066i	0.253945	−	0.0293303i
$217$	−3.73386	+	3.54549i	−0.253471	+	0.240683i
$218$	1.95341	−	3.70437i	0.132302	−	0.250892i
$219$	−1.48535	+	0.397999i	−0.100371	+	0.0268943i
$220$	−4.97977	+	10.3900i	−0.335736	+	0.700492i
$221$	−14.6867	−	3.93529i	−0.987935	−	0.264716i
$222$	−0.620887	+	2.73199i	−0.0416712	+	0.183359i
$223$	6.39219			0.428053			0.214026	−	0.976828i	$-0.431342\pi$
$223$	6.39219			0.428053			0.214026	+	0.976828i	$0.431342\pi$
$224$	9.51961	+	11.5489i	0.636056	+	0.771643i
$225$	−2.95016			−0.196678
$226$	0.482296	−	2.12217i	0.0320819	−	0.141165i
$227$	−4.03125	−	1.08017i	−0.267563	−	0.0716933i	0.122543	−	0.992463i	$-0.460895\pi$
$227$	−4.03125	−	1.08017i	−0.267563	−	0.0716933i	−0.390106	+	0.920770i	$0.627562\pi$
$228$	−1.26544	+	2.64025i	−0.0838055	+	0.174855i
$229$	−15.0141	+	4.02301i	−0.992159	+	0.265848i	−0.718157	−	0.695881i	$-0.755014\pi$
$229$	−15.0141	+	4.02301i	−0.992159	+	0.265848i	−0.274002	+	0.961729i	$0.588347\pi$
$230$	2.79742	−	5.30491i	0.184456	−	0.349795i
$231$	3.26274	+	0.965374i	0.214673	+	0.0635169i
$232$	1.65849	+	14.3594i	0.108885	+	0.942740i
$233$	4.87165	+	2.81265i	0.319152	+	0.184263i	0.651015	−	0.759065i	$-0.274344\pi$
$233$	4.87165	+	2.81265i	0.319152	+	0.184263i	−0.331862	+	0.943328i	$0.607677\pi$
$234$	0.464107	+	12.1024i	0.0303396	+	0.791156i
$235$	1.71343	−	6.39460i	0.111772	−	0.417138i
$236$	7.70160	−	8.98315i	0.501331	−	0.584753i
$237$	−0.578298	+	0.578298i	−0.0375645	+	0.0375645i
$238$	−10.0098	−	16.8492i	−0.648838	−	1.09217i
$239$	−14.7265			−0.952576			−0.476288	−	0.879289i	$-0.658018\pi$
$239$	−14.7265			−0.952576			−0.476288	+	0.879289i	$0.658018\pi$
$240$	0.559342	+	0.696067i	0.0361054	+	0.0449309i
$241$	−14.0953	−	24.4138i	−0.907960	−	1.57263i	−0.816894	−	0.576788i	$-0.804306\pi$
$241$	−14.0953	−	24.4138i	−0.907960	−	1.57263i	−0.0910656	−	0.995845i	$-0.529027\pi$
$242$	−21.3209	+	23.0213i	−1.37056	+	1.47987i
$243$	1.52561	+	5.69366i	0.0978681	+	0.365249i
$244$	0.549198	−	2.93242i	0.0351588	−	0.187729i
$245$	−5.19912	+	4.68712i	−0.332160	+	0.299449i
$246$	2.49534	+	1.31586i	0.159097	+	0.0838962i
$247$	−16.4856	−	9.51799i	−1.04896	−	0.605615i
$248$	−5.44530	−	0.805219i	−0.345777	−	0.0511315i
$249$	1.63510	−	0.944023i	0.103620	−	0.0598250i
$250$	−0.753520	−	1.19675i	−0.0476568	−	0.0756890i
$251$	0.533730	+	0.533730i	0.0336888	+	0.0336888i	0.723751	−	0.690062i	$-0.242417\pi$
$251$	0.533730	+	0.533730i	0.0336888	+	0.0336888i	−0.690062	+	0.723751i	$0.742417\pi$
$252$	−10.4639	+	11.5847i	−0.659163	+	0.729765i
$253$	17.2748	−	17.2748i	1.08606	−	1.08606i
$254$	−0.555767	+	2.44545i	−0.0348719	+	0.153441i
$255$	−0.584646	−	1.01264i	−0.0366120	−	0.0634138i
$256$	−3.44421	+	15.6249i	−0.215263	+	0.976556i
$257$	−3.74201	+	6.48134i	−0.233420	+	0.404295i	−0.958812	−	0.284040i	$-0.908325\pi$
$257$	−3.74201	+	6.48134i	−0.233420	+	0.404295i	0.725392	+	0.688336i	$0.241658\pi$
$258$	3.64277	−	1.12736i	0.226789	−	0.0701861i
$259$	−11.2095	−	20.6302i	−0.696527	−	1.28190i
$260$	−4.79084	+	3.27941i	−0.297115	+	0.203380i
$261$	−14.5633	+	3.90221i	−0.901443	+	0.241541i
$262$	13.9822	−	0.536195i	0.863822	−	0.0331263i
$263$	14.9230	−	8.61582i	0.920194	−	0.531274i	0.0364971	−	0.999334i	$-0.488380\pi$
$263$	14.9230	−	8.61582i	0.920194	−	0.531274i	0.883697	+	0.468059i	$0.155047\pi$
$264$	1.33837	+	3.38233i	0.0823707	+	0.208168i
$265$		−	1.05202i		−	0.0646252i
$266$	−6.64526	−	23.6194i	−0.407447	−	1.44820i
$267$	−1.70293	−	1.70293i	−0.104218	−	0.104218i
$268$	−6.37621	−	5.46657i	−0.389489	−	0.333924i
$269$	28.3048	+	7.58425i	1.72578	+	0.462420i	0.979203	−	0.202884i	$-0.0650315\pi$
$269$	28.3048	+	7.58425i	1.72578	+	0.462420i	0.746572	+	0.665304i	$0.231698\pi$
$270$	−1.27643	+	1.37824i	−0.0776813	+	0.0838768i
$271$	−10.5929	+	18.3474i	−0.643473	+	1.11453i	0.341179	+	0.939998i	$0.389174\pi$
$271$	−10.5929	+	18.3474i	−0.643473	+	1.11453i	−0.984652	+	0.174529i	$0.944160\pi$
$272$	7.58181	−	19.5314i	0.459715	−	1.18427i
$273$	1.18060	+	1.24332i	0.0714529	+	0.0752491i
$274$	−3.52643	−	11.3948i	−0.213039	−	0.688383i
$275$	−1.49102	−	5.56455i	−0.0899118	−	0.335555i
$276$	−0.628671	−	1.78598i	−0.0378416	−	0.107503i
$277$	4.42520	−	16.5151i	0.265884	−	0.992294i	−0.695822	−	0.718214i	$-0.744960\pi$
$277$	4.42520	−	16.5151i	0.265884	−	0.992294i	0.961707	−	0.274080i	$-0.0883734\pi$
$278$	−1.18429	+	0.745673i	−0.0710288	+	0.0447225i
$279$		−	5.74143i		−	0.343730i
$280$	−7.37202	−	1.28582i	−0.440562	−	0.0768424i
$281$			14.7831i			0.881886i	0.897535	+	0.440943i	$0.145356\pi$
$281$			14.7831i			0.881886i	−0.897535	+	0.440943i	$0.854644\pi$
$282$	−1.11362	−	1.76866i	−0.0663148	−	0.105322i
$283$	3.91731	−	14.6196i	0.232860	−	0.869045i	−0.746242	−	0.665675i	$-0.768144\pi$
$283$	3.91731	−	14.6196i	0.232860	−	0.869045i	0.979102	−	0.203370i	$-0.0651895\pi$
$284$	−8.14645	+	16.9971i	−0.483403	+	1.00859i
$285$	−0.378891	−	1.41404i	−0.0224436	−	0.0837605i
$286$	−22.5927	+	6.99194i	−1.33594	+	0.413442i
$287$	−22.9864	+	5.52604i	−1.35684	+	0.326192i
$288$	−16.6476	−	1.16976i	−0.980969	−	0.0689290i
$289$	−5.21751	+	9.03699i	−0.306912	+	0.531587i
$290$	−5.30264	−	4.91097i	−0.311382	−	0.288382i
$291$	1.43592	+	0.384755i	0.0841753	+	0.0225547i
$292$	13.7362	−	1.05508i	0.803853	−	0.0617438i
$293$	4.30786	+	4.30786i	0.251668	+	0.251668i	0.821654	−	0.569986i	$-0.193052\pi$
$293$	4.30786	+	4.30786i	0.251668	+	0.251668i	−0.569986	+	0.821654i	$0.693052\pi$
$294$	−0.0296415	+	2.20976i	−0.00172873	+	0.128876i
$295$			5.91632i			0.344462i
$296$	9.97309	−	23.0336i	0.579674	−	1.33880i
$297$	−6.62700	+	3.82610i	−0.384537	+	0.222013i
$298$	−0.504022	−	13.1432i	−0.0291972	−	0.761365i
$299$	11.8908	−	3.18614i	0.687665	−	0.184259i
$300$	−0.438849	−	0.0821896i	−0.0253369	−	0.00474522i
$301$	−16.6887	+	27.2523i	−0.961920	+	1.57080i
$302$	−6.79289	−	21.9495i	−0.390887	−	1.26305i
$303$	−2.00611	+	3.47468i	−0.115248	+	0.199615i
$304$	15.4976	−	21.1628i	0.888849	−	1.21377i
$305$	0.745852	+	1.29185i	0.0427074	+	0.0739714i
$306$	21.3097	+	4.84297i	1.21820	+	0.276854i
$307$	−7.60236	+	7.60236i	−0.433889	+	0.433889i	−0.889949	−	0.456060i	$-0.849260\pi$
$307$	−7.60236	+	7.60236i	−0.433889	+	0.433889i	0.456060	+	0.889949i	$0.349260\pi$
$308$	−27.1393	−	13.8819i	−1.54640	−	0.790996i
$309$	1.20754	+	1.20754i	0.0686945	+	0.0686945i
$310$	2.32904	−	1.46645i	0.132280	−	0.0832890i
$311$	11.7927	−	6.80854i	0.668704	−	0.386077i	−0.126881	−	0.991918i	$-0.540497\pi$
$311$	11.7927	−	6.80854i	0.668704	−	0.386077i	0.795586	+	0.605841i	$0.207163\pi$
$312$	−0.268126	+	1.81320i	−0.0151797	+	0.102652i
$313$	−8.89311	−	5.13444i	−0.502668	−	0.290216i	0.227146	−	0.973861i	$-0.427060\pi$
$313$	−8.89311	−	5.13444i	−0.502668	−	0.290216i	−0.729815	+	0.683645i	$0.760394\pi$
$314$	−1.41703	+	2.68720i	−0.0799679	+	0.151648i
$315$	0.201914	−	7.80279i	0.0113766	−	0.439637i
$316$	6.04617	−	4.13870i	0.340124	−	0.232820i
$317$	7.25057	+	27.0595i	0.407233	+	1.51981i	0.799900	+	0.600133i	$0.204886\pi$
$317$	7.25057	+	27.0595i	0.407233	+	1.51981i	−0.392667	+	0.919681i	$0.628448\pi$
$318$	−0.243680	−	0.225681i	−0.0136649	−	0.0126555i
$319$	−14.7206	−	25.4968i	−0.824195	−	1.42755i
$320$	−3.77755	−	7.05196i	−0.211171	−	0.394217i
$321$	1.92988			0.107716
$322$	13.8393	+	7.76188i	0.771235	+	0.432552i
$323$	−24.2876	+	24.2876i	−1.35140	+	1.35140i
$324$	−1.31020	−	17.0577i	−0.0727888	−	0.947649i
$325$	0.751319	−	2.80396i	0.0416757	−	0.155536i
$326$	−8.29619	+	0.318146i	−0.459483	+	0.0176205i
$327$	0.572504	+	0.330535i	0.0316595	+	0.0182786i
$328$	−19.8036	−	15.7027i	−1.09347	−	0.867034i
$329$	16.7956	+	4.96945i	0.925971	+	0.273974i
$330$	−1.60877	−	0.848348i	−0.0885600	−	0.0467000i
$331$	−19.6363	+	5.26153i	−1.07931	+	0.289200i	−0.754312	−	0.656516i	$-0.772030\pi$
$331$	−19.6363	+	5.26153i	−1.07931	+	0.289200i	−0.324996	+	0.945715i	$0.605363\pi$
$332$	−15.9554	+	5.61635i	−0.875665	+	0.308237i
$333$	25.2883	+	6.77597i	1.38579	+	0.371321i
$334$	33.5028	+	7.61402i	1.83319	+	0.416621i
$335$	4.19939			0.229437
$336$	−1.87929	+	1.43175i	−0.102523	+	0.0781081i
$337$	10.5657			0.575552			0.287776	−	0.957698i	$-0.407084\pi$
$337$	10.5657			0.575552			0.287776	+	0.957698i	$0.407084\pi$
$338$	6.30684	+	1.43333i	0.343047	+	0.0779627i
$339$	0.331830	+	0.0889135i	0.0180225	+	0.00482912i
$340$	3.47828	+	9.88138i	0.188636	+	0.535893i
$341$	10.8294	−	2.90173i	0.586444	−	0.157137i
$342$	24.2008	+	12.7617i	1.30863	+	0.690076i
$343$	−12.0410	−	14.0718i	−0.650152	−	0.759805i
$344$	−33.9371	+	3.91968i	−1.82976	+	0.211335i
$345$	0.819865	+	0.473349i	0.0441400	+	0.0254843i
$346$	1.24335	−	0.0476805i	0.0668428	−	0.00256332i
$347$	−7.64828	+	28.5438i	−0.410581	+	1.53231i	0.382944	+	0.923771i	$0.374910\pi$
$347$	−7.64828	+	28.5438i	−0.410581	+	1.53231i	−0.793525	+	0.608537i	$0.791757\pi$
$348$	−2.27505	+	0.174747i	−0.121956	+	0.00936741i
$349$	3.81912	−	3.81912i	0.204433	−	0.204433i	−0.597463	−	0.801896i	$-0.703825\pi$
$349$	3.81912	−	3.81912i	0.204433	−	0.204433i	0.801896	+	0.597463i	$0.203825\pi$
$350$	3.21681	−	1.91105i	0.171946	−	0.102150i
$351$	−3.85592			−0.205814
$352$	−6.20733	−	31.9916i	−0.330852	−	1.70516i
$353$	−12.1188	−	20.9904i	−0.645019	−	1.11721i	−0.984297	−	0.176519i	$-0.943516\pi$
$353$	−12.1188	−	20.9904i	−0.645019	−	1.11721i	0.339278	−	0.940686i	$-0.389817\pi$
$354$	1.37040	+	1.26917i	0.0728358	+	0.0674559i
$355$	−2.43917	−	9.10311i	−0.129458	−	0.483143i
$356$	12.1873	+	17.8043i	0.645927	+	0.943626i
$357$	2.71830	−	1.47700i	0.143868	−	0.0781714i
$358$	13.5065	−	25.6132i	0.713841	−	1.35370i
$359$	−23.2323	−	13.4132i	−1.22616	−	0.707921i	−0.259932	−	0.965627i	$-0.583700\pi$
$359$	−23.2323	−	13.4132i	−1.22616	−	0.707921i	−0.966223	+	0.257706i	$0.917033\pi$
$360$	6.69998	−	4.97374i	0.353120	−	0.262139i
$361$	−20.7868	+	12.0013i	−1.09404	+	0.631646i
$362$	−19.1916	+	12.0838i	−1.00869	+	0.635108i
$363$	−3.50237	−	3.50237i	−0.183827	−	0.183827i
$364$	−8.34570	−	12.8956i	−0.437434	−	0.675912i
$365$	−4.87080	+	4.87080i	−0.254949	+	0.254949i
$366$	0.459233	+	0.104368i	0.0240045	+	0.00545539i
$367$	16.5458	+	28.6582i	0.863684	+	1.49594i	0.868348	+	0.495956i	$0.165182\pi$
$367$	16.5458	+	28.6582i	0.863684	+	1.49594i	−0.00466368	+	0.999989i	$0.501485\pi$
$368$	2.59056	+	16.7639i	0.135042	+	0.873881i
$369$	13.1807	−	22.8296i	0.686160	−	1.18846i
$370$	3.71033	+	11.9890i	0.192891	+	0.623278i
$371$	2.78246	+	0.0720021i	0.144458	+	0.00373817i
$372$	0.159952	−	0.854060i	0.00829314	−	0.0442809i
$373$	7.95284	−	2.13096i	0.411783	−	0.110337i	−0.0469797	−	0.998896i	$-0.514960\pi$
$373$	7.95284	−	2.13096i	0.411783	−	0.110337i	0.458762	+	0.888559i	$0.348293\pi$
$374$	1.63525	+	42.6418i	0.0845566	+	2.20495i
$375$	0.193331	−	0.111620i	0.00998357	−	0.00576401i
$376$	6.88949	+	17.4112i	0.355298	+	0.897913i
$377$		−	14.8353i		−	0.764057i
$378$	−3.55789	−	3.47032i	−0.182998	−	0.178494i
$379$	12.6669	+	12.6669i	0.650653	+	0.650653i	0.953150	−	0.302497i	$-0.0978202\pi$
$379$	12.6669	+	12.6669i	0.650653	+	0.650653i	−0.302497	+	0.953150i	$0.597820\pi$
$380$	1.00442	+	13.0767i	0.0515259	+	0.670823i
$381$	−0.382379	−	0.102458i	−0.0195899	−	0.00524910i
$382$	−8.70380	−	8.06090i	−0.445325	−	0.412431i
$383$	4.12415	−	7.14324i	0.210734	−	0.365003i	−0.741210	−	0.671273i	$-0.765748\pi$
$383$	4.12415	−	7.14324i	0.210734	−	0.365003i	0.951945	+	0.306270i	$0.0990811\pi$
$384$	−2.44381	−	0.637798i	−0.124710	−	0.0325475i
$385$	14.8195	−	3.56269i	0.755274	−	0.181572i
$386$	−18.6168	+	5.76149i	−0.947571	+	0.293252i
$387$	−9.22251	−	34.4189i	−0.468807	−	1.74961i
$388$	−12.0100	−	5.75624i	−0.609718	−	0.292229i
$389$	5.31265	−	19.8271i	0.269362	−	1.00527i	−0.690164	−	0.723653i	$-0.742462\pi$
$389$	5.31265	−	19.8271i	0.269362	−	1.00527i	0.959526	−	0.281620i	$-0.0908717\pi$
$390$	−0.488308	−	0.775536i	−0.0247264	−	0.0392708i
$391$		−	22.2123i		−	1.12332i
$392$	3.90537	−	19.4100i	0.197251	−	0.980353i
$393$			2.20877i			0.111417i
$394$	10.9708	−	6.90764i	0.552700	−	0.348002i
$395$	−0.948184	+	3.53867i	−0.0477083	+	0.178050i
$396$	32.0625	−	11.2861i	1.61120	−	0.567149i
$397$	−3.25763	−	12.1577i	−0.163496	−	0.610175i	−0.998227	−	0.0595177i	$-0.981044\pi$
$397$	−3.25763	−	12.1577i	−0.163496	−	0.610175i	0.834731	−	0.550657i	$-0.185623\pi$
$398$	3.29872	+	10.6590i	0.165350	+	0.534287i
$399$	3.76588	−	0.905336i	0.188530	−	0.0453235i
$400$	3.72890	+	1.44751i	0.186445	+	0.0723753i
$401$	6.34725	−	10.9938i	0.316967	−	0.549002i	−0.662887	−	0.748719i	$-0.730669\pi$
$401$	6.34725	−	10.9938i	0.316967	−	0.549002i	0.979854	+	0.199717i	$0.0640024\pi$
$402$	0.900856	−	0.972704i	0.0449306	−	0.0485141i
$403$	5.45689	+	1.46217i	0.271827	+	0.0728359i
$404$	23.3961	−	27.2892i	1.16400	−	1.35769i
$405$	6.04856	+	6.04856i	0.300556	+	0.300556i
$406$	13.3518	−	13.6887i	0.662637	−	0.679357i
$407$			51.1229i			2.53407i
$408$	3.03499	+	1.31409i	0.150254	+	0.0650570i
$409$	1.91938	−	1.10816i	0.0949073	−	0.0547948i	−0.451795	−	0.892122i	$-0.649216\pi$
$409$	1.91938	−	1.10816i	0.0949073	−	0.0547948i	0.546702	+	0.837327i	$0.315883\pi$
$410$	12.6275	−	0.484246i	0.623629	−	0.0239152i
$411$	1.81872	−	0.487325i	0.0897109	−	0.0240380i
$412$	−8.64198	−	12.6249i	−0.425760	−	0.621987i
$413$	−15.6479	−	0.404923i	−0.769982	−	0.0199250i
$414$	−16.9021	+	5.23083i	−0.830694	+	0.257081i
$415$	4.22875	−	7.32441i	0.207581	−	0.359541i
$416$	5.35144	−	15.5247i	0.262376	−	0.761160i
$417$	−0.110457	−	0.191318i	−0.00540912	−	0.00936887i
$418$	−11.8399	+	52.0971i	−0.579107	+	2.54815i
$419$	−17.3509	+	17.3509i	−0.847645	+	0.847645i	−0.989839	−	0.142194i	$-0.954584\pi$
$419$	−17.3509	+	17.3509i	−0.847645	+	0.847645i	0.142194	+	0.989839i	$0.454584\pi$
$420$	0.247416	−	1.15507i	0.0120727	−	0.0563617i
$421$	14.5307	+	14.5307i	0.708184	+	0.708184i	0.966153	−	0.257969i	$-0.0830533\pi$
$421$	14.5307	+	14.5307i	0.708184	+	0.708184i	−0.257969	+	0.966153i	$0.583053\pi$
$422$	0.0219818	+	0.0349117i	0.00107006	+	0.00169948i
$423$	−16.9140	+	9.76531i	−0.822387	+	0.474806i
$424$	1.77362	+	2.38920i	0.0861348	+	0.116030i
$425$	−4.53611	−	2.61892i	−0.220033	−	0.127036i
$426$	−2.63180	−	1.38782i	−0.127511	−	0.0672401i
$427$	−3.46783	+	1.88426i	−0.167820	+	0.0911859i
$428$	−16.9944	−	3.18278i	−0.821453	−	0.153846i
$429$	−0.966232	−	3.60603i	−0.0466501	−	0.174101i
$430$	11.6066	−	12.5323i	0.559721	−	0.604361i
$431$	9.30550	+	16.1176i	0.448230	+	0.776358i	0.998271	−	0.0587803i	$-0.0187211\pi$
$431$	9.30550	+	16.1176i	0.448230	+	0.776358i	−0.550041	+	0.835138i	$0.685388\pi$
$432$	0.575254	−	5.28201i	0.0276769	−	0.254131i
$433$	1.63177			0.0784176			0.0392088	−	0.999231i	$-0.487516\pi$
$433$	1.63177			0.0784176			0.0392088	+	0.999231i	$0.487516\pi$
$434$	3.71917	+	6.26036i	0.178526	+	0.300507i
$435$	0.806723	−	0.806723i	0.0386794	−	0.0386794i
$436$	−4.49629	−	3.85484i	−0.215333	−	0.184613i
$437$	7.19754	−	26.8616i	0.344305	−	1.28496i
$438$	0.0833355	+	2.17311i	0.00398192	+	0.103835i
$439$	−18.5073	−	10.6852i	−0.883306	−	0.509977i	−0.0115589	−	0.999933i	$-0.503679\pi$
$439$	−18.5073	−	10.6852i	−0.883306	−	0.509977i	−0.871747	+	0.489956i	$0.837013\pi$
$440$	12.7676	+	10.1237i	0.608670	+	0.482627i
$441$	20.6235	+	1.06807i	0.982072	+	0.0508606i
$442$	−10.0299	+	19.0203i	−0.477075	+	0.904704i
$443$	4.06854	−	1.09016i	0.193302	−	0.0517952i	−0.160869	−	0.986976i	$-0.551430\pi$
$443$	4.06854	−	1.09016i	0.193302	−	0.0517952i	0.354171	+	0.935181i	$0.384763\pi$
$444$	3.57295	+	1.71247i	0.169565	+	0.0812701i
$445$	−10.4204	−	2.79214i	−0.493975	−	0.132360i
$446$	2.00338	−	8.81513i	0.0948626	−	0.417409i
$447$	2.07623			0.0982024
$448$	18.9100	−	9.50846i	0.893415	−	0.449233i
$449$	27.8414			1.31392			0.656959	−	0.753926i	$-0.271842\pi$
$449$	27.8414			1.31392			0.656959	+	0.753926i	$0.271842\pi$
$450$	−0.924611	+	4.06842i	−0.0435866	+	0.191787i
$451$	49.7225	+	13.3231i	2.34134	+	0.627360i
$452$	−2.77542	−	1.33022i	−0.130545	−	0.0625682i
$453$	3.50337	−	0.938725i	0.164603	−	0.0441052i
$454$	−2.75304	+	5.22075i	−0.129206	+	0.245022i
$455$	7.36468	+	2.17905i	0.345261	+	0.102155i
$456$	3.24444	+	2.57258i	0.151935	+	0.120472i
$457$	3.21806	+	1.85795i	0.150534	+	0.0869110i	0.573375	−	0.819293i	$-0.305634\pi$
$457$	3.21806	+	1.85795i	0.150534	+	0.0869110i	−0.422841	+	0.906204i	$0.638967\pi$
$458$	0.842363	+	21.9660i	0.0393610	+	1.02640i
$459$	−1.80073	+	6.72041i	−0.0840509	+	0.313682i
$460$	−6.43899	−	5.52039i	−0.300219	−	0.257389i
$461$	26.9397	−	26.9397i	1.25471	−	1.25471i	0.301123	−	0.953585i	$-0.402638\pi$
$461$	26.9397	−	26.9397i	1.25471	−	1.25471i	0.953585	−	0.301123i	$-0.0973616\pi$
$462$	2.35387	−	4.19692i	0.109512	−	0.195259i
$463$	−9.29658			−0.432049			−0.216024	−	0.976388i	$-0.569309\pi$
$463$	−9.29658			−0.432049			−0.216024	+	0.976388i	$0.569309\pi$
$464$	20.3221	+	2.21324i	0.943429	+	0.102747i
$465$	0.217227	+	0.376249i	0.0100737	+	0.0174481i
$466$	5.40560	−	5.83672i	0.250409	−	0.270381i
$467$	−0.684051	−	2.55291i	−0.0316541	−	0.118135i	0.948291	−	0.317402i	$-0.102810\pi$
$467$	−0.684051	−	2.55291i	−0.0316541	−	0.118135i	−0.979945	+	0.199267i	$0.936144\pi$
$468$	16.8352	+	3.15298i	0.778207	+	0.145746i
$469$	−0.287413	+	11.1068i	−0.0132715	+	0.512865i
$470$	−8.28146	−	4.36703i	−0.381995	−	0.201436i
$471$	−0.415303	−	0.239775i	−0.0191361	−	0.0110483i
$472$	−9.97444	−	13.4363i	−0.459111	−	0.618455i
$473$	60.2593	−	34.7907i	2.77073	−	1.59968i
$474$	0.616257	+	0.978746i	0.0283056	+	0.0449553i
$475$	−4.63695	−	4.63695i	−0.212758	−	0.212758i
$476$	−26.3730	+	8.52329i	−1.20880	+	0.390664i
$477$	−2.19460	+	2.19460i	−0.100484	+	0.100484i
$478$	−4.61542	+	20.3085i	−0.211105	+	0.928890i
$479$	12.3301	+	21.3564i	0.563378	+	0.975799i	0.997199	+	0.0747997i	$0.0238317\pi$
$479$	12.3301	+	21.3564i	0.563378	+	0.975799i	−0.433821	+	0.900999i	$0.642835\pi$
$480$	1.13521	−	0.553206i	0.0518152	−	0.0252503i
$481$	−12.8803	+	22.3094i	−0.587293	+	1.01722i
$482$	−38.0855	+	11.7866i	−1.73474	+	0.536865i
$483$	−1.30806	+	2.13604i	−0.0595187	+	0.0971930i
$484$	25.0653	+	36.6176i	1.13933	+	1.66444i
$485$	6.43222	−	1.72351i	0.292072	−	0.0782604i
$486$	8.32998	−	0.319442i	0.377855	−	0.0144902i
$487$	13.5303	−	7.81170i	0.613114	−	0.353982i	−0.161069	−	0.986943i	$-0.551494\pi$
$487$	13.5303	−	7.81170i	0.613114	−	0.353982i	0.774183	+	0.632961i	$0.218161\pi$
$488$	−3.87183	−	1.67642i	−0.175270	−	0.0758881i
$489$		−	1.31055i		−	0.0592651i
$490$	4.83431	+	8.63883i	0.218392	+	0.390263i
$491$	−18.2600	−	18.2600i	−0.824061	−	0.824061i	0.162626	−	0.986688i	$-0.448003\pi$
$491$	−18.2600	−	18.2600i	−0.824061	−	0.824061i	−0.986688	+	0.162626i	$0.948003\pi$
$492$	2.59670	−	3.02879i	0.117068	−	0.136549i
$493$	−25.8562	−	6.92815i	−1.16451	−	0.312028i
$494$	−18.2925	+	19.7515i	−0.823020	+	0.888660i
$495$	−8.49773	+	14.7185i	−0.381944	+	0.661547i
$496$	−2.81705	+	7.25696i	−0.126489	+	0.325847i
$497$	24.2434	−	5.82825i	1.08747	−	0.261433i
$498$	−0.789398	−	2.55074i	−0.0353738	−	0.114302i
$499$	8.56308	+	31.9578i	0.383336	+	1.43063i	0.840773	+	0.541388i	$0.182101\pi$
$499$	8.56308	+	31.9578i	0.383336	+	1.43063i	−0.457437	+	0.889242i	$0.651233\pi$
$500$	−1.88654	+	0.664067i	−0.0843684	+	0.0296980i
$501$	−1.40368	+	5.23860i	−0.0627118	+	0.234044i
$502$	0.903317	−	0.568764i	0.0403170	−	0.0253852i
$503$		−	19.1718i		−	0.854828i	−0.904056	−	0.427414i	$-0.859425\pi$
$503$		−	19.1718i		−	0.854828i	0.904056	−	0.427414i	$-0.140575\pi$
$504$	12.6963	+	18.0610i	0.565538	+	0.804499i
$505$			17.9727i			0.799776i
$506$	−18.4087	−	29.2368i	−0.818365	−	1.29974i
$507$	−0.264241	+	0.986159i	−0.0117353	+	0.0437969i
$508$	3.19822	+	1.53286i	0.141898	+	0.0680096i
$509$	−5.74863	−	21.4542i	−0.254803	−	0.950939i	−0.968200	−	0.250178i	$-0.919511\pi$
$509$	−5.74863	−	21.4542i	−0.254803	−	0.950939i	0.713396	−	0.700761i	$-0.247156\pi$
$510$	−1.57971	+	0.488885i	−0.0699507	+	0.0216482i
$511$	−12.5492	−	13.2160i	−0.555146	−	0.584640i
$512$	20.4680	+	9.64673i	0.904568	+	0.426329i
$513$	−4.35529	+	7.54358i	−0.192291	+	0.333057i
$514$	7.76530	+	7.19172i	0.342513	+	0.317213i
$515$	7.38907	+	1.97989i	0.325601	+	0.0872446i
$516$	−0.412998	−	5.37688i	−0.0181812	−	0.236704i
$517$	−26.9675	−	26.9675i	−1.18603	−	1.18603i
$518$	−31.9632	+	8.99277i	−1.40438	+	0.395120i
$519$			0.196412i			0.00862152i
$520$	3.02096	+	7.63460i	0.132478	+	0.334799i
$521$	−23.9506	+	13.8279i	−1.04929	+	0.605811i	−0.922452	−	0.386112i	$-0.873818\pi$
$521$	−23.9506	+	13.8279i	−1.04929	+	0.605811i	−0.126843	+	0.991923i	$0.540484\pi$
$522$	0.817069	+	21.3064i	0.0357621	+	0.932557i
$523$	1.32821	−	0.355891i	0.0580784	−	0.0155620i	−0.229663	−	0.973270i	$-0.573762\pi$
$523$	1.32821	−	0.355891i	0.0580784	−	0.0155620i	0.287741	+	0.957708i	$0.407096\pi$
$524$	3.64272	−	19.4501i	0.159133	−	0.849684i
$525$	0.281987	+	0.518974i	0.0123069	+	0.0226499i
$526$	−7.20460	−	23.2799i	−0.314136	−	1.01505i
$527$	5.09678	−	8.82789i	0.222019	−	0.384549i
$528$	5.08385	−	0.785615i	0.221246	−	0.0341895i
$529$	−2.50809	−	4.34415i	−0.109048	−	0.188876i
$530$	−1.45079	−	0.329714i	−0.0630183	−	0.0143219i
$531$	12.3419	−	12.3419i	0.535594	−	0.535594i
$532$	−34.6550	+	1.76157i	−1.50248	+	0.0763738i
$533$	18.3415	+	18.3415i	0.794459	+	0.794459i
$534$	−2.88214	+	1.81471i	−0.124722	+	0.0785300i
$535$	7.48671	−	4.32246i	0.323679	−	0.186876i
$536$	−9.53703	+	7.07983i	−0.411937	+	0.305802i
$537$	3.95847	+	2.28542i	0.170821	+	0.0986234i
$538$	19.3301	−	36.6567i	0.833378	−	1.58038i
$539$	8.40858	+	39.4396i	0.362183	+	1.69878i
$540$	1.50061	+	2.19222i	0.0645759	+	0.0943380i
$541$	0.0514911	+	0.192167i	0.00221378	+	0.00826192i	0.967024	−	0.254686i	$-0.0819720\pi$
$541$	0.0514911	+	0.192167i	0.00221378	+	0.00826192i	−0.964810	+	0.262948i	$0.915305\pi$
$542$	21.9821	+	20.3584i	0.944211	+	0.874468i
$543$	−1.78998	−	3.10034i	−0.0768154	−	0.133048i
$544$	−24.5586	−	16.5770i	−1.05294	−	0.710734i
$545$	2.96126			0.126847
$546$	2.08461	−	1.23843i	0.0892130	−	0.0529999i
$547$	28.5981	−	28.5981i	1.22276	−	1.22276i	0.256120	−	0.966645i	$-0.417556\pi$
$547$	28.5981	−	28.5981i	1.22276	−	1.22276i	0.966645	−	0.256120i	$-0.0824441\pi$
$548$	−16.8192	+	1.29188i	−0.718479	+	0.0551863i
$549$	1.13900	−	4.25082i	0.0486115	−	0.181421i
$550$	−8.14109	+	0.312198i	−0.347137	+	0.0133122i
$551$	−29.0233	−	16.7566i	−1.23643	−	0.713855i
$552$	−2.65998	+	0.307224i	−0.113216	+	0.0130763i
$553$	−9.29441	−	2.75001i	−0.395239	−	0.116942i
$554$	−21.3882	−	11.2785i	−0.908696	−	0.479180i
$555$	−1.91357	+	0.512738i	−0.0812264	+	0.0217645i
$556$	0.657152	+	1.86689i	0.0278695	+	0.0791738i
$557$	19.3026	+	5.17212i	0.817878	+	0.219150i	0.643418	−	0.765515i	$-0.277516\pi$
$557$	19.3026	+	5.17212i	0.817878	+	0.219150i	0.174459	+	0.984664i	$0.444182\pi$
$558$	−7.91770	−	1.79942i	−0.335183	−	0.0761756i
$559$	35.0619			1.48296
$560$	−4.08367	+	9.76338i	−0.172567	+	0.412578i
$561$	−6.73612			−0.284399
$562$	20.3866	+	4.63318i	0.859958	+	0.195439i
$563$	−32.9874	−	8.83896i	−1.39025	−	0.372518i	−0.515419	−	0.856938i	$-0.672364\pi$
$563$	−32.9874	−	8.83896i	−1.39025	−	0.372518i	−0.874835	+	0.484420i	$0.839031\pi$
$564$	−2.78808	+	0.981415i	−0.117399	+	0.0413250i
$565$	1.48643	−	0.398288i	0.0625346	−	0.0167561i
$566$	−18.9334	−	9.98409i	−0.795830	−	0.419663i
$567$	−16.4116	+	15.5837i	−0.689223	+	0.654453i
$568$	20.8866	+	16.5614i	0.876381	+	0.694901i
$569$	7.71087	+	4.45187i	0.323256	+	0.186632i	0.652843	−	0.757493i	$-0.273576\pi$
$569$	7.71087	+	4.45187i	0.323256	+	0.186632i	−0.329587	+	0.944125i	$0.606909\pi$
$570$	−2.06878	+	0.0793344i	−0.0866515	+	0.00332295i
$571$	−0.961559	+	3.58859i	−0.0402400	+	0.150178i	−0.983123	−	0.182947i	$-0.941436\pi$
$571$	−0.961559	+	3.58859i	−0.0402400	+	0.150178i	0.942883	+	0.333125i	$0.108103\pi$
$572$	2.56144	+	33.3478i	0.107099	+	1.39434i
$573$	1.32416	−	1.32416i	0.0553176	−	0.0553176i
$574$	0.416518	+	33.4312i	0.0173851	+	1.39539i
$575$	4.24073			0.176851
$576$	−6.83069	+	22.5912i	−0.284612	+	0.941301i
$577$	17.1055	+	29.6276i	0.712112	+	1.23341i	0.964063	+	0.265675i	$0.0855947\pi$
$577$	17.1055	+	29.6276i	0.712112	+	1.23341i	−0.251950	+	0.967740i	$0.581072\pi$
$578$	10.8272	+	10.0275i	0.450353	+	0.417088i
$579$	−0.796193	−	2.97143i	−0.0330886	−	0.123488i
$580$	−8.43436	+	5.77346i	−0.350218	+	0.239730i
$581$	19.0827	+	11.6858i	0.791682	+	0.484807i
$582$	0.980628	−	1.85962i	0.0406483	−	0.0770838i
$583$	−5.24858	−	3.03027i	−0.217374	−	0.125501i
$584$	2.85007	−	19.2736i	0.117937	−	0.797548i
$585$	−7.41660	+	4.28198i	−0.306639	+	0.177038i
$586$	7.29087	−	4.59062i	0.301183	−	0.189637i
$587$	−16.8395	−	16.8395i	−0.695039	−	0.695039i	0.268297	−	0.963336i	$-0.413539\pi$
$587$	−16.8395	−	16.8395i	−0.695039	−	0.695039i	−0.963336	+	0.268297i	$0.913539\pi$
$588$	3.03807	+	0.733437i	0.125288	+	0.0302464i
$589$	9.02414	−	9.02414i	0.371833	−	0.371833i
$590$	8.15890	+	1.85424i	0.335896	+	0.0763377i
$591$	1.02323	+	1.77229i	0.0420903	+	0.0729025i
$592$	−28.6388	−	20.9723i	−1.17705	−	0.861958i
$593$	−16.3114	+	28.2521i	−0.669828	+	1.16018i	0.308124	+	0.951346i	$0.400299\pi$
$593$	−16.3114	+	28.2521i	−0.669828	+	1.16018i	−0.977952	+	0.208830i	$0.933035\pi$
$594$	3.19941	+	10.3381i	0.131273	+	0.424177i
$595$	7.23716	−	11.8181i	0.296695	−	0.484497i
$596$	−18.2831	−	3.42414i	−0.748904	−	0.140258i
$597$	−1.70128	+	0.455857i	−0.0696288	+	0.0186570i
$598$	−0.667134	−	17.3966i	−0.0272811	−	0.711401i
$599$	−0.153274	+	0.0884929i	−0.00626262	+	0.00361572i	−0.503128	−	0.864212i	$-0.667818\pi$
$599$	−0.153274	+	0.0884929i	−0.00626262	+	0.00361572i	0.496865	+	0.867828i	$0.334484\pi$
$600$	−0.250883	+	0.579434i	−0.0102423	+	0.0236553i
$601$			23.4355i			0.955955i	0.878372	+	0.477977i	$0.158630\pi$
$601$			23.4355i			0.955955i	−0.878372	+	0.477977i	$0.841370\pi$
$602$	32.3519	+	31.5557i	1.31856	+	1.28611i
$603$	−8.76027	−	8.76027i	−0.356746	−	0.356746i
$604$	−32.3984	+	2.48852i	−1.31827	+	0.101257i
$605$	−21.4314	−	5.74252i	−0.871309	−	0.233467i
$606$	4.16302	+	3.85552i	0.169111	+	0.156620i
$607$	−1.99926	+	3.46282i	−0.0811474	+	0.140551i	−0.903743	−	0.428075i	$-0.859192\pi$
$607$	−1.99926	+	3.46282i	−0.0811474	+	0.140551i	0.822596	+	0.568627i	$0.192525\pi$
$608$	−24.3274	−	28.0046i	−0.986608	−	1.13574i
$609$	2.07846	+	2.18889i	0.0842234	+	0.0886981i
$610$	2.01529	−	0.623686i	0.0815966	−	0.0252523i
$611$	−4.97386	−	18.5627i	−0.201221	−	0.750967i
$612$	13.3574	−	27.8693i	0.539940	−	1.12655i
$613$	−7.97906	+	29.7783i	−0.322271	+	1.20273i	0.594755	+	0.803907i	$0.297249\pi$
$613$	−7.97906	+	29.7783i	−0.322271	+	1.20273i	−0.917027	+	0.398826i	$0.869418\pi$
$614$	8.10136	+	12.8667i	0.326944	+	0.519257i
$615$			1.99477i			0.0804369i
$616$	−27.6496	+	33.0756i	−1.11403	+	1.33265i
$617$		−	35.2198i		−	1.41790i	−0.705260	−	0.708949i	$-0.749170\pi$
$617$		−	35.2198i		−	1.41790i	0.705260	−	0.708949i	$-0.250830\pi$
$618$	2.04371	−	1.28680i	0.0822101	−	0.0517627i
$619$	−2.77743	+	10.3655i	−0.111634	+	0.416626i	−0.999013	−	0.0444158i	$-0.985857\pi$
$619$	−2.77743	+	10.3655i	−0.111634	+	0.416626i	0.887379	+	0.461041i	$0.152524\pi$
$620$	−1.29237	−	3.67146i	−0.0519027	−	0.147449i
$621$	−1.45793	−	5.44107i	−0.0585047	−	0.218343i
$622$	−5.69334	−	18.3966i	−0.228282	−	0.737637i
$623$	8.09803	−	27.3695i	0.324441	−	1.09654i
$624$	2.41646	+	0.938035i	0.0967359	+	0.0375515i
$625$	0.500000	−	0.866025i	0.0200000	−	0.0346410i
$626$	−9.86783	+	10.6548i	−0.394398	+	0.425853i
$627$	−8.14607	−	2.18273i	−0.325323	−	0.0871700i
$628$	3.26167	+	2.79636i	0.130155	+	0.111587i
$629$	32.8675	+	32.8675i	1.31051	+	1.31051i
$630$	−10.6971	−	2.72392i	−0.426184	−	0.108524i
$631$			29.5619i			1.17684i	0.808555	+	0.588420i	$0.200250\pi$
$631$			29.5619i			1.17684i	−0.808555	+	0.588420i	$0.799750\pi$
$632$	−3.81253	−	9.63507i	−0.151654	−	0.383262i
$633$	−0.00563987	+	0.00325618i	−0.000224165	+	0.000129422i
$634$	39.5888	−	1.51817i	1.57227	−	0.0602942i
$635$	−1.71287	+	0.458961i	−0.0679731	+	0.0182133i
$636$	−0.387596	+	0.265316i	−0.0153692	+	0.0105205i
$637$	−6.26733	+	19.3294i	−0.248321	+	0.765860i
$638$	−39.7749	+	12.3094i	−1.57470	+	0.487336i
$639$	−13.9015	+	24.0781i	−0.549935	+	0.952516i
$640$	−10.9089	+	2.99927i	−0.431213	+	0.118556i
$641$	−13.5805	−	23.5221i	−0.536397	−	0.929066i	−0.999094	−	0.0425503i	$-0.986452\pi$
$641$	−13.5805	−	23.5221i	−0.536397	−	0.929066i	0.462698	−	0.886516i	$-0.346882\pi$
$642$	0.604845	−	2.66140i	0.0238713	−	0.105037i
$643$	30.6989	−	30.6989i	1.21065	−	1.21065i	0.239832	−	0.970814i	$-0.422908\pi$
$643$	30.6989	−	30.6989i	1.21065	−	1.21065i	0.970814	−	0.239832i	$-0.0770924\pi$
$644$	15.0414	−	16.6524i	0.592714	−	0.656198i
$645$	1.90661	+	1.90661i	0.0750728	+	0.0750728i
$646$	25.8818	+	41.1058i	1.01831	+	1.61728i
$647$	11.0182	−	6.36139i	0.433172	−	0.250092i	−0.267525	−	0.963551i	$-0.586206\pi$
$647$	11.0182	−	6.36139i	0.433172	−	0.250092i	0.700697	+	0.713459i	$0.252873\pi$
$648$	−23.9340	−	3.53922i	−0.940216	−	0.139034i
$649$	29.5168	+	17.0415i	1.15864	+	0.668939i
$650$	−3.63133	−	1.91489i	−0.142432	−	0.0751083i
$651$	−1.00999	+	0.548786i	−0.0395848	+	0.0215086i
$652$	−2.16137	+	11.5406i	−0.0846458	+	0.451963i
$653$	4.67610	+	17.4514i	0.182990	+	0.682927i	0.995052	+	0.0993564i	$0.0316784\pi$
$653$	4.67610	+	17.4514i	0.182990	+	0.682927i	−0.812062	+	0.583571i	$0.801655\pi$
$654$	0.635253	−	0.685918i	0.0248403	−	0.0268215i
$655$	4.94708	+	8.56859i	0.193298	+	0.334803i
$656$	−27.8614	+	22.3887i	−1.08780	+	0.874133i
$657$	20.3218			0.792827
$658$	12.1170	−	21.6045i	0.472370	−	0.842230i
$659$	−14.4418	+	14.4418i	−0.562572	+	0.562572i	−0.930037	−	0.367465i	$-0.880226\pi$
$659$	−14.4418	+	14.4418i	−0.562572	+	0.562572i	0.367465	+	0.930037i	$0.380226\pi$
$660$	−1.67412	+	1.95269i	−0.0651650	+	0.0760085i
$661$	0.110124	−	0.410987i	0.00428331	−	0.0159855i	−0.963751	−	0.266803i	$-0.914033\pi$
$661$	0.110124	−	0.410987i	0.00428331	−	0.0159855i	0.968034	+	0.250817i	$0.0806994\pi$
$662$	1.10169	+	28.7284i	0.0428184	+	1.11656i
$663$	−2.93956	−	1.69715i	−0.114163	−	0.0659120i
$664$	2.74464	+	23.7634i	0.106513	+	0.922200i
$665$	12.5815	−	11.9467i	0.487888	−	0.463275i
$666$	17.2700	−	32.7501i	0.669198	−	1.26904i
$667$	20.9340	−	5.60926i	0.810569	−	0.217191i
$668$	21.0002	−	43.8156i	0.812522	−	1.69528i
$669$	1.37836	+	0.369332i	0.0532906	+	0.0142792i
$670$	1.31613	−	5.79116i	0.0508466	−	0.223732i
$671$	8.59349			0.331748
$672$	1.38546	+	3.04035i	0.0534453	+	0.117284i
$673$	10.7925			0.416022			0.208011	−	0.978126i	$-0.433301\pi$
$673$	10.7925			0.416022			0.208011	+	0.978126i	$0.433301\pi$
$674$	3.31140	−	14.5706i	0.127551	−	0.561240i
$675$	−1.28305	−	0.343792i	−0.0493846	−	0.0132326i
$676$	3.95326	−	8.24822i	0.152048	−	0.317239i
$677$	9.97534	−	2.67288i	0.383384	−	0.102727i	−0.0619794	−	0.998077i	$-0.519741\pi$
$677$	9.97534	−	2.67288i	0.383384	−	0.102727i	0.445363	+	0.895350i	$0.353075\pi$
$678$	0.226615	−	0.429743i	0.00870309	−	0.0165042i
$679$	4.11821	+	17.1303i	0.158043	+	0.657401i
$680$	14.7170	−	1.69980i	0.564372	−	0.0651842i
$681$	−0.806857	−	0.465839i	−0.0309188	−	0.0178510i
$682$	−0.607581	−	15.8437i	−0.0232655	−	0.606686i
$683$	−8.11335	+	30.2794i	−0.310449	+	1.15861i	0.617704	+	0.786411i	$0.288063\pi$
$683$	−8.11335	+	30.2794i	−0.310449	+	1.15861i	−0.928153	+	0.372200i	$0.878604\pi$
$684$	25.1838	−	29.3745i	0.962928	−	1.12316i
$685$	5.96399	−	5.96399i	0.227872	−	0.227872i
$686$	−23.1794	+	12.1949i	−0.884994	+	0.465602i
$687$	−3.46997			−0.132388
$688$	−5.23079	+	48.0293i	−0.199422	+	1.83110i
$689$	−1.52694	−	2.64474i	−0.0581719	−	0.100757i
$690$	0.909725	−	0.982281i	0.0346326	−	0.0373948i
$691$	1.39965	+	5.22357i	0.0532453	+	0.198714i	0.987425	−	0.158089i	$-0.0505333\pi$
$691$	1.39965	+	5.22357i	0.0532453	+	0.198714i	−0.934180	+	0.356803i	$0.883867\pi$
$692$	0.323924	−	1.72958i	0.0123137	−	0.0657488i
$693$	−38.3468	−	23.4827i	−1.45668	−	0.892034i
$694$	36.9662	+	19.4932i	1.40322	+	0.739953i
$695$	−0.857007	−	0.494793i	−0.0325081	−	0.0187686i
$696$	−0.472041	+	3.19218i	−0.0178927	+	0.120999i
$697$	40.5327	−	23.4016i	1.53529	−	0.886397i
$698$	−4.06980	−	6.46371i	−0.154044	−	0.244655i
$699$	0.887975	+	0.887975i	0.0335863	+	0.0335863i
$700$	−1.62725	−	5.03508i	−0.0615043	−	0.190308i
$701$	15.1255	−	15.1255i	0.571283	−	0.571283i	−0.361204	−	0.932487i	$-0.617634\pi$
$701$	15.1255	−	15.1255i	0.571283	−	0.571283i	0.932487	+	0.361204i	$0.117634\pi$
$702$	−1.20848	+	5.31750i	−0.0456113	+	0.200696i
$703$	29.0969	+	50.3972i	1.09741	+	1.90077i
$704$	−46.0635	−	1.46629i	−1.73608	−	0.0552629i
$705$	0.738942	−	1.27989i	0.0278302	−	0.0482033i
$706$	−32.7449	+	10.1338i	−1.23237	+	0.381391i
$707$	−47.5355	−	1.23008i	−1.78775	−	0.0462620i
$708$	2.17975	−	1.49207i	0.0819200	−	0.0560755i
$709$	20.7160	−	5.55084i	0.778006	−	0.208466i	0.152101	−	0.988365i	$-0.451396\pi$
$709$	20.7160	−	5.55084i	0.778006	−	0.208466i	0.625906	+	0.779899i	$0.284730\pi$
$710$	−13.3181	+	0.510728i	−0.499819	+	0.0191673i
$711$	9.35994	−	5.40396i	0.351025	−	0.202665i
$712$	28.3726	−	11.2269i	1.06331	−	0.420744i
$713$			8.25305i			0.309079i
$714$	−1.18492	−	4.21158i	−0.0443444	−	0.157614i
$715$	−11.8250	−	11.8250i	−0.442228	−	0.442228i
$716$	−31.0887	−	26.6535i	−1.16184	−	0.996090i
$717$	−3.17551	−	0.850875i	−0.118591	−	0.0317765i
$718$	−25.7787	+	27.8347i	−0.962052	+	1.03878i
$719$	14.9028	−	25.8124i	0.555780	−	0.962639i	−0.442062	−	0.896984i	$-0.645753\pi$
$719$	14.9028	−	25.8124i	0.555780	−	0.962639i	0.997842	−	0.0656550i	$-0.0209137\pi$
$720$	−4.75918	−	10.7984i	−0.177364	−	0.402433i
$721$	−5.74227	+	19.4076i	−0.213853	+	0.722776i
$722$	10.0355	+	32.4273i	0.373484	+	1.20682i
$723$	−1.62882	−	6.07882i	−0.0605763	−	0.226074i
$724$	10.6493	+	30.2533i	0.395777	+	1.12435i
$725$	1.32271	−	4.93642i	0.0491242	−	0.183334i
$726$	−5.92762	+	3.73226i	−0.219994	+	0.138517i
$727$			32.8773i			1.21935i	0.792651	+	0.609676i	$0.208701\pi$
$727$			32.8773i			1.21935i	−0.792651	+	0.609676i	$0.791299\pi$
$728$	−20.3993	+	7.46752i	−0.756047	+	0.276765i
$729$		−	24.3460i		−	0.901704i
$730$	5.19051	+	8.24362i	0.192109	+	0.305110i
$731$	16.3740	−	61.1087i	0.605616	−	2.26019i
$732$	0.287856	−	0.600595i	0.0106395	−	0.0221986i
$733$	−6.90977	−	25.7876i	−0.255218	−	0.952487i	−0.967969	−	0.251070i	$-0.919218\pi$
$733$	−6.90977	−	25.7876i	−0.255218	−	0.952487i	0.712751	−	0.701417i	$-0.247449\pi$
$734$	44.7066	−	13.8357i	1.65015	−	0.510685i
$735$	−1.39192	+	0.710299i	−0.0513416	+	0.0261998i
$736$	23.9302	+	1.68148i	0.882079	+	0.0619804i
$737$	12.0960	−	20.9509i	0.445563	−	0.771737i
$738$	−27.3522	−	25.3319i	−1.00685	−	0.932479i
$739$	−8.04324	−	2.15518i	−0.295875	−	0.0792795i	0.107828	−	0.994170i	$-0.465610\pi$
$739$	−8.04324	−	2.15518i	−0.295875	−	0.0792795i	−0.403703	+	0.914890i	$0.632277\pi$
$740$	17.6963	−	1.35925i	0.650528	−	0.0499670i
$741$	−3.00491	−	3.00491i	−0.110388	−	0.110388i
$742$	0.971345	−	3.81458i	0.0356592	−	0.140038i
$743$		−	22.1610i		−	0.813006i	−0.913649	−	0.406503i	$-0.866748\pi$
$743$		−	22.1610i		−	0.813006i	0.913649	−	0.406503i	$-0.133252\pi$
$744$	−1.12766	−	0.488253i	−0.0413420	−	0.0179002i
$745$	8.05445	−	4.65024i	0.295092	−	0.170372i
$746$	−0.446193	−	11.6352i	−0.0163363	−	0.425996i
$747$	−24.1008	+	6.45780i	−0.881803	+	0.236278i
$748$	59.3175	+	11.1093i	2.16886	+	0.406195i
$749$	10.9199	+	20.0972i	0.399005	+	0.734335i
$750$	−0.0933370	−	0.301595i	−0.00340819	−	0.0110127i
$751$	3.90262	−	6.75954i	0.142409	−	0.246659i	−0.785995	−	0.618233i	$-0.787849\pi$
$751$	3.90262	−	6.75954i	0.142409	−	0.246659i	0.928403	+	0.371574i	$0.121182\pi$
$752$	26.1701	−	4.04410i	0.954325	−	0.147473i
$753$	0.0842515	+	0.145928i	0.00307030	+	0.00531791i
$754$	−20.4586	−	4.64953i	−0.745058	−	0.169326i
$755$	11.4883	−	11.4883i	0.418103	−	0.418103i
$756$	−5.90082	+	3.81887i	−0.214611	+	0.138891i
$757$	−31.6550	−	31.6550i	−1.15052	−	1.15052i	−0.986448	−	0.164074i	$-0.947536\pi$
$757$	−31.6550	−	31.6550i	−1.15052	−	1.15052i	−0.164074	−	0.986448i	$-0.552464\pi$
$758$	21.4382	−	13.4983i	0.778669	−	0.490280i
$759$	4.72312	−	2.72689i	0.171438	−	0.0989800i
$760$	18.3483	+	2.71324i	0.665561	+	0.0984194i
$761$	−26.1855	−	15.1182i	−0.949222	−	0.548034i	−0.0563828	−	0.998409i	$-0.517957\pi$
$761$	−26.1855	−	15.1182i	−0.949222	−	0.548034i	−0.892839	+	0.450376i	$0.851290\pi$
$762$	−0.261136	+	0.495208i	−0.00945997	+	0.0179395i
$763$	−0.202674	+	7.83215i	−0.00733729	+	0.283543i
$764$	−13.8442	+	9.47659i	−0.500866	+	0.342851i
$765$	3.99940	+	14.9260i	0.144599	+	0.539650i
$766$	−8.55833	−	7.92617i	−0.309225	−	0.286384i
$767$	8.58717	+	14.8734i	0.310065	+	0.537048i
$768$	−1.64547	+	3.17024i	−0.0593757	+	0.114396i
$769$	−32.7068			−1.17944			−0.589719	−	0.807608i	$-0.700762\pi$
$769$	−32.7068			−1.17944			−0.589719	+	0.807608i	$0.700762\pi$
$770$	−0.268533	−	21.5535i	−0.00967726	−	0.776733i
$771$	−1.18138	+	1.18138i	−0.0425464	+	0.0425464i
$772$	2.11067	+	27.4792i	0.0759648	+	0.988998i
$773$	−0.817224	+	3.04992i	−0.0293935	+	0.109698i	−0.979064	−	0.203552i	$-0.934751\pi$
$773$	−0.817224	+	3.04992i	−0.0293935	+	0.109698i	0.949671	+	0.313250i	$0.101418\pi$
$774$	−50.3557	+	1.93107i	−1.81000	+	0.0694107i
$775$	1.68540	+	0.973069i	0.0605415	+	0.0349537i
$776$	−11.7022	+	14.7584i	−0.420085	+	0.529795i
$777$	−1.22516	−	5.09622i	−0.0439523	−	0.182826i
$778$	−25.6775	−	13.5404i	−0.920582	−	0.485447i
$779$	56.5996	−	15.1658i	2.02789	−	0.543372i
$780$	−1.22254	+	0.430339i	−0.0437740	+	0.0154086i
$781$	−52.4416	−	14.0517i	−1.87651	−	0.502809i
$782$	−30.6318	−	6.96156i	−1.09539	−	0.248945i
$783$	−6.78841			−0.242598
$784$	−25.5433	−	11.4690i	−0.912262	−	0.409607i
$785$	−2.14815			−0.0766706
$786$	3.04599	+	0.692249i	0.108647	+	0.0246917i
$787$	14.4065	+	3.86020i	0.513535	+	0.137601i	0.506275	−	0.862372i	$-0.331022\pi$
$787$	14.4065	+	3.86020i	0.513535	+	0.137601i	0.00726045	+	0.999974i	$0.497689\pi$
$788$	−6.08761	−	17.2942i	−0.216862	−	0.616079i
$789$	3.71570	−	0.995620i	0.132283	−	0.0354450i
$790$	4.58283	+	2.41665i	0.163050	+	0.0859804i
$791$	0.951684	+	3.95867i	0.0338380	+	0.140754i
$792$	−5.51540	−	47.7529i	−0.195981	−	1.69683i
$793$	3.75009	+	2.16511i	0.133170	+	0.0768855i
$794$	−17.7870	+	0.682103i	−0.631236	+	0.0242069i
$795$	0.0607844	−	0.226850i	0.00215580	−	0.00804555i
$796$	15.7331	−	1.20846i	0.557645	−	0.0428327i
$797$	−35.5594	+	35.5594i	−1.25958	+	1.25958i	−0.308286	+	0.951294i	$0.599755\pi$
$797$	−35.5594	+	35.5594i	−1.25958	+	1.25958i	−0.951294	+	0.308286i	$0.900245\pi$
$798$	−0.0682384	−	5.47707i	−0.00241561	−	0.193886i
$799$	−34.6755			−1.22673
$800$	3.16486	−	4.68868i	0.111895	−	0.165770i
$801$	15.9132	+	27.5624i	0.562265	+	0.973871i
$802$	−13.1716	−	12.1987i	−0.465106	−	0.430752i
$803$	10.2707	+	38.3306i	0.362443	+	1.35266i
$804$	−1.05907	−	1.54718i	−0.0373505	−	0.0545648i
$805$	−0.290243	+	11.2162i	−0.0102297	+	0.395318i
$806$	3.72665	−	7.06706i	0.131266	−	0.248927i
$807$	5.66523	+	3.27082i	0.199426	+	0.115138i
$808$	−30.3006	−	40.8170i	−1.06597	−	1.43594i
$809$	−18.8852	+	10.9034i	−0.663970	+	0.383343i	−0.793788	−	0.608195i	$-0.791894\pi$
$809$	−18.8852	+	10.9034i	−0.663970	+	0.383343i	0.129818	+	0.991538i	$0.458561\pi$
$810$	10.2369	−	6.44558i	0.359690	−	0.226475i
$811$	−21.8890	−	21.8890i	−0.768628	−	0.768628i	0.209237	−	0.977865i	$-0.432902\pi$
$811$	−21.8890	−	21.8890i	−0.768628	−	0.768628i	−0.977865	+	0.209237i	$0.932902\pi$
$812$	−14.6928	−	22.7029i	−0.515615	−	0.796716i
$813$	−3.34426	+	3.34426i	−0.117288	+	0.117288i
$814$	70.5010	+	16.0224i	2.47106	+	0.561586i
$815$	−2.93530	−	5.08409i	−0.102819	−	0.178088i
$816$	2.76338	−	3.77355i	0.0967378	−	0.132101i
$817$	39.6026	−	68.5938i	1.38552	−	2.39979i
$818$	−0.926646	−	2.99423i	−0.0323994	−	0.104691i
$819$	−10.8176	−	19.9090i	−0.377999	−	0.695676i
$820$	3.28979	−	17.5657i	0.114885	−	0.613422i
$821$	6.18763	−	1.65797i	0.215950	−	0.0578636i	−0.149222	−	0.988804i	$-0.547677\pi$
$821$	6.18763	−	1.65797i	0.215950	−	0.0578636i	0.365172	+	0.930940i	$0.381010\pi$
$822$	−0.102039	−	2.66084i	−0.00355902	−	0.0928073i
$823$	4.23201	−	2.44335i	0.147518	−	0.0851698i	−0.424424	−	0.905464i	$-0.639523\pi$
$823$	4.23201	−	2.44335i	0.147518	−	0.0851698i	0.571942	+	0.820294i	$0.306190\pi$
$824$	−20.1189	+	7.96092i	−0.700875	+	0.277332i
$825$		−	1.28605i		−	0.0447745i
$826$	−5.46261	+	21.4523i	−0.190069	+	0.746420i
$827$	−26.5265	−	26.5265i	−0.922417	−	0.922417i	0.0747830	−	0.997200i	$-0.476174\pi$
$827$	−26.5265	−	26.5265i	−0.922417	−	0.922417i	−0.997200	+	0.0747830i	$0.976174\pi$
$828$	1.91627	+	24.9482i	0.0665950	+	0.867011i
$829$	−48.3487	−	12.9550i	−1.67922	−	0.449945i	−0.711646	−	0.702538i	$-0.752050\pi$
$829$	−48.3487	−	12.9550i	−1.67922	−	0.449945i	−0.967573	+	0.252593i	$0.918717\pi$
$830$	−8.77538	−	8.12719i	−0.304598	−	0.282099i
$831$	1.90843	−	3.30551i	0.0662029	−	0.114667i
$832$	−19.7321	−	12.2455i	−0.684087	−	0.424536i
$833$	30.7621	+	19.9502i	1.06584	+	0.691232i
$834$	−0.298455	+	0.0923651i	−0.0103346	+	0.00319834i
$835$	6.28778	+	23.4663i	0.217598	+	0.812085i
$836$	68.1336	+	32.6555i	2.35645	+	1.12941i
$837$	0.669067	−	2.49699i	0.0231263	−	0.0863087i
$838$	18.4897	+	29.3656i	0.638718	+	1.01442i
$839$		−	19.2811i		−	0.665656i	−0.942987	−	0.332828i	$-0.891997\pi$
$839$		−	19.2811i		−	0.665656i	0.942987	−	0.332828i	$-0.108003\pi$
$840$	−1.51536	−	0.703209i	−0.0522847	−	0.0242630i
$841$			2.88218i			0.0993855i
$842$	24.5926	−	15.4845i	0.847518	−	0.533631i
$843$	−0.854147	+	3.18772i	−0.0294184	+	0.109791i
$844$	0.0550342	−	0.0193723i	0.00189436	−	0.000666821i
$845$	1.18366	+	4.41750i	0.0407193	+	0.151967i
$846$	8.16581	+	26.3858i	0.280746	+	0.907162i
$847$	16.6550	−	56.2901i	0.572272	−	1.93415i
$848$	3.85069	−	1.69711i	0.132233	−	0.0582791i
$849$	1.68940	−	2.92613i	0.0579800	−	0.100424i
$850$	−5.03328	+	5.43471i	−0.172640	+	0.186409i
$851$	−36.3508	−	9.74016i	−1.24609	−	0.333888i
$852$	−2.73871	+	3.19443i	−0.0938265	+	0.109439i
$853$	−35.6558	−	35.6558i	−1.22083	−	1.22083i	−0.967337	−	0.253492i	$-0.918421\pi$
$853$	−35.6558	−	35.6558i	−1.22083	−	1.22083i	−0.253492	−	0.967337i	$-0.581579\pi$
$854$	1.51164	+	5.37285i	0.0517272	+	0.183855i
$855$			19.3461i			0.661622i
$856$	−9.71541	+	22.4385i	−0.332066	+	0.766933i
$857$	4.93440	−	2.84888i	0.168556	−	0.0973159i	−0.413349	−	0.910573i	$-0.635641\pi$
$857$	4.93440	−	2.84888i	0.168556	−	0.0973159i	0.581905	+	0.813257i	$0.302308\pi$
$858$	−5.27571	+	0.202316i	−0.180110	+	0.00690694i
$859$	−12.6001	+	3.37619i	−0.429910	+	0.115194i	−0.467284	−	0.884107i	$-0.654767\pi$
$859$	−12.6001	+	3.37619i	−0.429910	+	0.115194i	0.0373739	+	0.999301i	$0.488101\pi$
$860$	−13.6450	−	19.9338i	−0.465291	−	0.679738i
$861$	−5.27590	−	0.136525i	−0.179802	−	0.00465277i
$862$	25.1434	−	7.78132i	0.856387	−	0.265033i
$863$	−16.2390	+	28.1268i	−0.552782	+	0.957447i	0.445290	+	0.895386i	$0.353100\pi$
$863$	−16.2390	+	28.1268i	−0.552782	+	0.957447i	−0.998072	+	0.0620605i	$0.980233\pi$
$864$	−7.10386	−	2.44874i	−0.241678	−	0.0833078i
$865$	0.439913	+	0.761951i	0.0149575	+	0.0259071i
$866$	0.511412	−	2.25028i	0.0173785	−	0.0764677i
$867$	−1.64721	+	1.64721i	−0.0559422	+	0.0559422i
$868$	9.79896	−	3.16686i	0.332599	−	0.107490i
$869$	14.9234	+	14.9234i	0.506242	+	0.506242i
$870$	−0.859674	−	1.36534i	−0.0291457	−	0.0462895i
$871$	10.5571	−	6.09515i	0.357714	−	0.206526i
$872$	−6.72519	+	4.99245i	−0.227744	+	0.169066i
$873$	−17.0135	−	9.82275i	−0.575820	−	0.332450i
$874$	−34.7877	−	18.3445i	−1.17671	−	0.620510i
$875$	2.25630	+	1.38171i	0.0762769	+	0.0467102i
$876$	3.02294	+	0.566151i	0.102136	+	0.0191285i
$877$	10.5967	+	39.5475i	0.357825	+	1.33542i	0.876891	+	0.480688i	$0.159613\pi$
$877$	10.5967	+	39.5475i	0.357825	+	1.33542i	−0.519066	+	0.854734i	$0.673720\pi$
$878$	−20.5358	+	22.1736i	−0.693049	+	0.748324i
$879$	0.680013	+	1.17782i	0.0229363	+	0.0397268i
$880$	17.9625	−	14.4342i	0.605516	−	0.486578i
$881$	−34.0142			−1.14597			−0.572984	−	0.819567i	$-0.694214\pi$
$881$	−34.0142			−1.14597			−0.572984	+	0.819567i	$0.694214\pi$
$882$	7.93654	−	28.1061i	0.267237	−	0.946381i
$883$	−8.25371	+	8.25371i	−0.277759	+	0.277759i	−0.832214	−	0.554455i	$-0.812927\pi$
$883$	−8.25371	+	8.25371i	−0.277759	+	0.277759i	0.554455	+	0.832214i	$0.312927\pi$
$884$	23.0865	+	19.7929i	0.776482	+	0.665707i
$885$	−0.341837	+	1.27575i	−0.0114907	+	0.0428840i
$886$	−0.228265	−	5.95238i	−0.00766870	−	0.199974i
$887$	−11.6294	−	6.71424i	−0.390477	−	0.225442i	0.291890	−	0.956452i	$-0.405716\pi$
$887$	−11.6294	−	6.71424i	−0.390477	−	0.225442i	−0.682367	+	0.731010i	$0.739049\pi$
$888$	3.48137	−	4.39057i	0.116827	−	0.147338i
$889$	−1.09666	−	4.56172i	−0.0367808	−	0.152995i
$890$	−7.11636	+	13.4952i	−0.238541	+	0.452359i
$891$	47.5990	−	12.7541i	1.59463	−	0.427279i
$892$	−11.5286	−	5.52550i	−0.386007	−	0.185008i
$893$	−41.9335	−	11.2360i	−1.40325	−	0.376000i
$894$	0.650712	−	2.86322i	0.0217631	−	0.0957605i
$895$	20.4751			0.684407
$896$	−7.18603	−	29.0579i	−0.240069	−	0.970756i
$897$	2.74814			0.0917579
$898$	8.72579	−	38.3947i	0.291183	−	1.28125i
$899$	9.60696	+	2.57418i	0.320410	+	0.0858536i
$900$	5.32076	+	2.55017i	0.177359	+	0.0850056i
$901$	−5.32257	+	1.42618i	−0.177320	+	0.0475129i
$902$	33.9567	−	64.3941i	1.13063	−	2.14409i
$903$	−5.17323	+	4.91224i	−0.172154	+	0.163469i
$904$	−2.70428	+	3.41053i	−0.0899430	+	0.113433i
$905$	−13.8879	−	8.01821i	−0.461651	−	0.266534i
$906$	−0.196556	−	5.12552i	−0.00653013	−	0.170284i
$907$	7.51316	−	28.0395i	0.249470	−	0.931036i	−0.721613	−	0.692296i	$-0.756599\pi$
$907$	7.51316	−	28.0395i	0.249470	−	0.931036i	0.971084	−	0.238740i	$-0.0767342\pi$
$908$	6.33683	+	5.43281i	0.210295	+	0.180294i
$909$	37.4926	−	37.4926i	1.24355	−	1.24355i
$910$	5.31317	−	9.47331i	0.176130	−	0.314037i
$911$	36.4821			1.20871			0.604353	−	0.796717i	$-0.293432\pi$
$911$	36.4821			1.20871			0.604353	+	0.796717i	$0.293432\pi$
$912$	4.56455	−	3.66796i	0.151147	−	0.121458i
$913$	−24.3612	−	42.1948i	−0.806238	−	1.39644i
$914$	3.57077	−	3.85556i	0.118111	−	0.127530i
$915$	0.0861886	+	0.321660i	0.00284931	+	0.0106338i
$916$	30.5562	+	5.72271i	1.00960	+	0.189084i
$917$	−23.0014	+	12.4979i	−0.759572	+	0.412717i
$918$	8.70341	+	4.58954i	0.287255	+	0.151477i
$919$	−37.5156	−	21.6597i	−1.23753	−	0.714487i	−0.268939	−	0.963157i	$-0.586673\pi$
$919$	−37.5156	−	21.6597i	−1.23753	−	0.714487i	−0.968588	+	0.248671i	$0.920006\pi$
$920$	−9.63093	+	7.14953i	−0.317522	+	0.235713i
$921$	−2.07857	+	1.20006i	−0.0684912	+	0.0395434i
$922$	−28.7080	−	45.5944i	−0.945448	−	1.50157i
$923$	−19.3446	−	19.3446i	−0.636734	−	0.636734i
$924$	−5.05003	−	4.56146i	−0.166134	−	0.150061i
$925$	−6.27500	+	6.27500i	−0.206321	+	0.206321i
$926$	−2.91364	+	12.8204i	−0.0957482	+	0.421306i
$927$	−11.2840	−	19.5444i	−0.370614	−	0.641923i
$928$	9.42131	−	27.3315i	0.309270	−	0.897199i
$929$	−24.9290	+	43.1783i	−0.817893	+	1.41663i	0.0893382	+	0.996001i	$0.471525\pi$
$929$	−24.9290	+	43.1783i	−0.817893	+	1.41663i	−0.907232	+	0.420632i	$0.861809\pi$
$930$	0.586946	−	0.181647i	0.0192467	−	0.00595643i
$931$	30.7364	+	34.0939i	1.00735	+	1.11738i
$932$	−6.35495	−	9.28387i	−0.208163	−	0.304103i
$933$	2.93629	−	0.786775i	0.0961297	−	0.0257579i
$934$	−3.73498	+	0.143231i	−0.122212	+	0.00468665i
$935$	−26.1318	+	15.0872i	−0.854602	+	0.493405i
$936$	9.62442	−	22.2284i	0.314584	−	0.726557i
$937$			56.1234i			1.83347i	0.399493	+	0.916736i	$0.369186\pi$
$937$			56.1234i			1.83347i	−0.399493	+	0.916736i	$0.630814\pi$
$938$	15.2268	+	3.87735i	0.497171	+	0.126600i
$939$	−1.62098	−	1.62098i	−0.0528988	−	0.0528988i
$940$	−8.61784	+	10.0519i	−0.281083	+	0.327856i
$941$	−13.9543	−	3.73904i	−0.454897	−	0.121889i	0.0240930	−	0.999710i	$-0.492330\pi$
$941$	−13.9543	−	3.73904i	−0.454897	−	0.121889i	−0.478990	+	0.877821i	$0.658997\pi$
$942$	−0.460822	+	0.497575i	−0.0150144	+	0.0162119i
$943$	−18.9467	+	32.8166i	−0.616989	+	1.06866i
$944$	−21.6554	+	9.54417i	−0.704822	+	0.310636i
$945$	0.997098	−	3.36996i	0.0324356	−	0.109625i
$946$	−29.0922	−	94.0042i	−0.945870	−	3.05634i
$947$	5.28517	+	19.7245i	0.171745	+	0.640961i	0.997083	+	0.0763221i	$0.0243177\pi$
$947$	5.28517	+	19.7245i	0.171745	+	0.640961i	−0.825338	+	0.564638i	$0.809016\pi$
$948$	1.54288	−	0.543099i	0.0501104	−	0.0176390i
$949$	−5.17535	+	19.3147i	−0.167999	+	0.626980i
$950$	−7.84784	+	4.94131i	−0.254618	+	0.160317i
$951$			6.25384i			0.202795i
$952$	3.48847	+	39.0409i	0.113062	+	1.26532i
$953$		−	24.8086i		−	0.803631i	−0.915721	−	0.401815i	$-0.868379\pi$
$953$		−	24.8086i		−	0.803631i	0.915721	−	0.401815i	$-0.131621\pi$
$954$	2.33865	+	3.71428i	0.0757167	+	0.120254i
$955$	2.17111	−	8.10268i	0.0702553	−	0.262196i
$956$	26.5599	+	12.7298i	0.859008	+	0.411711i
$957$	−1.70107	−	6.34848i	−0.0549878	−	0.205217i
$958$	33.3159	−	10.3105i	1.07639	−	0.333118i
$959$	15.3658	+	16.1821i	0.496186	+	0.522548i
$960$	−0.407110	−	1.73889i	−0.0131394	−	0.0561226i
$961$	13.6063	−	23.5668i	0.438912	−	0.760218i
$962$	26.7289	+	24.7546i	0.861774	+	0.798120i
$963$	−24.6349	−	6.60090i	−0.793848	−	0.212711i
$964$	4.31792	+	56.2157i	0.139071	+	1.81059i
$965$	−9.74398	−	9.74398i	−0.313670	−	0.313670i
$966$	2.53574	+	2.47333i	0.0815860	+	0.0795781i
$967$			17.2584i			0.554991i	0.960727	+	0.277496i	$0.0895044\pi$
$967$			17.2584i			0.554991i	−0.960727	+	0.277496i	$0.910496\pi$
$968$	58.3532	−	23.0900i	1.87554	−	0.742140i
$969$	−6.64050	+	3.83390i	−0.213324	+	0.123163i
$970$	−0.360878	−	9.41050i	−0.0115871	−	0.302153i
$971$	14.9512	−	4.00615i	0.479805	−	0.128563i	−0.0108066	−	0.999942i	$-0.503440\pi$
$971$	14.9512	−	4.00615i	0.479805	−	0.128563i	0.490612	+	0.871378i	$0.336773\pi$
$972$	2.17017	−	11.5876i	0.0696083	−	0.371671i
$973$	1.36732	−	2.23280i	0.0438342	−	0.0715804i
$974$	−6.53219	−	21.1071i	−0.209305	−	0.676316i
$975$	0.324018	−	0.561215i	0.0103769	−	0.0179733i
$976$	−3.52534	+	4.81403i	−0.112843	+	0.154093i
$977$	20.6390	+	35.7477i	0.660299	+	1.14367i	0.980537	+	0.196334i	$0.0629037\pi$
$977$	20.6390	+	35.7477i	0.660299	+	1.14367i	−0.320238	+	0.947337i	$0.603763\pi$
$978$	−1.80731	−	0.410739i	−0.0577914	−	0.0131340i
$979$	−43.9453	+	43.9453i	−1.40450	+	1.40450i
$980$	13.4285	−	3.95925i	0.428957	−	0.126474i
$981$	−6.17744	−	6.17744i	−0.197230	−	0.197230i
$982$	−30.9043	+	19.4585i	−0.986194	+	0.620947i
$983$	−20.1079	+	11.6093i	−0.641342	+	0.370279i	−0.785131	−	0.619329i	$-0.787405\pi$
$983$	−20.1079	+	11.6093i	−0.641342	+	0.370279i	0.143789	+	0.989608i	$0.454071\pi$
$984$	−3.36302	−	4.53023i	−0.107209	−	0.144418i
$985$	7.93899	+	4.58358i	0.252957	+	0.146045i
$986$	−17.6578	+	33.4856i	−0.562340	+	1.06640i
$987$	3.33455	+	2.04200i	0.106140	+	0.0649976i
$988$	21.5052	+	31.4166i	0.684170	+	0.999495i
$989$	13.2570	+	49.4757i	0.421547	+	1.57323i
$990$	17.6342	+	16.3317i	0.560453	+	0.519055i
$991$	−11.4179	−	19.7765i	−0.362703	−	0.628220i	0.625702	−	0.780062i	$-0.284813\pi$
$991$	−11.4179	−	19.7765i	−0.362703	−	0.628220i	−0.988405	+	0.151842i	$0.951479\pi$
$992$	9.12481	+	6.15925i	0.289713	+	0.195556i
$993$	−4.53823			−0.144016
$994$	−0.439296	−	35.2595i	−0.0139336	−	1.11836i
$995$	−5.57888	+	5.57888i	−0.176862	+	0.176862i
$996$	−3.76500	+	0.289190i	−0.119299	+	0.00916332i
$997$	−9.04976	+	33.7742i	−0.286609	+	1.06964i	0.661047	+	0.750345i	$0.270112\pi$
$997$	−9.04976	+	33.7742i	−0.286609	+	1.06964i	−0.947656	+	0.319294i	$0.896554\pi$
$998$	46.7552	−	1.79299i	1.48001	−	0.0567561i
$999$	10.2084	+	5.89384i	0.322981	+	0.186473i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.cp.a.261.38	yes	256
7.4	even	3	inner	560.2.cp.a.501.48	yes	256
16.13	even	4	inner	560.2.cp.a.541.48	yes	256
112.109	even	12	inner	560.2.cp.a.221.38	✓	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.cp.a.221.38	✓	256	112.109	even	12	inner
560.2.cp.a.261.38	yes	256	1.1	even	1	trivial
560.2.cp.a.501.48	yes	256	7.4	even	3	inner
560.2.cp.a.541.48	yes	256	16.13	even	4	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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.cp (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.313410 - 1.37905i) q^{2} +(0.215633 + 0.0577786i) q^{3} +(-1.80355 - 0.864415i) q^{4} +(0.965926 - 0.258819i) q^{5} +(0.147261 - 0.279259i) q^{6} +(0.618432 + 2.57246i) q^{7} +(-1.75732 + 2.21626i) q^{8} +(-2.55492 - 1.47508i) q^{9} +(-0.0541931 - 1.41317i) q^{10} +(1.49102 - 5.56455i) q^{11} +(-0.338959 - 0.290603i) q^{12} +(2.05264 - 2.05264i) q^{13} +(3.74137 - 0.0466135i) q^{14} +0.223239 q^{15} +(2.50557 + 3.11803i) q^{16} +(-2.61892 - 4.53611i) q^{17} +(-2.83495 + 3.06105i) q^{18} +(-1.69724 - 6.33419i) q^{19} +(-1.96582 - 0.368168i) q^{20} +(-0.0152789 + 0.590438i) q^{21} +(-7.20649 - 3.80017i) q^{22} +(3.67258 + 2.12037i) q^{23} +(-0.506988 + 0.376363i) q^{24} +(0.866025 - 0.500000i) q^{25} +(-2.18737 - 3.47401i) q^{26} +(-0.939257 - 0.939257i) q^{27} +(1.10830 - 5.17413i) q^{28} +(3.61371 - 3.61371i) q^{29} +(0.0699654 - 0.307858i) q^{30} +(0.973069 + 1.68540i) q^{31} +(5.08518 - 2.47808i) q^{32} +(0.643024 - 1.11375i) q^{33} +(-7.07631 + 2.18996i) q^{34} +(1.26316 + 2.32474i) q^{35} +(3.33283 + 4.86889i) q^{36} +(-8.57181 + 2.29681i) q^{37} +(-9.26708 + 0.355378i) q^{38} +(0.561215 - 0.324018i) q^{39} +(-1.12383 + 2.59557i) q^{40} +8.93557i q^{41} +(0.809454 + 0.206120i) q^{42} +(8.54067 + 8.54067i) q^{43} +(-7.49921 + 8.74708i) q^{44} +(-2.84964 - 0.763559i) q^{45} +(4.07511 - 4.40012i) q^{46} +(3.31009 - 5.73324i) q^{47} +(0.360128 + 0.817117i) q^{48} +(-6.23508 + 3.18178i) q^{49} +(-0.418103 - 1.35100i) q^{50} +(-0.302635 - 1.12945i) q^{51} +(-5.47637 + 1.92770i) q^{52} +(0.272283 - 1.01618i) q^{53} +(-1.58965 + 1.00091i) q^{54} -5.76085i q^{55} +(-6.78803 - 3.15002i) q^{56} -1.46392i q^{57} +(-3.85091 - 6.11606i) q^{58} +(-1.53126 + 5.71473i) q^{59} +(-0.402623 - 0.192971i) q^{60} +(0.386082 + 1.44088i) q^{61} +(2.62922 - 0.813686i) q^{62} +(2.21454 - 7.48466i) q^{63} +(-1.82365 - 7.78937i) q^{64} +(1.45144 - 2.51396i) q^{65} +(-1.33439 - 1.23582i) q^{66} +(4.05630 + 1.08688i) q^{67} +(0.802274 + 10.4449i) q^{68} +(0.669417 + 0.669417i) q^{69} +(3.60182 - 1.01336i) q^{70} -9.42423i q^{71} +(7.75898 - 3.07018i) q^{72} +(-5.96549 + 3.44417i) q^{73} +(0.480920 + 12.5408i) q^{74} +(0.215633 - 0.0577786i) q^{75} +(-2.41431 + 12.8911i) q^{76} +(15.2367 + 0.394282i) q^{77} +(-0.270946 - 0.875493i) q^{78} +(-1.83175 + 3.17269i) q^{79} +(3.22720 + 2.36329i) q^{80} +(4.27698 + 7.40795i) q^{81} +(12.3226 + 2.80050i) q^{82} +(5.98035 - 5.98035i) q^{83} +(0.537940 - 1.05168i) q^{84} +(-3.70372 - 3.70372i) q^{85} +(14.4547 - 9.10126i) q^{86} +(0.988029 - 0.570439i) q^{87} +(9.71232 + 13.0832i) q^{88} +(-9.34268 - 5.39400i) q^{89} +(-1.94609 + 3.69048i) q^{90} +(6.54975 + 4.01091i) q^{91} +(-4.79080 - 6.99882i) q^{92} +(0.112445 + 0.419651i) q^{93} +(-6.86900 - 6.36163i) q^{94} +(-3.27882 - 5.67908i) q^{95} +(1.23971 - 0.240541i) q^{96} +6.65912 q^{97} +(2.43369 + 9.59568i) q^{98} +(-12.0176 + 12.0176i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 4 q^{4} + 8 q^{11} + 16 q^{14} - 20 q^{16} - 40 q^{18} - 16 q^{20} + 56 q^{22} - 40 q^{24} + 4 q^{28} - 32 q^{29} - 20 q^{32} + 16 q^{37} - 40 q^{38} - 60 q^{42} + 16 q^{43} + 32 q^{44} - 20 q^{46}+ \cdots - 80 q^{99}+O(q^{100}) \) 256 * q + 4 * q^4 + 8 * q^11 + 16 * q^14 - 20 * q^16 - 40 * q^18 - 16 * q^20 + 56 * q^22 - 40 * q^24 + 4 * q^28 - 32 * q^29 - 20 * q^32 + 16 * q^37 - 40 * q^38 - 60 * q^42 + 16 * q^43 + 32 * q^44 - 20 * q^46 + 80 * q^47 - 160 * q^48 - 8 * q^50 - 40 * q^51 + 24 * q^52 - 16 * q^53 - 116 * q^54 - 96 * q^56 - 8 * q^58 + 16 * q^59 - 28 * q^60 + 88 * q^62 - 56 * q^64 - 16 * q^66 - 40 * q^67 - 20 * q^68 - 16 * q^70 + 76 * q^72 + 52 * q^74 - 48 * q^78 + 128 * q^81 - 80 * q^83 - 68 * q^84 + 52 * q^86 + 20 * q^88 - 72 * q^90 - 32 * q^91 - 112 * q^92 + 120 * q^94 + 140 * q^96 + 24 * q^98 - 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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