LMFDB - Embedded newform 680.2.cf.a.533.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(37,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 8, 4, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.37"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.cf (of order $16$, degree $8$, 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:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$832$
Relative dimension:	$104$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			533.13
Character	$\chi$	$=$	680.533
Dual form			680.2.cf.a.37.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.33961 - 0.453250i) q^{2} +(1.50989 - 2.25971i) q^{3} +(1.58913 + 1.21436i) q^{4} +(-1.01577 - 1.99204i) q^{5} +(-3.04688 + 2.34278i) q^{6} +(1.91012 + 0.379947i) q^{7} +(-1.57841 - 2.34704i) q^{8} +(-1.67846 - 4.05216i) q^{9} +(0.457849 + 3.12896i) q^{10} +(4.06379 + 0.808338i) q^{11} +(5.14350 - 1.75742i) q^{12} -2.33036i q^{13} +(-2.38661 - 1.37474i) q^{14} +(-6.03511 - 0.712409i) q^{15} +(1.05067 + 3.85955i) q^{16} +(-2.91956 - 2.91139i) q^{17} +(0.411847 + 6.18909i) q^{18} +(6.47634 + 2.68259i) q^{19} +(0.804857 - 4.39911i) q^{20} +(3.74263 - 3.74263i) q^{21} +(-5.07753 - 2.92477i) q^{22} +(-3.00926 - 4.50368i) q^{23} +(-7.68685 + 0.0229749i) q^{24} +(-2.93642 + 4.04690i) q^{25} +(-1.05623 + 3.12178i) q^{26} +(-3.69445 - 0.734872i) q^{27} +(2.57404 + 2.92336i) q^{28} +(-2.68219 - 1.79218i) q^{29} +(7.76182 + 3.68977i) q^{30} +(-0.632315 - 3.17886i) q^{31} +(0.341853 - 5.64652i) q^{32} +(7.96247 - 7.96247i) q^{33} +(2.59150 + 5.22342i) q^{34} +(-1.18338 - 4.19097i) q^{35} +(2.25349 - 8.47766i) q^{36} +(-2.73456 - 1.82717i) q^{37} +(-7.45991 - 6.52903i) q^{38} +(-5.26592 - 3.51857i) q^{39} +(-3.07209 + 5.52831i) q^{40} +(5.30100 + 7.93351i) q^{41} +(-6.71003 + 3.31734i) q^{42} +(-2.27201 + 5.48512i) q^{43} +(5.47628 + 6.21946i) q^{44} +(-6.36712 + 7.45961i) q^{45} +(1.98996 + 7.39714i) q^{46} +12.1107i q^{47} +(10.3078 + 3.45328i) q^{48} +(-2.96295 - 1.22730i) q^{49} +(5.76793 - 4.09035i) q^{50} +(-10.9871 + 2.20148i) q^{51} +(2.82989 - 3.70324i) q^{52} +(1.41644 - 0.586711i) q^{53} +(4.61606 + 2.65895i) q^{54} +(-2.51764 - 8.91631i) q^{55} +(-2.12321 - 5.08285i) q^{56} +(15.8404 - 10.5842i) q^{57} +(2.78080 + 3.61654i) q^{58} +(-3.26263 - 7.87669i) q^{59} +(-8.72546 - 8.46090i) q^{60} +(8.05380 + 12.0534i) q^{61} +(-0.593761 + 4.54505i) q^{62} +(-1.66646 - 8.37784i) q^{63} +(-3.01723 + 7.40920i) q^{64} +(-4.64216 + 2.36711i) q^{65} +(-14.2756 + 7.05765i) q^{66} +(0.918910 - 0.918910i) q^{67} +(-1.10409 - 8.17196i) q^{68} -14.7206 q^{69} +(-0.314289 + 6.15065i) q^{70} +(-2.92256 + 0.581333i) q^{71} +(-6.86129 + 10.3354i) q^{72} +(-2.11104 + 0.419911i) q^{73} +(2.83509 + 3.68714i) q^{74} +(4.71114 + 12.7458i) q^{75} +(7.03412 + 12.1276i) q^{76} +(7.45521 + 3.08805i) q^{77} +(5.45950 + 7.10031i) q^{78} +(-11.5007 - 2.28762i) q^{79} +(6.62113 - 6.01338i) q^{80} +(2.06536 - 2.06536i) q^{81} +(-3.50543 - 13.0305i) q^{82} +(-2.70583 - 6.53244i) q^{83} +(10.4924 - 1.40263i) q^{84} +(-2.83399 + 8.77317i) q^{85} +(5.52974 - 6.31815i) q^{86} +(-8.09962 + 3.35497i) q^{87} +(-4.51713 - 10.8138i) q^{88} +(-6.40177 + 6.40177i) q^{89} +(11.9105 - 7.10710i) q^{90} +(0.885411 - 4.45126i) q^{91} +(0.686975 - 10.8113i) q^{92} +(-8.13802 - 3.37088i) q^{93} +(5.48917 - 16.2237i) q^{94} +(-1.23466 - 15.6260i) q^{95} +(-12.2433 - 9.29808i) q^{96} +(11.5896 - 2.30532i) q^{97} +(3.41294 + 2.98706i) q^{98} +(-3.54539 - 17.8239i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 832 q - 8 q^{2} - 16 q^{6} - 16 q^{7} - 8 q^{8} - 8 q^{10} - 32 q^{12} - 32 q^{14} - 16 q^{15} - 16 q^{17} - 16 q^{18} - 8 q^{20} - 8 q^{22} - 16 q^{23} - 16 q^{25} - 48 q^{26} - 40 q^{28} - 72 q^{30} - 32 q^{31}+ \cdots - 16 q^{98}+O(q^{100}) $ 832 * q - 8 * q^2 - 16 * q^6 - 16 * q^7 - 8 * q^8 - 8 * q^10 - 32 * q^12 - 32 * q^14 - 16 * q^15 - 16 * q^17 - 16 * q^18 - 8 * q^20 - 8 * q^22 - 16 * q^23 - 16 * q^25 - 48 * q^26 - 40 * q^28 - 72 * q^30 - 32 * q^31 - 8 * q^32 + 48 * q^36 + 96 * q^39 + 48 * q^40 - 32 * q^41 + 8 * q^42 - 32 * q^46 + 72 * q^48 - 16 * q^52 - 64 * q^54 - 16 * q^55 - 16 * q^56 - 16 * q^57 - 64 * q^58 - 8 * q^60 - 8 * q^62 - 64 * q^63 + 64 * q^65 - 16 * q^66 - 128 * q^68 - 72 * q^70 - 32 * q^71 - 16 * q^72 - 96 * q^73 - 16 * q^76 - 64 * q^78 - 136 * q^80 - 32 * q^81 - 8 * q^82 - 96 * q^84 - 32 * q^86 - 16 * q^87 + 80 * q^88 + 136 * q^90 + 104 * q^92 + 48 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{15}{16}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.33961	−	0.453250i	−0.947250	−	0.320496i
$2$	−1.33961	−	0.453250i	−0.947250	−	0.320496i
$3$	1.50989	−	2.25971i	0.871733	−	1.30464i	−0.0797101	−	0.996818i	$-0.525399\pi$
$3$	1.50989	−	2.25971i	0.871733	−	1.30464i	0.951444	−	0.307823i	$-0.0996005\pi$
$4$	1.58913	+	1.21436i	0.794565	+	0.607179i
$5$	−1.01577	−	1.99204i	−0.454266	−	0.890866i
$5$	−1.01577	−	1.99204i	−0.454266	−	0.890866i
$6$	−3.04688	+	2.34278i	−1.24388	+	0.956434i
$7$	1.91012	+	0.379947i	0.721958	+	0.143606i	0.542375	−	0.840137i	$-0.317525\pi$
$7$	1.91012	+	0.379947i	0.721958	+	0.143606i	0.179583	+	0.983743i	$0.442525\pi$
$8$	−1.57841	−	2.34704i	−0.558053	−	0.829805i
$9$	−1.67846	−	4.05216i	−0.559486	−	1.35072i
$10$	0.457849	+	3.12896i	0.144785	+	0.989463i
$11$	4.06379	+	0.808338i	1.22528	+	0.243723i	0.764988	−	0.644045i	$-0.222745\pi$
$11$	4.06379	+	0.808338i	1.22528	+	0.243723i	0.460291	+	0.887768i	$0.347745\pi$
$12$	5.14350	−	1.75742i	1.48480	−	0.507323i
$13$		−	2.33036i		−	0.646325i	−0.946344	−	0.323162i	$-0.895254\pi$
$13$		−	2.33036i		−	0.646325i	0.946344	−	0.323162i	$-0.104746\pi$
$14$	−2.38661	−	1.37474i	−0.637849	−	0.367416i
$15$	−6.03511	−	0.712409i	−1.55826	−	0.183943i
$16$	1.05067	+	3.85955i	0.262666	+	0.964887i
$17$	−2.91956	−	2.91139i	−0.708097	−	0.706115i
$17$	−2.91956	−	2.91139i	−0.708097	−	0.706115i
$18$	0.411847	+	6.18909i	0.0970733	+	1.45878i
$19$	6.47634	+	2.68259i	1.48577	+	0.615428i	0.970393	−	0.241533i	$-0.0776503\pi$
$19$	6.47634	+	2.68259i	1.48577	+	0.615428i	0.515381	+	0.856961i	$0.327650\pi$
$20$	0.804857	−	4.39911i	0.179972	−	0.983672i
$21$	3.74263	−	3.74263i	0.816710	−	0.816710i
$22$	−5.07753	−	2.92477i	−1.08253	−	0.623564i
$23$	−3.00926	−	4.50368i	−0.627475	−	0.939082i	−0.999939	−	0.0110359i	$-0.996487\pi$
$23$	−3.00926	−	4.50368i	−0.627475	−	0.939082i	0.372464	−	0.928047i	$-0.378513\pi$
$24$	−7.68685	+	0.0229749i	−1.56907	+	0.00468974i
$25$	−2.93642	+	4.04690i	−0.587284	+	0.809381i
$26$	−1.05623	+	3.12178i	−0.207144	+	0.612231i
$27$	−3.69445	−	0.734872i	−0.710998	−	0.141426i
$28$	2.57404	+	2.92336i	0.486447	+	0.552463i
$29$	−2.68219	−	1.79218i	−0.498071	−	0.332800i	0.281030	−	0.959699i	$-0.409324\pi$
$29$	−2.68219	−	1.79218i	−0.498071	−	0.332800i	−0.779101	+	0.626899i	$0.784324\pi$
$30$	7.76182	+	3.68977i	1.41711	+	0.673656i
$31$	−0.632315	−	3.17886i	−0.113567	−	0.570941i	−0.995105	−	0.0988267i	$-0.968491\pi$
$31$	−0.632315	−	3.17886i	−0.113567	−	0.570941i	0.881537	−	0.472114i	$-0.156509\pi$
$32$	0.341853	−	5.64652i	0.0604316	−	0.998172i
$33$	7.96247	−	7.96247i	1.38609	−	1.38609i
$34$	2.59150	+	5.22342i	0.444438	+	0.895810i
$35$	−1.18338	−	4.19097i	−0.200027	−	0.708403i
$36$	2.25349	−	8.47766i	0.375581	−	1.41294i
$37$	−2.73456	−	1.82717i	−0.449559	−	0.300385i	0.310104	−	0.950703i	$-0.399636\pi$
$37$	−2.73456	−	1.82717i	−0.449559	−	0.300385i	−0.759663	+	0.650317i	$0.774636\pi$
$38$	−7.45991	−	6.52903i	−1.21016	−	1.05915i
$39$	−5.26592	−	3.51857i	−0.843222	−	0.563423i
$40$	−3.07209	+	5.52831i	−0.485741	+	0.874103i
$41$	5.30100	+	7.93351i	0.827877	+	1.23901i	0.968518	+	0.248945i	$0.0800839\pi$
$41$	5.30100	+	7.93351i	0.827877	+	1.23901i	−0.140640	+	0.990061i	$0.544916\pi$
$42$	−6.71003	+	3.31734i	−1.03538	+	0.511876i
$43$	−2.27201	+	5.48512i	−0.346478	+	0.836472i	0.650552	+	0.759462i	$0.274538\pi$
$43$	−2.27201	+	5.48512i	−0.346478	+	0.836472i	−0.997030	+	0.0770107i	$0.975462\pi$
$44$	5.47628	+	6.21946i	0.825580	+	0.937618i
$45$	−6.36712	+	7.45961i	−0.949154	+	1.11201i
$46$	1.98996	+	7.39714i	0.293403	+	1.09065i
$47$			12.1107i			1.76653i	0.468877	+	0.883264i	$0.344659\pi$
$47$			12.1107i			1.76653i	−0.468877	+	0.883264i	$0.655341\pi$
$48$	10.3078	+	3.45328i	1.48781	+	0.498439i
$49$	−2.96295	−	1.22730i	−0.423279	−	0.175328i
$50$	5.76793	−	4.09035i	0.815708	−	0.578463i
$51$	−10.9871	+	2.20148i	−1.53850	+	0.308269i
$52$	2.82989	−	3.70324i	0.392435	−	0.513547i
$53$	1.41644	−	0.586711i	0.194564	−	0.0805909i	−0.283274	−	0.959039i	$-0.591421\pi$
$53$	1.41644	−	0.586711i	0.194564	−	0.0805909i	0.477838	+	0.878448i	$0.341421\pi$
$54$	4.61606	+	2.65895i	0.628166	+	0.361838i
$55$	−2.51764	−	8.91631i	−0.339478	−	1.20227i
$56$	−2.12321	−	5.08285i	−0.283725	−	0.679224i
$57$	15.8404	−	10.5842i	2.09811	−	1.40191i
$58$	2.78080	+	3.61654i	0.365136	+	0.474875i
$59$	−3.26263	−	7.87669i	−0.424758	−	1.02546i	−0.980925	−	0.194386i	$-0.937728\pi$
$59$	−3.26263	−	7.87669i	−0.424758	−	1.02546i	0.556167	−	0.831071i	$-0.312272\pi$
$60$	−8.72546	−	8.46090i	−1.12645	−	1.09230i
$61$	8.05380	+	12.0534i	1.03118	+	1.54327i	0.825297	+	0.564698i	$0.191007\pi$
$61$	8.05380	+	12.0534i	1.03118	+	1.54327i	0.205886	+	0.978576i	$0.433993\pi$
$62$	−0.593761	+	4.54505i	−0.0754077	+	0.577221i
$63$	−1.66646	−	8.37784i	−0.209954	−	1.05551i
$64$	−3.01723	+	7.40920i	−0.377154	+	0.926151i
$65$	−4.64216	+	2.36711i	−0.575789	+	0.293603i
$66$	−14.2756	+	7.05765i	−1.75721	+	0.868736i
$67$	0.918910	−	0.918910i	0.112263	−	0.112263i	−0.648744	−	0.761007i	$-0.724705\pi$
$67$	0.918910	−	0.918910i	0.112263	−	0.112263i	0.761007	+	0.648744i	$0.224705\pi$
$68$	−1.10409	−	8.17196i	−0.133891	−	0.990996i
$69$	−14.7206			−1.77216
$70$	−0.314289	+	6.15065i	−0.0375647	+	0.735143i
$71$	−2.92256	+	0.581333i	−0.346844	+	0.0689916i	−0.365438	−	0.930836i	$-0.619081\pi$
$71$	−2.92256	+	0.581333i	−0.346844	+	0.0689916i	0.0185943	+	0.999827i	$0.494081\pi$
$72$	−6.86129	+	10.3354i	−0.808611	+	1.21804i
$73$	−2.11104	+	0.419911i	−0.247078	+	0.0491469i	−0.317076	−	0.948400i	$-0.602701\pi$
$73$	−2.11104	+	0.419911i	−0.247078	+	0.0491469i	0.0699975	+	0.997547i	$0.477701\pi$
$74$	2.83509	+	3.68714i	0.329572	+	0.428622i
$75$	4.71114	+	12.7458i	0.543996	+	1.47176i
$76$	7.03412	+	12.1276i	0.806869	+	1.39113i
$77$	7.45521	+	3.08805i	0.849600	+	0.351916i
$78$	5.45950	+	7.10031i	0.618167	+	0.803951i
$79$	−11.5007	−	2.28762i	−1.29393	−	0.257378i	−0.500336	−	0.865831i	$-0.666790\pi$
$79$	−11.5007	−	2.28762i	−1.29393	−	0.257378i	−0.793589	+	0.608454i	$0.791790\pi$
$80$	6.62113	−	6.01338i	0.740264	−	0.672316i
$81$	2.06536	−	2.06536i	0.229485	−	0.229485i
$82$	−3.50543	−	13.0305i	−0.387110	−	1.43898i
$83$	−2.70583	−	6.53244i	−0.297003	−	0.717029i	−0.999983	−	0.00581915i	$-0.998148\pi$
$83$	−2.70583	−	6.53244i	−0.297003	−	0.717029i	0.702980	−	0.711210i	$-0.251852\pi$
$84$	10.4924	−	1.40263i	1.14482	−	0.153039i
$85$	−2.83399	+	8.77317i	−0.307389	+	0.951584i
$86$	5.52974	−	6.31815i	0.596287	−	0.681304i
$87$	−8.09962	+	3.35497i	−0.868370	+	0.359691i
$88$	−4.51713	−	10.8138i	−0.481528	−	1.15275i
$89$	−6.40177	+	6.40177i	−0.678586	+	0.678586i	−0.959680	−	0.281094i	$-0.909303\pi$
$89$	−6.40177	+	6.40177i	−0.678586	+	0.678586i	0.281094	+	0.959680i	$0.409303\pi$
$90$	11.9105	−	7.10710i	1.25548	−	0.749155i
$91$	0.885411	−	4.45126i	0.0928163	−	0.466619i
$92$	0.686975	−	10.8113i	0.0716221	−	1.12715i
$93$	−8.13802	−	3.37088i	−0.843873	−	0.349544i
$94$	5.48917	−	16.2237i	0.566165	−	1.67334i
$95$	−1.23466	−	15.6260i	−0.126673	−	1.60319i
$96$	−12.2433	−	9.29808i	−1.24958	−	0.948982i
$97$	11.5896	−	2.30532i	1.17675	−	0.234070i	0.432289	−	0.901735i	$-0.357706\pi$
$97$	11.5896	−	2.30532i	1.17675	−	0.234070i	0.744462	+	0.667665i	$0.232706\pi$
$98$	3.41294	+	2.98706i	0.344759	+	0.301739i
$99$	−3.54539	−	17.8239i	−0.356325	−	1.79137i
$100$	−9.58075	+	2.86518i	−0.958075	+	0.286518i
$101$	−7.74711			−0.770866			−0.385433	−	0.922736i	$-0.625948\pi$
$101$	−7.74711			−0.770866			−0.385433	+	0.922736i	$0.625948\pi$
$102$	15.7163	+	2.03076i	1.55614	+	0.201075i
$103$	0.257098	+	0.257098i	0.0253326	+	0.0253326i	0.719660	−	0.694327i	$-0.244298\pi$
$103$	0.257098	+	0.257098i	0.0253326	+	0.0253326i	−0.694327	+	0.719660i	$0.744298\pi$
$104$	−5.46945	+	3.67826i	−0.536324	+	0.360683i
$105$	−11.2571	−	3.65381i	−1.09858	−	0.356575i
$106$	−2.16341	+	0.143962i	−0.210129	+	0.0139829i
$107$	11.1715	−	2.22215i	1.07999	−	0.214823i	0.377136	−	0.926158i	$-0.376909\pi$
$107$	11.1715	−	2.22215i	1.07999	−	0.214823i	0.702853	+	0.711335i	$0.251909\pi$
$108$	−4.97857	−	5.65420i	−0.479063	−	0.544076i
$109$	−2.77195	−	4.14852i	−0.265505	−	0.397356i	0.674631	−	0.738155i	$-0.264303\pi$
$109$	−2.77195	−	4.14852i	−0.265505	−	0.397356i	−0.940136	+	0.340799i	$0.889303\pi$
$110$	−0.668651	+	13.0855i	−0.0637534	+	1.24766i
$111$	−8.25775	+	3.42047i	−0.783791	+	0.324657i
$112$	0.540476	+	7.77140i	0.0510702	+	0.734328i
$113$	8.26725	−	5.52400i	0.777718	−	0.519654i	−0.102209	−	0.994763i	$-0.532591\pi$
$113$	8.26725	−	5.52400i	0.777718	−	0.519654i	0.879927	+	0.475108i	$0.157591\pi$
$114$	−26.0173	+	6.99910i	−2.43674	+	0.655526i
$115$	−5.91478	+	10.5693i	−0.551556	+	0.985589i
$116$	−2.08600	−	6.10516i	−0.193680	−	0.566850i
$117$	−9.44297	+	3.91141i	−0.873003	+	0.361610i
$118$	0.800559	+	12.0305i	0.0736974	+	1.10750i
$119$	−4.47054	−	6.67038i	−0.409814	−	0.611473i
$120$	7.85384	+	15.2892i	0.716954	+	1.39570i
$121$	5.69832	+	2.36032i	0.518029	+	0.214575i
$122$	−5.32580	−	19.7972i	−0.482175	−	1.79236i
$123$	25.9313			2.33815
$124$	2.85545	−	5.81948i	0.256427	−	0.522605i
$125$	11.0443	+	1.73874i	0.987833	+	0.155517i
$126$	−1.56485	+	11.9784i	−0.139407	+	1.06712i
$127$	5.65659	+	2.34303i	0.501941	+	0.207911i	0.619264	−	0.785183i	$-0.287431\pi$
$127$	5.65659	+	2.34303i	0.501941	+	0.207911i	−0.117323	+	0.993094i	$0.537431\pi$
$128$	7.40014	−	8.55791i	0.654086	−	0.756420i
$129$	8.96427	+	13.4160i	0.789260	+	1.18121i
$130$	7.29159	−	1.06695i	0.639514	−	0.0935779i
$131$	−0.612815	+	0.917143i	−0.0535419	+	0.0801312i	−0.857275	−	0.514859i	$-0.827844\pi$
$131$	−0.612815	+	0.917143i	−0.0535419	+	0.0801312i	0.803733	+	0.594990i	$0.202844\pi$
$132$	22.3227	−	2.98410i	1.94294	−	0.259733i
$133$	11.3513	+	7.58473i	0.984287	+	0.657679i
$134$	−1.64748	+	0.814489i	−0.142321	+	0.0703611i
$135$	2.28882	+	8.10595i	0.196990	+	0.697649i
$136$	−2.22489	+	11.4477i	−0.190782	+	0.981632i
$137$	−13.9924	+	13.9924i	−1.19545	+	1.19545i	−0.219933	+	0.975515i	$0.570584\pi$
$137$	−13.9924	+	13.9924i	−1.19545	+	1.19545i	−0.975515	+	0.219933i	$0.929416\pi$
$138$	19.7200	+	6.67212i	1.67868	+	0.567969i
$139$	16.8872	−	3.35907i	1.43235	−	0.284913i	0.582886	−	0.812554i	$-0.301923\pi$
$139$	16.8872	−	3.35907i	1.43235	−	0.284913i	0.849467	+	0.527641i	$0.176923\pi$
$140$	3.20880	−	8.09704i	0.271193	−	0.684325i
$141$	27.3666	+	18.2858i	2.30468	+	1.53994i
$142$	4.17859	+	0.545887i	0.350659	+	0.0458098i
$143$	1.88372	−	9.47008i	0.157524	−	0.791928i
$144$	13.8760	−	10.7356i	1.15633	−	0.894629i
$145$	−0.845606	+	7.16348i	−0.0702237	+	0.594894i
$146$	3.01830	+	0.394308i	0.249796	+	0.0326331i
$147$	−7.24705	+	4.84232i	−0.597727	+	0.399388i
$148$	−2.12672	−	6.22435i	−0.174816	−	0.511638i
$149$	13.4577	−	13.4577i	1.10250	−	1.10250i	0.108390	−	0.994108i	$-0.465431\pi$
$149$	13.4577	−	13.4577i	1.10250	−	1.10250i	0.994108	−	0.108390i	$-0.0345695\pi$
$150$	−0.534076	−	19.2098i	−0.0436071	−	1.56847i
$151$	−2.04079	+	4.92690i	−0.166077	+	0.400946i	−0.984906	−	0.173093i	$-0.944624\pi$
$151$	−2.04079	+	4.92690i	−0.166077	+	0.400946i	0.818828	+	0.574038i	$0.194624\pi$
$152$	−3.92618	−	19.4345i	−0.318455	−	1.57634i
$153$	−6.89704	+	16.7172i	−0.557593	+	1.35150i
$154$	−8.58744	−	7.51586i	−0.691996	−	0.605645i
$155$	−5.69013	+	4.48859i	−0.457042	+	0.360532i
$156$	−4.09542	−	11.9862i	−0.327896	−	0.959663i
$157$		−	0.551312i		−	0.0439995i	−0.999758	−	0.0219997i	$-0.992997\pi$
$157$		−	0.551312i		−	0.0439995i	0.999758	−	0.0219997i	$-0.00700330\pi$
$158$	14.3696	+	8.27720i	1.14318	+	0.658499i
$159$	0.812878	−	4.08661i	0.0644654	−	0.324089i
$160$	−11.5953	+	5.05458i	−0.916690	+	0.399600i
$161$	−4.03690	−	9.74594i	−0.318152	−	0.768087i
$162$	−3.70291	+	1.83066i	−0.290928	+	0.143830i
$163$	−2.63247	+	13.2343i	−0.206191	+	1.03659i	0.729556	+	0.683921i	$0.239727\pi$
$163$	−2.63247	+	13.2343i	−0.206191	+	1.03659i	−0.935747	+	0.352672i	$0.885273\pi$
$164$	−1.21015	+	19.0447i	−0.0944968	+	1.48714i
$165$	−23.9496	−	7.77350i	−1.86447	−	0.605166i
$166$	0.663935	+	9.97736i	0.0515313	+	0.774394i
$167$	15.0051	+	10.0261i	1.16113	+	0.775843i	0.978278	−	0.207297i	$-0.0664667\pi$
$167$	15.0051	+	10.0261i	1.16113	+	0.775843i	0.182853	+	0.983140i	$0.441467\pi$
$168$	−14.6915	−	2.87671i	−1.13348	−	0.221943i
$169$	7.56944			0.582264
$170$	7.77289	−	10.4682i	0.596153	−	0.802871i
$171$		−	30.7458i		−	2.35119i
$172$	−10.2714	+	5.95753i	−0.783188	+	0.454257i
$173$	−4.69250	+	7.02283i	−0.356764	+	0.533936i	−0.965827	−	0.259186i	$-0.916546\pi$
$173$	−4.69250	+	7.02283i	−0.356764	+	0.533936i	0.609063	+	0.793122i	$0.291546\pi$
$174$	12.3710	−	0.823217i	0.937843	−	0.0624079i
$175$	−7.14653	+	6.61439i	−0.540227	+	0.500001i
$176$	1.14986	+	16.5337i	0.0866743	+	1.24627i
$177$	−22.7252	−	4.52032i	−1.70813	−	0.339768i
$178$	11.4775	−	5.67430i	0.860275	−	0.425307i
$179$	18.4001	−	7.62156i	1.37529	−	0.569662i	0.432070	−	0.901840i	$-0.357783\pi$
$179$	18.4001	−	7.62156i	1.37529	−	0.569662i	0.943217	+	0.332178i	$0.107783\pi$
$180$	−19.1768	+	4.12232i	−1.42936	+	0.307260i
$181$	7.32451	+	1.45693i	0.544426	+	0.108293i	0.459639	−	0.888106i	$-0.347979\pi$
$181$	7.32451	+	1.45693i	0.544426	+	0.108293i	0.0847874	+	0.996399i	$0.472979\pi$
$182$	−3.20364	+	5.56166i	−0.237470	+	0.412258i
$183$	39.3974			2.91234
$184$	−5.82048	+	14.1715i	−0.429092	+	1.04474i
$185$	−0.862114	+	7.30333i	−0.0633839	+	0.536951i
$186$	9.37395	+	8.20423i	0.687332	+	0.601563i
$187$	−9.51110	−	14.1913i	−0.695520	−	1.03777i
$188$	−14.7067	+	19.2455i	−1.07260	+	1.40362i
$189$	−6.77764	−	2.80739i	−0.493001	−	0.204208i
$190$	−5.42851	+	21.4924i	−0.393826	+	1.55922i
$191$	3.58146	+	3.58146i	0.259145	+	0.259145i	0.824706	−	0.565561i	$-0.191340\pi$
$191$	3.58146	+	3.58146i	0.259145	+	0.259145i	−0.565561	+	0.824706i	$0.691340\pi$
$192$	12.1869	+	18.0051i	0.879517	+	1.29941i
$193$	−3.96075	−	5.92768i	−0.285101	−	0.426683i	0.661083	−	0.750313i	$-0.270097\pi$
$193$	−3.96075	−	5.92768i	−0.285101	−	0.426683i	−0.946184	+	0.323629i	$0.895097\pi$
$194$	−16.5705	−	2.16476i	−1.18970	−	0.155421i
$195$	−1.66017	+	14.0640i	−0.118887	+	1.00714i
$196$	−3.21814	−	5.54842i	−0.229867	−	0.396316i
$197$	11.8980	+	2.36666i	0.847698	+	0.168618i	0.599781	−	0.800164i	$-0.295254\pi$
$197$	11.8980	+	2.36666i	0.847698	+	0.168618i	0.247916	+	0.968781i	$0.420254\pi$
$198$	−3.32922	+	25.4841i	−0.236597	+	1.81107i
$199$	−4.55161	+	6.81197i	−0.322655	+	0.482888i	−0.956970	−	0.290187i	$-0.906282\pi$
$199$	−4.55161	+	6.81197i	−0.322655	+	0.482888i	0.634315	+	0.773075i	$0.281282\pi$
$200$	14.1331	+	0.504232i	0.999364	+	0.0356546i
$201$	−0.689016	−	3.46392i	−0.0485994	−	0.244326i
$202$	10.3781	+	3.51138i	0.730203	+	0.247060i
$203$	−4.44238	−	4.44238i	−0.311794	−	0.311794i
$204$	−20.1333	−	9.84382i	−1.40961	−	0.689205i
$205$	10.4192	−	18.6184i	0.727712	−	1.30037i
$206$	−0.227882	−	0.460941i	−0.0158773	−	0.0321153i
$207$	−13.1987	+	19.7533i	−0.917373	+	1.37295i
$208$	8.99412	−	2.44842i	0.623630	−	0.169768i
$209$	24.1501	+	16.1365i	1.67049	+	1.11619i
$210$	13.4241	+	9.99698i	0.926351	+	0.689857i
$211$	−0.402060	+	0.268648i	−0.0276789	+	0.0184945i	−0.569333	−	0.822107i	$-0.692798\pi$
$211$	−0.402060	+	0.268648i	−0.0276789	+	0.0184945i	0.541654	+	0.840602i	$0.317798\pi$
$212$	2.96339	+	0.787713i	0.203527	+	0.0541003i
$213$	−3.09909	+	7.48187i	−0.212346	+	0.512649i
$214$	−15.9727	−	2.08666i	−1.09187	−	0.142641i
$215$	13.2344	−	1.04569i	0.902578	−	0.0713155i
$216$	4.10659	+	9.83098i	0.279418	+	0.668913i
$217$		−	6.31226i		−	0.428504i
$218$	1.83303	+	6.81380i	0.124148	+	0.461489i
$219$	−2.23855	+	5.40434i	−0.151267	+	0.365191i
$220$	6.82675	−	17.2265i	0.460259	−	1.16141i
$221$	−6.78457	+	6.80361i	−0.456380	+	0.457661i
$222$	12.6125	−	0.839288i	0.846497	−	0.0563294i
$223$	3.14773	+	7.59929i	0.210787	+	0.508886i	0.993545	−	0.113441i	$-0.0361873\pi$
$223$	3.14773	+	7.59929i	0.210787	+	0.508886i	−0.782757	+	0.622327i	$0.786187\pi$
$224$	2.79835	−	10.6556i	0.186973	−	0.711960i
$225$	21.3274	+	5.10629i	1.42182	+	0.340419i
$226$	−13.5787	+	3.65290i	−0.903240	+	0.242987i
$227$	−8.46190	−	12.6641i	−0.561636	−	0.840548i	0.436616	−	0.899648i	$-0.356177\pi$
$227$	−8.46190	−	12.6641i	−0.561636	−	0.840548i	−0.998252	+	0.0591001i	$0.981177\pi$
$228$	38.0255	+	2.41624i	2.51830	+	0.160019i
$229$	−0.256873	−	0.620146i	−0.0169746	−	0.0409804i	0.915165	−	0.403079i	$-0.132060\pi$
$229$	−0.256873	−	0.620146i	−0.0169746	−	0.0409804i	−0.932140	+	0.362099i	$0.882060\pi$
$230$	12.7140	−	11.4779i	0.838339	−	0.756828i
$231$	18.2346	−	12.1840i	1.19975	−	0.801646i
$232$	0.0272705	+	9.12403i	0.00179039	+	0.599022i
$233$	4.08960	+	20.5598i	0.267919	+	1.34692i	0.846976	+	0.531632i	$0.178421\pi$
$233$	4.08960	+	20.5598i	0.267919	+	1.34692i	−0.579057	+	0.815287i	$0.696579\pi$
$234$	14.4228	−	0.959751i	0.942847	−	0.0627409i
$235$	24.1250	−	12.3017i	1.57374	−	0.802474i
$236$	4.38038	−	16.4791i	0.285138	−	1.07270i
$237$	−22.5340	+	22.5340i	−1.46374	+	1.46374i
$238$	2.96545	+	10.9620i	0.192222	+	0.710561i
$239$		−	24.2813i		−	1.57063i	−0.619096	−	0.785315i	$-0.712501\pi$
$239$		−	24.2813i		−	1.57063i	0.619096	−	0.785315i	$-0.287499\pi$
$240$	−3.59131	−	24.0413i	−0.231818	−	1.55186i
$241$	2.47544	−	0.492395i	0.159457	−	0.0317180i	−0.114716	−	0.993398i	$-0.536596\pi$
$241$	2.47544	−	0.492395i	0.159457	−	0.0317180i	0.274173	+	0.961680i	$0.411596\pi$
$242$	−6.56373	−	5.74468i	−0.421933	−	0.369282i
$243$	−3.75326	−	18.8689i	−0.240772	−	1.21044i
$244$	−1.83858	+	28.9345i	−0.117703	+	1.85234i
$245$	0.564862	+	7.14896i	0.0360877	+	0.456731i
$246$	−34.7379	−	11.7534i	−2.21481	−	0.749367i
$247$	6.25139	−	15.0922i	0.397766	−	0.960292i
$248$	−6.46288	+	6.50163i	−0.410393	+	0.412854i
$249$	−18.8469	−	3.74888i	−1.19437	−	0.237576i
$250$	−14.0070	−	7.33507i	−0.885882	−	0.463910i
$251$	−0.317560	−	0.317560i	−0.0200442	−	0.0200442i	0.697014	−	0.717058i	$-0.254512\pi$
$251$	−0.317560	−	0.317560i	−0.0200442	−	0.0200442i	−0.717058	+	0.697014i	$0.754512\pi$
$252$	7.52549	−	15.3371i	0.474061	−	0.966149i
$253$	−8.58852	−	20.7345i	−0.539956	−	1.30357i
$254$	−6.51566	−	5.70261i	−0.408829	−	0.357813i
$255$	15.5458	+	19.6505i	0.973514	+	1.23056i
$256$	−13.7922	+	8.11018i	−0.862013	+	0.506887i
$257$	7.42509	−	3.07557i	0.463164	−	0.191849i	−0.138884	−	0.990309i	$-0.544351\pi$
$257$	7.42509	−	3.07557i	0.463164	−	0.191849i	0.602048	+	0.798460i	$0.294351\pi$
$258$	−5.92787	−	22.0353i	−0.369053	−	1.37186i
$259$	−4.52911	−	4.52911i	−0.281425	−	0.281425i
$260$	−10.2515	−	1.87560i	−0.635771	−	0.116320i
$261$	−2.76026	+	13.8768i	−0.170856	+	0.858951i
$262$	1.23663	−	0.950859i	0.0763993	−	0.0587443i
$263$	−0.341696	+	0.824927i	−0.0210699	+	0.0508672i	−0.934064	−	0.357105i	$-0.883764\pi$
$263$	−0.341696	+	0.824927i	−0.0210699	+	0.0508672i	0.912994	+	0.407972i	$0.133764\pi$
$264$	−31.2563	−	6.12021i	−1.92369	−	0.376673i
$265$	−2.60753	−	2.22565i	−0.160179	−	0.136720i
$266$	−11.7686	−	15.3056i	−0.721582	−	0.938447i
$267$	4.80017	+	24.1321i	0.293765	+	1.47686i
$268$	2.57615	−	0.344381i	0.157364	−	0.0210364i
$269$	4.08019	+	20.5125i	0.248773	+	1.25067i	0.879964	+	0.475040i	$0.157567\pi$
$269$	4.08019	+	20.5125i	0.248773	+	1.25067i	−0.631191	+	0.775628i	$0.717433\pi$
$270$	0.607881	−	11.8962i	0.0369945	−	0.723983i
$271$		−	19.9074i		−	1.20929i	−0.796495	−	0.604645i	$-0.793315\pi$
$271$		−	19.9074i		−	1.20929i	0.796495	−	0.604645i	$-0.206685\pi$
$272$	8.16915	−	14.3271i	0.495328	−	0.868706i
$273$	−8.72167	−	8.72167i	−0.527860	−	0.527860i
$274$	25.0864	−	12.4023i	1.51552	−	0.749252i
$275$	−15.2043	+	14.0721i	−0.916852	+	0.848583i
$276$	−23.3930	−	17.8761i	−1.40809	−	1.07602i
$277$	21.4444	−	4.26555i	1.28847	−	0.256292i	0.497133	−	0.867675i	$-0.334386\pi$
$277$	21.4444	−	4.26555i	1.28847	−	0.256292i	0.791335	+	0.611382i	$0.209386\pi$
$278$	−24.1448	−	3.15426i	−1.44811	−	0.189180i
$279$	−11.8199	+	7.89783i	−0.707642	+	0.472831i
$280$	−7.96854	+	9.39251i	−0.476211	+	0.561310i
$281$	−9.56327	+	3.96124i	−0.570497	+	0.236307i	−0.649235	−	0.760588i	$-0.724911\pi$
$281$	−9.56327	+	3.96124i	−0.570497	+	0.236307i	0.0787383	+	0.996895i	$0.474911\pi$
$282$	−28.3727	−	36.8998i	−1.68957	−	2.19735i
$283$	0.00879277	+	0.0131593i	0.000522676	+	0.000782239i	0.831731	−	0.555179i	$-0.187350\pi$
$283$	0.00879277	+	0.0131593i	0.000522676	+	0.000782239i	−0.831208	+	0.555961i	$0.812350\pi$
$284$	−5.35027	−	2.62522i	−0.317480	−	0.155778i
$285$	−37.1743	−	20.8035i	−2.20202	−	1.23229i
$286$	−6.81577	+	11.8325i	−0.403025	+	0.699668i
$287$	7.11124	+	17.1681i	0.419763	+	1.01340i
$288$	−23.4544	+	8.09220i	−1.38206	+	0.476838i
$289$	0.0476546	+	16.9999i	0.00280321	+	0.999996i
$290$	4.37963	−	9.21302i	0.257181	−	0.541007i
$291$	12.2897	−	29.6700i	0.720435	−	1.73928i
$292$	−3.86463	−	1.89626i	−0.226161	−	0.110970i
$293$	−7.37954			−0.431117			−0.215559	−	0.976491i	$-0.569157\pi$
$293$	−7.37954			−0.431117			−0.215559	+	0.976491i	$0.569157\pi$
$294$	11.9030	−	3.20212i	0.694199	−	0.186751i
$295$	−12.3766	+	14.5002i	−0.720592	+	0.844233i
$296$	0.0278029	+	9.30216i	0.00161601	+	0.540677i
$297$	−14.4195	−	5.97274i	−0.836702	−	0.346573i
$298$	−24.1278	+	11.9284i	−1.39769	+	0.690995i
$299$	−10.4952	+	7.01266i	−0.606952	+	0.405552i
$300$	−7.99137	+	25.9758i	−0.461382	+	1.49971i
$301$	−6.42387	+	9.61399i	−0.370265	+	0.554141i
$302$	4.96699	−	5.67516i	0.285818	−	0.326569i
$303$	−11.6973	+	17.5062i	−0.671990	+	1.00570i
$304$	−3.54911	+	27.8142i	−0.203555	+	1.59526i
$305$	15.8299	−	28.2869i	0.906419	−	1.61970i
$306$	16.8164	−	19.2685i	0.961330	−	1.10150i
$307$	−19.3372	−	19.3372i	−1.10363	−	1.10363i	−0.993969	−	0.109663i	$-0.965023\pi$
$307$	−19.3372	−	19.3372i	−1.10363	−	1.10363i	−0.109663	−	0.993969i	$-0.534977\pi$
$308$	8.09729	+	13.9606i	0.461386	+	0.795479i
$309$	0.969154	−	0.192777i	0.0551332	−	0.0109667i
$310$	9.65702	−	3.43393i	0.548482	−	0.195034i
$311$	−0.121348	+	0.181610i	−0.00688101	+	0.0102982i	−0.834894	−	0.550410i	$-0.814471\pi$
$311$	−0.121348	+	0.181610i	−0.00688101	+	0.0102982i	0.828013	+	0.560709i	$0.189471\pi$
$312$	0.0535398	+	17.9131i	0.00303109	+	1.01413i
$313$	2.79070	−	14.0298i	0.157740	−	0.793012i	−0.818194	−	0.574943i	$-0.805024\pi$
$313$	2.79070	−	14.0298i	0.157740	−	0.793012i	0.975933	−	0.218069i	$-0.0699758\pi$
$314$	−0.249882	+	0.738545i	−0.0141017	+	0.0416785i
$315$	−14.9962	+	11.8296i	−0.844942	+	0.666522i
$316$	−15.4980	−	17.6013i	−0.871833	−	0.990148i
$317$	19.7139	−	13.1724i	1.10724	−	0.739836i	0.139111	−	0.990277i	$-0.455576\pi$
$317$	19.7139	−	13.1724i	1.10724	−	0.739836i	0.968132	+	0.250441i	$0.0805755\pi$
$318$	−2.94120	+	5.10605i	−0.164934	+	0.286333i
$319$	−9.45119	−	9.45119i	−0.529165	−	0.529165i
$320$	17.8242	−	1.51561i	0.996404	−	0.0847253i
$321$	11.8463	−	28.5995i	0.661195	−	1.59627i
$322$	0.990543	+	14.8855i	0.0552008	+	0.829537i
$323$	−11.0980	−	26.6871i	−0.617510	−	1.48491i
$324$	5.79022	−	0.774037i	0.321679	−	0.0430021i
$325$	9.43073	+	6.84291i	0.523123	+	0.379576i
$326$	9.52496	−	16.5357i	0.527539	−	0.915830i
$327$	−13.5598			−0.749857
$328$	10.2531	−	24.9640i	0.566135	−	1.37841i
$329$	−4.60142	+	23.1329i	−0.253685	+	1.27536i
$330$	28.5598	+	21.2686i	1.57217	+	1.17080i
$331$	−2.82447	+	1.16993i	−0.155247	+	0.0643053i	−0.458954	−	0.888460i	$-0.651776\pi$
$331$	−2.82447	+	1.16993i	−0.155247	+	0.0643053i	0.303707	+	0.952765i	$0.401776\pi$
$332$	3.63282	−	13.6667i	0.199377	−	0.750060i
$333$	−2.81415	+	14.1477i	−0.154215	+	0.775289i
$334$	−15.5567	−	20.2322i	−0.851227	−	1.10706i
$335$	−2.76390	−	0.897102i	−0.151008	−	0.0490139i
$336$	18.3771	+	10.5126i	1.00255	+	0.573510i
$337$	−14.4474	−	9.65344i	−0.787000	−	0.525856i	0.0959152	−	0.995390i	$-0.469422\pi$
$337$	−14.4474	−	9.65344i	−0.787000	−	0.525856i	−0.882915	+	0.469533i	$0.844422\pi$
$338$	−10.1401	−	3.43084i	−0.551550	−	0.186613i
$339$		−	27.0222i		−	1.46764i
$340$	−15.1574	+	10.5002i	−0.822023	+	0.569455i
$341$		−	13.4294i		−	0.727241i
$342$	−13.9355	+	41.1874i	−0.753546	+	2.22716i
$343$	−16.5286	−	11.0440i	−0.892458	−	0.596321i
$344$	16.4600	−	3.32527i	0.887462	−	0.179286i
$345$	14.9528	+	29.3241i	0.805031	+	1.57875i
$346$	9.46923	−	7.28100i	0.509069	−	0.391429i
$347$	−5.31259	+	26.7082i	−0.285195	+	1.43377i	0.526742	+	0.850025i	$0.323413\pi$
$347$	−5.31259	+	26.7082i	−0.285195	+	1.43377i	−0.811937	+	0.583745i	$0.801587\pi$
$348$	−16.9455	−	4.50436i	−0.908373	−	0.241459i
$349$	14.1237	−	5.85024i	0.756026	−	0.313156i	0.0288287	−	0.999584i	$-0.490822\pi$
$349$	14.1237	−	5.85024i	0.756026	−	0.313156i	0.727198	+	0.686428i	$0.240822\pi$
$350$	12.5716	−	5.62157i	0.671978	−	0.300485i
$351$	−1.71251	+	8.60939i	−0.0914073	+	0.459535i
$352$	5.95351	−	22.6699i	0.317323	−	1.20831i
$353$	−26.1196			−1.39021			−0.695104	−	0.718909i	$-0.744642\pi$
$353$	−26.1196			−1.39021			−0.695104	+	0.718909i	$0.744642\pi$
$354$	28.3941	+	16.3557i	1.50913	+	0.869294i
$355$	4.12669	+	5.23135i	0.219022	+	0.277651i
$356$	−17.9473	+	2.39920i	−0.951205	+	0.127157i
$357$	−21.8231	+	0.0305874i	−1.15500	+	0.00161886i
$358$	−28.1035	+	1.87012i	−1.48531	+	0.0988389i
$359$	−9.34864	+	22.5696i	−0.493402	+	1.19118i	0.459575	+	0.888139i	$0.348002\pi$
$359$	−9.34864	+	22.5696i	−0.493402	+	1.19118i	−0.952978	+	0.303040i	$0.901998\pi$
$360$	27.5580	+	3.16957i	1.45243	+	0.167051i
$361$	21.3117	+	21.3117i	1.12167	+	1.12167i
$362$	−9.15165	−	5.27156i	−0.481000	−	0.277067i
$363$	13.9374	−	9.31270i	0.731526	−	0.488790i
$364$	6.81246	−	5.99843i	0.357070	−	0.314403i
$365$	2.98081	+	3.77873i	0.156023	+	0.197788i
$366$	−52.7772	−	17.8568i	−2.75871	−	0.933392i
$367$	−1.14912	+	5.77702i	−0.0599836	+	0.301558i	−0.999118	−	0.0419922i	$-0.986630\pi$
$367$	−1.14912	+	5.77702i	−0.0599836	+	0.301558i	0.939134	+	0.343550i	$0.111630\pi$
$368$	14.2204	−	16.3463i	0.741292	−	0.852107i
$369$	23.2503	−	34.7966i	1.21036	−	1.81144i
$370$	4.46513	−	9.39289i	0.232131	−	0.488313i
$371$	2.92850	−	0.582515i	0.152040	−	0.0302427i
$372$	−8.83891	−	15.2392i	−0.458276	−	0.790118i
$373$	2.01100	+	2.01100i	0.104126	+	0.104126i	0.757250	−	0.653125i	$-0.226542\pi$
$373$	2.01100	+	2.01100i	0.104126	+	0.104126i	−0.653125	+	0.757250i	$0.726542\pi$
$374$	6.30901	+	23.3217i	0.326231	+	1.20594i
$375$	20.6047	−	22.3316i	1.06402	−	1.15320i
$376$	28.4243	−	19.1157i	1.46587	−	0.985816i
$377$	−4.17643	+	6.25047i	−0.215097	+	0.321915i
$378$	7.80697	+	6.83278i	0.401547	+	0.351440i
$379$	−9.40345	+	14.0733i	−0.483023	+	0.722895i	−0.990309	−	0.138883i	$-0.955649\pi$
$379$	−9.40345	+	14.0733i	−0.483023	+	0.722895i	0.507286	+	0.861778i	$0.330649\pi$
$380$	17.0135	−	26.3311i	0.872776	−	1.35075i
$381$	13.8354	−	9.24450i	0.708807	−	0.473610i
$382$	−3.17448	−	6.42106i	−0.162420	−	0.328530i
$383$	13.1907	+	5.46379i	0.674016	+	0.279186i	0.693323	−	0.720627i	$-0.256146\pi$
$383$	13.1907	+	5.46379i	0.674016	+	0.279186i	−0.0193072	+	0.999814i	$0.506146\pi$
$384$	−8.16498	−	29.6436i	−0.416667	−	1.51274i
$385$	−1.42127	−	17.9878i	−0.0724347	−	0.916743i
$386$	2.61915	+	9.73600i	0.133311	+	0.495550i
$387$	26.0400			1.32369
$388$	21.2169	+	10.4105i	1.07713	+	0.528515i
$389$	−14.6452	+	35.3566i	−0.742540	+	1.79265i	−0.147316	+	0.989090i	$0.547063\pi$
$389$	−14.6452	+	35.3566i	−0.742540	+	1.79265i	−0.595224	+	0.803560i	$0.702937\pi$
$390$	8.59847	−	18.0878i	0.435400	−	0.915912i
$391$	−4.32623	+	21.9099i	−0.218787	+	1.10803i
$392$	1.79624	+	8.89136i	0.0907241	+	0.449082i
$393$	1.14719	+	2.76956i	0.0578681	+	0.139706i
$394$	−14.8660	−	8.56318i	−0.748940	−	0.431407i
$395$	7.12500	+	25.2334i	0.358497	+	1.26963i
$396$	16.0105	−	32.6298i	0.804558	−	1.63971i
$397$	−15.3975	−	23.0440i	−0.772780	−	1.15655i	−0.983836	−	0.179072i	$-0.942690\pi$
$397$	−15.3975	−	23.0440i	−0.772780	−	1.15655i	0.211056	−	0.977474i	$-0.432310\pi$
$398$	9.18492	−	7.06239i	0.460399	−	0.354006i
$399$	34.2785	−	14.1986i	1.71607	−	0.710820i
$400$	−18.7044	−	7.08132i	−0.935220	−	0.354066i
$401$	−18.2714	+	12.2086i	−0.912430	+	0.609666i	−0.920688	−	0.390300i	$-0.872371\pi$
$401$	−18.2714	+	12.2086i	−0.912430	+	0.609666i	0.00825787	+	0.999966i	$0.497371\pi$
$402$	−0.647004	+	4.95261i	−0.0322696	+	0.247014i
$403$	−7.40789	+	1.47352i	−0.369013	+	0.0734013i
$404$	−12.3112	−	9.40777i	−0.612503	−	0.468054i
$405$	−6.21221	−	2.01634i	−0.308687	−	0.100193i
$406$	3.93757	+	7.96458i	0.195418	+	0.395275i
$407$	−9.63570	−	9.63570i	−0.477624	−	0.477624i
$408$	22.5091	+	22.3123i	1.11437	+	1.10462i
$409$		−	11.0950i		−	0.548611i	−0.961643	−	0.274306i	$-0.911552\pi$
$409$		−	11.0950i		−	0.548611i	0.961643	−	0.274306i	$-0.0884480\pi$
$410$	−22.3966	+	20.2190i	−1.10609	+	0.998543i
$411$	10.4917	+	52.7455i	0.517519	+	2.60174i
$412$	0.0963527	+	0.720771i	0.00474696	+	0.0355098i
$413$	−3.23930	−	16.2850i	−0.159395	−	0.801335i
$414$	26.6343	−	20.4794i	1.30901	−	1.00651i
$415$	−10.2644	+	12.0256i	−0.503858	+	0.590312i
$416$	−13.1584	−	0.796639i	−0.645143	−	0.0390584i
$417$	17.9072	−	43.2319i	0.876921	−	2.11708i
$418$	−25.0379	−	32.5627i	−1.22464	−	1.59270i
$419$	−4.63451	+	23.2993i	−0.226411	+	1.13824i	0.685569	+	0.728008i	$0.259554\pi$
$419$	−4.63451	+	23.2993i	−0.226411	+	1.13824i	−0.911980	+	0.410236i	$0.865446\pi$
$420$	−13.4520	−	19.4766i	−0.656390	−	0.950359i
$421$	13.3082	+	13.3082i	0.648602	+	0.648602i	0.952655	−	0.304053i	$-0.0983400\pi$
$421$	13.3082	+	13.3082i	0.648602	+	0.648602i	−0.304053	+	0.952655i	$0.598340\pi$
$422$	0.660369	−	0.177651i	0.0321463	−	0.00864790i
$423$	49.0745	−	20.3273i	2.38608	−	0.988348i
$424$	−3.61277	−	2.39839i	−0.175452	−	0.116476i
$425$	20.3552	−	3.26611i	0.987370	−	0.158430i
$426$	7.54274	−	8.61815i	0.365447	−	0.417551i
$427$	10.8041	+	26.0834i	0.522847	+	1.26226i
$428$	20.4514	+	10.0349i	0.988558	+	0.485056i
$429$	−18.5554	−	18.5554i	−0.895863	−	0.895863i
$430$	−18.2029	−	4.59766i	−0.877823	−	0.221719i
$431$	−23.2866	−	4.63199i	−1.12168	−	0.223115i	−0.400791	−	0.916170i	$-0.631265\pi$
$431$	−23.2866	−	4.63199i	−1.12168	−	0.223115i	−0.720885	+	0.693054i	$0.756265\pi$
$432$	−1.04536	−	15.0310i	−0.0502949	−	0.723180i
$433$	−4.83247	+	11.6666i	−0.232234	+	0.560662i	−0.996440	−	0.0843108i	$-0.973131\pi$
$433$	−4.83247	+	11.6666i	−0.232234	+	0.560662i	0.764206	+	0.644972i	$0.223131\pi$
$434$	−2.86103	+	8.45599i	−0.137334	+	0.405901i
$435$	14.9106	+	12.7269i	0.714907	+	0.610206i
$436$	0.632800	−	9.95868i	0.0303056	−	0.476934i
$437$	−7.40749	−	37.2400i	−0.354348	−	1.78143i
$438$	5.44831	−	6.22510i	0.260330	−	0.297447i
$439$	15.7674	−	3.13633i	0.752537	−	0.149689i	0.196106	−	0.980583i	$-0.437170\pi$
$439$	15.7674	−	3.13633i	0.752537	−	0.149689i	0.556431	+	0.830894i	$0.312170\pi$
$440$	−16.9531	+	19.9826i	−0.808207	+	0.952634i
$441$			14.0663i			0.669825i
$442$	12.1724	−	6.03911i	0.578984	−	0.287251i
$443$	−15.4262	+	15.4262i	−0.732920	+	0.732920i	−0.971197	−	0.238277i	$-0.923417\pi$
$443$	−15.4262	+	15.4262i	−0.732920	+	0.732920i	0.238277	+	0.971197i	$0.423417\pi$
$444$	−17.2763	−	4.59230i	−0.819897	−	0.217941i
$445$	19.2553	+	6.24984i	0.912788	+	0.296271i
$446$	−0.772365	−	11.6068i	−0.0365726	−	0.549599i
$447$	−10.0908	−	50.7301i	−0.477280	−	2.39945i
$448$	−8.57838	+	13.0061i	−0.405290	+	0.614480i
$449$	9.17205	−	6.12857i	0.432856	−	0.289225i	−0.319991	−	0.947421i	$-0.603680\pi$
$449$	9.17205	−	6.12857i	0.432856	−	0.289225i	0.752847	+	0.658195i	$0.228680\pi$
$450$	−26.2560	−	16.5071i	−1.23772	−	0.778151i
$451$	15.1292	+	36.5251i	0.712407	+	1.71990i
$452$	19.8459	+	1.26106i	0.933471	+	0.0593151i
$453$	8.05199	+	12.0507i	0.378315	+	0.566189i
$454$	5.59567	+	20.8004i	0.262618	+	0.976211i
$455$	−9.76646	+	2.75769i	−0.457858	+	0.129282i
$456$	−49.8443	−	20.4719i	−2.33417	−	0.958682i
$457$	−3.35913	−	8.10966i	−0.157134	−	0.379354i	0.825632	−	0.564209i	$-0.190819\pi$
$457$	−3.35913	−	8.10966i	−0.157134	−	0.379354i	−0.982766	+	0.184855i	$0.940819\pi$
$458$	0.0630295	+	0.947183i	0.00294517	+	0.0442590i
$459$	8.64668	+	12.9015i	0.403592	+	0.602190i
$460$	−22.2342	+	9.61327i	−1.03668	+	0.448221i
$461$	9.18322	−	22.1703i	0.427705	−	1.03257i	−0.552308	−	0.833640i	$-0.686253\pi$
$461$	9.18322	−	22.1703i	0.427705	−	1.03257i	0.980013	−	0.198932i	$-0.0637472\pi$
$462$	−29.9497	+	8.05699i	−1.39339	+	0.374845i
$463$			35.5713i			1.65314i	0.562835	+	0.826569i	$0.309711\pi$
$463$			35.5713i			1.65314i	−0.562835	+	0.826569i	$0.690289\pi$
$464$	4.09893	−	12.2350i	0.190288	−	0.567997i
$465$	1.55144	+	19.6353i	0.0719465	+	0.910564i
$466$	3.84024	−	29.3958i	0.177896	−	1.36174i
$467$	4.31331	−	10.4132i	0.199596	−	0.481867i	−0.792112	−	0.610375i	$-0.791019\pi$
$467$	4.31331	−	10.4132i	0.199596	−	0.481867i	0.991709	+	0.128508i	$0.0410187\pi$
$468$	−19.7560	−	5.25142i	−0.913220	−	0.242747i
$469$	2.10437	−	1.40609i	0.0971706	−	0.0649273i
$470$	−37.8939	+	5.54488i	−1.74791	+	0.255766i
$471$	−1.24580	−	0.832419i	−0.0574036	−	0.0383558i
$472$	−13.3372	+	20.0902i	−0.613892	+	0.924726i
$473$	−13.6668	+	20.4538i	−0.628400	+	0.940468i
$474$	40.4005	−	19.9734i	1.85565	−	0.917407i
$475$	−29.8734	+	18.3319i	−1.37069	+	0.841126i
$476$	0.995965	−	16.0289i	0.0456500	−	0.734685i
$477$	−4.75489	−	4.75489i	−0.217711	−	0.217711i
$478$	−11.0055	+	32.5276i	−0.503380	+	1.48778i
$479$	−3.32771	−	16.7295i	−0.152047	−	0.764391i	−0.979277	−	0.202527i	$-0.935084\pi$
$479$	−3.32771	−	16.7295i	−0.152047	−	0.764391i	0.827230	−	0.561864i	$-0.189916\pi$
$480$	−6.08575	+	33.8338i	−0.277775	+	1.54430i
$481$	−4.25797	+	6.37250i	−0.194147	+	0.290561i
$482$	−3.53931	−	0.462372i	−0.161211	−	0.0210605i
$483$	−28.1182	−	5.59306i	−1.27942	−	0.254493i
$484$	6.18909	+	10.6707i	0.281322	+	0.485030i
$485$	−16.3647	−	20.7453i	−0.743083	−	0.941997i
$486$	−3.52441	+	26.9782i	−0.159871	+	1.22376i
$487$	20.8642	+	31.2254i	0.945446	+	1.41496i	0.909545	+	0.415605i	$0.136430\pi$
$487$	20.8642	+	31.2254i	0.945446	+	1.41496i	0.0359007	+	0.999355i	$0.488570\pi$
$488$	15.5776	−	37.9278i	0.705163	−	1.71691i
$489$	25.9310	+	25.9310i	1.17264	+	1.17264i
$490$	2.48357	−	9.83287i	0.112196	−	0.444204i
$491$	5.44368	+	2.25485i	0.245670	+	0.101760i	0.502121	−	0.864797i	$-0.332553\pi$
$491$	5.44368	+	2.25485i	0.245670	+	0.101760i	−0.256451	+	0.966557i	$0.582553\pi$
$492$	41.2082	+	31.4899i	1.85781	+	1.41967i
$493$	2.61308	+	13.0413i	0.117687	+	0.587350i
$494$	−15.2150	+	17.3843i	−0.684554	+	0.782154i
$495$	−31.9045	+	25.1675i	−1.43400	+	1.13120i
$496$	11.6046	−	5.78037i	0.521063	−	0.259546i
$497$	−5.80332			−0.260314
$498$	23.5484	+	13.5644i	1.05523	+	0.607835i
$499$	−26.1558	−	5.20270i	−1.17089	−	0.232905i	−0.428925	−	0.903340i	$-0.641107\pi$
$499$	−26.1558	−	5.20270i	−1.17089	−	0.232905i	−0.741968	+	0.670435i	$0.766107\pi$
$500$	15.4394	+	16.1748i	0.690470	+	0.723361i
$501$	45.3121	−	18.7689i	2.02439	−	0.838531i
$502$	0.281474	+	0.569342i	0.0125628	+	0.0254110i
$503$	−34.3025	−	6.82320i	−1.52947	−	0.304231i	−0.642585	−	0.766214i	$-0.722138\pi$
$503$	−34.3025	−	6.82320i	−1.52947	−	0.304231i	−0.886889	+	0.461983i	$0.847138\pi$
$504$	−17.0328	+	17.1349i	−0.758701	+	0.763250i
$505$	7.86928	+	15.4325i	0.350179	+	0.686739i
$506$	2.10738	+	31.6690i	0.0936847	+	1.40786i
$507$	11.4290	−	17.1047i	0.507579	−	0.759646i
$508$	6.14376	+	10.5925i	0.272585	+	0.469967i
$509$		−	16.4098i		−	0.727354i	−0.931525	−	0.363677i	$-0.881521\pi$
$509$		−	16.4098i		−	0.727354i	0.931525	−	0.363677i	$-0.118479\pi$
$510$	−11.9188	−	33.3702i	−0.527772	−	1.47766i
$511$	−4.19188			−0.185438
$512$	22.1522	−	4.61320i	0.978997	−	0.203877i
$513$	−21.9552	−	14.6700i	−0.969344	−	0.647695i
$514$	−11.3408	+	0.754660i	−0.500219	+	0.0332866i
$515$	0.250996	−	0.773301i	0.0110602	−	0.0340757i
$516$	−2.04642	+	32.2056i	−0.0900888	+	1.41777i
$517$	−9.78955	+	49.2154i	−0.430544	+	2.16449i
$518$	4.01444	+	8.12007i	0.176384	+	0.356776i
$519$	8.78437	+	21.2073i	0.385591	+	0.930899i
$520$	12.8829	+	7.15908i	0.564954	+	0.313946i
$521$	−6.99311	+	35.1567i	−0.306374	+	1.54024i	0.454145	+	0.890928i	$0.349945\pi$
$521$	−6.99311	+	35.1567i	−0.306374	+	1.54024i	−0.760518	+	0.649317i	$0.775055\pi$
$522$	9.98733	−	17.3384i	0.437134	−	0.758883i
$523$		−	2.85903i		−	0.125017i	−0.998044	−	0.0625084i	$-0.980090\pi$
$523$		−	2.85903i		−	0.125017i	0.998044	−	0.0625084i	$-0.0199100\pi$
$524$	−2.08758	+	0.713281i	−0.0911965	+	0.0311598i
$525$	4.15612	+	26.1360i	0.181388	+	1.14067i
$526$	0.831639	−	0.950210i	0.0362612	−	0.0414311i
$527$	−7.40882	+	11.1218i	−0.322733	+	0.484473i
$528$	39.0974	+	22.3656i	1.70150	+	0.973340i
$529$	−2.42576	+	5.85630i	−0.105468	+	0.254622i
$530$	2.48431	+	4.16337i	0.107912	+	0.180845i
$531$	−26.4414	+	26.4414i	−1.14746	+	1.14746i
$532$	8.82818	+	25.8377i	0.382750	+	1.12021i
$533$	18.4879	−	12.3532i	0.800800	−	0.535078i
$534$	4.50748	−	34.5033i	0.195058	−	1.49310i
$535$	−15.7743	−	19.9968i	−0.681981	−	0.864539i
$536$	−3.60714	−	0.706304i	−0.155805	−	0.0305077i
$537$	10.5595	−	53.0864i	0.455678	−	2.29085i
$538$	3.83140	−	29.3281i	0.165183	−	1.26443i
$539$	−11.0488	−	7.38254i	−0.475904	−	0.317989i
$540$	−6.20630	+	15.6609i	−0.267076	+	0.673936i
$541$	−1.27592	+	0.253797i	−0.0548562	+	0.0109116i	−0.222442	−	0.974946i	$-0.571403\pi$
$541$	−1.27592	+	0.253797i	−0.0548562	+	0.0109116i	0.167586	+	0.985857i	$0.446403\pi$
$542$	−9.02304	+	26.6683i	−0.387573	+	1.14550i
$543$	14.3514	−	14.3514i	0.615878	−	0.615878i
$544$	−17.4372	+	15.4901i	−0.747616	+	0.664131i
$545$	−5.44834	+	9.73577i	−0.233381	+	0.417035i
$546$	7.73058	+	15.6368i	0.330838	+	0.669192i
$547$	16.6477	+	11.1236i	0.711805	+	0.475613i	0.858004	−	0.513643i	$-0.171704\pi$
$547$	16.6477	+	11.1236i	0.711805	+	0.475613i	−0.146200	+	0.989255i	$0.546704\pi$
$548$	−39.2274	+	5.24393i	−1.67571	+	0.224010i
$549$	35.3241	−	52.8663i	1.50760	−	2.25628i
$550$	26.7461	−	11.9599i	1.14046	−	0.509972i
$551$	−12.5631	−	18.8020i	−0.535206	−	0.800993i
$552$	23.2352	+	34.5500i	0.988957	+	1.47055i
$553$	−21.0985	−	8.73927i	−0.897198	−	0.371632i
$554$	−30.6605	−	4.00547i	−1.30264	−	0.170176i
$555$	15.2017	+	12.9753i	0.645275	+	0.550772i
$556$	30.9151	+	15.1691i	1.31109	+	0.643314i
$557$	−19.8267			−0.840086			−0.420043	−	0.907504i	$-0.637985\pi$
$557$	−19.8267			−0.840086			−0.420043	+	0.907504i	$0.637985\pi$
$558$	19.4138	−	5.22266i	0.821854	−	0.221093i
$559$	12.7823	+	5.29459i	0.540633	+	0.223937i
$560$	14.9319	−	8.97060i	0.630989	−	0.379077i
$561$	−46.4287	+	0.0650749i	−1.96022	+	0.00274747i
$562$	14.6065	−	0.971977i	0.616139	−	0.0410004i
$563$	−25.3200	+	10.4879i	−1.06711	+	0.442011i	−0.845970	−	0.533231i	$-0.820978\pi$
$563$	−25.3200	+	10.4879i	−1.06711	+	0.442011i	−0.221140	+	0.975242i	$0.570978\pi$
$564$	21.2836	+	62.2914i	0.896201	+	2.62294i
$565$	−19.4016	−	10.8576i	−0.816233	−	0.456781i
$566$	−0.00581446	−	0.0216137i	−0.000244400	−	0.000908492i
$567$	4.72982	−	3.16036i	0.198634	−	0.132723i
$568$	5.97742	+	5.94179i	0.250807	+	0.249312i
$569$	34.2005	−	14.1663i	1.43376	−	0.593883i	0.475483	−	0.879725i	$-0.342273\pi$
$569$	34.2005	−	14.1663i	1.43376	−	0.593883i	0.958277	+	0.285842i	$0.0922734\pi$
$570$	40.3701	+	44.7179i	1.69092	+	1.87303i
$571$	−19.5011	−	29.1855i	−0.816096	−	1.22137i	−0.972320	−	0.233653i	$-0.924932\pi$
$571$	−19.5011	−	29.1855i	−0.816096	−	1.22137i	0.156224	−	0.987722i	$-0.450068\pi$
$572$	14.4936	−	12.7617i	0.606006	−	0.533593i
$573$	13.5006	−	2.68544i	0.563997	−	0.112186i
$574$	−1.74490	−	26.2217i	−0.0728308	−	1.09447i
$575$	27.0624	+	1.04651i	1.12858	+	0.0436425i
$576$	35.0876	−	0.209746i	1.46198	−	0.00873940i
$577$	9.33306	+	9.33306i	0.388540	+	0.388540i	0.874167	−	0.485626i	$-0.161408\pi$
$577$	9.33306	+	9.33306i	0.388540	+	0.388540i	−0.485626	+	0.874167i	$0.661408\pi$
$578$	7.64137	−	22.7949i	0.317839	−	0.948145i
$579$	−19.3751			−0.805201
$580$	−10.0428	+	10.3568i	−0.417005	+	0.430044i
$581$	−2.68648	−	13.5058i	−0.111454	−	0.560316i
$582$	−29.9114	+	34.1760i	−1.23987	+	1.41664i
$583$	6.23040	−	1.23930i	0.258037	−	0.0513267i
$584$	4.31763	+	4.29190i	0.178665	+	0.177600i
$585$	17.3836	+	14.8377i	0.718722	+	0.613462i
$586$	9.88573	+	3.34477i	0.408376	+	0.138171i
$587$	−26.5199	−	10.9849i	−1.09459	−	0.453395i	−0.238987	−	0.971023i	$-0.576815\pi$
$587$	−26.5199	−	10.9849i	−1.09459	−	0.453395i	−0.855606	+	0.517628i	$0.826815\pi$
$588$	−17.3968	−	1.10544i	−0.717433	−	0.0455875i
$589$	4.43249	−	22.2836i	0.182638	−	0.918181i
$590$	23.1520	−	13.8150i	0.953153	−	0.568753i
$591$	23.3126	−	23.3126i	0.958952	−	0.958952i
$592$	4.17896	−	12.4739i	0.171754	−	0.512674i
$593$	2.89772	−	1.20027i	0.118995	−	0.0492893i	−0.322392	−	0.946606i	$-0.604487\pi$
$593$	2.89772	−	1.20027i	0.118995	−	0.0492893i	0.441387	+	0.897317i	$0.354487\pi$
$594$	16.6094	+	14.5368i	0.681491	+	0.596451i
$595$	−8.74660	+	15.6811i	−0.358576	+	0.642860i
$596$	37.7285	−	5.04355i	1.54542	−	0.206592i
$597$	8.52062	+	20.5706i	0.348726	+	0.841899i
$598$	17.2380	−	4.63731i	0.704913	−	0.189634i
$599$	−21.8568	+	21.8568i	−0.893044	+	0.893044i	−0.994809	−	0.101765i	$-0.967551\pi$
$599$	−21.8568	+	21.8568i	−0.893044	+	0.893044i	0.101765	+	0.994809i	$0.467551\pi$
$600$	22.4789	−	31.1754i	0.917696	−	1.27273i
$601$	−1.73066	−	0.344250i	−0.0705951	−	0.0140422i	0.159666	−	0.987171i	$-0.448958\pi$
$601$	−1.73066	−	0.344250i	−0.0705951	−	0.0140422i	−0.230261	+	0.973129i	$0.573958\pi$
$602$	12.9630	−	9.96742i	0.528334	−	0.406242i
$603$	−5.26592	−	2.18122i	−0.214445	−	0.0888260i
$604$	−9.22611	+	5.35124i	−0.375405	+	0.217739i
$605$	−1.08634	−	13.7488i	−0.0441658	−	0.558968i
$606$	23.6045	−	18.1497i	0.958866	−	0.737283i
$607$	−27.5866	+	5.48731i	−1.11970	+	0.222723i	−0.720036	−	0.693937i	$-0.755875\pi$
$607$	−27.5866	+	5.48731i	−1.11970	+	0.222723i	−0.399668	+	0.916660i	$0.630875\pi$
$608$	17.3612	−	35.6517i	0.704091	−	1.44587i
$609$	−16.7460	+	3.33098i	−0.678580	+	0.134978i
$610$	−34.0270	+	30.7186i	−1.37771	+	1.24376i
$611$	28.2223			1.14175
$612$	−31.2609	+	18.1903i	−1.26365	+	0.735297i
$613$	29.4717	−	29.4717i	1.19035	−	1.19035i	0.213379	−	0.976969i	$-0.431553\pi$
$613$	29.4717	−	29.4717i	1.19035	−	1.19035i	0.976969	−	0.213379i	$-0.0684471\pi$
$614$	17.1398	+	34.6689i	0.691706	+	1.39912i
$615$	−26.3402	−	51.6561i	−1.06214	−	2.08298i
$616$	−4.51960	−	22.3719i	−0.182100	−	0.901390i
$617$	6.64912	+	33.4274i	0.267684	+	1.34574i	0.847416	+	0.530929i	$0.178157\pi$
$617$	6.64912	+	33.4274i	0.267684	+	1.34574i	−0.579732	+	0.814807i	$0.696843\pi$
$618$	−1.38567	−	0.181022i	−0.0557397	−	0.00728179i
$619$	−2.57775	−	3.85787i	−0.103608	−	0.155061i	0.776043	−	0.630680i	$-0.217224\pi$
$619$	−2.57775	−	3.85787i	−0.103608	−	0.155061i	−0.879651	+	0.475619i	$0.842224\pi$
$620$	−14.4931	+	0.223095i	−0.582057	+	0.00895973i
$621$	7.80795	+	18.8501i	0.313322	+	0.756427i
$622$	0.244874	−	0.188286i	0.00981856	−	0.00754960i
$623$	−14.6605	+	9.79583i	−0.587360	+	0.392462i
$624$	8.04738	−	24.0209i	0.322153	−	0.961606i
$625$	−7.75485	−	23.7668i	−0.310194	−	0.950673i
$626$	−10.0975	+	17.5296i	−0.403576	+	0.700625i
$627$	72.9277	−	30.2076i	2.91245	−	1.20638i
$628$	0.669491	−	0.876106i	0.0267156	−	0.0349605i
$629$	2.66410	+	13.2959i	0.106225	+	0.530142i
$630$	25.4509	−	9.05006i	1.01399	−	0.360563i
$631$	9.14014	+	3.78597i	0.363863	+	0.150717i	0.557122	−	0.830431i	$-0.311906\pi$
$631$	9.14014	+	3.78597i	0.363863	+	0.150717i	−0.193259	+	0.981148i	$0.561906\pi$
$632$	12.7836	+	30.6034i	0.508505	+	1.21734i
$633$			1.31416i			0.0522333i
$634$	−32.3794	+	8.71062i	−1.28595	+	0.345943i
$635$	−1.07838	−	13.6481i	−0.0427942	−	0.541609i
$636$	6.25438	−	5.50703i	0.248002	−	0.218368i
$637$	−2.86004	+	6.90474i	−0.113319	+	0.273576i
$638$	8.37719	+	16.9447i	0.331656	+	0.670846i
$639$	7.26105	+	10.8669i	0.287243	+	0.429889i
$640$	−24.5645	−	6.04849i	−0.970998	−	0.239087i
$641$	−23.6918	−	15.8303i	−0.935769	−	0.625261i	−0.00862371	−	0.999963i	$-0.502745\pi$
$641$	−23.6918	−	15.8303i	−0.935769	−	0.625261i	−0.927145	+	0.374702i	$0.877745\pi$
$642$	−28.8322	+	32.9429i	−1.13791	+	1.30015i
$643$	−10.0414	−	6.70944i	−0.395994	−	0.264595i	0.341592	−	0.939848i	$-0.389034\pi$
$643$	−10.0414	−	6.70944i	−0.395994	−	0.264595i	−0.737585	+	0.675254i	$0.764034\pi$
$644$	5.41991	−	20.3898i	0.213574	−	0.803471i
$645$	17.6195	−	31.4847i	0.693766	−	1.23971i
$646$	2.77112	+	40.7806i	0.109028	+	1.60449i
$647$	10.0825	−	10.0825i	0.396385	−	0.396385i	−0.480571	−	0.876956i	$-0.659571\pi$
$647$	10.0825	−	10.0825i	0.396385	−	0.396385i	0.876956	+	0.480571i	$0.159571\pi$
$648$	−8.10749	−	1.58750i	−0.318492	−	0.0623630i
$649$	−6.89162	−	34.6465i	−0.270520	−	1.35999i
$650$	−9.53198	−	13.4413i	−0.373875	−	0.527212i
$651$	−14.2638	−	9.53080i	−0.559044	−	0.373541i
$652$	−20.2546	+	17.8343i	−0.793231	+	0.698446i
$653$	−15.8304	−	3.14887i	−0.619493	−	0.123225i	−0.124641	−	0.992202i	$-0.539778\pi$
$653$	−15.8304	−	3.14887i	−0.619493	−	0.123225i	−0.494852	+	0.868977i	$0.664778\pi$
$654$	18.1648	+	6.14596i	0.710302	+	0.240326i
$655$	2.44946	+	0.289144i	0.0957084	+	0.0112978i
$656$	−25.0502	+	28.7949i	−0.978045	+	1.12425i
$657$	5.24483	+	7.84945i	0.204620	+	0.306236i
$658$	16.6491	−	28.9036i	0.649050	−	1.12678i
$659$	27.3135	−	27.3135i	1.06398	−	1.06398i	0.0661730	−	0.997808i	$-0.478921\pi$
$659$	27.3135	−	27.3135i	1.06398	−	1.06398i	0.997808	−	0.0661730i	$-0.0210789\pi$
$660$	−28.6192	−	41.4365i	−1.11400	−	1.61291i
$661$	−10.1463	−	4.20275i	−0.394647	−	0.163468i	0.176530	−	0.984295i	$-0.443513\pi$
$661$	−10.1463	−	4.20275i	−0.394647	−	0.163468i	−0.571177	+	0.820827i	$0.693513\pi$
$662$	4.31396	−	0.287069i	0.167667	−	0.0111572i
$663$	5.13023	+	25.6038i	0.199242	+	0.994370i
$664$	−11.0610	+	16.6616i	−0.429251	+	0.646595i
$665$	3.57870	−	30.3166i	0.138776	−	1.17563i
$666$	10.1823	−	17.6769i	0.394557	−	0.684967i
$667$			17.4729i			0.676553i
$668$	11.6698	+	34.1544i	0.451518	+	1.32147i
$669$	21.9249	+	4.36113i	0.847664	+	0.168611i
$670$	3.29595	+	2.45451i	0.127334	+	0.0948259i
$671$	22.9858	+	55.4925i	0.887355	+	2.14227i
$672$	−19.8534	−	22.4123i	−0.765862	−	0.864572i
$673$	−0.574371	−	0.114249i	−0.0221404	−	0.00440399i	0.184008	−	0.982925i	$-0.441093\pi$
$673$	−0.574371	−	0.114249i	−0.0221404	−	0.00440399i	−0.206148	+	0.978521i	$0.566093\pi$
$674$	14.9785	+	19.4802i	0.576950	+	0.750347i
$675$	13.8224	−	12.7932i	0.532026	−	0.492410i
$676$	12.0288	+	9.19201i	0.462647	+	0.353539i
$677$	−25.7780	+	38.5795i	−0.990730	+	1.48273i	−0.118910	+	0.992905i	$0.537940\pi$
$677$	−25.7780	+	38.5795i	−0.990730	+	1.48273i	−0.871820	+	0.489827i	$0.837060\pi$
$678$	−12.2478	+	36.1993i	−0.470374	+	1.39022i
$679$	23.0135			0.883178
$680$	25.0642	−	7.19618i	0.961169	−	0.275961i
$681$	−41.3937			−1.58621
$682$	−6.08686	+	17.9902i	−0.233078	+	0.688879i
$683$	14.8557	−	22.2331i	0.568436	−	0.850725i	−0.430211	−	0.902728i	$-0.641561\pi$
$683$	14.8557	−	22.2331i	0.568436	−	0.850725i	0.998647	+	0.0520038i	$0.0165608\pi$
$684$	37.3364	−	48.8590i	1.42759	−	1.86817i
$685$	42.0863	+	13.6603i	1.60804	+	0.521933i
$686$	17.1362	+	22.2863i	0.654262	+	0.850894i
$687$	−1.78920	−	0.355893i	−0.0682621	−	0.0135782i
$688$	−23.5572	−	3.00591i	−0.898109	−	0.114599i
$689$	−1.36724	−	3.30082i	−0.0520879	−	0.125751i
$690$	−6.73984	−	46.0602i	−0.256581	−	1.75348i
$691$	−18.8010	−	3.73976i	−0.715225	−	0.142267i	−0.175953	−	0.984399i	$-0.556301\pi$
$691$	−18.8010	−	3.73976i	−0.715225	−	0.142267i	−0.539272	+	0.842132i	$0.681301\pi$
$692$	−15.9852	+	5.46180i	−0.607667	+	0.207626i
$693$		−	35.3928i		−	1.34446i
$694$	19.2223	−	33.3707i	0.729668	−	1.26673i
$695$	−23.8449	−	30.2279i	−0.904489	−	1.14661i
$696$	20.6588	+	13.7146i	0.783070	+	0.519852i
$697$	7.62093	−	38.5956i	0.288663	−	1.46191i
$698$	−21.5720	+	1.43549i	−0.816511	+	0.0543340i
$699$	52.6340	+	21.8017i	1.99080	+	0.824616i
$700$	−19.3890	+	1.83267i	−0.732835	+	0.0692685i
$701$	−2.76608	+	2.76608i	−0.104473	+	0.104473i	−0.757411	−	0.652938i	$-0.773536\pi$
$701$	−2.76608	+	2.76608i	−0.104473	+	0.104473i	0.652938	+	0.757411i	$0.273536\pi$
$702$	6.19631	−	10.7571i	0.233865	−	0.405999i
$703$	−12.8084	−	19.1691i	−0.483077	−	0.722976i
$704$	−18.2505	+	27.6705i	−0.687843	+	1.04287i
$705$	8.62777	−	73.0895i	0.324941	−	2.75271i
$706$	34.9902	+	11.8387i	1.31687	+	0.445556i
$707$	−14.7979	−	2.94349i	−0.556533	−	0.110701i
$708$	−30.6240	−	34.7799i	−1.15092	−	1.30711i
$709$	28.3646	+	18.9526i	1.06525	+	0.711780i	0.959242	−	0.282585i	$-0.0911920\pi$
$709$	28.3646	+	18.9526i	1.06525	+	0.711780i	0.106011	+	0.994365i	$0.466192\pi$
$710$	−3.15706	−	8.87840i	−0.118482	−	0.333200i
$711$	10.0336	+	50.4422i	0.376288	+	1.89173i
$712$	25.1299	+	4.92061i	0.941782	+	0.184408i
$713$	−12.4138	+	12.4138i	−0.464900	+	0.464900i
$714$	29.2484	+	9.85033i	1.09459	+	0.368640i
$715$	−20.7782	+	5.86700i	−0.777060	+	0.219413i
$716$	38.4954	+	10.2326i	1.43864	+	0.382412i
$717$	−54.8687	−	36.6621i	−2.04911	−	1.36917i
$718$	22.7532	−	25.9973i	0.849143	−	0.970211i
$719$	19.3582	+	12.9348i	0.721940	+	0.482385i	0.861454	−	0.507835i	$-0.169554\pi$
$719$	19.3582	+	12.9348i	0.721940	+	0.482385i	−0.139514	+	0.990220i	$0.544554\pi$
$720$	−35.4804	−	16.7366i	−1.32228	−	0.623738i
$721$	0.393404	+	0.588771i	0.0146511	+	0.0219270i
$722$	−18.8899	−	38.2089i	−0.703009	−	1.42199i
$723$	2.62496	−	6.33722i	0.0976234	−	0.235684i
$724$	9.87035	+	11.2098i	0.366829	+	0.416610i
$725$	15.1289	−	5.59197i	0.561871	−	0.207680i
$726$	−22.8918	+	6.15828i	−0.849593	+	0.228555i
$727$		−	3.91712i		−	0.145278i	−0.997358	−	0.0726391i	$-0.976858\pi$
$727$		−	3.91712i		−	0.145278i	0.997358	−	0.0726391i	$-0.0231421\pi$
$728$	−11.8449	+	4.94783i	−0.439000	+	0.183379i
$729$	−40.2096	−	16.6554i	−1.48925	−	0.616866i
$730$	−2.28042	−	6.41309i	−0.0844022	−	0.237359i
$731$	22.6026	−	9.39942i	0.835986	−	0.347650i
$732$	62.6075	+	47.8425i	2.31404	+	1.76831i
$733$	8.89200	−	3.68319i	0.328433	−	0.136042i	−0.212373	−	0.977189i	$-0.568119\pi$
$733$	8.89200	−	3.68319i	0.328433	−	0.136042i	0.540806	+	0.841147i	$0.318119\pi$
$734$	4.15781	−	7.21813i	0.153468	−	0.266426i
$735$	17.0074	+	9.51770i	0.627328	+	0.351066i
$736$	−26.4588	+	15.4523i	−0.975285	+	0.569578i
$737$	4.47705	−	2.99147i	0.164914	−	0.110192i
$738$	−46.9180	+	36.0758i	−1.72707	+	1.32797i
$739$	−12.5665	−	30.3383i	−0.462267	−	1.11601i	−0.967464	−	0.253008i	$-0.918580\pi$
$739$	−12.5665	−	30.3383i	−0.462267	−	1.11601i	0.505197	−	0.863004i	$-0.331420\pi$
$740$	−10.2389	+	10.5590i	−0.376388	+	0.388157i
$741$	−24.6650	−	36.9138i	−0.906091	−	1.35606i
$742$	−4.18708	−	0.546997i	−0.153713	−	0.0200809i
$743$	−3.27265	−	16.4527i	−0.120062	−	0.603591i	−0.993229	−	0.116171i	$-0.962938\pi$
$743$	−3.27265	−	16.4527i	−0.120062	−	0.603591i	0.873167	−	0.487420i	$-0.162062\pi$
$744$	4.93355	+	24.4209i	0.180873	+	0.895315i
$745$	−40.4782	−	13.1383i	−1.48301	−	0.481351i
$746$	−1.78248	−	3.60545i	−0.0652612	−	0.132005i
$747$	−21.9289	+	21.9289i	−0.802335	+	0.802335i
$748$	2.11892	−	34.1016i	0.0774754	−	1.24688i
$749$	22.1832			0.810557
$750$	−37.7241	+	20.5766i	−1.37749	+	0.751352i
$751$	43.8097	−	8.71429i	1.59864	−	0.317989i	0.686267	−	0.727350i	$-0.259248\pi$
$751$	43.8097	−	8.71429i	1.59864	−	0.317989i	0.912373	+	0.409361i	$0.134248\pi$
$752$	−46.7418	+	12.7243i	−1.70450	+	0.464007i
$753$	−1.19707	+	0.238112i	−0.0436237	+	0.00867729i
$754$	8.42782	−	6.48025i	0.306923	−	0.235997i
$755$	11.8876	−	0.939272i	0.432632	−	0.0341836i
$756$	−7.36137	−	12.6918i	−0.267730	−	0.461596i
$757$	14.2816	+	5.91563i	0.519073	+	0.215007i	0.626810	−	0.779172i	$-0.284360\pi$
$757$	14.2816	+	5.91563i	0.519073	+	0.215007i	−0.107737	+	0.994179i	$0.534360\pi$
$758$	18.9757	−	14.5906i	0.689228	−	0.529955i
$759$	−59.8216	−	11.8993i	−2.17139	−	0.431916i
$760$	−34.7261	+	27.5621i	−1.25965	+	0.999781i
$761$	−17.2556	+	17.2556i	−0.625516	+	0.625516i	−0.946936	−	0.321421i	$-0.895840\pi$
$761$	−17.2556	+	17.2556i	−0.625516	+	0.625516i	0.321421	+	0.946936i	$0.395840\pi$
$762$	−22.7241	+	6.11318i	−0.823208	+	0.221457i
$763$	−3.71855	−	8.97737i	−0.134620	−	0.325002i
$764$	1.34223	+	10.0406i	0.0485600	+	0.363255i
$765$	40.3070	−	3.24163i	1.45730	−	0.117202i
$766$	−15.1940	−	13.2981i	−0.548983	−	0.480478i
$767$	−18.3555	+	7.60309i	−0.662778	+	0.274532i
$768$	−2.49804	+	43.4118i	−0.0901403	+	1.56649i
$769$	8.71938	−	8.71938i	0.314429	−	0.314429i	−0.532194	−	0.846623i	$-0.678632\pi$
$769$	8.71938	−	8.71938i	0.314429	−	0.314429i	0.846623	+	0.532194i	$0.178632\pi$
$770$	−6.24901	+	24.7409i	−0.225199	+	0.891600i
$771$	4.26116	−	21.4223i	0.153462	−	0.771504i
$772$	0.904187	−	14.2296i	0.0325424	−	0.512135i
$773$	−4.50970	−	1.86798i	−0.162203	−	0.0671865i	0.300105	−	0.953906i	$-0.402978\pi$
$773$	−4.50970	−	1.86798i	−0.162203	−	0.0671865i	−0.462307	+	0.886720i	$0.652978\pi$
$774$	−34.8836	−	11.8026i	−1.25386	−	0.424237i
$775$	14.7213	+	6.77557i	0.528805	+	0.243386i
$776$	−23.7039	−	23.5627i	−0.850922	−	0.845850i
$777$	−17.0729	+	3.39601i	−0.612487	+	0.121831i
$778$	35.6442	−	40.7262i	1.27791	−	1.46011i
$779$	13.0488	+	65.6005i	0.467520	+	2.35038i
$780$	−19.7169	+	20.3334i	−0.705979	+	0.728053i
$781$	−12.3466			−0.441796
$782$	15.7261	−	27.3899i	0.562365	−	0.979462i
$783$	8.59221	+	8.59221i	0.307061	+	0.307061i
$784$	1.62373	−	12.7251i	0.0579904	−	0.454469i
$785$	−1.09823	+	0.560006i	−0.0391977	+	0.0199875i
$786$	−0.281489	−	4.23011i	−0.0100404	−	0.150883i
$787$	−17.6291	+	3.50665i	−0.628410	+	0.124999i	−0.499013	−	0.866594i	$-0.666304\pi$
$787$	−17.6291	+	3.50665i	−0.628410	+	0.124999i	−0.129397	+	0.991593i	$0.541304\pi$
$788$	16.0335	+	18.2094i	0.571170	+	0.648682i
$789$	1.34817	+	2.01768i	0.0479961	+	0.0718313i
$790$	1.89230	−	37.0325i	0.0673252	−	1.31756i
$791$	17.8903	−	7.41040i	0.636105	−	0.263483i
$792$	−36.2374	+	36.4546i	−1.28764	+	1.29536i
$793$	28.0886	−	18.7682i	0.997456	−	0.666479i
$794$	10.1820	+	37.8490i	0.361347	+	1.34321i
$795$	−8.96638	+	2.53178i	−0.318005	+	0.0897929i
$796$	−15.5053	+	5.29781i	−0.549570	+	0.187776i
$797$	−26.5638	+	11.0031i	−0.940937	+	0.389749i	−0.799817	−	0.600244i	$-0.795070\pi$
$797$	−26.5638	+	11.0031i	−0.940937	+	0.389749i	−0.141120	+	0.989993i	$0.545070\pi$
$798$	−52.3555	+	3.48395i	−1.85336	+	0.123330i
$799$	35.2589	−	35.3579i	1.24737	−	1.25087i
$800$	21.8471	+	17.9640i	0.772411	+	0.635123i
$801$	36.6861	+	15.1959i	1.29624	+	0.536920i
$802$	30.0101	−	8.07325i	1.05969	−	0.285076i
$803$	−8.91824			−0.314718
$804$	3.11150	−	6.34132i	0.109734	−	0.223641i
$805$	−15.3137	+	17.9413i	−0.539737	+	0.632347i
$806$	10.5916	+	1.38367i	0.373072	+	0.0487378i
$807$	52.5128	+	21.7515i	1.84854	+	0.765689i
$808$	12.2281	+	18.1828i	0.430184	+	0.639669i
$809$	10.5964	+	15.8586i	0.372550	+	0.557560i	0.969616	−	0.244632i	$-0.0786671\pi$
$809$	10.5964	+	15.8586i	0.372550	+	0.557560i	−0.597066	+	0.802192i	$0.703667\pi$
$810$	7.40806	+	5.51681i	0.260293	+	0.193841i
$811$	13.2716	−	19.8624i	0.466030	−	0.697464i	−0.521788	−	0.853075i	$-0.674735\pi$
$811$	13.2716	−	19.8624i	0.466030	−	0.697464i	0.987818	+	0.155612i	$0.0497348\pi$
$812$	−1.66487	−	12.4542i	−0.0584256	−	0.437055i
$813$	−44.9849	−	30.0580i	−1.57769	−	1.05418i
$814$	8.54074	+	17.2755i	0.299353	+	0.605506i
$815$	29.0373	−	8.19906i	1.01713	−	0.287201i
$816$	−20.0405	−	40.0921i	−0.701556	−	1.40351i
$817$	−29.4286	+	29.4286i	−1.02958	+	1.02958i
$818$	−5.02880	+	14.8630i	−0.175828	+	0.519672i
$819$	−19.5233	+	3.88344i	−0.682201	+	0.135698i
$820$	39.1670	−	16.9344i	1.36777	−	0.591374i
$821$	−13.3245	−	8.90313i	−0.465027	−	0.310721i	0.300892	−	0.953658i	$-0.402716\pi$
$821$	−13.3245	−	8.90313i	−0.465027	−	0.310721i	−0.765919	+	0.642937i	$0.777716\pi$
$822$	9.85201	−	75.4140i	0.343628	−	2.63036i
$823$	−6.16487	+	30.9929i	−0.214894	+	1.08034i	0.711182	+	0.703008i	$0.248160\pi$
$823$	−6.16487	+	30.9929i	−0.214894	+	1.08034i	−0.926076	+	0.377337i	$0.876840\pi$
$824$	0.197614	−	1.00923i	0.00688420	−	0.0351581i
$825$	8.84217	+	55.6045i	0.307845	+	1.93590i
$826$	−3.04178	+	23.2839i	−0.105837	+	0.810150i
$827$	20.6870	−	13.8226i	0.719356	−	0.480658i	−0.141221	−	0.989978i	$-0.545103\pi$
$827$	20.6870	−	13.8226i	0.719356	−	0.480658i	0.860577	+	0.509320i	$0.170103\pi$
$828$	−44.9620	+	15.3625i	−1.56254	+	0.533884i
$829$	−16.2859	+	16.2859i	−0.565634	+	0.565634i	−0.930902	−	0.365268i	$-0.880977\pi$
$829$	−16.2859	+	16.2859i	−0.565634	+	0.565634i	0.365268	+	0.930902i	$0.380977\pi$
$830$	19.2009	−	11.4573i	0.666472	−	0.397688i
$831$	22.7397	−	54.8985i	0.788831	−	1.90441i
$832$	17.2661	+	7.03123i	0.598594	+	0.243764i
$833$	5.07739	+	12.2095i	0.175921	+	0.423033i
$834$	−43.5836	+	49.7976i	−1.50918	+	1.72435i
$835$	4.73061	−	40.0750i	0.163710	−	1.38685i
$836$	18.7820	+	54.9699i	0.649589	+	1.90117i
$837$			12.2088i			0.421999i
$838$	16.7688	−	29.1114i	0.579270	−	1.00564i
$839$	1.22719	−	6.16949i	0.0423672	−	0.212994i	−0.953803	−	0.300434i	$-0.902868\pi$
$839$	1.22719	−	6.16949i	0.0423672	−	0.212994i	0.996170	+	0.0874396i	$0.0278685\pi$
$840$	9.19272	+	32.1882i	0.317179	+	1.11060i
$841$	−7.11558	−	17.1785i	−0.245365	−	0.592363i
$842$	−11.7959	−	23.8598i	−0.406514	−	0.822263i
$843$	−5.48823	+	27.5912i	−0.189025	+	0.950291i
$844$	−0.965160	−	0.0613287i	−0.0332222	−	0.00211102i
$845$	−7.68881	−	15.0786i	−0.264503	−	0.518720i
$846$	−74.9542	+	4.98776i	−2.57698	+	0.171483i
$847$	9.98768	+	6.67356i	0.343181	+	0.229306i
$848$	3.75265	+	4.85040i	0.128866	+	0.166563i
$849$	0.0430122			0.00147618
$850$	−28.7484	−	4.85064i	−0.986062	−	0.166376i
$851$			17.8140i			0.610657i
$852$	−14.0105	+	8.12625i	−0.479993	+	0.278401i
$853$	−16.2009	+	24.2464i	−0.554709	+	0.830180i	−0.997800	−	0.0662964i	$-0.978882\pi$
$853$	−16.2009	+	24.2464i	−0.554709	+	0.830180i	0.443091	+	0.896476i	$0.353882\pi$
$854$	−2.65102	−	39.8386i	−0.0907162	−	1.36325i
$855$	−61.2467	+	31.2306i	−2.09459	+	1.06806i
$856$	−22.8487	−	22.7125i	−0.780952	−	0.776298i
$857$	−6.55466	−	1.30380i	−0.223903	−	0.0445371i	0.0818637	−	0.996644i	$-0.473913\pi$
$857$	−6.55466	−	1.30380i	−0.223903	−	0.0445371i	−0.305767	+	0.952106i	$0.598913\pi$
$858$	16.4468	+	33.2673i	0.561486	+	1.13573i
$859$	−15.9873	+	6.62215i	−0.545479	+	0.225945i	−0.638368	−	0.769732i	$-0.720390\pi$
$859$	−15.9873	+	6.62215i	−0.545479	+	0.225945i	0.0928884	+	0.995677i	$0.470390\pi$
$860$	22.3010	+	14.4096i	0.760458	+	0.491362i
$861$	49.5319	+	9.85251i	1.68804	+	0.335773i
$862$	29.0956	+	16.7597i	0.991000	+	0.570839i
$863$	−40.4473			−1.37684			−0.688421	−	0.725312i	$-0.741696\pi$
$863$	−40.4473			−1.37684			−0.688421	+	0.725312i	$0.741696\pi$
$864$	−5.41243	+	20.6096i	−0.184135	+	0.701152i
$865$	18.7562	+	2.21406i	0.637731	+	0.0752803i
$866$	11.7615	−	13.4384i	0.399673	−	0.456657i
$867$	38.4868	+	25.5603i	1.30708	+	0.868073i
$868$	7.66535	−	10.0310i	0.260179	−	0.340474i
$869$	−44.8871	−	18.5928i	−1.52269	−	0.630719i
$870$	−14.2060	−	23.8073i	−0.481627	−	0.807143i
$871$	−2.14139	−	2.14139i	−0.0725582	−	0.0725582i
$872$	−5.36147	+	13.0540i	−0.181562	+	0.442063i
$873$	−28.7943	−	43.0937i	−0.974539	−	1.45850i
$874$	−6.95583	+	53.2446i	−0.235284	+	1.80103i
$875$	20.4353	+	7.51745i	0.690841	+	0.254136i
$876$	−10.1202	+	5.86979i	−0.341928	+	0.198322i
$877$	29.4222	+	5.85244i	0.993517	+	0.197623i	0.664974	−	0.746866i	$-0.268443\pi$
$877$	29.4222	+	5.85244i	0.993517	+	0.197623i	0.328542	+	0.944489i	$0.393443\pi$
$878$	−22.5438	−	2.94510i	−0.760815	−	0.0993922i
$879$	−11.1423	+	16.6756i	−0.375819	+	0.562453i
$880$	31.7677	−	19.0850i	1.07089	−	0.643355i
$881$	7.85664	+	39.4980i	0.264697	+	1.33072i	0.852928	+	0.522028i	$0.174824\pi$
$881$	7.85664	+	39.4980i	0.264697	+	1.33072i	−0.588231	+	0.808693i	$0.700176\pi$
$882$	6.37556	−	18.8434i	0.214676	−	0.634492i
$883$	7.85896	+	7.85896i	0.264475	+	0.264475i	0.826869	−	0.562394i	$-0.190120\pi$
$883$	7.85896	+	7.85896i	0.264475	+	0.264475i	−0.562394	+	0.826869i	$0.690120\pi$
$884$	−19.0436	+	2.57292i	−0.640505	+	0.0865368i
$885$	14.0789	+	49.8610i	0.473258	+	1.67606i
$886$	27.6570	−	13.6732i	0.929156	−	0.459360i
$887$	11.4762	−	17.1753i	0.385332	−	0.576690i	−0.587205	−	0.809438i	$-0.699772\pi$
$887$	11.4762	−	17.1753i	0.385332	−	0.576690i	0.972537	+	0.232748i	$0.0747718\pi$
$888$	21.0621	+	13.9824i	0.706798	+	0.469218i
$889$	9.91453	+	6.62468i	0.332523	+	0.222185i
$890$	−22.9619	−	17.0998i	−0.769685	−	0.573187i
$891$	10.0627	−	6.72369i	0.337114	−	0.225252i
$892$	−4.22612	+	15.8987i	−0.141501	+	0.532329i
$893$	−32.4880	+	78.4330i	−1.08717	+	2.62466i
$894$	−9.47556	+	72.5323i	−0.316910	+	2.42584i
$895$	−33.8727	−	28.9119i	−1.13224	−	0.966418i
$896$	17.3867	−	13.5350i	0.580850	−	0.452172i
$897$			34.3043i			1.14539i
$898$	−15.0648	+	4.05269i	−0.502718	+	0.135240i
$899$	−4.00112	+	9.65956i	−0.133445	+	0.322164i
$900$	27.6911	+	34.0136i	0.923036	+	1.13379i
$901$	−5.84354	−	2.41088i	−0.194676	−	0.0803181i
$902$	−3.71229	−	55.7869i	−0.123606	−	1.85750i
$903$	12.0255	+	29.0321i	0.400183	+	0.966127i
$904$	−26.0142	−	10.6845i	−0.865220	−	0.355360i
$905$	−4.53775	−	16.0706i	−0.150840	−	0.534205i
$906$	−5.32460	−	19.7928i	−0.176898	−	0.657571i
$907$	−26.4760	−	39.6241i	−0.879121	−	1.31570i	−0.948065	−	0.318077i	$-0.896963\pi$
$907$	−26.4760	−	39.6241i	−0.879121	−	1.31570i	0.0689439	−	0.997621i	$-0.478037\pi$
$908$	1.93174	−	30.4007i	0.0641071	−	1.00888i
$909$	13.0032	+	31.3925i	0.431289	+	1.04122i
$910$	14.3332	+	0.732406i	0.475141	+	0.0242790i
$911$	12.7486	−	8.51834i	0.422380	−	0.282225i	−0.326161	−	0.945314i	$-0.605755\pi$
$911$	12.7486	−	8.51834i	0.422380	−	0.282225i	0.748540	+	0.663089i	$0.230755\pi$
$912$	57.4932	+	50.0163i	1.90379	+	1.65620i
$913$	−5.71549	−	28.7337i	−0.189155	−	0.950947i
$914$	0.824238	+	12.3863i	0.0272634	+	0.409704i
$915$	−40.0187	−	78.4810i	−1.32298	−	2.59450i
$916$	0.344875	−	1.29743i	0.0113950	−	0.0428682i
$917$	−1.51902	+	1.51902i	−0.0501624	+	0.0501624i
$918$	−5.73561	−	21.2021i	−0.189303	−	0.699774i
$919$		−	35.0456i		−	1.15605i	−0.816020	−	0.578023i	$-0.803824\pi$
$919$		−	35.0456i		−	1.15605i	0.816020	−	0.578023i	$-0.196176\pi$
$920$	34.1425	−	2.80041i	1.12564	−	0.0923269i
$921$	−72.8933	+	14.4994i	−2.40192	+	0.477771i
$922$	−22.3506	+	25.5373i	−0.736079	+	0.841026i
$923$	1.35471	+	6.81061i	0.0445910	+	0.224174i
$924$	43.7729	+	2.78144i	1.44002	+	0.0915027i
$925$	15.4242	−	5.70114i	0.507145	−	0.187452i
$926$	16.1227	−	47.6518i	0.529824	−	1.56594i
$927$	0.610273	−	1.47333i	0.0200440	−	0.0483905i
$928$	−11.0365	+	14.5324i	−0.362291	+	0.477049i
$929$	−46.3250	−	9.21461i	−1.51987	−	0.302322i	−0.636605	−	0.771190i	$-0.719662\pi$
$929$	−46.3250	−	9.21461i	−1.51987	−	0.302322i	−0.883268	+	0.468869i	$0.844662\pi$
$930$	6.82135	−	27.0069i	0.223681	−	0.885590i
$931$	−15.8968	−	15.8968i	−0.520995	−	0.520995i
$932$	−18.4681	+	37.6385i	−0.604942	+	1.23289i
$933$	0.227164	+	0.548421i	0.00743700	+	0.0179545i
$934$	−10.4980	+	11.9947i	−0.343504	+	0.392479i
$935$	−18.6084	+	33.3615i	−0.608561	+	1.09104i
$936$	24.0851	+	15.9893i	0.787248	+	0.522625i
$937$	32.5577	−	13.4858i	1.06361	−	0.440563i	0.218881	−	0.975752i	$-0.429760\pi$
$937$	32.5577	−	13.4858i	1.06361	−	0.440563i	0.844733	+	0.535189i	$0.179760\pi$
$938$	−3.45635	+	0.929818i	−0.112854	+	0.0303596i
$939$	−27.4896	−	27.4896i	−0.897089	−	0.897089i
$940$	53.2764	+	9.74739i	1.73768	+	0.317925i
$941$	−9.20654	+	46.2844i	−0.300125	+	1.50883i	0.476674	+	0.879080i	$0.341842\pi$
$941$	−9.20654	+	46.2844i	−0.300125	+	1.50883i	−0.776799	+	0.629749i	$0.783158\pi$
$942$	1.29160	+	1.67978i	0.0420826	+	0.0547302i
$943$	19.7779	−	47.7480i	0.644057	−	1.55489i
$944$	26.9725	−	20.8680i	0.877880	−	0.679197i
$945$	1.29210	+	16.3530i	0.0420320	+	0.531962i
$946$	27.5789	−	21.2057i	0.896668	−	0.689458i
$947$	−0.943761	−	4.74461i	−0.0306681	−	0.154179i	0.962417	−	0.271576i	$-0.0875449\pi$
$947$	−0.943761	−	4.74461i	−0.0306681	−	0.154179i	−0.993085	+	0.117397i	$0.962545\pi$
$948$	−63.1739	+	8.44510i	−2.05179	+	0.274284i
$949$	0.978543	+	4.91947i	0.0317648	+	0.159693i
$950$	48.3278	−	11.0175i	1.56796	−	0.357456i
$951$		−	64.4364i		−	2.08949i
$952$	−8.59932	+	21.0212i	−0.278705	+	0.681300i
$953$	23.3999	+	23.3999i	0.757997	+	0.757997i	0.975958	−	0.217961i	$-0.0699405\pi$
$953$	23.3999	+	23.3999i	0.757997	+	0.757997i	−0.217961	+	0.975958i	$0.569941\pi$
$954$	4.21456	+	8.52486i	0.136451	+	0.276003i
$955$	3.49646	−	10.7723i	0.113143	−	0.348585i
$956$	29.4863	−	38.5862i	0.953654	−	1.24797i
$957$	−35.6271	+	7.08667i	−1.15166	+	0.229080i
$958$	−3.12481	+	23.9194i	−0.100958	+	0.772800i
$959$	−32.0435	+	21.4108i	−1.03474	+	0.691389i
$960$	23.4877	−	42.5659i	0.758063	−	1.37381i
$961$	18.9349	−	7.84310i	0.610804	−	0.253003i
$962$	8.59236	−	6.60676i	0.277029	−	0.213011i
$963$	−27.7554	−	41.5389i	−0.894405	−	1.33857i
$964$	4.53174	+	2.22359i	0.145957	+	0.0716170i
$965$	−7.78494	+	13.9111i	−0.250606	+	0.447814i
$966$	35.1325	+	20.2371i	1.13037	+	0.651118i
$967$	22.0051	+	53.1251i	0.707637	+	1.70839i	0.705823	+	0.708388i	$0.250577\pi$
$967$	22.0051	+	53.1251i	0.707637	+	1.70839i	0.00181418	+	0.999998i	$0.499423\pi$
$968$	−3.45452	−	17.0998i	−0.111032	−	0.549607i
$969$	−77.0617	−	15.2163i	−2.47558	−	0.488817i
$970$	12.5196	+	35.2080i	0.401979	+	1.13046i
$971$	−6.96830	+	16.8230i	−0.223624	+	0.539875i	−0.995377	−	0.0960472i	$-0.969380\pi$
$971$	−6.96830	+	16.8230i	−0.223624	+	0.539875i	0.771753	+	0.635922i	$0.219380\pi$
$972$	16.9492	−	34.5430i	0.543647	−	1.10797i
$973$	33.5329			1.07501
$974$	−13.7970	−	51.2867i	−0.442085	−	1.64333i
$975$	29.7023	−	10.9786i	0.951235	−	0.351598i
$976$	−38.0587	+	43.7481i	−1.21823	+	1.40034i
$977$	−0.297898	−	0.123393i	−0.00953059	−	0.00394770i	0.377913	−	0.925841i	$-0.376642\pi$
$977$	−0.297898	−	0.123393i	−0.00953059	−	0.00394770i	−0.387444	+	0.921893i	$0.626642\pi$
$978$	−22.9843	−	46.4907i	−0.734956	−	1.48661i
$979$	−31.1903	+	20.8407i	−0.996845	+	0.666071i
$980$	−7.78377	+	12.0466i	−0.248643	+	0.384814i
$981$	−12.1578	+	18.1955i	−0.388170	+	0.580938i
$982$	−6.27042	−	5.48797i	−0.200097	−	0.175128i
$983$	−21.7237	+	32.5118i	−0.692878	+	1.03696i	0.303575	+	0.952808i	$0.401820\pi$
$983$	−21.7237	+	32.5118i	−0.692878	+	1.03696i	−0.996453	+	0.0841570i	$0.973180\pi$
$984$	−40.9303	−	60.8619i	−1.30481	−	1.94021i
$985$	−7.37116	−	26.1052i	−0.234865	−	0.831782i
$986$	2.41044	−	18.6547i	0.0767641	−	0.594086i
$987$	45.3259	+	45.3259i	1.44274	+	1.44274i
$988$	28.2616	−	16.3920i	0.899121	−	0.521499i
$989$	31.5403	−	6.27375i	1.00292	−	0.199494i
$990$	54.1469	−	19.2540i	1.72090	−	0.611934i
$991$	29.6409	−	44.3608i	0.941575	−	1.40917i	0.0293089	−	0.999570i	$-0.490669\pi$
$991$	29.6409	−	44.3608i	0.941575	−	1.40917i	0.912267	−	0.409597i	$-0.134331\pi$
$992$	−18.1657	+	2.48368i	−0.576760	+	0.0788568i
$993$	−1.62092	+	8.14892i	−0.0514384	+	0.258598i
$994$	7.77420	+	2.63035i	0.246583	+	0.0834297i
$995$	18.1931	+	2.14758i	0.576759	+	0.0680830i
$996$	−25.3977	−	28.8443i	−0.804756	−	0.913968i
$997$	−19.1030	+	12.7642i	−0.604997	+	0.404246i	−0.819997	−	0.572368i	$-0.806025\pi$
$997$	−19.1030	+	12.7642i	−0.604997	+	0.404246i	0.215000	+	0.976614i	$0.431025\pi$
$998$	32.6805	+	18.8247i	1.03448	+	0.595885i
$999$	8.75996	+	8.75996i	0.277153	+	0.277153i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.cf.a.533.13	yes	832
5.2	odd	4		680.2.ct.a.397.65	yes	832
8.5	even	2	inner	680.2.cf.a.533.40	yes	832
17.3	odd	16		680.2.ct.a.173.15	yes	832
40.37	odd	4		680.2.ct.a.397.15	yes	832
85.37	even	16	inner	680.2.cf.a.37.40	yes	832
136.37	odd	16		680.2.ct.a.173.65	yes	832
680.37	even	16	inner	680.2.cf.a.37.13	✓	832

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.cf.a.37.13	✓	832	680.37	even	16	inner
680.2.cf.a.37.40	yes	832	85.37	even	16	inner
680.2.cf.a.533.13	yes	832	1.1	even	1	trivial
680.2.cf.a.533.40	yes	832	8.5	even	2	inner
680.2.ct.a.173.15	yes	832	17.3	odd	16
680.2.ct.a.173.65	yes	832	136.37	odd	16
680.2.ct.a.397.15	yes	832	40.37	odd	4
680.2.ct.a.397.65	yes	832	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.cf (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33961 - 0.453250i) q^{2} +(1.50989 - 2.25971i) q^{3} +(1.58913 + 1.21436i) q^{4} +(-1.01577 - 1.99204i) q^{5} +(-3.04688 + 2.34278i) q^{6} +(1.91012 + 0.379947i) q^{7} +(-1.57841 - 2.34704i) q^{8} +(-1.67846 - 4.05216i) q^{9} +(0.457849 + 3.12896i) q^{10} +(4.06379 + 0.808338i) q^{11} +(5.14350 - 1.75742i) q^{12} -2.33036i q^{13} +(-2.38661 - 1.37474i) q^{14} +(-6.03511 - 0.712409i) q^{15} +(1.05067 + 3.85955i) q^{16} +(-2.91956 - 2.91139i) q^{17} +(0.411847 + 6.18909i) q^{18} +(6.47634 + 2.68259i) q^{19} +(0.804857 - 4.39911i) q^{20} +(3.74263 - 3.74263i) q^{21} +(-5.07753 - 2.92477i) q^{22} +(-3.00926 - 4.50368i) q^{23} +(-7.68685 + 0.0229749i) q^{24} +(-2.93642 + 4.04690i) q^{25} +(-1.05623 + 3.12178i) q^{26} +(-3.69445 - 0.734872i) q^{27} +(2.57404 + 2.92336i) q^{28} +(-2.68219 - 1.79218i) q^{29} +(7.76182 + 3.68977i) q^{30} +(-0.632315 - 3.17886i) q^{31} +(0.341853 - 5.64652i) q^{32} +(7.96247 - 7.96247i) q^{33} +(2.59150 + 5.22342i) q^{34} +(-1.18338 - 4.19097i) q^{35} +(2.25349 - 8.47766i) q^{36} +(-2.73456 - 1.82717i) q^{37} +(-7.45991 - 6.52903i) q^{38} +(-5.26592 - 3.51857i) q^{39} +(-3.07209 + 5.52831i) q^{40} +(5.30100 + 7.93351i) q^{41} +(-6.71003 + 3.31734i) q^{42} +(-2.27201 + 5.48512i) q^{43} +(5.47628 + 6.21946i) q^{44} +(-6.36712 + 7.45961i) q^{45} +(1.98996 + 7.39714i) q^{46} +12.1107i q^{47} +(10.3078 + 3.45328i) q^{48} +(-2.96295 - 1.22730i) q^{49} +(5.76793 - 4.09035i) q^{50} +(-10.9871 + 2.20148i) q^{51} +(2.82989 - 3.70324i) q^{52} +(1.41644 - 0.586711i) q^{53} +(4.61606 + 2.65895i) q^{54} +(-2.51764 - 8.91631i) q^{55} +(-2.12321 - 5.08285i) q^{56} +(15.8404 - 10.5842i) q^{57} +(2.78080 + 3.61654i) q^{58} +(-3.26263 - 7.87669i) q^{59} +(-8.72546 - 8.46090i) q^{60} +(8.05380 + 12.0534i) q^{61} +(-0.593761 + 4.54505i) q^{62} +(-1.66646 - 8.37784i) q^{63} +(-3.01723 + 7.40920i) q^{64} +(-4.64216 + 2.36711i) q^{65} +(-14.2756 + 7.05765i) q^{66} +(0.918910 - 0.918910i) q^{67} +(-1.10409 - 8.17196i) q^{68} -14.7206 q^{69} +(-0.314289 + 6.15065i) q^{70} +(-2.92256 + 0.581333i) q^{71} +(-6.86129 + 10.3354i) q^{72} +(-2.11104 + 0.419911i) q^{73} +(2.83509 + 3.68714i) q^{74} +(4.71114 + 12.7458i) q^{75} +(7.03412 + 12.1276i) q^{76} +(7.45521 + 3.08805i) q^{77} +(5.45950 + 7.10031i) q^{78} +(-11.5007 - 2.28762i) q^{79} +(6.62113 - 6.01338i) q^{80} +(2.06536 - 2.06536i) q^{81} +(-3.50543 - 13.0305i) q^{82} +(-2.70583 - 6.53244i) q^{83} +(10.4924 - 1.40263i) q^{84} +(-2.83399 + 8.77317i) q^{85} +(5.52974 - 6.31815i) q^{86} +(-8.09962 + 3.35497i) q^{87} +(-4.51713 - 10.8138i) q^{88} +(-6.40177 + 6.40177i) q^{89} +(11.9105 - 7.10710i) q^{90} +(0.885411 - 4.45126i) q^{91} +(0.686975 - 10.8113i) q^{92} +(-8.13802 - 3.37088i) q^{93} +(5.48917 - 16.2237i) q^{94} +(-1.23466 - 15.6260i) q^{95} +(-12.2433 - 9.29808i) q^{96} +(11.5896 - 2.30532i) q^{97} +(3.41294 + 2.98706i) q^{98} +(-3.54539 - 17.8239i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 832 q - 8 q^{2} - 16 q^{6} - 16 q^{7} - 8 q^{8} - 8 q^{10} - 32 q^{12} - 32 q^{14} - 16 q^{15} - 16 q^{17} - 16 q^{18} - 8 q^{20} - 8 q^{22} - 16 q^{23} - 16 q^{25} - 48 q^{26} - 40 q^{28} - 72 q^{30} - 32 q^{31}+ \cdots - 16 q^{98}+O(q^{100}) \) 832 * q - 8 * q^2 - 16 * q^6 - 16 * q^7 - 8 * q^8 - 8 * q^10 - 32 * q^12 - 32 * q^14 - 16 * q^15 - 16 * q^17 - 16 * q^18 - 8 * q^20 - 8 * q^22 - 16 * q^23 - 16 * q^25 - 48 * q^26 - 40 * q^28 - 72 * q^30 - 32 * q^31 - 8 * q^32 + 48 * q^36 + 96 * q^39 + 48 * q^40 - 32 * q^41 + 8 * q^42 - 32 * q^46 + 72 * q^48 - 16 * q^52 - 64 * q^54 - 16 * q^55 - 16 * q^56 - 16 * q^57 - 64 * q^58 - 8 * q^60 - 8 * q^62 - 64 * q^63 + 64 * q^65 - 16 * q^66 - 128 * q^68 - 72 * q^70 - 32 * q^71 - 16 * q^72 - 96 * q^73 - 16 * q^76 - 64 * q^78 - 136 * q^80 - 32 * q^81 - 8 * q^82 - 96 * q^84 - 32 * q^86 - 16 * q^87 + 80 * q^88 + 136 * q^90 + 104 * q^92 + 48 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more