LMFDB - Embedded newform 1295.2.j.a.926.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1295,2,Mod(186,1295)] 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("1295.186"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1295, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1295 = 5 \cdot 7 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1295.j (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [38] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$10.3406270618$
Analytic rank:	$0$
Dimension:	$38$
Relative dimension:	$19$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			926.10
Character	$\chi$	$=$	1295.926
Dual form			1295.2.j.a.186.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.189789 - 0.328725i) q^{2} +(-0.313780 - 0.543483i) q^{3} +(0.927960 + 1.60727i) q^{4} +(-0.500000 + 0.866025i) q^{5} -0.238209 q^{6} +(-2.24021 - 1.40764i) q^{7} +1.46363 q^{8} +(1.30308 - 2.25701i) q^{9} +(0.189789 + 0.328725i) q^{10} +(-0.195253 - 0.338188i) q^{11} +(0.582351 - 1.00866i) q^{12} -5.61090 q^{13} +(-0.887895 + 0.469260i) q^{14} +0.627560 q^{15} +(-1.57814 + 2.73342i) q^{16} +(-1.36583 - 2.36568i) q^{17} +(-0.494623 - 0.856713i) q^{18} +(-3.29786 + 5.71206i) q^{19} -1.85592 q^{20} +(-0.0620924 + 1.65921i) q^{21} -0.148228 q^{22} +(0.941721 - 1.63111i) q^{23} +(-0.459257 - 0.795456i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.06489 + 1.84444i) q^{26} -3.51821 q^{27} +(0.183629 - 4.90687i) q^{28} +1.03928 q^{29} +(0.119104 - 0.206295i) q^{30} +(-1.06268 - 1.84061i) q^{31} +(2.06265 + 3.57262i) q^{32} +(-0.122533 + 0.212234i) q^{33} -1.03688 q^{34} +(2.33916 - 1.23626i) q^{35} +4.83684 q^{36} +(-0.500000 + 0.866025i) q^{37} +(1.25180 + 2.16818i) q^{38} +(1.76059 + 3.04943i) q^{39} +(-0.731813 + 1.26754i) q^{40} -9.05677 q^{41} +(0.533638 + 0.335311i) q^{42} -5.44088 q^{43} +(0.362374 - 0.627650i) q^{44} +(1.30308 + 2.25701i) q^{45} +(-0.357457 - 0.619135i) q^{46} +(-0.0948253 + 0.164242i) q^{47} +1.98075 q^{48} +(3.03712 + 6.30682i) q^{49} -0.379579 q^{50} +(-0.857140 + 1.48461i) q^{51} +(-5.20669 - 9.01824i) q^{52} +(-3.49439 - 6.05246i) q^{53} +(-0.667719 + 1.15652i) q^{54} +0.390506 q^{55} +(-3.27884 - 2.06025i) q^{56} +4.13921 q^{57} +(0.197244 - 0.341637i) q^{58} +(-3.28538 - 5.69044i) q^{59} +(0.582351 + 1.00866i) q^{60} +(2.21331 - 3.83357i) q^{61} -0.806738 q^{62} +(-6.09623 + 3.22191i) q^{63} -4.74668 q^{64} +(2.80545 - 4.85918i) q^{65} +(0.0465110 + 0.0805594i) q^{66} +(-5.06590 - 8.77439i) q^{67} +(2.53487 - 4.39052i) q^{68} -1.18197 q^{69} +(0.0375565 - 1.00357i) q^{70} -7.15892 q^{71} +(1.90723 - 3.30342i) q^{72} +(-0.00378823 - 0.00656140i) q^{73} +(0.189789 + 0.328725i) q^{74} +(-0.313780 + 0.543483i) q^{75} -12.2411 q^{76} +(-0.0386377 + 1.03246i) q^{77} +1.33656 q^{78} +(0.674724 - 1.16866i) q^{79} +(-1.57814 - 2.73342i) q^{80} +(-2.80531 - 4.85894i) q^{81} +(-1.71888 + 2.97719i) q^{82} +11.5548 q^{83} +(-2.72442 + 1.43988i) q^{84} +2.73166 q^{85} +(-1.03262 + 1.78855i) q^{86} +(-0.326105 - 0.564831i) q^{87} +(-0.285778 - 0.494981i) q^{88} +(-2.78198 + 4.81854i) q^{89} +0.989247 q^{90} +(12.5696 + 7.89810i) q^{91} +3.49552 q^{92} +(-0.666893 + 1.15509i) q^{93} +(0.0359937 + 0.0623429i) q^{94} +(-3.29786 - 5.71206i) q^{95} +(1.29444 - 2.24204i) q^{96} -15.2161 q^{97} +(2.64962 + 0.198591i) q^{98} -1.01772 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q + 3 q^{2} + q^{3} - 11 q^{4} - 19 q^{5} - 8 q^{6} - 18 q^{8} - 12 q^{9} + 3 q^{10} + 13 q^{11} + 4 q^{12} - 6 q^{13} - q^{14} - 2 q^{15} + 5 q^{16} + 2 q^{17} + 11 q^{18} + 12 q^{19} + 22 q^{20}+ \cdots - 142 q^{99}+O(q^{100}) $ 38 * q + 3 * q^2 + q^3 - 11 * q^4 - 19 * q^5 - 8 * q^6 - 18 * q^8 - 12 * q^9 + 3 * q^10 + 13 * q^11 + 4 * q^12 - 6 * q^13 - q^14 - 2 * q^15 + 5 * q^16 + 2 * q^17 + 11 * q^18 + 12 * q^19 + 22 * q^20 - 8 * q^21 - 20 * q^22 + 16 * q^23 - 15 * q^24 - 19 * q^25 + 3 * q^26 - 14 * q^27 + 27 * q^28 - 2 * q^29 + 4 * q^30 + 8 * q^31 + 16 * q^32 + 2 * q^33 - 28 * q^34 + 10 * q^36 - 19 * q^37 - 2 * q^38 + 45 * q^39 + 9 * q^40 - 36 * q^41 + 29 * q^42 - 74 * q^43 - q^44 - 12 * q^45 + 29 * q^46 - 2 * q^47 - 70 * q^48 + 6 * q^49 - 6 * q^50 + 43 * q^51 - 40 * q^52 + 10 * q^53 + 38 * q^54 - 26 * q^55 + 21 * q^56 + 24 * q^57 + 13 * q^58 + 28 * q^59 + 4 * q^60 - 22 * q^61 - 20 * q^62 - 27 * q^63 - 14 * q^64 + 3 * q^65 - 34 * q^66 + 61 * q^67 + 17 * q^68 - 40 * q^69 + 5 * q^70 - 34 * q^71 - 17 * q^72 - 16 * q^73 + 3 * q^74 + q^75 - 90 * q^76 + 5 * q^77 + 106 * q^78 + 63 * q^79 + 5 * q^80 + 5 * q^81 - 37 * q^82 - 48 * q^83 + 40 * q^84 - 4 * q^85 + 19 * q^86 - 32 * q^87 + 58 * q^88 + 16 * q^89 - 22 * q^90 - 11 * q^91 + 14 * q^92 + 31 * q^93 + 12 * q^95 - 40 * q^96 - 48 * q^97 + 66 * q^98 - 142 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1295\mathbb{Z}\right)^\times$.

$n$	$556$	$631$	$1037$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.189789	−	0.328725i	0.134201	−	0.232444i	−0.791091	−	0.611699i	$-0.790486\pi$
$2$	0.189789	−	0.328725i	0.134201	−	0.232444i	0.925292	+	0.379255i	$0.123820\pi$
$3$	−0.313780	−	0.543483i	−0.181161	−	0.313780i	0.761115	−	0.648617i	$-0.224652\pi$
$3$	−0.313780	−	0.543483i	−0.181161	−	0.313780i	−0.942276	+	0.334837i	$0.891319\pi$
$4$	0.927960	+	1.60727i	0.463980	+	0.803637i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−0.238209			−0.0972483
$7$	−2.24021	−	1.40764i	−0.846721	−	0.532037i
$7$	−2.24021	−	1.40764i	−0.846721	−	0.532037i
$8$	1.46363			0.517470
$9$	1.30308	−	2.25701i	0.434361	−	0.752336i
$10$	0.189789	+	0.328725i	0.0600167	+	0.103952i
$11$	−0.195253	−	0.338188i	−0.0588710	−	0.101968i	0.835088	−	0.550117i	$-0.185417\pi$
$11$	−0.195253	−	0.338188i	−0.0588710	−	0.101968i	−0.893959	+	0.448149i	$0.852083\pi$
$12$	0.582351	−	1.00866i	0.168110	−	0.291175i
$13$	−5.61090			−1.55618			−0.778091	−	0.628151i	$-0.783812\pi$
$13$	−5.61090			−1.55618			−0.778091	+	0.628151i	$0.783812\pi$
$14$	−0.887895	+	0.469260i	−0.237300	+	0.125415i
$15$	0.627560			0.162035
$16$	−1.57814	+	2.73342i	−0.394535	+	0.683354i
$17$	−1.36583	−	2.36568i	−0.331262	−	0.573763i	0.651498	−	0.758651i	$-0.274141\pi$
$17$	−1.36583	−	2.36568i	−0.331262	−	0.573763i	−0.982760	+	0.184888i	$0.940808\pi$
$18$	−0.494623	−	0.856713i	−0.116584	−	0.201929i
$19$	−3.29786	+	5.71206i	−0.756581	+	1.31044i	0.188003	+	0.982168i	$0.439799\pi$
$19$	−3.29786	+	5.71206i	−0.756581	+	1.31044i	−0.944584	+	0.328269i	$0.893535\pi$
$20$	−1.85592			−0.414996
$21$	−0.0620924	+	1.65921i	−0.0135497	+	0.362069i
$22$	−0.148228			−0.0316023
$23$	0.941721	−	1.63111i	0.196362	−	0.340110i	−0.750984	−	0.660321i	$-0.770420\pi$
$23$	0.941721	−	1.63111i	0.196362	−	0.340110i	0.947346	+	0.320211i	$0.103754\pi$
$24$	−0.459257	−	0.795456i	−0.0937454	−	0.162372i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−1.06489	+	1.84444i	−0.208842	+	0.361725i
$27$	−3.51821			−0.677080
$28$	0.183629	−	4.90687i	0.0347027	−	0.927311i
$29$	1.03928			0.192989			0.0964947	−	0.995334i	$-0.469237\pi$
$29$	1.03928			0.192989			0.0964947	+	0.995334i	$0.469237\pi$
$30$	0.119104	−	0.206295i	0.0217454	−	0.0376641i
$31$	−1.06268	−	1.84061i	−0.190862	−	0.330583i	0.754674	−	0.656100i	$-0.227795\pi$
$31$	−1.06268	−	1.84061i	−0.190862	−	0.330583i	−0.945536	+	0.325517i	$0.894462\pi$
$32$	2.06265	+	3.57262i	0.364629	+	0.631556i
$33$	−0.122533	+	0.212234i	−0.0213303	+	0.0369451i
$34$	−1.03688			−0.177823
$35$	2.33916	−	1.23626i	0.395390	−	0.208967i
$36$	4.83684			0.806140
$37$	−0.500000	+	0.866025i	−0.0821995	+	0.142374i
$37$	−0.500000	+	0.866025i	−0.0821995	+	0.142374i
$38$	1.25180	+	2.16818i	0.203069	+	0.351725i
$39$	1.76059	+	3.04943i	0.281920	+	0.488299i
$40$	−0.731813	+	1.26754i	−0.115710	+	0.200415i
$41$	−9.05677			−1.41443			−0.707215	−	0.706998i	$-0.750049\pi$
$41$	−9.05677			−1.41443			−0.707215	+	0.706998i	$0.750049\pi$
$42$	0.533638	+	0.335311i	0.0823422	+	0.0517397i
$43$	−5.44088			−0.829726			−0.414863	−	0.909884i	$-0.636171\pi$
$43$	−5.44088			−0.829726			−0.414863	+	0.909884i	$0.636171\pi$
$44$	0.362374	−	0.627650i	0.0546300	−	0.0946219i
$45$	1.30308	+	2.25701i	0.194252	+	0.336455i
$46$	−0.357457	−	0.619135i	−0.0527042	−	0.0912864i
$47$	−0.0948253	+	0.164242i	−0.0138317	+	0.0239572i	−0.872858	−	0.487974i	$-0.837736\pi$
$47$	−0.0948253	+	0.164242i	−0.0138317	+	0.0239572i	0.859027	+	0.511931i	$0.171070\pi$
$48$	1.98075			0.285897
$49$	3.03712	+	6.30682i	0.433874	+	0.900974i
$50$	−0.379579			−0.0536806
$51$	−0.857140	+	1.48461i	−0.120024	+	0.207887i
$52$	−5.20669	−	9.01824i	−0.722037	−	1.25061i
$53$	−3.49439	−	6.05246i	−0.479991	−	0.831369i	0.519746	−	0.854321i	$-0.326027\pi$
$53$	−3.49439	−	6.05246i	−0.479991	−	0.831369i	−0.999737	+	0.0229523i	$0.992693\pi$
$54$	−0.667719	+	1.15652i	−0.0908651	+	0.157383i
$55$	0.390506			0.0526559
$56$	−3.27884	−	2.06025i	−0.438153	−	0.275313i
$57$	4.13921			0.548252
$58$	0.197244	−	0.341637i	0.0258994	−	0.0448592i
$59$	−3.28538	−	5.69044i	−0.427720	−	0.740833i	0.568950	−	0.822372i	$-0.307350\pi$
$59$	−3.28538	−	5.69044i	−0.427720	−	0.740833i	−0.996670	+	0.0815393i	$0.974016\pi$
$60$	0.582351	+	1.00866i	0.0751812	+	0.130218i
$61$	2.21331	−	3.83357i	0.283385	−	0.490838i	−0.688831	−	0.724922i	$-0.741876\pi$
$61$	2.21331	−	3.83357i	0.283385	−	0.490838i	0.972216	+	0.234084i	$0.0752091\pi$
$62$	−0.806738			−0.102456
$63$	−6.09623	+	3.22191i	−0.768053	+	0.405923i
$64$	−4.74668			−0.593334
$65$	2.80545	−	4.85918i	0.347973	−	0.602707i
$66$	0.0465110	+	0.0805594i	0.00572511	+	0.00991618i
$67$	−5.06590	−	8.77439i	−0.618898	−	1.07196i	−0.989687	−	0.143245i	$-0.954246\pi$
$67$	−5.06590	−	8.77439i	−0.618898	−	1.07196i	0.370790	−	0.928717i	$-0.379087\pi$
$68$	2.53487	−	4.39052i	0.307398	−	0.532429i
$69$	−1.18197			−0.142293
$70$	0.0375565	−	1.00357i	0.00448886	−	0.119949i
$71$	−7.15892			−0.849608			−0.424804	−	0.905285i	$-0.639657\pi$
$71$	−7.15892			−0.849608			−0.424804	+	0.905285i	$0.639657\pi$
$72$	1.90723	−	3.30342i	0.224769	−	0.389311i
$73$	−0.00378823	−	0.00656140i	−0.000443379	−	0.000767954i	0.865804	−	0.500384i	$-0.166808\pi$
$73$	−0.00378823	−	0.00656140i	−0.000443379	−	0.000767954i	−0.866247	+	0.499616i	$0.833474\pi$
$74$	0.189789	+	0.328725i	0.0220626	+	0.0382135i
$75$	−0.313780	+	0.543483i	−0.0362322	+	0.0627560i
$76$	−12.2411			−1.40415
$77$	−0.0386377	+	1.03246i	−0.00440317	+	0.117660i
$78$	1.33656			0.151336
$79$	0.674724	−	1.16866i	0.0759124	−	0.131484i	−0.825570	−	0.564299i	$-0.809146\pi$
$79$	0.674724	−	1.16866i	0.0759124	−	0.131484i	0.901483	+	0.432815i	$0.142480\pi$
$80$	−1.57814	−	2.73342i	−0.176441	−	0.305605i
$81$	−2.80531	−	4.85894i	−0.311701	−	0.539882i
$82$	−1.71888	+	2.97719i	−0.189819	+	0.328775i
$83$	11.5548			1.26831			0.634153	−	0.773208i	$-0.281349\pi$
$83$	11.5548			1.26831			0.634153	+	0.773208i	$0.281349\pi$
$84$	−2.72442	+	1.43988i	−0.297259	+	0.157104i
$85$	2.73166			0.296290
$86$	−1.03262	+	1.78855i	−0.111350	+	0.192865i
$87$	−0.326105	−	0.564831i	−0.0349622	−	0.0605562i
$88$	−0.285778	−	0.494981i	−0.0304640	−	0.0527652i
$89$	−2.78198	+	4.81854i	−0.294890	+	0.510764i	−0.974959	−	0.222384i	$-0.928616\pi$
$89$	−2.78198	+	4.81854i	−0.294890	+	0.510764i	0.680070	+	0.733148i	$0.261950\pi$
$90$	0.989247			0.104276
$91$	12.5696	+	7.89810i	1.31765	+	0.827946i
$92$	3.49552			0.364433
$93$	−0.666893	+	1.15509i	−0.0691536	+	0.119777i
$94$	0.0359937	+	0.0623429i	0.00371247	+	0.00643018i
$95$	−3.29786	−	5.71206i	−0.338353	−	0.586045i
$96$	1.29444	−	2.24204i	0.132113	−	0.228827i
$97$	−15.2161			−1.54496			−0.772480	−	0.635039i	$-0.780984\pi$
$97$	−15.2161			−1.54496			−0.772480	+	0.635039i	$0.780984\pi$
$98$	2.64962	+	0.198591i	0.267652	+	0.0200608i
$99$	−1.01772			−0.102285
$100$	0.927960	−	1.60727i	0.0927960	−	0.160727i
$101$	8.80119	+	15.2441i	0.875751	+	1.51685i	0.855960	+	0.517042i	$0.172967\pi$
$101$	8.80119	+	15.2441i	0.875751	+	1.51685i	0.0197910	+	0.999804i	$0.493700\pi$
$102$	0.325352	+	0.563527i	0.0322147	+	0.0557974i
$103$	0.619523	−	1.07305i	0.0610434	−	0.105730i	−0.833889	−	0.551933i	$-0.813891\pi$
$103$	0.619523	−	1.07305i	0.0610434	−	0.105730i	0.894932	+	0.446202i	$0.147224\pi$
$104$	−8.21225			−0.805278
$105$	−1.40587	−	0.883377i	−0.137199	−	0.0862088i
$106$	−2.65279			−0.257662
$107$	−6.08099	+	10.5326i	−0.587872	+	1.01822i	0.406639	+	0.913589i	$0.366701\pi$
$107$	−6.08099	+	10.5326i	−0.587872	+	1.01822i	−0.994511	+	0.104635i	$0.966633\pi$
$108$	−3.26476	−	5.65472i	−0.314151	−	0.544126i
$109$	0.864560	+	1.49746i	0.0828098	+	0.143431i	0.904456	−	0.426567i	$-0.140277\pi$
$109$	0.864560	+	1.49746i	0.0828098	+	0.143431i	−0.821646	+	0.569998i	$0.806944\pi$
$110$	0.0741140	−	0.128369i	0.00706649	−	0.0122395i
$111$	0.627560			0.0595654
$112$	7.38303	−	3.90199i	0.697631	−	0.368704i
$113$	6.76591			0.636484			0.318242	−	0.948010i	$-0.396908\pi$
$113$	6.76591			0.636484			0.318242	+	0.948010i	$0.396908\pi$
$114$	0.785579	−	1.36066i	0.0735763	−	0.127438i
$115$	0.941721	+	1.63111i	0.0878159	+	0.152102i
$116$	0.964410	+	1.67041i	0.0895432	+	0.155093i
$117$	−7.31147	+	12.6638i	−0.675945	+	1.17077i
$118$	−2.49412			−0.229603
$119$	−0.270277	+	7.22223i	−0.0247763	+	0.662061i
$120$	0.918514			0.0838484
$121$	5.42375	−	9.39421i	0.493068	−	0.854020i
$122$	−0.840126	−	1.45514i	−0.0760615	−	0.131742i
$123$	2.84184	+	4.92220i	0.256240	+	0.443820i
$124$	1.97224	−	3.41602i	0.177112	−	0.306768i
$125$	1.00000			0.0894427
$126$	−0.0978786	+	2.61547i	−0.00871972	+	0.233005i
$127$	4.30548			0.382050			0.191025	−	0.981585i	$-0.438819\pi$
$127$	4.30548			0.382050			0.191025	+	0.981585i	$0.438819\pi$
$128$	−5.02618	+	8.70560i	−0.444256	+	0.769473i
$129$	1.70724	+	2.95703i	0.150314	+	0.260352i
$130$	−1.06489	−	1.84444i	−0.0933969	−	0.161768i
$131$	−3.71178	+	6.42900i	−0.324300	+	0.561704i	−0.981370	−	0.192125i	$-0.938462\pi$
$131$	−3.71178	+	6.42900i	−0.324300	+	0.561704i	0.657070	+	0.753829i	$0.271795\pi$
$132$	−0.454823			−0.0395873
$133$	15.4284	−	8.15405i	1.33781	−	0.707046i
$134$	−3.84581			−0.332228
$135$	1.75910	−	3.04686i	0.151400	−	0.262232i
$136$	−1.99906	−	3.46248i	−0.171418	−	0.296905i
$137$	−3.61949	−	6.26914i	−0.309234	−	0.535609i	0.668961	−	0.743297i	$-0.266739\pi$
$137$	−3.61949	−	6.26914i	−0.309234	−	0.535609i	−0.978195	+	0.207689i	$0.933406\pi$
$138$	−0.224326	+	0.388544i	−0.0190959	+	0.0330751i
$139$	15.4159			1.30756			0.653780	−	0.756685i	$-0.273182\pi$
$139$	15.4159			1.30756			0.653780	+	0.756685i	$0.273182\pi$
$140$	4.15766	+	2.61246i	0.351386	+	0.220793i
$141$	0.119017			0.0100231
$142$	−1.35869	+	2.35332i	−0.114019	+	0.197486i
$143$	1.09554	+	1.89754i	0.0916141	+	0.158680i
$144$	4.11290	+	7.12374i	0.342741	+	0.593645i
$145$	−0.519640	+	0.900042i	−0.0431537	+	0.0747444i
$146$	−0.00287586			−0.000238008
$147$	2.47466	−	3.62958i	0.204107	−	0.299362i
$148$	−1.85592			−0.152556
$149$	5.28228	−	9.14917i	0.432741	−	0.749530i	−0.564367	−	0.825524i	$-0.690880\pi$
$149$	5.28228	−	9.14917i	0.432741	−	0.749530i	0.997108	+	0.0759943i	$0.0242131\pi$
$150$	0.119104	+	0.206295i	0.00972483	+	0.0168439i
$151$	8.98211	+	15.5575i	0.730954	+	1.26605i	0.956476	+	0.291811i	$0.0942579\pi$
$151$	8.98211	+	15.5575i	0.730954	+	1.26605i	−0.225522	+	0.974238i	$0.572409\pi$
$152$	−4.82684	+	8.36033i	−0.391508	+	0.678112i
$153$	−7.11916			−0.575550
$154$	0.332062	+	0.208651i	0.0267583	+	0.0168136i
$155$	2.12535			0.170712
$156$	−3.26751	+	5.65949i	−0.261610	+	0.453122i
$157$	5.80379	+	10.0525i	0.463193	+	0.802274i	0.999118	−	0.0419920i	$-0.0133704\pi$
$157$	5.80379	+	10.0525i	0.463193	+	0.802274i	−0.535925	+	0.844266i	$0.680037\pi$
$158$	−0.256111	−	0.443597i	−0.0203751	−	0.0352907i
$159$	−2.19294	+	3.79828i	−0.173911	+	0.301223i
$160$	−4.12531			−0.326134
$161$	−4.40567	+	2.32843i	−0.347215	+	0.183506i
$162$	−2.12967			−0.167323
$163$	1.93090	−	3.34442i	0.151240	−	0.261955i	−0.780444	−	0.625226i	$-0.785007\pi$
$163$	1.93090	−	3.34442i	0.151240	−	0.261955i	0.931684	+	0.363271i	$0.118340\pi$
$164$	−8.40432	−	14.5567i	−0.656267	−	1.13669i
$165$	−0.122533	−	0.212234i	−0.00953919	−	0.0165224i
$166$	2.19298	−	3.79836i	0.170208	−	0.294810i
$167$	−20.7281			−1.60399			−0.801994	−	0.597332i	$-0.796227\pi$
$167$	−20.7281			−1.60399			−0.801994	+	0.597332i	$0.796227\pi$
$168$	−0.0908801	+	2.42846i	−0.00701155	+	0.187360i
$169$	18.4821			1.42170
$170$	0.518440	−	0.897964i	0.0397625	−	0.0688707i
$171$	8.59478	+	14.8866i	0.657259	+	1.13841i
$172$	−5.04892	−	8.74498i	−0.384976	−	0.666799i
$173$	9.46016	−	16.3855i	0.719243	−	1.24577i	−0.242057	−	0.970262i	$-0.577822\pi$
$173$	9.46016	−	16.3855i	0.719243	−	1.24577i	0.961300	−	0.275503i	$-0.0888445\pi$
$174$	−0.247565			−0.0187679
$175$	−0.0989426	+	2.64390i	−0.00747935	+	0.199860i
$176$	1.23255			0.0929067
$177$	−2.06177	+	3.57110i	−0.154972	+	0.268420i
$178$	1.05598	+	1.82902i	0.0791492	+	0.137090i
$179$	6.34871	+	10.9963i	0.474525	+	0.821901i	0.999574	−	0.0291704i	$-0.00928654\pi$
$179$	6.34871	+	10.9963i	0.474525	+	0.821901i	−0.525050	+	0.851072i	$0.675953\pi$
$180$	−2.41842	+	4.18883i	−0.180258	+	0.312217i
$181$	−9.83041			−0.730689			−0.365344	−	0.930872i	$-0.619049\pi$
$181$	−9.83041			−0.730689			−0.365344	+	0.930872i	$0.619049\pi$
$182$	4.98188	−	2.63297i	0.369282	−	0.195168i
$183$	−2.77797			−0.205354
$184$	1.37833	−	2.38733i	0.101612	−	0.175997i
$185$	−0.500000	−	0.866025i	−0.0367607	−	0.0636715i
$186$	0.253138	+	0.438449i	0.0185610	+	0.0321486i
$187$	−0.533364	+	0.923814i	−0.0390035	+	0.0675560i
$188$	−0.351976			−0.0256705
$189$	7.88154	+	4.95236i	0.573298	+	0.360231i
$190$	−2.50360			−0.181630
$191$	−7.47397	+	12.9453i	−0.540797	+	0.936689i	0.458061	+	0.888921i	$0.348544\pi$
$191$	−7.47397	+	12.9453i	−0.540797	+	0.936689i	−0.998858	+	0.0477678i	$0.984789\pi$
$192$	1.48941	+	2.57974i	0.107489	+	0.186177i
$193$	−8.14197	−	14.1023i	−0.586072	−	1.01511i	−0.994741	−	0.102424i	$-0.967340\pi$
$193$	−8.14197	−	14.1023i	−0.586072	−	1.01511i	0.408669	−	0.912683i	$-0.365993\pi$
$194$	−2.88786	+	5.00191i	−0.207336	+	0.359116i
$195$	−3.52118			−0.252157
$196$	−7.31846	+	10.7339i	−0.522747	+	0.766711i
$197$	−8.74693			−0.623193			−0.311596	−	0.950215i	$-0.600864\pi$
$197$	−8.74693			−0.623193			−0.311596	+	0.950215i	$0.600864\pi$
$198$	−0.193153	+	0.334552i	−0.0137268	+	0.0237756i
$199$	−4.77656	−	8.27324i	−0.338601	−	0.586474i	0.645569	−	0.763702i	$-0.276620\pi$
$199$	−4.77656	−	8.27324i	−0.338601	−	0.586474i	−0.984170	+	0.177228i	$0.943287\pi$
$200$	−0.731813	−	1.26754i	−0.0517470	−	0.0896284i
$201$	−3.17916	+	5.50646i	−0.224240	+	0.388396i
$202$	6.68149			0.470108
$203$	−2.32821	−	1.46293i	−0.163408	−	0.102677i
$204$	−3.18156			−0.222754
$205$	4.52839	−	7.84339i	0.316276	−	0.547806i
$206$	−0.235158	−	0.407306i	−0.0163842	−	0.0283783i
$207$	−2.45428	−	4.25094i	−0.170584	−	0.295461i
$208$	8.85477	−	15.3369i	0.613968	−	1.06342i
$209$	2.57567			0.178163
$210$	−0.557207	+	0.294489i	−0.0384510	+	0.0203217i
$211$	−2.93456			−0.202023			−0.101012	−	0.994885i	$-0.532208\pi$
$211$	−2.93456			−0.202023			−0.101012	+	0.994885i	$0.532208\pi$
$212$	6.48530	−	11.2329i	0.445412	−	0.771477i
$213$	2.24633	+	3.89075i	0.153916	+	0.266590i
$214$	2.30822	+	3.99795i	0.157786	+	0.273294i
$215$	2.72044	−	4.71194i	0.185532	−	0.321352i
$216$	−5.14934			−0.350368
$217$	−0.210288	+	5.61921i	−0.0142753	+	0.381457i
$218$	0.656337			0.0444528
$219$	−0.00237734	+	0.00411768i	−0.000160646	+	0.000278247i
$220$	0.362374	+	0.627650i	0.0244313	+	0.0423162i
$221$	7.66352	+	13.2736i	0.515504	+	0.892879i
$222$	0.119104	−	0.206295i	0.00799376	−	0.0138456i
$223$	−3.55216			−0.237870			−0.118935	−	0.992902i	$-0.537948\pi$
$223$	−3.55216			−0.237870			−0.118935	+	0.992902i	$0.537948\pi$
$224$	0.408169	−	10.9069i	0.0272719	−	0.728748i
$225$	−2.60617			−0.173745
$226$	1.28410	−	2.22413i	0.0854170	−	0.147947i
$227$	12.9292	+	22.3940i	0.858142	+	1.48635i	0.873699	+	0.486466i	$0.161714\pi$
$227$	12.9292	+	22.3940i	0.858142	+	1.48635i	−0.0155576	+	0.999879i	$0.504952\pi$
$228$	3.84103	+	6.65285i	0.254378	+	0.440596i
$229$	13.3126	−	23.0581i	0.879721	−	1.52372i	0.0280729	−	0.999606i	$-0.491063\pi$
$229$	13.3126	−	23.0581i	0.879721	−	1.52372i	0.851648	−	0.524115i	$-0.175604\pi$
$230$	0.714915			0.0471401
$231$	0.573248	−	0.302966i	0.0377170	−	0.0199337i
$232$	1.52112			0.0998662
$233$	4.02298	−	6.96801i	0.263554	−	0.456489i	−0.703630	−	0.710567i	$-0.748439\pi$
$233$	4.02298	−	6.96801i	0.263554	−	0.456489i	0.967184	+	0.254078i	$0.0817719\pi$
$234$	2.77528	+	4.80692i	0.181426	+	0.314239i
$235$	−0.0948253	−	0.164242i	−0.00618572	−	0.0107140i
$236$	6.09740	−	10.5610i	0.396907	−	0.687463i
$237$	−0.846860			−0.0550095
$238$	2.32283	+	1.45955i	0.150567	+	0.0946086i
$239$	12.5935			0.814605			0.407302	−	0.913293i	$-0.366470\pi$
$239$	12.5935			0.814605			0.407302	+	0.913293i	$0.366470\pi$
$240$	−0.990377	+	1.71538i	−0.0639286	+	0.110728i
$241$	−4.68609	−	8.11654i	−0.301857	−	0.522832i	0.674699	−	0.738093i	$-0.264273\pi$
$241$	−4.68609	−	8.11654i	−0.301857	−	0.522832i	−0.976557	+	0.215260i	$0.930940\pi$
$242$	−2.05874	−	3.56585i	−0.132341	−	0.229221i
$243$	−7.03781	+	12.1899i	−0.451476	+	0.781979i
$244$	8.21545			0.525941
$245$	−6.98042	−	0.523189i	−0.445963	−	0.0334253i
$246$	2.15740			0.137551
$247$	18.5040	−	32.0498i	1.17738	−	2.03928i
$248$	−1.55536	−	2.69396i	−0.0987654	−	0.171067i
$249$	−3.62567	−	6.27985i	−0.229768	−	0.397969i
$250$	0.189789	−	0.328725i	0.0120033	−	0.0207904i
$251$	−9.30369			−0.587244			−0.293622	−	0.955922i	$-0.594861\pi$
$251$	−9.30369			−0.587244			−0.293622	+	0.955922i	$0.594861\pi$
$252$	−10.8356	−	6.80851i	−0.682576	−	0.428896i
$253$	−0.735496			−0.0462402
$254$	0.817135	−	1.41532i	0.0512716	−	0.0888050i
$255$	−0.857140	−	1.48461i	−0.0536762	−	0.0929698i
$256$	−2.83884	−	4.91702i	−0.177428	−	0.307314i
$257$	−0.454749	+	0.787648i	−0.0283665	+	0.0491322i	−0.879860	−	0.475233i	$-0.842364\pi$
$257$	−0.454749	+	0.787648i	−0.0283665	+	0.0491322i	0.851494	+	0.524365i	$0.175697\pi$
$258$	1.29606			0.0806895
$259$	2.33916	−	1.23626i	0.145348	−	0.0768177i
$260$	10.4134			0.645810
$261$	1.35427	−	2.34566i	0.0838271	−	0.145193i
$262$	1.40891	+	2.44031i	0.0870430	+	0.150763i
$263$	13.9114	+	24.0953i	0.857814	+	1.48578i	0.874009	+	0.485909i	$0.161511\pi$
$263$	13.9114	+	24.0953i	0.857814	+	1.48578i	−0.0161951	+	0.999869i	$0.505155\pi$
$264$	−0.179343	+	0.310631i	−0.0110378	+	0.0191180i
$265$	6.98877			0.429317
$266$	0.247712	−	6.61926i	0.0151882	−	0.405853i
$267$	3.49173			0.213690
$268$	9.40190	−	16.2846i	0.574312	−	0.994738i
$269$	−4.77597	−	8.27222i	−0.291196	−	0.504366i	0.682897	−	0.730515i	$-0.260720\pi$
$269$	−4.77597	−	8.27222i	−0.291196	−	0.504366i	−0.974093	+	0.226149i	$0.927386\pi$
$270$	−0.667719	−	1.15652i	−0.0406361	−	0.0703838i
$271$	−5.58048	+	9.66568i	−0.338990	+	0.587148i	−0.984243	−	0.176821i	$-0.943419\pi$
$271$	−5.58048	+	9.66568i	−0.338990	+	0.587148i	0.645253	+	0.763969i	$0.276752\pi$
$272$	8.62187			0.522777
$273$	0.348394	−	9.30964i	0.0210858	−	0.563445i
$274$	−2.74776			−0.165998
$275$	−0.195253	+	0.338188i	−0.0117742	+	0.0203935i
$276$	−1.09682	−	1.89975i	−0.0660210	−	0.114352i
$277$	12.2028	+	21.1359i	0.733195	+	1.26993i	0.955511	+	0.294956i	$0.0953049\pi$
$277$	12.2028	+	21.1359i	0.733195	+	1.26993i	−0.222316	+	0.974975i	$0.571362\pi$
$278$	2.92578	−	5.06759i	0.175476	−	0.303934i
$279$	−5.53902			−0.331612
$280$	3.42365	−	1.80943i	0.204602	−	0.108134i
$281$	−27.3226			−1.62993			−0.814965	−	0.579510i	$-0.803244\pi$
$281$	−27.3226			−1.62993			−0.814965	+	0.579510i	$0.803244\pi$
$282$	0.0225882	−	0.0391239i	0.00134511	−	0.00232980i
$283$	−6.45199	−	11.1752i	−0.383531	−	0.664295i	0.608033	−	0.793912i	$-0.291959\pi$
$283$	−6.45199	−	11.1752i	−0.383531	−	0.664295i	−0.991564	+	0.129616i	$0.958625\pi$
$284$	−6.64319	−	11.5063i	−0.394201	−	0.682776i
$285$	−2.06961	+	3.58467i	−0.122593	+	0.212337i
$286$	0.831692			0.0491790
$287$	20.2891	+	12.7486i	1.19763	+	0.752529i
$288$	10.7512			0.633523
$289$	4.76903	−	8.26020i	0.280531	−	0.485894i
$290$	0.197244	+	0.341637i	0.0115826	+	0.0200616i
$291$	4.77451	+	8.26969i	0.279887	+	0.484778i
$292$	0.00703065	−	0.0121774i	0.000411438	−	0.000712631i
$293$	13.0076			0.759914			0.379957	−	0.925004i	$-0.375939\pi$
$293$	13.0076			0.759914			0.379957	+	0.925004i	$0.375939\pi$
$294$	−0.723467	−	1.50234i	−0.0421935	−	0.0876182i
$295$	6.57076			0.382564
$296$	−0.731813	+	1.26754i	−0.0425358	+	0.0736741i
$297$	0.686941	+	1.18982i	0.0398604	+	0.0690402i
$298$	−2.00504	−	3.47283i	−0.116149	−	0.201176i
$299$	−5.28390	+	9.15198i	−0.305576	+	0.529273i
$300$	−1.16470			−0.0672441
$301$	12.1887	+	7.65878i	0.702547	+	0.441445i
$302$	6.81884			0.392380
$303$	5.52328	−	9.56660i	0.317304	−	0.549587i
$304$	−10.4090	−	18.0289i	−0.596995	−	1.03403i
$305$	2.21331	+	3.83357i	0.126734	+	0.219509i
$306$	−1.35114	+	2.34024i	−0.0772396	+	0.133783i
$307$	15.9317			0.909269			0.454634	−	0.890678i	$-0.349770\pi$
$307$	15.9317			0.909269			0.454634	+	0.890678i	$0.349770\pi$
$308$	−1.69530	+	0.895980i	−0.0965987	+	0.0510532i
$309$	−0.777576			−0.0442348
$310$	0.403369	−	0.698656i	0.0229098	−	0.0396810i
$311$	13.8855	+	24.0505i	0.787377	+	1.36378i	0.927569	+	0.373653i	$0.121895\pi$
$311$	13.8855	+	24.0505i	0.787377	+	1.36378i	−0.140191	+	0.990124i	$0.544772\pi$
$312$	2.57684	+	4.46322i	0.145885	+	0.252680i
$313$	15.0252	−	26.0244i	0.849276	−	1.47099i	−0.0325798	−	0.999469i	$-0.510372\pi$
$313$	15.0252	−	26.0244i	0.849276	−	1.47099i	0.881856	−	0.471520i	$-0.156294\pi$
$314$	4.40599			0.248645
$315$	0.257861	−	6.89045i	0.0145288	−	0.388233i
$316$	2.50447			0.140887
$317$	−0.760583	+	1.31737i	−0.0427186	+	0.0739908i	−0.886594	−	0.462548i	$-0.846935\pi$
$317$	−0.760583	+	1.31737i	−0.0427186	+	0.0739908i	0.843876	+	0.536539i	$0.180269\pi$
$318$	0.832394	+	1.44175i	0.0466783	+	0.0808492i
$319$	−0.202923	−	0.351472i	−0.0113615	−	0.0196787i
$320$	2.37334	−	4.11074i	0.132674	−	0.229797i
$321$	7.63238			0.425998
$322$	−0.0707355	+	1.89016i	−0.00394194	+	0.105335i
$323$	18.0173			1.00251
$324$	5.20643	−	9.01779i	0.289246	−	0.500989i
$325$	2.80545	+	4.85918i	0.155618	+	0.269539i
$326$	−0.732930	−	1.26947i	−0.0405932	−	0.0703096i
$327$	0.542563	−	0.939747i	0.0300038	−	0.0519681i
$328$	−13.2557			−0.731925
$329$	0.443623	−	0.234458i	0.0244577	−	0.0129261i
$330$	−0.0930220			−0.00512069
$331$	−2.79070	+	4.83363i	−0.153391	+	0.265680i	−0.932472	−	0.361243i	$-0.882353\pi$
$331$	−2.79070	+	4.83363i	−0.153391	+	0.265680i	0.779081	+	0.626923i	$0.215686\pi$
$332$	10.7224	+	18.5717i	0.588468	+	1.01926i
$333$	1.30308	+	2.25701i	0.0714086	+	0.123683i
$334$	−3.93397	+	6.81384i	−0.215257	+	0.372837i
$335$	10.1318			0.553559
$336$	−4.43731	−	2.78818i	−0.242075	−	0.152108i
$337$	−7.61503			−0.414817			−0.207409	−	0.978254i	$-0.566503\pi$
$337$	−7.61503			−0.414817			−0.207409	+	0.978254i	$0.566503\pi$
$338$	3.50772	−	6.07554i	0.190795	−	0.330466i
$339$	−2.12301	−	3.67716i	−0.115306	−	0.199716i
$340$	2.53487	+	4.39052i	0.137472	+	0.238109i
$341$	−0.414981	+	0.718769i	−0.0224725	+	0.0389235i
$342$	6.52480			0.352821
$343$	2.07392	−	18.4038i	0.111981	−	0.993710i
$344$	−7.96341			−0.429358
$345$	0.590987	−	1.02362i	0.0318177	−	0.0551098i
$346$	−3.59088	−	6.21959i	−0.193047	−	0.334367i
$347$	13.6764	+	23.6882i	0.734188	+	1.27165i	0.955079	+	0.296352i	$0.0957703\pi$
$347$	13.6764	+	23.6882i	0.734188	+	1.27165i	−0.220891	+	0.975299i	$0.570896\pi$
$348$	0.605225	−	1.04828i	0.0324435	−	0.0561938i
$349$	10.1015			0.540719			0.270359	−	0.962759i	$-0.412857\pi$
$349$	10.1015			0.540719			0.270359	+	0.962759i	$0.412857\pi$
$350$	0.850338	+	0.534309i	0.0454525	+	0.0285600i
$351$	19.7403			1.05366
$352$	0.805479	−	1.39513i	0.0429322	−	0.0743608i
$353$	−2.59131	−	4.48828i	−0.137921	−	0.238887i	0.788788	−	0.614665i	$-0.210709\pi$
$353$	−2.59131	−	4.48828i	−0.137921	−	0.238887i	−0.926710	+	0.375778i	$0.877375\pi$
$354$	0.782606	+	1.35551i	0.0415950	+	0.0720447i
$355$	3.57946	−	6.19981i	0.189978	−	0.329052i
$356$	−10.3263			−0.547292
$357$	4.00997	−	2.11930i	0.212230	−	0.112165i
$358$	4.81967			0.254728
$359$	2.84279	−	4.92386i	0.150037	−	0.259871i	−0.781204	−	0.624276i	$-0.785394\pi$
$359$	2.84279	−	4.92386i	0.150037	−	0.259871i	0.931241	+	0.364405i	$0.118727\pi$
$360$	1.90723	+	3.30342i	0.100520	+	0.174105i
$361$	−12.2518	−	21.2207i	−0.644831	−	1.11688i
$362$	−1.86571	+	3.23150i	−0.0980595	+	0.169844i
$363$	−6.80746			−0.357299
$364$	−1.03033	+	27.5319i	−0.0540037	+	1.44306i
$365$	0.00757646			0.000396570
$366$	−0.527230	+	0.913189i	−0.0275587	+	0.0477332i
$367$	−17.5071	−	30.3231i	−0.913861	−	1.58285i	−0.808561	−	0.588413i	$-0.799753\pi$
$367$	−17.5071	−	30.3231i	−0.913861	−	1.58285i	−0.105300	−	0.994440i	$-0.533580\pi$
$368$	2.97233	+	5.14823i	0.154944	+	0.268370i
$369$	−11.8017	+	20.4412i	−0.614374	+	1.06413i
$370$	−0.379579			−0.0197334
$371$	−0.691487	+	18.4776i	−0.0359002	+	0.959311i
$372$	−2.47540			−0.128343
$373$	−0.344592	+	0.596852i	−0.0178423	+	0.0309038i	−0.874809	−	0.484469i	$-0.839013\pi$
$373$	−0.344592	+	0.596852i	−0.0178423	+	0.0309038i	0.856966	+	0.515372i	$0.172346\pi$
$374$	0.202454	+	0.350661i	0.0104686	+	0.0181322i
$375$	−0.313780	−	0.543483i	−0.0162035	−	0.0280654i
$376$	−0.138789	+	0.240389i	−0.00715749	+	0.0123971i
$377$	−5.83129			−0.300327
$378$	3.12380	−	1.65095i	0.160671	−	0.0849159i
$379$	−33.3391			−1.71251			−0.856257	−	0.516551i	$-0.827216\pi$
$379$	−33.3391			−1.71251			−0.856257	+	0.516551i	$0.827216\pi$
$380$	6.12057	−	10.6011i	0.313978	−	0.543827i
$381$	−1.35097	−	2.33996i	−0.0692125	−	0.119880i
$382$	2.83696	+	4.91376i	0.145152	+	0.251410i
$383$	−8.76733	+	15.1855i	−0.447990	+	0.775941i	−0.998255	−	0.0590491i	$-0.981193\pi$
$383$	−8.76733	+	15.1855i	−0.447990	+	0.775941i	0.550266	+	0.834990i	$0.314526\pi$
$384$	6.30846			0.321927
$385$	−0.874818	−	0.549691i	−0.0445848	−	0.0280149i
$386$	−6.18104			−0.314607
$387$	−7.08992	+	12.2801i	−0.360401	+	0.624233i
$388$	−14.1199	−	24.4564i	−0.716831	−	1.24159i
$389$	3.76343	+	6.51846i	0.190814	+	0.330499i	0.945520	−	0.325564i	$-0.105554\pi$
$389$	3.76343	+	6.51846i	0.190814	+	0.330499i	−0.754706	+	0.656063i	$0.772221\pi$
$390$	−0.668282	+	1.15750i	−0.0338398	+	0.0586122i
$391$	−5.14492			−0.260190
$392$	4.44520	+	9.23082i	0.224517	+	0.466227i
$393$	4.65873			0.235002
$394$	−1.66008	+	2.87533i	−0.0836334	+	0.144857i
$395$	0.674724	+	1.16866i	0.0339491	+	0.0588015i
$396$	−0.944408	−	1.63576i	−0.0474583	−	0.0822002i
$397$	−13.6276	+	23.6037i	−0.683950	+	1.18464i	0.289816	+	0.957082i	$0.406406\pi$
$397$	−13.6276	+	23.6037i	−0.683950	+	1.18464i	−0.973766	+	0.227554i	$0.926927\pi$
$398$	−3.62616			−0.181763
$399$	−9.27273	−	5.82651i	−0.464217	−	0.291690i
$400$	3.15628			0.157814
$401$	16.8645	−	29.2102i	0.842175	−	1.45869i	−0.0458776	−	0.998947i	$-0.514608\pi$
$401$	16.8645	−	29.2102i	0.842175	−	1.45869i	0.888052	−	0.459742i	$-0.152058\pi$
$402$	1.20674	+	2.09014i	0.0601867	+	0.104247i
$403$	5.96256	+	10.3275i	0.297016	+	0.514447i
$404$	−16.3343	+	28.2918i	−0.812662	+	1.40757i
$405$	5.61062			0.278794
$406$	−0.922771	+	0.487692i	−0.0457963	+	0.0242037i
$407$	0.390506			0.0193567
$408$	−1.25453	+	2.17291i	−0.0621086	+	0.107575i
$409$	−15.7979	−	27.3628i	−0.781156	−	1.35300i	−0.931269	−	0.364333i	$-0.881297\pi$
$409$	−15.7979	−	27.3628i	−0.781156	−	1.35300i	0.150112	−	0.988669i	$-0.452036\pi$
$410$	−1.71888	−	2.97719i	−0.0848894	−	0.147033i
$411$	−2.27145	+	3.93426i	−0.112042	+	0.194063i
$412$	2.29957			0.113292
$413$	−0.650128	+	17.3724i	−0.0319907	+	0.854841i
$414$	−1.86319			−0.0915707
$415$	−5.77741	+	10.0068i	−0.283602	+	0.491213i
$416$	−11.5733	−	20.0456i	−0.567430	−	0.982817i
$417$	−4.83720	−	8.37828i	−0.236879	−	0.410286i
$418$	0.488835	−	0.846688i	0.0239097	−	0.0414128i
$419$	4.44414			0.217111			0.108555	−	0.994090i	$-0.465378\pi$
$419$	4.44414			0.217111			0.108555	+	0.994090i	$0.465378\pi$
$420$	0.115239	−	3.07936i	0.00562307	−	0.150257i
$421$	13.7138			0.668370			0.334185	−	0.942507i	$-0.391539\pi$
$421$	13.7138			0.668370			0.334185	+	0.942507i	$0.391539\pi$
$422$	−0.556948	+	0.964663i	−0.0271118	+	0.0469590i
$423$	0.247131	+	0.428043i	0.0120159	+	0.0208122i
$424$	−5.11448	−	8.85853i	−0.248381	−	0.430208i
$425$	−1.36583	+	2.36568i	−0.0662524	+	0.114753i
$426$	1.70532			0.0826229
$427$	−10.3546	+	5.47247i	−0.501092	+	0.264831i
$428$	−22.5717			−1.09104
$429$	0.687521	−	1.19082i	0.0331938	−	0.0574934i
$430$	−1.03262	−	1.78855i	−0.0497974	−	0.0862517i
$431$	−2.77959	−	4.81439i	−0.133888	−	0.231901i	0.791284	−	0.611449i	$-0.209413\pi$
$431$	−2.77959	−	4.81439i	−0.133888	−	0.231901i	−0.925172	+	0.379548i	$0.876080\pi$
$432$	5.55222	−	9.61673i	0.267131	−	0.462685i
$433$	2.77663			0.133436			0.0667181	−	0.997772i	$-0.478747\pi$
$433$	2.77663			0.133436			0.0667181	+	0.997772i	$0.478747\pi$
$434$	1.80727	+	1.13559i	0.0867516	+	0.0545103i
$435$	0.652211			0.0312711
$436$	−1.60455	+	2.77917i	−0.0768442	+	0.133098i
$437$	6.21133	+	10.7583i	0.297128	+	0.514641i
$438$	0.000902389		0.00156298i	4.31178e−5		7.46823e-5i
$439$	−8.44995	+	14.6357i	−0.403294	+	0.698526i	−0.994121	−	0.108272i	$-0.965468\pi$
$439$	−8.44995	+	14.6357i	−0.403294	+	0.698526i	0.590827	+	0.806798i	$0.298801\pi$
$440$	0.571555			0.0272478
$441$	18.1921	+	1.36352i	0.866293	+	0.0649294i
$442$	5.81782			0.276726
$443$	8.22139	−	14.2399i	0.390610	−	0.676557i	−0.601920	−	0.798556i	$-0.705597\pi$
$443$	8.22139	−	14.2399i	0.390610	−	0.676557i	0.992530	+	0.122000i	$0.0389307\pi$
$444$	0.582351	+	1.00866i	0.0276371	+	0.0478689i
$445$	−2.78198	−	4.81854i	−0.131879	−	0.228421i
$446$	−0.674162	+	1.16768i	−0.0319225	+	0.0552914i
$447$	−6.62990			−0.313583
$448$	10.6336	+	6.68160i	0.502389	+	0.315676i
$449$	−3.70476			−0.174839			−0.0874193	−	0.996172i	$-0.527862\pi$
$449$	−3.70476			−0.174839			−0.0874193	+	0.996172i	$0.527862\pi$
$450$	−0.494623	+	0.856713i	−0.0233168	+	0.0403858i
$451$	1.76836	+	3.06289i	0.0832690	+	0.144226i
$452$	6.27850	+	10.8747i	0.295316	+	0.511502i
$453$	5.63682	−	9.76325i	0.264841	−	0.458718i
$454$	9.81531			0.460655
$455$	−13.1248	+	6.93654i	−0.615298	+	0.325190i
$456$	6.05826			0.283704
$457$	−6.76255	+	11.7131i	−0.316339	+	0.547915i	−0.979721	−	0.200366i	$-0.935787\pi$
$457$	−6.76255	+	11.7131i	−0.316339	+	0.547915i	0.663382	+	0.748281i	$0.269120\pi$
$458$	−5.05318	−	8.75236i	−0.236120	−	0.408971i
$459$	4.80527	+	8.32297i	0.224291	+	0.388483i
$460$	−1.74776	+	3.02721i	−0.0814897	+	0.141144i
$461$	−14.0320			−0.653537			−0.326769	−	0.945104i	$-0.605960\pi$
$461$	−14.0320			−0.653537			−0.326769	+	0.945104i	$0.605960\pi$
$462$	0.00920383	−	0.245941i	0.000428201	−	0.0114422i
$463$	−9.81181			−0.455993			−0.227997	−	0.973662i	$-0.573218\pi$
$463$	−9.81181			−0.455993			−0.227997	+	0.973662i	$0.573218\pi$
$464$	−1.64013	+	2.84078i	−0.0761410	+	0.131880i
$465$	−0.666893	−	1.15509i	−0.0309264	−	0.0535661i
$466$	−1.52704	−	2.64491i	−0.0707387	−	0.122523i
$467$	−1.04247	+	1.80561i	−0.0482398	+	0.0835537i	−0.889137	−	0.457641i	$-0.848694\pi$
$467$	−1.04247	+	1.80561i	−0.0482398	+	0.0835537i	0.840897	+	0.541195i	$0.182028\pi$
$468$	−27.1390			−1.25450
$469$	−1.00247	+	26.7874i	−0.0462895	+	1.23693i
$470$	−0.0719874			−0.00332053
$471$	3.64223	−	6.30852i	0.167825	−	0.290681i
$472$	−4.80857	−	8.32868i	−0.221332	−	0.383359i
$473$	1.06235	+	1.84004i	0.0488468	+	0.0846052i
$474$	−0.160725	+	0.278384i	−0.00738235	+	0.0127866i
$475$	6.59572			0.302633
$476$	−11.8589	+	6.26753i	−0.543552	+	0.287272i
$477$	−18.2139			−0.833958
$478$	2.39011	−	4.13979i	0.109321	−	0.189350i
$479$	13.6102	+	23.5735i	0.621864	+	1.07710i	0.989138	+	0.146987i	$0.0469576\pi$
$479$	13.6102	+	23.5735i	0.621864	+	1.07710i	−0.367275	+	0.930113i	$0.619709\pi$
$480$	1.29444	+	2.24204i	0.0590828	+	0.102334i
$481$	2.80545	−	4.85918i	0.127917	−	0.221559i
$482$	−3.55748			−0.162039
$483$	2.64787	+	1.66379i	0.120482	+	0.0757051i
$484$	20.1321			0.915095
$485$	7.60805	−	13.1775i	0.345464	−	0.598361i
$486$	2.67141	+	4.62701i	0.121177	+	0.209885i
$487$	13.8477	+	23.9849i	0.627498	+	1.08686i	0.988052	+	0.154120i	$0.0492543\pi$
$487$	13.8477	+	23.9849i	0.627498	+	1.08686i	−0.360554	+	0.932738i	$0.617412\pi$
$488$	3.23946	−	5.61091i	0.146643	−	0.253994i
$489$	−2.42352			−0.109595
$490$	−1.49680	+	2.19534i	−0.0676183	+	0.0991755i
$491$	−29.8219			−1.34584			−0.672922	−	0.739713i	$-0.734961\pi$
$491$	−29.8219			−1.34584			−0.672922	+	0.739713i	$0.734961\pi$
$492$	−5.27422	+	9.13522i	−0.237780	+	0.411847i
$493$	−1.41948	−	2.45861i	−0.0639300	−	0.110730i
$494$	−7.02371	−	12.1654i	−0.316012	−	0.547348i
$495$	0.508862	−	0.881376i	0.0228717	−	0.0396149i
$496$	6.70820			0.301207
$497$	16.0375	+	10.0772i	0.719381	+	0.452023i
$498$	−2.75246			−0.123341
$499$	−15.3062	+	26.5111i	−0.685198	+	1.18680i	0.288177	+	0.957577i	$0.406951\pi$
$499$	−15.3062	+	26.5111i	−0.685198	+	1.18680i	−0.973375	+	0.229220i	$0.926382\pi$
$500$	0.927960	+	1.60727i	0.0414996	+	0.0718795i
$501$	6.50407	+	11.2654i	0.290580	+	0.503300i
$502$	−1.76574	+	3.05836i	−0.0788089	+	0.136501i
$503$	−5.72398			−0.255220			−0.127610	−	0.991824i	$-0.540731\pi$
$503$	−5.72398			−0.255220			−0.127610	+	0.991824i	$0.540731\pi$
$504$	−8.92261	+	4.71567i	−0.397445	+	0.210053i
$505$	−17.6024			−0.783296
$506$	−0.139589	+	0.241776i	−0.00620551	+	0.0107483i
$507$	−5.79933	−	10.0447i	−0.257557	−	0.446102i
$508$	3.99531	+	6.92008i	0.177263	+	0.307029i
$509$	21.4471	−	37.1474i	0.950624	−	1.64653i	0.206546	−	0.978437i	$-0.433778\pi$
$509$	21.4471	−	37.1474i	0.950624	−	1.64653i	0.744078	−	0.668092i	$-0.232889\pi$
$510$	−0.650704			−0.0288137
$511$	−0.000749634		0.0200314i	−3.31619e−5		0.000886137i
$512$	−22.2598			−0.983755
$513$	11.6026	−	20.0962i	0.512266	−	0.887270i
$514$	0.172613	+	0.298975i	0.00761364	+	0.0131872i
$515$	0.619523	+	1.07305i	0.0272995	+	0.0472840i
$516$	−3.16850	+	5.48800i	−0.139485	+	0.241596i
$517$	0.0740598			0.00325714
$518$	0.0375565	−	1.00357i	0.00165014	−	0.0440943i
$519$	−11.8736			−0.521195
$520$	4.10613	−	7.11202i	0.180066	−	0.311883i
$521$	−8.69893	−	15.0670i	−0.381107	−	0.660096i	0.610114	−	0.792314i	$-0.291124\pi$
$521$	−8.69893	−	15.0670i	−0.381107	−	0.660096i	−0.991221	+	0.132217i	$0.957790\pi$
$522$	−0.514052	−	0.890364i	−0.0224994	−	0.0389702i
$523$	11.1040	−	19.2328i	0.485546	−	0.840990i	−0.514316	−	0.857601i	$-0.671954\pi$
$523$	11.1040	−	19.2328i	0.485546	−	0.840990i	0.999862	+	0.0166106i	$0.00528756\pi$
$524$	−13.7775			−0.601875
$525$	1.46796	−	0.775830i	0.0640671	−	0.0338600i
$526$	10.5610			0.460480
$527$	−2.90286	+	5.02791i	−0.126451	+	0.219019i
$528$	−0.386749	−	0.669868i	−0.0168311	−	0.0291523i
$529$	9.72632	+	16.8465i	0.422884	+	0.732456i
$530$	1.32640	−	2.29739i	0.0576150	−	0.0997920i
$531$	−17.1245			−0.743140
$532$	27.4228	+	17.2311i	1.18893	+	0.747062i
$533$	50.8166			2.20111
$534$	0.662693	−	1.14782i	0.0286775	−	0.0496709i
$535$	−6.08099	−	10.5326i	−0.262904	−	0.455363i
$536$	−7.41458	−	12.8424i	−0.320261	−	0.554708i
$537$	3.98420	−	6.90084i	0.171931	−	0.297793i
$538$	−3.62571			−0.156316
$539$	1.53989	−	2.25854i	0.0663276	−	0.0972823i
$540$	6.52951			0.280986
$541$	20.3414	−	35.2323i	0.874545	−	1.51476i	0.0172980	−	0.999850i	$-0.494494\pi$
$541$	20.3414	−	35.2323i	0.874545	−	1.51476i	0.857247	−	0.514906i	$-0.172173\pi$
$542$	2.11823	+	3.66889i	0.0909860	+	0.157592i
$543$	3.08459	+	5.34267i	0.132372	+	0.229276i
$544$	5.63446	−	9.75918i	0.241576	−	0.418421i
$545$	−1.72912			−0.0740673
$546$	−2.99419	−	1.88140i	−0.128139	−	0.0805164i
$547$	−35.5004			−1.51789			−0.758944	−	0.651156i	$-0.774284\pi$
$547$	−35.5004			−1.51789			−0.758944	+	0.651156i	$0.774284\pi$
$548$	6.71748	−	11.6350i	0.286956	−	0.497023i
$549$	−5.76826	−	9.99092i	−0.246183	−	0.426402i
$550$	0.0741140	+	0.128369i	0.00316023	+	0.00547368i
$551$	−3.42740	+	5.93643i	−0.146012	+	0.252900i
$552$	−1.72997			−0.0736323
$553$	−3.15657	+	1.66827i	−0.134231	+	0.0709422i
$554$	9.26385			0.393583
$555$	−0.313780	+	0.543483i	−0.0133192	+	0.0230696i
$556$	14.3053	+	24.7776i	0.606681	+	1.05080i
$557$	8.38325	+	14.5202i	0.355210	+	0.615242i	0.987154	−	0.159772i	$-0.0510761\pi$
$557$	8.38325	+	14.5202i	0.355210	+	0.615242i	−0.631944	+	0.775014i	$0.717743\pi$
$558$	−1.05125	+	1.82081i	−0.0445029	+	0.0770812i
$559$	30.5282			1.29121
$560$	−0.312290	+	8.34489i	−0.0131967	+	0.352636i
$561$	0.669437			0.0282636
$562$	−5.18554	+	8.98162i	−0.218739	+	0.378867i
$563$	−9.51736	−	16.4845i	−0.401109	−	0.694741i	0.592751	−	0.805386i	$-0.298042\pi$
$563$	−9.51736	−	16.4845i	−0.401109	−	0.694741i	−0.993860	+	0.110645i	$0.964708\pi$
$564$	0.110443	+	0.191293i	0.00465050	+	0.00805490i
$565$	−3.38296	+	5.85945i	−0.142322	+	0.246509i
$566$	−4.89808			−0.205882
$567$	−0.555129	+	14.8339i	−0.0233132	+	0.622966i
$568$	−10.4780			−0.439647
$569$	−10.2347	+	17.7270i	−0.429062	+	0.743157i	−0.996790	−	0.0800593i	$-0.974489\pi$
$569$	−10.2347	+	17.7270i	−0.429062	+	0.743157i	0.567728	+	0.823216i	$0.307822\pi$
$570$	0.785579	+	1.36066i	0.0329043	+	0.0569919i
$571$	9.00268	+	15.5931i	0.376751	+	0.652551i	0.990587	−	0.136882i	$-0.0437080\pi$
$571$	9.00268	+	15.5931i	0.376751	+	0.652551i	−0.613837	+	0.789433i	$0.710375\pi$
$572$	−2.03324	+	3.52168i	−0.0850142	+	0.147249i
$573$	9.38073			0.391886
$574$	8.04146	−	4.24998i	0.335644	−	0.177391i
$575$	−1.88344			−0.0785450
$576$	−6.18532	+	10.7133i	−0.257722	+	0.446387i
$577$	−20.6932	−	35.8416i	−0.861468	−	1.49211i	−0.870512	−	0.492148i	$-0.836212\pi$
$577$	−20.6932	−	35.8416i	−0.861468	−	1.49211i	0.00904305	−	0.999959i	$-0.497121\pi$
$578$	−1.81022	−	3.13540i	−0.0752953	−	0.130415i
$579$	−5.10958	+	8.85005i	−0.212347	+	0.367796i
$580$	−1.92882			−0.0800899
$581$	−25.8852	−	16.2650i	−1.07390	−	0.674785i
$582$	3.62461			0.150245
$583$	−1.36458	+	2.36352i	−0.0565151	+	0.0978871i
$584$	−0.00554455	−	0.00960344i	−0.000229435	−	0.000397393i
$585$	−7.31147	−	12.6638i	−0.302292	−	0.523585i
$586$	2.46871	−	4.27594i	0.101982	−	0.176637i
$587$	−15.4408			−0.637309			−0.318655	−	0.947871i	$-0.603231\pi$
$587$	−15.4408			−0.637309			−0.318655	+	0.947871i	$0.603231\pi$
$588$	8.13011	+	0.609359i	0.335280	+	0.0251295i
$589$	14.0182			0.577611
$590$	1.24706	−	2.15997i	0.0513407	−	0.0889247i
$591$	2.74461	+	4.75381i	0.112898	+	0.195546i
$592$	−1.57814	−	2.73342i	−0.0648611	−	0.112343i
$593$	−4.27749	+	7.40884i	−0.175656	+	0.304245i	−0.940388	−	0.340104i	$-0.889538\pi$
$593$	−4.27749	+	7.40884i	−0.175656	+	0.304245i	0.764732	+	0.644348i	$0.222871\pi$
$594$	0.521497			0.0213973
$595$	−6.11949	−	3.84518i	−0.250875	−	0.157637i
$596$	19.6070			0.803133
$597$	−2.99758	+	5.19196i	−0.122683	+	0.212493i
$598$	2.00566	+	3.47390i	0.0820174	+	0.142058i
$599$	−22.2221	−	38.4899i	−0.907972	−	1.57265i	−0.816878	−	0.576811i	$-0.804297\pi$
$599$	−22.2221	−	38.4899i	−0.907972	−	1.57265i	−0.0910936	−	0.995842i	$-0.529036\pi$
$600$	−0.459257	+	0.795456i	−0.0187491	+	0.0324744i
$601$	−38.4364			−1.56785			−0.783926	−	0.620854i	$-0.786786\pi$
$601$	−38.4364			−1.56785			−0.783926	+	0.620854i	$0.786786\pi$
$602$	4.83093	−	2.55318i	0.196894	−	0.104060i
$603$	−26.4051			−1.07530
$604$	−16.6701	+	28.8734i	−0.678296	+	1.17484i
$605$	5.42375	+	9.39421i	0.220507	+	0.381929i
$606$	−2.09652	−	3.63128i	−0.0851653	−	0.147511i
$607$	21.1565	−	36.6442i	0.858717	−	1.48734i	−0.0144357	−	0.999896i	$-0.504595\pi$
$607$	21.1565	−	36.6442i	0.858717	−	1.48734i	0.873153	−	0.487446i	$-0.162071\pi$
$608$	−27.2094			−1.10349
$609$	−0.0645314	+	1.72438i	−0.00261494	+	0.0698754i
$610$	1.68025			0.0680314
$611$	0.532055	−	0.921546i	0.0215246	−	0.0372818i
$612$	−6.60629	−	11.4424i	−0.267043	−	0.462533i
$613$	17.0125	+	29.4664i	0.687126	+	1.19014i	0.972763	+	0.231800i	$0.0744615\pi$
$613$	17.0125	+	29.4664i	0.687126	+	1.19014i	−0.285637	+	0.958338i	$0.592205\pi$
$614$	3.02366	−	5.23714i	0.122025	−	0.211354i
$615$	−5.68367			−0.229188
$616$	−0.0565511	+	1.51114i	−0.00227851	+	0.0608854i
$617$	−38.6719			−1.55687			−0.778437	−	0.627723i	$-0.783987\pi$
$617$	−38.6719			−1.55687			−0.778437	+	0.627723i	$0.783987\pi$
$618$	−0.147576	+	0.255609i	−0.00593637	+	0.0102821i
$619$	−14.2752	−	24.7254i	−0.573770	−	0.993799i	−0.996174	−	0.0873913i	$-0.972147\pi$
$619$	−14.2752	−	24.7254i	−0.573770	−	0.993799i	0.422404	−	0.906408i	$-0.361186\pi$
$620$	1.97224	+	3.41602i	0.0792071	+	0.137191i
$621$	−3.31317	+	5.73858i	−0.132953	+	0.230281i
$622$	10.5413			0.422669
$623$	13.0150	−	6.87853i	0.521434	−	0.275582i
$624$	−11.1138			−0.444908
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−5.70326	−	9.87833i	−0.227948	−	0.394818i
$627$	−0.808195	−	1.39983i	−0.0322762	−	0.0559040i
$628$	−10.7714	+	18.6566i	−0.429824	+	0.744478i
$629$	2.73166			0.108918
$630$	−2.21612	−	1.39250i	−0.0882925	−	0.0554785i
$631$	26.6796			1.06210			0.531049	−	0.847341i	$-0.321798\pi$
$631$	26.6796			1.06210			0.531049	+	0.847341i	$0.321798\pi$
$632$	0.987544	−	1.71048i	0.0392824	−	0.0680391i
$633$	0.920806	+	1.59488i	0.0365988	+	0.0633909i
$634$	0.288701	+	0.500045i	0.0114658	+	0.0198593i
$635$	−2.15274	+	3.72866i	−0.0854289	+	0.147967i
$636$	−8.13984			−0.322766
$637$	−17.0409	−	35.3869i	−0.675187	−	1.40208i
$638$	−0.154050			−0.00609891
$639$	−9.32868	+	16.1577i	−0.369037	+	0.639190i
$640$	−5.02618	−	8.70560i	−0.198677	−	0.344119i
$641$	8.08283	+	13.9999i	0.319253	+	0.552962i	0.980332	−	0.197354i	$-0.0632348\pi$
$641$	8.08283	+	13.9999i	0.319253	+	0.552962i	−0.661080	+	0.750316i	$0.729901\pi$
$642$	1.44855	−	2.50895i	0.0571695	−	0.0990205i
$643$	10.0326			0.395647			0.197823	−	0.980238i	$-0.436613\pi$
$643$	10.0326			0.395647			0.197823	+	0.980238i	$0.436613\pi$
$644$	−7.83071	−	4.92042i	−0.308573	−	0.193892i
$645$	−3.41448			−0.134445
$646$	3.41948	−	5.92272i	0.134538	−	0.233026i
$647$	−5.32980	−	9.23148i	−0.209536	−	0.362927i	0.742032	−	0.670364i	$-0.233862\pi$
$647$	−5.32980	−	9.23148i	−0.209536	−	0.362927i	−0.951568	+	0.307437i	$0.900529\pi$
$648$	−4.10592	−	7.11166i	−0.161296	−	0.279373i
$649$	−1.28296	+	2.22215i	−0.0503606	+	0.0872272i
$650$	2.12978			0.0835368
$651$	3.11993	−	1.64891i	0.122280	−	0.0646259i
$652$	7.16720			0.280689
$653$	−15.7969	+	27.3610i	−0.618179	+	1.07072i	0.371639	+	0.928377i	$0.378796\pi$
$653$	−15.7969	+	27.3610i	−0.618179	+	1.07072i	−0.989818	+	0.142340i	$0.954537\pi$
$654$	−0.205946	−	0.356708i	−0.00805311	−	0.0139484i
$655$	−3.71178	−	6.42900i	−0.145031	−	0.251202i
$656$	14.2928	−	24.7559i	0.558042	−	0.966557i
$657$	−0.0197455			−0.000770346
$658$	0.00712262	−	0.190328i	0.000277669	−	0.00741974i
$659$	−2.67426			−0.104174			−0.0520871	−	0.998643i	$-0.516587\pi$
$659$	−2.67426			−0.104174			−0.0520871	+	0.998643i	$0.516587\pi$
$660$	0.227412	−	0.393889i	0.00885199	−	0.0153321i
$661$	10.7230	+	18.5727i	0.417076	+	0.722396i	0.995644	−	0.0932379i	$-0.0297217\pi$
$661$	10.7230	+	18.5727i	0.417076	+	0.722396i	−0.578568	+	0.815634i	$0.696388\pi$
$662$	1.05929	+	1.83474i	0.0411705	+	0.0713094i
$663$	4.80932	−	8.32999i	0.186779	−	0.323510i
$664$	16.9119			0.656310
$665$	−0.652598	+	17.4384i	−0.0253067	+	0.676234i
$666$	0.989247			0.0383325
$667$	0.978711	−	1.69518i	0.0378958	−	0.0656375i
$668$	−19.2348	−	33.3157i	−0.744218	−	1.28902i
$669$	1.11460	+	1.93054i	0.0430928	+	0.0746389i
$670$	1.92291	−	3.33057i	0.0742884	−	0.128671i
$671$	−1.72862			−0.0667328
$672$	−6.05580	+	3.20054i	−0.233607	+	0.123463i
$673$	−0.232291			−0.00895417			−0.00447708	−	0.999990i	$-0.501425\pi$
$673$	−0.232291			−0.00895417			−0.00447708	+	0.999990i	$0.501425\pi$
$674$	−1.44525	+	2.50325i	−0.0556691	+	0.0964216i
$675$	1.75910	+	3.04686i	0.0677080	+	0.117274i
$676$	17.1507	+	29.7059i	0.659642	+	1.14253i
$677$	5.13468	−	8.89352i	0.197342	−	0.341806i	−0.750324	−	0.661070i	$-0.770103\pi$
$677$	5.13468	−	8.89352i	0.197342	−	0.341806i	0.947666	+	0.319265i	$0.103436\pi$
$678$	−1.61170			−0.0618970
$679$	34.0873	+	21.4187i	1.30815	+	0.821976i
$680$	3.99812			0.153321
$681$	8.11386	−	14.0536i	0.310924	−	0.538536i
$682$	0.157518	+	0.272829i	0.00603168	+	0.0104472i
$683$	−3.50847	−	6.07685i	−0.134248	−	0.232524i	0.791062	−	0.611736i	$-0.209529\pi$
$683$	−3.50847	−	6.07685i	−0.134248	−	0.232524i	−0.925310	+	0.379212i	$0.876195\pi$
$684$	−15.9512	+	27.6283i	−0.609910	+	1.05640i
$685$	7.23898			0.276587
$686$	−5.65617	−	4.17459i	−0.215954	−	0.159387i
$687$	−16.7089			−0.637484
$688$	8.58646	−	14.8722i	0.327356	−	0.566997i
$689$	19.6066	+	33.9597i	0.746954	+	1.29376i
$690$	−0.224326	−	0.388544i	−0.00853995	−	0.0147916i
$691$	−1.47283	+	2.55102i	−0.0560292	+	0.0970453i	−0.892680	−	0.450692i	$-0.851177\pi$
$691$	−1.47283	+	2.55102i	−0.0560292	+	0.0970453i	0.836650	+	0.547737i	$0.184511\pi$
$692$	35.1146			1.33486
$693$	2.27992	+	1.43259i	0.0866071	+	0.0544195i
$694$	10.3826			0.394116
$695$	−7.70795	+	13.3506i	−0.292379	+	0.506416i
$696$	−0.477296	−	0.826701i	−0.0180919	−	0.0313360i
$697$	12.3700	+	21.4255i	0.468547	+	0.811547i
$698$	1.91715	−	3.32060i	0.0725652	−	0.125687i
$699$	−5.04933			−0.190983
$700$	−4.34129	+	2.29441i	−0.164085	+	0.0867204i
$701$	−33.7709			−1.27551			−0.637755	−	0.770239i	$-0.720137\pi$
$701$	−33.7709			−1.27551			−0.637755	+	0.770239i	$0.720137\pi$
$702$	3.74650	−	6.48913i	0.141403	−	0.244916i
$703$	−3.29786	−	5.71206i	−0.124381	−	0.215435i
$704$	0.926803	+	1.60527i	0.0349302	+	0.0605009i
$705$	−0.0595086	+	0.103072i	−0.00224122	+	0.00388191i
$706$	−1.96721			−0.0740370
$707$	1.74162	−	46.5390i	0.0655005	−	1.75028i
$708$	−7.65297			−0.287616
$709$	20.9877	−	36.3517i	0.788209	−	1.36522i	−0.138855	−	0.990313i	$-0.544342\pi$
$709$	20.9877	−	36.3517i	0.788209	−	1.36522i	0.927063	−	0.374905i	$-0.122325\pi$
$710$	−1.35869	−	2.35332i	−0.0509907	−	0.0883184i
$711$	−1.75844	−	3.04572i	−0.0659468	−	0.114223i
$712$	−4.07178	+	7.05254i	−0.152597	+	0.264305i
$713$	−4.00297			−0.149913
$714$	0.0643824	−	1.72040i	0.00240945	−	0.0643843i
$715$	−2.19109			−0.0819421
$716$	−11.7827	+	20.4082i	−0.440340	+	0.762691i
$717$	−3.95158	−	6.84435i	−0.147575	−	0.255607i
$718$	−1.07906	−	1.86899i	−0.0402703	−	0.0697502i
$719$	−0.323198	+	0.559795i	−0.0120532	+	0.0208768i	−0.871989	−	0.489525i	$-0.837170\pi$
$719$	−0.323198	+	0.559795i	−0.0120532	+	0.0208768i	0.859936	+	0.510402i	$0.170503\pi$
$720$	−8.22579			−0.306557
$721$	−2.89832	+	1.53179i	−0.107939	+	0.0570468i
$722$	−9.30104			−0.346149
$723$	−2.94080	+	5.09362i	−0.109370	+	0.189434i
$724$	−9.12223	−	15.8002i	−0.339025	−	0.587209i
$725$	−0.519640	−	0.900042i	−0.0192989	−	0.0334267i
$726$	−1.29199	+	2.23778i	−0.0479501	+	0.0830520i
$727$	−2.31066			−0.0856975			−0.0428488	−	0.999082i	$-0.513643\pi$
$727$	−2.31066			−0.0856975			−0.0428488	+	0.999082i	$0.513643\pi$
$728$	18.3972	+	11.5599i	0.681846	+	0.428437i
$729$	−7.99854			−0.296242
$730$	0.00143793	−	0.00249057i	5.32202e−5	−	9.21802e-5i
$731$	7.43131	+	12.8714i	0.274857	+	0.476066i
$732$	−2.57785	−	4.46496i	−0.0952800	−	0.165030i
$733$	−12.1894	+	21.1126i	−0.450224	+	0.779811i	−0.998400	−	0.0565520i	$-0.981989\pi$
$733$	−12.1894	+	21.1126i	−0.450224	+	0.779811i	0.548175	+	0.836363i	$0.315323\pi$
$734$	−13.2906			−0.490566
$735$	1.90597	+	3.95791i	0.0703029	+	0.145990i
$736$	7.76978			0.286398
$737$	−1.97826	+	3.42645i	−0.0728703	+	0.126215i
$738$	4.47969	+	7.75905i	0.164900	+	0.285615i
$739$	−16.4247	−	28.4485i	−0.604194	−	1.04649i	−0.992178	−	0.124829i	$-0.960162\pi$
$739$	−16.4247	−	28.4485i	−0.604194	−	1.04649i	0.387984	−	0.921666i	$-0.373171\pi$
$740$	0.927960	−	1.60727i	0.0341125	−	0.0590846i
$741$	−23.2247			−0.853181
$742$	5.94282	+	3.73417i	0.218168	+	0.137086i
$743$	17.3661			0.637100			0.318550	−	0.947906i	$-0.396804\pi$
$743$	17.3661			0.637100			0.318550	+	0.947906i	$0.396804\pi$
$744$	−0.976082	+	1.69062i	−0.0357849	+	0.0619813i
$745$	5.28228	+	9.14917i	0.193528	+	0.335200i
$746$	0.130800	+	0.226552i	0.00478893	+	0.00829467i
$747$	15.0569	−	26.0793i	0.550903	−	0.954192i
$748$	−1.97976			−0.0723873
$749$	28.4488	−	15.0354i	1.03950	−	0.549382i
$750$	−0.238209			−0.00869815
$751$	−1.41771	+	2.45554i	−0.0517330	+	0.0896041i	−0.890732	−	0.454528i	$-0.849808\pi$
$751$	−1.41771	+	2.45554i	−0.0517330	+	0.0896041i	0.838999	+	0.544133i	$0.183141\pi$
$752$	−0.299295	−	0.518394i	−0.0109142	−	0.0189039i
$753$	2.91931	+	5.05640i	0.106386	+	0.184265i
$754$	−1.10672	+	1.91689i	−0.0403043	+	0.0698090i
$755$	−17.9642			−0.653785
$756$	−0.646047	+	17.2634i	−0.0234965	+	0.627863i
$757$	−9.26175			−0.336624			−0.168312	−	0.985734i	$-0.553832\pi$
$757$	−9.26175			−0.336624			−0.168312	+	0.985734i	$0.553832\pi$
$758$	−6.32741	+	10.9594i	−0.229822	+	0.398063i
$759$	0.230784	+	0.399730i	0.00837693	+	0.0145093i
$760$	−4.82684	−	8.36033i	−0.175088	−	0.303261i
$761$	−13.6533	+	23.6482i	−0.494931	+	0.857246i	−0.999983	−	0.00584327i	$-0.998140\pi$
$761$	−13.6533	+	23.6482i	−0.494931	+	0.857246i	0.505052	+	0.863089i	$0.331473\pi$
$762$	−1.02560			−0.0371537
$763$	0.171083	−	4.57162i	0.00619364	−	0.165504i
$764$	−27.7422			−1.00368
$765$	3.55958	−	6.16537i	0.128697	−	0.222909i
$766$	3.32789	+	5.76408i	0.120242	+	0.208265i
$767$	18.4339	+	31.9285i	0.665610	+	1.15287i
$768$	−1.78155	+	3.08573i	−0.0642860	+	0.111347i
$769$	−48.3748			−1.74444			−0.872221	−	0.489112i	$-0.837321\pi$
$769$	−48.3748			−1.74444			−0.872221	+	0.489112i	$0.837321\pi$
$770$	−0.346728	+	0.183249i	−0.0124952	+	0.00660383i
$771$	0.570765			0.0205556
$772$	15.1108	−	26.1728i	0.543851	−	0.941978i
$773$	3.91660	+	6.78375i	0.140870	+	0.243994i	0.927825	−	0.373017i	$-0.121677\pi$
$773$	3.91660	+	6.78375i	0.140870	+	0.243994i	−0.786954	+	0.617011i	$0.788343\pi$
$774$	2.69119	+	4.66127i	0.0967327	+	0.167546i
$775$	−1.06268	+	1.84061i	−0.0381724	+	0.0661166i
$776$	−22.2707			−0.799471
$777$	−1.40587	−	0.883377i	−0.0504353	−	0.0316910i
$778$	2.85704			0.102430
$779$	29.8680	−	51.7329i	1.07013	−	1.85352i
$780$	−3.26751	−	5.65949i	−0.116996	−	0.202642i
$781$	1.39780	+	2.42106i	0.0500173	+	0.0866325i
$782$	−0.976451	+	1.69126i	−0.0349178	+	0.0604794i
$783$	−3.65640			−0.130669
$784$	−22.0321	−	1.65133i	−0.786862	−	0.0589760i
$785$	−11.6076			−0.414292
$786$	0.884179	−	1.53144i	0.0315376	−	0.0546248i
$787$	−18.2320	−	31.5787i	−0.649900	−	1.12566i	−0.983146	−	0.182820i	$-0.941477\pi$
$787$	−18.2320	−	31.5787i	−0.649900	−	1.12566i	0.333247	−	0.942840i	$-0.391856\pi$
$788$	−8.11680	−	14.0587i	−0.289149	−	0.500821i
$789$	8.73025	−	15.1212i	0.310805	−	0.538330i
$790$	0.512222			0.0182240
$791$	−15.1571	−	9.52395i	−0.538924	−	0.338633i
$792$	−1.48957			−0.0529295
$793$	−12.4187	+	21.5097i	−0.440999	+	0.763833i
$794$	5.17275	+	8.95947i	0.183574	+	0.317960i
$795$	−2.19294	−	3.79828i	−0.0777755	−	0.134711i
$796$	8.86490	−	15.3545i	0.314208	−	0.544225i
$797$	4.65973			0.165056			0.0825280	−	0.996589i	$-0.473701\pi$
$797$	4.65973			0.165056			0.0825280	+	0.996589i	$0.473701\pi$
$798$	−3.67519	+	1.94237i	−0.130100	+	0.0687590i
$799$	0.518060			0.0183277
$800$	2.06265	−	3.57262i	0.0729258	−	0.126311i
$801$	7.25032	+	12.5579i	0.256177	+	0.443712i
$802$	−6.40142	−	11.0876i	−0.226042	−	0.391516i
$803$	−0.00147933	+	0.00256227i	−5.22043e−5	+	9.04205e-5i
$804$	−11.8005			−0.416172
$805$	0.186353	−	4.97963i	0.00656806	−	0.175509i
$806$	4.52652			0.159440
$807$	−2.99721	+	5.19132i	−0.105507	+	0.182743i
$808$	12.8817	+	22.3117i	0.453175	+	0.784922i
$809$	−7.48427	−	12.9631i	−0.263133	−	0.455759i	0.703940	−	0.710259i	$-0.251422\pi$
$809$	−7.48427	−	12.9631i	−0.263133	−	0.455759i	−0.967073	+	0.254500i	$0.918089\pi$
$810$	1.06484	−	1.84435i	0.0374145	−	0.0648038i
$811$	−37.4641			−1.31554			−0.657771	−	0.753218i	$-0.728500\pi$
$811$	−37.4641			−1.31554			−0.657771	+	0.753218i	$0.728500\pi$
$812$	0.190842	−	5.09961i	0.00669725	−	0.178961i
$813$	7.00418			0.245647
$814$	0.0741140	−	0.128369i	0.00259769	−	0.00449934i
$815$	1.93090	+	3.34442i	0.0676366	+	0.117150i
$816$	−2.70537	−	4.68584i	−0.0947069	−	0.164037i
$817$	17.9433	−	31.0786i	0.627755	−	1.08730i
$818$	−11.9931			−0.419329
$819$	34.2053	−	18.0778i	1.19523	−	0.631690i
$820$	16.8086			0.586983
$821$	25.9075	−	44.8731i	0.904178	−	1.56608i	0.0821611	−	0.996619i	$-0.473818\pi$
$821$	25.9075	−	44.8731i	0.904178	−	1.56608i	0.822017	−	0.569463i	$-0.192849\pi$
$822$	0.862194	+	1.49336i	0.0300725	+	0.0520870i
$823$	10.2048	+	17.6752i	0.355715	+	0.616117i	0.987240	−	0.159239i	$-0.0509039\pi$
$823$	10.2048	+	17.6752i	0.355715	+	0.616117i	−0.631525	+	0.775356i	$0.717571\pi$
$824$	0.906750	−	1.57054i	0.0315881	−	0.0547123i
$825$	0.245066			0.00853211
$826$	5.58737	+	3.51082i	0.194409	+	0.122157i
$827$	−55.1680			−1.91838			−0.959190	−	0.282761i	$-0.908750\pi$
$827$	−55.1680			−1.91838			−0.959190	+	0.282761i	$0.908750\pi$
$828$	4.55495	−	7.88941i	0.158296	−	0.274176i
$829$	22.4399	+	38.8671i	0.779372	+	1.34991i	0.932304	+	0.361675i	$0.117795\pi$
$829$	22.4399	+	38.8671i	0.779372	+	1.34991i	−0.152933	+	0.988237i	$0.548872\pi$
$830$	2.19298	+	3.79836i	0.0761195	+	0.131843i
$831$	7.65799	−	13.2640i	0.265653	−	0.460124i
$832$	26.6331			0.923336
$833$	10.7718	−	15.7989i	0.373219	−	0.547399i
$834$	−3.67220			−0.127158
$835$	10.3640	−	17.9511i	0.358663	−	0.621222i
$836$	2.39012	+	4.13981i	0.0826640	+	0.143178i
$837$	3.73871	+	6.47564i	0.129229	+	0.223831i
$838$	0.843452	−	1.46090i	0.0291366	−	0.0504660i
$839$	−27.0715			−0.934612			−0.467306	−	0.884096i	$-0.654775\pi$
$839$	−27.0715			−0.934612			−0.467306	+	0.884096i	$0.654775\pi$
$840$	−2.05767	−	1.29293i	−0.0709963	−	0.0446105i
$841$	−27.9199			−0.962755
$842$	2.60274	−	4.50807i	0.0896963	−	0.155358i
$843$	8.57329	+	14.8494i	0.295280	+	0.511440i
$844$	−2.72315	−	4.71664i	−0.0937348	−	0.162353i
$845$	−9.24107	+	16.0060i	−0.317903	+	0.550623i
$846$	0.187611			0.00645021
$847$	−25.3740	+	13.4104i	−0.871861	+	0.460786i
$848$	22.0585			0.757493
$849$	−4.04902	+	7.01310i	−0.138962	+	0.240689i
$850$	0.518440	+	0.897964i	0.0177823	+	0.0307999i
$851$	0.941721	+	1.63111i	0.0322818	+	0.0559137i
$852$	−4.16900	+	7.22093i	−0.142828	+	0.247385i
$853$	−51.0117			−1.74661			−0.873303	−	0.487177i	$-0.838026\pi$
$853$	−51.0117			−1.74661			−0.873303	+	0.487177i	$0.838026\pi$
$854$	−0.166248	+	4.44242i	−0.00568891	+	0.152016i
$855$	−17.1896			−0.587871
$856$	−8.90030	+	15.4158i	−0.304206	+	0.526900i
$857$	10.9192	+	18.9126i	0.372992	+	0.646041i	0.990024	−	0.140897i	$-0.0449986\pi$
$857$	10.9192	+	18.9126i	0.372992	+	0.646041i	−0.617033	+	0.786938i	$0.711665\pi$
$858$	−0.260968	−	0.452010i	−0.00890931	−	0.0154314i
$859$	2.22433	−	3.85265i	0.0758930	−	0.131451i	−0.825581	−	0.564283i	$-0.809153\pi$
$859$	2.22433	−	3.85265i	0.0758930	−	0.131451i	0.901474	+	0.432833i	$0.142486\pi$
$860$	10.0978			0.344333
$861$	0.562357	−	15.0271i	0.0191651	−	0.512121i
$862$	−2.11015			−0.0718720
$863$	−20.5255	+	35.5511i	−0.698695	+	1.21017i	0.270225	+	0.962797i	$0.412902\pi$
$863$	−20.5255	+	35.5511i	−0.698695	+	1.21017i	−0.968919	+	0.247377i	$0.920431\pi$
$864$	−7.25685	−	12.5692i	−0.246883	−	0.427614i
$865$	9.46016	+	16.3855i	0.321655	+	0.557123i
$866$	0.526975	−	0.912747i	0.0179073	−	0.0310164i
$867$	−5.98570			−0.203285
$868$	−9.22675	+	4.87642i	−0.313176	+	0.165516i
$869$	−0.526968			−0.0178762
$870$	0.123783	−	0.214398i	0.00419663	−	0.00726877i
$871$	28.4242	+	49.2322i	0.963118	+	1.66817i
$872$	1.26539	+	2.19172i	0.0428516	+	0.0742211i
$873$	−19.8279	+	34.3428i	−0.671071	+	1.16233i
$874$	4.71538			0.159500
$875$	−2.24021	−	1.40764i	−0.0757330	−	0.0475868i
$876$	−0.00882431			−0.000298146
$877$	12.7474	−	22.0792i	0.430449	−	0.745560i	−0.566463	−	0.824087i	$-0.691688\pi$
$877$	12.7474	−	22.0792i	0.430449	−	0.745560i	0.996912	+	0.0785273i	$0.0250218\pi$
$878$	3.20742	+	5.55542i	0.108245	+	0.187486i
$879$	−4.08154	−	7.06943i	−0.137667	−	0.238446i
$880$	−0.616273	+	1.06742i	−0.0207746	+	0.0359826i
$881$	20.9833			0.706946			0.353473	−	0.935445i	$-0.385001\pi$
$881$	20.9833			0.706946			0.353473	+	0.935445i	$0.385001\pi$
$882$	3.90090	−	5.72143i	0.131350	−	0.192651i
$883$	28.9427			0.974000			0.487000	−	0.873402i	$-0.338091\pi$
$883$	28.9427			0.974000			0.487000	+	0.873402i	$0.338091\pi$
$884$	−14.2229	+	24.6347i	−0.478367	+	0.828556i
$885$	−2.06177	−	3.57110i	−0.0693058	−	0.120041i
$886$	−3.12067	−	5.40516i	−0.104841	−	0.181590i
$887$	−18.4323	+	31.9256i	−0.618895	+	1.07196i	0.370792	+	0.928716i	$0.379086\pi$
$887$	−18.4323	+	31.9256i	−0.618895	+	1.07196i	−0.989688	+	0.143243i	$0.954247\pi$
$888$	0.918514			0.0308233
$889$	−9.64520	−	6.06055i	−0.323489	−	0.203264i
$890$	−2.11196			−0.0707932
$891$	−1.09549	+	1.89744i	−0.0367003	+	0.0635668i
$892$	−3.29626	−	5.70929i	−0.110367	−	0.191161i
$893$	−0.625442	−	1.08330i	−0.0209296	−	0.0362511i
$894$	−1.25828	+	2.17941i	−0.0420833	+	0.0728905i
$895$	−12.6974			−0.424428
$896$	23.5140	−	12.4274i	0.785549	−	0.415169i
$897$	6.63193			0.221434
$898$	−0.703125	+	1.21785i	−0.0234636	+	0.0406401i
$899$	−1.10442	−	1.91291i	−0.0368343	−	0.0637990i
$900$	−2.41842	−	4.18883i	−0.0806140	−	0.139628i
$901$	−9.54547	+	16.5332i	−0.318006	+	0.550802i
$902$	1.34247			0.0446993
$903$	0.337837	−	9.02755i	0.0112425	−	0.300418i
$904$	9.90277			0.329361
$905$	4.91521	−	8.51339i	0.163387	−	0.282995i
$906$	−2.13962	−	3.70593i	−0.0710840	−	0.123121i
$907$	−2.16283	−	3.74614i	−0.0718157	−	0.124388i	0.827881	−	0.560903i	$-0.189546\pi$
$907$	−2.16283	−	3.74614i	−0.0718157	−	0.124388i	−0.899697	+	0.436515i	$0.856213\pi$
$908$	−23.9956	+	41.5616i	−0.796321	+	1.37927i
$909$	45.8748			1.52157
$910$	−0.210726	+	5.63092i	−0.00698549	+	0.186663i
$911$	−23.0427			−0.763438			−0.381719	−	0.924278i	$-0.624668\pi$
$911$	−23.0427			−0.763438			−0.381719	+	0.924278i	$0.624668\pi$
$912$	−6.53226	+	11.3142i	−0.216305	+	0.374651i
$913$	−2.25611	−	3.90770i	−0.0746664	−	0.129326i
$914$	2.56692	+	4.44604i	0.0849063	+	0.147062i
$915$	1.38899	−	2.40579i	0.0459185	−	0.0795331i
$916$	49.4142			1.63269
$917$	17.3649	−	9.17748i	0.573439	−	0.303067i
$918$	3.64796			0.120401
$919$	−8.84248	+	15.3156i	−0.291687	+	0.505216i	−0.974209	−	0.225649i	$-0.927550\pi$
$919$	−8.84248	+	15.3156i	−0.291687	+	0.505216i	0.682522	+	0.730865i	$0.260883\pi$
$920$	1.37833	+	2.38733i	0.0454421	+	0.0787080i
$921$	−4.99904	−	8.65860i	−0.164724	−	0.285311i
$922$	−2.66313	+	4.61268i	−0.0877056	+	0.151911i
$923$	40.1680			1.32214
$924$	1.01890	+	0.640226i	0.0335194	+	0.0210619i
$925$	1.00000			0.0328798
$926$	−1.86218	+	3.22539i	−0.0611950	+	0.105993i
$927$	−1.61458	−	2.79654i	−0.0530298	−	0.0918503i
$928$	2.14367	+	3.71295i	0.0703696	+	0.121884i
$929$	0.638091	−	1.10521i	0.0209351	−	0.0362606i	−0.855368	−	0.518021i	$-0.826669\pi$
$929$	0.638091	−	1.10521i	0.0209351	−	0.0362606i	0.876303	+	0.481760i	$0.160002\pi$
$930$	−0.506277			−0.0166015
$931$	−46.0409	−	3.45081i	−1.50893	−	0.113096i
$932$	14.9327			0.489135
$933$	8.71402	−	15.0931i	0.285284	−	0.494127i
$934$	0.395700	+	0.685372i	0.0129477	+	0.0224261i
$935$	−0.533364	−	0.923814i	−0.0174429	−	0.0302120i
$936$	−10.7013	+	18.5351i	−0.349781	+	0.605839i
$937$	7.60829			0.248552			0.124276	−	0.992248i	$-0.460339\pi$
$937$	7.60829			0.248552			0.124276	+	0.992248i	$0.460339\pi$
$938$	8.61545	+	5.41351i	0.281304	+	0.176757i
$939$	−18.8585			−0.615423
$940$	0.175988	−	0.304821i	0.00574010	−	0.00994215i
$941$	12.3256	+	21.3485i	0.401802	+	0.695941i	0.993943	−	0.109893i	$-0.0350507\pi$
$941$	12.3256	+	21.3485i	0.401802	+	0.695941i	−0.592141	+	0.805834i	$0.701717\pi$
$942$	−1.38251	−	2.39458i	−0.0450447	−	0.0780197i
$943$	−8.52895	+	14.7726i	−0.277741	+	0.481061i
$944$	20.7391			0.675001
$945$	−8.22964	+	4.34943i	−0.267710	+	0.141487i
$946$	0.806490			0.0262213
$947$	−9.37698	+	16.2414i	−0.304711	+	0.527775i	−0.977197	−	0.212335i	$-0.931893\pi$
$947$	−9.37698	+	16.2414i	−0.304711	+	0.527775i	0.672486	+	0.740110i	$0.265227\pi$
$948$	−0.785852	−	1.36114i	−0.0255233	−	0.0442076i
$949$	0.0212554	+	0.0368154i	0.000689978	+	0.00119508i
$950$	1.25180	−	2.16818i	0.0406137	−	0.0703450i
$951$	0.954624			0.0309558
$952$	−0.395585	+	10.5706i	−0.0128210	+	0.342596i
$953$	−42.9712			−1.39198			−0.695988	−	0.718054i	$-0.745033\pi$
$953$	−42.9712			−1.39198			−0.695988	+	0.718054i	$0.745033\pi$
$954$	−3.45681	+	5.98737i	−0.111918	+	0.193848i
$955$	−7.47397	−	12.9453i	−0.241852	−	0.418900i
$956$	11.6862	+	20.2412i	0.377960	+	0.654646i
$957$	−0.127346	+	0.220570i	−0.00411652	+	0.00713002i
$958$	10.3323			0.333820
$959$	−0.716243	+	19.1391i	−0.0231287	+	0.618035i
$960$	−2.97883			−0.0961412
$961$	13.2414	−	22.9349i	0.427143	−	0.739834i
$962$	−1.06489	−	1.84444i	−0.0343334	−	0.0594672i
$963$	15.8481	+	27.4497i	0.510697	+	0.884554i
$964$	8.69700	−	15.0636i	0.280112	−	0.485167i
$965$	16.2839			0.524199
$966$	1.04947	−	0.554652i	0.0337661	−	0.0178457i
$967$	−12.0686			−0.388102			−0.194051	−	0.980991i	$-0.562163\pi$
$967$	−12.0686			−0.388102			−0.194051	+	0.980991i	$0.562163\pi$
$968$	7.93835	−	13.7496i	0.255148	−	0.441929i
$969$	−5.65346	−	9.79207i	−0.181615	−	0.314567i
$970$	−2.88786	−	5.00191i	−0.0927234	−	0.160602i
$971$	−2.43590	+	4.21910i	−0.0781717	+	0.135397i	−0.902461	−	0.430771i	$-0.858242\pi$
$971$	−2.43590	+	4.21910i	−0.0781717	+	0.135397i	0.824289	+	0.566169i	$0.191575\pi$
$972$	−26.1232			−0.837903
$973$	−34.5349	−	21.7000i	−1.10714	−	0.695670i
$974$	10.5126			0.336845
$975$	1.76059	−	3.04943i	0.0563839	−	0.0976598i
$976$	6.98582	+	12.0998i	0.223611	+	0.387305i
$977$	−22.1634	−	38.3881i	−0.709070	−	1.22814i	−0.965203	−	0.261503i	$-0.915782\pi$
$977$	−22.1634	−	38.3881i	−0.709070	−	1.22814i	0.256133	−	0.966642i	$-0.417552\pi$
$978$	−0.459958	+	0.796670i	−0.0147078	+	0.0254747i
$979$	2.17276			0.0694418
$980$	−5.63664	−	11.7049i	−0.180056	−	0.373901i
$981$	4.50637			0.143877
$982$	−5.65989	+	9.80321i	−0.180614	+	0.312833i
$983$	−10.1216	−	17.5312i	−0.322830	−	0.559158i	0.658241	−	0.752807i	$-0.271301\pi$
$983$	−10.1216	−	17.5312i	−0.322830	−	0.559158i	−0.981071	+	0.193650i	$0.937968\pi$
$984$	4.15938	+	7.20427i	0.132596	+	0.229664i
$985$	4.37346	−	7.57506i	0.139350	−	0.241362i
$986$	−1.07761			−0.0343180
$987$	−0.266624	−	0.167533i	−0.00848674	−	0.00533264i
$988$	68.6837			2.18512
$989$	−5.12379	+	8.87466i	−0.162927	+	0.282198i
$990$	−0.193153	−	0.334552i	−0.00613882	−	0.0106327i
$991$	−21.2705	−	36.8416i	−0.675681	−	1.17031i	−0.976269	−	0.216559i	$-0.930516\pi$
$991$	−21.2705	−	36.8416i	−0.675681	−	1.17031i	0.300589	−	0.953754i	$-0.402817\pi$
$992$	4.38386	−	7.59307i	0.139188	−	0.241080i
$993$	3.50266			0.111154
$994$	6.35637	−	3.35939i	0.201612	−	0.106553i
$995$	9.55311			0.302854
$996$	6.72895	−	11.6549i	0.213215	−	0.369299i
$997$	−26.3445	−	45.6301i	−0.834340	−	1.44512i	−0.894567	−	0.446934i	$-0.852516\pi$
$997$	−26.3445	−	45.6301i	−0.834340	−	1.44512i	0.0602268	−	0.998185i	$-0.480818\pi$
$998$	5.80990	+	10.0630i	0.183909	+	0.318540i
$999$	1.75910	−	3.04686i	0.0556556	−	0.0963983i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1295.2.j.a.926.10	yes	38
7.2	even	3		9065.2.a.r.1.10		19
7.4	even	3	inner	1295.2.j.a.186.10	✓	38
7.5	odd	6		9065.2.a.s.1.10		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1295.2.j.a.186.10	✓	38	7.4	even	3	inner
1295.2.j.a.926.10	yes	38	1.1	even	1	trivial
9065.2.a.r.1.10		19	7.2	even	3
9065.2.a.s.1.10		19	7.5	odd	6

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:	\( N \)	\(=\)	\( 1295 = 5 \cdot 7 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1295.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.189789 - 0.328725i) q^{2} +(-0.313780 - 0.543483i) q^{3} +(0.927960 + 1.60727i) q^{4} +(-0.500000 + 0.866025i) q^{5} -0.238209 q^{6} +(-2.24021 - 1.40764i) q^{7} +1.46363 q^{8} +(1.30308 - 2.25701i) q^{9} +(0.189789 + 0.328725i) q^{10} +(-0.195253 - 0.338188i) q^{11} +(0.582351 - 1.00866i) q^{12} -5.61090 q^{13} +(-0.887895 + 0.469260i) q^{14} +0.627560 q^{15} +(-1.57814 + 2.73342i) q^{16} +(-1.36583 - 2.36568i) q^{17} +(-0.494623 - 0.856713i) q^{18} +(-3.29786 + 5.71206i) q^{19} -1.85592 q^{20} +(-0.0620924 + 1.65921i) q^{21} -0.148228 q^{22} +(0.941721 - 1.63111i) q^{23} +(-0.459257 - 0.795456i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.06489 + 1.84444i) q^{26} -3.51821 q^{27} +(0.183629 - 4.90687i) q^{28} +1.03928 q^{29} +(0.119104 - 0.206295i) q^{30} +(-1.06268 - 1.84061i) q^{31} +(2.06265 + 3.57262i) q^{32} +(-0.122533 + 0.212234i) q^{33} -1.03688 q^{34} +(2.33916 - 1.23626i) q^{35} +4.83684 q^{36} +(-0.500000 + 0.866025i) q^{37} +(1.25180 + 2.16818i) q^{38} +(1.76059 + 3.04943i) q^{39} +(-0.731813 + 1.26754i) q^{40} -9.05677 q^{41} +(0.533638 + 0.335311i) q^{42} -5.44088 q^{43} +(0.362374 - 0.627650i) q^{44} +(1.30308 + 2.25701i) q^{45} +(-0.357457 - 0.619135i) q^{46} +(-0.0948253 + 0.164242i) q^{47} +1.98075 q^{48} +(3.03712 + 6.30682i) q^{49} -0.379579 q^{50} +(-0.857140 + 1.48461i) q^{51} +(-5.20669 - 9.01824i) q^{52} +(-3.49439 - 6.05246i) q^{53} +(-0.667719 + 1.15652i) q^{54} +0.390506 q^{55} +(-3.27884 - 2.06025i) q^{56} +4.13921 q^{57} +(0.197244 - 0.341637i) q^{58} +(-3.28538 - 5.69044i) q^{59} +(0.582351 + 1.00866i) q^{60} +(2.21331 - 3.83357i) q^{61} -0.806738 q^{62} +(-6.09623 + 3.22191i) q^{63} -4.74668 q^{64} +(2.80545 - 4.85918i) q^{65} +(0.0465110 + 0.0805594i) q^{66} +(-5.06590 - 8.77439i) q^{67} +(2.53487 - 4.39052i) q^{68} -1.18197 q^{69} +(0.0375565 - 1.00357i) q^{70} -7.15892 q^{71} +(1.90723 - 3.30342i) q^{72} +(-0.00378823 - 0.00656140i) q^{73} +(0.189789 + 0.328725i) q^{74} +(-0.313780 + 0.543483i) q^{75} -12.2411 q^{76} +(-0.0386377 + 1.03246i) q^{77} +1.33656 q^{78} +(0.674724 - 1.16866i) q^{79} +(-1.57814 - 2.73342i) q^{80} +(-2.80531 - 4.85894i) q^{81} +(-1.71888 + 2.97719i) q^{82} +11.5548 q^{83} +(-2.72442 + 1.43988i) q^{84} +2.73166 q^{85} +(-1.03262 + 1.78855i) q^{86} +(-0.326105 - 0.564831i) q^{87} +(-0.285778 - 0.494981i) q^{88} +(-2.78198 + 4.81854i) q^{89} +0.989247 q^{90} +(12.5696 + 7.89810i) q^{91} +3.49552 q^{92} +(-0.666893 + 1.15509i) q^{93} +(0.0359937 + 0.0623429i) q^{94} +(-3.29786 - 5.71206i) q^{95} +(1.29444 - 2.24204i) q^{96} -15.2161 q^{97} +(2.64962 + 0.198591i) q^{98} -1.01772 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 3 q^{2} + q^{3} - 11 q^{4} - 19 q^{5} - 8 q^{6} - 18 q^{8} - 12 q^{9} + 3 q^{10} + 13 q^{11} + 4 q^{12} - 6 q^{13} - q^{14} - 2 q^{15} + 5 q^{16} + 2 q^{17} + 11 q^{18} + 12 q^{19} + 22 q^{20}+ \cdots - 142 q^{99}+O(q^{100}) \) 38 * q + 3 * q^2 + q^3 - 11 * q^4 - 19 * q^5 - 8 * q^6 - 18 * q^8 - 12 * q^9 + 3 * q^10 + 13 * q^11 + 4 * q^12 - 6 * q^13 - q^14 - 2 * q^15 + 5 * q^16 + 2 * q^17 + 11 * q^18 + 12 * q^19 + 22 * q^20 - 8 * q^21 - 20 * q^22 + 16 * q^23 - 15 * q^24 - 19 * q^25 + 3 * q^26 - 14 * q^27 + 27 * q^28 - 2 * q^29 + 4 * q^30 + 8 * q^31 + 16 * q^32 + 2 * q^33 - 28 * q^34 + 10 * q^36 - 19 * q^37 - 2 * q^38 + 45 * q^39 + 9 * q^40 - 36 * q^41 + 29 * q^42 - 74 * q^43 - q^44 - 12 * q^45 + 29 * q^46 - 2 * q^47 - 70 * q^48 + 6 * q^49 - 6 * q^50 + 43 * q^51 - 40 * q^52 + 10 * q^53 + 38 * q^54 - 26 * q^55 + 21 * q^56 + 24 * q^57 + 13 * q^58 + 28 * q^59 + 4 * q^60 - 22 * q^61 - 20 * q^62 - 27 * q^63 - 14 * q^64 + 3 * q^65 - 34 * q^66 + 61 * q^67 + 17 * q^68 - 40 * q^69 + 5 * q^70 - 34 * q^71 - 17 * q^72 - 16 * q^73 + 3 * q^74 + q^75 - 90 * q^76 + 5 * q^77 + 106 * q^78 + 63 * q^79 + 5 * q^80 + 5 * q^81 - 37 * q^82 - 48 * q^83 + 40 * q^84 - 4 * q^85 + 19 * q^86 - 32 * q^87 + 58 * q^88 + 16 * q^89 - 22 * q^90 - 11 * q^91 + 14 * q^92 + 31 * q^93 + 12 * q^95 - 40 * q^96 - 48 * q^97 + 66 * q^98 - 142 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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