LMFDB - Embedded newform 425.2.k.b.86.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,2,Mod(86,425)] 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("425.86"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.k (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [76] 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:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$19$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			86.7
Character	$\chi$	$=$	425.86
Dual form			425.2.k.b.341.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.18469 + 0.860728i) q^{2} +(-0.207649 + 0.639078i) q^{3} +(0.0446047 - 0.137279i) q^{4} +(-0.708744 + 2.12077i) q^{5} +(-0.304073 - 0.935839i) q^{6} +4.82170 q^{7} +(-0.839706 - 2.58435i) q^{8} +(2.06175 + 1.49795i) q^{9} +(-0.985767 - 3.12250i) q^{10} +(3.05345 - 2.21846i) q^{11} +(0.0784700 + 0.0570118i) q^{12} +(4.36092 + 3.16840i) q^{13} +(-5.71222 + 4.15017i) q^{14} +(-1.20817 - 0.893320i) q^{15} +(3.45277 + 2.50858i) q^{16} +(0.309017 + 0.951057i) q^{17} -3.73186 q^{18} +(-1.42855 - 4.39662i) q^{19} +(0.259525 + 0.191892i) q^{20} +(-1.00122 + 3.08145i) q^{21} +(-1.70790 + 5.25638i) q^{22} +(-3.28257 + 2.38493i) q^{23} +1.82596 q^{24} +(-3.99536 - 3.00617i) q^{25} -7.89347 q^{26} +(-3.01632 + 2.19149i) q^{27} +(0.215071 - 0.661920i) q^{28} +(0.708132 - 2.17940i) q^{29} +(2.20021 + 0.0184015i) q^{30} +(-0.964101 - 2.96720i) q^{31} -0.814975 q^{32} +(0.783725 + 2.41206i) q^{33} +(-1.18469 - 0.860728i) q^{34} +(-3.41735 + 10.2257i) q^{35} +(0.297601 - 0.216220i) q^{36} +(7.01575 + 5.09724i) q^{37} +(5.47668 + 3.97904i) q^{38} +(-2.93040 + 2.12906i) q^{39} +(6.07595 + 0.0508163i) q^{40} +(-5.75637 - 4.18225i) q^{41} +(-1.46615 - 4.51234i) q^{42} -8.80722 q^{43} +(-0.168350 - 0.518129i) q^{44} +(-4.63806 + 3.31084i) q^{45} +(1.83606 - 5.65080i) q^{46} +(2.09118 - 6.43600i) q^{47} +(-2.32014 + 1.68568i) q^{48} +16.2488 q^{49} +(7.32077 + 0.122463i) q^{50} -0.671967 q^{51} +(0.629473 - 0.457339i) q^{52} +(-2.69710 + 8.30083i) q^{53} +(1.68714 - 5.19247i) q^{54} +(2.54074 + 8.04800i) q^{55} +(-4.04881 - 12.4610i) q^{56} +3.10642 q^{57} +(1.03696 + 3.19143i) q^{58} +(-11.0489 - 8.02748i) q^{59} +(-0.176524 + 0.126010i) q^{60} +(0.537472 - 0.390496i) q^{61} +(3.69611 + 2.68538i) q^{62} +(9.94113 + 7.22266i) q^{63} +(-5.94004 + 4.31569i) q^{64} +(-9.81023 + 7.00295i) q^{65} +(-3.00460 - 2.18297i) q^{66} +(-1.06508 - 3.27799i) q^{67} +0.144344 q^{68} +(-0.842532 - 2.59305i) q^{69} +(-4.75307 - 15.0557i) q^{70} +(3.67724 - 11.3174i) q^{71} +(2.13996 - 6.58611i) q^{72} +(-6.11218 + 4.44076i) q^{73} -12.6988 q^{74} +(2.75081 - 1.92912i) q^{75} -0.667284 q^{76} +(14.7228 - 10.6968i) q^{77} +(1.63907 - 5.04455i) q^{78} +(-1.38095 + 4.25012i) q^{79} +(-7.76726 + 5.54459i) q^{80} +(1.58836 + 4.88846i) q^{81} +10.4193 q^{82} +(2.89920 + 8.92283i) q^{83} +(0.378359 + 0.274894i) q^{84} +(-2.23599 - 0.0187007i) q^{85} +(10.4338 - 7.58062i) q^{86} +(1.24577 + 0.905103i) q^{87} +(-8.29728 - 6.02833i) q^{88} +(-0.145061 + 0.105393i) q^{89} +(2.64493 - 7.91443i) q^{90} +(21.0271 + 15.2771i) q^{91} +(0.180983 + 0.557008i) q^{92} +2.09647 q^{93} +(3.06224 + 9.42461i) q^{94} +(10.3367 + 0.0864511i) q^{95} +(0.169229 - 0.520833i) q^{96} +(4.59316 - 14.1363i) q^{97} +(-19.2498 + 13.9858i) q^{98} +9.61859 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 6 q^{2} - 7 q^{3} - 26 q^{4} + 13 q^{5} + 12 q^{6} + 22 q^{7} + 10 q^{8} - 24 q^{9} - 6 q^{10} - 16 q^{11} - 15 q^{12} - q^{13} - 19 q^{14} - 3 q^{15} + 30 q^{16} - 19 q^{17} + 6 q^{18} + 18 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) $ 76 * q - 6 * q^2 - 7 * q^3 - 26 * q^4 + 13 * q^5 + 12 * q^6 + 22 * q^7 + 10 * q^8 - 24 * q^9 - 6 * q^10 - 16 * q^11 - 15 * q^12 - q^13 - 19 * q^14 - 3 * q^15 + 30 * q^16 - 19 * q^17 + 6 * q^18 + 18 * q^19 - 23 * q^20 - 22 * q^21 - 15 * q^22 - 8 * q^23 - 22 * q^24 + 35 * q^25 - 14 * q^26 - 10 * q^27 - 29 * q^28 - 25 * q^29 + 57 * q^30 + 22 * q^31 + 54 * q^32 - 22 * q^33 - 6 * q^34 - 19 * q^35 - 91 * q^36 - 49 * q^37 + 15 * q^38 + 25 * q^39 - 2 * q^40 + 16 * q^41 - 28 * q^42 + 104 * q^43 + 18 * q^44 + 10 * q^45 - 55 * q^46 - 26 * q^47 - 86 * q^48 + 2 * q^49 - 17 * q^50 + 18 * q^51 + 53 * q^52 - 41 * q^53 - 6 * q^54 + 67 * q^55 + 115 * q^56 + 84 * q^57 - 12 * q^58 - 7 * q^59 - 32 * q^60 - 21 * q^61 - 23 * q^62 - 21 * q^63 + 6 * q^64 - 72 * q^65 + 102 * q^66 - 15 * q^67 + 74 * q^68 + 48 * q^69 - 60 * q^70 - 8 * q^71 + 9 * q^72 - 25 * q^73 - 60 * q^74 + 68 * q^75 - 76 * q^76 - 36 * q^77 - 51 * q^78 + 2 * q^79 + 217 * q^80 + 20 * q^81 - 12 * q^82 - 41 * q^83 - 48 * q^84 - 7 * q^85 - 87 * q^86 - 54 * q^87 - 4 * q^88 + 77 * q^89 - 93 * q^90 + 79 * q^91 - 19 * q^92 + 72 * q^93 + 15 * q^94 + 57 * q^95 + 28 * q^96 + 13 * q^97 - 62 * q^98 - 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.18469	+	0.860728i	−0.837703	+	0.608627i	−0.921728	−	0.387837i	$-0.873222\pi$
$2$	−1.18469	+	0.860728i	−0.837703	+	0.608627i	0.0840253	+	0.996464i	$0.473222\pi$
$3$	−0.207649	+	0.639078i	−0.119886	+	0.368972i	−0.992935	−	0.118661i	$-0.962140\pi$
$3$	−0.207649	+	0.639078i	−0.119886	+	0.368972i	0.873049	+	0.487633i	$0.162140\pi$
$4$	0.0446047	−	0.137279i	0.0223024	−	0.0686396i
$5$	−0.708744	+	2.12077i	−0.316960	+	0.948439i
$5$	−0.708744	+	2.12077i	−0.316960	+	0.948439i
$6$	−0.304073	−	0.935839i	−0.124137	−	0.382055i
$7$	4.82170			1.82243			0.911216	−	0.411929i	$-0.135145\pi$
$7$	4.82170			1.82243			0.911216	+	0.411929i	$0.135145\pi$
$8$	−0.839706	−	2.58435i	−0.296881	−	0.913705i
$9$	2.06175	+	1.49795i	0.687249	+	0.499316i
$10$	−0.985767	−	3.12250i	−0.311727	−	0.987420i
$11$	3.05345	−	2.21846i	0.920650	−	0.668892i	−0.0230355	−	0.999735i	$-0.507333\pi$
$11$	3.05345	−	2.21846i	0.920650	−	0.668892i	0.943686	+	0.330843i	$0.107333\pi$
$12$	0.0784700	+	0.0570118i	0.0226524	+	0.0164579i
$13$	4.36092	+	3.16840i	1.20950	+	0.878755i	0.995186	−	0.0980090i	$-0.0312474\pi$
$13$	4.36092	+	3.16840i	1.20950	+	0.878755i	0.214317	+	0.976764i	$0.431247\pi$
$14$	−5.71222	+	4.15017i	−1.52666	+	1.10918i
$15$	−1.20817	−	0.893320i	−0.311948	−	0.230654i
$16$	3.45277	+	2.50858i	0.863191	+	0.627145i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$18$	−3.73186			−0.879608
$19$	−1.42855	−	4.39662i	−0.327731	−	1.00865i	−0.970193	−	0.242335i	$-0.922087\pi$
$19$	−1.42855	−	4.39662i	−0.327731	−	1.00865i	0.642461	−	0.766318i	$-0.277913\pi$
$20$	0.259525	+	0.191892i	0.0580315	+	0.0429084i
$21$	−1.00122	+	3.08145i	−0.218485	+	0.672426i
$22$	−1.70790	+	5.25638i	−0.364126	+	1.12066i
$23$	−3.28257	+	2.38493i	−0.684463	+	0.497292i	−0.874835	−	0.484420i	$-0.839031\pi$
$23$	−3.28257	+	2.38493i	−0.684463	+	0.497292i	0.190372	+	0.981712i	$0.439031\pi$
$24$	1.82596			0.372724
$25$	−3.99536	−	3.00617i	−0.799073	−	0.601235i
$26$	−7.89347			−1.54804
$27$	−3.01632	+	2.19149i	−0.580492	+	0.421752i
$28$	0.215071	−	0.661920i	0.0406445	−	0.125091i
$29$	0.708132	−	2.17940i	0.131497	−	0.404705i	−0.863532	−	0.504294i	$-0.831753\pi$
$29$	0.708132	−	2.17940i	0.131497	−	0.404705i	0.995029	+	0.0995888i	$0.0317527\pi$
$30$	2.20021	+	0.0184015i	0.401702	+	0.00335964i
$31$	−0.964101	−	2.96720i	−0.173158	−	0.532925i	0.826387	−	0.563103i	$-0.190392\pi$
$31$	−0.964101	−	2.96720i	−0.173158	−	0.532925i	−0.999545	+	0.0301783i	$0.990392\pi$
$32$	−0.814975			−0.144069
$33$	0.783725	+	2.41206i	0.136429	+	0.419885i
$34$	−1.18469	−	0.860728i	−0.203173	−	0.147614i
$35$	−3.41735	+	10.2257i	−0.577638	+	1.72847i
$36$	0.297601	−	0.216220i	0.0496001	−	0.0360366i
$37$	7.01575	+	5.09724i	1.15338	+	0.837982i	0.988927	−	0.148403i	$-0.0474132\pi$
$37$	7.01575	+	5.09724i	1.15338	+	0.837982i	0.164456	+	0.986384i	$0.447413\pi$
$38$	5.47668	+	3.97904i	0.888434	+	0.645485i
$39$	−2.93040	+	2.12906i	−0.469239	+	0.340922i
$40$	6.07595	+	0.0508163i	0.960693	+	0.00803476i
$41$	−5.75637	−	4.18225i	−0.898994	−	0.653157i	0.0392134	−	0.999231i	$-0.487515\pi$
$41$	−5.75637	−	4.18225i	−0.898994	−	0.653157i	−0.938207	+	0.346073i	$0.887515\pi$
$42$	−1.46615	−	4.51234i	−0.226231	−	0.696269i
$43$	−8.80722			−1.34309			−0.671544	−	0.740964i	$-0.734369\pi$
$43$	−8.80722			−1.34309			−0.671544	+	0.740964i	$0.734369\pi$
$44$	−0.168350	−	0.518129i	−0.0253798	−	0.0781109i
$45$	−4.63806	+	3.31084i	−0.691401	+	0.493551i
$46$	1.83606	−	5.65080i	0.270712	−	0.833165i
$47$	2.09118	−	6.43600i	0.305030	−	0.938787i	−0.674635	−	0.738151i	$-0.735699\pi$
$47$	2.09118	−	6.43600i	0.305030	−	0.938787i	0.979666	−	0.200636i	$-0.0643009\pi$
$48$	−2.32014	+	1.68568i	−0.334884	+	0.243307i
$49$	16.2488			2.32126
$50$	7.32077	+	0.122463i	1.03531	+	0.0173189i
$51$	−0.671967			−0.0940942
$52$	0.629473	−	0.457339i	0.0872922	−	0.0634215i
$53$	−2.69710	+	8.30083i	−0.370476	+	1.14021i	0.576005	+	0.817446i	$0.304611\pi$
$53$	−2.69710	+	8.30083i	−0.370476	+	1.14021i	−0.946481	+	0.322761i	$0.895389\pi$
$54$	1.68714	−	5.19247i	0.229590	−	0.706605i
$55$	2.54074	+	8.04800i	0.342593	+	1.08519i
$56$	−4.04881	−	12.4610i	−0.541045	−	1.66517i
$57$	3.10642			0.411455
$58$	1.03696	+	3.19143i	0.136159	+	0.419055i
$59$	−11.0489	−	8.02748i	−1.43844	−	1.04509i	−0.988365	−	0.152098i	$-0.951397\pi$
$59$	−11.0489	−	8.02748i	−1.43844	−	1.04509i	−0.450075	−	0.892991i	$-0.648603\pi$
$60$	−0.176524	+	0.126010i	−0.0227892	+	0.0162679i
$61$	0.537472	−	0.390496i	0.0688162	−	0.0499979i	−0.552845	−	0.833284i	$-0.686458\pi$
$61$	0.537472	−	0.390496i	0.0688162	−	0.0499979i	0.621662	+	0.783286i	$0.286458\pi$
$62$	3.69611	+	2.68538i	0.469407	+	0.341044i
$63$	9.94113	+	7.22266i	1.25247	+	0.909969i
$64$	−5.94004	+	4.31569i	−0.742505	+	0.539461i
$65$	−9.81023	+	7.00295i	−1.21681	+	0.868609i
$66$	−3.00460	−	2.18297i	−0.369840	−	0.268705i
$67$	−1.06508	−	3.27799i	−0.130121	−	0.400470i	0.864679	−	0.502325i	$-0.167522\pi$
$67$	−1.06508	−	3.27799i	−0.130121	−	0.400470i	−0.994799	+	0.101856i	$0.967522\pi$
$68$	0.144344			0.0175043
$69$	−0.842532	−	2.59305i	−0.101429	−	0.312166i
$70$	−4.75307	−	15.0557i	−0.568101	−	1.79951i
$71$	3.67724	−	11.3174i	0.436408	−	1.34313i	−0.455229	−	0.890374i	$-0.650443\pi$
$71$	3.67724	−	11.3174i	0.436408	−	1.34313i	0.891637	−	0.452751i	$-0.149557\pi$
$72$	2.13996	−	6.58611i	0.252196	−	0.776181i
$73$	−6.11218	+	4.44076i	−0.715376	+	0.519751i	−0.884904	−	0.465774i	$-0.845776\pi$
$73$	−6.11218	+	4.44076i	−0.715376	+	0.519751i	0.169527	+	0.985525i	$0.445776\pi$
$74$	−12.6988			−1.47621
$75$	2.75081	−	1.92912i	0.317637	−	0.222756i
$76$	−0.667284			−0.0765427
$77$	14.7228	−	10.6968i	1.67782	−	1.21901i
$78$	1.63907	−	5.04455i	0.185588	−	0.571182i
$79$	−1.38095	+	4.25012i	−0.155369	+	0.478176i	−0.998198	−	0.0600053i	$-0.980888\pi$
$79$	−1.38095	+	4.25012i	−0.155369	+	0.478176i	0.842829	+	0.538181i	$0.180888\pi$
$80$	−7.76726	+	5.54459i	−0.868406	+	0.619904i
$81$	1.58836	+	4.88846i	0.176484	+	0.543163i
$82$	10.4193			1.15062
$83$	2.89920	+	8.92283i	0.318229	+	0.979408i	0.974405	+	0.224800i	$0.0721729\pi$
$83$	2.89920	+	8.92283i	0.318229	+	0.979408i	−0.656176	+	0.754608i	$0.727827\pi$
$84$	0.378359	+	0.274894i	0.0412824	+	0.0299934i
$85$	−2.23599	−	0.0187007i	−0.242527	−	0.00202838i
$86$	10.4338	−	7.58062i	1.12511	−	0.817439i
$87$	1.24577	+	0.905103i	0.133560	+	0.0970372i
$88$	−8.29728	−	6.02833i	−0.884493	−	0.642622i
$89$	−0.145061	+	0.105393i	−0.0153764	+	0.0111716i	−0.595447	−	0.803395i	$-0.703025\pi$
$89$	−0.145061	+	0.105393i	−0.0153764	+	0.0111716i	0.580071	+	0.814566i	$0.303025\pi$
$90$	2.64493	−	7.91443i	0.278800	−	0.834254i
$91$	21.0271	+	15.2771i	2.20424	+	1.60147i
$92$	0.180983	+	0.557008i	0.0188688	+	0.0580721i
$93$	2.09647			0.217393
$94$	3.06224	+	9.42461i	0.315846	+	0.972074i
$95$	10.3367	+	0.0864511i	1.06052	+	0.00886969i
$96$	0.169229	−	0.520833i	0.0172718	−	0.0531572i
$97$	4.59316	−	14.1363i	0.466365	−	1.43532i	−0.390894	−	0.920436i	$-0.627834\pi$
$97$	4.59316	−	14.1363i	0.466365	−	1.43532i	0.857258	−	0.514887i	$-0.172166\pi$
$98$	−19.2498	+	13.9858i	−1.94452	+	1.41278i
$99$	9.61859			0.966705
$100$	−0.590897	+	0.414391i	−0.0590897	+	0.0414391i
$101$	−2.70613			−0.269270			−0.134635	−	0.990895i	$-0.542986\pi$
$101$	−2.70613			−0.269270			−0.134635	+	0.990895i	$0.542986\pi$
$102$	0.796072	−	0.578380i	0.0788229	−	0.0572682i
$103$	2.92904	−	9.01464i	0.288606	−	0.888239i	−0.696688	−	0.717374i	$-0.745344\pi$
$103$	2.92904	−	9.01464i	0.288606	−	0.888239i	0.985294	−	0.170865i	$-0.0546562\pi$
$104$	4.52635	−	13.9307i	0.443845	−	1.36601i
$105$	−5.82544	−	4.30732i	−0.568504	−	0.420352i
$106$	−3.94952	−	12.1554i	−0.383612	−	1.18064i
$107$	−5.44857			−0.526733			−0.263366	−	0.964696i	$-0.584833\pi$
$107$	−5.44857			−0.526733			−0.263366	+	0.964696i	$0.584833\pi$
$108$	0.166303	+	0.511829i	0.0160026	+	0.0492508i
$109$	−13.1095	−	9.52461i	−1.25566	−	0.912293i	−0.257127	−	0.966378i	$-0.582776\pi$
$109$	−13.1095	−	9.52461i	−1.25566	−	0.912293i	−0.998536	+	0.0540851i	$0.982776\pi$
$110$	−9.93713	−	7.34750i	−0.947468	−	0.700557i
$111$	−4.71435	+	3.42518i	−0.447467	+	0.325104i
$112$	16.6482	+	12.0956i	1.57311	+	1.14293i
$113$	5.06450	+	3.67957i	0.476428	+	0.346145i	0.799941	−	0.600079i	$-0.204864\pi$
$113$	5.06450	+	3.67957i	0.476428	+	0.346145i	−0.323513	+	0.946224i	$0.604864\pi$
$114$	−3.68014	+	2.67378i	−0.344677	+	0.250423i
$115$	−2.73139	−	8.65189i	−0.254703	−	0.806793i
$116$	−0.267601	−	0.194424i	−0.0248461	−	0.0180518i
$117$	4.24503	+	13.0649i	0.392454	+	1.20785i
$118$	19.9990			1.84105
$119$	1.48999	+	4.58571i	0.136587	+	0.420371i
$120$	−1.29414	+	3.87246i	−0.118138	+	0.353505i
$121$	1.00280	−	3.08631i	0.0911640	−	0.280574i
$122$	−0.300627	+	0.925234i	−0.0272175	+	0.0837668i
$123$	3.86809	−	2.81033i	0.348774	−	0.253399i
$124$	−0.450338			−0.0404416
$125$	9.20710	−	6.34265i	0.823508	−	0.567304i
$126$	−17.9939			−1.60302
$127$	−3.64573	+	2.64878i	−0.323506	+	0.235041i	−0.737670	−	0.675161i	$-0.764074\pi$
$127$	−3.64573	+	2.64878i	−0.323506	+	0.235041i	0.414164	+	0.910202i	$0.364074\pi$
$128$	3.82615	−	11.7757i	0.338187	−	1.04083i
$129$	1.82881	−	5.62850i	0.161018	−	0.495562i
$130$	5.59445	−	16.7403i	0.490666	−	1.46822i
$131$	2.36542	+	7.28000i	0.206667	+	0.636057i	0.999641	+	0.0268004i	$0.00853185\pi$
$131$	2.36542	+	7.28000i	0.206667	+	0.636057i	−0.792974	+	0.609256i	$0.791468\pi$
$132$	0.366083			0.0318634
$133$	−6.88803	−	21.1992i	−0.597268	−	1.83820i
$134$	4.08325	+	2.96665i	0.352739	+	0.256280i
$135$	−2.50985	−	7.95014i	−0.216013	−	0.684239i
$136$	2.19838	−	1.59722i	0.188509	−	0.136960i
$137$	−8.44300	−	6.13420i	−0.721334	−	0.524080i	0.165476	−	0.986214i	$-0.447084\pi$
$137$	−8.44300	−	6.13420i	−0.721334	−	0.524080i	−0.886810	+	0.462134i	$0.847084\pi$
$138$	3.23005	+	2.34677i	0.274960	+	0.199770i
$139$	5.45704	−	3.96477i	0.462860	−	0.336288i	−0.331792	−	0.943353i	$-0.607653\pi$
$139$	5.45704	−	3.96477i	0.462860	−	0.336288i	0.794652	+	0.607065i	$0.207653\pi$
$140$	1.25135	+	0.925248i	0.105759	+	0.0781977i
$141$	3.67888	+	2.67286i	0.309817	+	0.225095i
$142$	5.38479	+	16.5727i	0.451882	+	1.39075i
$143$	20.3448			1.70132
$144$	3.36101	+	10.3441i	0.280084	+	0.862010i
$145$	4.12014	+	3.04643i	0.342159	+	0.252992i
$146$	3.41875	−	10.5218i	0.282938	−	0.870794i
$147$	−3.37405	+	10.3843i	−0.278287	+	0.856479i
$148$	1.01268	−	0.735756i	0.0832419	−	0.0604788i
$149$	−9.32348			−0.763809			−0.381905	−	0.924202i	$-0.624732\pi$
$149$	−9.32348			−0.763809			−0.381905	+	0.924202i	$0.624732\pi$
$150$	−1.59841	+	4.65311i	−0.130510	+	0.379925i
$151$	8.86005			0.721021			0.360510	−	0.932755i	$-0.382603\pi$
$151$	8.86005			0.721021			0.360510	+	0.932755i	$0.382603\pi$
$152$	−10.1628	+	7.38373i	−0.824314	+	0.598899i
$153$	−0.787518	+	2.42373i	−0.0636670	+	0.195947i
$154$	−8.23500	+	25.3447i	−0.663595	+	2.04233i
$155$	6.97606	+	0.0583443i	0.560330	+	0.00468633i
$156$	0.161566	+	0.497248i	0.0129356	+	0.0398117i
$157$	5.10549			0.407462			0.203731	−	0.979027i	$-0.434693\pi$
$157$	5.10549			0.407462			0.203731	+	0.979027i	$0.434693\pi$
$158$	−2.02220	−	6.22369i	−0.160878	−	0.495130i
$159$	−4.74483	−	3.44732i	−0.376289	−	0.273390i
$160$	0.577609	−	1.72838i	0.0456640	−	0.136640i
$161$	−15.8276	+	11.4994i	−1.24739	+	0.906280i
$162$	−6.08935	−	4.42417i	−0.478425	−	0.347596i
$163$	−6.03263	−	4.38296i	−0.472512	−	0.343300i	0.325908	−	0.945402i	$-0.394330\pi$
$163$	−6.03263	−	4.38296i	−0.472512	−	0.343300i	−0.798419	+	0.602102i	$0.794330\pi$
$164$	−0.830897	+	0.603682i	−0.0648822	+	0.0471397i
$165$	−5.67089	−	0.0474285i	−0.441478	−	0.00369230i
$166$	−11.1148	−	8.07537i	−0.862675	−	0.626770i
$167$	−0.0950279	−	0.292466i	−0.00735348	−	0.0226317i	0.947312	−	0.320311i	$-0.103787\pi$
$167$	−0.0950279	−	0.292466i	−0.00735348	−	0.0226317i	−0.954666	+	0.297679i	$0.903787\pi$
$168$	8.80426			0.679263
$169$	4.96170	+	15.2705i	0.381669	+	1.17466i
$170$	2.66505	−	1.90242i	0.204400	−	0.145909i
$171$	3.64060	−	11.2046i	0.278403	−	0.856837i
$172$	−0.392844	+	1.20905i	−0.0299541	+	0.0921891i
$173$	−10.1977	+	7.40908i	−0.775319	+	0.563302i	−0.903571	−	0.428439i	$-0.859064\pi$
$173$	−10.1977	+	7.40908i	−0.775319	+	0.563302i	0.128251	+	0.991742i	$0.459064\pi$
$174$	−2.25490			−0.170943
$175$	−19.2645	−	14.4949i	−1.45626	−	1.09571i
$176$	16.1080			1.21419
$177$	7.42447	−	5.39420i	0.558058	−	0.405453i
$178$	0.0811375	−	0.249715i	0.00608151	−	0.0187170i
$179$	−5.49777	+	16.9204i	−0.410923	+	1.26469i	0.504925	+	0.863163i	$0.331520\pi$
$179$	−5.49777	+	16.9204i	−0.410923	+	1.26469i	−0.915847	+	0.401526i	$0.868480\pi$
$180$	0.247630	+	0.784388i	0.0184573	+	0.0584649i
$181$	2.24706	+	6.91575i	0.167023	+	0.514044i	0.999180	−	0.0404969i	$-0.0128941\pi$
$181$	2.24706	+	6.91575i	0.167023	+	0.514044i	−0.832157	+	0.554540i	$0.812894\pi$
$182$	−38.0600			−2.82119
$183$	0.137952	+	0.424573i	0.0101977	+	0.0313853i
$184$	8.91987	+	6.48067i	0.657582	+	0.477761i
$185$	−15.7825	+	11.2662i	−1.16035	+	0.828306i
$186$	−2.48366	+	1.80449i	−0.182111	+	0.132311i
$187$	3.05345	+	2.21846i	0.223290	+	0.162230i
$188$	−0.790253	−	0.574152i	−0.0576351	−	0.0418743i
$189$	−14.5438	+	10.5667i	−1.05791	+	0.768614i
$190$	−12.3202	+	8.79467i	−0.893802	+	0.638033i
$191$	8.13871	+	5.91312i	0.588896	+	0.427858i	0.841920	−	0.539602i	$-0.181425\pi$
$191$	8.13871	+	5.91312i	0.588896	+	0.427858i	−0.253024	+	0.967460i	$0.581425\pi$
$192$	−1.52462	−	4.69230i	−0.110030	−	0.338637i
$193$	−22.1775			−1.59637			−0.798187	−	0.602410i	$-0.794207\pi$
$193$	−22.1775			−1.59637			−0.798187	+	0.602410i	$0.794207\pi$
$194$	6.72603	+	20.7006i	0.482901	+	1.48622i
$195$	−2.43835	−	7.72366i	−0.174614	−	0.553103i
$196$	0.724774	−	2.23062i	0.0517696	−	0.159330i
$197$	−5.95000	+	18.3122i	−0.423920	+	1.30469i	0.480104	+	0.877212i	$0.340599\pi$
$197$	−5.95000	+	18.3122i	−0.423920	+	1.30469i	−0.904024	+	0.427481i	$0.859401\pi$
$198$	−11.3950	+	8.27899i	−0.809811	+	0.588362i
$199$	−4.88667			−0.346407			−0.173203	−	0.984886i	$-0.555412\pi$
$199$	−4.88667			−0.346407			−0.173203	+	0.984886i	$0.555412\pi$
$200$	−4.41407	+	12.8497i	−0.312122	+	0.908612i
$201$	2.31605			0.163362
$202$	3.20592	−	2.32924i	0.225568	−	0.163885i
$203$	3.41440	−	10.5084i	0.239644	−	0.737548i
$204$	−0.0299729	+	0.0922471i	−0.00209852	+	0.00645859i
$205$	12.9494	−	9.24382i	0.904425	−	0.645616i
$206$	4.28916	+	13.2007i	0.298840	+	0.919734i
$207$	−10.3403			−0.718702
$208$	7.10907	+	21.8795i	0.492925	+	1.51707i
$209$	−14.1157	−	10.2557i	−0.976405	−	0.709400i
$210$	10.6088	+	0.0887265i	0.732075	+	0.00612271i
$211$	−6.47686	+	4.70571i	−0.445885	+	0.323955i	−0.787969	−	0.615715i	$-0.788867\pi$
$211$	−6.47686	+	4.70571i	−0.445885	+	0.323955i	0.342084	+	0.939669i	$0.388867\pi$
$212$	1.01923	+	0.740512i	0.0700009	+	0.0508586i
$213$	6.46911	+	4.70009i	0.443256	+	0.322045i
$214$	6.45487	−	4.68973i	0.441246	−	0.320584i
$215$	6.24207	−	18.6781i	0.425705	−	1.27384i
$216$	8.19639	+	5.95503i	0.557694	+	0.405188i
$217$	−4.64861	−	14.3069i	−0.315568	−	0.971219i
$218$	23.7288			1.60712
$219$	−1.56880	−	4.82828i	−0.106010	−	0.326265i
$220$	1.21815	+	0.0101880i	0.0821278	+	0.000686877i
$221$	−1.66572	+	5.12657i	−0.112049	+	0.344851i
$222$	2.63690	−	8.11555i	0.176977	−	0.544680i
$223$	9.06564	−	6.58657i	0.607080	−	0.441070i	−0.241305	−	0.970449i	$-0.577575\pi$
$223$	9.06564	−	6.58657i	0.607080	−	0.441070i	0.848385	+	0.529380i	$0.177575\pi$
$224$	−3.92956			−0.262555
$225$	−3.73434	−	12.1828i	−0.248956	−	0.812188i
$226$	−9.16697			−0.609778
$227$	10.3426	−	7.51437i	0.686466	−	0.498747i	−0.189031	−	0.981971i	$-0.560535\pi$
$227$	10.3426	−	7.51437i	0.686466	−	0.498747i	0.875496	+	0.483225i	$0.160535\pi$
$228$	0.138561	−	0.426447i	0.00917642	−	0.0282421i
$229$	1.56668	−	4.82174i	0.103529	−	0.318630i	−0.885853	−	0.463965i	$-0.846426\pi$
$229$	1.56668	−	4.82174i	0.103529	−	0.318630i	0.989382	+	0.145336i	$0.0464262\pi$
$230$	10.6828	+	7.89883i	0.704401	+	0.520834i
$231$	3.77889	+	11.6302i	0.248632	+	0.765212i
$232$	−6.22696			−0.408820
$233$	−2.45452	−	7.55423i	−0.160801	−	0.494894i	0.837902	−	0.545821i	$-0.183782\pi$
$233$	−2.45452	−	7.55423i	−0.160801	−	0.494894i	−0.998702	+	0.0509273i	$0.983782\pi$
$234$	−16.2744	−	11.8240i	−1.06389	−	0.772960i
$235$	12.1672	+	8.99641i	0.793700	+	0.586861i
$236$	−1.59484	+	1.15872i	−0.103815	+	0.0754261i
$237$	−2.42941	−	1.76507i	−0.157807	−	0.114653i
$238$	−5.71222	−	4.15017i	−0.370268	−	0.269016i
$239$	3.86727	−	2.80973i	0.250153	−	0.181747i	−0.455642	−	0.890163i	$-0.650590\pi$
$239$	3.86727	−	2.80973i	0.250153	−	0.181747i	0.705795	+	0.708417i	$0.250590\pi$
$240$	−1.93056	−	6.11522i	−0.124617	−	0.394736i
$241$	−0.585723	−	0.425552i	−0.0377297	−	0.0274122i	0.568761	−	0.822503i	$-0.307423\pi$
$241$	−0.585723	−	0.425552i	−0.0377297	−	0.0274122i	−0.606490	+	0.795091i	$0.707423\pi$
$242$	1.46846	+	4.51947i	0.0943964	+	0.290522i
$243$	−14.6391			−0.939097
$244$	−0.0296332	−	0.0912017i	−0.00189707	−	0.00583859i
$245$	−11.5163	+	34.4601i	−0.735746	+	2.20157i
$246$	−2.16356	+	6.65874i	−0.137943	+	0.424546i
$247$	7.70044	−	23.6995i	0.489967	−	1.50796i
$248$	−6.85871	+	4.98315i	−0.435529	+	0.316430i
$249$	−6.30440			−0.399525
$250$	−5.44827	+	15.4389i	−0.344579	+	0.976441i
$251$	27.0984			1.71043			0.855216	−	0.518271i	$-0.173424\pi$
$251$	27.0984			1.71043			0.855216	+	0.518271i	$0.173424\pi$
$252$	1.43494	−	1.04255i	0.0903929	−	0.0656743i
$253$	−4.73230	+	14.5645i	−0.297517	+	0.915663i
$254$	2.03918	−	6.27596i	0.127950	−	0.393789i
$255$	0.476253	−	1.42509i	0.0298241	−	0.0892426i
$256$	1.06507	+	3.27795i	0.0665670	+	0.204872i
$257$	19.4817			1.21524			0.607618	−	0.794229i	$-0.292125\pi$
$257$	19.4817			1.21524			0.607618	+	0.794229i	$0.292125\pi$
$258$	2.67803	+	8.24214i	0.166727	+	0.513133i
$259$	33.8279	+	24.5774i	2.10196	+	1.52716i
$260$	0.523777	+	1.65911i	0.0324833	+	0.102893i
$261$	4.72462	−	3.43264i	0.292447	−	0.212475i
$262$	−9.06838	−	6.58857i	−0.560247	−	0.407043i
$263$	−7.39938	−	5.37596i	−0.456265	−	0.331496i	0.335799	−	0.941934i	$-0.390994\pi$
$263$	−7.39938	−	5.37596i	−0.456265	−	0.331496i	−0.792064	+	0.610437i	$0.790994\pi$
$264$	5.57550	−	4.05083i	0.343148	−	0.249312i
$265$	−15.6926	−	11.6031i	−0.963990	−	0.712773i
$266$	26.4069	+	19.1857i	1.61911	+	1.17635i
$267$	−0.0372325	−	0.114590i	−0.00227859	−	0.00701278i
$268$	−0.497507			−0.0303901
$269$	−2.84530	−	8.75694i	−0.173481	−	0.533920i	0.826080	−	0.563553i	$-0.190566\pi$
$269$	−2.84530	−	8.75694i	−0.173481	−	0.533920i	−0.999561	+	0.0296333i	$0.990566\pi$
$270$	9.81630	+	7.25816i	0.597401	+	0.441718i
$271$	0.767617	−	2.36248i	0.0466294	−	0.143511i	−0.925031	−	0.379891i	$-0.875961\pi$
$271$	0.767617	−	2.36248i	0.0466294	−	0.143511i	0.971660	+	0.236381i	$0.0759613\pi$
$272$	−1.31884	+	4.05897i	−0.0799664	+	0.246111i
$273$	−14.1295	+	10.2657i	−0.855156	+	0.621307i
$274$	15.2822			0.923233
$275$	−18.8687	−	0.315640i	−1.13783	−	0.0190338i
$276$	−0.393552			−0.0236891
$277$	−18.1359	+	13.1765i	−1.08968	+	0.791701i	−0.979346	−	0.202193i	$-0.935193\pi$
$277$	−18.1359	+	13.1765i	−1.08968	+	0.791701i	−0.110338	+	0.993894i	$0.535193\pi$
$278$	−3.05232	+	9.39406i	−0.183066	+	0.563418i
$279$	2.45697	−	7.56179i	0.147095	−	0.452712i
$280$	29.2964	+	0.245021i	1.75080	+	0.0146428i
$281$	−5.32866	−	16.3999i	−0.317881	−	0.978337i	−0.974552	−	0.224160i	$-0.928036\pi$
$281$	−5.32866	−	16.3999i	−0.317881	−	0.978337i	0.656671	−	0.754177i	$-0.271964\pi$
$282$	−6.65893			−0.396534
$283$	−3.18005	−	9.78718i	−0.189034	−	0.581787i	0.810960	−	0.585101i	$-0.198945\pi$
$283$	−3.18005	−	9.78718i	−0.189034	−	0.581787i	−0.999995	+	0.00331386i	$0.998945\pi$
$284$	−1.38962	−	1.00962i	−0.0824587	−	0.0599097i
$285$	−2.20166	+	6.58801i	−0.130415	+	0.390240i
$286$	−24.1023	+	17.5114i	−1.42520	+	1.03547i
$287$	−27.7555	−	20.1656i	−1.63836	−	1.19033i
$288$	−1.68027	−	1.22079i	−0.0990110	−	0.0719357i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	−7.50324	−	0.0627534i	−0.440605	−	0.00368500i
$291$	8.08043	+	5.87077i	0.473683	+	0.344151i
$292$	0.336992	+	1.03715i	0.0197209	+	0.0606948i
$293$	27.3815			1.59965			0.799823	−	0.600236i	$-0.204927\pi$
$293$	27.3815			1.59965			0.799823	+	0.600236i	$0.204927\pi$
$294$	−4.94082	−	15.2063i	−0.288154	−	0.886848i
$295$	24.8553	−	17.7427i	1.44713	−	1.03302i
$296$	7.28188	−	22.4113i	0.423251	−	1.30263i
$297$	−4.34847	+	13.3832i	−0.252324	+	0.776572i
$298$	11.0454	−	8.02498i	0.639845	−	0.464875i
$299$	−21.8714			−1.26486
$300$	−0.142129	−	0.463677i	−0.00820582	−	0.0267704i
$301$	−42.4658			−2.44769
$302$	−10.4964	+	7.62609i	−0.604001	+	0.438832i
$303$	0.561925	−	1.72943i	0.0322818	−	0.0993530i
$304$	6.09683	−	18.7641i	0.349677	−	1.07620i
$305$	0.447224	+	1.41662i	0.0256080	+	0.0811153i
$306$	−1.15321	−	3.54921i	−0.0659245	−	0.202895i
$307$	18.5382			1.05803			0.529016	−	0.848612i	$-0.322561\pi$
$307$	18.5382			1.05803			0.529016	+	0.848612i	$0.322561\pi$
$308$	−0.811736	−	2.49827i	−0.0462529	−	0.142352i
$309$	5.15285	+	3.74377i	0.293135	+	0.212975i
$310$	−8.31469	+	5.93537i	−0.472242	+	0.337106i
$311$	−2.73974	+	1.99054i	−0.155356	+	0.112873i	−0.662748	−	0.748843i	$-0.730610\pi$
$311$	−2.73974	+	1.99054i	−0.155356	+	0.112873i	0.507391	+	0.861716i	$0.330610\pi$
$312$	7.96289	+	5.78538i	0.450810	+	0.327533i
$313$	8.86949	+	6.44406i	0.501333	+	0.364240i	0.809526	−	0.587084i	$-0.199724\pi$
$313$	8.86949	+	6.44406i	0.501333	+	0.364240i	−0.308193	+	0.951324i	$0.599724\pi$
$314$	−6.04842	+	4.39443i	−0.341332	+	0.247992i
$315$	−22.3633	+	15.9639i	−1.26003	+	0.899463i
$316$	0.521856	+	0.379151i	0.0293567	+	0.0213289i
$317$	6.08701	+	18.7339i	0.341881	+	1.05220i	0.963233	+	0.268669i	$0.0865838\pi$
$317$	6.08701	+	18.7339i	0.341881	+	1.05220i	−0.621352	+	0.783532i	$0.713416\pi$
$318$	8.58836			0.481611
$319$	−2.67268	−	8.22567i	−0.149641	−	0.460549i
$320$	−4.94264	−	15.6562i	−0.276302	−	0.875208i
$321$	1.13139	−	3.48206i	0.0631481	−	0.194350i
$322$	8.85292	−	27.2465i	0.493354	−	1.51839i
$323$	3.73999	−	2.71726i	0.208098	−	0.151192i
$324$	0.741933			0.0412185
$325$	−7.89873	−	25.7686i	−0.438143	−	1.42938i
$326$	10.9193			0.604766
$327$	8.80915	−	6.40022i	0.487147	−	0.353933i
$328$	−5.97473	+	18.3883i	−0.329899	+	1.01533i
$329$	10.0831	−	31.0325i	0.555897	−	1.71088i
$330$	6.75907	−	4.82490i	0.372074	−	0.265602i
$331$	−3.98810	−	12.2741i	−0.219206	−	0.674645i	−0.998828	−	0.0483959i	$-0.984589\pi$
$331$	−3.98810	−	12.2741i	−0.219206	−	0.674645i	0.779623	−	0.626250i	$-0.215411\pi$
$332$	1.35424			0.0743234
$333$	6.82931	+	21.0185i	0.374244	+	1.15180i
$334$	0.364312	+	0.264688i	0.0199343	+	0.0144831i
$335$	7.70674	+	0.0644553i	0.421064	+	0.00352157i
$336$	−11.1870	+	8.12786i	−0.610303	+	0.443411i
$337$	2.49958	+	1.81605i	0.136161	+	0.0989267i	0.653781	−	0.756684i	$-0.273182\pi$
$337$	2.49958	+	1.81605i	0.136161	+	0.0989267i	−0.517620	+	0.855611i	$0.673182\pi$
$338$	−19.0219	−	13.8202i	−1.03465	−	0.751719i
$339$	−3.40317	+	2.47255i	−0.184835	+	0.134291i
$340$	−0.102303	+	0.306121i	−0.00554816	+	0.0166017i
$341$	−9.52645	−	6.92137i	−0.515886	−	0.374813i
$342$	5.33114	+	16.4075i	0.288275	+	0.887219i
$343$	44.5950			2.40790
$344$	7.39547	+	22.7609i	0.398737	+	1.22719i
$345$	6.09641	+	0.0509873i	0.328219	+	0.00274507i
$346$	5.70395	−	17.5549i	0.306646	−	0.943760i
$347$	−8.19442	+	25.2198i	−0.439899	+	1.35387i	0.448082	+	0.893992i	$0.352107\pi$
$347$	−8.19442	+	25.2198i	−0.439899	+	1.35387i	−0.887982	+	0.459879i	$0.847893\pi$
$348$	0.179819	−	0.130646i	0.00963931	−	0.00700337i
$349$	16.4007			0.877911			0.438956	−	0.898509i	$-0.355349\pi$
$349$	16.4007			0.877911			0.438956	+	0.898509i	$0.355349\pi$
$350$	35.2985	+	0.590481i	1.88679	+	0.0315625i
$351$	−20.0975			−1.07272
$352$	−2.48849	+	1.80799i	−0.132637	+	0.0963662i
$353$	8.80000	−	27.0836i	0.468377	−	1.44152i	−0.386308	−	0.922370i	$-0.626250\pi$
$353$	8.80000	−	27.0836i	0.468377	−	1.44152i	0.854685	−	0.519146i	$-0.173750\pi$
$354$	−4.15277	+	12.7809i	−0.220717	+	0.679297i
$355$	21.3954	+	15.8197i	1.13555	+	0.839623i
$356$	0.00799784	+	0.0246148i	0.000423885	+	0.00130458i
$357$	−3.24002			−0.171480
$358$	−8.05070	−	24.7775i	−0.425493	−	1.30953i
$359$	4.01209	+	2.91495i	0.211750	+	0.153845i	0.688605	−	0.725137i	$-0.258223\pi$
$359$	4.01209	+	2.91495i	0.211750	+	0.153845i	−0.476855	+	0.878982i	$0.658223\pi$
$360$	12.4510	+	9.20623i	0.656224	+	0.485211i
$361$	−1.91816	+	1.39363i	−0.100956	+	0.0733488i
$362$	−8.61465	−	6.25891i	−0.452776	−	0.328961i
$363$	1.76416	+	1.28174i	0.0925946	+	0.0672739i
$364$	3.03513	−	2.20515i	0.159084	−	0.115581i
$365$	−5.08587	−	16.1099i	−0.266207	−	0.843231i
$366$	−0.528872	−	0.384248i	−0.0276446	−	0.0200850i
$367$	−3.10169	−	9.54602i	−0.161907	−	0.498298i	0.836888	−	0.547374i	$-0.184372\pi$
$367$	−3.10169	−	9.54602i	−0.161907	−	0.498298i	−0.998795	+	0.0490758i	$0.984372\pi$
$368$	−17.3167			−0.902697
$369$	−5.60340	−	17.2455i	−0.291701	−	0.897764i
$370$	9.00023	−	26.9314i	0.467900	−	1.40009i
$371$	−13.0046	+	40.0241i	−0.675167	+	2.07795i
$372$	0.0935123	−	0.287801i	0.00484839	−	0.0149218i
$373$	8.46641	−	6.15121i	0.438374	−	0.318497i	−0.346614	−	0.938008i	$-0.612669\pi$
$373$	8.46641	−	6.15121i	0.438374	−	0.318497i	0.784989	+	0.619510i	$0.212669\pi$
$374$	−5.52689			−0.285789
$375$	2.14161	+	7.20111i	0.110592	+	0.371864i
$376$	−18.3888			−0.948332
$377$	9.99333	−	7.26058i	0.514683	−	0.373939i
$378$	8.13486	−	25.0365i	0.418412	−	1.28774i
$379$	−1.47100	+	4.52728i	−0.0755604	+	0.232551i	−0.981702	−	0.190423i	$-0.939014\pi$
$379$	−1.47100	+	4.52728i	−0.0755604	+	0.232551i	0.906142	+	0.422974i	$0.139014\pi$
$380$	0.472934	−	1.41516i	0.0242610	−	0.0725961i
$381$	−0.935743	−	2.87992i	−0.0479396	−	0.147543i
$382$	−14.7314			−0.753726
$383$	−3.78577	−	11.6514i	−0.193444	−	0.595359i	−0.999991	−	0.00418954i	$-0.998666\pi$
$383$	−3.78577	−	11.6514i	−0.193444	−	0.595359i	0.806547	−	0.591170i	$-0.201334\pi$
$384$	6.73109	+	4.89042i	0.343494	+	0.249563i
$385$	12.2507	+	38.8051i	0.624353	+	1.97769i
$386$	26.2735	−	19.0888i	1.33729	−	0.971595i
$387$	−18.1583	−	13.1928i	−0.923037	−	0.670626i
$388$	−1.73574	−	1.26109i	−0.0881189	−	0.0640222i
$389$	−9.87863	+	7.17725i	−0.500867	+	0.363901i	−0.809348	−	0.587329i	$-0.800179\pi$
$389$	−9.87863	+	7.17725i	−0.500867	+	0.363901i	0.308481	+	0.951230i	$0.400179\pi$
$390$	9.53666	+	7.05140i	0.482907	+	0.357061i
$391$	−3.28257	−	2.38493i	−0.166007	−	0.120611i
$392$	−13.6442	−	41.9926i	−0.689137	−	2.12095i
$393$	−5.14367			−0.259464
$394$	−8.71294	−	26.8157i	−0.438951	−	1.35095i
$395$	−8.03480	−	5.94092i	−0.404275	−	0.298920i
$396$	0.429035	−	1.32043i	0.0215598	−	0.0663542i
$397$	−11.7855	+	36.2719i	−0.591495	+	1.82044i	−0.0200438	+	0.999799i	$0.506381\pi$
$397$	−11.7855	+	36.2719i	−0.591495	+	1.82044i	−0.571451	+	0.820636i	$0.693619\pi$
$398$	5.78919	−	4.20610i	0.290186	−	0.210832i
$399$	14.9782			0.749849
$400$	−6.25382	−	20.4023i	−0.312691	−	1.02012i
$401$	13.6183			0.680068			0.340034	−	0.940413i	$-0.389561\pi$
$401$	13.6183			0.680068			0.340034	+	0.940413i	$0.389561\pi$
$402$	−2.74381	+	1.99349i	−0.136849	+	0.0994263i
$403$	5.19689	−	15.9944i	0.258875	−	0.796737i
$404$	−0.120706	+	0.371495i	−0.00600535	+	0.0184826i
$405$	−11.4931	−	0.0961223i	−0.571095	−	0.00477636i
$406$	4.99990	+	15.3881i	0.248141	+	0.763700i
$407$	32.7303			1.62238
$408$	0.564254	+	1.73660i	0.0279347	+	0.0859743i
$409$	3.03882	+	2.20783i	0.150260	+	0.109170i	0.660375	−	0.750936i	$-0.270397\pi$
$409$	3.03882	+	2.20783i	0.150260	+	0.109170i	−0.510115	+	0.860106i	$0.670397\pi$
$410$	−7.38462	+	22.0970i	−0.364700	+	1.09129i
$411$	5.67342	−	4.12198i	0.279849	−	0.203322i
$412$	−1.10687	−	0.804191i	−0.0545318	−	0.0396197i
$413$	−53.2744	−	38.7061i	−2.62146	−	1.90460i
$414$	12.2501	−	8.90021i	0.602059	−	0.437421i
$415$	−20.9781	−	0.175450i	−1.02977	−	0.00861252i
$416$	−3.55404	−	2.58216i	−0.174251	−	0.126601i
$417$	1.40065	+	4.31076i	0.0685902	+	0.211099i
$418$	25.5501			1.24970
$419$	−4.09932	−	12.6164i	−0.200265	−	0.616352i	−0.999875	−	0.0158319i	$-0.994960\pi$
$419$	−4.09932	−	12.6164i	−0.200265	−	0.616352i	0.799610	−	0.600520i	$-0.205040\pi$
$420$	−0.851148	+	0.607585i	−0.0415318	+	0.0296471i
$421$	6.21881	−	19.1395i	0.303086	−	0.932804i	−0.677298	−	0.735709i	$-0.736849\pi$
$421$	6.21881	−	19.1395i	0.303086	−	0.932804i	0.980384	−	0.197095i	$-0.0631508\pi$
$422$	3.62273	−	11.1496i	0.176352	−	0.542755i
$423$	13.9523	−	10.1369i	0.678383	−	0.492874i
$424$	23.7170			1.15180
$425$	1.62440	−	4.72877i	0.0787952	−	0.229379i
$426$	−11.7094			−0.567322
$427$	2.59153	−	1.88286i	0.125413	−	0.0911178i
$428$	−0.243032	+	0.747975i	−0.0117474	+	0.0361547i
$429$	−4.22459	+	13.0019i	−0.203965	+	0.627740i
$430$	8.68187	+	27.5005i	0.418677	+	1.32619i
$431$	5.18295	+	15.9515i	0.249654	+	0.768355i	0.994836	+	0.101495i	$0.0323624\pi$
$431$	5.18295	+	15.9515i	0.249654	+	0.768355i	−0.745182	+	0.666861i	$0.767638\pi$
$432$	−15.9122			−0.765575
$433$	−5.75874	−	17.7236i	−0.276747	−	0.851741i	−0.988752	−	0.149566i	$-0.952212\pi$
$433$	−5.75874	−	17.7236i	−0.276747	−	0.851741i	0.712004	−	0.702175i	$-0.247788\pi$
$434$	17.8215	+	12.9481i	0.855462	+	0.621529i
$435$	−2.80245	+	2.00050i	−0.134367	+	0.0959168i
$436$	−1.89228	+	1.37482i	−0.0906237	+	0.0658420i
$437$	15.1749	+	11.0252i	0.725915	+	0.527408i
$438$	6.01438	+	4.36970i	0.287378	+	0.208792i
$439$	12.1468	−	8.82517i	0.579735	−	0.421202i	−0.258893	−	0.965906i	$-0.583358\pi$
$439$	12.1468	−	8.82517i	0.579735	−	0.421202i	0.838629	+	0.544703i	$0.183358\pi$
$440$	18.6654	−	13.3241i	0.889836	−	0.635202i
$441$	33.5010	+	24.3399i	1.59528	+	1.15904i
$442$	−2.43922	−	7.50714i	−0.116022	−	0.357078i
$443$	38.3692			1.82298			0.911489	−	0.411325i	$-0.134934\pi$
$443$	38.3692			1.82298			0.911489	+	0.411325i	$0.134934\pi$
$444$	0.259923	+	0.799962i	0.0123354	+	0.0379645i
$445$	−0.120703	−	0.382337i	−0.00572188	−	0.0181245i
$446$	−5.07073	+	15.6061i	−0.240106	+	0.738970i
$447$	1.93601	−	5.95843i	0.0915702	−	0.281824i
$448$	−28.6411	+	20.8090i	−1.35316	+	0.983132i
$449$	12.7787			0.603066			0.301533	−	0.953456i	$-0.402502\pi$
$449$	12.7787			0.603066			0.301533	+	0.953456i	$0.402502\pi$
$450$	14.9101	+	11.2186i	0.702870	+	0.528850i
$451$	−26.8550			−1.26455
$452$	0.731030	−	0.531124i	0.0343847	−	0.0249820i
$453$	−1.83978	+	5.66227i	−0.0864405	+	0.266036i
$454$	−5.78500	+	17.8044i	−0.271504	+	0.835603i
$455$	−47.3020	+	33.7661i	−2.21755	+	1.58298i
$456$	−2.60848	−	8.02807i	−0.122153	−	0.375949i
$457$	12.8715			0.602106			0.301053	−	0.953607i	$-0.402662\pi$
$457$	12.8715			0.602106			0.301053	+	0.953607i	$0.402662\pi$
$458$	2.29418	+	7.06076i	0.107200	+	0.329927i
$459$	−3.01632	−	2.19149i	−0.140790	−	0.102290i
$460$	−1.30956	−	0.0109525i	−0.0610585	−	0.000510663i
$461$	−4.12219	+	2.99495i	−0.191989	+	0.139489i	−0.679628	−	0.733557i	$-0.737859\pi$
$461$	−4.12219	+	2.99495i	−0.191989	+	0.139489i	0.487638	+	0.873046i	$0.337859\pi$
$462$	−14.4873	−	10.5256i	−0.674008	−	0.489696i
$463$	−31.3274	−	22.7607i	−1.45591	−	1.05778i	−0.984405	−	0.175917i	$-0.943711\pi$
$463$	−31.3274	−	22.7607i	−1.45591	−	1.05778i	−0.471504	−	0.881864i	$-0.656289\pi$
$464$	7.91223	−	5.74857i	0.367316	−	0.266871i
$465$	−1.48586	+	4.44613i	−0.0689050	+	0.206184i
$466$	9.40998	+	6.83675i	0.435909	+	0.316706i
$467$	−1.48122	−	4.55872i	−0.0685426	−	0.210953i	0.910918	−	0.412587i	$-0.135375\pi$
$467$	−1.48122	−	4.55872i	−0.0685426	−	0.210953i	−0.979461	+	0.201634i	$0.935375\pi$
$468$	1.98288			0.0916589
$469$	−5.13551	−	15.8055i	−0.237136	−	0.729829i
$470$	−22.1578	−	0.185317i	−1.02206	−	0.00854803i
$471$	−1.06015	+	3.26281i	−0.0488491	+	0.150342i
$472$	−11.4680	+	35.2949i	−0.527857	+	1.62458i
$473$	−26.8924	+	19.5385i	−1.23651	+	0.898381i
$474$	4.39734			0.201976
$475$	−7.50942	+	21.8605i	−0.344556	+	1.00303i
$476$	0.695983			0.0319003
$477$	−17.9950	+	13.0741i	−0.823932	+	0.598622i
$478$	−2.16310	+	6.65733i	−0.0989378	+	0.304499i
$479$	−2.86967	+	8.83194i	−0.131119	+	0.403542i	−0.994966	−	0.100212i	$-0.968048\pi$
$479$	−2.86967	+	8.83194i	−0.131119	+	0.403542i	0.863847	+	0.503753i	$0.168048\pi$
$480$	0.984628	+	0.728033i	0.0449419	+	0.0332300i
$481$	14.4451	+	44.4574i	0.658639	+	2.02708i
$482$	1.06018			0.0482901
$483$	−4.06244	−	12.5029i	−0.184847	−	0.568902i
$484$	−0.378957	−	0.275328i	−0.0172253	−	0.0125149i
$485$	26.7245	+	19.7601i	1.21350	+	0.897258i
$486$	17.3428	−	12.6003i	0.786684	−	0.571559i
$487$	−18.7197	−	13.6006i	−0.848269	−	0.616304i	0.0763990	−	0.997077i	$-0.475658\pi$
$487$	−18.7197	−	13.6006i	−0.848269	−	0.616304i	−0.924668	+	0.380774i	$0.875658\pi$
$488$	−1.46050	−	1.06111i	−0.0661136	−	0.0480343i
$489$	4.05372	−	2.94520i	0.183316	−	0.133187i
$490$	−16.0175	−	50.7369i	−0.723599	−	2.29206i
$491$	14.7469	+	10.7142i	0.665518	+	0.483527i	0.868522	−	0.495651i	$-0.165070\pi$
$491$	14.7469	+	10.7142i	0.665518	+	0.483527i	−0.203004	+	0.979178i	$0.565070\pi$
$492$	−0.213265	−	0.656362i	−0.00961473	−	0.0295911i
$493$	2.29156			0.103207
$494$	11.2762	+	34.7046i	0.507340	+	1.56143i
$495$	−6.81712	+	20.3989i	−0.306407	+	0.916860i
$496$	4.11464	−	12.6636i	0.184753	−	0.568611i
$497$	17.7305	−	54.5690i	0.795324	−	2.44775i
$498$	7.46877	−	5.42638i	0.334683	−	0.243162i
$499$	−12.0134			−0.537794			−0.268897	−	0.963169i	$-0.586659\pi$
$499$	−12.0134			−0.537794			−0.268897	+	0.963169i	$0.586659\pi$
$500$	−0.460034	−	1.54686i	−0.0205734	−	0.0691775i
$501$	0.206641			0.00923204
$502$	−32.1032	+	23.3243i	−1.43283	+	1.04101i
$503$	0.745667	−	2.29493i	0.0332476	−	0.102326i	−0.933056	−	0.359732i	$-0.882868\pi$
$503$	0.745667	−	2.29493i	0.0332476	−	0.102326i	0.966303	+	0.257407i	$0.0828680\pi$
$504$	10.3182	−	31.7563i	0.459611	−	1.41454i
$505$	1.91795	−	5.73909i	0.0853478	−	0.255386i
$506$	−6.92978	−	21.3277i	−0.308066	−	0.948130i
$507$	−10.7894			−0.479172
$508$	0.201005	+	0.618631i	0.00891817	+	0.0274473i
$509$	−16.7201	−	12.1478i	−0.741104	−	0.538444i	0.151953	−	0.988388i	$-0.451444\pi$
$509$	−16.7201	−	12.1478i	−0.741104	−	0.538444i	−0.893057	+	0.449944i	$0.851444\pi$
$510$	0.662402	+	2.09821i	0.0293317	+	0.0929105i
$511$	−29.4711	+	21.4120i	−1.30372	+	0.947211i
$512$	15.9508	+	11.5889i	0.704932	+	0.512163i
$513$	13.9441	+	10.1310i	0.615647	+	0.447293i
$514$	−23.0798	+	16.7685i	−1.01801	+	0.739625i
$515$	17.0421	+	12.6009i	0.750964	+	0.555262i
$516$	−0.691103	−	0.502116i	−0.0304241	−	0.0221044i
$517$	−7.89270	−	24.2912i	−0.347120	−	1.06833i
$518$	−61.2300			−2.69029
$519$	−2.61744	−	8.05564i	−0.114893	−	0.353603i
$520$	26.3358	+	19.4726i	1.15490	+	0.853932i
$521$	9.20530	−	28.3310i	0.403292	−	1.24120i	−0.519022	−	0.854761i	$-0.673704\pi$
$521$	9.20530	−	28.3310i	0.403292	−	1.24120i	0.922313	−	0.386443i	$-0.126296\pi$
$522$	−2.64265	+	8.13323i	−0.115666	+	0.355982i
$523$	−22.9150	+	16.6487i	−1.00200	+	0.727997i	−0.962516	−	0.271224i	$-0.912572\pi$
$523$	−22.9150	+	16.6487i	−1.00200	+	0.727997i	−0.0394849	+	0.999220i	$0.512572\pi$
$524$	1.10490			0.0482678
$525$	13.2636	−	9.30165i	0.578871	−	0.405957i
$526$	13.3932			0.583972
$527$	2.52405	−	1.83383i	0.109949	−	0.0798829i
$528$	−3.34482	+	10.2943i	−0.145565	+	0.448002i
$529$	−2.02000	+	6.21692i	−0.0878261	+	0.270301i
$530$	28.5780	+	0.239012i	1.24135	+	0.0103820i
$531$	−10.7553	−	33.1013i	−0.466738	−	1.43647i
$532$	−3.21744			−0.139494
$533$	−11.8521	−	36.4769i	−0.513370	−	1.57999i
$534$	0.142740	+	0.103706i	0.00617695	+	0.00448781i
$535$	3.86164	−	11.5552i	0.166953	−	0.499574i
$536$	−7.57710	+	5.50509i	−0.327281	+	0.237784i
$537$	−9.67185	−	7.02701i	−0.417371	−	0.303238i
$538$	10.9081	+	7.92523i	0.470284	+	0.341681i
$539$	49.6150	−	36.0474i	2.13707	−	1.55267i
$540$	−1.20334	−	0.0100641i	−0.0517835	−	0.000433092i
$541$	−20.6208	−	14.9819i	−0.886555	−	0.644120i	0.0484222	−	0.998827i	$-0.484581\pi$
$541$	−20.6208	−	14.9819i	−0.886555	−	0.644120i	−0.934978	+	0.354707i	$0.884581\pi$
$542$	1.12407	+	3.45952i	0.0482828	+	0.148599i
$543$	−4.88631			−0.209691
$544$	−0.251841	−	0.775087i	−0.0107976	−	0.0332316i
$545$	29.4908	−	21.0518i	1.26325	−	0.901759i
$546$	7.90312	−	24.3233i	0.338222	−	1.04094i
$547$	1.90558	−	5.86478i	0.0814768	−	0.250760i	−0.902017	−	0.431700i	$-0.857914\pi$
$547$	1.90558	−	5.86478i	0.0814768	−	0.250760i	0.983494	+	0.180940i	$0.0579140\pi$
$548$	−1.21870	+	0.885435i	−0.0520601	+	0.0378239i
$549$	1.69307			0.0722587
$550$	22.6253	−	15.8669i	0.964745	−	0.676567i
$551$	−10.5936			−0.451303
$552$	−5.99386	+	4.35479i	−0.255116	+	0.185352i
$553$	−6.65851	+	20.4928i	−0.283149	+	0.871442i
$554$	10.1441	−	31.2202i	0.430980	−	1.32642i
$555$	−3.92276	−	12.4257i	−0.166512	−	0.527440i
$556$	−0.300871	−	0.925987i	−0.0127598	−	0.0392706i
$557$	2.28829			0.0969581			0.0484790	−	0.998824i	$-0.484563\pi$
$557$	2.28829			0.0969581			0.0484790	+	0.998824i	$0.484563\pi$
$558$	3.59789	+	11.0732i	0.152311	+	0.468764i
$559$	−38.4076	−	27.9048i	−1.62447	−	1.18025i
$560$	−37.4514	+	26.7344i	−1.58261	+	1.12973i
$561$	−2.05182	+	1.49073i	−0.0866278	+	0.0629388i
$562$	20.4287	+	14.8423i	0.861732	+	0.626085i
$563$	1.18822	+	0.863296i	0.0500777	+	0.0363836i	0.612543	−	0.790438i	$-0.290147\pi$
$563$	1.18822	+	0.863296i	0.0500777	+	0.0363836i	−0.562465	+	0.826821i	$0.690147\pi$
$564$	0.531023	−	0.385811i	0.0223601	−	0.0162456i
$565$	−11.3930	+	8.13278i	−0.479306	+	0.342149i
$566$	12.1915	+	8.85762i	0.512446	+	0.372313i
$567$	7.65859	+	23.5707i	0.321631	+	0.989877i
$568$	−32.3358			−1.35678
$569$	1.01445	+	3.12215i	0.0425279	+	0.130887i	0.970066	−	0.242841i	$-0.0780793\pi$
$569$	1.01445	+	3.12215i	0.0425279	+	0.130887i	−0.927538	+	0.373728i	$0.878079\pi$
$570$	−3.06220	−	9.69978i	−0.128262	−	0.406279i
$571$	−12.2269	+	37.6306i	−0.511680	+	1.57479i	0.277561	+	0.960708i	$0.410474\pi$
$571$	−12.2269	+	37.6306i	−0.511680	+	1.57479i	−0.789242	+	0.614083i	$0.789526\pi$
$572$	0.907476	−	2.79292i	0.0379435	−	0.116778i
$573$	−5.46894	+	3.97342i	−0.228468	+	0.165992i
$574$	50.2387			2.09692
$575$	20.2846	+	0.339324i	0.845925	+	0.0141508i
$576$	−18.7115			−0.779648
$577$	−36.3556	+	26.4139i	−1.51350	+	1.09962i	−0.548909	+	0.835882i	$0.684957\pi$
$577$	−36.3556	+	26.4139i	−1.51350	+	1.09962i	−0.964593	+	0.263741i	$0.915043\pi$
$578$	0.452511	−	1.39269i	0.0188220	−	0.0579281i
$579$	4.60515	−	14.1732i	0.191383	−	0.589017i
$580$	0.601989	−	0.429725i	0.0249962	−	0.0178433i
$581$	13.9791	+	43.0232i	0.579951	+	1.78490i
$582$	−14.6259			−0.606265
$583$	10.1796	+	31.3296i	0.421596	+	1.29754i
$584$	16.6089	+	12.0671i	0.687281	+	0.499339i
$585$	−30.7163	−	0.256896i	−1.26996	−	0.0106213i
$586$	−32.4386	+	23.5680i	−1.34003	+	0.973587i
$587$	−6.33046	−	4.59935i	−0.261286	−	0.189835i	0.449428	−	0.893317i	$-0.351628\pi$
$587$	−6.33046	−	4.59935i	−0.261286	−	0.189835i	−0.710714	+	0.703481i	$0.751628\pi$
$588$	1.27504	+	0.926374i	0.0525820	+	0.0382030i
$589$	−11.6684	+	8.47757i	−0.480787	+	0.349312i
$590$	−14.1742	+	42.4133i	−0.583541	+	1.74613i
$591$	−10.4674	−	7.60504i	−0.430573	−	0.312829i
$592$	11.4369	+	35.1992i	0.470054	+	1.44668i
$593$	11.3987			0.468090			0.234045	−	0.972226i	$-0.424804\pi$
$593$	11.3987			0.468090			0.234045	+	0.972226i	$0.424804\pi$
$594$	−6.36771	−	19.5978i	−0.261270	−	0.804107i
$595$	−10.7813	−	0.0901693i	−0.441989	−	0.00369658i
$596$	−0.415871	+	1.27992i	−0.0170348	+	0.0524276i
$597$	1.01471	−	3.12297i	0.0415294	−	0.127814i
$598$	25.9109	−	18.8254i	1.05957	−	0.769826i
$599$	29.9222			1.22259			0.611295	−	0.791403i	$-0.290649\pi$
$599$	29.9222			1.22259			0.611295	+	0.791403i	$0.290649\pi$
$600$	−7.29539	−	5.48917i	−0.297833	−	0.224094i
$601$	−11.6958			−0.477082			−0.238541	−	0.971132i	$-0.576669\pi$
$601$	−11.6958			−0.477082			−0.238541	+	0.971132i	$0.576669\pi$
$602$	50.3088	−	36.5515i	2.05043	−	1.48973i
$603$	2.71432	−	8.35382i	0.110536	−	0.340194i
$604$	0.395200	−	1.21630i	0.0160805	−	0.0494906i
$605$	5.83464	+	4.31413i	0.237212	+	0.175394i
$606$	0.822859	+	2.53250i	0.0334264	+	0.102876i
$607$	−7.45335			−0.302522			−0.151261	−	0.988494i	$-0.548333\pi$
$607$	−7.45335			−0.302522			−0.151261	+	0.988494i	$0.548333\pi$
$608$	1.16423	+	3.58313i	0.0472157	+	0.145315i
$609$	6.00672	+	4.36414i	0.243405	+	0.176844i
$610$	−1.74914	−	1.29332i	−0.0708208	−	0.0523648i
$611$	29.5113	−	21.4412i	1.19390	−	0.867418i
$612$	0.297601	+	0.216220i	0.0120298	+	0.00874016i
$613$	29.9514	+	21.7610i	1.20973	+	0.878917i	0.995206	−	0.0978024i	$-0.0311813\pi$
$613$	29.9514	+	21.7610i	1.20973	+	0.878917i	0.214520	+	0.976720i	$0.431181\pi$
$614$	−21.9621	+	15.9564i	−0.886316	+	0.643946i
$615$	3.21859	+	10.1951i	0.129786	+	0.411108i
$616$	−40.0070	−	29.0668i	−1.61193	−	1.17113i
$617$	−5.79909	−	17.8478i	−0.233463	−	0.718524i	−0.997322	−	0.0731411i	$-0.976698\pi$
$617$	−5.79909	−	17.8478i	−0.233463	−	0.718524i	0.763859	−	0.645383i	$-0.223302\pi$
$618$	−9.32690			−0.375183
$619$	10.3839	+	31.9585i	0.417366	+	1.28452i	0.910118	+	0.414350i	$0.135991\pi$
$619$	10.3839	+	31.9585i	0.417366	+	1.28452i	−0.492752	+	0.870170i	$0.664009\pi$
$620$	0.319175	−	0.955065i	0.0128184	−	0.0383563i
$621$	4.67476	−	14.3874i	0.187592	−	0.577347i
$622$	1.53243	−	4.71634i	0.0614450	−	0.189108i
$623$	−0.699439	+	0.508172i	−0.0280224	+	0.0203595i
$624$	−15.4589			−0.618850
$625$	6.92585	+	24.0215i	0.277034	+	0.960860i
$626$	−16.0542			−0.641654
$627$	9.48530	−	6.89147i	0.378806	−	0.275219i
$628$	0.227729	−	0.700877i	0.00908737	−	0.0279680i
$629$	−2.67978	+	8.24751i	−0.106850	+	0.328850i
$630$	12.7531	−	38.1610i	0.508095	−	1.52037i
$631$	5.03116	+	15.4843i	0.200287	+	0.616421i	0.999874	+	0.0158702i	$0.00505186\pi$
$631$	5.03116	+	15.4843i	0.200287	+	0.616421i	−0.799587	+	0.600550i	$0.794948\pi$
$632$	12.1434			0.483037
$633$	−1.66240	−	5.11635i	−0.0660746	−	0.203357i
$634$	−23.3360	−	16.9546i	−0.926792	−	0.673353i
$635$	−3.03357	−	9.60907i	−0.120383	−	0.381324i
$636$	−0.684887	+	0.497600i	−0.0271575	+	0.0197311i
$637$	70.8598	+	51.4827i	2.80757	+	2.03982i
$638$	10.2464	+	7.44442i	0.405658	+	0.294727i
$639$	24.5344	−	17.8253i	0.970565	−	0.705157i
$640$	22.2618	+	16.4604i	0.879975	+	0.650653i
$641$	21.9212	+	15.9267i	0.865835	+	0.629066i	0.929466	−	0.368908i	$-0.120268\pi$
$641$	21.9212	+	15.9267i	0.865835	+	0.629066i	−0.0636311	+	0.997973i	$0.520268\pi$
$642$	1.65676	+	5.09898i	0.0653871	+	0.201241i
$643$	−32.1021			−1.26598			−0.632992	−	0.774158i	$-0.718174\pi$
$643$	−32.1021			−1.26598			−0.632992	+	0.774158i	$0.718174\pi$
$644$	0.872645	+	2.68573i	0.0343870	+	0.105832i
$645$	10.6406	+	7.86767i	0.418974	+	0.309789i
$646$	−2.09190	+	6.43822i	−0.0823049	+	0.253308i
$647$	−5.64636	+	17.3777i	−0.221981	+	0.683188i	0.776603	+	0.629990i	$0.216941\pi$
$647$	−5.64636	+	17.3777i	−0.221981	+	0.683188i	−0.998584	+	0.0531973i	$0.983059\pi$
$648$	11.2997	−	8.20974i	0.443896	−	0.322509i
$649$	−51.5459			−2.02335
$650$	31.5373	+	23.7291i	1.23699	+	0.930733i
$651$	10.1085			0.396185
$652$	−0.870773	+	0.632654i	−0.0341021	+	0.0247766i
$653$	6.54384	−	20.1399i	0.256080	−	0.788134i	−0.737535	−	0.675309i	$-0.764010\pi$
$653$	6.54384	−	20.1399i	0.256080	−	0.788134i	0.993615	−	0.112825i	$-0.0359899\pi$
$654$	−4.92727	+	15.1646i	−0.192671	+	0.592981i
$655$	−17.1157	−	0.143147i	−0.668766	−	0.00559323i
$656$	−9.38389	−	28.8806i	−0.366379	−	1.12760i
$657$	−19.2538			−0.751162
$658$	14.7652	+	45.4427i	0.575608	+	1.77154i
$659$	14.8605	+	10.7968i	0.578882	+	0.420582i	0.838321	−	0.545177i	$-0.183538\pi$
$659$	14.8605	+	10.7968i	0.578882	+	0.420582i	−0.259439	+	0.965759i	$0.583538\pi$
$660$	−0.259459	+	0.776379i	−0.0100994	+	0.0302205i
$661$	15.4072	−	11.1940i	0.599271	−	0.435396i	−0.246349	−	0.969181i	$-0.579231\pi$
$661$	15.4072	−	11.1940i	0.599271	−	0.435396i	0.845620	+	0.533785i	$0.179231\pi$
$662$	15.2893	+	11.1083i	0.594236	+	0.431738i
$663$	−2.93040	−	2.12906i	−0.113807	−	0.0826857i
$664$	20.6252	−	14.9851i	0.800414	−	0.581535i
$665$	49.8405	+	0.416841i	1.93273	+	0.0161644i
$666$	−26.1818	−	19.0222i	−1.01452	−	0.737095i
$667$	2.87323	+	8.84289i	0.111252	+	0.342398i
$668$	−0.0443882			−0.00171743
$669$	2.32686	+	7.16135i	0.0899618	+	0.276874i
$670$	−9.18558	+	6.55705i	−0.354870	+	0.253321i
$671$	0.774843	−	2.38472i	0.0299125	−	0.0920612i
$672$	0.815971	−	2.51130i	0.0314767	−	0.0968755i
$673$	−34.8437	+	25.3154i	−1.34312	+	0.975837i	−0.343801	+	0.939042i	$0.611715\pi$
$673$	−34.8437	+	25.3154i	−1.34312	+	0.975837i	−0.999323	+	0.0367944i	$0.988285\pi$
$674$	−4.52436			−0.174272
$675$	18.6393	+	0.311802i	0.717427	+	0.0120012i
$676$	2.31764			0.0891401
$677$	4.69926	−	3.41421i	0.180607	−	0.131219i	−0.493808	−	0.869571i	$-0.664396\pi$
$677$	4.69926	−	3.41421i	0.180607	−	0.131219i	0.674416	+	0.738352i	$0.264396\pi$
$678$	1.90351	−	5.85841i	0.0731040	−	0.224991i
$679$	22.1468	−	68.1610i	0.849918	−	2.61578i
$680$	1.82924	+	5.79428i	0.0701483	+	0.222200i
$681$	2.65463	+	8.17012i	0.101726	+	0.313079i
$682$	17.2433			0.660281
$683$	13.0003	+	40.0107i	0.497441	+	1.53097i	0.813118	+	0.582099i	$0.197769\pi$
$683$	13.0003	+	40.0107i	0.497441	+	1.53097i	−0.315677	+	0.948867i	$0.602231\pi$
$684$	−1.37577	−	0.999557i	−0.0526039	−	0.0382190i
$685$	18.9932	−	13.5581i	0.725692	−	0.518029i
$686$	−52.8313	+	38.3842i	−2.01711	+	1.46551i
$687$	2.75615	+	2.00246i	0.105154	+	0.0763986i
$688$	−30.4093	−	22.0936i	−1.15934	−	0.842312i
$689$	−38.0622	+	27.6538i	−1.45005	+	1.05353i
$690$	−7.26624	+	5.18694i	−0.276621	+	0.197464i
$691$	−1.91267	−	1.38964i	−0.0727614	−	0.0528643i	0.550810	−	0.834631i	$-0.314319\pi$
$691$	−1.91267	−	1.38964i	−0.0727614	−	0.0528643i	−0.623571	+	0.781766i	$0.714319\pi$
$692$	0.562247	+	1.73042i	0.0213734	+	0.0657806i
$693$	46.3780			1.76175
$694$	−11.9996	−	36.9308i	−0.455497	−	1.40188i
$695$	4.54074	+	14.3832i	0.172240	+	0.545585i
$696$	1.29302	−	3.97952i	0.0490119	−	0.150843i
$697$	2.19874	−	6.76702i	0.0832831	−	0.256319i
$698$	−19.4298	+	14.1166i	−0.735428	+	0.534320i
$699$	5.33742			0.201880
$700$	−2.84913	+	1.99807i	−0.107687	+	0.0755199i
$701$	−14.6281			−0.552494			−0.276247	−	0.961087i	$-0.589091\pi$
$701$	−14.6281			−0.552494			−0.276247	+	0.961087i	$0.589091\pi$
$702$	23.8093	−	17.2984i	0.898623	−	0.652888i
$703$	12.3883	−	38.1272i	0.467233	−	1.43800i
$704$	−8.56342	+	26.3555i	−0.322746	+	0.993310i
$705$	−8.27591	+	5.90769i	−0.311689	+	0.222496i
$706$	12.8864	+	39.6601i	0.484984	+	1.49263i
$707$	−13.0481			−0.490726
$708$	−0.409345	−	1.25983i	−0.0153841	−	0.0473474i
$709$	−22.1213	−	16.0721i	−0.830784	−	0.603600i	0.0889972	−	0.996032i	$-0.471634\pi$
$709$	−22.1213	−	16.0721i	−0.830784	−	0.603600i	−0.919781	+	0.392432i	$0.871634\pi$
$710$	−38.9634	−	0.325870i	−1.46227	−	0.0122297i
$711$	−9.21362	+	6.69409i	−0.345538	+	0.251048i
$712$	0.394180	+	0.286388i	0.0147725	+	0.0107329i
$713$	10.2413	+	7.44073i	0.383539	+	0.278657i
$714$	3.83842	−	2.78878i	0.143649	−	0.104367i
$715$	−14.4193	+	43.1468i	−0.539251	+	1.61360i
$716$	2.07759	+	1.50946i	0.0776433	+	0.0564111i
$717$	0.992606	+	3.05493i	0.0370695	+	0.114088i
$718$	−7.26207			−0.271018
$719$	6.04655	+	18.6094i	0.225498	+	0.694013i	0.998241	+	0.0592928i	$0.0188846\pi$
$719$	6.04655	+	18.6094i	0.225498	+	0.694013i	−0.772742	+	0.634720i	$0.781115\pi$
$720$	−24.3196	−	0.203397i	−0.906340	−	0.00758018i
$721$	14.1229	−	43.4659i	0.525966	−	1.61876i
$722$	1.07290	−	3.30203i	0.0399290	−	0.122889i
$723$	0.393586	−	0.285957i	0.0146376	−	0.0106349i
$724$	1.04962			0.0390088
$725$	−9.38091	+	6.57875i	−0.348398	+	0.244329i
$726$	−3.19322			−0.118511
$727$	18.7511	−	13.6235i	0.695441	−	0.505267i	−0.183003	−	0.983112i	$-0.558582\pi$
$727$	18.7511	−	13.6235i	0.695441	−	0.505267i	0.878444	+	0.477845i	$0.158582\pi$
$728$	21.8247	−	67.1695i	0.808877	−	2.48947i
$729$	−1.72528	+	5.30988i	−0.0638994	+	0.196662i
$730$	19.8914	+	14.7077i	0.736215	+	0.544356i
$731$	−2.72158	−	8.37617i	−0.100661	−	0.309804i
$732$	0.0644383			0.00238171
$733$	−3.76594	−	11.5904i	−0.139098	−	0.428100i	0.857107	−	0.515139i	$-0.172260\pi$
$733$	−3.76594	−	11.5904i	−0.139098	−	0.428100i	−0.996205	+	0.0870388i	$0.972260\pi$
$734$	11.8911	+	8.63936i	0.438907	+	0.318885i
$735$	−19.6313	−	14.5154i	−0.724113	−	0.535408i
$736$	2.67521	−	1.94365i	0.0986096	−	0.0716441i
$737$	−10.5243	−	7.64633i	−0.387666	−	0.281656i
$738$	21.4820	+	15.6076i	0.790762	+	0.574522i
$739$	14.9030	−	10.8276i	0.548214	−	0.398301i	−0.278913	−	0.960316i	$-0.589974\pi$
$739$	14.9030	−	10.8276i	0.548214	−	0.398301i	0.827127	+	0.562016i	$0.189974\pi$
$740$	0.842640	+	2.66913i	0.0309761	+	0.0981192i
$741$	13.5469	+	9.84237i	0.497656	+	0.361568i
$742$	−19.0434	−	58.6096i	−0.699106	−	2.15163i
$743$	−27.1298			−0.995297			−0.497648	−	0.867379i	$-0.665803\pi$
$743$	−27.1298			−0.995297			−0.497648	+	0.867379i	$0.665803\pi$
$744$	−1.76041	−	5.41800i	−0.0645399	−	0.198634i
$745$	6.60796	−	19.7730i	0.242097	−	0.724426i
$746$	−4.73556	+	14.5746i	−0.173381	+	0.533612i
$747$	−7.38851	+	22.7395i	−0.270331	+	0.831994i
$748$	0.440747	−	0.320222i	0.0161153	−	0.0117085i
$749$	−26.2714			−0.959935
$750$	−8.73533	−	6.68774i	−0.318969	−	0.244202i
$751$	−30.8170			−1.12453			−0.562263	−	0.826958i	$-0.690069\pi$
$751$	−30.8170			−1.12453			−0.562263	+	0.826958i	$0.690069\pi$
$752$	23.3656	−	16.9761i	0.852056	−	0.619055i
$753$	−5.62695	+	17.3180i	−0.205057	+	0.631102i
$754$	−5.58962	+	17.2031i	−0.203562	+	0.626499i
$755$	−6.27951	+	18.7902i	−0.228535	+	0.683844i
$756$	0.801865	+	2.46789i	0.0291636	+	0.0897562i
$757$	38.0445			1.38275			0.691375	−	0.722496i	$-0.257005\pi$
$757$	38.0445			1.38275			0.691375	+	0.722496i	$0.257005\pi$
$758$	−2.15408	−	6.62956i	−0.0782395	−	0.240797i
$759$	−8.32521	−	6.04862i	−0.302186	−	0.219551i
$760$	−8.45637	−	26.7862i	−0.306745	−	0.971639i
$761$	4.77807	−	3.47147i	0.173205	−	0.125841i	−0.497805	−	0.867289i	$-0.665861\pi$
$761$	4.77807	−	3.47147i	0.173205	−	0.125841i	0.671010	+	0.741448i	$0.265861\pi$
$762$	3.58740	+	2.60640i	0.129958	+	0.0944197i
$763$	−63.2101	−	45.9249i	−2.28836	−	1.66259i
$764$	1.17477	−	0.853523i	0.0425018	−	0.0308794i
$765$	−4.58203	−	3.38795i	−0.165664	−	0.122492i
$766$	14.5137	+	10.5448i	0.524400	+	0.380999i
$767$	−22.7491	−	70.0144i	−0.821421	−	2.52807i
$768$	−2.31603			−0.0835725
$769$	9.77817	+	30.0941i	0.352610	+	1.08522i	0.957382	+	0.288823i	$0.0932640\pi$
$769$	9.77817	+	30.0941i	0.352610	+	1.08522i	−0.604772	+	0.796398i	$0.706736\pi$
$770$	−47.9139	−	35.4275i	−1.72670	−	1.27672i
$771$	−4.04536	+	12.4503i	−0.145690	+	0.448388i
$772$	−0.989223	+	3.04451i	−0.0356029	+	0.109574i
$773$	−9.41935	+	6.84355i	−0.338790	+	0.246146i	−0.744151	−	0.668011i	$-0.767146\pi$
$773$	−9.41935	+	6.84355i	−0.338790	+	0.246146i	0.405361	+	0.914157i	$0.367146\pi$
$774$	32.8673			1.18139
$775$	−5.06798	+	14.7533i	−0.182047	+	0.529954i
$776$	−40.3900			−1.44992
$777$	−22.7312	+	16.5152i	−0.815477	+	0.592479i
$778$	5.52547	−	17.0056i	0.198098	−	0.609682i
$779$	−10.1645	+	31.2831i	−0.364181	+	1.12083i
$780$	−1.16906	−	0.00977744i	−0.0418591	−	0.000350089i
$781$	−13.8789	−	42.7149i	−0.496626	−	1.52846i
$782$	5.94160			0.212471
$783$	2.64018	+	8.12565i	0.0943525	+	0.290387i
$784$	56.1033	+	40.7615i	2.00369	+	1.45577i
$785$	−3.61848	+	10.8276i	−0.129149	+	0.386453i
$786$	6.09365	−	4.42730i	0.217353	−	0.157916i
$787$	−3.03440	−	2.20462i	−0.108165	−	0.0785862i	0.532388	−	0.846500i	$-0.321295\pi$
$787$	−3.03440	−	2.20462i	−0.108165	−	0.0785862i	−0.640553	+	0.767914i	$0.721295\pi$
$788$	2.24849	+	1.63362i	0.0800992	+	0.0581955i
$789$	4.97214	−	3.61247i	0.177013	−	0.128607i
$790$	14.6323	+	0.122377i	0.520593	+	0.00435398i
$791$	24.4195	+	17.7418i	0.868257	+	0.630826i
$792$	−8.07678	−	24.8578i	−0.286996	−	0.883283i
$793$	3.58112			0.127169
$794$	−17.2581	−	53.1151i	−0.612468	−	1.88498i
$795$	10.6739	−	7.61944i	0.378563	−	0.270234i
$796$	−0.217969	+	0.670839i	−0.00772569	+	0.0237772i
$797$	−2.69627	+	8.29827i	−0.0955069	+	0.293940i	−0.987385	−	0.158335i	$-0.949387\pi$
$797$	−2.69627	+	8.29827i	−0.0955069	+	0.293940i	0.891879	+	0.452275i	$0.149387\pi$
$798$	−17.7446	+	12.8922i	−0.628151	+	0.456378i
$799$	6.76721			0.239407
$800$	3.25612	+	2.44995i	0.115121	+	0.0866190i
$801$	−0.456951			−0.0161456
$802$	−16.1335	+	11.7217i	−0.569695	+	0.413907i
$803$	−8.81158	+	27.1193i	−0.310954	+	0.957018i
$804$	0.103307	−	0.317946i	0.00364335	−	0.0112131i
$805$	−13.1699	−	41.7168i	−0.464179	−	1.47033i
$806$	7.61011	+	23.4215i	0.268055	+	0.824987i
$807$	6.18719			0.217800
$808$	2.27235	+	6.99358i	0.0799410	+	0.246033i
$809$	−18.3556	−	13.3361i	−0.645350	−	0.468874i	0.216334	−	0.976319i	$-0.430590\pi$
$809$	−18.3556	−	13.3361i	−0.645350	−	0.468874i	−0.861684	+	0.507445i	$0.830590\pi$
$810$	13.6985	−	9.77853i	0.481315	−	0.343582i
$811$	−10.3578	+	7.52537i	−0.363711	+	0.264251i	−0.754598	−	0.656187i	$-0.772168\pi$
$811$	−10.3578	+	7.52537i	−0.363711	+	0.264251i	0.390887	+	0.920439i	$0.372168\pi$
$812$	−1.29029	−	0.937452i	−0.0452804	−	0.0328981i
$813$	1.35042	+	0.981134i	0.0473611	+	0.0344099i
$814$	−38.7753	+	28.1719i	−1.35907	+	0.987424i
$815$	13.5709	−	9.68744i	0.475366	−	0.339336i
$816$	−2.32014	−	1.68568i	−0.0812213	−	0.0590107i
$817$	12.5815	+	38.7220i	0.440172	+	1.35471i
$818$	−5.50040			−0.192317
$819$	20.4683	+	62.9949i	0.715220	+	2.20122i
$820$	−0.691380	−	2.19000i	−0.0241440	−	0.0764782i
$821$	9.90907	−	30.4970i	0.345829	−	1.06435i	−0.615310	−	0.788285i	$-0.710969\pi$
$821$	9.90907	−	30.4970i	0.345829	−	1.06435i	0.961139	−	0.276066i	$-0.0890310\pi$
$822$	−3.17334	+	9.76654i	−0.110683	+	0.340647i
$823$	40.3262	−	29.2987i	1.40568	−	1.02129i	0.411751	−	0.911296i	$-0.364917\pi$
$823$	40.3262	−	29.2987i	1.40568	−	1.02129i	0.993932	−	0.109992i	$-0.0350827\pi$
$824$	−25.7565			−0.897270
$825$	4.11979	−	11.9931i	0.143433	−	0.417544i
$826$	96.4291			3.35520
$827$	−22.4214	+	16.2901i	−0.779670	+	0.566463i	−0.904880	−	0.425667i	$-0.860040\pi$
$827$	−22.4214	+	16.2901i	−0.779670	+	0.566463i	0.125210	+	0.992130i	$0.460040\pi$
$828$	−0.461228	+	1.41951i	−0.0160288	+	0.0493315i
$829$	−5.36585	+	16.5144i	−0.186364	+	0.573568i	−0.999969	−	0.00784914i	$-0.997502\pi$
$829$	−5.36585	+	16.5144i	−0.186364	+	0.573568i	0.813606	+	0.581417i	$0.197502\pi$
$830$	25.0036	−	17.8486i	0.867887	−	0.619533i
$831$	−4.65492	−	14.3264i	−0.161478	−	0.496977i
$832$	−39.5779			−1.37212
$833$	5.02116	+	15.4535i	0.173973	+	0.535433i
$834$	−5.36973	−	3.90134i	−0.185939	−	0.135092i
$835$	0.687604	+	0.00575078i	0.0237955	+	0.000199014i
$836$	−2.03752	+	1.48034i	−0.0704691	+	0.0511988i
$837$	9.41062	+	6.83721i	0.325279	+	0.236329i
$838$	15.7157	+	11.4181i	0.542890	+	0.394433i
$839$	18.7826	−	13.6463i	0.648446	−	0.471124i	−0.214295	−	0.976769i	$-0.568745\pi$
$839$	18.7826	−	13.6463i	0.648446	−	0.471124i	0.862742	+	0.505645i	$0.168745\pi$
$840$	−6.23997	+	18.6718i	−0.215299	+	0.644240i
$841$	19.2131	+	13.9592i	0.662522	+	0.481350i
$842$	9.10657	+	28.0271i	0.313833	+	0.965879i
$843$	11.5873			0.399089
$844$	0.357098	+	1.09903i	0.0122918	+	0.0378303i
$845$	−35.9019	−	0.300266i	−1.23506	−	0.0103295i
$846$	−7.80400	+	24.0182i	−0.268307	+	0.825764i
$847$	4.83522	−	14.8813i	0.166140	−	0.511327i
$848$	−30.1358	+	21.8949i	−1.03487	+	0.751874i
$849$	6.91511			0.237326
$850$	2.14577	+	7.00030i	0.0735994	+	0.240108i
$851$	−35.1863			−1.20617
$852$	0.933777	−	0.678429i	0.0319907	−	0.0232426i
$853$	13.2845	−	40.8856i	0.454854	−	1.39990i	−0.416452	−	0.909157i	$-0.636727\pi$
$853$	13.2845	−	40.8856i	0.454854	−	1.39990i	0.871307	−	0.490739i	$-0.163273\pi$
$854$	−1.44953	+	4.46120i	−0.0496020	+	0.152659i
$855$	21.1822	+	15.6621i	0.724415	+	0.535632i
$856$	4.57519	+	14.0810i	0.156377	+	0.481279i
$857$	−1.20306			−0.0410958			−0.0205479	−	0.999789i	$-0.506541\pi$
$857$	−1.20306			−0.0410958			−0.0205479	+	0.999789i	$0.506541\pi$
$858$	−6.18631	−	19.0395i	−0.211197	−	0.649998i
$859$	17.6459	+	12.8205i	0.602071	+	0.437430i	0.846613	−	0.532208i	$-0.178638\pi$
$859$	17.6459	+	12.8205i	0.602071	+	0.437430i	−0.244542	+	0.969639i	$0.578638\pi$
$860$	−2.28569	−	1.69004i	−0.0779415	−	0.0576299i
$861$	18.6508	−	13.5506i	0.635617	−	0.461803i
$862$	−19.8701	−	14.4364i	−0.676777	−	0.491707i
$863$	20.4426	+	14.8524i	0.695874	+	0.505582i	0.878586	−	0.477584i	$-0.158487\pi$
$863$	20.4426	+	14.8524i	0.695874	+	0.505582i	−0.182712	+	0.983167i	$0.558487\pi$
$864$	2.45823	−	1.78601i	0.0836306	−	0.0607612i
$865$	−8.48541	−	26.8782i	−0.288513	−	0.913887i
$866$	22.0775	+	16.0402i	0.750224	+	0.545070i
$867$	−0.207649	−	0.639078i	−0.00705213	−	0.0217042i
$868$	−2.17140			−0.0737020
$869$	5.21207	+	16.0411i	0.176807	+	0.544157i
$870$	1.59814	−	4.78212i	0.0541822	−	0.162129i
$871$	5.74122	−	17.6696i	0.194534	−	0.598713i
$872$	−13.6068	+	41.8774i	−0.460784	+	1.41815i
$873$	30.6454	−	22.2652i	1.03719	−	0.753561i
$874$	−27.4673			−0.929095
$875$	44.3939	−	30.5824i	1.50079	−	1.03387i
$876$	−0.732798			−0.0247590
$877$	−27.1365	+	19.7158i	−0.916333	+	0.665755i	−0.942609	−	0.333900i	$-0.891635\pi$
$877$	−27.1365	+	19.7158i	−0.916333	+	0.665755i	0.0262756	+	0.999655i	$0.491635\pi$
$878$	−6.79413	+	20.9102i	−0.229291	+	0.705685i
$879$	−5.68575	+	17.4989i	−0.191776	+	0.590224i
$880$	−11.4165	+	34.1615i	−0.384850	+	1.15158i
$881$	1.79959	+	5.53857i	0.0606298	+	0.186599i	0.976784	−	0.214227i	$-0.0687232\pi$
$881$	1.79959	+	5.53857i	0.0606298	+	0.186599i	−0.916154	+	0.400826i	$0.868723\pi$
$882$	−60.6383			−2.04180
$883$	10.5267	+	32.3980i	0.354253	+	1.09028i	0.956441	+	0.291925i	$0.0942956\pi$
$883$	10.5267	+	32.3980i	0.354253	+	1.09028i	−0.602188	+	0.798354i	$0.705704\pi$
$884$	0.629473	+	0.457339i	0.0211715	+	0.0153820i
$885$	6.17782	+	19.5687i	0.207665	+	0.657796i
$886$	−45.4557	+	33.0255i	−1.52711	+	1.10951i
$887$	−27.7085	−	20.1314i	−0.930360	−	0.675946i	0.0157207	−	0.999876i	$-0.494996\pi$
$887$	−27.7085	−	20.1314i	−0.930360	−	0.675946i	−0.946081	+	0.323930i	$0.894996\pi$
$888$	12.8105	+	9.30739i	0.429893	+	0.312336i
$889$	−17.5786	+	12.7716i	−0.589568	+	0.428346i
$890$	0.472084	+	0.349059i	0.0158243	+	0.0117005i
$891$	15.6948	+	11.4030i	0.525797	+	0.382014i
$892$	−0.499829	−	1.53832i	−0.0167355	−	0.0515067i
$893$	−31.2840			−1.04688
$894$	2.83502	+	8.72528i	0.0948171	+	0.291817i
$895$	−31.9878	−	23.6518i	−1.06923	−	0.790591i
$896$	18.4486	−	56.7789i	0.616323	−	1.89685i
$897$	4.54158	−	13.9776i	0.151639	−	0.466697i
$898$	−15.1388	+	10.9990i	−0.505190	+	0.367042i
$899$	−7.14944			−0.238447
$900$	−1.83902	−	0.0307634i	−0.0613006	−	0.00102545i
$901$	−8.72801			−0.290772
$902$	31.8148	−	23.1148i	1.05932	−	0.769639i
$903$	8.81799	−	27.1390i	0.293444	−	0.903128i
$904$	5.25661	−	16.1782i	0.174832	−	0.538078i
$905$	−16.2593	−	0.135985i	−0.540478	−	0.00452029i
$906$	−2.69410	−	8.29158i	−0.0895054	−	0.275469i
$907$	28.1688			0.935331			0.467666	−	0.883906i	$-0.345095\pi$
$907$	28.1688			0.935331			0.467666	+	0.883906i	$0.345095\pi$
$908$	−0.570237	−	1.75501i	−0.0189240	−	0.0582420i
$909$	−5.57935	−	4.05364i	−0.185055	−	0.134451i
$910$	26.9748	−	80.7166i	0.894205	−	2.67573i
$911$	−1.01660	+	0.738604i	−0.0336815	+	0.0244710i	−0.604499	−	0.796606i	$-0.706627\pi$
$911$	−1.01660	+	0.738604i	−0.0336815	+	0.0244710i	0.570817	+	0.821077i	$0.306627\pi$
$912$	10.7257	+	7.79270i	0.355165	+	0.258042i
$913$	28.6475	+	20.8137i	0.948095	+	0.688832i
$914$	−15.2488	+	11.0789i	−0.504385	+	0.366457i
$915$	−0.998196	−	0.00834842i	−0.0329993	−	0.000275990i
$916$	−0.592044	−	0.430145i	−0.0195617	−	0.0142124i
$917$	11.4053	+	35.1020i	0.376637	+	1.15917i
$918$	5.45968			0.180196
$919$	1.85946	+	5.72284i	0.0613381	+	0.188779i	0.977030	−	0.213102i	$-0.0683566\pi$
$919$	1.85946	+	5.72284i	0.0613381	+	0.188779i	−0.915692	+	0.401881i	$0.868357\pi$
$920$	−20.0659	+	14.3239i	−0.661554	+	0.472245i
$921$	−3.84945	+	11.8474i	−0.126844	+	0.390384i
$922$	2.30568	−	7.09617i	0.0759337	−	0.233700i
$923$	51.8941	−	37.7033i	1.70811	−	1.24102i
$924$	1.76514			0.0580690
$925$	−12.7073	−	41.4559i	−0.417813	−	1.36306i
$926$	56.7041			1.86341
$927$	19.5424	−	14.1984i	0.641856	−	0.466336i
$928$	−0.577109	+	1.77616i	−0.0189445	+	0.0583053i
$929$	−7.38701	+	22.7349i	−0.242360	+	0.745907i	0.753700	+	0.657219i	$0.228267\pi$
$929$	−7.38701	+	22.7349i	−0.242360	+	0.745907i	−0.996059	+	0.0886879i	$0.971733\pi$
$930$	−2.06663	−	6.54621i	−0.0677674	−	0.214659i
$931$	−23.2122	−	71.4398i	−0.760749	−	2.34134i
$932$	−1.14652			−0.0375556
$933$	−0.703205	−	2.16424i	−0.0230219	−	0.0708541i
$934$	5.67861	+	4.12575i	0.185810	+	0.134999i
$935$	−6.86897	+	4.90336i	−0.224639	+	0.160357i
$936$	30.1996	−	21.9413i	0.987105	−	0.717174i
$937$	−0.0353101	−	0.0256543i	−0.00115353	−	0.000838088i	0.587208	−	0.809436i	$-0.300227\pi$
$937$	−0.0353101	−	0.0256543i	−0.00115353	−	0.000838088i	−0.588362	+	0.808598i	$0.700227\pi$
$938$	19.6882	+	14.3043i	0.642843	+	0.467052i
$939$	−5.96000	+	4.33020i	−0.194497	+	0.141311i
$940$	1.77773	−	1.26902i	0.0579833	−	0.0413909i
$941$	22.8239	+	16.5825i	0.744037	+	0.540575i	0.893973	−	0.448121i	$-0.147907\pi$
$941$	22.8239	+	16.5825i	0.744037	+	0.540575i	−0.149936	+	0.988696i	$0.547907\pi$
$942$	−1.55244	−	4.77791i	−0.0505812	−	0.155673i
$943$	28.8700			0.940138
$944$	−18.0116	−	55.4340i	−0.586227	−	1.80422i
$945$	−12.1017	−	38.3332i	−0.393669	−	1.24698i
$946$	15.0419	−	46.2941i	0.489053	−	1.50515i
$947$	−7.94145	+	24.4413i	−0.258062	+	0.794234i	0.735148	+	0.677906i	$0.237112\pi$
$947$	−7.94145	+	24.4413i	−0.258062	+	0.794234i	−0.993211	+	0.116328i	$0.962888\pi$
$948$	−0.350670	+	0.254777i	−0.0113892	+	0.00827476i
$949$	−40.7248			−1.32198
$950$	−9.91964	−	32.3615i	−0.321835	−	1.04995i
$951$	−13.2364			−0.429219
$952$	10.5999	−	7.70129i	0.343545	−	0.249600i
$953$	−3.06802	+	9.44241i	−0.0993831	+	0.305870i	−0.988371	−	0.152061i	$-0.951409\pi$
$953$	−3.06802	+	9.44241i	−0.0993831	+	0.305870i	0.888988	+	0.457930i	$0.151409\pi$
$954$	10.0652	−	30.9775i	0.325873	−	1.00293i
$955$	−18.3087	+	13.0695i	−0.592454	+	0.422918i
$956$	−0.213220	−	0.656223i	−0.00689602	−	0.0212238i
$957$	5.81183			0.187870
$958$	−4.20223	−	12.9331i	−0.135768	−	0.417850i
$959$	−40.7096	−	29.5773i	−1.31458	−	0.955100i
$960$	11.0319	+	0.0922651i	0.356052	+	0.00297784i
$961$	17.2048	−	12.5000i	0.554992	−	0.403225i
$962$	−55.3787	−	40.2350i	−1.78548	−	1.29723i
$963$	−11.2336	−	8.16167i	−0.361997	−	0.263006i
$964$	−0.0845455	+	0.0614259i	−0.00272303	+	0.00197840i
$965$	15.7182	−	47.0335i	0.505987	−	1.51406i
$966$	15.5743	+	11.3154i	0.501096	+	0.364067i
$967$	15.3591	+	47.2703i	0.493914	+	1.52011i	0.818642	+	0.574303i	$0.194727\pi$
$967$	15.3591	+	47.2703i	0.493914	+	1.52011i	−0.324729	+	0.945807i	$0.605273\pi$
$968$	−8.81817			−0.283427
$969$	0.959936	+	2.95438i	0.0308376	+	0.0949083i
$970$	−48.6683	−	0.407037i	−1.56264	−	0.0130692i
$971$	15.6683	−	48.2222i	0.502821	−	1.54752i	−0.301583	−	0.953440i	$-0.597515\pi$
$971$	15.6683	−	48.2222i	0.502821	−	1.54752i	0.804404	−	0.594083i	$-0.202485\pi$
$972$	−0.652972	+	2.00964i	−0.0209441	+	0.0644593i
$973$	26.3122	−	19.1170i	0.843532	−	0.612862i
$974$	33.8835			1.08570
$975$	18.1083	+	0.302919i	0.579930	+	0.00970117i
$976$	2.83536			0.0907575
$977$	13.9304	−	10.1210i	0.445673	−	0.323801i	−0.342212	−	0.939623i	$-0.611176\pi$
$977$	13.9304	−	10.1210i	0.445673	−	0.323801i	0.787885	+	0.615822i	$0.211176\pi$
$978$	−2.26739	+	6.97831i	−0.0725031	+	0.223142i
$979$	−0.209126	+	0.643623i	−0.00668369	+	0.0205703i
$980$	4.21697	+	3.11802i	0.134706	+	0.0996016i
$981$	−12.7611	−	39.2747i	−0.407431	−	1.25395i
$982$	−26.6925			−0.851793
$983$	4.17384	+	12.8458i	0.133125	+	0.409716i	0.995294	−	0.0969050i	$-0.0308943\pi$
$983$	4.17384	+	12.8458i	0.133125	+	0.409716i	−0.862169	+	0.506621i	$0.830894\pi$
$984$	−10.5109	−	7.63664i	−0.335076	−	0.243447i
$985$	−34.6191	−	25.5973i	−1.10306	−	0.815598i
$986$	−2.71479	+	1.97241i	−0.0864566	+	0.0628144i
$987$	17.7384	+	12.8877i	0.564621	+	0.410221i
$988$	−2.90997	−	2.11422i	−0.0925786	−	0.0672623i
$989$	28.9103	−	21.0046i	0.919295	−	0.667907i
$990$	−9.48168	−	30.0340i	−0.301348	−	0.954543i
$991$	3.08711	+	2.24292i	0.0980653	+	0.0712486i	0.635737	−	0.771905i	$-0.280696\pi$
$991$	3.08711	+	2.24292i	0.0980653	+	0.0712486i	−0.537672	+	0.843154i	$0.680696\pi$
$992$	0.785718	+	2.41819i	0.0249466	+	0.0767776i
$993$	8.67223			0.275205
$994$	25.9639	+	79.9086i	0.823524	+	2.53455i
$995$	3.46340	−	10.3635i	0.109797	−	0.328546i
$996$	−0.281206	+	0.865464i	−0.00891036	+	0.0274233i
$997$	6.03776	−	18.5823i	0.191218	−	0.588508i	−0.808782	−	0.588109i	$-0.799873\pi$
$997$	6.03776	−	18.5823i	0.191218	−	0.588508i	1.00000		0.000399635i	$-0.000127208\pi$
$998$	14.2322	−	10.3403i	0.450512	−	0.327316i
$999$	−32.3323			−1.02295

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.k.b.86.7	✓	76
25.16	even	5	inner	425.2.k.b.341.7	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.k.b.86.7	✓	76	1.1	even	1	trivial
425.2.k.b.341.7	yes	76	25.16	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18469 + 0.860728i) q^{2} +(-0.207649 + 0.639078i) q^{3} +(0.0446047 - 0.137279i) q^{4} +(-0.708744 + 2.12077i) q^{5} +(-0.304073 - 0.935839i) q^{6} +4.82170 q^{7} +(-0.839706 - 2.58435i) q^{8} +(2.06175 + 1.49795i) q^{9} +(-0.985767 - 3.12250i) q^{10} +(3.05345 - 2.21846i) q^{11} +(0.0784700 + 0.0570118i) q^{12} +(4.36092 + 3.16840i) q^{13} +(-5.71222 + 4.15017i) q^{14} +(-1.20817 - 0.893320i) q^{15} +(3.45277 + 2.50858i) q^{16} +(0.309017 + 0.951057i) q^{17} -3.73186 q^{18} +(-1.42855 - 4.39662i) q^{19} +(0.259525 + 0.191892i) q^{20} +(-1.00122 + 3.08145i) q^{21} +(-1.70790 + 5.25638i) q^{22} +(-3.28257 + 2.38493i) q^{23} +1.82596 q^{24} +(-3.99536 - 3.00617i) q^{25} -7.89347 q^{26} +(-3.01632 + 2.19149i) q^{27} +(0.215071 - 0.661920i) q^{28} +(0.708132 - 2.17940i) q^{29} +(2.20021 + 0.0184015i) q^{30} +(-0.964101 - 2.96720i) q^{31} -0.814975 q^{32} +(0.783725 + 2.41206i) q^{33} +(-1.18469 - 0.860728i) q^{34} +(-3.41735 + 10.2257i) q^{35} +(0.297601 - 0.216220i) q^{36} +(7.01575 + 5.09724i) q^{37} +(5.47668 + 3.97904i) q^{38} +(-2.93040 + 2.12906i) q^{39} +(6.07595 + 0.0508163i) q^{40} +(-5.75637 - 4.18225i) q^{41} +(-1.46615 - 4.51234i) q^{42} -8.80722 q^{43} +(-0.168350 - 0.518129i) q^{44} +(-4.63806 + 3.31084i) q^{45} +(1.83606 - 5.65080i) q^{46} +(2.09118 - 6.43600i) q^{47} +(-2.32014 + 1.68568i) q^{48} +16.2488 q^{49} +(7.32077 + 0.122463i) q^{50} -0.671967 q^{51} +(0.629473 - 0.457339i) q^{52} +(-2.69710 + 8.30083i) q^{53} +(1.68714 - 5.19247i) q^{54} +(2.54074 + 8.04800i) q^{55} +(-4.04881 - 12.4610i) q^{56} +3.10642 q^{57} +(1.03696 + 3.19143i) q^{58} +(-11.0489 - 8.02748i) q^{59} +(-0.176524 + 0.126010i) q^{60} +(0.537472 - 0.390496i) q^{61} +(3.69611 + 2.68538i) q^{62} +(9.94113 + 7.22266i) q^{63} +(-5.94004 + 4.31569i) q^{64} +(-9.81023 + 7.00295i) q^{65} +(-3.00460 - 2.18297i) q^{66} +(-1.06508 - 3.27799i) q^{67} +0.144344 q^{68} +(-0.842532 - 2.59305i) q^{69} +(-4.75307 - 15.0557i) q^{70} +(3.67724 - 11.3174i) q^{71} +(2.13996 - 6.58611i) q^{72} +(-6.11218 + 4.44076i) q^{73} -12.6988 q^{74} +(2.75081 - 1.92912i) q^{75} -0.667284 q^{76} +(14.7228 - 10.6968i) q^{77} +(1.63907 - 5.04455i) q^{78} +(-1.38095 + 4.25012i) q^{79} +(-7.76726 + 5.54459i) q^{80} +(1.58836 + 4.88846i) q^{81} +10.4193 q^{82} +(2.89920 + 8.92283i) q^{83} +(0.378359 + 0.274894i) q^{84} +(-2.23599 - 0.0187007i) q^{85} +(10.4338 - 7.58062i) q^{86} +(1.24577 + 0.905103i) q^{87} +(-8.29728 - 6.02833i) q^{88} +(-0.145061 + 0.105393i) q^{89} +(2.64493 - 7.91443i) q^{90} +(21.0271 + 15.2771i) q^{91} +(0.180983 + 0.557008i) q^{92} +2.09647 q^{93} +(3.06224 + 9.42461i) q^{94} +(10.3367 + 0.0864511i) q^{95} +(0.169229 - 0.520833i) q^{96} +(4.59316 - 14.1363i) q^{97} +(-19.2498 + 13.9858i) q^{98} +9.61859 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 6 q^{2} - 7 q^{3} - 26 q^{4} + 13 q^{5} + 12 q^{6} + 22 q^{7} + 10 q^{8} - 24 q^{9} - 6 q^{10} - 16 q^{11} - 15 q^{12} - q^{13} - 19 q^{14} - 3 q^{15} + 30 q^{16} - 19 q^{17} + 6 q^{18} + 18 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) \) 76 * q - 6 * q^2 - 7 * q^3 - 26 * q^4 + 13 * q^5 + 12 * q^6 + 22 * q^7 + 10 * q^8 - 24 * q^9 - 6 * q^10 - 16 * q^11 - 15 * q^12 - q^13 - 19 * q^14 - 3 * q^15 + 30 * q^16 - 19 * q^17 + 6 * q^18 + 18 * q^19 - 23 * q^20 - 22 * q^21 - 15 * q^22 - 8 * q^23 - 22 * q^24 + 35 * q^25 - 14 * q^26 - 10 * q^27 - 29 * q^28 - 25 * q^29 + 57 * q^30 + 22 * q^31 + 54 * q^32 - 22 * q^33 - 6 * q^34 - 19 * q^35 - 91 * q^36 - 49 * q^37 + 15 * q^38 + 25 * q^39 - 2 * q^40 + 16 * q^41 - 28 * q^42 + 104 * q^43 + 18 * q^44 + 10 * q^45 - 55 * q^46 - 26 * q^47 - 86 * q^48 + 2 * q^49 - 17 * q^50 + 18 * q^51 + 53 * q^52 - 41 * q^53 - 6 * q^54 + 67 * q^55 + 115 * q^56 + 84 * q^57 - 12 * q^58 - 7 * q^59 - 32 * q^60 - 21 * q^61 - 23 * q^62 - 21 * q^63 + 6 * q^64 - 72 * q^65 + 102 * q^66 - 15 * q^67 + 74 * q^68 + 48 * q^69 - 60 * q^70 - 8 * q^71 + 9 * q^72 - 25 * q^73 - 60 * q^74 + 68 * q^75 - 76 * q^76 - 36 * q^77 - 51 * q^78 + 2 * q^79 + 217 * q^80 + 20 * q^81 - 12 * q^82 - 41 * q^83 - 48 * q^84 - 7 * q^85 - 87 * q^86 - 54 * q^87 - 4 * q^88 + 77 * q^89 - 93 * q^90 + 79 * q^91 - 19 * q^92 + 72 * q^93 + 15 * q^94 + 57 * q^95 + 28 * q^96 + 13 * q^97 - 62 * q^98 - 64 * q^99

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