LMFDB - Embedded newform 425.2.k.c.86.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(86,425)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			86.15
Character	$\chi$	$=$	425.86
Dual form			425.2.k.c.341.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.15223 - 0.837145i) q^{2} +(-0.390637 + 1.20226i) q^{3} +(0.00879129 - 0.0270568i) q^{4} +(-0.580418 - 2.15942i) q^{5} +(0.556359 + 1.71230i) q^{6} +0.714392 q^{7} +(0.867706 + 2.67052i) q^{8} +(1.13423 + 0.824064i) q^{9} +(-2.47653 - 2.00226i) q^{10} +(2.01947 - 1.46723i) q^{11} +(0.0290950 + 0.0211388i) q^{12} +(3.63648 + 2.64206i) q^{13} +(0.823145 - 0.598050i) q^{14} +(2.82292 + 0.145740i) q^{15} +(3.28144 + 2.38411i) q^{16} +(-0.309017 - 0.951057i) q^{17} +1.99675 q^{18} +(-0.0462935 - 0.142477i) q^{19} +(-0.0635297 - 0.00327987i) q^{20} +(-0.279068 + 0.858883i) q^{21} +(1.09861 - 3.38118i) q^{22} +(2.26373 - 1.64470i) q^{23} -3.54961 q^{24} +(-4.32623 + 2.50674i) q^{25} +6.40185 q^{26} +(-4.50191 + 3.27083i) q^{27} +(0.00628043 - 0.0193292i) q^{28} +(0.542467 - 1.66954i) q^{29} +(3.37466 - 2.19526i) q^{30} +(-0.524693 - 1.61484i) q^{31} +0.160921 q^{32} +(0.975108 + 3.00107i) q^{33} +(-1.15223 - 0.837145i) q^{34} +(-0.414646 - 1.54268i) q^{35} +(0.0322678 - 0.0234440i) q^{36} +(0.0115674 + 0.00840422i) q^{37} +(-0.172614 - 0.125412i) q^{38} +(-4.59698 + 3.33990i) q^{39} +(5.26316 - 3.42376i) q^{40} +(-1.78837 - 1.29932i) q^{41} +(0.397459 + 1.22325i) q^{42} +2.75327 q^{43} +(-0.0219448 - 0.0675392i) q^{44} +(1.12118 - 2.92758i) q^{45} +(1.23149 - 3.79015i) q^{46} +(0.580598 - 1.78690i) q^{47} +(-4.14817 + 3.01382i) q^{48} -6.48964 q^{49} +(-2.88632 + 6.51002i) q^{50} +1.26413 q^{51} +(0.103455 - 0.0751644i) q^{52} +(-0.891803 + 2.74469i) q^{53} +(-2.44908 + 7.53750i) q^{54} +(-4.34051 - 3.50928i) q^{55} +(0.619882 + 1.90780i) q^{56} +0.189377 q^{57} +(-0.772602 - 2.37782i) q^{58} +(-10.5878 - 7.69248i) q^{59} +(0.0287603 - 0.0750978i) q^{60} +(-5.42647 + 3.94256i) q^{61} +(-1.95642 - 1.42142i) q^{62} +(0.810283 + 0.588705i) q^{63} +(-6.37747 + 4.63350i) q^{64} +(3.59465 - 9.38620i) q^{65} +(3.63588 + 2.64162i) q^{66} +(-0.334538 - 1.02960i) q^{67} -0.0284492 q^{68} +(1.09305 + 3.36407i) q^{69} +(-1.76921 - 1.43040i) q^{70} +(0.794366 - 2.44481i) q^{71} +(-1.21651 + 3.74402i) q^{72} +(-4.81434 + 3.49783i) q^{73} +0.0203639 q^{74} +(-1.32376 - 6.18046i) q^{75} -0.00426194 q^{76} +(1.44269 - 1.04818i) q^{77} +(-2.50080 + 7.69667i) q^{78} +(5.35194 - 16.4716i) q^{79} +(3.24370 - 8.46981i) q^{80} +(-0.874056 - 2.69007i) q^{81} -3.14833 q^{82} +(-4.52083 - 13.9137i) q^{83} +(0.0207853 + 0.0151014i) q^{84} +(-1.87438 + 1.21931i) q^{85} +(3.17240 - 2.30489i) q^{86} +(1.79531 + 1.30437i) q^{87} +(5.67057 + 4.11991i) q^{88} +(-1.94404 + 1.41243i) q^{89} +(-1.15895 - 4.31184i) q^{90} +(2.59787 + 1.88747i) q^{91} +(-0.0245992 - 0.0757084i) q^{92} +2.14641 q^{93} +(-0.826908 - 2.54496i) q^{94} +(-0.280798 + 0.182663i) q^{95} +(-0.0628616 + 0.193468i) q^{96} +(-2.42168 + 7.45316i) q^{97} +(-7.47757 + 5.43277i) q^{98} +3.49963 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 2 q^{2} + 2 q^{3} - 20 q^{4} - 17 q^{6} - 44 q^{7} + 15 q^{8} - 22 q^{9} - 2 q^{10} + 4 q^{11} + 14 q^{12} + 6 q^{13} - 10 q^{14} + 14 q^{15} - 32 q^{16} + 20 q^{17} - 62 q^{18} - 3 q^{19} + 16 q^{21}+ \cdots + 76 q^{99}+O(q^{100}) $ 80 * q + 2 * q^2 + 2 * q^3 - 20 * q^4 - 17 * q^6 - 44 * q^7 + 15 * q^8 - 22 * q^9 - 2 * q^10 + 4 * q^11 + 14 * q^12 + 6 * q^13 - 10 * q^14 + 14 * q^15 - 32 * q^16 + 20 * q^17 - 62 * q^18 - 3 * q^19 + 16 * q^21 + 17 * q^22 - 5 * q^23 + 30 * q^24 - 14 * q^25 + 18 * q^26 + 17 * q^27 + 32 * q^28 + 20 * q^29 - 114 * q^30 - 21 * q^31 - 88 * q^32 - 2 * q^34 - 2 * q^35 + 47 * q^36 + 6 * q^37 + 22 * q^38 - 46 * q^39 + 59 * q^40 - 26 * q^41 - 3 * q^42 - 102 * q^43 - 44 * q^44 + 74 * q^45 + 2 * q^46 + 2 * q^47 + 72 * q^48 + 108 * q^49 + 7 * q^50 + 18 * q^51 + 65 * q^52 - 18 * q^53 - 29 * q^54 - 49 * q^55 - 117 * q^56 + 2 * q^57 + 42 * q^58 + 21 * q^59 + 112 * q^60 + 4 * q^61 + 15 * q^62 + 41 * q^63 - 11 * q^64 + 8 * q^65 - 156 * q^66 + 21 * q^67 - 80 * q^68 - 67 * q^69 + 32 * q^70 - 4 * q^71 + 83 * q^72 - 2 * q^73 + 78 * q^74 - 68 * q^75 + 16 * q^76 + 2 * q^77 - 2 * q^78 - 53 * q^79 - 54 * q^80 - 21 * q^81 - 72 * q^82 - 42 * q^83 - 52 * q^84 + 42 * q^86 - 8 * q^87 + 68 * q^88 - 73 * q^89 + 97 * q^90 - 83 * q^91 + 117 * q^92 - 120 * q^93 + 80 * q^94 + 16 * q^95 + 88 * q^96 + 57 * q^97 + 17 * q^98 + 76 * 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 $

$2$	1.15223	−	0.837145i	0.814751	−	0.591951i	−0.100453	−	0.994942i	$-0.532029\pi$
$2$	1.15223	−	0.837145i	0.814751	−	0.591951i	0.915204	+	0.402991i	$0.132029\pi$
$3$	−0.390637	+	1.20226i	−0.225534	+	0.694123i	0.772703	+	0.634768i	$0.218904\pi$
$3$	−0.390637	+	1.20226i	−0.225534	+	0.694123i	−0.998237	+	0.0593551i	$0.981096\pi$
$4$	0.00879129	−	0.0270568i	0.00439564	−	0.0135284i
$5$	−0.580418	−	2.15942i	−0.259571	−	0.965724i
$5$	−0.580418	−	2.15942i	−0.259571	−	0.965724i
$6$	0.556359	+	1.71230i	0.227133	+	0.699043i
$7$	0.714392			0.270015			0.135007	−	0.990845i	$-0.456894\pi$
$7$	0.714392			0.270015			0.135007	+	0.990845i	$0.456894\pi$
$8$	0.867706	+	2.67052i	0.306780	+	0.944173i
$9$	1.13423	+	0.824064i	0.378076	+	0.274688i
$10$	−2.47653	−	2.00226i	−0.783147	−	0.633171i
$11$	2.01947	−	1.46723i	0.608893	−	0.442386i	−0.240132	−	0.970740i	$-0.577191\pi$
$11$	2.01947	−	1.46723i	0.608893	−	0.442386i	0.849024	+	0.528354i	$0.177191\pi$
$12$	0.0290950	+	0.0211388i	0.00839901	+	0.00610224i
$13$	3.63648	+	2.64206i	1.00858	+	0.732775i	0.963910	−	0.266227i	$-0.0857771\pi$
$13$	3.63648	+	2.64206i	1.00858	+	0.732775i	0.0446678	+	0.999002i	$0.485777\pi$
$14$	0.823145	−	0.598050i	0.219995	−	0.159836i
$15$	2.82292	+	0.145740i	0.728874	+	0.0376298i
$16$	3.28144	+	2.38411i	0.820361	+	0.596027i
$17$	−0.309017	−	0.951057i	−0.0749476	−	0.230665i
$17$	−0.309017	−	0.951057i	−0.0749476	−	0.230665i
$18$	1.99675			0.470639
$19$	−0.0462935	−	0.142477i	−0.0106204	−	0.0326864i	0.945606	−	0.325315i	$-0.105470\pi$
$19$	−0.0462935	−	0.142477i	−0.0106204	−	0.0326864i	−0.956226	+	0.292628i	$0.905470\pi$
$20$	−0.0635297	−	0.00327987i	−0.0142057	−	0.000733402i
$21$	−0.279068	+	0.858883i	−0.0608976	+	0.187424i
$22$	1.09861	−	3.38118i	0.234225	−	0.720869i
$23$	2.26373	−	1.64470i	0.472021	−	0.342944i	−0.326207	−	0.945298i	$-0.605771\pi$
$23$	2.26373	−	1.64470i	0.472021	−	0.342944i	0.798229	+	0.602355i	$0.205771\pi$
$24$	−3.54961			−0.724562
$25$	−4.32623	+	2.50674i	−0.865246	+	0.501348i
$26$	6.40185			1.25551
$27$	−4.50191	+	3.27083i	−0.866393	+	0.629471i
$28$	0.00628043	−	0.0193292i	0.00118689	−	0.00365287i
$29$	0.542467	−	1.66954i	0.100734	−	0.310026i	−0.887972	−	0.459898i	$-0.847886\pi$
$29$	0.542467	−	1.66954i	0.100734	−	0.310026i	0.988705	+	0.149872i	$0.0478860\pi$
$30$	3.37466	−	2.19526i	0.616125	−	0.400799i
$31$	−0.524693	−	1.61484i	−0.0942376	−	0.290033i	0.892817	−	0.450420i	$-0.148726\pi$
$31$	−0.524693	−	1.61484i	−0.0942376	−	0.290033i	−0.987054	+	0.160387i	$0.948726\pi$
$32$	0.160921			0.0284471
$33$	0.975108	+	3.00107i	0.169744	+	0.522420i
$34$	−1.15223	−	0.837145i	−0.197606	−	0.143569i
$35$	−0.414646	−	1.54268i	−0.0700880	−	0.260760i
$36$	0.0322678	−	0.0234440i	0.00537797	−	0.00390733i
$37$	0.0115674	+	0.00840422i	0.00190167	+	0.00138164i	0.588736	−	0.808326i	$-0.299626\pi$
$37$	0.0115674	+	0.00840422i	0.00190167	+	0.00138164i	−0.586834	+	0.809707i	$0.699626\pi$
$38$	−0.172614	−	0.125412i	−0.0280017	−	0.0203445i
$39$	−4.59698	+	3.33990i	−0.736105	+	0.534812i
$40$	5.26316	−	3.42376i	0.832179	−	0.541345i
$41$	−1.78837	−	1.29932i	−0.279296	−	0.202920i	0.439314	−	0.898333i	$-0.355221\pi$
$41$	−1.78837	−	1.29932i	−0.279296	−	0.202920i	−0.718610	+	0.695413i	$0.755221\pi$
$42$	0.397459	+	1.22325i	0.0613292	+	0.188752i
$43$	2.75327			0.419869			0.209935	−	0.977715i	$-0.432675\pi$
$43$	2.75327			0.419869			0.209935	+	0.977715i	$0.432675\pi$
$44$	−0.0219448	−	0.0675392i	−0.00330830	−	0.0101819i
$45$	1.12118	−	2.92758i	0.167135	−	0.436418i
$46$	1.23149	−	3.79015i	0.181574	−	0.558827i
$47$	0.580598	−	1.78690i	0.0846889	−	0.260646i	−0.899741	−	0.436425i	$-0.856245\pi$
$47$	0.580598	−	1.78690i	0.0846889	−	0.260646i	0.984430	+	0.175779i	$0.0562445\pi$
$48$	−4.14817	+	3.01382i	−0.598736	+	0.435007i
$49$	−6.48964			−0.927092
$50$	−2.88632	+	6.51002i	−0.408187	+	0.920656i
$51$	1.26413			0.177013
$52$	0.103455	−	0.0751644i	0.0143466	−	0.0104234i
$53$	−0.891803	+	2.74469i	−0.122499	+	0.377012i	−0.993437	−	0.114380i	$-0.963512\pi$
$53$	−0.891803	+	2.74469i	−0.122499	+	0.377012i	0.870939	+	0.491392i	$0.163512\pi$
$54$	−2.44908	+	7.53750i	−0.333278	+	1.02572i
$55$	−4.34051	−	3.50928i	−0.585274	−	0.473192i
$56$	0.619882	+	1.90780i	0.0828352	+	0.254941i
$57$	0.189377			0.0250836
$58$	−0.772602	−	2.37782i	−0.101448	−	0.312223i
$59$	−10.5878	−	7.69248i	−1.37841	−	1.00148i	−0.997026	−	0.0770603i	$-0.975447\pi$
$59$	−10.5878	−	7.69248i	−1.37841	−	1.00148i	−0.381387	−	0.924416i	$-0.624553\pi$
$60$	0.0287603	−	0.0750978i	0.00371294	−	0.00969509i
$61$	−5.42647	+	3.94256i	−0.694789	+	0.504794i	−0.878231	−	0.478237i	$-0.841276\pi$
$61$	−5.42647	+	3.94256i	−0.694789	+	0.504794i	0.183442	+	0.983031i	$0.441276\pi$
$62$	−1.95642	−	1.42142i	−0.248466	−	0.180521i
$63$	0.810283	+	0.588705i	0.102086	+	0.0741698i
$64$	−6.37747	+	4.63350i	−0.797184	+	0.579188i
$65$	3.59465	−	9.38620i	0.445861	−	1.16422i
$66$	3.63588	+	2.64162i	0.447546	+	0.325161i
$67$	−0.334538	−	1.02960i	−0.0408703	−	0.125786i	0.928540	−	0.371233i	$-0.121065\pi$
$67$	−0.334538	−	1.02960i	−0.0408703	−	0.125786i	−0.969410	+	0.245448i	$0.921065\pi$
$68$	−0.0284492			−0.00344997
$69$	1.09305	+	3.36407i	0.131588	+	0.404987i
$70$	−1.76921	−	1.43040i	−0.211461	−	0.170966i
$71$	0.794366	−	2.44481i	0.0942739	−	0.290145i	−0.892790	−	0.450473i	$-0.851255\pi$
$71$	0.794366	−	2.44481i	0.0942739	−	0.290145i	0.987064	+	0.160328i	$0.0512552\pi$
$72$	−1.21651	+	3.74402i	−0.143367	+	0.441237i
$73$	−4.81434	+	3.49783i	−0.563476	+	0.409389i	−0.832730	−	0.553680i	$-0.813223\pi$
$73$	−4.81434	+	3.49783i	−0.563476	+	0.409389i	0.269253	+	0.963069i	$0.413223\pi$
$74$	0.0203639			0.00236725
$75$	−1.32376	−	6.18046i	−0.152854	−	0.713658i
$76$	−0.00426194			−0.000488878
$77$	1.44269	−	1.04818i	0.164410	−	0.119451i
$78$	−2.50080	+	7.69667i	−0.283160	+	0.871476i
$79$	5.35194	−	16.4716i	0.602140	−	1.85320i	0.0867725	−	0.996228i	$-0.472345\pi$
$79$	5.35194	−	16.4716i	0.602140	−	1.85320i	0.515368	−	0.856969i	$-0.327655\pi$
$80$	3.24370	−	8.46981i	0.362656	−	0.946954i
$81$	−0.874056	−	2.69007i	−0.0971173	−	0.298896i
$82$	−3.14833			−0.347675
$83$	−4.52083	−	13.9137i	−0.496225	−	1.52722i	−0.815038	−	0.579407i	$-0.803284\pi$
$83$	−4.52083	−	13.9137i	−0.496225	−	1.52722i	0.318813	−	0.947818i	$-0.396716\pi$
$84$	0.0207853	+	0.0151014i	0.00226786	+	0.00164769i
$85$	−1.87438	+	1.21931i	−0.203305	+	0.132253i
$86$	3.17240	−	2.30489i	0.342089	−	0.248542i
$87$	1.79531	+	1.30437i	0.192478	+	0.139843i
$88$	5.67057	+	4.11991i	0.604485	+	0.439184i
$89$	−1.94404	+	1.41243i	−0.206068	+	0.149717i	−0.686033	−	0.727571i	$-0.740649\pi$
$89$	−1.94404	+	1.41243i	−0.206068	+	0.149717i	0.479965	+	0.877288i	$0.340649\pi$
$90$	−1.15895	−	4.31184i	−0.122164	−	0.454508i
$91$	2.59787	+	1.88747i	0.272331	+	0.197860i
$92$	−0.0245992	−	0.0757084i	−0.00256464	−	0.00789315i
$93$	2.14641			0.222573
$94$	−0.826908	−	2.54496i	−0.0852891	−	0.262493i
$95$	−0.280798	+	0.182663i	−0.0288093	+	0.0187408i
$96$	−0.0628616	+	0.193468i	−0.00641579	+	0.0197458i
$97$	−2.42168	+	7.45316i	−0.245884	+	0.756754i	0.749606	+	0.661885i	$0.230243\pi$
$97$	−2.42168	+	7.45316i	−0.245884	+	0.756754i	−0.995490	+	0.0948689i	$0.969757\pi$
$98$	−7.47757	+	5.43277i	−0.755349	+	0.548793i
$99$	3.49963			0.351726
$100$	0.0297912	+	0.139091i	0.00297912	+	0.0139091i
$101$	6.38663			0.635494			0.317747	−	0.948176i	$-0.397074\pi$
$101$	6.38663			0.635494			0.317747	+	0.948176i	$0.397074\pi$
$102$	1.45657	−	1.05826i	0.144222	−	0.104783i
$103$	−1.64991	+	5.07789i	−0.162570	+	0.500339i	−0.998849	−	0.0479651i	$-0.984726\pi$
$103$	−1.64991	+	5.07789i	−0.162570	+	0.500339i	0.836279	+	0.548304i	$0.184726\pi$
$104$	−3.90028	+	12.0038i	−0.382454	+	1.17707i
$105$	2.01667	+	0.104115i	0.196807	+	0.0101606i
$106$	1.27014	+	3.90908i	0.123367	+	0.379684i
$107$	13.4093			1.29632			0.648161	−	0.761504i	$-0.275538\pi$
$107$	13.4093			1.29632			0.648161	+	0.761504i	$0.275538\pi$
$108$	0.0489206	+	0.150562i	0.00470738	+	0.0144878i
$109$	−7.07100	−	5.13738i	−0.677279	−	0.492072i	0.195175	−	0.980768i	$-0.437473\pi$
$109$	−7.07100	−	5.13738i	−0.677279	−	0.492072i	−0.872454	+	0.488697i	$0.837473\pi$
$110$	−7.93905	−	0.409872i	−0.756958	−	0.0390798i
$111$	−0.0146227	+	0.0106240i	−0.00138792	+	0.00100839i
$112$	2.34424	+	1.70319i	0.221510	+	0.160936i
$113$	4.11523	+	2.98989i	0.387128	+	0.281265i	0.764278	−	0.644887i	$-0.223096\pi$
$113$	4.11523	+	2.98989i	0.387128	+	0.281265i	−0.377150	+	0.926152i	$0.623096\pi$
$114$	0.218207	−	0.158536i	0.0204369	−	0.0148483i
$115$	−4.86552	−	3.93375i	−0.453712	−	0.366824i
$116$	−0.0404035	−	0.0293549i	−0.00375137	−	0.00272553i
$117$	1.94737	+	5.99339i	0.180034	+	0.554089i
$118$	−18.6393			−1.71589
$119$	−0.220759	−	0.679427i	−0.0202370	−	0.0622830i
$120$	2.06026	+	7.66512i	0.188075	+	0.699727i
$121$	−1.47370	+	4.53558i	−0.133973	+	0.412325i
$122$	−2.95205	+	9.08549i	−0.267266	+	0.822562i
$123$	2.26072	−	1.64251i	0.203843	−	0.148100i
$124$	−0.0483051			−0.00433792
$125$	7.92413	+	7.88721i	0.708756	+	0.705454i
$126$	1.42646			0.127080
$127$	−11.6120	+	8.43663i	−1.03040	+	0.748630i	−0.968389	−	0.249445i	$-0.919752\pi$
$127$	−11.6120	+	8.43663i	−1.03040	+	0.748630i	−0.0620122	+	0.998075i	$0.519752\pi$
$128$	−3.56886	+	10.9838i	−0.315446	+	0.970842i
$129$	−1.07553	+	3.31014i	−0.0946950	+	0.291441i
$130$	−3.71575	−	13.8243i	−0.325893	−	1.21247i
$131$	−2.96717	−	9.13202i	−0.259243	−	0.797869i	−0.992964	−	0.118417i	$-0.962218\pi$
$131$	−2.96717	−	9.13202i	−0.259243	−	0.797869i	0.733721	−	0.679451i	$-0.237782\pi$
$132$	0.0897719			0.00781364
$133$	−0.0330717	−	0.101784i	−0.00286768	−	0.00882581i
$134$	−1.24739	−	0.906282i	−0.107758	−	0.0782909i
$135$	9.67610	+	7.82309i	0.832786	+	0.673304i
$136$	2.27168	−	1.65047i	0.194795	−	0.141527i
$137$	13.1003	+	9.51794i	1.11924	+	0.813173i	0.984093	−	0.177653i	$-0.0568506\pi$
$137$	13.1003	+	9.51794i	1.11924	+	0.813173i	0.135143	+	0.990826i	$0.456851\pi$
$138$	4.07567	+	2.96114i	0.346944	+	0.252069i
$139$	−5.09327	+	3.70047i	−0.432005	+	0.313870i	−0.782450	−	0.622713i	$-0.786030\pi$
$139$	−5.09327	+	3.70047i	−0.432005	+	0.313870i	0.350445	+	0.936583i	$0.386030\pi$
$140$	−0.0453851	−	0.00234311i	−0.00383574	−	0.000198029i
$141$	1.92150	+	1.39605i	0.161820	+	0.117569i
$142$	−1.13136	−	3.48198i	−0.0949420	−	0.292201i
$143$	11.2203			0.938285
$144$	1.75724	+	5.40824i	0.146437	+	0.450687i
$145$	−3.92011	−	0.202385i	−0.325547	−	0.0168071i
$146$	−2.61905	+	8.06061i	−0.216754	+	0.667101i
$147$	2.53509	−	7.80222i	0.209091	−	0.643516i
$148$	0.000329084	0	0.000239093i	2.70505e−5	0	1.96533e-5i
$149$	−2.16707			−0.177533			−0.0887667	−	0.996052i	$-0.528293\pi$
$149$	−2.16707			−0.177533			−0.0887667	+	0.996052i	$0.528293\pi$
$150$	−6.69922	−	6.01315i	−0.546989	−	0.490971i
$151$	3.85870			0.314016			0.157008	−	0.987597i	$-0.449815\pi$
$151$	3.85870			0.314016			0.157008	+	0.987597i	$0.449815\pi$
$152$	0.340318	−	0.247255i	0.0276034	−	0.0200551i
$153$	0.433236	−	1.33336i	0.0350251	−	0.107796i
$154$	0.784839	−	2.41549i	0.0632441	−	0.194645i
$155$	−3.18258	+	2.07032i	−0.255631	+	0.166292i
$156$	0.0499536	+	0.153741i	0.00399949	+	0.0123092i
$157$	17.8723			1.42637			0.713184	−	0.700977i	$-0.247252\pi$
$157$	17.8723			1.42637			0.713184	+	0.700977i	$0.247252\pi$
$158$	−7.62243	−	23.4594i	−0.606408	−	1.86633i
$159$	−2.95145	−	2.14435i	−0.234065	−	0.170058i
$160$	−0.0934013	−	0.347496i	−0.00738402	−	0.0274720i
$161$	1.61719	−	1.17496i	0.127453	−	0.0925998i
$162$	−3.25909	−	2.36787i	−0.256058	−	0.186037i
$163$	10.7501	+	7.81038i	0.842010	+	0.611756i	0.922931	−	0.384965i	$-0.125786\pi$
$163$	10.7501	+	7.81038i	0.842010	+	0.611756i	−0.0809216	+	0.996720i	$0.525786\pi$
$164$	−0.0508776	+	0.0369647i	−0.00397287	+	0.00288646i
$165$	5.91462	−	3.84755i	0.460453	−	0.299531i
$166$	−16.8568	−	12.2472i	−1.30834	−	0.950566i
$167$	−1.04953	−	3.23012i	−0.0812151	−	0.249954i	0.902202	−	0.431314i	$-0.141950\pi$
$167$	−1.04953	−	3.23012i	−0.0812151	−	0.249954i	−0.983417	+	0.181360i	$0.941950\pi$
$168$	−2.53582			−0.195642
$169$	2.22630	+	6.85185i	0.171254	+	0.527065i
$170$	−1.13898	+	2.97405i	−0.0873555	+	0.228099i
$171$	0.0649026	−	0.199750i	0.00496322	−	0.0152752i
$172$	0.0242048	−	0.0744946i	0.00184560	−	0.00568016i
$173$	2.22257	−	1.61479i	0.168979	−	0.122770i	−0.500082	−	0.865978i	$-0.666697\pi$
$173$	2.22257	−	1.61479i	0.168979	−	0.122770i	0.669060	+	0.743208i	$0.266697\pi$
$174$	3.16056			0.239602
$175$	−3.09062	+	1.79079i	−0.233629	+	0.135371i
$176$	10.1248			0.763186
$177$	13.3843	−	9.72428i	1.00603	−	0.730922i
$178$	−1.05758	+	3.25489i	−0.0792688	+	0.243964i
$179$	2.47002	−	7.60195i	0.184618	−	0.568196i	−0.815323	−	0.579006i	$-0.803441\pi$
$179$	2.47002	−	7.60195i	0.184618	−	0.568196i	0.999942	+	0.0108095i	$0.00344085\pi$
$180$	−0.0693543	−	0.0560727i	−0.00516936	−	0.00417941i
$181$	−5.45841	−	16.7992i	−0.405720	−	1.24868i	−0.920292	−	0.391231i	$-0.872049\pi$
$181$	−5.45841	−	16.7992i	−0.405720	−	1.24868i	0.514572	−	0.857447i	$-0.327951\pi$
$182$	4.57343			0.339005
$183$	−2.62019	−	8.06412i	−0.193690	−	0.596117i
$184$	6.35646	+	4.61824i	0.468605	+	0.340461i
$185$	0.0114343	−	0.0298569i	0.000840669	−	0.00219512i
$186$	2.47317	−	1.79686i	0.181341	−	0.131752i
$187$	−2.01947	−	1.46723i	−0.147678	−	0.107294i
$188$	−0.0432435	−	0.0314182i	−0.00315385	−	0.00229141i
$189$	−3.21613	+	2.33665i	−0.233939	+	0.169967i
$190$	−0.170629	+	0.445539i	−0.0123787	+	0.0323228i
$191$	−15.9902	−	11.6176i	−1.15701	−	0.840618i	−0.167615	−	0.985853i	$-0.553606\pi$
$191$	−15.9902	−	11.6176i	−1.15701	−	0.840618i	−0.989397	+	0.145234i	$0.953606\pi$
$192$	−3.07939	−	9.47738i	−0.222236	−	0.683971i
$193$	−3.79437			−0.273125			−0.136562	−	0.990631i	$-0.543605\pi$
$193$	−3.79437			−0.273125			−0.136562	+	0.990631i	$0.543605\pi$
$194$	3.44904	+	10.6151i	0.247627	+	0.762117i
$195$	9.88043	+	7.98829i	0.707552	+	0.572053i
$196$	−0.0570523	+	0.175589i	−0.00407517	+	0.0125421i
$197$	−8.38486	+	25.8060i	−0.597397	+	1.83860i	−0.0549818	+	0.998487i	$0.517510\pi$
$197$	−8.38486	+	25.8060i	−0.597397	+	1.83860i	−0.542415	+	0.840111i	$0.682490\pi$
$198$	4.03238	−	2.92969i	0.286569	−	0.208204i
$199$	−5.16301			−0.365996			−0.182998	−	0.983113i	$-0.558580\pi$
$199$	−5.16301			−0.365996			−0.182998	+	0.983113i	$0.558580\pi$
$200$	−10.4482	−	9.37819i	−0.738799	−	0.663138i
$201$	1.36853			0.0965285
$202$	7.35888	−	5.34654i	0.517769	−	0.376181i
$203$	0.387534	−	1.19271i	0.0271996	−	0.0837117i
$204$	0.0111133	−	0.0342032i	0.000778087	−	0.00239471i
$205$	−1.76779	+	4.61599i	−0.123468	+	0.322395i
$206$	2.34985	+	7.23211i	0.163722	+	0.503885i
$207$	3.92293			0.272662
$208$	5.63396	+	17.3395i	0.390645	+	1.20228i
$209$	−0.302534	−	0.219804i	−0.0209267	−	0.0152041i
$210$	2.41083	−	1.56828i	0.166363	−	0.108222i
$211$	19.4083	−	14.1009i	1.33612	−	0.970749i	0.336544	−	0.941668i	$-0.390742\pi$
$211$	19.4083	−	14.1009i	1.33612	−	0.970749i	0.999577	−	0.0290808i	$-0.00925800\pi$
$212$	0.0664223	+	0.0482586i	0.00456190	+	0.00331442i
$213$	2.62898	+	1.91006i	0.180135	+	0.130875i
$214$	15.4506	−	11.2255i	1.05618	−	0.767359i
$215$	−1.59805	−	5.94548i	−0.108986	−	0.405478i
$216$	−12.6412	−	9.18434i	−0.860122	−	0.624915i
$217$	−0.374836	−	1.15363i	−0.0254455	−	0.0783133i
$218$	−12.4482			−0.843096
$219$	−2.32462	−	7.15446i	−0.157084	−	0.483453i
$220$	−0.133109	+	0.0865891i	−0.00897418	+	0.00583784i
$221$	1.38901	−	4.27494i	0.0934351	−	0.287564i
$222$	−0.00795488	+	0.0244826i	−0.000533897	+	0.00164317i
$223$	−10.6580	+	7.74349i	−0.713712	+	0.518542i	−0.884369	−	0.466788i	$-0.845411\pi$
$223$	−10.6580	+	7.74349i	−0.713712	+	0.518542i	0.170657	+	0.985331i	$0.445411\pi$
$224$	0.114961			0.00768113
$225$	−6.97264	−	0.721882i	−0.464843	−	0.0481254i
$226$	7.24466			0.481908
$227$	−0.784624	+	0.570063i	−0.0520773	+	0.0378364i	−0.613519	−	0.789680i	$-0.710247\pi$
$227$	−0.784624	+	0.570063i	−0.0520773	+	0.0378364i	0.561442	+	0.827516i	$0.310247\pi$
$228$	0.00166487	−	0.00512395i	0.000110259	−	0.000339342i
$229$	8.08790	−	24.8920i	0.534463	−	1.64491i	−0.210343	−	0.977628i	$-0.567458\pi$
$229$	8.08790	−	24.8920i	0.534463	−	1.64491i	0.744806	−	0.667281i	$-0.232542\pi$
$230$	−8.89932	−	0.459448i	−0.586804	−	0.0302951i
$231$	0.696609	+	2.14394i	0.0458335	+	0.141061i
$232$	4.92925			0.323621
$233$	−7.48855	−	23.0474i	−0.490591	−	1.50988i	−0.823717	−	0.567002i	$-0.808103\pi$
$233$	−7.48855	−	23.0474i	−0.490591	−	1.50988i	0.333126	−	0.942882i	$-0.391897\pi$
$234$	7.26115	+	5.27554i	0.474676	+	0.344873i
$235$	−4.19566	−	0.216611i	−0.273694	−	0.0141301i
$236$	−0.301214	+	0.218845i	−0.0196074	+	0.0142456i
$237$	17.7124	+	12.8688i	1.15054	+	0.835919i
$238$	−0.823145	−	0.598050i	−0.0533566	−	0.0387658i
$239$	−12.4075	+	9.01457i	−0.802574	+	0.583104i	−0.911668	−	0.410927i	$-0.865205\pi$
$239$	−12.4075	+	9.01457i	−0.802574	+	0.583104i	0.109094	+	0.994031i	$0.465205\pi$
$240$	8.91578	+	7.20838i	0.575511	+	0.465299i
$241$	−15.4498	−	11.2249i	−0.995209	−	0.723062i	−0.0341536	−	0.999417i	$-0.510874\pi$
$241$	−15.4498	−	11.2249i	−0.995209	−	0.723062i	−0.961056	+	0.276355i	$0.910874\pi$
$242$	2.09889	+	6.45973i	0.134922	+	0.415247i
$243$	−13.1184			−0.841546
$244$	0.0589675	+	0.181483i	0.00377500	+	0.0116183i
$245$	3.76671	+	14.0139i	0.240646	+	0.895315i
$246$	1.22986	−	3.78511i	0.0784127	−	0.241330i
$247$	0.208086	−	0.640423i	0.0132402	−	0.0407492i
$248$	3.85718	−	2.80241i	0.244931	−	0.177953i
$249$	18.4938			1.17200
$250$	15.7332	+	2.45425i	0.995053	+	0.155220i
$251$	4.22737			0.266829			0.133415	−	0.991060i	$-0.457406\pi$
$251$	4.22737			0.266829			0.133415	+	0.991060i	$0.457406\pi$
$252$	0.0230519	−	0.0167482i	0.00145213	−	0.00105504i
$253$	2.15839	−	6.64284i	0.135697	−	0.417632i
$254$	−6.31706	+	19.4419i	−0.396368	+	1.21989i
$255$	−0.733722	−	2.72979i	−0.0459475	−	0.170946i
$256$	0.210948	+	0.649232i	0.0131843	+	0.0405770i
$257$	19.7121			1.22961			0.614805	−	0.788679i	$-0.289235\pi$
$257$	19.7121			1.22961			0.614805	+	0.788679i	$0.289235\pi$
$258$	1.53181	+	4.71442i	0.0953661	+	0.293507i
$259$	0.00826367	+	0.00600391i	0.000513479	+	0.000373065i
$260$	−0.222359	−	0.179776i	−0.0137901	−	0.0111493i
$261$	1.99109	−	1.44661i	0.123245	−	0.0895430i
$262$	−11.0637	−	8.03825i	−0.683518	−	0.496605i
$263$	1.63607	+	1.18868i	0.100885	+	0.0732970i	0.637084	−	0.770794i	$-0.280140\pi$
$263$	1.63607	+	1.18868i	0.100885	+	0.0732970i	−0.536199	+	0.844091i	$0.680140\pi$
$264$	−7.16833	+	5.20810i	−0.441180	+	0.320536i
$265$	6.44456	+	0.332716i	0.395886	+	0.0204386i
$266$	−0.123314	−	0.0895931i	−0.00756089	−	0.00549331i
$267$	−0.938687	−	2.88898i	−0.0574467	−	0.176803i
$268$	−0.0307987			−0.00188133
$269$	−1.72689	−	5.31482i	−0.105290	−	0.324051i	0.884508	−	0.466525i	$-0.154494\pi$
$269$	−1.72689	−	5.31482i	−0.105290	−	0.324051i	−0.989799	+	0.142474i	$0.954494\pi$
$270$	17.6982	+	0.913709i	1.07708	+	0.0556066i
$271$	−6.90485	+	21.2509i	−0.419440	+	1.29090i	0.488779	+	0.872407i	$0.337442\pi$
$271$	−6.90485	+	21.2509i	−0.419440	+	1.29090i	−0.908219	+	0.418495i	$0.862558\pi$
$272$	1.25340	−	3.85757i	0.0759986	−	0.233900i
$273$	−3.28404	+	2.38600i	−0.198759	+	0.144407i
$274$	23.0625			1.39326
$275$	−5.05872	+	11.4098i	−0.305053	+	0.688040i
$276$	0.100630			0.00605723
$277$	−10.9594	+	7.96245i	−0.658485	+	0.478417i	−0.866151	−	0.499783i	$-0.833413\pi$
$277$	−10.9594	+	7.96245i	−0.658485	+	0.478417i	0.207666	+	0.978200i	$0.433413\pi$
$278$	−2.77079	+	8.52761i	−0.166181	+	0.511452i
$279$	0.735609	−	2.26397i	0.0440398	−	0.135541i
$280$	3.75996	−	2.44591i	0.224701	−	0.146171i
$281$	9.17276	+	28.2309i	0.547201	+	1.68411i	0.715698	+	0.698409i	$0.246108\pi$
$281$	9.17276	+	28.2309i	0.547201	+	1.68411i	−0.168497	+	0.985702i	$0.553892\pi$
$282$	3.38272			0.201438
$283$	−7.82168	−	24.0727i	−0.464951	−	1.43097i	−0.859044	−	0.511901i	$-0.828941\pi$
$283$	−7.82168	−	24.0727i	−0.464951	−	1.43097i	0.394094	−	0.919070i	$-0.371059\pi$
$284$	−0.0591651	−	0.0429860i	−0.00351081	−	0.00255075i
$285$	−0.109918	−	0.408946i	−0.00651098	−	0.0242239i
$286$	12.9283	−	9.39299i	0.764469	−	0.555419i
$287$	−1.27759	−	0.928227i	−0.0754140	−	0.0547915i
$288$	0.182521	+	0.132609i	0.0107551	+	0.00781406i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	−4.68630	+	3.04851i	−0.275189	+	0.179014i
$291$	−8.01461	−	5.82296i	−0.469825	−	0.341348i
$292$	0.0523157	+	0.161011i	0.00306154	+	0.00942246i
$293$	21.4400			1.25254			0.626269	−	0.779607i	$-0.284581\pi$
$293$	21.4400			1.25254			0.626269	+	0.779607i	$0.284581\pi$
$294$	−3.61057	−	11.1122i	−0.210573	−	0.648077i
$295$	−10.4660	+	27.3284i	−0.609354	+	1.59112i
$296$	−0.0124065	+	0.0381834i	−0.000721116	+	0.00221937i
$297$	−4.29241	+	13.2107i	−0.249071	+	0.766561i
$298$	−2.49697	+	1.81415i	−0.144646	+	0.105091i
$299$	12.5774			0.727371
$300$	−0.178861	−	0.0185176i	−0.0103265	−	0.00106911i
$301$	1.96691			0.113371
$302$	4.44611	−	3.23029i	0.255845	−	0.185882i
$303$	−2.49485	+	7.67837i	−0.143326	+	0.441111i
$304$	0.187770	−	0.577898i	0.0107694	−	0.0331447i
$305$	11.6633	+	9.42973i	0.667838	+	0.539944i
$306$	−0.617031	−	1.89902i	−0.0352733	−	0.108560i
$307$	−26.6977			−1.52372			−0.761858	−	0.647744i	$-0.775713\pi$
$307$	−26.6977			−1.52372			−0.761858	+	0.647744i	$0.775713\pi$
$308$	−0.0156772	−	0.0482494i	−0.000893291	−	0.00274927i
$309$	−5.46041	−	3.96722i	−0.310632	−	0.225687i
$310$	−1.93391	+	5.04976i	−0.109839	+	0.286807i
$311$	−17.6916	+	12.8537i	−1.00320	+	0.728865i	−0.962771	−	0.270318i	$-0.912871\pi$
$311$	−17.6916	+	12.8537i	−1.00320	+	0.728865i	−0.0404250	+	0.999183i	$0.512871\pi$
$312$	−12.9081	−	9.37828i	−0.730777	−	0.530941i
$313$	13.2646	+	9.63730i	0.749760	+	0.544733i	0.895752	−	0.444553i	$-0.146638\pi$
$313$	13.2646	+	9.63730i	0.749760	+	0.544733i	−0.145992	+	0.989286i	$0.546638\pi$
$314$	20.5931	−	14.9617i	1.16213	−	0.844340i
$315$	0.800961	−	2.09144i	0.0451290	−	0.117839i
$316$	−0.398618	−	0.289613i	−0.0224240	−	0.0162920i
$317$	8.72299	+	26.8466i	0.489932	+	1.50786i	0.824709	+	0.565558i	$0.191339\pi$
$317$	8.72299	+	26.8466i	0.489932	+	1.50786i	−0.334777	+	0.942297i	$0.608661\pi$
$318$	−5.19588			−0.291371
$319$	−1.35411	−	4.16751i	−0.0758154	−	0.233336i
$320$	13.7073	+	11.0823i	0.766262	+	0.619519i
$321$	−5.23815	+	16.1214i	−0.292365	+	0.899807i
$322$	0.879770	−	2.70765i	0.0490276	−	0.150892i
$323$	−0.121198	+	0.0880554i	−0.00674363	+	0.00489953i
$324$	−0.0804687			−0.00447048
$325$	−22.3552	−	2.31445i	−1.24004	−	0.128382i
$326$	18.9250			1.04816
$327$	8.93864	−	6.49431i	0.494308	−	0.359136i
$328$	1.91810	−	5.90330i	0.105909	−	0.325955i
$329$	0.414774	−	1.27654i	0.0228672	−	0.0703782i
$330$	3.59406	−	9.38466i	0.197846	−	0.516609i
$331$	4.47077	+	13.7596i	0.245736	+	0.756297i	0.995515	+	0.0946082i	$0.0301598\pi$
$331$	4.47077	+	13.7596i	0.245736	+	0.756297i	−0.749779	+	0.661688i	$0.769840\pi$
$332$	−0.416204			−0.0228421
$333$	0.00619446	+	0.0190646i	0.000339454	+	0.00104473i
$334$	−3.91338	−	2.84324i	−0.214131	−	0.155575i
$335$	−2.02917	+	1.32001i	−0.110866	+	0.0721197i
$336$	−2.96342	+	2.15305i	−0.161668	+	0.117458i
$337$	−24.5634	−	17.8463i	−1.33805	−	0.972152i	−0.999513	−	0.0312002i	$-0.990067\pi$
$337$	−24.5634	−	17.8463i	−1.33805	−	0.972152i	−0.338540	−	0.940952i	$-0.609933\pi$
$338$	8.30120	+	6.03118i	0.451526	+	0.328053i
$339$	−5.20217	+	3.77960i	−0.282543	+	0.205280i
$340$	0.0165124	+	0.0614339i	0.000895512	+	0.00333172i
$341$	−3.42894	−	2.49127i	−0.185687	−	0.134910i
$342$	−0.0924366	−	0.284491i	−0.00499840	−	0.0153835i
$343$	−9.63689			−0.520343
$344$	2.38903	+	7.35267i	0.128808	+	0.396429i
$345$	6.63003	−	4.31293i	0.356949	−	0.232200i
$346$	1.20910	−	3.72122i	0.0650015	−	0.200054i
$347$	−0.216697	+	0.666924i	−0.0116329	+	0.0358023i	−0.956704	−	0.291061i	$-0.905992\pi$
$347$	−0.216697	+	0.666924i	−0.0116329	+	0.0358023i	0.945072	+	0.326863i	$0.105992\pi$
$348$	0.0510752	−	0.0371083i	0.00273792	−	0.00198921i
$349$	16.5119			0.883859			0.441930	−	0.897050i	$-0.354294\pi$
$349$	16.5119			0.883859			0.441930	+	0.897050i	$0.354294\pi$
$350$	−2.06196	+	4.65071i	−0.110216	+	0.248591i
$351$	−25.0128			−1.33509
$352$	0.324974	−	0.236108i	0.0173212	−	0.0125846i
$353$	8.01334	−	24.6625i	0.426507	−	1.31265i	−0.475037	−	0.879966i	$-0.657565\pi$
$353$	8.01334	−	24.6625i	0.426507	−	1.31265i	0.901544	−	0.432687i	$-0.142435\pi$
$354$	7.28120	−	22.4092i	0.386992	−	1.19104i
$355$	−5.74044	−	0.296364i	−0.304671	−	0.0157293i
$356$	0.0211252	+	0.0650166i	0.00111963	+	0.00344587i
$357$	0.903083			0.0477962
$358$	−3.51790	−	10.8270i	−0.185927	−	0.572223i
$359$	10.1721	+	7.39050i	0.536865	+	0.390055i	0.822920	−	0.568158i	$-0.192344\pi$
$359$	10.1721	+	7.39050i	0.536865	+	0.390055i	−0.286054	+	0.958213i	$0.592344\pi$
$360$	8.79102	+	0.453857i	0.463327	+	0.0239204i
$361$	15.3532	−	11.1547i	0.808061	−	0.587091i
$362$	−20.3528	−	14.7871i	−1.06972	−	0.777195i
$363$	−4.87725	−	3.54353i	−0.255989	−	0.185987i
$364$	0.0739074	−	0.0536969i	0.00387380	−	0.00281448i
$365$	10.3476	+	8.36601i	0.541619	+	0.437897i
$366$	−9.76991	−	7.09826i	−0.510681	−	0.371032i
$367$	0.650318	+	2.00147i	0.0339463	+	0.104476i	0.966594	−	0.256312i	$-0.0825076\pi$
$367$	0.650318	+	2.00147i	0.0339463	+	0.104476i	−0.932648	+	0.360789i	$0.882508\pi$
$368$	11.3495			0.591632
$369$	−0.957687	−	2.94746i	−0.0498552	−	0.153438i
$370$	−0.0118196	−	0.0439743i	−0.000614470	−	0.00228611i
$371$	−0.637097	+	1.96078i	−0.0330764	+	0.101799i
$372$	0.0188697	−	0.0580751i	0.000978351	−	0.00301105i
$373$	−13.2077	+	9.59594i	−0.683868	+	0.496859i	−0.874639	−	0.484776i	$-0.838901\pi$
$373$	−13.2077	+	9.59594i	−0.683868	+	0.496859i	0.190771	+	0.981635i	$0.438901\pi$
$374$	−3.55518			−0.183834
$375$	−12.5779	+	6.44581i	−0.649521	+	0.332860i
$376$	5.27573			0.272075
$377$	6.38370	−	4.63803i	0.328777	−	0.238871i
$378$	−1.74961	+	5.38473i	−0.0899900	+	0.276961i
$379$	9.54259	−	29.3691i	0.490170	−	1.50859i	−0.334182	−	0.942509i	$-0.608460\pi$
$379$	9.54259	−	29.3691i	0.490170	−	1.50859i	0.824351	−	0.566079i	$-0.191540\pi$
$380$	0.00247371	+	0.00920334i	0.000126898	+	0.000472121i
$381$	−5.60691	−	17.2563i	−0.287251	−	0.884067i
$382$	−28.1500			−1.44028
$383$	3.28716	+	10.1168i	0.167966	+	0.516947i	0.999243	−	0.0389126i	$-0.0123894\pi$
$383$	3.28716	+	10.1168i	0.167966	+	0.516947i	−0.831277	+	0.555859i	$0.812389\pi$
$384$	−11.8113	−	8.58138i	−0.602740	−	0.437917i
$385$	−3.10082	−	2.50700i	−0.158033	−	0.127769i
$386$	−4.37199	+	3.17644i	−0.222528	+	0.161676i
$387$	3.12283	+	2.26887i	0.158742	+	0.115333i
$388$	0.180369	+	0.131046i	0.00915685	+	0.00665284i
$389$	−0.871150	+	0.632927i	−0.0441691	+	0.0320907i	−0.609651	−	0.792670i	$-0.708690\pi$
$389$	−0.871150	+	0.632927i	−0.0441691	+	0.0320907i	0.565482	+	0.824761i	$0.308690\pi$
$390$	18.0719	+	0.933004i	0.915106	+	0.0472445i
$391$	−2.26373	−	1.64470i	−0.114482	−	0.0831760i
$392$	−5.63110	−	17.3307i	−0.284414	−	0.875335i
$393$	12.1381			0.612288
$394$	11.9420	+	36.7538i	0.601631	+	1.85163i
$395$	−38.6755	−	1.99671i	−1.94598	−	0.100466i
$396$	0.0307662	−	0.0946887i	0.00154606	−	0.00475828i
$397$	−5.71992	+	17.6041i	−0.287074	+	0.883524i	0.698695	+	0.715420i	$0.253765\pi$
$397$	−5.71992	+	17.6041i	−0.287074	+	0.883524i	−0.985769	+	0.168104i	$0.946235\pi$
$398$	−5.94898	+	4.32219i	−0.298196	+	0.216652i
$399$	0.135290			0.00677296
$400$	−20.1726	−	2.08848i	−1.00863	−	0.104424i
$401$	3.70518			0.185028			0.0925138	−	0.995711i	$-0.470510\pi$
$401$	3.70518			0.185028			0.0925138	+	0.995711i	$0.470510\pi$
$402$	1.57686	−	1.14566i	0.0786467	−	0.0571402i
$403$	2.35846	−	7.25860i	0.117483	−	0.361576i
$404$	0.0561467	−	0.172802i	0.00279340	−	0.00859721i
$405$	−5.30168	+	3.44882i	−0.263443	+	0.171373i
$406$	−0.551940	−	1.69870i	−0.0273923	−	0.0843050i
$407$	0.0356909			0.00176913
$408$	1.09689	+	3.37588i	0.0543042	+	0.167131i
$409$	−11.2860	−	8.19978i	−0.558059	−	0.405453i	0.272689	−	0.962102i	$-0.412087\pi$
$409$	−11.2860	−	8.19978i	−0.558059	−	0.405453i	−0.830748	+	0.556649i	$0.812087\pi$
$410$	1.82735	+	6.79859i	0.0902464	+	0.335759i
$411$	−16.5605	+	12.0319i	−0.816868	+	0.593489i
$412$	0.122887	+	0.0892823i	0.00605419	+	0.00439862i
$413$	−7.56384	−	5.49545i	−0.372192	−	0.270413i
$414$	4.52012	−	3.28406i	0.222152	−	0.161403i
$415$	−27.4216	+	17.8381i	−1.34607	+	0.875640i
$416$	0.585185	+	0.425162i	0.0286911	+	0.0208453i
$417$	−2.45930	−	7.56896i	−0.120433	−	0.370653i
$418$	−0.532597			−0.0260502
$419$	−0.162778	−	0.500980i	−0.00795223	−	0.0244745i	0.947002	−	0.321229i	$-0.104096\pi$
$419$	−0.162778	−	0.500980i	−0.00795223	−	0.0244745i	−0.954954	+	0.296754i	$0.904096\pi$
$420$	0.0205461	−	0.0536493i	0.00100255	−	0.00261782i
$421$	−4.93054	+	15.1747i	−0.240300	+	0.739567i	0.756074	+	0.654486i	$0.227115\pi$
$421$	−4.93054	+	15.1747i	−0.240300	+	0.739567i	−0.996374	+	0.0850811i	$0.972885\pi$
$422$	10.5583	−	32.4951i	0.513970	−	1.58184i
$423$	2.13105	−	1.54830i	0.103615	−	0.0752807i
$424$	−8.10357			−0.393544
$425$	3.72093	+	3.33986i	0.180492	+	0.162007i
$426$	4.62819			0.224237
$427$	−3.87663	+	2.81654i	−0.187603	+	0.136302i
$428$	0.117885	−	0.362811i	0.00569817	−	0.0175372i
$429$	−4.38305	+	13.4896i	−0.211616	+	0.651286i
$430$	−6.81855	−	5.51277i	−0.328819	−	0.265849i
$431$	11.3820	+	35.0301i	0.548249	+	1.68734i	0.713136	+	0.701026i	$0.247274\pi$
$431$	11.3820	+	35.0301i	0.548249	+	1.68734i	−0.164886	+	0.986313i	$0.552726\pi$
$432$	−22.5708			−1.08594
$433$	−1.10631	−	3.40488i	−0.0531660	−	0.163628i	0.920948	−	0.389686i	$-0.127416\pi$
$433$	−1.10631	−	3.40488i	−0.0531660	−	0.163628i	−0.974114	+	0.226057i	$0.927416\pi$
$434$	−1.39765	−	1.01545i	−0.0670894	−	0.0487433i
$435$	1.77466	−	4.63392i	0.0850883	−	0.222179i
$436$	−0.201164	+	0.146154i	−0.00963402	+	0.00699953i
$437$	−0.339127	−	0.246390i	−0.0162227	−	0.0117865i
$438$	−8.66782	−	6.29754i	−0.414165	−	0.300908i
$439$	−10.4289	+	7.57706i	−0.497746	+	0.361634i	−0.808155	−	0.588969i	$-0.799534\pi$
$439$	−10.4289	+	7.57706i	−0.497746	+	0.361634i	0.310409	+	0.950603i	$0.399534\pi$
$440$	5.60534	−	14.6364i	0.267224	−	0.697765i
$441$	−7.36073	−	5.34788i	−0.350511	−	0.254661i
$442$	−1.97828	−	6.08852i	−0.0940972	−	0.289602i
$443$	15.0335			0.714262			0.357131	−	0.934054i	$-0.383755\pi$
$443$	15.0335			0.714262			0.357131	+	0.934054i	$0.383755\pi$
$444$	0.000158899	0	0.000489042i	7.54103e−6	0	2.32089e-5i
$445$	4.17839	+	3.37821i	0.198075	+	0.160143i
$446$	−5.79806	+	17.8446i	−0.274546	+	0.844965i
$447$	0.846538	−	2.60538i	0.0400399	−	0.123230i
$448$	−4.55602	+	3.31014i	−0.215251	+	0.156389i
$449$	−27.3740			−1.29186			−0.645929	−	0.763398i	$-0.723530\pi$
$449$	−27.3740			−1.29186			−0.645929	+	0.763398i	$0.723530\pi$
$450$	−8.63841	+	5.00534i	−0.407219	+	0.235954i
$451$	−5.51796			−0.259830
$452$	0.117075	−	0.0850599i	0.00550674	−	0.00400088i
$453$	−1.50735	+	4.63915i	−0.0708215	+	0.217966i
$454$	−0.426843	+	1.31369i	−0.0200327	+	0.0616544i
$455$	2.56799	−	6.70543i	0.120389	−	0.314355i
$456$	0.164324	+	0.505737i	0.00769517	+	0.0236833i
$457$	−32.1594			−1.50435			−0.752176	−	0.658962i	$-0.770996\pi$
$457$	−32.1594			−1.50435			−0.752176	+	0.658962i	$0.770996\pi$
$458$	−11.5191	−	35.4521i	−0.538251	−	1.65657i
$459$	4.50191	+	3.27083i	0.210131	+	0.152669i
$460$	−0.149209	+	0.0970626i	−0.00695690	+	0.00452557i
$461$	13.9722	−	10.1514i	0.650751	−	0.472799i	−0.212776	−	0.977101i	$-0.568250\pi$
$461$	13.9722	−	10.1514i	0.650751	−	0.472799i	0.863527	+	0.504302i	$0.168250\pi$
$462$	2.59745	+	1.88716i	0.120844	+	0.0877984i
$463$	34.1813	+	24.8341i	1.58854	+	1.15414i	0.905989	+	0.423301i	$0.139129\pi$
$463$	34.1813	+	24.8341i	1.58854	+	1.15414i	0.682549	+	0.730840i	$0.260871\pi$
$464$	5.76045	−	4.18521i	0.267422	−	0.194294i
$465$	−1.24582	−	4.63502i	−0.0577734	−	0.214944i
$466$	−27.9225	−	20.2869i	−1.29349	−	0.939773i
$467$	−12.1400	−	37.3631i	−0.561772	−	1.72896i	−0.677353	−	0.735658i	$-0.736873\pi$
$467$	−12.1400	−	37.3631i	−0.561772	−	1.72896i	0.115581	−	0.993298i	$-0.463127\pi$
$468$	0.179282			0.00828730
$469$	−0.238991	−	0.735539i	−0.0110356	−	0.0339640i
$470$	−5.01570	+	3.26279i	−0.231357	+	0.150501i
$471$	−6.98160	+	21.4871i	−0.321695	+	0.990075i
$472$	11.3559	−	34.9498i	0.522696	−	1.60869i
$473$	5.56014	−	4.03968i	0.255655	−	0.185745i
$474$	31.1818			1.43223
$475$	0.557428	+	0.500341i	0.0255765	+	0.0229572i
$476$	−0.0203239			−0.000931544
$477$	−3.27330	+	2.37819i	−0.149874	+	0.108890i
$478$	−6.74980	+	20.7738i	−0.308729	+	0.950169i
$479$	−5.69283	+	17.5207i	−0.260112	+	0.800542i	0.732667	+	0.680587i	$0.238275\pi$
$479$	−5.69283	+	17.5207i	−0.260112	+	0.800542i	−0.992779	+	0.119955i	$0.961725\pi$
$480$	0.454266	+	0.0234525i	0.0207343	+	0.00107046i
$481$	0.0198602	+	0.0611235i	0.000905549	+	0.00278699i
$482$	−27.1987			−1.23886
$483$	0.780868	+	2.40327i	0.0355307	+	0.109352i
$484$	0.109762	+	0.0797471i	0.00498920	+	0.00362487i
$485$	17.5001	+	0.903485i	0.794640	+	0.0410251i
$486$	−15.1154	+	10.9820i	−0.685650	+	0.498154i
$487$	−13.2382	−	9.61814i	−0.599882	−	0.435840i	0.245955	−	0.969281i	$-0.420898\pi$
$487$	−13.2382	−	9.61814i	−0.599882	−	0.435840i	−0.845837	+	0.533442i	$0.820898\pi$
$488$	−15.2373	−	11.0705i	−0.689760	−	0.501140i
$489$	−13.5894	+	9.87331i	−0.614536	+	0.446487i
$490$	16.0718	+	12.9940i	0.726049	+	0.587008i
$491$	8.03540	+	5.83806i	0.362633	+	0.263468i	0.754149	−	0.656703i	$-0.228049\pi$
$491$	8.03540	+	5.83806i	0.362633	+	0.263468i	−0.391517	+	0.920171i	$0.628049\pi$
$492$	−0.0245664	−	0.0756077i	−0.00110754	−	0.00340866i
$493$	−1.75546			−0.0790620
$494$	−0.296364	−	0.912114i	−0.0133340	−	0.0410380i
$495$	−2.03125	−	7.55718i	−0.0912977	−	0.339670i
$496$	2.12820	−	6.54993i	0.0955590	−	0.294100i
$497$	0.567489	−	1.74655i	0.0254553	−	0.0783435i
$498$	21.3092	−	15.4820i	0.954886	−	0.693766i
$499$	25.1462			1.12570			0.562849	−	0.826560i	$-0.309705\pi$
$499$	25.1462			1.12570			0.562849	+	0.826560i	$0.309705\pi$
$500$	0.283066	−	0.145063i	0.0126591	−	0.00648741i
$501$	4.29342			0.191816
$502$	4.87091	−	3.53893i	0.217399	−	0.157950i
$503$	8.20594	−	25.2553i	0.365885	−	1.12608i	−0.583540	−	0.812084i	$-0.698333\pi$
$503$	8.20594	−	25.2553i	0.365885	−	1.12608i	0.949425	−	0.313993i	$-0.101667\pi$
$504$	−0.869063	+	2.67470i	−0.0387111	+	0.119141i
$505$	−3.70692	−	13.7915i	−0.164956	−	0.613711i
$506$	−3.07406	−	9.46097i	−0.136658	−	0.420591i
$507$	−9.10736			−0.404472
$508$	0.126184	+	0.388353i	0.00559849	+	0.0172304i
$509$	14.6671	+	10.6563i	0.650110	+	0.472332i	0.863309	−	0.504676i	$-0.168388\pi$
$509$	14.6671	+	10.6563i	0.650110	+	0.472332i	−0.213199	+	0.977009i	$0.568388\pi$
$510$	−3.13065	−	2.53112i	−0.138627	−	0.112080i
$511$	−3.43933	+	2.49882i	−0.152147	+	0.110541i
$512$	−17.9002	−	13.0053i	−0.791086	−	0.574758i
$513$	0.674425	+	0.489999i	0.0297766	+	0.0216340i
$514$	22.7129	−	16.5019i	1.00183	−	0.727869i
$515$	11.9229	+	0.615550i	0.525388	+	0.0271244i
$516$	0.0801064	+	0.0582007i	0.00352649	+	0.00256214i
$517$	−1.44929	−	4.46045i	−0.0637396	−	0.196170i
$518$	0.0145478			0.000639193
$519$	1.07317	+	3.30289i	0.0471071	+	0.144981i
$520$	28.1852	+	1.45513i	1.23600	+	0.0638115i
$521$	−13.6600	+	42.0412i	−0.598455	+	1.84186i	−0.0617414	+	0.998092i	$0.519665\pi$
$521$	−13.6600	+	42.0412i	−0.598455	+	1.84186i	−0.536714	+	0.843764i	$0.680335\pi$
$522$	1.08317	−	3.33366i	0.0474092	−	0.145911i
$523$	23.0778	−	16.7670i	1.00912	−	0.733170i	0.0450974	−	0.998983i	$-0.485640\pi$
$523$	23.0778	−	16.7670i	1.00912	−	0.733170i	0.964025	+	0.265812i	$0.0856402\pi$
$524$	−0.273169			−0.0119334
$525$	−0.945682	−	4.41527i	−0.0412729	−	0.192698i
$526$	2.88023			0.125584
$527$	−1.37366	+	0.998025i	−0.0598377	+	0.0434746i
$528$	−3.95512	+	12.1726i	−0.172125	+	0.529745i
$529$	−4.68793	+	14.4280i	−0.203823	+	0.627303i
$530$	7.70416	−	5.01167i	0.334647	−	0.217693i
$531$	−5.66986	−	17.4500i	−0.246051	−	0.757267i
$532$	−0.00304470			−0.000132004
$533$	−3.07047	−	9.44993i	−0.132997	−	0.409322i
$534$	−3.50008	−	2.54296i	−0.151463	−	0.110045i
$535$	−7.78297	−	28.9563i	−0.336487	−	1.25189i
$536$	2.45929	−	1.78678i	0.106225	−	0.0771772i
$537$	8.17461	+	5.93920i	0.352761	+	0.256296i
$538$	−6.43906	−	4.67825i	−0.277607	−	0.201694i
$539$	−13.1056	+	9.52180i	−0.564499	+	0.410133i
$540$	0.296733	−	0.193029i	0.0127694	−	0.00830665i
$541$	31.8723	+	23.1566i	1.37030	+	0.995578i	0.997714	+	0.0675784i	$0.0215273\pi$
$541$	31.8723	+	23.1566i	1.37030	+	0.995578i	0.372581	+	0.928000i	$0.378473\pi$
$542$	9.83414	+	30.2664i	0.422412	+	1.30005i
$543$	22.3293			0.958240
$544$	−0.0497273	−	0.153045i	−0.00213204	−	0.00656174i
$545$	−6.98965	+	18.2511i	−0.299404	+	0.781792i
$546$	−1.78655	+	5.49844i	−0.0764574	+	0.235312i
$547$	6.25301	−	19.2448i	0.267359	−	0.822848i	−0.723781	−	0.690030i	$-0.757597\pi$
$547$	6.25301	−	19.2448i	0.267359	−	0.822848i	0.991140	−	0.132818i	$-0.0424026\pi$
$548$	0.372694	−	0.270778i	0.0159207	−	0.0115671i
$549$	−9.40378			−0.401343
$550$	3.72288	+	17.3817i	0.158744	+	0.741157i
$551$	−0.262983			−0.0112035
$552$	−8.03538	+	5.83805i	−0.342009	+	0.248484i
$553$	3.82338	−	11.7672i	0.162587	−	0.500391i
$554$	−5.96200	+	18.3492i	−0.253301	+	0.779581i
$555$	0.0314290	+	0.0254102i	0.00133409	+	0.00107860i
$556$	0.0553466	+	0.170339i	0.00234722	+	0.00722400i
$557$	43.0923			1.82588			0.912940	−	0.408093i	$-0.133806\pi$
$557$	43.0923			1.82588			0.912940	+	0.408093i	$0.133806\pi$
$558$	−1.04768	−	3.22443i	−0.0443519	−	0.136501i
$559$	10.0122	+	7.27429i	0.423471	+	0.307670i
$560$	2.31727	−	6.05077i	0.0979225	−	0.255692i
$561$	2.55287	−	1.85477i	0.107782	−	0.0783082i
$562$	34.2025	+	24.8495i	1.44274	+	1.04821i
$563$	6.20346	+	4.50708i	0.261445	+	0.189951i	0.710784	−	0.703411i	$-0.248340\pi$
$563$	6.20346	+	4.50708i	0.261445	+	0.189951i	−0.449339	+	0.893361i	$0.648340\pi$
$564$	0.0546653	−	0.0397166i	0.00230182	−	0.00167237i
$565$	4.06789	−	10.6219i	0.171137	−	0.446867i
$566$	−29.1647	−	21.1894i	−1.22588	−	0.890657i
$567$	−0.624419	−	1.92176i	−0.0262231	−	0.0807064i
$568$	7.21819			0.302868
$569$	−9.76666	−	30.0587i	−0.409440	−	1.26013i	−0.917131	−	0.398586i	$-0.869501\pi$
$569$	−9.76666	−	30.0587i	−0.409440	−	1.26013i	0.507691	−	0.861539i	$-0.330499\pi$
$570$	−0.468998	−	0.379183i	−0.0196442	−	0.0158822i
$571$	−7.00128	+	21.5477i	−0.292994	+	0.901744i	0.690893	+	0.722957i	$0.257217\pi$
$571$	−7.00128	+	21.5477i	−0.292994	+	0.901744i	−0.983888	+	0.178787i	$0.942783\pi$
$572$	0.0986405	−	0.303584i	0.00412437	−	0.0126935i
$573$	20.2137	−	14.6861i	0.844439	−	0.613521i
$574$	−2.24915			−0.0938775
$575$	−5.67061	+	12.7899i	−0.236481	+	0.533377i
$576$	−11.0518			−0.460492
$577$	−23.1995	+	16.8555i	−0.965810	+	0.701702i	−0.954493	−	0.298234i	$-0.903602\pi$
$577$	−23.1995	+	16.8555i	−0.965810	+	0.701702i	−0.0113170	+	0.999936i	$0.503602\pi$
$578$	−0.440113	+	1.35453i	−0.0183063	+	0.0563410i
$579$	1.48222	−	4.56181i	0.0615990	−	0.189582i
$580$	−0.0399387	+	0.104286i	−0.00165836	+	0.00433026i
$581$	−3.22964	−	9.93982i	−0.133988	−	0.412373i
$582$	−14.1094			−0.584851
$583$	2.22612	+	6.85128i	0.0921964	+	0.283751i
$584$	−13.5185	−	9.82173i	−0.559398	−	0.406426i
$585$	11.8120	−	7.68386i	0.488365	−	0.317689i
$586$	24.7038	−	17.9484i	1.02051	−	0.741441i
$587$	12.8502	+	9.33623i	0.530385	+	0.385347i	0.820502	−	0.571644i	$-0.193694\pi$
$587$	12.8502	+	9.33623i	0.530385	+	0.385347i	−0.290117	+	0.956991i	$0.593694\pi$
$588$	−0.188816	−	0.137183i	−0.00778665	−	0.00565733i
$589$	−0.205787	+	0.149513i	−0.00847930	+	0.00616057i
$590$	10.8186	+	40.2502i	0.445394	+	1.65707i
$591$	−27.7499	−	20.1615i	−1.14148	−	0.829334i
$592$	0.0179213	+	0.0551559i	0.000736559	+	0.00226690i
$593$	−36.1000			−1.48245			−0.741225	−	0.671256i	$-0.765755\pi$
$593$	−36.1000			−1.48245			−0.741225	+	0.671256i	$0.765755\pi$
$594$	6.11340	+	18.8151i	0.250836	+	0.771993i
$595$	−1.33904	+	0.871065i	−0.0548953	+	0.0357102i
$596$	−0.0190514	+	0.0586340i	−0.000780374	+	0.00240174i
$597$	2.01686	−	6.20726i	0.0825447	−	0.254046i
$598$	14.4921	−	10.5291i	0.592626	−	0.430568i
$599$	−2.60840			−0.106576			−0.0532882	−	0.998579i	$-0.516970\pi$
$599$	−2.60840			−0.106576			−0.0532882	+	0.998579i	$0.516970\pi$
$600$	15.3564	−	8.89795i	0.626924	−	0.363257i
$601$	33.8225			1.37965			0.689825	−	0.723977i	$-0.257688\pi$
$601$	33.8225			1.37965			0.689825	+	0.723977i	$0.257688\pi$
$602$	2.26634	−	1.64659i	0.0923691	−	0.0671101i
$603$	0.469016	−	1.44348i	0.0190998	−	0.0587831i
$604$	0.0339229	−	0.104404i	0.00138030	−	0.00424814i
$605$	10.6496	+	0.549810i	0.432968	+	0.0223530i
$606$	3.55326	+	10.9358i	0.144341	+	0.444237i
$607$	−5.28976			−0.214705			−0.107352	−	0.994221i	$-0.534237\pi$
$607$	−5.28976			−0.214705			−0.107352	+	0.994221i	$0.534237\pi$
$608$	−0.00744958	−	0.0229275i	−0.000302120	−	0.000929831i
$609$	1.28256	+	0.931832i	0.0519718	+	0.0377597i
$610$	21.3329	+	1.10136i	0.863742	+	0.0445927i
$611$	6.83241	−	4.96404i	0.276410	−	0.200824i
$612$	−0.0322678	−	0.0234440i	−0.00130435	−	0.000947666i
$613$	39.3923	+	28.6202i	1.59104	+	1.15596i	0.902440	+	0.430816i	$0.141774\pi$
$613$	39.3923	+	28.6202i	1.59104	+	1.15596i	0.688599	+	0.725142i	$0.258226\pi$
$614$	−30.7619	+	22.3498i	−1.24145	+	0.901966i
$615$	−4.85904	−	3.92852i	−0.195936	−	0.158413i
$616$	4.05101	+	2.94323i	0.163220	+	0.118586i
$617$	4.72304	+	14.5360i	0.190143	+	0.585199i	0.999999	−	0.00142943i	$-0.000455003\pi$
$617$	4.72304	+	14.5360i	0.190143	+	0.585199i	−0.809856	+	0.586628i	$0.800455\pi$
$618$	−9.61279			−0.386683
$619$	15.0360	+	46.2761i	0.604348	+	1.85999i	0.501209	+	0.865326i	$0.332889\pi$
$619$	15.0360	+	46.2761i	0.604348	+	1.85999i	0.103139	+	0.994667i	$0.467111\pi$
$620$	0.0280371	+	0.104311i	0.00112600	+	0.00418924i
$621$	−4.81160	+	14.8086i	−0.193083	+	0.594248i
$622$	−9.62438	+	29.6208i	−0.385903	+	1.18769i
$623$	−1.38881	+	1.00903i	−0.0556414	+	0.0404258i
$624$	−23.0474			−0.922635
$625$	12.4325	−	21.6894i	0.497301	−	0.867578i
$626$	23.3517			0.933323
$627$	0.382442	−	0.277860i	0.0152732	−	0.0110967i
$628$	0.157121	−	0.483568i	0.00626981	−	0.0192965i
$629$	0.00441836	−	0.0135983i	0.000176171	−	0.000542200i
$630$	−0.827945	−	3.08034i	−0.0329861	−	0.122724i
$631$	−2.43461	−	7.49295i	−0.0969202	−	0.298290i	0.890829	−	0.454338i	$-0.150124\pi$
$631$	−2.43461	−	7.49295i	−0.0969202	−	0.298290i	−0.987749	+	0.156049i	$0.950124\pi$
$632$	48.6316			1.93446
$633$	9.37136	+	28.8421i	0.372478	+	1.14637i
$634$	32.5254	+	23.6311i	1.29175	+	0.938510i
$635$	24.9581	+	20.1785i	0.990432	+	0.800761i
$636$	−0.0839663	+	0.0610051i	−0.00332948	+	0.00241901i
$637$	−23.5995	−	17.1460i	−0.935045	−	0.679350i
$638$	−5.04906	−	3.66835i	−0.199894	−	0.145232i
$639$	2.91567	−	2.11836i	0.115342	−	0.0838009i
$640$	25.7902	+	1.33148i	1.01945	+	0.0526313i
$641$	7.02336	+	5.10277i	0.277406	+	0.201547i	0.717785	−	0.696265i	$-0.245156\pi$
$641$	7.02336	+	5.10277i	0.277406	+	0.201547i	−0.440379	+	0.897812i	$0.645156\pi$
$642$	7.46036	+	22.9606i	0.294437	+	0.906184i
$643$	−4.66249			−0.183871			−0.0919353	−	0.995765i	$-0.529305\pi$
$643$	−4.66249			−0.183871			−0.0919353	+	0.995765i	$0.529305\pi$
$644$	−0.0175734	−	0.0540855i	−0.000692491	−	0.00213127i
$645$	7.77224	+	0.401260i	0.306032	+	0.0157996i
$646$	−0.0659328	+	0.202920i	−0.00259409	+	0.00798379i
$647$	10.2265	−	31.4738i	0.402044	−	1.23736i	−0.521295	−	0.853377i	$-0.674551\pi$
$647$	10.2265	−	31.4738i	0.402044	−	1.23736i	0.923338	−	0.383987i	$-0.125449\pi$
$648$	6.42546	−	4.66837i	0.252416	−	0.183391i
$649$	−32.6683			−1.28234
$650$	−27.6959	+	16.0478i	−1.08632	+	0.629445i
$651$	1.53338			0.0600980
$652$	0.305831	−	0.222199i	0.0119773	−	0.00870198i
$653$	1.93524	−	5.95605i	0.0757317	−	0.233078i	−0.906023	−	0.423227i	$-0.860897\pi$
$653$	1.93524	−	5.95605i	0.0757317	−	0.233078i	0.981755	+	0.190149i	$0.0608971\pi$
$654$	4.86271	−	14.9659i	0.190147	−	0.585212i
$655$	−17.9977	+	11.7078i	−0.703229	+	0.457461i
$656$	−2.77069	−	8.52732i	−0.108177	−	0.332936i
$657$	−8.34299			−0.325491
$658$	−0.590737	−	1.81810i	−0.0230293	−	0.0708769i
$659$	14.4174	+	10.4748i	0.561622	+	0.408042i	0.832052	−	0.554697i	$-0.187166\pi$
$659$	14.4174	+	10.4748i	0.561622	+	0.408042i	−0.270430	+	0.962740i	$0.587166\pi$
$660$	−0.0521052	−	0.193856i	−0.00202819	−	0.00754582i
$661$	−32.4398	+	23.5689i	−1.26176	+	0.916723i	−0.998843	−	0.0480951i	$-0.984685\pi$
$661$	−32.4398	+	23.5689i	−1.26176	+	0.916723i	−0.262918	+	0.964818i	$0.584685\pi$
$662$	16.6702	+	12.1116i	0.647904	+	0.470730i
$663$	4.59698	+	3.33990i	0.178532	+	0.129711i
$664$	33.2341	−	24.1460i	1.28973	−	0.937045i
$665$	−0.200600	+	0.130493i	−0.00777893	+	0.00506031i
$666$	0.0230973	+	0.0167811i	0.000895001	+	0.000650256i
$667$	−1.51789	−	4.67160i	−0.0587731	−	0.180885i
$668$	−0.0966235			−0.00373848
$669$	−5.14625	−	15.8385i	−0.198966	−	0.612353i
$670$	−1.23304	+	3.21967i	−0.0476365	+	0.124387i
$671$	−5.17394	+	15.9238i	−0.199738	+	0.614730i
$672$	−0.0449078	+	0.138212i	−0.00173236	+	0.00533165i
$673$	21.8257	−	15.8573i	0.841319	−	0.611254i	−0.0814199	−	0.996680i	$-0.525945\pi$
$673$	21.8257	−	15.8573i	0.841319	−	0.611254i	0.922739	+	0.385426i	$0.125945\pi$
$674$	−43.2427			−1.66565
$675$	11.2772	−	25.4355i	0.434059	−	0.979011i
$676$	0.204961			0.00788312
$677$	2.64869	−	1.92439i	0.101798	−	0.0739603i	−0.535722	−	0.844394i	$-0.679960\pi$
$677$	2.64869	−	1.92439i	0.101798	−	0.0739603i	0.637520	+	0.770434i	$0.279960\pi$
$678$	−2.83003	+	8.70995i	−0.108687	+	0.334503i
$679$	−1.73003	+	5.32448i	−0.0663924	+	0.204335i
$680$	−4.88260	−	3.94756i	−0.187239	−	0.151382i
$681$	−0.378859	−	1.16601i	−0.0145179	−	0.0446815i
$682$	−6.03648			−0.231149
$683$	−13.2057	−	40.6429i	−0.505302	−	1.55516i	−0.800263	−	0.599650i	$-0.795307\pi$
$683$	−13.2057	−	40.6429i	−0.505302	−	1.55516i	0.294961	−	0.955509i	$-0.404693\pi$
$684$	−0.00483401	−	0.00351211i	−0.000184833	−	0.000134289i
$685$	12.9496	−	33.8135i	0.494779	−	1.29195i
$686$	−11.1039	+	8.06748i	−0.423950	+	0.308018i
$687$	26.7671	+	19.4475i	1.02123	+	0.741967i
$688$	9.03470	+	6.56409i	0.344445	+	0.250254i
$689$	−10.4946	+	7.62480i	−0.399814	+	0.290482i
$690$	4.02878	−	10.5198i	0.153373	−	0.400482i
$691$	20.0521	+	14.5687i	0.762817	+	0.554219i	0.899773	−	0.436358i	$-0.143732\pi$
$691$	20.0521	+	14.5687i	0.762817	+	0.554219i	−0.136956	+	0.990577i	$0.543732\pi$
$692$	−0.0241518	−	0.0743316i	−0.000918114	−	0.00282566i
$693$	2.50010			0.0949711
$694$	0.308627	+	0.949857i	0.0117153	+	0.0360561i
$695$	10.9471	+	8.85070i	0.415248	+	0.335726i
$696$	−1.92555	+	5.92623i	−0.0729877	+	0.224633i
$697$	−0.683095	+	2.10235i	−0.0258741	+	0.0796322i
$698$	19.0255	−	13.8228i	0.720125	−	0.523201i
$699$	30.6342			1.15869
$700$	0.0212826	+	0.0993658i	0.000804406	+	0.00375567i
$701$	−12.6607			−0.478188			−0.239094	−	0.970996i	$-0.576850\pi$
$701$	−12.6607			−0.478188			−0.239094	+	0.970996i	$0.576850\pi$
$702$	−28.8206	+	20.9394i	−1.08776	+	0.790305i
$703$	0.000661909	−	0.00203715i	2.49644e−5	−	7.68324e-5i
$704$	−6.08069	+	18.7144i	−0.229174	+	0.705327i
$705$	1.89940	−	4.95964i	0.0715355	−	0.186791i
$706$	−11.4129	−	35.1252i	−0.429530	−	1.32196i
$707$	4.56256			0.171593
$708$	−0.145442	−	0.447626i	−0.00546606	−	0.0168228i
$709$	10.2869	+	7.47389i	0.386333	+	0.280688i	0.763951	−	0.645274i	$-0.223257\pi$
$709$	10.2869	+	7.47389i	0.386333	+	0.280688i	−0.377618	+	0.925962i	$0.623257\pi$
$710$	−6.86241	+	4.46410i	−0.257542	+	0.167535i
$711$	19.6439	−	14.2722i	0.736706	−	0.535248i
$712$	−5.45878	−	3.96603i	−0.204576	−	0.148633i
$713$	−3.84369	−	2.79260i	−0.143947	−	0.104584i
$714$	1.04056	−	0.756011i	0.0389420	−	0.0282930i
$715$	−6.51244	−	24.2293i	−0.243551	−	0.906125i
$716$	−0.183970	−	0.133662i	−0.00687527	−	0.00499518i
$717$	−5.99101	−	18.4384i	−0.223738	−	0.688596i
$718$	17.9076			0.668305
$719$	−10.7809	−	33.1802i	−0.402060	−	1.23741i	−0.923325	−	0.384019i	$-0.874540\pi$
$719$	−10.7809	−	33.1802i	−0.402060	−	1.23741i	0.521265	−	0.853395i	$-0.325460\pi$
$720$	10.6588	−	6.93368i	0.397228	−	0.258403i
$721$	−1.17868	+	3.62760i	−0.0438963	+	0.135099i
$722$	8.35227	−	25.7057i	0.310839	−	0.956665i
$723$	19.5305	−	14.1898i	0.726348	−	0.527723i
$724$	−0.502520			−0.0186760
$725$	1.83827	+	8.58265i	0.0682715	+	0.318752i
$726$	−8.58616			−0.318662
$727$	−1.75120	+	1.27232i	−0.0649484	+	0.0471877i	−0.619786	−	0.784771i	$-0.712780\pi$
$727$	−1.75120	+	1.27232i	−0.0649484	+	0.0471877i	0.554837	+	0.831959i	$0.312780\pi$
$728$	−2.78633	+	8.57544i	−0.103268	+	0.317827i
$729$	7.74670	−	23.8419i	0.286915	−	0.883033i
$730$	18.9264	+	0.977121i	0.700498	+	0.0361649i
$731$	−0.850807	−	2.61851i	−0.0314682	−	0.0968492i
$732$	−0.241224			−0.00891591
$733$	4.90138	+	15.0849i	0.181036	+	0.557173i	0.999858	−	0.0168758i	$-0.00537198\pi$
$733$	4.90138	+	15.0849i	0.181036	+	0.557173i	−0.818821	+	0.574049i	$0.805372\pi$
$734$	2.42484	+	1.76175i	0.0895025	+	0.0650274i
$735$	−18.3197	−	0.945798i	−0.675733	−	0.0348863i
$736$	0.364282	−	0.264666i	0.0134276	−	0.00975573i
$737$	−2.18625	−	1.58840i	−0.0805315	−	0.0585096i
$738$	−3.57093	−	2.59443i	−0.131448	−	0.0955023i
$739$	40.5235	−	29.4420i	1.49068	−	1.08304i	0.516765	−	0.856127i	$-0.327136\pi$
$739$	40.5235	−	29.4420i	1.49068	−	1.08304i	0.973915	−	0.226915i	$-0.0728638\pi$
$740$	−0.000707310	0	0.000571857i	−2.60012e−5	0	2.10219e-5i
$741$	0.688667	+	0.500346i	0.0252988	+	0.0183807i
$742$	0.907376	+	2.79262i	0.0333108	+	0.102520i
$743$	−30.8400			−1.13141			−0.565705	−	0.824607i	$-0.691396\pi$
$743$	−30.8400			−1.13141			−0.565705	+	0.824607i	$0.691396\pi$
$744$	1.86246	+	5.73205i	0.0682809	+	0.210147i
$745$	1.25781	+	4.67963i	0.0460825	+	0.171448i
$746$	−7.18511	+	22.1135i	−0.263066	+	0.809633i
$747$	6.33812	−	19.5067i	0.231900	−	0.713714i
$748$	−0.0574523	+	0.0417415i	−0.00210066	+	0.00152622i
$749$	9.57946			0.350026
$750$	−9.09659	+	17.9566i	−0.332161	+	0.655682i
$751$	−26.4955			−0.966834			−0.483417	−	0.875390i	$-0.660605\pi$
$751$	−26.4955			−0.966834			−0.483417	+	0.875390i	$0.660605\pi$
$752$	6.16535	−	4.47939i	0.224827	−	0.163347i
$753$	−1.65137	+	5.08239i	−0.0601792	+	0.185213i
$754$	3.47280	−	10.6882i	0.126472	−	0.389240i
$755$	−2.23966	−	8.33257i	−0.0815095	−	0.303253i
$756$	0.0349485	+	0.107560i	0.00127106	+	0.00391193i
$757$	−7.76603			−0.282261			−0.141131	−	0.989991i	$-0.545074\pi$
$757$	−7.76603			−0.282261			−0.141131	+	0.989991i	$0.545074\pi$
$758$	−13.5909	−	41.8285i	−0.493644	−	1.51928i
$759$	7.14325	+	5.18987i	0.259284	+	0.188380i
$760$	−0.731456	−	0.591380i	−0.0265327	−	0.0214516i
$761$	26.4865	−	19.2436i	0.960134	−	0.697578i	0.00695224	−	0.999976i	$-0.497787\pi$
$761$	26.4865	−	19.2436i	0.960134	−	0.697578i	0.953182	+	0.302398i	$0.0977870\pi$
$762$	−20.9065	−	15.1895i	−0.757362	−	0.550256i
$763$	−5.05147	−	3.67010i	−0.182875	−	0.132867i
$764$	−0.454909	+	0.330511i	−0.0164580	+	0.0119575i
$765$	−3.13076	−	0.161633i	−0.113193	−	0.00584384i
$766$	12.2568	+	8.90511i	0.442857	+	0.321755i
$767$	−18.1783	−	55.9471i	−0.656381	−	2.02013i
$768$	−0.862948			−0.0311390
$769$	−0.757106	−	2.33013i	−0.0273019	−	0.0840267i	0.936477	−	0.350729i	$-0.114066\pi$
$769$	−0.757106	−	2.33013i	−0.0273019	−	0.0840267i	−0.963779	+	0.266702i	$0.914066\pi$
$770$	−5.67159	−	0.292809i	−0.204390	−	0.0105521i

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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.15223 - 0.837145i) q^{2} +(-0.390637 + 1.20226i) q^{3} +(0.00879129 - 0.0270568i) q^{4} +(-0.580418 - 2.15942i) q^{5} +(0.556359 + 1.71230i) q^{6} +0.714392 q^{7} +(0.867706 + 2.67052i) q^{8} +(1.13423 + 0.824064i) q^{9} +(-2.47653 - 2.00226i) q^{10} +(2.01947 - 1.46723i) q^{11} +(0.0290950 + 0.0211388i) q^{12} +(3.63648 + 2.64206i) q^{13} +(0.823145 - 0.598050i) q^{14} +(2.82292 + 0.145740i) q^{15} +(3.28144 + 2.38411i) q^{16} +(-0.309017 - 0.951057i) q^{17} +1.99675 q^{18} +(-0.0462935 - 0.142477i) q^{19} +(-0.0635297 - 0.00327987i) q^{20} +(-0.279068 + 0.858883i) q^{21} +(1.09861 - 3.38118i) q^{22} +(2.26373 - 1.64470i) q^{23} -3.54961 q^{24} +(-4.32623 + 2.50674i) q^{25} +6.40185 q^{26} +(-4.50191 + 3.27083i) q^{27} +(0.00628043 - 0.0193292i) q^{28} +(0.542467 - 1.66954i) q^{29} +(3.37466 - 2.19526i) q^{30} +(-0.524693 - 1.61484i) q^{31} +0.160921 q^{32} +(0.975108 + 3.00107i) q^{33} +(-1.15223 - 0.837145i) q^{34} +(-0.414646 - 1.54268i) q^{35} +(0.0322678 - 0.0234440i) q^{36} +(0.0115674 + 0.00840422i) q^{37} +(-0.172614 - 0.125412i) q^{38} +(-4.59698 + 3.33990i) q^{39} +(5.26316 - 3.42376i) q^{40} +(-1.78837 - 1.29932i) q^{41} +(0.397459 + 1.22325i) q^{42} +2.75327 q^{43} +(-0.0219448 - 0.0675392i) q^{44} +(1.12118 - 2.92758i) q^{45} +(1.23149 - 3.79015i) q^{46} +(0.580598 - 1.78690i) q^{47} +(-4.14817 + 3.01382i) q^{48} -6.48964 q^{49} +(-2.88632 + 6.51002i) q^{50} +1.26413 q^{51} +(0.103455 - 0.0751644i) q^{52} +(-0.891803 + 2.74469i) q^{53} +(-2.44908 + 7.53750i) q^{54} +(-4.34051 - 3.50928i) q^{55} +(0.619882 + 1.90780i) q^{56} +0.189377 q^{57} +(-0.772602 - 2.37782i) q^{58} +(-10.5878 - 7.69248i) q^{59} +(0.0287603 - 0.0750978i) q^{60} +(-5.42647 + 3.94256i) q^{61} +(-1.95642 - 1.42142i) q^{62} +(0.810283 + 0.588705i) q^{63} +(-6.37747 + 4.63350i) q^{64} +(3.59465 - 9.38620i) q^{65} +(3.63588 + 2.64162i) q^{66} +(-0.334538 - 1.02960i) q^{67} -0.0284492 q^{68} +(1.09305 + 3.36407i) q^{69} +(-1.76921 - 1.43040i) q^{70} +(0.794366 - 2.44481i) q^{71} +(-1.21651 + 3.74402i) q^{72} +(-4.81434 + 3.49783i) q^{73} +0.0203639 q^{74} +(-1.32376 - 6.18046i) q^{75} -0.00426194 q^{76} +(1.44269 - 1.04818i) q^{77} +(-2.50080 + 7.69667i) q^{78} +(5.35194 - 16.4716i) q^{79} +(3.24370 - 8.46981i) q^{80} +(-0.874056 - 2.69007i) q^{81} -3.14833 q^{82} +(-4.52083 - 13.9137i) q^{83} +(0.0207853 + 0.0151014i) q^{84} +(-1.87438 + 1.21931i) q^{85} +(3.17240 - 2.30489i) q^{86} +(1.79531 + 1.30437i) q^{87} +(5.67057 + 4.11991i) q^{88} +(-1.94404 + 1.41243i) q^{89} +(-1.15895 - 4.31184i) q^{90} +(2.59787 + 1.88747i) q^{91} +(-0.0245992 - 0.0757084i) q^{92} +2.14641 q^{93} +(-0.826908 - 2.54496i) q^{94} +(-0.280798 + 0.182663i) q^{95} +(-0.0628616 + 0.193468i) q^{96} +(-2.42168 + 7.45316i) q^{97} +(-7.47757 + 5.43277i) q^{98} +3.49963 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 2 q^{2} + 2 q^{3} - 20 q^{4} - 17 q^{6} - 44 q^{7} + 15 q^{8} - 22 q^{9} - 2 q^{10} + 4 q^{11} + 14 q^{12} + 6 q^{13} - 10 q^{14} + 14 q^{15} - 32 q^{16} + 20 q^{17} - 62 q^{18} - 3 q^{19} + 16 q^{21}+ \cdots + 76 q^{99}+O(q^{100}) \) 80 * q + 2 * q^2 + 2 * q^3 - 20 * q^4 - 17 * q^6 - 44 * q^7 + 15 * q^8 - 22 * q^9 - 2 * q^10 + 4 * q^11 + 14 * q^12 + 6 * q^13 - 10 * q^14 + 14 * q^15 - 32 * q^16 + 20 * q^17 - 62 * q^18 - 3 * q^19 + 16 * q^21 + 17 * q^22 - 5 * q^23 + 30 * q^24 - 14 * q^25 + 18 * q^26 + 17 * q^27 + 32 * q^28 + 20 * q^29 - 114 * q^30 - 21 * q^31 - 88 * q^32 - 2 * q^34 - 2 * q^35 + 47 * q^36 + 6 * q^37 + 22 * q^38 - 46 * q^39 + 59 * q^40 - 26 * q^41 - 3 * q^42 - 102 * q^43 - 44 * q^44 + 74 * q^45 + 2 * q^46 + 2 * q^47 + 72 * q^48 + 108 * q^49 + 7 * q^50 + 18 * q^51 + 65 * q^52 - 18 * q^53 - 29 * q^54 - 49 * q^55 - 117 * q^56 + 2 * q^57 + 42 * q^58 + 21 * q^59 + 112 * q^60 + 4 * q^61 + 15 * q^62 + 41 * q^63 - 11 * q^64 + 8 * q^65 - 156 * q^66 + 21 * q^67 - 80 * q^68 - 67 * q^69 + 32 * q^70 - 4 * q^71 + 83 * q^72 - 2 * q^73 + 78 * q^74 - 68 * q^75 + 16 * q^76 + 2 * q^77 - 2 * q^78 - 53 * q^79 - 54 * q^80 - 21 * q^81 - 72 * q^82 - 42 * q^83 - 52 * q^84 + 42 * q^86 - 8 * q^87 + 68 * q^88 - 73 * q^89 + 97 * q^90 - 83 * q^91 + 117 * q^92 - 120 * q^93 + 80 * q^94 + 16 * q^95 + 88 * q^96 + 57 * q^97 + 17 * q^98 + 76 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

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