LMFDB - Embedded newform 315.2.l.c.121.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(121,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("315.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.l (of order $3$, degree $2$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.18
Character	$\chi$	$=$	315.121
Dual form			315.2.l.c.151.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.75701 q^{2} +(-0.581455 - 1.63154i) q^{3} +5.60109 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.60307 - 4.49816i) q^{6} +(-2.40845 + 1.09515i) q^{7} +9.92824 q^{8} +(-2.32382 + 1.89733i) q^{9} +O(q^{10})$	\(q+2.75701 q^{2} +(-0.581455 - 1.63154i) q^{3} +5.60109 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.60307 - 4.49816i) q^{6} +(-2.40845 + 1.09515i) q^{7} +9.92824 q^{8} +(-2.32382 + 1.89733i) q^{9} +(-1.37850 - 2.38764i) q^{10} +(-1.14040 + 1.97523i) q^{11} +(-3.25678 - 9.13838i) q^{12} +(1.37896 - 2.38844i) q^{13} +(-6.64012 + 3.01934i) q^{14} +(-1.12222 + 1.31932i) q^{15} +16.1700 q^{16} +(1.01423 + 1.75669i) q^{17} +(-6.40679 + 5.23095i) q^{18} +(-3.03493 + 5.25665i) q^{19} +(-2.80055 - 4.85069i) q^{20} +(3.18719 + 3.29270i) q^{21} +(-3.14410 + 5.44574i) q^{22} +(-1.49557 - 2.59040i) q^{23} +(-5.77282 - 16.1983i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(3.80182 - 6.58494i) q^{26} +(4.44676 + 2.68819i) q^{27} +(-13.4900 + 6.13405i) q^{28} +(-2.78655 - 4.82644i) q^{29} +(-3.09398 + 3.63738i) q^{30} -0.333000 q^{31} +24.7245 q^{32} +(3.88576 + 0.712099i) q^{33} +(2.79623 + 4.84321i) q^{34} +(2.15266 + 1.53820i) q^{35} +(-13.0159 + 10.6271i) q^{36} +(0.0601415 - 0.104168i) q^{37} +(-8.36733 + 14.4926i) q^{38} +(-4.69863 - 0.861064i) q^{39} +(-4.96412 - 8.59810i) q^{40} +(-0.237341 + 0.411087i) q^{41} +(8.78710 + 9.07799i) q^{42} +(3.43450 + 5.94872i) q^{43} +(-6.38750 + 11.0635i) q^{44} +(2.80505 + 1.06382i) q^{45} +(-4.12329 - 7.14174i) q^{46} +7.21451 q^{47} +(-9.40214 - 26.3820i) q^{48} +(4.60128 - 5.27524i) q^{49} +(-1.37850 + 2.38764i) q^{50} +(2.27638 - 2.67618i) q^{51} +(7.72371 - 13.3779i) q^{52} +(-4.25673 - 7.37287i) q^{53} +(12.2597 + 7.41136i) q^{54} +2.28080 q^{55} +(-23.9117 + 10.8729i) q^{56} +(10.3411 + 1.89509i) q^{57} +(-7.68253 - 13.3065i) q^{58} -8.64149 q^{59} +(-6.28568 + 7.38965i) q^{60} -11.2957 q^{61} -0.918083 q^{62} +(3.51895 - 7.11456i) q^{63} +35.8254 q^{64} -2.75793 q^{65} +(10.7131 + 1.96326i) q^{66} -6.78119 q^{67} +(5.68077 + 9.83938i) q^{68} +(-3.35672 + 3.94627i) q^{69} +(5.93489 + 4.24084i) q^{70} +12.3927 q^{71} +(-23.0714 + 18.8371i) q^{72} +(0.0952946 + 0.165055i) q^{73} +(0.165811 - 0.287192i) q^{74} +(1.70368 + 0.312214i) q^{75} +(-16.9989 + 29.4430i) q^{76} +(0.583422 - 6.00617i) q^{77} +(-12.9542 - 2.37396i) q^{78} -11.5433 q^{79} +(-8.08502 - 14.0037i) q^{80} +(1.80029 - 8.81810i) q^{81} +(-0.654352 + 1.13337i) q^{82} +(-3.98395 - 6.90040i) q^{83} +(17.8517 + 18.4427i) q^{84} +(1.01423 - 1.75669i) q^{85} +(9.46893 + 16.4007i) q^{86} +(-6.25426 + 7.35271i) q^{87} +(-11.3222 + 19.6106i) q^{88} +(1.05443 - 1.82633i) q^{89} +(7.73353 + 2.93297i) q^{90} +(-0.705469 + 7.26261i) q^{91} +(-8.37680 - 14.5090i) q^{92} +(0.193624 + 0.543302i) q^{93} +19.8904 q^{94} +6.06986 q^{95} +(-14.3761 - 40.3388i) q^{96} +(-3.42650 - 5.93488i) q^{97} +(12.6858 - 14.5439i) q^{98} +(-1.09758 - 6.75381i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9}+O(q^{10}) $ 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9	\( 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9} + q^{11} + 8 q^{12} + 2 q^{13} + 9 q^{14} - q^{15} + 60 q^{16} - 5 q^{17} - 21 q^{18} - 2 q^{19} - 22 q^{20} - 23 q^{21} - 19 q^{22} - 3 q^{23} - 32 q^{24} - 18 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} + 2 q^{30} - 20 q^{32} - 35 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} - 22 q^{38} + 7 q^{39} - 4 q^{41} + 57 q^{42} - 29 q^{43} - 7 q^{44} + 6 q^{45} - 24 q^{46} + 46 q^{47} - 19 q^{48} - 7 q^{49} + 42 q^{51} - 7 q^{52} + 21 q^{54} - 2 q^{55} - 12 q^{56} + 21 q^{57} - 20 q^{58} + 10 q^{59} - 13 q^{60} + 6 q^{61} - 12 q^{62} + 2 q^{63} + 128 q^{64} - 4 q^{65} - 12 q^{66} + 70 q^{67} - 17 q^{68} - 50 q^{69} - 3 q^{70} + 24 q^{71} - 10 q^{72} - 10 q^{73} + 22 q^{74} + 2 q^{75} + 10 q^{76} + 35 q^{77} + 66 q^{78} + 56 q^{79} - 30 q^{80} - 49 q^{81} - 8 q^{82} - 22 q^{83} - 86 q^{84} - 5 q^{85} + 19 q^{86} - 42 q^{87} - 50 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - q^{93} + 4 q^{94} + 4 q^{95} - 179 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9 + q^11 + 8 * q^12 + 2 * q^13 + 9 * q^14 - q^15 + 60 * q^16 - 5 * q^17 - 21 * q^18 - 2 * q^19 - 22 * q^20 - 23 * q^21 - 19 * q^22 - 3 * q^23 - 32 * q^24 - 18 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 + 2 * q^30 - 20 * q^32 - 35 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 - 22 * q^38 + 7 * q^39 - 4 * q^41 + 57 * q^42 - 29 * q^43 - 7 * q^44 + 6 * q^45 - 24 * q^46 + 46 * q^47 - 19 * q^48 - 7 * q^49 + 42 * q^51 - 7 * q^52 + 21 * q^54 - 2 * q^55 - 12 * q^56 + 21 * q^57 - 20 * q^58 + 10 * q^59 - 13 * q^60 + 6 * q^61 - 12 * q^62 + 2 * q^63 + 128 * q^64 - 4 * q^65 - 12 * q^66 + 70 * q^67 - 17 * q^68 - 50 * q^69 - 3 * q^70 + 24 * q^71 - 10 * q^72 - 10 * q^73 + 22 * q^74 + 2 * q^75 + 10 * q^76 + 35 * q^77 + 66 * q^78 + 56 * q^79 - 30 * q^80 - 49 * q^81 - 8 * q^82 - 22 * q^83 - 86 * q^84 - 5 * q^85 + 19 * q^86 - 42 * q^87 - 50 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - q^93 + 4 * q^94 + 4 * q^95 - 179 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	2.75701			1.94950			0.974749	−	0.223302i	$-0.0716835\pi$
$2$	2.75701			1.94950			0.974749	+	0.223302i	$0.0716835\pi$
$3$	−0.581455	−	1.63154i	−0.335703	−	0.941968i
$3$	−0.581455	−	1.63154i	−0.335703	−	0.941968i
$4$	5.60109			2.80055
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−1.60307	−	4.49816i	−0.654452	−	1.83637i
$7$	−2.40845	+	1.09515i	−0.910309	+	0.413929i
$7$	−2.40845	+	1.09515i	−0.910309	+	0.413929i
$8$	9.92824			3.51016
$9$	−2.32382	+	1.89733i	−0.774607	+	0.632443i
$10$	−1.37850	−	2.38764i	−0.435921	−	0.755038i
$11$	−1.14040	+	1.97523i	−0.343844	+	0.595556i	−0.985143	−	0.171735i	$-0.945063\pi$
$11$	−1.14040	+	1.97523i	−0.343844	+	0.595556i	0.641299	+	0.767291i	$0.278396\pi$
$12$	−3.25678	−	9.13838i	−0.940151	−	2.63802i
$13$	1.37896	−	2.38844i	0.382456	−	0.662433i	−0.608957	−	0.793203i	$-0.708412\pi$
$13$	1.37896	−	2.38844i	0.382456	−	0.662433i	0.991413	+	0.130770i	$0.0417450\pi$
$14$	−6.64012	+	3.01934i	−1.77465	+	0.806953i
$15$	−1.12222	+	1.31932i	−0.289757	+	0.340648i
$16$	16.1700			4.04251
$17$	1.01423	+	1.75669i	0.245986	+	0.426060i	0.962408	−	0.271607i	$-0.0875550\pi$
$17$	1.01423	+	1.75669i	0.245986	+	0.426060i	−0.716422	+	0.697667i	$0.754222\pi$
$18$	−6.40679	+	5.23095i	−1.51010	+	1.23295i
$19$	−3.03493	+	5.25665i	−0.696261	+	1.20596i	0.273493	+	0.961874i	$0.411821\pi$
$19$	−3.03493	+	5.25665i	−0.696261	+	1.20596i	−0.969754	+	0.244085i	$0.921512\pi$
$20$	−2.80055	−	4.85069i	−0.626221	−	1.08465i
$21$	3.18719	+	3.29270i	0.695501	+	0.718525i
$22$	−3.14410	+	5.44574i	−0.670324	+	1.16104i
$23$	−1.49557	−	2.59040i	−0.311847	−	0.540135i	0.666915	−	0.745134i	$-0.267614\pi$
$23$	−1.49557	−	2.59040i	−0.311847	−	0.540135i	−0.978762	+	0.204999i	$0.934281\pi$
$24$	−5.77282	−	16.1983i	−1.17837	−	3.30646i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	3.80182	−	6.58494i	0.745598	−	1.29141i
$27$	4.44676	+	2.68819i	0.855779	+	0.517342i
$28$	−13.4900	+	6.13405i	−2.54936	+	1.15923i
$29$	−2.78655	−	4.82644i	−0.517449	−	0.896248i	−0.999795	−	0.0202667i	$-0.993548\pi$
$29$	−2.78655	−	4.82644i	−0.517449	−	0.896248i	0.482346	−	0.875981i	$-0.339785\pi$
$30$	−3.09398	+	3.63738i	−0.564881	+	0.664092i
$31$	−0.333000			−0.0598086			−0.0299043	−	0.999553i	$-0.509520\pi$
$31$	−0.333000			−0.0598086			−0.0299043	+	0.999553i	$0.509520\pi$
$32$	24.7245			4.37071
$33$	3.88576	+	0.712099i	0.676424	+	0.123960i
$34$	2.79623	+	4.84321i	0.479549	+	0.830604i
$35$	2.15266	+	1.53820i	0.363865	+	0.260004i
$36$	−13.0159	+	10.6271i	−2.16932	+	1.77118i
$37$	0.0601415	−	0.104168i	0.00988720	−	0.0171251i	−0.861039	−	0.508538i	$-0.830186\pi$
$37$	0.0601415	−	0.104168i	0.00988720	−	0.0171251i	0.870927	+	0.491413i	$0.163519\pi$
$38$	−8.36733	+	14.4926i	−1.35736	+	2.35102i
$39$	−4.69863	−	0.861064i	−0.752382	−	0.137881i
$40$	−4.96412	−	8.59810i	−0.784896	−	1.35948i
$41$	−0.237341	+	0.411087i	−0.0370665	+	0.0642010i	−0.883964	−	0.467556i	$-0.845135\pi$
$41$	−0.237341	+	0.411087i	−0.0370665	+	0.0642010i	0.846897	+	0.531757i	$0.178468\pi$
$42$	8.78710	+	9.07799i	1.35588	+	1.40076i
$43$	3.43450	+	5.94872i	0.523756	+	0.907171i	0.999618	+	0.0276514i	$0.00880283\pi$
$43$	3.43450	+	5.94872i	0.523756	+	0.907171i	−0.475862	+	0.879520i	$0.657864\pi$
$44$	−6.38750	+	11.0635i	−0.962952	+	1.66788i
$45$	2.80505	+	1.06382i	0.418151	+	0.158586i
$46$	−4.12329	−	7.14174i	−0.607946	−	1.05299i
$47$	7.21451			1.05234			0.526172	−	0.850378i	$-0.323627\pi$
$47$	7.21451			1.05234			0.526172	+	0.850378i	$0.323627\pi$
$48$	−9.40214	−	26.3820i	−1.35708	−	3.80791i
$49$	4.60128	−	5.27524i	0.657326	−	0.753606i
$50$	−1.37850	+	2.38764i	−0.194950	+	0.337663i
$51$	2.27638	−	2.67618i	0.318757	−	0.374740i
$52$	7.72371	−	13.3779i	1.07109	−	1.85517i
$53$	−4.25673	−	7.37287i	−0.584707	−	1.01274i	−0.994912	−	0.100748i	$-0.967876\pi$
$53$	−4.25673	−	7.37287i	−0.584707	−	1.01274i	0.410205	−	0.911993i	$-0.365457\pi$
$54$	12.2597	+	7.41136i	1.66834	+	1.00856i
$55$	2.28080			0.307544
$56$	−23.9117	+	10.8729i	−3.19533	+	1.45296i
$57$	10.3411	+	1.89509i	1.36971	+	0.251011i
$58$	−7.68253	−	13.3065i	−1.00877	−	1.74723i
$59$	−8.64149			−1.12503			−0.562513	−	0.826788i	$-0.690165\pi$
$59$	−8.64149			−1.12503			−0.562513	+	0.826788i	$0.690165\pi$
$60$	−6.28568	+	7.38965i	−0.811478	+	0.953999i
$61$	−11.2957			−1.44627			−0.723135	−	0.690706i	$-0.757300\pi$
$61$	−11.2957			−1.44627			−0.723135	+	0.690706i	$0.757300\pi$
$62$	−0.918083			−0.116597
$63$	3.51895	−	7.11456i	0.443346	−	0.896351i
$64$	35.8254			4.47818
$65$	−2.75793			−0.342079
$66$	10.7131	+	1.96326i	1.31869	+	0.241661i
$67$	−6.78119			−0.828454			−0.414227	−	0.910174i	$-0.635948\pi$
$67$	−6.78119			−0.828454			−0.414227	+	0.910174i	$0.635948\pi$
$68$	5.68077	+	9.83938i	0.688895	+	1.19320i
$69$	−3.35672	+	3.94627i	−0.404102	+	0.475075i
$70$	5.93489	+	4.24084i	0.709355	+	0.506878i
$71$	12.3927			1.47074			0.735369	−	0.677667i	$-0.237009\pi$
$71$	12.3927			1.47074			0.735369	+	0.677667i	$0.237009\pi$
$72$	−23.0714	+	18.8371i	−2.71900	+	2.21998i
$73$	0.0952946	+	0.165055i	0.0111534	+	0.0193182i	0.871548	−	0.490310i	$-0.163116\pi$
$73$	0.0952946	+	0.165055i	0.0111534	+	0.0193182i	−0.860395	+	0.509628i	$0.829783\pi$
$74$	0.165811	−	0.287192i	0.0192751	−	0.0333854i
$75$	1.70368	+	0.312214i	0.196724	+	0.0360513i
$76$	−16.9989	+	29.4430i	−1.94991	+	3.37734i
$77$	0.583422	−	6.00617i	0.0664871	−	0.684467i
$78$	−12.9542	−	2.37396i	−1.46677	−	0.268798i
$79$	−11.5433			−1.29873			−0.649363	−	0.760478i	$-0.724964\pi$
$79$	−11.5433			−1.29873			−0.649363	+	0.760478i	$0.724964\pi$
$80$	−8.08502	−	14.0037i	−0.903933	−	1.56566i
$81$	1.80029	−	8.81810i	0.200032	−	0.979789i
$82$	−0.654352	+	1.13337i	−0.0722611	+	0.125160i
$83$	−3.98395	−	6.90040i	−0.437295	−	0.757418i	0.560185	−	0.828368i	$-0.310730\pi$
$83$	−3.98395	−	6.90040i	−0.437295	−	0.757418i	−0.997480	+	0.0709503i	$0.977397\pi$
$84$	17.8517	+	18.4427i	1.94778	+	2.01226i
$85$	1.01423	−	1.75669i	0.110008	−	0.190540i
$86$	9.46893	+	16.4007i	1.02106	+	1.76853i
$87$	−6.25426	+	7.35271i	−0.670527	+	0.788293i
$88$	−11.3222	+	19.6106i	−1.20695	+	2.09050i
$89$	1.05443	−	1.82633i	0.111770	−	0.193591i	−0.804714	−	0.593662i	$-0.797681\pi$
$89$	1.05443	−	1.82633i	0.111770	−	0.193591i	0.916484	+	0.400072i	$0.131015\pi$
$90$	7.73353	+	2.93297i	0.815186	+	0.309162i
$91$	−0.705469	+	7.26261i	−0.0739532	+	0.761329i
$92$	−8.37680	−	14.5090i	−0.873342	−	1.51267i
$93$	0.193624	+	0.543302i	0.0200779	+	0.0563377i
$94$	19.8904			2.05154
$95$	6.06986			0.622755
$96$	−14.3761	−	40.3388i	−1.46726	−	4.11707i
$97$	−3.42650	−	5.93488i	−0.347909	−	0.602596i	0.637969	−	0.770062i	$-0.279775\pi$
$97$	−3.42650	−	5.93488i	−0.347909	−	0.602596i	−0.985878	+	0.167466i	$0.946441\pi$
$98$	12.6858	−	14.5439i	1.28146	−	1.46915i
$99$	−1.09758	−	6.75381i	−0.110311	−	0.678784i
$100$	−2.80055	+	4.85069i	−0.280055	+	0.485069i
$101$	6.27474	−	10.8682i	0.624360	−	1.08142i	−0.364305	−	0.931280i	$-0.618693\pi$
$101$	6.27474	−	10.8682i	0.624360	−	1.08142i	0.988664	−	0.150143i	$-0.0479734\pi$
$102$	6.27599	−	7.37825i	0.621416	−	0.730556i
$103$	7.45281	+	12.9087i	0.734348	+	1.27193i	0.955009	+	0.296577i	$0.0958451\pi$
$103$	7.45281	+	12.9087i	0.734348	+	1.27193i	−0.220661	+	0.975350i	$0.570822\pi$
$104$	13.6907	−	23.7130i	1.34248	−	2.32525i
$105$	1.25797	−	4.40653i	0.122765	−	0.430033i
$106$	−11.7358	−	20.3271i	−1.13989	−	1.97434i
$107$	8.79267	−	15.2293i	0.850019	−	1.47228i	−0.0311708	−	0.999514i	$-0.509924\pi$
$107$	8.79267	−	15.2293i	0.850019	−	1.47228i	0.881190	−	0.472762i	$-0.156743\pi$
$108$	24.9067	+	15.0568i	2.39665	+	1.44884i
$109$	−2.07627	−	3.59620i	−0.198870	−	0.344454i	0.749292	−	0.662240i	$-0.230394\pi$
$109$	−2.07627	−	3.59620i	−0.198870	−	0.344454i	−0.948162	+	0.317786i	$0.897061\pi$
$110$	6.28820			0.599556
$111$	−0.204924	−	0.0375540i	−0.0194505	−	0.00356447i
$112$	−38.9448	+	17.7087i	−3.67993	+	1.67331i
$113$	3.40667	−	5.90053i	0.320473	−	0.555075i	−0.660113	−	0.751166i	$-0.729492\pi$
$113$	3.40667	−	5.90053i	0.320473	−	0.555075i	0.980586	+	0.196091i	$0.0628250\pi$
$114$	28.5105	+	5.22479i	2.67025	+	0.489346i
$115$	−1.49557	+	2.59040i	−0.139462	+	0.241556i
$116$	−15.6077	−	27.0333i	−1.44914	−	2.50998i
$117$	1.32718	+	8.16665i	0.122698	+	0.755007i
$118$	−23.8247			−2.19324
$119$	−4.36656	−	3.12017i	−0.400282	−	0.286026i
$120$	−11.1417	+	13.0985i	−1.01709	+	1.19573i
$121$	2.89896	+	5.02115i	0.263542	+	0.456469i
$122$	−31.1424			−2.81950
$123$	0.808707	+	0.148202i	0.0729186	+	0.0133630i
$124$	−1.86516			−0.167497
$125$	1.00000			0.0894427
$126$	9.70177	−	19.6149i	0.864302	−	1.74743i
$127$	15.5473			1.37960			0.689799	−	0.724001i	$-0.257699\pi$
$127$	15.5473			1.37960			0.689799	+	0.724001i	$0.257699\pi$
$128$	49.3221			4.35950
$129$	7.70855	−	9.06241i	0.678700	−	0.797901i
$130$	−7.60363			−0.666883
$131$	4.39898	+	7.61925i	0.384340	+	0.665697i	0.991677	−	0.128747i	$-0.0410956\pi$
$131$	4.39898	+	7.61925i	0.384340	+	0.665697i	−0.607337	+	0.794444i	$0.707762\pi$
$132$	21.7645	+	3.98853i	1.89436	+	0.347157i
$133$	1.55265	−	15.9841i	0.134632	−	1.38600i
$134$	−18.6958			−1.61507
$135$	0.104661	−	5.19510i	0.00900782	−	0.447123i
$136$	10.0695	+	17.4408i	0.863450	+	1.49554i
$137$	−0.216678	+	0.375298i	−0.0185121	+	0.0320639i	−0.875133	−	0.483882i	$-0.839226\pi$
$137$	−0.216678	+	0.375298i	−0.0185121	+	0.0320639i	0.856621	+	0.515946i	$0.172560\pi$
$138$	−9.25451	+	10.8799i	−0.787796	+	0.926158i
$139$	−1.11053	+	1.92350i	−0.0941940	+	0.163149i	−0.909272	−	0.416203i	$-0.863361\pi$
$139$	−1.11053	+	1.92350i	−0.0941940	+	0.163149i	0.815078	+	0.579351i	$0.196694\pi$
$140$	12.0572	+	8.61562i	1.01902	+	0.728153i
$141$	−4.19491	−	11.7707i	−0.353275	−	0.991274i
$142$	34.1666			2.86720
$143$	3.14515	+	5.44756i	0.263011	+	0.455548i
$144$	−37.5763	+	30.6799i	−3.13136	+	2.55666i
$145$	−2.78655	+	4.82644i	−0.231410	+	0.400814i
$146$	0.262728	+	0.455058i	0.0217435	+	0.0376609i
$147$	−11.2822	−	4.43985i	−0.930539	−	0.366192i
$148$	0.336858	−	0.583455i	0.0276895	−	0.0479597i
$149$	4.15666	+	7.19954i	0.340527	+	0.589809i	0.984531	−	0.175213i	$-0.0560613\pi$
$149$	4.15666	+	7.19954i	0.340527	+	0.589809i	−0.644004	+	0.765022i	$0.722728\pi$
$150$	4.69706	+	0.860776i	0.383513	+	0.0702820i
$151$	−10.3673	+	17.9567i	−0.843680	+	1.46130i	0.0430819	+	0.999072i	$0.486282\pi$
$151$	−10.3673	+	17.9567i	−0.843680	+	1.46130i	−0.886762	+	0.462226i	$0.847051\pi$
$152$	−30.1315	+	52.1893i	−2.44399	+	4.23311i
$153$	−5.68990	−	2.15792i	−0.460001	−	0.174457i
$154$	1.60850	−	16.5591i	0.129616	−	1.33437i
$155$	0.166500	+	0.288386i	0.0133736	+	0.0231638i
$156$	−26.3174	−	4.82290i	−2.10708	−	0.386141i
$157$	14.2316			1.13580			0.567902	−	0.823096i	$-0.307755\pi$
$157$	14.2316			1.13580			0.567902	+	0.823096i	$0.307755\pi$
$158$	−31.8251			−2.53187
$159$	−9.55401	+	11.2320i	−0.757682	+	0.890755i
$160$	−12.3622	−	21.4120i	−0.977320	−	1.69277i
$161$	6.43888	+	4.60097i	0.507455	+	0.362608i
$162$	4.96342	−	24.3116i	0.389963	−	1.91010i
$163$	−3.08319	+	5.34024i	−0.241494	+	0.418280i	−0.961140	−	0.276061i	$-0.910971\pi$
$163$	−3.08319	+	5.34024i	−0.241494	+	0.418280i	0.719646	+	0.694341i	$0.244304\pi$
$164$	−1.32937	+	2.30254i	−0.103806	+	0.179798i
$165$	−1.32618	−	3.72122i	−0.103243	−	0.289696i
$166$	−10.9838	−	19.0245i	−0.852506	−	1.47658i
$167$	−2.22416	+	3.85236i	−0.172111	+	0.298105i	−0.939158	−	0.343487i	$-0.888392\pi$
$167$	−2.22416	+	3.85236i	−0.172111	+	0.298105i	0.767047	+	0.641591i	$0.221725\pi$
$168$	31.6431	+	32.6907i	2.44132	+	2.52214i
$169$	2.69691	+	4.67119i	0.207455	+	0.359322i
$170$	2.79623	−	4.84321i	0.214461	−	0.371457i
$171$	−2.92096	−	17.9738i	−0.223372	−	1.37449i
$172$	19.2369	+	33.3193i	1.46680	+	2.54057i
$173$	17.9135			1.36194			0.680969	−	0.732312i	$-0.261559\pi$
$173$	17.9135			1.36194			0.680969	+	0.732312i	$0.261559\pi$
$174$	−17.2431	+	20.2715i	−1.30719	+	1.53678i
$175$	0.255796	−	2.63336i	0.0193364	−	0.199063i
$176$	−18.4404	+	31.9396i	−1.38999	+	2.40754i
$177$	5.02464	+	14.0989i	0.377675	+	1.05974i
$178$	2.90708	−	5.03521i	0.217895	−	0.377405i
$179$	−9.04272	−	15.6625i	−0.675885	−	1.17067i	−0.976209	−	0.216830i	$-0.930428\pi$
$179$	−9.04272	−	15.6625i	−0.675885	−	1.17067i	0.300325	−	0.953837i	$-0.402905\pi$
$180$	15.7113	+	5.95858i	1.17105	+	0.444126i
$181$	5.03221			0.374041			0.187021	−	0.982356i	$-0.440117\pi$
$181$	5.03221			0.374041			0.187021	+	0.982356i	$0.440117\pi$
$182$	−1.94498	+	20.0231i	−0.144172	+	1.48421i
$183$	6.56796	+	18.4294i	0.485517	+	1.36234i
$184$	−14.8483	−	25.7181i	−1.09463	−	1.89596i
$185$	−0.120283			−0.00884338
$186$	0.533824	+	1.49789i	0.0391419	+	0.109830i
$187$	−4.62650			−0.338323
$188$	40.4091			2.94714
$189$	−13.6538	−	1.60450i	−0.993166	−	0.116710i
$190$	16.7347			1.21406
$191$	−12.0171			−0.869526			−0.434763	−	0.900545i	$-0.643168\pi$
$191$	−12.0171			−0.869526			−0.434763	+	0.900545i	$0.643168\pi$
$192$	−20.8309	−	58.4505i	−1.50334	−	4.21830i
$193$	−10.1945			−0.733813			−0.366907	−	0.930258i	$-0.619583\pi$
$193$	−10.1945			−0.733813			−0.366907	+	0.930258i	$0.619583\pi$
$194$	−9.44690	−	16.3625i	−0.678248	−	1.17476i
$195$	1.60361	+	4.49966i	0.114837	+	0.322227i
$196$	25.7722	−	29.5471i	1.84087	−	2.11051i
$197$	8.70110			0.619928			0.309964	−	0.950748i	$-0.399683\pi$
$197$	8.70110			0.619928			0.309964	+	0.950748i	$0.399683\pi$
$198$	−3.02603	−	18.6203i	−0.215051	−	1.32329i
$199$	−2.25588	−	3.90730i	−0.159915	−	0.276981i	0.774923	−	0.632056i	$-0.217789\pi$
$199$	−2.25588	−	3.90730i	−0.159915	−	0.276981i	−0.934838	+	0.355075i	$0.884455\pi$
$200$	−4.96412	+	8.59810i	−0.351016	+	0.607978i
$201$	3.94295	+	11.0638i	0.278114	+	0.780377i
$202$	17.2995	−	29.9636i	1.21719	−	2.10823i
$203$	11.9970	+	8.57256i	0.842021	+	0.601676i
$204$	12.7502	−	14.9895i	0.892693	−	1.04948i
$205$	0.474683			0.0331533
$206$	20.5475	+	35.5893i	1.43161	+	2.47962i
$207$	8.39026	+	3.18204i	0.583164	+	0.221167i
$208$	22.2979	−	38.6211i	1.54608	−	2.67789i
$209$	−6.92208	−	11.9894i	−0.478811	−	0.829324i
$210$	3.46822	−	12.1488i	0.239330	−	0.838350i
$211$	−9.86770	+	17.0914i	−0.679320	+	1.17662i	0.295866	+	0.955230i	$0.404392\pi$
$211$	−9.86770	+	17.0914i	−0.679320	+	1.17662i	−0.975186	+	0.221388i	$0.928941\pi$
$212$	−23.8423	−	41.2961i	−1.63750	−	2.83623i
$213$	−7.20576	−	20.2191i	−0.493731	−	1.38539i
$214$	24.2414	−	41.9874i	1.65711	−	2.87020i
$215$	3.43450	−	5.94872i	0.234231	−	0.405699i
$216$	44.1484	+	26.6890i	3.00392	+	1.81595i
$217$	0.802014	−	0.364686i	0.0544443	−	0.0247565i
$218$	−5.72429	−	9.91476i	−0.387698	−	0.671512i
$219$	0.213884	−	0.251449i	0.0144529	−	0.0169913i
$220$	12.7750			0.861290
$221$	5.59433			0.376315
$222$	−0.564976	−	0.103537i	−0.0379187	−	0.00694892i
$223$	3.33721	+	5.78023i	0.223476	+	0.387073i	0.955861	−	0.293818i	$-0.0949261\pi$
$223$	3.33721	+	5.78023i	0.223476	+	0.387073i	−0.732385	+	0.680891i	$0.761593\pi$
$224$	−59.5477	+	27.0770i	−3.97870	+	1.80916i
$225$	−0.481224	−	2.96115i	−0.0320816	−	0.197410i
$226$	9.39222	−	16.2678i	0.624761	−	1.08212i
$227$	1.36965	−	2.37230i	0.0909068	−	0.157455i	−0.816986	−	0.576657i	$-0.804357\pi$
$227$	1.36965	−	2.37230i	0.0909068	−	0.157455i	0.907893	+	0.419202i	$0.137690\pi$
$228$	57.9214	+	10.6146i	3.83594	+	0.702969i
$229$	−2.36355	−	4.09379i	−0.156188	−	0.270526i	0.777303	−	0.629126i	$-0.216587\pi$
$229$	−2.36355	−	4.09379i	−0.156188	−	0.270526i	−0.933491	+	0.358601i	$0.883254\pi$
$230$	−4.12329	+	7.14174i	−0.271882	+	0.470913i
$231$	−10.1385	+	2.54044i	−0.667066	+	0.167149i
$232$	−27.6655	−	47.9180i	−1.81633	−	3.14597i
$233$	−12.2018	+	21.1341i	−0.799365	+	1.38454i	0.120665	+	0.992693i	$0.461497\pi$
$233$	−12.2018	+	21.1341i	−0.799365	+	1.38454i	−0.920030	+	0.391848i	$0.871836\pi$
$234$	3.65905	+	22.5155i	0.239200	+	1.47189i
$235$	−3.60725	−	6.24794i	−0.235311	−	0.407571i
$236$	−48.4018			−3.15069
$237$	6.71192	+	18.8334i	0.435986	+	1.22336i
$238$	−12.0386	−	8.60234i	−0.780349	−	0.557607i
$239$	1.18546	−	2.05327i	0.0766809	−	0.132815i	−0.825135	−	0.564935i	$-0.808901\pi$
$239$	1.18546	−	2.05327i	0.0766809	−	0.132815i	0.901816	+	0.432120i	$0.142234\pi$
$240$	−18.1464	+	21.3335i	−1.17135	+	1.37707i
$241$	−5.57694	+	9.65954i	−0.359242	+	0.622225i	−0.987834	−	0.155509i	$-0.950298\pi$
$241$	−5.57694	+	9.65954i	−0.359242	+	0.622225i	0.628592	+	0.777735i	$0.283631\pi$
$242$	7.99247	+	13.8434i	0.513775	+	0.889885i
$243$	−15.4338	+	2.19009i	−0.990082	+	0.140494i
$244$	−63.2685			−4.05035
$245$	−6.86914	−	1.34721i	−0.438853	−	0.0860699i
$246$	2.22961	+	0.408595i	0.142155	+	0.0260511i
$247$	8.37012	+	14.4975i	0.532578	+	0.922453i
$248$	−3.30610			−0.209938
$249$	−8.94177	+	10.5122i	−0.566662	+	0.666185i
$250$	2.75701			0.174368
$251$	−1.86691			−0.117838			−0.0589192	−	0.998263i	$-0.518765\pi$
$251$	−1.86691			−0.117838			−0.0589192	+	0.998263i	$0.518765\pi$
$252$	19.7100	−	39.8493i	1.24161	−	2.51027i
$253$	6.82219			0.428907
$254$	42.8640			2.68952
$255$	−3.45583	−	0.633310i	−0.216413	−	0.0396594i
$256$	64.3305			4.02065
$257$	0.753875	+	1.30575i	0.0470254	+	0.0814504i	0.888580	−	0.458722i	$-0.151692\pi$
$257$	0.753875	+	1.30575i	0.0470254	+	0.0814504i	−0.841555	+	0.540172i	$0.818359\pi$
$258$	21.2525	−	24.9851i	1.32312	−	1.55551i
$259$	−0.0307680	+	0.316748i	−0.00191183	+	0.0196818i
$260$	−15.4474			−0.958008
$261$	15.6328	+	5.92879i	0.967645	+	0.366983i
$262$	12.1280	+	21.0063i	0.749271	+	1.29778i
$263$	0.964200	−	1.67004i	0.0594551	−	0.102979i	−0.834766	−	0.550605i	$-0.814397\pi$
$263$	0.964200	−	1.67004i	0.0594551	−	0.102979i	0.894221	+	0.447626i	$0.147730\pi$
$264$	38.5787	+	7.06988i	2.37436	+	0.435121i
$265$	−4.25673	+	7.37287i	−0.261489	+	0.452912i
$266$	4.28066	−	44.0683i	0.262464	−	2.70200i
$267$	−3.59283	−	0.658416i	−0.219878	−	0.0402944i
$268$	−37.9820			−2.32012
$269$	5.62853	+	9.74890i	0.343177	+	0.594401i	0.985021	−	0.172435i	$-0.0551634\pi$
$269$	5.62853	+	9.74890i	0.343177	+	0.594401i	−0.641843	+	0.766836i	$0.721830\pi$
$270$	0.288552	−	14.3229i	0.0175607	−	0.871666i
$271$	9.11902	−	15.7946i	0.553941	−	0.959454i	−0.444044	−	0.896005i	$-0.646457\pi$
$271$	9.11902	−	15.7946i	0.553941	−	0.959454i	0.997985	−	0.0634494i	$-0.0202101\pi$
$272$	16.4001	+	28.4058i	0.994400	+	1.72235i
$273$	12.2594	−	3.07188i	0.741973	−	0.185919i
$274$	−0.597384	+	1.03470i	−0.0360893	+	0.0625085i
$275$	−1.14040	−	1.97523i	−0.0687689	−	0.119111i
$276$	−18.8013	+	22.1034i	−1.13171	+	1.33047i
$277$	2.51744	−	4.36034i	0.151258	−	0.261987i	−0.780432	−	0.625241i	$-0.785001\pi$
$277$	2.51744	−	4.36034i	0.151258	−	0.261987i	0.931690	+	0.363254i	$0.118334\pi$
$278$	−3.06174	+	5.30309i	−0.183631	+	0.318058i
$279$	0.773832	−	0.631810i	0.0463281	−	0.0378255i
$280$	21.3721	+	15.2717i	1.27723	+	0.912656i
$281$	−5.29241	−	9.16672i	−0.315719	−	0.546841i	0.663871	−	0.747847i	$-0.268912\pi$
$281$	−5.29241	−	9.16672i	−0.315719	−	0.546841i	−0.979590	+	0.201006i	$0.935579\pi$
$282$	−11.5654	−	32.4520i	−0.688709	−	1.93249i
$283$	2.52352			0.150008			0.0750039	−	0.997183i	$-0.476103\pi$
$283$	2.52352			0.150008			0.0750039	+	0.997183i	$0.476103\pi$
$284$	69.4124			4.11887
$285$	−3.52935	−	9.90320i	−0.209061	−	0.586615i
$286$	8.67120	+	15.0190i	0.512739	+	0.888090i
$287$	0.121422	−	1.25001i	0.00716732	−	0.0737857i
$288$	−57.4552	+	46.9104i	−3.38558	+	2.76422i
$289$	6.44269	−	11.1591i	0.378982	−	0.656416i
$290$	−7.68253	+	13.3065i	−0.451134	+	0.781387i
$291$	−7.69061	+	9.04133i	−0.450832	+	0.530012i
$292$	0.533754	+	0.924489i	0.0312356	+	0.0541016i
$293$	−12.4897	+	21.6328i	−0.729655	+	1.26380i	0.227374	+	0.973808i	$0.426986\pi$
$293$	−12.4897	+	21.6328i	−0.729655	+	1.26380i	−0.957029	+	0.289992i	$0.906347\pi$
$294$	−31.1051	−	12.2407i	−1.81409	−	0.713892i
$295$	4.32075	+	7.48375i	0.251564	+	0.435721i
$296$	0.597099	−	1.03421i	0.0347057	−	0.0601120i
$297$	−10.3809	+	5.71777i	−0.602361	+	0.331779i
$298$	11.4599	+	19.8492i	0.663856	+	1.14983i
$299$	−8.24933			−0.477071
$300$	9.54246	+	1.74874i	0.550934	+	0.100963i
$301$	−14.7866	−	10.5659i	−0.852284	−	0.609009i
$302$	−28.5828	+	49.5068i	−1.64475	+	2.84880i
$303$	−21.3803	−	3.91812i	−1.22826	−	0.225090i
$304$	−49.0750	+	85.0003i	−2.81464	+	4.87510i
$305$	5.64787	+	9.78239i	0.323396	+	0.560138i
$306$	−15.6871	−	5.94939i	−0.896771	−	0.340104i
$307$	−16.5452			−0.944287			−0.472143	−	0.881522i	$-0.656520\pi$
$307$	−16.5452			−0.944287			−0.472143	+	0.881522i	$0.656520\pi$
$308$	3.26780	−	33.6411i	0.186200	−	1.91688i
$309$	16.7275	−	19.6653i	0.951592	−	1.11872i
$310$	0.459042	+	0.795084i	0.0260718	+	0.0451577i
$311$	10.2315			0.580175			0.290088	−	0.957000i	$-0.406316\pi$
$311$	10.2315			0.580175			0.290088	+	0.957000i	$0.406316\pi$
$312$	−46.6491	−	8.54884i	−2.64098	−	0.483983i
$313$	11.6672			0.659471			0.329735	−	0.944073i	$-0.393040\pi$
$313$	11.6672			0.659471			0.329735	+	0.944073i	$0.393040\pi$
$314$	39.2366			2.21425
$315$	−7.92087	+	0.509782i	−0.446290	+	0.0287230i
$316$	−64.6553			−3.63714
$317$	−3.05697			−0.171696			−0.0858482	−	0.996308i	$-0.527360\pi$
$317$	−3.05697			−0.171696			−0.0858482	+	0.996308i	$0.527360\pi$
$318$	−26.3405	+	30.9667i	−1.47710	+	1.73653i
$319$	12.7111			0.711687
$320$	−17.9127	−	31.0257i	−1.00135	−	1.73439i
$321$	−29.9598	−	5.49038i	−1.67219	−	0.306443i
$322$	17.7520	+	12.6849i	0.989282	+	0.706903i
$323$	−12.3124			−0.685081
$324$	10.0836	−	49.3910i	0.560200	−	2.74394i
$325$	1.37896	+	2.38844i	0.0764912	+	0.132487i
$326$	−8.50038	+	14.7231i	−0.470793	+	0.815437i
$327$	−4.66008	+	5.47853i	−0.257703	+	0.302964i
$328$	−2.35638	+	4.08137i	−0.130109	+	0.225356i
$329$	−17.3758	+	7.90098i	−0.957958	+	0.435595i
$330$	−3.65630	−	10.2594i	−0.201273	−	0.564763i
$331$	0.408975			0.0224793			0.0112396	−	0.999937i	$-0.496422\pi$
$331$	0.408975			0.0224793			0.0112396	+	0.999937i	$0.496422\pi$
$332$	−22.3145	−	38.6498i	−1.22467	−	2.12118i
$333$	0.0578830	+	0.356176i	0.00317197	+	0.0195183i
$334$	−6.13203	+	10.6210i	−0.335530	+	0.581154i
$335$	3.39059	+	5.87268i	0.185248	+	0.320859i
$336$	51.5369	+	53.2430i	2.81157	+	2.90465i
$337$	5.32468	−	9.22262i	0.290054	−	0.502388i	−0.683768	−	0.729699i	$-0.739660\pi$
$337$	5.32468	−	9.22262i	0.290054	−	0.502388i	0.973822	+	0.227311i	$0.0729934\pi$
$338$	7.43541	+	12.8785i	0.404433	+	0.700498i
$339$	−11.6077	−	2.12722i	−0.630446	−	0.115535i
$340$	5.68077	−	9.83938i	0.308083	−	0.533616i
$341$	0.379754	−	0.657753i	0.0205648	−	0.0356193i
$342$	−8.05311	−	49.5539i	−0.435463	−	2.67957i
$343$	−5.30478	+	17.7443i	−0.286431	+	0.958101i
$344$	34.0985	+	59.0603i	1.83847	+	3.18432i
$345$	5.09593	+	0.933873i	0.274356	+	0.0502780i
$346$	49.3877			2.65510
$347$	−24.3109			−1.30508			−0.652540	−	0.757754i	$-0.726296\pi$
$347$	−24.3109			−1.30508			−0.652540	+	0.757754i	$0.726296\pi$
$348$	−35.0307	+	41.1832i	−1.87784	+	2.20765i
$349$	10.7597	+	18.6364i	0.575955	+	0.997584i	0.995937	+	0.0900511i	$0.0287030\pi$
$349$	10.7597	+	18.6364i	0.575955	+	0.997584i	−0.419982	+	0.907532i	$0.637964\pi$
$350$	0.705233	−	7.26018i	0.0376963	−	0.388073i
$351$	12.5525	−	6.91388i	0.670002	−	0.369036i
$352$	−28.1958	+	48.8366i	−1.50284	+	2.60300i
$353$	−4.77583	+	8.27197i	−0.254192	+	0.440273i	−0.964676	−	0.263441i	$-0.915143\pi$
$353$	−4.77583	+	8.27197i	−0.254192	+	0.440273i	0.710484	+	0.703713i	$0.248476\pi$
$354$	13.8530	+	38.8708i	0.736276	+	2.06596i
$355$	−6.19633	−	10.7324i	−0.328867	−	0.569614i
$356$	5.90597	−	10.2294i	0.313016	−	0.542159i
$357$	−2.55172	+	8.93844i	−0.135051	+	0.473072i
$358$	−24.9309	−	43.1815i	−1.31764	−	2.28221i
$359$	−3.89960	+	6.75430i	−0.205813	+	0.356478i	−0.950391	−	0.311057i	$-0.899317\pi$
$359$	−3.89960	+	6.75430i	−0.205813	+	0.356478i	0.744579	+	0.667535i	$0.232650\pi$
$360$	27.8492	+	10.5619i	1.46778	+	0.556661i
$361$	−8.92161	−	15.4527i	−0.469558	−	0.813299i
$362$	13.8738			0.729193
$363$	6.50658	−	7.64934i	0.341507	−	0.401486i
$364$	−3.95139	+	40.6786i	−0.207109	+	2.13214i
$365$	0.0952946	−	0.165055i	0.00498795	−	0.00863938i
$366$	18.1079	+	50.8100i	0.946516	+	2.65588i
$367$	8.16980	−	14.1505i	0.426460	−	0.738650i	−0.570095	−	0.821578i	$-0.693094\pi$
$367$	8.16980	−	14.1505i	0.426460	−	0.738650i	0.996556	+	0.0829280i	$0.0264271\pi$
$368$	−24.1834	−	41.8868i	−1.26065	−	2.18350i
$369$	−0.228429	−	1.40561i	−0.0118915	−	0.0731730i
$370$	−0.331621			−0.0172402
$371$	18.3265	+	13.0954i	0.951467	+	0.679881i
$372$	1.08451	+	3.04308i	0.0562291	+	0.157776i
$373$	−4.45892	−	7.72308i	−0.230874	−	0.399886i	0.727191	−	0.686435i	$-0.240825\pi$
$373$	−4.45892	−	7.72308i	−0.230874	−	0.399886i	−0.958066	+	0.286549i	$0.907492\pi$
$374$	−12.7553			−0.659561
$375$	−0.581455	−	1.63154i	−0.0300262	−	0.0842522i
$376$	71.6273			3.69390
$377$	−15.3702			−0.791606
$378$	−37.6436	−	4.42361i	−1.93618	−	0.227526i
$379$	1.27870			0.0656824			0.0328412	−	0.999461i	$-0.489544\pi$
$379$	1.27870			0.0656824			0.0328412	+	0.999461i	$0.489544\pi$
$380$	33.9978			1.74405
$381$	−9.04003	−	25.3659i	−0.463135	−	1.29954i
$382$	−33.1312			−1.69514
$383$	−0.686580	−	1.18919i	−0.0350826	−	0.0607649i	0.847951	−	0.530075i	$-0.177836\pi$
$383$	−0.686580	−	1.18919i	−0.0350826	−	0.0607649i	−0.883034	+	0.469310i	$0.844503\pi$
$384$	−28.6785	−	80.4707i	−1.46350	−	4.10651i
$385$	−5.49321	+	2.49783i	−0.279960	+	0.127301i
$386$	−28.1062			−1.43057
$387$	−19.2678	−	7.30740i	−0.979439	−	0.371456i
$388$	−19.1922	−	33.2418i	−0.974334	−	1.68760i
$389$	5.39811	−	9.34980i	0.273695	−	0.474054i	−0.696110	−	0.717935i	$-0.745087\pi$
$389$	5.39811	−	9.34980i	0.273695	−	0.474054i	0.969805	+	0.243881i	$0.0784208\pi$
$390$	4.42117	+	12.4056i	0.223874	+	0.628182i
$391$	3.03368	−	5.25449i	0.153420	−	0.265731i
$392$	45.6826	−	52.3739i	2.30732	−	2.64528i
$393$	9.87328	−	11.6073i	0.498041	−	0.585513i
$394$	23.9890			1.20855
$395$	5.77167	+	9.99682i	0.290404	+	0.502995i
$396$	−6.14763	−	37.8287i	−0.308930	−	1.90096i
$397$	1.10939	−	1.92153i	0.0556789	−	0.0964386i	−0.836843	−	0.547444i	$-0.815601\pi$
$397$	1.10939	−	1.92153i	0.0556789	−	0.0964386i	0.892521	+	0.451005i	$0.148934\pi$
$398$	−6.21948	−	10.7725i	−0.311754	−	0.539974i
$399$	−26.9815	+	6.76083i	−1.35076	+	0.338465i
$400$	−8.08502	+	14.0037i	−0.404251	+	0.700183i
$401$	10.7445	+	18.6101i	0.536557	+	0.929344i	0.999086	+	0.0427400i	$0.0136087\pi$
$401$	10.7445	+	18.6101i	0.536557	+	0.929344i	−0.462529	+	0.886604i	$0.653058\pi$
$402$	10.8707	+	30.5029i	0.542184	+	1.52134i
$403$	−0.459195	+	0.795349i	−0.0228741	+	0.0396192i
$404$	35.1454	−	60.8736i	1.74855	−	3.02857i
$405$	−8.53685	+	2.84995i	−0.424199	+	0.141615i
$406$	33.0757	+	23.6346i	1.64152	+	1.17297i
$407$	0.137171	+	0.237587i	0.00679931	+	0.0117768i
$408$	22.6004	−	26.5698i	1.11889	−	1.31540i
$409$	3.28309			0.162339			0.0811693	−	0.996700i	$-0.474135\pi$
$409$	3.28309			0.162339			0.0811693	+	0.996700i	$0.474135\pi$
$410$	1.30870			0.0646323
$411$	0.738301	+	0.135300i	0.0364177	+	0.00667386i
$412$	41.7439	+	72.3025i	2.05657	+	3.56209i
$413$	20.8126	−	9.46375i	1.02412	−	0.465681i
$414$	23.1320	+	8.77291i	1.13688	+	0.431165i
$415$	−3.98395	+	6.90040i	−0.195564	+	0.338727i
$416$	34.0942	−	59.0528i	1.67160	−	2.89530i
$417$	3.78398	+	0.693446i	0.185302	+	0.0339582i
$418$	−19.0842	−	33.0549i	−0.933441	−	1.61677i
$419$	−15.4340	+	26.7325i	−0.754001	+	1.30597i	0.191869	+	0.981421i	$0.438545\pi$
$419$	−15.4340	+	26.7325i	−0.754001	+	1.30597i	−0.945870	+	0.324547i	$0.894788\pi$
$420$	7.04598	−	24.6814i	0.343809	−	1.20433i
$421$	14.4175	+	24.9718i	0.702665	+	1.21705i	0.967528	+	0.252765i	$0.0813401\pi$
$421$	14.4175	+	24.9718i	0.702665	+	1.21705i	−0.264863	+	0.964286i	$0.585327\pi$
$422$	−27.2053	+	47.1210i	−1.32433	+	2.29381i
$423$	−16.7652	+	13.6883i	−0.815153	+	0.665547i
$424$	−42.2618	−	73.1996i	−2.05242	−	3.55489i
$425$	−2.02845			−0.0983944
$426$	−19.8663	−	55.7441i	−0.962528	−	2.70081i
$427$	27.2052	−	12.3706i	1.31655	−	0.598653i
$428$	49.2485	−	85.3010i	2.38052	−	4.12318i
$429$	7.05913	−	8.29893i	0.340818	−	0.400676i
$430$	9.46893	−	16.4007i	0.456632	−	0.790910i
$431$	11.0677	+	19.1699i	0.533114	+	0.923380i	0.999252	+	0.0386684i	$0.0123116\pi$
$431$	11.0677	+	19.1699i	0.533114	+	0.923380i	−0.466138	+	0.884712i	$0.654355\pi$
$432$	71.9042	+	43.4681i	3.45949	+	2.09136i
$433$	12.9721			0.623400			0.311700	−	0.950181i	$-0.399102\pi$
$433$	12.9721			0.623400			0.311700	+	0.950181i	$0.399102\pi$
$434$	2.21116	−	1.00544i	0.106139	−	0.0482627i
$435$	9.49476	+	1.74000i	0.455239	+	0.0834264i
$436$	−11.6294	−	20.1427i	−0.556946	−	0.964658i
$437$	18.1558			0.868508
$438$	0.589680	−	0.693246i	0.0281760	−	0.0331246i
$439$	−39.2494			−1.87327			−0.936636	−	0.350304i	$-0.886078\pi$
$439$	−39.2494			−1.87327			−0.936636	+	0.350304i	$0.886078\pi$
$440$	22.6444			1.07953
$441$	−0.683692	+	20.9889i	−0.0325568	+	0.999470i
$442$	15.4236			0.733626
$443$	5.18810			0.246494			0.123247	−	0.992376i	$-0.460669\pi$
$443$	5.18810			0.246494			0.123247	+	0.992376i	$0.460669\pi$
$444$	−1.14780	−	0.210343i	−0.0544720	−	0.00998245i
$445$	−2.10886			−0.0999698
$446$	9.20073	+	15.9361i	0.435667	+	0.754597i
$447$	9.32940	−	10.9679i	0.441266	−	0.518766i
$448$	−86.2838	+	39.2343i	−4.07653	+	1.85365i
$449$	−14.2836			−0.674084			−0.337042	−	0.941490i	$-0.609426\pi$
$449$	−14.2836			−0.674084			−0.337042	+	0.941490i	$0.609426\pi$
$450$	−1.32674	−	8.16392i	−0.0625430	−	0.384851i
$451$	−0.541329	−	0.937610i	−0.0254902	−	0.0441503i
$452$	19.0811	−	33.0494i	0.897498	−	1.55451i
$453$	35.3252	+	6.47364i	1.65972	+	0.304158i
$454$	3.77613	−	6.54045i	0.177223	−	0.306959i
$455$	6.64234	−	3.02035i	0.311398	−	0.141596i
$456$	102.669	+	18.8149i	4.80791	+	0.881090i
$457$	16.1354			0.754780			0.377390	−	0.926054i	$-0.376822\pi$
$457$	16.1354			0.754780			0.377390	+	0.926054i	$0.376822\pi$
$458$	−6.51633	−	11.2866i	−0.304488	−	0.527389i
$459$	−0.212301	+	10.5380i	−0.00990935	+	0.491872i
$460$	−8.37680	+	14.5090i	−0.390570	+	0.676488i
$461$	−13.0362	−	22.5794i	−0.607157	−	1.05163i	−0.991707	−	0.128523i	$-0.958976\pi$
$461$	−13.0362	−	22.5794i	−0.607157	−	1.05163i	0.384549	−	0.923104i	$-0.374357\pi$
$462$	−27.9520	+	7.00402i	−1.30044	+	0.325856i
$463$	−17.6259	+	30.5290i	−0.819146	+	1.41880i	0.0871659	+	0.996194i	$0.472219\pi$
$463$	−17.6259	+	30.5290i	−0.819146	+	1.41880i	−0.906312	+	0.422609i	$0.861114\pi$
$464$	−45.0586	−	78.0437i	−2.09179	−	3.62309i
$465$	0.373701	−	0.439334i	0.0173300	−	0.0203736i
$466$	−33.6404	+	58.2669i	−1.55836	+	2.69916i
$467$	13.6311	−	23.6098i	0.630774	−	1.09253i	−0.356620	−	0.934250i	$-0.616071\pi$
$467$	13.6311	−	23.6098i	0.630774	−	1.09253i	0.987394	−	0.158283i	$-0.0505959\pi$
$468$	7.43366	+	45.7422i	0.343621	+	2.11443i
$469$	16.3322	−	7.42643i	0.754149	−	0.342921i
$470$	−9.94522	−	17.2256i	−0.458739	−	0.794559i
$471$	−8.27502	−	23.2194i	−0.381293	−	1.06989i
$472$	−85.7948			−3.94902
$473$	−15.6668			−0.720361
$474$	18.5048	+	51.9237i	0.849955	+	2.38494i
$475$	−3.03493	−	5.25665i	−0.139252	−	0.241192i
$476$	−24.4575	−	17.4764i	−1.12101	−	0.801028i
$477$	23.8806	+	9.05682i	1.09342	+	0.414683i
$478$	3.26832	−	5.66089i	0.149489	−	0.258923i
$479$	4.21047	−	7.29275i	0.192381	−	0.333214i	−0.753658	−	0.657267i	$-0.771712\pi$
$479$	4.21047	−	7.29275i	0.192381	−	0.333214i	0.946039	+	0.324053i	$0.105046\pi$
$480$	−27.7464	+	32.6195i	−1.26644	+	1.48887i
$481$	−0.165866	−	0.287288i	−0.00756284	−	0.0130992i
$482$	−15.3757	+	26.6314i	−0.700342	+	1.21303i
$483$	3.76274	−	13.1805i	0.171211	−	0.599735i
$484$	16.2374	+	28.1239i	0.738062	+	1.27836i
$485$	−3.42650	+	5.93488i	−0.155589	+	0.269489i
$486$	−42.5512	+	6.03809i	−1.93016	+	0.273893i
$487$	−12.3605	−	21.4090i	−0.560108	−	0.970135i	−0.997486	−	0.0708579i	$-0.977426\pi$
$487$	−12.3605	−	21.4090i	−0.560108	−	0.970135i	0.437379	−	0.899278i	$-0.355907\pi$
$488$	−112.147			−5.07664
$489$	10.5055	+	1.92523i	0.475077	+	0.0870619i
$490$	−18.9383	−	3.71426i	−0.855543	−	0.167793i
$491$	−2.31133	+	4.00335i	−0.104309	+	0.180668i	−0.913456	−	0.406938i	$-0.866596\pi$
$491$	−2.31133	+	4.00335i	−0.104309	+	0.180668i	0.809147	+	0.587607i	$0.199930\pi$
$492$	4.52964	+	0.830095i	0.204212	+	0.0374236i
$493$	5.65238	−	9.79020i	0.254570	−	0.440928i
$494$	23.0765	+	39.9697i	1.03826	+	1.79832i
$495$	−5.30018	+	4.32744i	−0.238225	+	0.194504i
$496$	−5.38462			−0.241777
$497$	−29.8471	+	13.5718i	−1.33883	+	0.608780i
$498$	−24.6525	+	28.9823i	−1.10471	+	1.29873i
$499$	11.2805	+	19.5385i	0.504987	+	0.874662i	0.999983	+	0.00576754i	$0.00183588\pi$
$499$	11.2805	+	19.5385i	0.504987	+	0.874662i	−0.494997	+	0.868895i	$0.664831\pi$
$500$	5.60109			0.250488
$501$	7.57851	+	1.38883i	0.338583	+	0.0620482i
$502$	−5.14708			−0.229726
$503$	−14.9141			−0.664988			−0.332494	−	0.943105i	$-0.607890\pi$
$503$	−14.9141			−0.664988			−0.332494	+	0.943105i	$0.607890\pi$
$504$	34.9370	−	70.6351i	1.55622	−	3.14634i
$505$	−12.5495			−0.558444
$506$	18.8088			0.836154
$507$	6.05308	−	7.11619i	0.268827	−	0.316041i
$508$	87.0817			3.86363
$509$	0.618180	+	1.07072i	0.0274003	+	0.0474588i	0.879400	−	0.476083i	$-0.157944\pi$
$509$	0.618180	+	1.07072i	0.0274003	+	0.0474588i	−0.852000	+	0.523542i	$0.824610\pi$
$510$	−9.52775	−	1.74604i	−0.421896	−	0.0773160i
$511$	−0.410273	−	0.293165i	−0.0181494	−	0.0129689i
$512$	78.7155			3.47876
$513$	−27.6265	+	15.2166i	−1.21974	+	0.671829i
$514$	2.07844	+	3.59996i	0.0916760	+	0.158788i
$515$	7.45281	−	12.9087i	0.328410	−	0.568823i
$516$	43.1763	−	50.7594i	1.90073	−	2.23456i
$517$	−8.22744	+	14.2503i	−0.361842	+	0.626729i
$518$	−0.0848275	+	0.873277i	−0.00372711	+	0.0383696i
$519$	−10.4159	−	29.2265i	−0.457207	−	1.28290i
$520$	−27.3814			−1.20075
$521$	21.3625	+	37.0009i	0.935908	+	1.62104i	0.773007	+	0.634398i	$0.218752\pi$
$521$	21.3625	+	37.0009i	0.935908	+	1.62104i	0.162901	+	0.986642i	$0.447915\pi$
$522$	43.0997	+	16.3457i	1.88642	+	0.715433i
$523$	19.9386	−	34.5347i	0.871855	−	1.51010i	0.0117804	−	0.999931i	$-0.496250\pi$
$523$	19.9386	−	34.5347i	0.871855	−	1.51010i	0.860075	−	0.510167i	$-0.170417\pi$
$524$	24.6391	+	42.6761i	1.07636	+	1.86431i
$525$	−4.44515	+	1.11384i	−0.194002	+	0.0486118i
$526$	2.65831	−	4.60432i	0.115908	−	0.200758i
$527$	−0.337737	−	0.584978i	−0.0147121	−	0.0254820i
$528$	62.8329	+	11.5147i	2.73445	+	0.501111i
$529$	7.02656	−	12.1704i	0.305503	−	0.529146i
$530$	−11.7358	+	20.3271i	−0.509772	+	0.882951i
$531$	20.0813	−	16.3957i	0.871454	−	0.711515i
$532$	8.69653	−	89.5285i	0.377042	−	3.88155i
$533$	0.654571	+	1.13375i	0.0283526	+	0.0491081i
$534$	−9.90545	−	1.81526i	−0.428651	−	0.0785539i
$535$	−17.5853			−0.760280
$536$	−67.3252			−2.90801
$537$	−20.2959	+	23.8605i	−0.875834	+	1.02966i
$538$	15.5179	+	26.8778i	0.669024	+	1.15878i
$539$	5.17253	+	15.1045i	0.222797	+	0.650598i
$540$	0.586218	−	29.0982i	0.0252268	−	1.25219i
$541$	8.42859	−	14.5987i	0.362373	−	0.627649i	−0.625978	−	0.779841i	$-0.715300\pi$
$541$	8.42859	−	14.5987i	0.362373	−	0.627649i	0.988351	+	0.152192i	$0.0486332\pi$
$542$	25.1412	−	43.5459i	1.07991	−	1.87046i
$543$	−2.92600	−	8.21023i	−0.125567	−	0.352335i
$544$	25.0762	+	43.4332i	1.07513	+	1.86218i
$545$	−2.07627	+	3.59620i	−0.0889376	+	0.154044i
$546$	33.7993	−	8.46920i	1.44648	−	0.362448i
$547$	−20.1819	−	34.9560i	−0.862915	−	1.49461i	−0.869103	−	0.494631i	$-0.835303\pi$
$547$	−20.1819	−	34.9560i	−0.862915	−	1.49461i	0.00618833	−	0.999981i	$-0.498030\pi$
$548$	−1.21364	+	2.10208i	−0.0518440	+	0.0897964i
$549$	26.2493	−	21.4317i	1.12029	−	0.914684i
$550$	−3.14410	−	5.44574i	−0.134065	−	0.232207i
$551$	33.8279			1.44112
$552$	−33.3263	+	39.1795i	−1.41846	+	1.66759i
$553$	27.8016	−	12.6417i	1.18224	−	0.537580i
$554$	6.94060	−	12.0215i	0.294878	−	0.510744i
$555$	0.0699391	+	0.196246i	0.00296875	+	0.00833018i
$556$	−6.22018	+	10.7737i	−0.263795	+	0.456905i
$557$	−2.17500	−	3.76721i	−0.0921578	−	0.159622i	0.816261	−	0.577683i	$-0.196043\pi$
$557$	−2.17500	−	3.76721i	−0.0921578	−	0.159622i	−0.908419	+	0.418061i	$0.862710\pi$
$558$	2.13346	−	1.74191i	0.0903166	−	0.0737408i
$559$	18.9442			0.801254
$560$	34.8085	+	24.8728i	1.47093	+	1.05107i
$561$	2.69010	+	7.54831i	0.113576	+	0.318690i
$562$	−14.5912	−	25.2727i	−0.615493	−	1.06607i
$563$	5.48221			0.231048			0.115524	−	0.993305i	$-0.463145\pi$
$563$	5.48221			0.231048			0.115524	+	0.993305i	$0.463145\pi$
$564$	−23.4961	−	65.9289i	−0.989362	−	2.77611i
$565$	−6.81334			−0.286639
$566$	6.95737			0.292440
$567$	5.32125	+	23.2096i	0.223472	+	0.974710i
$568$	123.037			5.16253
$569$	−31.0759			−1.30277			−0.651384	−	0.758748i	$-0.725811\pi$
$569$	−31.0759			−1.30277			−0.651384	+	0.758748i	$0.725811\pi$
$570$	−9.73044	−	27.3032i	−0.407563	−	1.14360i
$571$	6.79721			0.284454			0.142227	−	0.989834i	$-0.454574\pi$
$571$	6.79721			0.284454			0.142227	+	0.989834i	$0.454574\pi$
$572$	17.6163	+	30.5123i	0.736573	+	1.27578i
$573$	6.98739	+	19.6063i	0.291902	+	0.819066i
$574$	0.334762	−	3.44628i	0.0139727	−	0.143845i
$575$	2.99113			0.124739
$576$	−83.2519	+	67.9726i	−3.46883	+	2.83219i
$577$	−7.43866	−	12.8841i	−0.309676	−	0.536374i	0.668616	−	0.743608i	$-0.266887\pi$
$577$	−7.43866	−	12.8841i	−0.309676	−	0.536374i	−0.978291	+	0.207234i	$0.933554\pi$
$578$	17.7626	−	30.7656i	0.738825	−	1.27968i
$579$	5.92761	+	16.6326i	0.246343	+	0.691229i
$580$	−15.6077	+	27.0333i	−0.648075	+	1.12250i
$581$	17.1521	+	12.2563i	0.711591	+	0.508475i
$582$	−21.2031	+	24.9270i	−0.878896	+	1.03326i
$583$	19.4175			0.804192
$584$	0.946107	+	1.63871i	0.0391502	+	0.0678101i
$585$	6.40894	−	5.23270i	0.264977	−	0.216345i
$586$	−34.4341	+	59.6417i	−1.42246	+	2.46378i
$587$	−20.2119	−	35.0081i	−0.834235	−	1.44494i	−0.894652	−	0.446764i	$-0.852576\pi$
$587$	−20.2119	−	35.0081i	−0.834235	−	1.44494i	0.0604165	−	0.998173i	$-0.480757\pi$
$588$	−63.1926	−	24.8680i	−2.60602	−	1.02554i
$589$	1.01063	−	1.75047i	0.0416424	−	0.0721267i
$590$	11.9123	+	20.6328i	0.490423	+	0.849437i
$591$	−5.05929	−	14.1962i	−0.208112	−	0.583952i
$592$	0.972490	−	1.68440i	0.0399691	−	0.0692285i
$593$	−2.11725	+	3.66719i	−0.0869451	+	0.150593i	−0.906218	−	0.422810i	$-0.861044\pi$
$593$	−2.11725	+	3.66719i	−0.0869451	+	0.150593i	0.819273	+	0.573403i	$0.194377\pi$
$594$	−28.6202	+	15.7639i	−1.17430	+	0.646802i
$595$	−0.518871	+	5.34164i	−0.0212716	+	0.218986i
$596$	23.2818	+	40.3253i	0.953660	+	1.65179i
$597$	−5.06321	+	5.95247i	−0.207223	+	0.243618i
$598$	−22.7435			−0.930050
$599$	4.11637			0.168190			0.0840951	−	0.996458i	$-0.473200\pi$
$599$	4.11637			0.168190			0.0840951	+	0.996458i	$0.473200\pi$
$600$	16.9145	+	3.09973i	0.690533	+	0.126546i
$601$	−21.2127	−	36.7416i	−0.865286	−	1.49872i	−0.866763	−	0.498720i	$-0.833803\pi$
$601$	−21.2127	−	36.7416i	−0.865286	−	1.49872i	0.00147704	−	0.999999i	$-0.499530\pi$
$602$	−40.7667	−	29.1303i	−1.66153	−	1.18726i
$603$	15.7583	−	12.8661i	0.641726	−	0.523950i
$604$	−58.0683	+	100.577i	−2.36277	+	4.09243i
$605$	2.89896	−	5.02115i	0.117860	−	0.204139i
$606$	−58.9456	−	10.8023i	−2.39450	−	0.438813i
$607$	22.0283	+	38.1542i	0.894102	+	1.54863i	0.834913	+	0.550382i	$0.185518\pi$
$607$	22.0283	+	38.1542i	0.894102	+	1.54863i	0.0591889	+	0.998247i	$0.481149\pi$
$608$	−75.0370	+	129.968i	−3.04315	+	5.27089i
$609$	7.01076	−	24.5580i	0.284090	−	0.995141i
$610$	15.5712	+	26.9701i	0.630460	+	1.09199i
$611$	9.94855	−	17.2314i	0.402475	−	0.697107i
$612$	−31.8696	−	12.0867i	−1.28825	−	0.488575i
$613$	6.78432	+	11.7508i	0.274016	+	0.474610i	0.969886	−	0.243558i	$-0.0783145\pi$
$613$	6.78432	+	11.7508i	0.274016	+	0.474610i	−0.695870	+	0.718167i	$0.744981\pi$
$614$	−45.6154			−1.84089
$615$	−0.276006	−	0.774462i	−0.0111297	−	0.0312293i
$616$	5.79235	−	59.6307i	0.233380	−	2.40259i
$617$	13.5005	−	23.3835i	0.543509	−	0.941384i	−0.455191	−	0.890394i	$-0.650429\pi$
$617$	13.5005	−	23.3835i	0.543509	−	0.941384i	0.998699	−	0.0509904i	$-0.0162378\pi$
$618$	46.1177	−	54.2175i	1.85513	−	2.18095i
$619$	10.3531	−	17.9322i	0.416128	−	0.720755i	−0.579418	−	0.815031i	$-0.696720\pi$
$619$	10.3531	−	17.9322i	0.416128	−	0.720755i	0.995546	+	0.0942754i	$0.0300534\pi$
$620$	0.932582	+	1.61528i	0.0374534	+	0.0648712i
$621$	0.313056	−	15.5392i	0.0125625	−	0.623568i
$622$	28.2083			1.13105
$623$	−0.539440	+	5.55339i	−0.0216122	+	0.222492i
$624$	−75.9770	−	13.9234i	−3.04151	−	0.557383i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	32.1666			1.28564
$627$	−15.5363	+	18.2649i	−0.620459	+	0.729431i
$628$	79.7125			3.18087
$629$	0.243988			0.00972844
$630$	−21.8379	+	1.40547i	−0.870042	+	0.0559954i
$631$	10.8873			0.433416			0.216708	−	0.976237i	$-0.430468\pi$
$631$	10.8873			0.433416			0.216708	+	0.976237i	$0.430468\pi$
$632$	−114.605			−4.55874
$633$	33.6228	+	6.16166i	1.33639	+	0.244904i
$634$	−8.42808			−0.334722
$635$	−7.77364	−	13.4643i	−0.308487	−	0.534316i
$636$	−53.5129	+	62.9114i	−2.12192	+	2.49460i
$637$	−6.25458	−	18.2643i	−0.247815	−	0.723656i
$638$	35.0447			1.38743
$639$	−28.7983	+	23.5129i	−1.13924	+	0.930157i
$640$	−24.6610	−	42.7142i	−0.974813	−	1.68843i
$641$	8.22677	−	14.2492i	0.324938	−	0.562809i	−0.656562	−	0.754272i	$-0.727990\pi$
$641$	8.22677	−	14.2492i	0.324938	−	0.562809i	0.981500	+	0.191463i	$0.0613232\pi$
$642$	−82.5993	−	15.1370i	−3.25993	−	0.597411i
$643$	17.2233	−	29.8317i	0.679221	−	1.17645i	−0.295994	−	0.955190i	$-0.595651\pi$
$643$	17.2233	−	29.8317i	0.679221	−	1.17645i	0.975216	−	0.221256i	$-0.0710157\pi$
$644$	36.0647	+	25.7705i	1.42115	+	1.01550i
$645$	−11.7026	−	2.14459i	−0.460788	−	0.0844433i
$646$	−33.9454			−1.33557
$647$	−6.32211	−	10.9502i	−0.248548	−	0.430498i	0.714575	−	0.699559i	$-0.246620\pi$
$647$	−6.32211	−	10.9502i	−0.248548	−	0.430498i	−0.963123	+	0.269061i	$0.913287\pi$
$648$	17.8737	−	87.5482i	0.702146	−	3.43922i
$649$	9.85478	−	17.0690i	0.386834	−	0.670016i
$650$	3.80182	+	6.58494i	0.149120	+	0.258283i
$651$	−1.06133	−	1.09647i	−0.0415969	−	0.0429740i
$652$	−17.2692	+	29.9112i	−0.676315	+	1.17141i
$653$	−14.3832	−	24.9124i	−0.562856	−	0.974896i	−0.997246	−	0.0741704i	$-0.976369\pi$
$653$	−14.3832	−	24.9124i	−0.562856	−	0.974896i	0.434389	−	0.900725i	$-0.356964\pi$
$654$	−12.8479	+	15.1044i	−0.502392	+	0.590627i
$655$	4.39898	−	7.61925i	0.171882	−	0.297709i
$656$	−3.83782	+	6.64730i	−0.149842	+	0.259533i
$657$	−0.534611	−	0.202753i	−0.0208572	−	0.00791016i
$658$	−47.9052	+	21.7831i	−1.86754	+	0.849192i
$659$	16.4699	+	28.5267i	0.641576	+	1.11124i	0.985081	+	0.172091i	$0.0550523\pi$
$659$	16.4699	+	28.5267i	0.641576	+	1.11124i	−0.343506	+	0.939151i	$0.611614\pi$
$660$	−7.42808	−	20.8429i	−0.289138	−	0.811308i
$661$	−36.5045			−1.41986			−0.709930	−	0.704273i	$-0.751273\pi$
$661$	−36.5045			−1.41986			−0.709930	+	0.704273i	$0.751273\pi$
$662$	1.12755			0.0438233
$663$	−3.25285	−	9.12735i	−0.126330	−	0.354477i
$664$	−39.5536	−	68.5088i	−1.53498	−	2.65866i
$665$	−14.6190	+	6.64742i	−0.566899	+	0.257776i
$666$	0.159584	+	0.981980i	0.00618375	+	0.0380510i
$667$	−8.33493	+	14.4365i	−0.322730	+	0.558984i
$668$	−12.4577	+	21.5774i	−0.482004	+	0.834855i
$669$	7.49021	−	8.80572i	0.289588	−	0.340449i
$670$	9.34789	+	16.1910i	0.361141	+	0.625514i
$671$	12.8817	−	22.3117i	0.497292	−	0.861335i
$672$	78.8014	+	81.4101i	3.03983	+	3.14046i
$673$	21.7574	+	37.6849i	0.838685	+	1.45265i	0.890994	+	0.454014i	$0.150008\pi$
$673$	21.7574	+	37.6849i	0.838685	+	1.45265i	−0.0523094	+	0.998631i	$0.516658\pi$
$674$	14.6802	−	25.4268i	0.565460	−	0.979405i
$675$	−4.55142	+	2.50691i	−0.175184	+	0.0964910i
$676$	15.1057	+	26.1638i	0.580987	+	1.00630i
$677$	42.2727			1.62467			0.812336	−	0.583189i	$-0.198195\pi$
$677$	42.2727			1.62467			0.812336	+	0.583189i	$0.198195\pi$
$678$	−32.0026	−	5.86476i	−1.22905	−	0.225235i
$679$	14.7522	+	10.5413i	0.566136	+	0.404539i
$680$	10.0695	−	17.4408i	0.386147	−	0.668826i
$681$	−4.66689	−	0.855247i	−0.178835	−	0.0327731i
$682$	1.04698	−	1.81343i	0.0400911	−	0.0694398i
$683$	−12.1766	−	21.0904i	−0.465923	−	0.807003i	0.533319	−	0.845914i	$-0.320944\pi$
$683$	−12.1766	−	21.0904i	−0.465923	−	0.807003i	−0.999243	+	0.0389112i	$0.987611\pi$
$684$	−16.3606	−	100.673i	−0.625562	−	3.84932i
$685$	0.433357			0.0165577
$686$	−14.6253	+	48.9211i	−0.558397	+	1.86782i
$687$	−5.30487	+	6.23658i	−0.202394	+	0.237940i
$688$	55.5359	+	96.1910i	2.11729	+	3.66725i
$689$	−23.4795			−0.894498
$690$	14.0495	+	2.57469i	0.534856	+	0.0980169i
$691$	−18.5890			−0.707158			−0.353579	−	0.935405i	$-0.615035\pi$
$691$	−18.5890			−0.707158			−0.353579	+	0.935405i	$0.615035\pi$
$692$	100.335			3.81417
$693$	10.0399	+	15.0642i	0.381385	+	0.572242i
$694$	−67.0254			−2.54425
$695$	2.22106			0.0842496
$696$	−62.0938	+	72.9994i	−2.35366	+	2.76704i
$697$	−0.962871			−0.0364713
$698$	29.6647	+	51.3807i	1.12282	+	1.94479i
$699$	41.5758	+	7.61913i	1.57254	+	0.288182i
$700$	1.43274	−	14.7497i	0.0541525	−	0.557485i
$701$	−23.3630			−0.882409			−0.441205	−	0.897407i	$-0.645449\pi$
$701$	−23.3630			−0.882409			−0.441205	+	0.897407i	$0.645449\pi$
$702$	34.6073	−	19.0616i	1.30617	−	0.719435i
$703$	0.365050	+	0.632286i	0.0137681	+	0.0238471i
$704$	−40.8554	+	70.7636i	−1.53980	+	2.66700i
$705$	−8.09630	+	9.51826i	−0.304924	+	0.358478i
$706$	−13.1670	+	22.8059i	−0.495546	+	0.858311i
$707$	−3.21011	+	33.0472i	−0.120729	+	1.24287i
$708$	28.1434	+	78.9693i	1.05770	+	2.96785i
$709$	43.3833			1.62929			0.814647	−	0.579957i	$-0.196930\pi$
$709$	43.3833			1.62929			0.814647	+	0.579957i	$0.196930\pi$
$710$	−17.0833	−	29.5892i	−0.641125	−	1.11046i
$711$	26.8246	−	21.9015i	1.00600	−	0.821370i
$712$	10.4687	−	18.1322i	0.392329	−	0.679534i
$713$	0.498024	+	0.862602i	0.0186511	+	0.0323047i
$714$	−7.03512	+	24.6433i	−0.263283	+	0.922254i
$715$	3.14515	−	5.44756i	0.117622	−	0.203727i
$716$	−50.6491	−	87.7268i	−1.89285	−	3.27851i
$717$	−4.03928	−	0.740233i	−0.150850	−	0.0276445i
$718$	−10.7512	+	18.6216i	−0.401232	+	0.694954i
$719$	21.0553	−	36.4688i	0.785230	−	1.36006i	−0.143632	−	0.989631i	$-0.545878\pi$
$719$	21.0553	−	36.4688i	0.785230	−	1.36006i	0.928862	−	0.370427i	$-0.120789\pi$
$720$	45.3577	+	17.2021i	1.69038	+	0.641084i
$721$	−32.0867	−	22.9279i	−1.19497	−	0.853880i
$722$	−24.5969	−	42.6031i	−0.915403	−	1.58552i
$723$	19.0026	+	3.48239i	0.706715	+	0.129512i
$724$	28.1859			1.04752
$725$	5.57309			0.206980
$726$	17.9387	−	21.0893i	0.665767	−	0.782697i
$727$	−23.4220	−	40.5680i	−0.868673	−	1.50459i	−0.863354	−	0.504599i	$-0.831640\pi$
$727$	−23.4220	−	40.5680i	−0.868673	−	1.50459i	−0.00531918	−	0.999986i	$-0.501693\pi$
$728$	−7.00406	+	72.1049i	−0.259588	+	2.67239i
$729$	12.5473	+	23.9074i	0.464714	+	0.885461i
$730$	0.262728	−	0.455058i	0.00972400	−	0.0168425i
$731$	−6.96671	+	12.0667i	−0.257673	+	0.446303i
$732$	36.7877	+	103.225i	1.35971	+	3.81530i
$733$	−25.1880	−	43.6270i	−0.930341	−	1.61140i	−0.782738	−	0.622352i	$-0.786177\pi$
$733$	−25.1880	−	43.6270i	−0.930341	−	1.61140i	−0.147603	−	0.989047i	$-0.547156\pi$
$734$	22.5242	−	39.0131i	0.831383	−	1.44000i
$735$	1.79607	+	11.9906i	0.0662492	+	0.442279i
$736$	−36.9771	−	64.0461i	−1.36299	−	2.36077i
$737$	7.73328	−	13.3944i	0.284859	−	0.493390i
$738$	−0.629779	−	3.87527i	−0.0231825	−	0.142651i
$739$	24.8224	+	42.9937i	0.913108	+	1.58155i	0.809648	+	0.586915i	$0.199658\pi$
$739$	24.8224	+	42.9937i	0.913108	+	1.58155i	0.103460	+	0.994634i	$0.467009\pi$
$740$	−0.673716			−0.0247663
$741$	18.7863	−	22.0858i	0.690133	−	0.811342i
$742$	50.5264	+	36.1042i	1.85488	+	1.32543i
$743$	−6.76254	+	11.7131i	−0.248093	+	0.429710i	−0.962997	−	0.269513i	$-0.913137\pi$
$743$	−6.76254	+	11.7131i	−0.248093	+	0.429710i	0.714903	+	0.699223i	$0.246471\pi$
$744$	1.92235	+	5.39403i	0.0704767	+	0.197755i
$745$	4.15666	−	7.19954i	0.152288	−	0.263771i
$746$	−12.2933	−	21.2926i	−0.450089	−	0.779577i
$747$	22.3503	+	8.47644i	0.817755	+	0.310137i
$748$	−25.9135			−0.947490
$749$	−4.49827	+	46.3085i	−0.164363	+	1.69207i
$750$	−1.60307	−	4.49816i	−0.0585360	−	0.164250i
$751$	20.2889	+	35.1414i	0.740351	+	1.28233i	0.952335	+	0.305053i	$0.0986742\pi$
$751$	20.2889	+	35.1414i	0.740351	+	1.28233i	−0.211984	+	0.977273i	$0.567992\pi$
$752$	116.659			4.25411
$753$	1.08552	+	3.04593i	0.0395587	+	0.111000i
$754$	−42.3758			−1.54323
$755$	20.7346			0.754611
$756$	−76.4760	−	8.98694i	−2.78141	−	0.326852i
$757$	−0.0588390			−0.00213854			−0.00106927	−	0.999999i	$-0.500340\pi$
$757$	−0.0588390			−0.00213854			−0.00106927	+	0.999999i	$0.500340\pi$
$758$	3.52538			0.128048
$759$	−3.96679	−	11.1307i	−0.143985	−	0.404017i
$760$	60.2630			2.18597
$761$	0.872297	+	1.51086i	0.0316207	+	0.0547687i	0.881403	−	0.472366i	$-0.156600\pi$
$761$	0.872297	+	1.51086i	0.0316207	+	0.0547687i	−0.849782	+	0.527134i	$0.823266\pi$
$762$	−24.9234	−	69.9341i	−0.902881	−	2.53345i
$763$	8.93898	+	6.38745i	0.323613	+	0.231241i
$764$	−67.3088			−2.43515
$765$	0.976139	+	6.00655i	0.0352924	+	0.217167i
$766$	−1.89291	−	3.27861i	−0.0683935	−	0.118461i
$767$	−11.9163	+	20.6397i	−0.430273	+	0.745255i
$768$	−37.4052	−	104.957i	−1.34975	−	3.78733i
$769$	−2.67448	+	4.63234i	−0.0964444	+	0.167047i	−0.910210	−	0.414146i	$-0.864080\pi$
$769$	−2.67448	+	4.63234i	−0.0964444	+	0.167047i	0.813766	+	0.581192i	$0.197414\pi$
$770$	−15.1448	+	6.88653i	−0.545781	+	0.248173i
$771$	1.69203	−	1.98921i	0.0609371	−	0.0716396i
$772$	−57.1001			−2.05508
$773$	16.5833	+	28.7231i	0.596460	+	1.03310i	0.993339	+	0.115228i	$0.0367597\pi$
$773$	16.5833	+	28.7231i	0.596460	+	1.03310i	−0.396880	+	0.917871i	$0.629907\pi$
$774$	−53.1216	−	20.1466i	−1.90941	−	0.724153i
$775$	0.166500	−	0.288386i	0.00598086	−	0.0103591i
$776$	−34.0191	−	58.9229i	−1.22122	−	2.11521i
$777$	0.534676	−	0.133975i	0.0191814	−	0.00480634i
$778$	14.8826	−	25.7775i	0.533568	−	0.924167i
$779$	−1.44063	−	2.49524i	−0.0516159	−	0.0894013i
$780$	8.98197	+	25.2030i	0.321606	+	0.902413i
$781$	−14.1326	+	24.4784i	−0.505705	+	0.875906i
$782$	8.36389	−	14.4867i	0.299092	−	0.518043i
$783$	0.583288	−	28.9528i	0.0208450	−	1.03469i
$784$	74.4029	−	85.3009i	2.65725	−	3.04646i
$785$	−7.11580	−	12.3249i	−0.253974	−	0.439895i
$786$	27.2207	−	32.0015i	0.970930	−	1.14146i
$787$	0.794698			0.0283279			0.0141640	−	0.999900i	$-0.495491\pi$
$787$	0.794698			0.0283279			0.0141640	+	0.999900i	$0.495491\pi$
$788$	48.7357			1.73614
$789$	−3.28537	−	0.602073i	−0.116962	−	0.0214344i
$790$	15.9125	+	27.5613i	0.566142	+	0.980587i
$791$	−1.74283	+	17.9420i	−0.0619678	+	0.637943i
$792$	−10.8970	−	67.0534i	−0.387208	−	2.38264i
$793$	−15.5764	+	26.9792i	−0.553135	+	0.958058i
$794$	3.05861	−	5.29766i	0.108546	−	0.188007i
$795$	14.5042	+	2.65802i	0.514411	+	0.0942702i
$796$	−12.6354	−	21.8851i	−0.447849	−	0.775698i
$797$	6.14419	−	10.6421i	0.217638	−	0.376961i	−0.736447	−	0.676495i	$-0.763498\pi$
$797$	6.14419	−	10.6421i	0.217638	−	0.376961i	0.954086	+	0.299534i	$0.0968313\pi$
$798$	−74.3881	+	18.6397i	−2.63331	+	0.659837i
$799$	7.31714	+	12.6737i	0.258862	+	0.448362i
$800$	−12.3622	+	21.4120i	−0.437071	+	0.757029i
$801$	1.01484	+	6.24467i	0.0358575	+	0.220645i
$802$	29.6228	+	51.3082i	1.04602	+	1.81176i
$803$	−0.434697			−0.0153401
$804$	22.0848	+	61.9691i	0.778872	+	2.18548i
$805$	0.765121	−	7.87672i	0.0269670	−	0.277618i
$806$	−1.26600	+	2.19278i	−0.0445931	+	0.0772375i
$807$	12.6329	−	14.8517i	0.444701	−	0.522804i
$808$	62.2971	−	107.902i	2.19160	−	3.79597i
$809$	−7.69807	−	13.3334i	−0.270650	−	0.468779i	0.698379	−	0.715728i	$-0.253905\pi$
$809$	−7.69807	−	13.3334i	−0.270650	−	0.468779i	−0.969028	+	0.246950i	$0.920572\pi$
$810$	−23.5362	+	7.85735i	−0.826976	+	0.276079i
$811$	48.7158			1.71064			0.855321	−	0.518098i	$-0.173360\pi$
$811$	48.7158			1.71064			0.855321	+	0.518098i	$0.173360\pi$
$812$	67.1960	+	48.0157i	2.35812	+	1.68502i
$813$	−31.0718	−	5.69417i	−1.08974	−	0.199703i
$814$	0.378181	+	0.655029i	0.0132553	+	0.0229588i
$815$	6.16638			0.215999
$816$	36.8091	−	43.2740i	1.28858	−	1.51489i
$817$	−41.6938			−1.45868
$818$	9.05152			0.316479
$819$	−12.1402	−	18.2155i	−0.424212	−	0.636502i
$820$	2.65874			0.0928473
$821$	−41.5631			−1.45056			−0.725282	−	0.688452i	$-0.758290\pi$
$821$	−41.5631			−1.45056			−0.725282	+	0.688452i	$0.758290\pi$
$822$	2.03550	+	0.373023i	0.0709963	+	0.0130107i
$823$	−18.2402			−0.635813			−0.317907	−	0.948122i	$-0.602980\pi$
$823$	−18.2402			−0.635813			−0.317907	+	0.948122i	$0.602980\pi$
$824$	73.9933	+	128.160i	2.57768	+	4.46467i
$825$	−2.55958	+	3.00912i	−0.0891130	+	0.104764i
$826$	57.3806	−	26.0916i	1.99652	−	0.907844i
$827$	−42.1614			−1.46610			−0.733048	−	0.680177i	$-0.761903\pi$
$827$	−42.1614			−1.46610			−0.733048	+	0.680177i	$0.761903\pi$
$828$	46.9946	+	17.8229i	1.63318	+	0.619388i
$829$	−3.57036	−	6.18404i	−0.124004	−	0.214781i	0.797339	−	0.603531i	$-0.206240\pi$
$829$	−3.57036	−	6.18404i	−0.124004	−	0.214781i	−0.921343	+	0.388751i	$0.872907\pi$
$830$	−10.9838	+	19.0245i	−0.381252	+	0.660349i
$831$	−8.57782	−	1.57196i	−0.297561	−	0.0545307i
$832$	49.4020	−	85.5668i	1.71271	−	2.96649i
$833$	13.9337	+	2.73274i	0.482774	+	0.0946839i
$834$	10.4324	+	1.91184i	0.361246	+	0.0662014i
$835$	4.44832			0.153941
$836$	−38.7712	−	67.1537i	−1.34093	−	2.32256i
$837$	−1.48077	−	0.895167i	−0.0511829	−	0.0309415i
$838$	−42.5517	+	73.7017i	−1.46992	+	2.54598i
$839$	18.6903	+	32.3725i	0.645260	+	1.11762i	0.984241	+	0.176830i	$0.0565843\pi$
$839$	18.6903	+	32.3725i	0.645260	+	1.11762i	−0.338981	+	0.940793i	$0.610082\pi$
$840$	12.4894	−	43.7491i	0.430924	−	1.50949i
$841$	−1.02969	+	1.78347i	−0.0355065	+	0.0614990i
$842$	39.7491	+	68.8475i	1.36984	+	2.37264i
$843$	−11.8785	+	13.9648i	−0.409119	+	0.480973i
$844$	−55.2699	+	95.7302i	−1.90247	+	3.29517i
$845$	2.69691	−	4.67119i	0.0927766	−	0.160694i
$846$	−46.2218	+	37.7387i	−1.58914	+	1.29748i
$847$	−12.4809	−	8.91840i	−0.428850	−	0.306440i
$848$	−68.8315	−	119.220i	−2.36368	−	4.09402i
$849$	−1.46731	−	4.11722i	−0.0503580	−	0.141302i
$850$	−5.59246			−0.191820
$851$	−0.359782			−0.0123332
$852$	−40.3601	−	113.249i	−1.38272	−	3.87984i
$853$	−2.46029	−	4.26134i	−0.0842386	−	0.145906i	0.820828	−	0.571176i	$-0.193512\pi$
$853$	−2.46029	−	4.26134i	−0.0842386	−	0.145906i	−0.905067	+	0.425270i	$0.860179\pi$
$854$	75.0051	−	34.1057i	2.56662	−	1.16707i
$855$	−14.1053	+	11.5165i	−0.482390	+	0.393857i
$856$	87.2957	−	151.201i	2.98370	−	5.16793i
$857$	−24.0601	+	41.6734i	−0.821878	+	1.42353i	0.0824040	+	0.996599i	$0.473740\pi$
$857$	−24.0601	+	41.6734i	−0.821878	+	1.42353i	−0.904282	+	0.426936i	$0.859593\pi$
$858$	19.4621	−	22.8802i	0.664424	−	0.781118i
$859$	−16.4250	−	28.4489i	−0.560414	−	0.970666i	−0.997460	−	0.0712265i	$-0.977309\pi$
$859$	−16.4250	−	28.4489i	−0.560414	−	0.970666i	0.437046	−	0.899439i	$-0.356025\pi$
$860$	19.2369	−	33.3193i	0.655974	−	1.13618i
$861$	−2.11004	+	0.528719i	−0.0719098	+	0.0180187i
$862$	30.5138	+	52.8515i	1.03930	+	1.80013i
$863$	20.3542	−	35.2544i	0.692864	−	1.20007i	−0.278032	−	0.960572i	$-0.589682\pi$
$863$	20.3542	−	35.2544i	0.692864	−	1.20007i	0.970896	−	0.239503i	$-0.0769845\pi$
$864$	109.944	+	66.4640i	3.74036	+	2.26115i
$865$	−8.95676	−	15.5136i	−0.304539	−	0.527477i
$866$	35.7642			1.21532
$867$	−21.9526	−	4.02299i	−0.745548	−	0.136628i
$868$	4.49216	−	2.04264i	0.152474	−	0.0693316i
$869$	13.1640	−	22.8008i	0.446560	−	0.773464i
$870$	26.1771	+	4.79718i	0.887488	+	0.162640i
$871$	−9.35102	+	16.1964i	−0.316847	+	0.548795i
$872$	−20.6137	−	35.7039i	−0.698067	−	1.20909i
$873$	19.2230	+	7.29039i	0.650600	+	0.246742i
$874$	50.0556			1.69315
$875$	−2.40845	+	1.09515i	−0.0814205	+	0.0370229i
$876$	1.19798	−	1.40839i	0.0404761	−	0.0475850i
$877$	−11.9782	−	20.7469i	−0.404476	−	0.700573i	0.589784	−	0.807561i	$-0.299213\pi$
$877$	−11.9782	−	20.7469i	−0.404476	−	0.700573i	−0.994260	+	0.106988i	$0.965879\pi$
$878$	−108.211			−3.65194
$879$	42.5568	+	7.79890i	1.43541	+	0.263050i
$880$	36.8807			1.24325
$881$	−2.59131			−0.0873035			−0.0436518	−	0.999047i	$-0.513899\pi$
$881$	−2.59131			−0.0873035			−0.0436518	+	0.999047i	$0.513899\pi$
$882$	−1.88494	+	57.8665i	−0.0634693	+	1.94847i
$883$	−38.0612			−1.28086			−0.640431	−	0.768015i	$-0.721244\pi$
$883$	−38.0612			−1.28086			−0.640431	+	0.768015i	$0.721244\pi$
$884$	31.3343			1.05389
$885$	9.69770	−	11.4009i	0.325984	−	0.383238i
$886$	14.3036			0.480540
$887$	−23.8669	−	41.3386i	−0.801371	−	1.38801i	−0.918714	−	0.394924i	$-0.870771\pi$
$887$	−23.8669	−	41.3386i	−0.801371	−	1.38801i	0.117343	−	0.993091i	$-0.462562\pi$
$888$	−2.03453	−	0.372845i	−0.0682743	−	0.0125119i
$889$	−37.4449	+	17.0266i	−1.25586	+	0.571055i
$890$	−5.81415			−0.194891
$891$	15.3648	+	13.6122i	0.514739	+	0.456025i
$892$	18.6920	+	32.3756i	0.625856	+	1.08401i
$893$	−21.8955	+	37.9242i	−0.732706	+	1.26908i
$894$	25.7212	−	30.2387i	0.860247	−	1.01133i
$895$	−9.04272	+	15.6625i	−0.302265	+	0.523538i
$896$	−118.790	+	54.0152i	−3.96849	+	1.80452i
$897$	4.79661	+	13.4591i	0.160154	+	0.449386i
$898$	−39.3800			−1.31413
$899$	0.927920	+	1.60720i	0.0309479	+	0.0536033i
$900$	−2.69538	−	16.5857i	−0.0898460	−	0.552856i
$901$	8.63457	−	14.9555i	0.287659	−	0.498240i
$902$	−1.49245	−	2.58500i	−0.0496931	−	0.0860710i
$903$	−8.64095	+	30.2684i	−0.287553	+	1.00727i
$904$	33.8222	−	58.5818i	1.12491	−	1.94840i
$905$	−2.51610	−	4.35802i	−0.0836382	−	0.144866i
$906$	97.3918	+	17.8479i	3.23562	+	0.592956i
$907$	7.11975	−	12.3318i	0.236407	−	0.409470i	−0.723273	−	0.690562i	$-0.757363\pi$
$907$	7.11975	−	12.3318i	0.236407	−	0.409470i	0.959681	+	0.281092i	$0.0906966\pi$
$908$	7.67153	−	13.2875i	0.254589	−	0.440960i
$909$	6.03911	+	37.1609i	0.200305	+	1.23255i
$910$	18.3130	−	8.32714i	0.607070	−	0.276042i
$911$	15.6619	+	27.1272i	0.518902	+	0.898764i	0.999759	+	0.0219651i	$0.00699228\pi$
$911$	15.6619	+	27.1272i	0.518902	+	0.898764i	−0.480857	+	0.876799i	$0.659674\pi$
$912$	167.216	+	30.6437i	5.53707	+	1.01472i
$913$	18.1732			0.601446
$914$	44.4853			1.47144
$915$	12.6764	−	14.9027i	0.419067	−	0.492669i
$916$	−13.2385	−	22.9297i	−0.437412	−	0.757619i
$917$	−18.9390	−	13.5331i	−0.625420	−	0.446901i
$918$	−0.585315	+	29.0534i	−0.0193183	+	0.958904i
$919$	14.9287	−	25.8572i	0.492451	−	0.852951i	−0.507511	−	0.861645i	$-0.669434\pi$
$919$	14.9287	−	25.8572i	0.492451	−	0.852951i	0.999962	+	0.00869473i	$0.00276765\pi$
$920$	−14.8483	+	25.7181i	−0.489535	+	0.847900i
$921$	9.62030	+	26.9942i	0.317000	+	0.889488i
$922$	−35.9410	−	62.2516i	−1.18365	−	2.05015i
$923$	17.0890	−	29.5991i	0.562492	−	0.974265i
$924$	−56.7868	+	14.2293i	−1.86815	+	0.468108i
$925$	0.0601415	+	0.104168i	0.00197744	+	0.00342503i
$926$	−48.5948	+	84.1687i	−1.59692	+	2.76595i
$927$	−41.8110	−	15.8570i	−1.37325	−	0.520811i
$928$	−68.8958	−	119.331i	−2.26162	−	3.91724i
$929$	−20.9883			−0.688604			−0.344302	−	0.938859i	$-0.611884\pi$
$929$	−20.9883			−0.688604			−0.344302	+	0.938859i	$0.611884\pi$
$930$	1.03030	−	1.21125i	0.0337847	−	0.0397184i
$931$	13.7656	+	40.1974i	0.451148	+	1.31741i
$932$	−68.3433	+	118.374i	−2.23866	+	3.87747i
$933$	−5.94915	−	16.6931i	−0.194767	−	0.546507i
$934$	37.5812	−	65.0925i	1.22969	−	2.12989i
$935$	2.31325	+	4.00667i	0.0756514	+	0.131032i
$936$	13.1766	+	81.0804i	0.430690	+	2.65020i
$937$	−22.0134			−0.719147			−0.359573	−	0.933117i	$-0.617078\pi$
$937$	−22.0134			−0.719147			−0.359573	+	0.933117i	$0.617078\pi$
$938$	45.0279	−	20.4747i	1.47021	−	0.668524i
$939$	−6.78396	−	19.0355i	−0.221386	−	0.621200i
$940$	−20.2046	−	34.9953i	−0.659000	−	1.14142i
$941$	−55.2078			−1.79972			−0.899862	−	0.436176i	$-0.856333\pi$
$941$	−55.2078			−1.79972			−0.899862	+	0.436176i	$0.856333\pi$
$942$	−22.8143	−	64.0160i	−0.743330	−	2.08575i
$943$	1.41984			0.0462363
$944$	−139.733			−4.54793
$945$	5.43735	+	12.6268i	0.176877	+	0.410749i
$946$	−43.1936			−1.40434
$947$	−7.75878			−0.252126			−0.126063	−	0.992022i	$-0.540234\pi$
$947$	−7.75878			−0.252126			−0.126063	+	0.992022i	$0.540234\pi$
$948$	37.5941	+	105.487i	1.22100	+	3.42607i
$949$	0.525632			0.0170627
$950$	−8.36733	−	14.4926i	−0.271472	−	0.470203i
$951$	1.77749	+	4.98755i	0.0576390	+	0.161732i
$952$	−43.3522	−	30.9778i	−1.40505	−	1.00400i
$953$	−21.6205			−0.700356			−0.350178	−	0.936683i	$-0.613879\pi$
$953$	−21.6205			−0.700356			−0.350178	+	0.936683i	$0.613879\pi$
$954$	65.8391	+	24.9697i	2.13162	+	0.808425i
$955$	6.00854	+	10.4071i	0.194432	+	0.336766i
$956$	6.63986	−	11.5006i	0.214748	−	0.371955i
$957$	−7.39095	−	20.7387i	−0.238915	−	0.670386i
$958$	11.6083	−	20.1062i	0.375047	−	0.649601i
$959$	0.110851	−	1.14118i	0.00357957	−	0.0368507i
$960$	−40.2042	+	47.2653i	−1.29758	+	1.52548i
$961$	−30.8891			−0.996423
$962$	−0.457294	−	0.792056i	−0.0147437	−	0.0255369i
$963$	8.46248	+	52.0729i	0.272700	+	1.67802i
$964$	−31.2369	+	54.1039i	−1.00607	+	1.74257i
$965$	5.09723	+	8.82866i	0.164086	+	0.284205i
$966$	10.3739	−	36.3388i	0.333775	−	1.16918i
$967$	−28.5905	+	49.5202i	−0.919408	+	1.59246i	−0.119092	+	0.992883i	$0.537998\pi$
$967$	−28.5905	+	49.5202i	−0.919408	+	1.59246i	−0.800316	+	0.599579i	$0.795335\pi$
$968$	28.7816	+	49.8512i	0.925076	+	1.60228i
$969$	7.15911	+	20.0882i	0.229984	+	0.645325i
$970$	−9.44690	+	16.3625i	−0.303322	+	0.525368i
$971$	−7.15219	+	12.3879i	−0.229525	+	0.397548i	−0.957667	−	0.287877i	$-0.907050\pi$
$971$	−7.15219	+	12.3879i	−0.229525	+	0.397548i	0.728143	+	0.685426i	$0.240384\pi$
$972$	−86.4464	+	12.2669i	−2.77277	+	0.393460i
$973$	0.568140	−	5.84885i	0.0182137	−	0.187505i
$974$	−34.0780	−	59.0248i	−1.09193	−	1.89128i
$975$	3.09502	−	3.63860i	0.0991199	−	0.116528i
$976$	−182.653			−5.84656
$977$	−12.4472			−0.398222			−0.199111	−	0.979977i	$-0.563805\pi$
$977$	−12.4472			−0.398222			−0.199111	+	0.979977i	$0.563805\pi$
$978$	28.9638	+	5.30787i	0.926162	+	0.169727i
$979$	2.40495	+	4.16550i	0.0768627	+	0.133130i
$980$	−38.4747	−	7.54583i	−1.22903	−	0.241043i
$981$	11.6481	+	4.41757i	0.371894	+	0.141042i
$982$	−6.37236	+	11.0373i	−0.203350	+	0.352213i
$983$	7.83067	−	13.5631i	0.249759	−	0.432596i	−0.713700	−	0.700452i	$-0.752982\pi$
$983$	7.83067	−	13.5631i	0.249759	−	0.432596i	0.963459	+	0.267856i	$0.0863151\pi$
$984$	8.02903	+	1.47139i	0.255956	+	0.0469062i
$985$	−4.35055	−	7.53537i	−0.138620	−	0.240097i
$986$	15.5836	−	26.9917i	0.496284	−	0.859590i
$987$	22.9940	+	23.7552i	0.731906	+	0.756135i
$988$	46.8818	+	81.2017i	1.49151	+	2.58337i
$989$	10.2730	−	17.7934i	0.326663	−	0.565798i
$990$	−14.6126	+	11.9308i	−0.464420	+	0.379185i
$991$	18.0010	+	31.1787i	0.571821	+	0.990423i	0.996379	+	0.0850224i	$0.0270962\pi$
$991$	18.0010	+	31.1787i	0.571821	+	0.990423i	−0.424558	+	0.905401i	$0.639570\pi$
$992$	−8.23324			−0.261406
$993$	−0.237800	−	0.667257i	−0.00754636	−	0.0211748i
$994$	−82.2887	+	37.4177i	−2.61004	+	1.18682i
$995$	−2.25588	+	3.90730i	−0.0715162	+	0.123870i
$996$	−50.0837	+	58.8799i	−1.58696	+	1.86568i
$997$	−3.83251	+	6.63811i	−0.121377	+	0.210231i	−0.920311	−	0.391188i	$-0.872064\pi$
$997$	−3.83251	+	6.63811i	−0.121377	+	0.210231i	0.798934	+	0.601419i	$0.205398\pi$
$998$	31.1005	+	53.8677i	0.984471	+	1.70515i
$999$	0.547458	−	0.301539i	0.0173208	−	0.00954026i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.l.c.121.18	yes	36
3.2	odd	2		945.2.l.c.226.1		36
7.4	even	3		315.2.k.c.256.1	yes	36
9.2	odd	6		945.2.k.c.856.18		36
9.7	even	3		315.2.k.c.16.1	✓	36
21.11	odd	6		945.2.k.c.361.18		36
63.11	odd	6		945.2.l.c.46.1		36
63.25	even	3	inner	315.2.l.c.151.18	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.c.16.1	✓	36	9.7	even	3
315.2.k.c.256.1	yes	36	7.4	even	3
315.2.l.c.121.18	yes	36	1.1	even	1	trivial
315.2.l.c.151.18	yes	36	63.25	even	3	inner
945.2.k.c.361.18		36	21.11	odd	6
945.2.k.c.856.18		36	9.2	odd	6
945.2.l.c.46.1		36	63.11	odd	6
945.2.l.c.226.1		36	3.2	odd	2

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.75701 q^{2} +(-0.581455 - 1.63154i) q^{3} +5.60109 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.60307 - 4.49816i) q^{6} +(-2.40845 + 1.09515i) q^{7} +9.92824 q^{8} +(-2.32382 + 1.89733i) q^{9} +O(q^{10})\)	\(q+2.75701 q^{2} +(-0.581455 - 1.63154i) q^{3} +5.60109 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.60307 - 4.49816i) q^{6} +(-2.40845 + 1.09515i) q^{7} +9.92824 q^{8} +(-2.32382 + 1.89733i) q^{9} +(-1.37850 - 2.38764i) q^{10} +(-1.14040 + 1.97523i) q^{11} +(-3.25678 - 9.13838i) q^{12} +(1.37896 - 2.38844i) q^{13} +(-6.64012 + 3.01934i) q^{14} +(-1.12222 + 1.31932i) q^{15} +16.1700 q^{16} +(1.01423 + 1.75669i) q^{17} +(-6.40679 + 5.23095i) q^{18} +(-3.03493 + 5.25665i) q^{19} +(-2.80055 - 4.85069i) q^{20} +(3.18719 + 3.29270i) q^{21} +(-3.14410 + 5.44574i) q^{22} +(-1.49557 - 2.59040i) q^{23} +(-5.77282 - 16.1983i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(3.80182 - 6.58494i) q^{26} +(4.44676 + 2.68819i) q^{27} +(-13.4900 + 6.13405i) q^{28} +(-2.78655 - 4.82644i) q^{29} +(-3.09398 + 3.63738i) q^{30} -0.333000 q^{31} +24.7245 q^{32} +(3.88576 + 0.712099i) q^{33} +(2.79623 + 4.84321i) q^{34} +(2.15266 + 1.53820i) q^{35} +(-13.0159 + 10.6271i) q^{36} +(0.0601415 - 0.104168i) q^{37} +(-8.36733 + 14.4926i) q^{38} +(-4.69863 - 0.861064i) q^{39} +(-4.96412 - 8.59810i) q^{40} +(-0.237341 + 0.411087i) q^{41} +(8.78710 + 9.07799i) q^{42} +(3.43450 + 5.94872i) q^{43} +(-6.38750 + 11.0635i) q^{44} +(2.80505 + 1.06382i) q^{45} +(-4.12329 - 7.14174i) q^{46} +7.21451 q^{47} +(-9.40214 - 26.3820i) q^{48} +(4.60128 - 5.27524i) q^{49} +(-1.37850 + 2.38764i) q^{50} +(2.27638 - 2.67618i) q^{51} +(7.72371 - 13.3779i) q^{52} +(-4.25673 - 7.37287i) q^{53} +(12.2597 + 7.41136i) q^{54} +2.28080 q^{55} +(-23.9117 + 10.8729i) q^{56} +(10.3411 + 1.89509i) q^{57} +(-7.68253 - 13.3065i) q^{58} -8.64149 q^{59} +(-6.28568 + 7.38965i) q^{60} -11.2957 q^{61} -0.918083 q^{62} +(3.51895 - 7.11456i) q^{63} +35.8254 q^{64} -2.75793 q^{65} +(10.7131 + 1.96326i) q^{66} -6.78119 q^{67} +(5.68077 + 9.83938i) q^{68} +(-3.35672 + 3.94627i) q^{69} +(5.93489 + 4.24084i) q^{70} +12.3927 q^{71} +(-23.0714 + 18.8371i) q^{72} +(0.0952946 + 0.165055i) q^{73} +(0.165811 - 0.287192i) q^{74} +(1.70368 + 0.312214i) q^{75} +(-16.9989 + 29.4430i) q^{76} +(0.583422 - 6.00617i) q^{77} +(-12.9542 - 2.37396i) q^{78} -11.5433 q^{79} +(-8.08502 - 14.0037i) q^{80} +(1.80029 - 8.81810i) q^{81} +(-0.654352 + 1.13337i) q^{82} +(-3.98395 - 6.90040i) q^{83} +(17.8517 + 18.4427i) q^{84} +(1.01423 - 1.75669i) q^{85} +(9.46893 + 16.4007i) q^{86} +(-6.25426 + 7.35271i) q^{87} +(-11.3222 + 19.6106i) q^{88} +(1.05443 - 1.82633i) q^{89} +(7.73353 + 2.93297i) q^{90} +(-0.705469 + 7.26261i) q^{91} +(-8.37680 - 14.5090i) q^{92} +(0.193624 + 0.543302i) q^{93} +19.8904 q^{94} +6.06986 q^{95} +(-14.3761 - 40.3388i) q^{96} +(-3.42650 - 5.93488i) q^{97} +(12.6858 - 14.5439i) q^{98} +(-1.09758 - 6.75381i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9}+O(q^{10}) \) 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9	\( 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9} + q^{11} + 8 q^{12} + 2 q^{13} + 9 q^{14} - q^{15} + 60 q^{16} - 5 q^{17} - 21 q^{18} - 2 q^{19} - 22 q^{20} - 23 q^{21} - 19 q^{22} - 3 q^{23} - 32 q^{24} - 18 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} + 2 q^{30} - 20 q^{32} - 35 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} - 22 q^{38} + 7 q^{39} - 4 q^{41} + 57 q^{42} - 29 q^{43} - 7 q^{44} + 6 q^{45} - 24 q^{46} + 46 q^{47} - 19 q^{48} - 7 q^{49} + 42 q^{51} - 7 q^{52} + 21 q^{54} - 2 q^{55} - 12 q^{56} + 21 q^{57} - 20 q^{58} + 10 q^{59} - 13 q^{60} + 6 q^{61} - 12 q^{62} + 2 q^{63} + 128 q^{64} - 4 q^{65} - 12 q^{66} + 70 q^{67} - 17 q^{68} - 50 q^{69} - 3 q^{70} + 24 q^{71} - 10 q^{72} - 10 q^{73} + 22 q^{74} + 2 q^{75} + 10 q^{76} + 35 q^{77} + 66 q^{78} + 56 q^{79} - 30 q^{80} - 49 q^{81} - 8 q^{82} - 22 q^{83} - 86 q^{84} - 5 q^{85} + 19 q^{86} - 42 q^{87} - 50 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - q^{93} + 4 q^{94} + 4 q^{95} - 179 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9 + q^11 + 8 * q^12 + 2 * q^13 + 9 * q^14 - q^15 + 60 * q^16 - 5 * q^17 - 21 * q^18 - 2 * q^19 - 22 * q^20 - 23 * q^21 - 19 * q^22 - 3 * q^23 - 32 * q^24 - 18 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 + 2 * q^30 - 20 * q^32 - 35 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 - 22 * q^38 + 7 * q^39 - 4 * q^41 + 57 * q^42 - 29 * q^43 - 7 * q^44 + 6 * q^45 - 24 * q^46 + 46 * q^47 - 19 * q^48 - 7 * q^49 + 42 * q^51 - 7 * q^52 + 21 * q^54 - 2 * q^55 - 12 * q^56 + 21 * q^57 - 20 * q^58 + 10 * q^59 - 13 * q^60 + 6 * q^61 - 12 * q^62 + 2 * q^63 + 128 * q^64 - 4 * q^65 - 12 * q^66 + 70 * q^67 - 17 * q^68 - 50 * q^69 - 3 * q^70 + 24 * q^71 - 10 * q^72 - 10 * q^73 + 22 * q^74 + 2 * q^75 + 10 * q^76 + 35 * q^77 + 66 * q^78 + 56 * q^79 - 30 * q^80 - 49 * q^81 - 8 * q^82 - 22 * q^83 - 86 * q^84 - 5 * q^85 + 19 * q^86 - 42 * q^87 - 50 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - q^93 + 4 * q^94 + 4 * q^95 - 179 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more