LMFDB - Embedded newform 495.2.i.f.166.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [495,2,Mod(166,495)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(495, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("495.166");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.i (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:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			166.4
Character	$\chi$	$=$	495.166
Dual form			495.2.i.f.331.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.350077 - 0.606351i) q^{2} +(1.65559 - 0.508929i) q^{3} +(0.754892 - 1.30751i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.888175 - 0.825707i) q^{6} +(-0.588842 - 1.01990i) q^{7} -2.45739 q^{8} +(2.48198 - 1.68516i) q^{9} +O(q^{10})$	\(q+(-0.350077 - 0.606351i) q^{2} +(1.65559 - 0.508929i) q^{3} +(0.754892 - 1.30751i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.888175 - 0.825707i) q^{6} +(-0.588842 - 1.01990i) q^{7} -2.45739 q^{8} +(2.48198 - 1.68516i) q^{9} -0.700154 q^{10} +(0.500000 + 0.866025i) q^{11} +(0.584365 - 2.54890i) q^{12} +(-0.148320 + 0.256897i) q^{13} +(-0.412280 + 0.714090i) q^{14} +(0.387052 - 1.68825i) q^{15} +(-0.649509 - 1.12498i) q^{16} -2.34305 q^{17} +(-1.89068 - 0.915018i) q^{18} +2.93247 q^{19} +(-0.754892 - 1.30751i) q^{20} +(-1.49394 - 1.38887i) q^{21} +(0.350077 - 0.606351i) q^{22} +(-1.56787 + 2.71564i) q^{23} +(-4.06844 + 1.25064i) q^{24} +(-0.500000 - 0.866025i) q^{25} +0.207693 q^{26} +(3.25153 - 4.05309i) q^{27} -1.77805 q^{28} +(1.88017 + 3.25655i) q^{29} +(-1.15917 + 0.356328i) q^{30} +(-0.622676 + 1.07851i) q^{31} +(-2.91215 + 5.04398i) q^{32} +(1.26854 + 1.17932i) q^{33} +(0.820249 + 1.42071i) q^{34} -1.17768 q^{35} +(-0.329734 - 4.51734i) q^{36} +6.86836 q^{37} +(-1.02659 - 1.77811i) q^{38} +(-0.114815 + 0.500802i) q^{39} +(-1.22869 + 2.12816i) q^{40} +(-2.14122 + 3.70870i) q^{41} +(-0.319148 + 1.39206i) q^{42} +(-0.917946 - 1.58993i) q^{43} +1.50978 q^{44} +(-0.218398 - 2.99204i) q^{45} +2.19551 q^{46} +(3.61066 + 6.25385i) q^{47} +(-1.64786 - 1.53196i) q^{48} +(2.80653 - 4.86105i) q^{49} +(-0.350077 + 0.606351i) q^{50} +(-3.87914 + 1.19245i) q^{51} +(0.223931 + 0.387859i) q^{52} -8.03651 q^{53} +(-3.59588 - 0.552677i) q^{54} +1.00000 q^{55} +(1.44701 + 2.50630i) q^{56} +(4.85499 - 1.49242i) q^{57} +(1.31641 - 2.28009i) q^{58} +(3.81600 - 6.60951i) q^{59} +(-1.91523 - 1.78052i) q^{60} +(-0.821792 - 1.42339i) q^{61} +0.871938 q^{62} +(-3.18020 - 1.53909i) q^{63} +1.47986 q^{64} +(0.148320 + 0.256897i) q^{65} +(0.270996 - 1.18204i) q^{66} +(4.05754 - 7.02787i) q^{67} +(-1.76875 + 3.06357i) q^{68} +(-1.21370 + 5.29393i) q^{69} +(0.412280 + 0.714090i) q^{70} +4.12642 q^{71} +(-6.09920 + 4.14109i) q^{72} -7.20957 q^{73} +(-2.40445 - 4.16463i) q^{74} +(-1.26854 - 1.17932i) q^{75} +(2.21370 - 3.83425i) q^{76} +(0.588842 - 1.01990i) q^{77} +(0.343856 - 0.105701i) q^{78} +(4.40381 + 7.62762i) q^{79} -1.29902 q^{80} +(3.32048 - 8.36507i) q^{81} +2.99836 q^{82} +(-0.522997 - 0.905858i) q^{83} +(-2.94373 + 0.904900i) q^{84} +(-1.17153 + 2.02914i) q^{85} +(-0.642704 + 1.11320i) q^{86} +(4.77016 + 4.43466i) q^{87} +(-1.22869 - 2.12816i) q^{88} +1.35499 q^{89} +(-1.73777 + 1.17987i) q^{90} +0.349348 q^{91} +(2.36715 + 4.10003i) q^{92} +(-0.482016 + 2.10247i) q^{93} +(2.52802 - 4.37866i) q^{94} +(1.46624 - 2.53960i) q^{95} +(-2.25430 + 9.83286i) q^{96} +(5.57188 + 9.65078i) q^{97} -3.93000 q^{98} +(2.70038 + 1.30688i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 3 q^{2} - 13 q^{4} + 11 q^{5} + 13 q^{6} - 3 q^{7} - 6 q^{8} - 4 q^{9}+O(q^{10}) $ 22 * q + 3 * q^2 - 13 * q^4 + 11 * q^5 + 13 * q^6 - 3 * q^7 - 6 * q^8 - 4 * q^9	\( 22 q + 3 q^{2} - 13 q^{4} + 11 q^{5} + 13 q^{6} - 3 q^{7} - 6 q^{8} - 4 q^{9} + 6 q^{10} + 11 q^{11} - 9 q^{12} - 9 q^{13} + 5 q^{14} - 17 q^{16} - 28 q^{17} - 7 q^{18} - 6 q^{19} + 13 q^{20} - 8 q^{21} - 3 q^{22} + 16 q^{23} - 18 q^{24} - 11 q^{25} - 28 q^{26} - 18 q^{27} - 12 q^{28} + 16 q^{29} + 11 q^{30} - 4 q^{31} + 34 q^{32} + 39 q^{34} - 6 q^{35} - 55 q^{36} + 40 q^{37} + 4 q^{38} - 4 q^{39} - 3 q^{40} + 26 q^{41} + 59 q^{42} + 3 q^{43} - 26 q^{44} - 2 q^{45} - 16 q^{46} + 8 q^{47} + 28 q^{48} - 10 q^{49} + 3 q^{50} + 7 q^{51} - 31 q^{52} - 52 q^{53} - 20 q^{54} + 22 q^{55} + 30 q^{56} + 3 q^{57} - 6 q^{58} + 10 q^{59} + 25 q^{61} + 40 q^{62} - 9 q^{63} + 26 q^{64} + 9 q^{65} + 2 q^{66} - 13 q^{67} + 20 q^{68} + 28 q^{69} - 5 q^{70} - 48 q^{71} - 114 q^{72} + 18 q^{73} + 10 q^{74} + 25 q^{76} + 3 q^{77} + 13 q^{78} + q^{79} - 34 q^{80} - 4 q^{81} + 34 q^{82} - 2 q^{83} + 89 q^{84} - 14 q^{85} + 15 q^{86} - 31 q^{87} - 3 q^{88} - 44 q^{89} + 13 q^{90} - 2 q^{91} + 44 q^{92} + 29 q^{93} + 36 q^{94} - 3 q^{95} + 42 q^{96} - 33 q^{97} - 38 q^{98} - 2 q^{99}+O(q^{100}) \) 22 * q + 3 * q^2 - 13 * q^4 + 11 * q^5 + 13 * q^6 - 3 * q^7 - 6 * q^8 - 4 * q^9 + 6 * q^10 + 11 * q^11 - 9 * q^12 - 9 * q^13 + 5 * q^14 - 17 * q^16 - 28 * q^17 - 7 * q^18 - 6 * q^19 + 13 * q^20 - 8 * q^21 - 3 * q^22 + 16 * q^23 - 18 * q^24 - 11 * q^25 - 28 * q^26 - 18 * q^27 - 12 * q^28 + 16 * q^29 + 11 * q^30 - 4 * q^31 + 34 * q^32 + 39 * q^34 - 6 * q^35 - 55 * q^36 + 40 * q^37 + 4 * q^38 - 4 * q^39 - 3 * q^40 + 26 * q^41 + 59 * q^42 + 3 * q^43 - 26 * q^44 - 2 * q^45 - 16 * q^46 + 8 * q^47 + 28 * q^48 - 10 * q^49 + 3 * q^50 + 7 * q^51 - 31 * q^52 - 52 * q^53 - 20 * q^54 + 22 * q^55 + 30 * q^56 + 3 * q^57 - 6 * q^58 + 10 * q^59 + 25 * q^61 + 40 * q^62 - 9 * q^63 + 26 * q^64 + 9 * q^65 + 2 * q^66 - 13 * q^67 + 20 * q^68 + 28 * q^69 - 5 * q^70 - 48 * q^71 - 114 * q^72 + 18 * q^73 + 10 * q^74 + 25 * q^76 + 3 * q^77 + 13 * q^78 + q^79 - 34 * q^80 - 4 * q^81 + 34 * q^82 - 2 * q^83 + 89 * q^84 - 14 * q^85 + 15 * q^86 - 31 * q^87 - 3 * q^88 - 44 * q^89 + 13 * q^90 - 2 * q^91 + 44 * q^92 + 29 * q^93 + 36 * q^94 - 3 * q^95 + 42 * q^96 - 33 * q^97 - 38 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.350077	−	0.606351i	−0.247542	−	0.428755i	0.715301	−	0.698816i	$-0.246289\pi$
$2$	−0.350077	−	0.606351i	−0.247542	−	0.428755i	−0.962843	+	0.270061i	$0.912956\pi$
$3$	1.65559	−	0.508929i	0.955858	−	0.293830i
$3$	1.65559	−	0.508929i	0.955858	−	0.293830i
$4$	0.754892	−	1.30751i	0.377446	−	0.653756i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−0.888175	−	0.825707i	−0.362596	−	0.337093i
$7$	−0.588842	−	1.01990i	−0.222561	−	0.385488i	0.733024	−	0.680203i	$-0.238108\pi$
$7$	−0.588842	−	1.01990i	−0.222561	−	0.385488i	−0.955585	+	0.294715i	$0.904775\pi$
$8$	−2.45739			−0.868818
$9$	2.48198	−	1.68516i	0.827328	−	0.561719i
$10$	−0.700154			−0.221408
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	0.584365	−	2.54890i	0.168692	−	0.735803i
$13$	−0.148320	+	0.256897i	−0.0411365	+	0.0712505i	−0.885861	−	0.463952i	$-0.846431\pi$
$13$	−0.148320	+	0.256897i	−0.0411365	+	0.0712505i	0.844724	+	0.535202i	$0.179765\pi$
$14$	−0.412280	+	0.714090i	−0.110187	+	0.190849i
$15$	0.387052	−	1.68825i	0.0999364	−	0.435904i
$16$	−0.649509	−	1.12498i	−0.162377	−	0.281246i
$17$	−2.34305			−0.568274			−0.284137	−	0.958784i	$-0.591707\pi$
$17$	−2.34305			−0.568274			−0.284137	+	0.958784i	$0.591707\pi$
$18$	−1.89068	−	0.915018i	−0.445638	−	0.215672i
$19$	2.93247			0.672756			0.336378	−	0.941727i	$-0.390798\pi$
$19$	2.93247			0.672756			0.336378	+	0.941727i	$0.390798\pi$
$20$	−0.754892	−	1.30751i	−0.168799	−	0.292369i
$21$	−1.49394	−	1.38887i	−0.326005	−	0.303076i
$22$	0.350077	−	0.606351i	0.0746367	−	0.129274i
$23$	−1.56787	+	2.71564i	−0.326924	+	0.566250i	−0.981900	−	0.189400i	$-0.939346\pi$
$23$	−1.56787	+	2.71564i	−0.326924	+	0.566250i	0.654976	+	0.755650i	$0.272679\pi$
$24$	−4.06844	+	1.25064i	−0.830467	+	0.255285i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	0.207693			0.0407320
$27$	3.25153	−	4.05309i	0.625758	−	0.780018i
$28$	−1.77805			−0.336020
$29$	1.88017	+	3.25655i	0.349139	+	0.604727i	0.986097	−	0.166172i	$-0.0531407\pi$
$29$	1.88017	+	3.25655i	0.349139	+	0.604727i	−0.636958	+	0.770899i	$0.719807\pi$
$30$	−1.15917	+	0.356328i	−0.211635	+	0.0650563i
$31$	−0.622676	+	1.07851i	−0.111836	+	0.193706i	−0.916511	−	0.400011i	$-0.869006\pi$
$31$	−0.622676	+	1.07851i	−0.111836	+	0.193706i	0.804675	+	0.593716i	$0.202340\pi$
$32$	−2.91215	+	5.04398i	−0.514799	+	0.891659i
$33$	1.26854	+	1.17932i	0.220825	+	0.205294i
$34$	0.820249	+	1.42071i	0.140671	+	0.243650i
$35$	−1.17768			−0.199065
$36$	−0.329734	−	4.51734i	−0.0549556	−	0.752889i
$37$	6.86836			1.12915			0.564575	−	0.825381i	$-0.309040\pi$
$37$	6.86836			1.12915			0.564575	+	0.825381i	$0.309040\pi$
$38$	−1.02659	−	1.77811i	−0.166535	−	0.288447i
$39$	−0.114815	+	0.500802i	−0.0183851	+	0.0801924i
$40$	−1.22869	+	2.12816i	−0.194274	+	0.336492i
$41$	−2.14122	+	3.70870i	−0.334402	+	0.579201i	−0.983370	−	0.181615i	$-0.941868\pi$
$41$	−2.14122	+	3.70870i	−0.334402	+	0.579201i	0.648968	+	0.760816i	$0.275201\pi$
$42$	−0.319148	+	1.39206i	−0.0492456	+	0.214800i
$43$	−0.917946	−	1.58993i	−0.139986	−	0.242462i	0.787505	−	0.616308i	$-0.211372\pi$
$43$	−0.917946	−	1.58993i	−0.139986	−	0.242462i	−0.927491	+	0.373846i	$0.878039\pi$
$44$	1.50978			0.227609
$45$	−0.218398	−	2.99204i	−0.0325568	−	0.446027i
$46$	2.19551			0.323710
$47$	3.61066	+	6.25385i	0.526669	+	0.912218i	0.999517	+	0.0310737i	$0.00989265\pi$
$47$	3.61066	+	6.25385i	0.526669	+	0.912218i	−0.472848	+	0.881144i	$0.656774\pi$
$48$	−1.64786	−	1.53196i	−0.237848	−	0.221120i
$49$	2.80653	−	4.86105i	0.400933	−	0.694436i
$50$	−0.350077	+	0.606351i	−0.0495084	+	0.0857510i
$51$	−3.87914	+	1.19245i	−0.543189	+	0.166976i
$52$	0.223931	+	0.387859i	0.0310536	+	0.0537864i
$53$	−8.03651			−1.10390			−0.551950	−	0.833877i	$-0.686116\pi$
$53$	−8.03651			−1.10390			−0.551950	+	0.833877i	$0.686116\pi$
$54$	−3.59588	−	0.552677i	−0.489338	−	0.0752098i
$55$	1.00000			0.134840
$56$	1.44701	+	2.50630i	0.193365	+	0.334919i
$57$	4.85499	−	1.49242i	0.643059	−	0.197676i
$58$	1.31641	−	2.28009i	0.172853	−	0.299390i
$59$	3.81600	−	6.60951i	0.496802	−	0.860485i	−0.503192	−	0.864175i	$-0.667841\pi$
$59$	3.81600	−	6.60951i	0.496802	−	0.860485i	0.999993	+	0.00368938i	$0.00117437\pi$
$60$	−1.91523	−	1.78052i	−0.247255	−	0.229864i
$61$	−0.821792	−	1.42339i	−0.105220	−	0.182246i	0.808608	−	0.588347i	$-0.200221\pi$
$61$	−0.821792	−	1.42339i	−0.105220	−	0.182246i	−0.913828	+	0.406102i	$0.866888\pi$
$62$	0.871938			0.110736
$63$	−3.18020	−	1.53909i	−0.400667	−	0.193908i
$64$	1.47986			0.184983
$65$	0.148320	+	0.256897i	0.0183968	+	0.0318642i
$66$	0.270996	−	1.18204i	0.0333573	−	0.145498i
$67$	4.05754	−	7.02787i	0.495708	−	0.858591i	−0.504280	−	0.863540i	$-0.668242\pi$
$67$	4.05754	−	7.02787i	0.495708	−	0.858591i	0.999988	+	0.00494904i	$0.00157533\pi$
$68$	−1.76875	+	3.06357i	−0.214493	+	0.371512i
$69$	−1.21370	+	5.29393i	−0.146112	+	0.637314i
$70$	0.412280	+	0.714090i	0.0492769	+	0.0853501i
$71$	4.12642			0.489716			0.244858	−	0.969559i	$-0.421259\pi$
$71$	4.12642			0.489716			0.244858	+	0.969559i	$0.421259\pi$
$72$	−6.09920	+	4.14109i	−0.718798	+	0.488032i
$73$	−7.20957			−0.843816			−0.421908	−	0.906639i	$-0.638639\pi$
$73$	−7.20957			−0.843816			−0.421908	+	0.906639i	$0.638639\pi$
$74$	−2.40445	−	4.16463i	−0.279512	−	0.484129i
$75$	−1.26854	−	1.17932i	−0.146479	−	0.136176i
$76$	2.21370	−	3.83425i	0.253929	−	0.439818i
$77$	0.588842	−	1.01990i	0.0671048	−	0.116229i
$78$	0.343856	−	0.105701i	0.0389340	−	0.0119683i
$79$	4.40381	+	7.62762i	0.495467	+	0.858174i	0.999986	−	0.00522632i	$-0.00166360\pi$
$79$	4.40381	+	7.62762i	0.495467	+	0.858174i	−0.504519	+	0.863400i	$0.668330\pi$
$80$	−1.29902			−0.145235
$81$	3.32048	−	8.36507i	0.368943	−	0.929452i
$82$	2.99836			0.331114
$83$	−0.522997	−	0.905858i	−0.0574064	−	0.0994308i	0.835894	−	0.548891i	$-0.184950\pi$
$83$	−0.522997	−	0.905858i	−0.0574064	−	0.0994308i	−0.893300	+	0.449460i	$0.851616\pi$
$84$	−2.94373	+	0.904900i	−0.321187	+	0.0987327i
$85$	−1.17153	+	2.02914i	−0.127070	+	0.220091i
$86$	−0.642704	+	1.11320i	−0.0693045	+	0.120039i
$87$	4.77016	+	4.43466i	0.511414	+	0.475445i
$88$	−1.22869	−	2.12816i	−0.130979	−	0.226863i
$89$	1.35499			0.143628			0.0718141	−	0.997418i	$-0.477121\pi$
$89$	1.35499			0.143628			0.0718141	+	0.997418i	$0.477121\pi$
$90$	−1.73777	+	1.17987i	−0.183177	+	0.124369i
$91$	0.349348			0.0366216
$92$	2.36715	+	4.10003i	0.246793	+	0.427458i
$93$	−0.482016	+	2.10247i	−0.0499828	+	0.218016i
$94$	2.52802	−	4.37866i	0.260745	−	0.451624i
$95$	1.46624	−	2.53960i	0.150433	−	0.260557i
$96$	−2.25430	+	9.83286i	−0.230079	+	1.00356i
$97$	5.57188	+	9.65078i	0.565739	+	0.979888i	0.996981	+	0.0776519i	$0.0247423\pi$
$97$	5.57188	+	9.65078i	0.565739	+	0.979888i	−0.431242	+	0.902236i	$0.641924\pi$
$98$	−3.93000			−0.396990
$99$	2.70038	+	1.30688i	0.271399	+	0.131347i
$100$	−1.50978			−0.150978
$101$	6.99330	+	12.1127i	0.695859	+	1.20526i	0.969890	+	0.243543i	$0.0783096\pi$
$101$	6.99330	+	12.1127i	0.695859	+	1.20526i	−0.274031	+	0.961721i	$0.588357\pi$
$102$	2.08104	+	1.93468i	0.206054	+	0.191561i
$103$	0.434939	−	0.753336i	0.0428558	−	0.0742284i	−0.843802	−	0.536655i	$-0.819688\pi$
$103$	0.434939	−	0.753336i	0.0428558	−	0.0742284i	0.886658	+	0.462426i	$0.153021\pi$
$104$	0.364479	−	0.631297i	0.0357401	−	0.0619037i
$105$	−1.94977	+	0.599357i	−0.190278	+	0.0584913i
$106$	2.81340	+	4.87295i	0.273261	+	0.473302i
$107$	−9.31200			−0.900225			−0.450113	−	0.892972i	$-0.648616\pi$
$107$	−9.31200			−0.900225			−0.450113	+	0.892972i	$0.648616\pi$
$108$	−2.84491	−	7.31106i	−0.273751	−	0.703507i
$109$	5.36336			0.513716			0.256858	−	0.966449i	$-0.417313\pi$
$109$	5.36336			0.513716			0.256858	+	0.966449i	$0.417313\pi$
$110$	−0.350077	−	0.606351i	−0.0333785	−	0.0578133i
$111$	11.3712	−	3.49550i	1.07931	−	0.331778i
$112$	−0.764917	+	1.32488i	−0.0722779	+	0.125189i
$113$	−9.39187	+	16.2672i	−0.883513	+	1.53029i	−0.0361036	+	0.999348i	$0.511495\pi$
$113$	−9.39187	+	16.2672i	−0.883513	+	1.53029i	−0.847409	+	0.530941i	$0.821839\pi$
$114$	−2.60455	−	2.42136i	−0.243938	−	0.226782i
$115$	1.56787	+	2.71564i	0.146205	+	0.253235i
$116$	5.67731			0.527125
$117$	0.0647854	+	0.887557i	0.00598942	+	0.0820547i
$118$	−5.34358			−0.491916
$119$	1.37969	+	2.38969i	0.126476	+	0.219063i
$120$	−0.951137	+	4.14869i	−0.0868266	+	0.378722i
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−0.575381	+	0.996589i	−0.0520925	+	0.0902269i
$123$	−1.65752	+	7.22982i	−0.149454	+	0.651891i
$124$	0.940107	+	1.62831i	0.0844241	+	0.146227i
$125$	−1.00000			−0.0894427
$126$	0.180082	+	2.46712i	0.0160430	+	0.219788i
$127$	6.93697			0.615556			0.307778	−	0.951458i	$-0.400415\pi$
$127$	6.93697			0.615556			0.307778	+	0.951458i	$0.400415\pi$
$128$	5.30623	+	9.19065i	0.469009	+	0.812347i
$129$	−2.32891	−	2.16511i	−0.205049	−	0.190627i
$130$	0.103847	−	0.179868i	0.00910795	−	0.0157754i
$131$	3.02099	−	5.23250i	0.263945	−	0.457166i	−0.703342	−	0.710852i	$-0.748310\pi$
$131$	3.02099	−	5.23250i	0.263945	−	0.457166i	0.967287	+	0.253686i	$0.0816430\pi$
$132$	2.49959	−	0.768372i	0.217561	−	0.0668782i
$133$	−1.72677	−	2.99085i	−0.149730	−	0.259339i
$134$	−5.68181			−0.490834
$135$	−1.88431	−	4.84245i	−0.162176	−	0.416772i
$136$	5.75779			0.493727
$137$	0.382667	+	0.662799i	0.0326935	+	0.0566267i	0.881909	−	0.471419i	$-0.156258\pi$
$137$	0.382667	+	0.662799i	0.0326935	+	0.0566267i	−0.849216	+	0.528046i	$0.822925\pi$
$138$	3.63487	−	1.11736i	0.309420	−	0.0951156i
$139$	−3.94005	+	6.82437i	−0.334191	+	0.578835i	−0.983329	−	0.181835i	$-0.941796\pi$
$139$	−3.94005	+	6.82437i	−0.334191	+	0.578835i	0.649138	+	0.760670i	$0.275130\pi$
$140$	−0.889025	+	1.53984i	−0.0751363	+	0.130140i
$141$	9.16055	+	8.51627i	0.771458	+	0.717199i
$142$	−1.44456	−	2.50206i	−0.121225	−	0.209968i
$143$	−0.296639			−0.0248062
$144$	−3.50785	−	1.69766i	−0.292320	−	0.141472i
$145$	3.76035			0.312280
$146$	2.52390	+	4.37153i	0.208880	+	0.361790i
$147$	2.17255	−	9.47625i	0.179189	−	0.781588i
$148$	5.18487	−	8.98046i	0.426194	−	0.738189i
$149$	9.53540	−	16.5158i	0.781170	−	1.35303i	−0.150091	−	0.988672i	$-0.547957\pi$
$149$	9.53540	−	16.5158i	0.781170	−	1.35303i	0.931261	−	0.364354i	$-0.118710\pi$
$150$	−0.270996	+	1.18204i	−0.0221267	+	0.0965128i
$151$	9.18407	+	15.9073i	0.747389	+	1.29452i	0.949070	+	0.315065i	$0.102026\pi$
$151$	9.18407	+	15.9073i	0.747389	+	1.29452i	−0.201681	+	0.979451i	$0.564640\pi$
$152$	−7.20623			−0.584503
$153$	−5.81542	+	3.94841i	−0.470149	+	0.319210i
$154$	−0.824560			−0.0664450
$155$	0.622676	+	1.07851i	0.0500146	+	0.0866278i
$156$	0.568131	+	0.528173i	0.0454869	+	0.0422877i
$157$	−10.0952	+	17.4853i	−0.805681	+	1.39548i	0.110150	+	0.993915i	$0.464867\pi$
$157$	−10.0952	+	17.4853i	−0.805681	+	1.39548i	−0.915831	+	0.401565i	$0.868466\pi$
$158$	3.08334	−	5.34051i	0.245298	−	0.424868i
$159$	−13.3052	+	4.09001i	−1.05517	+	0.324359i
$160$	2.91215	+	5.04398i	0.230225	+	0.398762i
$161$	3.69292			0.291043
$162$	−6.23459	+	0.915039i	−0.489836	+	0.0718922i
$163$	−22.6695			−1.77562			−0.887808	−	0.460215i	$-0.847772\pi$
$163$	−22.6695			−1.77562			−0.887808	+	0.460215i	$0.847772\pi$
$164$	3.23278	+	5.59933i	0.252437	+	0.437234i
$165$	1.65559	−	0.508929i	0.128888	−	0.0396200i
$166$	−0.366179	+	0.634240i	−0.0284210	+	0.0492266i
$167$	4.21060	−	7.29297i	0.325826	−	0.564347i	−0.655853	−	0.754888i	$-0.727691\pi$
$167$	4.21060	−	7.29297i	0.325826	−	0.564347i	0.981679	+	0.190541i	$0.0610243\pi$
$168$	3.67120	+	3.41299i	0.283239	+	0.263318i
$169$	6.45600	+	11.1821i	0.496616	+	0.860163i
$170$	1.64050			0.125820
$171$	7.27835	−	4.94168i	0.556590	−	0.377900i
$172$	−2.77180			−0.211348
$173$	−2.52945	−	4.38113i	−0.192310	−	0.333091i	0.753705	−	0.657213i	$-0.228265\pi$
$173$	−2.52945	−	4.38113i	−0.192310	−	0.333091i	−0.946015	+	0.324121i	$0.894931\pi$
$174$	1.01904	−	4.44486i	0.0772531	−	0.336964i
$175$	−0.588842	+	1.01990i	−0.0445123	+	0.0770976i
$176$	0.649509	−	1.12498i	0.0489586	−	0.0847988i
$177$	2.95398	−	12.8847i	0.222035	−	0.968477i
$178$	−0.474350	−	0.821598i	−0.0355540	−	0.0615813i
$179$	−1.46529			−0.109521			−0.0547606	−	0.998500i	$-0.517440\pi$
$179$	−1.46529			−0.109521			−0.0547606	+	0.998500i	$0.517440\pi$
$180$	−4.07699	−	1.97311i	−0.303881	−	0.147067i
$181$	4.87403			0.362284			0.181142	−	0.983457i	$-0.442021\pi$
$181$	4.87403			0.362284			0.181142	+	0.983457i	$0.442021\pi$
$182$	−0.122299	−	0.211827i	−0.00906537	−	0.0157017i
$183$	−2.08495	−	1.93831i	−0.154124	−	0.143284i
$184$	3.85288	−	6.67338i	0.284038	−	0.491968i
$185$	3.43418	−	5.94817i	0.252486	−	0.437318i
$186$	1.44358	−	0.443754i	0.105848	−	0.0325376i
$187$	−1.17153	−	2.02914i	−0.0856705	−	0.148386i
$188$	10.9026			0.795157
$189$	−6.04841	−	0.929622i	−0.439957	−	0.0676201i
$190$	−2.05318			−0.148954
$191$	2.22495	+	3.85372i	0.160991	+	0.278845i	0.935225	−	0.354055i	$-0.115198\pi$
$191$	2.22495	+	3.85372i	0.160991	+	0.278845i	−0.774233	+	0.632901i	$0.781864\pi$
$192$	2.45005	−	0.753144i	0.176817	−	0.0543535i
$193$	7.03592	−	12.1866i	0.506456	−	0.877208i	−0.493516	−	0.869737i	$-0.664288\pi$
$193$	7.03592	−	12.1866i	0.506456	−	0.877208i	0.999972	−	0.00747135i	$-0.00237823\pi$
$194$	3.90117	−	6.75703i	0.280088	−	0.485127i
$195$	0.376300	+	0.349833i	0.0269474	+	0.0250521i
$196$	−4.23725	−	7.33914i	−0.302661	−	0.524224i
$197$	−18.6989			−1.33224			−0.666121	−	0.745843i	$-0.732047\pi$
$197$	−18.6989			−1.33224			−0.666121	+	0.745843i	$0.732047\pi$
$198$	−0.152912	−	2.09489i	−0.0108670	−	0.148877i
$199$	−11.0690			−0.784662			−0.392331	−	0.919824i	$-0.628331\pi$
$199$	−11.0690			−0.784662			−0.392331	+	0.919824i	$0.628331\pi$
$200$	1.22869	+	2.12816i	0.0868818	+	0.150484i
$201$	3.14096	−	13.7003i	0.221546	−	0.966345i
$202$	4.89639	−	8.48079i	0.344508	−	0.596706i
$203$	2.21425	−	3.83519i	0.155410	−	0.269178i
$204$	−1.36920	+	5.97220i	−0.0958631	+	0.418137i
$205$	2.14122	+	3.70870i	0.149549	+	0.259027i
$206$	−0.609048			−0.0424344
$207$	0.684841	+	9.38228i	0.0475998	+	0.652114i
$208$	0.385340			0.0267185
$209$	1.46624	+	2.53960i	0.101422	+	0.175668i
$210$	1.04599	+	0.972423i	0.0721801	+	0.0671035i
$211$	−10.1785	+	17.6297i	−0.700716	+	1.21368i	0.267500	+	0.963558i	$0.413803\pi$
$211$	−10.1785	+	17.6297i	−0.700716	+	1.21368i	−0.968215	+	0.250118i	$0.919531\pi$
$212$	−6.06670	+	10.5078i	−0.416663	+	0.721681i
$213$	6.83167	−	2.10005i	0.468099	−	0.143893i
$214$	3.25992	+	5.64634i	0.222843	+	0.385976i
$215$	−1.83589			−0.125207
$216$	−7.99028	+	9.96002i	−0.543670	+	0.677693i
$217$	1.46663			0.0995615
$218$	−1.87759	−	3.25208i	−0.127166	−	0.220258i
$219$	−11.9361	+	3.66915i	−0.806568	+	0.247938i
$220$	0.754892	−	1.30751i	0.0508948	−	0.0881524i
$221$	0.347521	−	0.601924i	0.0233768	−	0.0404898i
$222$	−6.10030	−	5.67125i	−0.409425	−	0.380629i
$223$	−6.86450	−	11.8897i	−0.459681	−	0.796191i	0.539263	−	0.842137i	$-0.318703\pi$
$223$	−6.86450	−	11.8897i	−0.459681	−	0.796191i	−0.998944	+	0.0459468i	$0.985370\pi$
$224$	6.85918			0.458298
$225$	−2.70038	−	1.30688i	−0.180025	−	0.0871254i
$226$	13.1515			0.874825
$227$	−8.34587	−	14.4555i	−0.553935	−	0.959443i	−0.997986	−	0.0634416i	$-0.979792\pi$
$227$	−8.34587	−	14.4555i	−0.553935	−	0.959443i	0.444051	−	0.896002i	$-0.353541\pi$
$228$	1.71364	−	7.47457i	0.113488	−	0.495015i
$229$	−7.71466	+	13.3622i	−0.509799	+	0.882997i	0.490137	+	0.871646i	$0.336947\pi$
$229$	−7.71466	+	13.3622i	−0.509799	+	0.882997i	−0.999936	+	0.0113519i	$0.996387\pi$
$230$	1.09775	−	1.90136i	0.0723837	−	0.125372i
$231$	0.455825	−	1.98823i	0.0299911	−	0.130816i
$232$	−4.62032	−	8.00262i	−0.303339	−	0.525398i
$233$	−19.5945			−1.28368			−0.641838	−	0.766840i	$-0.721828\pi$
$233$	−19.5945			−1.28368			−0.641838	+	0.766840i	$0.721828\pi$
$234$	0.515491	−	0.349996i	0.0336987	−	0.0228799i
$235$	7.22132			0.471067
$236$	−5.76135	−	9.97894i	−0.375032	−	0.649574i
$237$	11.1728	+	10.3870i	0.725753	+	0.674709i
$238$	0.965994	−	1.67315i	0.0626161	−	0.108454i
$239$	14.4503	−	25.0286i	0.934712	−	1.61897i	0.159564	−	0.987188i	$-0.448991\pi$
$239$	14.4503	−	25.0286i	0.934712	−	1.61897i	0.775147	−	0.631781i	$-0.217676\pi$
$240$	−2.15065	+	0.661108i	−0.138824	+	0.0426743i
$241$	−13.6522	−	23.6464i	−0.879419	−	1.52320i	−0.851980	−	0.523574i	$-0.824598\pi$
$241$	−13.6522	−	23.6464i	−0.879419	−	1.52320i	−0.0274387	−	0.999623i	$-0.508735\pi$
$242$	0.700154			0.0450076
$243$	1.24015	−	15.5390i	0.0795558	−	0.996830i
$244$	−2.48146			−0.158859
$245$	−2.80653	−	4.86105i	−0.179303	−	0.310561i
$246$	4.96407	−	1.52595i	0.316498	−	0.0972912i
$247$	−0.434944	+	0.753345i	−0.0276748	+	0.0479342i
$248$	1.53016	−	2.65031i	0.0971651	−	0.168295i
$249$	−1.32689	−	1.23357i	−0.0840881	−	0.0781740i
$250$	0.350077	+	0.606351i	0.0221408	+	0.0383490i
$251$	−0.551662			−0.0348206			−0.0174103	−	0.999848i	$-0.505542\pi$
$251$	−0.551662			−0.0348206			−0.0174103	+	0.999848i	$0.505542\pi$
$252$	−4.41309	+	2.99630i	−0.277999	+	0.188749i
$253$	−3.13575			−0.197143
$254$	−2.42847	−	4.20624i	−0.152376	−	0.263923i
$255$	−0.906883	+	3.95566i	−0.0567912	+	0.247713i
$256$	5.19504	−	8.99807i	0.324690	−	0.562379i
$257$	11.7403	−	20.3348i	0.732339	−	1.26845i	−0.223542	−	0.974694i	$-0.571762\pi$
$257$	11.7403	−	20.3348i	0.732339	−	1.26845i	0.955881	−	0.293754i	$-0.0949046\pi$
$258$	−0.497520	+	2.17009i	−0.0309742	+	0.135104i
$259$	−4.04438	−	7.00507i	−0.251306	−	0.435274i
$260$	0.447862			0.0277752
$261$	10.1544	+	4.91433i	0.628540	+	0.304189i
$262$	−4.23031			−0.261349
$263$	7.94281	+	13.7574i	0.489775	+	0.848315i	0.999931	−	0.0117672i	$-0.00374569\pi$
$263$	7.94281	+	13.7574i	0.489775	+	0.848315i	−0.510156	+	0.860082i	$0.670412\pi$
$264$	−3.11730	−	2.89805i	−0.191857	−	0.178363i
$265$	−4.01825	+	6.95982i	−0.246839	+	0.427538i
$266$	−1.20900	+	2.09405i	−0.0741286	+	0.128395i
$267$	2.24331	−	0.689591i	0.137288	−	0.0422023i
$268$	−6.12602	−	10.6106i	−0.374206	−	0.648144i
$269$	−17.9606			−1.09508			−0.547539	−	0.836780i	$-0.684435\pi$
$269$	−17.9606			−1.09508			−0.547539	+	0.836780i	$0.684435\pi$
$270$	−2.27657	+	2.83779i	−0.138548	+	0.172702i
$271$	−29.3222			−1.78120			−0.890599	−	0.454790i	$-0.849714\pi$
$271$	−29.3222			−1.78120			−0.890599	+	0.454790i	$0.849714\pi$
$272$	1.52183	+	2.63589i	0.0922748	+	0.159825i
$273$	0.578378	−	0.177793i	0.0350050	−	0.0107605i
$274$	0.267926	−	0.464061i	0.0161860	−	0.0280350i
$275$	0.500000	−	0.866025i	0.0301511	−	0.0522233i
$276$	6.00567	+	5.58327i	0.361499	+	0.336073i
$277$	−0.200453	−	0.347195i	−0.0120441	−	0.0208609i	0.859941	−	0.510394i	$-0.170500\pi$
$277$	−0.200453	−	0.347195i	−0.0120441	−	0.0208609i	−0.871985	+	0.489533i	$0.837167\pi$
$278$	5.51728			0.330905
$279$	0.271982	+	3.72614i	0.0162832	+	0.223078i
$280$	2.89403			0.172951
$281$	−15.9252	−	27.5832i	−0.950015	−	1.64547i	−0.745384	−	0.666635i	$-0.767734\pi$
$281$	−15.9252	−	27.5832i	−0.950015	−	1.64547i	−0.204631	−	0.978839i	$-0.565599\pi$
$282$	1.95695	−	8.53586i	0.116535	−	0.508303i
$283$	12.7775	−	22.1312i	0.759541	−	1.31556i	−0.183543	−	0.983012i	$-0.558757\pi$
$283$	12.7775	−	22.1312i	0.759541	−	1.31556i	0.943085	−	0.332553i	$-0.107910\pi$
$284$	3.11500	−	5.39534i	0.184841	−	0.320155i
$285$	1.13502	−	4.95075i	0.0672328	−	0.293257i
$286$	0.103847	+	0.179868i	0.00614058	+	0.0106358i
$287$	5.04336			0.297700
$288$	1.27201	+	17.4265i	0.0749541	+	1.02687i
$289$	−11.5101			−0.677065
$290$	−1.31641	−	2.28009i	−0.0773023	−	0.133891i
$291$	14.1363	+	13.1421i	0.828686	+	0.770403i
$292$	−5.44245	+	9.42659i	−0.318495	+	0.551650i
$293$	−5.92972	+	10.2706i	−0.346418	+	0.600014i	−0.985610	−	0.169033i	$-0.945935\pi$
$293$	−5.92972	+	10.2706i	−0.346418	+	0.600014i	0.639192	+	0.769047i	$0.279269\pi$
$294$	−6.50649	+	2.00009i	−0.379466	+	0.116648i
$295$	−3.81600	−	6.60951i	−0.222176	−	0.384821i
$296$	−16.8782			−0.981027
$297$	5.13584	+	0.789364i	0.298012	+	0.0458036i
$298$	−13.3525			−0.773489
$299$	−0.465093	−	0.805565i	−0.0268970	−	0.0465870i
$300$	−2.49959	+	0.768372i	−0.144314	+	0.0443620i
$301$	−1.08105	+	1.87244i	−0.0623108	+	0.107925i
$302$	6.43026	−	11.1375i	0.370020	−	0.640894i
$303$	17.7426	+	16.4947i	1.01929	+	0.947596i
$304$	−1.90467	−	3.29898i	−0.109240	−	0.189210i
$305$	−1.64358			−0.0941113
$306$	4.42997	+	2.14394i	0.253244	+	0.122561i
$307$	18.0183			1.02836			0.514181	−	0.857682i	$-0.328096\pi$
$307$	18.0183			1.02836			0.514181	+	0.857682i	$0.328096\pi$
$308$	−0.889025	−	1.53984i	−0.0506569	−	0.0877403i
$309$	0.336688	−	1.46857i	0.0191535	−	0.0835441i
$310$	0.435969	−	0.755121i	0.0247614	−	0.0428880i
$311$	1.34574	−	2.33088i	0.0763097	−	0.132172i	−0.825345	−	0.564628i	$-0.809020\pi$
$311$	1.34574	−	2.33088i	0.0763097	−	0.132172i	0.901655	+	0.432456i	$0.142353\pi$
$312$	0.282145	−	1.23066i	0.0159733	−	0.0696727i
$313$	7.50952	+	13.0069i	0.424463	+	0.735192i	0.996370	−	0.0851269i	$-0.0271296\pi$
$313$	7.50952	+	13.0069i	0.424463	+	0.735192i	−0.571907	+	0.820318i	$0.693796\pi$
$314$	14.1363			0.797759
$315$	−2.92299	+	1.98458i	−0.164692	+	0.111819i
$316$	13.2976			0.748049
$317$	7.89780	+	13.6794i	0.443584	+	0.768311i	0.997952	−	0.0639609i	$-0.0203733\pi$
$317$	7.89780	+	13.6794i	0.443584	+	0.768311i	−0.554368	+	0.832272i	$0.687040\pi$
$318$	7.13782	+	6.63580i	0.400269	+	0.372117i
$319$	−1.88017	+	3.25655i	−0.105269	+	0.182332i
$320$	0.739931	−	1.28160i	0.0413634	−	0.0716435i
$321$	−15.4169	+	4.73914i	−0.860487	+	0.264513i
$322$	−1.29281	−	2.23921i	−0.0720453	−	0.124786i
$323$	−6.87094			−0.382309
$324$	−8.43082	−	10.6563i	−0.468379	−	0.592017i
$325$	0.296639			0.0164546
$326$	7.93608	+	13.7457i	0.439539	+	0.761304i
$327$	8.87954	−	2.72956i	0.491040	−	0.150945i
$328$	5.26180	−	9.11371i	0.290534	−	0.503220i
$329$	4.25222	−	7.36506i	0.234433	−	0.406049i
$330$	−0.888175	−	0.825707i	−0.0488924	−	0.0454537i
$331$	−15.0418	−	26.0532i	−0.826772	−	1.43201i	−0.900558	−	0.434737i	$-0.856841\pi$
$331$	−15.0418	−	26.0532i	−0.826772	−	1.43201i	0.0737857	−	0.997274i	$-0.476492\pi$
$332$	−1.57923			−0.0866713
$333$	17.0471	−	11.5743i	0.934178	−	0.634266i
$334$	−5.89613			−0.322622
$335$	−4.05754	−	7.02787i	−0.221687	−	0.383974i
$336$	−0.592125	+	2.58274i	−0.0323031	+	0.140900i
$337$	−11.2817	+	19.5405i	−0.614555	+	1.06444i	0.375908	+	0.926657i	$0.377331\pi$
$337$	−11.2817	+	19.5405i	−0.614555	+	1.06444i	−0.990462	+	0.137783i	$0.956002\pi$
$338$	4.52020	−	7.82921i	0.245866	−	0.425853i
$339$	−7.27028	+	31.7117i	−0.394868	+	1.72234i
$340$	1.76875	+	3.06357i	0.0959241	+	0.166145i
$341$	−1.24535			−0.0674396
$342$	−5.54438	−	2.68327i	−0.299806	−	0.145095i
$343$	−14.8542			−0.802052
$344$	2.25575	+	3.90708i	0.121622	+	0.210655i
$345$	3.97783	+	3.69806i	0.214159	+	0.199097i
$346$	−1.77100	+	3.06747i	−0.0952097	+	0.164908i
$347$	15.0524	−	26.0716i	0.808057	−	1.39960i	−0.106150	−	0.994350i	$-0.533852\pi$
$347$	15.0524	−	26.0716i	0.808057	−	1.39960i	0.914208	−	0.405246i	$-0.132814\pi$
$348$	9.39932	−	2.88935i	0.503857	−	0.154885i
$349$	13.1576	+	22.7896i	0.704309	+	1.21990i	0.966940	+	0.255002i	$0.0820762\pi$
$349$	13.1576	+	22.7896i	0.704309	+	1.21990i	−0.262632	+	0.964896i	$0.584590\pi$
$350$	0.824560			0.0440746
$351$	0.558961	+	1.43646i	0.0298352	+	0.0766727i
$352$	−5.82429			−0.310436
$353$	15.4574	+	26.7731i	0.822717	+	1.42499i	0.903652	+	0.428268i	$0.140876\pi$
$353$	15.4574	+	26.7731i	0.822717	+	1.42499i	−0.0809346	+	0.996719i	$0.525790\pi$
$354$	−8.84680	+	2.71950i	−0.470202	+	0.144540i
$355$	2.06321	−	3.57358i	0.109504	−	0.189666i
$356$	1.02287	−	1.77166i	0.0542119	−	0.0938978i
$357$	3.50039	+	3.25420i	0.185260	+	0.172230i
$358$	0.512965	+	0.888482i	0.0271111	+	0.0469577i
$359$	12.3437			0.651477			0.325739	−	0.945460i	$-0.394387\pi$
$359$	12.3437			0.651477			0.325739	+	0.945460i	$0.394387\pi$
$360$	0.536689	+	7.35261i	0.0282860	+	0.387516i
$361$	−10.4006			−0.547400
$362$	−1.70629	−	2.95538i	−0.0896805	−	0.155331i
$363$	−0.387052	+	1.68825i	−0.0203150	+	0.0886102i
$364$	0.263720	−	0.456776i	0.0138227	−	0.0239416i
$365$	−3.60478	+	6.24367i	−0.188683	+	0.326808i
$366$	−0.445404	+	1.94277i	−0.0232817	+	0.101550i
$367$	−10.2280	−	17.7155i	−0.533899	−	0.924741i	−0.999216	−	0.0395965i	$-0.987393\pi$
$367$	−10.2280	−	17.7155i	−0.533899	−	0.924741i	0.465316	−	0.885144i	$-0.345941\pi$
$368$	4.07340			0.212340
$369$	0.935275	+	12.8132i	0.0486885	+	0.667029i
$370$	−4.80891			−0.250003
$371$	4.73224	+	8.19647i	0.245686	+	0.425540i
$372$	2.38513	+	2.21738i	0.123663	+	0.114966i
$373$	−14.6674	+	25.4047i	−0.759448	+	1.31540i	0.183684	+	0.982985i	$0.441198\pi$
$373$	−14.6674	+	25.4047i	−0.759448	+	1.31540i	−0.943132	+	0.332418i	$0.892136\pi$
$374$	−0.820249	+	1.42071i	−0.0424141	+	0.0734633i
$375$	−1.65559	+	0.508929i	−0.0854945	+	0.0262810i
$376$	−8.87280	−	15.3681i	−0.457580	−	0.792551i
$377$	−1.11547			−0.0574494
$378$	1.55373	+	3.99290i	0.0799152	+	0.205372i
$379$	8.14294			0.418275			0.209137	−	0.977886i	$-0.432934\pi$
$379$	8.14294			0.418275			0.209137	+	0.977886i	$0.432934\pi$
$380$	−2.21370	−	3.83425i	−0.113561	−	0.196693i
$381$	11.4848	−	3.53042i	0.588384	−	0.180869i
$382$	1.55780	−	2.69820i	0.0797042	−	0.138052i
$383$	11.0219	−	19.0905i	0.563192	−	0.975478i	−0.434023	−	0.900902i	$-0.642906\pi$
$383$	11.0219	−	19.0905i	0.563192	−	0.975478i	0.997215	−	0.0745759i	$-0.0237603\pi$
$384$	13.4623	+	12.5155i	0.686997	+	0.638679i
$385$	−0.588842	−	1.01990i	−0.0300102	−	0.0519792i
$386$	−9.85245			−0.501476
$387$	−4.95761	−	2.39929i	−0.252010	−	0.121963i
$388$	16.8247			0.854144
$389$	7.09347	+	12.2863i	0.359653	+	0.622938i	0.987903	−	0.155074i	$-0.0495616\pi$
$389$	7.09347	+	12.2863i	0.359653	+	0.622938i	−0.628249	+	0.778012i	$0.716228\pi$
$390$	0.0803881	−	0.350638i	0.00407061	−	0.0177553i
$391$	3.67361	−	6.36288i	0.185783	−	0.321785i
$392$	−6.89673	+	11.9455i	−0.348338	+	0.603339i
$393$	2.33856	−	10.2004i	0.117965	−	0.514540i
$394$	6.54606	+	11.3381i	0.329786	+	0.571206i
$395$	8.80761			0.443159
$396$	3.74726	−	2.54423i	0.188307	−	0.127852i
$397$	−12.2954			−0.617090			−0.308545	−	0.951210i	$-0.599842\pi$
$397$	−12.2954			−0.617090			−0.308545	+	0.951210i	$0.599842\pi$
$398$	3.87501	+	6.71171i	0.194237	+	0.336428i
$399$	−4.38095	−	4.07283i	−0.219322	−	0.203896i
$400$	−0.649509	+	1.12498i	−0.0324755	+	0.0562492i
$401$	−10.3097	+	17.8569i	−0.514840	+	0.891729i	0.485012	+	0.874508i	$0.338815\pi$
$401$	−10.3097	+	17.8569i	−0.514840	+	0.891729i	−0.999852	+	0.0172211i	$0.994518\pi$
$402$	−9.40677	+	2.89164i	−0.469167	+	0.144222i
$403$	−0.184710	−	0.319928i	−0.00920108	−	0.0159367i
$404$	21.1168			1.05060
$405$	−5.58412	−	7.05816i	−0.277477	−	0.350723i
$406$	−3.10063			−0.153882
$407$	3.43418	+	5.94817i	0.170226	+	0.294840i
$408$	9.53257	−	2.93030i	0.471932	−	0.145072i
$409$	−12.4106	+	21.4957i	−0.613663	+	1.06290i	0.376954	+	0.926232i	$0.376971\pi$
$409$	−12.4106	+	21.4957i	−0.613663	+	1.06290i	−0.990617	+	0.136664i	$0.956362\pi$
$410$	1.49918	−	2.59666i	0.0740393	−	0.128240i
$411$	0.970859	+	0.902576i	0.0478889	+	0.0445208i
$412$	−0.656664	−	1.13738i	−0.0323515	−	0.0560345i
$413$	−8.98810			−0.442276
$414$	5.44921	−	3.69978i	0.267814	−	0.181834i
$415$	−1.04599			−0.0513459
$416$	−0.863857	−	1.49624i	−0.0423541	−	0.0733594i
$417$	−3.05001	+	13.3036i	−0.149360	+	0.651479i
$418$	1.02659	−	1.77811i	0.0502122	−	0.0869702i
$419$	7.02800	−	12.1728i	0.343340	−	0.594682i	−0.641711	−	0.766947i	$-0.721775\pi$
$419$	7.02800	−	12.1728i	0.343340	−	0.594682i	0.985051	+	0.172264i	$0.0551083\pi$
$420$	−0.688198	+	3.00179i	−0.0335806	+	0.146473i
$421$	−11.9831	−	20.7553i	−0.584019	−	1.01155i	−0.994997	−	0.0999049i	$-0.968146\pi$
$421$	−11.9831	−	20.7553i	−0.584019	−	1.01155i	0.410978	−	0.911645i	$-0.365187\pi$
$422$	14.2530			0.693826
$423$	19.5003	+	9.43742i	0.948138	+	0.458863i
$424$	19.7488			0.959088
$425$	1.17153	+	2.02914i	0.0568274	+	0.0984279i
$426$	−3.66498	−	3.40721i	−0.177569	−	0.165080i
$427$	−0.967812	+	1.67630i	−0.0468357	+	0.0811218i
$428$	−7.02956	+	12.1756i	−0.339786	+	0.588527i
$429$	−0.491114	+	0.150968i	−0.0237112	+	0.00728882i
$430$	0.642704	+	1.11320i	0.0309939	+	0.0536831i
$431$	19.5979			0.943998			0.471999	−	0.881599i	$-0.343533\pi$
$431$	19.5979			0.943998			0.471999	+	0.881599i	$0.343533\pi$
$432$	−6.67156	−	1.02540i	−0.320986	−	0.0493345i
$433$	−7.54039			−0.362368			−0.181184	−	0.983449i	$-0.557993\pi$
$433$	−7.54039			−0.362368			−0.181184	+	0.983449i	$0.557993\pi$
$434$	−0.513434	−	0.889294i	−0.0246456	−	0.0426875i
$435$	6.22561	−	1.91375i	0.298495	−	0.0917571i
$436$	4.04876	−	7.01265i	0.193900	−	0.335845i
$437$	−4.59775	+	7.96354i	−0.219940	+	0.380948i
$438$	6.40335	+	5.95299i	0.305964	+	0.284445i
$439$	12.1734	+	21.0850i	0.581007	+	1.00633i	0.995360	+	0.0962174i	$0.0306744\pi$
$439$	12.1734	+	21.0850i	0.581007	+	1.00633i	−0.414353	+	0.910116i	$0.635992\pi$
$440$	−2.45739			−0.117151
$441$	−1.22588	−	16.7945i	−0.0583753	−	0.799738i
$442$	−0.486636			−0.0231469
$443$	−0.0833848	−	0.144427i	−0.00396173	−	0.00686192i	0.864038	−	0.503427i	$-0.167928\pi$
$443$	−0.0833848	−	0.144427i	−0.00396173	−	0.00686192i	−0.867999	+	0.496565i	$0.834594\pi$
$444$	4.01363	−	17.5067i	0.190478	−	0.830832i
$445$	0.677493	−	1.17345i	0.0321163	−	0.0556270i
$446$	−4.80621	+	8.32459i	−0.227580	+	0.394181i
$447$	7.38139	−	32.1963i	0.349128	−	1.52283i
$448$	−0.871406	−	1.50932i	−0.0411701	−	0.0713086i
$449$	−12.7098			−0.599815			−0.299907	−	0.953968i	$-0.596956\pi$
$449$	−12.7098			−0.599815			−0.299907	+	0.953968i	$0.596956\pi$
$450$	0.152912	+	2.09489i	0.00720835	+	0.0987540i
$451$	−4.28243			−0.201652
$452$	14.1797	+	24.5600i	0.666957	+	1.15520i
$453$	23.3008	+	21.6620i	1.09477	+	1.01777i
$454$	−5.84339	+	10.1211i	−0.274244	+	0.475005i
$455$	0.174674	−	0.302544i	0.00818884	−	0.0141835i
$456$	−11.9306	+	3.66746i	−0.558701	+	0.171744i
$457$	−11.5561	−	20.0158i	−0.540574	−	0.936301i	−0.998871	−	0.0475022i	$-0.984874\pi$
$457$	−11.5561	−	20.0158i	−0.540574	−	0.936301i	0.458297	−	0.888799i	$-0.348459\pi$
$458$	10.8029			0.504786
$459$	−7.61851	+	9.49660i	−0.355602	+	0.443264i
$460$	4.73430			0.220738
$461$	−15.6081	−	27.0340i	−0.726941	−	1.25910i	−0.958170	−	0.286200i	$-0.907608\pi$
$461$	−15.6081	−	27.0340i	−0.726941	−	1.25910i	0.231229	−	0.972899i	$-0.425725\pi$
$462$	−1.36514	+	0.419642i	−0.0635119	+	0.0195235i
$463$	−10.3805	+	17.9796i	−0.482425	+	0.835584i	−0.999796	−	0.0201764i	$-0.993577\pi$
$463$	−10.3805	+	17.9796i	−0.482425	+	0.835584i	0.517372	+	0.855761i	$0.326911\pi$
$464$	2.44238	−	4.23033i	0.113385	−	0.196388i
$465$	1.57978	+	1.46867i	0.0732606	+	0.0681080i
$466$	6.85957	+	11.8811i	0.317764	+	0.550383i
$467$	−9.27177			−0.429046			−0.214523	−	0.976719i	$-0.568820\pi$
$467$	−9.27177			−0.429046			−0.214523	+	0.976719i	$0.568820\pi$
$468$	1.20940	+	0.585302i	0.0559044	+	0.0270556i
$469$	−9.55701			−0.441302
$470$	−2.52802	−	4.37866i	−0.116609	−	0.201972i
$471$	−7.81470	+	34.0863i	−0.360082	+	1.57061i
$472$	−9.37741	+	16.2421i	−0.431630	+	0.747605i
$473$	0.917946	−	1.58993i	0.0422072	−	0.0731051i
$474$	2.38683	−	10.4109i	0.109631	−	0.478189i
$475$	−1.46624	−	2.53960i	−0.0672756	−	0.116525i
$476$	4.16607			0.190951
$477$	−19.9465	+	13.5428i	−0.913287	+	0.620082i
$478$	−20.2349			−0.925521
$479$	−18.0496	−	31.2628i	−0.824705	−	1.42843i	−0.902144	−	0.431434i	$-0.858008\pi$
$479$	−18.0496	−	31.2628i	−0.824705	−	1.42843i	0.0774389	−	0.996997i	$-0.475326\pi$
$480$	7.38836	+	6.86872i	0.337231	+	0.313513i
$481$	−1.01871	+	1.76446i	−0.0464493	+	0.0804525i
$482$	−9.55867	+	16.5561i	−0.435386	+	0.754110i
$483$	6.11398	−	1.87943i	0.278196	−	0.0855172i
$484$	0.754892	+	1.30751i	0.0343133	+	0.0594324i
$485$	11.1438			0.506012
$486$	−9.85627	+	4.68790i	−0.447089	+	0.212647i
$487$	23.0753			1.04564			0.522820	−	0.852443i	$-0.324880\pi$
$487$	23.0753			1.04564			0.522820	+	0.852443i	$0.324880\pi$
$488$	2.01946	+	3.49781i	0.0914168	+	0.158338i
$489$	−37.5315	+	11.5372i	−1.69724	+	0.521729i
$490$	−1.96500	+	3.40348i	−0.0887698	+	0.153754i
$491$	−14.4475	+	25.0238i	−0.652007	+	1.12931i	0.330628	+	0.943761i	$0.392739\pi$
$491$	−14.4475	+	25.0238i	−0.652007	+	1.12931i	−0.982635	+	0.185548i	$0.940594\pi$
$492$	8.20182	+	7.62497i	0.369767	+	0.343760i
$493$	−4.40534	−	7.63028i	−0.198407	−	0.343651i
$494$	0.609055			0.0274027
$495$	2.48198	−	1.68516i	0.111557	−	0.0757422i
$496$	1.61774			0.0726385
$497$	−2.42981	−	4.20855i	−0.108992	−	0.188779i
$498$	−0.283460	+	1.23640i	−0.0127022	+	0.0554045i
$499$	17.3107	−	29.9830i	0.774933	−	1.34222i	−0.159900	−	0.987133i	$-0.551117\pi$
$499$	17.3107	−	29.9830i	0.774933	−	1.34222i	0.934832	−	0.355089i	$-0.115550\pi$
$500$	−0.754892	+	1.30751i	−0.0337598	+	0.0584737i
$501$	3.25944	−	14.2171i	0.145621	−	0.635173i
$502$	0.193124	+	0.334501i	0.00861956	+	0.0149295i
$503$	−16.8626			−0.751868			−0.375934	−	0.926646i	$-0.622678\pi$
$503$	−16.8626			−0.751868			−0.375934	+	0.926646i	$0.622678\pi$
$504$	7.81498	+	3.78215i	0.348107	+	0.168471i
$505$	13.9866			0.622395
$506$	1.09775	+	1.90136i	0.0488011	+	0.0845260i
$507$	16.3794	+	15.2274i	0.727436	+	0.676273i
$508$	5.23666	−	9.07017i	0.232339	−	0.402424i
$509$	0.244591	−	0.423644i	0.0108413	−	0.0187777i	−0.860554	−	0.509359i	$-0.829882\pi$
$509$	0.244591	−	0.423644i	0.0108413	−	0.0187777i	0.871395	+	0.490582i	$0.163216\pi$
$510$	2.71600	−	0.834896i	0.120266	−	0.0369698i
$511$	4.24530	+	7.35307i	0.187801	+	0.325281i
$512$	13.9503			0.616520
$513$	9.53504	−	11.8856i	0.420982	−	0.524761i
$514$	−16.4400			−0.725138
$515$	−0.434939	−	0.753336i	−0.0191657	−	0.0331960i
$516$	−4.58898	+	1.41065i	−0.202019	+	0.0621004i
$517$	−3.61066	+	6.25385i	−0.158797	+	0.275044i
$518$	−2.83169	+	4.90463i	−0.124417	+	0.215497i
$519$	−6.41742	−	5.96607i	−0.281693	−	0.261881i
$520$	−0.364479	−	0.631297i	−0.0159835	−	0.0276842i
$521$	−35.6875			−1.56350			−0.781750	−	0.623592i	$-0.785673\pi$
$521$	−35.6875			−1.56350			−0.781750	+	0.623592i	$0.785673\pi$
$522$	−0.575003	−	7.87750i	−0.0251672	−	0.344789i
$523$	36.9484			1.61564			0.807820	−	0.589430i	$-0.200648\pi$
$523$	36.9484			1.61564			0.807820	+	0.589430i	$0.200648\pi$
$524$	−4.56104	−	7.89995i	−0.199250	−	0.345111i
$525$	−0.455825	+	1.98823i	−0.0198938	+	0.0867733i
$526$	5.56119	−	9.63226i	0.242479	−	0.419987i
$527$	1.45896	−	2.52700i	0.0635534	−	0.110078i
$528$	0.502788	−	2.19307i	0.0218810	−	0.0954411i
$529$	6.58354	+	11.4030i	0.286241	+	0.495784i
$530$	5.62679			0.244412
$531$	−1.66682	−	22.8353i	−0.0723336	−	0.990967i
$532$	−5.21409			−0.226059
$533$	−0.635169	−	1.10015i	−0.0275122	−	0.0476526i
$534$	−1.20346	−	1.11882i	−0.0520790	−	0.0484162i
$535$	−4.65600	+	8.06443i	−0.201296	+	0.348656i
$536$	−9.97096	+	17.2702i	−0.430680	+	0.745960i
$537$	−2.42593	+	0.745730i	−0.104687	+	0.0321806i
$538$	6.28759	+	10.8904i	0.271077	+	0.469520i
$539$	5.61306			0.241772
$540$	−7.75402	−	1.19177i	−0.333680	−	0.0512856i
$541$	−33.1526			−1.42534			−0.712670	−	0.701499i	$-0.752515\pi$
$541$	−33.1526			−1.42534			−0.712670	+	0.701499i	$0.752515\pi$
$542$	10.2650	+	17.7796i	0.440921	+	0.763697i
$543$	8.06942	−	2.48054i	0.346292	−	0.106450i
$544$	6.82331	−	11.8183i	0.292547	−	0.506706i
$545$	2.68168	−	4.64480i	0.114870	−	0.198961i
$546$	−0.310282	−	0.288459i	−0.0132788	−	0.0123449i
$547$	−2.65701	−	4.60208i	−0.113606	−	0.196771i	0.803616	−	0.595148i	$-0.202907\pi$
$547$	−2.65701	−	4.60208i	−0.113606	−	0.196771i	−0.917221	+	0.398378i	$0.869573\pi$
$548$	1.15549			0.0493601
$549$	−4.43830	−	2.14797i	−0.189422	−	0.0916731i
$550$	−0.700154			−0.0298547
$551$	5.51356	+	9.54976i	0.234885	+	0.406834i
$552$	2.98253	−	13.0092i	0.126945	−	0.553710i
$553$	5.18630	−	8.98293i	0.220544	−	0.381993i
$554$	−0.140348	+	0.243090i	−0.00596281	+	0.0103279i
$555$	2.65841	−	11.5955i	0.112843	−	0.492202i
$556$	5.94863	+	10.3033i	0.252278	+	0.436958i
$557$	1.18653			0.0502749			0.0251374	−	0.999684i	$-0.491998\pi$
$557$	1.18653			0.0502749			0.0251374	+	0.999684i	$0.491998\pi$
$558$	2.16414	−	1.46935i	0.0916152	−	0.0622027i
$559$	0.544598			0.0230340
$560$	0.764917	+	1.32488i	0.0323237	+	0.0559862i
$561$	−2.97226	−	2.76321i	−0.125489	−	0.116663i
$562$	−11.1501	+	19.3125i	−0.470337	+	0.814647i
$563$	3.17803	−	5.50452i	0.133938	−	0.231988i	−0.791253	−	0.611489i	$-0.790571\pi$
$563$	3.17803	−	5.50452i	0.133938	−	0.231988i	0.925191	+	0.379501i	$0.123904\pi$
$564$	18.0504	−	5.54867i	0.760057	−	0.233641i
$565$	9.39187	+	16.2672i	0.395119	+	0.684366i
$566$	−17.8924			−0.752073
$567$	−10.4868	+	1.53913i	−0.440405	+	0.0646373i
$568$	−10.1402			−0.425474
$569$	−11.2265	−	19.4448i	−0.470639	−	0.815170i	0.528797	−	0.848748i	$-0.322643\pi$
$569$	−11.2265	−	19.4448i	−0.470639	−	0.815170i	−0.999436	+	0.0335778i	$0.989310\pi$
$570$	−3.39924	+	1.04492i	−0.142378	+	0.0437670i
$571$	13.0324	−	22.5728i	0.545390	−	0.944643i	−0.453193	−	0.891413i	$-0.649715\pi$
$571$	13.0324	−	22.5728i	0.545390	−	0.944643i	0.998582	−	0.0532300i	$-0.0169517\pi$
$572$	−0.223931	+	0.387859i	−0.00936302	+	0.0162172i
$573$	5.64487	+	5.24786i	0.235818	+	0.219232i
$574$	−1.76556	−	3.05804i	−0.0736932	−	0.127640i
$575$	3.13575			0.130770
$576$	3.67299	−	2.49380i	0.153041	−	0.103908i
$577$	30.2301			1.25850			0.629249	−	0.777204i	$-0.283363\pi$
$577$	30.2301			1.25850			0.629249	+	0.777204i	$0.283363\pi$
$578$	4.02942	+	6.97916i	0.167602	+	0.290295i
$579$	5.44653	−	23.7568i	0.226350	−	0.987298i
$580$	2.83866	−	4.91670i	0.117869	−	0.204155i
$581$	−0.615926	+	1.06682i	−0.0255529	+	0.0442590i
$582$	3.01991	−	13.1723i	0.125179	−	0.546010i
$583$	−4.01825	−	6.95982i	−0.166419	−	0.288246i
$584$	17.7167			0.733123
$585$	0.801040	+	0.387673i	0.0331189	+	0.0160283i
$586$	8.30344			0.343012
$587$	−1.66191	−	2.87850i	−0.0685942	−	0.118809i	0.829689	−	0.558227i	$-0.188518\pi$
$587$	−1.66191	−	2.87850i	−0.0685942	−	0.118809i	−0.898283	+	0.439418i	$0.855185\pi$
$588$	−10.7503	−	9.99418i	−0.443334	−	0.412153i
$589$	−1.82598	+	3.16269i	−0.0752383	+	0.130317i
$590$	−2.67179	+	4.62768i	−0.109996	+	0.190518i
$591$	−30.9578	+	9.51641i	−1.27343	+	0.391453i
$592$	−4.46106	−	7.72679i	−0.183349	−	0.317569i
$593$	−2.52778			−0.103804			−0.0519018	−	0.998652i	$-0.516528\pi$
$593$	−2.52778			−0.103804			−0.0519018	+	0.998652i	$0.516528\pi$
$594$	−1.31931	−	3.39046i	−0.0541319	−	0.139112i
$595$	2.75938			0.113123
$596$	−14.3964	−	24.9353i	−0.589699	−	1.02139i
$597$	−18.3258	+	5.63334i	−0.750026	+	0.230557i
$598$	−0.325637	+	0.564020i	−0.0133163	+	0.0230645i
$599$	−17.8169	+	30.8598i	−0.727980	+	1.26090i	0.229756	+	0.973248i	$0.426207\pi$
$599$	−17.8169	+	30.8598i	−0.727980	+	1.26090i	−0.957736	+	0.287650i	$0.907126\pi$
$600$	3.11730	+	2.89805i	0.127263	+	0.118313i
$601$	2.19130	+	3.79543i	0.0893848	+	0.154819i	0.907251	−	0.420589i	$-0.138177\pi$
$601$	2.19130	+	3.79543i	0.0893848	+	0.154819i	−0.817866	+	0.575408i	$0.804843\pi$
$602$	1.51380			0.0616981
$603$	−1.77232	−	24.2807i	−0.0721744	−	0.988785i
$604$	27.7319			1.12840
$605$	0.500000	+	0.866025i	0.0203279	+	0.0352089i
$606$	3.79031	−	16.5327i	0.153971	−	0.671593i
$607$	1.62794	−	2.81968i	0.0660761	−	0.114447i	−0.831095	−	0.556131i	$-0.812285\pi$
$607$	1.62794	−	2.81968i	0.0660761	−	0.114447i	0.897171	+	0.441684i	$0.145619\pi$
$608$	−8.53979	+	14.7914i	−0.346334	+	0.599869i
$609$	1.71406	−	7.47642i	0.0694572	−	0.302960i
$610$	0.575381	+	0.996589i	0.0232965	+	0.0403507i
$611$	−2.14213			−0.0866613
$612$	0.772584	+	10.5844i	0.0312299	+	0.427847i
$613$	31.8613			1.28686			0.643432	−	0.765503i	$-0.277510\pi$
$613$	31.8613			1.28686			0.643432	+	0.765503i	$0.277510\pi$
$614$	−6.30781	−	10.9254i	−0.254562	−	0.440915i
$615$	5.43245	+	5.05037i	0.219057	+	0.203651i
$616$	−1.44701	+	2.50630i	−0.0583019	+	0.100982i
$617$	−9.48411	+	16.4270i	−0.381816	+	0.661325i	−0.991322	−	0.131457i	$-0.958035\pi$
$617$	−9.48411	+	16.4270i	−0.381816	+	0.661325i	0.609506	+	0.792782i	$0.291368\pi$
$618$	−1.00834	+	0.309962i	−0.0405613	+	0.0124685i
$619$	−2.43379	−	4.21545i	−0.0978224	−	0.169433i	0.812961	−	0.582319i	$-0.197854\pi$
$619$	−2.43379	−	4.21545i	−0.0978224	−	0.169433i	−0.910783	+	0.412885i	$0.864521\pi$
$620$	1.88021			0.0755112
$621$	5.90873	+	15.1847i	0.237109	+	0.609342i
$622$	−1.88444			−0.0755593
$623$	−0.797874	−	1.38196i	−0.0319661	−	0.0553670i
$624$	0.637967	−	0.196111i	0.0255391	−	0.00785071i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	5.25782	−	9.10681i	0.210145	−	0.363981i
$627$	3.71997	+	3.45833i	0.148561	+	0.138112i
$628$	15.2415	+	26.3991i	0.608202	+	1.05344i
$629$	−16.0929			−0.641667
$630$	2.22663	+	1.07760i	0.0887110	+	0.0429327i
$631$	−15.4696			−0.615834			−0.307917	−	0.951413i	$-0.599632\pi$
$631$	−15.4696			−0.615834			−0.307917	+	0.951413i	$0.599632\pi$
$632$	−10.8219	−	18.7440i	−0.430471	−	0.745597i
$633$	−7.87921	+	34.3677i	−0.313170	+	1.36599i
$634$	5.52967	−	9.57767i	0.219611	−	0.380378i
$635$	3.46848	−	6.00759i	0.137643	−	0.238404i
$636$	−4.69626	+	20.4842i	−0.186219	+	0.812252i
$637$	0.832527	+	1.44198i	0.0329859	+	0.0571333i
$638$	2.63282			0.104234
$639$	10.2417	−	6.95367i	0.405155	−	0.275083i
$640$	10.6125			0.419494
$641$	4.43570	+	7.68286i	0.175200	+	0.303455i	0.940230	−	0.340539i	$-0.110610\pi$
$641$	4.43570	+	7.68286i	0.175200	+	0.303455i	−0.765031	+	0.643994i	$0.777276\pi$
$642$	8.27068	+	7.68898i	0.326418	+	0.303460i
$643$	0.0457665	−	0.0792700i	0.00180486	−	0.00312610i	−0.865122	−	0.501562i	$-0.832759\pi$
$643$	0.0457665	−	0.0792700i	0.00180486	−	0.00312610i	0.866926	+	0.498436i	$0.166092\pi$
$644$	2.78776	−	4.82854i	0.109853	−	0.190271i
$645$	−3.03949	+	0.934338i	−0.119680	+	0.0367895i
$646$	2.40536	+	4.16620i	0.0946376	+	0.163917i
$647$	13.8790			0.545641			0.272821	−	0.962065i	$-0.412043\pi$
$647$	13.8790			0.545641			0.272821	+	0.962065i	$0.412043\pi$
$648$	−8.15972	+	20.5562i	−0.320544	+	0.807525i
$649$	7.63201			0.299583
$650$	−0.103847	−	0.179868i	−0.00407320	−	0.00705499i
$651$	2.42815	−	0.746411i	0.0951666	−	0.0292542i
$652$	−17.1131	+	29.6407i	−0.670199	+	1.16082i
$653$	−15.6959	+	27.1861i	−0.614228	+	1.06387i	0.376292	+	0.926501i	$0.377199\pi$
$653$	−15.6959	+	27.1861i	−0.614228	+	1.06387i	−0.990519	+	0.137372i	$0.956134\pi$
$654$	−4.76360	−	4.42856i	−0.186271	−	0.173170i
$655$	−3.02099	−	5.23250i	−0.118040	−	0.204451i
$656$	5.56296			0.217197
$657$	−17.8940	+	12.1493i	−0.698112	+	0.473988i
$658$	−5.95442			−0.232127
$659$	−7.84555	−	13.5889i	−0.305619	−	0.529348i	0.671780	−	0.740751i	$-0.265530\pi$
$659$	−7.84555	−	13.5889i	−0.305619	−	0.529348i	−0.977399	+	0.211403i	$0.932197\pi$
$660$	0.584365	−	2.54890i	0.0227464	−	0.0992156i
$661$	−4.59347	+	7.95612i	−0.178665	+	0.309457i	−0.941424	−	0.337226i	$-0.890511\pi$
$661$	−4.59347	+	7.95612i	−0.178665	+	0.309457i	0.762758	+	0.646684i	$0.223845\pi$
$662$	−10.5316	+	18.2412i	−0.409321	+	0.708965i
$663$	0.269017	−	1.17340i	0.0104478	−	0.0455713i
$664$	1.28521	+	2.22605i	0.0498758	+	0.0863873i
$665$	−3.45353			−0.133922
$666$	−12.9859	−	6.28467i	−0.503193	−	0.243526i
$667$	−11.7915			−0.456569
$668$	−6.35710	−	11.0108i	−0.245963	−	0.426021i
$669$	−17.4158	−	16.1909i	−0.673334	−	0.625977i
$670$	−2.84090	+	4.92059i	−0.109754	+	0.190099i
$671$	0.821792	−	1.42339i	0.0317249	−	0.0549492i
$672$	11.3560	−	3.49083i	0.438068	−	0.134662i
$673$	9.83989	+	17.0432i	0.379300	+	0.656967i	0.990961	−	0.134154i	$-0.0428316\pi$
$673$	9.83989	+	17.0432i	0.379300	+	0.656967i	−0.611661	+	0.791120i	$0.709498\pi$
$674$	15.7979			0.608512
$675$	−5.13584	−	0.789364i	−0.197679	−	0.0303827i
$676$	19.4943			0.749783
$677$	−13.9690	−	24.1951i	−0.536874	−	0.929892i	−0.999070	−	0.0431148i	$-0.986272\pi$
$677$	−13.9690	−	24.1951i	−0.536874	−	0.929892i	0.462197	−	0.886777i	$-0.347061\pi$
$678$	21.7736	−	6.69318i	0.836208	−	0.257050i
$679$	6.56192	−	11.3656i	0.251823	−	0.436171i
$680$	2.87890	−	4.98639i	0.110401	−	0.191220i
$681$	−21.1742	−	19.6849i	−0.811396	−	0.754329i
$682$	0.435969	+	0.755121i	0.0166941	+	0.0289151i
$683$	38.6180			1.47768			0.738838	−	0.673883i	$-0.235375\pi$
$683$	38.6180			1.47768			0.738838	+	0.673883i	$0.235375\pi$
$684$	−0.966936	−	13.2470i	−0.0369717	−	0.506511i
$685$	0.765334			0.0292419
$686$	5.20011	+	9.00686i	0.198541	+	0.343884i
$687$	−5.97195	+	26.0485i	−0.227844	+	0.993814i
$688$	−1.19243	+	2.06535i	−0.0454610	+	0.0787407i
$689$	1.19197	−	2.06456i	0.0454105	−	0.0786534i
$690$	0.849775	−	3.70657i	0.0323504	−	0.141107i
$691$	13.3727	+	23.1621i	0.508720	+	0.881130i	0.999949	+	0.0100989i	$0.00321464\pi$
$691$	13.3727	+	23.1621i	0.508720	+	0.881130i	−0.491229	+	0.871031i	$0.663452\pi$
$692$	−7.63784			−0.290347
$693$	−0.257204	−	3.52368i	−0.00977037	−	0.133854i
$694$	−21.0780			−0.800112
$695$	3.94005	+	6.82437i	0.149455	+	0.258863i
$696$	−11.7221	−	10.8977i	−0.444326	−	0.413076i
$697$	5.01698	−	8.68967i	0.190032	−	0.329145i
$698$	9.21232	−	15.9562i	0.348692	−	0.603952i
$699$	−32.4405	+	9.97219i	−1.22701	+	0.377183i
$700$	0.889025	+	1.53984i	0.0336020	+	0.0582004i
$701$	−5.12083			−0.193411			−0.0967055	−	0.995313i	$-0.530831\pi$
$701$	−5.12083			−0.193411			−0.0967055	+	0.995313i	$0.530831\pi$
$702$	0.675321	−	0.841799i	0.0254884	−	0.0317717i
$703$	20.1413			0.759643
$704$	0.739931	+	1.28160i	0.0278872	+	0.0483021i
$705$	11.9556	−	3.67514i	0.450273	−	0.138414i
$706$	10.8226	−	18.7453i	0.407314	−	0.705488i
$707$	8.23590	−	14.2650i	0.309743	−	0.536491i
$708$	−14.6170	−	13.5890i	−0.549341	−	0.510705i
$709$	20.4851	+	35.4812i	0.769334	+	1.33253i	0.937924	+	0.346840i	$0.112745\pi$
$709$	20.4851	+	35.4812i	0.769334	+	1.33253i	−0.168590	+	0.985686i	$0.553921\pi$
$710$	−2.88913			−0.108427
$711$	23.7839	+	11.5105i	0.891967	+	0.431678i
$712$	−3.32973			−0.124787
$713$	−1.95256	−	3.38193i	−0.0731238	−	0.126654i
$714$	0.747780	−	3.26168i	0.0279850	−	0.122065i
$715$	−0.148320	+	0.256897i	−0.00554684	+	0.00960741i
$716$	−1.10614	+	1.91589i	−0.0413383	+	0.0716001i
$717$	11.1860	−	48.7914i	0.417750	−	1.82215i
$718$	−4.32125	−	7.48463i	−0.161268	−	0.279324i
$719$	−6.76466			−0.252279			−0.126140	−	0.992012i	$-0.540259\pi$
$719$	−6.76466			−0.252279			−0.126140	+	0.992012i	$0.540259\pi$
$720$	−3.22414	+	2.18905i	−0.120157	+	0.0815811i
$721$	−1.02444			−0.0381522
$722$	3.64101	+	6.30641i	0.135504	+	0.234700i
$723$	−34.6369	−	32.2008i	−1.28816	−	1.19756i
$724$	3.67937	−	6.37286i	0.136743	−	0.236845i
$725$	1.88017	−	3.25655i	0.0698279	−	0.120945i
$726$	1.15917	−	0.356328i	0.0430209	−	0.0132246i
$727$	−23.3952	−	40.5218i	−0.867682	−	1.50287i	−0.864360	−	0.502874i	$-0.832276\pi$
$727$	−23.3952	−	40.5218i	−0.867682	−	1.50287i	−0.00332210	−	0.999994i	$-0.501057\pi$
$728$	−0.858483			−0.0318175
$729$	−5.85508	−	26.3575i	−0.216855	−	0.976204i
$730$	5.04781			0.186828
$731$	2.15080	+	3.72529i	0.0795501	+	0.137785i
$732$	−4.10829	+	1.26288i	−0.151847	+	0.0466775i
$733$	11.7840	−	20.4105i	0.435251	−	0.753877i	−0.562065	−	0.827093i	$-0.689993\pi$
$733$	11.7840	−	20.4105i	0.435251	−	0.753877i	0.997316	+	0.0732158i	$0.0233262\pi$
$734$	−7.16120	+	12.4036i	−0.264325	+	0.457824i
$735$	−7.12040	−	6.61961i	−0.262640	−	0.244168i
$736$	−9.13176	−	15.8167i	−0.336601	−	0.583010i
$737$	8.11509			0.298923
$738$	7.44189	−	5.05271i	0.273940	−	0.185993i
$739$	36.5947			1.34616			0.673080	−	0.739570i	$-0.264971\pi$
$739$	36.5947			1.34616			0.673080	+	0.739570i	$0.264971\pi$
$740$	−5.18487	−	8.98046i	−0.190600	−	0.330128i
$741$	−0.336692	+	1.46859i	−0.0123687	+	0.0539499i
$742$	3.31329	−	5.73879i	0.121635	−	0.210678i
$743$	−3.07707	+	5.32963i	−0.112887	+	0.195525i	−0.916933	−	0.399041i	$-0.869343\pi$
$743$	−3.07707	+	5.32963i	−0.112887	+	0.195525i	0.804046	+	0.594567i	$0.202676\pi$
$744$	1.18450	−	5.16658i	0.0434259	−	0.189416i
$745$	−9.53540	−	16.5158i	−0.349350	−	0.605092i
$746$	20.5389			0.751981
$747$	−2.82459	−	1.36699i	−0.103346	−	0.0500156i
$748$	−3.53751			−0.129344
$749$	5.48330	+	9.49735i	0.200355	+	0.347026i
$750$	0.888175	+	0.825707i	0.0324316	+	0.0301506i
$751$	−16.1910	+	28.0436i	−0.590818	+	1.02333i	0.403305	+	0.915066i	$0.367861\pi$
$751$	−16.1910	+	28.0436i	−0.590818	+	1.02333i	−0.994123	+	0.108261i	$0.965472\pi$
$752$	4.69032	−	8.12387i	0.171038	−	0.296247i
$753$	−0.913329	+	0.280757i	−0.0332836	+	0.0102313i
$754$	0.390499	+	0.676364i	0.0142211	+	0.0246317i
$755$	18.3681			0.668485
$756$	−5.78139	+	7.20660i	−0.210267	+	0.262101i
$757$	29.3918			1.06826			0.534132	−	0.845401i	$-0.320638\pi$
$757$	29.3918			1.06826			0.534132	+	0.845401i	$0.320638\pi$
$758$	−2.85065	−	4.93748i	−0.103540	−	0.179337i
$759$	−5.19153	+	1.59587i	−0.188440	+	0.0579265i
$760$	−3.60312	+	6.24078i	−0.130699	+	0.226377i
$761$	18.7387	−	32.4564i	0.679278	−	1.17654i	−0.295921	−	0.955212i	$-0.595627\pi$
$761$	18.7387	−	32.4564i	0.679278	−	1.17654i	0.975199	−	0.221331i	$-0.0710401\pi$
$762$	−6.16124	−	5.72790i	−0.223198	−	0.207500i
$763$	−3.15817	−	5.47011i	−0.114333	−	0.198031i
$764$	6.71838			0.243062
$765$	0.511718	+	7.01051i	0.0185012	+	0.253465i
$766$	−15.4340			−0.557655
$767$	1.13198	+	1.96064i	0.0408733	+	0.0707947i
$768$	4.02150	−	17.5411i	0.145113	−	0.632958i
$769$	−2.79653	+	4.84374i	−0.100846	+	0.174670i	−0.912033	−	0.410116i	$-0.865488\pi$
$769$	−2.79653	+	4.84374i	−0.100846	+	0.174670i	0.811188	+	0.584786i	$0.198821\pi$
$770$	−0.412280	+	0.714090i	−0.0148575	+	0.0257340i
$771$	9.08820	−	39.6411i	0.327304	−	1.42764i
$772$	−10.6227	−	18.3991i	−0.382320	−	0.662198i
$773$	−18.5787			−0.668230			−0.334115	−	0.942532i	$-0.608437\pi$
$773$	−18.5787			−0.668230			−0.334115	+	0.942532i	$0.608437\pi$
$774$	0.280730	+	3.84599i	0.0100906	+	0.138241i
$775$	1.24535			0.0447344
$776$	−13.6923	−	23.7157i	−0.491524	−	0.851345i
$777$	−10.2609	−	9.53925i	−0.368109	−	0.342219i
$778$	4.96652	−	8.60227i	0.178058	−	0.308406i
$779$	−6.27906	+	10.8757i	−0.224971	+	0.389661i
$780$	0.741477	−	0.227930i	0.0265491	−	0.00816119i
$781$	2.06321	+	3.57358i	0.0738274	+	0.127873i
$782$	−5.14419			−0.183956
$783$	19.3126	+	2.96828i	0.690174	+	0.106078i
$784$	−7.29147			−0.260410
$785$	10.0952	+	17.4853i	0.360311	+	0.624078i
$786$	−7.00367	+	2.15292i	−0.249813	+	0.0767923i
$787$	10.9843	−	19.0253i	0.391547	−	0.678180i	−0.601106	−	0.799169i	$-0.705273\pi$
$787$	10.9843	−	19.0253i	0.391547	−	0.678180i	0.992654	+	0.120989i	$0.0386066\pi$
$788$	−14.1157	+	24.4491i	−0.502850	+	0.870961i
$789$	20.1516	+	18.7343i	0.717415	+	0.666958i
$790$	−3.08334	−	5.34051i	−0.109700	−	0.190007i
$791$	22.1213			0.786544
$792$	−6.63589	−	3.21152i	−0.235796	−	0.114116i
$793$	0.487552			0.0173135
$794$	4.30435	+	7.45535i	0.152756	+	0.264580i
$795$	−3.11055	+	13.5676i	−0.110320	+	0.481195i
$796$	−8.35592	+	14.4729i	−0.296168	+	0.512978i
$797$	4.37943	−	7.58540i	0.155127	−	0.268688i	−0.777978	−	0.628291i	$-0.783755\pi$
$797$	4.37943	−	7.58540i	0.155127	−	0.268688i	0.933105	+	0.359603i	$0.117088\pi$
$798$	−0.935893	+	4.08219i	−0.0331302	+	0.144508i
$799$	−8.45997	−	14.6531i	−0.299292	−	0.518389i
$800$	5.82429			0.205920
$801$	3.36305	−	2.28337i	0.118828	−	0.0806788i
$802$	14.4367			0.509777
$803$	−3.60478	−	6.24367i	−0.127210	−	0.220334i
$804$	−15.5422	−	14.4491i	−0.548132	−	0.509580i
$805$	1.84646	−	3.19817i	0.0650792	−	0.112721i
$806$	−0.129326	+	0.223999i	−0.00455530	+	0.00789001i
$807$	−29.7355	+	9.14066i	−1.04674	+	0.321767i
$808$	−17.1853	−	29.7657i	−0.604575	−	1.04716i
$809$	−30.7507			−1.08114			−0.540569	−	0.841300i	$-0.681791\pi$
$809$	−30.7507			−1.08114			−0.540569	+	0.841300i	$0.681791\pi$
$810$	−2.32485	+	5.85684i	−0.0816869	+	0.205788i
$811$	−8.03066			−0.281995			−0.140997	−	0.990010i	$-0.545031\pi$
$811$	−8.03066			−0.281995			−0.140997	+	0.990010i	$0.545031\pi$
$812$	−3.34304	−	5.79032i	−0.117318	−	0.203200i
$813$	−48.5457	+	14.9229i	−1.70257	+	0.523369i
$814$	2.40445	−	4.16463i	0.0842760	−	0.145970i
$815$	−11.3348	+	19.6324i	−0.397040	+	0.687693i
$816$	3.86102	+	3.58947i	0.135163	+	0.125656i
$817$	−2.69185	−	4.66243i	−0.0941761	−	0.163118i
$818$	17.3786			0.607629
$819$	0.867075	−	0.588706i	0.0302981	−	0.0205711i
$820$	6.46555			0.225787
$821$	17.6651	+	30.5969i	0.616517	+	1.06784i	0.990116	+	0.140249i	$0.0447903\pi$
$821$	17.6651	+	30.5969i	0.616517	+	1.06784i	−0.373599	+	0.927590i	$0.621876\pi$
$822$	0.207403	−	0.904652i	0.00723399	−	0.0315534i
$823$	14.9294	−	25.8586i	0.520408	−	0.901373i	−0.479311	−	0.877645i	$-0.659113\pi$
$823$	14.9294	−	25.8586i	0.520408	−	0.901373i	0.999718	−	0.0237274i	$-0.00755337\pi$
$824$	−1.06881	+	1.85124i	−0.0372339	+	0.0644910i
$825$	0.387052	−	1.68825i	0.0134754	−	0.0587773i
$826$	3.14653	+	5.44994i	0.109482	+	0.189628i
$827$	−9.81251			−0.341214			−0.170607	−	0.985339i	$-0.554573\pi$
$827$	−9.81251			−0.341214			−0.170607	+	0.985339i	$0.554573\pi$
$828$	12.7844	+	6.18718i	0.444290	+	0.215019i
$829$	−3.17106			−0.110135			−0.0550677	−	0.998483i	$-0.517537\pi$
$829$	−3.17106			−0.110135			−0.0550677	+	0.998483i	$0.517537\pi$
$830$	0.366179	+	0.634240i	0.0127102	+	0.0220148i
$831$	−0.508566	−	0.472797i	−0.0176420	−	0.0164012i
$832$	−0.219493	+	0.380173i	−0.00760954	+	0.0131801i
$833$	−6.57585	+	11.3897i	−0.227840	+	0.394630i
$834$	9.13438	−	2.80790i	0.316298	−	0.0972297i
$835$	−4.21060	−	7.29297i	−0.145714	−	0.252384i
$836$	4.42740			0.153125
$837$	2.34663	+	6.03056i	0.0811115	+	0.208447i
$838$	−9.84136			−0.339964
$839$	−3.23041	−	5.59524i	−0.111526	−	0.193169i	0.804860	−	0.593465i	$-0.202241\pi$
$839$	−3.23041	−	5.59524i	−0.111526	−	0.193169i	−0.916386	+	0.400296i	$0.868907\pi$
$840$	4.79134	−	1.47285i	0.165317	−	0.0508183i
$841$	7.42990	−	12.8690i	0.256204	−	0.443757i
$842$	−8.38999	+	14.5319i	−0.289138	+	0.500802i
$843$	−40.4035	−	37.5618i	−1.39157	−	1.29370i
$844$	15.3673	+	26.6170i	0.528965	+	0.916194i
$845$	12.9120			0.444186
$846$	−1.10423	−	15.1279i	−0.0379642	−	0.520107i
$847$	1.17768			0.0404657
$848$	5.21979	+	9.04094i	0.179248	+	0.310467i
$849$	9.89109	−	43.1431i	0.339461	−	1.48067i
$850$	0.820249	−	1.42071i	0.0281343	−	0.0487300i
$851$	−10.7687	+	18.6520i	−0.369147	+	0.639381i
$852$	2.41133	−	10.5178i	0.0826110	−	0.360334i
$853$	20.4548	+	35.4287i	0.700359	+	1.21306i	0.968341	+	0.249633i	$0.0803100\pi$
$853$	20.4548	+	35.4287i	0.700359	+	1.21306i	−0.267982	+	0.963424i	$0.586357\pi$
$854$	1.35523			0.0463752
$855$	−0.640447	−	8.77408i	−0.0219028	−	0.300067i
$856$	22.8832			0.782132
$857$	−22.5708	−	39.0938i	−0.771004	−	1.33542i	−0.937013	−	0.349294i	$-0.886421\pi$
$857$	−22.5708	−	39.0938i	−0.771004	−	1.33542i	0.166009	−	0.986124i	$-0.446912\pi$
$858$	0.263468	+	0.244937i	0.00899463	+	0.00836202i
$859$	−10.7884	+	18.6861i	−0.368096	+	0.637560i	−0.989268	−	0.146114i	$-0.953323\pi$
$859$	−10.7884	+	18.6861i	−0.368096	+	0.637560i	0.621172	+	0.783674i	$0.286657\pi$
$860$	−1.38590	+	2.40045i	−0.0472588	+	0.0818547i
$861$	8.34975	−	2.56671i	0.284559	−	0.0874732i
$862$	−6.86078	−	11.8832i	−0.233679	−	0.404744i
$863$	20.6987			0.704591			0.352296	−	0.935889i	$-0.385401\pi$
$863$	20.6987			0.704591			0.352296	+	0.935889i	$0.385401\pi$
$864$	10.9748	+	28.2039i	0.373370	+	0.959515i
$865$	−5.05889			−0.172008
$866$	2.63972	+	4.57213i	0.0897013	+	0.155367i
$867$	−19.0561	+	5.85782i	−0.647178	+	0.198942i
$868$	1.10715	−	1.91764i	0.0375791	−	0.0650889i
$869$	−4.40381	+	7.62762i	−0.149389	+	0.258749i
$870$	−3.33984	−	3.10494i	−0.113231	−	0.105267i
$871$	1.20363	+	2.08474i	0.0407834	+	0.0706388i
$872$	−13.1799			−0.446326
$873$	30.0924	+	14.5636i	1.01847	+	0.492902i
$874$	6.43827			0.217778
$875$	0.588842	+	1.01990i	0.0199065	+	0.0344791i
$876$	−4.21302	+	18.3764i	−0.142345	+	0.620882i
$877$	19.1881	−	33.2347i	0.647935	−	1.12226i	−0.335680	−	0.941976i	$-0.608966\pi$
$877$	19.1881	−	33.2347i	0.647935	−	1.12226i	0.983615	−	0.180280i	$-0.0577005\pi$
$878$	8.52329	−	14.7628i	0.287647	−	0.498219i
$879$	−4.59022	+	20.0217i	−0.154824	+	0.675316i
$880$	−0.649509	−	1.12498i	−0.0218950	−	0.0379232i
$881$	−19.8755			−0.669622			−0.334811	−	0.942285i	$-0.608672\pi$
$881$	−19.8755			−0.669622			−0.334811	+	0.942285i	$0.608672\pi$
$882$	−9.75421	+	6.62268i	−0.328441	+	0.222997i
$883$	21.7955			0.733476			0.366738	−	0.930324i	$-0.380475\pi$
$883$	21.7955			0.733476			0.366738	+	0.930324i	$0.380475\pi$
$884$	−0.524682	−	0.908775i	−0.0176470	−	0.0305654i
$885$	−9.68153	−	9.00060i	−0.325441	−	0.302552i
$886$	−0.0583822	+	0.101121i	−0.00196139	+	0.00339722i
$887$	3.37517	−	5.84597i	0.113327	−	0.196289i	−0.803783	−	0.594923i	$-0.797182\pi$
$887$	3.37517	−	5.84597i	0.113327	−	0.196289i	0.917110	+	0.398635i	$0.130516\pi$
$888$	−27.9435	+	8.58981i	−0.937722	+	0.288255i
$889$	−4.08478	−	7.07505i	−0.136999	−	0.237290i
$890$	−0.948699			−0.0318005
$891$	8.90460	−	1.30691i	0.298315	−	0.0437832i
$892$	−20.7278			−0.694019
$893$	10.5882	+	18.3393i	0.354320	+	0.613700i
$894$	−22.1063	+	6.79546i	−0.739345	+	0.227274i
$895$	−0.732647	+	1.26898i	−0.0244897	+	0.0424174i
$896$	6.24906	−	10.8237i	0.208766	−	0.361594i
$897$	−1.17998	−	1.09699i	−0.0393984	−	0.0366274i
$898$	4.44942	+	7.70663i	0.148479	+	0.257174i
$899$	−4.68296			−0.156185
$900$	−3.74726	+	2.54423i	−0.124909	+	0.0848075i
$901$	18.8300			0.627317
$902$	1.49918	+	2.59666i	0.0499173	+	0.0864593i
$903$	−0.836846	+	3.65017i	−0.0278485	+	0.121470i
$904$	23.0795	−	39.9748i	0.767612	−	1.32954i
$905$	2.43702	−	4.22104i	0.0810092	−	0.140312i
$906$	4.97769	−	21.7118i	0.165373	−	0.721326i
$907$	−2.64943	−	4.58895i	−0.0879730	−	0.152374i	0.818681	−	0.574248i	$-0.194706\pi$
$907$	−2.64943	−	4.58895i	−0.0879730	−	0.152374i	−0.906654	+	0.421875i	$0.861372\pi$
$908$	−25.2009			−0.836322
$909$	37.7692	+	18.2788i	1.25272	+	0.606271i
$910$	−0.244597			−0.00810832
$911$	19.9173	+	34.4977i	0.659888	+	1.14296i	0.980644	+	0.195798i	$0.0627296\pi$
$911$	19.9173	+	34.4977i	0.659888	+	1.14296i	−0.320756	+	0.947162i	$0.603937\pi$
$912$	−4.83231	−	4.49244i	−0.160014	−	0.148760i
$913$	0.522997	−	0.905858i	0.0173087	−	0.0299795i
$914$	−8.09108	+	14.0142i	−0.267629	+	0.463547i
$915$	−2.72111	+	0.836467i	−0.0899570	+	0.0276527i
$916$	11.6475	+	20.1740i	0.384843	+	0.666568i
$917$	−7.11554			−0.234976
$918$	8.42534	+	1.29495i	0.278078	+	0.0427397i
$919$	−41.9573			−1.38404			−0.692021	−	0.721877i	$-0.743280\pi$
$919$	−41.9573			−1.38404			−0.692021	+	0.721877i	$0.743280\pi$
$920$	−3.85288	−	6.67338i	−0.127026	−	0.220015i
$921$	29.8311	−	9.17005i	0.982967	−	0.302163i
$922$	−10.9281	+	18.9280i	−0.359897	+	0.623359i
$923$	−0.612029	+	1.06007i	−0.0201452	+	0.0348925i
$924$	−2.25553	−	2.09689i	−0.0742015	−	0.0689828i
$925$	−3.43418	−	5.94817i	−0.112915	−	0.195575i
$926$	14.5360			0.477681
$927$	−0.189980	−	2.60271i	−0.00623975	−	0.0854842i
$928$	−21.9013			−0.718947
$929$	2.60094	+	4.50496i	0.0853340	+	0.147803i	0.905533	−	0.424275i	$-0.139471\pi$
$929$	2.60094	+	4.50496i	0.0853340	+	0.147803i	−0.820199	+	0.572078i	$0.806138\pi$
$930$	0.337485	−	1.47205i	0.0110666	−	0.0482704i
$931$	8.23008	−	14.2549i	0.269730	−	0.467186i
$932$	−14.7917	+	25.6200i	−0.484519	+	0.839211i
$933$	1.04174	−	4.54388i	0.0341050	−	0.148760i
$934$	3.24583	+	5.62195i	0.106207	+	0.183956i
$935$	−2.34305			−0.0766260
$936$	−0.159203	−	2.18107i	−0.00520371	−	0.0712906i
$937$	23.9767			0.783285			0.391642	−	0.920118i	$-0.371907\pi$
$937$	23.9767			0.783285			0.391642	+	0.920118i	$0.371907\pi$
$938$	3.34569	+	5.79491i	0.109241	+	0.189210i
$939$	19.0523	+	17.7123i	0.621748	+	0.578019i
$940$	5.45132	−	9.44197i	0.177802	−	0.307963i
$941$	−11.3692	+	19.6921i	−0.370627	+	0.641944i	−0.989662	−	0.143419i	$-0.954190\pi$
$941$	−11.3692	+	19.6921i	−0.370627	+	0.641944i	0.619035	+	0.785363i	$0.287524\pi$
$942$	23.4040	−	7.19438i	0.762544	−	0.234405i
$943$	−6.71432	−	11.6295i	−0.218648	−	0.378710i
$944$	−9.91412			−0.322677
$945$	−3.82928	+	4.77326i	−0.124566	+	0.155274i
$946$	−1.28541			−0.0417922
$947$	18.5951	+	32.2077i	0.604261	+	1.04661i	0.992168	+	0.124912i	$0.0398648\pi$
$947$	18.5951	+	32.2077i	0.604261	+	1.04661i	−0.387907	+	0.921698i	$0.626802\pi$
$948$	22.0154	−	6.76753i	0.715028	−	0.219799i
$949$	1.06932	−	1.85212i	0.0347116	−	0.0601223i
$950$	−1.02659	+	1.77811i	−0.0333070	+	0.0576895i
$951$	20.0374	+	18.6281i	0.649756	+	0.604057i
$952$	−3.39043	−	5.87240i	−0.109885	−	0.190326i
$953$	6.74353			0.218444			0.109222	−	0.994017i	$-0.465164\pi$
$953$	6.74353			0.218444			0.109222	+	0.994017i	$0.465164\pi$
$954$	15.1945	+	7.35355i	0.491940	+	0.238080i
$955$	4.44989			0.143995
$956$	−21.8168	−	37.7879i	−0.705607	−	1.22215i
$957$	−1.45545	+	6.34841i	−0.0470480	+	0.205215i
$958$	−12.6375	+	21.8887i	−0.408298	+	0.707193i
$959$	0.450661	−	0.780568i	0.0145526	−	0.0252059i
$960$	0.572784	−	2.49838i	0.0184865	−	0.0806348i
$961$	14.7245	+	25.5037i	0.474985	+	0.822699i
$962$	1.42651			0.0459926
$963$	−23.1122	+	15.6922i	−0.744781	+	0.505674i
$964$	−41.2239			−1.32773
$965$	−7.03592	−	12.1866i	−0.226494	−	0.392299i
$966$	−3.27996	−	3.04927i	−0.105531	−	0.0981087i
$967$	−1.84522	+	3.19601i	−0.0593382	+	0.102777i	−0.894169	−	0.447731i	$-0.852232\pi$
$967$	−1.84522	+	3.19601i	−0.0593382	+	0.102777i	0.834830	+	0.550507i	$0.185566\pi$
$968$	1.22869	−	2.12816i	0.0394917	−	0.0684017i
$969$	−11.3755	+	3.49682i	−0.365433	+	0.112334i
$970$	−3.90117	−	6.75703i	−0.125259	−	0.216955i
$971$	35.8356			1.15002			0.575009	−	0.818147i	$-0.304998\pi$
$971$	35.8356			1.15002			0.575009	+	0.818147i	$0.304998\pi$
$972$	−19.3813	−	13.3518i	−0.621656	−	0.428260i
$973$	9.28027			0.297512
$974$	−8.07812	−	13.9917i	−0.258840	−	0.448323i
$975$	0.491114	−	0.150968i	0.0157282	−	0.00483485i
$976$	−1.06752	+	1.84900i	−0.0341706	+	0.0591852i
$977$	15.9580	−	27.6400i	0.510541	−	0.884283i	−0.489384	−	0.872068i	$-0.662778\pi$
$977$	15.9580	−	27.6400i	0.510541	−	0.884283i	0.999925	−	0.0122151i	$-0.00388829\pi$
$978$	20.1345	+	18.7184i	0.643830	+	0.598548i
$979$	0.677493	+	1.17345i	0.0216528	+	0.0375037i
$980$	−8.47451			−0.270708
$981$	13.3118	−	9.03810i	0.425012	−	0.288564i
$982$	20.2310			0.645596
$983$	−6.37670	−	11.0448i	−0.203385	−	0.352274i	0.746232	−	0.665686i	$-0.231861\pi$
$983$	−6.37670	−	11.0448i	−0.203385	−	0.352274i	−0.949617	+	0.313413i	$0.898528\pi$
$984$	4.07318	−	17.7665i	0.129848	−	0.566375i
$985$	−9.34946	+	16.1937i	−0.297898	+	0.515975i
$986$	−3.08442	+	5.34237i	−0.0982279	+	0.170136i
$987$	3.29166	−	14.3576i	0.104775	−	0.457008i
$988$	0.656671	+	1.13739i	0.0208915	+	0.0361851i
$989$	5.75690			0.183059
$990$	−1.89068	−	0.915018i	−0.0600898	−	0.0290812i
$991$	5.93839			0.188639			0.0943195	−	0.995542i	$-0.469932\pi$
$991$	5.93839			0.188639			0.0943195	+	0.995542i	$0.469932\pi$
$992$	−3.62665	−	6.28154i	−0.115146	−	0.199439i
$993$	−38.1623	−	35.4783i	−1.21104	−	1.12587i
$994$	−1.70124	+	2.94664i	−0.0539601	+	0.0934616i
$995$	−5.53451	+	9.58606i	−0.175456	+	0.303898i
$996$	−2.61456	+	0.803714i	−0.0828455	+	0.0254666i
$997$	0.646629	+	1.11999i	0.0204789	+	0.0354706i	0.876083	−	0.482160i	$-0.160148\pi$
$997$	0.646629	+	1.11999i	0.0204789	+	0.0354706i	−0.855604	+	0.517630i	$0.826814\pi$
$998$	−24.2403			−0.767313
$999$	22.3327	−	27.8381i	0.706575	−	0.880757i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.i.f.166.4	✓	22
3.2	odd	2		1485.2.i.f.496.8		22
9.2	odd	6		1485.2.i.f.991.8		22
9.4	even	3		4455.2.a.u.1.8		11
9.5	odd	6		4455.2.a.v.1.4		11
9.7	even	3	inner	495.2.i.f.331.4	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
495.2.i.f.166.4	✓	22	1.1	even	1	trivial
495.2.i.f.331.4	yes	22	9.7	even	3	inner
1485.2.i.f.496.8		22	3.2	odd	2
1485.2.i.f.991.8		22	9.2	odd	6
4455.2.a.u.1.8		11	9.4	even	3
4455.2.a.v.1.4		11	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.350077 - 0.606351i) q^{2} +(1.65559 - 0.508929i) q^{3} +(0.754892 - 1.30751i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.888175 - 0.825707i) q^{6} +(-0.588842 - 1.01990i) q^{7} -2.45739 q^{8} +(2.48198 - 1.68516i) q^{9} +O(q^{10})\)	\(q+(-0.350077 - 0.606351i) q^{2} +(1.65559 - 0.508929i) q^{3} +(0.754892 - 1.30751i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.888175 - 0.825707i) q^{6} +(-0.588842 - 1.01990i) q^{7} -2.45739 q^{8} +(2.48198 - 1.68516i) q^{9} -0.700154 q^{10} +(0.500000 + 0.866025i) q^{11} +(0.584365 - 2.54890i) q^{12} +(-0.148320 + 0.256897i) q^{13} +(-0.412280 + 0.714090i) q^{14} +(0.387052 - 1.68825i) q^{15} +(-0.649509 - 1.12498i) q^{16} -2.34305 q^{17} +(-1.89068 - 0.915018i) q^{18} +2.93247 q^{19} +(-0.754892 - 1.30751i) q^{20} +(-1.49394 - 1.38887i) q^{21} +(0.350077 - 0.606351i) q^{22} +(-1.56787 + 2.71564i) q^{23} +(-4.06844 + 1.25064i) q^{24} +(-0.500000 - 0.866025i) q^{25} +0.207693 q^{26} +(3.25153 - 4.05309i) q^{27} -1.77805 q^{28} +(1.88017 + 3.25655i) q^{29} +(-1.15917 + 0.356328i) q^{30} +(-0.622676 + 1.07851i) q^{31} +(-2.91215 + 5.04398i) q^{32} +(1.26854 + 1.17932i) q^{33} +(0.820249 + 1.42071i) q^{34} -1.17768 q^{35} +(-0.329734 - 4.51734i) q^{36} +6.86836 q^{37} +(-1.02659 - 1.77811i) q^{38} +(-0.114815 + 0.500802i) q^{39} +(-1.22869 + 2.12816i) q^{40} +(-2.14122 + 3.70870i) q^{41} +(-0.319148 + 1.39206i) q^{42} +(-0.917946 - 1.58993i) q^{43} +1.50978 q^{44} +(-0.218398 - 2.99204i) q^{45} +2.19551 q^{46} +(3.61066 + 6.25385i) q^{47} +(-1.64786 - 1.53196i) q^{48} +(2.80653 - 4.86105i) q^{49} +(-0.350077 + 0.606351i) q^{50} +(-3.87914 + 1.19245i) q^{51} +(0.223931 + 0.387859i) q^{52} -8.03651 q^{53} +(-3.59588 - 0.552677i) q^{54} +1.00000 q^{55} +(1.44701 + 2.50630i) q^{56} +(4.85499 - 1.49242i) q^{57} +(1.31641 - 2.28009i) q^{58} +(3.81600 - 6.60951i) q^{59} +(-1.91523 - 1.78052i) q^{60} +(-0.821792 - 1.42339i) q^{61} +0.871938 q^{62} +(-3.18020 - 1.53909i) q^{63} +1.47986 q^{64} +(0.148320 + 0.256897i) q^{65} +(0.270996 - 1.18204i) q^{66} +(4.05754 - 7.02787i) q^{67} +(-1.76875 + 3.06357i) q^{68} +(-1.21370 + 5.29393i) q^{69} +(0.412280 + 0.714090i) q^{70} +4.12642 q^{71} +(-6.09920 + 4.14109i) q^{72} -7.20957 q^{73} +(-2.40445 - 4.16463i) q^{74} +(-1.26854 - 1.17932i) q^{75} +(2.21370 - 3.83425i) q^{76} +(0.588842 - 1.01990i) q^{77} +(0.343856 - 0.105701i) q^{78} +(4.40381 + 7.62762i) q^{79} -1.29902 q^{80} +(3.32048 - 8.36507i) q^{81} +2.99836 q^{82} +(-0.522997 - 0.905858i) q^{83} +(-2.94373 + 0.904900i) q^{84} +(-1.17153 + 2.02914i) q^{85} +(-0.642704 + 1.11320i) q^{86} +(4.77016 + 4.43466i) q^{87} +(-1.22869 - 2.12816i) q^{88} +1.35499 q^{89} +(-1.73777 + 1.17987i) q^{90} +0.349348 q^{91} +(2.36715 + 4.10003i) q^{92} +(-0.482016 + 2.10247i) q^{93} +(2.52802 - 4.37866i) q^{94} +(1.46624 - 2.53960i) q^{95} +(-2.25430 + 9.83286i) q^{96} +(5.57188 + 9.65078i) q^{97} -3.93000 q^{98} +(2.70038 + 1.30688i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 3 q^{2} - 13 q^{4} + 11 q^{5} + 13 q^{6} - 3 q^{7} - 6 q^{8} - 4 q^{9}+O(q^{10}) \) 22 * q + 3 * q^2 - 13 * q^4 + 11 * q^5 + 13 * q^6 - 3 * q^7 - 6 * q^8 - 4 * q^9	\( 22 q + 3 q^{2} - 13 q^{4} + 11 q^{5} + 13 q^{6} - 3 q^{7} - 6 q^{8} - 4 q^{9} + 6 q^{10} + 11 q^{11} - 9 q^{12} - 9 q^{13} + 5 q^{14} - 17 q^{16} - 28 q^{17} - 7 q^{18} - 6 q^{19} + 13 q^{20} - 8 q^{21} - 3 q^{22} + 16 q^{23} - 18 q^{24} - 11 q^{25} - 28 q^{26} - 18 q^{27} - 12 q^{28} + 16 q^{29} + 11 q^{30} - 4 q^{31} + 34 q^{32} + 39 q^{34} - 6 q^{35} - 55 q^{36} + 40 q^{37} + 4 q^{38} - 4 q^{39} - 3 q^{40} + 26 q^{41} + 59 q^{42} + 3 q^{43} - 26 q^{44} - 2 q^{45} - 16 q^{46} + 8 q^{47} + 28 q^{48} - 10 q^{49} + 3 q^{50} + 7 q^{51} - 31 q^{52} - 52 q^{53} - 20 q^{54} + 22 q^{55} + 30 q^{56} + 3 q^{57} - 6 q^{58} + 10 q^{59} + 25 q^{61} + 40 q^{62} - 9 q^{63} + 26 q^{64} + 9 q^{65} + 2 q^{66} - 13 q^{67} + 20 q^{68} + 28 q^{69} - 5 q^{70} - 48 q^{71} - 114 q^{72} + 18 q^{73} + 10 q^{74} + 25 q^{76} + 3 q^{77} + 13 q^{78} + q^{79} - 34 q^{80} - 4 q^{81} + 34 q^{82} - 2 q^{83} + 89 q^{84} - 14 q^{85} + 15 q^{86} - 31 q^{87} - 3 q^{88} - 44 q^{89} + 13 q^{90} - 2 q^{91} + 44 q^{92} + 29 q^{93} + 36 q^{94} - 3 q^{95} + 42 q^{96} - 33 q^{97} - 38 q^{98} - 2 q^{99}+O(q^{100}) \) 22 * q + 3 * q^2 - 13 * q^4 + 11 * q^5 + 13 * q^6 - 3 * q^7 - 6 * q^8 - 4 * q^9 + 6 * q^10 + 11 * q^11 - 9 * q^12 - 9 * q^13 + 5 * q^14 - 17 * q^16 - 28 * q^17 - 7 * q^18 - 6 * q^19 + 13 * q^20 - 8 * q^21 - 3 * q^22 + 16 * q^23 - 18 * q^24 - 11 * q^25 - 28 * q^26 - 18 * q^27 - 12 * q^28 + 16 * q^29 + 11 * q^30 - 4 * q^31 + 34 * q^32 + 39 * q^34 - 6 * q^35 - 55 * q^36 + 40 * q^37 + 4 * q^38 - 4 * q^39 - 3 * q^40 + 26 * q^41 + 59 * q^42 + 3 * q^43 - 26 * q^44 - 2 * q^45 - 16 * q^46 + 8 * q^47 + 28 * q^48 - 10 * q^49 + 3 * q^50 + 7 * q^51 - 31 * q^52 - 52 * q^53 - 20 * q^54 + 22 * q^55 + 30 * q^56 + 3 * q^57 - 6 * q^58 + 10 * q^59 + 25 * q^61 + 40 * q^62 - 9 * q^63 + 26 * q^64 + 9 * q^65 + 2 * q^66 - 13 * q^67 + 20 * q^68 + 28 * q^69 - 5 * q^70 - 48 * q^71 - 114 * q^72 + 18 * q^73 + 10 * q^74 + 25 * q^76 + 3 * q^77 + 13 * q^78 + q^79 - 34 * q^80 - 4 * q^81 + 34 * q^82 - 2 * q^83 + 89 * q^84 - 14 * q^85 + 15 * q^86 - 31 * q^87 - 3 * q^88 - 44 * q^89 + 13 * q^90 - 2 * q^91 + 44 * q^92 + 29 * q^93 + 36 * q^94 - 3 * q^95 + 42 * q^96 - 33 * q^97 - 38 * q^98 - 2 * q^99

Introduction

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