LMFDB - Embedded newform 315.2.bl.j.146.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(41,315)]

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([5, 0, 3]))

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

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

chi := DirichletCharacter("315.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bl (of order $6$, 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:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			146.3
Character	$\chi$	$=$	315.146
Dual form			315.2.bl.j.41.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41561 - 0.817305i) q^{2} +(1.73161 + 0.0392468i) q^{3} +(0.335974 + 0.581925i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.41921 - 1.47081i) q^{6} +(2.11432 + 1.59049i) q^{7} +2.17085i q^{8} +(2.99692 + 0.135920i) q^{9} +O(q^{10})$	\(q+(-1.41561 - 0.817305i) q^{2} +(1.73161 + 0.0392468i) q^{3} +(0.335974 + 0.581925i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.41921 - 1.47081i) q^{6} +(2.11432 + 1.59049i) q^{7} +2.17085i q^{8} +(2.99692 + 0.135920i) q^{9} +1.63461i q^{10} +(1.25981 + 0.727354i) q^{11} +(0.558937 + 1.02085i) q^{12} +(4.17130 - 2.40830i) q^{13} +(-1.69314 - 3.97956i) q^{14} +(-0.831814 - 1.51924i) q^{15} +(2.44619 - 4.23693i) q^{16} -6.37049 q^{17} +(-4.13139 - 2.64181i) q^{18} +1.12941i q^{19} +(0.335974 - 0.581925i) q^{20} +(3.59874 + 2.83709i) q^{21} +(-1.18894 - 2.05931i) q^{22} +(7.62029 - 4.39958i) q^{23} +(-0.0851986 + 3.75905i) q^{24} +(-0.500000 + 0.866025i) q^{25} -7.87327 q^{26} +(5.18415 + 0.352979i) q^{27} +(-0.215191 + 1.76474i) q^{28} +(-3.63049 - 2.09607i) q^{29} +(-0.0641531 + 2.83050i) q^{30} +(-6.94505 + 4.00973i) q^{31} +(-3.16571 + 1.82772i) q^{32} +(2.15296 + 1.30893i) q^{33} +(9.01815 + 5.20663i) q^{34} +(0.320249 - 2.62630i) q^{35} +(0.927793 + 1.78965i) q^{36} +4.26717 q^{37} +(0.923070 - 1.59880i) q^{38} +(7.31757 - 4.00652i) q^{39} +(1.88001 - 1.08542i) q^{40} +(-4.21764 - 7.30517i) q^{41} +(-2.77566 - 6.95749i) q^{42} +(3.35714 - 5.81474i) q^{43} +0.977490i q^{44} +(-1.38075 - 2.66337i) q^{45} -14.3832 q^{46} +(0.739160 - 1.28026i) q^{47} +(4.40213 - 7.24068i) q^{48} +(1.94067 + 6.72561i) q^{49} +(1.41561 - 0.817305i) q^{50} +(-11.0312 - 0.250021i) q^{51} +(2.80290 + 1.61826i) q^{52} +9.46524i q^{53} +(-7.05026 - 4.73671i) q^{54} -1.45471i q^{55} +(-3.45271 + 4.58985i) q^{56} +(-0.0443256 + 1.95569i) q^{57} +(3.42625 + 5.93444i) q^{58} +(1.63609 + 2.83379i) q^{59} +(0.604614 - 0.994478i) q^{60} +(-6.44991 - 3.72386i) q^{61} +13.1087 q^{62} +(6.12026 + 5.05396i) q^{63} -3.80954 q^{64} +(-4.17130 - 2.40830i) q^{65} +(-1.97796 - 3.61257i) q^{66} +(-0.282624 - 0.489519i) q^{67} +(-2.14032 - 3.70715i) q^{68} +(13.3680 - 7.31926i) q^{69} +(-2.59983 + 3.45608i) q^{70} +15.7089i q^{71} +(-0.295061 + 6.50585i) q^{72} +6.61409i q^{73} +(-6.04067 - 3.48758i) q^{74} +(-0.899792 + 1.47999i) q^{75} +(-0.657230 + 0.379452i) q^{76} +(1.50679 + 3.54158i) q^{77} +(-13.6334 - 0.309000i) q^{78} +(-3.80625 + 6.59262i) q^{79} -4.89238 q^{80} +(8.96305 + 0.814682i) q^{81} +13.7884i q^{82} +(-1.62896 + 2.82144i) q^{83} +(-0.441886 + 3.04738i) q^{84} +(3.18524 + 5.51701i) q^{85} +(-9.50483 + 5.48762i) q^{86} +(-6.20432 - 3.77204i) q^{87} +(-1.57897 + 2.73486i) q^{88} -3.18080 q^{89} +(-0.222176 + 4.89879i) q^{90} +(12.6498 + 1.54251i) q^{91} +(5.12044 + 2.95629i) q^{92} +(-12.1835 + 6.67070i) q^{93} +(-2.09273 + 1.20824i) q^{94} +(0.978095 - 0.564704i) q^{95} +(-5.55349 + 3.04065i) q^{96} +(-10.0401 - 5.79666i) q^{97} +(2.74964 - 11.1070i) q^{98} +(3.67670 + 2.35106i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{2} + 5 q^{3} + 18 q^{4} - 12 q^{5} + q^{6} + 9 q^{7} + q^{9}+O(q^{10}) $ 24 * q + 6 * q^2 + 5 * q^3 + 18 * q^4 - 12 * q^5 + q^6 + 9 * q^7 + q^9	$ 24 q + 6 q^{2} + 5 q^{3} + 18 q^{4} - 12 q^{5} + q^{6} + 9 q^{7} + q^{9} + 9 q^{11} - 18 q^{12} + 3 q^{13} + 18 q^{14} + 2 q^{15} - 18 q^{16} + 18 q^{17} + 2 q^{18} + 18 q^{20} + 8 q^{21} - 9 q^{22} + 9 q^{23} - 7 q^{24} - 12 q^{25} - 18 q^{26} - 4 q^{27} - 9 q^{28} + 9 q^{29} - 5 q^{30} - 42 q^{31} + 18 q^{32} + 13 q^{33} - 39 q^{34} - 9 q^{35} - 21 q^{36} - 12 q^{38} - 21 q^{39} - 6 q^{40} - 33 q^{41} - 65 q^{42} + 18 q^{43} + q^{45} - 30 q^{46} - 17 q^{48} + 9 q^{49} - 6 q^{50} - 12 q^{51} + 129 q^{52} + 52 q^{54} - 9 q^{56} + 6 q^{57} - 15 q^{58} + 12 q^{59} + 15 q^{60} - 15 q^{61} + 12 q^{62} + 46 q^{63} - 60 q^{64} - 3 q^{65} + 29 q^{66} - 15 q^{67} + 9 q^{68} + 61 q^{69} - 9 q^{70} + 61 q^{72} - 18 q^{74} - 7 q^{75} + 54 q^{76} - 45 q^{77} - 66 q^{78} + 21 q^{79} + 36 q^{80} + q^{81} - 30 q^{83} + 15 q^{84} - 9 q^{85} - 102 q^{86} + 10 q^{87} - 9 q^{88} + 102 q^{89} - 37 q^{90} + 42 q^{91} - 3 q^{92} - 6 q^{93} - 156 q^{94} - 18 q^{95} - 42 q^{96} - 45 q^{97} + 3 q^{98} + 23 q^{99}+O(q^{100}) $ 24 * q + 6 * q^2 + 5 * q^3 + 18 * q^4 - 12 * q^5 + q^6 + 9 * q^7 + q^9 + 9 * q^11 - 18 * q^12 + 3 * q^13 + 18 * q^14 + 2 * q^15 - 18 * q^16 + 18 * q^17 + 2 * q^18 + 18 * q^20 + 8 * q^21 - 9 * q^22 + 9 * q^23 - 7 * q^24 - 12 * q^25 - 18 * q^26 - 4 * q^27 - 9 * q^28 + 9 * q^29 - 5 * q^30 - 42 * q^31 + 18 * q^32 + 13 * q^33 - 39 * q^34 - 9 * q^35 - 21 * q^36 - 12 * q^38 - 21 * q^39 - 6 * q^40 - 33 * q^41 - 65 * q^42 + 18 * q^43 + q^45 - 30 * q^46 - 17 * q^48 + 9 * q^49 - 6 * q^50 - 12 * q^51 + 129 * q^52 + 52 * q^54 - 9 * q^56 + 6 * q^57 - 15 * q^58 + 12 * q^59 + 15 * q^60 - 15 * q^61 + 12 * q^62 + 46 * q^63 - 60 * q^64 - 3 * q^65 + 29 * q^66 - 15 * q^67 + 9 * q^68 + 61 * q^69 - 9 * q^70 + 61 * q^72 - 18 * q^74 - 7 * q^75 + 54 * q^76 - 45 * q^77 - 66 * q^78 + 21 * q^79 + 36 * q^80 + q^81 - 30 * q^83 + 15 * q^84 - 9 * q^85 - 102 * q^86 + 10 * q^87 - 9 * q^88 + 102 * q^89 - 37 * q^90 + 42 * q^91 - 3 * q^92 - 6 * q^93 - 156 * q^94 - 18 * q^95 - 42 * q^96 - 45 * q^97 + 3 * q^98 + 23 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.41561	−	0.817305i	−1.00099	−	0.577922i	−0.0924489	−	0.995717i	$-0.529469\pi$
$2$	−1.41561	−	0.817305i	−1.00099	−	0.577922i	−0.908541	+	0.417796i	$0.862803\pi$
$3$	1.73161	+	0.0392468i	0.999743	+	0.0226591i
$3$	1.73161	+	0.0392468i	0.999743	+	0.0226591i
$4$	0.335974	+	0.581925i	0.167987	+	0.290962i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−2.41921	−	1.47081i	−0.987638	−	0.600455i
$7$	2.11432	+	1.59049i	0.799136	+	0.601150i
$7$	2.11432	+	1.59049i	0.799136	+	0.601150i
$8$			2.17085i			0.767510i
$9$	2.99692	+	0.135920i	0.998973	+	0.0453066i
$10$			1.63461i			0.516909i
$11$	1.25981	+	0.727354i	0.379848	+	0.219306i	0.677752	−	0.735290i	$-0.262954\pi$
$11$	1.25981	+	0.727354i	0.379848	+	0.219306i	−0.297904	+	0.954596i	$0.596288\pi$
$12$	0.558937	+	1.02085i	0.161351	+	0.294694i
$13$	4.17130	−	2.40830i	1.15691	−	0.667943i	0.206350	−	0.978478i	$-0.433842\pi$
$13$	4.17130	−	2.40830i	1.15691	−	0.667943i	0.950562	+	0.310535i	$0.100508\pi$
$14$	−1.69314	−	3.97956i	−0.452510	−	1.06358i
$15$	−0.831814	−	1.51924i	−0.214774	−	0.392266i
$16$	2.44619	−	4.23693i	0.611548	−	1.05923i
$17$	−6.37049			−1.54507			−0.772535	−	0.634972i	$-0.781012\pi$
$17$	−6.37049			−1.54507			−0.772535	+	0.634972i	$0.781012\pi$
$18$	−4.13139	−	2.64181i	−0.973778	−	0.622680i
$19$			1.12941i			0.259104i	0.991573	+	0.129552i	$0.0413539\pi$
$19$			1.12941i			0.259104i	−0.991573	+	0.129552i	$0.958646\pi$
$20$	0.335974	−	0.581925i	0.0751262	−	0.130122i
$21$	3.59874	+	2.83709i	0.785310	+	0.619103i
$22$	−1.18894	−	2.05931i	−0.253483	−	0.439045i
$23$	7.62029	−	4.39958i	1.58894	−	0.917375i	0.595458	−	0.803386i	$-0.296971\pi$
$23$	7.62029	−	4.39958i	1.58894	−	0.917375i	0.993482	−	0.113988i	$-0.0363627\pi$
$24$	−0.0851986	+	3.75905i	−0.0173911	+	0.767313i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−7.87327			−1.54408
$27$	5.18415	+	0.352979i	0.997690	+	0.0679308i
$28$	−0.215191	+	1.76474i	−0.0406673	+	0.333504i
$29$	−3.63049	−	2.09607i	−0.674165	−	0.389230i	0.123488	−	0.992346i	$-0.460592\pi$
$29$	−3.63049	−	2.09607i	−0.674165	−	0.389230i	−0.797653	+	0.603117i	$0.793925\pi$
$30$	−0.0641531	+	2.83050i	−0.0117127	+	0.516776i
$31$	−6.94505	+	4.00973i	−1.24737	+	0.720169i	−0.970584	−	0.240763i	$-0.922602\pi$
$31$	−6.94505	+	4.00973i	−1.24737	+	0.720169i	−0.276785	+	0.960932i	$0.589269\pi$
$32$	−3.16571	+	1.82772i	−0.559623	+	0.323099i
$33$	2.15296	+	1.30893i	0.374782	+	0.227856i
$34$	9.01815	+	5.20663i	1.54660	+	0.892930i
$35$	0.320249	−	2.62630i	0.0541319	−	0.443925i
$36$	0.927793	+	1.78965i	0.154632	+	0.298274i
$37$	4.26717			0.701519			0.350760	−	0.936466i	$-0.385923\pi$
$37$	4.26717			0.701519			0.350760	+	0.936466i	$0.385923\pi$
$38$	0.923070	−	1.59880i	0.149742	−	0.259360i
$39$	7.31757	−	4.00652i	1.17175	−	0.641557i
$40$	1.88001	−	1.08542i	0.297255	−	0.171620i
$41$	−4.21764	−	7.30517i	−0.658685	−	1.14088i	−0.980956	−	0.194229i	$-0.937780\pi$
$41$	−4.21764	−	7.30517i	−0.658685	−	1.14088i	0.322271	−	0.946647i	$-0.395554\pi$
$42$	−2.77566	−	6.95749i	−0.428294	−	1.07356i
$43$	3.35714	−	5.81474i	0.511960	−	0.886740i	−0.487944	−	0.872875i	$-0.662253\pi$
$43$	3.35714	−	5.81474i	0.511960	−	0.886740i	0.999904	−	0.0138652i	$-0.00441358\pi$
$44$			0.977490i			0.147362i
$45$	−1.38075	−	2.66337i	−0.205830	−	0.397031i
$46$	−14.3832			−2.12068
$47$	0.739160	−	1.28026i	0.107818	−	0.186745i	−0.807068	−	0.590458i	$-0.798947\pi$
$47$	0.739160	−	1.28026i	0.107818	−	0.186745i	0.914886	+	0.403713i	$0.132280\pi$
$48$	4.40213	−	7.24068i	0.635392	−	1.04510i
$49$	1.94067	+	6.72561i	0.277238	+	0.960801i
$50$	1.41561	−	0.817305i	0.200198	−	0.115584i
$51$	−11.0312	−	0.250021i	−1.54467	−	0.0350099i
$52$	2.80290	+	1.61826i	0.388693	+	0.224412i
$53$			9.46524i			1.30015i	0.759870	+	0.650075i	$0.225263\pi$
$53$			9.46524i			1.30015i	−0.759870	+	0.650075i	$0.774737\pi$
$54$	−7.05026	−	4.73671i	−0.959419	−	0.644585i
$55$		−	1.45471i		−	0.196153i
$56$	−3.45271	+	4.58985i	−0.461388	+	0.613345i
$57$	−0.0443256	+	1.95569i	−0.00587106	+	0.259037i
$58$	3.42625	+	5.93444i	0.449888	+	0.779230i
$59$	1.63609	+	2.83379i	0.213001	+	0.368928i	0.952652	−	0.304062i	$-0.0983431\pi$
$59$	1.63609	+	2.83379i	0.213001	+	0.368928i	−0.739652	+	0.672990i	$0.765010\pi$
$60$	0.604614	−	0.994478i	0.0780553	−	0.128387i
$61$	−6.44991	−	3.72386i	−0.825827	−	0.476791i	0.0265950	−	0.999646i	$-0.491534\pi$
$61$	−6.44991	−	3.72386i	−0.825827	−	0.476791i	−0.852422	+	0.522855i	$0.824867\pi$
$62$	13.1087			1.66480
$63$	6.12026	+	5.05396i	0.771080	+	0.636739i
$64$	−3.80954			−0.476192
$65$	−4.17130	−	2.40830i	−0.517386	−	0.298713i
$66$	−1.97796	−	3.61257i	−0.243469	−	0.444676i
$67$	−0.282624	−	0.489519i	−0.0345280	−	0.0598042i	0.848245	−	0.529604i	$-0.177659\pi$
$67$	−0.282624	−	0.489519i	−0.0345280	−	0.0598042i	−0.882773	+	0.469800i	$0.844326\pi$
$68$	−2.14032	−	3.70715i	−0.259552	−	0.449557i
$69$	13.3680	−	7.31926i	1.60932	−	0.881135i
$70$	−2.59983	+	3.45608i	−0.310740	+	0.413081i
$71$			15.7089i			1.86430i	0.362070	+	0.932151i	$0.382070\pi$
$71$			15.7089i			1.86430i	−0.362070	+	0.932151i	$0.617930\pi$
$72$	−0.295061	+	6.50585i	−0.0347733	+	0.766722i
$73$			6.61409i			0.774120i	0.922054	+	0.387060i	$0.126509\pi$
$73$			6.61409i			0.774120i	−0.922054	+	0.387060i	$0.873491\pi$
$74$	−6.04067	−	3.48758i	−0.702214	−	0.405423i
$75$	−0.899792	+	1.47999i	−0.103899	+	0.170895i
$76$	−0.657230	+	0.379452i	−0.0753894	+	0.0435261i
$77$	1.50679	+	3.54158i	0.171715	+	0.403601i
$78$	−13.6334	−	0.309000i	−1.54368	−	0.0349874i
$79$	−3.80625	+	6.59262i	−0.428236	+	0.741727i	−0.996717	−	0.0809697i	$-0.974198\pi$
$79$	−3.80625	+	6.59262i	−0.428236	+	0.741727i	0.568480	+	0.822697i	$0.307532\pi$
$80$	−4.89238			−0.546985
$81$	8.96305	+	0.814682i	0.995895	+	0.0905202i
$82$			13.7884i			1.52267i
$83$	−1.62896	+	2.82144i	−0.178802	+	0.309694i	−0.941470	−	0.337096i	$-0.890555\pi$
$83$	−1.62896	+	2.82144i	−0.178802	+	0.309694i	0.762669	+	0.646789i	$0.223889\pi$
$84$	−0.441886	+	3.04738i	−0.0482137	+	0.332497i
$85$	3.18524	+	5.51701i	0.345488	+	0.598403i
$86$	−9.50483	+	5.48762i	−1.02493	+	0.591745i
$87$	−6.20432	−	3.77204i	−0.665173	−	0.404406i
$88$	−1.57897	+	2.73486i	−0.168319	+	0.291537i
$89$	−3.18080			−0.337164			−0.168582	−	0.985688i	$-0.553919\pi$
$89$	−3.18080			−0.337164			−0.168582	+	0.985688i	$0.553919\pi$
$90$	−0.222176	+	4.89879i	−0.0234194	+	0.516378i
$91$	12.6498	+	1.54251i	1.32606	+	0.161699i
$92$	5.12044	+	2.95629i	0.533843	+	0.308214i
$93$	−12.1835	+	6.67070i	−1.26337	+	0.691719i
$94$	−2.09273	+	1.20824i	−0.215849	+	0.124620i
$95$	0.978095	−	0.564704i	0.100350	−	0.0579374i
$96$	−5.55349	+	3.04065i	−0.566801	+	0.310335i
$97$	−10.0401	−	5.79666i	−1.01942	−	0.588562i	−0.105483	−	0.994421i	$-0.533639\pi$
$97$	−10.0401	−	5.79666i	−1.01942	−	0.588562i	−0.913935	+	0.405860i	$0.866972\pi$
$98$	2.74964	−	11.1070i	0.277756	−	1.12197i
$99$	3.67670	+	2.35106i	0.369522	+	0.236290i
$100$	−0.671949			−0.0671949
$101$	−3.36000	+	5.81970i	−0.334333	+	0.579082i	−0.983356	−	0.181687i	$-0.941844\pi$
$101$	−3.36000	+	5.81970i	−0.334333	+	0.579082i	0.649023	+	0.760768i	$0.275178\pi$
$102$	15.4115	+	9.36977i	1.52597	+	0.927745i
$103$	−6.37897	+	3.68290i	−0.628539	+	0.362887i	−0.780186	−	0.625548i	$-0.784876\pi$
$103$	−6.37897	+	3.68290i	−0.628539	+	0.362887i	0.151647	+	0.988435i	$0.451542\pi$
$104$	5.22805	+	9.05525i	0.512653	+	0.887941i
$105$	0.657619	−	4.53514i	0.0641770	−	0.442585i
$106$	7.73599	−	13.3991i	0.751385	−	1.30144i
$107$		−	4.77802i		−	0.461909i	−0.972965	−	0.230954i	$-0.925815\pi$
$107$		−	4.77802i		−	0.461909i	0.972965	−	0.230954i	$-0.0741848\pi$
$108$	1.53633	+	3.13538i	0.147834	+	0.301702i
$109$	−15.5253			−1.48705			−0.743525	−	0.668708i	$-0.766848\pi$
$109$	−15.5253			−1.48705			−0.743525	+	0.668708i	$0.766848\pi$
$110$	−1.18894	+	2.05931i	−0.113361	+	0.196347i
$111$	7.38907	+	0.167473i	0.701339	+	0.0158958i
$112$	11.9108	−	5.06756i	1.12547	−	0.478839i
$113$	7.57031	−	4.37072i	0.712155	−	0.411163i	−0.0997035	−	0.995017i	$-0.531789\pi$
$113$	7.57031	−	4.37072i	0.712155	−	0.411163i	0.811858	+	0.583854i	$0.198456\pi$
$114$	1.66114	−	2.73227i	0.155580	−	0.255901i
$115$	−7.62029	−	4.39958i	−0.710596	−	0.410263i
$116$		−	2.81690i		−	0.261542i
$117$	12.8284	−	6.65053i	1.18599	−	0.614841i
$118$		−	5.34873i		−	0.492391i
$119$	−13.4692	−	10.1322i	−1.23472	−	0.928819i
$120$	3.29803	−	1.80574i	0.301068	−	0.164841i
$121$	−4.44191	−	7.69362i	−0.403810	−	0.699420i
$122$	6.08705	+	10.5431i	0.551096	+	0.954526i
$123$	−7.01659	−	12.8152i	−0.632665	−	1.15551i
$124$	−4.66672	−	2.69433i	−0.419084	−	0.241958i
$125$	1.00000			0.0894427
$126$	−4.53329	−	12.1566i	−0.403858	−	1.08299i
$127$	−11.1422			−0.988708			−0.494354	−	0.869261i	$-0.664595\pi$
$127$	−11.1422			−0.988708			−0.494354	+	0.869261i	$0.664595\pi$
$128$	11.7243	+	6.76900i	1.03629	+	0.598301i
$129$	6.04146	−	9.93709i	0.531921	−	0.874912i
$130$	3.93664	+	6.81845i	0.345266	+	0.598018i
$131$	0.968463	+	1.67743i	0.0846150	+	0.146557i	0.905227	−	0.424928i	$-0.139701\pi$
$131$	0.968463	+	1.67743i	0.0846150	+	0.146557i	−0.820612	+	0.571486i	$0.806367\pi$
$132$	−0.0383633	+	1.69263i	−0.00333910	+	0.147324i
$133$	−1.79631	+	2.38792i	−0.155760	+	0.207059i
$134$			0.923959i			0.0798179i
$135$	−2.28639	−	4.66609i	−0.196781	−	0.401593i
$136$		−	13.8293i		−	1.18586i
$137$	10.8085	+	6.24029i	0.923433	+	0.533144i	0.884729	−	0.466106i	$-0.154344\pi$
$137$	10.8085	+	6.24029i	0.923433	+	0.533144i	0.0387043	+	0.999251i	$0.487677\pi$
$138$	−24.9060	−	0.564493i	−2.12014	−	0.0480528i
$139$	−4.57102	+	2.63908i	−0.387709	+	0.223844i	−0.681167	−	0.732128i	$-0.738527\pi$
$139$	−4.57102	+	2.63908i	−0.387709	+	0.223844i	0.293458	+	0.955972i	$0.405194\pi$
$140$	1.63590	−	0.696008i	0.138259	−	0.0588234i
$141$	1.33018	−	2.18790i	0.112021	−	0.184254i
$142$	12.8390	−	22.2377i	1.07742	−	1.86615i
$143$	7.00676			0.585935
$144$	7.90692	−	12.3652i	0.658910	−	1.03044i
$145$			4.19213i			0.348137i
$146$	5.40573	−	9.36299i	0.447381	−	0.774887i
$147$	3.09651	+	11.7223i	0.255396	+	0.966837i
$148$	1.43366	+	2.48317i	0.117846	+	0.204116i
$149$	8.13399	−	4.69616i	0.666362	−	0.384724i	−0.128335	−	0.991731i	$-0.540963\pi$
$149$	8.13399	−	4.69616i	0.666362	−	0.384724i	0.794697	+	0.607007i	$0.207630\pi$
$150$	2.48336	−	1.35969i	0.202766	−	0.111018i
$151$	4.57554	−	7.92506i	0.372352	−	0.644932i	−0.617575	−	0.786512i	$-0.711885\pi$
$151$	4.57554	−	7.92506i	0.372352	−	0.644932i	0.989927	+	0.141580i	$0.0452181\pi$
$152$	−2.45177			−0.198865
$153$	−19.0918	−	0.865876i	−1.54348	−	0.0700019i
$154$	0.761514	−	6.24502i	0.0613645	−	0.503238i
$155$	6.94505	+	4.00973i	0.557840	+	0.322069i
$156$	4.79001	+	2.91219i	0.383508	+	0.233162i
$157$	2.77373	−	1.60141i	0.221367	−	0.127807i	−0.385216	−	0.922826i	$-0.625873\pi$
$157$	2.77373	−	1.60141i	0.221367	−	0.127807i	0.606583	+	0.795020i	$0.292540\pi$
$158$	10.7764	−	6.22173i	0.857321	−	0.494974i
$159$	−0.371480	+	16.3901i	−0.0294603	+	1.29982i
$160$	3.16571	+	1.82772i	0.250271	+	0.144494i
$161$	23.1092	+	2.81792i	1.82126	+	0.222083i
$162$	−12.0224	−	8.47882i	−0.944567	−	0.666159i
$163$	2.29873			0.180050			0.0900252	−	0.995939i	$-0.471305\pi$
$163$	2.29873			0.180050			0.0900252	+	0.995939i	$0.471305\pi$
$164$	2.83404	−	4.90870i	0.221301	−	0.383305i
$165$	0.0570926	−	2.51898i	0.00444465	−	0.196103i
$166$	4.61196	−	2.66272i	0.357957	−	0.206667i
$167$	−6.51434	−	11.2832i	−0.504095	−	0.873118i	−0.999989	−	0.00473508i	$-0.998493\pi$
$167$	−6.51434	−	11.2832i	−0.504095	−	0.873118i	0.495894	−	0.868383i	$-0.334841\pi$
$168$	−6.15888	+	7.81231i	−0.475168	+	0.602733i
$169$	5.09985	−	8.83319i	0.392296	−	0.679477i
$170$		−	10.4133i		−	0.798661i
$171$	−0.153509	+	3.38474i	−0.0117391	+	0.258838i
$172$	4.51166			0.344011
$173$	−5.41379	+	9.37697i	−0.411603	+	0.712918i	−0.995065	−	0.0992228i	$-0.968364\pi$
$173$	−5.41379	+	9.37697i	−0.411603	+	0.712918i	0.583462	+	0.812140i	$0.301698\pi$
$174$	5.70001	+	10.4106i	0.432116	+	0.789224i
$175$	−2.43457	+	1.03581i	−0.184036	+	0.0782995i
$176$	6.16349	−	3.55850i	0.464591	−	0.268232i
$177$	2.72184	+	4.97122i	0.204586	+	0.373659i
$178$	4.50278	+	2.59968i	0.337498	+	0.194854i
$179$		−	8.57422i		−	0.640868i	−0.947271	−	0.320434i	$-0.896171\pi$
$179$		−	8.57422i		−	0.640868i	0.947271	−	0.320434i	$-0.103829\pi$
$180$	1.08598	−	1.69832i	0.0809444	−	0.126585i
$181$			12.4134i			0.922682i	0.887223	+	0.461341i	$0.152631\pi$
$181$			12.4134i			0.922682i	−0.887223	+	0.461341i	$0.847369\pi$
$182$	−16.6466	−	12.5224i	−1.23393	−	0.928221i
$183$	−11.0226	−	6.70139i	−0.814811	−	0.495381i
$184$	9.55080	+	16.5425i	0.704094	+	1.21953i
$185$	−2.13359	−	3.69548i	−0.156864	−	0.271697i
$186$	22.6991	+	0.514473i	1.66438	+	0.0377230i
$187$	−8.02564	−	4.63360i	−0.586893	−	0.338843i
$188$	0.993355			0.0724479
$189$	10.3995	+	8.99166i	0.756454	+	0.654047i
$190$	−1.84614			−0.133933
$191$	−11.2345	−	6.48623i	−0.812898	−	0.469327i	0.0350632	−	0.999385i	$-0.488837\pi$
$191$	−11.2345	−	6.48623i	−0.812898	−	0.469327i	−0.847961	+	0.530058i	$0.822170\pi$
$192$	−6.59662	−	0.149512i	−0.476070	−	0.0107901i
$193$	1.43033	+	2.47741i	0.102957	+	0.178328i	0.912902	−	0.408179i	$-0.133836\pi$
$193$	1.43033	+	2.47741i	0.102957	+	0.178328i	−0.809944	+	0.586507i	$0.800503\pi$
$194$	9.47527	+	16.4117i	0.680285	+	1.17829i
$195$	−7.12854	−	4.33394i	−0.510485	−	0.310360i
$196$	−3.26178	+	3.38895i	−0.232985	+	0.242068i
$197$			16.0891i			1.14630i	0.819450	+	0.573151i	$0.194279\pi$
$197$			16.0891i			1.14630i	−0.819450	+	0.573151i	$0.805721\pi$
$198$	−3.28326	−	6.33317i	−0.233331	−	0.450079i
$199$		−	23.5913i		−	1.67235i	−0.548466	−	0.836173i	$-0.684788\pi$
$199$		−	23.5913i		−	1.67235i	0.548466	−	0.836173i	$-0.315212\pi$
$200$	−1.88001	−	1.08542i	−0.132937	−	0.0767510i
$201$	−0.470181	−	0.858746i	−0.0331640	−	0.0605713i
$202$	9.51294	−	5.49230i	0.669328	−	0.386437i
$203$	−4.34223	−	10.2060i	−0.304765	−	0.716322i
$204$	−3.56070	−	6.50332i	−0.249299	−	0.455323i
$205$	−4.21764	+	7.30517i	−0.294573	+	0.510215i
$206$	12.0402			0.838882
$207$	23.4354	−	12.1494i	1.62887	−	0.844443i
$208$		−	23.5647i		−	1.63392i
$209$	−0.821479	+	1.42284i	−0.0568229	+	0.0984202i
$210$	−4.63753	+	5.88254i	−0.320020	+	0.405934i
$211$	−4.69979	−	8.14028i	−0.323547	−	0.560400i	0.657670	−	0.753306i	$-0.271542\pi$
$211$	−4.69979	−	8.14028i	−0.323547	−	0.560400i	−0.981217	+	0.192906i	$0.938209\pi$
$212$	−5.50806	+	3.18008i	−0.378295	+	0.218409i
$213$	−0.616523	+	27.2016i	−0.0422435	+	1.86382i
$214$	−3.90510	+	6.76383i	−0.266947	+	0.462366i
$215$	−6.71429			−0.457911
$216$	−0.766263	+	11.2540i	−0.0521376	+	0.765737i
$217$	−21.0615	−	2.56822i	−1.42975	−	0.174342i
$218$	21.9778	+	12.6889i	1.48852	+	0.859399i
$219$	−0.259581	+	11.4530i	−0.0175409	+	0.773922i
$220$	0.846531	−	0.488745i	0.0570731	−	0.0329512i
$221$	−26.5732	+	15.3421i	−1.78751	+	1.03202i
$222$	−10.3232	−	6.27620i	−0.692847	−	0.421231i
$223$	−3.23735	−	1.86908i	−0.216789	−	0.125163i	0.387674	−	0.921797i	$-0.373279\pi$
$223$	−3.23735	−	1.86908i	−0.216789	−	0.125163i	−0.604463	+	0.796634i	$0.706612\pi$
$224$	−9.60029	−	1.17065i	−0.641446	−	0.0782175i
$225$	−1.61617	+	2.52745i	−0.107745	+	0.168497i
$226$	−14.2888			−0.950480
$227$	8.25962	−	14.3061i	0.548210	−	0.949527i	−0.450187	−	0.892934i	$-0.648643\pi$
$227$	8.25962	−	14.3061i	0.548210	−	0.949527i	0.998397	−	0.0565933i	$-0.0180239\pi$
$228$	−1.15296	+	0.631267i	−0.0763563	+	0.0418067i
$229$	1.00736	−	0.581599i	0.0665682	−	0.0384332i	−0.466346	−	0.884602i	$-0.654430\pi$
$229$	1.00736	−	0.581599i	0.0665682	−	0.0384332i	0.532915	+	0.846169i	$0.321097\pi$
$230$	7.19159	+	12.4562i	0.474199	+	0.821337i
$231$	2.47018	+	6.19176i	0.162526	+	0.407388i
$232$	4.55023	−	7.88124i	0.298737	−	0.517428i
$233$		−	18.4853i		−	1.21101i	−0.795841	−	0.605506i	$-0.792971\pi$
$233$		−	18.4853i		−	1.21101i	0.795841	−	0.605506i	$-0.207029\pi$
$234$	−23.5956	−	1.07013i	−1.54249	−	0.0699568i
$235$	−1.47832			−0.0964349
$236$	−1.09937	+	1.90416i	−0.0715627	+	0.123950i
$237$	−6.84966	+	11.2664i	−0.444933	+	0.731833i
$238$	10.7861	+	25.3518i	0.699160	+	1.64331i
$239$	−10.4020	+	6.00563i	−0.672853	+	0.388472i	−0.797157	−	0.603773i	$-0.793664\pi$
$239$	−10.4020	+	6.00563i	−0.672853	+	0.388472i	0.124304	+	0.992244i	$0.460330\pi$
$240$	−8.47168	−	0.192010i	−0.546845	−	0.0123942i
$241$	22.5257	+	13.0052i	1.45101	+	0.837740i	0.998539	−	0.0540393i	$-0.0172096\pi$
$241$	22.5257	+	13.0052i	1.45101	+	0.837740i	0.452470	+	0.891780i	$0.350543\pi$
$242$			14.5216i			0.933483i
$243$	15.4885	+	1.76248i	0.993588	+	0.113063i
$244$		−	5.00448i		−	0.320379i
$245$	4.85422	−	5.04347i	0.310124	−	0.322216i
$246$	−0.541150	+	23.8761i	−0.0345025	+	1.52228i
$247$	2.71995	+	4.71110i	0.173067	+	0.299760i
$248$	−8.70450	−	15.0766i	−0.552736	−	0.957367i
$249$	−2.93145	+	4.82170i	−0.185773	+	0.305563i
$250$	−1.41561	−	0.817305i	−0.0895313	−	0.0516909i
$251$	5.52002			0.348421			0.174210	−	0.984708i	$-0.444263\pi$
$251$	5.52002			0.348421			0.174210	+	0.984708i	$0.444263\pi$
$252$	−0.884772	+	5.25953i	−0.0557354	+	0.331319i
$253$	12.8002			0.804742
$254$	15.7730	+	9.10655i	0.989686	+	0.571396i
$255$	5.29906	+	9.67829i	0.331840	+	0.606078i
$256$	−7.25513	−	12.5663i	−0.453446	−	0.785391i
$257$	0.303064	+	0.524923i	0.0189046	+	0.0327438i	0.875323	−	0.483539i	$-0.160649\pi$
$257$	0.303064	+	0.524923i	0.0189046	+	0.0327438i	−0.856418	+	0.516283i	$0.827315\pi$
$258$	−16.6740	+	9.12936i	−1.03808	+	0.568369i
$259$	9.02216	+	6.78691i	0.560610	+	0.421718i
$260$		−	3.23651i		−	0.200720i
$261$	−10.5954	−	6.77519i	−0.655838	−	0.419374i
$262$		−	3.16612i		−	0.195603i
$263$	−11.7103	−	6.76094i	−0.722088	−	0.416897i	0.0934330	−	0.995626i	$-0.470216\pi$
$263$	−11.7103	−	6.76094i	−0.722088	−	0.416897i	−0.815521	+	0.578728i	$0.803549\pi$
$264$	−2.84150	+	4.67374i	−0.174882	+	0.287649i
$265$	8.19714	−	4.73262i	0.503546	−	0.290723i
$266$	4.49455	−	1.91224i	0.275578	−	0.117247i
$267$	−5.50789	−	0.124836i	−0.337077	−	0.00763984i
$268$	0.189909	−	0.328932i	0.0116005	−	0.0200927i
$269$	−19.2253			−1.17219			−0.586093	−	0.810244i	$-0.699335\pi$
$269$	−19.2253			−1.17219			−0.586093	+	0.810244i	$0.699335\pi$
$270$	−0.576983	+	8.47406i	−0.0351141	+	0.515715i
$271$		−	14.2264i		−	0.864191i	−0.901828	−	0.432096i	$-0.857774\pi$
$271$		−	14.2264i		−	0.864191i	0.901828	−	0.432096i	$-0.142226\pi$
$272$	−15.5834	+	26.9913i	−0.944885	+	1.63659i
$273$	21.8440	+	3.16749i	1.32206	+	0.191705i
$274$	−10.2004	−	17.6677i	−0.616231	−	1.06734i
$275$	−1.25981	+	0.727354i	−0.0759697	+	0.0438611i
$276$	8.75057	+	5.32009i	0.526722	+	0.320232i
$277$	−12.6825	+	21.9668i	−0.762019	+	1.31986i	0.179790	+	0.983705i	$0.442458\pi$
$277$	−12.6825	+	21.9668i	−0.762019	+	1.31986i	−0.941808	+	0.336150i	$0.890875\pi$
$278$	8.62773			0.517457
$279$	−21.3588	+	11.0729i	−1.27872	+	0.662915i
$280$	5.70129	+	0.695211i	0.340717	+	0.0415468i
$281$	15.8465	+	9.14899i	0.945324	+	0.545783i	0.891625	−	0.452774i	$-0.149566\pi$
$281$	15.8465	+	9.14899i	0.945324	+	0.545783i	0.0536985	+	0.998557i	$0.482899\pi$
$282$	−3.67120	+	2.01006i	−0.218617	+	0.119697i
$283$	−12.3263	+	7.11659i	−0.732722	+	0.423037i	−0.819417	−	0.573198i	$-0.805703\pi$
$283$	−12.3263	+	7.11659i	−0.732722	+	0.423037i	0.0866953	+	0.996235i	$0.472369\pi$
$284$	−9.14139	+	5.27778i	−0.542442	+	0.313179i
$285$	1.71584	−	0.939457i	0.101638	−	0.0556486i
$286$	−9.91886	−	5.72666i	−0.586515	−	0.338624i
$287$	2.70139	−	22.1536i	0.159458	−	1.30768i
$288$	−9.73580	+	5.04725i	−0.573687	+	0.297412i
$289$	23.5831			1.38724
$290$	3.42625	−	5.93444i	0.201196	−	0.348482i
$291$	−17.1580	−	10.4316i	−1.00582	−	0.611510i
$292$	−3.84890	+	2.22216i	−0.225240	+	0.130042i
$293$	−0.556616	−	0.964087i	−0.0325178	−	0.0563226i	0.849308	−	0.527897i	$-0.177019\pi$
$293$	−0.556616	−	0.964087i	−0.0325178	−	0.0563226i	−0.881826	+	0.471574i	$0.843686\pi$
$294$	5.19721	−	19.1250i	0.303107	−	1.11539i
$295$	1.63609	−	2.83379i	0.0952567	−	0.164990i
$296$			9.26338i			0.538423i
$297$	6.27433	+	4.21540i	0.364073	+	0.244602i
$298$	−15.3528			−0.889362
$299$	21.1910	−	36.7039i	1.22551	−	2.12264i
$300$	−1.16355	−	0.0263718i	−0.0671776	−	0.00152258i
$301$	16.3464	−	6.95469i	0.942189	−	0.400862i
$302$	−12.9544	+	7.47922i	−0.745441	+	0.430381i
$303$	−6.04661	+	9.94556i	−0.347369	+	0.571357i
$304$	4.78522	+	2.76275i	0.274451	+	0.158454i
$305$			7.44772i			0.426455i
$306$	26.3190	+	16.8296i	1.50456	+	0.962084i
$307$			5.82101i			0.332223i	0.986107	+	0.166111i	$0.0531211\pi$
$307$			5.82101i			0.332223i	−0.986107	+	0.166111i	$0.946879\pi$
$308$	−1.55469	+	2.06672i	−0.0885867	+	0.117762i
$309$	−11.1904	+	6.12698i	−0.636600	+	0.348552i
$310$	−6.55434	−	11.3525i	−0.372262	−	0.644776i
$311$	2.35308	+	4.07566i	0.133431	+	0.231110i	0.924997	−	0.379974i	$-0.124067\pi$
$311$	2.35308	+	4.07566i	0.133431	+	0.231110i	−0.791566	+	0.611084i	$0.790734\pi$
$312$	8.69754	+	15.8853i	0.492401	+	0.899329i
$313$	10.4213	+	6.01675i	0.589048	+	0.340087i	0.764721	−	0.644362i	$-0.222877\pi$
$313$	10.4213	+	6.01675i	0.589048	+	0.340087i	−0.175673	+	0.984449i	$0.556210\pi$
$314$	−5.23536			−0.295449
$315$	1.31673	−	7.82727i	0.0741891	−	0.441017i
$316$	−5.11521			−0.287753
$317$	−3.23415	−	1.86724i	−0.181648	−	0.104874i	0.406419	−	0.913687i	$-0.366777\pi$
$317$	−3.23415	−	1.86724i	−0.181648	−	0.104874i	−0.588067	+	0.808812i	$0.700111\pi$
$318$	13.9216	−	22.8984i	0.780682	−	1.28408i
$319$	−3.04916	−	5.28131i	−0.170720	−	0.295696i
$320$	1.90477	+	3.29916i	0.106480	+	0.184429i
$321$	0.187522	−	8.27365i	0.0104664	−	0.461790i
$322$	−30.4106	−	22.8763i	−1.69472	−	1.27485i
$323$		−	7.19488i		−	0.400334i
$324$	2.53727	+	5.48953i	0.140960	+	0.304974i
$325$			4.81661i			0.267177i
$326$	−3.25411	−	1.87876i	−0.180229	−	0.104055i
$327$	−26.8836	−	0.609316i	−1.48667	−	0.0336953i
$328$	15.8584	−	9.15585i	0.875633	−	0.505547i
$329$	3.59907	−	1.53125i	0.198423	−	0.0844206i
$330$	−2.13960	+	3.51924i	−0.117781	+	0.193728i
$331$	2.04517	−	3.54235i	0.112413	−	0.194705i	−0.804330	−	0.594183i	$-0.797475\pi$
$331$	2.04517	−	3.54235i	0.112413	−	0.194705i	0.916743	+	0.399478i	$0.130809\pi$
$332$	−2.18916			−0.120146
$333$	12.7884	+	0.579994i	0.700799	+	0.0317835i
$334$			21.2968i			1.16531i
$335$	−0.282624	+	0.489519i	−0.0154414	+	0.0267453i
$336$	20.8237	−	8.30755i	1.13603	−	0.453214i
$337$	−15.3123	−	26.5217i	−0.834113	−	1.44473i	−0.894750	−	0.446567i	$-0.852647\pi$
$337$	−15.3123	−	26.5217i	−0.834113	−	1.44473i	0.0606369	−	0.998160i	$-0.480687\pi$
$338$	−14.4388	+	8.33626i	−0.785369	+	0.453433i
$339$	13.2803	−	7.27126i	0.721289	−	0.394920i
$340$	−2.14032	+	3.70715i	−0.116075	+	0.201048i
$341$	−11.6660			−0.631748
$342$	2.98368	−	4.66602i	0.161339	−	0.252310i
$343$	−6.59385	+	17.3067i	−0.356034	+	0.934473i
$344$	12.6229	+	7.28784i	0.680582	+	0.392934i
$345$	−13.0227	−	7.91740i	−0.701117	−	0.426259i
$346$	15.3277	−	8.84944i	0.824021	−	0.475749i
$347$	2.29025	−	1.32227i	0.122947	−	0.0709834i	−0.437265	−	0.899333i	$-0.644053\pi$
$347$	2.29025	−	1.32227i	0.122947	−	0.0709834i	0.560212	+	0.828349i	$0.310720\pi$
$348$	0.110554	−	4.87776i	0.00592632	−	0.261475i
$349$	3.40959	+	1.96853i	0.182511	+	0.105373i	0.588472	−	0.808518i	$-0.299730\pi$
$349$	3.40959	+	1.96853i	0.182511	+	0.105373i	−0.405961	+	0.913890i	$0.633063\pi$
$350$	4.29297	+	0.523482i	0.229469	+	0.0279813i
$351$	22.4747	−	11.0126i	1.19961	−	0.587810i
$352$	−5.31761			−0.283429
$353$	4.13508	−	7.16216i	0.220088	−	0.381204i	−0.734746	−	0.678342i	$-0.762699\pi$
$353$	4.13508	−	7.16216i	0.220088	−	0.381204i	0.954834	+	0.297138i	$0.0960322\pi$
$354$	0.209920	−	9.26190i	0.0111571	−	0.492264i
$355$	13.6043	−	7.85444i	0.722041	−	0.416871i
$356$	−1.06867	−	1.85098i	−0.0566392	−	0.0981020i
$357$	−22.9257	−	18.0736i	−1.21336	−	0.956558i
$358$	−7.00775	+	12.1378i	−0.370371	+	0.641502i
$359$			1.45601i			0.0768453i	0.999262	+	0.0384226i	$0.0122333\pi$
$359$			1.45601i			0.0768453i	−0.999262	+	0.0384226i	$0.987767\pi$
$360$	5.78176	−	2.99739i	0.304726	−	0.157977i
$361$	17.7244			0.932865
$362$	10.1455	−	17.5726i	0.533238	−	0.923595i
$363$	−7.38969	−	13.4966i	−0.387858	−	0.708390i
$364$	3.35240	+	7.87950i	0.175713	+	0.412998i
$365$	5.72797	−	3.30704i	0.299816	−	0.173099i
$366$	10.1266	+	18.4954i	0.529326	+	0.966769i
$367$	−2.13524	−	1.23278i	−0.111459	−	0.0643507i	0.443234	−	0.896406i	$-0.353831\pi$
$367$	−2.13524	−	1.23278i	−0.111459	−	0.0643507i	−0.554693	+	0.832055i	$0.687164\pi$
$368$		−	43.0488i		−	2.24407i
$369$	−11.6470	−	22.4663i	−0.606319	−	1.16955i
$370$			6.97517i			0.362622i
$371$	−15.0544	+	20.0125i	−0.781585	+	1.03900i
$372$	−7.97518	−	4.84868i	−0.413494	−	0.251392i
$373$	13.2071	+	22.8754i	0.683839	+	1.18444i	0.973800	+	0.227406i	$0.0730244\pi$
$373$	13.2071	+	22.8754i	0.683839	+	1.18444i	−0.289961	+	0.957039i	$0.593642\pi$
$374$	7.57413	+	13.1188i	0.391649	+	0.678356i
$375$	1.73161	+	0.0392468i	0.0894198	+	0.00202669i
$376$	2.77925	+	1.60460i	0.143329	+	0.0827510i
$377$	−20.1918			−1.03993
$378$	−7.37277	−	21.2283i	−0.379215	−	1.09187i
$379$	8.35948			0.429398			0.214699	−	0.976680i	$-0.431123\pi$
$379$	8.35948			0.429398			0.214699	+	0.976680i	$0.431123\pi$
$380$	0.657230	+	0.379452i	0.0337152	+	0.0194655i
$381$	−19.2938	−	0.437294i	−0.988454	−	0.0224032i
$382$	10.6024	+	18.3640i	0.542469	+	0.939583i
$383$	12.7643	+	22.1084i	0.652223	+	1.12968i	0.982582	+	0.185829i	$0.0594969\pi$
$383$	12.7643	+	22.1084i	0.652223	+	1.12968i	−0.330359	+	0.943855i	$0.607170\pi$
$384$	20.0361	+	12.1814i	1.02246	+	0.621628i
$385$	2.31370	−	3.07571i	0.117917	−	0.156753i
$386$		−	4.67606i		−	0.238005i
$387$	10.8514	−	16.9700i	0.551609	−	0.862634i
$388$		−	7.79012i		−	0.395483i
$389$	−14.6697	−	8.46958i	−0.743786	−	0.429425i	0.0796586	−	0.996822i	$-0.474617\pi$
$389$	−14.6697	−	8.46958i	−0.743786	−	0.429425i	−0.823444	+	0.567397i	$0.807950\pi$
$390$	6.54910	+	11.9614i	0.331627	+	0.605688i
$391$	−48.5450	+	28.0275i	−2.45502	+	1.41741i
$392$	−14.6003	+	4.21289i	−0.737424	+	0.212783i
$393$	1.61116	+	2.94265i	0.0812724	+	0.148437i
$394$	13.1497	−	22.7760i	0.662472	−	1.14744i
$395$	7.61250			0.383026
$396$	−0.132860	+	2.92946i	−0.00667648	+	0.147211i
$397$			38.1097i			1.91267i	0.292275	+	0.956334i	$0.405588\pi$
$397$			38.1097i			1.91267i	−0.292275	+	0.956334i	$0.594412\pi$
$398$	−19.2813	+	33.3962i	−0.966485	+	1.67400i
$399$	−3.20423	+	4.06444i	−0.160412	+	0.203477i
$400$	2.44619	+	4.23693i	0.122310	+	0.211846i
$401$	5.03914	−	2.90935i	0.251643	−	0.145286i	−0.368874	−	0.929480i	$-0.620256\pi$
$401$	5.03914	−	2.90935i	0.251643	−	0.145286i	0.620516	+	0.784194i	$0.286923\pi$
$402$	−0.0362624	+	1.59993i	−0.00180860	+	0.0797974i
$403$	−19.3133	+	33.4516i	−0.962063	+	1.66634i
$404$	−4.51550			−0.224655
$405$	−3.77599	−	8.16957i	−0.187630	−	0.405949i
$406$	−2.19450	+	17.9967i	−0.108911	+	0.893161i
$407$	5.37585	+	3.10375i	0.266471	+	0.153847i
$408$	0.542757	−	23.9470i	0.0268705	−	1.18555i
$409$	−25.1434	+	14.5165i	−1.24326	+	0.717797i	−0.969757	−	0.244074i	$-0.921516\pi$
$409$	−25.1434	+	14.5165i	−1.24326	+	0.717797i	−0.273504	+	0.961871i	$0.588183\pi$
$410$	11.9411	−	6.89420i	0.589729	−	0.340480i
$411$	18.4712	+	11.2299i	0.911115	+	0.553932i
$412$	−4.28634	−	2.47472i	−0.211173	−	0.121921i
$413$	−1.04791	+	8.59371i	−0.0515643	+	0.422869i
$414$	−43.1052	−	1.95496i	−2.11851	−	0.0960810i
$415$	3.25792			0.159925
$416$	−8.80342	+	15.2480i	−0.431623	+	0.747593i
$417$	−8.01878	+	4.39045i	−0.392681	+	0.215001i
$418$	2.32579	−	1.34280i	0.113758	−	0.0656784i
$419$	−14.7033	−	25.4669i	−0.718305	−	1.24414i	−0.961671	−	0.274207i	$-0.911585\pi$
$419$	−14.7033	−	25.4669i	−0.718305	−	1.24414i	0.243365	−	0.969935i	$-0.421749\pi$
$420$	2.86006	−	1.14101i	0.139556	−	0.0556755i
$421$	12.0041	−	20.7918i	0.585046	−	1.01333i	−0.409824	−	0.912165i	$-0.634410\pi$
$421$	12.0041	−	20.7918i	0.585046	−	1.01333i	0.994870	−	0.101164i	$-0.0322568\pi$
$422$			15.3647i			0.747939i
$423$	2.38922	−	3.73638i	0.116168	−	0.181669i
$424$	−20.5476			−0.997878
$425$	3.18524	−	5.51701i	0.154507	−	0.267614i
$426$	23.1048	−	38.0031i	1.11943	−	1.84126i
$427$	−7.71438	−	18.1320i	−0.373325	−	0.877467i
$428$	2.78045	−	1.60529i	0.134398	−	0.0775947i
$429$	12.1329	+	0.274993i	0.585784	+	0.0132768i
$430$	9.50483	+	5.48762i	0.458364	+	0.264636i
$431$		−	10.2871i		−	0.495510i	−0.968823	−	0.247755i	$-0.920307\pi$
$431$		−	10.2871i		−	0.495510i	0.968823	−	0.247755i	$-0.0796928\pi$
$432$	14.1770	−	21.1014i	0.682090	−	1.01524i
$433$		−	23.1127i		−	1.11073i	−0.831608	−	0.555363i	$-0.812579\pi$
$433$		−	23.1127i		−	1.11073i	0.831608	−	0.555363i	$-0.187421\pi$
$434$	27.7159	+	20.8493i	1.33041	+	1.00080i
$435$	−0.164528	+	7.25912i	−0.00788849	+	0.348048i
$436$	−5.21609	−	9.03454i	−0.249806	−	0.432676i
$437$	4.96891	+	8.60641i	0.237695	+	0.411700i
$438$	9.72806	−	16.0009i	0.464824	−	0.764551i
$439$	−2.97538	−	1.71784i	−0.142007	−	0.0819879i	0.427313	−	0.904104i	$-0.359460\pi$
$439$	−2.97538	−	1.71784i	−0.142007	−	0.0819879i	−0.569320	+	0.822116i	$0.692794\pi$
$440$	3.15795			0.150549
$441$	4.90188	+	20.4199i	0.233423	+	0.972375i
$442$	50.1566			2.38571
$443$	16.2377	+	9.37484i	0.771476	+	0.445412i	0.833401	−	0.552669i	$-0.186391\pi$
$443$	16.2377	+	9.37484i	0.771476	+	0.445412i	−0.0619247	+	0.998081i	$0.519724\pi$
$444$	2.38508	+	4.35615i	0.113191	+	0.206734i
$445$	1.59040	+	2.75465i	0.0753921	+	0.130583i
$446$	3.05522	+	5.29180i	0.144669	+	0.250574i
$447$	14.2692	−	7.81266i	0.674908	−	0.369526i
$448$	−8.05457	−	6.05904i	−0.380543	−	0.286263i
$449$			19.9704i			0.942461i	0.882010	+	0.471231i	$0.156190\pi$
$449$			19.9704i			0.942461i	−0.882010	+	0.471231i	$0.843810\pi$
$450$	4.35357	−	2.25699i	0.205229	−	0.106395i
$451$		−	12.2709i		−	0.577813i
$452$	5.08686	+	2.93690i	0.239266	+	0.138140i
$453$	8.23406	−	13.5435i	0.386870	−	0.636330i
$454$	−23.3848	+	13.5012i	−1.09751	+	0.633645i
$455$	−4.98907	−	11.7263i	−0.233891	−	0.549739i
$456$	−4.24550	−	0.0962239i	−0.198814	−	0.00450610i
$457$	−15.0331	+	26.0381i	−0.703219	+	1.21801i	0.264112	+	0.964492i	$0.414921\pi$
$457$	−15.0331	+	26.0381i	−0.703219	+	1.21801i	−0.967331	+	0.253518i	$0.918412\pi$
$458$	−1.90138			−0.0888455
$459$	−33.0256	−	2.24865i	−1.54150	−	0.104958i
$460$		−	5.91258i		−	0.275675i
$461$	11.0089	−	19.0680i	0.512736	−	0.888085i	−0.487155	−	0.873316i	$-0.661965\pi$
$461$	11.0089	−	19.0680i	0.512736	−	0.888085i	0.999891	−	0.0147696i	$-0.00470148\pi$
$462$	1.56374	−	10.7840i	0.0727517	−	0.501719i
$463$	−10.2509	−	17.7550i	−0.476398	−	0.825145i	0.523237	−	0.852188i	$-0.324724\pi$
$463$	−10.2509	−	17.7550i	−0.476398	−	0.825145i	−0.999634	+	0.0270424i	$0.991391\pi$
$464$	−17.7618	+	10.2548i	−0.824569	+	0.476065i
$465$	11.8687	+	7.21584i	0.550399	+	0.334627i
$466$	−15.1081	+	26.1680i	−0.699870	+	1.21221i
$467$	−2.21159			−0.102340			−0.0511701	−	0.998690i	$-0.516295\pi$
$467$	−2.21159			−0.102340			−0.0511701	+	0.998690i	$0.516295\pi$
$468$	8.18012	+	5.23075i	0.378126	+	0.241792i
$469$	0.181020	−	1.48451i	0.00835873	−	0.0685483i
$470$	2.09273	+	1.20824i	0.0965304	+	0.0557319i
$471$	4.86585	−	2.66415i	0.224207	−	0.122758i
$472$	−6.15172	+	3.55169i	−0.283156	+	0.163480i
$473$	8.45876	−	4.88367i	0.388934	−	0.224551i
$474$	18.9046	−	10.3507i	0.868316	−	0.475421i
$475$	−0.978095	−	0.564704i	−0.0448781	−	0.0259104i
$476$	1.37087	−	11.2422i	0.0628338	−	0.515287i
$477$	−1.28651	+	28.3666i	−0.0589054	+	1.29882i
$478$	19.6337			0.898025
$479$	−1.55167	+	2.68757i	−0.0708975	+	0.122798i	−0.899295	−	0.437343i	$-0.855920\pi$
$479$	−1.55167	+	2.68757i	−0.0708975	+	0.122798i	0.828397	+	0.560141i	$0.189253\pi$
$480$	5.41003	+	3.28914i	0.246933	+	0.150128i
$481$	17.7997	−	10.2767i	0.811596	−	0.468575i
$482$	−21.2585	−	36.8208i	−0.968297	−	1.67714i
$483$	39.9054	+	5.78649i	1.81576	+	0.263294i
$484$	2.98474	−	5.16972i	0.135670	−	0.234987i
$485$			11.5933i			0.526425i
$486$	−20.4852	−	15.1538i	−0.929230	−	0.687391i
$487$	28.9402			1.31141			0.655703	−	0.755019i	$-0.272372\pi$
$487$	28.9402			1.31141			0.655703	+	0.755019i	$0.272372\pi$
$488$	8.08392	−	14.0018i	0.365942	−	0.633830i
$489$	3.98050	+	0.0902177i	0.180004	+	0.00407979i
$490$	−10.9937	+	3.17223i	−0.496647	+	0.143307i
$491$	−18.6279	+	10.7548i	−0.840666	+	0.485359i	−0.857490	−	0.514500i	$-0.827978\pi$
$491$	−18.6279	+	10.7548i	−0.840666	+	0.485359i	0.0168248	+	0.999858i	$0.494644\pi$
$492$	5.10009	−	8.38871i	0.229930	−	0.378192i
$493$	23.1280	+	13.3530i	1.04163	+	0.601387i
$494$		−	8.89213i		−	0.400076i
$495$	0.197724	−	4.35964i	0.00888702	−	0.195951i
$496$			39.2343i			1.76167i
$497$	−24.9849	+	33.2136i	−1.12072	+	1.48983i
$498$	8.09060	−	4.42977i	0.362548	−	0.198503i
$499$	−15.3022	−	26.5042i	−0.685020	−	1.18649i	−0.973431	−	0.228983i	$-0.926460\pi$
$499$	−15.3022	−	26.5042i	−0.685020	−	1.18649i	0.288410	−	0.957507i	$-0.406873\pi$
$500$	0.335974	+	0.581925i	0.0150252	+	0.0260245i
$501$	−10.8375	−	19.7937i	−0.484182	−	0.884316i
$502$	−7.81422	−	4.51154i	−0.348766	−	0.201360i
$503$	29.3667			1.30940			0.654699	−	0.755890i	$-0.272795\pi$
$503$	29.3667			1.30940			0.654699	+	0.755890i	$0.272795\pi$
$504$	−10.9714	+	13.2861i	−0.488703	+	0.591811i
$505$	6.72001			0.299037
$506$	−18.1201	−	10.4617i	−0.805538	−	0.465078i
$507$	9.17760	−	15.0955i	0.407592	−	0.670413i
$508$	−3.74348	−	6.48390i	−0.166090	−	0.287677i
$509$	11.2559	+	19.4957i	0.498907	+	0.864132i	0.999999	−	0.00126186i	$-0.000401663\pi$
$509$	11.2559	+	19.4957i	0.498907	+	0.864132i	−0.501092	+	0.865394i	$0.667068\pi$
$510$	0.408687	−	18.0317i	0.0180970	−	0.798456i
$511$	−10.5197	+	13.9843i	−0.465362	+	0.618628i
$512$		−	3.35738i		−	0.148377i
$513$	−0.398657	+	5.85502i	−0.0176011	+	0.258505i
$514$		−	0.990783i		−	0.0437016i
$515$	6.37897	+	3.68290i	0.281091	+	0.162288i
$516$	7.81241	+	0.177068i	0.343922	+	0.00779498i
$517$	1.86241	−	1.07526i	0.0819086	−	0.0472900i
$518$	−7.22491	−	16.9815i	−0.317444	−	0.746124i
$519$	−9.74257	+	16.0247i	−0.427652	+	0.703408i
$520$	5.22805	−	9.05525i	0.229265	−	0.397099i
$521$	−3.86417			−0.169292			−0.0846461	−	0.996411i	$-0.526976\pi$
$521$	−3.86417			−0.169292			−0.0846461	+	0.996411i	$0.526976\pi$
$522$	9.46158	+	18.2507i	0.414122	+	0.798812i
$523$			13.6894i			0.598596i	0.954160	+	0.299298i	$0.0967525\pi$
$523$			13.6894i			0.598596i	−0.954160	+	0.299298i	$0.903248\pi$
$524$	−0.650757	+	1.12714i	−0.0284285	+	0.0492396i
$525$	−4.25636	+	1.69806i	−0.185763	+	0.0741093i
$526$	11.0515	+	19.1418i	0.481868	+	0.834620i
$527$	44.2434	−	25.5439i	1.92727	−	1.11271i
$528$	10.8124	−	5.92002i	0.470550	−	0.257636i
$529$	27.2125	−	47.1335i	1.18315	−	2.04928i
$530$	−15.4720			−0.672060
$531$	4.51806	+	8.71501i	0.196067	+	0.378199i
$532$	−1.99311	−	0.243038i	−0.0864122	−	0.0105370i
$533$	−35.1861	−	20.3147i	−1.52408	−	0.879928i
$534$	7.69501	+	4.67834i	0.332996	+	0.202452i
$535$	−4.13789	+	2.38901i	−0.178896	+	0.103286i
$536$	1.06267	−	0.613533i	0.0459003	−	0.0265006i
$537$	0.336510	−	14.8472i	0.0145215	−	0.640703i
$538$	27.2156	+	15.7129i	1.17335	+	0.677432i
$539$	−2.44702	+	9.88457i	−0.105401	+	0.425759i
$540$	1.94715	−	2.89819i	0.0837919	−	0.124718i
$541$	−8.51509			−0.366092			−0.183046	−	0.983104i	$-0.558596\pi$
$541$	−8.51509			−0.366092			−0.183046	+	0.983104i	$0.558596\pi$
$542$	−11.6273	+	20.1391i	−0.499435	+	0.865046i
$543$	−0.487186	+	21.4951i	−0.0209072	+	0.922445i
$544$	20.1671	−	11.6435i	0.864658	−	0.499210i
$545$	7.76263	+	13.4453i	0.332515	+	0.575932i
$546$	−28.3339	−	22.3372i	−1.21258	−	0.955942i
$547$	−9.11195	+	15.7824i	−0.389599	+	0.674805i	−0.992396	−	0.123090i	$-0.960720\pi$
$547$	−9.11195	+	15.7824i	−0.389599	+	0.674805i	0.602797	+	0.797895i	$0.294053\pi$
$548$			8.38632i			0.358246i
$549$	−18.8237	−	12.0368i	−0.803377	−	0.513717i
$550$	2.37788			0.101393
$551$	2.36731	−	4.10030i	0.100851	−	0.174679i
$552$	15.8890	+	29.0199i	0.676280	+	1.23517i
$553$	−18.5331	+	7.88506i	−0.788108	+	0.335307i
$554$	35.9071	−	20.7310i	1.52555	−	0.880775i
$555$	−3.54950	−	6.48286i	−0.150668	−	0.275182i
$556$	−3.07149	−	1.77333i	−0.130260	−	0.0752058i
$557$		−	0.206472i		−	0.00874851i	−0.999990	−	0.00437426i	$-0.998608\pi$
$557$		−	0.206472i		−	0.00874851i	0.999990	−	0.00437426i	$-0.00139237\pi$
$558$	39.2857	+	1.78173i	1.66309	+	0.0754266i
$559$		−	32.3401i		−	1.36784i
$560$	−10.3440	−	7.78130i	−0.437116	−	0.328820i
$561$	−13.7154	−	8.33856i	−0.579064	−	0.352054i
$562$	−14.9550	−	25.9029i	−0.630840	−	1.09265i
$563$	−21.7058	−	37.5956i	−0.914791	−	1.58447i	−0.807206	−	0.590269i	$-0.799022\pi$
$563$	−21.7058	−	37.5956i	−0.914791	−	1.58447i	−0.107585	−	0.994196i	$-0.534312\pi$
$564$	1.72010	+	0.0389860i	0.0724293	+	0.00164161i
$565$	−7.57031	−	4.37072i	−0.318485	−	0.183878i
$566$	23.2657			0.977929
$567$	17.6550	+	15.9782i	0.741439	+	0.671020i
$568$	−34.1016			−1.43087
$569$	18.7566	+	10.8291i	0.786318	+	0.453981i	0.838665	−	0.544648i	$-0.183337\pi$
$569$	18.7566	+	10.8291i	0.786318	+	0.453981i	−0.0523465	+	0.998629i	$0.516670\pi$
$570$	−3.19679	−	0.0724550i	−0.133899	−	0.00303481i
$571$	6.87597	+	11.9095i	0.287750	+	0.498398i	0.973272	−	0.229653i	$-0.0737593\pi$
$571$	6.87597	+	11.9095i	0.287750	+	0.498398i	−0.685522	+	0.728052i	$0.740426\pi$
$572$	2.35409	+	4.07741i	0.0984295	+	0.170485i
$573$	−19.1991	−	11.6725i	−0.802055	−	0.487626i
$574$	−21.9303	+	29.1530i	−0.915355	+	1.21682i
$575$			8.79915i			0.366950i
$576$	−11.4169	−	0.517792i	−0.475703	−	0.0215747i
$577$			9.29586i			0.386992i	0.981101	+	0.193496i	$0.0619826\pi$
$577$			9.29586i			0.386992i	−0.981101	+	0.193496i	$0.938017\pi$
$578$	−33.3846	−	19.2746i	−1.38862	−	0.801718i
$579$	2.37954	+	4.34603i	0.0988903	+	0.180615i
$580$	−2.43950	+	1.40845i	−0.101295	+	0.0584826i
$581$	−7.93162	+	3.37457i	−0.329059	+	0.140001i
$582$	15.7633	+	28.7904i	0.653411	+	1.19340i
$583$	−6.88458	+	11.9244i	−0.285130	+	0.493860i
$584$	−14.3582			−0.594145
$585$	−12.1737	−	7.78445i	−0.503322	−	0.321848i
$586$			1.81970i			0.0751711i
$587$	16.4314	−	28.4600i	0.678197	−	1.17467i	−0.297326	−	0.954776i	$-0.596095\pi$
$587$	16.4314	−	28.4600i	0.678197	−	1.17467i	0.975523	−	0.219896i	$-0.0705718\pi$
$588$	−5.78113	+	5.74032i	−0.238410	+	0.236727i
$589$	−4.52862	−	7.84379i	−0.186598	−	0.323198i
$590$	−4.63214	+	2.67437i	−0.190702	+	0.110102i
$591$	−0.631445	+	27.8600i	−0.0259742	+	1.14601i
$592$	10.4383	−	18.0797i	0.429013	−	0.743071i
$593$	−9.23970			−0.379429			−0.189715	−	0.981839i	$-0.560756\pi$
$593$	−9.23970			−0.379429			−0.189715	+	0.981839i	$0.560756\pi$
$594$	−5.43675	−	11.0954i	−0.223073	−	0.455250i
$595$	−2.04014	+	16.7308i	−0.0836377	+	0.685896i
$596$	5.46562	+	3.15558i	0.223881	+	0.129258i
$597$	0.925884	−	40.8509i	0.0378939	−	1.67192i
$598$	−59.9966	+	34.6391i	−2.45344	+	1.41650i
$599$	−3.33402	+	1.92490i	−0.136224	+	0.0786493i	−0.566563	−	0.824018i	$-0.691727\pi$
$599$	−3.33402	+	1.92490i	−0.136224	+	0.0786493i	0.430339	+	0.902667i	$0.358394\pi$
$600$	−3.21283	−	1.95331i	−0.131163	−	0.0797435i
$601$	11.5016	+	6.64047i	0.469161	+	0.270870i	0.715888	−	0.698215i	$-0.246022\pi$
$601$	11.5016	+	6.64047i	0.469161	+	0.270870i	−0.246727	+	0.969085i	$0.579355\pi$
$602$	−28.8242	−	3.51481i	−1.17479	−	0.143253i
$603$	−0.780466	−	1.50546i	−0.0317830	−	0.0613072i
$604$	6.14905			0.250201
$605$	−4.44191	+	7.69362i	−0.180589	+	0.312790i
$606$	16.6882	−	9.13714i	0.677912	−	0.371171i
$607$	14.8801	−	8.59105i	0.603966	−	0.348700i	−0.166634	−	0.986019i	$-0.553290\pi$
$607$	14.8801	−	8.59105i	0.603966	−	0.348700i	0.770600	+	0.637319i	$0.219957\pi$
$608$	−2.06424	−	3.57537i	−0.0837161	−	0.145001i
$609$	−7.11848	−	17.8432i	−0.288455	−	0.723044i
$610$	6.08705	−	10.5431i	0.246458	−	0.426877i
$611$		−	7.12048i		−	0.288064i
$612$	−5.91050	−	11.4009i	−0.238918	−	0.460855i
$613$	42.9512			1.73478			0.867390	−	0.497628i	$-0.165796\pi$
$613$	42.9512			1.73478			0.867390	+	0.497628i	$0.165796\pi$
$614$	4.75754	−	8.24030i	0.191999	−	0.332551i
$615$	−7.59000	+	12.4841i	−0.306058	+	0.503409i
$616$	−7.68823	+	3.27102i	−0.309768	+	0.131793i
$617$	21.6606	−	12.5058i	0.872025	−	0.503464i	0.00400404	−	0.999992i	$-0.498725\pi$
$617$	21.6606	−	12.5058i	0.872025	−	0.503464i	0.868020	+	0.496528i	$0.165392\pi$
$618$	20.8489	+	0.472539i	0.838666	+	0.0190083i
$619$	14.6924	+	8.48266i	0.590537	+	0.340947i	0.765310	−	0.643662i	$-0.222586\pi$
$619$	14.6924	+	8.48266i	0.590537	+	0.340947i	−0.174773	+	0.984609i	$0.555919\pi$
$620$			5.38866i			0.216414i
$621$	41.0577	−	20.1183i	1.64759	−	0.807318i
$622$		−	7.69275i		−	0.308451i
$623$	−6.72521	−	5.05904i	−0.269440	−	0.202686i
$624$	0.924837	−	40.8047i	0.0370231	−	1.63350i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−9.83504	−	17.0348i	−0.393087	−	0.680847i
$627$	−1.47832	+	2.43156i	−0.0590384	+	0.0971073i
$628$	1.86380	+	1.07607i	0.0743738	+	0.0429397i
$629$	−27.1840			−1.08390
$630$	−8.26124	+	10.0042i	−0.329136	+	0.398578i
$631$	25.4056			1.01138			0.505690	−	0.862716i	$-0.331238\pi$
$631$	25.4056			1.01138			0.505690	+	0.862716i	$0.331238\pi$
$632$	−14.3116	−	8.26278i	−0.569283	−	0.328676i
$633$	−7.81871	−	14.2802i	−0.310766	−	0.567587i
$634$	3.05220	+	5.28657i	0.121218	+	0.209956i
$635$	5.57108	+	9.64940i	0.221082	+	0.382925i
$636$	−9.66259	+	5.29047i	−0.383147	+	0.209781i
$637$	24.2924	+	23.3808i	0.962500	+	0.926383i
$638$			9.96839i			0.394652i
$639$	−2.13515	+	47.0783i	−0.0844652	+	1.86239i
$640$		−	13.5380i		−	0.535136i
$641$	−4.95438	−	2.86041i	−0.195686	−	0.112979i	0.398956	−	0.916970i	$-0.369373\pi$
$641$	−4.95438	−	2.86041i	−0.195686	−	0.112979i	−0.594642	+	0.803991i	$0.702706\pi$
$642$	−7.02755	+	11.5590i	−0.277355	+	0.456198i
$643$	33.7595	−	19.4911i	1.33134	−	0.768652i	0.345839	−	0.938294i	$-0.387594\pi$
$643$	33.7595	−	19.4911i	1.33134	−	0.768652i	0.985506	+	0.169642i	$0.0542611\pi$
$644$	6.12428	+	14.3946i	0.241330	+	0.567225i
$645$	−11.6265	−	0.263514i	−0.457793	−	0.0103759i
$646$	−5.88041	+	10.1852i	−0.231362	+	0.400730i
$647$	47.2192			1.85638			0.928189	−	0.372110i	$-0.121365\pi$
$647$	47.2192			1.85638			0.928189	+	0.372110i	$0.121365\pi$
$648$	−1.76855	+	19.4574i	−0.0694751	+	0.764359i
$649$			4.76006i			0.186849i
$650$	3.93664	−	6.81845i	0.154408	−	0.267442i
$651$	−36.3694	−	5.27374i	−1.42543	−	0.206694i
$652$	0.772315	+	1.33769i	0.0302462	+	0.0523879i
$653$	−15.8290	+	9.13890i	−0.619438	+	0.357633i	−0.776650	−	0.629932i	$-0.783083\pi$
$653$	−15.8290	+	9.13890i	−0.619438	+	0.357633i	0.157212	+	0.987565i	$0.449749\pi$
$654$	37.5589	+	22.8347i	1.46867	+	0.892907i
$655$	0.968463	−	1.67743i	0.0378410	−	0.0655425i
$656$	−41.2686			−1.61127
$657$	−0.898986	+	19.8219i	−0.0350728	+	0.773326i
$658$	−6.34638	−	0.773874i	−0.247408	−	0.0301687i
$659$	2.38069	+	1.37449i	0.0927386	+	0.0535426i	0.545652	−	0.838012i	$-0.316282\pi$
$659$	2.38069	+	1.37449i	0.0927386	+	0.0535426i	−0.452913	+	0.891554i	$0.649615\pi$
$660$	1.48504	−	0.813090i	0.0578051	−	0.0316495i
$661$	28.5264	−	16.4697i	1.10955	−	0.640599i	0.170837	−	0.985299i	$-0.445353\pi$
$661$	28.5264	−	16.4697i	1.10955	−	0.640599i	0.938713	+	0.344701i	$0.112020\pi$
$662$	−5.79035	+	3.34306i	−0.225048	+	0.129932i
$663$	−46.6165	+	25.5235i	−1.81044	+	0.991251i
$664$	−6.12492	−	3.53622i	−0.237693	−	0.137232i
$665$	2.96616	+	0.361691i	0.115023	+	0.0140258i
$666$	−17.6294	−	11.2731i	−0.683124	−	0.436822i
$667$	−36.8872			−1.42828
$668$	4.37731	−	7.58172i	0.169363	−	0.293345i
$669$	−5.53246	−	3.36357i	−0.213897	−	0.130043i
$670$	0.800172	−	0.461980i	0.0309134	−	0.0178478i
$671$	−5.41713	−	9.38274i	−0.209126	−	0.362217i
$672$	−16.5780	−	2.40389i	−0.639509	−	0.0927320i
$673$	6.94958	−	12.0370i	0.267887	−	0.463993i	−0.700429	−	0.713722i	$-0.747008\pi$
$673$	6.94958	−	12.0370i	0.267887	−	0.463993i	0.968316	+	0.249729i	$0.0803414\pi$
$674$			50.0592i			1.92821i
$675$	−2.89776	+	4.31312i	−0.111535	+	0.166012i
$676$	6.85367			0.263603
$677$	7.77408	−	13.4651i	0.298782	−	0.517506i	−0.677075	−	0.735914i	$-0.736753\pi$
$677$	7.77408	−	13.4651i	0.298782	−	0.517506i	0.975858	+	0.218408i	$0.0700862\pi$
$678$	−24.7427	−	0.560791i	−0.950236	−	0.0215370i
$679$	−12.0084	−	28.2247i	−0.460841	−	1.08316i
$680$	−11.9766	+	6.91467i	−0.459280	+	0.265166i
$681$	14.8639	−	24.4483i	0.569585	−	0.936862i
$682$	16.5145	+	9.53466i	0.632373	+	0.365101i
$683$			17.7234i			0.678168i	0.940756	+	0.339084i	$0.110117\pi$
$683$			17.7234i			0.678168i	−0.940756	+	0.339084i	$0.889883\pi$
$684$	−2.02124	+	1.04786i	−0.0772840	+	0.0400658i
$685$		−	12.4806i		−	0.476859i
$686$	23.4792	−	19.1104i	0.896439	−	0.729638i
$687$	1.76718	−	0.967566i	0.0674220	−	0.0369149i
$688$	−16.4244	−	28.4479i	−0.626175	−	1.08457i
$689$	22.7952	+	39.4824i	0.868427	+	1.50416i
$690$	11.9641	+	21.8515i	0.455467	+	0.831871i
$691$	−10.6786	−	6.16531i	−0.406234	−	0.234539i	0.282936	−	0.959139i	$-0.408692\pi$
$691$	−10.6786	−	6.16531i	−0.406234	−	0.234539i	−0.689170	+	0.724599i	$0.742025\pi$
$692$	−7.27558			−0.276576
$693$	4.03437	+	10.8186i	0.153253	+	0.410966i
$694$	−4.32280			−0.164091
$695$	4.57102	+	2.63908i	0.173389	+	0.100106i
$696$	8.18853	−	13.4686i	0.310385	−	0.510526i
$697$	26.8684	+	46.5375i	1.01772	+	1.76273i
$698$	−3.21777	−	5.57335i	−0.121795	−	0.210954i
$699$	0.725488	−	32.0092i	0.0274405	−	1.21070i
$700$	−1.42071	−	1.06873i	−0.0536979	−	0.0403942i
$701$			18.0864i			0.683114i	0.939861	+	0.341557i	$0.110954\pi$
$701$			18.0864i			0.683114i	−0.939861	+	0.341557i	$0.889046\pi$
$702$	−40.8162	−	2.77910i	−1.54051	−	0.104890i
$703$			4.81938i			0.181766i
$704$	−4.79931	−	2.77089i	−0.180881	−	0.104432i
$705$	−2.55987	−	0.0580192i	−0.0964102	−	0.00218513i
$706$	−11.7073	+	6.75924i	−0.440612	+	0.254387i
$707$	−16.3603	+	6.96062i	−0.615292	+	0.261781i
$708$	−1.97840	+	3.25411i	−0.0743530	+	0.122297i
$709$	−21.0823	+	36.5155i	−0.791761	+	1.37137i	0.133115	+	0.991101i	$0.457502\pi$
$709$	−21.0823	+	36.5155i	−0.791761	+	1.37137i	−0.924876	+	0.380269i	$0.875831\pi$
$710$	−25.6779			−0.963674
$711$	−12.3031	+	19.2402i	−0.461402	+	0.721564i
$712$		−	6.90502i		−	0.258777i
$713$	−35.2822	+	61.1106i	−1.32133	+	2.28861i
$714$	17.6823	+	44.3226i	0.661744	+	1.65873i
$715$	−3.50338	−	6.06803i	−0.131019	−	0.226931i
$716$	4.98955	−	2.88072i	0.186468	−	0.107658i
$717$	−18.2480	+	9.99113i	−0.681482	+	0.373126i
$718$	1.19000	−	2.06115i	0.0444106	−	0.0769213i
$719$	−11.4453			−0.426839			−0.213420	−	0.976961i	$-0.568460\pi$
$719$	−11.4453			−0.426839			−0.213420	+	0.976961i	$0.568460\pi$
$720$	−14.6621	−	0.664972i	−0.546423	−	0.0247820i
$721$	−19.3448	−	2.35889i	−0.720438	−	0.0878497i
$722$	−25.0910	−	14.4863i	−0.933789	−	0.539123i
$723$	38.4953	+	23.4040i	1.43165	+	0.870404i
$724$	−7.22367	+	4.17059i	−0.268466	+	0.154999i
$725$	3.63049	−	2.09607i	0.134833	−	0.0778459i
$726$	−0.569925	+	25.1457i	−0.0211519	+	0.933243i
$727$	1.99593	+	1.15235i	0.0740249	+	0.0427383i	0.536556	−	0.843865i	$-0.319725\pi$
$727$	1.99593	+	1.15235i	0.0740249	+	0.0427383i	−0.462531	+	0.886603i	$0.653059\pi$
$728$	−3.34856	+	27.4609i	−0.124106	+	1.01777i
$729$	26.7508	+	3.65979i	0.990771	+	0.135548i
$730$	−10.8115			−0.400150
$731$	−21.3866	+	37.0428i	−0.791014	+	1.37008i
$732$	0.196410	−	8.66579i	0.00725951	−	0.320297i
$733$	43.1657	−	24.9217i	1.59436	−	0.920504i	0.601813	−	0.798637i	$-0.294445\pi$
$733$	43.1657	−	24.9217i	1.59436	−	0.920504i	0.992546	−	0.121867i	$-0.0388883\pi$
$734$	2.01512	+	3.49029i	0.0743794	+	0.128829i
$735$	8.60353	−	8.54279i	0.317346	−	0.315106i
$736$	−16.0824	+	27.8555i	−0.592805	+	1.02677i
$737$		−	0.822271i		−	0.0302887i
$738$	−1.87412	+	41.3227i	−0.0689872	+	1.52111i
$739$	23.2021			0.853505			0.426752	−	0.904369i	$-0.359658\pi$
$739$	23.2021			0.853505			0.426752	+	0.904369i	$0.359658\pi$
$740$	1.43366	−	2.48317i	0.0527024	−	0.0912833i
$741$	4.52499	+	8.26452i	0.166230	+	0.303605i
$742$	37.6675	−	16.0259i	1.38282	−	0.588331i
$743$	−22.7634	+	13.1425i	−0.835109	+	0.482151i	−0.855599	−	0.517640i	$-0.826811\pi$
$743$	−22.7634	+	13.1425i	−0.835109	+	0.482151i	0.0204896	+	0.999790i	$0.493477\pi$
$744$	−14.4811	−	26.4484i	−0.530901	−	0.969646i
$745$	−8.13399	−	4.69616i	−0.298006	−	0.172054i
$746$		−	43.1770i		−	1.58082i
$747$	−5.26535	+	8.23423i	−0.192649	+	0.301275i
$748$		−	6.22709i		−	0.227685i
$749$	7.59940	−	10.1022i	0.277676	−	0.369128i
$750$	−2.41921	−	1.47081i	−0.0883370	−	0.0537063i
$751$	13.8847	+	24.0489i	0.506658	+	0.877558i	0.999970	+	0.00770566i	$0.00245281\pi$
$751$	13.8847	+	24.0489i	0.506658	+	0.877558i	−0.493312	+	0.869853i	$0.664214\pi$
$752$	−3.61625	−	6.26353i	−0.131871	−	0.228408i
$753$	9.55850	+	0.216643i	0.348331	+	0.00789491i
$754$	28.5838	+	16.5029i	1.04096	+	0.601000i
$755$	−9.15107			−0.333042
$756$	−1.73850	+	9.07271i	−0.0632285	+	0.329971i
$757$	−5.00655			−0.181966			−0.0909831	−	0.995852i	$-0.529001\pi$
$757$	−5.00655			−0.181966			−0.0909831	+	0.995852i	$0.529001\pi$
$758$	−11.8338	−	6.83224i	−0.429823	−	0.248158i
$759$	22.1649	+	0.502366i	0.804535	+	0.0182347i
$760$	1.22588	+	2.12329i	0.0444675	+	0.0770200i
$761$	−23.5905	−	40.8599i	−0.855155	−	1.48117i	−0.876501	−	0.481400i	$-0.840129\pi$
$761$	−23.5905	−	40.8599i	−0.855155	−	1.48117i	0.0213461	−	0.999772i	$-0.493205\pi$
$762$	26.9552	+	16.3880i	0.976485	+	0.593674i
$763$	−32.8253	−	24.6928i	−1.18836	−	0.893940i
$764$		−	8.71682i		−	0.315364i
$765$	8.79605	+	16.9670i	0.318022	+	0.613442i
$766$		−	41.7292i		−	1.50774i
$767$	13.6492	+	7.88039i	0.492845	+	0.284544i
$768$	−12.0698	−	22.0446i	−0.435533	−	0.795464i
$769$	22.3667	−	12.9134i	0.806564	−	0.465670i	−0.0391974	−	0.999231i	$-0.512480\pi$
$769$	22.3667	−	12.9134i	0.806564	−	0.465670i	0.845761	+	0.533562i	$0.179147\pi$
$770$	−5.78911	+	2.46302i	−0.208625	+	0.0887611i
$771$	0.504186	+	0.920854i	0.0181578	+	0.0331637i
$772$	−0.961109	+	1.66469i	−0.0345911	+	0.0599135i
$773$	−1.15100			−0.0413984			−0.0206992	−	0.999786i	$-0.506589\pi$
$773$	−1.15100			−0.0413984			−0.0206992	+	0.999786i	$0.506589\pi$
$774$	−29.2311	+	15.1541i	−1.05069	+	0.544701i
$775$		−	8.01946i		−	0.288067i
$776$	12.5837	−	21.7955i	0.451727	−	0.782414i
$777$	15.3565	+	12.1063i	0.550910	+	0.434313i
$778$	13.8445	+	23.9793i	0.496348	+	0.859700i
$779$	8.25051	−	4.76344i	0.295605	−	0.170668i
$780$	0.127023	−	5.60436i	0.00454814	−	0.200668i
$781$	−11.4259	+	19.7903i	−0.408852	+	0.708152i
$782$	91.6279			3.27661
$783$	−18.0811	−	12.1478i	−0.646167	−	0.434127i
$784$	33.2432	+	8.22966i	1.18726	+	0.293917i
$785$	−2.77373	−	1.60141i	−0.0989985	−	0.0571568i
$786$	0.124260	−	5.48247i	0.00443220	−	0.195553i
$787$	5.44315	−	3.14261i	0.194027	−	0.112022i	−0.399839	−	0.916585i	$-0.630934\pi$
$787$	5.44315	−	3.14261i	0.194027	−	0.112022i	0.593867	+	0.804564i	$0.297601\pi$
$788$	−9.36265	+	5.40553i	−0.333530	+	0.192564i
$789$	−20.0123	−	12.1669i	−0.712456	−	0.433152i
$790$	−10.7764	−	6.22173i	−0.383405	−	0.221359i
$791$	22.9576	+	2.79944i	0.816279	+	0.0995365i
$792$	−5.10378	+	7.98155i	−0.181355	+	0.283612i
$793$	−35.8727			−1.27388
$794$	31.1472	−	53.9485i	1.10537	−	1.91456i
$795$	14.3800	−	7.87332i	0.510004	−	0.279238i
$796$	13.7284	−	7.92609i	0.486590	−	0.280933i
$797$	7.23122	+	12.5248i	0.256143	+	0.443653i	0.965205	−	0.261493i	$-0.0842149\pi$
$797$	7.23122	+	12.5248i	0.256143	+	0.443653i	−0.709062	+	0.705146i	$0.750882\pi$
$798$	7.85784	−	3.13485i	0.278164	−	0.110973i
$799$	−4.70881	+	8.15590i	−0.166586	+	0.288535i
$800$		−	3.65544i		−	0.129239i
$801$	−9.53259	−	0.432334i	−0.336818	−	0.0152758i
$802$	−9.51130			−0.335856
$803$	−4.81079	+	8.33252i	−0.169769	+	0.294048i
$804$	0.341757	−	0.562127i	0.0120528	−	0.0198247i
$805$	−9.11421	−	21.4221i	−0.321234	−	0.755030i
$806$	54.6803	−	31.5697i	1.92603	−	1.11199i
$807$	−33.2906	−	0.754530i	−1.17189	−	0.0265607i
$808$	−12.6337	−	7.29405i	−0.444451	−	0.256604i
$809$		−	28.3908i		−	0.998167i	−0.866554	−	0.499083i	$-0.833670\pi$
$809$		−	28.3908i		−	0.998167i	0.866554	−	0.499083i	$-0.166330\pi$
$810$	−1.33169	+	14.6511i	−0.0467907	+	0.514787i
$811$		−	4.01801i		−	0.141092i	−0.997509	−	0.0705458i	$-0.977526\pi$
$811$		−	4.01801i		−	0.141092i	0.997509	−	0.0705458i	$-0.0224741\pi$
$812$	4.48025	−	5.95581i	0.157226	−	0.209008i
$813$	0.558339	−	24.6345i	0.0195818	−	0.863969i
$814$	−5.07342	−	8.78741i	−0.177823	−	0.307999i
$815$	−1.14937	−	1.99076i	−0.0402605	−	0.0697333i
$816$	−28.0437	+	46.1267i	−0.981726	+	1.61476i
$817$	6.56721	+	3.79158i	0.229758	+	0.132651i
$818$	47.4578			1.65932
$819$	37.7009	+	6.34215i	1.31738	+	0.221613i
$820$	−5.66808			−0.197938
$821$	31.1099	+	17.9613i	1.08574	+	0.626854i	0.932440	−	0.361325i	$-0.117676\pi$
$821$	31.1099	+	17.9613i	1.08574	+	0.626854i	0.153303	+	0.988179i	$0.451009\pi$
$822$	−16.9698	−	30.9938i	−0.591888	−	1.08103i
$823$	−22.5092	−	38.9871i	−0.784622	−	1.35900i	−0.929225	−	0.369515i	$-0.879524\pi$
$823$	−22.5092	−	38.9871i	−0.784622	−	1.35900i	0.144603	−	0.989490i	$-0.453810\pi$
$824$	−7.99501	−	13.8478i	−0.278519	−	0.482410i
$825$	−2.21005	+	1.21005i	−0.0769440	+	0.0421284i
$826$	8.50712	−	11.3089i	0.296000	−	0.393487i
$827$		−	5.95051i		−	0.206920i	−0.994634	−	0.103460i	$-0.967009\pi$
$827$		−	5.95051i		−	0.206920i	0.994634	−	0.103460i	$-0.0329913\pi$
$828$	14.9437	+	9.55573i	0.519331	+	0.332085i
$829$		−	3.36094i		−	0.116730i	−0.998295	−	0.0583652i	$-0.981411\pi$
$829$		−	3.36094i		−	0.116730i	0.998295	−	0.0583652i	$-0.0185888\pi$
$830$	−4.61196	−	2.66272i	−0.160083	−	0.0924242i
$831$	−22.8233	+	37.5400i	−0.791730	+	1.30225i
$832$	−15.8907	+	9.17453i	−0.550912	+	0.318069i
$833$	−12.3630	−	42.8454i	−0.428352	−	1.48451i
$834$	14.9398	+	0.338610i	0.517324	+	0.0117251i
$835$	−6.51434	+	11.2832i	−0.225438	+	0.390470i
$836$	−1.10398			−0.0381821
$837$	−37.4195	+	18.3356i	−1.29341	+	0.633770i
$838$			48.0685i			1.66050i
$839$	−0.948753	+	1.64329i	−0.0327546	+	0.0567326i	−0.881938	−	0.471365i	$-0.843761\pi$
$839$	−0.948753	+	1.64329i	−0.0327546	+	0.0567326i	0.849183	+	0.528098i	$0.177095\pi$
$840$	9.84510	+	1.42759i	0.339688	+	0.0492565i
$841$	−5.71302	−	9.89524i	−0.197001	−	0.341215i
$842$	−33.9864	+	19.6221i	−1.17125	+	0.676221i
$843$	27.0808	+	16.4644i	0.932714	+	0.567063i
$844$	3.15802	−	5.46985i	0.108704	−	0.188280i
$845$	−10.1997			−0.350880
$846$	−6.43596	+	3.33655i	−0.221273	+	0.114713i
$847$	2.84503	−	23.3316i	0.0977566	−	0.801682i
$848$	40.1035	+	23.1538i	1.37716	+	0.795104i
$849$	−21.6236	+	11.8394i	−0.742119	+	0.406326i
$850$	−9.01815	+	5.20663i	−0.309320	+	0.178586i
$851$	32.5171	−	18.7738i	1.11467	−	0.643556i
$852$	−16.0364	+	8.78027i	−0.549399	+	0.300807i
$853$	−1.38628	−	0.800367i	−0.0474652	−	0.0274040i	0.476080	−	0.879402i	$-0.342057\pi$
$853$	−1.38628	−	0.800367i	−0.0474652	−	0.0274040i	−0.523545	+	0.851998i	$0.675391\pi$
$854$	−3.89875	+	31.9728i	−0.133412	+	1.09409i
$855$	3.00803	−	1.55943i	0.102872	−	0.0533313i
$856$	10.3723			0.354519
$857$	−3.02250	+	5.23513i	−0.103247	+	0.178828i	−0.913021	−	0.407914i	$-0.866256\pi$
$857$	−3.02250	+	5.23513i	−0.103247	+	0.178828i	0.809774	+	0.586742i	$0.199590\pi$
$858$	−16.9508	−	10.3056i	−0.578691	−	0.351827i
$859$	−38.6087	+	22.2908i	−1.31731	+	0.760551i	−0.983296	−	0.182016i	$-0.941738\pi$
$859$	−38.6087	+	22.2908i	−1.31731	+	0.760551i	−0.334018	+	0.942567i	$0.608404\pi$
$860$	−2.25583	−	3.90721i	−0.0769231	−	0.133235i
$861$	5.54720	−	38.2552i	0.189048	−	1.30373i
$862$	−8.40766	+	14.5625i	−0.286366	+	0.496001i
$863$			26.0301i			0.886076i	0.896503	+	0.443038i	$0.146099\pi$
$863$			26.0301i			0.886076i	−0.896503	+	0.443038i	$0.853901\pi$
$864$	−17.0567	+	8.35776i	−0.580279	+	0.284337i
$865$	10.8276			0.368149
$866$	−18.8901	+	32.7187i	−0.641913	+	1.11183i
$867$	40.8367	+	0.925562i	1.38689	+	0.0314337i
$868$	−5.58161	−	13.1191i	−0.189452	−	0.445290i
$869$	−9.59034	+	5.53698i	−0.325330	+	0.187829i
$870$	6.16582	−	10.1416i	0.209041	−	0.343834i
$871$	−2.35782	−	1.36129i	−0.0798917	−	0.0461255i
$872$		−	33.7030i		−	1.14133i
$873$	−29.3015	−	18.7368i	−0.991706	−	0.634144i
$874$		−	16.2445i		−	0.549477i
$875$	2.11432	+	1.59049i	0.0714769	+	0.0537685i
$876$	−6.75199	+	3.69686i	−0.228129	+	0.124905i
$877$	−18.4461	−	31.9496i	−0.622881	−	1.07886i	−0.988947	−	0.148272i	$-0.952629\pi$
$877$	−18.4461	−	31.9496i	−0.622881	−	1.07886i	0.366066	−	0.930589i	$-0.380704\pi$
$878$	2.80799	+	4.86359i	0.0947652	+	0.164138i
$879$	−0.926002	−	1.69126i	−0.0312333	−	0.0570449i
$880$	−6.16349	−	3.55850i	−0.207771	−	0.119957i
$881$	6.15732			0.207445			0.103723	−	0.994606i	$-0.466925\pi$
$881$	6.15732			0.207445			0.103723	+	0.994606i	$0.466925\pi$
$882$	9.75011	−	32.9130i	0.328303	−	1.10824i
$883$	29.9261			1.00709			0.503546	−	0.863968i	$-0.332028\pi$
$883$	29.9261			1.00709			0.503546	+	0.863968i	$0.332028\pi$
$884$	−17.8559	−	10.3091i	−0.600558	−	0.346732i
$885$	2.94428	−	4.84279i	0.0989708	−	0.162789i
$886$	−15.3242	−	26.5423i	−0.514827	−	0.891706i
$887$	28.5822	+	49.5058i	0.959697	+	1.66224i	0.723234	+	0.690603i	$0.242655\pi$
$887$	28.5822	+	49.5058i	0.959697	+	1.66224i	0.236463	+	0.971641i	$0.424012\pi$
$888$	−0.363557	+	16.0405i	−0.0122002	+	0.538285i
$889$	−23.5581	−	17.7215i	−0.790112	−	0.594361i
$890$		−	5.19936i		−	0.174283i
$891$	10.6992	+	7.54566i	0.358437	+	0.252789i
$892$		−	2.51186i		−	0.0841032i
$893$	1.44594	+	0.834812i	0.0483865	+	0.0279359i
$894$	−26.5850	−	0.602546i	−0.889134	−	0.0201522i
$895$	−7.42550	+	4.28711i	−0.248207	+	0.143302i
$896$	14.0227	+	32.9591i	0.468467	+	1.10109i
$897$	38.1350	−	62.7251i	1.27329	−	2.09433i
$898$	16.3219	−	28.2704i	0.544669	−	0.943394i
$899$	33.6186			1.12124
$900$	−2.01378	−	0.0913312i	−0.0671259	−	0.00304437i
$901$		−	60.2982i		−	2.00882i
$902$	−10.0291	+	17.3708i	−0.333931	+	0.578385i
$903$	28.5784	−	11.4012i	0.951030	−	0.379410i
$904$	9.48816	+	16.4340i	0.315572	+	0.546586i
$905$	10.7503	−	6.20671i	0.357353	−	0.206318i
$906$	−22.7254	+	12.4426i	−0.755002	+	0.413379i
$907$	4.19628	−	7.26817i	0.139335	−	0.241336i	−0.787910	−	0.615790i	$-0.788837\pi$
$907$	4.19628	−	7.26817i	0.139335	−	0.241336i	0.927245	+	0.374455i	$0.122170\pi$
$908$	11.1001			0.368369
$909$	−10.8607	+	16.9845i	−0.360226	+	0.563340i
$910$	−2.52141	+	20.6776i	−0.0835838	+	0.685454i
$911$	−46.9250	−	27.0922i	−1.55469	−	0.897603i	−0.997749	−	0.0670542i	$-0.978640\pi$
$911$	−46.9250	−	27.0922i	−1.55469	−	0.897603i	−0.556945	−	0.830549i	$-0.688027\pi$
$912$	8.17768	+	4.97179i	0.270790	+	0.164632i
$913$	−4.10438	+	2.36966i	−0.135835	+	0.0784244i
$914$	42.5621	−	24.5732i	1.40783	−	0.812811i
$915$	−0.292299	+	12.8965i	−0.00966310	+	0.426346i
$916$	0.676894	+	0.390805i	0.0223652	+	0.0129126i
$917$	−0.620298	+	5.08694i	−0.0204841	+	0.167986i
$918$	44.9136	+	30.1752i	1.48237	+	0.995929i
$919$	29.4897			0.972775			0.486387	−	0.873743i	$-0.338314\pi$
$919$	29.4897			0.972775			0.486387	+	0.873743i	$0.338314\pi$
$920$	9.55080	−	16.5425i	0.314881	−	0.545389i
$921$	−0.228456	+	10.0797i	−0.00752787	+	0.332137i
$922$	−31.1687	+	17.9953i	−1.02649	+	0.592643i
$923$	37.8318	+	65.5265i	1.24525	+	2.15683i
$924$	−2.77322	+	3.51773i	−0.0912323	+	0.115725i
$925$	−2.13359	+	3.69548i	−0.0701519	+	0.121507i
$926$			33.5123i			1.10128i
$927$	−19.6179	+	10.1703i	−0.644335	+	0.334038i
$928$	15.3241			0.503038
$929$	3.33959	−	5.78434i	0.109568	−	0.189778i	−0.806027	−	0.591879i	$-0.798386\pi$
$929$	3.33959	−	5.78434i	0.109568	−	0.189778i	0.915595	+	0.402101i	$0.131720\pi$
$930$	−10.9040	−	19.9152i	−0.357556	−	0.653045i
$931$	−7.59595	+	2.19180i	−0.248947	+	0.0718334i
$932$	10.7570	−	6.21058i	0.352359	−	0.203434i
$933$	3.91466	+	7.14979i	0.128160	+	0.234074i
$934$	3.13076	+	1.80754i	0.102442	+	0.0591446i
$935$			9.26721i			0.303070i
$936$	14.4373	+	27.8485i	0.471897	+	0.910256i
$937$		−	26.7523i		−	0.873959i	−0.899472	−	0.436979i	$-0.856048\pi$
$937$		−	26.7523i		−	0.873959i	0.899472	−	0.436979i	$-0.143952\pi$
$938$	−1.46955	+	1.95354i	−0.0479825	+	0.0637854i
$939$	17.8095	+	10.8277i	0.581191	+	0.353347i
$940$	−0.496678	−	0.860271i	−0.0161998	−	0.0280589i
$941$	26.1593	+	45.3092i	0.852768	+	1.47704i	0.878700	+	0.477374i	$0.158411\pi$
$941$	26.1593	+	45.3092i	0.852768	+	1.47704i	−0.0259320	+	0.999664i	$0.508255\pi$
$942$	−9.06559	−	0.205471i	−0.295373	−	0.00669461i
$943$	−64.2793	−	37.1117i	−2.09322	−	1.20852i
$944$	16.0087			0.521040
$945$	2.58725	−	13.5021i	0.0841631	−	0.439223i
$946$	−15.9658			−0.519092
$947$	−7.24519	−	4.18301i	−0.235437	−	0.135930i	0.377641	−	0.925952i	$-0.376735\pi$
$947$	−7.24519	−	4.18301i	−0.235437	−	0.135930i	−0.613078	+	0.790023i	$0.710069\pi$
$948$	−8.85753	−	0.200755i	−0.287679	−	0.00652023i
$949$	15.9287	+	27.5894i	0.517068	+	0.895589i
$950$	0.923070	+	1.59880i	0.0299483	+	0.0518721i
$951$	−5.52699	−	3.36025i	−0.179225	−	0.108963i
$952$	21.9955	−	29.2396i	0.712878	−	0.947661i
$953$		−	58.9752i		−	1.91040i	−0.295969	−	0.955198i	$-0.595642\pi$
$953$		−	58.9752i		−	1.91040i	0.295969	−	0.955198i	$-0.404358\pi$
$954$	25.0053	−	39.1046i	0.809578	−	1.26606i
$955$			12.9725i			0.419779i
$956$	−6.98964	−	4.03547i	−0.226061	−	0.130517i
$957$	−5.07268	−	9.26481i	−0.163976	−	0.299489i
$958$	4.39312	−	2.53637i	0.141935	−	0.0819464i
$959$	12.9275	+	30.3848i	0.417449	+	0.981177i
$960$	3.16883	+	5.78760i	0.102274	+	0.186794i
$961$	16.6558	−	28.8488i	0.537285	−	0.930606i
$962$	−33.5966			−1.08320
$963$	0.649428	−	14.3193i	0.0209275	−	0.461434i
$964$			17.4777i			0.562919i
$965$	1.43033	−	2.47741i	0.0460440	−	0.0797505i
$966$	−51.7613	−	40.8063i	−1.66539	−	1.31292i
$967$	25.7118	+	44.5341i	0.826835	+	1.43212i	0.900509	+	0.434838i	$0.143194\pi$
$967$	25.7118	+	44.5341i	0.826835	+	1.43212i	−0.0736739	+	0.997282i	$0.523472\pi$
$968$	16.7017	−	9.64270i	0.536811	−	0.309928i
$969$	0.282376	−	12.4587i	0.00907121	−	0.400231i
$970$	9.47527	−	16.4117i	0.304233	−	0.526947i
$971$	−26.2726			−0.843129			−0.421564	−	0.906798i	$-0.638519\pi$
$971$	−26.2726			−0.843129			−0.421564	+	0.906798i	$0.638519\pi$
$972$	4.17811	+	9.60529i	0.134013	+	0.308090i
$973$	−13.8620	−	1.69032i	−0.444396	−	0.0541893i
$974$	−40.9682	−	23.6530i	−1.31270	−	0.757890i
$975$	−0.189036	+	8.34046i	−0.00605400	+	0.267109i
$976$	−31.5554	+	18.2185i	−1.01006	+	0.583161i
$977$	27.5820	−	15.9245i	0.882428	−	0.509470i	0.0109695	−	0.999940i	$-0.496508\pi$
$977$	27.5820	−	15.9245i	0.882428	−	0.509470i	0.871458	+	0.490470i	$0.163175\pi$
$978$	−5.56111	−	3.38099i	−0.177825	−	0.108112i
$979$	−4.00722	−	2.31357i	−0.128071	−	0.0739419i
$980$	4.56581	+	1.13031i	0.145850	+	0.0361064i
$981$	−46.5280	−	2.11019i	−1.48552	−	0.0673732i
$982$	35.1599			1.12200
$983$	11.6123	−	20.1132i	0.370376	−	0.641510i	−0.619247	−	0.785196i	$-0.712562\pi$
$983$	11.6123	−	20.1132i	0.370376	−	0.641510i	0.989623	+	0.143686i	$0.0458955\pi$
$984$	27.8198	−	15.2319i	0.886864	−	0.485576i
$985$	13.9336	−	8.04455i	0.443961	−	0.256321i
$986$	−21.8269	−	37.8053i	−0.695109	−	1.20396i
$987$	6.29226	−	2.51027i	0.200285	−	0.0799029i
$988$	−1.82767	+	3.16562i	−0.0581459	+	0.100712i
$989$		−	59.0800i		−	1.87864i
$990$	−3.84306	+	6.00997i	−0.122140	+	0.191009i
$991$	56.9448			1.80891			0.904456	−	0.426567i	$-0.140277\pi$
$991$	56.9448			1.80891			0.904456	+	0.426567i	$0.140277\pi$
$992$	14.6573	−	25.3873i	0.465371	−	0.806046i
$993$	3.68046	−	6.05368i	0.116796	−	0.192108i
$994$	62.5145	−	26.5973i	1.98284	−	0.843615i
$995$	−20.4307	+	11.7957i	−0.647697	+	0.373948i
$996$	−3.79076	−	0.0859173i	−0.120115	−	0.00272239i
$997$	2.27939	+	1.31601i	0.0721890	+	0.0416784i	0.535660	−	0.844434i	$-0.320063\pi$
$997$	2.27939	+	1.31601i	0.0721890	+	0.0416784i	−0.463471	+	0.886112i	$0.653396\pi$
$998$			50.0262i			1.58355i
$999$	22.1217	+	1.50622i	0.699899	+	0.0476548i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bl.j.146.3	yes	24
3.2	odd	2		945.2.bl.j.251.10		24
7.6	odd	2		315.2.bl.i.146.3	yes	24
9.4	even	3		945.2.bl.i.881.10		24
9.5	odd	6		315.2.bl.i.41.3	✓	24
21.20	even	2		945.2.bl.i.251.10		24
63.13	odd	6		945.2.bl.j.881.10		24
63.41	even	6	inner	315.2.bl.j.41.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bl.i.41.3	✓	24	9.5	odd	6
315.2.bl.i.146.3	yes	24	7.6	odd	2
315.2.bl.j.41.3	yes	24	63.41	even	6	inner
315.2.bl.j.146.3	yes	24	1.1	even	1	trivial
945.2.bl.i.251.10		24	21.20	even	2
945.2.bl.i.881.10		24	9.4	even	3
945.2.bl.j.251.10		24	3.2	odd	2
945.2.bl.j.881.10		24	63.13	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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41561 - 0.817305i) q^{2} +(1.73161 + 0.0392468i) q^{3} +(0.335974 + 0.581925i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.41921 - 1.47081i) q^{6} +(2.11432 + 1.59049i) q^{7} +2.17085i q^{8} +(2.99692 + 0.135920i) q^{9} +O(q^{10})\)	\(q+(-1.41561 - 0.817305i) q^{2} +(1.73161 + 0.0392468i) q^{3} +(0.335974 + 0.581925i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.41921 - 1.47081i) q^{6} +(2.11432 + 1.59049i) q^{7} +2.17085i q^{8} +(2.99692 + 0.135920i) q^{9} +1.63461i q^{10} +(1.25981 + 0.727354i) q^{11} +(0.558937 + 1.02085i) q^{12} +(4.17130 - 2.40830i) q^{13} +(-1.69314 - 3.97956i) q^{14} +(-0.831814 - 1.51924i) q^{15} +(2.44619 - 4.23693i) q^{16} -6.37049 q^{17} +(-4.13139 - 2.64181i) q^{18} +1.12941i q^{19} +(0.335974 - 0.581925i) q^{20} +(3.59874 + 2.83709i) q^{21} +(-1.18894 - 2.05931i) q^{22} +(7.62029 - 4.39958i) q^{23} +(-0.0851986 + 3.75905i) q^{24} +(-0.500000 + 0.866025i) q^{25} -7.87327 q^{26} +(5.18415 + 0.352979i) q^{27} +(-0.215191 + 1.76474i) q^{28} +(-3.63049 - 2.09607i) q^{29} +(-0.0641531 + 2.83050i) q^{30} +(-6.94505 + 4.00973i) q^{31} +(-3.16571 + 1.82772i) q^{32} +(2.15296 + 1.30893i) q^{33} +(9.01815 + 5.20663i) q^{34} +(0.320249 - 2.62630i) q^{35} +(0.927793 + 1.78965i) q^{36} +4.26717 q^{37} +(0.923070 - 1.59880i) q^{38} +(7.31757 - 4.00652i) q^{39} +(1.88001 - 1.08542i) q^{40} +(-4.21764 - 7.30517i) q^{41} +(-2.77566 - 6.95749i) q^{42} +(3.35714 - 5.81474i) q^{43} +0.977490i q^{44} +(-1.38075 - 2.66337i) q^{45} -14.3832 q^{46} +(0.739160 - 1.28026i) q^{47} +(4.40213 - 7.24068i) q^{48} +(1.94067 + 6.72561i) q^{49} +(1.41561 - 0.817305i) q^{50} +(-11.0312 - 0.250021i) q^{51} +(2.80290 + 1.61826i) q^{52} +9.46524i q^{53} +(-7.05026 - 4.73671i) q^{54} -1.45471i q^{55} +(-3.45271 + 4.58985i) q^{56} +(-0.0443256 + 1.95569i) q^{57} +(3.42625 + 5.93444i) q^{58} +(1.63609 + 2.83379i) q^{59} +(0.604614 - 0.994478i) q^{60} +(-6.44991 - 3.72386i) q^{61} +13.1087 q^{62} +(6.12026 + 5.05396i) q^{63} -3.80954 q^{64} +(-4.17130 - 2.40830i) q^{65} +(-1.97796 - 3.61257i) q^{66} +(-0.282624 - 0.489519i) q^{67} +(-2.14032 - 3.70715i) q^{68} +(13.3680 - 7.31926i) q^{69} +(-2.59983 + 3.45608i) q^{70} +15.7089i q^{71} +(-0.295061 + 6.50585i) q^{72} +6.61409i q^{73} +(-6.04067 - 3.48758i) q^{74} +(-0.899792 + 1.47999i) q^{75} +(-0.657230 + 0.379452i) q^{76} +(1.50679 + 3.54158i) q^{77} +(-13.6334 - 0.309000i) q^{78} +(-3.80625 + 6.59262i) q^{79} -4.89238 q^{80} +(8.96305 + 0.814682i) q^{81} +13.7884i q^{82} +(-1.62896 + 2.82144i) q^{83} +(-0.441886 + 3.04738i) q^{84} +(3.18524 + 5.51701i) q^{85} +(-9.50483 + 5.48762i) q^{86} +(-6.20432 - 3.77204i) q^{87} +(-1.57897 + 2.73486i) q^{88} -3.18080 q^{89} +(-0.222176 + 4.89879i) q^{90} +(12.6498 + 1.54251i) q^{91} +(5.12044 + 2.95629i) q^{92} +(-12.1835 + 6.67070i) q^{93} +(-2.09273 + 1.20824i) q^{94} +(0.978095 - 0.564704i) q^{95} +(-5.55349 + 3.04065i) q^{96} +(-10.0401 - 5.79666i) q^{97} +(2.74964 - 11.1070i) q^{98} +(3.67670 + 2.35106i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} + 5 q^{3} + 18 q^{4} - 12 q^{5} + q^{6} + 9 q^{7} + q^{9}+O(q^{10}) \) 24 * q + 6 * q^2 + 5 * q^3 + 18 * q^4 - 12 * q^5 + q^6 + 9 * q^7 + q^9	\( 24 q + 6 q^{2} + 5 q^{3} + 18 q^{4} - 12 q^{5} + q^{6} + 9 q^{7} + q^{9} + 9 q^{11} - 18 q^{12} + 3 q^{13} + 18 q^{14} + 2 q^{15} - 18 q^{16} + 18 q^{17} + 2 q^{18} + 18 q^{20} + 8 q^{21} - 9 q^{22} + 9 q^{23} - 7 q^{24} - 12 q^{25} - 18 q^{26} - 4 q^{27} - 9 q^{28} + 9 q^{29} - 5 q^{30} - 42 q^{31} + 18 q^{32} + 13 q^{33} - 39 q^{34} - 9 q^{35} - 21 q^{36} - 12 q^{38} - 21 q^{39} - 6 q^{40} - 33 q^{41} - 65 q^{42} + 18 q^{43} + q^{45} - 30 q^{46} - 17 q^{48} + 9 q^{49} - 6 q^{50} - 12 q^{51} + 129 q^{52} + 52 q^{54} - 9 q^{56} + 6 q^{57} - 15 q^{58} + 12 q^{59} + 15 q^{60} - 15 q^{61} + 12 q^{62} + 46 q^{63} - 60 q^{64} - 3 q^{65} + 29 q^{66} - 15 q^{67} + 9 q^{68} + 61 q^{69} - 9 q^{70} + 61 q^{72} - 18 q^{74} - 7 q^{75} + 54 q^{76} - 45 q^{77} - 66 q^{78} + 21 q^{79} + 36 q^{80} + q^{81} - 30 q^{83} + 15 q^{84} - 9 q^{85} - 102 q^{86} + 10 q^{87} - 9 q^{88} + 102 q^{89} - 37 q^{90} + 42 q^{91} - 3 q^{92} - 6 q^{93} - 156 q^{94} - 18 q^{95} - 42 q^{96} - 45 q^{97} + 3 q^{98} + 23 q^{99}+O(q^{100}) \) 24 * q + 6 * q^2 + 5 * q^3 + 18 * q^4 - 12 * q^5 + q^6 + 9 * q^7 + q^9 + 9 * q^11 - 18 * q^12 + 3 * q^13 + 18 * q^14 + 2 * q^15 - 18 * q^16 + 18 * q^17 + 2 * q^18 + 18 * q^20 + 8 * q^21 - 9 * q^22 + 9 * q^23 - 7 * q^24 - 12 * q^25 - 18 * q^26 - 4 * q^27 - 9 * q^28 + 9 * q^29 - 5 * q^30 - 42 * q^31 + 18 * q^32 + 13 * q^33 - 39 * q^34 - 9 * q^35 - 21 * q^36 - 12 * q^38 - 21 * q^39 - 6 * q^40 - 33 * q^41 - 65 * q^42 + 18 * q^43 + q^45 - 30 * q^46 - 17 * q^48 + 9 * q^49 - 6 * q^50 - 12 * q^51 + 129 * q^52 + 52 * q^54 - 9 * q^56 + 6 * q^57 - 15 * q^58 + 12 * q^59 + 15 * q^60 - 15 * q^61 + 12 * q^62 + 46 * q^63 - 60 * q^64 - 3 * q^65 + 29 * q^66 - 15 * q^67 + 9 * q^68 + 61 * q^69 - 9 * q^70 + 61 * q^72 - 18 * q^74 - 7 * q^75 + 54 * q^76 - 45 * q^77 - 66 * q^78 + 21 * q^79 + 36 * q^80 + q^81 - 30 * q^83 + 15 * q^84 - 9 * q^85 - 102 * q^86 + 10 * q^87 - 9 * q^88 + 102 * q^89 - 37 * q^90 + 42 * q^91 - 3 * q^92 - 6 * q^93 - 156 * q^94 - 18 * q^95 - 42 * q^96 - 45 * q^97 + 3 * q^98 + 23 * q^99

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