LMFDB - Embedded newform 95.2.p.a.9.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [95,2,Mod(4,95)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(95, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("95.4"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 95 = 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	95.p (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.758578819202$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			9.4
Character	$\chi$	$=$	95.9
Dual form			95.2.p.a.74.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.240763 + 0.0424530i) q^{2} +(-1.76019 - 2.09771i) q^{3} +(-1.82322 + 0.663598i) q^{4} +(-1.42562 + 1.72267i) q^{5} +(0.512843 + 0.430326i) q^{6} +(-1.68032 - 0.970136i) q^{7} +(0.834240 - 0.481648i) q^{8} +(-0.781184 + 4.43031i) q^{9} +(0.270105 - 0.475278i) q^{10} +(-2.11666 - 3.66617i) q^{11} +(4.60125 + 2.65653i) q^{12} +(0.816227 - 0.972742i) q^{13} +(0.445745 + 0.162238i) q^{14} +(6.12303 - 0.0416827i) q^{15} +(2.79220 - 2.34293i) q^{16} +(-2.42284 + 0.427212i) q^{17} -1.09982i q^{18} +(-1.64247 - 4.03761i) q^{19} +(1.45606 - 4.08685i) q^{20} +(0.922623 + 5.23246i) q^{21} +(0.665255 + 0.792820i) q^{22} +(1.75701 + 4.82735i) q^{23} +(-2.47878 - 0.902202i) q^{24} +(-0.935198 - 4.91176i) q^{25} +(-0.155222 + 0.268852i) q^{26} +(3.55406 - 2.05194i) q^{27} +(3.70738 + 0.653712i) q^{28} +(-1.50053 + 8.50995i) q^{29} +(-1.47243 + 0.269977i) q^{30} +(-2.55042 + 4.41746i) q^{31} +(-1.81118 + 2.15849i) q^{32} +(-3.96484 + 10.8933i) q^{33} +(0.565193 - 0.205714i) q^{34} +(4.06673 - 1.51160i) q^{35} +(-1.51568 - 8.59583i) q^{36} -11.0305i q^{37} +(0.566855 + 0.902380i) q^{38} -3.47724 q^{39} +(-0.359589 + 2.12377i) q^{40} +(1.91387 - 1.60593i) q^{41} +(-0.444267 - 1.22061i) q^{42} +(1.52842 - 4.19929i) q^{43} +(6.29201 + 5.27962i) q^{44} +(-6.51830 - 7.66168i) q^{45} +(-0.627959 - 1.08766i) q^{46} +(-6.66617 - 1.17543i) q^{47} +(-9.82960 - 1.73322i) q^{48} +(-1.61767 - 2.80189i) q^{49} +(0.433680 + 1.14287i) q^{50} +(5.16082 + 4.33044i) q^{51} +(-0.842653 + 2.31517i) q^{52} +(-0.235926 - 0.648201i) q^{53} +(-0.768575 + 0.644911i) q^{54} +(9.33317 + 1.58026i) q^{55} -1.86906 q^{56} +(-5.57868 + 10.5524i) q^{57} -2.11258i q^{58} +(-0.901817 - 5.11446i) q^{59} +(-11.1360 + 4.13923i) q^{60} +(-2.63378 + 0.958619i) q^{61} +(0.426513 - 1.17183i) q^{62} +(5.61065 - 6.68651i) q^{63} +(-3.30053 + 5.71668i) q^{64} +(0.512083 + 2.79285i) q^{65} +(0.492133 - 2.79103i) q^{66} +(5.13308 + 0.905101i) q^{67} +(4.13387 - 2.38669i) q^{68} +(7.03371 - 12.1828i) q^{69} +(-0.914948 + 0.536583i) q^{70} +(-0.744158 - 0.270851i) q^{71} +(1.48216 + 4.07220i) q^{72} +(0.910034 + 1.08454i) q^{73} +(0.468279 + 2.65574i) q^{74} +(-8.65733 + 10.6074i) q^{75} +(5.67394 + 6.27151i) q^{76} +8.21381i q^{77} +(0.837192 - 0.147620i) q^{78} +(4.64448 - 3.89718i) q^{79} +(0.0554826 + 8.15018i) q^{80} +(2.12188 + 0.772300i) q^{81} +(-0.392614 + 0.467899i) q^{82} +(-10.2643 - 5.92611i) q^{83} +(-5.15439 - 8.92767i) q^{84} +(2.71811 - 4.78280i) q^{85} +(-0.189714 + 1.07592i) q^{86} +(20.4926 - 11.8314i) q^{87} +(-3.53161 - 2.03898i) q^{88} +(1.71051 + 1.43529i) q^{89} +(1.89463 + 1.56793i) q^{90} +(-2.31522 + 0.842670i) q^{91} +(-6.40684 - 7.63537i) q^{92} +(13.7558 - 2.42551i) q^{93} +1.65487 q^{94} +(9.29702 + 2.92667i) q^{95} +7.71591 q^{96} +(-8.47901 + 1.49508i) q^{97} +(0.508425 + 0.605917i) q^{98} +(17.8958 - 6.51353i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 18 q^{4} - 6 q^{5} - 6 q^{6} - 12 q^{9} - 15 q^{10} - 12 q^{11} + 6 q^{14} + 3 q^{15} - 42 q^{16} + 12 q^{19} + 42 q^{20} - 54 q^{21} + 24 q^{24} + 12 q^{25} + 12 q^{26} + 18 q^{30} - 42 q^{31} - 36 q^{34}+ \cdots - 36 q^{99}+O(q^{100}) $ 48 * q - 18 * q^4 - 6 * q^5 - 6 * q^6 - 12 * q^9 - 15 * q^10 - 12 * q^11 + 6 * q^14 + 3 * q^15 - 42 * q^16 + 12 * q^19 + 42 * q^20 - 54 * q^21 + 24 * q^24 + 12 * q^25 + 12 * q^26 + 18 * q^30 - 42 * q^31 - 36 * q^34 + 6 * q^35 + 18 * q^36 - 48 * q^39 + 66 * q^40 + 6 * q^41 - 6 * q^44 - 9 * q^45 - 6 * q^46 + 12 * q^49 - 18 * q^50 + 108 * q^51 + 24 * q^54 + 36 * q^56 - 36 * q^59 - 114 * q^60 + 48 * q^61 - 18 * q^65 + 180 * q^66 + 66 * q^69 - 123 * q^70 - 24 * q^71 + 84 * q^74 + 72 * q^75 + 66 * q^76 + 48 * q^79 - 39 * q^80 - 78 * q^81 - 54 * q^84 - 84 * q^85 - 42 * q^86 - 12 * q^89 + 18 * q^90 - 30 * q^91 - 72 * q^94 - 63 * q^95 - 240 * q^96 - 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/95\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$-1$

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 $

$2$	−0.240763	+	0.0424530i	−0.170245	+	0.0300188i	−0.258121	−	0.966113i	$-0.583103\pi$
$2$	−0.240763	+	0.0424530i	−0.170245	+	0.0300188i	0.0878757	+	0.996131i	$0.471992\pi$
$3$	−1.76019	−	2.09771i	−1.01625	−	1.21111i	−0.977297	−	0.211873i	$-0.932044\pi$
$3$	−1.76019	−	2.09771i	−1.01625	−	1.21111i	−0.0389482	−	0.999241i	$-0.512401\pi$
$4$	−1.82322	+	0.663598i	−0.911610	+	0.331799i
$5$	−1.42562	+	1.72267i	−0.637558	+	0.770402i
$5$	−1.42562	+	1.72267i	−0.637558	+	0.770402i
$6$	0.512843	+	0.430326i	0.209367	+	0.175680i
$7$	−1.68032	−	0.970136i	−0.635103	−	0.366677i	0.147623	−	0.989044i	$-0.452838\pi$
$7$	−1.68032	−	0.970136i	−0.635103	−	0.366677i	−0.782726	+	0.622367i	$0.786171\pi$
$8$	0.834240	−	0.481648i	0.294948	−	0.170288i
$9$	−0.781184	+	4.43031i	−0.260395	+	1.47677i
$10$	0.270105	−	0.475278i	0.0854146	−	0.150296i
$11$	−2.11666	−	3.66617i	−0.638198	−	1.10539i	−0.985828	−	0.167760i	$-0.946347\pi$
$11$	−2.11666	−	3.66617i	−0.638198	−	1.10539i	0.347630	−	0.937632i	$-0.386987\pi$
$12$	4.60125	+	2.65653i	1.32827	+	0.766875i
$13$	0.816227	−	0.972742i	0.226381	−	0.269790i	−0.640884	−	0.767638i	$-0.721432\pi$
$13$	0.816227	−	0.972742i	0.226381	−	0.269790i	0.867264	+	0.497848i	$0.165876\pi$
$14$	0.445745	+	0.162238i	0.119130	+	0.0433599i
$15$	6.12303	−	0.0416827i	1.58096	−	0.0107624i
$16$	2.79220	−	2.34293i	0.698050	−	0.585733i
$17$	−2.42284	+	0.427212i	−0.587624	+	0.103614i	−0.459552	−	0.888151i	$-0.651990\pi$
$17$	−2.42284	+	0.427212i	−0.587624	+	0.103614i	−0.128072	+	0.991765i	$0.540879\pi$
$18$		−	1.09982i		−	0.259230i
$19$	−1.64247	−	4.03761i	−0.376809	−	0.926291i
$19$	−1.64247	−	4.03761i	−0.376809	−	0.926291i
$20$	1.45606	−	4.08685i	0.325586	−	0.913848i
$21$	0.922623	+	5.23246i	0.201333	+	1.14182i
$22$	0.665255	+	0.792820i	0.141833	+	0.169030i
$23$	1.75701	+	4.82735i	0.366362	+	1.00657i	0.976734	+	0.214457i	$0.0687981\pi$
$23$	1.75701	+	4.82735i	0.366362	+	1.00657i	−0.610371	+	0.792115i	$0.708980\pi$
$24$	−2.47878	−	0.902202i	−0.505979	−	0.184161i
$25$	−0.935198	−	4.91176i	−0.187040	−	0.982352i
$26$	−0.155222	+	0.268852i	−0.0304415	+	0.0527261i
$27$	3.55406	−	2.05194i	0.683979	−	0.394895i
$28$	3.70738	+	0.653712i	0.700629	+	0.123540i
$29$	−1.50053	+	8.50995i	−0.278642	+	1.58026i	0.448508	+	0.893779i	$0.351956\pi$
$29$	−1.50053	+	8.50995i	−0.278642	+	1.58026i	−0.727150	+	0.686479i	$0.759155\pi$
$30$	−1.47243	+	0.269977i	−0.268828	+	0.0492908i
$31$	−2.55042	+	4.41746i	−0.458069	+	0.793399i	−0.998859	−	0.0477591i	$-0.984792\pi$
$31$	−2.55042	+	4.41746i	−0.458069	+	0.793399i	0.540790	+	0.841158i	$0.318125\pi$
$32$	−1.81118	+	2.15849i	−0.320175	+	0.381570i
$33$	−3.96484	+	10.8933i	−0.690190	+	1.89628i
$34$	0.565193	−	0.205714i	0.0969299	−	0.0352796i
$35$	4.06673	−	1.51160i	0.687404	−	0.255507i
$36$	−1.51568	−	8.59583i	−0.252613	−	1.43264i
$37$		−	11.0305i		−	1.81341i	−0.421770	−	0.906703i	$-0.638591\pi$
$37$		−	11.0305i		−	1.81341i	0.421770	−	0.906703i	$-0.361409\pi$
$38$	0.566855	+	0.902380i	0.0919561	+	0.146385i
$39$	−3.47724			−0.556805
$40$	−0.359589	+	2.12377i	−0.0568560	+	0.335798i
$41$	1.91387	−	1.60593i	0.298897	−	0.250804i	−0.480988	−	0.876727i	$-0.659722\pi$
$41$	1.91387	−	1.60593i	0.298897	−	0.250804i	0.779885	+	0.625923i	$0.215278\pi$
$42$	−0.444267	−	1.22061i	−0.0685519	−	0.188345i
$43$	1.52842	−	4.19929i	0.233081	−	0.640386i	−0.766918	−	0.641745i	$-0.778211\pi$
$43$	1.52842	−	4.19929i	0.233081	−	0.640386i	0.999999	+	0.00135976i	$0.000432826\pi$
$44$	6.29201	+	5.27962i	0.948556	+	0.795933i
$45$	−6.51830	−	7.66168i	−0.971691	−	1.14214i
$46$	−0.627959	−	1.08766i	−0.0925876	−	0.160366i
$47$	−6.66617	−	1.17543i	−0.972362	−	0.171454i	−0.335169	−	0.942158i	$-0.608793\pi$
$47$	−6.66617	−	1.17543i	−0.972362	−	0.171454i	−0.637193	+	0.770705i	$0.719904\pi$
$48$	−9.82960	−	1.73322i	−1.41878	−	0.250169i
$49$	−1.61767	−	2.80189i	−0.231096	−	0.400270i
$50$	0.433680	+	1.14287i	0.0613317	+	0.161626i
$51$	5.16082	+	4.33044i	0.722659	+	0.606383i
$52$	−0.842653	+	2.31517i	−0.116855	+	0.321056i
$53$	−0.235926	−	0.648201i	−0.0324069	−	0.0890373i	0.922434	−	0.386155i	$-0.126197\pi$
$53$	−0.235926	−	0.648201i	−0.0324069	−	0.0890373i	−0.954841	+	0.297117i	$0.903975\pi$
$54$	−0.768575	+	0.644911i	−0.104590	+	0.0877613i
$55$	9.33317	+	1.58026i	1.25849	+	0.213082i
$56$	−1.86906			−0.249763
$57$	−5.57868	+	10.5524i	−0.738914	+	1.39770i
$58$		−	2.11258i		−	0.277396i
$59$	−0.901817	−	5.11446i	−0.117407	−	0.665846i	−0.985530	−	0.169498i	$-0.945785\pi$
$59$	−0.901817	−	5.11446i	−0.117407	−	0.665846i	0.868124	−	0.496348i	$-0.165326\pi$
$60$	−11.1360	+	4.13923i	−1.43765	+	0.534372i
$61$	−2.63378	+	0.958619i	−0.337221	+	0.122739i	−0.505080	−	0.863073i	$-0.668537\pi$
$61$	−2.63378	+	0.958619i	−0.337221	+	0.122739i	0.167859	+	0.985811i	$0.446315\pi$
$62$	0.426513	−	1.17183i	0.0541672	−	0.148823i
$63$	5.61065	−	6.68651i	0.706875	−	0.842421i
$64$	−3.30053	+	5.71668i	−0.412566	+	0.714585i
$65$	0.512083	+	2.79285i	0.0635160	+	0.346411i
$66$	0.492133	−	2.79103i	0.0605774	−	0.343551i
$67$	5.13308	+	0.905101i	0.627106	+	0.110576i	0.478164	−	0.878270i	$-0.341302\pi$
$67$	5.13308	+	0.905101i	0.627106	+	0.110576i	0.148941	+	0.988846i	$0.452413\pi$
$68$	4.13387	−	2.38669i	0.501305	−	0.289429i
$69$	7.03371	−	12.1828i	0.846760	−	1.46663i
$70$	−0.914948	+	0.536583i	−0.109357	+	0.0641339i
$71$	−0.744158	−	0.270851i	−0.0883153	−	0.0321441i	0.297485	−	0.954727i	$-0.403852\pi$
$71$	−0.744158	−	0.270851i	−0.0883153	−	0.0321441i	−0.385800	+	0.922582i	$0.626075\pi$
$72$	1.48216	+	4.07220i	0.174674	+	0.479913i
$73$	0.910034	+	1.08454i	0.106511	+	0.126935i	0.816666	−	0.577110i	$-0.195820\pi$
$73$	0.910034	+	1.08454i	0.106511	+	0.126935i	−0.710155	+	0.704045i	$0.751375\pi$
$74$	0.468279	+	2.65574i	0.0544363	+	0.308724i
$75$	−8.65733	+	10.6074i	−0.999663	+	1.22484i
$76$	5.67394	+	6.27151i	0.650845	+	0.719392i
$77$			8.21381i			0.936050i
$78$	0.837192	−	0.147620i	0.0947934	−	0.0167146i
$79$	4.64448	−	3.89718i	0.522545	−	0.438467i	−0.342973	−	0.939345i	$-0.611434\pi$
$79$	4.64448	−	3.89718i	0.522545	−	0.438467i	0.865518	+	0.500878i	$0.166989\pi$
$80$	0.0554826	+	8.15018i	0.00620315	+	0.911218i
$81$	2.12188	+	0.772300i	0.235764	+	0.0858112i
$82$	−0.392614	+	0.467899i	−0.0433569	+	0.0516708i
$83$	−10.2643	−	5.92611i	−1.12666	−	0.650476i	−0.183565	−	0.983008i	$-0.558764\pi$
$83$	−10.2643	−	5.92611i	−1.12666	−	0.650476i	−0.943092	+	0.332532i	$0.892097\pi$
$84$	−5.15439	−	8.92767i	−0.562391	−	0.974089i
$85$	2.71811	−	4.78280i	0.294820	−	0.518767i
$86$	−0.189714	+	1.07592i	−0.0204574	+	0.116019i
$87$	20.4926	−	11.8314i	2.19704	−	1.26846i
$88$	−3.53161	−	2.03898i	−0.376471	−	0.217356i
$89$	1.71051	+	1.43529i	0.181314	+	0.152140i	0.728927	−	0.684591i	$-0.240019\pi$
$89$	1.71051	+	1.43529i	0.181314	+	0.152140i	−0.547614	+	0.836731i	$0.684464\pi$
$90$	1.89463	+	1.56793i	0.199711	+	0.165274i
$91$	−2.31522	+	0.842670i	−0.242701	+	0.0883358i
$92$	−6.40684	−	7.63537i	−0.667959	−	0.796043i
$93$	13.7558	−	2.42551i	1.42641	−	0.251514i
$94$	1.65487			0.170687
$95$	9.29702	+	2.92667i	0.953854	+	0.300270i
$96$	7.71591			0.787501
$97$	−8.47901	+	1.49508i	−0.860913	+	0.151802i	−0.586638	−	0.809849i	$-0.699549\pi$
$97$	−8.47901	+	1.49508i	−0.860913	+	0.151802i	−0.274275	+	0.961651i	$0.588438\pi$
$98$	0.508425	+	0.605917i	0.0513587	+	0.0612069i
$99$	17.8958	−	6.51353i	1.79859	−	0.654635i
$100$	4.96451	+	8.33463i	0.496451	+	0.833463i
$101$	−10.3041	−	8.64614i	−1.02529	−	0.860323i	−0.0350095	−	0.999387i	$-0.511146\pi$
$101$	−10.3041	−	8.64614i	−1.02529	−	0.860323i	−0.990283	+	0.139064i	$0.955591\pi$
$102$	−1.42637	−	0.823518i	−0.141232	−	0.0815404i
$103$	3.49510	−	2.01789i	0.344382	−	0.198829i	−0.317826	−	0.948149i	$-0.602953\pi$
$103$	3.49510	−	2.01789i	0.344382	−	0.198829i	0.662208	+	0.749320i	$0.269619\pi$
$104$	0.212409	−	1.20463i	0.0208285	−	0.118124i
$105$	−10.3291	−	5.87013i	−1.00802	−	0.572866i
$106$	0.0843204	+	0.146047i	0.00818992	+	0.0141854i
$107$	14.6869	+	8.47947i	1.41983	+	0.819741i	0.996284	−	0.0861313i	$-0.0274505\pi$
$107$	14.6869	+	8.47947i	1.41983	+	0.819741i	0.423550	+	0.905873i	$0.360784\pi$
$108$	−5.11817	+	6.09960i	−0.492496	+	0.586934i
$109$	6.42343	+	2.33794i	0.615253	+	0.223934i	0.630800	−	0.775945i	$-0.282727\pi$
$109$	6.42343	+	2.33794i	0.615253	+	0.223934i	−0.0155471	+	0.999879i	$0.504949\pi$
$110$	−2.31417	+	0.0157538i	−0.220648	+	0.00150207i
$111$	−23.1388	+	19.4158i	−2.19624	+	1.84287i
$112$	−6.96476	+	1.22808i	−0.658108	+	0.116042i
$113$			5.92416i			0.557298i	0.960393	+	0.278649i	$0.0898867\pi$
$113$			5.92416i			0.557298i	−0.960393	+	0.278649i	$0.910113\pi$
$114$	0.895159	−	2.77746i	0.0838394	−	0.260133i
$115$	−10.8208	−	3.85523i	−1.00904	−	0.359502i
$116$	−2.91138	−	16.5113i	−0.270315	−	1.53303i
$117$	3.67193	+	4.37603i	0.339470	+	0.404564i
$118$	0.434249	+	1.19309i	0.0399758	+	0.109833i
$119$	4.48561	+	1.63263i	0.411195	+	0.149663i
$120$	5.08800	−	2.98392i	0.464469	−	0.272394i
$121$	−3.46054	+	5.99383i	−0.314594	+	0.544893i
$122$	0.593422	−	0.342612i	0.0537259	−	0.0310186i
$123$	−6.73756	−	1.18801i	−0.607505	−	0.107120i
$124$	1.71856	−	9.74645i	0.154331	−	0.875257i
$125$	9.79460	+	5.39128i	0.876055	+	0.482211i
$126$	−1.06697	+	1.84805i	−0.0950536	+	0.164638i
$127$	−12.3288	+	14.6929i	−1.09400	+	1.30378i	−0.144680	+	0.989479i	$0.546215\pi$
$127$	−12.3288	+	14.6929i	−1.09400	+	1.30378i	−0.949323	+	0.314303i	$0.898229\pi$
$128$	2.47938	−	6.81203i	0.219148	−	0.602104i
$129$	−11.4992	+	4.18537i	−1.01245	+	0.368501i
$130$	−0.241856	−	0.650677i	−0.0212122	−	0.0570681i
$131$	−0.0534819	−	0.303311i	−0.00467273	−	0.0265004i	0.982382	−	0.186883i	$-0.0598384\pi$
$131$	−0.0534819	−	0.303311i	−0.00467273	−	0.0265004i	−0.987055	+	0.160382i	$0.948727\pi$
$132$		−	22.4920i		−	1.95767i
$133$	−1.15714	+	8.37791i	−0.100337	+	0.726457i
$134$	−1.27428			−0.110081
$135$	−1.53193	+	9.04777i	−0.131848	+	0.778708i
$136$	−1.81546	+	1.52335i	−0.155674	+	0.130626i
$137$	−4.95907	−	13.6249i	−0.423682	−	1.16406i	−0.949584	−	0.313512i	$-0.898494\pi$
$137$	−4.95907	−	13.6249i	−0.423682	−	1.16406i	0.525902	−	0.850545i	$-0.323728\pi$
$138$	−1.17626	+	3.23176i	−0.100130	+	0.275106i
$139$	−12.1014	−	10.1543i	−1.02643	−	0.861278i	−0.0360091	−	0.999351i	$-0.511465\pi$
$139$	−12.1014	−	10.1543i	−1.02643	−	0.861278i	−0.990422	+	0.138074i	$0.955909\pi$
$140$	−6.41146	+	5.45466i	−0.541867	+	0.461003i
$141$	9.26802	+	16.0527i	0.780508	+	1.35188i
$142$	0.190664	+	0.0336192i	0.0160002	+	0.00282126i
$143$	−5.29391	−	0.933460i	−0.442699	−	0.0780598i
$144$	8.19871	+	14.2006i	0.683226	+	1.18338i
$145$	−12.5207	−	14.7169i	−1.03978	−	1.22217i
$146$	−0.265144	−	0.222483i	−0.0219435	−	0.0184128i
$147$	−3.03015	+	8.32527i	−0.249923	+	0.686657i
$148$	7.31983	+	20.1111i	0.601686	+	1.65312i
$149$	9.54872	−	8.01233i	0.782262	−	0.656396i	−0.161555	−	0.986864i	$-0.551651\pi$
$149$	9.54872	−	8.01233i	0.782262	−	0.656396i	0.943817	+	0.330468i	$0.107207\pi$
$150$	1.63405	−	2.92140i	0.133420	−	0.238531i
$151$	13.8400			1.12629			0.563143	−	0.826360i	$-0.309592\pi$
$151$	13.8400			1.12629			0.563143	+	0.826360i	$0.309592\pi$
$152$	−3.31492	−	2.57724i	−0.268876	−	0.209042i
$153$		−	11.0677i		−	0.894767i
$154$	−0.348701	−	1.97758i	−0.0280991	−	0.159358i
$155$	−3.97389	−	10.6912i	−0.319191	−	0.858735i
$156$	6.33978	−	2.30749i	0.507589	−	0.184747i
$157$	6.22373	−	17.0996i	0.496708	−	1.36469i	−0.397731	−	0.917502i	$-0.630202\pi$
$157$	6.22373	−	17.0996i	0.496708	−	1.36469i	0.894438	−	0.447191i	$-0.147576\pi$
$158$	−0.952772	+	1.13547i	−0.0757985	+	0.0903331i
$159$	−0.944465	+	1.63586i	−0.0749010	+	0.129732i
$160$	−1.13630	−	6.19726i	−0.0898322	−	0.489937i
$161$	1.73084	−	9.81605i	0.136409	−	0.773613i
$162$	−0.543656	−	0.0958613i	−0.0427137	−	0.00753158i
$163$	−13.2794	+	7.66687i	−1.04012	+	0.600516i	−0.919868	−	0.392227i	$-0.871705\pi$
$163$	−13.2794	+	7.66687i	−1.04012	+	0.600516i	−0.120256	+	0.992743i	$0.538371\pi$
$164$	−2.42372	+	4.19801i	−0.189261	+	0.327809i
$165$	−13.1132	−	22.3599i	−1.02086	−	1.74071i
$166$	2.72285	+	0.991038i	0.211334	+	0.0769195i
$167$	−2.12631	−	5.84198i	−0.164539	−	0.452066i	0.829833	−	0.558011i	$-0.188435\pi$
$167$	−2.12631	−	5.84198i	−0.164539	−	0.452066i	−0.994372	+	0.105945i	$0.966213\pi$
$168$	3.28989	+	3.92074i	0.253821	+	0.302492i
$169$	1.97743	+	11.2145i	0.152110	+	0.862657i
$170$	−0.451376	+	1.26691i	−0.0346189	+	0.0971678i
$171$	19.1709	−	4.12255i	1.46604	−	0.315259i
$172$			8.67048i			0.661118i
$173$	−2.72401	+	0.480317i	−0.207103	+	0.0365178i	−0.276237	−	0.961090i	$-0.589087\pi$
$173$	−2.72401	+	0.480317i	−0.207103	+	0.0365178i	0.0691341	+	0.997607i	$0.477976\pi$
$174$	−4.43159	+	3.71855i	−0.335958	+	0.281902i
$175$	−3.19364	+	9.16062i	−0.241416	+	0.692478i
$176$	−14.4997	−	5.27747i	−1.09296	−	0.397805i
$177$	−9.14129	+	10.8942i	−0.687102	+	0.818856i
$178$	−0.472760	−	0.272948i	−0.0354349	−	0.0204583i
$179$	−5.68916	−	9.85392i	−0.425228	−	0.736516i	0.571214	−	0.820801i	$-0.306473\pi$
$179$	−5.68916	−	9.85392i	−0.425228	−	0.736516i	−0.996442	+	0.0842849i	$0.973139\pi$
$180$	16.9686	+	9.64340i	1.26476	+	0.718776i
$181$	0.619323	−	3.51236i	0.0460339	−	0.261071i	−0.953101	−	0.302652i	$-0.902128\pi$
$181$	0.619323	−	3.51236i	0.0460339	−	0.261071i	0.999135	+	0.0415803i	$0.0132392\pi$
$182$	0.521645	−	0.301172i	0.0386669	−	0.0223243i
$183$	6.64686	+	3.83757i	0.491350	+	0.283681i
$184$	3.79085	+	3.18090i	0.279466	+	0.234499i
$185$	19.0020	+	15.7254i	1.39705	+	1.15615i
$186$	−3.20891	+	1.16795i	−0.235289	+	0.0856381i
$187$	6.69456	+	7.97827i	0.489555	+	0.583429i
$188$	12.9339	−	2.28060i	0.943303	−	0.166330i
$189$	−7.96263			−0.579196
$190$	−2.36263	−	0.309947i	−0.171403	−	0.0224859i
$191$	−8.67323			−0.627573			−0.313786	−	0.949494i	$-0.601598\pi$
$191$	−8.67323			−0.627573			−0.313786	+	0.949494i	$0.601598\pi$
$192$	17.8015	−	3.13888i	1.28471	−	0.226529i
$193$	−0.271327	−	0.323355i	−0.0195306	−	0.0232756i	0.756191	−	0.654351i	$-0.227058\pi$
$193$	−0.271327	−	0.323355i	−0.0195306	−	0.0232756i	−0.775721	+	0.631076i	$0.782614\pi$
$194$	1.97796	−	0.719919i	0.142009	−	0.0516872i
$195$	4.95724	−	5.99015i	0.354995	−	0.428964i
$196$	4.80871	+	4.03498i	0.343479	+	0.288213i
$197$	13.1995	+	7.62075i	0.940427	+	0.542956i	0.890094	−	0.455777i	$-0.150638\pi$
$197$	13.1995	+	7.62075i	0.940427	+	0.542956i	0.0503329	+	0.998732i	$0.483972\pi$
$198$	−4.03213	+	2.32795i	−0.286551	+	0.165440i
$199$	−2.24465	+	12.7301i	−0.159119	+	0.902410i	0.795803	+	0.605555i	$0.207049\pi$
$199$	−2.24465	+	12.7301i	−0.159119	+	0.902410i	−0.954923	+	0.296855i	$0.904062\pi$
$200$	−3.14592	−	3.64715i	−0.222450	−	0.257892i
$201$	−7.13656	−	12.3609i	−0.503374	−	0.871869i
$202$	2.84789	+	1.64423i	0.200377	+	0.115688i
$203$	10.7772	−	12.8438i	0.756410	−	0.901455i
$204$	−12.2830	−	4.47064i	−0.859981	−	0.313007i
$205$	0.0380298	+	5.58643i	0.00265612	+	0.390173i
$206$	−0.755824	+	0.634212i	−0.0526608	+	0.0441876i
$207$	−22.7592	+	4.01306i	−1.58188	+	0.278927i
$208$		−	4.62845i		−	0.320926i
$209$	−11.3260	+	14.5678i	−0.783436	+	1.00768i
$210$	2.73608	+	0.974809i	0.188807	+	0.0672682i
$211$	−0.772073	−	4.37864i	−0.0531517	−	0.301438i	0.946630	−	0.322322i	$-0.104463\pi$
$211$	−0.772073	−	4.37864i	−0.0531517	−	0.301438i	−0.999782	+	0.0208833i	$0.993352\pi$
$212$	0.860290	+	1.02525i	0.0590850	+	0.0704148i
$213$	0.741690	+	2.03778i	0.0508198	+	0.139626i
$214$	−3.89604	−	1.41804i	−0.266328	−	0.0969353i
$215$	5.05505	+	8.61956i	0.344752	+	0.587849i
$216$	1.97662	−	3.42361i	0.134492	−	0.232947i
$217$	8.57106	−	4.94851i	0.581842	−	0.335926i
$218$	−1.64578	−	0.290195i	−0.111466	−	0.0196545i
$219$	0.673212	−	3.81798i	0.0454915	−	0.257995i
$220$	−18.0651	+	3.31232i	−1.21795	+	0.223316i
$221$	−1.56202	+	2.70550i	−0.105073	+	0.181991i
$222$	4.74672	−	5.65692i	0.318579	−	0.379668i
$223$	3.14622	−	8.64417i	0.210687	−	0.578856i	−0.788667	−	0.614821i	$-0.789228\pi$
$223$	3.14622	−	8.64417i	0.210687	−	0.578856i	0.999353	+	0.0359647i	$0.0114504\pi$
$224$	5.13740	−	1.86986i	0.343257	−	0.124935i
$225$	22.4912	−	0.306233i	1.49941	−	0.0204156i
$226$	−0.251499	−	1.42632i	−0.0167294	−	0.0948774i
$227$		−	0.600308i		−	0.0398438i	−0.999802	−	0.0199219i	$-0.993658\pi$
$227$		−	0.600308i		−	0.0398438i	0.999802	−	0.0199219i	$-0.00634176\pi$
$228$	3.16862	−	22.9413i	0.209847	−	1.51933i
$229$	7.11499			0.470172			0.235086	−	0.971975i	$-0.424463\pi$
$229$	7.11499			0.470172			0.235086	+	0.971975i	$0.424463\pi$
$230$	2.76891	+	0.468821i	0.182577	+	0.0309132i
$231$	17.2302	−	14.4579i	1.13366	−	0.951257i
$232$	2.84700	+	7.82207i	0.186915	+	0.513544i
$233$	−6.89726	+	18.9501i	−0.451854	+	1.24146i	0.479563	+	0.877507i	$0.340795\pi$
$233$	−6.89726	+	18.9501i	−0.451854	+	1.24146i	−0.931418	+	0.363952i	$0.881427\pi$
$234$	−1.06984	−	0.897702i	−0.0699376	−	0.0586846i
$235$	11.5283	−	9.80792i	0.752025	−	0.639798i
$236$	5.03816	+	8.72635i	0.327956	+	0.568037i
$237$	−16.3503	−	2.88300i	−1.06207	−	0.187271i
$238$	−1.14928	−	0.202649i	−0.0744967	−	0.0131358i
$239$	−5.81710	−	10.0755i	−0.376277	−	0.651731i	0.614240	−	0.789119i	$-0.289463\pi$
$239$	−5.81710	−	10.0755i	−0.376277	−	0.651731i	−0.990517	+	0.137388i	$0.956129\pi$
$240$	16.9991	−	14.4622i	1.09729	−	0.933534i
$241$	19.5572	+	16.4104i	1.25979	+	1.05709i	0.995704	+	0.0925884i	$0.0295141\pi$
$241$	19.5572	+	16.4104i	1.25979	+	1.05709i	0.264084	+	0.964500i	$0.414930\pi$
$242$	0.578714	−	1.59000i	0.0372011	−	0.102209i
$243$	−6.32567	−	17.3796i	−0.405792	−	1.11490i
$244$	4.16583	−	3.49555i	0.266690	−	0.223779i
$245$	7.13293	+	1.20772i	0.455706	+	0.0771585i
$246$	1.67259			0.106640
$247$	−5.26818	−	1.69791i	−0.335206	−	0.108035i
$248$			4.91362i			0.312015i
$249$	5.63588	+	31.9627i	0.357160	+	2.02555i
$250$	−2.58705	−	0.882211i	−0.163620	−	0.0557959i
$251$	−14.4509	+	5.25969i	−0.912131	+	0.331988i	−0.755103	−	0.655606i	$-0.772413\pi$
$251$	−14.4509	+	5.25969i	−0.912131	+	0.331988i	−0.157027	+	0.987594i	$0.550191\pi$
$252$	−5.79229	+	15.9142i	−0.364880	+	1.00250i
$253$	13.9789	−	16.6594i	0.878845	−	1.04737i
$254$	2.34456	−	4.06090i	0.147111	−	0.254803i
$255$	−14.8173	+	2.71682i	−0.927896	+	0.170134i
$256$	1.98477	−	11.2562i	0.124048	−	0.703512i
$257$	15.8096	+	2.78765i	0.986173	+	0.173889i	0.643401	−	0.765530i	$-0.277523\pi$
$257$	15.8096	+	2.78765i	0.986173	+	0.173889i	0.342772	+	0.939419i	$0.388634\pi$
$258$	2.59090	−	1.49586i	0.161302	−	0.0931280i
$259$	−10.7011	+	18.5348i	−0.664934	+	1.15170i
$260$	−2.78697	−	4.75217i	−0.172841	−	0.294717i
$261$	−36.5295	−	13.2957i	−2.26112	−	0.822981i
$262$	0.0257529	+	0.0707556i	0.00159102	+	0.00437129i
$263$	−9.15308	−	10.9082i	−0.564403	−	0.672629i	0.406069	−	0.913842i	$-0.366899\pi$
$263$	−9.15308	−	10.9082i	−0.564403	−	0.672629i	−0.970472	+	0.241213i	$0.922455\pi$
$264$	1.93912	+	10.9973i	0.119344	+	0.676836i
$265$	1.45298	+	0.517668i	0.0892559	+	0.0318001i
$266$	−0.0770701	−	2.06622i	−0.00472547	−	0.126688i
$267$		−	6.11453i		−	0.374203i
$268$	−9.95937	+	1.75611i	−0.608365	+	0.107271i
$269$	−12.4416	+	10.4398i	−0.758579	+	0.636523i	−0.937756	−	0.347294i	$-0.887101\pi$
$269$	−12.4416	+	10.4398i	−0.758579	+	0.636523i	0.179178	+	0.983817i	$0.442656\pi$
$270$	−0.0152720	−	2.24340i	−0.000929427	−	0.136529i
$271$	5.56796	+	2.02657i	0.338230	+	0.123106i	0.505551	−	0.862797i	$-0.331289\pi$
$271$	5.56796	+	2.02657i	0.338230	+	0.123106i	−0.167321	+	0.985902i	$0.553512\pi$
$272$	−5.76412	+	6.86941i	−0.349501	+	0.416519i
$273$	5.84290	+	3.37340i	0.353628	+	0.204167i
$274$	1.77238	+	3.06985i	0.107073	+	0.185457i
$275$	−16.0279	+	13.8251i	−0.966516	+	0.833688i
$276$	−4.73956	+	26.8794i	−0.285288	+	1.61795i
$277$	−5.46407	+	3.15468i	−0.328304	+	0.189546i	−0.655088	−	0.755553i	$-0.727368\pi$
$277$	−5.46407	+	3.15468i	−0.328304	+	0.189546i	0.326784	+	0.945099i	$0.394035\pi$
$278$	3.34466	+	1.93104i	0.200600	+	0.115816i
$279$	−17.5784	−	14.7500i	−1.05239	−	0.883059i
$280$	2.66457	−	3.21977i	0.159239	−	0.192418i
$281$	2.51801	−	0.916481i	0.150212	−	0.0546727i	−0.265820	−	0.964023i	$-0.585643\pi$
$281$	2.51801	−	0.916481i	0.150212	−	0.0546727i	0.416032	+	0.909350i	$0.363420\pi$
$282$	−2.91288	−	3.47144i	−0.173460	−	0.206721i
$283$	−30.5923	+	5.39425i	−1.81853	+	0.320655i	−0.975962	−	0.217942i	$-0.930066\pi$
$283$	−30.5923	+	5.39425i	−1.81853	+	0.320655i	−0.842564	+	0.538597i	$0.818955\pi$
$284$	1.53650			0.0911745
$285$	−10.2252	−	24.6540i	−0.605689	−	1.46037i
$286$	1.31421			0.0777107
$287$	−4.77390	+	0.841767i	−0.281794	+	0.0496880i
$288$	−8.14790	−	9.71029i	−0.480120	−	0.572184i
$289$	−10.2871	+	3.74421i	−0.605126	+	0.220248i
$290$	3.63929	+	3.01175i	0.213706	+	0.176856i
$291$	18.0609	+	15.1549i	1.05875	+	0.888396i
$292$	−2.37889	−	1.37345i	−0.139214	−	0.0803752i
$293$	0.749675	−	0.432825i	0.0437965	−	0.0252859i	−0.477942	−	0.878391i	$-0.658617\pi$
$293$	0.749675	−	0.432825i	0.0437965	−	0.0252859i	0.521738	+	0.853106i	$0.325284\pi$
$294$	0.376116	−	2.13306i	0.0219355	−	0.124402i
$295$	10.0962	+	5.73776i	0.587823	+	0.334065i
$296$	−5.31283	−	9.20209i	−0.308802	−	0.534861i
$297$	−15.0455	−	8.68652i	−0.873029	−	0.504043i
$298$	−1.95883	+	2.33445i	−0.113472	+	0.135231i
$299$	6.12988	+	2.23110i	0.354500	+	0.129028i
$300$	8.74517	−	25.0846i	0.504903	−	1.44826i
$301$	−6.64212	+	5.57340i	−0.382845	+	0.321245i
$302$	−3.33217	+	0.587551i	−0.191745	+	0.0338098i
$303$			36.8338i			2.11605i
$304$	−14.0460	−	7.42561i	−0.805591	−	0.425888i
$305$	2.10340	−	5.90377i	0.120440	−	0.338049i
$306$	0.469856	+	2.66468i	0.0268599	+	0.152330i
$307$	5.77995	+	6.88828i	0.329879	+	0.393135i	0.905335	−	0.424698i	$-0.139620\pi$
$307$	5.77995	+	6.88828i	0.329879	+	0.393135i	−0.575456	+	0.817833i	$0.695175\pi$
$308$	−5.45067	−	14.9756i	−0.310581	−	0.853313i
$309$	−10.3850	−	3.77983i	−0.590781	−	0.215027i
$310$	1.41064	+	2.40533i	0.0801189	+	0.136614i
$311$	5.72035	−	9.90793i	0.324371	−	0.561827i	−0.657014	−	0.753879i	$-0.728181\pi$
$311$	5.72035	−	9.90793i	0.324371	−	0.561827i	0.981385	+	0.192051i	$0.0615140\pi$
$312$	−2.90086	+	1.67481i	−0.164229	+	0.0948174i
$313$	7.74572	+	1.36578i	0.437814	+	0.0771984i	0.388211	−	0.921571i	$-0.373093\pi$
$313$	7.74572	+	1.36578i	0.437814	+	0.0771984i	0.0496032	+	0.998769i	$0.484204\pi$
$314$	−0.772517	+	4.38116i	−0.0435956	+	0.247243i
$315$	3.51999	+	19.1977i	0.198329	+	1.08167i
$316$	−5.88175	+	10.1875i	−0.330874	+	0.573091i
$317$	10.6230	−	12.6600i	0.596647	−	0.711056i	−0.380222	−	0.924895i	$-0.624152\pi$
$317$	10.6230	−	12.6600i	0.596647	−	0.711056i	0.976869	+	0.213839i	$0.0685968\pi$
$318$	0.157945	−	0.433951i	0.00885712	−	0.0243347i
$319$	34.3750	−	12.5115i	1.92463	−	0.700509i
$320$	−5.14266	−	13.8355i	−0.287483	−	0.773431i
$321$	−8.06419	−	45.7343i	−0.450099	−	2.55264i
$322$			2.43682i			0.135799i
$323$	5.70435	+	9.08079i	0.317399	+	0.505269i
$324$	−4.38115			−0.243397
$325$	−5.54121	−	3.09941i	−0.307371	−	0.171924i
$326$	2.87171	−	2.40965i	0.159049	−	0.133458i
$327$	−6.40213	−	17.5897i	−0.354039	−	0.972713i
$328$	0.823135	−	2.26155i	0.0454500	−	0.124873i
$329$	10.0610	+	8.44219i	0.554682	+	0.465433i
$330$	4.10642	+	4.82673i	0.226051	+	0.265703i
$331$	−3.95723	−	6.85412i	−0.217509	−	0.376736i	0.736537	−	0.676397i	$-0.236460\pi$
$331$	−3.95723	−	6.85412i	−0.217509	−	0.376736i	−0.954046	+	0.299661i	$0.903126\pi$
$332$	22.6467	+	3.99322i	1.24290	+	0.219157i
$333$	48.8686	+	8.61686i	2.67798	+	0.472201i
$334$	0.759946	+	1.31627i	0.0415824	+	0.0720228i
$335$	−8.87703	+	7.55229i	−0.485004	+	0.412626i
$336$	14.8354	+	12.4484i	0.809340	+	0.679117i
$337$	6.51071	−	17.8880i	0.354661	−	0.974423i	−0.626191	−	0.779670i	$-0.715387\pi$
$337$	6.51071	−	17.8880i	0.354661	−	0.974423i	0.980852	−	0.194754i	$-0.0623908\pi$
$338$	−0.952183	−	2.61610i	−0.0517919	−	0.142297i
$339$	12.4272	−	10.4276i	0.674952	−	0.566352i
$340$	−1.78185	+	10.5238i	−0.0966346	+	0.570734i
$341$	21.5935			1.16936
$342$	−4.44064	+	1.80642i	−0.240122	+	0.0976801i
$343$			19.8594i			1.07230i
$344$	−0.747516	−	4.23937i	−0.0403034	−	0.228572i
$345$	10.9595	+	29.4848i	0.590038	+	1.58741i
$346$	0.635451	−	0.231285i	0.0341621	−	0.0124340i
$347$	1.86887	−	5.13467i	0.100326	−	0.275644i	−0.879368	−	0.476143i	$-0.842034\pi$
$347$	1.86887	−	5.13467i	0.100326	−	0.275644i	0.979694	+	0.200500i	$0.0642566\pi$
$348$	−29.5113	+	35.1702i	−1.58197	+	1.88532i
$349$	−3.13218	+	5.42509i	−0.167662	+	0.290398i	−0.937597	−	0.347723i	$-0.886955\pi$
$349$	−3.13218	+	5.42509i	−0.167662	+	0.290398i	0.769936	+	0.638121i	$0.220288\pi$
$350$	0.380014	−	2.34112i	0.0203126	−	0.125138i
$351$	0.904915	−	5.13203i	0.0483008	−	0.273927i
$352$	11.7470	+	2.07132i	0.626120	+	0.110402i
$353$	−7.18280	+	4.14699i	−0.382302	+	0.220722i	−0.678819	−	0.734305i	$-0.737508\pi$
$353$	−7.18280	+	4.14699i	−0.382302	+	0.220722i	0.296517	+	0.955027i	$0.404175\pi$
$354$	1.73840	−	3.01099i	0.0923947	−	0.160032i
$355$	1.52748	−	0.895808i	0.0810700	−	0.0475446i
$356$	−4.07109	−	1.48176i	−0.215767	−	0.0785329i
$357$	−4.47073	−	12.2832i	−0.236616	−	0.650098i
$358$	1.78807	+	2.13094i	0.0945024	+	0.112624i
$359$	−2.27231	−	12.8869i	−0.119928	−	0.680145i	−0.984192	−	0.177106i	$-0.943326\pi$
$359$	−2.27231	−	12.8869i	−0.119928	−	0.680145i	0.864264	−	0.503039i	$-0.167785\pi$
$360$	−9.12806	−	3.25215i	−0.481091	−	0.171403i
$361$	−13.6046	+	13.2633i	−0.716030	+	0.698069i
$362$			0.871938i			0.0458281i
$363$	18.6645	−	3.29106i	0.979633	−	0.172736i
$364$	3.66196	−	3.07275i	0.191939	−	0.161056i
$365$	−3.16567	+	0.0215504i	−0.165699	+	0.00112800i
$366$	−1.76324	−	0.641765i	−0.0921658	−	0.0335456i
$367$	16.7730	−	19.9893i	0.875545	−	1.04343i	−0.123151	−	0.992388i	$-0.539300\pi$
$367$	16.7730	−	19.9893i	0.875545	−	1.04343i	0.998696	−	0.0510458i	$-0.0162555\pi$
$368$	16.2161	+	9.36236i	0.845322	+	0.488047i
$369$	5.61969	+	9.73359i	0.292549	+	0.506710i
$370$	−5.24256	−	2.97940i	−0.272548	−	0.154891i
$371$	−0.232411	+	1.31807i	−0.0120662	+	0.0684307i
$372$	−23.4702	+	13.5505i	−1.21687	+	0.702563i
$373$	−23.5532	−	13.5984i	−1.21954	−	0.704100i	−0.254718	−	0.967015i	$-0.581983\pi$
$373$	−23.5532	−	13.5984i	−1.21954	−	0.704100i	−0.964819	+	0.262915i	$0.915316\pi$
$374$	−1.95051	−	1.63667i	−0.100858	−	0.0846301i
$375$	−5.93099	−	30.0359i	−0.306275	−	1.55105i
$376$	−6.12733	+	2.23017i	−0.315993	+	0.115012i
$377$	7.05320	+	8.40568i	0.363258	+	0.432915i
$378$	1.91711	−	0.338038i	0.0986054	−	0.0173868i
$379$	−13.6999			−0.703714			−0.351857	−	0.936054i	$-0.614450\pi$
$379$	−13.6999			−0.703714			−0.351857	+	0.936054i	$0.614450\pi$
$380$	−18.8927	+	0.833522i	−0.969173	+	0.0427588i
$381$	52.5224			2.69080
$382$	2.08819	−	0.368205i	0.106841	−	0.0188390i
$383$	6.58953	+	7.85310i	0.336709	+	0.401275i	0.907658	−	0.419711i	$-0.137869\pi$
$383$	6.58953	+	7.85310i	0.336709	+	0.401275i	−0.570948	+	0.820986i	$0.693424\pi$
$384$	−18.6538	+	6.78945i	−0.951925	+	0.346472i
$385$	−14.1497	−	11.7098i	−0.721135	−	0.596786i
$386$	0.0790530	+	0.0663333i	0.00402369	+	0.00337628i
$387$	17.4102	+	10.0518i	0.885010	+	0.510961i
$388$	14.4670	−	8.35251i	0.734449	−	0.424035i
$389$	0.878089	−	4.97989i	0.0445209	−	0.252490i	−0.954422	−	0.298461i	$-0.903527\pi$
$389$	0.878089	−	4.97989i	0.0445209	−	0.252490i	0.998943	+	0.0459703i	$0.0146380\pi$
$390$	−0.939220	+	1.65266i	−0.0475593	+	0.0836856i
$391$	−6.31925	−	10.9453i	−0.319578	−	0.553526i
$392$	−2.69905	−	1.55830i	−0.136323	−	0.0787060i
$393$	−0.542120	+	0.646074i	−0.0273463	+	0.0325901i
$394$	−3.50148	−	1.27444i	−0.176402	−	0.0642051i
$395$	0.0922885	+	13.5568i	0.00464354	+	0.682118i
$396$	−28.3056	+	23.7512i	−1.42241	+	1.19354i
$397$	23.5131	−	4.14599i	1.18009	−	0.208081i	0.451014	−	0.892517i	$-0.351062\pi$
$397$	23.5131	−	4.14599i	1.18009	−	0.208081i	0.729073	+	0.684435i	$0.239951\pi$
$398$		−	3.16022i		−	0.158408i
$399$	19.6112	−	12.3194i	0.981790	−	0.616739i
$400$	−14.1192	−	11.5235i	−0.705960	−	0.576176i
$401$	−4.30049	−	24.3893i	−0.214756	−	1.21794i	−0.881329	−	0.472503i	$-0.843351\pi$
$401$	−4.30049	−	24.3893i	−0.214756	−	1.21794i	0.666573	−	0.745440i	$-0.267760\pi$
$402$	2.24298	+	2.67307i	0.111869	+	0.133321i
$403$	2.21532	+	6.08655i	0.110353	+	0.303192i
$404$	24.5241	+	8.92606i	1.22012	+	0.444088i
$405$	−4.35542	+	2.55429i	−0.216422	+	0.126924i
$406$	−2.04949	+	3.54983i	−0.101715	+	0.176175i
$407$	−40.4398	+	23.3479i	−2.00452	+	1.15731i
$408$	6.39111	+	1.12692i	0.316407	+	0.0557911i
$409$	1.71911	−	9.74958i	0.0850047	−	0.482086i	−0.912351	−	0.409409i	$-0.865735\pi$
$409$	1.71911	−	9.74958i	0.0850047	−	0.482086i	0.997356	−	0.0726764i	$-0.0231540\pi$
$410$	−0.246317	−	1.34339i	−0.0121647	−	0.0663454i
$411$	−19.8523	+	34.3852i	−0.979241	+	1.69609i
$412$	−5.03326	+	5.99841i	−0.247971	+	0.295520i
$413$	−3.44637	+	9.46884i	−0.169585	+	0.465931i
$414$	5.30921	−	1.93240i	0.260934	−	0.0949721i
$415$	24.8418	−	9.23367i	1.21944	−	0.453263i
$416$	0.621311	+	3.52363i	0.0304623	+	0.172760i
$417$			43.2588i			2.11839i
$418$	2.10843	−	3.98822i	0.103127	−	0.195070i
$419$	−4.00810			−0.195808			−0.0979042	−	0.995196i	$-0.531214\pi$
$419$	−4.00810			−0.195808			−0.0979042	+	0.995196i	$0.531214\pi$
$420$	22.7277	+	3.84816i	1.10900	+	0.187771i
$421$	15.5339	−	13.0345i	0.757077	−	0.635263i	−0.180287	−	0.983614i	$-0.557703\pi$
$421$	15.5339	−	13.0345i	0.757077	−	0.635263i	0.937364	+	0.348351i	$0.113258\pi$
$422$	0.371774	+	1.02144i	0.0180977	+	0.0497229i
$423$	10.4150	−	28.6150i	0.506395	−	1.39131i
$424$	−0.509024	−	0.427122i	−0.0247204	−	0.0207429i
$425$	4.36419	+	11.5009i	0.211695	+	0.557874i
$426$	−0.265082	−	0.459135i	−0.0128432	−	0.0222451i
$427$	5.35560	+	0.944337i	0.259176	+	0.0456997i
$428$	−32.4044	−	5.71377i	−1.56632	−	0.276185i
$429$	7.36016	+	12.7482i	0.355352	+	0.615487i
$430$	−1.58300	−	1.86067i	−0.0763389	−	0.0897295i
$431$	10.3250	+	8.66371i	0.497338	+	0.417316i	0.856648	−	0.515902i	$-0.172543\pi$
$431$	10.3250	+	8.66371i	0.497338	+	0.417316i	−0.359309	+	0.933219i	$0.616988\pi$
$432$	5.11609	−	14.0563i	0.246148	−	0.676286i
$433$	−11.7578	−	32.3043i	−0.565045	−	1.55245i	−0.812144	−	0.583458i	$-0.801699\pi$
$433$	−11.7578	−	32.3043i	−0.565045	−	1.55245i	0.247099	−	0.968990i	$-0.420523\pi$
$434$	−1.85352	+	1.55529i	−0.0889717	+	0.0746561i
$435$	−8.83310	+	52.1693i	−0.423515	+	2.50132i
$436$	−13.2628			−0.635172
$437$	16.6051	−	15.0229i	0.794330	−	0.718643i
$438$			0.947808i			0.0452880i
$439$	−4.06648	−	23.0621i	−0.194082	−	1.10070i	−0.913720	−	0.406345i	$-0.866803\pi$
$439$	−4.06648	−	23.0621i	−0.194082	−	1.10070i	0.719637	−	0.694350i	$-0.244308\pi$
$440$	8.54723	−	3.17700i	0.407473	−	0.151457i
$441$	13.6770	−	4.97801i	0.651284	−	0.237048i
$442$	0.261220	−	0.717696i	0.0124250	−	0.0341373i
$443$	1.54197	−	1.83765i	0.0732612	−	0.0873093i	−0.728169	−	0.685398i	$-0.759628\pi$
$443$	1.54197	−	1.83765i	0.0732612	−	0.0873093i	0.801430	+	0.598088i	$0.204073\pi$
$444$	29.3029	−	50.7542i	1.39066	−	2.40869i
$445$	−4.91107	+	0.900468i	−0.232807	+	0.0426863i
$446$	−0.390523	+	2.21476i	−0.0184918	+	0.104872i
$447$	−33.6151	−	5.92725i	−1.58994	−	0.280349i
$448$	11.0919	−	6.40391i	0.524043	−	0.302557i
$449$	19.1010	−	33.0838i	0.901430	−	1.56132i	0.0757922	−	0.997124i	$-0.475851\pi$
$449$	19.1010	−	33.0838i	0.901430	−	1.56132i	0.825638	−	0.564200i	$-0.190815\pi$
$450$	−5.40205	+	1.02855i	−0.254655	+	0.0484863i
$451$	−9.93864	−	3.61737i	−0.467992	−	0.170335i
$452$	−3.93126	−	10.8011i	−0.184911	−	0.508039i
$453$	−24.3611	−	29.0324i	−1.14458	−	1.36406i
$454$	0.0254849	+	0.144532i	0.00119606	+	0.00678322i
$455$	1.84898	−	5.18969i	0.0866816	−	0.243296i
$456$	0.428585	+	11.4902i	0.0200703	+	0.538077i
$457$		−	1.87605i		−	0.0877581i	−0.999037	−	0.0438790i	$-0.986028\pi$
$457$		−	1.87605i		−	0.0877581i	0.999037	−	0.0438790i	$-0.0139716\pi$
$458$	−1.71303	+	0.302053i	−0.0800445	+	0.0141140i
$459$	−7.73430	+	6.48984i	−0.361006	+	0.302920i
$460$	22.2870	−	0.151719i	1.03914	−	0.00707395i
$461$	−15.8060	−	5.75290i	−0.736157	−	0.267939i	−0.0533885	−	0.998574i	$-0.517002\pi$
$461$	−15.8060	−	5.75290i	−0.736157	−	0.267939i	−0.682769	+	0.730634i	$0.739224\pi$
$462$	−3.53462	+	4.21239i	−0.164445	+	0.195978i
$463$	21.0999	+	12.1821i	0.980598	+	0.566148i	0.902450	−	0.430794i	$-0.141766\pi$
$463$	21.0999	+	12.1821i	0.980598	+	0.566148i	0.0781471	+	0.996942i	$0.475100\pi$
$464$	15.7485	+	27.2771i	0.731104	+	1.26631i
$465$	−15.4322	+	27.1545i	−0.715650	+	1.25926i
$466$	0.856118	−	4.85529i	0.0396589	−	0.224917i
$467$	−11.8222	+	6.82553i	−0.547065	+	0.315848i	−0.747937	−	0.663770i	$-0.768956\pi$
$467$	−11.8222	+	6.82553i	−0.547065	+	0.315848i	0.200873	+	0.979617i	$0.435622\pi$
$468$	−9.59866	−	5.54179i	−0.443698	−	0.256169i
$469$	−7.74717	−	6.50065i	−0.357731	−	0.300172i
$470$	−2.35922	+	2.85080i	−0.108823	+	0.131497i
$471$	−46.8249	+	17.0429i	−2.15758	+	0.785293i
$472$	−3.21570	−	3.83233i	−0.148015	−	0.176397i
$473$	−18.6305	+	3.28505i	−0.856629	+	0.151047i
$474$	4.05895			0.186434
$475$	−18.2957	+	11.8434i	−0.839466	+	0.543412i
$476$	−9.26166			−0.424507
$477$	3.05604	−	0.538862i	0.139926	−	0.0246728i
$478$	1.82828	+	2.17886i	0.0836236	+	0.0996587i
$479$	−20.4294	+	7.43570i	−0.933444	+	0.339746i	−0.763574	−	0.645720i	$-0.776557\pi$
$479$	−20.4294	+	7.43570i	−0.933444	+	0.339746i	−0.169870	+	0.985466i	$0.554335\pi$
$480$	−11.0000	+	13.2920i	−0.502078	+	0.606693i
$481$	−10.7298	−	9.00341i	−0.489239	−	0.410520i
$482$	−5.40532	−	3.12076i	−0.246206	−	0.142147i
$483$	−23.6378	+	13.6473i	−1.07556	+	0.620974i
$484$	2.33183	−	13.2245i	0.105992	−	0.601112i
$485$	9.51234	−	16.7380i	0.431933	−	0.760032i
$486$	2.26080	+	3.91583i	0.102552	+	0.177626i
$487$	−25.3273	−	14.6227i	−1.14769	−	0.662618i	−0.199366	−	0.979925i	$-0.563888\pi$
$487$	−25.3273	−	14.6227i	−1.14769	−	0.662618i	−0.948323	+	0.317307i	$0.897222\pi$
$488$	−1.73549	+	2.06828i	−0.0785619	+	0.0936264i
$489$	39.4572	+	14.3612i	1.78431	+	0.649437i
$490$	−1.76862	+	0.0120399i	−0.0798981	+	0.000543909i
$491$	−14.0612	+	11.7987i	−0.634572	+	0.532469i	−0.902346	−	0.431012i	$-0.858157\pi$
$491$	−14.0612	+	11.7987i	−0.634572	+	0.532469i	0.267774	+	0.963482i	$0.413712\pi$
$492$	13.0724	−	2.30502i	0.589350	−	0.103918i
$493$		−	21.2593i		−	0.957469i
$494$	1.34046	+	0.185143i	0.0603104	+	0.00832997i
$495$	−14.2920	+	40.1144i	−0.642376	+	1.80301i
$496$	3.22853	+	18.3099i	0.144965	+	0.822138i
$497$	0.987664	+	1.17705i	0.0443028	+	0.0527980i
$498$	−2.71383	−	7.45618i	−0.121609	−	0.334119i
$499$	9.78774	+	3.56245i	0.438159	+	0.159477i	0.551675	−	0.834059i	$-0.313989\pi$
$499$	9.78774	+	3.56245i	0.438159	+	0.159477i	−0.113516	+	0.993536i	$0.536211\pi$
$500$	−21.4354	−	3.32982i	−0.958618	−	0.148914i
$501$	−8.51208	+	14.7434i	−0.380292	+	0.658685i
$502$	3.25595	−	1.87982i	0.145320	−	0.0839006i
$503$	4.29111	+	0.756638i	0.191331	+	0.0337368i	0.268492	−	0.963282i	$-0.413475\pi$
$503$	4.29111	+	0.756638i	0.191331	+	0.0337368i	−0.0771614	+	0.997019i	$0.524586\pi$
$504$	1.46008	−	8.28051i	0.0650370	−	0.368843i
$505$	29.5842	−	5.42439i	1.31648	−	0.241382i
$506$	−2.65836	+	4.60441i	−0.118178	+	0.204691i
$507$	20.0442	−	23.8878i	0.890196	−	1.06089i
$508$	12.7279	−	34.9697i	0.564711	−	1.55153i
$509$	−35.9534	+	13.0860i	−1.59361	+	0.580026i	−0.978106	−	0.208109i	$-0.933269\pi$
$509$	−35.9534	+	13.0860i	−1.59361	+	0.580026i	−0.615502	+	0.788135i	$0.711047\pi$
$510$	3.45212	−	1.28315i	0.152863	−	0.0568188i
$511$	−0.477005	−	2.70523i	−0.0211015	−	0.119672i
$512$			17.2928i			0.764239i
$513$	−14.1224	−	10.9797i	−0.623517	−	0.484764i
$514$	−3.92470			−0.173111
$515$	−1.50652	+	8.89766i	−0.0663851	+	0.392078i
$516$	18.1882	−	15.2617i	0.800690	−	0.671858i
$517$	9.80074	+	26.9273i	0.431036	+	1.18426i
$518$	1.78957	−	4.91680i	0.0786292	−	0.216032i
$519$	5.80235	+	4.86875i	0.254695	+	0.213714i
$520$	1.77237	+	2.08327i	0.0777237	+	0.0913573i
$521$	1.24406	+	2.15478i	0.0545033	+	0.0944025i	0.891990	−	0.452056i	$-0.149309\pi$
$521$	1.24406	+	2.15478i	0.0545033	+	0.0944025i	−0.837486	+	0.546458i	$0.815976\pi$
$522$	9.35941	+	1.65032i	0.409650	+	0.0722324i
$523$	19.1578	+	3.37803i	0.837712	+	0.147711i	0.576015	−	0.817439i	$-0.304607\pi$
$523$	19.1578	+	3.37803i	0.837712	+	0.147711i	0.261696	+	0.965150i	$0.415718\pi$
$524$	0.298786	+	0.517512i	0.0130525	+	0.0226076i
$525$	24.8377	−	9.42509i	1.08401	−	0.411345i
$526$	2.66681	+	2.23772i	0.116278	+	0.0975692i
$527$	4.29206	−	11.7923i	0.186965	−	0.513683i
$528$	14.4517	+	39.7056i	0.628928	+	1.72797i
$529$	−2.59720	+	2.17931i	−0.112922	+	0.0947525i
$530$	−0.371801	−	0.0629519i	−0.0161500	−	0.00273445i
$531$	23.3631			1.01387
$532$	−3.44984	−	16.0427i	−0.149569	−	0.695538i
$533$		−	3.17251i		−	0.137417i
$534$	0.259581	+	1.47215i	0.0112332	+	0.0637064i
$535$	−35.5453	+	13.2121i	−1.53676	+	0.571211i
$536$	4.71816	−	1.71727i	0.203794	−	0.0741748i
$537$	−10.6567	+	29.2790i	−0.459869	+	1.26348i
$538$	2.55228	−	3.04169i	0.110037	−	0.131137i
$539$	−6.84814	+	11.8613i	−0.294970	+	0.510904i
$540$	−3.21103	−	17.5127i	−0.138181	−	0.753625i
$541$	2.51035	−	14.2369i	0.107928	−	0.612093i	−0.882082	−	0.471097i	$-0.843858\pi$
$541$	2.51035	−	14.2369i	0.107928	−	0.612093i	0.990010	−	0.140996i	$-0.0450305\pi$
$542$	−1.42659	−	0.251547i	−0.0612775	−	0.0108049i
$543$	−8.45804	+	4.88325i	−0.362969	+	0.209560i
$544$	3.46608	−	6.00342i	0.148607	−	0.257394i
$545$	−13.1849	+	7.73245i	−0.564779	+	0.331222i
$546$	−1.54997	−	0.564141i	−0.0663324	−	0.0241430i
$547$	10.7381	+	29.5027i	0.459128	+	1.26144i	0.926136	+	0.377191i	$0.123110\pi$
$547$	10.7381	+	29.5027i	0.459128	+	1.26144i	−0.467007	+	0.884253i	$0.654668\pi$
$548$	18.0830	+	21.5504i	0.772466	+	0.920589i
$549$	−2.18951	−	12.4173i	−0.0934461	−	0.529959i
$550$	3.27200	−	4.00902i	0.139518	−	0.170945i
$551$	36.8244	−	7.91878i	1.56877	−	0.337351i
$552$		−	13.5511i		−	0.576774i
$553$	−11.5850	+	2.04275i	−0.492646	+	0.0868667i
$554$	1.18162	−	0.991497i	0.0502022	−	0.0421247i
$555$	−0.459782	−	67.5402i	−0.0195167	−	2.86692i
$556$	28.8020	+	10.4831i	1.22148	+	0.444581i
$557$	−19.5718	+	23.3248i	−0.829286	+	0.988304i	0.170710	+	0.985321i	$0.445394\pi$
$557$	−19.5718	+	23.3248i	−0.829286	+	0.988304i	−0.999996	+	0.00298303i	$0.999050\pi$
$558$	4.85840	+	2.80500i	0.205673	+	0.118745i
$559$	−2.83729	−	4.91433i	−0.120005	−	0.207854i
$560$	7.81356	−	13.7488i	0.330183	−	0.580992i
$561$	4.95241	−	28.0865i	0.209091	−	1.18581i
$562$	−0.567337	+	0.327552i	−0.0239317	+	0.0138169i
$563$	23.1239	+	13.3506i	0.974558	+	0.562661i	0.900623	−	0.434602i	$-0.143111\pi$
$563$	23.1239	+	13.3506i	0.974558	+	0.562661i	0.0739355	+	0.997263i	$0.476444\pi$
$564$	−27.5502	−	23.1173i	−1.16007	−	0.973416i
$565$	−10.2054	−	8.44562i	−0.429344	−	0.355310i
$566$	7.13650	−	2.59747i	0.299970	−	0.109180i
$567$	−2.81621	−	3.35622i	−0.118270	−	0.140948i
$568$	−0.751261	+	0.132468i	−0.0315222	+	0.00555822i
$569$	25.6513			1.07536			0.537679	−	0.843150i	$-0.319301\pi$
$569$	25.6513			1.07536			0.537679	+	0.843150i	$0.319301\pi$
$570$	3.50849	+	5.50167i	0.146954	+	0.230440i
$571$	2.93559			0.122851			0.0614253	−	0.998112i	$-0.480435\pi$
$571$	2.93559			0.122851			0.0614253	+	0.998112i	$0.480435\pi$
$572$	10.2714	−	1.81113i	0.429470	−	0.0757271i
$573$	15.2665	+	18.1939i	0.637768	+	0.760062i
$574$	1.11364	−	0.405333i	0.0464826	−	0.0169183i
$575$	22.0676	−	13.1446i	0.920284	−	0.548166i
$576$	−22.7484	−	19.0881i	−0.947848	−	0.795339i
$577$	−15.3921	−	8.88661i	−0.640780	−	0.369954i	0.144135	−	0.989558i	$-0.453960\pi$
$577$	−15.3921	−	8.88661i	−0.640780	−	0.369954i	−0.784915	+	0.619604i	$0.787293\pi$
$578$	2.31781	−	1.33819i	0.0964083	−	0.0556613i
$579$	−0.200719	+	1.13833i	−0.00834158	+	0.0473075i
$580$	32.5940	+	18.5235i	1.35339	+	0.769146i
$581$	11.4983	+	19.9156i	0.477029	+	0.826238i
$582$	−4.99177	−	2.88200i	−0.206916	−	0.119463i
$583$	−1.87704	+	2.23697i	−0.0777391	+	0.0926458i
$584$	1.28155	+	0.466447i	0.0530310	+	0.0193017i
$585$	−12.7732	+	0.0869543i	−0.528109	+	0.00359512i
$586$	−0.162119	+	0.136034i	−0.00669709	+	0.00561952i
$587$	22.7723	−	4.01538i	0.939915	−	0.165732i	0.317357	−	0.948306i	$-0.397205\pi$
$587$	22.7723	−	4.01538i	0.939915	−	0.165732i	0.622558	+	0.782574i	$0.286094\pi$
$588$		−	17.1896i		−	0.708887i
$589$	22.0250	+	3.04205i	0.907522	+	0.125346i
$590$	−2.67438	−	0.952826i	−0.110102	−	0.0392272i
$591$	−7.24752	−	41.1027i	−0.298123	−	1.69074i
$592$	−25.8438	−	30.7994i	−1.06217	−	1.26585i
$593$	−5.86817	−	16.1227i	−0.240977	−	0.662078i	−0.999940	−	0.0109447i	$-0.996516\pi$
$593$	−5.86817	−	16.1227i	−0.240977	−	0.662078i	0.758963	−	0.651133i	$-0.225706\pi$
$594$	3.99117	+	1.45267i	0.163760	+	0.0596037i
$595$	−9.20726	+	5.39972i	−0.377461	+	0.221367i
$596$	−12.0925	+	20.9448i	−0.495327	+	0.857931i
$597$	30.6550	−	17.6987i	1.25463	−	0.724358i
$598$	−1.57057	−	0.276933i	−0.0642253	−	0.0113246i
$599$	2.32632	−	13.1932i	0.0950508	−	0.539060i	−0.899681	−	0.436548i	$-0.856201\pi$
$599$	2.32632	−	13.1932i	0.0950508	−	0.539060i	0.994732	−	0.102512i	$-0.0326880\pi$
$600$	−2.11325	+	13.0189i	−0.0862731	+	0.531495i
$601$	−4.13126	+	7.15554i	−0.168517	+	0.291881i	−0.937899	−	0.346909i	$-0.887231\pi$
$601$	−4.13126	+	7.15554i	−0.168517	+	0.291881i	0.769381	+	0.638790i	$0.220565\pi$
$602$	1.36257	−	1.62385i	0.0555342	−	0.0661830i
$603$	−8.01976	+	22.0341i	−0.326590	+	0.897298i
$604$	−25.2334	+	9.18421i	−1.02673	+	0.373700i
$605$	−5.39198	−	14.5063i	−0.219215	−	0.589765i
$606$	−1.56371	−	8.86822i	−0.0635212	−	0.360247i
$607$			23.5191i			0.954612i	0.878737	+	0.477306i	$0.158387\pi$
$607$			23.5191i			0.954612i	−0.878737	+	0.477306i	$0.841613\pi$
$608$	11.6899	+	3.76761i	0.474090	+	0.152797i
$609$	−45.9124			−1.86046
$610$	−0.255787	+	1.51071i	−0.0103565	+	0.0611667i
$611$	−6.58450	+	5.52505i	−0.266380	+	0.223520i
$612$	7.34447	+	20.1788i	0.296883	+	0.815679i
$613$	−10.2029	+	28.0323i	−0.412092	+	1.13221i	0.543984	+	0.839095i	$0.316915\pi$
$613$	−10.2029	+	28.0323i	−0.412092	+	1.13221i	−0.956076	+	0.293118i	$0.905307\pi$
$614$	−1.68403	−	1.41307i	−0.0679619	−	0.0570268i
$615$	11.6518	−	9.91295i	0.469845	−	0.399729i
$616$	3.95617	+	6.85228i	0.159399	+	0.276086i
$617$	−11.4142	−	2.01262i	−0.459516	−	0.0810251i	−0.0609020	−	0.998144i	$-0.519398\pi$
$617$	−11.4142	−	2.01262i	−0.459516	−	0.0810251i	−0.398614	+	0.917119i	$0.630509\pi$
$618$	2.66079	+	0.469169i	0.107033	+	0.0188727i
$619$	14.8349	+	25.6947i	0.596264	+	1.03276i	0.993367	+	0.114985i	$0.0366820\pi$
$619$	14.8349	+	25.6947i	0.596264	+	1.03276i	−0.397104	+	0.917774i	$0.629985\pi$
$620$	14.3399	+	16.8553i	0.575905	+	0.676924i
$621$	16.1499	+	13.5514i	0.648075	+	0.543799i
$622$	−0.956627	+	2.62831i	−0.0383573	+	0.105386i
$623$	−1.48179	−	4.07118i	−0.0593666	−	0.163108i
$624$	−9.70916	+	8.14695i	−0.388677	+	0.326139i
$625$	−23.2508	+	9.18694i	−0.930032	+	0.367478i
$626$	−1.92287			−0.0768532
$627$	50.4950	−	1.88347i	2.01658	−	0.0752185i
$628$			35.3063i			1.40888i
$629$	4.71236	+	26.7251i	0.187894	+	1.06560i
$630$	−1.66249	−	4.47267i	−0.0662351	−	0.178196i
$631$	23.0191	−	8.37827i	0.916376	−	0.333534i	0.159580	−	0.987185i	$-0.448986\pi$
$631$	23.0191	−	8.37827i	0.916376	−	0.333534i	0.756796	+	0.653651i	$0.226764\pi$
$632$	1.99754	−	5.48819i	0.0794578	−	0.218308i
$633$	−7.82614	+	9.32683i	−0.311061	+	0.370708i
$634$	−2.02017	+	3.49904i	−0.0802313	+	0.138965i
$635$	−7.73480	−	42.1849i	−0.306946	−	1.67406i
$636$	0.636414	−	3.60928i	0.0252354	−	0.143117i
$637$	−4.04591	−	0.713402i	−0.160305	−	0.0282660i
$638$	−7.74509	+	4.47163i	−0.306631	+	0.177034i
$639$	1.78128	−	3.08527i	0.0704663	−	0.122051i
$640$	8.20024	+	13.9825i	0.324143	+	0.552709i
$641$	−11.6336	−	4.23428i	−0.459499	−	0.167244i	0.101890	−	0.994796i	$-0.467511\pi$
$641$	−11.6336	−	4.23428i	−0.459499	−	0.167244i	−0.561390	+	0.827552i	$0.689733\pi$
$642$	3.88312	+	10.6688i	0.153254	+	0.421063i
$643$	29.5099	+	35.1685i	1.16376	+	1.38691i	0.907369	+	0.420336i	$0.138088\pi$
$643$	29.5099	+	35.1685i	1.16376	+	1.38691i	0.256387	+	0.966574i	$0.417468\pi$
$644$	3.35822	+	19.0454i	0.132332	+	0.750494i
$645$	9.18351	−	25.7761i	0.361600	−	1.01493i
$646$	−1.75891	−	1.94415i	−0.0692032	−	0.0764916i
$647$		−	33.6773i		−	1.32399i	−0.749508	−	0.661996i	$-0.769710\pi$
$647$		−	33.6773i		−	1.32399i	0.749508	−	0.661996i	$-0.230290\pi$
$648$	2.14213	−	0.377716i	0.0841509	−	0.0148381i
$649$	−16.8416	+	14.1318i	−0.661092	+	0.554722i
$650$	1.46570	+	0.510982i	0.0574894	+	0.0200424i
$651$	−25.4672	−	9.26931i	−0.998139	−	0.363293i
$652$	19.1236	−	22.7906i	0.748937	−	0.892549i
$653$	−17.0057	−	9.81827i	−0.665486	−	0.384219i	0.128878	−	0.991660i	$-0.458862\pi$
$653$	−17.0057	−	9.81827i	−0.665486	−	0.384219i	−0.794364	+	0.607442i	$0.792196\pi$
$654$	2.28813	+	3.96316i	0.0894731	+	0.154972i
$655$	0.598750	+	0.340275i	0.0233951	+	0.0132956i
$656$	1.58133	−	8.96816i	0.0617405	−	0.350148i
$657$	−5.51574	+	3.18451i	−0.215189	+	0.124240i
$658$	−2.78072	−	1.60545i	−0.108404	−	0.0625869i
$659$	−15.9102	−	13.3503i	−0.619775	−	0.520053i	0.277958	−	0.960593i	$-0.410342\pi$
$659$	−15.9102	−	13.3503i	−0.619775	−	0.520053i	−0.897733	+	0.440540i	$0.854787\pi$
$660$	38.7463	+	32.0650i	1.50820	+	1.24813i
$661$	−12.4567	+	4.53386i	−0.484508	+	0.176347i	−0.572713	−	0.819756i	$-0.694109\pi$
$661$	−12.4567	+	4.53386i	−0.484508	+	0.176347i	0.0882049	+	0.996102i	$0.471887\pi$
$662$	1.24373	+	1.48222i	0.0483390	+	0.0576082i
$663$	8.42480	−	1.48552i	0.327192	−	0.0576928i
$664$	−11.4172			−0.443074
$665$	−12.7827	−	13.9371i	−0.495694	−	0.540459i
$666$	−12.1316			−0.470089
$667$	−43.7170	+	7.70848i	−1.69273	+	0.298473i
$668$	7.75345	+	9.24020i	0.299990	+	0.357514i
$669$	−23.6709	+	8.61551i	−0.915171	+	0.333095i
$670$	1.81665	−	2.19517i	0.0701831	−	0.0848068i
$671$	9.08930	+	7.62682i	0.350888	+	0.294430i
$672$	−12.9652	−	7.48548i	−0.500144	−	0.288759i
$673$	11.1350	−	6.42879i	0.429223	−	0.247812i	−0.269793	−	0.962918i	$-0.586955\pi$
$673$	11.1350	−	6.42879i	0.429223	−	0.247812i	0.699015	+	0.715107i	$0.253622\pi$
$674$	−0.808138	+	4.58318i	−0.0311283	+	0.176537i
$675$	−13.4024	−	15.5377i	−0.515858	−	0.598047i
$676$	−11.0472	−	19.1344i	−0.424894	−	0.735937i
$677$	−22.1332	−	12.7786i	−0.850649	−	0.491122i	0.0102207	−	0.999948i	$-0.496747\pi$
$677$	−22.1332	−	12.7786i	−0.850649	−	0.491122i	−0.860870	+	0.508825i	$0.830080\pi$
$678$	−2.54932	+	3.03816i	−0.0979062	+	0.116680i
$679$	15.6979	+	5.71357i	0.602431	+	0.219267i
$680$	−0.0360743	−	5.29917i	−0.00138338	−	0.203214i
$681$	−1.25927	+	1.05665i	−0.0482554	+	0.0404911i
$682$	−5.19893	+	0.916711i	−0.199077	+	0.0351027i
$683$		−	22.8692i		−	0.875064i	−0.899203	−	0.437532i	$-0.855853\pi$
$683$		−	22.8692i		−	0.875064i	0.899203	−	0.437532i	$-0.144147\pi$
$684$	−32.2171	+	20.2381i	−1.23185	+	0.773824i
$685$	30.5411	+	10.8812i	1.16691	+	0.415748i
$686$	−0.843090	−	4.78140i	−0.0321893	−	0.182555i
$687$	−12.5237	−	14.9252i	−0.477810	−	0.569432i
$688$	−5.57101	−	15.3062i	−0.212393	−	0.583545i
$689$	−0.823102	−	0.299585i	−0.0313577	−	0.0114133i
$690$	−3.89035	−	6.63359i	−0.148103	−	0.252536i
$691$	16.1574	−	27.9854i	0.614657	−	1.06462i	−0.375788	−	0.926706i	$-0.622628\pi$
$691$	16.1574	−	27.9854i	0.614657	−	1.06462i	0.990445	−	0.137911i	$-0.0440388\pi$
$692$	4.64774	−	2.68337i	0.176681	−	0.102007i
$693$	−36.3897	−	6.41649i	−1.38233	−	0.243742i
$694$	−0.231972	+	1.31558i	−0.00880554	+	0.0499387i
$695$	34.7447	−	6.37059i	1.31794	−	0.241650i
$696$	11.3972	−	19.7405i	0.432009	−	0.748262i
$697$	−3.95093	+	4.70854i	−0.149652	+	0.178349i
$698$	0.523801	−	1.43913i	0.0198262	−	0.0544719i
$699$	51.8922	−	18.8872i	1.96274	−	0.714381i
$700$	−0.256263	−	18.8211i	−0.00968582	−	0.711372i
$701$	6.03353	+	34.2179i	0.227883	+	1.29239i	0.857096	+	0.515157i	$0.172266\pi$
$701$	6.03353	+	34.2179i	0.227883	+	1.29239i	−0.629212	+	0.777233i	$0.716622\pi$
$702$			1.27402i			0.0480848i
$703$	−44.5369	+	18.1173i	−1.67974	+	0.683307i
$704$	27.9444			1.05319
$705$	−40.8662	−	6.91931i	−1.53911	−	0.260596i
$706$	1.55330	−	1.30337i	0.0584593	−	0.0490531i
$707$	8.92625	+	24.5247i	0.335706	+	0.922345i
$708$	9.43724	−	25.9286i	0.354673	−	0.974457i
$709$	−6.13431	−	5.14730i	−0.230379	−	0.193311i	0.520290	−	0.853990i	$-0.325824\pi$
$709$	−6.13431	−	5.14730i	−0.230379	−	0.193311i	−0.750669	+	0.660679i	$0.770268\pi$
$710$	−0.329730	+	0.280524i	−0.0123746	+	0.0105279i
$711$	13.6375	+	23.6209i	0.511448	+	0.885853i
$712$	2.11828	+	0.373510i	0.0793859	+	0.0139979i
$713$	−25.8057	−	4.55025i	−0.966432	−	0.170408i
$714$	1.59785	+	2.76755i	0.0597980	+	0.103573i
$715$	9.15517	−	7.78892i	0.342384	−	0.291289i
$716$	16.9116	+	14.1905i	0.632018	+	0.530326i
$717$	−10.8963	+	29.9374i	−0.406931	+	1.11803i
$718$	1.09418	+	3.00622i	0.0408343	+	0.112191i
$719$	−10.9307	+	9.17191i	−0.407645	+	0.342055i	−0.823440	−	0.567404i	$-0.807948\pi$
$719$	−10.9307	+	9.17191i	−0.407645	+	0.342055i	0.415795	+	0.909458i	$0.363503\pi$
$720$	−36.1512	−	6.12098i	−1.34728	−	0.228116i
$721$	−7.83053			−0.291624
$722$	2.71241	−	3.77087i	0.100946	−	0.140337i
$723$		−	69.9107i		−	2.60001i
$724$	1.20163	+	6.81478i	0.0446582	+	0.253269i
$725$	43.2021	−	0.588227i	1.60449	−	0.0218462i
$726$	−4.35401	+	1.58473i	−0.161593	+	0.0588149i
$727$	−1.07271	+	2.94724i	−0.0397846	+	0.109307i	−0.957994	−	0.286788i	$-0.907413\pi$
$727$	−1.07271	+	2.94724i	−0.0397846	+	0.109307i	0.918210	+	0.396095i	$0.129635\pi$
$728$	−1.52558	+	1.81811i	−0.0565416	+	0.0673836i
$729$	−21.9360	+	37.9942i	−0.812444	+	1.40719i
$730$	0.761261	−	0.139581i	0.0281755	−	0.00516611i
$731$	−1.90912	+	10.8272i	−0.0706113	+	0.400457i
$732$	−14.6653	−	2.58589i	−0.542045	−	0.0955772i
$733$	10.7391	−	6.20021i	0.396657	−	0.229010i	−0.288384	−	0.957515i	$-0.593118\pi$
$733$	10.7391	−	6.20021i	0.396657	−	0.229010i	0.685041	+	0.728505i	$0.259784\pi$
$734$	−3.18972	+	5.52476i	−0.117735	+	0.203922i
$735$	−10.0219	−	17.0887i	−0.369662	−	0.630325i
$736$	−13.6020	−	4.95074i	−0.501378	−	0.182487i
$737$	−7.54676	−	20.7346i	−0.277988	−	0.763767i
$738$	−1.76623	−	2.10492i	−0.0650160	−	0.0774830i
$739$	1.62242	+	9.20119i	0.0596816	+	0.338471i	0.999998	−	0.00182926i	$-0.000582271\pi$
$739$	1.62242	+	9.20119i	0.0596816	+	0.338471i	−0.940317	+	0.340301i	$0.889471\pi$
$740$	−45.0801	−	16.0611i	−1.65718	−	0.590419i
$741$	5.71127	+	14.0398i	0.209809	+	0.515763i
$742$		−	0.327209i		−	0.0120122i
$743$	37.7365	−	6.65396i	1.38442	−	0.244110i	0.568692	−	0.822551i	$-0.307450\pi$
$743$	37.7365	−	6.65396i	1.38442	−	0.244110i	0.815725	+	0.578441i	$0.196339\pi$
$744$	10.3074	−	8.64890i	0.377886	−	0.317084i
$745$	0.189739	+	27.8719i	0.00695149	+	1.02115i
$746$	6.24803	+	2.27410i	0.228757	+	0.0832606i
$747$	34.2729	−	40.8448i	1.25398	−	1.49443i
$748$	−17.5000	−	10.1036i	−0.639864	−	0.369426i
$749$	−16.4525	−	28.4965i	−0.601160	−	1.04124i
$750$	2.70308	+	6.97975i	0.0987025	+	0.254864i
$751$	−8.51519	+	48.2921i	−0.310724	+	1.76220i	0.284533	+	0.958666i	$0.408162\pi$
$751$	−8.51519	+	48.2921i	−0.310724	+	1.76220i	−0.595257	+	0.803536i	$0.702950\pi$
$752$	−21.3672	+	12.3364i	−0.779183	+	0.449861i
$753$	36.4696	+	21.0557i	1.32902	+	0.767313i
$754$	−2.05500	−	1.72435i	−0.0748386	−	0.0627971i
$755$	−19.7307	+	23.8418i	−0.718072	+	0.867693i
$756$	14.5176	−	5.28399i	0.528001	−	0.192177i
$757$	23.6504	+	28.1855i	0.859590	+	1.02442i	0.999414	+	0.0342429i	$0.0109020\pi$
$757$	23.6504	+	28.1855i	0.859590	+	1.02442i	−0.139824	+	0.990176i	$0.544654\pi$
$758$	3.29842	−	0.581600i	0.119804	−	0.0211247i
$759$	−59.5521			−2.16160
$760$	9.16557	−	2.03635i	0.332470	−	0.0738663i
$761$	−0.255560			−0.00926406			−0.00463203	−	0.999989i	$-0.501474\pi$
$761$	−0.255560			−0.00926406			−0.00463203	+	0.999989i	$0.501474\pi$
$762$	−12.6455	+	2.22973i	−0.458096	+	0.0807748i
$763$	−8.52533	−	10.1601i	−0.308638	−	0.367820i
$764$	15.8132	−	5.75554i	0.572102	−	0.208228i
$765$	19.0659	+	15.7783i	0.689331	+	0.570466i
$766$	−1.91990	−	1.61099i	−0.0693690	−	0.0582075i
$767$	−5.71114	−	3.29733i	−0.206217	−	0.119060i
$768$	−27.1058	+	15.6495i	−0.978096	+	0.564704i
$769$	1.64209	−	9.31277i	0.0592154	−	0.335827i	−0.940780	−	0.339019i	$-0.889905\pi$
$769$	1.64209	−	9.31277i	0.0592154	−	0.335827i	0.999995	+	0.00319194i	$0.00101603\pi$
$770$	3.90384	+	2.21859i	0.140685	+	0.0799524i
$771$	−21.9801	−	38.0707i	−0.791594	−	1.37108i
$772$	0.709267	+	0.409495i	0.0255271	+	0.0147381i
$773$	19.4288	−	23.1544i	0.698807	−	0.832806i	−0.293584	−	0.955933i	$-0.594848\pi$
$773$	19.4288	−	23.1544i	0.698807	−	0.832806i	0.992391	+	0.123128i	$0.0392925\pi$
$774$	−4.61846	−	1.68098i	−0.166007	−	0.0604217i
$775$	24.0826	+	8.39586i	0.865074	+	0.301588i
$776$	−6.35342	+	5.33116i	−0.228075	+	0.191377i
$777$	57.7167	−	10.1770i	2.07058	−	0.365098i
$778$			1.23625i			0.0443217i
$779$	−9.62760	−	5.08978i	−0.344945	−	0.182360i
$780$	−5.06309	+	14.2110i	−0.181288	+	0.508835i
$781$	0.582145	+	3.30151i	0.0208308	+	0.118137i
$782$	1.98610	+	2.36695i	0.0710229	+	0.0846418i
$783$	12.1289	+	33.3239i	0.433451	+	1.19090i
$784$	−11.0815	−	4.03334i	−0.395768	−	0.144048i
$785$	20.5842	+	35.0990i	0.734683	+	1.25274i
$786$	0.103095	−	0.178565i	0.00367727	−	0.00636922i
$787$	−31.5212	+	18.1988i	−1.12361	+	0.648717i	−0.942320	−	0.334712i	$-0.891361\pi$
$787$	−31.5212	+	18.1988i	−1.12361	+	0.648717i	−0.181291	+	0.983430i	$0.558027\pi$
$788$	−29.1228	−	5.13513i	−1.03746	−	0.182931i
$789$	−6.77114	+	38.4010i	−0.241059	+	1.36711i
$790$	−0.597748	−	3.26007i	−0.0212669	−	0.115988i
$791$	5.74724	−	9.95452i	0.204348	−	0.353942i
$792$	11.7921	−	14.0533i	0.419015	−	0.499363i
$793$	−1.21728	+	3.34444i	−0.0432268	+	0.118765i
$794$	−5.48507	+	1.99640i	−0.194658	+	0.0708497i
$795$	−1.47160	−	3.95913i	−0.0521923	−	0.140416i
$796$	−4.35514	−	24.6993i	−0.154364	−	0.875442i
$797$			19.2118i			0.680517i	0.940332	+	0.340258i	$0.110515\pi$
$797$			19.2118i			0.680517i	−0.940332	+	0.340258i	$0.889485\pi$
$798$	−4.19867	+	3.79860i	−0.148631	+	0.134469i
$799$	16.6532			0.589148
$800$	12.2958	+	6.87750i	0.434722	+	0.243156i
$801$	−7.69500	+	6.45687i	−0.271889	+	0.228142i
$802$	2.07080	+	5.68947i	0.0731224	+	0.200902i
$803$	2.04986	−	5.63194i	0.0723379	−	0.198747i
$804$	21.2142	+	17.8008i	0.748166	+	0.627786i
$805$	14.4423	+	16.9757i	0.509025	+	0.598313i
$806$	−0.791760	−	1.37137i	−0.0278886	−	0.0483044i
$807$	43.7992	+	7.72298i	1.54180	+	0.271862i
$808$	−12.7605	−	2.25001i	−0.448911	−	0.0791552i
$809$	−21.5251	−	37.2825i	−0.756781	−	1.31078i	−0.944484	−	0.328557i	$-0.893438\pi$
$809$	−21.5251	−	37.2825i	−0.756781	−	1.31078i	0.187703	−	0.982226i	$-0.439896\pi$
$810$	0.940187	−	0.799880i	0.0330348	−	0.0281049i
$811$	−23.9988	−	20.1373i	−0.842710	−	0.707118i	0.115461	−	0.993312i	$-0.463165\pi$
$811$	−23.9988	−	20.1373i	−0.842710	−	0.707118i	−0.958172	+	0.286194i	$0.907610\pi$
$812$	−11.1261	+	30.5687i	−0.390450	+	1.07275i
$813$	−5.54950	−	15.2471i	−0.194629	−	0.534740i
$814$	8.74521	−	7.33810i	0.306520	−	0.257200i
$815$	5.72393	−	33.8062i	0.200501	−	1.18418i
$816$	24.5560			0.859631
$817$	−19.4655	+	0.726064i	−0.681011	+	0.0254018i
$818$			2.42032i			0.0846245i
$819$	−1.92468	−	10.9154i	−0.0672539	−	0.381416i
$820$	−3.77648	−	10.1601i	−0.131880	−	0.354805i
$821$	−16.0413	+	5.83857i	−0.559847	+	0.203768i	−0.606416	−	0.795148i	$-0.707393\pi$
$821$	−16.0413	+	5.83857i	−0.559847	+	0.203768i	0.0465693	+	0.998915i	$0.485171\pi$
$822$	3.31994	−	9.12147i	0.115796	−	0.318148i
$823$	23.3420	−	27.8179i	0.813650	−	0.969670i	−0.186268	−	0.982499i	$-0.559639\pi$
$823$	23.3420	−	27.8179i	0.813650	−	0.969670i	0.999918	+	0.0128292i	$0.00408378\pi$
$824$	1.94383	−	3.36682i	0.0677166	−	0.117289i
$825$	57.2132	+	9.28694i	1.99191	+	0.323330i
$826$	0.427779	−	2.42606i	0.0148843	−	0.0844133i
$827$	−19.0492	−	3.35888i	−0.662404	−	0.116800i	−0.167669	−	0.985843i	$-0.553624\pi$
$827$	−19.0492	−	3.35888i	−0.662404	−	0.116800i	−0.494735	+	0.869044i	$0.664735\pi$
$828$	38.8320	−	22.4197i	1.34951	−	0.779138i
$829$	−10.0921	+	17.4801i	−0.350514	+	0.607109i	−0.986340	−	0.164724i	$-0.947327\pi$
$829$	−10.0921	+	17.4801i	−0.350514	+	0.607109i	0.635825	+	0.771833i	$0.280660\pi$
$830$	−5.58900	+	3.27774i	−0.193997	+	0.113772i
$831$	16.2354	+	5.90920i	0.563200	+	0.204988i
$832$	2.86687	+	7.87666i	0.0993909	+	0.273074i
$833$	5.11636	+	6.09744i	0.177271	+	0.211264i
$834$	−1.83647	−	10.4151i	−0.0635917	−	0.360647i
$835$	13.0951	+	4.66553i	0.453176	+	0.161457i
$836$	10.9826	−	34.0763i	0.379841	−	1.17855i
$837$			20.9332i			0.723557i
$838$	0.965002	−	0.170156i	0.0333355	−	0.00587794i
$839$	−19.7800	+	16.5974i	−0.682880	+	0.573005i	−0.916846	−	0.399240i	$-0.869274\pi$
$839$	−19.7800	+	16.5974i	−0.682880	+	0.573005i	0.233966	+	0.972245i	$0.424830\pi$
$840$	−11.4443	+	0.0779074i	−0.394866	+	0.00268806i
$841$	−42.9165	−	15.6203i	−1.47988	−	0.538632i
$842$	−3.18664	+	3.79769i	−0.109819	+	0.130877i
$843$	−6.35469	−	3.66888i	−0.218867	−	0.126363i
$844$	4.31332	+	7.47089i	0.148471	+	0.257159i
$845$	−22.1380	−	12.5813i	−0.761572	−	0.432808i
$846$	−1.29276	+	7.33159i	−0.0444459	+	0.252065i
$847$	11.6296	−	6.71438i	0.399599	−	0.230709i
$848$	−2.17745	−	1.25715i	−0.0747738	−	0.0431707i
$849$	65.1639	+	54.6790i	2.23642	+	1.87658i
$850$	−1.53898	−	2.58371i	−0.0527867	−	0.0886206i
$851$	53.2482	−	19.3807i	1.82532	−	0.664363i
$852$	−2.70453	−	3.22313i	−0.0926557	−	0.110423i
$853$	−14.1058	+	2.48724i	−0.482974	+	0.0851613i	−0.409834	−	0.912160i	$-0.634413\pi$
$853$	−14.1058	+	2.48724i	−0.482974	+	0.0851613i	−0.0731404	+	0.997322i	$0.523302\pi$
$854$	−1.32952			−0.0454953
$855$	−20.2287	+	38.9024i	−0.691808	+	1.33044i
$856$	16.3365			0.558370
$857$	23.8963	−	4.21356i	0.816281	−	0.143932i	0.250107	−	0.968218i	$-0.419534\pi$
$857$	23.8963	−	4.21356i	0.816281	−	0.143932i	0.566174	+	0.824286i	$0.308423\pi$
$858$	−2.31325	−	2.75683i	−0.0789732	−	0.0941166i
$859$	38.0794	−	13.8598i	1.29925	−	0.472889i	0.402499	−	0.915421i	$-0.368142\pi$
$859$	38.0794	−	13.8598i	1.29925	−	0.472889i	0.896753	+	0.442532i	$0.145920\pi$
$860$	−14.9364	−	12.3608i	−0.509327	−	0.421501i
$861$	10.1687	+	8.53259i	0.346550	+	0.290790i
$862$	−2.85368	−	1.64757i	−0.0971968	−	0.0561166i
$863$	19.8458	−	11.4580i	0.675560	−	0.390035i	−0.122620	−	0.992454i	$-0.539130\pi$
$863$	19.8458	−	11.4580i	0.675560	−	0.390035i	0.798180	+	0.602419i	$0.205796\pi$
$864$	−2.00798	+	11.3878i	−0.0683129	+	0.387422i
$865$	3.05599	−	5.37733i	0.103907	−	0.182835i
$866$	4.20227	+	7.27854i	0.142799	+	0.247335i
$867$	25.9616	+	14.9889i	0.881702	+	0.509051i
$868$	−12.3431	+	14.7100i	−0.418953	+	0.499289i
$869$	−24.1185	−	8.77843i	−0.818165	−	0.297788i
$870$	−0.0880583	−	12.9354i	−0.00298546	−	0.438552i
$871$	5.07019	−	4.25440i	0.171797	−	0.144155i
$872$	6.48474	−	1.14344i	0.219601	−	0.0387216i
$873$		−	38.7326i		−	1.31090i
$874$	−3.36013	+	4.32190i	−0.113658	+	0.146190i
$875$	−11.2278	−	18.5612i	−0.379570	−	0.627483i
$876$	1.30619	+	7.40776i	0.0441320	+	0.250285i
$877$	−31.9434	−	38.0686i	−1.07865	−	1.28549i	−0.956105	−	0.293024i	$-0.905338\pi$
$877$	−31.9434	−	38.0686i	−1.07865	−	1.28549i	−0.122546	−	0.992463i	$-0.539106\pi$
$878$	1.95812	+	5.37988i	0.0660832	+	0.181562i
$879$	−2.22751	−	0.810748i	−0.0751321	−	0.0273458i
$880$	29.7625	−	17.4546i	1.00329	−	0.588395i
$881$	5.51788	−	9.55725i	0.185902	−	0.321992i	−0.757978	−	0.652280i	$-0.773813\pi$
$881$	5.51788	−	9.55725i	0.185902	−	0.321992i	0.943880	+	0.330288i	$0.107146\pi$
$882$	−3.08158	+	1.77915i	−0.103762	+	0.0599071i
$883$	21.7883	+	3.84187i	0.733235	+	0.129289i	0.527785	−	0.849378i	$-0.323023\pi$
$883$	21.7883	+	3.84187i	0.733235	+	0.129289i	0.205451	+	0.978667i	$0.434134\pi$
$884$	1.05254	−	5.96927i	0.0354009	−	0.200768i
$885$	−5.73504	−	31.2784i	−0.192781	−	1.05141i
$886$	−0.293236	+	0.507899i	−0.00985145	+	0.0170632i
$887$	−12.8769	+	15.3461i	−0.432365	+	0.515272i	−0.937603	−	0.347708i	$-0.886960\pi$
$887$	−12.8769	+	15.3461i	−0.432365	+	0.515272i	0.505238	+	0.862980i	$0.331405\pi$
$888$	−9.95175	+	27.3422i	−0.333959	+	0.917544i
$889$	34.9704	−	12.7282i	1.17287	−	0.426890i
$890$	1.14418	−	0.425289i	0.0383529	−	0.0142557i
$891$	−1.65992	−	9.41387i	−0.0556094	−	0.315376i
$892$			17.8481i			0.597597i
$893$	6.20309	+	28.8460i	0.207578	+	0.965295i
$894$	8.34491			0.279095
$895$	25.0857	+	4.24741i	0.838521	+	0.141975i
$896$	−10.7748	+	9.04109i	−0.359959	+	0.302042i
$897$	−6.10956	−	16.7859i	−0.203992	−	0.560464i
$898$	−3.19430	+	8.77627i	−0.106595	+	0.292868i
$899$	−33.7653	−	28.3325i	−1.12614	−	0.944941i
$900$	−40.8032	+	15.4834i	−1.36011	+	0.516115i
$901$	0.848530	+	1.46970i	0.0282686	+	0.0489627i
$902$	2.54643	+	0.449004i	0.0847868	+	0.0149502i
$903$	23.3828	+	4.12301i	0.778129	+	0.137205i
$904$	2.85336	+	4.94217i	0.0949015	+	0.164374i
$905$	5.16772	+	6.07419i	0.171781	+	0.201913i
$906$	7.09776	+	5.95572i	0.235807	+	0.197866i
$907$	−0.233041	+	0.640274i	−0.00773799	+	0.0212600i	−0.943501	−	0.331368i	$-0.892490\pi$
$907$	−0.233041	+	0.640274i	−0.00773799	+	0.0212600i	0.935763	+	0.352628i	$0.114712\pi$
$908$	0.398363	+	1.09449i	0.0132201	+	0.0363220i
$909$	46.3545	−	38.8960i	1.53748	−	1.29010i
$910$	−0.224849	+	1.32798i	−0.00745366	+	0.0440221i
$911$	28.7169			0.951433			0.475716	−	0.879599i	$-0.342189\pi$
$911$	28.7169			0.951433			0.475716	+	0.879599i	$0.342189\pi$
$912$	9.14675	+	42.5348i	0.302879	+	1.40847i
$913$			50.1744i			1.66053i
$914$	0.0796442	+	0.451684i	0.00263439	+	0.0149404i
$915$	−16.0868	+	5.97944i	−0.531813	+	0.197674i
$916$	−12.9722	+	4.72149i	−0.428613	+	0.156002i
$917$	−0.204386	+	0.561545i	−0.00674941	+	0.0185439i
$918$	1.58662	−	1.89086i	0.0523663	−	0.0624077i
$919$	3.45629	−	5.98648i	0.114013	−	0.197476i	−0.803372	−	0.595477i	$-0.796963\pi$
$919$	3.45629	−	5.98648i	0.114013	−	0.197476i	0.917385	+	0.398002i	$0.130296\pi$
$920$	−10.8840	+	1.99563i	−0.358834	+	0.0657939i
$921$	4.27581	−	24.2494i	0.140893	−	0.799043i
$922$	4.04972	+	0.714075i	0.133371	+	0.0235168i
$923$	−0.870870	+	0.502797i	−0.0286650	+	0.0165498i
$924$	−21.8202	+	37.7938i	−0.717833	+	1.24332i
$925$	−54.1793	+	10.3157i	−1.78140	+	0.339179i
$926$	−5.59725	−	2.03723i	−0.183937	−	0.0669477i
$927$	6.20959	+	17.0607i	0.203950	+	0.560347i
$928$	−15.6509	−	18.6520i	−0.513765	−	0.612281i
$929$	−7.09009	−	40.2099i	−0.232618	−	1.31924i	−0.847572	−	0.530681i	$-0.821936\pi$
$929$	−7.09009	−	40.2099i	−0.232618	−	1.31924i	0.614953	−	0.788563i	$-0.289175\pi$
$930$	2.56271	−	7.19296i	0.0840344	−	0.235866i
$931$	−8.65596	+	11.1336i	−0.283688	+	0.364888i
$932$		−	39.1272i		−	1.28165i
$933$	−30.8529	+	5.44020i	−1.01008	+	0.178104i
$934$	2.55658	−	2.14522i	0.0836538	−	0.0701938i
$935$	−23.2879	+	0.158533i	−0.761595	+	0.00518458i
$936$	5.17097	+	1.88208i	0.169019	+	0.0615177i
$937$	9.47723	−	11.2945i	0.309608	−	0.368976i	−0.588694	−	0.808356i	$-0.700358\pi$
$937$	9.47723	−	11.2945i	0.309608	−	0.368976i	0.898301	+	0.439380i	$0.144802\pi$
$938$	2.14121	+	1.23623i	0.0699129	+	0.0403642i
$939$	−10.7689	−	18.6523i	−0.351430	−	0.608695i
$940$	−14.5102	+	25.5322i	−0.473269	+	0.832768i
$941$	−9.06681	+	51.4204i	−0.295570	+	1.67626i	0.369309	+	0.929307i	$0.379594\pi$
$941$	−9.06681	+	51.4204i	−0.295570	+	1.67626i	−0.664878	+	0.746952i	$0.731517\pi$
$942$	10.5502	−	6.09115i	0.343743	−	0.198460i
$943$	11.1151	+	6.41730i	0.361957	+	0.208976i
$944$	−14.5009	−	12.1677i	−0.471964	−	0.396025i
$945$	11.3517	−	13.7170i	0.369271	−	0.446214i
$946$	4.34607	−	1.58184i	0.141303	−	0.0514300i
$947$	−36.8577	−	43.9252i	−1.19771	−	1.42738i	−0.877194	−	0.480137i	$-0.840587\pi$
$947$	−36.8577	−	43.9252i	−1.19771	−	1.42738i	−0.320519	−	0.947242i	$-0.603857\pi$
$948$	31.7234	−	5.59369i	1.03033	−	0.181675i
$949$	1.79777			0.0583580
$950$	3.90215	−	3.62816i	0.126603	−	0.117713i
$951$	−45.2555			−1.46751
$952$	4.52842	−	0.798483i	0.146767	−	0.0258790i
$953$	5.98927	+	7.13773i	0.194011	+	0.231214i	0.854277	−	0.519819i	$-0.174001\pi$
$953$	5.98927	+	7.13773i	0.194011	+	0.231214i	−0.660265	+	0.751033i	$0.729556\pi$
$954$	−0.712905	+	0.259476i	−0.0230811	+	0.00840085i
$955$	12.3648	−	14.9411i	0.400114	−	0.483484i
$956$	17.2920	+	14.5097i	0.559262	+	0.469277i
$957$	−86.7521	−	50.0863i	−2.80430	−	1.61906i
$958$	4.60298	−	2.65753i	0.148716	−	0.0858610i
$959$	−4.88519	+	27.7053i	−0.157751	+	0.894650i
$960$	−19.9709	+	35.1410i	−0.644559	+	1.13417i
$961$	2.49072	+	4.31405i	0.0803458	+	0.139163i
$962$	2.96557	+	1.71217i	0.0956139	+	0.0552027i
$963$	−49.0399	+	58.4434i	−1.58029	+	1.88331i
$964$	−46.5470	−	16.9417i	−1.49918	−	0.545656i
$965$	0.943845	−	0.00642525i	0.0303834	−	0.000206836i
$966$	5.11175	−	4.28927i	0.164468	−	0.138005i
$967$	−8.69287	+	1.53279i	−0.279544	+	0.0492911i	−0.311662	−	0.950193i	$-0.600886\pi$
$967$	−8.69287	+	1.53279i	−0.279544	+	0.0492911i	0.0321185	+	0.999484i	$0.489775\pi$
$968$			6.66705i			0.214287i
$969$	9.00813	−	27.9500i	0.289383	−	0.897883i
$970$	−1.57964	+	4.43371i	−0.0507193	+	0.142358i
$971$	9.72287	+	55.1412i	0.312022	+	1.76956i	0.588454	+	0.808531i	$0.299737\pi$
$971$	9.72287	+	55.1412i	0.312022	+	1.76956i	−0.276432	+	0.961033i	$0.589152\pi$
$972$	23.0662	+	27.4892i	0.739848	+	0.881716i
$973$	10.4833	+	28.8026i	0.336079	+	0.923369i
$974$	6.71866	+	2.44539i	0.215280	+	0.0783554i
$975$	3.25191	+	17.0794i	0.104145	+	0.546978i
$976$	−5.10807	+	8.84743i	−0.163505	+	0.283199i
$977$	35.5965	−	20.5517i	1.13883	−	0.657506i	0.192693	−	0.981259i	$-0.438278\pi$
$977$	35.5965	−	20.5517i	1.13883	−	0.657506i	0.946142	+	0.323753i	$0.104945\pi$
$978$	−10.1095	−	1.78258i	−0.323266	−	0.0570006i
$979$	1.64144	−	9.30905i	0.0524605	−	0.297518i
$980$	−13.8064	+	2.53146i	−0.441028	+	0.0808645i
$981$	−15.3757	+	26.6314i	−0.490907	+	0.850277i
$982$	2.88452	−	3.43764i	0.0920488	−	0.109700i
$983$	0.854584	−	2.34795i	0.0272570	−	0.0748880i	−0.925318	−	0.379193i	$-0.876202\pi$
$983$	0.854584	−	2.34795i	0.0272570	−	0.0748880i	0.952575	+	0.304305i	$0.0984240\pi$
$984$	−6.19294	+	2.25405i	−0.197424	+	0.0718564i
$985$	−31.9456	+	11.8741i	−1.01787	+	0.378341i
$986$	0.902520	+	5.11845i	0.0287421	+	0.163005i
$987$		−	35.9650i		−	1.14478i
$988$	10.7318	−	0.400297i	0.341423	−	0.0127351i
$989$	22.9569			0.729986
$990$	1.73800	−	10.2648i	0.0552372	−	0.326237i
$991$	13.3471	−	11.1995i	0.423983	−	0.355764i	−0.405693	−	0.914010i	$-0.632970\pi$
$991$	13.3471	−	11.1995i	0.423983	−	0.355764i	0.829676	+	0.558245i	$0.188525\pi$
$992$	−4.91574	−	13.5059i	−0.156075	−	0.428812i
$993$	−7.41250	+	20.3657i	−0.235228	+	0.646285i
$994$	−0.287762	−	0.241461i	−0.00912727	−	0.00765869i
$995$	−18.7297	−	22.0151i	−0.593771	−	0.697924i
$996$	−31.4858	−	54.5351i	−0.997667	−	1.72801i
$997$	−12.6065	−	2.22287i	−0.399253	−	0.0703990i	−0.0295832	−	0.999562i	$-0.509418\pi$
$997$	−12.6065	−	2.22287i	−0.399253	−	0.0703990i	−0.369670	+	0.929163i	$0.620529\pi$
$998$	−2.50776	−	0.442186i	−0.0793819	−	0.0139972i
$999$	−22.6339	−	39.2031i	−0.716106	−	1.24033i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	95.2.p.a.9.4	✓	48
3.2	odd	2		855.2.da.b.199.5		48
5.2	odd	4		475.2.l.f.351.4		48
5.3	odd	4		475.2.l.f.351.5		48
5.4	even	2	inner	95.2.p.a.9.5	yes	48
15.14	odd	2		855.2.da.b.199.4		48
19.6	even	9		1805.2.b.k.1084.13		24
19.13	odd	18		1805.2.b.l.1084.12		24
19.17	even	9	inner	95.2.p.a.74.5	yes	48
57.17	odd	18		855.2.da.b.739.4		48
95.13	even	36		9025.2.a.ct.1.12		24
95.17	odd	36		475.2.l.f.226.4		48
95.32	even	36		9025.2.a.ct.1.13		24
95.44	even	18		1805.2.b.k.1084.12		24
95.63	odd	36		9025.2.a.cu.1.13		24
95.74	even	18	inner	95.2.p.a.74.4	yes	48
95.82	odd	36		9025.2.a.cu.1.12		24
95.89	odd	18		1805.2.b.l.1084.13		24
95.93	odd	36		475.2.l.f.226.5		48
285.74	odd	18		855.2.da.b.739.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.9.4	✓	48	1.1	even	1	trivial
95.2.p.a.9.5	yes	48	5.4	even	2	inner
95.2.p.a.74.4	yes	48	95.74	even	18	inner
95.2.p.a.74.5	yes	48	19.17	even	9	inner
475.2.l.f.226.4		48	95.17	odd	36
475.2.l.f.226.5		48	95.93	odd	36
475.2.l.f.351.4		48	5.2	odd	4
475.2.l.f.351.5		48	5.3	odd	4
855.2.da.b.199.4		48	15.14	odd	2
855.2.da.b.199.5		48	3.2	odd	2
855.2.da.b.739.4		48	57.17	odd	18
855.2.da.b.739.5		48	285.74	odd	18
1805.2.b.k.1084.12		24	95.44	even	18
1805.2.b.k.1084.13		24	19.6	even	9
1805.2.b.l.1084.12		24	19.13	odd	18
1805.2.b.l.1084.13		24	95.89	odd	18
9025.2.a.ct.1.12		24	95.13	even	36
9025.2.a.ct.1.13		24	95.32	even	36
9025.2.a.cu.1.12		24	95.82	odd	36
9025.2.a.cu.1.13		24	95.63	odd	36

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	95.p (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.240763 + 0.0424530i) q^{2} +(-1.76019 - 2.09771i) q^{3} +(-1.82322 + 0.663598i) q^{4} +(-1.42562 + 1.72267i) q^{5} +(0.512843 + 0.430326i) q^{6} +(-1.68032 - 0.970136i) q^{7} +(0.834240 - 0.481648i) q^{8} +(-0.781184 + 4.43031i) q^{9} +(0.270105 - 0.475278i) q^{10} +(-2.11666 - 3.66617i) q^{11} +(4.60125 + 2.65653i) q^{12} +(0.816227 - 0.972742i) q^{13} +(0.445745 + 0.162238i) q^{14} +(6.12303 - 0.0416827i) q^{15} +(2.79220 - 2.34293i) q^{16} +(-2.42284 + 0.427212i) q^{17} -1.09982i q^{18} +(-1.64247 - 4.03761i) q^{19} +(1.45606 - 4.08685i) q^{20} +(0.922623 + 5.23246i) q^{21} +(0.665255 + 0.792820i) q^{22} +(1.75701 + 4.82735i) q^{23} +(-2.47878 - 0.902202i) q^{24} +(-0.935198 - 4.91176i) q^{25} +(-0.155222 + 0.268852i) q^{26} +(3.55406 - 2.05194i) q^{27} +(3.70738 + 0.653712i) q^{28} +(-1.50053 + 8.50995i) q^{29} +(-1.47243 + 0.269977i) q^{30} +(-2.55042 + 4.41746i) q^{31} +(-1.81118 + 2.15849i) q^{32} +(-3.96484 + 10.8933i) q^{33} +(0.565193 - 0.205714i) q^{34} +(4.06673 - 1.51160i) q^{35} +(-1.51568 - 8.59583i) q^{36} -11.0305i q^{37} +(0.566855 + 0.902380i) q^{38} -3.47724 q^{39} +(-0.359589 + 2.12377i) q^{40} +(1.91387 - 1.60593i) q^{41} +(-0.444267 - 1.22061i) q^{42} +(1.52842 - 4.19929i) q^{43} +(6.29201 + 5.27962i) q^{44} +(-6.51830 - 7.66168i) q^{45} +(-0.627959 - 1.08766i) q^{46} +(-6.66617 - 1.17543i) q^{47} +(-9.82960 - 1.73322i) q^{48} +(-1.61767 - 2.80189i) q^{49} +(0.433680 + 1.14287i) q^{50} +(5.16082 + 4.33044i) q^{51} +(-0.842653 + 2.31517i) q^{52} +(-0.235926 - 0.648201i) q^{53} +(-0.768575 + 0.644911i) q^{54} +(9.33317 + 1.58026i) q^{55} -1.86906 q^{56} +(-5.57868 + 10.5524i) q^{57} -2.11258i q^{58} +(-0.901817 - 5.11446i) q^{59} +(-11.1360 + 4.13923i) q^{60} +(-2.63378 + 0.958619i) q^{61} +(0.426513 - 1.17183i) q^{62} +(5.61065 - 6.68651i) q^{63} +(-3.30053 + 5.71668i) q^{64} +(0.512083 + 2.79285i) q^{65} +(0.492133 - 2.79103i) q^{66} +(5.13308 + 0.905101i) q^{67} +(4.13387 - 2.38669i) q^{68} +(7.03371 - 12.1828i) q^{69} +(-0.914948 + 0.536583i) q^{70} +(-0.744158 - 0.270851i) q^{71} +(1.48216 + 4.07220i) q^{72} +(0.910034 + 1.08454i) q^{73} +(0.468279 + 2.65574i) q^{74} +(-8.65733 + 10.6074i) q^{75} +(5.67394 + 6.27151i) q^{76} +8.21381i q^{77} +(0.837192 - 0.147620i) q^{78} +(4.64448 - 3.89718i) q^{79} +(0.0554826 + 8.15018i) q^{80} +(2.12188 + 0.772300i) q^{81} +(-0.392614 + 0.467899i) q^{82} +(-10.2643 - 5.92611i) q^{83} +(-5.15439 - 8.92767i) q^{84} +(2.71811 - 4.78280i) q^{85} +(-0.189714 + 1.07592i) q^{86} +(20.4926 - 11.8314i) q^{87} +(-3.53161 - 2.03898i) q^{88} +(1.71051 + 1.43529i) q^{89} +(1.89463 + 1.56793i) q^{90} +(-2.31522 + 0.842670i) q^{91} +(-6.40684 - 7.63537i) q^{92} +(13.7558 - 2.42551i) q^{93} +1.65487 q^{94} +(9.29702 + 2.92667i) q^{95} +7.71591 q^{96} +(-8.47901 + 1.49508i) q^{97} +(0.508425 + 0.605917i) q^{98} +(17.8958 - 6.51353i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 18 q^{4} - 6 q^{5} - 6 q^{6} - 12 q^{9} - 15 q^{10} - 12 q^{11} + 6 q^{14} + 3 q^{15} - 42 q^{16} + 12 q^{19} + 42 q^{20} - 54 q^{21} + 24 q^{24} + 12 q^{25} + 12 q^{26} + 18 q^{30} - 42 q^{31} - 36 q^{34}+ \cdots - 36 q^{99}+O(q^{100}) \) 48 * q - 18 * q^4 - 6 * q^5 - 6 * q^6 - 12 * q^9 - 15 * q^10 - 12 * q^11 + 6 * q^14 + 3 * q^15 - 42 * q^16 + 12 * q^19 + 42 * q^20 - 54 * q^21 + 24 * q^24 + 12 * q^25 + 12 * q^26 + 18 * q^30 - 42 * q^31 - 36 * q^34 + 6 * q^35 + 18 * q^36 - 48 * q^39 + 66 * q^40 + 6 * q^41 - 6 * q^44 - 9 * q^45 - 6 * q^46 + 12 * q^49 - 18 * q^50 + 108 * q^51 + 24 * q^54 + 36 * q^56 - 36 * q^59 - 114 * q^60 + 48 * q^61 - 18 * q^65 + 180 * q^66 + 66 * q^69 - 123 * q^70 - 24 * q^71 + 84 * q^74 + 72 * q^75 + 66 * q^76 + 48 * q^79 - 39 * q^80 - 78 * q^81 - 54 * q^84 - 84 * q^85 - 42 * q^86 - 12 * q^89 + 18 * q^90 - 30 * q^91 - 72 * q^94 - 63 * q^95 - 240 * q^96 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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