LMFDB - Embedded newform 416.2.bf.a.53.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,2,Mod(53,416)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(416, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 5, 0]))

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

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

chi := DirichletCharacter("416.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.bf (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			53.15
Character	$\chi$	$=$	416.53
Dual form			416.2.bf.a.157.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.884565 - 1.10342i) q^{2} +(-0.349851 + 0.144913i) q^{3} +(-0.435089 + 1.95210i) q^{4} +(1.55977 - 3.76561i) q^{5} +(0.469367 + 0.257849i) q^{6} +(3.21782 + 3.21782i) q^{7} +(2.53886 - 1.24667i) q^{8} +(-2.01992 + 2.01992i) q^{9} +(-5.53478 + 1.60984i) q^{10} +(3.33191 + 1.38012i) q^{11} +(-0.130669 - 0.745995i) q^{12} +(0.382683 + 0.923880i) q^{13} +(0.704248 - 6.39699i) q^{14} +1.54343i q^{15} +(-3.62140 - 1.69867i) q^{16} +4.55727i q^{17} +(4.01559 + 0.442078i) q^{18} +(-0.372913 - 0.900292i) q^{19} +(6.67222 + 4.68320i) q^{20} +(-1.59206 - 0.659453i) q^{21} +(-1.42443 - 4.89732i) q^{22} +(0.896482 - 0.896482i) q^{23} +(-0.707563 + 0.804064i) q^{24} +(-8.21142 - 8.21142i) q^{25} +(0.680922 - 1.23949i) q^{26} +(0.848698 - 2.04894i) q^{27} +(-7.68154 + 4.88147i) q^{28} +(6.52827 - 2.70410i) q^{29} +(1.70306 - 1.36527i) q^{30} +5.60889 q^{31} +(1.32900 + 5.49852i) q^{32} -1.36567 q^{33} +(5.02860 - 4.03120i) q^{34} +(17.1361 - 7.09801i) q^{35} +(-3.06425 - 4.82194i) q^{36} +(1.78152 - 4.30096i) q^{37} +(-0.663538 + 1.20785i) q^{38} +(-0.267764 - 0.267764i) q^{39} +(-0.734457 - 11.5049i) q^{40} +(-0.255937 + 0.255937i) q^{41} +(0.680625 + 2.34005i) q^{42} +(-7.06466 - 2.92628i) q^{43} +(-4.14382 + 5.90375i) q^{44} +(4.45564 + 10.7569i) q^{45} +(-1.78220 - 0.196203i) q^{46} -4.48241i q^{47} +(1.51311 + 0.0694955i) q^{48} +13.7087i q^{49} +(-1.79714 + 16.3242i) q^{50} +(-0.660408 - 1.59436i) q^{51} +(-1.97001 + 0.345067i) q^{52} +(-5.86345 - 2.42872i) q^{53} +(-3.01158 + 0.875946i) q^{54} +(10.3940 - 10.3940i) q^{55} +(12.1812 + 4.15802i) q^{56} +(0.260928 + 0.260928i) q^{57} +(-8.75844 - 4.81150i) q^{58} +(0.698645 - 1.68668i) q^{59} +(-3.01294 - 0.671531i) q^{60} +(-10.3825 + 4.30056i) q^{61} +(-4.96143 - 6.18898i) q^{62} -12.9995 q^{63} +(4.89161 - 6.33026i) q^{64} +4.07587 q^{65} +(1.20802 + 1.50691i) q^{66} +(1.55466 - 0.643963i) q^{67} +(-8.89625 - 1.98282i) q^{68} +(-0.183723 + 0.443547i) q^{69} +(-22.9901 - 12.6297i) q^{70} +(-5.65597 - 5.65597i) q^{71} +(-2.61012 + 7.64649i) q^{72} +(1.51942 - 1.51942i) q^{73} +(-6.32166 + 1.83871i) q^{74} +(4.06272 + 1.68283i) q^{75} +(1.91971 - 0.336257i) q^{76} +(6.28050 + 15.1625i) q^{77} +(-0.0586026 + 0.532313i) q^{78} +16.0902i q^{79} +(-12.0451 + 10.9872i) q^{80} -7.73000i q^{81} +(0.508799 + 0.0560140i) q^{82} +(1.23518 + 2.98198i) q^{83} +(1.98001 - 2.82094i) q^{84} +(17.1609 + 7.10828i) q^{85} +(3.02023 + 10.3838i) q^{86} +(-1.89206 + 1.89206i) q^{87} +(10.1798 - 0.649867i) q^{88} +(-10.8072 - 10.8072i) q^{89} +(7.92808 - 14.4316i) q^{90} +(-1.74147 + 4.20428i) q^{91} +(1.35997 + 2.14007i) q^{92} +(-1.96228 + 0.812801i) q^{93} +(-4.94600 + 3.96499i) q^{94} -3.97181 q^{95} +(-1.26176 - 1.73107i) q^{96} +2.93479 q^{97} +(15.1265 - 12.1262i) q^{98} +(-9.51795 + 3.94247i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 16 q^{10} - 16 q^{12} - 40 q^{16} - 40 q^{18} - 8 q^{22} - 16 q^{23} + 24 q^{24} + 80 q^{30} - 48 q^{31} - 48 q^{35} + 80 q^{36} - 56 q^{38} - 64 q^{40} - 16 q^{43} - 80 q^{44} + 24 q^{50} + 32 q^{51}+ \cdots + 56 q^{98}+O(q^{100}) $ 192 * q - 16 * q^10 - 16 * q^12 - 40 * q^16 - 40 * q^18 - 8 * q^22 - 16 * q^23 + 24 * q^24 + 80 * q^30 - 48 * q^31 - 48 * q^35 + 80 * q^36 - 56 * q^38 - 64 * q^40 - 16 * q^43 - 80 * q^44 + 24 * q^50 + 32 * q^51 - 32 * q^53 - 24 * q^54 + 32 * q^55 + 16 * q^56 - 64 * q^58 - 56 * q^60 - 64 * q^61 + 24 * q^62 + 80 * q^63 + 72 * q^64 + 96 * q^66 + 80 * q^67 - 32 * q^68 - 64 * q^69 - 120 * q^72 - 32 * q^74 + 32 * q^75 + 64 * q^76 - 32 * q^77 - 56 * q^80 - 80 * q^82 - 80 * q^83 + 112 * q^84 - 112 * q^87 - 88 * q^88 - 120 * q^90 + 144 * q^92 + 40 * q^94 + 136 * q^96 + 56 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$1$	$1$

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 $

$2$	−0.884565	−	1.10342i	−0.625482	−	0.780239i
$2$	−0.884565	−	1.10342i	−0.625482	−	0.780239i
$3$	−0.349851	+	0.144913i	−0.201987	+	0.0836656i	−0.481383	−	0.876510i	$-0.659866\pi$
$3$	−0.349851	+	0.144913i	−0.201987	+	0.0836656i	0.279397	+	0.960176i	$0.409866\pi$
$4$	−0.435089	+	1.95210i	−0.217544	+	0.976050i
$5$	1.55977	−	3.76561i	0.697549	−	1.68403i	−0.0314383	−	0.999506i	$-0.510009\pi$
$5$	1.55977	−	3.76561i	0.697549	−	1.68403i	0.728987	−	0.684527i	$-0.239991\pi$
$6$	0.469367	+	0.257849i	0.191618	+	0.105266i
$7$	3.21782	+	3.21782i	1.21622	+	1.21622i	0.968945	+	0.247276i	$0.0795354\pi$
$7$	3.21782	+	3.21782i	1.21622	+	1.21622i	0.247276	+	0.968945i	$0.420465\pi$
$8$	2.53886	−	1.24667i	0.897622	−	0.440766i
$9$	−2.01992	+	2.01992i	−0.673308	+	0.673308i
$10$	−5.53478	+	1.60984i	−1.75025	+	0.509078i
$11$	3.33191	+	1.38012i	1.00461	+	0.416123i	0.823485	−	0.567338i	$-0.192027\pi$
$11$	3.33191	+	1.38012i	1.00461	+	0.416123i	0.181124	+	0.983460i	$0.442027\pi$
$12$	−0.130669	−	0.745995i	−0.0377208	−	0.215350i
$13$	0.382683	+	0.923880i	0.106137	+	0.256238i
$13$	0.382683	+	0.923880i	0.106137	+	0.256238i
$14$	0.704248	−	6.39699i	0.188218	−	1.70967i
$15$			1.54343i			0.398513i
$16$	−3.62140	−	1.69867i	−0.905349	−	0.424669i
$17$			4.55727i			1.10530i	0.833414	+	0.552650i	$0.186383\pi$
$17$			4.55727i			1.10530i	−0.833414	+	0.552650i	$0.813617\pi$
$18$	4.01559	+	0.442078i	0.946483	+	0.104199i
$19$	−0.372913	−	0.900292i	−0.0855521	−	0.206541i	0.875314	−	0.483556i	$-0.160655\pi$
$19$	−0.372913	−	0.900292i	−0.0855521	−	0.206541i	−0.960866	+	0.277015i	$0.910655\pi$
$20$	6.67222	+	4.68320i	1.49195	+	1.04720i
$21$	−1.59206	−	0.659453i	−0.347416	−	0.143905i
$22$	−1.42443	−	4.89732i	−0.303690	−	1.04411i
$23$	0.896482	−	0.896482i	0.186929	−	0.186929i	−0.607438	−	0.794367i	$-0.707803\pi$
$23$	0.896482	−	0.896482i	0.186929	−	0.186929i	0.794367	+	0.607438i	$0.207803\pi$
$24$	−0.707563	+	0.804064i	−0.144431	+	0.164129i
$25$	−8.21142	−	8.21142i	−1.64228	−	1.64228i
$26$	0.680922	−	1.23949i	0.133540	−	0.243085i
$27$	0.848698	−	2.04894i	0.163332	−	0.394319i
$28$	−7.68154	+	4.88147i	−1.45168	+	0.922511i
$29$	6.52827	−	2.70410i	1.21227	−	0.502138i	0.317325	−	0.948317i	$-0.397215\pi$
$29$	6.52827	−	2.70410i	1.21227	−	0.502138i	0.894944	+	0.446179i	$0.147215\pi$
$30$	1.70306	−	1.36527i	0.310935	−	0.249263i
$31$	5.60889			1.00739			0.503693	−	0.863883i	$-0.331974\pi$
$31$	5.60889			1.00739			0.503693	+	0.863883i	$0.331974\pi$
$32$	1.32900	+	5.49852i	0.234937	+	0.972011i
$33$	−1.36567			−0.237733
$34$	5.02860	−	4.03120i	0.862397	−	0.691345i
$35$	17.1361	−	7.09801i	2.89653	−	1.19978i
$36$	−3.06425	−	4.82194i	−0.510708	−	0.803657i
$37$	1.78152	−	4.30096i	0.292880	−	0.707074i	−0.707120	−	0.707093i	$-0.750006\pi$
$37$	1.78152	−	4.30096i	0.292880	−	0.707074i	1.00000		1.90889e-5i	$6.07619e-6\pi$
$38$	−0.663538	+	1.20785i	−0.107640	+	0.195939i
$39$	−0.267764	−	0.267764i	−0.0428766	−	0.0428766i
$40$	−0.734457	−	11.5049i	−0.116128	−	1.81908i
$41$	−0.255937	+	0.255937i	−0.0399706	+	0.0399706i	−0.726810	−	0.686839i	$-0.758998\pi$
$41$	−0.255937	+	0.255937i	−0.0399706	+	0.0399706i	0.686839	+	0.726810i	$0.258998\pi$
$42$	0.680625	+	2.34005i	0.105023	+	0.361077i
$43$	−7.06466	−	2.92628i	−1.07735	−	0.446253i	−0.227771	−	0.973715i	$-0.573144\pi$
$43$	−7.06466	−	2.92628i	−1.07735	−	0.446253i	−0.849579	+	0.527462i	$0.823144\pi$
$44$	−4.14382	+	5.90375i	−0.624704	+	0.890024i
$45$	4.45564	+	10.7569i	0.664207	+	1.60354i
$46$	−1.78220	−	0.196203i	−0.262771	−	0.0289285i
$47$		−	4.48241i		−	0.653827i	−0.945054	−	0.326913i	$-0.893991\pi$
$47$		−	4.48241i		−	0.653827i	0.945054	−	0.326913i	$-0.106009\pi$
$48$	1.51311	+	0.0694955i	0.218399	+	0.0100308i
$49$			13.7087i			1.95839i
$50$	−1.79714	+	16.3242i	−0.254154	+	2.30859i
$51$	−0.660408	−	1.59436i	−0.0924756	−	0.223256i
$52$	−1.97001	+	0.345067i	−0.273191	+	0.0478522i
$53$	−5.86345	−	2.42872i	−0.805407	−	0.333611i	−0.0582872	−	0.998300i	$-0.518564\pi$
$53$	−5.86345	−	2.42872i	−0.805407	−	0.333611i	−0.747120	+	0.664689i	$0.768564\pi$
$54$	−3.01158	+	0.875946i	−0.409824	+	0.119201i
$55$	10.3940	−	10.3940i	1.40153	−	1.40153i
$56$	12.1812	+	4.15802i	1.62778	+	0.555639i
$57$	0.260928	+	0.260928i	0.0345608	+	0.0345608i
$58$	−8.75844	−	4.81150i	−1.15004	−	0.631780i
$59$	0.698645	−	1.68668i	0.0909559	−	0.219587i	−0.871854	−	0.489765i	$-0.837083\pi$
$59$	0.698645	−	1.68668i	0.0909559	−	0.219587i	0.962810	+	0.270178i	$0.0870826\pi$
$60$	−3.01294	−	0.671531i	−0.388969	−	0.0866942i
$61$	−10.3825	+	4.30056i	−1.32934	+	0.550630i	−0.930467	−	0.366376i	$-0.880598\pi$
$61$	−10.3825	+	4.30056i	−1.32934	+	0.550630i	−0.398872	+	0.917007i	$0.630598\pi$
$62$	−4.96143	−	6.18898i	−0.630102	−	0.786001i
$63$	−12.9995			−1.63778
$64$	4.89161	−	6.33026i	0.611451	−	0.791282i
$65$	4.07587			0.505549
$66$	1.20802	+	1.50691i	0.148698	+	0.185488i
$67$	1.55466	−	0.643963i	0.189932	−	0.0786726i	−0.285690	−	0.958322i	$-0.592223\pi$
$67$	1.55466	−	0.643963i	0.189932	−	0.0786726i	0.475623	+	0.879649i	$0.342223\pi$
$68$	−8.89625	−	1.98282i	−1.07883	−	0.240452i
$69$	−0.183723	+	0.443547i	−0.0221177	+	0.0533968i
$70$	−22.9901	−	12.6297i	−2.74784	−	1.50954i
$71$	−5.65597	−	5.65597i	−0.671240	−	0.671240i	0.286762	−	0.958002i	$-0.407421\pi$
$71$	−5.65597	−	5.65597i	−0.671240	−	0.671240i	−0.958002	+	0.286762i	$0.907421\pi$
$72$	−2.61012	+	7.64649i	−0.307605	+	0.901147i
$73$	1.51942	−	1.51942i	0.177835	−	0.177835i	−0.612577	−	0.790411i	$-0.709867\pi$
$73$	1.51942	−	1.51942i	0.177835	−	0.177835i	0.790411	+	0.612577i	$0.209867\pi$
$74$	−6.32166	+	1.83871i	−0.734878	+	0.213746i
$75$	4.06272	+	1.68283i	0.469122	+	0.194317i
$76$	1.91971	−	0.336257i	0.220206	−	0.0385713i
$77$	6.28050	+	15.1625i	0.715730	+	1.72792i
$78$	−0.0586026	+	0.532313i	−0.00663543	+	0.0602726i
$79$			16.0902i			1.81029i	0.425105	+	0.905144i	$0.360237\pi$
$79$			16.0902i			1.81029i	−0.425105	+	0.905144i	$0.639763\pi$
$80$	−12.0451	+	10.9872i	−1.34668	+	1.22841i
$81$		−	7.73000i		−	0.858889i
$82$	0.508799	+	0.0560140i	0.0561875	+	0.00618571i
$83$	1.23518	+	2.98198i	0.135578	+	0.327314i	0.977058	−	0.212974i	$-0.0683150\pi$
$83$	1.23518	+	2.98198i	0.135578	+	0.327314i	−0.841480	+	0.540289i	$0.818315\pi$
$84$	1.98001	−	2.82094i	0.216037	−	0.307790i
$85$	17.1609	+	7.10828i	1.86136	+	0.771001i
$86$	3.02023	+	10.3838i	0.325679	+	1.11971i
$87$	−1.89206	+	1.89206i	−0.202850	+	0.202850i
$88$	10.1798	−	0.649867i	1.08517	−	0.0692761i
$89$	−10.8072	−	10.8072i	−1.14556	−	1.14556i	−0.987417	−	0.158140i	$-0.949450\pi$
$89$	−10.8072	−	10.8072i	−1.14556	−	1.14556i	−0.158140	−	0.987417i	$-0.550550\pi$
$90$	7.92808	−	14.4316i	0.835693	−	1.52122i
$91$	−1.74147	+	4.20428i	−0.182556	+	0.440729i
$92$	1.35997	+	2.14007i	0.141787	+	0.223118i
$93$	−1.96228	+	0.812801i	−0.203478	+	0.0842835i
$94$	−4.94600	+	3.96499i	−0.510141	+	0.408957i
$95$	−3.97181			−0.407499
$96$	−1.26176	−	1.73107i	−0.128778	−	0.176677i
$97$	2.93479			0.297983			0.148992	−	0.988838i	$-0.452397\pi$
$97$	2.93479			0.297983			0.148992	+	0.988838i	$0.452397\pi$
$98$	15.1265	−	12.1262i	1.52801	−	1.22494i
$99$	−9.51795	+	3.94247i	−0.956590	+	0.396233i
$100$	19.6022	−	12.4568i	1.96022	−	1.24568i
$101$	−5.43119	+	13.1120i	−0.540423	+	1.30470i	0.384002	+	0.923332i	$0.374546\pi$
$101$	−5.43119	+	13.1120i	−0.540423	+	1.30470i	−0.924425	+	0.381364i	$0.875454\pi$
$102$	−1.17509	+	2.13903i	−0.116351	+	0.211795i
$103$	−1.92234	−	1.92234i	−0.189414	−	0.189414i	0.606029	−	0.795443i	$-0.292762\pi$
$103$	−1.92234	−	1.92234i	−0.189414	−	0.189414i	−0.795443	+	0.606029i	$0.792762\pi$
$104$	2.12336	+	1.86852i	0.208212	+	0.183223i
$105$	−4.96649	+	4.96649i	−0.484680	+	0.484680i
$106$	2.50670	+	8.61824i	0.243472	+	0.837077i
$107$	18.3479	+	7.59996i	1.77376	+	0.734716i	0.994094	+	0.108523i	$0.0346120\pi$
$107$	18.3479	+	7.59996i	1.77376	+	0.734716i	0.779668	+	0.626193i	$0.215388\pi$
$108$	3.63048	+	2.54822i	0.349343	+	0.245202i
$109$	2.43235	+	5.87222i	0.232977	+	0.562456i	0.996525	−	0.0832949i	$-0.0265443\pi$
$109$	2.43235	+	5.87222i	0.232977	+	0.562456i	−0.763548	+	0.645751i	$0.776544\pi$
$110$	−20.6632	−	2.27482i	−1.97016	−	0.216896i
$111$			1.76286i			0.167323i
$112$	−6.18697	−	17.1190i	−0.584614	−	1.61760i
$113$		−	5.98905i		−	0.563403i	−0.959502	−	0.281701i	$-0.909101\pi$
$113$		−	5.98905i		−	0.563403i	0.959502	−	0.281701i	$-0.0908987\pi$
$114$	0.0571064	−	0.518722i	0.00534850	−	0.0485828i
$115$	−1.97750	−	4.77411i	−0.184403	−	0.445188i
$116$	2.43829	+	13.9204i	0.226390	+	1.29247i
$117$	−2.63916	−	1.09318i	−0.243990	−	0.101064i
$118$	−2.47912	+	0.721076i	−0.228221	+	0.0663804i
$119$	−14.6645	+	14.6645i	−1.34429	+	1.34429i
$120$	1.92416	+	3.91856i	0.175651	+	0.357714i
$121$	1.41872	+	1.41872i	0.128975	+	0.128975i
$122$	13.9293	+	7.65214i	1.26110	+	0.692792i
$123$	0.0524511	−	0.126628i	0.00472936	−	0.0114177i
$124$	−2.44036	+	10.9491i	−0.219151	+	0.983260i
$125$	−24.9009	+	10.3143i	−2.22720	+	0.922538i
$126$	11.4989	+	14.3440i	1.02440	+	1.27786i
$127$	11.8228			1.04910			0.524550	−	0.851379i	$-0.324233\pi$
$127$	11.8228			1.04910			0.524550	+	0.851379i	$0.324233\pi$
$128$	−11.3119	+	0.202002i	−0.999841	+	0.0178546i
$129$	2.89563			0.254946
$130$	−3.60537	−	4.49741i	−0.316212	−	0.394449i
$131$	3.19155	−	1.32198i	0.278847	−	0.115502i	−0.238877	−	0.971050i	$-0.576779\pi$
$131$	3.19155	−	1.32198i	0.278847	−	0.115502i	0.517724	+	0.855548i	$0.326779\pi$
$132$	0.594188	−	2.66593i	0.0517174	−	0.232039i
$133$	1.69701	−	4.09694i	0.147149	−	0.355250i
$134$	−2.08577	−	1.14583i	−0.180183	−	0.0989843i
$135$	−6.39174	−	6.39174i	−0.550113	−	0.550113i
$136$	5.68142	+	11.5703i	0.487178	+	0.992142i
$137$	5.89020	−	5.89020i	0.503234	−	0.503234i	−0.409208	−	0.912441i	$-0.634195\pi$
$137$	5.89020	−	5.89020i	0.503234	−	0.503234i	0.912441	+	0.409208i	$0.134195\pi$
$138$	0.651936	−	0.189622i	0.0554965	−	0.0161417i
$139$	−7.81989	−	3.23910i	−0.663274	−	0.274737i	0.0255415	−	0.999674i	$-0.491869\pi$
$139$	−7.81989	−	3.23910i	−0.663274	−	0.274737i	−0.688816	+	0.724937i	$0.741869\pi$
$140$	6.40030	+	36.5397i	0.540924	+	3.08817i
$141$	0.649560	+	1.56818i	0.0547028	+	0.132064i
$142$	−1.23786	+	11.2440i	−0.103879	+	0.943576i
$143$			3.60644i			0.301585i
$144$	10.7461	−	3.88375i	0.895512	−	0.323646i
$145$		−	28.8007i		−	2.39177i
$146$	−3.02059	−	0.332538i	−0.249986	−	0.0275211i
$147$	−1.98657	−	4.79601i	−0.163850	−	0.395568i
$148$	7.62080	+	5.34900i	0.626426	+	0.439685i
$149$	−12.7662	−	5.28795i	−1.04585	−	0.433205i	−0.207442	−	0.978247i	$-0.566514\pi$
$149$	−12.7662	−	5.28795i	−1.04585	−	0.433205i	−0.838409	+	0.545042i	$0.816514\pi$
$150$	−1.73686	−	5.97148i	−0.141814	−	0.487569i
$151$	−12.9731	+	12.9731i	−1.05574	+	1.05574i	−0.0573862	+	0.998352i	$0.518277\pi$
$151$	−12.9731	+	12.9731i	−1.05574	+	1.05574i	−0.998352	+	0.0573862i	$0.981723\pi$
$152$	−2.06914	−	1.82081i	−0.167830	−	0.147687i
$153$	−9.20534	−	9.20534i	−0.744207	−	0.744207i
$154$	11.1751	−	20.3423i	0.900517	−	1.63923i
$155$	8.74856	−	21.1209i	0.702701	−	1.69647i
$156$	0.639204	−	0.406202i	0.0511773	−	0.0325222i
$157$	−4.88363	+	2.02287i	−0.389756	+	0.161442i	−0.568951	−	0.822371i	$-0.692651\pi$
$157$	−4.88363	+	2.02287i	−0.389756	+	0.161442i	0.179195	+	0.983814i	$0.442651\pi$
$158$	17.7543	−	14.2328i	1.41246	−	1.13230i
$159$	2.40329			0.190593
$160$	22.7782	+	3.57191i	1.80078	+	0.282384i
$161$	5.76943			0.454695
$162$	−8.52947	+	6.83769i	−0.670138	+	0.537220i
$163$	7.07871	−	2.93210i	0.554447	−	0.229660i	−0.0878252	−	0.996136i	$-0.527992\pi$
$163$	7.07871	−	2.93210i	0.554447	−	0.229660i	0.642273	+	0.766476i	$0.277992\pi$
$164$	−0.388259	−	0.610969i	−0.0303179	−	0.0477087i
$165$	−2.13013	+	5.14259i	−0.165830	+	0.400350i
$166$	2.19779	−	4.00068i	0.170582	−	0.310513i
$167$	5.35486	+	5.35486i	0.414371	+	0.414371i	0.883258	−	0.468887i	$-0.155345\pi$
$167$	5.35486	+	5.35486i	0.414371	+	0.414371i	−0.468887	+	0.883258i	$0.655345\pi$
$168$	−4.86414	+	0.310521i	−0.375277	+	0.0239572i
$169$	−0.707107	+	0.707107i	−0.0543928	+	0.0543928i
$170$	−7.33649	−	25.2235i	−0.562683	−	1.93455i
$171$	2.57178	+	1.06527i	0.196669	+	0.0814629i
$172$	8.78614	−	12.5177i	0.669937	−	0.954468i
$173$	−3.02283	−	7.29776i	−0.229822	−	0.554839i	0.766334	−	0.642443i	$-0.222079\pi$
$173$	−3.02283	−	7.29776i	−0.229822	−	0.554839i	−0.996155	+	0.0876041i	$0.972079\pi$
$174$	3.76140	+	0.414094i	0.285151	+	0.0313924i
$175$		−	52.8457i		−	3.99476i
$176$	−9.72179	−	10.6578i	−0.732808	−	0.803362i
$177$			0.691329i			0.0519635i
$178$	−2.36524	+	21.4845i	−0.177282	+	1.61033i
$179$	−0.114440	−	0.276282i	−0.00855364	−	0.0206503i	0.919545	−	0.392985i	$-0.128557\pi$
$179$	−0.114440	−	0.276282i	−0.00855364	−	0.0206503i	−0.928099	+	0.372334i	$0.878557\pi$
$180$	−22.9371	+	4.01767i	−1.70963	+	0.299459i
$181$	−16.9008	−	7.00053i	−1.25622	−	0.520345i	−0.347476	−	0.937689i	$-0.612961\pi$
$181$	−16.9008	−	7.00053i	−1.25622	−	0.520345i	−0.908749	+	0.417344i	$0.862961\pi$
$182$	6.17955	−	1.79738i	0.458059	−	0.133231i
$183$	3.00911	−	3.00911i	0.222440	−	0.222440i
$184$	1.15842	−	3.39366i	0.0854000	−	0.250184i
$185$	−13.4170	−	13.4170i	−0.986438	−	0.986438i
$186$	2.63262	+	1.44625i	0.193033	+	0.106044i
$187$	−6.28959	+	15.1844i	−0.459940	+	1.11039i
$188$	8.75012	+	1.95025i	0.638168	+	0.142236i
$189$	9.32407	−	3.86216i	0.678226	−	0.280931i
$190$	3.51332	+	4.38259i	0.254883	+	0.317946i
$191$	16.3870			1.18572			0.592861	−	0.805305i	$-0.297998\pi$
$191$	16.3870			1.18572			0.592861	+	0.805305i	$0.297998\pi$
$192$	−0.793999	+	2.92351i	−0.0573019	+	0.210986i
$193$	−24.3652			−1.75385			−0.876923	−	0.480631i	$-0.840408\pi$
$193$	−24.3652			−1.75385			−0.876923	+	0.480631i	$0.840408\pi$
$194$	−2.59602	−	3.23832i	−0.186383	−	0.232498i
$195$	−1.42595	+	0.590647i	−0.102114	+	0.0422971i
$196$	−26.7608	−	5.96451i	−1.91148	−	0.426036i
$197$	5.47434	−	13.2162i	0.390030	−	0.941616i	−0.599902	−	0.800074i	$-0.704794\pi$
$197$	5.47434	−	13.2162i	0.390030	−	0.941616i	0.989932	−	0.141543i	$-0.0452063\pi$
$198$	12.7695	+	7.01497i	0.907486	+	0.498532i
$199$	−5.44203	−	5.44203i	−0.385775	−	0.385775i	0.487402	−	0.873177i	$-0.337945\pi$
$199$	−5.44203	−	5.44203i	−0.385775	−	0.385775i	−0.873177	+	0.487402i	$0.837945\pi$
$200$	−31.0846	−	10.6107i	−2.19801	−	0.750289i
$201$	−0.450582	+	0.450582i	−0.0317816	+	0.0317816i
$202$	19.2724	−	5.60556i	1.35600	−	0.394406i
$203$	29.7081	+	12.3055i	2.08510	+	0.863676i
$204$	3.39970	−	0.595492i	0.238026	−	0.0416928i
$205$	0.564556	+	1.36296i	0.0394303	+	0.0951932i
$206$	−0.420721	+	3.82159i	−0.0293130	+	0.266263i
$207$			3.62165i			0.251722i
$208$	0.183522	−	3.99579i	0.0127250	−	0.277058i
$209$		−	3.51436i		−	0.243093i
$210$	9.87333	+	1.08696i	0.681324	+	0.0750073i
$211$	3.72815	+	9.00054i	0.256656	+	0.619623i	0.998713	−	0.0507138i	$-0.0161496\pi$
$211$	3.72815	+	9.00054i	0.256656	+	0.619623i	−0.742057	+	0.670337i	$0.766150\pi$
$212$	7.29223	−	10.3893i	0.500833	−	0.713543i
$213$	2.79837	+	1.15912i	0.191741	+	0.0794218i
$214$	−7.84396	−	26.9682i	−0.536202	−	1.84351i
$215$	−22.0384	+	22.0384i	−1.50301	+	1.50301i
$216$	−0.399632	−	6.26002i	−0.0271915	−	0.425940i
$217$	18.0484	+	18.0484i	1.22520	+	1.22520i
$218$	4.32797	−	7.87827i	0.293127	−	0.533584i
$219$	−0.311387	+	0.751754i	−0.0210416	+	0.0507988i
$220$	15.7678	+	24.8125i	1.06307	+	1.67286i
$221$	−4.21037	+	1.74399i	−0.283220	+	0.117314i
$222$	1.94518	−	1.55937i	0.130552	−	0.104658i
$223$	−6.21427			−0.416138			−0.208069	−	0.978114i	$-0.566718\pi$
$223$	−6.21427			−0.416138			−0.208069	+	0.978114i	$0.566718\pi$
$224$	−13.4168	+	21.9697i	−0.896445	+	1.46791i
$225$	33.1729			2.21153
$226$	−6.60846	+	5.29771i	−0.439588	+	0.352398i
$227$	−9.38046	+	3.88551i	−0.622603	+	0.257891i	−0.671607	−	0.740908i	$-0.734395\pi$
$227$	−9.38046	+	3.88551i	−0.622603	+	0.257891i	0.0490035	+	0.998799i	$0.484395\pi$
$228$	−0.622885	+	0.395831i	−0.0412516	+	0.0262146i
$229$	1.82760	−	4.41221i	0.120771	−	0.291567i	−0.851920	−	0.523673i	$-0.824562\pi$
$229$	1.82760	−	4.41221i	0.120771	−	0.291567i	0.972691	+	0.232106i	$0.0745615\pi$
$230$	−3.51864	+	6.40503i	−0.232012	+	0.422335i
$231$	−4.39448	−	4.39448i	−0.289136	−	0.289136i
$232$	13.2032	−	15.0039i	0.866834	−	0.985057i
$233$	−6.74417	+	6.74417i	−0.441825	+	0.441825i	−0.892625	−	0.450800i	$-0.851139\pi$
$233$	−6.74417	+	6.74417i	−0.441825	+	0.441825i	0.450800	+	0.892625i	$0.351139\pi$
$234$	1.12827	+	3.87910i	0.0737575	+	0.253584i
$235$	−16.8790	−	6.99152i	−1.10107	−	0.456076i
$236$	2.98859	+	2.09768i	0.194541	+	0.136547i
$237$	−2.33168	−	5.62917i	−0.151459	−	0.365654i
$238$	29.1528	+	3.20944i	1.88969	+	0.208037i
$239$			10.3547i			0.669788i	0.942256	+	0.334894i	$0.108701\pi$
$239$			10.3547i			0.669788i	−0.942256	+	0.334894i	$0.891299\pi$
$240$	2.62179	−	5.58938i	0.169236	−	0.360793i
$241$			1.92458i			0.123973i	0.998077	+	0.0619867i	$0.0197436\pi$
$241$			1.92458i			0.123973i	−0.998077	+	0.0619867i	$0.980256\pi$
$242$	0.310499	−	2.82040i	0.0199597	−	0.181302i
$243$	3.66627	+	8.85117i	0.235192	+	0.567803i
$244$	−3.87783	−	22.1388i	−0.248253	−	1.41729i
$245$	51.6217	+	21.3824i	3.29799	+	1.36607i
$246$	−0.186121	+	0.0541351i	−0.0118666	+	0.00345153i
$247$	0.689054	−	0.689054i	0.0438434	−	0.0438434i
$248$	14.2402	−	6.99245i	0.904252	−	0.444021i
$249$	−0.864255	−	0.864255i	−0.0547699	−	0.0547699i
$250$	33.4075	+	18.3526i	2.11287	+	1.16072i
$251$	3.70885	−	8.95395i	0.234101	−	0.565169i	−0.762552	−	0.646927i	$-0.776054\pi$
$251$	3.70885	−	8.95395i	0.234101	−	0.565169i	0.996652	+	0.0817587i	$0.0260537\pi$
$252$	5.65594	−	25.3763i	0.356290	−	1.59856i
$253$	4.22425	−	1.74974i	0.265577	−	0.110005i
$254$	−10.4580	−	13.0455i	−0.656194	−	0.818549i
$255$	−7.03384			−0.440476
$256$	10.2290	+	12.3031i	0.639313	+	0.768946i
$257$	−9.39814			−0.586240			−0.293120	−	0.956076i	$-0.594694\pi$
$257$	−9.39814			−0.586240			−0.293120	+	0.956076i	$0.594694\pi$
$258$	−2.56138	−	3.19511i	−0.159464	−	0.198919i
$259$	19.5723	−	8.10712i	1.21617	−	0.503752i
$260$	−1.77336	+	7.95651i	−0.109979	+	0.493442i
$261$	−7.72453	+	18.6487i	−0.478137	+	1.15432i
$262$	−4.28184	−	2.35225i	−0.264533	−	0.145323i
$263$	−11.8201	−	11.8201i	−0.728861	−	0.728861i	0.241532	−	0.970393i	$-0.422350\pi$
$263$	−11.8201	−	11.8201i	−0.728861	−	0.728861i	−0.970393	+	0.241532i	$0.922350\pi$
$264$	−3.46725	+	1.70254i	−0.213394	+	0.104784i
$265$	−18.2912	+	18.2912i	−1.12362	+	1.12362i
$266$	−6.02178	+	1.75149i	−0.369219	+	0.107391i
$267$	5.34699	+	2.21480i	0.327231	+	0.135543i
$268$	0.580664	+	3.31504i	0.0354697	+	0.202498i
$269$	0.574436	+	1.38681i	0.0350240	+	0.0845553i	0.940424	−	0.340005i	$-0.110429\pi$
$269$	0.574436	+	1.38681i	0.0350240	+	0.0845553i	−0.905400	+	0.424560i	$0.860429\pi$
$270$	−1.39889	+	12.7067i	−0.0851336	+	0.773305i
$271$			23.1139i			1.40407i	0.712142	+	0.702036i	$0.247725\pi$
$271$			23.1139i			1.40407i	−0.712142	+	0.702036i	$0.752275\pi$
$272$	7.74131	−	16.5037i	0.469386	−	1.00068i
$273$		−	1.72323i		−	0.104295i
$274$	−11.7097	−	1.28912i	−0.707406	−	0.0778787i
$275$	−16.0270	−	38.6925i	−0.966462	−	2.33325i
$276$	−0.785913	−	0.551629i	−0.0473064	−	0.0332041i
$277$	12.4884	+	5.17285i	0.750353	+	0.310807i	0.724886	−	0.688869i	$-0.241893\pi$
$277$	12.4884	+	5.17285i	0.750353	+	0.310807i	0.0254676	+	0.999676i	$0.491893\pi$
$278$	3.34310	+	11.4938i	0.200506	+	0.689355i
$279$	−11.3295	+	11.3295i	−0.678281	+	0.678281i
$280$	34.6573	−	39.3840i	2.07117	−	2.35364i
$281$	6.56824	+	6.56824i	0.391829	+	0.391829i	0.875339	−	0.483510i	$-0.160638\pi$
$281$	6.56824	+	6.56824i	0.391829	+	0.391829i	−0.483510	+	0.875339i	$0.660638\pi$
$282$	1.15579	−	2.10389i	0.0688260	−	0.125285i
$283$	5.18493	−	12.5175i	0.308212	−	0.744090i	−0.691551	−	0.722328i	$-0.743072\pi$
$283$	5.18493	−	12.5175i	0.308212	−	0.744090i	0.999763	−	0.0217622i	$-0.00692768\pi$
$284$	13.5019	−	8.58018i	0.801189	−	0.509140i
$285$	1.38954	−	0.575567i	0.0823093	−	0.0340936i
$286$	3.97943	−	3.19013i	0.235308	−	0.188636i
$287$	−1.64712			−0.0972261
$288$	−13.7911	−	8.42211i	−0.812647	−	0.496278i
$289$	−3.76869			−0.221687
$290$	−31.7794	+	25.4761i	−1.86615	+	1.49601i
$291$	−1.02674	+	0.425290i	−0.0601886	+	0.0249309i
$292$	2.30498	+	3.62714i	0.134889	+	0.212262i
$293$	5.82556	−	14.0641i	0.340333	−	0.821636i	−0.657349	−	0.753586i	$-0.728322\pi$
$293$	5.82556	−	14.0641i	0.340333	−	0.821636i	0.997682	−	0.0680498i	$-0.0216777\pi$
$294$	−3.53478	+	6.43441i	−0.206152	+	0.375263i
$295$	−5.26165	−	5.26165i	−0.306345	−	0.306345i
$296$	−0.838874	−	13.1405i	−0.0487586	−	0.763777i
$297$	5.65558	−	5.65558i	0.328170	−	0.328170i
$298$	5.45772	+	18.7641i	0.316157	+	1.08697i
$299$	1.17131	+	0.485173i	0.0677386	+	0.0280583i
$300$	−5.05270	+	7.19865i	−0.291718	+	0.415614i
$301$	−13.3166	−	32.1490i	−0.767554	−	1.85304i
$302$	25.7904	+	2.83928i	1.48407	+	0.163382i
$303$		−	5.37431i		−	0.308746i
$304$	−0.178837	+	3.89377i	−0.0102570	+	0.223323i
$305$			45.8042i			2.62274i
$306$	−2.01467	+	18.3001i	−0.115171	+	1.04615i
$307$	−9.16200	−	22.1190i	−0.522903	−	1.26240i	−0.936093	−	0.351754i	$-0.885585\pi$
$307$	−9.16200	−	22.1190i	−0.522903	−	1.26240i	0.413190	−	0.910645i	$-0.364415\pi$
$308$	−32.3312	+	5.66315i	−1.84224	+	0.322688i
$309$	0.951106	+	0.393961i	0.0541065	+	0.0224117i
$310$	−31.0440	+	9.02944i	−1.76318	+	0.512838i
$311$	−21.8070	+	21.8070i	−1.23656	+	1.23656i	−0.275163	+	0.961398i	$0.588732\pi$
$311$	−21.8070	+	21.8070i	−1.23656	+	1.23656i	−0.961398	+	0.275163i	$0.911268\pi$
$312$	−1.01363	−	0.346001i	−0.0573855	−	0.0195885i
$313$	−12.3386	−	12.3386i	−0.697421	−	0.697421i	0.266433	−	0.963853i	$-0.414155\pi$
$313$	−12.3386	−	12.3386i	−0.697421	−	0.697421i	−0.963853	+	0.266433i	$0.914155\pi$
$314$	6.55197	+	3.59936i	0.369749	+	0.203124i
$315$	−20.2762	+	48.9511i	−1.14243	+	2.75808i
$316$	−31.4097	−	7.00066i	−1.76693	−	0.393818i
$317$	19.8477	−	8.22117i	1.11476	−	0.461747i	0.252183	−	0.967680i	$-0.418851\pi$
$317$	19.8477	−	8.22117i	1.11476	−	0.461747i	0.862573	+	0.505932i	$0.168851\pi$
$318$	−2.12587	−	2.65185i	−0.119213	−	0.148708i
$319$	25.4836			1.42681
$320$	−16.2075	−	28.2936i	−0.906027	−	1.58166i
$321$	−7.52038			−0.419747
$322$	−5.10344	−	6.36613i	−0.284404	−	0.354771i
$323$	4.10287	−	1.69946i	0.228290	−	0.0945607i
$324$	15.0897	+	3.36324i	0.838319	+	0.186846i
$325$	4.44399	−	10.7287i	0.246508	−	0.595123i
$326$	−9.49693	−	5.21719i	−0.525986	−	0.288953i
$327$	−1.70192	−	1.70192i	−0.0941165	−	0.0941165i
$328$	−0.330718	+	0.968856i	−0.0182608	+	0.0534962i
$329$	14.4236	−	14.4236i	0.795198	−	0.795198i
$330$	7.55869	−	2.19852i	0.416092	−	0.121024i
$331$	−11.7026	−	4.84736i	−0.643230	−	0.266435i	0.0371323	−	0.999310i	$-0.488178\pi$
$331$	−11.7026	−	4.84736i	−0.643230	−	0.266435i	−0.680363	+	0.732876i	$0.738178\pi$
$332$	−6.35853	+	1.11376i	−0.348970	+	0.0611256i
$333$	5.08909	+	12.2862i	0.278881	+	0.673277i
$334$	1.17196	−	10.6454i	0.0641267	−	0.582490i
$335$		−	6.85869i		−	0.374730i
$336$	4.64529	+	5.09253i	0.253421	+	0.277821i
$337$		−	12.8700i		−	0.701075i	−0.936549	−	0.350538i	$-0.885999\pi$
$337$		−	12.8700i		−	0.701075i	0.936549	−	0.350538i	$-0.114001\pi$
$338$	1.40572	+	0.154756i	0.0764611	+	0.00841764i
$339$	0.867892	+	2.09528i	0.0471374	+	0.113800i
$340$	−21.3426	+	30.4071i	−1.15746	+	1.64906i
$341$	18.6883	+	7.74095i	1.01203	+	0.419196i
$342$	−1.09947	−	3.78006i	−0.0594523	−	0.204402i
$343$	−21.5874	+	21.5874i	−1.16561	+	1.16561i
$344$	−21.5843	+	1.37791i	−1.16375	+	0.0742922i
$345$	1.38366	+	1.38366i	0.0744938	+	0.0744938i
$346$	−5.37863	+	9.79081i	−0.289157	+	0.526357i
$347$	−5.00595	+	12.0854i	−0.268733	+	0.648780i	−0.999424	−	0.0339288i	$-0.989198\pi$
$347$	−5.00595	+	12.0854i	−0.268733	+	0.648780i	0.730691	+	0.682708i	$0.239198\pi$
$348$	−2.87028	−	4.51671i	−0.153863	−	0.242121i
$349$	13.3622	−	5.53481i	0.715263	−	0.296272i	0.00478248	−	0.999989i	$-0.498478\pi$
$349$	13.3622	−	5.53481i	0.715263	−	0.296272i	0.710480	+	0.703717i	$0.248478\pi$
$350$	−58.3113	+	46.7455i	−3.11687	+	2.49865i
$351$	2.21776			0.118375
$352$	−3.16052	+	20.1548i	−0.168456	+	1.07425i
$353$	−15.0762			−0.802427			−0.401214	−	0.915984i	$-0.631412\pi$
$353$	−15.0762			−0.802427			−0.401214	+	0.915984i	$0.631412\pi$
$354$	0.762829	−	0.611526i	0.0405439	−	0.0325022i
$355$	−30.1202	+	12.4762i	−1.59861	+	0.662168i
$356$	25.7987	−	16.3946i	1.36733	−	0.868911i
$357$	3.00531	−	7.25545i	0.159058	−	0.383999i
$358$	−0.203627	+	0.370665i	−0.0107620	+	0.0195903i
$359$	5.48515	+	5.48515i	0.289495	+	0.289495i	0.836881	−	0.547385i	$-0.184377\pi$
$359$	5.48515	+	5.48515i	0.289495	+	0.289495i	−0.547385	+	0.836881i	$0.684377\pi$
$360$	24.7225	+	21.7554i	1.30299	+	1.14661i
$361$	12.7636	−	12.7636i	0.671767	−	0.671767i
$362$	7.22528	+	24.8411i	0.379752	+	1.30562i
$363$	−0.701932	−	0.290750i	−0.0368419	−	0.0152604i
$364$	−7.44949	−	5.22876i	−0.390459	−	0.274062i
$365$	−3.35160	−	8.09148i	−0.175431	−	0.423528i
$366$	−5.98208	−	0.658570i	−0.312688	−	0.0344240i
$367$		−	23.8161i		−	1.24319i	−0.783339	−	0.621594i	$-0.786485\pi$
$367$		−	23.8161i		−	1.24319i	0.783339	−	0.621594i	$-0.213515\pi$
$368$	−4.76935	+	1.72369i	−0.248619	+	0.0898533i
$369$		−	1.03395i		−	0.0538250i
$370$	−2.93643	+	26.6729i	−0.152658	+	1.38666i
$371$	−11.0523	−	26.6827i	−0.573809	−	1.38530i
$372$	−0.732906	−	4.18420i	−0.0379994	−	0.216941i
$373$	−15.8573	−	6.56831i	−0.821060	−	0.340094i	−0.0677025	−	0.997706i	$-0.521567\pi$
$373$	−15.8573	−	6.56831i	−0.821060	−	0.340094i	−0.753357	+	0.657611i	$0.771567\pi$
$374$	22.3184	−	6.49152i	1.15406	−	0.335668i
$375$	7.21693	−	7.21693i	0.372680	−	0.372680i
$376$	−5.58810	−	11.3802i	−0.288184	−	0.586890i
$377$	4.99652	+	4.99652i	0.257334	+	0.257334i
$378$	−12.5093	−	6.87207i	−0.643411	−	0.353461i
$379$	−7.59746	+	18.3419i	−0.390255	+	0.942160i	0.599628	+	0.800279i	$0.295315\pi$
$379$	−7.59746	+	18.3419i	−0.390255	+	0.942160i	−0.989884	+	0.141881i	$0.954685\pi$
$380$	1.72809	−	7.75337i	0.0886491	−	0.397739i
$381$	−4.13621	+	1.71327i	−0.211904	+	0.0877736i
$382$	−14.4954	−	18.0818i	−0.741648	−	0.925146i
$383$	33.0584			1.68920			0.844602	−	0.535395i	$-0.179837\pi$
$383$	33.0584			1.68920			0.844602	+	0.535395i	$0.179837\pi$
$384$	3.92821	−	1.70991i	0.200461	−	0.0872587i
$385$	66.8921			3.40914
$386$	21.5526	+	26.8851i	1.09700	+	1.36842i
$387$	20.1809	−	8.35922i	1.02585	−	0.424923i
$388$	−1.27690	+	5.72902i	−0.0648246	+	0.290847i
$389$	11.1498	−	26.9181i	0.565320	−	1.36480i	−0.340142	−	0.940374i	$-0.610475\pi$
$389$	11.1498	−	26.9181i	0.565320	−	1.36480i	0.905462	−	0.424428i	$-0.139525\pi$
$390$	1.91308	+	1.05096i	0.0968724	+	0.0532174i
$391$	4.08551	+	4.08551i	0.206613	+	0.206613i
$392$	17.0903	+	34.8045i	0.863190	+	1.75789i
$393$	−0.924994	+	0.924994i	−0.0466598	+	0.0466598i
$394$	−19.4255	+	5.65009i	−0.978642	+	0.284647i
$395$	60.5894	+	25.0970i	3.04858	+	1.26276i
$396$	−3.55494	−	20.2953i	−0.178642	−	1.01988i
$397$	14.3290	+	34.5932i	0.719151	+	1.73619i	0.675754	+	0.737127i	$0.263818\pi$
$397$	14.3290	+	34.5932i	0.719151	+	1.73619i	0.0433976	+	0.999058i	$0.486182\pi$
$398$	−1.19104	+	10.8187i	−0.0597012	+	0.542292i
$399$			1.67924i			0.0840671i
$400$	15.7883	+	43.6853i	0.789414	+	2.18427i
$401$			11.7744i			0.587984i	0.955808	+	0.293992i	$0.0949839\pi$
$401$			11.7744i			0.587984i	−0.955808	+	0.293992i	$0.905016\pi$
$402$	0.895753	+	0.0986138i	0.0446761	+	0.00491841i
$403$	2.14643	+	5.18194i	0.106921	+	0.258131i
$404$	−23.2330	−	16.3071i	−1.15588	−	0.811310i
$405$	−29.1082	−	12.0570i	−1.44640	−	0.599117i
$406$	−12.7006	−	43.6656i	−0.630318	−	2.16709i
$407$	11.8717	−	11.8717i	0.588459	−	0.588459i
$408$	−3.66433	−	3.22456i	−0.181412	−	0.159639i
$409$	−7.75244	−	7.75244i	−0.383334	−	0.383334i	0.488968	−	0.872302i	$-0.337373\pi$
$409$	−7.75244	−	7.75244i	−0.383334	−	0.383334i	−0.872302	+	0.488968i	$0.837373\pi$
$410$	1.00454	−	1.82857i	0.0496105	−	0.0903067i
$411$	−1.20713	+	2.91426i	−0.0595431	+	0.143750i
$412$	4.58899	−	2.91622i	0.226084	−	0.143672i
$413$	7.67554	−	3.17931i	0.377689	−	0.156444i
$414$	3.99622	−	3.20359i	0.196403	−	0.157448i
$415$	13.1556			0.645781
$416$	−4.57139	+	3.33203i	−0.224131	+	0.163366i
$417$	3.20518			0.156959
$418$	−3.87783	+	3.10868i	−0.189671	+	0.152050i
$419$	−35.5284	+	14.7163i	−1.73568	+	0.718940i	−0.736583	+	0.676347i	$0.763562\pi$
$419$	−35.5284	+	14.7163i	−1.73568	+	0.718940i	−0.999093	+	0.0425931i	$0.986438\pi$
$420$	−7.53423	−	11.8560i	−0.367633	−	0.578511i
$421$	−11.7867	+	28.4557i	−0.574450	+	1.38685i	0.323282	+	0.946303i	$0.395214\pi$
$421$	−11.7867	+	28.4557i	−0.574450	+	1.38685i	−0.897732	+	0.440542i	$0.854786\pi$
$422$	6.63363	−	12.0753i	0.322920	−	0.587816i
$423$	9.05413	+	9.05413i	0.440227	+	0.440227i
$424$	−17.9143	+	1.14363i	−0.869995	+	0.0555394i
$425$	37.4216	−	37.4216i	1.81522	−	1.81522i
$426$	−1.19634	−	4.11311i	−0.0579628	−	0.199281i
$427$	−47.2473	−	19.5705i	−2.28646	−	0.947082i
$428$	−22.8189	+	32.5104i	−1.10299	+	1.57145i
$429$	−0.522620	−	1.26172i	−0.0252323	−	0.0609162i
$430$	43.8122	+	4.82331i	2.11281	+	0.232600i
$431$			19.6215i			0.945132i	0.881295	+	0.472566i	$0.156672\pi$
$431$			19.6215i			0.945132i	−0.881295	+	0.472566i	$0.843328\pi$
$432$	−6.55395	+	5.97836i	−0.315327	+	0.287634i
$433$			20.3797i			0.979387i	0.871895	+	0.489694i	$0.162891\pi$
$433$			20.3797i			0.979387i	−0.871895	+	0.489694i	$0.837109\pi$
$434$	3.95005	−	35.8800i	0.189608	−	1.72229i
$435$	4.17359	+	10.0759i	0.200109	+	0.483105i
$436$	−12.5214	+	2.19326i	−0.599669	+	0.105038i
$437$	−1.14141	−	0.472786i	−0.0546008	−	0.0226164i
$438$	1.10495	−	0.321384i	0.0527963	−	0.0153563i
$439$	−10.1282	+	10.1282i	−0.483392	+	0.483392i	−0.906213	−	0.422821i	$-0.861040\pi$
$439$	−10.1282	+	10.1282i	−0.483392	+	0.483392i	0.422821	+	0.906213i	$0.361040\pi$
$440$	13.4310	−	39.3469i	0.640298	−	1.87579i
$441$	−27.6906	−	27.6906i	−1.31860	−	1.31860i
$442$	5.64870	+	3.10315i	0.268681	+	0.147602i
$443$	−0.591943	+	1.42908i	−0.0281241	+	0.0678975i	−0.937318	−	0.348476i	$-0.886699\pi$
$443$	−0.591943	+	1.42908i	−0.0281241	+	0.0678975i	0.909194	+	0.416374i	$0.136699\pi$
$444$	−3.44128	−	0.767001i	−0.163316	−	0.0364003i
$445$	−57.5522	+	23.8389i	−2.72824	+	1.13007i
$446$	5.49692	+	6.85697i	0.260287	+	0.324687i
$447$	5.23257			0.247492
$448$	36.1099	−	4.62929i	1.70603	−	0.218714i
$449$	−17.2816			−0.815571			−0.407785	−	0.913078i	$-0.633699\pi$
$449$	−17.2816			−0.815571			−0.407785	+	0.913078i	$0.633699\pi$
$450$	−29.3436	−	36.6038i	−1.38327	−	1.72552i
$451$	−1.20598	+	0.499534i	−0.0567875	+	0.0235221i
$452$	11.6912	+	2.60577i	0.549909	+	0.122565i
$453$	2.65869	−	6.41864i	0.124916	−	0.301574i
$454$	12.5850	+	6.91363i	0.590643	+	0.324473i
$455$	13.1154	+	13.1154i	0.614860	+	0.614860i
$456$	0.987752	+	0.337168i	0.0462557	+	0.0157893i
$457$	−15.5287	+	15.5287i	−0.726403	+	0.726403i	−0.969901	−	0.243498i	$-0.921705\pi$
$457$	−15.5287	+	15.5287i	−0.726403	+	0.726403i	0.243498	+	0.969901i	$0.421705\pi$
$458$	−6.48516	+	1.88627i	−0.303032	+	0.0881397i
$459$	9.33756	+	3.86775i	0.435840	+	0.180531i
$460$	10.1799	−	1.78312i	0.474642	−	0.0831384i
$461$	−1.01958	−	2.46148i	−0.0474865	−	0.114643i	0.898356	−	0.439267i	$-0.144762\pi$
$461$	−1.01958	−	2.46148i	−0.0474865	−	0.114643i	−0.945843	+	0.324625i	$0.894762\pi$
$462$	−0.961770	+	8.73618i	−0.0447456	+	0.406444i
$463$		−	4.76539i		−	0.221466i	−0.993850	−	0.110733i	$-0.964680\pi$
$463$		−	4.76539i		−	0.221466i	0.993850	−	0.110733i	$-0.0353199\pi$
$464$	−28.2348	−	1.29679i	−1.31077	−	0.0602022i
$465$			8.65695i			0.401456i
$466$	13.4073	+	1.47602i	0.621083	+	0.0683753i
$467$	−11.0898	−	26.7731i	−0.513174	−	1.23891i	−0.942027	−	0.335538i	$-0.891082\pi$
$467$	−11.0898	−	26.7731i	−0.513174	−	1.23891i	0.428853	−	0.903374i	$-0.358918\pi$
$468$	3.28226	−	4.67628i	0.151722	−	0.216161i
$469$	7.07478	+	2.93047i	0.326683	+	0.135317i
$470$	7.21599	+	24.8092i	0.332849	+	1.14436i
$471$	1.41540	−	1.41540i	0.0652184	−	0.0652184i
$472$	−0.328975	−	5.15322i	−0.0151423	−	0.237196i
$473$	−19.5002	−	19.5002i	−0.896620	−	0.896620i
$474$	−4.14884	+	7.55220i	−0.190562	+	0.346884i
$475$	−4.33053	+	10.4548i	−0.198698	+	0.479700i
$476$	−22.2462	−	35.0068i	−1.01965	−	1.60454i
$477$	16.7496	−	6.93790i	0.766910	−	0.317664i
$478$	11.4256	−	9.15939i	0.522595	−	0.418941i
$479$	−33.6247			−1.53635			−0.768175	−	0.640240i	$-0.778835\pi$
$479$	−33.6247			−1.53635			−0.768175	+	0.640240i	$0.778835\pi$
$480$	−8.48661	+	2.05123i	−0.387359	+	0.0936253i
$481$	4.65533			0.212265
$482$	2.12363	−	1.70242i	0.0967288	−	0.0775431i
$483$	−2.01844	+	0.836066i	−0.0918423	+	0.0380423i
$484$	−3.38675	+	2.15222i	−0.153943	+	0.0978280i
$485$	4.57760	−	11.0513i	0.207858	−	0.501814i
$486$	6.52353	−	11.8749i	0.295913	−	0.538656i
$487$	5.86696	+	5.86696i	0.265857	+	0.265857i	0.827428	−	0.561571i	$-0.189803\pi$
$487$	5.86696	+	5.86696i	0.265857	+	0.265857i	−0.561571	+	0.827428i	$0.689803\pi$
$488$	−20.9982	+	23.8621i	−0.950545	+	1.08018i
$489$	−2.05160	+	2.05160i	−0.0927763	+	0.0927763i
$490$	−22.0689	−	75.8747i	−0.996971	−	3.42767i
$491$	−21.4780	−	8.89648i	−0.969288	−	0.401492i	−0.158841	−	0.987304i	$-0.550776\pi$
$491$	−21.4780	−	8.89648i	−0.969288	−	0.401492i	−0.810447	+	0.585812i	$0.800776\pi$
$492$	0.224370	+	0.157484i	0.0101154	+	0.00709995i
$493$	12.3233	+	29.7511i	0.555013	+	1.33992i
$494$	−1.36983	−	0.150805i	−0.0616316	−	0.00678505i
$495$			41.9902i			1.88732i
$496$	−20.3120	−	9.52767i	−0.912036	−	0.427805i
$497$		−	36.3998i		−	1.63275i
$498$	−0.189150	+	1.71813i	−0.00847600	+	0.0769912i
$499$	−14.6607	−	35.3940i	−0.656303	−	1.58445i	−0.803471	−	0.595343i	$-0.797016\pi$
$499$	−14.6607	−	35.3940i	−0.656303	−	1.58445i	0.147169	−	0.989111i	$-0.452984\pi$
$500$	−9.30043	−	53.0967i	−0.415928	−	2.37455i
$501$	−2.64939	−	1.09741i	−0.118366	−	0.0490288i
$502$	−13.1607	+	3.82792i	−0.587392	+	0.170849i
$503$	12.0326	−	12.0326i	0.536506	−	0.536506i	−0.385995	−	0.922501i	$-0.626142\pi$
$503$	12.0326	−	12.0326i	0.536506	−	0.536506i	0.922501	+	0.385995i	$0.126142\pi$
$504$	−33.0039	+	16.2061i	−1.47011	+	0.721878i
$505$	40.9035	+	40.9035i	1.82018	+	1.82018i
$506$	−5.66734	−	3.11338i	−0.251944	−	0.138407i
$507$	0.144913	−	0.349851i	0.00643581	−	0.0155374i
$508$	−5.14395	+	23.0792i	−0.228226	+	1.02398i
$509$	13.4319	−	5.56367i	0.595358	−	0.246605i	−0.0645959	−	0.997912i	$-0.520576\pi$
$509$	13.4319	−	5.56367i	0.595358	−	0.246605i	0.659954	+	0.751306i	$0.270576\pi$
$510$	6.22189	+	7.76131i	0.275510	+	0.343677i
$511$	9.77843			0.432572
$512$	4.52735	−	22.1699i	0.200083	−	0.979779i
$513$	−2.16113			−0.0954164
$514$	8.31327	+	10.3701i	0.366683	+	0.457407i
$515$	−10.2372	+	4.24039i	−0.451105	+	0.186854i
$516$	−1.25986	+	5.65257i	−0.0554621	+	0.248841i
$517$	6.18628	−	14.9350i	0.272072	−	0.656841i
$518$	−26.2586	−	14.4253i	−1.15374	−	0.633811i
$519$	2.11508	+	2.11508i	0.0928418	+	0.0928418i
$520$	10.3481	−	5.08128i	0.453792	−	0.222829i
$521$	25.6220	−	25.6220i	1.12252	−	1.12252i	0.131160	−	0.991361i	$-0.458130\pi$
$521$	25.6220	−	25.6220i	1.12252	−	1.12252i	0.991361	−	0.131160i	$-0.0418701\pi$
$522$	27.4103	−	7.97253i	1.19971	−	0.348948i
$523$	21.0493	+	8.71890i	0.920422	+	0.381251i	0.792037	−	0.610473i	$-0.209021\pi$
$523$	21.0493	+	8.71890i	0.920422	+	0.381251i	0.128385	+	0.991724i	$0.459021\pi$
$524$	1.19204	+	6.80541i	0.0520744	+	0.297296i
$525$	7.65804	+	18.4881i	0.334224	+	0.806889i
$526$	−2.58694	+	23.4983i	−0.112796	+	1.02458i
$527$			25.5612i			1.11346i
$528$	4.94563	+	2.31983i	0.215231	+	0.100958i
$529$			21.3926i			0.930115i
$530$	36.3628	+	4.00320i	1.57950	+	0.173888i
$531$	1.99575	+	4.81817i	0.0866083	+	0.209091i
$532$	7.25930	+	5.09527i	0.314730	+	0.220908i
$533$	−0.334397	−	0.138512i	−0.0144844	−	0.00599962i
$534$	−2.28590	−	7.85913i	−0.0989208	−	0.340098i
$535$	57.2370	−	57.2370i	2.47457	−	2.47457i
$536$	3.14426	−	3.57309i	0.135811	−	0.154334i
$537$	0.0800738	+	0.0800738i	0.00345544	+	0.00345544i
$538$	1.02211	−	1.86057i	0.0440665	−	0.0802149i
$539$	−18.9197	+	45.6762i	−0.814930	+	1.96741i
$540$	15.2583	−	9.69634i	0.656612	−	0.417264i
$541$	−3.81264	+	1.57925i	−0.163918	+	0.0678971i	−0.463134	−	0.886288i	$-0.653275\pi$
$541$	−3.81264	+	1.57925i	−0.163918	+	0.0678971i	0.299216	+	0.954186i	$0.403275\pi$
$542$	25.5045	−	20.4458i	1.09551	−	0.878221i
$543$	6.92722			0.297275
$544$	−25.0582	+	6.05662i	−1.07436	+	0.259675i
$545$	25.9064			1.10971
$546$	−1.90146	+	1.52431i	−0.0813749	+	0.0652346i
$547$	32.8939	−	13.6251i	1.40644	−	0.582567i	0.455027	−	0.890478i	$-0.349630\pi$
$547$	32.8939	−	13.6251i	1.40644	−	0.582567i	0.951415	+	0.307911i	$0.0996298\pi$
$548$	8.93551	+	14.0610i	0.381706	+	0.600657i
$549$	12.2850	−	29.6586i	0.524311	−	1.26580i
$550$	−28.5173	+	51.9106i	−1.21598	+	2.21347i
$551$	−4.86895	−	4.86895i	−0.207424	−	0.207424i
$552$	0.0865109	+	1.35515i	0.00368215	+	0.0576789i
$553$	−51.7753	+	51.7753i	−2.20171	+	2.20171i
$554$	−5.33893	−	18.3557i	−0.226829	−	0.779859i
$555$	6.63825	+	2.74966i	0.281778	+	0.116716i
$556$	9.72540	−	13.8559i	0.412449	−	0.587621i
$557$	−6.34923	−	15.3284i	−0.269025	−	0.649485i	0.730413	−	0.683006i	$-0.239328\pi$
$557$	−6.34923	−	15.3284i	−0.269025	−	0.649485i	−0.999438	+	0.0335214i	$0.989328\pi$
$558$	22.5230	+	2.47957i	0.953474	+	0.104968i
$559$		−	7.64673i		−	0.323422i
$560$	−74.1138	−	3.40397i	−3.13188	−	0.143844i
$561$		−	6.22373i		−	0.262766i
$562$	1.43752	−	13.0576i	0.0606380	−	0.550802i
$563$	−4.98573	−	12.0366i	−0.210123	−	0.507283i	0.783319	−	0.621621i	$-0.213525\pi$
$563$	−4.98573	−	12.0366i	−0.210123	−	0.507283i	−0.993442	+	0.114338i	$0.963525\pi$
$564$	−3.34386	+	0.585711i	−0.140802	+	0.0246629i
$565$	−22.5524	−	9.34153i	−0.948789	−	0.393001i
$566$	−18.3985	+	5.35139i	−0.773349	+	0.224936i
$567$	24.8737	−	24.8737i	1.04460	−	1.04460i
$568$	−21.4109	−	7.30857i	−0.898380	−	0.306661i
$569$	4.93822	+	4.93822i	0.207021	+	0.207021i	0.803000	−	0.595979i	$-0.203236\pi$
$569$	4.93822	+	4.93822i	0.207021	+	0.207021i	−0.595979	+	0.803000i	$0.703236\pi$
$570$	−1.86423	−	1.02413i	−0.0780842	−	0.0428959i
$571$	6.45176	−	15.5759i	0.269998	−	0.651832i	−0.729485	−	0.683997i	$-0.760240\pi$
$571$	6.45176	−	15.5759i	0.269998	−	0.651832i	0.999483	+	0.0321648i	$0.0102401\pi$
$572$	−7.04012	−	1.56912i	−0.294362	−	0.0656082i
$573$	−5.73301	+	2.37469i	−0.239500	+	0.0992042i
$574$	1.45698	+	1.81747i	0.0608132	+	0.0758596i
$575$	−14.7228			−0.613983
$576$	2.90595	+	22.6673i	0.121081	+	0.944472i
$577$	−11.5813			−0.482136			−0.241068	−	0.970508i	$-0.577498\pi$
$577$	−11.5813			−0.482136			−0.241068	+	0.970508i	$0.577498\pi$
$578$	3.33365	+	4.15846i	0.138661	+	0.172969i
$579$	8.52419	−	3.53084i	0.354253	−	0.146737i
$580$	56.2218	+	12.5309i	2.33448	+	0.520315i
$581$	−5.62089	+	13.5700i	−0.233194	+	0.562980i
$582$	1.37749	+	0.756734i	0.0570990	+	0.0313676i
$583$	−16.1846	−	16.1846i	−0.670296	−	0.670296i
$584$	1.96337	−	5.75181i	0.0812449	−	0.238012i
$585$	−8.23295	+	8.23295i	−0.340390	+	0.340390i
$586$	−20.6718	+	6.01259i	−0.853944	+	0.248378i
$587$	22.3352	+	9.25154i	0.921872	+	0.381852i	0.792589	−	0.609756i	$-0.208732\pi$
$587$	22.3352	+	9.25154i	0.921872	+	0.381852i	0.129283	+	0.991608i	$0.458732\pi$
$588$	10.2266	−	1.79130i	0.421739	−	0.0738719i
$589$	−2.09163	−	5.04964i	−0.0861840	−	0.208067i
$590$	−1.15156	+	10.4601i	−0.0474089	+	0.430636i
$591$			5.41701i			0.222826i
$592$	−13.7575	+	12.5493i	−0.565431	+	0.515772i
$593$		−	37.2011i		−	1.52767i	−0.645413	−	0.763834i	$-0.723315\pi$
$593$		−	37.2011i		−	1.52767i	0.645413	−	0.763834i	$-0.276685\pi$
$594$	−11.2432	−	1.23777i	−0.461315	−	0.0507864i
$595$	32.3475	+	78.0938i	1.32612	+	3.20153i
$596$	15.8770	−	22.6202i	0.650349	−	0.926561i
$597$	2.69252	+	1.11528i	0.110198	+	0.0456453i
$598$	−0.500749	−	1.72162i	−0.0204772	−	0.0704022i
$599$	2.44032	−	2.44032i	0.0997088	−	0.0997088i	−0.655493	−	0.755201i	$-0.727539\pi$
$599$	2.44032	−	2.44032i	0.0997088	−	0.0997088i	0.755201	+	0.655493i	$0.227539\pi$
$600$	12.4126	−	0.792406i	0.506743	−	0.0323498i
$601$	28.6379	+	28.6379i	1.16816	+	1.16816i	0.982640	+	0.185522i	$0.0593977\pi$
$601$	28.6379	+	28.6379i	1.16816	+	1.16816i	0.185522	+	0.982640i	$0.440602\pi$
$602$	−23.6946	+	43.1317i	−0.965721	+	1.75792i
$603$	−1.83955	+	4.44106i	−0.0749122	+	0.180854i
$604$	−19.6804	−	30.9693i	−0.800784	−	1.26012i
$605$	7.55522	−	3.12948i	0.307164	−	0.127231i
$606$	−5.93014	+	4.75393i	−0.240896	+	0.193115i
$607$	−28.9756			−1.17608			−0.588042	−	0.808830i	$-0.700101\pi$
$607$	−28.9756			−1.17608			−0.588042	+	0.808830i	$0.700101\pi$
$608$	4.45467	−	3.24696i	0.180661	−	0.131682i
$609$	−12.1766			−0.493422
$610$	50.5415	−	40.5168i	2.04636	−	1.64048i
$611$	4.14121	−	1.71534i	0.167535	−	0.0693954i
$612$	21.9749	−	13.9646i	0.888282	−	0.564486i
$613$	5.44671	−	13.1495i	0.219991	−	0.531105i	−0.774898	−	0.632087i	$-0.782199\pi$
$613$	5.44671	−	13.1495i	0.219991	−	0.531105i	0.994888	+	0.100982i	$0.0321986\pi$
$614$	−16.3023	+	29.6753i	−0.657906	+	1.19760i
$615$	−0.395021	−	0.395021i	−0.0159288	−	0.0159288i
$616$	34.8480	+	30.6656i	1.40406	+	1.23555i
$617$	1.40968	−	1.40968i	0.0567516	−	0.0567516i	−0.678161	−	0.734913i	$-0.737223\pi$
$617$	1.40968	−	1.40968i	0.0567516	−	0.0567516i	0.734913	+	0.678161i	$0.237223\pi$
$618$	−0.406609	−	1.39796i	−0.0163562	−	0.0562341i
$619$	−11.0671	−	4.58416i	−0.444826	−	0.184253i	0.149016	−	0.988835i	$-0.452390\pi$
$619$	−11.0671	−	4.58416i	−0.444826	−	0.184253i	−0.593842	+	0.804582i	$0.702390\pi$
$620$	37.4237	+	26.2675i	1.50297	+	1.05493i
$621$	−1.07599	−	2.59768i	−0.0431782	−	0.104241i
$622$	43.3521	+	4.77265i	1.73826	+	0.191366i
$623$		−	69.5509i		−	2.78650i
$624$	0.514836	+	1.42453i	0.0206099	+	0.0570267i
$625$			51.7914i			2.07166i
$626$	−2.70042	+	24.5291i	−0.107930	+	0.980378i
$627$	0.509276	+	1.22950i	0.0203385	+	0.0491016i
$628$	−1.82403	−	10.4135i	−0.0727865	−	0.415542i
$629$	19.6006	+	8.11885i	0.781529	+	0.323720i
$630$	71.9494	−	20.9272i	2.86653	−	0.833759i
$631$	13.8071	−	13.8071i	0.549650	−	0.549650i	−0.376690	−	0.926340i	$-0.622938\pi$
$631$	13.8071	−	13.8071i	0.549650	−	0.549650i	0.926340	+	0.376690i	$0.122938\pi$
$632$	20.0592	+	40.8507i	0.797912	+	1.62495i
$633$	−2.60859	−	2.60859i	−0.103682	−	0.103682i
$634$	−26.6280	−	14.6282i	−1.05753	−	0.580961i
$635$	18.4408	−	44.5199i	0.731799	−	1.76672i
$636$	−1.04564	+	4.69146i	−0.0414625	+	0.186029i
$637$	−12.6652	+	5.24610i	−0.501813	+	0.207858i
$638$	−22.5419	−	28.1192i	−0.892442	−	1.11325i
$639$	22.8493			0.903903
$640$	−16.8833	+	42.9113i	−0.667370	+	1.69622i
$641$	23.6169			0.932813			0.466406	−	0.884571i	$-0.345548\pi$
$641$	23.6169			0.932813			0.466406	+	0.884571i	$0.345548\pi$
$642$	6.65227	+	8.29817i	0.262544	+	0.327502i
$643$	−15.9142	+	6.59190i	−0.627597	+	0.259959i	−0.673732	−	0.738976i	$-0.735310\pi$
$643$	−15.9142	+	6.59190i	−0.627597	+	0.259959i	0.0461349	+	0.998935i	$0.485310\pi$
$644$	−2.51022	+	11.2625i	−0.0989163	+	0.443805i
$645$	4.51652	−	10.9038i	0.177838	−	0.429338i
$646$	−5.50449	−	3.02392i	−0.216571	−	0.118974i
$647$	10.6265	+	10.6265i	0.417770	+	0.417770i	0.884434	−	0.466664i	$-0.154544\pi$
$647$	10.6265	+	10.6265i	0.417770	+	0.417770i	−0.466664	+	0.884434i	$0.654544\pi$
$648$	−9.63679	−	19.6254i	−0.378569	−	0.770958i
$649$	4.65565	−	4.65565i	0.182750	−	0.182750i
$650$	−15.7693	+	4.58667i	−0.618525	+	0.179904i
$651$	−8.92969	−	3.69880i	−0.349982	−	0.144967i
$652$	2.64388	+	15.0941i	0.103542	+	0.591130i
$653$	−10.8391	−	26.1680i	−0.424168	−	1.02403i	−0.981105	−	0.193477i	$-0.938023\pi$
$653$	−10.8391	−	26.1680i	−0.424168	−	1.02403i	0.556937	−	0.830555i	$-0.311977\pi$
$654$	−0.372480	+	3.38340i	−0.0145651	+	0.132301i
$655$		−	14.0801i		−	0.550156i
$656$	1.36160	−	0.492095i	0.0531616	−	0.0192131i
$657$			6.13822i			0.239475i
$658$	−28.6739	−	3.15673i	−1.11783	−	0.123062i
$659$	7.99883	+	19.3109i	0.311590	+	0.752245i	0.999646	+	0.0265878i	$0.00846416\pi$
$659$	7.99883	+	19.3109i	0.311590	+	0.752245i	−0.688056	+	0.725657i	$0.741536\pi$
$660$	−9.11205	−	6.39571i	−0.354686	−	0.248953i
$661$	18.5687	+	7.69141i	0.722239	+	0.299161i	0.713359	−	0.700799i	$-0.247173\pi$
$661$	18.5687	+	7.69141i	0.722239	+	0.299161i	0.00888078	+	0.999961i	$0.497173\pi$
$662$	5.00298	+	17.2007i	0.194446	+	0.668523i
$663$	1.22027	−	1.22027i	0.0473915	−	0.0473915i
$664$	6.85349	+	6.03096i	0.265967	+	0.234047i
$665$	−12.7806	−	12.7806i	−0.495609	−	0.495609i
$666$	9.05520	−	16.4833i	0.350882	−	0.638716i
$667$	3.42830	−	8.27665i	0.132744	−	0.320473i
$668$	−12.7831	+	8.12339i	−0.494592	+	0.314303i
$669$	2.17407	−	0.900528i	0.0840543	−	0.0348164i
$670$	−7.56805	+	6.06696i	−0.292379	+	0.234387i
$671$	−40.5288			−1.56460
$672$	1.51017	−	9.63040i	0.0582559	−	0.371501i
$673$	23.8555			0.919563			0.459782	−	0.888032i	$-0.347928\pi$
$673$	23.8555			0.919563			0.459782	+	0.888032i	$0.347928\pi$
$674$	−14.2011	+	11.3844i	−0.547006	+	0.438510i
$675$	−23.7937	+	9.85569i	−0.915821	+	0.379346i
$676$	−1.07269	−	1.68800i	−0.0412573	−	0.0649230i
$677$	9.53221	−	23.0128i	0.366353	−	0.884454i	−0.627989	−	0.778222i	$-0.716122\pi$
$677$	9.53221	−	23.0128i	0.366353	−	0.884454i	0.994341	−	0.106231i	$-0.0338784\pi$
$678$	1.54427	−	2.81106i	0.0593074	−	0.107958i
$679$	9.44364	+	9.44364i	0.362414	+	0.362414i
$680$	52.4308	−	3.34712i	2.01063	−	0.128356i
$681$	2.71870	−	2.71870i	0.104181	−	0.104181i
$682$	−7.98948	−	27.4685i	−0.305933	−	1.05182i
$683$	−17.5064	−	7.25140i	−0.669865	−	0.277467i	0.0217181	−	0.999764i	$-0.493086\pi$
$683$	−17.5064	−	7.25140i	−0.669865	−	0.277467i	−0.691583	+	0.722297i	$0.743086\pi$
$684$	−3.19846	+	4.55688i	−0.122296	+	0.174237i
$685$	−12.9929	−	31.3675i	−0.496432	−	1.19849i
$686$	42.9156	+	4.72459i	1.63852	+	0.180386i
$687$			1.80846i			0.0689970i
$688$	20.6131	+	22.5978i	0.785868	+	0.861532i
$689$		−	6.34656i		−	0.241785i
$690$	0.302826	−	2.75070i	0.0115284	−	0.104717i
$691$	−1.81082	−	4.37171i	−0.0688869	−	0.166308i	0.885686	−	0.464284i	$-0.153688\pi$
$691$	−1.81082	−	4.37171i	−0.0688869	−	0.166308i	−0.954573	+	0.297976i	$0.903688\pi$
$692$	15.5612	−	2.72570i	0.591547	−	0.103616i
$693$	−43.3132	−	17.9409i	−1.64533	−	0.681519i
$694$	17.7634	−	5.16666i	0.674291	−	0.196124i
$695$	−24.3944	+	24.3944i	−0.925333	+	0.925333i
$696$	−2.44490	+	7.16246i	−0.0926736	+	0.271492i
$697$	−1.16637	−	1.16637i	−0.0441795	−	0.0441795i
$698$	−17.9270	−	9.84829i	−0.678547	−	0.372763i
$699$	1.38214	−	3.33677i	0.0522772	−	0.126208i
$700$	103.160	+	22.9926i	3.89909	+	0.869038i
$701$	−6.99824	+	2.89876i	−0.264320	+	0.109485i	−0.510908	−	0.859636i	$-0.670691\pi$
$701$	−6.99824	+	2.89876i	−0.264320	+	0.109485i	0.246588	+	0.969120i	$0.420691\pi$
$702$	−1.96175	−	2.44712i	−0.0740415	−	0.0923608i
$703$	−4.53647			−0.171096
$704$	25.0349	−	14.3408i	0.943540	−	0.540490i
$705$	6.91831			0.260559
$706$	13.3359	+	16.6355i	0.501904	+	0.626085i
$707$	−59.6687	+	24.7156i	−2.24407	+	0.929526i
$708$	−1.34954	−	0.300790i	−0.0507190	−	0.0113044i
$709$	−12.4013	+	29.9394i	−0.465741	+	1.12440i	0.500263	+	0.865874i	$0.333237\pi$
$709$	−12.4013	+	29.9394i	−0.465741	+	1.12440i	−0.966004	+	0.258526i	$0.916763\pi$
$710$	40.4098	+	22.1993i	1.51655	+	0.833126i
$711$	−32.5010	−	32.5010i	−1.21888	−	1.21888i
$712$	−40.9108	−	13.9649i	−1.53320	−	0.523355i
$713$	5.02827	−	5.02827i	0.188310	−	0.188310i
$714$	−10.6642	+	3.10179i	−0.399099	+	0.116082i
$715$	13.5804	+	5.62520i	0.507879	+	0.210371i
$716$	0.589122	−	0.103191i	0.0220165	−	0.00385642i
$717$	−1.50053	−	3.62260i	−0.0560382	−	0.135288i
$718$	1.20047	−	10.9044i	0.0448013	−	0.406950i
$719$		−	21.0993i		−	0.786871i	−0.919352	−	0.393436i	$-0.871286\pi$
$719$		−	21.0993i		−	0.786871i	0.919352	−	0.393436i	$-0.128714\pi$
$720$	2.13678	−	46.5235i	0.0796329	−	1.73383i
$721$		−	12.3715i		−	0.460739i
$722$	−25.3738	−	2.79342i	−0.944316	−	0.103960i
$723$	−0.278897	−	0.673318i	−0.0103723	−	0.0250410i
$724$	21.0191	−	29.9462i	0.781167	−	1.11294i
$725$	−75.8108	−	31.4019i	−2.81554	−	1.16624i
$726$	0.300084	+	1.03172i	0.0111372	+	0.0382906i
$727$	−18.0057	+	18.0057i	−0.667795	+	0.667795i	−0.957205	−	0.289410i	$-0.906541\pi$
$727$	−18.0057	+	18.0057i	−0.667795	+	0.667795i	0.289410	+	0.957205i	$0.406541\pi$
$728$	0.820017	+	12.8451i	0.0303919	+	0.476072i
$729$	13.8325	+	13.8325i	0.512315	+	0.512315i
$730$	−5.96363	+	10.8557i	−0.220724	+	0.401787i
$731$	13.3358	−	32.1955i	0.493243	−	1.19079i
$732$	4.56486	+	7.18332i	0.168722	+	0.265503i
$733$	10.9534	−	4.53704i	0.404573	−	0.167579i	−0.171112	−	0.985252i	$-0.554736\pi$
$733$	10.9534	−	4.53704i	0.404573	−	0.167579i	0.575684	+	0.817672i	$0.304736\pi$
$734$	−26.2792	+	21.0669i	−0.969984	+	0.777592i
$735$	−21.1585			−0.780443
$736$	6.12075	+	3.73790i	0.225614	+	0.137781i
$737$	6.06875			0.223545
$738$	−1.14088	+	0.914592i	−0.0419964	+	0.0336666i
$739$	36.4442	−	15.0957i	1.34062	−	0.555303i	0.406955	−	0.913448i	$-0.366591\pi$
$739$	36.4442	−	15.0957i	1.34062	−	0.555303i	0.933666	+	0.358145i	$0.116591\pi$
$740$	32.0289	−	20.3538i	1.17741	−	0.748219i
$741$	−0.141213	+	0.340919i	−0.00518760	+	0.0125240i
$742$	−19.6658	+	35.7980i	−0.721955	+	1.31419i
$743$	1.42019	+	1.42019i	0.0521018	+	0.0521018i	0.732678	−	0.680576i	$-0.238270\pi$
$743$	1.42019	+	1.42019i	0.0521018	+	0.0521018i	−0.680576	+	0.732678i	$0.738270\pi$
$744$	−3.96864	+	4.50990i	−0.145498	+	0.165341i
$745$	−39.8247	+	39.8247i	−1.45906	+	1.45906i
$746$	6.77919	+	23.3074i	0.248204	+	0.853345i
$747$	−8.51833	−	3.52841i	−0.311669	−	0.129098i
$748$	−26.9050	−	18.8845i	−0.983743	−	0.690485i
$749$	34.5850	+	83.4956i	1.26371	+	3.05086i
$750$	−14.3472	−	1.57949i	−0.523885	−	0.0576747i
$751$			29.0582i			1.06035i	0.847889	+	0.530174i	$0.177873\pi$
$751$			29.0582i			1.06035i	−0.847889	+	0.530174i	$0.822127\pi$
$752$	−7.61416	+	16.2326i	−0.277660	+	0.591942i
$753$			3.67001i			0.133743i
$754$	1.09353	−	9.93303i	0.0398241	−	0.361739i
$755$	28.6167	+	69.0868i	1.04147	+	2.51433i
$756$	3.48252	+	19.8819i	0.126658	+	0.723098i
$757$	−18.9923	−	7.86686i	−0.690286	−	0.285926i	0.00983311	−	0.999952i	$-0.496870\pi$
$757$	−18.9923	−	7.86686i	−0.690286	−	0.285926i	−0.700120	+	0.714026i	$0.746870\pi$
$758$	26.9593	−	7.84138i	0.979207	−	0.284812i
$759$	−1.22430	+	1.22430i	−0.0444392	+	0.0444392i
$760$	−10.0839	+	4.95155i	−0.365780	+	0.179611i
$761$	−27.4131	−	27.4131i	−0.993725	−	0.993725i	0.00625520	−	0.999980i	$-0.498009\pi$
$761$	−27.4131	−	27.4131i	−0.993725	−	0.993725i	−0.999980	+	0.00625520i	$0.998009\pi$
$762$	5.54921	+	3.04849i	0.201027	+	0.110435i
$763$	−11.0689	+	26.7226i	−0.400720	+	0.967423i
$764$	−7.12980	+	31.9891i	−0.257947	+	1.15732i
$765$	−49.0219	+	20.3055i	−1.77239	+	0.734148i
$766$	−29.2423	−	36.4774i	−1.05657	−	1.31798i
$767$	1.82565			0.0659203
$768$	−5.36152	−	2.82195i	−0.193467	−	0.101828i
$769$	−10.1532			−0.366133			−0.183066	−	0.983101i	$-0.558602\pi$
$769$	−10.1532			−0.366133			−0.183066	+	0.983101i	$0.558602\pi$
$770$	−59.1704	−	73.8103i	−2.13235	−	2.65994i
$771$	3.28795	−	1.36191i	0.118413	−	0.0490481i
$772$	10.6010	−	47.5633i	0.381539	−	1.71184i
$773$	3.60232	−	8.69677i	0.129566	−	0.312801i	−0.845762	−	0.533561i	$-0.820854\pi$
$773$	3.60232	−	8.69677i	0.129566	−	0.312801i	0.975328	+	0.220760i	$0.0708536\pi$
$774$	−27.0751	−	14.8739i	−0.973195	−	0.534630i
$775$	−46.0569	−	46.0569i	−1.65441	−	1.65441i
$776$	7.45103	−	3.65873i	0.267476	−	0.131341i
$777$	−5.67257	+	5.67257i	−0.203502	+	0.203502i
$778$	−39.5649	+	11.5078i	−1.41847	+	0.412575i
$779$	0.325860	+	0.134976i	0.0116751	+	0.00483600i
$780$	−0.532588	−	3.04058i	−0.0190697	−	0.108870i
$781$	−11.0393	−	26.6511i	−0.395016	−	0.953653i
$782$	0.894149	−	8.12195i	0.0319747	−	0.290440i
$783$		−	15.6710i		−	0.560035i
$784$	23.2866	−	49.6447i	0.831666	−	1.77302i
$785$			21.5451i			0.768976i
$786$	1.83888	+	0.202443i	0.0655906	+	0.00722090i
$787$	2.19648	+	5.30278i	0.0782962	+	0.189024i	0.958181	−	0.286164i	$-0.0923802\pi$
$787$	2.19648	+	5.30278i	0.0782962	+	0.189024i	−0.879885	+	0.475188i	$0.842380\pi$
$788$	23.4176	+	16.4367i	0.834216	+	0.585533i
$789$	5.84818	+	2.42240i	0.208201	+	0.0862396i
$790$	−25.9027	−	89.0557i	−0.921577	−	3.16846i
$791$	19.2717	−	19.2717i	0.685222	−	0.685222i
$792$	−19.2498	+	21.8751i	−0.684011	+	0.777299i
$793$	−7.94640	−	7.94640i	−0.282185	−	0.282185i
$794$	25.4961	−	46.4109i	0.904822	−	1.64706i
$795$	3.74857	−	9.04985i	0.132948	−	0.320965i
$796$	12.9912	−	8.25562i	0.460459	−	0.292613i
$797$	5.00233	−	2.07203i	0.177192	−	0.0733952i	−0.292324	−	0.956319i	$-0.594429\pi$
$797$	5.00233	−	2.07203i	0.177192	−	0.0733952i	0.469516	+	0.882924i	$0.344429\pi$
$798$	1.85291	−	1.48540i	0.0655924	−	0.0525824i
$799$	20.4275			0.722675
$800$	34.2377	−	56.0637i	1.21049	−	1.98215i
$801$	43.6593			1.54262
$802$	12.9921	−	10.4152i	0.458768	−	0.367773i
$803$	7.15956	−	2.96559i	0.252655	−	0.104653i
$804$	−0.683539	−	1.07563i	−0.0241066	−	0.0379344i
$805$	8.99897	−	21.7254i	0.317172	−	0.765721i
$806$	3.81922	−	6.95218i	0.134526	−	0.244880i
$807$	−0.401934	−	0.401934i	−0.0141487	−	0.0141487i
$808$	2.55742	+	40.0605i	0.0899696	+	1.40932i
$809$	−22.4126	+	22.4126i	−0.787986	+	0.787986i	−0.981164	−	0.193178i	$-0.938120\pi$
$809$	−22.4126	+	22.4126i	−0.787986	+	0.787986i	0.193178	+	0.981164i	$0.438120\pi$
$810$	12.4441	+	42.7839i	0.437241	+	1.50327i
$811$	−8.88819	−	3.68161i	−0.312107	−	0.129279i	0.221131	−	0.975244i	$-0.429025\pi$
$811$	−8.88819	−	3.68161i	−0.312107	−	0.129279i	−0.533238	+	0.845965i	$0.679025\pi$
$812$	−36.9472	+	52.6392i	−1.29659	+	1.84727i
$813$	−3.34951	−	8.08643i	−0.117472	−	0.283604i
$814$	−23.6008	−	2.59823i	−0.827209	−	0.0910679i
$815$		−	31.2291i		−	1.09391i
$816$	−0.316709	+	6.89564i	−0.0110870	+	0.241396i
$817$			7.45150i			0.260695i
$818$	−1.69669	+	15.4118i	−0.0593234	+	0.538860i
$819$	−4.97469	−	12.0100i	−0.173830	−	0.419662i
$820$	−2.90627	+	0.509063i	−0.101491	+	0.0177772i
$821$	42.3378	+	17.5369i	1.47760	+	0.612042i	0.968578	−	0.248712i	$-0.0800071\pi$
$821$	42.3378	+	17.5369i	1.47760	+	0.612042i	0.509022	+	0.860753i	$0.330007\pi$
$822$	4.28345	−	1.24588i	0.149402	−	0.0434551i
$823$	25.7454	−	25.7454i	0.897429	−	0.897429i	−0.0977795	−	0.995208i	$-0.531174\pi$
$823$	25.7454	−	25.7454i	0.897429	−	0.897429i	0.995208	+	0.0977795i	$0.0311740\pi$
$824$	−7.27709	−	2.48402i	−0.253509	−	0.0865351i
$825$	11.2141	+	11.2141i	0.390425	+	0.390425i
$826$	−10.2976	−	5.65707i	−0.358301	−	0.196834i
$827$	−13.7026	+	33.0811i	−0.476487	+	1.15034i	0.484758	+	0.874648i	$0.338908\pi$
$827$	−13.7026	+	33.0811i	−0.476487	+	1.15034i	−0.961246	+	0.275694i	$0.911092\pi$
$828$	−7.06983	−	1.57574i	−0.245694	−	0.0547608i
$829$	2.95125	−	1.22245i	0.102501	−	0.0424574i	−0.330844	−	0.943686i	$-0.607333\pi$
$829$	2.95125	−	1.22245i	0.102501	−	0.0424574i	0.433345	+	0.901228i	$0.357333\pi$
$830$	−11.6369	−	14.5162i	−0.403924	−	0.503863i
$831$	−5.11868			−0.177565
$832$	7.72033	+	2.09678i	0.267654	+	0.0726926i
$833$	−62.4743			−2.16460
$834$	−2.83519	−	3.53668i	−0.0981747	−	0.122465i
$835$	28.5167	−	11.8120i	0.986859	−	0.408771i
$836$	6.86038	+	1.52906i	0.237271	+	0.0528836i
$837$	4.76025	−	11.4923i	0.164538	−	0.397231i
$838$	47.6655	+	26.1853i	1.64658	+	0.904557i
$839$	40.0010	+	40.0010i	1.38099	+	1.38099i	0.842868	+	0.538120i	$0.180865\pi$
$839$	40.0010	+	40.0010i	1.38099	+	1.38099i	0.538120	+	0.842868i	$0.319135\pi$
$840$	−6.41763	+	18.8008i	−0.221429	+	0.648690i
$841$	14.8000	−	14.8000i	0.510346	−	0.510346i
$842$	41.8248	−	12.1651i	1.44138	−	0.419239i
$843$	−3.24973	−	1.34608i	−0.111927	−	0.0463616i
$844$	−19.1920	+	3.36168i	−0.660617	+	0.115714i
$845$	1.55977	+	3.76561i	0.0536576	+	0.129541i
$846$	1.98158	−	17.9995i	0.0681280	−	0.618836i
$847$			9.13037i			0.313723i
$848$	17.1083	+	18.7555i	0.587501	+	0.644065i
$849$			5.13063i			0.176083i
$850$	−74.3938	−	8.19005i	−2.55169	−	0.280917i
$851$	−2.25864	−	5.45284i	−0.0774251	−	0.186921i
$852$	−3.48027	+	4.95838i	−0.119232	+	0.169871i
$853$	2.53287	+	1.04915i	0.0867237	+	0.0359221i	0.425624	−	0.904900i	$-0.360055\pi$
$853$	2.53287	+	1.04915i	0.0867237	+	0.0359221i	−0.338900	+	0.940822i	$0.610055\pi$
$854$	20.1988	+	69.4452i	0.691189	+	2.37637i
$855$	8.02275	−	8.02275i	0.274372	−	0.274372i
$856$	56.0575	−	3.57864i	1.91601	−	0.122315i
$857$	−25.2252	−	25.2252i	−0.861676	−	0.861676i	0.129856	−	0.991533i	$-0.458548\pi$
$857$	−25.2252	−	25.2252i	−0.861676	−	0.861676i	−0.991533	+	0.129856i	$0.958548\pi$
$858$	−0.929916	+	1.69274i	−0.0317468	+	0.0577892i
$859$	2.68209	−	6.47514i	0.0915117	−	0.220929i	−0.871496	−	0.490403i	$-0.836850\pi$
$859$	2.68209	−	6.47514i	0.0915117	−	0.220929i	0.963008	+	0.269474i	$0.0868497\pi$
$860$	−33.4326	−	52.6100i	−1.14004	−	1.79398i
$861$	0.576245	−	0.238689i	0.0196384	−	0.00813448i
$862$	21.6508	−	17.3565i	0.737428	−	0.591163i
$863$	54.0682			1.84050			0.920251	−	0.391328i	$-0.127984\pi$
$863$	54.0682			1.84050			0.920251	+	0.391328i	$0.127984\pi$
$864$	12.3941	+	1.94354i	0.421655	+	0.0661206i
$865$	−32.1955			−1.09468
$866$	22.4875	−	18.0272i	0.764156	−	0.612589i
$867$	1.31848	−	0.546132i	0.0447779	−	0.0185476i
$868$	−43.0849	+	27.3796i	−1.46240	+	0.929325i
$869$	−22.2064	+	53.6111i	−0.753302	+	1.81863i
$870$	7.42623	−	13.5181i	0.251773	−	0.458306i
$871$	1.18989	+	1.18989i	0.0403178	+	0.0403178i
$872$	13.4961	+	11.8764i	0.457037	+	0.402185i
$873$	−5.92806	+	5.92806i	−0.200635	+	0.200635i
$874$	0.487965	+	1.67766i	0.0165056	+	0.0567478i
$875$	−113.316	−	46.9370i	−3.83078	−	1.58676i
$876$	−1.33202	−	0.934938i	−0.0450048	−	0.0315886i
$877$	6.72569	+	16.2372i	0.227110	+	0.548293i	0.995823	−	0.0913010i	$-0.0291025\pi$
$877$	6.72569	+	16.2372i	0.227110	+	0.548293i	−0.768713	+	0.639594i	$0.779103\pi$
$878$	20.1347	+	2.21664i	0.679514	+	0.0748081i
$879$			5.76456i			0.194434i
$880$	−55.2969	+	19.9848i	−1.86406	+	0.673687i
$881$		−	5.12129i		−	0.172541i	−0.996272	−	0.0862703i	$-0.972505\pi$
$881$		−	5.12129i		−	0.172541i	0.996272	−	0.0862703i	$-0.0274949\pi$
$882$	−6.06032	+	55.0485i	−0.204062	+	1.85358i
$883$	14.9701	+	36.1410i	0.503784	+	1.21624i	0.947408	+	0.320029i	$0.103693\pi$
$883$	14.9701	+	36.1410i	0.503784	+	1.21624i	−0.443624	+	0.896213i	$0.646307\pi$
$884$	−1.57256	−	8.97785i	−0.0528910	−	0.301958i
$885$	2.60328	+	1.07831i	0.0875082	+	0.0362471i
$886$	2.10049	−	0.610948i	0.0705674	−	0.0205252i
$887$	−2.15113	+	2.15113i	−0.0722278	+	0.0722278i	−0.742298	−	0.670070i	$-0.766264\pi$
$887$	−2.15113	+	2.15113i	−0.0722278	+	0.0722278i	0.670070	+	0.742298i	$0.266264\pi$
$888$	2.19771	+	4.47566i	0.0737504	+	0.150193i
$889$	38.0435	+	38.0435i	1.27594	+	1.27594i
$890$	77.2131	+	42.4174i	2.58819	+	1.42184i
$891$	10.6684	−	25.7557i	0.357403	−	0.862848i
$892$	2.70376	−	12.1309i	0.0905285	−	0.406172i
$893$	−4.03548	+	1.67155i	−0.135042	+	0.0559363i
$894$	−4.62855	−	5.77374i	−0.154802	−	0.193103i
$895$	−1.21887			−0.0407424
$896$	−37.0497	−	35.7497i	−1.23774	−	1.19431i
$897$	−0.480092			−0.0160298
$898$	15.2867	+	19.0690i	0.510125	+	0.636340i
$899$	36.6163	−	15.1670i	1.22122	−	0.505847i
$900$	−14.4332	+	64.7569i	−0.481105	+	2.15856i
$901$	11.0683	−	26.7213i	0.368740	−	0.890216i
$902$	1.61797	+	0.888839i	0.0538724	+	0.0295951i
$903$	9.31763	+	9.31763i	0.310071	+	0.310071i
$904$	−7.46639	−	15.2054i	−0.248328	−	0.505723i
$905$	−52.7225	+	52.7225i	−1.75256	+	1.75256i
$906$	−9.43426	+	2.74405i	−0.313432	+	0.0911648i
$907$	−12.5625	−	5.20355i	−0.417130	−	0.172781i	0.164240	−	0.986420i	$-0.447483\pi$
$907$	−12.5625	−	5.20355i	−0.417130	−	0.172781i	−0.581370	+	0.813640i	$0.697483\pi$
$908$	−3.50358	−	20.0021i	−0.116270	−	0.663795i
$909$	−15.5147	−	37.4559i	−0.514592	−	1.24233i
$910$	2.87042	−	26.0733i	0.0951535	−	0.864321i
$911$			34.4951i			1.14287i	0.820646	+	0.571437i	$0.193614\pi$
$911$			34.4951i			1.14287i	−0.820646	+	0.571437i	$0.806386\pi$
$912$	−0.501692	−	1.38816i	−0.0166127	−	0.0459664i
$913$			11.6404i			0.385240i
$914$	30.8709	+	3.39860i	1.02112	+	0.112416i
$915$	−6.63763	−	16.0247i	−0.219433	−	0.529759i
$916$	7.81791	+	5.48735i	0.258311	+	0.181307i
$917$	14.5237	+	6.01592i	0.479616	+	0.198663i
$918$	−3.99192	−	13.7246i	−0.131753	−	0.452978i
$919$	−10.2509	+	10.2509i	−0.338146	+	0.338146i	−0.855669	−	0.517523i	$-0.826854\pi$
$919$	−10.2509	+	10.2509i	−0.338146	+	0.338146i	0.517523	+	0.855669i	$0.326854\pi$
$920$	−10.9723	−	9.65549i	−0.361748	−	0.318332i
$921$	6.41067	+	6.41067i	0.211239	+	0.211239i
$922$	−1.81417	+	3.30237i	−0.0597466	+	0.108758i
$923$	3.06099	−	7.38988i	0.100754	−	0.243241i
$924$	10.4905	−	6.66648i	0.345111	−	0.219311i
$925$	−49.9458	+	20.6882i	−1.64221	+	0.680225i
$926$	−5.25825	+	4.21530i	−0.172797	+	0.138523i
$927$	7.76597			0.255068
$928$	23.5446	+	32.3021i	0.772890	+	1.06037i
$929$	16.4667			0.540254			0.270127	−	0.962825i	$-0.412934\pi$
$929$	16.4667			0.540254			0.270127	+	0.962825i	$0.412934\pi$
$930$	9.55228	−	7.65763i	0.313232	−	0.251104i
$931$	12.3418	−	5.11216i	0.404488	−	0.167544i
$932$	−10.2310	−	16.0996i	−0.335127	−	0.527360i
$933$	4.46908	−	10.7893i	0.146311	−	0.353226i
$934$	−19.7325	+	35.9193i	−0.645666	+	1.17532i
$935$	47.3683	+	47.3683i	1.54911	+	1.54911i
$936$	−8.06328	+	0.514750i	−0.263557	+	0.0168251i
$937$	5.26752	−	5.26752i	0.172082	−	0.172082i	−0.615811	−	0.787894i	$-0.711172\pi$
$937$	5.26752	−	5.26752i	0.172082	−	0.172082i	0.787894	+	0.615811i	$0.211172\pi$
$938$	−3.02455	−	10.3987i	−0.0987552	−	0.339529i
$939$	6.10471	+	2.52865i	0.199220	+	0.0825195i
$940$	20.9920	−	29.9076i	0.684684	−	0.975479i
$941$	−19.2255	−	46.4144i	−0.626732	−	1.51306i	−0.843660	−	0.536877i	$-0.819604\pi$
$941$	−19.2255	−	46.4144i	−0.626732	−	1.51306i	0.216928	−	0.976188i	$-0.430396\pi$
$942$	−2.81381	−	0.309773i	−0.0916788	−	0.0100930i
$943$			0.458885i			0.0149434i
$944$	−5.39519	+	4.92136i	−0.175598	+	0.160177i
$945$		−	41.1349i		−	1.33812i
$946$	−4.26779	+	38.7662i	−0.138758	+	1.26040i
$947$	−5.60086	−	13.5217i	−0.182003	−	0.439395i	0.806376	−	0.591404i	$-0.201426\pi$
$947$	−5.60086	−	13.5217i	−0.182003	−	0.439395i	−0.988379	+	0.152008i	$0.951426\pi$
$948$	12.0032	−	2.10248i	0.389846	−	0.0682855i
$949$	1.98522	+	0.822304i	0.0644429	+	0.0266931i
$950$	15.3667	−	4.46956i	0.498563	−	0.145012i
$951$	−5.75237	+	5.75237i	−0.186533	+	0.186533i
$952$	−18.9492	+	55.5128i	−0.614147	+	1.79918i
$953$	24.7058	+	24.7058i	0.800298	+	0.800298i	0.983142	−	0.182844i	$-0.0585303\pi$
$953$	24.7058	+	24.7058i	0.800298	+	0.800298i	−0.182844	+	0.983142i	$0.558530\pi$
$954$	−22.4715	−	12.3448i	−0.727542	−	0.399679i
$955$	25.5599	−	61.7071i	0.827100	−	1.99680i
$956$	−20.2134	−	4.50520i	−0.653747	−	0.145709i
$957$	−8.91546	+	3.69291i	−0.288196	+	0.119375i
$958$	29.7432	+	37.1023i	0.960959	+	1.19872i
$959$	37.9072			1.22409
$960$	9.77033	+	7.54988i	0.315336	+	0.243671i
$961$	0.459621			0.0148265
$962$	−4.11794	−	5.13680i	−0.132768	−	0.165617i
$963$	−52.4128	+	21.7101i	−1.68898	+	0.699598i
$964$	−3.75698	−	0.837365i	−0.121004	−	0.0269697i
$965$	−38.0040	+	91.7499i	−1.22339	+	2.95353i
$966$	2.70798	+	1.48764i	0.0871278	+	0.0478641i
$967$	38.5177	+	38.5177i	1.23865	+	1.23865i	0.960554	+	0.278092i	$0.0897020\pi$
$967$	38.5177	+	38.5177i	1.23865	+	1.23865i	0.278092	+	0.960554i	$0.410298\pi$
$968$	5.37061	+	1.83325i	0.172618	+	0.0589229i
$969$	−1.18912	+	1.18912i	−0.0382000	+	0.0382000i
$970$	−16.2434	+	4.72456i	−0.521546	+	0.151697i
$971$	−29.7628	−	12.3282i	−0.955134	−	0.395629i	−0.149976	−	0.988690i	$-0.547920\pi$
$971$	−29.7628	−	12.3282i	−0.955134	−	0.395629i	−0.805158	+	0.593060i	$0.797920\pi$
$972$	−18.8735	+	3.30589i	−0.605369	+	0.106037i
$973$	−14.7401	−	35.5858i	−0.472547	−	1.14083i
$974$	1.28404	−	11.6635i	0.0411431	−	0.373721i
$975$			4.39745i			0.140831i
$976$	44.9043	+	2.06241i	1.43735	+	0.0660160i
$977$			35.3308i			1.13033i	0.824977	+	0.565166i	$0.191188\pi$
$977$			35.3308i			1.13033i	−0.824977	+	0.565166i	$0.808812\pi$
$978$	4.07855	+	0.449009i	0.130418	+	0.0143577i
$979$	−21.0933	−	50.9237i	−0.674144	−	1.62753i
$980$	−64.2006	+	91.4675i	−2.05081	+	2.92182i
$981$	−16.7746	−	6.94827i	−0.535572	−	0.221841i
$982$	9.18210	+	31.5688i	0.293013	+	1.00740i
$983$	−26.3513	+	26.3513i	−0.840475	+	0.840475i	−0.988921	−	0.148446i	$-0.952573\pi$
$983$	−26.3513	+	26.3513i	−0.840475	+	0.840475i	0.148446	+	0.988921i	$0.452573\pi$
$984$	−0.0246980	−	0.386881i	−0.000787343	−	0.0123333i
$985$	−41.2284	−	41.2284i	−1.31365	−	1.31365i
$986$	21.9273	−	39.9146i	0.698307	−	1.27114i
$987$	−2.95594	+	7.13627i	−0.0940887	+	0.227150i
$988$	1.04530	+	1.64490i	0.0332555	+	0.0523313i
$989$	−8.95670	+	3.70998i	−0.284806	+	0.117971i
$990$	46.3330	−	37.1431i	1.47256	−	1.18049i
$991$	18.0474			0.573294			0.286647	−	0.958036i	$-0.407459\pi$
$991$	18.0474			0.573294			0.286647	+	0.958036i	$0.407459\pi$
$992$	7.45423	+	30.8406i	0.236672	+	0.979190i
$993$	4.79660			0.152215
$994$	−40.1644	+	32.1980i	−1.27394	+	1.02126i
$995$	−28.9809	+	12.0043i	−0.918755	+	0.380561i
$996$	2.06314	−	1.31108i	0.0653731	−	0.0415433i
$997$	−23.4141	+	56.5266i	−0.741531	+	1.79021i	−0.141995	+	0.989867i	$0.545352\pi$
$997$	−23.4141	+	56.5266i	−0.741531	+	1.79021i	−0.599537	+	0.800347i	$0.704648\pi$
$998$	−26.0863	+	47.4853i	−0.825747	+	1.50312i
$999$	−7.30044	−	7.30044i	−0.230976	−	0.230976i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.2.bf.a.53.15	✓	192
32.29	even	8	inner	416.2.bf.a.157.15	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
416.2.bf.a.53.15	✓	192	1.1	even	1	trivial
416.2.bf.a.157.15	yes	192	32.29	even	8	inner

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:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.bf (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.884565 - 1.10342i) q^{2} +(-0.349851 + 0.144913i) q^{3} +(-0.435089 + 1.95210i) q^{4} +(1.55977 - 3.76561i) q^{5} +(0.469367 + 0.257849i) q^{6} +(3.21782 + 3.21782i) q^{7} +(2.53886 - 1.24667i) q^{8} +(-2.01992 + 2.01992i) q^{9} +(-5.53478 + 1.60984i) q^{10} +(3.33191 + 1.38012i) q^{11} +(-0.130669 - 0.745995i) q^{12} +(0.382683 + 0.923880i) q^{13} +(0.704248 - 6.39699i) q^{14} +1.54343i q^{15} +(-3.62140 - 1.69867i) q^{16} +4.55727i q^{17} +(4.01559 + 0.442078i) q^{18} +(-0.372913 - 0.900292i) q^{19} +(6.67222 + 4.68320i) q^{20} +(-1.59206 - 0.659453i) q^{21} +(-1.42443 - 4.89732i) q^{22} +(0.896482 - 0.896482i) q^{23} +(-0.707563 + 0.804064i) q^{24} +(-8.21142 - 8.21142i) q^{25} +(0.680922 - 1.23949i) q^{26} +(0.848698 - 2.04894i) q^{27} +(-7.68154 + 4.88147i) q^{28} +(6.52827 - 2.70410i) q^{29} +(1.70306 - 1.36527i) q^{30} +5.60889 q^{31} +(1.32900 + 5.49852i) q^{32} -1.36567 q^{33} +(5.02860 - 4.03120i) q^{34} +(17.1361 - 7.09801i) q^{35} +(-3.06425 - 4.82194i) q^{36} +(1.78152 - 4.30096i) q^{37} +(-0.663538 + 1.20785i) q^{38} +(-0.267764 - 0.267764i) q^{39} +(-0.734457 - 11.5049i) q^{40} +(-0.255937 + 0.255937i) q^{41} +(0.680625 + 2.34005i) q^{42} +(-7.06466 - 2.92628i) q^{43} +(-4.14382 + 5.90375i) q^{44} +(4.45564 + 10.7569i) q^{45} +(-1.78220 - 0.196203i) q^{46} -4.48241i q^{47} +(1.51311 + 0.0694955i) q^{48} +13.7087i q^{49} +(-1.79714 + 16.3242i) q^{50} +(-0.660408 - 1.59436i) q^{51} +(-1.97001 + 0.345067i) q^{52} +(-5.86345 - 2.42872i) q^{53} +(-3.01158 + 0.875946i) q^{54} +(10.3940 - 10.3940i) q^{55} +(12.1812 + 4.15802i) q^{56} +(0.260928 + 0.260928i) q^{57} +(-8.75844 - 4.81150i) q^{58} +(0.698645 - 1.68668i) q^{59} +(-3.01294 - 0.671531i) q^{60} +(-10.3825 + 4.30056i) q^{61} +(-4.96143 - 6.18898i) q^{62} -12.9995 q^{63} +(4.89161 - 6.33026i) q^{64} +4.07587 q^{65} +(1.20802 + 1.50691i) q^{66} +(1.55466 - 0.643963i) q^{67} +(-8.89625 - 1.98282i) q^{68} +(-0.183723 + 0.443547i) q^{69} +(-22.9901 - 12.6297i) q^{70} +(-5.65597 - 5.65597i) q^{71} +(-2.61012 + 7.64649i) q^{72} +(1.51942 - 1.51942i) q^{73} +(-6.32166 + 1.83871i) q^{74} +(4.06272 + 1.68283i) q^{75} +(1.91971 - 0.336257i) q^{76} +(6.28050 + 15.1625i) q^{77} +(-0.0586026 + 0.532313i) q^{78} +16.0902i q^{79} +(-12.0451 + 10.9872i) q^{80} -7.73000i q^{81} +(0.508799 + 0.0560140i) q^{82} +(1.23518 + 2.98198i) q^{83} +(1.98001 - 2.82094i) q^{84} +(17.1609 + 7.10828i) q^{85} +(3.02023 + 10.3838i) q^{86} +(-1.89206 + 1.89206i) q^{87} +(10.1798 - 0.649867i) q^{88} +(-10.8072 - 10.8072i) q^{89} +(7.92808 - 14.4316i) q^{90} +(-1.74147 + 4.20428i) q^{91} +(1.35997 + 2.14007i) q^{92} +(-1.96228 + 0.812801i) q^{93} +(-4.94600 + 3.96499i) q^{94} -3.97181 q^{95} +(-1.26176 - 1.73107i) q^{96} +2.93479 q^{97} +(15.1265 - 12.1262i) q^{98} +(-9.51795 + 3.94247i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 16 q^{10} - 16 q^{12} - 40 q^{16} - 40 q^{18} - 8 q^{22} - 16 q^{23} + 24 q^{24} + 80 q^{30} - 48 q^{31} - 48 q^{35} + 80 q^{36} - 56 q^{38} - 64 q^{40} - 16 q^{43} - 80 q^{44} + 24 q^{50} + 32 q^{51}+ \cdots + 56 q^{98}+O(q^{100}) \) 192 * q - 16 * q^10 - 16 * q^12 - 40 * q^16 - 40 * q^18 - 8 * q^22 - 16 * q^23 + 24 * q^24 + 80 * q^30 - 48 * q^31 - 48 * q^35 + 80 * q^36 - 56 * q^38 - 64 * q^40 - 16 * q^43 - 80 * q^44 + 24 * q^50 + 32 * q^51 - 32 * q^53 - 24 * q^54 + 32 * q^55 + 16 * q^56 - 64 * q^58 - 56 * q^60 - 64 * q^61 + 24 * q^62 + 80 * q^63 + 72 * q^64 + 96 * q^66 + 80 * q^67 - 32 * q^68 - 64 * q^69 - 120 * q^72 - 32 * q^74 + 32 * q^75 + 64 * q^76 - 32 * q^77 - 56 * q^80 - 80 * q^82 - 80 * q^83 + 112 * q^84 - 112 * q^87 - 88 * q^88 - 120 * q^90 + 144 * q^92 + 40 * q^94 + 136 * q^96 + 56 * q^98

Introduction

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