LMFDB - Embedded newform 525.2.w.a.104.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(104,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 1, 5]))

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

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

chi := DirichletCharacter("525.104");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.w (of order $10$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$304$
Relative dimension:	$76$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			104.11
Character	$\chi$	$=$	525.104
Dual form			525.2.w.a.419.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.677246 + 2.08435i) q^{2} +(-1.04597 + 1.38056i) q^{3} +(-2.26781 - 1.64766i) q^{4} +(-2.02988 + 0.937853i) q^{5} +(-2.16919 - 3.11514i) q^{6} +(-2.59371 - 0.522162i) q^{7} +(1.42406 - 1.03464i) q^{8} +(-0.811893 - 2.88805i) q^{9} +O(q^{10})$	\(q+(-0.677246 + 2.08435i) q^{2} +(-1.04597 + 1.38056i) q^{3} +(-2.26781 - 1.64766i) q^{4} +(-2.02988 + 0.937853i) q^{5} +(-2.16919 - 3.11514i) q^{6} +(-2.59371 - 0.522162i) q^{7} +(1.42406 - 1.03464i) q^{8} +(-0.811893 - 2.88805i) q^{9} +(-0.580080 - 4.86614i) q^{10} +(0.285649 + 0.0928130i) q^{11} +(4.64676 - 1.40745i) q^{12} +(1.41023 + 4.34026i) q^{13} +(2.84495 - 5.05257i) q^{14} +(0.828437 - 3.78334i) q^{15} +(-0.540342 - 1.66300i) q^{16} +(-1.66821 - 2.29609i) q^{17} +(6.56955 + 0.263651i) q^{18} +(3.24751 + 4.46982i) q^{19} +(6.14866 + 1.21769i) q^{20} +(3.43382 - 3.03461i) q^{21} +(-0.386909 + 0.532535i) q^{22} +(-0.170045 + 0.523346i) q^{23} +(-0.0611411 + 3.04820i) q^{24} +(3.24087 - 3.80747i) q^{25} -10.0017 q^{26} +(4.83634 + 1.89995i) q^{27} +(5.02171 + 5.45772i) q^{28} +(-1.33191 + 1.83322i) q^{29} +(7.32475 + 4.28900i) q^{30} +(-4.61943 - 6.35810i) q^{31} +7.35269 q^{32} +(-0.426914 + 0.297276i) q^{33} +(5.91565 - 1.92211i) q^{34} +(5.75465 - 1.37259i) q^{35} +(-2.91731 + 7.88728i) q^{36} +(-1.07493 + 0.349266i) q^{37} +(-11.5160 + 3.74178i) q^{38} +(-7.46705 - 2.59286i) q^{39} +(-1.92034 + 3.43576i) q^{40} +(-2.86405 - 8.81464i) q^{41} +(3.99965 + 9.21246i) q^{42} +4.94132i q^{43} +(-0.494874 - 0.681135i) q^{44} +(4.35661 + 5.10097i) q^{45} +(-0.975672 - 0.708867i) q^{46} +(-2.09215 + 2.87960i) q^{47} +(2.86105 + 0.993475i) q^{48} +(6.45469 + 2.70867i) q^{49} +(5.74122 + 9.33368i) q^{50} +(4.91479 + 0.0985814i) q^{51} +(3.95313 - 12.1665i) q^{52} +(-0.862770 - 0.626839i) q^{53} +(-7.23554 + 8.79389i) q^{54} +(-0.666880 + 0.0794970i) q^{55} +(-4.23385 + 1.93997i) q^{56} +(-9.56766 - 0.191909i) q^{57} +(-2.91904 - 4.01772i) q^{58} +(-3.24014 - 9.97212i) q^{59} +(-8.11241 + 7.21493i) q^{60} +(0.214027 + 0.0695416i) q^{61} +(16.3810 - 5.32250i) q^{62} +(0.597789 + 7.91471i) q^{63} +(-3.89889 + 11.9996i) q^{64} +(-6.93313 - 7.48763i) q^{65} +(-0.330501 - 1.09117i) q^{66} +(-7.08216 - 9.74776i) q^{67} +7.95575i q^{68} +(-0.544648 - 0.782162i) q^{69} +(-1.03635 + 12.9243i) q^{70} +(-5.02433 + 6.91539i) q^{71} +(-4.14428 - 3.27274i) q^{72} +(2.90010 - 8.92560i) q^{73} -2.47707i q^{74} +(1.86659 + 8.45670i) q^{75} -15.4875i q^{76} +(-0.692428 - 0.389885i) q^{77} +(10.4615 - 13.8079i) q^{78} +(12.5110 + 9.08978i) q^{79} +(2.65648 + 2.86894i) q^{80} +(-7.68166 + 4.68957i) q^{81} +20.3124 q^{82} +(5.74177 + 7.90287i) q^{83} +(-12.7873 + 1.22415i) q^{84} +(5.53967 + 3.09627i) q^{85} +(-10.2994 - 3.34649i) q^{86} +(-1.13773 - 3.75629i) q^{87} +(0.502810 - 0.163373i) q^{88} +(2.22429 - 6.84565i) q^{89} +(-13.5827 + 5.62609i) q^{90} +(-1.39143 - 11.9937i) q^{91} +(1.24793 - 0.906672i) q^{92} +(13.6095 + 0.272981i) q^{93} +(-4.58519 - 6.31097i) q^{94} +(-10.7841 - 6.02753i) q^{95} +(-7.69069 + 10.1508i) q^{96} +(-8.44677 - 6.13693i) q^{97} +(-10.0172 + 11.6194i) q^{98} +(0.0361320 - 0.900323i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 304 q - 84 q^{4} - 6 q^{9}+O(q^{10}) $ 304 * q - 84 * q^4 - 6 * q^9	$ 304 q - 84 q^{4} - 6 q^{9} - 36 q^{15} - 60 q^{16} - 18 q^{21} - 40 q^{22} - 8 q^{25} + 60 q^{28} + 14 q^{30} + 28 q^{36} - 20 q^{37} - 2 q^{39} - 35 q^{42} - 24 q^{46} - 20 q^{49} - 52 q^{51} - 80 q^{58} + 4 q^{60} + 55 q^{63} - 76 q^{64} - 20 q^{67} + 6 q^{70} + 30 q^{72} - 40 q^{78} - 68 q^{79} - 10 q^{81} + 80 q^{84} - 88 q^{85} - 20 q^{88} - 82 q^{91} - 36 q^{99}+O(q^{100}) $ 304 * q - 84 * q^4 - 6 * q^9 - 36 * q^15 - 60 * q^16 - 18 * q^21 - 40 * q^22 - 8 * q^25 + 60 * q^28 + 14 * q^30 + 28 * q^36 - 20 * q^37 - 2 * q^39 - 35 * q^42 - 24 * q^46 - 20 * q^49 - 52 * q^51 - 80 * q^58 + 4 * q^60 + 55 * q^63 - 76 * q^64 - 20 * q^67 + 6 * q^70 + 30 * q^72 - 40 * q^78 - 68 * q^79 - 10 * q^81 + 80 * q^84 - 88 * q^85 - 20 * q^88 - 82 * q^91 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$-1$	$-1$

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 $

$2$	−0.677246	+	2.08435i	−0.478885	+	1.47386i	0.361761	+	0.932271i	$0.382176\pi$
$2$	−0.677246	+	2.08435i	−0.478885	+	1.47386i	−0.840646	+	0.541586i	$0.817824\pi$
$3$	−1.04597	+	1.38056i	−0.603891	+	0.797067i
$3$	−1.04597	+	1.38056i	−0.603891	+	0.797067i
$4$	−2.26781	−	1.64766i	−1.13391	−	0.823831i
$5$	−2.02988	+	0.937853i	−0.907792	+	0.419420i
$5$	−2.02988	+	0.937853i	−0.907792	+	0.419420i
$6$	−2.16919	−	3.11514i	−0.885568	−	1.27175i
$7$	−2.59371	−	0.522162i	−0.980331	−	0.197359i
$7$	−2.59371	−	0.522162i	−0.980331	−	0.197359i
$8$	1.42406	−	1.03464i	0.503481	−	0.365801i
$9$	−0.811893	−	2.88805i	−0.270631	−	0.962683i
$10$	−0.580080	−	4.86614i	−0.183438	−	1.53881i
$11$	0.285649	+	0.0928130i	0.0861264	+	0.0279842i	0.351763	−	0.936089i	$-0.385582\pi$
$11$	0.285649	+	0.0928130i	0.0861264	+	0.0279842i	−0.265637	+	0.964073i	$0.585582\pi$
$12$	4.64676	−	1.40745i	1.34140	−	0.406295i
$13$	1.41023	+	4.34026i	0.391129	+	1.20377i	0.931936	+	0.362624i	$0.118119\pi$
$13$	1.41023	+	4.34026i	0.391129	+	1.20377i	−0.540807	+	0.841147i	$0.681881\pi$
$14$	2.84495	−	5.05257i	0.760344	−	1.35036i
$15$	0.828437	−	3.78334i	0.213901	−	0.976855i
$16$	−0.540342	−	1.66300i	−0.135085	−	0.415750i
$17$	−1.66821	−	2.29609i	−0.404600	−	0.556885i	0.557291	−	0.830317i	$-0.311841\pi$
$17$	−1.66821	−	2.29609i	−0.404600	−	0.556885i	−0.961891	+	0.273433i	$0.911841\pi$
$18$	6.56955	+	0.263651i	1.54846	+	0.0621432i
$19$	3.24751	+	4.46982i	0.745031	+	1.02545i	0.998313	+	0.0580547i	$0.0184898\pi$
$19$	3.24751	+	4.46982i	0.745031	+	1.02545i	−0.253282	+	0.967392i	$0.581510\pi$
$20$	6.14866	+	1.21769i	1.37488	+	0.272284i
$21$	3.43382	−	3.03461i	0.749321	−	0.662207i
$22$	−0.386909	+	0.532535i	−0.0824893	+	0.113537i
$23$	−0.170045	+	0.523346i	−0.0354569	+	0.109125i	−0.967219	−	0.253945i	$-0.918272\pi$
$23$	−0.170045	+	0.523346i	−0.0354569	+	0.109125i	0.931762	+	0.363071i	$0.118272\pi$
$24$	−0.0611411	+	3.04820i	−0.0124804	+	0.622212i
$25$	3.24087	−	3.80747i	0.648173	−	0.761493i
$26$	−10.0017			−1.96149
$27$	4.83634	+	1.89995i	0.930754	+	0.365645i
$28$	5.02171	+	5.45772i	0.949013	+	1.03141i
$29$	−1.33191	+	1.83322i	−0.247330	+	0.340421i	−0.914574	−	0.404418i	$-0.867474\pi$
$29$	−1.33191	+	1.83322i	−0.247330	+	0.340421i	0.667244	+	0.744839i	$0.267474\pi$
$30$	7.32475	+	4.28900i	1.33731	+	0.783062i
$31$	−4.61943	−	6.35810i	−0.829674	−	1.14195i	−0.987984	−	0.154559i	$-0.950604\pi$
$31$	−4.61943	−	6.35810i	−0.829674	−	1.14195i	0.158310	−	0.987389i	$-0.449396\pi$
$32$	7.35269			1.29978
$33$	−0.426914	+	0.297276i	−0.0743162	+	0.0517491i
$34$	5.91565	−	1.92211i	1.01453	−	0.329639i
$35$	5.75465	−	1.37259i	0.972713	−	0.232010i
$36$	−2.91731	+	7.88728i	−0.486218	+	1.31455i
$37$	−1.07493	+	0.349266i	−0.176718	+	0.0574190i	−0.396039	−	0.918234i	$-0.629616\pi$
$37$	−1.07493	+	0.349266i	−0.176718	+	0.0574190i	0.219322	+	0.975653i	$0.429616\pi$
$38$	−11.5160	+	3.74178i	−1.86815	+	0.606998i
$39$	−7.46705	−	2.59286i	−1.19568	−	0.415191i
$40$	−1.92034	+	3.43576i	−0.303632	+	0.543241i
$41$	−2.86405	−	8.81464i	−0.447289	−	1.37662i	−0.879953	−	0.475060i	$-0.842426\pi$
$41$	−2.86405	−	8.81464i	−0.447289	−	1.37662i	0.432664	−	0.901555i	$-0.357574\pi$
$42$	3.99965	+	9.21246i	0.617159	+	1.42151i
$43$			4.94132i			0.753544i	0.926306	+	0.376772i	$0.122966\pi$
$43$			4.94132i			0.753544i	−0.926306	+	0.376772i	$0.877034\pi$
$44$	−0.494874	−	0.681135i	−0.0746050	−	0.102685i
$45$	4.35661	+	5.10097i	0.649446	+	0.760408i
$46$	−0.975672	−	0.708867i	−0.143855	−	0.104517i
$47$	−2.09215	+	2.87960i	−0.305172	+	0.420033i	−0.933868	−	0.357618i	$-0.883589\pi$
$47$	−2.09215	+	2.87960i	−0.305172	+	0.420033i	0.628696	+	0.777651i	$0.283589\pi$
$48$	2.86105	+	0.993475i	0.412957	+	0.143396i
$49$	6.45469	+	2.70867i	0.922099	+	0.386954i
$50$	5.74122	+	9.33368i	0.811931	+	1.31998i
$51$	4.91479	+	0.0985814i	0.688209	+	0.0138042i
$52$	3.95313	−	12.1665i	0.548200	−	1.68719i
$53$	−0.862770	−	0.626839i	−0.118511	−	0.0861030i	0.526951	−	0.849896i	$-0.323335\pi$
$53$	−0.862770	−	0.626839i	−0.118511	−	0.0861030i	−0.645462	+	0.763793i	$0.723335\pi$
$54$	−7.23554	+	8.79389i	−0.984632	+	1.19670i
$55$	−0.666880	+	0.0794970i	−0.0899220	+	0.0107194i
$56$	−4.23385	+	1.93997i	−0.565773	+	0.259240i
$57$	−9.56766	−	0.191909i	−1.26727	−	0.0254190i
$58$	−2.91904	−	4.01772i	−0.383289	−	0.527552i
$59$	−3.24014	−	9.97212i	−0.421830	−	1.29826i	−0.905997	−	0.423284i	$-0.860877\pi$
$59$	−3.24014	−	9.97212i	−0.421830	−	1.29826i	0.484167	−	0.874975i	$-0.339123\pi$
$60$	−8.11241	+	7.21493i	−1.04731	+	0.931443i
$61$	0.214027	+	0.0695416i	0.0274033	+	0.00890388i	0.322687	−	0.946506i	$-0.395414\pi$
$61$	0.214027	+	0.0695416i	0.0274033	+	0.00890388i	−0.295283	+	0.955410i	$0.595414\pi$
$62$	16.3810	−	5.32250i	2.08039	−	0.675958i
$63$	0.597789	+	7.91471i	0.0753144	+	0.997160i
$64$	−3.89889	+	11.9996i	−0.487362	+	1.49994i
$65$	−6.93313	−	7.48763i	−0.859949	−	0.928726i
$66$	−0.330501	−	1.09117i	−0.0406819	−	0.134313i
$67$	−7.08216	−	9.74776i	−0.865223	−	1.19088i	−0.980299	−	0.197521i	$-0.936711\pi$
$67$	−7.08216	−	9.74776i	−0.865223	−	1.19088i	0.115075	−	0.993357i	$-0.463289\pi$
$68$			7.95575i			0.964777i
$69$	−0.544648	−	0.782162i	−0.0655679	−	0.0941612i
$70$	−1.03635	+	12.9243i	−0.123868	+	1.54475i
$71$	−5.02433	+	6.91539i	−0.596278	+	0.820706i	−0.995361	−	0.0962086i	$-0.969328\pi$
$71$	−5.02433	+	6.91539i	−0.596278	+	0.820706i	0.399083	+	0.916915i	$0.369328\pi$
$72$	−4.14428	−	3.27274i	−0.488408	−	0.385696i
$73$	2.90010	−	8.92560i	0.339431	−	1.04466i	−0.625067	−	0.780571i	$-0.714928\pi$
$73$	2.90010	−	8.92560i	0.339431	−	1.04466i	0.964498	−	0.264091i	$-0.0850718\pi$
$74$		−	2.47707i		−	0.287953i
$75$	1.86659	+	8.45670i	0.215535	+	0.976496i
$76$		−	15.4875i		−	1.77654i
$77$	−0.692428	−	0.389885i	−0.0789095	−	0.0444316i
$78$	10.4615	−	13.8079i	1.18453	−	1.56344i
$79$	12.5110	+	9.08978i	1.40760	+	1.02268i	0.993666	+	0.112373i	$0.0358451\pi$
$79$	12.5110	+	9.08978i	1.40760	+	1.02268i	0.413933	+	0.910307i	$0.364155\pi$
$80$	2.65648	+	2.86894i	0.297004	+	0.320757i
$81$	−7.68166	+	4.68957i	−0.853518	+	0.521064i
$82$	20.3124			2.24313
$83$	5.74177	+	7.90287i	0.630241	+	0.867452i	0.998048	−	0.0624499i	$-0.0198914\pi$
$83$	5.74177	+	7.90287i	0.630241	+	0.867452i	−0.367807	+	0.929902i	$0.619891\pi$
$84$	−12.7873	+	1.22415i	−1.39521	+	0.133566i
$85$	5.53967	+	3.09627i	0.600862	+	0.335838i
$86$	−10.2994	−	3.34649i	−1.11062	−	0.360861i
$87$	−1.13773	−	3.75629i	−0.121978	−	0.402716i
$88$	0.502810	−	0.163373i	0.0535997	−	0.0174156i
$89$	2.22429	−	6.84565i	0.235774	−	0.725637i	−0.761244	−	0.648466i	$-0.775411\pi$
$89$	2.22429	−	6.84565i	0.235774	−	0.725637i	0.997018	−	0.0771717i	$-0.0245890\pi$
$90$	−13.5827	+	5.62609i	−1.43174	+	0.593042i
$91$	−1.39143	−	11.9937i	−0.145861	−	1.25729i
$92$	1.24793	−	0.906672i	0.130105	−	0.0945271i
$93$	13.6095	+	0.272981i	1.41124	+	0.0283068i
$94$	−4.58519	−	6.31097i	−0.472926	−	0.650927i
$95$	−10.7841	−	6.02753i	−1.10643	−	0.618412i
$96$	−7.69069	+	10.1508i	−0.784928	+	1.03601i
$97$	−8.44677	−	6.13693i	−0.857639	−	0.623111i	0.0696025	−	0.997575i	$-0.477827\pi$
$97$	−8.44677	−	6.13693i	−0.857639	−	0.623111i	−0.927242	+	0.374463i	$0.877827\pi$
$98$	−10.0172	+	11.6194i	−1.01189	+	1.17374i
$99$	0.0361320	−	0.900323i	0.00363141	−	0.0904859i
$100$	−13.6231	+	3.29477i	−1.36231	+	0.329477i
$101$	−6.05598			−0.602593			−0.301296	−	0.953531i	$-0.597419\pi$
$101$	−6.05598			−0.602593			−0.301296	+	0.953531i	$0.597419\pi$
$102$	−3.53400	+	10.1774i	−0.349918	+	1.00771i
$103$	−7.20680	−	5.23605i	−0.710107	−	0.515923i	0.173101	−	0.984904i	$-0.444621\pi$
$103$	−7.20680	−	5.23605i	−0.710107	−	0.515923i	−0.883208	+	0.468981i	$0.844621\pi$
$104$	6.49886	+	4.72170i	0.637266	+	0.463001i
$105$	−4.12424	+	9.38033i	−0.402485	+	0.915427i
$106$	1.89086	−	1.37379i	0.183656	−	0.133434i
$107$	2.93038			0.283290			0.141645	−	0.989918i	$-0.454761\pi$
$107$	2.93038			0.283290			0.141645	+	0.989918i	$0.454761\pi$
$108$	−7.83744	−	12.2774i	−0.754158	−	1.18139i
$109$	−0.558938	−	1.72023i	−0.0535365	−	0.164768i	0.920713	−	0.390240i	$-0.127608\pi$
$109$	−0.558938	−	1.72023i	−0.0535365	−	0.164768i	−0.974250	+	0.225471i	$0.927608\pi$
$110$	0.285942	−	1.44385i	0.0272635	−	0.137666i
$111$	0.642162	−	1.84933i	0.0609514	−	0.175531i
$112$	0.533136	+	4.59549i	0.0503766	+	0.434233i
$113$	−6.20835	−	19.1073i	−0.584032	−	1.79747i	−0.603122	−	0.797649i	$-0.706077\pi$
$113$	−6.20835	−	19.1073i	−0.584032	−	1.79747i	0.0190891	−	0.999818i	$-0.493923\pi$
$114$	6.87966	−	19.8124i	0.644339	−	1.85560i
$115$	−0.145649	−	1.22181i	−0.0135818	−	0.113934i
$116$	6.04106	−	1.96286i	0.560899	−	0.182247i
$117$	11.3899	−	7.59665i	1.05300	−	0.702311i
$118$	22.9797			2.11546
$119$	3.12793	+	6.82648i	0.286736	+	0.625783i
$120$	−2.73466	−	6.24485i	−0.249639	−	0.570074i
$121$	−8.82621	−	6.41261i	−0.802382	−	0.582965i
$122$	−0.289898	+	0.399010i	−0.0262461	+	0.0361247i
$123$	15.1649	+	5.26586i	1.36737	+	0.474806i
$124$			22.0302i			1.97837i
$125$	−3.00774	+	10.7682i	−0.269021	+	0.963134i
$126$	−16.9019	−	4.11420i	−1.50574	−	0.366522i
$127$	−10.3866	−	3.37481i	−0.921662	−	0.299466i	−0.190513	−	0.981685i	$-0.561015\pi$
$127$	−10.3866	−	3.37481i	−0.921662	−	0.299466i	−0.731148	+	0.682219i	$0.761015\pi$
$128$	−10.4739	−	7.60970i	−0.925766	−	0.672609i
$129$	−6.82179	−	5.16847i	−0.600625	−	0.455059i
$130$	20.3023	−	9.38010i	1.78063	−	0.822689i
$131$	3.99547	−	2.90288i	0.349085	−	0.253625i	−0.399400	−	0.916777i	$-0.630781\pi$
$131$	3.99547	−	2.90288i	0.349085	−	0.253625i	0.748485	+	0.663151i	$0.230781\pi$
$132$	1.45797	+	0.0292441i	0.126900	+	0.00254537i
$133$	−6.08915	−	13.2892i	−0.527996	−	1.15232i
$134$	25.1141	−	8.16006i	2.16953	−	0.704922i
$135$	−11.5991	+	0.679104i	−0.998290	+	0.0584480i
$136$	−4.75126	−	1.54378i	−0.407417	−	0.132378i
$137$	−0.467744	−	1.43957i	−0.0399620	−	0.122991i	0.929085	−	0.369866i	$-0.120596\pi$
$137$	−0.467744	−	1.43957i	−0.0399620	−	0.122991i	−0.969047	+	0.246875i	$0.920596\pi$
$138$	1.99916	−	0.605520i	0.170180	−	0.0515453i
$139$	−12.9929	−	4.22166i	−1.10205	−	0.358076i	−0.299156	−	0.954204i	$-0.596705\pi$
$139$	−12.9929	−	4.22166i	−1.10205	−	0.358076i	−0.802890	+	0.596128i	$0.796705\pi$
$140$	−15.3120	−	6.36893i	−1.29410	−	0.538273i
$141$	−1.78713	−	5.90032i	−0.150504	−	0.496896i
$142$	−11.0114	−	15.1559i	−0.924054	−	1.27185i
$143$			1.37068i			0.114622i
$144$	−4.36413	+	2.91071i	−0.363677	+	0.242559i
$145$	0.984340	−	4.97037i	0.0817450	−	0.412767i
$146$	16.6400	+	12.0896i	1.37713	+	1.00055i
$147$	−10.4909	+	6.07790i	−0.865275	+	0.501297i
$148$	3.01321	+	0.979052i	0.247685	+	0.0804776i
$149$		−	9.15699i		−	0.750170i	−0.926990	−	0.375085i	$-0.877614\pi$
$149$		−	9.15699i		−	0.750170i	0.926990	−	0.375085i	$-0.122386\pi$
$150$	−18.8909	−	1.83665i	−1.54243	−	0.149962i
$151$	17.4967			1.42386			0.711932	−	0.702249i	$-0.247821\pi$
$151$	17.4967			1.42386			0.711932	+	0.702249i	$0.247821\pi$
$152$	9.24931	+	3.00528i	0.750218	+	0.243761i
$153$	−5.27682	+	6.68206i	−0.426606	+	0.540212i
$154$	1.28160	−	1.17921i	0.103274	−	0.0950237i
$155$	15.3399	+	8.57386i	1.23213	+	0.688669i
$156$	12.6617	+	18.1833i	1.01375	+	1.45583i
$157$	9.36674			0.747547			0.373774	−	0.927520i	$-0.378064\pi$
$157$	9.36674			0.747547			0.373774	+	0.927520i	$0.378064\pi$
$158$	−27.4193	+	19.9213i	−2.18136	+	1.58485i
$159$	1.76782	−	0.535451i	0.140197	−	0.0424640i
$160$	−14.9251	+	6.89574i	−1.17993	+	0.545156i
$161$	0.714320	−	1.26862i	0.0562963	−	0.0999811i
$162$	−4.57234	−	19.1872i	−0.359237	−	1.50749i
$163$	−18.2745	+	5.93774i	−1.43137	+	0.465080i	−0.919195	−	0.393803i	$-0.871159\pi$
$163$	−18.2745	+	5.93774i	−1.43137	+	0.465080i	−0.512173	+	0.858882i	$0.671159\pi$
$164$	−8.02842	+	24.7089i	−0.626914	+	1.92944i
$165$	0.587786	−	1.00382i	0.0457591	−	0.0781472i
$166$	−20.3609	+	6.61566i	−1.58031	+	0.513475i
$167$	−7.88643	−	10.8547i	−0.610270	−	0.839965i	0.386329	−	0.922361i	$-0.373743\pi$
$167$	−7.88643	−	10.8547i	−0.610270	−	0.839965i	−0.996600	+	0.0823958i	$0.973743\pi$
$168$	1.75024	−	7.87424i	0.135034	−	0.607511i
$169$	−6.33184	+	4.60035i	−0.487064	+	0.353873i
$170$	−10.2054	+	9.44967i	−0.782720	+	0.724756i
$171$	10.2724	−	13.0080i	0.785552	−	0.994747i
$172$	8.14162	−	11.2060i	0.620793	−	0.854448i
$173$	14.8239	+	4.81658i	1.12704	+	0.366198i	0.812451	−	0.583030i	$-0.198133\pi$
$173$	14.8239	+	4.81658i	1.12704	+	0.366198i	0.314590	+	0.949228i	$0.398133\pi$
$174$	8.59993	+	0.172498i	0.651959	+	0.0130771i
$175$	−10.3940	+	8.18322i	−0.785711	+	0.618593i
$176$		−	0.525185i		−	0.0395873i
$177$	17.1562	+	5.95733i	1.28954	+	0.447780i
$178$	12.7623	+	9.27237i	0.956577	+	0.694994i
$179$	−13.1520	+	18.1022i	−0.983026	+	1.35302i	−0.0478421	+	0.998855i	$0.515234\pi$
$179$	−13.1520	+	18.1022i	−0.983026	+	1.35302i	−0.935183	+	0.354164i	$0.884766\pi$
$180$	−1.47530	−	18.7463i	−0.109963	−	1.39726i
$181$	8.66852	+	11.9312i	0.644326	+	0.886838i	0.998837	−	0.0482135i	$-0.0153528\pi$
$181$	8.66852	+	11.9312i	0.644326	+	0.886838i	−0.354511	+	0.935052i	$0.615353\pi$
$182$	25.9415	+	5.22249i	1.92291	+	0.387117i
$183$	−0.319872	+	0.222739i	−0.0236456	+	0.0164653i
$184$	0.299320	+	0.921212i	0.0220662	+	0.0679126i
$185$	1.85443	−	1.71710i	0.136340	−	0.126243i
$186$	−9.78598	+	28.1821i	−0.717543	+	2.06641i
$187$	−0.263415	−	0.810709i	−0.0192628	−	0.0592849i
$188$	9.48921	−	3.08323i	0.692072	−	0.224868i
$189$	−11.5520	−	7.45327i	−0.840285	−	0.542145i
$190$	19.8670	−	18.3957i	1.44130	−	1.33457i
$191$	−12.5051	+	4.06315i	−0.904838	+	0.294000i	−0.724232	−	0.689556i	$-0.757806\pi$
$191$	−12.5051	+	4.06315i	−0.904838	+	0.294000i	−0.180605	+	0.983556i	$0.557806\pi$
$192$	−12.4880	−	17.9338i	−0.901243	−	1.29426i
$193$			11.7673i			0.847027i	0.905890	+	0.423513i	$0.139203\pi$
$193$			11.7673i			0.847027i	−0.905890	+	0.423513i	$0.860797\pi$
$194$	18.5120	−	13.4498i	1.32909	−	0.965639i
$195$	17.5890	−	1.73977i	1.25957	−	0.124588i
$196$	−10.1751	−	16.7779i	−0.726789	−	1.19842i
$197$	−14.9529	−	10.8640i	−1.06535	−	0.774025i	−0.0902822	−	0.995916i	$-0.528777\pi$
$197$	−14.9529	−	10.8640i	−1.06535	−	0.774025i	−0.975071	+	0.221892i	$0.928777\pi$
$198$	1.85212	+	0.685052i	0.131624	+	0.0486845i
$199$			20.3538i			1.44285i	0.692495	+	0.721423i	$0.256511\pi$
$199$			20.3538i			1.44285i	−0.692495	+	0.721423i	$0.743489\pi$
$200$	0.675830	−	8.77519i	0.0477884	−	0.620500i
$201$	20.8651	+	0.418514i	1.47171	+	0.0295197i
$202$	4.10139	−	12.6228i	0.288573	−	0.888136i
$203$	4.41184	−	4.05938i	0.309651	−	0.284913i
$204$	−10.9834	−	8.32148i	−0.768991	−	0.582620i
$205$	14.0805	+	15.2066i	0.983426	+	1.06208i
$206$	15.7945	−	11.4754i	1.10046	−	0.799528i
$207$	1.64951	+	0.0661986i	0.114649	+	0.00460112i
$208$	6.45584	−	4.69044i	0.447632	−	0.325224i
$209$	0.512792	+	1.57821i	0.0354706	+	0.109167i
$210$	−16.7587	−	14.9492i	−1.15646	−	1.03159i
$211$	−6.99608	+	21.5317i	−0.481630	+	1.48230i	0.355174	+	0.934800i	$0.384422\pi$
$211$	−6.99608	+	21.5317i	−0.481630	+	1.48230i	−0.836803	+	0.547504i	$0.815578\pi$
$212$	0.923781	+	2.84311i	0.0634455	+	0.195265i
$213$	−4.29182	−	14.1697i	−0.294071	−	0.970890i
$214$	−1.98458	+	6.10792i	−0.135663	+	0.417529i
$215$	−4.63423	−	10.0303i	−0.316052	−	0.684062i
$216$	8.85300	−	2.29824i	0.602371	−	0.156375i
$217$	8.66152	+	18.9032i	0.587982	+	1.28323i
$218$	3.96410			0.268483
$219$	9.28890	+	13.3397i	0.627686	+	0.901412i
$220$	1.64334	+	0.918508i	0.110794	+	0.0619258i
$221$	7.61307	−	10.4785i	0.512110	−	0.704859i
$222$	3.41974	+	2.59094i	0.229518	+	0.173893i
$223$	−6.23868	+	19.2007i	−0.417773	+	1.28577i	0.491975	+	0.870610i	$0.336275\pi$
$223$	−6.23868	+	19.2007i	−0.417773	+	1.28577i	−0.909747	+	0.415162i	$0.863725\pi$
$224$	−19.0708	−	3.83929i	−1.27422	−	0.256523i
$225$	−13.6274	−	6.26852i	−0.908492	−	0.417902i
$226$	44.0309			2.92889
$227$	−12.8552	−	4.17691i	−0.853231	−	0.277231i	−0.150432	−	0.988620i	$-0.548066\pi$
$227$	−12.8552	−	4.17691i	−0.853231	−	0.277231i	−0.702799	+	0.711389i	$0.748066\pi$
$228$	21.3814	+	16.1995i	1.41602	+	1.07284i
$229$	3.90169	−	5.37022i	0.257831	−	0.354874i	−0.660403	−	0.750911i	$-0.729615\pi$
$229$	3.90169	−	5.37022i	0.257831	−	0.354874i	0.918235	+	0.396037i	$0.129615\pi$
$230$	2.64532	+	0.523882i	0.174427	+	0.0345438i
$231$	1.26252	−	0.548131i	0.0830677	−	0.0360643i
$232$			3.98867i			0.261869i
$233$	1.67790	−	1.21906i	0.109923	−	0.0798636i	−0.531466	−	0.847080i	$-0.678359\pi$
$233$	1.67790	−	1.21906i	0.109923	−	0.0798636i	0.641389	+	0.767216i	$0.278359\pi$
$234$	8.12029	+	28.8853i	0.530840	+	1.88829i
$235$	1.54619	−	7.80739i	0.100862	−	0.509298i
$236$	−9.08265	+	27.9535i	−0.591230	+	1.81962i
$237$	−25.6351	+	7.76456i	−1.66518	+	0.504363i
$238$	−16.3471	+	1.89648i	−1.05963	+	0.122930i
$239$	18.3866	+	5.97416i	1.18933	+	0.386436i	0.835824	−	0.548997i	$-0.184990\pi$
$239$	18.3866	+	5.97416i	1.18933	+	0.386436i	0.353504	+	0.935433i	$0.384990\pi$
$240$	−6.73934	+	0.666607i	−0.435023	+	0.0430293i
$241$	−10.2203	+	3.32078i	−0.658348	+	0.213910i	−0.619091	−	0.785319i	$-0.712499\pi$
$241$	−10.2203	+	3.32078i	−0.658348	+	0.213910i	−0.0392566	+	0.999229i	$0.512499\pi$
$242$	19.3436	−	14.0540i	1.24346	−	0.903423i
$243$	1.56055	−	15.5101i	0.100109	−	0.994976i
$244$	−0.370792	−	0.510351i	−0.0237375	−	0.0326719i
$245$	−15.6426	+	0.555254i	−0.999371	+	0.0354739i
$246$	−21.2462	+	28.0425i	−1.35461	+	1.78793i
$247$	−14.8204	+	20.3985i	−0.943000	+	1.29793i
$248$	−13.1567	−	4.27487i	−0.835451	−	0.271454i
$249$	−16.9161	−	0.339305i	−1.07201	−	0.0215026i
$250$	−20.4076	−	13.5619i	−1.29069	−	0.857728i
$251$	20.7720			1.31112			0.655559	−	0.755144i	$-0.272433\pi$
$251$	20.7720			1.31112			0.655559	+	0.755144i	$0.272433\pi$
$252$	11.6851	−	18.9340i	0.736091	−	1.19273i
$253$	−0.0971466	+	0.133711i	−0.00610755	+	0.00840633i
$254$	14.0686	−	19.3637i	0.882740	−	1.21499i
$255$	−10.0689	+	4.40924i	−0.630540	+	0.276118i
$256$	2.53976	−	1.84525i	0.158735	−	0.115328i
$257$			18.3986i			1.14767i	0.818971	+	0.573836i	$0.194545\pi$
$257$			18.3986i			1.14767i	−0.818971	+	0.573836i	$0.805455\pi$
$258$	15.3929	−	10.7187i	0.958322	−	0.667315i
$259$	2.97044	−	0.344609i	0.184574	−	0.0214129i
$260$	3.38597	+	28.4040i	0.209989	+	1.76154i
$261$	6.37581	+	2.35825i	0.394653	+	0.145972i
$262$	3.34469	+	10.2939i	0.206636	+	0.635959i
$263$	1.46293	+	4.50243i	0.0902080	+	0.277632i	0.985975	−	0.166892i	$-0.0533731\pi$
$263$	1.46293	+	4.50243i	0.0902080	+	0.277632i	−0.895767	+	0.444523i	$0.853373\pi$
$264$	−0.300378	+	0.865042i	−0.0184870	+	0.0532397i
$265$	2.33921	+	0.463260i	0.143696	+	0.0284578i
$266$	31.8231	−	3.69189i	1.95120	−	0.226364i
$267$	7.12429	+	10.2311i	0.436000	+	0.626133i
$268$			33.7751i			2.06314i
$269$	−10.1984	+	7.40960i	−0.621810	+	0.451772i	−0.853553	−	0.521005i	$-0.825557\pi$
$269$	−10.1984	+	7.40960i	−0.621810	+	0.451772i	0.231743	+	0.972777i	$0.425557\pi$
$270$	6.43994	−	24.6365i	0.391922	−	1.49933i
$271$	15.5963	−	21.4665i	0.947410	−	1.30400i	−0.00525837	−	0.999986i	$-0.501674\pi$
$271$	15.5963	−	21.4665i	0.947410	−	1.30400i	0.952668	−	0.304012i	$-0.0983262\pi$
$272$	−2.91700	+	4.01491i	−0.176869	+	0.243440i
$273$	18.0135	+	10.6242i	1.09023	+	0.643003i
$274$	3.31734			0.200408
$275$	1.27913	−	0.786805i	0.0771346	−	0.0474461i
$276$	−0.0535790	+	2.67119i	−0.00322508	+	0.160787i
$277$	−21.9435	−	7.12987i	−1.31846	−	0.428392i	−0.436491	−	0.899709i	$-0.643779\pi$
$277$	−21.9435	−	7.12987i	−1.31846	−	0.428392i	−0.881964	+	0.471316i	$0.843779\pi$
$278$	17.5988	−	24.2227i	1.05551	−	1.45278i
$279$	−14.6120	+	18.5032i	−0.874799	+	1.10776i
$280$	6.77483	−	7.90865i	0.404873	−	0.472632i
$281$	1.32360	+	1.82178i	0.0789596	+	0.108679i	0.846670	−	0.532119i	$-0.178604\pi$
$281$	1.32360	+	1.82178i	0.0789596	+	0.108679i	−0.767710	+	0.640797i	$0.778604\pi$
$282$	13.5086	+	0.270958i	0.804428	+	0.0161353i
$283$	−23.2304	+	16.8779i	−1.38090	+	1.00328i	−0.384107	+	0.923289i	$0.625491\pi$
$283$	−23.2304	+	16.8779i	−1.38090	+	1.00328i	−0.996795	+	0.0799954i	$0.974509\pi$
$284$	22.7884	−	7.40442i	1.35225	−	0.439371i
$285$	19.6012	−	8.58350i	1.16108	−	0.508443i
$286$	−2.85697	−	0.928286i	−0.168936	−	0.0548907i
$287$	2.82586	+	24.3581i	0.166805	+	1.43782i
$288$	−5.96960	−	21.2349i	−0.351762	−	1.25128i
$289$	2.76417	−	8.50723i	0.162598	−	0.500425i
$290$	9.69335	+	5.41787i	0.569213	+	0.318148i
$291$	17.3075	−	5.24222i	1.01458	−	0.307304i
$292$	−21.2832	+	15.4632i	−1.24551	+	0.904914i
$293$		−	28.9815i		−	1.69312i	−0.532294	−	0.846560i	$-0.678670\pi$
$293$		−	28.9815i		−	1.69312i	0.532294	−	0.846560i	$-0.321330\pi$
$294$	−5.56354	−	25.9829i	−0.324472	−	1.51536i
$295$	15.9295	+	17.2035i	0.927450	+	1.00163i
$296$	−1.16940	+	1.60954i	−0.0679701	+	0.0935528i
$297$	1.20516	+	0.991593i	0.0699303	+	0.0575381i
$298$	19.0864	+	6.20153i	1.10564	+	0.359245i
$299$	−2.51126			−0.145230
$300$	9.70072	−	22.2537i	0.560071	−	1.28482i
$301$	2.58017	−	12.8164i	0.148718	−	0.738723i
$302$	−11.8496	+	36.4693i	−0.681867	+	2.09857i
$303$	6.33438	−	8.36065i	0.363901	−	0.480307i
$304$	5.67855	−	7.81585i	0.325687	−	0.448270i
$305$	−0.499670	+	0.0595643i	−0.0286110	+	0.00341064i
$306$	−10.3540	−	15.5241i	−0.591900	−	0.887456i
$307$	−13.2165			−0.754303			−0.377151	−	0.926152i	$-0.623096\pi$
$307$	−13.2165			−0.754303			−0.377151	+	0.926152i	$0.623096\pi$
$308$	0.927898	+	2.02507i	0.0528719	+	0.115389i
$309$	14.7668	−	4.47267i	0.840053	−	0.254441i
$310$	−28.2598	+	26.1670i	−1.60505	+	1.48619i
$311$	7.14488	−	21.9897i	0.405149	−	1.24692i	−0.515622	−	0.856816i	$-0.672439\pi$
$311$	7.14488	−	21.9897i	0.405149	−	1.24692i	0.920771	−	0.390104i	$-0.127561\pi$
$312$	−13.3162	+	4.03331i	−0.753882	+	0.228341i
$313$	1.03834	+	3.19567i	0.0586902	+	0.180630i	0.976104	−	0.217306i	$-0.0697268\pi$
$313$	1.03834	+	3.19567i	0.0586902	+	0.180630i	−0.917413	+	0.397935i	$0.869727\pi$
$314$	−6.34358	+	19.5235i	−0.357989	+	1.10178i
$315$	−8.63628	−	15.5053i	−0.486599	−	0.873625i
$316$	−13.3957	−	41.2278i	−0.753569	−	2.31925i
$317$	−7.59024	+	5.51463i	−0.426310	+	0.309733i	−0.780172	−	0.625565i	$-0.784868\pi$
$317$	−7.59024	+	5.51463i	−0.426310	+	0.309733i	0.353862	+	0.935298i	$0.384868\pi$
$318$	−0.0811828	+	4.04739i	−0.00455251	+	0.226966i
$319$	−0.550607	+	0.400040i	−0.0308281	+	0.0223979i
$320$	−3.33951	−	28.0143i	−0.186684	−	1.56605i
$321$	−3.06508	+	4.04556i	−0.171076	+	0.225801i
$322$	2.16047	+	2.34806i	0.120398	+	0.130852i
$323$	4.84559	−	14.9132i	0.269616	−	0.829792i
$324$	25.1474	+	2.02170i	1.39708	+	0.112317i
$325$	21.0958	+	8.69676i	1.17018	+	0.482410i
$326$		−	42.1117i		−	2.33235i
$327$	2.95952	+	1.02767i	0.163662	+	0.0568300i
$328$	−13.1986	−	9.58932i	−0.728769	−	0.529481i
$329$	6.93006	−	6.37642i	0.382067	−	0.351543i
$330$	1.69423	+	1.90498i	0.0932644	+	0.104866i
$331$	−1.47580	+	1.07223i	−0.0811171	+	0.0589350i	−0.627605	−	0.778532i	$-0.715965\pi$
$331$	−1.47580	+	1.07223i	−0.0811171	+	0.0589350i	0.546488	+	0.837467i	$0.315965\pi$
$332$		−	27.3827i		−	1.50282i
$333$	1.88143	+	2.82089i	0.103102	+	0.154584i
$334$	27.9661	−	9.08674i	1.53024	−	0.497204i
$335$	23.5179	+	13.1448i	1.28492	+	0.718177i
$336$	−6.90200	−	4.07072i	−0.376535	−	0.222076i
$337$	10.3243	−	3.35458i	0.562402	−	0.182735i	−0.0139999	−	0.999902i	$-0.504456\pi$
$337$	10.3243	−	3.35458i	0.562402	−	0.182735i	0.576402	+	0.817167i	$0.304456\pi$
$338$	−5.30052	−	16.3133i	−0.288310	−	0.887327i
$339$	32.8726	+	11.4147i	1.78539	+	0.619961i
$340$	−7.46132	−	16.1493i	−0.404647	−	0.875817i
$341$	−0.729421	−	2.24493i	−0.0395004	−	0.121570i
$342$	20.1562	+	30.2209i	1.08992	+	1.63416i
$343$	−15.3273	−	10.3959i	−0.827594	−	0.561327i
$344$	5.11249	+	7.03674i	0.275647	+	0.379396i
$345$	1.83913	+	1.07690i	0.0990152	+	0.0579783i
$346$	−20.0789	+	27.6362i	−1.07945	+	1.48573i
$347$	19.4710	+	14.1465i	1.04526	+	0.759424i	0.971305	−	0.237837i	$-0.0764386\pi$
$347$	19.4710	+	14.1465i	1.04526	+	0.759424i	0.0739528	+	0.997262i	$0.476439\pi$
$348$	−3.60892	+	10.3931i	−0.193459	+	0.557131i
$349$			1.15222i			0.0616769i	0.999524	+	0.0308385i	$0.00981774\pi$
$349$			1.15222i			0.0616769i	−0.999524	+	0.0308385i	$0.990182\pi$
$350$	−10.0174	−	27.2067i	−0.535452	−	1.45426i
$351$	−1.42587	+	23.6703i	−0.0761076	+	1.26343i
$352$	2.10029	+	0.682425i	0.111946	+	0.0363734i
$353$	5.58638	−	7.68900i	0.297333	−	0.409244i	−0.634046	−	0.773296i	$-0.718607\pi$
$353$	5.58638	−	7.68900i	0.297333	−	0.409244i	0.931379	+	0.364052i	$0.118607\pi$
$354$	−24.0361	+	31.7249i	−1.27750	+	1.68616i
$355$	3.71319	−	18.7495i	0.197075	−	0.995122i
$356$	−16.3236	+	11.8598i	−0.865147	+	0.628566i
$357$	−12.6961	−	2.82201i	−0.671948	−	0.149357i
$358$	−28.8241	−	39.6729i	−1.52340	−	2.09678i
$359$	−12.1983	+	3.96346i	−0.643800	+	0.209183i	−0.612678	−	0.790332i	$-0.709908\pi$
$359$	−12.1983	+	3.96346i	−0.643800	+	0.209183i	−0.0311214	+	0.999516i	$0.509908\pi$
$360$	11.4818	+	2.75656i	0.605142	+	0.145284i
$361$	−3.56162	+	10.9615i	−0.187454	+	0.576923i
$362$	−30.7395	+	9.98786i	−1.61563	+	0.524950i
$363$	18.0849	−	5.47771i	0.949214	−	0.287505i
$364$	−16.6061	+	29.4922i	−0.870398	+	1.54581i
$365$	2.48402	+	20.8378i	0.130020	+	1.09070i
$366$	−0.247633	−	0.817574i	−0.0129440	−	0.0427353i
$367$	−5.89403	+	4.28226i	−0.307666	+	0.223532i	−0.730894	−	0.682491i	$-0.760897\pi$
$367$	−5.89403	+	4.28226i	−0.307666	+	0.223532i	0.423228	+	0.906023i	$0.360897\pi$
$368$	0.962207			0.0501585
$369$	−23.1318	+	15.4281i	−1.20419	+	0.803153i
$370$	2.32313	+	5.02817i	0.120774	+	0.261402i
$371$	1.91047	+	2.07635i	0.0991865	+	0.107799i
$372$	−30.4140	−	23.0430i	−1.57689	−	1.19472i
$373$	3.87244	+	1.25823i	0.200508	+	0.0651489i	0.407549	−	0.913183i	$-0.366384\pi$
$373$	3.87244	+	1.25823i	0.200508	+	0.0651489i	−0.207042	+	0.978332i	$0.566384\pi$
$374$	1.86820			0.0966021
$375$	−11.7201	−	15.4156i	−0.605223	−	0.796056i
$376$			6.26535i			0.323111i
$377$	−9.83497	−	3.19558i	−0.506527	−	0.164581i
$378$	23.3587	−	19.0307i	1.20144	−	0.978834i
$379$	−7.76568	−	5.64209i	−0.398896	−	0.289815i	0.370195	−	0.928954i	$-0.379291\pi$
$379$	−7.76568	−	5.64209i	−0.398896	−	0.289815i	−0.769091	+	0.639139i	$0.779291\pi$
$380$	14.5250	+	31.4379i	0.745117	+	1.61273i
$381$	15.5232	−	10.8094i	0.795278	−	0.553781i
$382$		−	28.8167i		−	1.47439i
$383$	14.7824	+	20.3462i	0.755345	+	1.03964i	0.997587	+	0.0694278i	$0.0221173\pi$
$383$	14.7824	+	20.3462i	0.755345	+	1.03964i	−0.242242	+	0.970216i	$0.577883\pi$
$384$	21.4610	−	6.50027i	1.09518	−	0.331715i
$385$	1.77120	+	0.142027i	0.0902690	+	0.00723834i
$386$	−24.5271	−	7.96934i	−1.24840	−	0.405629i
$387$	14.2708	−	4.01182i	0.725424	−	0.203933i
$388$	9.04408	+	27.8348i	0.459144	+	1.41310i
$389$	−25.5854	−	8.31321i	−1.29723	−	0.421497i	−0.422615	−	0.906309i	$-0.638888\pi$
$389$	−25.5854	−	8.31321i	−1.29723	−	0.421497i	−0.874618	+	0.484813i	$0.838888\pi$
$390$	−8.28576	+	37.8398i	−0.419566	+	1.91609i
$391$	1.48532	−	0.482611i	0.0751160	−	0.0244067i
$392$	11.9944	−	2.82097i	0.605808	−	0.142481i
$393$	−0.171543	+	8.55230i	−0.00865319	+	0.431407i
$394$	32.7711	−	23.8096i	1.65098	−	1.19951i
$395$	−33.9208	−	6.71773i	−1.70674	−	0.338005i
$396$	−1.56537	+	1.98223i	−0.0786627	+	0.0996108i
$397$	−27.6210	−	20.0678i	−1.38626	−	1.00718i	−0.996264	−	0.0863585i	$-0.972477\pi$
$397$	−27.6210	−	20.0678i	−1.38626	−	1.00718i	−0.389994	−	0.920817i	$-0.627523\pi$
$398$	−42.4245	−	13.7845i	−2.12655	−	0.690957i
$399$	24.7156	+	5.49362i	1.23733	+	0.275025i
$400$	−8.08299	−	3.33223i	−0.404150	−	0.166611i
$401$		−	34.1504i		−	1.70539i	−0.522408	−	0.852696i	$-0.674966\pi$
$401$		−	34.1504i		−	1.70539i	0.522408	−	0.852696i	$-0.325034\pi$
$402$	−15.0031	+	43.2067i	−0.748288	+	2.15495i
$403$	21.0813	−	29.0159i	1.05013	−	1.44539i
$404$	13.7338	+	9.97821i	0.683283	+	0.496435i
$405$	11.1948	−	16.7236i	0.556272	−	0.831000i
$406$	5.47326	+	11.9450i	0.271633	+	0.592821i
$407$	−0.339469			−0.0168269
$408$	7.10096	−	4.94466i	0.351550	−	0.244797i
$409$	−5.67442	+	1.84373i	−0.280582	+	0.0911666i	−0.445927	−	0.895069i	$-0.647126\pi$
$409$	−5.67442	+	1.84373i	−0.280582	+	0.0911666i	0.165346	+	0.986236i	$0.447126\pi$
$410$	−41.2319	+	19.0501i	−2.03630	+	0.940816i
$411$	2.47666	+	0.859996i	0.122164	+	0.0424205i
$412$	7.71643	+	23.7487i	0.380161	+	1.17002i
$413$	3.19693	+	27.5567i	0.157311	+	1.35598i
$414$	−1.25510	+	3.39331i	−0.0616849	+	0.166772i
$415$	−19.0668	−	10.6570i	−0.935955	−	0.523130i
$416$	10.3690	+	31.9125i	0.508383	+	1.56464i
$417$	19.4185	−	13.5218i	0.950927	−	0.662165i
$418$	−3.63683			−0.177883
$419$	2.62834	−	1.90960i	0.128403	−	0.0932902i	−0.521730	−	0.853111i	$-0.674713\pi$
$419$	2.62834	−	1.90960i	0.128403	−	0.0932902i	0.650133	+	0.759820i	$0.274713\pi$
$420$	24.8086	−	14.4775i	1.21054	−	0.706428i
$421$	−12.7854	−	9.28914i	−0.623123	−	0.452725i	0.230888	−	0.972980i	$-0.425837\pi$
$421$	−12.7854	−	9.28914i	−0.623123	−	0.452725i	−0.854011	+	0.520255i	$0.825837\pi$
$422$	−40.1415	−	29.1645i	−1.95406	−	1.41971i
$423$	10.0150	+	3.70431i	0.486948	+	0.180110i
$424$	−1.87719			−0.0911644
$425$	−14.1487	−	1.08968i	−0.686315	−	0.0528572i
$426$	32.4412	+	0.650708i	1.57178	+	0.0315269i
$427$	−0.518812	−	0.292128i	−0.0251071	−	0.0141370i
$428$	−6.64554	−	4.82827i	−0.321224	−	0.233383i
$429$	−1.89230	−	1.43369i	−0.0913613	−	0.0692191i
$430$	24.0452	−	2.86636i	1.15956	−	0.138228i
$431$	10.0311	+	13.8066i	0.483180	+	0.665040i	0.979112	−	0.203321i	$-0.0651736\pi$
$431$	10.0311	+	13.8066i	0.483180	+	0.665040i	−0.495932	+	0.868361i	$0.665174\pi$
$432$	0.546334	−	9.06946i	0.0262855	−	0.436355i
$433$	−20.5354	+	14.9198i	−0.986868	+	0.717002i	−0.959233	−	0.282616i	$-0.908798\pi$
$433$	−20.5354	+	14.9198i	−0.986868	+	0.717002i	−0.0276351	+	0.999618i	$0.508798\pi$
$434$	−45.2668	+	5.25153i	−2.17287	+	0.252081i
$435$	5.83231	+	6.55780i	0.279638	+	0.314423i
$436$	−1.56680	+	4.82211i	−0.0750360	+	0.230937i
$437$	−2.89149	+	0.939501i	−0.138319	+	0.0449424i
$438$	−34.0954	+	10.3271i	−1.62914	+	0.493447i
$439$	−19.2332	−	6.24926i	−0.917952	−	0.298261i	−0.188326	−	0.982107i	$-0.560306\pi$
$439$	−19.2332	−	6.24926i	−0.917952	−	0.298261i	−0.729626	+	0.683846i	$0.760306\pi$
$440$	−0.867426	+	0.803189i	−0.0413529	+	0.0382905i
$441$	2.58226	−	20.8406i	0.122965	−	0.992411i
$442$	16.6849	+	22.9648i	0.793620	+	1.09232i
$443$	−15.3838			−0.730906			−0.365453	−	0.930830i	$-0.619086\pi$
$443$	−15.3838			−0.730906			−0.365453	+	0.930830i	$0.619086\pi$
$444$	−4.50337	+	3.13586i	−0.213721	+	0.148821i
$445$	1.90516	+	15.9819i	0.0903135	+	0.757616i
$446$	−35.7958	−	26.0071i	−1.69498	−	1.23147i
$447$	12.6418	+	9.57794i	0.597936	+	0.453021i
$448$	16.3783	−	29.0876i	0.773803	−	1.37426i
$449$		−	22.6874i		−	1.07068i	−0.844636	−	0.535342i	$-0.820183\pi$
$449$		−	22.6874i		−	1.07068i	0.844636	−	0.535342i	$-0.179817\pi$
$450$	22.2949	−	24.1589i	1.05099	−	1.13886i
$451$		−	2.78371i		−	0.131080i
$452$	−17.4031	+	53.5611i	−0.818571	+	2.51930i
$453$	−18.3010	+	24.1553i	−0.859858	+	1.13491i
$454$	17.4123	−	23.9659i	0.817199	−	1.12478i
$455$	14.0728	+	23.0410i	0.659743	+	1.08018i
$456$	−13.8235	+	9.62580i	−0.647344	+	0.450769i
$457$		−	27.4568i		−	1.28438i	−0.766547	−	0.642188i	$-0.778027\pi$
$457$		−	27.4568i		−	1.28438i	0.766547	−	0.642188i	$-0.221973\pi$
$458$	8.55100	+	11.7694i	0.399562	+	0.549950i
$459$	−3.70558	−	14.2742i	−0.172962	−	0.666263i
$460$	−1.68282	+	3.01081i	−0.0784621	+	0.140380i
$461$	−5.28271	+	16.2585i	−0.246040	+	0.757234i	0.749423	+	0.662091i	$0.230331\pi$
$461$	−5.28271	+	16.2585i	−0.246040	+	0.757234i	−0.995464	+	0.0951429i	$0.969669\pi$
$462$	0.287459	+	3.00275i	0.0133738	+	0.139701i
$463$	28.7673	−	9.34705i	1.33693	−	0.434394i	0.448653	−	0.893706i	$-0.351904\pi$
$463$	28.7673	−	9.34705i	1.33693	−	0.434394i	0.888275	+	0.459312i	$0.151904\pi$
$464$	3.76834	+	1.22441i	0.174941	+	0.0568417i
$465$	−27.8818	+	12.2096i	−1.29299	+	0.566207i
$466$	1.40461	+	4.32293i	0.0650671	+	0.200256i
$467$	5.09919	+	7.01843i	0.235962	+	0.324774i	0.910533	−	0.413436i	$-0.135671\pi$
$467$	5.09919	+	7.01843i	0.235962	+	0.324774i	−0.674571	+	0.738210i	$0.735671\pi$
$468$	−38.3469	−	1.53895i	−1.77259	−	0.0711380i
$469$	13.2792	+	28.9809i	0.613176	+	1.33821i
$470$	15.2262	+	8.51031i	0.702331	+	0.392551i
$471$	−9.79733	+	12.9313i	−0.451437	+	0.595845i
$472$	−14.9317	−	10.8485i	−0.687288	−	0.499344i
$473$	−0.458619	+	1.41148i	−0.0210873	+	0.0649001i
$474$	1.17723	−	58.6911i	0.0540720	−	2.69577i
$475$	27.5434	+	2.12128i	1.26378	+	0.0973312i
$476$	4.15419	−	20.6349i	0.190407	−	0.945801i
$477$	−1.10987	+	3.00065i	−0.0508172	+	0.137390i
$478$	−24.9044	+	34.2780i	−1.13910	+	1.56784i
$479$	−3.26421	−	2.37159i	−0.149146	−	0.108361i	0.510710	−	0.859753i	$-0.329383\pi$
$479$	−3.26421	−	2.37159i	−0.149146	−	0.108361i	−0.659856	+	0.751392i	$0.729383\pi$
$480$	6.09124	−	27.8177i	0.278026	−	1.26970i
$481$	−3.03181	−	4.17293i	−0.138239	−	0.190269i
$482$		−	23.5517i		−	1.07275i
$483$	1.00425	+	2.31310i	0.0456948	+	0.105250i
$484$	9.45035	+	29.0852i	0.429561	+	1.32205i
$485$	22.9015	+	4.53545i	1.03990	+	0.205944i
$486$	31.2717	+	13.7569i	1.41851	+	0.624026i
$487$	12.0439	−	3.91330i	0.545761	−	0.177329i	−0.0231433	−	0.999732i	$-0.507367\pi$
$487$	12.0439	−	3.91330i	0.545761	−	0.177329i	0.568905	+	0.822404i	$0.307367\pi$
$488$	0.376738	−	0.122410i	0.0170541	−	0.00554122i
$489$	10.9172	−	31.4397i	0.493691	−	1.42175i
$490$	9.43656	−	32.9807i	0.426300	−	1.48992i
$491$	−14.1025	+	4.58218i	−0.636437	+	0.206791i	−0.609424	−	0.792844i	$-0.708599\pi$
$491$	−14.1025	+	4.58218i	−0.636437	+	0.206791i	−0.0270124	+	0.999635i	$0.508599\pi$
$492$	−25.7147	−	36.9285i	−1.15931	−	1.66487i
$493$	6.43117			0.289645
$494$	−32.4806	−	44.7057i	−1.46137	−	2.01140i
$495$	0.771026	+	1.86144i	0.0346551	+	0.0836654i
$496$	−8.07745	+	11.1177i	−0.362688	+	0.499197i
$497$	16.6426	−	15.3130i	0.746523	−	0.686883i
$498$	12.1636	−	35.0292i	0.545063	−	1.56970i
$499$	4.76429			0.213279			0.106639	−	0.994298i	$-0.465991\pi$
$499$	4.76429			0.213279			0.106639	+	0.994298i	$0.465991\pi$
$500$	24.5633	−	19.4644i	1.09850	−	0.870476i
$501$	23.2346	+	0.466041i	1.03805	+	0.0208212i
$502$	−14.0678	+	43.2961i	−0.627875	+	1.93240i
$503$	−2.26139	+	3.11253i	−0.100830	+	0.138781i	−0.856451	−	0.516229i	$-0.827335\pi$
$503$	−2.26139	+	3.11253i	−0.100830	+	0.138781i	0.755621	+	0.655010i	$0.227335\pi$
$504$	9.04017	+	10.6525i	0.402681	+	0.474501i
$505$	12.2929	−	5.67962i	0.547029	−	0.252740i
$506$	−0.212908	−	0.293042i	−0.00946491	−	0.0130273i
$507$	0.271853	−	13.5533i	0.0120734	−	0.601924i
$508$	17.9943	+	24.7670i	0.798368	+	1.09886i
$509$	−2.94120	−	9.05209i	−0.130367	−	0.401227i	0.864474	−	0.502677i	$-0.167652\pi$
$509$	−2.94120	−	9.05209i	−0.130367	−	0.401227i	−0.994841	+	0.101450i	$0.967652\pi$
$510$	−2.37126	−	23.9733i	−0.105001	−	1.06155i
$511$	−12.1826	+	21.6361i	−0.538928	+	0.957125i
$512$	−5.87522	−	18.0821i	−0.259650	−	0.799122i
$513$	7.21367	+	27.7877i	0.318492	+	1.22686i
$514$	−38.3490	−	12.4604i	−1.69150	−	0.549603i
$515$	19.5396	+	3.86966i	0.861018	+	0.170517i
$516$	6.95464	+	22.9611i	0.306161	+	1.01081i
$517$	−0.864886	+	0.628376i	−0.0380376	+	0.0276360i
$518$	−1.29343	+	6.42481i	−0.0568301	+	0.282290i
$519$	−22.1549	+	15.4273i	−0.972494	+	0.677183i
$520$	−17.6202	−	3.48953i	−0.772697	−	0.153026i
$521$	−12.1364	−	8.81760i	−0.531705	−	0.386306i	0.289290	−	0.957241i	$-0.406581\pi$
$521$	−12.1364	−	8.81760i	−0.531705	−	0.386306i	−0.820995	+	0.570935i	$0.806581\pi$
$522$	−9.23342	+	11.6923i	−0.404136	+	0.511758i
$523$	7.28242	−	22.4130i	0.318438	−	0.980052i	−0.655878	−	0.754867i	$-0.727701\pi$
$523$	7.28242	−	22.4130i	0.318438	−	0.980052i	0.974316	−	0.225185i	$-0.0722986\pi$
$524$	−13.8439			−0.604774
$525$	−0.425626	−	22.9089i	−0.0185759	−	0.999827i
$526$	−10.3754			−0.452388
$527$	−6.89261	+	21.2133i	−0.300247	+	0.924065i
$528$	0.725050	+	0.549328i	0.0315537	+	0.0239064i
$529$	18.3624	+	13.3411i	0.798366	+	0.580047i
$530$	−2.54981	+	4.56198i	−0.110757	+	0.198160i
$531$	−26.1693	+	17.4540i	−1.13565	+	0.757438i
$532$	−8.08698	+	40.1702i	−0.350615	+	1.74160i
$533$	34.2188	−	24.8614i	1.48218	−	1.07687i
$534$	−26.1501	+	7.92053i	−1.13162	+	0.342755i
$535$	−5.94832	+	2.74826i	−0.257168	+	0.118818i
$536$	−20.1708	−	6.55391i	−0.871248	−	0.283086i
$537$	−11.2345	−	37.0914i	−0.484806	−	1.60061i
$538$	−8.53734	−	26.2752i	−0.368071	−	1.13281i
$539$	1.59238	+	1.37281i	0.0685885	+	0.0591311i
$540$	27.4235	+	17.5713i	1.18012	+	0.756148i
$541$	4.19009	+	12.8958i	0.180146	+	0.554432i	0.999831	−	0.0183821i	$-0.00585154\pi$
$541$	4.19009	+	12.8958i	0.180146	+	0.554432i	−0.819685	+	0.572815i	$0.805852\pi$
$542$	34.1811	+	47.0463i	1.46821	+	2.02081i
$543$	−25.5387	−	0.512258i	−1.09597	−	0.0219831i
$544$	−12.2658	−	16.8825i	−0.525893	−	0.723829i
$545$	2.74790	+	2.96767i	0.117707	+	0.127121i
$546$	−34.3440	+	30.3512i	−1.46979	+	1.29891i
$547$	5.99272	−	8.24827i	0.256230	−	0.352670i	−0.661451	−	0.749988i	$-0.730059\pi$
$547$	5.99272	−	8.24827i	0.256230	−	0.352670i	0.917681	+	0.397318i	$0.130059\pi$
$548$	−1.31116	+	4.03535i	−0.0560102	+	0.172382i
$549$	0.0270725	−	0.674581i	0.00115543	−	0.0287904i
$550$	0.773688	+	3.19902i	0.0329902	+	0.136407i
$551$	−12.5196			−0.533353
$552$	−1.58487	−	0.550331i	−0.0674565	−	0.0234236i
$553$	−27.7036	−	30.1091i	−1.17808	−	1.28037i
$554$	29.7222	−	40.9092i	1.26278	−	1.73806i
$555$	0.430882	+	4.35618i	0.0182899	+	0.184909i
$556$	22.5096	+	30.9819i	0.954622	+	1.31392i
$557$	15.8017			0.669538			0.334769	−	0.942300i	$-0.391342\pi$
$557$	15.8017			0.669538			0.334769	+	0.942300i	$0.391342\pi$
$558$	−28.6713	−	42.9878i	−1.21375	−	1.81982i
$559$	−21.4466	+	6.96842i	−0.907094	+	0.294733i
$560$	−5.39210	−	8.82832i	−0.227858	−	0.373064i
$561$	1.39476	+	0.484316i	0.0588867	+	0.0204479i
$562$	−4.69364	+	1.52505i	−0.197989	+	0.0643306i
$563$	−34.4780	+	11.2026i	−1.45307	+	0.472132i	−0.925947	−	0.377655i	$-0.876731\pi$
$563$	−34.4780	+	11.2026i	−1.45307	+	0.472132i	−0.527127	+	0.849787i	$0.676731\pi$
$564$	−5.66884	+	16.3254i	−0.238701	+	0.687423i
$565$	30.5221	+	32.9632i	1.28407	+	1.38677i
$566$	−19.4466	−	59.8506i	−0.817404	−	2.51571i
$567$	22.3727	−	8.15234i	0.939567	−	0.342366i
$568$			15.0463i			0.631329i
$569$	12.9814	+	17.8674i	0.544208	+	0.749038i	0.989212	−	0.146490i	$-0.0467977\pi$
$569$	12.9814	+	17.8674i	0.544208	+	0.749038i	−0.445004	+	0.895529i	$0.646798\pi$
$570$	4.61616	+	46.6689i	0.193349	+	1.95475i
$571$	−5.51138	−	4.00425i	−0.230644	−	0.167573i	0.466461	−	0.884542i	$-0.345529\pi$
$571$	−5.51138	−	4.00425i	−0.230644	−	0.167573i	−0.697105	+	0.716969i	$0.745529\pi$
$572$	2.25841	−	3.10844i	0.0944290	−	0.129970i
$573$	7.47053	−	21.5140i	0.312086	−	0.898760i
$574$	−52.6846	−	10.6064i	−2.19901	−	0.442702i
$575$	1.44153	+	2.34354i	0.0601158	+	0.0977322i
$576$	37.8208	+	1.51784i	1.57587	+	0.0632432i
$577$	3.52857	−	10.8598i	0.146896	−	0.452100i	−0.850354	−	0.526212i	$-0.823612\pi$
$577$	3.52857	−	10.8598i	0.146896	−	0.452100i	0.997250	+	0.0741113i	$0.0236120\pi$
$578$	15.8600	+	11.5230i	0.659689	+	0.479292i
$579$	−16.2454	−	12.3082i	−0.675137	−	0.511512i
$580$	−10.4218	+	9.65001i	−0.432741	+	0.400695i
$581$	−10.7659	−	23.4959i	−0.446646	−	0.974774i
$582$	−0.794803	+	39.6251i	−0.0329456	+	1.64251i
$583$	−0.188271	−	0.259132i	−0.00779737	−	0.0107322i
$584$	−5.10486	−	15.7112i	−0.211241	−	0.650132i
$585$	−15.9957	+	26.1024i	−0.661340	+	1.07920i
$586$	60.4076	+	19.6276i	2.49542	+	0.810810i
$587$	19.9739	−	6.48991i	0.824411	−	0.267867i	0.133722	−	0.991019i	$-0.457307\pi$
$587$	19.9739	−	6.48991i	0.824411	−	0.267867i	0.690689	+	0.723151i	$0.257307\pi$
$588$	33.8057	+	3.50193i	1.39412	+	0.144417i
$589$	13.4179	−	41.2960i	0.552875	−	1.70157i
$590$	−46.6462	+	21.5516i	−1.92039	+	0.887265i
$591$	30.6387	−	9.28008i	1.26031	−	0.381731i
$592$	1.16166	+	1.59889i	0.0477439	+	0.0657139i
$593$			30.2720i			1.24312i	0.783366	+	0.621561i	$0.213501\pi$
$593$			30.2720i			1.24312i	−0.783366	+	0.621561i	$0.786499\pi$
$594$	−2.88301	+	1.84041i	−0.118291	+	0.0755131i
$595$	−12.7516	−	10.9234i	−0.522763	−	0.447818i
$596$	−15.0876	+	20.7663i	−0.618013	+	0.850622i
$597$	−28.0997	−	21.2895i	−1.15004	−	0.871321i
$598$	1.70074	−	5.23434i	0.0695484	−	0.214048i
$599$			41.6105i			1.70016i	0.526653	+	0.850080i	$0.323447\pi$
$599$			41.6105i			1.70016i	−0.526653	+	0.850080i	$0.676553\pi$
$600$	11.4078	+	10.1116i	0.465721	+	0.412805i
$601$			25.8395i			1.05401i	0.849861	+	0.527007i	$0.176686\pi$
$601$			25.8395i			1.05401i	−0.849861	+	0.527007i	$0.823314\pi$
$602$	24.9664	+	14.0578i	1.01755	+	0.572953i
$603$	−22.4020	+	28.3678i	−0.912282	+	1.15522i
$604$	−39.6793	−	28.8287i	−1.61453	−	1.17302i
$605$	23.9303	+	4.73919i	0.972904	+	0.192675i
$606$	13.1366	+	18.8653i	0.533637	+	0.766349i
$607$	27.0197			1.09670			0.548348	−	0.836250i	$-0.315257\pi$
$607$	27.0197			1.09670			0.548348	+	0.836250i	$0.315257\pi$
$608$	23.8780	+	32.8652i	0.968379	+	1.33286i
$609$	0.989563	+	10.3368i	0.0400991	+	0.418869i
$610$	0.214246	−	1.08183i	0.00867458	−	0.0438018i
$611$	−15.4486	−	5.01956i	−0.624985	−	0.203070i
$612$	22.9766	−	6.45922i	0.928774	−	0.261099i
$613$	−13.6664	+	4.44047i	−0.551979	+	0.179349i	−0.571709	−	0.820457i	$-0.693719\pi$
$613$	−13.6664	+	4.44047i	−0.551979	+	0.179349i	0.0197300	+	0.999805i	$0.493719\pi$
$614$	8.95079	−	27.5477i	0.361224	−	1.11173i
$615$	−35.7215	+	3.53331i	−1.44043	+	0.142477i
$616$	−1.38945	+	0.161194i	−0.0559826	+	0.00649470i
$617$	−1.54495	+	1.12247i	−0.0621972	+	0.0451889i	−0.618449	−	0.785825i	$-0.712239\pi$
$617$	−1.54495	+	1.12247i	−0.0621972	+	0.0451889i	0.556252	+	0.831014i	$0.312239\pi$
$618$	−0.678128	+	33.8082i	−0.0272783	+	1.35997i
$619$	−13.1123	−	18.0475i	−0.527028	−	0.725391i	0.459646	−	0.888102i	$-0.347976\pi$
$619$	−13.1123	−	18.0475i	−0.527028	−	0.725391i	−0.986674	+	0.162711i	$0.947976\pi$
$620$	−20.6611	−	44.7188i	−0.829770	−	1.79595i
$621$	−1.81673	+	2.20800i	−0.0729027	+	0.0886041i
$622$	40.9953	+	29.7848i	1.64376	+	1.19426i
$623$	−9.34369	+	16.5942i	−0.374347	+	0.664833i
$624$	−0.277177	+	13.8187i	−0.0110960	+	0.553192i
$625$	−3.99359	−	24.6790i	−0.159744	−	0.987159i
$626$	−7.36409			−0.294328
$627$	−2.71518	−	0.942822i	−0.108434	−	0.0376527i
$628$	−21.2420	−	15.4332i	−0.847648	−	0.615852i
$629$	2.59516	+	1.88549i	0.103476	+	0.0751795i
$630$	38.1674	−	7.50010i	1.52062	−	0.298811i
$631$	11.7988	−	8.57231i	0.469701	−	0.341258i	−0.327623	−	0.944808i	$-0.606248\pi$
$631$	11.7988	−	8.57231i	0.469701	−	0.341258i	0.797325	+	0.603550i	$0.206248\pi$
$632$	27.2211			1.08280
$633$	−22.4081	−	32.1800i	−0.890643	−	1.27904i
$634$	−6.35395	−	19.5555i	−0.252348	−	0.776646i
$635$	24.2487	−	2.89062i	0.962279	−	0.114711i
$636$	−4.89133	−	1.69847i	−0.193954	−	0.0673486i
$637$	−2.65371	+	31.8349i	−0.105144	+	1.26134i
$638$	−0.460925	−	1.41858i	−0.0182482	−	0.0561622i
$639$	24.0512	+	8.89594i	0.951451	+	0.351918i
$640$	28.3975	+	5.62388i	1.12251	+	0.222303i
$641$	23.1298	−	7.51532i	0.913572	−	0.296837i	0.185745	−	0.982598i	$-0.440530\pi$
$641$	23.1298	−	7.51532i	0.913572	−	0.296837i	0.727827	+	0.685761i	$0.240530\pi$
$642$	−6.35654	−	9.12854i	−0.250873	−	0.360275i
$643$	6.65789			0.262561			0.131281	−	0.991345i	$-0.458091\pi$
$643$	6.65789			0.262561			0.131281	+	0.991345i	$0.458091\pi$
$644$	−3.71020	+	1.70003i	−0.146202	+	0.0669905i
$645$	18.6947	+	4.09357i	0.736104	+	0.161184i
$646$	27.8026	+	20.1998i	1.09388	+	0.794750i
$647$	−5.87802	+	8.09041i	−0.231089	+	0.318067i	−0.908776	−	0.417283i	$-0.862982\pi$
$647$	−5.87802	+	8.09041i	−0.231089	+	0.318067i	0.677687	+	0.735350i	$0.262982\pi$
$648$	−6.08712	+	14.6260i	−0.239125	+	0.574563i
$649$		−	3.14925i		−	0.123619i
$650$	−32.4141	+	38.0810i	−1.27139	+	1.49366i
$651$	−35.1567	−	7.81440i	−1.37790	−	0.306271i
$652$	51.2265	+	16.6445i	2.00618	+	0.651848i
$653$	−21.2243	−	15.4204i	−0.830573	−	0.603447i	0.0891484	−	0.996018i	$-0.471585\pi$
$653$	−21.2243	−	15.4204i	−0.830573	−	0.603447i	−0.919721	+	0.392572i	$0.871585\pi$
$654$	−4.14633	+	5.47268i	−0.162134	+	0.213999i
$655$	−5.38787	+	9.63966i	−0.210521	+	0.376653i
$656$	−13.1112	+	9.52583i	−0.511906	+	0.371921i
$657$	−28.1321	−	1.12901i	−1.09754	−	0.0440468i
$658$	8.59732	+	18.7631i	0.335158	+	0.731460i
$659$	1.02209	−	0.332097i	0.0398150	−	0.0129367i	−0.289042	−	0.957316i	$-0.593337\pi$
$659$	1.02209	−	0.332097i	0.0398150	−	0.0129367i	0.328857	+	0.944380i	$0.393337\pi$
$660$	−2.98694	+	1.30800i	−0.116267	+	0.0509138i
$661$	3.28096	+	1.06605i	0.127615	+	0.0414645i	0.372128	−	0.928181i	$-0.378628\pi$
$661$	3.28096	+	1.06605i	0.127615	+	0.0414645i	−0.244513	+	0.969646i	$0.578628\pi$
$662$	−1.23542	−	3.80223i	−0.0480160	−	0.147778i
$663$	6.50314	+	21.4705i	0.252561	+	0.833844i
$664$	16.3532	+	5.31349i	0.634629	+	0.206204i
$665$	24.8235	+	21.2647i	0.962616	+	0.824611i
$666$	−7.15390	+	2.01112i	−0.277208	+	0.0779291i
$667$	−0.732924	−	1.00878i	−0.0283789	−	0.0390602i
$668$			37.6107i			1.45520i
$669$	−19.9822	−	28.6962i	−0.772557	−	1.10946i
$670$	−43.3258	+	40.1173i	−1.67382	+	1.54987i
$671$	0.0546822	+	0.0397290i	0.00211098	+	0.00153372i
$672$	25.2478	−	22.3125i	0.973956	−	0.860725i
$673$	−22.3114	−	7.24941i	−0.860040	−	0.279444i	−0.154395	−	0.988009i	$-0.549343\pi$
$673$	−22.3114	−	7.24941i	−0.860040	−	0.279444i	−0.705645	+	0.708565i	$0.749343\pi$
$674$			23.7914i			0.916409i
$675$	22.9079	−	12.2567i	0.881726	−	0.471762i
$676$	21.9392			0.843816
$677$	30.5820	+	9.93669i	1.17536	+	0.381898i	0.830641	−	0.556808i	$-0.187974\pi$
$677$	30.5820	+	9.93669i	1.17536	+	0.381898i	0.344720	+	0.938706i	$0.387974\pi$
$678$	−46.0550	+	60.7873i	−1.76873	+	2.33452i
$679$	18.7040	+	20.3280i	0.717794	+	0.780118i
$680$	11.0924	−	1.32229i	0.425372	−	0.0507075i
$681$	19.2126	−	13.3785i	0.736230	−	0.512664i
$682$	5.17321			0.198092
$683$	15.2288	−	11.0644i	0.582713	−	0.423366i	−0.256988	−	0.966415i	$-0.582730\pi$
$683$	15.2288	−	11.0644i	0.582713	−	0.423366i	0.839701	+	0.543049i	$0.182730\pi$
$684$	−44.7287	+	12.5742i	−1.71024	+	0.480787i
$685$	2.29957	+	2.48348i	0.0878620	+	0.0948889i
$686$	32.0490	−	24.9068i	1.22364	−	0.950944i
$687$	3.33286	+	11.0036i	0.127156	+	0.419814i
$688$	8.21742	−	2.67000i	0.313286	−	0.101793i
$689$	1.50393	−	4.62863i	0.0572953	−	0.176337i
$690$	−3.49017	+	3.10405i	−0.132869	+	0.118169i
$691$	24.9463	−	8.10553i	0.949000	−	0.308349i	0.206691	−	0.978406i	$-0.433731\pi$
$691$	24.9463	−	8.10553i	0.949000	−	0.308349i	0.742309	+	0.670057i	$0.233731\pi$
$692$	−25.6817	−	35.3479i	−0.976273	−	1.34372i
$693$	−0.563830	+	2.31631i	−0.0214181	+	0.0879894i
$694$	−42.6729	+	31.0037i	−1.61984	+	1.17688i
$695$	30.3334	−	3.61597i	1.15061	−	0.137162i
$696$	−5.50661	−	4.17203i	−0.208727	−	0.158141i
$697$	−15.4614	+	21.2808i	−0.585642	+	0.806068i
$698$	−2.40163	−	0.780336i	−0.0909030	−	0.0295362i
$699$	−0.0720395	+	3.59154i	−0.00272478	+	0.135845i
$700$	37.0548	−	1.43222i	1.40054	−	0.0541330i
$701$			14.2919i			0.539799i	0.962889	+	0.269899i	$0.0869905\pi$
$701$			14.2919i			0.539799i	−0.962889	+	0.269899i	$0.913010\pi$
$702$	−48.3715	−	19.0026i	−1.82567	−	0.717209i
$703$	−5.05201	−	3.67050i	−0.190540	−	0.138436i
$704$	−2.22743	+	3.06579i	−0.0839494	+	0.115546i
$705$	9.16130	+	10.3009i	0.345035	+	0.387954i
$706$	12.2432	+	16.8513i	0.460779	+	0.634207i
$707$	15.7075	+	3.16220i	0.590741	+	0.118927i
$708$	−29.0913	−	41.7777i	−1.09332	−	1.57010i
$709$	−9.64890	−	29.6962i	−0.362372	−	1.11527i	−0.951610	−	0.307307i	$-0.900572\pi$
$709$	−9.64890	−	29.6962i	−0.362372	−	1.11527i	0.589239	−	0.807959i	$-0.299428\pi$
$710$	36.5658	+	20.4376i	1.37229	+	0.767010i
$711$	16.0941	−	43.5124i	0.603577	−	1.63184i
$712$	−3.91527	−	12.0500i	−0.146731	−	0.451591i
$713$	4.11300	−	1.33639i	0.154033	−	0.0500483i
$714$	14.4804	−	24.5519i	0.541916	−	0.918831i
$715$	−1.28549	−	2.78232i	−0.0480748	−	0.104053i
$716$	59.6524	−	19.3823i	2.22932	−	0.724349i
$717$	−27.4795	+	19.1350i	−1.02624	+	0.714609i
$718$		−	28.1097i		−	1.04904i
$719$	18.6554	−	13.5540i	0.695730	−	0.505478i	−0.182809	−	0.983149i	$-0.558519\pi$
$719$	18.6554	−	13.5540i	0.695730	−	0.505478i	0.878539	+	0.477671i	$0.158519\pi$
$720$	6.12886	−	10.0013i	0.228409	−	0.372727i
$721$	15.9583	+	17.3439i	0.594318	+	0.645921i
$722$	−20.4356	−	14.8473i	−0.760533	−	0.552560i
$723$	6.10560	−	17.5832i	0.227070	−	0.653926i
$724$		−	41.3405i		−	1.53641i
$725$	2.66338	+	11.0125i	0.0989154	+	0.408992i
$726$	−0.830507	+	41.4051i	−0.0308230	+	1.53669i
$727$	14.7435	−	45.3759i	0.546807	−	1.68290i	−0.169847	−	0.985470i	$-0.554327\pi$
$727$	14.7435	−	45.3759i	0.546807	−	1.68290i	0.716654	−	0.697429i	$-0.245673\pi$
$728$	−14.3907	−	15.6402i	−0.533355	−	0.579664i
$729$	19.7804	+	18.3776i	0.732608	+	0.680651i
$730$	−45.1155	−	8.93475i	−1.66980	−	0.330690i
$731$	11.3457	−	8.24316i	0.419637	−	0.304884i
$732$	1.09241	+	0.0219116i	0.0403765	+	0.000809876i
$733$	2.10318	−	1.52805i	0.0776826	−	0.0564397i	−0.548266	−	0.836304i	$-0.684712\pi$
$733$	2.10318	−	1.52805i	0.0776826	−	0.0564397i	0.625949	+	0.779864i	$0.284712\pi$
$734$	−4.93402	−	15.1854i	−0.182118	−	0.560502i
$735$	15.5952	−	22.1764i	0.575236	−	0.817988i
$736$	−1.25029	+	3.84800i	−0.0460863	+	0.141839i
$737$	−1.11829	−	3.44175i	−0.0411929	−	0.126779i
$738$	−16.4915	−	58.6633i	−0.607062	−	2.15943i
$739$	9.12250	−	28.0762i	0.335577	−	1.03280i	−0.630861	−	0.775896i	$-0.717298\pi$
$739$	9.12250	−	28.0762i	0.335577	−	1.03280i	0.966437	−	0.256902i	$-0.0827019\pi$
$740$	−7.03468	+	0.838586i	−0.258600	+	0.0308270i
$741$	−12.6597	−	41.7967i	−0.465066	−	1.53544i
$742$	−5.62168	+	2.57588i	−0.206379	+	0.0945636i
$743$	−39.7204			−1.45720			−0.728600	−	0.684940i	$-0.759829\pi$
$743$	−39.7204			−1.45720			−0.728600	+	0.684940i	$0.759829\pi$
$744$	19.6632	−	13.6922i	0.720889	−	0.501981i
$745$	8.58791	+	18.5876i	0.314637	+	0.680998i
$746$	−5.24519	+	7.21939i	−0.192040	+	0.264321i
$747$	18.1622	−	22.9988i	0.664519	−	0.841482i
$748$	−0.738397	+	2.27255i	−0.0269985	+	0.0830928i
$749$	−7.60055	−	1.53013i	−0.277718	−	0.0559097i
$750$	40.0688	−	13.9887i	1.46310	−	0.510793i
$751$	−25.8070			−0.941711			−0.470856	−	0.882210i	$-0.656055\pi$
$751$	−25.8070			−0.941711			−0.470856	+	0.882210i	$0.656055\pi$
$752$	5.91925	+	1.92328i	0.215853	+	0.0701349i
$753$	−21.7269	+	28.6770i	−0.791772	+	1.04505i
$754$	13.3214	−	18.3353i	0.485136	−	0.667733i
$755$	−35.5163	+	16.4093i	−1.29257	+	0.597197i
$756$	13.9173	+	35.9364i	0.506168	+	1.30699i
$757$			9.39690i			0.341536i	0.985311	+	0.170768i	$0.0546249\pi$
$757$			9.39690i			0.341536i	−0.985311	+	0.170768i	$0.945375\pi$
$758$	17.0194	−	12.3653i	0.618171	−	0.449127i
$759$	−0.0829834	−	0.273974i	−0.00301211	−	0.00994464i
$760$	−21.5936	+	2.57411i	−0.783281	+	0.0933729i
$761$	−3.18153	+	9.79174i	−0.115330	+	0.354950i	−0.992016	−	0.126114i	$-0.959750\pi$
$761$	−3.18153	+	9.79174i	−0.115330	+	0.354950i	0.876685	+	0.481064i	$0.159750\pi$
$762$	12.0175	+	39.6764i	0.435347	+	1.43732i
$763$	0.551484	+	4.75365i	0.0199651	+	0.172094i
$764$	35.0539	+	11.3897i	1.26821	+	0.412065i
$765$	4.44456	−	18.5127i	0.160694	−	0.669328i
$766$	−52.4199	+	17.0323i	−1.89401	+	0.615401i
$767$	38.7122	−	28.1260i	1.39782	−	1.01557i
$768$	−0.109043	+	5.43637i	−0.00393475	+	0.196168i
$769$	7.38461	+	10.1640i	0.266296	+	0.366525i	0.921135	−	0.389244i	$-0.127264\pi$
$769$	7.38461	+	10.1640i	0.266296	+	0.366525i	−0.654839	+	0.755768i	$0.727264\pi$
$770$	−1.49557	+	3.59562i	−0.0538967	+	0.129577i
$771$	−25.4003	−	19.2444i	−0.914771	−	0.693068i
$772$	19.3885	−	26.6860i	0.697807	−	0.960449i
$773$	6.85717	+	2.22803i	0.246635	+	0.0801367i	0.429726	−	0.902959i	$-0.358610\pi$
$773$	6.85717	+	2.22803i	0.246635	+	0.0801367i	−0.183091	+	0.983096i	$0.558610\pi$
$774$	−1.30279	+	32.4623i	−0.0468277	+	1.16683i
$775$	−39.1792	−	3.01742i	−1.40736	−	0.108389i
$776$	−18.3782			−0.659740
$777$	−2.63123	+	4.46132i	−0.0943950	+	0.160049i
$778$	34.6553	−	47.6989i	1.24245	−	1.71009i
$779$	30.0988	−	41.4275i	1.07840	−	1.48429i
$780$	−42.7550	−	25.0352i	−1.53088	−	0.896403i
$781$	−2.07703	+	1.50905i	−0.0743221	+	0.0539981i
$782$			3.42278i			0.122398i
$783$	−9.92462	+	6.33553i	−0.354677	+	0.226413i
$784$	1.01679	−	12.1978i	0.0363138	−	0.435635i
$785$	−19.0134	+	8.78462i	−0.678617	+	0.313537i
$786$	−17.7098	−	6.14957i	−0.631688	−	0.219348i
$787$	−10.7933	−	33.2183i	−0.384738	−	1.18410i	−0.936670	−	0.350213i	$-0.886109\pi$
$787$	−10.7933	−	33.2183i	−0.384738	−	1.18410i	0.551932	−	0.833889i	$-0.313891\pi$
$788$	16.0104	+	49.2748i	0.570345	+	1.75534i
$789$	−7.74605	−	2.68975i	−0.275767	−	0.0957575i
$790$	36.9748	−	66.1532i	1.31550	−	2.35362i
$791$	6.12556	+	52.8007i	0.217800	+	1.87738i
$792$	−0.880056	−	1.31950i	−0.0312714	−	0.0468863i
$793$			1.02700i			0.0364699i
$794$	60.5346	−	43.9809i	2.14829	−	1.56082i
$795$	−3.08630	+	2.74486i	−0.109460	+	0.0973501i
$796$	33.5362	−	46.1587i	1.18866	−	1.63605i
$797$	10.1307	−	13.9437i	0.358848	−	0.493911i	−0.590980	−	0.806686i	$-0.701259\pi$
$797$	10.1307	−	13.9437i	0.358848	−	0.493911i	0.949827	+	0.312775i	$0.101259\pi$
$798$	−28.1891	+	47.7953i	−0.997884	+	1.69193i
$799$	10.1020			0.357382
$800$	23.8291	−	27.9951i	0.842485	−	0.989776i
$801$	−21.5765	−	0.865913i	−0.762366	−	0.0305955i
$802$	71.1814	+	23.1282i	2.51350	+	0.816686i
$803$	1.65682	−	2.28042i	0.0584680	−	0.0804743i
$804$	−46.6285	−	35.3277i	−1.64446	−	1.24591i
$805$	−0.260211	+	3.24507i	−0.00917123	+	0.114374i
$806$	46.2020	+	63.5917i	1.62740	+	2.23992i
$807$	0.437864	−	21.8298i	0.0154135	−	0.768445i
$808$	−8.62409	+	6.26577i	−0.303394	+	0.220429i
$809$	10.7648	−	3.49770i	0.378470	−	0.122973i	−0.113603	−	0.993526i	$-0.536239\pi$
$809$	10.7648	−	3.49770i	0.378470	−	0.122973i	0.492073	+	0.870554i	$0.336239\pi$
$810$	27.2761	+	34.6597i	0.958385	+	1.21782i
$811$	−29.9718	−	9.73841i	−1.05245	−	0.341962i	−0.268821	−	0.963190i	$-0.586634\pi$
$811$	−29.9718	−	9.73841i	−1.05245	−	0.341962i	−0.783630	+	0.621228i	$0.786634\pi$
$812$	−16.6937	+	1.93669i	−0.585835	+	0.0679643i
$813$	13.3225	+	43.9850i	0.467241	+	1.54262i
$814$	0.229904	−	0.707573i	0.00805814	−	0.0248004i
$815$	31.5264	−	29.1917i	1.10432	−	1.02254i
$816$	−2.49173	−	8.22657i	−0.0872279	−	0.287988i
$817$	−22.0868	+	16.0470i	−0.772720	+	0.561414i
$818$		−	13.0761i		−	0.457196i
$819$	−33.5088	+	13.7562i	−1.17089	+	0.480679i
$820$	−6.87657	−	57.6857i	−0.240140	−	2.01447i
$821$	−25.1940	+	34.6765i	−0.879276	+	1.21022i	0.0973454	+	0.995251i	$0.468965\pi$
$821$	−25.1940	+	34.6765i	−0.879276	+	1.21022i	−0.976621	+	0.214968i	$0.931035\pi$
$822$	−3.46984	+	4.57978i	−0.121024	+	0.159738i
$823$	−32.3993	−	10.5272i	−1.12937	−	0.366954i	−0.316032	−	0.948748i	$-0.602351\pi$
$823$	−32.3993	−	10.5272i	−1.12937	−	0.366954i	−0.813336	+	0.581795i	$0.802351\pi$
$824$	−15.6803			−0.546251
$825$	−0.251703	+	2.58889i	−0.00876318	+	0.0901337i
$826$	−59.6028	−	11.9991i	−2.07385	−	0.417503i
$827$	11.3349	−	34.8851i	0.394152	−	1.21307i	−0.535468	−	0.844555i	$-0.679865\pi$
$827$	11.3349	−	34.8851i	0.394152	−	1.21307i	0.929620	−	0.368519i	$-0.120135\pi$
$828$	−3.63170	−	2.86796i	−0.126210	−	0.0996683i
$829$	18.6186	−	25.6263i	0.646651	−	0.890039i	−0.352297	−	0.935888i	$-0.614599\pi$
$829$	18.6186	−	25.6263i	0.646651	−	0.890039i	0.998948	+	0.0458491i	$0.0145993\pi$
$830$	35.1258	−	32.5246i	1.21923	−	1.12894i
$831$	32.7954	−	22.8367i	1.13766	−	0.792195i
$832$	−57.5795			−1.99621
$833$	−4.54841	−	19.3392i	−0.157593	−	0.670064i
$834$	15.0330	+	49.6324i	0.520552	+	1.71863i
$835$	26.1887	+	14.6376i	0.906297	+	0.506554i
$836$	1.43744	−	4.42399i	0.0497150	−	0.153007i
$837$	−10.2611	−	39.5266i	−0.354675	−	1.36624i
$838$	2.20024	+	6.77165i	0.0760061	+	0.233923i
$839$	−11.4043	+	35.0987i	−0.393719	+	1.21174i	0.536236	+	0.844068i	$0.319846\pi$
$839$	−11.4043	+	35.0987i	−0.393719	+	1.21174i	−0.929955	+	0.367674i	$0.880154\pi$
$840$	3.83210	+	17.6253i	0.132220	+	0.608130i
$841$	7.37478	+	22.6972i	0.254303	+	0.782664i
$842$	28.0207	−	20.3582i	0.965656	−	0.701590i
$843$	−3.89953	−	0.0782171i	−0.134307	−	0.00269394i
$844$	51.3427	−	37.3027i	1.76729	−	1.28401i
$845$	8.53845	−	15.2765i	0.293732	−	0.525528i
$846$	−14.5037	+	18.3661i	−0.498648	+	0.631439i
$847$	19.5442	+	21.2412i	0.671547	+	0.729856i
$848$	−0.576243	+	1.77349i	−0.0197883	+	0.0609020i
$849$	0.997381	−	49.7247i	0.0342300	−	1.70655i
$850$	11.8534	−	28.7529i	0.406570	−	0.986217i
$851$		−	0.621952i		−	0.0213202i
$852$	−13.6138	+	39.2056i	−0.466401	+	1.34316i
$853$	9.69544	+	7.04415i	0.331966	+	0.241187i	0.741264	−	0.671213i	$-0.234227\pi$
$853$	9.69544	+	7.04415i	0.331966	+	0.241187i	−0.409299	+	0.912401i	$0.634227\pi$
$854$	0.960259	−	0.883544i	0.0328594	−	0.0302342i
$855$	−8.65226	+	36.0388i	−0.295901	+	1.23250i
$856$	4.17303	−	3.03188i	0.142631	−	0.103628i
$857$			4.22577i			0.144350i	0.997392	+	0.0721748i	$0.0229939\pi$
$857$			4.22577i			0.144350i	−0.997392	+	0.0721748i	$0.977006\pi$
$858$	4.26986	−	2.97326i	0.145771	−	0.101505i
$859$	−1.73445	+	0.563556i	−0.0591785	+	0.0192283i	−0.338457	−	0.940982i	$-0.609905\pi$
$859$	−1.73445	+	0.563556i	−0.0591785	+	0.0192283i	0.279278	+	0.960210i	$0.409905\pi$
$860$	−6.01700	+	30.3825i	−0.205178	+	1.03603i
$861$	−36.5836	−	21.5766i	−1.24677	−	0.735329i
$862$	−35.5712	+	11.5578i	−1.21156	+	0.393660i
$863$	14.5552	+	44.7962i	0.495463	+	1.52488i	0.816233	+	0.577722i	$0.196058\pi$
$863$	14.5552	+	44.7962i	0.495463	+	1.52488i	−0.320770	+	0.947157i	$0.603942\pi$
$864$	35.5601	+	13.9697i	1.20978	+	0.475259i
$865$	−34.6081	+	4.12554i	−1.17671	+	0.140273i
$866$	−17.1906	−	52.9073i	−0.584161	−	1.79786i
$867$	8.85351	+	12.7144i	0.300681	+	0.431804i
$868$	11.5033	−	57.1401i	0.390449	−	1.93946i
$869$	2.73011	+	3.75767i	0.0926126	+	0.127470i
$870$	−17.6186	+	7.71532i	−0.597328	+	0.261574i
$871$	32.3202	−	44.4850i	1.09513	−	1.50732i
$872$	−2.57578	−	1.87142i	−0.0872271	−	0.0633742i
$873$	−10.8659	+	29.3772i	−0.367755	+	0.994268i
$874$		−	6.66314i		−	0.225384i
$875$	13.4239	−	26.3590i	0.453812	−	0.891097i
$876$	0.913783	−	45.5568i	0.0308739	−	1.53922i
$877$	−50.2291	−	16.3204i	−1.69612	−	0.551102i	−0.708190	−	0.706022i	$-0.750488\pi$
$877$	−50.2291	−	16.3204i	−1.69612	−	0.551102i	−0.987927	+	0.154921i	$0.950488\pi$
$878$	26.0513	−	35.8565i	0.879187	−	1.21010i
$879$	40.0108	+	30.3138i	1.34953	+	1.02246i
$880$	0.492546	+	1.06607i	0.0166037	+	0.0359371i
$881$	−36.8094	+	26.7436i	−1.24014	+	0.901015i	−0.997608	−	0.0691287i	$-0.977978\pi$
$881$	−36.8094	+	26.7436i	−1.24014	+	0.901015i	−0.242532	+	0.970143i	$0.577978\pi$
$882$	41.6903	+	19.4966i	1.40379	+	0.656484i
$883$	9.80538	+	13.4960i	0.329977	+	0.454175i	0.941481	−	0.337067i	$-0.109435\pi$
$883$	9.80538	+	13.4960i	0.329977	+	0.454175i	−0.611503	+	0.791242i	$0.709435\pi$
$884$	−34.5300	+	11.2195i	−1.16137	+	0.377352i
$885$	−40.4122	+	3.99728i	−1.35844	+	0.134367i
$886$	10.4186	−	32.0652i	0.350020	−	1.07725i
$887$	20.1947	−	6.56166i	0.678072	−	0.220319i	0.0503212	−	0.998733i	$-0.483976\pi$
$887$	20.1947	−	6.56166i	0.678072	−	0.220319i	0.627751	+	0.778414i	$0.283976\pi$
$888$	−0.998912	−	3.29796i	−0.0335213	−	0.110672i
$889$	25.1777	+	14.1768i	0.844432	+	0.475474i
$890$	−34.6022	−	6.85267i	−1.15987	−	0.229702i
$891$	−2.62951	+	0.626615i	−0.0880920	+	0.0209924i
$892$	45.7843	−	33.2643i	1.53297	−	1.11377i
$893$	−19.6656			−0.658084
$894$	−28.5254	+	19.8632i	−0.954030	+	0.664326i
$895$	9.71986	−	49.0799i	0.324899	−	1.64056i
$896$	23.1927	+	25.2064i	0.774813	+	0.842087i
$897$	2.62670	−	3.46694i	0.0877030	−	0.115758i
$898$	47.2884	+	15.3649i	1.57803	+	0.512734i
$899$	17.8085			0.593947
$900$	20.5759	+	36.6691i	0.685864	+	1.22230i
$901$			3.02670i			0.100834i
$902$	5.80223	+	1.88526i	0.193193	+	0.0627723i
$903$	14.9950	+	16.9676i	0.499002	+	0.564647i
$904$	−28.6103	−	20.7866i	−0.951564	−	0.691352i
$905$	−28.7858	−	16.0891i	−0.956872	−	0.534821i
$906$	−37.9537	−	54.5048i	−1.26093	−	1.81080i
$907$			30.3376i			1.00734i	0.863895	+	0.503672i	$0.168018\pi$
$907$			30.3376i			1.00734i	−0.863895	+	0.503672i	$0.831982\pi$
$908$	22.2711	+	30.6535i	0.739091	+	1.01727i
$909$	4.91681	+	17.4900i	0.163080	+	0.580106i
$910$	−57.5562	+	13.7282i	−1.90797	+	0.455086i
$911$	−45.9707	−	14.9368i	−1.52308	−	0.494877i	−0.576428	−	0.817148i	$-0.695554\pi$
$911$	−45.9707	−	14.9368i	−1.52308	−	0.494877i	−0.946648	+	0.322271i	$0.895554\pi$
$912$	4.85066	+	16.0147i	0.160621	+	0.530300i
$913$	0.906642	+	2.79036i	0.0300055	+	0.0923473i
$914$	57.2296	+	18.5950i	1.89299	+	0.615068i
$915$	0.440407	−	0.752127i	0.0145594	−	0.0248645i
$916$	−17.6966	+	5.74998i	−0.584712	+	0.189985i
$917$	−11.8789	+	5.44295i	−0.392275	+	0.179742i
$918$	32.2620	+	1.94343i	1.06480	+	0.0641427i
$919$	−17.6871	+	12.8504i	−0.583444	+	0.423897i	−0.839964	−	0.542642i	$-0.817424\pi$
$919$	−17.6871	+	12.8504i	−0.583444	+	0.423897i	0.256520	+	0.966539i	$0.417424\pi$
$920$	−1.47155	−	1.58924i	−0.0485154	−	0.0523956i
$921$	13.8240	−	18.2461i	0.455517	−	0.601230i
$922$	−30.3107	−	22.0220i	−0.998229	−	0.725256i
$923$	−37.1000	−	12.0545i	−1.22116	−	0.396780i
$924$	−3.76629	−	0.837148i	−0.123902	−	0.0275401i
$925$	−2.15389	+	5.22469i	−0.0708194	+	0.171787i
$926$			66.2912i			2.17846i
$927$	−9.27081	+	25.0647i	−0.304493	+	0.823233i
$928$	−9.79315	+	13.4791i	−0.321476	+	0.442474i
$929$	31.5281	+	22.9065i	1.03440	+	0.751538i	0.969185	−	0.246333i	$-0.0792256\pi$
$929$	31.5281	+	22.9065i	1.03440	+	0.751538i	0.0652185	+	0.997871i	$0.479226\pi$
$930$	−6.56625	−	66.3842i	−0.215316	−	2.17682i
$931$	8.85442	+	37.6478i	0.290192	+	1.23386i
$932$	−5.81376			−0.190436
$933$	22.8847	+	32.8645i	0.749212	+	1.07593i
$934$	−18.0823	+	5.87528i	−0.591670	+	0.192245i
$935$	1.29503	+	1.39860i	0.0423519	+	0.0457391i
$936$	8.36012	−	22.6026i	0.273259	−	0.738788i
$937$	−7.37908	−	22.7105i	−0.241064	−	0.741919i	−0.996259	−	0.0864186i	$-0.972458\pi$
$937$	−7.37908	−	22.7105i	−0.241064	−	0.741919i	0.755195	−	0.655500i	$-0.227542\pi$
$938$	−69.3996	+	8.05124i	−2.26598	+	0.262882i
$939$	−5.49788	−	1.90909i	−0.179416	−	0.0623007i
$940$	−16.3704	+	15.1581i	−0.533943	+	0.494402i
$941$	14.4829	+	44.5738i	0.472129	+	1.45306i	0.849791	+	0.527120i	$0.176728\pi$
$941$	14.4829	+	44.5738i	0.472129	+	1.45306i	−0.377662	+	0.925944i	$0.623272\pi$
$942$	−20.3182	−	29.1787i	−0.662004	−	0.950695i
$943$	5.10012			0.166083
$944$	−14.8329	+	10.7767i	−0.482768	+	0.350752i
$945$	30.4393	+	4.29520i	0.990191	+	0.139723i
$946$	−2.63143	−	1.91184i	−0.0855550	−	0.0621594i
$947$	20.3312	+	14.7715i	0.660675	+	0.480009i	0.866891	−	0.498498i	$-0.166115\pi$
$947$	20.3312	+	14.7715i	0.660675	+	0.480009i	−0.206216	+	0.978507i	$0.566115\pi$
$948$	70.9290	+	24.6295i	2.30367	+	0.799927i
$949$	42.8292			1.39029
$950$	−23.0752	+	55.9735i	−0.748658	+	1.81602i
$951$	0.325882	−	16.2469i	0.0105675	−	0.526842i
$952$	11.5173	+	6.48505i	0.373278	+	0.210182i
$953$	−30.0408	−	21.8260i	−0.973119	−	0.707012i	−0.0169584	−	0.999856i	$-0.505398\pi$
$953$	−30.0408	−	21.8260i	−0.973119	−	0.707012i	−0.956160	+	0.292844i	$0.905398\pi$
$954$	−5.50275	−	4.34552i	−0.178158	−	0.140691i
$955$	21.5733	−	19.9757i	0.698095	−	0.646398i
$956$	−31.8539	−	43.8431i	−1.03023	−	1.41799i
$957$	0.0236400	−	1.17858i	0.000764172	−	0.0380979i
$958$	7.15389	−	5.19760i	0.231132	−	0.167927i
$959$	0.461506	+	3.97806i	0.0149028	+	0.128458i
$960$	42.1685	+	24.6917i	1.36098	+	0.796922i
$961$	−9.50676	+	29.2588i	−0.306670	+	0.943832i
$962$	10.7511	−	3.49325i	0.346630	−	0.112627i
$963$	−2.37915	−	8.46307i	−0.0766671	−	0.272719i
$964$	28.6493	+	9.30871i	0.922730	+	0.299813i
$965$	−11.0360	−	23.8862i	−0.355260	−	0.768924i
$966$	−5.50142	+	0.526662i	−0.177005	+	0.0169451i
$967$	7.28009	+	10.0202i	0.234112	+	0.322227i	0.909868	−	0.414898i	$-0.136183\pi$
$967$	7.28009	+	10.0202i	0.234112	+	0.322227i	−0.675756	+	0.737125i	$0.736183\pi$
$968$	−19.2038			−0.617234
$969$	15.5202	+	22.2884i	0.498581	+	0.716006i
$970$	−24.9634	+	44.6631i	−0.801527	+	1.43405i
$971$	13.5966	+	9.87849i	0.436335	+	0.317016i	0.784177	−	0.620537i	$-0.213085\pi$
$971$	13.5966	+	9.87849i	0.436335	+	0.317016i	−0.347842	+	0.937553i	$0.613085\pi$
$972$	−29.0945	+	32.6028i	−0.933206	+	1.04574i
$973$	31.4955	+	17.7342i	1.00970	+	0.568532i
$974$			27.7539i			0.889294i
$975$	−34.0719	+	20.0274i	−1.09118	+	0.641390i
$976$		−	0.393503i		−	0.0125957i
$977$	−10.0426	+	30.9078i	−0.321290	+	0.988829i	0.651798	+	0.758393i	$0.274015\pi$
$977$	−10.0426	+	30.9078i	−0.321290	+	0.988829i	−0.973088	+	0.230436i	$0.925985\pi$
$978$	58.1377	+	44.0476i	1.85904	+	1.40849i
$979$	1.27073	−	1.74901i	0.0406127	−	0.0558986i
$980$	36.3894	+	24.5145i	1.16242	+	0.783088i
$981$	−4.51432	+	3.01089i	−0.144131	+	0.0961302i
$982$		−	32.4978i		−	1.03705i
$983$	−2.78417	−	3.83208i	−0.0888012	−	0.122224i	0.762305	−	0.647218i	$-0.224068\pi$
$983$	−2.78417	−	3.83208i	−0.0888012	−	0.122224i	−0.851106	+	0.524994i	$0.824068\pi$
$984$	27.0439	−	8.19127i	0.862129	−	0.261128i
$985$	40.5416	+	8.02891i	1.29176	+	0.255822i
$986$	−4.35548	+	13.4048i	−0.138707	+	0.426896i
$987$	1.55439	+	16.2369i	0.0494768	+	0.516826i
$988$	67.2198	−	21.8410i	2.13855	−	0.694856i
$989$	−2.58602	−	0.840249i	−0.0822306	−	0.0267184i
$990$	−4.40206	+	0.346436i	−0.139907	+	0.0110105i
$991$	−2.76721	−	8.51661i	−0.0879034	−	0.270539i	0.897436	−	0.441145i	$-0.145428\pi$
$991$	−2.76721	−	8.51661i	−0.0879034	−	0.270539i	−0.985339	+	0.170606i	$0.945428\pi$
$992$	−33.9652	−	46.7491i	−1.07840	−	1.48429i
$993$	0.0633624	−	3.15894i	0.00201074	−	0.100246i
$994$	20.6465	+	45.0597i	0.654869	+	1.42921i
$995$	−19.0889	−	41.3159i	−0.605159	−	1.30980i
$996$	37.8035	+	28.6415i	1.19785	+	0.907540i
$997$	−0.240901	−	0.175025i	−0.00762940	−	0.00554308i	0.583964	−	0.811780i	$-0.301501\pi$
$997$	−0.240901	−	0.175025i	−0.00762940	−	0.00554308i	−0.591593	+	0.806236i	$0.701501\pi$
$998$	−3.22659	+	9.93043i	−0.102136	+	0.314342i
$999$	−5.86232	−	0.353140i	−0.185476	−	0.0111728i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.w.a.104.11	✓	304
3.2	odd	2	inner	525.2.w.a.104.66	yes	304
7.6	odd	2	inner	525.2.w.a.104.12	yes	304
21.20	even	2	inner	525.2.w.a.104.65	yes	304
25.19	even	10	inner	525.2.w.a.419.65	yes	304
75.44	odd	10	inner	525.2.w.a.419.12	yes	304
175.69	odd	10	inner	525.2.w.a.419.66	yes	304
525.419	even	10	inner	525.2.w.a.419.11	yes	304

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.w.a.104.11	✓	304	1.1	even	1	trivial
525.2.w.a.104.12	yes	304	7.6	odd	2	inner
525.2.w.a.104.65	yes	304	21.20	even	2	inner
525.2.w.a.104.66	yes	304	3.2	odd	2	inner
525.2.w.a.419.11	yes	304	525.419	even	10	inner
525.2.w.a.419.12	yes	304	75.44	odd	10	inner
525.2.w.a.419.65	yes	304	25.19	even	10	inner
525.2.w.a.419.66	yes	304	175.69	odd	10	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.677246 + 2.08435i) q^{2} +(-1.04597 + 1.38056i) q^{3} +(-2.26781 - 1.64766i) q^{4} +(-2.02988 + 0.937853i) q^{5} +(-2.16919 - 3.11514i) q^{6} +(-2.59371 - 0.522162i) q^{7} +(1.42406 - 1.03464i) q^{8} +(-0.811893 - 2.88805i) q^{9} +O(q^{10})\)	\(q+(-0.677246 + 2.08435i) q^{2} +(-1.04597 + 1.38056i) q^{3} +(-2.26781 - 1.64766i) q^{4} +(-2.02988 + 0.937853i) q^{5} +(-2.16919 - 3.11514i) q^{6} +(-2.59371 - 0.522162i) q^{7} +(1.42406 - 1.03464i) q^{8} +(-0.811893 - 2.88805i) q^{9} +(-0.580080 - 4.86614i) q^{10} +(0.285649 + 0.0928130i) q^{11} +(4.64676 - 1.40745i) q^{12} +(1.41023 + 4.34026i) q^{13} +(2.84495 - 5.05257i) q^{14} +(0.828437 - 3.78334i) q^{15} +(-0.540342 - 1.66300i) q^{16} +(-1.66821 - 2.29609i) q^{17} +(6.56955 + 0.263651i) q^{18} +(3.24751 + 4.46982i) q^{19} +(6.14866 + 1.21769i) q^{20} +(3.43382 - 3.03461i) q^{21} +(-0.386909 + 0.532535i) q^{22} +(-0.170045 + 0.523346i) q^{23} +(-0.0611411 + 3.04820i) q^{24} +(3.24087 - 3.80747i) q^{25} -10.0017 q^{26} +(4.83634 + 1.89995i) q^{27} +(5.02171 + 5.45772i) q^{28} +(-1.33191 + 1.83322i) q^{29} +(7.32475 + 4.28900i) q^{30} +(-4.61943 - 6.35810i) q^{31} +7.35269 q^{32} +(-0.426914 + 0.297276i) q^{33} +(5.91565 - 1.92211i) q^{34} +(5.75465 - 1.37259i) q^{35} +(-2.91731 + 7.88728i) q^{36} +(-1.07493 + 0.349266i) q^{37} +(-11.5160 + 3.74178i) q^{38} +(-7.46705 - 2.59286i) q^{39} +(-1.92034 + 3.43576i) q^{40} +(-2.86405 - 8.81464i) q^{41} +(3.99965 + 9.21246i) q^{42} +4.94132i q^{43} +(-0.494874 - 0.681135i) q^{44} +(4.35661 + 5.10097i) q^{45} +(-0.975672 - 0.708867i) q^{46} +(-2.09215 + 2.87960i) q^{47} +(2.86105 + 0.993475i) q^{48} +(6.45469 + 2.70867i) q^{49} +(5.74122 + 9.33368i) q^{50} +(4.91479 + 0.0985814i) q^{51} +(3.95313 - 12.1665i) q^{52} +(-0.862770 - 0.626839i) q^{53} +(-7.23554 + 8.79389i) q^{54} +(-0.666880 + 0.0794970i) q^{55} +(-4.23385 + 1.93997i) q^{56} +(-9.56766 - 0.191909i) q^{57} +(-2.91904 - 4.01772i) q^{58} +(-3.24014 - 9.97212i) q^{59} +(-8.11241 + 7.21493i) q^{60} +(0.214027 + 0.0695416i) q^{61} +(16.3810 - 5.32250i) q^{62} +(0.597789 + 7.91471i) q^{63} +(-3.89889 + 11.9996i) q^{64} +(-6.93313 - 7.48763i) q^{65} +(-0.330501 - 1.09117i) q^{66} +(-7.08216 - 9.74776i) q^{67} +7.95575i q^{68} +(-0.544648 - 0.782162i) q^{69} +(-1.03635 + 12.9243i) q^{70} +(-5.02433 + 6.91539i) q^{71} +(-4.14428 - 3.27274i) q^{72} +(2.90010 - 8.92560i) q^{73} -2.47707i q^{74} +(1.86659 + 8.45670i) q^{75} -15.4875i q^{76} +(-0.692428 - 0.389885i) q^{77} +(10.4615 - 13.8079i) q^{78} +(12.5110 + 9.08978i) q^{79} +(2.65648 + 2.86894i) q^{80} +(-7.68166 + 4.68957i) q^{81} +20.3124 q^{82} +(5.74177 + 7.90287i) q^{83} +(-12.7873 + 1.22415i) q^{84} +(5.53967 + 3.09627i) q^{85} +(-10.2994 - 3.34649i) q^{86} +(-1.13773 - 3.75629i) q^{87} +(0.502810 - 0.163373i) q^{88} +(2.22429 - 6.84565i) q^{89} +(-13.5827 + 5.62609i) q^{90} +(-1.39143 - 11.9937i) q^{91} +(1.24793 - 0.906672i) q^{92} +(13.6095 + 0.272981i) q^{93} +(-4.58519 - 6.31097i) q^{94} +(-10.7841 - 6.02753i) q^{95} +(-7.69069 + 10.1508i) q^{96} +(-8.44677 - 6.13693i) q^{97} +(-10.0172 + 11.6194i) q^{98} +(0.0361320 - 0.900323i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 304 q - 84 q^{4} - 6 q^{9}+O(q^{10}) \) 304 * q - 84 * q^4 - 6 * q^9	\( 304 q - 84 q^{4} - 6 q^{9} - 36 q^{15} - 60 q^{16} - 18 q^{21} - 40 q^{22} - 8 q^{25} + 60 q^{28} + 14 q^{30} + 28 q^{36} - 20 q^{37} - 2 q^{39} - 35 q^{42} - 24 q^{46} - 20 q^{49} - 52 q^{51} - 80 q^{58} + 4 q^{60} + 55 q^{63} - 76 q^{64} - 20 q^{67} + 6 q^{70} + 30 q^{72} - 40 q^{78} - 68 q^{79} - 10 q^{81} + 80 q^{84} - 88 q^{85} - 20 q^{88} - 82 q^{91} - 36 q^{99}+O(q^{100}) \) 304 * q - 84 * q^4 - 6 * q^9 - 36 * q^15 - 60 * q^16 - 18 * q^21 - 40 * q^22 - 8 * q^25 + 60 * q^28 + 14 * q^30 + 28 * q^36 - 20 * q^37 - 2 * q^39 - 35 * q^42 - 24 * q^46 - 20 * q^49 - 52 * q^51 - 80 * q^58 + 4 * q^60 + 55 * q^63 - 76 * q^64 - 20 * q^67 + 6 * q^70 + 30 * q^72 - 40 * q^78 - 68 * q^79 - 10 * q^81 + 80 * q^84 - 88 * q^85 - 20 * q^88 - 82 * q^91 - 36 * q^99

Introduction

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