LMFDB - Embedded newform 525.2.bv.a.52.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(52,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("525.52");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bv (of order $60$, degree $16$, 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:	$640$
Relative dimension:	$40$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			52.9
Character	$\chi$	$=$	525.52
Dual form			525.2.bv.a.313.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.641755 - 1.67183i) q^{2} +(-0.0523360 + 0.998630i) q^{3} +(-0.896875 + 0.807550i) q^{4} +(-0.674040 + 2.13206i) q^{5} +(1.70313 - 0.553379i) q^{6} +(0.561772 - 2.58542i) q^{7} +(-1.26552 - 0.644814i) q^{8} +(-0.994522 - 0.104528i) q^{9} +O(q^{10})$	\(q+(-0.641755 - 1.67183i) q^{2} +(-0.0523360 + 0.998630i) q^{3} +(-0.896875 + 0.807550i) q^{4} +(-0.674040 + 2.13206i) q^{5} +(1.70313 - 0.553379i) q^{6} +(0.561772 - 2.58542i) q^{7} +(-1.26552 - 0.644814i) q^{8} +(-0.994522 - 0.104528i) q^{9} +(3.99701 - 0.241379i) q^{10} +(0.150578 + 1.43266i) q^{11} +(-0.759505 - 0.937910i) q^{12} +(-0.455949 - 2.87875i) q^{13} +(-4.68291 + 0.720022i) q^{14} +(-2.09386 - 0.784700i) q^{15} +(-0.518169 + 4.93005i) q^{16} +(5.90257 - 3.83317i) q^{17} +(0.463486 + 1.72975i) q^{18} +(3.28699 - 3.65057i) q^{19} +(-1.11721 - 2.45651i) q^{20} +(2.55248 + 0.696312i) q^{21} +(2.29852 - 1.17116i) q^{22} +(2.37937 - 0.913356i) q^{23} +(0.710162 - 1.23004i) q^{24} +(-4.09134 - 2.87419i) q^{25} +(-4.52017 + 2.60972i) q^{26} +(0.156434 - 0.987688i) q^{27} +(1.58402 + 2.77246i) q^{28} +(-0.717661 - 0.233182i) q^{29} +(0.0318609 + 4.00416i) q^{30} +(1.62131 - 7.62767i) q^{31} +(5.83089 - 1.56238i) q^{32} +(-1.43857 + 0.0753925i) q^{33} +(-10.1964 - 7.40813i) q^{34} +(5.13361 + 2.94041i) q^{35} +(0.976374 - 0.709377i) q^{36} +(7.81349 - 6.32724i) q^{37} +(-8.21257 - 3.15251i) q^{38} +(2.89867 - 0.304662i) q^{39} +(2.22779 - 2.26353i) q^{40} +(0.632836 - 0.871024i) q^{41} +(-0.473951 - 4.71417i) q^{42} +(-0.968165 + 0.968165i) q^{43} +(-1.29199 - 1.16332i) q^{44} +(0.893208 - 2.04992i) q^{45} +(-3.05395 - 3.39176i) q^{46} +(-4.87986 + 7.51433i) q^{47} +(-4.89618 - 0.775478i) q^{48} +(-6.36883 - 2.90483i) q^{49} +(-2.17951 + 8.68455i) q^{50} +(3.51900 + 6.09510i) q^{51} +(2.73366 + 2.21368i) q^{52} +(1.31802 + 0.0690744i) q^{53} +(-1.75164 + 0.372322i) q^{54} +(-3.15600 - 0.644627i) q^{55} +(-2.37805 + 2.90966i) q^{56} +(3.47354 + 3.47354i) q^{57} +(0.0707219 + 1.34945i) q^{58} +(-7.93303 + 3.53201i) q^{59} +(2.51161 - 0.987118i) q^{60} +(-3.56190 + 8.00017i) q^{61} +(-13.7927 + 2.18454i) q^{62} +(-0.828945 + 2.51254i) q^{63} +(-0.526493 - 0.724655i) q^{64} +(6.44498 + 0.968283i) q^{65} +(1.04926 + 2.35667i) q^{66} +(-0.527324 - 0.812008i) q^{67} +(-2.19839 + 8.20450i) q^{68} +(0.787578 + 2.42392i) q^{69} +(1.62134 - 10.4696i) q^{70} +(0.608425 - 1.87254i) q^{71} +(1.19118 + 0.773564i) q^{72} +(3.62327 - 4.47436i) q^{73} +(-15.5924 - 9.00229i) q^{74} +(3.08437 - 3.93531i) q^{75} +5.92851i q^{76} +(3.78862 + 0.415517i) q^{77} +(-2.36958 - 4.65056i) q^{78} +(2.32380 + 10.9326i) q^{79} +(-10.1619 - 4.42782i) q^{80} +(0.978148 + 0.207912i) q^{81} +(-1.86233 - 0.499010i) q^{82} +(2.97329 - 5.83542i) q^{83} +(-2.85156 + 1.43675i) q^{84} +(4.19398 + 15.1683i) q^{85} +(2.23993 + 0.997282i) q^{86} +(0.270422 - 0.704474i) q^{87} +(0.733238 - 1.91015i) q^{88} +(-6.65249 - 2.96188i) q^{89} +(-4.00034 - 0.177744i) q^{90} +(-7.69892 - 0.438378i) q^{91} +(-1.39642 + 2.74063i) q^{92} +(7.53236 + 2.01829i) q^{93} +(15.6944 + 3.33594i) q^{94} +(5.56766 + 9.46868i) q^{95} +(1.25508 + 5.90467i) q^{96} +(-7.28555 - 14.2987i) q^{97} +(-0.769162 + 12.5118i) q^{98} -1.44055i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 640 q + 12 q^{5} - 8 q^{7} + 24 q^{8}+O(q^{10}) $ 640 * q + 12 * q^5 - 8 * q^7 + 24 * q^8	$ 640 q + 12 q^{5} - 8 q^{7} + 24 q^{8} + 12 q^{10} + 8 q^{15} - 80 q^{16} - 72 q^{22} + 48 q^{23} - 12 q^{25} - 36 q^{28} - 80 q^{29} + 32 q^{30} - 24 q^{32} + 36 q^{33} - 64 q^{35} + 160 q^{36} - 4 q^{37} - 192 q^{38} - 12 q^{40} - 16 q^{42} + 120 q^{43} + 60 q^{47} + 288 q^{50} - 432 q^{52} - 136 q^{53} - 16 q^{57} - 4 q^{58} - 240 q^{59} - 20 q^{60} - 4 q^{63} + 120 q^{64} + 4 q^{65} - 8 q^{67} - 132 q^{68} + 76 q^{70} - 12 q^{72} - 36 q^{73} - 48 q^{75} - 60 q^{77} - 80 q^{78} + 12 q^{80} - 80 q^{81} - 252 q^{82} - 160 q^{84} + 72 q^{85} + 24 q^{87} + 152 q^{88} + 56 q^{92} - 96 q^{93} + 172 q^{95} - 488 q^{98}+O(q^{100}) $ 640 * q + 12 * q^5 - 8 * q^7 + 24 * q^8 + 12 * q^10 + 8 * q^15 - 80 * q^16 - 72 * q^22 + 48 * q^23 - 12 * q^25 - 36 * q^28 - 80 * q^29 + 32 * q^30 - 24 * q^32 + 36 * q^33 - 64 * q^35 + 160 * q^36 - 4 * q^37 - 192 * q^38 - 12 * q^40 - 16 * q^42 + 120 * q^43 + 60 * q^47 + 288 * q^50 - 432 * q^52 - 136 * q^53 - 16 * q^57 - 4 * q^58 - 240 * q^59 - 20 * q^60 - 4 * q^63 + 120 * q^64 + 4 * q^65 - 8 * q^67 - 132 * q^68 + 76 * q^70 - 12 * q^72 - 36 * q^73 - 48 * q^75 - 60 * q^77 - 80 * q^78 + 12 * q^80 - 80 * q^81 - 252 * q^82 - 160 * q^84 + 72 * q^85 + 24 * q^87 + 152 * q^88 + 56 * q^92 - 96 * q^93 + 172 * q^95 - 488 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{20}\right)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.641755	−	1.67183i	−0.453790	−	1.18216i	−0.949526	−	0.313689i	$-0.898435\pi$
$2$	−0.641755	−	1.67183i	−0.453790	−	1.18216i	0.495736	−	0.868473i	$-0.334898\pi$
$3$	−0.0523360	+	0.998630i	−0.0302162	+	0.576559i
$3$	−0.0523360	+	0.998630i	−0.0302162	+	0.576559i
$4$	−0.896875	+	0.807550i	−0.448438	+	0.403775i
$5$	−0.674040	+	2.13206i	−0.301440	+	0.953485i
$5$	−0.674040	+	2.13206i	−0.301440	+	0.953485i
$6$	1.70313	−	0.553379i	0.695298	−	0.225916i
$7$	0.561772	−	2.58542i	0.212330	−	0.977198i
$7$	0.561772	−	2.58542i	0.212330	−	0.977198i
$8$	−1.26552	−	0.644814i	−0.447428	−	0.227976i
$9$	−0.994522	−	0.104528i	−0.331507	−	0.0348428i
$10$	3.99701	−	0.241379i	1.26396	−	0.0763307i
$11$	0.150578	+	1.43266i	0.0454011	+	0.431962i	0.993487	+	0.113947i	$0.0363495\pi$
$11$	0.150578	+	1.43266i	0.0454011	+	0.431962i	−0.948086	+	0.318015i	$0.896984\pi$
$12$	−0.759505	−	0.937910i	−0.219250	−	0.270751i
$13$	−0.455949	−	2.87875i	−0.126457	−	0.798421i	−0.966644	−	0.256124i	$-0.917555\pi$
$13$	−0.455949	−	2.87875i	−0.126457	−	0.798421i	0.840187	−	0.542297i	$-0.182445\pi$
$14$	−4.68291	+	0.720022i	−1.25156	+	0.192434i
$15$	−2.09386	−	0.784700i	−0.540632	−	0.202609i
$16$	−0.518169	+	4.93005i	−0.129542	+	1.23251i
$17$	5.90257	−	3.83317i	1.43158	−	0.929681i	0.431970	−	0.901888i	$-0.357819\pi$
$17$	5.90257	−	3.83317i	1.43158	−	0.929681i	0.999614	−	0.0277935i	$-0.00884809\pi$
$18$	0.463486	+	1.72975i	0.109245	+	0.407707i
$19$	3.28699	−	3.65057i	0.754087	−	0.837498i	−0.236889	−	0.971537i	$-0.576128\pi$
$19$	3.28699	−	3.65057i	0.754087	−	0.837498i	0.990976	+	0.134038i	$0.0427946\pi$
$20$	−1.11721	−	2.45651i	−0.249817	−	0.549293i
$21$	2.55248	+	0.696312i	0.556997	+	0.151948i
$22$	2.29852	−	1.17116i	0.490047	−	0.249691i
$23$	2.37937	−	0.913356i	0.496134	−	0.190448i	−0.0974181	−	0.995244i	$-0.531058\pi$
$23$	2.37937	−	0.913356i	0.496134	−	0.190448i	0.593552	+	0.804796i	$0.297725\pi$
$24$	0.710162	−	1.23004i	0.144961	−	0.251080i
$25$	−4.09134	−	2.87419i	−0.818268	−	0.574837i
$26$	−4.52017	+	2.60972i	−0.886478	+	0.511808i
$27$	0.156434	−	0.987688i	0.0301058	−	0.190081i
$28$	1.58402	+	2.77246i	0.299352	+	0.523946i
$29$	−0.717661	−	0.233182i	−0.133266	−	0.0433009i	0.241624	−	0.970370i	$-0.422320\pi$
$29$	−0.717661	−	0.233182i	−0.133266	−	0.0433009i	−0.374891	+	0.927069i	$0.622320\pi$
$30$	0.0318609	+	4.00416i	0.00581698	+	0.731057i
$31$	1.62131	−	7.62767i	0.291196	−	1.36997i	−0.552663	−	0.833405i	$-0.686388\pi$
$31$	1.62131	−	7.62767i	0.291196	−	1.36997i	0.843859	−	0.536565i	$-0.180278\pi$
$32$	5.83089	−	1.56238i	1.03076	−	0.276193i
$33$	−1.43857	+	0.0753925i	−0.250424	+	0.0131241i
$34$	−10.1964	−	7.40813i	−1.74867	−	1.27048i
$35$	5.13361	+	2.94041i	0.867739	+	0.497020i
$36$	0.976374	−	0.709377i	0.162729	−	0.118230i
$37$	7.81349	−	6.32724i	1.28453	−	1.04019i	0.287943	−	0.957648i	$-0.407029\pi$
$37$	7.81349	−	6.32724i	1.28453	−	1.04019i	0.996587	−	0.0825447i	$-0.0263047\pi$
$38$	−8.21257	−	3.15251i	−1.33226	−	0.511405i
$39$	2.89867	−	0.304662i	0.464158	−	0.0487850i
$40$	2.22779	−	2.26353i	0.352245	−	0.357895i
$41$	0.632836	−	0.871024i	0.0988324	−	0.136031i	−0.756737	−	0.653720i	$-0.773207\pi$
$41$	0.632836	−	0.871024i	0.0988324	−	0.136031i	0.855569	+	0.517689i	$0.173207\pi$
$42$	−0.473951	−	4.71417i	−0.0731323	−	0.727413i
$43$	−0.968165	+	0.968165i	−0.147644	+	0.147644i	−0.777065	−	0.629421i	$-0.783292\pi$
$43$	−0.968165	+	0.968165i	−0.147644	+	0.147644i	0.629421	+	0.777065i	$0.283292\pi$
$44$	−1.29199	−	1.16332i	−0.194775	−	0.175376i
$45$	0.893208	−	2.04992i	0.133152	−	0.305584i
$46$	−3.05395	−	3.39176i	−0.450281	−	0.500088i
$47$	−4.87986	+	7.51433i	−0.711801	+	1.09608i	0.278939	+	0.960309i	$0.410017\pi$
$47$	−4.87986	+	7.51433i	−0.711801	+	1.09608i	−0.990741	+	0.135769i	$0.956650\pi$
$48$	−4.89618	−	0.775478i	−0.706702	−	0.111931i
$49$	−6.36883	−	2.90483i	−0.909832	−	0.414976i
$50$	−2.17951	+	8.68455i	−0.308229	+	1.22818i
$51$	3.51900	+	6.09510i	0.492759	+	0.853484i
$52$	2.73366	+	2.21368i	0.379091	+	0.306982i
$53$	1.31802	+	0.0690744i	0.181044	+	0.00948810i	0.142642	−	0.989774i	$-0.454440\pi$
$53$	1.31802	+	0.0690744i	0.181044	+	0.00948810i	0.0384013	+	0.999262i	$0.487773\pi$
$54$	−1.75164	+	0.372322i	−0.238368	+	0.0506667i
$55$	−3.15600	−	0.644627i	−0.425555	−	0.0869215i
$56$	−2.37805	+	2.90966i	−0.317780	+	0.388820i
$57$	3.47354	+	3.47354i	0.460082	+	0.460082i
$58$	0.0707219	+	1.34945i	0.00928624	+	0.177192i
$59$	−7.93303	+	3.53201i	−1.03279	+	0.459829i	−0.851917	−	0.523677i	$-0.824560\pi$
$59$	−7.93303	+	3.53201i	−1.03279	+	0.459829i	−0.180876	+	0.983506i	$0.557893\pi$
$60$	2.51161	−	0.987118i	0.324248	−	0.127436i
$61$	−3.56190	+	8.00017i	−0.456055	+	1.02432i	0.528451	+	0.848964i	$0.322773\pi$
$61$	−3.56190	+	8.00017i	−0.456055	+	1.02432i	−0.984506	+	0.175352i	$0.943894\pi$
$62$	−13.7927	+	2.18454i	−1.75167	+	0.277437i
$63$	−0.828945	+	2.51254i	−0.104437	+	0.316550i
$64$	−0.526493	−	0.724655i	−0.0658116	−	0.0905819i
$65$	6.44498	+	0.968283i	0.799402	+	0.120101i
$66$	1.04926	+	2.35667i	0.129155	+	0.290086i
$67$	−0.527324	−	0.812008i	−0.0644229	−	0.0992025i	0.804991	−	0.593287i	$-0.202170\pi$
$67$	−0.527324	−	0.812008i	−0.0644229	−	0.0992025i	−0.869414	+	0.494084i	$0.835503\pi$
$68$	−2.19839	+	8.20450i	−0.266594	+	0.994942i
$69$	0.787578	+	2.42392i	0.0948132	+	0.291805i
$70$	1.62134	−	10.4696i	0.193787	−	1.25135i
$71$	0.608425	−	1.87254i	0.0722067	−	0.222230i	−0.908440	−	0.418015i	$-0.862726\pi$
$71$	0.608425	−	1.87254i	0.0722067	−	0.222230i	0.980647	+	0.195786i	$0.0627258\pi$
$72$	1.19118	+	0.773564i	0.140382	+	0.0911654i
$73$	3.62327	−	4.47436i	0.424071	−	0.523684i	−0.519671	−	0.854366i	$-0.673945\pi$
$73$	3.62327	−	4.47436i	0.424071	−	0.523684i	0.943742	+	0.330682i	$0.107279\pi$
$74$	−15.5924	−	9.00229i	−1.81258	−	1.04649i
$75$	3.08437	−	3.93531i	0.356152	−	0.454410i
$76$			5.92851i			0.680047i
$77$	3.78862	+	0.415517i	0.431753	+	0.0473526i
$78$	−2.36958	−	4.65056i	−0.268302	−	0.526572i
$79$	2.32380	+	10.9326i	0.261448	+	1.23002i	0.891340	+	0.453335i	$0.149766\pi$
$79$	2.32380	+	10.9326i	0.261448	+	1.23002i	−0.629892	+	0.776683i	$0.716901\pi$
$80$	−10.1619	−	4.42782i	−1.13613	−	0.495045i
$81$	0.978148	+	0.207912i	0.108683	+	0.0231013i
$82$	−1.86233	−	0.499010i	−0.205660	−	0.0551064i
$83$	2.97329	−	5.83542i	0.326361	−	0.640520i	−0.668279	−	0.743910i	$-0.732969\pi$
$83$	2.97329	−	5.83542i	0.326361	−	0.640520i	0.994641	+	0.103390i	$0.0329690\pi$
$84$	−2.85156	+	1.43675i	−0.311131	+	0.156762i
$85$	4.19398	+	15.1683i	0.454901	+	1.64524i
$86$	2.23993	+	0.997282i	0.241538	+	0.107540i
$87$	0.270422	−	0.704474i	0.0289923	−	0.0755275i
$88$	0.733238	−	1.91015i	0.0781634	−	0.203623i
$89$	−6.65249	−	2.96188i	−0.705163	−	0.313959i	0.0226416	−	0.999744i	$-0.492792\pi$
$89$	−6.65249	−	2.96188i	−0.705163	−	0.313959i	−0.727804	+	0.685785i	$0.759459\pi$
$90$	−4.00034	−	0.177744i	−0.421673	−	0.0187359i
$91$	−7.69892	−	0.438378i	−0.807066	−	0.0459545i
$92$	−1.39642	+	2.74063i	−0.145587	+	0.285731i
$93$	7.53236	+	2.01829i	0.781070	+	0.209287i
$94$	15.6944	+	3.33594i	1.61875	+	0.344076i
$95$	5.56766	+	9.46868i	0.571230	+	0.971466i
$96$	1.25508	+	5.90467i	0.128096	+	0.602642i
$97$	−7.28555	−	14.2987i	−0.739736	−	1.45181i	−0.886542	−	0.462648i	$-0.846899\pi$
$97$	−7.28555	−	14.2987i	−0.739736	−	1.45181i	0.146807	−	0.989165i	$-0.453101\pi$
$98$	−0.769162	+	12.5118i	−0.0776971	+	1.26388i
$99$		−	1.44055i		−	0.144781i
$100$	5.99047	−	0.726176i	0.599047	−	0.0726176i
$101$	0.853490	+	0.492762i	0.0849254	+	0.0490317i	0.541861	−	0.840468i	$-0.317720\pi$
$101$	0.853490	+	0.492762i	0.0849254	+	0.0490317i	−0.456936	+	0.889500i	$0.651053\pi$
$102$	7.93162	−	9.79474i	0.785348	−	0.969823i
$103$	8.47928	+	5.50651i	0.835489	+	0.542573i	0.890011	−	0.455940i	$-0.150697\pi$
$103$	8.47928	+	5.50651i	0.835489	+	0.542573i	−0.0545220	+	0.998513i	$0.517364\pi$
$104$	−1.27924	+	3.93711i	−0.125440	+	0.386066i
$105$	−3.20505	+	4.97269i	−0.312781	+	0.485285i
$106$	−0.730364	−	2.24783i	−0.0709393	−	0.218329i
$107$	1.30387	−	4.86611i	0.126050	−	0.470425i	−0.873825	−	0.486241i	$-0.838368\pi$
$107$	1.30387	−	4.86611i	0.126050	−	0.470425i	0.999875	+	0.0158157i	$0.00503450\pi$
$108$	0.657306	+	1.01216i	0.0632493	+	0.0973953i
$109$	5.55731	+	12.4819i	0.532294	+	1.19555i	0.956965	+	0.290203i	$0.0937230\pi$
$109$	5.55731	+	12.4819i	0.532294	+	1.19555i	−0.424671	+	0.905348i	$0.639610\pi$
$110$	0.947676	+	5.68999i	0.0903573	+	0.542520i
$111$	5.90964	+	8.13393i	0.560919	+	0.772038i
$112$	12.4552	+	4.10925i	1.17690	+	0.388288i
$113$	−4.61241	+	0.730534i	−0.433899	+	0.0687229i	−0.369564	−	0.929205i	$-0.620493\pi$
$113$	−4.61241	+	0.730534i	−0.433899	+	0.0687229i	−0.0643355	+	0.997928i	$0.520493\pi$
$114$	3.57800	−	8.03633i	0.335111	−	0.752671i
$115$	0.343534	+	5.68860i	0.0320347	+	0.530465i
$116$	0.831959	−	0.370412i	0.0772455	−	0.0343919i
$117$	0.152540	+	2.91064i	0.0141023	+	0.269089i
$118$	10.9960	+	10.9960i	1.01226	+	1.01226i
$119$	−6.59448	−	17.4140i	−0.604515	−	1.59634i
$120$	2.14383	+	2.34320i	0.195704	+	0.213904i
$121$	8.72979	−	1.85557i	0.793617	−	0.168689i
$122$	15.6608	+	0.820747i	1.41786	+	0.0743070i
$123$	0.836710	+	0.677555i	0.0754436	+	0.0610930i
$124$	4.70561	+	8.15036i	0.422576	+	0.731924i
$125$	8.88566	−	6.78566i	0.794757	−	0.606927i
$126$	4.73252	−	0.226581i	0.421606	−	0.0201854i
$127$	−16.9825	−	2.68977i	−1.50696	−	0.238679i	−0.652336	−	0.757930i	$-0.726211\pi$
$127$	−16.9825	−	2.68977i	−1.50696	−	0.238679i	−0.854622	+	0.519251i	$0.826211\pi$
$128$	5.70189	−	8.78014i	0.503981	−	0.776062i
$129$	−0.916169	−	1.01751i	−0.0806641	−	0.0895866i
$130$	−2.51730	−	11.3963i	−0.220782	−	0.999523i
$131$	6.39768	+	5.76049i	0.558968	+	0.503297i	0.899491	−	0.436939i	$-0.143938\pi$
$131$	6.39768	+	5.76049i	0.558968	+	0.503297i	−0.340523	+	0.940236i	$0.610604\pi$
$132$	1.22934	−	1.22934i	0.107000	−	0.107000i
$133$	−7.59173	−	10.5490i	−0.658287	−	0.914718i
$134$	−1.01913	+	1.40271i	−0.0880390	+	0.121175i
$135$	2.00037	+	0.999269i	0.172164	+	0.0860034i
$136$	−9.94150	+	1.04489i	−0.852476	+	0.0895989i
$137$	7.88914	+	3.02836i	0.674015	+	0.258730i	0.671211	−	0.741266i	$-0.265774\pi$
$137$	7.88914	+	3.02836i	0.674015	+	0.258730i	0.00280334	+	0.999996i	$0.499108\pi$
$138$	3.54694	−	2.87226i	0.301936	−	0.244503i
$139$	12.3390	−	8.96482i	1.04658	−	0.760386i	0.0750220	−	0.997182i	$-0.476097\pi$
$139$	12.3390	−	8.96482i	1.04658	−	0.760386i	0.971559	+	0.236796i	$0.0760973\pi$
$140$	−6.97874	+	1.50847i	−0.589811	+	0.127489i
$141$	−7.24864	−	5.26644i	−0.610446	−	0.443515i
$142$	−3.52103	+	0.184529i	−0.295478	+	0.0154853i
$143$	4.05560	−	1.08670i	0.339147	−	0.0908740i
$144$	1.03066	−	4.84888i	0.0858884	−	0.404073i
$145$	0.980891	−	1.37292i	0.0814585	−	0.114015i
$146$	−9.80562	−	3.18604i	−0.811519	−	0.263678i
$147$	3.23417	−	6.20807i	0.266750	−	0.512033i
$148$	−1.89816	+	11.9845i	−0.156028	+	0.985123i
$149$	−6.49154	+	3.74789i	−0.531808	+	0.307039i	−0.741752	−	0.670674i	$-0.766005\pi$
$149$	−6.49154	+	3.74789i	−0.531808	+	0.307039i	0.209944	+	0.977713i	$0.432672\pi$
$150$	−8.55858	−	2.63104i	−0.698805	−	0.214823i
$151$	−8.46207	+	14.6567i	−0.688634	+	1.19275i	0.283647	+	0.958929i	$0.408456\pi$
$151$	−8.46207	+	14.6567i	−0.688634	+	1.19275i	−0.972280	+	0.233819i	$0.924878\pi$
$152$	−6.51368	+	2.50037i	−0.528329	+	0.202807i
$153$	−6.27091	+	3.19519i	−0.506973	+	0.258316i
$154$	−1.73669	−	6.60058i	−0.139946	−	0.531890i
$155$	15.1698	+	8.59809i	1.21847	+	0.690615i
$156$	−2.35371	+	2.61406i	−0.188448	+	0.209292i
$157$	4.42550	+	16.5162i	0.353193	+	1.31813i	0.882743	+	0.469856i	$0.155694\pi$
$157$	4.42550	+	16.5162i	0.353193	+	1.31813i	−0.529550	+	0.848279i	$0.677639\pi$
$158$	16.7862	−	10.9011i	1.33544	−	0.867243i
$159$	−0.137959	+	1.31260i	−0.0109409	+	0.104096i
$160$	−0.599165	+	13.4849i	−0.0473681	+	1.06607i
$161$	−1.02475	−	6.66479i	−0.0807614	−	0.525259i
$162$	−0.280138	−	1.76872i	−0.0220098	−	0.138964i
$163$	10.1515	+	12.5361i	0.795129	+	0.981903i	0.999995	+	0.00311297i	$0.000990890\pi$
$163$	10.1515	+	12.5361i	0.795129	+	0.981903i	−0.204866	+	0.978790i	$0.565676\pi$
$164$	0.135821	+	1.29225i	0.0106058	+	0.100907i
$165$	0.808916	−	3.11794i	0.0629740	−	0.242731i
$166$	−11.6640	−	1.22593i	−0.905298	−	0.0951507i
$167$	−12.0345	−	6.13191i	−0.931261	−	0.474501i	−0.0785651	−	0.996909i	$-0.525034\pi$
$167$	−12.0345	−	6.13191i	−0.931261	−	0.474501i	−0.852696	+	0.522408i	$0.825034\pi$
$168$	−2.78122	−	2.52707i	−0.214576	−	0.194968i
$169$	4.28443	−	1.39210i	0.329572	−	0.107084i
$170$	22.6674	−	16.7460i	1.73851	−	1.28436i
$171$	−3.65057	+	3.28699i	−0.279166	+	0.251362i
$172$	0.0864815	−	1.65017i	0.00659415	−	0.125824i
$173$	−1.68053	−	4.37794i	−0.127769	−	0.332849i	0.854743	−	0.519052i	$-0.173715\pi$
$173$	−1.68053	−	4.37794i	−0.127769	−	0.332849i	−0.982511	+	0.186203i	$0.940382\pi$
$174$	−1.35131			−0.102442
$175$	−9.72938	+	8.96321i	−0.735472	+	0.677555i
$176$	−7.14110			−0.538280
$177$	−3.11199	−	8.10701i	−0.233911	−	0.609360i
$178$	−0.682487	+	13.0226i	−0.0511546	+	0.976088i
$179$	−9.13908	+	8.22886i	−0.683087	+	0.615054i	−0.935818	−	0.352482i	$-0.885338\pi$
$179$	−9.13908	+	8.22886i	−0.683087	+	0.615054i	0.252732	+	0.967536i	$0.418671\pi$
$180$	0.854318	+	2.55983i	0.0636771	+	0.190799i
$181$	5.87982	−	1.91047i	0.437043	−	0.142004i	−0.0822277	−	0.996614i	$-0.526203\pi$
$181$	5.87982	−	1.91047i	0.437043	−	0.142004i	0.519271	+	0.854610i	$0.326203\pi$
$182$	4.20793	+	13.1526i	0.311913	+	0.974937i
$183$	−7.80279	−	3.97572i	−0.576799	−	0.293894i
$184$	−3.60009	−	0.378384i	−0.265402	−	0.0278949i
$185$	8.22344	+	20.9236i	0.604599	+	1.53834i
$186$	−1.45970	−	13.8881i	−0.107030	−	1.01832i
$187$	6.38042	+	7.87917i	0.466583	+	0.576182i
$188$	−1.69157	−	10.6802i	−0.123370	−	0.778930i
$189$	−2.46571	−	0.959305i	−0.179354	−	0.0697791i
$190$	12.2569	−	15.3848i	0.889212	−	1.11613i
$191$	−1.02601	+	9.76186i	−0.0742397	+	0.706344i	0.892581	+	0.450887i	$0.148892\pi$
$191$	−1.02601	+	9.76186i	−0.0742397	+	0.706344i	−0.966821	+	0.255456i	$0.917774\pi$
$192$	0.751216	−	0.487846i	0.0542144	−	0.0352072i
$193$	5.56660	+	20.7748i	0.400693	+	1.49541i	0.811863	+	0.583847i	$0.198453\pi$
$193$	5.56660	+	20.7748i	0.400693	+	1.49541i	−0.411171	+	0.911558i	$0.634880\pi$
$194$	−19.2294	+	21.3565i	−1.38059	+	1.53330i
$195$	−1.30426	+	6.38548i	−0.0934000	+	0.457273i
$196$	8.05784	−	2.53787i	0.575560	−	0.181276i
$197$	17.6974	−	9.01726i	1.26089	−	0.642453i	0.309630	−	0.950857i	$-0.399795\pi$
$197$	17.6974	−	9.01726i	1.26089	−	0.642453i	0.951255	+	0.308404i	$0.0997949\pi$
$198$	−2.40835	+	0.924480i	−0.171154	+	0.0656999i
$199$	3.16617	−	5.48396i	0.224444	−	0.388748i	−0.731709	−	0.681617i	$-0.761277\pi$
$199$	3.16617	−	5.48396i	0.224444	−	0.388748i	0.956152	+	0.292870i	$0.0946102\pi$
$200$	3.32435	+	6.27549i	0.235067	+	0.443744i
$201$	0.838493	−	0.484104i	0.0591427	−	0.0341461i
$202$	0.276083	−	1.74312i	0.0194252	−	0.122646i
$203$	−1.00604	+	1.72446i	−0.0706099	+	0.121034i
$204$	−8.07820	−	2.62477i	−0.565587	−	0.183770i
$205$	1.43052	+	1.93635i	0.0999116	+	0.135240i
$206$	3.76432	−	17.7097i	0.262273	−	1.23390i
$207$	−2.46181	+	0.659641i	−0.171108	+	0.0458482i
$208$	14.4286	−	0.756173i	1.00045	−	0.0524311i
$209$	5.72496	+	4.15943i	0.396004	+	0.287714i
$210$	10.3703	+	2.16705i	0.715622	+	0.149541i
$211$	−10.2653	+	7.45819i	−0.706694	+	0.513443i	−0.882105	−	0.471052i	$-0.843874\pi$
$211$	−10.2653	+	7.45819i	−0.706694	+	0.513443i	0.175411	+	0.984495i	$0.443874\pi$
$212$	−1.23788	+	1.00241i	−0.0850179	+	0.0688461i
$213$	1.83813	+	0.705592i	0.125947	+	0.0483464i
$214$	−8.97208	+	0.943004i	−0.613319	+	0.0644624i
$215$	−1.41160	−	2.71677i	−0.0962704	−	0.185282i
$216$	−0.834846	+	1.14907i	−0.0568041	+	0.0781841i
$217$	−18.8099	−	8.47678i	−1.27690	−	0.575442i
$218$	17.3012	−	17.3012i	1.17179	−	1.17179i
$219$	4.27860	+	3.85247i	0.289121	+	0.260326i
$220$	3.35111	−	1.97048i	0.225932	−	0.132850i
$221$	−13.7260	−	15.2443i	−0.923312	−	1.02544i
$222$	9.80600	−	15.0999i	0.658135	−	1.01344i
$223$	−24.3129	−	3.85079i	−1.62811	−	0.257868i	−0.725469	−	0.688255i	$-0.758377\pi$
$223$	−24.3129	−	3.85079i	−1.62811	−	0.257868i	−0.902644	+	0.430387i	$0.858377\pi$
$224$	−0.763790	−	15.9530i	−0.0510329	−	1.06591i
$225$	3.76849	+	3.28610i	0.251233	+	0.219073i
$226$	4.18137	+	7.24234i	0.278140	+	0.481753i
$227$	−20.6970	−	16.7601i	−1.37371	−	1.11241i	−0.981272	−	0.192628i	$-0.938299\pi$
$227$	−20.6970	−	16.7601i	−1.37371	−	1.11241i	−0.392436	−	0.919779i	$-0.628368\pi$
$228$	−5.92039	−	0.310274i	−0.392087	−	0.0205484i
$229$	19.1077	−	4.06147i	1.26267	−	0.268390i	0.472532	−	0.881313i	$-0.343340\pi$
$229$	19.1077	−	4.06147i	1.26267	−	0.268390i	0.790142	+	0.612924i	$0.210007\pi$
$230$	9.28991	−	4.22502i	0.612559	−	0.278590i
$231$	−0.613229	+	3.76168i	−0.0403475	+	0.247500i
$232$	0.757854	+	0.757854i	0.0497556	+	0.0497556i
$233$	0.940391	+	17.9437i	0.0616070	+	1.17553i	0.838140	+	0.545455i	$0.183643\pi$
$233$	0.940391	+	17.9437i	0.0616070	+	1.17553i	−0.776533	+	0.630077i	$0.783023\pi$
$234$	4.76820	−	2.12294i	0.311707	−	0.138781i
$235$	−12.7318	−	15.4691i	−0.830529	−	1.00909i
$236$	4.26266	−	9.57409i	0.277476	−	0.623220i
$237$	−11.0393	+	1.74845i	−0.717078	+	0.113574i
$238$	−24.8812	+	22.2004i	−1.61281	+	1.43904i
$239$	−7.33308	−	10.0931i	−0.474338	−	0.652870i	0.503067	−	0.864248i	$-0.332205\pi$
$239$	−7.33308	−	10.0931i	−0.474338	−	0.652870i	−0.977404	+	0.211378i	$0.932205\pi$
$240$	4.95358	−	9.91623i	0.319752	−	0.640090i
$241$	−5.49397	−	12.3397i	−0.353898	−	0.794868i	−0.999513	−	0.0312048i	$-0.990066\pi$
$241$	−5.49397	−	12.3397i	−0.353898	−	0.794868i	0.645615	−	0.763663i	$-0.276601\pi$
$242$	−8.70459	−	13.4039i	−0.559553	−	0.861635i
$243$	−0.258819	+	0.965926i	−0.0166032	+	0.0619642i
$244$	−3.26595	−	10.0516i	−0.209081	−	0.643486i
$245$	10.4861	−	11.6207i	0.669934	−	0.742421i
$246$	0.595793	−	1.83366i	0.0379864	−	0.116910i
$247$	−12.0078	−	7.79794i	−0.764036	−	0.496171i
$248$	−6.97023	+	8.60751i	−0.442610	+	0.546578i
$249$	5.67181	+	3.27462i	0.359436	+	0.207521i
$250$	−17.0469	−	10.5006i	−1.07814	−	0.664115i
$251$		−	21.6483i		−	1.36643i	−0.730218	−	0.683215i	$-0.760581\pi$
$251$		−	21.6483i		−	1.36643i	0.730218	−	0.683215i	$-0.239419\pi$
$252$	−1.28554	−	2.92285i	−0.0809815	−	0.184122i
$253$	1.66681	+	3.27130i	0.104791	+	0.205665i
$254$	6.40180	+	30.1181i	0.401685	+	1.88978i
$255$	−15.3670	+	3.39438i	−0.962322	+	0.212564i
$256$	−20.0904	−	4.27035i	−1.25565	−	0.266897i
$257$	−21.7461	−	5.82686i	−1.35649	−	0.363470i	−0.493962	−	0.869483i	$-0.664452\pi$
$257$	−21.7461	−	5.82686i	−1.35649	−	0.363470i	−0.862525	+	0.506014i	$0.831119\pi$
$258$	−1.11314	+	2.18467i	−0.0693014	+	0.136012i
$259$	−11.9692	−	23.7557i	−0.743730	−	1.47610i
$260$	−6.56228	+	4.33622i	−0.406976	+	0.268921i
$261$	0.689356	+	0.306921i	0.0426700	+	0.0189979i
$262$	5.52482	−	14.3927i	0.341325	−	0.889181i
$263$	4.12129	−	10.7363i	0.254129	−	0.662030i	−0.745862	−	0.666100i	$-0.767962\pi$
$263$	4.12129	−	10.7363i	0.254129	−	0.662030i	0.999992	+	0.00407045i	$0.00129567\pi$
$264$	1.86916	+	0.832202i	0.115039	+	0.0512185i
$265$	−1.03567	+	2.76353i	−0.0636206	+	0.169762i
$266$	−12.7642	+	19.4620i	−0.782621	+	1.19329i
$267$	3.30598	−	6.48836i	0.202323	−	0.397081i
$268$	1.12868	+	0.302429i	0.0689451	+	0.0184738i
$269$	28.3875	+	6.03396i	1.73082	+	0.367897i	0.962313	−	0.271946i	$-0.0876671\pi$
$269$	28.3875	+	6.03396i	1.73082	+	0.367897i	0.768506	+	0.639843i	$0.221000\pi$
$270$	0.386862	−	3.98556i	0.0235437	−	0.242553i
$271$	1.79081	+	8.42511i	0.108784	+	0.511789i	0.998474	+	0.0552238i	$0.0175872\pi$
$271$	1.79081	+	8.42511i	0.108784	+	0.511789i	−0.889690	+	0.456565i	$0.849079\pi$
$272$	15.8392	+	31.0862i	0.960394	+	1.88488i
$273$	0.840708	−	7.66543i	0.0508820	−	0.463933i
$274$		−	15.1328i		−	0.914204i
$275$	3.50165	−	6.29428i	0.211158	−	0.379559i
$276$	−2.66379	−	1.53794i	−0.160341	−	0.0925732i
$277$	−8.91218	+	11.0056i	−0.535481	+	0.661264i	−0.971046	−	0.238893i	$-0.923215\pi$
$277$	−8.91218	+	11.0056i	−0.535481	+	0.661264i	0.435565	+	0.900157i	$0.356549\pi$
$278$	−22.9063	−	14.8755i	−1.37383	−	0.892174i
$279$	−2.40974	+	7.41641i	−0.144267	+	0.444009i
$280$	−4.60067	−	7.03137i	−0.274942	−	0.420205i
$281$	6.91512	+	21.2826i	0.412522	+	1.26961i	0.914449	+	0.404701i	$0.132625\pi$
$281$	6.91512	+	21.2826i	0.412522	+	1.26961i	−0.501927	+	0.864910i	$0.667375\pi$
$282$	−4.15275	+	15.4983i	−0.247292	+	0.922908i
$283$	−1.85840	−	2.86168i	−0.110470	−	0.170109i	0.779111	−	0.626886i	$-0.215671\pi$
$283$	−1.85840	−	2.86168i	−0.110470	−	0.170109i	−0.889582	+	0.456776i	$0.849004\pi$
$284$	0.966488	+	2.17077i	0.0573505	+	0.128811i
$285$	−9.74709	+	5.06448i	−0.577368	+	0.299994i
$286$	−4.41947	−	6.08289i	−0.261329	−	0.359689i
$287$	−1.89646	−	2.12547i	−0.111944	−	0.125462i
$288$	−5.96226	+	0.944329i	−0.351329	+	0.0556451i
$289$	13.2326	−	29.7209i	0.778388	−	1.74829i
$290$	−2.92478	−	0.758803i	−0.171749	−	0.0445584i
$291$	14.6604	−	6.52723i	0.859408	−	0.382633i
$292$	0.363653	+	6.93891i	0.0212812	+	0.406069i
$293$	18.9084	+	18.9084i	1.10464	+	1.10464i	0.993843	+	0.110797i	$0.0353403\pi$
$293$	18.9084	+	18.9084i	1.10464	+	1.10464i	0.110797	+	0.993843i	$0.464660\pi$
$294$	−12.4544	−	1.42292i	−0.726354	−	0.0829866i
$295$	−2.18327	−	19.2944i	−0.127115	−	1.12336i
$296$	−13.9680	+	2.96899i	−0.811874	+	0.172569i
$297$	1.43857	+	0.0753925i	0.0834746	+	0.00437472i
$298$	10.4318	+	8.44752i	0.604299	+	0.489352i
$299$	−3.71420	−	6.43318i	−0.214798	−	0.372040i
$300$	0.411664	+	6.02027i	0.0237674	+	0.347580i
$301$	1.95923	+	3.04700i	0.112928	+	0.175626i
$302$	29.9341	+	4.74110i	1.72252	+	0.272820i
$303$	−0.536755	+	0.826531i	−0.0308358	+	0.0474829i
$304$	16.2943	+	18.0966i	0.934541	+	1.03791i
$305$	−14.6560	−	12.9866i	−0.839197	−	0.743612i
$306$	9.36620	+	8.43337i	0.535430	+	0.482104i
$307$	−10.2533	+	10.2533i	−0.585189	+	0.585189i	−0.936325	−	0.351136i	$-0.885796\pi$
$307$	−10.2533	+	10.2533i	−0.585189	+	0.585189i	0.351136	+	0.936325i	$0.385796\pi$
$308$	−3.73347	+	2.68683i	−0.212734	+	0.153096i
$309$	−5.94274	+	8.17947i	−0.338070	+	0.465314i
$310$	4.63923	−	30.8792i	0.263491	−	1.75382i
$311$	−31.1292	+	3.27181i	−1.76517	+	0.185527i	−0.930764	−	0.365620i	$-0.880857\pi$
$311$	−31.1292	+	3.27181i	−1.76517	+	0.185527i	−0.834408	+	0.551147i	$0.814190\pi$
$312$	−3.86476	−	1.48354i	−0.218799	−	0.0839892i
$313$	14.4104	−	11.6693i	0.814524	−	0.659588i	−0.128723	−	0.991681i	$-0.541088\pi$
$313$	14.4104	−	11.6693i	0.814524	−	0.659588i	0.943247	+	0.332092i	$0.107755\pi$
$314$	24.7721	−	17.9980i	1.39797	−	1.01569i
$315$	−4.79814	−	3.46091i	−0.270344	−	0.195000i
$316$	−10.9128	−	7.92862i	−0.613894	−	0.446020i
$317$	−7.29401	+	0.382263i	−0.409672	+	0.0214700i	−0.256059	−	0.966661i	$-0.582424\pi$
$317$	−7.29401	+	0.382263i	−0.409672	+	0.0214700i	−0.153613	+	0.988131i	$0.549091\pi$
$318$	2.28297	−	0.611721i	0.128023	−	0.0343036i
$319$	0.226006	−	1.06327i	0.0126539	−	0.0595320i
$320$	1.89988	−	0.634066i	0.106207	−	0.0354454i
$321$	4.79121	+	1.55676i	0.267419	+	0.0868897i
$322$	−10.4848	+	5.99037i	−0.584293	+	0.333830i
$323$	5.40841	−	34.1473i	0.300932	−	1.90001i
$324$	−1.04518	+	0.603432i	−0.0580653	+	0.0335240i
$325$	−6.40861	+	13.0884i	−0.355486	+	0.726015i
$326$	14.4434	−	25.0167i	0.799947	−	1.38555i
$327$	−12.7557	+	4.89644i	−0.705390	+	0.270774i
$328$	−1.36251	+	0.694235i	−0.0752322	+	0.0383327i
$329$	16.6864	+	16.8378i	0.919948	+	0.928301i
$330$	−5.73179	+	0.648586i	−0.315525	+	0.0357035i
$331$	−11.8006	+	13.1059i	−0.648618	+	0.720363i	−0.974335	−	0.225104i	$-0.927728\pi$
$331$	−11.8006	+	13.1059i	−0.648618	+	0.720363i	0.325717	+	0.945467i	$0.394394\pi$
$332$	2.04572	+	7.63473i	0.112273	+	0.419010i
$333$	−8.43207	+	5.47585i	−0.462074	+	0.300075i
$334$	−2.52827	+	24.0549i	−0.138341	+	1.31622i
$335$	2.08668	−	0.576959i	0.114008	−	0.0315227i
$336$	−4.75547	+	12.2230i	−0.259432	+	0.666822i
$337$	−3.55101	−	22.4202i	−0.193436	−	1.22130i	−0.873012	−	0.487699i	$-0.837836\pi$
$337$	−3.55101	−	22.4202i	−0.193436	−	1.22130i	0.679576	−	0.733605i	$-0.262164\pi$
$338$	−5.07691	−	6.26946i	−0.276147	−	0.341014i
$339$	−0.488138	−	4.64432i	−0.0265120	−	0.252245i
$340$	−16.0107	−	10.2173i	−0.868300	−	0.554109i
$341$	11.1720	+	1.17422i	0.604996	+	0.0635877i
$342$	7.83806	+	3.99369i	0.423834	+	0.215954i
$343$	−11.0881	+	14.8343i	−0.598699	+	0.800974i
$344$	1.84952	−	0.600945i	0.0997193	−	0.0324008i
$345$	−5.69879	+	0.0453450i	−0.306812	+	0.00244129i
$346$	−6.24068	+	5.61913i	−0.335501	+	0.302087i
$347$	−0.164275	+	3.13456i	−0.00881875	+	0.168272i	0.990670	+	0.136286i	$0.0435165\pi$
$347$	−0.164275	+	3.13456i	−0.00881875	+	0.168272i	−0.999488	+	0.0319861i	$0.989817\pi$
$348$	0.326363	+	0.850205i	0.0174949	+	0.0455758i
$349$	35.5336			1.90207			0.951035	−	0.309085i	$-0.100023\pi$
$349$	35.5336			1.90207			0.951035	+	0.309085i	$0.100023\pi$
$350$	21.2288	+	10.5137i	1.13473	+	0.561980i
$351$	−2.91463			−0.155572
$352$	3.11636	+	8.11840i	0.166103	+	0.432712i
$353$	0.160032	−	3.05359i	0.00851764	−	0.162526i	−0.991059	−	0.133426i	$-0.957402\pi$
$353$	0.160032	−	3.05359i	0.00851764	−	0.162526i	0.999576	−	0.0291007i	$-0.00926436\pi$
$354$	−11.5564	+	10.4054i	−0.614216	+	0.553042i
$355$	3.58226	+	2.55936i	0.190127	+	0.135837i
$356$	8.35832	−	2.71578i	0.442990	−	0.143936i
$357$	17.7353	−	5.67406i	0.938650	−	0.300303i
$358$	19.6223	+	9.99806i	1.03707	+	0.528414i
$359$	−15.3144	−	1.60961i	−0.808265	−	0.0849521i	−0.308624	−	0.951184i	$-0.599868\pi$
$359$	−15.3144	−	1.60961i	−0.808265	−	0.0849521i	−0.499642	+	0.866232i	$0.666535\pi$
$360$	−2.45219	+	2.01826i	−0.129242	+	0.106372i
$361$	−0.536330	−	5.10284i	−0.0282279	−	0.268571i
$362$	−6.96738	−	8.60400i	−0.366198	−	0.452216i
$363$	1.39615	+	8.81494i	0.0732788	+	0.462664i
$364$	7.25898	−	5.82409i	0.380474	−	0.305265i
$365$	7.09737	+	10.7409i	0.371493	+	0.562205i
$366$	−1.63924	+	15.5964i	−0.0856847	+	0.815235i
$367$	−18.8528	+	12.2431i	−0.984106	+	0.639086i	−0.933102	−	0.359613i	$-0.882909\pi$
$367$	−18.8528	+	12.2431i	−0.984106	+	0.639086i	−0.0510041	+	0.998698i	$0.516242\pi$
$368$	3.26997	+	12.2037i	0.170459	+	0.636163i
$369$	−0.720416	+	0.800103i	−0.0375034	+	0.0416517i
$370$	29.7033	−	27.1760i	1.54420	−	1.41281i
$371$	0.919012	−	3.36883i	0.0477127	−	0.174901i
$372$	−8.38546	+	4.27261i	−0.434766	+	0.221524i
$373$	−7.48037	+	2.87144i	−0.387319	+	0.148678i	−0.544232	−	0.838935i	$-0.683179\pi$
$373$	−7.48037	+	2.87144i	−0.387319	+	0.148678i	0.156914	+	0.987612i	$0.449846\pi$
$374$	9.07796	−	15.7235i	0.469410	−	0.813042i
$375$	6.31132	+	9.22861i	0.325915	+	0.476563i
$376$	11.0209	−	6.36292i	0.568360	−	0.328143i
$377$	−0.344056	+	2.17229i	−0.0177198	+	0.111878i
$378$	−0.0214103	+	4.73789i	−0.00110123	+	0.243691i
$379$	25.1057	+	8.15732i	1.28959	+	0.419013i	0.871948	−	0.489598i	$-0.162856\pi$
$379$	25.1057	+	8.15732i	1.28959	+	0.419013i	0.417642	+	0.908611i	$0.362856\pi$
$380$	−12.6399	−	3.99606i	−0.648415	−	0.204993i
$381$	3.57488	−	16.8185i	0.183147	−	0.861638i
$382$	16.9786	−	4.54941i	0.868702	−	0.232768i
$383$	31.5747	−	1.65476i	1.61339	−	0.0845544i	0.775847	−	0.630921i	$-0.217323\pi$
$383$	31.5747	−	1.65476i	1.61339	−	0.0845544i	0.837546	+	0.546366i	$0.183989\pi$
$384$	8.46970	+	6.15360i	0.432217	+	0.314024i
$385$	−3.43959	+	7.79747i	−0.175298	+	0.397396i
$386$	31.1596	−	22.6388i	1.58598	−	1.15228i
$387$	1.06406	−	0.861661i	0.0540893	−	0.0438007i
$388$	18.0811	+	6.94070i	0.917931	+	0.352361i
$389$	−2.60306	+	0.273593i	−0.131981	+	0.0138717i	−0.170288	−	0.985394i	$-0.554470\pi$
$389$	−2.60306	+	0.273593i	−0.131981	+	0.0138717i	0.0383078	+	0.999266i	$0.487803\pi$
$390$	11.5124	−	1.91741i	0.582955	−	0.0970920i
$391$	10.5434	−	14.5117i	0.533201	−	0.733889i
$392$	6.18679	+	7.78283i	0.312480	+	0.393092i
$393$	−6.08743	+	6.08743i	−0.307070	+	0.307070i
$394$	−26.4327	−	23.8001i	−1.33166	−	1.19903i
$395$	−24.8753	−	2.41455i	−1.25161	−	0.121489i
$396$	1.16332	+	1.29199i	0.0584588	+	0.0649251i
$397$	−13.7359	+	21.1515i	−0.689386	+	1.06156i	0.304645	+	0.952466i	$0.401462\pi$
$397$	−13.7359	+	21.1515i	−0.689386	+	1.06156i	−0.994031	+	0.109096i	$0.965205\pi$
$398$	−11.2002	−	1.77393i	−0.561413	−	0.0889191i
$399$	10.9319	−	7.02923i	0.547280	−	0.351902i
$400$	16.2899	−	18.6812i	0.814494	−	0.934060i
$401$	−1.31694	−	2.28101i	−0.0657650	−	0.113908i	0.831268	−	0.555872i	$-0.187615\pi$
$401$	−1.31694	−	2.28101i	−0.0657650	−	0.113908i	−0.897033	+	0.441963i	$0.854282\pi$
$402$	−1.34745	−	1.09114i	−0.0672045	−	0.0544212i
$403$	−22.6974	−	1.18952i	−1.13064	−	0.0592542i
$404$	−1.16340	+	0.247289i	−0.0578815	+	0.0123031i
$405$	−1.10259	+	1.94533i	−0.0547882	+	0.0966640i
$406$	3.52864	+	0.575239i	0.175123	+	0.0285486i
$407$	10.2413	+	10.2413i	0.507643	+	0.507643i
$408$	−0.523164	−	9.98256i	−0.0259005	−	0.494210i
$409$	11.7710	−	5.24080i	0.582040	−	0.259141i	−0.0945266	−	0.995522i	$-0.530134\pi$
$409$	11.7710	−	5.24080i	0.582040	−	0.259141i	0.676567	+	0.736381i	$0.263467\pi$
$410$	2.31920	−	3.63424i	0.114537	−	0.179482i
$411$	−3.43709	+	7.71983i	−0.169539	+	0.380791i
$412$	−12.0516	+	1.90879i	−0.593742	+	0.0940395i
$413$	4.67520	+	22.4944i	0.230051	+	1.10688i
$414$	2.68269	+	3.69240i	0.131847	+	0.181472i
$415$	10.4373	+	10.2725i	0.512348	+	0.504259i
$416$	−7.15629	−	16.0733i	−0.350866	−	0.788058i
$417$	8.30676	+	12.7913i	0.406784	+	0.626392i
$418$	3.27983	−	12.2405i	0.160422	−	0.598703i
$419$	−7.75375	−	23.8636i	−0.378796	−	1.16581i	−0.940882	−	0.338735i	$-0.890001\pi$
$419$	−7.75375	−	23.8636i	−0.378796	−	1.16581i	0.562086	−	0.827079i	$-0.309999\pi$
$420$	−1.14116	−	7.04812i	−0.0556831	−	0.343913i
$421$	10.8566	−	33.4131i	0.529118	−	1.62846i	−0.226909	−	0.973916i	$-0.572862\pi$
$421$	10.8566	−	33.4131i	0.529118	−	1.62846i	0.756026	−	0.654541i	$-0.227138\pi$
$422$	19.0567	+	12.3755i	0.927663	+	0.602432i
$423$	5.63859	−	6.96308i	0.274158	−	0.338557i
$424$	−1.62344	−	0.937291i	−0.0788410	−	0.0455189i
$425$	−35.1667	−	1.28226i	−1.70583	−	0.0621989i
$426$		−	3.52586i		−	0.170828i
$427$	18.6828	+	13.7033i	0.904126	+	0.663149i
$428$	2.76022	+	5.41724i	0.133420	+	0.261852i
$429$	0.872952	+	4.10692i	0.0421465	+	0.198284i
$430$	−3.63607	+	4.10346i	−0.175347	+	0.197886i
$431$	19.2597	+	4.09378i	0.927708	+	0.197190i	0.646901	−	0.762574i	$-0.276065\pi$
$431$	19.2597	+	4.09378i	0.927708	+	0.197190i	0.280807	+	0.959764i	$0.409398\pi$
$432$	4.78829	+	1.28302i	0.230377	+	0.0617293i
$433$	3.37294	−	6.61976i	0.162093	−	0.318125i	−0.795647	−	0.605760i	$-0.792869\pi$
$433$	3.37294	−	6.61976i	0.162093	−	0.318125i	0.957740	+	0.287635i	$0.0928690\pi$
$434$	−2.10036	+	36.8871i	−0.100820	+	1.77064i
$435$	1.31970	+	1.05140i	0.0632749	+	0.0504107i
$436$	−15.0640	−	6.70692i	−0.721434	−	0.321203i
$437$	4.48671	−	11.6883i	0.214628	−	0.559126i
$438$	3.69486	−	9.62544i	0.176547	−	0.459921i
$439$	29.0631	+	12.9397i	1.38710	+	0.617579i	0.958286	−	0.285812i	$-0.0922632\pi$
$439$	29.0631	+	12.9397i	1.38710	+	0.617579i	0.428819	+	0.903391i	$0.358930\pi$
$440$	3.57832	+	2.85082i	0.170590	+	0.135908i
$441$	6.03030	+	3.55465i	0.287157	+	0.169269i
$442$	−16.6771	+	32.7307i	−0.793249	+	1.55684i
$443$	5.35220	+	1.43412i	0.254291	+	0.0681369i	0.383712	−	0.923453i	$-0.374645\pi$
$443$	5.35220	+	1.43412i	0.254291	+	0.0681369i	−0.129422	+	0.991590i	$0.541312\pi$
$444$	−11.8688	−	2.52278i	−0.563267	−	0.119726i
$445$	10.7989	−	12.1871i	0.511919	−	0.577722i
$446$	9.16508	+	43.1183i	0.433979	+	2.04171i
$447$	−3.40302	−	6.67880i	−0.160957	−	0.315896i
$448$	−2.16931	+	0.954116i	−0.102490	+	0.0450777i
$449$		−	1.32047i		−	0.0623171i	−0.999514	−	0.0311585i	$-0.990080\pi$
$449$		−	1.32047i		−	0.0623171i	0.999514	−	0.0311585i	$-0.00991967\pi$
$450$	3.07535	−	8.40915i	0.144973	−	0.396411i
$451$	1.34317	+	0.775480i	0.0632474	+	0.0365159i
$452$	3.54681	−	4.37995i	0.166828	−	0.206016i
$453$	−14.1938	−	9.21755i	−0.666882	−	0.433078i
$454$	−14.7376	+	45.3577i	−0.691671	+	2.12874i
$455$	6.12403	−	16.1191i	0.287099	−	0.755673i
$456$	−2.15604	−	6.63561i	−0.100966	−	0.310741i
$457$	0.523772	−	1.95474i	0.0245010	−	0.0914390i	−0.952593	−	0.304248i	$-0.901595\pi$
$457$	0.523772	−	1.95474i	0.0245010	−	0.0914390i	0.977094	+	0.212809i	$0.0682614\pi$
$458$	−19.0526	−	29.3384i	−0.890269	−	1.37089i
$459$	−2.86262	−	6.42954i	−0.133615	−	0.300105i
$460$	−4.90194	−	4.82455i	−0.228554	−	0.224946i
$461$	15.3631	+	21.1455i	0.715533	+	0.984846i	0.999660	+	0.0260596i	$0.00829597\pi$
$461$	15.3631	+	21.1455i	0.715533	+	0.984846i	−0.284128	+	0.958786i	$0.591704\pi$
$462$	6.68243	−	1.38886i	0.310895	−	0.0646157i
$463$	−20.0012	+	3.16788i	−0.929536	+	0.147224i	−0.602801	−	0.797892i	$-0.705949\pi$
$463$	−20.0012	+	3.16788i	−0.929536	+	0.147224i	−0.326735	+	0.945116i	$0.605949\pi$
$464$	1.52147	−	3.41728i	0.0706325	−	0.158643i
$465$	−9.38023	+	14.6990i	−0.434998	+	0.681651i
$466$	29.3953	−	13.0877i	1.36171	−	0.606274i
$467$	0.681635	+	13.0064i	0.0315423	+	0.601863i	0.967980	+	0.251029i	$0.0807688\pi$
$467$	0.681635	+	13.0064i	0.0315423	+	0.601863i	−0.936437	+	0.350835i	$0.885898\pi$
$468$	−2.48730	−	2.48730i	−0.114975	−	0.114975i
$469$	−2.39562	+	0.907193i	−0.110619	+	0.0418903i
$470$	−17.6910	+	31.2127i	−0.816027	+	1.43974i
$471$	−16.7252	+	3.55504i	−0.770654	+	0.163808i
$472$	12.3169	+	0.645501i	0.566931	+	0.0297116i
$473$	−1.53283	−	1.24126i	−0.0704798	−	0.0570734i
$474$	10.0076	+	17.3337i	0.459665	+	0.796163i
$475$	−23.9406	+	5.48831i	−1.09847	+	0.251821i
$476$	19.9771	+	10.2928i	0.915650	+	0.471771i
$477$	−1.30358	−	0.206466i	−0.0596867	−	0.00945345i
$478$	−12.1679	+	18.7370i	−0.556549	+	0.857010i
$479$	−4.32522	−	4.80364i	−0.197624	−	0.219484i	0.636185	−	0.771536i	$-0.280511\pi$
$479$	−4.32522	−	4.80364i	−0.197624	−	0.219484i	−0.833809	+	0.552053i	$0.813845\pi$
$480$	−13.4351	−	1.30409i	−0.613224	−	0.0595232i
$481$	−21.7771	−	19.6082i	−0.992950	−	0.894056i
$482$	−17.1040	+	17.1040i	−0.779067	+	0.779067i
$483$	6.70929	−	0.674535i	0.305283	−	0.0306924i
$484$	−6.33106	+	8.71396i	−0.287776	+	0.396089i
$485$	35.3964	−	5.89532i	1.60727	−	0.267693i
$486$	1.78096	−	0.187187i	0.0807861	−	0.00849096i
$487$	10.8198	+	4.15332i	0.490291	+	0.188205i	0.590938	−	0.806717i	$-0.298758\pi$
$487$	10.8198	+	4.15332i	0.490291	+	0.188205i	−0.100647	+	0.994922i	$0.532091\pi$
$488$	9.66627	−	7.82759i	0.437572	−	0.354339i
$489$	−13.0502	+	9.48153i	−0.590151	+	0.428770i
$490$	−26.1574	−	10.0733i	−1.18167	−	0.455067i
$491$	23.7554	+	17.2593i	1.07207	+	0.778902i	0.976283	−	0.216501i	$-0.0694643\pi$
$491$	23.7554	+	17.2593i	1.07207	+	0.778902i	0.0957837	+	0.995402i	$0.469464\pi$
$492$	−1.29758	+	0.0680035i	−0.0584996	+	0.00306583i
$493$	−5.12988	+	1.37455i	−0.231038	+	0.0619064i
$494$	−5.33077	+	25.0793i	−0.239843	+	1.12837i
$495$	3.07133	+	0.970988i	0.138046	+	0.0436427i
$496$	36.7647	+	11.9456i	1.65078	+	0.536372i
$497$	−4.49951	−	2.62497i	−0.201831	−	0.117746i
$498$	1.83469	−	11.5838i	0.0822146	−	0.519083i
$499$	−18.3208	+	10.5775i	−0.820151	+	0.473514i	−0.850468	−	0.526026i	$-0.823681\pi$
$499$	−18.3208	+	10.5775i	−0.820151	+	0.473514i	0.0303176	+	0.999540i	$0.490348\pi$
$500$	−2.48957	+	13.2615i	−0.111337	+	0.593072i
$501$	6.75334	−	11.6971i	0.301717	−	0.522589i
$502$	−36.1923	+	13.8929i	−1.61534	+	0.620071i
$503$	−7.75553	+	3.95164i	−0.345802	+	0.176195i	−0.618262	−	0.785972i	$-0.712163\pi$
$503$	−7.75553	+	3.95164i	−0.345802	+	0.176195i	0.272460	+	0.962167i	$0.412163\pi$
$504$	2.66916	−	2.64515i	0.118894	−	0.117824i
$505$	−1.62588	+	1.48755i	−0.0723509	+	0.0661950i
$506$	4.39937	−	4.88599i	0.195576	−	0.217209i
$507$	1.16596	+	4.35142i	0.0517821	+	0.193253i
$508$	17.4034	−	11.3019i	0.772149	−	0.501439i
$509$	−0.247240	+	2.35233i	−0.0109587	+	0.104265i	−0.998634	−	0.0522522i	$-0.983360\pi$
$509$	−0.247240	+	2.35233i	−0.0109587	+	0.104265i	0.987675	+	0.156517i	$0.0500267\pi$
$510$	15.5367	+	23.5127i	0.687977	+	1.04116i
$511$	−9.53267	−	11.8812i	−0.421700	−	0.525595i
$512$	2.47837	+	15.6478i	0.109530	+	0.691543i
$513$	−3.09143	−	3.81759i	−0.136490	−	0.168551i
$514$	4.21418	+	40.0953i	0.185880	+	1.76853i
$515$	−17.4556	+	14.3667i	−0.769185	+	0.633073i
$516$	1.64338	+	0.172726i	0.0723457	+	0.00760384i
$517$	−11.5003	−	5.85968i	−0.505781	−	0.257708i
$518$	−32.0341	+	35.2558i	−1.40750	+	1.54905i
$519$	4.45989	−	1.44911i	0.195768	−	0.0636088i
$520$	−7.53189	−	5.38120i	−0.330295	−	0.235981i
$521$	18.4346	−	16.5986i	0.807634	−	0.727197i	−0.157905	−	0.987454i	$-0.550474\pi$
$521$	18.4346	−	16.5986i	0.807634	−	0.727197i	0.965539	+	0.260257i	$0.0838074\pi$
$522$	0.0707219	−	1.34945i	0.00309541	−	0.0590640i
$523$	−6.37286	−	16.6019i	−0.278666	−	0.725949i	−0.999462	−	0.0328016i	$-0.989557\pi$
$523$	−6.37286	−	16.6019i	−0.278666	−	0.725949i	0.720796	−	0.693147i	$-0.243776\pi$
$524$	−10.3898			−0.453881
$525$	−8.44173	−	10.1851i	−0.368427	−	0.444516i
$526$	−20.5942			−0.897948
$527$	−19.6683	−	51.2376i	−0.856764	−	2.23195i
$528$	0.373736	−	7.13131i	0.0162648	−	0.310350i
$529$	−12.2651	+	11.0436i	−0.533266	+	0.480155i
$530$	5.28480	−	0.0420509i	0.229557	−	0.00182657i
$531$	8.25877	−	2.68344i	0.358400	−	0.116451i
$532$	15.3277	+	3.33047i	0.664541	+	0.144394i
$533$	−2.79600	−	1.42463i	−0.121108	−	0.0617077i
$534$	−12.9691	−	1.36310i	−0.561226	−	0.0589873i
$535$	9.49597	+	6.05989i	0.410547	+	0.261992i
$536$	0.143744	+	1.36764i	0.00620881	+	0.0590729i
$537$	−7.73928	−	9.55722i	−0.333975	−	0.412424i
$538$	−8.13010	−	51.3314i	−0.350514	−	2.21306i
$539$	3.20263	−	9.56175i	0.137947	−	0.411854i
$540$	−2.60104	+	0.719176i	−0.111931	+	0.0309484i
$541$	−1.32153	+	12.5735i	−0.0568169	+	0.540576i	0.928680	+	0.370882i	$0.120945\pi$
$541$	−1.32153	+	12.5735i	−0.0568169	+	0.540576i	−0.985497	+	0.169694i	$0.945722\pi$
$542$	12.9361	−	8.40080i	0.555653	−	0.360845i
$543$	1.60012	+	5.97175i	0.0686679	+	0.256272i
$544$	28.4283	−	31.5729i	1.21886	−	1.35368i
$545$	−30.3580	+	3.43519i	−1.30039	+	0.147147i
$546$	−13.3548	+	3.51381i	−0.571533	+	0.150377i
$547$	−6.45718	+	3.29010i	−0.276089	+	0.140674i	−0.586553	−	0.809911i	$-0.699516\pi$
$547$	−6.45718	+	3.29010i	−0.276089	+	0.140674i	0.310464	+	0.950585i	$0.399516\pi$
$548$	−9.52112	+	3.65482i	−0.406722	+	0.156126i
$549$	4.37864	−	7.58402i	0.186876	−	0.323678i
$550$	−12.7702	−	1.81478i	−0.544522	−	0.0773827i
$551$	−3.21019	+	1.85341i	−0.136759	+	0.0789577i
$552$	0.566280	−	3.57535i	0.0241025	−	0.152177i
$553$	29.5709	+	0.133630i	1.25748	+	0.00568251i
$554$	24.1190	+	7.83673i	1.02472	+	0.332951i
$555$	−21.3253	+	7.11711i	−0.905210	+	0.302104i
$556$	−3.82702	+	18.0047i	−0.162302	+	0.763569i
$557$	−7.53065	+	2.01783i	−0.319084	+	0.0854983i	−0.414806	−	0.909910i	$-0.636151\pi$
$557$	−7.53065	+	2.01783i	−0.319084	+	0.0854983i	0.0957222	+	0.995408i	$0.469484\pi$
$558$	13.9454	−	0.730850i	0.590358	−	0.0309393i
$559$	3.22854	+	2.34567i	0.136553	+	0.0992113i
$560$	−17.1564	+	23.7854i	−0.724992	+	1.00511i
$561$	−8.20230	+	5.95932i	−0.346301	+	0.251603i
$562$	31.1430	−	25.2191i	1.31369	−	1.06380i
$563$	30.8874	+	11.8566i	1.30175	+	0.499694i	0.907787	−	0.419432i	$-0.137771\pi$
$563$	30.8874	+	11.8566i	1.30175	+	0.499694i	0.393962	+	0.919127i	$0.371104\pi$
$564$	10.7540	−	1.13030i	0.452827	−	0.0475940i
$565$	1.55141	−	10.3263i	0.0652683	−	0.434432i
$566$	−3.59161	+	4.94342i	−0.150966	+	0.207787i
$567$	1.08704	−	2.41213i	0.0456512	−	0.101300i
$568$	−1.97741	+	1.97741i	−0.0829704	+	0.0829704i
$569$	−14.1105	−	12.7051i	−0.591542	−	0.532627i	0.318080	−	0.948064i	$-0.396962\pi$
$569$	−14.1105	−	12.7051i	−0.591542	−	0.532627i	−0.909622	+	0.415437i	$0.863629\pi$
$570$	14.7222	+	13.0453i	0.616645	+	0.546408i
$571$	18.7832	+	20.8608i	0.786051	+	0.872998i	0.994468	−	0.105042i	$-0.0334978\pi$
$571$	18.7832	+	20.8608i	0.786051	+	0.872998i	−0.208417	+	0.978040i	$0.566831\pi$
$572$	−2.75981	+	4.24973i	−0.115393	+	0.177690i
$573$	−9.69479	−	1.53550i	−0.405006	−	0.0641466i
$574$	−2.33636	+	4.53458i	−0.0975176	+	0.189270i
$575$	−12.3600	−	3.10191i	−0.515447	−	0.129359i
$576$	0.447861	+	0.775719i	0.0186609	+	0.0323216i
$577$	11.1842	+	9.05681i	0.465606	+	0.377040i	0.833223	−	0.552937i	$-0.186493\pi$
$577$	11.1842	+	9.05681i	0.465606	+	0.377040i	−0.367617	+	0.929977i	$0.619826\pi$
$578$	−58.1804	−	3.04910i	−2.41998	−	0.126826i
$579$	−21.0377	+	4.47170i	−0.874297	+	0.185838i
$580$	0.228966	+	2.02346i	0.00950729	+	0.0840195i
$581$	−13.4167	−	10.9654i	−0.556619	−	0.454921i
$582$	−20.3208	−	20.3208i	−0.842325	−	0.842325i
$583$	0.0995050	+	1.89867i	0.00412108	+	0.0786348i
$584$	−7.47044	+	3.32605i	−0.309129	+	0.137633i
$585$	−6.30847	−	1.63666i	−0.260823	−	0.0676677i
$586$	19.4771	−	43.7462i	0.804590	−	1.80714i
$587$	10.5782	−	1.67542i	0.436608	−	0.0691519i	0.0657385	−	0.997837i	$-0.479060\pi$
$587$	10.5782	−	1.67542i	0.436608	−	0.0691519i	0.370870	+	0.928685i	$0.379060\pi$
$588$	2.11268	+	8.17962i	0.0871254	+	0.337322i
$589$	−22.5161	−	30.9908i	−0.927760	−	1.27695i
$590$	−30.8558	+	16.0323i	−1.27031	+	0.660041i
$591$	8.07869	+	18.1450i	0.332313	+	0.746387i
$592$	27.1449	+	41.7995i	1.11565	+	1.71795i
$593$	5.51623	−	20.5869i	0.226525	−	0.845401i	−0.755263	−	0.655421i	$-0.772491\pi$
$593$	5.51623	−	20.5869i	0.226525	−	0.845401i	0.981788	−	0.189980i	$-0.0608423\pi$
$594$	−0.797169	−	2.45343i	−0.0327083	−	0.100666i
$595$	41.5726	−	2.32207i	1.70431	−	0.0951955i
$596$	2.79549	−	8.60364i	0.114508	−	0.352419i
$597$	5.31074	+	3.44884i	0.217354	+	0.141151i
$598$	−8.37157	+	10.3380i	−0.342339	+	0.422753i
$599$	−0.330923	−	0.191059i	−0.0135212	−	0.00780644i	0.493224	−	0.869902i	$-0.335818\pi$
$599$	−0.330923	−	0.191059i	−0.0135212	−	0.00780644i	−0.506745	+	0.862096i	$0.669152\pi$
$600$	−6.44087	+	2.99136i	−0.262947	+	0.122122i
$601$			34.1965i			1.39490i	0.716632	+	0.697452i	$0.245683\pi$
$601$			34.1965i			1.39490i	−0.716632	+	0.697452i	$0.754317\pi$
$602$	3.83673	−	5.23093i	0.156373	−	0.213197i
$603$	0.439557	+	0.862680i	0.0179002	+	0.0351310i
$604$	−4.24663	−	19.9788i	−0.172793	−	0.812926i
$605$	−1.92804	+	19.8631i	−0.0783859	+	0.807552i
$606$	1.72628	+	0.366933i	0.0701255	+	0.0149056i
$607$	−25.9942	−	6.96513i	−1.05507	−	0.282706i	−0.310726	−	0.950499i	$-0.600572\pi$
$607$	−25.9942	−	6.96513i	−1.05507	−	0.282706i	−0.744347	+	0.667794i	$0.767239\pi$
$608$	13.4625	−	26.4216i	0.545975	−	1.07154i
$609$	−1.66945	−	1.09491i	−0.0676494	−	0.0443680i
$610$	−12.3059	+	32.8365i	−0.498251	+	1.32951i
$611$	23.8568	+	10.6217i	0.965144	+	0.429710i
$612$	3.04395	−	7.92976i	0.123044	−	0.320542i
$613$	8.33581	−	21.7155i	0.336680	−	0.877082i	−0.655829	−	0.754910i	$-0.727681\pi$
$613$	8.33581	−	21.7155i	0.336680	−	0.877082i	0.992509	−	0.122172i	$-0.0389860\pi$
$614$	23.7220	+	10.5617i	0.957341	+	0.426236i
$615$	−2.00856	+	1.32722i	−0.0809930	+	0.0535185i
$616$	−4.52663	−	2.96880i	−0.182383	−	0.119616i
$617$	8.52225	−	16.7258i	0.343093	−	0.673357i	−0.653402	−	0.757011i	$-0.726659\pi$
$617$	8.52225	−	16.7258i	0.343093	−	0.673357i	0.996495	+	0.0836536i	$0.0266589\pi$
$618$	17.4885	+	4.68602i	0.703489	+	0.188499i
$619$	−21.0650	−	4.47751i	−0.846675	−	0.179966i	−0.235907	−	0.971776i	$-0.575806\pi$
$619$	−21.0650	−	4.47751i	−0.846675	−	0.179966i	−0.610768	+	0.791809i	$0.709139\pi$
$620$	−20.5488	+	4.53897i	−0.825260	+	0.182289i
$621$	−0.529895	−	2.49296i	−0.0212640	−	0.100039i
$622$	25.4472	+	49.9429i	1.02034	+	2.00253i
$623$	−11.3949	+	15.5356i	−0.456527	+	0.622421i
$624$			14.4484i			0.578400i
$625$	8.47812	+	23.5185i	0.339125	+	0.940741i
$626$	−28.7570	−	16.6029i	−1.14936	−	0.663585i
$627$	−4.45335	+	5.49943i	−0.177850	+	0.219626i
$628$	−17.3068	−	11.2391i	−0.690615	−	0.448490i
$629$	21.8663	−	67.2975i	0.871866	−	2.68333i
$630$	−2.70682	+	10.2427i	−0.107842	+	0.408080i
$631$	−3.42229	−	10.5327i	−0.136239	−	0.419301i	0.859542	−	0.511066i	$-0.170749\pi$
$631$	−3.42229	−	10.5327i	−0.136239	−	0.419301i	−0.995781	+	0.0917648i	$0.970749\pi$
$632$	4.10870	−	15.3339i	0.163435	−	0.609949i
$633$	−6.91073	−	10.6416i	−0.274677	−	0.422965i
$634$	5.32005	+	11.9490i	0.211286	+	0.474556i
$635$	17.1817	−	34.3948i	0.681834	−	1.36491i
$636$	−0.936255	−	1.28864i	−0.0371249	−	0.0510981i
$637$	−5.45843	+	19.6587i	−0.216271	+	0.778906i
$638$	−1.92266	+	0.304519i	−0.0761186	+	0.0120560i
$639$	−0.800825	+	1.79868i	−0.0316802	+	0.0711548i
$640$	14.8765	+	18.0749i	0.588044	+	0.714475i
$641$	12.7393	−	5.67192i	0.503174	−	0.224027i	−0.139422	−	0.990233i	$-0.544524\pi$
$641$	12.7393	−	5.67192i	0.503174	−	0.224027i	0.642595	+	0.766206i	$0.277858\pi$
$642$	−0.472149	−	9.00914i	−0.0186342	−	0.355562i
$643$	−9.71117	−	9.71117i	−0.382971	−	0.382971i	0.489200	−	0.872171i	$-0.337289\pi$
$643$	−9.71117	−	9.71117i	−0.382971	−	0.382971i	−0.872171	+	0.489200i	$0.837289\pi$
$644$	6.30122	+	5.14995i	0.248303	+	0.202936i
$645$	2.78692	−	1.26748i	0.109735	−	0.0499071i
$646$	−60.5594	+	12.8723i	−2.38268	+	0.506454i
$647$	−14.5824	−	0.764231i	−0.573293	−	0.0300450i	−0.236513	−	0.971628i	$-0.576005\pi$
$647$	−14.5824	−	0.764231i	−0.573293	−	0.0300450i	−0.336780	+	0.941583i	$0.609338\pi$
$648$	−1.10380	−	0.893839i	−0.0433613	−	0.0351133i
$649$	−6.25471	−	10.8335i	−0.245519	−	0.425251i
$650$	25.9944	+	2.31455i	1.01958	+	0.0907841i
$651$	9.44960	−	18.3405i	0.370359	−	0.718822i
$652$	−19.2282	−	3.04545i	−0.753034	−	0.119269i
$653$	−15.4114	+	23.7314i	−0.603093	+	0.928682i	0.396848	+	0.917884i	$0.370104\pi$
$653$	−15.4114	+	23.7314i	−0.603093	+	0.928682i	−0.999942	+	0.0107981i	$0.996563\pi$
$654$	16.3720	+	18.1830i	0.640197	+	0.711011i
$655$	−16.5940	+	9.75741i	−0.648381	+	0.381254i
$656$	3.96628	+	3.57125i	0.154857	+	0.139434i
$657$	−4.07112	+	4.07112i	−0.158829	+	0.158829i
$658$	17.4415	−	38.7025i	0.679939	−	1.50878i
$659$	−16.2832	+	22.4119i	−0.634303	+	0.873043i	−0.998296	−	0.0583588i	$-0.981413\pi$
$659$	−16.2832	+	22.4119i	−0.634303	+	0.873043i	0.363993	+	0.931402i	$0.381413\pi$
$660$	1.79240	+	3.44964i	0.0697690	+	0.134277i
$661$	−4.33611	+	0.455744i	−0.168655	+	0.0177264i	−0.188480	−	0.982077i	$-0.560356\pi$
$661$	−4.33611	+	0.455744i	−0.168655	+	0.0177264i	0.0198244	+	0.999803i	$0.493689\pi$
$662$	29.4838	+	11.3178i	1.14592	+	0.439878i
$663$	15.9418	−	12.9094i	0.619127	−	0.501359i
$664$	−7.52552	+	5.46761i	−0.292047	+	0.212184i
$665$	27.6083	−	9.07553i	1.07060	−	0.351934i
$666$	14.5660	+	10.5828i	0.564421	+	0.410076i
$667$	−1.92056	+	0.100652i	−0.0743645	+	0.00389728i
$668$	15.7453	−	4.21894i	0.609204	−	0.163236i
$669$	5.11795	−	24.0781i	0.197871	−	0.930912i
$670$	−2.30372	−	3.11832i	−0.0890004	−	0.120471i
$671$	−11.9978	−	3.89833i	−0.463172	−	0.150494i
$672$	15.9711	+	0.0721728i	0.616099	+	0.00278413i
$673$	−0.667504	+	4.21445i	−0.0257304	+	0.162455i	−0.997208	−	0.0746769i	$-0.976207\pi$
$673$	−0.667504	+	4.21445i	−0.0257304	+	0.162455i	0.971477	+	0.237132i	$0.0762074\pi$
$674$	−35.2038	+	20.3249i	−1.35600	+	0.782888i
$675$	−3.47883	+	3.59135i	−0.133900	+	0.138231i
$676$	−2.71841	+	4.70843i	−0.104554	+	0.181094i
$677$	41.8788	−	16.0758i	1.60953	−	0.617842i	0.623121	−	0.782125i	$-0.285864\pi$
$677$	41.8788	−	16.0758i	1.60953	−	0.617842i	0.986413	+	0.164283i	$0.0525309\pi$
$678$	−7.45125	+	3.79660i	−0.286164	+	0.145808i
$679$	−41.0610	+	10.8036i	−1.57578	+	0.414605i
$680$	4.47320	−	21.9001i	0.171539	−	0.839832i
$681$	17.8203	−	19.7915i	0.682877	−	0.758411i
$682$	−5.20657	−	19.4312i	−0.199370	−	0.744059i
$683$	−22.4008	+	14.5472i	−0.857143	+	0.556635i	−0.896728	−	0.442581i	$-0.854063\pi$
$683$	−22.4008	+	14.5472i	−0.857143	+	0.556635i	0.0395857	+	0.999216i	$0.487396\pi$
$684$	0.619698	−	5.89604i	0.0236948	−	0.225441i
$685$	−11.7742	+	14.7789i	−0.449870	+	0.564671i
$686$	31.9162	+	9.01737i	1.21856	+	0.344285i
$687$	3.05589	+	19.2941i	0.116589	+	0.736116i
$688$	−4.27143	−	5.27478i	−0.162847	−	0.201099i
$689$	−0.402101	−	3.82574i	−0.0153188	−	0.145749i
$690$	3.73304	+	9.49830i	0.142114	+	0.361594i
$691$	34.4049	+	3.61610i	1.30882	+	0.137563i	0.733122	−	0.680097i	$-0.238062\pi$
$691$	34.4049	+	3.61610i	1.30882	+	0.137563i	0.575701	+	0.817660i	$0.304729\pi$
$692$	5.04264	+	2.56935i	0.191692	+	0.0976721i
$693$	−3.72443	−	0.809259i	−0.141479	−	0.0307412i
$694$	5.34587	−	1.73698i	0.202926	−	0.0659348i
$695$	10.7965	+	32.3501i	0.409535	+	1.22711i
$696$	−0.796479	+	0.717153i	−0.0301905	+	0.0271836i
$697$	0.396572	−	7.56705i	0.0150212	−	0.286623i
$698$	−22.8039	−	59.4061i	−0.863139	−	2.24855i
$699$	−17.9683			−0.679625
$700$	1.48780	−	15.8958i	0.0562337	−	0.600806i
$701$	−45.8468			−1.73161			−0.865804	−	0.500383i	$-0.833193\pi$
$701$	−45.8468			−1.73161			−0.865804	+	0.500383i	$0.833193\pi$
$702$	1.87048	+	4.87277i	0.0705967	+	0.183911i
$703$	2.58482	−	49.3213i	0.0974883	−	1.86019i
$704$	0.958904	−	0.863401i	0.0361400	−	0.0325406i
$705$	16.1142	−	11.9047i	0.606897	−	0.448358i
$706$	−5.20779	+	1.69211i	−0.195998	+	0.0636835i
$707$	1.75347	−	1.92981i	0.0659459	−	0.0725780i
$708$	9.33788	+	4.75789i	0.350939	+	0.178812i
$709$	−2.33717	−	0.245646i	−0.0877742	−	0.00922544i	0.0605395	−	0.998166i	$-0.480718\pi$
$709$	−2.33717	−	0.245646i	−0.0877742	−	0.00922544i	−0.148314	+	0.988940i	$0.547385\pi$
$710$	1.97989	−	7.63141i	0.0743038	−	0.286402i
$711$	−1.16830	−	11.1156i	−0.0438147	−	0.416869i
$712$	6.50899	+	8.03793i	0.243935	+	0.301234i
$713$	−3.10907	−	19.6299i	−0.116436	−	0.735146i
$714$	−20.8678	−	26.0090i	−0.780957	−	0.973362i
$715$	−0.416742	+	9.37926i	−0.0155853	+	0.350764i
$716$	1.55139	−	14.7605i	0.0579783	−	0.551627i
$717$	10.4631	−	6.79480i	0.390751	−	0.253757i
$718$	7.13713	+	26.6361i	0.266355	+	0.994051i
$719$	−31.0626	+	34.4985i	−1.15844	+	1.28658i	−0.207140	+	0.978311i	$0.566416\pi$
$719$	−31.0626	+	34.4985i	−1.15844	+	1.28658i	−0.951300	+	0.308267i	$0.900251\pi$
$720$	9.64338	+	5.46577i	0.359388	+	0.203697i
$721$	19.0001	−	18.8291i	0.707600	−	0.701233i
$722$	−8.18689	+	4.17143i	−0.304685	+	0.155245i
$723$	12.6103	−	4.84064i	0.468982	−	0.180025i
$724$	−3.73066	+	6.46170i	−0.138649	+	0.240147i
$725$	2.26599	+	3.01672i	0.0841566	+	0.112038i
$726$	13.8411	−	7.99116i	0.513691	−	0.296580i
$727$	−4.38202	+	27.6670i	−0.162520	+	1.02611i	0.762720	+	0.646729i	$0.223864\pi$
$727$	−4.38202	+	27.6670i	−0.162520	+	1.02611i	−0.925240	+	0.379383i	$0.876136\pi$
$728$	9.46045	+	5.51915i	0.350628	+	0.204553i
$729$	−0.951057	−	0.309017i	−0.0352243	−	0.0114451i
$730$	13.4022	−	18.7586i	0.496038	−	0.694288i
$731$	−2.00352	+	9.42581i	−0.0741028	+	0.348626i
$732$	10.2087	−	2.73542i	0.377325	−	0.101104i
$733$	23.1091	−	1.21110i	0.853553	−	0.0447328i	0.379461	−	0.925208i	$-0.376110\pi$
$733$	23.1091	−	1.21110i	0.853553	−	0.0447328i	0.474093	+	0.880475i	$0.342776\pi$
$734$	32.5673	+	23.6615i	1.20208	+	0.873362i
$735$	11.0560	+	11.0799i	0.407807	+	0.408689i
$736$	12.4469	−	9.04317i	0.458797	−	0.333336i
$737$	1.08393	−	0.877745i	0.0399269	−	0.0323322i
$738$	1.79997	+	0.690943i	0.0662577	+	0.0254339i
$739$	31.8585	−	3.34846i	1.17193	−	0.123175i	0.501508	−	0.865153i	$-0.332779\pi$
$739$	31.8585	−	3.34846i	1.17193	−	0.123175i	0.670424	+	0.741978i	$0.266112\pi$
$740$	−24.2723	−	12.1251i	−0.892267	−	0.445726i
$741$	8.41569	−	11.5832i	0.309158	−	0.425520i
$742$	−6.22189	+	0.625534i	−0.228413	+	0.0229641i
$743$	18.8587	−	18.8587i	0.691858	−	0.691858i	−0.270782	−	0.962641i	$-0.587282\pi$
$743$	18.8587	−	18.8587i	0.691858	−	0.691858i	0.962641	+	0.270782i	$0.0872823\pi$
$744$	−8.23092	−	7.41116i	−0.301760	−	0.271706i
$745$	−3.61516	−	16.3666i	−0.132449	−	0.599625i
$746$	9.60113	+	10.6631i	0.351522	+	0.390405i
$747$	−3.56697	+	5.49266i	−0.130509	+	0.200966i
$748$	−12.0853	−	1.91412i	−0.441881	−	0.0699871i
$749$	−11.8485	−	6.10470i	−0.432934	−	0.223061i
$750$	11.3783	−	16.4740i	0.415479	−	0.601544i
$751$	17.9590	+	31.1059i	0.655334	+	1.13507i	0.981810	+	0.189866i	$0.0608055\pi$
$751$	17.9590	+	31.1059i	0.655334	+	1.13507i	−0.326476	+	0.945206i	$0.605861\pi$
$752$	−34.5174	−	27.9517i	−1.25872	−	1.01929i
$753$	21.6186	+	1.13299i	0.787827	+	0.0412883i
$754$	3.85249	−	0.818872i	0.140299	−	0.0298216i
$755$	−25.5452	−	27.9209i	−0.929686	−	1.01614i
$756$	2.98612	−	1.13081i	0.108604	−	0.0411271i
$757$	3.27989	+	3.27989i	0.119210	+	0.119210i	0.764195	−	0.644985i	$-0.223137\pi$
$757$	3.27989	+	3.27989i	0.119210	+	0.119210i	−0.644985	+	0.764195i	$0.723137\pi$
$758$	−2.47403	−	47.2074i	−0.0898610	−	1.71465i
$759$	−3.35405	+	1.49332i	−0.121744	+	0.0542040i
$760$	−0.940446	−	15.5729i	−0.0341136	−	0.564888i
$761$	−1.83725	+	4.12653i	−0.0666002	+	0.149586i	−0.943779	−	0.330578i	$-0.892756\pi$
$761$	−1.83725	+	4.12653i	−0.0666002	+	0.149586i	0.877179	+	0.480164i	$0.159423\pi$
$762$	−30.4119	+	4.81677i	−1.10171	+	0.174493i
$763$	35.3930	−	7.35600i	1.28131	−	0.266305i
$764$	−6.96299	−	9.58373i	−0.251912	−	0.346727i
$765$	−2.58548	−	15.5236i	−0.0934783	−	0.561258i
$766$	−23.0297	−	51.7256i	−0.832098	−	1.86892i
$767$	13.7848	+	21.2268i	0.497741	+	0.766455i
$768$	5.31595	−	19.8394i	0.191823	−	0.715893i
$769$	−1.78874	−	5.50517i	−0.0645035	−	0.198521i	0.913611	−	0.406590i	$-0.133282\pi$
$769$	−1.78874	−	5.50517i	−0.0645035	−	0.198521i	−0.978114	+	0.208069i	$0.933282\pi$
$770$	15.2434	+	0.746334i	0.549335	+	0.0268960i
$771$	6.95698	−	21.4114i	0.250550	−	0.771112i
$772$	−21.7693	−	14.1371i	−0.783493	−	0.508806i
$773$	−24.7216	+	30.5286i	−0.889173	+	1.09804i	0.105445	+	0.994425i	$0.466373\pi$
$773$	−24.7216	+	30.5286i	−0.889173	+	1.09804i	−0.994618	+	0.103612i	$0.966960\pi$
$774$	−2.12342	−	1.22596i	−0.0763247	−	0.0440661i
$775$	−28.5567	+	26.5474i	−1.02579	+	0.953612i
$776$			22.7931i			0.818224i
$777$	24.3495	−	10.7095i	0.873534	−	0.384202i
$778$	2.12793	+	4.17630i	0.0762901	+	0.149728i
$779$	−1.09961	−	5.17326i	−0.0393976	−	0.185351i
$780$	−3.98683	−	6.78023i	−0.142752	−	0.242771i
$781$	2.77432	+	0.589700i	0.0992730	+	0.0211011i
$782$	−31.0274	−	8.31376i	−1.10954	−	0.297299i
$783$	−0.342578	+	0.672348i	−0.0122428	+	0.0240278i
$784$	17.6211	−	29.8934i	0.629325	−	1.06762i
$785$	−38.1964	−	1.69715i	−1.36329	−	0.0605740i
$786$	14.0838	+	6.27050i	0.502352	+	0.223661i
$787$	10.5020	−	27.3586i	0.374355	−	0.975227i	−0.608942	−	0.793215i	$-0.708406\pi$
$787$	10.5020	−	27.3586i	0.374355	−	0.975227i	0.983296	−	0.182012i	$-0.0582610\pi$
$788$	−8.59044	+	22.3789i	−0.306022	+	0.797214i
$789$	10.5059	+	4.67753i	0.374020	+	0.166525i
$790$	11.9272	+	43.1369i	0.424349	+	1.53474i
$791$	−0.702382	+	12.3354i	−0.0249738	+	0.438597i
$792$	−0.928886	+	1.82304i	−0.0330065	+	0.0647789i
$793$	24.6545	+	6.60616i	0.875507	+	0.234591i
$794$	44.1768	+	9.39006i	1.56777	+	0.333241i
$795$	−2.70554	−	1.17888i	−0.0959557	−	0.0418106i
$796$	1.58892	+	7.47527i	0.0563177	+	0.264954i
$797$	−6.10448	−	11.9807i	−0.216232	−	0.424379i	0.757256	−	0.653118i	$-0.226540\pi$
$797$	−6.10448	−	11.9807i	−0.216232	−	0.424379i	−0.973488	+	0.228739i	$0.926540\pi$
$798$	−18.7673	−	13.7652i	−0.664355	−	0.487284i
$799$			63.0592i			2.23088i
$800$	−28.3467	−	10.3668i	−1.00221	−	0.366522i
$801$	6.30645	+	3.64103i	0.222827	+	0.128649i
$802$	−2.96831	+	3.66556i	−0.104815	+	0.129435i
$803$	6.95581	+	4.51716i	0.245465	+	0.159407i
$804$	−0.361085	+	1.11131i	−0.0127345	+	0.0391927i
$805$	14.9004	+	2.30751i	0.525171	+	0.0813292i
$806$	12.5775	+	38.7095i	0.443023	+	1.36349i
$807$	−7.51138	+	28.0328i	−0.264413	+	0.986803i
$808$	−0.762367	−	1.17394i	−0.0268200	−	0.0412991i
$809$	19.0296	+	42.7411i	0.669044	+	1.50270i	0.854176	+	0.519984i	$0.174062\pi$
$809$	19.0296	+	42.7411i	0.669044	+	1.50270i	−0.185132	+	0.982714i	$0.559271\pi$
$810$	3.95985	+	0.594920i	0.139135	+	0.0209034i
$811$	24.3744	+	33.5484i	0.855900	+	1.17804i	0.982532	+	0.186095i	$0.0595832\pi$
$811$	24.3744	+	33.5484i	0.855900	+	1.17804i	−0.126632	+	0.991950i	$0.540417\pi$
$812$	−0.490301	−	2.35905i	−0.0172062	−	0.0827865i
$813$	−8.50729	+	1.34742i	−0.298364	+	0.0472562i
$814$	10.5493	−	23.6941i	0.369753	−	0.830479i
$815$	−33.5702	+	13.1938i	−1.17591	+	0.462159i
$816$	−31.8726	+	14.1906i	−1.11576	+	0.496770i
$817$	0.352007	+	6.71670i	0.0123152	+	0.234988i
$818$	−16.3158	−	16.3158i	−0.570470	−	0.570470i
$819$	7.61092	+	1.24073i	0.265947	+	0.0433547i
$820$	−2.84669	−	0.581449i	−0.0994108	−	0.0203051i
$821$	43.7114	−	9.29114i	1.52554	−	0.324263i	0.632612	−	0.774469i	$-0.281983\pi$
$821$	43.7114	−	9.29114i	1.52554	−	0.324263i	0.892925	+	0.450206i	$0.148649\pi$
$822$	15.1120	+	0.791988i	0.527092	+	0.0276237i
$823$	34.7768	+	28.1617i	1.21224	+	0.981654i	0.999990	+	0.00443894i	$0.00141296\pi$
$823$	34.7768	+	28.1617i	1.21224	+	0.981654i	0.212252	+	0.977215i	$0.431920\pi$
$824$	−7.18001	−	12.4361i	−0.250128	−	0.433234i
$825$	6.10239	+	3.82627i	0.212458	+	0.133214i
$826$	34.6065	−	22.2520i	1.20411	−	0.774248i
$827$	21.4835	+	3.40265i	0.747054	+	0.118322i	0.518343	−	0.855173i	$-0.326549\pi$
$827$	21.4835	+	3.40265i	0.747054	+	0.118322i	0.228711	+	0.973494i	$0.426549\pi$
$828$	1.67525	−	2.57965i	0.0582188	−	0.0896491i
$829$	−8.56650	−	9.51406i	−0.297527	−	0.330437i	0.575783	−	0.817603i	$-0.304697\pi$
$829$	−8.56650	−	9.51406i	−0.297527	−	0.330437i	−0.873309	+	0.487166i	$0.838031\pi$
$830$	10.4757	−	24.0419i	0.363618	−	0.834506i
$831$	−10.5241	−	9.47596i	−0.365078	−	0.328717i
$832$	−1.84605	+	1.84605i	−0.0640001	+	0.0640001i
$833$	−48.7272	+	7.26682i	−1.68830	+	0.251781i
$834$	16.0539	−	22.0964i	0.555903	−	0.765134i
$835$	21.1853	−	21.5252i	0.733149	−	0.744910i
$836$	−8.49353	+	0.892706i	−0.293755	+	0.0308749i
$837$	−7.28013	−	2.79458i	−0.251638	−	0.0965948i
$838$	−34.9199	+	28.2775i	−1.20629	+	0.976832i
$839$	35.8070	−	26.0153i	1.23619	−	0.898148i	0.238856	−	0.971055i	$-0.423228\pi$
$839$	35.8070	−	26.0153i	1.23619	−	0.898148i	0.997339	+	0.0729072i	$0.0232277\pi$
$840$	7.26251	−	4.22637i	0.250580	−	0.145824i
$841$	−23.0008	−	16.7111i	−0.793132	−	0.576244i
$842$	−62.8284	+	3.29270i	−2.16521	+	0.113474i
$843$	−21.6153	+	5.79180i	−0.744471	+	0.199480i
$844$	3.18385	−	14.9788i	0.109593	−	0.515593i
$845$	0.0801503	+	10.0730i	0.00275725	+	0.346521i
$846$	−15.2597	−	4.95817i	−0.524639	−	0.170465i
$847$	0.106704	−	23.6126i	0.00366640	−	0.811339i
$848$	−1.02350	+	6.46210i	−0.0351470	+	0.221910i
$849$	2.95502	−	1.70608i	0.101416	−	0.0585525i
$850$	20.4247	+	59.6156i	0.700561	+	2.04480i
$851$	12.8122	−	22.1914i	0.439197	−	0.760711i
$852$	−2.21837	+	0.851554i	−0.0760003	+	0.0291738i
$853$	−15.5885	+	7.94274i	−0.533740	+	0.271954i	−0.700019	−	0.714125i	$-0.746825\pi$
$853$	−15.5885	+	7.94274i	−0.533740	+	0.271954i	0.166278	+	0.986079i	$0.446825\pi$
$854$	10.9198	−	40.0287i	0.373667	−	1.36975i
$855$	−4.54742	−	9.99879i	−0.155518	−	0.341951i
$856$	−4.78781	+	5.31740i	−0.163644	+	0.181745i
$857$	−4.37055	−	16.3111i	−0.149295	−	0.557178i	−0.999527	−	0.0307683i	$-0.990205\pi$
$857$	−4.37055	−	16.3111i	−0.149295	−	0.557178i	0.850231	−	0.526409i	$-0.176462\pi$
$858$	6.30585	−	4.09506i	0.215278	−	0.139803i
$859$	1.87410	−	17.8309i	0.0639435	−	0.608382i	−0.914887	−	0.403710i	$-0.867720\pi$
$859$	1.87410	−	17.8309i	0.0639435	−	0.608382i	0.978831	−	0.204672i	$-0.0656128\pi$
$860$	3.45996	+	1.29666i	0.117984	+	0.0442158i
$861$	2.22181	−	1.78262i	0.0757189	−	0.0607515i
$862$	−5.51593	−	34.8262i	−0.187873	−	1.18618i
$863$	−9.69702	−	11.9748i	−0.330090	−	0.407628i	0.584899	−	0.811106i	$-0.301134\pi$
$863$	−9.69702	−	11.9748i	−0.330090	−	0.407628i	−0.914989	+	0.403479i	$0.867801\pi$
$864$	−0.630994	−	6.00351i	−0.0214669	−	0.204244i
$865$	10.4668	−	0.632087i	0.355881	−	0.0214916i
$866$	−13.2317	−	1.39071i	−0.449632	−	0.0472582i
$867$	28.9876	+	14.7699i	0.984472	+	0.501613i
$868$	23.7156	−	7.58736i	0.804960	−	0.257532i
$869$	−15.3128	+	4.97543i	−0.519451	+	0.168780i
$870$	0.910834	−	2.88106i	0.0308802	−	0.0976771i
$871$	−2.09713	+	1.88827i	−0.0710586	+	0.0639815i
$872$	1.01564	−	19.3795i	0.0343938	−	0.656274i
$873$	5.75102	+	14.9819i	0.194643	+	0.507061i
$874$	−22.4202			−0.758373
$875$	−12.5521	−	26.7852i	−0.424338	−	0.905504i
$876$	−6.94844			−0.234766
$877$	20.2782	+	52.8265i	0.684747	+	1.78383i	0.618170	+	0.786044i	$0.287874\pi$
$877$	20.2782	+	52.8265i	0.684747	+	1.78383i	0.0665763	+	0.997781i	$0.478792\pi$
$878$	2.98162	−	56.8926i	0.100625	−	1.92003i
$879$	−19.8721	+	17.8929i	−0.670268	+	0.603512i
$880$	4.81339	−	15.2252i	0.162259	−	0.513242i
$881$	−34.5383	+	11.2222i	−1.16363	+	0.378085i	−0.826260	−	0.563288i	$-0.809536\pi$
$881$	−34.5383	+	11.2222i	−1.16363	+	0.378085i	−0.337366	+	0.941374i	$0.609536\pi$
$882$	2.07279	−	12.3628i	0.0697943	−	0.416279i
$883$	−3.83057	−	1.95177i	−0.128909	−	0.0656824i	0.388347	−	0.921513i	$-0.373046\pi$
$883$	−3.83057	−	1.95177i	−0.128909	−	0.0656824i	−0.517256	+	0.855831i	$0.673046\pi$
$884$	24.6210	+	2.58778i	0.828095	+	0.0870363i
$885$	19.3822	−	1.17049i	0.651526	−	0.0393456i
$886$	−1.03720	−	9.86831i	−0.0348455	−	0.331532i
$887$	−18.1254	−	22.3830i	−0.608590	−	0.751546i	0.375963	−	0.926635i	$-0.377312\pi$
$887$	−18.1254	−	22.3830i	−0.608590	−	0.751546i	−0.984553	+	0.175089i	$0.943979\pi$
$888$	−2.23389	−	14.1043i	−0.0749646	−	0.473308i
$889$	−16.4945	+	42.3960i	−0.553208	+	1.42192i
$890$	−27.3050	−	10.2329i	−0.915265	−	0.343007i
$891$	−0.150578	+	1.43266i	−0.00504456	+	0.0479958i
$892$	24.9154	−	16.1802i	0.834228	−	0.541754i
$893$	11.3915	+	42.5138i	0.381203	+	1.42267i
$894$	−8.98191	+	9.97542i	−0.300400	+	0.333628i
$895$	−11.3843	−	25.0316i	−0.380535	−	0.836715i
$896$	−19.4972	−	19.6742i	−0.651357	−	0.657270i
$897$	6.61875	−	3.37242i	0.220994	−	0.112602i
$898$	−2.20761	+	0.847422i	−0.0736689	+	0.0282788i
$899$	−2.94219	+	5.09602i	−0.0981275	+	0.169962i
$900$	−6.03356	+	0.0960235i	−0.201119	+	0.00320078i
$901$	8.04447	−	4.64448i	0.268000	−	0.154730i
$902$	0.434483	−	2.74322i	0.0144667	−	0.0913392i
$903$	−3.14537	+	1.79708i	−0.104671	+	0.0598029i
$904$	6.30815	+	2.04964i	0.209806	+	0.0681701i
$905$	0.109996	+	13.8238i	0.00365638	+	0.459520i
$906$	−6.30124	+	29.6450i	−0.209345	+	0.984889i
$907$	−2.37659	+	0.636805i	−0.0789134	+	0.0211448i	−0.298060	−	0.954547i	$-0.596339\pi$
$907$	−2.37659	+	0.636805i	−0.0789134	+	0.0211448i	0.219146	+	0.975692i	$0.429673\pi$
$908$	32.0972	−	1.68215i	1.06518	−	0.0558240i
$909$	−0.797306	−	0.579277i	−0.0264450	−	0.0192134i
$910$	−30.8785	+	0.106156i	−1.02361	+	0.00351904i
$911$	−34.1838	+	24.8360i	−1.13256	+	0.822853i	−0.986065	−	0.166359i	$-0.946799\pi$
$911$	−34.1838	+	24.8360i	−1.13256	+	0.822853i	−0.146494	+	0.989212i	$0.546799\pi$
$912$	−18.9246	+	15.3248i	−0.626656	+	0.507456i
$913$	8.80787	+	3.38102i	0.291498	+	0.111896i
$914$	−3.60413	+	0.378809i	−0.119214	+	0.0125299i
$915$	13.7359	−	13.9562i	0.454093	−	0.461378i
$916$	−13.8574	+	19.0731i	−0.457862	+	0.630192i
$917$	18.4873	−	13.3046i	0.610506	−	0.439357i
$918$	−8.91200	+	8.91200i	−0.294140	+	0.294140i
$919$	29.9843	+	26.9980i	0.989091	+	0.890582i	0.993997	−	0.109406i	$-0.0348949\pi$
$919$	29.9843	+	26.9980i	0.989091	+	0.890582i	−0.00490567	+	0.999988i	$0.501562\pi$
$920$	3.23334	−	7.42055i	0.106600	−	0.244648i
$921$	−9.70267	−	10.7759i	−0.319714	−	0.355078i
$922$	25.4924	−	39.2548i	0.839547	−	1.29279i
$923$	−5.66798	−	0.897720i	−0.186564	−	0.0295488i
$924$	−2.48775	−	3.86897i	−0.0818411	−	0.127280i
$925$	−50.1533	+	3.42947i	−1.64903	+	0.112760i
$926$	18.1321	+	31.4056i	0.595856	+	1.03205i
$927$	−7.85724	−	6.36267i	−0.258066	−	0.208978i
$928$	−4.54892	−	0.238399i	−0.149326	−	0.00782583i
$929$	6.26250	−	1.33114i	0.205466	−	0.0436732i	−0.104029	−	0.994574i	$-0.533173\pi$
$929$	6.26250	−	1.33114i	0.205466	−	0.0436732i	0.309495	+	0.950901i	$0.399840\pi$
$930$	30.5941	+	6.24897i	1.00322	+	0.204912i
$931$	−31.5386	+	13.7017i	−1.03363	+	0.449055i
$932$	−15.3339	−	15.3339i	−0.502278	−	0.502278i
$933$	−1.63815	−	31.2577i	−0.0536306	−	1.02333i
$934$	21.3070	−	9.48649i	0.697187	−	0.310407i
$935$	−21.0995	+	8.29256i	−0.690028	+	0.271196i
$936$	1.68378	−	3.78183i	0.0550360	−	0.123613i
$937$	25.2168	−	3.99396i	0.823798	−	0.130477i	0.269717	−	0.962940i	$-0.413070\pi$
$937$	25.2168	−	3.99396i	0.823798	−	0.130477i	0.554081	+	0.832463i	$0.313070\pi$
$938$	3.05407	+	3.42287i	0.0997190	+	0.111761i
$939$	10.8991	+	15.0014i	0.355680	+	0.489551i
$940$	23.9109	+	3.59233i	0.779887	+	0.117169i
$941$	5.43036	+	12.1968i	0.177025	+	0.397604i	0.980164	−	0.198187i	$-0.0635054\pi$
$941$	5.43036	+	12.1968i	0.177025	+	0.397604i	−0.803140	+	0.595791i	$0.796839\pi$
$942$	16.6769	+	25.6801i	0.543362	+	0.836704i
$943$	0.710199	−	2.65050i	0.0231272	−	0.0863121i
$944$	−13.3023	−	40.9404i	−0.432955	−	1.33250i
$945$	3.70728	−	4.61043i	0.120598	−	0.149977i
$946$	−1.09148	+	3.35922i	−0.0354870	+	0.109218i
$947$	−15.1525	−	9.84013i	−0.492389	−	0.319761i	0.274449	−	0.961602i	$-0.411505\pi$
$947$	−15.1525	−	9.84013i	−0.492389	−	0.319761i	−0.766838	+	0.641840i	$0.778171\pi$
$948$	8.48889	−	10.4829i	0.275706	−	0.340469i
$949$	−14.5326	−	8.39039i	−0.471748	−	0.272364i
$950$	24.5395	+	36.5025i	0.796167	+	1.18430i
$951$		−	7.30402i		−	0.236849i
$952$	−2.88336	+	26.2900i	−0.0934502	+	0.852063i
$953$	16.9225	+	33.2122i	0.548173	+	1.07585i	0.984389	+	0.176008i	$0.0563184\pi$
$953$	16.9225	+	33.2122i	0.548173	+	1.07585i	−0.436216	+	0.899842i	$0.643682\pi$
$954$	0.491401	+	2.31186i	0.0159097	+	0.0748492i
$955$	−20.1213	−	8.76741i	−0.651109	−	0.283707i
$956$	14.7276	+	3.13044i	0.476324	+	0.101246i
$957$	1.04999	+	0.281344i	0.0339413	+	0.00909455i
$958$	−5.25514	+	10.3138i	−0.169786	+	0.333223i
$959$	12.2615	−	18.6955i	0.395944	−	0.603710i
$960$	0.533765	+	1.93046i	0.0172272	+	0.0623055i
$961$	−27.2328	−	12.1248i	−0.878477	−	0.391123i
$962$	−18.8060	+	48.9912i	−0.606329	+	1.57954i
$963$	−1.80538	+	4.70317i	−0.0581774	+	0.151557i
$964$	14.8923	+	6.63048i	0.479649	+	0.213553i
$965$	−48.0453	−	2.13476i	−1.54663	−	0.0687204i
$966$	−5.43343	−	10.7839i	−0.174818	−	0.346966i
$967$	−4.47583	+	8.78432i	−0.143933	+	0.282485i	−0.951707	−	0.307008i	$-0.900672\pi$
$967$	−4.47583	+	8.78432i	−0.143933	+	0.282485i	0.807774	+	0.589492i	$0.200672\pi$
$968$	−12.2442	−	3.28083i	−0.393544	−	0.105450i
$969$	33.8175	+	7.18813i	1.08637	+	0.230916i
$970$	−32.5718	−	55.3934i	−1.04582	−	1.77858i
$971$	−1.46946	−	6.91325i	−0.0471571	−	0.221857i	0.948259	−	0.317499i	$-0.102843\pi$
$971$	−1.46946	−	6.91325i	−0.0471571	−	0.221857i	−0.995416	+	0.0956420i	$0.969510\pi$
$972$	−0.547905	−	1.07532i	−0.0175741	−	0.0344910i
$973$	−16.2461	−	36.9377i	−0.520827	−	1.18417i
$974$		−	20.7543i		−	0.665009i
$975$	−12.7351	−	7.08483i	−0.407849	−	0.226896i
$976$	−37.5956	−	21.7058i	−1.20340	−	0.694786i
$977$	8.79620	−	10.8624i	0.281415	−	0.347519i	−0.616764	−	0.787148i	$-0.711557\pi$
$977$	8.79620	−	10.8624i	0.281415	−	0.347519i	0.898179	+	0.439629i	$0.144890\pi$
$978$	24.2265	+	15.7329i	0.774680	+	0.503083i
$979$	3.24164	−	9.97673i	0.103603	−	0.318858i
$980$	−0.0204218	+	18.8904i	−0.000652350	+	0.603432i
$981$	−4.22215	−	12.9944i	−0.134803	−	0.414880i
$982$	13.6095	−	50.7912i	0.434296	−	1.62081i
$983$	16.6726	+	25.6735i	0.531772	+	0.818858i	0.997826	−	0.0658987i	$-0.0209914\pi$
$983$	16.6726	+	25.6735i	0.531772	+	0.818858i	−0.466054	+	0.884756i	$0.654325\pi$
$984$	−0.621976	−	1.39698i	−0.0198279	−	0.0445341i
$985$	7.29658	+	43.8098i	0.232488	+	1.39590i
$986$	5.59013	+	7.69416i	0.178026	+	0.245032i
$987$	−17.6881	+	15.7823i	−0.563017	+	0.502355i
$988$	17.0667	−	2.70310i	0.542964	−	0.0859970i
$989$	−1.41935	+	3.18791i	−0.0451326	+	0.101370i
$990$	−0.347718	−	5.75788i	−0.0110512	−	0.182997i
$991$	5.70782	−	2.54129i	0.181315	−	0.0807266i	−0.314071	−	0.949399i	$-0.601693\pi$
$991$	5.70782	−	2.54129i	0.181315	−	0.0807266i	0.495386	+	0.868673i	$0.335026\pi$
$992$	−2.46365	−	47.0092i	−0.0782209	−	1.49254i
$993$	−12.4703	−	12.4703i	−0.395733	−	0.395733i
$994$	−1.50093	+	9.20701i	−0.0476065	+	0.292029i
$995$	9.55800	+	10.4469i	0.303009	+	0.331188i
$996$	−7.73133	+	1.64334i	−0.244976	+	0.0520714i
$997$	−21.0990	−	1.10575i	−0.668213	−	0.0350195i	−0.284786	−	0.958591i	$-0.591923\pi$
$997$	−21.0990	−	1.10575i	−0.668213	−	0.0350195i	−0.383426	+	0.923572i	$0.625256\pi$
$998$	29.4413	+	23.8411i	0.931947	+	0.754675i
$999$	−5.02704	−	8.70709i	−0.159049	−	0.275480i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bv.a.52.9	✓	640
7.5	odd	6	inner	525.2.bv.a.502.9	yes	640
25.13	odd	20	inner	525.2.bv.a.388.9	yes	640
175.138	even	60	inner	525.2.bv.a.313.9	yes	640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bv.a.52.9	✓	640	1.1	even	1	trivial
525.2.bv.a.313.9	yes	640	175.138	even	60	inner
525.2.bv.a.388.9	yes	640	25.13	odd	20	inner
525.2.bv.a.502.9	yes	640	7.5	odd	6	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.bv (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.641755 - 1.67183i) q^{2} +(-0.0523360 + 0.998630i) q^{3} +(-0.896875 + 0.807550i) q^{4} +(-0.674040 + 2.13206i) q^{5} +(1.70313 - 0.553379i) q^{6} +(0.561772 - 2.58542i) q^{7} +(-1.26552 - 0.644814i) q^{8} +(-0.994522 - 0.104528i) q^{9} +O(q^{10})\)	\(q+(-0.641755 - 1.67183i) q^{2} +(-0.0523360 + 0.998630i) q^{3} +(-0.896875 + 0.807550i) q^{4} +(-0.674040 + 2.13206i) q^{5} +(1.70313 - 0.553379i) q^{6} +(0.561772 - 2.58542i) q^{7} +(-1.26552 - 0.644814i) q^{8} +(-0.994522 - 0.104528i) q^{9} +(3.99701 - 0.241379i) q^{10} +(0.150578 + 1.43266i) q^{11} +(-0.759505 - 0.937910i) q^{12} +(-0.455949 - 2.87875i) q^{13} +(-4.68291 + 0.720022i) q^{14} +(-2.09386 - 0.784700i) q^{15} +(-0.518169 + 4.93005i) q^{16} +(5.90257 - 3.83317i) q^{17} +(0.463486 + 1.72975i) q^{18} +(3.28699 - 3.65057i) q^{19} +(-1.11721 - 2.45651i) q^{20} +(2.55248 + 0.696312i) q^{21} +(2.29852 - 1.17116i) q^{22} +(2.37937 - 0.913356i) q^{23} +(0.710162 - 1.23004i) q^{24} +(-4.09134 - 2.87419i) q^{25} +(-4.52017 + 2.60972i) q^{26} +(0.156434 - 0.987688i) q^{27} +(1.58402 + 2.77246i) q^{28} +(-0.717661 - 0.233182i) q^{29} +(0.0318609 + 4.00416i) q^{30} +(1.62131 - 7.62767i) q^{31} +(5.83089 - 1.56238i) q^{32} +(-1.43857 + 0.0753925i) q^{33} +(-10.1964 - 7.40813i) q^{34} +(5.13361 + 2.94041i) q^{35} +(0.976374 - 0.709377i) q^{36} +(7.81349 - 6.32724i) q^{37} +(-8.21257 - 3.15251i) q^{38} +(2.89867 - 0.304662i) q^{39} +(2.22779 - 2.26353i) q^{40} +(0.632836 - 0.871024i) q^{41} +(-0.473951 - 4.71417i) q^{42} +(-0.968165 + 0.968165i) q^{43} +(-1.29199 - 1.16332i) q^{44} +(0.893208 - 2.04992i) q^{45} +(-3.05395 - 3.39176i) q^{46} +(-4.87986 + 7.51433i) q^{47} +(-4.89618 - 0.775478i) q^{48} +(-6.36883 - 2.90483i) q^{49} +(-2.17951 + 8.68455i) q^{50} +(3.51900 + 6.09510i) q^{51} +(2.73366 + 2.21368i) q^{52} +(1.31802 + 0.0690744i) q^{53} +(-1.75164 + 0.372322i) q^{54} +(-3.15600 - 0.644627i) q^{55} +(-2.37805 + 2.90966i) q^{56} +(3.47354 + 3.47354i) q^{57} +(0.0707219 + 1.34945i) q^{58} +(-7.93303 + 3.53201i) q^{59} +(2.51161 - 0.987118i) q^{60} +(-3.56190 + 8.00017i) q^{61} +(-13.7927 + 2.18454i) q^{62} +(-0.828945 + 2.51254i) q^{63} +(-0.526493 - 0.724655i) q^{64} +(6.44498 + 0.968283i) q^{65} +(1.04926 + 2.35667i) q^{66} +(-0.527324 - 0.812008i) q^{67} +(-2.19839 + 8.20450i) q^{68} +(0.787578 + 2.42392i) q^{69} +(1.62134 - 10.4696i) q^{70} +(0.608425 - 1.87254i) q^{71} +(1.19118 + 0.773564i) q^{72} +(3.62327 - 4.47436i) q^{73} +(-15.5924 - 9.00229i) q^{74} +(3.08437 - 3.93531i) q^{75} +5.92851i q^{76} +(3.78862 + 0.415517i) q^{77} +(-2.36958 - 4.65056i) q^{78} +(2.32380 + 10.9326i) q^{79} +(-10.1619 - 4.42782i) q^{80} +(0.978148 + 0.207912i) q^{81} +(-1.86233 - 0.499010i) q^{82} +(2.97329 - 5.83542i) q^{83} +(-2.85156 + 1.43675i) q^{84} +(4.19398 + 15.1683i) q^{85} +(2.23993 + 0.997282i) q^{86} +(0.270422 - 0.704474i) q^{87} +(0.733238 - 1.91015i) q^{88} +(-6.65249 - 2.96188i) q^{89} +(-4.00034 - 0.177744i) q^{90} +(-7.69892 - 0.438378i) q^{91} +(-1.39642 + 2.74063i) q^{92} +(7.53236 + 2.01829i) q^{93} +(15.6944 + 3.33594i) q^{94} +(5.56766 + 9.46868i) q^{95} +(1.25508 + 5.90467i) q^{96} +(-7.28555 - 14.2987i) q^{97} +(-0.769162 + 12.5118i) q^{98} -1.44055i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q + 12 q^{5} - 8 q^{7} + 24 q^{8}+O(q^{10}) \) 640 * q + 12 * q^5 - 8 * q^7 + 24 * q^8	\( 640 q + 12 q^{5} - 8 q^{7} + 24 q^{8} + 12 q^{10} + 8 q^{15} - 80 q^{16} - 72 q^{22} + 48 q^{23} - 12 q^{25} - 36 q^{28} - 80 q^{29} + 32 q^{30} - 24 q^{32} + 36 q^{33} - 64 q^{35} + 160 q^{36} - 4 q^{37} - 192 q^{38} - 12 q^{40} - 16 q^{42} + 120 q^{43} + 60 q^{47} + 288 q^{50} - 432 q^{52} - 136 q^{53} - 16 q^{57} - 4 q^{58} - 240 q^{59} - 20 q^{60} - 4 q^{63} + 120 q^{64} + 4 q^{65} - 8 q^{67} - 132 q^{68} + 76 q^{70} - 12 q^{72} - 36 q^{73} - 48 q^{75} - 60 q^{77} - 80 q^{78} + 12 q^{80} - 80 q^{81} - 252 q^{82} - 160 q^{84} + 72 q^{85} + 24 q^{87} + 152 q^{88} + 56 q^{92} - 96 q^{93} + 172 q^{95} - 488 q^{98}+O(q^{100}) \) 640 * q + 12 * q^5 - 8 * q^7 + 24 * q^8 + 12 * q^10 + 8 * q^15 - 80 * q^16 - 72 * q^22 + 48 * q^23 - 12 * q^25 - 36 * q^28 - 80 * q^29 + 32 * q^30 - 24 * q^32 + 36 * q^33 - 64 * q^35 + 160 * q^36 - 4 * q^37 - 192 * q^38 - 12 * q^40 - 16 * q^42 + 120 * q^43 + 60 * q^47 + 288 * q^50 - 432 * q^52 - 136 * q^53 - 16 * q^57 - 4 * q^58 - 240 * q^59 - 20 * q^60 - 4 * q^63 + 120 * q^64 + 4 * q^65 - 8 * q^67 - 132 * q^68 + 76 * q^70 - 12 * q^72 - 36 * q^73 - 48 * q^75 - 60 * q^77 - 80 * q^78 + 12 * q^80 - 80 * q^81 - 252 * q^82 - 160 * q^84 + 72 * q^85 + 24 * q^87 + 152 * q^88 + 56 * q^92 - 96 * q^93 + 172 * q^95 - 488 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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