LMFDB - Embedded newform 800.2.be.a.369.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [800,2,Mod(209,800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(800, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 7]))

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

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

chi := DirichletCharacter("800.209");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 800 = 2^{5} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	800.be (of order $10$, degree $4$, not 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:	$6.38803216170$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			369.7
Character	$\chi$	$=$	800.369
Dual form			800.2.be.a.529.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39188 + 1.01126i) q^{3} +(0.122399 + 2.23272i) q^{5} +4.42380i q^{7} +(-0.0123697 + 0.0380700i) q^{9} +O(q^{10})$	\(q+(-1.39188 + 1.01126i) q^{3} +(0.122399 + 2.23272i) q^{5} +4.42380i q^{7} +(-0.0123697 + 0.0380700i) q^{9} +(-5.07953 + 1.65044i) q^{11} +(-0.237511 + 0.730985i) q^{13} +(-2.42822 - 2.98389i) q^{15} +(3.34610 - 4.60551i) q^{17} +(1.01760 - 1.40061i) q^{19} +(-4.47361 - 6.15740i) q^{21} +(5.01464 - 1.62935i) q^{23} +(-4.97004 + 0.546563i) q^{25} +(-1.61623 - 4.97425i) q^{27} +(1.21119 + 1.66707i) q^{29} +(2.10890 + 1.53221i) q^{31} +(5.40106 - 7.43393i) q^{33} +(-9.87709 + 0.541468i) q^{35} +(-2.01004 + 6.18628i) q^{37} +(-0.408628 - 1.25763i) q^{39} +(-0.754681 + 2.32267i) q^{41} +6.65200 q^{43} +(-0.0865136 - 0.0229583i) q^{45} +(-4.72720 - 6.50644i) q^{47} -12.5700 q^{49} +9.79409i q^{51} +(3.77778 - 2.74471i) q^{53} +(-4.30669 - 11.1391i) q^{55} +2.97854i q^{57} +(-1.02828 - 0.334110i) q^{59} +(-6.86954 + 2.23205i) q^{61} +(-0.168414 - 0.0547211i) q^{63} +(-1.66115 - 0.440824i) q^{65} +(-5.12879 - 3.72628i) q^{67} +(-5.33207 + 7.33896i) q^{69} +(-0.472812 + 0.343518i) q^{71} +(-5.48432 + 1.78197i) q^{73} +(6.36497 - 5.78674i) q^{75} +(-7.30121 - 22.4708i) q^{77} +(-6.27011 + 4.55550i) q^{79} +(7.18270 + 5.21854i) q^{81} +(5.49924 + 3.99543i) q^{83} +(10.6924 + 6.90718i) q^{85} +(-3.37167 - 1.09552i) q^{87} +(3.89405 + 11.9847i) q^{89} +(-3.23373 - 1.05070i) q^{91} -4.48479 q^{93} +(3.25171 + 2.10058i) q^{95} +(-1.90925 - 2.62786i) q^{97} -0.213793i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 30 q^{9}+O(q^{10}) $ 112 * q - 30 * q^9	$ 112 q - 30 q^{9} + 2 q^{15} - 10 q^{17} + 10 q^{23} - 6 q^{25} + 18 q^{31} - 10 q^{33} + 10 q^{39} - 10 q^{41} + 10 q^{47} - 80 q^{49} + 34 q^{55} - 60 q^{63} + 40 q^{65} - 22 q^{71} - 10 q^{73} - 14 q^{79} - 6 q^{81} + 10 q^{87} + 24 q^{89} + 86 q^{95} - 50 q^{97}+O(q^{100}) $ 112 * q - 30 * q^9 + 2 * q^15 - 10 * q^17 + 10 * q^23 - 6 * q^25 + 18 * q^31 - 10 * q^33 + 10 * q^39 - 10 * q^41 + 10 * q^47 - 80 * q^49 + 34 * q^55 - 60 * q^63 + 40 * q^65 - 22 * q^71 - 10 * q^73 - 14 * q^79 - 6 * q^81 + 10 * q^87 + 24 * q^89 + 86 * q^95 - 50 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/800\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$577$
$\chi(n)$	$-1$	$1$	$e\left(\frac{9}{10}\right)$

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			0
$2$		0			0
$3$	−1.39188	+	1.01126i	−0.803601	+	0.583851i	−0.911968	−	0.410260i	$-0.865438\pi$
$3$	−1.39188	+	1.01126i	−0.803601	+	0.583851i	0.108367	+	0.994111i	$0.465438\pi$
$4$		0			0
$5$	0.122399	+	2.23272i	0.0547384	+	0.998501i
$5$	0.122399	+	2.23272i	0.0547384	+	0.998501i
$6$		0			0
$7$			4.42380i			1.67204i	0.548699	+	0.836020i	$0.315123\pi$
$7$			4.42380i			1.67204i	−0.548699	+	0.836020i	$0.684877\pi$
$8$		0			0
$9$	−0.0123697	+	0.0380700i	−0.00412323	+	0.0126900i
$10$		0			0
$11$	−5.07953	+	1.65044i	−1.53153	+	0.497626i	−0.949026	−	0.315199i	$-0.897929\pi$
$11$	−5.07953	+	1.65044i	−1.53153	+	0.497626i	−0.582509	+	0.812824i	$0.697929\pi$
$12$		0			0
$13$	−0.237511	+	0.730985i	−0.0658738	+	0.202739i	−0.978576	−	0.205887i	$-0.933992\pi$
$13$	−0.237511	+	0.730985i	−0.0658738	+	0.202739i	0.912702	+	0.408626i	$0.133992\pi$
$14$		0			0
$15$	−2.42822	−	2.98389i	−0.626963	−	0.770438i
$16$		0			0
$17$	3.34610	−	4.60551i	0.811549	−	1.11700i	−0.179534	−	0.983752i	$-0.557459\pi$
$17$	3.34610	−	4.60551i	0.811549	−	1.11700i	0.991083	−	0.133249i	$-0.0425410\pi$
$18$		0			0
$19$	1.01760	−	1.40061i	0.233454	−	0.321322i	−0.676177	−	0.736739i	$-0.736365\pi$
$19$	1.01760	−	1.40061i	0.233454	−	0.321322i	0.909631	+	0.415418i	$0.136365\pi$
$20$		0			0
$21$	−4.47361	−	6.15740i	−0.976222	−	1.34365i
$22$		0			0
$23$	5.01464	−	1.62935i	1.04562	−	0.339744i	0.264675	−	0.964338i	$-0.414735\pi$
$23$	5.01464	−	1.62935i	1.04562	−	0.339744i	0.780950	+	0.624594i	$0.214735\pi$
$24$		0			0
$25$	−4.97004	+	0.546563i	−0.994007	+	0.109313i
$26$		0			0
$27$	−1.61623	−	4.97425i	−0.311044	−	0.957295i
$28$		0			0
$29$	1.21119	+	1.66707i	0.224913	+	0.309567i	0.906529	−	0.422144i	$-0.138722\pi$
$29$	1.21119	+	1.66707i	0.224913	+	0.309567i	−0.681616	+	0.731710i	$0.738722\pi$
$30$		0			0
$31$	2.10890	+	1.53221i	0.378770	+	0.275192i	0.760838	−	0.648942i	$-0.224788\pi$
$31$	2.10890	+	1.53221i	0.378770	+	0.275192i	−0.382068	+	0.924134i	$0.624788\pi$
$32$		0			0
$33$	5.40106	−	7.43393i	0.940204	−	1.29408i
$34$		0			0
$35$	−9.87709	+	0.541468i	−1.66953	+	0.0915248i
$36$		0			0
$37$	−2.01004	+	6.18628i	−0.330449	+	1.01702i	0.638471	+	0.769646i	$0.279567\pi$
$37$	−2.01004	+	6.18628i	−0.330449	+	1.01702i	−0.968921	+	0.247372i	$0.920433\pi$
$38$		0			0
$39$	−0.408628	−	1.25763i	−0.0654328	−	0.201382i
$40$		0			0
$41$	−0.754681	+	2.32267i	−0.117861	+	0.362740i	−0.992533	−	0.121976i	$-0.961077\pi$
$41$	−0.754681	+	2.32267i	−0.117861	+	0.362740i	0.874672	+	0.484716i	$0.161077\pi$
$42$		0			0
$43$	6.65200			1.01442			0.507210	−	0.861822i	$-0.330677\pi$
$43$	6.65200			1.01442			0.507210	+	0.861822i	$0.330677\pi$
$44$		0			0
$45$	−0.0865136	−	0.0229583i	−0.0128967	−	0.00342242i
$46$		0			0
$47$	−4.72720	−	6.50644i	−0.689534	−	0.949062i	0.310465	−	0.950585i	$-0.399515\pi$
$47$	−4.72720	−	6.50644i	−0.689534	−	0.949062i	−0.999999	+	0.00152305i	$0.999515\pi$
$48$		0			0
$49$	−12.5700			−1.79572
$50$		0			0
$51$			9.79409i			1.37145i
$52$		0			0
$53$	3.77778	−	2.74471i	0.518917	−	0.377016i	−0.297279	−	0.954791i	$-0.596079\pi$
$53$	3.77778	−	2.74471i	0.518917	−	0.377016i	0.816196	+	0.577775i	$0.196079\pi$
$54$		0			0
$55$	−4.30669	−	11.1391i	−0.580713	−	1.50200i
$56$		0			0
$57$			2.97854i			0.394517i
$58$		0			0
$59$	−1.02828	−	0.334110i	−0.133871	−	0.0434974i	0.241315	−	0.970447i	$-0.422421\pi$
$59$	−1.02828	−	0.334110i	−0.133871	−	0.0434974i	−0.375186	+	0.926949i	$0.622421\pi$
$60$		0			0
$61$	−6.86954	+	2.23205i	−0.879554	+	0.285785i	−0.713772	−	0.700378i	$-0.753015\pi$
$61$	−6.86954	+	2.23205i	−0.879554	+	0.285785i	−0.165782	+	0.986162i	$0.553015\pi$
$62$		0			0
$63$	−0.168414	−	0.0547211i	−0.0212182	−	0.00689422i
$64$		0			0
$65$	−1.66115	−	0.440824i	−0.206041	−	0.0546775i
$66$		0			0
$67$	−5.12879	−	3.72628i	−0.626581	−	0.455238i	0.228633	−	0.973513i	$-0.426574\pi$
$67$	−5.12879	−	3.72628i	−0.626581	−	0.455238i	−0.855214	+	0.518275i	$0.826574\pi$
$68$		0			0
$69$	−5.33207	+	7.33896i	−0.641905	+	0.883507i
$70$		0			0
$71$	−0.472812	+	0.343518i	−0.0561125	+	0.0407681i	−0.615488	−	0.788146i	$-0.711041\pi$
$71$	−0.472812	+	0.343518i	−0.0561125	+	0.0407681i	0.559375	+	0.828914i	$0.311041\pi$
$72$		0			0
$73$	−5.48432	+	1.78197i	−0.641892	+	0.208563i	−0.611836	−	0.790985i	$-0.709569\pi$
$73$	−5.48432	+	1.78197i	−0.641892	+	0.208563i	−0.0300561	+	0.999548i	$0.509569\pi$
$74$		0			0
$75$	6.36497	−	5.78674i	0.734964	−	0.668196i
$76$		0			0
$77$	−7.30121	−	22.4708i	−0.832050	−	2.56079i
$78$		0			0
$79$	−6.27011	+	4.55550i	−0.705442	+	0.512534i	−0.881700	−	0.471810i	$-0.843601\pi$
$79$	−6.27011	+	4.55550i	−0.705442	+	0.512534i	0.176258	+	0.984344i	$0.443601\pi$
$80$		0			0
$81$	7.18270	+	5.21854i	0.798078	+	0.579838i
$82$		0			0
$83$	5.49924	+	3.99543i	0.603619	+	0.438555i	0.847162	−	0.531335i	$-0.178309\pi$
$83$	5.49924	+	3.99543i	0.603619	+	0.438555i	−0.243542	+	0.969890i	$0.578309\pi$
$84$		0			0
$85$	10.6924	+	6.90718i	1.15975	+	0.749189i
$86$		0			0
$87$	−3.37167	−	1.09552i	−0.361481	−	0.117452i
$88$		0			0
$89$	3.89405	+	11.9847i	0.412769	+	1.27037i	0.914232	+	0.405192i	$0.132795\pi$
$89$	3.89405	+	11.9847i	0.412769	+	1.27037i	−0.501463	+	0.865179i	$0.667205\pi$
$90$		0			0
$91$	−3.23373	−	1.05070i	−0.338987	−	0.110144i
$92$		0			0
$93$	−4.48479			−0.465051
$94$		0			0
$95$	3.25171	+	2.10058i	0.333619	+	0.215515i
$96$		0			0
$97$	−1.90925	−	2.62786i	−0.193855	−	0.266819i	0.701014	−	0.713148i	$-0.252731\pi$
$97$	−1.90925	−	2.62786i	−0.193855	−	0.266819i	−0.894869	+	0.446329i	$0.852731\pi$
$98$		0			0
$99$		−	0.213793i		−	0.0214870i
$100$		0			0
$101$			3.90261i			0.388325i	0.980969	+	0.194162i	$0.0621989\pi$
$101$			3.90261i			0.388325i	−0.980969	+	0.194162i	$0.937801\pi$
$102$		0			0
$103$	11.2306	+	15.4576i	1.10659	+	1.52308i	0.826354	+	0.563151i	$0.190411\pi$
$103$	11.2306	+	15.4576i	1.10659	+	1.52308i	0.280231	+	0.959933i	$0.409589\pi$
$104$		0			0
$105$	13.2002	−	10.7420i	1.28820	−	1.04831i
$106$		0			0
$107$	12.2161			1.18098			0.590488	−	0.807046i	$-0.298935\pi$
$107$	12.2161			1.18098			0.590488	+	0.807046i	$0.298935\pi$
$108$		0			0
$109$	−8.01169	−	2.60316i	−0.767381	−	0.249337i	−0.100937	−	0.994893i	$-0.532184\pi$
$109$	−8.01169	−	2.60316i	−0.767381	−	0.249337i	−0.666443	+	0.745556i	$0.732184\pi$
$110$		0			0
$111$	−3.45819	−	10.6432i	−0.328237	−	1.01021i
$112$		0			0
$113$	5.14306	+	1.67108i	0.483818	+	0.157202i	0.540762	−	0.841175i	$-0.318136\pi$
$113$	5.14306	+	1.67108i	0.483818	+	0.157202i	−0.0569445	+	0.998377i	$0.518136\pi$
$114$		0			0
$115$	4.25167	+	10.9968i	0.396470	+	1.02546i
$116$		0			0
$117$	−0.0248907	−	0.0180841i	−0.00230114	−	0.00167188i
$118$		0			0
$119$	20.3739	+	14.8025i	1.86767	+	1.35694i
$120$		0			0
$121$	14.1785	−	10.3012i	1.28895	−	0.936477i
$122$		0			0
$123$	−1.29840	−	3.99605i	−0.117072	−	0.360312i
$124$		0			0
$125$	−1.82865	−	11.0298i	−0.163559	−	0.986534i
$126$		0			0
$127$	−12.7192	+	4.13273i	−1.12865	+	0.366721i	−0.813063	−	0.582175i	$-0.802202\pi$
$127$	−12.7192	+	4.13273i	−1.12865	+	0.366721i	−0.315588	+	0.948896i	$0.602202\pi$
$128$		0			0
$129$	−9.25877	+	6.72689i	−0.815190	+	0.592270i
$130$		0			0
$131$	2.07801	−	2.86013i	0.181556	−	0.249891i	−0.708532	−	0.705678i	$-0.750642\pi$
$131$	2.07801	−	2.86013i	0.181556	−	0.249891i	0.890089	+	0.455788i	$0.150642\pi$
$132$		0			0
$133$	6.19602	+	4.50167i	0.537263	+	0.390344i
$134$		0			0
$135$	10.9083	−	4.21743i	0.938834	−	0.362979i
$136$		0			0
$137$	−20.5757	−	6.68544i	−1.75790	−	0.571176i	−0.760919	−	0.648846i	$-0.775252\pi$
$137$	−20.5757	−	6.68544i	−1.75790	−	0.571176i	−0.996979	+	0.0776705i	$0.975252\pi$
$138$		0			0
$139$	−1.89983	+	0.617291i	−0.161141	+	0.0523579i	−0.388477	−	0.921459i	$-0.626999\pi$
$139$	−1.89983	+	0.617291i	−0.161141	+	0.0523579i	0.227336	+	0.973816i	$0.426999\pi$
$140$		0			0
$141$	13.1594	+	4.27575i	1.10822	+	0.360083i
$142$		0			0
$143$		−	4.10505i		−	0.343282i
$144$		0			0
$145$	−3.57384	+	2.90830i	−0.296791	+	0.241521i
$146$		0			0
$147$	17.4960	−	12.7116i	1.44304	−	1.04843i
$148$		0			0
$149$			4.60655i			0.377384i	0.982036	+	0.188692i	$0.0604247\pi$
$149$			4.60655i			0.377384i	−0.982036	+	0.188692i	$0.939575\pi$
$150$		0			0
$151$	−1.76177			−0.143371			−0.0716854	−	0.997427i	$-0.522838\pi$
$151$	−1.76177			−0.143371			−0.0716854	+	0.997427i	$0.522838\pi$
$152$		0			0
$153$	0.133942	+	0.184355i	0.0108285	+	0.0149042i
$154$		0			0
$155$	−3.16285	+	4.89611i	−0.254046	+	0.393265i
$156$		0			0
$157$	4.33632			0.346076			0.173038	−	0.984915i	$-0.444642\pi$
$157$	4.33632			0.346076			0.173038	+	0.984915i	$0.444642\pi$
$158$		0			0
$159$	−2.48259	+	7.64062i	−0.196882	+	0.605940i
$160$		0			0
$161$	7.20794	+	22.1838i	0.568066	+	1.74833i
$162$		0			0
$163$	2.23193	−	6.86918i	0.174818	−	0.538036i	−0.824807	−	0.565415i	$-0.808716\pi$
$163$	2.23193	−	6.86918i	0.174818	−	0.538036i	0.999625	+	0.0273790i	$0.00871610\pi$
$164$		0			0
$165$	17.2589	+	11.1491i	1.34361	+	0.867959i
$166$		0			0
$167$	−5.30895	+	7.30714i	−0.410819	+	0.565444i	−0.963418	−	0.268004i	$-0.913636\pi$
$167$	−5.30895	+	7.30714i	−0.410819	+	0.565444i	0.552599	+	0.833447i	$0.313636\pi$
$168$		0			0
$169$	10.0393	+	7.29397i	0.772253	+	0.561075i
$170$		0			0
$171$	0.0407338	+	0.0560652i	0.00311499	+	0.00428742i
$172$		0			0
$173$	4.23208	+	13.0250i	0.321759	+	0.990273i	0.972882	+	0.231301i	$0.0742982\pi$
$173$	4.23208	+	13.0250i	0.321759	+	0.990273i	−0.651123	+	0.758972i	$0.725702\pi$
$174$		0			0
$175$	−2.41789	−	21.9865i	−0.182775	−	1.66202i
$176$		0			0
$177$	1.76912	−	0.574821i	0.132975	−	0.0432062i
$178$		0			0
$179$	−4.19376	−	5.77221i	−0.313456	−	0.431435i	0.622999	−	0.782223i	$-0.285914\pi$
$179$	−4.19376	−	5.77221i	−0.313456	−	0.431435i	−0.936455	+	0.350787i	$0.885914\pi$
$180$		0			0
$181$	1.65805	−	2.28211i	0.123242	−	0.169628i	−0.742938	−	0.669360i	$-0.766568\pi$
$181$	1.65805	−	2.28211i	0.123242	−	0.169628i	0.866180	+	0.499732i	$0.166568\pi$
$182$		0			0
$183$	7.30439	−	10.0536i	0.539956	−	0.743185i
$184$		0			0
$185$	−14.0582	−	3.73066i	−1.03358	−	0.274284i
$186$		0			0
$187$	−9.39549	+	28.9163i	−0.687066	+	2.11457i
$188$		0			0
$189$	22.0051	−	7.14989i	1.60064	−	0.520078i
$190$		0			0
$191$	−4.36011	+	13.4190i	−0.315486	+	0.970968i	0.660067	+	0.751206i	$0.270528\pi$
$191$	−4.36011	+	13.4190i	−0.315486	+	0.970968i	−0.975554	+	0.219761i	$0.929472\pi$
$192$		0			0
$193$		−	6.87803i		−	0.495092i	−0.968876	−	0.247546i	$-0.920376\pi$
$193$		−	6.87803i		−	0.495092i	0.968876	−	0.247546i	$-0.0796241\pi$
$194$		0			0
$195$	2.75791	−	1.06628i	0.197498	−	0.0763580i
$196$		0			0
$197$	9.86331	−	7.16612i	0.702732	−	0.510565i	−0.178089	−	0.984014i	$-0.556991\pi$
$197$	9.86331	−	7.16612i	0.702732	−	0.510565i	0.880821	+	0.473450i	$0.156991\pi$
$198$		0			0
$199$	−14.7705			−1.04705			−0.523527	−	0.852009i	$-0.675384\pi$
$199$	−14.7705			−1.04705			−0.523527	+	0.852009i	$0.675384\pi$
$200$		0			0
$201$	10.9069			0.769313
$202$		0			0
$203$	−7.37478	+	5.35809i	−0.517608	+	0.376064i
$204$		0			0
$205$	−5.27823	−	1.40070i	−0.368648	−	0.0978289i
$206$		0			0
$207$			0.211062i			0.0146698i
$208$		0			0
$209$	−2.85732	+	8.79391i	−0.197645	+	0.608288i
$210$		0			0
$211$	−2.19369	+	0.712773i	−0.151020	+	0.0490693i	−0.383551	−	0.923520i	$-0.625299\pi$
$211$	−2.19369	+	0.712773i	−0.151020	+	0.0490693i	0.232532	+	0.972589i	$0.425299\pi$
$212$		0			0
$213$	0.310711	−	0.956271i	0.0212896	−	0.0655226i
$214$		0			0
$215$	0.814196	+	14.8520i	0.0555277	+	1.01290i
$216$		0			0
$217$	−6.77818	+	9.32936i	−0.460133	+	0.633318i
$218$		0			0
$219$	5.83149	−	8.02635i	0.394055	−	0.542371i
$220$		0			0
$221$	2.57182	+	3.53981i	0.173000	+	0.238113i
$222$		0			0
$223$	2.12152	−	0.689324i	0.142068	−	0.0461606i	−0.237120	−	0.971480i	$-0.576203\pi$
$223$	2.12152	−	0.689324i	0.142068	−	0.0461606i	0.379188	+	0.925320i	$0.376203\pi$
$224$		0			0
$225$	0.0406702	−	0.195970i	0.00271135	−	0.0130647i
$226$		0			0
$227$	2.05822	+	6.33454i	0.136609	+	0.420438i	0.995837	−	0.0911544i	$-0.0290557\pi$
$227$	2.05822	+	6.33454i	0.136609	+	0.420438i	−0.859228	+	0.511593i	$0.829056\pi$
$228$		0			0
$229$	−6.45978	−	8.89112i	−0.426874	−	0.587542i	0.540358	−	0.841435i	$-0.318289\pi$
$229$	−6.45978	−	8.89112i	−0.426874	−	0.587542i	−0.967232	+	0.253893i	$0.918289\pi$
$230$		0			0
$231$	32.8862	+	23.8932i	2.16375	+	1.57206i
$232$		0			0
$233$	16.0021	−	22.0251i	1.04834	−	1.44291i	0.158092	−	0.987424i	$-0.449466\pi$
$233$	16.0021	−	22.0251i	1.04834	−	1.44291i	0.890243	−	0.455485i	$-0.150534\pi$
$234$		0			0
$235$	13.9484	−	11.3509i	0.909895	−	0.740450i
$236$		0			0
$237$	4.12044	−	12.6814i	0.267651	−	0.823746i
$238$		0			0
$239$	−3.33646	−	10.2686i	−0.215817	−	0.664218i	−0.999095	−	0.0425450i	$-0.986453\pi$
$239$	−3.33646	−	10.2686i	−0.215817	−	0.664218i	0.783277	−	0.621673i	$-0.213547\pi$
$240$		0			0
$241$	−2.98946	+	9.20061i	−0.192568	+	0.592663i	0.807428	+	0.589966i	$0.200859\pi$
$241$	−2.98946	+	9.20061i	−0.192568	+	0.592663i	−0.999996	+	0.00269761i	$0.999141\pi$
$242$		0			0
$243$	0.415968			0.0266843
$244$		0			0
$245$	−1.53856	−	28.0653i	−0.0982947	−	1.79303i
$246$		0			0
$247$	0.782131	+	1.07651i	0.0497658	+	0.0684968i
$248$		0			0
$249$	−11.6947			−0.741120
$250$		0			0
$251$		−	19.3541i		−	1.22162i	−0.791778	−	0.610809i	$-0.790844\pi$
$251$		−	19.3541i		−	1.22162i	0.791778	−	0.610809i	$-0.209156\pi$
$252$		0			0
$253$	−22.7828	+	16.5527i	−1.43234	+	1.04066i
$254$		0			0
$255$	−21.8674	+	1.19878i	−1.36939	+	0.0750707i
$256$		0			0
$257$		−	11.0336i		−	0.688257i	−0.938923	−	0.344129i	$-0.888174\pi$
$257$		−	11.0336i		−	0.688257i	0.938923	−	0.344129i	$-0.111826\pi$
$258$		0			0
$259$	−27.3669	−	8.89204i	−1.70049	−	0.552524i
$260$		0			0
$261$	−0.0784474	+	0.0254891i	−0.00485577	+	0.00157774i
$262$		0			0
$263$	−7.35613	−	2.39015i	−0.453598	−	0.147383i	0.0733026	−	0.997310i	$-0.476646\pi$
$263$	−7.35613	−	2.39015i	−0.453598	−	0.147383i	−0.526901	+	0.849927i	$0.676646\pi$
$264$		0			0
$265$	6.59056	+	8.09875i	0.404855	+	0.497502i
$266$		0			0
$267$	−17.5396	−	12.7433i	−1.07341	−	0.779877i
$268$		0			0
$269$	10.4677	−	14.4075i	0.638224	−	0.878440i	−0.360295	−	0.932838i	$-0.617324\pi$
$269$	10.4677	−	14.4075i	0.638224	−	0.878440i	0.998519	+	0.0543984i	$0.0173241\pi$
$270$		0			0
$271$	−6.54444	+	4.75481i	−0.397546	+	0.288834i	−0.768541	−	0.639801i	$-0.779017\pi$
$271$	−6.54444	+	4.75481i	−0.397546	+	0.288834i	0.370994	+	0.928635i	$0.379017\pi$
$272$		0			0
$273$	5.56350	−	1.80769i	0.336718	−	0.109406i
$274$		0			0
$275$	24.3434	−	10.9790i	1.46796	−	0.662060i
$276$		0			0
$277$	6.31523	+	19.4363i	0.379445	+	1.16781i	0.940430	+	0.339987i	$0.110423\pi$
$277$	6.31523	+	19.4363i	0.379445	+	1.16781i	−0.560985	+	0.827826i	$0.689577\pi$
$278$		0			0
$279$	−0.0844176	+	0.0613330i	−0.00505395	+	0.00367191i
$280$		0			0
$281$	−26.1698	−	19.0135i	−1.56116	−	1.13425i	−0.935051	−	0.354513i	$-0.884647\pi$
$281$	−26.1698	−	19.0135i	−1.56116	−	1.13425i	−0.626108	−	0.779736i	$-0.715353\pi$
$282$		0			0
$283$	19.5207	+	14.1826i	1.16038	+	0.843067i	0.989826	−	0.142280i	$-0.0454435\pi$
$283$	19.5207	+	14.1826i	1.16038	+	0.843067i	0.170556	+	0.985348i	$0.445443\pi$
$284$		0			0
$285$	−6.65022	+	0.364569i	−0.393925	+	0.0215952i
$286$		0			0
$287$	−10.2750	−	3.33856i	−0.606516	−	0.197069i
$288$		0			0
$289$	−4.76106	−	14.6531i	−0.280063	−	0.861944i
$290$		0			0
$291$	5.31490	+	1.72691i	0.311565	+	0.101234i
$292$		0			0
$293$	10.3735			0.606027			0.303014	−	0.952986i	$-0.402007\pi$
$293$	10.3735			0.606027			0.303014	+	0.952986i	$0.402007\pi$
$294$		0			0
$295$	0.620111	−	2.33676i	0.0361043	−	0.136051i
$296$		0			0
$297$	16.4194	+	22.5994i	0.952750	+	1.31135i
$298$		0			0
$299$			4.05261i			0.234369i
$300$		0			0
$301$			29.4271i			1.69615i
$302$		0			0
$303$	−3.94655	−	5.43197i	−0.226724	−	0.312058i
$304$		0			0
$305$	−5.82435	−	15.0645i	−0.333501	−	0.862592i
$306$		0			0
$307$	−3.04330			−0.173690			−0.0868452	−	0.996222i	$-0.527679\pi$
$307$	−3.04330			−0.173690			−0.0868452	+	0.996222i	$0.527679\pi$
$308$		0			0
$309$	−31.2633	−	10.1581i	−1.77851	−	0.577872i
$310$		0			0
$311$	4.69469	+	14.4488i	0.266212	+	0.819315i	0.991412	+	0.130777i	$0.0417472\pi$
$311$	4.69469	+	14.4488i	0.266212	+	0.819315i	−0.725200	+	0.688538i	$0.758253\pi$
$312$		0			0
$313$	−0.113450	−	0.0368620i	−0.00641255	−	0.00208357i	0.305809	−	0.952093i	$-0.401073\pi$
$313$	−0.113450	−	0.0368620i	−0.00641255	−	0.00208357i	−0.312222	+	0.950009i	$0.601073\pi$
$314$		0			0
$315$	0.101563	−	0.382719i	0.00572243	−	0.0215638i
$316$		0			0
$317$	23.7579	+	17.2612i	1.33438	+	0.969483i	0.999631	+	0.0271752i	$0.00865119\pi$
$317$	23.7579	+	17.2612i	1.33438	+	0.969483i	0.334748	+	0.942308i	$0.391349\pi$
$318$		0			0
$319$	−8.90369	−	6.46891i	−0.498511	−	0.362189i
$320$		0			0
$321$	−17.0033	+	12.3537i	−0.949034	+	0.689514i
$322$		0			0
$323$	−3.04552	−	9.37315i	−0.169457	−	0.521536i
$324$		0			0
$325$	0.780911	−	3.76284i	0.0433172	−	0.208725i
$326$		0			0
$327$	13.7838	−	4.47862i	0.762244	−	0.247668i
$328$		0			0
$329$	28.7832	−	20.9122i	1.58687	−	1.15293i
$330$		0			0
$331$	−19.7316	+	27.1582i	−1.08455	+	1.49275i	−0.230129	+	0.973160i	$0.573915\pi$
$331$	−19.7316	+	27.1582i	−1.08455	+	1.49275i	−0.854416	+	0.519589i	$0.826085\pi$
$332$		0			0
$333$	−0.210648	−	0.153045i	−0.0115434	−	0.00838681i
$334$		0			0
$335$	7.69197	−	11.9072i	0.420257	−	0.650561i
$336$		0			0
$337$	−28.0105	−	9.10115i	−1.52583	−	0.495771i	−0.578403	−	0.815751i	$-0.696324\pi$
$337$	−28.0105	−	9.10115i	−1.52583	−	0.495771i	−0.947424	+	0.319980i	$0.896324\pi$
$338$		0			0
$339$	−8.84840	+	2.87502i	−0.480579	+	0.156150i
$340$		0			0
$341$	−13.2410	−	4.30227i	−0.717042	−	0.232981i
$342$		0			0
$343$		−	24.6407i		−	1.33048i
$344$		0			0
$345$	−17.0385	−	11.0067i	−0.917319	−	0.592581i
$346$		0			0
$347$	−3.43363	+	2.49468i	−0.184327	+	0.133921i	−0.676122	−	0.736789i	$-0.736341\pi$
$347$	−3.43363	+	2.49468i	−0.184327	+	0.133921i	0.491795	+	0.870711i	$0.336341\pi$
$348$		0			0
$349$			16.7792i			0.898172i	0.893488	+	0.449086i	$0.148250\pi$
$349$			16.7792i			0.898172i	−0.893488	+	0.449086i	$0.851750\pi$
$350$		0			0
$351$	4.01998			0.214570
$352$		0			0
$353$	20.2984	+	27.9383i	1.08037	+	1.48701i	0.859108	+	0.511794i	$0.171019\pi$
$353$	20.2984	+	27.9383i	1.08037	+	1.48701i	0.221266	+	0.975213i	$0.428981\pi$
$354$		0			0
$355$	−0.824850	−	1.01361i	−0.0437785	−	0.0537968i
$356$		0			0
$357$	−43.3271			−2.29311
$358$		0			0
$359$	−1.03463	+	3.18426i	−0.0546057	+	0.168059i	−0.974640	−	0.223779i	$-0.928161\pi$
$359$	−1.03463	+	3.18426i	−0.0546057	+	0.168059i	0.920034	+	0.391838i	$0.128161\pi$
$360$		0			0
$361$	4.94513	+	15.2196i	0.260270	+	0.801029i
$362$		0			0
$363$	−9.31745	+	28.6762i	−0.489039	+	1.50511i
$364$		0			0
$365$	−4.64990	−	12.0268i	−0.243387	−	0.629513i
$366$		0			0
$367$	−5.73261	+	7.89027i	−0.299240	+	0.411869i	−0.931988	−	0.362489i	$-0.881927\pi$
$367$	−5.73261	+	7.89027i	−0.299240	+	0.411869i	0.632748	+	0.774358i	$0.281927\pi$
$368$		0			0
$369$	−0.0790890	−	0.0574615i	−0.00411721	−	0.00299133i
$370$		0			0
$371$	12.1421	+	16.7121i	0.630385	+	0.867651i
$372$		0			0
$373$	−5.70667	−	17.5633i	−0.295480	−	0.909395i	−0.983060	−	0.183286i	$-0.941327\pi$
$373$	−5.70667	−	17.5633i	−0.295480	−	0.909395i	0.687579	−	0.726109i	$-0.258673\pi$
$374$		0			0
$375$	13.6992	+	13.5029i	0.707425	+	0.697286i
$376$		0			0
$377$	−1.50627	+	0.489418i	−0.0775770	+	0.0252063i
$378$		0			0
$379$	15.5245	+	21.3676i	0.797439	+	1.09758i	0.993142	+	0.116917i	$0.0373013\pi$
$379$	15.5245	+	21.3676i	0.797439	+	1.09758i	−0.195703	+	0.980663i	$0.562699\pi$
$380$		0			0
$381$	13.5244	−	18.6147i	0.692875	−	0.953661i
$382$		0			0
$383$	12.3447	−	16.9911i	0.630787	−	0.868203i	−0.367296	−	0.930104i	$-0.619716\pi$
$383$	12.3447	−	16.9911i	0.630787	−	0.868203i	0.998082	+	0.0619009i	$0.0197163\pi$
$384$		0			0
$385$	49.2773	−	19.0519i	2.51140	−	0.970976i
$386$		0			0
$387$	−0.0822833	+	0.253242i	−0.00418269	+	0.0128730i
$388$		0			0
$389$	−14.0198	+	4.55530i	−0.710830	+	0.230963i	−0.642043	−	0.766669i	$-0.721913\pi$
$389$	−14.0198	+	4.55530i	−0.710830	+	0.230963i	−0.0687872	+	0.997631i	$0.521913\pi$
$390$		0			0
$391$	9.27547	−	28.5470i	0.469081	−	1.44368i
$392$		0			0
$393$			6.08236i			0.306814i
$394$		0			0
$395$	−10.9386	−	13.4418i	−0.550380	−	0.676330i
$396$		0			0
$397$	−19.8855	+	14.4476i	−0.998023	+	0.725106i	−0.961663	−	0.274233i	$-0.911576\pi$
$397$	−19.8855	+	14.4476i	−0.998023	+	0.725106i	−0.0363595	+	0.999339i	$0.511576\pi$
$398$		0			0
$399$	−13.1765			−0.659648
$400$		0			0
$401$	3.41803			0.170688			0.0853441	−	0.996352i	$-0.472801\pi$
$401$	3.41803			0.170688			0.0853441	+	0.996352i	$0.472801\pi$
$402$		0			0
$403$	−1.62091	+	1.17766i	−0.0807431	+	0.0586633i
$404$		0			0
$405$	−10.7724	+	16.6757i	−0.535283	+	0.828621i
$406$		0			0
$407$		−	34.7408i		−	1.72204i
$408$		0			0
$409$	−1.50524	+	4.63264i	−0.0744292	+	0.229069i	−0.981349	−	0.192233i	$-0.938427\pi$
$409$	−1.50524	+	4.63264i	−0.0744292	+	0.229069i	0.906920	+	0.421303i	$0.138427\pi$
$410$		0			0
$411$	35.3996	−	11.5020i	1.74613	−	0.567352i
$412$		0			0
$413$	1.47804	−	4.54893i	0.0727294	−	0.223838i
$414$		0			0
$415$	−8.24756	+	12.7673i	−0.404857	+	0.626720i
$416$		0			0
$417$	2.02009	−	2.78041i	0.0989240	−	0.136157i
$418$		0			0
$419$	−2.28269	+	3.14185i	−0.111517	+	0.153489i	−0.861127	−	0.508390i	$-0.830241\pi$
$419$	−2.28269	+	3.14185i	−0.111517	+	0.153489i	0.749610	+	0.661879i	$0.230241\pi$
$420$		0			0
$421$	−4.13220	−	5.68749i	−0.201391	−	0.277191i	0.696361	−	0.717691i	$-0.254801\pi$
$421$	−4.13220	−	5.68749i	−0.201391	−	0.277191i	−0.897753	+	0.440500i	$0.854801\pi$
$422$		0			0
$423$	0.306175	−	0.0994821i	0.0148867	−	0.00483699i
$424$		0			0
$425$	−14.1130	+	24.7184i	−0.684583	+	1.19902i
$426$		0			0
$427$	−9.87415	−	30.3895i	−0.477843	−	1.47065i
$428$		0			0
$429$	4.15127	+	5.71374i	0.200425	+	0.275862i
$430$		0			0
$431$	1.52243	+	1.10611i	0.0733329	+	0.0532795i	0.623848	−	0.781546i	$-0.285569\pi$
$431$	1.52243	+	1.10611i	0.0733329	+	0.0532795i	−0.550515	+	0.834825i	$0.685569\pi$
$432$		0			0
$433$	−3.83776	+	5.28222i	−0.184431	+	0.253847i	−0.891214	−	0.453583i	$-0.850146\pi$
$433$	−3.83776	+	5.28222i	−0.184431	+	0.253847i	0.706783	+	0.707430i	$0.250146\pi$
$434$		0			0
$435$	2.03330	−	7.66208i	0.0974894	−	0.367368i
$436$		0			0
$437$	2.82082	−	8.68158i	0.134938	−	0.415296i
$438$		0			0
$439$	8.75988	+	26.9601i	0.418086	+	1.28674i	0.909461	+	0.415789i	$0.136494\pi$
$439$	8.75988	+	26.9601i	0.418086	+	1.28674i	−0.491375	+	0.870948i	$0.663506\pi$
$440$		0			0
$441$	0.155488	−	0.478542i	0.00740417	−	0.0227877i
$442$		0			0
$443$	−25.7646			−1.22412			−0.612058	−	0.790813i	$-0.709658\pi$
$443$	−25.7646			−1.22412			−0.612058	+	0.790813i	$0.709658\pi$
$444$		0			0
$445$	−26.2817	+	10.1612i	−1.24587	+	0.481688i
$446$		0			0
$447$	−4.65842	−	6.41176i	−0.220336	−	0.303266i
$448$		0			0
$449$	4.58045			0.216165			0.108082	−	0.994142i	$-0.465529\pi$
$449$	4.58045			0.216165			0.108082	+	0.994142i	$0.465529\pi$
$450$		0			0
$451$		−	13.0436i		−	0.614200i
$452$		0			0
$453$	2.45217	−	1.78161i	0.115213	−	0.0837072i
$454$		0			0
$455$	1.95012	−	7.34861i	0.0914229	−	0.344508i
$456$		0			0
$457$			10.4431i			0.488509i	0.969711	+	0.244255i	$0.0785433\pi$
$457$			10.4431i			0.488509i	−0.969711	+	0.244255i	$0.921457\pi$
$458$		0			0
$459$	−28.3171	−	9.20077i	−1.32173	−	0.429455i
$460$		0			0
$461$	−29.9901	+	9.74436i	−1.39678	+	0.453840i	−0.908147	−	0.418651i	$-0.862503\pi$
$461$	−29.9901	+	9.74436i	−1.39678	+	0.453840i	−0.488630	+	0.872491i	$0.662503\pi$
$462$		0			0
$463$	−12.8107	−	4.16244i	−0.595362	−	0.193445i	−0.00419137	−	0.999991i	$-0.501334\pi$
$463$	−12.8107	−	4.16244i	−0.595362	−	0.193445i	−0.591171	+	0.806546i	$0.701334\pi$
$464$		0			0
$465$	−0.548932	−	10.0133i	−0.0254561	−	0.464354i
$466$		0			0
$467$	15.5848	+	11.3230i	0.721180	+	0.523968i	0.886761	−	0.462228i	$-0.152950\pi$
$467$	15.5848	+	11.3230i	0.721180	+	0.523968i	−0.165581	+	0.986196i	$0.552950\pi$
$468$		0			0
$469$	16.4843	−	22.6888i	0.761176	−	1.04767i
$470$		0			0
$471$	−6.03563	+	4.38514i	−0.278107	+	0.202057i
$472$		0			0
$473$	−33.7890	+	10.9787i	−1.55362	+	0.504802i
$474$		0			0
$475$	−4.29200	+	7.51726i	−0.196930	+	0.344915i
$476$		0			0
$477$	0.0577614	+	0.177771i	0.00264471	+	0.00813959i
$478$		0			0
$479$	16.2835	−	11.8306i	0.744010	−	0.540555i	−0.149954	−	0.988693i	$-0.547913\pi$
$479$	16.2835	−	11.8306i	0.744010	−	0.540555i	0.893964	+	0.448138i	$0.147913\pi$
$480$		0			0
$481$	−4.04467	−	2.93862i	−0.184421	−	0.133990i
$482$		0			0
$483$	−32.4661	−	23.5880i	−1.47726	−	1.07329i
$484$		0			0
$485$	5.63358	−	4.58447i	0.255808	−	0.208170i
$486$		0			0
$487$	26.8399	+	8.72080i	1.21623	+	0.395177i	0.845708	−	0.533646i	$-0.179179\pi$
$487$	26.8399	+	8.72080i	1.21623	+	0.395177i	0.370523	+	0.928823i	$0.379179\pi$
$488$		0			0
$489$	3.83994	+	11.8181i	0.173648	+	0.534434i
$490$		0			0
$491$	−34.0495	−	11.0634i	−1.53663	−	0.499283i	−0.586189	−	0.810174i	$-0.699372\pi$
$491$	−34.0495	−	11.0634i	−1.53663	−	0.499283i	−0.950445	+	0.310892i	$0.899372\pi$
$492$		0			0
$493$	11.7305			0.528314
$494$		0			0
$495$	0.477339	−	0.0261680i	0.0214548	−	0.00117616i
$496$		0			0
$497$	−1.51966	−	2.09163i	−0.0681659	−	0.0938224i
$498$		0			0
$499$			26.6004i			1.19080i	0.803430	+	0.595399i	$0.203006\pi$
$499$			26.6004i			1.19080i	−0.803430	+	0.595399i	$0.796994\pi$
$500$		0			0
$501$		−	15.5394i		−	0.694248i
$502$		0			0
$503$	12.2552	+	16.8678i	0.546430	+	0.752097i	0.989522	−	0.144379i	$-0.0461185\pi$
$503$	12.2552	+	16.8678i	0.546430	+	0.752097i	−0.443092	+	0.896476i	$0.646118\pi$
$504$		0			0
$505$	−8.71343	+	0.477675i	−0.387742	+	0.0212563i
$506$		0			0
$507$	−21.3496			−0.948168
$508$		0			0
$509$	−34.2578	−	11.1310i	−1.51845	−	0.493374i	−0.573115	−	0.819475i	$-0.694265\pi$
$509$	−34.2578	−	11.1310i	−1.51845	−	0.493374i	−0.945335	+	0.326101i	$0.894265\pi$
$510$		0			0
$511$	−7.88306	−	24.2616i	−0.348726	−	1.07327i
$512$		0			0
$513$	−8.61166	−	2.79810i	−0.380214	−	0.123539i
$514$		0			0
$515$	−33.1378	+	26.9668i	−1.46023	+	1.18830i
$516$		0			0
$517$	34.7504	+	25.2477i	1.52832	+	1.11039i
$518$		0			0
$519$	−19.0622	−	13.8495i	−0.836738	−	0.607926i
$520$		0			0
$521$	27.8704	−	20.2490i	1.22102	−	0.887126i	0.224839	−	0.974396i	$-0.427814\pi$
$521$	27.8704	−	20.2490i	1.22102	−	0.887126i	0.996185	+	0.0872702i	$0.0278144\pi$
$522$		0			0
$523$	9.84654	+	30.3045i	0.430559	+	1.32512i	0.897570	+	0.440873i	$0.145331\pi$
$523$	9.84654	+	30.3045i	0.430559	+	1.32512i	−0.467011	+	0.884252i	$0.654669\pi$
$524$		0			0
$525$	25.5994	+	28.1574i	1.11725	+	1.22889i
$526$		0			0
$527$	14.1132	−	4.58565i	0.614780	−	0.199754i
$528$		0			0
$529$	3.88440	−	2.82218i	0.168887	−	0.122704i
$530$		0			0
$531$	0.0254391	−	0.0350140i	0.00110396	−	0.00151948i
$532$		0			0
$533$	−1.51859	−	1.10332i	−0.0657775	−	0.0477902i
$534$		0			0
$535$	1.49524	+	27.2751i	0.0646447	+	1.17921i
$536$		0			0
$537$	11.6744	+	3.79324i	0.503788	+	0.163691i
$538$		0			0
$539$	63.8498	−	20.7461i	2.75021	−	0.893596i
$540$		0			0
$541$	19.8645	+	6.45438i	0.854044	+	0.277496i	0.703139	−	0.711053i	$-0.251781\pi$
$541$	19.8645	+	6.45438i	0.854044	+	0.277496i	0.150905	+	0.988548i	$0.451781\pi$
$542$		0			0
$543$			4.85313i			0.208268i
$544$		0			0
$545$	4.83148	−	18.2064i	0.206958	−	0.779878i
$546$		0			0
$547$	24.4151	−	17.7386i	1.04392	−	0.758450i	0.0728702	−	0.997341i	$-0.476784\pi$
$547$	24.4151	−	17.7386i	1.04392	−	0.758450i	0.971046	+	0.238892i	$0.0767841\pi$
$548$		0			0
$549$		−	0.289133i		−	0.0123399i
$550$		0			0
$551$	3.56742			0.151977
$552$		0			0
$553$	−20.1526	−	27.7377i	−0.856978	−	1.17953i
$554$		0			0
$555$	23.3400	−	9.02388i	0.990728	−	0.383042i
$556$		0			0
$557$	−0.749572			−0.0317604			−0.0158802	−	0.999874i	$-0.505055\pi$
$557$	−0.749572			−0.0317604			−0.0158802	+	0.999874i	$0.505055\pi$
$558$		0			0
$559$	−1.57993	+	4.86251i	−0.0668237	+	0.205662i
$560$		0			0
$561$	−16.1645	−	49.7493i	−0.682467	−	2.10042i
$562$		0			0
$563$	7.19759	−	22.1519i	0.303342	−	0.933591i	−0.676949	−	0.736030i	$-0.736698\pi$
$563$	7.19759	−	22.1519i	0.303342	−	0.933591i	0.980291	−	0.197561i	$-0.0633020\pi$
$564$		0			0
$565$	−3.10154	+	11.6875i	−0.130483	+	0.491698i
$566$		0			0
$567$	−23.0858	+	31.7749i	−0.969512	+	1.33442i
$568$		0			0
$569$	6.07930	+	4.41687i	0.254858	+	0.185165i	0.707877	−	0.706336i	$-0.249653\pi$
$569$	6.07930	+	4.41687i	0.254858	+	0.185165i	−0.453019	+	0.891501i	$0.649653\pi$
$570$		0			0
$571$	1.37819	+	1.89691i	0.0576753	+	0.0793832i	0.836880	−	0.547386i	$-0.184377\pi$
$571$	1.37819	+	1.89691i	0.0576753	+	0.0793832i	−0.779205	+	0.626769i	$0.784377\pi$
$572$		0			0
$573$	−7.50138	−	23.0869i	−0.313375	−	0.964468i
$574$		0			0
$575$	−24.0324	+	10.8388i	−1.00222	+	0.452008i
$576$		0			0
$577$	−20.3396	+	6.60875i	−0.846750	+	0.275126i	−0.700084	−	0.714060i	$-0.746854\pi$
$577$	−20.3396	+	6.60875i	−0.846750	+	0.275126i	−0.146666	+	0.989186i	$0.546854\pi$
$578$		0			0
$579$	6.95547	+	9.57339i	0.289060	+	0.397856i
$580$		0			0
$581$	−17.6750	+	24.3275i	−0.733282	+	1.00928i
$582$		0			0
$583$	−14.6593	+	20.1768i	−0.607127	+	0.835639i
$584$		0			0
$585$	0.0373301	−	0.0577873i	0.00154341	−	0.00238921i
$586$		0			0
$587$	−2.16490	+	6.66288i	−0.0893551	+	0.275007i	−0.985741	−	0.168267i	$-0.946183\pi$
$587$	−2.16490	+	6.66288i	−0.0893551	+	0.275007i	0.896386	+	0.443274i	$0.146183\pi$
$588$		0			0
$589$	4.29204	−	1.39457i	0.176850	−	0.0574622i
$590$		0			0
$591$	−6.48173	+	19.9487i	−0.266623	+	0.820581i
$592$		0			0
$593$			28.8406i			1.18434i	0.805812	+	0.592171i	$0.201729\pi$
$593$			28.8406i			1.18434i	−0.805812	+	0.592171i	$0.798271\pi$
$594$		0			0
$595$	−30.5560	+	47.3009i	−1.25267	+	1.93915i
$596$		0			0
$597$	20.5587	−	14.9368i	0.841414	−	0.611323i
$598$		0			0
$599$	−2.36104			−0.0964695			−0.0482347	−	0.998836i	$-0.515360\pi$
$599$	−2.36104			−0.0964695			−0.0482347	+	0.998836i	$0.515360\pi$
$600$		0			0
$601$	−15.1806			−0.619228			−0.309614	−	0.950862i	$-0.600200\pi$
$601$	−15.1806			−0.619228			−0.309614	+	0.950862i	$0.600200\pi$
$602$		0			0
$603$	0.205301	−	0.149160i	0.00836052	−	0.00607427i
$604$		0			0
$605$	24.7352	+	30.3956i	1.00563	+	1.23576i
$606$		0			0
$607$		−	34.1325i		−	1.38540i	−0.721227	−	0.692699i	$-0.756422\pi$
$607$		−	34.1325i		−	1.38540i	0.721227	−	0.692699i	$-0.243578\pi$
$608$		0			0
$609$	4.84638	−	14.9156i	0.196385	−	0.604411i
$610$		0			0
$611$	5.87887	−	1.91016i	0.237834	−	0.0772769i
$612$		0			0
$613$	1.84281	−	5.67158i	0.0744303	−	0.229073i	−0.906919	−	0.421304i	$-0.861572\pi$
$613$	1.84281	−	5.67158i	0.0744303	−	0.229073i	0.981350	+	0.192231i	$0.0615724\pi$
$614$		0			0
$615$	8.76313	−	3.38806i	0.353363	−	0.136620i
$616$		0			0
$617$	4.47498	−	6.15928i	0.180156	−	0.247963i	−0.709383	−	0.704824i	$-0.751026\pi$
$617$	4.47498	−	6.15928i	0.180156	−	0.247963i	0.889538	+	0.456860i	$0.151026\pi$
$618$		0			0
$619$	16.7671	−	23.0779i	0.673925	−	0.927579i	−0.325916	−	0.945399i	$-0.605673\pi$
$619$	16.7671	−	23.0779i	0.673925	−	0.927579i	0.999841	+	0.0178200i	$0.00567259\pi$
$620$		0			0
$621$	−16.2096	−	22.3107i	−0.650470	−	0.895296i
$622$		0			0
$623$	−53.0178	+	17.2265i	−2.12411	+	0.690166i
$624$		0			0
$625$	24.4025	−	5.43288i	0.976102	−	0.217315i
$626$		0			0
$627$	−4.91589	−	15.1295i	−0.196322	−	0.604216i
$628$		0			0
$629$	21.7652	+	29.9572i	0.867834	+	1.19447i
$630$		0			0
$631$	−27.7571	−	20.1667i	−1.10499	−	0.802823i	−0.123124	−	0.992391i	$-0.539291\pi$
$631$	−27.7571	−	20.1667i	−1.10499	−	0.802823i	−0.981868	+	0.189568i	$0.939291\pi$
$632$		0			0
$633$	2.33255	−	3.21048i	0.0927106	−	0.127605i
$634$		0			0
$635$	−10.7840	−	27.8926i	−0.427952	−	1.10689i
$636$		0			0
$637$	2.98553	−	9.18851i	0.118291	−	0.364062i
$638$		0			0
$639$	−0.00722920	−	0.0222492i	−0.000285983	−	0.000880165i
$640$		0			0
$641$	11.8514	−	36.4748i	0.468102	−	1.44067i	−0.386938	−	0.922106i	$-0.626467\pi$
$641$	11.8514	−	36.4748i	0.468102	−	1.44067i	0.855039	−	0.518563i	$-0.173533\pi$
$642$		0			0
$643$	−4.80260			−0.189396			−0.0946980	−	0.995506i	$-0.530189\pi$
$643$	−4.80260			−0.189396			−0.0946980	+	0.995506i	$0.530189\pi$
$644$		0			0
$645$	−16.1525	−	19.8488i	−0.636004	−	0.781548i
$646$		0			0
$647$	−2.22128	−	3.05732i	−0.0873273	−	0.120196i	0.763118	−	0.646259i	$-0.223667\pi$
$647$	−2.22128	−	3.05732i	−0.0873273	−	0.120196i	−0.850445	+	0.526063i	$0.823667\pi$
$648$		0			0
$649$	5.77462			0.226674
$650$		0			0
$651$		−	19.8398i		−	0.777584i
$652$		0			0
$653$	32.1500	−	23.3583i	1.25813	−	0.914082i	0.259462	−	0.965753i	$-0.416455\pi$
$653$	32.1500	−	23.3583i	1.25813	−	0.914082i	0.998664	+	0.0516709i	$0.0164547\pi$
$654$		0			0
$655$	6.64020	+	4.28952i	0.259454	+	0.167605i
$656$		0			0
$657$		−	0.230831i		−	0.00900557i
$658$		0			0
$659$	−14.7150	−	4.78119i	−0.573214	−	0.186249i	0.00804417	−	0.999968i	$-0.497439\pi$
$659$	−14.7150	−	4.78119i	−0.573214	−	0.186249i	−0.581258	+	0.813719i	$0.697439\pi$
$660$		0			0
$661$	29.4671	−	9.57445i	1.14614	−	0.372403i	0.326451	−	0.945214i	$-0.394147\pi$
$661$	29.4671	−	9.57445i	1.14614	−	0.372403i	0.819687	+	0.572811i	$0.194147\pi$
$662$		0			0
$663$	−7.15933	−	2.32621i	−0.278045	−	0.0903424i
$664$		0			0
$665$	−9.29256	+	14.3849i	−0.360350	+	0.557824i
$666$		0			0
$667$	8.78995	+	6.38627i	0.340348	+	0.247277i
$668$		0			0
$669$	−2.25582	+	3.10486i	−0.0872149	+	0.120041i
$670$		0			0
$671$	31.2101	−	22.6755i	1.20485	−	0.875378i
$672$		0			0
$673$	27.2704	−	8.86070i	1.05120	−	0.341555i	0.268059	−	0.963402i	$-0.413618\pi$
$673$	27.2704	−	8.86070i	1.05120	−	0.341555i	0.783138	+	0.621848i	$0.213618\pi$
$674$		0			0
$675$	10.7515	+	23.8388i	0.413825	+	0.917558i
$676$		0			0
$677$	−9.18195	−	28.2591i	−0.352891	−	1.08609i	−0.957222	−	0.289353i	$-0.906560\pi$
$677$	−9.18195	−	28.2591i	−0.352891	−	1.08609i	0.604331	−	0.796733i	$-0.293440\pi$
$678$		0			0
$679$	11.6251	−	8.44616i	0.446132	−	0.324134i
$680$		0			0
$681$	−9.27065	−	6.73552i	−0.355252	−	0.258106i
$682$		0			0
$683$	−1.42936	−	1.03849i	−0.0546928	−	0.0397366i	0.560103	−	0.828423i	$-0.310762\pi$
$683$	−1.42936	−	1.03849i	−0.0546928	−	0.0397366i	−0.614796	+	0.788686i	$0.710762\pi$
$684$		0			0
$685$	12.4083	−	46.7579i	0.474095	−	1.78653i
$686$		0			0
$687$	17.9825	+	5.84285i	0.686073	+	0.222919i
$688$		0			0
$689$	1.10908	+	3.41340i	0.0422526	+	0.130040i
$690$		0			0
$691$	12.3432	+	4.01054i	0.469556	+	0.152568i	0.534231	−	0.845338i	$-0.320601\pi$
$691$	12.3432	+	4.01054i	0.469556	+	0.152568i	−0.0646751	+	0.997906i	$0.520601\pi$
$692$		0			0
$693$	0.945779			0.0359272
$694$		0			0
$695$	−1.61077	−	4.16622i	−0.0611000	−	0.158034i
$696$		0			0
$697$	8.17185	+	11.2476i	0.309531	+	0.426033i
$698$		0			0
$699$			46.8385i			1.77160i
$700$		0			0
$701$		−	9.99937i		−	0.377671i	−0.982009	−	0.188835i	$-0.939529\pi$
$701$		−	9.99937i		−	0.377671i	0.982009	−	0.188835i	$-0.0604713\pi$
$702$		0			0
$703$	6.61913	+	9.11045i	0.249645	+	0.343607i
$704$		0			0
$705$	−7.93583	+	29.9045i	−0.298881	+	1.12627i
$706$		0			0
$707$	−17.2644			−0.649295
$708$		0			0
$709$	39.3712	+	12.7925i	1.47862	+	0.480432i	0.933699	−	0.358058i	$-0.116561\pi$
$709$	39.3712	+	12.7925i	1.47862	+	0.480432i	0.544918	+	0.838490i	$0.316561\pi$
$710$		0			0
$711$	−0.0958687	−	0.295054i	−0.00359536	−	0.0110654i
$712$		0			0
$713$	13.0719	+	4.24731i	0.489546	+	0.159063i
$714$		0			0
$715$	9.16542	−	0.502453i	0.342767	−	0.0187907i
$716$		0			0
$717$	15.0281	+	10.9186i	0.561235	+	0.407761i
$718$		0			0
$719$	27.1580	+	19.7314i	1.01282	+	0.735858i	0.964799	−	0.262988i	$-0.0847080\pi$
$719$	27.1580	+	19.7314i	1.01282	+	0.735858i	0.0480227	+	0.998846i	$0.484708\pi$
$720$		0			0
$721$	−68.3814	+	49.6820i	−2.54666	+	1.85026i
$722$		0			0
$723$	−5.14323	−	15.8292i	−0.191279	−	0.588696i
$724$		0			0
$725$	−6.93084	−	7.62339i	−0.257405	−	0.283126i
$726$		0			0
$727$	42.4290	−	13.7860i	1.57360	−	0.511295i	0.613204	−	0.789924i	$-0.289880\pi$
$727$	42.4290	−	13.7860i	1.57360	−	0.511295i	0.960399	+	0.278630i	$0.0898803\pi$
$728$		0			0
$729$	−22.1271	+	16.0763i	−0.819522	+	0.595417i
$730$		0			0
$731$	22.2583	−	30.6359i	0.823251	−	1.13311i
$732$		0			0
$733$	35.1630	+	25.5474i	1.29877	+	0.943615i	0.999943	−	0.0106913i	$-0.00340322\pi$
$733$	35.1630	+	25.5474i	1.29877	+	0.943615i	0.298831	+	0.954306i	$0.403403\pi$
$734$		0			0
$735$	30.5228	+	37.5076i	1.12585	+	1.38349i
$736$		0			0
$737$	32.2018	+	10.4630i	1.18617	+	0.385410i
$738$		0			0
$739$	18.2840	−	5.94083i	0.672588	−	0.218537i	0.0472404	−	0.998884i	$-0.484957\pi$
$739$	18.2840	−	5.94083i	0.672588	−	0.218537i	0.625347	+	0.780347i	$0.284957\pi$
$740$		0			0
$741$	−2.17726	−	0.707436i	−0.0799838	−	0.0259883i
$742$		0			0
$743$			35.7627i			1.31200i	0.754759	+	0.656002i	$0.227754\pi$
$743$			35.7627i			1.31200i	−0.754759	+	0.656002i	$0.772246\pi$
$744$		0			0
$745$	−10.2851	+	0.563836i	−0.376818	+	0.0206574i
$746$		0			0
$747$	−0.220130	+	0.159934i	−0.00805414	+	0.00585167i
$748$		0			0
$749$			54.0417i			1.97464i
$750$		0			0
$751$	−8.13835			−0.296972			−0.148486	−	0.988914i	$-0.547440\pi$
$751$	−8.13835			−0.296972			−0.148486	+	0.988914i	$0.547440\pi$
$752$		0			0
$753$	19.5720	+	26.9385i	0.713243	+	0.981695i
$754$		0			0
$755$	−0.215638	−	3.93353i	−0.00784789	−	0.143156i
$756$		0			0
$757$	−42.4947			−1.54450			−0.772248	−	0.635321i	$-0.780868\pi$
$757$	−42.4947			−1.54450			−0.772248	+	0.635321i	$0.780868\pi$
$758$		0			0
$759$	14.9719	−	46.0787i	0.543445	−	1.67255i
$760$		0			0
$761$	11.9096	+	36.6540i	0.431723	+	1.32871i	0.896407	+	0.443231i	$0.146168\pi$
$761$	11.9096	+	36.6540i	0.431723	+	1.32871i	−0.464684	+	0.885477i	$0.653832\pi$
$762$		0			0
$763$	11.5158	−	35.4421i	0.416902	−	1.28309i
$764$		0			0
$765$	−0.395218	+	0.321619i	−0.0142891	+	0.0116281i
$766$		0			0
$767$	0.488458	−	0.672305i	0.0176372	−	0.0242755i
$768$		0			0
$769$	29.0252	+	21.0880i	1.04667	+	0.760454i	0.971577	−	0.236723i	$-0.0760733\pi$
$769$	29.0252	+	21.0880i	1.04667	+	0.760454i	0.0750973	+	0.997176i	$0.476073\pi$
$770$		0			0
$771$	11.1578	+	15.3574i	0.401839	+	0.553084i
$772$		0			0
$773$	0.547088	+	1.68376i	0.0196774	+	0.0605607i	0.960413	−	0.278580i	$-0.0898637\pi$
$773$	0.547088	+	1.68376i	0.0196774	+	0.0605607i	−0.940736	+	0.339141i	$0.889864\pi$
$774$		0			0
$775$	−11.3188	−	6.46247i	−0.406582	−	0.232139i
$776$		0			0
$777$	47.0835	−	15.2984i	1.68911	−	0.548826i
$778$		0			0
$779$	2.48519	+	3.42057i	0.0890411	+	0.122554i
$780$		0			0
$781$	1.83471	−	2.52526i	0.0656510	−	0.0903608i
$782$		0			0
$783$	6.33484	−	8.71916i	0.226389	−	0.311597i
$784$		0			0
$785$	0.530760	+	9.68176i	0.0189436	+	0.345557i
$786$		0			0
$787$	0.356070	−	1.09587i	0.0126925	−	0.0390636i	−0.944510	−	0.328484i	$-0.893462\pi$
$787$	0.356070	−	1.09587i	0.0126925	−	0.0390636i	0.957202	+	0.289420i	$0.0934624\pi$
$788$		0			0
$789$	12.6559	−	4.11215i	0.450562	−	0.146396i
$790$		0			0
$791$	−7.39253	+	22.7519i	−0.262848	+	0.808963i
$792$		0			0
$793$		−	5.55167i		−	0.197145i
$794$		0			0
$795$	−17.3632	−	4.60771i	−0.615809	−	0.163419i
$796$		0			0
$797$	−34.5173	+	25.0783i	−1.22267	+	0.888319i	−0.996319	−	0.0857282i	$-0.972678\pi$
$797$	−34.5173	+	25.0783i	−1.22267	+	0.888319i	−0.226347	+	0.974047i	$0.572678\pi$
$798$		0			0
$799$	−45.7832			−1.61969
$800$		0			0
$801$	−0.504425			−0.0178230
$802$		0			0
$803$	24.9167	−	18.1031i	0.879293	−	0.638844i
$804$		0			0
$805$	−48.6478	+	18.8086i	−1.71461	+	0.662914i
$806$		0			0
$807$			30.6390i			1.07854i
$808$		0			0
$809$	17.2761	−	53.1704i	0.607396	−	1.86937i	0.127999	−	0.991774i	$-0.459145\pi$
$809$	17.2761	−	53.1704i	0.607396	−	1.86937i	0.479397	−	0.877598i	$-0.340855\pi$
$810$		0			0
$811$	−27.5933	+	8.96560i	−0.968931	+	0.314825i	−0.750384	−	0.661002i	$-0.770132\pi$
$811$	−27.5933	+	8.96560i	−0.968931	+	0.314825i	−0.218547	+	0.975826i	$0.570132\pi$
$812$		0			0
$813$	4.30072	−	13.2362i	0.150833	−	0.464216i
$814$		0			0
$815$	15.6101	+	4.14249i	0.546798	+	0.145105i
$816$		0			0
$817$	6.76908	−	9.31684i	0.236820	−	0.325955i
$818$		0			0
$819$	0.0800007	−	0.110111i	0.00279545	−	0.00384761i
$820$		0			0
$821$	26.5861	+	36.5926i	0.927860	+	1.27709i	0.960689	+	0.277628i	$0.0895484\pi$
$821$	26.5861	+	36.5926i	0.927860	+	1.27709i	−0.0328288	+	0.999461i	$0.510452\pi$
$822$		0			0
$823$	22.3928	−	7.27585i	0.780562	−	0.253620i	0.108482	−	0.994098i	$-0.465401\pi$
$823$	22.3928	−	7.27585i	0.780562	−	0.253620i	0.672080	+	0.740478i	$0.265401\pi$
$824$		0			0
$825$	−22.7804	+	39.8989i	−0.793111	+	1.38910i
$826$		0			0
$827$	16.1742	+	49.7791i	0.562432	+	1.73099i	0.675460	+	0.737397i	$0.263945\pi$
$827$	16.1742	+	49.7791i	0.562432	+	1.73099i	−0.113028	+	0.993592i	$0.536055\pi$
$828$		0			0
$829$	−14.8801	−	20.4807i	−0.516808	−	0.711325i	0.468241	−	0.883601i	$-0.344888\pi$
$829$	−14.8801	−	20.4807i	−0.516808	−	0.711325i	−0.985049	+	0.172276i	$0.944888\pi$
$830$		0			0
$831$	−28.4451	−	20.6666i	−0.986751	−	0.716917i
$832$		0			0
$833$	−42.0606	+	57.8915i	−1.45731	+	2.00582i
$834$		0			0
$835$	−16.9646	−	10.9590i	−0.587083	−	0.379251i
$836$		0			0
$837$	4.21310	−	12.9666i	0.145626	−	0.448191i
$838$		0			0
$839$	−9.60794	−	29.5702i	−0.331703	−	1.02088i	−0.968323	−	0.249699i	$-0.919668\pi$
$839$	−9.60794	−	29.5702i	−0.331703	−	1.02088i	0.636620	−	0.771177i	$-0.280332\pi$
$840$		0			0
$841$	7.64937	−	23.5424i	0.263772	−	0.811805i
$842$		0			0
$843$	55.6527			1.91678
$844$		0			0
$845$	−15.0566	+	23.3077i	−0.517962	+	0.801808i
$846$		0			0
$847$	45.5707	+	62.7227i	1.56583	+	2.15518i
$848$		0			0
$849$	−41.5127			−1.42471
$850$		0			0
$851$			34.2970i			1.17569i
$852$		0			0
$853$	−33.2584	+	24.1636i	−1.13875	+	0.827347i	−0.986944	−	0.161064i	$-0.948507\pi$
$853$	−33.2584	+	24.1636i	−1.13875	+	0.827347i	−0.151801	+	0.988411i	$0.548507\pi$
$854$		0			0
$855$	−0.120192	+	0.0978092i	−0.00411048	+	0.00334501i
$856$		0			0
$857$		−	7.69778i		−	0.262951i	−0.991319	−	0.131476i	$-0.958029\pi$
$857$		−	7.69778i		−	0.262951i	0.991319	−	0.131476i	$-0.0419715\pi$
$858$		0			0
$859$	39.8085	+	12.9346i	1.35825	+	0.441322i	0.895458	−	0.445146i	$-0.146848\pi$
$859$	39.8085	+	12.9346i	1.35825	+	0.441322i	0.462791	+	0.886468i	$0.346848\pi$
$860$		0			0
$861$	17.6778	−	5.74385i	0.602456	−	0.195750i
$862$		0			0
$863$	16.4224	+	5.33595i	0.559024	+	0.181638i	0.574882	−	0.818236i	$-0.305048\pi$
$863$	16.4224	+	5.33595i	0.559024	+	0.181638i	−0.0158581	+	0.999874i	$0.505048\pi$
$864$		0			0
$865$	−28.5631	+	11.0433i	−0.971176	+	0.375483i
$866$		0			0
$867$	21.4449	+	15.5806i	0.728305	+	0.529145i
$868$		0			0
$869$	24.3306	−	33.4882i	0.825359	−	1.13601i
$870$		0			0
$871$	3.94200	−	2.86403i	0.133570	−	0.0970441i
$872$		0			0
$873$	0.123660	−	0.0401795i	0.00418525	−	0.00135987i
$874$		0			0
$875$	48.7936	−	8.08957i	1.64952	−	0.273477i
$876$		0			0
$877$	−4.64130	−	14.2844i	−0.156725	−	0.482351i	0.841606	−	0.540092i	$-0.181610\pi$
$877$	−4.64130	−	14.2844i	−0.156725	−	0.482351i	−0.998332	+	0.0577404i	$0.981610\pi$
$878$		0			0
$879$	−14.4387	+	10.4903i	−0.487004	+	0.353829i
$880$		0			0
$881$	37.8296	+	27.4848i	1.27451	+	0.925986i	0.999373	−	0.0354189i	$-0.0112766\pi$
$881$	37.8296	+	27.4848i	1.27451	+	0.925986i	0.275138	+	0.961405i	$0.411277\pi$
$882$		0			0
$883$	27.3068	+	19.8395i	0.918946	+	0.667653i	0.943261	−	0.332051i	$-0.107741\pi$
$883$	27.3068	+	19.8395i	0.918946	+	0.667653i	−0.0243155	+	0.999704i	$0.507741\pi$
$884$		0			0
$885$	1.49995	+	3.87958i	0.0504203	+	0.130411i
$886$		0			0
$887$	3.96211	+	1.28737i	0.133035	+	0.0432256i	0.374778	−	0.927115i	$-0.377719\pi$
$887$	3.96211	+	1.28737i	0.133035	+	0.0432256i	−0.241743	+	0.970340i	$0.577719\pi$
$888$		0			0
$889$	−18.2824	−	56.2675i	−0.613172	−	1.88715i
$890$		0			0
$891$	−45.0976	−	14.6531i	−1.51083	−	0.490897i
$892$		0			0
$893$	−13.9234			−0.465928
$894$		0			0
$895$	12.3744	−	10.0700i	0.413630	−	0.336602i
$896$		0			0
$897$	−4.09824	−	5.64075i	−0.136836	−	0.188339i
$898$		0			0
$899$			5.37148i			0.179149i
$900$		0			0
$901$		−	26.5827i		−	0.885597i
$902$		0			0
$903$	−29.7585	−	40.9590i	−0.990299	−	1.36303i
$904$		0			0
$905$	5.29824	+	3.42262i	0.176120	+	0.113772i
$906$		0			0
$907$	−44.9685			−1.49315			−0.746577	−	0.665299i	$-0.768304\pi$
$907$	−44.9685			−1.49315			−0.746577	+	0.665299i	$0.768304\pi$
$908$		0			0
$909$	−0.148573	−	0.0482742i	−0.00492784	−	0.00160115i
$910$		0			0
$911$	3.92631	+	12.0839i	0.130085	+	0.400359i	0.994793	−	0.101915i	$-0.0324969\pi$
$911$	3.92631	+	12.0839i	0.130085	+	0.400359i	−0.864709	+	0.502274i	$0.832497\pi$
$912$		0			0
$913$	−34.5277	−	11.2187i	−1.14270	−	0.371286i
$914$		0			0
$915$	23.3409	+	15.0781i	0.771627	+	0.498465i
$916$		0			0
$917$	12.6527	+	9.19269i	0.417827	+	0.303569i
$918$		0			0
$919$	18.4864	+	13.4312i	0.609810	+	0.443053i	0.849347	−	0.527834i	$-0.176996\pi$
$919$	18.4864	+	13.4312i	0.609810	+	0.443053i	−0.239537	+	0.970887i	$0.576996\pi$
$920$		0			0
$921$	4.23591	−	3.07757i	0.139578	−	0.101409i
$922$		0			0
$923$	−0.138808	−	0.427208i	−0.00456893	−	0.0140617i
$924$		0			0
$925$	6.60880	−	31.8446i	0.217296	−	1.04705i
$926$		0			0
$927$	−0.727391	+	0.236344i	−0.0238907	+	0.00776255i
$928$		0			0
$929$	−24.2098	+	17.5894i	−0.794297	+	0.577090i	−0.909236	−	0.416282i	$-0.863333\pi$
$929$	−24.2098	+	17.5894i	−0.794297	+	0.577090i	0.114939	+	0.993373i	$0.463333\pi$
$930$		0			0
$931$	−12.7913	+	17.6057i	−0.419218	+	0.577003i
$932$		0			0
$933$	−21.1459	−	15.3634i	−0.692286	−	0.502975i
$934$		0			0
$935$	−65.7120	−	17.4381i	−2.14901	−	0.570288i
$936$		0			0
$937$	44.9541	+	14.6065i	1.46859	+	0.477172i	0.930681	−	0.365833i	$-0.119216\pi$
$937$	44.9541	+	14.6065i	1.46859	+	0.477172i	0.537905	+	0.843005i	$0.319216\pi$
$938$		0			0
$939$	0.195185	−	0.0634195i	0.00636963	−	0.00206962i
$940$		0			0
$941$	−20.6937	−	6.72379i	−0.674595	−	0.219189i	−0.0483677	−	0.998830i	$-0.515402\pi$
$941$	−20.6937	−	6.72379i	−0.674595	−	0.219189i	−0.626228	+	0.779640i	$0.715402\pi$
$942$		0			0
$943$			12.8770i			0.419333i
$944$		0			0
$945$	18.6571	+	48.2560i	0.606915	+	1.56977i
$946$		0			0
$947$	43.9238	−	31.9125i	1.42733	−	1.03702i	0.436827	−	0.899546i	$-0.356102\pi$
$947$	43.9238	−	31.9125i	1.42733	−	1.03702i	0.990506	−	0.137472i	$-0.0438978\pi$
$948$		0			0
$949$		−	4.43220i		−	0.143875i
$950$		0			0
$951$	−50.5237			−1.63834
$952$		0			0
$953$	−26.3956	−	36.3305i	−0.855039	−	1.17686i	−0.982730	−	0.185046i	$-0.940757\pi$
$953$	−26.3956	−	36.3305i	−0.855039	−	1.17686i	0.127691	−	0.991814i	$-0.459243\pi$
$954$		0			0
$955$	−30.4946	−	8.09241i	−0.986781	−	0.261864i
$956$		0			0
$957$	18.9346			0.612068
$958$		0			0
$959$	29.5751	−	91.0227i	0.955029	−	2.93928i
$960$		0			0
$961$	−7.47972	−	23.0202i	−0.241281	−	0.742588i
$962$		0			0
$963$	−0.151110	+	0.465068i	−0.00486944	+	0.0149866i
$964$		0			0
$965$	15.3567	−	0.841862i	0.494349	−	0.0271005i
$966$		0			0
$967$	1.74121	−	2.39657i	0.0559936	−	0.0770686i	−0.780102	−	0.625652i	$-0.784833\pi$
$967$	1.74121	−	2.39657i	0.0559936	−	0.0770686i	0.836096	+	0.548584i	$0.184833\pi$
$968$		0			0
$969$	13.7177	+	9.96648i	0.440675	+	0.320169i
$970$		0			0
$971$	−15.2206	−	20.9493i	−0.488451	−	0.672295i	0.491650	−	0.870793i	$-0.336394\pi$
$971$	−15.2206	−	20.9493i	−0.488451	−	0.672295i	−0.980101	+	0.198497i	$0.936394\pi$
$972$		0			0
$973$	−2.73077	−	8.40446i	−0.0875446	−	0.269435i
$974$		0			0
$975$	2.71827	+	6.02712i	0.0870543	+	0.193022i
$976$		0			0
$977$	34.3875	−	11.1732i	1.10015	−	0.357461i	0.297991	−	0.954569i	$-0.403683\pi$
$977$	34.3875	−	11.1732i	1.10015	−	0.357461i	0.802161	+	0.597107i	$0.203683\pi$
$978$		0			0
$979$	−39.5599	−	54.4495i	−1.26434	−	1.74021i
$980$		0			0
$981$	0.198204	−	0.272805i	0.00632818	−	0.00870999i
$982$		0			0
$983$	−20.4443	+	28.1391i	−0.652071	+	0.897499i	−0.999187	−	0.0403234i	$-0.987161\pi$
$983$	−20.4443	+	28.1391i	−0.652071	+	0.897499i	0.347115	+	0.937822i	$0.387161\pi$
$984$		0			0
$985$	17.2072	+	21.1448i	0.548265	+	0.673731i
$986$		0			0
$987$	−18.9151	+	58.2146i	−0.602073	+	1.85299i
$988$		0			0
$989$	33.3574	−	10.8385i	1.06070	−	0.344643i
$990$		0			0
$991$	1.42805	−	4.39510i	0.0453636	−	0.139615i	−0.925809	−	0.377991i	$-0.876615\pi$
$991$	1.42805	−	4.39510i	0.0453636	−	0.139615i	0.971173	+	0.238376i	$0.0766151\pi$
$992$		0			0
$993$		−	57.7546i		−	1.83279i
$994$		0			0
$995$	−1.80789	−	32.9783i	−0.0573140	−	1.04548i
$996$		0			0
$997$	29.6486	−	21.5409i	0.938979	−	0.682209i	−0.00919532	−	0.999958i	$-0.502927\pi$
$997$	29.6486	−	21.5409i	0.938979	−	0.682209i	0.948175	+	0.317749i	$0.102927\pi$
$998$		0			0
$999$	34.0208			1.07637

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	800.2.be.a.369.7		112
4.3	odd	2		200.2.o.a.69.8	yes	112
8.3	odd	2		200.2.o.a.69.14	yes	112
8.5	even	2	inner	800.2.be.a.369.22		112
20.3	even	4		1000.2.t.b.901.16		224
20.7	even	4		1000.2.t.b.901.41		224
20.19	odd	2		1000.2.o.a.349.21		112
25.4	even	10	inner	800.2.be.a.529.22		112
40.3	even	4		1000.2.t.b.901.53		224
40.19	odd	2		1000.2.o.a.349.15		112
40.27	even	4		1000.2.t.b.901.4		224
100.3	even	20		1000.2.t.b.101.53		224
100.47	even	20		1000.2.t.b.101.4		224
100.71	odd	10		1000.2.o.a.149.15		112
100.79	odd	10		200.2.o.a.29.14	yes	112
200.3	even	20		1000.2.t.b.101.16		224
200.29	even	10	inner	800.2.be.a.529.7		112
200.147	even	20		1000.2.t.b.101.41		224
200.171	odd	10		1000.2.o.a.149.21		112
200.179	odd	10		200.2.o.a.29.8	✓	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.29.8	✓	112	200.179	odd	10
200.2.o.a.29.14	yes	112	100.79	odd	10
200.2.o.a.69.8	yes	112	4.3	odd	2
200.2.o.a.69.14	yes	112	8.3	odd	2
800.2.be.a.369.7		112	1.1	even	1	trivial
800.2.be.a.369.22		112	8.5	even	2	inner
800.2.be.a.529.7		112	200.29	even	10	inner
800.2.be.a.529.22		112	25.4	even	10	inner
1000.2.o.a.149.15		112	100.71	odd	10
1000.2.o.a.149.21		112	200.171	odd	10
1000.2.o.a.349.15		112	40.19	odd	2
1000.2.o.a.349.21		112	20.19	odd	2
1000.2.t.b.101.4		224	100.47	even	20
1000.2.t.b.101.16		224	200.3	even	20
1000.2.t.b.101.41		224	200.147	even	20
1000.2.t.b.101.53		224	100.3	even	20
1000.2.t.b.901.4		224	40.27	even	4
1000.2.t.b.901.16		224	20.3	even	4
1000.2.t.b.901.41		224	20.7	even	4
1000.2.t.b.901.53		224	40.3	even	4

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:	\( N \)	\(=\)	\( 800 = 2^{5} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	800.be (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.39188 + 1.01126i) q^{3} +(0.122399 + 2.23272i) q^{5} +4.42380i q^{7} +(-0.0123697 + 0.0380700i) q^{9} +O(q^{10})\)	\(q+(-1.39188 + 1.01126i) q^{3} +(0.122399 + 2.23272i) q^{5} +4.42380i q^{7} +(-0.0123697 + 0.0380700i) q^{9} +(-5.07953 + 1.65044i) q^{11} +(-0.237511 + 0.730985i) q^{13} +(-2.42822 - 2.98389i) q^{15} +(3.34610 - 4.60551i) q^{17} +(1.01760 - 1.40061i) q^{19} +(-4.47361 - 6.15740i) q^{21} +(5.01464 - 1.62935i) q^{23} +(-4.97004 + 0.546563i) q^{25} +(-1.61623 - 4.97425i) q^{27} +(1.21119 + 1.66707i) q^{29} +(2.10890 + 1.53221i) q^{31} +(5.40106 - 7.43393i) q^{33} +(-9.87709 + 0.541468i) q^{35} +(-2.01004 + 6.18628i) q^{37} +(-0.408628 - 1.25763i) q^{39} +(-0.754681 + 2.32267i) q^{41} +6.65200 q^{43} +(-0.0865136 - 0.0229583i) q^{45} +(-4.72720 - 6.50644i) q^{47} -12.5700 q^{49} +9.79409i q^{51} +(3.77778 - 2.74471i) q^{53} +(-4.30669 - 11.1391i) q^{55} +2.97854i q^{57} +(-1.02828 - 0.334110i) q^{59} +(-6.86954 + 2.23205i) q^{61} +(-0.168414 - 0.0547211i) q^{63} +(-1.66115 - 0.440824i) q^{65} +(-5.12879 - 3.72628i) q^{67} +(-5.33207 + 7.33896i) q^{69} +(-0.472812 + 0.343518i) q^{71} +(-5.48432 + 1.78197i) q^{73} +(6.36497 - 5.78674i) q^{75} +(-7.30121 - 22.4708i) q^{77} +(-6.27011 + 4.55550i) q^{79} +(7.18270 + 5.21854i) q^{81} +(5.49924 + 3.99543i) q^{83} +(10.6924 + 6.90718i) q^{85} +(-3.37167 - 1.09552i) q^{87} +(3.89405 + 11.9847i) q^{89} +(-3.23373 - 1.05070i) q^{91} -4.48479 q^{93} +(3.25171 + 2.10058i) q^{95} +(-1.90925 - 2.62786i) q^{97} -0.213793i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 30 q^{9}+O(q^{10}) \) 112 * q - 30 * q^9	\( 112 q - 30 q^{9} + 2 q^{15} - 10 q^{17} + 10 q^{23} - 6 q^{25} + 18 q^{31} - 10 q^{33} + 10 q^{39} - 10 q^{41} + 10 q^{47} - 80 q^{49} + 34 q^{55} - 60 q^{63} + 40 q^{65} - 22 q^{71} - 10 q^{73} - 14 q^{79} - 6 q^{81} + 10 q^{87} + 24 q^{89} + 86 q^{95} - 50 q^{97}+O(q^{100}) \) 112 * q - 30 * q^9 + 2 * q^15 - 10 * q^17 + 10 * q^23 - 6 * q^25 + 18 * q^31 - 10 * q^33 + 10 * q^39 - 10 * q^41 + 10 * q^47 - 80 * q^49 + 34 * q^55 - 60 * q^63 + 40 * q^65 - 22 * q^71 - 10 * q^73 - 14 * q^79 - 6 * q^81 + 10 * q^87 + 24 * q^89 + 86 * q^95 - 50 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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