LMFDB - Embedded newform 400.2.bi.d.223.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(47,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 17]))

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

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

chi := DirichletCharacter("400.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.bi (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			223.6
Character	$\chi$	$=$	400.223
Dual form			400.2.bi.d.287.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.157369 + 0.308855i) q^{3} +(-2.16783 + 0.548188i) q^{5} +(-1.64756 - 1.64756i) q^{7} +(1.69273 - 2.32984i) q^{9} +O(q^{10})$	\(q+(0.157369 + 0.308855i) q^{3} +(-2.16783 + 0.548188i) q^{5} +(-1.64756 - 1.64756i) q^{7} +(1.69273 - 2.32984i) q^{9} +(-2.02639 - 2.78909i) q^{11} +(-0.333359 - 2.10475i) q^{13} +(-0.510460 - 0.583277i) q^{15} +(4.32737 + 2.20491i) q^{17} +(-2.39074 - 7.35794i) q^{19} +(0.249580 - 0.768130i) q^{21} +(0.0697318 - 0.440270i) q^{23} +(4.39898 - 2.37676i) q^{25} +(2.01307 + 0.318839i) q^{27} +(1.71616 + 0.557615i) q^{29} +(-7.04868 + 2.29026i) q^{31} +(0.542530 - 1.06478i) q^{33} +(4.47479 + 2.66845i) q^{35} +(-4.39673 + 0.696374i) q^{37} +(0.597600 - 0.434182i) q^{39} +(-2.90521 - 2.11076i) q^{41} +(-7.50685 + 7.50685i) q^{43} +(-2.39236 + 5.97864i) q^{45} +(11.3009 - 5.75811i) q^{47} -1.57112i q^{49} +1.68351i q^{51} +(-7.81476 + 3.98182i) q^{53} +(5.92181 + 4.93542i) q^{55} +(1.89630 - 1.89630i) q^{57} +(1.55630 + 1.13072i) q^{59} +(5.52261 - 4.01241i) q^{61} +(-6.62741 + 1.04968i) q^{63} +(1.87646 + 4.37999i) q^{65} +(2.31499 - 4.54342i) q^{67} +(0.146953 - 0.0477479i) q^{69} +(-3.94277 - 1.28108i) q^{71} +(-5.07659 - 0.804053i) q^{73} +(1.42634 + 0.984617i) q^{75} +(-1.25658 + 7.93376i) q^{77} +(1.36639 - 4.20533i) q^{79} +(-2.45144 - 7.54476i) q^{81} +(11.6526 + 5.93732i) q^{83} +(-10.5897 - 2.40765i) q^{85} +(0.0978494 + 0.617797i) q^{87} +(8.50790 + 11.7101i) q^{89} +(-2.91846 + 4.01692i) q^{91} +(-1.81660 - 1.81660i) q^{93} +(9.21625 + 14.6402i) q^{95} +(4.61582 + 9.05905i) q^{97} -9.92826 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{5}+O(q^{10}) $ 80 * q + 4 * q^5	$ 80 q + 4 q^{5} - 4 q^{13} - 24 q^{17} - 48 q^{25} - 40 q^{29} - 64 q^{33} - 20 q^{37} - 24 q^{45} + 28 q^{53} + 48 q^{57} + 112 q^{65} + 140 q^{69} + 108 q^{73} + 136 q^{77} - 20 q^{81} - 24 q^{85} + 80 q^{89} - 116 q^{93} - 52 q^{97}+O(q^{100}) $ 80 * q + 4 * q^5 - 4 * q^13 - 24 * q^17 - 48 * q^25 - 40 * q^29 - 64 * q^33 - 20 * q^37 - 24 * q^45 + 28 * q^53 + 48 * q^57 + 112 * q^65 + 140 * q^69 + 108 * q^73 + 136 * q^77 - 20 * q^81 - 24 * q^85 + 80 * q^89 - 116 * q^93 - 52 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{11}{20}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.157369	+	0.308855i	0.0908572	+	0.178317i	0.931963	−	0.362553i	$-0.118095\pi$
$3$	0.157369	+	0.308855i	0.0908572	+	0.178317i	−0.841106	+	0.540871i	$0.818095\pi$
$4$		0			0
$5$	−2.16783	+	0.548188i	−0.969483	+	0.245157i
$5$	−2.16783	+	0.548188i	−0.969483	+	0.245157i
$6$		0			0
$7$	−1.64756	−	1.64756i	−0.622717	−	0.622717i	0.323508	−	0.946225i	$-0.395138\pi$
$7$	−1.64756	−	1.64756i	−0.622717	−	0.622717i	−0.946225	+	0.323508i	$0.895138\pi$
$8$		0			0
$9$	1.69273	−	2.32984i	0.564243	−	0.776614i
$10$		0			0
$11$	−2.02639	−	2.78909i	−0.610979	−	0.840941i	0.385678	−	0.922633i	$-0.373967\pi$
$11$	−2.02639	−	2.78909i	−0.610979	−	0.840941i	−0.996658	+	0.0816924i	$0.973967\pi$
$12$		0			0
$13$	−0.333359	−	2.10475i	−0.0924572	−	0.583752i	−0.989805	−	0.142428i	$-0.954509\pi$
$13$	−0.333359	−	2.10475i	−0.0924572	−	0.583752i	0.897348	−	0.441324i	$-0.145491\pi$
$14$		0			0
$15$	−0.510460	−	0.583277i	−0.131800	−	0.150601i
$16$		0			0
$17$	4.32737	+	2.20491i	1.04954	+	0.534768i	0.891667	−	0.452691i	$-0.149536\pi$
$17$	4.32737	+	2.20491i	1.04954	+	0.534768i	0.157874	+	0.987459i	$0.449536\pi$
$18$		0			0
$19$	−2.39074	−	7.35794i	−0.548473	−	1.68803i	−0.712585	−	0.701586i	$-0.752476\pi$
$19$	−2.39074	−	7.35794i	−0.548473	−	1.68803i	0.164112	−	0.986442i	$-0.447524\pi$
$20$		0			0
$21$	0.249580	−	0.768130i	0.0544629	−	0.167620i
$22$		0			0
$23$	0.0697318	−	0.440270i	0.0145401	−	0.0918025i	−0.979351	−	0.202167i	$-0.935202\pi$
$23$	0.0697318	−	0.440270i	0.0145401	−	0.0918025i	0.993891	+	0.110364i	$0.0352017\pi$
$24$		0			0
$25$	4.39898	−	2.37676i	0.879796	−	0.475351i
$26$		0			0
$27$	2.01307	+	0.318839i	0.387415	+	0.0613606i
$28$		0			0
$29$	1.71616	+	0.557615i	0.318684	+	0.103547i	0.463991	−	0.885840i	$-0.346417\pi$
$29$	1.71616	+	0.557615i	0.318684	+	0.103547i	−0.145307	+	0.989387i	$0.546417\pi$
$30$		0			0
$31$	−7.04868	+	2.29026i	−1.26598	+	0.411342i	−0.863622	−	0.504140i	$-0.831810\pi$
$31$	−7.04868	+	2.29026i	−1.26598	+	0.411342i	−0.402359	+	0.915482i	$0.631810\pi$
$32$		0			0
$33$	0.542530	−	1.06478i	0.0944424	−	0.185354i
$34$		0			0
$35$	4.47479	+	2.66845i	0.756378	+	0.451051i
$36$		0			0
$37$	−4.39673	+	0.696374i	−0.722818	+	0.114483i	−0.506994	−	0.861949i	$-0.669244\pi$
$37$	−4.39673	+	0.696374i	−0.722818	+	0.114483i	−0.215823	+	0.976432i	$0.569244\pi$
$38$		0			0
$39$	0.597600	−	0.434182i	0.0956927	−	0.0695248i
$40$		0			0
$41$	−2.90521	−	2.11076i	−0.453717	−	0.329645i	0.337344	−	0.941381i	$-0.390471\pi$
$41$	−2.90521	−	2.11076i	−0.453717	−	0.329645i	−0.791062	+	0.611736i	$0.790471\pi$
$42$		0			0
$43$	−7.50685	+	7.50685i	−1.14478	+	1.14478i	−0.157220	+	0.987564i	$0.550253\pi$
$43$	−7.50685	+	7.50685i	−1.14478	+	1.14478i	−0.987564	+	0.157220i	$0.949747\pi$
$44$		0			0
$45$	−2.39236	+	5.97864i	−0.356632	+	0.891243i
$46$		0			0
$47$	11.3009	−	5.75811i	1.64841	−	0.839907i	0.651734	−	0.758448i	$-0.274042\pi$
$47$	11.3009	−	5.75811i	1.64841	−	0.839907i	0.996677	−	0.0814592i	$-0.0259580\pi$
$48$		0			0
$49$		−	1.57112i		−	0.224446i
$50$		0			0
$51$			1.68351i			0.235739i
$52$		0			0
$53$	−7.81476	+	3.98182i	−1.07344	+	0.546945i	−0.899101	−	0.437741i	$-0.855779\pi$
$53$	−7.81476	+	3.98182i	−1.07344	+	0.546945i	−0.174338	+	0.984686i	$0.555779\pi$
$54$		0			0
$55$	5.92181	+	4.93542i	0.798497	+	0.665492i
$56$		0			0
$57$	1.89630	−	1.89630i	0.251172	−	0.251172i
$58$		0			0
$59$	1.55630	+	1.13072i	0.202613	+	0.147207i	0.684465	−	0.729046i	$-0.260036\pi$
$59$	1.55630	+	1.13072i	0.202613	+	0.147207i	−0.481852	+	0.876252i	$0.660036\pi$
$60$		0			0
$61$	5.52261	−	4.01241i	0.707098	−	0.513737i	−0.175138	−	0.984544i	$-0.556037\pi$
$61$	5.52261	−	4.01241i	0.707098	−	0.513737i	0.882236	+	0.470807i	$0.156037\pi$
$62$		0			0
$63$	−6.62741	+	1.04968i	−0.834975	+	0.132247i
$64$		0			0
$65$	1.87646	+	4.37999i	0.232747	+	0.543271i
$66$		0			0
$67$	2.31499	−	4.54342i	0.282821	−	0.555067i	−0.705270	−	0.708939i	$-0.749174\pi$
$67$	2.31499	−	4.54342i	0.282821	−	0.555067i	0.988091	+	0.153872i	$0.0491742\pi$
$68$		0			0
$69$	0.146953	−	0.0477479i	0.0176911	−	0.00574817i
$70$		0			0
$71$	−3.94277	−	1.28108i	−0.467921	−	0.152037i	0.0655604	−	0.997849i	$-0.479117\pi$
$71$	−3.94277	−	1.28108i	−0.467921	−	0.152037i	−0.533481	+	0.845812i	$0.679117\pi$
$72$		0			0
$73$	−5.07659	−	0.804053i	−0.594170	−	0.0941073i	−0.147895	−	0.989003i	$-0.547250\pi$
$73$	−5.07659	−	0.804053i	−0.594170	−	0.0941073i	−0.446275	+	0.894896i	$0.647250\pi$
$74$		0			0
$75$	1.42634	+	0.984617i	0.164699	+	0.113694i
$76$		0			0
$77$	−1.25658	+	7.93376i	−0.143201	+	0.904136i
$78$		0			0
$79$	1.36639	−	4.20533i	0.153731	−	0.473136i	−0.844299	−	0.535873i	$-0.819983\pi$
$79$	1.36639	−	4.20533i	0.153731	−	0.473136i	0.998030	+	0.0627363i	$0.0199827\pi$
$80$		0			0
$81$	−2.45144	−	7.54476i	−0.272382	−	0.838307i
$82$		0			0
$83$	11.6526	+	5.93732i	1.27904	+	0.651706i	0.955635	−	0.294554i	$-0.0951709\pi$
$83$	11.6526	+	5.93732i	1.27904	+	0.651706i	0.323409	+	0.946259i	$0.395171\pi$
$84$		0			0
$85$	−10.5897	−	2.40765i	−1.14862	−	0.261146i
$86$		0			0
$87$	0.0978494	+	0.617797i	0.0104906	+	0.0662348i
$88$		0			0
$89$	8.50790	+	11.7101i	0.901836	+	1.24127i	0.969879	+	0.243588i	$0.0783245\pi$
$89$	8.50790	+	11.7101i	0.901836	+	1.24127i	−0.0680431	+	0.997682i	$0.521676\pi$
$90$		0			0
$91$	−2.91846	+	4.01692i	−0.305938	+	0.421087i
$92$		0			0
$93$	−1.81660	−	1.81660i	−0.188373	−	0.188373i
$94$		0			0
$95$	9.21625	+	14.6402i	0.945568	+	1.50205i
$96$		0			0
$97$	4.61582	+	9.05905i	0.468665	+	0.919808i	0.997472	+	0.0710650i	$0.0226398\pi$
$97$	4.61582	+	9.05905i	0.468665	+	0.919808i	−0.528806	+	0.848743i	$0.677360\pi$
$98$		0			0
$99$	−9.92826			−0.997828
$100$		0			0
$101$	−4.46096			−0.443882			−0.221941	−	0.975060i	$-0.571239\pi$
$101$	−4.46096			−0.443882			−0.221941	+	0.975060i	$0.571239\pi$
$102$		0			0
$103$	6.65598	+	13.0631i	0.655834	+	1.28715i	0.944120	+	0.329602i	$0.106914\pi$
$103$	6.65598	+	13.0631i	0.655834	+	1.28715i	−0.288287	+	0.957544i	$0.593086\pi$
$104$		0			0
$105$	−0.119969	+	1.80199i	−0.0117078	+	0.175856i
$106$		0			0
$107$	7.43177	+	7.43177i	0.718456	+	0.718456i	0.968289	−	0.249833i	$-0.0803756\pi$
$107$	7.43177	+	7.43177i	0.718456	+	0.718456i	−0.249833	+	0.968289i	$0.580376\pi$
$108$		0			0
$109$	4.01366	−	5.52433i	0.384439	−	0.529135i	−0.572315	−	0.820034i	$-0.693954\pi$
$109$	4.01366	−	5.52433i	0.384439	−	0.529135i	0.956754	+	0.290899i	$0.0939544\pi$
$110$		0			0
$111$	−0.906988	−	1.24836i	−0.0860875	−	0.118489i
$112$		0			0
$113$	−1.73971	−	10.9841i	−0.163659	−	1.03330i	−0.923614	−	0.383324i	$-0.874779\pi$
$113$	−1.73971	−	10.9841i	−0.163659	−	1.03330i	0.759955	−	0.649975i	$-0.225221\pi$
$114$		0			0
$115$	0.0901836	+	0.992656i	0.00840966	+	0.0925656i
$116$		0			0
$117$	−5.46802	−	2.78609i	−0.505518	−	0.257575i
$118$		0			0
$119$	−3.49688	−	10.7623i	−0.320558	−	0.986577i
$120$		0			0
$121$	−0.273558	+	0.841925i	−0.0248689	+	0.0765386i
$122$		0			0
$123$	0.194726	−	1.22945i	0.0175579	−	0.110856i
$124$		0			0
$125$	−8.23334	+	7.56387i	−0.736412	+	0.676533i
$126$		0			0
$127$	0.214797	+	0.0340206i	0.0190602	+	0.00301884i	0.165957	−	0.986133i	$-0.446929\pi$
$127$	0.214797	+	0.0340206i	0.0190602	+	0.00301884i	−0.146897	+	0.989152i	$0.546929\pi$
$128$		0			0
$129$	−3.49987	−	1.13718i	−0.308146	−	0.100123i
$130$		0			0
$131$	−0.984606	+	0.319918i	−0.0860254	+	0.0279514i	−0.351714	−	0.936108i	$-0.614401\pi$
$131$	−0.984606	+	0.319918i	−0.0860254	+	0.0279514i	0.265688	+	0.964059i	$0.414401\pi$
$132$		0			0
$133$	−8.18374	+	16.0615i	−0.709620	+	1.39271i
$134$		0			0
$135$	−4.53878	+	0.412352i	−0.390636	+	0.0354896i
$136$		0			0
$137$	9.55851	−	1.51392i	0.816638	−	0.129343i	0.265878	−	0.964007i	$-0.414338\pi$
$137$	9.55851	−	1.51392i	0.816638	−	0.129343i	0.550760	+	0.834664i	$0.314338\pi$
$138$		0			0
$139$	13.1577	−	9.55965i	1.11602	−	0.810839i	0.132422	−	0.991193i	$-0.457724\pi$
$139$	13.1577	−	9.55965i	1.11602	−	0.810839i	0.983602	+	0.180354i	$0.0577245\pi$
$140$		0			0
$141$	3.55684	+	2.58419i	0.299540	+	0.217628i
$142$		0			0
$143$	−5.19481	+	5.19481i	−0.434412	+	0.434412i
$144$		0			0
$145$	−4.02603	−	0.268036i	−0.334344	−	0.0222592i
$146$		0			0
$147$	0.485249	−	0.247247i	0.0400226	−	0.0203926i
$148$		0			0
$149$		−	14.0114i		−	1.14786i	−0.818905	−	0.573929i	$-0.805418\pi$
$149$		−	14.0114i		−	1.14786i	0.818905	−	0.573929i	$-0.194582\pi$
$150$		0			0
$151$		−	2.40690i		−	0.195870i	−0.995193	−	0.0979352i	$-0.968776\pi$
$151$		−	2.40690i		−	0.195870i	0.995193	−	0.0979352i	$-0.0312238\pi$
$152$		0			0
$153$	12.4622	−	6.34978i	1.00751	−	0.513350i
$154$		0			0
$155$	14.0249	−	8.82889i	1.12650	−	0.709153i
$156$		0			0
$157$	4.45898	−	4.45898i	0.355865	−	0.355865i	−0.506421	−	0.862286i	$-0.669032\pi$
$157$	4.45898	−	4.45898i	0.355865	−	0.355865i	0.862286	+	0.506421i	$0.169032\pi$
$158$		0			0
$159$	−2.45961	−	1.78701i	−0.195059	−	0.141719i
$160$		0			0
$161$	−0.840255	+	0.610481i	−0.0662214	+	0.0481127i
$162$		0			0
$163$	−20.2451	+	3.20651i	−1.58572	+	0.251153i	−0.886145	−	0.463408i	$-0.846626\pi$
$163$	−20.2451	+	3.20651i	−1.58572	+	0.251153i	−0.699573	+	0.714561i	$0.746626\pi$
$164$		0			0
$165$	−0.592417	+	2.60566i	−0.0461196	+	0.202851i
$166$		0			0
$167$	2.33099	−	4.57483i	0.180378	−	0.354011i	−0.783059	−	0.621948i	$-0.786342\pi$
$167$	2.33099	−	4.57483i	0.180378	−	0.354011i	0.963437	+	0.267936i	$0.0863417\pi$
$168$		0			0
$169$	8.04490	−	2.61395i	0.618838	−	0.201073i
$170$		0			0
$171$	−21.1897	−	6.88496i	−1.62042	−	0.526506i
$172$		0			0
$173$	20.7780	+	3.29091i	1.57972	+	0.250204i	0.883783	−	0.467896i	$-0.154988\pi$
$173$	20.7780	+	3.29091i	1.57972	+	0.250204i	0.695940	+	0.718100i	$0.254988\pi$
$174$		0			0
$175$	−11.1634	−	3.33172i	−0.843874	−	0.251855i
$176$		0			0
$177$	−0.104314	+	0.658610i	−0.00784069	+	0.0495042i
$178$		0			0
$179$	−1.51271	+	4.65564i	−0.113065	+	0.347979i	−0.991539	−	0.129812i	$-0.958562\pi$
$179$	−1.51271	+	4.65564i	−0.113065	+	0.347979i	0.878473	+	0.477791i	$0.158562\pi$
$180$		0			0
$181$	1.18772	+	3.65542i	0.0882825	+	0.271705i	0.985445	−	0.169995i	$-0.0543753\pi$
$181$	1.18772	+	3.65542i	0.0882825	+	0.271705i	−0.897162	+	0.441701i	$0.854375\pi$
$182$		0			0
$183$	2.10834	+	1.07425i	0.155853	+	0.0794111i
$184$		0			0
$185$	9.14962	−	3.91985i	0.672694	−	0.288193i
$186$		0			0
$187$	−2.61927	−	16.5374i	−0.191540	−	1.20933i
$188$		0			0
$189$	−2.79134	−	3.84195i	−0.203040	−	0.279461i
$190$		0			0
$191$	4.10099	−	5.64453i	0.296737	−	0.408424i	−0.634451	−	0.772963i	$-0.718774\pi$
$191$	4.10099	−	5.64453i	0.296737	−	0.408424i	0.931188	+	0.364540i	$0.118774\pi$
$192$		0			0
$193$	−14.6474	−	14.6474i	−1.05435	−	1.05435i	−0.998436	−	0.0559101i	$-0.982194\pi$
$193$	−14.6474	−	14.6474i	−1.05435	−	1.05435i	−0.0559101	−	0.998436i	$-0.517806\pi$
$194$		0			0
$195$	−1.05748	+	1.26883i	−0.0757280	+	0.0908629i
$196$		0			0
$197$	−4.97346	−	9.76097i	−0.354345	−	0.695440i	0.643183	−	0.765712i	$-0.277613\pi$
$197$	−4.97346	−	9.76097i	−0.354345	−	0.695440i	−0.997528	+	0.0702719i	$0.977613\pi$
$198$		0			0
$199$	−9.42982			−0.668462			−0.334231	−	0.942491i	$-0.608477\pi$
$199$	−9.42982			−0.668462			−0.334231	+	0.942491i	$0.608477\pi$
$200$		0			0
$201$	1.76756			0.124674
$202$		0			0
$203$	−1.90877	−	3.74618i	−0.133970	−	0.262930i
$204$		0			0
$205$	7.45509	+	2.98316i	0.520686	+	0.208353i
$206$		0			0
$207$	−0.907722	−	0.907722i	−0.0630910	−	0.0630910i
$208$		0			0
$209$	−15.6774	+	21.5780i	−1.08443	+	1.49258i
$210$		0			0
$211$	1.89269	+	2.60506i	0.130298	+	0.179340i	0.869181	−	0.494494i	$-0.164647\pi$
$211$	1.89269	+	2.60506i	0.130298	+	0.179340i	−0.738883	+	0.673833i	$0.764647\pi$
$212$		0			0
$213$	−0.224802	−	1.41935i	−0.0154032	−	0.0972520i
$214$		0			0
$215$	12.1584	−	20.3887i	0.829197	−	1.39050i
$216$		0			0
$217$	15.3864	+	7.83977i	1.04450	+	0.532198i
$218$		0			0
$219$	−0.550564	−	1.69446i	−0.0372037	−	0.114501i
$220$		0			0
$221$	3.19820	−	9.84305i	0.215134	−	0.662115i
$222$		0			0
$223$	4.00808	−	25.3060i	0.268401	−	1.69462i	−0.373339	−	0.927695i	$-0.621787\pi$
$223$	4.00808	−	25.3060i	0.268401	−	1.69462i	0.641740	−	0.766922i	$-0.278213\pi$
$224$		0			0
$225$	1.90882	−	14.2721i	0.127254	−	0.951476i
$226$		0			0
$227$	8.49893	+	1.34610i	0.564094	+	0.0893437i	0.431968	−	0.901889i	$-0.357819\pi$
$227$	8.49893	+	1.34610i	0.564094	+	0.0893437i	0.132126	+	0.991233i	$0.457819\pi$
$228$		0			0
$229$	−0.143705	−	0.0466926i	−0.00949629	−	0.00308553i	0.304265	−	0.952587i	$-0.401589\pi$
$229$	−0.143705	−	0.0466926i	−0.00949629	−	0.00308553i	−0.313761	+	0.949502i	$0.601589\pi$
$230$		0			0
$231$	−2.64813	+	0.860428i	−0.174234	+	0.0566120i
$232$		0			0
$233$	−3.33372	+	6.54280i	−0.218399	+	0.428633i	−0.974047	−	0.226345i	$-0.927322\pi$
$233$	−3.33372	+	6.54280i	−0.218399	+	0.428633i	0.755648	+	0.654978i	$0.227322\pi$
$234$		0			0
$235$	−21.3420	+	18.6776i	−1.39220	+	1.21840i
$236$		0			0
$237$	1.51386	−	0.239772i	0.0983360	−	0.0155749i
$238$		0			0
$239$	0.364756	−	0.265011i	0.0235941	−	0.0171421i	−0.575926	−	0.817502i	$-0.695358\pi$
$239$	0.364756	−	0.265011i	0.0235941	−	0.0171421i	0.599520	+	0.800360i	$0.295358\pi$
$240$		0			0
$241$	−18.8526	−	13.6972i	−1.21440	−	0.882314i	−0.218778	−	0.975775i	$-0.570207\pi$
$241$	−18.8526	−	13.6972i	−1.21440	−	0.882314i	−0.995623	+	0.0934604i	$0.970207\pi$
$242$		0			0
$243$	6.26805	−	6.26805i	0.402096	−	0.402096i
$244$		0			0
$245$	0.861271	+	3.40593i	0.0550246	+	0.217597i
$246$		0			0
$247$	−14.6896	+	7.48474i	−0.934679	+	0.476243i
$248$		0			0
$249$			4.53333i			0.287288i
$250$		0			0
$251$		−	0.706581i		−	0.0445990i	−0.999751	−	0.0222995i	$-0.992901\pi$
$251$		−	0.706581i		−	0.0445990i	0.999751	−	0.0222995i	$-0.00709874\pi$
$252$		0			0
$253$	−1.36925	+	0.697669i	−0.0860842	+	0.0438621i
$254$		0			0
$255$	−0.922881	−	3.64957i	−0.0577931	−	0.228545i
$256$		0			0
$257$	−21.2988	+	21.2988i	−1.32858	+	1.32858i	−0.421976	+	0.906607i	$0.638663\pi$
$257$	−21.2988	+	21.2988i	−1.32858	+	1.32858i	−0.906607	+	0.421976i	$0.861337\pi$
$258$		0			0
$259$	8.39117	+	6.09654i	0.521402	+	0.378821i
$260$		0			0
$261$	4.20416	−	3.05450i	0.260231	−	0.189069i
$262$		0			0
$263$	−8.92677	+	1.41386i	−0.550448	+	0.0871825i	−0.425463	−	0.904976i	$-0.639889\pi$
$263$	−8.92677	+	1.41386i	−0.550448	+	0.0871825i	−0.124986	+	0.992159i	$0.539889\pi$
$264$		0			0
$265$	14.7583	−	12.9159i	0.906594	−	0.793415i
$266$		0			0
$267$	−2.27784	+	4.47052i	−0.139402	+	0.273591i
$268$		0			0
$269$	26.6700	−	8.66562i	1.62610	−	0.528352i	0.652730	−	0.757591i	$-0.273624\pi$
$269$	26.6700	−	8.66562i	1.62610	−	0.528352i	0.973370	+	0.229239i	$0.0736236\pi$
$270$		0			0
$271$	21.3414	+	6.93424i	1.29640	+	0.421225i	0.874327	−	0.485338i	$-0.161303\pi$
$271$	21.3414	+	6.93424i	1.29640	+	0.421225i	0.422071	+	0.906563i	$0.361303\pi$
$272$		0			0
$273$	−1.69992	−	0.269241i	−0.102884	−	0.0162952i
$274$		0			0
$275$	−15.5430	−	7.45290i	−0.937280	−	0.449427i
$276$		0			0
$277$	3.22339	−	20.3517i	0.193675	−	1.22282i	−0.678861	−	0.734266i	$-0.737526\pi$
$277$	3.22339	−	20.3517i	0.193675	−	1.22282i	0.872536	−	0.488549i	$-0.162474\pi$
$278$		0			0
$279$	−6.59558	+	20.2991i	−0.394867	+	1.21528i
$280$		0			0
$281$	4.63282	+	14.2584i	0.276371	+	0.850582i	0.988853	+	0.148892i	$0.0475708\pi$
$281$	4.63282	+	14.2584i	0.276371	+	0.850582i	−0.712482	+	0.701690i	$0.752429\pi$
$282$		0			0
$283$	18.9658	+	9.66354i	1.12740	+	0.574438i	0.915285	−	0.402807i	$-0.131966\pi$
$283$	18.9658	+	9.66354i	1.12740	+	0.574438i	0.212113	+	0.977245i	$0.431966\pi$
$284$		0			0
$285$	−3.07134	+	5.15040i	−0.181930	+	0.305083i
$286$		0			0
$287$	1.30890	+	8.26408i	0.0772620	+	0.487813i
$288$		0			0
$289$	3.87218	+	5.32960i	0.227775	+	0.313506i
$290$		0			0
$291$	−2.07154	+	2.85123i	−0.121436	+	0.167142i
$292$		0			0
$293$	11.8669	+	11.8669i	0.693275	+	0.693275i	0.962951	−	0.269676i	$-0.0869167\pi$
$293$	11.8669	+	11.8669i	0.693275	+	0.693275i	−0.269676	+	0.962951i	$0.586917\pi$
$294$		0			0
$295$	−3.99364	−	1.59806i	−0.232519	−	0.0930426i
$296$		0			0
$297$	−3.18999	−	6.26072i	−0.185102	−	0.363284i
$298$		0			0
$299$	−0.949902			−0.0549343
$300$		0			0
$301$	24.7359			1.42575
$302$		0			0
$303$	−0.702018	−	1.37779i	−0.0403299	−	0.0791519i
$304$		0			0
$305$	−9.77254	+	11.7257i	−0.559574	+	0.671410i
$306$		0			0
$307$	−14.3081	−	14.3081i	−0.816604	−	0.816604i	0.169010	−	0.985614i	$-0.445943\pi$
$307$	−14.3081	−	14.3081i	−0.816604	−	0.816604i	−0.985614	+	0.169010i	$0.945943\pi$
$308$		0			0
$309$	−2.98715	+	4.11146i	−0.169933	+	0.233893i
$310$		0			0
$311$	6.82825	+	9.39828i	0.387195	+	0.532928i	0.957473	−	0.288524i	$-0.0931646\pi$
$311$	6.82825	+	9.39828i	0.387195	+	0.532928i	−0.570278	+	0.821452i	$0.693165\pi$
$312$		0			0
$313$	−1.29209	−	8.15793i	−0.0730332	−	0.461113i	−0.996919	−	0.0784440i	$-0.975005\pi$
$313$	−1.29209	−	8.15793i	−0.0730332	−	0.461113i	0.923885	−	0.382669i	$-0.124995\pi$
$314$		0			0
$315$	13.7917	−	5.90859i	0.777073	−	0.332911i
$316$		0			0
$317$	−21.4391	−	10.9238i	−1.20414	−	0.613539i	−0.267405	−	0.963584i	$-0.586166\pi$
$317$	−21.4391	−	10.9238i	−1.20414	−	0.613539i	−0.936733	+	0.350045i	$0.886166\pi$
$318$		0			0
$319$	−1.92238	−	5.91647i	−0.107633	−	0.331259i
$320$		0			0
$321$	−1.12580	+	3.46487i	−0.0628363	+	0.193390i
$322$		0			0
$323$	5.87795	−	37.1119i	0.327058	−	2.06496i
$324$		0			0
$325$	−6.46892	−	8.46643i	−0.358831	−	0.469633i
$326$		0			0
$327$	2.33784	+	0.370278i	0.129283	+	0.0204764i
$328$		0			0
$329$	−28.1057	−	9.13210i	−1.54952	−	0.503469i
$330$		0			0
$331$	30.5187	−	9.91612i	1.67746	−	0.545039i	0.693042	−	0.720897i	$-0.256270\pi$
$331$	30.5187	−	9.91612i	1.67746	−	0.545039i	0.984416	+	0.175858i	$0.0562699\pi$
$332$		0			0
$333$	−5.82003	+	11.4225i	−0.318936	+	0.625947i
$334$		0			0
$335$	−2.52786	+	11.1184i	−0.138111	+	0.607464i
$336$		0			0
$337$	−2.70357	+	0.428204i	−0.147273	+	0.0233258i	−0.229636	−	0.973277i	$-0.573753\pi$
$337$	−2.70357	+	0.428204i	−0.147273	+	0.0233258i	0.0823626	+	0.996602i	$0.473753\pi$
$338$		0			0
$339$	3.11872	−	2.26588i	0.169386	−	0.123066i
$340$		0			0
$341$	20.6711	+	15.0184i	1.11940	+	0.813293i
$342$		0			0
$343$	−14.1214	+	14.1214i	−0.762484	+	0.762484i
$344$		0			0
$345$	−0.292394	+	0.184067i	−0.0157420	+	0.00990984i
$346$		0			0
$347$	−26.0565	+	13.2765i	−1.39879	+	0.712717i	−0.980669	−	0.195676i	$-0.937310\pi$
$347$	−26.0565	+	13.2765i	−1.39879	+	0.712717i	−0.418118	+	0.908393i	$0.637310\pi$
$348$		0			0
$349$			0.179332i			0.00959943i	0.999988	+	0.00479972i	$0.00152780\pi$
$349$			0.179332i			0.00959943i	−0.999988	+	0.00479972i	$0.998472\pi$
$350$		0			0
$351$		−	4.34329i		−	0.231828i
$352$		0			0
$353$	−11.7476	+	5.98569i	−0.625261	+	0.318586i	−0.737757	−	0.675066i	$-0.764115\pi$
$353$	−11.7476	+	5.98569i	−0.625261	+	0.318586i	0.112497	+	0.993652i	$0.464115\pi$
$354$		0			0
$355$	9.24953	+	0.615794i	0.490914	+	0.0326830i
$356$		0			0
$357$	2.77368	−	2.77368i	0.146799	−	0.146799i
$358$		0			0
$359$	29.3002	+	21.2879i	1.54641	+	1.12353i	0.946152	+	0.323722i	$0.104934\pi$
$359$	29.3002	+	21.2879i	1.54641	+	1.12353i	0.600255	+	0.799808i	$0.295066\pi$
$360$		0			0
$361$	−33.0523	+	24.0139i	−1.73960	+	1.26389i
$362$		0			0
$363$	−0.303082	+	0.0480035i	−0.0159077	+	0.00251953i
$364$		0			0
$365$	11.4460	−	1.03987i	0.599109	−	0.0544295i
$366$		0			0
$367$	−5.12861	+	10.0655i	−0.267711	+	0.525413i	−0.985253	−	0.171102i	$-0.945267\pi$
$367$	−5.12861	+	10.0655i	−0.267711	+	0.525413i	0.717542	+	0.696515i	$0.245267\pi$
$368$		0			0
$369$	−9.83546	+	3.19573i	−0.512014	+	0.166363i
$370$		0			0
$371$	19.4355	+	6.31498i	1.00904	+	0.327857i
$372$		0			0
$373$	24.4903	+	3.87888i	1.26806	+	0.200841i	0.753978	−	0.656900i	$-0.228133\pi$
$373$	24.4903	+	3.87888i	1.26806	+	0.200841i	0.514082	+	0.857741i	$0.328133\pi$
$374$		0			0
$375$	−3.63181	−	1.35258i	−0.187546	−	0.0698470i
$376$		0			0
$377$	0.601541	−	3.79798i	0.0309809	−	0.195606i
$378$		0			0
$379$	−8.56061	+	26.3468i	−0.439729	+	1.35335i	0.448434	+	0.893816i	$0.351982\pi$
$379$	−8.56061	+	26.3468i	−0.439729	+	1.35335i	−0.888162	+	0.459530i	$0.848018\pi$
$380$		0			0
$381$	0.0232951	+	0.0716950i	0.00119344	+	0.00367305i
$382$		0			0
$383$	27.3241	+	13.9223i	1.39620	+	0.711398i	0.980208	−	0.197972i	$-0.0634354\pi$
$383$	27.3241	+	13.9223i	1.39620	+	0.711398i	0.415989	+	0.909370i	$0.363435\pi$
$384$		0			0
$385$	−1.62513	−	17.8879i	−0.0828243	−	0.911652i
$386$		0			0
$387$	4.78271	+	30.1968i	0.243119	+	1.53499i
$388$		0			0
$389$	−15.1152	−	20.8043i	−0.766372	−	1.05482i	−0.996657	−	0.0816976i	$-0.973966\pi$
$389$	−15.1152	−	20.8043i	−0.766372	−	1.05482i	0.230285	−	0.973123i	$-0.426034\pi$
$390$		0			0
$391$	1.27251	−	1.75146i	0.0643535	−	0.0885750i
$392$		0			0
$393$	−0.253755	−	0.253755i	−0.0128002	−	0.0128002i
$394$		0			0
$395$	−0.656801	+	9.86548i	−0.0330472	+	0.496386i
$396$		0			0
$397$	1.03621	+	2.03367i	0.0520057	+	0.102067i	0.915547	−	0.402212i	$-0.131758\pi$
$397$	1.03621	+	2.03367i	0.0520057	+	0.102067i	−0.863541	+	0.504279i	$0.831758\pi$
$398$		0			0
$399$	−6.24853			−0.312818
$400$		0			0
$401$	−31.5582			−1.57594			−0.787971	−	0.615712i	$-0.788868\pi$
$401$	−31.5582			−1.57594			−0.787971	+	0.615712i	$0.788868\pi$
$402$		0			0
$403$	7.17015	+	14.0722i	0.357171	+	0.700987i
$404$		0			0
$405$	9.45026	+	15.0119i	0.469587	+	0.745948i
$406$		0			0
$407$	10.8517	+	10.8517i	0.537900	+	0.537900i
$408$		0			0
$409$	−15.6500	+	21.5404i	−0.773842	+	1.06510i	0.222093	+	0.975025i	$0.428711\pi$
$409$	−15.6500	+	21.5404i	−0.773842	+	1.06510i	−0.995935	+	0.0900763i	$0.971289\pi$
$410$		0			0
$411$	1.97180	+	2.71394i	0.0972615	+	0.133869i
$412$		0			0
$413$	−0.701169	−	4.42701i	−0.0345023	−	0.217839i
$414$		0			0
$415$	−28.5157	−	6.48327i	−1.39978	−	0.318251i
$416$		0			0
$417$	5.02316	+	2.55943i	0.245985	+	0.125336i
$418$		0			0
$419$	4.74322	+	14.5981i	0.231721	+	0.713165i	0.997539	+	0.0701078i	$0.0223343\pi$
$419$	4.74322	+	14.5981i	0.231721	+	0.713165i	−0.765818	+	0.643057i	$0.777666\pi$
$420$		0			0
$421$	−12.1430	+	37.3723i	−0.591813	+	1.82141i	−0.0218215	+	0.999762i	$0.506947\pi$
$421$	−12.1430	+	37.3723i	−0.591813	+	1.82141i	−0.569991	+	0.821651i	$0.693053\pi$
$422$		0			0
$423$	5.71393	−	36.0763i	0.277821	−	1.75409i
$424$		0			0
$425$	24.2765	−	0.585772i	1.17759	−	0.0284141i
$426$		0			0
$427$	−15.7095	−	2.48814i	−0.760235	−	0.120409i
$428$		0			0
$429$	−2.42194	−	0.786937i	−0.116932	−	0.0379937i
$430$		0			0
$431$	−10.5501	+	3.42794i	−0.508181	+	0.165118i	−0.551875	−	0.833927i	$-0.686087\pi$
$431$	−10.5501	+	3.42794i	−0.508181	+	0.165118i	0.0436939	+	0.999045i	$0.486087\pi$
$432$		0			0
$433$	3.37802	−	6.62974i	0.162337	−	0.318605i	−0.795481	−	0.605978i	$-0.792782\pi$
$433$	3.37802	−	6.62974i	0.162337	−	0.318605i	0.957819	+	0.287373i	$0.0927819\pi$
$434$		0			0
$435$	−0.550789	−	1.28564i	−0.0264083	−	0.0616417i
$436$		0			0
$437$	−3.40619	+	0.539487i	−0.162940	+	0.0258072i
$438$		0			0
$439$	29.3086	−	21.2940i	1.39882	−	1.01630i	0.403992	−	0.914762i	$-0.367622\pi$
$439$	29.3086	−	21.2940i	1.39882	−	1.01630i	0.994831	−	0.101543i	$-0.0323778\pi$
$440$		0			0
$441$	−3.66047	−	2.65949i	−0.174308	−	0.126642i
$442$		0			0
$443$	10.2479	−	10.2479i	0.486890	−	0.486890i	−0.420433	−	0.907324i	$-0.638122\pi$
$443$	10.2479	−	10.2479i	0.486890	−	0.486890i	0.907324	+	0.420433i	$0.138122\pi$
$444$		0			0
$445$	−24.8630	−	20.7216i	−1.17862	−	0.982300i
$446$		0			0
$447$	4.32748	−	2.20496i	0.204683	−	0.104291i
$448$		0			0
$449$			7.21911i			0.340691i	0.985384	+	0.170346i	$0.0544884\pi$
$449$			7.21911i			0.340691i	−0.985384	+	0.170346i	$0.945512\pi$
$450$		0			0
$451$			12.3801i			0.582955i
$452$		0			0
$453$	0.743381	−	0.378771i	0.0349271	−	0.0177962i
$454$		0			0
$455$	4.12470	−	10.3079i	0.193369	−	0.483240i
$456$		0			0
$457$	14.9794	−	14.9794i	0.700705	−	0.700705i	−0.263857	−	0.964562i	$-0.584995\pi$
$457$	14.9794	−	14.9794i	0.700705	−	0.700705i	0.964562	+	0.263857i	$0.0849946\pi$
$458$		0			0
$459$	8.00829	+	5.81836i	0.373795	+	0.271578i
$460$		0			0
$461$	31.3671	−	22.7895i	1.46091	−	1.06141i	0.477788	−	0.878475i	$-0.341439\pi$
$461$	31.3671	−	22.7895i	1.46091	−	1.06141i	0.983124	−	0.182940i	$-0.0585613\pi$
$462$		0			0
$463$	−2.56485	+	0.406232i	−0.119199	+	0.0188792i	−0.215749	−	0.976449i	$-0.569219\pi$
$463$	−2.56485	+	0.406232i	−0.119199	+	0.0188792i	0.0965501	+	0.995328i	$0.469219\pi$
$464$		0			0
$465$	4.93392	+	2.94225i	0.228805	+	0.136443i
$466$		0			0
$467$	−1.72887	+	3.39310i	−0.0800027	+	0.157014i	−0.927542	−	0.373718i	$-0.878083\pi$
$467$	−1.72887	+	3.39310i	−0.0800027	+	0.157014i	0.847540	+	0.530732i	$0.178083\pi$
$468$		0			0
$469$	−11.2996	+	3.67147i	−0.521767	+	0.169533i
$470$		0			0
$471$	2.07888	+	0.675470i	0.0957899	+	0.0311240i
$472$		0			0
$473$	36.1490	+	5.72544i	1.66213	+	0.263256i
$474$		0			0
$475$	−28.0049	−	26.6852i	−1.28495	−	1.22440i
$476$		0			0
$477$	−3.95126	+	24.9473i	−0.180916	+	1.14226i
$478$		0			0
$479$	−10.0595	+	30.9600i	−0.459631	+	1.41460i	0.405980	+	0.913882i	$0.366930\pi$
$479$	−10.0595	+	30.9600i	−0.459631	+	1.41460i	−0.865611	+	0.500717i	$0.833070\pi$
$480$		0			0
$481$	2.93138	+	9.02187i	0.133660	+	0.411362i
$482$		0			0
$483$	−0.320780	−	0.163446i	−0.0145960	−	0.00743704i
$484$		0			0
$485$	−14.9724	−	17.1082i	−0.679861	−	0.776841i
$486$		0			0
$487$	−1.74050	−	10.9891i	−0.0788696	−	0.497963i	−0.995226	−	0.0975990i	$-0.968884\pi$
$487$	−1.74050	−	10.9891i	−0.0788696	−	0.497963i	0.916356	−	0.400364i	$-0.131116\pi$
$488$		0			0
$489$	−4.17630	−	5.74818i	−0.188859	−	0.259942i
$490$		0			0
$491$	3.77311	−	5.19325i	0.170278	−	0.234368i	−0.715346	−	0.698770i	$-0.753731\pi$
$491$	3.77311	−	5.19325i	0.170278	−	0.234368i	0.885624	+	0.464403i	$0.153731\pi$
$492$		0			0
$493$	6.19699	+	6.19699i	0.279098	+	0.279098i
$494$		0			0
$495$	21.5228	−	5.44255i	0.967377	−	0.244624i
$496$		0			0
$497$	4.38528	+	8.60659i	0.196707	+	0.386058i
$498$		0			0
$499$	−12.3156			−0.551320			−0.275660	−	0.961255i	$-0.588896\pi$
$499$	−12.3156			−0.551320			−0.275660	+	0.961255i	$0.588896\pi$
$500$		0			0
$501$	1.77979			0.0795149
$502$		0			0
$503$	−14.8450	−	29.1349i	−0.661904	−	1.29906i	−0.940873	−	0.338759i	$-0.889993\pi$
$503$	−14.8450	−	29.1349i	−0.661904	−	1.29906i	0.278969	−	0.960300i	$-0.410007\pi$
$504$		0			0
$505$	9.67061	−	2.44544i	0.430336	−	0.108821i
$506$		0			0
$507$	2.07335	+	2.07335i	0.0920807	+	0.0920807i
$508$		0			0
$509$	10.5438	−	14.5123i	0.467345	−	0.643245i	−0.508667	−	0.860963i	$-0.669862\pi$
$509$	10.5438	−	14.5123i	0.467345	−	0.643245i	0.976012	+	0.217719i	$0.0698615\pi$
$510$		0			0
$511$	7.03924	+	9.68869i	0.311398	+	0.428602i
$512$		0			0
$513$	−2.46673	−	15.5743i	−0.108909	−	0.687623i
$514$		0			0
$515$	−21.5901	−	24.6699i	−0.951373	−	1.08708i
$516$		0			0
$517$	−38.9600	−	19.8511i	−1.71346	−	0.873050i
$518$		0			0
$519$	2.25341	+	6.93527i	0.0989136	+	0.304425i
$520$		0			0
$521$	2.98991	−	9.20201i	0.130991	−	0.403147i	−0.863954	−	0.503570i	$-0.832020\pi$
$521$	2.98991	−	9.20201i	0.130991	−	0.403147i	0.994945	+	0.100423i	$0.0320195\pi$
$522$		0			0
$523$	2.24651	−	14.1839i	0.0982331	−	0.620219i	−0.888626	−	0.458633i	$-0.848339\pi$
$523$	2.24651	−	14.1839i	0.0982331	−	0.620219i	0.986859	−	0.161586i	$-0.0516609\pi$
$524$		0			0
$525$	−0.727758	−	3.97218i	−0.0317620	−	0.173360i
$526$		0			0
$527$	−35.5521	−	5.63089i	−1.54867	−	0.245286i
$528$		0			0
$529$	21.6853	+	7.04599i	0.942840	+	0.306347i
$530$		0			0
$531$	5.26879	−	1.71193i	0.228646	−	0.0742915i
$532$		0			0
$533$	−3.47413	+	6.81837i	−0.150481	+	0.295336i
$534$		0			0
$535$	−20.1848	−	12.0368i	−0.872666	−	0.520397i
$536$		0			0
$537$	−1.67597	+	0.265447i	−0.0723234	+	0.0114549i
$538$		0			0
$539$	−4.38200	+	3.18371i	−0.188746	+	0.137132i
$540$		0			0
$541$	13.2387	+	9.61846i	0.569175	+	0.413530i	0.834805	−	0.550545i	$-0.185580\pi$
$541$	13.2387	+	9.61846i	0.569175	+	0.413530i	−0.265630	+	0.964075i	$0.585580\pi$
$542$		0			0
$543$	−0.942084	+	0.942084i	−0.0404287	+	0.0404287i
$544$		0			0
$545$	−5.67257	+	14.1761i	−0.242986	+	0.607235i
$546$		0			0
$547$	16.9259	−	8.62417i	0.723698	−	0.368743i	−0.0530177	−	0.998594i	$-0.516884\pi$
$547$	16.9259	−	8.62417i	0.723698	−	0.368743i	0.776716	+	0.629851i	$0.216884\pi$
$548$		0			0
$549$		−	19.6588i		−	0.839015i
$550$		0			0
$551$		−	13.9605i		−	0.594739i
$552$		0			0
$553$	−9.17972	+	4.67730i	−0.390361	+	0.198899i
$554$		0			0
$555$	2.65053	+	2.20904i	0.112509	+	0.0937684i
$556$		0			0
$557$	15.0408	−	15.0408i	0.637298	−	0.637298i	−0.312590	−	0.949888i	$-0.601197\pi$
$557$	15.0408	−	15.0408i	0.637298	−	0.637298i	0.949888	+	0.312590i	$0.101197\pi$
$558$		0			0
$559$	18.3025	+	13.2975i	0.774113	+	0.562426i
$560$		0			0
$561$	4.69546	−	3.41145i	0.198243	−	0.144032i
$562$		0			0
$563$	−34.3919	+	5.44714i	−1.44944	+	0.229569i	−0.831006	−	0.556264i	$-0.812234\pi$
$563$	−34.3919	+	5.44714i	−1.44944	+	0.229569i	−0.618439	+	0.785833i	$0.712234\pi$
$564$		0			0
$565$	9.79277	+	22.8580i	0.411985	+	0.961645i
$566$		0			0
$567$	−8.39153	+	16.4693i	−0.352411	+	0.691645i
$568$		0			0
$569$	−20.8584	+	6.77731i	−0.874431	+	0.284120i	−0.711643	−	0.702541i	$-0.752049\pi$
$569$	−20.8584	+	6.77731i	−0.874431	+	0.284120i	−0.162788	+	0.986661i	$0.552049\pi$
$570$		0			0
$571$	26.8000	+	8.70783i	1.12154	+	0.364411i	0.810356	−	0.585937i	$-0.199274\pi$
$571$	26.8000	+	8.70783i	1.12154	+	0.364411i	0.311187	+	0.950349i	$0.399274\pi$
$572$		0			0
$573$	2.38871	+	0.378334i	0.0997897	+	0.0158051i
$574$		0			0
$575$	−0.739665	−	2.10247i	−0.0308461	−	0.0876792i
$576$		0			0
$577$	3.99154	−	25.2016i	0.166170	−	1.04916i	−0.753782	−	0.657125i	$-0.771772\pi$
$577$	3.99154	−	25.2016i	0.166170	−	1.04916i	0.919952	−	0.392031i	$-0.128228\pi$
$578$		0			0
$579$	2.21887	−	6.82899i	0.0922132	−	0.283803i
$580$		0			0
$581$	−9.41632	−	28.9804i	−0.390655	−	1.20231i
$582$		0			0
$583$	26.9414	+	13.7273i	1.11580	+	0.568527i
$584$		0			0
$585$	13.3810	+	3.04228i	0.553238	+	0.125783i
$586$		0			0
$587$	0.0923130	+	0.582841i	0.00381016	+	0.0240564i	0.989520	−	0.144395i	$-0.0461235\pi$
$587$	0.0923130	+	0.582841i	0.00381016	+	0.0240564i	−0.985710	+	0.168451i	$0.946123\pi$
$588$		0			0
$589$	33.7031	+	46.3884i	1.38871	+	1.91140i
$590$		0			0
$591$	2.23205	−	3.07215i	0.0918143	−	0.126372i
$592$		0			0
$593$	−9.59028	−	9.59028i	−0.393826	−	0.393826i	0.482223	−	0.876049i	$-0.339830\pi$
$593$	−9.59028	−	9.59028i	−0.393826	−	0.393826i	−0.876049	+	0.482223i	$0.839830\pi$
$594$		0			0
$595$	13.4804	+	21.4139i	0.552642	+	0.877883i
$596$		0			0
$597$	−1.48396	−	2.91244i	−0.0607346	−	0.119198i
$598$		0			0
$599$	−41.1920			−1.68306			−0.841530	−	0.540210i	$-0.818345\pi$
$599$	−41.1920			−1.68306			−0.841530	+	0.540210i	$0.818345\pi$
$600$		0			0
$601$	0.602932			0.0245941			0.0122971	−	0.999924i	$-0.496086\pi$
$601$	0.602932			0.0245941			0.0122971	+	0.999924i	$0.496086\pi$
$602$		0			0
$603$	−6.66681	−	13.0843i	−0.271493	−	0.532836i
$604$		0			0
$605$	0.131494	−	1.97511i	0.00534601	−	0.0802997i
$606$		0			0
$607$	−20.4672	−	20.4672i	−0.830737	−	0.830737i	0.156880	−	0.987618i	$-0.449856\pi$
$607$	−20.4672	−	20.4672i	−0.830737	−	0.830737i	−0.987618	+	0.156880i	$0.949856\pi$
$608$		0			0
$609$	0.856642	−	1.17907i	0.0347129	−	0.0477782i
$610$		0			0
$611$	−15.8866	−	21.8661i	−0.642705	−	0.884607i
$612$		0			0
$613$	−0.106197	−	0.670499i	−0.00428924	−	0.0270812i	0.985451	−	0.169960i	$-0.0543640\pi$
$613$	−0.106197	−	0.670499i	−0.00428924	−	0.0270812i	−0.989740	+	0.142879i	$0.954364\pi$
$614$		0			0
$615$	0.251838	+	2.77200i	0.0101551	+	0.111778i
$616$		0			0
$617$	19.3389	+	9.85364i	0.778553	+	0.396693i	0.797647	−	0.603125i	$-0.206078\pi$
$617$	19.3389	+	9.85364i	0.778553	+	0.396693i	−0.0190934	+	0.999818i	$0.506078\pi$
$618$		0			0
$619$	−8.71819	−	26.8318i	−0.350414	−	1.07846i	−0.958621	−	0.284684i	$-0.908111\pi$
$619$	−8.71819	−	26.8318i	−0.350414	−	1.07846i	0.608208	−	0.793778i	$-0.291889\pi$
$620$		0			0
$621$	0.280750	−	0.864060i	0.0112661	−	0.0346735i
$622$		0			0
$623$	5.27583	−	33.3103i	0.211372	−	1.33455i
$624$		0			0
$625$	13.7021	−	20.9106i	0.548082	−	0.836425i
$626$		0			0
$627$	−9.13161	−	1.44630i	−0.364681	−	0.0577598i
$628$		0			0
$629$	−20.5617	−	6.68091i	−0.819849	−	0.266385i
$630$		0			0
$631$	28.0203	−	9.10433i	1.11547	−	0.362438i	0.307432	−	0.951570i	$-0.400530\pi$
$631$	28.0203	−	9.10433i	1.11547	−	0.362438i	0.808037	+	0.589132i	$0.200530\pi$
$632$		0			0
$633$	−0.506734	+	0.994522i	−0.0201409	+	0.0395287i
$634$		0			0
$635$	−0.484294	+	0.0439985i	−0.0192186	+	0.00174603i
$636$		0			0
$637$	−3.30682	+	0.523749i	−0.131021	+	0.0207517i
$638$		0			0
$639$	−9.65877	+	7.01751i	−0.382095	+	0.277608i
$640$		0			0
$641$	11.4507	+	8.31940i	0.452275	+	0.328597i	0.790493	−	0.612471i	$-0.209824\pi$
$641$	11.4507	+	8.31940i	0.452275	+	0.328597i	−0.338219	+	0.941068i	$0.609824\pi$
$642$		0			0
$643$	−14.9187	+	14.9187i	−0.588334	+	0.588334i	−0.937180	−	0.348846i	$-0.886574\pi$
$643$	−14.9187	+	14.9187i	−0.588334	+	0.588334i	0.348846	+	0.937180i	$0.386574\pi$
$644$		0			0
$645$	8.21051	+	0.546621i	0.323289	+	0.0215232i
$646$		0			0
$647$	−5.51212	+	2.80856i	−0.216704	+	0.110416i	−0.558973	−	0.829186i	$-0.688804\pi$
$647$	−5.51212	+	2.80856i	−0.216704	+	0.110416i	0.342269	+	0.939602i	$0.388804\pi$
$648$		0			0
$649$		−	6.63192i		−	0.260326i
$650$		0			0
$651$			5.98590i			0.234606i
$652$		0			0
$653$	9.79281	−	4.98969i	0.383222	−	0.195262i	−0.251757	−	0.967790i	$-0.581008\pi$
$653$	9.79281	−	4.98969i	0.383222	−	0.195262i	0.634980	+	0.772529i	$0.281008\pi$
$654$		0			0
$655$	1.95908	−	1.23328i	0.0765477	−	0.0481881i
$656$		0			0
$657$	−10.4666	+	10.4666i	−0.408342	+	0.408342i
$658$		0			0
$659$	−5.68138	−	4.12777i	−0.221315	−	0.160795i	0.471603	−	0.881811i	$-0.343675\pi$
$659$	−5.68138	−	4.12777i	−0.221315	−	0.160795i	−0.692919	+	0.721016i	$0.743675\pi$
$660$		0			0
$661$	−19.6925	+	14.3074i	−0.765948	+	0.556494i	−0.900729	−	0.434382i	$-0.856967\pi$
$661$	−19.6925	+	14.3074i	−0.765948	+	0.556494i	0.134781	+	0.990875i	$0.456967\pi$
$662$		0			0
$663$	3.54337	−	0.561215i	0.137613	−	0.0217958i
$664$		0			0
$665$	8.93624	−	39.3048i	0.346533	−	1.52418i
$666$		0			0
$667$	0.365172	−	0.716691i	0.0141395	−	0.0277504i
$668$		0			0
$669$	8.44663	−	2.74448i	0.326566	−	0.106108i
$670$		0			0
$671$	−22.3819	−	7.27233i	−0.864045	−	0.280745i
$672$		0			0
$673$	−1.95264	−	0.309268i	−0.0752688	−	0.0119214i	0.118686	−	0.992932i	$-0.462132\pi$
$673$	−1.95264	−	0.309268i	−0.0752688	−	0.0119214i	−0.193955	+	0.981010i	$0.562132\pi$
$674$		0			0
$675$	9.61326	−	3.38201i	0.370014	−	0.130174i
$676$		0			0
$677$	1.67655	−	10.5853i	0.0644350	−	0.406827i	−0.934298	−	0.356494i	$-0.883972\pi$
$677$	1.67655	−	10.5853i	0.0644350	−	0.406827i	0.998733	−	0.0503323i	$-0.0160280\pi$
$678$		0			0
$679$	7.32048	−	22.5301i	0.280934	−	0.864626i
$680$		0			0
$681$	0.921722	+	2.83677i	0.0353205	+	0.108705i
$682$		0			0
$683$	3.90373	+	1.98905i	0.149372	+	0.0761089i	0.527079	−	0.849816i	$-0.323287\pi$
$683$	3.90373	+	1.98905i	0.149372	+	0.0761089i	−0.377707	+	0.925925i	$0.623287\pi$
$684$		0			0
$685$	−19.8913	+	8.52178i	−0.760008	+	0.325600i
$686$		0			0
$687$	−0.00819353	−	0.0517319i	−0.000312603	−	0.00197370i
$688$		0			0
$689$	10.9858	+	15.1207i	0.418527	+	0.576054i
$690$		0			0
$691$	19.7436	−	27.1747i	0.751081	−	1.03377i	−0.246823	−	0.969061i	$-0.579387\pi$
$691$	19.7436	−	27.1747i	0.751081	−	1.03377i	0.997904	−	0.0647135i	$-0.0206134\pi$
$692$		0			0
$693$	16.3574	+	16.3574i	0.621365	+	0.621365i
$694$		0			0
$695$	−23.2832	+	27.9366i	−0.883184	+	1.05970i
$696$		0			0
$697$	−7.91789	−	15.5397i	−0.299911	−	0.588609i
$698$		0			0
$699$	−2.54540			−0.0962758
$700$		0			0
$701$	−12.5378			−0.473548			−0.236774	−	0.971565i	$-0.576090\pi$
$701$	−12.5378			−0.473548			−0.236774	+	0.971565i	$0.576090\pi$
$702$		0			0
$703$	15.6353	+	30.6860i	0.589697	+	1.15735i
$704$		0			0
$705$	−9.12725	−	3.65228i	−0.343752	−	0.137553i
$706$		0			0
$707$	7.34968	+	7.34968i	0.276413	+	0.276413i
$708$		0			0
$709$	−4.41846	+	6.08149i	−0.165939	+	0.228395i	−0.883886	−	0.467702i	$-0.845082\pi$
$709$	−4.41846	+	6.08149i	−0.165939	+	0.228395i	0.717947	+	0.696098i	$0.245082\pi$
$710$		0			0
$711$	−7.48482	−	10.3020i	−0.280703	−	0.386354i
$712$		0			0
$713$	0.516812	+	3.26302i	0.0193548	+	0.122201i
$714$		0			0
$715$	8.41373	−	14.1092i	0.314656	−	0.527654i
$716$		0			0
$717$	0.139251	+	0.0709521i	0.00520043	+	0.00264975i
$718$		0			0
$719$	−10.1211	−	31.1496i	−0.377454	−	1.16169i	−0.941808	−	0.336152i	$-0.890874\pi$
$719$	−10.1211	−	31.1496i	−0.377454	−	1.16169i	0.564353	−	0.825533i	$-0.309126\pi$
$720$		0			0
$721$	10.5561	−	32.4883i	0.393129	−	1.20993i
$722$		0			0
$723$	1.26363	−	7.97822i	0.0469948	−	0.296713i
$724$		0			0
$725$	8.87469	−	1.62597i	0.329598	−	0.0603868i
$726$		0			0
$727$	21.0297	+	3.33078i	0.779950	+	0.123532i	0.533699	−	0.845674i	$-0.320801\pi$
$727$	21.0297	+	3.33078i	0.779950	+	0.123532i	0.246250	+	0.969206i	$0.420801\pi$
$728$		0			0
$729$	−19.7120	−	6.40481i	−0.730073	−	0.237215i
$730$		0			0
$731$	−49.0368	+	15.9330i	−1.81369	+	0.589304i
$732$		0			0
$733$	−12.4043	+	24.3448i	−0.458163	+	0.899195i	0.540174	+	0.841553i	$0.318358\pi$
$733$	−12.4043	+	24.3448i	−0.458163	+	0.899195i	−0.998337	+	0.0576423i	$0.981642\pi$
$734$		0			0
$735$	−0.916399	+	0.801996i	−0.0338019	+	0.0295821i
$736$		0			0
$737$	−17.3631	+	2.75004i	−0.639576	+	0.101299i
$738$		0			0
$739$	13.7059	−	9.95788i	0.504178	−	0.366307i	−0.306433	−	0.951892i	$-0.599135\pi$
$739$	13.7059	−	9.95788i	0.504178	−	0.366307i	0.810611	+	0.585586i	$0.199135\pi$
$740$		0			0
$741$	−4.62339	−	3.35909i	−0.169845	−	0.123399i
$742$		0			0
$743$	5.57903	−	5.57903i	0.204675	−	0.204675i	−0.597325	−	0.801999i	$-0.703770\pi$
$743$	5.57903	−	5.57903i	0.204675	−	0.204675i	0.801999	+	0.597325i	$0.203770\pi$
$744$		0			0
$745$	7.68088	+	30.3743i	0.281406	+	1.11283i
$746$		0			0
$747$	33.5578	−	17.0986i	1.22782	−	0.625603i
$748$		0			0
$749$		−	24.4885i		−	0.894791i
$750$		0			0
$751$			22.8251i			0.832899i	0.909159	+	0.416450i	$0.136726\pi$
$751$			22.8251i			0.832899i	−0.909159	+	0.416450i	$0.863274\pi$
$752$		0			0
$753$	0.218231	−	0.111194i	0.00795277	−	0.00405214i
$754$		0			0
$755$	1.31943	+	5.21774i	0.0480190	+	0.189893i
$756$		0			0
$757$	11.8862	−	11.8862i	0.432012	−	0.432012i	−0.457300	−	0.889312i	$-0.651184\pi$
$757$	11.8862	−	11.8862i	0.432012	−	0.432012i	0.889312	+	0.457300i	$0.151184\pi$
$758$		0			0
$759$	−0.430957	−	0.313108i	−0.0156427	−	0.0113651i
$760$		0			0
$761$	−14.8155	+	10.7641i	−0.537061	+	0.390198i	−0.822992	−	0.568052i	$-0.807697\pi$
$761$	−14.8155	+	10.7641i	−0.537061	+	0.390198i	0.285931	+	0.958250i	$0.407697\pi$
$762$		0			0
$763$	−15.7144	+	2.48891i	−0.568898	+	0.0901046i
$764$		0			0
$765$	−23.5350	+	20.5969i	−0.850908	+	0.744681i
$766$		0			0
$767$	1.86107	−	3.65255i	0.0671993	−	0.131886i
$768$		0			0
$769$	33.9622	−	11.0350i	1.22471	−	0.397932i	0.375915	−	0.926654i	$-0.377329\pi$
$769$	33.9622	−	11.0350i	1.22471	−	0.397932i	0.848795	+	0.528722i	$0.177329\pi$
$770$		0			0
$771$	−9.93001	−	3.22646i	−0.357621	−	0.116198i
$772$		0			0
$773$	−4.78169	−	0.757345i	−0.171985	−	0.0272398i	0.0698478	−	0.997558i	$-0.477749\pi$
$773$	−4.78169	−	0.757345i	−0.171985	−	0.0272398i	−0.241833	+	0.970318i	$0.577749\pi$
$774$		0			0
$775$	−25.5636	+	26.8278i	−0.918273	+	0.963683i
$776$		0			0
$777$	−0.562433	+	3.55106i	−0.0201772	+	0.127394i
$778$		0			0
$779$	−8.58523	+	26.4226i	−0.307598	+	0.946688i
$780$		0			0
$781$	4.41654	+	13.5927i	0.158036	+	0.486385i
$782$		0			0
$783$	3.27697	+	1.66970i	0.117109	+	0.0596702i
$784$		0			0
$785$	−7.22196	+	12.1107i	−0.257763	+	0.432248i
$786$		0			0
$787$	0.344633	+	2.17593i	0.0122848	+	0.0775634i	0.993069	−	0.117532i	$-0.0374983\pi$
$787$	0.344633	+	2.17593i	0.0122848	+	0.0775634i	−0.980784	+	0.195096i	$0.937498\pi$
$788$		0			0
$789$	−1.84148	−	2.53458i	−0.0655583	−	0.0902333i
$790$		0			0
$791$	−15.2307	+	20.9632i	−0.541541	+	0.745367i
$792$		0			0
$793$	−10.2861	−	10.2861i	−0.365271	−	0.365271i
$794$		0			0
$795$	6.31162	+	2.52560i	0.223850	+	0.0895740i
$796$		0			0
$797$	−0.510571	−	1.00205i	−0.0180854	−	0.0354945i	0.881787	−	0.471648i	$-0.156341\pi$
$797$	−0.510571	−	1.00205i	−0.0180854	−	0.0354945i	−0.899872	+	0.436153i	$0.856341\pi$
$798$		0			0
$799$	61.5994			2.17923
$800$		0			0
$801$	41.6843			1.47284
$802$		0			0
$803$	8.04458	+	15.7884i	0.283887	+	0.557160i
$804$		0			0
$805$	1.48687	−	1.78404i	0.0524054	−	0.0628791i
$806$		0			0
$807$	6.87346	+	6.87346i	0.241957	+	0.241957i
$808$		0			0
$809$	3.49373	−	4.80871i	0.122833	−	0.169065i	−0.743172	−	0.669100i	$-0.766680\pi$
$809$	3.49373	−	4.80871i	0.122833	−	0.169065i	0.866005	+	0.500035i	$0.166680\pi$
$810$		0			0
$811$	15.8797	+	21.8566i	0.557613	+	0.767488i	0.991021	−	0.133710i	$-0.0426890\pi$
$811$	15.8797	+	21.8566i	0.557613	+	0.767488i	−0.433408	+	0.901198i	$0.642689\pi$
$812$		0			0
$813$	1.21681	+	7.68263i	0.0426753	+	0.269441i
$814$		0			0
$815$	42.1302	−	18.0493i	1.47575	−	0.632239i
$816$		0			0
$817$	73.1819	+	37.2880i	2.56031	+	1.30454i
$818$		0			0
$819$	4.41862	+	13.5991i	0.154399	+	0.475191i
$820$		0			0
$821$	0.109954	−	0.338404i	0.00383743	−	0.0118104i	−0.949119	−	0.314916i	$-0.898024\pi$
$821$	0.109954	−	0.338404i	0.00383743	−	0.0118104i	0.952957	+	0.303106i	$0.0980236\pi$
$822$		0			0
$823$	−8.92342	+	56.3403i	−0.311051	+	1.96390i	−0.0492043	+	0.998789i	$0.515669\pi$
$823$	−8.92342	+	56.3403i	−0.311051	+	1.96390i	−0.261847	+	0.965109i	$0.584331\pi$
$824$		0			0
$825$	−0.144133	−	5.97339i	−0.00501806	−	0.207967i
$826$		0			0
$827$	25.9409	+	4.10863i	0.902053	+	0.142871i	0.590198	−	0.807258i	$-0.299050\pi$
$827$	25.9409	+	4.10863i	0.902053	+	0.142871i	0.311855	+	0.950130i	$0.399050\pi$
$828$		0			0
$829$	−23.1049	−	7.50725i	−0.802468	−	0.260738i	−0.121063	−	0.992645i	$-0.538630\pi$
$829$	−23.1049	−	7.50725i	−0.802468	−	0.260738i	−0.681404	+	0.731907i	$0.738630\pi$
$830$		0			0
$831$	6.79298	−	2.20717i	0.235646	−	0.0765660i
$832$		0			0
$833$	3.46418	−	6.79883i	0.120027	−	0.235566i
$834$		0			0
$835$	−2.54533	+	11.1953i	−0.0880849	+	0.387429i
$836$		0			0
$837$	−14.9197	+	2.36305i	−0.515701	+	0.0816790i
$838$		0			0
$839$	−14.6750	+	10.6620i	−0.506637	+	0.368093i	−0.811546	−	0.584288i	$-0.801374\pi$
$839$	−14.6750	+	10.6620i	−0.506637	+	0.368093i	0.304910	+	0.952381i	$0.401374\pi$
$840$		0			0
$841$	−20.8272	−	15.1319i	−0.718180	−	0.521788i
$842$		0			0
$843$	−3.67469	+	3.67469i	−0.126563	+	0.126563i
$844$		0			0
$845$	−16.0070	+	10.0767i	−0.550659	+	0.346649i
$846$		0			0
$847$	1.83782	−	0.936416i	0.0631482	−	0.0321756i
$848$		0			0
$849$			7.37841i			0.253226i
$850$		0			0
$851$			1.98431i			0.0680211i
$852$		0			0
$853$	−8.54836	+	4.35561i	−0.292690	+	0.149133i	−0.594170	−	0.804339i	$-0.702519\pi$
$853$	−8.54836	+	4.35561i	−0.292690	+	0.149133i	0.301480	+	0.953473i	$0.402519\pi$
$854$		0			0
$855$	49.7100	+	3.30948i	1.70005	+	0.113182i
$856$		0			0
$857$	−27.5786	+	27.5786i	−0.942069	+	0.942069i	−0.998411	−	0.0563428i	$-0.982056\pi$
$857$	−27.5786	+	27.5786i	−0.942069	+	0.942069i	0.0563428	+	0.998411i	$0.482056\pi$
$858$		0			0
$859$	13.1839	+	9.57867i	0.449829	+	0.326820i	0.789528	−	0.613714i	$-0.210325\pi$
$859$	13.1839	+	9.57867i	0.449829	+	0.326820i	−0.339699	+	0.940534i	$0.610325\pi$
$860$		0			0
$861$	−2.34642	+	1.70477i	−0.0799657	+	0.0580985i
$862$		0			0
$863$	−43.2993	+	6.85794i	−1.47393	+	0.233447i	−0.841114	−	0.540858i	$-0.818100\pi$
$863$	−43.2993	+	6.85794i	−1.47393	+	0.233447i	−0.632813	+	0.774305i	$0.718100\pi$
$864$		0			0
$865$	−46.8473	+	4.25611i	−1.59285	+	0.144712i
$866$		0			0
$867$	−1.03671	+	2.03466i	−0.0352085	+	0.0691005i
$868$		0			0
$869$	−14.4979	+	4.71064i	−0.491806	+	0.159798i
$870$		0			0
$871$	−10.3345	−	3.35788i	−0.350170	−	0.113777i
$872$		0			0
$873$	28.9195	+	4.58040i	0.978777	+	0.155023i
$874$		0			0
$875$	26.0268	+	1.10297i	0.879866	+	0.0372873i
$876$		0			0
$877$	−7.95004	+	50.1946i	−0.268454	+	1.69495i	0.373035	+	0.927817i	$0.378317\pi$
$877$	−7.95004	+	50.1946i	−0.268454	+	1.69495i	−0.641489	+	0.767133i	$0.721683\pi$
$878$		0			0
$879$	−1.79767	+	5.53265i	−0.0606338	+	0.186612i
$880$		0			0
$881$	3.29679	+	10.1465i	0.111072	+	0.341844i	0.991107	−	0.133064i	$-0.0424815\pi$
$881$	3.29679	+	10.1465i	0.111072	+	0.341844i	−0.880036	+	0.474907i	$0.842482\pi$
$882$		0			0
$883$	27.4816	+	14.0026i	0.924829	+	0.471224i	0.850480	−	0.526008i	$-0.176312\pi$
$883$	27.4816	+	14.0026i	0.924829	+	0.471224i	0.0743498	+	0.997232i	$0.476312\pi$
$884$		0			0
$885$	−0.134908	−	1.48494i	−0.00453488	−	0.0499157i
$886$		0			0
$887$	−0.689610	−	4.35402i	−0.0231548	−	0.146194i	0.973402	−	0.229102i	$-0.0735791\pi$
$887$	−0.689610	−	4.35402i	−0.0231548	−	0.146194i	−0.996557	+	0.0829086i	$0.973579\pi$
$888$		0			0
$889$	−0.297840	−	0.409942i	−0.00998923	−	0.0137490i
$890$		0			0
$891$	−16.0754	+	22.1259i	−0.538547	+	0.741246i
$892$		0			0
$893$	−69.3854	−	69.3854i	−2.32190	−	2.32190i
$894$		0			0
$895$	0.727132	−	10.9219i	0.0243053	−	0.365078i
$896$		0			0
$897$	−0.149485	−	0.293382i	−0.00499117	−	0.00979573i
$898$		0			0
$899$	−13.3738			−0.446040
$900$		0			0
$901$	−42.5969			−1.41911
$902$		0			0
$903$	3.89267	+	7.63979i	0.129540	+	0.254236i
$904$		0			0
$905$	−4.57863	−	7.27325i	−0.152199	−	0.241771i
$906$		0			0
$907$	−14.5137	−	14.5137i	−0.481921	−	0.481921i	0.423824	−	0.905745i	$-0.360687\pi$
$907$	−14.5137	−	14.5137i	−0.481921	−	0.481921i	−0.905745	+	0.423824i	$0.860687\pi$
$908$		0			0
$909$	−7.55120	+	10.3933i	−0.250458	+	0.344725i
$910$		0			0
$911$	−15.6052	−	21.4787i	−0.517023	−	0.711622i	0.468061	−	0.883696i	$-0.344953\pi$
$911$	−15.6052	−	21.4787i	−0.517023	−	0.711622i	−0.985084	+	0.172075i	$0.944953\pi$
$912$		0			0
$913$	−7.05311	−	44.5316i	−0.233424	−	1.47378i
$914$		0			0
$915$	−5.15942	−	1.17303i	−0.170565	−	0.0387793i
$916$		0			0
$917$	2.14927	+	1.09511i	0.0709753	+	0.0361637i
$918$		0			0
$919$	−9.24808	−	28.4627i	−0.305066	−	0.938896i	−0.979653	−	0.200701i	$-0.935678\pi$
$919$	−9.24808	−	28.4627i	−0.305066	−	0.938896i	0.674587	−	0.738196i	$-0.264322\pi$
$920$		0			0
$921$	2.16746	−	6.67076i	0.0714203	−	0.219809i
$922$		0			0
$923$	−1.38200	+	8.72560i	−0.0454891	+	0.287207i
$924$		0			0
$925$	−17.6860	+	13.5133i	−0.581513	+	0.444314i
$926$		0			0
$927$	41.7018	+	6.60491i	1.36967	+	0.216934i
$928$		0			0
$929$	43.9815	+	14.2905i	1.44299	+	0.468855i	0.922827	−	0.385214i	$-0.125872\pi$
$929$	43.9815	+	14.2905i	1.44299	+	0.468855i	0.520160	+	0.854069i	$0.325872\pi$
$930$		0			0
$931$	−11.5602	+	3.75615i	−0.378871	+	0.123103i
$932$		0			0
$933$	−1.82814	+	3.58794i	−0.0598508	+	0.117464i
$934$		0			0
$935$	14.7437	+	34.4144i	0.482172	+	1.12547i
$936$		0			0
$937$	19.2814	−	3.05388i	0.629897	−	0.0997659i	0.166680	−	0.986011i	$-0.446695\pi$
$937$	19.2814	−	3.05388i	0.629897	−	0.0997659i	0.463217	+	0.886245i	$0.346695\pi$
$938$		0			0
$939$	2.31628	−	1.68287i	0.0755889	−	0.0549185i
$940$		0			0
$941$	−2.85440	−	2.07384i	−0.0930508	−	0.0676054i	0.540287	−	0.841481i	$-0.318316\pi$
$941$	−2.85440	−	2.07384i	−0.0930508	−	0.0676054i	−0.633338	+	0.773875i	$0.718316\pi$
$942$		0			0
$943$	−1.13189	+	1.13189i	−0.0368593	+	0.0368593i
$944$		0			0
$945$	8.15726	+	6.79852i	0.265356	+	0.221156i
$946$		0			0
$947$	−22.8923	+	11.6642i	−0.743901	+	0.379037i	−0.784492	−	0.620139i	$-0.787076\pi$
$947$	−22.8923	+	11.6642i	−0.743901	+	0.379037i	0.0405906	+	0.999176i	$0.487076\pi$
$948$		0			0
$949$			10.9530i			0.355549i
$950$		0			0
$951$		−	8.34062i		−	0.270463i
$952$		0			0
$953$	20.7915	−	10.5938i	0.673503	−	0.343167i	−0.0835655	−	0.996502i	$-0.526631\pi$
$953$	20.7915	−	10.5938i	0.673503	−	0.343167i	0.757069	+	0.653335i	$0.226631\pi$
$954$		0			0
$955$	−5.79599	+	14.4845i	−0.187554	+	0.468707i
$956$		0			0
$957$	1.52481	−	1.52481i	0.0492900	−	0.0492900i
$958$		0			0
$959$	−18.2424	−	13.2539i	−0.589079	−	0.427991i
$960$		0			0
$961$	19.3591	−	14.0652i	0.624487	−	0.453717i
$962$		0			0
$963$	29.8948	−	4.73488i	0.963348	−	0.152579i
$964$		0			0
$965$	39.7827	+	23.7236i	1.28065	+	0.763690i
$966$		0			0
$967$	17.5089	−	34.3632i	0.563049	−	1.10505i	−0.417483	−	0.908685i	$-0.637088\pi$
$967$	17.5089	−	34.3632i	0.563049	−	1.10505i	0.980532	−	0.196361i	$-0.0629124\pi$
$968$		0			0
$969$	12.3872	−	4.02484i	0.397934	−	0.129297i
$970$		0			0
$971$	−3.90481	−	1.26875i	−0.125311	−	0.0407161i	0.245690	−	0.969348i	$-0.420985\pi$
$971$	−3.90481	−	1.26875i	−0.125311	−	0.0407161i	−0.371001	+	0.928632i	$0.620985\pi$
$972$		0			0
$973$	−37.4281	−	5.92803i	−1.19989	−	0.190044i
$974$		0			0
$975$	1.59689	−	3.33031i	0.0511413	−	0.106655i
$976$		0			0
$977$	−0.524331	+	3.31050i	−0.0167748	+	0.105912i	−0.994655	−	0.103253i	$-0.967075\pi$
$977$	−0.524331	+	3.31050i	−0.0167748	+	0.105912i	0.977880	+	0.209166i	$0.0670748\pi$
$978$		0			0
$979$	15.4202	−	47.4585i	0.492832	−	1.51678i
$980$		0			0
$981$	−6.07678	−	18.7024i	−0.194017	−	0.597121i
$982$		0			0
$983$	−23.9917	−	12.2244i	−0.765216	−	0.389897i	0.0273949	−	0.999625i	$-0.491279\pi$
$983$	−23.9917	−	12.2244i	−0.765216	−	0.389897i	−0.792611	+	0.609728i	$0.791279\pi$
$984$		0			0
$985$	16.1325	+	18.4337i	0.514023	+	0.587348i
$986$		0			0
$987$	−1.60248	−	10.1177i	−0.0510077	−	0.322050i
$988$		0			0
$989$	2.78157	+	3.82850i	0.0884488	+	0.121739i
$990$		0			0
$991$	−12.7252	+	17.5147i	−0.404228	+	0.556372i	−0.961799	−	0.273757i	$-0.911733\pi$
$991$	−12.7252	+	17.5147i	−0.404228	+	0.556372i	0.557571	+	0.830129i	$0.311733\pi$
$992$		0			0
$993$	7.86534	+	7.86534i	0.249599	+	0.249599i
$994$		0			0
$995$	20.4423	−	5.16931i	0.648063	−	0.163878i
$996$		0			0
$997$	15.8642	+	31.1353i	0.502425	+	0.986064i	0.993380	+	0.114879i	$0.0366480\pi$
$997$	15.8642	+	31.1353i	0.502425	+	0.986064i	−0.490955	+	0.871185i	$0.663352\pi$
$998$		0			0
$999$	−9.07296			−0.287056

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.bi.d.223.6	yes	80
4.3	odd	2	inner	400.2.bi.d.223.5	✓	80
25.12	odd	20	inner	400.2.bi.d.287.5	yes	80
100.87	even	20	inner	400.2.bi.d.287.6	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.bi.d.223.5	✓	80	4.3	odd	2	inner
400.2.bi.d.223.6	yes	80	1.1	even	1	trivial
400.2.bi.d.287.5	yes	80	25.12	odd	20	inner
400.2.bi.d.287.6	yes	80	100.87	even	20	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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.bi (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.157369 + 0.308855i) q^{3} +(-2.16783 + 0.548188i) q^{5} +(-1.64756 - 1.64756i) q^{7} +(1.69273 - 2.32984i) q^{9} +O(q^{10})\)	\(q+(0.157369 + 0.308855i) q^{3} +(-2.16783 + 0.548188i) q^{5} +(-1.64756 - 1.64756i) q^{7} +(1.69273 - 2.32984i) q^{9} +(-2.02639 - 2.78909i) q^{11} +(-0.333359 - 2.10475i) q^{13} +(-0.510460 - 0.583277i) q^{15} +(4.32737 + 2.20491i) q^{17} +(-2.39074 - 7.35794i) q^{19} +(0.249580 - 0.768130i) q^{21} +(0.0697318 - 0.440270i) q^{23} +(4.39898 - 2.37676i) q^{25} +(2.01307 + 0.318839i) q^{27} +(1.71616 + 0.557615i) q^{29} +(-7.04868 + 2.29026i) q^{31} +(0.542530 - 1.06478i) q^{33} +(4.47479 + 2.66845i) q^{35} +(-4.39673 + 0.696374i) q^{37} +(0.597600 - 0.434182i) q^{39} +(-2.90521 - 2.11076i) q^{41} +(-7.50685 + 7.50685i) q^{43} +(-2.39236 + 5.97864i) q^{45} +(11.3009 - 5.75811i) q^{47} -1.57112i q^{49} +1.68351i q^{51} +(-7.81476 + 3.98182i) q^{53} +(5.92181 + 4.93542i) q^{55} +(1.89630 - 1.89630i) q^{57} +(1.55630 + 1.13072i) q^{59} +(5.52261 - 4.01241i) q^{61} +(-6.62741 + 1.04968i) q^{63} +(1.87646 + 4.37999i) q^{65} +(2.31499 - 4.54342i) q^{67} +(0.146953 - 0.0477479i) q^{69} +(-3.94277 - 1.28108i) q^{71} +(-5.07659 - 0.804053i) q^{73} +(1.42634 + 0.984617i) q^{75} +(-1.25658 + 7.93376i) q^{77} +(1.36639 - 4.20533i) q^{79} +(-2.45144 - 7.54476i) q^{81} +(11.6526 + 5.93732i) q^{83} +(-10.5897 - 2.40765i) q^{85} +(0.0978494 + 0.617797i) q^{87} +(8.50790 + 11.7101i) q^{89} +(-2.91846 + 4.01692i) q^{91} +(-1.81660 - 1.81660i) q^{93} +(9.21625 + 14.6402i) q^{95} +(4.61582 + 9.05905i) q^{97} -9.92826 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{5}+O(q^{10}) \) 80 * q + 4 * q^5	\( 80 q + 4 q^{5} - 4 q^{13} - 24 q^{17} - 48 q^{25} - 40 q^{29} - 64 q^{33} - 20 q^{37} - 24 q^{45} + 28 q^{53} + 48 q^{57} + 112 q^{65} + 140 q^{69} + 108 q^{73} + 136 q^{77} - 20 q^{81} - 24 q^{85} + 80 q^{89} - 116 q^{93} - 52 q^{97}+O(q^{100}) \) 80 * q + 4 * q^5 - 4 * q^13 - 24 * q^17 - 48 * q^25 - 40 * q^29 - 64 * q^33 - 20 * q^37 - 24 * q^45 + 28 * q^53 + 48 * q^57 + 112 * q^65 + 140 * q^69 + 108 * q^73 + 136 * q^77 - 20 * q^81 - 24 * q^85 + 80 * q^89 - 116 * q^93 - 52 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more