LMFDB - Embedded newform 400.2.bi.b.303.2

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:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{20})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 52 x^{14} - 224 x^{13} + 806 x^{12} - 2288 x^{11} + 5530 x^{10} - 11062 x^{9} + \cdots + 521 $ x^16 - 8x^15 + 52x^14 - 224x^13 + 806x^12 - 2288x^11 + 5530x^10 - 11062x^9 + 18924x^8 - 27056x^7 + 32750x^6 - 32636x^5 + 26711x^4 - 17122x^3 + 8368x^2 - 2746*x + 521
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			303.2
Root			$0.500000 + 1.94194i$ of defining polynomial
Character	$\chi$	$=$	400.303
Dual form			400.2.bi.b.367.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.01411 - 0.319003i) q^{3} +(-1.70582 - 1.44575i) q^{5} +(-3.13704 - 3.13704i) q^{7} +(1.10169 - 0.357960i) q^{9} +(3.22428 + 1.04763i) q^{11} +(1.73514 - 3.40540i) q^{13} +(-3.89690 - 2.36772i) q^{15} +(1.22123 - 7.71055i) q^{17} +(-0.375011 + 0.272461i) q^{19} +(-7.31906 - 5.31761i) q^{21} +(2.52419 + 4.95399i) q^{23} +(0.819639 + 4.93236i) q^{25} +(-3.34613 + 1.70494i) q^{27} +(0.719203 - 0.989898i) q^{29} +(4.50368 + 6.19878i) q^{31} +(6.82823 + 1.08149i) q^{33} +(0.815862 + 9.88660i) q^{35} +(1.21113 + 0.617102i) q^{37} +(2.40842 - 7.41234i) q^{39} +(-0.457300 - 1.40742i) q^{41} +(-5.57270 + 5.57270i) q^{43} +(-2.39680 - 0.982146i) q^{45} +(-0.197155 - 1.24479i) q^{47} +12.6821i q^{49} -15.9194i q^{51} +(0.141520 + 0.893520i) q^{53} +(-3.98543 - 6.44855i) q^{55} +(-0.668395 + 0.668395i) q^{57} +(-3.24696 - 9.99313i) q^{59} +(0.649536 - 1.99907i) q^{61} +(-4.57898 - 2.33311i) q^{63} +(-7.88316 + 3.30042i) q^{65} +(11.3499 + 1.79765i) q^{67} +(6.66432 + 9.17264i) q^{69} +(-1.00694 + 1.38593i) q^{71} +(5.49431 - 2.79949i) q^{73} +(3.22428 + 9.67283i) q^{75} +(-6.82823 - 13.4012i) q^{77} +(13.5517 + 9.84590i) q^{79} +(-9.00703 + 6.54399i) q^{81} +(1.12294 - 7.08995i) q^{83} +(-13.2307 + 11.3872i) q^{85} +(1.13277 - 2.22319i) q^{87} +(7.35916 + 2.39114i) q^{89} +(-16.1261 + 5.23968i) q^{91} +(11.0483 + 11.0483i) q^{93} +(1.03361 + 0.0774005i) q^{95} +(10.8914 - 1.72503i) q^{97} +3.92716 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 20 q^{9} + 20 q^{17} - 20 q^{21} - 20 q^{25} + 20 q^{29} + 60 q^{33} - 20 q^{37} + 28 q^{41} - 20 q^{45} + 60 q^{53} - 20 q^{57} - 12 q^{61} - 20 q^{65} - 80 q^{69} - 40 q^{73} - 60 q^{77} + 56 q^{81}+ \cdots + 40 q^{97}+O(q^{100}) $ 16 * q - 20 * q^9 + 20 * q^17 - 20 * q^21 - 20 * q^25 + 20 * q^29 + 60 * q^33 - 20 * q^37 + 28 * q^41 - 20 * q^45 + 60 * q^53 - 20 * q^57 - 12 * q^61 - 20 * q^65 - 80 * q^69 - 40 * q^73 - 60 * q^77 + 56 * q^81 - 60 * q^85 + 40 * q^97

Character values

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

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{7}{20}\right)$	$-1$

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
$3$	2.01411	−	0.319003i	1.16284	−	0.184176i	0.454965	−	0.890509i	$-0.349652\pi$
$3$	2.01411	−	0.319003i	1.16284	−	0.184176i	0.707880	+	0.706333i	$0.249652\pi$
$4$		0			0
$5$	−1.70582	−	1.44575i	−0.762866	−	0.646557i
$5$	−1.70582	−	1.44575i	−0.762866	−	0.646557i
$6$		0			0
$7$	−3.13704	−	3.13704i	−1.18569	−	1.18569i	−0.978247	−	0.207444i	$-0.933486\pi$
$7$	−3.13704	−	3.13704i	−1.18569	−	1.18569i	−0.207444	−	0.978247i	$-0.566514\pi$
$8$		0			0
$9$	1.10169	−	0.357960i	0.367230	−	0.119320i
$10$		0			0
$11$	3.22428	+	1.04763i	0.972156	+	0.315873i	0.751686	−	0.659521i	$-0.229241\pi$
$11$	3.22428	+	1.04763i	0.972156	+	0.315873i	0.220470	+	0.975394i	$0.429241\pi$
$12$		0			0
$13$	1.73514	−	3.40540i	0.481240	−	0.944487i	−0.514945	−	0.857223i	$-0.672188\pi$
$13$	1.73514	−	3.40540i	0.481240	−	0.944487i	0.996185	−	0.0872636i	$-0.0278123\pi$
$14$		0			0
$15$	−3.89690	−	2.36772i	−1.00617	−	0.611343i
$16$		0			0
$17$	1.22123	−	7.71055i	0.296192	−	1.87008i	−0.170062	−	0.985433i	$-0.554397\pi$
$17$	1.22123	−	7.71055i	0.296192	−	1.87008i	0.466254	−	0.884651i	$-0.345603\pi$
$18$		0			0
$19$	−0.375011	+	0.272461i	−0.0860333	+	0.0625069i	−0.629970	−	0.776619i	$-0.716933\pi$
$19$	−0.375011	+	0.272461i	−0.0860333	+	0.0625069i	0.543937	+	0.839126i	$0.316933\pi$
$20$		0			0
$21$	−7.31906	−	5.31761i	−1.59715	−	1.16040i
$22$		0			0
$23$	2.52419	+	4.95399i	0.526329	+	1.03298i	0.989203	+	0.146555i	$0.0468185\pi$
$23$	2.52419	+	4.95399i	0.526329	+	1.03298i	−0.462873	+	0.886424i	$0.653182\pi$
$24$		0			0
$25$	0.819639	+	4.93236i	0.163928	+	0.986472i
$26$		0			0
$27$	−3.34613	+	1.70494i	−0.643962	+	0.328115i
$28$		0			0
$29$	0.719203	−	0.989898i	0.133553	−	0.183819i	−0.737003	−	0.675890i	$-0.763760\pi$
$29$	0.719203	−	0.989898i	0.133553	−	0.183819i	0.870556	+	0.492070i	$0.163760\pi$
$30$		0			0
$31$	4.50368	+	6.19878i	0.808884	+	1.11333i	0.991495	+	0.130148i	$0.0415454\pi$
$31$	4.50368	+	6.19878i	0.808884	+	1.11333i	−0.182610	+	0.983185i	$0.558455\pi$
$32$		0			0
$33$	6.82823	+	1.08149i	1.18864	+	0.188262i
$34$		0			0
$35$	0.815862	+	9.88660i	0.137906	+	1.67114i
$36$		0			0
$37$	1.21113	+	0.617102i	0.199109	+	0.101451i	0.550702	−	0.834702i	$-0.314360\pi$
$37$	1.21113	+	0.617102i	0.199109	+	0.101451i	−0.351593	+	0.936153i	$0.614360\pi$
$38$		0			0
$39$	2.40842	−	7.41234i	0.385655	−	1.18692i
$40$		0			0
$41$	−0.457300	−	1.40742i	−0.0714182	−	0.219803i	0.908976	−	0.416848i	$-0.136865\pi$
$41$	−0.457300	−	1.40742i	−0.0714182	−	0.219803i	−0.980394	+	0.197046i	$0.936865\pi$
$42$		0			0
$43$	−5.57270	+	5.57270i	−0.849829	+	0.849829i	−0.990112	−	0.140283i	$-0.955199\pi$
$43$	−5.57270	+	5.57270i	−0.849829	+	0.849829i	0.140283	+	0.990112i	$0.455199\pi$
$44$		0			0
$45$	−2.39680	−	0.982146i	−0.357294	−	0.146410i
$46$		0			0
$47$	−0.197155	−	1.24479i	−0.0287580	−	0.181571i	0.969128	−	0.246558i	$-0.0792994\pi$
$47$	−0.197155	−	1.24479i	−0.0287580	−	0.181571i	−0.997886	+	0.0649869i	$0.979299\pi$
$48$		0			0
$49$			12.6821i			1.81173i
$50$		0			0
$51$		−	15.9194i		−	2.22917i
$52$		0			0
$53$	0.141520	+	0.893520i	0.0194392	+	0.122734i	0.995500	−	0.0947650i	$-0.0302100\pi$
$53$	0.141520	+	0.893520i	0.0194392	+	0.122734i	−0.976060	+	0.217499i	$0.930210\pi$
$54$		0			0
$55$	−3.98543	−	6.44855i	−0.537395	−	0.869523i
$56$		0			0
$57$	−0.668395	+	0.668395i	−0.0885311	+	0.0885311i
$58$		0			0
$59$	−3.24696	−	9.99313i	−0.422719	−	1.30099i	−0.905162	−	0.425067i	$-0.860250\pi$
$59$	−3.24696	−	9.99313i	−0.422719	−	1.30099i	0.482443	−	0.875927i	$-0.339750\pi$
$60$		0			0
$61$	0.649536	−	1.99907i	0.0831646	−	0.255954i	−0.900824	−	0.434184i	$-0.857037\pi$
$61$	0.649536	−	1.99907i	0.0831646	−	0.255954i	0.983989	+	0.178229i	$0.0570369\pi$
$62$		0			0
$63$	−4.57898	−	2.33311i	−0.576898	−	0.293944i
$64$		0			0
$65$	−7.88316	+	3.30042i	−0.977786	+	0.409367i
$66$		0			0
$67$	11.3499	+	1.79765i	1.38661	+	0.219618i	0.804724	−	0.593649i	$-0.202313\pi$
$67$	11.3499	+	1.79765i	1.38661	+	0.219618i	0.581890	+	0.813267i	$0.302313\pi$
$68$		0			0
$69$	6.66432	+	9.17264i	0.802289	+	1.10426i
$70$		0			0
$71$	−1.00694	+	1.38593i	−0.119502	+	0.164480i	−0.864577	−	0.502500i	$-0.832414\pi$
$71$	−1.00694	+	1.38593i	−0.119502	+	0.164480i	0.745075	+	0.666980i	$0.232414\pi$
$72$		0			0
$73$	5.49431	−	2.79949i	0.643061	−	0.327656i	−0.101870	−	0.994798i	$-0.532483\pi$
$73$	5.49431	−	2.79949i	0.643061	−	0.327656i	0.744931	+	0.667142i	$0.232483\pi$
$74$		0			0
$75$	3.22428	+	9.67283i	0.372307	+	1.11692i
$76$		0			0
$77$	−6.82823	−	13.4012i	−0.778149	−	1.52720i
$78$		0			0
$79$	13.5517	+	9.84590i	1.52469	+	1.10775i	0.959102	+	0.283061i	$0.0913501\pi$
$79$	13.5517	+	9.84590i	1.52469	+	1.10775i	0.565586	+	0.824689i	$0.308650\pi$
$80$		0			0
$81$	−9.00703	+	6.54399i	−1.00078	+	0.727110i
$82$		0			0
$83$	1.12294	−	7.08995i	0.123258	−	0.778223i	−0.846182	−	0.532895i	$-0.821104\pi$
$83$	1.12294	−	7.08995i	0.123258	−	0.778223i	0.969440	−	0.245328i	$-0.0788958\pi$
$84$		0			0
$85$	−13.2307	+	11.3872i	−1.43507	+	1.23512i
$86$		0			0
$87$	1.13277	−	2.22319i	0.121446	−	0.238351i
$88$		0			0
$89$	7.35916	+	2.39114i	0.780069	+	0.253460i	0.671870	−	0.740669i	$-0.265491\pi$
$89$	7.35916	+	2.39114i	0.780069	+	0.253460i	0.108199	+	0.994129i	$0.465491\pi$
$90$		0			0
$91$	−16.1261	+	5.23968i	−1.69047	+	0.549267i
$92$		0			0
$93$	11.0483	+	11.0483i	1.14566	+	1.14566i
$94$		0			0
$95$	1.03361	+	0.0774005i	0.106046	+	0.00794112i
$96$		0			0
$97$	10.8914	−	1.72503i	1.10586	−	0.175151i	0.423305	−	0.905987i	$-0.360870\pi$
$97$	10.8914	−	1.72503i	1.10586	−	0.175151i	0.682553	+	0.730837i	$0.260870\pi$
$98$		0			0
$99$	3.92716			0.394695
$100$		0			0
$101$	−14.0912			−1.40213			−0.701064	−	0.713098i	$-0.747291\pi$
$101$	−14.0912			−1.40213			−0.701064	+	0.713098i	$0.747291\pi$
$102$		0			0
$103$	5.29439	−	0.838549i	0.521672	−	0.0826247i	0.109955	−	0.993937i	$-0.464929\pi$
$103$	5.29439	−	0.838549i	0.521672	−	0.0826247i	0.411717	+	0.911312i	$0.364929\pi$
$104$		0			0
$105$	4.79709	+	19.6524i	0.468148	+	1.91788i
$106$		0			0
$107$	−2.89920	−	2.89920i	−0.280276	−	0.280276i	0.552943	−	0.833219i	$-0.313505\pi$
$107$	−2.89920	−	2.89920i	−0.280276	−	0.280276i	−0.833219	+	0.552943i	$0.813505\pi$
$108$		0			0
$109$	−1.50151	+	0.487870i	−0.143818	+	0.0467294i	−0.380042	−	0.924969i	$-0.624090\pi$
$109$	−1.50151	+	0.487870i	−0.143818	+	0.0467294i	0.236223	+	0.971699i	$0.424090\pi$
$110$		0			0
$111$	2.63620	+	0.856554i	0.250217	+	0.0813005i
$112$		0			0
$113$	0.368226	−	0.722684i	0.0346398	−	0.0679844i	−0.873038	−	0.487652i	$-0.837853\pi$
$113$	0.368226	−	0.722684i	0.0346398	−	0.0679844i	0.907678	+	0.419668i	$0.137853\pi$
$114$		0			0
$115$	2.85641	−	12.0999i	0.266362	−	1.12833i
$116$		0			0
$117$	0.692583	−	4.37280i	0.0640293	−	0.404265i
$118$		0			0
$119$	−28.0194	+	20.3573i	−2.56853	+	1.86615i
$120$		0			0
$121$	0.399243	+	0.290067i	0.0362948	+	0.0263698i
$122$		0			0
$123$	−1.37002	−	2.68882i	−0.123531	−	0.242443i
$124$		0			0
$125$	5.73279	−	9.59871i	0.512756	−	0.858534i
$126$		0			0
$127$	−4.49175	+	2.28866i	−0.398578	+	0.203086i	−0.641778	−	0.766890i	$-0.721803\pi$
$127$	−4.49175	+	2.28866i	−0.398578	+	0.203086i	0.243200	+	0.969976i	$0.421803\pi$
$128$		0			0
$129$	−9.44630	+	13.0017i	−0.831700	+	1.14474i
$130$		0			0
$131$	−0.911267	−	1.25425i	−0.0796178	−	0.109584i	0.767351	−	0.641228i	$-0.221575\pi$
$131$	−0.911267	−	1.25425i	−0.0796178	−	0.109584i	−0.846968	+	0.531643i	$0.821575\pi$
$132$		0			0
$133$	2.03115	+	0.321702i	0.176123	+	0.0278951i
$134$		0			0
$135$	8.17279	+	1.92933i	0.703402	+	0.166051i
$136$		0			0
$137$	11.2034	+	5.70842i	0.957172	+	0.487704i	0.861527	−	0.507712i	$-0.169509\pi$
$137$	11.2034	+	5.70842i	0.957172	+	0.487704i	0.0956453	+	0.995415i	$0.469509\pi$
$138$		0			0
$139$	−1.60657	+	4.94453i	−0.136268	+	0.419389i	−0.995785	−	0.0917174i	$-0.970764\pi$
$139$	−1.60657	+	4.94453i	−0.136268	+	0.419389i	0.859517	+	0.511107i	$0.170764\pi$
$140$		0			0
$141$	−0.794181	−	2.44424i	−0.0668821	−	0.205842i
$142$		0			0
$143$	9.16216	−	9.16216i	0.766178	−	0.766178i
$144$		0			0
$145$	−2.65797	+	0.648803i	−0.220733	+	0.0538801i
$146$		0			0
$147$	4.04562	+	25.5430i	0.333677	+	2.10675i
$148$		0			0
$149$		−	8.06154i		−	0.660427i	−0.943906	−	0.330213i	$-0.892879\pi$
$149$		−	8.06154i		−	0.660427i	0.943906	−	0.330213i	$-0.107121\pi$
$150$		0			0
$151$			15.8238i			1.28772i	0.765143	+	0.643860i	$0.222668\pi$
$151$			15.8238i			1.28772i	−0.765143	+	0.643860i	$0.777332\pi$
$152$		0			0
$153$	−1.41466	−	8.93179i	−0.114368	−	0.722092i
$154$		0			0
$155$	1.27940	−	17.0852i	0.102764	−	1.37231i
$156$		0			0
$157$	−7.45048	+	7.45048i	−0.594613	+	0.594613i	−0.938874	−	0.344261i	$-0.888130\pi$
$157$	−7.45048	+	7.45048i	−0.594613	+	0.594613i	0.344261	+	0.938874i	$0.388130\pi$
$158$		0			0
$159$	0.570071	+	1.75450i	0.0452096	+	0.139141i
$160$		0			0
$161$	7.62241	−	23.4594i	0.600730	−	1.84886i
$162$		0			0
$163$	−6.06500	−	3.09027i	−0.475048	−	0.242049i	0.200038	−	0.979788i	$-0.435893\pi$
$163$	−6.06500	−	3.09027i	−0.475048	−	0.242049i	−0.675086	+	0.737739i	$0.735893\pi$
$164$		0			0
$165$	−10.0842	−	11.7167i	−0.785052	−	0.912144i
$166$		0			0
$167$	−5.25160	−	0.831772i	−0.406381	−	0.0643645i	−0.0501023	−	0.998744i	$-0.515955\pi$
$167$	−5.25160	−	0.831772i	−0.406381	−	0.0643645i	−0.356279	+	0.934380i	$0.615955\pi$
$168$		0			0
$169$	−0.944813	−	1.30042i	−0.0726779	−	0.100033i
$170$		0			0
$171$	−0.315615	+	0.434406i	−0.0241357	+	0.0332199i
$172$		0			0
$173$	17.9448	−	9.14333i	1.36432	−	0.695154i	0.390101	−	0.920772i	$-0.372440\pi$
$173$	17.9448	−	9.14333i	1.36432	−	0.695154i	0.974216	+	0.225618i	$0.0724400\pi$
$174$		0			0
$175$	12.9018	−	18.0443i	0.975284	−	1.36402i
$176$		0			0
$177$	−9.72757	−	19.0914i	−0.731169	−	1.43500i
$178$		0			0
$179$	8.37543	+	6.08510i	0.626009	+	0.454822i	0.855015	−	0.518603i	$-0.173548\pi$
$179$	8.37543	+	6.08510i	0.626009	+	0.454822i	−0.229006	+	0.973425i	$0.573548\pi$
$180$		0			0
$181$	−11.8861	+	8.63577i	−0.883489	+	0.641892i	−0.934172	−	0.356823i	$-0.883860\pi$
$181$	−11.8861	+	8.63577i	−0.883489	+	0.641892i	0.0506835	+	0.998715i	$0.483860\pi$
$182$		0			0
$183$	0.670526	−	4.23354i	0.0495667	−	0.312952i
$184$		0			0
$185$	−1.17380	−	2.80365i	−0.0862993	−	0.206128i
$186$		0			0
$187$	12.0154	−	23.5816i	0.878653	−	1.72445i
$188$		0			0
$189$	15.8454	+	5.14848i	1.15258	+	0.374497i
$190$		0			0
$191$	9.35722	−	3.04034i	0.677064	−	0.219992i	0.0497547	−	0.998761i	$-0.484156\pi$
$191$	9.35722	−	3.04034i	0.677064	−	0.219992i	0.627310	+	0.778770i	$0.284156\pi$
$192$		0			0
$193$	−10.2775	−	10.2775i	−0.739792	−	0.739792i	0.232746	−	0.972538i	$-0.425229\pi$
$193$	−10.2775	−	10.2775i	−0.739792	−	0.739792i	−0.972538	+	0.232746i	$0.925229\pi$
$194$		0			0
$195$	−14.8247	+	9.16216i	−1.06162	+	0.656116i
$196$		0			0
$197$	−14.0391	+	2.22358i	−1.00025	+	0.158424i	−0.635021	−	0.772495i	$-0.719008\pi$
$197$	−14.0391	+	2.22358i	−1.00025	+	0.158424i	−0.365227	+	0.930919i	$0.619008\pi$
$198$		0			0
$199$	−15.1694			−1.07533			−0.537666	−	0.843158i	$-0.680694\pi$
$199$	−15.1694			−1.07533			−0.537666	+	0.843158i	$0.680694\pi$
$200$		0			0
$201$	23.4334			1.65287
$202$		0			0
$203$	−5.36152	+	0.849182i	−0.376305	+	0.0596009i
$204$		0			0
$205$	−1.25471	+	3.06195i	−0.0876325	+	0.213856i
$206$		0			0
$207$	4.55420	+	4.55420i	0.316539	+	0.316539i
$208$		0			0
$209$	−1.49458	+	0.485617i	−0.103382	+	0.0335909i
$210$		0			0
$211$	−6.62163	−	2.15150i	−0.455852	−	0.148115i	0.0720858	−	0.997398i	$-0.477034\pi$
$211$	−6.62163	−	2.15150i	−0.455852	−	0.148115i	−0.527937	+	0.849283i	$0.677034\pi$
$212$		0			0
$213$	−1.58597	+	3.11263i	−0.108669	+	0.213274i
$214$		0			0
$215$	17.5627	−	1.44931i	1.19777	−	0.0988423i
$216$		0			0
$217$	5.31761	−	33.5741i	0.360983	−	2.27916i
$218$		0			0
$219$	10.1731	−	7.39117i	0.687433	−	0.499449i
$220$		0			0
$221$	−24.1385	−	17.5376i	−1.62373	−	1.17971i
$222$		0			0
$223$	−5.44537	−	10.6871i	−0.364649	−	0.715664i	0.633671	−	0.773603i	$-0.281547\pi$
$223$	−5.44537	−	10.6871i	−0.364649	−	0.715664i	−0.998320	+	0.0579386i	$0.981547\pi$
$224$		0			0
$225$	2.66858	+	5.14053i	0.177905	+	0.342702i
$226$		0			0
$227$	−6.46387	+	3.29351i	−0.429022	+	0.218598i	−0.655148	−	0.755500i	$-0.727394\pi$
$227$	−6.46387	+	3.29351i	−0.429022	+	0.218598i	0.226126	+	0.974098i	$0.427394\pi$
$228$		0			0
$229$	9.02359	−	12.4199i	0.596296	−	0.820731i	−0.399067	−	0.916922i	$-0.630666\pi$
$229$	9.02359	−	12.4199i	0.596296	−	0.820731i	0.995363	+	0.0961910i	$0.0306659\pi$
$230$		0			0
$231$	−18.0278	−	24.8131i	−1.18614	−	1.63258i
$232$		0			0
$233$	−2.99885	−	0.474971i	−0.196461	−	0.0311164i	0.0574284	−	0.998350i	$-0.481710\pi$
$233$	−2.99885	−	0.474971i	−0.196461	−	0.0311164i	−0.253889	+	0.967233i	$0.581710\pi$
$234$		0			0
$235$	−1.46333	+	2.40842i	−0.0954573	+	0.157108i
$236$		0			0
$237$	30.4355	+	15.5076i	1.97700	+	1.00733i
$238$		0			0
$239$	6.57625	−	20.2396i	0.425382	−	1.30919i	−0.477245	−	0.878770i	$-0.658365\pi$
$239$	6.57625	−	20.2396i	0.425382	−	1.30919i	0.902628	−	0.430422i	$-0.141635\pi$
$240$		0			0
$241$	7.98714	+	24.5819i	0.514497	+	1.58346i	0.784196	+	0.620513i	$0.213076\pi$
$241$	7.98714	+	24.5819i	0.514497	+	1.58346i	−0.269699	+	0.962945i	$0.586924\pi$
$242$		0			0
$243$	−8.08705	+	8.08705i	−0.518785	+	0.518785i
$244$		0			0
$245$	18.3351	−	21.6333i	1.17138	−	1.38210i
$246$		0			0
$247$	0.277144	+	1.74982i	0.0176342	+	0.111338i
$248$		0			0
$249$		−	14.6381i		−	0.927653i
$250$		0			0
$251$			14.8326i			0.936228i	0.883668	+	0.468114i	$0.155066\pi$
$251$			14.8326i			0.936228i	−0.883668	+	0.468114i	$0.844934\pi$
$252$		0			0
$253$	2.94872	+	18.6175i	0.185384	+	1.17047i
$254$		0			0
$255$	−23.0155	+	27.1557i	−1.44128	+	1.70056i
$256$		0			0
$257$	−12.6464	+	12.6464i	−0.788861	+	0.788861i	−0.981307	−	0.192447i	$-0.938358\pi$
$257$	−12.6464	+	12.6464i	−0.788861	+	0.788861i	0.192447	+	0.981307i	$0.438358\pi$
$258$		0			0
$259$	−1.86349	−	5.73524i	−0.115792	−	0.356371i
$260$		0			0
$261$	0.437994	−	1.34801i	0.0271111	−	0.0834395i
$262$		0			0
$263$	24.4275	+	12.4464i	1.50626	+	0.767479i	0.995724	−	0.0923755i	$-0.0294460\pi$
$263$	24.4275	+	12.4464i	1.50626	+	0.767479i	0.510539	+	0.859855i	$0.329446\pi$
$264$		0			0
$265$	1.05040	−	1.72879i	0.0645253	−	0.106198i
$266$		0			0
$267$	15.5849	+	2.46841i	0.953780	+	0.151064i
$268$		0			0
$269$	−3.38943	−	4.66515i	−0.206657	−	0.284439i	0.693090	−	0.720851i	$-0.256249\pi$
$269$	−3.38943	−	4.66515i	−0.206657	−	0.284439i	−0.899747	+	0.436412i	$0.856249\pi$
$270$		0			0
$271$	5.76191	−	7.93059i	0.350011	−	0.481749i	−0.597321	−	0.802002i	$-0.703768\pi$
$271$	5.76191	−	7.93059i	0.350011	−	0.481749i	0.947332	+	0.320253i	$0.103768\pi$
$272$		0			0
$273$	−30.8081	+	15.6975i	−1.86459	+	0.950057i
$274$		0			0
$275$	−2.52455	+	16.7620i	−0.152236	+	1.01079i
$276$		0			0
$277$	4.24456	+	8.33042i	0.255031	+	0.500526i	0.982653	−	0.185451i	$-0.0593747\pi$
$277$	4.24456	+	8.33042i	0.255031	+	0.500526i	−0.727623	+	0.685978i	$0.759375\pi$
$278$		0			0
$279$	7.18057	+	5.21699i	0.429889	+	0.312333i
$280$		0			0
$281$	3.63235	−	2.63906i	0.216688	−	0.157433i	−0.474147	−	0.880446i	$-0.657243\pi$
$281$	3.63235	−	2.63906i	0.216688	−	0.157433i	0.690834	+	0.723013i	$0.257243\pi$
$282$		0			0
$283$	−3.98074	+	25.1334i	−0.236631	+	1.49403i	0.527827	+	0.849352i	$0.323007\pi$
$283$	−3.98074	+	25.1334i	−0.236631	+	1.49403i	−0.764457	+	0.644675i	$0.776993\pi$
$284$		0			0
$285$	2.10649	−	0.173832i	0.124778	−	0.0102969i
$286$		0			0
$287$	−2.98058	+	5.84972i	−0.175938	+	0.345298i
$288$		0			0
$289$	−41.7933	−	13.5795i	−2.45843	−	0.798792i
$290$		0			0
$291$	21.3862	−	6.94880i	1.25368	−	0.407346i
$292$		0			0
$293$	−8.29104	−	8.29104i	−0.484368	−	0.484368i	0.422156	−	0.906523i	$-0.361274\pi$
$293$	−8.29104	−	8.29104i	−0.484368	−	0.484368i	−0.906523	+	0.422156i	$0.861274\pi$
$294$		0			0
$295$	−8.90879	+	21.7408i	−0.518690	+	1.26580i
$296$		0			0
$297$	−12.5750	+	1.99168i	−0.729674	+	0.115569i
$298$		0			0
$299$	21.2501			1.22893
$300$		0			0
$301$	34.9636			2.01527
$302$		0			0
$303$	−28.3812	+	4.49514i	−1.63046	+	0.258239i
$304$		0			0
$305$	−3.99814	+	2.47098i	−0.228933	+	0.141488i
$306$		0			0
$307$	−15.0113	−	15.0113i	−0.856740	−	0.856740i	0.134212	−	0.990953i	$-0.457150\pi$
$307$	−15.0113	−	15.0113i	−0.856740	−	0.856740i	−0.990953	+	0.134212i	$0.957150\pi$
$308$		0			0
$309$	10.3960	−	3.37785i	0.591406	−	0.192159i
$310$		0			0
$311$	−17.8463	−	5.79862i	−1.01197	−	0.328810i	−0.244332	−	0.969692i	$-0.578569\pi$
$311$	−17.8463	−	5.79862i	−1.01197	−	0.328810i	−0.767639	+	0.640882i	$0.778569\pi$
$312$		0			0
$313$	6.73195	−	13.2122i	0.380513	−	0.746798i	−0.618734	−	0.785600i	$-0.712354\pi$
$313$	6.73195	−	13.2122i	0.380513	−	0.746798i	0.999247	+	0.0388023i	$0.0123543\pi$
$314$		0			0
$315$	4.43784	+	10.5999i	0.250044	+	0.597237i
$316$		0			0
$317$	−2.47741	+	15.6418i	−0.139145	+	0.878529i	0.815060	+	0.579377i	$0.196704\pi$
$317$	−2.47741	+	15.6418i	−0.139145	+	0.878529i	−0.954205	+	0.299152i	$0.903296\pi$
$318$		0			0
$319$	3.35596	−	2.43825i	0.187898	−	0.136516i
$320$		0			0
$321$	−6.76414	−	4.91444i	−0.377538	−	0.274297i
$322$		0			0
$323$	1.64285	+	3.22428i	0.0914107	+	0.179404i
$324$		0			0
$325$	18.2188	+	5.76712i	1.01060	+	0.319902i
$326$		0			0
$327$	−2.86857	+	1.46161i	−0.158632	+	0.0808271i
$328$		0			0
$329$	−3.28646	+	4.52343i	−0.181189	+	0.249385i
$330$		0			0
$331$	11.1337	+	15.3242i	0.611964	+	0.842296i	0.996737	−	0.0807153i	$-0.0257205\pi$
$331$	11.1337	+	15.3242i	0.611964	+	0.842296i	−0.384774	+	0.923011i	$0.625720\pi$
$332$		0			0
$333$	1.55519	+	0.246317i	0.0852237	+	0.0134981i
$334$		0			0
$335$	−16.7620	−	19.4756i	−0.915805	−	1.06406i
$336$		0			0
$337$	24.3115	+	12.3873i	1.32433	+	0.674780i	0.965934	−	0.258790i	$-0.0833237\pi$
$337$	24.3115	+	12.3873i	1.32433	+	0.674780i	0.358396	+	0.933570i	$0.383324\pi$
$338$		0			0
$339$	0.511107	−	1.57303i	0.0277595	−	0.0854351i
$340$		0			0
$341$	8.02707	+	24.7048i	0.434690	+	1.33784i
$342$		0			0
$343$	17.8249	−	17.8249i	0.962456	−	0.962456i
$344$		0			0
$345$	1.89319	−	25.2818i	0.101926	−	1.36113i
$346$		0			0
$347$	−3.77107	−	23.8096i	−0.202441	−	1.27816i	−0.854282	−	0.519809i	$-0.826003\pi$
$347$	−3.77107	−	23.8096i	−0.202441	−	1.27816i	0.651841	−	0.758356i	$-0.273997\pi$
$348$		0			0
$349$			17.6117i			0.942731i	0.881938	+	0.471366i	$0.156239\pi$
$349$			17.6117i			0.942731i	−0.881938	+	0.471366i	$0.843761\pi$
$350$		0			0
$351$			14.3532i			0.766116i
$352$		0			0
$353$	−1.73275	−	10.9402i	−0.0922250	−	0.582286i	−0.989915	−	0.141659i	$-0.954756\pi$
$353$	−1.73275	−	10.9402i	−0.0922250	−	0.582286i	0.897690	−	0.440627i	$-0.145244\pi$
$354$		0			0
$355$	3.72136	−	0.908373i	0.197509	−	0.0482114i
$356$		0			0
$357$	−49.9400	+	49.9400i	−2.64310	+	2.64310i
$358$		0			0
$359$	−8.01444	−	24.6659i	−0.422986	−	1.30182i	−0.904910	−	0.425603i	$-0.860062\pi$
$359$	−8.01444	−	24.6659i	−0.422986	−	1.30182i	0.481924	−	0.876213i	$-0.339938\pi$
$360$		0			0
$361$	−5.80493	+	17.8657i	−0.305522	+	0.940301i
$362$		0			0
$363$	0.896651	+	0.456866i	0.0470620	+	0.0239793i
$364$		0			0
$365$	−13.4197	−	3.16795i	−0.702417	−	0.165818i
$366$		0			0
$367$	−17.9407	−	2.84153i	−0.936497	−	0.148327i	−0.330511	−	0.943802i	$-0.607221\pi$
$367$	−17.9407	−	2.84153i	−0.936497	−	0.148327i	−0.605986	+	0.795476i	$0.707221\pi$
$368$		0			0
$369$	−1.00760	−	1.38685i	−0.0524538	−	0.0721964i
$370$		0			0
$371$	2.35906	−	3.24696i	0.122476	−	0.168574i
$372$		0			0
$373$	−2.07223	+	1.05585i	−0.107296	+	0.0546701i	−0.506815	−	0.862055i	$-0.669177\pi$
$373$	−2.07223	+	1.05585i	−0.107296	+	0.0546701i	0.399519	+	0.916725i	$0.369177\pi$
$374$		0			0
$375$	8.48442	−	21.1616i	0.438134	−	1.09278i
$376$		0			0
$377$	−2.12308	−	4.16678i	−0.109344	−	0.214600i
$378$		0			0
$379$	−22.5526	−	16.3854i	−1.15845	−	0.841664i	−0.168870	−	0.985638i	$-0.554012\pi$
$379$	−22.5526	−	16.3854i	−1.15845	−	0.841664i	−0.989581	+	0.143975i	$0.954012\pi$
$380$		0			0
$381$	−8.31677	+	6.04249i	−0.426081	+	0.309566i
$382$		0			0
$383$	−5.09982	+	32.1990i	−0.260589	+	1.64529i	0.416314	+	0.909221i	$0.363322\pi$
$383$	−5.09982	+	32.1990i	−0.260589	+	1.64529i	−0.676903	+	0.736072i	$0.736678\pi$
$384$		0			0
$385$	−7.72694	+	32.7318i	−0.393801	+	1.66817i
$386$		0			0
$387$	−4.14458	+	8.13419i	−0.210681	+	0.413484i
$388$		0			0
$389$	7.24292	+	2.35337i	0.367231	+	0.119321i	0.486819	−	0.873503i	$-0.338157\pi$
$389$	7.24292	+	2.35337i	0.367231	+	0.119321i	−0.119588	+	0.992824i	$0.538157\pi$
$390$		0			0
$391$	41.2807	−	13.4129i	2.08765	−	0.678319i
$392$		0			0
$393$	−2.23550	−	2.23550i	−0.112766	−	0.112766i
$394$		0			0
$395$	−8.88212	−	36.3877i	−0.446908	−	1.83086i
$396$		0			0
$397$	30.3958	−	4.81421i	1.52552	−	0.241619i	0.663377	−	0.748285i	$-0.269122\pi$
$397$	30.3958	−	4.81421i	1.52552	−	0.241619i	0.862142	+	0.506667i	$0.169122\pi$
$398$		0			0
$399$	4.19357			0.209941
$400$		0			0
$401$	20.2946			1.01346			0.506732	−	0.862104i	$-0.330853\pi$
$401$	20.2946			1.01346			0.506732	+	0.862104i	$0.330853\pi$
$402$		0			0
$403$	28.9238	−	4.58108i	1.44080	−	0.228200i
$404$		0			0
$405$	24.8253	+	1.85901i	1.23358	+	0.0923750i
$406$		0			0
$407$	3.25852	+	3.25852i	0.161519	+	0.161519i
$408$		0			0
$409$	−16.9278	+	5.50016i	−0.837024	+	0.271966i	−0.696001	−	0.718041i	$-0.745039\pi$
$409$	−16.9278	+	5.50016i	−0.837024	+	0.271966i	−0.141023	+	0.990006i	$0.545039\pi$
$410$		0			0
$411$	24.3859	+	7.92345i	1.20287	+	0.390835i
$412$		0			0
$413$	−21.1630	+	41.5347i	−1.04136	+	2.04379i
$414$		0			0
$415$	−12.1658	+	10.4707i	−0.597195	+	0.513986i
$416$		0			0
$417$	−1.65849	+	10.4713i	−0.0812167	+	0.512782i
$418$		0			0
$419$	−13.9634	+	10.1450i	−0.682159	+	0.495617i	−0.874073	−	0.485794i	$-0.838530\pi$
$419$	−13.9634	+	10.1450i	−0.682159	+	0.495617i	0.191914	+	0.981412i	$0.438530\pi$
$420$		0			0
$421$	22.6049	+	16.4235i	1.10170	+	0.800430i	0.981336	−	0.192300i	$-0.0615946\pi$
$421$	22.6049	+	16.4235i	1.10170	+	0.800430i	0.120362	+	0.992730i	$0.461595\pi$
$422$		0			0
$423$	−0.662787	−	1.30079i	−0.0322258	−	0.0632467i
$424$		0			0
$425$	39.0322	−	0.296310i	1.89334	−	0.0143732i
$426$		0			0
$427$	−8.30878	+	4.23354i	−0.402090	+	0.204875i
$428$		0			0
$429$	15.5308	−	21.3763i	0.749834	−	1.03206i
$430$		0			0
$431$	7.16187	+	9.85746i	0.344975	+	0.474817i	0.945886	−	0.324498i	$-0.105196\pi$
$431$	7.16187	+	9.85746i	0.344975	+	0.474817i	−0.600911	+	0.799316i	$0.705196\pi$
$432$		0			0
$433$	−34.4645	−	5.45864i	−1.65626	−	0.262326i	−0.742877	−	0.669428i	$-0.766539\pi$
$433$	−34.4645	−	5.45864i	−1.65626	−	0.262326i	−0.913383	+	0.407102i	$0.866539\pi$
$434$		0			0
$435$	−5.14647	+	2.15466i	−0.246754	+	0.103308i
$436$		0			0
$437$	−2.29637	−	1.17006i	−0.109850	−	0.0559714i
$438$		0			0
$439$	−1.07430	+	3.30636i	−0.0512736	+	0.157804i	−0.973415	−	0.229050i	$-0.926438\pi$
$439$	−1.07430	+	3.30636i	−0.0512736	+	0.157804i	0.922141	+	0.386854i	$0.126438\pi$
$440$		0			0
$441$	4.53968	+	13.9717i	0.216175	+	0.665319i
$442$		0			0
$443$	2.50489	−	2.50489i	0.119011	−	0.119011i	−0.645093	−	0.764104i	$-0.723181\pi$
$443$	2.50489	−	2.50489i	0.119011	−	0.119011i	0.764104	+	0.645093i	$0.223181\pi$
$444$		0			0
$445$	−9.09642	−	14.7183i	−0.431212	−	0.697715i
$446$		0			0
$447$	−2.57165	−	16.2368i	−0.121635	−	0.767974i
$448$		0			0
$449$		−	20.1589i		−	0.951358i	−0.879619	−	0.475679i	$-0.842202\pi$
$449$		−	20.1589i		−	0.951358i	0.879619	−	0.475679i	$-0.157798\pi$
$450$		0			0
$451$		−	5.01701i		−	0.236242i
$452$		0			0
$453$	5.04783	+	31.8708i	0.237168	+	1.49742i
$454$		0			0
$455$	35.0834	+	14.3763i	1.64473	+	0.673969i
$456$		0			0
$457$	−12.1697	+	12.1697i	−0.569275	+	0.569275i	−0.931925	−	0.362650i	$-0.881872\pi$
$457$	−12.1697	+	12.1697i	−0.569275	+	0.569275i	0.362650	+	0.931925i	$0.381872\pi$
$458$		0			0
$459$	9.05961	+	27.8826i	0.422866	+	1.30145i
$460$		0			0
$461$	5.73768	−	17.6588i	0.267231	−	0.822451i	−0.723941	−	0.689862i	$-0.757671\pi$
$461$	5.73768	−	17.6588i	0.267231	−	0.822451i	0.991171	−	0.132589i	$-0.0423290\pi$
$462$		0			0
$463$	11.7335	+	5.97851i	0.545301	+	0.277845i	0.704863	−	0.709343i	$-0.251008\pi$
$463$	11.7335	+	5.97851i	0.545301	+	0.277845i	−0.159562	+	0.987188i	$0.551008\pi$
$464$		0			0
$465$	−2.87337	−	34.8195i	−0.133249	−	1.61471i
$466$		0			0
$467$	−25.2095	−	3.99280i	−1.16656	−	0.184765i	−0.457036	−	0.889448i	$-0.651089\pi$
$467$	−25.2095	−	3.99280i	−1.16656	−	0.184765i	−0.709522	+	0.704684i	$0.751089\pi$
$468$		0			0
$469$	−29.9659	−	41.2445i	−1.38370	−	1.90450i
$470$		0			0
$471$	−12.6293	+	17.3828i	−0.581929	+	0.800956i
$472$		0			0
$473$	−23.8061	+	12.1298i	−1.09460	+	0.557729i
$474$		0			0
$475$	−1.65125	−	1.62637i	−0.0757645	−	0.0746229i
$476$		0			0
$477$	0.475756	+	0.933723i	0.0217833	+	0.0427522i
$478$		0			0
$479$	10.4934	+	7.62388i	0.479455	+	0.348344i	0.801114	−	0.598511i	$-0.204241\pi$
$479$	10.4934	+	7.62388i	0.479455	+	0.348344i	−0.321660	+	0.946855i	$0.604241\pi$
$480$		0			0
$481$	4.20295	−	3.05362i	0.191638	−	0.139233i
$482$		0			0
$483$	7.86873	−	49.6812i	0.358040	−	2.26057i
$484$		0			0
$485$	−21.0728	−	12.8036i	−0.956866	−	0.581384i
$486$		0			0
$487$	−12.8000	+	25.1215i	−0.580025	+	1.13836i	0.395498	+	0.918467i	$0.370572\pi$
$487$	−12.8000	+	25.1215i	−0.580025	+	1.13836i	−0.975523	+	0.219897i	$0.929428\pi$
$488$		0			0
$489$	−13.2014	−	4.28938i	−0.596986	−	0.193973i
$490$		0			0
$491$	−29.4078	+	9.55517i	−1.32716	+	0.431219i	−0.884946	−	0.465693i	$-0.845805\pi$
$491$	−29.4078	+	9.55517i	−1.32716	+	0.431219i	−0.442209	+	0.896912i	$0.645805\pi$
$492$		0			0
$493$	−6.75435	−	6.75435i	−0.304201	−	0.304201i
$494$		0			0
$495$	−6.69903	−	5.67768i	−0.301099	−	0.255193i
$496$		0			0
$497$	7.50654	−	1.18892i	0.336714	−	0.0533303i
$498$		0			0
$499$	−29.4300			−1.31747			−0.658733	−	0.752377i	$-0.728907\pi$
$499$	−29.4300			−1.31747			−0.658733	+	0.752377i	$0.728907\pi$
$500$		0			0
$501$	−10.8426			−0.484413
$502$		0			0
$503$	−17.2261	+	2.72834i	−0.768073	+	0.121651i	−0.528162	−	0.849144i	$-0.677118\pi$
$503$	−17.2261	+	2.72834i	−0.768073	+	0.121651i	−0.239912	+	0.970795i	$0.577118\pi$
$504$		0			0
$505$	24.0371	+	20.3723i	1.06963	+	0.906556i
$506$		0			0
$507$	−2.31779	−	2.31779i	−0.102937	−	0.102937i
$508$		0			0
$509$	19.0616	−	6.19349i	0.844891	−	0.274522i	0.145586	−	0.989346i	$-0.453493\pi$
$509$	19.0616	−	6.19349i	0.844891	−	0.274522i	0.699304	+	0.714824i	$0.253493\pi$
$510$		0			0
$511$	−26.0180	−	8.45377i	−1.15097	−	0.373973i
$512$		0			0
$513$	0.790303	−	1.55106i	0.0348927	−	0.0684809i
$514$		0			0
$515$	−10.2436	−	6.22393i	−0.451387	−	0.274259i
$516$		0			0
$517$	0.668395	−	4.22008i	0.0293960	−	0.185599i
$518$		0			0
$519$	33.2260	−	24.1401i	1.45846	−	1.05963i
$520$		0			0
$521$	17.0280	+	12.3716i	0.746011	+	0.542009i	0.894588	−	0.446892i	$-0.147469\pi$
$521$	17.0280	+	12.3716i	0.746011	+	0.542009i	−0.148577	+	0.988901i	$0.547469\pi$
$522$		0			0
$523$	5.05993	+	9.93068i	0.221255	+	0.434238i	0.974776	−	0.223186i	$-0.0716459\pi$
$523$	5.05993	+	9.93068i	0.221255	+	0.434238i	−0.753520	+	0.657425i	$0.771646\pi$
$524$		0			0
$525$	20.2294	−	40.4588i	0.882883	−	1.76577i
$526$		0			0
$527$	53.2961	−	27.1557i	2.32161	−	1.18292i
$528$		0			0
$529$	−4.65148	+	6.40221i	−0.202238	+	0.278357i
$530$		0			0
$531$	−7.15429	−	9.84703i	−0.310470	−	0.427325i
$532$		0			0
$533$	−5.58631	−	0.884785i	−0.241970	−	0.0383243i
$534$		0			0
$535$	0.754004	+	9.13701i	0.0325984	+	0.395027i
$536$		0			0
$537$	18.8102	+	9.58425i	0.811718	+	0.413591i
$538$		0			0
$539$	−13.2861	+	40.8905i	−0.572275	+	1.76128i
$540$		0			0
$541$	1.88970	+	5.81589i	0.0812444	+	0.250045i	0.983425	−	0.181313i	$-0.0580347\pi$
$541$	1.88970	+	5.81589i	0.0812444	+	0.250045i	−0.902181	+	0.431358i	$0.858035\pi$
$542$		0			0
$543$	−21.1851	+	21.1851i	−0.909138	+	0.909138i
$544$		0			0
$545$	3.26664	+	1.33858i	0.139927	+	0.0573386i
$546$		0			0
$547$	1.65747	+	10.4648i	0.0708682	+	0.447444i	0.997451	+	0.0713535i	$0.0227319\pi$
$547$	1.65747	+	10.4648i	0.0708682	+	0.447444i	−0.926583	+	0.376091i	$0.877268\pi$
$548$		0			0
$549$		−	2.43486i		−	0.103917i
$550$		0			0
$551$			0.567177i			0.0241626i
$552$		0			0
$553$	−11.6253	−	73.3994i	−0.494359	−	3.12126i
$554$		0			0
$555$	−3.25852	−	5.27240i	−0.138317	−	0.223801i
$556$		0			0
$557$	−23.5420	+	23.5420i	−0.997506	+	0.997506i	−0.999997	−	0.00249078i	$-0.999207\pi$
$557$	−23.5420	+	23.5420i	−0.997506	+	0.997506i	0.00249078	+	0.999997i	$0.499207\pi$
$558$		0			0
$559$	9.30786	+	28.6466i	0.393680	+	1.21162i
$560$		0			0
$561$	16.6777	−	51.3287i	0.704133	−	2.16710i
$562$		0			0
$563$	−16.5402	−	8.42768i	−0.697088	−	0.355184i	0.0692697	−	0.997598i	$-0.477933\pi$
$563$	−16.5402	−	8.42768i	−0.697088	−	0.355184i	−0.766358	+	0.642414i	$0.777933\pi$
$564$		0			0
$565$	−1.67294	+	0.700407i	−0.0703813	+	0.0294664i
$566$		0			0
$567$	48.7842	+	7.72666i	2.04874	+	0.324489i
$568$		0			0
$569$	17.9240	+	24.6702i	0.751412	+	1.03423i	0.997880	+	0.0650792i	$0.0207300\pi$
$569$	17.9240	+	24.6702i	0.751412	+	1.03423i	−0.246468	+	0.969151i	$0.579270\pi$
$570$		0			0
$571$	0.613924	−	0.844994i	0.0256919	−	0.0353619i	−0.795978	−	0.605326i	$-0.793043\pi$
$571$	0.613924	−	0.844994i	0.0256919	−	0.0353619i	0.821670	+	0.569964i	$0.193043\pi$
$572$		0			0
$573$	17.8765	−	9.10855i	0.746803	−	0.380515i
$574$		0			0
$575$	−22.3660	+	16.5107i	−0.932725	+	0.688543i
$576$		0			0
$577$	−14.6237	−	28.7007i	−0.608794	−	1.19483i	−0.965449	−	0.260590i	$-0.916083\pi$
$577$	−14.6237	−	28.7007i	−0.608794	−	1.19483i	0.356655	−	0.934236i	$-0.383917\pi$
$578$		0			0
$579$	−23.9786	−	17.4214i	−0.996515	−	0.724010i
$580$		0			0
$581$	−25.7642	+	18.7188i	−1.06888	+	0.776585i
$582$		0			0
$583$	−0.479781	+	3.02922i	−0.0198705	+	0.125457i
$584$		0			0
$585$	−7.50337	+	6.45790i	−0.310226	+	0.267001i
$586$		0			0
$587$	−12.5595	+	24.6494i	−0.518386	+	1.01739i	0.472327	+	0.881423i	$0.343414\pi$
$587$	−12.5595	+	24.6494i	−0.518386	+	1.01739i	−0.990713	+	0.135967i	$0.956586\pi$
$588$		0			0
$589$	−3.37785	−	1.09753i	−0.139182	−	0.0452230i
$590$		0			0
$591$	−27.5670	+	8.95706i	−1.13395	+	0.368444i
$592$		0			0
$593$	25.4162	+	25.4162i	1.04372	+	1.04372i	0.999000	+	0.0447166i	$0.0142385\pi$
$593$	25.4162	+	25.4162i	1.04372	+	1.04372i	0.0447166	+	0.999000i	$0.485762\pi$
$594$		0			0
$595$	77.2275	+	5.78308i	3.16602	+	0.237083i
$596$		0			0
$597$	−30.5528	+	4.83909i	−1.25044	+	0.198051i
$598$		0			0
$599$	17.7420			0.724918			0.362459	−	0.932000i	$-0.381937\pi$
$599$	17.7420			0.724918			0.362459	+	0.932000i	$0.381937\pi$
$600$		0			0
$601$	32.5333			1.32706			0.663531	−	0.748148i	$-0.269057\pi$
$601$	32.5333			1.32706			0.663531	+	0.748148i	$0.269057\pi$
$602$		0			0
$603$	13.1476	−	2.08237i	0.535411	−	0.0848008i
$604$		0			0
$605$	−0.261673	−	1.07201i	−0.0106385	−	0.0435833i
$606$		0			0
$607$	18.9437	+	18.9437i	0.768903	+	0.768903i	0.977913	−	0.209011i	$-0.0670244\pi$
$607$	18.9437	+	18.9437i	0.768903	+	0.768903i	−0.209011	+	0.977913i	$0.567024\pi$
$608$		0			0
$609$	−10.5278	+	3.42069i	−0.426607	+	0.138613i
$610$		0			0
$611$	−4.58108	−	1.48848i	−0.185331	−	0.0602176i
$612$		0			0
$613$	19.1250	−	37.5349i	0.772452	−	1.51602i	−0.0820818	−	0.996626i	$-0.526157\pi$
$613$	19.1250	−	37.5349i	0.772452	−	1.51602i	0.854534	−	0.519396i	$-0.173843\pi$
$614$		0			0
$615$	−1.55034	+	6.56735i	−0.0625157	+	0.264821i
$616$		0			0
$617$	2.30094	−	14.5276i	0.0926325	−	0.584859i	−0.897089	−	0.441850i	$-0.854322\pi$
$617$	2.30094	−	14.5276i	0.0926325	−	0.584859i	0.989721	−	0.143009i	$-0.0456777\pi$
$618$		0			0
$619$	28.6010	−	20.7799i	1.14957	−	0.835213i	0.161148	−	0.986930i	$-0.448480\pi$
$619$	28.6010	−	20.7799i	1.14957	−	0.835213i	0.988424	+	0.151717i	$0.0484802\pi$
$620$		0			0
$621$	−16.8925	−	12.2731i	−0.677872	−	0.492503i
$622$		0			0
$623$	−15.5849	−	30.5871i	−0.624396	−	1.22545i
$624$		0			0
$625$	−23.6564	+	8.08551i	−0.946255	+	0.323420i
$626$		0			0
$627$	−2.85532	+	1.45486i	−0.114031	+	0.0581015i
$628$		0			0
$629$	6.23727	−	8.58486i	0.248696	−	0.342301i
$630$		0			0
$631$	−15.8748	−	21.8497i	−0.631965	−	0.869825i	0.366190	−	0.930540i	$-0.380662\pi$
$631$	−15.8748	−	21.8497i	−0.631965	−	0.869825i	−0.998155	+	0.0607152i	$0.980662\pi$
$632$		0			0
$633$	−14.0230	−	2.22102i	−0.557364	−	0.0882777i
$634$		0			0
$635$	10.9709	+	2.58989i	0.435368	+	0.102777i
$636$		0			0
$637$	43.1875	+	22.0051i	1.71115	+	0.871875i
$638$		0			0
$639$	−0.613225	+	1.88731i	−0.0242588	+	0.0746609i
$640$		0			0
$641$	4.77172	+	14.6859i	0.188472	+	0.580057i	0.999991	−	0.00426935i	$-0.00135898\pi$
$641$	4.77172	+	14.6859i	0.188472	+	0.580057i	−0.811519	+	0.584326i	$0.801359\pi$
$642$		0			0
$643$	6.76567	−	6.76567i	0.266812	−	0.266812i	−0.561002	−	0.827814i	$-0.689584\pi$
$643$	6.76567	−	6.76567i	0.266812	−	0.266812i	0.827814	+	0.561002i	$0.189584\pi$
$644$		0			0
$645$	34.9109	−	8.52163i	1.37461	−	0.335539i
$646$		0			0
$647$	−0.544922	−	3.44050i	−0.0214231	−	0.135260i	0.974659	−	0.223697i	$-0.0718127\pi$
$647$	−0.544922	−	3.44050i	−0.0214231	−	0.135260i	−0.996082	+	0.0884372i	$0.971813\pi$
$648$		0			0
$649$		−	35.6222i		−	1.39829i
$650$		0			0
$651$		−	69.3181i		−	2.71679i
$652$		0			0
$653$	2.45959	+	15.5293i	0.0962513	+	0.607707i	0.987914	+	0.155006i	$0.0495396\pi$
$653$	2.45959	+	15.5293i	0.0962513	+	0.607707i	−0.891662	+	0.452701i	$0.850460\pi$
$654$		0			0
$655$	−0.258872	+	3.45699i	−0.0101150	+	0.135076i
$656$		0			0
$657$	5.05092	−	5.05092i	0.197055	−	0.197055i
$658$		0			0
$659$	1.70198	+	5.23816i	0.0662997	+	0.204050i	0.978718	−	0.205209i	$-0.0657874\pi$
$659$	1.70198	+	5.23816i	0.0662997	+	0.204050i	−0.912418	+	0.409259i	$0.865787\pi$
$660$		0			0
$661$	7.59689	−	23.3808i	0.295485	−	0.909409i	−0.687573	−	0.726115i	$-0.741324\pi$
$661$	7.59689	−	23.3808i	0.295485	−	0.909409i	0.983058	−	0.183294i	$-0.0586760\pi$
$662$		0			0
$663$	−54.2120	−	27.6224i	−2.10542	−	1.07277i
$664$		0			0
$665$	−2.99967	−	3.48529i	−0.116322	−	0.135154i
$666$		0			0
$667$	6.71935	+	1.06424i	0.260174	+	0.0412076i
$668$		0			0
$669$	−14.3768	−	19.7879i	−0.555838	−	0.765046i
$670$		0			0
$671$	4.18857	−	5.76507i	0.161698	−	0.222558i
$672$		0			0
$673$	−2.82484	+	1.43933i	−0.108890	+	0.0554821i	−0.507587	−	0.861601i	$-0.669462\pi$
$673$	−2.82484	+	1.43933i	−0.108890	+	0.0554821i	0.398697	+	0.917083i	$0.369462\pi$
$674$		0			0
$675$	−11.1520	−	15.1069i	−0.429240	−	0.581464i
$676$		0			0
$677$	−0.808560	−	1.58689i	−0.0310755	−	0.0609890i	0.874947	−	0.484219i	$-0.160896\pi$
$677$	−0.808560	−	1.58689i	−0.0310755	−	0.0609890i	−0.906022	+	0.423230i	$0.860896\pi$
$678$		0			0
$679$	−39.5784	−	28.7554i	−1.51888	−	1.10353i
$680$		0			0
$681$	−11.9683	+	8.69546i	−0.458625	+	0.333211i
$682$		0			0
$683$	5.36210	−	33.8550i	0.205175	−	1.29542i	−0.643065	−	0.765812i	$-0.722337\pi$
$683$	5.36210	−	33.8550i	0.205175	−	1.29542i	0.848240	−	0.529612i	$-0.177663\pi$
$684$		0			0
$685$	−10.8581	−	25.9348i	−0.414865	−	0.990919i
$686$		0			0
$687$	14.2125	−	27.8936i	0.542240	−	1.06421i
$688$		0			0
$689$	3.28834	+	1.06845i	0.125276	+	0.0407046i
$690$		0			0
$691$	−40.0444	+	13.0112i	−1.52336	+	0.494970i	−0.946728	−	0.322033i	$-0.895634\pi$
$691$	−40.0444	+	13.0112i	−1.52336	+	0.494970i	−0.576633	+	0.817003i	$0.695634\pi$
$692$		0			0
$693$	−12.3197	−	12.3197i	−0.467986	−	0.467986i
$694$		0			0
$695$	9.88906	−	6.11177i	0.375113	−	0.231833i
$696$		0			0
$697$	−11.4105	+	1.80724i	−0.432203	+	0.0684542i
$698$		0			0
$699$	−6.19151			−0.234185
$700$		0			0
$701$	−0.177945			−0.00672090			−0.00336045	−	0.999994i	$-0.501070\pi$
$701$	−0.177945			−0.00672090			−0.00336045	+	0.999994i	$0.501070\pi$
$702$		0			0
$703$	−0.622323	+	0.0985662i	−0.0234713	+	0.00371750i
$704$		0			0
$705$	−2.17902	+	5.31761i	−0.0820665	+	0.200273i
$706$		0			0
$707$	44.2047	+	44.2047i	1.66249	+	1.66249i
$708$		0			0
$709$	−31.1456	+	10.1198i	−1.16970	+	0.380057i	−0.828529	−	0.559945i	$-0.810822\pi$
$709$	−31.1456	+	10.1198i	−1.16970	+	0.380057i	−0.341167	+	0.940003i	$0.610822\pi$
$710$		0			0
$711$	18.4542	+	5.99614i	0.692088	+	0.224873i
$712$		0			0
$713$	−19.3406	+	37.9581i	−0.724311	+	1.42154i
$714$		0			0
$715$	−28.8751	+	2.38283i	−1.07987	+	0.0891129i
$716$		0			0
$717$	6.78877	−	42.8626i	0.253531	−	1.60073i
$718$		0			0
$719$	6.46726	−	4.69874i	0.241188	−	0.175233i	−0.460624	−	0.887595i	$-0.652374\pi$
$719$	6.46726	−	4.69874i	0.241188	−	0.175233i	0.701812	+	0.712362i	$0.252374\pi$
$720$		0			0
$721$	−19.2393	−	13.9782i	−0.716509	−	0.520574i
$722$		0			0
$723$	23.9286	+	46.9626i	0.889915	+	1.74656i
$724$		0			0
$725$	5.47202	+	2.73601i	0.203226	+	0.101613i
$726$		0			0
$727$	−23.4758	+	11.9615i	−0.870670	+	0.443629i	−0.831448	−	0.555602i	$-0.812488\pi$
$727$	−23.4758	+	11.9615i	−0.870670	+	0.443629i	−0.0392218	+	0.999231i	$0.512488\pi$
$728$		0			0
$729$	5.92358	−	8.15311i	0.219392	−	0.301967i
$730$		0			0
$731$	36.1631	+	49.7742i	1.33754	+	1.84096i
$732$		0			0
$733$	0.729982	+	0.115618i	0.0269625	+	0.00427044i	0.169901	−	0.985461i	$-0.445655\pi$
$733$	0.729982	+	0.115618i	0.0269625	+	0.00427044i	−0.142939	+	0.989732i	$0.545655\pi$
$734$		0			0
$735$	30.0277	−	49.4208i	1.10759	−	1.82291i
$736$		0			0
$737$	34.7120	+	17.6867i	1.27863	+	0.651497i
$738$		0			0
$739$	−3.59062	+	11.0508i	−0.132083	+	0.406510i	−0.995125	−	0.0986224i	$-0.968556\pi$
$739$	−3.59062	+	11.0508i	−0.132083	+	0.406510i	0.863042	+	0.505133i	$0.168556\pi$
$740$		0			0
$741$	1.11639	+	3.43590i	0.0410117	+	0.126221i
$742$		0			0
$743$	−17.6779	+	17.6779i	−0.648540	+	0.648540i	−0.952640	−	0.304100i	$-0.901644\pi$
$743$	−17.6779	+	17.6779i	−0.648540	+	0.648540i	0.304100	+	0.952640i	$0.401644\pi$
$744$		0			0
$745$	−11.6549	+	13.7515i	−0.427004	+	0.503817i
$746$		0			0
$747$	−1.30079	−	8.21289i	−0.0475935	−	0.300494i
$748$		0			0
$749$			18.1898i			0.664641i
$750$		0			0
$751$		−	8.62520i		−	0.314738i	−0.987540	−	0.157369i	$-0.949699\pi$
$751$		−	8.62520i		−	0.314738i	0.987540	−	0.157369i	$-0.0503012\pi$
$752$		0			0
$753$	4.73166	+	29.8745i	0.172431	+	1.08869i
$754$		0			0
$755$	22.8772	−	26.9925i	0.832585	−	0.982358i
$756$		0			0
$757$	20.2477	−	20.2477i	0.735915	−	0.735915i	−0.235870	−	0.971785i	$-0.575794\pi$
$757$	20.2477	−	20.2477i	0.735915	−	0.735915i	0.971785	+	0.235870i	$0.0757938\pi$
$758$		0			0
$759$	11.8781	+	36.5569i	0.431146	+	1.32693i
$760$		0			0
$761$	−10.9950	+	33.8391i	−0.398568	+	1.22667i	0.527580	+	0.849506i	$0.323100\pi$
$761$	−10.9950	+	33.8391i	−0.398568	+	1.22667i	−0.926148	+	0.377161i	$0.876900\pi$
$762$		0			0
$763$	6.24077	+	3.17983i	0.225931	+	0.115118i
$764$		0			0
$765$	−10.4999	+	17.2812i	−0.379626	+	0.624805i
$766$		0			0
$767$	−39.6645	−	6.28224i	−1.43220	−	0.226838i
$768$		0			0
$769$	5.38162	+	7.40717i	0.194066	+	0.267109i	0.894950	−	0.446166i	$-0.147211\pi$
$769$	5.38162	+	7.40717i	0.194066	+	0.267109i	−0.700884	+	0.713275i	$0.747211\pi$
$770$		0			0
$771$	−21.4369	+	29.5054i	−0.772033	+	1.06261i
$772$		0			0
$773$	−4.35369	+	2.21832i	−0.156591	+	0.0797873i	−0.530530	−	0.847666i	$-0.678007\pi$
$773$	−4.35369	+	2.21832i	−0.156591	+	0.0797873i	0.373939	+	0.927453i	$0.378007\pi$
$774$		0			0
$775$	−26.8832	+	27.2945i	−0.965674	+	0.980448i
$776$		0			0
$777$	−5.58283	−	10.9569i	−0.200283	−	0.393077i
$778$		0			0
$779$	0.554960	+	0.403202i	0.0198835	+	0.0144462i
$780$		0			0
$781$	−4.69860	+	3.41373i	−0.168129	+	0.122153i
$782$		0			0
$783$	−0.718831	+	4.53852i	−0.0256889	+	0.162193i
$784$		0			0
$785$	23.4807	−	1.93767i	0.838061	−	0.0691585i
$786$		0			0
$787$	−2.38805	+	4.68681i	−0.0851248	+	0.167067i	−0.929645	−	0.368458i	$-0.879886\pi$
$787$	−2.38805	+	4.68681i	−0.0851248	+	0.167067i	0.844520	+	0.535524i	$0.179886\pi$
$788$		0			0
$789$	53.1700	+	17.2760i	1.89290	+	0.615041i
$790$		0			0
$791$	−3.42223	+	1.11195i	−0.121681	+	0.0395364i
$792$		0			0
$793$	−5.68058	−	5.68058i	−0.201723	−	0.201723i
$794$		0			0
$795$	1.56412	−	3.81704i	0.0554736	−	0.135376i
$796$		0			0
$797$	−29.1549	+	4.61769i	−1.03272	+	0.163567i	−0.649714	−	0.760179i	$-0.725111\pi$
$797$	−29.1549	+	4.61769i	−1.03272	+	0.163567i	−0.383007	+	0.923746i	$0.625111\pi$
$798$		0			0
$799$	−9.83876			−0.348070
$800$		0			0
$801$	8.96344			0.316707
$802$		0			0
$803$	20.6480	−	3.27032i	0.728653	−	0.115407i
$804$		0			0
$805$	−46.9187	+	28.9974i	−1.65367	+	1.02202i
$806$		0			0
$807$	−8.31486	−	8.31486i	−0.292697	−	0.292697i
$808$		0			0
$809$	29.7303	−	9.65994i	1.04526	−	0.339626i	0.264453	−	0.964398i	$-0.414808\pi$
$809$	29.7303	−	9.65994i	1.04526	−	0.339626i	0.780807	+	0.624773i	$0.214808\pi$
$810$		0			0
$811$	41.3581	+	13.4380i	1.45228	+	0.471874i	0.925702	−	0.378254i	$-0.123476\pi$
$811$	41.3581	+	13.4380i	1.45228	+	0.471874i	0.526576	+	0.850128i	$0.323476\pi$
$812$		0			0
$813$	9.07522	−	17.8111i	0.318282	−	0.624663i
$814$		0			0
$815$	5.87805	+	14.0399i	0.205899	+	0.491796i
$816$		0			0
$817$	0.571477	−	3.60817i	0.0199935	−	0.126234i
$818$		0			0
$819$	−15.8903	+	11.5450i	−0.555253	+	0.403415i
$820$		0			0
$821$	−40.1380	−	29.1620i	−1.40083	−	1.01776i	−0.994578	−	0.103997i	$-0.966837\pi$
$821$	−40.1380	−	29.1620i	−1.40083	−	1.01776i	−0.406249	−	0.913763i	$-0.633163\pi$
$822$		0			0
$823$	−6.19436	−	12.1571i	−0.215922	−	0.423771i	0.757485	−	0.652852i	$-0.226428\pi$
$823$	−6.19436	−	12.1571i	−0.215922	−	0.423771i	−0.973407	+	0.229082i	$0.926428\pi$
$824$		0			0
$825$	0.262404	+	34.5657i	0.00913572	+	1.20342i
$826$		0			0
$827$	23.8274	−	12.1406i	0.828558	−	0.422171i	0.0123460	−	0.999924i	$-0.496070\pi$
$827$	23.8274	−	12.1406i	0.828558	−	0.422171i	0.816212	+	0.577752i	$0.196070\pi$
$828$		0			0
$829$	−26.5793	+	36.5832i	−0.923136	+	1.27059i	0.0393407	+	0.999226i	$0.487474\pi$
$829$	−26.5793	+	36.5832i	−0.923136	+	1.27059i	−0.962477	+	0.271363i	$0.912526\pi$
$830$		0			0
$831$	11.2064	+	15.4243i	0.388746	+	0.535064i
$832$		0			0
$833$	97.7858	+	15.4878i	3.38808	+	0.536619i
$834$		0			0
$835$	7.75576	+	9.01134i	0.268399	+	0.311850i
$836$		0			0
$837$	−25.6384	−	13.0634i	−0.886192	−	0.451538i
$838$		0			0
$839$	−11.1825	+	34.4161i	−0.386062	+	1.18818i	0.549645	+	0.835398i	$0.314763\pi$
$839$	−11.1825	+	34.4161i	−0.386062	+	1.18818i	−0.935707	+	0.352778i	$0.885237\pi$
$840$		0			0
$841$	8.49885	+	26.1568i	0.293064	+	0.901957i
$842$		0			0
$843$	6.47407	−	6.47407i	0.222979	−	0.222979i
$844$		0			0
$845$	−0.268402	+	3.58425i	−0.00923330	+	0.123302i
$846$		0			0
$847$	−0.342490	−	2.16240i	−0.0117681	−	0.0743008i
$848$		0			0
$849$			51.8912i			1.78090i
$850$		0			0
$851$			7.55761i			0.259072i
$852$		0			0
$853$	1.36501	+	8.61833i	0.0467371	+	0.295086i	0.999975	−	0.00713613i	$-0.00227152\pi$
$853$	1.36501	+	8.61833i	0.0467371	+	0.295086i	−0.953237	+	0.302222i	$0.902272\pi$
$854$		0			0
$855$	1.16642	−	0.284720i	0.0398908	−	0.00973722i
$856$		0			0
$857$	−33.2545	+	33.2545i	−1.13595	+	1.13595i	−0.146781	+	0.989169i	$0.546891\pi$
$857$	−33.2545	+	33.2545i	−1.13595	+	1.13595i	−0.989169	+	0.146781i	$0.953109\pi$
$858$		0			0
$859$	5.11046	+	15.7284i	0.174367	+	0.536645i	0.999604	−	0.0281409i	$-0.00895872\pi$
$859$	5.11046	+	15.7284i	0.174367	+	0.536645i	−0.825237	+	0.564786i	$0.808959\pi$
$860$		0			0
$861$	−4.13713	+	12.7328i	−0.140993	+	0.433931i
$862$		0			0
$863$	33.5995	+	17.1198i	1.14374	+	0.582764i	0.920013	−	0.391888i	$-0.128178\pi$
$863$	33.5995	+	17.1198i	1.14374	+	0.582764i	0.223726	+	0.974652i	$0.428178\pi$
$864$		0			0
$865$	−43.8295	−	10.3467i	−1.49025	−	0.351800i
$866$		0			0
$867$	−88.5080	−	14.0183i	−3.00589	−	0.476086i
$868$		0			0
$869$	33.3796	+	45.9431i	1.13233	+	1.55851i
$870$		0			0
$871$	25.8154	−	35.5318i	0.874721	−	1.20395i
$872$		0			0
$873$	11.3815	−	5.79915i	0.385205	−	0.196272i
$874$		0			0
$875$	−48.0956	+	12.1276i	−1.62593	+	0.409986i
$876$		0			0
$877$	−9.78063	−	19.1956i	−0.330269	−	0.648188i	0.664839	−	0.746987i	$-0.268500\pi$
$877$	−9.78063	−	19.1956i	−0.330269	−	0.648188i	−0.995107	+	0.0987983i	$0.968500\pi$
$878$		0			0
$879$	−19.3439	−	14.0542i	−0.652454	−	0.474035i
$880$		0			0
$881$	8.59034	−	6.24125i	0.289416	−	0.210273i	−0.433598	−	0.901106i	$-0.642756\pi$
$881$	8.59034	−	6.24125i	0.289416	−	0.210273i	0.723014	+	0.690833i	$0.242756\pi$
$882$		0			0
$883$	−2.52020	+	15.9119i	−0.0848116	+	0.535479i	0.908301	+	0.418317i	$0.137380\pi$
$883$	−2.52020	+	15.9119i	−0.0848116	+	0.535479i	−0.993113	+	0.117162i	$0.962620\pi$
$884$		0			0
$885$	−11.0079	+	46.6301i	−0.370026	+	1.56745i
$886$		0			0
$887$	−3.23809	+	6.35512i	−0.108725	+	0.213384i	−0.938958	−	0.344032i	$-0.888207\pi$
$887$	−3.23809	+	6.35512i	−0.108725	+	0.213384i	0.830233	+	0.557416i	$0.188207\pi$
$888$		0			0
$889$	21.2704	+	6.91118i	0.713388	+	0.231794i
$890$		0			0
$891$	−35.8968	+	11.6636i	−1.20259	+	0.390745i
$892$		0			0
$893$	0.413091	+	0.413091i	0.0138236	+	0.0138236i
$894$		0			0
$895$	−5.48945	−	22.4888i	−0.183492	−	0.751718i
$896$		0			0
$897$	42.8000	−	6.77885i	1.42905	−	0.226339i
$898$		0			0
$899$	9.37522			0.312681
$900$		0			0
$901$	7.06236			0.235281
$902$		0			0
$903$	70.4204	−	11.1535i	2.34344	−	0.371165i
$904$		0			0
$905$	32.7607	+	2.45324i	1.08900	+	0.0815485i
$906$		0			0
$907$	−19.7382	−	19.7382i	−0.655396	−	0.655396i	0.298891	−	0.954287i	$-0.403383\pi$
$907$	−19.7382	−	19.7382i	−0.655396	−	0.655396i	−0.954287	+	0.298891i	$0.903383\pi$
$908$		0			0
$909$	−15.5241	+	5.04410i	−0.514903	+	0.167302i
$910$		0			0
$911$	7.60272	+	2.47027i	0.251889	+	0.0818438i	0.432240	−	0.901759i	$-0.357723\pi$
$911$	7.60272	+	2.47027i	0.251889	+	0.0818438i	−0.180351	+	0.983602i	$0.557723\pi$
$912$		0			0
$913$	11.0483	−	21.6835i	0.365646	−	0.717620i
$914$		0			0
$915$	−7.26442	+	6.25224i	−0.240154	+	0.206693i
$916$		0			0
$917$	−1.07596	+	6.79332i	−0.0355312	+	0.224335i
$918$		0			0
$919$	45.7747	−	33.2573i	1.50997	−	1.09706i	0.543778	−	0.839229i	$-0.316993\pi$
$919$	45.7747	−	33.2573i	1.50997	−	1.09706i	0.966191	−	0.257827i	$-0.0830066\pi$
$920$		0			0
$921$	−35.0230	−	25.4457i	−1.15405	−	0.838464i
$922$		0			0
$923$	2.97247	+	5.83381i	0.0978402	+	0.192022i
$924$		0			0
$925$	−2.05108	+	6.47953i	−0.0674391	+	0.213046i
$926$		0			0
$927$	5.53260	−	2.81900i	0.181715	−	0.0925882i
$928$		0			0
$929$	−35.5268	+	48.8984i	−1.16560	+	1.60431i	−0.477635	+	0.878558i	$0.658506\pi$
$929$	−35.5268	+	48.8984i	−1.16560	+	1.60431i	−0.687961	+	0.725748i	$0.741494\pi$
$930$		0			0
$931$	−3.45537	−	4.75591i	−0.113245	−	0.155869i
$932$		0			0
$933$	−37.7941	−	5.98600i	−1.23732	−	0.195973i
$934$		0			0
$935$	−54.5890	+	22.8547i	−1.78525	+	0.747427i
$936$		0			0
$937$	−16.3594	−	8.33555i	−0.534440	−	0.272311i	0.165873	−	0.986147i	$-0.446956\pi$
$937$	−16.3594	−	8.33555i	−0.534440	−	0.272311i	−0.700312	+	0.713837i	$0.746956\pi$
$938$		0			0
$939$	9.34413	−	28.7583i	0.304934	−	0.938491i
$940$		0			0
$941$	−17.3832	−	53.5000i	−0.566676	−	1.74405i	−0.662918	−	0.748692i	$-0.730682\pi$
$941$	−17.3832	−	53.5000i	−0.566676	−	1.74405i	0.0962423	−	0.995358i	$-0.469318\pi$
$942$		0			0
$943$	5.81806	−	5.81806i	0.189462	−	0.189462i
$944$		0			0
$945$	−19.5860	−	31.6908i	−0.637132	−	1.03090i
$946$		0			0
$947$	−8.31394	−	52.4921i	−0.270167	−	1.70576i	−0.633200	−	0.773989i	$-0.718259\pi$
$947$	−8.31394	−	52.4921i	−0.270167	−	1.70576i	0.363033	−	0.931776i	$-0.381741\pi$
$948$		0			0
$949$		−	23.5678i		−	0.765043i
$950$		0			0
$951$			32.2945i			1.04722i
$952$		0			0
$953$	0.0979909	+	0.618690i	0.00317424	+	0.0200413i	0.989225	−	0.146406i	$-0.0467705\pi$
$953$	0.0979909	+	0.618690i	0.00317424	+	0.0200413i	−0.986050	+	0.166447i	$0.946771\pi$
$954$		0			0
$955$	−20.3573	−	8.34188i	−0.658746	−	0.269937i
$956$		0			0
$957$	5.98145	−	5.98145i	0.193353	−	0.193353i
$958$		0			0
$959$	−17.2380	−	53.0532i	−0.556645	−	1.71318i
$960$		0			0
$961$	−8.56224	+	26.3519i	−0.276201	+	0.850060i
$962$		0			0
$963$	−4.23181	−	2.15622i	−0.136368	−	0.0694831i
$964$		0			0
$965$	2.67291	+	32.3903i	0.0860440	+	1.04268i
$966$		0			0
$967$	−14.8068	−	2.34516i	−0.476154	−	0.0754153i	−0.0862550	−	0.996273i	$-0.527490\pi$
$967$	−14.8068	−	2.34516i	−0.476154	−	0.0754153i	−0.389899	+	0.920858i	$0.627490\pi$
$968$		0			0
$969$	4.33743	+	5.96996i	0.139338	+	0.191783i
$970$		0			0
$971$	33.6414	−	46.3034i	1.07960	−	1.48595i	0.219647	−	0.975579i	$-0.429509\pi$
$971$	33.6414	−	46.3034i	1.07960	−	1.48595i	0.859956	−	0.510368i	$-0.170491\pi$
$972$		0			0
$973$	20.5511	−	10.4713i	0.658838	−	0.335695i
$974$		0			0
$975$	38.5344	+	5.80374i	1.23409	+	0.185868i
$976$		0			0
$977$	6.58360	+	12.9210i	0.210628	+	0.413381i	0.972016	−	0.234916i	$-0.0754816\pi$
$977$	6.58360	+	12.9210i	0.210628	+	0.413381i	−0.761388	+	0.648297i	$0.775482\pi$
$978$		0			0
$979$	21.2229	+	15.4194i	0.678288	+	0.492805i
$980$		0			0
$981$	−1.47956	+	1.07496i	−0.0472386	+	0.0343209i
$982$		0			0
$983$	2.85036	−	17.9964i	0.0909122	−	0.573997i	−0.899615	−	0.436683i	$-0.856153\pi$
$983$	2.85036	−	17.9964i	0.0909122	−	0.573997i	0.990528	−	0.137314i	$-0.0438469\pi$
$984$		0			0
$985$	27.1630	+	16.5040i	0.865484	+	0.525861i
$986$		0			0
$987$	−5.17630	+	10.1591i	−0.164763	+	0.323366i
$988$		0			0
$989$	−41.6737	−	13.5406i	−1.32515	−	0.430566i
$990$		0			0
$991$	19.9240	−	6.47370i	0.632907	−	0.205644i	0.0250446	−	0.999686i	$-0.492027\pi$
$991$	19.9240	−	6.47370i	0.632907	−	0.205644i	0.607862	+	0.794042i	$0.292027\pi$
$992$		0			0
$993$	27.3129	+	27.3129i	0.866750	+	0.866750i
$994$		0			0
$995$	25.8763	+	21.9311i	0.820334	+	0.695264i
$996$		0			0
$997$	47.9547	−	7.59528i	1.51874	−	0.240545i	0.659339	−	0.751846i	$-0.270836\pi$
$997$	47.9547	−	7.59528i	1.51874	−	0.240545i	0.859402	+	0.511301i	$0.170836\pi$
$998$		0			0
$999$	−5.10471			−0.161506

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.bi.b.303.2	yes	16
4.3	odd	2	inner	400.2.bi.b.303.1	✓	16
25.17	odd	20	inner	400.2.bi.b.367.1	yes	16
100.67	even	20	inner	400.2.bi.b.367.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.bi.b.303.1	✓	16	4.3	odd	2	inner
400.2.bi.b.303.2	yes	16	1.1	even	1	trivial
400.2.bi.b.367.1	yes	16	25.17	odd	20	inner
400.2.bi.b.367.2	yes	16	100.67	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)

\(f(q)\)	\(=\)	\(q+(2.01411 - 0.319003i) q^{3} +(-1.70582 - 1.44575i) q^{5} +(-3.13704 - 3.13704i) q^{7} +(1.10169 - 0.357960i) q^{9} +(3.22428 + 1.04763i) q^{11} +(1.73514 - 3.40540i) q^{13} +(-3.89690 - 2.36772i) q^{15} +(1.22123 - 7.71055i) q^{17} +(-0.375011 + 0.272461i) q^{19} +(-7.31906 - 5.31761i) q^{21} +(2.52419 + 4.95399i) q^{23} +(0.819639 + 4.93236i) q^{25} +(-3.34613 + 1.70494i) q^{27} +(0.719203 - 0.989898i) q^{29} +(4.50368 + 6.19878i) q^{31} +(6.82823 + 1.08149i) q^{33} +(0.815862 + 9.88660i) q^{35} +(1.21113 + 0.617102i) q^{37} +(2.40842 - 7.41234i) q^{39} +(-0.457300 - 1.40742i) q^{41} +(-5.57270 + 5.57270i) q^{43} +(-2.39680 - 0.982146i) q^{45} +(-0.197155 - 1.24479i) q^{47} +12.6821i q^{49} -15.9194i q^{51} +(0.141520 + 0.893520i) q^{53} +(-3.98543 - 6.44855i) q^{55} +(-0.668395 + 0.668395i) q^{57} +(-3.24696 - 9.99313i) q^{59} +(0.649536 - 1.99907i) q^{61} +(-4.57898 - 2.33311i) q^{63} +(-7.88316 + 3.30042i) q^{65} +(11.3499 + 1.79765i) q^{67} +(6.66432 + 9.17264i) q^{69} +(-1.00694 + 1.38593i) q^{71} +(5.49431 - 2.79949i) q^{73} +(3.22428 + 9.67283i) q^{75} +(-6.82823 - 13.4012i) q^{77} +(13.5517 + 9.84590i) q^{79} +(-9.00703 + 6.54399i) q^{81} +(1.12294 - 7.08995i) q^{83} +(-13.2307 + 11.3872i) q^{85} +(1.13277 - 2.22319i) q^{87} +(7.35916 + 2.39114i) q^{89} +(-16.1261 + 5.23968i) q^{91} +(11.0483 + 11.0483i) q^{93} +(1.03361 + 0.0774005i) q^{95} +(10.8914 - 1.72503i) q^{97} +3.92716 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 20 q^{9} + 20 q^{17} - 20 q^{21} - 20 q^{25} + 20 q^{29} + 60 q^{33} - 20 q^{37} + 28 q^{41} - 20 q^{45} + 60 q^{53} - 20 q^{57} - 12 q^{61} - 20 q^{65} - 80 q^{69} - 40 q^{73} - 60 q^{77} + 56 q^{81}+ \cdots + 40 q^{97}+O(q^{100}) \) 16 * q - 20 * q^9 + 20 * q^17 - 20 * q^21 - 20 * q^25 + 20 * q^29 + 60 * q^33 - 20 * q^37 + 28 * q^41 - 20 * q^45 + 60 * q^53 - 20 * q^57 - 12 * q^61 - 20 * q^65 - 80 * q^69 - 40 * q^73 - 60 * q^77 + 56 * q^81 - 60 * q^85 + 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more