LMFDB - Embedded newform 855.2.n.d.647.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(647,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("855.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.n (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 101x^{16} + 2922x^{12} + 18746x^{8} + 4405x^{4} + 1 $ x^20 + 101x^16 + 2922x^12 + 18746x^8 + 4405x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			647.7
Root			$0.496954 - 0.496954i$ of defining polynomial
Character	$\chi$	$=$	855.647
Dual form			855.2.n.d.818.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.496954 - 0.496954i) q^{2} +1.50607i q^{4} +(0.496954 + 2.18015i) q^{5} +(1.19020 + 1.19020i) q^{7} +(1.74236 + 1.74236i) q^{8} +O(q^{10})$	\(q+(0.496954 - 0.496954i) q^{2} +1.50607i q^{4} +(0.496954 + 2.18015i) q^{5} +(1.19020 + 1.19020i) q^{7} +(1.74236 + 1.74236i) q^{8} +(1.33040 + 0.836469i) q^{10} +0.0469465i q^{11} +(2.19020 - 2.19020i) q^{13} +1.18295 q^{14} -1.28040 q^{16} +(-3.23322 + 3.23322i) q^{17} -1.00000i q^{19} +(-3.28346 + 0.748449i) q^{20} +(0.0233302 + 0.0233302i) q^{22} +(-1.50308 - 1.50308i) q^{23} +(-4.50607 + 2.16687i) q^{25} -2.17686i q^{26} +(-1.79252 + 1.79252i) q^{28} -2.41942 q^{29} +6.47151 q^{31} +(-4.12102 + 4.12102i) q^{32} +3.21353i q^{34} +(-2.00333 + 3.18627i) q^{35} +(3.95939 + 3.95939i) q^{37} +(-0.496954 - 0.496954i) q^{38} +(-2.93272 + 4.66447i) q^{40} +6.30116i q^{41} +(0.207478 - 0.207478i) q^{43} -0.0707048 q^{44} -1.49393 q^{46} +(-1.62073 + 1.62073i) q^{47} -4.16687i q^{49} +(-1.16248 + 3.31615i) q^{50} +(3.29859 + 3.29859i) q^{52} +(-7.52281 - 7.52281i) q^{53} +(-0.102350 + 0.0233302i) q^{55} +4.14750i q^{56} +(-1.20234 + 1.20234i) q^{58} +7.50855 q^{59} +2.12568 q^{61} +(3.21604 - 3.21604i) q^{62} +1.53511i q^{64} +(5.86337 + 3.68652i) q^{65} +(6.14958 + 6.14958i) q^{67} +(-4.86947 - 4.86947i) q^{68} +(0.587870 + 2.57900i) q^{70} -5.33044i q^{71} +(11.3753 - 11.3753i) q^{73} +3.93527 q^{74} +1.50607 q^{76} +(-0.0558755 + 0.0558755i) q^{77} +11.2925i q^{79} +(-0.636301 - 2.79146i) q^{80} +(3.13139 + 3.13139i) q^{82} +(-6.43501 - 6.43501i) q^{83} +(-8.65566 - 5.44213i) q^{85} -0.206214i q^{86} +(-0.0817975 + 0.0817975i) q^{88} +4.38348 q^{89} +5.21353 q^{91} +(2.26375 - 2.26375i) q^{92} +1.61086i q^{94} +(2.18015 - 0.496954i) q^{95} +(-2.85099 - 2.85099i) q^{97} +(-2.07074 - 2.07074i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q+O(q^{10}) $ 20 * q	$ 20 q + 28 q^{10} + 20 q^{13} - 76 q^{16} + 32 q^{22} - 32 q^{25} - 16 q^{28} - 16 q^{31} + 4 q^{37} - 64 q^{40} + 24 q^{43} - 88 q^{46} - 12 q^{52} + 40 q^{55} + 116 q^{58} + 32 q^{61} + 24 q^{67} - 16 q^{70} + 20 q^{73} - 28 q^{76} + 92 q^{82} - 16 q^{85} - 32 q^{88} + 112 q^{91} - 36 q^{97}+O(q^{100}) $ 20 * q + 28 * q^10 + 20 * q^13 - 76 * q^16 + 32 * q^22 - 32 * q^25 - 16 * q^28 - 16 * q^31 + 4 * q^37 - 64 * q^40 + 24 * q^43 - 88 * q^46 - 12 * q^52 + 40 * q^55 + 116 * q^58 + 32 * q^61 + 24 * q^67 - 16 * q^70 + 20 * q^73 - 28 * q^76 + 92 * q^82 - 16 * q^85 - 32 * q^88 + 112 * q^91 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.496954	−	0.496954i	0.351400	−	0.351400i	−0.509230	−	0.860630i	$-0.670070\pi$
$2$	0.496954	−	0.496954i	0.351400	−	0.351400i	0.860630	+	0.509230i	$0.170070\pi$
$3$		0			0
$3$		0			0
$4$			1.50607i			0.753036i
$5$	0.496954	+	2.18015i	0.222245	+	0.974991i
$5$	0.496954	+	2.18015i	0.222245	+	0.974991i
$6$		0			0
$7$	1.19020	+	1.19020i	0.449852	+	0.449852i	0.895305	−	0.445453i	$-0.146957\pi$
$7$	1.19020	+	1.19020i	0.449852	+	0.449852i	−0.445453	+	0.895305i	$0.646957\pi$
$8$	1.74236	+	1.74236i	0.616017	+	0.616017i
$9$		0			0
$10$	1.33040	+	0.836469i	0.420708	+	0.264515i
$11$			0.0469465i			0.0141549i	0.999975	+	0.00707744i	$0.00225284\pi$
$11$			0.0469465i			0.0141549i	−0.999975	+	0.00707744i	$0.997747\pi$
$12$		0			0
$13$	2.19020	−	2.19020i	0.607451	−	0.607451i	−0.334828	−	0.942279i	$-0.608678\pi$
$13$	2.19020	−	2.19020i	0.607451	−	0.607451i	0.942279	+	0.334828i	$0.108678\pi$
$14$	1.18295			0.316156
$15$		0			0
$16$	−1.28040			−0.320100
$17$	−3.23322	+	3.23322i	−0.784171	+	0.784171i	−0.980532	−	0.196360i	$-0.937088\pi$
$17$	−3.23322	+	3.23322i	−0.784171	+	0.784171i	0.196360	+	0.980532i	$0.437088\pi$
$18$		0			0
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	−3.28346	+	0.748449i	−0.734204	+	0.167358i
$21$		0			0
$22$	0.0233302	+	0.0233302i	0.00497402	+	0.00497402i
$23$	−1.50308	−	1.50308i	−0.313414	−	0.313414i	0.532816	−	0.846231i	$-0.321134\pi$
$23$	−1.50308	−	1.50308i	−0.313414	−	0.313414i	−0.846231	+	0.532816i	$0.821134\pi$
$24$		0			0
$25$	−4.50607	+	2.16687i	−0.901215	+	0.433373i
$26$		−	2.17686i		−	0.426916i
$27$		0			0
$28$	−1.79252	+	1.79252i	−0.338755	+	0.338755i
$29$	−2.41942			−0.449275			−0.224638	−	0.974442i	$-0.572120\pi$
$29$	−2.41942			−0.449275			−0.224638	+	0.974442i	$0.572120\pi$
$30$		0			0
$31$	6.47151			1.16232			0.581159	−	0.813790i	$-0.302600\pi$
$31$	6.47151			1.16232			0.581159	+	0.813790i	$0.302600\pi$
$32$	−4.12102	+	4.12102i	−0.728500	+	0.728500i
$33$		0			0
$34$			3.21353i			0.551115i
$35$	−2.00333	+	3.18627i	−0.338624	+	0.538579i
$36$		0			0
$37$	3.95939	+	3.95939i	0.650919	+	0.650919i	0.953214	−	0.302295i	$-0.0977528\pi$
$37$	3.95939	+	3.95939i	0.650919	+	0.650919i	−0.302295	+	0.953214i	$0.597753\pi$
$38$	−0.496954	−	0.496954i	−0.0806166	−	0.0806166i
$39$		0			0
$40$	−2.93272	+	4.66447i	−0.463704	+	0.737517i
$41$			6.30116i			0.984076i	0.870574	+	0.492038i	$0.163748\pi$
$41$			6.30116i			0.984076i	−0.870574	+	0.492038i	$0.836252\pi$
$42$		0			0
$43$	0.207478	−	0.207478i	0.0316401	−	0.0316401i	−0.691110	−	0.722750i	$-0.742878\pi$
$43$	0.207478	−	0.207478i	0.0316401	−	0.0316401i	0.722750	+	0.691110i	$0.242878\pi$
$44$	−0.0707048			−0.0106591
$45$		0			0
$46$	−1.49393			−0.220268
$47$	−1.62073	+	1.62073i	−0.236408	+	0.236408i	−0.815361	−	0.578953i	$-0.803462\pi$
$47$	−1.62073	+	1.62073i	−0.236408	+	0.236408i	0.578953	+	0.815361i	$0.303462\pi$
$48$		0			0
$49$		−	4.16687i		−	0.595267i
$50$	−1.16248	+	3.31615i	−0.164399	+	0.468974i
$51$		0			0
$52$	3.29859	+	3.29859i	0.457433	+	0.457433i
$53$	−7.52281	−	7.52281i	−1.03334	−	1.03334i	−0.999425	−	0.0339124i	$-0.989203\pi$
$53$	−7.52281	−	7.52281i	−1.03334	−	1.03334i	−0.0339124	−	0.999425i	$-0.510797\pi$
$54$		0			0
$55$	−0.102350	+	0.0233302i	−0.0138009	+	0.00314585i
$56$			4.14750i			0.554232i
$57$		0			0
$58$	−1.20234	+	1.20234i	−0.157875	+	0.157875i
$59$	7.50855			0.977530			0.488765	−	0.872416i	$-0.337448\pi$
$59$	7.50855			0.977530			0.488765	+	0.872416i	$0.337448\pi$
$60$		0			0
$61$	2.12568			0.272165			0.136083	−	0.990697i	$-0.456549\pi$
$61$	2.12568			0.272165			0.136083	+	0.990697i	$0.456549\pi$
$62$	3.21604	−	3.21604i	0.408438	−	0.408438i
$63$		0			0
$64$			1.53511i			0.191889i
$65$	5.86337	+	3.68652i	0.727262	+	0.457257i
$66$		0			0
$67$	6.14958	+	6.14958i	0.751291	+	0.751291i	0.974720	−	0.223429i	$-0.0717251\pi$
$67$	6.14958	+	6.14958i	0.751291	+	0.751291i	−0.223429	+	0.974720i	$0.571725\pi$
$68$	−4.86947	−	4.86947i	−0.590510	−	0.590510i
$69$		0			0
$70$	0.587870	+	2.57900i	0.0702639	+	0.308249i
$71$		−	5.33044i		−	0.632607i	−0.948658	−	0.316304i	$-0.897558\pi$
$71$		−	5.33044i		−	0.632607i	0.948658	−	0.316304i	$-0.102442\pi$
$72$		0			0
$73$	11.3753	−	11.3753i	1.33137	−	1.33137i	0.427230	−	0.904143i	$-0.359489\pi$
$73$	11.3753	−	11.3753i	1.33137	−	1.33137i	0.904143	−	0.427230i	$-0.140511\pi$
$74$	3.93527			0.457466
$75$		0			0
$76$	1.50607			0.172758
$77$	−0.0558755	+	0.0558755i	−0.00636760	+	0.00636760i
$78$		0			0
$79$			11.2925i			1.27051i	0.772302	+	0.635255i	$0.219105\pi$
$79$			11.2925i			1.27051i	−0.772302	+	0.635255i	$0.780895\pi$
$80$	−0.636301	−	2.79146i	−0.0711406	−	0.312095i
$81$		0			0
$82$	3.13139	+	3.13139i	0.345804	+	0.345804i
$83$	−6.43501	−	6.43501i	−0.706334	−	0.706334i	0.259429	−	0.965762i	$-0.416466\pi$
$83$	−6.43501	−	6.43501i	−0.706334	−	0.706334i	−0.965762	+	0.259429i	$0.916466\pi$
$84$		0			0
$85$	−8.65566	−	5.44213i	−0.938838	−	0.590282i
$86$		−	0.206214i		−	0.0222366i
$87$		0			0
$88$	−0.0817975	+	0.0817975i	−0.00871965	+	0.00871965i
$89$	4.38348			0.464648			0.232324	−	0.972638i	$-0.425367\pi$
$89$	4.38348			0.464648			0.232324	+	0.972638i	$0.425367\pi$
$90$		0			0
$91$	5.21353			0.546526
$92$	2.26375	−	2.26375i	0.236013	−	0.236013i
$93$		0			0
$94$			1.61086i			0.166148i
$95$	2.18015	−	0.496954i	0.223678	−	0.0509864i
$96$		0			0
$97$	−2.85099	−	2.85099i	−0.289474	−	0.289474i	0.547398	−	0.836872i	$-0.315618\pi$
$97$	−2.85099	−	2.85099i	−0.289474	−	0.289474i	−0.836872	+	0.547398i	$0.815618\pi$
$98$	−2.07074	−	2.07074i	−0.209177	−	0.209177i
$99$		0			0
$100$	−3.26346	−	6.78647i	−0.326346	−	0.678647i
$101$			12.8146i			1.27510i	0.770411	+	0.637548i	$0.220051\pi$
$101$			12.8146i			1.27510i	−0.770411	+	0.637548i	$0.779949\pi$
$102$		0			0
$103$	−2.12568	+	2.12568i	−0.209450	+	0.209450i	−0.804034	−	0.594584i	$-0.797317\pi$
$103$	−2.12568	+	2.12568i	−0.209450	+	0.209450i	0.594584	+	0.804034i	$0.297317\pi$
$104$	7.63221			0.748400
$105$		0			0
$106$	−7.47698			−0.726229
$107$	4.64241	−	4.64241i	0.448799	−	0.448799i	−0.446156	−	0.894955i	$-0.647207\pi$
$107$	4.64241	−	4.64241i	0.448799	−	0.448799i	0.894955	+	0.446156i	$0.147207\pi$
$108$		0			0
$109$		−	9.66742i		−	0.925970i	−0.886366	−	0.462985i	$-0.846778\pi$
$109$		−	9.66742i		−	0.925970i	0.886366	−	0.462985i	$-0.153222\pi$
$110$	−0.0392693	+	0.0624574i	−0.00374418	+	0.00595508i
$111$		0			0
$112$	−1.52393	−	1.52393i	−0.143998	−	0.143998i
$113$	1.48522	+	1.48522i	0.139718	+	0.139718i	0.773507	−	0.633788i	$-0.218501\pi$
$113$	1.48522	+	1.48522i	0.139718	+	0.139718i	−0.633788	+	0.773507i	$0.718501\pi$
$114$		0			0
$115$	2.52998	−	4.02390i	0.235922	−	0.375231i
$116$		−	3.64382i		−	0.338321i
$117$		0			0
$118$	3.73141	−	3.73141i	0.343504	−	0.343504i
$119$	−7.69633			−0.705522
$120$		0			0
$121$	10.9978			0.999800
$122$	1.05637	−	1.05637i	0.0956389	−	0.0956389i
$123$		0			0
$124$			9.74656i			0.875267i
$125$	−6.96340	−	8.74706i	−0.622825	−	0.782361i
$126$		0			0
$127$	−2.81038	−	2.81038i	−0.249381	−	0.249381i	0.571336	−	0.820716i	$-0.306425\pi$
$127$	−2.81038	−	2.81038i	−0.249381	−	0.249381i	−0.820716	+	0.571336i	$0.806425\pi$
$128$	−7.47915	−	7.47915i	−0.661070	−	0.661070i
$129$		0			0
$130$	4.74586	−	1.08180i	0.416240	−	0.0948799i
$131$			16.3700i			1.43025i	0.698996	+	0.715126i	$0.253631\pi$
$131$			16.3700i			1.43025i	−0.698996	+	0.715126i	$0.746369\pi$
$132$		0			0
$133$	1.19020	−	1.19020i	0.103203	−	0.103203i
$134$	6.11213			0.528007
$135$		0			0
$136$	−11.2669			−0.966125
$137$	9.99742	−	9.99742i	0.854137	−	0.854137i	−0.136502	−	0.990640i	$-0.543586\pi$
$137$	9.99742	−	9.99742i	0.854137	−	0.854137i	0.990640	+	0.136502i	$0.0435861\pi$
$138$		0			0
$139$		−	9.72627i		−	0.824971i	−0.910964	−	0.412486i	$-0.864661\pi$
$139$		−	9.72627i		−	0.824971i	0.910964	−	0.412486i	$-0.135339\pi$
$140$	−4.79876	−	3.01716i	−0.405569	−	0.254996i
$141$		0			0
$142$	−2.64899	−	2.64899i	−0.222298	−	0.222298i
$143$	0.102822	+	0.102822i	0.00859840	+	0.00859840i
$144$		0			0
$145$	−1.20234	−	5.27469i	−0.0998490	−	0.438039i
$146$		−	11.3060i		−	0.935688i
$147$		0			0
$148$	−5.96313	+	5.96313i	−0.490166	+	0.490166i
$149$	19.1930			1.57235			0.786176	−	0.618003i	$-0.212058\pi$
$149$	19.1930			1.57235			0.786176	+	0.618003i	$0.212058\pi$
$150$		0			0
$151$	4.75191			0.386705			0.193352	−	0.981129i	$-0.438064\pi$
$151$	4.75191			0.386705			0.193352	+	0.981129i	$0.438064\pi$
$152$	1.74236	−	1.74236i	0.141324	−	0.141324i
$153$		0			0
$154$			0.0555351i			0.00447515i
$155$	3.21604	+	14.1088i	0.258319	+	1.13325i
$156$		0			0
$157$	−11.7090	−	11.7090i	−0.934479	−	0.934479i	0.0635027	−	0.997982i	$-0.479773\pi$
$157$	−11.7090	−	11.7090i	−0.934479	−	0.934479i	−0.997982	+	0.0635027i	$0.979773\pi$
$158$	5.61188	+	5.61188i	0.446457	+	0.446457i
$159$		0			0
$160$	−11.0324	−	6.93646i	−0.872186	−	0.548375i
$161$		−	3.57793i		−	0.281980i
$162$		0			0
$163$	4.14901	−	4.14901i	0.324976	−	0.324976i	−0.525697	−	0.850672i	$-0.676195\pi$
$163$	4.14901	−	4.14901i	0.324976	−	0.324976i	0.850672	+	0.525697i	$0.176195\pi$
$164$	−9.49001			−0.741045
$165$		0			0
$166$	−6.39581			−0.496411
$167$	−2.71580	+	2.71580i	−0.210155	+	0.210155i	−0.804333	−	0.594178i	$-0.797477\pi$
$167$	−2.71580	+	2.71580i	−0.210155	+	0.210155i	0.594178	+	0.804333i	$0.297477\pi$
$168$		0			0
$169$			3.40608i			0.262006i
$170$	−7.00596	+	1.59698i	−0.537332	+	0.122482i
$171$		0			0
$172$	0.312477	+	0.312477i	0.0238261	+	0.0238261i
$173$	−2.71512	−	2.71512i	−0.206427	−	0.206427i	0.596320	−	0.802747i	$-0.296629\pi$
$173$	−2.71512	−	2.71512i	−0.206427	−	0.206427i	−0.802747	+	0.596320i	$0.796629\pi$
$174$		0			0
$175$	−7.94211	−	2.78412i	−0.600367	−	0.210459i
$176$		−	0.0601103i		−	0.00453098i
$177$		0			0
$178$	2.17839	−	2.17839i	0.163277	−	0.163277i
$179$	21.9449			1.64024			0.820120	−	0.572192i	$-0.193907\pi$
$179$	21.9449			1.64024			0.820120	+	0.572192i	$0.193907\pi$
$180$		0			0
$181$	−21.4749			−1.59622			−0.798109	−	0.602513i	$-0.794166\pi$
$181$	−21.4749			−1.59622			−0.798109	+	0.602513i	$0.794166\pi$
$182$	2.59088	−	2.59088i	0.192049	−	0.192049i
$183$		0			0
$184$		−	5.23782i		−	0.386137i
$185$	−6.66441	+	10.5997i	−0.489977	+	0.779304i
$186$		0			0
$187$	−0.151788	−	0.151788i	−0.0110999	−	0.0110999i
$188$	−2.44094	−	2.44094i	−0.178024	−	0.178024i
$189$		0			0
$190$	0.836469	−	1.33040i	0.0606839	−	0.0965171i
$191$		−	0.171861i		−	0.0124354i	−0.999981	−	0.00621772i	$-0.998021\pi$
$191$		−	0.171861i		−	0.0124354i	0.999981	−	0.00621772i	$-0.00197918\pi$
$192$		0			0
$193$	−3.95425	+	3.95425i	−0.284633	+	0.284633i	−0.834954	−	0.550320i	$-0.814506\pi$
$193$	−3.95425	+	3.95425i	−0.284633	+	0.284633i	0.550320	+	0.834954i	$0.314506\pi$
$194$	−2.83362			−0.203442
$195$		0			0
$196$	6.27560			0.448257
$197$	−1.10331	+	1.10331i	−0.0786078	+	0.0786078i	−0.745317	−	0.666710i	$-0.767702\pi$
$197$	−1.10331	+	1.10331i	−0.0786078	+	0.0786078i	0.666710	+	0.745317i	$0.267702\pi$
$198$		0			0
$199$			14.3701i			1.01867i	0.860568	+	0.509335i	$0.170109\pi$
$199$			14.3701i			1.01867i	−0.860568	+	0.509335i	$0.829891\pi$
$200$	−11.6266	−	4.07574i	−0.822128	−	0.288198i
$201$		0			0
$202$	6.36825	+	6.36825i	0.448068	+	0.448068i
$203$	−2.87959	−	2.87959i	−0.202107	−	0.202107i
$204$		0			0
$205$	−13.7375	+	3.13139i	−0.959465	+	0.218706i
$206$			2.11273i			0.147201i
$207$		0			0
$208$	−2.80433	+	2.80433i	−0.194445	+	0.194445i
$209$	0.0469465			0.00324735
$210$		0			0
$211$	−25.5572			−1.75943			−0.879713	−	0.475504i	$-0.842266\pi$
$211$	−25.5572			−1.75943			−0.879713	+	0.475504i	$0.842266\pi$
$212$	11.3299	−	11.3299i	0.778140	−	0.778140i
$213$		0			0
$214$		−	4.61413i		−	0.315416i
$215$	0.555439	+	0.349225i	0.0378806	+	0.0238170i
$216$		0			0
$217$	7.70237	+	7.70237i	0.522871	+	0.522871i
$218$	−4.80426	−	4.80426i	−0.325386	−	0.325386i
$219$		0			0
$220$	−0.0351370	−	0.154147i	−0.00236894	−	0.0103926i
$221$			14.1628i			0.952691i
$222$		0			0
$223$	17.4716	−	17.4716i	1.16998	−	1.16998i	0.187769	−	0.982213i	$-0.439874\pi$
$223$	17.4716	−	17.4716i	1.16998	−	1.16998i	0.982213	−	0.187769i	$-0.0601256\pi$
$224$	−9.80964			−0.655434
$225$		0			0
$226$	1.47618			0.0981939
$227$	4.74523	−	4.74523i	0.314952	−	0.314952i	−0.531872	−	0.846825i	$-0.678511\pi$
$227$	4.74523	−	4.74523i	0.314952	−	0.314952i	0.846825	+	0.531872i	$0.178511\pi$
$228$		0			0
$229$		−	19.8241i		−	1.31001i	−0.755624	−	0.655005i	$-0.772666\pi$
$229$		−	19.8241i		−	1.31001i	0.755624	−	0.655005i	$-0.227334\pi$
$230$	−0.742414	−	3.25698i	−0.0489533	−	0.214759i
$231$		0			0
$232$	−4.21550	−	4.21550i	−0.276761	−	0.276761i
$233$	−18.7470	−	18.7470i	−1.22815	−	1.22815i	−0.964661	−	0.263493i	$-0.915125\pi$
$233$	−18.7470	−	18.7470i	−1.22815	−	1.22815i	−0.263493	−	0.964661i	$-0.584875\pi$
$234$		0			0
$235$	−4.33887	−	2.72801i	−0.283037	−	0.177956i
$236$			11.3084i			0.736116i
$237$		0			0
$238$	−3.82473	+	3.82473i	−0.247920	+	0.247920i
$239$	25.3582			1.64029			0.820144	−	0.572157i	$-0.193893\pi$
$239$	25.3582			1.64029			0.820144	+	0.572157i	$0.193893\pi$
$240$		0			0
$241$	−0.795348			−0.0512329			−0.0256164	−	0.999672i	$-0.508155\pi$
$241$	−0.795348			−0.0512329			−0.0256164	+	0.999672i	$0.508155\pi$
$242$	5.46540	−	5.46540i	0.351329	−	0.351329i
$243$		0			0
$244$			3.20143i			0.204951i
$245$	9.08438	−	2.07074i	0.580379	−	0.132295i
$246$		0			0
$247$	−2.19020	−	2.19020i	−0.139359	−	0.139359i
$248$	11.2757	+	11.2757i	0.716007	+	0.716007i
$249$		0			0
$250$	−7.80738	−	0.886401i	−0.493782	−	0.0560609i
$251$		−	10.7805i		−	0.680457i	−0.940343	−	0.340229i	$-0.889496\pi$
$251$		−	10.7805i		−	0.680457i	0.940343	−	0.340229i	$-0.110504\pi$
$252$		0			0
$253$	0.0705644	−	0.0705644i	0.00443635	−	0.00443635i
$254$	−2.79326			−0.175265
$255$		0			0
$256$	−10.5038			−0.656489
$257$	7.59419	−	7.59419i	0.473713	−	0.473713i	−0.429401	−	0.903114i	$-0.641275\pi$
$257$	7.59419	−	7.59419i	0.473713	−	0.473713i	0.903114	+	0.429401i	$0.141275\pi$
$258$		0			0
$259$			9.42490i			0.585635i
$260$	−5.55217	+	8.83067i	−0.344331	+	0.547655i
$261$		0			0
$262$	8.13513	+	8.13513i	0.502590	+	0.502590i
$263$	4.02298	+	4.02298i	0.248068	+	0.248068i	0.820177	−	0.572110i	$-0.193875\pi$
$263$	4.02298	+	4.02298i	0.248068	+	0.248068i	−0.572110	+	0.820177i	$0.693875\pi$
$264$		0			0
$265$	12.6623	−	20.1393i	0.777841	−	1.23715i
$266$		−	1.18295i		−	0.0725311i
$267$		0			0
$268$	−9.26172	+	9.26172i	−0.565750	+	0.565750i
$269$	2.92888			0.178577			0.0892885	−	0.996006i	$-0.471541\pi$
$269$	2.92888			0.178577			0.0892885	+	0.996006i	$0.471541\pi$
$270$		0			0
$271$	−3.70198			−0.224879			−0.112440	−	0.993659i	$-0.535866\pi$
$271$	−3.70198			−0.224879			−0.112440	+	0.993659i	$0.535866\pi$
$272$	4.13982	−	4.13982i	0.251013	−	0.251013i
$273$		0			0
$274$		−	9.93653i		−	0.600287i
$275$	−0.101727	−	0.211544i	−0.00613435	−	0.0127566i
$276$		0			0
$277$	4.58182	+	4.58182i	0.275295	+	0.275295i	0.831227	−	0.555932i	$-0.187639\pi$
$277$	4.58182	+	4.58182i	0.275295	+	0.275295i	−0.555932	+	0.831227i	$0.687639\pi$
$278$	−4.83351	−	4.83351i	−0.289895	−	0.289895i
$279$		0			0
$280$	−9.04215	+	2.06112i	−0.540372	+	0.123175i
$281$		−	17.3770i		−	1.03663i	−0.855191	−	0.518314i	$-0.826560\pi$
$281$		−	17.3770i		−	1.03663i	0.855191	−	0.518314i	$-0.173440\pi$
$282$		0			0
$283$	12.0711	−	12.0711i	0.717555	−	0.717555i	−0.250549	−	0.968104i	$-0.580611\pi$
$283$	12.0711	−	12.0711i	0.717555	−	0.717555i	0.968104	+	0.250549i	$0.0806112\pi$
$284$	8.02803			0.476376
$285$		0			0
$286$	0.102196			0.00604295
$287$	−7.49962	+	7.49962i	−0.442689	+	0.442689i
$288$		0			0
$289$		−	3.90744i		−	0.229849i
$290$	−3.21879	−	2.02377i	−0.189014	−	0.118840i
$291$		0			0
$292$	17.1320	+	17.1320i	1.00257	+	1.00257i
$293$	16.7689	+	16.7689i	0.979649	+	0.979649i	0.999797	−	0.0201481i	$-0.00641376\pi$
$293$	16.7689	+	16.7689i	0.979649	+	0.979649i	−0.0201481	+	0.999797i	$0.506414\pi$
$294$		0			0
$295$	3.73141	+	16.3697i	0.217251	+	0.953083i
$296$			13.7973i			0.801954i
$297$		0			0
$298$	9.53804	−	9.53804i	0.552524	−	0.552524i
$299$	−6.58409			−0.380768
$300$		0			0
$301$	0.493879			0.0284667
$302$	2.36148	−	2.36148i	0.135888	−	0.135888i
$303$		0			0
$304$			1.28040i			0.0734360i
$305$	1.05637	+	4.63429i	0.0604873	+	0.265359i
$306$		0			0
$307$	−2.68648	−	2.68648i	−0.153326	−	0.153326i	0.626276	−	0.779602i	$-0.284578\pi$
$307$	−2.68648	−	2.68648i	−0.153326	−	0.153326i	−0.779602	+	0.626276i	$0.784578\pi$
$308$	−0.0841526	−	0.0841526i	−0.00479504	−	0.00479504i
$309$		0			0
$310$	8.60967	+	5.41322i	0.488997	+	0.307450i
$311$			16.0229i			0.908576i	0.890855	+	0.454288i	$0.150106\pi$
$311$			16.0229i			0.908576i	−0.890855	+	0.454288i	$0.849894\pi$
$312$		0			0
$313$	−11.4954	+	11.4954i	−0.649759	+	0.649759i	−0.952935	−	0.303176i	$-0.901953\pi$
$313$	−11.4954	+	11.4954i	−0.649759	+	0.649759i	0.303176	+	0.952935i	$0.401953\pi$
$314$	−11.6377			−0.656751
$315$		0			0
$316$	−17.0074			−0.956741
$317$	6.05173	−	6.05173i	0.339899	−	0.339899i	−0.516430	−	0.856329i	$-0.672739\pi$
$317$	6.05173	−	6.05173i	0.339899	−	0.339899i	0.856329	+	0.516430i	$0.172739\pi$
$318$		0			0
$319$		−	0.113583i		−	0.00635944i
$320$	−3.34677	+	0.762881i	−0.187090	+	0.0426463i
$321$		0			0
$322$	−1.77807	−	1.77807i	−0.0990878	−	0.0990878i
$323$	3.23322	+	3.23322i	0.179901	+	0.179901i
$324$		0			0
$325$	−5.12332	+	14.6150i	−0.284191	+	0.810697i
$326$		−	4.12374i		−	0.228393i
$327$		0			0
$328$	−10.9789	+	10.9789i	−0.606207	+	0.606207i
$329$	−3.85798			−0.212698
$330$		0			0
$331$	34.9307			1.91996			0.959982	−	0.280063i	$-0.0903553\pi$
$331$	34.9307			1.91996			0.959982	+	0.280063i	$0.0903553\pi$
$332$	9.69159	−	9.69159i	0.531895	−	0.531895i
$333$		0			0
$334$			2.69926i			0.147697i
$335$	−10.3509	+	16.4631i	−0.565532	+	0.899473i
$336$		0			0
$337$	−4.79252	−	4.79252i	−0.261065	−	0.261065i	0.564421	−	0.825487i	$-0.309099\pi$
$337$	−4.79252	−	4.79252i	−0.261065	−	0.261065i	−0.825487	+	0.564421i	$0.809099\pi$
$338$	1.69267	+	1.69267i	0.0920689	+	0.0920689i
$339$		0			0
$340$	8.19624	−	13.0360i	0.444504	−	0.706979i
$341$			0.303814i			0.0164525i
$342$		0			0
$343$	13.2908	−	13.2908i	0.717634	−	0.717634i
$344$	0.723002			0.0389816
$345$		0			0
$346$	−2.69858			−0.145077
$347$	−0.0862157	+	0.0862157i	−0.00462830	+	0.00462830i	−0.709417	−	0.704789i	$-0.751042\pi$
$347$	−0.0862157	+	0.0862157i	−0.00462830	+	0.00462830i	0.704789	+	0.709417i	$0.251042\pi$
$348$		0			0
$349$		−	12.0533i		−	0.645200i	−0.946535	−	0.322600i	$-0.895443\pi$
$349$		−	12.0533i		−	0.645200i	0.946535	−	0.322600i	$-0.104557\pi$
$350$	−5.33044	+	2.56329i	−0.284924	+	0.137013i
$351$		0			0
$352$	−0.193467	−	0.193467i	−0.0103118	−	0.0103118i
$353$	−18.0307	−	18.0307i	−0.959675	−	0.959675i	0.0395428	−	0.999218i	$-0.487410\pi$
$353$	−18.0307	−	18.0307i	−0.959675	−	0.959675i	−0.999218	+	0.0395428i	$0.987410\pi$
$354$		0			0
$355$	11.6211	−	2.64899i	0.616786	−	0.140594i
$356$			6.60184i			0.349897i
$357$		0			0
$358$	10.9056	−	10.9056i	0.576380	−	0.576380i
$359$	−13.9493			−0.736216			−0.368108	−	0.929783i	$-0.619994\pi$
$359$	−13.9493			−0.736216			−0.368108	+	0.929783i	$0.619994\pi$
$360$		0			0
$361$	−1.00000			−0.0526316
$362$	−10.6720	+	10.6720i	−0.560910	+	0.560910i
$363$		0			0
$364$			7.85195i			0.411554i
$365$	30.4527	+	19.1467i	1.59397	+	1.00219i
$366$		0			0
$367$	13.5945	+	13.5945i	0.709627	+	0.709627i	0.966457	−	0.256830i	$-0.0826780\pi$
$367$	13.5945	+	13.5945i	0.709627	+	0.709627i	−0.256830	+	0.966457i	$0.582678\pi$
$368$	1.92455	+	1.92455i	0.100324	+	0.100324i
$369$		0			0
$370$	1.95565	+	8.57946i	0.101669	+	0.446025i
$371$		−	17.9072i		−	0.929697i
$372$		0			0
$373$	13.3468	−	13.3468i	0.691071	−	0.691071i	−0.271397	−	0.962468i	$-0.587486\pi$
$373$	13.3468	−	13.3468i	0.691071	−	0.691071i	0.962468	+	0.271397i	$0.0874856\pi$
$374$	−0.150864			−0.00780097
$375$		0			0
$376$	−5.64780			−0.291263
$377$	−5.29901	+	5.29901i	−0.272913	+	0.272913i
$378$		0			0
$379$			32.6483i			1.67703i	0.544877	+	0.838516i	$0.316576\pi$
$379$			32.6483i			1.67703i	−0.544877	+	0.838516i	$0.683424\pi$
$380$	0.748449	+	3.28346i	0.0383946	+	0.168438i
$381$		0			0
$382$	−0.0854072	−	0.0854072i	−0.00436981	−	0.00436981i
$383$	−17.1927	−	17.1927i	−0.878506	−	0.878506i	0.114874	−	0.993380i	$-0.463354\pi$
$383$	−17.1927	−	17.1927i	−0.878506	−	0.878506i	−0.993380	+	0.114874i	$0.963354\pi$
$384$		0			0
$385$	−0.149584	−	0.0940492i	−0.00762352	−	0.00479319i
$386$			3.93017i			0.200040i
$387$		0			0
$388$	4.29380	−	4.29380i	0.217985	−	0.217985i
$389$	−15.8968			−0.805997			−0.402999	−	0.915201i	$-0.632032\pi$
$389$	−15.8968			−0.805997			−0.402999	+	0.915201i	$0.632032\pi$
$390$		0			0
$391$	9.71960			0.491541
$392$	7.26017	−	7.26017i	0.366694	−	0.366694i
$393$		0			0
$394$			1.09659i			0.0552455i
$395$	−24.6194	+	5.61188i	−1.23874	+	0.282364i
$396$		0			0
$397$	−8.61961	−	8.61961i	−0.432606	−	0.432606i	0.456908	−	0.889514i	$-0.348957\pi$
$397$	−8.61961	−	8.61961i	−0.432606	−	0.432606i	−0.889514	+	0.456908i	$0.848957\pi$
$398$	7.14129	+	7.14129i	0.357961	+	0.357961i
$399$		0			0
$400$	5.76958	−	2.77446i	0.288479	−	0.138723i
$401$		−	8.44961i		−	0.421953i	−0.977491	−	0.210977i	$-0.932336\pi$
$401$		−	8.44961i		−	0.421953i	0.977491	−	0.210977i	$-0.0676644\pi$
$402$		0			0
$403$	14.1739	−	14.1739i	0.706051	−	0.706051i
$404$	−19.2996			−0.960193
$405$		0			0
$406$	−2.86205			−0.142041
$407$	−0.185879	+	0.185879i	−0.00921369	+	0.00921369i
$408$		0			0
$409$			31.2423i			1.54483i	0.635116	+	0.772417i	$0.280952\pi$
$409$			31.2423i			1.54483i	−0.635116	+	0.772417i	$0.719048\pi$
$410$	−5.27073	+	8.38305i	−0.260303	+	0.414009i
$411$		0			0
$412$	−3.20143	−	3.20143i	−0.157723	−	0.157723i
$413$	8.93665	+	8.93665i	0.439744	+	0.439744i
$414$		0			0
$415$	10.8313	−	17.2272i	0.531690	−	0.845648i
$416$			18.0517i			0.885056i
$417$		0			0
$418$	0.0233302	−	0.0233302i	0.00114112	−	0.00114112i
$419$	−15.0509			−0.735284			−0.367642	−	0.929967i	$-0.619835\pi$
$419$	−15.0509			−0.735284			−0.367642	+	0.929967i	$0.619835\pi$
$420$		0			0
$421$	12.5215			0.610260			0.305130	−	0.952311i	$-0.401300\pi$
$421$	12.5215			0.610260			0.305130	+	0.952311i	$0.401300\pi$
$422$	−12.7007	+	12.7007i	−0.618262	+	0.618262i
$423$		0			0
$424$		−	26.2149i		−	1.27311i
$425$	7.56317	−	21.5751i	0.366868	−	1.04655i
$426$		0			0
$427$	2.52998	+	2.52998i	0.122434	+	0.122434i
$428$	6.99181	+	6.99181i	0.337962	+	0.337962i
$429$		0			0
$430$	0.449577	−	0.102479i	0.0216805	−	0.00494198i
$431$			4.24494i			0.204472i	0.994760	+	0.102236i	$0.0325997\pi$
$431$			4.24494i			0.204472i	−0.994760	+	0.102236i	$0.967400\pi$
$432$		0			0
$433$	−20.5170	+	20.5170i	−0.985984	+	0.985984i	−0.999903	−	0.0139187i	$-0.995569\pi$
$433$	−20.5170	+	20.5170i	−0.985984	+	0.985984i	0.0139187	+	0.999903i	$0.495569\pi$
$434$	7.65545			0.367473
$435$		0			0
$436$	14.5598			0.697289
$437$	−1.50308	+	1.50308i	−0.0719022	+	0.0719022i
$438$		0			0
$439$			37.7516i			1.80179i	0.434041	+	0.900893i	$0.357087\pi$
$439$			37.7516i			1.80179i	−0.434041	+	0.900893i	$0.642913\pi$
$440$	−0.218980	−	0.137681i	−0.0104395	−	0.00656368i
$441$		0			0
$442$	7.03825	+	7.03825i	0.334776	+	0.334776i
$443$	−6.40931	−	6.40931i	−0.304516	−	0.304516i	0.538262	−	0.842778i	$-0.319081\pi$
$443$	−6.40931	−	6.40931i	−0.304516	−	0.304516i	−0.842778	+	0.538262i	$0.819081\pi$
$444$		0			0
$445$	2.17839	+	9.55663i	0.103266	+	0.453028i
$446$		−	17.3651i		−	0.822263i
$447$		0			0
$448$	−1.82709	+	1.82709i	−0.0863217	+	0.0863217i
$449$	−12.9686			−0.612024			−0.306012	−	0.952028i	$-0.598995\pi$
$449$	−12.9686			−0.612024			−0.306012	+	0.952028i	$0.598995\pi$
$450$		0			0
$451$	−0.295817			−0.0139295
$452$	−2.23686	+	2.23686i	−0.105213	+	0.105213i
$453$		0			0
$454$		−	4.71633i		−	0.221348i
$455$	2.59088	+	11.3662i	0.121463	+	0.532858i
$456$		0			0
$457$	−19.9313	−	19.9313i	−0.932347	−	0.932347i	0.0655049	−	0.997852i	$-0.479134\pi$
$457$	−19.9313	−	19.9313i	−0.932347	−	0.932347i	−0.997852	+	0.0655049i	$0.979134\pi$
$458$	−9.85165	−	9.85165i	−0.460337	−	0.460337i
$459$		0			0
$460$	6.06029	+	3.81033i	0.282563	+	0.177658i
$461$		−	25.7083i		−	1.19736i	−0.800990	−	0.598678i	$-0.795693\pi$
$461$		−	25.7083i		−	1.19736i	0.800990	−	0.598678i	$-0.204307\pi$
$462$		0			0
$463$	−24.2972	+	24.2972i	−1.12919	+	1.12919i	−0.138877	+	0.990310i	$0.544349\pi$
$463$	−24.2972	+	24.2972i	−1.12919	+	1.12919i	−0.990310	+	0.138877i	$0.955651\pi$
$464$	3.09783			0.143813
$465$		0			0
$466$	−18.6328			−0.863146
$467$	−17.5684	+	17.5684i	−0.812970	+	0.812970i	−0.985078	−	0.172108i	$-0.944942\pi$
$467$	−17.5684	+	17.5684i	−0.812970	+	0.812970i	0.172108	+	0.985078i	$0.444942\pi$
$468$		0			0
$469$			14.6384i			0.675940i
$470$	−3.51191	+	0.800525i	−0.161993	+	0.0369255i
$471$		0			0
$472$	13.0826	+	13.0826i	0.602175	+	0.602175i
$473$	0.00974035	+	0.00974035i	0.000447862	+	0.000447862i
$474$		0			0
$475$	2.16687	+	4.50607i	0.0994226	+	0.206753i
$476$		−	11.5912i		−	0.531284i
$477$		0			0
$478$	12.6019	−	12.6019i	0.576397	−	0.576397i
$479$	33.8559			1.54692			0.773458	−	0.633848i	$-0.218526\pi$
$479$	33.8559			1.54692			0.773458	+	0.633848i	$0.218526\pi$
$480$		0			0
$481$	17.3437			0.790803
$482$	−0.395252	+	0.395252i	−0.0180032	+	0.0180032i
$483$		0			0
$484$			16.5635i			0.752886i
$485$	4.79876	−	7.63238i	0.217901	−	0.346569i
$486$		0			0
$487$	20.0125	+	20.0125i	0.906852	+	0.906852i	0.996017	−	0.0891647i	$-0.0284197\pi$
$487$	20.0125	+	20.0125i	0.906852	+	0.906852i	−0.0891647	+	0.996017i	$0.528420\pi$
$488$	3.70370	+	3.70370i	0.167658	+	0.167658i
$489$		0			0
$490$	3.48546	−	5.54358i	0.157457	−	0.250434i
$491$			32.8613i			1.48301i	0.670947	+	0.741505i	$0.265888\pi$
$491$			32.8613i			1.48301i	−0.670947	+	0.741505i	$0.734112\pi$
$492$		0			0
$493$	7.82252	−	7.82252i	0.352309	−	0.352309i
$494$	−2.17686			−0.0979413
$495$		0			0
$496$	−8.28613			−0.372058
$497$	6.34427	−	6.34427i	0.284579	−	0.284579i
$498$		0			0
$499$			43.9806i			1.96884i	0.175827	+	0.984421i	$0.443740\pi$
$499$			43.9806i			1.96884i	−0.175827	+	0.984421i	$0.556260\pi$
$500$	13.1737	−	10.4874i	0.589146	−	0.469010i
$501$		0			0
$502$	−5.35740	−	5.35740i	−0.239113	−	0.239113i
$503$	−23.3284	−	23.3284i	−1.04016	−	1.04016i	−0.999159	−	0.0410035i	$-0.986945\pi$
$503$	−23.3284	−	23.3284i	−1.04016	−	1.04016i	−0.0410035	−	0.999159i	$-0.513055\pi$
$504$		0			0
$505$	−27.9376	+	6.36825i	−1.24321	+	0.283383i
$506$		−	0.0701346i		−	0.00311786i
$507$		0			0
$508$	4.23263	−	4.23263i	0.187793	−	0.187793i
$509$	10.4196			0.461839			0.230920	−	0.972973i	$-0.425827\pi$
$509$	10.4196			0.461839			0.230920	+	0.972973i	$0.425827\pi$
$510$		0			0
$511$	27.0776			1.19784
$512$	9.73839	−	9.73839i	0.430380	−	0.430380i
$513$		0			0
$514$		−	7.54794i		−	0.332925i
$515$	−5.69066	−	3.57793i	−0.250760	−	0.157662i
$516$		0			0
$517$	−0.0760877	−	0.0760877i	−0.00334633	−	0.00334633i
$518$	4.68374	+	4.68374i	0.205792	+	0.205792i
$519$		0			0
$520$	3.79286	+	16.6393i	0.166328	+	0.729683i
$521$		−	21.8409i		−	0.956866i	−0.878124	−	0.478433i	$-0.841205\pi$
$521$		−	21.8409i		−	0.956866i	0.878124	−	0.478433i	$-0.158795\pi$
$522$		0			0
$523$	−30.3595	+	30.3595i	−1.32753	+	1.32753i	−0.420005	+	0.907522i	$0.637972\pi$
$523$	−30.3595	+	30.3595i	−1.32753	+	1.32753i	−0.907522	+	0.420005i	$0.862028\pi$
$524$	−24.6544			−1.07703
$525$		0			0
$526$	3.99847			0.174342
$527$	−20.9238	+	20.9238i	−0.911456	+	0.911456i
$528$		0			0
$529$		−	18.4815i		−	0.803543i
$530$	−3.71572	−	16.3009i	−0.161401	−	0.708067i
$531$		0			0
$532$	1.79252	+	1.79252i	0.0777157	+	0.0777157i
$533$	13.8008	+	13.8008i	0.597778	+	0.597778i
$534$		0			0
$535$	12.4282	+	7.81407i	0.537318	+	0.337832i
$536$			21.4296i			0.925616i
$537$		0			0
$538$	1.45552	−	1.45552i	0.0627519	−	0.0627519i
$539$	0.195620			0.00842593
$540$		0			0
$541$	14.2168			0.611228			0.305614	−	0.952156i	$-0.401138\pi$
$541$	14.2168			0.611228			0.305614	+	0.952156i	$0.401138\pi$
$542$	−1.83971	+	1.83971i	−0.0790225	+	0.0790225i
$543$		0			0
$544$		−	26.6483i		−	1.14254i
$545$	21.0764	−	4.80426i	0.902813	−	0.205792i
$546$		0			0
$547$	−10.8108	−	10.8108i	−0.462235	−	0.462235i	0.437152	−	0.899387i	$-0.355987\pi$
$547$	−10.8108	−	10.8108i	−0.462235	−	0.462235i	−0.899387	+	0.437152i	$0.855987\pi$
$548$	15.0568	+	15.0568i	0.643197	+	0.643197i
$549$		0			0
$550$	−0.155681	−	0.0545743i	−0.00663827	−	0.00232705i
$551$			2.41942i			0.103071i
$552$		0			0
$553$	−13.4403	+	13.4403i	−0.571542	+	0.571542i
$554$	4.55391			0.193477
$555$		0			0
$556$	14.6485			0.621234
$557$	0.780431	−	0.780431i	0.0330679	−	0.0330679i	−0.690379	−	0.723447i	$-0.742556\pi$
$557$	0.780431	−	0.780431i	0.0330679	−	0.0330679i	0.723447	+	0.690379i	$0.242556\pi$
$558$		0			0
$559$		−	0.908835i		−	0.0384396i
$560$	2.56506	−	4.07971i	0.108394	−	0.172399i
$561$		0			0
$562$	−8.63560	−	8.63560i	−0.364271	−	0.364271i
$563$	3.19367	+	3.19367i	0.134597	+	0.134597i	0.771195	−	0.636598i	$-0.219659\pi$
$563$	3.19367	+	3.19367i	0.134597	+	0.134597i	−0.636598	+	0.771195i	$0.719659\pi$
$564$		0			0
$565$	−2.49992	+	3.97610i	−0.105172	+	0.167276i
$566$		−	11.9976i		−	0.504297i
$567$		0			0
$568$	9.28754	−	9.28754i	0.389696	−	0.389696i
$569$	20.8896			0.875737			0.437869	−	0.899039i	$-0.355733\pi$
$569$	20.8896			0.875737			0.437869	+	0.899039i	$0.355733\pi$
$570$		0			0
$571$	28.8153			1.20588			0.602941	−	0.797786i	$-0.293996\pi$
$571$	28.8153			1.20588			0.602941	+	0.797786i	$0.293996\pi$
$572$	−0.154857	+	0.154857i	−0.00647491	+	0.00647491i
$573$		0			0
$574$			7.45394i			0.311121i
$575$	10.0300	+	3.51602i	0.418279	+	0.146628i
$576$		0			0
$577$	−19.5130	−	19.5130i	−0.812338	−	0.812338i	0.172646	−	0.984984i	$-0.444768\pi$
$577$	−19.5130	−	19.5130i	−0.812338	−	0.812338i	−0.984984	+	0.172646i	$0.944768\pi$
$578$	−1.94182	−	1.94182i	−0.0807690	−	0.0807690i
$579$		0			0
$580$	7.94407	−	1.81081i	0.329859	−	0.0751900i
$581$		−	15.3178i		−	0.635491i
$582$		0			0
$583$	0.353169	−	0.353169i	0.0146268	−	0.0146268i
$584$	39.6395			1.64030
$585$		0			0
$586$	16.6667			0.688497
$587$	−9.20216	+	9.20216i	−0.379814	+	0.379814i	−0.871035	−	0.491221i	$-0.836551\pi$
$587$	−9.20216	+	9.20216i	−0.379814	+	0.379814i	0.491221	+	0.871035i	$0.336551\pi$
$588$		0			0
$589$		−	6.47151i		−	0.266654i
$590$	9.98935	+	6.28067i	0.411255	+	0.258571i
$591$		0			0
$592$	−5.06960	−	5.06960i	−0.208359	−	0.208359i
$593$	−8.03336	−	8.03336i	−0.329891	−	0.329891i	0.522654	−	0.852545i	$-0.324942\pi$
$593$	−8.03336	−	8.03336i	−0.329891	−	0.329891i	−0.852545	+	0.522654i	$0.824942\pi$
$594$		0			0
$595$	−3.82473	−	16.7791i	−0.156799	−	0.687877i
$596$			28.9061i			1.18404i
$597$		0			0
$598$	−3.27199	+	3.27199i	−0.133802	+	0.133802i
$599$	−38.2102			−1.56123			−0.780613	−	0.625015i	$-0.785093\pi$
$599$	−38.2102			−1.56123			−0.780613	+	0.625015i	$0.785093\pi$
$600$		0			0
$601$	−28.1731			−1.14921			−0.574603	−	0.818433i	$-0.694843\pi$
$601$	−28.1731			−1.14921			−0.574603	+	0.818433i	$0.694843\pi$
$602$	0.245435	−	0.245435i	0.0100032	−	0.0100032i
$603$		0			0
$604$			7.15672i			0.291203i
$605$	5.46540	+	23.9768i	0.222200	+	0.974796i
$606$		0			0
$607$	−16.0338	−	16.0338i	−0.650792	−	0.650792i	0.302392	−	0.953184i	$-0.402215\pi$
$607$	−16.0338	−	16.0338i	−0.650792	−	0.650792i	−0.953184	+	0.302392i	$0.902215\pi$
$608$	4.12102	+	4.12102i	0.167129	+	0.167129i
$609$		0			0
$610$	2.82800	+	1.77807i	0.114502	+	0.0719918i
$611$			7.09945i			0.287213i
$612$		0			0
$613$	−3.99159	+	3.99159i	−0.161219	+	0.161219i	−0.783107	−	0.621888i	$-0.786366\pi$
$613$	−3.99159	+	3.99159i	−0.161219	+	0.161219i	0.621888	+	0.783107i	$0.286366\pi$
$614$	−2.67012			−0.107757
$615$		0			0
$616$	−0.194710			−0.00784510
$617$	−15.1338	+	15.1338i	−0.609262	+	0.609262i	−0.942753	−	0.333491i	$-0.891773\pi$
$617$	−15.1338	+	15.1338i	−0.609262	+	0.609262i	0.333491	+	0.942753i	$0.391773\pi$
$618$		0			0
$619$			8.19331i			0.329317i	0.986351	+	0.164659i	$0.0526522\pi$
$619$			8.19331i			0.329317i	−0.986351	+	0.164659i	$0.947348\pi$
$620$	−21.2489	+	4.84360i	−0.853378	+	0.194524i
$621$		0			0
$622$	7.96266	+	7.96266i	0.319274	+	0.319274i
$623$	5.21720	+	5.21720i	0.209023	+	0.209023i
$624$		0			0
$625$	15.6094	−	19.5281i	0.624375	−	0.781124i
$626$			11.4254i			0.456650i
$627$		0			0
$628$	17.6346	−	17.6346i	0.703697	−	0.703697i
$629$	−25.6032			−1.02086
$630$		0			0
$631$	−7.19336			−0.286363			−0.143182	−	0.989696i	$-0.545733\pi$
$631$	−7.19336			−0.286363			−0.143182	+	0.989696i	$0.545733\pi$
$632$	−19.6757	+	19.6757i	−0.782656	+	0.782656i
$633$		0			0
$634$		−	6.01487i		−	0.238881i
$635$	4.73040	−	7.52366i	0.187720	−	0.298567i
$636$		0			0
$637$	−9.12625	−	9.12625i	−0.361595	−	0.361595i
$638$	−0.0564457	−	0.0564457i	−0.00223471	−	0.00223471i
$639$		0			0
$640$	12.5888	−	20.0224i	0.497618	−	0.791457i
$641$		−	4.15998i		−	0.164309i	−0.996620	−	0.0821546i	$-0.973820\pi$
$641$		−	4.15998i		−	0.164309i	0.996620	−	0.0821546i	$-0.0261801\pi$
$642$		0			0
$643$	13.3431	−	13.3431i	0.526202	−	0.526202i	−0.393236	−	0.919438i	$-0.628644\pi$
$643$	13.3431	−	13.3431i	0.526202	−	0.526202i	0.919438	+	0.393236i	$0.128644\pi$
$644$	5.38862			0.212341
$645$		0			0
$646$	3.21353			0.126435
$647$	−29.6236	+	29.6236i	−1.16462	+	1.16462i	−0.181171	+	0.983452i	$0.557989\pi$
$647$	−29.6236	+	29.6236i	−1.16462	+	1.16462i	−0.983452	+	0.181171i	$0.942011\pi$
$648$		0			0
$649$			0.352500i			0.0138368i
$650$	4.71695	+	9.80907i	0.185014	+	0.384743i
$651$		0			0
$652$	6.24871	+	6.24871i	0.244718	+	0.244718i
$653$	30.0782	+	30.0782i	1.17705	+	1.17705i	0.980492	+	0.196560i	$0.0629771\pi$
$653$	30.0782	+	30.0782i	1.17705	+	1.17705i	0.196560	+	0.980492i	$0.437023\pi$
$654$		0			0
$655$	−35.6889	+	8.13513i	−1.39448	+	0.317866i
$656$		−	8.06801i		−	0.315003i
$657$		0			0
$658$	−1.91724	+	1.91724i	−0.0747419	+	0.0747419i
$659$	−9.53805			−0.371550			−0.185775	−	0.982592i	$-0.559479\pi$
$659$	−9.53805			−0.371550			−0.185775	+	0.982592i	$0.559479\pi$
$660$		0			0
$661$	−33.6038			−1.30704			−0.653518	−	0.756911i	$-0.726708\pi$
$661$	−33.6038			−1.30704			−0.653518	+	0.756911i	$0.726708\pi$
$662$	17.3589	−	17.3589i	0.674675	−	0.674675i
$663$		0			0
$664$		−	22.4242i		−	0.870227i
$665$	3.18627	+	2.00333i	0.123558	+	0.0776857i
$666$		0			0
$667$	3.63659	+	3.63659i	0.140809	+	0.140809i
$668$	−4.09019	−	4.09019i	−0.158254	−	0.158254i
$669$		0			0
$670$	3.03745	+	13.3253i	0.117347	+	0.514802i
$671$			0.0997932i			0.00385247i
$672$		0			0
$673$	7.25193	−	7.25193i	0.279542	−	0.279542i	−0.553384	−	0.832926i	$-0.686664\pi$
$673$	7.25193	−	7.25193i	0.279542	−	0.279542i	0.832926	+	0.553384i	$0.186664\pi$
$674$	−4.76333			−0.183477
$675$		0			0
$676$	−5.12981			−0.197300
$677$	24.1273	−	24.1273i	0.927286	−	0.927286i	−0.0702435	−	0.997530i	$-0.522378\pi$
$677$	24.1273	−	24.1273i	0.927286	−	0.927286i	0.997530	+	0.0702435i	$0.0223776\pi$
$678$		0			0
$679$		−	6.78647i		−	0.260441i
$680$	−5.59911	−	24.5634i	−0.214716	−	0.941963i
$681$		0			0
$682$	0.150982	+	0.150982i	0.00578140	+	0.00578140i
$683$	8.00879	+	8.00879i	0.306448	+	0.306448i	0.843530	−	0.537082i	$-0.180473\pi$
$683$	8.00879	+	8.00879i	0.306448	+	0.306448i	−0.537082	+	0.843530i	$0.680473\pi$
$684$		0			0
$685$	26.7641	+	16.8276i	1.02260	+	0.642949i
$686$		−	13.2098i		−	0.504353i
$687$		0			0
$688$	−0.265655	+	0.265655i	−0.0101280	+	0.0101280i
$689$	−32.9529			−1.25540
$690$		0			0
$691$	−47.1210			−1.79257			−0.896283	−	0.443482i	$-0.853743\pi$
$691$	−47.1210			−1.79257			−0.896283	+	0.443482i	$0.853743\pi$
$692$	4.08916	−	4.08916i	0.155447	−	0.155447i
$693$		0			0
$694$			0.0856906i			0.00325277i
$695$	21.2047	−	4.83351i	0.804340	−	0.183346i
$696$		0			0
$697$	−20.3731	−	20.3731i	−0.771684	−	0.771684i
$698$	−5.98996	−	5.98996i	−0.226723	−	0.226723i
$699$		0			0
$700$	4.19308	−	11.9614i	0.158484	−	0.452098i
$701$		−	23.6908i		−	0.894791i	−0.894336	−	0.447395i	$-0.852352\pi$
$701$		−	23.6908i		−	0.894791i	0.894336	−	0.447395i	$-0.147648\pi$
$702$		0			0
$703$	3.95939	−	3.95939i	0.149331	−	0.149331i
$704$	−0.0720681			−0.00271617
$705$		0			0
$706$	−17.9208			−0.674459
$707$	−15.2518	+	15.2518i	−0.573604	+	0.573604i
$708$		0			0
$709$		−	9.90531i		−	0.372002i	−0.982550	−	0.186001i	$-0.940447\pi$
$709$		−	9.90531i		−	0.372002i	0.982550	−	0.186001i	$-0.0595527\pi$
$710$	4.45875	−	7.09160i	0.167334	−	0.266143i
$711$		0			0
$712$	7.63759	+	7.63759i	0.286231	+	0.286231i
$713$	−9.72722	−	9.72722i	−0.364287	−	0.364287i
$714$		0			0
$715$	−0.173069	+	0.275265i	−0.00647241	+	0.0102943i
$716$			33.0506i			1.23516i
$717$		0			0
$718$	−6.93216	+	6.93216i	−0.258706	+	0.258706i
$719$	11.8603			0.442316			0.221158	−	0.975238i	$-0.429016\pi$
$719$	11.8603			0.442316			0.221158	+	0.975238i	$0.429016\pi$
$720$		0			0
$721$	−5.05995			−0.188443
$722$	−0.496954	+	0.496954i	−0.0184947	+	0.0184947i
$723$		0			0
$724$		−	32.3428i		−	1.20201i
$725$	10.9021	−	5.24256i	0.404893	−	0.194704i
$726$		0			0
$727$	−26.4982	−	26.4982i	−0.982762	−	0.982762i	0.0170916	−	0.999854i	$-0.494559\pi$
$727$	−26.4982	−	26.4982i	−0.982762	−	0.982762i	−0.999854	+	0.0170916i	$0.994559\pi$
$728$	9.08383	+	9.08383i	0.336669	+	0.336669i
$729$		0			0
$730$	24.6487	−	5.61855i	0.912288	−	0.207952i
$731$			1.34164i			0.0496225i
$732$		0			0
$733$	−24.1651	+	24.1651i	−0.892558	+	0.892558i	−0.994763	−	0.102206i	$-0.967410\pi$
$733$	−24.1651	+	24.1651i	−0.892558	+	0.892558i	0.102206	+	0.994763i	$0.467410\pi$
$734$	13.5117			0.498725
$735$		0			0
$736$	12.3885			0.456645
$737$	−0.288701	+	0.288701i	−0.0106344	+	0.0106344i
$738$		0			0
$739$		−	43.3537i		−	1.59479i	−0.603457	−	0.797396i	$-0.706210\pi$
$739$		−	43.3537i		−	1.59479i	0.603457	−	0.797396i	$-0.293790\pi$
$740$	−15.9639	−	10.0371i	−0.586844	−	0.368971i
$741$		0			0
$742$	−8.89908	−	8.89908i	−0.326695	−	0.326695i
$743$	−35.2635	−	35.2635i	−1.29369	−	1.29369i	−0.932485	−	0.361209i	$-0.882364\pi$
$743$	−35.2635	−	35.2635i	−1.29369	−	1.29369i	−0.361209	−	0.932485i	$-0.617636\pi$
$744$		0			0
$745$	9.53804	+	41.8435i	0.349447	+	1.53303i
$746$		−	13.2655i		−	0.485684i
$747$		0			0
$748$	0.228604	−	0.228604i	0.00835860	−	0.00835860i
$749$	11.0508			0.403786
$750$		0			0
$751$	−27.7950			−1.01426			−0.507128	−	0.861871i	$-0.669293\pi$
$751$	−27.7950			−1.01426			−0.507128	+	0.861871i	$0.669293\pi$
$752$	2.07519	−	2.07519i	0.0756744	−	0.0756744i
$753$		0			0
$754$			5.26673i			0.191803i
$755$	2.36148	+	10.3599i	0.0859431	+	0.377034i
$756$		0			0
$757$	−13.2492	−	13.2492i	−0.481550	−	0.481550i	0.424076	−	0.905626i	$-0.360599\pi$
$757$	−13.2492	−	13.2492i	−0.481550	−	0.481550i	−0.905626	+	0.424076i	$0.860599\pi$
$758$	16.2247	+	16.2247i	0.589308	+	0.589308i
$759$		0			0
$760$	4.66447	+	2.93272i	0.169198	+	0.106381i
$761$		−	43.8017i		−	1.58781i	−0.608041	−	0.793906i	$-0.708044\pi$
$761$		−	43.8017i		−	1.58781i	0.608041	−	0.793906i	$-0.291956\pi$
$762$		0			0
$763$	11.5061	−	11.5061i	0.416550	−	0.416550i
$764$	0.258836			0.00936434
$765$		0			0
$766$	−17.0880			−0.617414
$767$	16.4452	−	16.4452i	0.593802	−	0.593802i
$768$		0			0
$769$			15.5451i			0.560570i	0.959917	+	0.280285i	$0.0904290\pi$
$769$			15.5451i			0.560570i	−0.959917	+	0.280285i	$0.909571\pi$
$770$	−0.121075	+	0.0275984i	−0.00436323	+	0.000994578i
$771$		0			0
$772$	−5.95539	−	5.95539i	−0.214339	−	0.214339i
$773$	37.8518	+	37.8518i	1.36144	+	1.36144i	0.872089	+	0.489347i	$0.162765\pi$
$773$	37.8518	+	37.8518i	1.36144	+	1.36144i	0.489347	+	0.872089i	$0.337235\pi$
$774$		0			0
$775$	−29.1611	+	14.0229i	−1.04750	+	0.503717i
$776$		−	9.93489i		−	0.356642i
$777$		0			0
$778$	−7.89996	+	7.89996i	−0.283227	+	0.283227i
$779$	6.30116			0.225763
$780$		0			0
$781$	0.250245			0.00895448
$782$	4.83020	−	4.83020i	0.172727	−	0.172727i
$783$		0			0
$784$			5.33526i			0.190545i
$785$	19.7085	−	31.3461i	0.703425	−	1.11879i
$786$		0			0
$787$	−0.871436	−	0.871436i	−0.0310633	−	0.0310633i	0.691405	−	0.722468i	$-0.256992\pi$
$787$	−0.871436	−	0.871436i	−0.0310633	−	0.0310633i	−0.722468	+	0.691405i	$0.756992\pi$
$788$	−1.66167	−	1.66167i	−0.0591945	−	0.0591945i
$789$		0			0
$790$	−9.44587	+	15.0236i	−0.336069	+	0.534514i
$791$			3.53542i			0.125705i
$792$		0			0
$793$	4.65566	−	4.65566i	0.165327	−	0.165327i
$794$	−8.56710			−0.304035
$795$		0			0
$796$	−21.6424			−0.767096
$797$	2.90993	−	2.90993i	0.103075	−	0.103075i	−0.653689	−	0.756764i	$-0.726779\pi$
$797$	2.90993	−	2.90993i	0.103075	−	0.103075i	0.756764	+	0.653689i	$0.226779\pi$
$798$		0			0
$799$		−	10.4804i		−	0.370769i
$800$	9.63991	−	27.4993i	0.340822	−	0.972247i
$801$		0			0
$802$	−4.19907	−	4.19907i	−0.148274	−	0.148274i
$803$	0.534028	+	0.534028i	0.0188454	+	0.0188454i
$804$		0			0
$805$	7.80040	−	1.77807i	0.274928	−	0.0626686i
$806$		−	14.0875i		−	0.496212i
$807$		0			0
$808$	−22.3275	+	22.3275i	−0.785480	+	0.785480i
$809$	27.3373			0.961128			0.480564	−	0.876960i	$-0.340432\pi$
$809$	27.3373			0.961128			0.480564	+	0.876960i	$0.340432\pi$
$810$		0			0
$811$	30.5057			1.07120			0.535600	−	0.844472i	$-0.320086\pi$
$811$	30.5057			1.07120			0.535600	+	0.844472i	$0.320086\pi$
$812$	4.33687	−	4.33687i	0.152194	−	0.152194i
$813$		0			0
$814$			0.184747i			0.00647538i
$815$	11.1073	+	6.98358i	0.389072	+	0.244624i
$816$		0			0
$817$	−0.207478	−	0.207478i	−0.00725873	−	0.00725873i
$818$	15.5260	+	15.5260i	0.542854	+	0.542854i
$819$		0			0
$820$	−4.71610	−	20.6896i	−0.164693	−	0.722512i
$821$		−	33.9744i		−	1.18571i	−0.805308	−	0.592857i	$-0.798000\pi$
$821$		−	33.9744i		−	1.18571i	0.805308	−	0.592857i	$-0.202000\pi$
$822$		0			0
$823$	−14.3397	+	14.3397i	−0.499851	+	0.499851i	−0.911391	−	0.411541i	$-0.864991\pi$
$823$	−14.3397	+	14.3397i	−0.499851	+	0.499851i	0.411541	+	0.911391i	$0.364991\pi$
$824$	−7.40739			−0.258049
$825$		0			0
$826$	8.88221			0.309052
$827$	23.5175	−	23.5175i	0.817782	−	0.817782i	−0.168004	−	0.985786i	$-0.553732\pi$
$827$	23.5175	−	23.5175i	0.817782	−	0.817782i	0.985786	+	0.168004i	$0.0537323\pi$
$828$		0			0
$829$		−	23.6486i		−	0.821351i	−0.911781	−	0.410676i	$-0.865293\pi$
$829$		−	23.6486i		−	0.821351i	0.911781	−	0.410676i	$-0.134707\pi$
$830$	−3.17842	−	13.9438i	−0.110325	−	0.483996i
$831$		0			0
$832$	3.36220	+	3.36220i	0.116563	+	0.116563i
$833$	13.4724	+	13.4724i	0.466791	+	0.466791i
$834$		0			0
$835$	−7.27047	−	4.57121i	−0.251605	−	0.158193i
$836$			0.0707048i			0.00244538i
$837$		0			0
$838$	−7.47960	+	7.47960i	−0.258379	+	0.258379i
$839$	−37.6489			−1.29979			−0.649893	−	0.760026i	$-0.725186\pi$
$839$	−37.6489			−1.29979			−0.649893	+	0.760026i	$0.725186\pi$
$840$		0			0
$841$	−23.1464			−0.798152
$842$	6.22261	−	6.22261i	0.214445	−	0.214445i
$843$		0			0
$844$		−	38.4909i		−	1.32491i
$845$	−7.42575	+	1.69267i	−0.255454	+	0.0582295i
$846$		0			0
$847$	13.0895	+	13.0895i	0.449762	+	0.449762i
$848$	9.63221	+	9.63221i	0.330771	+	0.330771i
$849$		0			0
$850$	−6.96328	−	14.4804i	−0.238839	−	0.496673i
$851$		−	11.9026i		−	0.408015i
$852$		0			0
$853$	0.903360	−	0.903360i	0.0309304	−	0.0309304i	−0.691472	−	0.722403i	$-0.743038\pi$
$853$	0.903360	−	0.903360i	0.0309304	−	0.0309304i	0.722403	+	0.691472i	$0.243038\pi$
$854$	2.51457			0.0860467
$855$		0			0
$856$	16.1775			0.552935
$857$	−27.9715	+	27.9715i	−0.955488	+	0.955488i	−0.999051	−	0.0435623i	$-0.986129\pi$
$857$	−27.9715	+	27.9715i	−0.955488	+	0.955488i	0.0435623	+	0.999051i	$0.486129\pi$
$858$		0			0
$859$			5.03464i			0.171780i	0.996305	+	0.0858899i	$0.0273733\pi$
$859$			5.03464i			0.171780i	−0.996305	+	0.0858899i	$0.972627\pi$
$860$	−0.525958	+	0.836532i	−0.0179350	+	0.0285255i
$861$		0			0
$862$	2.10954	+	2.10954i	0.0718513	+	0.0718513i
$863$	16.0343	+	16.0343i	0.545815	+	0.545815i	0.925228	−	0.379413i	$-0.123874\pi$
$863$	16.0343	+	16.0343i	0.545815	+	0.545815i	−0.379413	+	0.925228i	$0.623874\pi$
$864$		0			0
$865$	4.57006	−	7.26864i	0.155387	−	0.247141i
$866$			20.3920i			0.692949i
$867$		0			0
$868$	−11.6003	+	11.6003i	−0.393741	+	0.393741i
$869$	−0.530145			−0.0179839
$870$		0			0
$871$	26.9376			0.912745
$872$	16.8441	−	16.8441i	0.570413	−	0.570413i
$873$		0			0
$874$			1.49393i			0.0505328i
$875$	2.12291	−	18.6985i	0.0717676	−	0.632126i
$876$		0			0
$877$	25.5390	+	25.5390i	0.862391	+	0.862391i	0.991615	−	0.129224i	$-0.0412488\pi$
$877$	25.5390	+	25.5390i	0.862391	+	0.862391i	−0.129224	+	0.991615i	$0.541249\pi$
$878$	18.7608	+	18.7608i	0.633147	+	0.633147i
$879$		0			0
$880$	0.131049	−	0.0298721i	0.00441767	−	0.00100699i
$881$		−	45.1046i		−	1.51961i	−0.650150	−	0.759806i	$-0.725294\pi$
$881$		−	45.1046i		−	1.51961i	0.650150	−	0.759806i	$-0.274706\pi$
$882$		0			0
$883$	−29.5736	+	29.5736i	−0.995230	+	0.995230i	−0.999989	−	0.00475911i	$-0.998485\pi$
$883$	−29.5736	+	29.5736i	−0.995230	+	0.995230i	0.00475911	+	0.999989i	$0.498485\pi$
$884$	−21.3302			−0.717411
$885$		0			0
$886$	−6.37027			−0.214014
$887$	0.596883	−	0.596883i	0.0200414	−	0.0200414i	−0.697015	−	0.717056i	$-0.745489\pi$
$887$	0.596883	−	0.596883i	0.0200414	−	0.0200414i	0.717056	+	0.697015i	$0.245489\pi$
$888$		0			0
$889$		−	6.68980i		−	0.224369i
$890$	5.83177	+	3.66665i	0.195481	+	0.122906i
$891$		0			0
$892$	26.3134	+	26.3134i	0.881039	+	0.881039i
$893$	1.62073	+	1.62073i	0.0542358	+	0.0542358i
$894$		0			0
$895$	10.9056	+	47.8431i	0.364535	+	1.59922i
$896$		−	17.8033i		−	0.594767i
$897$		0			0
$898$	−6.44478	+	6.44478i	−0.215065	+	0.215065i
$899$	−15.6573			−0.522200
$900$		0			0
$901$	48.6458			1.62063
$902$	−0.147008	+	0.147008i	−0.00489482	+	0.00489482i
$903$		0			0
$904$			5.17559i			0.172137i
$905$	−10.6720	−	46.8184i	−0.354751	−	1.55630i
$906$		0			0
$907$	−7.45423	−	7.45423i	−0.247514	−	0.247514i	0.572436	−	0.819949i	$-0.305999\pi$
$907$	−7.45423	−	7.45423i	−0.247514	−	0.247514i	−0.819949	+	0.572436i	$0.805999\pi$
$908$	7.14667	+	7.14667i	0.237170	+	0.237170i
$909$		0			0
$910$	6.93606	+	4.36096i	0.229928	+	0.144564i
$911$			4.65162i			0.154115i	0.997027	+	0.0770576i	$0.0245525\pi$
$911$			4.65162i			0.154115i	−0.997027	+	0.0770576i	$0.975447\pi$
$912$		0			0
$913$	0.302101	−	0.302101i	0.00999807	−	0.00999807i
$914$	−19.8099			−0.655253
$915$		0			0
$916$	29.8565			0.986486
$917$	−19.4835	+	19.4835i	−0.643401	+	0.643401i
$918$		0			0
$919$		−	31.0340i		−	1.02372i	−0.859070	−	0.511858i	$-0.828957\pi$
$919$		−	31.0340i		−	1.02372i	0.859070	−	0.511858i	$-0.171043\pi$
$920$	11.4192	−	2.60296i	0.376480	−	0.0858169i
$921$		0			0
$922$	−12.7759	−	12.7759i	−0.420751	−	0.420751i
$923$	−11.6747	−	11.6747i	−0.384278	−	0.384278i
$924$		0			0
$925$	−26.4208	−	9.26183i	−0.868709	−	0.304527i
$926$			24.1492i			0.793592i
$927$		0			0
$928$	9.97047	−	9.97047i	0.327297	−	0.327297i
$929$	−16.3042			−0.534924			−0.267462	−	0.963568i	$-0.586185\pi$
$929$	−16.3042			−0.534924			−0.267462	+	0.963568i	$0.586185\pi$
$930$		0			0
$931$	−4.16687			−0.136564
$932$	28.2343	−	28.2343i	0.924845	−	0.924845i
$933$		0			0
$934$			17.4614i			0.571355i
$935$	0.255489	−	0.406352i	0.00835537	−	0.0132891i
$936$		0			0
$937$	−40.1633	−	40.1633i	−1.31208	−	1.31208i	−0.919882	−	0.392194i	$-0.871716\pi$
$937$	−40.1633	−	40.1633i	−1.31208	−	1.31208i	−0.392194	−	0.919882i	$-0.628284\pi$
$938$	7.27463	+	7.27463i	0.237525	+	0.237525i
$939$		0			0
$940$	4.10858	−	6.53465i	0.134007	−	0.213137i
$941$		−	10.2988i		−	0.335733i	−0.985810	−	0.167866i	$-0.946312\pi$
$941$		−	10.2988i		−	0.335733i	0.985810	−	0.167866i	$-0.0536877\pi$
$942$		0			0
$943$	9.47117	−	9.47117i	0.308424	−	0.308424i
$944$	−9.61395			−0.312907
$945$		0			0
$946$	0.00968102			0.000314757
$947$	10.5210	−	10.5210i	0.341888	−	0.341888i	−0.515189	−	0.857077i	$-0.672278\pi$
$947$	10.5210	−	10.5210i	0.341888	−	0.341888i	0.857077	+	0.515189i	$0.172278\pi$
$948$		0			0
$949$		−	49.8281i		−	1.61749i
$950$	3.31615	+	1.16248i	0.107590	+	0.0377158i
$951$		0			0
$952$	−13.4098	−	13.4098i	−0.434613	−	0.434613i
$953$	−30.5402	−	30.5402i	−0.989294	−	0.989294i	0.0106496	−	0.999943i	$-0.496610\pi$
$953$	−30.5402	−	30.5402i	−0.989294	−	0.989294i	−0.999943	+	0.0106496i	$0.996610\pi$
$954$		0			0
$955$	0.374683	−	0.0854072i	0.0121244	−	0.00276371i
$956$			38.1914i			1.23520i
$957$		0			0
$958$	16.8248	−	16.8248i	0.543586	−	0.543586i
$959$	23.7978			0.768471
$960$		0			0
$961$	10.8804			0.350982
$962$	8.61901	−	8.61901i	0.277888	−	0.277888i
$963$		0			0
$964$		−	1.19785i		−	0.0385802i
$965$	−10.5859	−	6.65576i	−0.340773	−	0.214257i
$966$		0			0
$967$	26.2211	+	26.2211i	0.843214	+	0.843214i	0.989276	−	0.146061i	$-0.0466597\pi$
$967$	26.2211	+	26.2211i	0.843214	+	0.843214i	−0.146061	+	0.989276i	$0.546660\pi$
$968$	19.1621	+	19.1621i	0.615893	+	0.615893i
$969$		0			0
$970$	−1.40818	−	6.17771i	−0.0452140	−	0.198354i
$971$		−	57.6993i		−	1.85166i	−0.377943	−	0.925829i	$-0.623369\pi$
$971$		−	57.6993i		−	1.85166i	0.377943	−	0.925829i	$-0.376631\pi$
$972$		0			0
$973$	11.5762	−	11.5762i	0.371115	−	0.371115i
$974$	19.8906			0.637335
$975$		0			0
$976$	−2.72172			−0.0871202
$977$	−40.6275	+	40.6275i	−1.29979	+	1.29979i	−0.371259	+	0.928529i	$0.621074\pi$
$977$	−40.6275	+	40.6275i	−1.29979	+	1.29979i	−0.928529	+	0.371259i	$0.878926\pi$
$978$		0			0
$979$			0.205789i			0.00657704i
$980$	3.11869	+	13.6817i	0.0996228	+	0.437047i
$981$		0			0
$982$	16.3306	+	16.3306i	0.521129	+	0.521129i
$983$	−31.3803	−	31.3803i	−1.00088	−	1.00088i	−1.00000		0.000877030i	$-0.999721\pi$
$983$	−31.3803	−	31.3803i	−1.00088	−	1.00088i	−0.000877030	−	1.00000i	$-0.500279\pi$
$984$		0			0
$985$	−2.95368	−	1.85709i	−0.0941120	−	0.0591717i
$986$		−	7.77487i		−	0.247602i
$987$		0			0
$988$	3.29859	−	3.29859i	0.104942	−	0.104942i
$989$	−0.623713			−0.0198329
$990$		0			0
$991$	−15.2289			−0.483763			−0.241882	−	0.970306i	$-0.577765\pi$
$991$	−15.2289			−0.483763			−0.241882	+	0.970306i	$0.577765\pi$
$992$	−26.6692	+	26.6692i	−0.846748	+	0.846748i
$993$		0			0
$994$		−	6.30563i		−	0.200002i
$995$	−31.3290	+	7.14129i	−0.993195	+	0.226394i
$996$		0			0
$997$	−30.4577	−	30.4577i	−0.964604	−	0.964604i	0.0347904	−	0.999395i	$-0.488924\pi$
$997$	−30.4577	−	30.4577i	−0.964604	−	0.964604i	−0.999395	+	0.0347904i	$0.988924\pi$
$998$	21.8564	+	21.8564i	0.691851	+	0.691851i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.n.d.647.7	yes	20
3.2	odd	2	inner	855.2.n.d.647.4	✓	20
5.3	odd	4	inner	855.2.n.d.818.4	yes	20
15.8	even	4	inner	855.2.n.d.818.7	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
855.2.n.d.647.4	✓	20	3.2	odd	2	inner
855.2.n.d.647.7	yes	20	1.1	even	1	trivial
855.2.n.d.818.4	yes	20	5.3	odd	4	inner
855.2.n.d.818.7	yes	20	15.8	even	4	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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.496954 - 0.496954i) q^{2} +1.50607i q^{4} +(0.496954 + 2.18015i) q^{5} +(1.19020 + 1.19020i) q^{7} +(1.74236 + 1.74236i) q^{8} +O(q^{10})\)	\(q+(0.496954 - 0.496954i) q^{2} +1.50607i q^{4} +(0.496954 + 2.18015i) q^{5} +(1.19020 + 1.19020i) q^{7} +(1.74236 + 1.74236i) q^{8} +(1.33040 + 0.836469i) q^{10} +0.0469465i q^{11} +(2.19020 - 2.19020i) q^{13} +1.18295 q^{14} -1.28040 q^{16} +(-3.23322 + 3.23322i) q^{17} -1.00000i q^{19} +(-3.28346 + 0.748449i) q^{20} +(0.0233302 + 0.0233302i) q^{22} +(-1.50308 - 1.50308i) q^{23} +(-4.50607 + 2.16687i) q^{25} -2.17686i q^{26} +(-1.79252 + 1.79252i) q^{28} -2.41942 q^{29} +6.47151 q^{31} +(-4.12102 + 4.12102i) q^{32} +3.21353i q^{34} +(-2.00333 + 3.18627i) q^{35} +(3.95939 + 3.95939i) q^{37} +(-0.496954 - 0.496954i) q^{38} +(-2.93272 + 4.66447i) q^{40} +6.30116i q^{41} +(0.207478 - 0.207478i) q^{43} -0.0707048 q^{44} -1.49393 q^{46} +(-1.62073 + 1.62073i) q^{47} -4.16687i q^{49} +(-1.16248 + 3.31615i) q^{50} +(3.29859 + 3.29859i) q^{52} +(-7.52281 - 7.52281i) q^{53} +(-0.102350 + 0.0233302i) q^{55} +4.14750i q^{56} +(-1.20234 + 1.20234i) q^{58} +7.50855 q^{59} +2.12568 q^{61} +(3.21604 - 3.21604i) q^{62} +1.53511i q^{64} +(5.86337 + 3.68652i) q^{65} +(6.14958 + 6.14958i) q^{67} +(-4.86947 - 4.86947i) q^{68} +(0.587870 + 2.57900i) q^{70} -5.33044i q^{71} +(11.3753 - 11.3753i) q^{73} +3.93527 q^{74} +1.50607 q^{76} +(-0.0558755 + 0.0558755i) q^{77} +11.2925i q^{79} +(-0.636301 - 2.79146i) q^{80} +(3.13139 + 3.13139i) q^{82} +(-6.43501 - 6.43501i) q^{83} +(-8.65566 - 5.44213i) q^{85} -0.206214i q^{86} +(-0.0817975 + 0.0817975i) q^{88} +4.38348 q^{89} +5.21353 q^{91} +(2.26375 - 2.26375i) q^{92} +1.61086i q^{94} +(2.18015 - 0.496954i) q^{95} +(-2.85099 - 2.85099i) q^{97} +(-2.07074 - 2.07074i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q+O(q^{10}) \) 20 * q	\( 20 q + 28 q^{10} + 20 q^{13} - 76 q^{16} + 32 q^{22} - 32 q^{25} - 16 q^{28} - 16 q^{31} + 4 q^{37} - 64 q^{40} + 24 q^{43} - 88 q^{46} - 12 q^{52} + 40 q^{55} + 116 q^{58} + 32 q^{61} + 24 q^{67} - 16 q^{70} + 20 q^{73} - 28 q^{76} + 92 q^{82} - 16 q^{85} - 32 q^{88} + 112 q^{91} - 36 q^{97}+O(q^{100}) \) 20 * q + 28 * q^10 + 20 * q^13 - 76 * q^16 + 32 * q^22 - 32 * q^25 - 16 * q^28 - 16 * q^31 + 4 * q^37 - 64 * q^40 + 24 * q^43 - 88 * q^46 - 12 * q^52 + 40 * q^55 + 116 * q^58 + 32 * q^61 + 24 * q^67 - 16 * q^70 + 20 * q^73 - 28 * q^76 + 92 * q^82 - 16 * q^85 - 32 * q^88 + 112 * q^91 - 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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