LMFDB - Embedded newform 855.2.n.d.818.7

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			818.7
Root			$0.496954 + 0.496954i$ of defining polynomial
Character	$\chi$	$=$	855.818
Dual form			855.2.n.d.647.7

$q$-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 $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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	0.860630	−	0.509230i	$-0.170070\pi$
$2$	0.496954	+	0.496954i	0.351400	+	0.351400i	−0.509230	+	0.860630i	$0.670070\pi$
$3$		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	−0.445453	−	0.895305i	$-0.646957\pi$
$7$	1.19020	−	1.19020i	0.449852	−	0.449852i	0.895305	+	0.445453i	$0.146957\pi$
$8$	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	$-0.997747\pi$
$11$		−	0.0469465i		−	0.0141549i	0.999975	−	0.00707744i	$-0.00225284\pi$
$12$		0			0
$13$	2.19020	+	2.19020i	0.607451	+	0.607451i	0.942279	−	0.334828i	$-0.108678\pi$
$13$	2.19020	+	2.19020i	0.607451	+	0.607451i	−0.334828	+	0.942279i	$0.608678\pi$
$14$	1.18295			0.316156
$15$		0			0
$16$	−1.28040			−0.320100
$17$	−3.23322	−	3.23322i	−0.784171	−	0.784171i	0.196360	−	0.980532i	$-0.437088\pi$
$17$	−3.23322	−	3.23322i	−0.784171	−	0.784171i	−0.980532	+	0.196360i	$0.937088\pi$
$18$		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	−0.846231	−	0.532816i	$-0.821134\pi$
$23$	−1.50308	+	1.50308i	−0.313414	+	0.313414i	0.532816	+	0.846231i	$0.321134\pi$
$24$		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	−0.302295	−	0.953214i	$-0.597753\pi$
$37$	3.95939	−	3.95939i	0.650919	−	0.650919i	0.953214	+	0.302295i	$0.0977528\pi$
$38$	−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	$-0.836252\pi$
$41$		−	6.30116i		−	0.984076i	0.870574	−	0.492038i	$-0.163748\pi$
$42$		0			0
$43$	0.207478	+	0.207478i	0.0316401	+	0.0316401i	0.722750	−	0.691110i	$-0.242878\pi$
$43$	0.207478	+	0.207478i	0.0316401	+	0.0316401i	−0.691110	+	0.722750i	$0.742878\pi$
$44$	−0.0707048			−0.0106591
$45$		0			0
$46$	−1.49393			−0.220268
$47$	−1.62073	−	1.62073i	−0.236408	−	0.236408i	0.578953	−	0.815361i	$-0.303462\pi$
$47$	−1.62073	−	1.62073i	−0.236408	−	0.236408i	−0.815361	+	0.578953i	$0.803462\pi$
$48$		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	−0.0339124	+	0.999425i	$0.510797\pi$
$53$	−7.52281	+	7.52281i	−1.03334	+	1.03334i	−0.999425	+	0.0339124i	$0.989203\pi$
$54$		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	−0.223429	−	0.974720i	$-0.571725\pi$
$67$	6.14958	−	6.14958i	0.751291	−	0.751291i	0.974720	+	0.223429i	$0.0717251\pi$
$68$	−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	$0.102442\pi$
$71$			5.33044i			0.632607i	−0.948658	+	0.316304i	$0.897558\pi$
$72$		0			0
$73$	11.3753	+	11.3753i	1.33137	+	1.33137i	0.904143	+	0.427230i	$0.140511\pi$
$73$	11.3753	+	11.3753i	1.33137	+	1.33137i	0.427230	+	0.904143i	$0.359489\pi$
$74$	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	$-0.780895\pi$
$79$		−	11.2925i		−	1.27051i	0.772302	−	0.635255i	$-0.219105\pi$
$80$	−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	−0.965762	−	0.259429i	$-0.916466\pi$
$83$	−6.43501	+	6.43501i	−0.706334	+	0.706334i	0.259429	+	0.965762i	$0.416466\pi$
$84$		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	−0.836872	−	0.547398i	$-0.815618\pi$
$97$	−2.85099	+	2.85099i	−0.289474	+	0.289474i	0.547398	+	0.836872i	$0.315618\pi$
$98$	−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	$-0.779949\pi$
$101$		−	12.8146i		−	1.27510i	0.770411	−	0.637548i	$-0.220051\pi$
$102$		0			0
$103$	−2.12568	−	2.12568i	−0.209450	−	0.209450i	0.594584	−	0.804034i	$-0.297317\pi$
$103$	−2.12568	−	2.12568i	−0.209450	−	0.209450i	−0.804034	+	0.594584i	$0.797317\pi$
$104$	7.63221			0.748400
$105$		0			0
$106$	−7.47698			−0.726229
$107$	4.64241	+	4.64241i	0.448799	+	0.448799i	0.894955	−	0.446156i	$-0.147207\pi$
$107$	4.64241	+	4.64241i	0.448799	+	0.448799i	−0.446156	+	0.894955i	$0.647207\pi$
$108$		0			0
$109$			9.66742i			0.925970i	0.886366	+	0.462985i	$0.153222\pi$
$109$			9.66742i			0.925970i	−0.886366	+	0.462985i	$0.846778\pi$
$110$	−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	−0.633788	−	0.773507i	$-0.718501\pi$
$113$	1.48522	−	1.48522i	0.139718	−	0.139718i	0.773507	+	0.633788i	$0.218501\pi$
$114$		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	−0.820716	−	0.571336i	$-0.806425\pi$
$127$	−2.81038	+	2.81038i	−0.249381	+	0.249381i	0.571336	+	0.820716i	$0.306425\pi$
$128$	−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	$-0.746369\pi$
$131$		−	16.3700i		−	1.43025i	0.698996	−	0.715126i	$-0.253631\pi$
$132$		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	0.990640	−	0.136502i	$-0.0435861\pi$
$137$	9.99742	+	9.99742i	0.854137	+	0.854137i	−0.136502	+	0.990640i	$0.543586\pi$
$138$		0			0
$139$			9.72627i			0.824971i	0.910964	+	0.412486i	$0.135339\pi$
$139$			9.72627i			0.824971i	−0.910964	+	0.412486i	$0.864661\pi$
$140$	−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	−0.997982	−	0.0635027i	$-0.979773\pi$
$157$	−11.7090	+	11.7090i	−0.934479	+	0.934479i	0.0635027	+	0.997982i	$0.479773\pi$
$158$	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	0.850672	−	0.525697i	$-0.176195\pi$
$163$	4.14901	+	4.14901i	0.324976	+	0.324976i	−0.525697	+	0.850672i	$0.676195\pi$
$164$	−9.49001			−0.741045
$165$		0			0
$166$	−6.39581			−0.496411
$167$	−2.71580	−	2.71580i	−0.210155	−	0.210155i	0.594178	−	0.804333i	$-0.297477\pi$
$167$	−2.71580	−	2.71580i	−0.210155	−	0.210155i	−0.804333	+	0.594178i	$0.797477\pi$
$168$		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	−0.802747	−	0.596320i	$-0.796629\pi$
$173$	−2.71512	+	2.71512i	−0.206427	+	0.206427i	0.596320	+	0.802747i	$0.296629\pi$
$174$		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	$0.00197918\pi$
$191$			0.171861i			0.0124354i	−0.999981	+	0.00621772i	$0.998021\pi$
$192$		0			0
$193$	−3.95425	−	3.95425i	−0.284633	−	0.284633i	0.550320	−	0.834954i	$-0.314506\pi$
$193$	−3.95425	−	3.95425i	−0.284633	−	0.284633i	−0.834954	+	0.550320i	$0.814506\pi$
$194$	−2.83362			−0.203442
$195$		0			0
$196$	6.27560			0.448257
$197$	−1.10331	−	1.10331i	−0.0786078	−	0.0786078i	0.666710	−	0.745317i	$-0.267702\pi$
$197$	−1.10331	−	1.10331i	−0.0786078	−	0.0786078i	−0.745317	+	0.666710i	$0.767702\pi$
$198$		0			0
$199$		−	14.3701i		−	1.01867i	−0.860568	−	0.509335i	$-0.829891\pi$
$199$		−	14.3701i		−	1.01867i	0.860568	−	0.509335i	$-0.170109\pi$
$200$	−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	0.982213	+	0.187769i	$0.0601256\pi$
$223$	17.4716	+	17.4716i	1.16998	+	1.16998i	0.187769	+	0.982213i	$0.439874\pi$
$224$	−9.80964			−0.655434
$225$		0			0
$226$	1.47618			0.0981939
$227$	4.74523	+	4.74523i	0.314952	+	0.314952i	0.846825	−	0.531872i	$-0.178511\pi$
$227$	4.74523	+	4.74523i	0.314952	+	0.314952i	−0.531872	+	0.846825i	$0.678511\pi$
$228$		0			0
$229$			19.8241i			1.31001i	0.755624	+	0.655005i	$0.227334\pi$
$229$			19.8241i			1.31001i	−0.755624	+	0.655005i	$0.772666\pi$
$230$	−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	−0.263493	+	0.964661i	$0.584875\pi$
$233$	−18.7470	+	18.7470i	−1.22815	+	1.22815i	−0.964661	+	0.263493i	$0.915125\pi$
$234$		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	$0.110504\pi$
$251$			10.7805i			0.680457i	−0.940343	+	0.340229i	$0.889496\pi$
$252$		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	0.903114	−	0.429401i	$-0.141275\pi$
$257$	7.59419	+	7.59419i	0.473713	+	0.473713i	−0.429401	+	0.903114i	$0.641275\pi$
$258$		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	−0.572110	−	0.820177i	$-0.693875\pi$
$263$	4.02298	−	4.02298i	0.248068	−	0.248068i	0.820177	+	0.572110i	$0.193875\pi$
$264$		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	−0.555932	−	0.831227i	$-0.687639\pi$
$277$	4.58182	−	4.58182i	0.275295	−	0.275295i	0.831227	+	0.555932i	$0.187639\pi$
$278$	−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	$0.173440\pi$
$281$			17.3770i			1.03663i	−0.855191	+	0.518314i	$0.826560\pi$
$282$		0			0
$283$	12.0711	+	12.0711i	0.717555	+	0.717555i	0.968104	−	0.250549i	$-0.0806112\pi$
$283$	12.0711	+	12.0711i	0.717555	+	0.717555i	−0.250549	+	0.968104i	$0.580611\pi$
$284$	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	−0.0201481	−	0.999797i	$-0.506414\pi$
$293$	16.7689	−	16.7689i	0.979649	−	0.979649i	0.999797	+	0.0201481i	$0.00641376\pi$
$294$		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	−0.779602	−	0.626276i	$-0.784578\pi$
$307$	−2.68648	+	2.68648i	−0.153326	+	0.153326i	0.626276	+	0.779602i	$0.284578\pi$
$308$	−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	$-0.849894\pi$
$311$		−	16.0229i		−	0.908576i	0.890855	−	0.454288i	$-0.150106\pi$
$312$		0			0
$313$	−11.4954	−	11.4954i	−0.649759	−	0.649759i	0.303176	−	0.952935i	$-0.401953\pi$
$313$	−11.4954	−	11.4954i	−0.649759	−	0.649759i	−0.952935	+	0.303176i	$0.901953\pi$
$314$	−11.6377			−0.656751
$315$		0			0
$316$	−17.0074			−0.956741
$317$	6.05173	+	6.05173i	0.339899	+	0.339899i	0.856329	−	0.516430i	$-0.172739\pi$
$317$	6.05173	+	6.05173i	0.339899	+	0.339899i	−0.516430	+	0.856329i	$0.672739\pi$
$318$		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	−0.825487	−	0.564421i	$-0.809099\pi$
$337$	−4.79252	+	4.79252i	−0.261065	+	0.261065i	0.564421	+	0.825487i	$0.309099\pi$
$338$	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	0.704789	−	0.709417i	$-0.251042\pi$
$347$	−0.0862157	−	0.0862157i	−0.00462830	−	0.00462830i	−0.709417	+	0.704789i	$0.751042\pi$
$348$		0			0
$349$			12.0533i			0.645200i	0.946535	+	0.322600i	$0.104557\pi$
$349$			12.0533i			0.645200i	−0.946535	+	0.322600i	$0.895443\pi$
$350$	−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	−0.999218	−	0.0395428i	$-0.987410\pi$
$353$	−18.0307	+	18.0307i	−0.959675	+	0.959675i	0.0395428	+	0.999218i	$0.487410\pi$
$354$		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	−0.256830	−	0.966457i	$-0.582678\pi$
$367$	13.5945	−	13.5945i	0.709627	−	0.709627i	0.966457	+	0.256830i	$0.0826780\pi$
$368$	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	0.962468	−	0.271397i	$-0.0874856\pi$
$373$	13.3468	+	13.3468i	0.691071	+	0.691071i	−0.271397	+	0.962468i	$0.587486\pi$
$374$	−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	$-0.683424\pi$
$379$		−	32.6483i		−	1.67703i	0.544877	−	0.838516i	$-0.316576\pi$
$380$	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	−0.993380	−	0.114874i	$-0.963354\pi$
$383$	−17.1927	+	17.1927i	−0.878506	+	0.878506i	0.114874	+	0.993380i	$0.463354\pi$
$384$		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	−0.889514	−	0.456908i	$-0.848957\pi$
$397$	−8.61961	+	8.61961i	−0.432606	+	0.432606i	0.456908	+	0.889514i	$0.348957\pi$
$398$	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	$0.0676644\pi$
$401$			8.44961i			0.421953i	−0.977491	+	0.210977i	$0.932336\pi$
$402$		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	$-0.719048\pi$
$409$		−	31.2423i		−	1.54483i	0.635116	−	0.772417i	$-0.280952\pi$
$410$	−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	$-0.967400\pi$
$431$		−	4.24494i		−	0.204472i	0.994760	−	0.102236i	$-0.0325997\pi$
$432$		0			0
$433$	−20.5170	−	20.5170i	−0.985984	−	0.985984i	0.0139187	−	0.999903i	$-0.495569\pi$
$433$	−20.5170	−	20.5170i	−0.985984	−	0.985984i	−0.999903	+	0.0139187i	$0.995569\pi$
$434$	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	$-0.642913\pi$
$439$		−	37.7516i		−	1.80179i	0.434041	−	0.900893i	$-0.357087\pi$
$440$	−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	−0.842778	−	0.538262i	$-0.819081\pi$
$443$	−6.40931	+	6.40931i	−0.304516	+	0.304516i	0.538262	+	0.842778i	$0.319081\pi$
$444$		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	−0.997852	−	0.0655049i	$-0.979134\pi$
$457$	−19.9313	+	19.9313i	−0.932347	+	0.932347i	0.0655049	+	0.997852i	$0.479134\pi$
$458$	−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	$0.204307\pi$
$461$			25.7083i			1.19736i	−0.800990	+	0.598678i	$0.795693\pi$
$462$		0			0
$463$	−24.2972	−	24.2972i	−1.12919	−	1.12919i	−0.990310	−	0.138877i	$-0.955651\pi$
$463$	−24.2972	−	24.2972i	−1.12919	−	1.12919i	−0.138877	−	0.990310i	$-0.544349\pi$
$464$	3.09783			0.143813
$465$		0			0
$466$	−18.6328			−0.863146
$467$	−17.5684	−	17.5684i	−0.812970	−	0.812970i	0.172108	−	0.985078i	$-0.444942\pi$
$467$	−17.5684	−	17.5684i	−0.812970	−	0.812970i	−0.985078	+	0.172108i	$0.944942\pi$
$468$		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	−0.0891647	−	0.996017i	$-0.528420\pi$
$487$	20.0125	−	20.0125i	0.906852	−	0.906852i	0.996017	+	0.0891647i	$0.0284197\pi$
$488$	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	$-0.734112\pi$
$491$		−	32.8613i		−	1.48301i	0.670947	−	0.741505i	$-0.265888\pi$
$492$		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	$-0.556260\pi$
$499$		−	43.9806i		−	1.96884i	0.175827	−	0.984421i	$-0.443740\pi$
$500$	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	−0.0410035	+	0.999159i	$0.513055\pi$
$503$	−23.3284	+	23.3284i	−1.04016	+	1.04016i	−0.999159	+	0.0410035i	$0.986945\pi$
$504$		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	$0.158795\pi$
$521$			21.8409i			0.956866i	−0.878124	+	0.478433i	$0.841205\pi$
$522$		0			0
$523$	−30.3595	−	30.3595i	−1.32753	−	1.32753i	−0.907522	−	0.420005i	$-0.862028\pi$
$523$	−30.3595	−	30.3595i	−1.32753	−	1.32753i	−0.420005	−	0.907522i	$-0.637972\pi$
$524$	−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	−0.899387	−	0.437152i	$-0.855987\pi$
$547$	−10.8108	+	10.8108i	−0.462235	+	0.462235i	0.437152	+	0.899387i	$0.355987\pi$
$548$	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	0.723447	−	0.690379i	$-0.242556\pi$
$557$	0.780431	+	0.780431i	0.0330679	+	0.0330679i	−0.690379	+	0.723447i	$0.742556\pi$
$558$		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	−0.636598	−	0.771195i	$-0.719659\pi$
$563$	3.19367	−	3.19367i	0.134597	−	0.134597i	0.771195	+	0.636598i	$0.219659\pi$
$564$		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	−0.984984	−	0.172646i	$-0.944768\pi$
$577$	−19.5130	+	19.5130i	−0.812338	+	0.812338i	0.172646	+	0.984984i	$0.444768\pi$
$578$	−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	0.491221	−	0.871035i	$-0.336551\pi$
$587$	−9.20216	−	9.20216i	−0.379814	−	0.379814i	−0.871035	+	0.491221i	$0.836551\pi$
$588$		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	−0.852545	−	0.522654i	$-0.824942\pi$
$593$	−8.03336	+	8.03336i	−0.329891	+	0.329891i	0.522654	+	0.852545i	$0.324942\pi$
$594$		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	−0.953184	−	0.302392i	$-0.902215\pi$
$607$	−16.0338	+	16.0338i	−0.650792	+	0.650792i	0.302392	+	0.953184i	$0.402215\pi$
$608$	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	0.621888	−	0.783107i	$-0.286366\pi$
$613$	−3.99159	−	3.99159i	−0.161219	−	0.161219i	−0.783107	+	0.621888i	$0.786366\pi$
$614$	−2.67012			−0.107757
$615$		0			0
$616$	−0.194710			−0.00784510
$617$	−15.1338	−	15.1338i	−0.609262	−	0.609262i	0.333491	−	0.942753i	$-0.391773\pi$
$617$	−15.1338	−	15.1338i	−0.609262	−	0.609262i	−0.942753	+	0.333491i	$0.891773\pi$
$618$		0			0
$619$		−	8.19331i		−	0.329317i	−0.986351	−	0.164659i	$-0.947348\pi$
$619$		−	8.19331i		−	0.329317i	0.986351	−	0.164659i	$-0.0526522\pi$
$620$	−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	$0.0261801\pi$
$641$			4.15998i			0.164309i	−0.996620	+	0.0821546i	$0.973820\pi$
$642$		0			0
$643$	13.3431	+	13.3431i	0.526202	+	0.526202i	0.919438	−	0.393236i	$-0.128644\pi$
$643$	13.3431	+	13.3431i	0.526202	+	0.526202i	−0.393236	+	0.919438i	$0.628644\pi$
$644$	5.38862			0.212341
$645$		0			0
$646$	3.21353			0.126435
$647$	−29.6236	−	29.6236i	−1.16462	−	1.16462i	−0.983452	−	0.181171i	$-0.942011\pi$
$647$	−29.6236	−	29.6236i	−1.16462	−	1.16462i	−0.181171	−	0.983452i	$-0.557989\pi$
$648$		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	0.196560	−	0.980492i	$-0.437023\pi$
$653$	30.0782	−	30.0782i	1.17705	−	1.17705i	0.980492	−	0.196560i	$-0.0629771\pi$
$654$		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	0.832926	−	0.553384i	$-0.186664\pi$
$673$	7.25193	+	7.25193i	0.279542	+	0.279542i	−0.553384	+	0.832926i	$0.686664\pi$
$674$	−4.76333			−0.183477
$675$		0			0
$676$	−5.12981			−0.197300
$677$	24.1273	+	24.1273i	0.927286	+	0.927286i	0.997530	−	0.0702435i	$-0.0223776\pi$
$677$	24.1273	+	24.1273i	0.927286	+	0.927286i	−0.0702435	+	0.997530i	$0.522378\pi$
$678$		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	−0.537082	−	0.843530i	$-0.680473\pi$
$683$	8.00879	−	8.00879i	0.306448	−	0.306448i	0.843530	+	0.537082i	$0.180473\pi$
$684$		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	$0.147648\pi$
$701$			23.6908i			0.894791i	−0.894336	+	0.447395i	$0.852352\pi$
$702$		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	$0.0595527\pi$
$709$			9.90531i			0.372002i	−0.982550	+	0.186001i	$0.940447\pi$
$710$	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	−0.999854	−	0.0170916i	$-0.994559\pi$
$727$	−26.4982	+	26.4982i	−0.982762	+	0.982762i	0.0170916	+	0.999854i	$0.494559\pi$
$728$	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	0.102206	−	0.994763i	$-0.467410\pi$
$733$	−24.1651	−	24.1651i	−0.892558	−	0.892558i	−0.994763	+	0.102206i	$0.967410\pi$
$734$	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	$0.293790\pi$
$739$			43.3537i			1.59479i	−0.603457	+	0.797396i	$0.706210\pi$
$740$	−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	−0.361209	+	0.932485i	$0.617636\pi$
$743$	−35.2635	+	35.2635i	−1.29369	+	1.29369i	−0.932485	+	0.361209i	$0.882364\pi$
$744$		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	−0.905626	−	0.424076i	$-0.860599\pi$
$757$	−13.2492	+	13.2492i	−0.481550	+	0.481550i	0.424076	+	0.905626i	$0.360599\pi$
$758$	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	$0.291956\pi$
$761$			43.8017i			1.58781i	−0.608041	+	0.793906i	$0.708044\pi$
$762$		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	$-0.909571\pi$
$769$		−	15.5451i		−	0.560570i	0.959917	−	0.280285i	$-0.0904290\pi$
$770$	−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	0.489347	−	0.872089i	$-0.337235\pi$
$773$	37.8518	−	37.8518i	1.36144	−	1.36144i	0.872089	−	0.489347i	$-0.162765\pi$
$774$		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	−0.722468	−	0.691405i	$-0.756992\pi$
$787$	−0.871436	+	0.871436i	−0.0310633	+	0.0310633i	0.691405	+	0.722468i	$0.256992\pi$
$788$	−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	0.756764	−	0.653689i	$-0.226779\pi$
$797$	2.90993	+	2.90993i	0.103075	+	0.103075i	−0.653689	+	0.756764i	$0.726779\pi$
$798$		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	$0.202000\pi$
$821$			33.9744i			1.18571i	−0.805308	+	0.592857i	$0.798000\pi$
$822$		0			0
$823$	−14.3397	−	14.3397i	−0.499851	−	0.499851i	0.411541	−	0.911391i	$-0.364991\pi$
$823$	−14.3397	−	14.3397i	−0.499851	−	0.499851i	−0.911391	+	0.411541i	$0.864991\pi$
$824$	−7.40739			−0.258049
$825$		0			0
$826$	8.88221			0.309052
$827$	23.5175	+	23.5175i	0.817782	+	0.817782i	0.985786	−	0.168004i	$-0.0537323\pi$
$827$	23.5175	+	23.5175i	0.817782	+	0.817782i	−0.168004	+	0.985786i	$0.553732\pi$
$828$		0			0
$829$			23.6486i			0.821351i	0.911781	+	0.410676i	$0.134707\pi$
$829$			23.6486i			0.821351i	−0.911781	+	0.410676i	$0.865293\pi$
$830$	−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	0.722403	−	0.691472i	$-0.243038\pi$
$853$	0.903360	+	0.903360i	0.0309304	+	0.0309304i	−0.691472	+	0.722403i	$0.743038\pi$
$854$	2.51457			0.0860467
$855$		0			0
$856$	16.1775			0.552935
$857$	−27.9715	−	27.9715i	−0.955488	−	0.955488i	0.0435623	−	0.999051i	$-0.486129\pi$
$857$	−27.9715	−	27.9715i	−0.955488	−	0.955488i	−0.999051	+	0.0435623i	$0.986129\pi$
$858$		0			0
$859$		−	5.03464i		−	0.171780i	−0.996305	−	0.0858899i	$-0.972627\pi$
$859$		−	5.03464i		−	0.171780i	0.996305	−	0.0858899i	$-0.0273733\pi$
$860$	−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	−0.379413	−	0.925228i	$-0.623874\pi$
$863$	16.0343	−	16.0343i	0.545815	−	0.545815i	0.925228	+	0.379413i	$0.123874\pi$
$864$		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	−0.129224	−	0.991615i	$-0.541249\pi$
$877$	25.5390	−	25.5390i	0.862391	−	0.862391i	0.991615	+	0.129224i	$0.0412488\pi$
$878$	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	$0.274706\pi$
$881$			45.1046i			1.51961i	−0.650150	+	0.759806i	$0.725294\pi$
$882$		0			0
$883$	−29.5736	−	29.5736i	−0.995230	−	0.995230i	0.00475911	−	0.999989i	$-0.498485\pi$
$883$	−29.5736	−	29.5736i	−0.995230	−	0.995230i	−0.999989	+	0.00475911i	$0.998485\pi$
$884$	−21.3302			−0.717411
$885$		0			0
$886$	−6.37027			−0.214014
$887$	0.596883	+	0.596883i	0.0200414	+	0.0200414i	0.717056	−	0.697015i	$-0.245489\pi$
$887$	0.596883	+	0.596883i	0.0200414	+	0.0200414i	−0.697015	+	0.717056i	$0.745489\pi$
$888$		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	−0.819949	−	0.572436i	$-0.805999\pi$
$907$	−7.45423	+	7.45423i	−0.247514	+	0.247514i	0.572436	+	0.819949i	$0.305999\pi$
$908$	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	$-0.975447\pi$
$911$		−	4.65162i		−	0.154115i	0.997027	−	0.0770576i	$-0.0245525\pi$
$912$		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	$0.171043\pi$
$919$			31.0340i			1.02372i	−0.859070	+	0.511858i	$0.828957\pi$
$920$	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	−0.392194	+	0.919882i	$0.628284\pi$
$937$	−40.1633	+	40.1633i	−1.31208	+	1.31208i	−0.919882	+	0.392194i	$0.871716\pi$
$938$	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	$0.0536877\pi$
$941$			10.2988i			0.335733i	−0.985810	+	0.167866i	$0.946312\pi$
$942$		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	0.857077	−	0.515189i	$-0.172278\pi$
$947$	10.5210	+	10.5210i	0.341888	+	0.341888i	−0.515189	+	0.857077i	$0.672278\pi$
$948$		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	−0.999943	−	0.0106496i	$-0.996610\pi$
$953$	−30.5402	+	30.5402i	−0.989294	+	0.989294i	0.0106496	+	0.999943i	$0.496610\pi$
$954$		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	−0.146061	−	0.989276i	$-0.546660\pi$
$967$	26.2211	−	26.2211i	0.843214	−	0.843214i	0.989276	+	0.146061i	$0.0466597\pi$
$968$	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	$0.376631\pi$
$971$			57.6993i			1.85166i	−0.377943	+	0.925829i	$0.623369\pi$
$972$		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	−0.928529	−	0.371259i	$-0.878926\pi$
$977$	−40.6275	−	40.6275i	−1.29979	−	1.29979i	−0.371259	−	0.928529i	$-0.621074\pi$
$978$		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	−0.000877030		1.00000i	$0.500279\pi$
$983$	−31.3803	+	31.3803i	−1.00088	+	1.00088i	−1.00000		0.000877030i	$0.999721\pi$
$984$		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	−0.999395	−	0.0347904i	$-0.988924\pi$
$997$	−30.4577	+	30.4577i	−0.964604	+	0.964604i	0.0347904	+	0.999395i	$0.488924\pi$
$998$	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.818.7	yes	20
3.2	odd	2	inner	855.2.n.d.818.4	yes	20
5.2	odd	4	inner	855.2.n.d.647.4	✓	20
15.2	even	4	inner	855.2.n.d.647.7	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
855.2.n.d.647.4	✓	20	5.2	odd	4	inner
855.2.n.d.647.7	yes	20	15.2	even	4	inner
855.2.n.d.818.4	yes	20	3.2	odd	2	inner
855.2.n.d.818.7	yes	20	1.1	even	1	trivial

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

Related objects

Downloads

Learn more