LMFDB - Embedded newform 855.2.n.e.647.10

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:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			647.10
Character	$\chi$	$=$	855.647
Dual form			855.2.n.e.818.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.196860 - 0.196860i) q^{2} +1.92249i q^{4} +(1.96089 + 1.07466i) q^{5} +(3.28026 + 3.28026i) q^{7} +(0.772182 + 0.772182i) q^{8} +O(q^{10})$	\(q+(0.196860 - 0.196860i) q^{2} +1.92249i q^{4} +(1.96089 + 1.07466i) q^{5} +(3.28026 + 3.28026i) q^{7} +(0.772182 + 0.772182i) q^{8} +(0.597579 - 0.174463i) q^{10} -2.84245i q^{11} +(3.00252 - 3.00252i) q^{13} +1.29151 q^{14} -3.54096 q^{16} +(2.57248 - 2.57248i) q^{17} +1.00000i q^{19} +(-2.06603 + 3.76980i) q^{20} +(-0.559566 - 0.559566i) q^{22} +(0.253403 + 0.253403i) q^{23} +(2.69020 + 4.21460i) q^{25} -1.18215i q^{26} +(-6.30628 + 6.30628i) q^{28} -3.39527 q^{29} -6.50994 q^{31} +(-2.24144 + 2.24144i) q^{32} -1.01284i q^{34} +(2.90706 + 9.95742i) q^{35} +(-4.02806 - 4.02806i) q^{37} +(0.196860 + 0.196860i) q^{38} +(0.684330 + 2.34400i) q^{40} -6.75296i q^{41} +(-5.59200 + 5.59200i) q^{43} +5.46460 q^{44} +0.0997698 q^{46} +(4.48496 - 4.48496i) q^{47} +14.5203i q^{49} +(1.35928 + 0.300094i) q^{50} +(5.77232 + 5.77232i) q^{52} +(-9.60045 - 9.60045i) q^{53} +(3.05468 - 5.57375i) q^{55} +5.06592i q^{56} +(-0.668392 + 0.668392i) q^{58} +12.3704 q^{59} +5.98606 q^{61} +(-1.28155 + 1.28155i) q^{62} -6.19942i q^{64} +(9.11432 - 2.66092i) q^{65} +(0.701938 + 0.701938i) q^{67} +(4.94557 + 4.94557i) q^{68} +(2.53250 + 1.38793i) q^{70} +14.5324i q^{71} +(-7.06563 + 7.06563i) q^{73} -1.58593 q^{74} -1.92249 q^{76} +(9.32400 - 9.32400i) q^{77} -12.4635i q^{79} +(-6.94344 - 3.80534i) q^{80} +(-1.32939 - 1.32939i) q^{82} +(-5.35197 - 5.35197i) q^{83} +(7.80890 - 2.27980i) q^{85} +2.20168i q^{86} +(2.19489 - 2.19489i) q^{88} -5.77421 q^{89} +19.6981 q^{91} +(-0.487166 + 0.487166i) q^{92} -1.76582i q^{94} +(-1.07466 + 1.96089i) q^{95} +(3.14970 + 3.14970i) q^{97} +(2.85846 + 2.85846i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{7}+O(q^{10}) $ 36 * q + 4 * q^7	$ 36 q + 4 q^{7} + 8 q^{10} + 4 q^{13} - 36 q^{16} - 80 q^{22} + 16 q^{25} - 24 q^{28} - 4 q^{37} + 76 q^{40} - 20 q^{43} + 96 q^{46} - 68 q^{52} + 48 q^{55} - 12 q^{58} + 56 q^{61} - 8 q^{67} - 16 q^{70} - 56 q^{73} + 36 q^{76} - 100 q^{82} + 80 q^{85} - 184 q^{88} + 92 q^{97}+O(q^{100}) $ 36 * q + 4 * q^7 + 8 * q^10 + 4 * q^13 - 36 * q^16 - 80 * q^22 + 16 * q^25 - 24 * q^28 - 4 * q^37 + 76 * q^40 - 20 * q^43 + 96 * q^46 - 68 * q^52 + 48 * q^55 - 12 * q^58 + 56 * q^61 - 8 * q^67 - 16 * q^70 - 56 * q^73 + 36 * q^76 - 100 * q^82 + 80 * q^85 - 184 * q^88 + 92 * 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 $

$2$	0.196860	−	0.196860i	0.139201	−	0.139201i	−0.634073	−	0.773274i	$-0.718618\pi$
$2$	0.196860	−	0.196860i	0.139201	−	0.139201i	0.773274	+	0.634073i	$0.218618\pi$
$3$		0			0
$3$		0			0
$4$			1.92249i			0.961246i
$5$	1.96089	+	1.07466i	0.876938	+	0.480604i
$5$	1.96089	+	1.07466i	0.876938	+	0.480604i
$6$		0			0
$7$	3.28026	+	3.28026i	1.23982	+	1.23982i	0.960073	+	0.279750i	$0.0902517\pi$
$7$	3.28026	+	3.28026i	1.23982	+	1.23982i	0.279750	+	0.960073i	$0.409748\pi$
$8$	0.772182	+	0.772182i	0.273007	+	0.273007i
$9$		0			0
$10$	0.597579	−	0.174463i	0.188971	−	0.0551700i
$11$		−	2.84245i		−	0.857032i	−0.903534	−	0.428516i	$-0.859036\pi$
$11$		−	2.84245i		−	0.857032i	0.903534	−	0.428516i	$-0.140964\pi$
$12$		0			0
$13$	3.00252	−	3.00252i	0.832749	−	0.832749i	−0.155143	−	0.987892i	$-0.549584\pi$
$13$	3.00252	−	3.00252i	0.832749	−	0.832749i	0.987892	+	0.155143i	$0.0495838\pi$
$14$	1.29151			0.345169
$15$		0			0
$16$	−3.54096			−0.885240
$17$	2.57248	−	2.57248i	0.623918	−	0.623918i	−0.322613	−	0.946531i	$-0.604561\pi$
$17$	2.57248	−	2.57248i	0.623918	−	0.623918i	0.946531	+	0.322613i	$0.104561\pi$
$18$		0			0
$19$			1.00000i			0.229416i
$19$			1.00000i			0.229416i
$20$	−2.06603	+	3.76980i	−0.461979	+	0.842953i
$21$		0			0
$22$	−0.559566	−	0.559566i	−0.119300	−	0.119300i
$23$	0.253403	+	0.253403i	0.0528382	+	0.0528382i	0.733032	−	0.680194i	$-0.238104\pi$
$23$	0.253403	+	0.253403i	0.0528382	+	0.0528382i	−0.680194	+	0.733032i	$0.738104\pi$
$24$		0			0
$25$	2.69020	+	4.21460i	0.538039	+	0.842920i
$26$		−	1.18215i		−	0.231839i
$27$		0			0
$28$	−6.30628	+	6.30628i	−1.19178	+	1.19178i
$29$	−3.39527			−0.630485			−0.315243	−	0.949011i	$-0.602086\pi$
$29$	−3.39527			−0.630485			−0.315243	+	0.949011i	$0.602086\pi$
$30$		0			0
$31$	−6.50994			−1.16922			−0.584610	−	0.811315i	$-0.698752\pi$
$31$	−6.50994			−1.16922			−0.584610	+	0.811315i	$0.698752\pi$
$32$	−2.24144	+	2.24144i	−0.396234	+	0.396234i
$33$		0			0
$34$		−	1.01284i		−	0.173700i
$35$	2.90706	+	9.95742i	0.491383	+	1.68311i
$36$		0			0
$37$	−4.02806	−	4.02806i	−0.662209	−	0.662209i	0.293691	−	0.955900i	$-0.405116\pi$
$37$	−4.02806	−	4.02806i	−0.662209	−	0.662209i	−0.955900	+	0.293691i	$0.905116\pi$
$38$	0.196860	+	0.196860i	0.0319349	+	0.0319349i
$39$		0			0
$40$	0.684330	+	2.34400i	0.108202	+	0.370619i
$41$		−	6.75296i		−	1.05464i	−0.849668	−	0.527318i	$-0.823198\pi$
$41$		−	6.75296i		−	1.05464i	0.849668	−	0.527318i	$-0.176802\pi$
$42$		0			0
$43$	−5.59200	+	5.59200i	−0.852772	+	0.852772i	−0.990474	−	0.137702i	$-0.956028\pi$
$43$	−5.59200	+	5.59200i	−0.852772	+	0.852772i	0.137702	+	0.990474i	$0.456028\pi$
$44$	5.46460			0.823819
$45$		0			0
$46$	0.0997698			0.0147103
$47$	4.48496	−	4.48496i	0.654198	−	0.654198i	−0.299803	−	0.954001i	$-0.596921\pi$
$47$	4.48496	−	4.48496i	0.654198	−	0.654198i	0.954001	+	0.299803i	$0.0969209\pi$
$48$		0			0
$49$			14.5203i			2.07432i
$50$	1.35928	+	0.300094i	0.192231	+	0.0424396i
$51$		0			0
$52$	5.77232	+	5.77232i	0.800477	+	0.800477i
$53$	−9.60045	−	9.60045i	−1.31872	−	1.31872i	−0.914787	−	0.403936i	$-0.867642\pi$
$53$	−9.60045	−	9.60045i	−1.31872	−	1.31872i	−0.403936	−	0.914787i	$-0.632358\pi$
$54$		0			0
$55$	3.05468	−	5.57375i	0.411893	−	0.751564i
$56$			5.06592i			0.676962i
$57$		0			0
$58$	−0.668392	+	0.668392i	−0.0877642	+	0.0877642i
$59$	12.3704			1.61049			0.805243	−	0.592946i	$-0.202035\pi$
$59$	12.3704			1.61049			0.805243	+	0.592946i	$0.202035\pi$
$60$		0			0
$61$	5.98606			0.766436			0.383218	−	0.923658i	$-0.374816\pi$
$61$	5.98606			0.766436			0.383218	+	0.923658i	$0.374816\pi$
$62$	−1.28155	+	1.28155i	−0.162756	+	0.162756i
$63$		0			0
$64$		−	6.19942i		−	0.774928i
$65$	9.11432	−	2.66092i	1.13049	−	0.330047i
$66$		0			0
$67$	0.701938	+	0.701938i	0.0857553	+	0.0857553i	0.748683	−	0.662928i	$-0.230686\pi$
$67$	0.701938	+	0.701938i	0.0857553	+	0.0857553i	−0.662928	+	0.748683i	$0.730686\pi$
$68$	4.94557	+	4.94557i	0.599739	+	0.599739i
$69$		0			0
$70$	2.53250	+	1.38793i	0.302692	+	0.165890i
$71$			14.5324i			1.72467i	0.506336	+	0.862336i	$0.331000\pi$
$71$			14.5324i			1.72467i	−0.506336	+	0.862336i	$0.669000\pi$
$72$		0			0
$73$	−7.06563	+	7.06563i	−0.826969	+	0.826969i	−0.987096	−	0.160127i	$-0.948809\pi$
$73$	−7.06563	+	7.06563i	−0.826969	+	0.826969i	0.160127	+	0.987096i	$0.448809\pi$
$74$	−1.58593			−0.184360
$75$		0			0
$76$	−1.92249			−0.220525
$77$	9.32400	−	9.32400i	1.06257	−	1.06257i
$78$		0			0
$79$		−	12.4635i		−	1.40226i	−0.713035	−	0.701128i	$-0.752680\pi$
$79$		−	12.4635i		−	1.40226i	0.713035	−	0.701128i	$-0.247320\pi$
$80$	−6.94344	−	3.80534i	−0.776301	−	0.425450i
$81$		0			0
$82$	−1.32939	−	1.32939i	−0.146806	−	0.146806i
$83$	−5.35197	−	5.35197i	−0.587455	−	0.587455i	0.349487	−	0.936941i	$-0.386356\pi$
$83$	−5.35197	−	5.35197i	−0.587455	−	0.587455i	−0.936941	+	0.349487i	$0.886356\pi$
$84$		0			0
$85$	7.80890	−	2.27980i	0.846994	−	0.247280i
$86$			2.20168i			0.237413i
$87$		0			0
$88$	2.19489	−	2.19489i	0.233976	−	0.233976i
$89$	−5.77421			−0.612065			−0.306033	−	0.952021i	$-0.599002\pi$
$89$	−5.77421			−0.612065			−0.306033	+	0.952021i	$0.599002\pi$
$90$		0			0
$91$	19.6981			2.06492
$92$	−0.487166	+	0.487166i	−0.0507905	+	0.0507905i
$93$		0			0
$94$		−	1.76582i		−	0.182130i
$95$	−1.07466	+	1.96089i	−0.110258	+	0.201183i
$96$		0			0
$97$	3.14970	+	3.14970i	0.319804	+	0.319804i	0.848692	−	0.528888i	$-0.177391\pi$
$97$	3.14970	+	3.14970i	0.319804	+	0.319804i	−0.528888	+	0.848692i	$0.677391\pi$
$98$	2.85846	+	2.85846i	0.288748	+	0.288748i
$99$		0			0
$100$	−8.10253	+	5.17188i	−0.810253	+	0.517188i
$101$			1.64693i			0.163875i	0.996637	+	0.0819376i	$0.0261108\pi$
$101$			1.64693i			0.163875i	−0.996637	+	0.0819376i	$0.973889\pi$
$102$		0			0
$103$	−9.45652	+	9.45652i	−0.931779	+	0.931779i	−0.997817	−	0.0660382i	$-0.978964\pi$
$103$	−9.45652	+	9.45652i	−0.931779	+	0.931779i	0.0660382	+	0.997817i	$0.478964\pi$
$104$	4.63698			0.454694
$105$		0			0
$106$	−3.77989			−0.367135
$107$	−12.8468	+	12.8468i	−1.24194	+	1.24194i	−0.282751	+	0.959193i	$0.591247\pi$
$107$	−12.8468	+	12.8468i	−1.24194	+	1.24194i	−0.959193	+	0.282751i	$0.908753\pi$
$108$		0			0
$109$		−	5.57072i		−	0.533579i	−0.963755	−	0.266789i	$-0.914037\pi$
$109$		−	5.57072i		−	0.533579i	0.963755	−	0.266789i	$-0.0859628\pi$
$110$	−0.495903	−	1.69859i	−0.0472825	−	0.161954i
$111$		0			0
$112$	−11.6153	−	11.6153i	−1.09754	−	1.09754i
$113$	−8.18267	−	8.18267i	−0.769761	−	0.769761i	0.208303	−	0.978064i	$-0.433206\pi$
$113$	−8.18267	−	8.18267i	−0.769761	−	0.769761i	−0.978064	+	0.208303i	$0.933206\pi$
$114$		0			0
$115$	0.224573	+	0.769219i	0.0209416	+	0.0717301i
$116$		−	6.52738i		−	0.606052i
$117$		0			0
$118$	2.43523	−	2.43523i	0.224181	−	0.224181i
$119$	16.8768			1.54710
$120$		0			0
$121$	2.92045			0.265495
$122$	1.17842	−	1.17842i	0.106689	−	0.106689i
$123$		0			0
$124$		−	12.5153i		−	1.12391i
$125$	0.745911	+	11.1554i	0.0667163	+	0.997772i
$126$		0			0
$127$	−0.708030	−	0.708030i	−0.0628275	−	0.0628275i	0.674995	−	0.737822i	$-0.264146\pi$
$127$	−0.708030	−	0.708030i	−0.0628275	−	0.0628275i	−0.737822	+	0.674995i	$0.764146\pi$
$128$	−5.70329	−	5.70329i	−0.504105	−	0.504105i
$129$		0			0
$130$	1.27042	−	2.31807i	0.111423	−	0.203308i
$131$		−	14.5949i		−	1.27517i	−0.770382	−	0.637583i	$-0.779934\pi$
$131$		−	14.5949i		−	1.27517i	0.770382	−	0.637583i	$-0.220066\pi$
$132$		0			0
$133$	−3.28026	+	3.28026i	−0.284435	+	0.284435i
$134$	0.276367			0.0238745
$135$		0			0
$136$	3.97284			0.340668
$137$	0.0445003	−	0.0445003i	0.00380192	−	0.00380192i	−0.705203	−	0.709005i	$-0.749144\pi$
$137$	0.0445003	−	0.0445003i	0.00380192	−	0.00380192i	0.709005	+	0.705203i	$0.249144\pi$
$138$		0			0
$139$		−	19.9136i		−	1.68905i	−0.535515	−	0.844526i	$-0.679882\pi$
$139$		−	19.9136i		−	1.68905i	0.535515	−	0.844526i	$-0.320118\pi$
$140$	−19.1431	+	5.58881i	−1.61788	+	0.472341i
$141$		0			0
$142$	2.86084	+	2.86084i	0.240076	+	0.240076i
$143$	−8.53453	−	8.53453i	−0.713693	−	0.713693i
$144$		0			0
$145$	−6.65775	−	3.64877i	−0.552896	−	0.303014i
$146$			2.78188i			0.230230i
$147$		0			0
$148$	7.74392	−	7.74392i	0.636546	−	0.636546i
$149$	−13.4325			−1.10043			−0.550216	−	0.835022i	$-0.685455\pi$
$149$	−13.4325			−1.10043			−0.550216	+	0.835022i	$0.685455\pi$
$150$		0			0
$151$	6.85582			0.557919			0.278959	−	0.960303i	$-0.410011\pi$
$151$	6.85582			0.557919			0.278959	+	0.960303i	$0.410011\pi$
$152$	−0.772182	+	0.772182i	−0.0626322	+	0.0626322i
$153$		0			0
$154$		−	3.67104i		−	0.295821i
$155$	−12.7653	−	6.99599i	−1.02533	−	0.561932i
$156$		0			0
$157$	10.6123	+	10.6123i	0.846954	+	0.846954i	0.989752	−	0.142798i	$-0.0456099\pi$
$157$	10.6123	+	10.6123i	0.846954	+	0.846954i	−0.142798	+	0.989752i	$0.545610\pi$
$158$	−2.45357	−	2.45357i	−0.195195	−	0.195195i
$159$		0			0
$160$	−6.80401	+	1.98643i	−0.537904	+	0.157041i
$161$			1.66246i			0.131020i
$162$		0			0
$163$	2.84105	−	2.84105i	0.222528	−	0.222528i	−0.587034	−	0.809562i	$-0.699705\pi$
$163$	2.84105	−	2.84105i	0.222528	−	0.222528i	0.809562	+	0.587034i	$0.199705\pi$
$164$	12.9825			1.01376
$165$		0			0
$166$	−2.10718			−0.163549
$167$	6.13455	−	6.13455i	0.474706	−	0.474706i	−0.428728	−	0.903434i	$-0.641038\pi$
$167$	6.13455	−	6.13455i	0.474706	−	0.474706i	0.903434	+	0.428728i	$0.141038\pi$
$168$		0			0
$169$		−	5.03026i		−	0.386943i
$170$	1.08846	−	1.98606i	0.0834809	−	0.152324i
$171$		0			0
$172$	−10.7506	−	10.7506i	−0.819724	−	0.819724i
$173$	−1.03653	−	1.03653i	−0.0788060	−	0.0788060i	0.666605	−	0.745411i	$-0.267747\pi$
$173$	−1.03653	−	1.03653i	−0.0788060	−	0.0788060i	−0.745411	+	0.666605i	$0.767747\pi$
$174$		0			0
$175$	−5.00044	+	22.6495i	−0.377998	+	1.71214i
$176$			10.0650i			0.758680i
$177$		0			0
$178$	−1.13671	+	1.13671i	−0.0852001	+	0.0852001i
$179$	9.34224			0.698272			0.349136	−	0.937072i	$-0.386475\pi$
$179$	9.34224			0.698272			0.349136	+	0.937072i	$0.386475\pi$
$180$		0			0
$181$	13.5363			1.00615			0.503073	−	0.864244i	$-0.332203\pi$
$181$	13.5363			1.00615			0.503073	+	0.864244i	$0.332203\pi$
$182$	3.87777	−	3.87777i	0.287439	−	0.287439i
$183$		0			0
$184$			0.391346i			0.0288504i
$185$	−3.56979	−	12.2274i	−0.262456	−	0.898977i
$186$		0			0
$187$	−7.31216	−	7.31216i	−0.534718	−	0.534718i
$188$	8.62230	+	8.62230i	0.628846	+	0.628846i
$189$		0			0
$190$	0.174463	+	0.597579i	0.0126569	+	0.0433530i
$191$			25.7618i			1.86406i	0.362384	+	0.932029i	$0.381963\pi$
$191$			25.7618i			1.86406i	−0.362384	+	0.932029i	$0.618037\pi$
$192$		0			0
$193$	13.3242	−	13.3242i	0.959098	−	0.959098i	−0.0400978	−	0.999196i	$-0.512767\pi$
$193$	13.3242	−	13.3242i	0.959098	−	0.959098i	0.999196	+	0.0400978i	$0.0127670\pi$
$194$	1.24010			0.0890341
$195$		0			0
$196$	−27.9151			−1.99393
$197$	−9.12930	+	9.12930i	−0.650436	+	0.650436i	−0.953098	−	0.302662i	$-0.902125\pi$
$197$	−9.12930	+	9.12930i	−0.650436	+	0.650436i	0.302662	+	0.953098i	$0.402125\pi$
$198$		0			0
$199$			6.83266i			0.484354i	0.970232	+	0.242177i	$0.0778615\pi$
$199$			6.83266i			0.484354i	−0.970232	+	0.242177i	$0.922138\pi$
$200$	−1.17711	+	5.33176i	−0.0832346	+	0.377012i
$201$		0			0
$202$	0.324214	+	0.324214i	0.0228116	+	0.0228116i
$203$	−11.1374	−	11.1374i	−0.781690	−	0.781690i
$204$		0			0
$205$	7.25716	−	13.2418i	0.506862	−	0.924849i
$206$			3.72322i			0.259409i
$207$		0			0
$208$	−10.6318	+	10.6318i	−0.737183	+	0.737183i
$209$	2.84245			0.196617
$210$		0			0
$211$	4.13944			0.284971			0.142485	−	0.989797i	$-0.454491\pi$
$211$	4.13944			0.284971			0.142485	+	0.989797i	$0.454491\pi$
$212$	18.4568	−	18.4568i	1.26762	−	1.26762i
$213$		0			0
$214$			5.05803i			0.345760i
$215$	−16.9748	+	4.95579i	−1.15767	+	0.337982i
$216$		0			0
$217$	−21.3543	−	21.3543i	−1.44962	−	1.44962i
$218$	−1.09665	−	1.09665i	−0.0742747	−	0.0742747i
$219$		0			0
$220$	10.7155	+	5.87260i	0.722438	+	0.395931i
$221$		−	15.4478i		−	1.03913i
$222$		0			0
$223$	−1.10160	+	1.10160i	−0.0737685	+	0.0737685i	−0.743028	−	0.669260i	$-0.766611\pi$
$223$	−1.10160	+	1.10160i	−0.0737685	+	0.0737685i	0.669260	+	0.743028i	$0.266611\pi$
$224$	−14.7050			−0.982520
$225$		0			0
$226$	−3.22168			−0.214303
$227$	−2.44141	+	2.44141i	−0.162042	+	0.162042i	−0.783471	−	0.621429i	$-0.786553\pi$
$227$	−2.44141	+	2.44141i	−0.162042	+	0.162042i	0.621429	+	0.783471i	$0.286553\pi$
$228$		0			0
$229$		−	2.55642i		−	0.168933i	−0.996426	−	0.0844665i	$-0.973081\pi$
$229$		−	2.55642i		−	0.168933i	0.996426	−	0.0844665i	$-0.0269186\pi$
$230$	0.195638	+	0.107219i	0.0129000	+	0.00706981i
$231$		0			0
$232$	−2.62176	−	2.62176i	−0.172127	−	0.172127i
$233$	−8.37313	−	8.37313i	−0.548542	−	0.548542i	0.377477	−	0.926019i	$-0.376792\pi$
$233$	−8.37313	−	8.37313i	−0.548542	−	0.548542i	−0.926019	+	0.377477i	$0.876792\pi$
$234$		0			0
$235$	13.6143	−	3.97470i	0.888101	−	0.259281i
$236$			23.7819i			1.54807i
$237$		0			0
$238$	3.32237	−	3.32237i	0.215357	−	0.215357i
$239$	−12.9049			−0.834747			−0.417374	−	0.908735i	$-0.637049\pi$
$239$	−12.9049			−0.834747			−0.417374	+	0.908735i	$0.637049\pi$
$240$		0			0
$241$	2.98783			0.192463			0.0962314	−	0.995359i	$-0.469321\pi$
$241$	2.98783			0.192463			0.0962314	+	0.995359i	$0.469321\pi$
$242$	0.574920	−	0.574920i	0.0369572	−	0.0369572i
$243$		0			0
$244$			11.5082i			0.736734i
$245$	−15.6044	+	28.4727i	−0.996928	+	1.81905i
$246$		0			0
$247$	3.00252	+	3.00252i	0.191046	+	0.191046i
$248$	−5.02685	−	5.02685i	−0.319206	−	0.319206i
$249$		0			0
$250$	2.34290	+	2.04922i	0.148178	+	0.129604i
$251$		−	2.30839i		−	0.145704i	−0.997343	−	0.0728522i	$-0.976790\pi$
$251$		−	2.30839i		−	0.145704i	0.997343	−	0.0728522i	$-0.0232101\pi$
$252$		0			0
$253$	0.720287	−	0.720287i	0.0452841	−	0.0452841i
$254$	−0.278766			−0.0174913
$255$		0			0
$256$	10.1533			0.634584
$257$	5.51697	−	5.51697i	0.344139	−	0.344139i	−0.513782	−	0.857921i	$-0.671756\pi$
$257$	5.51697	−	5.51697i	0.344139	−	0.344139i	0.857921	+	0.513782i	$0.171756\pi$
$258$		0			0
$259$		−	26.4262i		−	1.64205i
$260$	5.11560	+	17.5222i	0.317256	+	1.08668i
$261$		0			0
$262$	−2.87316	−	2.87316i	−0.177504	−	0.177504i
$263$	10.8028	+	10.8028i	0.666130	+	0.666130i	0.956818	−	0.290688i	$-0.0938842\pi$
$263$	10.8028	+	10.8028i	0.666130	+	0.666130i	−0.290688	+	0.956818i	$0.593884\pi$
$264$		0			0
$265$	−8.50820	−	29.1427i	−0.522654	−	1.79022i
$266$			1.29151i			0.0791873i
$267$		0			0
$268$	−1.34947	+	1.34947i	−0.0824320	+	0.0824320i
$269$	4.05850			0.247451			0.123725	−	0.992316i	$-0.460516\pi$
$269$	4.05850			0.247451			0.123725	+	0.992316i	$0.460516\pi$
$270$		0			0
$271$	20.1592			1.22458			0.612292	−	0.790632i	$-0.290248\pi$
$271$	20.1592			1.22458			0.612292	+	0.790632i	$0.290248\pi$
$272$	−9.10905	+	9.10905i	−0.552317	+	0.552317i
$273$		0			0
$274$		−	0.0175207i		−	0.00105846i
$275$	11.9798	−	7.64676i	0.722410	−	0.461117i
$276$		0			0
$277$	−5.84441	−	5.84441i	−0.351157	−	0.351157i	0.509383	−	0.860540i	$-0.329874\pi$
$277$	−5.84441	−	5.84441i	−0.351157	−	0.351157i	−0.860540	+	0.509383i	$0.829874\pi$
$278$	−3.92020	−	3.92020i	−0.235118	−	0.235118i
$279$		0			0
$280$	−5.44416	+	9.93372i	−0.325351	+	0.593653i
$281$			22.6267i			1.34980i	0.737910	+	0.674899i	$0.235813\pi$
$281$			22.6267i			1.34980i	−0.737910	+	0.674899i	$0.764187\pi$
$282$		0			0
$283$	0.149893	−	0.149893i	0.00891022	−	0.00891022i	−0.702638	−	0.711548i	$-0.747994\pi$
$283$	0.149893	−	0.149893i	0.00891022	−	0.00891022i	0.711548	+	0.702638i	$0.247994\pi$
$284$	−27.9383			−1.65784
$285$		0			0
$286$	−3.36021			−0.198694
$287$	22.1515	−	22.1515i	1.30756	−	1.30756i
$288$		0			0
$289$			3.76470i			0.221453i
$290$	−2.02894	+	0.592348i	−0.119144	+	0.0347839i
$291$		0			0
$292$	−13.5836	−	13.5836i	−0.794921	−	0.794921i
$293$	−23.2550	−	23.2550i	−1.35857	−	1.35857i	−0.875681	−	0.482890i	$-0.839587\pi$
$293$	−23.2550	−	23.2550i	−1.35857	−	1.35857i	−0.482890	−	0.875681i	$-0.660413\pi$
$294$		0			0
$295$	24.2570	+	13.2940i	1.41230	+	0.774006i
$296$		−	6.22079i		−	0.361576i
$297$		0			0
$298$	−2.64432	+	2.64432i	−0.153181	+	0.153181i
$299$	1.52170			0.0880019
$300$		0			0
$301$	−36.6865			−2.11457
$302$	1.34964	−	1.34964i	0.0776628	−	0.0776628i
$303$		0			0
$304$		−	3.54096i		−	0.203088i
$305$	11.7380	+	6.43300i	0.672117	+	0.368352i
$306$		0			0
$307$	10.6714	+	10.6714i	0.609046	+	0.609046i	0.942697	−	0.333650i	$-0.108281\pi$
$307$	10.6714	+	10.6714i	0.609046	+	0.609046i	−0.333650	+	0.942697i	$0.608281\pi$
$308$	17.9253	+	17.9253i	1.02139	+	1.02139i
$309$		0			0
$310$	−3.89020	+	1.13574i	−0.220949	+	0.0645059i
$311$		−	3.35074i		−	0.190003i	−0.995477	−	0.0950016i	$-0.969714\pi$
$311$		−	3.35074i		−	0.190003i	0.995477	−	0.0950016i	$-0.0302856\pi$
$312$		0			0
$313$	10.4058	−	10.4058i	0.588172	−	0.588172i	−0.348964	−	0.937136i	$-0.613466\pi$
$313$	10.4058	−	10.4058i	0.588172	−	0.588172i	0.937136	+	0.348964i	$0.113466\pi$
$314$	4.17827			0.235794
$315$		0			0
$316$	23.9610			1.34791
$317$	18.7671	−	18.7671i	1.05407	−	1.05407i	0.0556129	−	0.998452i	$-0.482289\pi$
$317$	18.7671	−	18.7671i	1.05407	−	1.05407i	0.998452	−	0.0556129i	$-0.0177113\pi$
$318$		0			0
$319$			9.65089i			0.540346i
$320$	6.66230	−	12.1564i	0.372434	−	0.679564i
$321$		0			0
$322$	0.327271	+	0.327271i	0.0182381	+	0.0182381i
$323$	2.57248	+	2.57248i	0.143137	+	0.143137i
$324$		0			0
$325$	20.7318	+	4.57705i	1.14999	+	0.253889i
$326$		−	1.11858i		−	0.0619523i
$327$		0			0
$328$	5.21451	−	5.21451i	0.287923	−	0.287923i
$329$	29.4237			1.62218
$330$		0			0
$331$	7.26043			0.399069			0.199535	−	0.979891i	$-0.436057\pi$
$331$	7.26043			0.399069			0.199535	+	0.979891i	$0.436057\pi$
$332$	10.2891	−	10.2891i	0.564688	−	0.564688i
$333$		0			0
$334$		−	2.41530i		−	0.132159i
$335$	0.622077	+	2.13077i	0.0339877	+	0.116416i
$336$		0			0
$337$	−5.18760	−	5.18760i	−0.282587	−	0.282587i	0.551553	−	0.834140i	$-0.314035\pi$
$337$	−5.18760	−	5.18760i	−0.282587	−	0.282587i	−0.834140	+	0.551553i	$0.814035\pi$
$338$	−0.990256	−	0.990256i	−0.0538628	−	0.0538628i
$339$		0			0
$340$	4.38291	+	15.0126i	0.237697	+	0.814170i
$341$			18.5042i			1.00206i
$342$		0			0
$343$	−24.6684	+	24.6684i	−1.33197	+	1.33197i
$344$	−8.63608			−0.465626
$345$		0			0
$346$	−0.408103			−0.0219398
$347$	8.09485	−	8.09485i	0.434554	−	0.434554i	−0.455620	−	0.890174i	$-0.650582\pi$
$347$	8.09485	−	8.09485i	0.434554	−	0.434554i	0.890174	+	0.455620i	$0.150582\pi$
$348$		0			0
$349$			7.68786i			0.411522i	0.978602	+	0.205761i	$0.0659669\pi$
$349$			7.68786i			0.411522i	−0.978602	+	0.205761i	$0.934033\pi$
$350$	3.47440	+	5.44318i	0.185715	+	0.290950i
$351$		0			0
$352$	6.37118	+	6.37118i	0.339585	+	0.339585i
$353$	−8.74952	−	8.74952i	−0.465690	−	0.465690i	0.434825	−	0.900515i	$-0.356810\pi$
$353$	−8.74952	−	8.74952i	−0.465690	−	0.465690i	−0.900515	+	0.434825i	$0.856810\pi$
$354$		0			0
$355$	−15.6174	+	28.4964i	−0.828885	+	1.51243i
$356$		−	11.1009i		−	0.588346i
$357$		0			0
$358$	1.83911	−	1.83911i	0.0972002	−	0.0972002i
$359$	18.2798			0.964773			0.482387	−	0.875958i	$-0.339770\pi$
$359$	18.2798			0.964773			0.482387	+	0.875958i	$0.339770\pi$
$360$		0			0
$361$	−1.00000			−0.0526316
$362$	2.66476	−	2.66476i	0.140057	−	0.140057i
$363$		0			0
$364$			37.8695i			1.98490i
$365$	−21.4481	+	6.26176i	−1.12264	+	0.327756i
$366$		0			0
$367$	12.2399	+	12.2399i	0.638917	+	0.638917i	0.950288	−	0.311372i	$-0.100788\pi$
$367$	12.2399	+	12.2399i	0.638917	+	0.638917i	−0.311372	+	0.950288i	$0.600788\pi$
$368$	−0.897291	−	0.897291i	−0.0467745	−	0.0467745i
$369$		0			0
$370$	−3.10983	−	1.70434i	−0.161673	−	0.0886044i
$371$		−	62.9840i		−	3.26997i
$372$		0			0
$373$	2.34385	−	2.34385i	0.121360	−	0.121360i	−0.643819	−	0.765178i	$-0.722651\pi$
$373$	2.34385	−	2.34385i	0.121360	−	0.121360i	0.765178	+	0.643819i	$0.222651\pi$
$374$	−2.87894			−0.148867
$375$		0			0
$376$	6.92640			0.357202
$377$	−10.1944	+	10.1944i	−0.525036	+	0.525036i
$378$		0			0
$379$			16.5772i			0.851514i	0.904838	+	0.425757i	$0.139992\pi$
$379$			16.5772i			0.851514i	−0.904838	+	0.425757i	$0.860008\pi$
$380$	−3.76980	−	2.06603i	−0.193387	−	0.105985i
$381$		0			0
$382$	5.07147	+	5.07147i	0.259479	+	0.259479i
$383$	17.1227	+	17.1227i	0.874929	+	0.874929i	0.993005	−	0.118076i	$-0.0376725\pi$
$383$	17.1227	+	17.1227i	0.874929	+	0.874929i	−0.118076	+	0.993005i	$0.537673\pi$
$384$		0			0
$385$	28.3035	−	8.26320i	1.44248	−	0.421132i
$386$		−	5.24601i		−	0.267015i
$387$		0			0
$388$	−6.05528	+	6.05528i	−0.307410	+	0.307410i
$389$	−33.9609			−1.72189			−0.860944	−	0.508700i	$-0.830126\pi$
$389$	−33.9609			−1.72189			−0.860944	+	0.508700i	$0.830126\pi$
$390$		0			0
$391$	1.30375			0.0659334
$392$	−11.2123	+	11.2123i	−0.566305	+	0.566305i
$393$		0			0
$394$			3.59439i			0.181083i
$395$	13.3941	−	24.4396i	0.673930	−	1.22969i
$396$		0			0
$397$	0.211422	+	0.211422i	0.0106110	+	0.0106110i	0.712392	−	0.701781i	$-0.247612\pi$
$397$	0.211422	+	0.211422i	0.0106110	+	0.0106110i	−0.701781	+	0.712392i	$0.747612\pi$
$398$	1.34508	+	1.34508i	0.0674226	+	0.0674226i
$399$		0			0
$400$	−9.52588	−	14.9237i	−0.476294	−	0.746187i
$401$		−	31.2069i		−	1.55840i	−0.626775	−	0.779200i	$-0.715626\pi$
$401$		−	31.2069i		−	1.55840i	0.626775	−	0.779200i	$-0.284374\pi$
$402$		0			0
$403$	−19.5462	+	19.5462i	−0.973667	+	0.973667i
$404$	−3.16620			−0.157524
$405$		0			0
$406$	−4.38500			−0.217624
$407$	−11.4496	+	11.4496i	−0.567535	+	0.567535i
$408$		0			0
$409$		−	11.8757i		−	0.587215i	−0.955926	−	0.293607i	$-0.905144\pi$
$409$		−	11.8757i		−	0.587215i	0.955926	−	0.293607i	$-0.0948559\pi$
$410$	−1.17814	−	4.03543i	−0.0581843	−	0.199296i
$411$		0			0
$412$	−18.1801	−	18.1801i	−0.895669	−	0.895669i
$413$	40.5781	+	40.5781i	1.99672	+	1.99672i
$414$		0			0
$415$	−4.74307	−	16.2462i	−0.232828	−	0.797494i
$416$			13.4599i			0.659927i
$417$		0			0
$418$	0.559566	−	0.559566i	0.0273692	−	0.0273692i
$419$	12.4413			0.607796			0.303898	−	0.952705i	$-0.401712\pi$
$419$	12.4413			0.607796			0.303898	+	0.952705i	$0.401712\pi$
$420$		0			0
$421$	−27.0263			−1.31718			−0.658591	−	0.752501i	$-0.728847\pi$
$421$	−27.0263			−1.31718			−0.658591	+	0.752501i	$0.728847\pi$
$422$	0.814890	−	0.814890i	0.0396682	−	0.0396682i
$423$		0			0
$424$		−	14.8266i		−	0.720042i
$425$	17.7624	+	3.92149i	0.861605	+	0.190220i
$426$		0			0
$427$	19.6358	+	19.6358i	0.950245	+	0.950245i
$428$	−24.6978	−	24.6978i	−1.19381	−	1.19381i
$429$		0			0
$430$	−2.36607	+	4.31726i	−0.114102	+	0.208197i
$431$			32.2593i			1.55388i	0.629577	+	0.776938i	$0.283228\pi$
$431$			32.2593i			1.55388i	−0.629577	+	0.776938i	$0.716772\pi$
$432$		0			0
$433$	−23.6058	+	23.6058i	−1.13442	+	1.13442i	−0.144988	+	0.989433i	$0.546314\pi$
$433$	−23.6058	+	23.6058i	−1.13442	+	1.13442i	−0.989433	+	0.144988i	$0.953686\pi$
$434$	−8.40762			−0.403579
$435$		0			0
$436$	10.7097			0.512900
$437$	−0.253403	+	0.253403i	−0.0121219	+	0.0121219i
$438$		0			0
$439$			16.0686i			0.766912i	0.923559	+	0.383456i	$0.125266\pi$
$439$			16.0686i			0.766912i	−0.923559	+	0.383456i	$0.874734\pi$
$440$	6.66272	−	1.94518i	0.317633	−	0.0927326i
$441$		0			0
$442$	−3.04106	−	3.04106i	−0.144649	−	0.144649i
$443$	−1.23540	−	1.23540i	−0.0586954	−	0.0586954i	0.677150	−	0.735845i	$-0.263215\pi$
$443$	−1.23540	−	1.23540i	−0.0586954	−	0.0586954i	−0.735845	+	0.677150i	$0.763215\pi$
$444$		0			0
$445$	−11.3226	−	6.20534i	−0.536743	−	0.294161i
$446$			0.433721i			0.0205373i
$447$		0			0
$448$	20.3357	−	20.3357i	0.960774	−	0.960774i
$449$	−0.0143358			−0.000676549			−0.000338275	−	1.00000i	$-0.500108\pi$
$449$	−0.0143358			−0.000676549			−0.000338275		1.00000i	$0.500108\pi$
$450$		0			0
$451$	−19.1950			−0.903857
$452$	15.7311	−	15.7311i	0.739930	−	0.739930i
$453$		0			0
$454$			0.961231i			0.0451128i
$455$	38.6259	+	21.1688i	1.81081	+	0.992411i
$456$		0			0
$457$	−2.37679	−	2.37679i	−0.111181	−	0.111181i	0.649328	−	0.760509i	$-0.275050\pi$
$457$	−2.37679	−	2.37679i	−0.111181	−	0.111181i	−0.760509	+	0.649328i	$0.775050\pi$
$458$	−0.503257	−	0.503257i	−0.0235156	−	0.0235156i
$459$		0			0
$460$	−1.47882	+	0.431740i	−0.0689502	+	0.0201300i
$461$		−	27.3369i		−	1.27321i	−0.771191	−	0.636604i	$-0.780339\pi$
$461$		−	27.3369i		−	1.27321i	0.771191	−	0.636604i	$-0.219661\pi$
$462$		0			0
$463$	−5.76332	+	5.76332i	−0.267844	+	0.267844i	−0.828231	−	0.560387i	$-0.810652\pi$
$463$	−5.76332	+	5.76332i	−0.267844	+	0.267844i	0.560387	+	0.828231i	$0.310652\pi$
$464$	12.0225			0.558131
$465$		0			0
$466$	−3.29667			−0.152715
$467$	−6.66825	+	6.66825i	−0.308570	+	0.308570i	−0.844355	−	0.535785i	$-0.820016\pi$
$467$	−6.66825	+	6.66825i	−0.308570	+	0.308570i	0.535785	+	0.844355i	$0.320016\pi$
$468$		0			0
$469$			4.60508i			0.212643i
$470$	1.89766	−	3.46258i	0.0875325	−	0.159717i
$471$		0			0
$472$	9.55217	+	9.55217i	0.439674	+	0.439674i
$473$	15.8950	+	15.8950i	0.730853	+	0.730853i
$474$		0			0
$475$	−4.21460	+	2.69020i	−0.193379	+	0.123435i
$476$			32.4456i			1.48714i
$477$		0			0
$478$	−2.54045	+	2.54045i	−0.116198	+	0.116198i
$479$	36.1338			1.65100			0.825498	−	0.564406i	$-0.190895\pi$
$479$	36.1338			1.65100			0.825498	+	0.564406i	$0.190895\pi$
$480$		0			0
$481$	−24.1887			−1.10291
$482$	0.588183	−	0.588183i	0.0267910	−	0.0267910i
$483$		0			0
$484$			5.61454i			0.255206i
$485$	2.79136	+	9.56110i	0.126749	+	0.434147i
$486$		0			0
$487$	5.43999	+	5.43999i	0.246509	+	0.246509i	0.819536	−	0.573027i	$-0.194231\pi$
$487$	5.43999	+	5.43999i	0.246509	+	0.246509i	−0.573027	+	0.819536i	$0.694231\pi$
$488$	4.62232	+	4.62232i	0.209243	+	0.209243i
$489$		0			0
$490$	2.53325	+	8.67701i	0.114440	+	0.391987i
$491$			26.8547i			1.21194i	0.795488	+	0.605969i	$0.207214\pi$
$491$			26.8547i			1.21194i	−0.795488	+	0.605969i	$0.792786\pi$
$492$		0			0
$493$	−8.73425	+	8.73425i	−0.393371	+	0.393371i
$494$	1.18215			0.0531875
$495$		0			0
$496$	23.0514			1.03504
$497$	−47.6699	+	47.6699i	−2.13829	+	2.13829i
$498$		0			0
$499$		−	7.27068i		−	0.325481i	−0.986669	−	0.162740i	$-0.947967\pi$
$499$		−	7.27068i		−	0.325481i	0.986669	−	0.162740i	$-0.0520333\pi$
$500$	−21.4462	+	1.43401i	−0.959104	+	0.0641308i
$501$		0			0
$502$	−0.454430	−	0.454430i	−0.0202822	−	0.0202822i
$503$	−8.94406	−	8.94406i	−0.398796	−	0.398796i	0.479012	−	0.877808i	$-0.340995\pi$
$503$	−8.94406	−	8.94406i	−0.398796	−	0.398796i	−0.877808	+	0.479012i	$0.840995\pi$
$504$		0			0
$505$	−1.76989	+	3.22945i	−0.0787591	+	0.143708i
$506$		−	0.283591i		−	0.0126072i
$507$		0			0
$508$	1.36118	−	1.36118i	0.0603927	−	0.0603927i
$509$	29.8639			1.32369			0.661847	−	0.749639i	$-0.269773\pi$
$509$	29.8639			1.32369			0.661847	+	0.749639i	$0.269773\pi$
$510$		0			0
$511$	−46.3542			−2.05059
$512$	13.4054	−	13.4054i	0.592439	−	0.592439i
$513$		0			0
$514$		−	2.17214i		−	0.0958091i
$515$	−28.7058	+	8.38064i	−1.26493	+	0.369295i
$516$		0			0
$517$	−12.7483	−	12.7483i	−0.560669	−	0.560669i
$518$	−5.20226	−	5.20226i	−0.228574	−	0.228574i
$519$		0			0
$520$	9.09262	+	4.98320i	0.398738	+	0.218528i
$521$			24.5231i			1.07438i	0.843462	+	0.537189i	$0.180514\pi$
$521$			24.5231i			1.07438i	−0.843462	+	0.537189i	$0.819486\pi$
$522$		0			0
$523$	11.6555	−	11.6555i	0.509660	−	0.509660i	−0.404762	−	0.914422i	$-0.632646\pi$
$523$	11.6555	−	11.6555i	0.509660	−	0.509660i	0.914422	+	0.404762i	$0.132646\pi$
$524$	28.0587			1.22575
$525$		0			0
$526$	4.25328			0.185452
$527$	−16.7467	+	16.7467i	−0.729497	+	0.729497i
$528$		0			0
$529$		−	22.8716i		−	0.994416i
$530$	−7.41195	−	4.06211i	−0.321955	−	0.176447i
$531$		0			0
$532$	−6.30628	−	6.30628i	−0.273412	−	0.273412i
$533$	−20.2759	−	20.2759i	−0.878247	−	0.878247i
$534$		0			0
$535$	−38.9971	+	11.3852i	−1.68599	+	0.492224i
$536$			1.08405i			0.0468237i
$537$		0			0
$538$	0.798955	−	0.798955i	0.0344454	−	0.0344454i
$539$	41.2732			1.77776
$540$		0			0
$541$	36.9585			1.58897			0.794485	−	0.607284i	$-0.207741\pi$
$541$	36.9585			1.58897			0.794485	+	0.607284i	$0.207741\pi$
$542$	3.96854	−	3.96854i	0.170463	−	0.170463i
$543$		0			0
$544$			11.5321i			0.494435i
$545$	5.98665	−	10.9236i	0.256440	−	0.467915i
$546$		0			0
$547$	25.5968	+	25.5968i	1.09444	+	1.09444i	0.995048	+	0.0993916i	$0.0316897\pi$
$547$	25.5968	+	25.5968i	1.09444	+	1.09444i	0.0993916	+	0.995048i	$0.468310\pi$
$548$	0.0855515	+	0.0855515i	0.00365458	+	0.00365458i
$549$		0			0
$550$	0.853003	−	3.86369i	0.0363722	−	0.164748i
$551$		−	3.39527i		−	0.144643i
$552$		0			0
$553$	40.8836	−	40.8836i	1.73855	−	1.73855i
$554$	−2.30106			−0.0977627
$555$		0			0
$556$	38.2838			1.62359
$557$	−15.3468	+	15.3468i	−0.650266	+	0.650266i	−0.953057	−	0.302791i	$-0.902082\pi$
$557$	−15.3468	+	15.3468i	−0.650266	+	0.650266i	0.302791	+	0.953057i	$0.402082\pi$
$558$		0			0
$559$			33.5802i			1.42029i
$560$	−10.2938	−	35.2588i	−0.434992	−	1.48996i
$561$		0			0
$562$	4.45430	+	4.45430i	0.187893	+	0.187893i
$563$	2.77754	+	2.77754i	0.117059	+	0.117059i	0.763210	−	0.646151i	$-0.223622\pi$
$563$	2.77754	+	2.77754i	0.117059	+	0.117059i	−0.646151	+	0.763210i	$0.723622\pi$
$564$		0			0
$565$	−7.25172	−	24.8390i	−0.305082	−	1.04498i
$566$		−	0.0590159i		−	0.00248062i
$567$		0			0
$568$	−11.2216	+	11.2216i	−0.470848	+	0.470848i
$569$	−6.43222			−0.269653			−0.134826	−	0.990869i	$-0.543048\pi$
$569$	−6.43222			−0.269653			−0.134826	+	0.990869i	$0.543048\pi$
$570$		0			0
$571$	22.5564			0.943957			0.471979	−	0.881610i	$-0.343540\pi$
$571$	22.5564			0.943957			0.471979	+	0.881610i	$0.343540\pi$
$572$	16.4076	−	16.4076i	0.686035	−	0.686035i
$573$		0			0
$574$		−	8.72148i		−	0.364028i
$575$	−0.386288	+	1.74970i	−0.0161093	+	0.0729674i
$576$		0			0
$577$	14.1411	+	14.1411i	0.588701	+	0.588701i	0.937280	−	0.348578i	$-0.113336\pi$
$577$	14.1411	+	14.1411i	0.588701	+	0.588701i	−0.348578	+	0.937280i	$0.613336\pi$
$578$	0.741119	+	0.741119i	0.0308265	+	0.0308265i
$579$		0			0
$580$	7.01473	−	12.7995i	0.291271	−	0.531469i
$581$		−	35.1117i		−	1.45668i
$582$		0			0
$583$	−27.2888	+	27.2888i	−1.13019	+	1.13019i
$584$	−10.9119			−0.451537
$585$		0			0
$586$	−9.15595			−0.378229
$587$	−30.3113	+	30.3113i	−1.25108	+	1.25108i	−0.295847	+	0.955235i	$0.595602\pi$
$587$	−30.3113	+	30.3113i	−1.25108	+	1.25108i	−0.955235	+	0.295847i	$0.904398\pi$
$588$		0			0
$589$		−	6.50994i		−	0.268237i
$590$	7.39228	−	2.15817i	0.304335	−	0.0888505i
$591$		0			0
$592$	14.2632	+	14.2632i	0.586215	+	0.586215i
$593$	7.53902	+	7.53902i	0.309590	+	0.309590i	0.844751	−	0.535160i	$-0.179749\pi$
$593$	7.53902	+	7.53902i	0.309590	+	0.309590i	−0.535160	+	0.844751i	$0.679749\pi$
$594$		0			0
$595$	33.0936	+	18.1369i	1.35671	+	0.743540i
$596$		−	25.8238i		−	1.05779i
$597$		0			0
$598$	0.299561	−	0.299561i	0.0122500	−	0.0122500i
$599$	19.3836			0.791991			0.395996	−	0.918252i	$-0.370400\pi$
$599$	19.3836			0.791991			0.395996	+	0.918252i	$0.370400\pi$
$600$		0			0
$601$	−38.6621			−1.57706			−0.788530	−	0.614996i	$-0.789157\pi$
$601$	−38.6621			−1.57706			−0.788530	+	0.614996i	$0.789157\pi$
$602$	−7.22210	+	7.22210i	−0.294351	+	0.294351i
$603$		0			0
$604$			13.1803i			0.536297i
$605$	5.72669	+	3.13850i	0.232823	+	0.127598i
$606$		0			0
$607$	0.301468	+	0.301468i	0.0122362	+	0.0122362i	0.713198	−	0.700962i	$-0.247246\pi$
$607$	0.301468	+	0.301468i	0.0122362	+	0.0122362i	−0.700962	+	0.713198i	$0.747246\pi$
$608$	−2.24144	−	2.24144i	−0.0909023	−	0.0909023i
$609$		0			0
$610$	3.57714	−	1.04435i	0.144834	−	0.0422843i
$611$		−	26.9323i		−	1.08957i
$612$		0			0
$613$	30.4937	−	30.4937i	1.23163	−	1.23163i	0.268293	−	0.963337i	$-0.413541\pi$
$613$	30.4937	−	30.4937i	1.23163	−	1.23163i	0.963337	−	0.268293i	$-0.0864595\pi$
$614$	4.20153			0.169560
$615$		0			0
$616$	14.3996			0.580178
$617$	17.4108	−	17.4108i	0.700931	−	0.700931i	−0.263679	−	0.964610i	$-0.584936\pi$
$617$	17.4108	−	17.4108i	0.700931	−	0.700931i	0.964610	+	0.263679i	$0.0849360\pi$
$618$		0			0
$619$		−	0.554678i		−	0.0222944i	−0.999938	−	0.0111472i	$-0.996452\pi$
$619$		−	0.554678i		−	0.0222944i	0.999938	−	0.0111472i	$-0.00354834\pi$
$620$	13.4497	−	24.5412i	0.540155	−	0.985597i
$621$		0			0
$622$	−0.659627	−	0.659627i	−0.0264486	−	0.0264486i
$623$	−18.9409	−	18.9409i	−0.758853	−	0.758853i
$624$		0			0
$625$	−10.5257	+	22.6762i	−0.421027	+	0.907048i
$626$		−	4.09698i		−	0.163748i
$627$		0			0
$628$	−20.4021	+	20.4021i	−0.814131	+	0.814131i
$629$	−20.7242			−0.826329
$630$		0			0
$631$	−45.0593			−1.79378			−0.896892	−	0.442249i	$-0.854181\pi$
$631$	−45.0593			−1.79378			−0.896892	+	0.442249i	$0.854181\pi$
$632$	9.62410	−	9.62410i	0.382826	−	0.382826i
$633$		0			0
$634$		−	7.38898i		−	0.293454i
$635$	−0.627477	−	2.14927i	−0.0249007	−	0.0852910i
$636$		0			0
$637$	43.5974	+	43.5974i	1.72739	+	1.72739i
$638$	1.89987	+	1.89987i	0.0752168	+	0.0752168i
$639$		0			0
$640$	−5.05442	−	17.3127i	−0.199794	−	0.684343i
$641$		−	9.70696i		−	0.383402i	−0.981453	−	0.191701i	$-0.938600\pi$
$641$		−	9.70696i		−	0.383402i	0.981453	−	0.191701i	$-0.0614004\pi$
$642$		0			0
$643$	−17.8061	+	17.8061i	−0.702206	+	0.702206i	−0.964884	−	0.262678i	$-0.915394\pi$
$643$	−17.8061	+	17.8061i	−0.702206	+	0.702206i	0.262678	+	0.964884i	$0.415394\pi$
$644$	−3.19606			−0.125943
$645$		0			0
$646$	1.01284			0.0398495
$647$	−14.2276	+	14.2276i	−0.559343	+	0.559343i	−0.929120	−	0.369777i	$-0.879434\pi$
$647$	−14.2276	+	14.2276i	−0.559343	+	0.559343i	0.369777	+	0.929120i	$0.379434\pi$
$648$		0			0
$649$		−	35.1622i		−	1.38024i
$650$	4.98230	−	3.18022i	0.195422	−	0.124739i
$651$		0			0
$652$	5.46190	+	5.46190i	0.213904	+	0.213904i
$653$	1.40028	+	1.40028i	0.0547973	+	0.0547973i	0.733974	−	0.679177i	$-0.237663\pi$
$653$	1.40028	+	1.40028i	0.0547973	+	0.0547973i	−0.679177	+	0.733974i	$0.737663\pi$
$654$		0			0
$655$	15.6847	−	28.6191i	0.612850	−	1.11824i
$656$			23.9120i			0.933606i
$657$		0			0
$658$	5.79234	−	5.79234i	0.225809	−	0.225809i
$659$	24.7015			0.962234			0.481117	−	0.876656i	$-0.340231\pi$
$659$	24.7015			0.962234			0.481117	+	0.876656i	$0.340231\pi$
$660$		0			0
$661$	44.0346			1.71275			0.856373	−	0.516357i	$-0.172712\pi$
$661$	44.0346			1.71275			0.856373	+	0.516357i	$0.172712\pi$
$662$	1.42929	−	1.42929i	0.0555509	−	0.0555509i
$663$		0			0
$664$		−	8.26538i		−	0.320759i
$665$	−9.95742	+	2.90706i	−0.386132	+	0.112731i
$666$		0			0
$667$	−0.860371	−	0.860371i	−0.0333137	−	0.0333137i
$668$	11.7936	+	11.7936i	0.456309	+	0.456309i
$669$		0			0
$670$	0.541926	+	0.297001i	0.0209364	+	0.0114742i
$671$		−	17.0151i		−	0.656861i
$672$		0			0
$673$	−4.80058	+	4.80058i	−0.185049	+	0.185049i	−0.793552	−	0.608503i	$-0.791770\pi$
$673$	−4.80058	+	4.80058i	−0.185049	+	0.185049i	0.608503	+	0.793552i	$0.291770\pi$
$674$	−2.04246			−0.0786727
$675$		0			0
$676$	9.67063			0.371947
$677$	−31.2272	+	31.2272i	−1.20016	+	1.20016i	−0.226040	+	0.974118i	$0.572578\pi$
$677$	−31.2272	+	31.2272i	−1.20016	+	1.20016i	−0.974118	+	0.226040i	$0.927422\pi$
$678$		0			0
$679$			20.6637i			0.793001i
$680$	7.79032	+	4.26947i	0.298745	+	0.163727i
$681$		0			0
$682$	3.64274	+	3.64274i	0.139488	+	0.139488i
$683$	−21.8048	−	21.8048i	−0.834338	−	0.834338i	0.153769	−	0.988107i	$-0.450859\pi$
$683$	−21.8048	−	21.8048i	−0.834338	−	0.834338i	−0.988107	+	0.153769i	$0.950859\pi$
$684$		0			0
$685$	0.135083	−	0.0394375i	0.00516126	−	0.00150683i
$686$			9.71245i			0.370823i
$687$		0			0
$688$	19.8011	−	19.8011i	0.754908	−	0.754908i
$689$	−57.6511			−2.19633
$690$		0			0
$691$	−23.7352			−0.902931			−0.451465	−	0.892289i	$-0.649099\pi$
$691$	−23.7352			−0.902931			−0.451465	+	0.892289i	$0.649099\pi$
$692$	1.99272	−	1.99272i	0.0757520	−	0.0757520i
$693$		0			0
$694$		−	3.18710i		−	0.120981i
$695$	21.4004	−	39.0485i	0.811765	−	1.48119i
$696$		0			0
$697$	−17.3718	−	17.3718i	−0.658006	−	0.658006i
$698$	1.51343	+	1.51343i	0.0572842	+	0.0572842i
$699$		0			0
$700$	−43.5436	−	9.61331i	−1.64579	−	0.363349i
$701$		−	5.70139i		−	0.215339i	−0.994187	−	0.107669i	$-0.965661\pi$
$701$		−	5.70139i		−	0.215339i	0.994187	−	0.107669i	$-0.0343388\pi$
$702$		0			0
$703$	4.02806	−	4.02806i	0.151921	−	0.151921i
$704$	−17.6216			−0.664138
$705$		0			0
$706$	−3.44486			−0.129649
$707$	−5.40235	+	5.40235i	−0.203176	+	0.203176i
$708$		0			0
$709$			6.83499i			0.256693i	0.991729	+	0.128347i	$0.0409670\pi$
$709$			6.83499i			0.256693i	−0.991729	+	0.128347i	$0.959033\pi$
$710$	2.53536	+	8.68423i	0.0951502	+	0.325913i
$711$		0			0
$712$	−4.45874	−	4.45874i	−0.167098	−	0.167098i
$713$	−1.64964	−	1.64964i	−0.0617794	−	0.0617794i
$714$		0			0
$715$	−7.56355	−	25.9070i	−0.282861	−	0.968868i
$716$			17.9604i			0.671211i
$717$		0			0
$718$	3.59857	−	3.59857i	0.134297	−	0.134297i
$719$	−25.6264			−0.955703			−0.477852	−	0.878441i	$-0.658584\pi$
$719$	−25.6264			−0.955703			−0.477852	+	0.878441i	$0.658584\pi$
$720$		0			0
$721$	−62.0398			−2.31048
$722$	−0.196860	+	0.196860i	−0.00732637	+	0.00732637i
$723$		0			0
$724$			26.0235i			0.967154i
$725$	−9.13394	−	14.3097i	−0.339226	−	0.531449i
$726$		0			0
$727$	−19.7895	−	19.7895i	−0.733951	−	0.733951i	0.237449	−	0.971400i	$-0.423689\pi$
$727$	−19.7895	−	19.7895i	−0.733951	−	0.733951i	−0.971400	+	0.237449i	$0.923689\pi$
$728$	15.2105	+	15.2105i	0.563739	+	0.563739i
$729$		0			0
$730$	−2.98958	+	5.45496i	−0.110649	+	0.201897i
$731$			28.7706i			1.06412i
$732$		0			0
$733$	22.9264	−	22.9264i	0.846805	−	0.846805i	−0.142928	−	0.989733i	$-0.545652\pi$
$733$	22.9264	−	22.9264i	0.846805	−	0.846805i	0.989733	+	0.142928i	$0.0456516\pi$
$734$	4.81909			0.177876
$735$		0			0
$736$	−1.13597			−0.0418726
$737$	1.99523	−	1.99523i	0.0734951	−	0.0734951i
$738$		0			0
$739$		−	20.3970i		−	0.750314i	−0.926961	−	0.375157i	$-0.877589\pi$
$739$		−	20.3970i		−	0.750314i	0.926961	−	0.375157i	$-0.122411\pi$
$740$	23.5071	−	6.86288i	0.864138	−	0.252285i
$741$		0			0
$742$	−12.3990	−	12.3990i	−0.455183	−	0.455183i
$743$	−12.4215	−	12.4215i	−0.455701	−	0.455701i	0.441540	−	0.897241i	$-0.354432\pi$
$743$	−12.4215	−	12.4215i	−0.455701	−	0.455701i	−0.897241	+	0.441540i	$0.854432\pi$
$744$		0			0
$745$	−26.3397	−	14.4354i	−0.965010	−	0.528872i
$746$		−	0.922818i		−	0.0337868i
$747$		0			0
$748$	14.0576	−	14.0576i	0.513995	−	0.513995i
$749$	−84.2816			−3.07958
$750$		0			0
$751$	46.9971			1.71495			0.857474	−	0.514527i	$-0.172033\pi$
$751$	46.9971			1.71495			0.857474	+	0.514527i	$0.172033\pi$
$752$	−15.8811	+	15.8811i	−0.579123	+	0.579123i
$753$		0			0
$754$			4.01372i			0.146171i
$755$	13.4435	+	7.36770i	0.489260	+	0.268138i
$756$		0			0
$757$	−31.5005	−	31.5005i	−1.14490	−	1.14490i	−0.987541	−	0.157363i	$-0.949701\pi$
$757$	−31.5005	−	31.5005i	−1.14490	−	1.14490i	−0.157363	−	0.987541i	$-0.550299\pi$
$758$	3.26339	+	3.26339i	0.118532	+	0.118532i
$759$		0			0
$760$	−2.34400	+	0.684330i	−0.0850258	+	0.0248232i
$761$			38.0826i			1.38049i	0.723575	+	0.690246i	$0.242498\pi$
$761$			38.0826i			1.38049i	−0.723575	+	0.690246i	$0.757502\pi$
$762$		0			0
$763$	18.2734	−	18.2734i	0.661543	−	0.661543i
$764$	−49.5269			−1.79182
$765$		0			0
$766$	6.74155			0.243582
$767$	37.1423	−	37.1423i	1.34113	−	1.34113i
$768$		0			0
$769$		−	15.7427i		−	0.567695i	−0.958869	−	0.283847i	$-0.908389\pi$
$769$		−	15.7427i		−	0.567695i	0.958869	−	0.283847i	$-0.0916109\pi$
$770$	3.94514	−	7.19852i	0.142173	−	0.259417i
$771$		0			0
$772$	25.6157	+	25.6157i	0.921929	+	0.921929i
$773$	22.0538	+	22.0538i	0.793220	+	0.793220i	0.982016	−	0.188796i	$-0.0604585\pi$
$773$	22.0538	+	22.0538i	0.793220	+	0.793220i	−0.188796	+	0.982016i	$0.560458\pi$
$774$		0			0
$775$	−17.5130	−	27.4368i	−0.629086	−	0.985558i
$776$			4.86429i			0.174618i
$777$		0			0
$778$	−6.68555	+	6.68555i	−0.239689	+	0.239689i
$779$	6.75296			0.241950
$780$		0			0
$781$	41.3076			1.47810
$782$	0.256656	−	0.256656i	0.00917799	−	0.00917799i
$783$		0			0
$784$		−	51.4157i		−	1.83627i
$785$	9.40493	+	32.2142i	0.335676	+	1.14978i
$786$		0			0
$787$	−20.7340	−	20.7340i	−0.739088	−	0.739088i	0.233314	−	0.972401i	$-0.425043\pi$
$787$	−20.7340	−	20.7340i	−0.739088	−	0.739088i	−0.972401	+	0.233314i	$0.925043\pi$
$788$	−17.5510	−	17.5510i	−0.625229	−	0.625229i
$789$		0			0
$790$	−2.17442	−	7.44794i	−0.0773625	−	0.264986i
$791$		−	53.6826i		−	1.90873i
$792$		0			0
$793$	17.9733	−	17.9733i	0.638249	−	0.638249i
$794$	0.0832409			0.00295411
$795$		0			0
$796$	−13.1357			−0.465584
$797$	−25.2451	+	25.2451i	−0.894226	+	0.894226i	−0.994918	−	0.100692i	$-0.967894\pi$
$797$	−25.2451	+	25.2451i	−0.894226	+	0.894226i	0.100692	+	0.994918i	$0.467894\pi$
$798$		0			0
$799$		−	23.0749i		−	0.816332i
$800$	−15.4767	−	3.41685i	−0.547183	−	0.120804i
$801$		0			0
$802$	−6.14340	−	6.14340i	−0.216931	−	0.216931i
$803$	20.0837	+	20.0837i	0.708739	+	0.708739i
$804$		0			0
$805$	−1.78658	+	3.25990i	−0.0629688	+	0.114896i
$806$			7.69574i			0.271071i
$807$		0			0
$808$	−1.27173	+	1.27173i	−0.0447392	+	0.0447392i
$809$	−15.2569			−0.536405			−0.268203	−	0.963363i	$-0.586430\pi$
$809$	−15.2569			−0.536405			−0.268203	+	0.963363i	$0.586430\pi$
$810$		0			0
$811$	−21.1266			−0.741857			−0.370928	−	0.928661i	$-0.620960\pi$
$811$	−21.1266			−0.741857			−0.370928	+	0.928661i	$0.620960\pi$
$812$	21.4115	−	21.4115i	0.751397	−	0.751397i
$813$		0			0
$814$			4.50793i			0.158003i
$815$	8.62417	−	2.51782i	0.302091	−	0.0881954i
$816$		0			0
$817$	−5.59200	−	5.59200i	−0.195639	−	0.195639i
$818$	−2.33785	−	2.33785i	−0.0817409	−	0.0817409i
$819$		0			0
$820$	25.4573	+	13.9518i	0.889008	+	0.487219i
$821$		−	9.42350i		−	0.328882i	−0.986387	−	0.164441i	$-0.947418\pi$
$821$		−	9.42350i		−	0.328882i	0.986387	−	0.164441i	$-0.0525821\pi$
$822$		0			0
$823$	−22.8717	+	22.8717i	−0.797258	+	0.797258i	−0.982662	−	0.185404i	$-0.940640\pi$
$823$	−22.8717	+	22.8717i	−0.797258	+	0.797258i	0.185404	+	0.982662i	$0.440640\pi$
$824$	−14.6043			−0.508765
$825$		0			0
$826$	15.9764			0.555890
$827$	−11.5961	+	11.5961i	−0.403235	+	0.403235i	−0.879371	−	0.476136i	$-0.842037\pi$
$827$	−11.5961	+	11.5961i	−0.403235	+	0.403235i	0.476136	+	0.879371i	$0.342037\pi$
$828$		0			0
$829$			49.4097i			1.71607i	0.513593	+	0.858034i	$0.328314\pi$
$829$			49.4097i			1.71607i	−0.513593	+	0.858034i	$0.671686\pi$
$830$	−4.13194	−	2.26450i	−0.143422	−	0.0786021i
$831$		0			0
$832$	−18.6139	−	18.6139i	−0.645321	−	0.645321i
$833$	37.3531	+	37.3531i	1.29421	+	1.29421i
$834$		0			0
$835$	18.6218	−	5.43662i	0.644433	−	0.188142i
$836$			5.46460i			0.188997i
$837$		0			0
$838$	2.44919	−	2.44919i	0.0846058	−	0.0846058i
$839$	−22.4894			−0.776420			−0.388210	−	0.921571i	$-0.626906\pi$
$839$	−22.4894			−0.776420			−0.388210	+	0.921571i	$0.626906\pi$
$840$		0			0
$841$	−17.4722			−0.602488
$842$	−5.32040	+	5.32040i	−0.183353	+	0.183353i
$843$		0			0
$844$			7.95804i			0.273927i
$845$	5.40583	−	9.86379i	0.185966	−	0.339325i
$846$		0			0
$847$	9.57984	+	9.57984i	0.329167	+	0.329167i
$848$	33.9948	+	33.9948i	1.16739	+	1.16739i
$849$		0			0
$850$	4.26870	−	2.72473i	0.146415	−	0.0934574i
$851$		−	2.04145i		−	0.0699799i
$852$		0			0
$853$	−8.92630	+	8.92630i	−0.305631	+	0.305631i	−0.843212	−	0.537581i	$-0.819338\pi$
$853$	−8.92630	+	8.92630i	−0.305631	+	0.305631i	0.537581	+	0.843212i	$0.319338\pi$
$854$	7.73102			0.264550
$855$		0			0
$856$	−19.8401			−0.678120
$857$	−23.0946	+	23.0946i	−0.788897	+	0.788897i	−0.981313	−	0.192416i	$-0.938368\pi$
$857$	−23.0946	+	23.0946i	−0.788897	+	0.788897i	0.192416	+	0.981313i	$0.438368\pi$
$858$		0			0
$859$			1.25456i			0.0428049i	0.999771	+	0.0214025i	$0.00681314\pi$
$859$			1.25456i			0.0428049i	−0.999771	+	0.0214025i	$0.993187\pi$
$860$	−9.52747	−	32.6340i	−0.324884	−	1.11281i
$861$		0			0
$862$	6.35056	+	6.35056i	0.216301	+	0.216301i
$863$	5.33530	+	5.33530i	0.181616	+	0.181616i	0.792060	−	0.610444i	$-0.209009\pi$
$863$	5.33530	+	5.33530i	0.181616	+	0.181616i	−0.610444	+	0.792060i	$0.709009\pi$
$864$		0			0
$865$	−0.918604	−	3.14645i	−0.0312335	−	0.106983i
$866$			9.29407i			0.315825i
$867$		0			0
$868$	41.0535	−	41.0535i	1.39345	−	1.39345i
$869$	−35.4270			−1.20178
$870$		0			0
$871$	4.21516			0.142825
$872$	4.30161	−	4.30161i	0.145671	−	0.145671i
$873$		0			0
$874$			0.0997698i			0.00337477i
$875$	−34.1460	+	39.0395i	−1.15434	+	1.31978i
$876$		0			0
$877$	29.0640	+	29.0640i	0.981422	+	0.981422i	0.999831	−	0.0184088i	$-0.00586003\pi$
$877$	29.0640	+	29.0640i	0.981422	+	0.981422i	−0.0184088	+	0.999831i	$0.505860\pi$
$878$	3.16326	+	3.16326i	0.106755	+	0.106755i
$879$		0			0
$880$	−10.8165	+	19.7364i	−0.364625	+	0.665315i
$881$		−	18.4567i		−	0.621823i	−0.950439	−	0.310911i	$-0.899366\pi$
$881$		−	18.4567i		−	0.621823i	0.950439	−	0.310911i	$-0.100634\pi$
$882$		0			0
$883$	21.3213	−	21.3213i	0.717519	−	0.717519i	−0.250577	−	0.968097i	$-0.580620\pi$
$883$	21.3213	−	21.3213i	0.717519	−	0.717519i	0.968097	+	0.250577i	$0.0806204\pi$
$884$	29.6984			0.998864
$885$		0			0
$886$	−0.486400			−0.0163409
$887$	−25.0749	+	25.0749i	−0.841933	+	0.841933i	−0.989110	−	0.147177i	$-0.952981\pi$
$887$	−25.0749	+	25.0749i	−0.841933	+	0.841933i	0.147177	+	0.989110i	$0.452981\pi$
$888$		0			0
$889$		−	4.64505i		−	0.155790i
$890$	−3.45055	+	1.00739i	−0.115663	+	0.0337677i
$891$		0			0
$892$	−2.11782	−	2.11782i	−0.0709097	−	0.0709097i
$893$	4.48496	+	4.48496i	0.150083	+	0.150083i
$894$		0			0
$895$	18.3191	+	10.0398i	0.612341	+	0.335592i
$896$		−	37.4166i		−	1.25000i
$897$		0			0
$898$	−0.00282215	+	0.00282215i	−9.41763e−5	+	9.41763e-5i
$899$	22.1030			0.737176
$900$		0			0
$901$	−49.3939			−1.64555
$902$	−3.77872	+	3.77872i	−0.125818	+	0.125818i
$903$		0			0
$904$		−	12.6370i		−	0.420301i
$905$	26.5433	+	14.5470i	0.882328	+	0.483558i
$906$		0			0
$907$	−9.41214	−	9.41214i	−0.312525	−	0.312525i	0.533362	−	0.845887i	$-0.320928\pi$
$907$	−9.41214	−	9.41214i	−0.312525	−	0.312525i	−0.845887	+	0.533362i	$0.820928\pi$
$908$	−4.69359	−	4.69359i	−0.155762	−	0.155762i
$909$		0			0
$910$	11.7712	−	3.43659i	0.390211	−	0.113922i
$911$			11.1658i			0.369940i	0.982744	+	0.184970i	$0.0592188\pi$
$911$			11.1658i			0.369940i	−0.982744	+	0.184970i	$0.940781\pi$
$912$		0			0
$913$	−15.2127	+	15.2127i	−0.503468	+	0.503468i
$914$	−0.935788			−0.0309531
$915$		0			0
$916$	4.91470			0.162386
$917$	47.8753	−	47.8753i	1.58098	−	1.58098i
$918$		0			0
$919$			2.91882i			0.0962828i	0.998841	+	0.0481414i	$0.0153298\pi$
$919$			2.91882i			0.0962828i	−0.998841	+	0.0481414i	$0.984670\pi$
$920$	−0.420566	+	0.767388i	−0.0138656	+	0.0253000i
$921$		0			0
$922$	−5.38155	−	5.38155i	−0.177232	−	0.177232i
$923$	43.6337	+	43.6337i	1.43622	+	1.43622i
$924$		0			0
$925$	6.14039	−	27.8129i	0.201895	−	0.914484i
$926$			2.26913i			0.0745683i
$927$		0			0
$928$	7.61028	−	7.61028i	0.249820	−	0.249820i
$929$	2.48012			0.0813701			0.0406850	−	0.999172i	$-0.487046\pi$
$929$	2.48012			0.0813701			0.0406850	+	0.999172i	$0.487046\pi$
$930$		0			0
$931$	−14.5203			−0.475882
$932$	16.0973	−	16.0973i	0.527284	−	0.527284i
$933$		0			0
$934$			2.62542i			0.0859064i
$935$	−6.48024	−	22.1965i	−0.211927	−	0.725902i
$936$		0			0
$937$	−26.1520	−	26.1520i	−0.854349	−	0.854349i	0.136316	−	0.990665i	$-0.456474\pi$
$937$	−26.1520	−	26.1520i	−0.854349	−	0.854349i	−0.990665	+	0.136316i	$0.956474\pi$
$938$	0.906556	+	0.906556i	0.0296001	+	0.0296001i
$939$		0			0
$940$	7.64133	+	26.1735i	0.249233	+	0.853684i
$941$		−	51.4117i		−	1.67597i	−0.545691	−	0.837987i	$-0.683733\pi$
$941$		−	51.4117i		−	1.67597i	0.545691	−	0.837987i	$-0.316267\pi$
$942$		0			0
$943$	1.71122	−	1.71122i	0.0557250	−	0.0557250i
$944$	−43.8030			−1.42567
$945$		0			0
$946$	6.25818			0.203471
$947$	−16.6633	+	16.6633i	−0.541485	+	0.541485i	−0.923964	−	0.382479i	$-0.875070\pi$
$947$	−16.6633	+	16.6633i	−0.541485	+	0.541485i	0.382479	+	0.923964i	$0.375070\pi$
$948$		0			0
$949$			42.4294i			1.37732i
$950$	−0.300094	+	1.35928i	−0.00973632	+	0.0441008i
$951$		0			0
$952$	13.0320	+	13.0320i	0.422369	+	0.422369i
$953$	15.8821	+	15.8821i	0.514471	+	0.514471i	0.915893	−	0.401422i	$-0.131484\pi$
$953$	15.8821	+	15.8821i	0.514471	+	0.514471i	−0.401422	+	0.915893i	$0.631484\pi$
$954$		0			0
$955$	−27.6853	+	50.5161i	−0.895874	+	1.63466i
$956$		−	24.8095i		−	0.802398i
$957$		0			0
$958$	7.11330	−	7.11330i	0.229820	−	0.229820i
$959$	0.291945			0.00942741
$960$		0			0
$961$	11.3793			0.367074
$962$	−4.76178	+	4.76178i	−0.153526	+	0.153526i
$963$		0			0
$964$			5.74407i			0.185004i
$965$	40.4464	−	11.8083i	1.30202	−	0.380123i
$966$		0			0
$967$	−5.99852	−	5.99852i	−0.192899	−	0.192899i	0.604048	−	0.796948i	$-0.293553\pi$
$967$	−5.99852	−	5.99852i	−0.192899	−	0.192899i	−0.796948	+	0.604048i	$0.793553\pi$
$968$	2.25512	+	2.25512i	0.0724822	+	0.0724822i
$969$		0			0
$970$	2.43171	+	1.33269i	0.0780773	+	0.0427901i
$971$		−	9.61709i		−	0.308627i	−0.988022	−	0.154314i	$-0.950683\pi$
$971$		−	9.61709i		−	0.308627i	0.988022	−	0.154314i	$-0.0493166\pi$
$972$		0			0
$973$	65.3219	−	65.3219i	2.09413	−	2.09413i
$974$	2.14183			0.0686287
$975$		0			0
$976$	−21.1964			−0.678480
$977$	14.2872	−	14.2872i	0.457088	−	0.457088i	−0.440610	−	0.897699i	$-0.645238\pi$
$977$	14.2872	−	14.2872i	0.457088	−	0.457088i	0.897699	+	0.440610i	$0.145238\pi$
$978$		0			0
$979$			16.4129i			0.524560i
$980$	−54.7385	−	29.9993i	−1.74856	−	0.958293i
$981$		0			0
$982$	5.28662	+	5.28662i	0.168703	+	0.168703i
$983$	−5.56834	−	5.56834i	−0.177603	−	0.177603i	0.612707	−	0.790310i	$-0.290080\pi$
$983$	−5.56834	−	5.56834i	−0.177603	−	0.177603i	−0.790310	+	0.612707i	$0.790080\pi$
$984$		0			0
$985$	−27.7125	+	8.09065i	−0.882994	+	0.257790i
$986$			3.43885i			0.109515i
$987$		0			0
$988$	−5.77232	+	5.77232i	−0.183642	+	0.183642i
$989$	−2.83406			−0.0901179
$990$		0			0
$991$	23.1676			0.735943			0.367972	−	0.929837i	$-0.380052\pi$
$991$	23.1676			0.735943			0.367972	+	0.929837i	$0.380052\pi$
$992$	14.5916	−	14.5916i	0.463284	−	0.463284i
$993$		0			0
$994$			18.7686i			0.595304i
$995$	−7.34281	+	13.3981i	−0.232783	+	0.424749i
$996$		0			0
$997$	−13.1051	−	13.1051i	−0.415042	−	0.415042i	0.468449	−	0.883491i	$-0.344813\pi$
$997$	−13.1051	−	13.1051i	−0.415042	−	0.415042i	−0.883491	+	0.468449i	$0.844813\pi$
$998$	−1.43131	−	1.43131i	−0.0453072	−	0.0453072i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.n.e.647.10	yes	36
3.2	odd	2	inner	855.2.n.e.647.9	✓	36
5.3	odd	4	inner	855.2.n.e.818.9	yes	36
15.8	even	4	inner	855.2.n.e.818.10	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
855.2.n.e.647.9	✓	36	3.2	odd	2	inner
855.2.n.e.647.10	yes	36	1.1	even	1	trivial
855.2.n.e.818.9	yes	36	5.3	odd	4	inner
855.2.n.e.818.10	yes	36	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)

\(f(q)\)	\(=\)	\(q+(0.196860 - 0.196860i) q^{2} +1.92249i q^{4} +(1.96089 + 1.07466i) q^{5} +(3.28026 + 3.28026i) q^{7} +(0.772182 + 0.772182i) q^{8} +O(q^{10})\)	\(q+(0.196860 - 0.196860i) q^{2} +1.92249i q^{4} +(1.96089 + 1.07466i) q^{5} +(3.28026 + 3.28026i) q^{7} +(0.772182 + 0.772182i) q^{8} +(0.597579 - 0.174463i) q^{10} -2.84245i q^{11} +(3.00252 - 3.00252i) q^{13} +1.29151 q^{14} -3.54096 q^{16} +(2.57248 - 2.57248i) q^{17} +1.00000i q^{19} +(-2.06603 + 3.76980i) q^{20} +(-0.559566 - 0.559566i) q^{22} +(0.253403 + 0.253403i) q^{23} +(2.69020 + 4.21460i) q^{25} -1.18215i q^{26} +(-6.30628 + 6.30628i) q^{28} -3.39527 q^{29} -6.50994 q^{31} +(-2.24144 + 2.24144i) q^{32} -1.01284i q^{34} +(2.90706 + 9.95742i) q^{35} +(-4.02806 - 4.02806i) q^{37} +(0.196860 + 0.196860i) q^{38} +(0.684330 + 2.34400i) q^{40} -6.75296i q^{41} +(-5.59200 + 5.59200i) q^{43} +5.46460 q^{44} +0.0997698 q^{46} +(4.48496 - 4.48496i) q^{47} +14.5203i q^{49} +(1.35928 + 0.300094i) q^{50} +(5.77232 + 5.77232i) q^{52} +(-9.60045 - 9.60045i) q^{53} +(3.05468 - 5.57375i) q^{55} +5.06592i q^{56} +(-0.668392 + 0.668392i) q^{58} +12.3704 q^{59} +5.98606 q^{61} +(-1.28155 + 1.28155i) q^{62} -6.19942i q^{64} +(9.11432 - 2.66092i) q^{65} +(0.701938 + 0.701938i) q^{67} +(4.94557 + 4.94557i) q^{68} +(2.53250 + 1.38793i) q^{70} +14.5324i q^{71} +(-7.06563 + 7.06563i) q^{73} -1.58593 q^{74} -1.92249 q^{76} +(9.32400 - 9.32400i) q^{77} -12.4635i q^{79} +(-6.94344 - 3.80534i) q^{80} +(-1.32939 - 1.32939i) q^{82} +(-5.35197 - 5.35197i) q^{83} +(7.80890 - 2.27980i) q^{85} +2.20168i q^{86} +(2.19489 - 2.19489i) q^{88} -5.77421 q^{89} +19.6981 q^{91} +(-0.487166 + 0.487166i) q^{92} -1.76582i q^{94} +(-1.07466 + 1.96089i) q^{95} +(3.14970 + 3.14970i) q^{97} +(2.85846 + 2.85846i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{7}+O(q^{10}) \) 36 * q + 4 * q^7	\( 36 q + 4 q^{7} + 8 q^{10} + 4 q^{13} - 36 q^{16} - 80 q^{22} + 16 q^{25} - 24 q^{28} - 4 q^{37} + 76 q^{40} - 20 q^{43} + 96 q^{46} - 68 q^{52} + 48 q^{55} - 12 q^{58} + 56 q^{61} - 8 q^{67} - 16 q^{70} - 56 q^{73} + 36 q^{76} - 100 q^{82} + 80 q^{85} - 184 q^{88} + 92 q^{97}+O(q^{100}) \) 36 * q + 4 * q^7 + 8 * q^10 + 4 * q^13 - 36 * q^16 - 80 * q^22 + 16 * q^25 - 24 * q^28 - 4 * q^37 + 76 * q^40 - 20 * q^43 + 96 * q^46 - 68 * q^52 + 48 * q^55 - 12 * q^58 + 56 * q^61 - 8 * q^67 - 16 * q^70 - 56 * q^73 + 36 * q^76 - 100 * q^82 + 80 * q^85 - 184 * q^88 + 92 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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