LMFDB - Embedded newform 1170.2.q.d.359.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1170,2,Mod(359,1170)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1170, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1170.359"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.q (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,0,0,0,0,0,0,0,0,20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			359.4
Character	$\chi$	$=$	1170.359
Dual form			1170.2.q.d.629.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(1.91575 + 1.15322i) q^{5} +(-1.29303 - 1.29303i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.539189 - 2.17009i) q^{10} +(-3.42313 - 3.42313i) q^{11} +(-3.25273 + 1.55555i) q^{13} +1.82862i q^{14} -1.00000 q^{16} +4.71368i q^{17} +(-3.83222 - 3.83222i) q^{19} +(-1.15322 + 1.91575i) q^{20} +4.84104i q^{22} +3.20573i q^{23} +(2.34017 + 4.41855i) q^{25} +(3.39997 + 1.20009i) q^{26} +(1.29303 - 1.29303i) q^{28} +7.09142i q^{29} +(-4.09901 - 4.09901i) q^{31} +(0.707107 + 0.707107i) q^{32} +(3.33308 - 3.33308i) q^{34} +(-0.985969 - 3.96825i) q^{35} +(-3.72990 - 3.72990i) q^{37} +5.41957i q^{38} +(2.17009 - 0.539189i) q^{40} +(4.42620 - 4.42620i) q^{41} -7.68861 q^{43} +(3.42313 - 3.42313i) q^{44} +(2.26679 - 2.26679i) q^{46} +(-8.97668 + 8.97668i) q^{47} -3.65617i q^{49} +(1.46963 - 4.77914i) q^{50} +(-1.55555 - 3.25273i) q^{52} +6.86336 q^{53} +(-2.61023 - 10.5055i) q^{55} -1.82862 q^{56} +(5.01439 - 5.01439i) q^{58} +(-1.67463 - 1.67463i) q^{59} -11.6690 q^{61} +5.79687i q^{62} -1.00000i q^{64} +(-8.02530 - 0.771077i) q^{65} +(-5.61487 + 5.61487i) q^{67} -4.71368 q^{68} +(-2.10879 + 3.50316i) q^{70} +(3.05893 - 3.05893i) q^{71} +(-0.453716 - 0.453716i) q^{73} +5.27488i q^{74} +(3.83222 - 3.83222i) q^{76} +8.85239i q^{77} +8.29230 q^{79} +(-1.91575 - 1.15322i) q^{80} -6.25959 q^{82} +(-2.48030 - 2.48030i) q^{83} +(-5.43591 + 9.03023i) q^{85} +(5.43667 + 5.43667i) q^{86} -4.84104 q^{88} +(-3.36649 - 3.36649i) q^{89} +(6.21723 + 2.19451i) q^{91} -3.20573 q^{92} +12.6949 q^{94} +(-2.92217 - 11.7609i) q^{95} +(-3.71551 + 3.71551i) q^{97} +(-2.58530 + 2.58530i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 20 q^{13} - 24 q^{16} - 48 q^{19} - 32 q^{25} - 8 q^{31} + 16 q^{34} + 32 q^{37} + 8 q^{40} - 80 q^{43} + 8 q^{46} + 12 q^{52} + 16 q^{55} + 24 q^{58} - 16 q^{61} + 8 q^{67} - 40 q^{70} - 48 q^{73}+ \cdots - 64 q^{97}+O(q^{100}) $ 24 * q + 20 * q^13 - 24 * q^16 - 48 * q^19 - 32 * q^25 - 8 * q^31 + 16 * q^34 + 32 * q^37 + 8 * q^40 - 80 * q^43 + 8 * q^46 + 12 * q^52 + 16 * q^55 + 24 * q^58 - 16 * q^61 + 8 * q^67 - 40 * q^70 - 48 * q^73 + 48 * q^76 - 96 * q^79 + 72 * q^82 + 104 * q^85 - 8 * q^88 + 48 * q^91 - 16 * q^94 - 64 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	1.91575	+	1.15322i	0.856748	+	0.515735i
$5$	1.91575	+	1.15322i	0.856748	+	0.515735i
$6$		0			0
$7$	−1.29303	−	1.29303i	−0.488718	−	0.488718i	0.419184	−	0.907902i	$-0.362316\pi$
$7$	−1.29303	−	1.29303i	−0.488718	−	0.488718i	−0.907902	+	0.419184i	$0.862316\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	−0.539189	−	2.17009i	−0.170506	−	0.686242i
$11$	−3.42313	−	3.42313i	−1.03211	−	1.03211i	−0.999467	−	0.0326453i	$-0.989607\pi$
$11$	−3.42313	−	3.42313i	−1.03211	−	1.03211i	−0.0326453	−	0.999467i	$-0.510393\pi$
$12$		0			0
$13$	−3.25273	+	1.55555i	−0.902146	+	0.431431i
$13$	−3.25273	+	1.55555i	−0.902146	+	0.431431i
$14$			1.82862i			0.488718i
$15$		0			0
$16$	−1.00000			−0.250000
$17$			4.71368i			1.14324i	0.820520	+	0.571618i	$0.193684\pi$
$17$			4.71368i			1.14324i	−0.820520	+	0.571618i	$0.806316\pi$
$18$		0			0
$19$	−3.83222	−	3.83222i	−0.879170	−	0.879170i	0.114278	−	0.993449i	$-0.463544\pi$
$19$	−3.83222	−	3.83222i	−0.879170	−	0.879170i	−0.993449	+	0.114278i	$0.963544\pi$
$20$	−1.15322	+	1.91575i	−0.257868	+	0.428374i
$21$		0			0
$22$			4.84104i			1.03211i
$23$			3.20573i			0.668440i	0.942495	+	0.334220i	$0.108473\pi$
$23$			3.20573i			0.668440i	−0.942495	+	0.334220i	$0.891527\pi$
$24$		0			0
$25$	2.34017	+	4.41855i	0.468035	+	0.883710i
$26$	3.39997	+	1.20009i	0.666789	+	0.235357i
$27$		0			0
$28$	1.29303	−	1.29303i	0.244359	−	0.244359i
$29$			7.09142i			1.31684i	0.752649	+	0.658422i	$0.228776\pi$
$29$			7.09142i			1.31684i	−0.752649	+	0.658422i	$0.771224\pi$
$30$		0			0
$31$	−4.09901	−	4.09901i	−0.736203	−	0.736203i	0.235638	−	0.971841i	$-0.424282\pi$
$31$	−4.09901	−	4.09901i	−0.736203	−	0.736203i	−0.971841	+	0.235638i	$0.924282\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$		0			0
$34$	3.33308	−	3.33308i	0.571618	−	0.571618i
$35$	−0.985969	−	3.96825i	−0.166659	−	0.670757i
$36$		0			0
$37$	−3.72990	−	3.72990i	−0.613192	−	0.613192i	0.330584	−	0.943776i	$-0.392754\pi$
$37$	−3.72990	−	3.72990i	−0.613192	−	0.613192i	−0.943776	+	0.330584i	$0.892754\pi$
$38$			5.41957i			0.879170i
$39$		0			0
$40$	2.17009	−	0.539189i	0.343121	−	0.0852532i
$41$	4.42620	−	4.42620i	0.691256	−	0.691256i	−0.271253	−	0.962508i	$-0.587438\pi$
$41$	4.42620	−	4.42620i	0.691256	−	0.691256i	0.962508	+	0.271253i	$0.0874379\pi$
$42$		0			0
$43$	−7.68861			−1.17250			−0.586251	−	0.810129i	$-0.699397\pi$
$43$	−7.68861			−1.17250			−0.586251	+	0.810129i	$0.699397\pi$
$44$	3.42313	−	3.42313i	0.516056	−	0.516056i
$45$		0			0
$46$	2.26679	−	2.26679i	0.334220	−	0.334220i
$47$	−8.97668	+	8.97668i	−1.30938	+	1.30938i	−0.387523	+	0.921860i	$0.626669\pi$
$47$	−8.97668	+	8.97668i	−1.30938	+	1.30938i	−0.921860	+	0.387523i	$0.873331\pi$
$48$		0			0
$49$		−	3.65617i		−	0.522309i
$50$	1.46963	−	4.77914i	0.207838	−	0.675872i
$51$		0			0
$52$	−1.55555	−	3.25273i	−0.215716	−	0.451073i
$53$	6.86336			0.942754			0.471377	−	0.881932i	$-0.343757\pi$
$53$	6.86336			0.942754			0.471377	+	0.881932i	$0.343757\pi$
$54$		0			0
$55$	−2.61023	−	10.5055i	−0.351964	−	1.41656i
$56$	−1.82862			−0.244359
$57$		0			0
$58$	5.01439	−	5.01439i	0.658422	−	0.658422i
$59$	−1.67463	−	1.67463i	−0.218018	−	0.218018i	0.589644	−	0.807663i	$-0.299268\pi$
$59$	−1.67463	−	1.67463i	−0.218018	−	0.218018i	−0.807663	+	0.589644i	$0.799268\pi$
$60$		0			0
$61$	−11.6690			−1.49407			−0.747033	−	0.664787i	$-0.768522\pi$
$61$	−11.6690			−1.49407			−0.747033	+	0.664787i	$0.768522\pi$
$62$			5.79687i			0.736203i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−8.02530	−	0.771077i	−0.995416	−	0.0956403i
$66$		0			0
$67$	−5.61487	+	5.61487i	−0.685966	+	0.685966i	−0.961338	−	0.275372i	$-0.911199\pi$
$67$	−5.61487	+	5.61487i	−0.685966	+	0.685966i	0.275372	+	0.961338i	$0.411199\pi$
$68$	−4.71368			−0.571618
$69$		0			0
$70$	−2.10879	+	3.50316i	−0.252049	+	0.418708i
$71$	3.05893	−	3.05893i	0.363028	−	0.363028i	−0.501898	−	0.864927i	$-0.667365\pi$
$71$	3.05893	−	3.05893i	0.363028	−	0.363028i	0.864927	+	0.501898i	$0.167365\pi$
$72$		0			0
$73$	−0.453716	−	0.453716i	−0.0531034	−	0.0531034i	0.680056	−	0.733160i	$-0.261955\pi$
$73$	−0.453716	−	0.453716i	−0.0531034	−	0.0531034i	−0.733160	+	0.680056i	$0.761955\pi$
$74$			5.27488i			0.613192i
$75$		0			0
$76$	3.83222	−	3.83222i	0.439585	−	0.439585i
$77$			8.85239i			1.00882i
$78$		0			0
$79$	8.29230			0.932957			0.466479	−	0.884533i	$-0.345522\pi$
$79$	8.29230			0.932957			0.466479	+	0.884533i	$0.345522\pi$
$80$	−1.91575	−	1.15322i	−0.214187	−	0.128934i
$81$		0			0
$82$	−6.25959			−0.691256
$83$	−2.48030	−	2.48030i	−0.272248	−	0.272248i	0.557756	−	0.830005i	$-0.311662\pi$
$83$	−2.48030	−	2.48030i	−0.272248	−	0.272248i	−0.830005	+	0.557756i	$0.811662\pi$
$84$		0			0
$85$	−5.43591	+	9.03023i	−0.589607	+	0.979465i
$86$	5.43667	+	5.43667i	0.586251	+	0.586251i
$87$		0			0
$88$	−4.84104			−0.516056
$89$	−3.36649	−	3.36649i	−0.356847	−	0.356847i	0.505802	−	0.862649i	$-0.331196\pi$
$89$	−3.36649	−	3.36649i	−0.356847	−	0.356847i	−0.862649	+	0.505802i	$0.831196\pi$
$90$		0			0
$91$	6.21723	+	2.19451i	0.651743	+	0.230047i
$92$	−3.20573			−0.334220
$93$		0			0
$94$	12.6949			1.30938
$95$	−2.92217	−	11.7609i	−0.299809	−	1.20665i
$96$		0			0
$97$	−3.71551	+	3.71551i	−0.377253	+	0.377253i	−0.870110	−	0.492857i	$-0.835952\pi$
$97$	−3.71551	+	3.71551i	−0.377253	+	0.377253i	0.492857	+	0.870110i	$0.335952\pi$
$98$	−2.58530	+	2.58530i	−0.261155	+	0.261155i
$99$		0			0
$100$	−4.41855	+	2.34017i	−0.441855	+	0.234017i
$101$	−16.9657			−1.68815			−0.844074	−	0.536227i	$-0.819849\pi$
$101$	−16.9657			−1.68815			−0.844074	+	0.536227i	$0.819849\pi$
$102$		0			0
$103$	15.3380			1.51129			0.755647	−	0.654979i	$-0.227322\pi$
$103$	15.3380			1.51129			0.755647	+	0.654979i	$0.227322\pi$
$104$	−1.20009	+	3.39997i	−0.117679	+	0.333394i
$105$		0			0
$106$	−4.85313	−	4.85313i	−0.471377	−	0.471377i
$107$	2.44651			0.236513			0.118256	−	0.992983i	$-0.462270\pi$
$107$	2.44651			0.236513			0.118256	+	0.992983i	$0.462270\pi$
$108$		0			0
$109$	11.7964	+	11.7964i	1.12989	+	1.12989i	0.990194	+	0.139700i	$0.0446137\pi$
$109$	11.7964	+	11.7964i	1.12989	+	1.12989i	0.139700	+	0.990194i	$0.455386\pi$
$110$	−5.58277	+	9.27420i	−0.532297	+	0.884260i
$111$		0			0
$112$	1.29303	+	1.29303i	0.122180	+	0.122180i
$113$	−7.30279			−0.686988			−0.343494	−	0.939155i	$-0.611611\pi$
$113$	−7.30279			−0.686988			−0.343494	+	0.939155i	$0.611611\pi$
$114$		0			0
$115$	−3.69690	+	6.14136i	−0.344738	+	0.572685i
$116$	−7.09142			−0.658422
$117$		0			0
$118$			2.36829i			0.218018i
$119$	6.09492	−	6.09492i	0.558720	−	0.558720i
$120$		0			0
$121$			12.4356i			1.13051i
$122$	8.25125	+	8.25125i	0.747033	+	0.747033i
$123$		0			0
$124$	4.09901	−	4.09901i	0.368102	−	0.368102i
$125$	−0.612376	+	11.1636i	−0.0547726	+	0.998499i
$126$		0			0
$127$	−9.77725			−0.867591			−0.433795	−	0.901011i	$-0.642826\pi$
$127$	−9.77725			−0.867591			−0.433795	+	0.901011i	$0.642826\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$		0			0
$130$	5.12951	+	6.21998i	0.449888	+	0.545528i
$131$			3.06190i			0.267520i	0.991014	+	0.133760i	$0.0427051\pi$
$131$			3.06190i			0.267520i	−0.991014	+	0.133760i	$0.957295\pi$
$132$		0			0
$133$			9.91031i			0.859333i
$134$	7.94063			0.685966
$135$		0			0
$136$	3.33308	+	3.33308i	0.285809	+	0.285809i
$137$	15.8693	−	15.8693i	1.35580	−	1.35580i	0.476779	−	0.879023i	$-0.341804\pi$
$137$	15.8693	−	15.8693i	1.35580	−	1.35580i	0.879023	−	0.476779i	$-0.158196\pi$
$138$		0			0
$139$	1.10199			0.0934697			0.0467349	−	0.998907i	$-0.485118\pi$
$139$	1.10199			0.0934697			0.0467349	+	0.998907i	$0.485118\pi$
$140$	3.96825	−	0.985969i	0.335379	−	0.0833296i
$141$		0			0
$142$	−4.32598			−0.363028
$143$	16.4594	+	5.80968i	1.37640	+	0.485830i
$144$		0			0
$145$	−8.17796	+	13.5854i	−0.679143	+	1.12820i
$146$			0.641651i			0.0531034i
$147$		0			0
$148$	3.72990	−	3.72990i	0.306596	−	0.306596i
$149$	−11.5204	+	11.5204i	−0.943788	+	0.943788i	−0.998502	−	0.0547142i	$-0.982575\pi$
$149$	−11.5204	+	11.5204i	−0.943788	+	0.943788i	0.0547142	+	0.998502i	$0.482575\pi$
$150$		0			0
$151$	−13.1195	+	13.1195i	−1.06765	+	1.06765i	−0.0701126	+	0.997539i	$0.522336\pi$
$151$	−13.1195	+	13.1195i	−1.06765	+	1.06765i	−0.997539	+	0.0701126i	$0.977664\pi$
$152$	−5.41957			−0.439585
$153$		0			0
$154$	6.25959	−	6.25959i	0.504412	−	0.504412i
$155$	−3.12561	−	12.5797i	−0.251055	−	1.01043i
$156$		0			0
$157$		−	18.1705i		−	1.45016i	−0.688664	−	0.725080i	$-0.741803\pi$
$157$		−	18.1705i		−	1.45016i	0.688664	−	0.725080i	$-0.258197\pi$
$158$	−5.86354	−	5.86354i	−0.466479	−	0.466479i
$159$		0			0
$160$	0.539189	+	2.17009i	0.0426266	+	0.171560i
$161$	4.14509	−	4.14509i	0.326679	−	0.326679i
$162$		0			0
$163$	−7.45812	−	7.45812i	−0.584165	−	0.584165i	0.351880	−	0.936045i	$-0.385542\pi$
$163$	−7.45812	−	7.45812i	−0.584165	−	0.584165i	−0.936045	+	0.351880i	$0.885542\pi$
$164$	4.42620	+	4.42620i	0.345628	+	0.345628i
$165$		0			0
$166$			3.50767i			0.272248i
$167$	−7.14982	+	7.14982i	−0.553269	+	0.553269i	−0.927383	−	0.374113i	$-0.877947\pi$
$167$	−7.14982	+	7.14982i	−0.553269	+	0.553269i	0.374113	+	0.927383i	$0.377947\pi$
$168$		0			0
$169$	8.16054	−	10.1196i	0.627734	−	0.778428i
$170$	10.2291	−	2.54157i	0.784536	−	0.194929i
$171$		0			0
$172$		−	7.68861i		−	0.586251i
$173$		−	15.0993i		−	1.14798i	−0.818864	−	0.573988i	$-0.805396\pi$
$173$		−	15.0993i		−	1.14798i	0.818864	−	0.573988i	$-0.194604\pi$
$174$		0			0
$175$	2.68740	−	8.73921i	0.203148	−	0.660622i
$176$	3.42313	+	3.42313i	0.258028	+	0.258028i
$177$		0			0
$178$			4.76093i			0.356847i
$179$	16.4200			1.22729			0.613645	−	0.789582i	$-0.289703\pi$
$179$	16.4200			1.22729			0.613645	+	0.789582i	$0.289703\pi$
$180$		0			0
$181$			4.47735i			0.332799i	0.986058	+	0.166399i	$0.0532141\pi$
$181$			4.47735i			0.332799i	−0.986058	+	0.166399i	$0.946786\pi$
$182$	−2.84450	−	5.94800i	−0.210848	−	0.440895i
$183$		0			0
$184$	2.26679	+	2.26679i	0.167110	+	0.167110i
$185$	−2.84416	−	11.4469i	−0.209107	−	0.841596i
$186$		0			0
$187$	16.1355	−	16.1355i	1.17995	−	1.17995i
$188$	−8.97668	−	8.97668i	−0.654691	−	0.654691i
$189$		0			0
$190$	−6.24995	+	10.3825i	−0.453419	+	0.753228i
$191$			10.5841i			0.765836i	0.923782	+	0.382918i	$0.125081\pi$
$191$			10.5841i			0.765836i	−0.923782	+	0.382918i	$0.874919\pi$
$192$		0			0
$193$	7.20113	+	7.20113i	0.518348	+	0.518348i	0.917071	−	0.398723i	$-0.130546\pi$
$193$	7.20113	+	7.20113i	0.518348	+	0.518348i	−0.398723	+	0.917071i	$0.630546\pi$
$194$	5.25453			0.377253
$195$		0			0
$196$	3.65617			0.261155
$197$	−9.16979	−	9.16979i	−0.653321	−	0.653321i	0.300470	−	0.953791i	$-0.402856\pi$
$197$	−9.16979	−	9.16979i	−0.653321	−	0.653321i	−0.953791	+	0.300470i	$0.902856\pi$
$198$		0			0
$199$		−	20.7555i		−	1.47132i	−0.677353	−	0.735658i	$-0.736873\pi$
$199$		−	20.7555i		−	1.47132i	0.677353	−	0.735658i	$-0.263127\pi$
$200$	4.77914	+	1.46963i	0.337936	+	0.103919i
$201$		0			0
$202$	11.9965	+	11.9965i	0.844074	+	0.844074i
$203$	9.16939	−	9.16939i	0.643565	−	0.643565i
$204$		0			0
$205$	13.5838	−	3.37510i	0.948737	−	0.235727i
$206$	−10.8456	−	10.8456i	−0.755647	−	0.755647i
$207$		0			0
$208$	3.25273	−	1.55555i	0.225536	−	0.107858i
$209$			26.2363i			1.81481i
$210$		0			0
$211$	−19.9602			−1.37412			−0.687058	−	0.726603i	$-0.741098\pi$
$211$	−19.9602			−1.37412			−0.687058	+	0.726603i	$0.741098\pi$
$212$			6.86336i			0.471377i
$213$		0			0
$214$	−1.72994	−	1.72994i	−0.118256	−	0.118256i
$215$	−14.7294	−	8.86665i	−1.00454	−	0.604700i
$216$		0			0
$217$			10.6002i			0.719591i
$218$		−	16.6827i		−	1.12989i
$219$		0			0
$220$	10.5055	−	2.61023i	0.708278	−	0.175982i
$221$	−7.33236	−	15.3324i	−0.493228	−	1.03137i
$222$		0			0
$223$	−9.64691	+	9.64691i	−0.646005	+	0.646005i	−0.952025	−	0.306020i	$-0.901002\pi$
$223$	−9.64691	+	9.64691i	−0.646005	+	0.646005i	0.306020	+	0.952025i	$0.401002\pi$
$224$		−	1.82862i		−	0.122180i
$225$		0			0
$226$	5.16385	+	5.16385i	0.343494	+	0.343494i
$227$	9.61668	+	9.61668i	0.638281	+	0.638281i	0.950131	−	0.311850i	$-0.100949\pi$
$227$	9.61668	+	9.61668i	0.638281	+	0.638281i	−0.311850	+	0.950131i	$0.600949\pi$
$228$		0			0
$229$	−0.831438	+	0.831438i	−0.0549429	+	0.0549429i	−0.734044	−	0.679101i	$-0.762370\pi$
$229$	−0.831438	+	0.831438i	−0.0549429	+	0.0549429i	0.679101	+	0.734044i	$0.262370\pi$
$230$	6.95670	−	1.72849i	0.458711	−	0.113973i
$231$		0			0
$232$	5.01439	+	5.01439i	0.329211	+	0.329211i
$233$			13.0922i			0.857698i	0.903376	+	0.428849i	$0.141081\pi$
$233$			13.0922i			0.857698i	−0.903376	+	0.428849i	$0.858919\pi$
$234$		0			0
$235$	−27.5491	+	6.84497i	−1.79711	+	0.446517i
$236$	1.67463	−	1.67463i	0.109009	−	0.109009i
$237$		0			0
$238$	−8.61951			−0.558720
$239$	8.83842	−	8.83842i	0.571710	−	0.571710i	−0.360896	−	0.932606i	$-0.617529\pi$
$239$	8.83842	−	8.83842i	0.571710	−	0.571710i	0.932606	+	0.360896i	$0.117529\pi$
$240$		0			0
$241$	5.80438	−	5.80438i	0.373893	−	0.373893i	−0.495000	−	0.868893i	$-0.664832\pi$
$241$	5.80438	−	5.80438i	0.373893	−	0.373893i	0.868893	+	0.495000i	$0.164832\pi$
$242$	8.79332	−	8.79332i	0.565256	−	0.565256i
$243$		0			0
$244$		−	11.6690i		−	0.747033i
$245$	4.21636	−	7.00429i	0.269373	−	0.447488i
$246$		0			0
$247$	18.4264	+	6.50398i	1.17244	+	0.413838i
$248$	−5.79687			−0.368102
$249$		0			0
$250$	8.32684	−	7.46081i	0.526636	−	0.471863i
$251$	26.8994			1.69787			0.848936	−	0.528495i	$-0.177244\pi$
$251$	26.8994			1.69787			0.848936	+	0.528495i	$0.177244\pi$
$252$		0			0
$253$	10.9736	−	10.9736i	0.689905	−	0.689905i
$254$	6.91356	+	6.91356i	0.433795	+	0.433795i
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	5.66502i		−	0.353374i	−0.984267	−	0.176687i	$-0.943462\pi$
$257$		−	5.66502i		−	0.353374i	0.984267	−	0.176687i	$-0.0565380\pi$
$258$		0			0
$259$			9.64572i			0.599356i
$260$	0.771077	−	8.02530i	0.0478202	−	0.497708i
$261$		0			0
$262$	2.16509	−	2.16509i	0.133760	−	0.133760i
$263$	−0.793522			−0.0489307			−0.0244653	−	0.999701i	$-0.507788\pi$
$263$	−0.793522			−0.0489307			−0.0244653	+	0.999701i	$0.507788\pi$
$264$		0			0
$265$	13.1485	+	7.91495i	0.807703	+	0.486212i
$266$	7.00765	−	7.00765i	0.429666	−	0.429666i
$267$		0			0
$268$	−5.61487	−	5.61487i	−0.342983	−	0.342983i
$269$			13.2877i			0.810165i	0.914280	+	0.405083i	$0.132757\pi$
$269$			13.2877i			0.810165i	−0.914280	+	0.405083i	$0.867243\pi$
$270$		0			0
$271$	15.5871	−	15.5871i	0.946849	−	0.946849i	−0.0518080	−	0.998657i	$-0.516498\pi$
$271$	15.5871	−	15.5871i	0.946849	−	0.946849i	0.998657	+	0.0518080i	$0.0164984\pi$
$272$		−	4.71368i		−	0.285809i
$273$		0			0
$274$	−22.4425			−1.35580
$275$	7.11456	−	23.1360i	0.429024	−	1.39515i
$276$		0			0
$277$	−11.4081			−0.685445			−0.342722	−	0.939437i	$-0.611349\pi$
$277$	−11.4081			−0.685445			−0.342722	+	0.939437i	$0.611349\pi$
$278$	−0.779226	−	0.779226i	−0.0467349	−	0.0467349i
$279$		0			0
$280$	−3.50316	−	2.10879i	−0.209354	−	0.126025i
$281$	−18.4689	−	18.4689i	−1.10176	−	1.10176i	−0.994198	−	0.107565i	$-0.965695\pi$
$281$	−18.4689	−	18.4689i	−1.10176	−	1.10176i	−0.107565	−	0.994198i	$-0.534305\pi$
$282$		0			0
$283$	24.4471			1.45323			0.726615	−	0.687045i	$-0.241092\pi$
$283$	24.4471			1.45323			0.726615	+	0.687045i	$0.241092\pi$
$284$	3.05893	+	3.05893i	0.181514	+	0.181514i
$285$		0			0
$286$	−7.53046	−	15.7466i	−0.445286	−	0.931116i
$287$	−11.4464			−0.675658
$288$		0			0
$289$	−5.21882			−0.306989
$290$	15.3890	−	3.82362i	0.903673	−	0.224530i
$291$		0			0
$292$	0.453716	−	0.453716i	0.0265517	−	0.0265517i
$293$	12.7581	−	12.7581i	0.745336	−	0.745336i	−0.228264	−	0.973599i	$-0.573305\pi$
$293$	12.7581	−	12.7581i	0.745336	−	0.745336i	0.973599	+	0.228264i	$0.0733048\pi$
$294$		0			0
$295$	−1.27695	−	5.13939i	−0.0743471	−	0.299227i
$296$	−5.27488			−0.306596
$297$		0			0
$298$	16.2923			0.943788
$299$	−4.98666	−	10.4274i	−0.288386	−	0.603030i
$300$		0			0
$301$	9.94158	+	9.94158i	0.573023	+	0.573023i
$302$	18.5538			1.06765
$303$		0			0
$304$	3.83222	+	3.83222i	0.219793	+	0.219793i
$305$	−22.3549	−	13.4569i	−1.28004	−	0.770543i
$306$		0			0
$307$	−1.54476	−	1.54476i	−0.0881641	−	0.0881641i	0.661649	−	0.749813i	$-0.269857\pi$
$307$	−1.54476	−	1.54476i	−0.0881641	−	0.0881641i	−0.749813	+	0.661649i	$0.769857\pi$
$308$	−8.85239			−0.504412
$309$		0			0
$310$	−6.68506	+	11.1053i	−0.379686	+	0.630741i
$311$	7.11421			0.403410			0.201705	−	0.979446i	$-0.435352\pi$
$311$	7.11421			0.403410			0.201705	+	0.979446i	$0.435352\pi$
$312$		0			0
$313$		−	4.63441i		−	0.261952i	−0.991386	−	0.130976i	$-0.958189\pi$
$313$		−	4.63441i		−	0.261952i	0.991386	−	0.130976i	$-0.0418112\pi$
$314$	−12.8485	+	12.8485i	−0.725080	+	0.725080i
$315$		0			0
$316$			8.29230i			0.466479i
$317$	−2.74539	−	2.74539i	−0.154196	−	0.154196i	0.625793	−	0.779989i	$-0.284775\pi$
$317$	−2.74539	−	2.74539i	−0.154196	−	0.154196i	−0.779989	+	0.625793i	$0.784775\pi$
$318$		0			0
$319$	24.2748	−	24.2748i	1.35913	−	1.35913i
$320$	1.15322	−	1.91575i	0.0644669	−	0.107094i
$321$		0			0
$322$	−5.86204			−0.326679
$323$	18.0639	−	18.0639i	1.00510	−	1.00510i
$324$		0			0
$325$	−14.4852	−	10.7321i	−0.803496	−	0.595311i
$326$			10.5474i			0.584165i
$327$		0			0
$328$		−	6.25959i		−	0.345628i
$329$	23.2142			1.27984
$330$		0			0
$331$	−4.29030	−	4.29030i	−0.235816	−	0.235816i	0.579299	−	0.815115i	$-0.303326\pi$
$331$	−4.29030	−	4.29030i	−0.235816	−	0.235816i	−0.815115	+	0.579299i	$0.803326\pi$
$332$	2.48030	−	2.48030i	0.136124	−	0.136124i
$333$		0			0
$334$	10.1114			0.553269
$335$	−17.2319	+	4.28150i	−0.941477	+	0.233923i
$336$		0			0
$337$	−2.00498			−0.109218			−0.0546092	−	0.998508i	$-0.517391\pi$
$337$	−2.00498			−0.109218			−0.0546092	+	0.998508i	$0.517391\pi$
$338$	−12.9260	+	1.38524i	−0.703081	+	0.0753469i
$339$		0			0
$340$	−9.03023	−	5.43591i	−0.489733	−	0.294804i
$341$			28.0628i			1.51969i
$342$		0			0
$343$	−13.7787	+	13.7787i	−0.743980	+	0.743980i
$344$	−5.43667	+	5.43667i	−0.293126	+	0.293126i
$345$		0			0
$346$	−10.6768	+	10.6768i	−0.573988	+	0.573988i
$347$	−17.8409			−0.957748			−0.478874	−	0.877884i	$-0.658955\pi$
$347$	−17.8409			−0.957748			−0.478874	+	0.877884i	$0.658955\pi$
$348$		0			0
$349$	19.2150	−	19.2150i	1.02855	−	1.02855i	0.0289745	−	0.999580i	$-0.490776\pi$
$349$	19.2150	−	19.2150i	1.02855	−	1.02855i	0.999580	−	0.0289745i	$-0.00922416\pi$
$350$	−8.07983	+	4.27928i	−0.431885	+	0.228737i
$351$		0			0
$352$		−	4.84104i		−	0.258028i
$353$	5.98145	+	5.98145i	0.318361	+	0.318361i	0.848137	−	0.529777i	$-0.177724\pi$
$353$	5.98145	+	5.98145i	0.318361	+	0.318361i	−0.529777	+	0.848137i	$0.677724\pi$
$354$		0			0
$355$	9.38776	−	2.33252i	0.498250	−	0.123797i
$356$	3.36649	−	3.36649i	0.178423	−	0.178423i
$357$		0			0
$358$	−11.6107	−	11.6107i	−0.613645	−	0.613645i
$359$	26.0867	+	26.0867i	1.37680	+	1.37680i	0.849966	+	0.526837i	$0.176622\pi$
$359$	26.0867	+	26.0867i	1.37680	+	1.37680i	0.526837	+	0.849966i	$0.323378\pi$
$360$		0			0
$361$			10.3717i			0.545881i
$362$	3.16597	−	3.16597i	0.166399	−	0.166399i
$363$		0			0
$364$	−2.19451	+	6.21723i	−0.115023	+	0.325872i
$365$	−0.345971	−	1.39244i	−0.0181090	−	0.0728836i
$366$		0			0
$367$			7.79988i			0.407150i	0.979059	+	0.203575i	$0.0652561\pi$
$367$			7.79988i			0.407150i	−0.979059	+	0.203575i	$0.934744\pi$
$368$		−	3.20573i		−	0.167110i
$369$		0			0
$370$	−6.08309	+	10.1053i	−0.316245	+	0.525351i
$371$	−8.87450	−	8.87450i	−0.460741	−	0.460741i
$372$		0			0
$373$			29.3018i			1.51719i	0.651563	+	0.758594i	$0.274114\pi$
$373$			29.3018i			1.51719i	−0.651563	+	0.758594i	$0.725886\pi$
$374$	−22.8191			−1.17995
$375$		0			0
$376$			12.6949i			0.654691i
$377$	−11.0310	−	23.0665i	−0.568128	−	1.18799i
$378$		0			0
$379$	−6.78165	−	6.78165i	−0.348350	−	0.348350i	0.511145	−	0.859495i	$-0.329222\pi$
$379$	−6.78165	−	6.78165i	−0.348350	−	0.348350i	−0.859495	+	0.511145i	$0.829222\pi$
$380$	11.7609	−	2.92217i	0.603323	−	0.149904i
$381$		0			0
$382$	7.48406	−	7.48406i	0.382918	−	0.382918i
$383$	9.46794	+	9.46794i	0.483789	+	0.483789i	0.906339	−	0.422550i	$-0.138865\pi$
$383$	9.46794	+	9.46794i	0.483789	+	0.483789i	−0.422550	+	0.906339i	$0.638865\pi$
$384$		0			0
$385$	−10.2087	+	16.9589i	−0.520286	+	0.864308i
$386$		−	10.1839i		−	0.518348i
$387$		0			0
$388$	−3.71551	−	3.71551i	−0.188627	−	0.188627i
$389$	26.5150			1.34436			0.672182	−	0.740386i	$-0.265357\pi$
$389$	26.5150			1.34436			0.672182	+	0.740386i	$0.265357\pi$
$390$		0			0
$391$	−15.1108			−0.764185
$392$	−2.58530	−	2.58530i	−0.130577	−	0.130577i
$393$		0			0
$394$			12.9680i			0.653321i
$395$	15.8860	+	9.56284i	0.799309	+	0.481159i
$396$		0			0
$397$	−13.5450	−	13.5450i	−0.679806	−	0.679806i	0.280150	−	0.959956i	$-0.409616\pi$
$397$	−13.5450	−	13.5450i	−0.679806	−	0.679806i	−0.959956	+	0.280150i	$0.909616\pi$
$398$	−14.6763	+	14.6763i	−0.735658	+	0.735658i
$399$		0			0
$400$	−2.34017	−	4.41855i	−0.117009	−	0.220928i
$401$	0.170681	+	0.170681i	0.00852341	+	0.00852341i	0.711356	−	0.702832i	$-0.248082\pi$
$401$	0.170681	+	0.170681i	0.00852341	+	0.00852341i	−0.702832	+	0.711356i	$0.748082\pi$
$402$		0			0
$403$	19.7092	+	6.95677i	0.981784	+	0.346541i
$404$		−	16.9657i		−	0.844074i
$405$		0			0
$406$	−12.9675			−0.643565
$407$			25.5359i			1.26577i
$408$		0			0
$409$	15.8128	+	15.8128i	0.781895	+	0.781895i	0.980150	−	0.198255i	$-0.0635276\pi$
$409$	15.8128	+	15.8128i	0.781895	+	0.781895i	−0.198255	+	0.980150i	$0.563528\pi$
$410$	−11.9918	−	7.21867i	−0.592232	−	0.356505i
$411$		0			0
$412$			15.3380i			0.755647i
$413$			4.33069i			0.213099i
$414$		0			0
$415$	−1.89130	−	7.61196i	−0.0928402	−	0.373656i
$416$	−3.39997	−	1.20009i	−0.166697	−	0.0588393i
$417$		0			0
$418$	18.5519	−	18.5519i	0.907403	−	0.907403i
$419$			9.92023i			0.484635i	0.970197	+	0.242318i	$0.0779076\pi$
$419$			9.92023i			0.484635i	−0.970197	+	0.242318i	$0.922092\pi$
$420$		0			0
$421$	16.6990	+	16.6990i	0.813862	+	0.813862i	0.985210	−	0.171349i	$-0.0548125\pi$
$421$	16.6990	+	16.6990i	0.813862	+	0.813862i	−0.171349	+	0.985210i	$0.554812\pi$
$422$	14.1140	+	14.1140i	0.687058	+	0.687058i
$423$		0			0
$424$	4.85313	−	4.85313i	0.235689	−	0.235689i
$425$	−20.8277	+	11.0308i	−1.01029	+	0.535074i
$426$		0			0
$427$	15.0884	+	15.0884i	0.730177	+	0.730177i
$428$			2.44651i			0.118256i
$429$		0			0
$430$	4.14561	+	16.6849i	0.199919	+	0.804620i
$431$	−17.0012	+	17.0012i	−0.818920	+	0.818920i	−0.985952	−	0.167032i	$-0.946582\pi$
$431$	−17.0012	+	17.0012i	−0.818920	+	0.818920i	0.167032	+	0.985952i	$0.446582\pi$
$432$		0			0
$433$	2.50595			0.120428			0.0602141	−	0.998185i	$-0.480822\pi$
$433$	2.50595			0.120428			0.0602141	+	0.998185i	$0.480822\pi$
$434$	7.49550	−	7.49550i	0.359796	−	0.359796i
$435$		0			0
$436$	−11.7964	+	11.7964i	−0.564947	+	0.564947i
$437$	12.2850	−	12.2850i	0.587673	−	0.587673i
$438$		0			0
$439$		−	29.9255i		−	1.42827i	−0.700009	−	0.714134i	$-0.746821\pi$
$439$		−	29.9255i		−	1.42827i	0.700009	−	0.714134i	$-0.253179\pi$
$440$	−9.27420	−	5.58277i	−0.442130	−	0.266148i
$441$		0			0
$442$	−5.65685	+	16.0264i	−0.269069	+	0.762297i
$443$	−7.51200			−0.356906			−0.178453	−	0.983948i	$-0.557109\pi$
$443$	−7.51200			−0.356906			−0.178453	+	0.983948i	$0.557109\pi$
$444$		0			0
$445$	−2.56704	−	10.3316i	−0.121689	−	0.489766i
$446$	13.6428			0.646005
$447$		0			0
$448$	−1.29303	+	1.29303i	−0.0610898	+	0.0610898i
$449$	−12.7797	−	12.7797i	−0.603113	−	0.603113i	0.338025	−	0.941137i	$-0.390241\pi$
$449$	−12.7797	−	12.7797i	−0.603113	−	0.603113i	−0.941137	+	0.338025i	$0.890241\pi$
$450$		0			0
$451$	−30.3029			−1.42691
$452$		−	7.30279i		−	0.343494i
$453$		0			0
$454$		−	13.6000i		−	0.638281i
$455$	9.37990	+	11.3739i	0.439737	+	0.533219i
$456$		0			0
$457$	1.41879	−	1.41879i	0.0663682	−	0.0663682i	−0.673144	−	0.739512i	$-0.735056\pi$
$457$	1.41879	−	1.41879i	0.0663682	−	0.0663682i	0.739512	+	0.673144i	$0.235056\pi$
$458$	1.17583			0.0549429
$459$		0			0
$460$	−6.14136	−	3.69690i	−0.286342	−	0.172369i
$461$	8.94270	−	8.94270i	0.416503	−	0.416503i	−0.467494	−	0.883996i	$-0.654843\pi$
$461$	8.94270	−	8.94270i	0.416503	−	0.416503i	0.883996	+	0.467494i	$0.154843\pi$
$462$		0			0
$463$	−1.64030	−	1.64030i	−0.0762314	−	0.0762314i	0.667963	−	0.744194i	$-0.267166\pi$
$463$	−1.64030	−	1.64030i	−0.0762314	−	0.0762314i	−0.744194	+	0.667963i	$0.767166\pi$
$464$		−	7.09142i		−	0.329211i
$465$		0			0
$466$	9.25758	−	9.25758i	0.428849	−	0.428849i
$467$		−	21.6984i		−	1.00408i	−0.864844	−	0.502040i	$-0.832583\pi$
$467$		−	21.6984i		−	1.00408i	0.864844	−	0.502040i	$-0.167417\pi$
$468$		0			0
$469$	14.5204			0.670488
$470$	24.3203	+	14.6400i	1.12181	+	0.675295i
$471$		0			0
$472$	−2.36829			−0.109009
$473$	26.3191	+	26.3191i	1.21015	+	1.21015i
$474$		0			0
$475$	7.96479	−	25.9009i	0.365450	−	1.18841i
$476$	6.09492	+	6.09492i	0.279360	+	0.279360i
$477$		0			0
$478$	−12.4994			−0.571710
$479$	−3.65613	−	3.65613i	−0.167053	−	0.167053i	0.618630	−	0.785683i	$-0.287688\pi$
$479$	−3.65613	−	3.65613i	−0.167053	−	0.167053i	−0.785683	+	0.618630i	$0.787688\pi$
$480$		0			0
$481$	17.9344	+	6.33034i	0.817739	+	0.288639i
$482$	−8.20864			−0.373893
$483$		0			0
$484$	−12.4356			−0.565256
$485$	−11.4028	+	2.83318i	−0.517773	+	0.128648i
$486$		0			0
$487$	−24.5766	+	24.5766i	−1.11367	+	1.11367i	−0.121021	+	0.992650i	$0.538617\pi$
$487$	−24.5766	+	24.5766i	−1.11367	+	1.11367i	−0.992650	+	0.121021i	$0.961383\pi$
$488$	−8.25125	+	8.25125i	−0.373517	+	0.373517i
$489$		0			0
$490$	−7.93420	+	1.97136i	−0.358430	+	0.0890571i
$491$	−35.0848			−1.58336			−0.791678	−	0.610939i	$-0.790792\pi$
$491$	−35.0848			−1.58336			−0.791678	+	0.610939i	$0.790792\pi$
$492$		0			0
$493$	−33.4267			−1.50546
$494$	−8.43040	−	17.6284i	−0.379302	−	0.793140i
$495$		0			0
$496$	4.09901	+	4.09901i	0.184051	+	0.184051i
$497$	−7.91056			−0.354837
$498$		0			0
$499$	6.90060	+	6.90060i	0.308913	+	0.308913i	0.844488	−	0.535575i	$-0.179905\pi$
$499$	6.90060	+	6.90060i	0.308913	+	0.308913i	−0.535575	+	0.844488i	$0.679905\pi$
$500$	−11.1636	−	0.612376i	−0.499249	−	0.0273863i
$501$		0			0
$502$	−19.0207	−	19.0207i	−0.848936	−	0.848936i
$503$	8.61769			0.384244			0.192122	−	0.981371i	$-0.438463\pi$
$503$	8.61769			0.384244			0.192122	+	0.981371i	$0.438463\pi$
$504$		0			0
$505$	−32.5019	−	19.5651i	−1.44632	−	0.870637i
$506$	−15.5190			−0.689905
$507$		0			0
$508$		−	9.77725i		−	0.433795i
$509$	12.3534	−	12.3534i	0.547555	−	0.547555i	−0.378178	−	0.925733i	$-0.623449\pi$
$509$	12.3534	−	12.3534i	0.547555	−	0.547555i	0.925733	+	0.378178i	$0.123449\pi$
$510$		0			0
$511$			1.17333i			0.0519052i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$	−4.00577	+	4.00577i	−0.176687	+	0.176687i
$515$	29.3837	+	17.6880i	1.29480	+	0.779428i
$516$		0			0
$517$	61.4567			2.70286
$518$	6.82056	−	6.82056i	0.299678	−	0.299678i
$519$		0			0
$520$	−6.21998	+	5.12951i	−0.272764	+	0.224944i
$521$			42.6428i			1.86822i	0.356991	+	0.934108i	$0.383803\pi$
$521$			42.6428i			1.86822i	−0.356991	+	0.934108i	$0.616197\pi$
$522$		0			0
$523$			9.80957i			0.428942i	0.976730	+	0.214471i	$0.0688028\pi$
$523$			9.80957i			0.428942i	−0.976730	+	0.214471i	$0.931197\pi$
$524$	−3.06190			−0.133760
$525$		0			0
$526$	0.561105	+	0.561105i	0.0244653	+	0.0244653i
$527$	19.3214	−	19.3214i	0.841654	−	0.841654i
$528$		0			0
$529$	12.7233			0.553188
$530$	−3.70065	−	14.8941i	−0.160746	−	0.646957i
$531$		0			0
$532$	−9.91031			−0.429666
$533$	−7.51208	+	21.2824i	−0.325384	+	0.921843i
$534$		0			0
$535$	4.68689	+	2.82136i	0.202632	+	0.121978i
$536$			7.94063i			0.342983i
$537$		0			0
$538$	9.39582	−	9.39582i	0.405083	−	0.405083i
$539$	−12.5155	+	12.5155i	−0.539082	+	0.539082i
$540$		0			0
$541$	21.5440	−	21.5440i	0.926250	−	0.926250i	−0.0712116	−	0.997461i	$-0.522687\pi$
$541$	21.5440	−	21.5440i	0.926250	−	0.926250i	0.997461	+	0.0712116i	$0.0226866\pi$
$542$	−22.0435			−0.946849
$543$		0			0
$544$	−3.33308	+	3.33308i	−0.142905	+	0.142905i
$545$	8.99512	+	36.2029i	0.385308	+	1.55076i
$546$		0			0
$547$		−	26.1118i		−	1.11646i	−0.829687	−	0.558229i	$-0.811481\pi$
$547$		−	26.1118i		−	1.11646i	0.829687	−	0.558229i	$-0.188519\pi$
$548$	15.8693	+	15.8693i	0.677901	+	0.677901i
$549$		0			0
$550$	−21.3904	+	11.3289i	−0.912088	+	0.483064i
$551$	27.1758	−	27.1758i	1.15773	−	1.15773i
$552$		0			0
$553$	−10.7222	−	10.7222i	−0.455953	−	0.455953i
$554$	8.06673	+	8.06673i	0.342722	+	0.342722i
$555$		0			0
$556$			1.10199i			0.0467349i
$557$	−24.5719	+	24.5719i	−1.04114	+	1.04114i	−0.0420278	+	0.999116i	$0.513382\pi$
$557$	−24.5719	+	24.5719i	−1.04114	+	1.04114i	−0.999116	+	0.0420278i	$0.986618\pi$
$558$		0			0
$559$	25.0090	−	11.9600i	1.05777	−	0.505854i
$560$	0.985969	+	3.96825i	0.0416648	+	0.167689i
$561$		0			0
$562$			26.1190i			1.10176i
$563$			4.81449i			0.202907i	0.994840	+	0.101453i	$0.0323493\pi$
$563$			4.81449i			0.202907i	−0.994840	+	0.101453i	$0.967651\pi$
$564$		0			0
$565$	−13.9903	−	8.42171i	−0.588576	−	0.354304i
$566$	−17.2867	−	17.2867i	−0.726615	−	0.726615i
$567$		0			0
$568$		−	4.32598i		−	0.181514i
$569$	−40.4223			−1.69459			−0.847295	−	0.531122i	$-0.821771\pi$
$569$	−40.4223			−1.69459			−0.847295	+	0.531122i	$0.821771\pi$
$570$		0			0
$571$		−	33.1629i		−	1.38782i	−0.720060	−	0.693911i	$-0.755886\pi$
$571$		−	33.1629i		−	1.38782i	0.720060	−	0.693911i	$-0.244114\pi$
$572$	−5.80968	+	16.4594i	−0.242915	+	0.688201i
$573$		0			0
$574$	8.09381	+	8.09381i	0.337829	+	0.337829i
$575$	−14.1647	+	7.50195i	−0.590707	+	0.312853i
$576$		0			0
$577$	5.26107	−	5.26107i	0.219021	−	0.219021i	−0.589065	−	0.808086i	$-0.700504\pi$
$577$	5.26107	−	5.26107i	0.219021	−	0.219021i	0.808086	+	0.589065i	$0.200504\pi$
$578$	3.69026	+	3.69026i	0.153495	+	0.153495i
$579$		0			0
$580$	−13.5854	−	8.17796i	−0.564102	−	0.339571i
$581$			6.41419i			0.266105i
$582$		0			0
$583$	−23.4942	−	23.4942i	−0.973028	−	0.973028i
$584$	−0.641651			−0.0265517
$585$		0			0
$586$	−18.0427			−0.745336
$587$	6.51985	+	6.51985i	0.269103	+	0.269103i	0.828739	−	0.559636i	$-0.189059\pi$
$587$	6.51985	+	6.51985i	0.269103	+	0.269103i	−0.559636	+	0.828739i	$0.689059\pi$
$588$		0			0
$589$			31.4165i			1.29450i
$590$	−2.73115	+	4.53704i	−0.112440	+	0.186787i
$591$		0			0
$592$	3.72990	+	3.72990i	0.153298	+	0.153298i
$593$	−17.8642	+	17.8642i	−0.733596	+	0.733596i	−0.971330	−	0.237734i	$-0.923595\pi$
$593$	−17.8642	+	17.8642i	−0.733596	+	0.733596i	0.237734	+	0.971330i	$0.423595\pi$
$594$		0			0
$595$	18.7051	−	4.64755i	0.766834	−	0.190531i
$596$	−11.5204	−	11.5204i	−0.471894	−	0.471894i
$597$		0			0
$598$	−3.84716	+	10.8994i	−0.157322	+	0.445708i
$599$			22.7673i			0.930246i	0.885246	+	0.465123i	$0.153990\pi$
$599$			22.7673i			0.930246i	−0.885246	+	0.465123i	$0.846010\pi$
$600$		0			0
$601$	21.8501			0.891283			0.445641	−	0.895212i	$-0.352976\pi$
$601$	21.8501			0.891283			0.445641	+	0.895212i	$0.352976\pi$
$602$		−	14.0595i		−	0.573023i
$603$		0			0
$604$	−13.1195	−	13.1195i	−0.533826	−	0.533826i
$605$	−14.3410	+	23.8235i	−0.583044	+	0.968564i
$606$		0			0
$607$		−	25.6082i		−	1.03941i	−0.854347	−	0.519703i	$-0.826043\pi$
$607$		−	25.6082i		−	1.03941i	0.854347	−	0.519703i	$-0.173957\pi$
$608$		−	5.41957i		−	0.219793i
$609$		0			0
$610$	6.29181	+	25.3228i	0.254748	+	1.02529i
$611$	15.2351	−	43.1624i	0.616346	−	1.74616i
$612$		0			0
$613$	−29.1287	+	29.1287i	−1.17650	+	1.17650i	−0.195866	+	0.980631i	$0.562752\pi$
$613$	−29.1287	+	29.1287i	−1.17650	+	1.17650i	−0.980631	+	0.195866i	$0.937248\pi$
$614$			2.18462i			0.0881641i
$615$		0			0
$616$	6.25959	+	6.25959i	0.252206	+	0.252206i
$617$	−26.1399	−	26.1399i	−1.05235	−	1.05235i	−0.998552	−	0.0537999i	$-0.982867\pi$
$617$	−26.1399	−	26.1399i	−1.05235	−	1.05235i	−0.0537999	−	0.998552i	$-0.517133\pi$
$618$		0			0
$619$	−14.5983	+	14.5983i	−0.586756	+	0.586756i	−0.936751	−	0.349995i	$-0.886183\pi$
$619$	−14.5983	+	14.5983i	−0.586756	+	0.586756i	0.349995	+	0.936751i	$0.386183\pi$
$620$	12.5797	−	3.12561i	0.505213	−	0.125527i
$621$		0			0
$622$	−5.03051	−	5.03051i	−0.201705	−	0.201705i
$623$			8.70591i			0.348795i
$624$		0			0
$625$	−14.0472	+	20.6803i	−0.561887	+	0.827214i
$626$	−3.27702	+	3.27702i	−0.130976	+	0.130976i
$627$		0			0
$628$	18.1705			0.725080
$629$	17.5816	−	17.5816i	0.701024	−	0.701024i
$630$		0			0
$631$	0.525820	−	0.525820i	0.0209326	−	0.0209326i	−0.696563	−	0.717496i	$-0.745288\pi$
$631$	0.525820	−	0.525820i	0.0209326	−	0.0209326i	0.717496	+	0.696563i	$0.245288\pi$
$632$	5.86354	−	5.86354i	0.233239	−	0.233239i
$633$		0			0
$634$			3.88256i			0.154196i
$635$	−18.7307	−	11.2753i	−0.743307	−	0.447447i
$636$		0			0
$637$	5.68734	+	11.8925i	0.225341	+	0.471199i
$638$	−34.3298			−1.35913
$639$		0			0
$640$	−2.17009	+	0.539189i	−0.0857802	+	0.0213133i
$641$	−22.8822			−0.903793			−0.451896	−	0.892070i	$-0.649252\pi$
$641$	−22.8822			−0.903793			−0.451896	+	0.892070i	$0.649252\pi$
$642$		0			0
$643$	−16.3799	+	16.3799i	−0.645961	+	0.645961i	−0.952014	−	0.306053i	$-0.900991\pi$
$643$	−16.3799	+	16.3799i	−0.645961	+	0.645961i	0.306053	+	0.952014i	$0.400991\pi$
$644$	4.14509	+	4.14509i	0.163339	+	0.163339i
$645$		0			0
$646$	−25.5461			−1.00510
$647$			36.9703i			1.45345i	0.686927	+	0.726727i	$0.258959\pi$
$647$			36.9703i			1.45345i	−0.686927	+	0.726727i	$0.741041\pi$
$648$		0			0
$649$			11.4650i			0.450039i
$650$	2.65385	+	17.8314i	0.104092	+	0.699403i
$651$		0			0
$652$	7.45812	−	7.45812i	0.292082	−	0.292082i
$653$	−19.2597			−0.753690			−0.376845	−	0.926276i	$-0.622991\pi$
$653$	−19.2597			−0.753690			−0.376845	+	0.926276i	$0.622991\pi$
$654$		0			0
$655$	−3.53104	+	5.86583i	−0.137969	+	0.229197i
$656$	−4.42620	+	4.42620i	−0.172814	+	0.172814i
$657$		0			0
$658$	−16.4149	−	16.4149i	−0.639919	−	0.639919i
$659$		−	9.15739i		−	0.356721i	−0.983965	−	0.178361i	$-0.942921\pi$
$659$		−	9.15739i		−	0.356721i	0.983965	−	0.178361i	$-0.0570794\pi$
$660$		0			0
$661$	6.14563	−	6.14563i	0.239037	−	0.239037i	−0.577414	−	0.816451i	$-0.695938\pi$
$661$	6.14563	−	6.14563i	0.239037	−	0.239037i	0.816451	+	0.577414i	$0.195938\pi$
$662$			6.06739i			0.235816i
$663$		0			0
$664$	−3.50767			−0.136124
$665$	−11.4288	+	18.9856i	−0.443188	+	0.736232i
$666$		0			0
$667$	−22.7331			−0.880231
$668$	−7.14982	−	7.14982i	−0.276635	−	0.276635i
$669$		0			0
$670$	15.2122	+	9.15728i	0.587700	+	0.353777i
$671$	39.9446	+	39.9446i	1.54204	+	1.54204i
$672$		0			0
$673$	−22.1797			−0.854964			−0.427482	−	0.904024i	$-0.640599\pi$
$673$	−22.1797			−0.854964			−0.427482	+	0.904024i	$0.640599\pi$
$674$	1.41774	+	1.41774i	0.0546092	+	0.0546092i
$675$		0			0
$676$	10.1196	+	8.16054i	0.389214	+	0.313867i
$677$	−1.47676			−0.0567566			−0.0283783	−	0.999597i	$-0.509034\pi$
$677$	−1.47676			−0.0567566			−0.0283783	+	0.999597i	$0.509034\pi$
$678$		0			0
$679$	9.60851			0.368741
$680$	2.54157	+	10.2291i	0.0974646	+	0.392268i
$681$		0			0
$682$	19.8434	−	19.8434i	0.759844	−	0.759844i
$683$	−4.17460	+	4.17460i	−0.159736	+	0.159736i	−0.782450	−	0.622713i	$-0.786030\pi$
$683$	−4.17460	+	4.17460i	−0.159736	+	0.159736i	0.622713	+	0.782450i	$0.286030\pi$
$684$		0			0
$685$	48.7022	−	12.1008i	1.86082	−	0.462346i
$686$	19.4860			0.743980
$687$		0			0
$688$	7.68861			0.293126
$689$	−22.3247	+	10.6763i	−0.850502	+	0.406734i
$690$		0			0
$691$	11.4564	+	11.4564i	0.435823	+	0.435823i	0.890604	−	0.454781i	$-0.150282\pi$
$691$	11.4564	+	11.4564i	0.435823	+	0.435823i	−0.454781	+	0.890604i	$0.650282\pi$
$692$	15.0993			0.573988
$693$		0			0
$694$	12.6154	+	12.6154i	0.478874	+	0.478874i
$695$	2.11114	+	1.27084i	0.0800800	+	0.0482056i
$696$		0			0
$697$	20.8637	+	20.8637i	0.790269	+	0.790269i
$698$	−27.1741			−1.02855
$699$		0			0
$700$	8.73921	+	2.68740i	0.330311	+	0.101574i
$701$	−35.5224			−1.34166			−0.670831	−	0.741611i	$-0.734062\pi$
$701$	−35.5224			−1.34166			−0.670831	+	0.741611i	$0.734062\pi$
$702$		0			0
$703$			28.5876i			1.07820i
$704$	−3.42313	+	3.42313i	−0.129014	+	0.129014i
$705$		0			0
$706$		−	8.45905i		−	0.318361i
$707$	21.9371	+	21.9371i	0.825028	+	0.825028i
$708$		0			0
$709$	−3.23400	+	3.23400i	−0.121455	+	0.121455i	−0.765222	−	0.643767i	$-0.777371\pi$
$709$	−3.23400	+	3.23400i	−0.121455	+	0.121455i	0.643767	+	0.765222i	$0.277371\pi$
$710$	−8.28749	−	4.98880i	−0.311024	−	0.187226i
$711$		0			0
$712$	−4.76093			−0.178423
$713$	13.1403	−	13.1403i	0.492108	−	0.492108i
$714$		0			0
$715$	24.8321	+	30.1111i	0.928669	+	1.12609i
$716$			16.4200i			0.613645i
$717$		0			0
$718$		−	36.8922i		−	1.37680i
$719$	11.9941			0.447304			0.223652	−	0.974669i	$-0.428202\pi$
$719$	11.9941			0.447304			0.223652	+	0.974669i	$0.428202\pi$
$720$		0			0
$721$	−19.8324	−	19.8324i	−0.738597	−	0.738597i
$722$	7.33393	−	7.33393i	0.272941	−	0.272941i
$723$		0			0
$724$	−4.47735			−0.166399
$725$	−31.3338	+	16.5952i	−1.16371	+	0.616328i
$726$		0			0
$727$	−45.7458			−1.69662			−0.848308	−	0.529503i	$-0.822379\pi$
$727$	−45.7458			−1.69662			−0.848308	+	0.529503i	$0.822379\pi$
$728$	5.94800	−	2.84450i	0.220447	−	0.105424i
$729$		0			0
$730$	−0.739964	+	1.22924i	−0.0273873	+	0.0454963i
$731$		−	36.2417i		−	1.34045i
$732$		0			0
$733$	−21.7680	+	21.7680i	−0.804018	+	0.804018i	−0.983721	−	0.179703i	$-0.942486\pi$
$733$	−21.7680	+	21.7680i	−0.804018	+	0.804018i	0.179703	+	0.983721i	$0.442486\pi$
$734$	5.51534	−	5.51534i	0.203575	−	0.203575i
$735$		0			0
$736$	−2.26679	+	2.26679i	−0.0835550	+	0.0835550i
$737$	38.4409			1.41599
$738$		0			0
$739$	−19.9122	+	19.9122i	−0.732484	+	0.732484i	−0.971111	−	0.238627i	$-0.923303\pi$
$739$	−19.9122	+	19.9122i	−0.732484	+	0.732484i	0.238627	+	0.971111i	$0.423303\pi$
$740$	11.4469	−	2.84416i	0.420798	−	0.104553i
$741$		0			0
$742$			12.5504i			0.460741i
$743$	−5.98788	−	5.98788i	−0.219674	−	0.219674i	0.588687	−	0.808361i	$-0.299645\pi$
$743$	−5.98788	−	5.98788i	−0.219674	−	0.219674i	−0.808361	+	0.588687i	$0.799645\pi$
$744$		0			0
$745$	−35.3557	+	8.78463i	−1.29533	+	0.321844i
$746$	20.7195	−	20.7195i	0.758594	−	0.758594i
$747$		0			0
$748$	16.1355	+	16.1355i	0.589974	+	0.589974i
$749$	−3.16340	−	3.16340i	−0.115588	−	0.115588i
$750$		0			0
$751$		−	22.9102i		−	0.836005i	−0.908446	−	0.418002i	$-0.862730\pi$
$751$		−	22.9102i		−	0.836005i	0.908446	−	0.418002i	$-0.137270\pi$
$752$	8.97668	−	8.97668i	0.327346	−	0.327346i
$753$		0			0
$754$	−8.51035	+	24.1106i	−0.309929	+	0.878056i
$755$	−40.2634	+	10.0040i	−1.46533	+	0.364083i
$756$		0			0
$757$			0.704519i			0.0256062i	0.999918	+	0.0128031i	$0.00407546\pi$
$757$			0.704519i			0.0256062i	−0.999918	+	0.0128031i	$0.995925\pi$
$758$			9.59070i			0.348350i
$759$		0			0
$760$	−10.3825	−	6.24995i	−0.376614	−	0.226710i
$761$	24.4534	+	24.4534i	0.886434	+	0.886434i	0.994179	−	0.107744i	$-0.0343628\pi$
$761$	24.4534	+	24.4534i	0.886434	+	0.886434i	−0.107744	+	0.994179i	$0.534363\pi$
$762$		0			0
$763$		−	30.5062i		−	1.10440i
$764$	−10.5841			−0.382918
$765$		0			0
$766$		−	13.3897i		−	0.483789i
$767$	8.05210	+	2.84216i	0.290744	+	0.102624i
$768$		0			0
$769$	−23.7953	−	23.7953i	−0.858080	−	0.858080i	0.133032	−	0.991112i	$-0.457529\pi$
$769$	−23.7953	−	23.7953i	−0.858080	−	0.858080i	−0.991112	+	0.133032i	$0.957529\pi$
$770$	19.2105	−	4.77311i	0.692297	−	0.172011i
$771$		0			0
$772$	−7.20113	+	7.20113i	−0.259174	+	0.259174i
$773$	2.81372	+	2.81372i	0.101202	+	0.101202i	0.755895	−	0.654693i	$-0.227202\pi$
$773$	2.81372	+	2.81372i	0.101202	+	0.101202i	−0.654693	+	0.755895i	$0.727202\pi$
$774$		0			0
$775$	8.51928	−	27.7040i	0.306022	−	0.995159i
$776$			5.25453i			0.188627i
$777$		0			0
$778$	−18.7489	−	18.7489i	−0.672182	−	0.672182i
$779$	−33.9243			−1.21546
$780$		0			0
$781$	−20.9422			−0.749372
$782$	10.6849	+	10.6849i	0.382092	+	0.382092i
$783$		0			0
$784$			3.65617i			0.130577i
$785$	20.9545	−	34.8100i	0.747899	−	1.24242i
$786$		0			0
$787$	−37.4915	−	37.4915i	−1.33643	−	1.33643i	−0.899493	−	0.436934i	$-0.856064\pi$
$787$	−37.4915	−	37.4915i	−1.33643	−	1.33643i	−0.436934	−	0.899493i	$-0.643936\pi$
$788$	9.16979	−	9.16979i	0.326660	−	0.326660i
$789$		0			0
$790$	−4.47112	−	17.9950i	−0.159075	−	0.640234i
$791$	9.44270	+	9.44270i	0.335744	+	0.335744i
$792$		0			0
$793$	37.9563	−	18.1517i	1.34787	−	0.644587i
$794$			19.1556i			0.679806i
$795$		0			0
$796$	20.7555			0.735658
$797$		−	17.4404i		−	0.617770i	−0.951099	−	0.308885i	$-0.900044\pi$
$797$		−	17.4404i		−	0.617770i	0.951099	−	0.308885i	$-0.0999557\pi$
$798$		0			0
$799$	−42.3132	−	42.3132i	−1.49693	−	1.49693i
$800$	−1.46963	+	4.77914i	−0.0519594	+	0.168968i
$801$		0			0
$802$		−	0.241380i		−	0.00852341i
$803$			3.10626i			0.109617i
$804$		0			0
$805$	12.7211	−	3.16075i	0.448361	−	0.111402i
$806$	−9.01731	−	18.8557i	−0.317621	−	0.664163i
$807$		0			0
$808$	−11.9965	+	11.9965i	−0.422037	+	0.422037i
$809$			42.5773i			1.49694i	0.663170	+	0.748469i	$0.269211\pi$
$809$			42.5773i			1.49694i	−0.663170	+	0.748469i	$0.730789\pi$
$810$		0			0
$811$	7.59986	+	7.59986i	0.266867	+	0.266867i	0.827837	−	0.560969i	$-0.189571\pi$
$811$	7.59986	+	7.59986i	0.266867	+	0.266867i	−0.560969	+	0.827837i	$0.689571\pi$
$812$	9.16939	+	9.16939i	0.321783	+	0.321783i
$813$		0			0
$814$	18.0566	−	18.0566i	0.632883	−	0.632883i
$815$	−5.68703	−	22.8887i	−0.199208	−	0.801756i
$816$		0			0
$817$	29.4644	+	29.4644i	1.03083	+	1.03083i
$818$		−	22.3627i		−	0.781895i
$819$		0			0
$820$	3.37510	+	13.5838i	0.117864	+	0.474368i
$821$	−1.44315	+	1.44315i	−0.0503664	+	0.0503664i	−0.731841	−	0.681475i	$-0.761339\pi$
$821$	−1.44315	+	1.44315i	−0.0503664	+	0.0503664i	0.681475	+	0.731841i	$0.261339\pi$
$822$		0			0
$823$	41.1421			1.43412			0.717061	−	0.697010i	$-0.245487\pi$
$823$	41.1421			1.43412			0.717061	+	0.697010i	$0.245487\pi$
$824$	10.8456	−	10.8456i	0.377824	−	0.377824i
$825$		0			0
$826$	3.06226	−	3.06226i	0.106550	−	0.106550i
$827$	−9.52443	+	9.52443i	−0.331197	+	0.331197i	−0.853041	−	0.521844i	$-0.825244\pi$
$827$	−9.52443	+	9.52443i	−0.331197	+	0.331197i	0.521844	+	0.853041i	$0.325244\pi$
$828$		0			0
$829$		−	8.86204i		−	0.307792i	−0.988087	−	0.153896i	$-0.950818\pi$
$829$		−	8.86204i		−	0.307792i	0.988087	−	0.153896i	$-0.0491820\pi$
$830$	−4.04512	+	6.71982i	−0.140408	+	0.233248i
$831$		0			0
$832$	1.55555	+	3.25273i	0.0539289	+	0.112768i
$833$	17.2340			0.597123
$834$		0			0
$835$	−21.9425	+	5.45194i	−0.759353	+	0.188672i
$836$	−26.2363			−0.907403
$837$		0			0
$838$	7.01466	−	7.01466i	0.242318	−	0.242318i
$839$	5.91015	+	5.91015i	0.204041	+	0.204041i	0.801729	−	0.597688i	$-0.203914\pi$
$839$	5.91015	+	5.91015i	0.204041	+	0.204041i	−0.597688	+	0.801729i	$0.703914\pi$
$840$		0			0
$841$	−21.2882			−0.734077
$842$		−	23.6160i		−	0.813862i
$843$		0			0
$844$		−	19.9602i		−	0.687058i
$845$	27.3036	−	9.97563i	0.939273	−	0.343172i
$846$		0			0
$847$	16.0796	−	16.0796i	0.552501	−	0.552501i
$848$	−6.86336			−0.235689
$849$		0			0
$850$	22.5274	+	6.92739i	0.772682	+	0.237608i
$851$	11.9570	−	11.9570i	0.409882	−	0.409882i
$852$		0			0
$853$	1.70532	+	1.70532i	0.0583891	+	0.0583891i	0.735698	−	0.677309i	$-0.236854\pi$
$853$	1.70532	+	1.70532i	0.0583891	+	0.0583891i	−0.677309	+	0.735698i	$0.736854\pi$
$854$		−	21.3382i		−	0.730177i
$855$		0			0
$856$	1.72994	−	1.72994i	0.0591281	−	0.0591281i
$857$		−	35.6660i		−	1.21833i	−0.793044	−	0.609164i	$-0.791505\pi$
$857$		−	35.6660i		−	1.21833i	0.793044	−	0.609164i	$-0.208495\pi$
$858$		0			0
$859$	−40.5671			−1.38413			−0.692065	−	0.721835i	$-0.743299\pi$
$859$	−40.5671			−1.38413			−0.692065	+	0.721835i	$0.743299\pi$
$860$	8.86665	−	14.7294i	0.302350	−	0.502269i
$861$		0			0
$862$	24.0434			0.818920
$863$	−8.23230	−	8.23230i	−0.280231	−	0.280231i	0.552970	−	0.833201i	$-0.313494\pi$
$863$	−8.23230	−	8.23230i	−0.280231	−	0.280231i	−0.833201	+	0.552970i	$0.813494\pi$
$864$		0			0
$865$	17.4128	−	28.9264i	0.592051	−	0.983526i
$866$	−1.77197	−	1.77197i	−0.0602141	−	0.0602141i
$867$		0			0
$868$	−10.6002			−0.359796
$869$	−28.3856	−	28.3856i	−0.962916	−	0.962916i
$870$		0			0
$871$	9.52948	−	26.9979i	0.322894	−	0.914789i
$872$	16.6827			0.564947
$873$		0			0
$874$	−17.3737			−0.587673
$875$	15.2266	−	13.6430i	0.514753	−	0.461216i
$876$		0			0
$877$	23.5233	−	23.5233i	0.794327	−	0.794327i	−0.187868	−	0.982194i	$-0.560158\pi$
$877$	23.5233	−	23.5233i	0.794327	−	0.794327i	0.982194	+	0.187868i	$0.0601576\pi$
$878$	−21.1606	+	21.1606i	−0.714134	+	0.714134i
$879$		0			0
$880$	2.61023	+	10.5055i	0.0879909	+	0.354139i
$881$	29.8500			1.00567			0.502837	−	0.864381i	$-0.332290\pi$
$881$	29.8500			1.00567			0.502837	+	0.864381i	$0.332290\pi$
$882$		0			0
$883$	23.1619			0.779459			0.389729	−	0.920929i	$-0.372569\pi$
$883$	23.1619			0.779459			0.389729	+	0.920929i	$0.372569\pi$
$884$	15.3324	−	7.33236i	0.515683	−	0.246614i
$885$		0			0
$886$	5.31179	+	5.31179i	0.178453	+	0.178453i
$887$	−46.8884			−1.57436			−0.787180	−	0.616723i	$-0.788460\pi$
$887$	−46.8884			−1.57436			−0.787180	+	0.616723i	$0.788460\pi$
$888$		0			0
$889$	12.6422	+	12.6422i	0.424007	+	0.424007i
$890$	−5.49040	+	9.12074i	−0.184039	+	0.305728i
$891$		0			0
$892$	−9.64691	−	9.64691i	−0.323002	−	0.323002i
$893$	68.8011			2.30234
$894$		0			0
$895$	31.4566	+	18.9359i	1.05148	+	0.632956i
$896$	1.82862			0.0610898
$897$		0			0
$898$			18.0733i			0.603113i
$899$	29.0678	−	29.0678i	0.969464	−	0.969464i
$900$		0			0
$901$			32.3517i			1.07779i
$902$	21.4274	+	21.4274i	0.713453	+	0.713453i
$903$		0			0
$904$	−5.16385	+	5.16385i	−0.171747	+	0.171747i
$905$	−5.16337	+	8.57747i	−0.171636	+	0.285125i
$906$		0			0
$907$	12.7144			0.422174			0.211087	−	0.977467i	$-0.432300\pi$
$907$	12.7144			0.422174			0.211087	+	0.977467i	$0.432300\pi$
$908$	−9.61668	+	9.61668i	−0.319141	+	0.319141i
$909$		0			0
$910$	1.41000	−	14.6752i	0.0467412	−	0.486478i
$911$		−	9.67389i		−	0.320510i	−0.987076	−	0.160255i	$-0.948768\pi$
$911$		−	9.67389i		−	0.320510i	0.987076	−	0.160255i	$-0.0512317\pi$
$912$		0			0
$913$			16.9808i			0.561982i
$914$	−2.00647			−0.0663682
$915$		0			0
$916$	−0.831438	−	0.831438i	−0.0274715	−	0.0274715i
$917$	3.95912	−	3.95912i	0.130742	−	0.130742i
$918$		0			0
$919$	−10.5683			−0.348616			−0.174308	−	0.984691i	$-0.555769\pi$
$919$	−10.5683			−0.348616			−0.174308	+	0.984691i	$0.555769\pi$
$920$	1.72849	+	6.95670i	0.0569867	+	0.229356i
$921$		0			0
$922$	−12.6469			−0.416503
$923$	−5.19157	+	14.7082i	−0.170883	+	0.484126i
$924$		0			0
$925$	7.75215	−	25.2094i	0.254889	−	0.828879i
$926$			2.31974i			0.0762314i
$927$		0			0
$928$	−5.01439	+	5.01439i	−0.164605	+	0.164605i
$929$	−7.91139	+	7.91139i	−0.259564	+	0.259564i	−0.824877	−	0.565313i	$-0.808756\pi$
$929$	−7.91139	+	7.91139i	−0.259564	+	0.259564i	0.565313	+	0.824877i	$0.308756\pi$
$930$		0			0
$931$	−14.0112	+	14.0112i	−0.459199	+	0.459199i
$932$	−13.0922			−0.428849
$933$		0			0
$934$	−15.3431	+	15.3431i	−0.502040	+	0.502040i
$935$	49.5194	−	12.3038i	1.61946	−	0.402378i
$936$		0			0
$937$		−	10.4694i		−	0.342020i	−0.985269	−	0.171010i	$-0.945297\pi$
$937$		−	10.4694i		−	0.342020i	0.985269	−	0.171010i	$-0.0547030\pi$
$938$	−10.2674	−	10.2674i	−0.335244	−	0.335244i
$939$		0			0
$940$	−6.84497	−	27.5491i	−0.223258	−	0.898553i
$941$	25.1112	−	25.1112i	0.818600	−	0.818600i	−0.167305	−	0.985905i	$-0.553506\pi$
$941$	25.1112	−	25.1112i	0.818600	−	0.818600i	0.985905	+	0.167305i	$0.0535064\pi$
$942$		0			0
$943$	14.1892	+	14.1892i	0.462063	+	0.462063i
$944$	1.67463	+	1.67463i	0.0545046	+	0.0545046i
$945$		0			0
$946$		−	37.2208i		−	1.21015i
$947$	6.75196	−	6.75196i	0.219409	−	0.219409i	−0.588840	−	0.808249i	$-0.700415\pi$
$947$	6.75196	−	6.75196i	0.219409	−	0.219409i	0.808249	+	0.588840i	$0.200415\pi$
$948$		0			0
$949$	2.18159	+	0.770040i	0.0708175	+	0.0249966i
$950$	−23.9466	+	12.6827i	−0.776932	+	0.411482i
$951$		0			0
$952$		−	8.61951i		−	0.279360i
$953$			36.1972i			1.17254i	0.810115	+	0.586271i	$0.199405\pi$
$953$			36.1972i			1.17254i	−0.810115	+	0.586271i	$0.800595\pi$
$954$		0			0
$955$	−12.2057	+	20.2764i	−0.394968	+	0.656128i
$956$	8.83842	+	8.83842i	0.285855	+	0.285855i
$957$		0			0
$958$			5.17055i			0.167053i
$959$	−41.0387			−1.32521
$960$		0			0
$961$			2.60369i			0.0839899i
$962$	−8.20533	−	17.1578i	−0.264550	−	0.553189i
$963$		0			0
$964$	5.80438	+	5.80438i	0.186947	+	0.186947i
$965$	5.49106	+	22.1000i	0.176764	+	0.711425i
$966$		0			0
$967$	26.5164	−	26.5164i	0.852709	−	0.852709i	−0.137757	−	0.990466i	$-0.543989\pi$
$967$	26.5164	−	26.5164i	0.852709	−	0.852709i	0.990466	+	0.137757i	$0.0439893\pi$
$968$	8.79332	+	8.79332i	0.282628	+	0.282628i
$969$		0			0
$970$	10.0663	+	6.05962i	0.323211	+	0.194563i
$971$			35.6136i			1.14290i	0.820638	+	0.571448i	$0.193618\pi$
$971$			35.6136i			1.14290i	−0.820638	+	0.571448i	$0.806382\pi$
$972$		0			0
$973$	−1.42490	−	1.42490i	−0.0456803	−	0.0456803i
$974$	34.7565			1.11367
$975$		0			0
$976$	11.6690			0.373517
$977$	−1.70264	−	1.70264i	−0.0544722	−	0.0544722i	0.679346	−	0.733818i	$-0.262264\pi$
$977$	−1.70264	−	1.70264i	−0.0544722	−	0.0544722i	−0.733818	+	0.679346i	$0.762264\pi$
$978$		0			0
$979$			23.0478i			0.736612i
$980$	7.00429	+	4.21636i	0.223744	+	0.134687i
$981$		0			0
$982$	24.8087	+	24.8087i	0.791678	+	0.791678i
$983$	11.2285	−	11.2285i	0.358134	−	0.358134i	−0.504991	−	0.863125i	$-0.668504\pi$
$983$	11.2285	−	11.2285i	0.358134	−	0.358134i	0.863125	+	0.504991i	$0.168504\pi$
$984$		0			0
$985$	−6.99223	−	28.1418i	−0.222791	−	0.896672i
$986$	23.6363	+	23.6363i	0.752732	+	0.752732i
$987$		0			0
$988$	−6.50398	+	18.4264i	−0.206919	+	0.586221i
$989$		−	24.6476i		−	0.783747i
$990$		0			0
$991$	−1.44965			−0.0460497			−0.0230248	−	0.999735i	$-0.507330\pi$
$991$	−1.44965			−0.0460497			−0.0230248	+	0.999735i	$0.507330\pi$
$992$		−	5.79687i		−	0.184051i
$993$		0			0
$994$	5.59361	+	5.59361i	0.177419	+	0.177419i
$995$	23.9356	−	39.7622i	0.758809	−	1.26055i
$996$		0			0
$997$			47.2336i			1.49590i	0.663753	+	0.747952i	$0.268963\pi$
$997$			47.2336i			1.49590i	−0.663753	+	0.747952i	$0.731037\pi$
$998$		−	9.75893i		−	0.308913i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.q.d.359.4	yes	24
3.2	odd	2	inner	1170.2.q.d.359.12	yes	24
5.4	even	2		1170.2.q.c.359.9	yes	24
13.5	odd	4		1170.2.q.c.629.1	yes	24
15.14	odd	2		1170.2.q.c.359.1	✓	24
39.5	even	4		1170.2.q.c.629.9	yes	24
65.44	odd	4	inner	1170.2.q.d.629.12	yes	24
195.44	even	4	inner	1170.2.q.d.629.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1170.2.q.c.359.1	✓	24	15.14	odd	2
1170.2.q.c.359.9	yes	24	5.4	even	2
1170.2.q.c.629.1	yes	24	13.5	odd	4
1170.2.q.c.629.9	yes	24	39.5	even	4
1170.2.q.d.359.4	yes	24	1.1	even	1	trivial
1170.2.q.d.359.12	yes	24	3.2	odd	2	inner
1170.2.q.d.629.4	yes	24	195.44	even	4	inner
1170.2.q.d.629.12	yes	24	65.44	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.q (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(1.91575 + 1.15322i) q^{5} +(-1.29303 - 1.29303i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.539189 - 2.17009i) q^{10} +(-3.42313 - 3.42313i) q^{11} +(-3.25273 + 1.55555i) q^{13} +1.82862i q^{14} -1.00000 q^{16} +4.71368i q^{17} +(-3.83222 - 3.83222i) q^{19} +(-1.15322 + 1.91575i) q^{20} +4.84104i q^{22} +3.20573i q^{23} +(2.34017 + 4.41855i) q^{25} +(3.39997 + 1.20009i) q^{26} +(1.29303 - 1.29303i) q^{28} +7.09142i q^{29} +(-4.09901 - 4.09901i) q^{31} +(0.707107 + 0.707107i) q^{32} +(3.33308 - 3.33308i) q^{34} +(-0.985969 - 3.96825i) q^{35} +(-3.72990 - 3.72990i) q^{37} +5.41957i q^{38} +(2.17009 - 0.539189i) q^{40} +(4.42620 - 4.42620i) q^{41} -7.68861 q^{43} +(3.42313 - 3.42313i) q^{44} +(2.26679 - 2.26679i) q^{46} +(-8.97668 + 8.97668i) q^{47} -3.65617i q^{49} +(1.46963 - 4.77914i) q^{50} +(-1.55555 - 3.25273i) q^{52} +6.86336 q^{53} +(-2.61023 - 10.5055i) q^{55} -1.82862 q^{56} +(5.01439 - 5.01439i) q^{58} +(-1.67463 - 1.67463i) q^{59} -11.6690 q^{61} +5.79687i q^{62} -1.00000i q^{64} +(-8.02530 - 0.771077i) q^{65} +(-5.61487 + 5.61487i) q^{67} -4.71368 q^{68} +(-2.10879 + 3.50316i) q^{70} +(3.05893 - 3.05893i) q^{71} +(-0.453716 - 0.453716i) q^{73} +5.27488i q^{74} +(3.83222 - 3.83222i) q^{76} +8.85239i q^{77} +8.29230 q^{79} +(-1.91575 - 1.15322i) q^{80} -6.25959 q^{82} +(-2.48030 - 2.48030i) q^{83} +(-5.43591 + 9.03023i) q^{85} +(5.43667 + 5.43667i) q^{86} -4.84104 q^{88} +(-3.36649 - 3.36649i) q^{89} +(6.21723 + 2.19451i) q^{91} -3.20573 q^{92} +12.6949 q^{94} +(-2.92217 - 11.7609i) q^{95} +(-3.71551 + 3.71551i) q^{97} +(-2.58530 + 2.58530i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 20 q^{13} - 24 q^{16} - 48 q^{19} - 32 q^{25} - 8 q^{31} + 16 q^{34} + 32 q^{37} + 8 q^{40} - 80 q^{43} + 8 q^{46} + 12 q^{52} + 16 q^{55} + 24 q^{58} - 16 q^{61} + 8 q^{67} - 40 q^{70} - 48 q^{73}+ \cdots - 64 q^{97}+O(q^{100}) \) 24 * q + 20 * q^13 - 24 * q^16 - 48 * q^19 - 32 * q^25 - 8 * q^31 + 16 * q^34 + 32 * q^37 + 8 * q^40 - 80 * q^43 + 8 * q^46 + 12 * q^52 + 16 * q^55 + 24 * q^58 - 16 * q^61 + 8 * q^67 - 40 * q^70 - 48 * q^73 + 48 * q^76 - 96 * q^79 + 72 * q^82 + 104 * q^85 - 8 * q^88 + 48 * q^91 - 16 * q^94 - 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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