LMFDB - Embedded newform 1170.2.q.c.629.1

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			629.1
Character	$\chi$	$=$	1170.629
Dual form			1170.2.q.c.359.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(1.15322 - 1.91575i) q^{5} +(1.29303 - 1.29303i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.539189 + 2.17009i) q^{10} +(3.42313 - 3.42313i) q^{11} +(3.25273 + 1.55555i) q^{13} +1.82862i q^{14} -1.00000 q^{16} -4.71368i q^{17} +(-3.83222 + 3.83222i) q^{19} +(-1.91575 - 1.15322i) q^{20} +4.84104i q^{22} -3.20573i q^{23} +(-2.34017 - 4.41855i) q^{25} +(-3.39997 + 1.20009i) q^{26} +(-1.29303 - 1.29303i) q^{28} +7.09142i q^{29} +(-4.09901 + 4.09901i) q^{31} +(0.707107 - 0.707107i) q^{32} +(3.33308 + 3.33308i) q^{34} +(-0.985969 - 3.96825i) q^{35} +(3.72990 - 3.72990i) q^{37} -5.41957i q^{38} +(2.17009 - 0.539189i) q^{40} +(-4.42620 - 4.42620i) q^{41} +7.68861 q^{43} +(-3.42313 - 3.42313i) q^{44} +(2.26679 + 2.26679i) q^{46} +(-8.97668 - 8.97668i) q^{47} +3.65617i q^{49} +(4.77914 + 1.46963i) q^{50} +(1.55555 - 3.25273i) q^{52} +6.86336 q^{53} +(-2.61023 - 10.5055i) q^{55} +1.82862 q^{56} +(-5.01439 - 5.01439i) q^{58} +(1.67463 - 1.67463i) q^{59} -11.6690 q^{61} -5.79687i q^{62} +1.00000i q^{64} +(6.73115 - 4.43753i) q^{65} +(5.61487 + 5.61487i) q^{67} -4.71368 q^{68} +(3.50316 + 2.10879i) q^{70} +(-3.05893 - 3.05893i) q^{71} +(0.453716 - 0.453716i) q^{73} +5.27488i q^{74} +(3.83222 + 3.83222i) q^{76} -8.85239i q^{77} +8.29230 q^{79} +(-1.15322 + 1.91575i) q^{80} +6.25959 q^{82} +(-2.48030 + 2.48030i) q^{83} +(-9.03023 - 5.43591i) q^{85} +(-5.43667 + 5.43667i) q^{86} +4.84104 q^{88} +(3.36649 - 3.36649i) q^{89} +(6.21723 - 2.19451i) q^{91} -3.20573 q^{92} +12.6949 q^{94} +(2.92217 + 11.7609i) q^{95} +(3.71551 + 3.71551i) q^{97} +(-2.58530 - 2.58530i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 24 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 - 24 * q^70 + 48 * q^73 + 48 * q^76 - 96 * q^79 - 72 * q^82 + 8 * 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 $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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
$5$	1.15322	−	1.91575i	0.515735	−	0.856748i
$5$	1.15322	−	1.91575i	0.515735	−	0.856748i
$6$		0			0
$7$	1.29303	−	1.29303i	0.488718	−	0.488718i	−0.419184	−	0.907902i	$-0.637684\pi$
$7$	1.29303	−	1.29303i	0.488718	−	0.488718i	0.907902	+	0.419184i	$0.137684\pi$
$8$	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	0.0326453	−	0.999467i	$-0.489607\pi$
$11$	3.42313	−	3.42313i	1.03211	−	1.03211i	0.999467	−	0.0326453i	$-0.0103932\pi$
$12$		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	$-0.806316\pi$
$17$		−	4.71368i		−	1.14324i	0.820520	−	0.571618i	$-0.193684\pi$
$18$		0			0
$19$	−3.83222	+	3.83222i	−0.879170	+	0.879170i	−0.993449	−	0.114278i	$-0.963544\pi$
$19$	−3.83222	+	3.83222i	−0.879170	+	0.879170i	0.114278	+	0.993449i	$0.463544\pi$
$20$	−1.91575	−	1.15322i	−0.428374	−	0.257868i
$21$		0			0
$22$			4.84104i			1.03211i
$23$		−	3.20573i		−	0.668440i	−0.942495	−	0.334220i	$-0.891527\pi$
$23$		−	3.20573i		−	0.668440i	0.942495	−	0.334220i	$-0.108473\pi$
$24$		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	−0.971841	−	0.235638i	$-0.924282\pi$
$31$	−4.09901	+	4.09901i	−0.736203	+	0.736203i	0.235638	+	0.971841i	$0.424282\pi$
$32$	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	$-0.607246\pi$
$37$	3.72990	−	3.72990i	0.613192	−	0.613192i	0.943776	+	0.330584i	$0.107246\pi$
$38$		−	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	$-0.412562\pi$
$41$	−4.42620	−	4.42620i	−0.691256	−	0.691256i	−0.962508	+	0.271253i	$0.912562\pi$
$42$		0			0
$43$	7.68861			1.17250			0.586251	−	0.810129i	$-0.300603\pi$
$43$	7.68861			1.17250			0.586251	+	0.810129i	$0.300603\pi$
$44$	−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	−0.921860	−	0.387523i	$-0.873331\pi$
$47$	−8.97668	−	8.97668i	−1.30938	−	1.30938i	−0.387523	−	0.921860i	$-0.626669\pi$
$48$		0			0
$49$			3.65617i			0.522309i
$50$	4.77914	+	1.46963i	0.675872	+	0.207838i
$51$		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	$-0.700732\pi$
$59$	1.67463	−	1.67463i	0.218018	−	0.218018i	0.807663	+	0.589644i	$0.200732\pi$
$60$		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
$65$	6.73115	−	4.43753i	0.834896	−	0.550407i
$66$		0			0
$67$	5.61487	+	5.61487i	0.685966	+	0.685966i	0.961338	−	0.275372i	$-0.0888010\pi$
$67$	5.61487	+	5.61487i	0.685966	+	0.685966i	−0.275372	+	0.961338i	$0.588801\pi$
$68$	−4.71368			−0.571618
$69$		0			0
$70$	3.50316	+	2.10879i	0.418708	+	0.252049i
$71$	−3.05893	−	3.05893i	−0.363028	−	0.363028i	0.501898	−	0.864927i	$-0.332635\pi$
$71$	−3.05893	−	3.05893i	−0.363028	−	0.363028i	−0.864927	+	0.501898i	$0.832635\pi$
$72$		0			0
$73$	0.453716	−	0.453716i	0.0531034	−	0.0531034i	−0.680056	−	0.733160i	$-0.738045\pi$
$73$	0.453716	−	0.453716i	0.0531034	−	0.0531034i	0.733160	+	0.680056i	$0.238045\pi$
$74$			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	$0.345522\pi$
$80$	−1.15322	+	1.91575i	−0.128934	+	0.214187i
$81$		0			0
$82$	6.25959			0.691256
$83$	−2.48030	+	2.48030i	−0.272248	+	0.272248i	−0.830005	−	0.557756i	$-0.811662\pi$
$83$	−2.48030	+	2.48030i	−0.272248	+	0.272248i	0.557756	+	0.830005i	$0.311662\pi$
$84$		0			0
$85$	−9.03023	−	5.43591i	−0.979465	−	0.589607i
$86$	−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	$-0.668804\pi$
$89$	3.36649	−	3.36649i	0.356847	−	0.356847i	0.862649	+	0.505802i	$0.168804\pi$
$90$		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	$-0.164048\pi$
$97$	3.71551	+	3.71551i	0.377253	+	0.377253i	−0.492857	+	0.870110i	$0.664048\pi$
$98$	−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	$-0.180151\pi$
$101$	16.9657			1.68815			0.844074	+	0.536227i	$0.180151\pi$
$102$		0			0
$103$	−15.3380			−1.51129			−0.755647	−	0.654979i	$-0.772678\pi$
$103$	−15.3380			−1.51129			−0.755647	+	0.654979i	$0.772678\pi$
$104$	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	0.139700	−	0.990194i	$-0.455386\pi$
$109$	11.7964	−	11.7964i	1.12989	−	1.12989i	0.990194	−	0.139700i	$-0.0446137\pi$
$110$	9.27420	+	5.58277i	0.884260	+	0.532297i
$111$		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
$115$	−6.14136	−	3.69690i	−0.572685	−	0.344738i
$116$	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
$125$	−11.1636	−	0.612376i	−0.998499	−	0.0547726i
$126$		0			0
$127$	9.77725			0.867591			0.433795	−	0.901011i	$-0.357174\pi$
$127$	9.77725			0.867591			0.433795	+	0.901011i	$0.357174\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	−1.62184	+	7.89745i	−0.142244	+	0.692652i
$131$			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	0.879023	+	0.476779i	$0.158196\pi$
$137$	15.8693	+	15.8693i	1.35580	+	1.35580i	0.476779	+	0.879023i	$0.341804\pi$
$138$		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
$145$	13.5854	+	8.17796i	1.12820	+	0.679143i
$146$			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	$-0.0174248\pi$
$149$	11.5204	+	11.5204i	0.943788	+	0.943788i	−0.0547142	+	0.998502i	$0.517425\pi$
$150$		0			0
$151$	−13.1195	−	13.1195i	−1.06765	−	1.06765i	−0.997539	−	0.0701126i	$-0.977664\pi$
$151$	−13.1195	−	13.1195i	−1.06765	−	1.06765i	−0.0701126	−	0.997539i	$-0.522336\pi$
$152$	−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	$-0.614458\pi$
$163$	7.45812	−	7.45812i	0.584165	−	0.584165i	0.936045	+	0.351880i	$0.114458\pi$
$164$	−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	0.374113	−	0.927383i	$-0.377947\pi$
$167$	−7.14982	−	7.14982i	−0.553269	−	0.553269i	−0.927383	+	0.374113i	$0.877947\pi$
$168$		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	$0.194604\pi$
$173$			15.0993i			1.14798i	−0.818864	+	0.573988i	$0.805396\pi$
$174$		0			0
$175$	−8.73921	−	2.68740i	−0.660622	−	0.203148i
$176$	−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	$-0.710297\pi$
$179$	−16.4200			−1.22729			−0.613645	+	0.789582i	$0.710297\pi$
$180$		0			0
$181$		−	4.47735i		−	0.332799i	−0.986058	−	0.166399i	$-0.946786\pi$
$181$		−	4.47735i		−	0.332799i	0.986058	−	0.166399i	$-0.0532141\pi$
$182$	−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
$190$	−10.3825	−	6.24995i	−0.753228	−	0.453419i
$191$			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	$-0.869454\pi$
$193$	−7.20113	+	7.20113i	−0.518348	+	0.518348i	0.398723	+	0.917071i	$0.369454\pi$
$194$	−5.25453			−0.377253
$195$		0			0
$196$	3.65617			0.261155
$197$	−9.16979	+	9.16979i	−0.653321	+	0.653321i	−0.953791	−	0.300470i	$-0.902856\pi$
$197$	−9.16979	+	9.16979i	−0.653321	+	0.653321i	0.300470	+	0.953791i	$0.402856\pi$
$198$		0			0
$199$			20.7555i			1.47132i	0.677353	+	0.735658i	$0.263127\pi$
$199$			20.7555i			1.47132i	−0.677353	+	0.735658i	$0.736873\pi$
$200$	1.46963	−	4.77914i	0.103919	−	0.337936i
$201$		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
$215$	8.86665	−	14.7294i	0.604700	−	1.00454i
$216$		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	$-0.0989976\pi$
$223$	9.64691	+	9.64691i	0.646005	+	0.646005i	−0.306020	+	0.952025i	$0.598998\pi$
$224$		−	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	−0.311850	−	0.950131i	$-0.600949\pi$
$227$	9.61668	−	9.61668i	0.638281	−	0.638281i	0.950131	+	0.311850i	$0.100949\pi$
$228$		0			0
$229$	−0.831438	−	0.831438i	−0.0549429	−	0.0549429i	0.679101	−	0.734044i	$-0.262370\pi$
$229$	−0.831438	−	0.831438i	−0.0549429	−	0.0549429i	−0.734044	+	0.679101i	$0.762370\pi$
$230$	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	$-0.858919\pi$
$233$		−	13.0922i		−	0.857698i	0.903376	−	0.428849i	$-0.141081\pi$
$234$		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	$-0.382471\pi$
$239$	−8.83842	−	8.83842i	−0.571710	−	0.571710i	−0.932606	+	0.360896i	$0.882471\pi$
$240$		0			0
$241$	5.80438	+	5.80438i	0.373893	+	0.373893i	0.868893	−	0.495000i	$-0.164832\pi$
$241$	5.80438	+	5.80438i	0.373893	+	0.373893i	−0.495000	+	0.868893i	$0.664832\pi$
$242$	8.79332	+	8.79332i	0.565256	+	0.565256i
$243$		0			0
$244$			11.6690i			0.747033i
$245$	7.00429	+	4.21636i	0.447488	+	0.269373i
$246$		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	$-0.822756\pi$
$251$	−26.8994			−1.69787			−0.848936	+	0.528495i	$0.822756\pi$
$252$		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	$0.0565380\pi$
$257$			5.66502i			0.353374i	−0.984267	+	0.176687i	$0.943462\pi$
$258$		0			0
$259$		−	9.64572i		−	0.599356i
$260$	−4.43753	−	6.73115i	−0.275204	−	0.417448i
$261$		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
$265$	7.91495	−	13.1485i	0.486212	−	0.807703i
$266$	−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	0.998657	−	0.0518080i	$-0.0164984\pi$
$271$	15.5871	+	15.5871i	0.946849	+	0.946849i	−0.0518080	+	0.998657i	$0.516498\pi$
$272$			4.71368i			0.285809i
$273$		0			0
$274$	−22.4425			−1.35580
$275$	−23.1360	−	7.11456i	−1.39515	−	0.429024i
$276$		0			0
$277$	11.4081			0.685445			0.342722	−	0.939437i	$-0.388651\pi$
$277$	11.4081			0.685445			0.342722	+	0.939437i	$0.388651\pi$
$278$	−0.779226	+	0.779226i	−0.0467349	+	0.0467349i
$279$		0			0
$280$	2.10879	−	3.50316i	0.126025	−	0.209354i
$281$	18.4689	−	18.4689i	1.10176	−	1.10176i	0.107565	−	0.994198i	$-0.465695\pi$
$281$	18.4689	−	18.4689i	1.10176	−	1.10176i	0.994198	−	0.107565i	$-0.0343052\pi$
$282$		0			0
$283$	−24.4471			−1.45323			−0.726615	−	0.687045i	$-0.758908\pi$
$283$	−24.4471			−1.45323			−0.726615	+	0.687045i	$0.758908\pi$
$284$	−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	0.973599	−	0.228264i	$-0.0733048\pi$
$293$	12.7581	+	12.7581i	0.745336	+	0.745336i	−0.228264	+	0.973599i	$0.573305\pi$
$294$		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
$305$	−13.4569	+	22.3549i	−0.770543	+	1.28004i
$306$		0			0
$307$	1.54476	−	1.54476i	0.0881641	−	0.0881641i	−0.661649	−	0.749813i	$-0.730143\pi$
$307$	1.54476	−	1.54476i	0.0881641	−	0.0881641i	0.749813	+	0.661649i	$0.230143\pi$
$308$	−8.85239			−0.504412
$309$		0			0
$310$	−11.1053	−	6.68506i	−0.630741	−	0.379686i
$311$	−7.11421			−0.403410			−0.201705	−	0.979446i	$-0.564648\pi$
$311$	−7.11421			−0.403410			−0.201705	+	0.979446i	$0.564648\pi$
$312$		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	−0.779989	−	0.625793i	$-0.784775\pi$
$317$	−2.74539	+	2.74539i	−0.154196	+	0.154196i	0.625793	+	0.779989i	$0.284775\pi$
$318$		0			0
$319$	24.2748	+	24.2748i	1.35913	+	1.35913i
$320$	1.91575	+	1.15322i	0.107094	+	0.0644669i
$321$		0			0
$322$	5.86204			0.326679
$323$	18.0639	+	18.0639i	1.00510	+	1.00510i
$324$		0			0
$325$	−0.738692	−	18.0126i	−0.0409753	−	0.999160i
$326$			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	−0.815115	−	0.579299i	$-0.803326\pi$
$331$	−4.29030	+	4.29030i	−0.235816	+	0.235816i	0.579299	+	0.815115i	$0.303326\pi$
$332$	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	$-0.482609\pi$
$337$	2.00498			0.109218			0.0546092	+	0.998508i	$0.482609\pi$
$338$	−12.9260	−	1.38524i	−0.703081	−	0.0753469i
$339$		0			0
$340$	−5.43591	+	9.03023i	−0.294804	+	0.489733i
$341$			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	0.999580	+	0.0289745i	$0.00922416\pi$
$349$	19.2150	+	19.2150i	1.02855	+	1.02855i	0.0289745	+	0.999580i	$0.490776\pi$
$350$	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	−0.529777	−	0.848137i	$-0.677724\pi$
$353$	5.98145	−	5.98145i	0.318361	−	0.318361i	0.848137	+	0.529777i	$0.177724\pi$
$354$		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	−0.526837	+	0.849966i	$0.676622\pi$
$359$	−26.0867	+	26.0867i	−1.37680	+	1.37680i	−0.849966	+	0.526837i	$0.823378\pi$
$360$		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
$370$	10.1053	+	6.08309i	0.525351	+	0.316245i
$371$	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	−0.859495	−	0.511145i	$-0.829222\pi$
$379$	−6.78165	+	6.78165i	−0.348350	+	0.348350i	0.511145	+	0.859495i	$0.329222\pi$
$380$	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	−0.422550	−	0.906339i	$-0.638865\pi$
$383$	9.46794	−	9.46794i	0.483789	−	0.483789i	0.906339	+	0.422550i	$0.138865\pi$
$384$		0			0
$385$	−16.9589	−	10.2087i	−0.864308	−	0.520286i
$386$		−	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	$-0.734643\pi$
$389$	−26.5150			−1.34436			−0.672182	+	0.740386i	$0.734643\pi$
$390$		0			0
$391$	−15.1108			−0.764185
$392$	−2.58530	+	2.58530i	−0.130577	+	0.130577i
$393$		0			0
$394$		−	12.9680i		−	0.653321i
$395$	9.56284	−	15.8860i	0.481159	−	0.799309i
$396$		0			0
$397$	13.5450	−	13.5450i	0.679806	−	0.679806i	−0.280150	−	0.959956i	$-0.590384\pi$
$397$	13.5450	−	13.5450i	0.679806	−	0.679806i	0.959956	+	0.280150i	$0.0903843\pi$
$398$	−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	$-0.751918\pi$
$401$	−0.170681	+	0.170681i	−0.00852341	+	0.00852341i	0.702832	+	0.711356i	$0.251918\pi$
$402$		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	−0.198255	−	0.980150i	$-0.563528\pi$
$409$	15.8128	−	15.8128i	0.781895	−	0.781895i	0.980150	+	0.198255i	$0.0635276\pi$
$410$	7.21867	−	11.9918i	0.356505	−	0.592232i
$411$		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	−0.171349	−	0.985210i	$-0.554812\pi$
$421$	16.6990	−	16.6990i	0.813862	−	0.813862i	0.985210	+	0.171349i	$0.0548125\pi$
$422$	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	$-0.0534182\pi$
$431$	17.0012	+	17.0012i	0.818920	+	0.818920i	−0.167032	+	0.985952i	$0.553418\pi$
$432$		0			0
$433$	−2.50595			−0.120428			−0.0602141	−	0.998185i	$-0.519178\pi$
$433$	−2.50595			−0.120428			−0.0602141	+	0.998185i	$0.519178\pi$
$434$	−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	$0.253179\pi$
$439$			29.9255i			1.42827i	−0.700009	+	0.714134i	$0.746821\pi$
$440$	5.58277	−	9.27420i	0.266148	−	0.442130i
$441$		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	$-0.609759\pi$
$449$	12.7797	−	12.7797i	0.603113	−	0.603113i	0.941137	+	0.338025i	$0.109759\pi$
$450$		0			0
$451$	−30.3029			−1.42691
$452$			7.30279i			0.343494i
$453$		0			0
$454$			13.6000i			0.638281i
$455$	2.96571	−	14.4414i	0.139035	−	0.677023i
$456$		0			0
$457$	−1.41879	−	1.41879i	−0.0663682	−	0.0663682i	0.673144	−	0.739512i	$-0.264944\pi$
$457$	−1.41879	−	1.41879i	−0.0663682	−	0.0663682i	−0.739512	+	0.673144i	$0.764944\pi$
$458$	1.17583			0.0549429
$459$		0			0
$460$	−3.69690	+	6.14136i	−0.172369	+	0.286342i
$461$	−8.94270	−	8.94270i	−0.416503	−	0.416503i	0.467494	−	0.883996i	$-0.345157\pi$
$461$	−8.94270	−	8.94270i	−0.416503	−	0.416503i	−0.883996	+	0.467494i	$0.845157\pi$
$462$		0			0
$463$	1.64030	−	1.64030i	0.0762314	−	0.0762314i	−0.667963	−	0.744194i	$-0.732834\pi$
$463$	1.64030	−	1.64030i	0.0762314	−	0.0762314i	0.744194	+	0.667963i	$0.232834\pi$
$464$		−	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	$0.167417\pi$
$467$			21.6984i			1.00408i	−0.864844	+	0.502040i	$0.832583\pi$
$468$		0			0
$469$	14.5204			0.670488
$470$	14.6400	−	24.3203i	0.675295	−	1.12181i
$471$		0			0
$472$	2.36829			0.109009
$473$	26.3191	−	26.3191i	1.21015	−	1.21015i
$474$		0			0
$475$	25.9009	+	7.96479i	1.18841	+	0.365450i
$476$	−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	$-0.712312\pi$
$479$	3.65613	−	3.65613i	0.167053	−	0.167053i	0.785683	+	0.618630i	$0.212312\pi$
$480$		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	0.992650	+	0.121021i	$0.0386169\pi$
$487$	24.5766	+	24.5766i	1.11367	+	1.11367i	0.121021	+	0.992650i	$0.461383\pi$
$488$	−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	$-0.209208\pi$
$491$	35.0848			1.58336			0.791678	+	0.610939i	$0.209208\pi$
$492$		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	−0.535575	−	0.844488i	$-0.679905\pi$
$499$	6.90060	−	6.90060i	0.308913	−	0.308913i	0.844488	+	0.535575i	$0.179905\pi$
$500$	−0.612376	+	11.1636i	−0.0273863	+	0.499249i
$501$		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
$505$	19.5651	−	32.5019i	0.870637	−	1.44632i
$506$	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	$-0.376551\pi$
$509$	−12.3534	−	12.3534i	−0.547555	−	0.547555i	−0.925733	+	0.378178i	$0.876551\pi$
$510$		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
$515$	−17.6880	+	29.3837i	−0.779428	+	1.29480i
$516$		0			0
$517$	−61.4567			−2.70286
$518$	6.82056	+	6.82056i	0.299678	+	0.299678i
$519$		0			0
$520$	7.89745	+	1.62184i	0.346326	+	0.0711222i
$521$			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
$535$	2.82136	−	4.68689i	0.121978	−	0.202632i
$536$			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	0.997461	−	0.0712116i	$-0.0226866\pi$
$541$	21.5440	+	21.5440i	0.926250	+	0.926250i	−0.0712116	+	0.997461i	$0.522687\pi$
$542$	−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	−0.999116	−	0.0420278i	$-0.986618\pi$
$557$	−24.5719	−	24.5719i	−1.04114	−	1.04114i	−0.0420278	−	0.999116i	$-0.513382\pi$
$558$		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	$-0.967651\pi$
$563$		−	4.81449i		−	0.202907i	0.994840	−	0.101453i	$-0.0323493\pi$
$564$		0			0
$565$	−8.42171	+	13.9903i	−0.354304	+	0.588576i
$566$	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	$-0.178229\pi$
$569$	40.4223			1.69459			0.847295	+	0.531122i	$0.178229\pi$
$570$		0			0
$571$			33.1629i			1.38782i	0.720060	+	0.693911i	$0.244114\pi$
$571$			33.1629i			1.38782i	−0.720060	+	0.693911i	$0.755886\pi$
$572$	−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	$-0.299496\pi$
$577$	−5.26107	−	5.26107i	−0.219021	−	0.219021i	−0.808086	+	0.589065i	$0.799496\pi$
$578$	3.69026	−	3.69026i	0.153495	−	0.153495i
$579$		0			0
$580$	8.17796	−	13.5854i	0.339571	−	0.564102i
$581$			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	−0.559636	−	0.828739i	$-0.689059\pi$
$587$	6.51985	−	6.51985i	0.269103	−	0.269103i	0.828739	+	0.559636i	$0.189059\pi$
$588$		0			0
$589$		−	31.4165i		−	1.29450i
$590$	4.53704	+	2.73115i	0.186787	+	0.112440i
$591$		0			0
$592$	−3.72990	+	3.72990i	−0.153298	+	0.153298i
$593$	−17.8642	−	17.8642i	−0.733596	−	0.733596i	0.237734	−	0.971330i	$-0.423595\pi$
$593$	−17.8642	−	17.8642i	−0.733596	−	0.733596i	−0.971330	+	0.237734i	$0.923595\pi$
$594$		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
$605$	−23.8235	−	14.3410i	−0.968564	−	0.583044i
$606$		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	0.980631	+	0.195866i	$0.0627519\pi$
$613$	29.1287	+	29.1287i	1.17650	+	1.17650i	0.195866	+	0.980631i	$0.437248\pi$
$614$			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	−0.0537999	+	0.998552i	$0.517133\pi$
$617$	−26.1399	+	26.1399i	−1.05235	+	1.05235i	−0.998552	+	0.0537999i	$0.982867\pi$
$618$		0			0
$619$	−14.5983	−	14.5983i	−0.586756	−	0.586756i	0.349995	−	0.936751i	$-0.386183\pi$
$619$	−14.5983	−	14.5983i	−0.586756	−	0.586756i	−0.936751	+	0.349995i	$0.886183\pi$
$620$	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	0.717496	−	0.696563i	$-0.245288\pi$
$631$	0.525820	+	0.525820i	0.0209326	+	0.0209326i	−0.696563	+	0.717496i	$0.745288\pi$
$632$	5.86354	+	5.86354i	0.233239	+	0.233239i
$633$		0			0
$634$		−	3.88256i		−	0.154196i
$635$	11.2753	−	18.7307i	0.447447	−	0.743307i
$636$		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	$-0.350748\pi$
$641$	22.8822			0.903793			0.451896	+	0.892070i	$0.350748\pi$
$642$		0			0
$643$	16.3799	+	16.3799i	0.645961	+	0.645961i	0.952014	−	0.306053i	$-0.0990085\pi$
$643$	16.3799	+	16.3799i	0.645961	+	0.645961i	−0.306053	+	0.952014i	$0.599009\pi$
$644$	−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	$-0.741041\pi$
$647$		−	36.9703i		−	1.45345i	0.686927	−	0.726727i	$-0.258959\pi$
$648$		0			0
$649$		−	11.4650i		−	0.450039i
$650$	13.2592	+	12.2145i	0.520068	+	0.479092i
$651$		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
$655$	5.86583	+	3.53104i	0.229197	+	0.137969i
$656$	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	0.816451	−	0.577414i	$-0.195938\pi$
$661$	6.14563	+	6.14563i	0.239037	+	0.239037i	−0.577414	+	0.816451i	$0.695938\pi$
$662$		−	6.06739i		−	0.235816i
$663$		0			0
$664$	−3.50767			−0.136124
$665$	18.9856	+	11.4288i	0.736232	+	0.443188i
$666$		0			0
$667$	22.7331			0.880231
$668$	−7.14982	+	7.14982i	−0.276635	+	0.276635i
$669$		0			0
$670$	−9.15728	+	15.2122i	−0.353777	+	0.587700i
$671$	−39.9446	+	39.9446i	−1.54204	+	1.54204i
$672$		0			0
$673$	22.1797			0.854964			0.427482	−	0.904024i	$-0.359401\pi$
$673$	22.1797			0.854964			0.427482	+	0.904024i	$0.359401\pi$
$674$	−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	0.622713	−	0.782450i	$-0.286030\pi$
$683$	−4.17460	−	4.17460i	−0.159736	−	0.159736i	−0.782450	+	0.622713i	$0.786030\pi$
$684$		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	−0.454781	−	0.890604i	$-0.650282\pi$
$691$	11.4564	−	11.4564i	0.435823	−	0.435823i	0.890604	+	0.454781i	$0.150282\pi$
$692$	15.0993			0.573988
$693$		0			0
$694$	12.6154	−	12.6154i	0.478874	−	0.478874i
$695$	1.27084	−	2.11114i	0.0482056	−	0.0800800i
$696$		0			0
$697$	−20.8637	+	20.8637i	−0.790269	+	0.790269i
$698$	−27.1741			−1.02855
$699$		0			0
$700$	−2.68740	+	8.73921i	−0.101574	+	0.330311i
$701$	35.5224			1.34166			0.670831	−	0.741611i	$-0.265938\pi$
$701$	35.5224			1.34166			0.670831	+	0.741611i	$0.265938\pi$
$702$		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	0.643767	−	0.765222i	$-0.277371\pi$
$709$	−3.23400	−	3.23400i	−0.121455	−	0.121455i	−0.765222	+	0.643767i	$0.777371\pi$
$710$	4.98880	−	8.28749i	0.187226	−	0.311024i
$711$		0			0
$712$	4.76093			0.178423
$713$	13.1403	+	13.1403i	0.492108	+	0.492108i
$714$		0			0
$715$	7.85136	−	38.2318i	0.293624	−	1.42979i
$716$			16.4200i			0.613645i
$717$		0			0
$718$		−	36.8922i		−	1.37680i
$719$	−11.9941			−0.447304			−0.223652	−	0.974669i	$-0.571798\pi$
$719$	−11.9941			−0.447304			−0.223652	+	0.974669i	$0.571798\pi$
$720$		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	$-0.177621\pi$
$727$	45.7458			1.69662			0.848308	+	0.529503i	$0.177621\pi$
$728$	5.94800	+	2.84450i	0.220447	+	0.105424i
$729$		0			0
$730$	1.22924	+	0.739964i	0.0454963	+	0.0273873i
$731$		−	36.2417i		−	1.34045i
$732$		0			0
$733$	21.7680	+	21.7680i	0.804018	+	0.804018i	0.983721	−	0.179703i	$-0.0575136\pi$
$733$	21.7680	+	21.7680i	0.804018	+	0.804018i	−0.179703	+	0.983721i	$0.557514\pi$
$734$	−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	0.238627	−	0.971111i	$-0.423303\pi$
$739$	−19.9122	−	19.9122i	−0.732484	−	0.732484i	−0.971111	+	0.238627i	$0.923303\pi$
$740$	−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	−0.808361	−	0.588687i	$-0.799645\pi$
$743$	−5.98788	+	5.98788i	−0.219674	+	0.219674i	0.588687	+	0.808361i	$0.299645\pi$
$744$		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	$0.137270\pi$
$751$			22.9102i			0.836005i	−0.908446	+	0.418002i	$0.862730\pi$
$752$	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
$760$	−6.24995	+	10.3825i	−0.226710	+	0.376614i
$761$	−24.4534	+	24.4534i	−0.886434	+	0.886434i	−0.994179	−	0.107744i	$-0.965637\pi$
$761$	−24.4534	+	24.4534i	−0.886434	+	0.886434i	0.107744	+	0.994179i	$0.465637\pi$
$762$		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	−0.991112	−	0.133032i	$-0.957529\pi$
$769$	−23.7953	+	23.7953i	−0.858080	+	0.858080i	0.133032	+	0.991112i	$0.457529\pi$
$770$	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	−0.654693	−	0.755895i	$-0.727202\pi$
$773$	2.81372	−	2.81372i	0.101202	−	0.101202i	0.755895	+	0.654693i	$0.227202\pi$
$774$		0			0
$775$	27.7040	+	8.51928i	0.995159	+	0.306022i
$776$			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
$785$	−34.8100	−	20.9545i	−1.24242	−	0.747899i
$786$		0			0
$787$	37.4915	−	37.4915i	1.33643	−	1.33643i	0.436934	−	0.899493i	$-0.356064\pi$
$787$	37.4915	−	37.4915i	1.33643	−	1.33643i	0.899493	−	0.436934i	$-0.143936\pi$
$788$	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	$0.0999557\pi$
$797$			17.4404i			0.617770i	−0.951099	+	0.308885i	$0.900044\pi$
$798$		0			0
$799$	−42.3132	+	42.3132i	−1.49693	+	1.49693i
$800$	−4.77914	−	1.46963i	−0.168968	−	0.0519594i
$801$		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	−0.560969	−	0.827837i	$-0.689571\pi$
$811$	7.59986	−	7.59986i	0.266867	−	0.266867i	0.827837	+	0.560969i	$0.189571\pi$
$812$	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	$-0.238661\pi$
$821$	1.44315	+	1.44315i	0.0503664	+	0.0503664i	−0.681475	+	0.731841i	$0.738661\pi$
$822$		0			0
$823$	−41.1421			−1.43412			−0.717061	−	0.697010i	$-0.754513\pi$
$823$	−41.1421			−1.43412			−0.717061	+	0.697010i	$0.754513\pi$
$824$	−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	0.521844	−	0.853041i	$-0.325244\pi$
$827$	−9.52443	−	9.52443i	−0.331197	−	0.331197i	−0.853041	+	0.521844i	$0.825244\pi$
$828$		0			0
$829$			8.86204i			0.307792i	0.988087	+	0.153896i	$0.0491820\pi$
$829$			8.86204i			0.307792i	−0.988087	+	0.153896i	$0.950818\pi$
$830$	−6.71982	−	4.04512i	−0.233248	−	0.140408i
$831$		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	$-0.796086\pi$
$839$	−5.91015	+	5.91015i	−0.204041	+	0.204041i	0.597688	+	0.801729i	$0.296086\pi$
$840$		0			0
$841$	−21.2882			−0.734077
$842$			23.6160i			0.813862i
$843$		0			0
$844$			19.9602i			0.687058i
$845$	28.7974	−	3.96347i	0.990661	−	0.136347i
$846$		0			0
$847$	−16.0796	−	16.0796i	−0.552501	−	0.552501i
$848$	−6.86336			−0.235689
$849$		0			0
$850$	6.92739	−	22.5274i	0.237608	−	0.772682i
$851$	−11.9570	−	11.9570i	−0.409882	−	0.409882i
$852$		0			0
$853$	−1.70532	+	1.70532i	−0.0583891	+	0.0583891i	−0.735698	−	0.677309i	$-0.763146\pi$
$853$	−1.70532	+	1.70532i	−0.0583891	+	0.0583891i	0.677309	+	0.735698i	$0.263146\pi$
$854$		−	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	$0.208495\pi$
$857$			35.6660i			1.21833i	−0.793044	+	0.609164i	$0.791505\pi$
$858$		0			0
$859$	−40.5671			−1.38413			−0.692065	−	0.721835i	$-0.743299\pi$
$859$	−40.5671			−1.38413			−0.692065	+	0.721835i	$0.743299\pi$
$860$	−14.7294	−	8.86665i	−0.502269	−	0.302350i
$861$		0			0
$862$	−24.0434			−0.818920
$863$	−8.23230	+	8.23230i	−0.280231	+	0.280231i	−0.833201	−	0.552970i	$-0.813494\pi$
$863$	−8.23230	+	8.23230i	−0.280231	+	0.280231i	0.552970	+	0.833201i	$0.313494\pi$
$864$		0			0
$865$	28.9264	+	17.4128i	0.983526	+	0.592051i
$866$	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	$-0.439842\pi$
$877$	−23.5233	−	23.5233i	−0.794327	−	0.794327i	−0.982194	+	0.187868i	$0.939842\pi$
$878$	−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	$-0.667710\pi$
$881$	−29.8500			−1.00567			−0.502837	+	0.864381i	$0.667710\pi$
$882$		0			0
$883$	−23.1619			−0.779459			−0.389729	−	0.920929i	$-0.627431\pi$
$883$	−23.1619			−0.779459			−0.389729	+	0.920929i	$0.627431\pi$
$884$	−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
$890$	9.12074	+	5.49040i	0.305728	+	0.184039i
$891$		0			0
$892$	9.64691	−	9.64691i	0.323002	−	0.323002i
$893$	68.8011			2.30234
$894$		0			0
$895$	−18.9359	+	31.4566i	−0.632956	+	1.05148i
$896$	−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
$905$	−8.57747	−	5.16337i	−0.285125	−	0.171636i
$906$		0			0
$907$	−12.7144			−0.422174			−0.211087	−	0.977467i	$-0.567700\pi$
$907$	−12.7144			−0.422174			−0.211087	+	0.977467i	$0.567700\pi$
$908$	−9.61668	−	9.61668i	−0.319141	−	0.319141i
$909$		0			0
$910$	8.11453	+	12.3087i	0.268994	+	0.408029i
$911$		−	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
$925$	−25.2094	−	7.75215i	−0.828879	−	0.254889i
$926$			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	$-0.191244\pi$
$929$	7.91139	+	7.91139i	0.259564	+	0.259564i	−0.565313	+	0.824877i	$0.691244\pi$
$930$		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	$-0.446494\pi$
$941$	−25.1112	−	25.1112i	−0.818600	−	0.818600i	−0.985905	+	0.167305i	$0.946494\pi$
$942$		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	0.808249	−	0.588840i	$-0.200415\pi$
$947$	6.75196	+	6.75196i	0.219409	+	0.219409i	−0.588840	+	0.808249i	$0.700415\pi$
$948$		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	$-0.800595\pi$
$953$		−	36.1972i		−	1.17254i	0.810115	−	0.586271i	$-0.199405\pi$
$954$		0			0
$955$	20.2764	+	12.2057i	0.656128	+	0.394968i
$956$	−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	$-0.456011\pi$
$967$	−26.5164	−	26.5164i	−0.852709	−	0.852709i	−0.990466	+	0.137757i	$0.956011\pi$
$968$	8.79332	−	8.79332i	0.282628	−	0.282628i
$969$		0			0
$970$	−6.05962	+	10.0663i	−0.194563	+	0.323211i
$971$			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	−0.733818	−	0.679346i	$-0.762264\pi$
$977$	−1.70264	+	1.70264i	−0.0544722	+	0.0544722i	0.679346	+	0.733818i	$0.262264\pi$
$978$		0			0
$979$		−	23.0478i		−	0.736612i
$980$	4.21636	−	7.00429i	0.134687	−	0.223744i
$981$		0			0
$982$	−24.8087	+	24.8087i	−0.791678	+	0.791678i
$983$	11.2285	+	11.2285i	0.358134	+	0.358134i	0.863125	−	0.504991i	$-0.168504\pi$
$983$	11.2285	+	11.2285i	0.358134	+	0.358134i	−0.504991	+	0.863125i	$0.668504\pi$
$984$		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
$995$	39.7622	+	23.9356i	1.26055	+	0.758809i
$996$		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.c.629.1	yes	24
3.2	odd	2	inner	1170.2.q.c.629.9	yes	24
5.4	even	2		1170.2.q.d.629.12	yes	24
13.8	odd	4		1170.2.q.d.359.4	yes	24
15.14	odd	2		1170.2.q.d.629.4	yes	24
39.8	even	4		1170.2.q.d.359.12	yes	24
65.34	odd	4	inner	1170.2.q.c.359.9	yes	24
195.164	even	4	inner	1170.2.q.c.359.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1170.2.q.c.359.1	✓	24	195.164	even	4	inner
1170.2.q.c.359.9	yes	24	65.34	odd	4	inner
1170.2.q.c.629.1	yes	24	1.1	even	1	trivial
1170.2.q.c.629.9	yes	24	3.2	odd	2	inner
1170.2.q.d.359.4	yes	24	13.8	odd	4
1170.2.q.d.359.12	yes	24	39.8	even	4
1170.2.q.d.629.4	yes	24	15.14	odd	2
1170.2.q.d.629.12	yes	24	5.4	even	2

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)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(1.15322 - 1.91575i) q^{5} +(1.29303 - 1.29303i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.539189 + 2.17009i) q^{10} +(3.42313 - 3.42313i) q^{11} +(3.25273 + 1.55555i) q^{13} +1.82862i q^{14} -1.00000 q^{16} -4.71368i q^{17} +(-3.83222 + 3.83222i) q^{19} +(-1.91575 - 1.15322i) q^{20} +4.84104i q^{22} -3.20573i q^{23} +(-2.34017 - 4.41855i) q^{25} +(-3.39997 + 1.20009i) q^{26} +(-1.29303 - 1.29303i) q^{28} +7.09142i q^{29} +(-4.09901 + 4.09901i) q^{31} +(0.707107 - 0.707107i) q^{32} +(3.33308 + 3.33308i) q^{34} +(-0.985969 - 3.96825i) q^{35} +(3.72990 - 3.72990i) q^{37} -5.41957i q^{38} +(2.17009 - 0.539189i) q^{40} +(-4.42620 - 4.42620i) q^{41} +7.68861 q^{43} +(-3.42313 - 3.42313i) q^{44} +(2.26679 + 2.26679i) q^{46} +(-8.97668 - 8.97668i) q^{47} +3.65617i q^{49} +(4.77914 + 1.46963i) q^{50} +(1.55555 - 3.25273i) q^{52} +6.86336 q^{53} +(-2.61023 - 10.5055i) q^{55} +1.82862 q^{56} +(-5.01439 - 5.01439i) q^{58} +(1.67463 - 1.67463i) q^{59} -11.6690 q^{61} -5.79687i q^{62} +1.00000i q^{64} +(6.73115 - 4.43753i) q^{65} +(5.61487 + 5.61487i) q^{67} -4.71368 q^{68} +(3.50316 + 2.10879i) q^{70} +(-3.05893 - 3.05893i) q^{71} +(0.453716 - 0.453716i) q^{73} +5.27488i q^{74} +(3.83222 + 3.83222i) q^{76} -8.85239i q^{77} +8.29230 q^{79} +(-1.15322 + 1.91575i) q^{80} +6.25959 q^{82} +(-2.48030 + 2.48030i) q^{83} +(-9.03023 - 5.43591i) q^{85} +(-5.43667 + 5.43667i) q^{86} +4.84104 q^{88} +(3.36649 - 3.36649i) q^{89} +(6.21723 - 2.19451i) q^{91} -3.20573 q^{92} +12.6949 q^{94} +(2.92217 + 11.7609i) q^{95} +(3.71551 + 3.71551i) q^{97} +(-2.58530 - 2.58530i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{13} - 24 q^{16} - 48 q^{19} + 32 q^{25} - 8 q^{31} + 16 q^{34} - 32 q^{37} + 8 q^{40} + 80 q^{43} + 8 q^{46} - 12 q^{52} + 16 q^{55} - 24 q^{58} - 16 q^{61} - 8 q^{67} - 24 q^{70} + 48 q^{73}+ \cdots + 64 q^{97}+O(q^{100}) \) 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 - 24 * q^70 + 48 * q^73 + 48 * q^76 - 96 * q^79 - 72 * q^82 + 8 * 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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