LMFDB - Embedded newform 740.2.cc.a.653.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [740,2,Mod(17,740)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(740, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([0, 9, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("740.17"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	740.cc (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.90892974957$
Analytic rank:	$0$
Dimension:	$228$
Relative dimension:	$19$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			653.10
Character	$\chi$	$=$	740.653
Dual form			740.2.cc.a.17.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0586331 + 0.0410554i) q^{3} +(1.91470 - 1.15496i) q^{5} +(-0.252966 + 2.89142i) q^{7} +(-1.02431 - 2.81426i) q^{9} +(3.18039 + 1.83620i) q^{11} +(0.615664 + 0.224083i) q^{13} +(0.159682 + 0.0108894i) q^{15} +(1.54808 + 4.25330i) q^{17} +(1.52167 - 2.17318i) q^{19} +(-0.133540 + 0.159147i) q^{21} +(0.987994 + 1.71126i) q^{23} +(2.33212 - 4.42281i) q^{25} +(0.111059 - 0.414479i) q^{27} +(-1.86162 - 6.94765i) q^{29} +(3.49362 + 3.49362i) q^{31} +(0.111090 + 0.238234i) q^{33} +(2.85513 + 5.82835i) q^{35} +(5.78774 - 1.87138i) q^{37} +(0.0268985 + 0.0384150i) q^{39} +(-2.44928 + 6.72933i) q^{41} -0.409897 q^{43} +(-5.21161 - 4.20542i) q^{45} +(0.396579 + 0.106263i) q^{47} +(-1.40264 - 0.247324i) q^{49} +(-0.0838524 + 0.312941i) q^{51} +(-0.141808 - 1.62087i) q^{53} +(8.21021 - 0.157473i) q^{55} +(0.178441 - 0.0649472i) q^{57} +(0.0782094 + 0.893937i) q^{59} +(-2.56682 - 5.50455i) q^{61} +(8.39632 - 2.24979i) q^{63} +(1.43762 - 0.282018i) q^{65} +(3.82527 + 0.334667i) q^{67} +(-0.0123270 + 0.140899i) q^{69} +(-1.24540 - 7.06302i) q^{71} +(-2.25715 + 2.25715i) q^{73} +(0.318319 - 0.163577i) q^{75} +(-6.11374 + 8.73133i) q^{77} +(4.33677 + 0.379418i) q^{79} +(-6.85910 + 5.75547i) q^{81} +(-0.740270 - 0.345193i) q^{83} +(7.87651 + 6.35581i) q^{85} +(0.176086 - 0.483792i) q^{87} +(3.98791 - 0.348897i) q^{89} +(-0.803661 + 1.72346i) q^{91} +(0.0614101 + 0.348274i) q^{93} +(0.403603 - 5.91845i) q^{95} +(-1.88605 + 1.08891i) q^{97} +(1.90985 - 10.8313i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 228 q + 6 q^{3} - 12 q^{25} + 12 q^{27} - 36 q^{31} + 6 q^{33} + 24 q^{35} + 24 q^{37} - 72 q^{39} - 54 q^{41} - 12 q^{45} + 36 q^{49} - 6 q^{53} - 72 q^{57} - 36 q^{61} + 18 q^{65} + 42 q^{67} + 96 q^{69}+ \cdots + 72 q^{97}+O(q^{100}) $ 228 * q + 6 * q^3 - 12 * q^25 + 12 * q^27 - 36 * q^31 + 6 * q^33 + 24 * q^35 + 24 * q^37 - 72 * q^39 - 54 * q^41 - 12 * q^45 + 36 * q^49 - 6 * q^53 - 72 * q^57 - 36 * q^61 + 18 * q^65 + 42 * q^67 + 96 * q^69 - 48 * q^71 - 6 * q^73 - 96 * q^75 - 114 * q^77 + 48 * q^79 - 36 * q^81 - 12 * q^83 + 72 * q^87 - 12 * q^89 + 24 * q^91 - 6 * q^93 + 90 * q^95 + 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.0586331	+	0.0410554i	0.0338519	+	0.0237033i	0.590380	−	0.807125i	$-0.298978\pi$
$3$	0.0586331	+	0.0410554i	0.0338519	+	0.0237033i	−0.556528	+	0.830829i	$0.687867\pi$
$4$		0			0
$5$	1.91470	−	1.15496i	0.856278	−	0.516515i
$5$	1.91470	−	1.15496i	0.856278	−	0.516515i
$6$		0			0
$7$	−0.252966	+	2.89142i	−0.0956122	+	1.09285i	0.785154	+	0.619301i	$0.212584\pi$
$7$	−0.252966	+	2.89142i	−0.0956122	+	1.09285i	−0.880766	+	0.473552i	$0.842972\pi$
$8$		0			0
$9$	−1.02431	−	2.81426i	−0.341436	−	0.938088i
$10$		0			0
$11$	3.18039	+	1.83620i	0.958923	+	0.553634i	0.895841	−	0.444374i	$-0.146574\pi$
$11$	3.18039	+	1.83620i	0.958923	+	0.553634i	0.0630814	+	0.998008i	$0.479907\pi$
$12$		0			0
$13$	0.615664	+	0.224083i	0.170755	+	0.0621496i	0.425983	−	0.904731i	$-0.359928\pi$
$13$	0.615664	+	0.224083i	0.170755	+	0.0621496i	−0.255228	+	0.966881i	$0.582151\pi$
$14$		0			0
$15$	0.159682	+	0.0108894i	0.0412297	+	0.00281163i
$16$		0			0
$17$	1.54808	+	4.25330i	0.375464	+	1.03158i	0.973215	+	0.229896i	$0.0738387\pi$
$17$	1.54808	+	4.25330i	0.375464	+	1.03158i	−0.597752	+	0.801681i	$0.703939\pi$
$18$		0			0
$19$	1.52167	−	2.17318i	0.349096	−	0.498561i	−0.605753	−	0.795653i	$-0.707128\pi$
$19$	1.52167	−	2.17318i	0.349096	−	0.498561i	0.954849	+	0.297092i	$0.0960169\pi$
$20$		0			0
$21$	−0.133540	+	0.159147i	−0.0291409	+	0.0347288i
$22$		0			0
$23$	0.987994	+	1.71126i	0.206011	+	0.356821i	0.950454	−	0.310864i	$-0.100618\pi$
$23$	0.987994	+	1.71126i	0.206011	+	0.356821i	−0.744443	+	0.667686i	$0.767285\pi$
$24$		0			0
$25$	2.33212	−	4.42281i	0.466424	−	0.884562i
$26$		0			0
$27$	0.111059	−	0.414479i	0.0213734	−	0.0797665i
$28$		0			0
$29$	−1.86162	−	6.94765i	−0.345693	−	1.29015i	−0.891800	−	0.452430i	$-0.850557\pi$
$29$	−1.86162	−	6.94765i	−0.345693	−	1.29015i	0.546107	−	0.837716i	$-0.316109\pi$
$30$		0			0
$31$	3.49362	+	3.49362i	0.627473	+	0.627473i	0.947432	−	0.319958i	$-0.103669\pi$
$31$	3.49362	+	3.49362i	0.627473	+	0.627473i	−0.319958	+	0.947432i	$0.603669\pi$
$32$		0			0
$33$	0.111090	+	0.238234i	0.0193383	+	0.0414712i
$34$		0			0
$35$	2.85513	+	5.82835i	0.482605	+	0.985171i
$36$		0			0
$37$	5.78774	−	1.87138i	0.951499	−	0.307653i
$37$	5.78774	−	1.87138i	0.951499	−	0.307653i
$38$		0			0
$39$	0.0268985	+	0.0384150i	0.00430721	+	0.00615133i
$40$		0			0
$41$	−2.44928	+	6.72933i	−0.382513	+	1.05095i	0.587782	+	0.809019i	$0.300001\pi$
$41$	−2.44928	+	6.72933i	−0.382513	+	1.05095i	−0.970295	+	0.241926i	$0.922221\pi$
$42$		0			0
$43$	−0.409897			−0.0625087			−0.0312543	−	0.999511i	$-0.509950\pi$
$43$	−0.409897			−0.0625087			−0.0312543	+	0.999511i	$0.509950\pi$
$44$		0			0
$45$	−5.21161	−	4.20542i	−0.776901	−	0.626907i
$46$		0			0
$47$	0.396579	+	0.106263i	0.0578470	+	0.0155001i	0.287626	−	0.957743i	$-0.407134\pi$
$47$	0.396579	+	0.106263i	0.0578470	+	0.0155001i	−0.229779	+	0.973243i	$0.573801\pi$
$48$		0			0
$49$	−1.40264	−	0.247324i	−0.200378	−	0.0353320i
$50$		0			0
$51$	−0.0838524	+	0.312941i	−0.0117417	+	0.0438206i
$52$		0			0
$53$	−0.141808	−	1.62087i	−0.0194788	−	0.222644i	−0.999695	−	0.0247122i	$-0.992133\pi$
$53$	−0.141808	−	1.62087i	−0.0194788	−	0.222644i	0.980216	−	0.197932i	$-0.0634225\pi$
$54$		0			0
$55$	8.21021	−	0.157473i	1.10706	−	0.0212336i
$56$		0			0
$57$	0.178441	−	0.0649472i	0.0236351	−	0.00860247i
$58$		0			0
$59$	0.0782094	+	0.893937i	0.0101820	+	0.116381i	0.999585	−	0.0288166i	$-0.00917387\pi$
$59$	0.0782094	+	0.893937i	0.0101820	+	0.116381i	−0.989403	+	0.145197i	$0.953618\pi$
$60$		0			0
$61$	−2.56682	−	5.50455i	−0.328647	−	0.704786i	0.670669	−	0.741757i	$-0.266007\pi$
$61$	−2.56682	−	5.50455i	−0.328647	−	0.704786i	−0.999316	+	0.0369705i	$0.988229\pi$
$62$		0			0
$63$	8.39632	−	2.24979i	1.05784	−	0.283447i
$64$		0			0
$65$	1.43762	−	0.282018i	0.178315	−	0.0349801i
$66$		0			0
$67$	3.82527	+	0.334667i	0.467331	+	0.0408861i	0.318390	−	0.947960i	$-0.396858\pi$
$67$	3.82527	+	0.334667i	0.467331	+	0.0408861i	0.148941	+	0.988846i	$0.452414\pi$
$68$		0			0
$69$	−0.0123270	+	0.140899i	−0.00148400	+	0.0169622i
$70$		0			0
$71$	−1.24540	−	7.06302i	−0.147802	−	0.838226i	−0.965075	−	0.261975i	$-0.915626\pi$
$71$	−1.24540	−	7.06302i	−0.147802	−	0.838226i	0.817273	−	0.576251i	$-0.195485\pi$
$72$		0			0
$73$	−2.25715	+	2.25715i	−0.264180	+	0.264180i	−0.826750	−	0.562570i	$-0.809813\pi$
$73$	−2.25715	+	2.25715i	−0.264180	+	0.264180i	0.562570	+	0.826750i	$0.309813\pi$
$74$		0			0
$75$	0.318319	−	0.163577i	0.0367564	−	0.0188883i
$76$		0			0
$77$	−6.11374	+	8.73133i	−0.696725	+	0.995027i
$78$		0			0
$79$	4.33677	+	0.379418i	0.487924	+	0.0426878i	0.328464	−	0.944517i	$-0.393469\pi$
$79$	4.33677	+	0.379418i	0.487924	+	0.0426878i	0.159460	+	0.987204i	$0.449025\pi$
$80$		0			0
$81$	−6.85910	+	5.75547i	−0.762122	+	0.639496i
$82$		0			0
$83$	−0.740270	−	0.345193i	−0.0812551	−	0.0378899i	0.381566	−	0.924342i	$-0.375385\pi$
$83$	−0.740270	−	0.345193i	−0.0812551	−	0.0378899i	−0.462821	+	0.886452i	$0.653163\pi$
$84$		0			0
$85$	7.87651	+	6.35581i	0.854327	+	0.689384i
$86$		0			0
$87$	0.176086	−	0.483792i	0.0188784	−	0.0518679i
$88$		0			0
$89$	3.98791	−	0.348897i	0.422717	−	0.0369830i	0.126187	−	0.992006i	$-0.459726\pi$
$89$	3.98791	−	0.348897i	0.422717	−	0.0369830i	0.296530	+	0.955023i	$0.404170\pi$
$90$		0			0
$91$	−0.803661	+	1.72346i	−0.0842465	+	0.180667i
$92$		0			0
$93$	0.0614101	+	0.348274i	0.00636793	+	0.0361143i
$94$		0			0
$95$	0.403603	−	5.91845i	0.0414088	−	0.607220i
$96$		0			0
$97$	−1.88605	+	1.08891i	−0.191499	+	0.110562i	−0.592684	−	0.805435i	$-0.701932\pi$
$97$	−1.88605	+	1.08891i	−0.191499	+	0.110562i	0.401185	+	0.915997i	$0.368598\pi$
$98$		0			0
$99$	1.90985	−	10.8313i	0.191947	−	1.08858i
$100$		0			0
$101$	−9.67703	+	5.58704i	−0.962901	+	0.555931i	−0.897065	−	0.441899i	$-0.854305\pi$
$101$	−9.67703	+	5.58704i	−0.962901	+	0.555931i	−0.0658361	+	0.997830i	$0.520971\pi$
$102$		0			0
$103$	11.4447	+	6.60760i	1.12768	+	0.651067i	0.943351	−	0.331798i	$-0.107655\pi$
$103$	11.4447	+	6.60760i	1.12768	+	0.651067i	0.184330	+	0.982864i	$0.440989\pi$
$104$		0			0
$105$	−0.0718799	+	0.458953i	−0.00701476	+	0.0447892i
$106$		0			0
$107$	6.96265	−	3.24674i	0.673105	−	0.313874i	−0.0558465	−	0.998439i	$-0.517786\pi$
$107$	6.96265	−	3.24674i	0.673105	−	0.313874i	0.728951	+	0.684565i	$0.240008\pi$
$108$		0			0
$109$	−11.6738	+	8.17412i	−1.11815	+	0.782938i	−0.978292	−	0.207233i	$-0.933554\pi$
$109$	−11.6738	+	8.17412i	−1.11815	+	0.782938i	−0.139860	+	0.990171i	$0.544665\pi$
$110$		0			0
$111$	0.416184	+	0.127893i	0.0395024	+	0.0121391i
$112$		0			0
$113$	−13.4908	−	2.37879i	−1.26911	−	0.223777i	−0.501757	−	0.865008i	$-0.667313\pi$
$113$	−13.4908	−	2.37879i	−1.26911	−	0.223777i	−0.767348	+	0.641231i	$0.778424\pi$
$114$		0			0
$115$	3.86815	+	2.13544i	0.360706	+	0.199130i
$116$		0			0
$117$		−	1.96217i		−	0.181403i
$118$		0			0
$119$	−12.6897	+	3.40019i	−1.16326	+	0.311695i
$120$		0			0
$121$	1.24324	+	2.15336i	0.113022	+	0.195760i
$122$		0			0
$123$	−0.419884	+	0.294006i	−0.0378597	+	0.0265096i
$124$		0			0
$125$	−0.642887	−	11.1618i	−0.0575015	−	0.998345i
$126$		0			0
$127$	−18.3599	+	1.60628i	−1.62918	+	0.142534i	−0.864759	−	0.502187i	$-0.832529\pi$
$127$	−18.3599	+	1.60628i	−1.62918	+	0.142534i	−0.764417	+	0.644722i	$0.776973\pi$
$128$		0			0
$129$	−0.0240335	−	0.0168285i	−0.00211603	−	0.00148166i
$130$		0			0
$131$	−13.8544	−	6.46042i	−1.21047	−	0.564450i	−0.290661	−	0.956826i	$-0.593875\pi$
$131$	−13.8544	−	6.46042i	−1.21047	−	0.564450i	−0.919805	+	0.392376i	$0.871653\pi$
$132$		0			0
$133$	5.89862	+	4.94953i	0.511476	+	0.429179i
$134$		0			0
$135$	−0.266064	−	0.921871i	−0.0228991	−	0.0793420i
$136$		0			0
$137$	0.685445	+	2.55811i	0.0585615	+	0.218555i	0.989005	−	0.147880i	$-0.0472450\pi$
$137$	0.685445	+	2.55811i	0.0585615	+	0.218555i	−0.930444	+	0.366435i	$0.880578\pi$
$138$		0			0
$139$	−16.4097	+	5.97265i	−1.39185	+	0.506593i	−0.925750	−	0.378136i	$-0.876565\pi$
$139$	−16.4097	+	5.97265i	−1.39185	+	0.506593i	−0.466104	+	0.884730i	$0.654343\pi$
$140$		0			0
$141$	0.0188900	+	0.0225122i	0.00159082	+	0.00189587i
$142$		0			0
$143$	1.54659	+	1.84315i	0.129332	+	0.154132i
$144$		0			0
$145$	−11.5887	−	11.1525i	−0.962390	−	0.926167i
$146$		0			0
$147$	−0.0720874	−	0.0720874i	−0.00594567	−	0.00594567i
$148$		0			0
$149$		−	18.5053i		−	1.51601i	−0.652248	−	0.758006i	$-0.726174\pi$
$149$		−	18.5053i		−	1.51601i	0.652248	−	0.758006i	$-0.273826\pi$
$150$		0			0
$151$	−11.2424	+	1.98234i	−0.914894	+	0.161321i	−0.611225	−	0.791457i	$-0.709323\pi$
$151$	−11.2424	+	1.98234i	−0.914894	+	0.161321i	−0.303669	+	0.952777i	$0.598212\pi$
$152$		0			0
$153$	10.3842	−	8.71339i	0.839514	−	0.704436i
$154$		0			0
$155$	10.7242	+	2.65422i	0.861391	+	0.213192i
$156$		0			0
$157$	−0.184904	+	0.396528i	−0.0147569	+	0.0316463i	−0.913548	−	0.406731i	$-0.866669\pi$
$157$	−0.184904	+	0.396528i	−0.0147569	+	0.0316463i	0.898791	+	0.438377i	$0.144447\pi$
$158$		0			0
$159$	0.0582309	−	0.100859i	0.00461801	−	0.00799863i
$160$		0			0
$161$	−5.19788	+	2.42381i	−0.409651	+	0.191023i
$162$		0			0
$163$	3.29387	−	3.92548i	0.257996	−	0.307468i	−0.621462	−	0.783444i	$-0.713461\pi$
$163$	3.29387	−	3.92548i	0.257996	−	0.307468i	0.879458	+	0.475977i	$0.157905\pi$
$164$		0			0
$165$	0.487856	+	0.327840i	0.0379795	+	0.0255223i
$166$		0			0
$167$	−17.1061	+	3.01627i	−1.32371	+	0.233406i	−0.790441	−	0.612538i	$-0.790149\pi$
$167$	−17.1061	+	3.01627i	−1.32371	+	0.233406i	−0.533272	+	0.845944i	$0.679038\pi$
$168$		0			0
$169$	−9.62975	−	8.08032i	−0.740750	−	0.621563i
$170$		0			0
$171$	−7.67455	−	2.05639i	−0.586888	−	0.157256i
$172$		0			0
$173$	−14.1109	−	20.1525i	−1.07283	−	1.53217i	−0.826463	−	0.562991i	$-0.809650\pi$
$173$	−14.1109	−	20.1525i	−1.07283	−	1.53217i	−0.246372	−	0.969175i	$-0.579238\pi$
$174$		0			0
$175$	12.1982	+	7.86194i	0.922100	+	0.594307i
$176$		0			0
$177$	−0.0321153	+	0.0556252i	−0.00241393	+	0.00418105i
$178$		0			0
$179$	−1.80862	+	1.80862i	−0.135183	+	0.135183i	−0.771460	−	0.636277i	$-0.780473\pi$
$179$	−1.80862	+	1.80862i	−0.135183	+	0.135183i	0.636277	+	0.771460i	$0.280473\pi$
$180$		0			0
$181$	6.00793	+	2.18671i	0.446566	+	0.162537i	0.555507	−	0.831512i	$-0.312524\pi$
$181$	6.00793	+	2.18671i	0.446566	+	0.162537i	−0.108942	+	0.994048i	$0.534746\pi$
$182$		0			0
$183$	0.0754910	−	0.428131i	0.00558046	−	0.0316483i
$184$		0			0
$185$	8.92039	−	10.2678i	0.655840	−	0.754900i
$186$		0			0
$187$	−2.88642	+	16.3697i	−0.211076	+	1.19707i
$188$		0			0
$189$	1.17034	+	0.425968i	0.0851295	+	0.0309846i
$190$		0			0
$191$	9.17431	−	9.17431i	0.663830	−	0.663830i	−0.292451	−	0.956281i	$-0.594471\pi$
$191$	9.17431	−	9.17431i	0.663830	−	0.663830i	0.956281	+	0.292451i	$0.0944707\pi$
$192$		0			0
$193$	−5.82815	+	10.0946i	−0.419519	+	0.726629i	−0.995891	−	0.0905588i	$-0.971135\pi$
$193$	−5.82815	+	10.0946i	−0.419519	+	0.726629i	0.576372	+	0.817188i	$0.304468\pi$
$194$		0			0
$195$	0.0958704	+	0.0424863i	0.00686542	+	0.00304251i
$196$		0			0
$197$	6.43257	+	9.18666i	0.458301	+	0.654522i	0.980090	−	0.198552i	$-0.0636240\pi$
$197$	6.43257	+	9.18666i	0.458301	+	0.654522i	−0.521789	+	0.853075i	$0.674735\pi$
$198$		0			0
$199$	−19.2377	−	5.15473i	−1.36372	−	0.365409i	−0.498542	−	0.866866i	$-0.666131\pi$
$199$	−19.2377	−	5.15473i	−1.36372	−	0.365409i	−0.865183	+	0.501457i	$0.832798\pi$
$200$		0			0
$201$	0.210547	+	0.176670i	0.0148509	+	0.0124614i
$202$		0			0
$203$	20.5595	−	3.62519i	1.44299	−	0.254438i
$204$		0			0
$205$	3.08252	+	15.7135i	0.215292	+	1.09748i
$206$		0			0
$207$	3.80391	−	4.53333i	0.264390	−	0.315088i
$208$		0			0
$209$	8.82989	−	4.11745i	0.610776	−	0.284810i
$210$		0			0
$211$	−1.42032	+	2.46006i	−0.0977786	+	0.169358i	−0.910765	−	0.412925i	$-0.864507\pi$
$211$	−1.42032	+	2.46006i	−0.0977786	+	0.169358i	0.812986	+	0.582283i	$0.197840\pi$
$212$		0			0
$213$	0.216953	−	0.465257i	0.0148654	−	0.0318789i
$214$		0			0
$215$	−0.784827	+	0.473416i	−0.0535248	+	0.0322867i
$216$		0			0
$217$	−10.9853	+	9.21775i	−0.745730	+	0.625742i
$218$		0			0
$219$	−0.225012	+	0.0396757i	−0.0152049	+	0.00268103i
$220$		0			0
$221$			2.96551i			0.199481i
$222$		0			0
$223$	10.6310	+	10.6310i	0.711907	+	0.711907i	0.966934	−	0.255027i	$-0.0820843\pi$
$223$	10.6310	+	10.6310i	0.711907	+	0.711907i	−0.255027	+	0.966934i	$0.582084\pi$
$224$		0			0
$225$	−14.8358	−	2.03288i	−0.989050	−	0.135525i
$226$		0			0
$227$	15.0951	+	17.9896i	1.00190	+	1.19401i	0.980956	+	0.194232i	$0.0622214\pi$
$227$	15.0951	+	17.9896i	1.00190	+	1.19401i	0.0209398	+	0.999781i	$0.493334\pi$
$228$		0			0
$229$	−10.3867	−	12.3784i	−0.686371	−	0.817985i	0.304541	−	0.952499i	$-0.401497\pi$
$229$	−10.3867	−	12.3784i	−0.686371	−	0.817985i	−0.990912	+	0.134515i	$0.957053\pi$
$230$		0			0
$231$	−0.716936	+	0.260943i	−0.0471709	+	0.0171688i
$232$		0			0
$233$	−0.540943	−	2.01883i	−0.0354384	−	0.132258i	0.945940	−	0.324341i	$-0.105142\pi$
$233$	−0.540943	−	2.01883i	−0.0354384	−	0.132258i	−0.981379	+	0.192083i	$0.938476\pi$
$234$		0			0
$235$	0.882058	−	0.254573i	0.0575391	−	0.0166065i
$236$		0			0
$237$	0.238701	+	0.200294i	0.0155053	+	0.0130105i
$238$		0			0
$239$	0.981773	+	0.457808i	0.0635056	+	0.0296132i	0.454112	−	0.890945i	$-0.349957\pi$
$239$	0.981773	+	0.457808i	0.0635056	+	0.0296132i	−0.390606	+	0.920558i	$0.627735\pi$
$240$		0			0
$241$	3.80575	+	2.66481i	0.245150	+	0.171656i	0.689693	−	0.724102i	$-0.257745\pi$
$241$	3.80575	+	2.66481i	0.245150	+	0.171656i	−0.444544	+	0.895757i	$0.646634\pi$
$242$		0			0
$243$	−1.92087	+	0.168054i	−0.123224	+	0.0107807i
$244$		0			0
$245$	−2.97128	+	1.14645i	−0.189828	+	0.0732441i
$246$		0			0
$247$	1.42381	−	0.996964i	0.0905950	−	0.0634353i
$248$		0			0
$249$	−0.0292323	−	0.0506318i	−0.00185252	−	0.00320866i
$250$		0			0
$251$	10.8225	−	2.89988i	0.683110	−	0.183039i	0.0994568	−	0.995042i	$-0.468289\pi$
$251$	10.8225	−	2.89988i	0.683110	−	0.183039i	0.583653	+	0.812003i	$0.301623\pi$
$252$		0			0
$253$			7.25661i			0.456219i
$254$		0			0
$255$	0.200884	+	0.696034i	0.0125799	+	0.0435873i
$256$		0			0
$257$	−21.9531	−	3.87093i	−1.36940	−	0.241462i	−0.559888	−	0.828568i	$-0.689156\pi$
$257$	−21.9531	−	3.87093i	−1.36940	−	0.241462i	−0.809510	+	0.587106i	$0.800267\pi$
$258$		0			0
$259$	3.94683	+	17.2082i	0.245244	+	1.06926i
$260$		0			0
$261$	−17.6456	+	12.3556i	−1.09224	+	0.764793i
$262$		0			0
$263$	−14.9554	+	6.97382i	−0.922190	+	0.430024i	−0.824930	−	0.565235i	$-0.808786\pi$
$263$	−14.9554	+	6.97382i	−0.922190	+	0.430024i	−0.0972600	+	0.995259i	$0.531008\pi$
$264$		0			0
$265$	−2.14357	−	2.93970i	−0.131678	−	0.180584i
$266$		0			0
$267$	0.248148	+	0.143268i	0.0151864	+	0.00876786i
$268$		0			0
$269$	8.49231	−	4.90303i	0.517785	−	0.298943i	−0.218243	−	0.975894i	$-0.570033\pi$
$269$	8.49231	−	4.90303i	0.517785	−	0.298943i	0.736028	+	0.676951i	$0.236699\pi$
$270$		0			0
$271$	−0.432338	+	2.45191i	−0.0262627	+	0.148943i	−0.995119	−	0.0986795i	$-0.968538\pi$
$271$	−0.432338	+	2.45191i	−0.0262627	+	0.148943i	0.968857	+	0.247622i	$0.0796493\pi$
$272$		0			0
$273$	−0.117878	+	0.0680571i	−0.00713432	+	0.00411900i
$274$		0			0
$275$	15.5382	−	9.78401i	0.936988	−	0.589998i
$276$		0			0
$277$	2.38285	+	13.5138i	0.143172	+	0.811967i	0.968817	+	0.247777i	$0.0797002\pi$
$277$	2.38285	+	13.5138i	0.143172	+	0.811967i	−0.825645	+	0.564190i	$0.809189\pi$
$278$		0			0
$279$	6.25343	−	13.4105i	0.374383	−	0.802867i
$280$		0			0
$281$	19.4107	−	1.69821i	1.15794	−	0.101307i	0.508047	−	0.861329i	$-0.330368\pi$
$281$	19.4107	−	1.69821i	1.15794	−	0.101307i	0.649897	+	0.760022i	$0.274812\pi$
$282$		0			0
$283$	−7.71458	+	21.1956i	−0.458584	+	1.25995i	0.467955	+	0.883752i	$0.344991\pi$
$283$	−7.71458	+	21.1956i	−0.458584	+	1.25995i	−0.926540	+	0.376197i	$0.877231\pi$
$284$		0			0
$285$	0.266649	−	0.330447i	0.0157949	−	0.0195740i
$286$		0			0
$287$	−18.8377	−	8.78418i	−1.11196	−	0.518513i
$288$		0			0
$289$	−2.67130	+	2.24149i	−0.157135	+	0.131852i
$290$		0			0
$291$	−0.155290	−	0.0135862i	−0.00910329	−	0.000796434i
$292$		0			0
$293$	11.1116	−	15.8689i	0.649144	−	0.927073i	−0.350812	−	0.936446i	$-0.614094\pi$
$293$	11.1116	−	15.8689i	0.649144	−	0.927073i	0.999956	+	0.00937240i	$0.00298337\pi$
$294$		0			0
$295$	1.18221	+	1.62129i	0.0688310	+	0.0943950i
$296$		0			0
$297$	1.11428	−	1.11428i	0.0646569	−	0.0646569i
$298$		0			0
$299$	0.224808	+	1.27495i	0.0130010	+	0.0737324i
$300$		0			0
$301$	0.103690	−	1.18518i	0.00597659	−	0.0683128i
$302$		0			0
$303$	−0.796773	−	0.0697086i	−0.0457734	−	0.00400465i
$304$		0			0
$305$	−11.2722	−	7.57497i	−0.645446	−	0.433741i
$306$		0			0
$307$	27.0123	−	7.23791i	1.54167	−	0.413089i	0.614866	−	0.788632i	$-0.289210\pi$
$307$	27.0123	−	7.23791i	1.54167	−	0.413089i	0.926805	+	0.375542i	$0.122544\pi$
$308$		0			0
$309$	0.399761	+	0.857291i	0.0227416	+	0.0487696i
$310$		0			0
$311$	−2.30598	−	26.3575i	−0.130760	−	1.49460i	−0.724128	−	0.689666i	$-0.757757\pi$
$311$	−2.30598	−	26.3575i	−0.130760	−	1.49460i	0.593367	−	0.804932i	$-0.297798\pi$
$312$		0			0
$313$	18.2704	−	6.64989i	1.03271	−	0.375874i	0.230595	−	0.973050i	$-0.425933\pi$
$313$	18.2704	−	6.64989i	1.03271	−	0.375874i	0.802111	+	0.597175i	$0.203710\pi$
$314$		0			0
$315$	13.4780	−	14.0051i	0.759398	−	0.789098i
$316$		0			0
$317$	−0.994146	−	11.3631i	−0.0558368	−	0.638218i	−0.971620	−	0.236546i	$-0.923985\pi$
$317$	−0.994146	−	11.3631i	−0.0558368	−	0.638218i	0.915784	−	0.401672i	$-0.131571\pi$
$318$		0			0
$319$	6.83659	−	25.5145i	0.382775	−	1.42854i
$320$		0			0
$321$	0.541538	+	0.0954878i	0.0302257	+	0.00532961i
$322$		0			0
$323$	11.5988	+	3.10790i	0.645377	+	0.172928i
$324$		0			0
$325$	2.42688	−	2.20038i	0.134619	−	0.122055i
$326$		0			0
$327$	−1.02007			−0.0564098
$328$		0			0
$329$	−0.407572	+	1.11979i	−0.0224702	+	0.0617362i
$330$		0			0
$331$	7.65788	+	10.9366i	0.420915	+	0.601129i	0.972475	−	0.233006i	$-0.0748562\pi$
$331$	7.65788	+	10.9366i	0.420915	+	0.601129i	−0.551560	+	0.834135i	$0.685967\pi$
$332$		0			0
$333$	−11.1950	−	14.3714i	−0.613481	−	0.787546i
$334$		0			0
$335$	7.71075	−	3.77726i	0.421283	−	0.206374i
$336$		0			0
$337$	−12.7538	−	27.3505i	−0.694742	−	1.48988i	−0.863568	−	0.504233i	$-0.831775\pi$
$337$	−12.7538	−	27.3505i	−0.694742	−	1.48988i	0.168826	−	0.985646i	$-0.446002\pi$
$338$		0			0
$339$	−0.693344	−	0.693344i	−0.0376573	−	0.0376573i
$340$		0			0
$341$	4.69609	+	17.5260i	0.254308	+	0.949089i
$342$		0			0
$343$	−4.18855	+	15.6319i	−0.226160	+	0.844042i
$344$		0			0
$345$	0.139130	+	0.284016i	0.00749053	+	0.0152909i
$346$		0			0
$347$	13.2363	+	22.9259i	0.710560	+	1.23073i	0.964647	+	0.263545i	$0.0848917\pi$
$347$	13.2363	+	22.9259i	0.710560	+	1.23073i	−0.254087	+	0.967181i	$0.581775\pi$
$348$		0			0
$349$	18.4695	−	22.0111i	0.988648	−	1.17823i	0.00466045	−	0.999989i	$-0.498517\pi$
$349$	18.4695	−	22.0111i	0.988648	−	1.17823i	0.983988	−	0.178236i	$-0.0570390\pi$
$350$		0			0
$351$	0.161253	−	0.230293i	0.00860706	−	0.0122922i
$352$		0			0
$353$	2.58163	+	7.09296i	0.137406	+	0.377520i	0.989242	−	0.146289i	$-0.0467328\pi$
$353$	2.58163	+	7.09296i	0.137406	+	0.377520i	−0.851836	+	0.523809i	$0.824511\pi$
$354$		0			0
$355$	−10.5421	−	12.0851i	−0.559516	−	0.641412i
$356$		0			0
$357$	−0.883632	−	0.321616i	−0.0467668	−	0.0170217i
$358$		0			0
$359$	−25.0776	−	14.4786i	−1.32354	−	0.764149i	−0.339252	−	0.940695i	$-0.610174\pi$
$359$	−25.0776	−	14.4786i	−1.32354	−	0.764149i	−0.984292	+	0.176547i	$0.943507\pi$
$360$		0			0
$361$	4.09118	+	11.2404i	0.215325	+	0.591602i
$362$		0			0
$363$	−0.0155117	+	0.177300i	−0.000814154	+	0.00930582i
$364$		0			0
$365$	−1.71483	+	6.92868i	−0.0897583	+	0.362664i
$366$		0			0
$367$	21.5483	+	15.0883i	1.12481	+	0.787603i	0.979432	−	0.201773i	$-0.0646704\pi$
$367$	21.5483	+	15.0883i	1.12481	+	0.787603i	0.145381	+	0.989376i	$0.453559\pi$
$368$		0			0
$369$	21.4469			1.11648
$370$		0			0
$371$	4.72250			0.245180
$372$		0			0
$373$	24.3654	+	17.0608i	1.26159	+	0.883376i	0.996722	−	0.0809085i	$-0.0257822\pi$
$373$	24.3654	+	17.0608i	1.26159	+	0.883376i	0.264870	+	0.964284i	$0.414671\pi$
$374$		0			0
$375$	0.420559	−	0.680848i	0.0217176	−	0.0351588i
$376$		0			0
$377$	0.410722	−	4.69457i	0.0211533	−	0.241783i
$378$		0			0
$379$	7.66587	+	21.0618i	0.393769	+	1.08187i	0.965266	+	0.261268i	$0.0841405\pi$
$379$	7.66587	+	21.0618i	0.393769	+	1.08187i	−0.571497	+	0.820604i	$0.693637\pi$
$380$		0			0
$381$	−1.14244	−	0.659590i	−0.0585292	−	0.0337918i
$382$		0			0
$383$	−34.9049	−	12.7044i	−1.78356	−	0.649162i	−0.999598	−	0.0283509i	$-0.990974\pi$
$383$	−34.9049	−	12.7044i	−1.78356	−	0.649162i	−0.783960	−	0.620811i	$-0.786803\pi$
$384$		0			0
$385$	−1.62159	+	23.7790i	−0.0826437	+	1.21189i
$386$		0			0
$387$	0.419861	+	1.15356i	0.0213427	+	0.0586386i
$388$		0			0
$389$	−7.77725	+	11.1071i	−0.394322	+	0.563150i	−0.966398	−	0.257050i	$-0.917249\pi$
$389$	−7.77725	+	11.1071i	−0.394322	+	0.563150i	0.572076	+	0.820201i	$0.306138\pi$
$390$		0			0
$391$	−5.74900	+	6.85139i	−0.290739	+	0.346490i
$392$		0			0
$393$	−0.547093	−	0.947593i	−0.0275972	−	0.0477997i
$394$		0			0
$395$	8.74180	−	4.28234i	0.439848	−	0.215468i
$396$		0			0
$397$	−2.26234	+	8.44315i	−0.113543	+	0.423750i	−0.999174	−	0.0406410i	$-0.987060\pi$
$397$	−2.26234	+	8.44315i	−0.113543	+	0.423750i	0.885630	+	0.464391i	$0.153727\pi$
$398$		0			0
$399$	0.142650	+	0.532377i	0.00714143	+	0.0266522i
$400$		0			0
$401$	4.56626	+	4.56626i	0.228028	+	0.228028i	0.811868	−	0.583840i	$-0.198451\pi$
$401$	4.56626	+	4.56626i	0.228028	+	0.228028i	−0.583840	+	0.811868i	$0.698451\pi$
$402$		0			0
$403$	1.36804	+	2.93376i	0.0681467	+	0.146141i
$404$		0			0
$405$	−6.48573	+	18.9420i	−0.322278	+	0.941234i
$406$		0			0
$407$	21.8435	+	4.67572i	1.08274	+	0.231767i
$408$		0			0
$409$	8.51380	+	12.1590i	0.420980	+	0.601222i	0.972490	−	0.232947i	$-0.0748367\pi$
$409$	8.51380	+	12.1590i	0.420980	+	0.601222i	−0.551509	+	0.834169i	$0.685948\pi$
$410$		0			0
$411$	−0.0648346	+	0.178132i	−0.00319805	+	0.00878658i
$412$		0			0
$413$	−2.60453			−0.128160
$414$		0			0
$415$	−1.81608	+	0.194044i	−0.0891477	+	0.00952526i
$416$		0			0
$417$	−1.20736	−	0.323512i	−0.0591248	−	0.0158424i
$418$		0			0
$419$	−8.93846	−	1.57609i	−0.436672	−	0.0769971i	−0.0490094	−	0.998798i	$-0.515606\pi$
$419$	−8.93846	−	1.57609i	−0.436672	−	0.0769971i	−0.387663	+	0.921801i	$0.626718\pi$
$420$		0			0
$421$	−2.70515	+	10.0957i	−0.131841	+	0.492036i	−0.999991	−	0.00426525i	$-0.998642\pi$
$421$	−2.70515	+	10.0957i	−0.131841	+	0.492036i	0.868150	+	0.496302i	$0.165309\pi$
$422$		0			0
$423$	−0.107167	−	1.22492i	−0.00521063	−	0.0595578i
$424$		0			0
$425$	22.4218	+	3.07236i	1.08762	+	0.149032i
$426$		0			0
$427$	16.5653	−	6.02927i	0.801650	−	0.291777i
$428$		0			0
$429$	0.0150100	+	0.171566i	0.000724692	+	0.00828327i
$430$		0			0
$431$	0.142560	+	0.305720i	0.00686685	+	0.0147260i	0.909711	−	0.415241i	$-0.136303\pi$
$431$	0.142560	+	0.305720i	0.00686685	+	0.0147260i	−0.902844	+	0.429967i	$0.858525\pi$
$432$		0			0
$433$	23.2361	−	6.22610i	1.11666	−	0.299207i	0.347127	−	0.937818i	$-0.387157\pi$
$433$	23.2361	−	6.22610i	1.11666	−	0.299207i	0.769530	+	0.638611i	$0.220490\pi$
$434$		0			0
$435$	−0.221611	−	1.12969i	−0.0106254	−	0.0541643i
$436$		0			0
$437$	5.22226	+	0.456889i	0.249815	+	0.0218560i
$438$		0			0
$439$	−1.82930	+	20.9090i	−0.0873076	+	0.997931i	0.818574	+	0.574400i	$0.194765\pi$
$439$	−1.82930	+	20.9090i	−0.0873076	+	0.997931i	−0.905882	+	0.423530i	$0.860791\pi$
$440$		0			0
$441$	0.740704	+	4.20074i	0.0352716	+	0.200035i
$442$		0			0
$443$	−10.8242	+	10.8242i	−0.514273	+	0.514273i	−0.915833	−	0.401560i	$-0.868468\pi$
$443$	−10.8242	+	10.8242i	−0.514273	+	0.514273i	0.401560	+	0.915833i	$0.368468\pi$
$444$		0			0
$445$	7.23266	−	5.27392i	0.342861	−	0.250008i
$446$		0			0
$447$	0.759741	−	1.08502i	0.0359345	−	0.0513198i
$448$		0			0
$449$	35.1649	+	3.07653i	1.65953	+	0.145190i	0.877996	−	0.478669i	$-0.158881\pi$
$449$	35.1649	+	3.07653i	1.65953	+	0.145190i	0.781537	+	0.623859i	$0.214436\pi$
$450$		0			0
$451$	−20.1460	+	16.9045i	−0.948640	+	0.796003i
$452$		0			0
$453$	−0.740563	−	0.345330i	−0.0347947	−	0.0162250i
$454$		0			0
$455$	0.451763	+	4.22809i	0.0211790	+	0.198216i
$456$		0			0
$457$	7.55671	−	20.7619i	0.353488	−	0.971200i	−0.627753	−	0.778413i	$-0.716025\pi$
$457$	7.55671	−	20.7619i	0.353488	−	0.971200i	0.981241	−	0.192787i	$-0.0617527\pi$
$458$		0			0
$459$	1.93483	−	0.169276i	0.0903103	−	0.00790113i
$460$		0			0
$461$	−0.826232	+	1.77186i	−0.0384815	+	0.0825238i	−0.924609	−	0.380918i	$-0.875608\pi$
$461$	−0.826232	+	1.77186i	−0.0384815	+	0.0825238i	0.886127	+	0.463442i	$0.153386\pi$
$462$		0			0
$463$	−4.46453	−	25.3196i	−0.207484	−	1.17670i	−0.893482	−	0.449098i	$-0.851745\pi$
$463$	−4.46453	−	25.3196i	−0.207484	−	1.17670i	0.685998	−	0.727603i	$-0.259366\pi$
$464$		0			0
$465$	0.519825	+	0.595912i	0.0241063	+	0.0276348i
$466$		0			0
$467$	18.8079	−	10.8587i	0.870324	−	0.502482i	0.00286793	−	0.999996i	$-0.499087\pi$
$467$	18.8079	−	10.8587i	0.870324	−	0.502482i	0.867456	+	0.497514i	$0.165754\pi$
$468$		0			0
$469$	−1.93533	+	10.9758i	−0.0893650	+	0.506814i
$470$		0			0
$471$	−0.0271211	+	0.0156584i	−0.00124967	+	0.000721499i
$472$		0			0
$473$	−1.30363	−	0.752651i	−0.0599410	−	0.0346069i
$474$		0			0
$475$	−6.06282	−	11.7982i	−0.278181	−	0.541337i
$476$		0			0
$477$	−4.41631	+	2.05936i	−0.202209	+	0.0942916i
$478$		0			0
$479$	−5.76161	+	4.03433i	−0.263255	+	0.184333i	−0.697750	−	0.716341i	$-0.745816\pi$
$479$	−5.76161	+	4.03433i	−0.263255	+	0.184333i	0.434496	+	0.900674i	$0.356927\pi$
$480$		0			0
$481$	3.98265	+	0.144796i	0.181593	+	0.00660211i
$482$		0			0
$483$	−0.404279	−	0.0712852i	−0.0183953	−	0.00324359i
$484$		0			0
$485$	−2.35355	+	4.26325i	−0.106869	+	0.193584i
$486$		0			0
$487$		−	25.9912i		−	1.17777i	−0.808216	−	0.588887i	$-0.799566\pi$
$487$		−	25.9912i		−	1.17777i	0.808216	−	0.588887i	$-0.200434\pi$
$488$		0			0
$489$	0.354292	−	0.0949323i	0.0160216	−	0.00429299i
$490$		0			0
$491$	−20.4462	−	35.4138i	−0.922723	−	1.59820i	−0.795184	−	0.606369i	$-0.792626\pi$
$491$	−20.4462	−	35.4138i	−0.922723	−	1.59820i	−0.127539	−	0.991834i	$-0.540708\pi$
$492$		0			0
$493$	26.6685	−	18.6735i	1.20109	−	0.841012i
$494$		0			0
$495$	−8.85296	−	22.9444i	−0.397911	−	1.03127i
$496$		0			0
$497$	20.7372	−	1.81427i	0.930189	−	0.0813810i
$498$		0			0
$499$	15.3836	+	10.7717i	0.688666	+	0.482209i	0.864774	−	0.502162i	$-0.167462\pi$
$499$	15.3836	+	10.7717i	0.688666	+	0.482209i	−0.176108	+	0.984371i	$0.556351\pi$
$500$		0			0
$501$	−1.12682	−	0.525445i	−0.0503427	−	0.0234752i
$502$		0			0
$503$	−21.2073	−	17.7950i	−0.945586	−	0.793441i	0.0329628	−	0.999457i	$-0.489506\pi$
$503$	−21.2073	−	17.7950i	−0.945586	−	0.793441i	−0.978549	+	0.206016i	$0.933950\pi$
$504$		0			0
$505$	−12.0757	+	21.8741i	−0.537364	+	0.973385i
$506$		0			0
$507$	−0.232882	−	0.869127i	−0.0103427	−	0.0385993i
$508$		0			0
$509$	−9.95374	+	3.62286i	−0.441192	+	0.160581i	−0.553058	−	0.833143i	$-0.686539\pi$
$509$	−9.95374	+	3.62286i	−0.441192	+	0.160581i	0.111867	+	0.993723i	$0.464317\pi$
$510$		0			0
$511$	−5.95538	−	7.09735i	−0.263451	−	0.313968i
$512$		0			0
$513$	−0.731740	−	0.872054i	−0.0323071	−	0.0385021i
$514$		0			0
$515$	29.5447	−	0.566670i	1.30189	−	0.0249705i
$516$		0			0
$517$	1.06615	+	1.06615i	0.0468894	+	0.0468894i
$518$		0			0
$519$		−	1.76093i		−	0.0772964i
$520$		0			0
$521$	35.9056	−	6.33113i	1.57306	−	0.277372i	0.682029	−	0.731325i	$-0.261098\pi$
$521$	35.9056	−	6.33113i	1.57306	−	0.277372i	0.891026	+	0.453953i	$0.149987\pi$
$522$		0			0
$523$	−23.8017	+	19.9720i	−1.04077	+	0.873313i	−0.992094	−	0.125501i	$-0.959946\pi$
$523$	−23.8017	+	19.9720i	−1.04077	+	0.873313i	−0.0486809	+	0.998814i	$0.515502\pi$
$524$		0			0
$525$	0.392446	+	0.961773i	0.0171277	+	0.0419752i
$526$		0			0
$527$	−9.45104	+	20.2678i	−0.411694	+	0.882881i
$528$		0			0
$529$	9.54774	−	16.5372i	0.415119	−	0.719007i
$530$		0			0
$531$	2.43566	−	1.13577i	0.105699	−	0.0492882i
$532$		0			0
$533$	−3.01586	+	3.59417i	−0.130632	+	0.155681i
$534$		0			0
$535$	9.58149	−	14.2581i	0.414244	−	0.616432i
$536$		0			0
$537$	−0.180299	+	0.0317916i	−0.00778048	+	0.00137191i
$538$		0			0
$539$	−4.00681	−	3.36212i	−0.172586	−	0.144817i
$540$		0			0
$541$	−6.33105	−	1.69640i	−0.272193	−	0.0729339i	0.120141	−	0.992757i	$-0.461665\pi$
$541$	−6.33105	−	1.69640i	−0.272193	−	0.0729339i	−0.392334	+	0.919823i	$0.628332\pi$
$542$		0			0
$543$	0.262488	+	0.374871i	0.0112644	+	0.0160873i
$544$		0			0
$545$	−12.9111	+	29.1338i	−0.553049	+	1.24796i
$546$		0			0
$547$	−10.2594	+	17.7697i	−0.438658	+	0.759779i	−0.997586	−	0.0694376i	$-0.977880\pi$
$547$	−10.2594	+	17.7697i	−0.438658	+	0.759779i	0.558928	+	0.829216i	$0.311213\pi$
$548$		0			0
$549$	−12.8621	+	12.8621i	−0.548939	+	0.548939i
$550$		0			0
$551$	−17.9312	−	6.52643i	−0.763896	−	0.278035i
$552$		0			0
$553$	−2.19411	+	12.4434i	−0.0933030	+	0.529148i
$554$		0			0
$555$	0.944577	−	0.235801i	0.0400950	−	0.0100092i
$556$		0			0
$557$	5.65277	−	32.0585i	0.239516	−	1.35836i	−0.593376	−	0.804925i	$-0.702205\pi$
$557$	5.65277	−	32.0585i	0.239516	−	1.35836i	0.832892	−	0.553436i	$-0.186684\pi$
$558$		0			0
$559$	−0.252359	−	0.0918511i	−0.0106736	−	0.00388489i
$560$		0			0
$561$	−0.841305	+	0.841305i	−0.0355199	+	0.0355199i
$562$		0			0
$563$	2.56205	−	4.43760i	0.107978	−	0.187023i	−0.806973	−	0.590588i	$-0.798896\pi$
$563$	2.56205	−	4.43760i	0.107978	−	0.187023i	0.914951	+	0.403565i	$0.132229\pi$
$564$		0			0
$565$	−28.5781	+	11.0267i	−1.20229	+	0.463897i
$566$		0			0
$567$	−14.9063	−	21.2884i	−0.626007	−	0.894031i
$568$		0			0
$569$	−44.0976	−	11.8159i	−1.84867	−	0.495349i	−0.849202	−	0.528068i	$-0.822917\pi$
$569$	−44.0976	−	11.8159i	−1.84867	−	0.495349i	−0.999465	+	0.0327189i	$0.989583\pi$
$570$		0			0
$571$	0.480315	+	0.403032i	0.0201005	+	0.0168664i	0.652783	−	0.757545i	$-0.273602\pi$
$571$	0.480315	+	0.403032i	0.0201005	+	0.0168664i	−0.632682	+	0.774412i	$0.718046\pi$
$572$		0			0
$573$	0.914574	−	0.161264i	0.0382069	−	0.00673690i
$574$		0			0
$575$	9.87267	−	0.378857i	0.411719	−	0.0157994i
$576$		0			0
$577$	12.0834	−	14.4004i	0.503039	−	0.599498i	−0.453445	−	0.891284i	$-0.649805\pi$
$577$	12.0834	−	14.4004i	0.503039	−	0.599498i	0.956484	+	0.291786i	$0.0942496\pi$
$578$		0			0
$579$	−0.756162	+	0.352604i	−0.0314250	+	0.0146537i
$580$		0			0
$581$	1.18536	−	2.05311i	0.0491771	−	0.0851772i
$582$		0			0
$583$	2.52524	−	5.41539i	0.104585	−	0.224283i
$584$		0			0
$585$	−2.26624	−	3.75696i	−0.0936974	−	0.155331i
$586$		0			0
$587$	−20.5545	+	17.2473i	−0.848375	+	0.711871i	−0.959431	−	0.281943i	$-0.909021\pi$
$587$	−20.5545	+	17.2473i	−0.848375	+	0.711871i	0.111056	+	0.993814i	$0.464577\pi$
$588$		0			0
$589$	12.9084	−	2.27610i	0.531882	−	0.0937851i
$590$		0			0
$591$			0.802734i			0.0330201i
$592$		0			0
$593$	−15.5723	−	15.5723i	−0.639476	−	0.639476i	0.310950	−	0.950426i	$-0.399353\pi$
$593$	−15.5723	−	15.5723i	−0.639476	−	0.639476i	−0.950426	+	0.310950i	$0.899353\pi$
$594$		0			0
$595$	−20.3698	+	21.1665i	−0.835080	+	0.867740i
$596$		0			0
$597$	−0.916337	−	1.09205i	−0.0375032	−	0.0446946i
$598$		0			0
$599$	−16.7504	−	19.9623i	−0.684401	−	0.815638i	0.306265	−	0.951946i	$-0.400921\pi$
$599$	−16.7504	−	19.9623i	−0.684401	−	0.815638i	−0.990666	+	0.136309i	$0.956476\pi$
$600$		0			0
$601$	12.9538	−	4.71480i	0.528396	−	0.192321i	−0.0640258	−	0.997948i	$-0.520394\pi$
$601$	12.9538	−	4.71480i	0.528396	−	0.192321i	0.592422	+	0.805628i	$0.298172\pi$
$602$		0			0
$603$	−2.97641	−	11.1081i	−0.121209	−	0.452357i
$604$		0			0
$605$	4.86748	+	2.68712i	0.197891	+	0.109247i
$606$		0			0
$607$	−23.5872	−	19.7920i	−0.957373	−	0.803331i	0.0231506	−	0.999732i	$-0.492630\pi$
$607$	−23.5872	−	19.7920i	−0.957373	−	0.803331i	−0.980524	+	0.196401i	$0.937075\pi$
$608$		0			0
$609$	1.35430	+	0.631520i	0.0548790	+	0.0255905i
$610$		0			0
$611$	0.220348	+	0.154289i	0.00891431	+	0.00624187i
$612$		0			0
$613$	−31.7202	+	2.77516i	−1.28117	+	0.112088i	−0.707331	−	0.706882i	$-0.750101\pi$
$613$	−31.7202	+	2.77516i	−1.28117	+	0.112088i	−0.573836	+	0.818970i	$0.694545\pi$
$614$		0			0
$615$	−0.464384	+	1.04788i	−0.0187258	+	0.0422547i
$616$		0			0
$617$	−37.0450	+	25.9392i	−1.49138	+	1.04427i	−0.508278	+	0.861193i	$0.669718\pi$
$617$	−37.0450	+	25.9392i	−1.49138	+	1.04427i	−0.983098	+	0.183080i	$0.941393\pi$
$618$		0			0
$619$	20.5297	+	35.5584i	0.825157	+	1.42921i	0.901800	+	0.432155i	$0.142247\pi$
$619$	20.5297	+	35.5584i	0.825157	+	1.42921i	−0.0766430	+	0.997059i	$0.524420\pi$
$620$		0			0
$621$	0.819006	−	0.219452i	0.0328656	−	0.00880630i
$622$		0			0
$623$			11.6190i			0.465504i
$624$		0			0
$625$	−14.1225	−	20.6290i	−0.564898	−	0.825161i
$626$		0			0
$627$	0.686768	+	0.121096i	0.0274269	+	0.00483609i
$628$		0			0
$629$	16.9194	+	21.7200i	0.674621	+	0.866032i
$630$		0			0
$631$	38.4114	−	26.8960i	1.52913	−	1.07071i	0.558692	−	0.829375i	$-0.311303\pi$
$631$	38.4114	−	26.8960i	1.52913	−	1.07071i	0.970442	−	0.241336i	$-0.0775855\pi$
$632$		0			0
$633$	−0.184276	+	0.0859295i	−0.00732433	+	0.00341539i
$634$		0			0
$635$	−33.2984	+	24.2805i	−1.32141	+	0.963544i
$636$		0			0
$637$	−0.808136	−	0.466578i	−0.0320195	−	0.0184865i
$638$		0			0
$639$	−18.6015	+	10.7396i	−0.735864	+	0.424852i
$640$		0			0
$641$	0.831751	−	4.71709i	0.0328522	−	0.186314i	−0.963966	−	0.266027i	$-0.914289\pi$
$641$	0.831751	−	4.71709i	0.0328522	−	0.186314i	0.996818	+	0.0797125i	$0.0254002\pi$
$642$		0			0
$643$	−22.4222	+	12.9455i	−0.884245	+	0.510519i	−0.872056	−	0.489406i	$-0.837213\pi$
$643$	−22.4222	+	12.9455i	−0.884245	+	0.510519i	−0.0121895	+	0.999926i	$0.503880\pi$
$644$		0			0
$645$	−0.0654532	−	0.00446352i	−0.00257722	−	0.000175751i
$646$		0			0
$647$	3.07212	+	17.4229i	0.120778	+	0.684963i	0.983727	+	0.179672i	$0.0575037\pi$
$647$	3.07212	+	17.4229i	0.120778	+	0.684963i	−0.862949	+	0.505291i	$0.831385\pi$
$648$		0			0
$649$	−1.39271	+	2.98667i	−0.0546686	+	0.117237i
$650$		0			0
$651$	−1.02254	+	0.0894606i	−0.0400765	+	0.00350624i
$652$		0			0
$653$	−0.597121	+	1.64058i	−0.0233672	+	0.0642007i	−0.950828	−	0.309720i	$-0.899765\pi$
$653$	−0.597121	+	1.64058i	−0.0233672	+	0.0642007i	0.927461	+	0.373921i	$0.121987\pi$
$654$		0			0
$655$	−33.9885	+	3.63161i	−1.32804	+	0.141899i
$656$		0			0
$657$	8.66424	+	4.04020i	0.338024	+	0.157623i
$658$		0			0
$659$	−11.6411	+	9.76806i	−0.453473	+	0.380509i	−0.840723	−	0.541466i	$-0.817870\pi$
$659$	−11.6411	+	9.76806i	−0.453473	+	0.380509i	0.387249	+	0.921975i	$0.373425\pi$
$660$		0			0
$661$	29.6079	+	2.59035i	1.15161	+	0.100753i	0.646928	−	0.762551i	$-0.276053\pi$
$661$	29.6079	+	2.59035i	1.15161	+	0.100753i	0.504684	+	0.863304i	$0.331609\pi$
$662$		0			0
$663$	−0.121750	+	0.173877i	−0.00472837	+	0.00675282i
$664$		0			0
$665$	17.0106	+	2.66415i	0.659643	+	0.103311i
$666$		0			0
$667$	10.0499	−	10.0499i	0.389135	−	0.389135i
$668$		0			0
$669$	0.186870	+	1.05979i	0.00722481	+	0.0409739i
$670$		0			0
$671$	1.94398	−	22.2198i	0.0750465	−	0.857786i
$672$		0			0
$673$	25.7568	+	2.25342i	0.992850	+	0.0868631i	0.571988	−	0.820262i	$-0.306172\pi$
$673$	25.7568	+	2.25342i	0.992850	+	0.0868631i	0.420862	+	0.907125i	$0.361728\pi$
$674$		0			0
$675$	−1.57416	−	1.45781i	−0.0605894	−	0.0561111i
$676$		0			0
$677$	4.22617	−	1.13240i	0.162425	−	0.0435216i	−0.176690	−	0.984267i	$-0.556539\pi$
$677$	4.22617	−	1.13240i	0.162425	−	0.0435216i	0.339115	+	0.940745i	$0.389872\pi$
$678$		0			0
$679$	−2.67139	−	5.72880i	−0.102518	−	0.219851i
$680$		0			0
$681$	0.146502	+	1.67452i	0.00561395	+	0.0641678i
$682$		0			0
$683$	−45.1568	+	16.4357i	−1.72788	+	0.628896i	−0.998476	−	0.0551905i	$-0.982423\pi$
$683$	−45.1568	+	16.4357i	−1.72788	+	0.628896i	−0.729401	+	0.684086i	$0.760201\pi$
$684$		0			0
$685$	4.26695	+	4.10635i	0.163032	+	0.156895i
$686$		0			0
$687$	−0.100805	−	1.15221i	−0.00384596	−	0.0439596i
$688$		0			0
$689$	0.275905	−	1.02969i	0.0105111	−	0.0392281i
$690$		0			0
$691$	37.9551	+	6.69252i	1.44388	+	0.254595i	0.840047	−	0.542514i	$-0.182527\pi$
$691$	37.9551	+	6.69252i	1.44388	+	0.254595i	0.603835	+	0.797109i	$0.293639\pi$
$692$		0			0
$693$	30.8346	+	8.26211i	1.17131	+	0.313852i
$694$		0			0
$695$	−24.5214	+	30.3884i	−0.930150	+	1.15270i
$696$		0			0
$697$	−32.4136			−1.22775
$698$		0			0
$699$	0.0511665	−	0.140579i	0.00193530	−	0.00531718i
$700$		0			0
$701$	−15.9836	−	22.8270i	−0.603693	−	0.862162i	0.394702	−	0.918809i	$-0.370848\pi$
$701$	−15.9836	−	22.8270i	−0.603693	−	0.862162i	−0.998394	+	0.0566470i	$0.981959\pi$
$702$		0			0
$703$	4.74022	−	15.4254i	0.178781	−	0.581780i
$704$		0			0
$705$	0.0621694	+	0.0212868i	0.00234144	+	0.000801707i
$706$		0			0
$707$	−13.7065	−	29.3937i	−0.515486	−	1.10546i
$708$		0			0
$709$	33.6760	+	33.6760i	1.26473	+	1.26473i	0.948774	+	0.315956i	$0.102325\pi$
$709$	33.6760	+	33.6760i	1.26473	+	1.26473i	0.315956	+	0.948774i	$0.397675\pi$
$710$		0			0
$711$	−3.37440	−	12.5934i	−0.126550	−	0.472291i
$712$		0			0
$713$	−2.52680	+	9.43016i	−0.0946295	+	0.353162i
$714$		0			0
$715$	5.09002	+	1.74282i	0.190356	+	0.0651779i
$716$		0			0
$717$	0.0387689	+	0.0671498i	0.00144785	+	0.00250775i
$718$		0			0
$719$	32.1115	−	38.2690i	1.19756	−	1.42719i	0.320201	−	0.947350i	$-0.396250\pi$
$719$	32.1115	−	38.2690i	1.19756	−	1.42719i	0.877355	−	0.479842i	$-0.159306\pi$
$720$		0			0
$721$	−22.0005	+	31.4199i	−0.819340	+	1.17014i
$722$		0			0
$723$	0.113738	+	0.312493i	0.00422996	+	0.0116217i
$724$		0			0
$725$	−35.0696	−	7.96916i	−1.30245	−	0.295967i
$726$		0			0
$727$	−43.1368	−	15.7005i	−1.59985	−	0.582300i	−0.620457	−	0.784240i	$-0.713053\pi$
$727$	−43.1368	−	15.7005i	−1.59985	−	0.582300i	−0.979398	+	0.201941i	$0.935275\pi$
$728$		0			0
$729$	23.1434	+	13.3619i	0.857164	+	0.494884i
$730$		0			0
$731$	−0.634551	−	1.74342i	−0.0234697	−	0.0644826i
$732$		0			0
$733$	2.92567	−	33.4406i	0.108062	−	1.23516i	−0.727635	−	0.685965i	$-0.759380\pi$
$733$	2.92567	−	33.4406i	0.108062	−	1.23516i	0.835697	−	0.549191i	$-0.185064\pi$
$734$		0			0
$735$	−0.221284	−	0.0547671i	−0.00816217	−	0.00202011i
$736$		0			0
$737$	11.5513	+	8.08831i	0.425498	+	0.297937i
$738$		0			0
$739$	29.9662			1.10232			0.551162	−	0.834398i	$-0.314184\pi$
$739$	29.9662			1.10232			0.551162	+	0.834398i	$0.314184\pi$
$740$		0			0
$741$	0.124413			0.00457044
$742$		0			0
$743$	41.2078	+	28.8540i	1.51177	+	1.05855i	0.976921	+	0.213601i	$0.0685194\pi$
$743$	41.2078	+	28.8540i	1.51177	+	1.05855i	0.534846	+	0.844949i	$0.320369\pi$
$744$		0			0
$745$	−21.3729	−	35.4320i	−0.783043	−	1.29813i
$746$		0			0
$747$	−0.213201	+	2.43690i	−0.00780062	+	0.0891614i
$748$		0			0
$749$	7.62636	+	20.9532i	0.278661	+	0.765615i
$750$		0			0
$751$	−42.0868	−	24.2989i	−1.53577	−	0.886678i	−0.999079	−	0.0428991i	$-0.986341\pi$
$751$	−42.0868	−	24.2989i	−1.53577	−	0.886678i	−0.536691	−	0.843779i	$-0.680326\pi$
$752$		0			0
$753$	0.753612	+	0.274292i	0.0274632	+	0.00999577i
$754$		0			0
$755$	−19.2363	+	16.7802i	−0.700079	+	0.610692i
$756$		0			0
$757$	−15.7677	−	43.3215i	−0.573088	−	1.57455i	−0.799597	−	0.600537i	$-0.794954\pi$
$757$	−15.7677	−	43.3215i	−0.573088	−	1.57455i	0.226509	−	0.974009i	$-0.427269\pi$
$758$		0			0
$759$	−0.297923	+	0.425478i	−0.0108139	+	0.0154439i
$760$		0			0
$761$	5.30651	−	6.32405i	0.192361	−	0.229247i	−0.661240	−	0.750175i	$-0.729969\pi$
$761$	5.30651	−	6.32405i	0.192361	−	0.229247i	0.853601	+	0.520928i	$0.174414\pi$
$762$		0			0
$763$	−20.6817	−	35.8217i	−0.748727	−	1.29683i
$764$		0			0
$765$	9.81896	−	28.6769i	0.355005	−	1.03681i
$766$		0			0
$767$	−0.152166	+	0.567890i	−0.00549439	+	0.0205053i
$768$		0			0
$769$	10.8657	+	40.5514i	0.391828	+	1.46232i	0.827117	+	0.562030i	$0.189980\pi$
$769$	10.8657	+	40.5514i	0.391828	+	1.46232i	−0.435289	+	0.900291i	$0.643354\pi$
$770$		0			0
$771$	−1.12826	−	1.12826i	−0.0406332	−	0.0406332i
$772$		0			0
$773$	6.10094	+	13.0835i	0.219435	+	0.470581i	0.984950	−	0.172837i	$-0.0552935\pi$
$773$	6.10094	+	13.0835i	0.219435	+	0.470581i	−0.765515	+	0.643418i	$0.777516\pi$
$774$		0			0
$775$	23.5992	−	7.30408i	0.847707	−	0.262370i
$776$		0			0
$777$	−0.475072	+	1.17101i	−0.0170431	+	0.0420097i
$778$		0			0
$779$	10.8970	+	15.5626i	0.390426	+	0.557587i
$780$		0			0
$781$	9.00824	−	24.7499i	0.322340	−	0.885622i
$782$		0			0
$783$	−3.08640			−0.110299
$784$		0			0
$785$	0.103940	+	0.972787i	0.00370979	+	0.0347203i
$786$		0			0
$787$	−15.4460	−	4.13874i	−0.550590	−	0.147530i	−0.0272102	−	0.999630i	$-0.508662\pi$
$787$	−15.4460	−	4.13874i	−0.550590	−	0.147530i	−0.523380	+	0.852100i	$0.675329\pi$
$788$		0			0
$789$	−1.16320	−	0.205103i	−0.0414109	−	0.00730185i
$790$		0			0
$791$	10.2908	−	38.4057i	0.365898	−	1.36555i
$792$		0			0
$793$	−0.346817	−	3.96414i	−0.0123158	−	0.140771i
$794$		0			0
$795$	−0.00499390	−	0.260369i	−0.000177115	−	0.00923433i
$796$		0			0
$797$	−19.5649	+	7.12103i	−0.693023	+	0.252240i	−0.664429	−	0.747351i	$-0.731325\pi$
$797$	−19.5649	+	7.12103i	−0.693023	+	0.252240i	−0.0285938	+	0.999591i	$0.509103\pi$
$798$		0			0
$799$	0.161965	+	1.85127i	0.00572993	+	0.0654934i
$800$		0			0
$801$	−5.06673	−	10.8656i	−0.179024	−	0.383919i
$802$		0			0
$803$	−11.3232	+	3.03404i	−0.399587	+	0.107069i
$804$		0			0
$805$	−7.15295	+	10.6442i	−0.252108	+	0.375160i
$806$		0			0
$807$	0.699226	+	0.0611744i	0.0246139	+	0.00215344i
$808$		0			0
$809$	−4.04776	+	46.2661i	−0.142312	+	1.62663i	0.504104	+	0.863643i	$0.331823\pi$
$809$	−4.04776	+	46.2661i	−0.142312	+	1.62663i	−0.646416	+	0.762985i	$0.723733\pi$
$810$		0			0
$811$	6.06376	+	34.3893i	0.212927	+	1.20757i	0.884467	+	0.466602i	$0.154522\pi$
$811$	6.06376	+	34.3893i	0.212927	+	1.20757i	−0.671540	+	0.740968i	$0.734367\pi$
$812$		0			0
$813$	−0.126013	+	0.126013i	−0.00441948	+	0.00441948i
$814$		0			0
$815$	1.77297	−	11.3204i	0.0621044	−	0.396537i
$816$		0			0
$817$	−0.623729	+	0.890778i	−0.0218215	+	0.0311644i
$818$		0			0
$819$	5.67346	+	0.496363i	0.198247	+	0.0173443i
$820$		0			0
$821$	19.2910	−	16.1870i	0.673260	−	0.564932i	−0.240769	−	0.970583i	$-0.577399\pi$
$821$	19.2910	−	16.1870i	0.673260	−	0.564932i	0.914028	+	0.405651i	$0.132955\pi$
$822$		0			0
$823$	−5.11708	−	2.38613i	−0.178370	−	0.0831754i	0.331382	−	0.943497i	$-0.392485\pi$
$823$	−5.11708	−	2.38613i	−0.178370	−	0.0831754i	−0.509752	+	0.860321i	$0.670263\pi$
$824$		0			0
$825$	1.31274	+	0.0642585i	0.0457037	+	0.00223720i
$826$		0			0
$827$	11.9833	−	32.9238i	0.416699	−	1.14487i	−0.536861	−	0.843670i	$-0.680390\pi$
$827$	11.9833	−	32.9238i	0.416699	−	1.14487i	0.953561	−	0.301201i	$-0.0973876\pi$
$828$		0			0
$829$	−33.8646	+	2.96276i	−1.17616	+	0.102901i	−0.658431	−	0.752641i	$-0.728780\pi$
$829$	−33.8646	+	2.96276i	−1.17616	+	0.102901i	−0.517733	+	0.855542i	$0.673224\pi$
$830$		0			0
$831$	−0.415101	+	0.890187i	−0.0143997	+	0.0308802i
$832$		0			0
$833$	−1.11945	−	6.34874i	−0.0387868	−	0.219971i
$834$		0			0
$835$	−29.2694	+	25.5322i	−1.01291	+	0.883579i
$836$		0			0
$837$	1.83603	−	1.06003i	0.0634626	−	0.0366401i
$838$		0			0
$839$	0.676517	−	3.83672i	0.0233560	−	0.132458i	−0.970900	−	0.239484i	$-0.923022\pi$
$839$	0.676517	−	3.83672i	0.0233560	−	0.132458i	0.994256	+	0.107026i	$0.0341328\pi$
$840$		0			0
$841$	−19.6894	+	11.3677i	−0.678946	+	0.391990i
$842$		0			0
$843$	1.20783	+	0.697341i	0.0415999	+	0.0240177i
$844$		0			0
$845$	−27.7705	−	4.34934i	−0.955335	−	0.149622i
$846$		0			0
$847$	−6.54075	+	3.05000i	−0.224743	+	0.104799i
$848$		0			0
$849$	−1.32252	+	0.926042i	−0.0453889	+	0.0317817i
$850$		0			0
$851$	8.92066	+	8.05539i	0.305796	+	0.276135i
$852$		0			0
$853$	6.35788	+	1.12107i	0.217690	+	0.0383846i	0.281429	−	0.959582i	$-0.409192\pi$
$853$	6.35788	+	1.12107i	0.217690	+	0.0383846i	−0.0637395	+	0.997967i	$0.520303\pi$
$854$		0			0
$855$	−17.0695	+	4.92647i	−0.583764	+	0.168482i
$856$		0			0
$857$			14.7846i			0.505031i	0.967593	+	0.252516i	$0.0812579\pi$
$857$			14.7846i			0.505031i	−0.967593	+	0.252516i	$0.918742\pi$
$858$		0			0
$859$	−33.1428	+	8.88059i	−1.13082	+	0.303002i	−0.775254	−	0.631650i	$-0.782378\pi$
$859$	−33.1428	+	8.88059i	−1.13082	+	0.303002i	−0.355565	+	0.934652i	$0.615711\pi$
$860$		0			0
$861$	−0.743877	−	1.28843i	−0.0253513	−	0.0439097i
$862$		0			0
$863$	−32.2997	+	22.6165i	−1.09950	+	0.769875i	−0.974969	−	0.222341i	$-0.928630\pi$
$863$	−32.2997	+	22.6165i	−1.09950	+	0.769875i	−0.124527	+	0.992216i	$0.539741\pi$
$864$		0			0
$865$	−50.2936	−	22.2883i	−1.71003	−	0.757825i
$866$		0			0
$867$	−0.248652	+	0.0217542i	−0.00844466	+	0.000738812i
$868$		0			0
$869$	13.0959	+	9.16985i	0.444248	+	0.311066i
$870$		0			0
$871$	2.28009	+	1.06322i	0.0772577	+	0.0360259i
$872$		0			0
$873$	4.99637	+	4.19245i	0.169102	+	0.141893i
$874$		0			0
$875$	32.4362	+	0.964715i	1.09654	+	0.0326133i
$876$		0			0
$877$	11.5209	+	42.9965i	0.389032	+	1.45189i	0.831711	+	0.555208i	$0.187361\pi$
$877$	11.5209	+	42.9965i	0.389032	+	1.45189i	−0.442679	+	0.896680i	$0.645972\pi$
$878$		0			0
$879$	1.30301	−	0.474257i	0.0439494	−	0.0159963i
$880$		0			0
$881$	16.2673	+	19.3866i	0.548059	+	0.653151i	0.966974	−	0.254874i	$-0.0820340\pi$
$881$	16.2673	+	19.3866i	0.548059	+	0.653151i	−0.418915	+	0.908025i	$0.637590\pi$
$882$		0			0
$883$	18.2298	+	21.7254i	0.613480	+	0.731117i	0.979935	−	0.199319i	$-0.0638729\pi$
$883$	18.2298	+	21.7254i	0.613480	+	0.731117i	−0.366455	+	0.930436i	$0.619428\pi$
$884$		0			0
$885$	0.00275421	+	0.143597i	9.25818e−5	+	0.00482697i
$886$		0			0
$887$	21.4435	+	21.4435i	0.720004	+	0.720004i	0.968606	−	0.248602i	$-0.0799711\pi$
$887$	21.4435	+	21.4435i	0.720004	+	0.720004i	−0.248602	+	0.968606i	$0.579971\pi$
$888$		0			0
$889$		−	53.4924i		−	1.79408i
$890$		0			0
$891$	−32.3828	+	5.70995i	−1.08486	+	0.191291i
$892$		0			0
$893$	0.834392	−	0.700138i	0.0279219	−	0.0234292i
$894$		0			0
$895$	−1.37407	+	5.55186i	−0.0459301	+	0.185578i
$896$		0			0
$897$	−0.0391624	+	0.0839840i	−0.00130759	+	0.00280415i
$898$		0			0
$899$	17.7687	−	30.7762i	0.592618	−	1.02644i
$900$		0			0
$901$	6.67454	−	3.11239i	0.222361	−	0.103689i
$902$		0			0
$903$	0.0547378	−	0.0652339i	0.00182156	−	0.00217085i
$904$		0			0
$905$	14.0289	−	2.75206i	0.466337	−	0.0914816i
$906$		0			0
$907$	39.4091	−	6.94888i	1.30856	−	0.230734i	0.524493	−	0.851414i	$-0.324255\pi$
$907$	39.4091	−	6.94888i	1.30856	−	0.230734i	0.784064	+	0.620681i	$0.213144\pi$
$908$		0			0
$909$	25.6357	+	21.5109i	0.850281	+	0.713471i
$910$		0			0
$911$	−2.26602	−	0.607178i	−0.0750766	−	0.0201167i	0.221085	−	0.975254i	$-0.429040\pi$
$911$	−2.26602	−	0.607178i	−0.0750766	−	0.0201167i	−0.296162	+	0.955138i	$0.595707\pi$
$912$		0			0
$913$	−1.72050	−	2.45713i	−0.0569403	−	0.0813191i
$914$		0			0
$915$	−0.349933	−	0.906930i	−0.0115684	−	0.0299822i
$916$		0			0
$917$	22.1845	−	38.4246i	0.732596	−	1.26889i
$918$		0			0
$919$	−22.0854	+	22.0854i	−0.728530	+	0.728530i	−0.970327	−	0.241797i	$-0.922263\pi$
$919$	−22.0854	+	22.0854i	−0.728530	+	0.728530i	0.241797	+	0.970327i	$0.422263\pi$
$920$		0			0
$921$	1.88097	+	0.684617i	0.0619800	+	0.0225589i
$922$		0			0
$923$	0.815956	−	4.62752i	0.0268575	−	0.152317i
$924$		0			0
$925$	5.22094	−	29.9623i	0.171664	−	0.985156i
$926$		0			0
$927$	6.87263	−	38.9766i	0.225727	−	1.28016i
$928$		0			0
$929$	−37.8784	−	13.7866i	−1.24275	−	0.452324i	−0.364805	−	0.931084i	$-0.618864\pi$
$929$	−37.8784	−	13.7866i	−1.24275	−	0.452324i	−0.877946	+	0.478760i	$0.841086\pi$
$930$		0			0
$931$	−2.67184	+	2.67184i	−0.0875662	+	0.0875662i
$932$		0			0
$933$	0.946910	−	1.64010i	0.0310005	−	0.0536944i
$934$		0			0
$935$	13.3798	+	34.6768i	0.437567	+	1.13405i
$936$		0			0
$937$	−14.1266	−	20.1749i	−0.461496	−	0.659085i	0.519193	−	0.854657i	$-0.326233\pi$
$937$	−14.1266	−	20.1749i	−0.461496	−	0.659085i	−0.980689	+	0.195572i	$0.937344\pi$
$938$		0			0
$939$	1.34427	+	0.360195i	0.0438685	+	0.0117545i
$940$		0			0
$941$	22.8515	+	19.1747i	0.744939	+	0.625078i	0.934159	−	0.356857i	$-0.116151\pi$
$941$	22.8515	+	19.1747i	0.744939	+	0.625078i	−0.189220	+	0.981935i	$0.560596\pi$
$942$		0			0
$943$	−13.9355	+	2.45720i	−0.453802	+	0.0800175i
$944$		0			0
$945$	2.73282	−	0.536098i	0.0888986	−	0.0174393i
$946$		0			0
$947$	21.0541	−	25.0913i	0.684166	−	0.815357i	−0.306471	−	0.951880i	$-0.599148\pi$
$947$	21.0541	−	25.0913i	0.684166	−	0.815357i	0.990637	+	0.136523i	$0.0435926\pi$
$948$		0			0
$949$	−1.89544	+	0.883857i	−0.0615285	+	0.0286912i
$950$		0			0
$951$	0.408228	−	0.707072i	0.0132377	−	0.0229284i
$952$		0			0
$953$	−11.5202	+	24.7052i	−0.373177	+	0.800282i	0.626603	+	0.779338i	$0.284445\pi$
$953$	−11.5202	+	24.7052i	−0.373177	+	0.800282i	−0.999781	+	0.0209431i	$0.993333\pi$
$954$		0			0
$955$	6.97002	−	28.1620i	0.225545	−	0.911302i
$956$		0			0
$957$	1.44836	−	1.21532i	0.0468188	−	0.0392856i
$958$		0			0
$959$	−7.56997	+	1.33479i	−0.244447	+	0.0431026i
$960$		0			0
$961$		−	6.58921i		−	0.212555i
$962$		0			0
$963$	−16.2691	−	16.2691i	−0.524264	−	0.524264i
$964$		0			0
$965$	0.499824	+	26.0595i	0.0160899	+	0.838884i
$966$		0			0
$967$	32.9854	+	39.3105i	1.06074	+	1.26414i	0.963164	+	0.268913i	$0.0866644\pi$
$967$	32.9854	+	39.3105i	1.06074	+	1.26414i	0.0975758	+	0.995228i	$0.468891\pi$
$968$		0			0
$969$	0.552481	+	0.658421i	0.0177482	+	0.0211515i
$970$		0			0
$971$	45.1071	−	16.4177i	1.44756	−	0.526868i	0.505649	−	0.862739i	$-0.331253\pi$
$971$	45.1071	−	16.4177i	1.44756	−	0.526868i	0.941908	+	0.335872i	$0.109031\pi$
$972$		0			0
$973$	−13.1183	−	48.9582i	−0.420554	−	1.56953i
$974$		0			0
$975$	0.232633	−	0.0293785i	0.00745021	−	0.000940865i
$976$		0			0
$977$	6.07520	+	5.09770i	0.194363	+	0.163090i	0.734776	−	0.678310i	$-0.237287\pi$
$977$	6.07520	+	5.09770i	0.194363	+	0.163090i	−0.540413	+	0.841400i	$0.681732\pi$
$978$		0			0
$979$	13.3237	+	6.21296i	0.425828	+	0.198567i
$980$		0			0
$981$	34.9617	+	24.4805i	1.11624	+	0.781601i
$982$		0			0
$983$	21.3921	−	1.87157i	0.682302	−	0.0596937i	0.259265	−	0.965806i	$-0.416520\pi$
$983$	21.3921	−	1.87157i	0.682302	−	0.0596937i	0.423037	+	0.906112i	$0.360964\pi$
$984$		0			0
$985$	22.9267	+	10.1603i	0.730504	+	0.323733i
$986$		0			0
$987$	−0.0698707	+	0.0489240i	−0.00222401	+	0.00155727i
$988$		0			0
$989$	−0.404976	−	0.701438i	−0.0128775	−	0.0223044i
$990$		0			0
$991$	−35.7492	+	9.57897i	−1.13561	+	0.304286i	−0.777185	−	0.629272i	$-0.783353\pi$
$991$	−35.7492	+	9.57897i	−1.13561	+	0.304286i	−0.358426	+	0.933558i	$0.616686\pi$
$992$		0			0
$993$			0.955643i			0.0303264i
$994$		0			0
$995$	−42.7879	+	12.3491i	−1.35647	+	0.391493i
$996$		0			0
$997$	−21.4471	−	3.78170i	−0.679235	−	0.119768i	−0.176622	−	0.984279i	$-0.556517\pi$
$997$	−21.4471	−	3.78170i	−0.679235	−	0.119768i	−0.502613	+	0.864511i	$0.667628\pi$
$998$		0			0
$999$	−0.132865	−	2.60673i	−0.00420366	−	0.0824733i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.cc.a.653.10	yes	228
5.2	odd	4		740.2.ch.a.357.10	yes	228
37.17	odd	36		740.2.ch.a.313.10	yes	228
185.17	even	36	inner	740.2.cc.a.17.10	✓	228

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.cc.a.17.10	✓	228	185.17	even	36	inner
740.2.cc.a.653.10	yes	228	1.1	even	1	trivial
740.2.ch.a.313.10	yes	228	37.17	odd	36
740.2.ch.a.357.10	yes	228	5.2	odd	4

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:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.cc (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0586331 + 0.0410554i) q^{3} +(1.91470 - 1.15496i) q^{5} +(-0.252966 + 2.89142i) q^{7} +(-1.02431 - 2.81426i) q^{9} +(3.18039 + 1.83620i) q^{11} +(0.615664 + 0.224083i) q^{13} +(0.159682 + 0.0108894i) q^{15} +(1.54808 + 4.25330i) q^{17} +(1.52167 - 2.17318i) q^{19} +(-0.133540 + 0.159147i) q^{21} +(0.987994 + 1.71126i) q^{23} +(2.33212 - 4.42281i) q^{25} +(0.111059 - 0.414479i) q^{27} +(-1.86162 - 6.94765i) q^{29} +(3.49362 + 3.49362i) q^{31} +(0.111090 + 0.238234i) q^{33} +(2.85513 + 5.82835i) q^{35} +(5.78774 - 1.87138i) q^{37} +(0.0268985 + 0.0384150i) q^{39} +(-2.44928 + 6.72933i) q^{41} -0.409897 q^{43} +(-5.21161 - 4.20542i) q^{45} +(0.396579 + 0.106263i) q^{47} +(-1.40264 - 0.247324i) q^{49} +(-0.0838524 + 0.312941i) q^{51} +(-0.141808 - 1.62087i) q^{53} +(8.21021 - 0.157473i) q^{55} +(0.178441 - 0.0649472i) q^{57} +(0.0782094 + 0.893937i) q^{59} +(-2.56682 - 5.50455i) q^{61} +(8.39632 - 2.24979i) q^{63} +(1.43762 - 0.282018i) q^{65} +(3.82527 + 0.334667i) q^{67} +(-0.0123270 + 0.140899i) q^{69} +(-1.24540 - 7.06302i) q^{71} +(-2.25715 + 2.25715i) q^{73} +(0.318319 - 0.163577i) q^{75} +(-6.11374 + 8.73133i) q^{77} +(4.33677 + 0.379418i) q^{79} +(-6.85910 + 5.75547i) q^{81} +(-0.740270 - 0.345193i) q^{83} +(7.87651 + 6.35581i) q^{85} +(0.176086 - 0.483792i) q^{87} +(3.98791 - 0.348897i) q^{89} +(-0.803661 + 1.72346i) q^{91} +(0.0614101 + 0.348274i) q^{93} +(0.403603 - 5.91845i) q^{95} +(-1.88605 + 1.08891i) q^{97} +(1.90985 - 10.8313i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 228 q + 6 q^{3} - 12 q^{25} + 12 q^{27} - 36 q^{31} + 6 q^{33} + 24 q^{35} + 24 q^{37} - 72 q^{39} - 54 q^{41} - 12 q^{45} + 36 q^{49} - 6 q^{53} - 72 q^{57} - 36 q^{61} + 18 q^{65} + 42 q^{67} + 96 q^{69}+ \cdots + 72 q^{97}+O(q^{100}) \) 228 * q + 6 * q^3 - 12 * q^25 + 12 * q^27 - 36 * q^31 + 6 * q^33 + 24 * q^35 + 24 * q^37 - 72 * q^39 - 54 * q^41 - 12 * q^45 + 36 * q^49 - 6 * q^53 - 72 * q^57 - 36 * q^61 + 18 * q^65 + 42 * q^67 + 96 * q^69 - 48 * q^71 - 6 * q^73 - 96 * q^75 - 114 * q^77 + 48 * q^79 - 36 * q^81 - 12 * q^83 + 72 * q^87 - 12 * q^89 + 24 * q^91 - 6 * q^93 + 90 * q^95 + 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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