LMFDB - Embedded newform 1170.2.bs.h.901.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,2,Mod(361,1170)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1170, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1170.361");

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.bs (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.1731891456.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 $ x^8 - 9x^6 + 65x^4 - 144*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.1
Root			$-1.35234 - 0.780776i$ of defining polynomial
Character	$\chi$	$=$	1170.901
Dual form			1170.2.bs.h.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000i q^{5} +(-2.34233 + 1.35234i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000i q^{5} +(-2.34233 + 1.35234i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{10} +(2.59808 + 1.50000i) q^{11} +(-3.34233 - 1.35234i) q^{13} +2.70469 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-5.34233 + 3.08440i) q^{19} +(-0.866025 + 0.500000i) q^{20} +(-1.50000 - 2.59808i) q^{22} +(3.95042 - 6.84233i) q^{23} -1.00000 q^{25} +(2.21837 + 2.84233i) q^{26} +(-2.34233 - 1.35234i) q^{28} +(-1.24573 + 2.15767i) q^{29} +0.972638i q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.35234 - 2.34233i) q^{35} +(-1.50000 - 0.866025i) q^{37} +6.16879 q^{38} +1.00000 q^{40} +(-5.19615 - 3.00000i) q^{41} +(-4.84233 - 8.38716i) q^{43} +3.00000i q^{44} +(-6.84233 + 3.95042i) q^{46} -3.00000i q^{47} +(0.157671 - 0.273094i) q^{49} +(0.866025 + 0.500000i) q^{50} +(-0.500000 - 3.57071i) q^{52} -2.70469 q^{53} +(-1.50000 + 2.59808i) q^{55} +(1.35234 + 2.34233i) q^{56} +(2.15767 - 1.24573i) q^{58} +(-6.65511 + 3.84233i) q^{59} +(-6.68466 - 11.5782i) q^{61} +(0.486319 - 0.842329i) q^{62} -1.00000 q^{64} +(1.35234 - 3.34233i) q^{65} +(-1.68466 - 0.972638i) q^{67} +2.70469i q^{70} +(5.19615 - 3.00000i) q^{71} +6.92820i q^{73} +(0.866025 + 1.50000i) q^{74} +(-5.34233 - 3.08440i) q^{76} -8.11407 q^{77} +5.68466 q^{79} +(-0.866025 - 0.500000i) q^{80} +(3.00000 + 5.19615i) q^{82} -15.3693i q^{83} +9.68466i q^{86} +(1.50000 - 2.59808i) q^{88} +(4.05703 + 2.34233i) q^{89} +(9.65767 - 1.35234i) q^{91} +7.90084 q^{92} +(-1.50000 + 2.59808i) q^{94} +(-3.08440 - 5.34233i) q^{95} +(-7.68466 + 4.43674i) q^{97} +(-0.273094 + 0.157671i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} + 6 q^{7}+O(q^{10}) $ 8 * q + 4 * q^4 + 6 * q^7	$ 8 q + 4 q^{4} + 6 q^{7} + 4 q^{10} - 2 q^{13} - 4 q^{16} - 18 q^{19} - 12 q^{22} - 8 q^{25} + 6 q^{28} - 12 q^{37} + 8 q^{40} - 14 q^{43} - 30 q^{46} + 26 q^{49} - 4 q^{52} - 12 q^{55} + 42 q^{58} - 4 q^{61} - 8 q^{64} + 36 q^{67} - 18 q^{76} - 4 q^{79} + 24 q^{82} + 12 q^{88} + 102 q^{91} - 12 q^{94} - 12 q^{97}+O(q^{100}) $ 8 * q + 4 * q^4 + 6 * q^7 + 4 * q^10 - 2 * q^13 - 4 * q^16 - 18 * q^19 - 12 * q^22 - 8 * q^25 + 6 * q^28 - 12 * q^37 + 8 * q^40 - 14 * q^43 - 30 * q^46 + 26 * q^49 - 4 * q^52 - 12 * q^55 + 42 * q^58 - 4 * q^61 - 8 * q^64 + 36 * q^67 - 18 * q^76 - 4 * q^79 + 24 * q^82 + 12 * q^88 + 102 * q^91 - 12 * q^94 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$911$	$937$	$1081$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		0			0
$7$	−2.34233	+	1.35234i	−0.885317	+	0.511138i	−0.872408	−	0.488779i	$-0.837443\pi$
$7$	−2.34233	+	1.35234i	−0.885317	+	0.511138i	−0.0129093	+	0.999917i	$0.504109\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	2.59808	+	1.50000i	0.783349	+	0.452267i	0.837616	−	0.546259i	$-0.183949\pi$
$11$	2.59808	+	1.50000i	0.783349	+	0.452267i	−0.0542666	+	0.998526i	$0.517282\pi$
$12$		0			0
$13$	−3.34233	−	1.35234i	−0.926995	−	0.375073i
$13$	−3.34233	−	1.35234i	−0.926995	−	0.375073i
$14$	2.70469			0.722858
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$		0			0
$19$	−5.34233	+	3.08440i	−1.22561	+	0.707609i	−0.966109	−	0.258133i	$-0.916893\pi$
$19$	−5.34233	+	3.08440i	−1.22561	+	0.707609i	−0.259505	+	0.965742i	$0.583559\pi$
$20$	−0.866025	+	0.500000i	−0.193649	+	0.111803i
$21$		0			0
$22$	−1.50000	−	2.59808i	−0.319801	−	0.553912i
$23$	3.95042	−	6.84233i	0.823720	−	1.42672i	−0.0791743	−	0.996861i	$-0.525228\pi$
$23$	3.95042	−	6.84233i	0.823720	−	1.42672i	0.902894	−	0.429863i	$-0.141438\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	2.21837	+	2.84233i	0.435058	+	0.557427i
$27$		0			0
$28$	−2.34233	−	1.35234i	−0.442659	−	0.255569i
$29$	−1.24573	+	2.15767i	−0.231327	+	0.400669i	−0.958199	−	0.286103i	$-0.907640\pi$
$29$	−1.24573	+	2.15767i	−0.231327	+	0.400669i	0.726872	+	0.686773i	$0.240973\pi$
$30$		0			0
$31$			0.972638i			0.174691i	0.996178	+	0.0873455i	$0.0278384\pi$
$31$			0.972638i			0.174691i	−0.996178	+	0.0873455i	$0.972162\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$		0			0
$35$	−1.35234	−	2.34233i	−0.228588	−	0.395926i
$36$		0			0
$37$	−1.50000	−	0.866025i	−0.246598	−	0.142374i	0.371607	−	0.928390i	$-0.378807\pi$
$37$	−1.50000	−	0.866025i	−0.246598	−	0.142374i	−0.618206	+	0.786016i	$0.712140\pi$
$38$	6.16879			1.00071
$39$		0			0
$40$	1.00000			0.158114
$41$	−5.19615	−	3.00000i	−0.811503	−	0.468521i	0.0359748	−	0.999353i	$-0.488546\pi$
$41$	−5.19615	−	3.00000i	−0.811503	−	0.468521i	−0.847477	+	0.530831i	$0.821880\pi$
$42$		0			0
$43$	−4.84233	−	8.38716i	−0.738448	−	1.27903i	−0.953194	−	0.302360i	$-0.902226\pi$
$43$	−4.84233	−	8.38716i	−0.738448	−	1.27903i	0.214746	−	0.976670i	$-0.431108\pi$
$44$			3.00000i			0.452267i
$45$		0			0
$46$	−6.84233	+	3.95042i	−1.00885	+	0.582458i
$47$		−	3.00000i		−	0.437595i	−0.975770	−	0.218797i	$-0.929787\pi$
$47$		−	3.00000i		−	0.437595i	0.975770	−	0.218797i	$-0.0702134\pi$
$48$		0			0
$49$	0.157671	−	0.273094i	0.0225244	−	0.0390134i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$		0			0
$52$	−0.500000	−	3.57071i	−0.0693375	−	0.495169i
$53$	−2.70469			−0.371518			−0.185759	−	0.982595i	$-0.559474\pi$
$53$	−2.70469			−0.371518			−0.185759	+	0.982595i	$0.559474\pi$
$54$		0			0
$55$	−1.50000	+	2.59808i	−0.202260	+	0.350325i
$56$	1.35234	+	2.34233i	0.180715	+	0.313007i
$57$		0			0
$58$	2.15767	−	1.24573i	0.283316	−	0.163573i
$59$	−6.65511	+	3.84233i	−0.866421	+	0.500229i	−0.866157	−	0.499771i	$-0.833417\pi$
$59$	−6.65511	+	3.84233i	−0.866421	+	0.500229i	−0.000264050		1.00000i	$0.500084\pi$
$60$		0			0
$61$	−6.68466	−	11.5782i	−0.855883	−	1.48243i	−0.875824	−	0.482631i	$-0.839681\pi$
$61$	−6.68466	−	11.5782i	−0.855883	−	1.48243i	0.0199408	−	0.999801i	$-0.493652\pi$
$62$	0.486319	−	0.842329i	0.0617626	−	0.106976i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	1.35234	−	3.34233i	0.167738	−	0.414565i
$66$		0			0
$67$	−1.68466	−	0.972638i	−0.205814	−	0.118827i	0.393551	−	0.919303i	$-0.371247\pi$
$67$	−1.68466	−	0.972638i	−0.205814	−	0.118827i	−0.599364	+	0.800476i	$0.704580\pi$
$68$		0			0
$69$		0			0
$70$			2.70469i			0.323272i
$71$	5.19615	−	3.00000i	0.616670	−	0.356034i	−0.158901	−	0.987294i	$-0.550795\pi$
$71$	5.19615	−	3.00000i	0.616670	−	0.356034i	0.775571	+	0.631260i	$0.217462\pi$
$72$		0			0
$73$			6.92820i			0.810885i	0.914121	+	0.405442i	$0.132883\pi$
$73$			6.92820i			0.810885i	−0.914121	+	0.405442i	$0.867117\pi$
$74$	0.866025	+	1.50000i	0.100673	+	0.174371i
$75$		0			0
$76$	−5.34233	−	3.08440i	−0.612807	−	0.353804i
$77$	−8.11407			−0.924684
$78$		0			0
$79$	5.68466			0.639574			0.319787	−	0.947489i	$-0.396389\pi$
$79$	5.68466			0.639574			0.319787	+	0.947489i	$0.396389\pi$
$80$	−0.866025	−	0.500000i	−0.0968246	−	0.0559017i
$81$		0			0
$82$	3.00000	+	5.19615i	0.331295	+	0.573819i
$83$		−	15.3693i		−	1.68700i	−0.537128	−	0.843501i	$-0.680491\pi$
$83$		−	15.3693i		−	1.68700i	0.537128	−	0.843501i	$-0.319509\pi$
$84$		0			0
$85$		0			0
$86$			9.68466i			1.04432i
$87$		0			0
$88$	1.50000	−	2.59808i	0.159901	−	0.276956i
$89$	4.05703	+	2.34233i	0.430045	+	0.248286i	0.699366	−	0.714764i	$-0.253466\pi$
$89$	4.05703	+	2.34233i	0.430045	+	0.248286i	−0.269321	+	0.963050i	$0.586799\pi$
$90$		0			0
$91$	9.65767	−	1.35234i	1.01240	−	0.141764i
$92$	7.90084			0.823720
$93$		0			0
$94$	−1.50000	+	2.59808i	−0.154713	+	0.267971i
$95$	−3.08440	−	5.34233i	−0.316452	−	0.548111i
$96$		0			0
$97$	−7.68466	+	4.43674i	−0.780259	+	0.450483i	−0.836522	−	0.547933i	$-0.815415\pi$
$97$	−7.68466	+	4.43674i	−0.780259	+	0.450483i	0.0562632	+	0.998416i	$0.482081\pi$
$98$	−0.273094	+	0.157671i	−0.0275866	+	0.0159272i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−5.40938	+	9.36932i	−0.538253	+	0.932282i	0.460745	+	0.887533i	$0.347582\pi$
$101$	−5.40938	+	9.36932i	−0.538253	+	0.932282i	−0.998998	+	0.0447493i	$0.985751\pi$
$102$		0			0
$103$	−14.6847			−1.44692			−0.723461	−	0.690365i	$-0.757450\pi$
$103$	−14.6847			−1.44692			−0.723461	+	0.690365i	$0.757450\pi$
$104$	−1.35234	+	3.34233i	−0.132608	+	0.327742i
$105$		0			0
$106$	2.34233	+	1.35234i	0.227507	+	0.131351i
$107$	−2.70469	+	4.68466i	−0.261472	+	0.452883i	−0.966633	−	0.256164i	$-0.917541\pi$
$107$	−2.70469	+	4.68466i	−0.261472	+	0.452883i	0.705161	+	0.709047i	$0.250875\pi$
$108$		0			0
$109$			12.3376i			1.18173i	0.806772	+	0.590863i	$0.201213\pi$
$109$			12.3376i			1.18173i	−0.806772	+	0.590863i	$0.798787\pi$
$110$	2.59808	−	1.50000i	0.247717	−	0.143019i
$111$		0			0
$112$		−	2.70469i		−	0.255569i
$113$	1.24573	+	2.15767i	0.117189	+	0.202977i	0.918653	−	0.395067i	$-0.129278\pi$
$113$	1.24573	+	2.15767i	0.117189	+	0.202977i	−0.801464	+	0.598043i	$0.795945\pi$
$114$		0			0
$115$	6.84233	+	3.95042i	0.638050	+	0.368379i
$116$	−2.49146			−0.231327
$117$		0			0
$118$	7.68466			0.707430
$119$		0			0
$120$		0			0
$121$	−1.00000	−	1.73205i	−0.0909091	−	0.157459i
$122$			13.3693i			1.21040i
$123$		0			0
$124$	−0.842329	+	0.486319i	−0.0756434	+	0.0436727i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$	−1.34233	+	2.32498i	−0.119112	+	0.206309i	−0.919416	−	0.393286i	$-0.871338\pi$
$127$	−1.34233	+	2.32498i	−0.119112	+	0.206309i	0.800304	+	0.599595i	$0.204672\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	−2.84233	+	2.21837i	−0.249289	+	0.194564i
$131$	−20.9978			−1.83459			−0.917295	−	0.398209i	$-0.869632\pi$
$131$	−20.9978			−1.83459			−0.917295	+	0.398209i	$0.869632\pi$
$132$		0			0
$133$	8.34233	−	14.4493i	0.723372	−	1.25292i
$134$	0.972638	+	1.68466i	0.0840231	+	0.145532i
$135$		0			0
$136$		0			0
$137$	−17.0474	+	9.84233i	−1.45646	+	0.840887i	−0.998835	−	0.0482589i	$-0.984633\pi$
$137$	−17.0474	+	9.84233i	−1.45646	+	0.840887i	−0.457624	+	0.889146i	$0.651299\pi$
$138$		0			0
$139$	−4.65767	−	8.06732i	−0.395058	−	0.684261i	0.598050	−	0.801459i	$-0.295942\pi$
$139$	−4.65767	−	8.06732i	−0.395058	−	0.684261i	−0.993109	+	0.117197i	$0.962609\pi$
$140$	1.35234	−	2.34233i	0.114294	−	0.197963i
$141$		0			0
$142$	−6.00000			−0.503509
$143$	−6.65511	−	8.52699i	−0.556528	−	0.713063i
$144$		0			0
$145$	−2.15767	−	1.24573i	−0.179185	−	0.103452i
$146$	3.46410	−	6.00000i	0.286691	−	0.496564i
$147$		0			0
$148$		−	1.73205i		−	0.142374i
$149$	8.93335	−	5.15767i	0.731848	−	0.422533i	−0.0872496	−	0.996186i	$-0.527808\pi$
$149$	8.93335	−	5.15767i	0.731848	−	0.422533i	0.819098	+	0.573654i	$0.194474\pi$
$150$		0			0
$151$		−	14.2829i		−	1.16232i	−0.813788	−	0.581161i	$-0.802599\pi$
$151$		−	14.2829i		−	1.16232i	0.813788	−	0.581161i	$-0.197401\pi$
$152$	3.08440	+	5.34233i	0.250177	+	0.433320i
$153$		0			0
$154$	7.02699	+	4.05703i	0.566251	+	0.326925i
$155$	−0.972638			−0.0781242
$156$		0			0
$157$	8.36932			0.667944			0.333972	−	0.942583i	$-0.391611\pi$
$157$	8.36932			0.667944			0.333972	+	0.942583i	$0.391611\pi$
$158$	−4.92306	−	2.84233i	−0.391658	−	0.226124i
$159$		0			0
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$			21.3693i			1.68414i
$162$		0			0
$163$	−15.8423	+	9.14657i	−1.24087	+	0.716415i	−0.969271	−	0.245996i	$-0.920885\pi$
$163$	−15.8423	+	9.14657i	−1.24087	+	0.716415i	−0.271596	+	0.962411i	$0.587552\pi$
$164$		−	6.00000i		−	0.468521i
$165$		0			0
$166$	−7.68466	+	13.3102i	−0.596445	+	1.03307i
$167$	−5.51599	−	3.18466i	−0.426840	−	0.246436i	0.271159	−	0.962534i	$-0.412593\pi$
$167$	−5.51599	−	3.18466i	−0.426840	−	0.246436i	−0.698000	+	0.716098i	$0.745926\pi$
$168$		0			0
$169$	9.34233	+	9.03996i	0.718641	+	0.695382i
$170$		0			0
$171$		0			0
$172$	4.84233	−	8.38716i	0.369224	−	0.639515i
$173$	−4.05703	−	7.02699i	−0.308451	−	0.534252i	0.669573	−	0.742746i	$-0.266477\pi$
$173$	−4.05703	−	7.02699i	−0.308451	−	0.534252i	−0.978024	+	0.208494i	$0.933144\pi$
$174$		0			0
$175$	2.34233	−	1.35234i	0.177063	−	0.102228i
$176$	−2.59808	+	1.50000i	−0.195837	+	0.113067i
$177$		0			0
$178$	−2.34233	−	4.05703i	−0.175565	−	0.304087i
$179$	6.44188	−	11.1577i	0.481489	−	0.833963i	−0.518285	−	0.855208i	$-0.673429\pi$
$179$	6.44188	−	11.1577i	0.481489	−	0.833963i	0.999774	+	0.0212443i	$0.00676279\pi$
$180$		0			0
$181$	5.36932			0.399098			0.199549	−	0.979888i	$-0.436052\pi$
$181$	5.36932			0.399098			0.199549	+	0.979888i	$0.436052\pi$
$182$	−9.03996	−	3.65767i	−0.670086	−	0.271125i
$183$		0			0
$184$	−6.84233	−	3.95042i	−0.504423	−	0.291229i
$185$	0.866025	−	1.50000i	0.0636715	−	0.110282i
$186$		0			0
$187$		0			0
$188$	2.59808	−	1.50000i	0.189484	−	0.109399i
$189$		0			0
$190$			6.16879i			0.447531i
$191$	10.6055	+	18.3693i	0.767389	+	1.32916i	0.938974	+	0.343988i	$0.111778\pi$
$191$	10.6055	+	18.3693i	0.767389	+	1.32916i	−0.171585	+	0.985169i	$0.554889\pi$
$192$		0			0
$193$	13.6847	+	7.90084i	0.985043	+	0.568715i	0.903789	−	0.427978i	$-0.140774\pi$
$193$	13.6847	+	7.90084i	0.985043	+	0.568715i	0.0812543	+	0.996693i	$0.474107\pi$
$194$	8.87348			0.637079
$195$		0			0
$196$	0.315342			0.0225244
$197$	17.3673	+	10.0270i	1.23737	+	0.714393i	0.968555	−	0.248800i	$-0.0800361\pi$
$197$	17.3673	+	10.0270i	1.23737	+	0.714393i	0.268811	+	0.963193i	$0.413369\pi$
$198$		0			0
$199$	8.68466	+	15.0423i	0.615639	+	1.06632i	0.990272	+	0.139145i	$0.0444354\pi$
$199$	8.68466	+	15.0423i	0.615639	+	1.06632i	−0.374633	+	0.927173i	$0.622231\pi$
$200$			1.00000i			0.0707107i
$201$		0			0
$202$	9.36932	−	5.40938i	0.659223	−	0.380602i
$203$		−	6.73863i		−	0.472959i
$204$		0			0
$205$	3.00000	−	5.19615i	0.209529	−	0.362915i
$206$	12.7173	+	7.34233i	0.886055	+	0.511564i
$207$		0			0
$208$	2.84233	−	2.21837i	0.197080	−	0.153816i
$209$	−18.5064			−1.28011
$210$		0			0
$211$	3.34233	−	5.78908i	0.230095	−	0.398537i	−0.727741	−	0.685853i	$-0.759429\pi$
$211$	3.34233	−	5.78908i	0.230095	−	0.398537i	0.957836	+	0.287316i	$0.0927628\pi$
$212$	−1.35234	−	2.34233i	−0.0928794	−	0.160872i
$213$		0			0
$214$	4.68466	−	2.70469i	0.320237	−	0.184889i
$215$	8.38716	−	4.84233i	0.572000	−	0.330244i
$216$		0			0
$217$	−1.31534	−	2.27824i	−0.0892912	−	0.154657i
$218$	6.16879	−	10.6847i	0.417803	−	0.723656i
$219$		0			0
$220$	−3.00000			−0.202260
$221$		0			0
$222$		0			0
$223$	6.65767	+	3.84381i	0.445831	+	0.257400i	0.706068	−	0.708144i	$-0.250467\pi$
$223$	6.65767	+	3.84381i	0.445831	+	0.257400i	−0.260237	+	0.965545i	$0.583801\pi$
$224$	−1.35234	+	2.34233i	−0.0903573	+	0.156503i
$225$		0			0
$226$		−	2.49146i		−	0.165730i
$227$	2.91791	−	1.68466i	0.193669	−	0.111815i	−0.400030	−	0.916502i	$-0.631000\pi$
$227$	2.91791	−	1.68466i	0.193669	−	0.111815i	0.593699	+	0.804687i	$0.297667\pi$
$228$		0			0
$229$			26.1940i			1.73095i	0.500954	+	0.865474i	$0.332982\pi$
$229$			26.1940i			1.73095i	−0.500954	+	0.865474i	$0.667018\pi$
$230$	−3.95042	−	6.84233i	−0.260483	−	0.451170i
$231$		0			0
$232$	2.15767	+	1.24573i	0.141658	+	0.0817863i
$233$	−12.8838			−0.844044			−0.422022	−	0.906586i	$-0.638679\pi$
$233$	−12.8838			−0.844044			−0.422022	+	0.906586i	$0.638679\pi$
$234$		0			0
$235$	3.00000			0.195698
$236$	−6.65511	−	3.84233i	−0.433211	−	0.250114i
$237$		0			0
$238$		0			0
$239$		−	24.7386i		−	1.60021i	−0.599861	−	0.800105i	$-0.704777\pi$
$239$		−	24.7386i		−	1.60021i	0.599861	−	0.800105i	$-0.295223\pi$
$240$		0			0
$241$	−5.81534	+	3.35749i	−0.374599	+	0.216275i	−0.675466	−	0.737391i	$-0.736057\pi$
$241$	−5.81534	+	3.35749i	−0.374599	+	0.216275i	0.300867	+	0.953666i	$0.402724\pi$
$242$			2.00000i			0.128565i
$243$		0			0
$244$	6.68466	−	11.5782i	0.427941	−	0.741216i
$245$	0.273094	+	0.157671i	0.0174473	+	0.0100732i
$246$		0			0
$247$	22.0270	−	3.08440i	1.40154	−	0.196255i
$248$	0.972638			0.0617626
$249$		0			0
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	2.59808	+	4.50000i	0.163989	+	0.284037i	0.936296	−	0.351212i	$-0.114230\pi$
$251$	2.59808	+	4.50000i	0.163989	+	0.284037i	−0.772307	+	0.635250i	$0.780897\pi$
$252$		0			0
$253$	20.5270	−	11.8513i	1.29052	−	0.745082i
$254$	2.32498	−	1.34233i	0.145882	−	0.0842252i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	11.6380	−	20.1577i	0.725961	−	1.25740i	−0.232617	−	0.972569i	$-0.574729\pi$
$257$	11.6380	−	20.1577i	0.725961	−	1.25740i	0.958577	−	0.284832i	$-0.0919380\pi$
$258$		0			0
$259$	4.68466			0.291091
$260$	3.57071	−	0.500000i	0.221446	−	0.0310087i
$261$		0			0
$262$	18.1847	+	10.4989i	1.12345	+	0.648625i
$263$	15.9083	−	27.5540i	0.980947	−	1.69905i	0.322228	−	0.946662i	$-0.395568\pi$
$263$	15.9083	−	27.5540i	0.980947	−	1.69905i	0.658719	−	0.752389i	$-0.271099\pi$
$264$		0			0
$265$		−	2.70469i		−	0.166148i
$266$	−14.4493	+	8.34233i	−0.885946	+	0.511501i
$267$		0			0
$268$		−	1.94528i		−	0.118827i
$269$	5.40938	+	9.36932i	0.329816	+	0.571257i	0.982475	−	0.186394i	$-0.0596801\pi$
$269$	5.40938	+	9.36932i	0.329816	+	0.571257i	−0.652659	+	0.757651i	$0.726347\pi$
$270$		0			0
$271$	11.5270	+	6.65511i	0.700215	+	0.404269i	0.807427	−	0.589967i	$-0.200859\pi$
$271$	11.5270	+	6.65511i	0.700215	+	0.404269i	−0.107213	+	0.994236i	$0.534193\pi$
$272$		0			0
$273$		0			0
$274$	19.6847			1.18919
$275$	−2.59808	−	1.50000i	−0.156670	−	0.0904534i
$276$		0			0
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	0.880656	−	0.473757i	$-0.157103\pi$
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	−0.850613	+	0.525792i	$0.823769\pi$
$278$			9.31534i			0.558697i
$279$		0			0
$280$	−2.34233	+	1.35234i	−0.139981	+	0.0808180i
$281$			24.7386i			1.47578i	0.674919	+	0.737892i	$0.264178\pi$
$281$			24.7386i			1.47578i	−0.674919	+	0.737892i	$0.735822\pi$
$282$		0			0
$283$	6.52699	−	11.3051i	0.387989	−	0.672017i	−0.604190	−	0.796840i	$-0.706503\pi$
$283$	6.52699	−	11.3051i	0.387989	−	0.672017i	0.992179	+	0.124824i	$0.0398365\pi$
$284$	5.19615	+	3.00000i	0.308335	+	0.178017i
$285$		0			0
$286$	1.50000	+	10.7121i	0.0886969	+	0.633422i
$287$	16.2281			0.957916
$288$		0			0
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$	1.24573	+	2.15767i	0.0731519	+	0.126703i
$291$		0			0
$292$	−6.00000	+	3.46410i	−0.351123	+	0.202721i
$293$	19.6455	−	11.3423i	1.14770	−	0.662626i	0.199376	−	0.979923i	$-0.436109\pi$
$293$	19.6455	−	11.3423i	1.14770	−	0.662626i	0.948326	+	0.317297i	$0.102775\pi$
$294$		0			0
$295$	−3.84233	−	6.65511i	−0.223709	−	0.387475i
$296$	−0.866025	+	1.50000i	−0.0503367	+	0.0871857i
$297$		0			0
$298$	−10.3153			−0.597552
$299$	−22.4568	+	17.5270i	−1.29871	+	1.01361i
$300$		0			0
$301$	22.6847	+	13.0970i	1.30752	+	0.754898i
$302$	−7.14143	+	12.3693i	−0.410943	+	0.711774i
$303$		0			0
$304$		−	6.16879i		−	0.353804i
$305$	11.5782	−	6.68466i	0.662964	−	0.382762i
$306$		0			0
$307$			14.2829i			0.815166i	0.913168	+	0.407583i	$0.133628\pi$
$307$			14.2829i			0.815166i	−0.913168	+	0.407583i	$0.866372\pi$
$308$	−4.05703	−	7.02699i	−0.231171	−	0.400400i
$309$		0			0
$310$	0.842329	+	0.486319i	0.0478411	+	0.0276211i
$311$	−4.98293			−0.282556			−0.141278	−	0.989970i	$-0.545121\pi$
$311$	−4.98293			−0.282556			−0.141278	+	0.989970i	$0.545121\pi$
$312$		0			0
$313$	−5.36932			−0.303492			−0.151746	−	0.988420i	$-0.548490\pi$
$313$	−5.36932			−0.303492			−0.151746	+	0.988420i	$0.548490\pi$
$314$	−7.24804	−	4.18466i	−0.409031	−	0.236154i
$315$		0			0
$316$	2.84233	+	4.92306i	0.159894	+	0.276944i
$317$			29.4233i			1.65258i	0.563247	+	0.826288i	$0.309552\pi$
$317$			29.4233i			1.65258i	−0.563247	+	0.826288i	$0.690448\pi$
$318$		0			0
$319$	−6.47301	+	3.73720i	−0.362419	+	0.209243i
$320$		−	1.00000i		−	0.0559017i
$321$		0			0
$322$	10.6847	−	18.5064i	0.595433	−	1.03132i
$323$		0			0
$324$		0			0
$325$	3.34233	+	1.35234i	0.185399	+	0.0750146i
$326$	18.2931			1.01316
$327$		0			0
$328$	−3.00000	+	5.19615i	−0.165647	+	0.286910i
$329$	4.05703	+	7.02699i	0.223671	+	0.387410i
$330$		0			0
$331$	8.05398	−	4.64996i	0.442687	−	0.255585i	−0.262050	−	0.965054i	$-0.584399\pi$
$331$	8.05398	−	4.64996i	0.442687	−	0.255585i	0.704737	+	0.709469i	$0.251065\pi$
$332$	13.3102	−	7.68466i	0.730493	−	0.421750i
$333$		0			0
$334$	3.18466	+	5.51599i	0.174257	+	0.301822i
$335$	0.972638	−	1.68466i	0.0531409	−	0.0920427i
$336$		0			0
$337$	−29.3693			−1.59985			−0.799924	−	0.600101i	$-0.795127\pi$
$337$	−29.3693			−1.59985			−0.799924	+	0.600101i	$0.795127\pi$
$338$	−3.57071	−	12.5000i	−0.194221	−	0.679910i
$339$		0			0
$340$		0			0
$341$	−1.45896	+	2.52699i	−0.0790070	+	0.136844i
$342$		0			0
$343$		−	18.0799i		−	0.976224i
$344$	−8.38716	+	4.84233i	−0.452205	+	0.261081i
$345$		0			0
$346$			8.11407i			0.436215i
$347$	2.49146	+	4.31534i	0.133749	+	0.231660i	0.925119	−	0.379678i	$-0.123965\pi$
$347$	2.49146	+	4.31534i	0.133749	+	0.231660i	−0.791370	+	0.611337i	$0.790632\pi$
$348$		0			0
$349$	−29.0540	−	16.7743i	−1.55522	−	0.897909i	−0.997703	−	0.0677460i	$-0.978419\pi$
$349$	−29.0540	−	16.7743i	−1.55522	−	0.897909i	−0.557521	−	0.830163i	$-0.688247\pi$
$350$	−2.70469			−0.144572
$351$		0			0
$352$	3.00000			0.159901
$353$	−13.3102	−	7.68466i	−0.708431	−	0.409013i	0.102049	−	0.994779i	$-0.467460\pi$
$353$	−13.3102	−	7.68466i	−0.708431	−	0.409013i	−0.810480	+	0.585766i	$0.800794\pi$
$354$		0			0
$355$	3.00000	+	5.19615i	0.159223	+	0.275783i
$356$			4.68466i			0.248286i
$357$		0			0
$358$	−11.1577	+	6.44188i	−0.589701	+	0.340464i
$359$			2.63068i			0.138842i	0.997587	+	0.0694211i	$0.0221152\pi$
$359$			2.63068i			0.138842i	−0.997587	+	0.0694211i	$0.977885\pi$
$360$		0			0
$361$	9.52699	−	16.5012i	0.501420	−	0.868486i
$362$	−4.64996	−	2.68466i	−0.244397	−	0.141103i
$363$		0			0
$364$	6.00000	+	7.68762i	0.314485	+	0.402941i
$365$	−6.92820			−0.362639
$366$		0			0
$367$	−11.6847	+	20.2384i	−0.609934	+	1.05644i	0.381317	+	0.924445i	$0.375471\pi$
$367$	−11.6847	+	20.2384i	−0.609934	+	1.05644i	−0.991251	+	0.131992i	$0.957863\pi$
$368$	3.95042	+	6.84233i	0.205930	+	0.356681i
$369$		0			0
$370$	−1.50000	+	0.866025i	−0.0779813	+	0.0450225i
$371$	6.33527	−	3.65767i	0.328911	−	0.189897i
$372$		0			0
$373$	0.526988	+	0.912769i	0.0272864	+	0.0472614i	0.879346	−	0.476183i	$-0.157980\pi$
$373$	0.526988	+	0.912769i	0.0272864	+	0.0472614i	−0.852060	+	0.523445i	$0.824647\pi$
$374$		0			0
$375$		0			0
$376$	−3.00000			−0.154713
$377$	7.08156	−	5.52699i	0.364719	−	0.284654i
$378$		0			0
$379$	−0.288354	−	0.166481i	−0.0148117	−	0.00855157i	0.492576	−	0.870270i	$-0.336055\pi$
$379$	−0.288354	−	0.166481i	−0.0148117	−	0.00855157i	−0.507388	+	0.861718i	$0.669389\pi$
$380$	3.08440	−	5.34233i	0.158226	−	0.274056i
$381$		0			0
$382$		−	21.2111i		−	1.08525i
$383$	6.65511	−	3.84233i	0.340060	−	0.196334i	−0.320238	−	0.947337i	$-0.603763\pi$
$383$	6.65511	−	3.84233i	0.340060	−	0.196334i	0.660299	+	0.751003i	$0.270430\pi$
$384$		0			0
$385$		−	8.11407i		−	0.413531i
$386$	−7.90084	−	13.6847i	−0.402142	−	0.696531i
$387$		0			0
$388$	−7.68466	−	4.43674i	−0.390129	−	0.225241i
$389$	24.1290			1.22339			0.611694	−	0.791095i	$-0.290488\pi$
$389$	24.1290			1.22339			0.611694	+	0.791095i	$0.290488\pi$
$390$		0			0
$391$		0			0
$392$	−0.273094	−	0.157671i	−0.0137933	−	0.00796358i
$393$		0			0
$394$	−10.0270	−	17.3673i	−0.505152	−	0.874950i
$395$			5.68466i			0.286026i
$396$		0			0
$397$	−30.1847	+	17.4271i	−1.51492	+	0.874642i	−0.515078	+	0.857143i	$0.672237\pi$
$397$	−30.1847	+	17.4271i	−1.51492	+	0.874642i	−0.999847	+	0.0174986i	$0.994430\pi$
$398$		−	17.3693i		−	0.870645i
$399$		0			0
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	1.77879	+	1.02699i	0.0888288	+	0.0512853i	0.543756	−	0.839243i	$-0.317002\pi$
$401$	1.77879	+	1.02699i	0.0888288	+	0.0512853i	−0.454928	+	0.890528i	$0.650335\pi$
$402$		0			0
$403$	1.31534	−	3.25088i	0.0655218	−	0.161938i
$404$	−10.8188			−0.538253
$405$		0			0
$406$	−3.36932	+	5.83583i	−0.167216	+	0.289627i
$407$	−2.59808	−	4.50000i	−0.128782	−	0.223057i
$408$		0			0
$409$	−11.7116	+	6.76172i	−0.579104	+	0.334346i	−0.760777	−	0.649013i	$-0.775182\pi$
$409$	−11.7116	+	6.76172i	−0.579104	+	0.334346i	0.181673	+	0.983359i	$0.441849\pi$
$410$	−5.19615	+	3.00000i	−0.256620	+	0.148159i
$411$		0			0
$412$	−7.34233	−	12.7173i	−0.361731	−	0.626536i
$413$	10.3923	−	18.0000i	0.511372	−	0.885722i
$414$		0			0
$415$	15.3693			0.754450
$416$	−3.57071	+	0.500000i	−0.175069	+	0.0245145i
$417$		0			0
$418$	16.0270	+	9.25319i	0.783906	+	0.452588i
$419$	0.213225	−	0.369317i	0.0104167	−	0.0180423i	−0.860770	−	0.508994i	$-0.830018\pi$
$419$	0.213225	−	0.369317i	0.0104167	−	0.0180423i	0.871187	+	0.490952i	$0.163351\pi$
$420$		0			0
$421$		−	26.6204i		−	1.29740i	−0.761044	−	0.648700i	$-0.775313\pi$
$421$		−	26.6204i		−	1.29740i	0.761044	−	0.648700i	$-0.224687\pi$
$422$	−5.78908	+	3.34233i	−0.281808	+	0.162702i
$423$		0			0
$424$			2.70469i			0.131351i
$425$		0			0
$426$		0			0
$427$	31.3153	+	18.0799i	1.51546	+	0.874949i
$428$	−5.40938			−0.261472
$429$		0			0
$430$	−9.68466			−0.467036
$431$	2.91791	+	1.68466i	0.140551	+	0.0811471i	0.568627	−	0.822596i	$-0.307475\pi$
$431$	2.91791	+	1.68466i	0.140551	+	0.0811471i	−0.428076	+	0.903743i	$0.640808\pi$
$432$		0			0
$433$	17.6847	+	30.6307i	0.849870	+	1.47202i	0.881323	+	0.472514i	$0.156653\pi$
$433$	17.6847	+	30.6307i	0.849870	+	1.47202i	−0.0314530	+	0.999505i	$0.510013\pi$
$434$			2.63068i			0.126277i
$435$		0			0
$436$	−10.6847	+	6.16879i	−0.511702	+	0.295431i
$437$			48.7386i			2.33149i
$438$		0			0
$439$	3.31534	−	5.74234i	0.158233	−	0.274067i	−0.775999	−	0.630734i	$-0.782754\pi$
$439$	3.31534	−	5.74234i	0.158233	−	0.274067i	0.934231	+	0.356667i	$0.116087\pi$
$440$	2.59808	+	1.50000i	0.123858	+	0.0715097i
$441$		0			0
$442$		0			0
$443$	10.3923			0.493753			0.246877	−	0.969047i	$-0.420596\pi$
$443$	10.3923			0.493753			0.246877	+	0.969047i	$0.420596\pi$
$444$		0			0
$445$	−2.34233	+	4.05703i	−0.111037	+	0.192322i
$446$	−3.84381	−	6.65767i	−0.182010	−	0.315250i
$447$		0			0
$448$	2.34233	−	1.35234i	0.110665	−	0.0638923i
$449$	−24.8416	+	14.3423i	−1.17235	+	0.676856i	−0.954232	−	0.299066i	$-0.903325\pi$
$449$	−24.8416	+	14.3423i	−1.17235	+	0.676856i	−0.218117	+	0.975923i	$0.569992\pi$
$450$		0			0
$451$	−9.00000	−	15.5885i	−0.423793	−	0.734032i
$452$	−1.24573	+	2.15767i	−0.0585943	+	0.101488i
$453$		0			0
$454$	−3.36932			−0.158130
$455$	1.35234	+	9.65767i	0.0633989	+	0.452759i
$456$		0			0
$457$	−3.00000	−	1.73205i	−0.140334	−	0.0810219i	0.428189	−	0.903689i	$-0.359152\pi$
$457$	−3.00000	−	1.73205i	−0.140334	−	0.0810219i	−0.568523	+	0.822667i	$0.692485\pi$
$458$	13.0970	−	22.6847i	0.611982	−	1.05998i
$459$		0			0
$460$			7.90084i			0.368379i
$461$	3.73720	−	2.15767i	0.174059	−	0.100493i	−0.410440	−	0.911888i	$-0.634625\pi$
$461$	3.73720	−	2.15767i	0.174059	−	0.100493i	0.584498	+	0.811395i	$0.301291\pi$
$462$		0			0
$463$			30.0845i			1.39815i	0.715050	+	0.699074i	$0.246404\pi$
$463$			30.0845i			1.39815i	−0.715050	+	0.699074i	$0.753596\pi$
$464$	−1.24573	−	2.15767i	−0.0578316	−	0.100167i
$465$		0			0
$466$	11.1577	+	6.44188i	0.516869	+	0.298415i
$467$	−21.6375			−1.00126			−0.500632	−	0.865660i	$-0.666899\pi$
$467$	−21.6375			−1.00126			−0.500632	+	0.865660i	$0.666899\pi$
$468$		0			0
$469$	5.26137			0.242947
$470$	−2.59808	−	1.50000i	−0.119840	−	0.0691898i
$471$		0			0
$472$	3.84233	+	6.65511i	0.176858	+	0.306326i
$473$		−	29.0540i		−	1.33590i
$474$		0			0
$475$	5.34233	−	3.08440i	0.245123	−	0.141522i
$476$		0			0
$477$		0			0
$478$	−12.3693	+	21.4243i	−0.565759	+	0.979924i
$479$	23.7025	+	13.6847i	1.08300	+	0.625268i	0.931703	−	0.363221i	$-0.118323\pi$
$479$	23.7025	+	13.6847i	1.08300	+	0.625268i	0.151293	+	0.988489i	$0.451656\pi$
$480$		0			0
$481$	3.84233	+	4.92306i	0.175195	+	0.224472i
$482$	6.71498			0.305859
$483$		0			0
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$	−4.43674	−	7.68466i	−0.201462	−	0.348942i
$486$		0			0
$487$	−17.3423	+	10.0126i	−0.785856	+	0.453714i	−0.838502	−	0.544899i	$-0.816568\pi$
$487$	−17.3423	+	10.0126i	−0.785856	+	0.453714i	0.0526457	+	0.998613i	$0.483235\pi$
$488$	−11.5782	+	6.68466i	−0.524119	+	0.302600i
$489$		0			0
$490$	−0.157671	−	0.273094i	−0.00712284	−	0.0123371i
$491$	6.54850	−	11.3423i	0.295530	−	0.511872i	−0.679578	−	0.733603i	$-0.737837\pi$
$491$	6.54850	−	11.3423i	0.295530	−	0.511872i	0.975108	+	0.221731i	$0.0711706\pi$
$492$		0			0
$493$		0			0
$494$	−20.6181	−	8.34233i	−0.927653	−	0.375339i
$495$		0			0
$496$	−0.842329	−	0.486319i	−0.0378217	−	0.0218364i
$497$	−8.11407	+	14.0540i	−0.363966	+	0.630407i
$498$		0			0
$499$		−	32.0298i		−	1.43385i	−0.697150	−	0.716926i	$-0.745549\pi$
$499$		−	32.0298i		−	1.43385i	0.697150	−	0.716926i	$-0.254451\pi$
$500$	0.866025	−	0.500000i	0.0387298	−	0.0223607i
$501$		0			0
$502$		−	5.19615i		−	0.231916i
$503$	14.2361	+	24.6577i	0.634757	+	1.09943i	0.986567	+	0.163360i	$0.0522331\pi$
$503$	14.2361	+	24.6577i	0.634757	+	1.09943i	−0.351810	+	0.936072i	$0.614434\pi$
$504$		0			0
$505$	−9.36932	−	5.40938i	−0.416929	−	0.240714i
$506$	−23.7025			−1.05371
$507$		0			0
$508$	−2.68466			−0.119112
$509$	8.93335	+	5.15767i	0.395964	+	0.228610i	0.684741	−	0.728787i	$-0.259915\pi$
$509$	8.93335	+	5.15767i	0.395964	+	0.228610i	−0.288777	+	0.957396i	$0.593249\pi$
$510$		0			0
$511$	−9.36932	−	16.2281i	−0.414474	−	0.717890i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−20.1577	+	11.6380i	−0.889117	+	0.513332i
$515$		−	14.6847i		−	0.647083i
$516$		0			0
$517$	4.50000	−	7.79423i	0.197910	−	0.342790i
$518$	−4.05703	−	2.34233i	−0.178256	−	0.102916i
$519$		0			0
$520$	−3.34233	−	1.35234i	−0.146571	−	0.0593042i
$521$	−13.0970			−0.573790			−0.286895	−	0.957962i	$-0.592623\pi$
$521$	−13.0970			−0.573790			−0.286895	+	0.957962i	$0.592623\pi$
$522$		0			0
$523$	−0.526988	+	0.912769i	−0.0230436	+	0.0399126i	−0.877317	−	0.479911i	$-0.840669\pi$
$523$	−0.526988	+	0.912769i	−0.0230436	+	0.0399126i	0.854274	+	0.519824i	$0.174002\pi$
$524$	−10.4989	−	18.1847i	−0.458647	−	0.794400i
$525$		0			0
$526$	−27.5540	+	15.9083i	−1.20141	+	0.693635i
$527$		0			0
$528$		0			0
$529$	−19.7116	−	34.1416i	−0.857028	−	1.48442i
$530$	−1.35234	+	2.34233i	−0.0587421	+	0.101744i
$531$		0			0
$532$	16.6847			0.723372
$533$	13.3102	+	17.0540i	0.576530	+	0.738690i
$534$		0			0
$535$	−4.68466	−	2.70469i	−0.202535	−	0.116934i
$536$	−0.972638	+	1.68466i	−0.0420116	+	0.0727662i
$537$		0			0
$538$		−	10.8188i		−	0.466430i
$539$	0.819281	−	0.473012i	0.0352889	−	0.0203741i
$540$		0			0
$541$			40.0504i			1.72190i	0.508689	+	0.860950i	$0.330130\pi$
$541$			40.0504i			1.72190i	−0.508689	+	0.860950i	$0.669870\pi$
$542$	−6.65511	−	11.5270i	−0.285861	−	0.495127i
$543$		0			0
$544$		0			0
$545$	−12.3376			−0.528484
$546$		0			0
$547$	−32.1080			−1.37284			−0.686418	−	0.727207i	$-0.740818\pi$
$547$	−32.1080			−1.37284			−0.686418	+	0.727207i	$0.740818\pi$
$548$	−17.0474	−	9.84233i	−0.728229	−	0.420443i
$549$		0			0
$550$	1.50000	+	2.59808i	0.0639602	+	0.110782i
$551$		−	15.3693i		−	0.654755i
$552$		0			0
$553$	−13.3153	+	7.68762i	−0.566226	+	0.326911i
$554$		−	1.00000i		−	0.0424859i
$555$		0			0
$556$	4.65767	−	8.06732i	0.197529	−	0.342131i
$557$	−1.13912	−	0.657671i	−0.0482660	−	0.0278664i	0.475673	−	0.879622i	$-0.342205\pi$
$557$	−1.13912	−	0.657671i	−0.0482660	−	0.0278664i	−0.523939	+	0.851756i	$0.675538\pi$
$558$		0			0
$559$	4.84233	+	34.5811i	0.204809	+	1.46263i
$560$	2.70469			0.114294
$561$		0			0
$562$	12.3693	−	21.4243i	0.521768	−	0.903729i
$563$	−12.8838	−	22.3153i	−0.542986	−	0.940480i	−0.998731	−	0.0503689i	$-0.983960\pi$
$563$	−12.8838	−	22.3153i	−0.542986	−	0.940480i	0.455745	−	0.890111i	$-0.349373\pi$
$564$		0			0
$565$	−2.15767	+	1.24573i	−0.0907739	+	0.0524083i
$566$	−11.3051	+	6.52699i	−0.475188	+	0.274350i
$567$		0			0
$568$	−3.00000	−	5.19615i	−0.125877	−	0.218026i
$569$	−14.6626	+	25.3963i	−0.614687	+	1.06467i	0.375753	+	0.926720i	$0.377384\pi$
$569$	−14.6626	+	25.3963i	−0.614687	+	1.06467i	−0.990439	+	0.137949i	$0.955949\pi$
$570$		0			0
$571$	−40.0540			−1.67621			−0.838103	−	0.545511i	$-0.816335\pi$
$571$	−40.0540			−1.67621			−0.838103	+	0.545511i	$0.816335\pi$
$572$	4.05703	−	10.0270i	0.169633	−	0.419249i
$573$		0			0
$574$	−14.0540	−	8.11407i	−0.586602	−	0.338675i
$575$	−3.95042	+	6.84233i	−0.164744	+	0.285345i
$576$		0			0
$577$		−	29.2316i		−	1.21693i	−0.793581	−	0.608465i	$-0.791786\pi$
$577$		−	29.2316i		−	1.21693i	0.793581	−	0.608465i	$-0.208214\pi$
$578$	−14.7224	+	8.50000i	−0.612372	+	0.353553i
$579$		0			0
$580$		−	2.49146i		−	0.103452i
$581$	20.7846	+	36.0000i	0.862291	+	1.49353i
$582$		0			0
$583$	−7.02699	−	4.05703i	−0.291028	−	0.168025i
$584$	6.92820			0.286691
$585$		0			0
$586$	−22.6847			−0.937095
$587$	8.11407	+	4.68466i	0.334903	+	0.193357i	0.658016	−	0.753004i	$-0.271396\pi$
$587$	8.11407	+	4.68466i	0.334903	+	0.193357i	−0.323113	+	0.946361i	$0.604729\pi$
$588$		0			0
$589$	−3.00000	−	5.19615i	−0.123613	−	0.214104i
$590$			7.68466i			0.316372i
$591$		0			0
$592$	1.50000	−	0.866025i	0.0616496	−	0.0355934i
$593$			38.4233i			1.57786i	0.614486	+	0.788928i	$0.289363\pi$
$593$			38.4233i			1.57786i	−0.614486	+	0.788928i	$0.710637\pi$
$594$		0			0
$595$		0			0
$596$	8.93335	+	5.15767i	0.365924	+	0.211266i
$597$		0			0
$598$	28.2116	−	3.95042i	1.15366	−	0.161545i
$599$	0.426450			0.0174243			0.00871215	−	0.999962i	$-0.497227\pi$
$599$	0.426450			0.0174243			0.00871215	+	0.999962i	$0.497227\pi$
$600$		0			0
$601$	17.5000	−	30.3109i	0.713840	−	1.23641i	−0.249565	−	0.968358i	$-0.580288\pi$
$601$	17.5000	−	30.3109i	0.713840	−	1.23641i	0.963405	−	0.268049i	$-0.0863789\pi$
$602$	−13.0970	−	22.6847i	−0.533794	−	0.924558i
$603$		0			0
$604$	12.3693	−	7.14143i	0.503300	−	0.290581i
$605$	1.73205	−	1.00000i	0.0704179	−	0.0406558i
$606$		0			0
$607$	−2.97301	−	5.14941i	−0.120671	−	0.209008i	0.799362	−	0.600850i	$-0.205171\pi$
$607$	−2.97301	−	5.14941i	−0.120671	−	0.209008i	−0.920032	+	0.391842i	$0.871838\pi$
$608$	−3.08440	+	5.34233i	−0.125089	+	0.216660i
$609$		0			0
$610$	−13.3693			−0.541308
$611$	−4.05703	+	10.0270i	−0.164130	+	0.405649i
$612$		0			0
$613$	−10.5000	−	6.06218i	−0.424091	−	0.244849i	0.272735	−	0.962089i	$-0.412072\pi$
$613$	−10.5000	−	6.06218i	−0.424091	−	0.244849i	−0.696826	+	0.717240i	$0.745405\pi$
$614$	7.14143	−	12.3693i	0.288205	−	0.499185i
$615$		0			0
$616$			8.11407i			0.326925i
$617$	11.8513	−	6.84233i	0.477114	−	0.275462i	−0.242099	−	0.970252i	$-0.577836\pi$
$617$	11.8513	−	6.84233i	0.477114	−	0.275462i	0.719213	+	0.694790i	$0.244503\pi$
$618$		0			0
$619$		−	3.13114i		−	0.125851i	−0.998018	−	0.0629256i	$-0.979957\pi$
$619$		−	3.13114i		−	0.125851i	0.998018	−	0.0629256i	$-0.0200431\pi$
$620$	−0.486319	−	0.842329i	−0.0195310	−	0.0338288i
$621$		0			0
$622$	4.31534	+	2.49146i	0.173029	+	0.0998986i
$623$	−12.6705			−0.507635
$624$		0			0
$625$	1.00000			0.0400000
$626$	4.64996	+	2.68466i	0.185850	+	0.107301i
$627$		0			0
$628$	4.18466	+	7.24804i	0.166986	+	0.289228i
$629$		0			0
$630$		0			0
$631$	−19.6847	+	11.3649i	−0.783634	+	0.452431i	−0.837717	−	0.546105i	$-0.816110\pi$
$631$	−19.6847	+	11.3649i	−0.783634	+	0.452431i	0.0540827	+	0.998536i	$0.482777\pi$
$632$		−	5.68466i		−	0.226124i
$633$		0			0
$634$	14.7116	−	25.4813i	0.584274	−	1.01199i
$635$	−2.32498	−	1.34233i	−0.0922641	−	0.0532687i
$636$		0			0
$637$	−0.896305	+	0.699544i	−0.0355129	+	0.0277170i
$638$	7.47439			0.295914
$639$		0			0
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	19.8587	+	34.3963i	0.784372	+	1.35857i	0.929373	+	0.369141i	$0.120348\pi$
$641$	19.8587	+	34.3963i	0.784372	+	1.35857i	−0.145001	+	0.989431i	$0.546319\pi$
$642$		0			0
$643$	−29.0540	+	16.7743i	−1.14578	+	0.661515i	−0.947855	−	0.318703i	$-0.896753\pi$
$643$	−29.0540	+	16.7743i	−1.14578	+	0.661515i	−0.197922	+	0.980218i	$0.563419\pi$
$644$	−18.5064	+	10.6847i	−0.729253	+	0.421035i
$645$		0			0
$646$		0			0
$647$	17.3673	−	30.0810i	0.682777	−	1.18260i	−0.291353	−	0.956616i	$-0.594105\pi$
$647$	17.3673	−	30.0810i	0.682777	−	1.18260i	0.974130	−	0.225989i	$-0.0725613\pi$
$648$		0			0
$649$	−23.0540			−0.904948
$650$	−2.21837	−	2.84233i	−0.0870116	−	0.111485i
$651$		0			0
$652$	−15.8423	−	9.14657i	−0.620433	−	0.358207i
$653$	−11.5314	+	19.9730i	−0.451259	+	0.781604i	−0.998465	−	0.0553942i	$-0.982358\pi$
$653$	−11.5314	+	19.9730i	−0.451259	+	0.781604i	0.547205	+	0.836999i	$0.315692\pi$
$654$		0			0
$655$		−	20.9978i		−	0.820453i
$656$	5.19615	−	3.00000i	0.202876	−	0.117130i
$657$		0			0
$658$		−	8.11407i		−	0.316319i
$659$	−16.8342	−	29.1577i	−0.655767	−	1.13582i	−0.981701	−	0.190429i	$-0.939012\pi$
$659$	−16.8342	−	29.1577i	−0.655767	−	1.13582i	0.325934	−	0.945393i	$-0.394321\pi$
$660$		0			0
$661$	9.00000	+	5.19615i	0.350059	+	0.202107i	0.664711	−	0.747100i	$-0.268554\pi$
$661$	9.00000	+	5.19615i	0.350059	+	0.202107i	−0.314652	+	0.949207i	$0.601888\pi$
$662$	−9.29993			−0.361452
$663$		0			0
$664$	−15.3693			−0.596445
$665$	14.4493	+	8.34233i	0.560321	+	0.323502i
$666$		0			0
$667$	9.84233	+	17.0474i	0.381097	+	0.660079i
$668$		−	6.36932i		−	0.246436i
$669$		0			0
$670$	−1.68466	+	0.972638i	−0.0650840	+	0.0375763i
$671$		−	40.1080i		−	1.54835i
$672$		0			0
$673$	−16.0000	+	27.7128i	−0.616755	+	1.06825i	0.373319	+	0.927703i	$0.378220\pi$
$673$	−16.0000	+	27.7128i	−0.616755	+	1.06825i	−0.990074	+	0.140548i	$0.955114\pi$
$674$	25.4346	+	14.6847i	0.979703	+	0.565632i
$675$		0			0
$676$	−3.15767	+	12.6107i	−0.121449	+	0.485026i
$677$	−36.5863			−1.40613			−0.703063	−	0.711128i	$-0.748185\pi$
$677$	−36.5863			−1.40613			−0.703063	+	0.711128i	$0.748185\pi$
$678$		0			0
$679$	12.0000	−	20.7846i	0.460518	−	0.797640i
$680$		0			0
$681$		0			0
$682$	2.52699	−	1.45896i	0.0967634	−	0.0558664i
$683$	2.27824	−	1.31534i	0.0871744	−	0.0503301i	−0.455779	−	0.890093i	$-0.650639\pi$
$683$	2.27824	−	1.31534i	0.0871744	−	0.0503301i	0.542954	+	0.839763i	$0.317306\pi$
$684$		0			0
$685$	−9.84233	−	17.0474i	−0.376056	−	0.651348i
$686$	−9.03996	+	15.6577i	−0.345147	+	0.597813i
$687$		0			0
$688$	9.68466			0.369224
$689$	9.03996	+	3.65767i	0.344395	+	0.139346i
$690$		0			0
$691$	−4.02699	−	2.32498i	−0.153194	−	0.0884465i	0.421444	−	0.906855i	$-0.361524\pi$
$691$	−4.02699	−	2.32498i	−0.153194	−	0.0884465i	−0.574637	+	0.818408i	$0.694857\pi$
$692$	4.05703	−	7.02699i	0.154225	−	0.267126i
$693$		0			0
$694$		−	4.98293i		−	0.189149i
$695$	8.06732	−	4.65767i	0.306011	−	0.176676i
$696$		0			0
$697$		0			0
$698$	16.7743	+	29.0540i	0.634917	+	1.09971i
$699$		0			0
$700$	2.34233	+	1.35234i	0.0885317	+	0.0511138i
$701$	−23.2761			−0.879125			−0.439563	−	0.898212i	$-0.644867\pi$
$701$	−23.2761			−0.879125			−0.439563	+	0.898212i	$0.644867\pi$
$702$		0			0
$703$	10.6847			0.402980
$704$	−2.59808	−	1.50000i	−0.0979187	−	0.0565334i
$705$		0			0
$706$	7.68466	+	13.3102i	0.289216	+	0.500937i
$707$		−	29.2614i		−	1.10049i
$708$		0			0
$709$	−27.3693	+	15.8017i	−1.02788	+	0.593445i	−0.916376	−	0.400320i	$-0.868899\pi$
$709$	−27.3693	+	15.8017i	−1.02788	+	0.593445i	−0.111501	+	0.993764i	$0.535566\pi$
$710$		−	6.00000i		−	0.225176i
$711$		0			0
$712$	2.34233	−	4.05703i	0.0877825	−	0.152044i
$713$	6.65511	+	3.84233i	0.249236	+	0.143896i
$714$		0			0
$715$	8.52699	−	6.65511i	0.318891	−	0.248887i
$716$	12.8838			0.481489
$717$		0			0
$718$	1.31534	−	2.27824i	0.0490881	−	0.0850231i
$719$	−4.98293	−	8.63068i	−0.185832	−	0.321870i	0.758025	−	0.652226i	$-0.226165\pi$
$719$	−4.98293	−	8.63068i	−0.185832	−	0.321870i	−0.943857	+	0.330356i	$0.892831\pi$
$720$		0			0
$721$	34.3963	−	19.8587i	1.28099	−	0.739577i
$722$	−16.5012	+	9.52699i	−0.614112	+	0.354558i
$723$		0			0
$724$	2.68466	+	4.64996i	0.0997745	+	0.172815i
$725$	1.24573	−	2.15767i	0.0462653	−	0.0801339i
$726$		0			0
$727$	−36.6847			−1.36056			−0.680279	−	0.732953i	$-0.738142\pi$
$727$	−36.6847			−1.36056			−0.680279	+	0.732953i	$0.738142\pi$
$728$	−1.35234	−	9.65767i	−0.0501212	−	0.357937i
$729$		0			0
$730$	6.00000	+	3.46410i	0.222070	+	0.128212i
$731$		0			0
$732$		0			0
$733$		−	26.5269i		−	0.979795i	−0.871780	−	0.489898i	$-0.837034\pi$
$733$		−	26.5269i		−	0.979795i	0.871780	−	0.489898i	$-0.162966\pi$
$734$	20.2384	−	11.6847i	0.747014	−	0.431289i
$735$		0			0
$736$		−	7.90084i		−	0.291229i
$737$	−2.91791	−	5.05398i	−0.107483	−	0.186166i
$738$		0			0
$739$	1.97301	+	1.13912i	0.0725784	+	0.0419032i	0.535850	−	0.844313i	$-0.319991\pi$
$739$	1.97301	+	1.13912i	0.0725784	+	0.0419032i	−0.463272	+	0.886216i	$0.653325\pi$
$740$	1.73205			0.0636715
$741$		0			0
$742$	−7.31534			−0.268555
$743$	17.0474	+	9.84233i	0.625409	+	0.361080i	0.778972	−	0.627059i	$-0.215741\pi$
$743$	17.0474	+	9.84233i	0.625409	+	0.361080i	−0.153563	+	0.988139i	$0.549075\pi$
$744$		0			0
$745$	5.15767	+	8.93335i	0.188962	+	0.327293i
$746$		−	1.05398i		−	0.0385888i
$747$		0			0
$748$		0			0
$749$		−	14.6307i		−	0.534594i
$750$		0			0
$751$	17.8423	−	30.9038i	0.651076	−	1.12770i	−0.331786	−	0.943355i	$-0.607651\pi$
$751$	17.8423	−	30.9038i	0.651076	−	1.12770i	0.982862	−	0.184342i	$-0.0590154\pi$
$752$	2.59808	+	1.50000i	0.0947421	+	0.0546994i
$753$		0			0
$754$	−8.89630	+	1.24573i	−0.323984	+	0.0453669i
$755$	14.2829			0.519806
$756$		0			0
$757$	−18.0270	+	31.2237i	−0.655202	+	1.13484i	0.326641	+	0.945148i	$0.394083\pi$
$757$	−18.0270	+	31.2237i	−0.655202	+	1.13484i	−0.981843	+	0.189695i	$0.939250\pi$
$758$	0.166481	+	0.288354i	0.00604687	+	0.0104735i
$759$		0			0
$760$	−5.34233	+	3.08440i	−0.193787	+	0.111883i
$761$	12.1711	−	7.02699i	0.441202	−	0.254728i	−0.262905	−	0.964822i	$-0.584681\pi$
$761$	12.1711	−	7.02699i	0.441202	−	0.254728i	0.704107	+	0.710094i	$0.251347\pi$
$762$		0			0
$763$	−16.6847	−	28.8987i	−0.604025	−	1.04620i
$764$	−10.6055	+	18.3693i	−0.383695	+	0.664579i
$765$		0			0
$766$	−7.68466			−0.277658
$767$	27.4397	−	3.84233i	0.990791	−	0.138738i
$768$		0			0
$769$	−19.2116	−	11.0918i	−0.692790	−	0.399982i	0.111867	−	0.993723i	$-0.464317\pi$
$769$	−19.2116	−	11.0918i	−0.692790	−	0.399982i	−0.804656	+	0.593741i	$0.797650\pi$
$770$	−4.05703	+	7.02699i	−0.146205	+	0.253235i
$771$		0			0
$772$			15.8017i			0.568715i
$773$	−35.2339	+	20.3423i	−1.26728	+	0.731663i	−0.974472	−	0.224509i	$-0.927922\pi$
$773$	−35.2339	+	20.3423i	−1.26728	+	0.731663i	−0.292805	+	0.956172i	$0.594589\pi$
$774$		0			0
$775$		−	0.972638i		−	0.0349382i
$776$	4.43674	+	7.68466i	0.159270	+	0.275863i
$777$		0			0
$778$	−20.8963	−	12.0645i	−0.749169	−	0.432533i
$779$	37.0127			1.32612
$780$		0			0
$781$	18.0000			0.644091
$782$		0			0
$783$		0			0
$784$	0.157671	+	0.273094i	0.00563110	+	0.00975335i
$785$			8.36932i			0.298714i
$786$		0			0
$787$	3.84233	−	2.21837i	0.136964	−	0.0790763i	−0.429952	−	0.902852i	$-0.641470\pi$
$787$	3.84233	−	2.21837i	0.136964	−	0.0790763i	0.566916	+	0.823775i	$0.308136\pi$
$788$			20.0540i			0.714393i
$789$		0			0
$790$	2.84233	−	4.92306i	0.101126	−	0.175155i
$791$	−5.83583	−	3.36932i	−0.207498	−	0.119799i
$792$		0			0
$793$	6.68466	+	47.7380i	0.237379	+	1.69523i
$794$	34.8542			1.23693
$795$		0			0
$796$	−8.68466	+	15.0423i	−0.307820	+	0.533159i
$797$	−10.8188	−	18.7386i	−0.383220	−	0.663756i	0.608301	−	0.793707i	$-0.291852\pi$
$797$	−10.8188	−	18.7386i	−0.383220	−	0.663756i	−0.991521	+	0.129950i	$0.958518\pi$
$798$		0			0
$799$		0			0
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$		0			0
$802$	−1.02699	−	1.77879i	−0.0362642	−	0.0628114i
$803$	−10.3923	+	18.0000i	−0.366736	+	0.635206i
$804$		0			0
$805$	−21.3693			−0.753169
$806$	−2.76456	+	2.15767i	−0.0973774	+	0.0760007i
$807$		0			0
$808$	9.36932	+	5.40938i	0.329611	+	0.190301i
$809$	−10.3923	+	18.0000i	−0.365374	+	0.632846i	−0.988836	−	0.149007i	$-0.952392\pi$
$809$	−10.3923	+	18.0000i	−0.365374	+	0.632846i	0.623462	+	0.781854i	$0.285726\pi$
$810$		0			0
$811$			27.3799i			0.961437i	0.876875	+	0.480718i	$0.159624\pi$
$811$			27.3799i			0.961437i	−0.876875	+	0.480718i	$0.840376\pi$
$812$	5.83583	−	3.36932i	0.204797	−	0.118240i
$813$		0			0
$814$			5.19615i			0.182125i
$815$	−9.14657	−	15.8423i	−0.320390	−	0.554933i
$816$		0			0
$817$	51.7386	+	29.8713i	1.81011	+	1.04506i
$818$	13.5234			0.472836
$819$		0			0
$820$	6.00000			0.209529
$821$	−35.5538	−	20.5270i	−1.24084	−	0.716397i	−0.271571	−	0.962418i	$-0.587543\pi$
$821$	−35.5538	−	20.5270i	−1.24084	−	0.716397i	−0.969264	+	0.246022i	$0.920877\pi$
$822$		0			0
$823$	5.65767	+	9.79937i	0.197214	+	0.341585i	0.947624	−	0.319388i	$-0.103477\pi$
$823$	5.65767	+	9.79937i	0.197214	+	0.341585i	−0.750410	+	0.660973i	$0.770144\pi$
$824$			14.6847i			0.511564i
$825$		0			0
$826$	−18.0000	+	10.3923i	−0.626300	+	0.361595i
$827$			14.6307i			0.508759i	0.967105	+	0.254379i	$0.0818712\pi$
$827$			14.6307i			0.508759i	−0.967105	+	0.254379i	$0.918129\pi$
$828$		0			0
$829$	−17.3693	+	30.0845i	−0.603261	+	1.04488i	0.389062	+	0.921211i	$0.372799\pi$
$829$	−17.3693	+	30.0845i	−0.603261	+	1.04488i	−0.992324	+	0.123668i	$0.960534\pi$
$830$	−13.3102	−	7.68466i	−0.462004	−	0.266738i
$831$		0			0
$832$	3.34233	+	1.35234i	0.115874	+	0.0468841i
$833$		0			0
$834$		0			0
$835$	3.18466	−	5.51599i	0.110210	−	0.190889i
$836$	−9.25319	−	16.0270i	−0.320028	−	0.554305i
$837$		0			0
$838$	−0.369317	+	0.213225i	−0.0127578	+	0.00736574i
$839$	42.2089	−	24.3693i	1.45721	−	0.841322i	0.458340	−	0.888777i	$-0.348444\pi$
$839$	42.2089	−	24.3693i	1.45721	−	0.841322i	0.998873	+	0.0474549i	$0.0151111\pi$
$840$		0			0
$841$	11.3963	+	19.7390i	0.392976	+	0.680654i
$842$	−13.3102	+	23.0540i	−0.458700	+	0.794492i
$843$		0			0
$844$	6.68466			0.230095
$845$	−9.03996	+	9.34233i	−0.310984	+	0.321386i
$846$		0			0
$847$	4.68466	+	2.70469i	0.160967	+	0.0929342i
$848$	1.35234	−	2.34233i	0.0464397	−	0.0804359i
$849$		0			0
$850$		0			0
$851$	−11.8513	+	6.84233i	−0.406256	+	0.234552i
$852$		0			0
$853$			2.49146i			0.0853061i	0.999090	+	0.0426530i	$0.0135810\pi$
$853$			2.49146i			0.0853061i	−0.999090	+	0.0426530i	$0.986419\pi$
$854$	−18.0799	−	31.3153i	−0.618682	−	1.07159i
$855$		0			0
$856$	4.68466	+	2.70469i	0.160118	+	0.0924444i
$857$	12.8838			0.440101			0.220051	−	0.975488i	$-0.429378\pi$
$857$	12.8838			0.440101			0.220051	+	0.975488i	$0.429378\pi$
$858$		0			0
$859$	18.0540			0.615994			0.307997	−	0.951387i	$-0.400341\pi$
$859$	18.0540			0.615994			0.307997	+	0.951387i	$0.400341\pi$
$860$	8.38716	+	4.84233i	0.286000	+	0.165122i
$861$		0			0
$862$	−1.68466	−	2.91791i	−0.0573797	−	0.0993845i
$863$		−	28.3153i		−	0.963865i	−0.876208	−	0.481933i	$-0.839935\pi$
$863$		−	28.3153i		−	0.963865i	0.876208	−	0.481933i	$-0.160065\pi$
$864$		0			0
$865$	7.02699	−	4.05703i	0.238925	−	0.137943i
$866$		−	35.3693i		−	1.20190i
$867$		0			0
$868$	1.31534	−	2.27824i	0.0446456	−	0.0773285i
$869$	14.7692	+	8.52699i	0.501010	+	0.289258i
$870$		0			0
$871$	4.31534	+	5.52911i	0.146220	+	0.187347i
$872$	12.3376			0.417803
$873$		0			0
$874$	24.3693	−	42.2089i	0.824304	−	1.42774i
$875$	1.35234	+	2.34233i	0.0457176	+	0.0791852i
$876$		0			0
$877$	−9.84233	+	5.68247i	−0.332352	+	0.191883i	−0.656885	−	0.753991i	$-0.728126\pi$
$877$	−9.84233	+	5.68247i	−0.332352	+	0.191883i	0.324533	+	0.945874i	$0.394793\pi$
$878$	−5.74234	+	3.31534i	−0.193795	+	0.111887i
$879$		0			0
$880$	−1.50000	−	2.59808i	−0.0505650	−	0.0875811i
$881$	17.1540	−	29.7116i	0.577934	−	1.00101i	−0.417782	−	0.908547i	$-0.637192\pi$
$881$	17.1540	−	29.7116i	0.577934	−	1.00101i	0.995716	−	0.0924636i	$-0.0294742\pi$
$882$		0			0
$883$	14.3153			0.481750			0.240875	−	0.970556i	$-0.422566\pi$
$883$	14.3153			0.481750			0.240875	+	0.970556i	$0.422566\pi$
$884$		0			0
$885$		0			0
$886$	−9.00000	−	5.19615i	−0.302361	−	0.174568i
$887$	−23.3827	+	40.5000i	−0.785114	+	1.35986i	0.143817	+	0.989604i	$0.454062\pi$
$887$	−23.3827	+	40.5000i	−0.785114	+	1.35986i	−0.928931	+	0.370253i	$0.879271\pi$
$888$		0			0
$889$		−	7.26117i		−	0.243532i
$890$	4.05703	−	2.34233i	0.135992	−	0.0785151i
$891$		0			0
$892$			7.68762i			0.257400i
$893$	9.25319	+	16.0270i	0.309646	+	0.536323i
$894$		0			0
$895$	11.1577	+	6.44188i	0.372960	+	0.215328i
$896$	−2.70469			−0.0903573
$897$		0			0
$898$	28.6847			0.957219
$899$	−2.09863	−	1.21165i	−0.0699933	−	0.0404107i
$900$		0			0
$901$		0			0
$902$			18.0000i			0.599334i
$903$		0			0
$904$	2.15767	−	1.24573i	0.0717631	−	0.0414324i
$905$			5.36932i			0.178482i
$906$		0			0
$907$	15.1577	−	26.2539i	0.503302	−	0.871745i	−0.496691	−	0.867928i	$-0.665452\pi$
$907$	15.1577	−	26.2539i	0.503302	−	0.871745i	0.999993	−	0.00381726i	$-0.00121507\pi$
$908$	2.91791	+	1.68466i	0.0968344	+	0.0559074i
$909$		0			0
$910$	3.65767	−	9.03996i	0.121251	−	0.299672i
$911$	37.4392			1.24042			0.620208	−	0.784437i	$-0.287048\pi$
$911$	37.4392			1.24042			0.620208	+	0.784437i	$0.287048\pi$
$912$		0			0
$913$	23.0540	−	39.9307i	0.762975	−	1.32151i
$914$	1.73205	+	3.00000i	0.0572911	+	0.0992312i
$915$		0			0
$916$	−22.6847	+	13.0970i	−0.749522	+	0.432737i
$917$	49.1838	−	28.3963i	1.62419	−	0.937729i
$918$		0			0
$919$	−0.684658	−	1.18586i	−0.0225848	−	0.0391180i	0.854512	−	0.519431i	$-0.173856\pi$
$919$	−0.684658	−	1.18586i	−0.0225848	−	0.0391180i	−0.877097	+	0.480313i	$0.840523\pi$
$920$	3.95042	−	6.84233i	0.130242	−	0.225585i
$921$		0			0
$922$	−4.31534			−0.142118
$923$	−21.4243	+	3.00000i	−0.705189	+	0.0987462i
$924$		0			0
$925$	1.50000	+	0.866025i	0.0493197	+	0.0284747i
$926$	15.0423	−	26.0540i	0.494320	−	0.856187i
$927$		0			0
$928$			2.49146i			0.0817863i
$929$	39.2910	−	22.6847i	1.28910	−	0.744260i	0.310602	−	0.950540i	$-0.399469\pi$
$929$	39.2910	−	22.6847i	1.28910	−	0.744260i	0.978493	+	0.206280i	$0.0661359\pi$
$930$		0			0
$931$			1.94528i			0.0637538i
$932$	−6.44188	−	11.1577i	−0.211011	−	0.365482i
$933$		0			0
$934$	18.7386	+	10.8188i	0.613147	+	0.354000i
$935$		0			0
$936$		0			0
$937$	28.7386			0.938850			0.469425	−	0.882972i	$-0.344461\pi$
$937$	28.7386			0.938850			0.469425	+	0.882972i	$0.344461\pi$
$938$	−4.55648	−	2.63068i	−0.148774	−	0.0858948i
$939$		0			0
$940$	1.50000	+	2.59808i	0.0489246	+	0.0847399i
$941$		−	27.3693i		−	0.892214i	−0.894980	−	0.446107i	$-0.852810\pi$
$941$		−	27.3693i		−	0.892214i	0.894980	−	0.446107i	$-0.147190\pi$
$942$		0			0
$943$	−41.0540	+	23.7025i	−1.33690	+	0.771860i
$944$		−	7.68466i		−	0.250114i
$945$		0			0
$946$	−14.5270	+	25.1615i	−0.472313	+	0.818070i
$947$	−31.8166	−	18.3693i	−1.03390	−	0.596923i	−0.115801	−	0.993272i	$-0.536943\pi$
$947$	−31.8166	−	18.3693i	−1.03390	−	0.596923i	−0.918100	+	0.396350i	$0.870277\pi$
$948$		0			0
$949$	9.36932	−	23.1563i	0.304141	−	0.751686i
$950$	−6.16879			−0.200142
$951$		0			0
$952$		0			0
$953$	25.1615	+	43.5810i	0.815060	+	1.41173i	0.909285	+	0.416175i	$0.136630\pi$
$953$	25.1615	+	43.5810i	0.815060	+	1.41173i	−0.0942243	+	0.995551i	$0.530037\pi$
$954$		0			0
$955$	−18.3693	+	10.6055i	−0.594417	+	0.343187i
$956$	21.4243	−	12.3693i	0.692911	−	0.400052i
$957$		0			0
$958$	−13.6847	−	23.7025i	−0.442131	−	0.765794i
$959$	26.6204	−	46.1080i	0.859619	−	1.48890i
$960$		0			0
$961$	30.0540			0.969483
$962$	−0.866025	−	6.18466i	−0.0279218	−	0.199401i
$963$		0			0
$964$	−5.81534	−	3.35749i	−0.187300	−	0.108137i
$965$	−7.90084	+	13.6847i	−0.254337	+	0.440525i
$966$		0			0
$967$			4.64996i			0.149533i	0.997201	+	0.0747664i	$0.0238211\pi$
$967$			4.64996i			0.149533i	−0.997201	+	0.0747664i	$0.976179\pi$
$968$	−1.73205	+	1.00000i	−0.0556702	+	0.0321412i
$969$		0			0
$970$			8.87348i			0.284910i
$971$	1.13912	+	1.97301i	0.0365561	+	0.0633170i	0.883725	−	0.468007i	$-0.155028\pi$
$971$	1.13912	+	1.97301i	0.0365561	+	0.0633170i	−0.847169	+	0.531324i	$0.821695\pi$
$972$		0			0
$973$	21.8196	+	12.5976i	0.699504	+	0.403859i
$974$	20.0252			0.641649
$975$		0			0
$976$	13.3693			0.427941
$977$	−25.8012	−	14.8963i	−0.825452	−	0.476575i	0.0268408	−	0.999640i	$-0.491455\pi$
$977$	−25.8012	−	14.8963i	−0.825452	−	0.476575i	−0.852293	+	0.523065i	$0.824789\pi$
$978$		0			0
$979$	7.02699	+	12.1711i	0.224583	+	0.388990i
$980$			0.315342i			0.0100732i
$981$		0			0
$982$	−11.3423	+	6.54850i	−0.361948	+	0.208971i
$983$			33.0000i			1.05254i	0.850319	+	0.526268i	$0.176409\pi$
$983$			33.0000i			1.05254i	−0.850319	+	0.526268i	$0.823591\pi$
$984$		0			0
$985$	−10.0270	+	17.3673i	−0.319486	+	0.553367i
$986$		0			0
$987$		0			0
$988$	13.6847	+	17.5337i	0.435367	+	0.557822i
$989$	−76.5169			−2.43310
$990$		0			0
$991$	25.8963	−	44.8537i	0.822623	−	1.42483i	−0.0810991	−	0.996706i	$-0.525843\pi$
$991$	25.8963	−	44.8537i	0.822623	−	1.42483i	0.903722	−	0.428119i	$-0.140824\pi$
$992$	0.486319	+	0.842329i	0.0154406	+	0.0267440i
$993$		0			0
$994$	14.0540	−	8.11407i	0.445765	−	0.257363i
$995$	−15.0423	+	8.68466i	−0.476872	+	0.275322i
$996$		0			0
$997$	−24.7116	−	42.8018i	−0.782626	−	1.35555i	−0.930407	−	0.366527i	$-0.880547\pi$
$997$	−24.7116	−	42.8018i	−0.782626	−	1.35555i	0.147782	−	0.989020i	$-0.452787\pi$
$998$	−16.0149	+	27.7386i	−0.506943	+	0.878051i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.bs.h.901.1	yes	8
3.2	odd	2	inner	1170.2.bs.h.901.3	yes	8
13.10	even	6	inner	1170.2.bs.h.361.1	✓	8
39.23	odd	6	inner	1170.2.bs.h.361.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1170.2.bs.h.361.1	✓	8	13.10	even	6	inner
1170.2.bs.h.361.3	yes	8	39.23	odd	6	inner
1170.2.bs.h.901.1	yes	8	1.1	even	1	trivial
1170.2.bs.h.901.3	yes	8	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.bs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000i q^{5} +(-2.34233 + 1.35234i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000i q^{5} +(-2.34233 + 1.35234i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{10} +(2.59808 + 1.50000i) q^{11} +(-3.34233 - 1.35234i) q^{13} +2.70469 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-5.34233 + 3.08440i) q^{19} +(-0.866025 + 0.500000i) q^{20} +(-1.50000 - 2.59808i) q^{22} +(3.95042 - 6.84233i) q^{23} -1.00000 q^{25} +(2.21837 + 2.84233i) q^{26} +(-2.34233 - 1.35234i) q^{28} +(-1.24573 + 2.15767i) q^{29} +0.972638i q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.35234 - 2.34233i) q^{35} +(-1.50000 - 0.866025i) q^{37} +6.16879 q^{38} +1.00000 q^{40} +(-5.19615 - 3.00000i) q^{41} +(-4.84233 - 8.38716i) q^{43} +3.00000i q^{44} +(-6.84233 + 3.95042i) q^{46} -3.00000i q^{47} +(0.157671 - 0.273094i) q^{49} +(0.866025 + 0.500000i) q^{50} +(-0.500000 - 3.57071i) q^{52} -2.70469 q^{53} +(-1.50000 + 2.59808i) q^{55} +(1.35234 + 2.34233i) q^{56} +(2.15767 - 1.24573i) q^{58} +(-6.65511 + 3.84233i) q^{59} +(-6.68466 - 11.5782i) q^{61} +(0.486319 - 0.842329i) q^{62} -1.00000 q^{64} +(1.35234 - 3.34233i) q^{65} +(-1.68466 - 0.972638i) q^{67} +2.70469i q^{70} +(5.19615 - 3.00000i) q^{71} +6.92820i q^{73} +(0.866025 + 1.50000i) q^{74} +(-5.34233 - 3.08440i) q^{76} -8.11407 q^{77} +5.68466 q^{79} +(-0.866025 - 0.500000i) q^{80} +(3.00000 + 5.19615i) q^{82} -15.3693i q^{83} +9.68466i q^{86} +(1.50000 - 2.59808i) q^{88} +(4.05703 + 2.34233i) q^{89} +(9.65767 - 1.35234i) q^{91} +7.90084 q^{92} +(-1.50000 + 2.59808i) q^{94} +(-3.08440 - 5.34233i) q^{95} +(-7.68466 + 4.43674i) q^{97} +(-0.273094 + 0.157671i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} + 6 q^{7}+O(q^{10}) \) 8 * q + 4 * q^4 + 6 * q^7	\( 8 q + 4 q^{4} + 6 q^{7} + 4 q^{10} - 2 q^{13} - 4 q^{16} - 18 q^{19} - 12 q^{22} - 8 q^{25} + 6 q^{28} - 12 q^{37} + 8 q^{40} - 14 q^{43} - 30 q^{46} + 26 q^{49} - 4 q^{52} - 12 q^{55} + 42 q^{58} - 4 q^{61} - 8 q^{64} + 36 q^{67} - 18 q^{76} - 4 q^{79} + 24 q^{82} + 12 q^{88} + 102 q^{91} - 12 q^{94} - 12 q^{97}+O(q^{100}) \) 8 * q + 4 * q^4 + 6 * q^7 + 4 * q^10 - 2 * q^13 - 4 * q^16 - 18 * q^19 - 12 * q^22 - 8 * q^25 + 6 * q^28 - 12 * q^37 + 8 * q^40 - 14 * q^43 - 30 * q^46 + 26 * q^49 - 4 * q^52 - 12 * q^55 + 42 * q^58 - 4 * q^61 - 8 * q^64 + 36 * q^67 - 18 * q^76 - 4 * q^79 + 24 * q^82 + 12 * q^88 + 102 * q^91 - 12 * q^94 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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