LMFDB - Embedded newform 1170.2.bs.h.901.4

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			901.4
Root			$-2.21837 - 1.28078i$ of defining polynomial
Character	$\chi$	$=$	1170.901
Dual form			1170.2.bs.h.361.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(3.84233 - 2.21837i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(3.84233 - 2.21837i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{10} +(-2.59808 - 1.50000i) q^{11} +(2.84233 + 2.21837i) q^{13} +4.43674 q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.842329 - 0.486319i) q^{19} +(0.866025 - 0.500000i) q^{20} +(-1.50000 - 2.59808i) q^{22} +(-0.379706 + 0.657671i) q^{23} -1.00000 q^{25} +(1.35234 + 3.34233i) q^{26} +(3.84233 + 2.21837i) q^{28} +(4.81645 - 8.34233i) q^{29} -6.16879i q^{31} +(-0.866025 + 0.500000i) q^{32} +(-2.21837 - 3.84233i) q^{35} +(-1.50000 - 0.866025i) q^{37} +0.972638 q^{38} +1.00000 q^{40} +(5.19615 + 3.00000i) q^{41} +(1.34233 + 2.32498i) q^{43} -3.00000i q^{44} +(-0.657671 + 0.379706i) q^{46} +3.00000i q^{47} +(6.34233 - 10.9852i) q^{49} +(-0.866025 - 0.500000i) q^{50} +(-0.500000 + 3.57071i) q^{52} -4.43674 q^{53} +(-1.50000 + 2.59808i) q^{55} +(2.21837 + 3.84233i) q^{56} +(8.34233 - 4.81645i) q^{58} +(-4.05703 + 2.34233i) q^{59} +(5.68466 + 9.84612i) q^{61} +(3.08440 - 5.34233i) q^{62} -1.00000 q^{64} +(2.21837 - 2.84233i) q^{65} +(10.6847 + 6.16879i) q^{67} -4.43674i q^{70} +(-5.19615 + 3.00000i) q^{71} +6.92820i q^{73} +(-0.866025 - 1.50000i) q^{74} +(0.842329 + 0.486319i) q^{76} -13.3102 q^{77} -6.68466 q^{79} +(0.866025 + 0.500000i) q^{80} +(3.00000 + 5.19615i) q^{82} -9.36932i q^{83} +2.68466i q^{86} +(1.50000 - 2.59808i) q^{88} +(6.65511 + 3.84233i) q^{89} +(15.8423 + 2.21837i) q^{91} -0.759413 q^{92} +(-1.50000 + 2.59808i) q^{94} +(-0.486319 - 0.842329i) q^{95} +(4.68466 - 2.70469i) q^{97} +(10.9852 - 6.34233i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	3.84233	−	2.21837i	1.45226	−	0.838465i	0.453654	−	0.891178i	$-0.350120\pi$
$7$	3.84233	−	2.21837i	1.45226	−	0.838465i	0.998610	+	0.0527128i	$0.0167868\pi$
$8$			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	0.0542666	−	0.998526i	$-0.482718\pi$
$11$	−2.59808	−	1.50000i	−0.783349	−	0.452267i	−0.837616	+	0.546259i	$0.816051\pi$
$12$		0			0
$13$	2.84233	+	2.21837i	0.788320	+	0.615265i
$13$	2.84233	+	2.21837i	0.788320	+	0.615265i
$14$	4.43674			1.18577
$15$		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
$19$	0.842329	−	0.486319i	0.193244	−	0.111569i	−0.400257	−	0.916403i	$-0.631079\pi$
$19$	0.842329	−	0.486319i	0.193244	−	0.111569i	0.593500	+	0.804834i	$0.297746\pi$
$20$	0.866025	−	0.500000i	0.193649	−	0.111803i
$21$		0			0
$22$	−1.50000	−	2.59808i	−0.319801	−	0.553912i
$23$	−0.379706	+	0.657671i	−0.0791743	+	0.137134i	−0.902894	−	0.429863i	$-0.858562\pi$
$23$	−0.379706	+	0.657671i	−0.0791743	+	0.137134i	0.823720	+	0.566997i	$0.191895\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	1.35234	+	3.34233i	0.265217	+	0.655485i
$27$		0			0
$28$	3.84233	+	2.21837i	0.726132	+	0.419232i
$29$	4.81645	−	8.34233i	0.894392	−	1.54913i	0.0598358	−	0.998208i	$-0.480942\pi$
$29$	4.81645	−	8.34233i	0.894392	−	1.54913i	0.834556	−	0.550923i	$-0.185724\pi$
$30$		0			0
$31$		−	6.16879i		−	1.10795i	−0.832534	−	0.553974i	$-0.813111\pi$
$31$		−	6.16879i		−	1.10795i	0.832534	−	0.553974i	$-0.186889\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$		0			0
$35$	−2.21837	−	3.84233i	−0.374973	−	0.649472i
$36$		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	$0.712140\pi$
$38$	0.972638			0.157783
$39$		0			0
$40$	1.00000			0.158114
$41$	5.19615	+	3.00000i	0.811503	+	0.468521i	0.847477	−	0.530831i	$-0.178120\pi$
$41$	5.19615	+	3.00000i	0.811503	+	0.468521i	−0.0359748	+	0.999353i	$0.511454\pi$
$42$		0			0
$43$	1.34233	+	2.32498i	0.204703	+	0.354556i	0.950038	−	0.312134i	$-0.101044\pi$
$43$	1.34233	+	2.32498i	0.204703	+	0.354556i	−0.745335	+	0.666690i	$0.767710\pi$
$44$		−	3.00000i		−	0.452267i
$45$		0			0
$46$	−0.657671	+	0.379706i	−0.0969683	+	0.0559847i
$47$			3.00000i			0.437595i	0.975770	+	0.218797i	$0.0702134\pi$
$47$			3.00000i			0.437595i	−0.975770	+	0.218797i	$0.929787\pi$
$48$		0			0
$49$	6.34233	−	10.9852i	0.906047	−	1.56932i
$50$	−0.866025	−	0.500000i	−0.122474	−	0.0707107i
$51$		0			0
$52$	−0.500000	+	3.57071i	−0.0693375	+	0.495169i
$53$	−4.43674			−0.609433			−0.304717	−	0.952443i	$-0.598562\pi$
$53$	−4.43674			−0.609433			−0.304717	+	0.952443i	$0.598562\pi$
$54$		0			0
$55$	−1.50000	+	2.59808i	−0.202260	+	0.350325i
$56$	2.21837	+	3.84233i	0.296442	+	0.513453i
$57$		0			0
$58$	8.34233	−	4.81645i	1.09540	−	0.632430i
$59$	−4.05703	+	2.34233i	−0.528181	+	0.304945i	−0.740275	−	0.672304i	$-0.765305\pi$
$59$	−4.05703	+	2.34233i	−0.528181	+	0.304945i	0.212095	+	0.977249i	$0.431972\pi$
$60$		0			0
$61$	5.68466	+	9.84612i	0.727846	+	1.26067i	0.957792	+	0.287463i	$0.0928117\pi$
$61$	5.68466	+	9.84612i	0.727846	+	1.26067i	−0.229946	+	0.973203i	$0.573855\pi$
$62$	3.08440	−	5.34233i	0.391719	−	0.678476i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	2.21837	−	2.84233i	0.275155	−	0.352548i
$66$		0			0
$67$	10.6847	+	6.16879i	1.30534	+	0.753638i	0.981314	−	0.192411i	$-0.0616307\pi$
$67$	10.6847	+	6.16879i	1.30534	+	0.753638i	0.324024	+	0.946049i	$0.394964\pi$
$68$		0			0
$69$		0			0
$70$		−	4.43674i		−	0.530292i
$71$	−5.19615	+	3.00000i	−0.616670	+	0.356034i	−0.775571	−	0.631260i	$-0.782538\pi$
$71$	−5.19615	+	3.00000i	−0.616670	+	0.356034i	0.158901	+	0.987294i	$0.449205\pi$
$72$		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
$76$	0.842329	+	0.486319i	0.0966218	+	0.0557846i
$77$	−13.3102			−1.51684
$78$		0			0
$79$	−6.68466			−0.752083			−0.376041	−	0.926603i	$-0.622715\pi$
$79$	−6.68466			−0.752083			−0.376041	+	0.926603i	$0.622715\pi$
$80$	0.866025	+	0.500000i	0.0968246	+	0.0559017i
$81$		0			0
$82$	3.00000	+	5.19615i	0.331295	+	0.573819i
$83$		−	9.36932i		−	1.02842i	−0.857665	−	0.514208i	$-0.828086\pi$
$83$		−	9.36932i		−	1.02842i	0.857665	−	0.514208i	$-0.171914\pi$
$84$		0			0
$85$		0			0
$86$			2.68466i			0.289494i
$87$		0			0
$88$	1.50000	−	2.59808i	0.159901	−	0.276956i
$89$	6.65511	+	3.84233i	0.705440	+	0.407286i	0.809370	−	0.587299i	$-0.199809\pi$
$89$	6.65511	+	3.84233i	0.705440	+	0.407286i	−0.103930	+	0.994585i	$0.533142\pi$
$90$		0			0
$91$	15.8423	+	2.21837i	1.66073	+	0.232548i
$92$	−0.759413			−0.0791743
$93$		0			0
$94$	−1.50000	+	2.59808i	−0.154713	+	0.267971i
$95$	−0.486319	−	0.842329i	−0.0498953	−	0.0864212i
$96$		0			0
$97$	4.68466	−	2.70469i	0.475655	−	0.274620i	−0.242949	−	0.970039i	$-0.578115\pi$
$97$	4.68466	−	2.70469i	0.475655	−	0.274620i	0.718604	+	0.695420i	$0.244781\pi$
$98$	10.9852	−	6.34233i	1.10968	−	0.640672i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−8.87348	+	15.3693i	−0.882944	+	1.52930i	−0.0348922	+	0.999391i	$0.511109\pi$
$101$	−8.87348	+	15.3693i	−0.882944	+	1.52930i	−0.848052	+	0.529913i	$0.822225\pi$
$102$		0			0
$103$	−2.31534			−0.228137			−0.114069	−	0.993473i	$-0.536388\pi$
$103$	−2.31534			−0.228137			−0.114069	+	0.993473i	$0.536388\pi$
$104$	−2.21837	+	2.84233i	−0.217529	+	0.278713i
$105$		0			0
$106$	−3.84233	−	2.21837i	−0.373200	−	0.215467i
$107$	−4.43674	+	7.68466i	−0.428916	+	0.742904i	−0.996777	−	0.0802202i	$-0.974438\pi$
$107$	−4.43674	+	7.68466i	−0.428916	+	0.742904i	0.567861	+	0.823124i	$0.307771\pi$
$108$		0			0
$109$		−	1.94528i		−	0.186324i	−0.995651	−	0.0931618i	$-0.970303\pi$
$109$		−	1.94528i		−	0.186324i	0.995651	−	0.0931618i	$-0.0296974\pi$
$110$	−2.59808	+	1.50000i	−0.247717	+	0.143019i
$111$		0			0
$112$			4.43674i			0.419232i
$113$	−4.81645	−	8.34233i	−0.453093	−	0.784780i	0.545483	−	0.838122i	$-0.316346\pi$
$113$	−4.81645	−	8.34233i	−0.453093	−	0.784780i	−0.998576	+	0.0533414i	$0.983013\pi$
$114$		0			0
$115$	0.657671	+	0.379706i	0.0613281	+	0.0354078i
$116$	9.63289			0.894392
$117$		0			0
$118$	−4.68466			−0.431258
$119$		0			0
$120$		0			0
$121$	−1.00000	−	1.73205i	−0.0909091	−	0.157459i
$122$			11.3693i			1.02933i
$123$		0			0
$124$	5.34233	−	3.08440i	0.479755	−	0.276987i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$	4.84233	−	8.38716i	0.429687	−	0.744240i	−0.567158	−	0.823609i	$-0.691957\pi$
$127$	4.84233	−	8.38716i	0.429687	−	0.744240i	0.996845	+	0.0793688i	$0.0252905\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	3.34233	−	1.35234i	0.293142	−	0.118608i
$131$	6.71498			0.586690			0.293345	−	0.956007i	$-0.405231\pi$
$131$	6.71498			0.586690			0.293345	+	0.956007i	$0.405231\pi$
$132$		0			0
$133$	2.15767	−	3.73720i	0.187094	−	0.324056i
$134$	6.16879	+	10.6847i	0.532902	+	0.923014i
$135$		0			0
$136$		0			0
$137$	6.33527	−	3.65767i	0.541259	−	0.312496i	−0.204330	−	0.978902i	$-0.565502\pi$
$137$	6.33527	−	3.65767i	0.541259	−	0.312496i	0.745589	+	0.666406i	$0.232168\pi$
$138$		0			0
$139$	−10.8423	−	18.7795i	−0.919634	−	1.59285i	−0.799971	−	0.600039i	$-0.795152\pi$
$139$	−10.8423	−	18.7795i	−0.919634	−	1.59285i	−0.119664	−	0.992814i	$-0.538182\pi$
$140$	2.21837	−	3.84233i	0.187486	−	0.324736i
$141$		0			0
$142$	−6.00000			−0.503509
$143$	−4.05703	−	10.0270i	−0.339266	−	0.838499i
$144$		0			0
$145$	−8.34233	−	4.81645i	−0.692793	−	0.399984i
$146$	−3.46410	+	6.00000i	−0.286691	+	0.496564i
$147$		0			0
$148$		−	1.73205i		−	0.142374i
$149$	−19.6455	+	11.3423i	−1.60942	+	0.929200i	−0.619922	+	0.784664i	$0.712836\pi$
$149$	−19.6455	+	11.3423i	−1.60942	+	0.929200i	−0.989500	+	0.144536i	$0.953831\pi$
$150$		0			0
$151$			14.2829i			1.16232i	0.813788	+	0.581161i	$0.197401\pi$
$151$			14.2829i			1.16232i	−0.813788	+	0.581161i	$0.802599\pi$
$152$	0.486319	+	0.842329i	0.0394457	+	0.0683219i
$153$		0			0
$154$	−11.5270	−	6.65511i	−0.928871	−	0.536284i
$155$	−6.16879			−0.495489
$156$		0			0
$157$	−16.3693			−1.30641			−0.653207	−	0.757180i	$-0.726577\pi$
$157$	−16.3693			−1.30641			−0.653207	+	0.757180i	$0.726577\pi$
$158$	−5.78908	−	3.34233i	−0.460555	−	0.265901i
$159$		0			0
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$			3.36932i			0.265539i
$162$		0			0
$163$	−9.65767	+	5.57586i	−0.756447	+	0.436735i	−0.828019	−	0.560701i	$-0.810532\pi$
$163$	−9.65767	+	5.57586i	−0.756447	+	0.436735i	0.0715715	+	0.997435i	$0.477199\pi$
$164$			6.00000i			0.468521i
$165$		0			0
$166$	4.68466	−	8.11407i	0.363600	−	0.629774i
$167$	−15.9083	−	9.18466i	−1.23102	−	0.710730i	−0.263778	−	0.964583i	$-0.584969\pi$
$167$	−15.9083	−	9.18466i	−1.23102	−	0.710730i	−0.967243	+	0.253853i	$0.918302\pi$
$168$		0			0
$169$	3.15767	+	12.6107i	0.242898	+	0.970052i
$170$		0			0
$171$		0			0
$172$	−1.34233	+	2.32498i	−0.102352	+	0.177278i
$173$	−6.65511	−	11.5270i	−0.505979	−	0.876381i	−0.999976	−	0.00691731i	$-0.997798\pi$
$173$	−6.65511	−	11.5270i	−0.505979	−	0.876381i	0.493997	−	0.869463i	$-0.335535\pi$
$174$		0			0
$175$	−3.84233	+	2.21837i	−0.290453	+	0.167693i
$176$	2.59808	−	1.50000i	0.195837	−	0.113067i
$177$		0			0
$178$	3.84233	+	6.65511i	0.287995	+	0.498822i
$179$	−10.0126	+	17.3423i	−0.748377	+	1.29623i	0.200224	+	0.979750i	$0.435833\pi$
$179$	−10.0126	+	17.3423i	−0.748377	+	1.29623i	−0.948600	+	0.316476i	$0.897500\pi$
$180$		0			0
$181$	−19.3693			−1.43971			−0.719855	−	0.694124i	$-0.755792\pi$
$181$	−19.3693			−1.43971			−0.719855	+	0.694124i	$0.755792\pi$
$182$	12.6107	+	9.84233i	0.934765	+	0.729562i
$183$		0			0
$184$	−0.657671	−	0.379706i	−0.0484841	−	0.0279923i
$185$	−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
$190$		−	0.972638i		−	0.0705626i
$191$	3.67733	+	6.36932i	0.266082	+	0.460868i	0.967847	−	0.251541i	$-0.0809375\pi$
$191$	3.67733	+	6.36932i	0.266082	+	0.460868i	−0.701765	+	0.712409i	$0.747604\pi$
$192$		0			0
$193$	1.31534	+	0.759413i	0.0946804	+	0.0546637i	0.546593	−	0.837399i	$-0.315925\pi$
$193$	1.31534	+	0.759413i	0.0946804	+	0.0546637i	−0.451912	+	0.892062i	$0.649258\pi$
$194$	5.40938			0.388371
$195$		0			0
$196$	12.6847			0.906047
$197$	14.7692	+	8.52699i	1.05226	+	0.607523i	0.923281	−	0.384125i	$-0.125497\pi$
$197$	14.7692	+	8.52699i	1.05226	+	0.607523i	0.128979	+	0.991647i	$0.458830\pi$
$198$		0			0
$199$	−3.68466	−	6.38202i	−0.261199	−	0.452409i	0.705362	−	0.708847i	$-0.250784\pi$
$199$	−3.68466	−	6.38202i	−0.261199	−	0.452409i	−0.966561	+	0.256438i	$0.917451\pi$
$200$		−	1.00000i		−	0.0707107i
$201$		0			0
$202$	−15.3693	+	8.87348i	−1.08138	+	0.624336i
$203$		−	42.7386i		−	2.99966i
$204$		0			0
$205$	3.00000	−	5.19615i	0.209529	−	0.362915i
$206$	−2.00514	−	1.15767i	−0.139705	−	0.0806587i
$207$		0			0
$208$	−3.34233	+	1.35234i	−0.231749	+	0.0937682i
$209$	−2.91791			−0.201836
$210$		0			0
$211$	−2.84233	+	4.92306i	−0.195674	+	0.338917i	−0.947121	−	0.320876i	$-0.896023\pi$
$211$	−2.84233	+	4.92306i	−0.195674	+	0.338917i	0.751447	+	0.659793i	$0.229356\pi$
$212$	−2.21837	−	3.84233i	−0.152358	−	0.263892i
$213$		0			0
$214$	−7.68466	+	4.43674i	−0.525312	+	0.303289i
$215$	2.32498	−	1.34233i	0.158562	−	0.0915461i
$216$		0			0
$217$	−13.6847	−	23.7025i	−0.928975	−	1.60903i
$218$	0.972638	−	1.68466i	0.0658754	−	0.114099i
$219$		0			0
$220$	−3.00000			−0.202260
$221$		0			0
$222$		0			0
$223$	12.8423	+	7.41452i	0.859986	+	0.496513i	0.864008	−	0.503479i	$-0.167947\pi$
$223$	12.8423	+	7.41452i	0.859986	+	0.496513i	−0.00402162	+	0.999992i	$0.501280\pi$
$224$	−2.21837	+	3.84233i	−0.148221	+	0.256726i
$225$		0			0
$226$		−	9.63289i		−	0.640770i
$227$	18.5064	−	10.6847i	1.22831	−	0.709166i	0.261635	−	0.965167i	$-0.415738\pi$
$227$	18.5064	−	10.6847i	1.22831	−	0.709166i	0.966676	+	0.256001i	$0.0824051\pi$
$228$		0			0
$229$			11.9111i			0.787110i	0.919301	+	0.393555i	$0.128755\pi$
$229$			11.9111i			0.787110i	−0.919301	+	0.393555i	$0.871245\pi$
$230$	0.379706	+	0.657671i	0.0250371	+	0.0433655i
$231$		0			0
$232$	8.34233	+	4.81645i	0.547701	+	0.316215i
$233$	20.0252			1.31189			0.655947	−	0.754807i	$-0.272269\pi$
$233$	20.0252			1.31189			0.655947	+	0.754807i	$0.272269\pi$
$234$		0			0
$235$	3.00000			0.195698
$236$	−4.05703	−	2.34233i	−0.264090	−	0.152473i
$237$		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
$241$	−18.1847	+	10.4989i	−1.17138	+	0.676295i	−0.954004	−	0.299794i	$-0.903082\pi$
$241$	−18.1847	+	10.4989i	−1.17138	+	0.676295i	−0.217373	+	0.976089i	$0.569749\pi$
$242$		−	2.00000i		−	0.128565i
$243$		0			0
$244$	−5.68466	+	9.84612i	−0.363923	+	0.630333i
$245$	−10.9852	−	6.34233i	−0.701821	−	0.405197i
$246$		0			0
$247$	3.47301	+	0.486319i	0.220982	+	0.0309437i
$248$	6.16879			0.391719
$249$		0			0
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	−2.59808	−	4.50000i	−0.163989	−	0.284037i	0.772307	−	0.635250i	$-0.219103\pi$
$251$	−2.59808	−	4.50000i	−0.163989	−	0.284037i	−0.936296	+	0.351212i	$0.885770\pi$
$252$		0			0
$253$	1.97301	−	1.13912i	0.124042	−	0.0716158i
$254$	8.38716	−	4.84233i	0.526257	−	0.303835i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−15.2088	+	26.3423i	−0.948696	+	1.64319i	−0.200519	+	0.979690i	$0.564263\pi$
$257$	−15.2088	+	26.3423i	−0.948696	+	1.64319i	−0.748177	+	0.663500i	$0.769070\pi$
$258$		0			0
$259$	−7.68466			−0.477501
$260$	3.57071	+	0.500000i	0.221446	+	0.0310087i
$261$		0			0
$262$	5.81534	+	3.35749i	0.359273	+	0.207426i
$263$	5.51599	−	9.55398i	0.340131	−	0.589123i	−0.644326	−	0.764751i	$-0.722862\pi$
$263$	5.51599	−	9.55398i	0.340131	−	0.589123i	0.984457	+	0.175627i	$0.0561954\pi$
$264$		0			0
$265$			4.43674i			0.272547i
$266$	3.73720	−	2.15767i	0.229142	−	0.132295i
$267$		0			0
$268$			12.3376i			0.753638i
$269$	8.87348	+	15.3693i	0.541026	+	0.937084i	0.998845	+	0.0480388i	$0.0152971\pi$
$269$	8.87348	+	15.3693i	0.541026	+	0.937084i	−0.457820	+	0.889045i	$0.651370\pi$
$270$		0			0
$271$	−7.02699	−	4.05703i	−0.426859	−	0.246447i	0.271149	−	0.962538i	$-0.412597\pi$
$271$	−7.02699	−	4.05703i	−0.426859	−	0.246447i	−0.698008	+	0.716090i	$0.745930\pi$
$272$		0			0
$273$		0			0
$274$	7.31534			0.441936
$275$	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	$0.823769\pi$
$278$		−	21.6847i		−	1.30056i
$279$		0			0
$280$	3.84233	−	2.21837i	0.229623	−	0.132573i
$281$			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
$283$	−12.0270	+	20.8314i	−0.714930	+	1.23830i	0.248056	+	0.968746i	$0.420208\pi$
$283$	−12.0270	+	20.8314i	−0.714930	+	1.23830i	−0.962986	+	0.269550i	$0.913125\pi$
$284$	−5.19615	−	3.00000i	−0.308335	−	0.178017i
$285$		0			0
$286$	1.50000	−	10.7121i	0.0886969	−	0.633422i
$287$	26.6204			1.57135
$288$		0			0
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$	−4.81645	−	8.34233i	−0.282831	−	0.489878i
$291$		0			0
$292$	−6.00000	+	3.46410i	−0.351123	+	0.202721i
$293$	−8.93335	+	5.15767i	−0.521892	+	0.301314i	−0.737708	−	0.675120i	$-0.764092\pi$
$293$	−8.93335	+	5.15767i	−0.521892	+	0.301314i	0.215817	+	0.976434i	$0.430759\pi$
$294$		0			0
$295$	2.34233	+	4.05703i	0.136376	+	0.236210i
$296$	0.866025	−	1.50000i	0.0503367	−	0.0871857i
$297$		0			0
$298$	−22.6847			−1.31409
$299$	−2.53821	+	1.02699i	−0.146788	+	0.0593922i
$300$		0			0
$301$	10.3153	+	5.95557i	0.594566	+	0.343273i
$302$	−7.14143	+	12.3693i	−0.410943	+	0.711774i
$303$		0			0
$304$			0.972638i			0.0557846i
$305$	9.84612	−	5.68466i	0.563787	−	0.325503i
$306$		0			0
$307$		−	14.2829i		−	0.815166i	−0.913168	−	0.407583i	$-0.866372\pi$
$307$		−	14.2829i		−	0.815166i	0.913168	−	0.407583i	$-0.133628\pi$
$308$	−6.65511	−	11.5270i	−0.379210	−	0.656811i
$309$		0			0
$310$	−5.34233	−	3.08440i	−0.303424	−	0.175182i
$311$	19.2658			1.09246			0.546231	−	0.837634i	$-0.316062\pi$
$311$	19.2658			1.09246			0.546231	+	0.837634i	$0.316062\pi$
$312$		0			0
$313$	19.3693			1.09482			0.547409	−	0.836865i	$-0.315614\pi$
$313$	19.3693			1.09482			0.547409	+	0.836865i	$0.315614\pi$
$314$	−14.1762	−	8.18466i	−0.800012	−	0.461887i
$315$		0			0
$316$	−3.34233	−	5.78908i	−0.188021	−	0.325661i
$317$			32.4233i			1.82107i	0.413428	+	0.910537i	$0.364331\pi$
$317$			32.4233i			1.82107i	−0.413428	+	0.910537i	$0.635669\pi$
$318$		0			0
$319$	−25.0270	+	14.4493i	−1.40124	+	0.809008i
$320$			1.00000i			0.0559017i
$321$		0			0
$322$	−1.68466	+	2.91791i	−0.0938823	+	0.162609i
$323$		0			0
$324$		0			0
$325$	−2.84233	−	2.21837i	−0.157664	−	0.123053i
$326$	−11.1517			−0.617637
$327$		0			0
$328$	−3.00000	+	5.19615i	−0.165647	+	0.286910i
$329$	6.65511	+	11.5270i	0.366908	+	0.635503i
$330$		0			0
$331$	−29.0540	+	16.7743i	−1.59695	+	0.922000i	−0.604881	+	0.796316i	$0.706779\pi$
$331$	−29.0540	+	16.7743i	−1.59695	+	0.922000i	−0.992070	+	0.125684i	$0.959888\pi$
$332$	8.11407	−	4.68466i	0.445317	−	0.257104i
$333$		0			0
$334$	−9.18466	−	15.9083i	−0.502562	−	0.870463i
$335$	6.16879	−	10.6847i	0.337037	−	0.583765i
$336$		0			0
$337$	−4.63068			−0.252249			−0.126125	−	0.992014i	$-0.540254\pi$
$337$	−4.63068			−0.252249			−0.126125	+	0.992014i	$0.540254\pi$
$338$	−3.57071	+	12.5000i	−0.194221	+	0.679910i
$339$		0			0
$340$		0			0
$341$	−9.25319	+	16.0270i	−0.501088	+	0.867910i
$342$		0			0
$343$		−	25.2213i		−	1.36182i
$344$	−2.32498	+	1.34233i	−0.125355	+	0.0723735i
$345$		0			0
$346$		−	13.3102i		−	0.715562i
$347$	−9.63289	−	16.6847i	−0.517121	−	0.895679i	−0.999802	−	0.0198835i	$-0.993670\pi$
$347$	−9.63289	−	16.6847i	−0.517121	−	0.895679i	0.482682	−	0.875796i	$-0.339663\pi$
$348$		0			0
$349$	8.05398	+	4.64996i	0.431119	+	0.248907i	0.699823	−	0.714316i	$-0.253262\pi$
$349$	8.05398	+	4.64996i	0.431119	+	0.248907i	−0.268704	+	0.963223i	$0.586595\pi$
$350$	−4.43674			−0.237154
$351$		0			0
$352$	3.00000			0.159901
$353$	−8.11407	−	4.68466i	−0.431868	−	0.249339i	0.268274	−	0.963343i	$-0.413547\pi$
$353$	−8.11407	−	4.68466i	−0.431868	−	0.249339i	−0.700142	+	0.714003i	$0.746880\pi$
$354$		0			0
$355$	3.00000	+	5.19615i	0.159223	+	0.275783i
$356$			7.68466i			0.407286i
$357$		0			0
$358$	−17.3423	+	10.0126i	−0.916571	+	0.529182i
$359$		−	27.3693i		−	1.44450i	−0.691633	−	0.722249i	$-0.743109\pi$
$359$		−	27.3693i		−	1.44450i	0.691633	−	0.722249i	$-0.256891\pi$
$360$		0			0
$361$	−9.02699	+	15.6352i	−0.475105	+	0.822905i
$362$	−16.7743	−	9.68466i	−0.881639	−	0.509014i
$363$		0			0
$364$	6.00000	+	14.8290i	0.314485	+	0.777253i
$365$	6.92820			0.362639
$366$		0			0
$367$	0.684658	−	1.18586i	0.0357389	−	0.0619016i	−0.847603	−	0.530631i	$-0.821955\pi$
$367$	0.684658	−	1.18586i	0.0357389	−	0.0619016i	0.883342	+	0.468730i	$0.155288\pi$
$368$	−0.379706	−	0.657671i	−0.0197936	−	0.0342835i
$369$		0			0
$370$	−1.50000	+	0.866025i	−0.0779813	+	0.0450225i
$371$	−17.0474	+	9.84233i	−0.885058	+	0.510988i
$372$		0			0
$373$	−18.0270	−	31.2237i	−0.933402	−	1.61670i	−0.777459	−	0.628934i	$-0.783492\pi$
$373$	−18.0270	−	31.2237i	−0.933402	−	1.61670i	−0.155943	−	0.987766i	$-0.549842\pi$
$374$		0			0
$375$		0			0
$376$	−3.00000			−0.154713
$377$	32.1963	−	13.0270i	1.65819	−	0.670924i
$378$		0			0
$379$	−31.2116	−	18.0201i	−1.60323	−	0.925628i	−0.990835	−	0.135080i	$-0.956871\pi$
$379$	−31.2116	−	18.0201i	−1.60323	−	0.925628i	−0.612400	−	0.790548i	$-0.709796\pi$
$380$	0.486319	−	0.842329i	0.0249476	−	0.0432106i
$381$		0			0
$382$			7.35465i			0.376297i
$383$	4.05703	−	2.34233i	0.207305	−	0.119687i	−0.392753	−	0.919644i	$-0.628477\pi$
$383$	4.05703	−	2.34233i	0.207305	−	0.119687i	0.600058	+	0.799956i	$0.295144\pi$
$384$		0			0
$385$			13.3102i			0.678352i
$386$	0.759413	+	1.31534i	0.0386531	+	0.0669491i
$387$		0			0
$388$	4.68466	+	2.70469i	0.237827	+	0.137310i
$389$	25.8610			1.31121			0.655603	−	0.755106i	$-0.272415\pi$
$389$	25.8610			1.31121			0.655603	+	0.755106i	$0.272415\pi$
$390$		0			0
$391$		0			0
$392$	10.9852	+	6.34233i	0.554838	+	0.320336i
$393$		0			0
$394$	8.52699	+	14.7692i	0.429583	+	0.744060i
$395$			6.68466i			0.336342i
$396$		0			0
$397$	−17.8153	+	10.2857i	−0.894126	+	0.516224i	−0.875290	−	0.483598i	$-0.839330\pi$
$397$	−17.8153	+	10.2857i	−0.894126	+	0.516224i	−0.0188364	+	0.999823i	$0.505996\pi$
$398$		−	7.36932i		−	0.369390i
$399$		0			0
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	30.3576	+	17.5270i	1.51599	+	0.875256i	0.999824	+	0.0187662i	$0.00597382\pi$
$401$	30.3576	+	17.5270i	1.51599	+	0.875256i	0.516164	+	0.856490i	$0.327360\pi$
$402$		0			0
$403$	13.6847	−	17.5337i	0.681681	−	0.873417i
$404$	−17.7470			−0.882944
$405$		0			0
$406$	21.3693	−	37.0127i	1.06054	−	1.83691i
$407$	2.59808	+	4.50000i	0.128782	+	0.223057i
$408$		0			0
$409$	19.2116	−	11.0918i	0.949955	−	0.548457i	0.0568879	−	0.998381i	$-0.481882\pi$
$409$	19.2116	−	11.0918i	0.949955	−	0.548457i	0.893067	+	0.449924i	$0.148549\pi$
$410$	5.19615	−	3.00000i	0.256620	−	0.148159i
$411$		0			0
$412$	−1.15767	−	2.00514i	−0.0570343	−	0.0987864i
$413$	−10.3923	+	18.0000i	−0.511372	+	0.885722i
$414$		0			0
$415$	−9.36932			−0.459922
$416$	−3.57071	−	0.500000i	−0.175069	−	0.0245145i
$417$		0			0
$418$	−2.52699	−	1.45896i	−0.123599	−	0.0713599i
$419$	14.0696	−	24.3693i	0.687346	−	1.19052i	−0.285347	−	0.958424i	$-0.592109\pi$
$419$	14.0696	−	24.3693i	0.687346	−	1.19052i	0.972693	−	0.232095i	$-0.0745579\pi$
$420$		0			0
$421$			16.2281i			0.790911i	0.918485	+	0.395455i	$0.129413\pi$
$421$			16.2281i			0.790911i	−0.918485	+	0.395455i	$0.870587\pi$
$422$	−4.92306	+	2.84233i	−0.239651	+	0.138362i
$423$		0			0
$424$		−	4.43674i		−	0.215467i
$425$		0			0
$426$		0			0
$427$	43.6847	+	25.2213i	2.11405	+	1.22055i
$428$	−8.87348			−0.428916
$429$		0			0
$430$	2.68466			0.129466
$431$	18.5064	+	10.6847i	0.891421	+	0.514662i	0.874407	−	0.485193i	$-0.161251\pi$
$431$	18.5064	+	10.6847i	0.891421	+	0.514662i	0.0170137	+	0.999855i	$0.494584\pi$
$432$		0			0
$433$	5.31534	+	9.20644i	0.255439	+	0.442433i	0.965015	−	0.262196i	$-0.0844467\pi$
$433$	5.31534	+	9.20644i	0.255439	+	0.442433i	−0.709576	+	0.704629i	$0.751113\pi$
$434$		−	27.3693i		−	1.31377i
$435$		0			0
$436$	1.68466	−	0.972638i	0.0806805	−	0.0465809i
$437$			0.738634i			0.0353336i
$438$		0			0
$439$	15.6847	−	27.1666i	0.748588	−	1.29659i	−0.199912	−	0.979814i	$-0.564066\pi$
$439$	15.6847	−	27.1666i	0.748588	−	1.29659i	0.948500	−	0.316778i	$-0.102601\pi$
$440$	−2.59808	−	1.50000i	−0.123858	−	0.0715097i
$441$		0			0
$442$		0			0
$443$	−10.3923			−0.493753			−0.246877	−	0.969047i	$-0.579404\pi$
$443$	−10.3923			−0.493753			−0.246877	+	0.969047i	$0.579404\pi$
$444$		0			0
$445$	3.84233	−	6.65511i	0.182144	−	0.315482i
$446$	7.41452	+	12.8423i	0.351088	+	0.608102i
$447$		0			0
$448$	−3.84233	+	2.21837i	−0.181533	+	0.104808i
$449$	14.1295	−	8.15767i	0.666812	−	0.384984i	−0.128055	−	0.991767i	$-0.540874\pi$
$449$	14.1295	−	8.15767i	0.666812	−	0.384984i	0.794868	+	0.606783i	$0.207540\pi$
$450$		0			0
$451$	−9.00000	−	15.5885i	−0.423793	−	0.734032i
$452$	4.81645	−	8.34233i	0.226547	−	0.392390i
$453$		0			0
$454$	21.3693			1.00291
$455$	2.21837	−	15.8423i	0.103999	−	0.742700i
$456$		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	$0.692485\pi$
$458$	−5.95557	+	10.3153i	−0.278285	+	0.482004i
$459$		0			0
$460$			0.759413i			0.0354078i
$461$	−14.4493	+	8.34233i	−0.672973	+	0.388541i	−0.797202	−	0.603713i	$-0.793687\pi$
$461$	−14.4493	+	8.34233i	−0.672973	+	0.388541i	0.124229	+	0.992254i	$0.460354\pi$
$462$		0			0
$463$		−	12.7640i		−	0.593195i	−0.955003	−	0.296597i	$-0.904148\pi$
$463$		−	12.7640i		−	0.593195i	0.955003	−	0.296597i	$-0.0958519\pi$
$464$	4.81645	+	8.34233i	0.223598	+	0.387283i
$465$		0			0
$466$	17.3423	+	10.0126i	0.803368	+	0.463825i
$467$	−35.4939			−1.64246			−0.821231	−	0.570595i	$-0.806712\pi$
$467$	−35.4939			−1.64246			−0.821231	+	0.570595i	$0.806712\pi$
$468$		0			0
$469$	54.7386			2.52760
$470$	2.59808	+	1.50000i	0.119840	+	0.0691898i
$471$		0			0
$472$	−2.34233	−	4.05703i	−0.107814	−	0.186740i
$473$		−	8.05398i		−	0.370322i
$474$		0			0
$475$	−0.842329	+	0.486319i	−0.0386487	+	0.0223138i
$476$		0			0
$477$		0			0
$478$	12.3693	−	21.4243i	0.565759	−	0.979924i
$479$	−2.27824	−	1.31534i	−0.104095	−	0.0600995i	0.447049	−	0.894510i	$-0.352475\pi$
$479$	−2.27824	−	1.31534i	−0.104095	−	0.0600995i	−0.551144	+	0.834410i	$0.685808\pi$
$480$		0			0
$481$	−2.34233	−	5.78908i	−0.106801	−	0.263960i
$482$	−20.9978			−0.956425
$483$		0			0
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$	−2.70469	−	4.68466i	−0.122814	−	0.212719i
$486$		0			0
$487$	−11.1577	+	6.44188i	−0.505602	+	0.291910i	−0.731024	−	0.682352i	$-0.760957\pi$
$487$	−11.1577	+	6.44188i	−0.505602	+	0.291910i	0.225422	+	0.974261i	$0.427624\pi$
$488$	−9.84612	+	5.68466i	−0.445713	+	0.257332i
$489$		0			0
$490$	−6.34233	−	10.9852i	−0.286517	−	0.496262i
$491$	−2.97778	+	5.15767i	−0.134385	+	0.232762i	−0.925363	−	0.379083i	$-0.876239\pi$
$491$	−2.97778	+	5.15767i	−0.134385	+	0.232762i	0.790977	+	0.611846i	$0.209573\pi$
$492$		0			0
$493$		0			0
$494$	2.76456	+	2.15767i	0.124383	+	0.0970782i
$495$		0			0
$496$	5.34233	+	3.08440i	0.239878	+	0.138493i
$497$	−13.3102	+	23.0540i	−0.597045	+	1.03411i
$498$		0			0
$499$			25.1016i			1.12370i	0.827238	+	0.561851i	$0.189911\pi$
$499$			25.1016i			1.12370i	−0.827238	+	0.561851i	$0.810089\pi$
$500$	−0.866025	+	0.500000i	−0.0387298	+	0.0223607i
$501$		0			0
$502$		−	5.19615i		−	0.231916i
$503$	−17.8068	−	30.8423i	−0.793967	−	1.37519i	−0.923493	−	0.383615i	$-0.874679\pi$
$503$	−17.8068	−	30.8423i	−0.793967	−	1.37519i	0.129526	−	0.991576i	$-0.458655\pi$
$504$		0			0
$505$	15.3693	+	8.87348i	0.683926	+	0.394865i
$506$	2.27824			0.101280
$507$		0			0
$508$	9.68466			0.429687
$509$	−19.6455	−	11.3423i	−0.870771	−	0.502740i	−0.00316666	−	0.999995i	$-0.501008\pi$
$509$	−19.6455	−	11.3423i	−0.870771	−	0.502740i	−0.867604	+	0.497255i	$0.834341\pi$
$510$		0			0
$511$	15.3693	+	26.6204i	0.679899	+	1.17762i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−26.3423	+	15.2088i	−1.16191	+	0.670829i
$515$			2.31534i			0.102026i
$516$		0			0
$517$	4.50000	−	7.79423i	0.197910	−	0.342790i
$518$	−6.65511	−	3.84233i	−0.292409	−	0.168822i
$519$		0			0
$520$	2.84233	+	2.21837i	0.124644	+	0.0972820i
$521$	5.95557			0.260918			0.130459	−	0.991454i	$-0.458355\pi$
$521$	5.95557			0.260918			0.130459	+	0.991454i	$0.458355\pi$
$522$		0			0
$523$	18.0270	−	31.2237i	0.788265	−	1.36532i	−0.138764	−	0.990326i	$-0.544313\pi$
$523$	18.0270	−	31.2237i	0.788265	−	1.36532i	0.927029	−	0.374990i	$-0.122354\pi$
$524$	3.35749	+	5.81534i	0.146673	+	0.254044i
$525$		0			0
$526$	9.55398	−	5.51599i	0.416573	−	0.240509i
$527$		0			0
$528$		0			0
$529$	11.2116	+	19.4191i	0.487463	+	0.844310i
$530$	−2.21837	+	3.84233i	−0.0963598	+	0.166900i
$531$		0			0
$532$	4.31534			0.187094
$533$	8.11407	+	20.0540i	0.351459	+	0.868634i
$534$		0			0
$535$	7.68466	+	4.43674i	0.332237	+	0.191817i
$536$	−6.16879	+	10.6847i	−0.266451	+	0.461507i
$537$		0			0
$538$			17.7470i			0.765126i
$539$	−32.9557	+	19.0270i	−1.41950	+	0.819550i
$540$		0			0
$541$			25.7675i			1.10783i	0.832572	+	0.553916i	$0.186867\pi$
$541$			25.7675i			1.10783i	−0.832572	+	0.553916i	$0.813133\pi$
$542$	−4.05703	−	7.02699i	−0.174264	−	0.301835i
$543$		0			0
$544$		0			0
$545$	−1.94528			−0.0833265
$546$		0			0
$547$	42.1080			1.80041			0.900203	−	0.435471i	$-0.143418\pi$
$547$	42.1080			1.80041			0.900203	+	0.435471i	$0.143418\pi$
$548$	6.33527	+	3.65767i	0.270629	+	0.156248i
$549$		0			0
$550$	1.50000	+	2.59808i	0.0639602	+	0.110782i
$551$		−	9.36932i		−	0.399146i
$552$		0			0
$553$	−25.6847	+	14.8290i	−1.09222	+	0.630595i
$554$			1.00000i			0.0424859i
$555$		0			0
$556$	10.8423	−	18.7795i	0.459817	−	0.796427i
$557$	11.8513	+	6.84233i	0.502154	+	0.289919i	0.729603	−	0.683871i	$-0.239705\pi$
$557$	11.8513	+	6.84233i	0.502154	+	0.289919i	−0.227449	+	0.973790i	$0.573038\pi$
$558$		0			0
$559$	−1.34233	+	9.58615i	−0.0567745	+	0.405451i
$560$	4.43674			0.187486
$561$		0			0
$562$	−12.3693	+	21.4243i	−0.521768	+	0.903729i
$563$	20.0252	+	34.6847i	0.843961	+	1.46178i	0.886520	+	0.462690i	$0.153116\pi$
$563$	20.0252	+	34.6847i	0.843961	+	1.46178i	−0.0425587	+	0.999094i	$0.513551\pi$
$564$		0			0
$565$	−8.34233	+	4.81645i	−0.350964	+	0.202629i
$566$	−20.8314	+	12.0270i	−0.875607	+	0.505532i
$567$		0			0
$568$	−3.00000	−	5.19615i	−0.125877	−	0.218026i
$569$	−10.3324	+	17.8963i	−0.433158	+	0.750252i	−0.997143	−	0.0755329i	$-0.975934\pi$
$569$	−10.3324	+	17.8963i	−0.433158	+	0.750252i	0.563985	+	0.825785i	$0.309268\pi$
$570$		0			0
$571$	−2.94602			−0.123287			−0.0616436	−	0.998098i	$-0.519634\pi$
$571$	−2.94602			−0.123287			−0.0616436	+	0.998098i	$0.519634\pi$
$572$	6.65511	−	8.52699i	0.278264	−	0.356531i
$573$		0			0
$574$	23.0540	+	13.3102i	0.962254	+	0.555558i
$575$	0.379706	−	0.657671i	0.0158349	−	0.0274268i
$576$		0			0
$577$		−	43.5145i		−	1.81153i	−0.423778	−	0.905766i	$-0.639296\pi$
$577$		−	43.5145i		−	1.81153i	0.423778	−	0.905766i	$-0.360704\pi$
$578$	14.7224	−	8.50000i	0.612372	−	0.353553i
$579$		0			0
$580$		−	9.63289i		−	0.399984i
$581$	−20.7846	−	36.0000i	−0.862291	−	1.49353i
$582$		0			0
$583$	11.5270	+	6.65511i	0.477399	+	0.275626i
$584$	−6.92820			−0.286691
$585$		0			0
$586$	−10.3153			−0.426123
$587$	13.3102	+	7.68466i	0.549372	+	0.317180i	0.748868	−	0.662719i	$-0.230597\pi$
$587$	13.3102	+	7.68466i	0.549372	+	0.317180i	−0.199497	+	0.979898i	$0.563931\pi$
$588$		0			0
$589$	−3.00000	−	5.19615i	−0.123613	−	0.214104i
$590$			4.68466i			0.192864i
$591$		0			0
$592$	1.50000	−	0.866025i	0.0616496	−	0.0355934i
$593$			23.4233i			0.961879i	0.876754	+	0.480940i	$0.159704\pi$
$593$			23.4233i			0.961879i	−0.876754	+	0.480940i	$0.840296\pi$
$594$		0			0
$595$		0			0
$596$	−19.6455	−	11.3423i	−0.804711	−	0.464600i
$597$		0			0
$598$	−2.71165	−	0.379706i	−0.110887	−	0.0155273i
$599$	28.1393			1.14974			0.574870	−	0.818245i	$-0.305053\pi$
$599$	28.1393			1.14974			0.574870	+	0.818245i	$0.305053\pi$
$600$		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	$-0.0863789\pi$
$602$	5.95557	+	10.3153i	0.242731	+	0.420422i
$603$		0			0
$604$	−12.3693	+	7.14143i	−0.503300	+	0.290581i
$605$	−1.73205	+	1.00000i	−0.0704179	+	0.0406558i
$606$		0			0
$607$	−21.5270	−	37.2858i	−0.873753	−	1.51339i	−0.858085	−	0.513508i	$-0.828346\pi$
$607$	−21.5270	−	37.2858i	−0.873753	−	1.51339i	−0.0156688	−	0.999877i	$-0.504988\pi$
$608$	−0.486319	+	0.842329i	−0.0197228	+	0.0341610i
$609$		0			0
$610$	11.3693			0.460330
$611$	−6.65511	+	8.52699i	−0.269237	+	0.344965i
$612$		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
$616$		−	13.3102i		−	0.536284i
$617$	−1.13912	+	0.657671i	−0.0458592	+	0.0264768i	−0.522754	−	0.852483i	$-0.675095\pi$
$617$	−1.13912	+	0.657671i	−0.0458592	+	0.0264768i	0.476895	+	0.878960i	$0.341762\pi$
$618$		0			0
$619$			32.5760i			1.30934i	0.755915	+	0.654670i	$0.227192\pi$
$619$			32.5760i			1.30934i	−0.755915	+	0.654670i	$0.772808\pi$
$620$	−3.08440	−	5.34233i	−0.123872	−	0.214553i
$621$		0			0
$622$	16.6847	+	9.63289i	0.668994	+	0.386244i
$623$	34.0948			1.36598
$624$		0			0
$625$	1.00000			0.0400000
$626$	16.7743	+	9.68466i	0.670437	+	0.387077i
$627$		0			0
$628$	−8.18466	−	14.1762i	−0.326603	−	0.565694i
$629$		0			0
$630$		0			0
$631$	−7.31534	+	4.22351i	−0.291219	+	0.168135i	−0.638492	−	0.769629i	$-0.720441\pi$
$631$	−7.31534	+	4.22351i	−0.291219	+	0.168135i	0.347272	+	0.937764i	$0.387108\pi$
$632$		−	6.68466i		−	0.265901i
$633$		0			0
$634$	−16.2116	+	28.0794i	−0.643847	+	1.11518i
$635$	−8.38716	−	4.84233i	−0.332834	−	0.192162i
$636$		0			0
$637$	42.3963	−	17.1540i	1.67980	−	0.679667i
$638$	−28.8987			−1.14411
$639$		0			0
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	5.13628	+	8.89630i	0.202871	+	0.351383i	0.949452	−	0.313911i	$-0.101639\pi$
$641$	5.13628	+	8.89630i	0.202871	+	0.351383i	−0.746581	+	0.665294i	$0.768306\pi$
$642$		0			0
$643$	8.05398	−	4.64996i	0.317618	−	0.183377i	−0.332712	−	0.943028i	$-0.607964\pi$
$643$	8.05398	−	4.64996i	0.317618	−	0.183377i	0.650330	+	0.759652i	$0.274631\pi$
$644$	−2.91791	+	1.68466i	−0.114982	+	0.0663848i
$645$		0			0
$646$		0			0
$647$	14.7692	−	25.5810i	0.580636	−	1.00569i	−0.414768	−	0.909927i	$-0.636137\pi$
$647$	14.7692	−	25.5810i	0.580636	−	1.00569i	0.995404	−	0.0957642i	$-0.0305295\pi$
$648$		0			0
$649$	14.0540			0.551667
$650$	−1.35234	−	3.34233i	−0.0530433	−	0.131097i
$651$		0			0
$652$	−9.65767	−	5.57586i	−0.378224	−	0.218367i
$653$	22.2436	−	38.5270i	0.870458	−	1.50768i	0.00893438	−	0.999960i	$-0.497156\pi$
$653$	22.2436	−	38.5270i	0.870458	−	1.50768i	0.861524	−	0.507717i	$-0.169511\pi$
$654$		0			0
$655$		−	6.71498i		−	0.262376i
$656$	−5.19615	+	3.00000i	−0.202876	+	0.117130i
$657$		0			0
$658$			13.3102i			0.518886i
$659$	20.4049	+	35.3423i	0.794862	+	1.37674i	0.922927	+	0.384976i	$0.125790\pi$
$659$	20.4049	+	35.3423i	0.794862	+	1.37674i	−0.128064	+	0.991766i	$0.540876\pi$
$660$		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	$0.601888\pi$
$662$	−33.5486			−1.30390
$663$		0			0
$664$	9.36932			0.363600
$665$	−3.73720	−	2.15767i	−0.144922	−	0.0836709i
$666$		0			0
$667$	3.65767	+	6.33527i	0.141626	+	0.245303i
$668$		−	18.3693i		−	0.710730i
$669$		0			0
$670$	10.6847	−	6.16879i	0.412784	−	0.238321i
$671$		−	34.1080i		−	1.31672i
$672$		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	$0.955114\pi$
$674$	−4.01029	−	2.31534i	−0.154471	−	0.0891836i
$675$		0			0
$676$	−9.34233	+	9.03996i	−0.359320	+	0.347691i
$677$	22.3034			0.857191			0.428595	−	0.903497i	$-0.359009\pi$
$677$	22.3034			0.857191			0.428595	+	0.903497i	$0.359009\pi$
$678$		0			0
$679$	12.0000	−	20.7846i	0.460518	−	0.797640i
$680$		0			0
$681$		0			0
$682$	−16.0270	+	9.25319i	−0.613705	+	0.354323i
$683$	−23.7025	+	13.6847i	−0.906952	+	0.523629i	−0.879449	−	0.475993i	$-0.842089\pi$
$683$	−23.7025	+	13.6847i	−0.906952	+	0.523629i	−0.0275027	+	0.999622i	$0.508755\pi$
$684$		0			0
$685$	−3.65767	−	6.33527i	−0.139752	−	0.242058i
$686$	12.6107	−	21.8423i	0.481478	−	0.833944i
$687$		0			0
$688$	−2.68466			−0.102352
$689$	−12.6107	−	9.84233i	−0.480428	−	0.374963i
$690$		0			0
$691$	14.5270	+	8.38716i	0.552633	+	0.319063i	0.750183	−	0.661230i	$-0.229965\pi$
$691$	14.5270	+	8.38716i	0.552633	+	0.319063i	−0.197550	+	0.980293i	$0.563299\pi$
$692$	6.65511	−	11.5270i	0.252989	−	0.438190i
$693$		0			0
$694$		−	19.2658i		−	0.731319i
$695$	−18.7795	+	10.8423i	−0.712346	+	0.411273i
$696$		0			0
$697$		0			0
$698$	4.64996	+	8.05398i	0.176004	+	0.304847i
$699$		0			0
$700$	−3.84233	−	2.21837i	−0.145226	−	0.0838465i
$701$	30.4175			1.14885			0.574427	−	0.818556i	$-0.305225\pi$
$701$	30.4175			1.14885			0.574427	+	0.818556i	$0.305225\pi$
$702$		0			0
$703$	−1.68466			−0.0635381
$704$	2.59808	+	1.50000i	0.0979187	+	0.0565334i
$705$		0			0
$706$	−4.68466	−	8.11407i	−0.176309	−	0.305377i
$707$			78.7386i			2.96127i
$708$		0			0
$709$	−2.63068	+	1.51883i	−0.0987974	+	0.0570407i	−0.548585	−	0.836095i	$-0.684833\pi$
$709$	−2.63068	+	1.51883i	−0.0987974	+	0.0570407i	0.449787	+	0.893136i	$0.351500\pi$
$710$			6.00000i			0.225176i
$711$		0			0
$712$	−3.84233	+	6.65511i	−0.143997	+	0.249411i
$713$	4.05703	+	2.34233i	0.151937	+	0.0877209i
$714$		0			0
$715$	−10.0270	+	4.05703i	−0.374988	+	0.151724i
$716$	−20.0252			−0.748377
$717$		0			0
$718$	13.6847	−	23.7025i	0.510707	−	0.884570i
$719$	19.2658	+	33.3693i	0.718493	+	1.24447i	0.961597	+	0.274465i	$0.0885009\pi$
$719$	19.2658	+	33.3693i	0.718493	+	1.24447i	−0.243104	+	0.970000i	$0.578166\pi$
$720$		0			0
$721$	−8.89630	+	5.13628i	−0.331316	+	0.191285i
$722$	−15.6352	+	9.02699i	−0.581882	+	0.335950i
$723$		0			0
$724$	−9.68466	−	16.7743i	−0.359927	−	0.623413i
$725$	−4.81645	+	8.34233i	−0.178878	+	0.309826i
$726$		0			0
$727$	−24.3153			−0.901806			−0.450903	−	0.892573i	$-0.648898\pi$
$727$	−24.3153			−0.901806			−0.450903	+	0.892573i	$0.648898\pi$
$728$	−2.21837	+	15.8423i	−0.0822183	+	0.587156i
$729$		0			0
$730$	6.00000	+	3.46410i	0.222070	+	0.128212i
$731$		0			0
$732$		0			0
$733$		−	47.9512i		−	1.77112i	−0.464526	−	0.885560i	$-0.653775\pi$
$733$		−	47.9512i		−	1.77112i	0.464526	−	0.885560i	$-0.346225\pi$
$734$	1.18586	−	0.684658i	0.0437710	−	0.0252712i
$735$		0			0
$736$		−	0.759413i		−	0.0279923i
$737$	−18.5064	−	32.0540i	−0.681691	−	1.18072i
$738$		0			0
$739$	20.5270	+	11.8513i	0.755097	+	0.435956i	0.827533	−	0.561417i	$-0.189744\pi$
$739$	20.5270	+	11.8513i	0.755097	+	0.435956i	−0.0724353	+	0.997373i	$0.523077\pi$
$740$	−1.73205			−0.0636715
$741$		0			0
$742$	−19.6847			−0.722647
$743$	−6.33527	−	3.65767i	−0.232419	−	0.134187i	0.379269	−	0.925287i	$-0.376176\pi$
$743$	−6.33527	−	3.65767i	−0.232419	−	0.134187i	−0.611687	+	0.791100i	$0.709509\pi$
$744$		0			0
$745$	11.3423	+	19.6455i	0.415551	+	0.719755i
$746$		−	36.0540i		−	1.32003i
$747$		0			0
$748$		0			0
$749$			39.3693i			1.43852i
$750$		0			0
$751$	11.6577	−	20.1917i	0.425394	−	0.736805i	−0.571063	−	0.820906i	$-0.693469\pi$
$751$	11.6577	−	20.1917i	0.425394	−	0.736805i	0.996457	+	0.0841016i	$0.0268020\pi$
$752$	−2.59808	−	1.50000i	−0.0947421	−	0.0546994i
$753$		0			0
$754$	34.3963	+	4.81645i	1.25264	+	0.175405i
$755$	14.2829			0.519806
$756$		0			0
$757$	0.526988	−	0.912769i	0.0191537	−	0.0331752i	−0.856290	−	0.516496i	$-0.827236\pi$
$757$	0.526988	−	0.912769i	0.0191537	−	0.0331752i	0.875443	+	0.483321i	$0.160569\pi$
$758$	−18.0201	−	31.2116i	−0.654518	−	1.13366i
$759$		0			0
$760$	0.842329	−	0.486319i	0.0305545	−	0.0176406i
$761$	19.9653	−	11.5270i	0.723743	−	0.417853i	−0.0923860	−	0.995723i	$-0.529449\pi$
$761$	19.9653	−	11.5270i	0.723743	−	0.417853i	0.816129	+	0.577870i	$0.196116\pi$
$762$		0			0
$763$	−4.31534	−	7.47439i	−0.156226	−	0.270591i
$764$	−3.67733	+	6.36932i	−0.133041	+	0.230434i
$765$		0			0
$766$	4.68466			0.169264
$767$	−16.7276	−	2.34233i	−0.603998	−	0.0845766i
$768$		0			0
$769$	11.7116	+	6.76172i	0.422333	+	0.243834i	0.696075	−	0.717969i	$-0.254928\pi$
$769$	11.7116	+	6.76172i	0.422333	+	0.243834i	−0.273742	+	0.961803i	$0.588261\pi$
$770$	−6.65511	+	11.5270i	−0.239833	+	0.415404i
$771$		0			0
$772$			1.51883i			0.0546637i
$773$	24.5218	−	14.1577i	0.881988	−	0.509216i	0.0106746	−	0.999943i	$-0.496602\pi$
$773$	24.5218	−	14.1577i	0.881988	−	0.509216i	0.871313	+	0.490727i	$0.163269\pi$
$774$		0			0
$775$			6.16879i			0.221589i
$776$	2.70469	+	4.68466i	0.0970927	+	0.168169i
$777$		0			0
$778$	22.3963	+	12.9305i	0.802946	+	0.463581i
$779$	5.83583			0.209090
$780$		0			0
$781$	18.0000			0.644091
$782$		0			0
$783$		0			0
$784$	6.34233	+	10.9852i	0.226512	+	0.392330i
$785$			16.3693i			0.584246i
$786$		0			0
$787$	−2.34233	+	1.35234i	−0.0834950	+	0.0482059i	−0.541166	−	0.840916i	$-0.682017\pi$
$787$	−2.34233	+	1.35234i	−0.0834950	+	0.0482059i	0.457671	+	0.889122i	$0.348684\pi$
$788$			17.0540i			0.607523i
$789$		0			0
$790$	−3.34233	+	5.78908i	−0.118915	+	0.205966i
$791$	−37.0127	−	21.3693i	−1.31602	−	0.759805i
$792$		0			0
$793$	−5.68466	+	40.5966i	−0.201868	+	1.44163i
$794$	−20.5714			−0.730051
$795$		0			0
$796$	3.68466	−	6.38202i	0.130599	−	0.226205i
$797$	−17.7470	−	30.7386i	−0.628630	−	1.08882i	−0.987827	−	0.155557i	$-0.950283\pi$
$797$	−17.7470	−	30.7386i	−0.628630	−	1.08882i	0.359197	−	0.933262i	$-0.383050\pi$
$798$		0			0
$799$		0			0
$800$	0.866025	−	0.500000i	0.0306186	−	0.0176777i
$801$		0			0
$802$	17.5270	+	30.3576i	0.618899	+	1.07197i
$803$	10.3923	−	18.0000i	0.366736	−	0.635206i
$804$		0			0
$805$	3.36932			0.118753
$806$	20.6181	−	8.34233i	0.726243	−	0.293846i
$807$		0			0
$808$	−15.3693	−	8.87348i	−0.540691	−	0.312168i
$809$	10.3923	−	18.0000i	0.365374	−	0.632846i	−0.623462	−	0.781854i	$-0.714274\pi$
$809$	10.3923	−	18.0000i	0.365374	−	0.632846i	0.988836	+	0.149007i	$0.0476078\pi$
$810$		0			0
$811$		−	8.32729i		−	0.292411i	−0.989254	−	0.146205i	$-0.953294\pi$
$811$		−	8.32729i		−	0.292411i	0.989254	−	0.146205i	$-0.0467060\pi$
$812$	37.0127	−	21.3693i	1.29889	−	0.749916i
$813$		0			0
$814$			5.19615i			0.182125i
$815$	5.57586	+	9.65767i	0.195314	+	0.338293i
$816$		0			0
$817$	2.26137	+	1.30560i	0.0791152	+	0.0456772i
$818$	22.1837			0.775635
$819$		0			0
$820$	6.00000			0.209529
$821$	3.41736	+	1.97301i	0.119267	+	0.0688586i	0.558447	−	0.829541i	$-0.311398\pi$
$821$	3.41736	+	1.97301i	0.119267	+	0.0688586i	−0.439180	+	0.898399i	$0.644731\pi$
$822$		0			0
$823$	11.8423	+	20.5115i	0.412798	+	0.714986i	0.995194	−	0.0979181i	$-0.0312183\pi$
$823$	11.8423	+	20.5115i	0.412798	+	0.714986i	−0.582397	+	0.812905i	$0.697885\pi$
$824$		−	2.31534i		−	0.0806587i
$825$		0			0
$826$	−18.0000	+	10.3923i	−0.626300	+	0.361595i
$827$		−	39.3693i		−	1.36901i	−0.729010	−	0.684503i	$-0.760019\pi$
$827$		−	39.3693i		−	1.36901i	0.729010	−	0.684503i	$-0.239981\pi$
$828$		0			0
$829$	7.36932	−	12.7640i	0.255947	−	0.443313i	−0.709205	−	0.705002i	$-0.750946\pi$
$829$	7.36932	−	12.7640i	0.255947	−	0.443313i	0.965152	+	0.261689i	$0.0842794\pi$
$830$	−8.11407	−	4.68466i	−0.281643	−	0.162607i
$831$		0			0
$832$	−2.84233	−	2.21837i	−0.0985400	−	0.0769081i
$833$		0			0
$834$		0			0
$835$	−9.18466	+	15.9083i	−0.317848	+	0.550529i
$836$	−1.45896	−	2.52699i	−0.0504591	−	0.0873977i
$837$		0			0
$838$	24.3693	−	14.0696i	0.841824	−	0.486027i
$839$	0.639676	−	0.369317i	0.0220841	−	0.0127502i	−0.488917	−	0.872330i	$-0.662608\pi$
$839$	0.639676	−	0.369317i	0.0220841	−	0.0127502i	0.511001	+	0.859580i	$0.329275\pi$
$840$		0			0
$841$	−31.8963	−	55.2460i	−1.09987	−	1.90504i
$842$	−8.11407	+	14.0540i	−0.279629	+	0.484332i
$843$		0			0
$844$	−5.68466			−0.195674
$845$	12.6107	−	3.15767i	0.433820	−	0.108627i
$846$		0			0
$847$	−7.68466	−	4.43674i	−0.264048	−	0.152448i
$848$	2.21837	−	3.84233i	0.0761791	−	0.131946i
$849$		0			0
$850$		0			0
$851$	1.13912	−	0.657671i	0.0390485	−	0.0225447i
$852$		0			0
$853$			9.63289i			0.329824i	0.986308	+	0.164912i	$0.0527340\pi$
$853$			9.63289i			0.329824i	−0.986308	+	0.164912i	$0.947266\pi$
$854$	25.2213	+	43.6847i	0.863057	+	1.49486i
$855$		0			0
$856$	−7.68466	−	4.43674i	−0.262656	−	0.151645i
$857$	−20.0252			−0.684048			−0.342024	−	0.939691i	$-0.611112\pi$
$857$	−20.0252			−0.684048			−0.342024	+	0.939691i	$0.611112\pi$
$858$		0			0
$859$	−19.0540			−0.650113			−0.325057	−	0.945695i	$-0.605383\pi$
$859$	−19.0540			−0.650113			−0.325057	+	0.945695i	$0.605383\pi$
$860$	2.32498	+	1.34233i	0.0792812	+	0.0457730i
$861$		0			0
$862$	10.6847	+	18.5064i	0.363921	+	0.630330i
$863$			40.6847i			1.38492i	0.721455	+	0.692461i	$0.243474\pi$
$863$			40.6847i			1.38492i	−0.721455	+	0.692461i	$0.756526\pi$
$864$		0			0
$865$	−11.5270	+	6.65511i	−0.391929	+	0.226281i
$866$			10.6307i			0.361245i
$867$		0			0
$868$	13.6847	−	23.7025i	0.464488	−	0.804516i
$869$	17.3673	+	10.0270i	0.589144	+	0.340142i
$870$		0			0
$871$	16.6847	+	41.2363i	0.565338	+	1.39724i
$872$	1.94528			0.0658754
$873$		0			0
$874$	−0.369317	+	0.639676i	−0.0124923	+	0.0216373i
$875$	2.21837	+	3.84233i	0.0749946	+	0.129894i
$876$		0			0
$877$	−3.65767	+	2.11176i	−0.123511	+	0.0713090i	−0.560483	−	0.828166i	$-0.689384\pi$
$877$	−3.65767	+	2.11176i	−0.123511	+	0.0713090i	0.436972	+	0.899475i	$0.356051\pi$
$878$	27.1666	−	15.6847i	0.916829	−	0.529332i
$879$		0			0
$880$	−1.50000	−	2.59808i	−0.0505650	−	0.0875811i
$881$	0.699544	−	1.21165i	0.0235682	−	0.0408214i	−0.854001	−	0.520272i	$-0.825831\pi$
$881$	0.699544	−	1.21165i	0.0235682	−	0.0408214i	0.877569	+	0.479450i	$0.159164\pi$
$882$		0			0
$883$	26.6847			0.898010			0.449005	−	0.893529i	$-0.351778\pi$
$883$	26.6847			0.898010			0.449005	+	0.893529i	$0.351778\pi$
$884$		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	$-0.545938\pi$
$887$	23.3827	−	40.5000i	0.785114	−	1.35986i	0.928931	−	0.370253i	$-0.120729\pi$
$888$		0			0
$889$		−	42.9683i		−	1.44111i
$890$	6.65511	−	3.84233i	0.223080	−	0.128795i
$891$		0			0
$892$			14.8290i			0.496513i
$893$	1.45896	+	2.52699i	0.0488221	+	0.0845624i
$894$		0			0
$895$	17.3423	+	10.0126i	0.579690	+	0.334684i
$896$	−4.43674			−0.148221
$897$		0			0
$898$	16.3153			0.544450
$899$	−51.4621	−	29.7116i	−1.71636	−	0.990939i
$900$		0			0
$901$		0			0
$902$		−	18.0000i		−	0.599334i
$903$		0			0
$904$	8.34233	−	4.81645i	0.277462	−	0.160193i
$905$			19.3693i			0.643858i
$906$		0			0
$907$	21.3423	−	36.9660i	0.708660	−	1.22744i	−0.256694	−	0.966493i	$-0.582633\pi$
$907$	21.3423	−	36.9660i	0.708660	−	1.22744i	0.965354	−	0.260943i	$-0.0840335\pi$
$908$	18.5064	+	10.6847i	0.614156	+	0.354583i
$909$		0			0
$910$	9.84233	−	12.6107i	0.326270	−	0.418040i
$911$	33.9751			1.12564			0.562822	−	0.826578i	$-0.309715\pi$
$911$	33.9751			1.12564			0.562822	+	0.826578i	$0.309715\pi$
$912$		0			0
$913$	−14.0540	+	24.3422i	−0.465119	+	0.805609i
$914$	−1.73205	−	3.00000i	−0.0572911	−	0.0992312i
$915$		0			0
$916$	−10.3153	+	5.95557i	−0.340828	+	0.196777i
$917$	25.8012	−	14.8963i	0.852029	−	0.491919i
$918$		0			0
$919$	11.6847	+	20.2384i	0.385441	+	0.667604i	0.991830	−	0.127564i	$-0.0407159\pi$
$919$	11.6847	+	20.2384i	0.385441	+	0.667604i	−0.606389	+	0.795168i	$0.707383\pi$
$920$	−0.379706	+	0.657671i	−0.0125185	+	0.0216828i
$921$		0			0
$922$	−16.6847			−0.549480
$923$	−21.4243	−	3.00000i	−0.705189	−	0.0987462i
$924$		0			0
$925$	1.50000	+	0.866025i	0.0493197	+	0.0284747i
$926$	6.38202	−	11.0540i	0.209726	−	0.363256i
$927$		0			0
$928$			9.63289i			0.316215i
$929$	−17.8667	+	10.3153i	−0.586187	+	0.338435i	−0.763588	−	0.645703i	$-0.776564\pi$
$929$	−17.8667	+	10.3153i	−0.586187	+	0.338435i	0.177401	+	0.984139i	$0.443231\pi$
$930$		0			0
$931$		−	12.3376i		−	0.404348i
$932$	10.0126	+	17.3423i	0.327974	+	0.568067i
$933$		0			0
$934$	−30.7386	−	17.7470i	−1.00580	−	0.580698i
$935$		0			0
$936$		0			0
$937$	−20.7386			−0.677502			−0.338751	−	0.940876i	$-0.610004\pi$
$937$	−20.7386			−0.677502			−0.338751	+	0.940876i	$0.610004\pi$
$938$	47.4050	+	27.3693i	1.54783	+	0.893640i
$939$		0			0
$940$	1.50000	+	2.59808i	0.0489246	+	0.0847399i
$941$			2.63068i			0.0857578i	0.999080	+	0.0428789i	$0.0136530\pi$
$941$			2.63068i			0.0857578i	−0.999080	+	0.0428789i	$0.986347\pi$
$942$		0			0
$943$	−3.94602	+	2.27824i	−0.128500	+	0.0741897i
$944$		−	4.68466i		−	0.152473i
$945$		0			0
$946$	4.02699	−	6.97495i	0.130929	−	0.226775i
$947$	−11.0320	−	6.36932i	−0.358491	−	0.206975i	0.309928	−	0.950760i	$-0.399695\pi$
$947$	−11.0320	−	6.36932i	−0.358491	−	0.206975i	−0.668419	+	0.743785i	$0.733029\pi$
$948$		0			0
$949$	−15.3693	+	19.6922i	−0.498909	+	0.639237i
$950$	−0.972638			−0.0315565
$951$		0			0
$952$		0			0
$953$	6.97495	+	12.0810i	0.225941	+	0.391341i	0.956601	−	0.291400i	$-0.0941211\pi$
$953$	6.97495	+	12.0810i	0.225941	+	0.391341i	−0.730661	+	0.682741i	$0.760788\pi$
$954$		0			0
$955$	6.36932	−	3.67733i	0.206106	−	0.118996i
$956$	21.4243	−	12.3693i	0.692911	−	0.400052i
$957$		0			0
$958$	−1.31534	−	2.27824i	−0.0424968	−	0.0736065i
$959$	16.2281	−	28.1080i	0.524034	−	0.907653i
$960$		0			0
$961$	−7.05398			−0.227548
$962$	0.866025	−	6.18466i	0.0279218	−	0.199401i
$963$		0			0
$964$	−18.1847	−	10.4989i	−0.585688	−	0.338147i
$965$	0.759413	−	1.31534i	0.0244464	−	0.0423423i
$966$		0			0
$967$		−	16.7743i		−	0.539426i	−0.962941	−	0.269713i	$-0.913071\pi$
$967$		−	16.7743i		−	0.539426i	0.962941	−	0.269713i	$-0.0869288\pi$
$968$	1.73205	−	1.00000i	0.0556702	−	0.0321412i
$969$		0			0
$970$		−	5.40938i		−	0.173685i
$971$	−11.8513	−	20.5270i	−0.380325	−	0.658742i	0.610784	−	0.791798i	$-0.290855\pi$
$971$	−11.8513	−	20.5270i	−0.380325	−	0.658742i	−0.991109	+	0.133055i	$0.957521\pi$
$972$		0			0
$973$	−83.3196	−	48.1046i	−2.67110	−	1.54216i
$974$	−12.8838			−0.412823
$975$		0			0
$976$	−11.3693			−0.363923
$977$	−49.1838	−	28.3963i	−1.57353	−	0.908478i	−0.995731	−	0.0922993i	$-0.970578\pi$
$977$	−49.1838	−	28.3963i	−1.57353	−	0.908478i	−0.577799	−	0.816179i	$-0.696088\pi$
$978$		0			0
$979$	−11.5270	−	19.9653i	−0.368404	−	0.638095i
$980$		−	12.6847i		−	0.405197i
$981$		0			0
$982$	−5.15767	+	2.97778i	−0.164588	+	0.0950249i
$983$		−	33.0000i		−	1.05254i	−0.850319	−	0.526268i	$-0.823591\pi$
$983$		−	33.0000i		−	1.05254i	0.850319	−	0.526268i	$-0.176409\pi$
$984$		0			0
$985$	8.52699	−	14.7692i	0.271692	−	0.470585i
$986$		0			0
$987$		0			0
$988$	1.31534	+	3.25088i	0.0418466	+	0.103424i
$989$	−2.03876			−0.0648289
$990$		0			0
$991$	−17.3963	+	30.1313i	−0.552612	+	0.957152i	0.445473	+	0.895295i	$0.353035\pi$
$991$	−17.3963	+	30.1313i	−0.552612	+	0.957152i	−0.998085	+	0.0618565i	$0.980298\pi$
$992$	3.08440	+	5.34233i	0.0979296	+	0.169619i
$993$		0			0
$994$	−23.0540	+	13.3102i	−0.731228	+	0.422175i
$995$	−6.38202	+	3.68466i	−0.202323	+	0.116812i
$996$		0			0
$997$	6.21165	+	10.7589i	0.196725	+	0.340737i	0.947465	−	0.319861i	$-0.103636\pi$
$997$	6.21165	+	10.7589i	0.196725	+	0.340737i	−0.750740	+	0.660598i	$0.770303\pi$
$998$	−12.5508	+	21.7386i	−0.397289	+	0.688124i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.bs.h.901.4	yes	8
3.2	odd	2	inner	1170.2.bs.h.901.2	yes	8
13.10	even	6	inner	1170.2.bs.h.361.4	yes	8
39.23	odd	6	inner	1170.2.bs.h.361.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1170.2.bs.h.361.2	✓	8	39.23	odd	6	inner
1170.2.bs.h.361.4	yes	8	13.10	even	6	inner
1170.2.bs.h.901.2	yes	8	3.2	odd	2	inner
1170.2.bs.h.901.4	yes	8	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(3.84233 - 2.21837i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(3.84233 - 2.21837i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{10} +(-2.59808 - 1.50000i) q^{11} +(2.84233 + 2.21837i) q^{13} +4.43674 q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.842329 - 0.486319i) q^{19} +(0.866025 - 0.500000i) q^{20} +(-1.50000 - 2.59808i) q^{22} +(-0.379706 + 0.657671i) q^{23} -1.00000 q^{25} +(1.35234 + 3.34233i) q^{26} +(3.84233 + 2.21837i) q^{28} +(4.81645 - 8.34233i) q^{29} -6.16879i q^{31} +(-0.866025 + 0.500000i) q^{32} +(-2.21837 - 3.84233i) q^{35} +(-1.50000 - 0.866025i) q^{37} +0.972638 q^{38} +1.00000 q^{40} +(5.19615 + 3.00000i) q^{41} +(1.34233 + 2.32498i) q^{43} -3.00000i q^{44} +(-0.657671 + 0.379706i) q^{46} +3.00000i q^{47} +(6.34233 - 10.9852i) q^{49} +(-0.866025 - 0.500000i) q^{50} +(-0.500000 + 3.57071i) q^{52} -4.43674 q^{53} +(-1.50000 + 2.59808i) q^{55} +(2.21837 + 3.84233i) q^{56} +(8.34233 - 4.81645i) q^{58} +(-4.05703 + 2.34233i) q^{59} +(5.68466 + 9.84612i) q^{61} +(3.08440 - 5.34233i) q^{62} -1.00000 q^{64} +(2.21837 - 2.84233i) q^{65} +(10.6847 + 6.16879i) q^{67} -4.43674i q^{70} +(-5.19615 + 3.00000i) q^{71} +6.92820i q^{73} +(-0.866025 - 1.50000i) q^{74} +(0.842329 + 0.486319i) q^{76} -13.3102 q^{77} -6.68466 q^{79} +(0.866025 + 0.500000i) q^{80} +(3.00000 + 5.19615i) q^{82} -9.36932i q^{83} +2.68466i q^{86} +(1.50000 - 2.59808i) q^{88} +(6.65511 + 3.84233i) q^{89} +(15.8423 + 2.21837i) q^{91} -0.759413 q^{92} +(-1.50000 + 2.59808i) q^{94} +(-0.486319 - 0.842329i) q^{95} +(4.68466 - 2.70469i) q^{97} +(10.9852 - 6.34233i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} + 6 q^{7}+O(q^{10}) \) 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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