LMFDB - Embedded newform 1638.2.j.l.235.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(235,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("1638.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.j (of order $3$, 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:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			235.2
Root			$-1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1638.235
Dual form			1638.2.j.l.1171.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.22474 + 2.12132i) q^{5} +(2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.22474 + 2.12132i) q^{5} +(2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(1.22474 - 2.12132i) q^{10} +(2.72474 - 4.71940i) q^{11} +1.00000 q^{13} +(-0.500000 - 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} +(-3.17423 - 5.49794i) q^{19} -2.44949 q^{20} -5.44949 q^{22} +(-3.67423 - 6.36396i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-0.500000 - 0.866025i) q^{26} +(-2.00000 + 1.73205i) q^{28} -0.550510 q^{29} +(-1.00000 + 1.73205i) q^{31} +(-0.500000 + 0.866025i) q^{32} -3.00000 q^{34} +(1.22474 + 6.36396i) q^{35} +(5.67423 + 9.82806i) q^{37} +(-3.17423 + 5.49794i) q^{38} +(1.22474 + 2.12132i) q^{40} +8.44949 q^{41} +2.00000 q^{43} +(2.72474 + 4.71940i) q^{44} +(-3.67423 + 6.36396i) q^{46} +(-3.94949 - 6.84072i) q^{47} +(5.50000 + 4.33013i) q^{49} +1.00000 q^{50} +(-0.500000 + 0.866025i) q^{52} +(3.27526 - 5.67291i) q^{53} +13.3485 q^{55} +(2.50000 + 0.866025i) q^{56} +(0.275255 + 0.476756i) q^{58} +(5.17423 - 8.96204i) q^{59} +(-6.17423 - 10.6941i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(1.22474 + 2.12132i) q^{65} +(-6.17423 + 10.6941i) q^{67} +(1.50000 + 2.59808i) q^{68} +(4.89898 - 4.24264i) q^{70} -6.79796 q^{71} +(-1.67423 + 2.89986i) q^{73} +(5.67423 - 9.82806i) q^{74} +6.34847 q^{76} +(10.8990 - 9.43879i) q^{77} +(5.00000 + 8.66025i) q^{79} +(1.22474 - 2.12132i) q^{80} +(-4.22474 - 7.31747i) q^{82} -6.00000 q^{83} +7.34847 q^{85} +(-1.00000 - 1.73205i) q^{86} +(2.72474 - 4.71940i) q^{88} +(6.67423 + 11.5601i) q^{89} +(2.50000 + 0.866025i) q^{91} +7.34847 q^{92} +(-3.94949 + 6.84072i) q^{94} +(7.77526 - 13.4671i) q^{95} +3.34847 q^{97} +(1.00000 - 6.92820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} + 10 q^{7} + 4 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^4 + 10 * q^7 + 4 * q^8	$ 4 q - 2 q^{2} - 2 q^{4} + 10 q^{7} + 4 q^{8} + 6 q^{11} + 4 q^{13} - 2 q^{14} - 2 q^{16} + 6 q^{17} + 2 q^{19} - 12 q^{22} - 2 q^{25} - 2 q^{26} - 8 q^{28} - 12 q^{29} - 4 q^{31} - 2 q^{32} - 12 q^{34} + 8 q^{37} + 2 q^{38} + 24 q^{41} + 8 q^{43} + 6 q^{44} - 6 q^{47} + 22 q^{49} + 4 q^{50} - 2 q^{52} + 18 q^{53} + 24 q^{55} + 10 q^{56} + 6 q^{58} + 6 q^{59} - 10 q^{61} + 8 q^{62} + 4 q^{64} - 10 q^{67} + 6 q^{68} + 12 q^{71} + 8 q^{73} + 8 q^{74} - 4 q^{76} + 24 q^{77} + 20 q^{79} - 12 q^{82} - 24 q^{83} - 4 q^{86} + 6 q^{88} + 12 q^{89} + 10 q^{91} - 6 q^{94} + 36 q^{95} - 16 q^{97} + 4 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 + 10 * q^7 + 4 * q^8 + 6 * q^11 + 4 * q^13 - 2 * q^14 - 2 * q^16 + 6 * q^17 + 2 * q^19 - 12 * q^22 - 2 * q^25 - 2 * q^26 - 8 * q^28 - 12 * q^29 - 4 * q^31 - 2 * q^32 - 12 * q^34 + 8 * q^37 + 2 * q^38 + 24 * q^41 + 8 * q^43 + 6 * q^44 - 6 * q^47 + 22 * q^49 + 4 * q^50 - 2 * q^52 + 18 * q^53 + 24 * q^55 + 10 * q^56 + 6 * q^58 + 6 * q^59 - 10 * q^61 + 8 * q^62 + 4 * q^64 - 10 * q^67 + 6 * q^68 + 12 * q^71 + 8 * q^73 + 8 * q^74 - 4 * q^76 + 24 * q^77 + 20 * q^79 - 12 * q^82 - 24 * q^83 - 4 * q^86 + 6 * q^88 + 12 * q^89 + 10 * q^91 - 6 * q^94 + 36 * q^95 - 16 * q^97 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.22474	+	2.12132i	0.547723	+	0.948683i	0.998430	+	0.0560116i	$0.0178384\pi$
$5$	1.22474	+	2.12132i	0.547723	+	0.948683i	−0.450708	+	0.892672i	$0.648828\pi$
$6$		0			0
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$8$	1.00000			0.353553
$9$		0			0
$10$	1.22474	−	2.12132i	0.387298	−	0.670820i
$11$	2.72474	−	4.71940i	0.821541	−	1.42295i	−0.0829925	−	0.996550i	$-0.526448\pi$
$11$	2.72474	−	4.71940i	0.821541	−	1.42295i	0.904534	−	0.426401i	$-0.140219\pi$
$12$		0			0
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	−0.500000	−	2.59808i	−0.133631	−	0.694365i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$		0			0
$19$	−3.17423	−	5.49794i	−0.728219	−	1.26131i	−0.957635	−	0.287984i	$-0.907015\pi$
$19$	−3.17423	−	5.49794i	−0.728219	−	1.26131i	0.229416	−	0.973329i	$-0.426318\pi$
$20$	−2.44949			−0.547723
$21$		0			0
$22$	−5.44949			−1.16184
$23$	−3.67423	−	6.36396i	−0.766131	−	1.32698i	−0.939647	−	0.342147i	$-0.888846\pi$
$23$	−3.67423	−	6.36396i	−0.766131	−	1.32698i	0.173516	−	0.984831i	$-0.444487\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.500000	−	0.866025i	−0.0980581	−	0.169842i
$27$		0			0
$28$	−2.00000	+	1.73205i	−0.377964	+	0.327327i
$29$	−0.550510			−0.102227			−0.0511136	−	0.998693i	$-0.516277\pi$
$29$	−0.550510			−0.102227			−0.0511136	+	0.998693i	$0.516277\pi$
$30$		0			0
$31$	−1.00000	+	1.73205i	−0.179605	+	0.311086i	−0.941745	−	0.336327i	$-0.890815\pi$
$31$	−1.00000	+	1.73205i	−0.179605	+	0.311086i	0.762140	+	0.647412i	$0.224149\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−3.00000			−0.514496
$35$	1.22474	+	6.36396i	0.207020	+	1.07571i
$36$		0			0
$37$	5.67423	+	9.82806i	0.932838	+	1.61572i	0.778444	+	0.627714i	$0.216009\pi$
$37$	5.67423	+	9.82806i	0.932838	+	1.61572i	0.154395	+	0.988009i	$0.450657\pi$
$38$	−3.17423	+	5.49794i	−0.514929	+	0.891883i
$39$		0			0
$40$	1.22474	+	2.12132i	0.193649	+	0.335410i
$41$	8.44949			1.31959			0.659794	−	0.751446i	$-0.270643\pi$
$41$	8.44949			1.31959			0.659794	+	0.751446i	$0.270643\pi$
$42$		0			0
$43$	2.00000			0.304997			0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$	2.72474	+	4.71940i	0.410771	+	0.711476i
$45$		0			0
$46$	−3.67423	+	6.36396i	−0.541736	+	0.938315i
$47$	−3.94949	−	6.84072i	−0.576092	−	0.997821i	−0.995922	−	0.0902182i	$-0.971244\pi$
$47$	−3.94949	−	6.84072i	−0.576092	−	0.997821i	0.419830	−	0.907603i	$-0.362090\pi$
$48$		0			0
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$	1.00000			0.141421
$51$		0			0
$52$	−0.500000	+	0.866025i	−0.0693375	+	0.120096i
$53$	3.27526	−	5.67291i	0.449891	−	0.779234i	−0.548488	−	0.836159i	$-0.684796\pi$
$53$	3.27526	−	5.67291i	0.449891	−	0.779234i	0.998378	+	0.0569248i	$0.0181295\pi$
$54$		0			0
$55$	13.3485			1.79991
$56$	2.50000	+	0.866025i	0.334077	+	0.115728i
$57$		0			0
$58$	0.275255	+	0.476756i	0.0361428	+	0.0626011i
$59$	5.17423	−	8.96204i	0.673628	−	1.16676i	−0.303240	−	0.952914i	$-0.598068\pi$
$59$	5.17423	−	8.96204i	0.673628	−	1.16676i	0.976868	−	0.213844i	$-0.0685983\pi$
$60$		0			0
$61$	−6.17423	−	10.6941i	−0.790530	−	1.36924i	−0.925639	−	0.378407i	$-0.876472\pi$
$61$	−6.17423	−	10.6941i	−0.790530	−	1.36924i	0.135110	−	0.990831i	$-0.456861\pi$
$62$	2.00000			0.254000
$63$		0			0
$64$	1.00000			0.125000
$65$	1.22474	+	2.12132i	0.151911	+	0.263117i
$66$		0			0
$67$	−6.17423	+	10.6941i	−0.754303	+	1.30649i	0.191417	+	0.981509i	$0.438692\pi$
$67$	−6.17423	+	10.6941i	−0.754303	+	1.30649i	−0.945720	+	0.324982i	$0.894642\pi$
$68$	1.50000	+	2.59808i	0.181902	+	0.315063i
$69$		0			0
$70$	4.89898	−	4.24264i	0.585540	−	0.507093i
$71$	−6.79796			−0.806769			−0.403385	−	0.915031i	$-0.632166\pi$
$71$	−6.79796			−0.806769			−0.403385	+	0.915031i	$0.632166\pi$
$72$		0			0
$73$	−1.67423	+	2.89986i	−0.195954	+	0.339403i	−0.947213	−	0.320605i	$-0.896114\pi$
$73$	−1.67423	+	2.89986i	−0.195954	+	0.339403i	0.751259	+	0.660008i	$0.229447\pi$
$74$	5.67423	−	9.82806i	0.659616	−	1.14249i
$75$		0			0
$76$	6.34847			0.728219
$77$	10.8990	−	9.43879i	1.24205	−	1.07565i
$78$		0			0
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	0.997274	+	0.0737937i	$0.0235106\pi$
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	−0.434730	+	0.900561i	$0.643156\pi$
$80$	1.22474	−	2.12132i	0.136931	−	0.237171i
$81$		0			0
$82$	−4.22474	−	7.31747i	−0.466545	−	0.808080i
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$		0			0
$85$	7.34847			0.797053
$86$	−1.00000	−	1.73205i	−0.107833	−	0.186772i
$87$		0			0
$88$	2.72474	−	4.71940i	0.290459	−	0.503089i
$89$	6.67423	+	11.5601i	0.707467	+	1.22537i	0.965794	+	0.259312i	$0.0834957\pi$
$89$	6.67423	+	11.5601i	0.707467	+	1.22537i	−0.258326	+	0.966058i	$0.583171\pi$
$90$		0			0
$91$	2.50000	+	0.866025i	0.262071	+	0.0907841i
$92$	7.34847			0.766131
$93$		0			0
$94$	−3.94949	+	6.84072i	−0.407359	+	0.705566i
$95$	7.77526	−	13.4671i	0.797724	−	1.38170i
$96$		0			0
$97$	3.34847			0.339986			0.169993	−	0.985445i	$-0.445626\pi$
$97$	3.34847			0.339986			0.169993	+	0.985445i	$0.445626\pi$
$98$	1.00000	−	6.92820i	0.101015	−	0.699854i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	0.550510	−	0.953512i	0.0547778	−	0.0948780i	−0.837336	−	0.546688i	$-0.815888\pi$
$101$	0.550510	−	0.953512i	0.0547778	−	0.0948780i	0.892114	+	0.451810i	$0.149222\pi$
$102$		0			0
$103$	6.34847	+	10.9959i	0.625533	+	1.08346i	0.988437	+	0.151629i	$0.0484519\pi$
$103$	6.34847	+	10.9959i	0.625533	+	1.08346i	−0.362904	+	0.931826i	$0.618215\pi$
$104$	1.00000			0.0980581
$105$		0			0
$106$	−6.55051			−0.636242
$107$	6.00000	+	10.3923i	0.580042	+	1.00466i	0.995474	+	0.0950377i	$0.0302972\pi$
$107$	6.00000	+	10.3923i	0.580042	+	1.00466i	−0.415432	+	0.909624i	$0.636370\pi$
$108$		0			0
$109$	−5.34847	+	9.26382i	−0.512290	+	0.887313i	0.487608	+	0.873063i	$0.337870\pi$
$109$	−5.34847	+	9.26382i	−0.512290	+	0.887313i	−0.999898	+	0.0142504i	$0.995464\pi$
$110$	−6.67423	−	11.5601i	−0.636363	−	1.10221i
$111$		0			0
$112$	−0.500000	−	2.59808i	−0.0472456	−	0.245495i
$113$	−12.7980			−1.20393			−0.601965	−	0.798522i	$-0.705615\pi$
$113$	−12.7980			−1.20393			−0.601965	+	0.798522i	$0.705615\pi$
$114$		0			0
$115$	9.00000	−	15.5885i	0.839254	−	1.45363i
$116$	0.275255	−	0.476756i	0.0255568	−	0.0442657i
$117$		0			0
$118$	−10.3485			−0.952654
$119$	6.00000	−	5.19615i	0.550019	−	0.476331i
$120$		0			0
$121$	−9.34847	−	16.1920i	−0.849861	−	1.47200i
$122$	−6.17423	+	10.6941i	−0.558989	+	0.968197i
$123$		0			0
$124$	−1.00000	−	1.73205i	−0.0898027	−	0.155543i
$125$	9.79796			0.876356
$126$		0			0
$127$	−11.3485			−1.00701			−0.503507	−	0.863991i	$-0.667957\pi$
$127$	−11.3485			−1.00701			−0.503507	+	0.863991i	$0.667957\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	1.22474	−	2.12132i	0.107417	−	0.186052i
$131$	−1.77526	−	3.07483i	−0.155105	−	0.268649i	0.777992	−	0.628274i	$-0.216238\pi$
$131$	−1.77526	−	3.07483i	−0.155105	−	0.268649i	−0.933097	+	0.359624i	$0.882905\pi$
$132$		0			0
$133$	−3.17423	−	16.4938i	−0.275241	−	1.43019i
$134$	12.3485			1.06675
$135$		0			0
$136$	1.50000	−	2.59808i	0.128624	−	0.222783i
$137$	−0.674235	+	1.16781i	−0.0576038	+	0.0997726i	−0.893389	−	0.449283i	$-0.851679\pi$
$137$	−0.674235	+	1.16781i	−0.0576038	+	0.0997726i	0.835786	+	0.549056i	$0.185013\pi$
$138$		0			0
$139$	−11.3485			−0.962565			−0.481282	−	0.876566i	$-0.659829\pi$
$139$	−11.3485			−0.962565			−0.481282	+	0.876566i	$0.659829\pi$
$140$	−6.12372	−	2.12132i	−0.517549	−	0.179284i
$141$		0			0
$142$	3.39898	+	5.88721i	0.285236	+	0.494043i
$143$	2.72474	−	4.71940i	0.227855	−	0.394656i
$144$		0			0
$145$	−0.674235	−	1.16781i	−0.0559921	−	0.0969812i
$146$	3.34847			0.277121
$147$		0			0
$148$	−11.3485			−0.932838
$149$	9.12372	+	15.8028i	0.747445	+	1.29461i	0.949044	+	0.315144i	$0.102053\pi$
$149$	9.12372	+	15.8028i	0.747445	+	1.29461i	−0.201599	+	0.979468i	$0.564614\pi$
$150$		0			0
$151$	10.8485	−	18.7901i	0.882836	−	1.52912i	0.0346618	−	0.999399i	$-0.488965\pi$
$151$	10.8485	−	18.7901i	0.882836	−	1.52912i	0.848174	−	0.529718i	$-0.177702\pi$
$152$	−3.17423	−	5.49794i	−0.257464	−	0.445941i
$153$		0			0
$154$	−13.6237	−	4.71940i	−1.09783	−	0.380300i
$155$	−4.89898			−0.393496
$156$		0			0
$157$	1.17423	−	2.03383i	0.0937141	−	0.162318i	−0.815357	−	0.578958i	$-0.803459\pi$
$157$	1.17423	−	2.03383i	0.0937141	−	0.162318i	0.909071	+	0.416641i	$0.136793\pi$
$158$	5.00000	−	8.66025i	0.397779	−	0.688973i
$159$		0			0
$160$	−2.44949			−0.193649
$161$	−3.67423	−	19.0919i	−0.289570	−	1.50465i
$162$		0			0
$163$	4.17423	+	7.22999i	0.326951	+	0.566296i	0.981905	−	0.189372i	$-0.0606454\pi$
$163$	4.17423	+	7.22999i	0.326951	+	0.566296i	−0.654954	+	0.755669i	$0.727312\pi$
$164$	−4.22474	+	7.31747i	−0.329897	+	0.571399i
$165$		0			0
$166$	3.00000	+	5.19615i	0.232845	+	0.403300i
$167$	−13.8990			−1.07554			−0.537768	−	0.843093i	$-0.680732\pi$
$167$	−13.8990			−1.07554			−0.537768	+	0.843093i	$0.680732\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	−3.67423	−	6.36396i	−0.281801	−	0.488094i
$171$		0			0
$172$	−1.00000	+	1.73205i	−0.0762493	+	0.132068i
$173$	−5.72474	−	9.91555i	−0.435244	−	0.753865i	0.562071	−	0.827089i	$-0.310005\pi$
$173$	−5.72474	−	9.91555i	−0.435244	−	0.753865i	−0.997316	+	0.0732236i	$0.976671\pi$
$174$		0			0
$175$	−2.00000	+	1.73205i	−0.151186	+	0.130931i
$176$	−5.44949			−0.410771
$177$		0			0
$178$	6.67423	−	11.5601i	0.500255	−	0.866467i
$179$	−5.44949	+	9.43879i	−0.407314	+	0.705489i	−0.994588	−	0.103900i	$-0.966868\pi$
$179$	−5.44949	+	9.43879i	−0.407314	+	0.705489i	0.587274	+	0.809388i	$0.300201\pi$
$180$		0			0
$181$	18.3485			1.36383			0.681915	−	0.731431i	$-0.261147\pi$
$181$	18.3485			1.36383			0.681915	+	0.731431i	$0.261147\pi$
$182$	−0.500000	−	2.59808i	−0.0370625	−	0.192582i
$183$		0			0
$184$	−3.67423	−	6.36396i	−0.270868	−	0.469157i
$185$	−13.8990	+	24.0737i	−1.02187	+	1.76994i
$186$		0			0
$187$	−8.17423	−	14.1582i	−0.597759	−	1.03535i
$188$	7.89898			0.576092
$189$		0			0
$190$	−15.5505			−1.12815
$191$	8.44949	+	14.6349i	0.611384	+	1.05895i	0.991007	+	0.133807i	$0.0427201\pi$
$191$	8.44949	+	14.6349i	0.611384	+	1.05895i	−0.379624	+	0.925141i	$0.623947\pi$
$192$		0			0
$193$	−4.67423	+	8.09601i	−0.336459	+	0.582764i	−0.983764	−	0.179467i	$-0.942563\pi$
$193$	−4.67423	+	8.09601i	−0.336459	+	0.582764i	0.647305	+	0.762231i	$0.275896\pi$
$194$	−1.67423	−	2.89986i	−0.120203	−	0.208198i
$195$		0			0
$196$	−6.50000	+	2.59808i	−0.464286	+	0.185577i
$197$	8.44949			0.602001			0.301001	−	0.953624i	$-0.402679\pi$
$197$	8.44949			0.602001			0.301001	+	0.953624i	$0.402679\pi$
$198$		0			0
$199$	11.6742	−	20.2204i	0.827565	−	1.43338i	−0.0723789	−	0.997377i	$-0.523059\pi$
$199$	11.6742	−	20.2204i	0.827565	−	1.43338i	0.899943	−	0.436007i	$-0.143608\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$		0			0
$202$	−1.10102			−0.0774675
$203$	−1.37628	−	0.476756i	−0.0965956	−	0.0334617i
$204$		0			0
$205$	10.3485	+	17.9241i	0.722768	+	1.25187i
$206$	6.34847	−	10.9959i	0.442319	−	0.766119i
$207$		0			0
$208$	−0.500000	−	0.866025i	−0.0346688	−	0.0600481i
$209$	−34.5959			−2.39305
$210$		0			0
$211$	−5.34847			−0.368204			−0.184102	−	0.982907i	$-0.558938\pi$
$211$	−5.34847			−0.368204			−0.184102	+	0.982907i	$0.558938\pi$
$212$	3.27526	+	5.67291i	0.224945	+	0.389617i
$213$		0			0
$214$	6.00000	−	10.3923i	0.410152	−	0.710403i
$215$	2.44949	+	4.24264i	0.167054	+	0.289346i
$216$		0			0
$217$	−4.00000	+	3.46410i	−0.271538	+	0.235159i
$218$	10.6969			0.724488
$219$		0			0
$220$	−6.67423	+	11.5601i	−0.449977	+	0.779383i
$221$	1.50000	−	2.59808i	0.100901	−	0.174766i
$222$		0			0
$223$	23.0000			1.54019			0.770097	−	0.637927i	$-0.220208\pi$
$223$	23.0000			1.54019			0.770097	+	0.637927i	$0.220208\pi$
$224$	−2.00000	+	1.73205i	−0.133631	+	0.115728i
$225$		0			0
$226$	6.39898	+	11.0834i	0.425654	+	0.737254i
$227$	1.34847	−	2.33562i	0.0895010	−	0.155020i	−0.817799	−	0.575504i	$-0.804806\pi$
$227$	1.34847	−	2.33562i	0.0895010	−	0.155020i	0.907300	+	0.420483i	$0.138139\pi$
$228$		0			0
$229$	−1.00000	−	1.73205i	−0.0660819	−	0.114457i	0.831092	−	0.556136i	$-0.187717\pi$
$229$	−1.00000	−	1.73205i	−0.0660819	−	0.114457i	−0.897173	+	0.441679i	$0.854383\pi$
$230$	−18.0000			−1.18688
$231$		0			0
$232$	−0.550510			−0.0361428
$233$	2.05051	+	3.55159i	0.134333	+	0.232672i	0.925343	−	0.379132i	$-0.123777\pi$
$233$	2.05051	+	3.55159i	0.134333	+	0.232672i	−0.791009	+	0.611804i	$0.790444\pi$
$234$		0			0
$235$	9.67423	−	16.7563i	0.631077	−	1.09306i
$236$	5.17423	+	8.96204i	0.336814	+	0.583379i
$237$		0			0
$238$	−7.50000	−	2.59808i	−0.486153	−	0.168408i
$239$	−0.303062			−0.0196034			−0.00980171	−	0.999952i	$-0.503120\pi$
$239$	−0.303062			−0.0196034			−0.00980171	+	0.999952i	$0.503120\pi$
$240$		0			0
$241$	−5.34847	+	9.26382i	−0.344525	+	0.596735i	−0.985267	−	0.171021i	$-0.945293\pi$
$241$	−5.34847	+	9.26382i	−0.344525	+	0.596735i	0.640742	+	0.767756i	$0.278627\pi$
$242$	−9.34847	+	16.1920i	−0.600942	+	1.04086i
$243$		0			0
$244$	12.3485			0.790530
$245$	−2.44949	+	16.9706i	−0.156492	+	1.08421i
$246$		0			0
$247$	−3.17423	−	5.49794i	−0.201972	−	0.349825i
$248$	−1.00000	+	1.73205i	−0.0635001	+	0.109985i
$249$		0			0
$250$	−4.89898	−	8.48528i	−0.309839	−	0.536656i
$251$	−3.79796			−0.239725			−0.119863	−	0.992790i	$-0.538245\pi$
$251$	−3.79796			−0.239725			−0.119863	+	0.992790i	$0.538245\pi$
$252$		0			0
$253$	−40.0454			−2.51763
$254$	5.67423	+	9.82806i	0.356033	+	0.616667i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.34847	+	12.7279i	0.458385	+	0.793946i	0.998876	−	0.0474039i	$-0.0150948\pi$
$257$	7.34847	+	12.7279i	0.458385	+	0.793946i	−0.540491	+	0.841350i	$0.681761\pi$
$258$		0			0
$259$	5.67423	+	29.4842i	0.352580	+	1.83206i
$260$	−2.44949			−0.151911
$261$		0			0
$262$	−1.77526	+	3.07483i	−0.109676	+	0.189964i
$263$	5.57321	−	9.65309i	0.343659	−	0.595235i	−0.641450	−	0.767165i	$-0.721667\pi$
$263$	5.57321	−	9.65309i	0.343659	−	0.595235i	0.985109	+	0.171930i	$0.0550002\pi$
$264$		0			0
$265$	16.0454			0.985662
$266$	−12.6969	+	10.9959i	−0.778499	+	0.674200i
$267$		0			0
$268$	−6.17423	−	10.6941i	−0.377151	−	0.653245i
$269$	−6.82577	+	11.8226i	−0.416174	+	0.720835i	−0.995551	−	0.0942250i	$-0.969963\pi$
$269$	−6.82577	+	11.8226i	−0.416174	+	0.720835i	0.579377	+	0.815060i	$0.303296\pi$
$270$		0			0
$271$	1.84847	+	3.20164i	0.112287	+	0.194486i	0.916692	−	0.399595i	$-0.130849\pi$
$271$	1.84847	+	3.20164i	0.112287	+	0.194486i	−0.804405	+	0.594081i	$0.797516\pi$
$272$	−3.00000			−0.181902
$273$		0			0
$274$	1.34847			0.0814640
$275$	2.72474	+	4.71940i	0.164308	+	0.284590i
$276$		0			0
$277$	4.17423	−	7.22999i	0.250805	−	0.434408i	−0.712942	−	0.701223i	$-0.752638\pi$
$277$	4.17423	−	7.22999i	0.250805	−	0.434408i	0.963748	+	0.266815i	$0.0859712\pi$
$278$	5.67423	+	9.82806i	0.340318	+	0.589448i
$279$		0			0
$280$	1.22474	+	6.36396i	0.0731925	+	0.380319i
$281$	−24.0000			−1.43172			−0.715860	−	0.698244i	$-0.753965\pi$
$281$	−24.0000			−1.43172			−0.715860	+	0.698244i	$0.753965\pi$
$282$		0			0
$283$	8.67423	−	15.0242i	0.515630	−	0.893097i	−0.484206	−	0.874954i	$-0.660891\pi$
$283$	8.67423	−	15.0242i	0.515630	−	0.893097i	0.999835	−	0.0181427i	$-0.00577531\pi$
$284$	3.39898	−	5.88721i	0.201692	−	0.349341i
$285$		0			0
$286$	−5.44949			−0.322235
$287$	21.1237	+	7.31747i	1.24689	+	0.431937i
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	−0.674235	+	1.16781i	−0.0395924	+	0.0685761i
$291$		0			0
$292$	−1.67423	−	2.89986i	−0.0979772	−	0.169701i
$293$	6.24745			0.364980			0.182490	−	0.983208i	$-0.441584\pi$
$293$	6.24745			0.364980			0.182490	+	0.983208i	$0.441584\pi$
$294$		0			0
$295$	25.3485			1.47584
$296$	5.67423	+	9.82806i	0.329808	+	0.571245i
$297$		0			0
$298$	9.12372	−	15.8028i	0.528523	−	0.915429i
$299$	−3.67423	−	6.36396i	−0.212486	−	0.368037i
$300$		0			0
$301$	5.00000	+	1.73205i	0.288195	+	0.0998337i
$302$	−21.6969			−1.24852
$303$		0			0
$304$	−3.17423	+	5.49794i	−0.182055	+	0.315328i
$305$	15.1237	−	26.1951i	0.865982	−	1.49992i
$306$		0			0
$307$	−11.0454			−0.630395			−0.315197	−	0.949026i	$-0.602071\pi$
$307$	−11.0454			−0.630395			−0.315197	+	0.949026i	$0.602071\pi$
$308$	2.72474	+	14.1582i	0.155257	+	0.806738i
$309$		0			0
$310$	2.44949	+	4.24264i	0.139122	+	0.240966i
$311$	10.4722	−	18.1384i	0.593824	−	1.02853i	−0.399888	−	0.916564i	$-0.630951\pi$
$311$	10.4722	−	18.1384i	0.593824	−	1.02853i	0.993712	−	0.111969i	$-0.0357156\pi$
$312$		0			0
$313$	15.3485	+	26.5843i	0.867547	+	1.50264i	0.864496	+	0.502640i	$0.167638\pi$
$313$	15.3485	+	26.5843i	0.867547	+	1.50264i	0.00305080	+	0.999995i	$0.499029\pi$
$314$	−2.34847			−0.132532
$315$		0			0
$316$	−10.0000			−0.562544
$317$	−6.79796	−	11.7744i	−0.381811	−	0.661317i	0.609510	−	0.792779i	$-0.291366\pi$
$317$	−6.79796	−	11.7744i	−0.381811	−	0.661317i	−0.991321	+	0.131462i	$0.958033\pi$
$318$		0			0
$319$	−1.50000	+	2.59808i	−0.0839839	+	0.145464i
$320$	1.22474	+	2.12132i	0.0684653	+	0.118585i
$321$		0			0
$322$	−14.6969	+	12.7279i	−0.819028	+	0.709299i
$323$	−19.0454			−1.05971
$324$		0			0
$325$	−0.500000	+	0.866025i	−0.0277350	+	0.0480384i
$326$	4.17423	−	7.22999i	0.231189	−	0.400432i
$327$		0			0
$328$	8.44949			0.466545
$329$	−3.94949	−	20.5222i	−0.217742	−	1.13142i
$330$		0			0
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	−0.998298	−	0.0583130i	$-0.981428\pi$
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	0.448649	−	0.893708i	$-0.351905\pi$
$332$	3.00000	−	5.19615i	0.164646	−	0.285176i
$333$		0			0
$334$	6.94949	+	12.0369i	0.380259	+	0.658628i
$335$	−30.2474			−1.65259
$336$		0			0
$337$	−21.6969			−1.18191			−0.590954	−	0.806705i	$-0.701248\pi$
$337$	−21.6969			−1.18191			−0.590954	+	0.806705i	$0.701248\pi$
$338$	−0.500000	−	0.866025i	−0.0271964	−	0.0471056i
$339$		0			0
$340$	−3.67423	+	6.36396i	−0.199263	+	0.345134i
$341$	5.44949	+	9.43879i	0.295106	+	0.511139i
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	2.00000			0.107833
$345$		0			0
$346$	−5.72474	+	9.91555i	−0.307764	+	0.533063i
$347$	−15.6742	+	27.1486i	−0.841437	+	1.45741i	0.0472429	+	0.998883i	$0.484957\pi$
$347$	−15.6742	+	27.1486i	−0.841437	+	1.45741i	−0.888680	+	0.458528i	$0.848377\pi$
$348$		0			0
$349$	−29.3485			−1.57099			−0.785494	−	0.618870i	$-0.787591\pi$
$349$	−29.3485			−1.57099			−0.785494	+	0.618870i	$0.787591\pi$
$350$	2.50000	+	0.866025i	0.133631	+	0.0462910i
$351$		0			0
$352$	2.72474	+	4.71940i	0.145229	+	0.251545i
$353$	0.550510	−	0.953512i	0.0293007	−	0.0507503i	−0.851003	−	0.525160i	$-0.824005\pi$
$353$	0.550510	−	0.953512i	0.0293007	−	0.0507503i	0.880304	+	0.474410i	$0.157339\pi$
$354$		0			0
$355$	−8.32577	−	14.4206i	−0.441886	−	0.765369i
$356$	−13.3485			−0.707467
$357$		0			0
$358$	10.8990			0.576029
$359$	12.5505	+	21.7381i	0.662391	+	1.14729i	0.979986	+	0.199068i	$0.0637914\pi$
$359$	12.5505	+	21.7381i	0.662391	+	1.14729i	−0.317595	+	0.948226i	$0.602875\pi$
$360$		0			0
$361$	−10.6515	+	18.4490i	−0.560607	+	0.971000i
$362$	−9.17423	−	15.8902i	−0.482187	−	0.835172i
$363$		0			0
$364$	−2.00000	+	1.73205i	−0.104828	+	0.0907841i
$365$	−8.20204			−0.429314
$366$		0			0
$367$	−8.34847	+	14.4600i	−0.435787	+	0.754804i	−0.997359	−	0.0726228i	$-0.976863\pi$
$367$	−8.34847	+	14.4600i	−0.435787	+	0.754804i	0.561573	+	0.827427i	$0.310196\pi$
$368$	−3.67423	+	6.36396i	−0.191533	+	0.331744i
$369$		0			0
$370$	27.7980			1.44515
$371$	13.1010	−	11.3458i	0.680171	−	0.589045i
$372$		0			0
$373$	16.1742	+	28.0146i	0.837470	+	1.45054i	0.892003	+	0.452029i	$0.149300\pi$
$373$	16.1742	+	28.0146i	0.837470	+	1.45054i	−0.0545332	+	0.998512i	$0.517367\pi$
$374$	−8.17423	+	14.1582i	−0.422680	+	0.732103i
$375$		0			0
$376$	−3.94949	−	6.84072i	−0.203679	−	0.352783i
$377$	−0.550510			−0.0283527
$378$		0			0
$379$	31.3939			1.61260			0.806298	−	0.591510i	$-0.201468\pi$
$379$	31.3939			1.61260			0.806298	+	0.591510i	$0.201468\pi$
$380$	7.77526	+	13.4671i	0.398862	+	0.690850i
$381$		0			0
$382$	8.44949	−	14.6349i	0.432314	−	0.748789i
$383$	−6.55051	−	11.3458i	−0.334715	−	0.579744i	0.648715	−	0.761032i	$-0.275307\pi$
$383$	−6.55051	−	11.3458i	−0.334715	−	0.579744i	−0.983430	+	0.181288i	$0.941974\pi$
$384$		0			0
$385$	33.3712	+	11.5601i	1.70075	+	0.589158i
$386$	9.34847			0.475825
$387$		0			0
$388$	−1.67423	+	2.89986i	−0.0849964	+	0.147218i
$389$	−13.0732	+	22.6435i	−0.662838	+	1.14807i	0.317028	+	0.948416i	$0.397315\pi$
$389$	−13.0732	+	22.6435i	−0.662838	+	1.14807i	−0.979867	+	0.199653i	$0.936018\pi$
$390$		0			0
$391$	−22.0454			−1.11488
$392$	5.50000	+	4.33013i	0.277792	+	0.218704i
$393$		0			0
$394$	−4.22474	−	7.31747i	−0.212840	−	0.368649i
$395$	−12.2474	+	21.2132i	−0.616236	+	1.06735i
$396$		0			0
$397$	−3.32577	−	5.76039i	−0.166915	−	0.289106i	0.770418	−	0.637539i	$-0.220047\pi$
$397$	−3.32577	−	5.76039i	−0.166915	−	0.289106i	−0.937334	+	0.348433i	$0.886714\pi$
$398$	−23.3485			−1.17035
$399$		0			0
$400$	1.00000			0.0500000
$401$	9.67423	+	16.7563i	0.483108	+	0.836768i	0.999812	−	0.0193963i	$-0.00617443\pi$
$401$	9.67423	+	16.7563i	0.483108	+	0.836768i	−0.516704	+	0.856164i	$0.672841\pi$
$402$		0			0
$403$	−1.00000	+	1.73205i	−0.0498135	+	0.0862796i
$404$	0.550510	+	0.953512i	0.0273889	+	0.0474390i
$405$		0			0
$406$	0.275255	+	1.43027i	0.0136607	+	0.0709830i
$407$	61.8434			3.06546
$408$		0			0
$409$	4.02270	−	6.96753i	0.198910	−	0.344522i	−0.749265	−	0.662270i	$-0.769593\pi$
$409$	4.02270	−	6.96753i	0.198910	−	0.344522i	0.948175	+	0.317748i	$0.102927\pi$
$410$	10.3485	−	17.9241i	0.511074	−	0.885207i
$411$		0			0
$412$	−12.6969			−0.625533
$413$	20.6969	−	17.9241i	1.01843	−	0.881986i
$414$		0			0
$415$	−7.34847	−	12.7279i	−0.360722	−	0.624789i
$416$	−0.500000	+	0.866025i	−0.0245145	+	0.0424604i
$417$		0			0
$418$	17.2980	+	29.9609i	0.846071	+	1.46544i
$419$	−34.8990			−1.70493			−0.852463	−	0.522787i	$-0.824892\pi$
$419$	−34.8990			−1.70493			−0.852463	+	0.522787i	$0.824892\pi$
$420$		0			0
$421$	−2.65153			−0.129228			−0.0646139	−	0.997910i	$-0.520582\pi$
$421$	−2.65153			−0.129228			−0.0646139	+	0.997910i	$0.520582\pi$
$422$	2.67423	+	4.63191i	0.130180	+	0.225478i
$423$		0			0
$424$	3.27526	−	5.67291i	0.159060	−	0.275501i
$425$	1.50000	+	2.59808i	0.0727607	+	0.126025i
$426$		0			0
$427$	−6.17423	−	32.0823i	−0.298792	−	1.55257i
$428$	−12.0000			−0.580042
$429$		0			0
$430$	2.44949	−	4.24264i	0.118125	−	0.204598i
$431$	6.55051	−	11.3458i	0.315527	−	0.546509i	−0.664022	−	0.747713i	$-0.731152\pi$
$431$	6.55051	−	11.3458i	0.315527	−	0.546509i	0.979549	+	0.201204i	$0.0644854\pi$
$432$		0			0
$433$	−15.6969			−0.754347			−0.377173	−	0.926143i	$-0.623104\pi$
$433$	−15.6969			−0.754347			−0.377173	+	0.926143i	$0.623104\pi$
$434$	5.00000	+	1.73205i	0.240008	+	0.0831411i
$435$		0			0
$436$	−5.34847	−	9.26382i	−0.256145	−	0.443657i
$437$	−23.3258	+	40.4014i	−1.11582	+	1.93266i
$438$		0			0
$439$	−3.02270	−	5.23548i	−0.144266	−	0.249876i	0.784833	−	0.619707i	$-0.212749\pi$
$439$	−3.02270	−	5.23548i	−0.144266	−	0.249876i	−0.929099	+	0.369832i	$0.879415\pi$
$440$	13.3485			0.636363
$441$		0			0
$442$	−3.00000			−0.142695
$443$	1.22474	+	2.12132i	0.0581894	+	0.100787i	0.893653	−	0.448759i	$-0.148134\pi$
$443$	1.22474	+	2.12132i	0.0581894	+	0.100787i	−0.835463	+	0.549546i	$0.814801\pi$
$444$		0			0
$445$	−16.3485	+	28.3164i	−0.774992	+	1.34233i
$446$	−11.5000	−	19.9186i	−0.544541	−	0.943172i
$447$		0			0
$448$	2.50000	+	0.866025i	0.118114	+	0.0409159i
$449$	−24.4949			−1.15599			−0.577993	−	0.816042i	$-0.696164\pi$
$449$	−24.4949			−1.15599			−0.577993	+	0.816042i	$0.696164\pi$
$450$		0			0
$451$	23.0227	−	39.8765i	1.08410	−	1.87771i
$452$	6.39898	−	11.0834i	0.300983	−	0.521317i
$453$		0			0
$454$	−2.69694			−0.126574
$455$	1.22474	+	6.36396i	0.0574169	+	0.298347i
$456$		0			0
$457$	10.3258	+	17.8848i	0.483019	+	0.836613i	0.999810	−	0.0194983i	$-0.00620689\pi$
$457$	10.3258	+	17.8848i	0.483019	+	0.836613i	−0.516791	+	0.856112i	$0.672874\pi$
$458$	−1.00000	+	1.73205i	−0.0467269	+	0.0809334i
$459$		0			0
$460$	9.00000	+	15.5885i	0.419627	+	0.726816i
$461$	19.5959			0.912673			0.456336	−	0.889807i	$-0.349161\pi$
$461$	19.5959			0.912673			0.456336	+	0.889807i	$0.349161\pi$
$462$		0			0
$463$	16.6969			0.775973			0.387986	−	0.921665i	$-0.373171\pi$
$463$	16.6969			0.775973			0.387986	+	0.921665i	$0.373171\pi$
$464$	0.275255	+	0.476756i	0.0127784	+	0.0221328i
$465$		0			0
$466$	2.05051	−	3.55159i	0.0949881	−	0.164524i
$467$	17.5732	+	30.4377i	0.813191	+	1.40849i	0.910619	+	0.413246i	$0.135605\pi$
$467$	17.5732	+	30.4377i	0.813191	+	1.40849i	−0.0974280	+	0.995243i	$0.531062\pi$
$468$		0			0
$469$	−24.6969	+	21.3882i	−1.14040	+	0.987614i
$470$	−19.3485			−0.892478
$471$		0			0
$472$	5.17423	−	8.96204i	0.238163	−	0.412511i
$473$	5.44949	−	9.43879i	0.250568	−	0.433996i
$474$		0			0
$475$	6.34847			0.291288
$476$	1.50000	+	7.79423i	0.0687524	+	0.357248i
$477$		0			0
$478$	0.151531	+	0.262459i	0.00693086	+	0.0120046i
$479$	−3.94949	+	6.84072i	−0.180457	+	0.312560i	−0.942036	−	0.335511i	$-0.891091\pi$
$479$	−3.94949	+	6.84072i	−0.180457	+	0.312560i	0.761579	+	0.648072i	$0.224424\pi$
$480$		0			0
$481$	5.67423	+	9.82806i	0.258723	+	0.448121i
$482$	10.6969			0.487232
$483$		0			0
$484$	18.6969			0.849861
$485$	4.10102	+	7.10318i	0.186218	+	0.322539i
$486$		0			0
$487$	3.50000	−	6.06218i	0.158600	−	0.274703i	−0.775764	−	0.631023i	$-0.782635\pi$
$487$	3.50000	−	6.06218i	0.158600	−	0.274703i	0.934364	+	0.356320i	$0.115969\pi$
$488$	−6.17423	−	10.6941i	−0.279494	−	0.484099i
$489$		0			0
$490$	15.9217	−	6.36396i	0.719268	−	0.287494i
$491$	3.79796			0.171399			0.0856997	−	0.996321i	$-0.472687\pi$
$491$	3.79796			0.171399			0.0856997	+	0.996321i	$0.472687\pi$
$492$		0			0
$493$	−0.825765	+	1.43027i	−0.0371906	+	0.0644160i
$494$	−3.17423	+	5.49794i	−0.142816	+	0.247364i
$495$		0			0
$496$	2.00000			0.0898027
$497$	−16.9949	−	5.88721i	−0.762325	−	0.264077i
$498$		0			0
$499$	−17.3485	−	30.0484i	−0.776624	−	1.34515i	−0.933877	−	0.357594i	$-0.883597\pi$
$499$	−17.3485	−	30.0484i	−0.776624	−	1.34515i	0.157253	−	0.987558i	$-0.449736\pi$
$500$	−4.89898	+	8.48528i	−0.219089	+	0.379473i
$501$		0			0
$502$	1.89898	+	3.28913i	0.0847556	+	0.146801i
$503$	−19.1010			−0.851672			−0.425836	−	0.904800i	$-0.640020\pi$
$503$	−19.1010			−0.851672			−0.425836	+	0.904800i	$0.640020\pi$
$504$		0			0
$505$	2.69694			0.120012
$506$	20.0227	+	34.6803i	0.890118	+	1.54173i
$507$		0			0
$508$	5.67423	−	9.82806i	0.251753	−	0.436050i
$509$	−14.6969	−	25.4558i	−0.651430	−	1.12831i	−0.982776	−	0.184801i	$-0.940836\pi$
$509$	−14.6969	−	25.4558i	−0.651430	−	1.12831i	0.331346	−	0.943509i	$-0.392497\pi$
$510$		0			0
$511$	−6.69694	+	5.79972i	−0.296255	+	0.256564i
$512$	1.00000			0.0441942
$513$		0			0
$514$	7.34847	−	12.7279i	0.324127	−	0.561405i
$515$	−15.5505	+	26.9343i	−0.685237	+	1.18687i
$516$		0			0
$517$	−43.0454			−1.89313
$518$	22.6969	−	19.6561i	0.997246	−	0.863641i
$519$		0			0
$520$	1.22474	+	2.12132i	0.0537086	+	0.0930261i
$521$	−10.8990	+	18.8776i	−0.477493	+	0.827042i	−0.999667	−	0.0257968i	$-0.991788\pi$
$521$	−10.8990	+	18.8776i	−0.477493	+	0.827042i	0.522174	+	0.852839i	$0.325121\pi$
$522$		0			0
$523$	−7.00000	−	12.1244i	−0.306089	−	0.530161i	0.671414	−	0.741082i	$-0.265687\pi$
$523$	−7.00000	−	12.1244i	−0.306089	−	0.530161i	−0.977503	+	0.210921i	$0.932354\pi$
$524$	3.55051			0.155105
$525$		0			0
$526$	−11.1464			−0.486007
$527$	3.00000	+	5.19615i	0.130682	+	0.226348i
$528$		0			0
$529$	−15.5000	+	26.8468i	−0.673913	+	1.16725i
$530$	−8.02270	−	13.8957i	−0.348484	−	0.603592i
$531$		0			0
$532$	15.8712	+	5.49794i	0.688103	+	0.238366i
$533$	8.44949			0.365988
$534$		0			0
$535$	−14.6969	+	25.4558i	−0.635404	+	1.10055i
$536$	−6.17423	+	10.6941i	−0.266686	+	0.461914i
$537$		0			0
$538$	13.6515			0.588559
$539$	35.4217	−	14.1582i	1.52572	−	0.609836i
$540$		0			0
$541$	−19.6742	−	34.0768i	−0.845861	−	1.46507i	−0.884871	−	0.465836i	$-0.845754\pi$
$541$	−19.6742	−	34.0768i	−0.845861	−	1.46507i	0.0390096	−	0.999239i	$-0.487580\pi$
$542$	1.84847	−	3.20164i	0.0793986	−	0.137522i
$543$		0			0
$544$	1.50000	+	2.59808i	0.0643120	+	0.111392i
$545$	−26.2020			−1.12237
$546$		0			0
$547$	33.3485			1.42588			0.712939	−	0.701226i	$-0.247364\pi$
$547$	33.3485			1.42588			0.712939	+	0.701226i	$0.247364\pi$
$548$	−0.674235	−	1.16781i	−0.0288019	−	0.0498863i
$549$		0			0
$550$	2.72474	−	4.71940i	0.116184	−	0.201236i
$551$	1.74745	+	3.02667i	0.0744438	+	0.128940i
$552$		0			0
$553$	5.00000	+	25.9808i	0.212622	+	1.10481i
$554$	−8.34847			−0.354692
$555$		0			0
$556$	5.67423	−	9.82806i	0.240641	−	0.416803i
$557$	12.5505	−	21.7381i	0.531782	−	0.921074i	−0.467530	−	0.883977i	$-0.654856\pi$
$557$	12.5505	−	21.7381i	0.531782	−	0.921074i	0.999312	−	0.0370963i	$-0.0118108\pi$
$558$		0			0
$559$	2.00000			0.0845910
$560$	4.89898	−	4.24264i	0.207020	−	0.179284i
$561$		0			0
$562$	12.0000	+	20.7846i	0.506189	+	0.876746i
$563$	−14.6969	+	25.4558i	−0.619402	+	1.07284i	0.370193	+	0.928955i	$0.379292\pi$
$563$	−14.6969	+	25.4558i	−0.619402	+	1.07284i	−0.989595	+	0.143881i	$0.954042\pi$
$564$		0			0
$565$	−15.6742	−	27.1486i	−0.659420	−	1.14215i
$566$	−17.3485			−0.729211
$567$		0			0
$568$	−6.79796			−0.285236
$569$	6.15153	+	10.6548i	0.257886	+	0.446671i	0.965675	−	0.259752i	$-0.0836409\pi$
$569$	6.15153	+	10.6548i	0.257886	+	0.446671i	−0.707790	+	0.706423i	$0.750308\pi$
$570$		0			0
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	−0.995788	−	0.0916910i	$-0.970773\pi$
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	0.577301	+	0.816532i	$0.304106\pi$
$572$	2.72474	+	4.71940i	0.113927	+	0.197328i
$573$		0			0
$574$	−4.22474	−	21.9524i	−0.176337	−	0.916276i
$575$	7.34847			0.306452
$576$		0			0
$577$	−8.34847	+	14.4600i	−0.347551	+	0.601977i	−0.985814	−	0.167842i	$-0.946320\pi$
$577$	−8.34847	+	14.4600i	−0.347551	+	0.601977i	0.638263	+	0.769819i	$0.279653\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$		0			0
$580$	1.34847			0.0559921
$581$	−15.0000	−	5.19615i	−0.622305	−	0.215573i
$582$		0			0
$583$	−17.8485	−	30.9145i	−0.739208	−	1.28035i
$584$	−1.67423	+	2.89986i	−0.0692803	+	0.119997i
$585$		0			0
$586$	−3.12372	−	5.41045i	−0.129040	−	0.223504i
$587$	−6.55051			−0.270368			−0.135184	−	0.990820i	$-0.543163\pi$
$587$	−6.55051			−0.270368			−0.135184	+	0.990820i	$0.543163\pi$
$588$		0			0
$589$	12.6969			0.523168
$590$	−12.6742	−	21.9524i	−0.521790	−	0.903767i
$591$		0			0
$592$	5.67423	−	9.82806i	0.233210	−	0.403931i
$593$	−16.4722	−	28.5307i	−0.676432	−	1.17161i	−0.976048	−	0.217555i	$-0.930192\pi$
$593$	−16.4722	−	28.5307i	−0.676432	−	1.17161i	0.299616	−	0.954060i	$-0.403141\pi$
$594$		0			0
$595$	18.3712	+	6.36396i	0.753145	+	0.260897i
$596$	−18.2474			−0.747445
$597$		0			0
$598$	−3.67423	+	6.36396i	−0.150251	+	0.260242i
$599$	−18.9217	+	32.7733i	−0.773119	+	1.33908i	0.162727	+	0.986671i	$0.447971\pi$
$599$	−18.9217	+	32.7733i	−0.773119	+	1.33908i	−0.935846	+	0.352410i	$0.885362\pi$
$600$		0			0
$601$	−45.6969			−1.86402			−0.932008	−	0.362436i	$-0.881945\pi$
$601$	−45.6969			−1.86402			−0.932008	+	0.362436i	$0.881945\pi$
$602$	−1.00000	−	5.19615i	−0.0407570	−	0.211779i
$603$		0			0
$604$	10.8485	+	18.7901i	0.441418	+	0.764558i
$605$	22.8990	−	39.6622i	0.930976	−	1.61250i
$606$		0			0
$607$	−6.32577	−	10.9565i	−0.256755	−	0.444713i	0.708616	−	0.705595i	$-0.249320\pi$
$607$	−6.32577	−	10.9565i	−0.256755	−	0.444713i	−0.965371	+	0.260882i	$0.915987\pi$
$608$	6.34847			0.257464
$609$		0			0
$610$	−30.2474			−1.22468
$611$	−3.94949	−	6.84072i	−0.159779	−	0.276746i
$612$		0			0
$613$	10.6969	−	18.5276i	0.432045	−	0.748324i	−0.565004	−	0.825088i	$-0.691125\pi$
$613$	10.6969	−	18.5276i	0.432045	−	0.748324i	0.997049	+	0.0767638i	$0.0244587\pi$
$614$	5.52270	+	9.56560i	0.222878	+	0.386036i
$615$		0			0
$616$	10.8990	−	9.43879i	0.439132	−	0.380300i
$617$	−6.49490			−0.261475			−0.130737	−	0.991417i	$-0.541734\pi$
$617$	−6.49490			−0.261475			−0.130737	+	0.991417i	$0.541734\pi$
$618$		0			0
$619$	−12.6969	+	21.9917i	−0.510333	+	0.883923i	0.489595	+	0.871950i	$0.337145\pi$
$619$	−12.6969	+	21.9917i	−0.510333	+	0.883923i	−0.999928	+	0.0119730i	$0.996189\pi$
$620$	2.44949	−	4.24264i	0.0983739	−	0.170389i
$621$		0			0
$622$	−20.9444			−0.839793
$623$	6.67423	+	34.6803i	0.267398	+	1.38944i
$624$		0			0
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$	15.3485	−	26.5843i	0.613448	−	1.06252i
$627$		0			0
$628$	1.17423	+	2.03383i	0.0468571	+	0.0811588i
$629$	34.0454			1.35748
$630$		0			0
$631$	−21.3939			−0.851677			−0.425838	−	0.904799i	$-0.640021\pi$
$631$	−21.3939			−0.851677			−0.425838	+	0.904799i	$0.640021\pi$
$632$	5.00000	+	8.66025i	0.198889	+	0.344486i
$633$		0			0
$634$	−6.79796	+	11.7744i	−0.269981	+	0.467622i
$635$	−13.8990	−	24.0737i	−0.551564	−	0.955337i
$636$		0			0
$637$	5.50000	+	4.33013i	0.217918	+	0.171566i
$638$	3.00000			0.118771
$639$		0			0
$640$	1.22474	−	2.12132i	0.0484123	−	0.0838525i
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	−0.401435	−	0.915888i	$-0.631488\pi$
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	0.993899	−	0.110291i	$-0.0351782\pi$
$642$		0			0
$643$	21.0454			0.829950			0.414975	−	0.909833i	$-0.363790\pi$
$643$	21.0454			0.829950			0.414975	+	0.909833i	$0.363790\pi$
$644$	18.3712	+	6.36396i	0.723926	+	0.250775i
$645$		0			0
$646$	9.52270	+	16.4938i	0.374666	+	0.648940i
$647$	0.550510	−	0.953512i	0.0216428	−	0.0374864i	−0.855001	−	0.518626i	$-0.826444\pi$
$647$	0.550510	−	0.953512i	0.0216428	−	0.0374864i	0.876644	+	0.481140i	$0.159777\pi$
$648$		0			0
$649$	−28.1969	−	48.8385i	−1.10683	−	1.91708i
$650$	1.00000			0.0392232
$651$		0			0
$652$	−8.34847			−0.326951
$653$	−1.65153	−	2.86054i	−0.0646294	−	0.111941i	0.831900	−	0.554925i	$-0.187253\pi$
$653$	−1.65153	−	2.86054i	−0.0646294	−	0.111941i	−0.896530	+	0.442984i	$0.853920\pi$
$654$		0			0
$655$	4.34847	−	7.53177i	0.169909	−	0.294291i
$656$	−4.22474	−	7.31747i	−0.164949	−	0.285699i
$657$		0			0
$658$	−15.7980	+	13.6814i	−0.615869	+	0.533358i
$659$	−29.1464			−1.13538			−0.567692	−	0.823241i	$-0.692163\pi$
$659$	−29.1464			−1.13538			−0.567692	+	0.823241i	$0.692163\pi$
$660$		0			0
$661$	19.0227	−	32.9483i	0.739897	−	1.28154i	−0.212644	−	0.977130i	$-0.568207\pi$
$661$	19.0227	−	32.9483i	0.739897	−	1.28154i	0.952541	−	0.304410i	$-0.0984593\pi$
$662$	−10.0000	+	17.3205i	−0.388661	+	0.673181i
$663$		0			0
$664$	−6.00000			−0.232845
$665$	31.1010	−	26.9343i	1.20605	−	1.04447i
$666$		0			0
$667$	2.02270	+	3.50343i	0.0783194	+	0.135653i
$668$	6.94949	−	12.0369i	0.268884	−	0.465720i
$669$		0			0
$670$	15.1237	+	26.1951i	0.584280	+	1.01200i
$671$	−67.2929			−2.59781
$672$		0			0
$673$	5.30306			0.204418			0.102209	−	0.994763i	$-0.467409\pi$
$673$	5.30306			0.204418			0.102209	+	0.994763i	$0.467409\pi$
$674$	10.8485	+	18.7901i	0.417867	+	0.723768i
$675$		0			0
$676$	−0.500000	+	0.866025i	−0.0192308	+	0.0333087i
$677$	−4.62372	−	8.00853i	−0.177704	−	0.307793i	0.763390	−	0.645938i	$-0.223534\pi$
$677$	−4.62372	−	8.00853i	−0.177704	−	0.307793i	−0.941094	+	0.338146i	$0.890200\pi$
$678$		0			0
$679$	8.37117	+	2.89986i	0.321256	+	0.111286i
$680$	7.34847			0.281801
$681$		0			0
$682$	5.44949	−	9.43879i	0.208672	−	0.361430i
$683$	25.3485	−	43.9048i	0.969932	−	1.67997i	0.274197	−	0.961674i	$-0.411588\pi$
$683$	25.3485	−	43.9048i	0.969932	−	1.67997i	0.695735	−	0.718298i	$-0.255079\pi$
$684$		0			0
$685$	−3.30306			−0.126203
$686$	8.50000	−	16.4545i	0.324532	−	0.628235i
$687$		0			0
$688$	−1.00000	−	1.73205i	−0.0381246	−	0.0660338i
$689$	3.27526	−	5.67291i	0.124777	−	0.216121i
$690$		0			0
$691$	8.52270	+	14.7618i	0.324219	+	0.561564i	0.981354	−	0.192209i	$-0.0615652\pi$
$691$	8.52270	+	14.7618i	0.324219	+	0.561564i	−0.657135	+	0.753773i	$0.728232\pi$
$692$	11.4495			0.435244
$693$		0			0
$694$	31.3485			1.18997
$695$	−13.8990	−	24.0737i	−0.527218	−	0.913169i
$696$		0			0
$697$	12.6742	−	21.9524i	0.480071	−	0.831507i
$698$	14.6742	+	25.4165i	0.555428	+	0.962029i
$699$		0			0
$700$	−0.500000	−	2.59808i	−0.0188982	−	0.0981981i
$701$	8.69694			0.328479			0.164239	−	0.986421i	$-0.447483\pi$
$701$	8.69694			0.328479			0.164239	+	0.986421i	$0.447483\pi$
$702$		0			0
$703$	36.0227	−	62.3932i	1.35862	−	2.35320i
$704$	2.72474	−	4.71940i	0.102693	−	0.177869i
$705$		0			0
$706$	−1.10102			−0.0414375
$707$	2.20204	−	1.90702i	0.0828163	−	0.0717210i
$708$		0			0
$709$	−10.6742	−	18.4883i	−0.400879	−	0.694343i	0.592953	−	0.805237i	$-0.297962\pi$
$709$	−10.6742	−	18.4883i	−0.400879	−	0.694343i	−0.993832	+	0.110894i	$0.964629\pi$
$710$	−8.32577	+	14.4206i	−0.312460	+	0.541197i
$711$		0			0
$712$	6.67423	+	11.5601i	0.250128	+	0.433234i
$713$	14.6969			0.550405
$714$		0			0
$715$	13.3485			0.499204
$716$	−5.44949	−	9.43879i	−0.203657	−	0.352744i
$717$		0			0
$718$	12.5505	−	21.7381i	0.468381	−	0.811259i
$719$	−6.55051	−	11.3458i	−0.244293	−	0.423128i	0.717640	−	0.696415i	$-0.245222\pi$
$719$	−6.55051	−	11.3458i	−0.244293	−	0.423128i	−0.961933	+	0.273287i	$0.911889\pi$
$720$		0			0
$721$	6.34847	+	32.9876i	0.236429	+	1.22852i
$722$	21.3031			0.792818
$723$		0			0
$724$	−9.17423	+	15.8902i	−0.340958	+	0.590556i
$725$	0.275255	−	0.476756i	0.0102227	−	0.0177063i
$726$		0			0
$727$	22.6969			0.841783			0.420891	−	0.907111i	$-0.361717\pi$
$727$	22.6969			0.841783			0.420891	+	0.907111i	$0.361717\pi$
$728$	2.50000	+	0.866025i	0.0926562	+	0.0320970i
$729$		0			0
$730$	4.10102	+	7.10318i	0.151786	+	0.262900i
$731$	3.00000	−	5.19615i	0.110959	−	0.192187i
$732$		0			0
$733$	2.67423	+	4.63191i	0.0987751	+	0.171084i	0.911178	−	0.412013i	$-0.135174\pi$
$733$	2.67423	+	4.63191i	0.0987751	+	0.171084i	−0.812403	+	0.583097i	$0.801841\pi$
$734$	16.6969			0.616295
$735$		0			0
$736$	7.34847			0.270868
$737$	33.6464	+	58.2773i	1.23938	+	2.14667i
$738$		0			0
$739$	−11.3485	+	19.6561i	−0.417460	+	0.723062i	−0.995683	−	0.0928165i	$-0.970413\pi$
$739$	−11.3485	+	19.6561i	−0.417460	+	0.723062i	0.578223	+	0.815879i	$0.303746\pi$
$740$	−13.8990	−	24.0737i	−0.510937	−	0.884968i
$741$		0			0
$742$	−16.3763	−	5.67291i	−0.601192	−	0.208259i
$743$	−1.89898			−0.0696668			−0.0348334	−	0.999393i	$-0.511090\pi$
$743$	−1.89898			−0.0696668			−0.0348334	+	0.999393i	$0.511090\pi$
$744$		0			0
$745$	−22.3485	+	38.7087i	−0.818785	+	1.41818i
$746$	16.1742	−	28.0146i	0.592181	−	1.02569i
$747$		0			0
$748$	16.3485			0.597759
$749$	6.00000	+	31.1769i	0.219235	+	1.13918i
$750$		0			0
$751$	24.0454	+	41.6479i	0.877429	+	1.51975i	0.854152	+	0.520023i	$0.174077\pi$
$751$	24.0454	+	41.6479i	0.877429	+	1.51975i	0.0232773	+	0.999729i	$0.492590\pi$
$752$	−3.94949	+	6.84072i	−0.144023	+	0.249455i
$753$		0			0
$754$	0.275255	+	0.476756i	0.0100242	+	0.0173624i
$755$	53.1464			1.93420
$756$		0			0
$757$	23.7423			0.862930			0.431465	−	0.902130i	$-0.357997\pi$
$757$	23.7423			0.862930			0.431465	+	0.902130i	$0.357997\pi$
$758$	−15.6969	−	27.1879i	−0.570138	−	0.987509i
$759$		0			0
$760$	7.77526	−	13.4671i	0.282038	−	0.488504i
$761$	−22.8990	−	39.6622i	−0.830087	−	1.43775i	−0.897968	−	0.440060i	$-0.854957\pi$
$761$	−22.8990	−	39.6622i	−0.830087	−	1.43775i	0.0678810	−	0.997693i	$-0.478376\pi$
$762$		0			0
$763$	−21.3939	+	18.5276i	−0.774510	+	0.670746i
$764$	−16.8990			−0.611384
$765$		0			0
$766$	−6.55051	+	11.3458i	−0.236680	+	0.409941i
$767$	5.17423	−	8.96204i	0.186831	−	0.323600i
$768$		0			0
$769$	−38.0454			−1.37195			−0.685976	−	0.727624i	$-0.740625\pi$
$769$	−38.0454			−1.37195			−0.685976	+	0.727624i	$0.740625\pi$
$770$	−6.67423	−	34.6803i	−0.240523	−	1.24979i
$771$		0			0
$772$	−4.67423	−	8.09601i	−0.168229	−	0.291382i
$773$	7.65153	−	13.2528i	0.275206	−	0.476672i	−0.694981	−	0.719028i	$-0.744587\pi$
$773$	7.65153	−	13.2528i	0.275206	−	0.476672i	0.970187	+	0.242357i	$0.0779205\pi$
$774$		0			0
$775$	−1.00000	−	1.73205i	−0.0359211	−	0.0622171i
$776$	3.34847			0.120203
$777$		0			0
$778$	26.1464			0.937395
$779$	−26.8207	−	46.4548i	−0.960950	−	1.66441i
$780$		0			0
$781$	−18.5227	+	32.0823i	−0.662794	+	1.14799i
$782$	11.0227	+	19.0919i	0.394171	+	0.682724i
$783$		0			0
$784$	1.00000	−	6.92820i	0.0357143	−	0.247436i
$785$	5.75255			0.205317
$786$		0			0
$787$	−0.477296	+	0.826701i	−0.0170138	+	0.0294687i	−0.874407	−	0.485193i	$-0.838749\pi$
$787$	−0.477296	+	0.826701i	−0.0170138	+	0.0294687i	0.857393	+	0.514662i	$0.172083\pi$
$788$	−4.22474	+	7.31747i	−0.150500	+	0.260674i
$789$		0			0
$790$	24.4949			0.871489
$791$	−31.9949	−	11.0834i	−1.13761	−	0.394079i
$792$		0			0
$793$	−6.17423	−	10.6941i	−0.219253	−	0.379758i
$794$	−3.32577	+	5.76039i	−0.118027	+	0.204429i
$795$		0			0
$796$	11.6742	+	20.2204i	0.413782	+	0.716692i
$797$	−15.7980			−0.559592			−0.279796	−	0.960059i	$-0.590267\pi$
$797$	−15.7980			−0.559592			−0.279796	+	0.960059i	$0.590267\pi$
$798$		0			0
$799$	−23.6969			−0.838337
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$		0			0
$802$	9.67423	−	16.7563i	0.341609	−	0.591684i
$803$	9.12372	+	15.8028i	0.321969	+	0.557667i
$804$		0			0
$805$	36.0000	−	31.1769i	1.26883	−	1.09884i
$806$	2.00000			0.0704470
$807$		0			0
$808$	0.550510	−	0.953512i	0.0193669	−	0.0335444i
$809$	7.74745	−	13.4190i	0.272386	−	0.471786i	−0.697086	−	0.716987i	$-0.745521\pi$
$809$	7.74745	−	13.4190i	0.272386	−	0.471786i	0.969472	+	0.245201i	$0.0788540\pi$
$810$		0			0
$811$	−40.0000			−1.40459			−0.702295	−	0.711886i	$-0.747841\pi$
$811$	−40.0000			−1.40459			−0.702295	+	0.711886i	$0.747841\pi$
$812$	1.10102	−	0.953512i	0.0386382	−	0.0334617i
$813$		0			0
$814$	−30.9217	−	53.5579i	−1.08380	−	1.87720i
$815$	−10.2247	+	17.7098i	−0.358157	+	0.620346i
$816$		0			0
$817$	−6.34847	−	10.9959i	−0.222105	−	0.384697i
$818$	−8.04541			−0.281301
$819$		0			0
$820$	−20.6969			−0.722768
$821$	−0.977296	−	1.69273i	−0.0341079	−	0.0590766i	0.848468	−	0.529247i	$-0.177526\pi$
$821$	−0.977296	−	1.69273i	−0.0341079	−	0.0590766i	−0.882575	+	0.470171i	$0.844192\pi$
$822$		0			0
$823$	−4.67423	+	8.09601i	−0.162934	+	0.282209i	−0.935920	−	0.352214i	$-0.885429\pi$
$823$	−4.67423	+	8.09601i	−0.162934	+	0.282209i	0.772986	+	0.634423i	$0.218762\pi$
$824$	6.34847	+	10.9959i	0.221159	+	0.383059i
$825$		0			0
$826$	−25.8712	−	8.96204i	−0.900173	−	0.311829i
$827$	54.4393			1.89304			0.946520	−	0.322646i	$-0.104572\pi$
$827$	54.4393			1.89304			0.946520	+	0.322646i	$0.104572\pi$
$828$		0			0
$829$	8.52270	−	14.7618i	0.296006	−	0.512697i	−0.679213	−	0.733942i	$-0.737679\pi$
$829$	8.52270	−	14.7618i	0.296006	−	0.512697i	0.975218	+	0.221245i	$0.0710119\pi$
$830$	−7.34847	+	12.7279i	−0.255069	+	0.441793i
$831$		0			0
$832$	1.00000			0.0346688
$833$	19.5000	−	7.79423i	0.675635	−	0.270054i
$834$		0			0
$835$	−17.0227	−	29.4842i	−0.589095	−	1.02034i
$836$	17.2980	−	29.9609i	0.598262	−	1.03622i
$837$		0			0
$838$	17.4495	+	30.2234i	0.602783	+	1.04405i
$839$	43.8990			1.51556			0.757781	−	0.652510i	$-0.226284\pi$
$839$	43.8990			1.51556			0.757781	+	0.652510i	$0.226284\pi$
$840$		0			0
$841$	−28.6969			−0.989550
$842$	1.32577	+	2.29629i	0.0456889	+	0.0791355i
$843$		0			0
$844$	2.67423	−	4.63191i	0.0920510	−	0.159437i
$845$	1.22474	+	2.12132i	0.0421325	+	0.0729756i
$846$		0			0
$847$	−9.34847	−	48.5761i	−0.321217	−	1.66909i
$848$	−6.55051			−0.224945
$849$		0			0
$850$	1.50000	−	2.59808i	0.0514496	−	0.0891133i
$851$	41.6969	−	72.2212i	1.42935	−	2.47571i
$852$		0			0
$853$	−17.3485			−0.594000			−0.297000	−	0.954877i	$-0.595986\pi$
$853$	−17.3485			−0.594000			−0.297000	+	0.954877i	$0.595986\pi$
$854$	−24.6969	+	21.3882i	−0.845112	+	0.731888i
$855$		0			0
$856$	6.00000	+	10.3923i	0.205076	+	0.355202i
$857$	−5.05051	+	8.74774i	−0.172522	+	0.298817i	−0.939301	−	0.343094i	$-0.888525\pi$
$857$	−5.05051	+	8.74774i	−0.172522	+	0.298817i	0.766779	+	0.641911i	$0.221858\pi$
$858$		0			0
$859$	8.00000	+	13.8564i	0.272956	+	0.472774i	0.969618	−	0.244626i	$-0.0786652\pi$
$859$	8.00000	+	13.8564i	0.272956	+	0.472774i	−0.696661	+	0.717400i	$0.745332\pi$
$860$	−4.89898			−0.167054
$861$		0			0
$862$	−13.1010			−0.446223
$863$	22.8990	+	39.6622i	0.779490	+	1.35012i	0.932236	+	0.361851i	$0.117855\pi$
$863$	22.8990	+	39.6622i	0.779490	+	1.35012i	−0.152746	+	0.988266i	$0.548811\pi$
$864$		0			0
$865$	14.0227	−	24.2880i	0.476786	−	0.825818i
$866$	7.84847	+	13.5939i	0.266702	+	0.461941i
$867$		0			0
$868$	−1.00000	−	5.19615i	−0.0339422	−	0.176369i
$869$	54.4949			1.84861
$870$		0			0
$871$	−6.17423	+	10.6941i	−0.209206	+	0.362355i
$872$	−5.34847	+	9.26382i	−0.181122	+	0.313713i
$873$		0			0
$874$	46.6515			1.57801
$875$	24.4949	+	8.48528i	0.828079	+	0.286855i
$876$		0			0
$877$	14.3712	+	24.8916i	0.485280	+	0.840530i	0.999857	−	0.0169146i	$-0.00538433\pi$
$877$	14.3712	+	24.8916i	0.485280	+	0.840530i	−0.514577	+	0.857444i	$0.672051\pi$
$878$	−3.02270	+	5.23548i	−0.102011	+	0.176689i
$879$		0			0
$880$	−6.67423	−	11.5601i	−0.224988	−	0.389691i
$881$	−16.8990			−0.569341			−0.284671	−	0.958625i	$-0.591884\pi$
$881$	−16.8990			−0.569341			−0.284671	+	0.958625i	$0.591884\pi$
$882$		0			0
$883$	−14.0454			−0.472666			−0.236333	−	0.971672i	$-0.575946\pi$
$883$	−14.0454			−0.472666			−0.236333	+	0.971672i	$0.575946\pi$
$884$	1.50000	+	2.59808i	0.0504505	+	0.0873828i
$885$		0			0
$886$	1.22474	−	2.12132i	0.0411461	−	0.0712672i
$887$	9.00000	+	15.5885i	0.302190	+	0.523409i	0.976632	−	0.214919i	$-0.0689488\pi$
$887$	9.00000	+	15.5885i	0.302190	+	0.523409i	−0.674441	+	0.738328i	$0.735615\pi$
$888$		0			0
$889$	−28.3712	−	9.82806i	−0.951539	−	0.329623i
$890$	32.6969			1.09600
$891$		0			0
$892$	−11.5000	+	19.9186i	−0.385048	+	0.666924i
$893$	−25.0732	+	43.4281i	−0.839043	+	1.45327i
$894$		0			0
$895$	−26.6969			−0.892380
$896$	−0.500000	−	2.59808i	−0.0167038	−	0.0867956i
$897$		0			0
$898$	12.2474	+	21.2132i	0.408703	+	0.707894i
$899$	0.550510	−	0.953512i	0.0183605	−	0.0318014i
$900$		0			0
$901$	−9.82577	−	17.0187i	−0.327344	−	0.566976i
$902$	−46.0454			−1.53314
$903$		0			0
$904$	−12.7980			−0.425654
$905$	22.4722	+	38.9230i	0.747001	+	1.29384i
$906$		0			0
$907$	1.32577	−	2.29629i	0.0440213	−	0.0762472i	−0.843175	−	0.537639i	$-0.819316\pi$
$907$	1.32577	−	2.29629i	0.0440213	−	0.0762472i	0.887197	+	0.461392i	$0.152650\pi$
$908$	1.34847	+	2.33562i	0.0447505	+	0.0775102i
$909$		0			0
$910$	4.89898	−	4.24264i	0.162400	−	0.140642i
$911$	−18.0000			−0.596367			−0.298183	−	0.954509i	$-0.596381\pi$
$911$	−18.0000			−0.596367			−0.298183	+	0.954509i	$0.596381\pi$
$912$		0			0
$913$	−16.3485	+	28.3164i	−0.541055	+	0.937135i
$914$	10.3258	−	17.8848i	0.341546	−	0.591575i
$915$		0			0
$916$	2.00000			0.0660819
$917$	−1.77526	−	9.22450i	−0.0586241	−	0.304620i
$918$		0			0
$919$	−5.65153	−	9.78874i	−0.186427	−	0.322901i	0.757630	−	0.652685i	$-0.226357\pi$
$919$	−5.65153	−	9.78874i	−0.186427	−	0.322901i	−0.944056	+	0.329784i	$0.893024\pi$
$920$	9.00000	−	15.5885i	0.296721	−	0.513936i
$921$		0			0
$922$	−9.79796	−	16.9706i	−0.322679	−	0.558896i
$923$	−6.79796			−0.223758
$924$		0			0
$925$	−11.3485			−0.373135
$926$	−8.34847	−	14.4600i	−0.274348	−	0.475184i
$927$		0			0
$928$	0.275255	−	0.476756i	0.00903569	−	0.0156503i
$929$	0.797959	+	1.38211i	0.0261802	+	0.0453454i	0.878819	−	0.477156i	$-0.158332\pi$
$929$	0.797959	+	1.38211i	0.0261802	+	0.0453454i	−0.852638	+	0.522501i	$0.824999\pi$
$930$		0			0
$931$	6.34847	−	43.9835i	0.208063	−	1.44150i
$932$	−4.10102			−0.134333
$933$		0			0
$934$	17.5732	−	30.4377i	0.575013	−	0.995952i
$935$	20.0227	−	34.6803i	0.654812	−	1.13417i
$936$		0			0
$937$	31.0908			1.01569			0.507846	−	0.861448i	$-0.330442\pi$
$937$	31.0908			1.01569			0.507846	+	0.861448i	$0.330442\pi$
$938$	30.8712	+	10.6941i	1.00798	+	0.349174i
$939$		0			0
$940$	9.67423	+	16.7563i	0.315539	+	0.546529i
$941$	21.7980	−	37.7552i	0.710593	−	1.23078i	−0.254042	−	0.967193i	$-0.581760\pi$
$941$	21.7980	−	37.7552i	0.710593	−	1.23078i	0.964635	−	0.263590i	$-0.0849066\pi$
$942$		0			0
$943$	−31.0454	−	53.7722i	−1.01098	−	1.75106i
$944$	−10.3485			−0.336814
$945$		0			0
$946$	−10.8990			−0.354356
$947$	−9.52270	−	16.4938i	−0.309446	−	0.535977i	0.668795	−	0.743447i	$-0.266810\pi$
$947$	−9.52270	−	16.4938i	−0.309446	−	0.535977i	−0.978241	+	0.207470i	$0.933477\pi$
$948$		0			0
$949$	−1.67423	+	2.89986i	−0.0543480	+	0.0941334i
$950$	−3.17423	−	5.49794i	−0.102986	−	0.178377i
$951$		0			0
$952$	6.00000	−	5.19615i	0.194461	−	0.168408i
$953$	8.50510			0.275507			0.137754	−	0.990467i	$-0.456012\pi$
$953$	8.50510			0.275507			0.137754	+	0.990467i	$0.456012\pi$
$954$		0			0
$955$	−20.6969	+	35.8481i	−0.669737	+	1.16002i
$956$	0.151531	−	0.262459i	0.00490086	−	0.00848853i
$957$		0			0
$958$	7.89898			0.255204
$959$	−2.69694	+	2.33562i	−0.0870887	+	0.0754210i
$960$		0			0
$961$	13.5000	+	23.3827i	0.435484	+	0.754280i
$962$	5.67423	−	9.82806i	0.182945	−	0.316869i
$963$		0			0
$964$	−5.34847	−	9.26382i	−0.172263	−	0.298368i
$965$	−22.8990			−0.737144
$966$		0			0
$967$	−33.6969			−1.08362			−0.541810	−	0.840501i	$-0.682261\pi$
$967$	−33.6969			−1.08362			−0.541810	+	0.840501i	$0.682261\pi$
$968$	−9.34847	−	16.1920i	−0.300471	−	0.520431i
$969$		0			0
$970$	4.10102	−	7.10318i	0.131676	−	0.228069i
$971$	−29.2702	−	50.6974i	−0.939324	−	1.62696i	−0.766736	−	0.641963i	$-0.778120\pi$
$971$	−29.2702	−	50.6974i	−0.939324	−	1.62696i	−0.172588	−	0.984994i	$-0.555213\pi$
$972$		0			0
$973$	−28.3712	−	9.82806i	−0.909538	−	0.315073i
$974$	−7.00000			−0.224294
$975$		0			0
$976$	−6.17423	+	10.6941i	−0.197632	+	0.342309i
$977$	1.89898	−	3.28913i	0.0607537	−	0.105229i	−0.834049	−	0.551691i	$-0.813983\pi$
$977$	1.89898	−	3.28913i	0.0607537	−	0.105229i	0.894803	+	0.446462i	$0.147316\pi$
$978$		0			0
$979$	72.7423			2.32486
$980$	−13.4722	−	10.6066i	−0.430353	−	0.338815i
$981$		0			0
$982$	−1.89898	−	3.28913i	−0.0605989	−	0.104960i
$983$	−11.0505	+	19.1400i	−0.352457	+	0.610473i	−0.986679	−	0.162678i	$-0.947987\pi$
$983$	−11.0505	+	19.1400i	−0.352457	+	0.610473i	0.634223	+	0.773150i	$0.281320\pi$
$984$		0			0
$985$	10.3485	+	17.9241i	0.329730	+	0.571109i
$986$	1.65153			0.0525955
$987$		0			0
$988$	6.34847			0.201972
$989$	−7.34847	−	12.7279i	−0.233668	−	0.404724i
$990$		0			0
$991$	−10.0000	+	17.3205i	−0.317660	+	0.550204i	−0.979999	−	0.199000i	$-0.936231\pi$
$991$	−10.0000	+	17.3205i	−0.317660	+	0.550204i	0.662339	+	0.749204i	$0.269564\pi$
$992$	−1.00000	−	1.73205i	−0.0317500	−	0.0549927i
$993$		0			0
$994$	3.39898	+	17.6616i	0.107809	+	0.560192i
$995$	57.1918			1.81310
$996$		0			0
$997$	−6.17423	+	10.6941i	−0.195540	+	0.338685i	−0.947077	−	0.321005i	$-0.895979\pi$
$997$	−6.17423	+	10.6941i	−0.195540	+	0.338685i	0.751537	+	0.659690i	$0.229313\pi$
$998$	−17.3485	+	30.0484i	−0.549156	+	0.951166i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.j.l.235.2	✓	4
3.2	odd	2		1638.2.j.o.235.1	yes	4
7.2	even	3	inner	1638.2.j.l.1171.2	yes	4
21.2	odd	6		1638.2.j.o.1171.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1638.2.j.l.235.2	✓	4	1.1	even	1	trivial
1638.2.j.l.1171.2	yes	4	7.2	even	3	inner
1638.2.j.o.235.1	yes	4	3.2	odd	2
1638.2.j.o.1171.1	yes	4	21.2	odd	6

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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.22474 + 2.12132i) q^{5} +(2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.22474 + 2.12132i) q^{5} +(2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(1.22474 - 2.12132i) q^{10} +(2.72474 - 4.71940i) q^{11} +1.00000 q^{13} +(-0.500000 - 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} +(-3.17423 - 5.49794i) q^{19} -2.44949 q^{20} -5.44949 q^{22} +(-3.67423 - 6.36396i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-0.500000 - 0.866025i) q^{26} +(-2.00000 + 1.73205i) q^{28} -0.550510 q^{29} +(-1.00000 + 1.73205i) q^{31} +(-0.500000 + 0.866025i) q^{32} -3.00000 q^{34} +(1.22474 + 6.36396i) q^{35} +(5.67423 + 9.82806i) q^{37} +(-3.17423 + 5.49794i) q^{38} +(1.22474 + 2.12132i) q^{40} +8.44949 q^{41} +2.00000 q^{43} +(2.72474 + 4.71940i) q^{44} +(-3.67423 + 6.36396i) q^{46} +(-3.94949 - 6.84072i) q^{47} +(5.50000 + 4.33013i) q^{49} +1.00000 q^{50} +(-0.500000 + 0.866025i) q^{52} +(3.27526 - 5.67291i) q^{53} +13.3485 q^{55} +(2.50000 + 0.866025i) q^{56} +(0.275255 + 0.476756i) q^{58} +(5.17423 - 8.96204i) q^{59} +(-6.17423 - 10.6941i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(1.22474 + 2.12132i) q^{65} +(-6.17423 + 10.6941i) q^{67} +(1.50000 + 2.59808i) q^{68} +(4.89898 - 4.24264i) q^{70} -6.79796 q^{71} +(-1.67423 + 2.89986i) q^{73} +(5.67423 - 9.82806i) q^{74} +6.34847 q^{76} +(10.8990 - 9.43879i) q^{77} +(5.00000 + 8.66025i) q^{79} +(1.22474 - 2.12132i) q^{80} +(-4.22474 - 7.31747i) q^{82} -6.00000 q^{83} +7.34847 q^{85} +(-1.00000 - 1.73205i) q^{86} +(2.72474 - 4.71940i) q^{88} +(6.67423 + 11.5601i) q^{89} +(2.50000 + 0.866025i) q^{91} +7.34847 q^{92} +(-3.94949 + 6.84072i) q^{94} +(7.77526 - 13.4671i) q^{95} +3.34847 q^{97} +(1.00000 - 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} + 10 q^{7} + 4 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^4 + 10 * q^7 + 4 * q^8	\( 4 q - 2 q^{2} - 2 q^{4} + 10 q^{7} + 4 q^{8} + 6 q^{11} + 4 q^{13} - 2 q^{14} - 2 q^{16} + 6 q^{17} + 2 q^{19} - 12 q^{22} - 2 q^{25} - 2 q^{26} - 8 q^{28} - 12 q^{29} - 4 q^{31} - 2 q^{32} - 12 q^{34} + 8 q^{37} + 2 q^{38} + 24 q^{41} + 8 q^{43} + 6 q^{44} - 6 q^{47} + 22 q^{49} + 4 q^{50} - 2 q^{52} + 18 q^{53} + 24 q^{55} + 10 q^{56} + 6 q^{58} + 6 q^{59} - 10 q^{61} + 8 q^{62} + 4 q^{64} - 10 q^{67} + 6 q^{68} + 12 q^{71} + 8 q^{73} + 8 q^{74} - 4 q^{76} + 24 q^{77} + 20 q^{79} - 12 q^{82} - 24 q^{83} - 4 q^{86} + 6 q^{88} + 12 q^{89} + 10 q^{91} - 6 q^{94} + 36 q^{95} - 16 q^{97} + 4 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 + 10 * q^7 + 4 * q^8 + 6 * q^11 + 4 * q^13 - 2 * q^14 - 2 * q^16 + 6 * q^17 + 2 * q^19 - 12 * q^22 - 2 * q^25 - 2 * q^26 - 8 * q^28 - 12 * q^29 - 4 * q^31 - 2 * q^32 - 12 * q^34 + 8 * q^37 + 2 * q^38 + 24 * q^41 + 8 * q^43 + 6 * q^44 - 6 * q^47 + 22 * q^49 + 4 * q^50 - 2 * q^52 + 18 * q^53 + 24 * q^55 + 10 * q^56 + 6 * q^58 + 6 * q^59 - 10 * q^61 + 8 * q^62 + 4 * q^64 - 10 * q^67 + 6 * q^68 + 12 * q^71 + 8 * q^73 + 8 * q^74 - 4 * q^76 + 24 * q^77 + 20 * q^79 - 12 * q^82 - 24 * q^83 - 4 * q^86 + 6 * q^88 + 12 * q^89 + 10 * q^91 - 6 * q^94 + 36 * q^95 - 16 * q^97 + 4 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more