LMFDB - Embedded newform 1710.2.t.b.1189.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(919,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("1710.919");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.t (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:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.89539436150784.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 $ x^12 - 2x^11 + 2x^10 - 8x^9 + 4x^8 + 16x^7 - 8x^6 + 20x^5 + 20x^4 - 24x^3 + 8x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 570)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1189.1
Root			$0.550552 + 0.147520i$ of defining polynomial
Character	$\chi$	$=$	1710.1189
Dual form			1710.2.t.b.919.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-2.12032 + 0.710109i) q^{5} +4.67513i q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-2.12032 + 0.710109i) q^{5} +4.67513i q^{7} -1.00000i q^{8} +(2.19130 + 0.445186i) q^{10} +3.96239 q^{11} +(-0.698071 + 0.403032i) q^{13} +(2.33757 - 4.04878i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(4.01621 + 2.31876i) q^{17} +(3.01270 - 3.15018i) q^{19} +(-1.67513 - 1.48119i) q^{20} +(-3.43153 - 1.98119i) q^{22} +(-5.52574 + 3.19029i) q^{23} +(3.99149 - 3.01131i) q^{25} +0.806063 q^{26} +(-4.04878 + 2.33757i) q^{28} +(2.03150 + 3.51866i) q^{29} +3.35026 q^{31} +(0.866025 - 0.500000i) q^{32} +(-2.31876 - 4.01621i) q^{34} +(-3.31985 - 9.91276i) q^{35} -2.19394i q^{37} +(-4.18416 + 1.22179i) q^{38} +(0.710109 + 2.12032i) q^{40} +(2.02785 - 3.51235i) q^{41} +(6.36551 + 3.67513i) q^{43} +(1.98119 + 3.43153i) q^{44} +6.38058 q^{46} +(-8.12382 + 4.69029i) q^{47} -14.8568 q^{49} +(-4.96239 + 0.612127i) q^{50} +(-0.698071 - 0.403032i) q^{52} +(-1.34790 + 0.778209i) q^{53} +(-8.40152 + 2.81373i) q^{55} +4.67513 q^{56} -4.06300i q^{58} +(-3.94723 + 6.83680i) q^{59} +(2.20299 + 3.81568i) q^{61} +(-2.90141 - 1.67513i) q^{62} -1.00000 q^{64} +(1.19394 - 1.35026i) q^{65} +(-6.42008 + 3.70663i) q^{67} +4.63752i q^{68} +(-2.08130 + 10.2446i) q^{70} +(-1.08427 + 1.87801i) q^{71} +(-10.2463 - 5.91573i) q^{73} +(-1.09697 + 1.90000i) q^{74} +(4.23449 + 1.03398i) q^{76} +18.5247i q^{77} +(-4.67513 + 8.09756i) q^{79} +(0.445186 - 2.19130i) q^{80} +(-3.51235 + 2.02785i) q^{82} -9.92478i q^{83} +(-10.1622 - 2.06456i) q^{85} +(-3.67513 - 6.36551i) q^{86} -3.96239i q^{88} +(9.13141 + 15.8161i) q^{89} +(-1.88423 - 3.26358i) q^{91} +(-5.52574 - 3.19029i) q^{92} +9.38058 q^{94} +(-4.15090 + 8.81873i) q^{95} +(10.7439 + 6.20299i) q^{97} +(12.8664 + 7.42842i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4}+O(q^{10}) $ 12 * q + 6 * q^4	$ 12 q + 6 q^{4} - 2 q^{10} + 4 q^{11} + 18 q^{14} - 6 q^{16} + 6 q^{19} - 2 q^{25} + 8 q^{26} + 16 q^{29} + 4 q^{34} - 2 q^{35} + 2 q^{40} - 10 q^{41} + 2 q^{44} + 28 q^{46} - 56 q^{49} - 16 q^{50} - 8 q^{55} + 36 q^{56} - 8 q^{59} - 28 q^{61} - 12 q^{64} + 16 q^{65} + 16 q^{70} - 44 q^{71} - 14 q^{74} - 12 q^{76} - 36 q^{79} - 32 q^{85} - 24 q^{86} - 6 q^{89} + 64 q^{94} + 12 q^{95}+O(q^{100}) $ 12 * q + 6 * q^4 - 2 * q^10 + 4 * q^11 + 18 * q^14 - 6 * q^16 + 6 * q^19 - 2 * q^25 + 8 * q^26 + 16 * q^29 + 4 * q^34 - 2 * q^35 + 2 * q^40 - 10 * q^41 + 2 * q^44 + 28 * q^46 - 56 * q^49 - 16 * q^50 - 8 * q^55 + 36 * q^56 - 8 * q^59 - 28 * q^61 - 12 * q^64 + 16 * q^65 + 16 * q^70 - 44 * q^71 - 14 * q^74 - 12 * q^76 - 36 * q^79 - 32 * q^85 - 24 * q^86 - 6 * q^89 + 64 * q^94 + 12 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

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
$5$	−2.12032	+	0.710109i	−0.948235	+	0.317570i
$5$	−2.12032	+	0.710109i	−0.948235	+	0.317570i
$6$		0			0
$7$			4.67513i			1.76703i	0.468400	+	0.883517i	$0.344831\pi$
$7$			4.67513i			1.76703i	−0.468400	+	0.883517i	$0.655169\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	2.19130	+	0.445186i	0.692951	+	0.140780i
$11$	3.96239			1.19471			0.597353	−	0.801979i	$-0.296219\pi$
$11$	3.96239			1.19471			0.597353	+	0.801979i	$0.296219\pi$
$12$		0			0
$13$	−0.698071	+	0.403032i	−0.193610	+	0.111781i	−0.593672	−	0.804707i	$-0.702322\pi$
$13$	−0.698071	+	0.403032i	−0.193610	+	0.111781i	0.400061	+	0.916488i	$0.368989\pi$
$14$	2.33757	−	4.04878i	0.624741	−	1.08208i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	4.01621	+	2.31876i	0.974074	+	0.562382i	0.900476	−	0.434906i	$-0.143218\pi$
$17$	4.01621	+	2.31876i	0.974074	+	0.562382i	0.0735981	+	0.997288i	$0.476552\pi$
$18$		0			0
$19$	3.01270	−	3.15018i	0.691160	−	0.722702i
$19$	3.01270	−	3.15018i	0.691160	−	0.722702i
$20$	−1.67513	−	1.48119i	−0.374571	−	0.331205i
$21$		0			0
$22$	−3.43153	−	1.98119i	−0.731604	−	0.422392i
$23$	−5.52574	+	3.19029i	−1.15220	+	0.665221i	−0.949422	−	0.314004i	$-0.898329\pi$
$23$	−5.52574	+	3.19029i	−1.15220	+	0.665221i	−0.202775	+	0.979225i	$0.564996\pi$
$24$		0			0
$25$	3.99149	−	3.01131i	0.798298	−	0.602262i
$26$	0.806063			0.158082
$27$		0			0
$28$	−4.04878	+	2.33757i	−0.765148	+	0.441758i
$29$	2.03150	+	3.51866i	0.377240	+	0.653400i	0.990660	−	0.136358i	$-0.0435397\pi$
$29$	2.03150	+	3.51866i	0.377240	+	0.653400i	−0.613419	+	0.789757i	$0.710206\pi$
$30$		0			0
$31$	3.35026			0.601725			0.300862	−	0.953668i	$-0.402726\pi$
$31$	3.35026			0.601725			0.300862	+	0.953668i	$0.402726\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$	−2.31876	−	4.01621i	−0.397664	−	0.688774i
$35$	−3.31985	−	9.91276i	−0.561157	−	1.67556i
$36$		0			0
$37$		−	2.19394i		−	0.360681i	−0.983604	−	0.180340i	$-0.942280\pi$
$37$		−	2.19394i		−	0.360681i	0.983604	−	0.180340i	$-0.0577200\pi$
$38$	−4.18416	+	1.22179i	−0.678761	+	0.198201i
$39$		0			0
$40$	0.710109	+	2.12032i	0.112278	+	0.335252i
$41$	2.02785	−	3.51235i	0.316698	−	0.548537i	−0.663099	−	0.748532i	$-0.730759\pi$
$41$	2.02785	−	3.51235i	0.316698	−	0.548537i	0.979797	+	0.199995i	$0.0640926\pi$
$42$		0			0
$43$	6.36551	+	3.67513i	0.970732	+	0.560452i	0.899459	−	0.437005i	$-0.143961\pi$
$43$	6.36551	+	3.67513i	0.970732	+	0.560452i	0.0712725	+	0.997457i	$0.477294\pi$
$44$	1.98119	+	3.43153i	0.298676	+	0.517322i
$45$		0			0
$46$	6.38058			0.940765
$47$	−8.12382	+	4.69029i	−1.18498	+	0.684149i	−0.957162	−	0.289554i	$-0.906493\pi$
$47$	−8.12382	+	4.69029i	−1.18498	+	0.684149i	−0.227819	+	0.973703i	$0.573160\pi$
$48$		0			0
$49$	−14.8568			−2.12241
$50$	−4.96239	+	0.612127i	−0.701788	+	0.0865678i
$51$		0			0
$52$	−0.698071	−	0.403032i	−0.0968051	−	0.0558904i
$53$	−1.34790	+	0.778209i	−0.185148	+	0.106895i	−0.589709	−	0.807616i	$-0.700758\pi$
$53$	−1.34790	+	0.778209i	−0.185148	+	0.106895i	0.404561	+	0.914511i	$0.367424\pi$
$54$		0			0
$55$	−8.40152	+	2.81373i	−1.13286	+	0.379403i
$56$	4.67513			0.624741
$57$		0			0
$58$		−	4.06300i		−	0.533499i
$59$	−3.94723	+	6.83680i	−0.513886	+	0.890076i	0.485985	+	0.873967i	$0.338461\pi$
$59$	−3.94723	+	6.83680i	−0.513886	+	0.890076i	−0.999870	+	0.0161086i	$0.994872\pi$
$60$		0			0
$61$	2.20299	+	3.81568i	0.282063	+	0.488548i	0.971893	−	0.235424i	$-0.0756478\pi$
$61$	2.20299	+	3.81568i	0.282063	+	0.488548i	−0.689829	+	0.723972i	$0.742314\pi$
$62$	−2.90141	−	1.67513i	−0.368480	−	0.212742i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	1.19394	−	1.35026i	0.148090	−	0.167479i
$66$		0			0
$67$	−6.42008	+	3.70663i	−0.784337	+	0.452837i	−0.837965	−	0.545724i	$-0.816255\pi$
$67$	−6.42008	+	3.70663i	−0.784337	+	0.452837i	0.0536280	+	0.998561i	$0.482921\pi$
$68$			4.63752i			0.562382i
$69$		0			0
$70$	−2.08130	+	10.2446i	−0.248764	+	1.22447i
$71$	−1.08427	+	1.87801i	−0.128679	+	0.222879i	−0.923165	−	0.384403i	$-0.874407\pi$
$71$	−1.08427	+	1.87801i	−0.128679	+	0.222879i	0.794486	+	0.607283i	$0.207740\pi$
$72$		0			0
$73$	−10.2463	−	5.91573i	−1.19924	−	0.692384i	−0.238857	−	0.971055i	$-0.576773\pi$
$73$	−10.2463	−	5.91573i	−1.19924	−	0.692384i	−0.960387	+	0.278671i	$0.910106\pi$
$74$	−1.09697	+	1.90000i	−0.127520	+	0.220871i
$75$		0			0
$76$	4.23449	+	1.03398i	0.485729	+	0.118606i
$77$			18.5247i			2.11108i
$78$		0			0
$79$	−4.67513	+	8.09756i	−0.525993	+	0.911047i	0.473548	+	0.880768i	$0.342973\pi$
$79$	−4.67513	+	8.09756i	−0.525993	+	0.911047i	−0.999541	+	0.0302792i	$0.990360\pi$
$80$	0.445186	−	2.19130i	0.0497734	−	0.244995i
$81$		0			0
$82$	−3.51235	+	2.02785i	−0.387874	+	0.223939i
$83$		−	9.92478i		−	1.08939i	−0.838636	−	0.544693i	$-0.816646\pi$
$83$		−	9.92478i		−	1.08939i	0.838636	−	0.544693i	$-0.183354\pi$
$84$		0			0
$85$	−10.1622	−	2.06456i	−1.10225	−	0.223933i
$86$	−3.67513	−	6.36551i	−0.396300	−	0.686411i
$87$		0			0
$88$		−	3.96239i		−	0.422392i
$89$	9.13141	+	15.8161i	0.967928	+	1.67650i	0.701535	+	0.712635i	$0.252498\pi$
$89$	9.13141	+	15.8161i	0.967928	+	1.67650i	0.266393	+	0.963865i	$0.414168\pi$
$90$		0			0
$91$	−1.88423	−	3.26358i	−0.197521	−	0.342116i
$92$	−5.52574	−	3.19029i	−0.576099	−	0.332611i
$93$		0			0
$94$	9.38058			0.967533
$95$	−4.15090	+	8.81873i	−0.425873	+	0.904783i
$96$		0			0
$97$	10.7439	+	6.20299i	1.09088	+	0.629818i	0.933810	−	0.357770i	$-0.116463\pi$
$97$	10.7439	+	6.20299i	1.09088	+	0.629818i	0.157067	+	0.987588i	$0.449796\pi$
$98$	12.8664	+	7.42842i	1.29970	+	0.750384i
$99$		0			0
$100$	4.60362	+	1.95108i	0.460362	+	0.195108i
$101$	−5.21933	−	9.04014i	−0.519343	−	0.899528i	−0.999747	−	0.0224809i	$-0.992844\pi$
$101$	−5.21933	−	9.04014i	−0.519343	−	0.899528i	0.480405	−	0.877047i	$-0.340490\pi$
$102$		0			0
$103$		−	2.13093i		−	0.209967i	−0.994474	−	0.104984i	$-0.966521\pi$
$103$		−	2.13093i		−	0.209967i	0.994474	−	0.104984i	$-0.0334790\pi$
$104$	0.403032	+	0.698071i	0.0395205	+	0.0684515i
$105$		0			0
$106$	1.55642			0.151173
$107$			7.95746i			0.769277i	0.923067	+	0.384639i	$0.125674\pi$
$107$			7.95746i			0.769277i	−0.923067	+	0.384639i	$0.874326\pi$
$108$		0			0
$109$	5.20299	−	9.01184i	0.498356	−	0.863177i	−0.501643	−	0.865075i	$-0.667271\pi$
$109$	5.20299	−	9.01184i	0.498356	−	0.863177i	0.999998	+	0.00189769i	$0.000604054\pi$
$110$	8.68279	+	1.76400i	0.827872	+	0.168191i
$111$		0			0
$112$	−4.04878	−	2.33757i	−0.382574	−	0.220879i
$113$		−	12.3004i		−	1.15713i	−0.815637	−	0.578564i	$-0.803613\pi$
$113$		−	12.3004i		−	1.15713i	0.815637	−	0.578564i	$-0.196387\pi$
$114$		0			0
$115$	9.45088	−	10.6883i	0.881299	−	0.996690i
$116$	−2.03150	+	3.51866i	−0.188620	+	0.326700i
$117$		0			0
$118$	6.83680	−	3.94723i	0.629379	−	0.363372i
$119$	−10.8405	+	18.7763i	−0.993747	+	1.72122i
$120$		0			0
$121$	4.70052			0.427320
$122$		−	4.40597i		−	0.398898i
$123$		0			0
$124$	1.67513	+	2.90141i	0.150431	+	0.260554i
$125$	−6.32487	+	9.21933i	−0.565713	+	0.824602i
$126$		0			0
$127$	−10.3754	+	5.99024i	−0.920668	+	0.531548i	−0.883848	−	0.467774i	$-0.845056\pi$
$127$	−10.3754	+	5.99024i	−0.920668	+	0.531548i	−0.0368202	+	0.999322i	$0.511723\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	−1.70911	+	0.572393i	−0.149899	+	0.0502022i
$131$	−6.30606	+	10.9224i	−0.550963	+	0.954296i	0.447242	+	0.894413i	$0.352406\pi$
$131$	−6.30606	+	10.9224i	−0.550963	+	0.954296i	−0.998205	+	0.0598835i	$0.980927\pi$
$132$		0			0
$133$	14.7275	+	14.0847i	1.27704	+	1.22130i
$134$	7.41327			0.640409
$135$		0			0
$136$	2.31876	−	4.01621i	0.198832	−	0.344387i
$137$	5.53206	−	3.19394i	0.472636	−	0.272876i	−0.244707	−	0.969597i	$-0.578692\pi$
$137$	5.53206	−	3.19394i	0.472636	−	0.272876i	0.717342	+	0.696721i	$0.245358\pi$
$138$		0			0
$139$	−6.63752	−	11.4965i	−0.562987	−	0.975122i	−0.997234	−	0.0743282i	$-0.976319\pi$
$139$	−6.63752	−	11.4965i	−0.562987	−	0.975122i	0.434247	−	0.900794i	$-0.357015\pi$
$140$	6.92478	−	7.83146i	0.585250	−	0.661879i
$141$		0			0
$142$	1.87801	−	1.08427i	0.157599	−	0.0909901i
$143$	−2.76603	+	1.59697i	−0.231307	+	0.133545i
$144$		0			0
$145$	−6.80606	−	6.01810i	−0.565213	−	0.499776i
$146$	5.91573	+	10.2463i	0.489589	+	0.847993i
$147$		0			0
$148$	1.90000	−	1.09697i	0.156179	−	0.0901702i
$149$	−0.449692	+	0.778890i	−0.0368402	+	0.0638091i	−0.883858	−	0.467756i	$-0.845063\pi$
$149$	−0.449692	+	0.778890i	−0.0368402	+	0.0638091i	0.847017	+	0.531565i	$0.178396\pi$
$150$		0			0
$151$	−10.3757			−0.844359			−0.422179	−	0.906512i	$-0.638735\pi$
$151$	−10.3757			−0.844359			−0.422179	+	0.906512i	$0.638735\pi$
$152$	−3.15018	−	3.01270i	−0.255514	−	0.244362i
$153$		0			0
$154$	9.26234	−	16.0428i	0.746381	−	1.29277i
$155$	−7.10362	+	2.37905i	−0.570576	+	0.191090i
$156$		0			0
$157$	−12.2534	−	7.07452i	−0.977929	−	0.564608i	−0.0762850	−	0.997086i	$-0.524306\pi$
$157$	−12.2534	−	7.07452i	−0.977929	−	0.564608i	−0.901644	+	0.432478i	$0.857639\pi$
$158$	8.09756	−	4.67513i	0.644208	−	0.371933i
$159$		0			0
$160$	−1.48119	+	1.67513i	−0.117099	+	0.132431i
$161$	−14.9150	−	25.8336i	−1.17547	−	2.03597i
$162$		0			0
$163$			17.4617i			1.36770i	0.729621	+	0.683852i	$0.239697\pi$
$163$			17.4617i			1.36770i	−0.729621	+	0.683852i	$0.760303\pi$
$164$	4.05571			0.316698
$165$		0			0
$166$	−4.96239	+	8.59511i	−0.385156	+	0.667110i
$167$	20.0979	−	11.6036i	1.55523	−	0.897910i	0.557523	−	0.830161i	$-0.311752\pi$
$167$	20.0979	−	11.6036i	1.55523	−	0.897910i	0.997702	−	0.0677489i	$-0.0215817\pi$
$168$		0			0
$169$	−6.17513	+	10.6956i	−0.475010	+	0.822742i
$170$	7.76845	+	6.86907i	0.595813	+	0.526833i
$171$		0			0
$172$			7.35026i			0.560452i
$173$	16.6055	+	9.58721i	1.26250	+	0.728902i	0.973557	−	0.228445i	$-0.0733642\pi$
$173$	16.6055	+	9.58721i	1.26250	+	0.728902i	0.288939	+	0.957348i	$0.406698\pi$
$174$		0			0
$175$	14.0783	+	18.6607i	1.06422	+	1.41062i
$176$	−1.98119	+	3.43153i	−0.149338	+	0.258661i
$177$		0			0
$178$		−	18.2628i		−	1.36886i
$179$	18.3707			1.37309			0.686546	−	0.727086i	$-0.259126\pi$
$179$	18.3707			1.37309			0.686546	+	0.727086i	$0.259126\pi$
$180$		0			0
$181$	3.10966	+	5.38610i	0.231140	+	0.400345i	0.958144	−	0.286288i	$-0.0924213\pi$
$181$	3.10966	+	5.38610i	0.231140	+	0.400345i	−0.727004	+	0.686633i	$0.759088\pi$
$182$			3.76845i			0.279336i
$183$		0			0
$184$	3.19029	+	5.52574i	0.235191	+	0.407363i
$185$	1.55793	+	4.65184i	0.114542	+	0.342010i
$186$		0			0
$187$	15.9138	+	9.18783i	1.16373	+	0.671880i
$188$	−8.12382	−	4.69029i	−0.592490	−	0.342075i
$189$		0			0
$190$	8.00415	−	5.56180i	0.580682	−	0.403495i
$191$	−3.47627			−0.251534			−0.125767	−	0.992060i	$-0.540139\pi$
$191$	−3.47627			−0.251534			−0.125767	+	0.992060i	$0.540139\pi$
$192$		0			0
$193$	−7.57171	−	4.37153i	−0.545024	−	0.314670i	0.202089	−	0.979367i	$-0.435227\pi$
$193$	−7.57171	−	4.37153i	−0.545024	−	0.314670i	−0.747112	+	0.664698i	$0.768560\pi$
$194$	−6.20299	−	10.7439i	−0.445348	−	0.771366i
$195$		0			0
$196$	−7.42842	−	12.8664i	−0.530602	−	0.919029i
$197$			12.6448i			0.900906i	0.892800	+	0.450453i	$0.148737\pi$
$197$			12.6448i			0.900906i	−0.892800	+	0.450453i	$0.851263\pi$
$198$		0			0
$199$	−2.18783	−	3.78943i	−0.155091	−	0.268625i	0.778001	−	0.628263i	$-0.216234\pi$
$199$	−2.18783	−	3.78943i	−0.155091	−	0.268625i	−0.933092	+	0.359637i	$0.882900\pi$
$200$	−3.01131	−	3.99149i	−0.212932	−	0.282241i
$201$		0			0
$202$			10.4387i			0.734461i
$203$	−16.4502	+	9.49754i	−1.15458	+	0.666596i
$204$		0			0
$205$	−1.80555	+	8.88729i	−0.126105	+	0.620715i
$206$	−1.06547	+	1.84544i	−0.0742346	+	0.128578i
$207$		0			0
$208$		−	0.806063i		−	0.0558904i
$209$	11.9375	−	12.4823i	0.825732	−	0.863416i
$210$		0			0
$211$	6.65022	−	11.5185i	0.457820	−	0.792967i	−0.541026	−	0.841006i	$-0.681964\pi$
$211$	6.65022	−	11.5185i	0.457820	−	0.792967i	0.998845	+	0.0480390i	$0.0152972\pi$
$212$	−1.34790	−	0.778209i	−0.0925739	−	0.0534476i
$213$		0			0
$214$	3.97873	−	6.89137i	0.271981	−	0.471084i
$215$	−16.1067	−	3.27224i	−1.09846	−	0.223165i
$216$		0			0
$217$			15.6629i			1.06327i
$218$	−9.01184	+	5.20299i	−0.610359	+	0.352391i
$219$		0			0
$220$	−6.63752	−	5.86907i	−0.447501	−	0.395692i
$221$	−3.73813			−0.251454
$222$		0			0
$223$	1.57468	+	0.909141i	0.105448	+	0.0608806i	0.551797	−	0.833979i	$-0.313942\pi$
$223$	1.57468	+	0.909141i	0.105448	+	0.0608806i	−0.446348	+	0.894859i	$0.647276\pi$
$224$	2.33757	+	4.04878i	0.156185	+	0.270521i
$225$		0			0
$226$	−6.15022	+	10.6525i	−0.409106	+	0.708593i
$227$		−	12.8691i		−	0.854150i	−0.904216	−	0.427075i	$-0.859544\pi$
$227$		−	12.8691i		−	0.854150i	0.904216	−	0.427075i	$-0.140456\pi$
$228$		0			0
$229$	−16.1114			−1.06467			−0.532336	−	0.846533i	$-0.678686\pi$
$229$	−16.1114			−1.06467			−0.532336	+	0.846533i	$0.678686\pi$
$230$	−13.5289	+	4.53090i	−0.892066	+	0.298759i
$231$		0			0
$232$	3.51866	−	2.03150i	0.231012	−	0.133375i
$233$	−1.90632	−	1.10062i	−0.124887	−	0.0721037i	0.436255	−	0.899823i	$-0.356305\pi$
$233$	−1.90632	−	1.10062i	−0.124887	−	0.0721037i	−0.561142	+	0.827719i	$0.689638\pi$
$234$		0			0
$235$	13.8945	−	15.7137i	0.906375	−	1.02505i
$236$	−7.89446			−0.513886
$237$		0			0
$238$	18.7763	−	10.8405i	1.21709	−	0.702686i
$239$	4.70052			0.304052			0.152026	−	0.988377i	$-0.451420\pi$
$239$	4.70052			0.304052			0.152026	+	0.988377i	$0.451420\pi$
$240$		0			0
$241$	−12.6405	−	21.8939i	−0.814244	−	1.41031i	−0.909870	−	0.414894i	$-0.863819\pi$
$241$	−12.6405	−	21.8939i	−0.814244	−	1.41031i	0.0956262	−	0.995417i	$-0.469515\pi$
$242$	−4.07077	−	2.35026i	−0.261679	−	0.151081i
$243$		0			0
$244$	−2.20299	+	3.81568i	−0.141032	+	0.244274i
$245$	31.5012	−	10.5500i	2.01254	−	0.674013i
$246$		0			0
$247$	−0.833453	+	3.41327i	−0.0530313	+	0.217181i
$248$		−	3.35026i		−	0.212742i
$249$		0			0
$250$	10.0872	−	4.82174i	0.637968	−	0.304954i
$251$	−6.21933	−	10.7722i	−0.392561	−	0.679935i	0.600226	−	0.799831i	$-0.295077\pi$
$251$	−6.21933	−	10.7722i	−0.392561	−	0.679935i	−0.992787	+	0.119896i	$0.961744\pi$
$252$		0			0
$253$	−21.8951	+	12.6412i	−1.37654	+	0.794743i
$254$	11.9805			0.751723
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−22.7011	+	13.1065i	−1.41606	+	0.817561i	−0.995950	−	0.0899138i	$-0.971341\pi$
$257$	−22.7011	+	13.1065i	−1.41606	+	0.817561i	−0.420107	+	0.907475i	$0.638008\pi$
$258$		0			0
$259$	10.2569			0.637335
$260$	1.76633	+	0.358849i	0.109543	+	0.0222548i
$261$		0			0
$262$	10.9224	−	6.30606i	0.674790	−	0.389590i
$263$	−5.03329	−	2.90597i	−0.310366	−	0.179190i	0.336724	−	0.941603i	$-0.390681\pi$
$263$	−5.03329	−	2.90597i	−0.310366	−	0.179190i	−0.647090	+	0.762413i	$0.724014\pi$
$264$		0			0
$265$	2.30536	−	2.60720i	0.141617	−	0.160159i
$266$	−5.71203	−	19.5615i	−0.350227	−	1.19939i
$267$		0			0
$268$	−6.42008	−	3.70663i	−0.392169	−	0.226419i
$269$	−11.7501	+	20.3518i	−0.716418	+	1.24087i	0.245992	+	0.969272i	$0.420886\pi$
$269$	−11.7501	+	20.3518i	−0.716418	+	1.24087i	−0.962410	+	0.271600i	$0.912447\pi$
$270$		0			0
$271$	−16.3430	+	28.3069i	−0.992765	+	1.71952i	−0.392393	+	0.919798i	$0.628353\pi$
$271$	−16.3430	+	28.3069i	−0.992765	+	1.71952i	−0.600372	+	0.799721i	$0.704981\pi$
$272$	−4.01621	+	2.31876i	−0.243518	+	0.140595i
$273$		0			0
$274$	−6.38787			−0.385906
$275$	15.8158	−	11.9320i	0.953731	−	0.719526i
$276$		0			0
$277$			19.6688i			1.18178i	0.806751	+	0.590892i	$0.201224\pi$
$277$			19.6688i			1.18178i	−0.806751	+	0.590892i	$0.798776\pi$
$278$			13.2750i			0.796184i
$279$		0			0
$280$	−9.91276	+	3.31985i	−0.592401	+	0.198399i
$281$	−5.79631	−	10.0395i	−0.345779	−	0.598906i	0.639716	−	0.768611i	$-0.279052\pi$
$281$	−5.79631	−	10.0395i	−0.345779	−	0.598906i	−0.985495	+	0.169705i	$0.945719\pi$
$282$		0			0
$283$	25.4621	+	14.7005i	1.51356	+	0.873855i	0.999874	+	0.0158784i	$0.00505446\pi$
$283$	25.4621	+	14.7005i	1.51356	+	0.873855i	0.513688	+	0.857977i	$0.328279\pi$
$284$	−2.16854			−0.128679
$285$		0			0
$286$	3.19394			0.188861
$287$	16.4207	+	9.48049i	0.969282	+	0.559615i
$288$		0			0
$289$	2.25329	+	3.90282i	0.132547	+	0.229578i
$290$	2.88517	+	8.61486i	0.169423	+	0.505882i
$291$		0			0
$292$		−	11.8315i		−	0.692384i
$293$		−	22.2628i		−	1.30061i	−0.759674	−	0.650304i	$-0.774642\pi$
$293$		−	22.2628i		−	1.30061i	0.759674	−	0.650304i	$-0.225358\pi$
$294$		0			0
$295$	3.51451	−	17.2992i	0.204622	−	1.00720i
$296$	−2.19394			−0.127520
$297$		0			0
$298$	0.778890	−	0.449692i	0.0451199	−	0.0260500i
$299$	2.57158	−	4.45410i	0.148718	−	0.257587i
$300$		0			0
$301$	−17.1817	+	29.7596i	−0.990338	+	1.71532i
$302$	8.98558	+	5.18783i	0.517062	+	0.298526i
$303$		0			0
$304$	1.22179	+	4.18416i	0.0700745	+	0.239978i
$305$	−7.38058	−	6.52610i	−0.422611	−	0.373683i
$306$		0			0
$307$	27.0744	+	15.6314i	1.54522	+	0.892132i	0.998496	+	0.0548168i	$0.0174575\pi$
$307$	27.0744	+	15.6314i	1.54522	+	0.892132i	0.546721	+	0.837315i	$0.315876\pi$
$308$	−16.0428	+	9.26234i	−0.914126	+	0.527771i
$309$		0			0
$310$	7.34144	+	1.49149i	0.416966	+	0.0847110i
$311$	17.7889			1.00872			0.504359	−	0.863494i	$-0.331729\pi$
$311$	17.7889			1.00872			0.504359	+	0.863494i	$0.331729\pi$
$312$		0			0
$313$	−5.40177	+	3.11871i	−0.305326	+	0.176280i	−0.644833	−	0.764323i	$-0.723073\pi$
$313$	−5.40177	+	3.11871i	−0.305326	+	0.176280i	0.339507	+	0.940604i	$0.389740\pi$
$314$	7.07452	+	12.2534i	0.399238	+	0.691501i
$315$		0			0
$316$	−9.35026			−0.525993
$317$	11.9018	−	6.87153i	0.668474	−	0.385944i	−0.127024	−	0.991900i	$-0.540543\pi$
$317$	11.9018	−	6.87153i	0.668474	−	0.385944i	0.795498	+	0.605956i	$0.207209\pi$
$318$		0			0
$319$	8.04960	+	13.9423i	0.450691	+	0.780620i
$320$	2.12032	−	0.710109i	0.118529	−	0.0396963i
$321$		0			0
$322$			29.8300i			1.66236i
$323$	19.4041	−	5.66608i	1.07968	−	0.315269i
$324$		0			0
$325$	−1.57269	+	3.71081i	−0.0872372	+	0.205839i
$326$	8.73084	−	15.1223i	0.483557	−	0.837544i
$327$		0			0
$328$	−3.51235	−	2.02785i	−0.193937	−	0.111970i
$329$	−21.9277	−	37.9799i	−1.20891	−	2.09390i
$330$		0			0
$331$	−1.56230			−0.0858716			−0.0429358	−	0.999078i	$-0.513671\pi$
$331$	−1.56230			−0.0858716			−0.0429358	+	0.999078i	$0.513671\pi$
$332$	8.59511	−	4.96239i	0.471718	−	0.272346i
$333$		0			0
$334$	−23.2071			−1.26984
$335$	10.9805	−	12.4182i	0.599928	−	0.678478i
$336$		0			0
$337$	−11.2909	−	6.51881i	−0.615055	−	0.355102i	0.159886	−	0.987135i	$-0.448887\pi$
$337$	−11.2909	−	6.51881i	−0.615055	−	0.355102i	−0.774941	+	0.632033i	$0.782221\pi$
$338$	10.6956	−	6.17513i	0.581766	−	0.335883i
$339$		0			0
$340$	−3.29314	−	9.83301i	−0.178596	−	0.533270i
$341$	13.2750			0.718884
$342$		0			0
$343$		−	36.7318i		−	1.98333i
$344$	3.67513	−	6.36551i	0.198150	−	0.343205i
$345$		0			0
$346$	−9.58721	−	16.6055i	−0.515412	−	0.892719i
$347$	−21.2610	−	12.2750i	−1.14135	−	0.658959i	−0.194585	−	0.980886i	$-0.562336\pi$
$347$	−21.2610	−	12.2750i	−1.14135	−	0.658959i	−0.946764	+	0.321927i	$0.895669\pi$
$348$		0			0
$349$	−6.86907			−0.367693			−0.183846	−	0.982955i	$-0.558855\pi$
$349$	−6.86907			−0.367693			−0.183846	+	0.982955i	$0.558855\pi$
$350$	−2.86177	−	23.1998i	−0.152968	−	1.24008i
$351$		0			0
$352$	3.43153	−	1.98119i	0.182901	−	0.105598i
$353$		−	29.1368i		−	1.55080i	−0.631473	−	0.775398i	$-0.717549\pi$
$353$		−	29.1368i		−	1.55080i	0.631473	−	0.775398i	$-0.282451\pi$
$354$		0			0
$355$	0.965406	−	4.75194i	0.0512385	−	0.252207i
$356$	−9.13141	+	15.8161i	−0.483964	+	0.838250i
$357$		0			0
$358$	−15.9095	−	9.18536i	−0.840844	−	0.485462i
$359$	−10.4223	+	18.0520i	−0.550069	+	0.952747i	0.448200	+	0.893933i	$0.352065\pi$
$359$	−10.4223	+	18.0520i	−0.550069	+	0.952747i	−0.998269	+	0.0588138i	$0.981268\pi$
$360$		0			0
$361$	−0.847322	−	18.9811i	−0.0445959	−	0.999005i
$362$		−	6.21933i		−	0.326881i
$363$		0			0
$364$	1.88423	−	3.26358i	0.0987603	−	0.171058i
$365$	25.9263	+	5.26720i	1.35704	+	0.275698i
$366$		0			0
$367$	23.1758	−	13.3806i	1.20977	−	0.698461i	0.247060	−	0.969000i	$-0.420535\pi$
$367$	23.1758	−	13.3806i	1.20977	−	0.698461i	0.962709	+	0.270540i	$0.0872021\pi$
$368$		−	6.38058i		−	0.332611i
$369$		0			0
$370$	0.976711	−	4.80758i	0.0507768	−	0.249934i
$371$	−3.63823	−	6.30159i	−0.188887	−	0.327162i
$372$		0			0
$373$		−	27.6312i		−	1.43069i	−0.698772	−	0.715344i	$-0.746270\pi$
$373$		−	27.6312i		−	1.43069i	0.698772	−	0.715344i	$-0.253730\pi$
$374$	−9.18783	−	15.9138i	−0.475091	−	0.822882i
$375$		0			0
$376$	4.69029	+	8.12382i	0.241883	+	0.418954i
$377$	−2.83627	−	1.63752i	−0.146075	−	0.0843365i
$378$		0			0
$379$	28.4387			1.46080			0.730398	−	0.683022i	$-0.239335\pi$
$379$	28.4387			1.46080			0.730398	+	0.683022i	$0.239335\pi$
$380$	−9.71270	+	0.814582i	−0.498251	+	0.0417872i
$381$		0			0
$382$	3.01054	+	1.73813i	0.154033	+	0.0889307i
$383$	14.7601	+	8.52175i	0.754206	+	0.435441i	0.827212	−	0.561891i	$-0.189926\pi$
$383$	14.7601	+	8.52175i	0.754206	+	0.435441i	−0.0730058	+	0.997332i	$0.523259\pi$
$384$		0			0
$385$	−13.1545	−	39.2782i	−0.670417	−	2.00180i
$386$	4.37153	+	7.57171i	0.222505	+	0.385390i
$387$		0			0
$388$			12.4060i			0.629818i
$389$	−1.28115	−	2.21901i	−0.0649568	−	0.112508i	0.831718	−	0.555198i	$-0.187358\pi$
$389$	−1.28115	−	2.21901i	−0.0649568	−	0.112508i	−0.896675	+	0.442690i	$0.854024\pi$
$390$		0			0
$391$	−29.5901			−1.49643
$392$			14.8568i			0.750384i
$393$		0			0
$394$	6.32241	−	10.9507i	0.318518	−	0.551690i
$395$	4.16261	−	20.4893i	0.209444	−	1.03093i
$396$		0			0
$397$	18.6367	+	10.7599i	0.935347	+	0.540023i	0.888499	−	0.458879i	$-0.151749\pi$
$397$	18.6367	+	10.7599i	0.935347	+	0.540023i	0.0468484	+	0.998902i	$0.485082\pi$
$398$			4.37565i			0.219332i
$399$		0			0
$400$	0.612127	+	4.96239i	0.0306063	+	0.248119i
$401$	−13.9502	+	24.1624i	−0.696638	+	1.20661i	0.272987	+	0.962018i	$0.411988\pi$
$401$	−13.9502	+	24.1624i	−0.696638	+	1.20661i	−0.969625	+	0.244595i	$0.921345\pi$
$402$		0			0
$403$	−2.33872	+	1.35026i	−0.116500	+	0.0672613i
$404$	5.21933	−	9.04014i	0.259671	−	0.449764i
$405$		0			0
$406$	18.9951			0.942710
$407$		−	8.69323i		−	0.430907i
$408$		0			0
$409$	18.6543	+	32.3103i	0.922398	+	1.59764i	0.795694	+	0.605699i	$0.207107\pi$
$409$	18.6543	+	32.3103i	0.922398	+	1.59764i	0.126704	+	0.991941i	$0.459560\pi$
$410$	6.00729	−	6.79384i	0.296679	−	0.335524i
$411$		0			0
$412$	1.84544	−	1.06547i	0.0909184	−	0.0524918i
$413$	−31.9629	−	18.4538i	−1.57279	−	0.908053i
$414$		0			0
$415$	7.04767	+	21.0437i	0.345957	+	1.03299i
$416$	−0.403032	+	0.698071i	−0.0197603	+	0.0342258i
$417$		0			0
$418$	−16.5793	+	4.84121i	−0.810919	+	0.236791i
$419$	−16.5271			−0.807399			−0.403700	−	0.914892i	$-0.632276\pi$
$419$	−16.5271			−0.807399			−0.403700	+	0.914892i	$0.632276\pi$
$420$		0			0
$421$	10.4902	−	18.1696i	0.511263	−	0.885534i	−0.488652	−	0.872479i	$-0.662511\pi$
$421$	10.4902	−	18.1696i	0.511263	−	0.885534i	0.999915	−	0.0130548i	$-0.00415559\pi$
$422$	−11.5185	+	6.65022i	−0.560712	+	0.323727i
$423$		0			0
$424$	0.778209	+	1.34790i	0.0377931	+	0.0654597i
$425$	23.0132	−	2.83875i	1.11630	−	0.137700i
$426$		0			0
$427$	−17.8388	+	10.2992i	−0.863281	+	0.498415i
$428$	−6.89137	+	3.97873i	−0.333107	+	0.192319i
$429$		0			0
$430$	12.3127	+	10.8872i	0.593769	+	0.525026i
$431$	−8.69640	−	15.0626i	−0.418891	−	0.725540i	0.576937	−	0.816788i	$-0.304248\pi$
$431$	−8.69640	−	15.0626i	−0.418891	−	0.725540i	−0.995828	+	0.0912482i	$0.970914\pi$
$432$		0			0
$433$	−0.124800	+	0.0720532i	−0.00599750	+	0.00346266i	−0.502996	−	0.864289i	$-0.667769\pi$
$433$	−0.124800	+	0.0720532i	−0.00599750	+	0.00346266i	0.496998	+	0.867752i	$0.334436\pi$
$434$	7.83146	−	13.5645i	0.375922	−	0.651116i
$435$		0			0
$436$	10.4060			0.498356
$437$	−6.59739	+	27.0185i	−0.315596	+	1.29247i
$438$		0			0
$439$	15.5381	−	26.9128i	0.741593	−	1.28448i	−0.210177	−	0.977663i	$-0.567404\pi$
$439$	15.5381	−	26.9128i	0.741593	−	1.28448i	0.951770	−	0.306813i	$-0.0992625\pi$
$440$	2.81373	+	8.40152i	0.134139	+	0.400527i
$441$		0			0
$442$	3.23732	+	1.86907i	0.153984	+	0.0889025i
$443$	26.7774	−	15.4599i	1.27223	−	0.734523i	0.296824	−	0.954932i	$-0.404073\pi$
$443$	26.7774	−	15.4599i	1.27223	−	0.734523i	0.975408	+	0.220409i	$0.0707392\pi$
$444$		0			0
$445$	−30.5926	−	27.0508i	−1.45023	−	1.28233i
$446$	−0.909141	−	1.57468i	−0.0430491	−	0.0745632i
$447$		0			0
$448$		−	4.67513i		−	0.220879i
$449$	−3.40009			−0.160460			−0.0802301	−	0.996776i	$-0.525566\pi$
$449$	−3.40009			−0.160460			−0.0802301	+	0.996776i	$0.525566\pi$
$450$		0			0
$451$	8.03515	−	13.9173i	0.378360	−	0.655339i
$452$	10.6525	−	6.15022i	0.501051	−	0.289282i
$453$		0			0
$454$	−6.43453	+	11.1449i	−0.301988	+	0.523058i
$455$	6.31265	+	5.58181i	0.295942	+	0.261679i
$456$		0			0
$457$			9.11634i			0.426445i	0.977004	+	0.213222i	$0.0683959\pi$
$457$			9.11634i			0.426445i	−0.977004	+	0.213222i	$0.931604\pi$
$458$	13.9529	+	8.05571i	0.651976	+	0.376419i
$459$		0			0
$460$	13.9818	+	2.84055i	0.651904	+	0.132441i
$461$	2.13823	−	3.70352i	0.0995871	−	0.172490i	−0.811927	−	0.583759i	$-0.801581\pi$
$461$	2.13823	−	3.70352i	0.0995871	−	0.172490i	0.911514	+	0.411269i	$0.134914\pi$
$462$		0			0
$463$		−	29.4871i		−	1.37038i	−0.728364	−	0.685190i	$-0.759719\pi$
$463$		−	29.4871i		−	1.37038i	0.728364	−	0.685190i	$-0.240281\pi$
$464$	−4.06300			−0.188620
$465$		0			0
$466$	1.10062	+	1.90632i	0.0509850	+	0.0883087i
$467$			15.9575i			0.738423i	0.929345	+	0.369212i	$0.120372\pi$
$467$			15.9575i			0.738423i	−0.929345	+	0.369212i	$0.879628\pi$
$468$		0			0
$469$	−17.3290	−	30.0147i	−0.800179	−	1.38595i
$470$	−19.8898	+	6.66123i	−0.917448	+	0.307260i
$471$		0			0
$472$	6.83680	+	3.94723i	0.314689	+	0.181686i
$473$	25.2226	+	14.5623i	1.15974	+	0.669575i
$474$		0			0
$475$	2.53896	−	21.6461i	0.116496	−	0.993191i
$476$	−21.6810			−0.993747
$477$		0			0
$478$	−4.07077	−	2.35026i	−0.186193	−	0.107498i
$479$	−10.5410	−	18.2576i	−0.481632	−	0.834211i	0.518146	−	0.855292i	$-0.326622\pi$
$479$	−10.5410	−	18.2576i	−0.481632	−	0.834211i	−0.999778	+	0.0210814i	$0.993289\pi$
$480$		0			0
$481$	0.884226	+	1.53152i	0.0403172	+	0.0698315i
$482$			25.2809i			1.15151i
$483$		0			0
$484$	2.35026	+	4.07077i	0.106830	+	0.185035i
$485$	−27.1852	−	5.52297i	−1.23442	−	0.250785i
$486$		0			0
$487$		−	10.2365i		−	0.463859i	−0.972733	−	0.231929i	$-0.925496\pi$
$487$		−	10.2365i		−	0.463859i	0.972733	−	0.231929i	$-0.0745038\pi$
$488$	3.81568	−	2.20299i	0.172728	−	0.0997245i
$489$		0			0
$490$	−32.5559	−	6.61407i	−1.47072	−	0.298793i
$491$	3.68901	−	6.38956i	0.166483	−	0.288357i	−0.770698	−	0.637200i	$-0.780092\pi$
$491$	3.68901	−	6.38956i	0.166483	−	0.288357i	0.937181	+	0.348844i	$0.113426\pi$
$492$		0			0
$493$			18.8423i			0.848613i
$494$	2.42842	−	2.53925i	0.109260	−	0.114246i
$495$		0			0
$496$	−1.67513	+	2.90141i	−0.0752156	+	0.130277i
$497$	−8.77996	−	5.06911i	−0.393835	−	0.227381i
$498$		0			0
$499$	−13.1944	+	22.8534i	−0.590663	+	1.02306i	0.403480	+	0.914988i	$0.367800\pi$
$499$	−13.1944	+	22.8534i	−0.590663	+	1.02306i	−0.994143	+	0.108070i	$0.965533\pi$
$500$	−11.1466	−	0.867833i	−0.498491	−	0.0388107i
$501$		0			0
$502$			12.4387i			0.555164i
$503$	27.0701	−	15.6289i	1.20700	−	0.696860i	0.244895	−	0.969550i	$-0.421246\pi$
$503$	27.0701	−	15.6289i	1.20700	−	0.696860i	0.962102	+	0.272689i	$0.0879131\pi$
$504$		0			0
$505$	17.4861	+	15.4617i	0.778122	+	0.688036i
$506$	25.2823			1.12394
$507$		0			0
$508$	−10.3754	−	5.99024i	−0.460334	−	0.265774i
$509$	−1.79384	−	3.10703i	−0.0795108	−	0.137717i	0.823528	−	0.567275i	$-0.192002\pi$
$509$	−1.79384	−	3.10703i	−0.0795108	−	0.137717i	−0.903039	+	0.429559i	$0.858669\pi$
$510$		0			0
$511$	27.6568	−	47.9030i	1.22346	−	2.11910i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	26.2130			1.15621
$515$	1.51319	+	4.51825i	0.0666793	+	0.199098i
$516$		0			0
$517$	−32.1897	+	18.5847i	−1.41570	+	0.817356i
$518$	−8.88277	−	5.12847i	−0.390287	−	0.225332i
$519$		0			0
$520$	−1.35026	−	1.19394i	−0.0592129	−	0.0523576i
$521$	−1.56134			−0.0684036			−0.0342018	−	0.999415i	$-0.510889\pi$
$521$	−1.56134			−0.0684036			−0.0342018	+	0.999415i	$0.510889\pi$
$522$		0			0
$523$	11.2025	−	6.46779i	0.489853	−	0.282817i	−0.234660	−	0.972077i	$-0.575398\pi$
$523$	11.2025	−	6.46779i	0.489853	−	0.282817i	0.724513	+	0.689261i	$0.242065\pi$
$524$	−12.6121			−0.550963
$525$		0			0
$526$	2.90597	+	5.03329i	0.126706	+	0.219462i
$527$	13.4554	+	7.76845i	0.586124	+	0.338399i
$528$		0			0
$529$	8.85589	−	15.3389i	0.385039	−	0.666907i
$530$	−3.30010	+	1.10523i	−0.143347	+	0.0480079i
$531$		0			0
$532$	−4.83399	+	19.7968i	−0.209580	+	0.858299i
$533$			3.26916i			0.141603i
$534$		0			0
$535$	−5.65066	−	16.8723i	−0.244300	−	0.729455i
$536$	3.70663	+	6.42008i	0.160102	+	0.277305i
$537$		0			0
$538$	20.3518	−	11.7501i	0.877429	−	0.506584i
$539$	−58.8686			−2.53565
$540$		0			0
$541$	−16.3004	−	28.2332i	−0.700810	−	1.21384i	−0.968182	−	0.250246i	$-0.919489\pi$
$541$	−16.3004	−	28.2332i	−0.700810	−	1.21384i	0.267372	−	0.963593i	$-0.413845\pi$
$542$	28.3069	−	16.3430i	1.21588	−	0.701991i
$543$		0			0
$544$	4.63752			0.198832
$545$	−4.63260	+	22.8026i	−0.198439	+	0.976758i
$546$		0			0
$547$	−24.6599	+	14.2374i	−1.05438	+	0.608748i	−0.923873	−	0.382699i	$-0.874995\pi$
$547$	−24.6599	+	14.2374i	−1.05438	+	0.608748i	−0.130510	+	0.991447i	$0.541661\pi$
$548$	5.53206	+	3.19394i	0.236318	+	0.136438i
$549$		0			0
$550$	−19.6629	+	2.42548i	−0.838429	+	0.103423i
$551$	17.2047	+	4.20106i	0.732947	+	0.178971i
$552$		0			0
$553$	−37.8572	−	21.8568i	−1.60985	−	0.929448i
$554$	9.83440	−	17.0337i	0.417823	−	0.723691i
$555$		0			0
$556$	6.63752	−	11.4965i	0.281494	−	0.487561i
$557$	−24.3934	+	14.0836i	−1.03358	+	0.596740i	−0.918009	−	0.396559i	$-0.870204\pi$
$557$	−24.3934	+	14.0836i	−1.03358	+	0.596740i	−0.115574	+	0.993299i	$0.536871\pi$
$558$		0			0
$559$	−5.92478			−0.250591
$560$	10.2446	+	2.08130i	0.432915	+	0.0879512i
$561$		0			0
$562$			11.5926i			0.489005i
$563$			7.02776i			0.296185i	0.988974	+	0.148092i	$0.0473133\pi$
$563$			7.02776i			0.296185i	−0.988974	+	0.148092i	$0.952687\pi$
$564$		0			0
$565$	8.73464	+	26.0808i	0.367469	+	1.09723i
$566$	−14.7005	−	25.4621i	−0.617909	−	1.07025i
$567$		0			0
$568$	1.87801	+	1.08427i	0.0787997	+	0.0454950i
$569$	21.5320			0.902668			0.451334	−	0.892355i	$-0.350948\pi$
$569$	21.5320			0.902668			0.451334	+	0.892355i	$0.350948\pi$
$570$		0			0
$571$	14.1417			0.591813			0.295907	−	0.955217i	$-0.404378\pi$
$571$	14.1417			0.591813			0.295907	+	0.955217i	$0.404378\pi$
$572$	−2.76603	−	1.59697i	−0.115654	−	0.0667726i
$573$		0			0
$574$	−9.48049	−	16.4207i	−0.395708	−	0.685386i
$575$	−12.4490	+	29.3737i	−0.519159	+	1.22497i
$576$		0			0
$577$		−	4.22918i		−	0.176063i	−0.996118	−	0.0880315i	$-0.971942\pi$
$577$		−	4.22918i		−	0.176063i	0.996118	−	0.0880315i	$-0.0280576\pi$
$578$		−	4.50659i		−	0.187449i
$579$		0			0
$580$	1.80879	−	8.90327i	0.0751061	−	0.369688i
$581$	46.3996			1.92498
$582$		0			0
$583$	−5.34089	+	3.08356i	−0.221197	+	0.127708i
$584$	−5.91573	+	10.2463i	−0.244795	+	0.423997i
$585$		0			0
$586$	−11.1314	+	19.2802i	−0.459834	+	0.796456i
$587$	2.11194	+	1.21933i	0.0871691	+	0.0503271i	0.542951	−	0.839764i	$-0.317307\pi$
$587$	2.11194	+	1.21933i	0.0871691	+	0.0503271i	−0.455782	+	0.890092i	$0.650640\pi$
$588$		0			0
$589$	10.0933	−	10.5539i	0.415888	−	0.434868i
$590$	−11.6932	+	13.2243i	−0.481403	+	0.544434i
$591$		0			0
$592$	1.90000	+	1.09697i	0.0780897	+	0.0450851i
$593$	2.19785	−	1.26893i	0.0902549	−	0.0521087i	−0.454193	−	0.890903i	$-0.650072\pi$
$593$	2.19785	−	1.26893i	0.0902549	−	0.0521087i	0.544448	+	0.838794i	$0.316739\pi$
$594$		0			0
$595$	9.65209	−	47.5097i	0.395697	−	1.94771i
$596$	−0.899385			−0.0368402
$597$		0			0
$598$	−4.45410	+	2.57158i	−0.182142	+	0.105160i
$599$	14.1776	+	24.5563i	0.579281	+	1.00334i	0.995562	+	0.0941078i	$0.0299998\pi$
$599$	14.1776	+	24.5563i	0.579281	+	1.00334i	−0.416281	+	0.909236i	$0.636667\pi$
$600$		0			0
$601$	23.5705			0.961463			0.480731	−	0.876868i	$-0.340371\pi$
$601$	23.5705			0.961463			0.480731	+	0.876868i	$0.340371\pi$
$602$	29.7596	−	17.1817i	1.21291	−	0.700275i
$603$		0			0
$604$	−5.18783	−	8.98558i	−0.211090	−	0.365618i
$605$	−9.96660	+	3.33788i	−0.405200	+	0.135704i
$606$		0			0
$607$		−	20.5042i		−	0.832241i	−0.909310	−	0.416120i	$-0.863390\pi$
$607$		−	20.5042i		−	0.832241i	0.909310	−	0.416120i	$-0.136610\pi$
$608$	1.03398	−	4.23449i	0.0419334	−	0.171731i
$609$		0			0
$610$	3.12872	+	9.34206i	0.126678	+	0.378249i
$611$	3.78067	−	6.54831i	0.152950	−	0.264916i
$612$		0			0
$613$	−0.211935	−	0.122361i	−0.00855999	−	0.00494211i	0.495714	−	0.868486i	$-0.334906\pi$
$613$	−0.211935	−	0.122361i	−0.00855999	−	0.00494211i	−0.504274	+	0.863544i	$0.668240\pi$
$614$	−15.6314	−	27.0744i	−0.630832	−	1.09263i
$615$		0			0
$616$	18.5247			0.746381
$617$	−0.401053	+	0.231548i	−0.0161458	+	0.00932177i	−0.508051	−	0.861327i	$-0.669634\pi$
$617$	−0.401053	+	0.231548i	−0.0161458	+	0.00932177i	0.491905	+	0.870649i	$0.336301\pi$
$618$		0			0
$619$	11.1685			0.448902			0.224451	−	0.974485i	$-0.427941\pi$
$619$	11.1685			0.448902			0.224451	+	0.974485i	$0.427941\pi$
$620$	−5.61213	−	4.96239i	−0.225388	−	0.199294i
$621$		0			0
$622$	−15.4057	−	8.89446i	−0.617711	−	0.356635i
$623$	−73.9422	+	42.6905i	−2.96243	+	1.71036i
$624$		0			0
$625$	6.86400	−	24.0392i	0.274560	−	0.961570i
$626$	6.23743			0.249298
$627$		0			0
$628$		−	14.1490i		−	0.564608i
$629$	5.08721	−	8.81131i	0.202840	−	0.351330i
$630$		0			0
$631$	20.9695	+	36.3202i	0.834781	+	1.44588i	0.894209	+	0.447650i	$0.147739\pi$
$631$	20.9695	+	36.3202i	0.834781	+	1.44588i	−0.0594281	+	0.998233i	$0.518928\pi$
$632$	8.09756	+	4.67513i	0.322104	+	0.185967i
$633$		0			0
$634$	−13.7431			−0.545807
$635$	17.7454	−	20.0689i	0.704206	−	0.796409i
$636$		0			0
$637$	10.3711	−	5.98778i	0.410920	−	0.237245i
$638$		−	16.0992i		−	0.637373i
$639$		0			0
$640$	−2.19130	−	0.445186i	−0.0866189	−	0.0175975i
$641$	−12.5999	+	21.8237i	−0.497666	+	0.861984i	−0.999996	−	0.00269246i	$-0.999143\pi$
$641$	−12.5999	+	21.8237i	−0.497666	+	0.861984i	0.502330	+	0.864676i	$0.332476\pi$
$642$		0			0
$643$	18.4581	+	10.6568i	0.727917	+	0.420263i	0.817660	−	0.575702i	$-0.195271\pi$
$643$	18.4581	+	10.6568i	0.727917	+	0.420263i	−0.0897424	+	0.995965i	$0.528604\pi$
$644$	14.9150	−	25.8336i	0.587734	−	1.01799i
$645$		0			0
$646$	−19.6375	−	4.79510i	−0.772628	−	0.188661i
$647$		−	22.0132i		−	0.865427i	−0.901531	−	0.432714i	$-0.857556\pi$
$647$		−	22.0132i		−	0.865427i	0.901531	−	0.432714i	$-0.142444\pi$
$648$		0			0
$649$	−15.6405	+	27.0901i	−0.613942	+	1.06338i
$650$	3.21740	−	2.42731i	0.126197	−	0.0952069i
$651$		0			0
$652$	−15.1223	+	8.73084i	−0.592233	+	0.341926i
$653$		−	33.6785i		−	1.31794i	−0.752169	−	0.658970i	$-0.770992\pi$
$653$		−	33.6785i		−	1.31794i	0.752169	−	0.658970i	$-0.229008\pi$
$654$		0			0
$655$	5.61475	−	27.6370i	0.219386	−	1.07987i
$656$	2.02785	+	3.51235i	0.0791744	+	0.137134i
$657$		0			0
$658$			43.8554i			1.70966i
$659$	22.9538	+	39.7572i	0.894154	+	1.54872i	0.834848	+	0.550480i	$0.185555\pi$
$659$	22.9538	+	39.7572i	0.894154	+	1.54872i	0.0593053	+	0.998240i	$0.481111\pi$
$660$		0			0
$661$	−7.24472	−	12.5482i	−0.281787	−	0.488069i	0.690038	−	0.723773i	$-0.257594\pi$
$661$	−7.24472	−	12.5482i	−0.281787	−	0.488069i	−0.971825	+	0.235704i	$0.924260\pi$
$662$	1.35299	+	0.781148i	0.0525854	+	0.0303602i
$663$		0			0
$664$	−9.92478			−0.385156
$665$	−41.2287	−	19.4060i	−1.59878	−	0.752532i
$666$		0			0
$667$	−22.4511	−	12.9622i	−0.869311	−	0.501897i
$668$	20.0979	+	11.6036i	0.777613	+	0.448955i
$669$		0			0
$670$	−15.7185	+	5.26422i	−0.607258	+	0.203375i
$671$	8.72909	+	15.1192i	0.336983	+	0.583671i
$672$		0			0
$673$		−	19.8397i		−	0.764764i	−0.924004	−	0.382382i	$-0.875104\pi$
$673$		−	19.8397i		−	0.764764i	0.924004	−	0.382382i	$-0.124896\pi$
$674$	6.51881	+	11.2909i	0.251095	+	0.434909i
$675$		0			0
$676$	−12.3503			−0.475010
$677$			10.3479i			0.397702i	0.980030	+	0.198851i	$0.0637209\pi$
$677$			10.3479i			0.397702i	−0.980030	+	0.198851i	$0.936279\pi$
$678$		0			0
$679$	−28.9998	+	50.2291i	−1.11291	+	1.92761i
$680$	−2.06456	+	10.1622i	−0.0791723	+	0.389703i
$681$		0			0
$682$	−11.4965	−	6.63752i	−0.440225	−	0.254164i
$683$			40.3307i			1.54321i	0.636100	+	0.771607i	$0.280547\pi$
$683$			40.3307i			1.54321i	−0.636100	+	0.771607i	$0.719453\pi$
$684$		0			0
$685$	−9.46168	+	10.7005i	−0.361512	+	0.408846i
$686$	−18.3659	+	31.8107i	−0.701213	+	1.21454i
$687$		0			0
$688$	−6.36551	+	3.67513i	−0.242683	+	0.140113i
$689$	0.627285	−	1.08649i	0.0238977	−	0.0413920i
$690$		0			0
$691$	45.8202			1.74308			0.871541	−	0.490322i	$-0.163121\pi$
$691$	45.8202			1.74308			0.871541	+	0.490322i	$0.163121\pi$
$692$			19.1744i			0.728902i
$693$		0			0
$694$	12.2750	+	21.2610i	0.465954	+	0.807056i
$695$	22.2374	+	19.6629i	0.843514	+	0.745857i
$696$		0			0
$697$	16.2886	−	9.40422i	0.616974	−	0.356210i
$698$	5.94879	+	3.43453i	0.225165	+	0.129999i
$699$		0			0
$700$	−9.12154	+	21.5225i	−0.344762	+	0.813475i
$701$	−18.6375	+	32.2811i	−0.703929	+	1.21924i	0.263147	+	0.964756i	$0.415240\pi$
$701$	−18.6375	+	32.2811i	−0.703929	+	1.21924i	−0.967077	+	0.254486i	$0.918094\pi$
$702$		0			0
$703$	−6.91130	−	6.60966i	−0.260665	−	0.249288i
$704$	−3.96239			−0.149338
$705$		0			0
$706$	−14.5684	+	25.2332i	−0.548289	+	0.949665i
$707$	42.2639	−	24.4010i	1.58950	−	0.917696i
$708$		0			0
$709$	22.8356	+	39.5524i	0.857608	+	1.48542i	0.874204	+	0.485559i	$0.161384\pi$
$709$	22.8356	+	39.5524i	0.857608	+	1.48542i	−0.0165958	+	0.999862i	$0.505283\pi$
$710$	−3.21203	+	3.63259i	−0.120546	+	0.136329i
$711$		0			0
$712$	15.8161	−	9.13141i	0.592732	−	0.342214i
$713$	−18.5127	+	10.6883i	−0.693306	+	0.400280i
$714$		0			0
$715$	4.73084	−	5.35026i	0.176923	−	0.200088i
$716$	9.18536	+	15.9095i	0.343273	+	0.594567i
$717$		0			0
$718$	18.0520	−	10.4223i	0.673694	−	0.388957i
$719$	14.5188	−	25.1473i	0.541460	−	0.937836i	−0.457360	−	0.889281i	$-0.651205\pi$
$719$	14.5188	−	25.1473i	0.541460	−	0.937836i	0.998821	−	0.0485550i	$-0.0154616\pi$
$720$		0			0
$721$	9.96239			0.371019
$722$	−8.75675	+	16.8618i	−0.325892	+	0.627530i
$723$		0			0
$724$	−3.10966	+	5.38610i	−0.115570	+	0.200173i
$725$	18.7045	+	7.92723i	0.694668	+	0.294410i
$726$		0			0
$727$	−11.6107	−	6.70346i	−0.430618	−	0.248618i	0.268992	−	0.963143i	$-0.413310\pi$
$727$	−11.6107	−	6.70346i	−0.430618	−	0.248618i	−0.699610	+	0.714525i	$0.746643\pi$
$728$	−3.26358	+	1.88423i	−0.120956	+	0.0698341i
$729$		0			0
$730$	−19.8192	−	17.5247i	−0.733543	−	0.648618i
$731$	17.0435	+	29.5202i	0.630376	+	1.09184i
$732$		0			0
$733$			8.72829i			0.322387i	0.986923	+	0.161193i	$0.0515343\pi$
$733$			8.72829i			0.322387i	−0.986923	+	0.161193i	$0.948466\pi$
$734$	−26.7612			−0.987772
$735$		0			0
$736$	−3.19029	+	5.52574i	−0.117596	+	0.203682i
$737$	−25.4388	+	14.6871i	−0.937052	+	0.541007i
$738$		0			0
$739$	−16.1661	+	28.0005i	−0.594679	+	1.03001i	0.398913	+	0.916989i	$0.369387\pi$
$739$	−16.1661	+	28.0005i	−0.594679	+	1.03001i	−0.993592	+	0.113025i	$0.963946\pi$
$740$	−3.24965	+	3.67513i	−0.119459	+	0.135100i
$741$		0			0
$742$			7.27645i			0.267127i
$743$	40.5255	+	23.3974i	1.48674	+	0.858367i	0.999886	−	0.0151182i	$-0.00481244\pi$
$743$	40.5255	+	23.3974i	1.48674	+	0.858367i	0.486850	+	0.873486i	$0.338146\pi$
$744$		0			0
$745$	0.400394	−	1.97082i	0.0146693	−	0.0722054i
$746$	−13.8156	+	23.9293i	−0.505825	+	0.876114i
$747$		0			0
$748$			18.3757i			0.671880i
$749$	−37.2022			−1.35934
$750$		0			0
$751$	19.6180	+	33.9794i	0.715871	+	1.23993i	0.962623	+	0.270846i	$0.0873036\pi$
$751$	19.6180	+	33.9794i	0.715871	+	1.23993i	−0.246751	+	0.969079i	$0.579363\pi$
$752$		−	9.38058i		−	0.342075i
$753$		0			0
$754$	1.63752	+	2.83627i	0.0596349	+	0.103291i
$755$	21.9997	−	7.36784i	0.800650	−	0.268143i
$756$		0			0
$757$	3.30977	+	1.91090i	0.120296	+	0.0694527i	0.558940	−	0.829208i	$-0.311208\pi$
$757$	3.30977	+	1.91090i	0.120296	+	0.0694527i	−0.438645	+	0.898661i	$0.644541\pi$
$758$	−24.6286	−	14.2193i	−0.894551	−	0.516469i
$759$		0			0
$760$	8.81873	+	4.15090i	0.319889	+	0.150569i
$761$	28.3928			1.02924			0.514619	−	0.857419i	$-0.327933\pi$
$761$	28.3928			1.02924			0.514619	+	0.857419i	$0.327933\pi$
$762$		0			0
$763$	42.1315	+	24.3246i	1.52526	+	0.880611i
$764$	−1.73813	−	3.01054i	−0.0628835	−	0.108917i
$765$		0			0
$766$	−8.52175	−	14.7601i	−0.307903	−	0.533304i
$767$		−	6.36344i		−	0.229770i
$768$		0			0
$769$	3.11577	+	5.39668i	0.112358	+	0.194609i	0.916720	−	0.399529i	$-0.130826\pi$
$769$	3.11577	+	5.39668i	0.112358	+	0.194609i	−0.804363	+	0.594139i	$0.797493\pi$
$770$	−8.24694	+	40.5932i	−0.297199	+	1.46288i
$771$		0			0
$772$		−	8.74306i		−	0.314670i
$773$	21.6189	−	12.4817i	0.777577	−	0.448935i	−0.0579936	−	0.998317i	$-0.518470\pi$
$773$	21.6189	−	12.4817i	0.777577	−	0.448935i	0.835571	+	0.549382i	$0.185137\pi$
$774$		0			0
$775$	13.3725	−	10.0887i	0.480356	−	0.362396i
$776$	6.20299	−	10.7439i	0.222674	−	0.385683i
$777$		0			0
$778$			2.56230i			0.0918628i
$779$	−4.95523	−	16.9698i	−0.177540	−	0.608005i
$780$		0			0
$781$	−4.29631	+	7.44142i	−0.153734	+	0.266275i
$782$	25.6257	+	14.7950i	0.916375	+	0.529069i
$783$		0			0
$784$	7.42842	−	12.8664i	0.265301	−	0.459515i
$785$	31.0048	+	6.29896i	1.10661	+	0.224819i
$786$		0			0
$787$			42.1744i			1.50336i	0.659530	+	0.751678i	$0.270755\pi$
$787$			42.1744i			1.50336i	−0.659530	+	0.751678i	$0.729245\pi$
$788$	−10.9507	+	6.32241i	−0.390104	+	0.225226i
$789$		0			0
$790$	−13.8496	+	15.6629i	−0.492745	+	0.557261i
$791$	57.5061			2.04468
$792$		0			0
$793$	−3.07568	−	1.77575i	−0.109221	−	0.0630586i
$794$	−10.7599	−	18.6367i	−0.381854	−	0.661390i
$795$		0			0
$796$	2.18783	−	3.78943i	0.0775455	−	0.134313i
$797$		−	11.1481i		−	0.394885i	−0.980314	−	0.197443i	$-0.936736\pi$
$797$		−	11.1481i		−	0.394885i	0.980314	−	0.197443i	$-0.0632636\pi$
$798$		0			0
$799$	−43.5026			−1.53901
$800$	1.95108	−	4.60362i	0.0689810	−	0.162762i
$801$		0			0
$802$	24.1624	−	13.9502i	0.853204	−	0.492598i
$803$	−40.6000	−	23.4404i	−1.43274	−	0.827194i
$804$		0			0
$805$	49.9692	+	44.1841i	1.76118	+	1.55728i
$806$	2.70052			0.0951219
$807$		0			0
$808$	−9.04014	+	5.21933i	−0.318031	+	0.183615i
$809$	13.3561			0.469577			0.234788	−	0.972046i	$-0.424560\pi$
$809$	13.3561			0.469577			0.234788	+	0.972046i	$0.424560\pi$
$810$		0			0
$811$	24.3781	+	42.2241i	0.856031	+	1.48269i	0.875685	+	0.482883i	$0.160410\pi$
$811$	24.3781	+	42.2241i	0.856031	+	1.48269i	−0.0196534	+	0.999807i	$0.506256\pi$
$812$	−16.4502	−	9.49754i	−0.577289	−	0.333298i
$813$		0			0
$814$	−4.34661	+	7.52856i	−0.152349	+	0.263876i
$815$	−12.3997	−	37.0243i	−0.434342	−	1.29690i
$816$		0			0
$817$	30.7547	−	8.98049i	1.07597	−	0.314187i
$818$		−	37.3087i		−	1.30447i
$819$		0			0
$820$	−8.59939	+	2.87999i	−0.300304	+	0.100574i
$821$	11.6448	+	20.1694i	0.406407	+	0.703917i	0.994484	−	0.104888i	$-0.0334483\pi$
$821$	11.6448	+	20.1694i	0.406407	+	0.703917i	−0.588077	+	0.808805i	$0.700115\pi$
$822$		0			0
$823$	−25.2481	+	14.5770i	−0.880092	+	0.508122i	−0.870689	−	0.491834i	$-0.836327\pi$
$823$	−25.2481	+	14.5770i	−0.880092	+	0.508122i	−0.00940343	+	0.999956i	$0.502993\pi$
$824$	−2.13093			−0.0742346
$825$		0			0
$826$	18.4538	+	31.9629i	0.642090	+	1.11213i
$827$	−21.7954	+	12.5836i	−0.757899	+	0.437573i	−0.828541	−	0.559928i	$-0.810829\pi$
$827$	−21.7954	+	12.5836i	−0.757899	+	0.437573i	0.0706416	+	0.997502i	$0.477495\pi$
$828$		0			0
$829$	16.7513			0.581797			0.290898	−	0.956754i	$-0.406046\pi$
$829$	16.7513			0.581797			0.290898	+	0.956754i	$0.406046\pi$
$830$	4.41838	−	21.7482i	0.153364	−	0.754891i
$831$		0			0
$832$	0.698071	−	0.403032i	0.0242013	−	0.0139726i
$833$	−59.6682	−	34.4495i	−2.06738	−	1.19360i
$834$		0			0
$835$	−34.3742	+	38.8749i	−1.18957	+	1.34532i
$836$	16.7787	+	4.09703i	0.580303	+	0.141699i
$837$		0			0
$838$	14.3128	+	8.26353i	0.494429	+	0.285459i
$839$	−9.18901	+	15.9158i	−0.317240	+	0.549476i	−0.979911	−	0.199435i	$-0.936089\pi$
$839$	−9.18901	+	15.9158i	−0.317240	+	0.549476i	0.662671	+	0.748910i	$0.269423\pi$
$840$		0			0
$841$	6.24600	−	10.8184i	0.215379	−	0.373048i
$842$	−18.1696	+	10.4902i	−0.626167	+	0.361518i
$843$		0			0
$844$	13.3004			0.457820
$845$	5.49817	−	27.0632i	0.189143	−	0.931001i
$846$		0			0
$847$			21.9756i			0.755089i
$848$		−	1.55642i		−	0.0534476i
$849$		0			0
$850$	−21.3494	−	9.04816i	−0.732277	−	0.310349i
$851$	6.99929	+	12.1231i	0.239933	+	0.415576i
$852$		0			0
$853$	13.9216	+	8.03761i	0.476665	+	0.275203i	0.719026	−	0.694984i	$-0.244588\pi$
$853$	13.9216	+	8.03761i	0.476665	+	0.275203i	−0.242361	+	0.970186i	$0.577922\pi$
$854$	20.5985			0.704866
$855$		0			0
$856$	7.95746			0.271981
$857$	3.85662	+	2.22662i	0.131740	+	0.0760600i	0.564422	−	0.825487i	$-0.309099\pi$
$857$	3.85662	+	2.22662i	0.131740	+	0.0760600i	−0.432682	+	0.901547i	$0.642433\pi$
$858$		0			0
$859$	23.8926	+	41.3831i	0.815204	+	1.41197i	0.909181	+	0.416400i	$0.136708\pi$
$859$	23.8926	+	41.3831i	0.815204	+	1.41197i	−0.0939775	+	0.995574i	$0.529958\pi$
$860$	−5.21949	−	15.5849i	−0.177983	−	0.531440i
$861$		0			0
$862$			17.3928i			0.592401i
$863$			20.6483i			0.702877i	0.936211	+	0.351439i	$0.114307\pi$
$863$			20.6483i			0.702877i	−0.936211	+	0.351439i	$0.885693\pi$
$864$		0			0
$865$	−42.0170	−	8.53619i	−1.42862	−	0.290239i
$866$	0.144106			0.00489693
$867$		0			0
$868$	−13.5645	+	7.83146i	−0.460408	+	0.265817i
$869$	−18.5247	+	32.0857i	−0.628407	+	1.08843i
$870$		0			0
$871$	2.98778	−	5.17499i	0.101237	−	0.175348i
$872$	−9.01184	−	5.20299i	−0.305179	−	0.176195i
$873$		0			0
$874$	19.2227	−	20.1000i	0.650219	−	0.679893i
$875$	−43.1016	−	29.5696i	−1.45710	−	0.999635i
$876$		0			0
$877$	14.2740	+	8.24107i	0.481997	+	0.278281i	0.721248	−	0.692676i	$-0.243569\pi$
$877$	14.2740	+	8.24107i	0.481997	+	0.278281i	−0.239251	+	0.970958i	$0.576902\pi$
$878$	−26.9128	+	15.5381i	−0.908262	+	0.524385i
$879$		0			0
$880$	1.76400	−	8.68279i	0.0594645	−	0.292697i
$881$	−31.1197			−1.04845			−0.524224	−	0.851580i	$-0.675645\pi$
$881$	−31.1197			−1.04845			−0.524224	+	0.851580i	$0.675645\pi$
$882$		0			0
$883$	7.20102	−	4.15751i	0.242334	−	0.139911i	−0.373915	−	0.927463i	$-0.621985\pi$
$883$	7.20102	−	4.15751i	0.242334	−	0.139911i	0.616249	+	0.787552i	$0.288652\pi$
$884$	−1.86907	−	3.23732i	−0.0628635	−	0.108883i
$885$		0			0
$886$	−30.9199			−1.03877
$887$	11.2435	−	6.49143i	0.377519	−	0.217961i	−0.299219	−	0.954184i	$-0.596726\pi$
$887$	11.2435	−	6.49143i	0.377519	−	0.217961i	0.676738	+	0.736224i	$0.263393\pi$
$888$		0			0
$889$	−28.0052	−	48.5064i	−0.939263	−	1.62685i
$890$	12.9686	+	38.7230i	0.434708	+	1.29800i
$891$		0			0
$892$			1.81828i			0.0608806i
$893$	−9.69933	+	39.7219i	−0.324576	+	1.32924i
$894$		0			0
$895$	−38.9518	+	13.0452i	−1.30201	+	0.436053i
$896$	−2.33757	+	4.04878i	−0.0780926	+	0.135260i
$897$		0			0
$898$	2.94457	+	1.70005i	0.0982614	+	0.0567313i
$899$	6.80606	+	11.7884i	0.226995	+	0.393167i
$900$		0			0
$901$	−7.21791			−0.240464
$902$	−13.9173	+	8.03515i	−0.463395	+	0.267541i
$903$		0			0
$904$	−12.3004			−0.409106
$905$	−10.4182	−	9.21203i	−0.346312	−	0.306218i
$906$		0			0
$907$	−35.8857	−	20.7186i	−1.19157	−	0.687951i	−0.232904	−	0.972500i	$-0.574823\pi$
$907$	−35.8857	−	20.7186i	−1.19157	−	0.687951i	−0.958661	+	0.284549i	$0.908156\pi$
$908$	11.1449	−	6.43453i	0.369858	−	0.213538i
$909$		0			0
$910$	−2.67601	−	7.99031i	−0.0887089	−	0.264876i
$911$	−12.4993			−0.414120			−0.207060	−	0.978328i	$-0.566390\pi$
$911$	−12.4993			−0.414120			−0.207060	+	0.978328i	$0.566390\pi$
$912$		0			0
$913$		−	39.3258i		−	1.30149i
$914$	4.55817	−	7.89499i	0.150771	−	0.261143i
$915$		0			0
$916$	−8.05571	−	13.9529i	−0.266168	−	0.461017i
$917$	−51.0638	−	29.4817i	−1.68627	−	0.973571i
$918$		0			0
$919$	−6.08744			−0.200806			−0.100403	−	0.994947i	$-0.532013\pi$
$919$	−6.08744			−0.200806			−0.100403	+	0.994947i	$0.532013\pi$
$920$	−10.6883	−	9.45088i	−0.352383	−	0.311586i
$921$		0			0
$922$	−3.70352	+	2.13823i	−0.121969	+	0.0704187i
$923$		−	1.74798i		−	0.0575356i
$924$		0			0
$925$	−6.60663	−	8.75708i	−0.217225	−	0.287931i
$926$	−14.7435	+	25.5366i	−0.484503	+	0.839183i
$927$		0			0
$928$	3.51866	+	2.03150i	0.115506	+	0.0666873i
$929$	14.6502	−	25.3749i	0.480658	−	0.832524i	−0.519096	−	0.854716i	$-0.673731\pi$
$929$	14.6502	−	25.3749i	0.480658	−	0.832524i	0.999754	+	0.0221920i	$0.00706453\pi$
$930$		0			0
$931$	−44.7592	+	46.8018i	−1.46692	+	1.53387i
$932$		−	2.20123i		−	0.0721037i
$933$		0			0
$934$	7.97873	−	13.8196i	0.261072	−	0.452190i
$935$	−40.2666	−	8.18059i	−1.31686	−	0.267534i
$936$		0			0
$937$	3.80715	−	2.19806i	0.124374	−	0.0718075i	−0.436522	−	0.899694i	$-0.643790\pi$
$937$	3.80715	−	2.19806i	0.124374	−	0.0718075i	0.560896	+	0.827886i	$0.310457\pi$
$938$			34.6580i			1.13162i
$939$		0			0
$940$	20.5557	+	4.17611i	0.670453	+	0.136210i
$941$	−28.6436	−	49.6122i	−0.933756	−	1.61731i	−0.776838	−	0.629700i	$-0.783178\pi$
$941$	−28.6436	−	49.6122i	−0.933756	−	1.61731i	−0.156918	−	0.987612i	$-0.550156\pi$
$942$		0			0
$943$			25.8778i			0.842696i
$944$	−3.94723	−	6.83680i	−0.128471	−	0.222519i
$945$		0			0
$946$	−14.5623	−	25.2226i	−0.473461	−	0.820059i
$947$	−6.56809	−	3.79209i	−0.213434	−	0.123226i	0.389472	−	0.921038i	$-0.372657\pi$
$947$	−6.56809	−	3.79209i	−0.213434	−	0.123226i	−0.602906	+	0.797812i	$0.705991\pi$
$948$		0			0
$949$	9.53690			0.309581
$950$	−13.0219	+	17.4766i	−0.422485	+	0.567015i
$951$		0			0
$952$	18.7763	+	10.8405i	0.608544	+	0.351343i
$953$	15.4370	+	8.91256i	0.500054	+	0.288706i	0.728736	−	0.684795i	$-0.240108\pi$
$953$	15.4370	+	8.91256i	0.500054	+	0.288706i	−0.228682	+	0.973501i	$0.573442\pi$
$954$		0			0
$955$	7.37079	−	2.46853i	0.238513	−	0.0798797i
$956$	2.35026	+	4.07077i	0.0760129	+	0.131658i
$957$		0			0
$958$			21.0821i			0.681130i
$959$	14.9321	+	25.8631i	0.482182	+	0.835163i
$960$		0			0
$961$	−19.7757			−0.637927
$962$		−	1.76845i		−	0.0570172i
$963$		0			0
$964$	12.6405	−	21.8939i	0.407122	−	0.705156i
$965$	19.1587	+	3.89229i	0.616740	+	0.125297i
$966$		0			0
$967$	−25.6974	−	14.8364i	−0.826372	−	0.477106i	0.0262371	−	0.999656i	$-0.491647\pi$
$967$	−25.6974	−	14.8364i	−0.826372	−	0.477106i	−0.852609	+	0.522550i	$0.824981\pi$
$968$		−	4.70052i		−	0.151081i
$969$		0			0
$970$	20.7816	+	18.3757i	0.667258	+	0.590007i
$971$	24.6840	−	42.7539i	0.792146	−	1.37204i	−0.132490	−	0.991184i	$-0.542297\pi$
$971$	24.6840	−	42.7539i	0.792146	−	1.37204i	0.924636	−	0.380852i	$-0.124369\pi$
$972$		0			0
$973$	53.7477	−	31.0313i	1.72307	−	0.994817i
$974$	−5.11824	+	8.86505i	−0.163999	+	0.284054i
$975$		0			0
$976$	−4.40597			−0.141032
$977$			14.5017i			0.463949i	0.972722	+	0.231975i	$0.0745186\pi$
$977$			14.5017i			0.463949i	−0.972722	+	0.231975i	$0.925481\pi$
$978$		0			0
$979$	36.1822	+	62.6694i	1.15639	+	2.00292i
$980$	24.8872	+	22.0059i	0.794991	+	0.702952i
$981$		0			0
$982$	−6.38956	+	3.68901i	−0.203899	+	0.117721i
$983$	5.97931	+	3.45215i	0.190710	+	0.110107i	0.592315	−	0.805706i	$-0.298214\pi$
$983$	5.97931	+	3.45215i	0.190710	+	0.110107i	−0.401605	+	0.915813i	$0.631547\pi$
$984$		0			0
$985$	−8.97919	−	26.8110i	−0.286101	−	0.854270i
$986$	9.42113	−	16.3179i	0.300030	−	0.519667i
$987$		0			0
$988$	−3.37270	+	0.984841i	−0.107300	+	0.0313320i
$989$	−46.8989			−1.49130
$990$		0			0
$991$	5.02421	−	8.70218i	0.159599	−	0.276434i	−0.775125	−	0.631808i	$-0.782313\pi$
$991$	5.02421	−	8.70218i	0.159599	−	0.276434i	0.934724	+	0.355374i	$0.115646\pi$
$992$	2.90141	−	1.67513i	0.0921199	−	0.0531855i
$993$		0			0
$994$	5.06911	+	8.77996i	0.160783	+	0.278483i
$995$	7.32979	+	6.48119i	0.232370	+	0.205468i
$996$		0			0
$997$	26.0709	−	15.0521i	0.825675	−	0.476704i	−0.0266946	−	0.999644i	$-0.508498\pi$
$997$	26.0709	−	15.0521i	0.825675	−	0.476704i	0.852369	+	0.522940i	$0.175165\pi$
$998$	22.8534	−	13.1944i	0.723412	−	0.417662i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.t.b.1189.1		12
3.2	odd	2		570.2.q.b.49.6	yes	12
5.4	even	2	inner	1710.2.t.b.1189.5		12
15.14	odd	2		570.2.q.b.49.2	✓	12
19.7	even	3	inner	1710.2.t.b.919.5		12
57.26	odd	6		570.2.q.b.349.2	yes	12
95.64	even	6	inner	1710.2.t.b.919.1		12
285.254	odd	6		570.2.q.b.349.6	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.q.b.49.2	✓	12	15.14	odd	2
570.2.q.b.49.6	yes	12	3.2	odd	2
570.2.q.b.349.2	yes	12	57.26	odd	6
570.2.q.b.349.6	yes	12	285.254	odd	6
1710.2.t.b.919.1		12	95.64	even	6	inner
1710.2.t.b.919.5		12	19.7	even	3	inner
1710.2.t.b.1189.1		12	1.1	even	1	trivial
1710.2.t.b.1189.5		12	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-2.12032 + 0.710109i) q^{5} +4.67513i q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-2.12032 + 0.710109i) q^{5} +4.67513i q^{7} -1.00000i q^{8} +(2.19130 + 0.445186i) q^{10} +3.96239 q^{11} +(-0.698071 + 0.403032i) q^{13} +(2.33757 - 4.04878i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(4.01621 + 2.31876i) q^{17} +(3.01270 - 3.15018i) q^{19} +(-1.67513 - 1.48119i) q^{20} +(-3.43153 - 1.98119i) q^{22} +(-5.52574 + 3.19029i) q^{23} +(3.99149 - 3.01131i) q^{25} +0.806063 q^{26} +(-4.04878 + 2.33757i) q^{28} +(2.03150 + 3.51866i) q^{29} +3.35026 q^{31} +(0.866025 - 0.500000i) q^{32} +(-2.31876 - 4.01621i) q^{34} +(-3.31985 - 9.91276i) q^{35} -2.19394i q^{37} +(-4.18416 + 1.22179i) q^{38} +(0.710109 + 2.12032i) q^{40} +(2.02785 - 3.51235i) q^{41} +(6.36551 + 3.67513i) q^{43} +(1.98119 + 3.43153i) q^{44} +6.38058 q^{46} +(-8.12382 + 4.69029i) q^{47} -14.8568 q^{49} +(-4.96239 + 0.612127i) q^{50} +(-0.698071 - 0.403032i) q^{52} +(-1.34790 + 0.778209i) q^{53} +(-8.40152 + 2.81373i) q^{55} +4.67513 q^{56} -4.06300i q^{58} +(-3.94723 + 6.83680i) q^{59} +(2.20299 + 3.81568i) q^{61} +(-2.90141 - 1.67513i) q^{62} -1.00000 q^{64} +(1.19394 - 1.35026i) q^{65} +(-6.42008 + 3.70663i) q^{67} +4.63752i q^{68} +(-2.08130 + 10.2446i) q^{70} +(-1.08427 + 1.87801i) q^{71} +(-10.2463 - 5.91573i) q^{73} +(-1.09697 + 1.90000i) q^{74} +(4.23449 + 1.03398i) q^{76} +18.5247i q^{77} +(-4.67513 + 8.09756i) q^{79} +(0.445186 - 2.19130i) q^{80} +(-3.51235 + 2.02785i) q^{82} -9.92478i q^{83} +(-10.1622 - 2.06456i) q^{85} +(-3.67513 - 6.36551i) q^{86} -3.96239i q^{88} +(9.13141 + 15.8161i) q^{89} +(-1.88423 - 3.26358i) q^{91} +(-5.52574 - 3.19029i) q^{92} +9.38058 q^{94} +(-4.15090 + 8.81873i) q^{95} +(10.7439 + 6.20299i) q^{97} +(12.8664 + 7.42842i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4}+O(q^{10}) \) 12 * q + 6 * q^4	\( 12 q + 6 q^{4} - 2 q^{10} + 4 q^{11} + 18 q^{14} - 6 q^{16} + 6 q^{19} - 2 q^{25} + 8 q^{26} + 16 q^{29} + 4 q^{34} - 2 q^{35} + 2 q^{40} - 10 q^{41} + 2 q^{44} + 28 q^{46} - 56 q^{49} - 16 q^{50} - 8 q^{55} + 36 q^{56} - 8 q^{59} - 28 q^{61} - 12 q^{64} + 16 q^{65} + 16 q^{70} - 44 q^{71} - 14 q^{74} - 12 q^{76} - 36 q^{79} - 32 q^{85} - 24 q^{86} - 6 q^{89} + 64 q^{94} + 12 q^{95}+O(q^{100}) \) 12 * q + 6 * q^4 - 2 * q^10 + 4 * q^11 + 18 * q^14 - 6 * q^16 + 6 * q^19 - 2 * q^25 + 8 * q^26 + 16 * q^29 + 4 * q^34 - 2 * q^35 + 2 * q^40 - 10 * q^41 + 2 * q^44 + 28 * q^46 - 56 * q^49 - 16 * q^50 - 8 * q^55 + 36 * q^56 - 8 * q^59 - 28 * q^61 - 12 * q^64 + 16 * q^65 + 16 * q^70 - 44 * q^71 - 14 * q^74 - 12 * q^76 - 36 * q^79 - 32 * q^85 - 24 * q^86 - 6 * q^89 + 64 * q^94 + 12 * q^95

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