LMFDB - Embedded newform 1197.2.db.a.647.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1197,2,Mod(647,1197)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1197, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 0]))

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

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

chi := DirichletCharacter("1197.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1197 = 3^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1197.db (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.55809312195$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			647.7
Character	$\chi$	$=$	1197.647
Dual form			1197.2.db.a.1160.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.97511 + 1.14033i) q^{2} +(1.60071 - 2.77251i) q^{4} +(0.970205 + 1.68044i) q^{5} +(-2.34380 + 1.22744i) q^{7} +2.74002i q^{8} +O(q^{10})$	\(q+(-1.97511 + 1.14033i) q^{2} +(1.60071 - 2.77251i) q^{4} +(0.970205 + 1.68044i) q^{5} +(-2.34380 + 1.22744i) q^{7} +2.74002i q^{8} +(-3.83252 - 2.21271i) q^{10} +(4.35215 + 2.51271i) q^{11} -5.69300i q^{13} +(3.22958 - 5.09703i) q^{14} +(0.0768845 + 0.133168i) q^{16} +(-0.0128670 + 0.0222863i) q^{17} +(0.866025 - 0.500000i) q^{19} +6.21206 q^{20} -11.4613 q^{22} +(6.92292 - 3.99695i) q^{23} +(0.617404 - 1.06938i) q^{25} +(6.49191 + 11.2443i) q^{26} +(-0.348666 + 8.46297i) q^{28} +1.11430i q^{29} +(3.97121 + 2.29278i) q^{31} +(-5.04957 - 2.91537i) q^{32} -0.0586904i q^{34} +(-4.33660 - 2.74776i) q^{35} +(-4.13836 - 7.16786i) q^{37} +(-1.14033 + 1.97511i) q^{38} +(-4.60446 + 2.65838i) q^{40} -7.17076 q^{41} -1.17085 q^{43} +(13.9330 - 8.04424i) q^{44} +(-9.11569 + 15.7888i) q^{46} +(3.90316 + 6.76047i) q^{47} +(3.98680 - 5.75373i) q^{49} +2.81618i q^{50} +(-15.7839 - 9.11284i) q^{52} +(8.88424 + 5.12932i) q^{53} +9.75139i q^{55} +(-3.36320 - 6.42207i) q^{56} +(-1.27067 - 2.20087i) q^{58} +(0.653821 - 1.13245i) q^{59} +(5.17540 - 2.98802i) q^{61} -10.4581 q^{62} +12.9904 q^{64} +(9.56678 - 5.52338i) q^{65} +(5.04341 - 8.73543i) q^{67} +(0.0411925 + 0.0713476i) q^{68} +(11.6986 + 0.481972i) q^{70} -9.79344i q^{71} +(11.5530 + 6.67014i) q^{73} +(16.3475 + 9.43820i) q^{74} -3.20142i q^{76} +(-13.2848 - 0.547319i) q^{77} +(3.70394 + 6.41542i) q^{79} +(-0.149188 + 0.258400i) q^{80} +(14.1630 - 8.17703i) q^{82} -16.2135 q^{83} -0.0499344 q^{85} +(2.31256 - 1.33515i) q^{86} +(-6.88489 + 11.9250i) q^{88} +(1.90428 + 3.29831i) q^{89} +(6.98780 + 13.3433i) q^{91} -25.5918i q^{92} +(-15.4183 - 8.90179i) q^{94} +(1.68044 + 0.970205i) q^{95} +3.05289i q^{97} +(-1.31322 + 15.9105i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 48 q^{4} + 8 q^{7}+O(q^{10}) $ 96 * q + 48 * q^4 + 8 * q^7	$ 96 q + 48 q^{4} + 8 q^{7} + 24 q^{10} - 56 q^{16} + 48 q^{22} - 24 q^{25} + 16 q^{28} - 24 q^{31} - 48 q^{40} - 24 q^{43} - 48 q^{46} + 52 q^{49} - 72 q^{52} + 48 q^{58} - 176 q^{64} + 32 q^{67} - 80 q^{70} - 12 q^{73} + 40 q^{79} + 72 q^{82} + 40 q^{85} - 16 q^{88} - 72 q^{91} + 72 q^{94}+O(q^{100}) $ 96 * q + 48 * q^4 + 8 * q^7 + 24 * q^10 - 56 * q^16 + 48 * q^22 - 24 * q^25 + 16 * q^28 - 24 * q^31 - 48 * q^40 - 24 * q^43 - 48 * q^46 + 52 * q^49 - 72 * q^52 + 48 * q^58 - 176 * q^64 + 32 * q^67 - 80 * q^70 - 12 * q^73 + 40 * q^79 + 72 * q^82 + 40 * q^85 - 16 * q^88 - 72 * q^91 + 72 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1197\mathbb{Z}\right)^\times$.

$n$	$514$	$533$	$1009$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$

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 $

$2$	−1.97511	+	1.14033i	−1.39661	+	0.806336i	−0.994036	−	0.109050i	$-0.965219\pi$
$2$	−1.97511	+	1.14033i	−1.39661	+	0.806336i	−0.402578	+	0.915386i	$0.631886\pi$
$3$		0			0
$3$		0			0
$4$	1.60071	−	2.77251i	0.800354	−	1.38625i
$5$	0.970205	+	1.68044i	0.433889	+	0.751518i	0.997204	−	0.0747244i	$-0.0238077\pi$
$5$	0.970205	+	1.68044i	0.433889	+	0.751518i	−0.563315	+	0.826242i	$0.690474\pi$
$6$		0			0
$7$	−2.34380	+	1.22744i	−0.885873	+	0.463927i
$7$	−2.34380	+	1.22744i	−0.885873	+	0.463927i
$8$			2.74002i			0.968744i
$9$		0			0
$10$	−3.83252	−	2.21271i	−1.21195	−	0.699720i
$11$	4.35215	+	2.51271i	1.31222	+	0.757612i	0.982464	−	0.186453i	$-0.0596994\pi$
$11$	4.35215	+	2.51271i	1.31222	+	0.757612i	0.329758	+	0.944065i	$0.393033\pi$
$12$		0			0
$13$		−	5.69300i		−	1.57896i	−0.613779	−	0.789478i	$-0.710352\pi$
$13$		−	5.69300i		−	1.57896i	0.613779	−	0.789478i	$-0.289648\pi$
$14$	3.22958	−	5.09703i	0.863142	−	1.36224i
$15$		0			0
$16$	0.0768845	+	0.133168i	0.0192211	+	0.0332920i
$17$	−0.0128670	+	0.0222863i	−0.00312070	+	0.00540521i	−0.867582	−	0.497295i	$-0.834327\pi$
$17$	−0.0128670	+	0.0222863i	−0.00312070	+	0.00540521i	0.864461	+	0.502700i	$0.167660\pi$
$18$		0			0
$19$	0.866025	−	0.500000i	0.198680	−	0.114708i
$19$	0.866025	−	0.500000i	0.198680	−	0.114708i
$20$	6.21206			1.38906
$21$		0			0
$22$	−11.4613			−2.44356
$23$	6.92292	−	3.99695i	1.44353	−	0.833421i	0.445445	−	0.895309i	$-0.353045\pi$
$23$	6.92292	−	3.99695i	1.44353	−	0.833421i	0.998083	+	0.0618879i	$0.0197121\pi$
$24$		0			0
$25$	0.617404	−	1.06938i	0.123481	−	0.213875i
$26$	6.49191	+	11.2443i	1.27317	+	2.20519i
$27$		0			0
$28$	−0.348666	+	8.46297i	−0.0658917	+	1.59935i
$29$			1.11430i			0.206921i	0.994634	+	0.103460i	$0.0329915\pi$
$29$			1.11430i			0.206921i	−0.994634	+	0.103460i	$0.967008\pi$
$30$		0			0
$31$	3.97121	+	2.29278i	0.713251	+	0.411796i	0.812264	−	0.583291i	$-0.198235\pi$
$31$	3.97121	+	2.29278i	0.713251	+	0.411796i	−0.0990126	+	0.995086i	$0.531568\pi$
$32$	−5.04957	−	2.91537i	−0.892646	−	0.515369i
$33$		0			0
$34$		−	0.0586904i		−	0.0100653i
$35$	−4.33660	−	2.74776i	−0.733020	−	0.464457i
$36$		0			0
$37$	−4.13836	−	7.16786i	−0.680343	−	1.17839i	−0.974876	−	0.222747i	$-0.928498\pi$
$37$	−4.13836	−	7.16786i	−0.680343	−	1.17839i	0.294534	−	0.955641i	$-0.404836\pi$
$38$	−1.14033	+	1.97511i	−0.184986	+	0.320405i
$39$		0			0
$40$	−4.60446	+	2.65838i	−0.728028	+	0.420327i
$41$	−7.17076			−1.11988			−0.559942	−	0.828532i	$-0.689177\pi$
$41$	−7.17076			−1.11988			−0.559942	+	0.828532i	$0.689177\pi$
$42$		0			0
$43$	−1.17085			−0.178553			−0.0892764	−	0.996007i	$-0.528455\pi$
$43$	−1.17085			−0.178553			−0.0892764	+	0.996007i	$0.528455\pi$
$44$	13.9330	−	8.04424i	2.10048	−	1.21272i
$45$		0			0
$46$	−9.11569	+	15.7888i	−1.34403	+	2.32794i
$47$	3.90316	+	6.76047i	0.569335	+	0.986116i	0.996632	+	0.0820052i	$0.0261324\pi$
$47$	3.90316	+	6.76047i	0.569335	+	0.986116i	−0.427297	+	0.904111i	$0.640534\pi$
$48$		0			0
$49$	3.98680	−	5.75373i	0.569543	−	0.821961i
$50$			2.81618i			0.398268i
$51$		0			0
$52$	−15.7839	−	9.11284i	−2.18883	−	1.26372i
$53$	8.88424	+	5.12932i	1.22034	+	0.704566i	0.964991	−	0.262282i	$-0.0844751\pi$
$53$	8.88424	+	5.12932i	1.22034	+	0.704566i	0.255353	+	0.966848i	$0.417808\pi$
$54$		0			0
$55$			9.75139i			1.31488i
$56$	−3.36320	−	6.42207i	−0.449427	−	0.858185i
$57$		0			0
$58$	−1.27067	−	2.20087i	−0.166848	−	0.288989i
$59$	0.653821	−	1.13245i	0.0851202	−	0.147433i	−0.820322	−	0.571902i	$-0.806206\pi$
$59$	0.653821	−	1.13245i	0.0851202	−	0.147433i	0.905442	+	0.424469i	$0.139539\pi$
$60$		0			0
$61$	5.17540	−	2.98802i	0.662642	−	0.382576i	−0.130641	−	0.991430i	$-0.541704\pi$
$61$	5.17540	−	2.98802i	0.662642	−	0.382576i	0.793283	+	0.608853i	$0.208370\pi$
$62$	−10.4581			−1.32818
$63$		0			0
$64$	12.9904			1.62380
$65$	9.56678	−	5.52338i	1.18661	−	0.685091i
$66$		0			0
$67$	5.04341	−	8.73543i	0.616150	−	1.06720i	−0.374032	−	0.927416i	$-0.622025\pi$
$67$	5.04341	−	8.73543i	0.616150	−	1.06720i	0.990182	−	0.139787i	$-0.0446418\pi$
$68$	0.0411925	+	0.0713476i	0.00499533	+	0.00865216i
$69$		0			0
$70$	11.6986	+	0.481972i	1.39825	+	0.0576067i
$71$		−	9.79344i		−	1.16227i	−0.813808	−	0.581134i	$-0.802609\pi$
$71$		−	9.79344i		−	1.16227i	0.813808	−	0.581134i	$-0.197391\pi$
$72$		0			0
$73$	11.5530	+	6.67014i	1.35218	+	0.780681i	0.988555	−	0.150864i	$-0.0482056\pi$
$73$	11.5530	+	6.67014i	1.35218	+	0.780681i	0.363625	+	0.931545i	$0.381539\pi$
$74$	16.3475	+	9.43820i	1.90035	+	1.09717i
$75$		0			0
$76$		−	3.20142i		−	0.367228i
$77$	−13.2848	−	0.547319i	−1.51394	−	0.0623728i
$78$		0			0
$79$	3.70394	+	6.41542i	0.416726	+	0.721791i	0.995608	−	0.0936206i	$-0.0298441\pi$
$79$	3.70394	+	6.41542i	0.416726	+	0.721791i	−0.578882	+	0.815411i	$0.696511\pi$
$80$	−0.149188	+	0.258400i	−0.0166797	+	0.0288900i
$81$		0			0
$82$	14.1630	−	8.17703i	1.56405	−	0.903002i
$83$	−16.2135			−1.77967			−0.889834	−	0.456285i	$-0.849180\pi$
$83$	−16.2135			−1.77967			−0.889834	+	0.456285i	$0.849180\pi$
$84$		0			0
$85$	−0.0499344			−0.00541615
$86$	2.31256	−	1.33515i	0.249369	−	0.143973i
$87$		0			0
$88$	−6.88489	+	11.9250i	−0.733932	+	1.27121i
$89$	1.90428	+	3.29831i	0.201853	+	0.349620i	0.949126	−	0.314898i	$-0.101970\pi$
$89$	1.90428	+	3.29831i	0.201853	+	0.349620i	−0.747272	+	0.664518i	$0.768637\pi$
$90$		0			0
$91$	6.98780	+	13.3433i	0.732520	+	1.39875i
$92$		−	25.5918i		−	2.66813i
$93$		0			0
$94$	−15.4183	−	8.90179i	−1.59028	−	0.918149i
$95$	1.68044	+	0.970205i	0.172410	+	0.0995409i
$96$		0			0
$97$			3.05289i			0.309974i	0.987917	+	0.154987i	$0.0495335\pi$
$97$			3.05289i			0.309974i	−0.987917	+	0.154987i	$0.950466\pi$
$98$	−1.31322	+	15.9105i	−0.132656	+	1.60721i
$99$		0			0
$100$	−1.97657	−	3.42352i	−0.197657	−	0.342352i
$101$	−3.58449	+	6.20851i	−0.356670	+	0.617770i	−0.987402	−	0.158230i	$-0.949421\pi$
$101$	−3.58449	+	6.20851i	−0.356670	+	0.617770i	0.630732	+	0.776000i	$0.282755\pi$
$102$		0			0
$103$	−1.76681	+	1.02007i	−0.174089	+	0.100510i	−0.584512	−	0.811385i	$-0.698714\pi$
$103$	−1.76681	+	1.02007i	−0.174089	+	0.100510i	0.410424	+	0.911895i	$0.365381\pi$
$104$	15.5990			1.52960
$105$		0			0
$106$	−23.3965			−2.27247
$107$	8.34931	−	4.82048i	0.807158	−	0.466013i	−0.0388098	−	0.999247i	$-0.512357\pi$
$107$	8.34931	−	4.82048i	0.807158	−	0.466013i	0.845968	+	0.533234i	$0.179023\pi$
$108$		0			0
$109$	−7.00954	+	12.1409i	−0.671392	+	1.16288i	0.306118	+	0.951994i	$0.400970\pi$
$109$	−7.00954	+	12.1409i	−0.671392	+	1.16288i	−0.977510	+	0.210891i	$0.932364\pi$
$110$	−11.1198	−	19.2601i	−1.06023	−	1.83638i
$111$		0			0
$112$	−0.343657	−	0.217748i	−0.0324725	−	0.0205753i
$113$			15.4033i			1.44903i	0.689262	+	0.724513i	$0.257935\pi$
$113$			15.4033i			1.44903i	−0.689262	+	0.724513i	$0.742065\pi$
$114$		0			0
$115$	13.4333	+	7.75572i	1.25266	+	0.723225i
$116$	3.08941	+	1.78367i	0.286845	+	0.165610i
$117$		0			0
$118$			2.98229i			0.274542i
$119$	0.00280268	−	0.0680279i	0.000256922	−	0.00623611i
$120$		0			0
$121$	7.12747	+	12.3451i	0.647951	+	1.12228i
$122$	−6.81466	+	11.8033i	−0.616970	+	1.06862i
$123$		0			0
$124$	12.7135	−	7.34015i	1.14171	−	0.659165i
$125$	12.0981			1.08209
$126$		0			0
$127$	10.9459			0.971289			0.485645	−	0.874156i	$-0.338585\pi$
$127$	10.9459			0.971289			0.485645	+	0.874156i	$0.338585\pi$
$128$	−15.5583	+	8.98262i	−1.37518	+	0.793959i
$129$		0			0
$130$	−12.5970	+	21.8186i	−1.10483	+	1.91362i
$131$	10.9454	+	18.9580i	0.956306	+	1.65637i	0.731351	+	0.682001i	$0.238890\pi$
$131$	10.9454	+	18.9580i	0.956306	+	1.65637i	0.224955	+	0.974369i	$0.427777\pi$
$132$		0			0
$133$	−1.41607	+	2.23489i	−0.122789	+	0.193790i
$134$			23.0046i			1.98729i
$135$		0			0
$136$	−0.0610648	−	0.0352558i	−0.00523627	−	0.00302316i
$137$	−3.28883	−	1.89880i	−0.280983	−	0.162226i	0.352885	−	0.935667i	$-0.385201\pi$
$137$	−3.28883	−	1.89880i	−0.280983	−	0.162226i	−0.633869	+	0.773441i	$0.718534\pi$
$138$		0			0
$139$		−	7.02004i		−	0.595432i	−0.954655	−	0.297716i	$-0.903775\pi$
$139$		−	7.02004i		−	0.595432i	0.954655	−	0.297716i	$-0.0962248\pi$
$140$	−14.5598	+	7.62490i	−1.23053	+	0.644422i
$141$		0			0
$142$	11.1678	+	19.3431i	0.937177	+	1.62324i
$143$	14.3049	−	24.7768i	1.19624	−	2.07194i
$144$		0			0
$145$	−1.87253	+	1.08110i	−0.155505	+	0.0897807i
$146$	−30.4247			−2.51796
$147$		0			0
$148$	−26.4972			−2.17806
$149$	−12.4160	+	7.16837i	−1.01716	+	0.587256i	−0.913279	−	0.407334i	$-0.866458\pi$
$149$	−12.4160	+	7.16837i	−1.01716	+	0.587256i	−0.103878	+	0.994590i	$0.533125\pi$
$150$		0			0
$151$	−5.36816	+	9.29792i	−0.436855	+	0.756654i	−0.997445	−	0.0714389i	$-0.977241\pi$
$151$	−5.36816	+	9.29792i	−0.436855	+	0.756654i	0.560590	+	0.828093i	$0.310574\pi$
$152$	1.37001	+	2.37293i	0.111123	+	0.192470i
$153$		0			0
$154$	26.8630	−	14.0680i	2.16468	−	1.13363i
$155$			8.89787i			0.714694i
$156$		0			0
$157$	−6.95897	−	4.01776i	−0.555386	−	0.320652i	0.195905	−	0.980623i	$-0.437235\pi$
$157$	−6.95897	−	4.01776i	−0.555386	−	0.320652i	−0.751292	+	0.659970i	$0.770569\pi$
$158$	−14.6314	−	8.44744i	−1.16401	−	0.672042i
$159$		0			0
$160$		−	11.3140i		−	0.894452i
$161$	−11.3199	+	17.8655i	−0.892137	+	1.40800i
$162$		0			0
$163$	−7.76923	−	13.4567i	−0.608533	−	1.05401i	−0.991482	−	0.130241i	$-0.958425\pi$
$163$	−7.76923	−	13.4567i	−0.608533	−	1.05401i	0.382949	−	0.923770i	$-0.374909\pi$
$164$	−11.4783	+	19.8810i	−0.896304	+	1.55244i
$165$		0			0
$166$	32.0235	−	18.4888i	2.48551	−	1.43501i
$167$	−7.72405			−0.597705			−0.298852	−	0.954299i	$-0.596604\pi$
$167$	−7.72405			−0.597705			−0.298852	+	0.954299i	$0.596604\pi$
$168$		0			0
$169$	−19.4103			−1.49310
$170$	0.0986260	−	0.0569417i	0.00756427	−	0.00436723i
$171$		0			0
$172$	−1.87419	+	3.24619i	−0.142905	+	0.247519i
$173$	6.47769	+	11.2197i	0.492490	+	0.853018i	0.999963	−	0.00865024i	$-0.00275349\pi$
$173$	6.47769	+	11.2197i	0.492490	+	0.853018i	−0.507473	+	0.861668i	$0.669420\pi$
$174$		0			0
$175$	−0.134483	+	3.26423i	−0.0101660	+	0.246752i
$176$			0.772755i			0.0582486i
$177$		0			0
$178$	−7.52232	−	4.34301i	−0.563822	−	0.325523i
$179$	−2.87583	−	1.66036i	−0.214950	−	0.124101i	0.388660	−	0.921381i	$-0.372938\pi$
$179$	−2.87583	−	1.66036i	−0.214950	−	0.124101i	−0.603610	+	0.797280i	$0.706271\pi$
$180$		0			0
$181$			24.5970i			1.82828i	0.405399	+	0.914140i	$0.367133\pi$
$181$			24.5970i			1.82828i	−0.405399	+	0.914140i	$0.632867\pi$
$182$	−29.0174	−	18.3860i	−2.15091	−	1.36286i
$183$		0			0
$184$	10.9517	+	18.9689i	0.807372	+	1.39841i
$185$	8.03012	−	13.9086i	0.590386	−	1.02258i
$186$		0			0
$187$	−0.111998	+	0.0646621i	−0.00819010	+	0.00472856i
$188$	24.9913			1.82268
$189$		0			0
$190$	−4.42542			−0.321054
$191$	14.0150	−	8.09156i	1.01409	−	0.585484i	0.101703	−	0.994815i	$-0.467571\pi$
$191$	14.0150	−	8.09156i	1.01409	−	0.585484i	0.912386	+	0.409330i	$0.134238\pi$
$192$		0			0
$193$	3.38230	−	5.85831i	0.243463	−	0.421690i	−0.718235	−	0.695800i	$-0.755050\pi$
$193$	3.38230	−	5.85831i	0.243463	−	0.421690i	0.961698	+	0.274110i	$0.0883832\pi$
$194$	−3.48130	−	6.02979i	−0.249943	−	0.432914i
$195$		0			0
$196$	−9.57055	−	20.2635i	−0.683611	−	1.44739i
$197$			8.12386i			0.578801i	0.957208	+	0.289401i	$0.0934560\pi$
$197$			8.12386i			0.578801i	−0.957208	+	0.289401i	$0.906544\pi$
$198$		0			0
$199$	6.71501	+	3.87692i	0.476015	+	0.274827i	0.718754	−	0.695264i	$-0.244713\pi$
$199$	6.71501	+	3.87692i	0.476015	+	0.274827i	−0.242739	+	0.970092i	$0.578046\pi$
$200$	2.93011	+	1.69170i	0.207190	+	0.119621i
$201$		0			0
$202$		−	16.3500i		−	1.15038i
$203$	−1.36774	−	2.61171i	−0.0959962	−	0.183306i
$204$		0			0
$205$	−6.95711	−	12.0501i	−0.485905	−	0.841613i
$206$	2.32643	−	4.02949i	0.162090	−	0.280748i
$207$		0			0
$208$	0.758125	−	0.437704i	0.0525665	−	0.0303493i
$209$	5.02543			0.347616
$210$		0			0
$211$	21.0503			1.44916			0.724582	−	0.689189i	$-0.242033\pi$
$211$	21.0503			1.44916			0.724582	+	0.689189i	$0.242033\pi$
$212$	28.4421	−	16.4211i	1.95341	−	1.12780i
$213$		0			0
$214$	−10.9939	+	19.0419i	−0.751526	+	1.30168i
$215$	−1.13596	−	1.96755i	−0.0774721	−	0.134186i
$216$		0			0
$217$	−12.1220	−	0.499413i	−0.822893	−	0.0339024i
$218$		−	31.9728i		−	2.16547i
$219$		0			0
$220$	27.0358	+	15.6091i	1.82275	+	1.05237i
$221$	0.126876	+	0.0732517i	0.00853458	+	0.00492744i
$222$		0			0
$223$		−	24.2161i		−	1.62163i	−0.585302	−	0.810815i	$-0.699024\pi$
$223$		−	24.2161i		−	1.62163i	0.585302	−	0.810815i	$-0.300976\pi$
$224$	15.4136	+	0.635026i	1.02987	+	0.0424294i
$225$		0			0
$226$	−17.5649	−	30.4233i	−1.16840	−	2.02373i
$227$	2.87742	−	4.98383i	0.190981	−	0.330789i	−0.754595	−	0.656191i	$-0.772166\pi$
$227$	2.87742	−	4.98383i	0.190981	−	0.330789i	0.945576	+	0.325403i	$0.105500\pi$
$228$		0			0
$229$	17.8264	−	10.2921i	1.17800	−	0.680118i	0.222448	−	0.974945i	$-0.428595\pi$
$229$	17.8264	−	10.2921i	1.17800	−	0.680118i	0.955551	+	0.294826i	$0.0952618\pi$
$230$	−35.3763			−2.33265
$231$		0			0
$232$	−3.05322			−0.200453
$233$	−3.94316	+	2.27658i	−0.258325	+	0.149144i	−0.623570	−	0.781767i	$-0.714318\pi$
$233$	−3.94316	+	2.27658i	−0.258325	+	0.149144i	0.365245	+	0.930911i	$0.380985\pi$
$234$		0			0
$235$	−7.57373	+	13.1181i	−0.494056	+	0.855730i
$236$	−2.09315	−	3.62545i	−0.136253	−	0.235996i
$237$		0			0
$238$	0.0720387	+	0.137559i	0.00466958	+	0.00891660i
$239$		−	7.83953i		−	0.507097i	−0.967323	−	0.253549i	$-0.918402\pi$
$239$		−	7.83953i		−	0.507097i	0.967323	−	0.253549i	$-0.0815978\pi$
$240$		0			0
$241$	−5.53599	−	3.19620i	−0.356604	−	0.205886i	0.310986	−	0.950415i	$-0.399341\pi$
$241$	−5.53599	−	3.19620i	−0.356604	−	0.205886i	−0.667590	+	0.744529i	$0.732674\pi$
$242$	−28.1551	−	16.2553i	−1.80988	−	1.04493i
$243$		0			0
$244$		−	19.1318i		−	1.22479i
$245$	13.5368	+	1.11731i	0.864837	+	0.0713820i
$246$		0			0
$247$	−2.84650	−	4.93029i	−0.181119	−	0.313707i
$248$	−6.28227	+	10.8812i	−0.398925	+	0.690958i
$249$		0			0
$250$	−23.8951	+	13.7958i	−1.51126	+	0.872524i
$251$	18.7077			1.18082			0.590410	−	0.807104i	$-0.298966\pi$
$251$	18.7077			1.18082			0.590410	+	0.807104i	$0.298966\pi$
$252$		0			0
$253$	40.1728			2.52564
$254$	−21.6193	+	12.4819i	−1.35652	+	0.783185i
$255$		0			0
$256$	7.49590	−	12.9833i	0.468494	−	0.811455i
$257$	−11.9181	−	20.6428i	−0.743432	−	1.28766i	−0.950924	−	0.309426i	$-0.899863\pi$
$257$	−11.9181	−	20.6428i	−0.743432	−	1.28766i	0.207491	−	0.978237i	$-0.433470\pi$
$258$		0			0
$259$	18.4976	+	11.7205i	1.14938	+	0.728273i
$260$		−	35.3653i		−	2.19326i
$261$		0			0
$262$	−43.2368	−	24.9628i	−2.67118	−	1.54221i
$263$	−3.72463	−	2.15042i	−0.229670	−	0.132600i	0.380750	−	0.924678i	$-0.375666\pi$
$263$	−3.72463	−	2.15042i	−0.229670	−	0.132600i	−0.610420	+	0.792078i	$0.708999\pi$
$264$		0			0
$265$			19.9060i			1.22281i
$266$	0.248387	−	6.02895i	0.0152296	−	0.369659i
$267$		0			0
$268$	−16.1460	−	27.9658i	−0.986276	−	1.70828i
$269$	−2.10080	+	3.63869i	−0.128088	+	0.221855i	−0.922936	−	0.384954i	$-0.874217\pi$
$269$	−2.10080	+	3.63869i	−0.128088	+	0.221855i	0.794848	+	0.606809i	$0.207551\pi$
$270$		0			0
$271$	0.295933	−	0.170857i	0.0179767	−	0.0103788i	−0.490985	−	0.871168i	$-0.663363\pi$
$271$	0.295933	−	0.170857i	0.0179767	−	0.0103788i	0.508961	+	0.860789i	$0.330030\pi$
$272$	−0.00395708			−0.000239934
$273$		0			0
$274$	8.66106			0.523234
$275$	5.37407	−	3.10272i	0.324069	−	0.187101i
$276$		0			0
$277$	−2.55975	+	4.43362i	−0.153801	+	0.266391i	−0.932622	−	0.360856i	$-0.882485\pi$
$277$	−2.55975	+	4.43362i	−0.153801	+	0.266391i	0.778821	+	0.627246i	$0.215818\pi$
$278$	8.00516	+	13.8653i	0.480118	+	0.831588i
$279$		0			0
$280$	7.52893	−	11.8824i	0.449940	−	0.710109i
$281$		−	20.4803i		−	1.22175i	−0.791727	−	0.610875i	$-0.790818\pi$
$281$		−	20.4803i		−	1.22175i	0.791727	−	0.610875i	$-0.209182\pi$
$282$		0			0
$283$	−15.0360	−	8.68102i	−0.893795	−	0.516033i	−0.0186132	−	0.999827i	$-0.505925\pi$
$283$	−15.0360	−	8.68102i	−0.893795	−	0.516033i	−0.875182	+	0.483794i	$0.839258\pi$
$284$	−27.1524	−	15.6764i	−1.61120	−	0.930225i
$285$		0			0
$286$			65.2492i			3.85827i
$287$	16.8068	−	8.80164i	0.992076	−	0.519545i
$288$		0			0
$289$	8.49967	+	14.7219i	0.499981	+	0.865992i
$290$	2.46563	−	4.27060i	0.144787	−	0.250778i
$291$		0			0
$292$	36.9860	−	21.3539i	2.16444	−	1.24964i
$293$	−0.209951			−0.0122655			−0.00613273	−	0.999981i	$-0.501952\pi$
$293$	−0.209951			−0.0122655			−0.00613273	+	0.999981i	$0.501952\pi$
$294$		0			0
$295$	2.53736			0.147731
$296$	19.6401	−	11.3392i	1.14156	−	0.659078i
$297$		0			0
$298$	16.3486	−	28.3166i	0.947050	−	1.64034i
$299$	−22.7546	−	39.4122i	−1.31593	−	2.27927i
$300$		0			0
$301$	2.74424	−	1.43714i	0.158175	−	0.0828355i
$302$		−	24.4859i		−	1.40901i
$303$		0			0
$304$	0.133168	+	0.0768845i	0.00763770	+	0.00440963i
$305$	10.0424	+	5.79798i	0.575026	+	0.331991i
$306$		0			0
$307$		−	5.31593i		−	0.303396i	−0.988427	−	0.151698i	$-0.951526\pi$
$307$		−	5.31593i		−	0.303396i	0.988427	−	0.151698i	$-0.0484742\pi$
$308$	−22.7825	+	35.9560i	−1.29815	+	2.04878i
$309$		0			0
$310$	−10.1465	−	17.5743i	−0.576283	−	0.998152i
$311$	−6.45534	+	11.1810i	−0.366049	+	0.634015i	−0.988944	−	0.148291i	$-0.952623\pi$
$311$	−6.45534	+	11.1810i	−0.366049	+	0.634015i	0.622895	+	0.782305i	$0.285956\pi$
$312$		0			0
$313$	−10.5493	+	6.09063i	−0.596280	+	0.344263i	−0.767577	−	0.640957i	$-0.778538\pi$
$313$	−10.5493	+	6.09063i	−0.596280	+	0.344263i	0.171296	+	0.985220i	$0.445204\pi$
$314$	18.3263			1.03421
$315$		0			0
$316$	23.7157			1.33411
$317$	16.9363	−	9.77816i	0.951235	−	0.549196i	0.0577710	−	0.998330i	$-0.481601\pi$
$317$	16.9363	−	9.77816i	0.951235	−	0.549196i	0.893465	+	0.449134i	$0.148267\pi$
$318$		0			0
$319$	−2.79993	+	4.84961i	−0.156766	+	0.271526i
$320$	12.6034	+	21.8297i	0.704549	+	1.22031i
$321$		0			0
$322$	1.98558	−	48.1948i	0.110652	−	2.68579i
$323$			0.0257339i			0.00143188i
$324$		0			0
$325$	−6.08796	−	3.51488i	−0.337699	−	0.194971i
$326$	30.6902	+	17.7190i	1.69977	+	0.981364i
$327$		0			0
$328$		−	19.6480i		−	1.08488i
$329$	−17.4463	−	11.0543i	−0.961844	−	0.609445i
$330$		0			0
$331$	−15.4160	−	26.7013i	−0.847339	−	1.46763i	−0.883575	−	0.468291i	$-0.844870\pi$
$331$	−15.4160	−	26.7013i	−0.847339	−	1.46763i	0.0362358	−	0.999343i	$-0.488463\pi$
$332$	−25.9531	+	44.9522i	−1.42436	+	2.46707i
$333$		0			0
$334$	15.2559	−	8.80797i	0.834763	−	0.481951i
$335$	19.5725			1.06936
$336$		0			0
$337$	18.6235			1.01449			0.507243	−	0.861803i	$-0.330664\pi$
$337$	18.6235			1.01449			0.507243	+	0.861803i	$0.330664\pi$
$338$	38.3375	−	22.1341i	2.08528	−	1.20394i
$339$		0			0
$340$	−0.0799304	+	0.138444i	−0.00433483	+	0.00750815i
$341$	11.5222	+	19.9570i	0.623963	+	1.08073i
$342$		0			0
$343$	−2.28194	+	18.3791i	−0.123213	+	0.992380i
$344$		−	3.20815i		−	0.172972i
$345$		0			0
$346$	−25.5883	−	14.7734i	−1.37564	−	0.794224i
$347$	−1.83614	−	1.06009i	−0.0985689	−	0.0569088i	0.449905	−	0.893076i	$-0.351458\pi$
$347$	−1.83614	−	1.06009i	−0.0985689	−	0.0569088i	−0.548474	+	0.836168i	$0.684791\pi$
$348$		0			0
$349$			6.98260i			0.373770i	0.982382	+	0.186885i	$0.0598392\pi$
$349$			6.98260i			0.373770i	−0.982382	+	0.186885i	$0.940161\pi$
$350$	−3.45668	−	6.60056i	−0.184767	−	0.352815i
$351$		0			0
$352$	−14.6510	−	25.3762i	−0.780900	−	1.35256i
$353$	−2.52197	+	4.36818i	−0.134231	+	0.232495i	−0.925303	−	0.379228i	$-0.876190\pi$
$353$	−2.52197	+	4.36818i	−0.134231	+	0.232495i	0.791073	+	0.611722i	$0.209523\pi$
$354$		0			0
$355$	16.4573	−	9.50164i	0.873464	−	0.504295i
$356$	12.1928			0.646216
$357$		0			0
$358$	7.57344			0.400269
$359$	7.10693	−	4.10319i	0.375089	−	0.216558i	−0.300590	−	0.953753i	$-0.597184\pi$
$359$	7.10693	−	4.10319i	0.375089	−	0.216558i	0.675680	+	0.737195i	$0.263850\pi$
$360$		0			0
$361$	0.500000	−	0.866025i	0.0263158	−	0.0455803i
$362$	−28.0487	−	48.5818i	−1.47421	−	2.55340i
$363$		0			0
$364$	48.1797	+	1.98496i	2.52530	+	0.104040i
$365$			25.8856i			1.35492i
$366$		0			0
$367$	−0.785866	−	0.453720i	−0.0410219	−	0.0236840i	0.479349	−	0.877624i	$-0.340873\pi$
$367$	−0.785866	−	0.453720i	−0.0410219	−	0.0236840i	−0.520371	+	0.853940i	$0.674206\pi$
$368$	1.06453	+	0.614607i	0.0554925	+	0.0320386i
$369$		0			0
$370$			36.6280i			1.90420i
$371$	−27.1188	−	1.11727i	−1.40794	−	0.0580056i
$372$		0			0
$373$	7.42878	+	12.8670i	0.384648	+	0.666230i	0.991720	−	0.128417i	$-0.0409896\pi$
$373$	7.42878	+	12.8670i	0.384648	+	0.666230i	−0.607072	+	0.794647i	$0.707656\pi$
$374$	0.147472	−	0.255429i	0.00762561	−	0.0132079i
$375$		0			0
$376$	−18.5238	+	10.6947i	−0.955294	+	0.551540i
$377$	6.34373			0.326719
$378$		0			0
$379$	−29.1286			−1.49624			−0.748118	−	0.663566i	$-0.769042\pi$
$379$	−29.1286			−1.49624			−0.748118	+	0.663566i	$0.769042\pi$
$380$	5.37980	−	3.10603i	0.275978	−	0.159336i
$381$		0			0
$382$	−18.4541	+	31.9634i	−0.944194	+	1.63539i
$383$	−10.8771	−	18.8397i	−0.555795	−	0.962666i	−0.997841	−	0.0656734i	$-0.979080\pi$
$383$	−10.8771	−	18.8397i	−0.555795	−	0.962666i	0.442046	−	0.896993i	$-0.354253\pi$
$384$		0			0
$385$	−11.9692	−	22.8553i	−0.610007	−	1.16482i
$386$			15.4277i			0.785251i
$387$		0			0
$388$	8.46415	+	4.88678i	0.429702	+	0.248089i
$389$	−2.10746	−	1.21674i	−0.106853	−	0.0616914i	0.445621	−	0.895222i	$-0.352983\pi$
$389$	−2.10746	−	1.21674i	−0.106853	−	0.0616914i	−0.552474	+	0.833530i	$0.686316\pi$
$390$		0			0
$391$			0.205715i			0.0104034i
$392$	15.7653	+	10.9239i	0.796270	+	0.551742i
$393$		0			0
$394$	−9.26389	−	16.0455i	−0.466708	−	0.808362i
$395$	−7.18717	+	12.4485i	−0.361626	+	0.626354i
$396$		0			0
$397$	−20.5816	+	11.8828i	−1.03296	+	0.596381i	−0.917832	−	0.396969i	$-0.870062\pi$
$397$	−20.5816	+	11.8828i	−1.03296	+	0.596381i	−0.115131	+	0.993350i	$0.536729\pi$
$398$	−17.6839			−0.886412
$399$		0			0
$400$	0.189875			0.00949377
$401$	−5.99029	+	3.45850i	−0.299141	+	0.172709i	−0.642057	−	0.766657i	$-0.721919\pi$
$401$	−5.99029	+	3.45850i	−0.299141	+	0.172709i	0.342916	+	0.939366i	$0.388585\pi$
$402$		0			0
$403$	13.0528	−	22.6081i	0.650207	−	1.12619i
$404$	11.4754	+	19.8760i	0.570924	+	0.988870i
$405$		0			0
$406$	5.67964	+	3.59874i	0.281876	+	0.178602i
$407$		−	41.5941i		−	2.06174i
$408$		0			0
$409$	−31.8609	−	18.3949i	−1.57542	−	0.909570i	−0.995486	−	0.0949079i	$-0.969744\pi$
$409$	−31.8609	−	18.3949i	−1.57542	−	0.909570i	−0.579936	−	0.814662i	$-0.696922\pi$
$410$	27.4821	+	15.8668i	1.35724	+	0.783605i
$411$		0			0
$412$			6.53132i			0.321775i
$413$	−0.142415	+	3.45676i	−0.00700779	+	0.170096i
$414$		0			0
$415$	−15.7305	−	27.2460i	−0.772178	−	1.33745i
$416$	−16.5972	+	28.7472i	−0.813745	+	1.40945i
$417$		0			0
$418$	−9.92578	+	5.73065i	−0.485486	+	0.280295i
$419$	−22.1381			−1.08152			−0.540758	−	0.841178i	$-0.681863\pi$
$419$	−22.1381			−1.08152			−0.540758	+	0.841178i	$0.681863\pi$
$420$		0			0
$421$	10.8606			0.529311			0.264656	−	0.964343i	$-0.414742\pi$
$421$	10.8606			0.529311			0.264656	+	0.964343i	$0.414742\pi$
$422$	−41.5767	+	24.0043i	−2.02392	+	1.16851i
$423$		0			0
$424$	−14.0544	+	24.3430i	−0.682544	+	1.18220i
$425$	0.0158882	+	0.0275193i	0.000770693	+	0.00133488i
$426$		0			0
$427$	−8.46250	+	13.3558i	−0.409529	+	0.646332i
$428$		−	30.8647i		−	1.49190i
$429$		0			0
$430$	4.48731	+	2.59075i	0.216397	+	0.124937i
$431$	1.34227	+	0.774961i	0.0646550	+	0.0373286i	0.531979	−	0.846758i	$-0.321449\pi$
$431$	1.34227	+	0.774961i	0.0646550	+	0.0373286i	−0.467324	+	0.884086i	$0.654782\pi$
$432$		0			0
$433$		−	18.5997i		−	0.893844i	−0.894573	−	0.446922i	$-0.852520\pi$
$433$		−	18.5997i		−	0.893844i	0.894573	−	0.446922i	$-0.147480\pi$
$434$	24.5117	−	12.8367i	1.17660	−	0.616179i
$435$		0			0
$436$	22.4404	+	38.8680i	1.07470	+	1.86144i
$437$	3.99695	−	6.92292i	0.191200	−	0.331168i
$438$		0			0
$439$	11.2019	−	6.46743i	0.534639	−	0.308674i	−0.208265	−	0.978073i	$-0.566782\pi$
$439$	11.2019	−	6.46743i	0.534639	−	0.308674i	0.742903	+	0.669399i	$0.233448\pi$
$440$	−26.7190			−1.27378
$441$		0			0
$442$	−0.334125			−0.0158927
$443$	25.3440	−	14.6324i	1.20413	−	0.695204i	0.242658	−	0.970112i	$-0.421981\pi$
$443$	25.3440	−	14.6324i	1.20413	−	0.695204i	0.961471	+	0.274908i	$0.0886472\pi$
$444$		0			0
$445$	−3.69508	+	6.40007i	−0.175164	+	0.303392i
$446$	27.6144	+	47.8295i	1.30758	+	2.26479i
$447$		0			0
$448$	−30.4469	+	15.9449i	−1.43848	+	0.753325i
$449$			1.99608i			0.0942007i	0.998890	+	0.0471004i	$0.0149981\pi$
$449$			1.99608i			0.0942007i	−0.998890	+	0.0471004i	$0.985002\pi$
$450$		0			0
$451$	−31.2082	−	18.0181i	−1.46954	−	0.848438i
$452$	42.7059	+	24.6563i	2.00872	+	1.15973i
$453$		0			0
$454$			13.1248i			0.615979i
$455$	−15.6430	+	24.6883i	−0.733356	+	1.15741i
$456$		0			0
$457$	−0.408227	−	0.707070i	−0.0190961	−	0.0330753i	0.856319	−	0.516446i	$-0.172746\pi$
$457$	−0.408227	−	0.707070i	−0.0190961	−	0.0330753i	−0.875416	+	0.483371i	$0.839412\pi$
$458$	−23.4727	+	40.6559i	−1.09681	+	1.89972i
$459$		0			0
$460$	43.0056	−	24.8293i	2.00515	−	1.15767i
$461$	19.2778			0.897856			0.448928	−	0.893568i	$-0.351806\pi$
$461$	19.2778			0.897856			0.448928	+	0.893568i	$0.351806\pi$
$462$		0			0
$463$	19.0383			0.884785			0.442393	−	0.896821i	$-0.354130\pi$
$463$	19.0383			0.884785			0.442393	+	0.896821i	$0.354130\pi$
$464$	−0.148389	+	0.0856727i	−0.00688881	+	0.00397726i
$465$		0			0
$466$	5.19212	−	8.99301i	0.240520	−	0.416593i
$467$	17.9962	+	31.1703i	0.832763	+	1.44239i	0.895839	+	0.444380i	$0.146576\pi$
$467$	17.9962	+	31.1703i	0.832763	+	1.44239i	−0.0630752	+	0.998009i	$0.520091\pi$
$468$		0			0
$469$	−1.09855	+	26.6646i	−0.0507265	+	1.23126i
$470$		−	34.5462i		−	1.59350i
$471$		0			0
$472$	3.10294	+	1.79148i	0.142824	+	0.0824597i
$473$	−5.09571	−	2.94201i	−0.234301	−	0.135274i
$474$		0			0
$475$		−	1.23481i		−	0.0566569i
$476$	−0.184122	−	0.116663i	−0.00843920	−	0.00534725i
$477$		0			0
$478$	8.93966	+	15.4839i	0.408890	+	0.708219i
$479$	−7.65134	+	13.2525i	−0.349599	+	0.605523i	−0.986178	−	0.165688i	$-0.947015\pi$
$479$	−7.65134	+	13.2525i	−0.349599	+	0.605523i	0.636579	+	0.771211i	$0.280349\pi$
$480$		0			0
$481$	−40.8066	+	23.5597i	−1.86062	+	1.07423i
$482$	14.5789			0.664051
$483$		0			0
$484$	45.6360			2.07436
$485$	−5.13021	+	2.96193i	−0.232951	+	0.134494i
$486$		0			0
$487$	−12.5698	+	21.7715i	−0.569592	+	0.986562i	0.427014	+	0.904245i	$0.359565\pi$
$487$	−12.5698	+	21.7715i	−0.569592	+	0.986562i	−0.996606	+	0.0823173i	$0.973768\pi$
$488$	8.18723	+	14.1807i	0.370619	+	0.641930i
$489$		0			0
$490$	−28.0109	+	13.2297i	−1.26540	+	0.597656i
$491$		−	28.6161i		−	1.29143i	−0.763579	−	0.645714i	$-0.776560\pi$
$491$		−	28.6161i		−	1.29143i	0.763579	−	0.645714i	$-0.223440\pi$
$492$		0			0
$493$	−0.0248336	−	0.0143377i	−0.00111845	−	0.000645738i
$494$	11.2443	+	6.49191i	0.505905	+	0.292085i
$495$		0			0
$496$			0.705118i			0.0316607i
$497$	12.0208	+	22.9539i	0.539207	+	1.02962i
$498$		0			0
$499$	−9.45082	−	16.3693i	−0.423077	−	0.732791i	0.573162	−	0.819442i	$-0.305717\pi$
$499$	−9.45082	−	16.3693i	−0.423077	−	0.732791i	−0.996239	+	0.0866515i	$0.972383\pi$
$500$	19.3655	−	33.5420i	0.866052	−	1.50005i
$501$		0			0
$502$	−36.9498	+	21.3330i	−1.64915	+	0.952137i
$503$	−14.9917			−0.668447			−0.334223	−	0.942494i	$-0.608474\pi$
$503$	−14.9917			−0.668447			−0.334223	+	0.942494i	$0.608474\pi$
$504$		0			0
$505$	−13.9108			−0.619020
$506$	−79.3456	+	45.8102i	−3.52734	+	2.03651i
$507$		0			0
$508$	17.5211	−	30.3475i	0.777375	−	1.34645i
$509$	8.51186	+	14.7430i	0.377282	+	0.653471i	0.990666	−	0.136314i	$-0.0435256\pi$
$509$	8.51186	+	14.7430i	0.377282	+	0.653471i	−0.613384	+	0.789785i	$0.710192\pi$
$510$		0			0
$511$	−35.2652	−	1.45289i	−1.56004	−	0.0642721i
$512$		−	1.73925i		−	0.0768647i
$513$		0			0
$514$	47.0792	+	27.1812i	2.07658	+	1.19891i
$515$	−3.42834	−	1.97935i	−0.151071	−	0.0872206i
$516$		0			0
$517$			39.2301i			1.72534i
$518$	−49.9000	−	2.05583i	−2.19248	−	0.0903279i
$519$		0			0
$520$	15.1342	+	26.2132i	0.663678	+	1.14952i
$521$	11.1307	−	19.2790i	0.487645	−	0.844627i	−0.512254	−	0.858834i	$-0.671189\pi$
$521$	11.1307	−	19.2790i	0.487645	−	0.844627i	0.999899	+	0.0142075i	$0.00452256\pi$
$522$		0			0
$523$	−4.55776	+	2.63142i	−0.199297	+	0.115064i	−0.596327	−	0.802741i	$-0.703374\pi$
$523$	−4.55776	+	2.63142i	−0.199297	+	0.115064i	0.397031	+	0.917805i	$0.370041\pi$
$524$	70.0817			3.06153
$525$		0			0
$526$	9.80874			0.427681
$527$	−0.102195	+	0.0590023i	−0.00445168	+	0.00257018i
$528$		0			0
$529$	20.4512	−	35.4225i	0.889182	−	1.54011i
$530$	−22.6994	−	39.3165i	−0.985998	−	1.70780i
$531$		0			0
$532$	3.92953	+	7.50348i	0.170367	+	0.325317i
$533$			40.8231i			1.76825i
$534$		0			0
$535$	16.2011	+	9.35370i	0.700434	+	0.404396i
$536$	23.9353	+	13.8190i	1.03385	+	0.596892i
$537$		0			0
$538$		−	9.58242i		−	0.413127i
$539$	31.8086	−	15.0234i	1.37010	−	0.647103i
$540$		0			0
$541$	−16.7083	−	28.9396i	−0.718345	−	1.24421i	−0.961655	−	0.274261i	$-0.911567\pi$
$541$	−16.7083	−	28.9396i	−0.718345	−	1.24421i	0.243310	−	0.969948i	$-0.421767\pi$
$542$	−0.389667	+	0.674923i	−0.0167376	+	0.0289904i
$543$		0			0
$544$	0.129945	−	0.0750240i	0.00557136	−	0.00321663i
$545$	−27.2027			−1.16524
$546$		0			0
$547$	11.7033			0.500397			0.250198	−	0.968195i	$-0.419504\pi$
$547$	11.7033			0.500397			0.250198	+	0.968195i	$0.419504\pi$
$548$	−10.5289	+	6.07886i	−0.449772	+	0.259676i
$549$		0			0
$550$	−7.07626	+	12.2564i	−0.301733	+	0.522616i
$551$	0.557152	+	0.965015i	0.0237355	+	0.0411110i
$552$		0			0
$553$	−16.5558	−	10.4901i	−0.704025	−	0.446085i
$554$		−	11.6759i		−	0.496060i
$555$		0			0
$556$	−19.4631	−	11.2370i	−0.825419	−	0.476556i
$557$	−22.5499	−	13.0192i	−0.955470	−	0.551641i	−0.0606943	−	0.998156i	$-0.519331\pi$
$557$	−22.5499	−	13.0192i	−0.955470	−	0.551641i	−0.894776	+	0.446515i	$0.852665\pi$
$558$		0			0
$559$			6.66565i			0.281927i
$560$	0.0324960	−	0.788757i	0.00137321	−	0.0333311i
$561$		0			0
$562$	23.3543	+	40.4508i	0.985140	+	1.70631i
$563$	−2.77808	+	4.81177i	−0.117082	+	0.202792i	−0.918610	−	0.395165i	$-0.870687\pi$
$563$	−2.77808	+	4.81177i	−0.117082	+	0.202792i	0.801528	+	0.597957i	$0.204021\pi$
$564$		0			0
$565$	−25.8845	+	14.9444i	−1.08897	+	0.628716i
$566$	39.5969			1.66438
$567$		0			0
$568$	26.8342			1.12594
$569$	0.0512521	−	0.0295904i	0.00214860	−	0.00124049i	−0.498925	−	0.866645i	$-0.666272\pi$
$569$	0.0512521	−	0.0295904i	0.00214860	−	0.00124049i	0.501074	+	0.865404i	$0.332938\pi$
$570$		0			0
$571$	2.72669	−	4.72277i	0.114108	−	0.197642i	−0.803315	−	0.595555i	$-0.796932\pi$
$571$	2.72669	−	4.72277i	0.114108	−	0.197642i	0.917423	+	0.397913i	$0.130266\pi$
$572$	−45.7959	−	79.3208i	−1.91482	−	3.31657i
$573$		0			0
$574$	−23.1586	+	36.5496i	−0.966620	+	1.52555i
$575$		−	9.87093i		−	0.411646i
$576$		0			0
$577$	6.65151	+	3.84025i	0.276906	+	0.159872i	0.632022	−	0.774951i	$-0.282225\pi$
$577$	6.65151	+	3.84025i	0.276906	+	0.159872i	−0.355116	+	0.934822i	$0.615559\pi$
$578$	−33.5756	−	19.3849i	−1.39656	−	0.806304i
$579$		0			0
$580$			6.92212i			0.287425i
$581$	38.0013	−	19.9011i	1.57656	−	0.825636i
$582$		0			0
$583$	25.7770	+	44.6471i	1.06757	+	1.84909i
$584$	−18.2763	+	31.6556i	−0.756280	+	1.30992i
$585$		0			0
$586$	0.414676	−	0.239413i	0.0171301	−	0.00989008i
$587$	−44.5414			−1.83842			−0.919209	−	0.393770i	$-0.871171\pi$
$587$	−44.5414			−1.83842			−0.919209	+	0.393770i	$0.871171\pi$
$588$		0			0
$589$	4.58556			0.188945
$590$	−5.01157	+	2.89343i	−0.206323	+	0.119121i
$591$		0			0
$592$	0.636352	−	1.10219i	0.0261539	−	0.0452999i
$593$	−19.9443	−	34.5445i	−0.819014	−	1.41857i	−0.906409	−	0.422400i	$-0.861188\pi$
$593$	−19.9443	−	34.5445i	−0.819014	−	1.41857i	0.0873951	−	0.996174i	$-0.472146\pi$
$594$		0			0
$595$	0.117036	−	0.0612913i	0.00479802	−	0.00251270i
$596$			45.8979i			1.88005i
$597$		0			0
$598$	89.8859	+	51.8956i	3.67571	+	2.12217i
$599$	−4.29413	−	2.47922i	−0.175453	−	0.101298i	0.409701	−	0.912220i	$-0.365633\pi$
$599$	−4.29413	−	2.47922i	−0.175453	−	0.101298i	−0.585155	+	0.810922i	$0.698966\pi$
$600$		0			0
$601$			20.7274i			0.845488i	0.906249	+	0.422744i	$0.138933\pi$
$601$			20.7274i			0.845488i	−0.906249	+	0.422744i	$0.861067\pi$
$602$	−3.78135	+	5.96785i	−0.154116	+	0.243231i
$603$		0			0
$604$	17.1857	+	29.7665i	0.699277	+	1.21118i
$605$	−13.8302	+	23.9546i	−0.562278	+	0.973894i
$606$		0			0
$607$	6.21489	−	3.58817i	0.252255	−	0.145639i	−0.368542	−	0.929611i	$-0.620143\pi$
$607$	6.21489	−	3.58817i	0.252255	−	0.145639i	0.620796	+	0.783972i	$0.286809\pi$
$608$	−5.83074			−0.236468
$609$		0			0
$610$	−26.4465			−1.07079
$611$	38.4874	−	22.2207i	1.55703	−	0.898954i
$612$		0			0
$613$	21.5467	−	37.3200i	0.870263	−	1.50734i	0.00853735	−	0.999964i	$-0.497282\pi$
$613$	21.5467	−	37.3200i	0.870263	−	1.50734i	0.861725	−	0.507375i	$-0.169384\pi$
$614$	6.06192	+	10.4996i	0.244639	+	0.423728i
$615$		0			0
$616$	1.49967	−	36.4005i	0.0604233	−	1.46662i
$617$			2.67002i			0.107491i	0.998555	+	0.0537454i	$0.0171160\pi$
$617$			2.67002i			0.107491i	−0.998555	+	0.0537454i	$0.982884\pi$
$618$		0			0
$619$	40.8686	+	23.5955i	1.64265	+	0.948384i	0.979887	+	0.199555i	$0.0639495\pi$
$619$	40.8686	+	23.5955i	1.64265	+	0.948384i	0.662763	+	0.748829i	$0.269384\pi$
$620$	24.6694	+	14.2429i	0.990747	+	0.572008i
$621$		0			0
$622$		−	29.4449i		−	1.18063i
$623$	−8.51171	−	5.39320i	−0.341014	−	0.216074i
$624$		0			0
$625$	8.65060	+	14.9833i	0.346024	+	0.599331i
$626$	13.8907	−	24.0593i	0.555182	−	0.961604i
$627$		0			0
$628$	−22.2786	+	12.8625i	−0.889011	+	0.513271i
$629$	0.212993			0.00849258
$630$		0			0
$631$	−13.5435			−0.539160			−0.269580	−	0.962978i	$-0.586885\pi$
$631$	−13.5435			−0.539160			−0.269580	+	0.962978i	$0.586885\pi$
$632$	−17.5784	+	10.1489i	−0.699231	+	0.403701i
$633$		0			0
$634$	−22.3007	+	38.6259i	−0.885673	+	1.53403i
$635$	10.6197	+	18.3939i	0.421432	+	0.729941i
$636$		0			0
$637$	−32.7560	−	22.6969i	−1.29784	−	0.899283i
$638$		−	12.7714i		−	0.505623i
$639$		0			0
$640$	−30.1896	−	17.4300i	−1.19335	−	0.688980i
$641$	8.19017	+	4.72860i	0.323492	+	0.186768i	0.652948	−	0.757403i	$-0.273532\pi$
$641$	8.19017	+	4.72860i	0.323492	+	0.186768i	−0.329456	+	0.944171i	$0.606865\pi$
$642$		0			0
$643$			24.1443i			0.952159i	0.879402	+	0.476079i	$0.157943\pi$
$643$			24.1443i			0.952159i	−0.879402	+	0.476079i	$0.842057\pi$
$644$	31.4123	+	59.9821i	1.23782	+	2.36362i
$645$		0			0
$646$	−0.0293452	−	0.0508274i	−0.00115457	−	0.00199978i
$647$	2.78316	−	4.82058i	0.109417	−	0.189517i	−0.806117	−	0.591756i	$-0.798435\pi$
$647$	2.78316	−	4.82058i	0.109417	−	0.189517i	0.915534	+	0.402240i	$0.131768\pi$
$648$		0			0
$649$	5.69105	−	3.28573i	0.223393	−	0.128976i
$650$	16.0325			0.628847
$651$		0			0
$652$	−49.7451			−1.94817
$653$	−29.3738	+	16.9590i	−1.14948	+	0.663655i	−0.948762	−	0.315993i	$-0.897662\pi$
$653$	−29.3738	+	16.9590i	−1.14948	+	0.663655i	−0.200723	+	0.979648i	$0.564329\pi$
$654$		0			0
$655$	−21.2386	+	36.7863i	−0.829861	+	1.43736i
$656$	−0.551320	−	0.954915i	−0.0215254	−	0.0372832i
$657$		0			0
$658$	47.0639	+	1.93899i	1.83474	+	0.0755896i
$659$			7.91562i			0.308349i	0.988044	+	0.154174i	$0.0492718\pi$
$659$			7.91562i			0.308349i	−0.988044	+	0.154174i	$0.950728\pi$
$660$		0			0
$661$	−23.4163	−	13.5194i	−0.910787	−	0.525843i	−0.0301028	−	0.999547i	$-0.509583\pi$
$661$	−23.4163	−	13.5194i	−0.910787	−	0.525843i	−0.880684	+	0.473704i	$0.842917\pi$
$662$	60.8965	+	35.1586i	2.36681	+	1.36648i
$663$		0			0
$664$		−	44.4255i		−	1.72404i
$665$	−5.12949	−	0.211330i	−0.198913	−	0.00819503i
$666$		0			0
$667$	4.45381	+	7.71423i	0.172452	+	0.298696i
$668$	−12.3639	+	21.4150i	−0.478375	+	0.828571i
$669$		0			0
$670$	−38.6579	+	22.3192i	−1.49349	+	0.862265i
$671$	30.0321			1.15938
$672$		0			0
$673$	34.8375			1.34289			0.671443	−	0.741056i	$-0.265675\pi$
$673$	34.8375			1.34289			0.671443	+	0.741056i	$0.265675\pi$
$674$	−36.7835	+	21.2370i	−1.41685	+	0.818017i
$675$		0			0
$676$	−31.0702	+	53.8152i	−1.19501	+	2.06981i
$677$	−4.01980	−	6.96249i	−0.154493	−	0.267590i	0.778381	−	0.627792i	$-0.216041\pi$
$677$	−4.01980	−	6.96249i	−0.154493	−	0.267590i	−0.932874	+	0.360202i	$0.882708\pi$
$678$		0			0
$679$	−3.74722	−	7.15536i	−0.143805	−	0.274597i
$680$		−	0.136821i		−	0.00524686i
$681$		0			0
$682$	−45.5153	−	26.2783i	−1.74287	−	1.00625i
$683$	−5.28721	−	3.05257i	−0.202310	−	0.116804i	0.395423	−	0.918499i	$-0.370598\pi$
$683$	−5.28721	−	3.05257i	−0.202310	−	0.116804i	−0.597732	+	0.801696i	$0.703931\pi$
$684$		0			0
$685$		−	7.36892i		−	0.281552i
$686$	−16.4512	−	38.9030i	−0.628110	−	1.48532i
$687$		0			0
$688$	−0.0900202	−	0.155919i	−0.00343199	−	0.00594437i
$689$	29.2012	−	50.5780i	1.11248	−	1.92687i
$690$		0			0
$691$	37.6270	−	21.7240i	1.43140	−	0.826419i	0.434172	−	0.900830i	$-0.357041\pi$
$691$	37.6270	−	21.7240i	1.43140	−	0.826419i	0.997228	+	0.0744114i	$0.0237078\pi$
$692$	41.4756			1.57667
$693$		0			0
$694$	4.83543			0.183550
$695$	11.7968	−	6.81087i	0.447477	−	0.258351i
$696$		0			0
$697$	0.0922659	−	0.159809i	0.00349482	−	0.00605321i
$698$	−7.96248	−	13.7914i	−0.301384	−	0.522013i
$699$		0			0
$700$	8.83483	+	5.59793i	0.333925	+	0.211582i
$701$		−	12.2615i		−	0.463110i	−0.972822	−	0.231555i	$-0.925619\pi$
$701$		−	12.2615i		−	0.463110i	0.972822	−	0.231555i	$-0.0743813\pi$
$702$		0			0
$703$	−7.16786	−	4.13836i	−0.270341	−	0.156081i
$704$	56.5362	+	32.6412i	2.13079	+	1.23021i
$705$		0			0
$706$		−	11.5035i		−	0.432940i
$707$	0.780773	−	18.9512i	0.0293640	−	0.712735i
$708$		0			0
$709$	11.2144	+	19.4239i	0.421165	+	0.729479i	0.996054	−	0.0887529i	$-0.0282881\pi$
$709$	11.2144	+	19.4239i	0.421165	+	0.729479i	−0.574889	+	0.818231i	$0.694955\pi$
$710$	−21.6700	+	37.5336i	−0.813262	+	1.40861i
$711$		0			0
$712$	−9.03743	+	5.21777i	−0.338692	+	0.195544i
$713$	36.6565			1.37280
$714$		0			0
$715$	55.5147			2.07613
$716$	−9.20672	+	5.31550i	−0.344071	+	0.198650i
$717$		0			0
$718$	−9.35798	+	16.2085i	−0.349237	+	0.604896i
$719$	13.9443	+	24.1523i	0.520035	+	0.900728i	0.999729	+	0.0232916i	$0.00741460\pi$
$719$	13.9443	+	24.1523i	0.520035	+	0.900728i	−0.479693	+	0.877436i	$0.659252\pi$
$720$		0			0
$721$	2.88898	−	4.55948i	0.107591	−	0.169804i
$722$			2.28066i			0.0848774i
$723$		0			0
$724$	68.1953	+	39.3726i	2.53446	+	1.46327i
$725$	1.19161	+	0.687976i	0.0442552	+	0.0255508i
$726$		0			0
$727$			4.93131i			0.182892i	0.995810	+	0.0914461i	$0.0291489\pi$
$727$			4.93131i			0.182892i	−0.995810	+	0.0914461i	$0.970851\pi$
$728$	−36.5608	+	19.1467i	−1.35503	+	0.709624i
$729$		0			0
$730$	−29.5182	−	51.1270i	−1.09252	−	1.89229i
$731$	0.0150653	−	0.0260938i	0.000557209	−	0.000965115i
$732$		0			0
$733$	−4.20275	+	2.42646i	−0.155232	+	0.0896234i	−0.575604	−	0.817729i	$-0.695233\pi$
$733$	−4.20275	+	2.42646i	−0.155232	+	0.0896234i	0.420372	+	0.907352i	$0.361900\pi$
$734$	2.06956			0.0763890
$735$		0			0
$736$	−46.6103			−1.71808
$737$	43.8993	−	25.3453i	1.61705	−	0.933605i
$738$		0			0
$739$	13.7412	−	23.8005i	0.505479	−	0.875515i	−0.494501	−	0.869177i	$-0.664649\pi$
$739$	13.7412	−	23.8005i	0.505479	−	0.875515i	0.999980	−	0.00633784i	$-0.00201741\pi$
$740$	−25.7078	−	44.5271i	−0.945036	−	1.63685i
$741$		0			0
$742$	54.8367	−	28.7177i	2.01312	−	1.05426i
$743$			36.1933i			1.32780i	0.747819	+	0.663902i	$0.231101\pi$
$743$			36.1933i			1.32780i	−0.747819	+	0.663902i	$0.768899\pi$
$744$		0			0
$745$	−24.0921	−	13.9096i	−0.882666	−	0.509608i
$746$	−29.3453	−	16.9425i	−1.07441	−	0.620310i
$747$		0			0
$748$			0.414020i			0.0151381i
$749$	−13.6523	+	21.5465i	−0.498844	+	0.787291i
$750$		0			0
$751$	10.9520	+	18.9694i	0.399644	+	0.692203i	0.993682	−	0.112234i	$-0.0358006\pi$
$751$	10.9520	+	18.9694i	0.399644	+	0.692203i	−0.594038	+	0.804437i	$0.702467\pi$
$752$	−0.600185	+	1.03955i	−0.0218865	+	0.0379085i
$753$		0			0
$754$	−12.5296	+	7.23395i	−0.456300	+	0.263445i
$755$	−20.8329			−0.758185
$756$		0			0
$757$	−45.1474			−1.64091			−0.820456	−	0.571710i	$-0.806280\pi$
$757$	−45.1474			−1.64091			−0.820456	+	0.571710i	$0.806280\pi$
$758$	57.5322	−	33.2162i	2.08966	−	1.20647i
$759$		0			0
$760$	−2.65838	+	4.60446i	−0.0964297	+	0.167021i
$761$	6.52858	+	11.3078i	0.236661	+	0.409908i	0.959754	−	0.280842i	$-0.0906137\pi$
$761$	6.52858	+	11.3078i	0.236661	+	0.409908i	−0.723093	+	0.690750i	$0.757280\pi$
$762$		0			0
$763$	1.52682	−	37.0595i	0.0552745	−	1.34165i
$764$		−	51.8089i		−	1.87438i
$765$		0			0
$766$	42.9671	+	24.8071i	1.55246	+	0.896315i
$767$	−6.44705	−	3.72220i	−0.232789	−	0.134401i
$768$		0			0
$769$		−	14.3213i		−	0.516439i	−0.966086	−	0.258219i	$-0.916864\pi$
$769$		−	14.3213i		−	0.516439i	0.966086	−	0.258219i	$-0.0831358\pi$
$770$	49.7031	+	31.4929i	1.79118	+	1.13493i
$771$		0			0
$772$	−10.8281	−	18.7549i	−0.389713	−	0.675003i
$773$	−17.0666	+	29.5603i	−0.613845	+	1.06321i	0.376741	+	0.926318i	$0.377045\pi$
$773$	−17.0666	+	29.5603i	−0.613845	+	1.06321i	−0.990586	+	0.136892i	$0.956289\pi$
$774$		0			0
$775$	4.90369	−	2.83115i	0.176146	−	0.101698i
$776$	−8.36498			−0.300285
$777$		0			0
$778$	5.54996			0.198976
$779$	−6.21006	+	3.58538i	−0.222498	+	0.128460i
$780$		0			0
$781$	24.6081	−	42.6225i	0.880548	−	1.52515i
$782$	−0.234583	−	0.406309i	−0.00838866	−	0.0145296i
$783$		0			0
$784$	1.07274	+	0.0885416i	0.0383120	+	0.00316220i
$785$		−	15.5922i		−	0.556510i
$786$		0			0
$787$	1.12517	+	0.649617i	0.0401080	+	0.0231563i	0.519920	−	0.854215i	$-0.325962\pi$
$787$	1.12517	+	0.649617i	0.0401080	+	0.0231563i	−0.479812	+	0.877371i	$0.659295\pi$
$788$	22.5235	+	13.0039i	0.802365	+	0.463246i
$789$		0			0
$790$		−	32.7830i		−	1.16637i
$791$	−18.9066	−	36.1024i	−0.672242	−	1.28365i
$792$		0			0
$793$	−17.0108	−	29.4636i	−0.604071	−	1.04628i
$794$	27.1007	−	46.9397i	0.961767	−	1.66583i
$795$		0			0
$796$	21.4976	−	12.4116i	0.761961	−	0.439918i
$797$	−16.6501			−0.589778			−0.294889	−	0.955532i	$-0.595283\pi$
$797$	−16.6501			−0.589778			−0.294889	+	0.955532i	$0.595283\pi$
$798$		0			0
$799$	−0.200887			−0.00710689
$800$	−6.23525	+	3.59992i	−0.220449	+	0.127277i
$801$		0			0
$802$	7.88766	−	13.6618i	0.278523	−	0.482416i
$803$	33.5203	+	58.0589i	1.18291	+	2.04885i
$804$		0			0
$805$	−41.0046	−	1.68935i	−1.44522	−	0.0595418i
$806$			59.5381i			2.09714i
$807$		0			0
$808$	−17.0115	−	9.82158i	−0.598461	−	0.345522i
$809$	1.59319	+	0.919826i	0.0560134	+	0.0323394i	0.527745	−	0.849403i	$-0.323038\pi$
$809$	1.59319	+	0.919826i	0.0560134	+	0.0323394i	−0.471732	+	0.881742i	$0.656371\pi$
$810$		0			0
$811$			47.1946i			1.65723i	0.559820	+	0.828614i	$0.310870\pi$
$811$			47.1946i			1.65723i	−0.559820	+	0.828614i	$0.689130\pi$
$812$	−9.43032	−	0.388520i	−0.330939	−	0.0136344i
$813$		0			0
$814$	47.4310	+	82.1529i	1.66246	+	2.87946i
$815$	15.0755	−	26.1115i	0.528072	−	0.914647i
$816$		0			0
$817$	−1.01398	+	0.585424i	−0.0354748	+	0.0204814i
$818$	83.9052			2.93367
$819$		0			0
$820$	−44.5452			−1.55558
$821$	11.1080	−	6.41321i	0.387672	−	0.223823i	−0.293479	−	0.955966i	$-0.594813\pi$
$821$	11.1080	−	6.41321i	0.387672	−	0.223823i	0.681151	+	0.732143i	$0.261480\pi$
$822$		0			0
$823$	17.6900	−	30.6400i	0.616635	−	1.06804i	−0.373460	−	0.927646i	$-0.621829\pi$
$823$	17.6900	−	30.6400i	0.616635	−	1.06804i	0.990095	−	0.140398i	$-0.0448381\pi$
$824$	−2.79501	−	4.84110i	−0.0973687	−	0.168648i
$825$		0			0
$826$	−3.66057	−	6.98989i	−0.127367	−	0.243209i
$827$		−	3.32086i		−	0.115477i	−0.998332	−	0.0577387i	$-0.981611\pi$
$827$		−	3.32086i		−	0.115477i	0.998332	−	0.0577387i	$-0.0183890\pi$
$828$		0			0
$829$	1.16859	+	0.674687i	0.0405869	+	0.0234329i	0.520156	−	0.854071i	$-0.325874\pi$
$829$	1.16859	+	0.674687i	0.0405869	+	0.0234329i	−0.479569	+	0.877504i	$0.659207\pi$
$830$	62.1388	+	35.8758i	2.15687	+	1.24527i
$831$		0			0
$832$		−	73.9544i		−	2.56391i
$833$	0.0769310	+	0.162884i	0.00266550	+	0.00564360i
$834$		0			0
$835$	−7.49391	−	12.9798i	−0.259338	−	0.449186i
$836$	8.04424	−	13.9330i	0.278216	−	0.481884i
$837$		0			0
$838$	43.7252	−	25.2447i	1.51046	−	0.872065i
$839$	−10.9817			−0.379130			−0.189565	−	0.981868i	$-0.560708\pi$
$839$	−10.9817			−0.379130			−0.189565	+	0.981868i	$0.560708\pi$
$840$		0			0
$841$	27.7583			0.957184
$842$	−21.4508	+	12.3846i	−0.739243	+	0.426802i
$843$		0			0
$844$	33.6954	−	58.3622i	1.15984	−	2.00891i
$845$	−18.8320	−	32.6179i	−0.647839	−	1.12209i
$846$		0			0
$847$	−31.8582	−	20.1860i	−1.09466	−	0.693600i
$848$			1.57746i			0.0541702i
$849$		0			0
$850$	−0.0627621	−	0.0362357i	−0.00215272	−	0.00124287i
$851$	−57.2991	−	33.0817i	−1.96419	−	1.13402i
$852$		0			0
$853$			37.4773i			1.28320i	0.767040	+	0.641599i	$0.221729\pi$
$853$			37.4773i			1.28320i	−0.767040	+	0.641599i	$0.778271\pi$
$854$	1.48437	−	36.0292i	0.0507940	−	1.23289i
$855$		0			0
$856$	13.2082	+	22.8773i	0.451447	+	0.781930i
$857$	−21.5845	+	37.3854i	−0.737312	+	1.27706i	0.216389	+	0.976307i	$0.430572\pi$
$857$	−21.5845	+	37.3854i	−0.737312	+	1.27706i	−0.953701	+	0.300755i	$0.902761\pi$
$858$		0			0
$859$	−17.3833	+	10.0362i	−0.593110	+	0.342432i	−0.766326	−	0.642452i	$-0.777917\pi$
$859$	−17.3833	+	10.0362i	−0.593110	+	0.342432i	0.173216	+	0.984884i	$0.444584\pi$
$860$	−7.27338			−0.248020
$861$		0			0
$862$	−3.53485			−0.120397
$863$	−6.12554	+	3.53658i	−0.208516	+	0.120387i	−0.600621	−	0.799534i	$-0.705080\pi$
$863$	−6.12554	+	3.53658i	−0.208516	+	0.120387i	0.392106	+	0.919920i	$0.371747\pi$
$864$		0			0
$865$	−12.5694	+	21.7708i	−0.427372	+	0.740230i
$866$	21.2098	+	36.7365i	0.720739	+	1.24836i
$867$		0			0
$868$	−20.7884	+	32.8088i	−0.705603	+	1.11360i
$869$			37.2278i			1.26287i
$870$		0			0
$871$	−49.7309	−	28.7121i	−1.68507	−	0.972873i
$872$	−33.2663	−	19.2063i	−1.12654	−	0.650407i
$873$		0			0
$874$			18.2314i			0.616685i
$875$	−28.3555	+	14.8496i	−0.958591	+	0.502009i
$876$		0			0
$877$	27.7815	+	48.1189i	0.938114	+	1.62486i	0.768984	+	0.639268i	$0.220762\pi$
$877$	27.7815	+	48.1189i	0.938114	+	1.62486i	0.169130	+	0.985594i	$0.445904\pi$
$878$	−14.7500	+	25.5478i	−0.497789	+	0.862196i
$879$		0			0
$880$	−1.29857	+	0.749731i	−0.0437749	+	0.0252734i
$881$	−35.8215			−1.20686			−0.603429	−	0.797417i	$-0.706199\pi$
$881$	−35.8215			−1.20686			−0.603429	+	0.797417i	$0.706199\pi$
$882$		0			0
$883$	35.9197			1.20879			0.604396	−	0.796684i	$-0.293414\pi$
$883$	35.9197			1.20879			0.604396	+	0.796684i	$0.293414\pi$
$884$	0.406182	−	0.234509i	0.0136614	−	0.00788740i
$885$		0			0
$886$	−33.3714	+	57.8010i	−1.12114	+	1.94186i
$887$	−8.44488	−	14.6270i	−0.283551	−	0.491125i	0.688706	−	0.725041i	$-0.258179\pi$
$887$	−8.44488	−	14.6270i	−0.283551	−	0.491125i	−0.972257	+	0.233916i	$0.924846\pi$
$888$		0			0
$889$	−25.6549	+	13.4354i	−0.860439	+	0.450607i
$890$		−	16.8545i		−	0.564963i
$891$		0			0
$892$	−67.1393	−	38.7629i	−2.24799	−	1.29788i
$893$	6.76047	+	3.90316i	0.226231	+	0.130614i
$894$		0			0
$895$		−	6.44356i		−	0.215385i
$896$	25.4401	−	40.1503i	0.849893	−	1.34133i
$897$		0			0
$898$	−2.27619	−	3.94247i	−0.0759574	−	0.131562i
$899$	−2.55485	+	4.42514i	−0.0852091	+	0.147587i
$900$		0			0
$901$	−0.228626	+	0.131998i	−0.00761665	+	0.00439748i
$902$	82.1862			2.73650
$903$		0			0
$904$	−42.2055			−1.40373
$905$	−41.3339	+	23.8641i	−1.37398	+	0.793270i
$906$		0			0
$907$	−13.5990	+	23.5542i	−0.451549	+	0.782106i	−0.998482	−	0.0550703i	$-0.982462\pi$
$907$	−13.5990	+	23.5542i	−0.451549	+	0.782106i	0.546934	+	0.837176i	$0.315795\pi$
$908$	−9.21181	−	15.9553i	−0.305705	−	0.529496i
$909$		0			0
$910$	2.74387	−	66.6004i	0.0909584	−	2.20778i
$911$			8.50006i			0.281620i	0.990037	+	0.140810i	$0.0449706\pi$
$911$			8.50006i			0.281620i	−0.990037	+	0.140810i	$0.955029\pi$
$912$		0			0
$913$	−70.5637	−	40.7400i	−2.33532	−	1.34830i
$914$	1.61259	+	0.931028i	0.0533396	+	0.0307957i
$915$		0			0
$916$		−	65.8983i		−	2.17734i
$917$	−48.9236	−	30.9990i	−1.61560	−	1.02368i
$918$		0			0
$919$	15.0341	+	26.0398i	0.495928	+	0.858973i	0.999989	−	0.00469504i	$-0.00149448\pi$
$919$	15.0341	+	26.0398i	0.495928	+	0.858973i	−0.504061	+	0.863668i	$0.668161\pi$
$920$	−21.2508	+	36.8075i	−0.700620	+	1.21351i
$921$		0			0
$922$	−38.0758	+	21.9830i	−1.25396	+	0.723973i
$923$	−55.7541			−1.83517
$924$		0			0
$925$	−10.2202			−0.336037
$926$	−37.6028	+	21.7100i	−1.23570	+	0.713434i
$927$		0			0
$928$	3.24861	−	5.62675i	0.106641	−	0.184707i
$929$	−24.8891	−	43.1092i	−0.816585	−	1.41437i	−0.908184	−	0.418571i	$-0.862531\pi$
$929$	−24.8891	−	43.1092i	−0.816585	−	1.41437i	0.0915993	−	0.995796i	$-0.470802\pi$
$930$		0			0
$931$	0.575809	−	6.97628i	0.0188714	−	0.228638i
$932$			14.5766i			0.477472i
$933$		0			0
$934$	−71.0888	−	41.0432i	−2.32610	−	1.34297i
$935$	−0.217322	−	0.125471i	−0.00710719	−	0.00410334i
$936$		0			0
$937$		−	37.8863i		−	1.23769i	−0.785512	−	0.618846i	$-0.787600\pi$
$937$		−	37.8863i		−	1.23769i	0.785512	−	0.618846i	$-0.212400\pi$
$938$	−28.2367	−	53.9182i	−0.921960	−	1.76049i
$939$		0			0
$940$	24.2467	+	41.9965i	0.790839	+	1.36977i
$941$	12.1974	−	21.1266i	0.397625	−	0.688706i	−0.595808	−	0.803127i	$-0.703168\pi$
$941$	12.1974	−	21.1266i	0.397625	−	0.688706i	0.993432	+	0.114421i	$0.0365013\pi$
$942$		0			0
$943$	−49.6426	+	28.6611i	−1.61658	+	0.933335i
$944$	0.201075			0.00654443
$945$		0			0
$946$	13.4194			0.436304
$947$	17.5034	−	10.1056i	0.568784	−	0.328388i	−0.187879	−	0.982192i	$-0.560161\pi$
$947$	17.5034	−	10.1056i	0.568784	−	0.328388i	0.756664	+	0.653804i	$0.226828\pi$
$948$		0			0
$949$	37.9732	−	65.7714i	1.23266	−	2.13503i
$950$	1.40809	+	2.43888i	0.0456845	+	0.0791278i
$951$		0			0
$952$	0.186398	+	0.00767941i	0.00604119	+	0.000248891i
$953$			38.4587i			1.24580i	0.782301	+	0.622900i	$0.214046\pi$
$953$			38.4587i			1.24580i	−0.782301	+	0.622900i	$0.785954\pi$
$954$		0			0
$955$	27.1948	+	15.7009i	0.880004	+	0.508070i
$956$	−21.7352	−	12.5488i	−0.702965	−	0.405857i
$957$		0			0
$958$		−	34.9002i		−	1.12758i
$959$	10.0390	+	0.413598i	0.324177	+	0.0133558i
$960$		0			0
$961$	−4.98631	−	8.63654i	−0.160849	−	0.278598i
$962$	53.7317	−	93.0661i	1.73238	−	3.00057i
$963$		0			0
$964$	−17.7230	+	10.2324i	−0.570819	+	0.329563i
$965$	13.1261			0.422543
$966$		0			0
$967$	−34.2960			−1.10289			−0.551443	−	0.834213i	$-0.685923\pi$
$967$	−34.2960			−1.10289			−0.551443	+	0.834213i	$0.685923\pi$
$968$	−33.8259	+	19.5294i	−1.08721	+	0.627699i
$969$		0			0
$970$	6.75515	−	11.7003i	0.216895	−	0.375673i
$971$	3.00399	+	5.20306i	0.0964025	+	0.166974i	0.910193	−	0.414184i	$-0.135933\pi$
$971$	3.00399	+	5.20306i	0.0964025	+	0.166974i	−0.813791	+	0.581158i	$0.802600\pi$
$972$		0			0
$973$	8.61664	+	16.4536i	0.276237	+	0.527477i
$974$		−	57.3349i		−	1.83713i
$975$		0			0
$976$	0.795816	+	0.459465i	0.0254735	+	0.0147071i
$977$	10.3238	+	5.96048i	0.330289	+	0.190693i	0.655969	−	0.754787i	$-0.272260\pi$
$977$	10.3238	+	5.96048i	0.330289	+	0.190693i	−0.325680	+	0.945480i	$0.605593\pi$
$978$		0			0
$979$			19.1396i			0.611705i
$980$	24.7663	−	35.7425i	0.791129	−	1.14175i
$981$		0			0
$982$	32.6319	+	56.5200i	1.04132	+	1.80363i
$983$	−3.63347	+	6.29336i	−0.115890	+	0.200727i	−0.918135	−	0.396268i	$-0.870305\pi$
$983$	−3.63347	+	6.29336i	−0.115890	+	0.200727i	0.802245	+	0.596995i	$0.203639\pi$
$984$		0			0
$985$	−13.6517	+	7.88181i	−0.434979	+	0.251135i
$986$	0.0653989			0.00208273
$987$		0			0
$988$	−18.2257			−0.579836
$989$	−8.10569	+	4.67982i	−0.257746	+	0.148810i
$990$		0			0
$991$	10.4235	−	18.0541i	0.331114	−	0.573506i	−0.651617	−	0.758548i	$-0.725909\pi$
$991$	10.4235	−	18.0541i	0.331114	−	0.573506i	0.982731	+	0.185042i	$0.0592423\pi$
$992$	−13.3686	−	23.1551i	−0.424454	−	0.735175i
$993$		0			0
$994$	−49.9174	−	31.6287i	−1.58329	−	1.00320i
$995$			15.0456i			0.476978i
$996$		0			0
$997$	−36.4114	−	21.0222i	−1.15316	−	0.665778i	−0.203506	−	0.979074i	$-0.565234\pi$
$997$	−36.4114	−	21.0222i	−1.15316	−	0.665778i	−0.949656	+	0.313295i	$0.898567\pi$
$998$	37.3328	+	21.5541i	1.18175	+	0.682284i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1197.2.db.a.647.7	✓	96
3.2	odd	2	inner	1197.2.db.a.647.42	yes	96
7.5	odd	6	inner	1197.2.db.a.1160.42	yes	96
21.5	even	6	inner	1197.2.db.a.1160.7	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1197.2.db.a.647.7	✓	96	1.1	even	1	trivial
1197.2.db.a.647.42	yes	96	3.2	odd	2	inner
1197.2.db.a.1160.7	yes	96	21.5	even	6	inner
1197.2.db.a.1160.42	yes	96	7.5	odd	6	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:	\( N \)	\(=\)	\( 1197 = 3^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1197.db (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.97511 + 1.14033i) q^{2} +(1.60071 - 2.77251i) q^{4} +(0.970205 + 1.68044i) q^{5} +(-2.34380 + 1.22744i) q^{7} +2.74002i q^{8} +O(q^{10})\)	\(q+(-1.97511 + 1.14033i) q^{2} +(1.60071 - 2.77251i) q^{4} +(0.970205 + 1.68044i) q^{5} +(-2.34380 + 1.22744i) q^{7} +2.74002i q^{8} +(-3.83252 - 2.21271i) q^{10} +(4.35215 + 2.51271i) q^{11} -5.69300i q^{13} +(3.22958 - 5.09703i) q^{14} +(0.0768845 + 0.133168i) q^{16} +(-0.0128670 + 0.0222863i) q^{17} +(0.866025 - 0.500000i) q^{19} +6.21206 q^{20} -11.4613 q^{22} +(6.92292 - 3.99695i) q^{23} +(0.617404 - 1.06938i) q^{25} +(6.49191 + 11.2443i) q^{26} +(-0.348666 + 8.46297i) q^{28} +1.11430i q^{29} +(3.97121 + 2.29278i) q^{31} +(-5.04957 - 2.91537i) q^{32} -0.0586904i q^{34} +(-4.33660 - 2.74776i) q^{35} +(-4.13836 - 7.16786i) q^{37} +(-1.14033 + 1.97511i) q^{38} +(-4.60446 + 2.65838i) q^{40} -7.17076 q^{41} -1.17085 q^{43} +(13.9330 - 8.04424i) q^{44} +(-9.11569 + 15.7888i) q^{46} +(3.90316 + 6.76047i) q^{47} +(3.98680 - 5.75373i) q^{49} +2.81618i q^{50} +(-15.7839 - 9.11284i) q^{52} +(8.88424 + 5.12932i) q^{53} +9.75139i q^{55} +(-3.36320 - 6.42207i) q^{56} +(-1.27067 - 2.20087i) q^{58} +(0.653821 - 1.13245i) q^{59} +(5.17540 - 2.98802i) q^{61} -10.4581 q^{62} +12.9904 q^{64} +(9.56678 - 5.52338i) q^{65} +(5.04341 - 8.73543i) q^{67} +(0.0411925 + 0.0713476i) q^{68} +(11.6986 + 0.481972i) q^{70} -9.79344i q^{71} +(11.5530 + 6.67014i) q^{73} +(16.3475 + 9.43820i) q^{74} -3.20142i q^{76} +(-13.2848 - 0.547319i) q^{77} +(3.70394 + 6.41542i) q^{79} +(-0.149188 + 0.258400i) q^{80} +(14.1630 - 8.17703i) q^{82} -16.2135 q^{83} -0.0499344 q^{85} +(2.31256 - 1.33515i) q^{86} +(-6.88489 + 11.9250i) q^{88} +(1.90428 + 3.29831i) q^{89} +(6.98780 + 13.3433i) q^{91} -25.5918i q^{92} +(-15.4183 - 8.90179i) q^{94} +(1.68044 + 0.970205i) q^{95} +3.05289i q^{97} +(-1.31322 + 15.9105i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 48 q^{4} + 8 q^{7}+O(q^{10}) \) 96 * q + 48 * q^4 + 8 * q^7	\( 96 q + 48 q^{4} + 8 q^{7} + 24 q^{10} - 56 q^{16} + 48 q^{22} - 24 q^{25} + 16 q^{28} - 24 q^{31} - 48 q^{40} - 24 q^{43} - 48 q^{46} + 52 q^{49} - 72 q^{52} + 48 q^{58} - 176 q^{64} + 32 q^{67} - 80 q^{70} - 12 q^{73} + 40 q^{79} + 72 q^{82} + 40 q^{85} - 16 q^{88} - 72 q^{91} + 72 q^{94}+O(q^{100}) \) 96 * q + 48 * q^4 + 8 * q^7 + 24 * q^10 - 56 * q^16 + 48 * q^22 - 24 * q^25 + 16 * q^28 - 24 * q^31 - 48 * q^40 - 24 * q^43 - 48 * q^46 + 52 * q^49 - 72 * q^52 + 48 * q^58 - 176 * q^64 + 32 * q^67 - 80 * q^70 - 12 * q^73 + 40 * q^79 + 72 * q^82 + 40 * q^85 - 16 * q^88 - 72 * q^91 + 72 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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