LMFDB - Embedded newform 414.3.k.a.179.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,3,Mod(35,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 20]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("414.35");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	414.k (of order $22$, degree $10$, 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:	$11.2806829445$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			179.3
Character	$\chi$	$=$	414.179
Dual form			414.3.k.a.377.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.398430 + 1.35693i) q^{2} +(-1.68251 - 1.08128i) q^{4} +(1.62786 + 0.234051i) q^{5} +(2.08299 + 4.56111i) q^{7} +(2.13758 - 1.85223i) q^{8} +O(q^{10})$	\(q+(-0.398430 + 1.35693i) q^{2} +(-1.68251 - 1.08128i) q^{4} +(1.62786 + 0.234051i) q^{5} +(2.08299 + 4.56111i) q^{7} +(2.13758 - 1.85223i) q^{8} +(-0.966179 + 2.11564i) q^{10} +(1.43035 + 4.87132i) q^{11} +(7.33521 - 16.0619i) q^{13} +(-7.01903 + 1.00918i) q^{14} +(1.66166 + 3.63853i) q^{16} +(13.7698 + 21.4263i) q^{17} +(-10.1680 - 6.53455i) q^{19} +(-2.48581 - 2.15397i) q^{20} -7.17993 q^{22} +(14.9955 + 17.4395i) q^{23} +(-21.3922 - 6.28131i) q^{25} +(18.8722 + 16.3529i) q^{26} +(1.42720 - 9.92640i) q^{28} +(5.07751 + 7.90075i) q^{29} +(28.5200 + 32.9138i) q^{31} +(-5.59928 + 0.805054i) q^{32} +(-34.5603 + 10.1478i) q^{34} +(2.32328 + 7.91238i) q^{35} +(3.41078 + 23.7225i) q^{37} +(12.9181 - 11.1936i) q^{38} +(3.91320 - 2.51486i) q^{40} +(56.6306 + 8.14224i) q^{41} +(-23.2569 + 26.8399i) q^{43} +(2.86070 - 9.74265i) q^{44} +(-29.6388 + 13.3994i) q^{46} +76.9599i q^{47} +(15.6233 - 18.0302i) q^{49} +(17.0466 - 26.5250i) q^{50} +(-29.7090 + 19.0928i) q^{52} +(-66.3491 + 30.3006i) q^{53} +(1.18827 + 8.26461i) q^{55} +(12.9008 + 5.89159i) q^{56} +(-12.7438 + 3.74191i) q^{58} +(-17.3351 - 7.91669i) q^{59} +(-19.6761 - 22.7074i) q^{61} +(-56.0249 + 25.5857i) q^{62} +(1.13852 - 7.91857i) q^{64} +(15.7000 - 24.4297i) q^{65} +(-33.8664 - 9.94408i) q^{67} -50.9390i q^{68} -11.6622 q^{70} +(6.16424 - 20.9935i) q^{71} +(48.8574 + 31.3987i) q^{73} +(-33.5487 - 4.82358i) q^{74} +(10.0420 + 21.9889i) q^{76} +(-19.2393 + 16.6709i) q^{77} +(34.7184 - 76.0226i) q^{79} +(1.85335 + 6.31193i) q^{80} +(-33.6117 + 73.5995i) q^{82} +(18.1157 - 2.60464i) q^{83} +(17.4005 + 38.1019i) q^{85} +(-27.1535 - 42.2517i) q^{86} +(12.0803 + 7.76353i) q^{88} +(-28.5760 - 24.7612i) q^{89} +88.5392 q^{91} +(-6.37299 - 45.5564i) q^{92} +(-104.429 - 30.6631i) q^{94} +(-15.0226 - 13.0172i) q^{95} +(11.9670 - 83.2320i) q^{97} +(18.2409 + 28.3834i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 16 q^{4} - 16 q^{7}+O(q^{10}) $ 80 * q + 16 * q^4 - 16 * q^7	$ 80 q + 16 q^{4} - 16 q^{7} + 8 q^{10} + 8 q^{13} - 32 q^{16} - 128 q^{19} - 32 q^{22} - 352 q^{25} + 32 q^{28} + 32 q^{31} - 300 q^{34} - 384 q^{37} - 16 q^{40} + 540 q^{43} - 80 q^{49} - 16 q^{52} + 1244 q^{55} + 424 q^{58} + 568 q^{61} + 64 q^{64} + 60 q^{67} + 296 q^{70} + 36 q^{73} - 96 q^{76} - 1476 q^{79} + 12 q^{82} - 276 q^{85} - 112 q^{88} - 368 q^{91} - 304 q^{94} + 712 q^{97}+O(q^{100}) $ 80 * q + 16 * q^4 - 16 * q^7 + 8 * q^10 + 8 * q^13 - 32 * q^16 - 128 * q^19 - 32 * q^22 - 352 * q^25 + 32 * q^28 + 32 * q^31 - 300 * q^34 - 384 * q^37 - 16 * q^40 + 540 * q^43 - 80 * q^49 - 16 * q^52 + 1244 * q^55 + 424 * q^58 + 568 * q^61 + 64 * q^64 + 60 * q^67 + 296 * q^70 + 36 * q^73 - 96 * q^76 - 1476 * q^79 + 12 * q^82 - 276 * q^85 - 112 * q^88 - 368 * q^91 - 304 * q^94 + 712 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$-1$	$e\left(\frac{6}{11}\right)$

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 $

$2$	−0.398430	+	1.35693i	−0.199215	+	0.678464i
$2$	−0.398430	+	1.35693i	−0.199215	+	0.678464i
$3$		0			0
$3$		0			0
$4$	−1.68251	−	1.08128i	−0.420627	−	0.270320i
$5$	1.62786	+	0.234051i	0.325572	+	0.0468102i	0.303163	−	0.952939i	$-0.401957\pi$
$5$	1.62786	+	0.234051i	0.325572	+	0.0468102i	0.0224090	+	0.999749i	$0.492866\pi$
$6$		0			0
$7$	2.08299	+	4.56111i	0.297570	+	0.651588i	0.998072	−	0.0620627i	$-0.0197679\pi$
$7$	2.08299	+	4.56111i	0.297570	+	0.651588i	−0.700502	+	0.713650i	$0.747041\pi$
$8$	2.13758	−	1.85223i	0.267198	−	0.231528i
$9$		0			0
$10$	−0.966179	+	2.11564i	−0.0966179	+	0.211564i
$11$	1.43035	+	4.87132i	0.130032	+	0.442848i	0.998610	−	0.0527042i	$-0.0167840\pi$
$11$	1.43035	+	4.87132i	0.130032	+	0.442848i	−0.868578	+	0.495552i	$0.834966\pi$
$12$		0			0
$13$	7.33521	−	16.0619i	0.564247	−	1.23553i	−0.385557	−	0.922684i	$-0.625991\pi$
$13$	7.33521	−	16.0619i	0.564247	−	1.23553i	0.949804	−	0.312845i	$-0.101282\pi$
$14$	−7.01903	+	1.00918i	−0.501359	+	0.0720846i
$15$		0			0
$16$	1.66166	+	3.63853i	0.103854	+	0.227408i
$17$	13.7698	+	21.4263i	0.809991	+	1.26037i	0.962287	+	0.272035i	$0.0876968\pi$
$17$	13.7698	+	21.4263i	0.809991	+	1.26037i	−0.152296	+	0.988335i	$0.548667\pi$
$18$		0			0
$19$	−10.1680	−	6.53455i	−0.535156	−	0.343924i	0.244986	−	0.969527i	$-0.421217\pi$
$19$	−10.1680	−	6.53455i	−0.535156	−	0.343924i	−0.780142	+	0.625603i	$0.784853\pi$
$20$	−2.48581	−	2.15397i	−0.124291	−	0.107698i
$21$		0			0
$22$	−7.17993			−0.326360
$23$	14.9955	+	17.4395i	0.651977	+	0.758239i
$23$	14.9955	+	17.4395i	0.651977	+	0.758239i
$24$		0			0
$25$	−21.3922	−	6.28131i	−0.855687	−	0.251252i
$26$	18.8722	+	16.3529i	0.725856	+	0.628957i
$27$		0			0
$28$	1.42720	−	9.92640i	0.0509715	−	0.354514i
$29$	5.07751	+	7.90075i	0.175086	+	0.272440i	0.917695	−	0.397286i	$-0.130048\pi$
$29$	5.07751	+	7.90075i	0.175086	+	0.272440i	−0.742608	+	0.669726i	$0.766412\pi$
$30$		0			0
$31$	28.5200	+	32.9138i	0.919999	+	1.06174i	0.997900	+	0.0647743i	$0.0206327\pi$
$31$	28.5200	+	32.9138i	0.919999	+	1.06174i	−0.0779010	+	0.996961i	$0.524822\pi$
$32$	−5.59928	+	0.805054i	−0.174977	+	0.0251579i
$33$		0			0
$34$	−34.5603	+	10.1478i	−1.01648	+	0.298465i
$35$	2.32328	+	7.91238i	0.0663796	+	0.226068i
$36$		0			0
$37$	3.41078	+	23.7225i	0.0921834	+	0.641149i	0.982563	+	0.185930i	$0.0595299\pi$
$37$	3.41078	+	23.7225i	0.0921834	+	0.641149i	−0.890380	+	0.455219i	$0.849561\pi$
$38$	12.9181	−	11.1936i	0.339951	−	0.294569i
$39$		0			0
$40$	3.91320	−	2.51486i	0.0978300	−	0.0628715i
$41$	56.6306	+	8.14224i	1.38123	+	0.198591i	0.792567	−	0.609785i	$-0.208744\pi$
$41$	56.6306	+	8.14224i	1.38123	+	0.198591i	0.588666	+	0.808376i	$0.299653\pi$
$42$		0			0
$43$	−23.2569	+	26.8399i	−0.540857	+	0.624183i	−0.958728	−	0.284324i	$-0.908231\pi$
$43$	−23.2569	+	26.8399i	−0.540857	+	0.624183i	0.417871	+	0.908506i	$0.362776\pi$
$44$	2.86070	−	9.74265i	0.0650159	−	0.221424i
$45$		0			0
$46$	−29.6388	+	13.3994i	−0.644321	+	0.291290i
$47$			76.9599i			1.63745i	0.574189	+	0.818723i	$0.305317\pi$
$47$			76.9599i			1.63745i	−0.574189	+	0.818723i	$0.694683\pi$
$48$		0			0
$49$	15.6233	−	18.0302i	0.318842	−	0.367964i
$50$	17.0466	−	26.5250i	0.340931	−	0.530500i
$51$		0			0
$52$	−29.7090	+	19.0928i	−0.571326	+	0.367169i
$53$	−66.3491	+	30.3006i	−1.25187	+	0.571710i	−0.927359	−	0.374173i	$-0.877927\pi$
$53$	−66.3491	+	30.3006i	−1.25187	+	0.571710i	−0.324510	+	0.945882i	$0.605199\pi$
$54$		0			0
$55$	1.18827	+	8.26461i	0.0216049	+	0.150266i
$56$	12.9008	+	5.89159i	0.230371	+	0.105207i
$57$		0			0
$58$	−12.7438	+	3.74191i	−0.219720	+	0.0645157i
$59$	−17.3351	−	7.91669i	−0.293816	−	0.134181i	0.263054	−	0.964781i	$-0.415270\pi$
$59$	−17.3351	−	7.91669i	−0.293816	−	0.134181i	−0.556869	+	0.830600i	$0.687998\pi$
$60$		0			0
$61$	−19.6761	−	22.7074i	−0.322559	−	0.372253i	0.571192	−	0.820816i	$-0.306481\pi$
$61$	−19.6761	−	22.7074i	−0.322559	−	0.372253i	−0.893751	+	0.448564i	$0.851936\pi$
$62$	−56.0249	+	25.5857i	−0.903627	+	0.412673i
$63$		0			0
$64$	1.13852	−	7.91857i	0.0177894	−	0.123728i
$65$	15.7000	−	24.4297i	0.241539	−	0.375841i
$66$		0			0
$67$	−33.8664	−	9.94408i	−0.505469	−	0.148419i	0.0190489	−	0.999819i	$-0.493936\pi$
$67$	−33.8664	−	9.94408i	−0.505469	−	0.148419i	−0.524518	+	0.851400i	$0.675754\pi$
$68$		−	50.9390i		−	0.749103i
$69$		0			0
$70$	−11.6622			−0.166603
$71$	6.16424	−	20.9935i	0.0868203	−	0.295683i	−0.904624	−	0.426210i	$-0.859849\pi$
$71$	6.16424	−	20.9935i	0.0868203	−	0.295683i	0.991445	+	0.130527i	$0.0416668\pi$
$72$		0			0
$73$	48.8574	+	31.3987i	0.669279	+	0.430120i	0.830666	−	0.556772i	$-0.187960\pi$
$73$	48.8574	+	31.3987i	0.669279	+	0.430120i	−0.161386	+	0.986891i	$0.551597\pi$
$74$	−33.5487	−	4.82358i	−0.453361	−	0.0651835i
$75$		0			0
$76$	10.0420	+	21.9889i	0.132131	+	0.289327i
$77$	−19.2393	+	16.6709i	−0.249860	+	0.216505i
$78$		0			0
$79$	34.7184	−	76.0226i	0.439473	−	0.962312i	−0.552222	−	0.833697i	$-0.686220\pi$
$79$	34.7184	−	76.0226i	0.439473	−	0.962312i	0.991695	−	0.128615i	$-0.0410530\pi$
$80$	1.85335	+	6.31193i	0.0231669	+	0.0788991i
$81$		0			0
$82$	−33.6117	+	73.5995i	−0.409899	+	0.897554i
$83$	18.1157	−	2.60464i	0.218261	−	0.0313812i	−0.0323166	−	0.999478i	$-0.510288\pi$
$83$	18.1157	−	2.60464i	0.218261	−	0.0313812i	0.250578	+	0.968096i	$0.419379\pi$
$84$		0			0
$85$	17.4005	+	38.1019i	0.204712	+	0.448257i
$86$	−27.1535	−	42.2517i	−0.315739	−	0.491299i
$87$		0			0
$88$	12.0803	+	7.76353i	0.137276	+	0.0882219i
$89$	−28.5760	−	24.7612i	−0.321078	−	0.278216i	0.479376	−	0.877610i	$-0.340863\pi$
$89$	−28.5760	−	24.7612i	−0.321078	−	0.278216i	−0.800454	+	0.599394i	$0.795408\pi$
$90$		0			0
$91$	88.5392			0.972959
$92$	−6.37299	−	45.5564i	−0.0692716	−	0.495178i
$93$		0			0
$94$	−104.429	−	30.6631i	−1.11095	−	0.326204i
$95$	−15.0226	−	13.0172i	−0.158133	−	0.137023i
$96$		0			0
$97$	11.9670	−	83.2320i	0.123371	−	0.858062i	−0.830323	−	0.557282i	$-0.811844\pi$
$97$	11.9670	−	83.2320i	0.123371	−	0.858062i	0.953694	−	0.300780i	$-0.0972468\pi$
$98$	18.2409	+	28.3834i	0.186132	+	0.289627i
$99$		0			0
$100$	29.2006	+	33.6993i	0.292006	+	0.336993i
$101$	55.9642	−	8.04643i	0.554101	−	0.0796676i	0.140424	−	0.990091i	$-0.455153\pi$
$101$	55.9642	−	8.04643i	0.554101	−	0.0796676i	0.413677	+	0.910424i	$0.364244\pi$
$102$		0			0
$103$	12.4855	−	3.66608i	0.121219	−	0.0355930i	−0.220561	−	0.975373i	$-0.570789\pi$
$103$	12.4855	−	3.66608i	0.121219	−	0.0355930i	0.341779	+	0.939780i	$0.388970\pi$
$104$	−14.0706	−	47.9201i	−0.135294	−	0.460770i
$105$		0			0
$106$	−14.6803	−	102.104i	−0.138493	−	0.963241i
$107$	45.6870	−	39.5880i	0.426982	−	0.369982i	−0.414698	−	0.909959i	$-0.636113\pi$
$107$	45.6870	−	39.5880i	0.426982	−	0.369982i	0.841679	+	0.539978i	$0.181567\pi$
$108$		0			0
$109$	−114.343	+	73.4838i	−1.04902	+	0.674163i	−0.947201	−	0.320640i	$-0.896102\pi$
$109$	−114.343	+	73.4838i	−1.04902	+	0.674163i	−0.101818	+	0.994803i	$0.532466\pi$
$110$	−11.6879	−	1.68047i	−0.106254	−	0.0152770i
$111$		0			0
$112$	−13.1345	+	15.1580i	−0.117272	+	0.135340i
$113$	5.43958	−	18.5255i	0.0481379	−	0.163942i	−0.931916	−	0.362674i	$-0.881864\pi$
$113$	5.43958	−	18.5255i	0.0481379	−	0.163942i	0.980054	+	0.198731i	$0.0636821\pi$
$114$		0			0
$115$	20.3288	+	31.8988i	0.176772	+	0.277381i
$116$		−	18.7833i		−	0.161925i
$117$		0			0
$118$	17.6492	−	20.3683i	0.149570	−	0.172613i
$119$	−69.0453	+	107.437i	−0.580213	+	0.902828i
$120$		0			0
$121$	80.1078	−	51.4821i	0.662048	−	0.425472i
$122$	38.6519	−	17.6517i	0.316818	−	0.144686i
$123$		0			0
$124$	−12.3960	−	86.2158i	−0.0999674	−	0.695289i
$125$	−70.7528	−	32.3117i	−0.566023	−	0.258494i
$126$		0			0
$127$	234.660	−	68.9024i	1.84772	−	0.542539i	0.847792	−	0.530329i	$-0.177932\pi$
$127$	234.660	−	68.9024i	1.84772	−	0.542539i	0.999925	−	0.0122100i	$-0.00388667\pi$
$128$	10.2913	+	4.69988i	0.0804009	+	0.0367178i
$129$		0			0
$130$	26.8940	+	31.0373i	0.206877	+	0.238748i
$131$	−0.683570	+	0.312176i	−0.00521809	+	0.00238302i	−0.418022	−	0.908437i	$-0.637277\pi$
$131$	−0.683570	+	0.312176i	−0.00521809	+	0.00238302i	0.412804	+	0.910820i	$0.364549\pi$
$132$		0			0
$133$	8.62506	−	59.9886i	0.0648501	−	0.451042i
$134$	26.9868	−	41.9923i	0.201394	−	0.313375i
$135$		0			0
$136$	69.1205	+	20.2956i	0.508239	+	0.149232i
$137$		−	84.6905i		−	0.618179i	−0.951033	−	0.309089i	$-0.899976\pi$
$137$		−	84.6905i		−	0.618179i	0.951033	−	0.309089i	$-0.100024\pi$
$138$		0			0
$139$	256.530			1.84554			0.922771	−	0.385349i	$-0.125919\pi$
$139$	256.530			1.84554			0.922771	+	0.385349i	$0.125919\pi$
$140$	4.64657	−	15.8248i	0.0331898	−	0.113034i
$141$		0			0
$142$	26.0306	+	16.7289i	0.183314	+	0.117809i
$143$	88.7345	+	12.7581i	0.620521	+	0.0892175i
$144$		0			0
$145$	6.41629	+	14.0497i	0.0442503	+	0.0968946i
$146$	−62.0721	+	53.7857i	−0.425151	+	0.368396i
$147$		0			0
$148$	19.9121	−	43.6013i	0.134541	−	0.294604i
$149$	−66.7872	−	227.456i	−0.448236	−	1.52655i	−0.805527	−	0.592560i	$-0.798117\pi$
$149$	−66.7872	−	227.456i	−0.448236	−	1.52655i	0.357290	−	0.933993i	$-0.383701\pi$
$150$		0			0
$151$	−23.2949	+	51.0087i	−0.154271	+	0.337806i	−0.970949	−	0.239288i	$-0.923086\pi$
$151$	−23.2949	+	51.0087i	−0.154271	+	0.337806i	0.816678	+	0.577094i	$0.195813\pi$
$152$	−33.8383	+	4.86522i	−0.222621	+	0.0320080i
$153$		0			0
$154$	−14.9557	−	32.7485i	−0.0971151	−	0.212652i
$155$	38.7230	+	60.2542i	0.249826	+	0.388737i
$156$		0			0
$157$	−234.074	−	150.430i	−1.49092	−	0.958154i	−0.996013	−	0.0892065i	$-0.971567\pi$
$157$	−234.074	−	150.430i	−1.49092	−	0.958154i	−0.494904	−	0.868948i	$-0.664797\pi$
$158$	89.3244	+	77.4000i	0.565344	+	0.489874i
$159$		0			0
$160$	−9.30326			−0.0581454
$161$	−48.3081	+	104.722i	−0.300050	+	0.650449i
$162$		0			0
$163$	61.5723	+	18.0793i	0.377744	+	0.110916i	0.465092	−	0.885262i	$-0.346021\pi$
$163$	61.5723	+	18.0793i	0.377744	+	0.110916i	−0.0873482	+	0.996178i	$0.527839\pi$
$164$	−86.4772	−	74.9330i	−0.527300	−	0.456908i
$165$		0			0
$166$	−3.68352	+	25.6195i	−0.0221899	+	0.154334i
$167$	−73.5147	−	114.391i	−0.440208	−	0.684977i	0.548277	−	0.836297i	$-0.315284\pi$
$167$	−73.5147	−	114.391i	−0.440208	−	0.684977i	−0.988485	+	0.151320i	$0.951648\pi$
$168$		0			0
$169$	−93.5071	−	107.913i	−0.553297	−	0.638538i
$170$	−58.6344	+	8.43035i	−0.344908	+	0.0495903i
$171$		0			0
$172$	68.1513	−	20.0110i	0.396228	−	0.116343i
$173$	−52.0397	−	177.231i	−0.300807	−	1.02446i	−0.961729	−	0.274001i	$-0.911653\pi$
$173$	−52.0397	−	177.231i	−0.300807	−	1.02446i	0.660922	−	0.750455i	$-0.270165\pi$
$174$		0			0
$175$	−15.9099	−	110.656i	−0.0909139	−	0.632320i
$176$	−15.3477	+	13.2989i	−0.0872028	+	0.0755617i
$177$		0			0
$178$	44.9847	−	28.9099i	0.252723	−	0.162415i
$179$	−171.409	−	24.6449i	−0.957594	−	0.137681i	−0.354240	−	0.935155i	$-0.615260\pi$
$179$	−171.409	−	24.6449i	−0.957594	−	0.137681i	−0.603354	+	0.797473i	$0.706169\pi$
$180$		0			0
$181$	40.7431	−	47.0200i	0.225100	−	0.259779i	−0.631954	−	0.775006i	$-0.717747\pi$
$181$	40.7431	−	47.0200i	0.225100	−	0.259779i	0.857054	+	0.515227i	$0.172292\pi$
$182$	−35.2767	+	120.141i	−0.193828	+	0.660117i
$183$		0			0
$184$	64.3559	+	9.50335i	0.349761	+	0.0516486i
$185$			39.4153i			0.213055i
$186$		0			0
$187$	−84.6787	+	97.7245i	−0.452827	+	0.522591i
$188$	83.2153	−	129.486i	0.442635	−	0.688753i
$189$		0			0
$190$	23.6488	−	15.1982i	0.124467	−	0.0799903i
$191$	−87.0803	+	39.7682i	−0.455918	+	0.208211i	−0.630118	−	0.776500i	$-0.716993\pi$
$191$	−87.0803	+	39.7682i	−0.455918	+	0.208211i	0.174200	+	0.984710i	$0.444266\pi$
$192$		0			0
$193$	4.76530	+	33.1434i	0.0246907	+	0.171728i	0.998436	−	0.0559146i	$-0.0178075\pi$
$193$	4.76530	+	33.1434i	0.0246907	+	0.171728i	−0.973745	+	0.227642i	$0.926898\pi$
$194$	108.172	+	49.4004i	0.557587	+	0.254641i
$195$		0			0
$196$	−45.7820	+	13.4428i	−0.233582	+	0.0685858i
$197$	251.286	+	114.759i	1.27556	+	0.582531i	0.933982	−	0.357321i	$-0.116310\pi$
$197$	251.286	+	114.759i	1.27556	+	0.582531i	0.341582	+	0.939852i	$0.389037\pi$
$198$		0			0
$199$	203.568	+	234.931i	1.02296	+	1.18056i	0.983421	+	0.181337i	$0.0580426\pi$
$199$	203.568	+	234.931i	1.02296	+	1.18056i	0.0395362	+	0.999218i	$0.487412\pi$
$200$	−57.3619	+	26.1963i	−0.286810	+	0.130982i
$201$		0			0
$202$	−11.3794	+	79.1453i	−0.0563335	+	0.391808i
$203$	−25.4598	+	39.6163i	−0.125418	+	0.195154i
$204$		0			0
$205$	90.2809	+	26.5089i	0.440395	+	0.129312i
$206$			18.4026i			0.0893332i
$207$		0			0
$208$	70.6302			0.339568
$209$	17.2882	−	58.8781i	0.0827186	−	0.281714i
$210$		0			0
$211$	−256.980	−	165.151i	−1.21791	−	0.782706i	−0.235948	−	0.971766i	$-0.575820\pi$
$211$	−256.980	−	165.151i	−1.21791	−	0.782706i	−0.981966	+	0.189060i	$0.939456\pi$
$212$	144.396	+	20.7610i	0.681114	+	0.0979295i
$213$		0			0
$214$	35.5150	+	77.7671i	0.165958	+	0.363398i
$215$	−44.1408	+	38.2482i	−0.205306	+	0.177899i
$216$		0			0
$217$	−90.7167	+	198.642i	−0.418049	+	0.915401i
$218$	−54.1545	−	184.433i	−0.248415	−	0.846025i
$219$		0			0
$220$	6.93710	−	15.1901i	0.0315323	−	0.0690460i
$221$	445.151	−	64.0031i	2.01426	−	0.289607i
$222$		0			0
$223$	−71.7613	−	157.135i	−0.321799	−	0.704642i	0.677730	−	0.735311i	$-0.262964\pi$
$223$	−71.7613	−	157.135i	−0.321799	−	0.704642i	−0.999530	+	0.0306682i	$0.990236\pi$
$224$	−15.3352	−	23.8620i	−0.0684606	−	0.106527i
$225$		0			0
$226$	22.9705	+	14.7622i	0.101639	+	0.0653196i
$227$	−2.14427	−	1.85802i	−0.00944610	−	0.00818510i	0.650125	−	0.759827i	$-0.274717\pi$
$227$	−2.14427	−	1.85802i	−0.00944610	−	0.00818510i	−0.659571	+	0.751642i	$0.729262\pi$
$228$		0			0
$229$	−229.677			−1.00296			−0.501478	−	0.865170i	$-0.667210\pi$
$229$	−229.677			−1.00296			−0.501478	+	0.865170i	$0.667210\pi$
$230$	−51.3839	+	14.8753i	−0.223408	+	0.0646752i
$231$		0			0
$232$	25.4876	+	7.48383i	0.109860	+	0.0322579i
$233$	−247.604	−	214.550i	−1.06268	−	0.920815i	−0.0656482	−	0.997843i	$-0.520912\pi$
$233$	−247.604	−	214.550i	−1.06268	−	0.920815i	−0.997029	+	0.0770279i	$0.975457\pi$
$234$		0			0
$235$	−18.0125	+	125.280i	−0.0766491	+	0.533106i
$236$	20.6063	+	32.0640i	0.0873149	+	0.135865i
$237$		0			0
$238$	−118.274	−	136.495i	−0.496950	−	0.573510i
$239$	−224.999	+	32.3500i	−0.941419	+	0.135356i	−0.595902	−	0.803057i	$-0.703205\pi$
$239$	−224.999	+	32.3500i	−0.941419	+	0.135356i	−0.345517	+	0.938413i	$0.612296\pi$
$240$		0			0
$241$	−286.783	+	84.2072i	−1.18997	+	0.349407i	−0.816011	−	0.578037i	$-0.803819\pi$
$241$	−286.783	+	84.2072i	−1.18997	+	0.349407i	−0.373961	+	0.927444i	$0.622001\pi$
$242$	37.9402	+	129.213i	0.156778	+	0.533936i
$243$		0			0
$244$	8.55204	+	59.4808i	0.0350493	+	0.243774i
$245$	29.6525	−	25.6940i	0.121031	−	0.104874i
$246$		0			0
$247$	−179.541	+	115.384i	−0.726888	+	0.467143i
$248$	121.928	+	17.5305i	0.491643	+	0.0706877i
$249$		0			0
$250$	72.0348	−	83.1326i	0.288139	−	0.332530i
$251$	−113.428	+	386.300i	−0.451903	+	1.53904i	0.347166	+	0.937804i	$0.387144\pi$
$251$	−113.428	+	386.300i	−0.451903	+	1.53904i	−0.799070	+	0.601238i	$0.794674\pi$
$252$		0			0
$253$	−63.5046	+	97.9924i	−0.251006	+	0.387322i
$254$			345.870i			1.36169i
$255$		0			0
$256$	−10.4778	+	12.0920i	−0.0409288	+	0.0472343i
$257$	106.725	−	166.068i	0.415273	−	0.646177i	−0.569101	−	0.822268i	$-0.692709\pi$
$257$	106.725	−	166.068i	0.415273	−	0.646177i	0.984374	+	0.176090i	$0.0563450\pi$
$258$		0			0
$259$	−101.096	+	64.9708i	−0.390334	+	0.250852i
$260$	−52.8307	+	24.1270i	−0.203195	+	0.0927961i
$261$		0			0
$262$	−0.151246	−	1.05194i	−0.000577273	−	0.00401502i
$263$	201.321	+	91.9403i	0.765480	+	0.349583i	0.759592	−	0.650400i	$-0.225399\pi$
$263$	201.321	+	91.9403i	0.765480	+	0.349583i	0.00588769	+	0.999983i	$0.498126\pi$
$264$		0			0
$265$	−115.099	+	33.7961i	−0.434336	+	0.127532i
$266$	77.9638	+	35.6049i	0.293097	+	0.133853i
$267$		0			0
$268$	46.2281	+	53.3501i	0.172493	+	0.199068i
$269$	−38.2388	+	17.4631i	−0.142151	+	0.0649184i	−0.485221	−	0.874392i	$-0.661261\pi$
$269$	−38.2388	+	17.4631i	−0.142151	+	0.0649184i	0.343069	+	0.939310i	$0.388533\pi$
$270$		0			0
$271$	2.43994	−	16.9701i	0.00900346	−	0.0626204i	−0.984824	−	0.173554i	$-0.944475\pi$
$271$	2.43994	−	16.9701i	0.00900346	−	0.0626204i	0.993828	+	0.110933i	$0.0353840\pi$
$272$	−55.0794	+	85.7052i	−0.202498	+	0.315093i
$273$		0			0
$274$	114.919	+	33.7432i	0.419412	+	0.123150i
$275$		−	113.193i		−	0.411610i
$276$		0			0
$277$	−144.368			−0.521185			−0.260593	−	0.965449i	$-0.583918\pi$
$277$	−144.368			−0.521185			−0.260593	+	0.965449i	$0.583918\pi$
$278$	−102.209	+	348.093i	−0.367660	+	1.25213i
$279$		0			0
$280$	19.6217	+	12.6101i	0.0700776	+	0.0450361i
$281$	−151.466	−	21.7775i	−0.539024	−	0.0775000i	−0.132574	−	0.991173i	$-0.542324\pi$
$281$	−151.466	−	21.7775i	−0.539024	−	0.0775000i	−0.406450	+	0.913673i	$0.633233\pi$
$282$		0			0
$283$	125.960	+	275.815i	0.445090	+	0.974611i	0.990636	+	0.136530i	$0.0435950\pi$
$283$	125.960	+	275.815i	0.445090	+	0.974611i	−0.545546	+	0.838081i	$0.683678\pi$
$284$	−33.0713	+	28.6564i	−0.116448	+	0.100903i
$285$		0			0
$286$	−52.6663	+	115.323i	−0.184148	+	0.403228i
$287$	80.8232	+	275.259i	0.281614	+	0.959089i
$288$		0			0
$289$	−149.423	+	327.190i	−0.517033	+	1.13214i
$290$	−21.6209	+	3.10862i	−0.0745548	+	0.0107194i
$291$		0			0
$292$	−48.2520	−	105.657i	−0.165247	−	0.361840i
$293$	12.1672	+	18.9326i	0.0415264	+	0.0646163i	0.861396	−	0.507934i	$-0.169591\pi$
$293$	12.1672	+	18.9326i	0.0415264	+	0.0646163i	−0.819870	+	0.572550i	$0.805954\pi$
$294$		0			0
$295$	−26.3663	−	16.9446i	−0.0893772	−	0.0574392i
$296$	51.2303	+	44.3913i	0.173075	+	0.149971i
$297$		0			0
$298$	335.252			1.12501
$299$	390.106	−	112.933i	1.30470	−	0.377703i
$300$		0			0
$301$	−170.863	−	50.1700i	−0.567653	−	0.166678i
$302$	−59.9337	−	51.9329i	−0.198456	−	0.171963i
$303$		0			0
$304$	6.88045	−	47.8546i	0.0226331	−	0.157416i
$305$	−26.7152	−	41.5697i	−0.0875909	−	0.136294i
$306$		0			0
$307$	135.132	+	155.951i	0.440170	+	0.507983i	0.931875	−	0.362778i	$-0.118172\pi$
$307$	135.132	+	155.951i	0.440170	+	0.507983i	−0.491706	+	0.870761i	$0.663626\pi$
$308$	50.3961	−	7.24587i	0.163624	−	0.0235256i
$309$		0			0
$310$	−97.1890	+	28.5373i	−0.313513	+	0.0920557i
$311$	37.9514	+	129.251i	0.122030	+	0.415597i	0.997736	−	0.0672478i	$-0.0214218\pi$
$311$	37.9514	+	129.251i	0.122030	+	0.415597i	−0.875706	+	0.482845i	$0.839604\pi$
$312$		0			0
$313$	−41.4178	−	288.067i	−0.132325	−	0.920342i	−0.942513	−	0.334171i	$-0.891544\pi$
$313$	−41.4178	−	288.067i	−0.132325	−	0.920342i	0.810187	−	0.586171i	$-0.199365\pi$
$314$	297.385	−	257.686i	0.947086	−	0.820655i
$315$		0			0
$316$	−140.616	+	90.3683i	−0.444987	+	0.285976i
$317$	531.672	+	76.4429i	1.67720	+	0.241145i	0.914203	−	0.405257i	$-0.132818\pi$
$317$	531.672	+	76.4429i	1.67720	+	0.241145i	0.762997	+	0.646402i	$0.223727\pi$
$318$		0			0
$319$	−31.2245	+	36.0350i	−0.0978825	+	0.112962i
$320$	3.70670	−	12.6239i	0.0115834	−	0.0394496i
$321$		0			0
$322$	−122.853	−	107.275i	−0.381532	−	0.333152i
$323$		−	307.841i		−	0.953070i
$324$		0			0
$325$	−257.806	+	297.524i	−0.793249	+	0.915458i
$326$	−49.0645	+	76.3459i	−0.150505	+	0.234190i
$327$		0			0
$328$	136.134	−	87.4879i	0.415042	−	0.266731i
$329$	−351.023	+	160.307i	−1.06694	+	0.487255i
$330$		0			0
$331$	−48.4181	−	336.755i	−0.146278	−	1.01739i	−0.922243	−	0.386611i	$-0.873646\pi$
$331$	−48.4181	−	336.755i	−0.146278	−	1.01739i	0.775965	−	0.630776i	$-0.217263\pi$
$332$	−33.2961	−	15.2058i	−0.100290	−	0.0458007i
$333$		0			0
$334$	184.511	−	54.1773i	0.552428	−	0.162208i
$335$	−52.8024	−	24.1140i	−0.157619	−	0.0719822i
$336$		0			0
$337$	8.30622	+	9.58589i	0.0246475	+	0.0284448i	0.767940	−	0.640522i	$-0.221282\pi$
$337$	8.30622	+	9.58589i	0.0246475	+	0.0284448i	−0.743292	+	0.668967i	$0.766737\pi$
$338$	183.686	−	83.8867i	0.543450	−	0.248185i
$339$		0			0
$340$	11.9223	−	82.9215i	0.0350656	−	0.243887i
$341$	−119.540	+	186.008i	−0.350558	+	0.545479i
$342$		0			0
$343$	350.526	+	102.924i	1.02194	+	0.300069i
$344$			100.449i			0.292004i
$345$		0			0
$346$	261.224			0.754982
$347$	−129.295	+	440.337i	−0.372607	+	1.26898i	0.533451	+	0.845831i	$0.320895\pi$
$347$	−129.295	+	440.337i	−0.372607	+	1.26898i	−0.906058	+	0.423153i	$0.860923\pi$
$348$		0			0
$349$	−318.328	−	204.577i	−0.912114	−	0.586180i	−0.00175438	−	0.999998i	$-0.500558\pi$
$349$	−318.328	−	204.577i	−0.912114	−	0.586180i	−0.910359	+	0.413819i	$0.864195\pi$
$350$	156.491	+	22.5000i	0.447118	+	0.0642858i
$351$		0			0
$352$	−11.9306	−	26.1244i	−0.0338938	−	0.0742170i
$353$	−193.712	+	167.853i	−0.548760	+	0.475503i	−0.884558	−	0.466431i	$-0.845540\pi$
$353$	−193.712	+	167.853i	−0.548760	+	0.475503i	0.335798	+	0.941934i	$0.390994\pi$
$354$		0			0
$355$	14.9481	−	32.7317i	0.0421073	−	0.0922020i
$356$	21.3054	+	72.5596i	0.0598467	+	0.203819i
$357$		0			0
$358$	101.736	−	222.771i	0.284179	−	0.622265i
$359$	292.026	−	41.9871i	0.813444	−	0.116956i	0.276977	−	0.960877i	$-0.410668\pi$
$359$	292.026	−	41.9871i	0.813444	−	0.116956i	0.536467	+	0.843921i	$0.319758\pi$
$360$		0			0
$361$	−89.2778	−	195.491i	−0.247307	−	0.541526i
$362$	47.5695	+	74.0196i	0.131407	+	0.204474i
$363$		0			0
$364$	−148.968	−	95.7358i	−0.409252	−	0.263011i
$365$	72.1841	+	62.5479i	0.197765	+	0.171364i
$366$		0			0
$367$	499.842			1.36197			0.680983	−	0.732299i	$-0.261553\pi$
$367$	499.842			1.36197			0.680983	+	0.732299i	$0.261553\pi$
$368$	−38.5367	+	83.5399i	−0.104719	+	0.227011i
$369$		0			0
$370$	−53.4837	−	15.7042i	−0.144550	−	0.0424438i
$371$	−276.409	−	239.510i	−0.745038	−	0.645579i
$372$		0			0
$373$	54.5239	−	379.222i	0.146177	−	1.01668i	−0.776227	−	0.630454i	$-0.782869\pi$
$373$	54.5239	−	379.222i	0.146177	−	1.01668i	0.922404	−	0.386228i	$-0.126222\pi$
$374$	−98.8665	−	153.839i	−0.264349	−	0.411335i
$375$		0			0
$376$	142.547	+	164.508i	0.379115	+	0.437522i
$377$	164.146	−	23.6006i	0.435399	−	0.0626010i
$378$		0			0
$379$	−452.872	+	132.975i	−1.19491	+	0.350858i	−0.817905	−	0.575353i	$-0.804865\pi$
$379$	−452.872	+	132.975i	−1.19491	+	0.350858i	−0.377006	+	0.926211i	$0.623047\pi$
$380$	11.2004	+	38.1451i	0.0294748	+	0.100382i
$381$		0			0
$382$	−19.2672	−	134.007i	−0.0504378	−	0.350803i
$383$	46.5559	−	40.3409i	0.121556	−	0.105329i	−0.591962	−	0.805966i	$-0.701646\pi$
$383$	46.5559	−	40.3409i	0.121556	−	0.105329i	0.713518	+	0.700637i	$0.247101\pi$
$384$		0			0
$385$	−35.2207	+	22.6349i	−0.0914822	+	0.0587921i
$386$	−46.8719	−	6.73916i	−0.121430	−	0.0174590i
$387$		0			0
$388$	−110.132	+	127.099i	−0.283845	+	0.327574i
$389$	116.753	−	397.625i	0.300137	−	1.02217i	−0.661977	−	0.749524i	$-0.730282\pi$
$389$	116.753	−	397.625i	0.300137	−	1.02217i	0.962114	−	0.272648i	$-0.0878995\pi$
$390$		0			0
$391$	−167.178	+	561.436i	−0.427566	+	1.43590i
$392$		−	67.4789i		−	0.172140i
$393$		0			0
$394$	−255.839	+	295.254i	−0.649338	+	0.749375i
$395$	74.3098	−	115.628i	0.188126	−	0.292730i
$396$		0			0
$397$	556.913	−	357.906i	1.40280	−	0.901528i	0.402898	−	0.915245i	$-0.368003\pi$
$397$	556.913	−	357.906i	1.40280	−	0.901528i	0.999906	+	0.0137173i	$0.00436647\pi$
$398$	−399.892	+	182.624i	−1.00475	+	0.458855i
$399$		0			0
$400$	−12.6918	−	88.2734i	−0.0317295	−	0.220684i
$401$	34.6553	+	15.8266i	0.0864222	+	0.0394677i	0.458157	−	0.888871i	$-0.348510\pi$
$401$	34.6553	+	15.8266i	0.0864222	+	0.0394677i	−0.371735	+	0.928339i	$0.621237\pi$
$402$		0			0
$403$	737.858	−	216.655i	1.83091	−	0.537604i
$404$	−102.861	−	46.9748i	−0.254605	−	0.116274i
$405$		0			0
$406$	−43.6125	−	50.3315i	−0.107420	−	0.123969i
$407$	−110.682	+	50.5466i	−0.271945	+	0.124193i
$408$		0			0
$409$	71.1746	−	495.030i	0.174021	−	1.21034i	−0.696261	−	0.717789i	$-0.745154\pi$
$409$	71.1746	−	495.030i	0.174021	−	1.21034i	0.870282	−	0.492554i	$-0.163937\pi$
$410$	−71.9413	+	111.943i	−0.175466	+	0.273031i
$411$		0			0
$412$	−24.9710	−	7.33216i	−0.0606093	−	0.0177965i
$413$		−	95.5579i		−	0.231375i
$414$		0			0
$415$	30.0994			0.0725287
$416$	−28.1412	+	95.8401i	−0.0676471	+	0.230385i
$417$		0			0
$418$	73.0052	+	46.9176i	0.174654	+	0.112243i
$419$	−177.045	−	25.4552i	−0.422541	−	0.0607522i	−0.0722351	−	0.997388i	$-0.523013\pi$
$419$	−177.045	−	25.4552i	−0.422541	−	0.0607522i	−0.350306	+	0.936635i	$0.613922\pi$
$420$		0			0
$421$	−262.835	−	575.528i	−0.624311	−	1.36705i	−0.912342	−	0.409430i	$-0.865728\pi$
$421$	−262.835	−	575.528i	−0.624311	−	1.36705i	0.288030	−	0.957621i	$-0.407000\pi$
$422$	326.486	−	282.902i	0.773664	−	0.670384i
$423$		0			0
$424$	−85.7031	+	187.664i	−0.202130	+	0.442603i
$425$	−159.982	−	544.848i	−0.376428	−	1.28199i
$426$		0			0
$427$	62.5860	−	137.044i	0.146571	−	0.320946i
$428$	−119.675	+	17.2066i	−0.279613	+	0.0402024i
$429$		0			0
$430$	−34.3131	−	75.1352i	−0.0797979	−	0.174733i
$431$	42.3589	+	65.9117i	0.0982805	+	0.152927i	0.886912	−	0.461939i	$-0.152846\pi$
$431$	42.3589	+	65.9117i	0.0982805	+	0.152927i	−0.788631	+	0.614867i	$0.789210\pi$
$432$		0			0
$433$	638.169	+	410.126i	1.47383	+	0.947174i	0.997699	+	0.0677999i	$0.0215980\pi$
$433$	638.169	+	410.126i	1.47383	+	0.947174i	0.476132	+	0.879374i	$0.342038\pi$
$434$	−233.399	−	202.241i	−0.537785	−	0.465993i
$435$		0			0
$436$	271.840			0.623486
$437$	−38.5141	−	275.313i	−0.0881330	−	0.630006i
$438$		0			0
$439$	−218.467	−	64.1476i	−0.497646	−	0.146122i	0.0232713	−	0.999729i	$-0.492592\pi$
$439$	−218.467	−	64.1476i	−0.497646	−	0.146122i	−0.520917	+	0.853607i	$0.674410\pi$
$440$	17.8480	+	15.4653i	0.0405635	+	0.0351485i
$441$		0			0
$442$	−90.5141	+	629.539i	−0.204783	+	1.42430i
$443$	192.235	+	299.123i	0.433938	+	0.675221i	0.987506	−	0.157583i	$-0.0503703\pi$
$443$	192.235	+	299.123i	0.433938	+	0.675221i	−0.553567	+	0.832804i	$0.686734\pi$
$444$		0			0
$445$	−40.7223	−	46.9960i	−0.0915108	−	0.105609i
$446$	241.813	−	34.7675i	0.542182	−	0.0779540i
$447$		0			0
$448$	38.4890	−	11.3014i	0.0859130	−	0.0252263i
$449$	67.0104	+	228.217i	0.149244	+	0.508277i	0.999846	−	0.0175318i	$-0.00558082\pi$
$449$	67.0104	+	228.217i	0.149244	+	0.508277i	−0.850603	+	0.525809i	$0.823763\pi$
$450$		0			0
$451$	41.3380	+	287.512i	0.0916585	+	0.637499i
$452$	−29.1834	+	25.2876i	−0.0645651	+	0.0559459i
$453$		0			0
$454$	3.37553	−	2.16932i	0.00743510	−	0.00477825i
$455$	144.130	+	20.7227i	0.316768	+	0.0455444i
$456$		0			0
$457$	−482.245	+	556.541i	−1.05524	+	1.21781i	−0.0799717	+	0.996797i	$0.525483\pi$
$457$	−482.245	+	556.541i	−1.05524	+	1.21781i	−0.975270	+	0.221017i	$0.929062\pi$
$458$	91.5102	−	311.655i	0.199804	−	0.680470i
$459$		0			0
$460$	0.288184	−	75.6511i	0.000626488	−	0.164459i
$461$			421.960i			0.915315i	0.889129	+	0.457658i	$0.151311\pi$
$461$			421.960i			0.915315i	−0.889129	+	0.457658i	$0.848689\pi$
$462$		0			0
$463$	296.290	−	341.937i	0.639936	−	0.738525i	−0.339428	−	0.940632i	$-0.610233\pi$
$463$	296.290	−	341.937i	0.639936	−	0.738525i	0.979363	+	0.202107i	$0.0647789\pi$
$464$	−20.3100	+	31.6030i	−0.0437716	+	0.0681099i
$465$		0			0
$466$	389.782	−	250.497i	0.836441	−	0.537548i
$467$	−662.339	+	302.480i	−1.41828	+	0.647709i	−0.969311	−	0.245836i	$-0.920938\pi$
$467$	−662.339	+	302.480i	−1.41828	+	0.647709i	−0.448973	+	0.893545i	$0.648210\pi$
$468$		0			0
$469$	−25.1874	−	175.182i	−0.0537044	−	0.373522i
$470$	−162.819	−	74.3570i	−0.346424	−	0.158206i
$471$		0			0
$472$	−51.7188	+	15.1860i	−0.109574	+	0.0321737i
$473$	−164.011	−	74.9013i	−0.346746	−	0.158354i
$474$		0			0
$475$	176.469	+	203.656i	0.371514	+	0.428750i
$476$	232.338	−	106.105i	0.488106	−	0.222911i
$477$		0			0
$478$	45.7498	−	318.197i	0.0957109	−	0.665684i
$479$	432.673	−	673.253i	0.903285	−	1.40554i	−0.0107676	−	0.999942i	$-0.503427\pi$
$479$	432.673	−	673.253i	0.903285	−	1.40554i	0.914052	−	0.405596i	$-0.132936\pi$
$480$		0			0
$481$	406.047	+	119.226i	0.844173	+	0.247872i
$482$		−	422.695i		−	0.876960i
$483$		0			0
$484$	−190.449			−0.393489
$485$	38.9611	−	132.689i	0.0803321	−	0.273586i
$486$		0			0
$487$	−64.6015	−	41.5168i	−0.132652	−	0.0852502i	0.472632	−	0.881260i	$-0.343304\pi$
$487$	−64.6015	−	41.5168i	−0.132652	−	0.0852502i	−0.605284	+	0.796010i	$0.706940\pi$
$488$	−84.1185	−	12.0944i	−0.172374	−	0.0247836i
$489$		0			0
$490$	23.0505	+	50.4736i	0.0470419	+	0.103007i
$491$	−440.091	+	381.341i	−0.896315	+	0.776661i	−0.975454	−	0.220202i	$-0.929328\pi$
$491$	−440.091	+	381.341i	−0.896315	+	0.776661i	0.0791393	+	0.996864i	$0.474783\pi$
$492$		0			0
$493$	−99.3674	+	217.584i	−0.201557	+	0.441347i
$494$	−85.0334	−	289.597i	−0.172132	−	0.586229i
$495$		0			0
$496$	−72.3673	+	158.462i	−0.145902	+	0.319480i
$497$	108.594	−	15.6134i	0.218498	−	0.0314153i
$498$		0			0
$499$	−28.3963	−	62.1792i	−0.0569064	−	0.124608i	0.879043	−	0.476743i	$-0.158183\pi$
$499$	−28.3963	−	62.1792i	−0.0569064	−	0.124608i	−0.935949	+	0.352136i	$0.885456\pi$
$500$	84.1041	+	130.868i	0.168208	+	0.261737i
$501$		0			0
$502$	−478.988	−	307.827i	−0.954159	−	0.613200i
$503$	−634.964	−	550.199i	−1.26235	−	1.09384i	−0.991348	−	0.131258i	$-0.958098\pi$
$503$	−634.964	−	550.199i	−1.26235	−	1.09384i	−0.271005	−	0.962578i	$-0.587356\pi$
$504$		0			0
$505$	92.9851			0.184129
$506$	−107.666	−	125.214i	−0.212780	−	0.247459i
$507$		0			0
$508$	−469.320	−	137.805i	−0.923859	−	0.271269i
$509$	−546.770	−	473.779i	−1.07420	−	0.930803i	−0.0764020	−	0.997077i	$-0.524343\pi$
$509$	−546.770	−	473.779i	−1.07420	−	0.930803i	−0.997801	+	0.0662745i	$0.978889\pi$
$510$		0			0
$511$	−41.4437	+	288.247i	−0.0811031	+	0.564085i
$512$	−12.2333	−	19.0354i	−0.0238932	−	0.0371785i
$513$		0			0
$514$	182.819	+	210.985i	0.355680	+	0.410476i
$515$	21.1827	−	3.04562i	0.0411315	−	0.00591382i
$516$		0			0
$517$	−374.897	+	110.080i	−0.725139	+	0.212920i
$518$	−47.8808	−	163.067i	−0.0924339	−	0.314801i
$519$		0			0
$520$	−11.6892	−	81.3004i	−0.0224793	−	0.156347i
$521$	660.213	−	572.078i	1.26720	−	1.09804i	0.276642	−	0.960973i	$-0.410778\pi$
$521$	660.213	−	572.078i	1.26720	−	1.09804i	0.990562	−	0.137065i	$-0.0437670\pi$
$522$		0			0
$523$	821.976	−	528.252i	1.57166	−	1.01004i	0.592835	−	0.805324i	$-0.298009\pi$
$523$	821.976	−	528.252i	1.57166	−	1.01004i	0.978821	−	0.204718i	$-0.0656278\pi$
$524$	1.48766	+	0.213893i	0.00283905	+	0.000408194i
$525$		0			0
$526$	−204.969	+	236.547i	−0.389674	+	0.449708i
$527$	−312.505	+	1064.30i	−0.592989	+	2.01954i
$528$		0			0
$529$	−79.2716	+	523.027i	−0.149852	+	0.988708i
$530$		−	169.646i		−	0.320087i
$531$		0			0
$532$	−79.3763	+	91.6052i	−0.149204	+	0.172190i
$533$	546.177	−	849.868i	1.02472	−	1.59450i
$534$		0			0
$535$	83.6377	−	53.7507i	0.156332	−	0.100469i
$536$	−90.8109	+	41.4720i	−0.169423	+	0.0773731i
$537$		0			0
$538$	−8.46064	−	58.8450i	−0.0157261	−	0.109377i
$539$	110.178	+	50.3165i	0.204411	+	0.0933516i
$540$		0			0
$541$	637.825	−	187.282i	1.17897	−	0.346178i	0.367196	−	0.930144i	$-0.380318\pi$
$541$	637.825	−	187.282i	1.17897	−	0.346178i	0.811778	+	0.583965i	$0.198500\pi$
$542$	22.0551	+	10.0722i	0.0406921	+	0.0185835i
$543$		0			0
$544$	−94.3505	−	108.886i	−0.173438	−	0.200159i
$545$	−203.333	+	92.8593i	−0.373089	+	0.170384i
$546$		0			0
$547$	93.6067	−	651.049i	0.171127	−	1.19022i	−0.705380	−	0.708829i	$-0.749224\pi$
$547$	93.6067	−	651.049i	0.171127	−	1.19022i	0.876508	−	0.481388i	$-0.159867\pi$
$548$	−91.5742	+	142.492i	−0.167106	+	0.260022i
$549$		0			0
$550$	153.594	+	45.0994i	0.279262	+	0.0819988i
$551$		−	113.514i		−	0.206014i
$552$		0			0
$553$	419.066			0.757805
$554$	57.5207	−	195.897i	0.103828	−	0.353605i
$555$		0			0
$556$	−431.614	−	277.381i	−0.776284	−	0.498888i
$557$	−982.264	−	141.228i	−1.76349	−	0.253552i	−0.817082	−	0.576522i	$-0.804410\pi$
$557$	−982.264	−	141.228i	−1.76349	−	0.253552i	−0.946409	+	0.322970i	$0.895319\pi$
$558$		0			0
$559$	260.504	+	570.425i	0.466019	+	1.02044i
$560$	−24.9289	+	21.6010i	−0.0445159	+	0.0385733i
$561$		0			0
$562$	89.8990	−	196.851i	0.159963	−	0.350269i
$563$	−105.918	−	360.722i	−0.188131	−	0.640715i	−0.998498	−	0.0547919i	$-0.982550\pi$
$563$	−105.918	−	360.722i	−0.188131	−	0.640715i	0.810367	−	0.585923i	$-0.199268\pi$
$564$		0			0
$565$	13.1908	−	28.8838i	0.0233465	−	0.0511217i
$566$	−424.447	+	61.0263i	−0.749907	+	0.107820i
$567$		0			0
$568$	−25.7081	−	56.2929i	−0.0452607	−	0.0991072i
$569$	457.558	+	711.975i	0.804145	+	1.25127i	0.964466	+	0.264208i	$0.0851107\pi$
$569$	457.558	+	711.975i	0.804145	+	1.25127i	−0.160321	+	0.987065i	$0.551253\pi$
$570$		0			0
$571$	−173.168	−	111.288i	−0.303271	−	0.194900i	0.380150	−	0.924925i	$-0.375872\pi$
$571$	−173.168	−	111.288i	−0.303271	−	0.194900i	−0.683421	+	0.730024i	$0.739509\pi$
$572$	−135.501	−	117.413i	−0.236891	−	0.205267i
$573$		0			0
$574$	−405.708			−0.706809
$575$	−211.243	−	467.260i	−0.367379	−	0.812626i
$576$		0			0
$577$	226.726	+	66.5727i	0.392939	+	0.115377i	0.472232	−	0.881474i	$-0.343448\pi$
$577$	226.726	+	66.5727i	0.392939	+	0.115377i	−0.0792937	+	0.996851i	$0.525266\pi$
$578$	−384.439	−	333.118i	−0.665119	−	0.576329i
$579$		0			0
$580$	4.39625	−	30.5766i	0.00757974	−	0.0527182i
$581$	49.6149	+	77.2023i	0.0853957	+	0.132878i
$582$		0			0
$583$	−242.506	−	279.867i	−0.415963	−	0.480047i
$584$	162.594	−	23.3775i	0.278415	−	0.0400300i
$585$		0			0
$586$	−30.5379	+	8.96675i	−0.0521125	+	0.0153016i
$587$	107.861	+	367.341i	0.183749	+	0.625793i	0.998915	+	0.0465655i	$0.0148276\pi$
$587$	107.861	+	367.341i	0.183749	+	0.625793i	−0.815166	+	0.579228i	$0.803354\pi$
$588$		0			0
$589$	−74.9130	−	521.031i	−0.127187	−	0.884603i
$590$	33.4977	−	29.0259i	0.0567757	−	0.0491964i
$591$		0			0
$592$	−80.6475	+	51.8290i	−0.136229	+	0.0875490i
$593$	−672.429	−	96.6807i	−1.13394	−	0.163037i	−0.450317	−	0.892869i	$-0.648689\pi$
$593$	−672.429	−	96.6807i	−1.13394	−	0.163037i	−0.683627	+	0.729832i	$0.739598\pi$
$594$		0			0
$595$	−137.542	+	158.732i	−0.231163	+	0.266776i
$596$	−133.574	+	454.913i	−0.224118	+	0.763277i
$597$		0			0
$598$	−2.18789	+	574.342i	−0.00365868	+	0.960438i
$599$			231.331i			0.386196i	0.981180	+	0.193098i	$0.0618535\pi$
$599$			231.331i			0.386196i	−0.981180	+	0.193098i	$0.938147\pi$
$600$		0			0
$601$	−290.465	+	335.214i	−0.483302	+	0.557761i	−0.944064	−	0.329763i	$-0.893031\pi$
$601$	−290.465	+	335.214i	−0.483302	+	0.557761i	0.460761	+	0.887524i	$0.347576\pi$
$602$	136.154	−	211.860i	0.226170	−	0.351927i
$603$		0			0
$604$	94.3486	−	60.6341i	0.156206	−	0.100388i
$605$	142.454	−	65.0564i	0.235461	−	0.107531i
$606$		0			0
$607$	−78.0689	−	542.981i	−0.128614	−	0.894532i	−0.947313	−	0.320309i	$-0.896213\pi$
$607$	−78.0689	−	542.981i	−0.128614	−	0.894532i	0.818699	−	0.574223i	$-0.194696\pi$
$608$	62.1939	+	28.4030i	0.102293	+	0.0467155i
$609$		0			0
$610$	67.0512	−	19.6880i	0.109920	−	0.0322754i
$611$	1236.12	+	564.517i	2.02311	+	0.923924i
$612$		0			0
$613$	−467.674	−	539.725i	−0.762927	−	0.880465i	0.232827	−	0.972518i	$-0.425202\pi$
$613$	−467.674	−	539.725i	−0.762927	−	0.880465i	−0.995754	+	0.0920532i	$0.970657\pi$
$614$	−265.455	+	121.229i	−0.432337	+	0.197442i
$615$		0			0
$616$	−10.2472	+	71.2709i	−0.0166351	+	0.115699i
$617$	−239.708	+	372.993i	−0.388506	+	0.604527i	−0.979329	−	0.202274i	$-0.935167\pi$
$617$	−239.708	+	372.993i	−0.388506	+	0.604527i	0.590823	+	0.806801i	$0.298803\pi$
$618$		0			0
$619$	578.597	+	169.891i	0.934728	+	0.274461i	0.713415	−	0.700742i	$-0.247147\pi$
$619$	578.597	+	169.891i	0.934728	+	0.274461i	0.221313	+	0.975203i	$0.428966\pi$
$620$		−	143.249i		−	0.231046i
$621$		0			0
$622$	−190.505			−0.306278
$623$	53.4152	−	181.916i	0.0857388	−	0.291999i
$624$		0			0
$625$	361.287	+	232.185i	0.578059	+	0.371496i
$626$	407.388	+	58.5736i	0.650780	+	0.0935680i
$627$		0			0
$628$	231.174	+	506.200i	0.368111	+	0.806051i
$629$	−461.320	+	399.736i	−0.733418	+	0.635510i
$630$		0			0
$631$	−169.404	+	370.942i	−0.268468	+	0.587864i	−0.995068	−	0.0991975i	$-0.968372\pi$
$631$	−169.404	+	370.942i	−0.268468	+	0.587864i	0.726599	+	0.687061i	$0.241100\pi$
$632$	−66.5977	−	226.811i	−0.105376	−	0.358878i
$633$		0			0
$634$	−315.562	+	690.984i	−0.497731	+	1.08988i
$635$	398.121	−	57.2411i	0.626962	−	0.0901435i
$636$		0			0
$637$	−174.999	−	383.195i	−0.274724	−	0.601561i
$638$	−36.4561	−	56.7269i	−0.0571413	−	0.0889136i
$639$		0			0
$640$	15.6528	+	10.0594i	0.0244575	+	0.0157179i
$641$	417.703	+	361.941i	0.651642	+	0.564651i	0.916697	−	0.399582i	$-0.130845\pi$
$641$	417.703	+	361.941i	0.651642	+	0.564651i	−0.265055	+	0.964233i	$0.585390\pi$
$642$		0			0
$643$	14.6169			0.0227324			0.0113662	−	0.999935i	$-0.496382\pi$
$643$	14.6169			0.0227324			0.0113662	+	0.999935i	$0.496382\pi$
$644$	194.513	−	123.961i	0.302039	−	0.192487i
$645$		0			0
$646$	417.719	+	122.653i	0.646623	+	0.189866i
$647$	114.406	+	99.1330i	0.176825	+	0.153219i	0.738776	−	0.673951i	$-0.235404\pi$
$647$	114.406	+	99.1330i	0.176825	+	0.153219i	−0.561952	+	0.827170i	$0.689949\pi$
$648$		0			0
$649$	13.7695	−	95.7687i	0.0212164	−	0.147563i
$650$	−301.001	−	468.366i	−0.463078	−	0.720564i
$651$		0			0
$652$	−84.0471	−	96.9955i	−0.128907	−	0.148766i
$653$	−207.401	+	29.8198i	−0.317613	+	0.0456658i	−0.299278	−	0.954166i	$-0.596746\pi$
$653$	−207.401	+	29.8198i	−0.317613	+	0.0456658i	−0.0183352	+	0.999832i	$0.505837\pi$
$654$		0			0
$655$	−1.18582	+	0.348189i	−0.00181042	+	0.000531586i
$656$	64.4749	+	219.581i	0.0982850	+	0.334728i
$657$		0			0
$658$	−77.6667	−	540.184i	−0.118035	−	0.820948i
$659$	225.089	−	195.041i	0.341562	−	0.295965i	−0.467140	−	0.884183i	$-0.654716\pi$
$659$	225.089	−	195.041i	0.341562	−	0.295965i	0.808702	+	0.588218i	$0.200170\pi$
$660$		0			0
$661$	−914.942	+	587.998i	−1.38418	+	0.889558i	−0.999440	−	0.0334680i	$-0.989345\pi$
$661$	−914.942	+	587.998i	−1.38418	+	0.889558i	−0.384739	+	0.923026i	$0.625708\pi$
$662$	476.244	+	68.4735i	0.719401	+	0.103434i
$663$		0			0
$664$	33.8994	−	39.1220i	0.0510533	−	0.0589187i
$665$	28.0808	−	95.6344i	0.0422268	−	0.143811i
$666$		0			0
$667$	−61.6455	+	207.025i	−0.0924221	+	0.310382i
$668$			271.954i			0.407117i
$669$		0			0
$670$	53.7591	−	62.0413i	0.0802374	−	0.0925989i
$671$	82.4715	−	128.328i	0.122908	−	0.191249i
$672$		0			0
$673$	867.474	−	557.492i	1.28897	−	0.828368i	0.297000	−	0.954877i	$-0.404014\pi$
$673$	867.474	−	557.492i	1.28897	−	0.828368i	0.991965	+	0.126510i	$0.0403775\pi$
$674$	−16.3168	+	7.45164i	−0.0242089	+	0.0110558i
$675$		0			0
$676$	40.6421	+	282.672i	0.0601214	+	0.418154i
$677$	648.376	+	296.103i	0.957720	+	0.437376i	0.832053	−	0.554697i	$-0.187166\pi$
$677$	648.376	+	296.103i	0.957720	+	0.437376i	0.125667	+	0.992072i	$0.459893\pi$
$678$		0			0
$679$	404.558	−	118.789i	0.595814	−	0.174947i
$680$	107.768	+	49.2162i	0.158483	+	0.0723767i
$681$		0			0
$682$	−204.771	−	236.319i	−0.300251	−	0.346508i
$683$	1170.44	−	534.522i	1.71367	−	0.782609i	0.717372	−	0.696691i	$-0.245345\pi$
$683$	1170.44	−	534.522i	1.71367	−	0.782609i	0.996302	−	0.0859181i	$-0.0273824\pi$
$684$		0			0
$685$	19.8219	−	137.864i	0.0289371	−	0.201262i
$686$	−279.320	+	434.631i	−0.407173	+	0.633573i
$687$		0			0
$688$	−136.303	−	40.0220i	−0.198114	−	0.0581716i
$689$			1287.95i			1.86931i
$690$		0			0
$691$	279.271			0.404155			0.202077	−	0.979370i	$-0.435231\pi$
$691$	279.271			0.404155			0.202077	+	0.979370i	$0.435231\pi$
$692$	−104.079	+	354.462i	−0.150404	+	0.512228i
$693$		0			0
$694$	−545.991	−	350.887i	−0.786731	−	0.505601i
$695$	417.595	+	60.0412i	0.600857	+	0.0863902i
$696$		0			0
$697$	605.336	+	1325.50i	0.868487	+	1.90172i
$698$	404.427	−	350.438i	0.579409	−	0.502061i
$699$		0			0
$700$	−92.8818	+	203.383i	−0.132688	+	0.290547i
$701$	168.154	+	572.678i	0.239877	+	0.816945i	0.988142	+	0.153545i	$0.0490690\pi$
$701$	168.154	+	572.678i	0.239877	+	0.816945i	−0.748265	+	0.663400i	$0.769113\pi$
$702$		0			0
$703$	120.335	−	263.498i	0.171174	−	0.374819i
$704$	40.2024	−	5.78023i	0.0571057	−	0.00821056i
$705$		0			0
$706$	−150.583	−	329.731i	−0.213291	−	0.467041i
$707$	153.273	+	238.498i	0.216794	+	0.337338i
$708$		0			0
$709$	−20.2649	−	13.0235i	−0.0285824	−	0.0183688i	0.526272	−	0.850317i	$-0.323590\pi$
$709$	−20.2649	−	13.0235i	−0.0285824	−	0.0183688i	−0.554854	+	0.831948i	$0.687226\pi$
$710$	38.4588	+	33.3248i	0.0541674	+	0.0469363i
$711$		0			0
$712$	−106.947			−0.150206
$713$	−146.329	+	990.932i	−0.205231	+	1.38981i
$714$		0			0
$715$	141.461	+	41.5368i	0.197848	+	0.0580934i
$716$	261.749	+	226.807i	0.365571	+	0.316770i
$717$		0			0
$718$	−59.3787	+	412.988i	−0.0827001	+	0.575192i
$719$	543.038	+	844.983i	0.755268	+	1.17522i	0.979649	+	0.200718i	$0.0643276\pi$
$719$	543.038	+	844.983i	0.755268	+	1.17522i	−0.224381	+	0.974501i	$0.572036\pi$
$720$		0			0
$721$	42.7286	+	49.3115i	0.0592630	+	0.0683932i
$722$	300.838	−	43.2540i	0.416673	−	0.0599086i
$723$		0			0
$724$	−119.392	+	35.0568i	−0.164907	+	0.0484209i
$725$	−58.9918	−	200.908i	−0.0813680	−	0.277114i
$726$		0			0
$727$	−113.332	−	788.244i	−0.155891	−	1.08424i	−0.906107	−	0.423050i	$-0.860960\pi$
$727$	−113.332	−	788.244i	−0.155891	−	1.08424i	0.750216	−	0.661193i	$-0.229949\pi$
$728$	189.260	−	163.995i	0.259972	−	0.225267i
$729$		0			0
$730$	−113.633	+	73.0277i	−0.155662	+	0.100038i
$731$	−895.322	−	128.728i	−1.22479	−	0.176098i
$732$		0			0
$733$	−533.338	+	615.505i	−0.727610	+	0.839707i	−0.992200	−	0.124654i	$-0.960218\pi$
$733$	−533.338	+	615.505i	−0.727610	+	0.839707i	0.264590	+	0.964361i	$0.414763\pi$
$734$	−199.152	+	678.249i	−0.271324	+	0.924045i
$735$		0			0
$736$	−98.0035	−	85.5763i	−0.133157	−	0.116272i
$737$		−	179.198i		−	0.243145i
$738$		0			0
$739$	−738.970	+	852.817i	−0.999960	+	1.15401i	−0.0119021	+	0.999929i	$0.503789\pi$
$739$	−738.970	+	852.817i	−0.999960	+	1.15401i	−0.988057	+	0.154086i	$0.950757\pi$
$740$	42.6190	−	66.3165i	0.0575932	−	0.0896168i
$741$		0			0
$742$	435.127	−	279.639i	0.586425	−	0.376872i
$743$	−963.757	+	440.133i	−1.29712	+	0.592373i	−0.939837	−	0.341624i	$-0.889023\pi$
$743$	−963.757	+	440.133i	−1.29712	+	0.592373i	−0.357280	+	0.933997i	$0.616296\pi$
$744$		0			0
$745$	−55.4839	−	385.899i	−0.0744750	−	0.517985i
$746$	492.853	+	225.078i	0.660661	+	0.301714i
$747$		0			0
$748$	248.140	−	72.8606i	0.331738	−	0.0974072i
$749$	275.731	+	125.922i	0.368132	+	0.168120i
$750$		0			0
$751$	−608.551	−	702.305i	−0.810321	−	0.935160i	0.188579	−	0.982058i	$-0.439612\pi$
$751$	−608.551	−	702.305i	−0.810321	−	0.935160i	−0.998900	+	0.0468978i	$0.985067\pi$
$752$	−280.021	+	127.881i	−0.372368	+	0.170055i
$753$		0			0
$754$	−33.3762	+	232.137i	−0.0442656	+	0.307874i
$755$	−49.8595	+	77.5828i	−0.0660390	+	0.102759i
$756$		0			0
$757$	502.167	+	147.450i	0.663365	+	0.194781i	0.596046	−	0.802950i	$-0.296737\pi$
$757$	502.167	+	147.450i	0.663365	+	0.194781i	0.0673184	+	0.997732i	$0.478556\pi$
$758$		−	667.495i		−	0.880601i
$759$		0			0
$760$	−56.2228			−0.0739773
$761$	−54.7768	+	186.553i	−0.0719800	+	0.245141i	−0.987622	−	0.156854i	$-0.949865\pi$
$761$	−54.7768	+	186.553i	−0.0719800	+	0.245141i	0.915642	+	0.401995i	$0.131683\pi$
$762$		0			0
$763$	−573.343	−	368.465i	−0.751433	−	0.482917i
$764$	189.514	+	27.2480i	0.248055	+	0.0356649i
$765$		0			0
$766$	36.1904	+	79.2460i	0.0472460	+	0.103454i
$767$	−254.314	+	220.364i	−0.331570	+	0.287307i
$768$		0			0
$769$	113.650	−	248.859i	0.147789	−	0.323614i	−0.821230	−	0.570597i	$-0.806712\pi$
$769$	113.650	−	248.859i	0.147789	−	0.323614i	0.969020	+	0.246983i	$0.0794392\pi$
$770$	−16.6810	−	56.8103i	−0.0216637	−	0.0737797i
$771$		0			0
$772$	27.8197	−	60.9167i	0.0360359	−	0.0789076i
$773$	1010.31	−	145.260i	1.30699	−	0.187917i	0.546608	−	0.837389i	$-0.315919\pi$
$773$	1010.31	−	145.260i	1.30699	−	0.187917i	0.760386	+	0.649471i	$0.225010\pi$
$774$		0			0
$775$	−403.362	−	883.240i	−0.520468	−	1.13967i
$776$	−128.584	−	200.081i	−0.165701	−	0.257836i
$777$		0			0
$778$	493.031	+	316.852i	0.633716	+	0.407264i
$779$	−522.611	−	452.845i	−0.670875	−	0.581316i
$780$		0			0
$781$	111.083			0.142232
$782$	−695.220	−	450.542i	−0.889028	−	0.576141i
$783$		0			0
$784$	91.5640	+	26.8856i	0.116791	+	0.0342929i
$785$	−345.831	−	299.665i	−0.440550	−	0.381738i
$786$		0			0
$787$	−84.5004	+	587.713i	−0.107370	+	0.746776i	0.863009	+	0.505189i	$0.168577\pi$
$787$	−84.5004	+	587.713i	−0.107370	+	0.746776i	−0.970379	+	0.241588i	$0.922332\pi$
$788$	−298.704	−	464.793i	−0.379066	−	0.589839i
$789$		0			0
$790$	127.292	+	146.903i	0.161129	+	0.185953i
$791$	95.8275	−	13.7779i	0.121147	−	0.0174183i
$792$		0			0
$793$	−509.052	+	149.471i	−0.641932	+	0.188488i
$794$	263.762	+	898.292i	0.332194	+	1.13135i
$795$		0			0
$796$	−88.4793	−	615.387i	−0.111155	−	0.773099i
$797$	58.8618	−	51.0041i	0.0738542	−	0.0639950i	−0.617151	−	0.786844i	$-0.711713\pi$
$797$	58.8618	−	51.0041i	0.0738542	−	0.0639950i	0.691006	+	0.722849i	$0.257168\pi$
$798$		0			0
$799$	−1648.97	+	1059.73i	−2.06379	+	1.32632i
$800$	124.837	+	17.9489i	0.156047	+	0.0224361i
$801$		0			0
$802$	−35.2832	+	40.7190i	−0.0439940	+	0.0507718i
$803$	−83.0702	+	282.911i	−0.103450	+	0.352318i
$804$		0			0
$805$	−103.149	+	159.167i	−0.128136	+	0.197723i
$806$			1087.54i			1.34931i
$807$		0			0
$808$	104.724	−	120.858i	0.129609	−	0.149577i
$809$	58.3011	−	90.7182i	0.0720656	−	0.112136i	−0.803350	−	0.595507i	$-0.796951\pi$
$809$	58.3011	−	90.7182i	0.0720656	−	0.112136i	0.875416	+	0.483371i	$0.160588\pi$
$810$		0			0
$811$	−601.902	+	386.819i	−0.742173	+	0.476965i	−0.856286	−	0.516502i	$-0.827234\pi$
$811$	−601.902	+	386.819i	−0.742173	+	0.476965i	0.114113	+	0.993468i	$0.463597\pi$
$812$	85.6727	−	39.1254i	0.105508	−	0.0481840i
$813$		0			0
$814$	−24.4892	−	170.326i	−0.0300850	−	0.209246i
$815$	95.9997	+	43.8416i	0.117791	+	0.0537933i
$816$		0			0
$817$	411.861	−	120.933i	0.504114	−	0.148021i
$818$	643.362	+	293.814i	0.786507	+	0.359186i
$819$		0			0
$820$	−123.235	−	142.220i	−0.150286	−	0.173440i
$821$	540.909	−	247.025i	0.658842	−	0.300883i	−0.0577962	−	0.998328i	$-0.518407\pi$
$821$	540.909	−	247.025i	0.658842	−	0.300883i	0.716638	+	0.697446i	$0.245680\pi$
$822$		0			0
$823$	−92.3729	+	642.468i	−0.112239	+	0.780641i	0.853494	+	0.521103i	$0.174479\pi$
$823$	−92.3729	+	642.468i	−0.112239	+	0.780641i	−0.965733	+	0.259538i	$0.916430\pi$
$824$	19.8984	−	30.9626i	0.0241486	−	0.0375759i
$825$		0			0
$826$	129.665	+	38.0731i	0.156980	+	0.0460934i
$827$		−	331.831i		−	0.401247i	−0.979668	−	0.200623i	$-0.935703\pi$
$827$		−	331.831i		−	0.401247i	0.979668	−	0.200623i	$-0.0642968\pi$
$828$		0			0
$829$	750.641			0.905478			0.452739	−	0.891643i	$-0.350447\pi$
$829$	750.641			0.905478			0.452739	+	0.891643i	$0.350447\pi$
$830$	−11.9925	+	40.8428i	−0.0144488	+	0.0492081i
$831$		0			0
$832$	−118.836	−	76.3712i	−0.142832	−	0.0917923i
$833$	601.451	+	86.4756i	0.722030	+	0.103812i
$834$		0			0
$835$	−92.8984	−	203.419i	−0.111256	−	0.243616i
$836$	−92.7513	+	80.3695i	−0.110947	+	0.0961357i
$837$		0			0
$838$	105.081	−	230.095i	0.125395	−	0.274576i
$839$	−405.861	−	1382.24i	−0.483744	−	1.64748i	−0.733887	−	0.679271i	$-0.762296\pi$
$839$	−405.861	−	1382.24i	−0.483744	−	1.64748i	0.250143	−	0.968209i	$-0.419522\pi$
$840$		0			0
$841$	312.723	−	684.768i	0.371847	−	0.814231i
$842$	885.672	−	127.340i	1.05187	−	0.151236i
$843$		0			0
$844$	253.796	+	555.735i	0.300706	+	0.658454i
$845$	−126.959	−	197.553i	−0.150248	−	0.233790i
$846$		0			0
$847$	401.680	+	258.144i	0.474238	+	0.304774i
$848$	−220.499	−	191.064i	−0.260023	−	0.225311i
$849$		0			0
$850$	803.061			0.944777
$851$	−362.562	+	415.213i	−0.426043	+	0.487912i
$852$		0			0
$853$	314.789	+	92.4305i	0.369038	+	0.108359i	0.460993	−	0.887404i	$-0.347493\pi$
$853$	314.789	+	92.4305i	0.369038	+	0.108359i	−0.0919549	+	0.995763i	$0.529312\pi$
$854$	161.023	+	139.527i	0.188551	+	0.163381i
$855$		0			0
$856$	24.3338	−	169.245i	0.0284274	−	0.197717i
$857$	317.415	+	493.907i	0.370379	+	0.576321i	0.975551	−	0.219774i	$-0.0705319\pi$
$857$	317.415	+	493.907i	0.370379	+	0.576321i	−0.605172	+	0.796095i	$0.706896\pi$
$858$		0			0
$859$	9.06121	+	10.4572i	0.0105486	+	0.0121737i	0.760999	−	0.648753i	$-0.224709\pi$
$859$	9.06121	+	10.4572i	0.0105486	+	0.0121737i	−0.750451	+	0.660926i	$0.770164\pi$
$860$	115.624	−	16.6243i	0.134447	−	0.0193306i
$861$		0			0
$862$	−106.315	+	31.2168i	−0.123335	+	0.0362143i
$863$	−165.250	−	562.791i	−0.191484	−	0.652133i	−0.998132	−	0.0611010i	$-0.980539\pi$
$863$	−165.250	−	562.791i	−0.191484	−	0.652133i	0.806648	−	0.591032i	$-0.201279\pi$
$864$		0			0
$865$	−43.2323	−	300.687i	−0.0499795	−	0.347615i
$866$	−810.777	+	702.543i	−0.936233	+	0.811250i
$867$		0			0
$868$	367.419	−	236.126i	0.423294	−	0.272035i
$869$	419.990	+	60.3855i	0.483303	+	0.0694885i
$870$		0			0
$871$	−408.138	+	471.016i	−0.468586	+	0.540776i
$872$	−108.309	+	368.867i	−0.124208	+	0.423012i
$873$		0			0
$874$	388.925	+	57.4320i	0.444994	+	0.0657116i
$875$		−	390.017i		−	0.445733i
$876$		0			0
$877$	−456.443	+	526.763i	−0.520459	+	0.600642i	−0.953746	−	0.300614i	$-0.902808\pi$
$877$	−456.443	+	526.763i	−0.520459	+	0.600642i	0.433287	+	0.901256i	$0.357354\pi$
$878$	174.087	−	270.885i	0.198277	−	0.308525i
$879$		0			0
$880$	−28.0965	+	18.0565i	−0.0319279	+	0.0205188i
$881$	−1206.83	+	551.141i	−1.36984	+	0.625586i	−0.958289	−	0.285800i	$-0.907741\pi$
$881$	−1206.83	+	551.141i	−1.36984	+	0.625586i	−0.411553	+	0.911386i	$0.635013\pi$
$882$		0			0
$883$	−130.008	−	904.224i	−0.147234	−	1.02404i	−0.920720	−	0.390223i	$-0.872398\pi$
$883$	−130.008	−	904.224i	−0.147234	−	1.02404i	0.773486	−	0.633813i	$-0.218511\pi$
$884$	−818.176	−	373.648i	−0.925538	−	0.422679i
$885$		0			0
$886$	−482.480	+	141.669i	−0.544560	+	0.159897i
$887$	−1032.50	−	471.526i	−1.16403	−	0.531597i	−0.262767	−	0.964859i	$-0.584635\pi$
$887$	−1032.50	−	471.526i	−1.16403	−	0.531597i	−0.901268	+	0.433263i	$0.857362\pi$
$888$		0			0
$889$	803.067	+	926.788i	0.903337	+	1.04251i
$890$	79.9952	−	36.5326i	0.0898823	−	0.0410479i
$891$		0			0
$892$	−49.1686	+	341.975i	−0.0551218	+	0.383380i
$893$	502.899	−	782.525i	0.563156	−	0.876288i
$894$		0			0
$895$	−273.262	−	80.2370i	−0.305321	−	0.0896503i
$896$			56.7296i			0.0633143i
$897$		0			0
$898$	−336.372			−0.374579
$899$	−115.233	+	392.449i	−0.128180	+	0.436540i
$900$		0			0
$901$	−1562.85	−	1004.38i	−1.73457	−	1.11474i
$902$	−406.603	−	58.4607i	−0.450780	−	0.0648124i
$903$		0			0
$904$	−22.6859	−	49.6751i	−0.0250950	−	0.0549503i
$905$	77.3291	−	67.0060i	0.0854465	−	0.0740398i
$906$		0			0
$907$	−338.223	+	740.604i	−0.372903	+	0.816543i	0.626411	+	0.779493i	$0.284523\pi$
$907$	−338.223	+	740.604i	−0.372903	+	0.816543i	−0.999313	+	0.0370498i	$0.988204\pi$
$908$	1.59870	+	5.44468i	0.00176069	+	0.00599635i
$909$		0			0
$910$	−85.5447	+	187.317i	−0.0940052	+	0.205843i
$911$	1066.16	−	153.290i	1.17031	−	0.168266i	0.470374	−	0.882467i	$-0.344119\pi$
$911$	1066.16	−	153.290i	1.17031	−	0.168266i	0.699940	+	0.714201i	$0.253210\pi$
$912$		0			0
$913$	38.5998	+	84.5218i	0.0422780	+	0.0925759i
$914$	−563.045	−	876.115i	−0.616023	−	0.958550i
$915$		0			0
$916$	386.433	+	248.345i	0.421870	+	0.271119i
$917$	−2.84774	−	2.46758i	−0.00310550	−	0.00269093i
$918$		0			0
$919$	−552.642			−0.601351			−0.300676	−	0.953726i	$-0.597212\pi$
$919$	−552.642			−0.601351			−0.300676	+	0.953726i	$0.597212\pi$
$920$	102.538	+	30.5327i	0.111455	+	0.0331877i
$921$		0			0
$922$	−572.570	−	168.122i	−0.621008	−	0.182344i
$923$	−291.979	−	253.001i	−0.316337	−	0.274107i
$924$		0			0
$925$	76.0444	−	528.901i	0.0822102	−	0.571784i
$926$	345.933	+	538.283i	0.373578	+	0.581299i
$927$		0			0
$928$	−34.7909	−	40.1508i	−0.0374902	−	0.0432660i
$929$	−463.342	+	66.6186i	−0.498754	+	0.0717100i	−0.387101	−	0.922037i	$-0.626524\pi$
$929$	−463.342	+	66.6186i	−0.498754	+	0.0717100i	−0.111653	+	0.993747i	$0.535614\pi$
$930$		0			0
$931$	−276.676	+	81.2395i	−0.297182	+	0.0872604i
$932$	184.606	+	628.711i	0.198075	+	0.674583i
$933$		0			0
$934$	−146.548	−	1019.26i	−0.156904	−	1.09129i
$935$	−160.718	+	139.263i	−0.171891	+	0.148944i
$936$		0			0
$937$	−632.931	+	406.760i	−0.675487	+	0.434109i	−0.832900	−	0.553424i	$-0.813321\pi$
$937$	−632.931	+	406.760i	−0.675487	+	0.434109i	0.157413	+	0.987533i	$0.449685\pi$
$938$	247.745	+	35.6203i	0.264120	+	0.0379747i
$939$		0			0
$940$	165.769	−	191.308i	0.176350	−	0.203519i
$941$	57.7076	−	196.534i	0.0613258	−	0.208856i	−0.923130	−	0.384487i	$-0.874378\pi$
$941$	57.7076	−	196.534i	0.0613258	−	0.208856i	0.984456	+	0.175631i	$0.0561965\pi$
$942$		0			0
$943$	707.205	+	1109.70i	0.749953	+	1.17678i
$944$		−	76.2292i		−	0.0807513i
$945$		0			0
$946$	166.983	−	192.708i	0.176514	−	0.203709i
$947$	850.836	−	1323.93i	0.898454	−	1.39802i	−0.0188450	−	0.999822i	$-0.505999\pi$
$947$	850.836	−	1323.93i	0.898454	−	1.39802i	0.917299	−	0.398199i	$-0.130365\pi$
$948$		0			0
$949$	862.702	−	554.425i	0.909064	−	0.584220i
$950$	−346.658	+	158.313i	−0.364903	+	0.166646i
$951$		0			0
$952$	51.4068	+	357.542i	0.0539987	+	0.375569i
$953$	−1363.64	−	622.752i	−1.43089	−	0.653465i	−0.458899	−	0.888488i	$-0.651756\pi$
$953$	−1363.64	−	622.752i	−1.43089	−	0.653465i	−0.971990	+	0.235023i	$0.924483\pi$
$954$		0			0
$955$	−151.062	+	44.3559i	−0.158180	+	0.0464460i
$956$	413.542	+	188.858i	0.432575	+	0.197551i
$957$		0			0
$958$	741.166	+	855.351i	0.773659	+	0.892850i
$959$	386.283	−	176.409i	0.402797	−	0.183951i
$960$		0			0
$961$	−133.165	+	926.182i	−0.138569	+	0.963769i
$962$	−323.563	+	503.474i	−0.336344	+	0.523361i
$963$		0			0
$964$	573.567	+	168.414i	0.594986	+	0.174704i
$965$			55.0682i			0.0570655i
$966$		0			0
$967$	1681.05			1.73842			0.869208	−	0.494447i	$-0.164629\pi$
$967$	1681.05			1.73842			0.869208	+	0.494447i	$0.164629\pi$
$968$	75.8804	−	258.425i	0.0783889	−	0.266968i
$969$		0			0
$970$	164.526	+	105.735i	0.169615	+	0.109005i
$971$	−1487.00	−	213.798i	−1.53141	−	0.220183i	−0.675519	−	0.737342i	$-0.736080\pi$
$971$	−1487.00	−	213.798i	−1.53141	−	0.220183i	−0.855889	+	0.517159i	$0.826990\pi$
$972$		0			0
$973$	534.350	+	1170.06i	0.549178	+	1.20253i
$974$	82.0745	−	71.1180i	0.0842654	−	0.0730164i
$975$		0			0
$976$	49.9266	−	109.324i	0.0511543	−	0.112012i
$977$	80.8084	+	275.208i	0.0827108	+	0.281687i	0.990455	−	0.137837i	$-0.0440151\pi$
$977$	80.8084	+	275.208i	0.0827108	+	0.281687i	−0.907744	+	0.419524i	$0.862197\pi$
$978$		0			0
$979$	79.7463	−	174.620i	0.0814569	−	0.178366i
$980$	−77.6730	+	11.1677i	−0.0792582	+	0.0113956i
$981$		0			0
$982$	−342.107	−	749.109i	−0.348377	−	0.762840i
$983$	−448.645	−	698.106i	−0.456404	−	0.710179i	0.534438	−	0.845208i	$-0.320523\pi$
$983$	−448.645	−	698.106i	−0.456404	−	0.710179i	−0.990842	+	0.135029i	$0.956887\pi$
$984$		0			0
$985$	382.199	+	245.625i	0.388020	+	0.249365i
$986$	−255.655	−	221.527i	−0.259285	−	0.224672i
$987$		0			0
$988$	426.842			0.432027
$989$	−816.821	−	3.11159i	−0.825906	−	0.00314620i
$990$		0			0
$991$	−1660.58	−	487.589i	−1.67566	−	0.492017i	−0.700522	−	0.713631i	$-0.747049\pi$
$991$	−1660.58	−	487.589i	−1.67566	−	0.492017i	−0.975134	+	0.221614i	$0.928867\pi$
$992$	−186.189	−	161.333i	−0.187690	−	0.162634i
$993$		0			0
$994$	−22.0807	+	153.575i	−0.0222140	+	0.154502i
$995$	276.395	+	430.080i	0.277784	+	0.432241i
$996$		0			0
$997$	−461.173	−	532.222i	−0.462560	−	0.533823i	0.475767	−	0.879571i	$-0.342171\pi$
$997$	−461.173	−	532.222i	−0.462560	−	0.533823i	−0.938327	+	0.345748i	$0.887625\pi$
$998$	95.6866	−	13.7577i	0.0958783	−	0.0137852i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.3.k.a.179.3	✓	80
3.2	odd	2	inner	414.3.k.a.179.6	yes	80
23.9	even	11	inner	414.3.k.a.377.6	yes	80
69.32	odd	22	inner	414.3.k.a.377.3	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.3.k.a.179.3	✓	80	1.1	even	1	trivial
414.3.k.a.179.6	yes	80	3.2	odd	2	inner
414.3.k.a.377.3	yes	80	69.32	odd	22	inner
414.3.k.a.377.6	yes	80	23.9	even	11	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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	414.k (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.398430 + 1.35693i) q^{2} +(-1.68251 - 1.08128i) q^{4} +(1.62786 + 0.234051i) q^{5} +(2.08299 + 4.56111i) q^{7} +(2.13758 - 1.85223i) q^{8} +O(q^{10})\)	\(q+(-0.398430 + 1.35693i) q^{2} +(-1.68251 - 1.08128i) q^{4} +(1.62786 + 0.234051i) q^{5} +(2.08299 + 4.56111i) q^{7} +(2.13758 - 1.85223i) q^{8} +(-0.966179 + 2.11564i) q^{10} +(1.43035 + 4.87132i) q^{11} +(7.33521 - 16.0619i) q^{13} +(-7.01903 + 1.00918i) q^{14} +(1.66166 + 3.63853i) q^{16} +(13.7698 + 21.4263i) q^{17} +(-10.1680 - 6.53455i) q^{19} +(-2.48581 - 2.15397i) q^{20} -7.17993 q^{22} +(14.9955 + 17.4395i) q^{23} +(-21.3922 - 6.28131i) q^{25} +(18.8722 + 16.3529i) q^{26} +(1.42720 - 9.92640i) q^{28} +(5.07751 + 7.90075i) q^{29} +(28.5200 + 32.9138i) q^{31} +(-5.59928 + 0.805054i) q^{32} +(-34.5603 + 10.1478i) q^{34} +(2.32328 + 7.91238i) q^{35} +(3.41078 + 23.7225i) q^{37} +(12.9181 - 11.1936i) q^{38} +(3.91320 - 2.51486i) q^{40} +(56.6306 + 8.14224i) q^{41} +(-23.2569 + 26.8399i) q^{43} +(2.86070 - 9.74265i) q^{44} +(-29.6388 + 13.3994i) q^{46} +76.9599i q^{47} +(15.6233 - 18.0302i) q^{49} +(17.0466 - 26.5250i) q^{50} +(-29.7090 + 19.0928i) q^{52} +(-66.3491 + 30.3006i) q^{53} +(1.18827 + 8.26461i) q^{55} +(12.9008 + 5.89159i) q^{56} +(-12.7438 + 3.74191i) q^{58} +(-17.3351 - 7.91669i) q^{59} +(-19.6761 - 22.7074i) q^{61} +(-56.0249 + 25.5857i) q^{62} +(1.13852 - 7.91857i) q^{64} +(15.7000 - 24.4297i) q^{65} +(-33.8664 - 9.94408i) q^{67} -50.9390i q^{68} -11.6622 q^{70} +(6.16424 - 20.9935i) q^{71} +(48.8574 + 31.3987i) q^{73} +(-33.5487 - 4.82358i) q^{74} +(10.0420 + 21.9889i) q^{76} +(-19.2393 + 16.6709i) q^{77} +(34.7184 - 76.0226i) q^{79} +(1.85335 + 6.31193i) q^{80} +(-33.6117 + 73.5995i) q^{82} +(18.1157 - 2.60464i) q^{83} +(17.4005 + 38.1019i) q^{85} +(-27.1535 - 42.2517i) q^{86} +(12.0803 + 7.76353i) q^{88} +(-28.5760 - 24.7612i) q^{89} +88.5392 q^{91} +(-6.37299 - 45.5564i) q^{92} +(-104.429 - 30.6631i) q^{94} +(-15.0226 - 13.0172i) q^{95} +(11.9670 - 83.2320i) q^{97} +(18.2409 + 28.3834i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 16 q^{4} - 16 q^{7}+O(q^{10}) \) 80 * q + 16 * q^4 - 16 * q^7	\( 80 q + 16 q^{4} - 16 q^{7} + 8 q^{10} + 8 q^{13} - 32 q^{16} - 128 q^{19} - 32 q^{22} - 352 q^{25} + 32 q^{28} + 32 q^{31} - 300 q^{34} - 384 q^{37} - 16 q^{40} + 540 q^{43} - 80 q^{49} - 16 q^{52} + 1244 q^{55} + 424 q^{58} + 568 q^{61} + 64 q^{64} + 60 q^{67} + 296 q^{70} + 36 q^{73} - 96 q^{76} - 1476 q^{79} + 12 q^{82} - 276 q^{85} - 112 q^{88} - 368 q^{91} - 304 q^{94} + 712 q^{97}+O(q^{100}) \) 80 * q + 16 * q^4 - 16 * q^7 + 8 * q^10 + 8 * q^13 - 32 * q^16 - 128 * q^19 - 32 * q^22 - 352 * q^25 + 32 * q^28 + 32 * q^31 - 300 * q^34 - 384 * q^37 - 16 * q^40 + 540 * q^43 - 80 * q^49 - 16 * q^52 + 1244 * q^55 + 424 * q^58 + 568 * q^61 + 64 * q^64 + 60 * q^67 + 296 * q^70 + 36 * q^73 - 96 * q^76 - 1476 * q^79 + 12 * q^82 - 276 * q^85 - 112 * q^88 - 368 * q^91 - 304 * q^94 + 712 * q^97

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