LMFDB - Embedded newform 414.3.k.a.377.3

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			377.3
Character	$\chi$	$=$	414.377
Dual form			414.3.k.a.179.3

$q$-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 $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$-1$	$e\left(\frac{5}{11}\right)$

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	0.0224090	−	0.999749i	$-0.492866\pi$
$5$	1.62786	−	0.234051i	0.325572	−	0.0468102i	0.303163	+	0.952939i	$0.401957\pi$
$6$		0			0
$7$	2.08299	−	4.56111i	0.297570	−	0.651588i	−0.700502	−	0.713650i	$-0.747041\pi$
$7$	2.08299	−	4.56111i	0.297570	−	0.651588i	0.998072	+	0.0620627i	$0.0197679\pi$
$8$	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	−0.868578	−	0.495552i	$-0.834966\pi$
$11$	1.43035	−	4.87132i	0.130032	−	0.442848i	0.998610	+	0.0527042i	$0.0167840\pi$
$12$		0			0
$13$	7.33521	+	16.0619i	0.564247	+	1.23553i	0.949804	+	0.312845i	$0.101282\pi$
$13$	7.33521	+	16.0619i	0.564247	+	1.23553i	−0.385557	+	0.922684i	$0.625991\pi$
$14$	−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	−0.152296	−	0.988335i	$-0.548667\pi$
$17$	13.7698	−	21.4263i	0.809991	−	1.26037i	0.962287	−	0.272035i	$-0.0876968\pi$
$18$		0			0
$19$	−10.1680	+	6.53455i	−0.535156	+	0.343924i	−0.780142	−	0.625603i	$-0.784853\pi$
$19$	−10.1680	+	6.53455i	−0.535156	+	0.343924i	0.244986	+	0.969527i	$0.421217\pi$
$20$	−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	−0.742608	−	0.669726i	$-0.766412\pi$
$29$	5.07751	−	7.90075i	0.175086	−	0.272440i	0.917695	+	0.397286i	$0.130048\pi$
$30$		0			0
$31$	28.5200	−	32.9138i	0.919999	−	1.06174i	−0.0779010	−	0.996961i	$-0.524822\pi$
$31$	28.5200	−	32.9138i	0.919999	−	1.06174i	0.997900	−	0.0647743i	$-0.0206327\pi$
$32$	−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	−0.890380	−	0.455219i	$-0.849561\pi$
$37$	3.41078	−	23.7225i	0.0921834	−	0.641149i	0.982563	−	0.185930i	$-0.0595299\pi$
$38$	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	0.588666	−	0.808376i	$-0.299653\pi$
$41$	56.6306	−	8.14224i	1.38123	−	0.198591i	0.792567	+	0.609785i	$0.208744\pi$
$42$		0			0
$43$	−23.2569	−	26.8399i	−0.540857	−	0.624183i	0.417871	−	0.908506i	$-0.362776\pi$
$43$	−23.2569	−	26.8399i	−0.540857	−	0.624183i	−0.958728	+	0.284324i	$0.908231\pi$
$44$	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	$-0.694683\pi$
$47$		−	76.9599i		−	1.63745i	0.574189	−	0.818723i	$-0.305317\pi$
$48$		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	−0.324510	−	0.945882i	$-0.605199\pi$
$53$	−66.3491	−	30.3006i	−1.25187	−	0.571710i	−0.927359	+	0.374173i	$0.877927\pi$
$54$		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	−0.556869	−	0.830600i	$-0.687998\pi$
$59$	−17.3351	+	7.91669i	−0.293816	+	0.134181i	0.263054	+	0.964781i	$0.415270\pi$
$60$		0			0
$61$	−19.6761	+	22.7074i	−0.322559	+	0.372253i	−0.893751	−	0.448564i	$-0.851936\pi$
$61$	−19.6761	+	22.7074i	−0.322559	+	0.372253i	0.571192	+	0.820816i	$0.306481\pi$
$62$	−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	−0.524518	−	0.851400i	$-0.675754\pi$
$67$	−33.8664	+	9.94408i	−0.505469	+	0.148419i	0.0190489	+	0.999819i	$0.493936\pi$
$68$			50.9390i			0.749103i
$69$		0			0
$70$	−11.6622			−0.166603
$71$	6.16424	+	20.9935i	0.0868203	+	0.295683i	0.991445	−	0.130527i	$-0.0416668\pi$
$71$	6.16424	+	20.9935i	0.0868203	+	0.295683i	−0.904624	+	0.426210i	$0.859849\pi$
$72$		0			0
$73$	48.8574	−	31.3987i	0.669279	−	0.430120i	−0.161386	−	0.986891i	$-0.551597\pi$
$73$	48.8574	−	31.3987i	0.669279	−	0.430120i	0.830666	+	0.556772i	$0.187960\pi$
$74$	−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	0.991695	+	0.128615i	$0.0410530\pi$
$79$	34.7184	+	76.0226i	0.439473	+	0.962312i	−0.552222	+	0.833697i	$0.686220\pi$
$80$	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	0.250578	−	0.968096i	$-0.419379\pi$
$83$	18.1157	+	2.60464i	0.218261	+	0.0313812i	−0.0323166	+	0.999478i	$0.510288\pi$
$84$		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	−0.800454	−	0.599394i	$-0.795408\pi$
$89$	−28.5760	+	24.7612i	−0.321078	+	0.278216i	0.479376	+	0.877610i	$0.340863\pi$
$90$		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	0.953694	+	0.300780i	$0.0972468\pi$
$97$	11.9670	+	83.2320i	0.123371	+	0.858062i	−0.830323	+	0.557282i	$0.811844\pi$
$98$	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	0.413677	−	0.910424i	$-0.364244\pi$
$101$	55.9642	+	8.04643i	0.554101	+	0.0796676i	0.140424	+	0.990091i	$0.455153\pi$
$102$		0			0
$103$	12.4855	+	3.66608i	0.121219	+	0.0355930i	0.341779	−	0.939780i	$-0.388970\pi$
$103$	12.4855	+	3.66608i	0.121219	+	0.0355930i	−0.220561	+	0.975373i	$0.570789\pi$
$104$	−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	0.841679	−	0.539978i	$-0.181567\pi$
$107$	45.6870	+	39.5880i	0.426982	+	0.369982i	−0.414698	+	0.909959i	$0.636113\pi$
$108$		0			0
$109$	−114.343	−	73.4838i	−1.04902	−	0.674163i	−0.101818	−	0.994803i	$-0.532466\pi$
$109$	−114.343	−	73.4838i	−1.04902	−	0.674163i	−0.947201	+	0.320640i	$0.896102\pi$
$110$	−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	0.980054	−	0.198731i	$-0.0636821\pi$
$113$	5.43958	+	18.5255i	0.0481379	+	0.163942i	−0.931916	+	0.362674i	$0.881864\pi$
$114$		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	0.999925	+	0.0122100i	$0.00388667\pi$
$127$	234.660	+	68.9024i	1.84772	+	0.542539i	0.847792	+	0.530329i	$0.177932\pi$
$128$	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	0.412804	−	0.910820i	$-0.364549\pi$
$131$	−0.683570	−	0.312176i	−0.00521809	−	0.00238302i	−0.418022	+	0.908437i	$0.637277\pi$
$132$		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	$0.100024\pi$
$137$			84.6905i			0.618179i	−0.951033	+	0.309089i	$0.899976\pi$
$138$		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	0.357290	+	0.933993i	$0.383701\pi$
$149$	−66.7872	+	227.456i	−0.448236	+	1.52655i	−0.805527	+	0.592560i	$0.798117\pi$
$150$		0			0
$151$	−23.2949	−	51.0087i	−0.154271	−	0.337806i	0.816678	−	0.577094i	$-0.195813\pi$
$151$	−23.2949	−	51.0087i	−0.154271	−	0.337806i	−0.970949	+	0.239288i	$0.923086\pi$
$152$	−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	−0.494904	+	0.868948i	$0.664797\pi$
$157$	−234.074	+	150.430i	−1.49092	+	0.958154i	−0.996013	+	0.0892065i	$0.971567\pi$
$158$	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	−0.0873482	−	0.996178i	$-0.527839\pi$
$163$	61.5723	−	18.0793i	0.377744	−	0.110916i	0.465092	+	0.885262i	$0.346021\pi$
$164$	−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	−0.988485	−	0.151320i	$-0.951648\pi$
$167$	−73.5147	+	114.391i	−0.440208	+	0.684977i	0.548277	+	0.836297i	$0.315284\pi$
$168$		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	0.660922	+	0.750455i	$0.270165\pi$
$173$	−52.0397	+	177.231i	−0.300807	+	1.02446i	−0.961729	+	0.274001i	$0.911653\pi$
$174$		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	−0.603354	−	0.797473i	$-0.706169\pi$
$179$	−171.409	+	24.6449i	−0.957594	+	0.137681i	−0.354240	+	0.935155i	$0.615260\pi$
$180$		0			0
$181$	40.7431	+	47.0200i	0.225100	+	0.259779i	0.857054	−	0.515227i	$-0.172292\pi$
$181$	40.7431	+	47.0200i	0.225100	+	0.259779i	−0.631954	+	0.775006i	$0.717747\pi$
$182$	−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	0.174200	−	0.984710i	$-0.444266\pi$
$191$	−87.0803	−	39.7682i	−0.455918	−	0.208211i	−0.630118	+	0.776500i	$0.716993\pi$
$192$		0			0
$193$	4.76530	−	33.1434i	0.0246907	−	0.171728i	−0.973745	−	0.227642i	$-0.926898\pi$
$193$	4.76530	−	33.1434i	0.0246907	−	0.171728i	0.998436	+	0.0559146i	$0.0178075\pi$
$194$	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	0.341582	−	0.939852i	$-0.389037\pi$
$197$	251.286	−	114.759i	1.27556	−	0.582531i	0.933982	+	0.357321i	$0.116310\pi$
$198$		0			0
$199$	203.568	−	234.931i	1.02296	−	1.18056i	0.0395362	−	0.999218i	$-0.487412\pi$
$199$	203.568	−	234.931i	1.02296	−	1.18056i	0.983421	−	0.181337i	$-0.0580426\pi$
$200$	−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	−0.981966	−	0.189060i	$-0.939456\pi$
$211$	−256.980	+	165.151i	−1.21791	+	0.782706i	−0.235948	+	0.971766i	$0.575820\pi$
$212$	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	−0.999530	−	0.0306682i	$-0.990236\pi$
$223$	−71.7613	+	157.135i	−0.321799	+	0.704642i	0.677730	+	0.735311i	$0.262964\pi$
$224$	−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	−0.659571	−	0.751642i	$-0.729262\pi$
$227$	−2.14427	+	1.85802i	−0.00944610	+	0.00818510i	0.650125	+	0.759827i	$0.274717\pi$
$228$		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	−0.997029	−	0.0770279i	$-0.975457\pi$
$233$	−247.604	+	214.550i	−1.06268	+	0.920815i	−0.0656482	+	0.997843i	$0.520912\pi$
$234$		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	−0.345517	−	0.938413i	$-0.612296\pi$
$239$	−224.999	−	32.3500i	−0.941419	−	0.135356i	−0.595902	+	0.803057i	$0.703205\pi$
$240$		0			0
$241$	−286.783	−	84.2072i	−1.18997	−	0.349407i	−0.373961	−	0.927444i	$-0.622001\pi$
$241$	−286.783	−	84.2072i	−1.18997	−	0.349407i	−0.816011	+	0.578037i	$0.803819\pi$
$242$	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	−0.799070	−	0.601238i	$-0.794674\pi$
$251$	−113.428	−	386.300i	−0.451903	−	1.53904i	0.347166	−	0.937804i	$-0.387144\pi$
$252$		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	0.984374	−	0.176090i	$-0.0563450\pi$
$257$	106.725	+	166.068i	0.415273	+	0.646177i	−0.569101	+	0.822268i	$0.692709\pi$
$258$		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	0.00588769	−	0.999983i	$-0.498126\pi$
$263$	201.321	−	91.9403i	0.765480	−	0.349583i	0.759592	+	0.650400i	$0.225399\pi$
$264$		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	0.343069	−	0.939310i	$-0.388533\pi$
$269$	−38.2388	−	17.4631i	−0.142151	−	0.0649184i	−0.485221	+	0.874392i	$0.661261\pi$
$270$		0			0
$271$	2.43994	+	16.9701i	0.00900346	+	0.0626204i	0.993828	−	0.110933i	$-0.0353840\pi$
$271$	2.43994	+	16.9701i	0.00900346	+	0.0626204i	−0.984824	+	0.173554i	$0.944475\pi$
$272$	−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	−0.406450	−	0.913673i	$-0.633233\pi$
$281$	−151.466	+	21.7775i	−0.539024	+	0.0775000i	−0.132574	+	0.991173i	$0.542324\pi$
$282$		0			0
$283$	125.960	−	275.815i	0.445090	−	0.974611i	−0.545546	−	0.838081i	$-0.683678\pi$
$283$	125.960	−	275.815i	0.445090	−	0.974611i	0.990636	−	0.136530i	$-0.0435950\pi$
$284$	−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	−0.819870	−	0.572550i	$-0.805954\pi$
$293$	12.1672	−	18.9326i	0.0415264	−	0.0646163i	0.861396	+	0.507934i	$0.169591\pi$
$294$		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	−0.491706	−	0.870761i	$-0.663626\pi$
$307$	135.132	−	155.951i	0.440170	−	0.507983i	0.931875	+	0.362778i	$0.118172\pi$
$308$	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	−0.875706	−	0.482845i	$-0.839604\pi$
$311$	37.9514	−	129.251i	0.122030	−	0.415597i	0.997736	+	0.0672478i	$0.0214218\pi$
$312$		0			0
$313$	−41.4178	+	288.067i	−0.132325	+	0.920342i	0.810187	+	0.586171i	$0.199365\pi$
$313$	−41.4178	+	288.067i	−0.132325	+	0.920342i	−0.942513	+	0.334171i	$0.891544\pi$
$314$	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	0.762997	−	0.646402i	$-0.223727\pi$
$317$	531.672	−	76.4429i	1.67720	−	0.241145i	0.914203	+	0.405257i	$0.132818\pi$
$318$		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	0.775965	+	0.630776i	$0.217263\pi$
$331$	−48.4181	+	336.755i	−0.146278	+	1.01739i	−0.922243	+	0.386611i	$0.873646\pi$
$332$	−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	−0.743292	−	0.668967i	$-0.766737\pi$
$337$	8.30622	−	9.58589i	0.0246475	−	0.0284448i	0.767940	+	0.640522i	$0.221282\pi$
$338$	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	−0.906058	−	0.423153i	$-0.860923\pi$
$347$	−129.295	−	440.337i	−0.372607	−	1.26898i	0.533451	−	0.845831i	$-0.320895\pi$
$348$		0			0
$349$	−318.328	+	204.577i	−0.912114	+	0.586180i	−0.910359	−	0.413819i	$-0.864195\pi$
$349$	−318.328	+	204.577i	−0.912114	+	0.586180i	−0.00175438	+	0.999998i	$0.500558\pi$
$350$	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	0.335798	−	0.941934i	$-0.390994\pi$
$353$	−193.712	−	167.853i	−0.548760	−	0.475503i	−0.884558	+	0.466431i	$0.845540\pi$
$354$		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	0.536467	−	0.843921i	$-0.319758\pi$
$359$	292.026	+	41.9871i	0.813444	+	0.116956i	0.276977	+	0.960877i	$0.410668\pi$
$360$		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	0.922404	+	0.386228i	$0.126222\pi$
$373$	54.5239	+	379.222i	0.146177	+	1.01668i	−0.776227	+	0.630454i	$0.782869\pi$
$374$	−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	−0.377006	−	0.926211i	$-0.623047\pi$
$379$	−452.872	−	132.975i	−1.19491	−	0.350858i	−0.817905	+	0.575353i	$0.804865\pi$
$380$	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	0.713518	−	0.700637i	$-0.247101\pi$
$383$	46.5559	+	40.3409i	0.121556	+	0.105329i	−0.591962	+	0.805966i	$0.701646\pi$
$384$		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	0.962114	+	0.272648i	$0.0878995\pi$
$389$	116.753	+	397.625i	0.300137	+	1.02217i	−0.661977	+	0.749524i	$0.730282\pi$
$390$		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	0.999906	−	0.0137173i	$-0.00436647\pi$
$397$	556.913	+	357.906i	1.40280	+	0.901528i	0.402898	+	0.915245i	$0.368003\pi$
$398$	−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	−0.371735	−	0.928339i	$-0.621237\pi$
$401$	34.6553	−	15.8266i	0.0864222	−	0.0394677i	0.458157	+	0.888871i	$0.348510\pi$
$402$		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	0.870282	+	0.492554i	$0.163937\pi$
$409$	71.1746	+	495.030i	0.174021	+	1.21034i	−0.696261	+	0.717789i	$0.745154\pi$
$410$	−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	−0.350306	−	0.936635i	$-0.613922\pi$
$419$	−177.045	+	25.4552i	−0.422541	+	0.0607522i	−0.0722351	+	0.997388i	$0.523013\pi$
$420$		0			0
$421$	−262.835	+	575.528i	−0.624311	+	1.36705i	0.288030	+	0.957621i	$0.407000\pi$
$421$	−262.835	+	575.528i	−0.624311	+	1.36705i	−0.912342	+	0.409430i	$0.865728\pi$
$422$	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	−0.788631	−	0.614867i	$-0.789210\pi$
$431$	42.3589	−	65.9117i	0.0982805	−	0.152927i	0.886912	+	0.461939i	$0.152846\pi$
$432$		0			0
$433$	638.169	−	410.126i	1.47383	−	0.947174i	0.476132	−	0.879374i	$-0.342038\pi$
$433$	638.169	−	410.126i	1.47383	−	0.947174i	0.997699	−	0.0677999i	$-0.0215980\pi$
$434$	−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	−0.520917	−	0.853607i	$-0.674410\pi$
$439$	−218.467	+	64.1476i	−0.497646	+	0.146122i	0.0232713	+	0.999729i	$0.492592\pi$
$440$	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	−0.553567	−	0.832804i	$-0.686734\pi$
$443$	192.235	−	299.123i	0.433938	−	0.675221i	0.987506	+	0.157583i	$0.0503703\pi$
$444$		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	−0.850603	−	0.525809i	$-0.823763\pi$
$449$	67.0104	−	228.217i	0.149244	−	0.508277i	0.999846	+	0.0175318i	$0.00558082\pi$
$450$		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	−0.975270	−	0.221017i	$-0.929062\pi$
$457$	−482.245	−	556.541i	−1.05524	−	1.21781i	−0.0799717	−	0.996797i	$-0.525483\pi$
$458$	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	$-0.848689\pi$
$461$		−	421.960i		−	0.915315i	0.889129	−	0.457658i	$-0.151311\pi$
$462$		0			0
$463$	296.290	+	341.937i	0.639936	+	0.738525i	0.979363	−	0.202107i	$-0.0647789\pi$
$463$	296.290	+	341.937i	0.639936	+	0.738525i	−0.339428	+	0.940632i	$0.610233\pi$
$464$	−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	−0.448973	−	0.893545i	$-0.648210\pi$
$467$	−662.339	−	302.480i	−1.41828	−	0.647709i	−0.969311	+	0.245836i	$0.920938\pi$
$468$		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	0.914052	+	0.405596i	$0.132936\pi$
$479$	432.673	+	673.253i	0.903285	+	1.40554i	−0.0107676	+	0.999942i	$0.503427\pi$
$480$		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	−0.605284	−	0.796010i	$-0.706940\pi$
$487$	−64.6015	+	41.5168i	−0.132652	+	0.0852502i	0.472632	+	0.881260i	$0.343304\pi$
$488$	−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	0.0791393	−	0.996864i	$-0.474783\pi$
$491$	−440.091	−	381.341i	−0.896315	−	0.776661i	−0.975454	+	0.220202i	$0.929328\pi$
$492$		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	−0.935949	−	0.352136i	$-0.885456\pi$
$499$	−28.3963	+	62.1792i	−0.0569064	+	0.124608i	0.879043	+	0.476743i	$0.158183\pi$
$500$	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	−0.271005	+	0.962578i	$0.587356\pi$
$503$	−634.964	+	550.199i	−1.26235	+	1.09384i	−0.991348	+	0.131258i	$0.958098\pi$
$504$		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	−0.997801	−	0.0662745i	$-0.978889\pi$
$509$	−546.770	+	473.779i	−1.07420	+	0.930803i	−0.0764020	+	0.997077i	$0.524343\pi$
$510$		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	0.990562	+	0.137065i	$0.0437670\pi$
$521$	660.213	+	572.078i	1.26720	+	1.09804i	0.276642	+	0.960973i	$0.410778\pi$
$522$		0			0
$523$	821.976	+	528.252i	1.57166	+	1.01004i	0.978821	+	0.204718i	$0.0656278\pi$
$523$	821.976	+	528.252i	1.57166	+	1.01004i	0.592835	+	0.805324i	$0.298009\pi$
$524$	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	0.811778	−	0.583965i	$-0.198500\pi$
$541$	637.825	+	187.282i	1.17897	+	0.346178i	0.367196	+	0.930144i	$0.380318\pi$
$542$	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	0.876508	+	0.481388i	$0.159867\pi$
$547$	93.6067	+	651.049i	0.171127	+	1.19022i	−0.705380	+	0.708829i	$0.749224\pi$
$548$	−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	−0.946409	−	0.322970i	$-0.895319\pi$
$557$	−982.264	+	141.228i	−1.76349	+	0.253552i	−0.817082	+	0.576522i	$0.804410\pi$
$558$		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	0.810367	+	0.585923i	$0.199268\pi$
$563$	−105.918	+	360.722i	−0.188131	+	0.640715i	−0.998498	+	0.0547919i	$0.982550\pi$
$564$		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	−0.160321	−	0.987065i	$-0.551253\pi$
$569$	457.558	−	711.975i	0.804145	−	1.25127i	0.964466	−	0.264208i	$-0.0851107\pi$
$570$		0			0
$571$	−173.168	+	111.288i	−0.303271	+	0.194900i	−0.683421	−	0.730024i	$-0.739509\pi$
$571$	−173.168	+	111.288i	−0.303271	+	0.194900i	0.380150	+	0.924925i	$0.375872\pi$
$572$	−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	−0.0792937	−	0.996851i	$-0.525266\pi$
$577$	226.726	−	66.5727i	0.392939	−	0.115377i	0.472232	+	0.881474i	$0.343448\pi$
$578$	−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	−0.815166	−	0.579228i	$-0.803354\pi$
$587$	107.861	−	367.341i	0.183749	−	0.625793i	0.998915	−	0.0465655i	$-0.0148276\pi$
$588$		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	−0.683627	−	0.729832i	$-0.739598\pi$
$593$	−672.429	+	96.6807i	−1.13394	+	0.163037i	−0.450317	+	0.892869i	$0.648689\pi$
$594$		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	$-0.938147\pi$
$599$		−	231.331i		−	0.386196i	0.981180	−	0.193098i	$-0.0618535\pi$
$600$		0			0
$601$	−290.465	−	335.214i	−0.483302	−	0.557761i	0.460761	−	0.887524i	$-0.347576\pi$
$601$	−290.465	−	335.214i	−0.483302	−	0.557761i	−0.944064	+	0.329763i	$0.893031\pi$
$602$	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	0.818699	+	0.574223i	$0.194696\pi$
$607$	−78.0689	+	542.981i	−0.128614	+	0.894532i	−0.947313	+	0.320309i	$0.896213\pi$
$608$	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	−0.995754	−	0.0920532i	$-0.970657\pi$
$613$	−467.674	+	539.725i	−0.762927	+	0.880465i	0.232827	+	0.972518i	$0.425202\pi$
$614$	−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	0.590823	−	0.806801i	$-0.298803\pi$
$617$	−239.708	−	372.993i	−0.388506	−	0.604527i	−0.979329	+	0.202274i	$0.935167\pi$
$618$		0			0
$619$	578.597	−	169.891i	0.934728	−	0.274461i	0.221313	−	0.975203i	$-0.428966\pi$
$619$	578.597	−	169.891i	0.934728	−	0.274461i	0.713415	+	0.700742i	$0.247147\pi$
$620$			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	0.726599	−	0.687061i	$-0.241100\pi$
$631$	−169.404	−	370.942i	−0.268468	−	0.587864i	−0.995068	+	0.0991975i	$0.968372\pi$
$632$	−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	−0.265055	−	0.964233i	$-0.585390\pi$
$641$	417.703	−	361.941i	0.651642	−	0.564651i	0.916697	+	0.399582i	$0.130845\pi$
$642$		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	−0.561952	−	0.827170i	$-0.689949\pi$
$647$	114.406	−	99.1330i	0.176825	−	0.153219i	0.738776	+	0.673951i	$0.235404\pi$
$648$		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	−0.0183352	−	0.999832i	$-0.505837\pi$
$653$	−207.401	−	29.8198i	−0.317613	−	0.0456658i	−0.299278	+	0.954166i	$0.596746\pi$
$654$		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	0.808702	−	0.588218i	$-0.200170\pi$
$659$	225.089	+	195.041i	0.341562	+	0.295965i	−0.467140	+	0.884183i	$0.654716\pi$
$660$		0			0
$661$	−914.942	−	587.998i	−1.38418	−	0.889558i	−0.384739	−	0.923026i	$-0.625708\pi$
$661$	−914.942	−	587.998i	−1.38418	−	0.889558i	−0.999440	+	0.0334680i	$0.989345\pi$
$662$	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	0.991965	−	0.126510i	$-0.0403775\pi$
$673$	867.474	+	557.492i	1.28897	+	0.828368i	0.297000	+	0.954877i	$0.404014\pi$
$674$	−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	0.125667	−	0.992072i	$-0.459893\pi$
$677$	648.376	−	296.103i	0.957720	−	0.437376i	0.832053	+	0.554697i	$0.187166\pi$
$678$		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	0.996302	+	0.0859181i	$0.0273824\pi$
$683$	1170.44	+	534.522i	1.71367	+	0.782609i	0.717372	+	0.696691i	$0.245345\pi$
$684$		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	−0.748265	−	0.663400i	$-0.769113\pi$
$701$	168.154	−	572.678i	0.239877	−	0.816945i	0.988142	−	0.153545i	$-0.0490690\pi$
$702$		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	−0.554854	−	0.831948i	$-0.687226\pi$
$709$	−20.2649	+	13.0235i	−0.0285824	+	0.0183688i	0.526272	+	0.850317i	$0.323590\pi$
$710$	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	−0.224381	−	0.974501i	$-0.572036\pi$
$719$	543.038	−	844.983i	0.755268	−	1.17522i	0.979649	−	0.200718i	$-0.0643276\pi$
$720$		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	0.750216	+	0.661193i	$0.229949\pi$
$727$	−113.332	+	788.244i	−0.155891	+	1.08424i	−0.906107	+	0.423050i	$0.860960\pi$
$728$	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	0.264590	−	0.964361i	$-0.414763\pi$
$733$	−533.338	−	615.505i	−0.727610	−	0.839707i	−0.992200	+	0.124654i	$0.960218\pi$
$734$	−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	−0.988057	−	0.154086i	$-0.950757\pi$
$739$	−738.970	−	852.817i	−0.999960	−	1.15401i	−0.0119021	−	0.999929i	$-0.503789\pi$
$740$	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	−0.357280	−	0.933997i	$-0.616296\pi$
$743$	−963.757	−	440.133i	−1.29712	−	0.592373i	−0.939837	+	0.341624i	$0.889023\pi$
$744$		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	−0.998900	−	0.0468978i	$-0.985067\pi$
$751$	−608.551	+	702.305i	−0.810321	+	0.935160i	0.188579	+	0.982058i	$0.439612\pi$
$752$	−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	0.0673184	−	0.997732i	$-0.478556\pi$
$757$	502.167	−	147.450i	0.663365	−	0.194781i	0.596046	+	0.802950i	$0.296737\pi$
$758$			667.495i			0.880601i
$759$		0			0
$760$	−56.2228			−0.0739773
$761$	−54.7768	−	186.553i	−0.0719800	−	0.245141i	0.915642	−	0.401995i	$-0.131683\pi$
$761$	−54.7768	−	186.553i	−0.0719800	−	0.245141i	−0.987622	+	0.156854i	$0.949865\pi$
$762$		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	0.969020	−	0.246983i	$-0.0794392\pi$
$769$	113.650	+	248.859i	0.147789	+	0.323614i	−0.821230	+	0.570597i	$0.806712\pi$
$770$	−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	0.760386	−	0.649471i	$-0.225010\pi$
$773$	1010.31	+	145.260i	1.30699	+	0.187917i	0.546608	+	0.837389i	$0.315919\pi$
$774$		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	−0.970379	−	0.241588i	$-0.922332\pi$
$787$	−84.5004	−	587.713i	−0.107370	−	0.746776i	0.863009	−	0.505189i	$-0.168577\pi$
$788$	−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	0.691006	−	0.722849i	$-0.257168\pi$
$797$	58.8618	+	51.0041i	0.0738542	+	0.0639950i	−0.617151	+	0.786844i	$0.711713\pi$
$798$		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	0.875416	−	0.483371i	$-0.160588\pi$
$809$	58.3011	+	90.7182i	0.0720656	+	0.112136i	−0.803350	+	0.595507i	$0.796951\pi$
$810$		0			0
$811$	−601.902	−	386.819i	−0.742173	−	0.476965i	0.114113	−	0.993468i	$-0.463597\pi$
$811$	−601.902	−	386.819i	−0.742173	−	0.476965i	−0.856286	+	0.516502i	$0.827234\pi$
$812$	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	0.716638	−	0.697446i	$-0.245680\pi$
$821$	540.909	+	247.025i	0.658842	+	0.300883i	−0.0577962	+	0.998328i	$0.518407\pi$
$822$		0			0
$823$	−92.3729	−	642.468i	−0.112239	−	0.780641i	−0.965733	−	0.259538i	$-0.916430\pi$
$823$	−92.3729	−	642.468i	−0.112239	−	0.780641i	0.853494	−	0.521103i	$-0.174479\pi$
$824$	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	$0.0642968\pi$
$827$			331.831i			0.401247i	−0.979668	+	0.200623i	$0.935703\pi$
$828$		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	0.250143	+	0.968209i	$0.419522\pi$
$839$	−405.861	+	1382.24i	−0.483744	+	1.64748i	−0.733887	+	0.679271i	$0.762296\pi$
$840$		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	−0.0919549	−	0.995763i	$-0.529312\pi$
$853$	314.789	−	92.4305i	0.369038	−	0.108359i	0.460993	+	0.887404i	$0.347493\pi$
$854$	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	−0.605172	−	0.796095i	$-0.706896\pi$
$857$	317.415	−	493.907i	0.370379	−	0.576321i	0.975551	+	0.219774i	$0.0705319\pi$
$858$		0			0
$859$	9.06121	−	10.4572i	0.0105486	−	0.0121737i	−0.750451	−	0.660926i	$-0.770164\pi$
$859$	9.06121	−	10.4572i	0.0105486	−	0.0121737i	0.760999	+	0.648753i	$0.224709\pi$
$860$	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	0.806648	+	0.591032i	$0.201279\pi$
$863$	−165.250	+	562.791i	−0.191484	+	0.652133i	−0.998132	+	0.0611010i	$0.980539\pi$
$864$		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	0.433287	−	0.901256i	$-0.357354\pi$
$877$	−456.443	−	526.763i	−0.520459	−	0.600642i	−0.953746	+	0.300614i	$0.902808\pi$
$878$	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	−0.411553	−	0.911386i	$-0.635013\pi$
$881$	−1206.83	−	551.141i	−1.36984	−	0.625586i	−0.958289	+	0.285800i	$0.907741\pi$
$882$		0			0
$883$	−130.008	+	904.224i	−0.147234	+	1.02404i	0.773486	+	0.633813i	$0.218511\pi$
$883$	−130.008	+	904.224i	−0.147234	+	1.02404i	−0.920720	+	0.390223i	$0.872398\pi$
$884$	−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	−0.901268	−	0.433263i	$-0.857362\pi$
$887$	−1032.50	+	471.526i	−1.16403	+	0.531597i	−0.262767	+	0.964859i	$0.584635\pi$
$888$		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	−0.999313	−	0.0370498i	$-0.988204\pi$
$907$	−338.223	−	740.604i	−0.372903	−	0.816543i	0.626411	−	0.779493i	$-0.284523\pi$
$908$	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	0.699940	−	0.714201i	$-0.253210\pi$
$911$	1066.16	+	153.290i	1.17031	+	0.168266i	0.470374	+	0.882467i	$0.344119\pi$
$912$		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	−0.111653	−	0.993747i	$-0.535614\pi$
$929$	−463.342	−	66.6186i	−0.498754	−	0.0717100i	−0.387101	+	0.922037i	$0.626524\pi$
$930$		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	0.157413	−	0.987533i	$-0.449685\pi$
$937$	−632.931	−	406.760i	−0.675487	−	0.434109i	−0.832900	+	0.553424i	$0.813321\pi$
$938$	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	0.984456	−	0.175631i	$-0.0561965\pi$
$941$	57.7076	+	196.534i	0.0613258	+	0.208856i	−0.923130	+	0.384487i	$0.874378\pi$
$942$		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	0.917299	+	0.398199i	$0.130365\pi$
$947$	850.836	+	1323.93i	0.898454	+	1.39802i	−0.0188450	+	0.999822i	$0.505999\pi$
$948$		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	−0.971990	−	0.235023i	$-0.924483\pi$
$953$	−1363.64	+	622.752i	−1.43089	+	0.653465i	−0.458899	+	0.888488i	$0.651756\pi$
$954$		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	−0.855889	−	0.517159i	$-0.826990\pi$
$971$	−1487.00	+	213.798i	−1.53141	+	0.220183i	−0.675519	+	0.737342i	$0.736080\pi$
$972$		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	−0.907744	−	0.419524i	$-0.862197\pi$
$977$	80.8084	−	275.208i	0.0827108	−	0.281687i	0.990455	+	0.137837i	$0.0440151\pi$
$978$		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	−0.990842	−	0.135029i	$-0.956887\pi$
$983$	−448.645	+	698.106i	−0.456404	+	0.710179i	0.534438	+	0.845208i	$0.320523\pi$
$984$		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	−0.975134	−	0.221614i	$-0.928867\pi$
$991$	−1660.58	+	487.589i	−1.67566	+	0.492017i	−0.700522	+	0.713631i	$0.747049\pi$
$992$	−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	−0.938327	−	0.345748i	$-0.887625\pi$
$997$	−461.173	+	532.222i	−0.462560	+	0.533823i	0.475767	+	0.879571i	$0.342171\pi$
$998$	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.377.3	yes	80
3.2	odd	2	inner	414.3.k.a.377.6	yes	80
23.18	even	11	inner	414.3.k.a.179.6	yes	80
69.41	odd	22	inner	414.3.k.a.179.3	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.3.k.a.179.3	✓	80	69.41	odd	22	inner
414.3.k.a.179.6	yes	80	23.18	even	11	inner
414.3.k.a.377.3	yes	80	1.1	even	1	trivial
414.3.k.a.377.6	yes	80	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
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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