LMFDB - Embedded newform 936.2.dg.e.829.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [936,2,Mod(829,936)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(936, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 5]))

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

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

chi := DirichletCharacter("936.829");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.dg (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			829.15
Character	$\chi$	$=$	936.829
Dual form			936.2.dg.e.901.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.203399 + 1.39951i) q^{2} +(-1.91726 + 0.569319i) q^{4} -3.13862 q^{5} +(-3.44764 - 1.99050i) q^{7} +(-1.18674 - 2.56742i) q^{8} +(-0.638393 - 4.39253i) q^{10} +(2.10717 + 3.64973i) q^{11} +(3.58133 - 0.417261i) q^{13} +(2.08447 - 5.22987i) q^{14} +(3.35175 - 2.18306i) q^{16} +(-0.962941 + 1.66786i) q^{17} +(1.67206 - 2.89609i) q^{19} +(6.01754 - 1.78688i) q^{20} +(-4.67924 + 3.69136i) q^{22} +(-1.84982 - 3.20398i) q^{23} +4.85094 q^{25} +(1.31240 + 4.92723i) q^{26} +(7.74324 + 1.85349i) q^{28} +(5.70476 - 3.29364i) q^{29} +6.35042i q^{31} +(3.73696 + 4.24678i) q^{32} +(-2.53005 - 1.00840i) q^{34} +(10.8208 + 6.24741i) q^{35} +(-0.708429 - 1.22703i) q^{37} +(4.39321 + 1.75100i) q^{38} +(3.72472 + 8.05817i) q^{40} +(2.47794 - 1.43064i) q^{41} +(10.0697 + 5.81376i) q^{43} +(-6.11785 - 5.79782i) q^{44} +(4.10776 - 3.24053i) q^{46} -9.74759i q^{47} +(4.42415 + 7.66285i) q^{49} +(0.986678 + 6.78894i) q^{50} +(-6.62877 + 2.83891i) q^{52} -2.32264i q^{53} +(-6.61361 - 11.4551i) q^{55} +(-1.01900 + 11.2137i) q^{56} +(5.76983 + 7.31394i) q^{58} +(0.0313645 - 0.0543248i) q^{59} +(6.32541 + 3.65198i) q^{61} +(-8.88748 + 1.29167i) q^{62} +(-5.18331 + 6.09371i) q^{64} +(-11.2404 + 1.30962i) q^{65} +(-5.97751 - 10.3534i) q^{67} +(0.896660 - 3.74594i) q^{68} +(-6.54237 + 16.4146i) q^{70} +(-5.28850 - 3.05332i) q^{71} -9.02220i q^{73} +(1.57315 - 1.24103i) q^{74} +(-1.55697 + 6.50449i) q^{76} -16.7773i q^{77} +12.0869 q^{79} +(-10.5199 + 6.85180i) q^{80} +(2.50621 + 3.17691i) q^{82} -5.10910 q^{83} +(3.02231 - 5.23479i) q^{85} +(-6.08824 + 15.2752i) q^{86} +(6.86974 - 9.74127i) q^{88} +(-1.29475 + 0.747522i) q^{89} +(-13.1777 - 5.69005i) q^{91} +(5.37067 + 5.08972i) q^{92} +(13.6419 - 1.98265i) q^{94} +(-5.24796 + 9.08974i) q^{95} +(5.07484 + 2.92996i) q^{97} +(-9.82437 + 7.75026i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 2 q^{4} - 12 q^{7} - 4 q^{10} + 36 q^{14} - 2 q^{16} - 12 q^{17} - 54 q^{20} - 14 q^{22} - 20 q^{23} + 48 q^{25} + 42 q^{26} + 6 q^{28} + 28 q^{38} - 8 q^{40} + 12 q^{41} - 30 q^{46} + 16 q^{49}+ \cdots - 24 q^{98}+O(q^{100}) $ 48 * q - 2 * q^4 - 12 * q^7 - 4 * q^10 + 36 * q^14 - 2 * q^16 - 12 * q^17 - 54 * q^20 - 14 * q^22 - 20 * q^23 + 48 * q^25 + 42 * q^26 + 6 * q^28 + 28 * q^38 - 8 * q^40 + 12 * q^41 - 30 * q^46 + 16 * q^49 + 84 * q^50 - 28 * q^52 - 68 * q^55 - 18 * q^56 - 24 * q^58 - 24 * q^62 - 68 * q^64 - 12 * q^65 - 4 * q^68 + 12 * q^71 - 54 * q^74 - 54 * q^76 - 192 * q^79 - 78 * q^80 - 6 * q^82 - 10 * q^88 + 48 * q^89 + 12 * q^92 + 54 * q^94 + 20 * q^95 + 144 * q^97 - 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.203399	+	1.39951i	0.143825	+	0.989603i
$2$	0.203399	+	1.39951i	0.143825	+	0.989603i
$3$		0			0
$3$		0			0
$4$	−1.91726	+	0.569319i	−0.958629	+	0.284659i
$5$	−3.13862			−1.40363			−0.701817	−	0.712357i	$-0.747628\pi$
$5$	−3.13862			−1.40363			−0.701817	+	0.712357i	$0.747628\pi$
$6$		0			0
$7$	−3.44764	−	1.99050i	−1.30309	−	0.752337i	−0.322154	−	0.946687i	$-0.604407\pi$
$7$	−3.44764	−	1.99050i	−1.30309	−	0.752337i	−0.980932	+	0.194351i	$0.937740\pi$
$8$	−1.18674	−	2.56742i	−0.419575	−	0.907721i
$9$		0			0
$10$	−0.638393	−	4.39253i	−0.201878	−	1.38904i
$11$	2.10717	+	3.64973i	0.635336	+	1.10043i	0.986444	+	0.164100i	$0.0524718\pi$
$11$	2.10717	+	3.64973i	0.635336	+	1.10043i	−0.351108	+	0.936335i	$0.614195\pi$
$12$		0			0
$13$	3.58133	−	0.417261i	0.993281	−	0.115727i
$13$	3.58133	−	0.417261i	0.993281	−	0.115727i
$14$	2.08447	−	5.22987i	0.557099	−	1.39774i
$15$		0			0
$16$	3.35175	−	2.18306i	0.837938	−	0.545765i
$17$	−0.962941	+	1.66786i	−0.233547	+	0.404516i	−0.958850	−	0.283915i	$-0.908367\pi$
$17$	−0.962941	+	1.66786i	−0.233547	+	0.404516i	0.725302	+	0.688431i	$0.241700\pi$
$18$		0			0
$19$	1.67206	−	2.89609i	0.383597	−	0.664409i	−0.607977	−	0.793955i	$-0.708019\pi$
$19$	1.67206	−	2.89609i	0.383597	−	0.664409i	0.991573	+	0.129546i	$0.0413519\pi$
$20$	6.01754	−	1.78688i	1.34556	−	0.399558i
$21$		0			0
$22$	−4.67924	+	3.69136i	−0.997616	+	0.787001i
$23$	−1.84982	−	3.20398i	−0.385714	−	0.668077i	0.606154	−	0.795348i	$-0.292712\pi$
$23$	−1.84982	−	3.20398i	−0.385714	−	0.668077i	−0.991868	+	0.127271i	$0.959378\pi$
$24$		0			0
$25$	4.85094			0.970188
$26$	1.31240	+	4.92723i	0.257383	+	0.966310i
$27$		0			0
$28$	7.74324	+	1.85349i	1.46334	+	0.350276i
$29$	5.70476	−	3.29364i	1.05935	−	0.611614i	0.134095	−	0.990968i	$-0.457187\pi$
$29$	5.70476	−	3.29364i	1.05935	−	0.611614i	0.925251	+	0.379354i	$0.123854\pi$
$30$		0			0
$31$			6.35042i			1.14057i	0.821447	+	0.570285i	$0.193167\pi$
$31$			6.35042i			1.14057i	−0.821447	+	0.570285i	$0.806833\pi$
$32$	3.73696	+	4.24678i	0.660608	+	0.750731i
$33$		0			0
$34$	−2.53005	−	1.00840i	−0.433900	−	0.172940i
$35$	10.8208	+	6.24741i	1.82906	+	1.05601i
$36$		0			0
$37$	−0.708429	−	1.22703i	−0.116465	−	0.201723i	0.801899	−	0.597459i	$-0.203823\pi$
$37$	−0.708429	−	1.22703i	−0.116465	−	0.201723i	−0.918364	+	0.395736i	$0.870490\pi$
$38$	4.39321	+	1.75100i	0.712672	+	0.284050i
$39$		0			0
$40$	3.72472	+	8.05817i	0.588929	+	1.27411i
$41$	2.47794	−	1.43064i	0.386989	−	0.223428i	−0.293866	−	0.955847i	$-0.594942\pi$
$41$	2.47794	−	1.43064i	0.386989	−	0.223428i	0.680855	+	0.732418i	$0.261608\pi$
$42$		0			0
$43$	10.0697	+	5.81376i	1.53562	+	0.886590i	0.999088	+	0.0427087i	$0.0135987\pi$
$43$	10.0697	+	5.81376i	1.53562	+	0.886590i	0.536531	+	0.843881i	$0.319735\pi$
$44$	−6.11785	−	5.79782i	−0.922301	−	0.874054i
$45$		0			0
$46$	4.10776	−	3.24053i	0.605656	−	0.477790i
$47$		−	9.74759i		−	1.42183i	−0.703277	−	0.710916i	$-0.748280\pi$
$47$		−	9.74759i		−	1.42183i	0.703277	−	0.710916i	$-0.251720\pi$
$48$		0			0
$49$	4.42415	+	7.66285i	0.632021	+	1.09469i
$50$	0.986678	+	6.78894i	0.139537	+	0.960101i
$51$		0			0
$52$	−6.62877	+	2.83891i	−0.919245	+	0.393686i
$53$		−	2.32264i		−	0.319039i	−0.987195	−	0.159519i	$-0.949006\pi$
$53$		−	2.32264i		−	0.319039i	0.987195	−	0.159519i	$-0.0509944\pi$
$54$		0			0
$55$	−6.61361	−	11.4551i	−0.891780	−	1.54461i
$56$	−1.01900	+	11.2137i	−0.136170	+	1.49850i
$57$		0			0
$58$	5.76983	+	7.31394i	0.757616	+	0.960367i
$59$	0.0313645	−	0.0543248i	0.00408331	−	0.00707249i	−0.863977	−	0.503532i	$-0.832034\pi$
$59$	0.0313645	−	0.0543248i	0.00408331	−	0.00707249i	0.868060	+	0.496460i	$0.165367\pi$
$60$		0			0
$61$	6.32541	+	3.65198i	0.809885	+	0.467588i	0.846916	−	0.531727i	$-0.178457\pi$
$61$	6.32541	+	3.65198i	0.809885	+	0.467588i	−0.0370307	+	0.999314i	$0.511790\pi$
$62$	−8.88748	+	1.29167i	−1.12871	+	0.164042i
$63$		0			0
$64$	−5.18331	+	6.09371i	−0.647914	+	0.761713i
$65$	−11.2404	+	1.30962i	−1.39420	+	0.162439i
$66$		0			0
$67$	−5.97751	−	10.3534i	−0.730269	−	1.26486i	−0.956768	−	0.290852i	$-0.906061\pi$
$67$	−5.97751	−	10.3534i	−0.730269	−	1.26486i	0.226498	−	0.974012i	$-0.427272\pi$
$68$	0.896660	−	3.74594i	0.108736	−	0.454262i
$69$		0			0
$70$	−6.54237	+	16.4146i	−0.781962	+	1.96192i
$71$	−5.28850	−	3.05332i	−0.627630	−	0.362362i	0.152204	−	0.988349i	$-0.451363\pi$
$71$	−5.28850	−	3.05332i	−0.627630	−	0.362362i	−0.779834	+	0.625987i	$0.784696\pi$
$72$		0			0
$73$		−	9.02220i		−	1.05597i	−0.849254	−	0.527984i	$-0.822948\pi$
$73$		−	9.02220i		−	1.05597i	0.849254	−	0.527984i	$-0.177052\pi$
$74$	1.57315	−	1.24103i	0.182875	−	0.144267i
$75$		0			0
$76$	−1.55697	+	6.50449i	−0.178597	+	0.746116i
$77$		−	16.7773i		−	1.91195i
$78$		0			0
$79$	12.0869			1.35989			0.679943	−	0.733265i	$-0.262005\pi$
$79$	12.0869			1.35989			0.679943	+	0.733265i	$0.262005\pi$
$80$	−10.5199	+	6.85180i	−1.17616	+	0.766055i
$81$		0			0
$82$	2.50621	+	3.17691i	0.276764	+	0.350831i
$83$	−5.10910			−0.560797			−0.280398	−	0.959884i	$-0.590467\pi$
$83$	−5.10910			−0.560797			−0.280398	+	0.959884i	$0.590467\pi$
$84$		0			0
$85$	3.02231	−	5.23479i	0.327815	−	0.567792i
$86$	−6.08824	+	15.2752i	−0.656511	+	1.64717i
$87$		0			0
$88$	6.86974	−	9.74127i	0.732316	−	1.03842i
$89$	−1.29475	+	0.747522i	−0.137243	+	0.0792372i	−0.567049	−	0.823684i	$-0.691915\pi$
$89$	−1.29475	+	0.747522i	−0.137243	+	0.0792372i	0.429806	+	0.902921i	$0.358582\pi$
$90$		0			0
$91$	−13.1777	−	5.69005i	−1.38140	−	0.596479i
$92$	5.37067	+	5.08972i	0.559931	+	0.530640i
$93$		0			0
$94$	13.6419	−	1.98265i	1.40705	−	0.204495i
$95$	−5.24796	+	9.08974i	−0.538429	+	0.932587i
$96$		0			0
$97$	5.07484	+	2.92996i	0.515272	+	0.297492i	0.734998	−	0.678069i	$-0.237183\pi$
$97$	5.07484	+	2.92996i	0.515272	+	0.297492i	−0.219726	+	0.975562i	$0.570516\pi$
$98$	−9.82437	+	7.75026i	−0.992411	+	0.782895i
$99$		0			0
$100$	−9.30050	+	2.76173i	−0.930050	+	0.276173i
$101$	6.98634	−	4.03356i	0.695166	−	0.401355i	−0.110378	−	0.993890i	$-0.535206\pi$
$101$	6.98634	−	4.03356i	0.695166	−	0.401355i	0.805545	+	0.592535i	$0.201873\pi$
$102$		0			0
$103$	−19.0873			−1.88073			−0.940363	−	0.340172i	$-0.889515\pi$
$103$	−19.0873			−1.88073			−0.940363	+	0.340172i	$0.889515\pi$
$104$	−5.32137	−	8.69960i	−0.521804	−	0.853066i
$105$		0			0
$106$	3.25055	−	0.472423i	0.315722	−	0.0458857i
$107$	5.69031	−	3.28530i	0.550103	−	0.317602i	−0.199060	−	0.979987i	$-0.563789\pi$
$107$	5.69031	−	3.28530i	0.550103	−	0.317602i	0.749164	+	0.662385i	$0.230456\pi$
$108$		0			0
$109$	12.1256			1.16142			0.580710	−	0.814110i	$-0.302775\pi$
$109$	12.1256			1.16142			0.580710	+	0.814110i	$0.302775\pi$
$110$	14.6863	−	11.5858i	1.40029	−	1.10466i
$111$		0			0
$112$	−15.9010	+	0.854762i	−1.50250	+	0.0807674i
$113$	9.34914	−	16.1932i	0.879493	−	1.52333i	0.0275947	−	0.999619i	$-0.491215\pi$
$113$	9.34914	−	16.1932i	0.879493	−	1.52333i	0.851898	−	0.523707i	$-0.175451\pi$
$114$		0			0
$115$	5.80589	+	10.0561i	0.541402	+	0.937735i
$116$	−9.06235	+	9.56258i	−0.841418	+	0.887864i
$117$		0			0
$118$	0.0824077	+	0.0328453i	0.00758624	+	0.00302365i
$119$	6.63975	−	3.83346i	0.608665	−	0.351413i
$120$		0			0
$121$	−3.38035	+	5.85493i	−0.307304	+	0.532267i
$122$	−3.82439	+	9.59528i	−0.346244	+	0.868716i
$123$		0			0
$124$	−3.61541	−	12.1754i	−0.324674	−	1.09338i
$125$	0.467837			0.0418446
$126$		0			0
$127$	−0.445189	−	0.771090i	−0.0395041	−	0.0684231i	0.845597	−	0.533821i	$-0.179244\pi$
$127$	−0.445189	−	0.771090i	−0.0395041	−	0.0684231i	−0.885101	+	0.465398i	$0.845911\pi$
$128$	−9.58249	−	6.01464i	−0.846980	−	0.531624i
$129$		0			0
$130$	−4.11913	−	15.4647i	−0.361271	−	1.35634i
$131$		−	3.32094i		−	0.290152i	−0.989421	−	0.145076i	$-0.953657\pi$
$131$		−	3.32094i		−	0.290152i	0.989421	−	0.145076i	$-0.0463426\pi$
$132$		0			0
$133$	−11.5293	+	6.65646i	−0.999719	+	0.577188i
$134$	13.2738	−	10.4715i	1.14668	−	0.904596i
$135$		0			0
$136$	5.42486	+	0.492963i	0.465178	+	0.0422712i
$137$	5.97444	+	3.44934i	0.510431	+	0.294697i	0.733011	−	0.680217i	$-0.238115\pi$
$137$	5.97444	+	3.44934i	0.510431	+	0.294697i	−0.222580	+	0.974914i	$0.571448\pi$
$138$		0			0
$139$	−4.32371	−	2.49629i	−0.366732	−	0.211733i	0.305298	−	0.952257i	$-0.401244\pi$
$139$	−4.32371	−	2.49629i	−0.366732	−	0.211733i	−0.672030	+	0.740524i	$0.734577\pi$
$140$	−24.3031	−	5.81739i	−2.05399	−	0.491659i
$141$		0			0
$142$	3.19747	−	8.02235i	0.268326	−	0.673221i
$143$	9.06936	+	12.1916i	0.758418	+	1.01952i
$144$		0			0
$145$	−17.9051	+	10.3375i	−1.48693	+	0.858482i
$146$	12.6267	−	1.83511i	1.04499	−	0.151875i
$147$		0			0
$148$	2.05681	+	1.94922i	0.169069	+	0.160225i
$149$	−10.5148	+	18.2122i	−0.861409	+	1.49200i	0.00916087	+	0.999958i	$0.497084\pi$
$149$	−10.5148	+	18.2122i	−0.861409	+	1.49200i	−0.870569	+	0.492045i	$0.836249\pi$
$150$		0			0
$151$		−	15.5772i		−	1.26765i	−0.773475	−	0.633827i	$-0.781483\pi$
$151$		−	15.5772i		−	1.26765i	0.773475	−	0.633827i	$-0.218517\pi$
$152$	−9.41978	−	0.855985i	−0.764045	−	0.0694295i
$153$		0			0
$154$	23.4800	−	3.41249i	1.89207	−	0.274986i
$155$		−	19.9316i		−	1.60094i
$156$		0			0
$157$			13.5871i			1.08437i	0.840260	+	0.542184i	$0.182402\pi$
$157$			13.5871i			1.08437i	−0.840260	+	0.542184i	$0.817598\pi$
$158$	2.45847	+	16.9158i	0.195586	+	1.34575i
$159$		0			0
$160$	−11.7289	−	13.3290i	−0.927251	−	1.05375i
$161$			14.7282i			1.16075i
$162$		0			0
$163$	−5.85529	+	10.1417i	−0.458622	+	0.794356i	−0.998888	−	0.0471375i	$-0.984990\pi$
$163$	−5.85529	+	10.1417i	−0.458622	+	0.794356i	0.540266	+	0.841494i	$0.318323\pi$
$164$	−3.93636	+	4.15364i	−0.307378	+	0.324345i
$165$		0			0
$166$	−1.03919	−	7.15024i	−0.0806566	−	0.554966i
$167$	−0.133302	+	0.0769619i	−0.0103152	+	0.00595549i	−0.505149	−	0.863032i	$-0.668562\pi$
$167$	−0.133302	+	0.0769619i	−0.0103152	+	0.00595549i	0.494834	+	0.868988i	$0.335229\pi$
$168$		0			0
$169$	12.6518	−	2.98869i	0.973214	−	0.229900i
$170$	7.94087	+	3.16500i	0.609037	+	0.242744i
$171$		0			0
$172$	−22.6161	−	5.41359i	−1.72446	−	0.412782i
$173$	22.4496	+	12.9613i	1.70681	+	0.985428i	0.938452	+	0.345408i	$0.112260\pi$
$173$	22.4496	+	12.9613i	1.70681	+	0.985428i	0.768359	+	0.640019i	$0.221074\pi$
$174$		0			0
$175$	−16.7243	−	9.65578i	−1.26424	−	0.729908i
$176$	15.0303	+	7.63290i	1.13295	+	0.575352i
$177$		0			0
$178$	−1.30952	−	1.65997i	−0.0981523	−	0.124420i
$179$	−10.9372	+	6.31460i	−0.817485	+	0.471975i	−0.849549	−	0.527510i	$-0.823126\pi$
$179$	−10.9372	+	6.31460i	−0.817485	+	0.471975i	0.0320632	+	0.999486i	$0.489792\pi$
$180$		0			0
$181$		−	18.4603i		−	1.37215i	−0.727533	−	0.686073i	$-0.759333\pi$
$181$		−	18.4603i		−	1.37215i	0.727533	−	0.686073i	$-0.240667\pi$
$182$	5.28295	−	19.5996i	0.391598	−	1.45282i
$183$		0			0
$184$	−6.03073	+	8.55156i	−0.444591	+	0.630429i
$185$	2.22349	+	3.85120i	0.163474	+	0.283146i
$186$		0			0
$187$	−8.11633			−0.593525
$188$	5.54949	+	18.6886i	0.404738	+	1.36301i
$189$		0			0
$190$	−13.7886	−	5.49573i	−1.00033	−	0.398702i
$191$	2.75962	−	4.77980i	0.199679	−	0.345854i	−0.748745	−	0.662858i	$-0.769343\pi$
$191$	2.75962	−	4.77980i	0.199679	−	0.345854i	0.948424	+	0.317004i	$0.102677\pi$
$192$		0			0
$193$	0.109080	−	0.0629771i	0.00785172	−	0.00453319i	−0.496069	−	0.868283i	$-0.665224\pi$
$193$	0.109080	−	0.0629771i	0.00785172	−	0.00453319i	0.503921	+	0.863750i	$0.331890\pi$
$194$	−3.06829	+	7.69824i	−0.220290	+	0.552701i
$195$		0			0
$196$	−12.8448	−	12.1729i	−0.917489	−	0.869494i
$197$	4.66226	+	8.07527i	0.332172	+	0.575339i	0.982938	−	0.183940i	$-0.0588851\pi$
$197$	4.66226	+	8.07527i	0.332172	+	0.575339i	−0.650765	+	0.759279i	$0.725552\pi$
$198$		0			0
$199$	−7.90454	+	13.6911i	−0.560338	+	0.970534i	0.437128	+	0.899399i	$0.355996\pi$
$199$	−7.90454	+	13.6911i	−0.560338	+	0.970534i	−0.997467	+	0.0711353i	$0.977338\pi$
$200$	−5.75679	−	12.4544i	−0.407066	−	0.880660i
$201$		0			0
$202$	7.06603	+	8.95702i	0.497164	+	0.630214i
$203$	−26.2239			−1.84056
$204$		0			0
$205$	−7.77732	+	4.49024i	−0.543191	+	0.313612i
$206$	−3.88234	−	26.7129i	−0.270496	−	1.86117i
$207$		0			0
$208$	11.0928	−	9.21681i	0.769148	−	0.639071i
$209$	14.0933			0.974852
$210$		0			0
$211$	16.2882	−	9.40397i	1.12132	−	0.647396i	0.179585	−	0.983742i	$-0.442525\pi$
$211$	16.2882	−	9.40397i	1.12132	−	0.647396i	0.941738	+	0.336346i	$0.109191\pi$
$212$	1.32232	+	4.45309i	0.0908174	+	0.305840i
$213$		0			0
$214$	5.75522	+	7.29542i	0.393419	+	0.498705i
$215$	−31.6050	−	18.2472i	−2.15545	−	1.24445i
$216$		0			0
$217$	12.6405	−	21.8940i	0.858092	−	1.48626i
$218$	2.46634	+	16.9699i	0.167041	+	1.14935i
$219$		0			0
$220$	19.2016	+	18.1972i	1.29457	+	1.22685i
$221$	−2.75267	+	6.37496i	−0.185165	+	0.428826i
$222$		0			0
$223$	−0.888282	+	0.512850i	−0.0594838	+	0.0343430i	−0.529447	−	0.848343i	$-0.677601\pi$
$223$	−0.888282	+	0.512850i	−0.0594838	+	0.0343430i	0.469963	+	0.882686i	$0.344267\pi$
$224$	−4.43050	−	22.0798i	−0.296025	−	1.47527i
$225$		0			0
$226$	24.5641	+	9.79053i	1.63398	+	0.651256i
$227$	3.67251	−	6.36098i	0.243753	−	0.422193i	−0.718027	−	0.696015i	$-0.754955\pi$
$227$	3.67251	−	6.36098i	0.243753	−	0.422193i	0.961780	+	0.273822i	$0.0882879\pi$
$228$		0			0
$229$	−2.10642			−0.139196			−0.0695982	−	0.997575i	$-0.522172\pi$
$229$	−2.10642			−0.139196			−0.0695982	+	0.997575i	$0.522172\pi$
$230$	−12.8927	+	10.1708i	−0.850119	+	0.670643i
$231$		0			0
$232$	−15.2262	−	10.7378i	−0.999650	−	0.704973i
$233$	30.1894			1.97777			0.988886	−	0.148674i	$-0.0475004\pi$
$233$	30.1894			1.97777			0.988886	+	0.148674i	$0.0475004\pi$
$234$		0			0
$235$			30.5940i			1.99573i
$236$	−0.0292056	+	0.122011i	−0.00190112	+	0.00794225i
$237$		0			0
$238$	6.71549	+	8.51267i	0.435300	+	0.551794i
$239$		−	18.4895i		−	1.19598i	−0.801502	−	0.597992i	$-0.795966\pi$
$239$		−	18.4895i		−	1.19598i	0.801502	−	0.597992i	$-0.204034\pi$
$240$		0			0
$241$	8.80353	+	5.08272i	0.567086	+	0.327407i	0.755984	−	0.654590i	$-0.227159\pi$
$241$	8.80353	+	5.08272i	0.567086	+	0.327407i	−0.188899	+	0.981997i	$0.560492\pi$
$242$	−8.88160	−	3.53994i	−0.570931	−	0.227556i
$243$		0			0
$244$	−14.2066	−	3.40060i	−0.909483	−	0.217701i
$245$	−13.8857	−	24.0508i	−0.887127	−	1.53655i
$246$		0			0
$247$	4.77976	−	11.0695i	0.304129	−	0.704338i
$248$	16.3042	−	7.53627i	1.03532	−	0.478554i
$249$		0			0
$250$	0.0951577	+	0.654743i	0.00601830	+	0.0414096i
$251$	1.44560	+	0.834618i	0.0912455	+	0.0526806i	0.544928	−	0.838483i	$-0.316557\pi$
$251$	1.44560	+	0.834618i	0.0912455	+	0.0526806i	−0.453683	+	0.891163i	$0.649890\pi$
$252$		0			0
$253$	7.79578	−	13.5027i	0.490117	−	0.848907i
$254$	0.988597	−	0.779885i	0.0620301	−	0.0489344i
$255$		0			0
$256$	6.46848	−	14.6342i	0.404280	−	0.914635i
$257$	−15.8839	−	27.5117i	−0.990809	−	1.71613i	−0.612553	−	0.790430i	$-0.709857\pi$
$257$	−15.8839	−	27.5117i	−0.990809	−	1.71613i	−0.378256	−	0.925701i	$-0.623476\pi$
$258$		0			0
$259$			5.64050i			0.350483i
$260$	20.8052	−	8.91027i	1.29028	−	0.552592i
$261$		0			0
$262$	4.64768	−	0.675476i	0.287135	−	0.0417311i
$263$	−1.42242	−	2.46371i	−0.0877102	−	0.151919i	0.818833	−	0.574032i	$-0.194622\pi$
$263$	−1.42242	−	2.46371i	−0.0877102	−	0.151919i	−0.906543	+	0.422114i	$0.861288\pi$
$264$		0			0
$265$			7.28988i			0.447813i
$266$	−11.6608	−	14.7815i	−0.714972	−	0.906311i
$267$		0			0
$268$	17.3548	+	16.4469i	1.06011	+	1.00466i
$269$	7.47092	+	4.31334i	0.455510	+	0.262989i	0.710155	−	0.704046i	$-0.248625\pi$
$269$	7.47092	+	4.31334i	0.455510	+	0.262989i	−0.254644	+	0.967035i	$0.581958\pi$
$270$		0			0
$271$	0.896928	−	0.517842i	0.0544845	−	0.0314566i	−0.472510	−	0.881325i	$-0.656652\pi$
$271$	0.896928	−	0.517842i	0.0544845	−	0.0314566i	0.526995	+	0.849869i	$0.323319\pi$
$272$	0.413507	+	7.69242i	0.0250726	+	0.466421i
$273$		0			0
$274$	−3.61219	+	9.06288i	−0.218221	+	0.547509i
$275$	10.2218	+	17.7046i	0.616396	+	1.06763i
$276$		0			0
$277$	−14.5234	−	8.38507i	−0.872625	−	0.503810i	−0.00440514	−	0.999990i	$-0.501402\pi$
$277$	−14.5234	−	8.38507i	−0.872625	−	0.503810i	−0.868220	+	0.496180i	$0.834736\pi$
$278$	2.61415	−	6.55882i	0.156786	−	0.393372i
$279$		0			0
$280$	3.19827	−	35.1957i	0.191133	−	2.10334i
$281$			17.7570i			1.05930i	0.848217	+	0.529648i	$0.177676\pi$
$281$			17.7570i			1.05930i	−0.848217	+	0.529648i	$0.822324\pi$
$282$		0			0
$283$	−10.5921	+	6.11533i	−0.629633	+	0.363519i	−0.780610	−	0.625019i	$-0.785091\pi$
$283$	−10.5921	+	6.11533i	−0.629633	+	0.363519i	0.150977	+	0.988537i	$0.451758\pi$
$284$	11.8777	+	2.84315i	0.704814	+	0.168710i
$285$		0			0
$286$	−15.2176	+	15.1724i	−0.899836	+	0.897164i
$287$	−11.3907			−0.672374
$288$		0			0
$289$	6.64549	+	11.5103i	0.390911	+	0.677078i
$290$	−18.1093	−	22.9557i	−1.06342	−	1.34800i
$291$		0			0
$292$	5.13651	+	17.2979i	0.300591	+	1.01228i
$293$	6.17354	−	10.6929i	0.360662	−	0.624686i	−0.627408	−	0.778691i	$-0.715884\pi$
$293$	6.17354	−	10.6929i	0.360662	−	0.624686i	0.988070	+	0.154005i	$0.0492173\pi$
$294$		0			0
$295$	−0.0984412	+	0.170505i	−0.00573147	+	0.00992719i
$296$	−2.30960	+	3.27500i	−0.134243	+	0.190356i
$297$		0			0
$298$	−27.6269	−	11.0113i	−1.60038	−	0.637865i
$299$	−7.96171	−	10.7027i	−0.460437	−	0.618950i
$300$		0			0
$301$	−23.1445	−	40.0875i	−1.33403	−	2.31060i
$302$	21.8004	−	3.16839i	1.25447	−	0.182320i
$303$		0			0
$304$	−0.718018	−	13.3572i	−0.0411812	−	0.766087i
$305$	−19.8531	−	11.4622i	−1.13678	−	0.656322i
$306$		0			0
$307$	−15.8252			−0.903189			−0.451595	−	0.892223i	$-0.649145\pi$
$307$	−15.8252			−0.903189			−0.451595	+	0.892223i	$0.649145\pi$
$308$	9.55162	+	32.1663i	0.544254	+	1.83285i
$309$		0			0
$310$	27.8944	−	4.05407i	1.58430	−	0.230255i
$311$	−17.0009			−0.964030			−0.482015	−	0.876163i	$-0.660095\pi$
$311$	−17.0009			−0.964030			−0.482015	+	0.876163i	$0.660095\pi$
$312$		0			0
$313$	3.56281			0.201382			0.100691	−	0.994918i	$-0.467895\pi$
$313$	3.56281			0.201382			0.100691	+	0.994918i	$0.467895\pi$
$314$	−19.0153	+	2.76361i	−1.07309	+	0.155959i
$315$		0			0
$316$	−23.1738	+	6.88132i	−1.30363	+	0.387104i
$317$	−6.07202			−0.341039			−0.170519	−	0.985354i	$-0.554545\pi$
$317$	−6.07202			−0.341039			−0.170519	+	0.985354i	$0.554545\pi$
$318$		0			0
$319$	24.0418	+	13.8805i	1.34608	+	0.777161i
$320$	16.2685	−	19.1258i	0.909434	−	1.06917i
$321$		0			0
$322$	−20.6123	+	2.99572i	−1.14868	+	0.166945i
$323$	3.22019	+	5.57753i	0.179176	+	0.310342i
$324$		0			0
$325$	17.3728	−	2.02411i	0.963670	−	0.112277i
$326$	−15.3843	−	6.13173i	−0.852059	−	0.339605i
$327$		0			0
$328$	−6.61372	−	4.66413i	−0.365182	−	0.257533i
$329$	−19.4025	+	33.6062i	−1.06970	+	1.85277i
$330$		0			0
$331$	8.39629	−	14.5428i	0.461502	−	0.799345i	−0.537534	−	0.843242i	$-0.680644\pi$
$331$	8.39629	−	14.5428i	0.461502	−	0.799345i	0.999036	+	0.0438972i	$0.0139774\pi$
$332$	9.79546	−	2.90871i	0.537596	−	0.159636i
$333$		0			0
$334$	−0.134822	−	0.170903i	−0.00737716	−	0.00935141i
$335$	18.7611	+	32.4953i	1.02503	+	1.77541i
$336$		0			0
$337$	28.8880			1.57363			0.786815	−	0.617189i	$-0.211729\pi$
$337$	28.8880			1.57363			0.786815	+	0.617189i	$0.211729\pi$
$338$	6.75607	+	17.0984i	0.367482	+	0.930031i
$339$		0			0
$340$	−2.81428	+	11.7571i	−0.152626	+	0.637618i
$341$	−23.1773	+	13.3814i	−1.25512	+	0.724645i
$342$		0			0
$343$		−	7.35807i		−	0.397299i
$344$	2.97626	−	32.7526i	0.160469	−	1.76590i
$345$		0			0
$346$	−13.5732	+	34.0548i	−0.729700	+	1.83079i
$347$	3.63911	+	2.10104i	0.195358	+	0.112790i	0.594488	−	0.804104i	$-0.297355\pi$
$347$	3.63911	+	2.10104i	0.195358	+	0.112790i	−0.399131	+	0.916894i	$0.630688\pi$
$348$		0			0
$349$	−3.16574	−	5.48322i	−0.169458	−	0.293510i	0.768771	−	0.639524i	$-0.220868\pi$
$349$	−3.16574	−	5.48322i	−0.169458	−	0.293510i	−0.938229	+	0.346014i	$0.887535\pi$
$350$	10.1117	−	25.3698i	0.540491	−	1.35607i
$351$		0			0
$352$	−7.62517	+	22.5876i	−0.406423	+	1.20392i
$353$	−7.42833	+	4.28875i	−0.395370	+	0.228267i	−0.684484	−	0.729028i	$-0.739973\pi$
$353$	−7.42833	+	4.28875i	−0.395370	+	0.228267i	0.289114	+	0.957295i	$0.406639\pi$
$354$		0			0
$355$	16.5986	+	9.58321i	0.880962	+	0.508624i
$356$	2.05678	−	2.17032i	0.109009	−	0.115027i
$357$		0			0
$358$	−11.0620	−	14.0223i	−0.584643	−	0.741104i
$359$			25.9007i			1.36699i	0.729956	+	0.683494i	$0.239541\pi$
$359$			25.9007i			1.36699i	−0.729956	+	0.683494i	$0.760459\pi$
$360$		0			0
$361$	3.90843	+	6.76961i	0.205707	+	0.356295i
$362$	25.8354	−	3.75482i	1.35788	−	0.197349i
$363$		0			0
$364$	28.5045	+	3.40699i	1.49404	+	0.178575i
$365$			28.3173i			1.48219i
$366$		0			0
$367$	−11.2481	−	19.4823i	−0.587148	−	1.01697i	−0.994604	−	0.103745i	$-0.966917\pi$
$367$	−11.2481	−	19.4823i	−0.587148	−	1.01697i	0.407456	−	0.913225i	$-0.366416\pi$
$368$	−13.1946	−	6.70069i	−0.687818	−	0.349297i
$369$		0			0
$370$	−4.93753	+	3.89513i	−0.256690	+	0.202498i
$371$	−4.62320	+	8.00762i	−0.240025	+	0.415735i
$372$		0			0
$373$	7.64709	+	4.41505i	0.395951	+	0.228603i	0.684736	−	0.728792i	$-0.259918\pi$
$373$	7.64709	+	4.41505i	0.395951	+	0.228603i	−0.288784	+	0.957394i	$0.593251\pi$
$374$	−1.65086	−	11.3589i	−0.0853637	−	0.587354i
$375$		0			0
$376$	−25.0262	+	11.5678i	−1.29063	+	0.596565i
$377$	19.0563	−	14.1760i	0.981448	−	0.730100i
$378$		0			0
$379$	−2.94384	−	5.09888i	−0.151215	−	0.261912i	0.780459	−	0.625206i	$-0.214985\pi$
$379$	−2.94384	−	5.09888i	−0.151215	−	0.261912i	−0.931674	+	0.363294i	$0.881652\pi$
$380$	4.88673	−	20.4151i	0.250684	−	1.04727i
$381$		0			0
$382$	7.25068	+	2.88990i	0.370977	+	0.147860i
$383$	10.8164	+	6.24483i	0.552691	+	0.319096i	0.750207	−	0.661204i	$-0.229954\pi$
$383$	10.8164	+	6.24483i	0.552691	+	0.319096i	−0.197516	+	0.980300i	$0.563287\pi$
$384$		0			0
$385$			52.6575i			2.68367i
$386$	0.110324	+	0.139849i	0.00561534	+	0.00711810i
$387$		0			0
$388$	−11.3979	−	2.72828i	−0.578638	−	0.138508i
$389$		−	7.83635i		−	0.397319i	−0.980069	−	0.198659i	$-0.936341\pi$
$389$		−	7.83635i		−	0.397319i	0.980069	−	0.198659i	$-0.0636587\pi$
$390$		0			0
$391$	7.12507			0.360330
$392$	14.4235	−	20.4524i	0.728496	−	1.03300i
$393$		0			0
$394$	−10.3531	+	8.16739i	−0.521583	+	0.411467i
$395$	−37.9363			−1.90878
$396$		0			0
$397$	−4.81455	+	8.33904i	−0.241635	+	0.418524i	−0.961180	−	0.275921i	$-0.911017\pi$
$397$	−4.81455	+	8.33904i	−0.241635	+	0.418524i	0.719545	+	0.694446i	$0.244350\pi$
$398$	−20.7686	−	8.27774i	−1.04103	−	0.414925i
$399$		0			0
$400$	16.2592	−	10.5899i	0.812958	−	0.529495i
$401$	32.5570	−	18.7968i	1.62582	−	0.938666i	0.640494	−	0.767963i	$-0.278729\pi$
$401$	32.5570	−	18.7968i	1.62582	−	0.938666i	0.985323	−	0.170703i	$-0.0546039\pi$
$402$		0			0
$403$	2.64978	+	22.7429i	0.131995	+	1.13291i
$404$	−11.0982	+	11.7108i	−0.552157	+	0.582636i
$405$		0			0
$406$	−5.33393	−	36.7007i	−0.264718	−	1.82142i
$407$	2.98556	−	5.17114i	0.147989	−	0.256324i
$408$		0			0
$409$	−30.8797	−	17.8284i	−1.52690	−	0.881557i	−0.999490	−	0.0319469i	$-0.989829\pi$
$409$	−30.8797	−	17.8284i	−1.52690	−	0.881557i	−0.527412	−	0.849610i	$-0.676837\pi$
$410$	−7.86603	−	9.97112i	−0.388476	−	0.492439i
$411$		0			0
$412$	36.5953	−	10.8668i	1.80292	−	0.535367i
$413$	−0.216267	+	0.124862i	−0.0106418	+	0.00614404i
$414$		0			0
$415$	16.0355			0.787153
$416$	15.1553	+	13.6498i	0.743049	+	0.669237i
$417$		0			0
$418$	2.86656	+	19.7237i	0.140208	+	0.964716i
$419$	11.0423	−	6.37526i	0.539450	−	0.311452i	−0.205406	−	0.978677i	$-0.565851\pi$
$419$	11.0423	−	6.37526i	0.539450	−	0.311452i	0.744856	+	0.667225i	$0.232518\pi$
$420$		0			0
$421$	−7.12038			−0.347026			−0.173513	−	0.984832i	$-0.555512\pi$
$421$	−7.12038			−0.347026			−0.173513	+	0.984832i	$0.555512\pi$
$422$	16.4740	+	20.8827i	0.801940	+	1.01655i
$423$		0			0
$424$	−5.96319	+	2.75636i	−0.289598	+	0.133861i
$425$	−4.67117	+	8.09070i	−0.226585	+	0.392457i
$426$		0			0
$427$	−14.5385	−	25.1814i	−0.703567	−	1.21861i
$428$	−9.03941	+	9.53838i	−0.436936	+	0.461055i
$429$		0			0
$430$	19.1087	−	47.9430i	0.921502	−	2.31202i
$431$	−0.125387	+	0.0723921i	−0.00603967	+	0.00348700i	−0.503017	−	0.864277i	$-0.667777\pi$
$431$	−0.125387	+	0.0723921i	−0.00603967	+	0.00348700i	0.496977	+	0.867764i	$0.334443\pi$
$432$		0			0
$433$	10.4272	−	18.0604i	0.501097	−	0.867925i	−0.498902	−	0.866658i	$-0.666263\pi$
$433$	10.4272	−	18.0604i	0.501097	−	0.867925i	0.999999	−	0.00126704i	$-0.000403311\pi$
$434$	33.2119	+	13.2373i	1.59422	+	0.635409i
$435$		0			0
$436$	−23.2479	+	6.90333i	−1.11337	+	0.330609i
$437$	−12.3720			−0.591835
$438$		0			0
$439$	12.9810	+	22.4838i	0.619550	+	1.07309i	0.989568	+	0.144068i	$0.0460183\pi$
$439$	12.9810	+	22.4838i	0.619550	+	1.07309i	−0.370018	+	0.929025i	$0.620648\pi$
$440$	−21.5615	+	30.5741i	−1.02790	+	1.45757i
$441$		0			0
$442$	−9.48171	−	2.55573i	−0.450999	−	0.121564i
$443$			5.43334i			0.258146i	0.991635	+	0.129073i	$0.0412001\pi$
$443$			5.43334i			0.258146i	−0.991635	+	0.129073i	$0.958800\pi$
$444$		0			0
$445$	4.06372	−	2.34619i	0.192639	−	0.111220i
$446$	−0.898415	−	1.13885i	−0.0425412	−	0.0539260i
$447$		0			0
$448$	29.9997	−	10.6915i	1.41735	−	0.505128i
$449$	6.29523	+	3.63455i	0.297090	+	0.171525i	0.641135	−	0.767428i	$-0.278464\pi$
$449$	6.29523	+	3.63455i	0.297090	+	0.171525i	−0.344045	+	0.938953i	$0.611797\pi$
$450$		0			0
$451$	10.4429	+	6.02921i	0.491737	+	0.283904i
$452$	−8.70562	+	36.3691i	−0.409478	+	1.71066i
$453$		0			0
$454$	9.64924	+	3.84590i	0.452861	+	0.180497i
$455$	41.3597	+	17.8589i	1.93897	+	0.837239i
$456$		0			0
$457$	−21.6279	+	12.4869i	−1.01171	+	0.584111i	−0.911692	−	0.410875i	$-0.865223\pi$
$457$	−21.6279	+	12.4869i	−1.01171	+	0.584111i	−0.100018	+	0.994986i	$0.531890\pi$
$458$	−0.428445	−	2.94796i	−0.0200199	−	0.137749i
$459$		0			0
$460$	−16.8565	−	15.9747i	−0.785938	−	0.744825i
$461$	−9.23732	+	15.9995i	−0.430225	+	0.745171i	−0.996892	−	0.0787751i	$-0.974899\pi$
$461$	−9.23732	+	15.9995i	−0.430225	+	0.745171i	0.566667	+	0.823947i	$0.308232\pi$
$462$		0			0
$463$			5.51017i			0.256079i	0.991769	+	0.128040i	$0.0408685\pi$
$463$			5.51017i			0.256079i	−0.991769	+	0.128040i	$0.959131\pi$
$464$	11.9307	−	23.4933i	0.553869	−	1.09065i
$465$		0			0
$466$	6.14050	+	42.2504i	0.284453	+	1.95721i
$467$			28.3047i			1.30979i	0.755722	+	0.654893i	$0.227286\pi$
$467$			28.3047i			1.30979i	−0.755722	+	0.654893i	$0.772714\pi$
$468$		0			0
$469$			47.5929i			2.19763i
$470$	−42.8166	+	6.22280i	−1.97498	+	0.287036i
$471$		0			0
$472$	−0.176696	−	0.0160566i	−0.00813310	−	0.000739063i
$473$			49.0023i			2.25313i
$474$		0			0
$475$	8.11106	−	14.0488i	0.372161	−	0.644602i
$476$	−10.5476	+	11.1299i	−0.483450	+	0.510136i
$477$		0			0
$478$	25.8762	−	3.76074i	1.18355	−	0.172012i
$479$	0.857951	−	0.495338i	0.0392008	−	0.0226326i	−0.480272	−	0.877120i	$-0.659462\pi$
$479$	0.857951	−	0.495338i	0.0392008	−	0.0226326i	0.519472	+	0.854487i	$0.326129\pi$
$480$		0			0
$481$	−3.04911	−	4.09881i	−0.139027	−	0.186890i
$482$	−5.32269	+	13.3545i	−0.242442	+	0.608279i
$483$		0			0
$484$	3.14767	−	13.1499i	0.143076	−	0.597723i
$485$	−15.9280	−	9.19603i	−0.723253	−	0.417570i
$486$		0			0
$487$	−17.0470	−	9.84212i	−0.772476	−	0.445989i	0.0612815	−	0.998121i	$-0.480481\pi$
$487$	−17.0470	−	9.84212i	−0.772476	−	0.445989i	−0.833757	+	0.552132i	$0.813815\pi$
$488$	1.86957	−	20.5739i	0.0846316	−	0.931338i
$489$		0			0
$490$	30.8350	−	24.3251i	1.39298	−	1.09890i
$491$	25.6962	−	14.8357i	1.15966	−	0.669527i	0.208434	−	0.978036i	$-0.433163\pi$
$491$	25.6962	−	14.8357i	1.15966	−	0.669527i	0.951221	+	0.308509i	$0.0998301\pi$
$492$		0			0
$493$			12.6863i			0.571364i
$494$	16.4641	+	4.43779i	0.740756	+	0.199666i
$495$		0			0
$496$	13.8634	+	21.2850i	0.622483	+	0.955726i
$497$	12.1552	+	21.0535i	0.545237	+	0.944378i
$498$		0			0
$499$	−6.24154			−0.279410			−0.139705	−	0.990193i	$-0.544615\pi$
$499$	−6.24154			−0.279410			−0.139705	+	0.990193i	$0.544615\pi$
$500$	−0.896964	+	0.266348i	−0.0401135	+	0.0119115i
$501$		0			0
$502$	−0.874022	+	2.19289i	−0.0390095	+	0.0978737i
$503$	−3.85799	+	6.68224i	−0.172019	+	0.297946i	−0.939126	−	0.343574i	$-0.888363\pi$
$503$	−3.85799	+	6.68224i	−0.172019	+	0.297946i	0.767106	+	0.641520i	$0.221696\pi$
$504$		0			0
$505$	−21.9275	+	12.6598i	−0.975759	+	0.563355i
$506$	20.4828	+	8.16384i	0.910572	+	0.362927i
$507$		0			0
$508$	1.29254	+	1.22492i	0.0573471	+	0.0543472i
$509$	−8.96597	−	15.5295i	−0.397409	−	0.688333i	0.595996	−	0.802987i	$-0.296757\pi$
$509$	−8.96597	−	15.5295i	−0.397409	−	0.688333i	−0.993405	+	0.114654i	$0.963424\pi$
$510$		0			0
$511$	−17.9587	+	31.1053i	−0.794444	+	1.37602i
$512$	21.7963	+	6.07613i	0.963271	+	0.268530i
$513$		0			0
$514$	35.2721	−	27.8255i	1.55579	−	1.22733i
$515$	59.9078			2.63985
$516$		0			0
$517$	35.5761	−	20.5399i	1.56463	−	0.903342i
$518$	−7.89393	+	1.14727i	−0.346840	+	0.0504083i
$519$		0			0
$520$	16.7018	+	27.3047i	0.732421	+	1.19739i
$521$	−30.0883			−1.31819			−0.659096	−	0.752059i	$-0.729061\pi$
$521$	−30.0883			−1.31819			−0.659096	+	0.752059i	$0.729061\pi$
$522$		0			0
$523$	31.8942	−	18.4142i	1.39464	−	0.805195i	0.400814	−	0.916160i	$-0.368727\pi$
$523$	31.8942	−	18.4142i	1.39464	−	0.805195i	0.993824	+	0.110965i	$0.0353941\pi$
$524$	1.89067	+	6.36709i	0.0825944	+	0.278148i
$525$		0			0
$526$	3.15866	−	2.49181i	0.137724	−	0.108648i
$527$	−10.5916	−	6.11508i	−0.461378	−	0.266377i
$528$		0			0
$529$	4.65633	−	8.06499i	0.202449	−	0.350652i
$530$	−10.2023	+	1.48276i	−0.443158	+	0.0644068i
$531$		0			0
$532$	18.3150	−	19.3260i	0.794057	−	0.837888i
$533$	8.27736	−	6.15753i	0.358532	−	0.266712i
$534$		0			0
$535$	−17.8597	+	10.3113i	−0.772144	+	0.445797i
$536$	−19.4877	+	27.6335i	−0.841741	+	1.19359i
$537$		0			0
$538$	−4.51698	+	11.3330i	−0.194741	+	0.488599i
$539$	−18.6449	+	32.2939i	−0.803092	+	1.39100i
$540$		0			0
$541$	−3.36378			−0.144620			−0.0723100	−	0.997382i	$-0.523037\pi$
$541$	−3.36378			−0.144620			−0.0723100	+	0.997382i	$0.523037\pi$
$542$	0.907159	+	1.14993i	0.0389658	+	0.0493938i
$543$		0			0
$544$	−10.6815	+	2.14334i	−0.457966	+	0.0918950i
$545$	−38.0576			−1.63021
$546$		0			0
$547$		−	29.3993i		−	1.25702i	−0.777801	−	0.628511i	$-0.783665\pi$
$547$		−	29.3993i		−	1.25702i	0.777801	−	0.628511i	$-0.216335\pi$
$548$	−13.4183	−	3.21192i	−0.573202	−	0.137206i
$549$		0			0
$550$	−22.6987	+	17.9066i	−0.967876	+	0.763539i
$551$		−	22.0287i		−	0.938453i
$552$		0			0
$553$	−41.6714	−	24.0590i	−1.77205	−	1.02309i
$554$	8.78095	−	22.0311i	0.373067	−	0.936013i
$555$		0			0
$556$	9.71085	+	2.32447i	0.411832	+	0.0985795i
$557$	−9.16684	−	15.8774i	−0.388412	−	0.672749i	0.603824	−	0.797117i	$-0.293643\pi$
$557$	−9.16684	−	15.8774i	−0.388412	−	0.672749i	−0.992236	+	0.124369i	$0.960309\pi$
$558$		0			0
$559$	38.4888	+	16.6193i	1.62790	+	0.702920i
$560$	49.9073	−	2.68277i	2.10897	−	0.113368i
$561$		0			0
$562$	−24.8512	+	3.61177i	−1.04828	+	0.152353i
$563$	−0.0171903	−	0.00992482i	−0.000724485	−	0.000418281i	0.499638	−	0.866234i	$-0.333466\pi$
$563$	−0.0171903	−	0.00992482i	−0.000724485	−	0.000418281i	−0.500362	+	0.865816i	$0.666800\pi$
$564$		0			0
$565$	−29.3434	+	50.8243i	−1.23449	+	2.13819i
$566$	−10.7129	−	13.5798i	−0.450296	−	0.570803i
$567$		0			0
$568$	−1.56310	+	17.2013i	−0.0655862	+	0.721750i
$569$	−4.01749	−	6.95849i	−0.168422	−	0.291715i	0.769443	−	0.638715i	$-0.220534\pi$
$569$	−4.01749	−	6.95849i	−0.168422	−	0.291715i	−0.937865	+	0.347000i	$0.887200\pi$
$570$		0			0
$571$			43.0575i			1.80190i	0.433922	+	0.900950i	$0.357129\pi$
$571$			43.0575i			1.80190i	−0.433922	+	0.900950i	$0.642871\pi$
$572$	−24.3292	−	18.2111i	−1.01726	−	0.761446i
$573$		0			0
$574$	−2.31687	−	15.9414i	−0.0967042	−	0.665383i
$575$	−8.97337	−	15.5423i	−0.374216	−	0.648160i
$576$		0			0
$577$		−	27.1370i		−	1.12973i	−0.825184	−	0.564864i	$-0.808929\pi$
$577$		−	27.1370i		−	1.12973i	0.825184	−	0.564864i	$-0.191071\pi$
$578$	−14.7571	+	11.6416i	−0.613816	+	0.484228i
$579$		0			0
$580$	28.4433	−	30.0133i	1.18104	−	1.24624i
$581$	17.6143	+	10.1696i	0.730766	+	0.421908i
$582$		0			0
$583$	8.47699	−	4.89419i	0.351081	−	0.202697i
$584$	−23.1638	+	10.7070i	−0.958525	+	0.443058i
$585$		0			0
$586$	16.2205	+	6.46501i	0.670063	+	0.267067i
$587$	−12.4090	−	21.4930i	−0.512175	−	0.887113i	−0.999900	−	0.0141157i	$-0.995507\pi$
$587$	−12.4090	−	21.4930i	−0.512175	−	0.887113i	0.487726	−	0.872997i	$-0.337827\pi$
$588$		0			0
$589$	18.3914	+	10.6183i	0.757804	+	0.437519i
$590$	−0.258647	−	0.103089i	−0.0106483	−	0.00424410i
$591$		0			0
$592$	−5.05317	−	2.56617i	−0.207684	−	0.105469i
$593$		−	21.5232i		−	0.883852i	−0.897051	−	0.441926i	$-0.854295\pi$
$593$		−	21.5232i		−	0.883852i	0.897051	−	0.441926i	$-0.145705\pi$
$594$		0			0
$595$	−20.8396	+	12.0318i	−0.854342	+	0.493255i
$596$	9.79108	−	40.9038i	0.401058	−	1.67549i
$597$		0			0
$598$	13.3591	−	13.3194i	0.546293	−	0.544671i
$599$	17.8112			0.727744			0.363872	−	0.931449i	$-0.381455\pi$
$599$	17.8112			0.727744			0.363872	+	0.931449i	$0.381455\pi$
$600$		0			0
$601$	−9.07847	−	15.7244i	−0.370319	−	0.641411i	0.619296	−	0.785158i	$-0.287418\pi$
$601$	−9.07847	−	15.7244i	−0.370319	−	0.641411i	−0.989614	+	0.143747i	$0.954085\pi$
$602$	51.3953	−	40.5448i	2.09471	−	1.65248i
$603$		0			0
$604$	8.86839	+	29.8655i	0.360850	+	1.21521i
$605$	10.6096	−	18.3764i	0.431343	−	0.747108i
$606$		0			0
$607$	−8.39617	+	14.5426i	−0.340790	+	0.590265i	−0.984580	−	0.174937i	$-0.944028\pi$
$607$	−8.39617	+	14.5426i	−0.340790	+	0.590265i	0.643790	+	0.765202i	$0.277361\pi$
$608$	18.5475	−	3.72172i	0.752200	−	0.150936i
$609$		0			0
$610$	12.0033	−	30.1159i	0.486000	−	1.21936i
$611$	−4.06729	−	34.9093i	−0.164545	−	1.41228i
$612$		0			0
$613$	6.93552	+	12.0127i	0.280123	+	0.485187i	0.971415	−	0.237388i	$-0.0762914\pi$
$613$	6.93552	+	12.0127i	0.280123	+	0.485187i	−0.691292	+	0.722576i	$0.742958\pi$
$614$	−3.21883	−	22.1475i	−0.129901	−	0.893799i
$615$		0			0
$616$	−43.0743	+	19.9102i	−1.73551	+	0.802205i
$617$	−13.9565	−	8.05780i	−0.561868	−	0.324395i	0.192027	−	0.981390i	$-0.438494\pi$
$617$	−13.9565	−	8.05780i	−0.561868	−	0.324395i	−0.753895	+	0.656995i	$0.771827\pi$
$618$		0			0
$619$	24.5032			0.984866			0.492433	−	0.870350i	$-0.336108\pi$
$619$	24.5032			0.984866			0.492433	+	0.870350i	$0.336108\pi$
$620$	11.3474	+	38.2139i	0.455723	+	1.53471i
$621$		0			0
$622$	−3.45796	−	23.7929i	−0.138652	−	0.954007i
$623$	5.95176			0.238452
$624$		0			0
$625$	−25.7231			−1.02892
$626$	0.724674	+	4.98619i	0.0289638	+	0.199288i
$627$		0			0
$628$	−7.73539	−	26.0500i	−0.308676	−	1.03951i
$629$	2.72870			0.108800
$630$		0			0
$631$	10.2300	+	5.90627i	0.407248	+	0.235125i	0.689607	−	0.724184i	$-0.257783\pi$
$631$	10.2300	+	5.90627i	0.407248	+	0.235125i	−0.282358	+	0.959309i	$0.591117\pi$
$632$	−14.3440	−	31.0323i	−0.570574	−	1.23440i
$633$		0			0
$634$	−1.23504	−	8.49785i	−0.0490499	−	0.337493i
$635$	1.39728	+	2.42016i	0.0554493	+	0.0960410i
$636$		0			0
$637$	19.0417	+	25.5971i	0.754461	+	1.01420i
$638$	−14.5359	+	36.4700i	−0.575481	+	1.44386i
$639$		0			0
$640$	30.0758	+	18.8777i	1.18885	+	0.746206i
$641$	−14.1841	+	24.5677i	−0.560240	+	0.970364i	0.437235	+	0.899347i	$0.355958\pi$
$641$	−14.1841	+	24.5677i	−0.560240	+	0.970364i	−0.997475	+	0.0710170i	$0.977376\pi$
$642$		0			0
$643$	6.21913	−	10.7718i	0.245258	−	0.424800i	−0.716946	−	0.697129i	$-0.754461\pi$
$643$	6.21913	−	10.7718i	0.245258	−	0.424800i	0.962204	+	0.272329i	$0.0877939\pi$
$644$	−8.38507	−	28.2378i	−0.330418	−	1.11273i
$645$		0			0
$646$	−7.15083	+	5.64115i	−0.281345	+	0.221948i
$647$	3.30728	+	5.72838i	0.130023	+	0.225206i	0.923685	−	0.383153i	$-0.125162\pi$
$647$	3.30728	+	5.72838i	0.130023	+	0.225206i	−0.793662	+	0.608358i	$0.791828\pi$
$648$		0			0
$649$	0.264361			0.0103771
$650$	6.36638	+	23.9017i	0.249710	+	0.937502i
$651$		0			0
$652$	5.45226	−	22.7777i	0.213527	−	0.892044i
$653$	23.5353	−	13.5881i	0.921009	−	0.531745i	0.0370519	−	0.999313i	$-0.488203\pi$
$653$	23.5353	−	13.5881i	0.921009	−	0.531745i	0.883957	+	0.467569i	$0.154870\pi$
$654$		0			0
$655$			10.4232i			0.407267i
$656$	5.18227	−	10.2046i	0.202334	−	0.398425i
$657$		0			0
$658$	−50.9787	−	20.3186i	−1.98736	−	0.792101i
$659$	−13.1651	−	7.60087i	−0.512839	−	0.296088i	0.221161	−	0.975237i	$-0.429015\pi$
$659$	−13.1651	−	7.60087i	−0.512839	−	0.296088i	−0.734000	+	0.679150i	$0.762349\pi$
$660$		0			0
$661$	−10.5180	−	18.2177i	−0.409102	−	0.708585i	0.585688	−	0.810537i	$-0.300825\pi$
$661$	−10.5180	−	18.2177i	−0.409102	−	0.708585i	−0.994789	+	0.101952i	$0.967491\pi$
$662$	22.0606	+	8.79270i	0.857410	+	0.341738i
$663$		0			0
$664$	6.06315	+	13.1172i	0.235296	+	0.509047i
$665$	36.1862	−	20.8921i	1.40324	−	0.810161i
$666$		0			0
$667$	−21.1056	−	12.1853i	−0.817210	−	0.471817i
$668$	0.211758	−	0.223447i	0.00819317	−	0.00864542i
$669$		0			0
$670$	−41.6614	+	32.8659i	−1.60952	+	1.26972i
$671$			30.7814i			1.18830i
$672$		0			0
$673$	−1.24365	−	2.15406i	−0.0479391	−	0.0830329i	0.841060	−	0.540942i	$-0.181932\pi$
$673$	−1.24365	−	2.15406i	−0.0479391	−	0.0830329i	−0.888999	+	0.457909i	$0.848599\pi$
$674$	5.87580	+	40.4290i	0.226327	+	1.55727i
$675$		0			0
$676$	−22.5552	+	12.9330i	−0.867508	+	0.497423i
$677$			3.55109i			0.136479i	0.997669	+	0.0682397i	$0.0217383\pi$
$677$			3.55109i			0.136479i	−0.997669	+	0.0682397i	$0.978262\pi$
$678$		0			0
$679$	−11.6641	−	20.2029i	−0.447629	−	0.775316i
$680$	−17.0266	−	1.54722i	−0.652940	−	0.0593333i
$681$		0			0
$682$	−23.4417	−	29.7151i	−0.897629	−	1.13785i
$683$	7.60672	−	13.1752i	0.291063	−	0.504136i	−0.682998	−	0.730420i	$-0.739324\pi$
$683$	7.60672	−	13.1752i	0.291063	−	0.504136i	0.974061	+	0.226284i	$0.0726577\pi$
$684$		0			0
$685$	−18.7515	−	10.8262i	−0.716458	−	0.413647i
$686$	10.2977	−	1.49663i	0.393168	−	0.0571415i
$687$		0			0
$688$	46.4430	−	2.49655i	1.77062	−	0.0951801i
$689$	−0.969146	−	8.31812i	−0.0369215	−	0.316895i
$690$		0			0
$691$	11.4909	+	19.9028i	0.437134	+	0.757137i	0.997467	−	0.0711296i	$-0.0226604\pi$
$691$	11.4909	+	19.9028i	0.437134	+	0.757137i	−0.560334	+	0.828267i	$0.689327\pi$
$692$	−50.4208	−	12.0691i	−1.91671	−	0.458800i
$693$		0			0
$694$	−2.20023	+	5.52032i	−0.0835197	+	0.209548i
$695$	13.5705	+	7.83492i	0.514758	+	0.297196i
$696$		0			0
$697$			5.51049i			0.208725i
$698$	7.02991	−	5.54576i	0.266086	−	0.209910i
$699$		0			0
$700$	37.5620	+	8.99116i	1.41971	+	0.339834i
$701$			13.4528i			0.508105i	0.967190	+	0.254053i	$0.0817636\pi$
$701$			13.4528i			0.508105i	−0.967190	+	0.254053i	$0.918236\pi$
$702$		0			0
$703$	−4.73814			−0.178702
$704$	−33.1625	−	6.07720i	−1.24986	−	0.229043i
$705$		0			0
$706$	−7.51306	−	9.52369i	−0.282758	−	0.358429i
$707$	−32.1152			−1.20782
$708$		0			0
$709$	−17.8824	+	30.9732i	−0.671587	+	1.16322i	0.305866	+	0.952074i	$0.401054\pi$
$709$	−17.8824	+	30.9732i	−0.671587	+	1.16322i	−0.977454	+	0.211149i	$0.932279\pi$
$710$	−10.0357	+	25.1791i	−0.376631	+	0.944956i
$711$		0			0
$712$	3.45573	+	2.43705i	0.129509	+	0.0913323i
$713$	20.3466	−	11.7471i	0.761988	−	0.439934i
$714$		0			0
$715$	−28.4653	−	38.2649i	−1.06454	−	1.43103i
$716$	17.3744	−	18.3335i	0.649313	−	0.685154i
$717$		0			0
$718$	−36.2483	+	5.26819i	−1.35278	+	0.196607i
$719$	6.16811	−	10.6835i	0.230032	−	0.398427i	−0.727785	−	0.685805i	$-0.759450\pi$
$719$	6.16811	−	10.6835i	0.230032	−	0.398427i	0.957817	+	0.287378i	$0.0927837\pi$
$720$		0			0
$721$	65.8061	+	37.9932i	2.45075	+	1.41494i
$722$	−8.67916	+	6.84683i	−0.323005	+	0.254812i
$723$		0			0
$724$	10.5098	+	35.3932i	0.390594	+	1.31538i
$725$	27.6734	−	15.9773i	1.02777	−	0.593381i
$726$		0			0
$727$	37.8521			1.40386			0.701928	−	0.712247i	$-0.252323\pi$
$727$	37.8521			1.40386			0.701928	+	0.712247i	$0.252323\pi$
$728$	1.02967	+	40.5853i	0.0381622	+	1.50419i
$729$		0			0
$730$	−39.6303	+	5.75971i	−1.46678	+	0.213177i
$731$	−19.3931	+	11.1966i	−0.717279	+	0.414121i
$732$		0			0
$733$	6.75241			0.249406			0.124703	−	0.992194i	$-0.460202\pi$
$733$	6.75241			0.249406			0.124703	+	0.992194i	$0.460202\pi$
$734$	24.9779	−	19.7046i	0.921950	−	0.727309i
$735$		0			0
$736$	6.69390	−	19.8289i	0.246740	−	0.730904i
$737$	25.1913	−	43.6326i	0.927933	−	1.60723i
$738$		0			0
$739$	0.391736	+	0.678507i	0.0144103	+	0.0249593i	0.873141	−	0.487468i	$-0.162080\pi$
$739$	0.391736	+	0.678507i	0.0144103	+	0.0249593i	−0.858730	+	0.512428i	$0.828746\pi$
$740$	−6.45556	−	6.11786i	−0.237311	−	0.224897i
$741$		0			0
$742$	−12.1471	−	4.84147i	−0.445934	−	0.177736i
$743$	41.1541	−	23.7603i	1.50980	−	0.871683i	0.509864	−	0.860255i	$-0.329696\pi$
$743$	41.1541	−	23.7603i	1.50980	−	0.871683i	0.999935	−	0.0114275i	$-0.00363755\pi$
$744$		0			0
$745$	33.0021	−	57.1613i	1.20910	−	2.09423i
$746$	−4.62349	+	11.6002i	−0.169278	+	0.424713i
$747$		0			0
$748$	15.5611	−	4.62078i	0.568970	−	0.168952i
$749$	−26.1575			−0.955776
$750$		0			0
$751$	−19.5727	−	33.9009i	−0.714218	−	1.23706i	−0.963260	−	0.268570i	$-0.913449\pi$
$751$	−19.5727	−	33.9009i	−0.714218	−	1.23706i	0.249042	−	0.968493i	$-0.419884\pi$
$752$	−21.2796	−	32.6715i	−0.775987	−	1.19141i
$753$		0			0
$754$	23.7155	+	23.7861i	0.863666	+	0.866238i
$755$			48.8909i			1.77932i
$756$		0			0
$757$	13.8830	−	8.01535i	0.504586	−	0.291323i	−0.226019	−	0.974123i	$-0.572571\pi$
$757$	13.8830	−	8.01535i	0.504586	−	0.291323i	0.730605	+	0.682800i	$0.239238\pi$
$758$	6.53716	−	5.15704i	0.237440	−	0.187312i
$759$		0			0
$760$	29.5651	+	2.68661i	1.07244	+	0.0974537i
$761$	−18.3101	−	10.5714i	−0.663742	−	0.383212i	0.129959	−	0.991519i	$-0.458515\pi$
$761$	−18.3101	−	10.5714i	−0.663742	−	0.383212i	−0.793701	+	0.608308i	$0.791849\pi$
$762$		0			0
$763$	−41.8047	−	24.1359i	−1.51343	−	0.873780i
$764$	−2.56967	+	10.7352i	−0.0929673	+	0.388386i
$765$		0			0
$766$	−6.53967	+	16.4078i	−0.236288	+	0.592838i
$767$	0.0896587	−	0.207642i	0.00323739	−	0.00749752i
$768$		0			0
$769$	−23.6873	+	13.6759i	−0.854185	+	0.493164i	−0.862061	−	0.506805i	$-0.830826\pi$
$769$	−23.6873	+	13.6759i	−0.854185	+	0.493164i	0.00787567	+	0.999969i	$0.497493\pi$
$770$	−73.6947	+	10.7105i	−2.65577	+	0.385980i
$771$		0			0
$772$	−0.173280	+	0.182844i	−0.00623647	+	0.00658072i
$773$	8.48123	−	14.6899i	0.305049	−	0.528360i	−0.672224	−	0.740348i	$-0.734661\pi$
$773$	8.48123	−	14.6899i	0.305049	−	0.528360i	0.977272	+	0.211989i	$0.0679939\pi$
$774$		0			0
$775$			30.8055i			1.10657i
$776$	1.49995	−	16.5063i	0.0538450	−	0.592543i
$777$		0			0
$778$	10.9670	−	1.59391i	0.393188	−	0.0571444i
$779$		−	9.56846i		−	0.342826i
$780$		0			0
$781$		−	25.7355i		−	0.920887i
$782$	1.44923	+	9.97161i	0.0518245	+	0.356584i
$783$		0			0
$784$	31.5571	+	16.0258i	1.12704	+	0.572350i
$785$		−	42.6447i		−	1.52206i
$786$		0			0
$787$	11.0502	−	19.1396i	0.393899	−	0.682252i	−0.599061	−	0.800703i	$-0.704459\pi$
$787$	11.0502	−	19.1396i	0.393899	−	0.682252i	0.992960	+	0.118451i	$0.0377928\pi$
$788$	−13.5362	−	12.8281i	−0.482206	−	0.456981i
$789$		0			0
$790$	−7.71622	−	53.0922i	−0.274531	−	1.88894i
$791$	−64.4649	+	37.2188i	−2.29211	+	1.32335i
$792$		0			0
$793$	24.1772	+	10.4396i	0.858556	+	0.370720i
$794$	−12.6498	−	5.04185i	−0.448926	−	0.178929i
$795$		0			0
$796$	7.36046	−	30.7495i	0.260885	−	1.08989i
$797$	−1.98959	−	1.14869i	−0.0704748	−	0.0406886i	0.464349	−	0.885653i	$-0.346289\pi$
$797$	−1.98959	−	1.14869i	−0.0704748	−	0.0406886i	−0.534823	+	0.844964i	$0.679622\pi$
$798$		0			0
$799$	16.2576	+	9.38635i	0.575154	+	0.332065i
$800$	18.1278	+	20.6009i	0.640914	+	0.728351i
$801$		0			0
$802$	32.9283	+	41.7405i	1.16274	+	1.47391i
$803$	32.9286	−	19.0113i	1.16202	−	0.670895i
$804$		0			0
$805$		−	46.2264i		−	1.62927i
$806$	−31.2900	+	8.33429i	−1.10214	+	0.293563i
$807$		0			0
$808$	−18.6468	−	13.1501i	−0.655992	−	0.462619i
$809$	−3.89606	−	6.74818i	−0.136978	−	0.237253i	0.789373	−	0.613914i	$-0.210406\pi$
$809$	−3.89606	−	6.74818i	−0.136978	−	0.237253i	−0.926351	+	0.376660i	$0.877072\pi$
$810$		0			0
$811$	−17.0777			−0.599679			−0.299840	−	0.953990i	$-0.596933\pi$
$811$	−17.0777			−0.599679			−0.299840	+	0.953990i	$0.596933\pi$
$812$	50.2780	−	14.9298i	1.76441	−	0.523932i
$813$		0			0
$814$	7.84433	+	3.12652i	0.274944	+	0.109584i
$815$	18.3775	−	31.8308i	0.643737	−	1.11499i
$816$		0			0
$817$	33.6743	−	19.4419i	1.17812	−	0.680186i
$818$	18.6701	−	46.8427i	0.652785	−	1.63782i
$819$		0			0
$820$	12.3547	−	13.0367i	0.431446	−	0.455262i
$821$	11.0400	+	19.1218i	0.385297	+	0.667354i	0.991810	−	0.127719i	$-0.0407657\pi$
$821$	11.0400	+	19.1218i	0.385297	+	0.667354i	−0.606513	+	0.795073i	$0.707432\pi$
$822$		0			0
$823$	−17.9141	+	31.0281i	−0.624447	+	1.08157i	0.364201	+	0.931320i	$0.381342\pi$
$823$	−17.9141	+	31.0281i	−0.624447	+	1.08157i	−0.988648	+	0.150253i	$0.951991\pi$
$824$	22.6516	+	49.0051i	0.789105	+	1.70717i
$825$		0			0
$826$	−0.218734	−	0.277271i	−0.00761072	−	0.00964749i
$827$	17.0225			0.591929			0.295964	−	0.955199i	$-0.404359\pi$
$827$	17.0225			0.591929			0.295964	+	0.955199i	$0.404359\pi$
$828$		0			0
$829$	−15.3179	+	8.84379i	−0.532013	+	0.307158i	−0.741836	−	0.670582i	$-0.766045\pi$
$829$	−15.3179	+	8.84379i	−0.532013	+	0.307158i	0.209823	+	0.977739i	$0.432711\pi$
$830$	3.26162	+	22.4419i	0.113212	+	0.778969i
$831$		0			0
$832$	−16.0205	+	23.9863i	−0.555410	+	0.831577i
$833$	−17.0408			−0.590428
$834$		0			0
$835$	0.418384	−	0.241554i	0.0144788	−	0.00835933i
$836$	−27.0204	+	8.02356i	−0.934521	+	0.277501i
$837$		0			0
$838$	11.1682	+	14.1570i	0.385800	+	0.489047i
$839$	21.4773	+	12.3999i	0.741478	+	0.428093i	0.822606	−	0.568611i	$-0.192519\pi$
$839$	21.4773	+	12.3999i	0.741478	+	0.428093i	−0.0811284	+	0.996704i	$0.525852\pi$
$840$		0			0
$841$	7.19616	−	12.4641i	0.248143	−	0.429797i
$842$	−1.44828	−	9.96504i	−0.0499110	−	0.343418i
$843$		0			0
$844$	−25.8747	+	27.3030i	−0.890645	+	0.939808i
$845$	−39.7092	+	9.38038i	−1.36604	+	0.322695i
$846$		0			0
$847$	23.3084	−	13.4571i	0.800888	−	0.462393i
$848$	−5.07046	−	7.78490i	−0.174120	−	0.267335i
$849$		0			0
$850$	−12.2731	−	4.89171i	−0.420965	−	0.167784i
$851$	−2.62093	+	4.53959i	−0.0898444	+	0.155615i
$852$		0			0
$853$	42.6375			1.45988			0.729941	−	0.683510i	$-0.239548\pi$
$853$	42.6375			1.45988			0.729941	+	0.683510i	$0.239548\pi$
$854$	32.2845	−	25.4686i	1.10475	−	0.871519i
$855$		0			0
$856$	−15.1877	−	10.7106i	−0.519104	−	0.366082i
$857$	−18.8716			−0.644640			−0.322320	−	0.946631i	$-0.604463\pi$
$857$	−18.8716			−0.644640			−0.322320	+	0.946631i	$0.604463\pi$
$858$		0			0
$859$		−	34.5624i		−	1.17926i	−0.807675	−	0.589628i	$-0.799274\pi$
$859$		−	34.5624i		−	1.17926i	0.807675	−	0.589628i	$-0.200726\pi$
$860$	70.9835	+	16.9912i	2.42052	+	0.579395i
$861$		0			0
$862$	−0.126817	−	0.160755i	−0.00431940	−	0.00547535i
$863$		−	13.9874i		−	0.476136i	−0.971249	−	0.238068i	$-0.923486\pi$
$863$		−	13.9874i		−	0.476136i	0.971249	−	0.238068i	$-0.0765141\pi$
$864$		0			0
$865$	−70.4608	−	40.6805i	−2.39574	−	1.38318i
$866$	27.3965	+	10.9194i	0.930972	+	0.371058i
$867$		0			0
$868$	−11.7704	+	49.1728i	−0.399514	+	1.66903i
$869$	25.4692	+	44.1140i	0.863985	+	1.49647i
$870$		0			0
$871$	−25.7275	−	34.5846i	−0.871742	−	1.17185i
$872$	−14.3899	−	31.1315i	−0.487303	−	1.05425i
$873$		0			0
$874$	−2.51647	−	17.3148i	−0.0851207	−	0.585682i
$875$	−1.61293	−	0.931228i	−0.0545271	−	0.0314812i
$876$		0			0
$877$	−25.6958	+	44.5064i	−0.867686	+	1.50288i	−0.00332994	+	0.999994i	$0.501060\pi$
$877$	−25.6958	+	44.5064i	−0.867686	+	1.50288i	−0.864356	+	0.502881i	$0.832273\pi$
$878$	−28.8260	+	22.7403i	−0.972829	+	0.767446i
$879$		0			0
$880$	−47.1744	−	23.9568i	−1.59025	−	0.807583i
$881$	12.8416	+	22.2423i	0.432644	+	0.749362i	0.997100	−	0.0761015i	$-0.0242473\pi$
$881$	12.8416	+	22.2423i	0.432644	+	0.749362i	−0.564456	+	0.825463i	$0.690914\pi$
$882$		0			0
$883$		−	1.54889i		−	0.0521242i	−0.999660	−	0.0260621i	$-0.991703\pi$
$883$		−	1.54889i		−	0.0521242i	0.999660	−	0.0260621i	$-0.00829676\pi$
$884$	1.64820	−	13.7896i	0.0554348	−	0.463794i
$885$		0			0
$886$	−7.60401	+	1.10514i	−0.255462	+	0.0371278i
$887$	−1.64662	−	2.85204i	−0.0552883	−	0.0957621i	0.837057	−	0.547116i	$-0.184274\pi$
$887$	−1.64662	−	2.85204i	−0.0552883	−	0.0957621i	−0.892345	+	0.451354i	$0.850941\pi$
$888$		0			0
$889$			3.54459i			0.118882i
$890$	4.11007	+	5.21000i	0.137770	+	0.174640i
$891$		0			0
$892$	1.41109	−	1.48898i	0.0472468	−	0.0498548i
$893$	−28.2299	−	16.2986i	−0.944679	−	0.545410i
$894$		0			0
$895$	34.3278	−	19.8191i	1.14745	−	0.662481i
$896$	21.0648	+	39.8102i	0.703727	+	1.32997i
$897$		0			0
$898$	−3.80615	+	9.54950i	−0.127013	+	0.318671i
$899$	20.9160	+	36.2276i	0.697588	+	1.20826i
$900$		0			0
$901$	3.87384	+	2.23656i	0.129056	+	0.0745107i
$902$	−6.31386	+	15.8413i	−0.210229	+	0.527457i
$903$		0			0
$904$	−52.6697	−	4.78615i	−1.75177	−	0.159185i
$905$			57.9400i			1.92599i
$906$		0			0
$907$	−9.53698	+	5.50618i	−0.316670	+	0.182830i	−0.649907	−	0.760013i	$-0.725192\pi$
$907$	−9.53698	+	5.50618i	−0.316670	+	0.182830i	0.333237	+	0.942843i	$0.391859\pi$
$908$	−3.41973	+	14.2865i	−0.113488	+	0.474113i
$909$		0			0
$910$	−16.5812	+	61.5159i	−0.549661	+	2.03923i
$911$	−57.1333			−1.89291			−0.946456	−	0.322833i	$-0.895365\pi$
$911$	−57.1333			−1.89291			−0.946456	+	0.322833i	$0.895365\pi$
$912$		0			0
$913$	−10.7658	−	18.6468i	−0.356294	−	0.617120i
$914$	−21.8746	−	27.7286i	−0.723547	−	0.917182i
$915$		0			0
$916$	4.03856	−	1.19923i	0.133438	−	0.0396236i
$917$	−6.61031	+	11.4494i	−0.218292	+	0.378092i
$918$		0			0
$919$	1.95754	−	3.39056i	0.0645734	−	0.111844i	−0.831931	−	0.554879i	$-0.812765\pi$
$919$	1.95754	−	3.39056i	0.0645734	−	0.111844i	0.896505	+	0.443034i	$0.146098\pi$
$920$	18.9282	−	26.8401i	0.624043	−	0.884892i
$921$		0			0
$922$	−24.2703	−	9.67344i	−0.799301	−	0.318578i
$923$	−20.2139	−	8.72824i	−0.665348	−	0.287293i
$924$		0			0
$925$	−3.43655	−	5.95227i	−0.112993	−	0.195709i
$926$	−7.71154	+	1.12077i	−0.253417	+	0.0368306i
$927$		0			0
$928$	35.3058	+	11.9186i	1.15897	+	0.391248i
$929$	−23.5063	−	13.5713i	−0.771215	−	0.445261i	0.0620927	−	0.998070i	$-0.480223\pi$
$929$	−23.5063	−	13.5713i	−0.771215	−	0.445261i	−0.833308	+	0.552809i	$0.813556\pi$
$930$		0			0
$931$	29.5898			0.969766
$932$	−57.8808	+	17.1874i	−1.89595	+	0.562992i
$933$		0			0
$934$	−39.6127	+	5.75716i	−1.29617	+	0.188380i
$935$	25.4741			0.833091
$936$		0			0
$937$	−15.1865			−0.496121			−0.248061	−	0.968745i	$-0.579793\pi$
$937$	−15.1865			−0.496121			−0.248061	+	0.968745i	$0.579793\pi$
$938$	−66.6067	+	9.68036i	−2.17479	+	0.316075i
$939$		0			0
$940$	−17.4177	−	58.6566i	−0.568104	−	1.91317i
$941$	23.8706			0.778158			0.389079	−	0.921204i	$-0.372793\pi$
$941$	23.8706			0.778158			0.389079	+	0.921204i	$0.372793\pi$
$942$		0			0
$943$	−9.16749	−	5.29285i	−0.298535	−	0.172359i
$944$	−0.0134686	−	0.250554i	−0.000438365	−	0.00815484i
$945$		0			0
$946$	−68.5793	+	9.96704i	−2.22970	+	0.324057i
$947$	−0.105623	−	0.182945i	−0.00343230	−	0.00594492i	0.864304	−	0.502970i	$-0.167759\pi$
$947$	−0.105623	−	0.182945i	−0.00343230	−	0.00594492i	−0.867736	+	0.497025i	$0.834426\pi$
$948$		0			0
$949$	−3.76461	−	32.3114i	−0.122204	−	1.04887i
$950$	21.3112	+	8.49400i	0.691426	+	0.275582i
$951$		0			0
$952$	−17.7217	−	12.4977i	−0.574365	−	0.405054i
$953$	14.5683	−	25.2330i	0.471913	−	0.817377i	−0.527571	−	0.849511i	$-0.676897\pi$
$953$	14.5683	−	25.2330i	0.471913	−	0.817377i	0.999484	+	0.0321343i	$0.0102304\pi$
$954$		0			0
$955$	−8.66139	+	15.0020i	−0.280276	+	0.485452i
$956$	10.5264	+	35.4490i	0.340448	+	1.14650i
$957$		0			0
$958$	0.867738	+	1.09996i	0.0280353	+	0.0355381i
$959$	−13.7318	−	23.7842i	−0.443423	−	0.768031i
$960$		0			0
$961$	−9.32783			−0.300898
$962$	5.11614	−	5.10095i	0.164951	−	0.164461i
$963$		0			0
$964$	−19.7723	−	4.73287i	−0.636824	−	0.152435i
$965$	−0.342360	+	0.197661i	−0.0110209	+	0.00636295i
$966$		0			0
$967$			7.86383i			0.252884i	0.991974	+	0.126442i	$0.0403557\pi$
$967$			7.86383i			0.252884i	−0.991974	+	0.126442i	$0.959644\pi$
$968$	19.0437	+	1.73052i	0.612087	+	0.0556209i
$969$		0			0
$970$	9.63019	−	24.1619i	0.309207	−	0.775790i
$971$	−45.0181	−	25.9912i	−1.44470	−	0.834098i	−0.446541	−	0.894763i	$-0.647344\pi$
$971$	−45.0181	−	25.9912i	−1.44470	−	0.834098i	−0.998158	+	0.0606655i	$0.980678\pi$
$972$		0			0
$973$	9.93773	+	17.2127i	0.318589	+	0.551812i
$974$	10.3068	−	25.8594i	0.330251	−	0.828589i
$975$		0			0
$976$	29.1737	−	1.56824i	0.933827	−	0.0501980i
$977$	−46.1724	+	26.6577i	−1.47719	+	0.852854i	−0.999668	−	0.0257671i	$-0.991797\pi$
$977$	−46.1724	+	26.6577i	−1.47719	+	0.852854i	−0.477519	+	0.878621i	$0.658464\pi$
$978$		0			0
$979$	−5.45651	−	3.15032i	−0.174391	−	0.100685i
$980$	40.3151	+	38.2062i	1.28782	+	1.22045i
$981$		0			0
$982$	25.9894	+	32.9446i	0.829354	+	1.05130i
$983$			5.04182i			0.160809i	0.996762	+	0.0804046i	$0.0256212\pi$
$983$			5.04182i			0.160809i	−0.996762	+	0.0804046i	$0.974379\pi$
$984$		0			0
$985$	−14.6331	−	25.3452i	−0.466248	−	0.807566i
$986$	−17.7546	+	2.58039i	−0.565423	+	0.0821764i
$987$		0			0
$988$	−2.86194	+	23.9444i	−0.0910505	+	0.761771i
$989$		−	43.0176i		−	1.36788i
$990$		0			0
$991$	2.07413	+	3.59249i	0.0658868	+	0.114119i	0.897087	−	0.441854i	$-0.145679\pi$
$991$	2.07413	+	3.59249i	0.0658868	+	0.114119i	−0.831200	+	0.555973i	$0.812346\pi$
$992$	−26.9688	+	23.7313i	−0.856261	+	0.753469i
$993$		0			0
$994$	−26.9922	+	21.2936i	−0.856141	+	0.675393i
$995$	24.8094	−	42.9711i	0.786510	−	1.36228i
$996$		0			0
$997$	−26.6284	−	15.3739i	−0.843330	−	0.486897i	0.0150648	−	0.999887i	$-0.495205\pi$
$997$	−26.6284	−	15.3739i	−0.843330	−	0.486897i	−0.858395	+	0.512990i	$0.828538\pi$
$998$	−1.26953	−	8.73510i	−0.0401861	−	0.276505i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.dg.e.829.15		48
3.2	odd	2		312.2.bk.b.205.10	✓	48
8.5	even	2	inner	936.2.dg.e.829.6		48
12.11	even	2		1248.2.ca.b.49.12		48
13.4	even	6	inner	936.2.dg.e.901.6		48
24.5	odd	2		312.2.bk.b.205.19	yes	48
24.11	even	2		1248.2.ca.b.49.13		48
39.17	odd	6		312.2.bk.b.277.19	yes	48
104.69	even	6	inner	936.2.dg.e.901.15		48
156.95	even	6		1248.2.ca.b.433.13		48
312.173	odd	6		312.2.bk.b.277.10	yes	48
312.251	even	6		1248.2.ca.b.433.12		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bk.b.205.10	✓	48	3.2	odd	2
312.2.bk.b.205.19	yes	48	24.5	odd	2
312.2.bk.b.277.10	yes	48	312.173	odd	6
312.2.bk.b.277.19	yes	48	39.17	odd	6
936.2.dg.e.829.6		48	8.5	even	2	inner
936.2.dg.e.829.15		48	1.1	even	1	trivial
936.2.dg.e.901.6		48	13.4	even	6	inner
936.2.dg.e.901.15		48	104.69	even	6	inner
1248.2.ca.b.49.12		48	12.11	even	2
1248.2.ca.b.49.13		48	24.11	even	2
1248.2.ca.b.433.12		48	312.251	even	6
1248.2.ca.b.433.13		48	156.95	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.dg (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.203399 + 1.39951i) q^{2} +(-1.91726 + 0.569319i) q^{4} -3.13862 q^{5} +(-3.44764 - 1.99050i) q^{7} +(-1.18674 - 2.56742i) q^{8} +(-0.638393 - 4.39253i) q^{10} +(2.10717 + 3.64973i) q^{11} +(3.58133 - 0.417261i) q^{13} +(2.08447 - 5.22987i) q^{14} +(3.35175 - 2.18306i) q^{16} +(-0.962941 + 1.66786i) q^{17} +(1.67206 - 2.89609i) q^{19} +(6.01754 - 1.78688i) q^{20} +(-4.67924 + 3.69136i) q^{22} +(-1.84982 - 3.20398i) q^{23} +4.85094 q^{25} +(1.31240 + 4.92723i) q^{26} +(7.74324 + 1.85349i) q^{28} +(5.70476 - 3.29364i) q^{29} +6.35042i q^{31} +(3.73696 + 4.24678i) q^{32} +(-2.53005 - 1.00840i) q^{34} +(10.8208 + 6.24741i) q^{35} +(-0.708429 - 1.22703i) q^{37} +(4.39321 + 1.75100i) q^{38} +(3.72472 + 8.05817i) q^{40} +(2.47794 - 1.43064i) q^{41} +(10.0697 + 5.81376i) q^{43} +(-6.11785 - 5.79782i) q^{44} +(4.10776 - 3.24053i) q^{46} -9.74759i q^{47} +(4.42415 + 7.66285i) q^{49} +(0.986678 + 6.78894i) q^{50} +(-6.62877 + 2.83891i) q^{52} -2.32264i q^{53} +(-6.61361 - 11.4551i) q^{55} +(-1.01900 + 11.2137i) q^{56} +(5.76983 + 7.31394i) q^{58} +(0.0313645 - 0.0543248i) q^{59} +(6.32541 + 3.65198i) q^{61} +(-8.88748 + 1.29167i) q^{62} +(-5.18331 + 6.09371i) q^{64} +(-11.2404 + 1.30962i) q^{65} +(-5.97751 - 10.3534i) q^{67} +(0.896660 - 3.74594i) q^{68} +(-6.54237 + 16.4146i) q^{70} +(-5.28850 - 3.05332i) q^{71} -9.02220i q^{73} +(1.57315 - 1.24103i) q^{74} +(-1.55697 + 6.50449i) q^{76} -16.7773i q^{77} +12.0869 q^{79} +(-10.5199 + 6.85180i) q^{80} +(2.50621 + 3.17691i) q^{82} -5.10910 q^{83} +(3.02231 - 5.23479i) q^{85} +(-6.08824 + 15.2752i) q^{86} +(6.86974 - 9.74127i) q^{88} +(-1.29475 + 0.747522i) q^{89} +(-13.1777 - 5.69005i) q^{91} +(5.37067 + 5.08972i) q^{92} +(13.6419 - 1.98265i) q^{94} +(-5.24796 + 9.08974i) q^{95} +(5.07484 + 2.92996i) q^{97} +(-9.82437 + 7.75026i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{4} - 12 q^{7} - 4 q^{10} + 36 q^{14} - 2 q^{16} - 12 q^{17} - 54 q^{20} - 14 q^{22} - 20 q^{23} + 48 q^{25} + 42 q^{26} + 6 q^{28} + 28 q^{38} - 8 q^{40} + 12 q^{41} - 30 q^{46} + 16 q^{49}+ \cdots - 24 q^{98}+O(q^{100}) \) 48 * q - 2 * q^4 - 12 * q^7 - 4 * q^10 + 36 * q^14 - 2 * q^16 - 12 * q^17 - 54 * q^20 - 14 * q^22 - 20 * q^23 + 48 * q^25 + 42 * q^26 + 6 * q^28 + 28 * q^38 - 8 * q^40 + 12 * q^41 - 30 * q^46 + 16 * q^49 + 84 * q^50 - 28 * q^52 - 68 * q^55 - 18 * q^56 - 24 * q^58 - 24 * q^62 - 68 * q^64 - 12 * q^65 - 4 * q^68 + 12 * q^71 - 54 * q^74 - 54 * q^76 - 192 * q^79 - 78 * q^80 - 6 * q^82 - 10 * q^88 + 48 * q^89 + 12 * q^92 + 54 * q^94 + 20 * q^95 + 144 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more