LMFDB - Embedded newform 429.2.bi.a.5.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(5,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 8, 15]))

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

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

chi := DirichletCharacter("429.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bi (of order $20$, degree $8$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$416$
Relative dimension:	$52$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			5.19
Character	$\chi$	$=$	429.5
Dual form			429.2.bi.a.86.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.339713 + 0.666725i) q^{2} +(-1.42645 - 0.982471i) q^{3} +(0.846454 + 1.16504i) q^{4} +(0.476840 - 0.242962i) q^{5} +(1.13962 - 0.617289i) q^{6} +(-1.13337 - 0.179507i) q^{7} +(-2.54245 + 0.402685i) q^{8} +(1.06950 + 2.80289i) q^{9} +O(q^{10})$	\(q+(-0.339713 + 0.666725i) q^{2} +(-1.42645 - 0.982471i) q^{3} +(0.846454 + 1.16504i) q^{4} +(0.476840 - 0.242962i) q^{5} +(1.13962 - 0.617289i) q^{6} +(-1.13337 - 0.179507i) q^{7} +(-2.54245 + 0.402685i) q^{8} +(1.06950 + 2.80289i) q^{9} +0.400459i q^{10} +(-2.58665 + 2.07588i) q^{11} +(-0.0627998 - 2.49349i) q^{12} +(3.35057 - 1.33180i) q^{13} +(0.504701 - 0.694662i) q^{14} +(-0.918891 - 0.121909i) q^{15} +(-0.294789 + 0.907268i) q^{16} +(-1.54087 + 4.74230i) q^{17} +(-2.23208 - 0.239114i) q^{18} +(0.744454 - 0.117910i) q^{19} +(0.686685 + 0.349884i) q^{20} +(1.44032 + 1.36956i) q^{21} +(-0.505321 - 2.42978i) q^{22} -7.06321 q^{23} +(4.02230 + 1.92348i) q^{24} +(-2.77058 + 3.81338i) q^{25} +(-0.250292 + 2.68634i) q^{26} +(1.22817 - 5.04892i) q^{27} +(-0.750208 - 1.47237i) q^{28} +(4.61078 + 6.34619i) q^{29} +(0.393439 - 0.571233i) q^{30} +(4.70833 + 2.39901i) q^{31} +(-4.14515 - 4.14515i) q^{32} +(5.72920 - 0.419825i) q^{33} +(-2.63836 - 2.63836i) q^{34} +(-0.584048 + 0.189769i) q^{35} +(-2.36020 + 3.61853i) q^{36} +(-5.59384 - 0.885977i) q^{37} +(-0.174287 + 0.536401i) q^{38} +(-6.08786 - 1.39210i) q^{39} +(-1.11451 + 0.809737i) q^{40} +(0.723922 + 4.57066i) q^{41} +(-1.40241 + 0.495044i) q^{42} +9.32757i q^{43} +(-4.60796 - 1.25642i) q^{44} +(1.19098 + 1.07668i) q^{45} +(2.39946 - 4.70921i) q^{46} +(-11.4859 + 1.81918i) q^{47} +(1.31187 - 1.00455i) q^{48} +(-5.40510 - 1.75622i) q^{49} +(-1.60127 - 3.14267i) q^{50} +(6.85714 - 5.25079i) q^{51} +(4.38770 + 2.77626i) q^{52} +(4.92630 - 1.60065i) q^{53} +(2.94902 + 2.53403i) q^{54} +(-0.729057 + 1.61832i) q^{55} +2.95382 q^{56} +(-1.17777 - 0.563212i) q^{57} +(-5.79751 + 0.918235i) q^{58} +(0.897818 - 5.66860i) q^{59} +(-0.635769 - 1.17374i) q^{60} +(0.874197 - 2.69050i) q^{61} +(-3.19896 + 2.32418i) q^{62} +(-0.708997 - 3.36868i) q^{63} +(2.35730 - 0.765932i) q^{64} +(1.27411 - 1.44912i) q^{65} +(-1.66638 + 3.96242i) q^{66} +(5.86648 - 5.86648i) q^{67} +(-6.82927 + 2.21896i) q^{68} +(10.0753 + 6.93940i) q^{69} +(0.0718853 - 0.453866i) q^{70} +(10.9118 - 5.55982i) q^{71} +(-3.84784 - 6.69554i) q^{72} +(10.4695 + 1.65821i) q^{73} +(2.49100 - 3.42857i) q^{74} +(7.69862 - 2.71756i) q^{75} +(0.767516 + 0.767516i) q^{76} +(3.30425 - 1.88841i) q^{77} +(2.99628 - 3.58601i) q^{78} +(0.921045 + 2.83468i) q^{79} +(0.0798645 + 0.504245i) q^{80} +(-6.71233 + 5.99538i) q^{81} +(-3.29330 - 1.07006i) q^{82} +(10.9893 - 5.59933i) q^{83} +(-0.376425 + 2.83731i) q^{84} +(0.417453 + 2.63569i) q^{85} +(-6.21892 - 3.16870i) q^{86} +(-0.342081 - 13.5825i) q^{87} +(5.74050 - 6.31943i) q^{88} +(6.39806 - 6.39806i) q^{89} +(-1.12244 + 0.428291i) q^{90} +(-4.03649 + 0.907958i) q^{91} +(-5.97868 - 8.22895i) q^{92} +(-4.35922 - 8.04786i) q^{93} +(2.68900 - 8.27590i) q^{94} +(0.326338 - 0.237098i) q^{95} +(1.84035 + 9.98532i) q^{96} +(8.66633 + 4.41571i) q^{97} +(3.00710 - 3.00710i) q^{98} +(-8.58487 - 5.02992i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9}+O(q^{10}) $ 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9	$ 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9} - 20 q^{13} - 30 q^{15} + 32 q^{16} + 2 q^{18} - 4 q^{19} - 12 q^{21} - 24 q^{22} - 78 q^{24} - 36 q^{27} - 84 q^{28} - 28 q^{31} - 44 q^{33} - 24 q^{34} - 12 q^{37} + 54 q^{39} + 88 q^{40} - 56 q^{42} + 8 q^{45} - 92 q^{46} + 40 q^{48} - 44 q^{52} - 176 q^{54} - 72 q^{55} - 6 q^{57} - 4 q^{58} + 12 q^{60} - 48 q^{61} - 46 q^{63} + 204 q^{66} - 64 q^{67} + 56 q^{70} - 66 q^{72} - 12 q^{73} - 104 q^{76} - 92 q^{78} + 104 q^{79} + 124 q^{81} + 16 q^{84} - 12 q^{85} - 24 q^{87} - 84 q^{91} - 124 q^{93} + 328 q^{94} - 152 q^{96} + 52 q^{97} - 142 q^{99}+O(q^{100}) $ 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9 - 20 * q^13 - 30 * q^15 + 32 * q^16 + 2 * q^18 - 4 * q^19 - 12 * q^21 - 24 * q^22 - 78 * q^24 - 36 * q^27 - 84 * q^28 - 28 * q^31 - 44 * q^33 - 24 * q^34 - 12 * q^37 + 54 * q^39 + 88 * q^40 - 56 * q^42 + 8 * q^45 - 92 * q^46 + 40 * q^48 - 44 * q^52 - 176 * q^54 - 72 * q^55 - 6 * q^57 - 4 * q^58 + 12 * q^60 - 48 * q^61 - 46 * q^63 + 204 * q^66 - 64 * q^67 + 56 * q^70 - 66 * q^72 - 12 * q^73 - 104 * q^76 - 92 * q^78 + 104 * q^79 + 124 * q^81 + 16 * q^84 - 12 * q^85 - 24 * q^87 - 84 * q^91 - 124 * q^93 + 328 * q^94 - 152 * q^96 + 52 * q^97 - 142 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{5}\right)$	$-1$

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 $

$2$	−0.339713	+	0.666725i	−0.240213	+	0.471445i	−0.979367	−	0.202092i	$-0.935226\pi$
$2$	−0.339713	+	0.666725i	−0.240213	+	0.471445i	0.739153	+	0.673537i	$0.235226\pi$
$3$	−1.42645	−	0.982471i	−0.823560	−	0.567230i
$3$	−1.42645	−	0.982471i	−0.823560	−	0.567230i
$4$	0.846454	+	1.16504i	0.423227	+	0.582522i
$5$	0.476840	−	0.242962i	0.213249	−	0.108656i	−0.344103	−	0.938932i	$-0.611817\pi$
$5$	0.476840	−	0.242962i	0.213249	−	0.108656i	0.557353	+	0.830276i	$0.311817\pi$
$6$	1.13962	−	0.617289i	0.465248	−	0.252007i
$7$	−1.13337	−	0.179507i	−0.428372	−	0.0678474i	−0.0614741	−	0.998109i	$-0.519580\pi$
$7$	−1.13337	−	0.179507i	−0.428372	−	0.0678474i	−0.366898	+	0.930261i	$0.619580\pi$
$8$	−2.54245	+	0.402685i	−0.898893	+	0.142371i
$9$	1.06950	+	2.80289i	0.356501	+	0.934295i
$10$			0.400459i			0.126636i
$11$	−2.58665	+	2.07588i	−0.779903	+	0.625900i
$11$	−2.58665	+	2.07588i	−0.779903	+	0.625900i
$12$	−0.0627998	−	2.49349i	−0.0181287	−	0.719808i
$13$	3.35057	−	1.33180i	0.929281	−	0.369374i
$13$	3.35057	−	1.33180i	0.929281	−	0.369374i
$14$	0.504701	−	0.694662i	0.134887	−	0.185656i
$15$	−0.918891	−	0.121909i	−0.237257	−	0.0314768i
$16$	−0.294789	+	0.907268i	−0.0736973	+	0.226817i
$17$	−1.54087	+	4.74230i	−0.373715	+	1.15018i	0.570626	+	0.821210i	$0.306701\pi$
$17$	−1.54087	+	4.74230i	−0.373715	+	1.15018i	−0.944341	+	0.328967i	$0.893299\pi$
$18$	−2.23208	−	0.239114i	−0.526105	−	0.0563597i
$19$	0.744454	−	0.117910i	0.170789	−	0.0270504i	−0.0704539	−	0.997515i	$-0.522445\pi$
$19$	0.744454	−	0.117910i	0.170789	−	0.0270504i	0.241243	+	0.970465i	$0.422445\pi$
$20$	0.686685	+	0.349884i	0.153547	+	0.0782363i
$21$	1.44032	+	1.36956i	0.314305	+	0.298862i
$22$	−0.505321	−	2.42978i	−0.107735	−	0.518031i
$23$	−7.06321			−1.47278			−0.736390	−	0.676557i	$-0.763471\pi$
$23$	−7.06321			−1.47278			−0.736390	+	0.676557i	$0.763471\pi$
$24$	4.02230	+	1.92348i	0.821049	+	0.392628i
$25$	−2.77058	+	3.81338i	−0.554116	+	0.762675i
$26$	−0.250292	+	2.68634i	−0.0490863	+	0.526834i
$27$	1.22817	−	5.04892i	0.236361	−	0.971665i
$28$	−0.750208	−	1.47237i	−0.141776	−	0.278251i
$29$	4.61078	+	6.34619i	0.856200	+	1.17846i	0.982462	+	0.186462i	$0.0597021\pi$
$29$	4.61078	+	6.34619i	0.856200	+	1.17846i	−0.126262	+	0.991997i	$0.540298\pi$
$30$	0.393439	−	0.571233i	0.0718318	−	0.104292i
$31$	4.70833	+	2.39901i	0.845641	+	0.430876i	0.822438	−	0.568855i	$-0.192613\pi$
$31$	4.70833	+	2.39901i	0.845641	+	0.430876i	0.0232033	+	0.999731i	$0.492613\pi$
$32$	−4.14515	−	4.14515i	−0.732765	−	0.732765i
$33$	5.72920	−	0.419825i	0.997326	−	0.0730821i
$34$	−2.63836	−	2.63836i	−0.452474	−	0.452474i
$35$	−0.584048	+	0.189769i	−0.0987221	+	0.0320768i
$36$	−2.36020	+	3.61853i	−0.393367	+	0.603088i
$37$	−5.59384	−	0.885977i	−0.919621	−	0.145654i	−0.321362	−	0.946956i	$-0.604141\pi$
$37$	−5.59384	−	0.885977i	−0.919621	−	0.145654i	−0.598259	+	0.801303i	$0.704141\pi$
$38$	−0.174287	+	0.536401i	−0.0282731	+	0.0870158i
$39$	−6.08786	−	1.39210i	−0.974838	−	0.222915i
$40$	−1.11451	+	0.809737i	−0.176219	+	0.128031i
$41$	0.723922	+	4.57066i	0.113058	+	0.713818i	0.977476	+	0.211045i	$0.0676867\pi$
$41$	0.723922	+	4.57066i	0.113058	+	0.713818i	−0.864419	+	0.502773i	$0.832313\pi$
$42$	−1.40241	+	0.495044i	−0.216397	+	0.0763869i
$43$			9.32757i			1.42244i	0.702969	+	0.711220i	$0.251857\pi$
$43$			9.32757i			1.42244i	−0.702969	+	0.711220i	$0.748143\pi$
$44$	−4.60796	−	1.25642i	−0.694677	−	0.189413i
$45$	1.19098	+	1.07668i	0.177540	+	0.160502i
$46$	2.39946	−	4.70921i	0.353782	−	0.694336i
$47$	−11.4859	+	1.81918i	−1.67538	+	0.265355i	−0.920568	−	0.390582i	$-0.872274\pi$
$47$	−11.4859	+	1.81918i	−1.67538	+	0.265355i	−0.754816	+	0.655937i	$0.772274\pi$
$48$	1.31187	−	1.00455i	0.189352	−	0.144994i
$49$	−5.40510	−	1.75622i	−0.772157	−	0.250889i
$50$	−1.60127	−	3.14267i	−0.226454	−	0.444440i
$51$	6.85714	−	5.25079i	0.960192	−	0.735257i
$52$	4.38770	+	2.77626i	0.608465	+	0.384998i
$53$	4.92630	−	1.60065i	0.676679	−	0.219866i	0.0495384	−	0.998772i	$-0.484225\pi$
$53$	4.92630	−	1.60065i	0.676679	−	0.219866i	0.627141	+	0.778906i	$0.284225\pi$
$54$	2.94902	+	2.53403i	0.401310	+	0.344838i
$55$	−0.729057	+	1.61832i	−0.0983060	+	0.218214i
$56$	2.95382			0.394720
$57$	−1.17777	−	0.563212i	−0.155999	−	0.0745993i
$58$	−5.79751	+	0.918235i	−0.761250	+	0.120570i
$59$	0.897818	−	5.66860i	0.116886	−	0.737989i	−0.857729	−	0.514102i	$-0.828125\pi$
$59$	0.897818	−	5.66860i	0.116886	−	0.737989i	0.974615	−	0.223887i	$-0.0718747\pi$
$60$	−0.635769	−	1.17374i	−0.0820775	−	0.151529i
$61$	0.874197	−	2.69050i	0.111929	−	0.344483i	−0.879365	−	0.476149i	$-0.842032\pi$
$61$	0.874197	−	2.69050i	0.111929	−	0.344483i	0.991294	+	0.131665i	$0.0420324\pi$
$62$	−3.19896	+	2.32418i	−0.406269	+	0.295171i
$63$	−0.708997	−	3.36868i	−0.0893253	−	0.424413i
$64$	2.35730	−	0.765932i	0.294662	−	0.0957415i
$65$	1.27411	−	1.44912i	0.158034	−	0.179741i
$66$	−1.66638	+	3.96242i	−0.205117	+	0.487740i
$67$	5.86648	−	5.86648i	0.716704	−	0.716704i	−0.251225	−	0.967929i	$-0.580833\pi$
$67$	5.86648	−	5.86648i	0.716704	−	0.716704i	0.967929	+	0.251225i	$0.0808333\pi$
$68$	−6.82927	+	2.21896i	−0.828170	+	0.269089i
$69$	10.0753	+	6.93940i	1.21292	+	0.835405i
$70$	0.0718853	−	0.453866i	0.00859194	−	0.0542474i
$71$	10.9118	−	5.55982i	1.29499	−	0.659829i	0.335622	−	0.941997i	$-0.391053\pi$
$71$	10.9118	−	5.55982i	1.29499	−	0.659829i	0.959365	+	0.282168i	$0.0910534\pi$
$72$	−3.84784	−	6.69554i	−0.453472	−	0.789076i
$73$	10.4695	+	1.65821i	1.22536	+	0.194078i	0.735381	−	0.677654i	$-0.237003\pi$
$73$	10.4695	+	1.65821i	1.22536	+	0.194078i	0.489982	+	0.871732i	$0.337003\pi$
$74$	2.49100	−	3.42857i	0.289573	−	0.398563i
$75$	7.69862	−	2.71756i	0.888960	−	0.313797i
$76$	0.767516	+	0.767516i	0.0880402	+	0.0880402i
$77$	3.30425	−	1.88841i	0.376554	−	0.215204i
$78$	2.99628	−	3.58601i	0.339261	−	0.406036i
$79$	0.921045	+	2.83468i	0.103626	+	0.318927i	0.989405	−	0.145179i	$-0.0463758\pi$
$79$	0.921045	+	2.83468i	0.103626	+	0.318927i	−0.885780	+	0.464106i	$0.846376\pi$
$80$	0.0798645	+	0.504245i	0.00892913	+	0.0563763i
$81$	−6.71233	+	5.99538i	−0.745815	+	0.666153i
$82$	−3.29330	−	1.07006i	−0.363684	−	0.118168i
$83$	10.9893	−	5.59933i	1.20623	−	0.614607i	0.268943	−	0.963156i	$-0.413326\pi$
$83$	10.9893	−	5.59933i	1.20623	−	0.614607i	0.937290	+	0.348549i	$0.113326\pi$
$84$	−0.376425	+	2.83731i	−0.0410713	+	0.309576i
$85$	0.417453	+	2.63569i	0.0452791	+	0.285881i
$86$	−6.21892	−	3.16870i	−0.670603	−	0.341689i
$87$	−0.342081	−	13.5825i	−0.0366750	−	1.45619i
$88$	5.74050	−	6.31943i	0.611940	−	0.673653i
$89$	6.39806	−	6.39806i	0.678193	−	0.678193i	−0.281398	−	0.959591i	$-0.590798\pi$
$89$	6.39806	−	6.39806i	0.678193	−	0.678193i	0.959591	+	0.281398i	$0.0907981\pi$
$90$	−1.12244	+	0.428291i	−0.118316	+	0.0451458i
$91$	−4.03649	+	0.907958i	−0.423139	+	0.0951799i
$92$	−5.97868	−	8.22895i	−0.623320	−	0.857927i
$93$	−4.35922	−	8.04786i	−0.452030	−	0.834525i
$94$	2.68900	−	8.27590i	0.277349	−	0.853594i
$95$	0.326338	−	0.237098i	0.0334816	−	0.0243258i
$96$	1.84035	+	9.98532i	0.187829	+	1.01912i
$97$	8.66633	+	4.41571i	0.879932	+	0.448348i	0.834749	−	0.550631i	$-0.185613\pi$
$97$	8.66633	+	4.41571i	0.879932	+	0.448348i	0.0451832	+	0.998979i	$0.485613\pi$
$98$	3.00710	−	3.00710i	0.303763	−	0.303763i
$99$	−8.58487	−	5.02992i	−0.862812	−	0.505526i
$100$	−6.78792			−0.678792
$101$	−2.38206	−	7.33123i	−0.237024	−	0.729485i	−0.996846	−	0.0793541i	$-0.974714\pi$
$101$	−2.38206	−	7.33123i	−0.237024	−	0.729485i	0.759823	−	0.650130i	$-0.225286\pi$
$102$	1.17137	+	6.35559i	0.115983	+	0.629297i
$103$	−5.07879	−	6.99036i	−0.500429	−	0.688781i	0.481840	−	0.876259i	$-0.339969\pi$
$103$	−5.07879	−	6.99036i	−0.500429	−	0.688781i	−0.982269	+	0.187478i	$0.939969\pi$
$104$	−7.98238	+	4.73525i	−0.782737	+	0.464330i
$105$	1.01956	+	0.303115i	0.0994984	+	0.0295810i
$106$	−0.606335	+	3.82825i	−0.0588924	+	0.371832i
$107$	−3.68239	+	5.06837i	−0.355990	+	0.489978i	−0.949026	−	0.315198i	$-0.897929\pi$
$107$	−3.68239	+	5.06837i	−0.355990	+	0.489978i	0.593036	+	0.805176i	$0.297929\pi$
$108$	6.92180	−	2.84281i	0.666051	−	0.273550i
$109$	−11.6731	+	11.6731i	−1.11808	+	1.11808i	−0.126052	+	0.992024i	$0.540231\pi$
$109$	−11.6731	+	11.6731i	−1.11808	+	1.11808i	−0.992024	+	0.126052i	$0.959769\pi$
$110$	−0.831303	−	1.03584i	−0.0792616	−	0.0987639i
$111$	7.10886	+	6.75958i	0.674744	+	0.641591i
$112$	0.496966	−	0.975350i	0.0469588	−	0.0921619i
$113$	11.3524	−	15.6252i	1.06794	−	1.46990i	0.195802	−	0.980643i	$-0.437269\pi$
$113$	11.3524	−	15.6252i	1.06794	−	1.46990i	0.872141	−	0.489255i	$-0.162731\pi$
$114$	0.775610	−	0.593916i	0.0726426	−	0.0556253i
$115$	−3.36802	+	1.71609i	−0.314070	+	0.160026i
$116$	−3.49078	+	10.7435i	−0.324111	+	0.997511i
$117$	7.31631	+	7.96691i	0.676393	+	0.736541i
$118$	3.47440	+	2.52430i	0.319844	+	0.232380i
$119$	2.59765	−	5.09817i	0.238126	−	0.467348i
$120$	2.38533	−	0.0600757i	0.217750	−	0.00548414i
$121$	2.38147	−	10.7391i	0.216497	−	0.976283i
$122$	1.49685	+	1.49685i	0.135518	+	0.135518i
$123$	3.45791	−	7.23104i	0.311789	−	0.652001i
$124$	1.19043	+	7.51607i	0.106904	+	0.674963i
$125$	−0.813213	+	5.13443i	−0.0727360	+	0.459237i
$126$	2.48684	+	0.671678i	0.221545	+	0.0598378i
$127$	−3.91000	−	1.27044i	−0.346957	−	0.112733i	0.130354	−	0.991467i	$-0.458389\pi$
$127$	−3.91000	−	1.27044i	−0.346957	−	0.112733i	−0.477311	+	0.878734i	$0.658389\pi$
$128$	1.54394	−	9.74804i	0.136466	−	0.861613i
$129$	9.16406	−	13.3053i	0.806851	−	1.17146i
$130$	0.533329	+	1.34176i	0.0467760	+	0.117681i
$131$			21.9114i			1.91441i	0.289412	+	0.957205i	$0.406540\pi$
$131$			21.9114i			1.91441i	−0.289412	+	0.957205i	$0.593460\pi$
$132$	5.33862	+	6.31941i	0.464667	+	0.550034i
$133$	−0.864904			−0.0749967
$134$	1.91840	+	5.90424i	0.165725	+	0.510049i
$135$	−0.641058	−	2.70593i	−0.0551735	−	0.232889i
$136$	2.00793	−	12.6776i	0.172179	−	1.08709i
$137$	4.57195	+	8.97297i	0.390608	+	0.766612i	0.999648	−	0.0265276i	$-0.00844499\pi$
$137$	4.57195	+	8.97297i	0.390608	+	0.766612i	−0.609040	+	0.793140i	$0.708445\pi$
$138$	−8.04937	+	4.36004i	−0.685208	+	0.371151i
$139$	−6.68174	+	4.85457i	−0.566737	+	0.411759i	−0.833919	−	0.551887i	$-0.813908\pi$
$139$	−6.68174	+	4.85457i	−0.566737	+	0.411759i	0.267181	+	0.963646i	$0.413908\pi$
$140$	−0.715458	−	0.519811i	−0.0604673	−	0.0439320i
$141$	18.1713	+	8.68955i	1.53030	+	0.731792i
$142$			9.16388i			0.769016i
$143$	−5.90209	+	10.4003i	−0.493558	+	0.869713i
$144$	−2.85825	+	0.144064i	−0.238187	+	0.0120053i
$145$	3.74049	+	1.90588i	0.310631	+	0.158274i
$146$	−4.66220	+	6.41696i	−0.385846	+	0.531072i
$147$	5.98465	+	7.81552i	0.493606	+	0.644613i
$148$	−3.70272	−	7.26700i	−0.304362	−	0.597344i
$149$	−2.10755	+	1.07385i	−0.172657	+	0.0879733i	−0.538183	−	0.842828i	$-0.680889\pi$
$149$	−2.10755	+	1.07385i	−0.172657	+	0.0879733i	0.365526	+	0.930801i	$0.380889\pi$
$150$	−0.803454	+	6.05605i	−0.0656018	+	0.494474i
$151$	−1.13012	−	7.13527i	−0.0919675	−	0.580660i	−0.990037	−	0.140807i	$-0.955030\pi$
$151$	−1.13012	−	7.13527i	−0.0919675	−	0.580660i	0.898070	−	0.439853i	$-0.144970\pi$
$152$	−1.84526	+	0.599561i	−0.149670	+	0.0486308i
$153$	−14.9401	+	0.753025i	−1.20783	+	0.0608785i
$154$	0.136549	+	2.84454i	0.0110034	+	0.229220i
$155$	2.82799			0.227150
$156$	−3.53123	−	8.27098i	−0.282725	−	0.662208i
$157$	−6.54568	−	4.75572i	−0.522402	−	0.379548i	0.295106	−	0.955465i	$-0.404645\pi$
$157$	−6.54568	−	4.75572i	−0.522402	−	0.379548i	−0.817508	+	0.575917i	$0.804645\pi$
$158$	−2.20284	−	0.348896i	−0.175249	−	0.0277567i
$159$	−8.59970	−	2.55670i	−0.682001	−	0.202760i
$160$	−2.98369	−	0.969459i	−0.235881	−	0.0766424i
$161$	8.00520	+	1.26790i	0.630898	+	0.0999244i
$162$	−1.71700	−	6.51199i	−0.134900	−	0.511630i
$163$	3.38200	−	6.63755i	0.264899	−	0.519893i	−0.719795	−	0.694187i	$-0.755764\pi$
$163$	3.38200	−	6.63755i	0.264899	−	0.519893i	0.984694	+	0.174294i	$0.0557642\pi$
$164$	−4.71226	+	4.71226i	−0.367965	+	0.367965i
$165$	2.62991	−	1.59217i	0.204738	−	0.123950i
$166$			9.22901i			0.716310i
$167$	−5.47143	−	2.78783i	−0.423392	−	0.215729i	0.229294	−	0.973357i	$-0.426358\pi$
$167$	−5.47143	−	2.78783i	−0.423392	−	0.215729i	−0.652687	+	0.757628i	$0.726358\pi$
$168$	−4.21346	−	2.90204i	−0.325076	−	0.223897i
$169$	9.45264	−	8.92455i	0.727126	−	0.686504i
$170$	−1.89910	−	0.617054i	−0.145654	−	0.0473259i
$171$	1.12668	+	1.96051i	0.0861596	+	0.149924i
$172$	−10.8670	+	7.89536i	−0.828603	+	0.602015i
$173$	10.5412	+	7.65864i	0.801434	+	0.582276i	0.911334	−	0.411667i	$-0.135053\pi$
$173$	10.5412	+	7.65864i	0.801434	+	0.582276i	−0.109901	+	0.993943i	$0.535053\pi$
$174$	9.17197	+	4.38607i	0.695326	+	0.332507i
$175$	3.82461	−	3.82461i	0.289113	−	0.289113i
$176$	−1.12086	−	2.95873i	−0.0844882	−	0.223023i
$177$	−6.84993	+	7.20388i	−0.514872	+	0.541477i
$178$	2.09224	+	6.43925i	0.156820	+	0.482642i
$179$	−0.279402	−	0.202998i	−0.0208835	−	0.0151727i	0.577295	−	0.816536i	$-0.304108\pi$
$179$	−0.279402	−	0.202998i	−0.0208835	−	0.0151727i	−0.598178	+	0.801363i	$0.704108\pi$
$180$	−0.246273	+	2.29890i	−0.0183561	+	0.171350i
$181$	−10.9108	−	3.54513i	−0.810992	−	0.263507i	−0.125974	−	0.992034i	$-0.540206\pi$
$181$	−10.9108	−	3.54513i	−0.810992	−	0.263507i	−0.685018	+	0.728526i	$0.740206\pi$
$182$	0.765890	−	2.99967i	0.0567715	−	0.222350i
$183$	−3.89033	+	2.97898i	−0.287582	+	0.220213i
$184$	17.9579	−	2.84425i	1.32387	−	0.209681i
$185$	−2.88263	+	0.936622i	−0.211935	+	0.0688618i
$186$	6.84659	−	0.172435i	0.502017	−	0.0126435i
$187$	−5.85876	−	15.4653i	−0.428435	−	1.13094i
$188$	−11.8417	−	11.8417i	−0.863643	−	0.863643i
$189$	−2.29828	+	5.50181i	−0.167175	+	0.400198i
$190$	0.0472181	+	0.298123i	0.00342556	+	0.0216281i
$191$	1.51479	+	2.08493i	0.109606	+	0.150860i	0.860296	−	0.509795i	$-0.170279\pi$
$191$	1.51479	+	2.08493i	0.109606	+	0.150860i	−0.750690	+	0.660655i	$0.770279\pi$
$192$	−4.11506	−	1.22341i	−0.296979	−	0.0882922i
$193$	4.42567	−	2.25499i	0.318567	−	0.162318i	−0.287394	−	0.957813i	$-0.592789\pi$
$193$	4.42567	−	2.25499i	0.318567	−	0.162318i	0.605961	+	0.795495i	$0.292789\pi$
$194$	−5.88813	+	4.27798i	−0.422743	+	0.307141i
$195$	−3.24117	+	0.815310i	−0.232105	+	0.0583855i
$196$	−2.52909	−	7.78374i	−0.180649	−	0.555982i
$197$	−0.474880	−	0.474880i	−0.0338338	−	0.0338338i	0.689987	−	0.723821i	$-0.257616\pi$
$197$	−0.474880	−	0.474880i	−0.0338338	−	0.0338338i	−0.723821	+	0.689987i	$0.757616\pi$
$198$	6.26996	−	4.01501i	0.445587	−	0.285335i
$199$			11.6860i			0.828399i	0.910186	+	0.414199i	$0.135938\pi$
$199$			11.6860i			0.828399i	−0.910186	+	0.414199i	$0.864062\pi$
$200$	5.50848	−	10.8110i	0.389509	−	0.764454i
$201$	−14.1319	+	2.60457i	−0.996784	+	0.183712i
$202$	5.69713	+	0.902336i	0.400849	+	0.0634882i
$203$	−4.08651	−	8.02023i	−0.286817	−	0.562910i
$204$	11.9217	+	3.54432i	0.834683	+	0.248152i
$205$	1.45569	+	2.00359i	0.101670	+	0.139937i
$206$	6.38598	−	1.01144i	0.444932	−	0.0704703i
$207$	−7.55411	−	19.7974i	−0.525047	−	1.37601i
$208$	0.220583	+	3.43247i	0.0152947	+	0.237999i
$209$	−1.68087	+	1.85039i	−0.116268	+	0.127994i
$210$	−0.548451	+	0.576790i	−0.0378467	+	0.0398023i
$211$	5.97326	+	18.3838i	0.411216	+	1.26559i	0.915592	+	0.402109i	$0.131723\pi$
$211$	5.97326	+	18.3838i	0.411216	+	1.26559i	−0.504376	+	0.863484i	$0.668277\pi$
$212$	6.03472	+	4.38448i	0.414466	+	0.301127i
$213$	−21.0274	−	2.78970i	−1.44077	−	0.191147i
$214$	−2.12825	−	4.17693i	−0.145484	−	0.285529i
$215$	2.26625	+	4.44776i	0.154557	+	0.303335i
$216$	−1.08943	+	13.3312i	−0.0741264	+	0.907074i
$217$	−4.90562	−	3.56414i	−0.333015	−	0.241950i
$218$	−3.81722	−	11.7482i	−0.258535	−	0.795688i
$219$	−13.3051	−	12.6513i	−0.899073	−	0.854898i
$220$	−2.50253	+	0.520449i	−0.168720	+	0.0350887i
$221$	1.15299	+	17.9415i	0.0775586	+	1.20688i
$222$	−6.92175	+	2.44334i	−0.464558	+	0.163986i
$223$	−26.2148	+	4.15202i	−1.75547	+	0.278040i	−0.949467	−	0.313866i	$-0.898376\pi$
$223$	−26.2148	+	4.15202i	−1.75547	+	0.278040i	−0.806007	+	0.591906i	$0.798376\pi$
$224$	3.95388	+	5.44205i	0.264180	+	0.363612i
$225$	−13.6516	−	3.68721i	−0.910106	−	0.245814i
$226$	6.56117	+	12.8770i	0.436442	+	0.856566i
$227$	−0.628697	−	0.0995758i	−0.0417281	−	0.00660908i	0.135536	−	0.990772i	$-0.456725\pi$
$227$	−0.628697	−	0.0995758i	−0.0417281	−	0.00660908i	−0.177264	+	0.984163i	$0.556725\pi$
$228$	−0.340759	−	1.84888i	−0.0225673	−	0.122445i
$229$	−6.33211	+	12.4275i	−0.418438	+	0.821230i	0.581533	+	0.813523i	$0.302453\pi$
$229$	−6.33211	+	12.4275i	−0.418438	+	0.821230i	−0.999970	+	0.00770721i	$0.997547\pi$
$230$		−	2.82852i		−	0.186507i
$231$	−6.56864	−	0.552620i	−0.432185	−	0.0363597i
$232$	−14.2782	−	14.2782i	−0.937411	−	0.937411i
$233$	8.74609	+	26.9177i	0.572975	+	1.76344i	0.642972	+	0.765890i	$0.277701\pi$
$233$	8.74609	+	26.9177i	0.572975	+	1.76344i	−0.0699963	+	0.997547i	$0.522299\pi$
$234$	−7.79718	+	2.17150i	−0.509718	+	0.141955i
$235$	−5.03493	+	3.65809i	−0.328442	+	0.238627i
$236$	7.36413	−	3.75221i	0.479364	−	0.244248i
$237$	1.47117	−	4.94843i	0.0955630	−	0.321435i
$238$	2.51662	+	3.46383i	0.163128	+	0.224527i
$239$	−3.73470	−	23.5800i	−0.241578	−	1.52526i	−0.748421	−	0.663224i	$-0.769188\pi$
$239$	−3.73470	−	23.5800i	−0.241578	−	1.52526i	0.506843	−	0.862038i	$-0.330812\pi$
$240$	0.381483	−	0.797743i	0.0246246	−	0.0514941i
$241$	−2.50437	−	2.50437i	−0.161321	−	0.161321i	0.621831	−	0.783152i	$-0.286389\pi$
$241$	−2.50437	−	2.50437i	−0.161321	−	0.161321i	−0.783152	+	0.621831i	$0.786389\pi$
$242$	6.35102	+	5.23600i	0.408259	+	0.336583i
$243$	15.4651	−	1.95742i	0.992085	−	0.125569i
$244$	3.87452	−	1.25891i	0.248041	−	0.0805933i
$245$	−3.00407	+	0.475797i	−0.191923	+	0.0303976i
$246$	3.64642	+	4.76195i	0.232487	+	0.303611i
$247$	2.33731	−	1.38653i	0.148720	−	0.0882225i
$248$	−12.9368	−	4.20341i	−0.821485	−	0.266917i
$249$	−21.1769	−	2.80953i	−1.34203	−	0.178047i
$250$	−3.14699	−	2.28642i	−0.199033	−	0.144606i
$251$	6.22864	+	19.1698i	0.393148	+	1.20999i	0.930394	+	0.366560i	$0.119465\pi$
$251$	6.22864	+	19.1698i	0.393148	+	1.20999i	−0.537246	+	0.843426i	$0.680535\pi$
$252$	3.32452	−	3.67744i	0.209425	−	0.231657i
$253$	18.2700	−	14.6624i	1.14863	−	0.921814i
$254$	2.17531	−	2.17531i	0.136491	−	0.136491i
$255$	1.99402	−	4.16981i	0.124870	−	0.261124i
$256$	9.98523	+	7.25469i	0.624077	+	0.453418i
$257$	1.48624	−	1.07982i	0.0927090	−	0.0673570i	−0.540465	−	0.841366i	$-0.681752\pi$
$257$	1.48624	−	1.07982i	0.0927090	−	0.0673570i	0.633174	+	0.774009i	$0.281752\pi$
$258$	5.75780	+	10.6299i	0.358465	+	0.661788i
$259$	6.18082	+	2.00827i	0.384058	+	0.124788i
$260$	2.76676	+	0.257785i	0.171587	+	0.0159872i
$261$	−12.8564	+	19.7108i	−0.795792	+	1.22007i
$262$	−14.6089	−	7.44360i	−0.902540	−	0.459867i
$263$		−	14.2726i		−	0.880087i	−0.897976	−	0.440043i	$-0.854963\pi$
$263$		−	14.2726i		−	0.880087i	0.897976	−	0.440043i	$-0.145037\pi$
$264$	−14.3972	+	3.37445i	−0.886085	+	0.207683i
$265$	1.96016	−	1.96016i	0.120412	−	0.120412i
$266$	0.293819	−	0.576653i	0.0180152	−	0.0353569i
$267$	−15.4124	+	2.84058i	−0.943224	+	0.173841i
$268$	11.8004	+	1.86900i	0.720824	+	0.114167i
$269$	7.38933	+	2.40094i	0.450535	+	0.146388i	0.525491	−	0.850799i	$-0.323882\pi$
$269$	7.38933	+	2.40094i	0.450535	+	0.146388i	−0.0749558	+	0.997187i	$0.523882\pi$
$270$	2.02188	+	0.491830i	0.123048	+	0.0299318i
$271$	29.1498	+	4.61688i	1.77073	+	0.280455i	0.954702	−	0.297563i	$-0.0961737\pi$
$271$	29.1498	+	4.61688i	1.77073	+	0.280455i	0.816024	+	0.578018i	$0.196174\pi$
$272$	−3.84831	−	2.79596i	−0.233338	−	0.169530i
$273$	6.64988	+	2.67058i	0.402469	+	0.161631i
$274$	−7.53565			−0.455245
$275$	−0.749592	−	15.6152i	−0.0452021	−	0.941634i
$276$	0.443568	+	17.6120i	0.0266997	+	1.06012i
$277$	12.9344	−	4.20264i	0.777152	−	0.252512i	0.106528	−	0.994310i	$-0.466027\pi$
$277$	12.9344	−	4.20264i	0.777152	−	0.252512i	0.670624	+	0.741798i	$0.266027\pi$
$278$	−0.966784	−	6.10404i	−0.0579839	−	0.366096i
$279$	−1.68859	+	15.7627i	−0.101094	+	0.943686i
$280$	1.40850	−	0.717666i	0.0841739	−	0.0428887i
$281$	−4.02152	−	7.89267i	−0.239904	−	0.470837i	0.739391	−	0.673276i	$-0.235113\pi$
$281$	−4.02152	−	7.89267i	−0.239904	−	0.470837i	−0.979295	+	0.202439i	$0.935113\pi$
$282$	−11.9666	+	9.16327i	−0.712598	+	0.545664i
$283$	11.9834	−	16.4938i	0.712341	−	0.980454i	−0.287402	−	0.957810i	$-0.592792\pi$
$283$	11.9834	−	16.4938i	0.712341	−	0.980454i	0.999744	−	0.0226437i	$-0.00720834\pi$
$284$	15.7137	+	8.00655i	0.932439	+	0.475101i
$285$	−0.698446	+	0.0175907i	−0.0413724	+	0.00104198i
$286$	−4.92909	−	7.46817i	−0.291463	−	0.441602i
$287$		−	5.31018i		−	0.313450i
$288$	7.18513	−	16.0516i	0.423388	−	0.945850i
$289$	−6.36188	−	4.62218i	−0.374228	−	0.271893i
$290$	−2.54139	+	1.84643i	−0.149235	+	0.108426i
$291$	−8.02374	−	14.8132i	−0.470360	−	0.868365i
$292$	6.93007	+	13.6010i	0.405552	+	0.795940i
$293$	0.387051	−	2.44374i	0.0226118	−	0.142765i	−0.973800	−	0.227408i	$-0.926975\pi$
$293$	0.387051	−	2.44374i	0.0226118	−	0.142765i	0.996411	+	0.0846428i	$0.0269749\pi$
$294$	−7.24386	+	1.33508i	−0.422470	+	0.0778635i
$295$	−0.949140	−	2.92115i	−0.0552611	−	0.170076i
$296$	14.5788			0.847378
$297$	7.30411	+	15.6093i	0.423827	+	0.905743i
$298$		−	1.76996i		−	0.102531i
$299$	−23.6658	+	9.40675i	−1.36863	+	0.544006i
$300$	9.68261	+	6.66893i	0.559026	+	0.385031i
$301$	1.67437	−	10.5715i	0.0965090	−	0.609334i
$302$	5.14117	+	1.67047i	0.295841	+	0.0961246i
$303$	−3.80484	+	12.7979i	−0.218582	+	0.735221i
$304$	−0.112481	+	0.710178i	−0.00645124	+	0.0407315i
$305$	−0.236838	−	1.49534i	−0.0135613	−	0.0856227i
$306$	4.57329	−	10.2167i	0.261437	−	0.584052i
$307$	5.32165	+	5.32165i	0.303723	+	0.303723i	0.842468	−	0.538746i	$-0.181102\pi$
$307$	5.32165	+	5.32165i	0.303723	+	0.303723i	−0.538746	+	0.842468i	$0.681102\pi$
$308$	4.99697	+	2.25115i	0.284729	+	0.128271i
$309$	0.376804	+	14.9611i	0.0214356	+	0.851110i
$310$	−0.960706	+	1.88549i	−0.0545644	+	0.107089i
$311$	13.7822	+	10.0134i	0.781519	+	0.567807i	0.905435	−	0.424486i	$-0.139545\pi$
$311$	13.7822	+	10.0134i	0.781519	+	0.567807i	−0.123915	+	0.992293i	$0.539545\pi$
$312$	16.0387	+	1.08787i	0.908012	+	0.0615883i
$313$	−4.54355	+	13.9836i	−0.256817	+	0.790400i	0.736650	+	0.676274i	$0.236407\pi$
$313$	−4.54355	+	13.9836i	−0.256817	+	0.790400i	−0.993466	+	0.114126i	$0.963593\pi$
$314$	5.39441	−	2.74859i	0.304424	−	0.155112i
$315$	−1.15654	−	1.43406i	−0.0651636	−	0.0808002i
$316$	−2.52291	+	3.47249i	−0.141925	+	0.195343i
$317$	−4.86550	+	9.54907i	−0.273273	+	0.536329i	−0.986331	−	0.164776i	$-0.947310\pi$
$317$	−4.86550	+	9.54907i	−0.273273	+	0.536329i	0.713058	+	0.701106i	$0.247310\pi$
$318$	4.62605	−	4.86509i	0.259416	−	0.272820i
$319$	−25.1004	−	6.84394i	−1.40535	−	0.383187i
$320$	0.937961	−	0.937961i	0.0524336	−	0.0524336i
$321$	10.2323	−	3.61193i	0.571109	−	0.201598i
$322$	−3.56481	+	4.90654i	−0.198659	+	0.273431i
$323$	−0.587941	+	3.71211i	−0.0327139	+	0.206547i
$324$	−12.6666	−	2.74535i	−0.703698	−	0.152519i
$325$	−4.20439	+	16.4668i	−0.233217	+	0.913415i
$326$	3.27651	+	4.50972i	0.181469	+	0.249771i
$327$	28.1194	−	5.18255i	1.55501	−	0.286596i
$328$	−3.68108	−	11.3292i	−0.203253	−	0.625550i
$329$	13.3442			0.735691
$330$	0.168122	+	2.29431i	0.00925483	+	0.126297i
$331$	−13.0037	+	13.0037i	−0.714747	+	0.714747i	−0.967524	−	0.252778i	$-0.918656\pi$
$331$	−13.0037	+	13.0037i	−0.714747	+	0.714747i	0.252778	+	0.967524i	$0.418656\pi$
$332$	15.8254	+	8.06345i	0.868533	+	0.442539i
$333$	−3.49933	−	16.6264i	−0.191762	−	0.911123i
$334$	3.71743	−	2.70087i	0.203409	−	0.147785i
$335$	1.37204	−	4.22270i	0.0749625	−	0.230711i
$336$	−1.66715	+	0.903030i	−0.0909504	+	0.0492644i
$337$	13.6892	+	18.8416i	0.745700	+	1.02637i	0.998270	+	0.0587892i	$0.0187240\pi$
$337$	13.6892	+	18.8416i	0.745700	+	1.02637i	−0.252571	+	0.967578i	$0.581276\pi$
$338$	2.73903	+	9.33409i	0.148983	+	0.507708i
$339$	−31.5449	+	11.1352i	−1.71328	+	0.604779i
$340$	−2.71734	+	2.71734i	−0.147369	+	0.147369i
$341$	−17.1588	+	3.56852i	−0.929203	+	0.193246i
$342$	−1.68987	+	0.0851746i	−0.0913778	+	0.00460572i
$343$	12.9677	+	6.60736i	0.700188	+	0.356764i
$344$	−3.75607	−	23.7149i	−0.202514	−	1.27862i
$345$	6.49032	+	0.861068i	0.349427	+	0.0463584i
$346$	−8.68719	+	4.42635i	−0.467026	+	0.237962i
$347$	−0.719294	−	0.233713i	−0.0386137	−	0.0125464i	0.289646	−	0.957134i	$-0.406462\pi$
$347$	−0.719294	−	0.233713i	−0.0386137	−	0.0125464i	−0.328260	+	0.944587i	$0.606462\pi$
$348$	15.5346	−	11.8955i	0.832743	−	0.637664i
$349$	1.41934	+	8.96135i	0.0759755	+	0.479690i	0.996112	+	0.0880932i	$0.0280773\pi$
$349$	1.41934	+	8.96135i	0.0759755	+	0.479690i	−0.920137	+	0.391597i	$0.871923\pi$
$350$	1.25069	+	3.84923i	0.0668522	+	0.205750i
$351$	−2.60907	−	18.5524i	−0.139262	−	0.990256i
$352$	19.3268	+	2.11721i	1.03012	+	0.112848i
$353$	−14.9401	−	14.9401i	−0.795181	−	0.795181i	0.187150	−	0.982331i	$-0.440075\pi$
$353$	−14.9401	−	14.9401i	−0.795181	−	0.795181i	−0.982331	+	0.187150i	$0.940075\pi$
$354$	−2.47599	−	7.01427i	−0.131598	−	0.372804i
$355$	3.85234	−	5.30229i	0.204461	−	0.281416i
$356$	12.8697	+	2.03836i	0.682092	+	0.108033i
$357$	−8.71420	+	4.72015i	−0.461205	+	0.249817i
$358$	0.230260	−	0.117323i	0.0121696	−	0.00620073i
$359$	1.57902	−	9.96955i	0.0833376	−	0.526173i	−0.910336	−	0.413869i	$-0.864177\pi$
$359$	1.57902	−	9.96955i	0.0833376	−	0.526173i	0.993674	−	0.112303i	$-0.0358229\pi$
$360$	−3.46157	−	2.25782i	−0.182441	−	0.118998i
$361$	−17.5298	+	5.69577i	−0.922619	+	0.299777i
$362$	6.07016	−	6.07016i	0.319041	−	0.319041i
$363$	−13.9479	+	12.9791i	−0.732075	+	0.681224i
$364$	−4.47451	−	3.93414i	−0.234528	−	0.206205i
$365$	5.39517	−	1.75300i	0.282396	−	0.0917560i
$366$	−0.664564	−	3.60578i	−0.0347373	−	0.188477i
$367$	−8.66975	+	6.29894i	−0.452557	+	0.328802i	−0.790605	−	0.612327i	$-0.790234\pi$
$367$	−8.66975	+	6.29894i	−0.452557	+	0.328802i	0.338047	+	0.941129i	$0.390234\pi$
$368$	2.08216	−	6.40822i	0.108540	−	0.334052i
$369$	−12.0368	+	6.91740i	−0.626611	+	0.360106i
$370$	0.354797	−	2.24010i	0.0184450	−	0.116457i
$371$	−5.87063	+	0.929816i	−0.304788	+	0.0482736i
$372$	5.68623	−	11.8908i	0.294818	−	0.616511i
$373$	−13.9328			−0.721411			−0.360706	−	0.932680i	$-0.617464\pi$
$373$	−13.9328			−0.721411			−0.360706	+	0.932680i	$0.617464\pi$
$374$	12.3014	+	1.34759i	0.636090	+	0.0696822i
$375$	6.20443	−	6.52503i	0.320395	−	0.336951i
$376$	28.4697	−	9.25037i	1.46821	−	0.477051i
$377$	23.9006	+	15.1228i	1.23094	+	0.778862i
$378$	−2.88743	−	3.40136i	−0.148514	−	0.174947i
$379$	3.91232	+	7.67835i	0.200962	+	0.394410i	0.969390	−	0.245526i	$-0.0789607\pi$
$379$	3.91232	+	7.67835i	0.200962	+	0.394410i	−0.768428	+	0.639936i	$0.778961\pi$
$380$	0.552460	+	0.179505i	0.0283406	+	0.00920842i
$381$	4.32925	+	5.65368i	0.221794	+	0.289647i
$382$	−1.90467	+	0.301669i	−0.0974512	+	0.0154348i
$383$	7.11570	−	13.9653i	0.363595	−	0.713596i	−0.634651	−	0.772799i	$-0.718856\pi$
$383$	7.11570	−	13.9653i	0.363595	−	0.713596i	0.998246	+	0.0592034i	$0.0188561\pi$
$384$	−11.7795	+	12.3882i	−0.601121	+	0.632182i
$385$	1.11679	−	1.70328i	0.0569168	−	0.0868070i
$386$			3.71676i			0.189178i
$387$	−26.1441	+	9.97585i	−1.32898	+	0.507101i
$388$	2.19115	+	13.8343i	0.111239	+	0.702333i
$389$	20.3462	−	14.7824i	1.03159	−	0.749496i	0.0629657	−	0.998016i	$-0.479944\pi$
$389$	20.3462	−	14.7824i	1.03159	−	0.749496i	0.968627	+	0.248520i	$0.0799441\pi$
$390$	0.557480	−	2.43794i	0.0282291	−	0.123450i
$391$	10.8835	−	33.4959i	0.550401	−	1.69396i
$392$	14.4494	+	2.28856i	0.729806	+	0.115590i
$393$	21.5273	−	31.2555i	1.08591	−	1.57663i
$394$	0.477937	−	0.155291i	0.0240781	−	0.00782346i
$395$	1.12791	+	1.12791i	0.0567514	+	0.0567514i
$396$	−1.40662	−	14.2593i	−0.0706854	−	0.716559i
$397$	4.28367	+	4.28367i	0.214991	+	0.214991i	0.806384	−	0.591393i	$-0.201422\pi$
$397$	4.28367	+	4.28367i	0.214991	+	0.214991i	−0.591393	+	0.806384i	$0.701422\pi$
$398$	−7.79134	−	3.96989i	−0.390545	−	0.198993i
$399$	1.23374	+	0.849743i	0.0617643	+	0.0425404i
$400$	−2.64302	−	3.63780i	−0.132151	−	0.181890i
$401$	−14.0935	−	27.6601i	−0.703797	−	1.38128i	−0.914846	−	0.403803i	$-0.867688\pi$
$401$	−14.0935	−	27.6601i	−0.703797	−	1.38128i	0.211049	−	0.977475i	$-0.432312\pi$
$402$	3.06424	−	10.3069i	0.152831	−	0.514060i
$403$	18.9706	+	1.76753i	0.944992	+	0.0880471i
$404$	6.52490	−	8.98075i	0.324626	−	0.446809i
$405$	−1.74406	+	4.48968i	−0.0866630	+	0.223094i
$406$	6.73552			0.334278
$407$	16.3085	−	9.32041i	0.808380	−	0.461996i
$408$	−15.3196	+	16.1112i	−0.758431	+	0.797621i
$409$	−8.54977	−	4.35633i	−0.422759	−	0.215406i	0.229650	−	0.973273i	$-0.426242\pi$
$409$	−8.54977	−	4.35633i	−0.422759	−	0.215406i	−0.652409	+	0.757867i	$0.726242\pi$
$410$	−1.83036	+	0.289901i	−0.0903951	+	0.0143172i
$411$	2.29403	−	17.2913i	0.113156	−	0.852915i
$412$	3.84511	−	11.8340i	0.189435	−	0.583021i
$413$	−2.03511	+	6.26343i	−0.100141	+	0.308203i
$414$	15.7656	+	1.68891i	0.774838	+	0.0830055i
$415$	3.87972	−	5.33998i	0.190448	−	0.262129i
$416$	−19.4091	−	8.36812i	−0.951609	−	0.410281i
$417$	14.3006	−	0.360168i	0.700304	−	0.0176375i
$418$	−0.662684	−	1.74928i	−0.0324129	−	0.0855601i
$419$		−	2.81147i		−	0.137349i	−0.997639	−	0.0686746i	$-0.978123\pi$
$419$		−	2.81147i		−	0.137349i	0.997639	−	0.0686746i	$-0.0218770\pi$
$420$	0.509864	+	1.44440i	0.0248788	+	0.0704795i
$421$	17.8274	−	2.82358i	0.868854	−	0.137613i	0.293937	−	0.955825i	$-0.405034\pi$
$421$	17.8274	−	2.82358i	0.868854	−	0.137613i	0.574917	+	0.818212i	$0.305034\pi$
$422$	−14.2861	−	2.26270i	−0.695438	−	0.110147i
$423$	−17.3831	−	30.2479i	−0.845195	−	1.47070i
$424$	−11.8803	+	6.05333i	−0.576960	+	0.293976i
$425$	−13.8151	−	19.0148i	−0.670130	−	0.922355i
$426$	9.00325	−	13.0718i	0.436209	−	0.633330i
$427$	−1.47375	+	2.89240i	−0.0713197	+	0.139973i
$428$	−9.02185			−0.436088
$429$	18.6370	−	9.03677i	0.899801	−	0.436300i
$430$	−3.73530			−0.180132
$431$	4.88114	−	9.57978i	0.235116	−	0.461442i	−0.743058	−	0.669227i	$-0.766625\pi$
$431$	4.88114	−	9.57978i	0.235116	−	0.461442i	0.978174	+	0.207785i	$0.0666255\pi$
$432$	4.21868	+	2.60264i	0.202971	+	0.125220i
$433$	−9.53972	−	13.1303i	−0.458450	−	0.631002i	0.515737	−	0.856747i	$-0.327518\pi$
$433$	−9.53972	−	13.1303i	−0.458450	−	0.631002i	−0.974186	+	0.225745i	$0.927518\pi$
$434$	4.04280	−	2.05991i	0.194061	−	0.0988789i
$435$	−3.46315	−	6.39355i	−0.166045	−	0.306547i
$436$	−23.4803	−	3.71892i	−1.12450	−	0.178104i
$437$	−5.25823	+	0.832823i	−0.251535	+	0.0398393i
$438$	12.9549	−	4.57298i	0.619007	−	0.218506i
$439$		−	2.35150i		−	0.112231i	−0.998424	−	0.0561154i	$-0.982129\pi$
$439$		−	2.35150i		−	0.112231i	0.998424	−	0.0561154i	$-0.0178715\pi$
$440$	1.20192	−	4.40808i	0.0572993	−	0.210147i
$441$	−0.858270	−	17.0282i	−0.0408700	−	0.810865i
$442$	−12.3538	−	5.32625i	−0.587608	−	0.253344i
$443$	−15.6413	+	21.5284i	−0.743141	+	1.02285i	0.255291	+	0.966864i	$0.417829\pi$
$443$	−15.6413	+	21.5284i	−0.743141	+	1.02285i	−0.998432	+	0.0559816i	$0.982171\pi$
$444$	−1.85788	+	14.0038i	−0.0881712	+	0.664592i
$445$	1.49637	−	4.60534i	0.0709345	−	0.218314i
$446$	6.13727	−	18.8886i	0.290608	−	0.894399i
$447$	4.06134	+	0.538817i	0.192095	+	0.0254852i
$448$	−2.80917	+	0.444928i	−0.132721	+	0.0210209i
$449$	4.53768	+	2.31206i	0.214146	+	0.109113i	0.557774	−	0.829993i	$-0.311656\pi$
$449$	4.53768	+	2.31206i	0.214146	+	0.109113i	−0.343627	+	0.939106i	$0.611656\pi$
$450$	7.09598	−	7.84926i	0.334508	−	0.370018i
$451$	−11.3607	−	10.3199i	−0.534953	−	0.485946i
$452$	27.8134			1.30823
$453$	−5.39814	+	11.2884i	−0.253627	+	0.530375i
$454$	0.279966	−	0.385340i	0.0131395	−	0.0180849i
$455$	−1.70416	+	1.41367i	−0.0798923	+	0.0662737i
$456$	3.22122	+	0.957672i	0.150847	+	0.0448471i
$457$	11.0634	+	21.7131i	0.517522	+	1.01569i	0.990870	+	0.134819i	$0.0430454\pi$
$457$	11.0634	+	21.7131i	0.517522	+	1.01569i	−0.473348	+	0.880876i	$0.656955\pi$
$458$	−6.13460	−	8.44355i	−0.286651	−	0.394541i
$459$	22.0511	+	13.6041i	1.02926	+	0.634983i
$460$	−4.85020	−	2.47130i	−0.226142	−	0.115225i
$461$	12.6257	+	12.6257i	0.588035	+	0.588035i	0.937099	−	0.349064i	$-0.113500\pi$
$461$	12.6257	+	12.6257i	0.588035	+	0.588035i	−0.349064	+	0.937099i	$0.613500\pi$
$462$	2.59990	−	4.19174i	0.120958	−	0.195017i
$463$	15.4024	+	15.4024i	0.715810	+	0.715810i	0.967744	−	0.251934i	$-0.0810666\pi$
$463$	15.4024	+	15.4024i	0.715810	+	0.715810i	−0.251934	+	0.967744i	$0.581067\pi$
$464$	−7.11691	+	2.31242i	−0.330394	+	0.107352i
$465$	−4.03398	−	2.77842i	−0.187071	−	0.128846i
$466$	−20.9179	−	3.31306i	−0.969001	−	0.153475i
$467$	−9.65628	+	29.7190i	−0.446839	+	1.37523i	0.433615	+	0.901098i	$0.357238\pi$
$467$	−9.65628	+	29.7190i	−0.446839	+	1.37523i	−0.880454	+	0.474131i	$0.842762\pi$
$468$	−3.08888	+	15.2674i	−0.142783	+	0.705738i
$469$	−7.70194	+	5.59578i	−0.355642	+	0.258389i
$470$	−0.728506	−	4.59961i	−0.0336035	−	0.212164i
$471$	4.66472	+	13.2147i	0.214939	+	0.608902i
$472$			14.7737i			0.680015i
$473$	−19.3629	−	24.1271i	−0.890306	−	1.10937i
$474$	2.79946	+	2.66191i	0.128583	+	0.122266i
$475$	−1.61293	+	3.16556i	−0.0740065	+	0.145246i
$476$	8.13837	−	1.28899i	0.373022	−	0.0590808i
$477$	9.75513	+	12.0960i	0.446657	+	0.553836i
$478$	16.9901	+	5.52041i	0.777108	+	0.252498i
$479$	−4.35453	−	8.54625i	−0.198964	−	0.390488i	0.769870	−	0.638201i	$-0.220321\pi$
$479$	−4.35453	−	8.54625i	−0.198964	−	0.390488i	−0.968834	+	0.247713i	$0.920321\pi$
$480$	3.30361	+	4.31427i	0.150788	+	0.196918i
$481$	−19.9225	+	4.48132i	−0.908387	+	0.204330i
$482$	2.52049	−	0.818958i	0.114805	−	0.0373025i
$483$	−10.1733	−	9.67346i	−0.462902	−	0.440158i
$484$	14.5273	−	6.31565i	0.660334	−	0.287075i
$485$	5.20530			0.236361
$486$	−3.94863	+	10.9759i	−0.179113	+	0.497877i
$487$	−11.7185	+	1.85604i	−0.531018	+	0.0841050i	−0.416185	−	0.909280i	$-0.636633\pi$
$487$	−11.7185	+	1.85604i	−0.531018	+	0.0841050i	−0.114833	+	0.993385i	$0.536633\pi$
$488$	−1.13918	+	7.19250i	−0.0515683	+	0.325589i
$489$	−11.3454	+	6.14539i	−0.513059	+	0.277904i
$490$	0.703295	−	2.16452i	0.0317716	−	0.0977830i
$491$	−0.644451	+	0.468221i	−0.0290837	+	0.0211305i	−0.602232	−	0.798321i	$-0.705722\pi$
$491$	−0.644451	+	0.468221i	−0.0290837	+	0.0211305i	0.573148	+	0.819452i	$0.305722\pi$
$492$	11.3514	−	2.09213i	0.511762	−	0.0943204i
$493$	−37.2002	+	12.0871i	−1.67541	+	0.544374i
$494$	0.130415	+	2.02937i	0.00586763	+	0.0913055i
$495$	−5.31569	−	0.312668i	−0.238923	−	0.0140534i
$496$	−3.56452	+	3.56452i	−0.160051	+	0.160051i
$497$	−13.3650	+	4.34256i	−0.599504	+	0.194791i
$498$	9.06724	−	13.1647i	0.406313	−	0.589924i
$499$	3.00517	−	18.9739i	0.134530	−	0.849388i	−0.824454	−	0.565928i	$-0.808518\pi$
$499$	3.00517	−	18.9739i	0.134530	−	0.849388i	0.958984	−	0.283459i	$-0.0914821\pi$
$500$	−6.67018	+	3.39863i	−0.298299	+	0.151991i
$501$	5.06574	+	9.35222i	0.226321	+	0.417826i
$502$	−14.8969	−	2.35944i	−0.664882	−	0.105307i
$503$	6.43734	−	8.86023i	0.287027	−	0.395058i	−0.641019	−	0.767525i	$-0.721488\pi$
$503$	6.43734	−	8.86023i	0.287027	−	0.395058i	0.928046	+	0.372467i	$0.121488\pi$
$504$	3.15911	+	8.27921i	0.140718	+	0.368785i
$505$	−2.91707	−	2.91707i	−0.129808	−	0.129808i
$506$	3.56919	+	17.1621i	0.158670	+	0.762947i
$507$	−22.2518	+	3.44344i	−0.988237	+	0.152929i
$508$	−1.82952	−	5.63069i	−0.0811720	−	0.249822i
$509$	−1.41705	−	8.94688i	−0.0628095	−	0.396563i	−0.998986	−	0.0450319i	$-0.985661\pi$
$509$	−1.41705	−	8.94688i	−0.0628095	−	0.396563i	0.936176	−	0.351531i	$-0.114339\pi$
$510$	2.10272	+	2.74600i	0.0931101	+	0.121595i
$511$	−11.5681	−	3.75871i	−0.511744	−	0.166276i
$512$	9.35867	−	4.76848i	0.413599	−	0.210739i
$513$	0.318995	−	3.90350i	0.0140840	−	0.172344i
$514$	0.215045	+	1.35774i	0.00948522	+	0.0598873i
$515$	−4.12017	−	2.09933i	−0.181556	−	0.0925076i
$516$	23.2582	−	0.585769i	1.02388	−	0.0257871i
$517$	25.9334	−	28.5488i	1.14055	−	1.25557i
$518$	−3.43867	+	3.43867i	−0.151086	+	0.151086i
$519$	−7.51209	−	21.2811i	−0.329744	−	0.934136i
$520$	−2.65583	+	4.19738i	−0.116466	+	0.184067i
$521$	15.1724	+	20.8830i	0.664715	+	0.914902i	0.999626	−	0.0273477i	$-0.00870613\pi$
$521$	15.1724	+	20.8830i	0.664715	+	0.914902i	−0.334911	+	0.942250i	$0.608706\pi$
$522$	−8.77415	−	15.2677i	−0.384034	−	0.668249i
$523$	3.83713	−	11.8095i	0.167786	−	0.516393i	−0.831445	−	0.555608i	$-0.812486\pi$
$523$	3.83713	−	11.8095i	0.167786	−	0.516393i	0.999231	+	0.0392149i	$0.0124857\pi$
$524$	−25.5278	+	18.5470i	−1.11519	+	0.810230i
$525$	−9.21317	+	1.69803i	−0.402096	+	0.0741083i
$526$	9.51590	+	4.84859i	0.414913	+	0.211409i
$527$	−18.6318	+	18.6318i	−0.811613	+	0.811613i
$528$	−1.30801	+	5.32168i	−0.0569240	+	0.231597i
$529$	26.8889			1.16908
$530$	0.640995	+	1.97278i	0.0278430	+	0.0856920i
$531$	16.8487	−	3.54610i	0.731170	−	0.153888i
$532$	−0.732102	−	1.00765i	−0.0317406	−	0.0436872i
$533$	8.51274	+	14.3502i	0.368728	+	0.621577i
$534$	3.34191	−	11.2408i	0.144618	−	0.486437i
$535$	−0.524488	+	3.31149i	−0.0226756	+	0.143168i
$536$	−12.5529	+	17.2776i	−0.542203	+	0.746278i
$537$	0.199113	+	0.564070i	0.00859237	+	0.0243414i
$538$	−4.11102	+	4.11102i	−0.177239	+	0.177239i
$539$	17.6268	−	6.67760i	0.759239	−	0.287624i
$540$	2.60990	−	3.03730i	0.112312	−	0.130705i
$541$	11.0721	−	21.7302i	0.476026	−	0.934255i	−0.520726	−	0.853724i	$-0.674339\pi$
$541$	11.0721	−	21.7302i	0.476026	−	0.934255i	0.996752	−	0.0805305i	$-0.0256614\pi$
$542$	−12.9808	+	17.8665i	−0.557572	+	0.767432i
$543$	12.0807	+	15.7765i	0.518431	+	0.677033i
$544$	26.0447	−	13.2704i	1.11666	−	0.568965i
$545$	−2.73007	+	8.40229i	−0.116943	+	0.359915i
$546$	−4.03959	+	3.52641i	−0.172879	+	0.150916i
$547$	13.4425	+	9.76653i	0.574759	+	0.417587i	0.836831	−	0.547462i	$-0.184406\pi$
$547$	13.4425	+	9.76653i	0.574759	+	0.417587i	−0.262072	+	0.965048i	$0.584406\pi$
$548$	−6.58395	+	12.9217i	−0.281252	+	0.551989i
$549$	8.47612	−	0.427222i	0.361752	−	0.0182334i
$550$	10.6657	+	4.80493i	0.454787	+	0.204883i
$551$	4.18079	+	4.18079i	0.178108	+	0.178108i
$552$	−28.4104	−	13.5859i	−1.20923	−	0.578256i
$553$	−0.535033	−	3.37807i	−0.0227519	−	0.143650i
$554$	−1.59198	+	10.0514i	−0.0676367	+	0.427042i
$555$	5.03212	+	1.49605i	0.213601	+	0.0635040i
$556$	−11.3116	−	3.67535i	−0.479717	−	0.155870i
$557$	−4.80468	+	30.3356i	−0.203581	+	1.28536i	0.648204	+	0.761467i	$0.275521\pi$
$557$	−4.80468	+	30.3356i	−0.203581	+	1.28536i	−0.851785	+	0.523892i	$0.824479\pi$
$558$	−9.93571	−	6.48061i	−0.420612	−	0.274346i
$559$	12.4224	+	31.2527i	0.525412	+	1.32185i
$560$		−	0.585830i		−	0.0247558i
$561$	−6.83701	+	27.8165i	−0.288659	+	1.17441i
$562$	6.62840			0.279602
$563$	1.97816	+	6.08814i	0.0833693	+	0.256584i	0.984049	−	0.177900i	$-0.0569305\pi$
$563$	1.97816	+	6.08814i	0.0833693	+	0.256584i	−0.900679	+	0.434485i	$0.856930\pi$
$564$	5.25742	+	28.5256i	0.221377	+	1.20115i
$565$	1.61694	−	10.2089i	0.0680251	−	0.429493i
$566$	6.92588	+	13.5928i	0.291116	+	0.571348i
$567$	8.68374	−	5.59004i	0.364683	−	0.234760i
$568$	−25.5038	+	18.5296i	−1.07012	+	0.777484i
$569$	−20.6397	−	14.9956i	−0.865263	−	0.628650i	0.0640487	−	0.997947i	$-0.479599\pi$
$569$	−20.6397	−	14.9956i	−0.865263	−	0.628650i	−0.929312	+	0.369296i	$0.879599\pi$
$570$	0.225543	−	0.471647i	0.00944697	−	0.0197551i
$571$			10.4104i			0.435661i	0.975987	+	0.217831i	$0.0698981\pi$
$571$			10.4104i			0.435661i	−0.975987	+	0.217831i	$0.930102\pi$
$572$	−17.1126	+	1.92714i	−0.715514	+	0.0805777i
$573$	−0.112385	−	4.46228i	−0.00469494	−	0.186414i
$574$	3.54043	+	1.80394i	0.147775	+	0.0752949i
$575$	19.5692	−	26.9347i	0.816091	−	1.12325i
$576$	4.66795	+	5.78806i	0.194498	+	0.241169i
$577$	−1.70464	−	3.34554i	−0.0709649	−	0.139276i	0.852799	−	0.522240i	$-0.174903\pi$
$577$	−1.70464	−	3.34554i	−0.0709649	−	0.139276i	−0.923763	+	0.382964i	$0.874903\pi$
$578$	5.24293	−	2.67141i	0.218077	−	0.111116i
$579$	−8.52845	−	1.13147i	−0.354430	−	0.0470222i
$580$	0.945725	+	5.97107i	0.0392691	+	0.247935i
$581$	−13.4600	+	4.37343i	−0.558416	+	0.181440i
$582$	12.6021	−	0.317390i	0.522373	−	0.0131562i
$583$	−9.41983	+	14.3667i	−0.390130	+	0.595008i
$584$	−27.2860			−1.12910
$585$	5.42437	+	2.02136i	0.224270	+	0.0835728i
$586$	1.49782	+	1.08823i	0.0618743	+	0.0449543i
$587$	−5.34038	−	0.845833i	−0.220421	−	0.0349113i	0.0452470	−	0.998976i	$-0.485593\pi$
$587$	−5.34038	−	0.845833i	−0.220421	−	0.0349113i	−0.265668	+	0.964065i	$0.585593\pi$
$588$	−4.03969	+	13.5879i	−0.166594	+	0.560354i
$589$	3.78800	+	1.23080i	0.156082	+	0.0507141i
$590$	2.27004	+	0.359539i	0.0934561	+	0.0148020i
$591$	0.210835	+	1.14395i	0.00867261	+	0.0470557i
$592$	2.45282	−	4.81393i	0.100810	−	0.197851i
$593$	−12.2970	+	12.2970i	−0.504976	+	0.504976i	−0.912980	−	0.408004i	$-0.866225\pi$
$593$	−12.2970	+	12.2970i	−0.504976	+	0.504976i	0.408004	+	0.912980i	$0.366225\pi$
$594$	−12.8884	−	0.432852i	−0.528817	−	0.0177601i
$595$		−	3.06214i		−	0.125536i
$596$	−3.03503	−	1.54642i	−0.124320	−	0.0633440i
$597$	11.4812	−	16.6695i	0.469893	−	0.682236i
$598$	1.76787	−	18.9741i	0.0722934	−	0.775911i
$599$	33.2366	+	10.7992i	1.35801	+	0.441245i	0.895379	−	0.445305i	$-0.146905\pi$
$599$	33.2366	+	10.7992i	1.35801	+	0.441245i	0.462633	+	0.886550i	$0.346905\pi$
$600$	−18.4791	+	10.0094i	−0.754404	+	0.408632i
$601$	17.8517	−	12.9700i	0.728184	−	0.529057i	−0.160804	−	0.986986i	$-0.551409\pi$
$601$	17.8517	−	12.9700i	0.728184	−	0.529057i	0.888988	+	0.457930i	$0.151409\pi$
$602$	6.47950	+	4.70763i	0.264085	+	0.191869i
$603$	22.7173	+	10.1689i	0.925118	+	0.414108i
$604$	7.35631	−	7.35631i	0.299324	−	0.299324i
$605$	−1.47362	−	5.69945i	−0.0599112	−	0.231716i
$606$	−7.24013	−	6.88440i	−0.294110	−	0.279660i
$607$	4.70316	+	14.4748i	0.190895	+	0.587516i	1.00000		0.000149093i	$-4.74578e-5\pi$
$607$	4.70316	+	14.4748i	0.190895	+	0.587516i	−0.809105	+	0.587665i	$0.800047\pi$
$608$	−3.57463	−	2.59712i	−0.144970	−	0.105327i
$609$	−2.05045	+	15.4553i	−0.0830885	+	0.626281i
$610$	1.07743	+	0.350080i	0.0436240	+	0.0141743i
$611$	−36.0614	+	21.3921i	−1.45889	+	0.865432i
$612$	−13.5234	−	16.7685i	−0.546651	−	0.677825i
$613$	−18.9121	+	2.99538i	−0.763853	+	0.120982i	−0.526192	−	0.850366i	$-0.676381\pi$
$613$	−18.9121	+	2.99538i	−0.763853	+	0.120982i	−0.237661	+	0.971348i	$0.576381\pi$
$614$	−5.35591	+	1.74024i	−0.216147	+	0.0702304i
$615$	−0.108000	−	4.28819i	−0.00435499	−	0.172917i
$616$	−7.64047	+	6.13176i	−0.307843	+	0.247056i
$617$	−10.0993	−	10.0993i	−0.406582	−	0.406582i	0.473963	−	0.880545i	$-0.342823\pi$
$617$	−10.0993	−	10.0993i	−0.406582	−	0.406582i	−0.880545	+	0.473963i	$0.842823\pi$
$618$	−10.1030	−	4.83127i	−0.406401	−	0.194342i
$619$	−3.13764	−	19.8103i	−0.126113	−	0.796243i	−0.966952	−	0.254959i	$-0.917938\pi$
$619$	−3.13764	−	19.8103i	−0.126113	−	0.796243i	0.840839	−	0.541285i	$-0.182062\pi$
$620$	2.39376	+	3.29473i	0.0961359	+	0.132320i
$621$	−8.67479	+	35.6616i	−0.348107	+	1.43105i
$622$	−11.3582	+	5.78728i	−0.455421	+	0.232049i
$623$	−8.39984	+	6.10284i	−0.336532	+	0.244505i
$624$	3.05765	−	5.11295i	0.122404	−	0.204682i
$625$	−6.42320	−	19.7686i	−0.256928	−	0.790743i
$626$	−7.77971	−	7.77971i	−0.310940	−	0.310940i
$627$	4.21563	−	0.988070i	0.168356	−	0.0394597i
$628$		−	11.6515i		−	0.464946i
$629$	12.8209	−	25.1625i	0.511204	−	1.00329i
$630$	1.34902	−	0.283924i	0.0537461	−	0.0113118i
$631$	−4.63183	−	0.733610i	−0.184390	−	0.0292046i	0.0635563	−	0.997978i	$-0.479756\pi$
$631$	−4.63183	−	0.733610i	−0.184390	−	0.0292046i	−0.247947	+	0.968774i	$0.579756\pi$
$632$	−3.48320	−	6.83616i	−0.138554	−	0.271928i
$633$	9.54101	−	32.0921i	0.379221	−	1.27555i
$634$	−4.71373	−	6.48789i	−0.187206	−	0.257667i
$635$	−2.17312	+	0.344188i	−0.0862375	+	0.0136587i
$636$	−4.30058	−	12.1832i	−0.170529	−	0.483094i
$637$	−20.4491	+	1.31414i	−0.810223	+	0.0520680i
$638$	13.0899	−	14.4101i	0.518236	−	0.570500i
$639$	27.2537	+	24.6382i	1.07814	+	0.974671i
$640$	−1.63219	−	5.02338i	−0.0645181	−	0.198566i
$641$	−36.3380	−	26.4011i	−1.43526	−	1.04278i	−0.989006	−	0.147877i	$-0.952756\pi$
$641$	−36.3380	−	26.4011i	−1.43526	−	1.04278i	−0.446259	−	0.894904i	$-0.647244\pi$
$642$	−1.06787	+	8.04912i	−0.0421456	+	0.317673i
$643$	19.9129	+	39.0812i	0.785287	+	1.54121i	0.839923	+	0.542706i	$0.182600\pi$
$643$	19.9129	+	39.0812i	0.785287	+	1.54121i	−0.0546363	+	0.998506i	$0.517400\pi$
$644$	5.29887	+	10.3996i	0.208805	+	0.409803i
$645$	1.13711	−	8.57102i	0.0447738	−	0.337483i
$646$	−2.27522	−	1.65305i	−0.0895175	−	0.0650383i
$647$	9.36960	+	28.8367i	0.368357	+	1.13369i	0.947852	+	0.318710i	$0.103250\pi$
$647$	9.36960	+	28.8367i	0.368357	+	1.13369i	−0.579495	+	0.814976i	$0.696750\pi$
$648$	14.6515	−	17.9459i	0.575567	−	0.704983i
$649$	9.44498	+	16.5264i	0.370748	+	0.648719i
$650$	−9.55055	−	8.39717i	−0.374604	−	0.329364i
$651$	3.49594	+	9.90368i	0.137017	+	0.388156i
$652$	10.5957	−	1.67820i	0.414961	−	0.0657234i
$653$	−2.03232	−	2.79725i	−0.0795308	−	0.109465i	0.767398	−	0.641171i	$-0.221551\pi$
$653$	−2.03232	−	2.79725i	−0.0795308	−	0.109465i	−0.846929	+	0.531706i	$0.821551\pi$
$654$	−6.09720	+	20.5085i	−0.238419	+	0.801945i
$655$	5.32365	+	10.4482i	0.208012	+	0.408247i
$656$	−4.36022	−	0.690591i	−0.170238	−	0.0269631i
$657$	6.54939	+	31.1183i	0.255516	+	1.21404i
$658$	−4.53321	+	8.89692i	−0.176723	+	0.346838i
$659$		−	3.13382i		−	0.122076i	−0.998135	−	0.0610382i	$-0.980559\pi$
$659$		−	3.13382i		−	0.122076i	0.998135	−	0.0610382i	$-0.0194411\pi$
$660$	4.08105	+	1.71627i	0.158855	+	0.0668056i
$661$	7.77634	+	7.77634i	0.302464	+	0.302464i	0.841977	−	0.539513i	$-0.181392\pi$
$661$	7.77634	+	7.77634i	0.302464	+	0.302464i	−0.539513	+	0.841977i	$0.681392\pi$
$662$	−4.25235	−	13.0874i	−0.165272	−	0.508656i
$663$	15.9824	−	26.7254i	0.620704	−	1.03793i
$664$	−25.6851	+	18.6613i	−0.996774	+	0.724198i
$665$	−0.412421	+	0.210139i	−0.0159930	+	0.00814885i
$666$	12.2740	+	3.31513i	0.475609	+	0.128459i
$667$	−32.5669	−	44.8245i	−1.26100	−	1.73561i
$668$	−1.38337	−	8.73423i	−0.0535240	−	0.337937i
$669$	41.4733	+	19.8327i	1.60345	+	0.766775i
$670$	2.34928	+	2.34928i	0.0907606	+	0.0907606i
$671$	3.32391	+	8.77410i	0.128318	+	0.338720i
$672$	−0.293345	−	11.6474i	−0.0113160	−	0.449307i
$673$	−17.7179	+	5.75689i	−0.682975	+	0.221912i	−0.629897	−	0.776678i	$-0.716903\pi$
$673$	−17.7179	+	5.75689i	−0.682975	+	0.221912i	−0.0530775	+	0.998590i	$0.516903\pi$
$674$	−17.2126	+	2.72620i	−0.663003	+	0.105009i
$675$	15.8507	+	18.6719i	0.610094	+	0.718682i
$676$	18.3987	+	3.45853i	0.707643	+	0.133020i
$677$	29.6052	+	9.61932i	1.13782	+	0.369701i	0.816543	−	0.577284i	$-0.195888\pi$
$677$	29.6052	+	9.61932i	1.13782	+	0.369701i	0.321278	+	0.946985i	$0.395888\pi$
$678$	3.29214	−	24.8145i	0.126434	−	0.952996i
$679$	−9.02946	−	6.56029i	−0.346519	−	0.251761i
$680$	−2.12271	−	6.53303i	−0.0814022	−	0.250530i
$681$	0.798972	+	0.759716i	0.0306167	+	0.0291124i
$682$	3.44987	−	12.6525i	0.132102	−	0.484489i
$683$	−15.9297	+	15.9297i	−0.609534	+	0.609534i	−0.942824	−	0.333290i	$-0.891841\pi$
$683$	−15.9297	+	15.9297i	−0.609534	+	0.609534i	0.333290	+	0.942824i	$0.391841\pi$
$684$	−1.33040	+	2.97212i	−0.0508691	+	0.113642i
$685$	4.36018	+	3.16786i	0.166594	+	0.121038i
$686$	−8.81057	+	6.40126i	−0.336389	+	0.244401i
$687$	21.2421	−	11.5060i	0.810435	−	0.438982i
$688$	−8.46261	−	2.74967i	−0.322634	−	0.104830i
$689$	14.3742	−	11.9239i	0.547612	−	0.454265i
$690$	−2.77894	+	4.03474i	−0.105792	+	0.153600i
$691$	−17.0132	−	8.66865i	−0.647212	−	0.329771i	0.0993837	−	0.995049i	$-0.468313\pi$
$691$	−17.0132	−	8.66865i	−0.647212	−	0.329771i	−0.746595	+	0.665278i	$0.768313\pi$
$692$			18.7637i			0.713288i
$693$	8.82688	+	7.24178i	0.335306	+	0.275093i
$694$	0.400176	−	0.400176i	0.0151905	−	0.0151905i
$695$	−2.00664	+	3.93826i	−0.0761164	+	0.149387i
$696$	6.33919	+	34.3951i	0.240286	+	1.30374i
$697$	−22.7909	−	3.60973i	−0.863268	−	0.136728i
$698$	−6.45692	−	2.09798i	−0.244398	−	0.0794098i
$699$	13.9700	−	46.9895i	0.528395	−	1.77730i
$700$	7.69319	+	1.21848i	0.290775	+	0.0460543i
$701$	1.48479	+	1.07877i	0.0560799	+	0.0407444i	0.615472	−	0.788159i	$-0.288965\pi$
$701$	1.48479	+	1.07877i	0.0560799	+	0.0407444i	−0.559392	+	0.828903i	$0.688965\pi$
$702$	13.2557	+	4.56297i	0.500304	+	0.172218i
$703$	−4.26882			−0.161002
$704$	−4.50751	+	6.87465i	−0.169883	+	0.259098i
$705$	10.7760	−	0.271400i	0.405848	−	0.0102215i
$706$	15.0363	−	4.88558i	0.565898	−	0.183871i
$707$	1.38374	+	8.73656i	0.0520407	+	0.328572i
$708$	−14.1910	−	1.88271i	−0.533330	−	0.0707567i
$709$	39.1719	−	19.9591i	1.47113	−	0.749579i	0.479362	−	0.877617i	$-0.340868\pi$
$709$	39.1719	−	19.9591i	1.47113	−	0.749579i	0.991769	+	0.128039i	$0.0408681\pi$
$710$	2.22648	+	4.36971i	0.0835582	+	0.163992i
$711$	−6.96024	+	5.61328i	−0.261029	+	0.210515i
$712$	−13.6904	+	18.8432i	−0.513068	+	0.706178i
$713$	−33.2559	−	16.9447i	−1.24544	−	0.634585i
$714$	−0.186712	−	7.41347i	−0.00698752	−	0.277442i
$715$	−0.287487	+	6.39325i	−0.0107514	+	0.239094i
$716$		−	0.497344i		−	0.0185866i
$717$	−17.8393	+	37.3048i	−0.666220	+	1.39317i
$718$	6.11053	+	4.43956i	0.228043	+	0.165683i
$719$	−5.93340	+	4.31087i	−0.221279	+	0.160768i	−0.692902	−	0.721032i	$-0.743668\pi$
$719$	−5.93340	+	4.31087i	−0.221279	+	0.160768i	0.471623	+	0.881800i	$0.343668\pi$
$720$	−1.32793	+	0.763142i	−0.0494888	+	0.0284406i
$721$	4.50131	+	8.83432i	0.167638	+	0.329007i
$722$	2.15758	−	13.6224i	0.0802970	−	0.506975i
$723$	1.11188	+	6.03283i	0.0413513	+	0.224363i
$724$	−5.10525	−	15.7123i	−0.189735	−	0.583944i
$725$	−36.9750			−1.37322
$726$	−3.91517	−	13.7086i	−0.145305	−	0.508773i
$727$		−	32.7041i		−	1.21293i	−0.795111	−	0.606464i	$-0.792587\pi$
$727$		−	32.7041i		−	1.21293i	0.795111	−	0.606464i	$-0.207413\pi$
$728$	9.89697	−	3.93388i	0.366806	−	0.145799i
$729$	−23.9832	−	12.4018i	−0.888267	−	0.459327i
$730$	−0.664043	+	4.19260i	−0.0245773	+	0.155175i
$731$	−44.2342	−	14.3725i	−1.63606	−	0.531588i
$732$	−6.76364	−	2.01084i	−0.249991	−	0.0743227i
$733$	4.11254	−	25.9655i	0.151900	−	0.959059i	−0.787520	−	0.616289i	$-0.788635\pi$
$733$	4.11254	−	25.9655i	0.151900	−	0.959059i	0.939420	−	0.342769i	$-0.111365\pi$
$734$	−1.25443	−	7.92017i	−0.0463019	−	0.292339i
$735$	4.75260	+	2.27271i	0.175302	+	0.0838301i
$736$	29.2780	+	29.2780i	1.07920	+	1.07920i
$737$	−2.99641	+	27.3526i	−0.110374	+	1.00755i
$738$	−0.522939	−	10.3752i	−0.0192497	−	0.381915i
$739$	16.3537	−	32.0960i	0.601582	−	1.18067i	−0.366589	−	0.930383i	$-0.619475\pi$
$739$	16.3537	−	32.0960i	0.601582	−	1.18067i	0.968171	−	0.250288i	$-0.0805254\pi$
$740$	−3.53122	−	2.56558i	−0.129810	−	0.0943125i
$741$	−4.69628	−	0.318537i	−0.172522	−	0.0117018i
$742$	1.37440	−	4.22996i	0.0504557	−	0.155287i
$743$	18.4918	−	9.42204i	0.678398	−	0.345661i	−0.0806069	−	0.996746i	$-0.525686\pi$
$743$	18.4918	−	9.42204i	0.678398	−	0.345661i	0.759005	+	0.651085i	$0.225686\pi$
$744$	14.3239	+	18.7059i	0.525139	+	0.685793i
$745$	−0.744060	+	1.02411i	−0.0272603	+	0.0375205i
$746$	4.73314	−	9.28932i	0.173293	−	0.340106i
$747$	27.4474	+	24.8133i	1.00425	+	0.907871i
$748$	13.0586	−	19.9164i	0.477469	−	0.728215i
$749$	5.08330	−	5.08330i	0.185740	−	0.185740i
$750$	2.24267	+	6.35328i	0.0818907	+	0.231989i
$751$	−15.4048	+	21.2029i	−0.562128	+	0.773703i	−0.991595	−	0.129379i	$-0.958701\pi$
$751$	−15.4048	+	21.2029i	−0.562128	+	0.773703i	0.429467	+	0.903083i	$0.358701\pi$
$752$	1.73542	−	10.9570i	0.0632844	−	0.399562i
$753$	9.94893	−	33.4641i	0.362559	−	1.21950i
$754$	−18.2021	+	10.7977i	−0.662880	+	0.393229i
$755$	−2.27249	−	3.12781i	−0.0827042	−	0.113833i
$756$	−8.35524	+	1.97943i	−0.303877	+	0.0719912i
$757$	−3.19718	−	9.83990i	−0.116203	−	0.357637i	0.875993	−	0.482324i	$-0.160207\pi$
$757$	−3.19718	−	9.83990i	−0.116203	−	0.357637i	−0.992196	+	0.124687i	$0.960207\pi$
$758$	−6.44841			−0.234217
$759$	−40.4665	+	2.96531i	−1.46884	+	0.107634i
$760$	−0.734224	+	0.734224i	−0.0266331	+	0.0266331i
$761$	9.26040	+	4.71841i	0.335689	+	0.171042i	0.613707	−	0.789534i	$-0.289678\pi$
$761$	9.26040	+	4.71841i	0.335689	+	0.171042i	−0.278018	+	0.960576i	$0.589678\pi$
$762$	−5.24015	+	0.965786i	−0.189830	+	0.0349867i
$763$	15.3252	−	11.1344i	0.554811	−	0.403094i
$764$	−1.14683	+	3.52959i	−0.0414910	+	0.127696i
$765$	−6.94108	+	3.98895i	−0.250955	+	0.144221i
$766$	6.89374	+	9.48842i	0.249081	+	0.342831i
$767$	−4.54121	−	20.1888i	−0.163974	−	0.728974i
$768$	−7.11587	−	20.1586i	−0.256772	−	0.727412i
$769$	−14.7868	+	14.7868i	−0.533226	+	0.533226i	−0.921531	−	0.388305i	$-0.873061\pi$
$769$	−14.7868	+	14.7868i	−0.533226	+	0.533226i	0.388305	+	0.921531i	$0.373061\pi$
$770$	0.756228	+	1.32322i	0.0272526	+	0.0476854i
$771$	−3.18093	+	0.0801133i	−0.114558	+	0.00288521i
$772$	6.37329	+	3.24736i	0.229380	+	0.116875i
$773$	4.97388	+	31.4038i	0.178898	+	1.12952i	0.899743	+	0.436421i	$0.143754\pi$
$773$	4.97388	+	31.4038i	0.178898	+	1.12952i	−0.720845	+	0.693097i	$0.756246\pi$
$774$	2.23035	−	20.8198i	0.0801683	−	0.748354i
$775$	−22.1932	+	11.3080i	−0.797202	+	0.406194i
$776$	−23.8119	−	7.73695i	−0.854797	−	0.277740i
$777$	−6.84355	−	8.93717i	−0.245511	−	0.320619i
$778$	2.94390	+	18.5871i	0.105544	+	0.666379i
$779$	1.07785	+	3.31729i	0.0386181	+	0.118854i
$780$	−3.69337	−	3.08598i	−0.132244	−	0.110496i
$781$	−16.6833	+	37.0327i	−0.596977	+	1.32514i
$782$	18.6353	+	18.6353i	0.666396	+	0.666396i
$783$	37.7042	−	15.4853i	1.34744	−	0.553399i
$784$	3.18673	−	4.38616i	0.113812	−	0.156649i
$785$	−4.27670	−	0.677364i	−0.152642	−	0.0241761i
$786$	13.5257	+	24.9707i	0.482445	+	0.890675i
$787$	−6.02173	+	3.06822i	−0.214651	+	0.109370i	−0.558011	−	0.829834i	$-0.688435\pi$
$787$	−6.02173	+	3.06822i	−0.214651	+	0.109370i	0.343359	+	0.939204i	$0.388435\pi$
$788$	0.151292	−	0.955220i	0.00538956	−	0.0340283i
$789$	−14.0224	+	20.3591i	−0.499212	+	0.724804i
$790$	−1.13517	+	0.368840i	−0.0403877	+	0.0131227i
$791$	−15.6713	+	15.6713i	−0.557206	+	0.557206i
$792$	23.8521	+	9.33133i	0.847548	+	0.331575i
$793$	−0.654138	−	10.1790i	−0.0232291	−	0.361466i
$794$	−4.31125	+	1.40081i	−0.153000	+	0.0497128i
$795$	−4.72187	+	0.870264i	−0.167467	+	0.0308651i
$796$	−13.6147	+	9.89166i	−0.482560	+	0.350601i
$797$	14.7516	−	45.4006i	0.522527	−	1.60817i	−0.246628	−	0.969110i	$-0.579323\pi$
$797$	14.7516	−	45.4006i	0.522527	−	1.60817i	0.769155	−	0.639062i	$-0.220677\pi$
$798$	−0.985663	+	0.533896i	−0.0348921	+	0.0188997i
$799$	9.07108	−	57.2725i	0.320912	−	2.02616i
$800$	27.2915	−	4.32254i	0.964899	−	0.152825i
$801$	24.7758	+	11.0903i	0.875409	+	0.391856i
$802$	23.2294			0.820259
$803$	−30.5231	+	17.4442i	−1.07714	+	0.615593i
$804$	−14.9964	−	14.2596i	−0.528883	−	0.502897i
$805$	4.12525	−	1.34038i	0.145396	−	0.0472420i
$806$	−7.62302	+	12.0477i	−0.268509	+	0.424362i
$807$	−8.18163	−	10.6846i	−0.288007	−	0.376116i
$808$	9.00846	+	17.6801i	0.316916	+	0.621984i
$809$	8.80342	+	2.86040i	0.309512	+	0.100566i	0.459654	−	0.888098i	$-0.347973\pi$
$809$	8.80342	+	2.86040i	0.309512	+	0.100566i	−0.150143	+	0.988664i	$0.547973\pi$
$810$	−2.40090	−	2.68801i	−0.0843591	−	0.0944471i
$811$	−16.4919	+	2.61207i	−0.579111	+	0.0917221i	−0.439116	−	0.898430i	$-0.644708\pi$
$811$	−16.4919	+	2.61207i	−0.579111	+	0.0917221i	−0.139994	+	0.990152i	$0.544708\pi$
$812$	5.88487	−	11.5497i	0.206519	−	0.405316i
$813$	−37.0447	−	35.2246i	−1.29922	−	1.23538i
$814$	0.673951	+	14.0395i	0.0236220	+	0.492085i
$815$		−	3.98675i		−	0.139650i
$816$	2.74246	+	7.76914i	0.0960053	+	0.271974i
$817$	1.09981	+	6.94395i	0.0384776	+	0.242938i
$818$	5.80894	−	4.22044i	0.203105	−	0.147564i
$819$	−6.86193	−	10.3428i	−0.239775	−	0.361405i
$820$	−1.10209	+	3.39189i	−0.0384868	+	0.118450i
$821$	−11.1574	−	1.76716i	−0.389396	−	0.0616742i	−0.0413330	−	0.999145i	$-0.513160\pi$
$821$	−11.1574	−	1.76716i	−0.389396	−	0.0616742i	−0.348063	+	0.937471i	$0.613160\pi$
$822$	10.7492	+	7.40356i	0.374921	+	0.258229i
$823$	−7.21302	+	2.34365i	−0.251430	+	0.0816946i	−0.432020	−	0.901864i	$-0.642199\pi$
$823$	−7.21302	+	2.34365i	−0.251430	+	0.0816946i	0.180590	+	0.983558i	$0.442199\pi$
$824$	15.7275	+	15.7275i	0.547894	+	0.547894i
$825$	−14.2723	+	23.0108i	−0.496896	+	0.801132i
$826$	−3.48463	−	3.48463i	−0.121246	−	0.121246i
$827$	18.3507	+	9.35015i	0.638117	+	0.325137i	0.742944	−	0.669354i	$-0.233429\pi$
$827$	18.3507	+	9.35015i	0.638117	+	0.325137i	−0.104827	+	0.994490i	$0.533429\pi$
$828$	16.6706	−	25.5584i	0.579343	−	0.888217i
$829$	0.190834	+	0.262660i	0.00662793	+	0.00912256i	0.812318	−	0.583215i	$-0.198205\pi$
$829$	0.190834	+	0.262660i	0.00662793	+	0.00912256i	−0.805690	+	0.592337i	$0.798205\pi$
$830$	2.24230	+	4.40076i	0.0778314	+	0.152753i
$831$	−22.5792	−	6.71282i	−0.783263	−	0.232865i
$832$	6.87822	−	5.70574i	0.238459	−	0.197811i
$833$	16.6571	−	22.9265i	0.577134	−	0.794357i
$834$	−4.61797	+	9.65692i	−0.159907	+	0.334392i
$835$	−3.28634			−0.113728
$836$	−3.57856	−	0.392023i	−0.123767	−	0.0135584i
$837$	17.8950	−	20.8256i	0.618543	−	0.719838i
$838$	1.87447	+	0.955092i	0.0647526	+	0.0329931i
$839$	12.9698	−	2.05421i	0.447766	−	0.0709192i	0.0715206	−	0.997439i	$-0.477215\pi$
$839$	12.9698	−	2.05421i	0.447766	−	0.0709192i	0.376246	+	0.926520i	$0.377215\pi$
$840$	−2.71423	−	0.360097i	−0.0936499	−	0.0124245i
$841$	−10.0534	+	30.9412i	−0.346669	+	1.06694i
$842$	−4.17365	+	12.8452i	−0.143833	+	0.442674i
$843$	−2.01784	+	15.2095i	−0.0694981	+	0.523843i
$844$	−16.3618	+	22.5202i	−0.563198	+	0.775176i
$845$	2.33907	−	6.55222i	0.0804666	−	0.225403i
$846$	26.0723	−	1.31412i	0.896384	−	0.0451804i
$847$	−4.62683	+	11.7439i	−0.158980	+	0.403524i
$848$			4.94133i			0.169686i
$849$	−33.2984	+	11.7541i	−1.14280	+	0.403401i
$850$	17.3708	−	2.75127i	0.595815	−	0.0943677i
$851$	39.5104	+	6.25784i	1.35440	+	0.214516i
$852$	−14.5486	−	26.8592i	−0.498427	−	0.920181i
$853$	32.3740	−	16.4954i	1.10846	−	0.564790i	0.198759	−	0.980048i	$-0.436309\pi$
$853$	32.3740	−	16.4954i	1.10846	−	0.564790i	0.909704	+	0.415258i	$0.136309\pi$
$854$	−1.42778	−	1.96517i	−0.0488576	−	0.0672467i
$855$	1.01358	+	0.661111i	0.0346637	+	0.0226095i
$856$	7.32135	−	14.3690i	0.250239	−	0.491121i
$857$	37.4467			1.27916			0.639578	−	0.768726i	$-0.279109\pi$
$857$	37.4467			1.27916			0.639578	+	0.768726i	$0.279109\pi$
$858$	−0.306185	+	15.4956i	−0.0104530	+	0.529012i
$859$	41.4918			1.41568			0.707841	−	0.706372i	$-0.249670\pi$
$859$	41.4918			1.41568			0.707841	+	0.706372i	$0.249670\pi$
$860$	−3.26356	+	6.40510i	−0.111287	+	0.218412i
$861$	−5.21710	+	7.57469i	−0.177798	+	0.258145i
$862$	4.72888	+	6.50875i	0.161066	+	0.221689i
$863$	−26.7522	+	13.6309i	−0.910656	+	0.464003i	−0.845562	−	0.533877i	$-0.820735\pi$
$863$	−26.7522	+	13.6309i	−0.910656	+	0.464003i	−0.0650940	+	0.997879i	$0.520735\pi$
$864$	−26.0195	+	15.8376i	−0.885200	+	0.538806i
$865$	6.88724	+	1.09083i	0.234173	+	0.0370894i
$866$	11.9951	−	1.89983i	0.407609	−	0.0645589i
$867$	4.53373	+	12.8437i	0.153974	+	0.436193i
$868$		−	8.73214i		−	0.296388i
$869$	−8.26687	−	5.42035i	−0.280434	−	0.183873i
$870$	5.43922	−	0.136989i	0.184407	−	0.00464438i
$871$	11.8431	−	27.4690i	0.401288	−	0.930751i
$872$	24.9776	−	34.3788i	0.845850	−	1.16421i
$873$	−3.10809	+	29.0133i	−0.105193	+	0.981952i
$874$	1.23103	−	3.78871i	0.0416401	−	0.128155i
$875$	1.84334	−	5.67320i	0.0623161	−	0.191789i
$876$	3.47724	−	26.2097i	0.117485	−	0.885545i
$877$	−57.2314	+	9.06457i	−1.93257	+	0.306089i	−0.998675	−	0.0514627i	$-0.983612\pi$
$877$	−57.2314	+	9.06457i	−1.93257	+	0.306089i	−0.933893	+	0.357551i	$0.883612\pi$
$878$	1.56780	+	0.798834i	0.0529107	+	0.0269593i
$879$	−2.95302	+	3.10561i	−0.0996027	+	0.104749i
$880$	−1.25333	−	1.13851i	−0.0422498	−	0.0383793i
$881$	21.1033			0.710987			0.355494	−	0.934679i	$-0.384313\pi$
$881$	21.1033			0.710987			0.355494	+	0.934679i	$0.384313\pi$
$882$	11.6447	+	5.21246i	0.392096	+	0.175513i
$883$	−1.23080	+	1.69405i	−0.0414198	+	0.0570094i	−0.829225	−	0.558916i	$-0.811218\pi$
$883$	−1.23080	+	1.69405i	−0.0414198	+	0.0570094i	0.787805	+	0.615925i	$0.211218\pi$
$884$	−19.9267	+	16.5300i	−0.670208	+	0.555963i
$885$	−1.51605	+	5.09937i	−0.0509615	+	0.171414i
$886$	−9.03996	−	17.7419i	−0.303704	−	0.596052i
$887$	−2.85066	−	3.92359i	−0.0957157	−	0.131741i	0.758473	−	0.651704i	$-0.225946\pi$
$887$	−2.85066	−	3.92359i	−0.0957157	−	0.131741i	−0.854189	+	0.519963i	$0.825946\pi$
$888$	−20.7959	−	14.3233i	−0.697866	−	0.480658i
$889$	4.20341	+	2.14174i	0.140978	+	0.0718318i
$890$	2.56216	+	2.56216i	0.0858837	+	0.0858837i
$891$	4.91675	−	29.4419i	0.164717	−	0.986341i
$892$	−27.0269	−	27.0269i	−0.904928	−	0.904928i
$893$	−8.33619	+	2.70859i	−0.278960	+	0.0906396i
$894$	−1.73893	+	2.52475i	−0.0581586	+	0.0844403i
$895$	−0.182551	−	0.0289132i	−0.00610200	−	0.000966463i
$896$	−3.49969	+	10.7709i	−0.116916	+	0.359832i
$897$	42.9998	+	9.83271i	1.43572	+	0.328305i
$898$	−3.08302	+	2.23995i	−0.102882	+	0.0747480i
$899$	6.48447	+	40.9413i	0.216269	+	1.36547i
$900$	−7.25969	−	19.0258i	−0.241990	−	0.634192i
$901$			25.8284i			0.860469i
$902$	10.7399	−	4.06862i	0.357600	−	0.135470i
$903$	−12.7746	+	13.4347i	−0.425113	+	0.447080i
$904$	−22.5709	+	44.2979i	−0.750697	+	1.47333i
$905$	−6.06403	+	0.960449i	−0.201575	+	0.0319264i
$906$	−5.69242	−	7.43389i	−0.189118	−	0.246974i
$907$	52.1531	+	16.9456i	1.73171	+	0.562668i	0.993695	−	0.112113i	$-0.0357618\pi$
$907$	52.1531	+	16.9456i	1.73171	+	0.562668i	0.738018	+	0.674781i	$0.235762\pi$
$908$	−0.416153	−	0.816745i	−0.0138105	−	0.0271046i
$909$	18.0010	−	14.5174i	0.597055	−	0.481512i
$910$	−0.363600	−	1.61645i	−0.0120532	−	0.0535847i
$911$	31.4399	−	10.2154i	1.04165	−	0.338453i	0.262264	−	0.964996i	$-0.415531\pi$
$911$	31.4399	−	10.2154i	1.04165	−	0.338453i	0.779386	+	0.626543i	$0.215531\pi$
$912$	0.858178	−	0.902522i	0.0284171	−	0.0298855i
$913$	−16.8019	+	37.2960i	−0.556063	+	1.23432i
$914$	−18.2350			−0.603160
$915$	−1.13129	+	2.36570i	−0.0373992	+	0.0782078i
$916$	−19.8384	+	3.14209i	−0.655479	+	0.103818i
$917$	3.93326	−	24.8336i	0.129888	−	0.820079i
$918$	−16.5612	+	10.0805i	−0.546601	+	0.332707i
$919$	8.23483	−	25.3442i	0.271642	−	0.836028i	−0.718447	−	0.695582i	$-0.755147\pi$
$919$	8.23483	−	25.3442i	0.271642	−	0.836028i	0.990088	−	0.140445i	$-0.0448535\pi$
$920$	7.87200	−	5.71934i	0.259532	−	0.188561i
$921$	−2.36269	−	12.8194i	−0.0778532	−	0.422415i
$922$	−12.7069	+	4.12873i	−0.418481	+	0.135973i
$923$	29.1561	−	33.1608i	0.959684	−	1.09150i
$924$	−4.91623	−	8.12052i	−0.161732	−	0.267146i
$925$	18.8767	−	18.8767i	0.620663	−	0.620663i
$926$	−15.5016	+	5.03676i	−0.509413	+	0.165518i
$927$	14.1614	−	21.7115i	0.465121	−	0.713099i
$928$	7.19355	−	45.4183i	0.236140	−	1.49093i
$929$	9.11898	−	4.64635i	0.299184	−	0.152442i	−0.297954	−	0.954580i	$-0.596304\pi$
$929$	9.11898	−	4.64635i	0.299184	−	0.152442i	0.597138	+	0.802138i	$0.296304\pi$
$930$	3.22284	−	1.74569i	0.105681	−	0.0572434i
$931$	−4.23093	−	0.670113i	−0.138663	−	0.0219621i
$932$	−23.9571	+	32.9742i	−0.784742	+	1.08010i
$933$	−9.82178	−	27.8242i	−0.321550	−	0.910924i
$934$	−16.5340	−	16.5340i	−0.541009	−	0.541009i
$935$	−6.55118	−	5.95103i	−0.214246	−	0.194619i
$936$	−21.8095	−	17.3093i	−0.712867	−	0.565773i
$937$	0.491724	+	1.51337i	0.0160639	+	0.0494396i	0.958767	−	0.284193i	$-0.0917256\pi$
$937$	0.491724	+	1.51337i	0.0160639	+	0.0494396i	−0.942703	+	0.333632i	$0.891726\pi$
$938$	−1.11440	−	7.03603i	−0.0363864	−	0.229735i
$939$	20.2196	−	15.4830i	0.659842	−	0.505267i
$940$	−8.52367	−	2.76951i	−0.278011	−	0.0903314i
$941$	−14.6078	+	7.44307i	−0.476202	+	0.242637i	−0.675581	−	0.737285i	$-0.736107\pi$
$941$	−14.6078	+	7.44307i	−0.476202	+	0.242637i	0.199380	+	0.979922i	$0.436107\pi$
$942$	−10.3952	−	1.37913i	−0.338695	−	0.0449346i
$943$	−5.11321	−	32.2835i	−0.166509	−	1.05130i
$944$	4.87828	+	2.48561i	0.158774	+	0.0808996i
$945$	0.240819	+	3.18188i	0.00783385	+	0.103507i
$946$	22.6640	−	4.71341i	0.736869	−	0.153246i
$947$	−29.2478	+	29.2478i	−0.950426	+	0.950426i	−0.998828	−	0.0484019i	$-0.984587\pi$
$947$	−29.2478	+	29.2478i	−0.950426	+	0.950426i	0.0484019	+	0.998828i	$0.484587\pi$
$948$	7.01041	−	2.47463i	0.227688	−	0.0803724i
$949$	37.2872	−	8.38730i	1.21039	−	0.272263i
$950$	−1.56262	−	2.15077i	−0.0506982	−	0.0697801i
$951$	16.3221	−	8.84104i	0.529279	−	0.286690i
$952$	−4.55144	+	14.0079i	−0.147513	+	0.453998i
$953$	4.54880	−	3.30490i	0.147350	−	0.107056i	−0.511668	−	0.859183i	$-0.670972\pi$
$953$	4.54880	−	3.30490i	0.147350	−	0.107056i	0.659018	+	0.752127i	$0.270972\pi$
$954$	−11.3786	+	2.39483i	−0.368396	+	0.0775355i
$955$	1.22887	+	0.626141i	0.0397653	+	0.0202615i
$956$	24.3105	−	24.3105i	0.786256	−	0.786256i
$957$	29.0804	+	34.4229i	0.940035	+	1.11273i
$958$	7.17729			0.231888
$959$	−3.57098	−	10.9903i	−0.115313	−	0.354897i
$960$	−2.25947	+	0.416432i	−0.0729241	+	0.0134403i
$961$	−1.80824	−	2.48883i	−0.0583302	−	0.0802847i
$962$	3.78012	−	14.8052i	0.121876	−	0.477338i
$963$	−18.1444	−	4.90068i	−0.584695	−	0.157922i
$964$	0.797868	−	5.03754i	0.0256976	−	0.162248i
$965$	1.56246	−	2.15054i	0.0502974	−	0.0692284i
$966$	9.90554	−	3.49660i	0.318706	−	0.112501i
$967$	−37.0576	+	37.0576i	−1.19169	+	1.19169i	−0.215099	+	0.976592i	$0.569007\pi$
$967$	−37.0576	+	37.0576i	−1.19169	+	1.19169i	−0.976592	+	0.215099i	$0.930993\pi$
$968$	−1.73029	+	28.2627i	−0.0556137	+	0.908397i
$969$	4.48571	−	4.71750i	0.144102	−	0.151548i
$970$	−1.76831	+	3.47050i	−0.0567770	+	0.111431i
$971$	7.26271	−	9.99627i	0.233072	−	0.320795i	−0.676421	−	0.736515i	$-0.736470\pi$
$971$	7.26271	−	9.99627i	0.233072	−	0.320795i	0.909493	+	0.415719i	$0.136470\pi$
$972$	15.3710	+	16.3606i	0.493024	+	0.524767i
$973$	8.44428	−	4.30258i	0.270711	−	0.137934i
$974$	2.74348	−	8.44356i	0.0879067	−	0.270549i
$975$	22.1755	−	19.3584i	0.710185	−	0.619964i
$976$	2.18330	+	1.58626i	0.0698858	+	0.0507750i
$977$	−3.62097	+	7.10656i	−0.115845	+	0.227359i	−0.941647	−	0.336601i	$-0.890723\pi$
$977$	−3.62097	+	7.10656i	−0.115845	+	0.227359i	0.825802	+	0.563960i	$0.190723\pi$
$978$	−0.243089	−	9.65196i	−0.00777314	−	0.308636i
$979$	−3.26793	+	29.8311i	−0.104443	+	0.953406i
$980$	−3.09713	−	3.09713i	−0.0989341	−	0.0989341i
$981$	−45.2026	−	20.2339i	−1.44321	−	0.646018i
$982$	−0.0932460	−	0.588732i	−0.00297560	−	0.0187872i
$983$	4.17586	−	26.3653i	0.133189	−	0.840924i	−0.827128	−	0.562014i	$-0.810027\pi$
$983$	4.17586	−	26.3653i	0.133189	−	0.840924i	0.960317	−	0.278910i	$-0.0899732\pi$
$984$	−5.87974	+	19.7770i	−0.187439	+	0.630469i
$985$	−0.341820	−	0.111064i	−0.0108913	−	0.00353879i
$986$	4.57864	−	28.9084i	0.145814	−	0.920631i
$987$	−19.0348	−	13.1103i	−0.605885	−	0.417306i
$988$	3.59379	+	1.54944i	0.114334	+	0.0492944i
$989$		−	65.8825i		−	2.09494i
$990$	2.01427	−	3.43788i	0.0640178	−	0.109263i
$991$	2.03846			0.0647539			0.0323770	−	0.999476i	$-0.489692\pi$
$991$	2.03846			0.0647539			0.0323770	+	0.999476i	$0.489692\pi$
$992$	−9.57246	−	29.4610i	−0.303926	−	0.935387i
$993$	31.3248	−	5.77332i	0.994062	−	0.183211i
$994$	1.64498	−	10.3860i	0.0521758	−	0.329425i
$995$	2.83926	+	5.57236i	0.0900105	+	0.176656i
$996$	−14.6520	−	27.0501i	−0.464267	−	0.857115i
$997$	−36.6592	+	26.6344i	−1.16101	+	0.843521i	−0.989905	−	0.141732i	$-0.954733\pi$
$997$	−36.6592	+	26.6344i	−1.16101	+	0.843521i	−0.171103	+	0.985253i	$0.554733\pi$
$998$	11.6295	+	8.44930i	0.368124	+	0.267458i
$999$	−11.3434	+	27.1547i	−0.358889	+	0.859137i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bi.a.5.19	✓	416
3.2	odd	2	inner	429.2.bi.a.5.34	yes	416
11.9	even	5	inner	429.2.bi.a.317.34	yes	416
13.8	odd	4	inner	429.2.bi.a.203.19	yes	416
33.20	odd	10	inner	429.2.bi.a.317.19	yes	416
39.8	even	4	inner	429.2.bi.a.203.34	yes	416
143.86	odd	20	inner	429.2.bi.a.86.34	yes	416
429.86	even	20	inner	429.2.bi.a.86.19	yes	416

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bi.a.5.19	✓	416	1.1	even	1	trivial
429.2.bi.a.5.34	yes	416	3.2	odd	2	inner
429.2.bi.a.86.19	yes	416	429.86	even	20	inner
429.2.bi.a.86.34	yes	416	143.86	odd	20	inner
429.2.bi.a.203.19	yes	416	13.8	odd	4	inner
429.2.bi.a.203.34	yes	416	39.8	even	4	inner
429.2.bi.a.317.19	yes	416	33.20	odd	10	inner
429.2.bi.a.317.34	yes	416	11.9	even	5	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bi (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.339713 + 0.666725i) q^{2} +(-1.42645 - 0.982471i) q^{3} +(0.846454 + 1.16504i) q^{4} +(0.476840 - 0.242962i) q^{5} +(1.13962 - 0.617289i) q^{6} +(-1.13337 - 0.179507i) q^{7} +(-2.54245 + 0.402685i) q^{8} +(1.06950 + 2.80289i) q^{9} +O(q^{10})\)	\(q+(-0.339713 + 0.666725i) q^{2} +(-1.42645 - 0.982471i) q^{3} +(0.846454 + 1.16504i) q^{4} +(0.476840 - 0.242962i) q^{5} +(1.13962 - 0.617289i) q^{6} +(-1.13337 - 0.179507i) q^{7} +(-2.54245 + 0.402685i) q^{8} +(1.06950 + 2.80289i) q^{9} +0.400459i q^{10} +(-2.58665 + 2.07588i) q^{11} +(-0.0627998 - 2.49349i) q^{12} +(3.35057 - 1.33180i) q^{13} +(0.504701 - 0.694662i) q^{14} +(-0.918891 - 0.121909i) q^{15} +(-0.294789 + 0.907268i) q^{16} +(-1.54087 + 4.74230i) q^{17} +(-2.23208 - 0.239114i) q^{18} +(0.744454 - 0.117910i) q^{19} +(0.686685 + 0.349884i) q^{20} +(1.44032 + 1.36956i) q^{21} +(-0.505321 - 2.42978i) q^{22} -7.06321 q^{23} +(4.02230 + 1.92348i) q^{24} +(-2.77058 + 3.81338i) q^{25} +(-0.250292 + 2.68634i) q^{26} +(1.22817 - 5.04892i) q^{27} +(-0.750208 - 1.47237i) q^{28} +(4.61078 + 6.34619i) q^{29} +(0.393439 - 0.571233i) q^{30} +(4.70833 + 2.39901i) q^{31} +(-4.14515 - 4.14515i) q^{32} +(5.72920 - 0.419825i) q^{33} +(-2.63836 - 2.63836i) q^{34} +(-0.584048 + 0.189769i) q^{35} +(-2.36020 + 3.61853i) q^{36} +(-5.59384 - 0.885977i) q^{37} +(-0.174287 + 0.536401i) q^{38} +(-6.08786 - 1.39210i) q^{39} +(-1.11451 + 0.809737i) q^{40} +(0.723922 + 4.57066i) q^{41} +(-1.40241 + 0.495044i) q^{42} +9.32757i q^{43} +(-4.60796 - 1.25642i) q^{44} +(1.19098 + 1.07668i) q^{45} +(2.39946 - 4.70921i) q^{46} +(-11.4859 + 1.81918i) q^{47} +(1.31187 - 1.00455i) q^{48} +(-5.40510 - 1.75622i) q^{49} +(-1.60127 - 3.14267i) q^{50} +(6.85714 - 5.25079i) q^{51} +(4.38770 + 2.77626i) q^{52} +(4.92630 - 1.60065i) q^{53} +(2.94902 + 2.53403i) q^{54} +(-0.729057 + 1.61832i) q^{55} +2.95382 q^{56} +(-1.17777 - 0.563212i) q^{57} +(-5.79751 + 0.918235i) q^{58} +(0.897818 - 5.66860i) q^{59} +(-0.635769 - 1.17374i) q^{60} +(0.874197 - 2.69050i) q^{61} +(-3.19896 + 2.32418i) q^{62} +(-0.708997 - 3.36868i) q^{63} +(2.35730 - 0.765932i) q^{64} +(1.27411 - 1.44912i) q^{65} +(-1.66638 + 3.96242i) q^{66} +(5.86648 - 5.86648i) q^{67} +(-6.82927 + 2.21896i) q^{68} +(10.0753 + 6.93940i) q^{69} +(0.0718853 - 0.453866i) q^{70} +(10.9118 - 5.55982i) q^{71} +(-3.84784 - 6.69554i) q^{72} +(10.4695 + 1.65821i) q^{73} +(2.49100 - 3.42857i) q^{74} +(7.69862 - 2.71756i) q^{75} +(0.767516 + 0.767516i) q^{76} +(3.30425 - 1.88841i) q^{77} +(2.99628 - 3.58601i) q^{78} +(0.921045 + 2.83468i) q^{79} +(0.0798645 + 0.504245i) q^{80} +(-6.71233 + 5.99538i) q^{81} +(-3.29330 - 1.07006i) q^{82} +(10.9893 - 5.59933i) q^{83} +(-0.376425 + 2.83731i) q^{84} +(0.417453 + 2.63569i) q^{85} +(-6.21892 - 3.16870i) q^{86} +(-0.342081 - 13.5825i) q^{87} +(5.74050 - 6.31943i) q^{88} +(6.39806 - 6.39806i) q^{89} +(-1.12244 + 0.428291i) q^{90} +(-4.03649 + 0.907958i) q^{91} +(-5.97868 - 8.22895i) q^{92} +(-4.35922 - 8.04786i) q^{93} +(2.68900 - 8.27590i) q^{94} +(0.326338 - 0.237098i) q^{95} +(1.84035 + 9.98532i) q^{96} +(8.66633 + 4.41571i) q^{97} +(3.00710 - 3.00710i) q^{98} +(-8.58487 - 5.02992i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9}+O(q^{10}) \) 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9	\( 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9} - 20 q^{13} - 30 q^{15} + 32 q^{16} + 2 q^{18} - 4 q^{19} - 12 q^{21} - 24 q^{22} - 78 q^{24} - 36 q^{27} - 84 q^{28} - 28 q^{31} - 44 q^{33} - 24 q^{34} - 12 q^{37} + 54 q^{39} + 88 q^{40} - 56 q^{42} + 8 q^{45} - 92 q^{46} + 40 q^{48} - 44 q^{52} - 176 q^{54} - 72 q^{55} - 6 q^{57} - 4 q^{58} + 12 q^{60} - 48 q^{61} - 46 q^{63} + 204 q^{66} - 64 q^{67} + 56 q^{70} - 66 q^{72} - 12 q^{73} - 104 q^{76} - 92 q^{78} + 104 q^{79} + 124 q^{81} + 16 q^{84} - 12 q^{85} - 24 q^{87} - 84 q^{91} - 124 q^{93} + 328 q^{94} - 152 q^{96} + 52 q^{97} - 142 q^{99}+O(q^{100}) \) 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9 - 20 * q^13 - 30 * q^15 + 32 * q^16 + 2 * q^18 - 4 * q^19 - 12 * q^21 - 24 * q^22 - 78 * q^24 - 36 * q^27 - 84 * q^28 - 28 * q^31 - 44 * q^33 - 24 * q^34 - 12 * q^37 + 54 * q^39 + 88 * q^40 - 56 * q^42 + 8 * q^45 - 92 * q^46 + 40 * q^48 - 44 * q^52 - 176 * q^54 - 72 * q^55 - 6 * q^57 - 4 * q^58 + 12 * q^60 - 48 * q^61 - 46 * q^63 + 204 * q^66 - 64 * q^67 + 56 * q^70 - 66 * q^72 - 12 * q^73 - 104 * q^76 - 92 * q^78 + 104 * q^79 + 124 * q^81 + 16 * q^84 - 12 * q^85 - 24 * q^87 - 84 * q^91 - 124 * q^93 + 328 * q^94 - 152 * q^96 + 52 * q^97 - 142 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more