LMFDB - Embedded newform 820.2.bw.b.11.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(11,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(40)) chi = DirichletCharacter(H, H._module([20, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.bw (of order $40$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [672,0,0,0,0,12,0,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$42$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			11.7
Character	$\chi$	$=$	820.11
Dual form			820.2.bw.b.671.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.23021 + 0.697547i) q^{2} +(-0.0404624 + 0.0976849i) q^{3} +(1.02686 - 1.71626i) q^{4} +(0.453990 - 0.891007i) q^{5} +(-0.0183623 - 0.148398i) q^{6} +(0.683689 + 2.84777i) q^{7} +(-0.0660801 + 2.82766i) q^{8} +(2.11342 + 2.11342i) q^{9} +(0.0630128 + 1.41281i) q^{10} +(2.02458 - 2.37048i) q^{11} +(0.126104 + 0.169753i) q^{12} +(2.83853 + 4.63206i) q^{13} +(-2.82754 - 3.02646i) q^{14} +(0.0686683 + 0.0804003i) q^{15} +(-1.89113 - 3.52472i) q^{16} +(-0.142473 - 1.81030i) q^{17} +(-4.07416 - 1.12575i) q^{18} +(-4.93456 - 3.02390i) q^{19} +(-1.06302 - 1.69410i) q^{20} +(-0.305848 - 0.0484416i) q^{21} +(-0.837150 + 4.32844i) q^{22} +(-0.442177 - 0.321261i) q^{23} +(-0.273545 - 0.120869i) q^{24} +(-0.587785 - 0.809017i) q^{25} +(-6.72308 - 3.71842i) q^{26} +(-0.585017 + 0.242322i) q^{27} +(5.58958 + 1.75086i) q^{28} +(0.000106835 - 0.00135747i) q^{29} +(-0.140560 - 0.0510103i) q^{30} +(-1.75563 + 5.40328i) q^{31} +(4.78515 + 3.01701i) q^{32} +(0.149641 + 0.293687i) q^{33} +(1.43804 + 2.12767i) q^{34} +(2.84777 + 0.683689i) q^{35} +(5.79736 - 1.45700i) q^{36} +(0.464392 + 1.42925i) q^{37} +(8.17988 + 0.277963i) q^{38} +(-0.567336 + 0.0898572i) q^{39} +(2.48946 + 1.34261i) q^{40} +(4.00583 + 4.99533i) q^{41} +(0.410049 - 0.153750i) q^{42} +(0.260780 + 1.64650i) q^{43} +(-1.98942 - 5.90887i) q^{44} +(2.84254 - 0.923596i) q^{45} +(0.768067 + 0.0867802i) q^{46} +(-1.02283 + 4.26040i) q^{47} +(0.420831 - 0.0421162i) q^{48} +(-1.40532 + 0.716047i) q^{49} +(1.28743 + 0.585257i) q^{50} +(0.182604 + 0.0593315i) q^{51} +(10.8646 - 0.115205i) q^{52} +(10.7647 + 0.847201i) q^{53} +(0.550666 - 0.706185i) q^{54} +(-1.19297 - 2.88009i) q^{55} +(-8.09769 + 1.74506i) q^{56} +(0.495054 - 0.359678i) q^{57} +(0.000815468 + 0.00174450i) q^{58} +(1.88962 - 2.60083i) q^{59} +(0.208501 - 0.0352934i) q^{60} +(-0.321828 + 2.03194i) q^{61} +(-1.60923 - 7.87183i) q^{62} +(-4.57360 + 7.46344i) q^{63} +(-7.99127 - 0.373703i) q^{64} +(5.41586 - 0.426237i) q^{65} +(-0.388951 - 0.256916i) q^{66} +(-2.92613 + 2.49915i) q^{67} +(-3.25325 - 1.61439i) q^{68} +(0.0492739 - 0.0301951i) q^{69} +(-3.98028 + 1.14537i) q^{70} +(10.5561 + 9.01579i) q^{71} +(-6.11566 + 5.83635i) q^{72} +(5.95234 - 5.95234i) q^{73} +(-1.56827 - 1.43435i) q^{74} +(0.102812 - 0.0246830i) q^{75} +(-10.2569 + 5.36390i) q^{76} +(8.13478 + 4.14488i) q^{77} +(0.635266 - 0.506287i) q^{78} +(-7.65804 - 3.17206i) q^{79} +(-3.99910 + 0.0848200i) q^{80} +8.89951i q^{81} +(-8.41251 - 3.35107i) q^{82} -3.14409i q^{83} +(-0.397201 + 0.475174i) q^{84} +(-1.67767 - 0.694913i) q^{85} +(-1.46933 - 1.84364i) q^{86} +(0.000128282 + 6.53627e-5i) q^{87} +(6.56912 + 5.88146i) q^{88} +(-1.78044 + 0.427445i) q^{89} +(-2.85268 + 3.11902i) q^{90} +(-11.2504 + 11.2504i) q^{91} +(-1.00542 + 0.429004i) q^{92} +(-0.456782 - 0.390128i) q^{93} +(-1.71352 - 5.95467i) q^{94} +(-4.93456 + 3.02390i) q^{95} +(-0.488335 + 0.345361i) q^{96} +(-4.19288 + 3.58106i) q^{97} +(1.22937 - 1.86117i) q^{98} +(9.28860 - 0.731029i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q + 12 q^{6} + 16 q^{9} - 124 q^{12} - 24 q^{14} - 32 q^{16} - 8 q^{17} + 40 q^{21} - 4 q^{22} - 24 q^{24} - 28 q^{28} - 12 q^{30} - 20 q^{32} + 40 q^{33} - 4 q^{34} - 60 q^{36} + 80 q^{37} - 172 q^{38}+ \cdots - 116 q^{98}+O(q^{100}) $ 672 * q + 12 * q^6 + 16 * q^9 - 124 * q^12 - 24 * q^14 - 32 * q^16 - 8 * q^17 + 40 * q^21 - 4 * q^22 - 24 * q^24 - 28 * q^28 - 12 * q^30 - 20 * q^32 + 40 * q^33 - 4 * q^34 - 60 * q^36 + 80 * q^37 - 172 * q^38 + 160 * q^42 - 24 * q^44 - 16 * q^46 + 40 * q^48 - 24 * q^52 - 64 * q^54 + 68 * q^56 - 112 * q^58 + 36 * q^62 - 120 * q^64 + 8 * q^65 + 144 * q^68 - 104 * q^69 + 24 * q^70 - 320 * q^72 - 92 * q^74 - 24 * q^76 + 160 * q^77 - 128 * q^78 - 192 * q^82 - 172 * q^84 - 32 * q^85 - 112 * q^88 + 8 * q^89 - 48 * q^90 + 24 * q^92 + 92 * q^94 + 56 * q^96 - 116 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$e\left(\frac{3}{40}\right)$	$1$

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 $

$2$	−1.23021	+	0.697547i	−0.869893	+	0.493240i
$2$	−1.23021	+	0.697547i	−0.869893	+	0.493240i
$3$	−0.0404624	+	0.0976849i	−0.0233610	+	0.0563984i	−0.935130	−	0.354306i	$-0.884717\pi$
$3$	−0.0404624	+	0.0976849i	−0.0233610	+	0.0563984i	0.911769	+	0.410704i	$0.134717\pi$
$4$	1.02686	−	1.71626i	0.513429	−	0.858132i
$5$	0.453990	−	0.891007i	0.203031	−	0.398470i
$5$	0.453990	−	0.891007i	0.203031	−	0.398470i
$6$	−0.0183623	−	0.148398i	−0.00749639	−	0.0605832i
$7$	0.683689	+	2.84777i	0.258410	+	1.07636i	0.939062	+	0.343749i	$0.111697\pi$
$7$	0.683689	+	2.84777i	0.258410	+	1.07636i	−0.680651	+	0.732607i	$0.738303\pi$
$8$	−0.0660801	+	2.82766i	−0.0233628	+	0.999727i
$9$	2.11342	+	2.11342i	0.704472	+	0.704472i
$10$	0.0630128	+	1.41281i	0.0199264	+	0.446769i
$11$	2.02458	−	2.37048i	0.610435	−	0.714727i	−0.365982	−	0.930622i	$-0.619267\pi$
$11$	2.02458	−	2.37048i	0.610435	−	0.714727i	0.976417	+	0.215895i	$0.0692668\pi$
$12$	0.126104	+	0.169753i	0.0364031	+	0.0490034i
$13$	2.83853	+	4.63206i	0.787266	+	1.28470i	0.954330	+	0.298756i	$0.0965716\pi$
$13$	2.83853	+	4.63206i	0.787266	+	1.28470i	−0.167063	+	0.985946i	$0.553428\pi$
$14$	−2.82754	−	3.02646i	−0.755691	−	0.808857i
$15$	0.0686683	+	0.0804003i	0.0177301	+	0.0207593i
$16$	−1.89113	−	3.52472i	−0.472782	−	0.881179i
$17$	−0.142473	−	1.81030i	−0.0345549	−	0.439062i	−0.989723	−	0.142998i	$-0.954326\pi$
$17$	−0.142473	−	1.81030i	−0.0345549	−	0.439062i	0.955168	−	0.296064i	$-0.0956741\pi$
$18$	−4.07416	−	1.12575i	−0.960289	−	0.265342i
$19$	−4.93456	−	3.02390i	−1.13207	−	0.693731i	−0.175279	−	0.984519i	$-0.556083\pi$
$19$	−4.93456	−	3.02390i	−1.13207	−	0.693731i	−0.956788	+	0.290788i	$0.906083\pi$
$20$	−1.06302	−	1.69410i	−0.237698	−	0.378813i
$21$	−0.305848	−	0.0484416i	−0.0667415	−	0.0105708i
$22$	−0.837150	+	4.32844i	−0.178481	+	0.922827i
$23$	−0.442177	−	0.321261i	−0.0922003	−	0.0669875i	0.540730	−	0.841196i	$-0.318148\pi$
$23$	−0.442177	−	0.321261i	−0.0922003	−	0.0669875i	−0.632930	+	0.774209i	$0.718148\pi$
$24$	−0.273545	−	0.120869i	−0.0558372	−	0.0246722i
$25$	−0.587785	−	0.809017i	−0.117557	−	0.161803i
$26$	−6.72308	−	3.71842i	−1.31850	−	0.729242i
$27$	−0.585017	+	0.242322i	−0.112587	+	0.0466349i
$28$	5.58958	+	1.75086i	1.05633	+	0.330882i
$29$	0.000106835	−	0.00135747i	1.98388e−5	−	0.000252076i	−0.996907	−	0.0785851i	$-0.974960\pi$
$29$	0.000106835	−	0.00135747i	1.98388e−5	−	0.000252076i	0.996927	+	0.0783331i	$0.0249598\pi$
$30$	−0.140560	−	0.0510103i	−0.0256626	−	0.00931316i
$31$	−1.75563	+	5.40328i	−0.315321	+	0.970457i	0.660302	+	0.751001i	$0.270428\pi$
$31$	−1.75563	+	5.40328i	−0.315321	+	0.970457i	−0.975622	+	0.219457i	$0.929572\pi$
$32$	4.78515	+	3.01701i	0.845903	+	0.533337i
$33$	0.149641	+	0.293687i	0.0260491	+	0.0511243i
$34$	1.43804	+	2.12767i	0.246622	+	0.364893i
$35$	2.84777	+	0.683689i	0.481361	+	0.115565i
$36$	5.79736	−	1.45700i	0.966226	−	0.242834i
$37$	0.464392	+	1.42925i	0.0763455	+	0.234967i	0.981945	−	0.189167i	$-0.0605786\pi$
$37$	0.464392	+	1.42925i	0.0763455	+	0.234967i	−0.905600	+	0.424134i	$0.860579\pi$
$38$	8.17988	+	0.277963i	1.32695	+	0.0450916i
$39$	−0.567336	+	0.0898572i	−0.0908465	+	0.0143887i
$40$	2.48946	+	1.34261i	0.393618	+	0.212285i
$41$	4.00583	+	4.99533i	0.625606	+	0.780139i
$41$	4.00583	+	4.99533i	0.625606	+	0.780139i
$42$	0.410049	−	0.153750i	0.0632719	−	0.0237241i
$43$	0.260780	+	1.64650i	0.0397686	+	0.251089i	0.999561	−	0.0296210i	$-0.00943003\pi$
$43$	0.260780	+	1.64650i	0.0397686	+	0.251089i	−0.959793	+	0.280710i	$0.909430\pi$
$44$	−1.98942	−	5.90887i	−0.299916	−	0.890795i
$45$	2.84254	−	0.923596i	0.423740	−	0.137682i
$46$	0.768067	+	0.0867802i	0.113245	+	0.0127950i
$47$	−1.02283	+	4.26040i	−0.149195	+	0.621442i	0.846790	+	0.531927i	$0.178532\pi$
$47$	−1.02283	+	4.26040i	−0.149195	+	0.621442i	−0.995985	+	0.0895156i	$0.971468\pi$
$48$	0.420831	−	0.0421162i	0.0607418	−	0.00607895i
$49$	−1.40532	+	0.716047i	−0.200760	+	0.102292i
$50$	1.28743	+	0.585257i	0.182070	+	0.0827678i
$51$	0.182604	+	0.0593315i	0.0255696	+	0.00830807i
$52$	10.8646	−	0.115205i	1.50665	−	0.0159760i
$53$	10.7647	+	0.847201i	1.47865	+	0.116372i	0.791956	−	0.610578i	$-0.209063\pi$
$53$	10.7647	+	0.847201i	1.47865	+	0.116372i	0.686690	+	0.726950i	$0.259063\pi$
$54$	0.550666	−	0.706185i	0.0749362	−	0.0960996i
$55$	−1.19297	−	2.88009i	−0.160861	−	0.388352i
$56$	−8.09769	+	1.74506i	−1.08210	+	0.233193i
$57$	0.495054	−	0.359678i	0.0655715	−	0.0476405i
$58$	0.000815468		0.00174450i	0.000107076		0.000229064i
$59$	1.88962	−	2.60083i	0.246007	−	0.338600i	−0.668101	−	0.744071i	$-0.732893\pi$
$59$	1.88962	−	2.60083i	0.246007	−	0.338600i	0.914108	+	0.405471i	$0.132893\pi$
$60$	0.208501	−	0.0352934i	0.0269173	−	0.00455636i
$61$	−0.321828	+	2.03194i	−0.0412058	+	0.260163i	−0.999688	−	0.0249902i	$-0.992045\pi$
$61$	−0.321828	+	2.03194i	−0.0412058	+	0.260163i	0.958482	+	0.285153i	$0.0920445\pi$
$62$	−1.60923	−	7.87183i	−0.204373	−	0.999723i
$63$	−4.57360	+	7.46344i	−0.576220	+	0.940305i
$64$	−7.99127	−	0.373703i	−0.998908	−	0.0467129i
$65$	5.41586	−	0.426237i	0.671755	−	0.0528682i
$66$	−0.388951	−	0.256916i	−0.0478765	−	0.0316242i
$67$	−2.92613	+	2.49915i	−0.357483	+	0.305319i	−0.809993	−	0.586440i	$-0.800529\pi$
$67$	−2.92613	+	2.49915i	−0.357483	+	0.305319i	0.452509	+	0.891760i	$0.350529\pi$
$68$	−3.25325	−	1.61439i	−0.394514	−	0.195774i
$69$	0.0492739	−	0.0301951i	0.00593188	−	0.00363506i
$70$	−3.98028	+	1.14537i	−0.475734	+	0.136898i
$71$	10.5561	+	9.01579i	1.25278	+	1.06998i	0.994589	+	0.103885i	$0.0331273\pi$
$71$	10.5561	+	9.01579i	1.25278	+	1.06998i	0.258194	+	0.966093i	$0.416873\pi$
$72$	−6.11566	+	5.83635i	−0.720738	+	0.687821i
$73$	5.95234	−	5.95234i	0.696669	−	0.696669i	−0.267021	−	0.963691i	$-0.586039\pi$
$73$	5.95234	−	5.95234i	0.696669	−	0.696669i	0.963691	+	0.267021i	$0.0860394\pi$
$74$	−1.56827	−	1.43435i	−0.182308	−	0.166740i
$75$	0.102812	−	0.0246830i	0.0118717	−	0.00285014i
$76$	−10.2569	+	5.36390i	−1.17655	+	0.615281i
$77$	8.13478	+	4.14488i	0.927044	+	0.472352i
$78$	0.635266	−	0.506287i	0.0719297	−	0.0573257i
$79$	−7.65804	−	3.17206i	−0.861597	−	0.356885i	−0.0922648	−	0.995735i	$-0.529411\pi$
$79$	−7.65804	−	3.17206i	−0.861597	−	0.356885i	−0.769332	+	0.638850i	$0.779411\pi$
$80$	−3.99910	+	0.0848200i	−0.447113	+	0.00948317i
$81$			8.89951i			0.988834i
$82$	−8.41251	−	3.35107i	−0.929006	−	0.370064i
$83$		−	3.14409i		−	0.345108i	−0.985000	−	0.172554i	$-0.944798\pi$
$83$		−	3.14409i		−	0.345108i	0.985000	−	0.172554i	$-0.0552020\pi$
$84$	−0.397201	+	0.475174i	−0.0433381	+	0.0518457i
$85$	−1.67767	−	0.694913i	−0.181969	−	0.0753739i
$86$	−1.46933	−	1.84364i	−0.158442	−	0.198805i
$87$	0.000128282	0	6.53627e-5i	1.37532e−5	0	7.00762e-6i
$88$	6.56912	+	5.88146i	0.700271	+	0.626966i
$89$	−1.78044	+	0.427445i	−0.188726	+	0.0453091i	−0.326706	−	0.945126i	$-0.605939\pi$
$89$	−1.78044	+	0.427445i	−0.188726	+	0.0453091i	0.137981	+	0.990435i	$0.455939\pi$
$90$	−2.85268	+	3.11902i	−0.300699	+	0.328774i
$91$	−11.2504	+	11.2504i	−1.17936	+	1.17936i
$92$	−1.00542	+	0.429004i	−0.104822	+	0.0447268i
$93$	−0.456782	−	0.390128i	−0.0473660	−	0.0404544i
$94$	−1.71352	−	5.95467i	−0.176736	−	0.614178i
$95$	−4.93456	+	3.02390i	−0.506275	+	0.310246i
$96$	−0.488335	+	0.345361i	−0.0498405	+	0.0352483i
$97$	−4.19288	+	3.58106i	−0.425723	+	0.363602i	−0.836345	−	0.548204i	$-0.815312\pi$
$97$	−4.19288	+	3.58106i	−0.425723	+	0.363602i	0.410622	+	0.911806i	$0.365312\pi$
$98$	1.22937	−	1.86117i	0.124185	−	0.188007i
$99$	9.28860	−	0.731029i	0.933539	−	0.0734711i
$100$	−1.99206	+	0.178050i	−0.199206	+	0.0178050i
$101$	10.4012	−	16.9731i	1.03495	−	1.68889i	0.399546	−	0.916713i	$-0.369168\pi$
$101$	10.4012	−	16.9731i	1.03495	−	1.68889i	0.635407	−	0.772177i	$-0.280832\pi$
$102$	−0.266028	+	0.0543840i	−0.0263407	+	0.00538482i
$103$	−1.83205	+	11.5671i	−0.180517	+	1.13974i	0.716449	+	0.697639i	$0.245766\pi$
$103$	−1.83205	+	11.5671i	−0.180517	+	1.13974i	−0.896966	+	0.442099i	$0.854234\pi$
$104$	−13.2854	+	7.72029i	−1.30274	+	0.757037i
$105$	−0.182014	+	0.250521i	−0.0177627	+	0.0244483i
$106$	−13.8339	+	6.46665i	−1.34366	+	0.628096i
$107$	−2.99450	+	2.17563i	−0.289489	+	0.210326i	−0.723046	−	0.690800i	$-0.757258\pi$
$107$	−2.99450	+	2.17563i	−0.289489	+	0.210326i	0.433557	+	0.901126i	$0.357258\pi$
$108$	−0.184840	+	1.25287i	−0.0177863	+	0.120558i
$109$	1.71632	+	4.14357i	0.164394	+	0.396882i	0.984513	−	0.175311i	$-0.0560930\pi$
$109$	1.71632	+	4.14357i	0.164394	+	0.396882i	−0.820119	+	0.572193i	$0.806093\pi$
$110$	3.47661	+	2.71098i	0.331482	+	0.258482i
$111$	−0.158407	−	0.0124669i	−0.0150353	−	0.00118330i
$112$	8.74464	−	7.79531i	0.826291	−	0.736588i
$113$	4.65905	+	1.51382i	0.438286	+	0.142408i	0.519845	−	0.854261i	$-0.325990\pi$
$113$	4.65905	+	1.51382i	0.438286	+	0.142408i	−0.0815585	+	0.996669i	$0.525990\pi$
$114$	−0.358131	+	0.787804i	−0.0335420	+	0.0737846i
$115$	−0.486989	+	0.248134i	−0.0454120	+	0.0231386i
$116$	−0.00222007	−	0.00157728i	−0.000206129	−	0.000146447i
$117$	−3.79047	+	15.7885i	−0.350429	+	1.45964i
$118$	−0.510431	+	4.51768i	−0.0469890	+	0.415886i
$119$	5.05790	−	1.64341i	0.463657	−	0.150651i
$120$	−0.231882	+	0.188858i	−0.0211678	+	0.0172403i
$121$	0.200530	+	1.26609i	0.0182300	+	0.115100i
$122$	−1.02146	−	2.72421i	−0.0924782	−	0.246639i
$123$	−0.650054	+	0.189187i	−0.0586134	+	0.0170584i
$124$	7.47067	+	8.56152i	0.670886	+	0.768847i
$125$	−0.987688	+	0.156434i	−0.0883415	+	0.0139919i
$126$	0.420415	−	12.3719i	0.0374535	−	1.10218i
$127$	−4.32430	−	13.3088i	−0.383720	−	1.18097i	−0.937405	−	0.348242i	$-0.886779\pi$
$127$	−4.32430	−	13.3088i	−0.383720	−	1.18097i	0.553685	−	0.832726i	$-0.313221\pi$
$128$	10.0917	−	5.11455i	0.891984	−	0.452066i
$129$	−0.171390	−	0.0411471i	−0.0150901	−	0.00362280i
$130$	−6.36535	+	4.30218i	−0.558278	+	0.377326i
$131$	−4.84749	−	9.51373i	−0.423527	−	0.831219i	−0.999902	−	0.0140329i	$-0.995533\pi$
$131$	−4.84749	−	9.51373i	−0.423527	−	0.831219i	0.576375	−	0.817186i	$-0.304467\pi$
$132$	0.657704	+	0.0447510i	0.0572458	+	0.00389507i
$133$	5.23768	−	16.1199i	0.454164	−	1.39777i
$134$	1.85649	−	5.11560i	0.160376	−	0.441920i
$135$	−0.0496817	+	0.631266i	−0.00427592	+	0.0543308i
$136$	5.12831	−	0.283241i	0.439749	−	0.0242877i
$137$	−17.3617	+	7.19144i	−1.48331	+	0.614406i	−0.969849	−	0.243708i	$-0.921636\pi$
$137$	−17.3617	+	7.19144i	−1.48331	+	0.614406i	−0.513459	+	0.858114i	$0.671636\pi$
$138$	−0.0395550	+	0.0715172i	−0.00336714	+	0.00608795i
$139$	−8.76218	−	12.0601i	−0.743198	−	1.02292i	−0.998428	−	0.0560444i	$-0.982151\pi$
$139$	−8.76218	−	12.0601i	−0.743198	−	1.02292i	0.255230	−	0.966880i	$-0.417849\pi$
$140$	4.09765	−	4.18548i	0.346314	−	0.353737i
$141$	−0.374790	−	0.272301i	−0.0315630	−	0.0229319i
$142$	−19.2753	−	3.72796i	−1.61754	−	0.312844i
$143$	16.7271	+	2.64930i	1.39879	+	0.221546i
$144$	3.45245	−	11.4459i	0.287704	−	0.953828i
$145$	−0.00116101		0.000711469i	−9.64168e−5		5.90843e-5i
$146$	−3.17062	+	11.4747i	−0.262403	+	0.949653i
$147$	−0.0130843	−	0.166252i	−0.00107917	−	0.0137122i
$148$	2.92984	+	0.670617i	0.240831	+	0.0551244i
$149$	−4.82862	−	5.65359i	−0.395576	−	0.463160i	0.526497	−	0.850177i	$-0.323505\pi$
$149$	−4.82862	−	5.65359i	−0.395576	−	0.463160i	−0.922072	+	0.387017i	$0.873505\pi$
$150$	−0.109263	+	0.102082i	−0.00892131	+	0.00833492i
$151$	−5.91416	−	9.65104i	−0.481288	−	0.785390i	0.516182	−	0.856479i	$-0.327353\pi$
$151$	−5.91416	−	9.65104i	−0.481288	−	0.785390i	−0.997470	+	0.0710884i	$0.977353\pi$
$152$	8.87663	−	13.7534i	0.719990	−	1.11555i
$153$	3.52480	−	4.12701i	0.284963	−	0.333649i
$154$	−12.8988	+	0.575299i	−1.03941	+	0.0463589i
$155$	4.01732	+	4.01732i	0.322679	+	0.322679i
$156$	−0.428354	+	1.06597i	−0.0342958	+	0.0853458i
$157$	3.11162	+	12.9608i	0.248335	+	1.03439i	0.947583	+	0.319510i	$0.103518\pi$
$157$	3.11162	+	12.9608i	0.248335	+	1.03439i	−0.699248	+	0.714879i	$0.746482\pi$
$158$	11.6337	−	1.43952i	0.925527	−	0.114522i
$159$	−0.518325	+	1.01727i	−0.0411058	+	0.0806747i
$160$	4.86059	−	2.89391i	0.384263	−	0.228783i
$161$	0.612565	−	1.47886i	0.0482768	−	0.116551i
$162$	−6.20782	−	10.9483i	−0.487733	−	0.860180i
$163$	20.9479			1.64077			0.820383	−	0.571814i	$-0.193760\pi$
$163$	20.9479			1.64077			0.820383	+	0.571814i	$0.193760\pi$
$164$	12.6867	−	1.74559i	0.990667	−	0.136307i
$165$	0.329612			0.0256603
$166$	2.19315	+	3.86790i	0.170221	+	0.300207i
$167$	5.82184	−	14.0552i	0.450507	−	1.08762i	−0.521622	−	0.853177i	$-0.674673\pi$
$167$	5.82184	−	14.0552i	0.450507	−	1.08762i	0.972130	−	0.234444i	$-0.0753271\pi$
$168$	0.157186	−	0.861632i	0.0121272	−	0.0664763i
$169$	−7.49684	+	14.7134i	−0.576680	+	1.13180i
$170$	2.54863	−	0.315360i	0.195471	−	0.0241870i
$171$	−4.03801	−	16.8195i	−0.308795	−	1.28622i
$172$	3.09362	+	1.24315i	0.235886	+	0.0947896i
$173$	−1.38293	−	1.38293i	−0.105142	−	0.105142i	0.652579	−	0.757721i	$-0.273687\pi$
$173$	−1.38293	−	1.38293i	−0.105142	−	0.105142i	−0.757721	+	0.652579i	$0.773687\pi$
$174$	−0.000203407	0	9.07219e-6i	−1.54203e−5	0	6.87761e-7i
$175$	1.90203	−	2.22699i	0.143780	−	0.168345i
$176$	−12.1840	−	2.65320i	−0.918406	−	0.199992i
$177$	0.177604	+	0.289823i	0.0133495	+	0.0217844i
$178$	1.89216	−	1.76779i	0.141823	−	0.132501i
$179$	9.42938	+	11.0404i	0.704785	+	0.825197i	0.991125	−	0.132931i	$-0.0424389\pi$
$179$	9.42938	+	11.0404i	0.704785	+	0.825197i	−0.286341	+	0.958128i	$0.592439\pi$
$180$	1.33374	−	5.82695i	0.0994114	−	0.434315i
$181$	−1.72266	−	21.8885i	−0.128044	−	1.62696i	−0.640302	−	0.768124i	$-0.721191\pi$
$181$	−1.72266	−	21.8885i	−0.128044	−	1.62696i	0.512257	−	0.858832i	$-0.328809\pi$
$182$	5.99271	−	21.6880i	0.444209	−	1.60762i
$183$	−0.185468	−	0.113655i	−0.0137102	−	0.00840161i
$184$	0.937633	−	1.22910i	0.0691232	−	0.0906101i
$185$	1.48430	+	0.235090i	0.109128	+	0.0172842i
$186$	0.834072	+	0.161315i	0.0611571	+	0.0118282i
$187$	−4.57973	−	3.32737i	−0.334903	−	0.243321i
$188$	6.26166	+	6.13026i	0.456679	+	0.447095i
$189$	−1.09005	−	1.50032i	−0.0792893	−	0.109132i
$190$	3.96126	−	7.16214i	0.287380	−	0.519596i
$191$	23.9146	−	9.90577i	1.73040	−	0.716757i	0.730994	−	0.682384i	$-0.239057\pi$
$191$	23.9146	−	9.90577i	1.73040	−	0.716757i	0.999409	−	0.0343729i	$-0.0109434\pi$
$192$	0.359851	−	0.765505i	0.0259700	−	0.0552456i
$193$	0.340275	−	4.32361i	0.0244936	−	0.311220i	−0.972451	−	0.233107i	$-0.925111\pi$
$193$	0.340275	−	4.32361i	0.0244936	−	0.311220i	0.996945	−	0.0781127i	$-0.0248894\pi$
$194$	2.66019	−	7.33021i	0.190991	−	0.526278i
$195$	−0.177502	+	0.546294i	−0.0127112	+	0.0391210i
$196$	−0.214138	+	3.14718i	−0.0152956	+	0.224799i
$197$	−7.29688	−	14.3209i	−0.519881	−	1.02032i	−0.990439	−	0.137955i	$-0.955947\pi$
$197$	−7.29688	−	14.3209i	−0.519881	−	1.02032i	0.470558	−	0.882369i	$-0.344053\pi$
$198$	−10.9170	+	7.37855i	−0.775841	+	0.524371i
$199$	−3.02400	−	0.725998i	−0.214366	−	0.0514646i	0.124840	−	0.992177i	$-0.460158\pi$
$199$	−3.02400	−	0.725998i	−0.214366	−	0.0514646i	−0.339206	+	0.940712i	$0.610158\pi$
$200$	2.32646	−	1.60859i	0.164506	−	0.113745i
$201$	−0.125731	−	0.386960i	−0.00886837	−	0.0272940i
$202$	−0.956095	+	28.1359i	−0.0672706	+	1.97963i
$203$	0.00393880		0.000623845i	0.000276450		4.37854e-5i
$204$	0.289336	−	0.252471i	0.0202576	−	0.0176765i
$205$	6.26948	−	1.30139i	0.437879	−	0.0908933i
$206$	−5.81477	−	15.5079i	−0.405134	−	1.08049i
$207$	−0.255547	−	1.61346i	−0.0177618	−	0.112143i
$208$	10.9587	−	18.7648i	0.759847	−	1.30111i
$209$	−17.1585	+	5.57515i	−1.18688	+	0.385641i
$210$	0.0491663	−	0.435157i	0.00339280	−	0.0300287i
$211$	−3.51809	+	14.6539i	−0.242195	+	1.00882i	0.710212	+	0.703988i	$0.248599\pi$
$211$	−3.51809	+	14.6539i	−0.242195	+	1.00882i	−0.952407	+	0.304828i	$0.901401\pi$
$212$	12.5078	−	17.6051i	0.859042	−	1.20913i
$213$	−1.30783	+	0.666375i	−0.0896113	+	0.0456592i
$214$	2.16627	−	4.76530i	0.148083	−	0.325749i
$215$	1.58544	+	0.515139i	0.108126	+	0.0351322i
$216$	−0.646545	−	1.67024i	−0.0439918	−	0.113645i
$217$	−16.5876	−	1.30547i	−1.12604	−	0.0886213i
$218$	−5.00178	−	3.90027i	−0.338763	−	0.264159i
$219$	0.340608	+	0.822301i	0.0230162	+	0.0555659i
$220$	−6.16802	−	0.909986i	−0.415848	−	0.0613512i
$221$	7.98099	−	5.79853i	0.536859	−	0.390051i
$222$	0.203570	−	0.0951591i	0.0136628	−	0.00638666i
$223$	−12.5130	+	17.2226i	−0.837929	+	1.15331i	0.148466	+	0.988918i	$0.452567\pi$
$223$	−12.5130	+	17.2226i	−0.837929	+	1.15331i	−0.986395	+	0.164393i	$0.947433\pi$
$224$	−5.32019	+	15.6897i	−0.355470	+	1.04831i
$225$	0.467555	−	2.95202i	0.0311703	−	0.196802i
$226$	−6.78759	+	1.38758i	−0.451504	+	0.0923007i
$227$	1.29201	−	2.10836i	0.0857534	−	0.139937i	−0.806888	−	0.590705i	$-0.798850\pi$
$227$	1.29201	−	2.10836i	0.0857534	−	0.139937i	0.892641	+	0.450768i	$0.148850\pi$
$228$	−0.108953	−	1.21898i	−0.00721556	−	0.0807290i
$229$	−12.1508	+	0.956291i	−0.802950	+	0.0631935i	−0.473290	−	0.880906i	$-0.656934\pi$
$229$	−12.1508	+	0.956291i	−0.802950	+	0.0631935i	−0.329659	+	0.944100i	$0.606934\pi$
$230$	0.426017	−	0.644955i	0.0280907	−	0.0425271i
$231$	−0.734044	+	0.626933i	−0.0482966	+	0.0412492i
$232$	0.00383140		0.000391795i	0.000251544		2.57226e-5i
$233$	−16.9308	+	10.3752i	−1.10917	+	0.679702i	−0.951457	−	0.307782i	$-0.900413\pi$
$233$	−16.9308	+	10.3752i	−1.10917	+	0.679702i	−0.157716	+	0.987484i	$0.550413\pi$
$234$	−6.35009	−	22.0672i	−0.415118	−	1.44258i
$235$	3.33168	+	2.84553i	0.217335	+	0.185622i
$236$	−2.52335	−	5.91377i	−0.164256	−	0.384953i
$237$	0.619725	−	0.619725i	0.0402555	−	0.0402555i
$238$	−5.07595	+	5.54987i	−0.329025	+	0.359745i
$239$	−4.88727	+	1.17333i	−0.316131	+	0.0758964i	−0.388406	−	0.921488i	$-0.626974\pi$
$239$	−4.88727	+	1.17333i	−0.316131	+	0.0758964i	0.0722747	+	0.997385i	$0.476974\pi$
$240$	0.153528	−	0.394084i	0.00991017	−	0.0254380i
$241$	−10.1860	−	5.19004i	−0.656140	−	0.334320i	0.0940260	−	0.995570i	$-0.470026\pi$
$241$	−10.1860	−	5.19004i	−0.656140	−	0.334320i	−0.750166	+	0.661250i	$0.770026\pi$
$242$	−1.12985	−	1.41769i	−0.0726298	−	0.0911325i
$243$	−2.62440	−	1.08706i	−0.168355	−	0.0697351i
$244$	3.15687	+	2.63885i	0.202098	+	0.168935i
$245$			1.57723i			0.100765i
$246$	0.667739	−	0.686183i	0.0425735	−	0.0437494i
$247$		−	31.4406i		−	2.00052i
$248$	−15.1626	−	5.32137i	−0.962826	−	0.337907i
$249$	0.307130	+	0.127217i	0.0194636	+	0.00806207i
$250$	1.10595	−	0.881407i	0.0699463	−	0.0557451i
$251$	−1.06373	−	0.541998i	−0.0671421	−	0.0342106i	0.420097	−	0.907479i	$-0.361996\pi$
$251$	−1.06373	−	0.541998i	−0.0671421	−	0.0342106i	−0.487239	+	0.873269i	$0.661996\pi$
$252$	8.11280	+	15.5134i	0.511059	+	0.977252i
$253$	−1.65677	+	0.397755i	−0.104160	+	0.0250066i
$254$	14.6034	+	13.3563i	0.916296	+	0.838051i
$255$	0.135765	−	0.135765i	0.00850193	−	0.00850193i
$256$	−8.84726	+	13.3314i	−0.552954	+	0.833212i
$257$	−18.3450	−	15.6681i	−1.14433	−	0.977349i	−0.144403	−	0.989519i	$-0.546126\pi$
$257$	−18.3450	−	15.6681i	−1.14433	−	0.977349i	−0.999926	+	0.0121697i	$0.996126\pi$
$258$	0.239549	−	0.0689328i	0.0149137	−	0.00429157i
$259$	−3.75268	+	2.29964i	−0.233180	+	0.142893i
$260$	4.82978	−	9.73273i	0.299530	−	0.603598i
$261$	0.00309468	−	0.00264311i	0.000191556	−	0.000163604i
$262$	12.5997	+	8.32258i	0.778414	+	0.514171i
$263$	8.14049	−	0.640671i	0.501964	−	0.0395055i	0.175050	−	0.984559i	$-0.443991\pi$
$263$	8.14049	−	0.640671i	0.501964	−	0.0395055i	0.326914	+	0.945054i	$0.393991\pi$
$264$	−0.840333	+	0.403726i	−0.0517189	+	0.0248476i
$265$	5.64194	−	9.20680i	0.346581	−	0.565569i
$266$	4.80092	+	23.4845i	0.294363	+	1.43993i
$267$	0.0302858	−	0.191217i	0.00185346	−	0.0117023i
$268$	1.28449	+	7.58827i	0.0784624	+	0.463528i
$269$	−0.771746	+	1.06222i	−0.0470542	+	0.0647645i	−0.831896	−	0.554932i	$-0.812744\pi$
$269$	−0.771746	+	1.06222i	−0.0470542	+	0.0647645i	0.784842	+	0.619696i	$0.212744\pi$
$270$	−0.379219	−	0.811248i	−0.0230785	−	0.0493710i
$271$	−6.80078	+	4.94106i	−0.413118	+	0.300148i	−0.774863	−	0.632129i	$-0.782181\pi$
$271$	−6.80078	+	4.94106i	−0.413118	+	0.300148i	0.361745	+	0.932277i	$0.382181\pi$
$272$	−6.11135	+	3.92568i	−0.370555	+	0.238030i
$273$	−0.643774	−	1.55421i	−0.0389630	−	0.0940650i
$274$	16.3422	−	20.9576i	0.987270	−	1.26609i
$275$	−3.10778	−	0.244588i	−0.187406	−	0.0147492i
$276$	−0.00122550	−	0.115573i	−7.37665e−5	−	0.00695668i
$277$	8.80511	+	2.86095i	0.529048	+	0.171898i	0.561347	−	0.827580i	$-0.310283\pi$
$277$	8.80511	+	2.86095i	0.529048	+	0.171898i	−0.0322999	+	0.999478i	$0.510283\pi$
$278$	19.1918	+	8.72449i	1.15105	+	0.523260i
$279$	−15.1297	+	7.70899i	−0.905794	+	0.461525i
$280$	−2.12142	+	8.00734i	−0.126779	+	0.478530i
$281$	1.46629	−	6.10753i	0.0874714	−	0.364345i	−0.911417	−	0.411484i	$-0.865011\pi$
$281$	1.46629	−	6.10753i	0.0874714	−	0.364345i	0.998888	+	0.0471395i	$0.0150105\pi$
$282$	0.651015	+	0.0735551i	0.0387674	+	0.00438014i
$283$	13.3712	−	4.34455i	0.794833	−	0.258257i	0.116672	−	0.993170i	$-0.462777\pi$
$283$	13.3712	−	4.34455i	0.794833	−	0.258257i	0.678161	+	0.734914i	$0.262777\pi$
$284$	26.3131	−	8.85920i	1.56140	−	0.525697i
$285$	−0.0957254	−	0.604387i	−0.00567029	−	0.0358008i
$286$	−22.4259	+	8.40869i	−1.32607	+	0.497216i
$287$	−11.4868	+	14.8229i	−0.678044	+	0.874971i
$288$	3.73682	+	16.4892i	0.220194	+	0.971635i
$289$	13.5338	−	2.14355i	0.796107	−	0.126091i
$290$	0.00192458		6.53997e-5i	0.000113015		3.84040e-6i
$291$	−0.180161	−	0.554480i	−0.0105613	−	0.0325042i
$292$	−4.10359	−	16.3280i	−0.240145	−	0.955524i
$293$	11.8961	+	2.85600i	0.694976	+	0.166849i	0.565518	−	0.824736i	$-0.308676\pi$
$293$	11.8961	+	2.85600i	0.694976	+	0.166849i	0.129458	+	0.991585i	$0.458676\pi$
$294$	0.132065	+	0.195398i	0.00770218	+	0.0113959i
$295$	−1.45949	−	2.86441i	−0.0849749	−	0.166773i
$296$	−4.07211	+	1.21869i	−0.236687	+	0.0708352i
$297$	−0.609996	+	1.87737i	−0.0353956	+	0.108936i
$298$	9.88388	+	3.58694i	0.572558	+	0.207786i
$299$	0.232965	−	2.96010i	0.0134727	−	0.171187i
$300$	0.0632107	−	0.201798i	0.00364947	−	0.0116508i
$301$	−4.51057	+	1.86834i	−0.259985	+	0.107689i
$302$	14.0077	+	7.74745i	0.806055	+	0.445815i
$303$	1.23716	+	1.70281i	0.0710732	+	0.0978239i
$304$	−1.32651	+	23.1115i	−0.0760807	+	1.32554i
$305$	1.66436	+	1.20923i	0.0953012	+	0.0692404i
$306$	−1.45748	+	7.53583i	−0.0833186	+	0.430795i
$307$	21.5974	+	3.42069i	1.23263	+	0.195229i	0.738556	−	0.674192i	$-0.235508\pi$
$307$	21.5974	+	3.42069i	1.23263	+	0.195229i	0.494072	+	0.869421i	$0.335508\pi$
$308$	15.4670	−	9.70523i	0.881312	−	0.553007i
$309$	−1.05580	−	0.646995i	−0.0600624	−	0.0368063i
$310$	−7.74443	−	2.13990i	−0.439854	−	0.121538i
$311$	−2.32195	−	29.5032i	−0.131666	−	1.67297i	−0.608174	−	0.793803i	$-0.708098\pi$
$311$	−2.32195	−	29.5032i	−0.131666	−	1.67297i	0.476509	−	0.879170i	$-0.341902\pi$
$312$	−0.216596	−	1.61017i	−0.0122623	−	0.0911578i
$313$	−0.914786	−	1.07108i	−0.0517068	−	0.0605408i	0.733950	−	0.679204i	$-0.237675\pi$
$313$	−0.914786	−	1.07108i	−0.0517068	−	0.0605408i	−0.785657	+	0.618663i	$0.787675\pi$
$314$	−12.8688	−	13.7741i	−0.726226	−	0.777319i
$315$	4.57360	+	7.46344i	0.257693	+	0.420517i
$316$	−13.3078	+	9.88596i	−0.748623	+	0.556129i
$317$	−6.58374	+	7.70857i	−0.369780	+	0.432957i	−0.913831	−	0.406096i	$-0.866890\pi$
$317$	−6.58374	+	7.70857i	−0.369780	+	0.432957i	0.544051	+	0.839052i	$0.316890\pi$
$318$	−0.0719423	−	1.61302i	−0.00403432	−	0.0904535i
$319$	−0.00300156	−	0.00300156i	−0.000168055	−	0.000168055i
$320$	−3.96093	+	6.95061i	−0.221423	+	0.388551i
$321$	−0.0913617	−	0.380549i	−0.00509931	−	0.0212402i
$322$	0.277989	+	2.24661i	0.0154917	+	0.125199i
$323$	−4.77112	+	9.36385i	−0.265472	+	0.521018i
$324$	15.2739	+	9.13852i	0.848551	+	0.507696i
$325$	2.07897	−	5.01907i	0.115320	−	0.278408i
$326$	−25.7704	+	14.6121i	−1.42729	+	0.809292i
$327$	−0.474211			−0.0262239
$328$	−14.3898	+	10.9970i	−0.794542	+	0.607209i
$329$	−12.8319			−0.707447
$330$	−0.405494	+	0.229920i	−0.0223217	+	0.0126567i
$331$	7.94384	−	19.1781i	0.436633	−	1.05412i	−0.540471	−	0.841363i	$-0.681754\pi$
$331$	7.94384	−	19.1781i	0.436633	−	1.05412i	0.977104	−	0.212762i	$-0.0682460\pi$
$332$	−5.39608	−	3.22853i	−0.296149	−	0.177188i
$333$	−2.03915	+	4.00205i	−0.111745	+	0.219311i
$334$	2.64202	+	21.3519i	0.144565	+	1.16832i
$335$	0.898323	+	3.74179i	0.0490806	+	0.204436i
$336$	0.407655	+	1.16964i	0.0222394	+	0.0638089i
$337$	−11.8563	−	11.8563i	−0.645854	−	0.645854i	0.306135	−	0.951988i	$-0.400964\pi$
$337$	−11.8563	−	11.8563i	−0.645854	−	0.645854i	−0.951988	+	0.306135i	$0.900964\pi$
$338$	−1.04054	−	23.3300i	−0.0565981	−	1.26899i
$339$	−0.336393	+	0.393866i	−0.0182704	+	0.0213919i
$340$	−2.91538	+	2.16575i	−0.158109	+	0.117454i
$341$	9.25395	+	15.1011i	0.501130	+	0.817769i
$342$	16.7000	+	17.8749i	0.903035	+	0.966566i
$343$	10.3143	+	12.0765i	0.556919	+	0.652068i
$344$	−4.67297	+	0.628596i	−0.251950	+	0.0338916i
$345$	−0.00453413	−	0.0576116i	−0.000244109	−	0.00310170i
$346$	2.66595	+	0.736640i	0.143322	+	0.0396020i
$347$	−25.8270	−	15.8268i	−1.38647	−	0.849627i	−0.389032	−	0.921224i	$-0.627190\pi$
$347$	−25.8270	−	15.8268i	−1.38647	−	0.849627i	−0.997434	+	0.0715970i	$0.977190\pi$
$348$	0.000243906	0	0.000153047i	1.30748e−5	0	8.20417e-6i
$349$	31.1198	+	4.92889i	1.66580	+	0.263837i	0.916980	−	0.398933i	$-0.130619\pi$
$349$	31.1198	+	4.92889i	1.66580	+	0.263837i	0.748823	+	0.662770i	$0.230619\pi$
$350$	−0.786476	+	4.06644i	−0.0420389	+	0.217360i
$351$	−2.78304	−	2.02200i	−0.148548	−	0.107926i
$352$	16.8397	−	5.23493i	0.897559	−	0.279023i
$353$	−13.7210	−	18.8853i	−0.730296	−	1.00517i	−0.999119	−	0.0419760i	$-0.986635\pi$
$353$	−13.7210	−	18.8853i	−0.730296	−	1.00517i	0.268823	−	0.963190i	$-0.413365\pi$
$354$	−0.420656	−	0.232658i	−0.0223576	−	0.0123656i
$355$	12.8255	−	5.31250i	0.680708	−	0.281958i
$356$	−1.09465	+	3.49463i	−0.0580161	+	0.185215i
$357$	−0.0441184	+	0.560577i	−0.00233499	+	0.0296689i
$358$	−19.3013	−	7.00461i	−1.02011	−	0.370205i
$359$	6.93399	−	21.3406i	0.365962	−	1.12632i	−0.583414	−	0.812175i	$-0.698284\pi$
$359$	6.93399	−	21.3406i	0.365962	−	1.12632i	0.949376	−	0.314141i	$-0.101716\pi$
$360$	2.42378	+	8.09875i	0.127744	+	0.426841i
$361$	6.58009	+	12.9141i	0.346320	+	0.679692i
$362$	17.3875	+	25.7259i	0.913864	+	1.35212i
$363$	−0.131792	−	0.0316405i	−0.00691730	−	0.00166070i
$364$	7.75609	+	30.8611i	0.406530	+	1.61756i
$365$	−2.60127	−	8.00589i	−0.136157	−	0.419047i
$366$	0.307445	+	0.0104474i	0.0160704	+	0.000546094i
$367$	−2.32057	+	0.367543i	−0.121133	+	0.0191856i	−0.216707	−	0.976237i	$-0.569531\pi$
$367$	−2.32057	+	0.367543i	−0.121133	+	0.0191856i	0.0955736	+	0.995422i	$0.469531\pi$
$368$	−0.296138	+	2.16609i	−0.0154373	+	0.112915i
$369$	−2.09121	+	19.0232i	−0.108864	+	0.990308i
$370$	−1.99000	+	0.746158i	−0.103455	+	0.0387909i
$371$	4.94708	+	31.2346i	0.256840	+	1.62162i
$372$	−1.13861	+	0.383352i	−0.0590343	+	0.0198759i
$373$	−19.0106	+	6.17693i	−0.984334	+	0.319829i	−0.756589	−	0.653891i	$-0.773135\pi$
$373$	−19.0106	+	6.17693i	−0.984334	+	0.319829i	−0.227745	+	0.973721i	$0.573135\pi$
$374$	7.95504	+	0.898802i	0.411345	+	0.0464759i
$375$	0.0246830	−	0.102812i	0.00127462	−	0.00530919i
$376$	−11.9793	−	3.17374i	−0.617787	−	0.163673i
$377$	0.00659113	−	0.00335835i	0.000339461	−	0.000172964i
$378$	2.38754	+	1.08536i	0.122802	+	0.0558249i
$379$	23.8448	+	7.74765i	1.22483	+	0.397970i	0.848837	−	0.528654i	$-0.177303\pi$
$379$	23.8448	+	7.74765i	1.22483	+	0.397970i	0.375989	+	0.926624i	$0.377303\pi$
$380$	0.122729	+	11.5741i	0.00629584	+	0.593740i
$381$	1.47504	+	0.116089i	0.0755688	+	0.00594740i
$382$	−22.5104	+	28.8678i	−1.15173	+	1.47701i
$383$	−7.76336	−	18.7424i	−0.396689	−	0.957692i	−0.988446	−	0.151575i	$-0.951565\pi$
$383$	−7.76336	−	18.7424i	−0.396689	−	0.957692i	0.591757	−	0.806117i	$-0.298435\pi$
$384$	0.0912815	+	1.19275i	0.00465819	+	0.0608672i
$385$	7.38622	−	5.36640i	0.376437	−	0.273497i
$386$	2.59731	+	5.55633i	0.132199	+	0.282810i
$387$	−2.92861	+	4.03088i	−0.148869	+	0.204901i
$388$	1.84056	+	10.8733i	0.0934401	+	0.552010i
$389$	1.90882	−	12.0518i	0.0967810	−	0.611051i	−0.890855	−	0.454288i	$-0.849894\pi$
$389$	1.90882	−	12.0518i	0.0967810	−	0.611051i	0.987636	−	0.156764i	$-0.0501061\pi$
$390$	−0.162700	−	0.795875i	−0.00823866	−	0.0403007i
$391$	−0.518578	+	0.846243i	−0.0262256	+	0.0427964i
$392$	−1.93187	−	4.02108i	−0.0975742	−	0.203095i
$393$	1.12549	−	0.0885779i	0.0567734	−	0.00446816i
$394$	18.9662	+	12.5279i	0.955505	+	0.631147i
$395$	−6.30301	+	5.38327i	−0.317139	+	0.270862i
$396$	8.28342	−	16.6924i	0.416258	−	0.838822i
$397$	−26.2668	+	16.0963i	−1.31830	+	0.807852i	−0.990581	−	0.136925i	$-0.956278\pi$
$397$	−26.2668	+	16.0963i	−1.31830	+	0.807852i	−0.327714	+	0.944777i	$0.606278\pi$
$398$	4.22659	−	1.21625i	0.211860	−	0.0609650i
$399$	1.36274	+	1.16389i	0.0682225	+	0.0582675i
$400$	−1.73998	+	3.60173i	−0.0869989	+	0.180087i
$401$	20.2245	−	20.2245i	1.00996	−	1.00996i	0.0100121	−	0.999950i	$-0.496813\pi$
$401$	20.2245	−	20.2245i	1.00996	−	1.00996i	0.999950	−	0.0100121i	$-0.00318700\pi$
$402$	0.424599	+	0.388341i	0.0211771	+	0.0193687i
$403$	−30.0117	+	7.20517i	−1.49499	+	0.358915i
$404$	−18.4499	−	35.2801i	−0.917917	−	1.75525i
$405$	7.92952	+	4.04029i	0.394021	+	0.200764i
$406$	−0.00441041	+	0.00351496i	−0.000218885	+	0.000174445i
$407$	4.32821	+	1.79280i	0.214542	+	0.0888660i
$408$	−0.179835	+	0.512419i	−0.00890318	+	0.0253685i
$409$		−	3.82069i		−	0.188921i	−0.995529	−	0.0944606i	$-0.969887\pi$
$409$		−	3.82069i		−	0.188921i	0.995529	−	0.0944606i	$-0.0301126\pi$
$410$	−6.80502	+	5.97425i	−0.336076	+	0.295047i
$411$		−	1.98696i		−	0.0980093i
$412$	17.9709	+	15.0220i	0.885364	+	0.740082i
$413$	8.69849	+	3.60303i	0.428025	+	0.177294i
$414$	1.43984	+	1.80665i	0.0707644	+	0.0887919i
$415$	−2.80140	−	1.42739i	−0.137515	−	0.0700676i
$416$	−0.392174	+	30.7290i	−0.0192279	+	1.50661i
$417$	1.53263	−	0.367952i	0.0750532	−	0.0180187i
$418$	17.2198	−	18.8275i	0.842246	−	0.920884i
$419$	−11.3242	+	11.3242i	−0.553225	+	0.553225i	−0.927370	−	0.374145i	$-0.877936\pi$
$419$	−11.3242	+	11.3242i	−0.553225	+	0.553225i	0.374145	+	0.927370i	$0.377936\pi$
$420$	0.243057	+	0.569633i	0.0118600	+	0.0277952i
$421$	−8.85477	−	7.56269i	−0.431555	−	0.368583i	0.406974	−	0.913440i	$-0.366584\pi$
$421$	−8.85477	−	7.56269i	−0.431555	−	0.368583i	−0.838529	+	0.544857i	$0.816584\pi$
$422$	−5.89377	−	20.4815i	−0.286904	−	0.997023i
$423$	−11.1656	+	6.84232i	−0.542892	+	0.332685i
$424$	−3.10692	+	30.3829i	−0.150886	+	1.47552i
$425$	−1.38082	+	1.17933i	−0.0669795	+	0.0572059i
$426$	1.14409	−	1.73206i	0.0554313	−	0.0839186i
$427$	−6.00653	+	0.472724i	−0.290676	+	0.0228767i
$428$	0.659036	+	7.37342i	0.0318557	+	0.356408i
$429$	−0.935614	+	1.52678i	−0.0451719	+	0.0737138i
$430$	−2.30976	+	0.472183i	−0.111387	+	0.0227707i
$431$	−6.01521	+	37.9785i	−0.289742	+	1.82936i	0.227806	+	0.973707i	$0.426845\pi$
$431$	−6.01521	+	37.9785i	−0.289742	+	1.82936i	−0.517548	+	0.855654i	$0.673155\pi$
$432$	1.96046	+	1.60376i	0.0943227	+	0.0771609i
$433$	−13.5265	+	18.6176i	−0.650040	+	0.894703i	−0.999101	−	0.0423969i	$-0.986501\pi$
$433$	−13.5265	+	18.6176i	−0.650040	+	0.894703i	0.349061	+	0.937100i	$0.386501\pi$
$434$	21.3169	−	9.96462i	1.02325	−	0.478317i
$435$	0.000116477	0	8.46256e-5i	5.58465e−6	0	4.05749e-6i
$436$	8.87388	+	1.30919i	0.424982	+	0.0626988i
$437$	1.21049	+	2.92238i	0.0579056	+	0.139796i
$438$	−0.992614	−	0.774016i	−0.0474289	−	0.0369839i
$439$	3.36975	+	0.265205i	0.160829	+	0.0126575i	0.158618	−	0.987340i	$-0.449296\pi$
$439$	3.36975	+	0.265205i	0.160829	+	0.0126575i	0.00221118	+	0.999998i	$0.499296\pi$
$440$	8.22274	−	3.18300i	0.392004	−	0.151744i
$441$	−4.48333	−	1.45672i	−0.213492	−	0.0693678i
$442$	−5.77358	+	12.7005i	−0.274621	+	0.604103i
$443$	−15.1628	+	7.72584i	−0.720407	+	0.367066i	−0.775442	−	0.631419i	$-0.782473\pi$
$443$	−15.1628	+	7.72584i	−0.720407	+	0.367066i	0.0550350	+	0.998484i	$0.482473\pi$
$444$	−0.184057	+	0.259066i	−0.00873498	+	0.0122947i
$445$	−0.427445	+	1.78044i	−0.0202628	+	0.0844008i
$446$	3.38005	−	29.9159i	0.160050	−	1.41656i
$447$	0.747648	−	0.242925i	0.0353625	−	0.0114900i
$448$	−4.39932	−	23.0128i	−0.207848	−	1.08725i
$449$	−2.70189	−	17.0591i	−0.127510	−	0.805067i	−0.965695	−	0.259681i	$-0.916383\pi$
$449$	−2.70189	−	17.0591i	−0.127510	−	0.805067i	0.838184	−	0.545387i	$-0.183617\pi$
$450$	1.48398	+	3.95776i	0.0699556	+	0.186571i
$451$	19.9515	+	0.617695i	0.939478	+	0.0290861i
$452$	7.38229	−	6.44169i	0.347234	−	0.302991i
$453$	1.18206	−	0.187220i	0.0555381	−	0.00879638i
$454$	−0.118764	+	3.49497i	−0.00557386	+	0.164027i
$455$	4.91659	+	15.1317i	0.230493	+	0.709386i
$456$	0.984332	+	1.42361i	0.0460955	+	0.0666666i
$457$	−15.3855	−	3.69372i	−0.719702	−	0.172785i	−0.142980	−	0.989726i	$-0.545668\pi$
$457$	−15.3855	−	3.69372i	−0.719702	−	0.172785i	−0.576722	+	0.816940i	$0.695668\pi$
$458$	14.2811	−	9.65222i	0.667311	−	0.451019i
$459$	0.522025	+	1.02453i	0.0243660	+	0.0478210i
$460$	−0.0742058	+	1.09060i	−0.00345986	+	0.0508495i
$461$	6.72774	−	20.7059i	0.313342	−	0.964368i	−0.663089	−	0.748540i	$-0.730755\pi$
$461$	6.72774	−	20.7059i	0.313342	−	0.964368i	0.976431	−	0.215828i	$-0.0692449\pi$
$462$	0.465717	−	1.28329i	0.0216671	−	0.0597042i
$463$	3.16519	−	40.2176i	0.147099	−	1.86907i	−0.273565	−	0.961854i	$-0.588203\pi$
$463$	3.16519	−	40.2176i	0.147099	−	1.86907i	0.420664	−	0.907217i	$-0.361797\pi$
$464$	−0.00498674	+	0.00219059i	−0.000231503	+	0.000101695i
$465$	−0.554981	+	0.229881i	−0.0257366	+	0.0106605i
$466$	13.5913	−	24.5737i	0.629606	−	1.13836i
$467$	−1.01675	−	1.39943i	−0.0470494	−	0.0647579i	0.784844	−	0.619693i	$-0.212743\pi$
$467$	−1.01675	−	1.39943i	−0.0470494	−	0.0647579i	−0.831893	+	0.554935i	$0.812743\pi$
$468$	23.2049	+	22.7179i	1.07265	+	1.05014i
$469$	−9.11756	−	6.62429i	−0.421010	−	0.305881i
$470$	−6.08358	−	1.17660i	−0.280614	−	0.0542727i
$471$	−1.39198	−	0.220468i	−0.0641392	−	0.0101587i
$472$	7.22939	+	5.51505i	0.332760	+	0.253851i
$473$	4.43097	+	2.71530i	0.203736	+	0.124850i
$474$	−0.330108	+	1.19468i	−0.0151624	+	0.0548736i
$475$	0.454073	+	5.76955i	0.0208343	+	0.264725i
$476$	2.37321	−	10.3683i	0.108776	−	0.475228i
$477$	20.9598	+	24.5408i	0.959684	+	1.12365i
$478$	5.19394	−	4.85255i	0.237565	−	0.221950i
$479$	−17.2208	−	28.1019i	−0.786841	−	1.28401i	−0.954514	−	0.298165i	$-0.903626\pi$
$479$	−17.2208	−	28.1019i	−0.786841	−	1.28401i	0.167674	−	0.985843i	$-0.446374\pi$
$480$	0.0860199	+	0.591900i	0.00392625	+	0.0270164i
$481$	−5.30218	+	6.20806i	−0.241759	+	0.283063i
$482$	16.1513	−	0.720366i	0.735671	−	0.0328118i
$483$	0.119677	+	0.119677i	0.00544548	+	0.00544548i
$484$	2.37887	+	0.955936i	0.108130	+	0.0434517i
$485$	1.28722	+	5.36166i	0.0584496	+	0.243460i
$486$	3.98685	−	0.493322i	0.180847	−	0.0223775i
$487$	−13.7110	+	26.9093i	−0.621304	+	1.21938i	0.339095	+	0.940752i	$0.389879\pi$
$487$	−13.7110	+	26.9093i	−0.621304	+	1.21938i	−0.960400	+	0.278626i	$0.910121\pi$
$488$	−5.72436	−	1.04429i	−0.259129	−	0.0472727i
$489$	−0.847603	+	2.04629i	−0.0383299	+	0.0925366i
$490$	−1.10019	−	1.94033i	−0.0497016	−	0.0876552i
$491$	−10.3665			−0.467836			−0.233918	−	0.972256i	$-0.575155\pi$
$491$	−10.3665			−0.467836			−0.233918	+	0.972256i	$0.575155\pi$
$492$	−0.342818	+	1.30993i	−0.0154554	+	0.0590563i
$493$	−0.00247264			−0.000111362
$494$	21.9313	+	38.6787i	0.986736	+	1.74024i
$495$	3.56558	−	8.60808i	0.160261	−	0.386904i
$496$	22.3652	−	4.03019i	1.00422	−	0.180961i
$497$	−18.4578	+	36.2255i	−0.827945	+	1.62493i
$498$	−0.466576	+	0.0577327i	−0.0209078	+	0.00258707i
$499$	7.52115	+	31.3279i	0.336693	+	1.40243i	0.841995	+	0.539485i	$0.181381\pi$
$499$	7.52115	+	31.3279i	0.336693	+	1.40243i	−0.505302	+	0.862943i	$0.668619\pi$
$500$	−0.745732	+	1.85577i	−0.0333501	+	0.0829926i
$501$	1.13741	+	1.13741i	0.0508158	+	0.0508158i
$502$	1.68669	−	0.0752281i	0.0752805	−	0.00335759i
$503$	−1.49187	+	1.74676i	−0.0665194	+	0.0778842i	−0.792668	−	0.609654i	$-0.791309\pi$
$503$	−1.49187	+	1.74676i	−0.0665194	+	0.0778842i	0.726148	+	0.687538i	$0.241309\pi$
$504$	−20.8018	−	13.4258i	−0.926586	−	0.598031i
$505$	−10.4012	−	16.9731i	−0.462845	−	0.755295i
$506$	1.76073	−	1.64500i	0.0782739	−	0.0731290i
$507$	−1.13393	−	1.32767i	−0.0503598	−	0.0589638i
$508$	−27.2819	−	6.24463i	−1.21044	−	0.277060i
$509$	1.30931	+	16.6364i	0.0580343	+	0.737396i	0.955249	+	0.295802i	$0.0955868\pi$
$509$	1.30931	+	16.6364i	0.0580343	+	0.737396i	−0.897215	+	0.441594i	$0.854413\pi$
$510$	−0.0723177	+	0.261723i	−0.00320228	+	0.0115893i
$511$	21.0205	+	12.8814i	0.929891	+	0.569838i
$512$	1.58477	−	22.5719i	0.0700375	−	0.997544i
$513$	3.61956	+	0.573282i	0.159808	+	0.0253110i
$514$	33.4975	+	6.47864i	1.47751	+	0.285761i
$515$	9.47462	+	6.88371i	0.417501	+	0.303333i
$516$	−0.246613	+	0.251899i	−0.0108565	+	0.0110892i
$517$	8.02839	+	11.0501i	0.353088	+	0.485984i
$518$	3.01249	−	5.44672i	0.132361	−	0.239315i
$519$	0.191047	−	0.0791344i	0.00838605	−	0.00347362i
$520$	0.847372	+	15.3423i	0.0371597	+	0.672806i
$521$	−1.30806	+	16.6204i	−0.0573070	+	0.728155i	0.899405	+	0.437117i	$0.144000\pi$
$521$	−1.30806	+	16.6204i	−0.0573070	+	0.728155i	−0.956712	+	0.291037i	$0.906000\pi$
$522$	−0.00196343	+	0.00541028i	−8.59372e−5	+	0.000236802i
$523$	12.0409	−	37.0580i	0.526511	−	1.62043i	−0.234798	−	0.972044i	$-0.575443\pi$
$523$	12.0409	−	37.0580i	0.526511	−	1.62043i	0.761309	−	0.648389i	$-0.224557\pi$
$524$	−21.3058	−	1.44967i	−0.930746	−	0.0633291i
$525$	0.140583	+	0.275909i	0.00613554	+	0.0120417i
$526$	−9.56766	+	6.46654i	−0.417170	+	0.281954i
$527$	10.0317	+	2.40839i	0.436986	+	0.104911i
$528$	0.752172	−	1.08284i	0.0327341	−	0.0471246i
$529$	−7.01508	−	21.5902i	−0.305003	−	0.938704i
$530$	−0.518618	+	15.2619i	−0.0225273	+	0.662933i
$531$	9.49019	−	1.50310i	0.411839	−	0.0652289i
$532$	−22.2877	−	25.5421i	−0.966294	−	1.10739i
$533$	−11.7680	+	32.7346i	−0.509727	+	1.41789i
$534$	0.0961249	+	0.256364i	0.00415973	+	0.0110940i
$535$	0.579027	+	3.65583i	0.0250335	+	0.158056i
$536$	−6.87337	−	8.43922i	−0.296884	−	0.364519i
$537$	−1.46001	+	0.474387i	−0.0630043	+	0.0204713i
$538$	0.208467	−	1.84508i	0.00898766	−	0.0795472i
$539$	−1.14781	+	4.78099i	−0.0494398	+	0.205932i
$540$	1.03240	+	0.733487i	0.0444276	+	0.0315643i
$541$	25.1773	−	12.8285i	1.08246	−	0.551539i	0.180592	−	0.983558i	$-0.442199\pi$
$541$	25.1773	−	12.8285i	1.08246	−	0.551539i	0.901865	+	0.432019i	$0.142199\pi$
$542$	4.91981	−	10.8224i	0.211324	−	0.464863i
$543$	2.20787	+	0.717382i	0.0947490	+	0.0307858i
$544$	4.77992	−	9.09239i	0.204938	−	0.389833i
$545$	4.47114	+	0.351887i	0.191523	+	0.0150732i
$546$	1.87611	+	1.46295i	0.0802902	+	0.0626084i
$547$	−5.88908	−	14.2175i	−0.251799	−	0.607897i	0.746550	−	0.665329i	$-0.231709\pi$
$547$	−5.88908	−	14.2175i	−0.251799	−	0.607897i	−0.998349	+	0.0574323i	$0.981709\pi$
$548$	−5.48554	+	37.1818i	−0.234331	+	1.58833i
$549$	−4.97449	+	3.61418i	−0.212306	+	0.154249i
$550$	3.99385	−	1.86693i	0.170298	−	0.0796060i
$551$	−0.00463204	+	0.00637546i	−0.000197332	+	0.000271604i
$552$	0.0821252	+	0.141325i	0.00349548	+	0.00601518i
$553$	3.79759	−	23.9770i	0.161490	−	1.01961i
$554$	−12.8278	+	2.62239i	−0.545002	+	0.111415i
$555$	−0.0830232	+	0.135481i	−0.00352414	+	0.00575087i
$556$	−29.6958	+	2.65421i	−1.25938	+	0.112564i
$557$	40.2757	−	3.16977i	1.70654	−	0.134307i	0.812694	−	0.582690i	$-0.198000\pi$
$557$	40.2757	−	3.16977i	1.70654	−	0.134307i	0.893842	+	0.448383i	$0.148000\pi$
$558$	13.2355	−	20.0374i	0.560302	−	0.848252i
$559$	−6.88646	+	5.88159i	−0.291266	+	0.248765i
$560$	−2.97569	−	11.3305i	−0.125746	−	0.478802i
$561$	0.510340	−	0.312737i	0.0215466	−	0.0132038i
$562$	2.45644	+	8.53638i	0.103619	+	0.360085i
$563$	−29.5879	−	25.2704i	−1.24698	−	1.06502i	−0.995263	−	0.0972202i	$-0.969005\pi$
$563$	−29.5879	−	25.2704i	−1.24698	−	1.06502i	−0.251717	−	0.967801i	$-0.580995\pi$
$564$	−0.852196	+	0.363625i	−0.0358839	+	0.0153114i
$565$	3.46398	−	3.46398i	0.145731	−	0.145731i
$566$	−13.4189	+	14.6717i	−0.564037	+	0.616699i
$567$	−25.3438	+	6.08450i	−1.06434	+	0.255525i
$568$	−26.1911	+	29.2534i	−1.09895	+	1.22744i
$569$	−26.7946	−	13.6525i	−1.12329	−	0.572343i	−0.209205	−	0.977872i	$-0.567087\pi$
$569$	−26.7946	−	13.6525i	−1.12329	−	0.572343i	−0.914082	+	0.405529i	$0.867087\pi$
$570$	0.539351	+	0.676752i	0.0225909	+	0.0283460i
$571$	6.14820	+	2.54667i	0.257294	+	0.106575i	0.507602	−	0.861591i	$-0.330532\pi$
$571$	6.14820	+	2.54667i	0.257294	+	0.106575i	−0.250308	+	0.968166i	$0.580532\pi$
$572$	21.7232	−	25.9876i	0.908293	−	1.08660i
$573$			2.73691i			0.114336i
$574$	3.79153	−	26.2480i	0.158255	−	1.09557i
$575$			0.546561i			0.0227932i
$576$	−16.0991	−	17.6787i	−0.670795	−	0.736611i
$577$	−33.2991	−	13.7929i	−1.38626	−	0.574207i	−0.440111	−	0.897943i	$-0.645061\pi$
$577$	−33.2991	−	13.7929i	−1.38626	−	0.574207i	−0.946147	+	0.323736i	$0.895061\pi$
$578$	−15.1543	+	12.0775i	−0.630335	+	0.502358i
$579$	0.408583	+	0.208183i	0.0169801	+	0.00865181i
$580$	−0.00241326	+	0.00126203i	−0.000100205	+	5.24028e-5i
$581$	8.95364	−	2.14958i	0.371459	−	0.0891795i
$582$	0.608413	+	0.556458i	0.0252195	+	0.0230659i
$583$	23.8023	−	23.8023i	0.985791	−	0.985791i
$584$	16.4378	+	17.2245i	0.680203	+	0.712755i
$585$	12.3468	+	10.5451i	0.510476	+	0.435988i
$586$	−16.6269	+	4.78458i	−0.686852	+	0.197649i
$587$	−18.0145	+	11.0393i	−0.743540	+	0.455642i	−0.841985	−	0.539501i	$-0.818613\pi$
$587$	−18.0145	+	11.0393i	−0.743540	+	0.455642i	0.0984455	+	0.995142i	$0.468613\pi$
$588$	−0.298768	−	0.148261i	−0.0123210	−	0.00611417i
$589$	25.0023	−	21.3539i	1.03020	−	0.879874i
$590$	3.79355	+	2.50578i	0.156178	+	0.103161i
$591$	1.69419	−	0.133335i	0.0696896	−	0.00548469i
$592$	4.15948	−	4.33975i	0.170954	−	0.178362i
$593$	−0.0229650	+	0.0374755i	−0.000943060	+	0.00153893i	−0.853111	−	0.521729i	$-0.825287\pi$
$593$	−0.0229650	+	0.0374755i	−0.000943060	+	0.00153893i	0.852168	+	0.523268i	$0.175287\pi$
$594$	−0.559130	−	2.73508i	−0.0229414	−	0.112221i
$595$	0.831949	−	5.25272i	0.0341066	−	0.215340i
$596$	−14.6614	+	2.48176i	−0.600552	+	0.101657i
$597$	0.193277	−	0.266023i	0.00791031	−	0.0108876i
$598$	1.77821	+	3.80406i	0.0727164	+	0.155560i
$599$	24.4330	−	17.7516i	0.998303	−	0.725310i	0.0365797	−	0.999331i	$-0.488354\pi$
$599$	24.4330	−	17.7516i	0.998303	−	0.725310i	0.961724	+	0.274021i	$0.0883537\pi$
$600$	0.0630011	+	0.292348i	0.00257201	+	0.0119351i
$601$	−10.0638	−	24.2961i	−0.410510	−	0.991058i	−0.985001	−	0.172547i	$-0.944800\pi$
$601$	−10.0638	−	24.2961i	−0.410510	−	0.991058i	0.574492	−	0.818510i	$-0.305200\pi$
$602$	4.24571	−	5.44479i	0.173042	−	0.221913i
$603$	−11.4659	−	0.902382i	−0.466926	−	0.0367478i
$604$	−22.6367	+	0.240033i	−0.921076	+	0.00976681i
$605$	1.21914	+	0.396122i	0.0495650	+	0.0161046i
$606$	−2.70977	−	1.23184i	−0.110077	−	0.0500402i
$607$	32.3811	−	16.4990i	1.31431	−	0.669674i	0.350575	−	0.936535i	$-0.385986\pi$
$607$	32.3811	−	16.4990i	1.31431	−	0.669674i	0.963735	+	0.266861i	$0.0859863\pi$
$608$	−14.4895	−	29.3574i	−0.587626	−	1.19060i
$609$	−9.84333e−5	0	0.000410004i	−3.98872e−6	0	1.66142e-5i
$610$	−2.89102	−	0.326643i	−0.117054	−	0.0132254i
$611$	−22.6377	+	7.35544i	−0.915825	+	0.297569i
$612$	−3.46358	−	10.2874i	−0.140007	−	0.415841i
$613$	1.27690	+	8.06204i	0.0515736	+	0.325623i	0.999964	+	0.00851689i	$0.00271104\pi$
$613$	1.27690	+	8.06204i	0.0515736	+	0.325623i	−0.948390	+	0.317106i	$0.897289\pi$
$614$	−28.9555	+	10.8570i	−1.16855	+	0.438153i
$615$	−0.126552	+	0.665091i	−0.00510306	+	0.0268191i
$616$	−12.2578	+	22.7284i	−0.493882	+	0.915755i
$617$	0.647180	−	0.102503i	0.0260545	−	0.00412663i	−0.143394	−	0.989666i	$-0.545801\pi$
$617$	0.647180	−	0.102503i	0.0260545	−	0.00412663i	0.169448	+	0.985539i	$0.445801\pi$
$618$	1.75017	+	0.0594731i	0.0704022	+	0.00239236i
$619$	5.79999	+	17.8505i	0.233121	+	0.717474i	0.997365	+	0.0725464i	$0.0231125\pi$
$619$	5.79999	+	17.8505i	0.233121	+	0.717474i	−0.764244	+	0.644928i	$0.776887\pi$
$620$	11.0200	−	2.76957i	0.442573	−	0.111229i
$621$	0.336530	+	0.0807937i	0.0135045	+	0.00324214i
$622$	23.4364	+	34.6756i	0.939713	+	1.39037i
$623$	−2.43453	−	4.77804i	−0.0975374	−	0.191428i
$624$	1.38963	+	1.82977i	0.0556296	+	0.0732493i
$625$	−0.309017	+	0.951057i	−0.0123607	+	0.0380423i
$626$	1.87251	+	0.679548i	0.0748405	+	0.0271602i
$627$	0.149668	−	1.90171i	0.00597717	−	0.0759472i
$628$	25.4394	+	7.96857i	1.01514	+	0.317981i
$629$	2.52120	−	1.04432i	0.100527	−	0.0416396i
$630$	−10.8326	−	5.99133i	−0.431582	−	0.238700i
$631$	11.7370	+	16.1546i	0.467241	+	0.643103i	0.975991	−	0.217812i	$-0.0698920\pi$
$631$	11.7370	+	16.1546i	0.467241	+	0.643103i	−0.508749	+	0.860915i	$0.669892\pi$
$632$	9.47554	−	21.4447i	0.376917	−	0.853024i
$633$	−1.28911	−	0.936597i	−0.0512377	−	0.0372264i
$634$	2.72233	−	14.0757i	0.108118	−	0.559016i
$635$	−13.8215	−	2.18910i	−0.548488	−	0.0868719i
$636$	1.21366	+	1.93417i	0.0481247	+	0.0766950i
$637$	−7.30582	−	4.47701i	−0.289467	−	0.177386i
$638$	0.00578629	+	0.00159884i	0.000229082	+	6.32985e-5i
$639$	3.25539	+	41.3636i	0.128781	+	1.63632i
$640$	0.0244192	−	11.3137i	0.000965252	−	0.447213i
$641$	5.96781	+	6.98741i	0.235714	+	0.275986i	0.865637	−	0.500672i	$-0.166914\pi$
$641$	5.96781	+	6.98741i	0.235714	+	0.275986i	−0.629923	+	0.776658i	$0.716914\pi$
$642$	0.377845	+	0.404428i	0.0149124	+	0.0159615i
$643$	−7.05747	−	11.5167i	−0.278320	−	0.454176i	0.682683	−	0.730714i	$-0.260813\pi$
$643$	−7.05747	−	11.5167i	−0.278320	−	0.454176i	−0.961003	+	0.276538i	$0.910813\pi$
$644$	−1.90910	−	2.56990i	−0.0752291	−	0.101268i
$645$	−0.114472	+	0.134029i	−0.00450733	+	0.00527740i
$646$	−0.662220	−	14.8476i	−0.0260547	−	0.584172i
$647$	27.7535	+	27.7535i	1.09110	+	1.09110i	0.995411	+	0.0956897i	$0.0305056\pi$
$647$	27.7535	+	27.7535i	1.09110	+	1.09110i	0.0956897	+	0.995411i	$0.469494\pi$
$648$	−25.1647	−	0.588080i	−0.988564	−	0.0231020i
$649$	−2.33954	−	9.74491i	−0.0918352	−	0.382521i
$650$	0.943461	+	7.62472i	0.0370056	+	0.299066i
$651$	0.798699	−	1.56754i	0.0313035	−	0.0614366i
$652$	21.5105	−	35.9522i	0.842417	−	1.40800i
$653$	8.51733	−	20.5626i	0.333309	−	0.804678i	−0.665017	−	0.746829i	$-0.731576\pi$
$653$	8.51733	−	20.5626i	0.333309	−	0.804678i	0.998325	−	0.0578498i	$-0.0184245\pi$
$654$	0.583381	−	0.330784i	0.0228120	−	0.0129347i
$655$	−10.6775			−0.417205
$656$	10.0316	−	23.5662i	0.391667	−	0.920107i
$657$	25.1596			0.981568
$658$	15.7860	−	8.95087i	0.615403	−	0.348941i
$659$	16.5935	−	40.0603i	0.646392	−	1.56053i	−0.171518	−	0.985181i	$-0.554867\pi$
$659$	16.5935	−	40.0603i	0.646392	−	1.56053i	0.817910	−	0.575347i	$-0.195133\pi$
$660$	0.338465	−	0.565702i	0.0131747	−	0.0220199i
$661$	12.2544	−	24.0506i	0.476640	−	0.935458i	−0.520048	−	0.854137i	$-0.674086\pi$
$661$	12.2544	−	24.0506i	0.476640	−	0.935458i	0.996688	−	0.0813213i	$-0.0259140\pi$
$662$	3.60501	+	29.1344i	0.140113	+	1.13234i
$663$	0.243499	+	1.01424i	0.00945670	+	0.0393900i
$664$	8.89039	+	0.207762i	0.345014	+	0.00806271i
$665$	−11.9851	−	11.9851i	−0.464762	−	0.464762i
$666$	−0.283029	−	6.34578i	−0.0109671	−	0.245894i
$667$	−0.000483342	0	0.000565920i	−1.87151e−5	0	2.19125e-5i
$668$	−18.1442	−	24.4245i	−0.702019	−	0.945011i
$669$	−1.17608	−	1.91919i	−0.0454700	−	0.0742003i
$670$	−3.71520	−	3.97658i	−0.143531	−	0.153629i
$671$	4.16511	+	4.87672i	0.160792	+	0.188264i
$672$	−1.31738	−	1.15455i	−0.0508190	−	0.0445376i
$673$	−0.552923	−	7.02556i	−0.0213136	−	0.270815i	−0.998335	−	0.0576757i	$-0.981631\pi$
$673$	−0.552923	−	7.02556i	−0.0213136	−	0.270815i	0.977022	−	0.213140i	$-0.0683689\pi$
$674$	22.8561	+	6.31547i	0.880385	+	0.243263i
$675$	0.539907	+	0.330856i	0.0207810	+	0.0127346i
$676$	17.5539	+	27.9751i	0.675149	+	1.07597i
$677$	−13.1708	−	2.08604i	−0.506193	−	0.0801731i	−0.101885	−	0.994796i	$-0.532488\pi$
$677$	−13.1708	−	2.08604i	−0.506193	−	0.0801731i	−0.404308	+	0.914623i	$0.632488\pi$
$678$	0.139096	−	0.719190i	0.00534196	−	0.0276203i
$679$	−13.0647	−	9.49204i	−0.501376	−	0.364271i
$680$	2.07583	−	4.69795i	0.0796046	−	0.180158i
$681$	0.153677	+	0.211519i	0.00588893	+	0.00810542i
$682$	−21.9181	−	12.1225i	−0.839286	−	0.464195i
$683$	29.9825	−	12.4192i	1.14725	−	0.475206i	0.273639	−	0.961832i	$-0.411773\pi$
$683$	29.9825	−	12.4192i	1.14725	−	0.475206i	0.873610	+	0.486626i	$0.161773\pi$
$684$	−33.0132	−	10.3410i	−1.26229	−	0.395397i
$685$	−1.47441	+	18.7342i	−0.0563345	+	0.715797i
$686$	−21.1127	−	7.66196i	−0.806086	−	0.292535i
$687$	0.398237	−	1.22565i	0.0151937	−	0.0467614i
$688$	5.31028	−	4.03292i	0.202453	−	0.153754i
$689$	26.6317	+	52.2676i	1.01459	+	1.99124i
$690$	0.0457647	+	0.0677119i	0.00174223	+	0.00257775i
$691$	−49.2413	−	11.8218i	−1.87323	−	0.449722i	−0.873891	−	0.486121i	$-0.838411\pi$
$691$	−49.2413	−	11.8218i	−1.87323	−	0.449722i	−0.999337	+	0.0363991i	$0.988411\pi$
$692$	−3.79353	+	0.953399i	−0.144208	+	0.0362428i
$693$	8.43232	+	25.9520i	0.320317	+	0.985835i
$694$	42.8127	+	1.45483i	1.62515	+	0.0552247i
$695$	−14.7236	+	2.33199i	−0.558497	+	0.0884573i
$696$	−0.000193300	0	0.000358417i	−7.32702e−6	0	1.35857e-5i
$697$	8.47230	−	7.96345i	0.320911	−	0.301637i
$698$	−41.7221	+	15.6439i	−1.57921	+	0.592130i
$699$	−0.328440	−	2.07369i	−0.0124227	−	0.0784341i
$700$	−1.86900	−	5.55120i	−0.0706414	−	0.209815i
$701$	36.1373	−	11.7417i	1.36489	−	0.443479i	0.467216	−	0.884143i	$-0.345257\pi$
$701$	36.1373	−	11.7417i	1.36489	−	0.443479i	0.897672	+	0.440664i	$0.145257\pi$
$702$	4.83417	+	0.546190i	0.182454	+	0.0206146i
$703$	2.03035	−	8.45700i	0.0765759	−	0.318962i
$704$	−17.0648	+	18.1866i	−0.643155	+	0.685432i
$705$	−0.412773	+	0.210318i	−0.0155459	+	0.00792105i
$706$	30.0532	+	13.6620i	1.13107	+	0.514176i
$707$	55.4468	+	18.0157i	2.08529	+	0.677552i
$708$	0.679787	−	0.00720825i	0.0255479	−	0.000270903i
$709$	−17.3717	−	1.36719i	−0.652409	−	0.0513457i	−0.252065	−	0.967710i	$-0.581110\pi$
$709$	−17.3717	−	1.36719i	−0.652409	−	0.0513457i	−0.400345	+	0.916365i	$0.631110\pi$
$710$	−12.0724	+	15.4819i	−0.453070	+	0.581026i
$711$	−9.48073	−	22.8885i	−0.355555	−	0.858386i
$712$	−1.09102	−	5.06271i	−0.0408875	−	0.189733i
$713$	2.51216	−	1.82519i	0.0940811	−	0.0683539i
$714$	−0.336754	−	0.720405i	−0.0126027	−	0.0269605i
$715$	9.95447	−	13.7012i	0.372276	−	0.512394i
$716$	28.6308	−	4.84641i	1.06998	−	0.181119i
$717$	0.0831341	−	0.524888i	0.00310470	−	0.0196023i
$718$	6.35579	+	31.0903i	0.237196	+	1.16028i
$719$	0.976901	−	1.59416i	0.0364323	−	0.0594521i	−0.833906	−	0.551907i	$-0.813900\pi$
$719$	0.976901	−	1.59416i	0.0364323	−	0.0594521i	0.870338	+	0.492455i	$0.163900\pi$
$720$	−8.63102	−	8.27250i	−0.321659	−	0.308298i
$721$	−34.1930	+	2.69104i	−1.27341	+	0.100220i
$722$	−17.1031	−	11.2973i	−0.636513	−	0.420440i
$723$	0.919140	−	0.785020i	0.0341832	−	0.0291952i
$724$	−39.3353	−	19.5198i	−1.46188	−	0.725447i
$725$	−0.00116101		0.000711469i	−4.31189e−5		2.64233e-5i
$726$	0.184204	−	0.0530066i	0.00683644	−	0.00196726i
$727$	−4.46537	−	3.81378i	−0.165611	−	0.141445i	0.562780	−	0.826607i	$-0.309732\pi$
$727$	−4.46537	−	3.81378i	−0.165611	−	0.141445i	−0.728391	+	0.685161i	$0.759732\pi$
$728$	−31.0687	−	32.5556i	−1.15148	−	1.20659i
$729$	−18.6663	+	18.6663i	−0.691346	+	0.691346i
$730$	8.78460	+	8.03445i	0.325133	+	0.297368i
$731$	2.94350	−	0.706673i	0.108869	−	0.0261372i
$732$	−0.385511	+	0.201605i	−0.0142489	+	0.00745152i
$733$	−43.7750	−	22.3045i	−1.61687	−	0.823835i	−0.999304	−	0.0373154i	$-0.988119\pi$
$733$	−43.7750	−	22.3045i	−1.61687	−	0.823835i	−0.617565	−	0.786520i	$-0.711881\pi$
$734$	2.59842	−	2.07086i	0.0959096	−	0.0764370i
$735$	−0.154072	−	0.0638185i	−0.00568301	−	0.00235398i
$736$	−1.14664	−	2.87133i	−0.0422656	−	0.105839i
$737$			11.9961i			0.441881i
$738$	−10.6969	−	24.8613i	−0.393759	−	0.915158i
$739$			39.7778i			1.46325i	0.681707	+	0.731626i	$0.261238\pi$
$739$			39.7778i			1.46325i	−0.681707	+	0.731626i	$0.738762\pi$
$740$	1.92764	−	2.30605i	0.0708615	−	0.0847721i
$741$	3.07127	+	1.27216i	0.112826	+	0.0467341i
$742$	−27.8736	−	34.9745i	−1.02327	−	1.28395i
$743$	−18.1856	−	9.26604i	−0.667166	−	0.339938i	0.0873896	−	0.996174i	$-0.472147\pi$
$743$	−18.1856	−	9.26604i	−0.667166	−	0.339938i	−0.754556	+	0.656236i	$0.772147\pi$
$744$	1.13333	−	1.26584i	0.0415500	−	0.0464080i
$745$	−7.22953	+	1.73566i	−0.264869	+	0.0635895i
$746$	19.0785	−	20.8598i	0.698513	−	0.763730i
$747$	6.64476	−	6.64476i	0.243119	−	0.243119i
$748$	−10.4134	+	4.44329i	−0.380750	+	0.162463i
$749$	−8.24301	−	7.04019i	−0.301193	−	0.257243i
$750$	0.0413508	+	0.143698i	0.00150992	+	0.00524712i
$751$	45.9681	−	28.1693i	1.67740	−	1.02791i	0.744608	−	0.667502i	$-0.232637\pi$
$751$	45.9681	−	28.1693i	1.67740	−	1.02791i	0.932794	−	0.360411i	$-0.117363\pi$
$752$	16.9510	−	4.45177i	0.618139	−	0.162339i
$753$	0.0959862	−	0.0819799i	0.00349793	−	0.00298752i
$754$	−0.00576590	+	0.00872912i	−0.000209982	+	0.000317896i
$755$	−11.2841	+	0.888079i	−0.410671	+	0.0323205i
$756$	−3.69427	+	0.330194i	−0.134359	+	0.0120090i
$757$	2.59681	−	4.23760i	0.0943825	−	0.154018i	−0.801964	−	0.597372i	$-0.796212\pi$
$757$	2.59681	−	4.23760i	0.0943825	−	0.154018i	0.896347	+	0.443354i	$0.146212\pi$
$758$	−34.7386	+	7.10160i	−1.26176	+	0.257942i
$759$	0.0281822	−	0.177935i	0.00102295	−	0.00645864i
$760$	−8.22448	−	14.1531i	−0.298333	−	0.513385i
$761$	−26.3789	+	36.3075i	−0.956235	+	1.31614i	−0.00753293	+	0.999972i	$0.502398\pi$
$761$	−26.3789	+	36.3075i	−0.956235	+	1.31614i	−0.948702	+	0.316172i	$0.897602\pi$
$762$	−1.89560	+	0.886099i	−0.0686703	+	0.0321000i
$763$	−10.6265	+	7.72061i	−0.384705	+	0.279505i
$764$	7.55600	−	51.2157i	0.273367	−	1.85292i
$765$	−2.07697	−	5.01425i	−0.0750930	−	0.181291i
$766$	22.6243	+	17.6419i	0.817449	+	0.637427i
$767$	17.4109	+	1.37027i	0.628673	+	0.0494776i
$768$	−0.944294	−	1.40366i	−0.0340743	−	0.0506504i
$769$	−16.0418	−	5.21229i	−0.578481	−	0.187960i	0.00513884	−	0.999987i	$-0.498364\pi$
$769$	−16.0418	−	5.21229i	−0.578481	−	0.187960i	−0.583620	+	0.812027i	$0.698364\pi$
$770$	−5.34332	+	11.7541i	−0.192560	+	0.423587i
$771$	2.27282	−	1.15806i	0.0818536	−	0.0417065i
$772$	−7.07104	−	5.02373i	−0.254492	−	0.180808i
$773$	−1.67868	+	6.99220i	−0.0603779	+	0.251492i	−0.994394	−	0.105739i	$-0.966279\pi$
$773$	−1.67868	+	6.99220i	−0.0603779	+	0.251492i	0.934016	+	0.357231i	$0.116279\pi$
$774$	0.791087	−	7.00169i	0.0284350	−	0.251670i
$775$	5.40328	−	1.75563i	0.194091	−	0.0630641i
$776$	−9.84894	−	12.0927i	−0.353556	−	0.434101i
$777$	−0.0727981	−	0.459629i	−0.00261162	−	0.0164891i
$778$	6.05845	+	16.1578i	0.217206	+	0.579286i
$779$	−4.66165	−	36.7630i	−0.167021	−	1.31717i
$780$	0.755317	+	0.865606i	0.0270447	+	0.0309937i
$781$	42.7436	−	6.76992i	1.52948	−	0.242247i
$782$	0.0476688	−	1.40279i	0.00170463	−	0.0501638i
$783$	0.000266445	0	0.000820032i	9.52195e−6	0	2.93056e-5i
$784$	5.18151	+	3.59922i	0.185054	+	0.128544i
$785$	12.9608	+	3.11162i	0.462593	+	0.111059i
$786$	−1.32281	+	0.894051i	−0.0471829	+	0.0318897i
$787$	8.56536	+	16.8105i	0.305322	+	0.599228i	0.991782	−	0.127939i	$-0.0408363\pi$
$787$	8.56536	+	16.8105i	0.305322	+	0.599228i	−0.686460	+	0.727168i	$0.740836\pi$
$788$	−32.0714	−	2.18217i	−1.14249	−	0.0777367i
$789$	−0.266800	+	0.821127i	−0.00949834	+	0.0292329i
$790$	3.99896	−	11.0192i	0.142277	−	0.392046i
$791$	−1.12566	+	14.3029i	−0.0400239	+	0.508552i
$792$	1.45331	+	26.3133i	0.0516410	+	0.935001i
$793$	−10.3256	+	4.27699i	−0.366672	+	0.151881i
$794$	21.0859	−	38.1243i	0.748311	−	1.35298i
$795$	0.671079	+	0.923662i	0.0238007	+	0.0327589i
$796$	−4.35122	+	4.44449i	−0.154225	+	0.157531i
$797$	−28.4730	−	20.6868i	−1.00856	−	0.732765i	−0.0446567	−	0.999002i	$-0.514219\pi$
$797$	−28.4730	−	20.6868i	−1.00856	−	0.732765i	−0.963907	+	0.266238i	$0.914219\pi$
$798$	−2.48834	−	0.481261i	−0.0880861	−	0.0170365i
$799$	7.85831	+	1.24463i	0.278007	+	0.0440320i
$800$	−0.371829	−	5.64462i	−0.0131461	−	0.199567i
$801$	−4.66617	−	2.85943i	−0.164871	−	0.101033i
$802$	−10.7729	+	38.9880i	−0.380405	+	1.37671i
$803$	−2.05891	−	26.1609i	−0.0726574	−	0.923200i
$804$	−0.793233	−	0.181565i	−0.0279752	−	0.00640330i
$805$	−1.03958	−	1.21719i	−0.0366403	−	0.0429002i
$806$	31.8949	−	29.7985i	1.12345	−	1.04961i
$807$	−0.0725359	−	0.118368i	−0.00255338	−	0.00416674i
$808$	47.3069	+	30.5325i	1.66425	+	1.07413i
$809$	−6.78451	+	7.94364i	−0.238531	+	0.279283i	−0.866739	−	0.498761i	$-0.833788\pi$
$809$	−6.78451	+	7.94364i	−0.238531	+	0.279283i	0.628209	+	0.778045i	$0.283788\pi$
$810$	−12.5733	+	0.560783i	−0.441781	+	0.0197039i
$811$	29.2530	+	29.2530i	1.02721	+	1.02721i	0.999619	+	0.0275918i	$0.00878386\pi$
$811$	29.2530	+	29.2530i	1.02721	+	1.02721i	0.0275918	+	0.999619i	$0.491216\pi$
$812$	0.00297391	−	0.00740063i	0.000104364	−	0.000259711i
$813$	−0.207491	−	0.864261i	−0.00727702	−	0.0303110i
$814$	−6.57520	+	0.813596i	−0.230460	+	0.0285165i
$815$	9.51015	−	18.6647i	0.333126	−	0.653797i
$816$	−0.136200	−	0.755829i	−0.00476796	−	0.0264593i
$817$	3.69203	−	8.91334i	0.129168	−	0.311838i
$818$	2.66511	+	4.70027i	0.0931835	+	0.164341i
$819$	−47.5534			−1.66165
$820$	4.20432	−	12.0964i	0.146821	−	0.422426i
$821$	29.1075			1.01586			0.507930	−	0.861398i	$-0.330411\pi$
$821$	29.1075			1.01586			0.507930	+	0.861398i	$0.330411\pi$
$822$	1.38599	+	2.44438i	0.0483421	+	0.0852576i
$823$	−12.9245	+	31.2025i	−0.450520	+	1.08765i	0.521604	+	0.853188i	$0.325334\pi$
$823$	−12.9245	+	31.2025i	−0.450520	+	1.08765i	−0.972125	+	0.234465i	$0.924666\pi$
$824$	−32.5867	−	5.94475i	−1.13521	−	0.207095i
$825$	0.149641	−	0.293687i	0.00520983	−	0.0102249i
$826$	−13.2143	+	1.63510i	−0.459784	+	0.0568924i
$827$	−5.32449	−	22.1781i	−0.185151	−	0.771208i	−0.985219	−	0.171299i	$-0.945204\pi$
$827$	−5.32449	−	22.1781i	−0.185151	−	0.771208i	0.800068	−	0.599909i	$-0.204796\pi$
$828$	−3.03154	−	1.21821i	−0.105353	−	0.0423356i
$829$	29.1225	+	29.1225i	1.01147	+	1.01147i	0.999933	+	0.0115340i	$0.00367147\pi$
$829$	29.1225	+	29.1225i	1.01147	+	1.01147i	0.0115340	+	0.999933i	$0.496329\pi$
$830$	4.44199	−	0.198118i	0.154184	−	0.00687677i
$831$	−0.635748	+	0.744365i	−0.0220538	+	0.0258217i
$832$	−20.9524	−	38.0768i	−0.726395	−	1.32007i
$833$	1.49648	+	2.44203i	0.0518499	+	0.0846114i
$834$	−1.62880	+	1.52174i	−0.0564007	+	0.0526936i
$835$	−9.88018	−	11.5682i	−0.341918	−	0.400334i
$836$	−8.05094	+	35.1735i	−0.278448	+	1.21650i
$837$	−0.282259	−	3.58644i	−0.00975630	−	0.123965i
$838$	6.03205	−	21.8304i	0.208374	−	0.754119i
$839$	−4.55402	−	2.79071i	−0.157222	−	0.0963459i	0.441662	−	0.897182i	$-0.354389\pi$
$839$	−4.55402	−	2.79071i	−0.157222	−	0.0963459i	−0.598884	+	0.800836i	$0.704389\pi$
$840$	−0.696358	−	0.531227i	−0.0240266	−	0.0183291i
$841$	28.6430	+	4.53660i	0.987688	+	0.156434i
$842$	16.1686	+	3.12712i	0.557207	+	0.107768i
$843$	0.537284	+	0.390360i	0.0185050	+	0.0134447i
$844$	21.5374	+	21.0854i	0.741348	+	0.725791i
$845$	9.70622	+	13.3595i	0.333904	+	0.459580i
$846$	8.96331	−	16.2061i	0.308165	−	0.557177i
$847$	−3.46845	+	1.43668i	−0.119177	+	0.0493648i
$848$	−17.3713	−	39.5447i	−0.596533	−	1.35797i
$849$	−0.116632	+	1.48195i	−0.00400281	+	0.0508605i
$850$	0.876065	−	2.41401i	0.0300488	−	0.0828000i
$851$	0.253818	−	0.781173i	0.00870078	−	0.0267783i
$852$	−0.199283	+	2.92886i	−0.00682733	+	0.100341i
$853$	22.3006	+	43.7673i	0.763556	+	1.49856i	0.863929	+	0.503614i	$0.167997\pi$
$853$	22.3006	+	43.7673i	0.763556	+	1.49856i	−0.100372	+	0.994950i	$0.532003\pi$
$854$	7.05957	−	4.77139i	0.241574	−	0.163273i
$855$	−16.8195	−	4.03801i	−0.575216	−	0.138097i
$856$	−5.95406	−	8.61118i	−0.203506	−	0.294324i
$857$	10.7043	+	32.9444i	0.365652	+	1.12536i	0.949572	+	0.313549i	$0.101518\pi$
$857$	10.7043	+	32.9444i	0.365652	+	1.12536i	−0.583920	+	0.811811i	$0.698482\pi$
$858$	0.0860035	−	2.53091i	0.00293611	−	0.0864037i
$859$	44.1255	−	6.98880i	1.50554	−	0.238455i	0.651497	−	0.758651i	$-0.274141\pi$
$859$	44.1255	−	6.98880i	1.50554	−	0.238455i	0.854046	+	0.520197i	$0.174141\pi$
$860$	2.51213	−	2.19205i	0.0856630	−	0.0747484i
$861$	−0.983195	−	1.72186i	−0.0335072	−	0.0586808i
$862$	−19.0918	−	50.9176i	−0.650269	−	1.73426i
$863$	7.79035	+	49.1863i	0.265187	+	1.67432i	0.656701	+	0.754151i	$0.271951\pi$
$863$	7.79035	+	49.1863i	0.265187	+	1.67432i	−0.391515	+	0.920172i	$0.628049\pi$
$864$	−3.53048	−	0.605455i	−0.120110	−	0.0205980i
$865$	−1.86003	+	0.604361i	−0.0632429	+	0.0205489i
$866$	3.65382	−	32.3389i	0.124162	−	1.09892i
$867$	−0.338219	+	1.40878i	−0.0114865	+	0.0478448i
$868$	−19.2736	+	27.1282i	−0.654190	+	0.920790i
$869$	−23.0237	+	11.7311i	−0.781024	+	0.397952i
$870$	−8.42616e−5	0	0.000185356i	−2.85674e−6	0	6.28416e-6i
$871$	−19.8821	−	6.46008i	−0.673679	−	0.218892i
$872$	−11.8300	+	4.57936i	−0.400614	+	0.155077i
$873$	−16.4296	−	1.29304i	−0.556057	−	0.0437626i
$874$	−3.52766	−	2.75078i	−0.119325	−	0.0930466i
$875$	−1.12076	−	2.70576i	−0.0378887	−	0.0914713i
$876$	1.76104	+	0.259812i	0.0595001	+	0.00877822i
$877$	38.3258	−	27.8453i	1.29417	−	0.940270i	0.294290	−	0.955716i	$-0.404917\pi$
$877$	38.3258	−	27.8453i	1.29417	−	0.940270i	0.999881	+	0.0154462i	$0.00491687\pi$
$878$	−4.33050	+	2.02430i	−0.146147	+	0.0683167i
$879$	−0.760332	+	1.04651i	−0.0256454	+	0.0352978i
$880$	−7.89545	+	9.65152i	−0.266155	+	0.325353i
$881$	7.95901	−	50.2512i	0.268146	−	1.69301i	−0.374810	−	0.927102i	$-0.622292\pi$
$881$	7.95901	−	50.2512i	0.268146	−	1.69301i	0.642955	−	0.765904i	$-0.277708\pi$
$882$	6.53160	−	1.33525i	0.219930	−	0.0449603i
$883$	−4.53920	+	7.40730i	−0.152756	+	0.249276i	−0.919859	−	0.392248i	$-0.871697\pi$
$883$	−4.53920	+	7.40730i	−0.152756	+	0.249276i	0.767103	+	0.641524i	$0.221697\pi$
$884$	−1.75647	−	19.6517i	−0.0590766	−	0.660960i
$885$	0.338865	−	0.0266692i	0.0113908	−	0.000896476i
$886$	13.2644	−	20.0812i	0.445626	−	0.674642i
$887$	−1.77977	+	1.52007i	−0.0597589	+	0.0510389i	−0.678826	−	0.734299i	$-0.737511\pi$
$887$	−1.77977	+	1.52007i	−0.0597589	+	0.0510389i	0.619067	+	0.785338i	$0.287511\pi$
$888$	0.0457195	−	0.447095i	0.00153425	−	0.0150035i
$889$	34.9440	−	21.4137i	1.17199	−	0.718194i
$890$	−0.716089	−	2.48848i	−0.0240033	−	0.0834141i
$891$	21.0961	+	18.0178i	0.706747	+	0.603619i
$892$	16.7095	+	39.1607i	0.559476	+	1.31120i
$893$	17.9302	−	17.9302i	0.600013	−	0.600013i
$894$	−0.750315	+	0.820370i	−0.0250943	+	0.0274373i
$895$	14.1179	−	3.38941i	0.471909	−	0.113295i
$896$	21.4646	+	25.2419i	0.717082	+	0.843274i
$897$	0.279731	+	0.142530i	0.00933993	+	0.00475893i
$898$	15.2234	+	19.1016i	0.508012	+	0.637430i
$899$	0.00714722	+	0.00296048i	0.000238373	+	9.87374e-5i
$900$	−4.58634	−	3.83375i	−0.152878	−	0.127792i
$901$		−	19.6080i		−	0.653238i
$902$	−24.9755	+	13.1572i	−0.831592	+	0.438087i
$903$		−	0.516212i		−	0.0171785i
$904$	−4.58842	+	13.0741i	−0.152609	+	0.434840i
$905$	−20.2848	−	8.40225i	−0.674290	−	0.279300i
$906$	−1.32360	+	1.05486i	−0.0439735	+	0.0350455i
$907$	−26.3073	−	13.4043i	−0.873521	−	0.445081i	−0.0410547	−	0.999157i	$-0.513072\pi$
$907$	−26.3073	−	13.4043i	−0.873521	−	0.445081i	−0.832466	+	0.554076i	$0.813072\pi$
$908$	−2.29180	−	4.38241i	−0.0760561	−	0.145435i
$909$	57.8532	−	13.8893i	1.91887	−	0.460680i
$910$	−16.6035	−	15.1857i	−0.550402	−	0.503401i
$911$	−28.3301	+	28.3301i	−0.938620	+	0.938620i	−0.998222	−	0.0596026i	$-0.981017\pi$
$911$	−28.3301	+	28.3301i	−0.938620	+	0.938620i	0.0596026	+	0.998222i	$0.481017\pi$
$912$	−2.20397	−	1.06473i	−0.0729809	−	0.0352567i
$913$	−7.45300	−	6.36546i	−0.246658	−	0.210666i
$914$	21.5040	−	6.18801i	0.711288	−	0.204681i
$915$	−0.185468	+	0.113655i	−0.00613138	+	0.00375731i
$916$	−10.8359	+	21.8360i	−0.358029	+	0.721483i
$917$	23.7787	−	20.3090i	0.785243	−	0.670661i
$918$	−1.35686	−	0.896256i	−0.0447831	−	0.0295809i
$919$	−50.4342	+	3.96926i	−1.66367	+	0.130934i	−0.875078	−	0.483983i	$-0.839190\pi$
$919$	−50.4342	+	3.96926i	−1.66367	+	0.130934i	−0.788592	+	0.614916i	$0.789190\pi$
$920$	−0.669456	−	1.39343i	−0.0220713	−	0.0459402i
$921$	−1.20803	+	1.97133i	−0.0398060	+	0.0649576i
$922$	6.16674	+	30.1656i	0.203091	+	0.993450i
$923$	−11.7978	+	74.4882i	−0.388329	+	2.45181i
$924$	0.322225	+	1.90359i	0.0106004	+	0.0626234i
$925$	0.883325	−	1.21579i	0.0290436	−	0.0399750i
$926$	24.1598	+	51.6842i	0.793940	+	1.69845i
$927$	−28.3179	+	20.5742i	−0.930083	+	0.675745i
$928$	0.00460672	−	0.00617337i	0.000151223	−	0.000202651i
$929$	12.0375	+	29.0612i	0.394939	+	0.953467i	0.988847	+	0.148934i	$0.0475843\pi$
$929$	12.0375	+	29.0612i	0.394939	+	0.953467i	−0.593908	+	0.804533i	$0.702416\pi$
$930$	0.522394	−	0.669928i	0.0171300	−	0.0219678i
$931$	9.09990	+	0.716178i	0.298237	+	0.0234718i
$932$	0.421089	+	39.7116i	0.0137932	+	1.30080i
$933$	2.97597	+	0.966951i	0.0974289	+	0.0316566i
$934$	2.22698	+	1.01237i	0.0728692	+	0.0331259i
$935$	−5.04386	+	2.56997i	−0.164952	+	0.0840471i
$936$	−44.3938	−	11.7615i	−1.45106	−	0.384435i
$937$	−9.16232	+	38.1638i	−0.299320	+	1.24676i	0.596599	+	0.802540i	$0.296518\pi$
$937$	−9.16232	+	38.1638i	−0.299320	+	1.24676i	−0.895919	+	0.444218i	$0.853482\pi$
$938$	15.8373	+	1.78938i	0.517107	+	0.0584254i
$939$	0.141642	−	0.0460224i	0.00462233	−	0.00150189i
$940$	8.30484	−	2.79610i	0.270874	−	0.0911988i
$941$	0.775714	+	4.89766i	0.0252875	+	0.159659i	0.997101	−	0.0760930i	$-0.0242446\pi$
$941$	0.775714	+	4.89766i	0.0252875	+	0.159659i	−0.971813	+	0.235752i	$0.924245\pi$
$942$	1.86623	−	0.699750i	0.0608049	−	0.0227991i
$943$	−0.166487	−	3.49574i	−0.00542157	−	0.113837i
$944$	−12.7407	−	1.74185i	−0.414675	−	0.0566924i
$945$	−1.83167	+	0.290108i	−0.0595842	+	0.00943721i
$946$	−7.34510	−	0.249596i	−0.238810	−	0.00811508i
$947$	−4.06949	−	12.5246i	−0.132241	−	0.406995i	0.862910	−	0.505358i	$-0.168639\pi$
$947$	−4.06949	−	12.5246i	−0.132241	−	0.406995i	−0.995151	+	0.0983628i	$0.968639\pi$
$948$	−0.427243	−	1.69998i	−0.0138762	−	0.0552129i
$949$	44.4675	+	10.6757i	1.44348	+	0.346548i
$950$	−4.58314	−	6.78105i	−0.148697	−	0.220006i
$951$	−0.486617	−	0.955040i	−0.0157796	−	0.0309693i
$952$	4.31278	+	14.4106i	0.139778	+	0.467050i
$953$	−0.247067	+	0.760395i	−0.00800330	+	0.0246316i	−0.954978	−	0.296675i	$-0.904122\pi$
$953$	−0.247067	+	0.760395i	−0.00800330	+	0.0246316i	0.946975	+	0.321307i	$0.104122\pi$
$954$	−42.9034	−	15.5700i	−1.38905	−	0.504097i
$955$	2.03092	−	25.8052i	0.0657189	−	0.835038i
$956$	−3.00478	+	9.59269i	−0.0971817	+	0.310250i
$957$	0.000414658	0	0.000171757i	1.34040e−5	0	5.55211e-6i
$958$	40.7877	+	22.5590i	1.31779	+	0.728848i
$959$	−32.3496	−	44.5253i	−1.04462	−	1.43780i
$960$	−0.518701	−	0.668162i	−0.0167410	−	0.0215648i
$961$	−1.03364	−	0.750983i	−0.0333432	−	0.0242253i
$962$	2.19241	−	11.3358i	0.0706862	−	0.365480i
$963$	−10.9266	−	1.73061i	−0.352106	−	0.0557681i
$964$	−19.3671	+	12.1525i	−0.623772	+	0.391405i
$965$	−3.69788	−	2.26607i	−0.119039	−	0.0729472i
$966$	−0.230708	−	0.0637479i	−0.00742291	−	0.00205106i
$967$	4.00828	+	50.9300i	0.128898	+	1.63780i	0.632998	+	0.774154i	$0.281824\pi$
$967$	4.00828	+	50.9300i	0.128898	+	1.63780i	−0.504100	+	0.863645i	$0.668176\pi$
$968$	−3.59333	+	0.483365i	−0.115494	+	0.0155359i
$969$	−0.721656	−	0.844950i	−0.0231829	−	0.0271437i
$970$	−5.32356	−	5.69809i	−0.170929	−	0.182955i
$971$	7.37561	+	12.0359i	0.236694	+	0.386250i	0.948828	−	0.315794i	$-0.102271\pi$
$971$	7.37561	+	12.0359i	0.236694	+	0.386250i	−0.712133	+	0.702044i	$0.752271\pi$
$972$	−4.56057	+	3.38791i	−0.146280	+	0.108667i
$973$	28.3538	−	33.1980i	0.908981	−	1.06428i
$974$	−1.90305	−	42.6683i	−0.0609778	−	1.36718i
$975$	0.406168	+	0.406168i	0.0130078	+	0.0130078i
$976$	7.77063	−	2.70831i	0.248732	−	0.0866908i
$977$	8.28039	+	34.4903i	0.264913	+	1.10344i	0.933148	+	0.359492i	$0.117050\pi$
$977$	8.28039	+	34.4903i	0.264913	+	1.10344i	−0.668235	+	0.743950i	$0.732950\pi$
$978$	−0.384652	−	3.10862i	−0.0122998	−	0.0994029i
$979$	−2.59139	+	5.08589i	−0.0828212	+	0.162546i
$980$	2.70694	+	1.61959i	0.0864701	+	0.0517359i
$981$	−5.12978	+	12.3844i	−0.163781	+	0.395403i
$982$	12.7531	−	7.23115i	0.406967	−	0.230755i
$983$	15.9148			0.507603			0.253802	−	0.967256i	$-0.418319\pi$
$983$	15.9148			0.507603			0.253802	+	0.967256i	$0.418319\pi$
$984$	−0.491999	−	1.85063i	−0.0156844	−	0.0589959i
$985$	−16.0728			−0.512120
$986$	0.00304188	−	0.00172479i	9.68733e−5	−	5.49283e-5i
$987$	0.519211	−	1.25349i	0.0165267	−	0.0398989i
$988$	−53.9604	−	32.2850i	−1.71671	−	1.02712i
$989$	0.413645	−	0.811824i	0.0131531	−	0.0258145i
$990$	1.61810	+	13.0770i	0.0514267	+	0.415613i
$991$	13.4420	+	55.9898i	0.426998	+	1.77857i	0.606783	+	0.794868i	$0.292460\pi$
$991$	13.4420	+	55.9898i	0.426998	+	1.77857i	−0.179785	+	0.983706i	$0.557540\pi$
$992$	−24.7027	+	20.5587i	−0.784311	+	0.652741i
$993$	1.55199	+	1.55199i	0.0492508	+	0.0492508i
$994$	−2.56190	−	57.4403i	−0.0812585	−	1.82190i
$995$	−2.01974	+	2.36481i	−0.0640299	+	0.0749694i
$996$	0.533717	−	0.396482i	0.0169115	−	0.0125630i
$997$	−21.8390	−	35.6381i	−0.691649	−	1.12867i	−0.984982	−	0.172659i	$-0.944764\pi$
$997$	−21.8390	−	35.6381i	−0.691649	−	1.12867i	0.293332	−	0.956011i	$-0.405236\pi$
$998$	−31.1053	−	33.2936i	−0.984620	−	1.05389i
$999$	−0.618016	−	0.723604i	−0.0195532	−	0.0228938i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bw.b.11.7	yes	672
4.3	odd	2	inner	820.2.bw.b.11.3	✓	672
41.15	odd	40	inner	820.2.bw.b.671.3	yes	672
164.15	even	40	inner	820.2.bw.b.671.7	yes	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bw.b.11.3	✓	672	4.3	odd	2	inner
820.2.bw.b.11.7	yes	672	1.1	even	1	trivial
820.2.bw.b.671.3	yes	672	41.15	odd	40	inner
820.2.bw.b.671.7	yes	672	164.15	even	40	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.bw (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23021 + 0.697547i) q^{2} +(-0.0404624 + 0.0976849i) q^{3} +(1.02686 - 1.71626i) q^{4} +(0.453990 - 0.891007i) q^{5} +(-0.0183623 - 0.148398i) q^{6} +(0.683689 + 2.84777i) q^{7} +(-0.0660801 + 2.82766i) q^{8} +(2.11342 + 2.11342i) q^{9} +(0.0630128 + 1.41281i) q^{10} +(2.02458 - 2.37048i) q^{11} +(0.126104 + 0.169753i) q^{12} +(2.83853 + 4.63206i) q^{13} +(-2.82754 - 3.02646i) q^{14} +(0.0686683 + 0.0804003i) q^{15} +(-1.89113 - 3.52472i) q^{16} +(-0.142473 - 1.81030i) q^{17} +(-4.07416 - 1.12575i) q^{18} +(-4.93456 - 3.02390i) q^{19} +(-1.06302 - 1.69410i) q^{20} +(-0.305848 - 0.0484416i) q^{21} +(-0.837150 + 4.32844i) q^{22} +(-0.442177 - 0.321261i) q^{23} +(-0.273545 - 0.120869i) q^{24} +(-0.587785 - 0.809017i) q^{25} +(-6.72308 - 3.71842i) q^{26} +(-0.585017 + 0.242322i) q^{27} +(5.58958 + 1.75086i) q^{28} +(0.000106835 - 0.00135747i) q^{29} +(-0.140560 - 0.0510103i) q^{30} +(-1.75563 + 5.40328i) q^{31} +(4.78515 + 3.01701i) q^{32} +(0.149641 + 0.293687i) q^{33} +(1.43804 + 2.12767i) q^{34} +(2.84777 + 0.683689i) q^{35} +(5.79736 - 1.45700i) q^{36} +(0.464392 + 1.42925i) q^{37} +(8.17988 + 0.277963i) q^{38} +(-0.567336 + 0.0898572i) q^{39} +(2.48946 + 1.34261i) q^{40} +(4.00583 + 4.99533i) q^{41} +(0.410049 - 0.153750i) q^{42} +(0.260780 + 1.64650i) q^{43} +(-1.98942 - 5.90887i) q^{44} +(2.84254 - 0.923596i) q^{45} +(0.768067 + 0.0867802i) q^{46} +(-1.02283 + 4.26040i) q^{47} +(0.420831 - 0.0421162i) q^{48} +(-1.40532 + 0.716047i) q^{49} +(1.28743 + 0.585257i) q^{50} +(0.182604 + 0.0593315i) q^{51} +(10.8646 - 0.115205i) q^{52} +(10.7647 + 0.847201i) q^{53} +(0.550666 - 0.706185i) q^{54} +(-1.19297 - 2.88009i) q^{55} +(-8.09769 + 1.74506i) q^{56} +(0.495054 - 0.359678i) q^{57} +(0.000815468 + 0.00174450i) q^{58} +(1.88962 - 2.60083i) q^{59} +(0.208501 - 0.0352934i) q^{60} +(-0.321828 + 2.03194i) q^{61} +(-1.60923 - 7.87183i) q^{62} +(-4.57360 + 7.46344i) q^{63} +(-7.99127 - 0.373703i) q^{64} +(5.41586 - 0.426237i) q^{65} +(-0.388951 - 0.256916i) q^{66} +(-2.92613 + 2.49915i) q^{67} +(-3.25325 - 1.61439i) q^{68} +(0.0492739 - 0.0301951i) q^{69} +(-3.98028 + 1.14537i) q^{70} +(10.5561 + 9.01579i) q^{71} +(-6.11566 + 5.83635i) q^{72} +(5.95234 - 5.95234i) q^{73} +(-1.56827 - 1.43435i) q^{74} +(0.102812 - 0.0246830i) q^{75} +(-10.2569 + 5.36390i) q^{76} +(8.13478 + 4.14488i) q^{77} +(0.635266 - 0.506287i) q^{78} +(-7.65804 - 3.17206i) q^{79} +(-3.99910 + 0.0848200i) q^{80} +8.89951i q^{81} +(-8.41251 - 3.35107i) q^{82} -3.14409i q^{83} +(-0.397201 + 0.475174i) q^{84} +(-1.67767 - 0.694913i) q^{85} +(-1.46933 - 1.84364i) q^{86} +(0.000128282 + 6.53627e-5i) q^{87} +(6.56912 + 5.88146i) q^{88} +(-1.78044 + 0.427445i) q^{89} +(-2.85268 + 3.11902i) q^{90} +(-11.2504 + 11.2504i) q^{91} +(-1.00542 + 0.429004i) q^{92} +(-0.456782 - 0.390128i) q^{93} +(-1.71352 - 5.95467i) q^{94} +(-4.93456 + 3.02390i) q^{95} +(-0.488335 + 0.345361i) q^{96} +(-4.19288 + 3.58106i) q^{97} +(1.22937 - 1.86117i) q^{98} +(9.28860 - 0.731029i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q + 12 q^{6} + 16 q^{9} - 124 q^{12} - 24 q^{14} - 32 q^{16} - 8 q^{17} + 40 q^{21} - 4 q^{22} - 24 q^{24} - 28 q^{28} - 12 q^{30} - 20 q^{32} + 40 q^{33} - 4 q^{34} - 60 q^{36} + 80 q^{37} - 172 q^{38}+ \cdots - 116 q^{98}+O(q^{100}) \) 672 * q + 12 * q^6 + 16 * q^9 - 124 * q^12 - 24 * q^14 - 32 * q^16 - 8 * q^17 + 40 * q^21 - 4 * q^22 - 24 * q^24 - 28 * q^28 - 12 * q^30 - 20 * q^32 + 40 * q^33 - 4 * q^34 - 60 * q^36 + 80 * q^37 - 172 * q^38 + 160 * q^42 - 24 * q^44 - 16 * q^46 + 40 * q^48 - 24 * q^52 - 64 * q^54 + 68 * q^56 - 112 * q^58 + 36 * q^62 - 120 * q^64 + 8 * q^65 + 144 * q^68 - 104 * q^69 + 24 * q^70 - 320 * q^72 - 92 * q^74 - 24 * q^76 + 160 * q^77 - 128 * q^78 - 192 * q^82 - 172 * q^84 - 32 * q^85 - 112 * q^88 + 8 * q^89 - 48 * q^90 + 24 * q^92 + 92 * q^94 + 56 * q^96 - 116 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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