LMFDB - Embedded newform 21.22.c.b.20.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,22,Mod(20,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 22, names="a")

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

chi := DirichletCharacter("21.20");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 22 $
Character orbit:	$[\chi]$	$=$	21.c (of order $2$, degree $1$, 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:	$58.6902423003$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			20.7
Character	$\chi$	$=$	21.20
Dual form			21.22.c.b.20.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-367.125i q^{2} +(-91325.3 - 46043.9i) q^{3} +1.96237e6 q^{4} -3.23352e7 q^{5} +(-1.69039e7 + 3.35278e7i) q^{6} +(-4.79207e8 - 5.73504e8i) q^{7} -1.49035e9i q^{8} +(6.22027e9 + 8.40995e9i) q^{9} +O(q^{10})$	\(q-367.125i q^{2} +(-91325.3 - 46043.9i) q^{3} +1.96237e6 q^{4} -3.23352e7 q^{5} +(-1.69039e7 + 3.35278e7i) q^{6} +(-4.79207e8 - 5.73504e8i) q^{7} -1.49035e9i q^{8} +(6.22027e9 + 8.40995e9i) q^{9} +1.18711e10i q^{10} -1.31196e11i q^{11} +(-1.79214e11 - 9.03553e10i) q^{12} -6.69122e11i q^{13} +(-2.10547e11 + 1.75929e11i) q^{14} +(2.95302e12 + 1.48884e12i) q^{15} +3.56825e12 q^{16} -9.54655e12 q^{17} +(3.08750e12 - 2.28361e12i) q^{18} -1.11389e13i q^{19} -6.34537e13 q^{20} +(1.73574e13 + 7.44400e13i) q^{21} -4.81652e13 q^{22} -2.12594e14i q^{23} +(-6.86216e13 + 1.36107e14i) q^{24} +5.68730e14 q^{25} -2.45651e14 q^{26} +(-1.80841e14 - 1.05445e15i) q^{27} +(-9.40382e14 - 1.12543e15i) q^{28} -1.26875e15i q^{29} +(5.46590e14 - 1.08413e15i) q^{30} -5.66433e15i q^{31} -4.43548e15i q^{32} +(-6.04077e15 + 1.19815e16i) q^{33} +3.50477e15i q^{34} +(1.54953e16 + 1.85444e16i) q^{35} +(1.22065e16 + 1.65034e16i) q^{36} -4.08103e16 q^{37} -4.08938e15 q^{38} +(-3.08090e16 + 6.11077e16i) q^{39} +4.81909e16i q^{40} +2.27791e16 q^{41} +(2.73288e16 - 6.37231e15i) q^{42} +1.15256e17 q^{43} -2.57455e17i q^{44} +(-2.01134e17 - 2.71938e17i) q^{45} -7.80486e16 q^{46} +1.81071e17 q^{47} +(-3.25871e17 - 1.64296e17i) q^{48} +(-9.92673e16 + 5.49654e17i) q^{49} -2.08795e17i q^{50} +(8.71841e17 + 4.39560e17i) q^{51} -1.31307e18i q^{52} +7.35468e17i q^{53} +(-3.87113e17 + 6.63911e16i) q^{54} +4.24225e18i q^{55} +(-8.54722e17 + 7.14187e17i) q^{56} +(-5.12881e17 + 1.01727e18i) q^{57} -4.65790e17 q^{58} -2.94154e18 q^{59} +(5.79493e18 + 2.92166e18i) q^{60} +1.08357e18i q^{61} -2.07951e18 q^{62} +(1.84234e18 - 7.59745e18i) q^{63} +5.85478e18 q^{64} +2.16362e19i q^{65} +(4.39870e18 + 2.21772e18i) q^{66} -6.78306e18 q^{67} -1.87339e19 q^{68} +(-9.78867e18 + 1.94152e19i) q^{69} +(6.80810e18 - 5.68869e18i) q^{70} +2.06767e19i q^{71} +(1.25338e19 - 9.27038e18i) q^{72} +4.03443e19i q^{73} +1.49825e19i q^{74} +(-5.19394e19 - 2.61866e19i) q^{75} -2.18587e19i q^{76} +(-7.52413e19 + 6.28700e19i) q^{77} +(2.24342e19 + 1.13107e19i) q^{78} +9.41640e19 q^{79} -1.15380e20 q^{80} +(-3.20355e19 + 1.04624e20i) q^{81} -8.36275e18i q^{82} -2.74031e19 q^{83} +(3.40616e19 + 1.46079e20i) q^{84} +3.08690e20 q^{85} -4.23135e19i q^{86} +(-5.84183e19 + 1.15869e20i) q^{87} -1.95528e20 q^{88} +4.43565e20 q^{89} +(-9.98350e19 + 7.38412e19i) q^{90} +(-3.83744e20 + 3.20648e20i) q^{91} -4.17189e20i q^{92} +(-2.60808e20 + 5.17296e20i) q^{93} -6.64757e19i q^{94} +3.60180e20i q^{95} +(-2.04227e20 + 4.05072e20i) q^{96} -8.62831e20i q^{97} +(2.01792e20 + 3.64435e19i) q^{98} +(1.10335e21 - 8.16073e20i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 58720260 q^{4} + 1422287188 q^{7} + 10150644696 q^{9}+O(q^{10}) $ 52 * q - 58720260 * q^4 + 1422287188 * q^7 + 10150644696 * q^9	$ 52 q - 58720260 q^{4} + 1422287188 q^{7} + 10150644696 q^{9} - 687153165468 q^{15} + 36241782390404 q^{16} + 36759093002772 q^{18} + 79412641656180 q^{21} + 228880341648112 q^{22} + 45\!\cdots\!12 q^{25}+ \cdots + 15\!\cdots\!28 q^{99}+O(q^{100}) $ 52 * q - 58720260 * q^4 + 1422287188 * q^7 + 10150644696 * q^9 - 687153165468 * q^15 + 36241782390404 * q^16 + 36759093002772 * q^18 + 79412641656180 * q^21 + 228880341648112 * q^22 + 4502168959229812 * q^25 - 328465100861772 * q^28 - 2422487119598196 * q^30 + 94669723666911312 * q^36 - 111253244635261912 * q^37 - 198389110134084780 * q^39 - 125754675449474820 * q^42 + 808208758088766656 * q^43 - 1124214920076830456 * q^46 + 760563680048831596 * q^49 + 4341973540932052200 * q^51 - 13080454499124088812 * q^57 - 10814528487339424568 * q^58 + 13643758017961015644 * q^60 - 38182310822257441896 * q^63 - 30480555033993680900 * q^64 - 25547251957658589040 * q^67 + 73727169165159410040 * q^70 + 39846964674222889428 * q^72 + 45848199464273536260 * q^78 + 199210197493083963080 * q^79 + 235499606962845306588 * q^81 - 373919224753720758924 * q^84 - 570842672309470848672 * q^85 - 1060053674241923431168 * q^88 - 923077800435233893128 * q^91 - 2832166256981601869904 * q^93 + 1525182290356701596928 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$		−	367.125i		−	0.253512i	−0.991934	−	0.126756i	$-0.959543\pi$
$2$		−	367.125i		−	0.253512i	0.991934	−	0.126756i	$-0.0404565\pi$
$3$	−91325.3	−	46043.9i	−0.892931	−	0.450193i
$3$	−91325.3	−	46043.9i	−0.892931	−	0.450193i
$4$	1.96237e6			0.935732
$5$	−3.23352e7			−1.48078			−0.740391	−	0.672177i	$-0.765359\pi$
$5$	−3.23352e7			−1.48078			−0.740391	+	0.672177i	$0.765359\pi$
$6$	−1.69039e7	+	3.35278e7i	−0.114129	+	0.226369i
$7$	−4.79207e8	−	5.73504e8i	−0.641200	−	0.767374i
$7$	−4.79207e8	−	5.73504e8i	−0.641200	−	0.767374i
$8$		−	1.49035e9i		−	0.490731i
$9$	6.22027e9	+	8.40995e9i	0.594652	+	0.803983i
$10$			1.18711e10i			0.375396i
$11$		−	1.31196e11i		−	1.52510i	−0.646932	−	0.762548i	$-0.723948\pi$
$11$		−	1.31196e11i		−	1.52510i	0.646932	−	0.762548i	$-0.276052\pi$
$12$	−1.79214e11	−	9.03553e10i	−0.835544	−	0.421260i
$13$		−	6.69122e11i		−	1.34617i	−0.739565	−	0.673085i	$-0.764969\pi$
$13$		−	6.69122e11i		−	1.34617i	0.739565	−	0.673085i	$-0.235031\pi$
$14$	−2.10547e11	+	1.75929e11i	−0.194538	+	0.162552i
$15$	2.95302e12	+	1.48884e12i	1.32224	+	0.666638i
$16$	3.56825e12			0.811325
$17$	−9.54655e12			−1.14850			−0.574252	−	0.818679i	$-0.694707\pi$
$17$	−9.54655e12			−1.14850			−0.574252	+	0.818679i	$0.694707\pi$
$18$	3.08750e12	−	2.28361e12i	0.203819	−	0.150751i
$19$		−	1.11389e13i		−	0.416803i	−0.978043	−	0.208402i	$-0.933174\pi$
$19$		−	1.11389e13i		−	0.416803i	0.978043	−	0.208402i	$-0.0668261\pi$
$20$	−6.34537e13			−1.38561
$21$	1.73574e13	+	7.44400e13i	0.227081	+	0.973876i
$22$	−4.81652e13			−0.386630
$23$		−	2.12594e14i		−	1.07006i	−0.844832	−	0.535031i	$-0.820300\pi$
$23$		−	2.12594e14i		−	1.07006i	0.844832	−	0.535031i	$-0.179700\pi$
$24$	−6.86216e13	+	1.36107e14i	−0.220924	+	0.438189i
$25$	5.68730e14			1.19271
$26$	−2.45651e14			−0.341270
$27$	−1.80841e14	−	1.05445e15i	−0.169035	−	0.985610i
$28$	−9.40382e14	−	1.12543e15i	−0.599991	−	0.718056i
$29$		−	1.26875e15i		−	0.560012i	−0.959998	−	0.280006i	$-0.909663\pi$
$29$		−	1.26875e15i		−	0.560012i	0.959998	−	0.280006i	$-0.0903365\pi$
$30$	5.46590e14	−	1.08413e15i	0.169001	−	0.335203i
$31$		−	5.66433e15i		−	1.24123i	−0.784117	−	0.620613i	$-0.786884\pi$
$31$		−	5.66433e15i		−	1.24123i	0.784117	−	0.620613i	$-0.213116\pi$
$32$		−	4.43548e15i		−	0.696412i
$33$	−6.04077e15	+	1.19815e16i	−0.686588	+	1.36180i
$34$			3.50477e15i			0.291160i
$35$	1.54953e16	+	1.85444e16i	0.949477	+	1.13631i
$36$	1.22065e16	+	1.65034e16i	0.556435	+	0.752313i
$37$	−4.08103e16			−1.39525			−0.697624	−	0.716464i	$-0.745759\pi$
$37$	−4.08103e16			−1.39525			−0.697624	+	0.716464i	$0.745759\pi$
$38$	−4.08938e15			−0.105665
$39$	−3.08090e16	+	6.11077e16i	−0.606037	+	1.20204i
$40$			4.81909e16i			0.726666i
$41$	2.27791e16			0.265036			0.132518	−	0.991181i	$-0.457694\pi$
$41$	2.27791e16			0.265036			0.132518	+	0.991181i	$0.457694\pi$
$42$	2.73288e16	−	6.37231e15i	0.246889	−	0.0575678i
$43$	1.15256e17			0.813292			0.406646	−	0.913586i	$-0.366698\pi$
$43$	1.15256e17			0.813292			0.406646	+	0.913586i	$0.366698\pi$
$44$		−	2.57455e17i		−	1.42708i
$45$	−2.01134e17	−	2.71938e17i	−0.880549	−	1.19052i
$46$	−7.80486e16			−0.271274
$47$	1.81071e17			0.502136			0.251068	−	0.967969i	$-0.419218\pi$
$47$	1.81071e17			0.502136			0.251068	+	0.967969i	$0.419218\pi$
$48$	−3.25871e17	−	1.64296e17i	−0.724458	−	0.365253i
$49$	−9.92673e16	+	5.49654e17i	−0.177725	+	0.984080i
$50$		−	2.08795e17i		−	0.302367i
$51$	8.71841e17	+	4.39560e17i	1.02554	+	0.517049i
$52$		−	1.31307e18i		−	1.25965i
$53$			7.35468e17i			0.577653i	0.957381	+	0.288826i	$0.0932650\pi$
$53$			7.35468e17i			0.577653i	−0.957381	+	0.288826i	$0.906735\pi$
$54$	−3.87113e17	+	6.63911e16i	−0.249864	+	0.0428524i
$55$			4.24225e18i			2.25833i
$56$	−8.54722e17	+	7.14187e17i	−0.376574	+	0.314657i
$57$	−5.12881e17	+	1.01727e18i	−0.187642	+	0.372177i
$58$	−4.65790e17			−0.141970
$59$	−2.94154e18			−0.749254			−0.374627	−	0.927176i	$-0.622229\pi$
$59$	−2.94154e18			−0.749254			−0.374627	+	0.927176i	$0.622229\pi$
$60$	5.79493e18	+	2.92166e18i	1.23726	+	0.623794i
$61$			1.08357e18i			0.194488i	0.995261	+	0.0972441i	$0.0310028\pi$
$61$			1.08357e18i			0.194488i	−0.995261	+	0.0972441i	$0.968997\pi$
$62$	−2.07951e18			−0.314666
$63$	1.84234e18	−	7.59745e18i	0.235665	−	0.971834i
$64$	5.85478e18			0.634776
$65$			2.16362e19i			1.99338i
$66$	4.39870e18	+	2.21772e18i	0.345234	+	0.174058i
$67$	−6.78306e18			−0.454611			−0.227306	−	0.973823i	$-0.572992\pi$
$67$	−6.78306e18			−0.454611			−0.227306	+	0.973823i	$0.572992\pi$
$68$	−1.87339e19			−1.07469
$69$	−9.78867e18	+	1.94152e19i	−0.481735	+	0.955492i
$70$	6.80810e18	−	5.68869e18i	0.288069	−	0.240704i
$71$			2.06767e19i			0.753822i	0.926250	+	0.376911i	$0.123014\pi$
$71$			2.06767e19i			0.753822i	−0.926250	+	0.376911i	$0.876986\pi$
$72$	1.25338e19	−	9.27038e18i	0.394540	−	0.291814i
$73$			4.03443e19i			1.09873i	0.835582	+	0.549366i	$0.185131\pi$
$73$			4.03443e19i			1.09873i	−0.835582	+	0.549366i	$0.814869\pi$
$74$			1.49825e19i			0.353712i
$75$	−5.19394e19	−	2.61866e19i	−1.06501	−	0.536952i
$76$		−	2.18587e19i		−	0.390016i
$77$	−7.52413e19	+	6.28700e19i	−1.17032	+	0.977891i
$78$	2.24342e19	+	1.13107e19i	0.304731	+	0.153638i
$79$	9.41640e19			1.11892			0.559462	−	0.828856i	$-0.311008\pi$
$79$	9.41640e19			1.11892			0.559462	+	0.828856i	$0.311008\pi$
$80$	−1.15380e20			−1.20140
$81$	−3.20355e19	+	1.04624e20i	−0.292778	+	0.956180i
$82$		−	8.36275e18i		−	0.0671899i
$83$	−2.74031e19			−0.193856			−0.0969281	−	0.995291i	$-0.530902\pi$
$83$	−2.74031e19			−0.193856			−0.0969281	+	0.995291i	$0.530902\pi$
$84$	3.40616e19	+	1.46079e20i	0.212487	+	0.911286i
$85$	3.08690e20			1.70068
$86$		−	4.23135e19i		−	0.206179i
$87$	−5.84183e19	+	1.15869e20i	−0.252114	+	0.500052i
$88$	−1.95528e20			−0.748412
$89$	4.43565e20			1.50786			0.753932	−	0.656953i	$-0.228155\pi$
$89$	4.43565e20			1.50786			0.753932	+	0.656953i	$0.228155\pi$
$90$	−9.98350e19	+	7.38412e19i	−0.301812	+	0.223230i
$91$	−3.83744e20	+	3.20648e20i	−1.03302	+	0.863165i
$92$		−	4.17189e20i		−	1.00129i
$93$	−2.60808e20	+	5.17296e20i	−0.558791	+	1.10833i
$94$		−	6.64757e19i		−	0.127298i
$95$			3.60180e20i			0.617195i
$96$	−2.04227e20	+	4.05072e20i	−0.313520	+	0.621848i
$97$		−	8.62831e20i		−	1.18802i	−0.804459	−	0.594008i	$-0.797545\pi$
$97$		−	8.62831e20i		−	1.18802i	0.804459	−	0.594008i	$-0.202455\pi$
$98$	2.01792e20	+	3.64435e19i	0.249476	+	0.0450553i
$99$	1.10335e21	−	8.16073e20i	1.22615	−	0.906901i
$100$	1.11606e21			1.11606
$101$	−5.09810e20			−0.459234			−0.229617	−	0.973281i	$-0.573747\pi$
$101$	−5.09810e20			−0.459234			−0.229617	+	0.973281i	$0.573747\pi$
$102$	1.61373e20	−	3.20074e20i	0.131078	−	0.259985i
$103$			1.30498e20i			0.0956782i	0.998855	+	0.0478391i	$0.0152335\pi$
$103$			1.30498e20i			0.0956782i	−0.998855	+	0.0478391i	$0.984767\pi$
$104$	−9.97226e20			−0.660608
$105$	−5.61254e20	−	2.40703e21i	−0.336257	−	1.44210i
$106$	2.70008e20			0.146442
$107$		−	2.46662e21i		−	1.21220i	−0.795390	−	0.606098i	$-0.792734\pi$
$107$		−	2.46662e21i		−	1.21220i	0.795390	−	0.606098i	$-0.207266\pi$
$108$	−3.54877e20	−	2.06922e21i	−0.158172	−	0.922266i
$109$	−4.07891e21			−1.65031			−0.825155	−	0.564907i	$-0.808912\pi$
$109$	−4.07891e21			−1.65031			−0.825155	+	0.564907i	$0.808912\pi$
$110$	1.55743e21			0.572514
$111$	3.72701e21	+	1.87906e21i	1.24586	+	0.628131i
$112$	−1.70993e21	−	2.04640e21i	−0.520222	−	0.622590i
$113$		−	1.83094e21i		−	0.507401i	−0.967283	−	0.253701i	$-0.918352\pi$
$113$		−	1.83094e21i		−	0.507401i	0.967283	−	0.253701i	$-0.0816478\pi$
$114$	3.73464e20	+	1.88291e20i	0.0943513	+	0.0475695i
$115$			6.87428e21i			1.58453i
$116$		−	2.48976e21i		−	0.524021i
$117$	5.62728e21	−	4.16212e21i	1.08230	−	0.800503i
$118$			1.07991e21i			0.189945i
$119$	4.57477e21	+	5.47498e21i	0.736421	+	0.881332i
$120$	2.21890e21	−	4.40104e21i	0.327140	−	0.648862i
$121$	−9.81210e21			−1.32591
$122$	3.97805e20			0.0493051
$123$	−2.08030e21	−	1.04884e21i	−0.236659	−	0.119318i
$124$		−	1.11155e22i		−	1.16145i
$125$	−2.97138e21			−0.285366
$126$	−2.78921e21	−	6.76369e20i	−0.246372	−	0.0597438i
$127$	1.75513e22			1.42683			0.713413	−	0.700744i	$-0.247148\pi$
$127$	1.75513e22			1.42683			0.713413	+	0.700744i	$0.247148\pi$
$128$		−	1.14513e22i		−	0.857336i
$129$	−1.05258e22	−	5.30686e21i	−0.726213	−	0.366139i
$130$	7.94319e21			0.505347
$131$	3.21780e21			0.188891			0.0944453	−	0.995530i	$-0.469892\pi$
$131$	3.21780e21			0.188891			0.0944453	+	0.995530i	$0.469892\pi$
$132$	−1.18542e22	+	2.35122e22i	−0.642462	+	1.27428i
$133$	−6.38823e21	+	5.33786e21i	−0.319844	+	0.267254i
$134$			2.49023e21i			0.115249i
$135$	5.84753e21	+	3.40958e22i	0.250304	+	1.45947i
$136$			1.42277e22i			0.563607i
$137$		−	3.65830e22i		−	1.34188i	−0.741512	−	0.670940i	$-0.765891\pi$
$137$		−	3.65830e22i		−	1.34188i	0.741512	−	0.670940i	$-0.234109\pi$
$138$	7.12781e21	+	3.59366e21i	0.242229	+	0.122126i
$139$		−	4.00599e22i		−	1.26198i	−0.775789	−	0.630992i	$-0.782648\pi$
$139$		−	4.00599e22i		−	1.26198i	0.775789	−	0.630992i	$-0.217352\pi$
$140$	3.04075e22	+	3.63910e22i	0.888456	+	1.06328i
$141$	−1.65364e22	−	8.33722e21i	−0.448373	−	0.226058i
$142$	7.59093e21			0.191103
$143$	−8.77860e22			−2.05304
$144$	2.21955e22	+	3.00088e22i	0.482456	+	0.652292i
$145$			4.10254e22i			0.829256i
$146$	1.48114e22			0.278542
$147$	3.43738e22	−	4.56267e22i	0.601722	−	0.798705i
$148$	−8.00849e22			−1.30558
$149$			5.70779e22i			0.866986i	0.901157	+	0.433493i	$0.142719\pi$
$149$			5.70779e22i			0.866986i	−0.901157	+	0.433493i	$0.857281\pi$
$150$	−9.61373e21	+	1.90683e22i	−0.136124	+	0.269993i
$151$	1.37183e23			1.81151			0.905755	−	0.423801i	$-0.139304\pi$
$151$	1.37183e23			1.81151			0.905755	+	0.423801i	$0.139304\pi$
$152$	−1.66009e22			−0.204538
$153$	−5.93821e22	−	8.02860e22i	−0.682960	−	0.923378i
$154$	2.30811e22	+	2.76229e22i	0.247907	+	0.296690i
$155$			1.83157e23i			1.83798i
$156$	−6.04587e22	+	1.19916e23i	−0.567088	+	1.12478i
$157$			8.48354e22i			0.744099i	0.928213	+	0.372050i	$0.121345\pi$
$157$			8.48354e22i			0.744099i	−0.928213	+	0.372050i	$0.878655\pi$
$158$		−	3.45699e22i		−	0.283661i
$159$	3.38638e22	−	6.71668e22i	0.260055	−	0.515804i
$160$			1.43422e23i			1.03123i
$161$	−1.21924e23	+	1.01877e23i	−0.821138	+	0.686124i
$162$	3.84102e22	+	1.17610e22i	0.242403	+	0.0742228i
$163$	−2.44238e23			−1.44492			−0.722461	−	0.691412i	$-0.756989\pi$
$163$	−2.44238e23			−1.44492			−0.722461	+	0.691412i	$0.756989\pi$
$164$	4.47010e22			0.248003
$165$	1.95330e23	−	3.87425e23i	1.01669	−	2.01654i
$166$			1.00604e22i			0.0491449i
$167$	−4.94570e22			−0.226832			−0.113416	−	0.993548i	$-0.536179\pi$
$167$	−4.94570e22			−0.226832			−0.113416	+	0.993548i	$0.536179\pi$
$168$	1.10942e23	−	2.58686e22i	0.477911	−	0.111436i
$169$	−2.00659e23			−0.812174
$170$		−	1.13328e23i		−	0.431144i
$171$	9.36780e22	−	6.92872e22i	0.335103	−	0.247853i
$172$	2.26176e23			0.761023
$173$	1.35934e23			0.430371			0.215185	−	0.976573i	$-0.430964\pi$
$173$	1.35934e23			0.430371			0.215185	+	0.976573i	$0.430964\pi$
$174$	4.25384e22	+	2.14468e22i	0.126769	+	0.0639139i
$175$	−2.72539e23	−	3.26169e23i	−0.764768	−	0.915257i
$176$		−	4.68139e23i		−	1.23735i
$177$	2.68637e23	+	1.35440e23i	0.669032	+	0.337309i
$178$		−	1.62844e23i		−	0.382262i
$179$		−	5.09904e23i		−	1.12858i	−0.825578	−	0.564289i	$-0.809150\pi$
$179$		−	5.09904e23i		−	1.12858i	0.825578	−	0.564289i	$-0.190850\pi$
$180$	−3.94699e23	−	5.33643e23i	−0.823958	−	1.11401i
$181$			2.55697e23i			0.503617i	0.967777	+	0.251809i	$0.0810253\pi$
$181$			2.55697e23i			0.503617i	−0.967777	+	0.251809i	$0.918975\pi$
$182$	1.17718e23	+	1.40882e23i	0.218823	+	0.261882i
$183$	4.98918e22	−	9.89573e22i	0.0875573	−	0.173665i
$184$	−3.16840e23			−0.525113
$185$	1.31961e24			2.06606
$186$	1.89912e23	+	9.57490e22i	0.280975	+	0.141660i
$187$			1.25247e24i			1.75158i
$188$	3.55329e23			0.469865
$189$	−5.18069e23	+	6.09011e23i	−0.647946	+	0.761686i
$190$	1.32231e23			0.156466
$191$			9.41669e23i			1.05450i	0.849709	+	0.527252i	$0.176778\pi$
$191$			9.41669e23i			1.05450i	−0.849709	+	0.527252i	$0.823222\pi$
$192$	−5.34690e23	−	2.69577e23i	−0.566812	−	0.285772i
$193$	−1.22581e24			−1.23047			−0.615236	−	0.788343i	$-0.710939\pi$
$193$	−1.22581e24			−1.23047			−0.615236	+	0.788343i	$0.710939\pi$
$194$	−3.16767e23			−0.301176
$195$	9.96216e23	−	1.97593e24i	0.897408	−	1.77995i
$196$	−1.94799e23	+	1.07863e24i	−0.166302	+	0.920835i
$197$		−	1.96576e24i		−	1.59087i	−0.606040	−	0.795434i	$-0.707243\pi$
$197$		−	1.96576e24i		−	1.59087i	0.606040	−	0.795434i	$-0.292757\pi$
$198$	−2.99601e23	−	4.05067e23i	−0.229910	−	0.310844i
$199$		−	9.29643e23i		−	0.676642i	−0.941031	−	0.338321i	$-0.890141\pi$
$199$		−	9.29643e23i		−	0.676642i	0.941031	−	0.338321i	$-0.109859\pi$
$200$		−	8.47608e23i		−	0.585302i
$201$	6.19465e23	+	3.12319e23i	0.405937	+	0.204663i
$202$			1.87164e23i			0.116421i
$203$	−7.27634e23	+	6.07994e23i	−0.429739	+	0.359080i
$204$	1.71088e24	+	8.62581e23i	0.959626	+	0.483819i
$205$	−7.36566e23			−0.392461
$206$	4.79090e22			0.0242556
$207$	1.78791e24	−	1.32239e24i	0.860312	−	0.636314i
$208$		−	2.38759e24i		−	1.09218i
$209$	−1.46138e24			−0.635665
$210$	−8.83681e23	+	2.06050e23i	−0.365589	+	0.0852453i
$211$	2.16585e24			0.852436			0.426218	−	0.904621i	$-0.359846\pi$
$211$	2.16585e24			0.852436			0.426218	+	0.904621i	$0.359846\pi$
$212$			1.44326e24i			0.540528i
$213$	9.52036e23	−	1.88831e24i	0.339366	−	0.673111i
$214$	−9.05557e23			−0.307306
$215$	−3.72684e24			−1.20431
$216$	−1.57150e24	+	2.69516e23i	−0.483670	+	0.0829508i
$217$	−3.24851e24	+	2.71438e24i	−0.952483	+	0.795874i
$218$			1.49747e24i			0.418373i
$219$	1.85761e24	−	3.68445e24i	0.494642	−	0.981093i
$220$			8.32487e24i			2.11319i
$221$			6.38780e24i			1.54608i
$222$	6.89851e23	−	1.36828e24i	0.159239	−	0.315840i
$223$			1.09956e24i			0.242113i	0.992646	+	0.121056i	$0.0386282\pi$
$223$			1.09956e24i			0.242113i	−0.992646	+	0.121056i	$0.961372\pi$
$224$	−2.54377e24	+	2.12551e24i	−0.534408	+	0.446540i
$225$	3.53765e24	+	4.78299e24i	0.709249	+	0.958922i
$226$	−6.72185e23			−0.128632
$227$	3.04133e24			0.555638			0.277819	−	0.960633i	$-0.410388\pi$
$227$	3.04133e24			0.555638			0.277819	+	0.960633i	$0.410388\pi$
$228$	−1.00646e24	+	1.99626e24i	−0.175583	+	0.348257i
$229$			9.05432e24i			1.50863i	0.656511	+	0.754316i	$0.272031\pi$
$229$			9.05432e24i			1.50863i	−0.656511	+	0.754316i	$0.727969\pi$
$230$	2.52372e24			0.401697
$231$	9.76622e24	−	2.27721e24i	1.48525	−	0.346320i
$232$	−1.89089e24			−0.274816
$233$			8.39062e23i			0.116562i	0.998300	+	0.0582810i	$0.0185619\pi$
$233$			8.39062e23i			0.116562i	−0.998300	+	0.0582810i	$0.981438\pi$
$234$	−1.52802e24	−	2.06591e24i	−0.202937	−	0.274376i
$235$	−5.85498e24			−0.743554
$236$	−5.77240e24			−0.701100
$237$	−8.59956e24	−	4.33568e24i	−0.999122	−	0.503732i
$238$	2.01000e24	−	1.67951e24i	0.223428	−	0.186692i
$239$		−	1.16933e25i		−	1.24383i	−0.783087	−	0.621913i	$-0.786356\pi$
$239$		−	1.16933e25i		−	1.24383i	0.783087	−	0.621913i	$-0.213644\pi$
$240$	1.05371e25	+	5.31255e24i	1.07276	+	0.540860i
$241$			5.54789e24i			0.540691i	0.962763	+	0.270345i	$0.0871379\pi$
$241$			5.54789e24i			0.540691i	−0.962763	+	0.270345i	$0.912862\pi$
$242$			3.60226e24i			0.336135i
$243$	7.74297e24	−	8.07980e24i	0.691897	−	0.721996i
$244$			2.12637e24i			0.181989i
$245$	3.20983e24	−	1.77732e25i	0.263171	−	1.45721i
$246$	−3.85054e23	+	7.63731e23i	−0.0302484	+	0.0599959i
$247$	−7.45331e24			−0.561088
$248$	−8.44184e24			−0.609108
$249$	2.50260e24	+	1.26175e24i	0.173100	+	0.0872728i
$250$			1.09087e24i			0.0723438i
$251$	8.18893e24			0.520779			0.260389	−	0.965504i	$-0.416149\pi$
$251$	8.18893e24			0.520779			0.260389	+	0.965504i	$0.416149\pi$
$252$	3.61536e24	−	1.49090e25i	0.220519	−	0.909376i
$253$	−2.78915e25			−1.63195
$254$		−	6.44353e24i		−	0.361718i
$255$	−2.81912e25	−	1.42133e25i	−1.51859	−	0.765636i
$256$	8.07430e24			0.417432
$257$	1.49657e25			0.742674			0.371337	−	0.928498i	$-0.378900\pi$
$257$	1.49657e25			0.742674			0.371337	+	0.928498i	$0.378900\pi$
$258$	−1.94828e24	+	3.86429e24i	−0.0928205	+	0.184104i
$259$	1.95566e25	+	2.34048e25i	0.894633	+	1.07068i
$260$			4.24583e25i			1.86527i
$261$	1.06701e25	−	7.89197e24i	0.450241	−	0.333012i
$262$		−	1.18133e24i		−	0.0478860i
$263$		−	1.45078e25i		−	0.565024i	−0.959264	−	0.282512i	$-0.908832\pi$
$263$		−	1.45078e25i		−	0.565024i	0.959264	−	0.282512i	$-0.0911678\pi$
$264$	1.78566e25	+	9.00287e24i	0.668280	+	0.336930i
$265$		−	2.37815e25i		−	0.855377i
$266$	1.95966e24	+	2.34528e24i	0.0677522	+	0.0810843i
$267$	−4.05087e25	−	2.04235e25i	−1.34642	−	0.678830i
$268$	−1.33109e25			−0.425394
$269$	5.57484e25			1.71330			0.856650	−	0.515897i	$-0.172541\pi$
$269$	5.57484e25			1.71330			0.856650	+	0.515897i	$0.172541\pi$
$270$	1.25174e25	−	2.14677e24i	0.369994	−	0.0634551i
$271$		−	5.26405e25i		−	1.49673i	−0.663290	−	0.748363i	$-0.730840\pi$
$271$		−	5.26405e25i		−	1.49673i	0.663290	−	0.748363i	$-0.269160\pi$
$272$	−3.40644e25			−0.931810
$273$	4.98094e25	−	1.16142e25i	1.31100	−	0.305690i
$274$	−1.34305e25			−0.340183
$275$		−	7.46150e25i		−	1.81900i
$276$	−1.92090e25	+	3.80999e25i	−0.450775	+	0.894084i
$277$	−4.98204e25			−1.12556			−0.562781	−	0.826606i	$-0.690269\pi$
$277$	−4.98204e25			−1.12556			−0.562781	+	0.826606i	$0.690269\pi$
$278$	−1.47070e25			−0.319928
$279$	4.76367e25	−	3.52336e25i	0.997924	−	0.738097i
$280$	2.76376e25	−	2.30934e25i	0.557624	−	0.465938i
$281$			2.53148e25i			0.491992i	0.969271	+	0.245996i	$0.0791150\pi$
$281$			2.53148e25i			0.491992i	−0.969271	+	0.245996i	$0.920885\pi$
$282$	−3.06080e24	+	6.07091e24i	−0.0573085	+	0.113668i
$283$			5.18238e25i			0.934913i	0.884016	+	0.467457i	$0.154830\pi$
$283$			5.18238e25i			0.934913i	−0.884016	+	0.467457i	$0.845170\pi$
$284$			4.05754e25i			0.705375i
$285$	1.65841e25	−	3.28936e25i	0.277857	−	0.551112i
$286$			3.22284e25i			0.520470i
$287$	−1.09159e25	−	1.30639e25i	−0.169941	−	0.203382i
$288$	3.73022e25	−	2.75899e25i	0.559904	−	0.414123i
$289$	2.20446e25			0.319062
$290$	1.50614e25			0.210226
$291$	−3.97281e25	+	7.87983e25i	−0.534837	+	1.06082i
$292$			7.91705e25i			1.02812i
$293$	5.26755e25			0.659932			0.329966	−	0.943993i	$-0.392963\pi$
$293$	5.26755e25			0.659932			0.329966	+	0.943993i	$0.392963\pi$
$294$	−1.67507e25	−	1.26195e25i	−0.202481	−	0.152544i
$295$	9.51154e25			1.10948
$296$			6.08216e25i			0.684692i
$297$	−1.38339e26	+	2.37256e25i	−1.50315	+	0.257795i
$298$	2.09547e25			0.219792
$299$	−1.42251e26			−1.44049
$300$	−1.01924e26	−	5.13878e25i	−0.996564	−	0.502443i
$301$	−5.52317e25	−	6.61000e25i	−0.521483	−	0.624099i
$302$		−	5.03631e25i		−	0.459240i
$303$	4.65586e25	+	2.34737e25i	0.410064	+	0.206744i
$304$		−	3.97465e25i		−	0.338163i
$305$		−	3.50375e25i		−	0.287995i
$306$	−2.94750e25	+	2.18006e25i	−0.234087	+	0.173139i
$307$		−	3.81010e25i		−	0.292404i	−0.989255	−	0.146202i	$-0.953295\pi$
$307$		−	3.81010e25i		−	0.292404i	0.989255	−	0.146202i	$-0.0467050\pi$
$308$	−1.47651e26	+	1.23374e26i	−1.09510	+	0.915044i
$309$	6.00864e24	−	1.19178e25i	0.0430737	−	0.0854340i
$310$	6.72416e25			0.465951
$311$	2.86439e26			1.91888			0.959440	−	0.281914i	$-0.0909693\pi$
$311$	2.86439e26			1.91888			0.959440	+	0.281914i	$0.0909693\pi$
$312$	9.10720e25	+	4.59162e25i	0.589877	+	0.297401i
$313$			7.04402e25i			0.441169i	0.975368	+	0.220585i	$0.0707965\pi$
$313$			7.04402e25i			0.441169i	−0.975368	+	0.220585i	$0.929204\pi$
$314$	3.11452e25			0.188638
$315$	−5.95726e25	+	2.45665e26i	−0.348968	+	1.43907i
$316$	1.84785e26			1.04701
$317$			1.14082e25i			0.0625307i	0.999511	+	0.0312653i	$0.00995369\pi$
$317$			1.14082e25i			0.0625307i	−0.999511	+	0.0312653i	$0.990046\pi$
$318$	−2.46586e25	−	1.24322e25i	−0.130763	−	0.0659272i
$319$	−1.66455e26			−0.854072
$320$	−1.89316e26			−0.939965
$321$	−1.13573e26	+	2.25265e26i	−0.545723	+	1.08241i
$322$	3.74014e25	+	4.47611e25i	0.173941	+	0.208168i
$323$			1.06338e26i			0.478700i
$324$	−6.28656e25	+	2.05312e26i	−0.273962	+	0.894728i
$325$		−	3.80550e26i		−	1.60560i
$326$			8.96659e25i			0.366305i
$327$	3.72507e26	+	1.87809e26i	1.47361	+	0.742958i
$328$		−	3.39488e25i		−	0.130062i
$329$	−8.67705e25	−	1.03845e26i	−0.321970	−	0.385326i
$330$	−1.42233e26	−	7.17104e25i	−0.511216	−	0.257742i
$331$	−2.67563e26			−0.931605			−0.465802	−	0.884889i	$-0.654234\pi$
$331$	−2.67563e26			−0.931605			−0.465802	+	0.884889i	$0.654234\pi$
$332$	−5.37751e25			−0.181397
$333$	−2.53851e26	−	3.43212e26i	−0.829686	−	1.12176i
$334$			1.81569e25i			0.0575047i
$335$	2.19332e26			0.673180
$336$	6.19353e25	+	2.65620e26i	0.184237	+	0.790130i
$337$	5.06422e26			1.46015			0.730076	−	0.683366i	$-0.239485\pi$
$337$	5.06422e26			1.46015			0.730076	+	0.683366i	$0.239485\pi$
$338$			7.36670e25i			0.205896i
$339$	−8.43039e25	+	1.67212e26i	−0.228429	+	0.453074i
$340$	6.05764e26			1.59138
$341$	−7.43136e26			−1.89299
$342$	−2.54370e25	−	3.43915e25i	−0.0628337	−	0.0849526i
$343$	3.62798e26	−	2.06468e26i	0.869114	−	0.494611i
$344$		−	1.71773e26i		−	0.399108i
$345$	3.16519e26	−	6.27796e26i	0.713344	−	1.41487i
$346$		−	4.99046e25i		−	0.109104i
$347$		−	5.76925e26i		−	1.22366i	−0.790991	−	0.611828i	$-0.790434\pi$
$347$		−	5.76925e26i		−	1.22366i	0.790991	−	0.611828i	$-0.209566\pi$
$348$	−1.14638e26	+	2.27378e26i	−0.235911	+	0.467915i
$349$		−	7.69223e26i		−	1.53598i	−0.640463	−	0.767989i	$-0.721258\pi$
$349$		−	7.69223e26i		−	1.53598i	0.640463	−	0.767989i	$-0.278742\pi$
$350$	−1.19745e26	+	1.00056e26i	−0.232029	+	0.193878i
$351$	−7.05553e26	+	1.21005e26i	−1.32680	+	0.227550i
$352$	−5.81917e26			−1.06209
$353$	7.28618e26			1.29082			0.645410	−	0.763837i	$-0.276687\pi$
$353$	7.28618e26			1.29082			0.645410	+	0.763837i	$0.276687\pi$
$354$	4.97234e25	−	9.86233e25i	0.0855119	−	0.169608i
$355$		−	6.68586e26i		−	1.11625i
$356$	8.70439e26			1.41096
$357$	−1.65703e26	−	7.10645e26i	−0.260804	−	1.11850i
$358$	−1.87198e26			−0.286108
$359$			8.02107e26i			1.19053i	0.803529	+	0.595265i	$0.202953\pi$
$359$			8.02107e26i			1.19053i	−0.803529	+	0.595265i	$0.797047\pi$
$360$	−4.05283e26	+	2.99760e26i	−0.584227	+	0.432113i
$361$	5.90133e26			0.826275
$362$	9.38726e25			0.127673
$363$	8.96093e26	+	4.51788e26i	1.18395	+	0.596918i
$364$	−7.53048e26	+	6.29230e26i	−0.966625	+	0.807690i
$365$		−	1.30454e27i		−	1.62698i
$366$	−3.63297e25	−	1.83165e25i	−0.0440261	−	0.0221968i
$367$			1.07712e27i			1.26844i	0.773153	+	0.634219i	$0.218678\pi$
$367$			1.07712e27i			1.26844i	−0.773153	+	0.634219i	$0.781322\pi$
$368$		−	7.58588e26i		−	0.868169i
$369$	1.41692e26	+	1.91571e26i	0.157604	+	0.213085i
$370$		−	4.84461e26i		−	0.523770i
$371$	4.21793e26	−	3.52441e26i	0.443276	−	0.370391i
$372$	−5.11802e26	+	1.01513e27i	−0.522879	+	1.03710i
$373$	−3.65727e26			−0.363258			−0.181629	−	0.983367i	$-0.558137\pi$
$373$	−3.65727e26			−0.363258			−0.181629	+	0.983367i	$0.558137\pi$
$374$	4.59812e26			0.444046
$375$	2.71362e26	+	1.36814e26i	0.254813	+	0.128470i
$376$		−	2.69860e26i		−	0.246414i
$377$	−8.48949e26			−0.753872
$378$	2.23583e26	+	1.90196e26i	0.193097	+	0.164262i
$379$	−1.04194e27			−0.875250			−0.437625	−	0.899158i	$-0.644180\pi$
$379$	−1.04194e27			−0.875250			−0.437625	+	0.899158i	$0.644180\pi$
$380$			7.06808e26i			0.577529i
$381$	−1.60288e27	−	8.08132e26i	−1.27406	−	0.642347i
$382$	3.45710e26			0.267329
$383$	2.53492e26			0.190711			0.0953557	−	0.995443i	$-0.469601\pi$
$383$	2.53492e26			0.190711			0.0953557	+	0.995443i	$0.469601\pi$
$384$	−5.27264e26	+	1.04580e27i	−0.385967	+	0.765542i
$385$	2.43295e27	−	2.03291e27i	1.73298	−	1.44804i
$386$			4.50025e26i			0.311939i
$387$	7.16926e26	+	9.69301e26i	0.483625	+	0.653873i
$388$		−	1.69319e27i		−	1.11166i
$389$			1.49463e27i			0.955132i	0.878596	+	0.477566i	$0.158481\pi$
$389$			1.49463e27i			0.955132i	−0.878596	+	0.477566i	$0.841519\pi$
$390$	−7.25414e26	−	3.65735e26i	−0.451240	−	0.227504i
$391$			2.02954e27i			1.22897i
$392$	8.19177e26	+	1.47943e26i	0.482919	+	0.0872150i
$393$	−2.93866e26	−	1.48160e26i	−0.168666	−	0.0850373i
$394$	−7.21678e26			−0.403304
$395$	−3.04482e27			−1.65688
$396$	2.16518e27	−	1.60144e27i	1.14735	−	0.848616i
$397$			3.24066e27i			1.67237i	0.548446	+	0.836186i	$0.315220\pi$
$397$			3.24066e27i			1.67237i	−0.548446	+	0.836186i	$0.684780\pi$
$398$	−3.41295e26			−0.171537
$399$	8.29183e26	−	1.93343e26i	0.405915	−	0.0946482i
$400$	2.02937e27			0.967679
$401$		−	2.32859e27i		−	1.08163i	−0.841142	−	0.540814i	$-0.818116\pi$
$401$		−	2.32859e27i		−	1.08163i	0.841142	−	0.540814i	$-0.181884\pi$
$402$	1.14660e26	−	2.27421e26i	0.0518845	−	0.102910i
$403$	−3.79012e27			−1.67090
$404$	−1.00044e27			−0.429720
$405$	1.03588e27	−	3.38305e27i	0.433541	−	1.41589i
$406$	2.23210e26	+	2.67132e26i	0.0910311	+	0.108944i
$407$			5.35414e27i			2.12788i
$408$	6.55099e26	−	1.29935e27i	0.253732	−	0.503262i
$409$			2.01191e27i			0.759476i	0.925094	+	0.379738i	$0.123986\pi$
$409$			2.01191e27i			0.759476i	−0.925094	+	0.379738i	$0.876014\pi$
$410$			2.70412e26i			0.0994935i
$411$	−1.68443e27	+	3.34095e27i	−0.604105	+	1.19821i
$412$			2.56085e26i			0.0895291i
$413$	1.40961e27	+	1.68699e27i	0.480422	+	0.574957i
$414$	−4.85483e26	−	6.56384e26i	−0.161313	−	0.218100i
$415$	8.86086e26			0.287059
$416$	−2.96788e27			−0.937489
$417$	−1.84451e27	+	3.65848e27i	−0.568137	+	1.12686i
$418$			5.36510e26i			0.161149i
$419$	4.70631e27			1.37858			0.689292	−	0.724483i	$-0.257922\pi$
$419$	4.70631e27			1.37858			0.689292	+	0.724483i	$0.257922\pi$
$420$	−1.10139e27	−	4.72349e27i	−0.314647	−	1.34942i
$421$	2.99709e27			0.835099			0.417550	−	0.908654i	$-0.362889\pi$
$421$	2.99709e27			0.835099			0.417550	+	0.908654i	$0.362889\pi$
$422$		−	7.95135e26i		−	0.216103i
$423$	1.12631e27	+	1.52280e27i	0.298596	+	0.403709i
$424$	1.09610e27			0.283472
$425$	−5.42941e27			−1.36984
$426$	−6.93244e26	−	3.49516e26i	−0.170642	−	0.0860333i
$427$	6.21431e26	−	5.19254e26i	0.149245	−	0.124706i
$428$		−	4.84043e27i		−	1.13429i
$429$	8.01708e27	+	4.04201e27i	1.83322	+	0.924264i
$430$			1.36822e27i			0.305306i
$431$			7.88872e27i			1.71789i	0.512068	+	0.858945i	$0.328879\pi$
$431$			7.88872e27i			1.71789i	−0.512068	+	0.858945i	$0.671121\pi$
$432$	−6.45285e26	−	3.76253e27i	−0.137142	−	0.799650i
$433$			1.12507e27i			0.233377i	0.993169	+	0.116689i	$0.0372279\pi$
$433$			1.12507e27i			0.233377i	−0.993169	+	0.116689i	$0.962772\pi$
$434$	9.96518e26	+	1.19261e27i	0.201764	+	0.241466i
$435$	1.88897e27	−	3.74665e27i	0.373325	−	0.740468i
$436$	−8.00433e27			−1.54425
$437$	−2.36807e27			−0.446006
$438$	−1.35265e27	−	6.81974e26i	−0.248719	−	0.125398i
$439$		−	2.62451e26i		−	0.0471163i	−0.999722	−	0.0235582i	$-0.992501\pi$
$439$		−	2.62451e26i		−	0.0471163i	0.999722	−	0.0235582i	$-0.00749949\pi$
$440$	6.32244e27			1.10823
$441$	−5.24003e27	+	2.58416e27i	−0.896868	+	0.442298i
$442$	2.34512e27			0.391950
$443$		−	8.58094e27i		−	1.40054i	−0.713878	−	0.700270i	$-0.753063\pi$
$443$		−	8.58094e27i		−	1.40054i	0.713878	−	0.700270i	$-0.246937\pi$
$444$	7.31378e27	+	3.68742e27i	1.16579	+	0.587762i
$445$	−1.43428e28			−2.23282
$446$	4.03676e26			0.0613786
$447$	2.62809e27	−	5.21266e27i	0.390312	−	0.774159i
$448$	−2.80565e27	−	3.35774e27i	−0.407019	−	0.487111i
$449$		−	4.40140e27i		−	0.623741i	−0.950125	−	0.311871i	$-0.899044\pi$
$449$		−	4.40140e27i		−	0.623741i	0.950125	−	0.311871i	$-0.100956\pi$
$450$	1.75595e27	−	1.29876e27i	0.243098	−	0.179803i
$451$		−	2.98852e27i		−	0.404205i
$452$		−	3.59299e27i		−	0.474791i
$453$	−1.25282e28	−	6.31642e27i	−1.61755	−	0.815530i
$454$		−	1.11655e27i		−	0.140861i
$455$	1.24084e28	−	1.03682e28i	1.52967	−	1.27816i
$456$	1.51609e27	+	7.64372e26i	0.182639	+	0.0920819i
$457$	3.77890e27			0.444883			0.222441	−	0.974946i	$-0.428597\pi$
$457$	3.77890e27			0.444883			0.222441	+	0.974946i	$0.428597\pi$
$458$	3.32406e27			0.382456
$459$	1.72641e27	+	1.00663e28i	0.194138	+	1.13198i
$460$			1.34899e28i			1.48269i
$461$	3.80104e27			0.408359			0.204180	−	0.978933i	$-0.434547\pi$
$461$	3.80104e27			0.408359			0.204180	+	0.978933i	$0.434547\pi$
$462$	−8.36021e26	−	3.58542e27i	−0.0877964	−	0.376530i
$463$	−4.97281e27			−0.510507			−0.255253	−	0.966874i	$-0.582159\pi$
$463$	−4.97281e27			−0.510507			−0.255253	+	0.966874i	$0.582159\pi$
$464$		−	4.52722e27i		−	0.454352i
$465$	8.43328e27	−	1.67269e28i	0.827448	−	1.64119i
$466$	3.08040e26			0.0295499
$467$	−1.65815e28			−1.55523			−0.777617	−	0.628738i	$-0.783572\pi$
$467$	−1.65815e28			−1.55523			−0.777617	+	0.628738i	$0.783572\pi$
$468$	1.10428e28	−	8.16762e27i	1.01274	−	0.749056i
$469$	3.25049e27	+	3.89011e27i	0.291497	+	0.348857i
$470$			2.14951e27i			0.188500i
$471$	3.90615e27	−	7.74762e27i	0.334988	−	0.664429i
$472$			4.38393e27i			0.367682i
$473$		−	1.51212e28i		−	1.24035i
$474$	−1.59174e27	+	3.15711e27i	−0.127702	+	0.253290i
$475$		−	6.33505e27i		−	0.497127i
$476$	8.97740e27	+	1.07439e28i	0.689093	+	0.824690i
$477$	−6.18524e27	+	4.57481e27i	−0.464423	+	0.343502i
$478$	−4.29290e27			−0.315325
$479$	−1.67048e28			−1.20038			−0.600188	−	0.799859i	$-0.704908\pi$
$479$	−1.67048e28			−1.20038			−0.600188	+	0.799859i	$0.704908\pi$
$480$	6.60373e27	−	1.30981e28i	0.464255	−	0.920821i
$481$			2.73070e28i			1.87824i
$482$	2.03677e27			0.137072
$483$	1.58255e28	−	3.69007e27i	1.04211	−	0.242991i
$484$	−1.92550e28			−1.24070
$485$			2.78998e28i			1.75919i
$486$	−2.96630e27	−	2.84263e27i	−0.183035	−	0.175404i
$487$	1.69052e28			1.02086			0.510429	−	0.859920i	$-0.329487\pi$
$487$	1.69052e28			1.02086			0.510429	+	0.859920i	$0.329487\pi$
$488$	1.61490e27			0.0954415
$489$	2.23051e28	+	1.12457e28i	1.29021	+	0.650494i
$490$	−6.52498e27	−	1.17841e27i	−0.369420	−	0.0667171i
$491$			2.73101e28i			1.51345i	0.653734	+	0.756725i	$0.273202\pi$
$491$			2.73101e28i			1.51345i	−0.653734	+	0.756725i	$0.726798\pi$
$492$	−4.08233e27	−	2.05821e27i	−0.221449	−	0.111649i
$493$			1.21122e28i			0.643176i
$494$			2.73629e27i			0.142243i
$495$	−3.56771e28	+	2.63879e28i	−1.81566	+	1.34292i
$496$		−	2.02117e28i		−	1.00704i
$497$	1.18582e28	−	9.90842e27i	0.578463	−	0.483351i
$498$	4.63218e26	−	9.18765e26i	0.0221247	−	0.0438830i
$499$	−1.99149e28			−0.931372			−0.465686	−	0.884950i	$-0.654192\pi$
$499$	−1.99149e28			−0.931372			−0.465686	+	0.884950i	$0.654192\pi$
$500$	−5.83095e27			−0.267026
$501$	4.51668e27	+	2.27719e27i	0.202546	+	0.102118i
$502$		−	3.00636e27i		−	0.132024i
$503$	−1.58196e27			−0.0680350			−0.0340175	−	0.999421i	$-0.510830\pi$
$503$	−1.58196e27			−0.0680350			−0.0340175	+	0.999421i	$0.510830\pi$
$504$	−1.13229e28	−	2.74574e27i	−0.476910	−	0.115648i
$505$	1.64848e28			0.680025
$506$			1.02396e28i			0.413718i
$507$	1.83253e28	+	9.23915e27i	0.725216	+	0.365635i
$508$	3.44422e28			1.33513
$509$	−3.99452e28			−1.51680			−0.758400	−	0.651789i	$-0.774019\pi$
$509$	−3.99452e28			−1.51680			−0.758400	+	0.651789i	$0.774019\pi$
$510$	−5.21805e27	+	1.03497e28i	−0.194098	+	0.384982i
$511$	2.31376e28	−	1.93333e28i	0.843138	−	0.704508i
$512$		−	2.69794e28i		−	0.963159i
$513$	−1.17454e28	+	2.01438e27i	−0.410806	+	0.0704544i
$514$		−	5.49426e27i		−	0.188277i
$515$		−	4.21968e27i		−	0.141678i
$516$	−2.06556e28	−	1.04140e28i	−0.679541	−	0.342607i
$517$		−	2.37558e28i		−	0.765806i
$518$	8.59249e27	−	7.17969e27i	0.271429	−	0.226800i
$519$	−1.24142e28	−	6.25891e27i	−0.384291	−	0.193750i
$520$	3.22456e28			0.978216
$521$	−4.15617e28			−1.23565			−0.617827	−	0.786314i	$-0.711987\pi$
$521$	−4.15617e28			−1.23565			−0.617827	+	0.786314i	$0.711987\pi$
$522$	−2.89734e27	−	3.91727e27i	−0.0844226	−	0.114141i
$523$		−	4.59294e28i		−	1.31167i	−0.754906	−	0.655833i	$-0.772318\pi$
$523$		−	4.59294e28i		−	1.31167i	0.754906	−	0.655833i	$-0.227682\pi$
$524$	6.31451e27			0.176751
$525$	9.87165e27	+	4.23362e28i	0.270843	+	1.16155i
$526$	−5.32618e27			−0.143240
$527$			5.40748e28i			1.42555i
$528$	−2.15550e28	+	4.27529e28i	−0.557046	+	1.10487i
$529$	−5.72469e27			−0.145033
$530$	−8.73078e27			−0.216849
$531$	−1.82972e28	−	2.47382e28i	−0.445545	−	0.602387i
$532$	−1.25361e28	+	1.04749e28i	−0.299288	+	0.250078i
$533$		−	1.52420e28i		−	0.356784i
$534$	−7.49796e27	+	1.48717e28i	−0.172092	+	0.341333i
$535$			7.97588e28i			1.79500i
$536$			1.01091e28i			0.223092i
$537$	−2.34780e28	+	4.65671e28i	−0.508078	+	1.00774i
$538$		−	2.04666e28i		−	0.434342i
$539$	7.21123e28	+	1.30235e28i	1.50082	+	0.271047i
$540$	1.14750e28	+	6.69086e28i	0.234217	+	1.36568i
$541$	1.45892e28			0.292052			0.146026	−	0.989281i	$-0.453352\pi$
$541$	1.45892e28			0.292052			0.146026	+	0.989281i	$0.453352\pi$
$542$	−1.93256e28			−0.379438
$543$	1.17733e28	−	2.33516e28i	0.226725	−	0.449695i
$544$			4.23436e28i			0.799832i
$545$	1.31892e29			2.44375
$546$	−4.26385e27	−	1.82863e28i	−0.0774960	−	0.332355i
$547$	2.78371e28			0.496314			0.248157	−	0.968720i	$-0.420175\pi$
$547$	2.78371e28			0.496314			0.248157	+	0.968720i	$0.420175\pi$
$548$		−	7.17895e28i		−	1.25564i
$549$	−9.11276e27	+	6.74009e27i	−0.156365	+	0.115653i
$550$	−2.73930e28			−0.461139
$551$	−1.41326e28			−0.233415
$552$	2.89355e28	+	1.45886e28i	0.468890	+	0.236402i
$553$	−4.51241e28	−	5.40034e28i	−0.717454	−	0.858633i
$554$			1.82903e28i			0.285344i
$555$	−1.20514e29	−	6.07600e28i	−1.84485	−	0.930125i
$556$		−	7.86123e28i		−	1.18088i
$557$		−	8.40041e28i		−	1.23829i	−0.785278	−	0.619143i	$-0.787480\pi$
$557$		−	8.40041e28i		−	1.23829i	0.785278	−	0.619143i	$-0.212520\pi$
$558$	−1.29351e28	−	1.74886e28i	−0.187116	−	0.252986i
$559$		−	7.71206e28i		−	1.09483i
$560$	5.52909e28	+	6.61709e28i	0.770335	+	0.921919i
$561$	5.76685e28	−	1.14382e29i	0.788549	−	1.56404i
$562$	9.29368e27			0.124726
$563$	−4.44784e28			−0.585883			−0.292941	−	0.956130i	$-0.594634\pi$
$563$	−4.44784e28			−0.585883			−0.292941	+	0.956130i	$0.594634\pi$
$564$	−3.24505e28	−	1.63607e28i	−0.419557	−	0.211530i
$565$			5.92040e28i			0.751350i
$566$	1.90258e28			0.237012
$567$	7.53541e28	−	3.17642e28i	0.921477	−	0.388433i
$568$	3.08156e28			0.369924
$569$		−	3.84484e27i		−	0.0453106i	−0.999743	−	0.0226553i	$-0.992788\pi$
$569$		−	3.84484e27i		−	0.0453106i	0.999743	−	0.0226553i	$-0.00721202\pi$
$570$	−1.20760e28	−	6.08844e27i	−0.139714	−	0.0704401i
$571$	7.58051e28			0.861032			0.430516	−	0.902583i	$-0.358332\pi$
$571$	7.58051e28			0.861032			0.430516	+	0.902583i	$0.358332\pi$
$572$	−1.72269e29			−1.92109
$573$	4.33581e28	−	8.59982e28i	0.474731	−	0.941599i
$574$	−4.79607e27	+	4.00749e27i	−0.0515597	+	0.0430822i
$575$		−	1.20909e29i		−	1.27628i
$576$	3.64183e28	+	4.92384e28i	0.377471	+	0.510350i
$577$		−	1.48691e29i		−	1.51334i	−0.653795	−	0.756672i	$-0.726824\pi$
$577$		−	1.48691e29i		−	1.51334i	0.653795	−	0.756672i	$-0.273176\pi$
$578$		−	8.09311e27i		−	0.0808860i
$579$	1.11947e29	+	5.64411e28i	1.09873	+	0.553950i
$580$			8.05070e28i			0.775961i
$581$	1.31318e28	+	1.57158e28i	0.124301	+	0.148760i
$582$	2.89288e28	+	1.45852e28i	0.268930	+	0.135588i
$583$	9.64903e28			0.880975
$584$	6.01272e28			0.539183
$585$	−1.81959e29	+	1.34583e29i	−1.60265	+	1.18537i
$586$		−	1.93385e28i		−	0.167301i
$587$	9.38445e27			0.0797460			0.0398730	−	0.999205i	$-0.487305\pi$
$587$	9.38445e27			0.0797460			0.0398730	+	0.999205i	$0.487305\pi$
$588$	6.74542e28	−	8.95365e28i	0.563050	−	0.747374i
$589$	−6.30946e28			−0.517347
$590$		−	3.49192e28i		−	0.281267i
$591$	−9.05111e28	+	1.79523e29i	−0.716198	+	1.42054i
$592$	−1.45621e29			−1.13200
$593$	−1.65099e29			−1.26087			−0.630436	−	0.776241i	$-0.717124\pi$
$593$	−1.65099e29			−1.26087			−0.630436	+	0.776241i	$0.717124\pi$
$594$	8.71024e27	+	5.07877e28i	0.0653541	+	0.381066i
$595$	−1.47926e29	−	1.77035e29i	−1.09048	−	1.30506i
$596$			1.12008e29i			0.811267i
$597$	−4.28044e28	+	8.48999e28i	−0.304620	+	0.604194i
$598$			5.22240e28i			0.365181i
$599$			1.09948e29i			0.755452i	0.925917	+	0.377726i	$0.123294\pi$
$599$			1.09948e29i			0.755452i	−0.925917	+	0.377726i	$0.876706\pi$
$600$	−3.90272e28	+	7.74080e28i	−0.263499	+	0.522634i
$601$			1.93693e28i			0.128508i	0.997934	+	0.0642541i	$0.0204668\pi$
$601$			1.93693e28i			0.128508i	−0.997934	+	0.0642541i	$0.979533\pi$
$602$	−2.42669e28	+	2.02769e28i	−0.158217	+	0.132202i
$603$	−4.21924e28	−	5.70452e28i	−0.270335	−	0.365500i
$604$	2.69203e29			1.69509
$605$	3.17277e29			1.96339
$606$	8.61776e27	−	1.70928e28i	0.0524121	−	0.103956i
$607$		−	1.36592e28i		−	0.0816474i	−0.999166	−	0.0408237i	$-0.987002\pi$
$607$		−	1.36592e28i		−	0.0816474i	0.999166	−	0.0408237i	$-0.0129982\pi$
$608$	−4.94066e28			−0.290267
$609$	9.44458e28	−	2.20222e28i	0.545382	−	0.127168i
$610$	−1.28631e28			−0.0730101
$611$		−	1.21159e29i		−	0.675961i
$612$	−1.16530e29	−	1.57551e29i	−0.639067	−	0.864034i
$613$	1.87515e29			1.01089			0.505443	−	0.862860i	$-0.331329\pi$
$613$	1.87515e29			1.01089			0.505443	+	0.862860i	$0.331329\pi$
$614$	−1.39878e28			−0.0741280
$615$	6.72671e28	+	3.39144e28i	0.350440	+	0.176683i
$616$	9.36983e28	+	1.12136e29i	0.479882	+	0.574312i
$617$			7.21390e28i			0.363225i	0.983370	+	0.181613i	$0.0581317\pi$
$617$			7.21390e28i			0.363225i	−0.983370	+	0.181613i	$0.941868\pi$
$618$	−4.37531e27	−	2.20592e27i	−0.0216586	−	0.0109197i
$619$			9.03568e28i			0.439753i	0.975528	+	0.219877i	$0.0705655\pi$
$619$			9.03568e28i			0.439753i	−0.975528	+	0.219877i	$0.929434\pi$
$620$			3.59423e29i			1.71986i
$621$	−2.24169e29	+	3.84457e28i	−1.05466	+	0.180878i
$622$		−	1.05159e29i		−	0.486459i
$623$	−2.12559e29	−	2.54386e29i	−0.966843	−	1.15709i
$624$	−1.09934e29	+	2.18048e29i	−0.491693	+	0.975243i
$625$	−1.75111e29			−0.770148
$626$	2.58603e28			0.111842
$627$	1.33461e29	+	6.72878e28i	0.567605	+	0.286172i
$628$			1.66479e29i			0.696277i
$629$	3.89597e29			1.60245
$630$	9.01898e28	+	2.18706e28i	0.364823	+	0.0884676i
$631$	−1.32905e29			−0.528729			−0.264364	−	0.964423i	$-0.585162\pi$
$631$	−1.32905e29			−0.528729			−0.264364	+	0.964423i	$0.585162\pi$
$632$		−	1.40337e29i		−	0.549091i
$633$	−1.97796e29	−	9.97240e28i	−0.761166	−	0.383761i
$634$	4.18822e27			0.0158523
$635$	−5.67526e29			−2.11282
$636$	6.64534e28	−	1.31806e29i	0.243342	−	0.482654i
$637$	3.67785e29	+	6.64219e28i	1.32474	+	0.239247i
$638$			6.11097e28i			0.216518i
$639$	−1.73890e29	+	1.28615e29i	−0.606060	+	0.448261i
$640$			3.70281e29i			1.26953i
$641$		−	4.35352e29i		−	1.46836i	−0.678957	−	0.734178i	$-0.737568\pi$
$641$		−	4.35352e29i		−	1.46836i	0.678957	−	0.734178i	$-0.262432\pi$
$642$	8.27003e28	+	4.16954e28i	0.274403	+	0.138347i
$643$		−	2.05844e29i		−	0.671927i	−0.941875	−	0.335964i	$-0.890938\pi$
$643$		−	2.05844e29i		−	0.671927i	0.941875	−	0.335964i	$-0.109062\pi$
$644$	−2.39259e29	+	1.99920e29i	−0.768364	+	0.642028i
$645$	3.40355e29	+	1.71598e29i	1.07536	+	0.542171i
$646$	3.90395e28			0.121356
$647$	−2.25180e28			−0.0688709			−0.0344354	−	0.999407i	$-0.510963\pi$
$647$	−2.25180e28			−0.0688709			−0.0344354	+	0.999407i	$0.510963\pi$
$648$	1.55927e29	+	4.77442e28i	0.469228	+	0.143676i
$649$			3.85918e29i			1.14268i
$650$	−1.39709e29			−0.407038
$651$	4.21652e29	−	9.83177e28i	1.20880	−	0.281859i
$652$	−4.79286e29			−1.35206
$653$			4.78474e29i			1.32822i	0.747635	+	0.664110i	$0.231189\pi$
$653$			4.78474e29i			1.32822i	−0.747635	+	0.664110i	$0.768811\pi$
$654$	6.89492e28	−	1.36757e29i	0.188349	−	0.373579i
$655$	−1.04048e29			−0.279706
$656$	8.12813e28			0.215031
$657$	−3.39293e29	+	2.50952e29i	−0.883363	+	0.653363i
$658$	−3.81240e28	+	3.18556e28i	−0.0976848	+	0.0816233i
$659$			2.97678e29i			0.750672i	0.926889	+	0.375336i	$0.122473\pi$
$659$			2.97678e29i			0.750672i	−0.926889	+	0.375336i	$0.877527\pi$
$660$	3.83310e29	−	7.60271e29i	0.951345	−	1.88694i
$661$		−	5.59125e29i		−	1.36582i	−0.730503	−	0.682910i	$-0.760714\pi$
$661$		−	5.59125e29i		−	1.36582i	0.730503	−	0.682910i	$-0.239286\pi$
$662$			9.82289e28i			0.236173i
$663$	2.94119e29	−	5.83368e29i	0.696036	−	1.38054i
$664$			4.08403e28i			0.0951313i
$665$	2.06565e29	−	1.72601e29i	0.473619	−	0.395745i
$666$	−1.26002e29	+	9.31949e28i	−0.284379	+	0.210336i
$667$	−2.69729e29			−0.599248
$668$	−9.70530e28			−0.212254
$669$	5.06281e28	−	1.00418e29i	0.108998	−	0.216190i
$670$		−	8.05221e28i		−	0.170659i
$671$	1.42160e29			0.296613
$672$	3.30177e29	−	7.69883e28i	0.678219	−	0.158142i
$673$	−2.43237e29			−0.491893			−0.245947	−	0.969283i	$-0.579099\pi$
$673$	−2.43237e29			−0.491893			−0.245947	+	0.969283i	$0.579099\pi$
$674$		−	1.85920e29i		−	0.370166i
$675$	−1.02850e29	−	5.99696e29i	−0.201610	−	1.17555i
$676$	−3.93768e29			−0.759977
$677$	9.11748e29			1.73258			0.866291	−	0.499540i	$-0.166498\pi$
$677$	9.11748e29			1.73258			0.866291	+	0.499540i	$0.166498\pi$
$678$	6.13875e28	+	3.09500e28i	0.114860	+	0.0579094i
$679$	−4.94837e29	+	4.13475e29i	−0.911652	+	0.761756i
$680$		−	4.60056e29i		−	0.834579i
$681$	−2.77751e29	−	1.40035e29i	−0.496147	−	0.250145i
$682$			2.72824e29i			0.479895i
$683$		−	1.45654e29i		−	0.252293i	−0.992012	−	0.126146i	$-0.959739\pi$
$683$		−	1.45654e29i		−	0.252293i	0.992012	−	0.126146i	$-0.0402609\pi$
$684$	1.83831e29	−	1.35967e29i	0.313566	−	0.231924i
$685$			1.18292e30i			1.98703i
$686$	−7.57994e28	−	1.33192e29i	−0.125390	−	0.220331i
$687$	4.16896e29	−	8.26889e29i	0.679176	−	1.34710i
$688$	4.11263e29			0.659844
$689$	4.92117e29			0.777619
$690$	−2.30479e29	−	1.16202e29i	−0.358688	−	0.180841i
$691$		−	2.38869e29i		−	0.366135i	−0.983100	−	0.183067i	$-0.941397\pi$
$691$		−	2.38869e29i		−	0.366135i	0.983100	−	0.183067i	$-0.0586026\pi$
$692$	2.66752e29			0.402711
$693$	−9.96754e29	−	2.41708e29i	−1.48214	−	0.359411i
$694$	−2.11803e29			−0.310212
$695$			1.29534e30i			1.86872i
$696$	1.72686e29	+	8.70638e28i	0.245391	+	0.123720i
$697$	−2.17461e29			−0.304395
$698$	−2.82401e29			−0.389389
$699$	3.86337e28	−	7.66276e28i	0.0524754	−	0.104082i
$700$	−5.34824e29	−	6.40064e29i	−0.715618	−	0.856435i
$701$		−	1.08484e30i		−	1.42996i	−0.699143	−	0.714981i	$-0.746435\pi$
$701$		−	1.08484e30i		−	1.42996i	0.699143	−	0.714981i	$-0.253565\pi$
$702$	4.44238e28	+	2.59026e29i	0.0576867	+	0.336360i
$703$			4.54583e29i			0.581544i
$704$		−	7.68123e29i		−	0.968094i
$705$	5.34707e29	+	2.69586e29i	0.663943	+	0.334743i
$706$		−	2.67494e29i		−	0.327238i
$707$	2.44305e29	+	2.92378e29i	0.294461	+	0.352404i
$708$	5.27166e29	+	2.65784e29i	0.626034	+	0.315631i
$709$	−8.41126e29			−0.984182			−0.492091	−	0.870544i	$-0.663767\pi$
$709$	−8.41126e29			−0.984182			−0.492091	+	0.870544i	$0.663767\pi$
$710$	−2.45454e29			−0.282982
$711$	5.85726e29	+	7.91915e29i	0.665370	+	0.899596i
$712$		−	6.61067e29i		−	0.739956i
$713$	−1.20420e30			−1.32819
$714$	−2.60895e29	+	6.08336e28i	−0.283553	+	0.0661168i
$715$	2.83858e30			3.04010
$716$		−	1.00062e30i		−	1.05605i
$717$	−5.38406e29	+	1.06789e30i	−0.559962	+	1.11065i
$718$	2.94473e29			0.301814
$719$	4.13198e29			0.417354			0.208677	−	0.977985i	$-0.433084\pi$
$719$	4.13198e29			0.417354			0.208677	+	0.977985i	$0.433084\pi$
$720$	−7.17695e29	−	9.70341e29i	−0.714412	−	0.965902i
$721$	7.48411e28	−	6.25355e28i	0.0734209	−	0.0613489i
$722$		−	2.16653e29i		−	0.209471i
$723$	2.55447e29	−	5.06663e29i	0.243416	−	0.482800i
$724$			5.01772e29i			0.471250i
$725$		−	7.21577e29i		−	0.667934i
$726$	1.65862e29	−	3.28978e29i	0.151326	−	0.300146i
$727$		−	3.45036e29i		−	0.310279i	−0.987893	−	0.155140i	$-0.950417\pi$
$727$		−	3.45036e29i		−	0.310279i	0.987893	−	0.155140i	$-0.0495828\pi$
$728$	4.77878e29	+	5.71913e29i	0.423582	+	0.506933i
$729$	−1.07915e30	+	3.81374e29i	−0.942854	+	0.333205i
$730$	−4.78930e29			−0.412460
$731$	−1.10030e30			−0.934069
$732$	9.79062e28	−	1.94191e29i	0.0819302	−	0.162503i
$733$		−	5.24361e28i		−	0.0432553i	−0.999766	−	0.0216276i	$-0.993115\pi$
$733$		−	5.24361e28i		−	0.0432553i	0.999766	−	0.0216276i	$-0.00688482\pi$
$734$	3.95437e29			0.321565
$735$	−1.11149e30	+	1.47535e30i	−0.891019	+	1.18271i
$736$	−9.42958e29			−0.745204
$737$			8.89909e29i			0.693325i
$738$	7.03303e28	−	5.20186e28i	0.0540195	−	0.0399546i
$739$	3.97690e29			0.301147			0.150573	−	0.988599i	$-0.451888\pi$
$739$	3.97690e29			0.301147			0.150573	+	0.988599i	$0.451888\pi$
$740$	2.58956e30			1.93327
$741$	6.80676e29	+	3.43180e29i	0.501013	+	0.252598i
$742$	−1.29390e29	−	1.54851e29i	−0.0938986	−	0.112376i
$743$			1.67451e30i			1.19814i	0.800698	+	0.599068i	$0.204462\pi$
$743$			1.67451e30i			1.19814i	−0.800698	+	0.599068i	$0.795538\pi$
$744$	7.70953e29	+	3.88695e29i	0.543891	+	0.274216i
$745$		−	1.84563e30i		−	1.28382i
$746$			1.34268e29i			0.0920902i
$747$	−1.70455e29	−	2.30459e29i	−0.115277	−	0.155857i
$748$			2.45781e30i			1.63901i
$749$	−1.41462e30	+	1.18202e30i	−0.930207	+	0.777260i
$750$	5.02278e28	−	9.96237e28i	0.0325687	−	0.0645981i
$751$	6.70899e28			0.0428981			0.0214490	−	0.999770i	$-0.493172\pi$
$751$	6.70899e28			0.0428981			0.0214490	+	0.999770i	$0.493172\pi$
$752$	6.46106e29			0.407396
$753$	−7.47856e29	−	3.77050e29i	−0.465019	−	0.234451i
$754$			3.11670e29i			0.191116i
$755$	−4.43583e30			−2.68245
$756$	−1.01664e30	+	1.19511e30i	−0.606303	+	0.712734i
$757$	3.15591e29			0.185617			0.0928084	−	0.995684i	$-0.470416\pi$
$757$	3.15591e29			0.185617			0.0928084	+	0.995684i	$0.470416\pi$
$758$			3.82523e29i			0.221886i
$759$	2.54720e30	+	1.28423e30i	1.45722	+	0.734692i
$760$	5.36795e29			0.302877
$761$	1.60120e30			0.891062			0.445531	−	0.895267i	$-0.353015\pi$
$761$	1.60120e30			0.891062			0.445531	+	0.895267i	$0.353015\pi$
$762$	−2.96685e29	+	5.88457e29i	−0.162843	+	0.322989i
$763$	1.95464e30	+	2.33927e30i	1.05818	+	1.26640i
$764$			1.84790e30i			0.986732i
$765$	1.92013e30	+	2.59607e30i	1.01131	+	1.36732i
$766$		−	9.30631e28i		−	0.0483477i
$767$			1.96825e30i			1.00862i
$768$	−7.37388e29	−	3.71772e29i	−0.372738	−	0.187925i
$769$		−	2.32609e30i		−	1.15985i	−0.814671	−	0.579923i	$-0.803083\pi$
$769$		−	2.32609e30i		−	1.15985i	0.814671	−	0.579923i	$-0.196917\pi$
$770$	−7.46333e29	−	8.93194e29i	−0.367096	−	0.439333i
$771$	−1.36674e30	−	6.89078e29i	−0.663156	−	0.334347i
$772$	−2.40549e30			−1.15139
$773$	−3.42342e30			−1.61650			−0.808251	−	0.588839i	$-0.799585\pi$
$773$	−3.42342e30			−1.61650			−0.808251	+	0.588839i	$0.799585\pi$
$774$	3.55854e29	−	2.63201e29i	0.165765	−	0.122605i
$775$		−	3.22147e30i		−	1.48043i
$776$	−1.28592e30			−0.582997
$777$	−7.08358e29	−	3.03791e30i	−0.316834	−	1.35880i
$778$	5.48716e29			0.242138
$779$		−	2.53735e29i		−	0.110468i
$780$	1.95495e30	−	3.87752e30i	0.839733	−	1.66556i
$781$	2.71270e30			1.14965
$782$	7.45094e29			0.311559
$783$	−1.33783e30	+	2.29442e29i	−0.551954	+	0.0946618i
$784$	−3.54210e29	+	1.96130e30i	−0.144192	+	0.798409i
$785$		−	2.74317e30i		−	1.10185i
$786$	−5.43932e28	+	1.07886e29i	−0.0215580	+	0.0427589i
$787$		−	5.34698e29i		−	0.209110i	−0.994519	−	0.104555i	$-0.966658\pi$
$787$		−	5.34698e29i		−	0.209110i	0.994519	−	0.104555i	$-0.0333418\pi$
$788$		−	3.85754e30i		−	1.48863i
$789$	−6.67997e29	+	1.32493e30i	−0.254370	+	0.504528i
$790$			1.11783e30i			0.420040i
$791$	−1.05005e30	+	8.77401e29i	−0.389366	+	0.325346i
$792$	−1.21624e30	−	1.64438e30i	−0.445045	−	0.601711i
$793$	7.25040e29			0.261814
$794$	1.18973e30			0.423967
$795$	−1.09499e30	+	2.17185e30i	−0.385085	+	0.763793i
$796$		−	1.82430e30i		−	0.633155i
$797$	2.05810e30			0.704945			0.352472	−	0.935822i	$-0.385341\pi$
$797$	2.05810e30			0.704945			0.352472	+	0.935822i	$0.385341\pi$
$798$	−7.09808e28	−	3.04413e29i	−0.0239944	−	0.102904i
$799$	−1.72860e30			−0.576706
$800$		−	2.52259e30i		−	0.830620i
$801$	2.75909e30	+	3.73036e30i	0.896654	+	1.21230i
$802$	−8.54884e29			−0.274206
$803$	5.29300e30			1.67567
$804$	1.21562e30	+	6.12885e29i	0.379848	+	0.191510i
$805$	3.94243e30	−	3.29420e30i	1.21593	−	1.01600i
$806$			1.39145e30i			0.423593i
$807$	−5.09124e30	−	2.56688e30i	−1.52986	−	0.771317i
$808$			7.59796e29i			0.225361i
$809$		−	7.63848e29i		−	0.223639i	−0.993729	−	0.111820i	$-0.964332\pi$
$809$		−	7.63848e29i		−	0.223639i	0.993729	−	0.111820i	$-0.0356679\pi$
$810$	−1.24200e30	−	3.80296e29i	−0.358946	−	0.109908i
$811$		−	3.27107e29i		−	0.0933190i	−0.998911	−	0.0466595i	$-0.985142\pi$
$811$		−	3.27107e29i		−	0.0933190i	0.998911	−	0.0466595i	$-0.0148576\pi$
$812$	−1.42789e30	+	1.19311e30i	−0.402120	+	0.336003i
$813$	−2.42377e30	+	4.80741e30i	−0.673816	+	1.33647i
$814$	1.96564e30			0.539444
$815$	7.89751e30			2.13961
$816$	3.11094e30	+	1.56846e30i	0.832043	+	0.419495i
$817$		−	1.28383e30i		−	0.338983i
$818$	7.38622e29			0.192536
$819$	−5.08362e30	−	1.23275e30i	−1.30825	−	0.317245i
$820$	−1.44542e30			−0.367238
$821$		−	2.21419e30i		−	0.555408i	−0.960667	−	0.277704i	$-0.910427\pi$
$821$		−	2.21419e30i		−	0.555408i	0.960667	−	0.277704i	$-0.0895734\pi$
$822$	1.22655e30	+	6.18394e29i	0.303760	+	0.153148i
$823$	−6.59925e30			−1.61360			−0.806801	−	0.590823i	$-0.798803\pi$
$823$	−6.59925e30			−1.61360			−0.806801	+	0.590823i	$0.798803\pi$
$824$	1.94488e29			0.0469523
$825$	−3.43557e30	+	6.81424e30i	−0.818902	+	1.62424i
$826$	6.19334e29	−	5.17501e29i	0.145759	−	0.121793i
$827$		−	1.41248e30i		−	0.328228i	−0.986441	−	0.164114i	$-0.947524\pi$
$827$		−	1.41248e30i		−	0.328228i	0.986441	−	0.164114i	$-0.0524764\pi$
$828$	3.50854e30	−	2.59503e30i	0.805021	−	0.595420i
$829$		−	5.30162e30i		−	1.20112i	−0.799580	−	0.600559i	$-0.794945\pi$
$829$		−	5.30162e30i		−	1.20112i	0.799580	−	0.600559i	$-0.205055\pi$
$830$		−	3.25304e29i		−	0.0727729i
$831$	4.54986e30	+	2.29393e30i	1.00505	+	0.506720i
$832$		−	3.91756e30i		−	0.854517i
$833$	9.47660e29	−	5.24730e30i	0.204117	−	1.13022i
$834$	1.34312e30	+	6.77166e29i	0.285674	+	0.144030i
$835$	1.59920e30			0.335889
$836$	−2.86778e30			−0.594812
$837$	−5.97273e30	+	1.02434e30i	−1.22336	+	0.209811i
$838$		−	1.72780e30i		−	0.349488i
$839$	−5.61455e30			−1.12154			−0.560769	−	0.827972i	$-0.689495\pi$
$839$	−5.61455e30			−1.12154			−0.560769	+	0.827972i	$0.689495\pi$
$840$	−3.58733e30	+	8.36466e29i	−0.707682	+	0.165012i
$841$	3.52311e30			0.686386
$842$		−	1.10031e30i		−	0.211708i
$843$	1.16559e30	−	2.31188e30i	0.221491	−	0.439315i
$844$	4.25019e30			0.797651
$845$	6.48837e30			1.20265
$846$	5.59057e29	−	4.13496e29i	0.102345	−	0.0756978i
$847$	4.70203e30	+	5.62728e30i	0.850177	+	1.01747i
$848$			2.62433e30i			0.468664i
$849$	2.38617e30	−	4.73282e30i	0.420892	−	0.834813i
$850$			1.99327e30i			0.347270i
$851$			8.67602e30i			1.49300i
$852$	1.86825e30	−	3.70556e30i	0.317555	−	0.629851i
$853$		−	3.37502e30i		−	0.566645i	−0.959025	−	0.283323i	$-0.908563\pi$
$853$		−	3.37502e30i		−	0.566645i	0.959025	−	0.283323i	$-0.0914367\pi$
$854$	−1.90631e29	−	2.28143e29i	−0.0316145	−	0.0378355i
$855$	−3.02910e30	+	2.24042e30i	−0.496214	+	0.367016i
$856$	−3.67613e30			−0.594862
$857$	−3.90662e30			−0.624457			−0.312228	−	0.950007i	$-0.601075\pi$
$857$	−3.90662e30			−0.624457			−0.312228	+	0.950007i	$0.601075\pi$
$858$	1.48392e30	−	2.94327e30i	0.234312	−	0.464744i
$859$		−	4.65168e30i		−	0.725574i	−0.931872	−	0.362787i	$-0.881825\pi$
$859$		−	4.65168e30i		−	0.725574i	0.931872	−	0.362787i	$-0.118175\pi$
$860$	−7.31345e30			−1.12691
$861$	3.95384e29	+	1.69567e30i	0.0601847	+	0.258112i
$862$	2.89614e30			0.435506
$863$			7.36536e30i			1.09416i	0.837080	+	0.547080i	$0.184261\pi$
$863$			7.36536e30i			1.09416i	−0.837080	+	0.547080i	$0.815739\pi$
$864$	−4.67698e30	+	8.02117e29i	−0.686391	+	0.117718i
$865$	−4.39544e30			−0.637285
$866$	4.13043e29			0.0591639
$867$	−2.01323e30	−	1.01502e30i	−0.284900	−	0.143639i
$868$	−6.37479e30	+	5.32663e30i	−0.891269	+	0.744724i
$869$		−	1.23539e31i		−	1.70647i
$870$	−1.37549e30	−	6.93487e29i	−0.187718	−	0.0946425i
$871$			4.53869e30i			0.611984i
$872$			6.07900e30i			0.809858i
$873$	7.25636e30	−	5.36704e30i	0.955145	−	0.706456i
$874$			8.69379e29i			0.113068i
$875$	1.42391e30	+	1.70410e30i	0.182977	+	0.218983i
$876$	3.64532e30	−	7.23027e30i	0.462852	−	0.918039i
$877$	3.02934e30			0.380060			0.190030	−	0.981778i	$-0.439141\pi$
$877$	3.02934e30			0.380060			0.190030	+	0.981778i	$0.439141\pi$
$878$	−9.63524e28			−0.0119446
$879$	−4.81061e30	−	2.42539e30i	−0.589273	−	0.297097i
$880$			1.51374e31i			1.83224i
$881$	3.23996e30			0.387519			0.193759	−	0.981049i	$-0.437932\pi$
$881$	3.23996e30			0.387519			0.193759	+	0.981049i	$0.437932\pi$
$882$	9.48710e29	+	1.92374e30i	0.112128	+	0.227367i
$883$	6.38595e30			0.745827			0.372913	−	0.927866i	$-0.378359\pi$
$883$	6.38595e30			0.745827			0.372913	+	0.927866i	$0.378359\pi$
$884$			1.25352e31i			1.44672i
$885$	−8.68644e30	−	4.37949e30i	−0.990690	−	0.499481i
$886$	−3.15027e30			−0.355054
$887$	−8.04598e30			−0.896150			−0.448075	−	0.893996i	$-0.647890\pi$
$887$	−8.04598e30			−0.896150			−0.448075	+	0.893996i	$0.647890\pi$
$888$	2.80047e30	−	5.55455e30i	0.308244	−	0.611382i
$889$	−8.41072e30	−	1.00658e31i	−0.914881	−	1.09491i
$890$			5.26559e30i			0.566046i
$891$	1.37263e31	+	4.20293e30i	1.45827	+	0.446515i
$892$			2.15775e30i			0.226553i
$893$		−	2.01694e30i		−	0.209292i
$894$	−1.91370e30	−	9.64837e29i	−0.196259	−	0.0989487i
$895$			1.64879e31i			1.67118i
$896$	−6.56737e30	+	5.48755e30i	−0.657897	+	0.549724i
$897$	1.29911e31	+	6.54981e30i	1.28625	+	0.648497i
$898$	−1.61586e30			−0.158126
$899$	−7.18662e30			−0.695101
$900$	6.94219e30	+	9.38601e30i	0.663667	+	0.897293i
$901$		−	7.02117e30i		−	0.663437i
$902$	−1.09716e30			−0.102471
$903$	2.00055e30	+	8.57968e30i	0.184683	+	0.792045i
$904$	−2.72875e30			−0.248998
$905$		−	8.26802e30i		−	0.745747i
$906$	−2.31891e30	+	4.59942e30i	−0.206747	+	0.410069i
$907$	7.97062e30			0.702450			0.351225	−	0.936291i	$-0.385765\pi$
$907$	7.97062e30			0.702450			0.351225	+	0.936291i	$0.385765\pi$
$908$	5.96822e30			0.519928
$909$	−3.17116e30	−	4.28748e30i	−0.273084	−	0.369217i
$910$	−3.80643e30	−	4.55545e30i	−0.324028	−	0.387790i
$911$			4.16999e29i			0.0350907i	0.999846	+	0.0175453i	$0.00558514\pi$
$911$			4.16999e29i			0.0350907i	−0.999846	+	0.0175453i	$0.994415\pi$
$912$	−1.83008e30	+	3.62986e30i	−0.152239	+	0.301956i
$913$			3.59517e30i			0.295649i
$914$		−	1.38733e30i		−	0.112783i
$915$	−1.61326e30	+	3.19981e30i	−0.129653	+	0.257159i
$916$			1.77679e31i			1.41167i
$917$	−1.54199e30	−	1.84542e30i	−0.121117	−	0.144950i
$918$	3.69560e30	−	6.33806e29i	0.286970	−	0.0492162i
$919$	4.12496e30			0.316670			0.158335	−	0.987385i	$-0.449387\pi$
$919$	4.12496e30			0.316670			0.158335	+	0.987385i	$0.449387\pi$
$920$	1.02451e31			0.777578
$921$	−1.75432e30	+	3.47959e30i	−0.131639	+	0.261097i
$922$		−	1.39546e30i		−	0.103524i
$923$	1.38352e31			1.01477
$924$	1.91649e31	−	4.46874e30i	1.38980	−	0.324063i
$925$	−2.32100e31			−1.66413
$926$			1.82564e30i			0.129420i
$927$	−1.09748e30	+	8.11732e29i	−0.0769237	+	0.0568952i
$928$	−5.62753e30			−0.389999
$929$	−3.85340e30			−0.264046			−0.132023	−	0.991247i	$-0.542147\pi$
$929$	−3.85340e30			−0.264046			−0.132023	+	0.991247i	$0.542147\pi$
$930$	−6.14086e30	−	3.09607e30i	−0.416062	−	0.209768i
$931$	6.12256e30	+	1.10573e30i	0.410168	+	0.0740762i
$932$			1.64655e30i			0.109071i
$933$	−2.61591e31	−	1.31888e31i	−1.71343	−	0.863867i
$934$			6.08747e30i			0.394271i
$935$		−	4.04988e31i		−	2.59370i
$936$	−6.20302e30	−	8.38662e30i	−0.392832	−	0.531118i
$937$			1.95142e30i			0.122204i	0.998132	+	0.0611020i	$0.0194615\pi$
$937$			1.95142e30i			0.122204i	−0.998132	+	0.0611020i	$0.980539\pi$
$938$	1.42816e30	−	1.19333e30i	0.0884394	−	0.0738980i
$939$	3.24334e30	−	6.43297e30i	0.198611	−	0.393934i
$940$	−1.14896e31			−0.695767
$941$	1.60469e31			0.960947			0.480474	−	0.877009i	$-0.340465\pi$
$941$	1.60469e31			0.960947			0.480474	+	0.877009i	$0.340465\pi$
$942$	−2.84434e30	−	1.43405e30i	−0.168441	−	0.0849236i
$943$		−	4.84269e30i		−	0.283605i
$944$	−1.04961e31			−0.607888
$945$	1.67519e31	−	1.96925e31i	0.959466	−	1.12789i
$946$	−5.55135e30			−0.314443
$947$		−	4.95459e30i		−	0.277544i	−0.990324	−	0.138772i	$-0.955684\pi$
$947$		−	4.95459e30i		−	0.277544i	0.990324	−	0.138772i	$-0.0443156\pi$
$948$	−1.68755e31	−	8.50822e30i	−0.934910	−	0.471358i
$949$	2.69952e31			1.47908
$950$	−2.32575e30			−0.126028
$951$	5.25276e29	−	1.04185e30i	0.0281509	−	0.0558356i
$952$	8.15964e30	−	6.81801e30i	0.432497	−	0.361385i
$953$			1.14242e31i			0.598895i	0.954113	+	0.299447i	$0.0968023\pi$
$953$			1.14242e31i			0.598895i	−0.954113	+	0.299447i	$0.903198\pi$
$954$	1.67952e30	+	2.27076e30i	0.0870820	+	0.117737i
$955$		−	3.04491e31i		−	1.56149i
$956$		−	2.29466e31i		−	1.16389i
$957$	1.52015e31	+	7.66424e30i	0.762627	+	0.384498i
$958$			6.13273e30i			0.304310i
$959$	−2.09805e31	+	1.75308e31i	−1.02972	+	0.860413i
$960$	1.72893e31	+	8.71683e30i	0.839324	+	0.423166i
$961$	−1.12591e31			−0.540640
$962$	1.00251e31			0.476157
$963$	2.07442e31	−	1.53430e31i	0.974585	−	0.720834i
$964$			1.08870e31i			0.505942i
$965$	3.96369e31			1.82206
$966$	−1.35472e30	−	5.80993e30i	−0.0616011	−	0.264187i
$967$	−3.41790e31			−1.53738			−0.768690	−	0.639622i	$-0.779091\pi$
$967$	−3.41790e31			−1.53738			−0.768690	+	0.639622i	$0.779091\pi$
$968$			1.46235e31i			0.650668i
$969$	4.89624e30	−	9.71139e30i	0.215508	−	0.427446i
$970$	1.02427e31			0.445977
$971$	−3.79278e31			−1.63364			−0.816818	−	0.576896i	$-0.804264\pi$
$971$	−3.79278e31			−1.63364			−0.816818	+	0.576896i	$0.804264\pi$
$972$	1.51946e31	−	1.58556e31i	0.647430	−	0.675595i
$973$	−2.29745e31	+	1.91970e31i	−0.968413	+	0.809185i
$974$		−	6.20631e30i		−	0.258800i
$975$	−1.75220e31	+	3.47538e31i	−0.722828	+	1.43369i
$976$			3.86644e30i			0.157793i
$977$			2.50257e31i			1.01040i	0.863003	+	0.505200i	$0.168581\pi$
$977$			2.50257e31i			1.01040i	−0.863003	+	0.505200i	$0.831419\pi$
$978$	4.12857e30	−	8.18877e30i	0.164908	−	0.327085i
$979$		−	5.81939e31i		−	2.29964i
$980$	6.29888e30	−	3.48776e31i	0.246258	−	1.36356i
$981$	−2.53719e31	−	3.43034e31i	−0.981360	−	1.32682i
$982$	1.00262e31			0.383678
$983$	−3.40644e30			−0.128970			−0.0644851	−	0.997919i	$-0.520540\pi$
$983$	−3.40644e30			−0.128970			−0.0644851	+	0.997919i	$0.520540\pi$
$984$	−1.56314e30	+	3.10038e30i	−0.0585529	+	0.116136i
$985$			6.35632e31i			2.35573i
$986$	4.44668e30			0.163053
$987$	3.14292e30	+	1.34789e31i	0.114026	+	0.489018i
$988$	−1.46262e31			−0.525028
$989$		−	2.45028e31i		−	0.870273i
$990$	9.68766e30	+	1.30979e31i	0.340447	+	0.460292i
$991$	1.23866e31			0.430702			0.215351	−	0.976537i	$-0.430910\pi$
$991$	1.23866e31			0.430702			0.215351	+	0.976537i	$0.430910\pi$
$992$	−2.51240e31			−0.864404
$993$	2.44352e31	+	1.23196e31i	0.831859	+	0.419402i
$994$	−3.63763e30	−	4.35343e30i	−0.122535	−	0.146647i
$995$			3.00602e31i			1.00196i
$996$	4.91103e30	+	2.47602e30i	0.161975	+	0.0816639i
$997$			1.86025e31i			0.607116i	0.952813	+	0.303558i	$0.0981745\pi$
$997$			1.86025e31i			0.607116i	−0.952813	+	0.303558i	$0.901825\pi$
$998$			7.31126e30i			0.236114i
$999$	7.38016e30	+	4.30322e31i	0.235846	+	1.37517i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.22.c.b.20.7	✓	52
3.2	odd	2	inner	21.22.c.b.20.46	yes	52
7.6	odd	2	inner	21.22.c.b.20.45	yes	52
21.20	even	2	inner	21.22.c.b.20.8	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.22.c.b.20.7	✓	52	1.1	even	1	trivial
21.22.c.b.20.8	yes	52	21.20	even	2	inner
21.22.c.b.20.45	yes	52	7.6	odd	2	inner
21.22.c.b.20.46	yes	52	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	21.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-367.125i q^{2} +(-91325.3 - 46043.9i) q^{3} +1.96237e6 q^{4} -3.23352e7 q^{5} +(-1.69039e7 + 3.35278e7i) q^{6} +(-4.79207e8 - 5.73504e8i) q^{7} -1.49035e9i q^{8} +(6.22027e9 + 8.40995e9i) q^{9} +O(q^{10})\)	\(q-367.125i q^{2} +(-91325.3 - 46043.9i) q^{3} +1.96237e6 q^{4} -3.23352e7 q^{5} +(-1.69039e7 + 3.35278e7i) q^{6} +(-4.79207e8 - 5.73504e8i) q^{7} -1.49035e9i q^{8} +(6.22027e9 + 8.40995e9i) q^{9} +1.18711e10i q^{10} -1.31196e11i q^{11} +(-1.79214e11 - 9.03553e10i) q^{12} -6.69122e11i q^{13} +(-2.10547e11 + 1.75929e11i) q^{14} +(2.95302e12 + 1.48884e12i) q^{15} +3.56825e12 q^{16} -9.54655e12 q^{17} +(3.08750e12 - 2.28361e12i) q^{18} -1.11389e13i q^{19} -6.34537e13 q^{20} +(1.73574e13 + 7.44400e13i) q^{21} -4.81652e13 q^{22} -2.12594e14i q^{23} +(-6.86216e13 + 1.36107e14i) q^{24} +5.68730e14 q^{25} -2.45651e14 q^{26} +(-1.80841e14 - 1.05445e15i) q^{27} +(-9.40382e14 - 1.12543e15i) q^{28} -1.26875e15i q^{29} +(5.46590e14 - 1.08413e15i) q^{30} -5.66433e15i q^{31} -4.43548e15i q^{32} +(-6.04077e15 + 1.19815e16i) q^{33} +3.50477e15i q^{34} +(1.54953e16 + 1.85444e16i) q^{35} +(1.22065e16 + 1.65034e16i) q^{36} -4.08103e16 q^{37} -4.08938e15 q^{38} +(-3.08090e16 + 6.11077e16i) q^{39} +4.81909e16i q^{40} +2.27791e16 q^{41} +(2.73288e16 - 6.37231e15i) q^{42} +1.15256e17 q^{43} -2.57455e17i q^{44} +(-2.01134e17 - 2.71938e17i) q^{45} -7.80486e16 q^{46} +1.81071e17 q^{47} +(-3.25871e17 - 1.64296e17i) q^{48} +(-9.92673e16 + 5.49654e17i) q^{49} -2.08795e17i q^{50} +(8.71841e17 + 4.39560e17i) q^{51} -1.31307e18i q^{52} +7.35468e17i q^{53} +(-3.87113e17 + 6.63911e16i) q^{54} +4.24225e18i q^{55} +(-8.54722e17 + 7.14187e17i) q^{56} +(-5.12881e17 + 1.01727e18i) q^{57} -4.65790e17 q^{58} -2.94154e18 q^{59} +(5.79493e18 + 2.92166e18i) q^{60} +1.08357e18i q^{61} -2.07951e18 q^{62} +(1.84234e18 - 7.59745e18i) q^{63} +5.85478e18 q^{64} +2.16362e19i q^{65} +(4.39870e18 + 2.21772e18i) q^{66} -6.78306e18 q^{67} -1.87339e19 q^{68} +(-9.78867e18 + 1.94152e19i) q^{69} +(6.80810e18 - 5.68869e18i) q^{70} +2.06767e19i q^{71} +(1.25338e19 - 9.27038e18i) q^{72} +4.03443e19i q^{73} +1.49825e19i q^{74} +(-5.19394e19 - 2.61866e19i) q^{75} -2.18587e19i q^{76} +(-7.52413e19 + 6.28700e19i) q^{77} +(2.24342e19 + 1.13107e19i) q^{78} +9.41640e19 q^{79} -1.15380e20 q^{80} +(-3.20355e19 + 1.04624e20i) q^{81} -8.36275e18i q^{82} -2.74031e19 q^{83} +(3.40616e19 + 1.46079e20i) q^{84} +3.08690e20 q^{85} -4.23135e19i q^{86} +(-5.84183e19 + 1.15869e20i) q^{87} -1.95528e20 q^{88} +4.43565e20 q^{89} +(-9.98350e19 + 7.38412e19i) q^{90} +(-3.83744e20 + 3.20648e20i) q^{91} -4.17189e20i q^{92} +(-2.60808e20 + 5.17296e20i) q^{93} -6.64757e19i q^{94} +3.60180e20i q^{95} +(-2.04227e20 + 4.05072e20i) q^{96} -8.62831e20i q^{97} +(2.01792e20 + 3.64435e19i) q^{98} +(1.10335e21 - 8.16073e20i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 58720260 q^{4} + 1422287188 q^{7} + 10150644696 q^{9}+O(q^{10}) \) 52 * q - 58720260 * q^4 + 1422287188 * q^7 + 10150644696 * q^9	\( 52 q - 58720260 q^{4} + 1422287188 q^{7} + 10150644696 q^{9} - 687153165468 q^{15} + 36241782390404 q^{16} + 36759093002772 q^{18} + 79412641656180 q^{21} + 228880341648112 q^{22} + 45\!\cdots\!12 q^{25}+ \cdots + 15\!\cdots\!28 q^{99}+O(q^{100}) \) 52 * q - 58720260 * q^4 + 1422287188 * q^7 + 10150644696 * q^9 - 687153165468 * q^15 + 36241782390404 * q^16 + 36759093002772 * q^18 + 79412641656180 * q^21 + 228880341648112 * q^22 + 4502168959229812 * q^25 - 328465100861772 * q^28 - 2422487119598196 * q^30 + 94669723666911312 * q^36 - 111253244635261912 * q^37 - 198389110134084780 * q^39 - 125754675449474820 * q^42 + 808208758088766656 * q^43 - 1124214920076830456 * q^46 + 760563680048831596 * q^49 + 4341973540932052200 * q^51 - 13080454499124088812 * q^57 - 10814528487339424568 * q^58 + 13643758017961015644 * q^60 - 38182310822257441896 * q^63 - 30480555033993680900 * q^64 - 25547251957658589040 * q^67 + 73727169165159410040 * q^70 + 39846964674222889428 * q^72 + 45848199464273536260 * q^78 + 199210197493083963080 * q^79 + 235499606962845306588 * q^81 - 373919224753720758924 * q^84 - 570842672309470848672 * q^85 - 1060053674241923431168 * q^88 - 923077800435233893128 * q^91 - 2832166256981601869904 * q^93 + 1525182290356701596928 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more