LMFDB - Embedded newform 21.22.c.b.20.34

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			20.34
Character	$\chi$	$=$	21.20
Dual form			21.22.c.b.20.33

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1077.74i q^{2} +(-64855.1 - 79083.3i) q^{3} +935630. q^{4} +7.14030e6 q^{5} +(8.52312e7 - 6.98969e7i) q^{6} +(-3.76236e8 + 6.45749e8i) q^{7} +3.26855e9i q^{8} +(-2.04799e9 + 1.02579e10i) q^{9} +O(q^{10})$	\(q+1077.74i q^{2} +(-64855.1 - 79083.3i) q^{3} +935630. q^{4} +7.14030e6 q^{5} +(8.52312e7 - 6.98969e7i) q^{6} +(-3.76236e8 + 6.45749e8i) q^{7} +3.26855e9i q^{8} +(-2.04799e9 + 1.02579e10i) q^{9} +7.69538e9i q^{10} +6.21657e8i q^{11} +(-6.06803e10 - 7.39927e10i) q^{12} -3.37753e11i q^{13} +(-6.95949e11 - 4.05485e11i) q^{14} +(-4.63085e11 - 5.64679e11i) q^{15} -1.56049e12 q^{16} +6.87345e12 q^{17} +(-1.10554e13 - 2.20720e12i) q^{18} +1.17334e13i q^{19} +6.68068e12 q^{20} +(7.54688e13 - 1.21261e13i) q^{21} -6.69984e11 q^{22} -8.43774e13i q^{23} +(2.58488e14 - 2.11982e14i) q^{24} -4.25853e14 q^{25} +3.64010e14 q^{26} +(9.44052e14 - 5.03316e14i) q^{27} +(-3.52018e14 + 6.04182e14i) q^{28} +6.05365e14i q^{29} +(6.08576e14 - 4.99085e14i) q^{30} +1.22561e15i q^{31} +5.17285e15i q^{32} +(4.91627e13 - 4.03176e13i) q^{33} +7.40779e15i q^{34} +(-2.68644e15 + 4.61084e15i) q^{35} +(-1.91616e15 + 9.59760e15i) q^{36} -3.62083e16 q^{37} -1.26456e16 q^{38} +(-2.67107e16 + 2.19050e16i) q^{39} +2.33384e16i q^{40} +1.58503e16 q^{41} +(1.30688e16 + 8.13357e16i) q^{42} -2.84588e16 q^{43} +5.81640e14i q^{44} +(-1.46233e16 + 7.32446e16i) q^{45} +9.09368e16 q^{46} +2.36994e17 q^{47} +(1.01205e17 + 1.23408e17i) q^{48} +(-2.75438e17 - 4.85909e17i) q^{49} -4.58959e17i q^{50} +(-4.45778e17 - 5.43575e17i) q^{51} -3.16012e17i q^{52} -6.88418e17i q^{53} +(5.42443e17 + 1.01744e18i) q^{54} +4.43881e15i q^{55} +(-2.11066e18 - 1.22975e18i) q^{56} +(9.27917e17 - 7.60972e17i) q^{57} -6.52426e17 q^{58} -4.19426e18 q^{59} +(-4.33276e17 - 5.28330e17i) q^{60} +5.56709e18i q^{61} -1.32089e18 q^{62} +(-5.85351e18 - 5.18189e18i) q^{63} -8.84756e18 q^{64} -2.41166e18i q^{65} +(4.34519e16 + 5.29845e16i) q^{66} -1.57639e19 q^{67} +6.43100e18 q^{68} +(-6.67284e18 + 5.47230e18i) q^{69} +(-4.96929e18 - 2.89528e18i) q^{70} -7.43701e18i q^{71} +(-3.35285e19 - 6.69396e18i) q^{72} +4.27354e19i q^{73} -3.90231e19i q^{74} +(2.76187e19 + 3.36779e19i) q^{75} +1.09781e19i q^{76} +(-4.01434e17 - 2.33890e17i) q^{77} +(-2.36079e19 - 2.87871e19i) q^{78} -1.56226e20 q^{79} -1.11423e19 q^{80} +(-1.01030e20 - 4.20162e19i) q^{81} +1.70825e19i q^{82} -1.29172e20 q^{83} +(7.06109e19 - 1.13455e19i) q^{84} +4.90785e19 q^{85} -3.06712e19i q^{86} +(4.78743e19 - 3.92610e19i) q^{87} -2.03191e18 q^{88} -4.94133e20 q^{89} +(-7.89385e19 - 1.57601e19i) q^{90} +(2.18104e20 + 1.27075e20i) q^{91} -7.89460e19i q^{92} +(9.69253e19 - 7.94870e19i) q^{93} +2.55418e20i q^{94} +8.37801e19i q^{95} +(4.09086e20 - 3.35485e20i) q^{96} -5.62341e19i q^{97} +(5.23683e20 - 2.96851e20i) q^{98} +(-6.37690e18 - 1.27315e18i) 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 $

$2$			1077.74i			0.744216i	0.928189	+	0.372108i	$0.121365\pi$
$2$			1077.74i			0.744216i	−0.928189	+	0.372108i	$0.878635\pi$
$3$	−64855.1	−	79083.3i	−0.634119	−	0.773235i
$3$	−64855.1	−	79083.3i	−0.634119	−	0.773235i
$4$	935630.			0.446143
$5$	7.14030e6			0.326988			0.163494	−	0.986544i	$-0.447724\pi$
$5$	7.14030e6			0.326988			0.163494	+	0.986544i	$0.447724\pi$
$6$	8.52312e7	−	6.98969e7i	0.575454	−	0.471921i
$7$	−3.76236e8	+	6.45749e8i	−0.503421	+	0.864041i
$7$	−3.76236e8	+	6.45749e8i	−0.503421	+	0.864041i
$8$			3.26855e9i			1.07624i
$9$	−2.04799e9	+	1.02579e10i	−0.195786	+	0.980647i
$10$			7.69538e9i			0.243349i
$11$			6.21657e8i			0.00722649i	0.999993	+	0.00361324i	$0.00115013\pi$
$11$			6.21657e8i			0.00722649i	−0.999993	+	0.00361324i	$0.998850\pi$
$12$	−6.06803e10	−	7.39927e10i	−0.282908	−	0.344974i
$13$		−	3.37753e11i		−	0.679508i	−0.940514	−	0.339754i	$-0.889656\pi$
$13$		−	3.37753e11i		−	0.679508i	0.940514	−	0.339754i	$-0.110344\pi$
$14$	−6.95949e11	−	4.05485e11i	−0.643033	−	0.374654i
$15$	−4.63085e11	−	5.64679e11i	−0.207349	−	0.252838i
$16$	−1.56049e12			−0.354813
$17$	6.87345e12			0.826915			0.413458	−	0.910523i	$-0.364321\pi$
$17$	6.87345e12			0.826915			0.413458	+	0.910523i	$0.364321\pi$
$18$	−1.10554e13	−	2.20720e12i	−0.729813	−	0.145707i
$19$			1.17334e13i			0.439048i	0.975607	+	0.219524i	$0.0704504\pi$
$19$			1.17334e13i			0.439048i	−0.975607	+	0.219524i	$0.929550\pi$
$20$	6.68068e12			0.145883
$21$	7.54688e13	−	1.21261e13i	0.987336	−	0.158642i
$22$	−6.69984e11			−0.00537807
$23$		−	8.43774e13i		−	0.424701i	−0.977194	−	0.212351i	$-0.931888\pi$
$23$		−	8.43774e13i		−	0.424701i	0.977194	−	0.212351i	$-0.0681119\pi$
$24$	2.58488e14	−	2.11982e14i	0.832189	−	0.682466i
$25$	−4.25853e14			−0.893079
$26$	3.64010e14			0.505700
$27$	9.44052e14	−	5.03316e14i	0.882422	−	0.470458i
$28$	−3.52018e14	+	6.04182e14i	−0.224598	+	0.385486i
$29$			6.05365e14i			0.267201i	0.991035	+	0.133601i	$0.0426539\pi$
$29$			6.05365e14i			0.267201i	−0.991035	+	0.133601i	$0.957346\pi$
$30$	6.08576e14	−	4.99085e14i	0.188166	−	0.154312i
$31$			1.22561e15i			0.268568i	0.990943	+	0.134284i	$0.0428734\pi$
$31$			1.22561e15i			0.268568i	−0.990943	+	0.134284i	$0.957127\pi$
$32$			5.17285e15i			0.812185i
$33$	4.91627e13	−	4.03176e13i	0.00558778	−	0.00458245i
$34$			7.40779e15i			0.615403i
$35$	−2.68644e15	+	4.61084e15i	−0.164612	+	0.282531i
$36$	−1.91616e15	+	9.59760e15i	−0.0873485	+	0.437509i
$37$	−3.62083e16			−1.23791			−0.618957	−	0.785425i	$-0.712444\pi$
$37$	−3.62083e16			−1.23791			−0.618957	+	0.785425i	$0.712444\pi$
$38$	−1.26456e16			−0.326746
$39$	−2.67107e16	+	2.19050e16i	−0.525420	+	0.430889i
$40$			2.33384e16i			0.351918i
$41$	1.58503e16			0.184420			0.0922100	−	0.995740i	$-0.470607\pi$
$41$	1.58503e16			0.184420			0.0922100	+	0.995740i	$0.470607\pi$
$42$	1.30688e16	+	8.13357e16i	0.118064	+	0.734791i
$43$	−2.84588e16			−0.200816			−0.100408	−	0.994946i	$-0.532015\pi$
$43$	−2.84588e16			−0.200816			−0.100408	+	0.994946i	$0.532015\pi$
$44$			5.81640e14i			0.00322405i
$45$	−1.46233e16	+	7.32446e16i	−0.0640196	+	0.320659i
$46$	9.09368e16			0.316069
$47$	2.36994e17			0.657219			0.328609	−	0.944466i	$-0.393420\pi$
$47$	2.36994e17			0.657219			0.328609	+	0.944466i	$0.393420\pi$
$48$	1.01205e17	+	1.23408e17i	0.224994	+	0.274354i
$49$	−2.75438e17	−	4.85909e17i	−0.493134	−	0.869953i
$50$		−	4.58959e17i		−	0.664643i
$51$	−4.45778e17	−	5.43575e17i	−0.524363	−	0.639400i
$52$		−	3.16012e17i		−	0.303158i
$53$		−	6.88418e17i		−	0.540699i	−0.962762	−	0.270350i	$-0.912861\pi$
$53$		−	6.88418e17i		−	0.540699i	0.962762	−	0.270350i	$-0.0871393\pi$
$54$	5.42443e17	+	1.01744e18i	0.350122	+	0.656713i
$55$			4.43881e15i			0.00236297i
$56$	−2.11066e18	−	1.22975e18i	−0.929918	−	0.541803i
$57$	9.27917e17	−	7.60972e17i	0.339487	−	0.278408i
$58$	−6.52426e17			−0.198855
$59$	−4.19426e18			−1.06834			−0.534170	−	0.845377i	$-0.679376\pi$
$59$	−4.19426e18			−1.06834			−0.534170	+	0.845377i	$0.679376\pi$
$60$	−4.33276e17	−	5.28330e17i	−0.0925074	−	0.112802i
$61$			5.56709e18i			0.999229i	0.866248	+	0.499615i	$0.166525\pi$
$61$			5.56709e18i			0.999229i	−0.866248	+	0.499615i	$0.833475\pi$
$62$	−1.32089e18			−0.199873
$63$	−5.85351e18	−	5.18189e18i	−0.748756	−	0.662845i
$64$	−8.84756e18			−0.959254
$65$		−	2.41166e18i		−	0.222191i
$66$	4.34519e16	+	5.29845e16i	0.00341033	+	0.00415851i
$67$	−1.57639e19			−1.05652			−0.528261	−	0.849082i	$-0.677156\pi$
$67$	−1.57639e19			−1.05652			−0.528261	+	0.849082i	$0.677156\pi$
$68$	6.43100e18			0.368922
$69$	−6.67284e18	+	5.47230e18i	−0.328394	+	0.269311i
$70$	−4.96929e18	−	2.89528e18i	−0.210264	−	0.122507i
$71$		−	7.43701e18i		−	0.271135i	−0.990768	−	0.135567i	$-0.956714\pi$
$71$		−	7.43701e18i		−	0.271135i	0.990768	−	0.135567i	$-0.0432857\pi$
$72$	−3.35285e19	−	6.69396e18i	−1.05541	−	0.210713i
$73$			4.27354e19i			1.16385i	0.813242	+	0.581926i	$0.197701\pi$
$73$			4.27354e19i			1.16385i	−0.813242	+	0.581926i	$0.802299\pi$
$74$		−	3.90231e19i		−	0.921275i
$75$	2.76187e19	+	3.36779e19i	0.566318	+	0.690560i
$76$			1.09781e19i			0.195878i
$77$	−4.01434e17	−	2.33890e17i	−0.00624398	−	0.00363797i
$78$	−2.36079e19	−	2.87871e19i	−0.320674	−	0.391026i
$79$	−1.56226e20			−1.85639			−0.928196	−	0.372092i	$-0.878641\pi$
$79$	−1.56226e20			−1.85639			−0.928196	+	0.372092i	$0.878641\pi$
$80$	−1.11423e19			−0.116020
$81$	−1.01030e20	−	4.20162e19i	−0.923336	−	0.383994i
$82$			1.70825e19i			0.137248i
$83$	−1.29172e20			−0.913793			−0.456897	−	0.889520i	$-0.651039\pi$
$83$	−1.29172e20			−0.913793			−0.456897	+	0.889520i	$0.651039\pi$
$84$	7.06109e19	−	1.13455e19i	0.440493	−	0.0707770i
$85$	4.90785e19			0.270391
$86$		−	3.06712e19i		−	0.149450i
$87$	4.78743e19	−	3.92610e19i	0.206609	−	0.169437i
$88$	−2.03191e18			−0.00777745
$89$	−4.94133e20			−1.67977			−0.839883	−	0.542767i	$-0.817377\pi$
$89$	−4.94133e20			−1.67977			−0.839883	+	0.542767i	$0.817377\pi$
$90$	−7.89385e19	−	1.57601e19i	−0.238640	−	0.0476444i
$91$	2.18104e20	+	1.27075e20i	0.587123	+	0.342079i
$92$		−	7.89460e19i		−	0.189478i
$93$	9.69253e19	−	7.94870e19i	0.207666	−	0.170304i
$94$			2.55418e20i			0.489112i
$95$			8.37801e19i			0.143563i
$96$	4.09086e20	−	3.35485e20i	0.628010	−	0.515022i
$97$		−	5.62341e19i		−	0.0774277i	−0.999250	−	0.0387139i	$-0.987674\pi$
$97$		−	5.62341e19i		−	0.0774277i	0.999250	−	0.0387139i	$-0.0123261\pi$
$98$	5.23683e20	−	2.96851e20i	0.647433	−	0.366998i
$99$	−6.37690e18	−	1.27315e18i	−0.00708663	−	0.00141485i
$100$	−3.98441e20			−0.398441
$101$	−7.78423e20			−0.701199			−0.350599	−	0.936526i	$-0.614022\pi$
$101$	−7.78423e20			−0.701199			−0.350599	+	0.936526i	$0.614022\pi$
$102$	5.85832e20	−	4.80433e20i	0.475852	−	0.390239i
$103$		−	1.44000e21i		−	1.05578i	−0.849314	−	0.527888i	$-0.822984\pi$
$103$		−	1.44000e21i		−	1.05578i	0.849314	−	0.527888i	$-0.177016\pi$
$104$	1.10396e21			0.731315
$105$	5.38870e20	−	8.65839e19i	0.322847	−	0.0518740i
$106$	7.41936e20			0.402397
$107$			2.60763e21i			1.28149i	0.767752	+	0.640747i	$0.221375\pi$
$107$			2.60763e21i			1.28149i	−0.767752	+	0.640747i	$0.778625\pi$
$108$	8.83283e20	−	4.70917e20i	0.393687	−	0.209892i
$109$	1.47050e21			0.594957			0.297479	−	0.954728i	$-0.403854\pi$
$109$	1.47050e21			0.594957			0.297479	+	0.954728i	$0.403854\pi$
$110$	−4.78389e18			−0.00175856
$111$	2.34829e21	+	2.86347e21i	0.784985	+	0.957199i
$112$	5.87112e20	−	1.00768e21i	0.178621	−	0.306573i
$113$			6.05155e21i			1.67704i	0.544873	+	0.838519i	$0.316578\pi$
$113$			6.05155e21i			1.67704i	−0.544873	+	0.838519i	$0.683422\pi$
$114$	8.20129e20	+	1.00005e21i	0.207196	+	0.252652i
$115$		−	6.02480e20i		−	0.138872i
$116$			5.66397e20i			0.119210i
$117$	3.46464e21	+	6.91716e20i	0.666357	+	0.133038i
$118$		−	4.52032e21i		−	0.795076i
$119$	−2.58604e21	+	4.43852e21i	−0.416287	+	0.714489i
$120$	1.84568e21	−	1.51361e21i	0.272115	−	0.223158i
$121$	7.39986e21			0.999948
$122$	−5.99987e21			−0.743642
$123$	−1.02798e21	−	1.25350e21i	−0.116944	−	0.142600i
$124$			1.14672e21i			0.119820i
$125$	−6.44548e21			−0.619014
$126$	5.58472e21	−	6.30856e21i	0.493300	−	0.557236i
$127$	−7.21609e21			−0.586628			−0.293314	−	0.956016i	$-0.594758\pi$
$127$	−7.21609e21			−0.586628			−0.293314	+	0.956016i	$0.594758\pi$
$128$			1.31288e21i			0.0982926i
$129$	1.84570e21	+	2.25062e21i	0.127341	+	0.155278i
$130$	2.59914e21			0.165358
$131$	1.65885e22			0.973778			0.486889	−	0.873464i	$-0.338132\pi$
$131$	1.65885e22			0.973778			0.486889	+	0.873464i	$0.338132\pi$
$132$	4.59980e19	−	3.77223e19i	0.00249295	−	0.00204443i
$133$	−7.57684e21	−	4.41454e21i	−0.379355	−	0.221026i
$134$		−	1.69894e22i		−	0.786281i
$135$	6.74082e21	−	3.59383e21i	0.288541	−	0.153834i
$136$			2.24662e22i			0.889961i
$137$		−	4.04119e22i		−	1.48232i	−0.671327	−	0.741161i	$-0.734275\pi$
$137$		−	4.04119e22i		−	1.48232i	0.671327	−	0.741161i	$-0.265725\pi$
$138$	−5.89771e21	−	7.19159e21i	−0.200426	−	0.244396i
$139$		−	7.25523e21i		−	0.228558i	−0.993449	−	0.114279i	$-0.963544\pi$
$139$		−	7.25523e21i		−	0.228558i	0.993449	−	0.114279i	$-0.0364557\pi$
$140$	−2.51351e21	+	4.31404e21i	−0.0734407	+	0.126049i
$141$	−1.53703e22	−	1.87423e22i	−0.416755	−	0.508185i
$142$	8.01515e21			0.201783
$143$	2.09967e20			0.00491046
$144$	3.19586e21	−	1.60073e22i	0.0694675	−	0.347947i
$145$			4.32249e21i			0.0873715i
$146$	−4.60576e22			−0.866157
$147$	−2.05637e22	+	5.32962e22i	−0.359973	+	0.932963i
$148$	−3.38776e22			−0.552286
$149$			5.74877e22i			0.873210i	0.899653	+	0.436605i	$0.143819\pi$
$149$			5.74877e22i			0.873210i	−0.899653	+	0.436605i	$0.856181\pi$
$150$	−3.62960e22	+	2.97658e22i	−0.513926	+	0.421463i
$151$	−1.09733e23			−1.44903			−0.724515	−	0.689259i	$-0.757936\pi$
$151$	−1.09733e23			−1.44903			−0.724515	+	0.689259i	$0.757936\pi$
$152$	−3.83512e22			−0.472522
$153$	−1.40768e22	+	7.05072e22i	−0.161898	+	0.810912i
$154$	2.52072e20	−	4.32642e20i	0.00270743	−	0.00464687i
$155$			8.75122e21i			0.0878184i
$156$	−2.49913e22	+	2.04950e22i	−0.234412	+	0.192238i
$157$		−	7.99062e21i		−	0.0700865i	−0.999386	−	0.0350432i	$-0.988843\pi$
$157$		−	7.99062e21i		−	0.0700865i	0.999386	−	0.0350432i	$-0.0111569\pi$
$158$		−	1.68371e23i		−	1.38156i
$159$	−5.44424e22	+	4.46474e22i	−0.418088	+	0.342868i
$160$			3.69357e22i			0.265574i
$161$	5.44866e22	+	3.17458e22i	0.366959	+	0.213804i
$162$	4.52825e22	−	1.08885e23i	0.285774	−	0.687161i
$163$	−1.71233e23			−1.01302			−0.506510	−	0.862234i	$-0.669065\pi$
$163$	−1.71233e23			−1.01302			−0.506510	+	0.862234i	$0.669065\pi$
$164$	1.48300e22			0.0822777
$165$	3.51036e20	−	2.87880e20i	0.00182713	−	0.00149841i
$166$		−	1.39214e23i		−	0.680059i
$167$	3.54755e23			1.62707			0.813533	−	0.581519i	$-0.197541\pi$
$167$	3.54755e23			1.62707			0.813533	+	0.581519i	$0.197541\pi$
$168$	3.96347e22	+	2.46674e23i	0.170737	+	1.06261i
$169$	1.32987e23			0.538269
$170$			5.28938e22i			0.201229i
$171$	−1.20360e23	−	2.40299e22i	−0.430551	−	0.0859594i
$172$	−2.66269e22			−0.0895926
$173$	1.34777e23			0.426709			0.213354	−	0.976975i	$-0.431561\pi$
$173$	1.34777e23			0.426709			0.213354	+	0.976975i	$0.431561\pi$
$174$	4.23131e22	+	5.15960e22i	0.126098	+	0.153762i
$175$	1.60222e23	−	2.74994e23i	0.449595	−	0.771657i
$176$		−	9.70087e20i		−	0.00256406i
$177$	2.72019e23	+	3.31696e23i	0.677455	+	0.826079i
$178$		−	5.32547e23i		−	1.25011i
$179$		−	6.29190e23i		−	1.39260i	−0.717753	−	0.696298i	$-0.754829\pi$
$179$		−	6.29190e23i		−	1.39260i	0.717753	−	0.696298i	$-0.245171\pi$
$180$	−1.36820e22	+	6.85298e22i	−0.0285619	+	0.143060i
$181$		−	8.74990e22i		−	0.172337i	−0.996281	−	0.0861684i	$-0.972538\pi$
$181$		−	8.74990e22i		−	0.172337i	0.996281	−	0.0861684i	$-0.0274623\pi$
$182$	−1.36954e23	+	2.35059e23i	−0.254580	+	0.436946i
$183$	4.40264e23	−	3.61054e23i	0.772639	−	0.633630i
$184$	2.75792e23			0.457082
$185$	−2.58538e23			−0.404783
$186$	8.56663e22	+	1.04460e23i	0.126743	+	0.154549i
$187$			4.27293e21i			0.00597569i
$188$	2.21739e23			0.293213
$189$	−3.01711e22	+	7.98987e23i	−0.0377348	+	0.999288i
$190$	−9.02931e22			−0.106842
$191$			1.61611e24i			1.80976i	0.425668	+	0.904879i	$0.360039\pi$
$191$			1.61611e24i			1.80976i	−0.425668	+	0.904879i	$0.639961\pi$
$192$	5.73809e23	+	6.99694e23i	0.608281	+	0.741729i
$193$	1.92008e23			0.192738			0.0963691	−	0.995346i	$-0.469277\pi$
$193$	1.92008e23			0.192738			0.0963691	+	0.995346i	$0.469277\pi$
$194$	6.06057e22			0.0576229
$195$	−1.90722e23	+	1.56408e23i	−0.171806	+	0.140895i
$196$	−2.57708e23	−	4.54631e23i	−0.220008	−	0.388123i
$197$			1.23814e24i			1.00202i	0.865443	+	0.501008i	$0.167037\pi$
$197$			1.23814e24i			1.00202i	−0.865443	+	0.501008i	$0.832963\pi$
$198$	1.37212e21	−	6.87263e21i	0.00105295	−	0.00527398i
$199$		−	1.90069e24i		−	1.38342i	−0.722176	−	0.691710i	$-0.756858\pi$
$199$		−	1.90069e24i		−	1.38342i	0.722176	−	0.691710i	$-0.243142\pi$
$200$		−	1.39192e24i		−	0.961169i
$201$	1.02237e24	+	1.24666e24i	0.669961	+	0.816941i
$202$		−	8.38937e23i		−	0.521843i
$203$	−3.90914e23	−	2.27760e23i	−0.230873	−	0.134515i
$204$	−4.17083e23	−	5.08585e23i	−0.233941	−	0.285264i
$205$	1.13176e23			0.0603031
$206$	1.55195e24			0.785725
$207$	8.65535e23	+	1.72804e23i	0.416482	+	0.0831506i
$208$			5.27060e23i			0.241099i
$209$	−7.29415e21			−0.00317277
$210$	9.33149e22	+	5.80762e23i	0.0386054	+	0.240268i
$211$	−2.81290e24			−1.10710			−0.553552	−	0.832815i	$-0.686728\pi$
$211$	−2.81290e24			−1.10710			−0.553552	+	0.832815i	$0.686728\pi$
$212$		−	6.44105e23i		−	0.241229i
$213$	−5.88143e23	+	4.82328e23i	−0.209651	+	0.171932i
$214$	−2.81035e24			−0.953708
$215$	−2.03204e23			−0.0656643
$216$	1.64511e24	+	3.08568e24i	0.506327	+	0.949700i
$217$	−7.91436e23	−	4.61119e23i	−0.232054	−	0.135203i
$218$			1.58481e24i			0.442777i
$219$	3.37966e24	−	2.77161e24i	0.899931	−	0.738021i
$220$			4.15309e21i			0.00105422i
$221$		−	2.32153e24i		−	0.561896i
$222$	−3.08608e24	+	2.53085e24i	−0.712362	+	0.584198i
$223$			2.45705e23i			0.0541021i	0.999634	+	0.0270510i	$0.00861166\pi$
$223$			2.45705e23i			0.0541021i	−0.999634	+	0.0270510i	$0.991388\pi$
$224$	−3.34036e24	−	1.94621e24i	−0.701761	−	0.408871i
$225$	8.72143e23	−	4.36836e24i	0.174852	−	0.875795i
$226$	−6.52199e24			−1.24808
$227$	−1.08437e25			−1.98109			−0.990545	−	0.137190i	$-0.956193\pi$
$227$	−1.08437e25			−1.98109			−0.990545	+	0.137190i	$0.956193\pi$
$228$	8.68187e23	−	7.11988e23i	0.151460	−	0.124210i
$229$		−	7.03610e24i		−	1.17236i	−0.810183	−	0.586178i	$-0.800632\pi$
$229$		−	7.03610e24i		−	1.17236i	0.810183	−	0.586178i	$-0.199368\pi$
$230$	6.49316e23			0.103351
$231$	7.53827e21	+	4.69157e22i	0.00114642	+	0.00713497i
$232$	−1.97866e24			−0.287573
$233$		−	3.24912e24i		−	0.451366i	−0.974201	−	0.225683i	$-0.927539\pi$
$233$		−	3.24912e24i		−	0.451366i	0.974201	−	0.225683i	$-0.0724613\pi$
$234$	−7.45489e23	+	3.73398e24i	−0.0990091	+	0.495913i
$235$	1.69221e24			0.214902
$236$	−3.92428e24			−0.476633
$237$	1.01321e25	+	1.23549e25i	1.17717	+	1.43543i
$238$	−4.78357e24	−	2.78708e24i	−0.531734	−	0.309807i
$239$			1.00716e24i			0.107132i	0.998564	+	0.0535662i	$0.0170588\pi$
$239$			1.00716e24i			0.107132i	−0.998564	+	0.0535662i	$0.982941\pi$
$240$	7.22637e23	+	8.81173e23i	0.0735703	+	0.0897105i
$241$		−	1.65145e25i		−	1.60949i	−0.593623	−	0.804743i	$-0.702303\pi$
$241$		−	1.65145e25i		−	1.60949i	0.593623	−	0.804743i	$-0.297697\pi$
$242$			7.97513e24i			0.744177i
$243$	3.22956e24	+	1.07148e25i	0.288587	+	0.957454i
$244$			5.20874e24i			0.445799i
$245$	−1.96671e24	−	3.46953e24i	−0.161249	−	0.284464i
$246$	1.35094e24	−	1.10789e24i	0.106125	−	0.0870318i
$247$	3.96300e24			0.298336
$248$	−4.00596e24			−0.289044
$249$	8.37745e24	+	1.02153e25i	0.579454	+	0.706577i
$250$		−	6.94655e24i		−	0.460680i
$251$	2.59270e25			1.64884			0.824418	−	0.565981i	$-0.191502\pi$
$251$	2.59270e25			1.64884			0.824418	+	0.565981i	$0.191502\pi$
$252$	−5.47672e24	−	4.84833e24i	−0.334052	−	0.295724i
$253$	5.24537e22			0.00306910
$254$		−	7.77707e24i		−	0.436578i
$255$	−3.18299e24	−	3.88129e24i	−0.171460	−	0.209076i
$256$	−1.99696e25			−1.03240
$257$	2.85855e25			1.41856			0.709279	−	0.704927i	$-0.249020\pi$
$257$	2.85855e25			1.41856			0.709279	+	0.704927i	$0.249020\pi$
$258$	−2.42558e24	+	1.98918e24i	−0.115560	+	0.0947693i
$259$	1.36229e25	−	2.33815e25i	0.623192	−	1.06961i
$260$		−	2.25642e24i		−	0.0991288i
$261$	−6.20978e24	−	1.23978e24i	−0.262030	−	0.0523142i
$262$			1.78781e25i			0.724701i
$263$			4.87018e25i			1.89675i	0.317153	+	0.948374i	$0.397273\pi$
$263$			4.87018e25i			1.89675i	−0.317153	+	0.948374i	$0.602727\pi$
$264$	1.31780e23	+	1.60691e23i	0.00493183	+	0.00601380i
$265$		−	4.91551e24i		−	0.176802i
$266$	4.75772e24	−	8.16586e24i	0.164491	−	0.282322i
$267$	3.20471e25	+	3.90777e25i	1.06517	+	1.29886i
$268$	−1.47492e25			−0.471360
$269$	−1.71594e25			−0.527355			−0.263678	−	0.964611i	$-0.584936\pi$
$269$	−1.71594e25			−0.527355			−0.263678	+	0.964611i	$0.584936\pi$
$270$	3.87321e24	+	7.26484e24i	0.114486	+	0.214737i
$271$			5.72937e24i			0.162903i	0.996677	+	0.0814515i	$0.0259556\pi$
$271$			5.72937e24i			0.162903i	−0.996677	+	0.0814515i	$0.974044\pi$
$272$	−1.07259e25			−0.293401
$273$	−4.09563e24	−	2.54899e25i	−0.107799	−	0.670903i
$274$	4.35535e25			1.10317
$275$		−	2.64734e23i		−	0.00645383i
$276$	−6.24331e24	+	5.12005e24i	−0.146511	+	0.120151i
$277$	6.39436e25			1.44464			0.722320	−	0.691559i	$-0.243076\pi$
$277$	6.39436e25			1.44464			0.722320	+	0.691559i	$0.243076\pi$
$278$	7.81925e24			0.170096
$279$	−1.25722e25	−	2.51004e24i	−0.263370	−	0.0525819i
$280$	−1.50708e25	−	8.78076e24i	−0.304072	−	0.177163i
$281$		−	5.72925e24i		−	0.111348i	−0.998449	−	0.0556739i	$-0.982269\pi$
$281$		−	5.72925e24i		−	0.111348i	0.998449	−	0.0556739i	$-0.0177307\pi$
$282$	2.01993e25	−	1.65651e25i	0.378199	−	0.310155i
$283$		−	5.34411e25i		−	0.964090i	−0.876147	−	0.482045i	$-0.839894\pi$
$283$		−	5.34411e25i		−	0.964090i	0.876147	−	0.482045i	$-0.160106\pi$
$284$		−	6.95828e24i		−	0.120965i
$285$	6.62561e24	−	5.43357e24i	0.111008	−	0.0910361i
$286$			2.26289e23i			0.00365444i
$287$	−5.96348e24	+	1.02353e25i	−0.0928409	+	0.159347i
$288$	−5.30626e25	−	1.05939e25i	−0.796466	−	0.159014i
$289$	−2.18476e25			−0.316211
$290$	−4.65851e24			−0.0650232
$291$	−4.44718e24	+	3.64707e24i	−0.0598699	+	0.0490984i
$292$			3.99845e25i			0.519244i
$293$	1.11333e26			1.39480			0.697402	−	0.716680i	$-0.254339\pi$
$293$	1.11333e26			1.39480			0.697402	+	0.716680i	$0.254339\pi$
$294$	−5.74394e25	−	2.21623e25i	−0.694326	−	0.267897i
$295$	−2.99483e25			−0.349334
$296$		−	1.18349e26i		−	1.33230i
$297$	3.12890e23	+	5.86876e23i	0.00339976	+	0.00637682i
$298$	−6.19567e25			−0.649857
$299$	−2.84987e25			−0.288588
$300$	2.58409e25	+	3.15100e25i	0.252659	+	0.308089i
$301$	1.07072e25	−	1.83773e25i	0.101095	−	0.173513i
$302$		−	1.18263e26i		−	1.07839i
$303$	5.04847e25	+	6.15602e25i	0.444643	+	0.542192i
$304$		−	1.83098e25i		−	0.155780i
$305$			3.97507e25i			0.326736i
$306$	−7.59884e25	−	1.51711e25i	−0.603493	−	0.120487i
$307$			2.15589e26i			1.65452i	0.561817	+	0.827261i	$0.310102\pi$
$307$			2.15589e26i			1.65452i	−0.561817	+	0.827261i	$0.689898\pi$
$308$	−3.75594e23	−	2.18834e23i	−0.00278571	−	0.00162305i
$309$	−1.13880e26	+	9.33914e25i	−0.816364	+	0.669488i
$310$	−9.43154e24			−0.0653559
$311$	−1.36821e26			−0.916576			−0.458288	−	0.888804i	$-0.651537\pi$
$311$	−1.36821e26			−0.916576			−0.458288	+	0.888804i	$0.651537\pi$
$312$	−7.15976e25	−	8.73051e25i	−0.463741	−	0.565479i
$313$			1.05616e26i			0.661474i	0.943723	+	0.330737i	$0.107297\pi$
$313$			1.05616e26i			0.661474i	−0.943723	+	0.330737i	$0.892703\pi$
$314$	8.61181e24			0.0521595
$315$	−4.17958e25	−	3.70002e25i	−0.244834	−	0.216742i
$316$	−1.46170e26			−0.828216
$317$			1.49928e26i			0.821790i	0.911683	+	0.410895i	$0.134784\pi$
$317$			1.49928e26i			0.821790i	−0.911683	+	0.410895i	$0.865216\pi$
$318$	−4.81183e25	−	5.86747e25i	−0.255168	−	0.311148i
$319$	−3.76329e23			−0.00193093
$320$	−6.31742e25			−0.313664
$321$	2.06220e26	−	1.69118e26i	0.990897	−	0.812620i
$322$	−3.42137e25	+	5.87224e25i	−0.159116	+	0.273097i
$323$			8.06490e25i			0.363055i
$324$	−9.45271e25	−	3.93116e25i	−0.411940	−	0.171316i
$325$			1.43833e26i			0.606854i
$326$		−	1.84545e26i		−	0.753905i
$327$	−9.53692e25	−	1.16292e26i	−0.377274	−	0.460042i
$328$			5.18076e25i			0.198481i
$329$	−8.91658e25	+	1.53039e26i	−0.330858	+	0.567864i
$330$	3.10259e23	+	3.78326e23i	0.00111514	+	0.00135978i
$331$	1.65667e26			0.576822			0.288411	−	0.957507i	$-0.406873\pi$
$331$	1.65667e26			0.576822			0.288411	+	0.957507i	$0.406873\pi$
$332$	−1.20857e26			−0.407682
$333$	7.41543e25	−	3.71422e26i	0.242366	−	1.21396i
$334$			3.82333e26i			1.21089i
$335$	−1.12559e26			−0.345470
$336$	−1.17768e26	+	1.89226e25i	−0.350320	+	0.0562883i
$337$	3.84946e26			1.10991			0.554953	−	0.831882i	$-0.312736\pi$
$337$	3.84946e26			1.10991			0.554953	+	0.831882i	$0.312736\pi$
$338$			1.43326e26i			0.400588i
$339$	4.78576e26	−	3.92474e26i	1.29674	−	1.06344i
$340$	4.59193e25			0.120633
$341$	−7.61908e23			−0.00194080
$342$	2.58980e25	−	1.29717e26i	0.0639723	−	0.320423i
$343$	4.17405e26	+	4.95254e24i	0.999930	+	0.0118642i
$344$		−	9.30190e25i		−	0.216126i
$345$	−4.76461e25	+	3.90739e25i	−0.107381	+	0.0880615i
$346$			1.45254e26i			0.317563i
$347$		−	2.57009e26i		−	0.545116i	−0.962139	−	0.272558i	$-0.912130\pi$
$347$		−	2.57009e26i		−	0.545116i	0.962139	−	0.272558i	$-0.0878697\pi$
$348$	4.47926e25	−	3.67337e25i	0.0921773	−	0.0755933i
$349$		−	6.70849e26i		−	1.33955i	−0.742565	−	0.669773i	$-0.766391\pi$
$349$		−	6.70849e26i		−	1.33955i	0.742565	−	0.669773i	$-0.233609\pi$
$350$	2.96372e26	+	1.72677e26i	0.574279	+	0.334596i
$351$	−1.69997e26	−	3.18857e26i	−0.319680	−	0.599613i
$352$	−3.21573e24			−0.00586924
$353$	5.19858e26			0.920980			0.460490	−	0.887665i	$-0.347674\pi$
$353$	5.19858e26			0.920980			0.460490	+	0.887665i	$0.347674\pi$
$354$	−3.57482e26	+	2.93166e26i	−0.614781	+	0.504173i
$355$		−	5.31024e25i		−	0.0886578i
$356$	−4.62326e26			−0.749416
$357$	5.18731e26	−	8.33481e25i	0.816443	−	0.131184i
$358$	6.78103e26			1.03639
$359$			6.53139e26i			0.969424i	0.874674	+	0.484712i	$0.161076\pi$
$359$			6.53139e26i			0.969424i	−0.874674	+	0.484712i	$0.838924\pi$
$360$	−2.39403e26	−	4.77969e25i	−0.345107	−	0.0689006i
$361$	5.76536e26			0.807237
$362$	9.43011e25			0.128256
$363$	−4.79919e26	−	5.85206e26i	−0.634086	−	0.773195i
$364$	2.04065e26	+	1.18895e26i	0.261941	+	0.152616i
$365$			3.05144e26i			0.380565i
$366$	3.89122e26	+	4.74490e26i	0.471558	+	0.575010i
$367$			1.07354e27i			1.26423i	0.774874	+	0.632115i	$0.217813\pi$
$367$			1.07354e27i			1.26423i	−0.774874	+	0.632115i	$0.782187\pi$
$368$			1.31670e26i			0.150690i
$369$	−3.24613e25	+	1.62591e26i	−0.0361069	+	0.180851i
$370$		−	2.78637e26i		−	0.301246i
$371$	4.44546e26	+	2.59008e26i	0.467187	+	0.272199i
$372$	9.06862e25	−	7.43704e25i	0.0926489	−	0.0759800i
$373$	−2.84476e26			−0.282555			−0.141278	−	0.989970i	$-0.545121\pi$
$373$	−2.84476e26			−0.282555			−0.141278	+	0.989970i	$0.545121\pi$
$374$	−4.60510e24			−0.00444721
$375$	4.18022e26	+	5.09730e26i	0.392528	+	0.478643i
$376$			7.74626e26i			0.707326i
$377$	2.04464e26			0.181565
$378$	−8.61099e26	−	3.25166e25i	−0.743686	−	0.0280828i
$379$	−1.97170e26			−0.165626			−0.0828129	−	0.996565i	$-0.526390\pi$
$379$	−1.97170e26			−0.165626			−0.0828129	+	0.996565i	$0.526390\pi$
$380$			7.83871e25i			0.0640497i
$381$	4.68000e26	+	5.70673e26i	0.371992	+	0.453602i
$382$	−1.74175e27			−1.34685
$383$	−1.51088e27			−1.13669			−0.568347	−	0.822789i	$-0.692417\pi$
$383$	−1.51088e27			−1.13669			−0.568347	+	0.822789i	$0.692417\pi$
$384$	1.03827e26	−	8.51471e25i	0.0760034	−	0.0623292i
$385$	−2.86636e24	−	1.67004e24i	−0.00204171	−	0.00118957i
$386$			2.06935e26i			0.143439i
$387$	5.82834e25	−	2.91928e26i	0.0393169	−	0.196929i
$388$		−	5.26143e25i		−	0.0345438i
$389$		−	1.62998e27i		−	1.04163i	−0.853671	−	0.520813i	$-0.825629\pi$
$389$		−	1.62998e27i		−	1.04163i	0.853671	−	0.520813i	$-0.174371\pi$
$390$	−1.68568e26	−	2.05549e26i	−0.104857	−	0.127861i
$391$		−	5.79964e26i		−	0.351192i
$392$	1.58822e27	−	9.00283e26i	0.936280	−	0.530732i
$393$	−1.07585e27	−	1.31188e27i	−0.617491	−	0.752959i
$394$	−1.33439e27			−0.745715
$395$	−1.11550e27			−0.607017
$396$	−5.96641e24	−	1.19119e24i	−0.00316165	−	0.000631223i
$397$		−	2.20610e26i		−	0.113848i	−0.998379	−	0.0569239i	$-0.981871\pi$
$397$		−	2.20610e26i		−	0.113848i	0.998379	−	0.0569239i	$-0.0181292\pi$
$398$	2.04845e27			1.02956
$399$	1.42280e26	+	8.85507e26i	0.0696514	+	0.433488i
$400$	6.64538e26			0.316876
$401$		−	1.71853e27i		−	0.798256i	−0.916895	−	0.399128i	$-0.869313\pi$
$401$		−	1.71853e27i		−	0.798256i	0.916895	−	0.399128i	$-0.130687\pi$
$402$	−1.34358e27	+	1.10185e27i	−0.607980	+	0.498596i
$403$	4.13954e26			0.182494
$404$	−7.28315e26			−0.312835
$405$	−7.21388e26	−	3.00008e26i	−0.301919	−	0.125561i
$406$	2.45466e26	−	4.21303e26i	0.100108	−	0.171819i
$407$		−	2.25091e25i		−	0.00894577i
$408$	1.77670e27	−	1.45705e27i	0.688150	−	0.564341i
$409$			1.01469e27i			0.383037i	0.981489	+	0.191518i	$0.0613411\pi$
$409$			1.01469e27i			0.383037i	−0.981489	+	0.191518i	$0.938659\pi$
$410$			1.21974e26i			0.0448785i
$411$	−3.19590e27	+	2.62091e27i	−1.14618	+	0.939969i
$412$		−	1.34731e27i		−	0.471027i
$413$	1.57803e27	−	2.70844e27i	0.537825	−	0.923090i
$414$	−1.86238e26	+	9.32822e26i	−0.0618820	+	0.309952i
$415$	−9.22326e26			−0.298799
$416$	1.74715e27			0.551886
$417$	−5.73768e26	+	4.70539e26i	−0.176729	+	0.144933i
$418$		−	7.86120e24i		−	0.00236123i
$419$	−3.27068e27			−0.958056			−0.479028	−	0.877800i	$-0.659011\pi$
$419$	−3.27068e27			−0.958056			−0.479028	+	0.877800i	$0.659011\pi$
$420$	5.04183e26	−	8.10105e25i	0.144036	−	0.0231432i
$421$	−4.01568e27			−1.11892			−0.559458	−	0.828859i	$-0.688991\pi$
$421$	−4.01568e27			−1.11892			−0.559458	+	0.828859i	$0.688991\pi$
$422$		−	3.03157e27i		−	0.823924i
$423$	−4.85361e26	+	2.43106e27i	−0.128674	+	0.644499i
$424$	2.25013e27			0.581923
$425$	−2.92708e27			−0.738501
$426$	−5.19823e26	−	6.33865e26i	−0.127954	−	0.156026i
$427$	−3.59494e27	−	2.09454e27i	−0.863375	−	0.503033i
$428$			2.43978e27i			0.571730i
$429$	−1.36174e25	−	1.66049e25i	−0.00311381	−	0.00379694i
$430$		−	2.19001e26i		−	0.0488684i
$431$			6.37440e27i			1.38812i	0.719916	+	0.694061i	$0.244180\pi$
$431$			6.37440e27i			1.38812i	−0.719916	+	0.694061i	$0.755820\pi$
$432$	−1.47318e27	+	7.85417e26i	−0.313095	+	0.166925i
$433$		−	6.23955e27i		−	1.29429i	−0.762369	−	0.647143i	$-0.775964\pi$
$433$		−	6.23955e27i		−	1.29429i	0.762369	−	0.647143i	$-0.224036\pi$
$434$	4.96966e26	−	8.52962e26i	0.100620	−	0.172698i
$435$	3.41837e26	−	2.80335e26i	0.0675587	−	0.0554039i
$436$	1.37584e27			0.265436
$437$	9.90035e26			0.186464
$438$	2.98707e27	+	3.64239e27i	0.549247	+	0.669743i
$439$			8.26648e27i			1.48403i	0.670383	+	0.742015i	$0.266130\pi$
$439$			8.26648e27i			1.48403i	−0.670383	+	0.742015i	$0.733870\pi$
$440$	−1.45085e25			−0.00254313
$441$	5.54850e27	−	1.83028e27i	0.949665	−	0.313266i
$442$	2.50201e27			0.418172
$443$			1.94582e27i			0.317587i	0.987312	+	0.158794i	$0.0507604\pi$
$443$			1.94582e27i			0.317587i	−0.987312	+	0.158794i	$0.949240\pi$
$444$	2.19713e27	+	2.67915e27i	0.350215	+	0.427047i
$445$	−3.52826e27			−0.549263
$446$	−2.64806e26			−0.0402636
$447$	4.54632e27	−	3.72837e27i	0.675197	−	0.553719i
$448$	3.32877e27	−	5.71330e27i	0.482909	−	0.828835i
$449$			1.69203e27i			0.239785i	0.992787	+	0.119893i	$0.0382550\pi$
$449$			1.69203e27i			0.239785i	−0.992787	+	0.119893i	$0.961745\pi$
$450$	4.70796e27	+	9.39943e26i	0.651780	+	0.130128i
$451$			9.85347e24i			0.00133271i
$452$			5.66201e27i			0.748198i
$453$	7.11671e27	+	8.67801e27i	0.918858	+	1.12044i
$454$		−	1.16866e28i		−	1.47436i
$455$	1.55733e27	+	9.07354e26i	0.191982	+	0.111855i
$456$	2.48727e27	+	3.03294e27i	0.299635	+	0.365370i
$457$	−7.92917e27			−0.933486			−0.466743	−	0.884393i	$-0.654573\pi$
$457$	−7.92917e27			−0.933486			−0.466743	+	0.884393i	$0.654573\pi$
$458$	7.58308e27			0.872485
$459$	6.48890e27	−	3.45952e27i	0.729689	−	0.389029i
$460$		−	5.63698e26i		−	0.0619568i
$461$	5.88926e27			0.632705			0.316352	−	0.948642i	$-0.397542\pi$
$461$	5.88926e27			0.632705			0.316352	+	0.948642i	$0.397542\pi$
$462$	−5.05629e25	+	8.12429e24i	−0.00530996	+	0.000853187i
$463$	2.89487e27			0.297186			0.148593	−	0.988898i	$-0.452526\pi$
$463$	2.89487e27			0.297186			0.148593	+	0.988898i	$0.452526\pi$
$464$		−	9.44664e26i		−	0.0948066i
$465$	6.92076e26	−	5.67561e26i	0.0679043	−	0.0556874i
$466$	3.50170e27			0.335913
$467$	−1.50197e28			−1.40875			−0.704374	−	0.709829i	$-0.748772\pi$
$467$	−1.50197e28			−1.40875			−0.704374	+	0.709829i	$0.748772\pi$
$468$	3.24162e27	+	6.47190e26i	0.297291	+	0.0593540i
$469$	5.93096e27	−	1.01795e28i	0.531876	−	0.912879i
$470$			1.82376e27i			0.159934i
$471$	−6.31925e26	+	5.18233e26i	−0.0541934	+	0.0444432i
$472$		−	1.37092e28i		−	1.14979i
$473$		−	1.76916e25i		−	0.00145119i
$474$	−1.33154e28	+	1.09197e28i	−1.06827	+	0.876071i
$475$		−	4.99671e27i		−	0.392104i
$476$	−2.41958e27	+	4.15282e27i	−0.185723	+	0.318764i
$477$	7.06173e27	+	1.40987e27i	0.530235	+	0.105861i
$478$	−1.08546e27			−0.0797297
$479$	−2.05235e28			−1.47478			−0.737391	−	0.675467i	$-0.763942\pi$
$479$	−2.05235e28			−1.47478			−0.737391	+	0.675467i	$0.763942\pi$
$480$	2.92100e27	−	2.39547e27i	0.205351	−	0.168406i
$481$			1.22295e28i			0.841172i
$482$	1.77984e28			1.19780
$483$	−1.02317e27	−	6.36786e27i	−0.0673755	−	0.419323i
$484$	6.92353e27			0.446120
$485$		−	4.01528e26i		−	0.0253179i
$486$	−1.15478e28	+	3.48062e27i	−0.712552	+	0.214771i
$487$	−1.39386e28			−0.841712			−0.420856	−	0.907127i	$-0.638270\pi$
$487$	−1.39386e28			−0.841712			−0.420856	+	0.907127i	$0.638270\pi$
$488$	−1.81963e28			−1.07541
$489$	1.11053e28	+	1.35417e28i	0.642375	+	0.783302i
$490$	3.73925e27	−	2.11960e27i	0.211703	−	0.120004i
$491$		−	2.14939e28i		−	1.19113i	−0.803308	−	0.595564i	$-0.796929\pi$
$491$		−	2.14939e28i		−	1.19113i	0.803308	−	0.595564i	$-0.203071\pi$
$492$	−9.61804e26	−	1.17281e27i	−0.0521739	−	0.0636200i
$493$			4.16095e27i			0.220953i
$494$			4.27108e27i			0.222027i
$495$	−4.55330e25	−	9.09065e24i	−0.00231724	−	0.000462637i
$496$		−	1.91255e27i		−	0.0952916i
$497$	4.80244e27	+	2.79807e27i	0.234272	+	0.136495i
$498$	−1.10095e28	+	9.02871e27i	−0.525846	+	0.431239i
$499$	−4.87093e27			−0.227801			−0.113901	−	0.993492i	$-0.536335\pi$
$499$	−4.87093e27			−0.227801			−0.113901	+	0.993492i	$0.536335\pi$
$500$	−6.03058e27			−0.276169
$501$	−2.30076e28	−	2.80552e28i	−1.03175	−	1.25811i
$502$			2.79425e28i			1.22709i
$503$	3.80145e28			1.63488			0.817439	−	0.576015i	$-0.195393\pi$
$503$	3.80145e28			1.63488			0.817439	+	0.576015i	$0.195393\pi$
$504$	1.69373e28	−	1.91325e28i	0.713382	−	0.805843i
$505$	−5.55817e27			−0.229283
$506$			5.65315e25i			0.00228407i
$507$	−8.62489e27	−	1.05171e28i	−0.341327	−	0.416209i
$508$	−6.75159e27			−0.261720
$509$	−3.14244e28			−1.19325			−0.596623	−	0.802521i	$-0.703491\pi$
$509$	−3.14244e28			−1.19325			−0.596623	+	0.802521i	$0.703491\pi$
$510$	4.18302e27	−	3.43043e27i	0.155598	−	0.127603i
$511$	−2.75963e28	−	1.60786e28i	−1.00562	−	0.585908i
$512$		−	1.87687e28i		−	0.670039i
$513$	5.90561e27	+	1.10770e28i	0.206554	+	0.387425i
$514$			3.08077e28i			1.05571i
$515$		−	1.02820e28i		−	0.345226i
$516$	1.72689e27	+	2.10574e27i	0.0568124	+	0.0692761i
$517$			1.47329e26i			0.00474938i
$518$	2.51992e28	+	1.46819e28i	0.796019	+	0.463789i
$519$	−8.74097e27	−	1.06586e28i	−0.270584	−	0.329946i
$520$	7.88263e27			0.239131
$521$	−1.29490e28			−0.384982			−0.192491	−	0.981299i	$-0.561657\pi$
$521$	−1.29490e28			−0.384982			−0.192491	+	0.981299i	$0.561657\pi$
$522$	1.33616e27	−	6.69252e27i	0.0389331	−	0.195007i
$523$			5.98374e28i			1.70885i	0.519571	+	0.854427i	$0.326092\pi$
$523$			5.98374e28i			1.70885i	−0.519571	+	0.854427i	$0.673908\pi$
$524$	1.55207e28			0.434444
$525$	−3.21387e28	+	5.16394e27i	−0.881769	+	0.141680i
$526$	−5.24879e28			−1.41159
$527$			8.42417e27i			0.222083i
$528$	−7.67177e25	+	6.29150e25i	−0.00198262	+	0.00162592i
$529$	3.23520e28			0.819629
$530$	5.29764e27			0.131579
$531$	8.58981e27	−	4.30244e28i	0.209166	−	1.04766i
$532$	−7.08912e27	−	4.13037e27i	−0.169247	−	0.0986091i
$533$		−	5.35351e27i		−	0.125315i
$534$	−4.21156e28	+	3.45384e28i	−0.966629	+	0.792718i
$535$			1.86193e28i			0.419033i
$536$		−	5.15251e28i		−	1.13707i
$537$	−4.97584e28	+	4.08062e28i	−1.07680	+	0.883071i
$538$		−	1.84934e28i		−	0.392466i
$539$	3.02068e26	−	1.71228e26i	0.00628671	−	0.00356363i
$540$	6.30691e27	−	3.36249e27i	0.128731	−	0.0686320i
$541$	7.37106e28			1.47557			0.737783	−	0.675038i	$-0.235873\pi$
$541$	7.37106e28			1.47557			0.737783	+	0.675038i	$0.235873\pi$
$542$	−6.17476e27			−0.121235
$543$	−6.91971e27	+	5.67475e27i	−0.133257	+	0.109282i
$544$			3.55553e28i			0.671608i
$545$	1.04998e28			0.194544
$546$	2.74714e28	−	4.41402e27i	0.499296	−	0.0802254i
$547$	6.40075e28			1.14121			0.570603	−	0.821226i	$-0.306709\pi$
$547$	6.40075e28			1.14121			0.570603	+	0.821226i	$0.306709\pi$
$548$		−	3.78105e28i		−	0.661328i
$549$	−5.71067e28	−	1.14013e28i	−0.979891	−	0.195635i
$550$	2.85315e26			0.00480304
$551$	−7.10300e27			−0.117314
$552$	−1.78865e28	−	2.18105e28i	−0.289844	−	0.353432i
$553$	5.87780e28	−	1.00883e29i	0.934547	−	1.60400i
$554$			6.89145e28i			1.07512i
$555$	1.67675e28	+	2.04461e28i	0.256680	+	0.312992i
$556$		−	6.78821e27i		−	0.101969i
$557$			2.96472e28i			0.437023i	0.975834	+	0.218512i	$0.0701202\pi$
$557$			2.96472e28i			0.437023i	−0.975834	+	0.218512i	$0.929880\pi$
$558$	2.70517e27	−	1.35495e28i	0.0391322	−	0.196004i
$559$			9.61206e27i			0.136456i
$560$	4.19215e27	−	7.19516e27i	0.0584067	−	0.100246i
$561$	3.37917e26	−	2.77121e26i	0.00462062	−	0.00378930i
$562$	6.17464e27			0.0828668
$563$	2.39088e28			0.314934			0.157467	−	0.987524i	$-0.449667\pi$
$563$	2.39088e28			0.314934			0.157467	+	0.987524i	$0.449667\pi$
$564$	−1.43809e28	−	1.75358e28i	−0.185932	−	0.226723i
$565$			4.32099e28i			0.548371i
$566$	5.75955e28			0.717491
$567$	6.51433e28	−	4.94323e28i	0.796613	−	0.604490i
$568$	2.43082e28			0.291807
$569$			9.30524e28i			1.09660i	0.836281	+	0.548300i	$0.184725\pi$
$569$			9.30524e28i			1.09660i	−0.836281	+	0.548300i	$0.815275\pi$
$570$	5.85597e27	+	7.14068e27i	0.0677505	+	0.0826140i
$571$	3.32995e28			0.378232			0.189116	−	0.981955i	$-0.439438\pi$
$571$	3.32995e28			0.378232			0.189116	+	0.981955i	$0.439438\pi$
$572$	1.96451e26			0.00219077
$573$	1.27807e29	−	1.04813e29i	1.39937	−	1.14760i
$574$	−1.10310e28	−	6.42707e27i	−0.118588	−	0.0690937i
$575$			3.59324e28i			0.379292i
$576$	1.81197e28	−	9.07574e28i	0.187808	−	0.940689i
$577$			5.75601e28i			0.585835i	0.956138	+	0.292917i	$0.0946261\pi$
$577$			5.75601e28i			0.585835i	−0.956138	+	0.292917i	$0.905374\pi$
$578$		−	2.35460e28i		−	0.235329i
$579$	−1.24527e28	−	1.51846e28i	−0.122219	−	0.149032i
$580$			4.04425e27i			0.0389802i
$581$	4.85991e28	−	8.34126e28i	0.460023	−	0.789555i
$582$	−3.93059e27	−	4.79290e27i	−0.0365398	−	0.0445561i
$583$	4.27960e26			0.00390736
$584$	−1.39683e29			−1.25259
$585$	2.47386e28	+	4.93906e27i	0.217891	+	0.0435018i
$586$			1.19988e29i			1.03804i
$587$	1.17507e29			0.998540			0.499270	−	0.866447i	$-0.333602\pi$
$587$	1.17507e29			0.998540			0.499270	+	0.866447i	$0.333602\pi$
$588$	−1.92400e28	+	4.98655e28i	−0.160599	+	0.416235i
$589$	−1.43806e28			−0.117914
$590$		−	3.22765e28i		−	0.259980i
$591$	9.79162e28	−	8.02996e28i	0.774793	−	0.635397i
$592$	5.65026e28			0.439228
$593$	−1.36983e29			−1.04614			−0.523072	−	0.852289i	$-0.675214\pi$
$593$	−1.36983e29			−1.04614			−0.523072	+	0.852289i	$0.675214\pi$
$594$	−6.32500e26	+	3.37213e26i	−0.00474573	+	0.00253016i
$595$	−1.84651e28	+	3.16924e28i	−0.136121	+	0.233629i
$596$			5.37872e28i			0.389577i
$597$	−1.50313e29	+	1.23269e29i	−1.06971	+	0.877252i
$598$		−	3.07142e28i		−	0.214772i
$599$			2.40682e29i			1.65372i	0.562410	+	0.826859i	$0.309874\pi$
$599$			2.40682e29i			1.65372i	−0.562410	+	0.826859i	$0.690126\pi$
$600$	−1.10078e29	+	9.02732e28i	−0.743210	+	0.609496i
$601$		−	3.96548e28i		−	0.263096i	−0.991310	−	0.131548i	$-0.958005\pi$
$601$		−	3.96548e28i		−	0.263096i	0.991310	−	0.131548i	$-0.0419947\pi$
$602$	1.98059e28	+	1.15396e28i	0.129131	+	0.0752364i
$603$	3.22844e28	−	1.61705e29i	0.206852	−	1.03608i
$604$	−1.02669e29			−0.646475
$605$	5.28372e28			0.326971
$606$	−6.63459e28	+	5.44093e28i	−0.403507	+	0.330911i
$607$			1.06491e29i			0.636546i	0.947999	+	0.318273i	$0.103103\pi$
$607$			1.06491e29i			0.636546i	−0.947999	+	0.318273i	$0.896897\pi$
$608$	−6.06951e28			−0.356588
$609$	7.34071e27	+	4.56862e28i	0.0423893	+	0.263817i
$610$	−4.28409e28			−0.243162
$611$		−	8.00455e28i		−	0.446585i
$612$	−1.31706e28	+	6.59687e28i	−0.0722298	+	0.361783i
$613$	−6.00070e28			−0.323494			−0.161747	−	0.986832i	$-0.551713\pi$
$613$	−6.00070e28			−0.323494			−0.161747	+	0.986832i	$0.551713\pi$
$614$	−2.32348e29			−1.23132
$615$	−7.34005e27	−	8.95035e27i	−0.0382393	−	0.0466285i
$616$	7.64480e26	−	1.31211e27i	0.00391533	−	0.00672004i
$617$			4.47628e28i			0.225384i	0.993630	+	0.112692i	$0.0359473\pi$
$617$			4.47628e28i			0.225384i	−0.993630	+	0.112692i	$0.964053\pi$
$618$	−1.00652e29	−	1.22733e29i	−0.498243	−	0.607551i
$619$			9.07018e28i			0.441432i	0.975338	+	0.220716i	$0.0708394\pi$
$619$			9.07018e28i			0.441432i	−0.975338	+	0.220716i	$0.929161\pi$
$620$			8.18790e27i			0.0391796i
$621$	−4.24685e28	−	7.96566e28i	−0.199804	−	0.374766i
$622$		−	1.47457e29i		−	0.682130i
$623$	1.85911e29	−	3.19086e29i	0.845630	−	1.45139i
$624$	4.16816e28	−	3.41825e28i	0.186426	−	0.152885i
$625$	1.57040e29			0.690669
$626$	−1.13826e29			−0.492280
$627$	4.73063e26	+	5.76846e26i	0.00201192	+	0.00245330i
$628$		−	7.47626e27i		−	0.0312686i
$629$	−2.48876e29			−1.02365
$630$	3.98766e28	−	4.50450e28i	0.161303	−	0.182209i
$631$	−6.30668e28			−0.250895			−0.125448	−	0.992100i	$-0.540037\pi$
$631$	−6.30668e28			−0.250895			−0.125448	+	0.992100i	$0.540037\pi$
$632$		−	5.10633e29i		−	1.99793i
$633$	1.82431e29	+	2.22453e29i	0.702036	+	0.856052i
$634$	−1.61583e29			−0.611589
$635$	−5.15251e28			−0.191820
$636$	−5.09379e28	+	4.17735e28i	−0.186527	+	0.152968i
$637$	−1.64117e29	+	9.30302e28i	−0.591140	+	0.335089i
$638$		−	4.05585e26i		−	0.00143703i
$639$	7.62881e28	+	1.52309e28i	0.265888	+	0.0530844i
$640$			9.37437e27i			0.0321405i
$641$			2.58094e29i			0.870501i	0.900309	+	0.435250i	$0.143340\pi$
$641$			2.58094e29i			0.870501i	−0.900309	+	0.435250i	$0.856660\pi$
$642$	1.82265e29	+	2.22252e29i	0.604765	+	0.737441i
$643$		−	3.31180e29i		−	1.08106i	−0.841325	−	0.540529i	$-0.818224\pi$
$643$		−	3.31180e29i		−	1.08106i	0.841325	−	0.540529i	$-0.181776\pi$
$644$	5.09793e28	+	2.97023e28i	0.163716	+	0.0953870i
$645$	1.31788e28	+	1.60701e28i	0.0416390	+	0.0507740i
$646$	−8.69187e28			−0.270191
$647$	2.95666e29			0.904287			0.452143	−	0.891945i	$-0.350660\pi$
$647$	2.95666e29			0.904287			0.452143	+	0.891945i	$0.350660\pi$
$648$	1.37332e29	−	3.30223e29i	0.413270	−	0.993733i
$649$		−	2.60739e27i		−	0.00772035i
$650$	−1.55015e29			−0.451631
$651$	1.48619e28	+	9.24953e28i	0.0426062	+	0.265167i
$652$	−1.60211e29			−0.451951
$653$		−	4.60468e28i		−	0.127824i	−0.997956	−	0.0639118i	$-0.979642\pi$
$653$		−	4.60468e28i		−	0.127824i	0.997956	−	0.0639118i	$-0.0203576\pi$
$654$	1.25332e29	−	1.02783e29i	0.342371	−	0.280773i
$655$	1.18447e29			0.318413
$656$	−2.47342e28			−0.0654347
$657$	−4.38376e29	−	8.75217e28i	−1.14133	−	0.227866i
$658$	−1.64936e29	−	9.60975e28i	−0.422613	−	0.246229i
$659$		−	5.55268e28i		−	0.140025i	−0.997546	−	0.0700126i	$-0.977696\pi$
$659$		−	5.55268e28i		−	0.140025i	0.997546	−	0.0700126i	$-0.0223039\pi$
$660$	3.28440e26	−	2.69349e26i	0.000815163	−	0.000668503i
$661$		−	3.21572e28i		−	0.0785530i	−0.999228	−	0.0392765i	$-0.987495\pi$
$661$		−	3.21572e28i		−	0.0785530i	0.999228	−	0.0392765i	$-0.0125053\pi$
$662$			1.78546e29i			0.429280i
$663$	−1.83594e29	+	1.50563e29i	−0.434478	+	0.356309i
$664$		−	4.22204e29i		−	0.983463i
$665$	−5.41009e28	−	3.15211e28i	−0.124044	−	0.0722727i
$666$	4.00296e29	+	7.99190e28i	0.903445	+	0.180373i
$667$	5.10791e28			0.113481
$668$	3.31919e29			0.725904
$669$	1.94312e28	−	1.59352e28i	0.0418336	−	0.0343071i
$670$		−	1.21309e29i		−	0.257104i
$671$	−3.46082e27			−0.00722092
$672$	6.27264e28	+	3.90389e29i	0.128847	+	0.801899i
$673$	−1.37267e29			−0.277592			−0.138796	−	0.990321i	$-0.544323\pi$
$673$	−1.37267e29			−0.277592			−0.138796	+	0.990321i	$0.544323\pi$
$674$			4.14872e29i			0.826010i
$675$	−4.02028e29	+	2.14339e29i	−0.788073	+	0.420156i
$676$	1.24427e29			0.240145
$677$	6.52328e29			1.23961			0.619805	−	0.784756i	$-0.287212\pi$
$677$	6.52328e29			1.23961			0.619805	+	0.784756i	$0.287212\pi$
$678$	4.22984e29	+	5.15781e29i	0.791430	+	0.965058i
$679$	3.63131e28	+	2.11573e28i	0.0669008	+	0.0389788i
$680$			1.60415e29i			0.291006i
$681$	7.03266e29	+	8.57552e29i	1.25625	+	1.53185i
$682$		−	8.21139e26i		−	0.00144438i
$683$			3.61830e29i			0.626740i	0.949631	+	0.313370i	$0.101458\pi$
$683$			3.61830e29i			0.626740i	−0.949631	+	0.313370i	$0.898542\pi$
$684$	−1.12613e29	−	2.24831e28i	−0.192087	−	0.0383502i
$685$		−	2.88553e29i		−	0.484701i
$686$	−5.33755e27	+	4.49854e29i	−0.00882955	+	0.744163i
$687$	−5.56438e29	+	4.56327e29i	−0.906506	+	0.743413i
$688$	4.44096e28			0.0712522
$689$	−2.32516e29			−0.367409
$690$	−4.21114e28	−	5.13501e28i	−0.0655367	−	0.0799145i
$691$		−	6.57444e29i		−	1.00772i	−0.863786	−	0.503859i	$-0.831913\pi$
$691$		−	6.57444e29i		−	1.00772i	0.863786	−	0.503859i	$-0.168087\pi$
$692$	1.26101e29			0.190373
$693$	3.22135e27	−	3.63887e27i	0.00479004	−	0.00541088i
$694$	2.76989e29			0.405684
$695$		−	5.18045e28i		−	0.0747356i
$696$	1.28326e29	+	1.56479e29i	0.182356	+	0.222362i
$697$	1.08947e29			0.152500
$698$	7.23001e29			0.996912
$699$	−2.56951e29	+	2.10722e29i	−0.349012	+	0.286220i
$700$	1.49908e29	−	2.57293e29i	0.200584	−	0.344269i
$701$		−	8.98314e29i		−	1.18410i	−0.805901	−	0.592051i	$-0.798318\pi$
$701$		−	8.98314e29i		−	1.18410i	0.805901	−	0.592051i	$-0.201682\pi$
$702$	3.43645e29	−	1.83212e29i	0.446241	−	0.237911i
$703$		−	4.24847e29i		−	0.543503i
$704$		−	5.50014e27i		−	0.00693204i
$705$	−1.09748e29	−	1.33825e29i	−0.136274	−	0.166170i
$706$			5.60271e29i			0.685408i
$707$	2.92871e29	−	5.02666e29i	0.352998	−	0.605864i
$708$	2.54509e29	+	3.10345e29i	0.302242	+	0.368549i
$709$	−2.07195e29			−0.242435			−0.121217	−	0.992626i	$-0.538680\pi$
$709$	−2.07195e29			−0.242435			−0.121217	+	0.992626i	$0.538680\pi$
$710$	5.72306e28			0.0659805
$711$	3.19950e29	−	1.60256e30i	0.363455	−	1.82046i
$712$		−	1.61510e30i		−	1.80784i
$713$	1.03414e29			0.114061
$714$	8.98275e28	+	5.59057e29i	0.0976289	+	0.607610i
$715$	1.49922e27			0.00160566
$716$		−	5.88689e29i		−	0.621297i
$717$	7.96497e28	−	6.53195e28i	0.0828386	−	0.0679347i
$718$	−7.03914e29			−0.721461
$719$	−4.91706e29			−0.496651			−0.248326	−	0.968677i	$-0.579880\pi$
$719$	−4.91706e29			−0.496651			−0.248326	+	0.968677i	$0.579880\pi$
$720$	2.28194e28	−	1.14297e29i	0.0227150	−	0.113774i
$721$	9.29879e29	+	5.41781e29i	0.912234	+	0.531500i
$722$			6.21356e29i			0.600759i
$723$	−1.30602e30	+	1.07105e30i	−1.24451	+	1.02061i
$724$		−	8.18666e28i		−	0.0768868i
$725$		−	2.57797e29i		−	0.238632i
$726$	6.30699e29	−	5.17227e29i	0.575424	−	0.471897i
$727$			1.76811e30i			1.59000i	0.606609	+	0.795001i	$0.292529\pi$
$727$			1.76811e30i			1.59000i	−0.606609	+	0.795001i	$0.707471\pi$
$728$	−4.15351e29	+	7.12883e29i	−0.368159	+	0.631886i
$729$	6.37908e29	−	9.50313e29i	0.557338	−	0.830286i
$730$	−3.28865e29			−0.283223
$731$	−1.95610e29			−0.166058
$732$	4.11924e29	−	3.37813e29i	0.344708	−	0.282690i
$733$			3.09927e29i			0.255663i	0.991796	+	0.127832i	$0.0408017\pi$
$733$			3.09927e29i			0.255663i	−0.991796	+	0.127832i	$0.959198\pi$
$734$	−1.15700e30			−0.940860
$735$	−1.46831e29	+	3.80551e29i	−0.117707	+	0.305067i
$736$	4.36471e29			0.344936
$737$		−	9.79974e27i		−	0.00763495i
$738$	−1.75231e29	−	3.49849e28i	−0.134592	−	0.0268713i
$739$	−1.92783e29			−0.145983			−0.0729915	−	0.997333i	$-0.523255\pi$
$739$	−1.92783e29			−0.145983			−0.0729915	+	0.997333i	$0.523255\pi$
$740$	−2.41896e29			−0.180591
$741$	−2.57021e29	−	3.13407e29i	−0.189181	−	0.230684i
$742$	−2.79143e29	+	4.79104e29i	−0.202575	+	0.347688i
$743$		−	8.09967e29i		−	0.579542i	−0.957096	−	0.289771i	$-0.906421\pi$
$743$		−	8.09967e29i		−	0.579542i	0.957096	−	0.289771i	$-0.0935791\pi$
$744$	2.59807e29	+	3.16805e29i	0.183289	+	0.223499i
$745$			4.10479e29i			0.285529i
$746$		−	3.06591e29i		−	0.210282i
$747$	2.64543e29	−	1.32503e30i	0.178908	−	0.896108i
$748$			3.99788e27i			0.00266601i
$749$	−1.68388e30	−	9.81086e29i	−1.10726	−	0.645131i
$750$	−5.49356e29	+	4.50519e29i	−0.356214	+	0.292126i
$751$	−9.79340e29			−0.626201			−0.313101	−	0.949720i	$-0.601368\pi$
$751$	−9.79340e29			−0.626201			−0.313101	+	0.949720i	$0.601368\pi$
$752$	−3.69826e29			−0.233190
$753$	−1.68150e30	−	2.05039e30i	−1.04556	−	1.27494i
$754$			2.20359e29i			0.135124i
$755$	−7.83523e29			−0.473815
$756$	−2.82289e28	+	7.47556e29i	−0.0168351	+	0.445825i
$757$	−1.72229e30			−1.01298			−0.506489	−	0.862246i	$-0.669057\pi$
$757$	−1.72229e30			−1.01298			−0.506489	+	0.862246i	$0.669057\pi$
$758$		−	2.12497e29i		−	0.123261i
$759$	−3.40189e27	−	4.14822e27i	−0.00194617	−	0.00237314i
$760$	−2.73839e29			−0.154509
$761$	2.24991e30			1.25206			0.626032	−	0.779797i	$-0.284678\pi$
$761$	2.24991e30			1.25206			0.626032	+	0.779797i	$0.284678\pi$
$762$	−6.15036e29	+	5.04382e29i	−0.337578	+	0.276842i
$763$	−5.53254e29	+	9.49572e29i	−0.299514	+	0.514068i
$764$			1.51208e30i			0.807411i
$765$	−1.00512e29	+	5.03443e29i	−0.0529388	+	0.265158i
$766$		−	1.62834e30i		−	0.845945i
$767$			1.41663e30i			0.725946i
$768$	1.29513e30	+	1.57926e30i	0.654668	+	0.798292i
$769$			3.91252e30i			1.95088i	0.220271	+	0.975439i	$0.429306\pi$
$769$			3.91252e30i			1.95088i	−0.220271	+	0.975439i	$0.570694\pi$
$770$	1.79987e27	−	3.08919e27i	0.000885297	−	0.00151947i
$771$	−1.85391e30	−	2.26063e30i	−0.899535	−	1.09688i
$772$	1.79648e29			0.0859888
$773$	9.37932e29			0.442881			0.221440	−	0.975174i	$-0.428924\pi$
$773$	9.37932e29			0.442881			0.221440	+	0.975174i	$0.428924\pi$
$774$	3.14622e29	+	6.28143e28i	0.146558	+	0.0292603i
$775$		−	5.21930e29i		−	0.239853i
$776$	1.83804e29			0.0833310
$777$	−2.73260e30	+	4.39066e29i	−1.22224	+	0.196385i
$778$	1.75670e30			0.775195
$779$			1.85979e29i			0.0809692i
$780$	−1.78445e29	+	1.46340e29i	−0.0766499	+	0.0628595i
$781$	4.62326e27			0.00195935
$782$	6.25050e29			0.261363
$783$	3.04690e29	+	5.71496e29i	0.125707	+	0.235784i
$784$	4.29818e29	+	7.58254e29i	0.174971	+	0.308671i
$785$		−	5.70555e28i		−	0.0229174i
$786$	1.41386e30	−	1.15949e30i	0.560364	−	0.459546i
$787$			5.38816e29i			0.210720i	0.994434	+	0.105360i	$0.0335995\pi$
$787$			5.38816e29i			0.210720i	−0.994434	+	0.105360i	$0.966400\pi$
$788$			1.15844e30i			0.447042i
$789$	3.85150e30	−	3.15856e30i	1.46663	−	1.20276i
$790$		−	1.20222e30i		−	0.451752i
$791$	−3.90778e30	−	2.27681e30i	−1.44903	−	0.844256i
$792$	4.16134e27	−	2.08432e28i	0.00152272	−	0.00762693i
$793$	1.88030e30			0.678984
$794$	2.37760e29			0.0847273
$795$	−3.88735e29	+	3.18796e29i	−0.136710	+	0.112114i
$796$		−	1.77834e30i		−	0.617203i
$797$	1.93642e30			0.663264			0.331632	−	0.943409i	$-0.392401\pi$
$797$	1.93642e30			0.663264			0.331632	+	0.943409i	$0.392401\pi$
$798$	−9.54346e29	+	1.53341e29i	−0.322608	+	0.0518357i
$799$	1.62897e30			0.543464
$800$		−	2.20287e30i		−	0.725345i
$801$	1.01198e30	−	5.06877e30i	0.328875	−	1.64726i
$802$	1.85213e30			0.594075
$803$	−2.65667e28			−0.00841056
$804$	9.56560e29	+	1.16641e30i	0.298898	+	0.364472i
$805$	3.89051e29	+	2.26675e29i	0.119991	+	0.0699112i
$806$			4.46134e29i			0.135815i
$807$	1.11287e30	+	1.35702e30i	0.334406	+	0.407770i
$808$		−	2.54431e30i		−	0.754660i
$809$			5.89657e30i			1.72639i	0.504867	+	0.863197i	$0.331542\pi$
$809$			5.89657e30i			1.72639i	−0.504867	+	0.863197i	$0.668458\pi$
$810$	3.23331e29	−	7.77468e29i	0.0934446	−	0.224693i
$811$			5.40534e30i			1.54207i	0.636793	+	0.771035i	$0.280261\pi$
$811$			5.40534e30i			1.54207i	−0.636793	+	0.771035i	$0.719739\pi$
$812$	−3.65751e29	−	2.13099e29i	−0.103002	−	0.0600128i
$813$	4.53097e29	−	3.71578e29i	0.125962	−	0.103300i
$814$	2.42590e28			0.00665758
$815$	−1.22265e30			−0.331245
$816$	6.95631e29	+	8.48242e29i	0.186051	+	0.226868i
$817$		−	3.33919e29i		−	0.0881677i
$818$	−1.09358e30			−0.285062
$819$	−1.75020e30	+	1.97704e30i	−0.450409	+	0.508786i
$820$	1.05891e29			0.0269038
$821$		−	2.36026e30i		−	0.592047i	−0.955181	−	0.296024i	$-0.904339\pi$
$821$		−	2.36026e30i		−	0.592047i	0.955181	−	0.296024i	$-0.0956607\pi$
$822$	−2.82466e30	−	3.44435e30i	−0.699540	−	0.853009i
$823$	4.60455e30			1.12587			0.562936	−	0.826501i	$-0.309672\pi$
$823$	4.60455e30			1.12587			0.562936	+	0.826501i	$0.309672\pi$
$824$	4.70671e30			1.13627
$825$	−2.09361e28	+	1.71694e28i	−0.00499033	+	0.00409249i
$826$	2.91900e30	+	1.70071e30i	0.686978	+	0.400258i
$827$			5.99819e30i			1.39384i	0.717150	+	0.696919i	$0.245446\pi$
$827$			5.99819e30i			1.39384i	−0.717150	+	0.696919i	$0.754554\pi$
$828$	8.09821e29	+	1.61681e29i	0.185811	+	0.0370970i
$829$			2.77814e30i			0.629406i	0.949190	+	0.314703i	$0.101905\pi$
$829$			2.77814e30i			0.629406i	−0.949190	+	0.314703i	$0.898095\pi$
$830$		−	9.94027e29i		−	0.222371i
$831$	−4.14707e30	−	5.05687e30i	−0.916073	−	1.11705i
$832$			2.98829e30i			0.651821i
$833$	−1.89321e30	−	3.33987e30i	−0.407780	−	0.719378i
$834$	−5.07118e29	−	6.18372e29i	−0.107861	−	0.131524i
$835$	2.53305e30			0.532031
$836$	−6.82463e27			−0.00141551
$837$	6.16869e29	+	1.15704e30i	0.126350	+	0.236990i
$838$		−	3.52494e30i		−	0.713000i
$839$	1.52551e30			0.304730			0.152365	−	0.988324i	$-0.451311\pi$
$839$	1.52551e30			0.304730			0.152365	+	0.988324i	$0.451311\pi$
$840$	2.83004e29	+	1.76132e30i	0.0558290	+	0.347461i
$841$	4.76638e30			0.928604
$842$		−	4.32786e30i		−	0.832714i
$843$	−4.53088e29	+	3.71571e29i	−0.0860981	+	0.0706078i
$844$	−2.63183e30			−0.493927
$845$	9.49568e29			0.176007
$846$	−2.62005e30	−	5.23093e29i	−0.479646	−	0.0957613i
$847$	−2.78410e30	+	4.77846e30i	−0.503395	+	0.863996i
$848$			1.07427e30i			0.191847i
$849$	−4.22630e30	+	3.46592e30i	−0.745468	+	0.611348i
$850$		−	3.15463e30i		−	0.549604i
$851$			3.05516e30i			0.525744i
$852$	−5.50284e29	+	4.51280e29i	−0.0935344	+	0.0767062i
$853$		−	1.94054e30i		−	0.325806i	−0.986642	−	0.162903i	$-0.947914\pi$
$853$		−	1.94054e30i		−	0.325806i	0.986642	−	0.162903i	$-0.0520857\pi$
$854$	2.25737e30	−	3.87441e30i	0.374365	−	0.642537i
$855$	−8.59409e29	−	1.71581e29i	−0.140785	−	0.0281077i
$856$	−8.52317e30			−1.37920
$857$	1.03943e31			1.66149			0.830744	−	0.556655i	$-0.187915\pi$
$857$	1.03943e31			1.66149			0.830744	+	0.556655i	$0.187915\pi$
$858$	1.78957e28	−	1.46760e28i	0.00282574	−	0.00231735i
$859$		−	3.88737e30i		−	0.606356i	−0.952934	−	0.303178i	$-0.901952\pi$
$859$		−	3.88737e30i		−	0.606356i	0.952934	−	0.303178i	$-0.0980476\pi$
$860$	−1.90124e29			−0.0292957
$861$	1.19621e30	−	1.92203e29i	0.182085	−	0.0292568i
$862$	−6.86994e30			−1.03306
$863$		−	5.66899e29i		−	0.0842155i	−0.999113	−	0.0421078i	$-0.986593\pi$
$863$		−	5.66899e29i		−	0.0842155i	0.999113	−	0.0421078i	$-0.0134073\pi$
$864$	2.60357e30	+	4.88344e30i	0.382099	+	0.716690i
$865$	9.62347e29			0.139528
$866$	6.72461e30			0.963228
$867$	1.41693e30	+	1.72778e30i	0.200515	+	0.244505i
$868$	−7.40491e29	−	4.31437e29i	−0.103529	−	0.0603198i
$869$		−	9.71191e28i		−	0.0134152i
$870$	3.02128e29	+	3.68411e29i	0.0412325	+	0.0502783i
$871$			5.32432e30i			0.717915i
$872$			4.80639e30i			0.640318i
$873$	5.76844e29	+	1.15167e29i	0.0759293	+	0.0151593i
$874$			1.06700e30i			0.138770i
$875$	2.42502e30	−	4.16216e30i	0.311624	−	0.534853i
$876$	3.16211e30	−	2.59320e30i	0.401498	−	0.329263i
$877$	3.63806e29			0.0456430			0.0228215	−	0.999740i	$-0.492735\pi$
$877$	3.63806e29			0.0456430			0.0228215	+	0.999740i	$0.492735\pi$
$878$	−8.90911e30			−1.10444
$879$	−7.22050e30	−	8.80457e30i	−0.884472	−	1.07851i
$880$		−	6.92671e27i		−	0.000838415i
$881$	−1.48754e31			−1.77918			−0.889591	−	0.456758i	$-0.849010\pi$
$881$	−1.48754e31			−1.77918			−0.889591	+	0.456758i	$0.849010\pi$
$882$	1.97257e30	+	5.97984e30i	0.233138	+	0.706756i
$883$	8.98766e29			0.104969			0.0524843	−	0.998622i	$-0.483286\pi$
$883$	8.98766e29			0.104969			0.0524843	+	0.998622i	$0.483286\pi$
$884$		−	2.17209e30i		−	0.250686i
$885$	1.94230e30	+	2.36841e30i	0.221519	+	0.270118i
$886$	−2.09708e30			−0.236353
$887$	−1.04913e30			−0.116851			−0.0584253	−	0.998292i	$-0.518608\pi$
$887$	−1.04913e30			−0.116851			−0.0584253	+	0.998292i	$0.518608\pi$
$888$	−9.35941e30	+	7.67551e30i	−1.03018	+	0.844834i
$889$	2.71496e30	−	4.65979e30i	0.295321	−	0.506871i
$890$		−	3.80254e30i		−	0.408770i
$891$	2.61196e28	−	6.28063e28i	0.00277493	−	0.00667248i
$892$			2.29889e29i			0.0241373i
$893$			2.78075e30i			0.288550i
$894$	4.01821e30	+	4.89974e30i	0.412087	+	0.502492i
$895$		−	4.49260e30i		−	0.455362i
$896$	−8.47793e29	−	4.93954e29i	−0.0849289	−	0.0494826i
$897$	1.84829e30	+	2.25378e30i	0.182999	+	0.223146i
$898$	−1.82357e30			−0.178452
$899$	−7.41941e29			−0.0717617
$900$	8.16003e29	−	4.08717e30i	0.0780091	−	0.390730i
$901$		−	4.73181e30i		−	0.447113i
$902$	−1.06195e28			−0.000991823
$903$	−2.14775e30	+	3.45094e29i	−0.198273	+	0.0318578i
$904$	−1.97798e31			−1.80490
$905$		−	6.24769e29i		−	0.0563520i
$906$	−9.35264e30	+	7.66996e30i	−0.833850	+	0.683828i
$907$	−8.65904e30			−0.763120			−0.381560	−	0.924344i	$-0.624613\pi$
$907$	−8.65904e30			−0.763120			−0.381560	+	0.924344i	$0.624613\pi$
$908$	−1.01456e31			−0.883849
$909$	1.59420e30	−	7.98499e30i	0.137285	−	0.687628i
$910$	−9.77892e29	+	1.67839e30i	−0.0832446	+	0.142876i
$911$		−	1.30878e31i		−	1.10135i	−0.834720	−	0.550674i	$-0.814371\pi$
$911$		−	1.30878e31i		−	1.10135i	0.834720	−	0.550674i	$-0.185629\pi$
$912$	−1.44800e30	+	1.18749e30i	−0.120455	+	0.0987831i
$913$		−	8.03005e28i		−	0.00660352i
$914$		−	8.54558e30i		−	0.694715i
$915$	3.14362e30	−	2.57803e30i	0.252644	−	0.207189i
$916$		−	6.58318e30i		−	0.523038i
$917$	−6.24122e30	+	1.07120e31i	−0.490220	+	0.841384i
$918$	3.72846e30	+	6.99334e30i	0.289522	+	0.543046i
$919$	−6.25718e29			−0.0480359			−0.0240179	−	0.999712i	$-0.507646\pi$
$919$	−6.25718e29			−0.0480359			−0.0240179	+	0.999712i	$0.507646\pi$
$920$	1.96923e30			0.149460
$921$	1.70495e31	−	1.39820e31i	1.27934	−	1.04916i
$922$			6.34709e30i			0.470869i
$923$	−2.51187e30			−0.184238
$924$	7.05302e27	+	4.38957e28i	0.000511469	+	0.00318322i
$925$	1.54194e31			1.10555
$926$			3.11992e30i			0.221171i
$927$	1.47714e31	+	2.94911e30i	1.03534	+	0.206706i
$928$	−3.13146e30			−0.217017
$929$	3.76917e30			0.258274			0.129137	−	0.991627i	$-0.458779\pi$
$929$	3.76917e30			0.258274			0.129137	+	0.991627i	$0.458779\pi$
$930$	6.11683e29	+	7.45877e29i	0.0414434	+	0.0505355i
$931$	5.70137e30	−	3.23183e30i	0.381951	−	0.216510i
$932$		−	3.03997e30i		−	0.201374i
$933$	8.87353e30	+	1.08202e31i	0.581218	+	0.708729i
$934$		−	1.61873e31i		−	1.04841i
$935$			3.05100e28i			0.00195398i
$936$	−2.26091e30	+	1.13244e31i	−0.143181	+	0.717162i
$937$		−	5.44084e30i		−	0.340722i	−0.985382	−	0.170361i	$-0.945507\pi$
$937$		−	5.44084e30i		−	0.340722i	0.985382	−	0.170361i	$-0.0544934\pi$
$938$	1.09709e31	+	6.39203e30i	0.679379	+	0.395830i
$939$	8.35244e30	−	6.84971e30i	0.511475	−	0.419453i
$940$	1.58328e30			0.0958772
$941$	1.75096e29			0.0104854			0.00524270	−	0.999986i	$-0.498331\pi$
$941$	1.75096e29			0.0104854			0.00524270	+	0.999986i	$0.498331\pi$
$942$	−5.58520e29	−	6.81051e29i	−0.0330753	−	0.0403316i
$943$		−	1.33741e30i		−	0.0783234i
$944$	6.54509e30			0.379062
$945$	−2.15431e29	+	5.70500e30i	−0.0123388	+	0.326755i
$946$	1.90669e28			0.00108000
$947$		−	1.67680e30i		−	0.0939305i	−0.998897	−	0.0469652i	$-0.985045\pi$
$947$		−	1.67680e30i		−	0.0939305i	0.998897	−	0.0469652i	$-0.0149550\pi$
$948$	9.47986e30	+	1.15596e31i	0.525188	+	0.640406i
$949$	1.44340e31			0.790847
$950$	5.38516e30			0.291810
$951$	1.18568e31	−	9.72360e30i	0.635437	−	0.521113i
$952$	−1.45075e31	−	8.45260e30i	−0.768963	−	0.448025i
$953$			2.58264e31i			1.35390i	0.736027	+	0.676952i	$0.236700\pi$
$953$			2.58264e31i			1.35390i	−0.736027	+	0.676952i	$0.763300\pi$
$954$	−1.51948e30	+	7.61071e30i	−0.0787837	+	0.394609i
$955$			1.15395e31i			0.591769i
$956$			9.42330e29i			0.0477964i
$957$	2.44069e28	+	2.97614e28i	0.00122444	+	0.00149306i
$958$		−	2.21189e31i		−	1.09756i
$959$	2.60959e31	+	1.52044e31i	1.28079	+	0.746233i
$960$	4.09717e30	+	4.99603e30i	0.198900	+	0.242536i
$961$	1.93234e31			0.927871
$962$	−1.31802e31			−0.626014
$963$	−2.67489e31	−	5.34041e30i	−1.25669	−	0.250899i
$964$		−	1.54515e31i		−	0.718061i
$965$	1.37100e30			0.0630230
$966$	6.86290e30	−	1.10271e30i	0.312067	−	0.0501419i
$967$	−2.54600e31			−1.14520			−0.572599	−	0.819836i	$-0.694065\pi$
$967$	−2.54600e31			−1.14520			−0.572599	+	0.819836i	$0.694065\pi$
$968$			2.41868e31i			1.07619i
$969$	6.37799e30	−	5.23050e30i	0.280727	−	0.230220i
$970$	4.32743e29			0.0188420
$971$	−4.36527e31			−1.88022			−0.940111	−	0.340868i	$-0.889279\pi$
$971$	−4.36527e31			−1.88022			−0.940111	+	0.340868i	$0.889279\pi$
$972$	3.02167e30	+	1.00251e31i	0.128751	+	0.427161i
$973$	4.68506e30	+	2.72968e30i	0.197483	+	0.115061i
$974$		−	1.50221e31i		−	0.626415i
$975$	1.13748e31	−	9.32833e30i	0.469241	−	0.384818i
$976$		−	8.68737e30i		−	0.354540i
$977$			2.05782e31i			0.830833i	0.909631	+	0.415416i	$0.136364\pi$
$977$			2.05782e31i			0.830833i	−0.909631	+	0.415416i	$0.863636\pi$
$978$	−1.45944e31	+	1.19687e31i	−0.582946	+	0.478065i
$979$		−	3.07181e29i		−	0.0121388i
$980$	−1.84011e30	−	3.24620e30i	−0.0719401	−	0.126912i
$981$	−3.01156e30	+	1.50842e31i	−0.116484	+	0.583443i
$982$	2.31648e31			0.886457
$983$	1.33127e31			0.504027			0.252013	−	0.967724i	$-0.418907\pi$
$983$	1.33127e31			0.504027			0.252013	+	0.967724i	$0.418907\pi$
$984$	4.09712e30	−	3.35999e30i	0.153472	−	0.125860i
$985$			8.84069e30i			0.327647i
$986$	−4.48441e30			−0.164436
$987$	1.78857e31	−	2.87381e30i	0.648896	−	0.104262i
$988$	3.70790e30			0.133101
$989$			2.40128e30i			0.0852868i
$990$	9.79735e27	−	4.90727e28i	0.000344302	−	0.00172453i
$991$	1.15424e31			0.401350			0.200675	−	0.979658i	$-0.435686\pi$
$991$	1.15424e31			0.401350			0.200675	+	0.979658i	$0.435686\pi$
$992$	−6.33989e30			−0.218127
$993$	−1.07443e31	−	1.31015e31i	−0.365774	−	0.446019i
$994$	−3.01559e30	+	5.17578e30i	−0.101582	+	0.174349i
$995$		−	1.35715e31i		−	0.452361i
$996$	7.83819e30	+	9.55777e30i	0.258519	+	0.315234i
$997$			3.21188e31i			1.04824i	0.851645	+	0.524119i	$0.175605\pi$
$997$			3.21188e31i			1.04824i	−0.851645	+	0.524119i	$0.824395\pi$
$998$		−	5.24959e30i		−	0.169533i
$999$	−3.41825e31	+	1.82242e31i	−1.09236	+	0.582387i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.22.c.b.20.34	yes	52
3.2	odd	2	inner	21.22.c.b.20.19	✓	52
7.6	odd	2	inner	21.22.c.b.20.20	yes	52
21.20	even	2	inner	21.22.c.b.20.33	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.22.c.b.20.19	✓	52	3.2	odd	2	inner
21.22.c.b.20.20	yes	52	7.6	odd	2	inner
21.22.c.b.20.33	yes	52	21.20	even	2	inner
21.22.c.b.20.34	yes	52	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+1077.74i q^{2} +(-64855.1 - 79083.3i) q^{3} +935630. q^{4} +7.14030e6 q^{5} +(8.52312e7 - 6.98969e7i) q^{6} +(-3.76236e8 + 6.45749e8i) q^{7} +3.26855e9i q^{8} +(-2.04799e9 + 1.02579e10i) q^{9} +O(q^{10})\)	\(q+1077.74i q^{2} +(-64855.1 - 79083.3i) q^{3} +935630. q^{4} +7.14030e6 q^{5} +(8.52312e7 - 6.98969e7i) q^{6} +(-3.76236e8 + 6.45749e8i) q^{7} +3.26855e9i q^{8} +(-2.04799e9 + 1.02579e10i) q^{9} +7.69538e9i q^{10} +6.21657e8i q^{11} +(-6.06803e10 - 7.39927e10i) q^{12} -3.37753e11i q^{13} +(-6.95949e11 - 4.05485e11i) q^{14} +(-4.63085e11 - 5.64679e11i) q^{15} -1.56049e12 q^{16} +6.87345e12 q^{17} +(-1.10554e13 - 2.20720e12i) q^{18} +1.17334e13i q^{19} +6.68068e12 q^{20} +(7.54688e13 - 1.21261e13i) q^{21} -6.69984e11 q^{22} -8.43774e13i q^{23} +(2.58488e14 - 2.11982e14i) q^{24} -4.25853e14 q^{25} +3.64010e14 q^{26} +(9.44052e14 - 5.03316e14i) q^{27} +(-3.52018e14 + 6.04182e14i) q^{28} +6.05365e14i q^{29} +(6.08576e14 - 4.99085e14i) q^{30} +1.22561e15i q^{31} +5.17285e15i q^{32} +(4.91627e13 - 4.03176e13i) q^{33} +7.40779e15i q^{34} +(-2.68644e15 + 4.61084e15i) q^{35} +(-1.91616e15 + 9.59760e15i) q^{36} -3.62083e16 q^{37} -1.26456e16 q^{38} +(-2.67107e16 + 2.19050e16i) q^{39} +2.33384e16i q^{40} +1.58503e16 q^{41} +(1.30688e16 + 8.13357e16i) q^{42} -2.84588e16 q^{43} +5.81640e14i q^{44} +(-1.46233e16 + 7.32446e16i) q^{45} +9.09368e16 q^{46} +2.36994e17 q^{47} +(1.01205e17 + 1.23408e17i) q^{48} +(-2.75438e17 - 4.85909e17i) q^{49} -4.58959e17i q^{50} +(-4.45778e17 - 5.43575e17i) q^{51} -3.16012e17i q^{52} -6.88418e17i q^{53} +(5.42443e17 + 1.01744e18i) q^{54} +4.43881e15i q^{55} +(-2.11066e18 - 1.22975e18i) q^{56} +(9.27917e17 - 7.60972e17i) q^{57} -6.52426e17 q^{58} -4.19426e18 q^{59} +(-4.33276e17 - 5.28330e17i) q^{60} +5.56709e18i q^{61} -1.32089e18 q^{62} +(-5.85351e18 - 5.18189e18i) q^{63} -8.84756e18 q^{64} -2.41166e18i q^{65} +(4.34519e16 + 5.29845e16i) q^{66} -1.57639e19 q^{67} +6.43100e18 q^{68} +(-6.67284e18 + 5.47230e18i) q^{69} +(-4.96929e18 - 2.89528e18i) q^{70} -7.43701e18i q^{71} +(-3.35285e19 - 6.69396e18i) q^{72} +4.27354e19i q^{73} -3.90231e19i q^{74} +(2.76187e19 + 3.36779e19i) q^{75} +1.09781e19i q^{76} +(-4.01434e17 - 2.33890e17i) q^{77} +(-2.36079e19 - 2.87871e19i) q^{78} -1.56226e20 q^{79} -1.11423e19 q^{80} +(-1.01030e20 - 4.20162e19i) q^{81} +1.70825e19i q^{82} -1.29172e20 q^{83} +(7.06109e19 - 1.13455e19i) q^{84} +4.90785e19 q^{85} -3.06712e19i q^{86} +(4.78743e19 - 3.92610e19i) q^{87} -2.03191e18 q^{88} -4.94133e20 q^{89} +(-7.89385e19 - 1.57601e19i) q^{90} +(2.18104e20 + 1.27075e20i) q^{91} -7.89460e19i q^{92} +(9.69253e19 - 7.94870e19i) q^{93} +2.55418e20i q^{94} +8.37801e19i q^{95} +(4.09086e20 - 3.35485e20i) q^{96} -5.62341e19i q^{97} +(5.23683e20 - 2.96851e20i) q^{98} +(-6.37690e18 - 1.27315e18i) 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

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