LMFDB - Embedded newform 21.22.c.b.20.16

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			20.16
Character	$\chi$	$=$	21.20
Dual form			21.22.c.b.20.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2502.20i q^{2} +(-102208. - 3714.28i) q^{3} -4.16388e6 q^{4} -1.82569e7 q^{5} +(9.29389e6 - 2.55746e8i) q^{6} +(-7.47262e8 - 1.20672e7i) q^{7} -5.17136e9i q^{8} +(1.04328e10 + 7.59261e8i) q^{9} +O(q^{10})$	\(q+2502.20i q^{2} +(-102208. - 3714.28i) q^{3} -4.16388e6 q^{4} -1.82569e7 q^{5} +(9.29389e6 - 2.55746e8i) q^{6} +(-7.47262e8 - 1.20672e7i) q^{7} -5.17136e9i q^{8} +(1.04328e10 + 7.59261e8i) q^{9} -4.56824e10i q^{10} -6.04302e10i q^{11} +(4.25583e11 + 1.54658e10i) q^{12} +4.37169e11i q^{13} +(3.01945e10 - 1.86980e12i) q^{14} +(1.86601e12 + 6.78111e10i) q^{15} +4.20753e12 q^{16} +1.17175e13 q^{17} +(-1.89983e12 + 2.61049e13i) q^{18} -1.52935e13i q^{19} +7.60193e13 q^{20} +(7.63316e13 + 4.00890e12i) q^{21} +1.51209e14 q^{22} -2.33876e14i q^{23} +(-1.92079e13 + 5.28557e14i) q^{24} -1.43524e14 q^{25} -1.09389e15 q^{26} +(-1.06350e15 - 1.16353e14i) q^{27} +(3.11151e15 + 5.02462e13i) q^{28} -1.65948e15i q^{29} +(-1.69677e14 + 4.66913e15i) q^{30} +6.51175e15i q^{31} -3.17034e14i q^{32} +(-2.24455e14 + 6.17647e15i) q^{33} +2.93196e16i q^{34} +(1.36427e16 + 2.20309e14i) q^{35} +(-4.34407e16 - 3.16147e15i) q^{36} +5.22826e15 q^{37} +3.82675e16 q^{38} +(1.62377e15 - 4.46824e16i) q^{39} +9.44129e16i q^{40} -5.69124e15 q^{41} +(-1.00311e16 + 1.90997e17i) q^{42} -1.25962e17 q^{43} +2.51624e17i q^{44} +(-1.90470e17 - 1.38617e16i) q^{45} +5.85206e17 q^{46} -2.94625e17 q^{47} +(-4.30045e17 - 1.56279e16i) q^{48} +(5.58255e17 + 1.80347e16i) q^{49} -3.59126e17i q^{50} +(-1.19763e18 - 4.35221e16i) q^{51} -1.82032e18i q^{52} -2.27799e18i q^{53} +(2.91139e17 - 2.66108e18i) q^{54} +1.10327e18i q^{55} +(-6.24037e16 + 3.86436e18i) q^{56} +(-5.68044e16 + 1.56313e18i) q^{57} +4.15236e18 q^{58} +3.70144e18 q^{59} +(-7.76981e18 - 2.82357e17i) q^{60} -1.05348e19i q^{61} -1.62937e19 q^{62} +(-7.78684e18 - 6.93261e17i) q^{63} +9.61712e18 q^{64} -7.98134e18i q^{65} +(-1.54548e19 - 5.61631e17i) q^{66} -2.59967e18 q^{67} -4.87903e19 q^{68} +(-8.68682e17 + 2.39041e19i) q^{69} +(-5.51257e17 + 3.41367e19i) q^{70} +3.94068e19i q^{71} +(3.92642e18 - 5.39516e19i) q^{72} +1.65922e19i q^{73} +1.30822e19i q^{74} +(1.46694e19 + 5.33088e17i) q^{75} +6.36803e19i q^{76} +(-7.29221e17 + 4.51572e19i) q^{77} +(1.11804e20 + 4.06300e18i) q^{78} -5.35555e19 q^{79} -7.68163e19 q^{80} +(1.08266e20 + 1.58424e19i) q^{81} -1.42406e19i q^{82} -2.97531e19 q^{83} +(-3.17835e20 - 1.66926e19i) q^{84} -2.13925e20 q^{85} -3.15182e20i q^{86} +(-6.16378e18 + 1.69613e20i) q^{87} -3.12507e20 q^{88} -3.34783e20 q^{89} +(3.46849e19 - 4.76594e20i) q^{90} +(5.27540e18 - 3.26680e20i) q^{91} +9.73832e20i q^{92} +(2.41865e19 - 6.65556e20i) q^{93} -7.37211e20i q^{94} +2.79212e20i q^{95} +(-1.17755e18 + 3.24035e19i) q^{96} -6.17354e20i q^{97} +(-4.51264e19 + 1.39687e21i) q^{98} +(4.58823e19 - 6.30454e20i) 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 $

$2$			2502.20i			1.72786i	0.503614	+	0.863929i	$0.332003\pi$
$2$			2502.20i			1.72786i	−0.503614	+	0.863929i	$0.667997\pi$
$3$	−102208.	−	3714.28i	−0.999340	−	0.0363163i
$3$	−102208.	−	3714.28i	−0.999340	−	0.0363163i
$4$	−4.16388e6			−1.98549
$5$	−1.82569e7			−0.836067			−0.418034	−	0.908432i	$-0.637281\pi$
$5$	−1.82569e7			−0.836067			−0.418034	+	0.908432i	$0.637281\pi$
$6$	9.29389e6	−	2.55746e8i	0.0627493	−	1.72672i
$7$	−7.47262e8	−	1.20672e7i	−0.999870	−	0.0161464i
$7$	−7.47262e8	−	1.20672e7i	−0.999870	−	0.0161464i
$8$		−	5.17136e9i		−	1.70279i
$9$	1.04328e10	+	7.59261e8i	0.997362	+	0.0725846i
$10$		−	4.56824e10i		−	1.44460i
$11$		−	6.04302e10i		−	0.702475i	−0.936286	−	0.351237i	$-0.885761\pi$
$11$		−	6.04302e10i		−	0.702475i	0.936286	−	0.351237i	$-0.114239\pi$
$12$	4.25583e11	+	1.54658e10i	1.98418	+	0.0721056i
$13$			4.37169e11i			0.879517i	0.898116	+	0.439759i	$0.144936\pi$
$13$			4.37169e11i			0.879517i	−0.898116	+	0.439759i	$0.855064\pi$
$14$	3.01945e10	−	1.86980e12i	0.0278987	−	1.72763i
$15$	1.86601e12	+	6.78111e10i	0.835516	+	0.0303629i
$16$	4.20753e12			0.956682
$17$	1.17175e13			1.40968			0.704842	−	0.709364i	$-0.251018\pi$
$17$	1.17175e13			1.40968			0.704842	+	0.709364i	$0.251018\pi$
$18$	−1.89983e12	+	2.61049e13i	−0.125416	+	1.72330i
$19$		−	1.52935e13i		−	0.572261i	−0.958191	−	0.286131i	$-0.907631\pi$
$19$		−	1.52935e13i		−	0.572261i	0.958191	−	0.286131i	$-0.0923691\pi$
$20$	7.60193e13			1.66000
$21$	7.63316e13	+	4.00890e12i	0.998624	+	0.0524473i
$22$	1.51209e14			1.21378
$23$		−	2.33876e14i		−	1.17718i	−0.808431	−	0.588592i	$-0.799683\pi$
$23$		−	2.33876e14i		−	1.17718i	0.808431	−	0.588592i	$-0.200317\pi$
$24$	−1.92079e13	+	5.28557e14i	−0.0618389	+	1.70166i
$25$	−1.43524e14			−0.300992
$26$	−1.09389e15			−1.51968
$27$	−1.06350e15	−	1.16353e14i	−0.994068	−	0.108757i
$28$	3.11151e15	+	5.02462e13i	1.98523	+	0.0320585i
$29$		−	1.65948e15i		−	0.732477i	−0.930521	−	0.366238i	$-0.880646\pi$
$29$		−	1.65948e15i		−	0.732477i	0.930521	−	0.366238i	$-0.119354\pi$
$30$	−1.69677e14	+	4.66913e15i	−0.0524627	+	1.44365i
$31$			6.51175e15i			1.42692i	0.700696	+	0.713460i	$0.252873\pi$
$31$			6.51175e15i			1.42692i	−0.700696	+	0.713460i	$0.747127\pi$
$32$		−	3.17034e14i		−	0.0497772i
$33$	−2.24455e14	+	6.17647e15i	−0.0255113	+	0.702012i
$34$			2.93196e16i			2.43573i
$35$	1.36427e16	+	2.20309e14i	0.835958	+	0.0134995i
$36$	−4.34407e16	−	3.16147e15i	−1.98025	−	0.144116i
$37$	5.22826e15			0.178747			0.0893735	−	0.995998i	$-0.471514\pi$
$37$	5.22826e15			0.178747			0.0893735	+	0.995998i	$0.471514\pi$
$38$	3.82675e16			0.988786
$39$	1.62377e15	−	4.46824e16i	0.0319408	−	0.878937i
$40$			9.44129e16i			1.42364i
$41$	−5.69124e15			−0.0662180			−0.0331090	−	0.999452i	$-0.510541\pi$
$41$	−5.69124e15			−0.0662180			−0.0331090	+	0.999452i	$0.510541\pi$
$42$	−1.00311e16	+	1.90997e17i	−0.0906214	+	1.72548i
$43$	−1.25962e17			−0.888833			−0.444416	−	0.895820i	$-0.646589\pi$
$43$	−1.25962e17			−0.888833			−0.444416	+	0.895820i	$0.646589\pi$
$44$			2.51624e17i			1.39476i
$45$	−1.90470e17	−	1.38617e16i	−0.833862	−	0.0606856i
$46$	5.85206e17			2.03400
$47$	−2.94625e17			−0.817037			−0.408518	−	0.912750i	$-0.633954\pi$
$47$	−2.94625e17			−0.817037			−0.408518	+	0.912750i	$0.633954\pi$
$48$	−4.30045e17	−	1.56279e16i	−0.956051	−	0.0347431i
$49$	5.58255e17	+	1.80347e16i	0.999479	+	0.0322886i
$50$		−	3.59126e17i		−	0.520070i
$51$	−1.19763e18	−	4.35221e16i	−1.40875	−	0.0511945i
$52$		−	1.82032e18i		−	1.74627i
$53$		−	2.27799e18i		−	1.78918i	−0.446886	−	0.894591i	$-0.647467\pi$
$53$		−	2.27799e18i		−	1.78918i	0.446886	−	0.894591i	$-0.352533\pi$
$54$	2.91139e17	−	2.66108e18i	0.187917	−	1.71761i
$55$			1.10327e18i			0.587316i
$56$	−6.24037e16	+	3.86436e18i	−0.0274939	+	1.70256i
$57$	−5.68044e16	+	1.56313e18i	−0.0207824	+	0.571884i
$58$	4.15236e18			1.26561
$59$	3.70144e18			0.942811			0.471405	−	0.881917i	$-0.343747\pi$
$59$	3.70144e18			0.942811			0.471405	+	0.881917i	$0.343747\pi$
$60$	−7.76981e18	−	2.82357e17i	−1.65891	−	0.0602852i
$61$		−	1.05348e19i		−	1.89087i	−0.325809	−	0.945436i	$-0.605637\pi$
$61$		−	1.05348e19i		−	1.89087i	0.325809	−	0.945436i	$-0.394363\pi$
$62$	−1.62937e19			−2.46552
$63$	−7.78684e18	−	6.93261e17i	−0.996060	−	0.0886790i
$64$	9.61712e18			1.04269
$65$		−	7.98134e18i		−	0.735336i
$66$	−1.54548e19	−	5.61631e17i	−1.21298	−	0.0440798i
$67$	−2.59967e18			−0.174234			−0.0871169	−	0.996198i	$-0.527765\pi$
$67$	−2.59967e18			−0.174234			−0.0871169	+	0.996198i	$0.527765\pi$
$68$	−4.87903e19			−2.79891
$69$	−8.68682e17	+	2.39041e19i	−0.0427509	+	1.17641i
$70$	−5.51257e17	+	3.41367e19i	−0.0233252	+	1.44442i
$71$			3.94068e19i			1.43668i	0.695694	+	0.718338i	$0.255097\pi$
$71$			3.94068e19i			1.43668i	−0.695694	+	0.718338i	$0.744903\pi$
$72$	3.92642e18	−	5.39516e19i	0.123596	−	1.69830i
$73$			1.65922e19i			0.451871i	0.974142	+	0.225936i	$0.0725439\pi$
$73$			1.65922e19i			0.451871i	−0.974142	+	0.225936i	$0.927456\pi$
$74$			1.30822e19i			0.308849i
$75$	1.46694e19	+	5.33088e17i	0.300793	+	0.0109309i
$76$			6.36803e19i			1.13622i
$77$	−7.29221e17	+	4.51572e19i	−0.0113424	+	0.702383i
$78$	1.11804e20	+	4.06300e18i	1.51868	+	0.0551891i
$79$	−5.35555e19			−0.636384			−0.318192	−	0.948026i	$-0.603076\pi$
$79$	−5.35555e19			−0.636384			−0.318192	+	0.948026i	$0.603076\pi$
$80$	−7.68163e19			−0.799850
$81$	1.08266e20	+	1.58424e19i	0.989463	+	0.144786i
$82$		−	1.42406e19i		−	0.114415i
$83$	−2.97531e19			−0.210480			−0.105240	−	0.994447i	$-0.533561\pi$
$83$	−2.97531e19			−0.210480			−0.105240	+	0.994447i	$0.533561\pi$
$84$	−3.17835e20	−	1.66926e19i	−1.98276	−	0.104134i
$85$	−2.13925e20			−1.17859
$86$		−	3.15182e20i		−	1.53578i
$87$	−6.16378e18	+	1.69613e20i	−0.0266008	+	0.731993i
$88$	−3.12507e20			−1.19617
$89$	−3.34783e20			−1.13807			−0.569034	−	0.822314i	$-0.692683\pi$
$89$	−3.34783e20			−1.13807			−0.569034	+	0.822314i	$0.692683\pi$
$90$	3.46849e19	−	4.76594e20i	0.104856	−	1.44079i
$91$	5.27540e18	−	3.26680e20i	0.0142010	−	0.879403i
$92$			9.73832e20i			2.33729i
$93$	2.41865e19	−	6.65556e20i	0.0518205	−	1.42598i
$94$		−	7.37211e20i		−	1.41172i
$95$			2.79212e20i			0.478449i
$96$	−1.17755e18	+	3.24035e19i	−0.00180772	+	0.0497444i
$97$		−	6.17354e20i		−	0.850023i	−0.905188	−	0.425012i	$-0.860270\pi$
$97$		−	6.17354e20i		−	0.850023i	0.905188	−	0.425012i	$-0.139730\pi$
$98$	−4.51264e19	+	1.39687e21i	−0.0557901	+	1.72696i
$99$	4.58823e19	−	6.30454e20i	0.0509889	−	0.700622i
$100$	5.97616e20			0.597616
$101$	1.89205e21			1.70435			0.852176	−	0.523255i	$-0.175283\pi$
$101$	1.89205e21			1.70435			0.852176	+	0.523255i	$0.175283\pi$
$102$	1.08901e20	−	2.99671e21i	0.0884568	−	2.43413i
$103$			2.49585e21i			1.82990i	0.403563	+	0.914952i	$0.367771\pi$
$103$			2.49585e21i			1.82990i	−0.403563	+	0.914952i	$0.632229\pi$
$104$	2.26076e21			1.49763
$105$	−1.39358e21	−	7.31900e19i	−0.834917	−	0.0438495i
$106$	5.69999e21			3.09145
$107$			1.21577e21i			0.597480i	0.954335	+	0.298740i	$0.0965663\pi$
$107$			1.21577e21i			0.597480i	−0.954335	+	0.298740i	$0.903434\pi$
$108$	4.42826e21	+	4.84480e20i	1.97371	+	0.215936i
$109$	−2.44406e21			−0.988856			−0.494428	−	0.869219i	$-0.664622\pi$
$109$	−2.44406e21			−0.988856			−0.494428	+	0.869219i	$0.664622\pi$
$110$	−2.76060e21			−1.01480
$111$	−5.34372e20	−	1.94192e19i	−0.178629	−	0.00649143i
$112$	−3.14413e21	−	5.07730e19i	−0.956557	−	0.0154470i
$113$			1.46567e21i			0.406173i	0.979161	+	0.203087i	$0.0650973\pi$
$113$			1.46567e21i			0.406173i	−0.979161	+	0.203087i	$0.934903\pi$
$114$	−3.91126e21	−	1.42136e20i	−0.988134	−	0.0359090i
$115$			4.26985e21i			0.984204i
$116$			6.90988e21i			1.45433i
$117$	−3.31926e20	+	4.56088e21i	−0.0638395	+	0.877198i
$118$			9.26176e21i			1.62904i
$119$	−8.75605e21	−	1.41397e20i	−1.40950	−	0.0227613i
$120$	3.50676e20	−	9.64979e21i	0.0517015	−	1.42271i
$121$	3.74844e21			0.506529
$122$	2.63602e22			3.26716
$123$	5.81692e20	+	2.11388e19i	0.0661743	+	0.00240479i
$124$		−	2.71141e22i		−	2.83314i
$125$	1.13259e22			1.08772
$126$	1.73468e21	−	1.94843e22i	0.153225	−	1.72105i
$127$	−1.56943e22			−1.27586			−0.637928	−	0.770096i	$-0.720208\pi$
$127$	−1.56943e22			−1.27586			−0.637928	+	0.770096i	$0.720208\pi$
$128$			2.33991e22i			1.75184i
$129$	1.28744e22	+	4.67857e20i	0.888247	+	0.0322791i
$130$	1.99710e22			1.27056
$131$	−1.89203e22			−1.11066			−0.555328	−	0.831632i	$-0.687407\pi$
$131$	−1.89203e22			−1.11066			−0.555328	+	0.831632i	$0.687407\pi$
$132$	9.34601e20	−	2.57181e22i	0.0506524	−	1.39384i
$133$	−1.84549e20	+	1.14283e22i	−0.00923997	+	0.572187i
$134$		−	6.50490e21i		−	0.301051i
$135$	1.94161e22	+	2.12424e21i	0.831108	+	0.0909284i
$136$		−	6.05955e22i		−	2.40039i
$137$			1.55013e22i			0.568594i	0.958736	+	0.284297i	$0.0917602\pi$
$137$			1.55013e22i			0.568594i	−0.958736	+	0.284297i	$0.908240\pi$
$138$	−5.98130e22	−	2.17362e21i	−2.03266	−	0.0738675i
$139$			4.26773e22i			1.34444i	0.740352	+	0.672220i	$0.234659\pi$
$139$			4.26773e22i			1.34444i	−0.740352	+	0.672220i	$0.765341\pi$
$140$	−5.68063e22	−	9.17338e20i	−1.65979	−	0.0268031i
$141$	3.01131e22	+	1.09432e21i	0.816498	+	0.0296717i
$142$	−9.86040e22			−2.48237
$143$	2.64182e22			0.617839
$144$	4.38962e22	+	3.19461e21i	0.954158	+	0.0694404i
$145$			3.02970e22i			0.612400i
$146$	−4.15171e22			−0.780769
$147$	−5.69913e22	−	3.91681e21i	−0.997647	−	0.0685647i
$148$	−2.17698e22			−0.354901
$149$		−	5.72238e22i		−	0.869203i	−0.900623	−	0.434601i	$-0.856889\pi$
$149$		−	5.72238e22i		−	0.869203i	0.900623	−	0.434601i	$-0.143111\pi$
$150$	−1.33390e21	+	3.67057e22i	−0.0188870	+	0.519727i
$151$	7.59752e22			1.00326			0.501631	−	0.865082i	$-0.332734\pi$
$151$	7.59752e22			1.00326			0.501631	+	0.865082i	$0.332734\pi$
$152$	−7.90883e22			−0.974439
$153$	1.22246e23	+	8.89665e21i	1.40597	+	0.102321i
$154$	−1.12993e23	−	1.82466e21i	−1.21362	−	0.0195981i
$155$		−	1.18884e23i		−	1.19300i
$156$	−6.76117e21	+	1.86052e23i	−0.0634182	+	1.74512i
$157$			1.67270e23i			1.46714i	0.679613	+	0.733571i	$0.262148\pi$
$157$			1.67270e23i			1.46714i	−0.679613	+	0.733571i	$0.737852\pi$
$158$		−	1.34007e23i		−	1.09958i
$159$	−8.46108e21	+	2.32829e23i	−0.0649764	+	1.78800i
$160$			5.78804e21i			0.0416171i
$161$	−2.82223e21	+	1.74767e23i	−0.0190073	+	1.17703i
$162$	−3.96409e22	+	2.70904e23i	−0.250170	+	1.70965i
$163$	8.95540e20			0.00529804			0.00264902	−	0.999996i	$-0.499157\pi$
$163$	8.95540e20			0.00529804			0.00264902	+	0.999996i	$0.499157\pi$
$164$	2.36976e22			0.131475
$165$	4.09784e21	−	1.12763e23i	0.0213291	−	0.586929i
$166$		−	7.44483e22i		−	0.363680i
$167$	−1.42420e23			−0.653204			−0.326602	−	0.945162i	$-0.605904\pi$
$167$	−1.42420e23			−0.653204			−0.326602	+	0.945162i	$0.605904\pi$
$168$	2.07315e22	−	3.94739e23i	0.0893066	−	1.70044i
$169$	5.59475e22			0.226449
$170$		−	5.35284e23i		−	2.03644i
$171$	1.16118e22	−	1.59554e23i	0.0415374	−	0.570752i
$172$	5.24489e23			1.76477
$173$	4.51867e22			0.143063			0.0715314	−	0.997438i	$-0.477211\pi$
$173$	4.51867e22			0.143063			0.0715314	+	0.997438i	$0.477211\pi$
$174$	−4.24407e23	−	1.54230e22i	−1.26478	−	0.0459624i
$175$	1.07250e23	+	1.73193e21i	0.300952	+	0.00485993i
$176$		−	2.54262e23i		−	0.672045i
$177$	−3.78318e23	−	1.37482e22i	−0.942189	−	0.0342394i
$178$		−	8.37695e23i		−	1.96642i
$179$			3.13845e23i			0.694637i	0.937747	+	0.347318i	$0.112908\pi$
$179$			3.13845e23i			0.694637i	−0.937747	+	0.347318i	$0.887092\pi$
$180$	7.93091e23	+	5.77185e22i	1.65562	+	0.120491i
$181$			2.93796e23i			0.578657i	0.957230	+	0.289329i	$0.0934321\pi$
$181$			2.93796e23i			0.578657i	−0.957230	+	0.289329i	$0.906568\pi$
$182$	8.17420e23	+	1.32001e22i	1.51948	+	0.0245374i
$183$	−3.91291e22	+	1.07674e24i	−0.0686694	+	1.88962i
$184$	−1.20946e24			−2.00449
$185$	−9.54516e22			−0.149445
$186$	1.66536e24	+	6.05195e22i	2.46389	+	0.0895383i
$187$		−	7.08092e23i		−	0.990268i
$188$	1.22678e24			1.62222
$189$	7.93306e23	+	9.97796e22i	0.992183	+	0.124794i
$190$	−6.98645e23			−0.826691
$191$		−	1.16683e24i		−	1.30665i	−0.757079	−	0.653323i	$-0.773374\pi$
$191$		−	1.16683e24i		−	1.30665i	0.757079	−	0.653323i	$-0.226626\pi$
$192$	−9.82950e23	−	3.57206e22i	−1.04200	−	0.0378666i
$193$	−1.14336e24			−1.14771			−0.573856	−	0.818957i	$-0.694553\pi$
$193$	−1.14336e24			−1.14771			−0.573856	+	0.818957i	$0.694553\pi$
$194$	1.54475e24			1.46872
$195$	−2.96449e22	+	8.15760e23i	−0.0267047	+	0.734851i
$196$	−2.32450e24	−	7.50941e22i	−1.98446	−	0.0641087i
$197$		−	1.16336e24i		−	0.941499i	−0.882267	−	0.470750i	$-0.843984\pi$
$197$		−	1.16336e24i		−	0.941499i	0.882267	−	0.470750i	$-0.156016\pi$
$198$	1.57752e24	+	1.14807e23i	1.21057	+	0.0881015i
$199$			2.86453e23i			0.208495i	0.994551	+	0.104248i	$0.0332435\pi$
$199$			2.86453e23i			0.208495i	−0.994551	+	0.104248i	$0.966757\pi$
$200$			7.42215e23i			0.512524i
$201$	2.65708e23	+	9.65589e21i	0.174119	+	0.00632752i
$202$			4.73431e24i			2.94488i
$203$	−2.00253e22	+	1.24007e24i	−0.0118269	+	0.732381i
$204$	4.98678e24	+	1.81221e23i	2.79707	+	0.101646i
$205$	1.03904e23			0.0553627
$206$	−6.24513e24			−3.16181
$207$	1.77573e23	−	2.43998e24i	0.0854454	−	1.17408i
$208$			1.83940e24i			0.841418i
$209$	−9.24190e23			−0.401999
$210$	1.83136e23	−	3.48701e24i	0.0757656	−	1.44262i
$211$	5.84219e23			0.229938			0.114969	−	0.993369i	$-0.463323\pi$
$211$	5.84219e23			0.229938			0.114969	+	0.993369i	$0.463323\pi$
$212$			9.48525e24i			3.55240i
$213$	1.46368e23	−	4.02771e24i	0.0521747	−	1.43573i
$214$	−3.04211e24			−1.03236
$215$	2.29967e24			0.743124
$216$	−6.01704e23	+	5.49972e24i	−0.185190	+	1.69269i
$217$	7.85784e22	−	4.86598e24i	0.0230396	−	1.42673i
$218$		−	6.11553e24i		−	1.70860i
$219$	6.16282e22	−	1.69586e24i	0.0164103	−	0.451573i
$220$		−	4.59386e24i		−	1.16611i
$221$			5.12254e24i			1.23984i
$222$	4.85908e22	−	1.33711e24i	0.0112163	−	0.308646i
$223$		−	4.55822e24i		−	1.00368i	−0.864961	−	0.501838i	$-0.832657\pi$
$223$		−	4.55822e24i		−	1.00368i	0.864961	−	0.501838i	$-0.167343\pi$
$224$	−3.82570e21	+	2.36907e23i	−0.000803724	+	0.0497707i
$225$	−1.49735e24	−	1.08972e23i	−0.300198	−	0.0218474i
$226$	−3.66740e24			−0.701809
$227$	5.13660e24			0.938434			0.469217	−	0.883083i	$-0.344536\pi$
$227$	5.13660e24			0.938434			0.469217	+	0.883083i	$0.344536\pi$
$228$	2.36526e23	−	6.50866e24i	0.0412633	−	1.13547i
$229$			7.47039e24i			1.24472i	0.782732	+	0.622359i	$0.213825\pi$
$229$			7.47039e24i			1.24472i	−0.782732	+	0.622359i	$0.786175\pi$
$230$	−1.06840e25			−1.70056
$231$	2.42259e23	−	4.61274e24i	0.0368429	−	0.701508i
$232$	−8.58179e24			−1.24725
$233$		−	1.62336e23i		−	0.0225516i	−0.999936	−	0.0112758i	$-0.996411\pi$
$233$		−	1.62336e23i		−	0.0225516i	0.999936	−	0.0112758i	$-0.00358928\pi$
$234$	−1.14123e25	−	8.30546e23i	−1.51567	−	0.110305i
$235$	5.37892e24			0.683098
$236$	−1.54123e25			−1.87194
$237$	5.47382e24	+	1.98920e23i	0.635964	+	0.0231111i
$238$	3.53805e23	−	2.19094e25i	0.0393283	−	2.43542i
$239$			6.66887e24i			0.709372i	0.934985	+	0.354686i	$0.115412\pi$
$239$			6.66887e24i			0.709372i	−0.934985	+	0.354686i	$0.884588\pi$
$240$	7.85127e24	+	2.85317e23i	0.799323	+	0.0290476i
$241$		−	1.61013e25i		−	1.56921i	−0.619995	−	0.784606i	$-0.712865\pi$
$241$		−	1.61013e25i		−	1.56921i	0.619995	−	0.784606i	$-0.287135\pi$
$242$			9.37936e24i			0.875210i
$243$	−1.10069e25	−	2.02135e24i	−0.983552	−	0.180624i
$244$			4.38655e25i			3.75431i
$245$	−1.01920e25	−	3.29257e23i	−0.835631	−	0.0269954i
$246$	−5.28937e22	+	1.45551e24i	−0.00415514	+	0.114340i
$247$	6.68585e24			0.503314
$248$	3.36746e25			2.42974
$249$	3.04101e24	+	1.10511e23i	0.210342	+	0.00764387i
$250$			2.83396e25i			1.87942i
$251$	2.18605e25			1.39023			0.695113	−	0.718900i	$-0.255354\pi$
$251$	2.18605e25			1.39023			0.695113	+	0.718900i	$0.255354\pi$
$252$	3.24234e25	+	2.88665e24i	1.97767	+	0.176071i
$253$	−1.41332e25			−0.826942
$254$		−	3.92702e25i		−	2.20450i
$255$	2.18649e25	+	7.94578e23i	1.17781	+	0.0428020i
$256$	−3.83808e25			−1.98424
$257$	4.67336e24			0.231916			0.115958	−	0.993254i	$-0.463006\pi$
$257$	4.67336e24			0.231916			0.115958	+	0.993254i	$0.463006\pi$
$258$	−1.17067e24	+	3.22143e25i	−0.0557737	+	1.53476i
$259$	−3.90688e24	−	6.30903e22i	−0.178724	−	0.00288612i
$260$			3.32333e25i			1.46000i
$261$	1.25998e24	−	1.73130e25i	0.0531665	−	0.730544i
$262$		−	4.73425e25i		−	1.91905i
$263$		−	2.03251e25i		−	0.791586i	−0.918340	−	0.395793i	$-0.870470\pi$
$263$		−	2.03251e25i		−	0.791586i	0.918340	−	0.395793i	$-0.129530\pi$
$264$	3.19408e25	+	1.16074e24i	1.19538	+	0.0434403i
$265$			4.15889e25i			1.49588i
$266$	−2.85958e25	−	4.61780e23i	−0.988657	−	0.0159653i
$267$	3.42176e25	+	1.24348e24i	1.13732	+	0.0413304i
$268$	1.08247e25			0.345940
$269$	5.17550e25			1.59057			0.795286	−	0.606235i	$-0.207321\pi$
$269$	5.17550e25			1.59057			0.795286	+	0.606235i	$0.207321\pi$
$270$	−5.31529e24	+	4.85831e25i	−0.157111	+	1.43604i
$271$		−	1.89000e25i		−	0.537384i	−0.963226	−	0.268692i	$-0.913409\pi$
$271$		−	1.89000e25i		−	0.537384i	0.963226	−	0.268692i	$-0.0865913\pi$
$272$	4.93018e25			1.34862
$273$	−1.75257e24	+	3.33698e25i	−0.0461283	+	0.878307i
$274$	−3.87874e25			−0.982449
$275$			8.67318e24i			0.211439i
$276$	3.61708e24	−	9.95338e25i	0.0848815	−	2.33574i
$277$	−3.71578e25			−0.839485			−0.419743	−	0.907643i	$-0.637880\pi$
$277$	−3.71578e25			−0.839485			−0.419743	+	0.907643i	$0.637880\pi$
$278$	−1.06787e26			−2.32300
$279$	−4.94412e24	+	6.79355e25i	−0.103573	+	1.42316i
$280$	1.13930e24	−	7.05512e25i	0.0229867	−	1.42346i
$281$		−	6.37724e25i		−	1.23941i	−0.784833	−	0.619707i	$-0.787251\pi$
$281$		−	6.37724e25i		−	1.23941i	0.784833	−	0.619707i	$-0.212749\pi$
$282$	−2.73821e24	+	7.53492e25i	−0.0512685	+	1.41079i
$283$		−	2.65862e25i		−	0.479621i	−0.970820	−	0.239810i	$-0.922915\pi$
$283$		−	2.65862e25i		−	0.479621i	0.970820	−	0.239810i	$-0.0770853\pi$
$284$		−	1.64085e26i		−	2.85251i
$285$	1.03707e24	−	2.85378e25i	0.0173755	−	0.478133i
$286$			6.61038e25i			1.06754i
$287$	4.25285e24	+	6.86771e22i	0.0662094	+	0.00106918i
$288$	2.40711e23	−	3.30754e24i	0.00361306	−	0.0496459i
$289$	6.82082e25			0.987210
$290$	−7.58092e25			−1.05814
$291$	−2.29302e24	+	6.30987e25i	−0.0308697	+	0.849463i
$292$		−	6.90880e25i		−	0.897186i
$293$	8.54153e25			1.07010			0.535052	−	0.844819i	$-0.320292\pi$
$293$	8.54153e25			1.07010			0.535052	+	0.844819i	$0.320292\pi$
$294$	9.80065e24	−	1.42604e26i	0.118470	−	1.72379i
$295$	−6.75767e25			−0.788253
$296$		−	2.70372e25i		−	0.304368i
$297$	−7.03124e24	+	6.42673e25i	−0.0763992	+	0.698308i
$298$	1.43186e26			1.50186
$299$	1.02244e26			1.03535
$300$	−6.10814e25	−	2.21971e24i	−0.597222	−	0.0217032i
$301$	9.41265e25	+	1.52000e24i	0.888717	+	0.0143515i
$302$			1.90106e26i			1.73349i
$303$	−1.93384e26	−	7.02762e24i	−1.70323	−	0.0618957i
$304$		−	6.43479e25i		−	0.547472i
$305$			1.92332e26i			1.58090i
$306$	−2.22612e25	+	3.05885e26i	−0.176797	+	2.42931i
$307$			1.95485e26i			1.50024i	0.661302	+	0.750120i	$0.270004\pi$
$307$			1.95485e26i			1.50024i	−0.661302	+	0.750120i	$0.729996\pi$
$308$	3.03639e24	−	1.88029e26i	0.0225203	−	1.39458i
$309$	9.27029e24	−	2.55097e26i	0.0664553	−	1.82870i
$310$	2.97472e26			2.06134
$311$	−6.31627e25			−0.423133			−0.211566	−	0.977364i	$-0.567856\pi$
$311$	−6.31627e25			−0.423133			−0.211566	+	0.977364i	$0.567856\pi$
$312$	−2.31069e26	−	8.39710e24i	−1.49664	−	0.0543884i
$313$			2.52571e26i			1.58186i	0.611907	+	0.790930i	$0.290403\pi$
$313$			2.52571e26i			1.58186i	−0.611907	+	0.790930i	$0.709597\pi$
$314$	−4.18544e26			−2.53501
$315$	1.42163e26	+	1.26568e25i	0.832773	+	0.0741416i
$316$	2.22998e26			1.26353
$317$			2.59156e26i			1.42050i	0.703952	+	0.710248i	$0.251417\pi$
$317$			2.59156e26i			1.42050i	−0.703952	+	0.710248i	$0.748583\pi$
$318$	−5.82587e26	−	2.11713e25i	−3.08941	−	0.112270i
$319$	−1.00283e26			−0.514546
$320$	−1.75578e26			−0.871759
$321$	4.51572e24	−	1.24262e26i	0.0216982	−	0.597085i
$322$	−4.37302e26	−	7.06178e24i	−2.03374	−	0.0328419i
$323$		−	1.79202e26i		−	0.806708i
$324$	−4.50806e26	−	6.59657e25i	−1.96457	−	0.287472i
$325$		−	6.27443e25i		−	0.264727i
$326$			2.24082e24i			0.00915426i
$327$	2.49803e26	+	9.07791e24i	0.988203	+	0.0359116i
$328$			2.94315e25i			0.112755i
$329$	2.20162e26	+	3.55529e24i	0.816930	+	0.0131922i
$330$	2.82156e26	+	1.02536e25i	1.01413	+	0.0368537i
$331$	1.71522e26			0.597209			0.298605	−	0.954377i	$-0.403479\pi$
$331$	1.71522e26			0.597209			0.298605	+	0.954377i	$0.403479\pi$
$332$	1.23888e26			0.417907
$333$	5.45452e25	+	3.96961e24i	0.178276	+	0.0129743i
$334$		−	3.56365e26i		−	1.12864i
$335$	4.74618e25			0.145671
$336$	3.21168e26	+	1.68676e25i	0.955365	+	0.0501754i
$337$	3.61345e25			0.104186			0.0520928	−	0.998642i	$-0.483411\pi$
$337$	3.61345e25			0.104186			0.0520928	+	0.998642i	$0.483411\pi$
$338$			1.39992e26i			0.391272i
$339$	5.44389e24	−	1.49803e26i	0.0147507	−	0.405905i
$340$	8.90758e26			2.34008
$341$	3.93506e26			1.00238
$342$	3.99236e26	+	2.90550e25i	0.986178	+	0.0717707i
$343$	−4.16945e26	−	2.02132e25i	−0.998827	−	0.0484224i
$344$			6.51394e26i			1.51349i
$345$	1.58594e25	−	4.36414e26i	0.0357426	−	0.983555i
$346$			1.13066e26i			0.247192i
$347$			3.43480e26i			0.728520i	0.931297	+	0.364260i	$0.118678\pi$
$347$			3.43480e26i			0.728520i	−0.931297	+	0.364260i	$0.881322\pi$
$348$	2.56652e25	−	7.06248e26i	0.0528157	−	1.45337i
$349$		−	7.52353e26i		−	1.50229i	−0.660135	−	0.751147i	$-0.729501\pi$
$349$		−	7.52353e26i		−	1.50229i	0.660135	−	0.751147i	$-0.270499\pi$
$350$	−4.33364e24	+	2.68361e26i	−0.00839727	+	0.520003i
$351$	5.08660e25	−	4.64928e26i	0.0956539	−	0.874300i
$352$	−1.91584e25			−0.0349673
$353$	−5.74039e26			−1.01697			−0.508484	−	0.861072i	$-0.669794\pi$
$353$	−5.74039e26			−1.01697			−0.508484	+	0.861072i	$0.669794\pi$
$354$	3.44007e25	−	9.46629e26i	0.0591607	−	1.62797i
$355$		−	7.19445e26i		−	1.20116i
$356$	1.39399e27			2.25962
$357$	8.94417e26	+	4.69744e25i	1.40774	+	0.0739341i
$358$	−7.85303e26			−1.20023
$359$		−	2.32932e26i		−	0.345730i	−0.984946	−	0.172865i	$-0.944698\pi$
$359$		−	2.32932e26i		−	0.345730i	0.984946	−	0.172865i	$-0.0553024\pi$
$360$	−7.16840e25	+	9.84987e26i	−0.103335	+	1.41989i
$361$	4.80318e26			0.672517
$362$	−7.35139e26			−0.999837
$363$	−3.83122e26	−	1.39228e25i	−0.506195	−	0.0183952i
$364$	−2.19661e25	+	1.36025e27i	−0.0281960	+	1.74605i
$365$		−	3.02922e26i		−	0.377795i
$366$	−2.69423e27	−	9.79090e25i	−3.26500	−	0.118651i
$367$			6.36769e26i			0.749874i	0.927050	+	0.374937i	$0.122336\pi$
$367$			6.36769e26i			0.749874i	−0.927050	+	0.374937i	$0.877664\pi$
$368$		−	9.84042e26i		−	1.12619i
$369$	−5.93753e25	−	4.32114e24i	−0.0660434	−	0.00480641i
$370$		−	2.38839e26i		−	0.258219i
$371$	−2.74889e25	+	1.70225e27i	−0.0288889	+	1.78895i
$372$	−1.00709e26	+	2.77129e27i	−0.102889	+	2.83127i
$373$	1.89302e27			1.88024			0.940119	−	0.340848i	$-0.110714\pi$
$373$	1.89302e27			1.88024			0.940119	+	0.340848i	$0.110714\pi$
$374$	1.77179e27			1.71104
$375$	−1.15760e27	−	4.20674e25i	−1.08700	−	0.0395018i
$376$			1.52361e27i			1.39124i
$377$	7.25475e26			0.644226
$378$	−2.49669e26	+	1.98501e27i	−0.215626	+	1.71435i
$379$	−1.36236e27			−1.14441			−0.572205	−	0.820111i	$-0.693912\pi$
$379$	−1.36236e27			−1.14441			−0.572205	+	0.820111i	$0.693912\pi$
$380$		−	1.16260e27i		−	0.949956i
$381$	1.60409e27	+	5.82929e25i	1.27501	+	0.0463344i
$382$	2.91965e27			2.25770
$383$	−1.42413e27			−1.07143			−0.535713	−	0.844400i	$-0.679957\pi$
$383$	−1.42413e27			−1.07143			−0.535713	+	0.844400i	$0.679957\pi$
$384$	8.69109e25	−	2.39159e27i	0.0636204	−	1.75069i
$385$	1.33133e25	−	8.24429e26i	0.00948305	−	0.587240i
$386$		−	2.86093e27i		−	1.98308i
$387$	−1.31413e27	−	9.56379e25i	−0.886488	−	0.0645156i
$388$			2.57058e27i			1.68771i
$389$			1.78241e27i			1.13904i	0.821979	+	0.569518i	$0.192870\pi$
$389$			1.78241e27i			1.13904i	−0.821979	+	0.569518i	$0.807130\pi$
$390$	−2.04120e27	−	7.41777e25i	−1.26972	−	0.0461418i
$391$		−	2.74045e27i		−	1.65946i
$392$	9.32638e25	−	2.88694e27i	0.0549806	−	1.70190i
$393$	1.93381e27	+	7.02753e25i	1.10992	+	0.0403349i
$394$	2.91097e27			1.62678
$395$	9.77755e26			0.532060
$396$	−1.91048e26	+	2.62513e27i	−0.101238	+	1.39108i
$397$			4.68315e26i			0.241678i	0.992672	+	0.120839i	$0.0385585\pi$
$397$			4.68315e26i			0.241678i	−0.992672	+	0.120839i	$0.961441\pi$
$398$	−7.16764e26			−0.360250
$399$	6.13102e25	−	1.16738e27i	0.0300136	−	0.571474i
$400$	−6.03881e26			−0.287953
$401$		−	8.07972e26i		−	0.375302i	−0.982236	−	0.187651i	$-0.939913\pi$
$401$		−	8.07972e26i		−	0.375302i	0.982236	−	0.187651i	$-0.0600873\pi$
$402$	−2.41610e25	+	6.64855e26i	−0.0109331	+	0.300853i
$403$	−2.84674e27			−1.25500
$404$	−7.87828e27			−3.38397
$405$	−1.97660e27	−	2.89232e26i	−0.827258	−	0.121051i
$406$	−3.10290e27	−	5.01073e25i	−1.26545	−	0.0204351i
$407$		−	3.15945e26i		−	0.125565i
$408$	−2.25069e26	+	6.19337e27i	−0.0871733	+	2.39881i
$409$			9.79040e26i			0.369578i	0.982778	+	0.184789i	$0.0591601\pi$
$409$			9.79040e26i			0.369578i	−0.982778	+	0.184789i	$0.940840\pi$
$410$			2.59990e26i			0.0956589i
$411$	5.75762e25	−	1.58436e27i	0.0206492	−	0.568219i
$412$		−	1.03924e28i		−	3.63326i
$413$	−2.76594e27	−	4.46659e25i	−0.942688	−	0.0152230i
$414$	6.10532e27	+	4.44324e26i	2.02864	+	0.147637i
$415$	5.43198e26			0.175976
$416$	1.38597e26			0.0437799
$417$	1.58515e26	−	4.36198e27i	0.0488250	−	1.34355i
$418$		−	2.31251e27i		−	0.694597i
$419$	7.96227e26			0.233233			0.116616	−	0.993177i	$-0.462795\pi$
$419$	7.96227e26			0.233233			0.116616	+	0.993177i	$0.462795\pi$
$420$	5.80268e27	+	3.04754e26i	1.65772	+	0.0870627i
$421$	−4.25993e27			−1.18697			−0.593486	−	0.804844i	$-0.702249\pi$
$421$	−4.25993e27			−1.18697			−0.593486	+	0.804844i	$0.702249\pi$
$422$			1.46184e27i			0.397299i
$423$	−3.07375e27	−	2.23697e26i	−0.814882	−	0.0593043i
$424$	−1.17803e28			−3.04660
$425$	−1.68174e27			−0.424303
$426$	1.00782e28	+	3.66243e26i	2.48073	+	0.0901505i
$427$	−1.27125e26	+	7.87224e27i	−0.0305308	+	1.89062i
$428$		−	5.06233e27i		−	1.18629i
$429$	−2.70017e27	−	9.81247e25i	−0.617431	−	0.0224376i
$430$			5.75424e27i			1.28401i
$431$			2.53784e27i			0.552654i	0.961064	+	0.276327i	$0.0891173\pi$
$431$			2.53784e27i			0.552654i	−0.961064	+	0.276327i	$0.910883\pi$
$432$	−4.47469e27	−	4.89559e26i	−0.951007	−	0.104046i
$433$			1.66290e27i			0.344940i	0.985015	+	0.172470i	$0.0551747\pi$
$433$			1.66290e27i			0.344940i	−0.985015	+	0.172470i	$0.944825\pi$
$434$	1.21757e28	+	1.96619e26i	2.46519	+	0.0398092i
$435$	1.12531e26	−	3.09660e27i	0.0222401	−	0.611996i
$436$	1.01767e28			1.96336
$437$	−3.57679e27			−0.673656
$438$	4.24340e27	+	1.54206e26i	0.780254	+	0.0283546i
$439$			2.77213e27i			0.497664i	0.968547	+	0.248832i	$0.0800466\pi$
$439$			2.77213e27i			0.497664i	−0.968547	+	0.248832i	$0.919953\pi$
$440$	5.70539e27			1.00007
$441$	5.81044e27	+	6.12012e26i	0.994499	+	0.104750i
$442$	−1.28176e28			−2.14227
$443$			1.08786e27i			0.177555i	0.996051	+	0.0887775i	$0.0282960\pi$
$443$			1.08786e27i			0.177555i	−0.996051	+	0.0887775i	$0.971704\pi$
$444$	2.22506e27	+	8.08592e25i	0.354667	+	0.0128887i
$445$	6.11209e27			0.951502
$446$	1.14056e28			1.73421
$447$	−2.12545e26	+	5.84876e27i	−0.0315662	+	0.868629i
$448$	−7.18650e27	−	1.16051e26i	−1.04255	−	0.0168357i
$449$			1.24861e28i			1.76946i	0.466103	+	0.884730i	$0.345658\pi$
$449$			1.24861e28i			1.76946i	−0.466103	+	0.884730i	$0.654342\pi$
$450$	2.72671e26	−	3.74668e27i	0.0377491	−	0.518699i
$451$			3.43923e26i			0.0465165i
$452$		−	6.10285e27i		−	0.806453i
$453$	−7.76530e27	−	2.82193e26i	−1.00260	−	0.0364347i
$454$			1.28528e28i			1.62148i
$455$	−9.63122e25	+	5.96415e27i	−0.0118730	+	0.735240i
$456$	8.08349e27	+	2.93756e26i	0.973796	+	0.0353880i
$457$	1.54742e27			0.182175			0.0910874	−	0.995843i	$-0.470966\pi$
$457$	1.54742e27			0.182175			0.0910874	+	0.995843i	$0.470966\pi$
$458$	−1.86924e28			−2.15069
$459$	−1.24615e28	−	1.36337e27i	−1.40132	−	0.153313i
$460$		−	1.77791e28i		−	1.95413i
$461$	−1.68747e27			−0.181291			−0.0906457	−	0.995883i	$-0.528893\pi$
$461$	−1.68747e27			−0.181291			−0.0906457	+	0.995883i	$0.528893\pi$
$462$	1.15420e28	+	6.06181e26i	1.21211	+	0.0636593i
$463$	1.68626e28			1.73111			0.865554	−	0.500816i	$-0.166967\pi$
$463$	1.68626e28			1.73111			0.865554	+	0.500816i	$0.166967\pi$
$464$		−	6.98232e27i		−	0.700747i
$465$	−4.41569e26	+	1.21510e28i	−0.0433254	+	1.19221i
$466$	4.06198e26			0.0389660
$467$	7.78290e27			0.729985			0.364993	−	0.931010i	$-0.381072\pi$
$467$	7.78290e27			0.729985			0.364993	+	0.931010i	$0.381072\pi$
$468$	1.38210e27	−	1.89909e28i	0.126753	−	1.74167i
$469$	1.94263e27	+	3.13706e25i	0.174211	+	0.00281325i
$470$			1.34592e28i			1.18030i
$471$	6.21288e26	−	1.70964e28i	0.0532811	−	1.46617i
$472$		−	1.91415e28i		−	1.60541i
$473$			7.61190e27i			0.624383i
$474$	−4.97738e26	+	1.36966e28i	−0.0399327	+	1.09886i
$475$			2.19498e27i			0.172246i
$476$	3.64591e28	+	5.88760e26i	2.79855	+	0.0451924i
$477$	1.72959e27	−	2.37657e28i	0.129867	−	1.78446i
$478$	−1.66869e28			−1.22569
$479$	−1.15541e28			−0.830257			−0.415128	−	0.909763i	$-0.636263\pi$
$479$	−1.15541e28			−0.830257			−0.415128	+	0.909763i	$0.636263\pi$
$480$	2.14984e25	−	5.91587e26i	0.00151138	−	0.0415897i
$481$			2.28563e27i			0.157211i
$482$	4.02887e28			2.71137
$483$	9.37588e26	−	1.78522e28i	0.0617401	−	1.17556i
$484$	−1.56080e28			−1.00571
$485$			1.12709e28i			0.710677i
$486$	5.05784e27	−	2.75414e28i	0.312093	−	1.69944i
$487$	−1.21726e28			−0.735071			−0.367536	−	0.930009i	$-0.619798\pi$
$487$	−1.21726e28			−0.735071			−0.367536	+	0.930009i	$0.619798\pi$
$488$	−5.44792e28			−3.21975
$489$	−9.15317e25	−	3.32629e24i	−0.00529455	−	0.000192405i
$490$	8.23867e26	−	2.55024e28i	0.0466443	−	1.44385i
$491$			2.96382e28i			1.64246i	0.570595	+	0.821232i	$0.306713\pi$
$491$			2.96382e28i			1.64246i	−0.570595	+	0.821232i	$0.693287\pi$
$492$	−2.42209e27	−	8.80195e25i	−0.131389	−	0.00477469i
$493$		−	1.94450e28i		−	1.03256i
$494$			1.67294e28i			0.869654i
$495$	−8.37667e26	+	1.15101e28i	−0.0426301	+	0.585767i
$496$			2.73984e28i			1.36511i
$497$	4.75529e26	−	2.94472e28i	0.0231972	−	1.43649i
$498$	−2.76522e26	+	7.60924e27i	−0.0132075	+	0.363440i
$499$	1.71476e28			0.801952			0.400976	−	0.916089i	$-0.368671\pi$
$499$	1.71476e28			0.801952			0.400976	+	0.916089i	$0.368671\pi$
$500$	−4.71594e28			−2.15965
$501$	1.45566e28	+	5.28989e26i	0.652773	+	0.0237219i
$502$			5.46994e28i			2.40211i
$503$	−3.99652e28			−1.71877			−0.859386	−	0.511327i	$-0.829154\pi$
$503$	−3.99652e28			−1.71877			−0.859386	+	0.511327i	$0.829154\pi$
$504$	−3.58510e27	+	4.02686e28i	−0.151001	+	1.69608i
$505$	−3.45430e28			−1.42495
$506$		−	3.53641e28i		−	1.42884i
$507$	−5.71831e27	−	2.07805e26i	−0.226300	−	0.00822379i
$508$	6.53489e28			2.53320
$509$	−1.77023e28			−0.672192			−0.336096	−	0.941828i	$-0.609107\pi$
$509$	−1.77023e28			−0.672192			−0.336096	+	0.941828i	$0.609107\pi$
$510$	−1.98820e27	+	5.47106e28i	−0.0739558	+	2.03509i
$511$	2.00221e26	−	1.23987e28i	0.00729610	−	0.451812i
$512$		−	4.69652e28i		−	1.67665i
$513$	−1.77945e27	+	1.62646e28i	−0.0622376	+	0.568867i
$514$			1.16937e28i			0.400718i
$515$		−	4.55665e28i		−	1.52992i
$516$	−5.36072e28	−	1.94810e27i	−1.76360	−	0.0640898i
$517$			1.78042e28i			0.573948i
$518$	1.57865e26	−	9.77581e27i	0.00498681	−	0.308809i
$519$	−4.61846e27	−	1.67836e26i	−0.142968	−	0.00519551i
$520$	−4.12744e28			−1.25212
$521$	5.91540e28			1.75869			0.879343	−	0.476189i	$-0.157982\pi$
$521$	5.91540e28			1.75869			0.879343	+	0.476189i	$0.157982\pi$
$522$	4.33206e28	+	3.15273e27i	1.26228	+	0.0918642i
$523$		−	1.74278e28i		−	0.497709i	−0.968541	−	0.248854i	$-0.919946\pi$
$523$		−	1.74278e28i		−	0.497709i	0.968541	−	0.248854i	$-0.0800540\pi$
$524$	7.87818e28			2.20520
$525$	−1.09554e28	−	5.75374e26i	−0.300577	−	0.0157862i
$526$	5.08576e28			1.36775
$527$			7.63015e28i			2.01151i
$528$	−9.44400e26	+	2.59877e28i	−0.0244062	+	0.671602i
$529$	−1.52266e28			−0.385760
$530$	−1.04064e29			−2.58466
$531$	3.86162e28	+	2.81036e27i	0.940324	+	0.0684336i
$532$	7.68441e26	−	4.75858e28i	0.0183459	−	1.13607i
$533$		−	2.48803e27i		−	0.0582399i
$534$	−3.11143e27	+	8.56195e28i	−0.0714130	+	1.96512i
$535$		−	2.21962e28i		−	0.499533i
$536$			1.34438e28i			0.296683i
$537$	1.16571e27	−	3.20776e28i	0.0252266	−	0.694179i
$538$			1.29502e29i			2.74828i
$539$	1.08984e27	−	3.37354e28i	0.0226819	−	0.702109i
$540$	−8.08462e28	−	8.84508e27i	−1.65016	−	0.180537i
$541$	−7.84416e28			−1.57027			−0.785137	−	0.619322i	$-0.787407\pi$
$541$	−7.84416e28			−1.57027			−0.785137	+	0.619322i	$0.787407\pi$
$542$	4.72917e28			0.928522
$543$	1.09124e27	−	3.00285e28i	0.0210147	−	0.578276i
$544$		−	3.71485e27i		−	0.0701702i
$545$	4.46208e28			0.826750
$546$	−8.34982e28	−	4.38529e27i	−1.51759	−	0.0797031i
$547$	8.11851e28			1.44747			0.723734	−	0.690079i	$-0.242424\pi$
$547$	8.11851e28			1.44747			0.723734	+	0.690079i	$0.242424\pi$
$548$		−	6.45455e28i		−	1.12894i
$549$	7.99864e27	−	1.09907e29i	0.137248	−	1.88588i
$550$	−2.17021e28			−0.365336
$551$	−2.53793e28			−0.419168
$552$	1.23617e29	+	4.49227e27i	2.00317	+	0.0727957i
$553$	4.00200e28	+	6.46263e26i	0.636301	+	0.0102753i
$554$		−	9.29765e28i		−	1.45051i
$555$	9.75596e27	+	3.54534e26i	0.149346	+	0.00542727i
$556$		−	1.77703e29i		−	2.66937i
$557$			6.86762e28i			1.01234i	0.862433	+	0.506170i	$0.168939\pi$
$557$			6.86762e28i			1.01234i	−0.862433	+	0.506170i	$0.831061\pi$
$558$	−1.69989e29	−	1.23712e28i	−2.45901	−	0.178959i
$559$		−	5.50666e28i		−	0.781744i
$560$	5.74019e28	+	9.26956e26i	0.799746	+	0.0129147i
$561$	−2.63005e27	+	7.23729e28i	−0.0359628	+	0.989615i
$562$	1.59572e29			2.14153
$563$	−2.72494e28			−0.358938			−0.179469	−	0.983764i	$-0.557438\pi$
$563$	−2.72494e28			−0.358938			−0.179469	+	0.983764i	$0.557438\pi$
$564$	−1.25387e29	−	4.55661e27i	−1.62115	−	0.0589130i
$565$		−	2.67585e28i		−	0.339588i
$566$	6.65240e28			0.828716
$567$	−8.07119e28	−	1.31449e28i	−0.986996	−	0.160744i
$568$	2.03787e29			2.44635
$569$		−	7.84585e28i		−	0.924616i	−0.886719	−	0.462308i	$-0.847021\pi$
$569$		−	7.84585e28i		−	0.924616i	0.886719	−	0.462308i	$-0.152979\pi$
$570$	7.14073e28	+	2.59496e27i	0.826146	+	0.0300224i
$571$	2.92469e28			0.332201			0.166100	−	0.986109i	$-0.446882\pi$
$571$	2.92469e28			0.332201			0.166100	+	0.986109i	$0.446882\pi$
$572$	−1.10002e29			−1.22671
$573$	−4.33394e27	+	1.19260e29i	−0.0474525	+	1.30578i
$574$	−1.71844e26	+	1.06415e28i	−0.00184740	+	0.114400i
$575$			3.35669e28i			0.354322i
$576$	1.00333e29	+	7.30190e27i	1.03994	+	0.0756833i
$577$			1.12472e29i			1.14472i	0.820003	+	0.572359i	$0.193971\pi$
$577$			1.12472e29i			1.14472i	−0.820003	+	0.572359i	$0.806029\pi$
$578$			1.70671e29i			1.70576i
$579$	1.16861e29	+	4.24677e27i	1.14695	+	0.0416806i
$580$		−	1.26153e29i		−	1.21591i
$581$	2.22333e28	+	3.59035e26i	0.210453	+	0.00339850i
$582$	−1.57886e29	−	5.73761e27i	−1.46775	−	0.0533384i
$583$	−1.37659e29			−1.25686
$584$	8.58044e28			0.769440
$585$	6.05992e27	−	8.32674e28i	0.0533741	−	0.733396i
$586$			2.13727e29i			1.84899i
$587$	7.19101e28			0.611069			0.305534	−	0.952181i	$-0.401165\pi$
$587$	7.19101e28			0.611069			0.305534	+	0.952181i	$0.401165\pi$
$588$	2.37305e29	+	1.63091e28i	1.98082	+	0.136134i
$589$	9.95875e28			0.816572
$590$		−	1.69091e29i		−	1.36199i
$591$	−4.32106e27	+	1.18905e29i	−0.0341917	+	0.940878i
$592$	2.19981e28			0.171004
$593$	1.05302e29			0.804198			0.402099	−	0.915596i	$-0.368281\pi$
$593$	1.05302e29			0.804198			0.402099	+	0.915596i	$0.368281\pi$
$594$	−1.60810e29	−	1.75936e28i	−1.20658	−	0.132007i
$595$	1.59858e29	+	2.58147e27i	1.17844	+	0.0190300i
$596$			2.38273e29i			1.72579i
$597$	1.06397e27	−	2.92779e28i	0.00757177	−	0.208358i
$598$			2.55834e29i			1.78894i
$599$		−	5.84017e28i		−	0.401277i	−0.979665	−	0.200638i	$-0.935698\pi$
$599$		−	5.84017e28i		−	0.401277i	0.979665	−	0.200638i	$-0.0643016\pi$
$600$	2.75679e27	−	7.58606e28i	0.0186130	−	0.512186i
$601$		−	1.06053e29i		−	0.703625i	−0.936070	−	0.351813i	$-0.885565\pi$
$601$		−	1.06053e29i		−	0.703625i	0.936070	−	0.351813i	$-0.114435\pi$
$602$	−3.80336e27	+	2.35524e29i	−0.0247973	+	1.53558i
$603$	−2.71217e28	−	1.97383e27i	−0.173774	−	0.0126467i
$604$	−3.16351e29			−1.99197
$605$	−6.84348e28			−0.423492
$606$	1.75845e28	−	4.83886e29i	0.106947	−	2.94293i
$607$			1.21676e29i			0.727317i	0.931532	+	0.363659i	$0.118473\pi$
$607$			1.21676e29i			0.727317i	−0.931532	+	0.363659i	$0.881527\pi$
$608$	−4.84856e27			−0.0284856
$609$	6.65271e27	−	1.26671e29i	0.0384164	−	0.731468i
$610$	−4.81254e29			−2.73156
$611$		−	1.28801e29i		−	0.718598i
$612$	−5.09017e29	−	3.70446e28i	−2.79153	−	0.203158i
$613$	−8.15440e28			−0.439599			−0.219800	−	0.975545i	$-0.570540\pi$
$613$	−8.15440e28			−0.439599			−0.219800	+	0.975545i	$0.570540\pi$
$614$	−4.89144e29			−2.59220
$615$	−1.06199e28	−	3.85929e26i	−0.0553262	−	0.00201057i
$616$	2.33524e29	+	3.77107e27i	1.19601	+	0.0193138i
$617$			8.97288e28i			0.451791i	0.974152	+	0.225895i	$0.0725308\pi$
$617$			8.97288e28i			0.451791i	−0.974152	+	0.225895i	$0.927469\pi$
$618$	6.38305e29	+	2.31962e28i	3.15973	+	0.114825i
$619$			2.44203e29i			1.18850i	0.804280	+	0.594250i	$0.202551\pi$
$619$			2.44203e29i			1.18850i	−0.804280	+	0.594250i	$0.797449\pi$
$620$			4.95019e29i			2.36869i
$621$	−2.72122e28	+	2.48726e29i	−0.128027	+	1.17020i
$622$		−	1.58046e29i		−	0.731113i
$623$	2.50171e29	+	4.03988e27i	1.13792	+	0.0183757i
$624$	6.83206e27	−	1.88002e29i	0.0305572	−	0.840863i
$625$	−1.38337e29			−0.608413
$626$	−6.31984e29			−2.73323
$627$	9.44600e28	+	3.43270e27i	0.401734	+	0.0145991i
$628$		−	6.96492e29i		−	2.91300i
$629$	6.12622e28			0.251977
$630$	−3.16698e28	+	3.55722e29i	−0.128106	+	1.43891i
$631$	3.66064e29			1.45629			0.728146	−	0.685422i	$-0.240382\pi$
$631$	3.66064e29			1.45629			0.728146	+	0.685422i	$0.240382\pi$
$632$			2.76955e29i			1.08363i
$633$	−5.97121e28	−	2.16995e27i	−0.229786	−	0.00835048i
$634$	−6.48462e29			−2.45441
$635$	2.86528e29			1.06670
$636$	3.52309e28	−	9.69473e29i	0.129010	−	3.55006i
$637$	−7.88420e27	+	2.44052e29i	−0.0283984	+	0.879059i
$638$		−	2.50928e29i		−	0.889063i
$639$	−2.99201e28	+	4.11122e29i	−0.104281	+	1.43289i
$640$		−	4.27195e29i		−	1.46466i
$641$			1.23048e29i			0.415015i	0.978233	+	0.207508i	$0.0665352\pi$
$641$			1.23048e29i			0.415015i	−0.978233	+	0.207508i	$0.933465\pi$
$642$	3.10930e29	+	1.12993e28i	1.03168	+	0.0374915i
$643$		−	2.14552e29i		−	0.700352i	−0.936684	−	0.350176i	$-0.886122\pi$
$643$		−	2.14552e29i		−	0.700352i	0.936684	−	0.350176i	$-0.113878\pi$
$644$	1.17514e28	−	7.27707e29i	0.0377388	−	2.33698i
$645$	−2.35045e29	−	8.54161e27i	−0.742634	−	0.0269875i
$646$	4.48400e29			1.39388
$647$	2.98765e28			0.0913766			0.0456883	−	0.998956i	$-0.485452\pi$
$647$	2.98765e28			0.0913766			0.0456883	+	0.998956i	$0.485452\pi$
$648$	8.19267e28	−	5.59883e29i	0.246540	−	1.68484i
$649$		−	2.23679e29i		−	0.662301i
$650$	1.56999e29			0.457411
$651$	−2.61050e28	+	4.97052e29i	−0.0748382	+	1.42496i
$652$	−3.72892e27			−0.0105192
$653$		−	3.85689e29i		−	1.07065i	−0.844645	−	0.535326i	$-0.820189\pi$
$653$		−	3.85689e29i		−	1.07065i	0.844645	−	0.535326i	$-0.179811\pi$
$654$	−2.27148e28	+	6.25058e29i	−0.0620501	+	1.70747i
$655$	3.45425e29			0.928583
$656$	−2.39461e28			−0.0633496
$657$	−1.25978e28	+	1.73103e29i	−0.0327989	+	0.450679i
$658$	−8.89605e27	+	5.50890e29i	−0.0227943	+	1.41154i
$659$		−	4.97164e29i		−	1.25373i	−0.779129	−	0.626863i	$-0.784339\pi$
$659$		−	4.97164e29i		−	1.25373i	0.779129	−	0.626863i	$-0.215661\pi$
$660$	−1.70629e28	+	4.69531e29i	−0.0423488	+	1.16534i
$661$			2.77713e29i			0.678392i	0.940716	+	0.339196i	$0.110155\pi$
$661$			2.77713e29i			0.678392i	−0.940716	+	0.339196i	$0.889845\pi$
$662$			4.29184e29i			1.03189i
$663$	1.90265e28	−	5.23566e29i	0.0450264	−	1.23902i
$664$			1.53864e29i			0.358403i
$665$	3.36929e27	−	2.08644e29i	0.00772523	−	0.478387i
$666$	−9.93278e27	+	1.36483e29i	−0.0224177	+	0.308035i
$667$	−3.88114e29			−0.862259
$668$	5.93020e29			1.29693
$669$	−1.69305e28	+	4.65888e29i	−0.0364498	+	1.00301i
$670$			1.18759e29i			0.251699i
$671$	−6.36619e29			−1.32829
$672$	1.27096e27	−	2.41997e28i	0.00261068	−	0.0497087i
$673$	1.68936e29			0.341637			0.170818	−	0.985303i	$-0.445359\pi$
$673$	1.68936e29			0.341637			0.170818	+	0.985303i	$0.445359\pi$
$674$			9.04159e28i			0.180018i
$675$	1.52637e29	+	1.66994e28i	0.299206	+	0.0327350i
$676$	−2.32959e29			−0.449612
$677$	−6.40443e29			−1.21702			−0.608512	−	0.793544i	$-0.708233\pi$
$677$	−6.40443e29			−1.21702			−0.608512	+	0.793544i	$0.708233\pi$
$678$	3.74839e29	+	1.36217e28i	0.701346	+	0.0254871i
$679$	−7.44971e27	+	4.61325e29i	−0.0137248	+	0.849912i
$680$			1.10628e30i			2.00689i
$681$	−5.25003e29	−	1.90787e28i	−0.937815	−	0.0340804i
$682$			9.84633e29i			1.73196i
$683$			1.21336e29i			0.210171i	0.994463	+	0.105086i	$0.0335116\pi$
$683$			1.21336e29i			0.210171i	−0.994463	+	0.105086i	$0.966488\pi$
$684$	−4.83499e28	+	6.64361e29i	−0.0824721	+	1.13322i
$685$		−	2.83005e29i		−	0.475383i
$686$	5.05775e28	−	1.04328e30i	0.0836670	−	1.72583i
$687$	2.77471e28	−	7.63537e29i	0.0452035	−	1.24390i
$688$	−5.29988e29			−0.850330
$689$	9.95866e29			1.57362
$690$	1.09200e30	+	3.96835e28i	1.69944	+	0.0617582i
$691$		−	4.79509e29i		−	0.734983i	−0.930027	−	0.367491i	$-0.880217\pi$
$691$		−	4.79509e29i		−	0.734983i	0.930027	−	0.367491i	$-0.119783\pi$
$692$	−1.88152e29			−0.284050
$693$	−4.18939e28	+	4.70560e29i	−0.0622948	+	0.699707i
$694$	−8.59456e29			−1.25878
$695$		−	7.79153e29i		−	1.12404i
$696$	8.77131e29	+	3.18752e28i	1.24643	+	0.0452955i
$697$	−6.66872e28			−0.0933465
$698$	1.88254e30			2.59575
$699$	−6.02962e26	+	1.65921e28i	−0.000818991	+	0.0225368i
$700$	−4.46575e29	−	7.21153e27i	−0.597538	−	0.00964935i
$701$		−	3.19313e29i		−	0.420898i	−0.977605	−	0.210449i	$-0.932507\pi$
$701$		−	3.19313e29i		−	0.420898i	0.977605	−	0.210449i	$-0.0674926\pi$
$702$	1.16334e30	+	1.27277e29i	1.51067	+	0.165276i
$703$		−	7.99584e28i		−	0.102290i
$704$		−	5.81164e29i		−	0.732463i
$705$	−5.49771e29	−	1.99788e28i	−0.682647	−	0.0248076i
$706$		−	1.43636e30i		−	1.75717i
$707$	−1.41386e30	−	2.28317e28i	−1.70413	−	0.0275192i
$708$	1.57527e30	+	5.72457e28i	1.87071	+	0.0679819i
$709$	−2.31583e29			−0.270970			−0.135485	−	0.990779i	$-0.543259\pi$
$709$	−2.31583e29			−0.270970			−0.135485	+	0.990779i	$0.543259\pi$
$710$	1.80020e30			2.07543
$711$	−5.58731e29	−	4.06626e28i	−0.634706	−	0.0461917i
$712$			1.73128e30i			1.93789i
$713$	1.52294e30			1.67975
$714$	−1.17540e29	+	2.23801e30i	−0.127748	+	2.43238i
$715$	−4.82314e29			−0.516555
$716$		−	1.30681e30i		−	1.37919i
$717$	2.47700e28	−	6.81614e29i	0.0257618	−	0.708904i
$718$	5.82842e29			0.597372
$719$	−9.43702e29			−0.953194			−0.476597	−	0.879122i	$-0.658130\pi$
$719$	−9.43702e29			−0.953194			−0.476597	+	0.879122i	$0.658130\pi$
$720$	−8.01406e29	−	5.83236e28i	−0.797741	−	0.0580569i
$721$	3.01179e28	−	1.86506e30i	0.0295464	−	1.82966i
$722$			1.20185e30i			1.16201i
$723$	−5.98046e28	+	1.64569e30i	−0.0569879	+	1.56818i
$724$		−	1.22333e30i		−	1.14892i
$725$			2.38175e29i			0.220469i
$726$	3.48376e28	−	9.58650e29i	0.0317844	−	0.874632i
$727$		−	4.36564e29i		−	0.392587i	−0.980545	−	0.196294i	$-0.937109\pi$
$727$		−	4.36564e29i		−	0.392587i	0.980545	−	0.196294i	$-0.0628906\pi$
$728$	−1.68938e30	−	2.72810e28i	−1.49744	−	0.0241814i
$729$	1.11749e30	+	2.47482e29i	0.976344	+	0.216224i
$730$	7.57973e29			0.652775
$731$	−1.47596e30			−1.25297
$732$	1.62929e29	−	4.48342e30i	0.136342	−	3.75183i
$733$		−	7.74686e29i		−	0.639049i	−0.947578	−	0.319524i	$-0.896477\pi$
$733$		−	7.74686e29i		−	0.639049i	0.947578	−	0.319524i	$-0.103523\pi$
$734$	−1.59333e30			−1.29568
$735$	1.04048e30	+	7.15086e28i	0.834100	+	0.0573247i
$736$	−7.41467e28			−0.0585969
$737$			1.57098e29i			0.122395i
$738$	1.08124e28	−	1.48569e29i	0.00830479	−	0.114114i
$739$	7.52141e29			0.569551			0.284775	−	0.958594i	$-0.408081\pi$
$739$	7.52141e29			0.569551			0.284775	+	0.958594i	$0.408081\pi$
$740$	3.97449e29			0.296721
$741$	−6.83350e29	−	2.48331e28i	−0.502982	−	0.0182785i
$742$	−4.25938e30	−	6.87827e28i	−3.09105	−	0.0499158i
$743$			2.56667e29i			0.183649i	0.995775	+	0.0918243i	$0.0292698\pi$
$743$			2.56667e29i			0.183649i	−0.995775	+	0.0918243i	$0.970730\pi$
$744$	−3.44183e30	−	1.25077e29i	−2.42814	−	0.0882392i
$745$			1.04473e30i			0.726712i
$746$			4.73672e30i			3.24878i
$747$	−3.10407e29	−	2.25903e28i	−0.209925	−	0.0152777i
$748$			2.94841e30i			1.96617i
$749$	1.46709e28	−	9.08501e29i	0.00964715	−	0.597402i
$750$	1.05261e29	−	2.89654e30i	0.0682535	−	1.87818i
$751$	−3.92938e29			−0.251249			−0.125625	−	0.992078i	$-0.540093\pi$
$751$	−3.92938e29			−0.251249			−0.125625	+	0.992078i	$0.540093\pi$
$752$	−1.23964e30			−0.781644
$753$	−2.23432e30	−	8.11959e28i	−1.38931	−	0.0504879i
$754$			1.81529e30i			1.11313i
$755$	−1.38707e30			−0.838794
$756$	−3.30323e30	−	4.15470e29i	−1.96997	−	0.247777i
$757$	3.06495e30			1.80267			0.901337	−	0.433119i	$-0.142587\pi$
$757$	3.06495e30			1.80267			0.901337	+	0.433119i	$0.142587\pi$
$758$		−	3.40891e30i		−	1.97738i
$759$	1.44453e30	+	5.24946e28i	0.826396	+	0.0300314i
$760$	1.44390e30			0.814696
$761$	1.21051e30			0.673643			0.336822	−	0.941568i	$-0.390648\pi$
$761$	1.21051e30			0.673643			0.336822	+	0.941568i	$0.390648\pi$
$762$	−1.45861e29	+	4.01375e30i	−0.0800591	+	2.20304i
$763$	1.82635e30	+	2.94928e28i	0.988727	+	0.0159665i
$764$			4.85854e30i			2.59433i
$765$	−2.23183e30	−	1.62425e29i	−1.17548	−	0.0855476i
$766$		−	3.56346e30i		−	1.85127i
$767$			1.61816e30i			0.829218i
$768$	3.92284e30	+	1.42557e29i	1.98293	+	0.0720603i
$769$			2.92363e30i			1.45779i	0.684624	+	0.728896i	$0.259966\pi$
$769$			2.92363e30i			1.45779i	−0.684624	+	0.728896i	$0.740034\pi$
$770$	2.06289e30	+	3.33126e28i	1.01467	+	0.0163854i
$771$	−4.77657e29	−	1.73582e28i	−0.231763	−	0.00842234i
$772$	4.76082e30			2.27877
$773$	−2.60630e30			−1.23066			−0.615331	−	0.788269i	$-0.710978\pi$
$773$	−2.60630e30			−1.23066			−0.615331	+	0.788269i	$0.710978\pi$
$774$	2.39306e29	−	3.28822e30i	0.111474	−	1.53173i
$775$		−	9.34592e29i		−	0.429491i
$776$	−3.19256e30			−1.44741
$777$	3.99081e29	+	2.09596e28i	0.178501	+	0.00937480i
$778$	−4.45996e30			−1.96809
$779$			8.70390e28i			0.0378940i
$780$	1.23438e29	−	3.39672e30i	0.0530218	−	1.45904i
$781$	2.38136e30			1.00923
$782$	6.85716e30			2.86730
$783$	−1.93086e29	+	1.76485e30i	−0.0796621	+	0.728132i
$784$	2.34887e30	+	7.58814e28i	0.956183	+	0.0308899i
$785$		−	3.05383e30i		−	1.22663i
$786$	−1.75843e29	+	4.83880e30i	−0.0696929	+	1.91779i
$787$			2.79596e30i			1.09344i	0.837314	+	0.546722i	$0.184124\pi$
$787$			2.79596e30i			1.09344i	−0.837314	+	0.546722i	$0.815876\pi$
$788$			4.84410e30i			1.86934i
$789$	−7.54932e28	+	2.07740e30i	−0.0287475	+	0.791064i
$790$			2.44654e30i			0.919324i
$791$	1.76864e28	−	1.09524e30i	0.00655824	−	0.406120i
$792$	−3.26031e30	−	2.37274e29i	−1.19301	−	0.0868232i
$793$	4.60548e30			1.66305
$794$	−1.17182e30			−0.417586
$795$	1.54473e29	−	4.25074e30i	0.0543247	−	1.49489i
$796$		−	1.19276e30i		−	0.413965i
$797$	−1.70407e30			−0.583680			−0.291840	−	0.956467i	$-0.594268\pi$
$797$	−1.70407e30			−0.583680			−0.291840	+	0.956467i	$0.594268\pi$
$798$	2.92102e30	+	1.53411e29i	0.987425	+	0.0518591i
$799$	−3.45227e30			−1.15176
$800$			4.55019e28i			0.0149825i
$801$	−3.49271e30	−	2.54188e29i	−1.13507	−	0.0826063i
$802$	2.02171e30			0.648468
$803$	1.00267e30			0.317428
$804$	−1.10637e30	−	4.02059e28i	−0.345711	−	0.0125632i
$805$	5.15250e28	−	3.19070e30i	0.0158914	−	0.984076i
$806$		−	7.12312e30i		−	2.16846i
$807$	−5.28979e30	−	1.92232e29i	−1.58952	−	0.0577636i
$808$		−	9.78450e30i		−	2.90215i
$809$			4.11056e30i			1.20349i	0.798689	+	0.601744i	$0.205527\pi$
$809$			4.11056e30i			1.20349i	−0.798689	+	0.601744i	$0.794473\pi$
$810$	7.23718e29	−	4.94585e30i	0.209159	−	1.42938i
$811$			6.74352e29i			0.192384i	0.995363	+	0.0961918i	$0.0306662\pi$
$811$			6.74352e29i			0.192384i	−0.995363	+	0.0961918i	$0.969334\pi$
$812$	8.33827e28	−	5.16349e30i	0.0234821	−	1.45414i
$813$	−7.01999e28	+	1.93174e30i	−0.0195158	+	0.537029i
$814$	7.90558e29			0.216959
$815$	−1.63498e28			−0.00442952
$816$	−5.03906e30	−	1.83121e29i	−1.34773	−	0.0489768i
$817$			1.92640e30i			0.508645i
$818$	−2.44976e30			−0.638578
$819$	3.03072e29	−	3.40417e30i	0.0779947	−	0.876052i
$820$	−4.32644e29			−0.109922
$821$			8.34544e29i			0.209337i	0.994507	+	0.104668i	$0.0333781\pi$
$821$			8.34544e29i			0.209337i	−0.994507	+	0.104668i	$0.966622\pi$
$822$	3.96440e30	+	1.44067e29i	0.981801	+	0.0356789i
$823$	−6.65471e30			−1.62716			−0.813582	−	0.581451i	$-0.802485\pi$
$823$	−6.65471e30			−1.62716			−0.813582	+	0.581451i	$0.802485\pi$
$824$	1.29070e31			3.11593
$825$	3.22146e28	−	8.86472e29i	0.00767868	−	0.211300i
$826$	1.11763e29	−	6.92096e30i	0.0263032	−	1.62883i
$827$			5.95478e30i			1.38375i	0.722017	+	0.691875i	$0.243215\pi$
$827$			5.95478e30i			1.38375i	−0.722017	+	0.691875i	$0.756785\pi$
$828$	−7.39393e29	+	1.01598e31i	−0.169651	+	2.33112i
$829$			4.17490e30i			0.945852i	0.881102	+	0.472926i	$0.156802\pi$
$829$			4.17490e30i			0.945852i	−0.881102	+	0.472926i	$0.843198\pi$
$830$			1.35919e30i			0.304061i
$831$	3.79784e30	+	1.38015e29i	0.838931	+	0.0304870i
$832$			4.20431e30i			0.917064i
$833$	6.54136e30	+	2.11322e29i	1.40895	+	0.0455167i
$834$	1.09146e31	+	3.96638e29i	2.32147	+	0.0843627i
$835$	2.60015e30			0.546123
$836$	3.84821e30			0.798166
$837$	7.57662e29	−	6.92522e30i	0.155188	−	1.41846i
$838$			1.99232e30i			0.402993i
$839$	3.22056e30			0.643326			0.321663	−	0.946854i	$-0.395758\pi$
$839$	3.22056e30			0.643326			0.321663	+	0.946854i	$0.395758\pi$
$840$	−3.78492e29	+	7.20669e30i	−0.0746663	+	1.42168i
$841$	2.37896e30			0.463478
$842$		−	1.06592e31i		−	2.05092i
$843$	−2.36869e29	+	6.51808e30i	−0.0450109	+	1.23860i
$844$	−2.43261e30			−0.456539
$845$	−1.02143e30			−0.189327
$846$	5.59736e29	−	7.69115e30i	0.102469	−	1.40800i
$847$	−2.80107e30	−	4.52331e28i	−0.506463	−	0.00817862i
$848$		−	9.58470e30i		−	1.71168i
$849$	−9.87484e28	+	2.71733e30i	−0.0174180	+	0.479304i
$850$		−	4.20807e30i		−	0.733135i
$851$		−	1.22277e30i		−	0.210418i
$852$	−6.09458e29	+	1.67709e31i	−0.103592	+	2.85063i
$853$			5.64652e30i			0.948018i	0.880520	+	0.474009i	$0.157194\pi$
$853$			5.64652e30i			0.948018i	−0.880520	+	0.474009i	$0.842806\pi$
$854$	−1.96979e31	−	3.18093e29i	−3.26673	−	0.0527528i
$855$	−2.11994e29	+	2.91295e30i	−0.0347280	+	0.477187i
$856$	6.28721e30			1.01738
$857$	3.54661e30			0.566910			0.283455	−	0.958985i	$-0.408519\pi$
$857$	3.54661e30			0.566910			0.283455	+	0.958985i	$0.408519\pi$
$858$	2.45528e29	−	6.75636e30i	0.0387690	−	1.06683i
$859$		−	2.64120e30i		−	0.411977i	−0.978554	−	0.205988i	$-0.933959\pi$
$859$		−	2.64120e30i		−	0.411977i	0.978554	−	0.205988i	$-0.0660409\pi$
$860$	−9.57553e30			−1.47547
$861$	−4.34421e29	−	2.28156e28i	−0.0661269	−	0.00347296i
$862$	−6.35020e30			−0.954908
$863$		−	3.86700e30i		−	0.574461i	−0.957861	−	0.287231i	$-0.907265\pi$
$863$		−	3.86700e30i		−	0.574461i	0.957861	−	0.287231i	$-0.0927346\pi$
$864$	−3.68878e28	+	3.37164e29i	−0.00541364	+	0.0494820i
$865$	−8.24968e29			−0.119610
$866$	−4.16091e30			−0.596006
$867$	−6.97145e30	−	2.53344e29i	−0.986559	−	0.0358518i
$868$	−3.27191e29	+	2.02613e31i	−0.0457450	+	2.83277i
$869$			3.23637e30i			0.447044i
$870$	7.74833e30	+	2.81576e29i	1.05744	+	0.0384277i
$871$		−	1.13649e30i		−	0.153242i
$872$			1.26391e31i			1.68381i
$873$	4.68733e29	−	6.44070e30i	0.0616986	−	0.847781i
$874$		−	8.94986e30i		−	1.16398i
$875$	−8.46338e30	−	1.36671e29i	−1.08757	−	0.0175627i
$876$	−2.56612e29	+	7.06137e30i	−0.0325825	+	0.896594i
$877$	3.61378e30			0.453384			0.226692	−	0.973967i	$-0.427209\pi$
$877$	3.61378e30			0.453384			0.226692	+	0.973967i	$0.427209\pi$
$878$	−6.93643e30			−0.859892
$879$	−8.73017e30	−	3.17256e29i	−1.06940	−	0.0388622i
$880$			4.64203e30i			0.561875i
$881$	1.06397e31			1.27257			0.636286	−	0.771453i	$-0.280470\pi$
$881$	1.06397e31			1.27257			0.636286	+	0.771453i	$0.280470\pi$
$882$	−1.53138e30	+	1.45389e31i	−0.180993	+	1.71835i
$883$	6.65519e30			0.777272			0.388636	−	0.921391i	$-0.372946\pi$
$883$	6.65519e30			0.777272			0.388636	+	0.921391i	$0.372946\pi$
$884$		−	2.13296e31i		−	2.46169i
$885$	6.90690e30	+	2.50999e29i	0.787733	+	0.0286264i
$886$	−2.72204e30			−0.306790
$887$	−2.96444e30			−0.330175			−0.165087	−	0.986279i	$-0.552791\pi$
$887$	−2.96444e30			−0.330175			−0.165087	+	0.986279i	$0.552791\pi$
$888$	−1.00424e29	+	2.76343e30i	−0.0110535	+	0.304167i
$889$	1.17277e31	+	1.89385e29i	1.27569	+	0.0206005i
$890$			1.52937e31i			1.64406i
$891$	9.57358e29	−	6.54254e30i	0.101709	−	0.695073i
$892$			1.89798e31i			1.99279i
$893$			4.50585e30i			0.467559i
$894$	−1.46348e31	−	5.31832e29i	−1.50087	−	0.0545419i
$895$		−	5.72982e30i		−	0.580763i
$896$	2.82361e29	−	1.74853e31i	0.0282860	−	1.75161i
$897$	−1.04502e31	−	3.79761e29i	−1.03467	−	0.0376002i
$898$	−3.12428e31			−3.05738
$899$	1.08061e31			1.04519
$900$	6.23478e30	+	4.53746e29i	0.596039	+	0.0433777i
$901$		−	2.66923e31i		−	2.52218i
$902$	−8.60565e29			−0.0803739
$903$	−9.61487e30	−	5.04969e29i	−0.887610	−	0.0466169i
$904$	7.57949e30			0.691626
$905$		−	5.36380e30i		−	0.483797i
$906$	7.06105e29	−	1.94304e31i	0.0629540	−	1.73235i
$907$	1.57592e31			1.38886			0.694428	−	0.719562i	$-0.255657\pi$
$907$	1.57592e31			1.38886			0.694428	+	0.719562i	$0.255657\pi$
$908$	−2.13881e31			−1.86325
$909$	1.97394e31	+	1.43656e30i	1.69986	+	0.123710i
$910$	−1.49235e31	−	2.40993e29i	−1.27039	−	0.0205149i
$911$			1.02264e31i			0.860557i	0.902696	+	0.430279i	$0.141585\pi$
$911$			1.02264e31i			0.860557i	−0.902696	+	0.430279i	$0.858415\pi$
$912$	−2.39006e29	+	6.57690e30i	−0.0198821	+	0.547111i
$913$			1.79798e30i			0.147857i
$914$			3.87196e30i			0.314772i
$915$	7.14375e29	−	1.96579e31i	0.0574123	−	1.57985i
$916$		−	3.11058e31i		−	2.47137i
$917$	1.41384e31	+	2.28314e29i	1.11051	+	0.0179331i
$918$	3.41143e30	−	3.11813e31i	0.264904	−	2.42129i
$919$	9.00430e29			0.0691253			0.0345627	−	0.999403i	$-0.488996\pi$
$919$	9.00430e29			0.0691253			0.0345627	+	0.999403i	$0.488996\pi$
$920$	2.20809e31			1.67589
$921$	7.26086e29	−	1.99802e31i	0.0544831	−	1.49925i
$922$		−	4.22241e30i		−	0.313246i
$923$	−1.72275e31			−1.26358
$924$	−1.00874e30	+	1.92069e31i	−0.0731513	+	1.39284i
$925$	−7.50380e29			−0.0538014
$926$			4.21937e31i			2.99111i
$927$	−1.89500e30	+	2.60386e31i	−0.132823	+	1.82508i
$928$	−5.26112e29			−0.0364607
$929$	−4.42530e30			−0.303234			−0.151617	−	0.988439i	$-0.548448\pi$
$929$	−4.42530e30			−0.303234			−0.151617	+	0.988439i	$0.548448\pi$
$930$	−3.04042e31	−	1.10490e30i	−2.05998	−	0.0748601i
$931$	2.75813e29	−	8.53767e30i	0.0184775	−	0.571963i
$932$			6.75947e29i			0.0447760i
$933$	6.45576e30	+	2.34604e29i	0.422853	+	0.0153666i
$934$			1.94744e31i			1.26131i
$935$			1.29275e31i			0.827931i
$936$	2.35860e31	+	1.71651e30i	1.49368	+	0.108705i
$937$		−	4.25212e30i		−	0.266281i	−0.991097	−	0.133141i	$-0.957494\pi$
$937$		−	4.25212e30i		−	0.266281i	0.991097	−	0.133141i	$-0.0425062\pi$
$938$	−7.84957e28	+	4.86086e30i	−0.00486089	+	0.301012i
$939$	9.38119e29	−	2.58149e31i	0.0574472	−	1.58082i
$940$	−2.23972e31			−1.35628
$941$	1.23676e31			0.740618			0.370309	−	0.928909i	$-0.379252\pi$
$941$	1.23676e31			0.740618			0.370309	+	0.928909i	$0.379252\pi$
$942$	4.27787e31	+	1.55459e30i	2.53334	+	0.0920622i
$943$			1.33105e30i			0.0779507i
$944$	1.55739e31			0.901970
$945$	−1.44833e31	−	1.82166e30i	−0.829531	−	0.104336i
$946$	−1.90465e31			−1.07884
$947$			1.46118e31i			0.818519i	0.912418	+	0.409260i	$0.134213\pi$
$947$			1.46118e31i			0.818519i	−0.912418	+	0.409260i	$0.865787\pi$
$948$	−2.27923e31	−	8.28278e29i	−1.26270	−	0.0458869i
$949$	−7.25361e30			−0.397429
$950$	−5.49230e30			−0.297616
$951$	9.62579e29	−	2.64880e31i	0.0515871	−	1.41956i
$952$	−7.31217e29	+	4.52807e31i	−0.0387577	+	2.40008i
$953$			2.04242e31i			1.07071i	0.844628	+	0.535353i	$0.179821\pi$
$953$			2.04242e31i			1.07071i	−0.844628	+	0.535353i	$0.820179\pi$
$954$	5.94666e31	+	4.32778e30i	3.08330	+	0.224392i
$955$			2.13027e31i			1.09244i
$956$		−	2.77683e31i		−	1.40845i
$957$	1.02498e31	+	3.72479e29i	0.514207	+	0.0186864i
$958$		−	2.89107e31i		−	1.43457i
$959$	1.87057e29	−	1.15835e31i	0.00918075	−	0.568520i
$960$	1.79456e31	+	6.52147e29i	0.871184	+	0.0316590i
$961$	−2.15774e31			−1.03610
$962$	−5.71912e30			−0.271638
$963$	−9.23090e29	+	1.26839e31i	−0.0433678	+	0.595904i
$964$			6.70437e31i			3.11565i
$965$	2.08742e31			0.959564
$966$	4.46698e31	+	2.34604e30i	2.03120	+	0.106678i
$967$	3.06812e31			1.38005			0.690025	−	0.723785i	$-0.257599\pi$
$967$	3.06812e31			1.38005			0.690025	+	0.723785i	$0.257599\pi$
$968$		−	1.93846e31i		−	0.862511i
$969$	−6.65606e29	+	1.83159e31i	−0.0292966	+	0.806176i
$970$	−2.82022e31			−1.22795
$971$	7.67233e30			0.330465			0.165232	−	0.986255i	$-0.447163\pi$
$971$	7.67233e30			0.330465			0.165232	+	0.986255i	$0.447163\pi$
$972$	4.58312e31	+	8.41667e30i	1.95283	+	0.358628i
$973$	5.14994e29	−	3.18911e31i	0.0217079	−	1.34426i
$974$		−	3.04583e31i		−	1.27010i
$975$	−2.33050e29	+	6.41299e30i	−0.00961391	+	0.264553i
$976$		−	4.43254e31i		−	1.80896i
$977$		−	7.79765e29i		−	0.0314826i	−0.999876	−	0.0157413i	$-0.994989\pi$
$977$		−	7.79765e29i		−	0.0314826i	0.999876	−	0.0157413i	$-0.00501082\pi$
$978$	8.32305e27	−	2.29031e29i	0.000332449	−	0.00914822i
$979$			2.02310e31i			0.799464i
$980$	4.24381e31	+	1.37098e30i	1.65914	+	0.0535992i
$981$	−2.54983e31	−	1.85568e30i	−0.986247	−	0.0717757i
$982$	−7.41608e31			−2.83794
$983$	−3.28437e31			−1.24348			−0.621741	−	0.783223i	$-0.713574\pi$
$983$	−3.28437e31			−1.24348			−0.621741	+	0.783223i	$0.713574\pi$
$984$	1.09317e29	−	3.00814e30i	0.00409485	−	0.112681i
$985$			2.12394e31i			0.787157i
$986$	4.86554e31			1.78412
$987$	−2.24892e31	−	1.18112e30i	−0.815912	−	0.0428514i
$988$	−2.78391e31			−0.999325
$989$			2.94595e31i			1.04632i
$990$	−2.88007e31	−	2.09601e30i	−1.01212	−	0.0736588i
$991$	2.67744e31			0.930995			0.465497	−	0.885049i	$-0.345875\pi$
$991$	2.67744e31			0.930995			0.465497	+	0.885049i	$0.345875\pi$
$992$	2.06444e30			0.0710282
$993$	−1.75310e31	−	6.37081e29i	−0.596815	−	0.0216884i
$994$	7.36830e31	+	1.18987e30i	2.48205	+	0.0400814i
$995$		−	5.22974e30i		−	0.174316i
$996$	−1.26624e31	−	4.60155e29i	−0.417631	−	0.0151768i
$997$			5.74615e31i			1.87533i	0.347542	+	0.937664i	$0.387016\pi$
$997$			5.74615e31i			1.87533i	−0.347542	+	0.937664i	$0.612984\pi$
$998$			4.29069e31i			1.38566i
$999$	−5.56023e30	−	6.08324e29i	−0.177687	−	0.0194400i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.22.c.b.20.16	yes	52
3.2	odd	2	inner	21.22.c.b.20.37	yes	52
7.6	odd	2	inner	21.22.c.b.20.38	yes	52
21.20	even	2	inner	21.22.c.b.20.15	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.22.c.b.20.15	✓	52	21.20	even	2	inner
21.22.c.b.20.16	yes	52	1.1	even	1	trivial
21.22.c.b.20.37	yes	52	3.2	odd	2	inner
21.22.c.b.20.38	yes	52	7.6	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)

\(f(q)\)	\(=\)	\(q+2502.20i q^{2} +(-102208. - 3714.28i) q^{3} -4.16388e6 q^{4} -1.82569e7 q^{5} +(9.29389e6 - 2.55746e8i) q^{6} +(-7.47262e8 - 1.20672e7i) q^{7} -5.17136e9i q^{8} +(1.04328e10 + 7.59261e8i) q^{9} +O(q^{10})\)	\(q+2502.20i q^{2} +(-102208. - 3714.28i) q^{3} -4.16388e6 q^{4} -1.82569e7 q^{5} +(9.29389e6 - 2.55746e8i) q^{6} +(-7.47262e8 - 1.20672e7i) q^{7} -5.17136e9i q^{8} +(1.04328e10 + 7.59261e8i) q^{9} -4.56824e10i q^{10} -6.04302e10i q^{11} +(4.25583e11 + 1.54658e10i) q^{12} +4.37169e11i q^{13} +(3.01945e10 - 1.86980e12i) q^{14} +(1.86601e12 + 6.78111e10i) q^{15} +4.20753e12 q^{16} +1.17175e13 q^{17} +(-1.89983e12 + 2.61049e13i) q^{18} -1.52935e13i q^{19} +7.60193e13 q^{20} +(7.63316e13 + 4.00890e12i) q^{21} +1.51209e14 q^{22} -2.33876e14i q^{23} +(-1.92079e13 + 5.28557e14i) q^{24} -1.43524e14 q^{25} -1.09389e15 q^{26} +(-1.06350e15 - 1.16353e14i) q^{27} +(3.11151e15 + 5.02462e13i) q^{28} -1.65948e15i q^{29} +(-1.69677e14 + 4.66913e15i) q^{30} +6.51175e15i q^{31} -3.17034e14i q^{32} +(-2.24455e14 + 6.17647e15i) q^{33} +2.93196e16i q^{34} +(1.36427e16 + 2.20309e14i) q^{35} +(-4.34407e16 - 3.16147e15i) q^{36} +5.22826e15 q^{37} +3.82675e16 q^{38} +(1.62377e15 - 4.46824e16i) q^{39} +9.44129e16i q^{40} -5.69124e15 q^{41} +(-1.00311e16 + 1.90997e17i) q^{42} -1.25962e17 q^{43} +2.51624e17i q^{44} +(-1.90470e17 - 1.38617e16i) q^{45} +5.85206e17 q^{46} -2.94625e17 q^{47} +(-4.30045e17 - 1.56279e16i) q^{48} +(5.58255e17 + 1.80347e16i) q^{49} -3.59126e17i q^{50} +(-1.19763e18 - 4.35221e16i) q^{51} -1.82032e18i q^{52} -2.27799e18i q^{53} +(2.91139e17 - 2.66108e18i) q^{54} +1.10327e18i q^{55} +(-6.24037e16 + 3.86436e18i) q^{56} +(-5.68044e16 + 1.56313e18i) q^{57} +4.15236e18 q^{58} +3.70144e18 q^{59} +(-7.76981e18 - 2.82357e17i) q^{60} -1.05348e19i q^{61} -1.62937e19 q^{62} +(-7.78684e18 - 6.93261e17i) q^{63} +9.61712e18 q^{64} -7.98134e18i q^{65} +(-1.54548e19 - 5.61631e17i) q^{66} -2.59967e18 q^{67} -4.87903e19 q^{68} +(-8.68682e17 + 2.39041e19i) q^{69} +(-5.51257e17 + 3.41367e19i) q^{70} +3.94068e19i q^{71} +(3.92642e18 - 5.39516e19i) q^{72} +1.65922e19i q^{73} +1.30822e19i q^{74} +(1.46694e19 + 5.33088e17i) q^{75} +6.36803e19i q^{76} +(-7.29221e17 + 4.51572e19i) q^{77} +(1.11804e20 + 4.06300e18i) q^{78} -5.35555e19 q^{79} -7.68163e19 q^{80} +(1.08266e20 + 1.58424e19i) q^{81} -1.42406e19i q^{82} -2.97531e19 q^{83} +(-3.17835e20 - 1.66926e19i) q^{84} -2.13925e20 q^{85} -3.15182e20i q^{86} +(-6.16378e18 + 1.69613e20i) q^{87} -3.12507e20 q^{88} -3.34783e20 q^{89} +(3.46849e19 - 4.76594e20i) q^{90} +(5.27540e18 - 3.26680e20i) q^{91} +9.73832e20i q^{92} +(2.41865e19 - 6.65556e20i) q^{93} -7.37211e20i q^{94} +2.79212e20i q^{95} +(-1.17755e18 + 3.24035e19i) q^{96} -6.17354e20i q^{97} +(-4.51264e19 + 1.39687e21i) q^{98} +(4.58823e19 - 6.30454e20i) 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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