LMFDB - Embedded newform 21.22.c.b.20.30

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			20.30
Character	$\chi$	$=$	21.20
Dual form			21.22.c.b.20.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1485.79i q^{2} +(56903.5 - 84984.4i) q^{3} -110413. q^{4} +3.09347e6 q^{5} +(1.26269e8 + 8.45465e7i) q^{6} +(4.84831e8 - 5.68758e8i) q^{7} +2.95187e9i q^{8} +(-3.98433e9 - 9.67182e9i) q^{9} +O(q^{10})$	\(q+1485.79i q^{2} +(56903.5 - 84984.4i) q^{3} -110413. q^{4} +3.09347e6 q^{5} +(1.26269e8 + 8.45465e7i) q^{6} +(4.84831e8 - 5.68758e8i) q^{7} +2.95187e9i q^{8} +(-3.98433e9 - 9.67182e9i) q^{9} +4.59624e9i q^{10} -1.18376e11i q^{11} +(-6.28290e9 + 9.38340e9i) q^{12} -4.83935e11i q^{13} +(8.45053e11 + 7.20355e11i) q^{14} +(1.76029e11 - 2.62897e11i) q^{15} -4.61741e12 q^{16} -9.41748e10 q^{17} +(1.43703e13 - 5.91988e12i) q^{18} +3.71365e13i q^{19} -3.41560e11 q^{20} +(-2.07469e13 - 7.35673e13i) q^{21} +1.75882e14 q^{22} -1.88841e14i q^{23} +(2.50863e14 + 1.67972e14i) q^{24} -4.67268e14 q^{25} +7.19024e14 q^{26} +(-1.04868e15 - 2.11754e14i) q^{27} +(-5.35317e13 + 6.27984e13i) q^{28} -3.79278e15i q^{29} +(3.90609e14 + 2.61542e14i) q^{30} +7.93042e15i q^{31} -6.69965e14i q^{32} +(-1.00601e16 - 6.73602e15i) q^{33} -1.39924e14i q^{34} +(1.49981e15 - 1.75944e15i) q^{35} +(4.39923e14 + 1.06790e15i) q^{36} -4.02246e16 q^{37} -5.51769e16 q^{38} +(-4.11269e16 - 2.75376e16i) q^{39} +9.13153e15i q^{40} -1.25820e17 q^{41} +(1.09305e17 - 3.08255e16i) q^{42} -3.23401e15 q^{43} +1.30703e16i q^{44} +(-1.23254e16 - 2.99195e16i) q^{45} +2.80578e17 q^{46} +4.91893e17 q^{47} +(-2.62747e17 + 3.92408e17i) q^{48} +(-8.84243e16 - 5.51502e17i) q^{49} -6.94260e17i q^{50} +(-5.35888e15 + 8.00339e15i) q^{51} +5.34328e16i q^{52} -5.38384e15i q^{53} +(3.14622e17 - 1.55811e18i) q^{54} -3.66193e17i q^{55} +(1.67890e18 + 1.43116e18i) q^{56} +(3.15602e18 + 2.11320e18i) q^{57} +5.63527e18 q^{58} +9.12302e17 q^{59} +(-1.94360e16 + 2.90273e16i) q^{60} -6.80147e18i q^{61} -1.17829e19 q^{62} +(-7.43265e18 - 2.42307e18i) q^{63} -8.68798e18 q^{64} -1.49704e18i q^{65} +(1.00083e19 - 1.49472e19i) q^{66} +2.32626e19 q^{67} +1.03981e16 q^{68} +(-1.60485e19 - 1.07457e19i) q^{69} +(2.61415e18 + 2.22840e18i) q^{70} -2.32191e19i q^{71} +(2.85500e19 - 1.17612e19i) q^{72} -1.56191e19i q^{73} -5.97652e19i q^{74} +(-2.65892e19 + 3.97104e19i) q^{75} -4.10036e18i q^{76} +(-6.73273e19 - 5.73924e19i) q^{77} +(4.09150e19 - 6.11058e19i) q^{78} +8.59048e19 q^{79} -1.42838e19 q^{80} +(-7.76691e19 + 7.70715e19i) q^{81} -1.86942e20i q^{82} +1.01334e20 q^{83} +(2.29074e18 + 8.12281e18i) q^{84} -2.91327e17 q^{85} -4.80505e18i q^{86} +(-3.22327e20 - 2.15823e20i) q^{87} +3.49431e20 q^{88} +5.73582e19 q^{89} +(4.44540e19 - 1.83130e19i) q^{90} +(-2.75242e20 - 2.34626e20i) q^{91} +2.08506e19i q^{92} +(6.73962e20 + 4.51269e20i) q^{93} +7.30848e20i q^{94} +1.14881e20i q^{95} +(-5.69365e19 - 3.81233e19i) q^{96} -6.72755e20i q^{97} +(8.19415e20 - 1.31380e20i) q^{98} +(-1.14491e21 + 4.71650e20i) 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 $

$2$			1485.79i			1.02599i	0.858393	+	0.512993i	$0.171463\pi$
$2$			1485.79i			1.02599i	−0.858393	+	0.512993i	$0.828537\pi$
$3$	56903.5	−	84984.4i	0.556373	−	0.830933i
$3$	56903.5	−	84984.4i	0.556373	−	0.830933i
$4$	−110413.			−0.0526491
$5$	3.09347e6			0.141665			0.0708323	−	0.997488i	$-0.477434\pi$
$5$	3.09347e6			0.141665			0.0708323	+	0.997488i	$0.477434\pi$
$6$	1.26269e8	+	8.45465e7i	0.852526	+	0.570831i
$7$	4.84831e8	−	5.68758e8i	0.648725	−	0.761023i
$7$	4.84831e8	−	5.68758e8i	0.648725	−	0.761023i
$8$			2.95187e9i			0.971970i
$9$	−3.98433e9	−	9.67182e9i	−0.380899	−	0.924617i
$10$			4.59624e9i			0.145346i
$11$		−	1.18376e11i		−	1.37607i	−0.725677	−	0.688035i	$-0.758473\pi$
$11$		−	1.18376e11i		−	1.37607i	0.725677	−	0.688035i	$-0.241527\pi$
$12$	−6.28290e9	+	9.38340e9i	−0.0292925	+	0.0437479i
$13$		−	4.83935e11i		−	0.973602i	−0.873513	−	0.486801i	$-0.838164\pi$
$13$		−	4.83935e11i		−	0.973602i	0.873513	−	0.486801i	$-0.161836\pi$
$14$	8.45053e11	+	7.20355e11i	0.780800	+	0.665583i
$15$	1.76029e11	−	2.62897e11i	0.0788183	−	0.117714i
$16$	−4.61741e12			−1.04988
$17$	−9.41748e10			−0.0113298			−0.00566489	−	0.999984i	$-0.501803\pi$
$17$	−9.41748e10			−0.0113298			−0.00566489	+	0.999984i	$0.501803\pi$
$18$	1.43703e13	−	5.91988e12i	0.948645	−	0.390797i
$19$			3.71365e13i			1.38959i	0.719206	+	0.694797i	$0.244506\pi$
$19$			3.71365e13i			1.38959i	−0.719206	+	0.694797i	$0.755494\pi$
$20$	−3.41560e11			−0.00745851
$21$	−2.07469e13	−	7.35673e13i	−0.271426	−	0.962459i
$22$	1.75882e14			1.41183
$23$		−	1.88841e14i		−	0.950505i	−0.879850	−	0.475252i	$-0.842357\pi$
$23$		−	1.88841e14i		−	0.950505i	0.879850	−	0.475252i	$-0.157643\pi$
$24$	2.50863e14	+	1.67972e14i	0.807641	+	0.540777i
$25$	−4.67268e14			−0.979931
$26$	7.19024e14			0.998903
$27$	−1.04868e15	−	2.11754e14i	−0.980216	−	0.197930i
$28$	−5.35317e13	+	6.27984e13i	−0.0341548	+	0.0400672i
$29$		−	3.79278e15i		−	1.67409i	−0.547134	−	0.837045i	$-0.684281\pi$
$29$		−	3.79278e15i		−	1.67409i	0.547134	−	0.837045i	$-0.315719\pi$
$30$	3.90609e14	+	2.61542e14i	0.120773	+	0.0808665i
$31$			7.93042e15i			1.73779i	0.494993	+	0.868897i	$0.335171\pi$
$31$			7.93042e15i			1.73779i	−0.494993	+	0.868897i	$0.664829\pi$
$32$		−	6.69965e14i		−	0.105191i
$33$	−1.00601e16	−	6.73602e15i	−1.14342	−	0.765608i
$34$		−	1.39924e14i		−	0.0116242i
$35$	1.49981e15	−	1.75944e15i	0.0919013	−	0.107810i
$36$	4.39923e14	+	1.06790e15i	0.0200540	+	0.0486803i
$37$	−4.02246e16			−1.37522			−0.687612	−	0.726078i	$-0.741341\pi$
$37$	−4.02246e16			−1.37522			−0.687612	+	0.726078i	$0.741341\pi$
$38$	−5.51769e16			−1.42571
$39$	−4.11269e16	−	2.75376e16i	−0.808998	−	0.541686i
$40$			9.13153e15i			0.137694i
$41$	−1.25820e17			−1.46393			−0.731963	−	0.681344i	$-0.761396\pi$
$41$	−1.25820e17			−1.46393			−0.731963	+	0.681344i	$0.761396\pi$
$42$	1.09305e17	−	3.08255e16i	0.987471	−	0.278479i
$43$	−3.23401e15			−0.0228203			−0.0114102	−	0.999935i	$-0.503632\pi$
$43$	−3.23401e15			−0.0228203			−0.0114102	+	0.999935i	$0.503632\pi$
$44$			1.30703e16i			0.0724489i
$45$	−1.23254e16	−	2.99195e16i	−0.0539598	−	0.130985i
$46$	2.80578e17			0.975205
$47$	4.91893e17			1.36409			0.682045	−	0.731311i	$-0.261091\pi$
$47$	4.91893e17			1.36409			0.682045	+	0.731311i	$0.261091\pi$
$48$	−2.62747e17	+	3.92408e17i	−0.584123	+	0.872377i
$49$	−8.84243e16	−	5.51502e17i	−0.158312	−	0.987389i
$50$		−	6.94260e17i		−	1.00540i
$51$	−5.35888e15	+	8.00339e15i	−0.00630358	+	0.00941428i
$52$			5.34328e16i			0.0512593i
$53$		−	5.38384e15i		−	0.00422859i	−0.999998	−	0.00211429i	$-0.999327\pi$
$53$		−	5.38384e15i		−	0.00422859i	0.999998	−	0.00211429i	$-0.000673001\pi$
$54$	3.14622e17	−	1.55811e18i	0.203074	−	1.00569i
$55$		−	3.66193e17i		−	0.194940i
$56$	1.67890e18	+	1.43116e18i	0.739691	+	0.630541i
$57$	3.15602e18	+	2.11320e18i	1.15466	+	0.773132i
$58$	5.63527e18			1.71759
$59$	9.12302e17			0.232377			0.116188	−	0.993227i	$-0.462932\pi$
$59$	9.12302e17			0.232377			0.116188	+	0.993227i	$0.462932\pi$
$60$	−1.94360e16	+	2.90273e16i	−0.00414971	+	0.00619752i
$61$		−	6.80147e18i		−	1.22079i	−0.792099	−	0.610393i	$-0.791012\pi$
$61$		−	6.80147e18i		−	1.22079i	0.792099	−	0.610393i	$-0.208988\pi$
$62$	−1.17829e19			−1.78295
$63$	−7.43265e18	−	2.42307e18i	−0.950753	−	0.309949i
$64$	−8.68798e18			−0.941953
$65$		−	1.49704e18i		−	0.137925i
$66$	1.00083e19	−	1.49472e19i	0.785504	−	1.17314i
$67$	2.32626e19			1.55909			0.779547	−	0.626344i	$-0.215449\pi$
$67$	2.32626e19			1.55909			0.779547	+	0.626344i	$0.215449\pi$
$68$	1.03981e16			0.000596503
$69$	−1.60485e19	−	1.07457e19i	−0.789805	−	0.528835i
$70$	2.61415e18	+	2.22840e18i	0.110612	+	0.0942895i
$71$		−	2.32191e19i		−	0.846510i	−0.906011	−	0.423255i	$-0.860887\pi$
$71$		−	2.32191e19i		−	0.846510i	0.906011	−	0.423255i	$-0.139113\pi$
$72$	2.85500e19	−	1.17612e19i	0.898699	−	0.370222i
$73$		−	1.56191e19i		−	0.425368i	−0.977121	−	0.212684i	$-0.931779\pi$
$73$		−	1.56191e19i		−	0.425368i	0.977121	−	0.212684i	$-0.0682206\pi$
$74$		−	5.97652e19i		−	1.41096i
$75$	−2.65892e19	+	3.97104e19i	−0.545207	+	0.814257i
$76$		−	4.10036e18i		−	0.0731609i
$77$	−6.73273e19	−	5.73924e19i	−1.04722	−	0.892692i
$78$	4.09150e19	−	6.11058e19i	0.555763	−	0.830022i
$79$	8.59048e19			1.02078			0.510391	−	0.859942i	$-0.329501\pi$
$79$	8.59048e19			1.02078			0.510391	+	0.859942i	$0.329501\pi$
$80$	−1.42838e19			−0.148730
$81$	−7.76691e19	+	7.70715e19i	−0.709832	+	0.704371i
$82$		−	1.86942e20i		−	1.50197i
$83$	1.01334e20			0.716858			0.358429	−	0.933557i	$-0.383312\pi$
$83$	1.01334e20			0.716858			0.358429	+	0.933557i	$0.383312\pi$
$84$	2.29074e18	+	8.12281e18i	0.0142903	+	0.0506726i
$85$	−2.91327e17			−0.00160503
$86$		−	4.80505e18i		−	0.0234134i
$87$	−3.22327e20	−	2.15823e20i	−1.39106	−	0.931418i
$88$	3.49431e20			1.33750
$89$	5.73582e19			0.194984			0.0974922	−	0.995236i	$-0.468918\pi$
$89$	5.73582e19			0.194984			0.0974922	+	0.995236i	$0.468918\pi$
$90$	4.44540e19	−	1.83130e19i	0.134389	−	0.0553621i
$91$	−2.75242e20	−	2.34626e20i	−0.740934	−	0.631600i
$92$			2.08506e19i			0.0500432i
$93$	6.73962e20	+	4.51269e20i	1.44399	+	0.966861i
$94$			7.30848e20i			1.39954i
$95$			1.14881e20i			0.196856i
$96$	−5.69365e19	−	3.81233e19i	−0.0874064	−	0.0585252i
$97$		−	6.72755e20i		−	0.926304i	−0.886279	−	0.463152i	$-0.846718\pi$
$97$		−	6.72755e20i		−	0.926304i	0.886279	−	0.463152i	$-0.153282\pi$
$98$	8.19415e20	−	1.31380e20i	1.01305	−	0.162426i
$99$	−1.14491e21	+	4.71650e20i	−1.27234	+	0.524144i
$100$	5.15925e19			0.0515925
$101$	3.07186e20			0.276711			0.138356	−	0.990383i	$-0.455818\pi$
$101$	3.07186e20			0.276711			0.138356	+	0.990383i	$0.455818\pi$
$102$	−1.18913e19	−	7.96216e18i	−0.00965893	−	0.00646739i
$103$			1.57884e21i			1.15757i	0.815481	+	0.578784i	$0.196472\pi$
$103$			1.57884e21i			1.15757i	−0.815481	+	0.578784i	$0.803528\pi$
$104$	1.42851e21			0.946312
$105$	−6.41801e19	−	2.27578e20i	−0.0384514	−	0.136346i
$106$	7.99924e18			0.00433848
$107$		−	2.36014e21i		−	1.15987i	−0.814664	−	0.579933i	$-0.803079\pi$
$107$		−	2.36014e21i		−	1.15987i	0.814664	−	0.579933i	$-0.196921\pi$
$108$	1.15788e20	+	2.33805e19i	0.0516075	+	0.0104209i
$109$	−2.59276e21			−1.04902			−0.524510	−	0.851404i	$-0.675752\pi$
$109$	−2.59276e21			−1.04902			−0.524510	+	0.851404i	$0.675752\pi$
$110$	5.44085e20			0.200006
$111$	−2.28892e21	+	3.41846e21i	−0.765137	+	1.14272i
$112$	−2.23866e21	+	2.62619e21i	−0.681082	+	0.798981i
$113$			3.71329e20i			0.102905i	0.998675	+	0.0514524i	$0.0163850\pi$
$113$			3.71329e20i			0.102905i	−0.998675	+	0.0514524i	$0.983615\pi$
$114$	−3.13976e21	+	4.68918e21i	−0.793224	+	1.18467i
$115$		−	5.84175e20i		−	0.134653i
$116$			4.18773e20i			0.0881394i
$117$	−4.68053e21	+	1.92816e21i	−0.900209	+	0.370844i
$118$			1.35549e21i			0.238415i
$119$	−4.56588e19	+	5.35626e19i	−0.00734991	+	0.00862222i
$120$	7.76038e20	+	5.19616e20i	0.114414	+	0.0766090i
$121$	−6.61265e21			−0.893571
$122$	1.01055e22			1.25251
$123$	−7.15960e21	+	1.06927e22i	−0.814489	+	1.21642i
$124$		−	8.75623e20i		−	0.0914933i
$125$	−2.92056e21			−0.280486
$126$	3.60017e21	−	1.10433e22i	0.318004	−	0.975460i
$127$	2.82420e21			0.229592			0.114796	−	0.993389i	$-0.463379\pi$
$127$	2.82420e21			0.229592			0.114796	+	0.993389i	$0.463379\pi$
$128$		−	1.43135e22i		−	1.07162i
$129$	−1.84026e20	+	2.74840e20i	−0.0126966	+	0.0189622i
$130$	2.22428e21			0.141509
$131$	2.27036e22			1.33274			0.666370	−	0.745621i	$-0.267847\pi$
$131$	2.27036e22			1.33274			0.666370	+	0.745621i	$0.267847\pi$
$132$	1.11077e21	+	7.43745e20i	0.0602002	+	0.0403086i
$133$	2.11217e22	+	1.80049e22i	1.05751	+	0.901464i
$134$			3.45632e22i			1.59961i
$135$	−3.24405e21	−	6.55056e20i	−0.138862	−	0.0280397i
$136$		−	2.77992e20i		−	0.0110122i
$137$		−	1.20737e22i		−	0.442869i	−0.975175	−	0.221435i	$-0.928926\pi$
$137$		−	1.20737e22i		−	0.442869i	0.975175	−	0.221435i	$-0.0710739\pi$
$138$	1.59659e22	−	2.38447e22i	0.542578	−	0.810330i
$139$		−	2.72336e22i		−	0.857926i	−0.903322	−	0.428963i	$-0.858879\pi$
$139$		−	2.72336e22i		−	0.857926i	0.903322	−	0.428963i	$-0.141121\pi$
$140$	−1.65599e20	+	1.94265e20i	−0.00483852	+	0.00567610i
$141$	2.79904e22	−	4.18032e22i	0.758942	−	1.13347i
$142$	3.44986e22			0.868508
$143$	−5.72863e22			−1.33975
$144$	1.83973e22	+	4.46587e22i	0.399897	+	0.970734i
$145$		−	1.17329e22i		−	0.237159i
$146$	2.32066e22			0.436422
$147$	−5.19007e22	−	2.38677e22i	−0.908534	−	0.417810i
$148$	4.44133e21			0.0724044
$149$		−	1.25411e23i		−	1.90493i	−0.304654	−	0.952463i	$-0.598541\pi$
$149$		−	1.25411e23i		−	1.90493i	0.304654	−	0.952463i	$-0.401459\pi$
$150$	−5.90013e22	−	3.95059e22i	−0.835417	−	0.559375i
$151$	−3.64033e22			−0.480710			−0.240355	−	0.970685i	$-0.577264\pi$
$151$	−3.64033e22			−0.480710			−0.240355	+	0.970685i	$0.577264\pi$
$152$	−1.09622e23			−1.35064
$153$	3.75224e20	+	9.10842e20i	0.00431550	+	0.0104757i
$154$	8.52729e22	−	1.00034e23i	0.915890	−	1.07444i
$155$			2.45325e22i			0.246184i
$156$	4.54095e21	+	3.04051e21i	0.0425931	+	0.0285193i
$157$			7.80839e22i			0.684881i	0.939540	+	0.342441i	$0.111254\pi$
$157$			7.80839e22i			0.684881i	−0.939540	+	0.342441i	$0.888746\pi$
$158$			1.27636e23i			1.04731i
$159$	−4.57542e20	−	3.06359e20i	−0.00351367	−	0.00235267i
$160$		−	2.07252e21i		−	0.0149018i
$161$	−1.07405e23	−	9.15559e22i	−0.723356	−	0.616616i
$162$	−1.14512e23	−	1.15400e23i	−0.722675	−	0.728279i
$163$	1.28355e23			0.759351			0.379675	−	0.925120i	$-0.376036\pi$
$163$	1.28355e23			0.759351			0.379675	+	0.925120i	$0.376036\pi$
$164$	1.38922e22			0.0770745
$165$	−3.11207e22	−	2.08377e22i	−0.161982	−	0.108460i
$166$			1.50560e23i			0.735487i
$167$	−3.33949e22			−0.153164			−0.0765822	−	0.997063i	$-0.524401\pi$
$167$	−3.33949e22			−0.153164			−0.0765822	+	0.997063i	$0.524401\pi$
$168$	2.17161e23	−	6.12423e22i	0.935481	−	0.263818i
$169$	1.28717e22			0.0520984
$170$		−	4.32850e20i		−	0.00164674i
$171$	3.59177e23	−	1.47964e23i	1.28484	−	0.529295i
$172$	3.57077e20			0.00120147
$173$	−1.89907e22			−0.0601252			−0.0300626	−	0.999548i	$-0.509571\pi$
$173$	−1.89907e22			−0.0601252			−0.0300626	+	0.999548i	$0.509571\pi$
$174$	3.20667e23	−	4.78910e23i	0.955623	−	1.42721i
$175$	−2.26546e23	+	2.65762e23i	−0.635706	+	0.745750i
$176$			5.46591e23i			1.44471i
$177$	5.19132e22	−	7.75314e22i	0.129288	−	0.193089i
$178$			8.52220e22i			0.200052i
$179$			8.17687e23i			1.80980i	0.425626	+	0.904899i	$0.360054\pi$
$179$			8.17687e23i			1.80980i	−0.425626	+	0.904899i	$0.639946\pi$
$180$	1.36089e21	+	3.30351e21i	0.00284094	+	0.00689627i
$181$			5.72727e23i			1.12803i	0.825763	+	0.564017i	$0.190745\pi$
$181$			5.72727e23i			1.12803i	−0.825763	+	0.564017i	$0.809255\pi$
$182$	3.48605e23	−	4.08951e23i	0.648014	−	0.760188i
$183$	−5.78018e23	−	3.87027e23i	−1.01439	−	0.679212i
$184$	5.57435e23			0.923862
$185$	−1.24434e23			−0.194820
$186$	−6.70489e23	+	1.00136e24i	−0.991987	+	1.48151i
$187$			1.11481e22i			0.0155906i
$188$	−5.43114e22			−0.0718181
$189$	−6.28867e23	+	4.93777e23i	−0.786520	+	0.617564i
$190$	−1.70688e23			−0.201972
$191$			1.42400e23i			0.159463i	0.996816	+	0.0797314i	$0.0254062\pi$
$191$			1.42400e23i			0.159463i	−0.996816	+	0.0797314i	$0.974594\pi$
$192$	−4.94377e23	+	7.38343e23i	−0.524077	+	0.782700i
$193$	−3.26333e23			−0.327574			−0.163787	−	0.986496i	$-0.552371\pi$
$193$	−3.26333e23			−0.327574			−0.163787	+	0.986496i	$0.552371\pi$
$194$	9.99571e23			0.950376
$195$	−1.27225e23	−	8.51867e22i	−0.114606	−	0.0767377i
$196$	9.76322e21	+	6.08931e22i	0.00833497	+	0.0519852i
$197$			1.17460e24i			0.950591i	0.879826	+	0.475295i	$0.157659\pi$
$197$			1.17460e24i			0.950591i	−0.879826	+	0.475295i	$0.842341\pi$
$198$	−7.00772e23	−	1.70110e24i	−0.537765	−	1.30540i
$199$			1.38417e24i			1.00747i	0.863858	+	0.503735i	$0.168041\pi$
$199$			1.38417e24i			1.00747i	−0.863858	+	0.503735i	$0.831959\pi$
$200$		−	1.37931e24i		−	0.952463i
$201$	1.32372e24	−	1.97695e24i	0.867437	−	1.29550i
$202$			4.56413e23i			0.283902i
$203$	−2.15717e24	−	1.83886e24i	−1.27402	−	1.08602i
$204$	5.91691e20	−	8.83680e20i	0.000331878	−	0.000495654i
$205$	−3.89221e23			−0.207387
$206$	−2.34582e24			−1.18765
$207$	−1.82644e24	+	7.52406e23i	−0.878852	+	0.362046i
$208$			2.23452e24i			1.02216i
$209$	4.39607e24			1.91218
$210$	3.38133e23	−	9.53579e22i	0.139890	−	0.0394507i
$211$	1.69822e24			0.668386			0.334193	−	0.942505i	$-0.391536\pi$
$211$	1.69822e24			0.668386			0.334193	+	0.942505i	$0.391536\pi$
$212$			5.94447e20i			0.000222632i
$213$	−1.97326e24	−	1.32125e24i	−0.703393	−	0.470975i
$214$	3.50666e24			1.19001
$215$	−1.00043e22			−0.00323283
$216$	6.25071e23	−	3.09556e24i	0.192382	−	0.952740i
$217$	4.51049e24	+	3.84491e24i	1.32250	+	1.12735i
$218$		−	3.85229e24i		−	1.07628i
$219$	−1.32738e24	−	8.88780e23i	−0.353453	−	0.236663i
$220$			4.04326e22i			0.0102634i
$221$			4.55745e22i			0.0110307i
$222$	−5.07911e24	−	3.40085e24i	−1.17241	−	0.785021i
$223$		−	6.19989e24i		−	1.36516i	−0.730812	−	0.682579i	$-0.760858\pi$
$223$		−	6.19989e24i		−	1.36516i	0.730812	−	0.682579i	$-0.239142\pi$
$224$	−3.81048e23	−	3.24819e23i	−0.0800525	−	0.0682398i
$225$	1.86175e24	+	4.51933e24i	0.373254	+	0.906061i
$226$	−5.51717e23			−0.105579
$227$	4.35156e24			0.795012			0.397506	−	0.917600i	$-0.369876\pi$
$227$	4.35156e24			0.795012			0.397506	+	0.917600i	$0.369876\pi$
$228$	−3.48466e23	−	2.33325e23i	−0.0607918	−	0.0407047i
$229$		−	1.17904e24i		−	0.196451i	−0.995164	−	0.0982257i	$-0.968683\pi$
$229$		−	1.17904e24i		−	0.196451i	0.995164	−	0.0982257i	$-0.0313167\pi$
$230$	8.67959e23			0.138152
$231$	−8.70861e24	+	2.45594e24i	−1.32441	+	0.373501i
$232$	1.11958e25			1.62716
$233$			2.29783e24i			0.319214i	0.987181	+	0.159607i	$0.0510226\pi$
$233$			2.29783e24i			0.319214i	−0.987181	+	0.159607i	$0.948977\pi$
$234$	−2.86483e24	−	6.95427e24i	−0.380481	−	0.923603i
$235$	1.52166e24			0.193243
$236$	−1.00730e23			−0.0122344
$237$	4.88828e24	−	7.30057e24i	0.567935	−	0.848201i
$238$	−7.95827e22	−	6.78394e22i	−0.00884628	−	0.00754091i
$239$			8.93905e23i			0.0950853i	0.998869	+	0.0475426i	$0.0151390\pi$
$239$			8.93905e23i			0.0950853i	−0.998869	+	0.0475426i	$0.984861\pi$
$240$	−8.12800e23	+	1.21390e24i	−0.0827495	+	0.123585i
$241$			1.69279e25i			1.64978i	0.565296	+	0.824888i	$0.308762\pi$
$241$			1.69279e25i			1.64978i	−0.565296	+	0.824888i	$0.691238\pi$
$242$		−	9.82500e24i		−	0.916793i
$243$	2.13023e24	+	1.09863e25i	0.190353	+	0.981716i
$244$			7.50972e23i			0.0642733i
$245$	−2.73538e23	−	1.70606e24i	−0.0224271	−	0.139878i
$246$	−1.58871e25	−	1.06377e25i	−1.24804	−	0.835655i
$247$	1.79716e25			1.35291
$248$	−2.34096e25			−1.68908
$249$	5.76624e24	−	8.61177e24i	0.398840	−	0.595661i
$250$		−	4.33933e24i		−	0.287775i
$251$	2.53859e25			1.61443			0.807213	−	0.590260i	$-0.200975\pi$
$251$	2.53859e25			1.61443			0.807213	+	0.590260i	$0.200975\pi$
$252$	8.20663e23	+	2.67539e23i	0.0500563	+	0.0163186i
$253$	−2.23543e25			−1.30796
$254$			4.19616e24i			0.235558i
$255$	−1.65775e22	+	2.47583e22i	−0.000892993	+	0.00133367i
$256$	3.04683e24			0.157517
$257$	1.29746e25			0.643868			0.321934	−	0.946762i	$-0.395667\pi$
$257$	1.29746e25			0.643868			0.321934	+	0.946762i	$0.395667\pi$
$258$	−4.08354e23	−	2.73424e23i	−0.0194549	−	0.0130266i
$259$	−1.95021e25	+	2.28780e25i	−0.892142	+	1.04658i
$260$			1.65293e23i			0.00726163i
$261$	−3.66831e25	+	1.51117e25i	−1.54789	+	0.637659i
$262$			3.37327e25i			1.36737i
$263$		−	6.73076e24i		−	0.262137i	−0.991373	−	0.131069i	$-0.958159\pi$
$263$		−	6.73076e24i		−	0.262137i	0.991373	−	0.131069i	$-0.0418408\pi$
$264$	1.98839e25	−	2.96962e25i	0.744148	−	1.11137i
$265$		−	1.66548e22i		−	0.000599041i
$266$	−2.67515e25	+	3.13823e25i	−0.924891	+	1.08499i
$267$	3.26388e24	−	4.87455e24i	0.108484	−	0.162019i
$268$	−2.56849e24			−0.0820849
$269$	−3.23796e25			−0.995115			−0.497557	−	0.867431i	$-0.665770\pi$
$269$	−3.23796e25			−0.995115			−0.497557	+	0.867431i	$0.665770\pi$
$270$	9.73273e23	−	4.81997e24i	0.0287684	−	0.142470i
$271$			2.34627e25i			0.667115i	0.942730	+	0.333558i	$0.108249\pi$
$271$			2.34627e25i			0.667115i	−0.942730	+	0.333558i	$0.891751\pi$
$272$	4.34844e23			0.0118949
$273$	−3.56018e25	+	1.00402e25i	−0.937053	+	0.264261i
$274$	1.79390e25			0.454378
$275$			5.53133e25i			1.34845i
$276$	1.77197e24	+	1.18647e24i	0.0415826	+	0.0278427i
$277$	−6.09072e24			−0.137604			−0.0688020	−	0.997630i	$-0.521918\pi$
$277$	−6.09072e24			−0.137604			−0.0688020	+	0.997630i	$0.521918\pi$
$278$	4.04633e25			0.880220
$279$	7.67016e25	−	3.15974e25i	1.60679	−	0.661923i
$280$	5.19363e24	+	4.42725e24i	0.104788	+	0.0893253i
$281$			1.02487e24i			0.0199183i	0.999950	+	0.00995916i	$0.00317015\pi$
$281$			1.02487e24i			0.0199183i	−0.999950	+	0.00995916i	$0.996830\pi$
$282$	6.21107e25	+	4.15878e25i	1.16292	+	0.778665i
$283$		−	7.57297e24i		−	0.136618i	−0.997664	−	0.0683092i	$-0.978240\pi$
$283$		−	7.57297e24i		−	0.136618i	0.997664	−	0.0683092i	$-0.0217604\pi$
$284$			2.56369e24i			0.0445680i
$285$	9.76306e24	+	6.53711e24i	0.163574	+	0.109525i
$286$		−	8.51153e25i		−	1.37456i
$287$	−6.10014e25	+	7.15611e25i	−0.949686	+	1.11408i
$288$	−6.47978e24	+	2.66936e24i	−0.0972611	+	0.0400670i
$289$	−6.90831e25			−0.999872
$290$	1.74325e25			0.243322
$291$	−5.71736e25	−	3.82821e25i	−0.769696	−	0.515370i
$292$			1.72455e24i			0.0223953i
$293$	1.04502e26			1.30922			0.654612	−	0.755965i	$-0.272832\pi$
$293$	1.04502e26			1.30922			0.654612	+	0.755965i	$0.272832\pi$
$294$	3.54624e25	−	7.71135e25i	0.428668	−	0.932144i
$295$	2.82218e24			0.0329195
$296$		−	1.18738e26i		−	1.33668i
$297$	−2.50666e25	+	1.24138e26i	−0.272366	+	1.34885i
$298$	1.86333e26			1.95443
$299$	−9.13868e25			−0.925414
$300$	2.93580e24	−	4.38456e24i	0.0287047	−	0.0428699i
$301$	−1.56795e24	+	1.83937e24i	−0.0148041	+	0.0173668i
$302$		−	5.40876e25i		−	0.493202i
$303$	1.74800e25	−	2.61060e25i	0.153955	−	0.229928i
$304$		−	1.71474e26i		−	1.45890i
$305$		−	2.10401e25i		−	0.172942i
$306$	−1.35332e24	+	5.57503e23i	−0.0107479	+	0.00442764i
$307$			4.30569e25i			0.330438i	0.986257	+	0.165219i	$0.0528331\pi$
$307$			4.30569e25i			0.330438i	−0.986257	+	0.165219i	$0.947167\pi$
$308$	7.43382e24	+	6.33688e24i	0.0551353	+	0.0469994i
$309$	1.34176e26	+	8.98413e25i	0.961861	+	0.644039i
$310$	−3.64501e25			−0.252581
$311$	−1.60452e26			−1.07488			−0.537442	−	0.843301i	$-0.680609\pi$
$311$	−1.60452e26			−1.07488			−0.537442	+	0.843301i	$0.680609\pi$
$312$	8.12874e25	−	1.21401e26i	0.526502	−	0.786322i
$313$		−	5.34989e25i		−	0.335065i	−0.985867	−	0.167533i	$-0.946420\pi$
$313$		−	5.34989e25i		−	0.335065i	0.985867	−	0.167533i	$-0.0535799\pi$
$314$	−1.16016e26			−0.702679
$315$	−2.29927e25	−	7.49571e24i	−0.134688	−	0.0439088i
$316$	−9.48503e24			−0.0537433
$317$		−	1.46935e26i		−	0.805382i	−0.915336	−	0.402691i	$-0.868075\pi$
$317$		−	1.46935e26i		−	0.805382i	0.915336	−	0.402691i	$-0.131925\pi$
$318$	4.55185e23	−	6.79811e23i	0.00241381	−	0.00360498i
$319$	−4.48975e26			−2.30367
$320$	−2.68760e25			−0.133441
$321$	−2.00575e26	−	1.34300e26i	−0.963771	−	0.645318i
$322$	1.36033e26	−	1.59581e26i	0.632640	−	0.742154i
$323$		−	3.49732e24i		−	0.0157438i
$324$	8.57570e24	−	8.50972e24i	0.0373721	−	0.0370845i
$325$			2.26127e26i			0.954063i
$326$			1.90708e26i			0.779084i
$327$	−1.47537e26	+	2.20344e26i	−0.583646	+	0.871666i
$328$		−	3.71405e26i		−	1.42289i
$329$	2.38485e26	−	2.79768e26i	0.884919	−	1.03810i
$330$	3.09604e25	−	4.62387e25i	0.111278	−	0.166192i
$331$	1.02111e26			0.355530			0.177765	−	0.984073i	$-0.443113\pi$
$331$	1.02111e26			0.355530			0.177765	+	0.984073i	$0.443113\pi$
$332$	−1.11886e25			−0.0377420
$333$	1.60268e26	+	3.89045e26i	0.523821	+	1.27156i
$334$		−	4.96178e25i		−	0.157145i
$335$	7.19621e25			0.220868
$336$	9.57971e25	+	3.39690e26i	0.284964	+	1.01046i
$337$	1.09301e26			0.315145			0.157572	−	0.987507i	$-0.449633\pi$
$337$	1.09301e26			0.315145			0.157572	+	0.987507i	$0.449633\pi$
$338$			1.91246e25i			0.0534522i
$339$	3.15572e25	+	2.11299e25i	0.0855070	+	0.0572534i
$340$	3.21664e22			8.45033e−5
$341$	9.38772e26			2.39133
$342$	2.19843e26	+	5.33661e26i	0.543049	+	1.31823i
$343$	−3.56542e26	−	2.17093e26i	−0.854127	−	0.520065i
$344$		−	9.54637e24i		−	0.0221807i
$345$	−4.96457e25	−	3.32416e25i	−0.111887	−	0.0749171i
$346$		−	2.82161e25i		−	0.0616877i
$347$			2.32919e26i			0.494021i	0.969013	+	0.247011i	$0.0794483\pi$
$347$			2.32919e26i			0.494021i	−0.969013	+	0.247011i	$0.920552\pi$
$348$	3.55892e25	+	2.38297e25i	0.0732379	+	0.0490384i
$349$			1.17165e26i			0.233954i	0.993135	+	0.116977i	$0.0373203\pi$
$349$			1.17165e26i			0.233954i	−0.993135	+	0.116977i	$0.962680\pi$
$350$	−3.94866e26	−	3.36599e26i	−0.765130	−	0.652226i
$351$	−1.02475e26	+	5.07491e26i	−0.192705	+	0.954341i
$352$	−7.93078e25			−0.144750
$353$	9.25968e26			1.64044			0.820222	−	0.572045i	$-0.193850\pi$
$353$	9.25968e26			1.64044			0.820222	+	0.572045i	$0.193850\pi$
$354$	1.15195e26	+	7.71320e25i	0.198107	+	0.132648i
$355$		−	7.18275e25i		−	0.119920i
$356$	−6.33310e24			−0.0102658
$357$	1.95384e24	+	6.92819e24i	0.00307519	+	0.0109044i
$358$	−1.21491e27			−1.85683
$359$			4.54615e26i			0.674765i	0.941368	+	0.337382i	$0.109542\pi$
$359$			4.54615e26i			0.674765i	−0.941368	+	0.337382i	$0.890458\pi$
$360$	8.83185e25	−	3.63831e25i	0.127314	−	0.0524473i
$361$	−6.64909e26			−0.930971
$362$	−8.50950e26			−1.15735
$363$	−3.76283e26	+	5.61972e26i	−0.497159	+	0.742498i
$364$	3.03903e25	+	2.59059e25i	0.0390095	+	0.0332532i
$365$		−	4.83172e25i		−	0.0602596i
$366$	5.75041e26	−	8.58813e26i	0.696862	−	1.04075i
$367$		−	5.33160e26i		−	0.627862i	−0.949446	−	0.313931i	$-0.898354\pi$
$367$		−	5.33160e26i		−	0.627862i	0.949446	−	0.313931i	$-0.101646\pi$
$368$			8.71956e26i			0.997913i
$369$	5.01309e26	+	1.21691e27i	0.557608	+	1.35357i
$370$		−	1.84882e26i		−	0.199883i
$371$	−3.06210e24	−	2.61025e24i	−0.00321805	−	0.00274319i
$372$	−7.44143e25	−	4.98260e25i	−0.0760248	−	0.0509044i
$373$	7.93244e26			0.787887			0.393944	−	0.919135i	$-0.371111\pi$
$373$	7.93244e26			0.787887			0.393944	+	0.919135i	$0.371111\pi$
$374$	−1.65636e25			−0.0159957
$375$	−1.66190e26	+	2.48202e26i	−0.156055	+	0.233065i
$376$			1.45200e27i			1.32585i
$377$	−1.83546e27			−1.62990
$378$	−7.33648e26	−	9.34363e26i	−0.633613	−	0.806959i
$379$	−2.47846e26			−0.208195			−0.104098	−	0.994567i	$-0.533195\pi$
$379$	−2.47846e26			−0.208195			−0.104098	+	0.994567i	$0.533195\pi$
$380$		−	1.26843e25i		−	0.0103643i
$381$	1.60707e26	−	2.40013e26i	0.127739	−	0.190775i
$382$	−2.11576e26			−0.163607
$383$	2.81912e26			0.212093			0.106046	−	0.994361i	$-0.466181\pi$
$383$	2.81912e26			0.212093			0.106046	+	0.994361i	$0.466181\pi$
$384$	−1.21643e27	−	8.14489e26i	−0.890446	−	0.596221i
$385$	−2.08275e26	−	1.77542e26i	−0.148354	−	0.126463i
$386$		−	4.84862e26i		−	0.336086i
$387$	1.28854e25	+	3.12787e25i	0.00869224	+	0.0211001i
$388$			7.42810e25i			0.0487691i
$389$		−	1.60857e27i		−	1.02794i	−0.857807	−	0.513972i	$-0.828174\pi$
$389$		−	1.60857e27i		−	1.02794i	0.857807	−	0.513972i	$-0.171826\pi$
$390$	1.26569e26	−	1.89029e26i	0.0787318	−	0.117585i
$391$			1.77841e25i			0.0107690i
$392$	1.62796e27	−	2.61017e26i	0.959712	−	0.153874i
$393$	1.29191e27	−	1.92945e27i	0.741501	−	1.10742i
$394$	−1.74520e27			−0.975294
$395$	2.65744e26			0.144609
$396$	1.26413e26	−	5.20764e25i	0.0669875	−	0.0275957i
$397$		−	7.69315e26i		−	0.397012i	−0.980100	−	0.198506i	$-0.936391\pi$
$397$		−	7.69315e26i		−	0.397012i	0.980100	−	0.198506i	$-0.0636090\pi$
$398$	−2.05658e27			−1.03365
$399$	2.73203e27	−	7.70468e26i	1.33743	−	0.377172i
$400$	2.15757e27			1.02881
$401$		−	5.00705e26i		−	0.232577i	−0.993215	−	0.116288i	$-0.962900\pi$
$401$		−	5.00705e26i		−	0.232577i	0.993215	−	0.116288i	$-0.0370997\pi$
$402$	2.93733e27	+	1.96677e27i	1.32917	+	0.889979i
$403$	3.83781e27			1.69192
$404$	−3.39174e25			−0.0145686
$405$	−2.40267e26	+	2.38419e26i	−0.100558	+	0.0997843i
$406$	2.73215e27	−	3.20510e27i	1.11425	−	1.30713i
$407$			4.76163e27i			1.89241i
$408$	−2.36250e25	−	1.58187e25i	−0.00915039	−	0.00612689i
$409$		−	2.15827e27i		−	0.814725i	−0.913267	−	0.407363i	$-0.866449\pi$
$409$		−	2.15827e27i		−	0.814725i	0.913267	−	0.407363i	$-0.133551\pi$
$410$		−	5.78299e26i		−	0.212776i
$411$	−1.02608e27	−	6.87037e26i	−0.367995	−	0.246400i
$412$		−	1.74324e26i		−	0.0609449i
$413$	4.42312e26	−	5.18878e26i	0.150749	−	0.176844i
$414$	−1.11792e27	−	2.71370e27i	−0.371454	−	0.901691i
$415$	3.13473e26			0.101553
$416$	−3.24219e26			−0.102414
$417$	−2.31443e27	−	1.54969e27i	−0.712879	−	0.477326i
$418$			6.53163e27i			1.96187i
$419$	−5.64002e27			−1.65209			−0.826044	−	0.563606i	$-0.809414\pi$
$419$	−5.64002e27			−1.65209			−0.826044	+	0.563606i	$0.809414\pi$
$420$	7.08633e24	+	2.51277e25i	0.00202443	+	0.00717852i
$421$	3.13387e27			0.873210			0.436605	−	0.899653i	$-0.356181\pi$
$421$	3.13387e27			0.873210			0.436605	+	0.899653i	$0.356181\pi$
$422$			2.52319e27i			0.685755i
$423$	−1.95986e27	−	4.75750e27i	−0.519580	−	1.26126i
$424$	1.58924e25			0.00411006
$425$	4.40049e25			0.0111024
$426$	1.96309e27	−	2.93184e27i	0.483214	−	0.721672i
$427$	−3.86839e27	−	3.29756e27i	−0.929046	−	0.791954i
$428$			2.60590e26i			0.0610659i
$429$	−3.25979e27	+	4.86844e27i	−0.745398	+	1.11324i
$430$		−	1.48643e25i		−	0.00331684i
$431$		−	4.68316e27i		−	1.01983i	−0.860225	−	0.509915i	$-0.829677\pi$
$431$		−	4.68316e27i		−	1.01983i	0.860225	−	0.509915i	$-0.170323\pi$
$432$	4.84217e27	+	9.77756e26i	1.02911	+	0.207803i
$433$			9.28397e26i			0.192580i	0.995353	+	0.0962899i	$0.0306976\pi$
$433$			9.28397e26i			0.192580i	−0.995353	+	0.0962899i	$0.969302\pi$
$434$	−5.71272e27	+	6.70162e27i	−1.15665	+	1.35687i
$435$	−9.97110e26	−	6.67641e26i	−0.197063	−	0.131949i
$436$	2.86275e26			0.0552300
$437$	7.01289e27			1.32082
$438$	1.32054e27	−	1.97220e27i	0.242814	−	0.362638i
$439$			8.27480e27i			1.48553i	0.669555	+	0.742763i	$0.266485\pi$
$439$			8.27480e27i			1.48553i	−0.669555	+	0.742763i	$0.733515\pi$
$440$	1.08096e27			0.189476
$441$	−4.98172e27	+	3.05259e27i	−0.852656	+	0.522473i
$442$	−6.77140e25			−0.0113173
$443$		−	1.03727e28i		−	1.69298i	−0.532401	−	0.846492i	$-0.678710\pi$
$443$		−	1.03727e28i		−	1.69298i	0.532401	−	0.846492i	$-0.321290\pi$
$444$	2.52727e26	−	3.77443e26i	0.0402838	−	0.0601632i
$445$	1.77436e26			0.0276224
$446$	9.21172e27			1.40063
$447$	−1.06579e28	−	7.13630e27i	−1.58287	−	1.05985i
$448$	−4.21220e27	+	4.94136e27i	−0.611068	+	0.716848i
$449$		−	8.27111e27i		−	1.17213i	−0.810263	−	0.586067i	$-0.800676\pi$
$449$		−	8.27111e27i		−	1.17213i	0.810263	−	0.586067i	$-0.199324\pi$
$450$	−6.71476e27	+	2.76617e27i	−0.929607	+	0.382954i
$451$			1.48941e28i			2.01447i
$452$		−	4.09997e25i		−	0.00541785i
$453$	−2.07148e27	+	3.09371e27i	−0.267454	+	0.399437i
$454$			6.46550e27i			0.815672i
$455$	−8.51452e26	−	7.25810e26i	−0.104964	−	0.0894753i
$456$	−6.23788e27	+	9.31617e27i	−0.751461	+	1.12229i
$457$	5.65235e27			0.665440			0.332720	−	0.943026i	$-0.392034\pi$
$457$	5.65235e27			0.665440			0.332720	+	0.943026i	$0.392034\pi$
$458$	1.75180e27			0.201557
$459$	9.87589e25	+	1.99419e25i	0.0111056	+	0.00224251i
$460$			6.45006e25i			0.00708935i
$461$	9.95162e27			1.06914			0.534569	−	0.845125i	$-0.320474\pi$
$461$	9.95162e27			1.06914			0.534569	+	0.845125i	$0.320474\pi$
$462$	−3.64901e27	−	1.29392e28i	−0.383208	−	1.35883i
$463$	−5.94443e27			−0.610253			−0.305126	−	0.952312i	$-0.598699\pi$
$463$	−5.94443e27			−0.610253			−0.305126	+	0.952312i	$0.598699\pi$
$464$			1.75128e28i			1.75759i
$465$	2.08488e27	+	1.39599e27i	0.204562	+	0.136970i
$466$	−3.41409e27			−0.327509
$467$	6.07954e27			0.570221			0.285111	−	0.958495i	$-0.407970\pi$
$467$	6.07954e27			0.570221			0.285111	+	0.958495i	$0.407970\pi$
$468$	5.16792e26	−	2.12894e26i	0.0473952	−	0.0195246i
$469$	1.12784e28	−	1.32308e28i	1.01142	−	1.18651i
$470$			2.26086e27i			0.198265i
$471$	6.63591e27	+	4.44325e27i	0.569090	+	0.381049i
$472$			2.69300e27i			0.225863i
$473$			3.82829e26i			0.0314024i
$474$	1.08471e28	+	7.26295e27i	0.870243	+	0.582694i
$475$		−	1.73527e28i		−	1.36171i
$476$	5.04134e24	−	5.91402e24i	0.000386966	−	0.000453952i
$477$	−5.20715e25	+	2.14510e25i	−0.00390982	+	0.00161066i
$478$	−1.32815e27			−0.0975562
$479$	−1.64367e27			−0.118112			−0.0590558	−	0.998255i	$-0.518809\pi$
$479$	−1.64367e27			−0.118112			−0.0590558	+	0.998255i	$0.518809\pi$
$480$	−1.76132e26	−	1.17933e26i	−0.0123824	−	0.00829095i
$481$			1.94661e28i			1.33892i
$482$	−2.51513e28			−1.69265
$483$	−1.38925e28	+	3.91787e27i	−0.914822	+	0.257992i
$484$	7.30124e26			0.0470458
$485$		−	2.08115e27i		−	0.131224i
$486$	−1.63233e28	+	3.16507e27i	−1.00723	+	0.195300i
$487$	8.83430e27			0.533480			0.266740	−	0.963769i	$-0.414054\pi$
$487$	8.83430e27			0.533480			0.266740	+	0.963769i	$0.414054\pi$
$488$	2.00771e28			1.18657
$489$	7.30384e27	−	1.09082e28i	0.422482	−	0.630970i
$490$	2.53484e27	−	4.06420e26i	0.143513	−	0.0230100i
$491$		−	1.12407e28i		−	0.622928i	−0.950258	−	0.311464i	$-0.899181\pi$
$491$		−	1.12407e28i		−	0.622928i	0.950258	−	0.311464i	$-0.100819\pi$
$492$	7.90515e26	−	1.18062e27i	0.0428821	−	0.0640437i
$493$			3.57185e26i			0.0189671i
$494$			2.67020e28i			1.38807i
$495$	−3.54175e27	+	1.45904e27i	−0.180245	+	0.0742526i
$496$		−	3.66180e28i		−	1.82447i
$497$	−1.32060e28	−	1.12573e28i	−0.644213	−	0.549152i
$498$	1.27953e28	+	8.56740e27i	0.611141	+	0.409205i
$499$	1.18575e28			0.554545			0.277272	−	0.960791i	$-0.410570\pi$
$499$	1.18575e28			0.554545			0.277272	+	0.960791i	$0.410570\pi$
$500$	3.22469e26			0.0147673
$501$	−1.90029e27	+	2.83805e27i	−0.0852164	+	0.127269i
$502$			3.77180e28i			1.65638i
$503$	2.35921e28			1.01462			0.507309	−	0.861764i	$-0.330640\pi$
$503$	2.35921e28			1.01462			0.507309	+	0.861764i	$0.330640\pi$
$504$	7.15260e27	−	2.19402e28i	0.301261	−	0.924103i
$505$	9.50271e26			0.0392002
$506$		−	3.32137e28i		−	1.34195i
$507$	7.32442e26	−	1.09389e27i	0.0289861	−	0.0432902i
$508$	−3.11829e26			−0.0120878
$509$	−3.23971e27			−0.123018			−0.0615091	−	0.998107i	$-0.519591\pi$
$509$	−3.23971e27			−0.123018			−0.0615091	+	0.998107i	$0.519591\pi$
$510$	−3.67855e25	−	2.46307e25i	−0.00136833	−	0.000916199i
$511$	−8.88346e27	−	7.57261e27i	−0.323715	−	0.275947i
$512$		−	2.54907e28i		−	0.910011i
$513$	7.86380e27	−	3.89441e28i	0.275043	−	1.36210i
$514$			1.92775e28i			0.660600i
$515$			4.88409e27i			0.163986i
$516$	2.03189e25	−	3.03460e25i	0.000668466	−	0.000998342i
$517$		−	5.82283e28i		−	1.87708i
$518$	−3.39919e28	−	2.89760e28i	−1.07377	−	0.915326i
$519$	−1.08064e27	+	1.61391e27i	−0.0334520	+	0.0499600i
$520$	4.41907e27			0.134059
$521$	−3.45890e28			−1.02835			−0.514175	−	0.857685i	$-0.671902\pi$
$521$	−3.45890e28			−1.02835			−0.514175	+	0.857685i	$0.671902\pi$
$522$	−2.24528e28	−	5.45033e28i	−0.654230	−	1.58812i
$523$			1.02373e28i			0.292360i	0.989258	+	0.146180i	$0.0466978\pi$
$523$			1.02373e28i			0.292360i	−0.989258	+	0.146180i	$0.953302\pi$
$524$	−2.50678e27			−0.0701677
$525$	9.69437e27	+	3.43756e28i	0.265979	+	0.943144i
$526$	1.00005e28			0.268949
$527$		−	7.46846e26i		−	0.0196888i
$528$	4.64517e28	+	3.11029e28i	1.20045	+	0.803795i
$529$	3.81063e27			0.0965410
$530$	2.47454e25			0.000614608
$531$	−3.63492e27	−	8.82362e27i	−0.0885119	−	0.214859i
$532$	−2.33211e27	−	1.98798e27i	−0.0556771	−	0.0474613i
$533$			6.08887e28i			1.42528i
$534$	7.24254e27	+	4.84943e27i	0.166229	+	0.111303i
$535$		−	7.30102e27i		−	0.164312i
$536$			6.86681e28i			1.51539i
$537$	6.94906e28	+	4.65293e28i	1.50382	+	1.00692i
$538$		−	4.81093e28i		−	1.02097i
$539$	−6.52847e28	+	1.04673e28i	−1.35872	+	0.217848i
$540$	3.58186e26	+	7.23268e25i	0.00731095	+	0.00147627i
$541$	−6.92446e28			−1.38616			−0.693082	−	0.720859i	$-0.743748\pi$
$541$	−6.92446e28			−1.38616			−0.693082	+	0.720859i	$0.743748\pi$
$542$	−3.48606e28			−0.684452
$543$	4.86728e28	+	3.25901e28i	0.937321	+	0.627607i
$544$			6.30938e25i			0.00119179i
$545$	−8.02063e27			−0.148609
$546$	−1.49176e28	−	5.28967e28i	−0.271128	−	0.961404i
$547$	−1.84212e28			−0.328436			−0.164218	−	0.986424i	$-0.552510\pi$
$547$	−1.84212e28			−0.328436			−0.164218	+	0.986424i	$0.552510\pi$
$548$			1.33310e27i			0.0233167i
$549$	−6.57826e28	+	2.70993e28i	−1.12876	+	0.464996i
$550$	−8.21838e28			−1.38350
$551$	1.40851e29			2.32631
$552$	3.17200e28	−	4.73732e28i	0.514011	−	0.767667i
$553$	4.16493e28	−	4.88590e28i	0.662207	−	0.776838i
$554$		−	9.04952e27i		−	0.141180i
$555$	−7.08071e27	+	1.05749e28i	−0.108393	+	0.161883i
$556$			3.00695e27i			0.0451690i
$557$			5.54215e28i			0.816956i	0.912768	+	0.408478i	$0.133940\pi$
$557$			5.54215e28i			0.816956i	−0.912768	+	0.408478i	$0.866060\pi$
$558$	4.69471e28	+	1.13962e29i	0.679125	+	1.64855i
$559$			1.56505e27i			0.0222179i
$560$	−6.92524e27	+	8.12403e27i	−0.0964851	+	0.113187i
$561$	9.47410e26	+	6.34363e26i	0.0129547	+	0.00867417i
$562$	−1.52274e27			−0.0204359
$563$	7.07778e28			0.932307			0.466154	−	0.884704i	$-0.345639\pi$
$563$	7.07778e28			0.932307			0.466154	+	0.884704i	$0.345639\pi$
$564$	−3.09051e27	+	4.61562e27i	−0.0399576	+	0.0596760i
$565$			1.14870e27i			0.0145780i
$566$	1.12518e28			0.140169
$567$	6.17863e27	+	8.15415e28i	0.0755561	+	0.997142i
$568$	6.85397e28			0.822782
$569$		−	1.81397e28i		−	0.213772i	−0.994271	−	0.106886i	$-0.965912\pi$
$569$		−	1.81397e28i		−	0.213772i	0.994271	−	0.106886i	$-0.0340880\pi$
$570$	−9.71276e27	+	1.45058e28i	−0.112372	+	0.167825i
$571$	−6.72310e28			−0.763643			−0.381822	−	0.924236i	$-0.624703\pi$
$571$	−6.72310e28			−0.763643			−0.381822	+	0.924236i	$0.624703\pi$
$572$	6.32517e27			0.0705365
$573$	1.21018e28	+	8.10305e27i	0.132503	+	0.0887207i
$574$	−1.06325e29	−	9.06352e28i	−1.14303	−	0.974365i
$575$			8.82393e28i			0.931429i
$576$	3.46158e28	+	8.40286e28i	0.358789	+	0.870946i
$577$			1.11053e29i			1.13027i	0.824997	+	0.565136i	$0.191176\pi$
$577$			1.11053e29i			1.13027i	−0.824997	+	0.565136i	$0.808824\pi$
$578$		−	1.02643e29i		−	1.02586i
$579$	−1.85695e28	+	2.77332e28i	−0.182253	+	0.272192i
$580$			1.29546e27i			0.0124862i
$581$	4.91296e28	−	5.76342e28i	0.465044	−	0.545546i
$582$	5.68791e28	−	8.49479e28i	0.528763	−	0.789698i
$583$	−6.37318e26			−0.00581884
$584$	4.61055e28			0.413445
$585$	−1.44791e28	+	5.96470e27i	−0.127528	+	0.0525354i
$586$			1.55268e29i			1.34325i
$587$	−1.58188e29			−1.34423			−0.672116	−	0.740446i	$-0.734614\pi$
$587$	−1.58188e29			−1.34423			−0.672116	+	0.740446i	$0.734614\pi$
$588$	5.73053e27	+	2.63531e27i	0.0478335	+	0.0219973i
$589$	−2.94508e29			−2.41483
$590$			4.19316e27i			0.0337750i
$591$	9.98224e28	+	6.68387e28i	0.789877	+	0.528883i
$592$	1.85733e29			1.44382
$593$	4.33232e28			0.330861			0.165431	−	0.986221i	$-0.447099\pi$
$593$	4.33232e28			0.330861			0.165431	+	0.986221i	$0.447099\pi$
$594$	−1.84443e29	−	3.72437e28i	−1.38390	−	0.279444i
$595$	−1.41244e26	+	1.65695e26i	−0.00104122	+	0.00122146i
$596$			1.38470e28i			0.100293i
$597$	1.17633e29	+	7.87642e28i	0.837140	+	0.560529i
$598$		−	1.35781e29i		−	0.949462i
$599$		−	1.56320e29i		−	1.07407i	−0.843560	−	0.537035i	$-0.819544\pi$
$599$		−	1.56320e29i		−	1.07407i	0.843560	−	0.537035i	$-0.180456\pi$
$600$	−1.17220e29	−	7.84878e28i	−0.791433	−	0.529925i
$601$		−	1.18315e29i		−	0.784980i	−0.919756	−	0.392490i	$-0.871614\pi$
$601$		−	1.18315e29i		−	0.784980i	0.919756	−	0.392490i	$-0.128386\pi$
$602$	−2.73291e27	−	2.32963e27i	−0.0178181	−	0.0151888i
$603$	−9.26858e28	−	2.24991e29i	−0.593857	−	1.44156i
$604$	4.01941e27			0.0253089
$605$	−2.04560e28			−0.126587
$606$	3.87880e28	+	2.59715e28i	0.235904	+	0.157955i
$607$			2.03805e29i			1.21824i	0.793077	+	0.609122i	$0.208478\pi$
$607$			2.03805e29i			1.21824i	−0.793077	+	0.609122i	$0.791522\pi$
$608$	2.48801e28			0.146172
$609$	−2.79025e29	+	7.86886e28i	−1.61124	+	0.454392i
$610$	3.12612e28			0.177436
$611$		−	2.38044e29i		−	1.32808i
$612$	−4.14297e25	−	1.00569e26i	−0.000227207	−	0.000551536i
$613$	−9.25714e28			−0.499047			−0.249524	−	0.968369i	$-0.580274\pi$
$613$	−9.25714e28			−0.499047			−0.249524	+	0.968369i	$0.580274\pi$
$614$	−6.39734e28			−0.339025
$615$	−2.21480e28	+	3.30777e28i	−0.115384	+	0.172324i
$616$	1.69415e29	−	1.98742e29i	0.867669	−	1.01787i
$617$			1.93357e29i			0.973566i	0.873523	+	0.486783i	$0.161830\pi$
$617$			1.93357e29i			0.973566i	−0.873523	+	0.486783i	$0.838170\pi$
$618$	−1.33485e29	+	1.99358e29i	−0.660776	+	0.986857i
$619$		−	1.19009e29i		−	0.579200i	−0.957148	−	0.289600i	$-0.906478\pi$
$619$		−	1.19009e29i		−	0.579200i	0.957148	−	0.289600i	$-0.0935222\pi$
$620$		−	2.70872e27i		−	0.0129614i
$621$	−3.99879e28	+	1.98033e29i	−0.188134	+	0.931700i
$622$		−	2.38398e29i		−	1.10282i
$623$	2.78090e28	−	3.26229e28i	0.126491	−	0.148388i
$624$	1.89900e29	+	1.27152e29i	0.849349	+	0.568704i
$625$	2.13776e29			0.940196
$626$	7.94880e28			0.343772
$627$	2.50152e29	−	3.73597e29i	1.06388	−	1.58889i
$628$		−	8.62150e27i		−	0.0360584i
$629$	3.78814e27			0.0155810
$630$	1.11370e28	−	3.41622e28i	0.0450499	−	0.138188i
$631$	4.47316e29			1.77953			0.889766	−	0.456416i	$-0.150867\pi$
$631$	4.47316e29			1.77953			0.889766	+	0.456416i	$0.150867\pi$
$632$			2.53580e29i			0.992169i
$633$	9.66345e28	−	1.44322e29i	0.371872	−	0.555384i
$634$	2.18314e29			0.826312
$635$	8.73657e27			0.0325250
$636$	5.05187e25	+	3.38261e25i	0.000184992	+	0.000123866i
$637$	−2.66891e29	+	4.27916e28i	−0.961324	+	0.154133i
$638$		−	6.67081e29i		−	2.36353i
$639$	−2.24571e29	+	9.25125e28i	−0.782697	+	0.322434i
$640$		−	4.42785e28i		−	0.151811i
$641$			2.76478e29i			0.932507i	0.884651	+	0.466253i	$0.154396\pi$
$641$			2.76478e29i			0.932507i	−0.884651	+	0.466253i	$0.845604\pi$
$642$	1.99541e29	−	2.98012e29i	0.662088	−	0.988816i
$643$			4.86411e29i			1.58777i	0.608067	+	0.793886i	$0.291945\pi$
$643$			4.86411e29i			1.58777i	−0.608067	+	0.793886i	$0.708055\pi$
$644$	1.18589e28	+	1.01090e28i	0.0380841	+	0.0324643i
$645$	−5.69280e26	+	8.50210e26i	−0.00179866	+	0.00268627i
$646$	5.19628e27			0.0161529
$647$	2.18028e29			0.666834			0.333417	−	0.942779i	$-0.391798\pi$
$647$	2.18028e29			0.666834			0.333417	+	0.942779i	$0.391798\pi$
$648$	−2.27505e29	−	2.29269e29i	−0.684627	−	0.689935i
$649$		−	1.07995e29i		−	0.319767i
$650$	−3.35977e29			−0.978856
$651$	5.83420e29	−	1.64532e29i	1.67256	−	0.471682i
$652$	−1.41721e28			−0.0399792
$653$		−	3.14849e29i		−	0.874005i	−0.899460	−	0.437002i	$-0.856040\pi$
$653$		−	3.14849e29i		−	0.874005i	0.899460	−	0.437002i	$-0.143960\pi$
$654$	−3.27384e29	−	2.19209e29i	−0.894317	−	0.598814i
$655$	7.02329e28			0.188802
$656$	5.80963e29			1.53694
$657$	−1.51065e29	+	6.22316e28i	−0.393303	+	0.162022i
$658$	4.15675e29	+	3.54338e29i	1.06508	+	0.907915i
$659$			4.76961e29i			1.20278i	0.798956	+	0.601389i	$0.205386\pi$
$659$			4.76961e29i			1.20278i	−0.798956	+	0.601389i	$0.794614\pi$
$660$	3.43614e27	+	2.30075e27i	0.00852823	+	0.00571030i
$661$			2.59847e28i			0.0634749i	0.999496	+	0.0317375i	$0.0101040\pi$
$661$			2.59847e28i			0.0634749i	−0.999496	+	0.0317375i	$0.989896\pi$
$662$			1.51715e29i			0.364769i
$663$	3.87312e27	+	2.59335e27i	0.00916577	+	0.00613718i
$664$			2.99124e29i			0.696765i
$665$	6.53392e28	+	5.56977e28i	0.149812	+	0.127706i
$666$	−5.78038e29	+	2.38125e29i	−1.30460	+	0.537434i
$667$	−7.16233e29			−1.59123
$668$	3.68724e27			0.00806397
$669$	−5.26894e29	−	3.52796e29i	−1.13436	−	0.759537i
$670$			1.06920e29i			0.226608i
$671$	−8.05131e29			−1.67989
$672$	−4.92875e28	+	1.38997e28i	−0.101242	+	0.0285515i
$673$	2.52103e29			0.509824			0.254912	−	0.966964i	$-0.417954\pi$
$673$	2.52103e29			0.509824			0.254912	+	0.966964i	$0.417954\pi$
$674$			1.62398e29i			0.323334i
$675$	4.90012e29	+	9.89459e28i	0.960544	+	0.193958i
$676$	−1.42120e27			−0.00274293
$677$	−9.65507e29			−1.83474			−0.917370	−	0.398035i	$-0.869692\pi$
$677$	−9.65507e29			−1.83474			−0.917370	+	0.398035i	$0.869692\pi$
$678$	−3.13946e28	+	4.68873e28i	−0.0587413	+	0.0877291i
$679$	−3.82634e29	−	3.26172e29i	−0.704939	−	0.600917i
$680$		−	8.59961e26i		−	0.00156004i
$681$	2.47619e29	−	3.69815e29i	0.442323	−	0.660601i
$682$			1.39482e30i			2.45347i
$683$			6.57041e29i			1.13809i	0.822308	+	0.569043i	$0.192686\pi$
$683$			6.57041e29i			1.13809i	−0.822308	+	0.569043i	$0.807314\pi$
$684$	−3.96579e28	+	1.63372e28i	−0.0676458	+	0.0278669i
$685$		−	3.73497e28i		−	0.0627388i
$686$	3.22554e29	−	5.29745e29i	0.533580	−	0.876323i
$687$	−1.00200e29	−	6.70914e28i	−0.163238	−	0.109300i
$688$	1.49327e28			0.0239586
$689$	−2.60543e27			−0.00411696
$690$	4.93899e28	−	7.37630e28i	0.0768640	−	0.114795i
$691$			2.43529e29i			0.373277i	0.982429	+	0.186638i	$0.0597593\pi$
$691$			2.43529e29i			0.373277i	−0.982429	+	0.186638i	$0.940241\pi$
$692$	2.09682e27			0.00316554
$693$	−2.86834e29	+	8.79848e29i	−0.426512	+	1.30830i
$694$	−3.46068e29			−0.506859
$695$		−	8.42464e28i		−	0.121538i
$696$	6.37081e29	−	9.51469e29i	0.905310	−	1.35206i
$697$	1.18491e28			0.0165860
$698$	−1.74082e29			−0.240033
$699$	1.95280e29	+	1.30755e29i	0.265245	+	0.177602i
$700$	2.50136e28	−	2.93436e28i	0.0334694	−	0.0392631i
$701$			4.20767e29i			0.554629i	0.960779	+	0.277315i	$0.0894444\pi$
$701$			4.20767e29i			0.554629i	−0.960779	+	0.277315i	$0.910556\pi$
$702$	−7.54024e29	−	1.52256e29i	−0.979141	−	0.197713i
$703$		−	1.49380e30i		−	1.91100i
$704$			1.02845e30i			1.29619i
$705$	8.65876e28	−	1.29317e29i	0.107515	−	0.160572i
$706$			1.37579e30i			1.68307i
$707$	1.48933e29	−	1.74714e29i	0.179509	−	0.210584i
$708$	−5.73190e27	+	8.56049e27i	−0.00680690	+	0.0101660i
$709$	1.28022e30			1.49796			0.748980	−	0.662592i	$-0.230544\pi$
$709$	1.28022e30			1.49796			0.748980	+	0.662592i	$0.230544\pi$
$710$	1.06720e29			0.123037
$711$	−3.42274e29	−	8.30856e29i	−0.388815	−	0.943832i
$712$			1.69314e29i			0.189519i
$713$	1.49759e30			1.65178
$714$	−1.02938e28	+	2.90299e27i	−0.0111878	+	0.00315511i
$715$	−1.77214e29			−0.189794
$716$		−	9.02834e28i		−	0.0952843i
$717$	7.59679e28	+	5.08663e28i	0.0790095	+	0.0529029i
$718$	−6.75462e29			−0.692300
$719$	−6.56725e29			−0.663331			−0.331665	−	0.943397i	$-0.607610\pi$
$719$	−6.56725e29			−0.663331			−0.331665	+	0.943397i	$0.607610\pi$
$720$	5.69115e28	+	1.38151e29i	0.0566512	+	0.137519i
$721$	8.97975e29	+	7.65468e29i	0.880935	+	0.750943i
$722$		−	9.87913e29i		−	0.955165i
$723$	1.43861e30	+	9.63259e29i	1.37085	+	0.917891i
$724$		−	6.32366e28i		−	0.0593900i
$725$			1.77224e30i			1.64049i
$726$	−8.34971e29	−	5.59077e29i	−0.761793	−	0.510078i
$727$		−	5.36618e29i		−	0.482563i	−0.970455	−	0.241281i	$-0.922432\pi$
$727$		−	5.36618e29i		−	0.482563i	0.970455	−	0.241281i	$-0.0775677\pi$
$728$	6.92587e29	−	8.12478e29i	0.613896	−	0.720165i
$729$	1.05488e30	+	4.44123e29i	0.921647	+	0.388029i
$730$	7.17890e28			0.0618256
$731$	3.04562e26			0.000258549
$732$	6.38209e28	+	4.27329e28i	0.0534068	+	0.0357599i
$733$		−	1.18357e30i		−	0.976343i	−0.872748	−	0.488171i	$-0.837664\pi$
$733$		−	1.18357e30i		−	0.976343i	0.872748	−	0.488171i	$-0.162336\pi$
$734$	7.92163e29			0.644178
$735$	−1.60553e29	−	7.38341e28i	−0.128707	−	0.0591889i
$736$	−1.26517e29			−0.0999842
$737$		−	2.75373e30i		−	2.14542i
$738$	−1.80807e30	+	7.44839e29i	−1.38875	+	0.572098i
$739$	1.04586e30			0.791970			0.395985	−	0.918257i	$-0.370403\pi$
$739$	1.04586e30			0.791970			0.395985	+	0.918257i	$0.370403\pi$
$740$	1.37391e28			0.0102571
$741$	1.02265e30	−	1.52731e30i	0.752723	−	1.12418i
$742$	3.87828e27	−	4.54963e27i	0.00281448	−	0.00330168i
$743$			7.81081e29i			0.558873i	0.960164	+	0.279437i	$0.0901477\pi$
$743$			7.81081e29i			0.558873i	−0.960164	+	0.279437i	$0.909852\pi$
$744$	−1.33209e30	+	1.98945e30i	−0.939760	+	1.40351i
$745$		−	3.87954e29i		−	0.269860i
$746$			1.17859e30i			0.808362i
$747$	−4.03747e29	−	9.80080e29i	−0.273050	−	0.662819i
$748$		−	1.23089e27i		−	0.000820830i
$749$	−1.34235e30	−	1.14427e30i	−0.882684	−	0.752434i
$750$	−3.68776e29	−	2.46923e29i	−0.239122	−	0.160110i
$751$	1.34504e30			0.860034			0.430017	−	0.902821i	$-0.358508\pi$
$751$	1.34504e30			0.860034			0.430017	+	0.902821i	$0.358508\pi$
$752$	−2.27127e30			−1.43213
$753$	1.44455e30	−	2.15740e30i	0.898223	−	1.34148i
$754$		−	2.72710e30i		−	1.67225i
$755$	−1.12613e29			−0.0680995
$756$	6.94352e28	−	5.45196e28i	0.0414096	−	0.0325142i
$757$	−1.64153e30			−0.965477			−0.482738	−	0.875765i	$-0.660358\pi$
$757$	−1.64153e30			−0.965477			−0.482738	+	0.875765i	$0.660358\pi$
$758$		−	3.68247e29i		−	0.213605i
$759$	−1.27204e30	+	1.89976e30i	−0.727714	+	1.08683i
$760$	−3.39113e29			−0.191338
$761$	−5.46447e28			−0.0304095			−0.0152047	−	0.999884i	$-0.504840\pi$
$761$	−5.46447e28			−0.0304095			−0.0152047	+	0.999884i	$0.504840\pi$
$762$	3.56608e29	+	2.38776e29i	0.195733	+	0.131058i
$763$	−1.25705e30	+	1.47465e30i	−0.680526	+	0.798329i
$764$		−	1.57228e28i		−	0.00839557i
$765$	1.16075e27	+	2.81766e27i	0.000611353	+	0.00148403i
$766$			4.18861e29i			0.217604i
$767$		−	4.41495e29i		−	0.226242i
$768$	1.73375e29	−	2.58933e29i	0.0876383	−	0.130886i
$769$			7.28455e29i			0.363226i	0.983370	+	0.181613i	$0.0581317\pi$
$769$			7.28455e29i			0.363226i	−0.983370	+	0.181613i	$0.941868\pi$
$770$	2.63789e29	−	3.09453e29i	0.129749	−	0.152209i
$771$	7.38301e29	−	1.10264e30i	0.358231	−	0.535011i
$772$	3.60315e28			0.0172465
$773$	−4.05027e29			−0.191249			−0.0956245	−	0.995417i	$-0.530485\pi$
$773$	−4.05027e29			−0.191249			−0.0956245	+	0.995417i	$0.530485\pi$
$774$	−4.64735e28	+	1.91449e28i	−0.0216484	+	0.00891812i
$775$		−	3.70563e30i		−	1.70292i
$776$	1.98589e30			0.900339
$777$	8.34537e29	+	2.95922e30i	0.373272	+	1.32360i
$778$	2.39000e30			1.05466
$779$		−	4.67251e30i		−	2.03426i
$780$	1.40473e28	+	9.40574e27i	0.00603392	+	0.00404017i
$781$	−2.74858e30			−1.16486
$782$	−2.64234e28			−0.0110489
$783$	−8.03137e29	+	3.97740e30i	−0.331353	+	1.64097i
$784$	4.08291e29	+	2.54651e30i	0.166208	+	1.03664i
$785$			2.41550e29i			0.0970233i
$786$	2.86675e30	+	1.91951e30i	1.13620	+	0.760770i
$787$		−	3.62683e30i		−	1.41838i	−0.705018	−	0.709189i	$-0.749061\pi$
$787$		−	3.62683e30i		−	1.41838i	0.705018	−	0.709189i	$-0.250939\pi$
$788$		−	1.29691e29i		−	0.0500478i
$789$	−5.72009e29	−	3.83004e29i	−0.217818	−	0.145846i
$790$			3.94839e29i			0.148367i
$791$	2.11196e29	+	1.80032e29i	0.0783129	+	0.0667569i
$792$	−1.39225e30	−	3.37963e30i	−0.509452	−	1.23667i
$793$	−3.29147e30			−1.18856
$794$	1.14304e30			0.407329
$795$	−1.41539e27	−	9.47714e26i	−0.000497763	−	0.000333290i
$796$		−	1.52831e29i		−	0.0530424i
$797$	5.19369e30			1.77895			0.889476	−	0.456983i	$-0.151070\pi$
$797$	5.19369e30			1.77895			0.889476	+	0.456983i	$0.151070\pi$
$798$	1.14475e30	+	4.05922e30i	0.386973	+	1.37218i
$799$	−4.63239e28			−0.0154548
$800$			3.13053e29i			0.103080i
$801$	−2.28534e29	−	5.54758e29i	−0.0742693	−	0.180286i
$802$	7.43942e29			0.238621
$803$	−1.84892e30			−0.585337
$804$	−1.46156e29	+	2.18282e29i	−0.0456698	+	0.0682071i
$805$	−3.32254e29	−	2.83226e29i	−0.102474	−	0.0873526i
$806$			5.70216e30i			1.73589i
$807$	−1.84252e30	+	2.75176e30i	−0.553655	+	0.826873i
$808$			9.06773e29i			0.268955i
$809$		−	4.62788e29i		−	0.135495i	−0.997703	−	0.0677474i	$-0.978419\pi$
$809$		−	4.62788e29i		−	0.135495i	0.997703	−	0.0677474i	$-0.0215812\pi$
$810$	−3.54239e29	−	3.56986e29i	−0.102377	−	0.103171i
$811$		−	3.93765e30i		−	1.12336i	−0.827355	−	0.561679i	$-0.810156\pi$
$811$		−	3.93765e30i		−	1.12336i	0.827355	−	0.561679i	$-0.189844\pi$
$812$	2.38180e29	+	2.03034e29i	0.0670761	+	0.0571782i
$813$	1.99396e30	+	1.33511e30i	0.554328	+	0.371165i
$814$	−7.07477e30			−1.94158
$815$	3.97062e29			0.107573
$816$	2.47441e28	−	3.69549e28i	0.00661798	−	0.00988384i
$817$		−	1.20100e29i		−	0.0317110i
$818$	3.20673e30			0.835897
$819$	−1.17261e30	+	3.59692e30i	−0.301768	+	0.925655i
$820$	4.29751e28			0.0109187
$821$			5.89057e30i			1.47759i	0.673930	+	0.738796i	$0.264605\pi$
$821$			5.89057e30i			1.47759i	−0.673930	+	0.738796i	$0.735395\pi$
$822$	1.02079e30	−	1.52453e30i	0.252804	−	0.377558i
$823$	2.47341e30			0.604780			0.302390	−	0.953184i	$-0.402216\pi$
$823$	2.47341e30			0.604780			0.302390	+	0.953184i	$0.402216\pi$
$824$	−4.66052e30			−1.12512
$825$	4.70077e30	+	3.14752e30i	1.12048	+	0.750244i
$826$	7.70943e29	+	6.57182e29i	0.181440	+	0.154666i
$827$			8.02168e29i			0.186405i	0.995647	+	0.0932025i	$0.0297104\pi$
$827$			8.02168e29i			0.186405i	−0.995647	+	0.0932025i	$0.970290\pi$
$828$	2.01663e29	−	8.30756e28i	0.0462708	−	0.0190614i
$829$			7.37712e30i			1.67134i	0.549233	+	0.835669i	$0.314920\pi$
$829$			7.37712e30i			1.67134i	−0.549233	+	0.835669i	$0.685080\pi$
$830$			4.65754e29i			0.104192i
$831$	−3.46583e29	+	5.17616e29i	−0.0765591	+	0.114340i
$832$			4.20442e30i			0.917088i
$833$	8.32735e27	+	5.19376e28i	0.00179364	+	0.0111869i
$834$	2.30251e30	−	3.43875e30i	0.489731	−	0.731404i
$835$	−1.03306e29			−0.0216979
$836$	−4.85384e29			−0.100675
$837$	1.67930e30	−	8.31644e30i	0.343962	−	1.70341i
$838$		−	8.37987e30i		−	1.69502i
$839$	−5.53844e30			−1.10634			−0.553168	−	0.833070i	$-0.686581\pi$
$839$	−5.53844e30			−1.10634			−0.553168	+	0.833070i	$0.686581\pi$
$840$	6.71782e29	−	1.89451e29i	0.132524	−	0.0373736i
$841$	−9.25235e30			−1.80258
$842$			4.65626e30i			0.895902i
$843$	8.70980e28	+	5.83187e28i	0.0165508	+	0.0110820i
$844$	−1.87506e29			−0.0351899
$845$	3.98181e28			0.00738049
$846$	7.06863e30	−	2.91194e30i	1.29404	−	0.533082i
$847$	−3.20602e30	+	3.76100e30i	−0.579682	+	0.680028i
$848$			2.48594e28i			0.00443950i
$849$	−6.43584e29	−	4.30929e29i	−0.113521	−	0.0760107i
$850$			6.53819e28i			0.0113909i
$851$			7.59606e30i			1.30716i
$852$	2.17874e29	+	1.45883e29i	0.0370330	+	0.0247964i
$853$		−	3.48110e30i		−	0.584455i	−0.956349	−	0.292228i	$-0.905604\pi$
$853$		−	3.48110e30i		−	0.584455i	0.956349	−	0.292228i	$-0.0943965\pi$
$854$	4.89947e30	−	5.74760e30i	0.812535	−	0.953189i
$855$	1.11110e30	−	4.57723e29i	0.182017	−	0.0749823i
$856$	6.96683e30			1.12735
$857$	−8.72659e30			−1.39491			−0.697455	−	0.716629i	$-0.745684\pi$
$857$	−8.72659e30			−1.39491			−0.697455	+	0.716629i	$0.745684\pi$
$858$	−7.23347e30	−	4.84336e30i	−1.14217	−	0.764769i
$859$		−	2.42183e30i		−	0.377759i	−0.982000	−	0.188880i	$-0.939514\pi$
$859$		−	2.42183e30i		−	0.377759i	0.982000	−	0.188880i	$-0.0604856\pi$
$860$	1.10461e27			0.000170206
$861$	2.61038e30	+	9.25625e30i	0.397348	+	1.40897i
$862$	6.95819e30			1.04633
$863$		−	9.42768e30i		−	1.40053i	−0.713884	−	0.700264i	$-0.753066\pi$
$863$		−	9.42768e30i		−	1.40053i	0.713884	−	0.700264i	$-0.246934\pi$
$864$	−1.41868e29	+	7.02576e29i	−0.0208204	+	0.103110i
$865$	−5.87471e28			−0.00851761
$866$	−1.37940e30			−0.197584
$867$	−3.93107e30	+	5.87098e30i	−0.556301	+	0.830826i
$868$	−4.98017e29	−	4.24529e29i	−0.0696285	−	0.0593540i
$869$		−	1.01691e31i		−	1.40467i
$870$	9.91973e29	−	1.48149e30i	0.135378	−	0.202184i
$871$		−	1.12576e31i		−	1.51794i
$872$		−	7.65349e30i		−	1.01962i
$873$	−6.50676e30	+	2.68048e30i	−0.856476	+	0.352828i
$874$			1.04197e31i			1.35514i
$875$	−1.41598e30	+	1.66109e30i	−0.181958	+	0.213456i
$876$	1.46560e29	+	9.81331e28i	0.0186090	+	0.0124601i
$877$	1.82836e30			0.229386			0.114693	−	0.993401i	$-0.463412\pi$
$877$	1.82836e30			0.229386			0.114693	+	0.993401i	$0.463412\pi$
$878$	−1.22946e31			−1.52413
$879$	5.94652e30	−	8.88102e30i	0.728416	−	1.08788i
$880$			1.69086e30i			0.204664i
$881$	1.23115e31			1.47253			0.736267	−	0.676691i	$-0.236587\pi$
$881$	1.23115e31			1.47253			0.736267	+	0.676691i	$0.236587\pi$
$882$	−4.53551e30	−	7.40177e30i	−0.536050	−	0.874814i
$883$	−3.38640e30			−0.395504			−0.197752	−	0.980252i	$-0.563364\pi$
$883$	−3.38640e30			−0.395504			−0.197752	+	0.980252i	$0.563364\pi$
$884$		−	5.03203e27i		−	0.000580756i
$885$	1.60592e29	−	2.39841e29i	0.0183155	−	0.0273539i
$886$	1.54116e31			1.73698
$887$	−1.66615e30			−0.185573			−0.0927867	−	0.995686i	$-0.529577\pi$
$887$	−1.66615e30			−0.185573			−0.0927867	+	0.995686i	$0.529577\pi$
$888$	−1.00909e31	−	6.75660e30i	−1.11069	−	0.743690i
$889$	1.36926e30	−	1.60628e30i	0.148942	−	0.174724i
$890$			2.63632e29i			0.0283402i
$891$	9.12343e30	+	9.19417e30i	0.969264	+	0.976780i
$892$			6.84550e29i			0.0718744i
$893$			1.82672e31i			1.89553i
$894$	1.06030e31	−	1.58354e31i	1.08739	−	1.62400i
$895$			2.52949e30i			0.256384i
$896$	−8.14092e30	−	6.93963e30i	−0.815529	−	0.695188i
$897$	−5.20023e30	+	7.76645e30i	−0.514875	+	0.768956i
$898$	1.22891e31			1.20259
$899$	3.00783e31			2.90922
$900$	−2.05562e29	−	4.98993e29i	−0.0196515	−	0.0477033i
$901$			5.07022e26i			4.79089e-5i
$902$	−2.21295e31			−2.06682
$903$	6.70957e28	+	2.37917e29i	0.00619403	+	0.0219636i
$904$	−1.09612e30			−0.100020
$905$			1.77171e30i			0.159802i
$906$	−4.59660e30	−	3.07777e30i	−0.409818	−	0.274404i
$907$	−1.54297e31			−1.35982			−0.679908	−	0.733297i	$-0.737980\pi$
$907$	−1.54297e31			−1.35982			−0.679908	+	0.733297i	$0.737980\pi$
$908$	−4.80470e29			−0.0418567
$909$	−1.22393e30	−	2.97105e30i	−0.105399	−	0.255852i
$910$	1.07840e30	−	1.26508e30i	0.0918005	−	0.107692i
$911$			7.61143e30i			0.640506i	0.947332	+	0.320253i	$0.103768\pi$
$911$			7.61143e30i			0.640506i	−0.947332	+	0.320253i	$0.896232\pi$
$912$	−1.45726e31	−	9.75749e30i	−1.21225	−	0.811694i
$913$		−	1.19955e31i		−	0.986448i
$914$			8.39819e30i			0.682733i
$915$	−1.78808e30	−	1.19726e30i	−0.143703	−	0.0962202i
$916$			1.30181e29i			0.0103430i
$917$	1.10074e31	−	1.29128e31i	0.864582	−	1.01425i
$918$	−2.96295e28	+	1.46735e29i	−0.00230078	+	0.0113942i
$919$	1.21367e30			0.0931721			0.0465861	−	0.998914i	$-0.485166\pi$
$919$	1.21367e30			0.0931721			0.0465861	+	0.998914i	$0.485166\pi$
$920$	1.72441e30			0.130878
$921$	3.65916e30	+	2.45009e30i	0.274572	+	0.183847i
$922$			1.47860e31i			1.09692i
$923$	−1.12365e31			−0.824164
$924$	9.61546e29	−	2.71168e29i	0.0697292	−	0.0196645i
$925$	1.87956e31			1.34763
$926$		−	8.83216e30i		−	0.626111i
$927$	1.52702e31	−	6.29061e30i	1.07031	−	0.440916i
$928$	−2.54103e30			−0.176099
$929$	−7.74317e30			−0.530584			−0.265292	−	0.964168i	$-0.585468\pi$
$929$	−7.74317e30			−0.530584			−0.265292	+	0.964168i	$0.585468\pi$
$930$	−2.07414e30	+	3.09769e30i	−0.140529	+	0.209878i
$931$	2.04808e31	−	3.28377e30i	1.37207	−	0.219989i
$932$		−	2.53711e29i		−	0.0168063i
$933$	−9.13029e30	+	1.36359e31i	−0.598036	+	0.893156i
$934$			9.03291e30i			0.585040i
$935$			3.44862e28i			0.00220863i
$936$	−5.69168e30	−	1.38163e31i	−0.360449	−	0.874976i
$937$			2.41912e31i			1.51493i	0.652878	+	0.757463i	$0.273562\pi$
$937$			2.41912e31i			1.51493i	−0.652878	+	0.757463i	$0.726438\pi$
$938$	1.96581e31	+	1.67573e31i	1.21734	+	1.03771i
$939$	−4.54657e30	−	3.04427e30i	−0.278417	−	0.186421i
$940$	−1.68011e29			−0.0101741
$941$	3.12044e31			1.86863			0.934317	−	0.356442i	$-0.116010\pi$
$941$	3.12044e31			1.86863			0.934317	+	0.356442i	$0.116010\pi$
$942$	−6.60172e30	+	9.85956e30i	−0.390951	+	0.583879i
$943$			2.37600e31i			1.39147i
$944$	−4.21247e30			−0.243967
$945$	−1.94538e30	+	1.52749e30i	−0.111422	+	0.0874870i
$946$	−5.68803e29			−0.0322185
$947$		−	2.39780e31i		−	1.34319i	−0.740917	−	0.671596i	$-0.765609\pi$
$947$		−	2.39780e31i		−	1.34319i	0.740917	−	0.671596i	$-0.234391\pi$
$948$	−5.39731e29	+	8.06079e29i	−0.0299013	+	0.0446571i
$949$	−7.55861e30			−0.414140
$950$	2.57824e31			1.39709
$951$	−1.24872e31	−	8.36110e30i	−0.669218	−	0.448093i
$952$	−1.58110e29	−	1.34779e29i	−0.00838053	−	0.00714389i
$953$		−	1.08727e31i		−	0.569984i	−0.958530	−	0.284992i	$-0.908009\pi$
$953$		−	1.08727e31i		−	0.569984i	0.958530	−	0.284992i	$-0.0919909\pi$
$954$	−3.18717e28	−	7.73672e28i	−0.00165252	−	0.00401143i
$955$			4.40510e29i			0.0225902i
$956$		−	9.86989e28i		−	0.00500616i
$957$	−2.55482e31	+	3.81558e31i	−1.28170	+	1.91419i
$958$		−	2.44215e30i		−	0.121181i
$959$	−6.86702e30	−	5.85371e30i	−0.337034	−	0.287300i
$960$	−1.52934e30	+	2.28404e30i	−0.0742431	+	0.110881i
$961$	−4.20660e31			−2.01993
$962$	−2.89225e31			−1.37372
$963$	−2.28268e31	+	9.40358e30i	−1.07243	+	0.441791i
$964$		−	1.86907e30i		−	0.0868593i
$965$	−1.00950e30			−0.0464056
$966$	−5.82113e30	−	2.06414e31i	−0.264696	−	0.938595i
$967$	−2.01610e31			−0.906849			−0.453424	−	0.891295i	$-0.649798\pi$
$967$	−2.01610e31			−0.906849			−0.453424	+	0.891295i	$0.649798\pi$
$968$		−	1.95197e31i		−	0.868524i
$969$	−2.97218e29	−	1.99010e29i	−0.0130820	−	0.00875941i
$970$	3.09214e30			0.134635
$971$	1.62235e31			0.698782			0.349391	−	0.936977i	$-0.386389\pi$
$971$	1.62235e31			0.698782			0.349391	+	0.936977i	$0.386389\pi$
$972$	−2.35205e29	−	1.21303e30i	−0.0100219	−	0.0516865i
$973$	−1.54893e31	−	1.32037e31i	−0.652901	−	0.556558i
$974$			1.31259e31i			0.547343i
$975$	1.92173e31	+	1.28674e31i	0.792763	+	0.530815i
$976$			3.14052e31i			1.28167i
$977$			2.87785e31i			1.16192i	0.813932	+	0.580960i	$0.197323\pi$
$977$			2.87785e31i			1.16192i	−0.813932	+	0.580960i	$0.802677\pi$
$978$	1.62072e31	+	1.08520e31i	0.647367	+	0.433461i
$979$		−	6.78983e30i		−	0.268313i
$980$	3.02022e28	+	1.88371e29i	0.00118077	+	0.00736446i
$981$	1.03304e31	+	2.50767e31i	0.399571	+	0.969942i
$982$	1.67013e31			0.639116
$983$	−1.74400e31			−0.660289			−0.330144	−	0.943930i	$-0.607097\pi$
$983$	−1.74400e31			−0.660289			−0.330144	+	0.943930i	$0.607097\pi$
$984$	−3.15636e31	−	2.11342e31i	−1.18233	−	0.791659i
$985$			3.63358e30i			0.134665i
$986$	−5.30700e29			−0.0194600
$987$	−1.02053e31	−	3.61872e31i	−0.370249	−	1.31288i
$988$	−1.98431e30			−0.0712296
$989$			6.10713e29i			0.0216908i
$990$	−2.16782e30	−	5.26229e30i	−0.0761821	−	0.184929i
$991$	4.86682e31			1.69228			0.846139	−	0.532962i	$-0.178921\pi$
$991$	4.86682e31			1.69228			0.846139	+	0.532962i	$0.178921\pi$
$992$	5.31310e30			0.182800
$993$	5.81045e30	−	8.67780e30i	0.197807	−	0.295422i
$994$	1.67260e31	−	1.96213e31i	0.563423	−	0.660954i
$995$			4.28189e30i			0.142723i
$996$	−6.36669e29	+	9.50853e29i	−0.0209986	+	0.0313610i
$997$			1.20577e31i			0.393518i	0.980452	+	0.196759i	$0.0630417\pi$
$997$			1.20577e31i			0.393518i	−0.980452	+	0.196759i	$0.936958\pi$
$998$			1.76177e31i			0.568956i
$999$	4.21826e31	+	8.51773e30i	1.34802	+	0.272199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.22.c.b.20.30	yes	52
3.2	odd	2	inner	21.22.c.b.20.23	✓	52
7.6	odd	2	inner	21.22.c.b.20.24	yes	52
21.20	even	2	inner	21.22.c.b.20.29	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.22.c.b.20.23	✓	52	3.2	odd	2	inner
21.22.c.b.20.24	yes	52	7.6	odd	2	inner
21.22.c.b.20.29	yes	52	21.20	even	2	inner
21.22.c.b.20.30	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)

\(f(q)\)	\(=\)	\(q+1485.79i q^{2} +(56903.5 - 84984.4i) q^{3} -110413. q^{4} +3.09347e6 q^{5} +(1.26269e8 + 8.45465e7i) q^{6} +(4.84831e8 - 5.68758e8i) q^{7} +2.95187e9i q^{8} +(-3.98433e9 - 9.67182e9i) q^{9} +O(q^{10})\)	\(q+1485.79i q^{2} +(56903.5 - 84984.4i) q^{3} -110413. q^{4} +3.09347e6 q^{5} +(1.26269e8 + 8.45465e7i) q^{6} +(4.84831e8 - 5.68758e8i) q^{7} +2.95187e9i q^{8} +(-3.98433e9 - 9.67182e9i) q^{9} +4.59624e9i q^{10} -1.18376e11i q^{11} +(-6.28290e9 + 9.38340e9i) q^{12} -4.83935e11i q^{13} +(8.45053e11 + 7.20355e11i) q^{14} +(1.76029e11 - 2.62897e11i) q^{15} -4.61741e12 q^{16} -9.41748e10 q^{17} +(1.43703e13 - 5.91988e12i) q^{18} +3.71365e13i q^{19} -3.41560e11 q^{20} +(-2.07469e13 - 7.35673e13i) q^{21} +1.75882e14 q^{22} -1.88841e14i q^{23} +(2.50863e14 + 1.67972e14i) q^{24} -4.67268e14 q^{25} +7.19024e14 q^{26} +(-1.04868e15 - 2.11754e14i) q^{27} +(-5.35317e13 + 6.27984e13i) q^{28} -3.79278e15i q^{29} +(3.90609e14 + 2.61542e14i) q^{30} +7.93042e15i q^{31} -6.69965e14i q^{32} +(-1.00601e16 - 6.73602e15i) q^{33} -1.39924e14i q^{34} +(1.49981e15 - 1.75944e15i) q^{35} +(4.39923e14 + 1.06790e15i) q^{36} -4.02246e16 q^{37} -5.51769e16 q^{38} +(-4.11269e16 - 2.75376e16i) q^{39} +9.13153e15i q^{40} -1.25820e17 q^{41} +(1.09305e17 - 3.08255e16i) q^{42} -3.23401e15 q^{43} +1.30703e16i q^{44} +(-1.23254e16 - 2.99195e16i) q^{45} +2.80578e17 q^{46} +4.91893e17 q^{47} +(-2.62747e17 + 3.92408e17i) q^{48} +(-8.84243e16 - 5.51502e17i) q^{49} -6.94260e17i q^{50} +(-5.35888e15 + 8.00339e15i) q^{51} +5.34328e16i q^{52} -5.38384e15i q^{53} +(3.14622e17 - 1.55811e18i) q^{54} -3.66193e17i q^{55} +(1.67890e18 + 1.43116e18i) q^{56} +(3.15602e18 + 2.11320e18i) q^{57} +5.63527e18 q^{58} +9.12302e17 q^{59} +(-1.94360e16 + 2.90273e16i) q^{60} -6.80147e18i q^{61} -1.17829e19 q^{62} +(-7.43265e18 - 2.42307e18i) q^{63} -8.68798e18 q^{64} -1.49704e18i q^{65} +(1.00083e19 - 1.49472e19i) q^{66} +2.32626e19 q^{67} +1.03981e16 q^{68} +(-1.60485e19 - 1.07457e19i) q^{69} +(2.61415e18 + 2.22840e18i) q^{70} -2.32191e19i q^{71} +(2.85500e19 - 1.17612e19i) q^{72} -1.56191e19i q^{73} -5.97652e19i q^{74} +(-2.65892e19 + 3.97104e19i) q^{75} -4.10036e18i q^{76} +(-6.73273e19 - 5.73924e19i) q^{77} +(4.09150e19 - 6.11058e19i) q^{78} +8.59048e19 q^{79} -1.42838e19 q^{80} +(-7.76691e19 + 7.70715e19i) q^{81} -1.86942e20i q^{82} +1.01334e20 q^{83} +(2.29074e18 + 8.12281e18i) q^{84} -2.91327e17 q^{85} -4.80505e18i q^{86} +(-3.22327e20 - 2.15823e20i) q^{87} +3.49431e20 q^{88} +5.73582e19 q^{89} +(4.44540e19 - 1.83130e19i) q^{90} +(-2.75242e20 - 2.34626e20i) q^{91} +2.08506e19i q^{92} +(6.73962e20 + 4.51269e20i) q^{93} +7.30848e20i q^{94} +1.14881e20i q^{95} +(-5.69365e19 - 3.81233e19i) q^{96} -6.72755e20i q^{97} +(8.19415e20 - 1.31380e20i) q^{98} +(-1.14491e21 + 4.71650e20i) 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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