LMFDB - Embedded newform 21.30.c.a.20.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,30,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, 30, names="a")

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

chi := DirichletCharacter("21.20");

S:= CuspForms(chi, 30);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 30 $
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:	$111.883889004$
Analytic rank:	$0$
Dimension:	$76$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			20.1
Character	$\chi$	$=$	21.20
Dual form			21.30.c.a.20.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-27459.9i q^{2} +(-7.86336e6 - 2.60729e6i) q^{3} -2.17175e8 q^{4} -2.60713e10 q^{5} +(-7.15959e10 + 2.15927e11i) q^{6} +(-1.78867e12 - 1.43352e11i) q^{7} -8.77881e12i q^{8} +(5.50345e13 + 4.10041e13i) q^{9} +O(q^{10})$	\(q-27459.9i q^{2} +(-7.86336e6 - 2.60729e6i) q^{3} -2.17175e8 q^{4} -2.60713e10 q^{5} +(-7.15959e10 + 2.15927e11i) q^{6} +(-1.78867e12 - 1.43352e11i) q^{7} -8.77881e12i q^{8} +(5.50345e13 + 4.10041e13i) q^{9} +7.15915e14i q^{10} +1.84525e15i q^{11} +(1.70773e15 + 5.66239e14i) q^{12} -1.93886e14i q^{13} +(-3.93643e15 + 4.91168e16i) q^{14} +(2.05008e17 + 6.79754e16i) q^{15} -3.57660e17 q^{16} -8.05269e16 q^{17} +(1.12597e18 - 1.51124e18i) q^{18} -5.95624e18i q^{19} +5.66204e18 q^{20} +(1.36912e19 + 5.79082e18i) q^{21} +5.06704e19 q^{22} +6.15339e19i q^{23} +(-2.28889e19 + 6.90309e19i) q^{24} +4.93447e20 q^{25} -5.32409e18 q^{26} +(-3.25846e20 - 4.65921e20i) q^{27} +(3.88456e20 + 3.11325e19i) q^{28} -9.13257e20i q^{29} +(1.86660e21 - 5.62950e21i) q^{30} +3.13598e21i q^{31} +5.10823e21i q^{32} +(4.81110e21 - 1.45099e22i) q^{33} +2.21126e21i q^{34} +(4.66330e22 + 3.73737e21i) q^{35} +(-1.19521e22 - 8.90508e21i) q^{36} -2.79899e22 q^{37} -1.63558e23 q^{38} +(-5.05517e20 + 1.52460e21i) q^{39} +2.28875e23i q^{40} +2.23493e23 q^{41} +(1.59015e23 - 3.75960e23i) q^{42} +5.48297e23 q^{43} -4.00743e23i q^{44} +(-1.43482e24 - 1.06903e24i) q^{45} +1.68972e24 q^{46} -1.11402e24 q^{47} +(2.81241e24 + 9.32524e23i) q^{48} +(3.17881e24 + 5.12820e23i) q^{49} -1.35500e25i q^{50} +(6.33212e23 + 2.09957e23i) q^{51} +4.21073e22i q^{52} +1.03543e25i q^{53} +(-1.27941e25 + 8.94770e24i) q^{54} -4.81080e25i q^{55} +(-1.25846e24 + 1.57024e25i) q^{56} +(-1.55296e25 + 4.68361e25i) q^{57} -2.50780e25 q^{58} -9.54320e24 q^{59} +(-4.45227e25 - 1.47626e25i) q^{60} -8.43183e25i q^{61} +8.61137e25 q^{62} +(-9.25607e25 - 8.12323e25i) q^{63} -5.17459e25 q^{64} +5.05486e24i q^{65} +(-3.98439e26 - 1.32112e26i) q^{66} +2.14590e26 q^{67} +1.74884e25 q^{68} +(1.60437e26 - 4.83863e26i) q^{69} +(1.02628e26 - 1.28054e27i) q^{70} +7.65917e26i q^{71} +(3.59967e26 - 4.83137e26i) q^{72} +7.98935e26i q^{73} +7.68601e26i q^{74} +(-3.88015e27 - 1.28656e27i) q^{75} +1.29355e27i q^{76} +(2.64520e26 - 3.30055e27i) q^{77} +(4.18652e25 + 1.38815e25i) q^{78} -2.93271e27 q^{79} +9.32466e27 q^{80} +(1.34745e27 + 4.51328e27i) q^{81} -6.13708e27i q^{82} -5.11580e27 q^{83} +(-2.97340e27 - 1.25762e27i) q^{84} +2.09944e27 q^{85} -1.50562e28i q^{86} +(-2.38113e27 + 7.18127e27i) q^{87} +1.61991e28 q^{88} +2.50441e28 q^{89} +(-2.93555e28 + 3.94000e28i) q^{90} +(-2.77939e25 + 3.46799e26i) q^{91} -1.33637e28i q^{92} +(8.17641e27 - 2.46593e28i) q^{93} +3.05909e28i q^{94} +1.55287e29i q^{95} +(1.33186e28 - 4.01679e28i) q^{96} +1.08394e29i q^{97} +(1.40820e28 - 8.72897e28i) q^{98} +(-7.56629e28 + 1.01552e29i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 20401094660 q^{4} + 1962751543872 q^{7} - 89581451225964 q^{9}+O(q^{10}) $ 76 * q - 20401094660 * q^4 + 1962751543872 * q^7 - 89581451225964 * q^9	$ 76 q - 20401094660 q^{4} + 1962751543872 q^{7} - 89581451225964 q^{9} - 11\!\cdots\!48 q^{15}+ \cdots - 23\!\cdots\!24 q^{99}+O(q^{100}) $ 76 * q - 20401094660 * q^4 + 1962751543872 * q^7 - 89581451225964 * q^9 - 116668222909200048 * q^15 + 4964525139713333892 * q^16 + 1542346202347854996 * q^18 + 33840646982361357348 * q^21 - 9870996616978150672 * q^22 + 3225406746743103424612 * q^25 - 3181907581338093199564 * q^28 + 5113912044496410095244 * q^30 - 85758641407134848258352 * q^36 - 17812771227715200149976 * q^37 + 388095283792424641491696 * q^39 + 804036587819434104664956 * q^42 + 2391536152977907871782320 * q^43 - 1070985628070611677307000 * q^46 - 512656982878691867441540 * q^49 - 961431915936904000664400 * q^51 + 20345422731681279280765248 * q^57 - 40096240109469024574169272 * q^58 - 164991837955115951799442596 * q^60 - 360764839802574990409097184 * q^63 - 1608343949909674725081473028 * q^64 + 483978610969894046870693264 * q^67 - 656026306765550013508448520 * q^70 + 1937172856654554597960695124 * q^72 - 8054141680325499868559088636 * q^78 - 11740735193468750125742145952 * q^79 + 18477545939654446572971367132 * q^81 - 7249045143271847568431965452 * q^84 + 14576359553686844022629140848 * q^85 - 1685535263940707754634995584 * q^88 + 44135166284535829618726469040 * q^91 + 226499776928895503792863540632 * q^93 - 231093384978708762520959066624 * 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 $

$2$		−	27459.9i		−	1.18512i	−0.805525	−	0.592562i	$-0.798116\pi$
$2$		−	27459.9i		−	1.18512i	0.805525	−	0.592562i	$-0.201884\pi$
$3$	−7.86336e6	−	2.60729e6i	−0.949183	−	0.314725i
$3$	−7.86336e6	−	2.60729e6i	−0.949183	−	0.314725i
$4$	−2.17175e8			−0.404521
$5$	−2.60713e10			−1.91028			−0.955141	−	0.296153i	$-0.904296\pi$
$5$	−2.60713e10			−1.91028			−0.955141	+	0.296153i	$0.904296\pi$
$6$	−7.15959e10	+	2.15927e11i	−0.372988	+	1.12490i
$7$	−1.78867e12	−	1.43352e11i	−0.996804	−	0.0798881i
$7$	−1.78867e12	−	1.43352e11i	−0.996804	−	0.0798881i
$8$		−	8.77881e12i		−	0.705717i
$9$	5.50345e13	+	4.10041e13i	0.801896	+	0.597463i
$10$			7.15915e14i			2.26392i
$11$			1.84525e15i			1.46508i	0.680724	+	0.732540i	$0.261665\pi$
$11$			1.84525e15i			1.46508i	−0.680724	+	0.732540i	$0.738335\pi$
$12$	1.70773e15	+	5.66239e14i	0.383964	+	0.127313i
$13$		−	1.93886e14i		−	0.0136574i	−0.999977	−	0.00682870i	$-0.997826\pi$
$13$		−	1.93886e14i		−	0.0136574i	0.999977	−	0.00682870i	$-0.00217366\pi$
$14$	−3.93643e15	+	4.91168e16i	−0.0946773	+	1.18134i
$15$	2.05008e17	+	6.79754e16i	1.81321	+	0.601213i
$16$	−3.57660e17			−1.24088
$17$	−8.05269e16			−0.115993			−0.0579964	−	0.998317i	$-0.518471\pi$
$17$	−8.05269e16			−0.115993			−0.0579964	+	0.998317i	$0.518471\pi$
$18$	1.12597e18	−	1.51124e18i	0.708068	−	0.950347i
$19$		−	5.95624e18i		−	1.71019i	−0.518469	−	0.855096i	$-0.673498\pi$
$19$		−	5.95624e18i		−	1.71019i	0.518469	−	0.855096i	$-0.326502\pi$
$20$	5.66204e18			0.772748
$21$	1.36912e19	+	5.79082e18i	0.921006	+	0.389547i
$22$	5.06704e19			1.73630
$23$			6.15339e19i			1.10678i	0.832922	+	0.553390i	$0.186666\pi$
$23$			6.15339e19i			1.10678i	−0.832922	+	0.553390i	$0.813334\pi$
$24$	−2.28889e19	+	6.90309e19i	−0.222107	+	0.669855i
$25$	4.93447e20			2.64917
$26$	−5.32409e18			−0.0161857
$27$	−3.25846e20	−	4.65921e20i	−0.573110	−	0.819479i
$28$	3.88456e20	+	3.11325e19i	0.403228	+	0.0323164i
$29$		−	9.13257e20i		−	0.569931i	−0.958538	−	0.284965i	$-0.908018\pi$
$29$		−	9.13257e20i		−	0.569931i	0.958538	−	0.284965i	$-0.0919821\pi$
$30$	1.86660e21	−	5.62950e21i	0.712513	−	2.14888i
$31$			3.13598e21i			0.744096i	0.928214	+	0.372048i	$0.121344\pi$
$31$			3.13598e21i			0.744096i	−0.928214	+	0.372048i	$0.878656\pi$
$32$			5.10823e21i			0.764885i
$33$	4.81110e21	−	1.45099e22i	0.461097	−	1.39063i
$34$			2.21126e21i			0.137466i
$35$	4.66330e22	+	3.73737e21i	1.90418	+	0.152609i
$36$	−1.19521e22	−	8.90508e21i	−0.324384	−	0.241686i
$37$	−2.79899e22			−0.510595			−0.255298	−	0.966863i	$-0.582173\pi$
$37$	−2.79899e22			−0.510595			−0.255298	+	0.966863i	$0.582173\pi$
$38$	−1.63558e23			−2.02679
$39$	−5.05517e20	+	1.52460e21i	−0.00429832	+	0.0129634i
$40$			2.28875e23i			1.34812i
$41$	2.23493e23			0.920232			0.460116	−	0.887859i	$-0.347808\pi$
$41$	2.23493e23			0.920232			0.460116	+	0.887859i	$0.347808\pi$
$42$	1.59015e23	−	3.75960e23i	0.461662	−	1.09151i
$43$	5.48297e23			1.13168			0.565840	−	0.824515i	$-0.308552\pi$
$43$	5.48297e23			1.13168			0.565840	+	0.824515i	$0.308552\pi$
$44$		−	4.00743e23i		−	0.592655i
$45$	−1.43482e24	−	1.06903e24i	−1.53185	−	1.14132i
$46$	1.68972e24			1.31167
$47$	−1.11402e24			−0.633103			−0.316552	−	0.948575i	$-0.602525\pi$
$47$	−1.11402e24			−0.633103			−0.316552	+	0.948575i	$0.602525\pi$
$48$	2.81241e24	+	9.32524e23i	1.17783	+	0.390537i
$49$	3.17881e24	+	5.12820e23i	0.987236	+	0.159265i
$50$		−	1.35500e25i		−	3.13960i
$51$	6.33212e23	+	2.09957e23i	0.110098	+	0.0365059i
$52$			4.21073e22i			0.00552470i
$53$			1.03543e25i			1.03067i	0.856988	+	0.515336i	$0.172333\pi$
$53$			1.03543e25i			1.03067i	−0.856988	+	0.515336i	$0.827667\pi$
$54$	−1.27941e25	+	8.94770e24i	−0.971184	+	0.679207i
$55$		−	4.81080e25i		−	2.79871i
$56$	−1.25846e24	+	1.57024e25i	−0.0563784	+	0.703462i
$57$	−1.55296e25	+	4.68361e25i	−0.538240	+	1.62329i
$58$	−2.50780e25			−0.675439
$59$	−9.54320e24			−0.200604			−0.100302	−	0.994957i	$-0.531981\pi$
$59$	−9.54320e24			−0.200604			−0.100302	+	0.994957i	$0.531981\pi$
$60$	−4.45227e25	−	1.47626e25i	−0.733479	−	0.243203i
$61$		−	8.43183e25i		−	1.09305i	−0.837444	−	0.546524i	$-0.815951\pi$
$61$		−	8.43183e25i		−	1.09305i	0.837444	−	0.546524i	$-0.184049\pi$
$62$	8.61137e25			0.881846
$63$	−9.25607e25	−	8.12323e25i	−0.751603	−	0.659615i
$64$	−5.17459e25			−0.334400
$65$			5.05486e24i			0.0260895i
$66$	−3.98439e26	−	1.32112e26i	−1.64807	−	0.546458i
$67$	2.14590e26			0.713716			0.356858	−	0.934159i	$-0.383848\pi$
$67$	2.14590e26			0.713716			0.356858	+	0.934159i	$0.383848\pi$
$68$	1.74884e25			0.0469215
$69$	1.60437e26	−	4.83863e26i	0.348331	−	1.05054i
$70$	1.02628e26	−	1.28054e27i	0.180860	−	2.25669i
$71$			7.65917e26i			1.09884i	0.835545	+	0.549422i	$0.185152\pi$
$71$			7.65917e26i			1.09884i	−0.835545	+	0.549422i	$0.814848\pi$
$72$	3.59967e26	−	4.83137e26i	0.421640	−	0.565912i
$73$			7.98935e26i			0.766178i	0.923711	+	0.383089i	$0.125140\pi$
$73$			7.98935e26i			0.766178i	−0.923711	+	0.383089i	$0.874860\pi$
$74$			7.68601e26i			0.605119i
$75$	−3.88015e27	−	1.28656e27i	−2.51455	−	0.833761i
$76$			1.29355e27i			0.691808i
$77$	2.64520e26	−	3.30055e27i	0.117042	−	1.46040i
$78$	4.18652e25	+	1.38815e25i	0.0153632	+	0.00509405i
$79$	−2.93271e27			−0.894697			−0.447349	−	0.894360i	$-0.647632\pi$
$79$	−2.93271e27			−0.894697			−0.447349	+	0.894360i	$0.647632\pi$
$80$	9.32466e27			2.37044
$81$	1.34745e27	+	4.51328e27i	0.286076	+	0.958207i
$82$		−	6.13708e27i		−	1.09059i
$83$	−5.11580e27			−0.762573			−0.381286	−	0.924457i	$-0.624519\pi$
$83$	−5.11580e27			−0.762573			−0.381286	+	0.924457i	$0.624519\pi$
$84$	−2.97340e27	−	1.25762e27i	−0.372566	−	0.157580i
$85$	2.09944e27			0.221579
$86$		−	1.50562e28i		−	1.34118i
$87$	−2.38113e27	+	7.18127e27i	−0.179371	+	0.540969i
$88$	1.61991e28			1.03393
$89$	2.50441e28			1.35691			0.678454	−	0.734643i	$-0.262650\pi$
$89$	2.50441e28			1.35691			0.678454	+	0.734643i	$0.262650\pi$
$90$	−2.93555e28	+	3.94000e28i	−1.35261	+	1.81543i
$91$	−2.77939e25	+	3.46799e26i	−0.00109106	+	0.0136137i
$92$		−	1.33637e28i		−	0.447715i
$93$	8.17641e27	−	2.46593e28i	0.234186	−	0.706283i
$94$			3.05909e28i			0.750306i
$95$			1.55287e29i			3.26695i
$96$	1.33186e28	−	4.01679e28i	0.240728	−	0.726015i
$97$			1.08394e29i			1.68584i	0.538042	+	0.842918i	$0.319164\pi$
$97$			1.08394e29i			1.68584i	−0.538042	+	0.842918i	$0.680836\pi$
$98$	1.40820e28	−	8.72897e28i	0.188749	−	1.17000i
$99$	−7.56629e28	+	1.01552e29i	−0.875331	+	1.17484i
$100$	−1.07165e29			−1.07165
$101$	−6.79883e28			−0.588538			−0.294269	−	0.955723i	$-0.595076\pi$
$101$	−6.79883e28			−0.588538			−0.294269	+	0.955723i	$0.595076\pi$
$102$	5.76540e27	−	1.73879e28i	0.0432640	−	0.130480i
$103$			1.35130e29i			0.880261i	0.897934	+	0.440130i	$0.145068\pi$
$103$			1.35130e29i			0.880261i	−0.897934	+	0.440130i	$0.854932\pi$
$104$	−1.70209e27			−0.00963826
$105$	−3.56948e29	−	1.50974e29i	−1.75938	−	0.744145i
$106$	2.84328e29			1.22147
$107$		−	2.32027e29i		−	0.869908i	−0.900453	−	0.434954i	$-0.856765\pi$
$107$		−	2.32027e29i		−	0.869908i	0.900453	−	0.434954i	$-0.143235\pi$
$108$	7.07657e28	+	1.01187e29i	0.231835	+	0.331496i
$109$	1.37524e29			0.394180			0.197090	−	0.980385i	$-0.436851\pi$
$109$	1.37524e29			0.394180			0.197090	+	0.980385i	$0.436851\pi$
$110$	−1.32104e30			−3.31683
$111$	2.20095e29	+	7.29779e28i	0.484648	+	0.160697i
$112$	6.39738e29	+	5.12713e28i	1.23692	+	0.0991318i
$113$			1.01708e29i			0.172869i	0.996258	+	0.0864344i	$0.0275473\pi$
$113$			1.01708e29i			0.172869i	−0.996258	+	0.0864344i	$0.972453\pi$
$114$	1.28611e30	+	4.26443e29i	1.92380	+	0.637882i
$115$		−	1.60427e30i		−	2.11426i
$116$			1.98337e29i			0.230549i
$117$	7.95013e27	−	1.06704e28i	0.00815979	−	0.0109518i
$118$			2.62055e29i			0.237741i
$119$	1.44036e29	+	1.15437e28i	0.115622	+	0.00926645i
$120$	5.96743e29	−	1.79972e30i	0.424287	−	1.27961i
$121$	−1.81864e30			−1.14646
$122$	−2.31537e30			−1.29540
$123$	−1.75740e30	−	5.82710e29i	−0.873468	−	0.289620i
$124$		−	6.81058e29i		−	0.301002i
$125$	−8.00864e30			−3.15039
$126$	−2.23063e30	+	2.54171e30i	−0.781727	+	0.890744i
$127$	−3.24278e30			−1.01336			−0.506679	−	0.862135i	$-0.669127\pi$
$127$	−3.24278e30			−1.01336			−0.506679	+	0.862135i	$0.669127\pi$
$128$			4.16340e30i			1.16119i
$129$	−4.31146e30	−	1.42957e30i	−1.07417	−	0.356168i
$130$	1.38806e29			0.0309193
$131$	2.26554e30			0.451583			0.225791	−	0.974176i	$-0.427503\pi$
$131$	2.26554e30			0.451583			0.225791	+	0.974176i	$0.427503\pi$
$132$	−1.04485e30	+	3.15119e30i	−0.186523	+	0.562538i
$133$	−8.53839e29	+	1.06538e31i	−0.136624	+	1.70473i
$134$		−	5.89262e30i		−	0.845842i
$135$	8.49522e30	+	1.21472e31i	1.09480	+	1.56543i
$136$			7.06930e29i			0.0818582i
$137$		−	8.13564e30i		−	0.847117i	−0.905869	−	0.423558i	$-0.860781\pi$
$137$		−	8.13564e30i		−	0.847117i	0.905869	−	0.423558i	$-0.139219\pi$
$138$	−1.32868e31	−	4.40558e30i	−1.24502	−	0.412816i
$139$			8.04462e30i			0.678877i	0.940628	+	0.339438i	$0.110237\pi$
$139$			8.04462e30i			0.678877i	−0.940628	+	0.339438i	$0.889763\pi$
$140$	−1.01275e31	−	8.11664e29i	−0.770278	−	0.0617334i
$141$	8.75995e30	+	2.90458e30i	0.600931	+	0.199253i
$142$	2.10320e31			1.30227
$143$	3.57768e29			0.0200092
$144$	−1.96836e31	−	1.46655e31i	−0.995060	−	0.741382i
$145$			2.38098e31i			1.08873i
$146$	2.19387e31			0.908017
$147$	−2.36590e31	−	1.23206e31i	−0.886943	−	0.461880i
$148$	6.07872e30			0.206546
$149$			2.94023e31i			0.906109i	0.891483	+	0.453054i	$0.149666\pi$
$149$			2.94023e31i			0.906109i	−0.891483	+	0.453054i	$0.850334\pi$
$150$	−3.53288e31	+	1.06549e32i	−0.988111	+	2.98006i
$151$	1.57029e31			0.398855			0.199428	−	0.979913i	$-0.436092\pi$
$151$	1.57029e31			0.398855			0.199428	+	0.979913i	$0.436092\pi$
$152$	−5.22887e31			−1.20691
$153$	−4.43175e30	−	3.30193e30i	−0.0930143	−	0.0693015i
$154$	−9.06328e31	−	7.26370e30i	−1.73075	−	0.138710i
$155$		−	8.17591e31i		−	1.42143i
$156$	1.09786e29	−	3.31105e29i	0.00173876	−	0.00524395i
$157$			2.67475e31i			0.386134i	0.981186	+	0.193067i	$0.0618435\pi$
$157$			2.67475e31i			0.386134i	−0.981186	+	0.193067i	$0.938157\pi$
$158$			8.05319e31i			1.06033i
$159$	2.69966e31	−	8.14195e31i	0.324378	−	0.978295i
$160$		−	1.33178e32i		−	1.46114i
$161$	8.82101e30	−	1.10064e32i	0.0884185	−	1.10324i
$162$	1.23934e32	−	3.70009e31i	1.13559	−	0.339035i
$163$	1.09229e32			0.915412			0.457706	−	0.889104i	$-0.348671\pi$
$163$	1.09229e32			0.915412			0.457706	+	0.889104i	$0.348671\pi$
$164$	−4.85371e31			−0.372253
$165$	−1.25432e32	+	3.78291e32i	−0.880825	+	2.65649i
$166$			1.40479e32i			0.903744i
$167$	−1.79477e32			−1.05832			−0.529162	−	0.848521i	$-0.677494\pi$
$167$	−1.79477e32			−1.05832			−0.529162	+	0.848521i	$0.677494\pi$
$168$	5.08365e31	−	1.20193e32i	0.274910	−	0.649970i
$169$	2.01501e32			0.999813
$170$		−	5.76504e31i		−	0.262599i
$171$	2.44230e32	−	3.27798e32i	1.02178	−	1.37140i
$172$	−1.19077e32			−0.457788
$173$	−1.76120e31			−0.0622502			−0.0311251	−	0.999515i	$-0.509909\pi$
$173$	−1.76120e31			−0.0622502			−0.0311251	+	0.999515i	$0.509909\pi$
$174$	1.97197e32	+	6.53855e31i	0.641115	+	0.212578i
$175$	−8.82616e32	−	7.07366e31i	−2.64071	−	0.211637i
$176$		−	6.59973e32i		−	1.81799i
$177$	7.50416e31	+	2.48819e31i	0.190410	+	0.0631352i
$178$		−	6.87709e32i		−	1.60810i
$179$			1.46675e32i			0.316219i	0.987422	+	0.158110i	$0.0505400\pi$
$179$			1.46675e32i			0.316219i	−0.987422	+	0.158110i	$0.949460\pi$
$180$	3.11607e32	+	2.32167e32i	0.619664	+	0.461689i
$181$			3.40067e31i			0.0624058i	0.999513	+	0.0312029i	$0.00993380\pi$
$181$			3.40067e31i			0.0624058i	−0.999513	+	0.0312029i	$0.990066\pi$
$182$	9.52307e30	+	7.63219e29i	0.0161340	+	0.00129305i
$183$	−2.19842e32	+	6.63025e32i	−0.344009	+	1.03750i
$184$	5.40195e32			0.781073
$185$	7.29733e32			0.975380
$186$	−6.77143e32	−	2.24524e32i	−0.837034	−	0.277539i
$187$		−	1.48592e32i		−	0.169939i
$188$	2.41938e32			0.256103
$189$	5.16042e32	+	8.80091e32i	0.505812	+	0.862644i
$190$	4.26416e33			3.87174
$191$		−	2.40802e32i		−	0.202617i	−0.994855	−	0.101308i	$-0.967697\pi$
$191$		−	2.40802e32i		−	0.202617i	0.994855	−	0.101308i	$-0.0323029\pi$
$192$	4.06897e32	+	1.34917e32i	0.317407	+	0.105244i
$193$	−1.66406e33			−1.20389			−0.601947	−	0.798536i	$-0.705608\pi$
$193$	−1.66406e33			−1.20389			−0.601947	+	0.798536i	$0.705608\pi$
$194$	2.97649e33			1.99793
$195$	1.31795e31	−	3.97482e31i	0.00821101	−	0.0247637i
$196$	−6.90358e32	−	1.11372e32i	−0.399357	−	0.0644262i
$197$		−	2.90596e33i		−	1.56146i	−0.624870	−	0.780728i	$-0.714848\pi$
$197$		−	2.90596e33i		−	1.56146i	0.624870	−	0.780728i	$-0.285152\pi$
$198$	2.78862e33	+	2.07769e33i	1.39233	+	1.03738i
$199$			1.38700e33i			0.643732i	0.946785	+	0.321866i	$0.104310\pi$
$199$			1.38700e33i			0.643732i	−0.946785	+	0.321866i	$0.895690\pi$
$200$		−	4.33188e33i		−	1.86957i
$201$	−1.68740e33	−	5.59499e32i	−0.677447	−	0.224624i
$202$			1.86695e33i			0.697490i
$203$	−1.30917e32	+	1.63352e33i	−0.0455307	+	0.568109i
$204$	−1.37518e32	−	4.55975e31i	−0.0445371	−	0.0147674i
$205$	−5.82674e33			−1.75790
$206$	3.71065e33			1.04322
$207$	−2.52314e33	+	3.38649e33i	−0.661260	+	0.887522i
$208$			6.93453e31i			0.0169472i
$209$	1.09908e34			2.50557
$210$	−4.14573e33	+	9.80175e33i	−0.881905	+	2.08509i
$211$	3.16343e33			0.628148			0.314074	−	0.949398i	$-0.398306\pi$
$211$	3.16343e33			0.628148			0.314074	+	0.949398i	$0.398306\pi$
$212$		−	2.24870e33i		−	0.416928i
$213$	1.99697e33	−	6.02268e33i	0.345833	−	1.04300i
$214$	−6.37143e33			−1.03095
$215$	−1.42948e34			−2.16183
$216$	−4.09023e33	+	2.86054e33i	−0.578320	+	0.404454i
$217$	4.49549e32	−	5.60925e33i	0.0594444	−	0.741718i
$218$		−	3.77640e33i		−	0.467153i
$219$	2.08306e33	−	6.28231e33i	0.241135	−	0.727243i
$220$			1.04479e34i			1.13214i
$221$			1.56130e31i			0.00158416i
$222$	2.00396e33	−	6.04378e33i	0.190446	−	0.574369i
$223$		−	1.87524e34i		−	1.66969i	−0.550486	−	0.834845i	$-0.685557\pi$
$223$		−	1.87524e34i		−	1.66969i	0.550486	−	0.834845i	$-0.314443\pi$
$224$	7.32275e32	−	9.13696e33i	0.0611052	−	0.762440i
$225$	2.71566e34	+	2.02334e34i	2.12436	+	1.58278i
$226$	2.79288e33			0.204871
$227$	−1.65372e34			−1.13786			−0.568929	−	0.822387i	$-0.692642\pi$
$227$	−1.65372e34			−1.13786			−0.568929	+	0.822387i	$0.692642\pi$
$228$	3.37266e33	−	1.01716e34i	0.217729	−	0.656653i
$229$		−	9.33470e33i		−	0.565569i	−0.959183	−	0.282785i	$-0.908742\pi$
$229$		−	9.33470e33i		−	0.565569i	0.959183	−	0.282785i	$-0.0912582\pi$
$230$	−4.40531e34			−2.50566
$231$	−1.06855e34	+	2.52637e34i	−0.570718	+	1.34935i
$232$	−8.01731e33			−0.402210
$233$		−	1.40299e34i		−	0.661291i	−0.943755	−	0.330645i	$-0.892734\pi$
$233$		−	1.40299e34i		−	0.661291i	0.943755	−	0.330645i	$-0.107266\pi$
$234$	−2.93008e32	−	2.18310e32i	−0.0129793	−	0.00967037i
$235$	2.90440e34			1.20941
$236$	2.07255e33			0.0811485
$237$	2.30609e34	+	7.64642e33i	0.849231	+	0.281584i
$238$	3.16988e32	−	3.95522e33i	0.0109819	−	0.137027i
$239$		−	1.47077e34i		−	0.479484i	−0.970837	−	0.239742i	$-0.922937\pi$
$239$		−	1.47077e34i		−	0.479484i	0.970837	−	0.239742i	$-0.0770628\pi$
$240$	−7.33232e34	−	2.43121e34i	−2.24998	−	0.746036i
$241$		−	2.73665e33i		−	0.0790629i	−0.999218	−	0.0395315i	$-0.987413\pi$
$241$		−	2.73665e33i		−	0.0790629i	0.999218	−	0.0395315i	$-0.0125865\pi$
$242$			4.99396e34i			1.35870i
$243$	1.17192e33	−	3.90027e34i	0.0300335	−	0.999549i
$244$			1.83118e34i			0.442160i
$245$	−8.28755e34	−	1.33699e34i	−1.88590	−	0.304242i
$246$	−1.60012e34	+	4.82581e34i	−0.343236	+	1.03517i
$247$	−1.15483e33			−0.0233568
$248$	2.75302e34			0.525121
$249$	4.02274e34	+	1.33384e34i	0.723821	+	0.240001i
$250$			2.19917e35i			3.73360i
$251$	2.11420e34			0.338748			0.169374	−	0.985552i	$-0.445825\pi$
$251$	2.11420e34			0.338748			0.169374	+	0.985552i	$0.445825\pi$
$252$	2.01019e34	+	1.76417e34i	0.304039	+	0.266828i
$253$	−1.13546e35			−1.62152
$254$			8.90463e34i			1.20096i
$255$	−1.65086e34	−	5.47384e33i	−0.210319	−	0.0697365i
$256$	8.65457e34			1.04176
$257$	−7.36616e34			−0.837936			−0.418968	−	0.908001i	$-0.637608\pi$
$257$	−7.36616e34			−0.837936			−0.418968	+	0.908001i	$0.637608\pi$
$258$	−3.92559e34	+	1.18392e35i	−0.422103	+	1.27303i
$259$	5.00649e34	+	4.01241e33i	0.508963	+	0.0407905i
$260$		−	1.09779e33i		−	0.0105537i
$261$	3.74473e34	−	5.02606e34i	0.340513	−	0.457026i
$262$		−	6.22114e34i		−	0.535182i
$263$		−	2.37182e35i		−	1.93074i	−0.260883	−	0.965370i	$-0.584014\pi$
$263$		−	2.37182e35i		−	1.93074i	0.260883	−	0.965370i	$-0.415986\pi$
$264$	−1.27379e35	−	4.22358e34i	−0.981391	−	0.325404i
$265$		−	2.69950e35i		−	1.96887i
$266$	2.92552e35	+	2.34463e34i	2.02031	+	0.161916i
$267$	−1.96931e35	−	6.52972e34i	−1.28795	−	0.427053i
$268$	−4.66037e34			−0.288713
$269$	8.81222e34			0.517223			0.258611	−	0.965981i	$-0.416735\pi$
$269$	8.81222e34			0.517223			0.258611	+	0.965981i	$0.416735\pi$
$270$	3.33560e35	−	2.33278e35i	1.85524	−	1.29748i
$271$			1.51177e35i			0.796951i	0.917179	+	0.398476i	$0.130461\pi$
$271$			1.51177e35i			0.796951i	−0.917179	+	0.398476i	$0.869539\pi$
$272$	2.88013e34			0.143934
$273$	1.12276e33	−	2.65454e33i	0.00532020	−	0.0125785i
$274$	−2.23404e35			−1.00394
$275$			9.10533e35i			3.88125i
$276$	−3.48429e34	+	1.05083e35i	−0.140907	+	0.424964i
$277$	1.02040e35			0.391574			0.195787	−	0.980646i	$-0.437274\pi$
$277$	1.02040e35			0.391574			0.195787	+	0.980646i	$0.437274\pi$
$278$	2.20904e35			0.804554
$279$	−1.28588e35	+	1.72587e35i	−0.444570	+	0.596688i
$280$	3.28096e34	−	4.09382e35i	0.107699	−	1.34381i
$281$		−	2.27657e35i		−	0.709641i	−0.934934	−	0.354821i	$-0.884542\pi$
$281$		−	2.27657e35i		−	0.709641i	0.934934	−	0.354821i	$-0.115458\pi$
$282$	7.97594e34	−	2.40547e35i	0.236140	−	0.712178i
$283$		−	1.56973e35i		−	0.441490i	−0.975332	−	0.220745i	$-0.929151\pi$
$283$		−	1.56973e35i		−	0.441490i	0.975332	−	0.220745i	$-0.0708488\pi$
$284$		−	1.66338e35i		−	0.444505i
$285$	4.04878e35	−	1.22108e36i	1.02819	−	3.10093i
$286$		−	9.82428e33i		−	0.0237134i
$287$	−3.99755e35	−	3.20381e34i	−0.917290	−	0.0735155i
$288$	−2.09459e35	+	2.81129e35i	−0.456990	+	0.613358i
$289$	−4.75484e35			−0.986546
$290$	6.53815e35			1.29028
$291$	2.82615e35	−	8.52342e35i	0.530575	−	1.60017i
$292$		−	1.73509e35i		−	0.309935i
$293$	3.63411e35			0.617758			0.308879	−	0.951101i	$-0.400046\pi$
$293$	3.63411e35			0.617758			0.308879	+	0.951101i	$0.400046\pi$
$294$	−3.38321e35	+	6.49675e35i	−0.547385	+	1.05114i
$295$	2.48804e35			0.383210
$296$			2.45718e35i			0.360336i
$297$	8.59741e35	−	6.01267e35i	1.20060	−	0.839652i
$298$	8.07384e35			1.07385
$299$	1.19306e34			0.0151157
$300$	8.42673e35	+	2.79409e35i	1.01719	+	0.337274i
$301$	−9.80726e35	−	7.85995e34i	−1.12806	−	0.0904077i
$302$		−	4.31201e35i		−	0.472693i
$303$	5.34616e35	+	1.77265e35i	0.558630	+	0.185227i
$304$			2.13031e36i			2.12215i
$305$			2.19829e36i			2.08803i
$306$	−9.06708e34	+	1.21695e35i	−0.0821309	+	0.110234i
$307$		−	1.68415e36i		−	1.45503i	−0.686090	−	0.727517i	$-0.740674\pi$
$307$		−	1.68415e36i		−	1.45503i	0.686090	−	0.727517i	$-0.259326\pi$
$308$	−5.74473e34	+	7.16799e35i	−0.0473461	+	0.590761i
$309$	3.52323e35	−	1.06257e36i	0.277040	−	0.835528i
$310$	−2.24510e36			−1.68457
$311$	−2.55264e36			−1.82795			−0.913974	−	0.405773i	$-0.867002\pi$
$311$	−2.55264e36			−1.82795			−0.913974	+	0.405773i	$0.867002\pi$
$312$	1.33841e34	+	4.43784e33i	0.00914847	+	0.00303340i
$313$			1.65771e36i			1.08172i	0.841112	+	0.540862i	$0.181902\pi$
$313$			1.65771e36i			1.08172i	−0.841112	+	0.540862i	$0.818098\pi$
$314$	7.34484e35			0.457617
$315$	2.41318e36	+	2.11783e36i	1.43577	+	1.26005i
$316$	6.36912e35			0.361923
$317$		−	1.10890e36i		−	0.601910i	−0.953638	−	0.300955i	$-0.902695\pi$
$317$		−	1.10890e36i		−	0.601910i	0.953638	−	0.300955i	$-0.0973054\pi$
$318$	−2.23577e36	−	7.41325e35i	−1.15940	−	0.384428i
$319$	1.68519e36			0.834994
$320$	1.34908e36			0.638798
$321$	−6.04961e35	+	1.82451e36i	−0.273782	+	0.825701i
$322$	−3.02235e36	−	2.42224e35i	−1.30748	−	0.104787i
$323$			4.79637e35i			0.198370i
$324$	−2.92634e35	−	9.80173e35i	−0.115724	−	0.387615i
$325$		−	9.56725e34i		−	0.0361808i
$326$		−	2.99941e36i		−	1.08488i
$327$	−1.08140e36	−	3.58565e35i	−0.374149	−	0.124058i
$328$		−	1.96200e36i		−	0.649423i
$329$	1.99262e36	+	1.59697e35i	0.631080	+	0.0505774i
$330$	1.03878e37	+	3.44434e36i	3.14827	+	1.04389i
$331$	−4.19132e34			−0.0121575			−0.00607876	−	0.999982i	$-0.501935\pi$
$331$	−4.19132e34			−0.0121575			−0.00607876	+	0.999982i	$0.501935\pi$
$332$	1.11103e36			0.308476
$333$	−1.54041e36	−	1.14770e36i	−0.409444	−	0.305062i
$334$			4.92841e36i			1.25425i
$335$	−5.59464e36			−1.36340
$336$	−4.89681e36	−	2.07115e36i	−1.14286	−	0.483383i
$337$	2.76289e36			0.617631			0.308816	−	0.951122i	$-0.400067\pi$
$337$	2.76289e36			0.617631			0.308816	+	0.951122i	$0.400067\pi$
$338$		−	5.53319e36i		−	1.18490i
$339$	2.65181e35	−	7.99764e35i	0.0544061	−	0.164084i
$340$	−4.55946e35			−0.0896333
$341$	−5.78667e36			−1.09016
$342$	−9.00131e36	−	6.70654e36i	−1.62528	−	1.21093i
$343$	−5.61234e36	−	1.37296e36i	−0.971357	−	0.237625i
$344$		−	4.81340e36i		−	0.798646i
$345$	−4.18279e36	+	1.26149e37i	−0.665410	+	2.00682i
$346$			4.83625e35i			0.0737743i
$347$		−	6.10380e36i		−	0.892941i	−0.894798	−	0.446471i	$-0.852681\pi$
$347$		−	6.10380e36i		−	0.892941i	0.894798	−	0.446471i	$-0.147319\pi$
$348$	5.17122e35	−	1.55960e36i	0.0725595	−	0.218833i
$349$			7.10404e36i			0.956174i	0.878312	+	0.478087i	$0.158670\pi$
$349$			7.10404e36i			0.956174i	−0.878312	+	0.478087i	$0.841330\pi$
$350$	−1.94242e36	+	2.42366e37i	−0.250817	+	3.12957i
$351$	−9.03355e34	+	6.31770e34i	−0.0111919	+	0.00782719i
$352$	−9.42597e36			−1.12062
$353$	1.68355e36			0.192085			0.0960423	−	0.995377i	$-0.469382\pi$
$353$	1.68355e36			0.192085			0.0960423	+	0.995377i	$0.469382\pi$
$354$	6.83255e35	−	2.06064e36i	0.0748230	−	0.225660i
$355$		−	1.99684e37i		−	2.09910i
$356$	−5.43896e36			−0.548897
$357$	−1.10251e36	−	4.66317e35i	−0.106830	−	0.0451847i
$358$	4.02769e36			0.374759
$359$			3.39910e36i			0.303734i	0.988401	+	0.151867i	$0.0485286\pi$
$359$			3.39910e36i			0.303734i	−0.988401	+	0.151867i	$0.951471\pi$
$360$	−9.38481e36	+	1.25960e37i	−0.805451	+	1.08105i
$361$	−2.33470e37			−1.92476
$362$	9.33820e35			0.0739586
$363$	1.43006e37	+	4.74172e36i	1.08820	+	0.360819i
$364$	6.03616e33	−	7.53162e34i	0.000441357	−	0.00550704i
$365$		−	2.08293e37i		−	1.46362i
$366$	1.82066e37	+	6.03684e36i	1.22957	+	0.407694i
$367$			1.85685e37i			1.20536i	0.797981	+	0.602682i	$0.205901\pi$
$367$			1.85685e37i			1.20536i	−0.797981	+	0.602682i	$0.794099\pi$
$368$		−	2.20083e37i		−	1.37338i
$369$	1.22998e37	+	9.16412e36i	0.737930	+	0.549804i
$370$		−	2.00384e37i		−	1.15595i
$371$	1.48431e36	−	1.85204e37i	0.0823383	−	1.02738i
$372$	−1.77572e36	+	5.35540e36i	−0.0947329	+	0.285706i
$373$	−8.33812e34			−0.00427848			−0.00213924	−	0.999998i	$-0.500681\pi$
$373$	−8.33812e34			−0.00427848			−0.00213924	+	0.999998i	$0.500681\pi$
$374$	−4.08033e36			−0.201399
$375$	6.29748e37	+	2.08809e37i	2.99029	+	0.991505i
$376$			9.77978e36i			0.446792i
$377$	−1.77068e35			−0.00778377
$378$	2.41672e37	−	1.41705e37i	1.02234	−	0.599450i
$379$	1.91804e36			0.0780888			0.0390444	−	0.999237i	$-0.487569\pi$
$379$	1.91804e36			0.0780888			0.0390444	+	0.999237i	$0.487569\pi$
$380$		−	3.37245e37i		−	1.32155i
$381$	2.54991e37	+	8.45486e36i	0.961863	+	0.318929i
$382$	−6.61239e36			−0.240126
$383$	−3.60082e36			−0.125898			−0.0629490	−	0.998017i	$-0.520051\pi$
$383$	−3.60082e36			−0.125898			−0.0629490	+	0.998017i	$0.520051\pi$
$384$	1.08552e37	−	3.27383e37i	0.365456	−	1.10218i
$385$	−6.89638e36	+	8.60496e37i	−0.223584	+	2.78977i
$386$			4.56949e37i			1.42676i
$387$	3.01752e37	+	2.24825e37i	0.907490	+	0.676137i
$388$		−	2.35405e37i		−	0.681956i
$389$			2.94788e37i			0.822699i	0.911478	+	0.411350i	$0.134942\pi$
$389$			2.94788e37i			0.822699i	−0.911478	+	0.411350i	$0.865058\pi$
$390$	−1.09148e36	−	3.61907e35i	−0.0293480	−	0.00973107i
$391$		−	4.95513e36i		−	0.128379i
$392$	4.50195e36	−	2.79061e37i	0.112396	−	0.696709i
$393$	−1.78147e37	−	5.90691e36i	−0.428634	−	0.142124i
$394$	−7.97975e37			−1.85052
$395$	7.64595e37			1.70912
$396$	1.64321e37	−	2.20547e37i	0.354090	−	0.475248i
$397$		−	2.63789e37i		−	0.548018i	−0.961727	−	0.274009i	$-0.911650\pi$
$397$		−	2.63789e37i		−	0.548018i	0.961727	−	0.274009i	$-0.0883499\pi$
$398$	3.80868e37			0.762903
$399$	3.44915e37	−	8.15483e37i	0.666201	−	1.57510i
$400$	−1.76486e38			−3.28732
$401$			3.97992e37i			0.714958i	0.933921	+	0.357479i	$0.116364\pi$
$401$			3.97992e37i			0.714958i	−0.933921	+	0.357479i	$0.883636\pi$
$402$	−1.53638e37	+	4.63358e37i	−0.266208	+	0.802859i
$403$	6.08023e35			0.0101624
$404$	1.47654e37			0.238076
$405$	−3.51298e37	−	1.17667e38i	−0.546485	−	1.83044i
$406$	4.48563e37	+	3.59497e36i	0.673280	+	0.0539595i
$407$		−	5.16484e37i		−	0.748063i
$408$	1.84317e36	−	5.55884e36i	0.0257628	−	0.0776984i
$409$		−	4.93049e37i		−	0.665124i	−0.943081	−	0.332562i	$-0.892087\pi$
$409$		−	4.93049e37i		−	0.665124i	0.943081	−	0.332562i	$-0.107913\pi$
$410$			1.60002e38i			2.08333i
$411$	−2.12120e37	+	6.39734e37i	−0.266609	+	0.804069i
$412$		−	2.93469e37i		−	0.356084i
$413$	1.70697e37	+	1.36804e36i	0.199963	+	0.0160259i
$414$	9.29926e37	+	6.92853e37i	1.05182	+	0.783675i
$415$	1.33375e38			1.45673
$416$	9.90415e35			0.0104463
$417$	2.09747e37	−	6.32577e37i	0.213659	−	0.644378i
$418$		−	3.01805e38i		−	2.96941i
$419$	6.58531e37			0.625854			0.312927	−	0.949777i	$-0.398691\pi$
$419$	6.58531e37			0.625854			0.312927	+	0.949777i	$0.398691\pi$
$420$	7.75203e37	+	3.27879e37i	0.711706	+	0.301022i
$421$	−2.19764e38			−1.94924			−0.974622	−	0.223856i	$-0.928135\pi$
$421$	−2.19764e38			−1.94924			−0.974622	+	0.223856i	$0.928135\pi$
$422$		−	8.68674e37i		−	0.744434i
$423$	−6.13095e37	−	4.56795e37i	−0.507683	−	0.378256i
$424$	9.08983e37			0.727362
$425$	−3.97357e37			−0.307285
$426$	−1.65382e38	−	5.48366e37i	−1.23609	−	0.409856i
$427$	−1.20872e37	+	1.50818e38i	−0.0873215	+	1.08955i
$428$			5.03905e37i			0.351896i
$429$	−2.81326e36	−	9.32806e35i	−0.0189924	−	0.00629739i
$430$			3.92534e38i			2.56203i
$431$		−	1.17334e38i		−	0.740464i	−0.928939	−	0.370232i	$-0.879278\pi$
$431$		−	1.17334e38i		−	0.740464i	0.928939	−	0.370232i	$-0.120722\pi$
$432$	1.16542e38	+	1.66641e38i	0.711163	+	1.01688i
$433$		−	2.48867e38i		−	1.46856i	−0.678844	−	0.734282i	$-0.737519\pi$
$433$		−	2.48867e38i		−	1.46856i	0.678844	−	0.734282i	$-0.262481\pi$
$434$	−1.54029e38	−	1.23446e37i	−0.879028	−	0.0704490i
$435$	6.20790e37	−	1.87225e38i	0.342650	−	1.03340i
$436$	−2.98669e37			−0.159454
$437$	3.66511e38			1.89281
$438$	−1.72512e38	−	5.72005e37i	−0.861874	−	0.285776i
$439$			1.35398e38i			0.654451i	0.944946	+	0.327225i	$0.106114\pi$
$439$			1.35398e38i			0.654451i	−0.944946	+	0.327225i	$0.893886\pi$
$440$	−4.22331e38			−1.97510
$441$	1.53916e38	+	1.58567e38i	0.696506	+	0.717551i
$442$	4.28732e35			0.00187743
$443$			3.89269e38i			1.64967i	0.565376	+	0.824833i	$0.308731\pi$
$443$			3.89269e38i			1.64967i	−0.565376	+	0.824833i	$0.691269\pi$
$444$	−4.77992e37	−	1.58490e37i	−0.196050	−	0.0650053i
$445$	−6.52932e38			−2.59208
$446$	−5.14938e38			−1.97879
$447$	7.66603e37	−	2.31201e38i	0.285175	−	0.860063i
$448$	9.25566e37	+	7.41787e36i	0.333331	+	0.0267146i
$449$			3.93055e38i			1.37051i	0.728304	+	0.685254i	$0.240309\pi$
$449$			3.93055e38i			1.37051i	−0.728304	+	0.685254i	$0.759691\pi$
$450$	5.55606e38	−	7.45717e38i	1.87580	−	2.51764i
$451$			4.12400e38i			1.34821i
$452$		−	2.20884e37i		−	0.0699290i
$453$	−1.23478e38	−	4.09421e37i	−0.378586	−	0.125530i
$454$			4.54111e38i			1.34850i
$455$	7.24623e35	−	9.04149e36i	0.00208424	−	0.0260061i
$456$	4.11165e38	+	1.36332e38i	1.14558	+	0.379846i
$457$	−4.02004e38			−1.08504			−0.542520	−	0.840043i	$-0.682530\pi$
$457$	−4.02004e38			−1.08504			−0.542520	+	0.840043i	$0.682530\pi$
$458$	−2.56330e38			−0.670270
$459$	2.62394e37	+	3.75191e37i	0.0664767	+	0.0950537i
$460$			3.48408e38i			0.855262i
$461$	−1.92578e38			−0.458081			−0.229040	−	0.973417i	$-0.573559\pi$
$461$	−1.92578e38			−0.458081			−0.229040	+	0.973417i	$0.573559\pi$
$462$	6.93740e38	+	2.93423e38i	1.59915	+	0.676372i
$463$	7.75241e38			1.73186			0.865929	−	0.500166i	$-0.166728\pi$
$463$	7.75241e38			1.73186			0.865929	+	0.500166i	$0.166728\pi$
$464$			3.26636e38i			0.707218i
$465$	−2.13170e38	+	6.42901e38i	−0.447360	+	1.34920i
$466$	−3.85258e38			−0.783712
$467$	−4.16159e37			−0.0820663			−0.0410331	−	0.999158i	$-0.513065\pi$
$467$	−4.16159e37			−0.0820663			−0.0410331	+	0.999158i	$0.513065\pi$
$468$	−1.72657e36	+	2.31735e36i	−0.00330080	+	0.00443024i
$469$	−3.83832e38	−	3.07619e37i	−0.711434	−	0.0570174i
$470$		−	7.97544e38i		−	1.43330i
$471$	6.97385e37	−	2.10325e38i	0.121526	−	0.366512i
$472$			8.37780e37i			0.141570i
$473$			1.01175e39i			1.65800i
$474$	2.09970e38	−	6.33251e38i	0.333712	−	1.00644i
$475$		−	2.93909e39i		−	4.53060i
$476$	−3.12811e37	−	2.50700e36i	−0.0467716	−	0.00374847i
$477$	−4.24568e38	+	5.69843e38i	−0.615788	+	0.826491i
$478$	−4.03871e38			−0.568248
$479$	1.11054e39			1.51589			0.757946	−	0.652317i	$-0.226203\pi$
$479$	1.11054e39			1.51589			0.757946	+	0.652317i	$0.226203\pi$
$480$	−3.47234e38	+	1.04723e39i	−0.459859	+	1.38689i
$481$			5.42686e36i			0.00697340i
$482$	−7.51483e37			−0.0936994
$483$	−3.56332e38	+	8.42475e38i	−0.431143	+	1.01935i
$484$	3.94964e38			0.463766
$485$		−	2.82597e39i		−	3.22042i
$486$	−1.07101e39	−	3.21807e37i	−1.18459	−	0.0355935i
$487$	−9.46464e38			−1.01610			−0.508048	−	0.861329i	$-0.669633\pi$
$487$	−9.46464e38			−1.01610			−0.508048	+	0.861329i	$0.669633\pi$
$488$	−7.40214e38			−0.771383
$489$	−8.58905e38	−	2.84791e38i	−0.868893	−	0.288103i
$490$	−3.67135e38	+	2.27575e39i	−0.360565	+	2.23502i
$491$			2.79679e38i			0.266673i	0.991071	+	0.133336i	$0.0425691\pi$
$491$			2.79679e38i			0.266673i	−0.991071	+	0.133336i	$0.957431\pi$
$492$	3.81664e38	+	1.26550e38i	0.353336	+	0.117157i
$493$			7.35417e37i			0.0661079i
$494$			3.17116e37i			0.0276807i
$495$	1.97263e39	−	2.64760e39i	1.67213	−	2.24428i
$496$		−	1.12162e39i		−	0.923337i
$497$	1.09796e38	−	1.36998e39i	0.0877845	−	1.09533i
$498$	3.66270e38	−	1.10464e39i	0.284431	−	0.857818i
$499$	2.38891e39			1.80195			0.900975	−	0.433872i	$-0.142853\pi$
$499$	2.38891e39			1.80195			0.900975	+	0.433872i	$0.142853\pi$
$500$	1.73928e39			1.27440
$501$	1.41129e39	+	4.67947e38i	1.00454	+	0.333081i
$502$		−	5.80556e38i		−	0.401458i
$503$	2.00686e39			1.34828			0.674142	−	0.738602i	$-0.264514\pi$
$503$	2.00686e39			1.34828			0.674142	+	0.738602i	$0.264514\pi$
$504$	−7.13123e38	+	8.12573e38i	−0.465502	+	0.530419i
$505$	1.77254e39			1.12427
$506$			3.11795e39i			1.92170i
$507$	−1.58447e39	−	5.25370e38i	−0.949006	−	0.314666i
$508$	7.04251e38			0.409924
$509$	2.23697e39			1.26547			0.632737	−	0.774367i	$-0.281932\pi$
$509$	2.23697e39			1.26547			0.632737	+	0.774367i	$0.281932\pi$
$510$	−1.50311e38	+	4.53326e38i	−0.0826464	+	0.249254i
$511$	1.14529e38	−	1.42903e39i	0.0612085	−	0.763730i
$512$		−	1.41328e38i		−	0.0734198i
$513$	−2.77514e39	+	1.94082e39i	−1.40147	+	0.980128i
$514$			2.02274e39i			0.993059i
$515$		−	3.52301e39i		−	1.68155i
$516$	9.36343e38	+	3.10467e38i	0.434524	+	0.144077i
$517$		−	2.05565e39i		−	0.927547i
$518$	1.10180e38	−	1.37478e39i	0.0483418	−	0.603185i
$519$	1.38490e38	+	4.59197e37i	0.0590869	+	0.0195917i
$520$	4.43756e37			0.0184118
$521$	2.75049e39			1.10985			0.554923	−	0.831901i	$-0.312748\pi$
$521$	2.75049e39			1.10985			0.554923	+	0.831901i	$0.312748\pi$
$522$	−1.38015e39	−	1.02830e39i	−0.541632	−	0.403550i
$523$			2.90751e39i			1.10980i	0.831916	+	0.554902i	$0.187244\pi$
$523$			2.90751e39i			1.10980i	−0.831916	+	0.554902i	$0.812756\pi$
$524$	−4.92019e38			−0.182674
$525$	6.75590e39	+	2.85746e39i	2.43991	+	1.03198i
$526$	−6.51300e39			−2.28817
$527$		−	2.52531e38i		−	0.0863098i
$528$	−1.72074e39	+	5.18960e39i	−0.572168	+	1.72561i
$529$	−6.95367e38			−0.224961
$530$	−7.41279e39			−2.33336
$531$	−5.25205e38	−	3.91311e38i	−0.160864	−	0.119854i
$532$	1.85433e38	−	2.31374e39i	0.0552672	−	0.689597i
$533$		−	4.33321e37i		−	0.0125680i
$534$	−1.79306e39	+	5.40770e39i	−0.506111	+	1.52639i
$535$			6.04923e39i			1.66177i
$536$		−	1.88385e39i		−	0.503681i
$537$	3.82426e38	−	1.15336e39i	0.0995221	−	0.300150i
$538$		−	2.41983e39i		−	0.612973i
$539$	−9.46281e38	+	5.86569e39i	−0.233337	+	1.44638i
$540$	−1.84495e39	−	2.63806e39i	−0.442870	−	0.633251i
$541$	5.32128e39			1.24353			0.621764	−	0.783205i	$-0.286416\pi$
$541$	5.32128e39			1.24353			0.621764	+	0.783205i	$0.286416\pi$
$542$	4.15131e39			0.944487
$543$	8.86652e37	−	2.67407e38i	0.0196406	−	0.0592345i
$544$		−	4.11350e38i		−	0.0887212i
$545$	−3.58543e39			−0.752995
$546$	−7.28933e37	−	3.08309e37i	−0.0149071	−	0.00630510i
$547$	−4.81769e39			−0.959451			−0.479726	−	0.877419i	$-0.659264\pi$
$547$	−4.81769e39			−0.959451			−0.479726	+	0.877419i	$0.659264\pi$
$548$			1.76686e39i			0.342676i
$549$	3.45740e39	−	4.64041e39i	0.653056	−	0.876511i
$550$	2.50032e40			4.59977
$551$	−5.43958e39			−0.974692
$552$	−4.24774e39	−	1.40844e39i	−0.741382	−	0.245823i
$553$	5.24566e39	+	4.20409e38i	0.891838	+	0.0714756i
$554$		−	2.80201e39i		−	0.464064i
$555$	−5.73815e39	−	1.90263e39i	−0.925814	−	0.306977i
$556$		−	1.74709e39i		−	0.274620i
$557$		−	9.50433e39i		−	1.45553i	−0.685827	−	0.727765i	$-0.740559\pi$
$557$		−	9.50433e39i		−	1.45553i	0.685827	−	0.727765i	$-0.259441\pi$
$558$	4.73922e39	+	3.53102e39i	0.707150	+	0.526871i
$559$		−	1.06307e38i		−	0.0154558i
$560$	−1.66788e40	−	1.33671e39i	−2.36286	−	0.189370i
$561$	−3.87423e38	+	1.16843e39i	−0.0534840	+	0.161303i
$562$	−6.25143e39			−0.841013
$563$	3.75617e39			0.492463			0.246231	−	0.969211i	$-0.420808\pi$
$563$	3.75617e39			0.492463			0.246231	+	0.969211i	$0.420808\pi$
$564$	−1.90245e39	−	6.30802e38i	−0.243089	−	0.0806021i
$565$		−	2.65165e39i		−	0.330228i
$566$	−4.31045e39			−0.523220
$567$	−1.76317e39	−	8.26595e39i	−0.208612	−	0.977998i
$568$	6.72384e39			0.775473
$569$		−	2.36168e39i		−	0.265518i	−0.991148	−	0.132759i	$-0.957616\pi$
$569$		−	2.36168e39i		−	0.265518i	0.991148	−	0.132759i	$-0.0423836\pi$
$570$	−3.35306e40	−	1.11179e40i	−3.67499	−	1.21853i
$571$	−3.21874e39			−0.343924			−0.171962	−	0.985104i	$-0.555011\pi$
$571$	−3.21874e39			−0.343924			−0.171962	+	0.985104i	$0.555011\pi$
$572$	−7.76984e37			−0.00809412
$573$	−6.27839e38	+	1.89351e39i	−0.0637686	+	0.192320i
$574$	−8.79763e38	+	1.09772e40i	−0.0871251	+	1.08710i
$575$			3.03637e40i			2.93205i
$576$	−2.84781e39	−	2.12179e39i	−0.268154	−	0.199792i
$577$		−	6.93567e39i		−	0.636853i	−0.947948	−	0.318426i	$-0.896846\pi$
$577$		−	6.93567e39i		−	0.636853i	0.947948	−	0.318426i	$-0.103154\pi$
$578$			1.30567e40i			1.16918i
$579$	1.30851e40	+	4.33869e39i	1.14271	+	0.378895i
$580$		−	5.17090e39i		−	0.440413i
$581$	9.15050e39	+	7.33360e38i	0.760135	+	0.0609205i
$582$	−2.34052e40	−	7.76058e39i	−1.89640	−	0.628797i
$583$	−1.91063e40			−1.51002
$584$	7.01370e39			0.540705
$585$	−2.07270e38	+	2.78191e38i	−0.0155875	+	0.0209210i
$586$		−	9.97924e39i		−	0.732120i
$587$	1.82904e40			1.30909			0.654547	−	0.756022i	$-0.272860\pi$
$587$	1.82904e40			1.30909			0.654547	+	0.756022i	$0.272860\pi$
$588$	5.13816e39	+	2.67572e39i	0.358787	+	0.186840i
$589$	1.86787e40			1.27255
$590$		−	6.83212e39i		−	0.454152i
$591$	−7.57669e39	+	2.28506e40i	−0.491429	+	1.48211i
$592$	1.00109e40			0.633589
$593$	−2.48997e40			−1.53781			−0.768903	−	0.639366i	$-0.779197\pi$
$593$	−2.48997e40			−1.53781			−0.768903	+	0.639366i	$0.779197\pi$
$594$	−1.65107e40	−	2.36084e40i	−0.995092	−	1.42286i
$595$	−3.75521e39	−	3.00958e38i	−0.220871	−	0.0177015i
$596$		−	6.38545e39i		−	0.366540i
$597$	3.61630e39	−	1.09064e40i	0.202599	−	0.611020i
$598$		−	3.27612e38i		−	0.0179140i
$599$			3.33529e39i			0.178010i	0.996031	+	0.0890051i	$0.0283688\pi$
$599$			3.33529e39i			0.178010i	−0.996031	+	0.0890051i	$0.971631\pi$
$600$	−1.12945e40	+	3.40631e40i	−0.588400	+	1.77456i
$601$			2.82826e40i			1.43827i	0.694873	+	0.719133i	$0.255461\pi$
$601$			2.82826e40i			1.43827i	−0.694873	+	0.719133i	$0.744539\pi$
$602$	−2.15833e39	+	2.69306e40i	−0.107144	+	1.33690i
$603$	1.18099e40	+	8.79908e39i	0.572326	+	0.426419i
$604$	−3.41029e39			−0.161345
$605$	4.74142e40			2.19006
$606$	4.86769e39	−	1.46805e40i	0.219518	−	0.662046i
$607$		−	1.30309e40i		−	0.573771i	−0.957965	−	0.286885i	$-0.907380\pi$
$607$		−	1.30309e40i		−	0.573771i	0.957965	−	0.286885i	$-0.0926199\pi$
$608$	3.04259e40			1.30810
$609$	5.28851e39	−	1.25036e40i	0.222015	−	0.524910i
$610$	6.03647e40			2.47457
$611$			2.15993e38i			0.00864654i
$612$	9.62467e38	+	7.17098e38i	0.0376262	+	0.0280339i
$613$	−1.11135e40			−0.424302			−0.212151	−	0.977237i	$-0.568047\pi$
$613$	−1.11135e40			−0.424302			−0.212151	+	0.977237i	$0.568047\pi$
$614$	−4.62465e40			−1.72440
$615$	4.58177e40	+	1.51920e40i	1.66857	+	0.553255i
$616$	−2.89749e40	−	2.32217e39i	−1.03063	−	0.0825989i
$617$		−	5.19429e40i		−	1.80464i	−0.431064	−	0.902322i	$-0.641862\pi$
$617$		−	5.19429e40i		−	1.80464i	0.431064	−	0.902322i	$-0.358138\pi$
$618$	−2.91782e40	−	9.67474e39i	−0.990205	−	0.328327i
$619$		−	8.01138e39i		−	0.265578i	−0.991144	−	0.132789i	$-0.957607\pi$
$619$		−	8.01138e39i		−	0.265578i	0.991144	−	0.132789i	$-0.0423933\pi$
$620$			1.77561e40i			0.574999i
$621$	2.86699e40	−	2.00506e40i	0.906982	−	0.634306i
$622$			7.00952e40i			2.16635i
$623$	−4.47957e40	−	3.59012e39i	−1.35257	−	0.108401i
$624$	1.80803e38	−	5.45287e38i	0.00533372	−	0.0160860i
$625$	1.16884e41			3.36895
$626$	4.55206e40			1.28198
$627$	−8.64243e40	−	2.86561e40i	−2.37824	−	0.788565i
$628$		−	5.80890e39i		−	0.156199i
$629$	2.25394e39			0.0592254
$630$	5.81554e40	−	6.62656e40i	1.49332	−	1.70157i
$631$	−4.96300e40			−1.24543			−0.622714	−	0.782450i	$-0.713970\pi$
$631$	−4.96300e40			−1.24543			−0.622714	+	0.782450i	$0.713970\pi$
$632$			2.57457e40i			0.631403i
$633$	−2.48752e40	−	8.24797e39i	−0.596228	−	0.197694i
$634$	−3.04502e40			−0.713338
$635$	8.45434e40			1.93580
$636$	−5.86300e39	+	1.76823e40i	−0.131218	+	0.395741i
$637$	9.94286e37	−	6.16326e38i	0.00217515	−	0.0134831i
$638$		−	4.62751e40i		−	0.989572i
$639$	−3.14058e40	+	4.21518e40i	−0.656518	+	0.881159i
$640$		−	1.08545e41i		−	2.21820i
$641$			6.33546e38i			0.0126572i	0.999980	+	0.00632859i	$0.00201446\pi$
$641$			6.33546e38i			0.0126572i	−0.999980	+	0.00632859i	$0.997986\pi$
$642$	5.01008e40	+	1.66122e40i	0.978559	+	0.324465i
$643$		−	3.01539e40i		−	0.575817i	−0.957658	−	0.287909i	$-0.907040\pi$
$643$		−	3.01539e40i		−	0.575817i	0.957658	−	0.287909i	$-0.0929599\pi$
$644$	−1.91571e39	+	2.39032e40i	−0.0357671	+	0.446284i
$645$	1.12405e41	+	3.72707e40i	2.05197	+	0.680381i
$646$	1.31708e40			0.235093
$647$	−8.84082e40			−1.54305			−0.771526	−	0.636198i	$-0.780506\pi$
$647$	−8.84082e40			−1.54305			−0.771526	+	0.636198i	$0.780506\pi$
$648$	3.96212e40	−	1.18290e40i	0.676223	−	0.201889i
$649$		−	1.76096e40i		−	0.293901i
$650$	−2.62716e39			−0.0428788
$651$	−1.81599e40	+	4.29354e40i	−0.289861	+	0.685317i
$652$	−2.37218e40			−0.370303
$653$			6.37221e40i			0.972857i	0.873720	+	0.486428i	$0.161701\pi$
$653$			6.37221e40i			0.972857i	−0.873720	+	0.486428i	$0.838299\pi$
$654$	−9.84617e39	+	2.96952e40i	−0.147025	+	0.443413i
$655$	−5.90654e40			−0.862650
$656$	−7.99344e40			−1.14190
$657$	−3.27596e40	+	4.39689e40i	−0.457763	+	0.614396i
$658$	4.38527e39	−	5.47172e40i	0.0599405	−	0.747908i
$659$			2.02299e39i			0.0270493i	0.999909	+	0.0135246i	$0.00430516\pi$
$659$			2.02299e39i			0.0270493i	−0.999909	+	0.0135246i	$0.995695\pi$
$660$	2.72407e40	−	8.21554e40i	0.356312	−	1.07461i
$661$		−	8.62348e40i		−	1.10347i	−0.834019	−	0.551736i	$-0.813965\pi$
$661$		−	8.62348e40i		−	1.10347i	0.834019	−	0.551736i	$-0.186035\pi$
$662$			1.15093e39i			0.0144082i
$663$	4.07077e37	−	1.22771e38i	0.000498575	−	0.00150366i
$664$			4.49106e40i			0.538161i
$665$	2.22607e40	−	2.77758e41i	0.260990	−	3.25651i
$666$	−3.15158e40	+	4.22995e40i	−0.361536	+	0.485243i
$667$	5.61963e40			0.630788
$668$	3.89779e40			0.428114
$669$	−4.88929e40	+	1.47457e41i	−0.525493	+	1.58484i
$670$			1.53628e41i			1.61580i
$671$	1.55588e41			1.60140
$672$	−2.95809e40	+	6.99380e40i	−0.297959	+	0.704464i
$673$	−1.47463e41			−1.45367			−0.726833	−	0.686815i	$-0.759008\pi$
$673$	−1.47463e41			−1.45367			−0.726833	+	0.686815i	$0.759008\pi$
$674$		−	7.58686e40i		−	0.731970i
$675$	−1.60788e41	−	2.29907e41i	−1.51827	−	2.17094i
$676$	−4.37610e40			−0.404445
$677$	−1.68380e41			−1.52320			−0.761598	−	0.648050i	$-0.775585\pi$
$677$	−1.68380e41			−1.52320			−0.761598	+	0.648050i	$0.775585\pi$
$678$	−2.19614e40	−	7.28186e39i	−0.194460	−	0.0644780i
$679$	1.55385e40	−	1.93882e41i	0.134678	−	1.68045i
$680$		−	1.84306e40i		−	0.156372i
$681$	1.30038e41	+	4.31174e40i	1.08003	+	0.358112i
$682$			1.58901e41i			1.29198i
$683$			1.93052e41i			1.53665i	0.640060	+	0.768325i	$0.278909\pi$
$683$			1.93052e41i			1.53665i	−0.640060	+	0.768325i	$0.721091\pi$
$684$	−5.30408e40	+	7.11898e40i	−0.413330	+	0.554759i
$685$			2.12106e41i			1.61823i
$686$	−3.77012e40	+	1.54114e41i	−0.281615	+	1.15118i
$687$	−2.43383e40	+	7.34021e40i	−0.177999	+	0.536829i
$688$	−1.96104e41			−1.40428
$689$	2.00755e39			0.0140763
$690$	3.46405e41	+	1.14859e41i	2.37833	+	0.788594i
$691$			2.46113e41i			1.65464i	0.561732	+	0.827319i	$0.310135\pi$
$691$			2.46113e41i			1.65464i	−0.561732	+	0.827319i	$0.689865\pi$
$692$	3.82490e39			0.0251815
$693$	1.49894e41	−	1.70798e41i	0.966389	−	1.10116i
$694$	−1.67610e41			−1.05825
$695$		−	2.09734e41i		−	1.29685i
$696$	6.30430e40	+	2.09035e40i	0.381771	+	0.126586i
$697$	−1.79972e40			−0.106740
$698$	1.95076e41			1.13319
$699$	−3.65799e40	+	1.10322e41i	−0.208125	+	0.627686i
$700$	1.91682e41	+	1.53622e40i	1.06822	+	0.0856117i
$701$		−	1.77281e41i		−	0.967725i	−0.875144	−	0.483862i	$-0.839234\pi$
$701$		−	1.77281e41i		−	0.967725i	0.875144	−	0.483862i	$-0.160766\pi$
$702$	1.73483e39	+	2.48061e39i	0.00927619	+	0.0132638i
$703$			1.66715e41i			0.873216i
$704$		−	9.54841e40i		−	0.489923i
$705$	−2.28383e41	−	7.57260e40i	−1.14795	−	0.380630i
$706$		−	4.62301e40i		−	0.227644i
$707$	1.21609e41	+	9.74625e39i	0.586657	+	0.0470171i
$708$	−1.62972e40	−	5.40374e39i	−0.0770248	−	0.0255395i
$709$	1.85949e41			0.861039			0.430519	−	0.902581i	$-0.358330\pi$
$709$	1.85949e41			0.861039			0.430519	+	0.902581i	$0.358330\pi$
$710$	−5.48332e41			−2.48770
$711$	−1.61400e41	−	1.20253e41i	−0.717454	−	0.534549i
$712$		−	2.19857e41i		−	0.957593i
$713$	−1.92969e41			−0.823550
$714$	−1.28050e40	+	3.02749e40i	−0.0535495	+	0.126607i
$715$	−9.32747e39			−0.0382232
$716$		−	3.18543e40i		−	0.127917i
$717$	−3.83471e40	+	1.15652e41i	−0.150906	+	0.455118i
$718$	9.33389e40			0.359963
$719$	−2.21601e41			−0.837537			−0.418768	−	0.908093i	$-0.637538\pi$
$719$	−2.21601e41			−0.837537			−0.418768	+	0.908093i	$0.637538\pi$
$720$	5.13178e41	+	3.82350e41i	1.90084	+	1.41625i
$721$	1.93711e40	−	2.41703e41i	0.0703223	−	0.877447i
$722$			6.41106e41i			2.28108i
$723$	−7.13525e39	+	2.15193e40i	−0.0248831	+	0.0750452i
$724$		−	7.38541e39i		−	0.0252444i
$725$		−	4.50644e41i		−	1.50985i
$726$	1.30207e41	−	3.92693e41i	0.427616	−	1.28965i
$727$		−	2.56606e41i		−	0.826072i	−0.910715	−	0.413036i	$-0.864468\pi$
$727$		−	2.56606e41i		−	0.826072i	0.910715	−	0.413036i	$-0.135532\pi$
$728$	3.04448e39	+	2.43998e38i	0.00960745	+	0.000769982i
$729$	−1.10907e41	+	3.03637e41i	−0.343090	+	0.939302i
$730$	−5.71969e41			−1.73457
$731$	−4.41527e40			−0.131267
$732$	4.77443e40	−	1.43993e41i	0.139159	−	0.419691i
$733$			2.64459e41i			0.755703i	0.925866	+	0.377851i	$0.123337\pi$
$733$			2.64459e41i			0.755703i	−0.925866	+	0.377851i	$0.876663\pi$
$734$	5.09888e41			1.42851
$735$	6.16821e41	+	3.21213e41i	1.69431	+	0.882320i
$736$	−3.14330e41			−0.846559
$737$			3.95973e41i			1.04565i
$738$	2.51646e41	−	3.37751e41i	0.651587	−	0.874540i
$739$	−5.53934e41			−1.40642			−0.703208	−	0.710985i	$-0.748250\pi$
$739$	−5.53934e41			−1.40642			−0.703208	+	0.710985i	$0.748250\pi$
$740$	−1.58480e41			−0.394562
$741$	9.08086e39	+	3.01098e39i	0.0221699	+	0.00735096i
$742$	−5.08570e41	−	4.07589e40i	−1.21757	−	0.0975812i
$743$			4.83025e41i			1.13405i	0.823701	+	0.567024i	$0.191906\pi$
$743$			4.83025e41i			1.13405i	−0.823701	+	0.567024i	$0.808094\pi$
$744$	−2.16480e41	−	7.17792e40i	−0.498436	−	0.165269i
$745$		−	7.66555e41i		−	1.73092i
$746$			2.28964e39i			0.00507054i
$747$	−2.81545e41	−	2.09769e41i	−0.611504	−	0.455609i
$748$			3.22706e40i			0.0687438i
$749$	−3.32615e40	+	4.15020e41i	−0.0694952	+	0.867127i
$750$	5.73386e41	−	1.72928e42i	1.17506	−	3.54387i
$751$	1.98960e41			0.399933			0.199966	−	0.979803i	$-0.435917\pi$
$751$	1.98960e41			0.399933			0.199966	+	0.979803i	$0.435917\pi$
$752$	3.98441e41			0.785607
$753$	−1.66247e41	−	5.51232e40i	−0.321533	−	0.106612i
$754$			4.86227e39i			0.00922474i
$755$	−4.09396e41			−0.761925
$756$	−1.12072e41	−	1.91134e41i	−0.204611	−	0.348957i
$757$	−1.85018e41			−0.331378			−0.165689	−	0.986178i	$-0.552985\pi$
$757$	−1.85018e41			−0.331378			−0.165689	+	0.986178i	$0.552985\pi$
$758$		−	5.26692e40i		−	0.0925450i
$759$	8.92849e41	+	2.96046e41i	1.53912	+	0.510333i
$760$	1.36323e42			2.30554
$761$	4.19703e41			0.696409			0.348204	−	0.937419i	$-0.386791\pi$
$761$	4.19703e41			0.696409			0.348204	+	0.937419i	$0.386791\pi$
$762$	2.32170e41	−	7.00203e41i	0.377971	−	1.13993i
$763$	−2.45986e41	−	1.97143e40i	−0.392920	−	0.0314903i
$764$			5.22962e40i			0.0819627i
$765$	1.15541e41	+	8.60856e40i	0.177683	+	0.132385i
$766$			9.88781e40i			0.149205i
$767$			1.85029e39i			0.00273973i
$768$	−6.80540e41	−	2.25650e41i	−0.988816	−	0.327866i
$769$			2.25526e41i			0.321562i	0.986990	+	0.160781i	$0.0514013\pi$
$769$			2.25526e41i			0.321562i	−0.986990	+	0.160781i	$0.948599\pi$
$770$	2.36291e42	+	1.89374e41i	3.30622	+	0.264975i
$771$	5.79228e41	+	1.92057e41i	0.795355	+	0.263719i
$772$	3.61393e41			0.487000
$773$	−4.58104e41			−0.605845			−0.302923	−	0.953015i	$-0.597962\pi$
$773$	−4.58104e41			−0.605845			−0.302923	+	0.953015i	$0.597962\pi$
$774$	6.17366e41	−	8.28609e41i	0.801307	−	1.07549i
$775$			1.54744e42i			1.97124i
$776$	9.51571e41			1.18972
$777$	−3.83216e41	−	1.62085e41i	−0.470261	−	0.198901i
$778$	8.09486e41			0.975001
$779$		−	1.33118e42i		−	1.57377i
$780$	−2.86226e39	+	8.63232e39i	−0.00332152	+	0.0100174i
$781$	−1.41331e42			−1.60989
$782$	−1.36068e41			−0.152145
$783$	−4.25506e41	+	2.97581e41i	−0.467046	+	0.326633i
$784$	−1.13693e42	−	1.83415e41i	−1.22504	−	0.197630i
$785$		−	6.97341e41i		−	0.737625i
$786$	−1.62203e41	+	4.89190e41i	−0.168435	+	0.507985i
$787$			5.27423e41i			0.537681i	0.963185	+	0.268841i	$0.0866405\pi$
$787$			5.27423e41i			0.537681i	−0.963185	+	0.268841i	$0.913359\pi$
$788$			6.31104e41i			0.631642i
$789$	−6.18403e41	+	1.86505e42i	−0.607652	+	1.83263i
$790$		−	2.09957e42i		−	2.02552i
$791$	1.45800e40	−	1.81922e41i	0.0138101	−	0.172316i
$792$	8.91509e41	+	6.64230e41i	0.829107	+	0.617736i
$793$	−1.63481e40			−0.0149282
$794$	−7.24363e41			−0.649470
$795$	−7.03837e41	+	2.12271e42i	−0.619653	+	1.86882i
$796$		−	3.01221e41i		−	0.260403i
$797$	1.44678e42			1.22816			0.614082	−	0.789242i	$-0.289526\pi$
$797$	1.44678e42			1.22816			0.614082	+	0.789242i	$0.289526\pi$
$798$	−2.23931e42	−	9.47134e41i	−1.86669	−	0.789532i
$799$	8.97086e40			0.0734355
$800$			2.52064e42i			2.02631i
$801$	1.37829e42	+	1.02691e42i	1.08810	+	0.810702i
$802$	1.09288e42			0.847314
$803$	−1.47423e42			−1.12251
$804$	3.66462e41	+	1.21509e41i	0.274041	+	0.0908651i
$805$	−2.29975e41	+	2.86951e42i	−0.168904	+	2.10750i
$806$		−	1.66963e40i		−	0.0120437i
$807$	−6.92937e41	−	2.29760e41i	−0.490939	−	0.162783i
$808$			5.96856e41i			0.415341i
$809$			6.29459e41i			0.430243i	0.976587	+	0.215121i	$0.0690147\pi$
$809$			6.29459e41i			0.430243i	−0.976587	+	0.215121i	$0.930985\pi$
$810$	−3.23112e42	+	9.64662e41i	−2.16931	+	0.647653i
$811$		−	5.18702e41i		−	0.342070i	−0.985265	−	0.171035i	$-0.945289\pi$
$811$		−	5.18702e41i		−	0.342070i	0.985265	−	0.171035i	$-0.0547112\pi$
$812$	2.84320e40	−	3.54760e41i	0.0184181	−	0.229812i
$813$	3.94163e41	−	1.18876e42i	0.250820	−	0.756453i
$814$	−1.41826e42			−0.886548
$815$	−2.84773e42			−1.74869
$816$	−2.26475e41	−	7.50933e40i	−0.136619	−	0.0452995i
$817$		−	3.26579e42i		−	1.93539i
$818$	−1.35391e42			−0.788255
$819$	−1.57498e40	+	1.79462e40i	−0.00900863	+	0.0102649i
$820$	1.26542e42			0.711107
$821$		−	8.40658e41i		−	0.464134i	−0.972700	−	0.232067i	$-0.925451\pi$
$821$		−	8.40658e41i		−	0.464134i	0.972700	−	0.232067i	$-0.0745489\pi$
$822$	1.75670e42	+	5.82479e41i	0.952922	+	0.315965i
$823$	7.67647e41			0.409133			0.204566	−	0.978853i	$-0.434422\pi$
$823$	7.67647e41			0.409133			0.204566	+	0.978853i	$0.434422\pi$
$824$	1.18628e42			0.621215
$825$	2.37402e42	−	7.15985e42i	1.22153	−	3.68402i
$826$	3.75662e40	−	4.68732e41i	0.0189927	−	0.236981i
$827$		−	8.95773e41i		−	0.445008i	−0.974932	−	0.222504i	$-0.928577\pi$
$827$		−	8.95773e41i		−	0.445008i	0.974932	−	0.222504i	$-0.0714231\pi$
$828$	5.47965e41	−	7.35461e41i	0.267493	−	0.359021i
$829$			3.49904e42i			1.67845i	0.543786	+	0.839224i	$0.316990\pi$
$829$			3.49904e42i			1.67845i	−0.543786	+	0.839224i	$0.683010\pi$
$830$		−	3.66248e42i		−	1.72640i
$831$	−8.02376e41	−	2.66048e41i	−0.371675	−	0.123238i
$832$			1.00328e40i			0.00456703i
$833$	−2.55979e41	−	4.12958e40i	−0.114512	−	0.0184737i
$834$	−1.73705e42	−	5.75962e41i	−0.763668	−	0.253213i
$835$	4.67918e42			2.02170
$836$	−2.38692e42			−1.01355
$837$	1.46112e42	−	1.02185e42i	0.609771	−	0.426449i
$838$		−	1.80832e42i		−	0.741715i
$839$	−3.78981e42			−1.52781			−0.763904	−	0.645329i	$-0.776720\pi$
$839$	−3.78981e42			−1.52781			−0.763904	+	0.645329i	$0.776720\pi$
$840$	−1.32537e42	+	3.13358e42i	−0.525156	+	1.24163i
$841$	1.73365e42			0.675179
$842$			6.03470e42i			2.31010i
$843$	−5.93567e41	+	1.79015e42i	−0.223342	+	0.673579i
$844$	−6.87018e41			−0.254099
$845$	−5.25338e42			−1.90992
$846$	−1.25435e42	+	1.68355e42i	−0.448280	+	0.601668i
$847$	3.25295e42	+	2.60705e41i	1.14279	+	0.0915884i
$848$		−	3.70332e42i		−	1.27894i
$849$	−4.09273e41	+	1.23433e42i	−0.138948	+	0.419055i
$850$			1.09114e42i			0.364171i
$851$		−	1.72233e42i		−	0.565116i
$852$	−4.33692e41	+	1.30798e42i	−0.139897	+	0.421916i
$853$			1.31506e42i			0.417048i	0.978017	+	0.208524i	$0.0668659\pi$
$853$			1.31506e42i			0.417048i	−0.978017	+	0.208524i	$0.933134\pi$
$854$	4.14145e42	+	3.31913e41i	1.29126	+	0.103487i
$855$	−6.36740e42	+	8.54613e42i	−1.95188	+	2.61975i
$856$	−2.03692e42			−0.613909
$857$	−2.60807e42			−0.772854			−0.386427	−	0.922320i	$-0.626291\pi$
$857$	−2.60807e42			−0.772854			−0.386427	+	0.922320i	$0.626291\pi$
$858$	−2.56147e40	+	7.72518e40i	−0.00746319	+	0.0225083i
$859$		−	6.29250e42i		−	1.80270i	−0.433096	−	0.901348i	$-0.642579\pi$
$859$		−	6.29250e42i		−	1.80270i	0.433096	−	0.901348i	$-0.357421\pi$
$860$	3.10448e42			0.874504
$861$	3.05989e42	+	1.29421e42i	0.847539	+	0.358474i
$862$	−3.22198e42			−0.877542
$863$		−	6.65231e42i		−	1.78162i	−0.454372	−	0.890812i	$-0.650136\pi$
$863$		−	6.65231e42i		−	1.78162i	0.454372	−	0.890812i	$-0.349864\pi$
$864$	2.38003e42	−	1.66450e42i	0.626807	−	0.438363i
$865$	4.59168e41			0.118915
$866$	−6.83387e42			−1.74043
$867$	3.73890e42	+	1.23972e42i	0.936412	+	0.310491i
$868$	−9.76310e40	+	1.21819e42i	−0.0240465	+	0.300040i
$869$		−	5.41158e42i		−	1.31080i
$870$	−5.14118e42	−	1.70468e42i	−1.22471	−	0.406083i
$871$		−	4.16060e40i		−	0.00974750i
$872$		−	1.20730e42i		−	0.278180i
$873$	−4.44460e42	+	5.96541e42i	−1.00723	+	1.35187i
$874$		−	1.00644e43i		−	2.24321i
$875$	1.43249e43	+	1.14805e42i	3.14032	+	0.251678i
$876$	−4.52388e41	+	1.36436e42i	−0.0975443	+	0.294185i
$877$	1.56359e41			0.0331610			0.0165805	−	0.999863i	$-0.494722\pi$
$877$	1.56359e41			0.0331610			0.0165805	+	0.999863i	$0.494722\pi$
$878$	3.71802e42			0.775606
$879$	−2.85763e42	−	9.47519e41i	−0.586365	−	0.194424i
$880$			1.72063e43i			3.47288i
$881$	5.62419e42			1.11663			0.558315	−	0.829629i	$-0.311448\pi$
$881$	5.62419e42			1.11663			0.558315	+	0.829629i	$0.311448\pi$
$882$	4.35423e42	−	4.22652e42i	0.850388	−	0.825446i
$883$	−7.84637e41			−0.150743			−0.0753717	−	0.997156i	$-0.524014\pi$
$883$	−7.84637e41			−0.150743			−0.0753717	+	0.997156i	$0.524014\pi$
$884$		−	3.39077e39i		−	0.000640826i
$885$	−1.95643e42	−	6.48703e41i	−0.363737	−	0.120606i
$886$	1.06893e43			1.95506
$887$	1.60597e42			0.288965			0.144483	−	0.989507i	$-0.453848\pi$
$887$	1.60597e42			0.288965			0.144483	+	0.989507i	$0.453848\pi$
$888$	6.40659e41	−	1.93217e42i	0.113407	−	0.342025i
$889$	5.80027e42	+	4.64858e41i	1.01012	+	0.0809553i
$890$			1.79294e43i			3.07193i
$891$	−8.32813e42	+	2.48639e42i	−1.40385	+	0.419124i
$892$			4.07255e42i			0.675424i
$893$			6.63538e42i			1.08273i
$894$	−6.34875e42	−	2.10508e42i	−1.01928	−	0.337968i
$895$		−	3.82402e42i		−	0.604068i
$896$	5.96831e41	−	7.44696e42i	0.0927653	−	1.15748i
$897$	−9.38144e40	−	3.11065e40i	−0.0143476	−	0.00475730i
$898$	1.07933e43			1.62422
$899$	2.86396e42			0.424083
$900$	−5.89774e42	−	4.39419e42i	−0.859349	−	0.640269i
$901$		−	8.33798e41i		−	0.119551i
$902$	1.13245e43			1.59780
$903$	7.50687e42	+	3.17509e42i	1.04228	+	0.440843i
$904$	8.92872e41			0.121996
$905$		−	8.86597e41i		−	0.119213i
$906$	−1.12427e42	+	3.39069e42i	−0.148768	+	0.448672i
$907$	−6.95849e42			−0.906169			−0.453085	−	0.891468i	$-0.649676\pi$
$907$	−6.95849e42			−0.906169			−0.453085	+	0.891468i	$0.649676\pi$
$908$	3.59148e42			0.460287
$909$	−3.74170e42	−	2.78780e42i	−0.471946	−	0.351630i
$910$	−2.48279e41	−	1.98981e40i	−0.0308204	−	0.00247008i
$911$		−	6.06042e42i		−	0.740433i	−0.928945	−	0.370217i	$-0.879283\pi$
$911$		−	6.06042e42i		−	0.740433i	0.928945	−	0.370217i	$-0.120717\pi$
$912$	5.55434e42	−	1.67514e43i	0.667894	−	2.01431i
$913$		−	9.43993e42i		−	1.11723i
$914$			1.10390e43i			1.28591i
$915$	5.73157e42	−	1.72859e43i	0.657155	−	1.98192i
$916$			2.02727e42i			0.228784i
$917$	−4.05231e42	−	3.24769e41i	−0.450139	−	0.0360761i
$918$	1.03027e42	−	7.20530e41i	0.112650	−	0.0787831i
$919$	−1.14023e43			−1.22720			−0.613602	−	0.789615i	$-0.710280\pi$
$919$	−1.14023e43			−1.22720			−0.613602	+	0.789615i	$0.710280\pi$
$920$	−1.40836e43			−1.49207
$921$	−4.39106e42	+	1.32430e43i	−0.457936	+	1.38109i
$922$			5.28816e42i			0.542883i
$923$	1.48501e41			0.0150073
$924$	2.32063e42	−	5.48666e42i	0.230867	−	0.545839i
$925$	−1.38115e43			−1.35266
$926$		−	2.12880e43i		−	2.05247i
$927$	−5.54088e42	+	7.43679e42i	−0.525923	+	0.705878i
$928$	4.66513e42			0.435931
$929$	1.70248e42			0.156622			0.0783110	−	0.996929i	$-0.475047\pi$
$929$	1.70248e42			0.156622			0.0783110	+	0.996929i	$0.475047\pi$
$930$	1.76540e43	+	5.85362e42i	1.59897	+	0.530178i
$931$	3.05448e42	−	1.89337e43i	0.272375	−	1.68836i
$932$			3.04694e42i			0.267506i
$933$	2.00723e43	+	6.65547e42i	1.73506	+	0.575301i
$934$			1.14277e42i			0.0972588i
$935$			3.87399e42i			0.324631i
$936$	−9.36735e40	−	6.97926e40i	−0.00772889	−	0.00575850i
$937$		−	1.20067e43i		−	0.975442i	−0.873000	−	0.487721i	$-0.837828\pi$
$937$		−	1.20067e43i		−	0.975442i	0.873000	−	0.487721i	$-0.162172\pi$
$938$	−8.44719e41	+	1.05400e43i	−0.0675727	+	0.843139i
$939$	4.32214e42	−	1.30352e43i	0.340445	−	1.02675i
$940$	−6.30763e42			−0.489229
$941$	1.62705e43			1.24266			0.621328	−	0.783550i	$-0.286593\pi$
$941$	1.62705e43			1.24266			0.621328	+	0.783550i	$0.286593\pi$
$942$	−5.77551e42	−	1.91501e42i	−0.434362	−	0.144023i
$943$			1.37524e43i			1.01849i
$944$	3.41323e42			0.248927
$945$	−1.34539e43	−	2.29451e43i	−0.966242	−	1.64789i
$946$	2.77824e43			1.96494
$947$			2.22922e43i			1.55266i	0.630324	+	0.776332i	$0.282922\pi$
$947$			2.22922e43i			1.55266i	−0.630324	+	0.776332i	$0.717078\pi$
$948$	−5.00827e42	−	1.66061e42i	−0.343532	−	0.113906i
$949$	1.54902e41			0.0104640
$950$	−8.07071e43			−5.36932
$951$	−2.89121e42	+	8.71965e42i	−0.189436	+	0.571323i
$952$	1.01340e41	−	1.26447e42i	0.00653949	−	0.0815966i
$953$		−	1.71692e43i		−	1.09119i	−0.838047	−	0.545597i	$-0.816303\pi$
$953$		−	1.71692e43i		−	1.09119i	0.838047	−	0.545597i	$-0.183697\pi$
$954$	1.56478e43	+	1.16586e43i	0.979496	+	0.729786i
$955$			6.27800e42i			0.387055i
$956$			3.19414e42i			0.193961i
$957$	−1.32512e43	−	4.39378e42i	−0.792562	−	0.262794i
$958$		−	3.04952e43i		−	1.79652i
$959$	−1.16626e42	+	1.45520e43i	−0.0676745	+	0.844409i
$960$	−1.06083e43	−	3.51745e42i	−0.606336	−	0.201046i
$961$	7.92751e42			0.446321
$962$	1.49021e41			0.00826435
$963$	9.51405e42	−	1.27695e43i	0.519738	−	0.697576i
$964$			5.94334e41i			0.0319826i
$965$	4.33842e43			2.29977
$966$	2.31343e43	+	9.78484e42i	1.20806	+	0.510958i
$967$	1.21025e43			0.622576			0.311288	−	0.950316i	$-0.399240\pi$
$967$	1.21025e43			0.622576			0.311288	+	0.950316i	$0.399240\pi$
$968$			1.59655e43i			0.809076i
$969$	1.25055e42	−	3.77156e42i	0.0624321	−	0.188290i
$970$	−7.76009e43			−3.81660
$971$	−2.09917e43			−1.01711			−0.508556	−	0.861029i	$-0.669821\pi$
$971$	−2.09917e43			−1.01711			−0.508556	+	0.861029i	$0.669821\pi$
$972$	−2.54512e41	+	8.47043e42i	−0.0121492	+	0.404338i
$973$	1.15321e42	−	1.43892e43i	0.0542341	−	0.676707i
$974$			2.59898e43i			1.20420i
$975$	−2.49446e41	+	7.52307e41i	−0.0113870	+	0.0343422i
$976$			3.01573e43i			1.35634i
$977$		−	1.47407e43i		−	0.653200i	−0.945163	−	0.326600i	$-0.894097\pi$
$977$		−	1.47407e43i		−	0.653200i	0.945163	−	0.326600i	$-0.105903\pi$
$978$	−7.82033e42	+	2.35854e43i	−0.341438	+	1.02975i
$979$			4.62126e43i			1.98798i
$980$	1.79985e43	+	2.90361e42i	0.762885	+	0.123072i
$981$	7.56857e42	+	5.63906e42i	0.316092	+	0.235508i
$982$	7.67997e42			0.316041
$983$	−1.75349e43			−0.711013			−0.355506	−	0.934674i	$-0.615692\pi$
$983$	−1.75349e43			−0.711013			−0.355506	+	0.934674i	$0.615692\pi$
$984$	−5.11550e42	+	1.54279e43i	−0.204390	+	0.616422i
$985$			7.57622e43i			2.98282i
$986$	2.01945e42			0.0783462
$987$	−1.52523e43	−	6.45110e42i	−0.583092	−	0.246624i
$988$	2.50801e41			0.00944830
$989$			3.37389e43i			1.25252i
$990$	−7.27028e43	−	5.41682e43i	−2.65975	−	1.98168i
$991$	1.87288e43			0.675214			0.337607	−	0.941287i	$-0.390383\pi$
$991$	1.87288e43			0.675214			0.337607	+	0.941287i	$0.390383\pi$
$992$	−1.60193e43			−0.569148
$993$	3.29579e41	+	1.09280e41i	0.0115397	+	0.00382627i
$994$	−3.76194e43	−	3.01498e42i	−1.29810	−	0.104036i
$995$		−	3.61607e43i		−	1.22971i
$996$	−8.73639e42	−	2.89677e42i	−0.292800	−	0.0970852i
$997$		−	4.04663e43i		−	1.33664i	−0.743875	−	0.668319i	$-0.767014\pi$
$997$		−	4.04663e43i		−	1.33664i	0.743875	−	0.668319i	$-0.232986\pi$
$998$		−	6.55993e43i		−	2.13553i
$999$	9.12041e42	+	1.30411e43i	0.292627	+	0.418422i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.30.c.a.20.1	✓	76
3.2	odd	2	inner	21.30.c.a.20.76	yes	76
7.6	odd	2	inner	21.30.c.a.20.75	yes	76
21.20	even	2	inner	21.30.c.a.20.2	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.30.c.a.20.1	✓	76	1.1	even	1	trivial
21.30.c.a.20.2	yes	76	21.20	even	2	inner
21.30.c.a.20.75	yes	76	7.6	odd	2	inner
21.30.c.a.20.76	yes	76	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 30 \)
Character orbit:	\([\chi]\)	\(=\)	21.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-27459.9i q^{2} +(-7.86336e6 - 2.60729e6i) q^{3} -2.17175e8 q^{4} -2.60713e10 q^{5} +(-7.15959e10 + 2.15927e11i) q^{6} +(-1.78867e12 - 1.43352e11i) q^{7} -8.77881e12i q^{8} +(5.50345e13 + 4.10041e13i) q^{9} +O(q^{10})\)	\(q-27459.9i q^{2} +(-7.86336e6 - 2.60729e6i) q^{3} -2.17175e8 q^{4} -2.60713e10 q^{5} +(-7.15959e10 + 2.15927e11i) q^{6} +(-1.78867e12 - 1.43352e11i) q^{7} -8.77881e12i q^{8} +(5.50345e13 + 4.10041e13i) q^{9} +7.15915e14i q^{10} +1.84525e15i q^{11} +(1.70773e15 + 5.66239e14i) q^{12} -1.93886e14i q^{13} +(-3.93643e15 + 4.91168e16i) q^{14} +(2.05008e17 + 6.79754e16i) q^{15} -3.57660e17 q^{16} -8.05269e16 q^{17} +(1.12597e18 - 1.51124e18i) q^{18} -5.95624e18i q^{19} +5.66204e18 q^{20} +(1.36912e19 + 5.79082e18i) q^{21} +5.06704e19 q^{22} +6.15339e19i q^{23} +(-2.28889e19 + 6.90309e19i) q^{24} +4.93447e20 q^{25} -5.32409e18 q^{26} +(-3.25846e20 - 4.65921e20i) q^{27} +(3.88456e20 + 3.11325e19i) q^{28} -9.13257e20i q^{29} +(1.86660e21 - 5.62950e21i) q^{30} +3.13598e21i q^{31} +5.10823e21i q^{32} +(4.81110e21 - 1.45099e22i) q^{33} +2.21126e21i q^{34} +(4.66330e22 + 3.73737e21i) q^{35} +(-1.19521e22 - 8.90508e21i) q^{36} -2.79899e22 q^{37} -1.63558e23 q^{38} +(-5.05517e20 + 1.52460e21i) q^{39} +2.28875e23i q^{40} +2.23493e23 q^{41} +(1.59015e23 - 3.75960e23i) q^{42} +5.48297e23 q^{43} -4.00743e23i q^{44} +(-1.43482e24 - 1.06903e24i) q^{45} +1.68972e24 q^{46} -1.11402e24 q^{47} +(2.81241e24 + 9.32524e23i) q^{48} +(3.17881e24 + 5.12820e23i) q^{49} -1.35500e25i q^{50} +(6.33212e23 + 2.09957e23i) q^{51} +4.21073e22i q^{52} +1.03543e25i q^{53} +(-1.27941e25 + 8.94770e24i) q^{54} -4.81080e25i q^{55} +(-1.25846e24 + 1.57024e25i) q^{56} +(-1.55296e25 + 4.68361e25i) q^{57} -2.50780e25 q^{58} -9.54320e24 q^{59} +(-4.45227e25 - 1.47626e25i) q^{60} -8.43183e25i q^{61} +8.61137e25 q^{62} +(-9.25607e25 - 8.12323e25i) q^{63} -5.17459e25 q^{64} +5.05486e24i q^{65} +(-3.98439e26 - 1.32112e26i) q^{66} +2.14590e26 q^{67} +1.74884e25 q^{68} +(1.60437e26 - 4.83863e26i) q^{69} +(1.02628e26 - 1.28054e27i) q^{70} +7.65917e26i q^{71} +(3.59967e26 - 4.83137e26i) q^{72} +7.98935e26i q^{73} +7.68601e26i q^{74} +(-3.88015e27 - 1.28656e27i) q^{75} +1.29355e27i q^{76} +(2.64520e26 - 3.30055e27i) q^{77} +(4.18652e25 + 1.38815e25i) q^{78} -2.93271e27 q^{79} +9.32466e27 q^{80} +(1.34745e27 + 4.51328e27i) q^{81} -6.13708e27i q^{82} -5.11580e27 q^{83} +(-2.97340e27 - 1.25762e27i) q^{84} +2.09944e27 q^{85} -1.50562e28i q^{86} +(-2.38113e27 + 7.18127e27i) q^{87} +1.61991e28 q^{88} +2.50441e28 q^{89} +(-2.93555e28 + 3.94000e28i) q^{90} +(-2.77939e25 + 3.46799e26i) q^{91} -1.33637e28i q^{92} +(8.17641e27 - 2.46593e28i) q^{93} +3.05909e28i q^{94} +1.55287e29i q^{95} +(1.33186e28 - 4.01679e28i) q^{96} +1.08394e29i q^{97} +(1.40820e28 - 8.72897e28i) q^{98} +(-7.56629e28 + 1.01552e29i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 20401094660 q^{4} + 1962751543872 q^{7} - 89581451225964 q^{9}+O(q^{10}) \) 76 * q - 20401094660 * q^4 + 1962751543872 * q^7 - 89581451225964 * q^9	\( 76 q - 20401094660 q^{4} + 1962751543872 q^{7} - 89581451225964 q^{9} - 11\!\cdots\!48 q^{15}+ \cdots - 23\!\cdots\!24 q^{99}+O(q^{100}) \) 76 * q - 20401094660 * q^4 + 1962751543872 * q^7 - 89581451225964 * q^9 - 116668222909200048 * q^15 + 4964525139713333892 * q^16 + 1542346202347854996 * q^18 + 33840646982361357348 * q^21 - 9870996616978150672 * q^22 + 3225406746743103424612 * q^25 - 3181907581338093199564 * q^28 + 5113912044496410095244 * q^30 - 85758641407134848258352 * q^36 - 17812771227715200149976 * q^37 + 388095283792424641491696 * q^39 + 804036587819434104664956 * q^42 + 2391536152977907871782320 * q^43 - 1070985628070611677307000 * q^46 - 512656982878691867441540 * q^49 - 961431915936904000664400 * q^51 + 20345422731681279280765248 * q^57 - 40096240109469024574169272 * q^58 - 164991837955115951799442596 * q^60 - 360764839802574990409097184 * q^63 - 1608343949909674725081473028 * q^64 + 483978610969894046870693264 * q^67 - 656026306765550013508448520 * q^70 + 1937172856654554597960695124 * q^72 - 8054141680325499868559088636 * q^78 - 11740735193468750125742145952 * q^79 + 18477545939654446572971367132 * q^81 - 7249045143271847568431965452 * q^84 + 14576359553686844022629140848 * q^85 - 1685535263940707754634995584 * q^88 + 44135166284535829618726469040 * q^91 + 226499776928895503792863540632 * q^93 - 231093384978708762520959066624 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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