LMFDB - Embedded newform 21.30.c.a.20.11

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			20.11
Character	$\chi$	$=$	21.20
Dual form			21.30.c.a.20.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-23469.1i q^{2} +(-4.70121e6 - 6.82122e6i) q^{3} -1.39279e7 q^{4} +1.98757e10 q^{5} +(-1.60088e11 + 1.10333e11i) q^{6} +(-7.54484e11 - 1.62808e12i) q^{7} -1.22730e13i q^{8} +(-2.44277e13 + 6.41359e13i) q^{9} +O(q^{10})$	\(q-23469.1i q^{2} +(-4.70121e6 - 6.82122e6i) q^{3} -1.39279e7 q^{4} +1.98757e10 q^{5} +(-1.60088e11 + 1.10333e11i) q^{6} +(-7.54484e11 - 1.62808e12i) q^{7} -1.22730e13i q^{8} +(-2.44277e13 + 6.41359e13i) q^{9} -4.66464e14i q^{10} -5.73249e14i q^{11} +(6.54778e13 + 9.50050e13i) q^{12} +2.54219e16i q^{13} +(-3.82097e16 + 1.77071e16i) q^{14} +(-9.34397e16 - 1.35576e17i) q^{15} -2.95514e17 q^{16} -7.73767e16 q^{17} +(1.50521e18 + 5.73296e17i) q^{18} -3.43827e18i q^{19} -2.76826e17 q^{20} +(-7.55853e18 + 1.28005e19i) q^{21} -1.34536e19 q^{22} -2.68583e19i q^{23} +(-8.37168e19 + 5.76979e19i) q^{24} +2.08778e20 q^{25} +5.96629e20 q^{26} +(5.52325e20 - 1.34890e20i) q^{27} +(1.05084e19 + 2.26757e19i) q^{28} +9.38030e20i q^{29} +(-3.18185e21 + 2.19294e21i) q^{30} +5.15944e21i q^{31} +3.46426e20i q^{32} +(-3.91025e21 + 2.69496e21i) q^{33} +1.81596e21i q^{34} +(-1.49959e22 - 3.23593e22i) q^{35} +(3.40225e20 - 8.93276e20i) q^{36} -3.88136e22 q^{37} -8.06931e22 q^{38} +(1.73408e23 - 1.19514e23i) q^{39} -2.43934e23i q^{40} -4.34123e23 q^{41} +(3.00415e23 + 1.77392e23i) q^{42} -5.92539e23 q^{43} +7.98413e21i q^{44} +(-4.85516e23 + 1.27474e24i) q^{45} -6.30341e23 q^{46} -1.14886e24 q^{47} +(1.38927e24 + 2.01576e24i) q^{48} +(-2.08141e24 + 2.45673e24i) q^{49} -4.89983e24i q^{50} +(3.63764e23 + 5.27803e23i) q^{51} -3.54072e23i q^{52} +1.25991e25i q^{53} +(-3.16574e24 - 1.29626e25i) q^{54} -1.13937e25i q^{55} +(-1.99815e25 + 9.25979e24i) q^{56} +(-2.34532e25 + 1.61640e25i) q^{57} +2.20147e25 q^{58} -6.30342e25 q^{59} +(1.30141e24 + 1.88829e24i) q^{60} -1.06559e26i q^{61} +1.21087e26 q^{62} +(1.22849e26 - 8.61923e24i) q^{63} -1.50522e26 q^{64} +5.05277e26i q^{65} +(6.32483e25 + 9.17701e25i) q^{66} -2.01956e26 q^{67} +1.07769e24 q^{68} +(-1.83207e26 + 1.26267e26i) q^{69} +(-7.59443e26 + 3.51940e26i) q^{70} +7.89239e26i q^{71} +(7.87141e26 + 2.99801e26i) q^{72} -1.48365e27i q^{73} +9.10920e26i q^{74} +(-9.81508e26 - 1.42412e27i) q^{75} +4.78877e25i q^{76} +(-9.33297e26 + 4.32507e26i) q^{77} +(-2.80488e27 - 4.06974e27i) q^{78} +4.39054e27 q^{79} -5.87354e27 q^{80} +(-3.51671e27 - 3.13338e27i) q^{81} +1.01885e28i q^{82} -4.23602e27 q^{83} +(1.05274e26 - 1.78283e26i) q^{84} -1.53791e27 q^{85} +1.39064e28i q^{86} +(6.39851e27 - 4.40987e27i) q^{87} -7.03548e27 q^{88} +1.28454e28 q^{89} +(2.99171e28 + 1.13946e28i) q^{90} +(4.13890e28 - 1.91804e28i) q^{91} +3.74079e26i q^{92} +(3.51936e28 - 2.42556e28i) q^{93} +2.69627e28i q^{94} -6.83379e28i q^{95} +(2.36305e27 - 1.62862e27i) q^{96} +1.72177e27i q^{97} +(5.76572e28 + 4.88489e28i) q^{98} +(3.67658e28 + 1.40031e28i) 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 $

$2$		−	23469.1i		−	1.01289i	−0.862273	−	0.506444i	$-0.830960\pi$
$2$		−	23469.1i		−	1.01289i	0.862273	−	0.506444i	$-0.169040\pi$
$3$	−4.70121e6	−	6.82122e6i	−0.567481	−	0.823387i
$3$	−4.70121e6	−	6.82122e6i	−0.567481	−	0.823387i
$4$	−1.39279e7			−0.0259427
$5$	1.98757e10			1.45632			0.728160	−	0.685407i	$-0.240376\pi$
$5$	1.98757e10			1.45632			0.728160	+	0.685407i	$0.240376\pi$
$6$	−1.60088e11	+	1.10333e11i	−0.833999	+	0.574795i
$7$	−7.54484e11	−	1.62808e12i	−0.420464	−	0.907309i
$7$	−7.54484e11	−	1.62808e12i	−0.420464	−	0.907309i
$8$		−	1.22730e13i		−	0.986611i
$9$	−2.44277e13	+	6.41359e13i	−0.355931	+	0.934512i
$10$		−	4.66464e14i		−	1.47509i
$11$		−	5.73249e14i		−	0.455144i	−0.973761	−	0.227572i	$-0.926921\pi$
$11$		−	5.73249e14i		−	0.455144i	0.973761	−	0.227572i	$-0.0730787\pi$
$12$	6.54778e13	+	9.50050e13i	0.0147220	+	0.0213608i
$13$			2.54219e16i			1.79073i	0.445337	+	0.895363i	$0.353084\pi$
$13$			2.54219e16i			1.79073i	−0.445337	+	0.895363i	$0.646916\pi$
$14$	−3.82097e16	+	1.77071e16i	−0.919003	+	0.425883i
$15$	−9.34397e16	−	1.35576e17i	−0.826434	−	1.19911i
$16$	−2.95514e17			−1.02527
$17$	−7.73767e16			−0.111455			−0.0557276	−	0.998446i	$-0.517748\pi$
$17$	−7.73767e16			−0.111455			−0.0557276	+	0.998446i	$0.517748\pi$
$18$	1.50521e18	+	5.73296e17i	0.946557	+	0.360518i
$19$		−	3.43827e18i		−	0.987217i	−0.869684	−	0.493608i	$-0.835678\pi$
$19$		−	3.43827e18i		−	0.987217i	0.869684	−	0.493608i	$-0.164322\pi$
$20$	−2.76826e17			−0.0377808
$21$	−7.55853e18	+	1.28005e19i	−0.508461	+	0.861085i
$22$	−1.34536e19			−0.461010
$23$		−	2.68583e19i		−	0.483087i	−0.970390	−	0.241544i	$-0.922346\pi$
$23$		−	2.68583e19i		−	0.483087i	0.970390	−	0.241544i	$-0.0776537\pi$
$24$	−8.37168e19	+	5.76979e19i	−0.812362	+	0.559883i
$25$	2.08778e20			1.12087
$26$	5.96629e20			1.81381
$27$	5.52325e20	−	1.34890e20i	0.971449	−	0.237249i
$28$	1.05084e19	+	2.26757e19i	0.0109079	+	0.0235380i
$29$			9.38030e20i			0.585390i	0.956206	+	0.292695i	$0.0945521\pi$
$29$			9.38030e20i			0.585390i	−0.956206	+	0.292695i	$0.905448\pi$
$30$	−3.18185e21	+	2.19294e21i	−1.21457	+	0.837085i
$31$			5.15944e21i			1.22422i	0.790775	+	0.612108i	$0.209678\pi$
$31$			5.15944e21i			1.22422i	−0.790775	+	0.612108i	$0.790322\pi$
$32$			3.46426e20i			0.0518723i
$33$	−3.91025e21	+	2.69496e21i	−0.374760	+	0.258286i
$34$			1.81596e21i			0.112892i
$35$	−1.49959e22	−	3.23593e22i	−0.612330	−	1.32133i
$36$	3.40225e20	−	8.93276e20i	0.00923380	−	0.0242437i
$37$	−3.88136e22			−0.708042			−0.354021	−	0.935238i	$-0.615186\pi$
$37$	−3.88136e22			−0.708042			−0.354021	+	0.935238i	$0.615186\pi$
$38$	−8.06931e22			−0.999940
$39$	1.73408e23	−	1.19514e23i	1.47446	−	1.01620i
$40$		−	2.43934e23i		−	1.43682i
$41$	−4.34123e23			−1.78751			−0.893753	−	0.448560i	$-0.851937\pi$
$41$	−4.34123e23			−1.78751			−0.893753	+	0.448560i	$0.851937\pi$
$42$	3.00415e23	+	1.77392e23i	0.872183	+	0.515014i
$43$	−5.92539e23			−1.22299			−0.611497	−	0.791247i	$-0.709432\pi$
$43$	−5.92539e23			−1.22299			−0.611497	+	0.791247i	$0.709432\pi$
$44$			7.98413e21i			0.0118077i
$45$	−4.85516e23	+	1.27474e24i	−0.518349	+	1.36095i
$46$	−6.30341e23			−0.489313
$47$	−1.14886e24			−0.652902			−0.326451	−	0.945214i	$-0.605853\pi$
$47$	−1.14886e24			−0.652902			−0.326451	+	0.945214i	$0.605853\pi$
$48$	1.38927e24	+	2.01576e24i	0.581821	+	0.844193i
$49$	−2.08141e24	+	2.45673e24i	−0.646420	+	0.762981i
$50$		−	4.89983e24i		−	1.13531i
$51$	3.63764e23	+	5.27803e23i	0.0632487	+	0.0917708i
$52$		−	3.54072e23i		−	0.0464562i
$53$			1.25991e25i			1.25412i	0.778970	+	0.627061i	$0.215742\pi$
$53$			1.25991e25i			1.25412i	−0.778970	+	0.627061i	$0.784258\pi$
$54$	−3.16574e24	−	1.29626e25i	−0.240307	−	0.983969i
$55$		−	1.13937e25i		−	0.662835i
$56$	−1.99815e25	+	9.25979e24i	−0.895162	+	0.414834i
$57$	−2.34532e25	+	1.61640e25i	−0.812861	+	0.560227i
$58$	2.20147e25			0.592935
$59$	−6.30342e25			−1.32502			−0.662509	−	0.749054i	$-0.730508\pi$
$59$	−6.30342e25			−1.32502			−0.662509	+	0.749054i	$0.730508\pi$
$60$	1.30141e24	+	1.88829e24i	0.0214399	+	0.0311082i
$61$		−	1.06559e26i		−	1.38136i	−0.723158	−	0.690682i	$-0.757310\pi$
$61$		−	1.06559e26i		−	1.38136i	0.723158	−	0.690682i	$-0.242690\pi$
$62$	1.21087e26			1.23999
$63$	1.22849e26	−	8.61923e24i	0.997548	−	0.0699891i
$64$	−1.50522e26			−0.972729
$65$			5.05277e26i			2.60787i
$66$	6.32483e25	+	9.17701e25i	0.261614	+	0.379590i
$67$	−2.01956e26			−0.671696			−0.335848	−	0.941916i	$-0.609023\pi$
$67$	−2.01956e26			−0.671696			−0.335848	+	0.941916i	$0.609023\pi$
$68$	1.07769e24			0.00289145
$69$	−1.83207e26	+	1.26267e26i	−0.397768	+	0.274143i
$70$	−7.59443e26	+	3.51940e26i	−1.33836	+	0.620222i
$71$			7.89239e26i			1.13230i	0.824302	+	0.566151i	$0.191568\pi$
$71$			7.89239e26i			1.13230i	−0.824302	+	0.566151i	$0.808432\pi$
$72$	7.87141e26	+	2.99801e26i	0.922000	+	0.351165i
$73$		−	1.48365e27i		−	1.42282i	−0.702776	−	0.711412i	$-0.748056\pi$
$73$		−	1.48365e27i		−	1.42282i	0.702776	−	0.711412i	$-0.251944\pi$
$74$			9.10920e26i			0.717167i
$75$	−9.81508e26	−	1.42412e27i	−0.636071	−	0.922907i
$76$			4.78877e25i			0.0256110i
$77$	−9.33297e26	+	4.32507e26i	−0.412957	+	0.191372i
$78$	−2.80488e27	−	4.06974e27i	−1.02930	−	1.49346i
$79$	4.39054e27			1.33944			0.669722	−	0.742612i	$-0.266413\pi$
$79$	4.39054e27			1.33944			0.669722	+	0.742612i	$0.266413\pi$
$80$	−5.87354e27			−1.49312
$81$	−3.51671e27	−	3.13338e27i	−0.746626	−	0.665244i
$82$			1.01885e28i			1.81054i
$83$	−4.23602e27			−0.631431			−0.315715	−	0.948854i	$-0.602244\pi$
$83$	−4.23602e27			−0.631431			−0.315715	+	0.948854i	$0.602244\pi$
$84$	1.05274e26	−	1.78283e26i	0.0131908	−	0.0223388i
$85$	−1.53791e27			−0.162315
$86$			1.39064e28i			1.23876i
$87$	6.39851e27	−	4.40987e27i	0.482003	−	0.332198i
$88$	−7.03548e27			−0.449050
$89$	1.28454e28			0.695975			0.347987	−	0.937499i	$-0.386865\pi$
$89$	1.28454e28			0.695975			0.347987	+	0.937499i	$0.386865\pi$
$90$	2.99171e28	+	1.13946e28i	1.37849	+	0.525030i
$91$	4.13890e28	−	1.91804e28i	1.62474	−	0.752935i
$92$			3.74079e26i			0.0125326i
$93$	3.51936e28	−	2.42556e28i	1.00800	−	0.694719i
$94$			2.69627e28i			0.661317i
$95$		−	6.83379e28i		−	1.43770i
$96$	2.36305e27	−	1.62862e27i	0.0427110	−	0.0294366i
$97$			1.72177e27i			0.0267785i	0.999910	+	0.0133892i	$0.00426205\pi$
$97$			1.72177e27i			0.0267785i	−0.999910	+	0.0133892i	$0.995738\pi$
$98$	5.76572e28	+	4.88489e28i	0.772815	+	0.654752i
$99$	3.67658e28	+	1.40031e28i	0.425338	+	0.162000i
$100$	−2.90783e27			−0.0290783
$101$	−1.79335e29			−1.55240			−0.776202	−	0.630484i	$-0.782856\pi$
$101$	−1.79335e29			−1.55240			−0.776202	+	0.630484i	$0.782856\pi$
$102$	1.23871e28	−	8.53721e27i	0.0929535	−	0.0640639i
$103$		−	8.70748e28i		−	0.567221i	−0.958940	−	0.283611i	$-0.908468\pi$
$103$		−	8.70748e28i		−	0.567221i	0.958940	−	0.283611i	$-0.0915323\pi$
$104$	3.12003e29			1.76675
$105$	−1.50231e29	+	2.54418e29i	−0.740482	+	1.25401i
$106$	2.95690e29			1.27028
$107$		−	8.17895e28i		−	0.306643i	−0.988176	−	0.153321i	$-0.951003\pi$
$107$		−	8.17895e28i		−	0.306643i	0.988176	−	0.153321i	$-0.0489970\pi$
$108$	−7.69270e27	+	1.87873e27i	−0.0252020	+	0.00615487i
$109$	−2.81481e29			−0.806800			−0.403400	−	0.915024i	$-0.632172\pi$
$109$	−2.81481e29			−0.806800			−0.403400	+	0.915024i	$0.632172\pi$
$110$	−2.67400e29			−0.671378
$111$	1.82471e29	+	2.64756e29i	0.401800	+	0.582992i
$112$	2.22961e29	+	4.81122e29i	0.431089	+	0.930237i
$113$			4.35011e29i			0.739372i	0.929157	+	0.369686i	$0.120535\pi$
$113$			4.35011e29i			0.739372i	−0.929157	+	0.369686i	$0.879465\pi$
$114$	3.79355e29	+	5.50425e29i	0.567447	+	0.823338i
$115$		−	5.33828e29i		−	0.703529i
$116$		−	1.30647e28i		−	0.0151866i
$117$	−1.63046e30	−	6.20997e29i	−1.67346	−	0.637375i
$118$			1.47936e30i			1.34210i
$119$	5.83795e28	+	1.25976e29i	0.0468629	+	0.101124i
$120$	−1.66393e30	+	1.14679e30i	−1.18306	+	0.815369i
$121$	1.25770e30			0.792844
$122$	−2.50085e30			−1.39917
$123$	2.04090e30	+	2.96125e30i	1.01438	+	1.47181i
$124$		−	7.18599e28i		−	0.0317594i
$125$	4.47466e29			0.176021
$126$	−2.02286e29	−	2.88316e30i	−0.0708912	−	1.01040i
$127$	1.01244e30			0.316385			0.158192	−	0.987408i	$-0.449433\pi$
$127$	1.01244e30			0.316385			0.158192	+	0.987408i	$0.449433\pi$
$128$			3.71861e30i			1.03714i
$129$	2.78565e30	+	4.04184e30i	0.694026	+	1.00700i
$130$	1.18584e31			2.64148
$131$	−2.09552e30			−0.417694			−0.208847	−	0.977948i	$-0.566971\pi$
$131$	−2.09552e30			−0.417694			−0.208847	+	0.977948i	$0.566971\pi$
$132$	5.44615e28	−	3.75350e28i	0.00972226	−	0.00670062i
$133$	−5.59779e30	+	2.59412e30i	−0.895711	+	0.415089i
$134$			4.73974e30i			0.680353i
$135$	1.09778e31	−	2.68103e30i	1.41474	−	0.345511i
$136$			9.49644e29i			0.109963i
$137$			1.03686e31i			1.07962i	0.841788	+	0.539809i	$0.181504\pi$
$137$			1.03686e31i			1.07962i	−0.841788	+	0.539809i	$0.818496\pi$
$138$	2.96336e30	+	4.29969e30i	0.277676	+	0.402894i
$139$			1.55704e30i			0.131397i	0.997840	+	0.0656986i	$0.0209276\pi$
$139$			1.55704e30i			0.131397i	−0.997840	+	0.0656986i	$0.979072\pi$
$140$	2.08861e29	+	4.50695e29i	0.0158855	+	0.0342789i
$141$	5.40103e30	+	7.83662e30i	0.370509	+	0.537591i
$142$	1.85227e31			1.14690
$143$	1.45731e31			0.815039
$144$	7.21872e30	−	1.89531e31i	0.364925	−	0.958127i
$145$			1.86440e31i			0.852516i
$146$	−3.48200e31			−1.44116
$147$	2.65430e31	+	2.64818e30i	0.995060	+	0.0992766i
$148$	5.40590e29			0.0183685
$149$		−	1.78985e31i		−	0.551590i	−0.961217	−	0.275795i	$-0.911059\pi$
$149$		−	1.78985e31i		−	0.551590i	0.961217	−	0.275795i	$-0.0889410\pi$
$150$	−3.34228e31	+	2.30351e31i	−0.934802	+	0.644269i
$151$	5.02949e31			1.27749			0.638746	−	0.769418i	$-0.279454\pi$
$151$	5.02949e31			1.27749			0.638746	+	0.769418i	$0.279454\pi$
$152$	−4.21979e31			−0.973999
$153$	1.89013e30	−	4.96262e30i	0.0396704	−	0.104156i
$154$	1.01505e31	+	2.19036e31i	0.193838	+	0.418279i
$155$			1.02547e32i			1.78285i
$156$	−2.41521e30	+	1.66457e30i	−0.0382514	+	0.0263630i
$157$		−	3.53151e31i		−	0.509818i	−0.966965	−	0.254909i	$-0.917955\pi$
$157$		−	3.53151e31i		−	0.509818i	0.966965	−	0.254909i	$-0.0820455\pi$
$158$		−	1.03042e32i		−	1.35671i
$159$	8.59413e31	−	5.92310e31i	1.03263	−	0.711690i
$160$			6.88545e30i			0.0755427i
$161$	−4.37276e31	+	2.02642e31i	−0.438310	+	0.203121i
$162$	−7.35377e31	+	8.25339e31i	−0.673817	+	0.756249i
$163$	1.19012e32			0.997399			0.498700	−	0.866775i	$-0.333811\pi$
$163$	1.19012e32			0.997399			0.498700	+	0.866775i	$0.333811\pi$
$164$	6.04641e30			0.0463726
$165$	−7.77189e31	+	5.35641e31i	−0.545770	+	0.376146i
$166$			9.94156e31i			0.639569i
$167$	−4.14758e31			−0.244572			−0.122286	−	0.992495i	$-0.539022\pi$
$167$	−4.14758e31			−0.244572			−0.122286	+	0.992495i	$0.539022\pi$
$168$	1.57100e32	+	9.27659e31i	0.849556	+	0.501654i
$169$	−4.44734e32			−2.20670
$170$			3.60934e31i			0.164406i
$171$	2.20517e32	+	8.39889e31i	0.922566	+	0.351381i
$172$	8.25280e30			0.0317277
$173$	1.76776e32			0.624820			0.312410	−	0.949947i	$-0.398864\pi$
$173$	1.76776e32			0.624820			0.312410	+	0.949947i	$0.398864\pi$
$174$	−1.03496e32	−	1.50167e32i	−0.336479	−	0.488215i
$175$	−1.57520e32	−	3.39908e32i	−0.471284	−	1.01697i
$176$			1.69403e32i			0.466646i
$177$	2.96337e32	+	4.29970e32i	0.751922	+	1.09100i
$178$		−	3.01471e32i		−	0.704944i
$179$		−	7.22462e32i		−	1.55756i	−0.627295	−	0.778782i	$-0.715838\pi$
$179$		−	7.22462e32i		−	1.55756i	0.627295	−	0.778782i	$-0.284162\pi$
$180$	6.76220e30	−	1.77545e31i	0.0134474	−	0.0353066i
$181$			1.20311e32i			0.220783i	0.993888	+	0.110391i	$0.0352104\pi$
$181$			1.20311e32i			0.220783i	−0.993888	+	0.110391i	$0.964790\pi$
$182$	−4.50147e32	−	9.71362e32i	−0.762639	−	1.64568i
$183$	−7.26864e32	+	5.00957e32i	−1.13740	+	0.783898i
$184$	−3.29633e32			−0.476619
$185$	−7.71446e32			−1.03113
$186$	−5.69257e32	−	8.25963e32i	−0.703672	−	1.02099i
$187$			4.43561e31i			0.0507282i
$188$	1.60012e31			0.0169380
$189$	−6.36332e32	−	7.97459e32i	−0.623717	−	0.781650i
$190$	−1.60383e33			−1.45623
$191$		−	8.95713e32i		−	0.753676i	−0.926279	−	0.376838i	$-0.877011\pi$
$191$		−	8.95713e32i		−	0.753676i	0.926279	−	0.376838i	$-0.122989\pi$
$192$	7.07637e32	+	1.02675e33i	0.552005	+	0.800932i
$193$	2.16008e33			1.56275			0.781374	−	0.624063i	$-0.214519\pi$
$193$	2.16008e33			1.56275			0.781374	+	0.624063i	$0.214519\pi$
$194$	4.04085e31			0.0271236
$195$	3.44661e33	−	2.37541e33i	2.14728	−	1.47992i
$196$	2.89896e31	−	3.42170e31i	0.0167699	−	0.0197938i
$197$			9.51350e32i			0.511187i	0.966784	+	0.255594i	$0.0822709\pi$
$197$			9.51350e32i			0.511187i	−0.966784	+	0.255594i	$0.917729\pi$
$198$	3.28641e32	−	8.62861e32i	0.164088	−	0.430820i
$199$		−	1.72725e33i		−	0.801651i	−0.916154	−	0.400826i	$-0.868723\pi$
$199$		−	1.72725e33i		−	0.801651i	0.916154	−	0.400826i	$-0.131277\pi$
$200$		−	2.56233e33i		−	1.10586i
$201$	9.49439e32	+	1.37759e33i	0.381175	+	0.553066i
$202$			4.20883e33i			1.57241i
$203$	1.52719e33	−	7.07729e32i	0.531130	−	0.246135i
$204$	−5.06645e30	−	7.35117e30i	−0.00164084	−	0.00238078i
$205$	−8.62850e33			−2.60318
$206$	−2.04357e33			−0.574532
$207$	1.72258e33	+	6.56087e32i	0.451451	+	0.171946i
$208$		−	7.51252e33i		−	1.83598i
$209$	−1.97098e33			−0.449326
$210$	5.97096e33	+	3.52579e33i	1.27018	+	0.750026i
$211$	3.23925e33			0.643205			0.321603	−	0.946875i	$-0.395778\pi$
$211$	3.23925e33			0.643205			0.321603	+	0.946875i	$0.395778\pi$
$212$		−	1.75479e32i		−	0.0325352i
$213$	5.38357e33	−	3.71037e33i	0.932322	−	0.642560i
$214$	−1.91953e33			−0.310595
$215$	−1.17771e34			−1.78107
$216$	−1.65550e33	−	6.77868e33i	−0.234073	−	0.958442i
$217$	8.40000e33	−	3.89271e33i	1.11074	−	0.514738i
$218$			6.60612e33i			0.817198i
$219$	−1.01203e34	+	6.97496e33i	−1.17153	+	0.807425i
$220$			1.58690e32i			0.0171957i
$221$		−	1.96706e33i		−	0.199586i
$222$	6.21358e33	−	4.28242e33i	0.590506	−	0.406979i
$223$			1.73026e34i			1.54060i	0.637682	+	0.770300i	$0.279893\pi$
$223$			1.73026e34i			1.54060i	−0.637682	+	0.770300i	$0.720107\pi$
$224$	5.64011e32	−	2.61373e32i	0.0470643	−	0.0218104i
$225$	−5.09996e33	+	1.33902e34i	−0.398951	+	1.04746i
$226$	1.02093e34			0.748902
$227$	−4.21542e33			−0.290046			−0.145023	−	0.989428i	$-0.546326\pi$
$227$	−4.21542e33			−0.290046			−0.145023	+	0.989428i	$0.546326\pi$
$228$	3.26653e32	−	2.25130e32i	0.0210878	−	0.0145338i
$229$			1.88113e34i			1.13974i	0.821736	+	0.569868i	$0.193006\pi$
$229$			1.88113e34i			1.13974i	−0.821736	+	0.569868i	$0.806994\pi$
$230$	−1.25285e34			−0.712597
$231$	7.33785e33	+	4.33292e33i	0.391918	+	0.231423i
$232$	1.15124e34			0.577553
$233$			2.37783e34i			1.12078i	0.828229	+	0.560389i	$0.189348\pi$
$233$			2.37783e34i			1.12078i	−0.828229	+	0.560389i	$0.810652\pi$
$234$	−1.45743e34	+	3.82653e34i	−0.645589	+	1.69502i
$235$	−2.28343e34			−0.950834
$236$	8.77931e32			0.0343745
$237$	−2.06408e34	−	2.99488e34i	−0.760109	−	1.10288i
$238$	2.95654e33	−	1.37011e33i	0.102428	−	0.0474669i
$239$		−	4.11101e34i		−	1.34023i	−0.742258	−	0.670115i	$-0.766245\pi$
$239$		−	4.11101e34i		−	1.34023i	0.742258	−	0.670115i	$-0.233755\pi$
$240$	2.76127e34	+	4.00647e34i	0.847317	+	1.22942i
$241$		−	3.28350e34i		−	0.948614i	−0.880359	−	0.474307i	$-0.842699\pi$
$241$		−	3.28350e34i		−	0.948614i	0.880359	−	0.474307i	$-0.157301\pi$
$242$		−	2.95170e34i		−	0.803062i
$243$	−4.84072e33	+	3.87189e34i	−0.124056	+	0.992275i
$244$			1.48414e33i			0.0358363i
$245$	−4.13695e34	+	4.88291e34i	−0.941395	+	1.11114i
$246$	6.94979e34	−	4.78982e34i	1.49078	−	1.02745i
$247$	8.74073e34			1.76784
$248$	6.33218e34			1.20782
$249$	1.99144e34	+	2.88948e34i	0.358325	+	0.519912i
$250$		−	1.05016e34i		−	0.178290i
$251$	1.41605e34			0.226887			0.113443	−	0.993544i	$-0.463812\pi$
$251$	1.41605e34			0.226887			0.113443	+	0.993544i	$0.463812\pi$
$252$	−1.71102e33	+	1.20047e32i	−0.0258790	+	0.00181570i
$253$	−1.53965e34			−0.219874
$254$		−	2.37611e34i		−	0.320462i
$255$	7.23005e33	+	1.04904e34i	0.0921104	+	0.133648i
$256$	6.46138e33			0.0777761
$257$	6.39890e34			0.727906			0.363953	−	0.931417i	$-0.381427\pi$
$257$	6.39890e34			0.727906			0.363953	+	0.931417i	$0.381427\pi$
$258$	9.48583e34	−	6.53767e34i	1.01998	−	0.702970i
$259$	2.92842e34	+	6.31918e34i	0.297706	+	0.642413i
$260$		−	7.03743e33i		−	0.0676551i
$261$	−6.01614e34	−	2.29139e34i	−0.547055	−	0.208359i
$262$			4.91800e34i			0.423078i
$263$			1.20189e35i			0.978374i	0.872179	+	0.489187i	$0.162706\pi$
$263$			1.20189e35i			0.978374i	−0.872179	+	0.489187i	$0.837294\pi$
$264$	3.30753e34	+	4.79906e34i	0.254828	+	0.369742i
$265$			2.50416e35i			1.82640i
$266$	6.08817e34	+	1.31375e35i	0.420439	+	0.907255i
$267$	−6.03890e34	−	8.76215e34i	−0.394952	−	0.573056i
$268$	2.81282e33			0.0174256
$269$	−2.28523e35			−1.34129			−0.670643	−	0.741780i	$-0.733982\pi$
$269$	−2.28523e35			−1.34129			−0.670643	+	0.741780i	$0.733982\pi$
$270$	−6.29213e34	−	2.57640e35i	−0.349964	−	1.43297i
$271$		−	2.80968e35i		−	1.48116i	−0.671968	−	0.740581i	$-0.734551\pi$
$271$		−	2.80968e35i		−	1.48116i	0.671968	−	0.740581i	$-0.265449\pi$
$272$	2.28659e34			0.114272
$273$	−3.25412e35	−	1.92152e35i	−1.54197	−	0.910515i
$274$	2.43341e35			1.09353
$275$		−	1.19682e35i		−	0.510156i
$276$	2.55168e33	−	1.75862e33i	0.0103191	−	0.00711199i
$277$	−3.34384e35			−1.28319			−0.641593	−	0.767046i	$-0.721726\pi$
$277$	−3.34384e35			−1.28319			−0.641593	+	0.767046i	$0.721726\pi$
$278$	3.65424e34			0.133091
$279$	−3.30905e35	−	1.26033e35i	−1.14404	−	0.435736i
$280$	−3.97145e35	+	1.84044e35i	−1.30364	+	0.604131i
$281$		−	2.59745e35i		−	0.809666i	−0.914391	−	0.404833i	$-0.867330\pi$
$281$		−	2.59745e35i		−	0.809666i	0.914391	−	0.404833i	$-0.132670\pi$
$282$	1.83918e35	−	1.26757e35i	0.544519	−	0.375285i
$283$		−	3.56363e35i		−	1.00228i	−0.865366	−	0.501140i	$-0.832914\pi$
$283$		−	3.56363e35i		−	1.00228i	0.865366	−	0.501140i	$-0.167086\pi$
$284$		−	1.09924e34i		−	0.0293749i
$285$	−4.66148e35	+	3.21271e35i	−1.18379	+	0.815869i
$286$		−	3.42017e35i		−	0.825543i
$287$	3.27539e35	+	7.06790e35i	0.751581	+	1.62182i
$288$	−2.22184e34	−	8.46238e33i	−0.0484753	−	0.0184630i
$289$	−4.75981e35			−0.987578
$290$	4.37557e35			0.863503
$291$	1.17446e34	−	8.09441e33i	0.0220490	−	0.0151963i
$292$			2.06641e34i			0.0369118i
$293$	5.56455e35			0.945910			0.472955	−	0.881087i	$-0.343187\pi$
$293$	5.56455e35			0.945910			0.472955	+	0.881087i	$0.343187\pi$
$294$	6.21505e34	−	6.22941e35i	0.100556	−	1.00788i
$295$	−1.25285e36			−1.92965
$296$			4.76359e35i			0.698562i
$297$	−7.73254e34	−	3.16619e35i	−0.107983	−	0.442149i
$298$	−4.20062e35			−0.558699
$299$	6.82790e35			0.865077
$300$	1.36703e34	+	1.98349e34i	0.0165014	+	0.0239427i
$301$	4.47061e35	+	9.64703e35i	0.514225	+	1.10963i
$302$		−	1.18038e36i		−	1.29396i
$303$	8.43091e35	+	1.22328e36i	0.880960	+	1.27823i
$304$			1.01606e36i			1.01216i
$305$		−	2.11794e36i		−	2.01171i
$306$	−1.16468e35	−	4.43597e34i	−0.105499	−	0.0401817i
$307$		−	8.46425e35i		−	0.731277i	−0.930757	−	0.365639i	$-0.880851\pi$
$307$		−	8.46425e35i		−	0.731277i	0.930757	−	0.365639i	$-0.119149\pi$
$308$	1.29988e34	−	6.02390e33i	0.0107132	−	0.00496469i
$309$	−5.93956e35	+	4.09357e35i	−0.467042	+	0.321887i
$310$	2.40669e36			1.80583
$311$	1.53663e36			1.10038			0.550192	−	0.835038i	$-0.314554\pi$
$311$	1.53663e36			1.10038			0.550192	+	0.835038i	$0.314554\pi$
$312$	−1.46679e36	−	2.12824e36i	−1.00260	−	1.45472i
$313$		−	2.33745e36i		−	1.52528i	−0.646824	−	0.762639i	$-0.723903\pi$
$313$		−	2.33745e36i		−	1.52528i	0.646824	−	0.762639i	$-0.276097\pi$
$314$	−8.28813e35			−0.516388
$315$	2.44171e36	−	1.71313e35i	1.45275	−	0.101927i
$316$	−6.11508e34			−0.0347488
$317$			9.66443e35i			0.524586i	0.964988	+	0.262293i	$0.0844787\pi$
$317$			9.66443e35i			0.524586i	−0.964988	+	0.262293i	$0.915521\pi$
$318$	−1.39010e36	−	2.01696e36i	−0.720862	−	1.04594i
$319$	5.37724e35			0.266437
$320$	−2.99174e36			−1.41660
$321$	−5.57904e35	+	3.84509e35i	−0.252485	+	0.174014i
$322$	4.75582e35	+	1.02625e36i	0.205739	+	0.443959i
$323$			2.66042e35i			0.110031i
$324$	4.89802e34	+	4.36413e34i	0.0193695	+	0.0172582i
$325$			5.30753e36i			2.00717i
$326$		−	2.79310e36i		−	1.01025i
$327$	1.32330e36	+	1.92005e36i	0.457843	+	0.664308i
$328$			5.32800e36i			1.76357i
$329$	8.66796e35	+	1.87044e36i	0.274522	+	0.592384i
$330$	1.25710e36	+	1.82399e36i	0.380994	+	0.552804i
$331$	−5.63257e36			−1.63381			−0.816903	−	0.576775i	$-0.804311\pi$
$331$	−5.63257e36			−1.63381			−0.816903	+	0.576775i	$0.804311\pi$
$332$	5.89987e34			0.0163810
$333$	9.48126e35	−	2.48935e36i	0.252014	−	0.661674i
$334$			9.73400e35i			0.247724i
$335$	−4.01402e36			−0.978205
$336$	2.23365e36	−	3.78271e36i	0.521310	−	0.882844i
$337$	4.78446e36			1.06955			0.534773	−	0.844996i	$-0.320397\pi$
$337$	4.78446e36			1.06955			0.534773	+	0.844996i	$0.320397\pi$
$338$			1.04375e37i			2.23514i
$339$	2.96731e36	−	2.04508e36i	0.608789	−	0.419580i
$340$	2.14198e34			0.00421087
$341$	2.95764e36			0.557194
$342$	1.97114e36	−	5.17533e36i	0.355910	−	0.934457i
$343$	5.57015e36	+	1.53515e36i	0.964056	+	0.265697i
$344$			7.27223e36i			1.20662i
$345$	−3.64135e36	+	2.50963e36i	−0.579277	+	0.399240i
$346$		−	4.14878e36i		−	0.632873i
$347$			1.75513e36i			0.256762i	0.991725	+	0.128381i	$0.0409781\pi$
$347$			1.75513e36i			0.256762i	−0.991725	+	0.128381i	$0.959022\pi$
$348$	−8.91175e34	+	6.14201e34i	−0.0125044	+	0.00861810i
$349$		−	8.95480e36i		−	1.20528i	−0.798014	−	0.602639i	$-0.794116\pi$
$349$		−	8.95480e36i		−	1.20528i	0.798014	−	0.602639i	$-0.205884\pi$
$350$	−7.97733e36	+	3.69684e36i	−1.03008	+	0.477358i
$351$	3.42915e36	+	1.40411e37i	0.424848	+	1.73960i
$352$	1.98588e35			0.0236094
$353$	−1.46102e37			−1.66695			−0.833473	−	0.552560i	$-0.813651\pi$
$353$	−1.46102e37			−1.66695			−0.833473	+	0.552560i	$0.813651\pi$
$354$	1.00910e37	−	6.95476e36i	1.10506	−	0.761613i
$355$			1.56866e37i			1.64899i
$356$	−1.78909e35			−0.0180554
$357$	5.84854e35	−	9.90457e35i	0.0566707	−	0.0959725i
$358$	−1.69555e37			−1.57764
$359$		−	1.05987e37i		−	0.947071i	−0.880775	−	0.473535i	$-0.842978\pi$
$359$		−	1.05987e37i		−	0.947071i	0.880775	−	0.473535i	$-0.157022\pi$
$360$	1.56449e37	+	5.95874e36i	1.34273	+	0.511409i
$361$	3.08130e35			0.0254027
$362$	2.82358e36			0.223628
$363$	−5.91269e36	−	8.57902e36i	−0.449924	−	0.652817i
$364$	−5.76460e35	+	2.67142e35i	−0.0421501	+	0.0195331i
$365$		−	2.94886e37i		−	2.07209i
$366$	1.17570e37	+	1.70588e37i	0.794001	+	1.15206i
$367$			1.41449e37i			0.918207i	0.888383	+	0.459103i	$0.151829\pi$
$367$			1.41449e37i			0.918207i	−0.888383	+	0.459103i	$0.848171\pi$
$368$			7.93701e36i			0.495295i
$369$	1.06046e37	−	2.78429e37i	0.636228	−	1.67045i
$370$			1.81051e37i			1.04442i
$371$	2.05124e37	−	9.50583e36i	1.13788	−	0.527313i
$372$	−4.90172e35	+	3.37828e35i	−0.0261503	+	0.0180229i
$373$	2.24839e36			0.115370			0.0576850	−	0.998335i	$-0.481628\pi$
$373$	2.24839e36			0.115370			0.0576850	+	0.998335i	$0.481628\pi$
$374$	1.04100e36			0.0513820
$375$	−2.10363e36	−	3.05227e36i	−0.0998887	−	0.144934i
$376$			1.41000e37i			0.644160i
$377$	−2.38465e37			−1.04827
$378$	−1.87157e37	+	1.49341e37i	−0.791724	+	0.631756i
$379$	7.15894e36			0.291461			0.145730	−	0.989324i	$-0.453447\pi$
$379$	7.15894e36			0.291461			0.145730	+	0.989324i	$0.453447\pi$
$380$			9.51801e35i			0.0372979i
$381$	−4.75969e36	−	6.90607e36i	−0.179542	−	0.260507i
$382$	−2.10216e37			−0.763390
$383$	−2.50212e37			−0.874833			−0.437416	−	0.899259i	$-0.644106\pi$
$383$	−2.50212e37			−0.874833			−0.437416	+	0.899259i	$0.644106\pi$
$384$	2.53655e37	−	1.74820e37i	0.853965	−	0.588556i
$385$	−1.85499e37	+	8.59637e36i	−0.601397	+	0.278698i
$386$		−	5.06952e37i		−	1.58289i
$387$	1.44743e37	−	3.80030e37i	0.435301	−	1.14290i
$388$		−	2.39806e34i		−	0.000694705i
$389$		−	5.39063e37i		−	1.50442i	−0.658922	−	0.752211i	$-0.728987\pi$
$389$		−	5.39063e37i		−	1.50442i	0.658922	−	0.752211i	$-0.271013\pi$
$390$	−5.57488e37	−	8.08887e37i	−1.49899	−	2.17496i
$391$			2.07821e36i			0.0538426i
$392$	3.01514e37	+	2.55452e37i	0.752766	+	0.637766i
$393$	9.85148e36	+	1.42940e37i	0.237033	+	0.343924i
$394$	2.23273e37			0.517776
$395$	8.72648e37			1.95066
$396$	−5.12069e35	−	1.95034e35i	−0.0110344	−	0.00420271i
$397$			4.27254e37i			0.887614i	0.896122	+	0.443807i	$0.146372\pi$
$397$			4.27254e37i			0.887614i	−0.896122	+	0.443807i	$0.853628\pi$
$398$	−4.05370e37			−0.811983
$399$	4.40114e37	+	2.59883e37i	0.850078	+	0.501962i
$400$	−6.16967e37			−1.14919
$401$		−	3.95033e37i		−	0.709644i	−0.934934	−	0.354822i	$-0.884542\pi$
$401$		−	3.95033e37i		−	0.709644i	0.934934	−	0.354822i	$-0.115458\pi$
$402$	3.23308e37	−	2.22825e37i	0.560194	−	0.386088i
$403$	−1.31163e38			−2.19223
$404$	2.49775e36			0.0402735
$405$	−6.98969e37	−	6.22781e37i	−1.08733	−	0.968807i
$406$	−1.66098e37	−	3.58418e37i	−0.249308	−	0.537976i
$407$			2.22498e37i			0.322261i
$408$	6.47773e36	−	4.46447e36i	0.0905421	−	0.0624019i
$409$			4.52233e37i			0.610062i	0.952342	+	0.305031i	$0.0986668\pi$
$409$			4.52233e37i			0.610062i	−0.952342	+	0.305031i	$0.901333\pi$
$410$			2.02503e38i			2.63673i
$411$	7.07262e37	−	4.87447e37i	0.888943	−	0.612662i
$412$			1.21277e36i			0.0147152i
$413$	4.75583e37	+	1.02625e38i	0.557122	+	1.20220i
$414$	1.53978e37	−	4.04275e37i	0.174162	−	0.457269i
$415$	−8.41938e37			−0.919565
$416$	−8.80680e36			−0.0928892
$417$	1.06209e37	−	7.31999e36i	0.108191	−	0.0745655i
$418$			4.62572e37i			0.455117i
$419$	−7.07947e36			−0.0672818			−0.0336409	−	0.999434i	$-0.510710\pi$
$419$	−7.07947e36			−0.0672818			−0.0336409	+	0.999434i	$0.510710\pi$
$420$	2.09240e36	−	3.54350e36i	0.0192101	−	0.0325325i
$421$	1.12032e38			0.993695			0.496847	−	0.867838i	$-0.334491\pi$
$421$	1.12032e38			0.993695			0.496847	+	0.867838i	$0.334491\pi$
$422$		−	7.60224e37i		−	0.651495i
$423$	2.80640e37	−	7.36832e37i	0.232388	−	0.610145i
$424$	1.54629e38			1.23733
$425$	−1.61545e37			−0.124927
$426$	−8.70792e37	−	1.26348e38i	−0.650841	−	0.944338i
$427$	−1.73487e38	+	8.03972e37i	−1.25333	+	0.580814i
$428$			1.13915e36i			0.00795513i
$429$	−6.85110e37	−	9.94060e37i	−0.462519	−	0.671092i
$430$			2.76398e38i			1.80402i
$431$			1.65534e38i			1.04464i	0.852750	+	0.522319i	$0.174933\pi$
$431$			1.65534e38i			1.04464i	−0.852750	+	0.522319i	$0.825067\pi$
$432$	−1.63220e38	+	3.98618e37i	−0.995997	+	0.243244i
$433$		−	1.72286e38i		−	1.01666i	−0.861163	−	0.508330i	$-0.830263\pi$
$433$		−	1.72286e38i		−	1.01666i	0.861163	−	0.508330i	$-0.169737\pi$
$434$	−9.13585e37	−	1.97140e38i	−0.521372	−	1.12506i
$435$	1.27175e38	−	8.76492e37i	0.701950	−	0.483786i
$436$	3.92044e36			0.0209305
$437$	−9.23462e37			−0.476912
$438$	1.63696e38	+	2.37515e38i	0.817831	+	1.18663i
$439$			2.02612e38i			0.979332i	0.871910	+	0.489666i	$0.162881\pi$
$439$			2.02612e38i			0.979332i	−0.871910	+	0.489666i	$0.837119\pi$
$440$	−1.39835e38			−0.653961
$441$	−1.06720e38	−	1.93506e38i	−0.482934	−	0.875657i
$442$	−4.61651e37			−0.202158
$443$			6.37635e37i			0.270220i	0.990831	+	0.135110i	$0.0431388\pi$
$443$			6.37635e37i			0.270220i	−0.990831	+	0.135110i	$0.956861\pi$
$444$	−2.54143e36	−	3.68748e36i	−0.0104238	−	0.0151244i
$445$	2.55311e38			1.01356
$446$	4.06075e38			1.56045
$447$	−1.22090e38	+	8.41446e37i	−0.454171	+	0.313017i
$448$	1.13567e38	+	2.45063e38i	0.408997	+	0.882566i
$449$			2.27296e38i			0.792536i	0.918135	+	0.396268i	$0.129695\pi$
$449$			2.27296e38i			0.792536i	−0.918135	+	0.396268i	$0.870305\pi$
$450$	3.14255e38	+	1.19691e38i	1.06096	+	0.404093i
$451$			2.48861e38i			0.813573i
$452$		−	6.05878e36i		−	0.0191813i
$453$	−2.36447e38	−	3.43072e38i	−0.724952	−	1.05187i
$454$			9.89322e37i			0.293784i
$455$	8.22634e38	−	3.81224e38i	2.36614	−	1.09651i
$456$	1.98381e38	+	2.87841e38i	0.552726	+	0.801978i
$457$	−1.56674e38			−0.422875			−0.211438	−	0.977391i	$-0.567815\pi$
$457$	−1.56674e38			−0.422875			−0.211438	+	0.977391i	$0.567815\pi$
$458$	4.41485e38			1.15443
$459$	−4.27370e37	+	1.04373e37i	−0.108273	+	0.0264427i
$460$			7.43508e36i			0.0182514i
$461$	−6.49971e38			−1.54607			−0.773037	−	0.634360i	$-0.781264\pi$
$461$	−6.49971e38			−1.54607			−0.773037	+	0.634360i	$0.781264\pi$
$462$	1.01690e38	−	1.72213e38i	0.234406	−	0.396969i
$463$	1.98052e38			0.442441			0.221220	−	0.975224i	$-0.428996\pi$
$463$	1.98052e38			0.442441			0.221220	+	0.975224i	$0.428996\pi$
$464$		−	2.77201e38i		−	0.600183i
$465$	6.99497e38	−	4.82096e38i	1.46797	−	1.01173i
$466$	5.58055e38			1.13522
$467$	1.84901e38			0.364624			0.182312	−	0.983241i	$-0.441642\pi$
$467$	1.84901e38			0.364624			0.182312	+	0.983241i	$0.441642\pi$
$468$	2.27088e37	+	8.64917e36i	0.0434139	+	0.0165352i
$469$	1.52373e38	+	3.28802e38i	0.282424	+	0.609436i
$470$			5.35902e38i			0.963088i
$471$	−2.40892e38	+	1.66023e38i	−0.419777	+	0.289312i
$472$			7.73619e38i			1.30728i
$473$			3.39672e38i			0.556638i
$474$	−7.02871e38	+	4.84421e38i	−1.11709	+	0.769906i
$475$		−	7.17834e38i		−	1.10654i
$476$	−8.13101e35	−	1.75457e36i	−0.00121575	−	0.00262344i
$477$	−8.08055e38	−	3.07767e38i	−1.17199	−	0.446381i
$478$	−9.64817e38			−1.35750
$479$	−5.59195e38			−0.763305			−0.381652	−	0.924306i	$-0.624645\pi$
$479$	−5.59195e38			−0.763305			−0.381652	+	0.924306i	$0.624645\pi$
$480$	4.69672e37	−	3.23699e37i	0.0622009	−	0.0428690i
$481$		−	9.86715e38i		−	1.26791i
$482$	−7.70608e38			−0.960840
$483$	3.43799e38	+	2.03010e38i	0.415979	+	0.245631i
$484$	−1.75170e37			−0.0205685
$485$			3.42214e37i			0.0389980i
$486$	9.08698e38	+	1.13607e38i	1.00506	+	0.125655i
$487$	−1.68468e39			−1.80862			−0.904309	−	0.426877i	$-0.859614\pi$
$487$	−1.68468e39			−1.80862			−0.904309	+	0.426877i	$0.859614\pi$
$488$	−1.30780e39			−1.36287
$489$	−5.59498e38	−	8.11804e38i	−0.566005	−	0.821245i
$490$	1.14598e39	+	9.70905e38i	1.12547	+	0.953528i
$491$			1.10505e39i			1.05366i	0.849972	+	0.526828i	$0.176619\pi$
$491$			1.10505e39i			1.05366i	−0.849972	+	0.526828i	$0.823381\pi$
$492$	−2.84254e37	−	4.12439e37i	−0.0263156	−	0.0381826i
$493$		−	7.25816e37i		−	0.0652448i
$494$		−	2.05137e39i		−	1.79062i
$495$	7.30745e38	+	2.78322e38i	0.619428	+	0.235924i
$496$		−	1.52468e39i		−	1.25515i
$497$	1.28495e39	−	5.95468e38i	1.02735	−	0.476092i
$498$	6.78136e38	−	4.67373e38i	0.526612	−	0.362943i
$499$	−6.45263e38			−0.486720			−0.243360	−	0.969936i	$-0.578250\pi$
$499$	−6.45263e38			−0.486720			−0.243360	+	0.969936i	$0.578250\pi$
$500$	−6.23225e36			−0.00456646
$501$	1.94986e38	+	2.82915e38i	0.138790	+	0.201377i
$502$		−	3.32334e38i		−	0.229811i
$503$	−1.83229e39			−1.23100			−0.615499	−	0.788138i	$-0.711045\pi$
$503$	−1.83229e39			−1.23100			−0.615499	+	0.788138i	$0.711045\pi$
$504$	−1.05784e38	−	1.50773e39i	−0.0690520	−	0.984192i
$505$	−3.56440e39			−2.26080
$506$			3.61342e38i			0.222708i
$507$	2.09079e39	+	3.03363e39i	1.25226	+	1.81697i
$508$	−1.41011e37			−0.00820786
$509$	−1.09277e39			−0.618190			−0.309095	−	0.951031i	$-0.600026\pi$
$509$	−1.09277e39			−0.618190			−0.309095	+	0.951031i	$0.600026\pi$
$510$	2.46201e38	−	1.69683e38i	0.135370	−	0.0932975i
$511$	−2.41551e39	+	1.11939e39i	−1.29094	+	0.598246i
$512$			1.84477e39i			0.958359i
$513$	−4.63788e38	−	1.89904e39i	−0.234216	−	0.959031i
$514$		−	1.50177e39i		−	0.737287i
$515$		−	1.73067e39i		−	0.826056i
$516$	−3.87981e37	−	5.62941e37i	−0.0180049	−	0.0261242i
$517$			6.58582e38i			0.297164i
$518$	1.48305e39	−	6.87275e38i	0.650692	−	0.301543i
$519$	−8.31061e38	−	1.20583e39i	−0.354573	−	0.514468i
$520$	6.20127e39			2.57295
$521$	3.12908e38			0.126261			0.0631305	−	0.998005i	$-0.479892\pi$
$521$	3.12908e38			0.126261			0.0631305	+	0.998005i	$0.479892\pi$
$522$	−5.37768e38	+	1.41193e39i	−0.211044	+	0.554105i
$523$		−	3.64988e39i		−	1.39317i	−0.717474	−	0.696586i	$-0.754702\pi$
$523$		−	3.64988e39i		−	1.39317i	0.717474	−	0.696586i	$-0.245298\pi$
$524$	2.91861e37			0.0108361
$525$	−1.57805e39	+	2.67245e39i	−0.569917	+	0.965162i
$526$	2.82072e39			0.990983
$527$		−	3.99220e38i		−	0.136445i
$528$	1.15553e39	−	7.96398e38i	0.384230	−	0.264812i
$529$	2.36969e39			0.766627
$530$	5.87703e39			1.84994
$531$	1.53978e39	−	4.04275e39i	0.471615	−	1.23825i
$532$	7.79653e37	−	3.61305e37i	0.0232371	−	0.0107685i
$533$		−	1.10362e40i		−	3.20093i
$534$	−2.05640e39	+	1.41728e39i	−0.580442	+	0.400043i
$535$		−	1.62562e39i		−	0.446570i
$536$			2.47861e39i			0.662703i
$537$	−4.92807e39	+	3.39644e39i	−1.28248	+	0.883888i
$538$			5.36323e39i			1.35857i
$539$	1.40832e39	+	1.19317e39i	0.347267	+	0.294215i
$540$	−1.52898e38	+	3.73410e37i	−0.0367021	+	0.00896347i
$541$	1.94010e39			0.453382			0.226691	−	0.973967i	$-0.427209\pi$
$541$	1.94010e39			0.453382			0.226691	+	0.973967i	$0.427209\pi$
$542$	−6.59407e39			−1.50025
$543$	8.20665e38	−	5.65605e38i	0.181789	−	0.125290i
$544$		−	2.68053e37i		−	0.00578145i
$545$	−5.59463e39			−1.17496
$546$	−4.50964e39	+	7.63713e39i	−0.922250	+	1.56184i
$547$	2.66457e39			0.530654			0.265327	−	0.964158i	$-0.414520\pi$
$547$	2.66457e39			0.530654			0.265327	+	0.964158i	$0.414520\pi$
$548$		−	1.44412e38i		−	0.0280082i
$549$	6.83427e39	+	2.60299e39i	1.29090	+	0.491670i
$550$	−2.80882e39			−0.516731
$551$	3.22520e39			0.577907
$552$	1.54967e39	+	2.24850e39i	0.270472	+	0.392442i
$553$	−3.31259e39	−	7.14816e39i	−0.563188	−	1.21529i
$554$			7.84770e39i			1.29972i
$555$	3.62673e39	+	5.26220e39i	0.585149	+	0.849023i
$556$		−	2.16863e37i		−	0.00340880i
$557$		−	5.86087e39i		−	0.897557i	−0.893643	−	0.448779i	$-0.851859\pi$
$557$		−	5.86087e39i		−	0.897557i	0.893643	−	0.448779i	$-0.148141\pi$
$558$	−2.95788e39	+	7.76605e39i	−0.441352	+	1.15879i
$559$		−	1.50635e40i		−	2.19005i
$560$	4.43149e39	+	9.56261e39i	0.627803	+	1.35472i
$561$	3.02562e38	−	2.08527e38i	0.0417689	−	0.0287873i
$562$	−6.09599e39			−0.820101
$563$	−2.96898e39			−0.389256			−0.194628	−	0.980877i	$-0.562350\pi$
$563$	−2.96898e39			−0.389256			−0.194628	+	0.980877i	$0.562350\pi$
$564$	−7.52247e37	−	1.09147e38i	−0.00961200	−	0.0139465i
$565$			8.64614e39i			1.07676i
$566$	−8.36352e39			−1.01520
$567$	−2.44811e39	+	8.08958e39i	−0.289652	+	0.957132i
$568$	9.68633e39			1.11714
$569$			9.01376e39i			1.01339i	0.862124	+	0.506697i	$0.169134\pi$
$569$			9.01376e39i			1.01339i	−0.862124	+	0.506697i	$0.830866\pi$
$570$	7.53993e39	+	1.09401e40i	0.826384	+	1.19904i
$571$	−6.18707e39			−0.661092			−0.330546	−	0.943790i	$-0.607233\pi$
$571$	−6.18707e39			−0.661092			−0.330546	+	0.943790i	$0.607233\pi$
$572$	−2.02972e38			−0.0211443
$573$	−6.10985e39	+	4.21093e39i	−0.620567	+	0.427697i
$574$	1.65877e40	−	7.68705e39i	1.64272	−	0.761268i
$575$		−	5.60742e39i		−	0.541477i
$576$	3.67691e39	−	9.65390e39i	0.346224	−	0.909027i
$577$			5.79829e39i			0.532416i	0.963916	+	0.266208i	$0.0857707\pi$
$577$			5.79829e39i			0.532416i	−0.963916	+	0.266208i	$0.914229\pi$
$578$			1.11709e40i			1.00031i
$579$	−1.01550e40	−	1.47344e40i	−0.886830	−	1.28675i
$580$		−	2.59671e38i		−	0.0221165i
$581$	3.19601e39	+	6.89660e39i	0.265494	+	0.572903i
$582$	−1.89969e38	−	2.75635e38i	−0.0153921	−	0.0223332i
$583$	7.22242e39			0.570806
$584$	−1.82089e40			−1.40377
$585$	−3.24064e40	−	1.23427e40i	−2.43709	−	0.928221i
$586$		−	1.30595e40i		−	0.958101i
$587$	2.32280e40			1.66249			0.831245	−	0.555907i	$-0.187629\pi$
$587$	2.32280e40			1.66249			0.831245	+	0.555907i	$0.187629\pi$
$588$	−3.69688e38	−	3.68835e37i	−0.0258145	−	0.00257550i
$589$	1.77395e40			1.20857
$590$			2.94032e40i			1.95452i
$591$	6.48937e39	−	4.47249e39i	0.420905	−	0.290089i
$592$	1.14700e40			0.725934
$593$	2.10136e40			1.29780			0.648899	−	0.760875i	$-0.275230\pi$
$593$	2.10136e40			1.29780			0.648899	+	0.760875i	$0.275230\pi$
$594$	−7.43077e39	+	1.81476e39i	−0.447848	+	0.109374i
$595$	1.16033e39	+	2.50385e39i	0.0682474	+	0.147269i
$596$			2.49288e38i			0.0143097i
$597$	−1.17819e40	+	8.12016e39i	−0.660069	+	0.454922i
$598$		−	1.60245e40i		−	0.876226i
$599$		−	1.68953e40i		−	0.901728i	−0.892593	−	0.450864i	$-0.851116\pi$
$599$		−	1.68953e40i		−	0.901728i	0.892593	−	0.450864i	$-0.148884\pi$
$600$	−1.74782e40	+	1.20460e40i	−0.910550	+	0.627555i
$601$			7.63589e39i			0.388311i	0.980971	+	0.194156i	$0.0621966\pi$
$601$			7.63589e39i			0.388311i	−0.980971	+	0.194156i	$0.937803\pi$
$602$	2.26407e40	−	1.04921e40i	1.12393	−	0.520852i
$603$	4.93333e39	−	1.29527e40i	0.239078	−	0.627709i
$604$	−7.00500e38			−0.0331415
$605$	2.49975e40			1.15463
$606$	2.87093e40	−	1.97866e40i	1.29470	−	0.892314i
$607$			1.38282e40i			0.608878i	0.952532	+	0.304439i	$0.0984690\pi$
$607$			1.38282e40i			0.608878i	−0.952532	+	0.304439i	$0.901531\pi$
$608$	1.19111e39			0.0512093
$609$	−1.20072e40	−	7.09013e39i	−0.504071	−	0.297648i
$610$	−4.97060e40			−2.03764
$611$		−	2.92062e40i		−	1.16917i
$612$	−2.63255e37	+	6.91187e37i	−0.00102916	+	0.00270209i
$613$	1.09697e40			0.418812			0.209406	−	0.977829i	$-0.432847\pi$
$613$	1.09697e40			0.418812			0.209406	+	0.977829i	$0.432847\pi$
$614$	−1.98648e40			−0.740702
$615$	4.05643e40	+	5.88569e40i	1.47725	+	2.14342i
$616$	5.30816e39	+	1.14544e40i	0.188809	+	0.407428i
$617$		−	4.32531e39i		−	0.150273i	−0.997173	−	0.0751367i	$-0.976061\pi$
$617$		−	4.32531e39i		−	0.150273i	0.997173	−	0.0751367i	$-0.0239393\pi$
$618$	9.60723e39	+	1.39396e40i	0.326036	+	0.473062i
$619$		−	4.58735e40i		−	1.52071i	−0.649506	−	0.760357i	$-0.725024\pi$
$619$		−	4.58735e40i		−	1.52071i	0.649506	−	0.760357i	$-0.274976\pi$
$620$		−	1.42826e39i		−	0.0462518i
$621$	−3.62292e39	−	1.48345e40i	−0.114612	−	0.469294i
$622$		−	3.60634e40i		−	1.11457i
$623$	−9.69167e39	−	2.09134e40i	−0.292632	−	0.631464i
$624$	−5.12445e40	+	3.53179e40i	−1.51172	+	1.04188i
$625$	−2.99942e40			−0.864524
$626$	−5.48578e40			−1.54494
$627$	9.26600e39	+	1.34445e40i	0.254984	+	0.369969i
$628$			4.91863e38i			0.0132260i
$629$	3.00327e39			0.0789150
$630$	−4.02056e39	−	5.73047e40i	−0.103240	−	1.47147i
$631$	−1.09303e40			−0.274288			−0.137144	−	0.990551i	$-0.543792\pi$
$631$	−1.09303e40			−0.274288			−0.137144	+	0.990551i	$0.543792\pi$
$632$		−	5.38851e40i		−	1.32151i
$633$	−1.52284e40	−	2.20957e40i	−0.365007	−	0.529606i
$634$	2.26815e40			0.531347
$635$	2.01229e40			0.460757
$636$	−1.19698e39	+	8.24961e38i	−0.0267891	+	0.0184631i
$637$	−6.24547e40	−	5.29134e40i	−1.36629	−	1.15756i
$638$		−	1.26199e40i		−	0.269871i
$639$	−5.06186e40	−	1.92793e40i	−1.05815	−	0.403021i
$640$			7.39099e40i			1.51040i
$641$		−	2.14381e40i		−	0.428297i	−0.976801	−	0.214149i	$-0.931302\pi$
$641$		−	2.14381e40i		−	0.428297i	0.976801	−	0.214149i	$-0.0686977\pi$
$642$	9.02409e39	+	1.30935e40i	0.176257	+	0.255740i
$643$		−	5.85246e40i		−	1.11758i	−0.829309	−	0.558791i	$-0.811266\pi$
$643$		−	5.85246e40i		−	1.11758i	0.829309	−	0.558791i	$-0.188734\pi$
$644$	6.09033e38	−	2.82237e38i	0.0113709	−	0.00526949i
$645$	5.53666e40	+	8.03342e40i	1.01072	+	1.46651i
$646$	6.24376e39			0.111449
$647$	−1.08177e41			−1.88809			−0.944045	−	0.329817i	$-0.893013\pi$
$647$	−1.08177e41			−1.88809			−0.944045	+	0.329817i	$0.893013\pi$
$648$	−3.84560e40	+	4.31606e40i	−0.656337	+	0.736630i
$649$			3.61342e40i			0.603074i
$650$	1.24563e41			2.03304
$651$	−6.60432e40	−	3.89978e40i	−1.05415	−	0.622466i
$652$	−1.65758e39			−0.0258752
$653$			1.08910e40i			0.166275i	0.996538	+	0.0831375i	$0.0264941\pi$
$653$			1.08910e40i			0.166275i	−0.996538	+	0.0831375i	$0.973506\pi$
$654$	4.50618e40	−	3.10567e40i	0.672870	−	0.463744i
$655$	−4.16499e40			−0.608296
$656$	1.28289e41			1.83267
$657$	9.51555e40	+	3.62422e40i	1.32965	+	0.506427i
$658$	4.38975e40	−	2.03429e40i	0.600019	−	0.278060i
$659$			7.93936e40i			1.06157i	0.847508	+	0.530783i	$0.178102\pi$
$659$			7.93936e40i			1.06157i	−0.847508	+	0.530783i	$0.821898\pi$
$660$	1.08246e39	−	7.46034e38i	0.0141587	−	0.00975824i
$661$		−	2.45659e39i		−	0.0314349i	−0.999876	−	0.0157174i	$-0.994997\pi$
$661$		−	2.45659e39i		−	0.0314349i	0.999876	−	0.0157174i	$-0.00500323\pi$
$662$			1.32191e41i			1.65486i
$663$	−1.34178e40	+	9.24756e39i	−0.164336	+	0.113261i
$664$			5.19887e40i			0.622977i
$665$	−1.11260e41	+	5.15599e40i	−1.30444	+	0.604502i
$666$	−5.84227e40	−	2.22517e40i	−0.670201	−	0.255262i
$667$	2.51939e40			0.282795
$668$	5.77669e38			0.00634484
$669$	1.18024e41	−	8.13429e40i	1.26851	−	0.874260i
$670$			9.42054e40i			0.990812i
$671$	−6.10849e40			−0.628720
$672$	−4.43441e39	−	2.61847e39i	−0.0446665	−	0.0263751i
$673$	−1.64622e40			−0.162281			−0.0811406	−	0.996703i	$-0.525856\pi$
$673$	−1.64622e40			−0.162281			−0.0811406	+	0.996703i	$0.525856\pi$
$674$		−	1.12287e41i		−	1.08333i
$675$	1.15313e41	−	2.81620e40i	1.08887	−	0.265925i
$676$	6.19420e39			0.0572477
$677$	−1.26236e41			−1.14195			−0.570975	−	0.820967i	$-0.693435\pi$
$677$	−1.26236e41			−1.14195			−0.570975	+	0.820967i	$0.693435\pi$
$678$	−4.79962e40	−	6.96401e40i	−0.424987	−	0.616636i
$679$	2.80319e39	−	1.29905e39i	0.0242963	−	0.0112594i
$680$			1.88748e40i			0.160141i
$681$	1.98176e40	+	2.87543e40i	0.164595	+	0.238820i
$682$		−	6.94131e40i		−	0.564376i
$683$			5.39341e40i			0.429302i	0.976691	+	0.214651i	$0.0688615\pi$
$683$			5.39341e40i			0.429302i	−0.976691	+	0.214651i	$0.931139\pi$
$684$	−3.07132e39	−	1.16979e39i	−0.0239338	−	0.00911576i
$685$			2.06082e41i			1.57227i
$686$	3.60287e40	−	1.30727e41i	0.269122	−	0.976482i
$687$	1.28316e41	−	8.84359e40i	0.938444	−	0.646779i
$688$	1.75103e41			1.25390
$689$	−3.20293e41			−2.24579
$690$	5.88989e40	+	8.54593e40i	0.404385	+	0.586743i
$691$			7.81794e40i			0.525606i	0.964849	+	0.262803i	$0.0846470\pi$
$691$			7.81794e40i			0.525606i	−0.964849	+	0.262803i	$0.915353\pi$
$692$	−2.46211e39			−0.0162095
$693$	−4.94096e39	−	7.04230e40i	−0.0318551	−	0.454028i
$694$	4.11913e40			0.260072
$695$			3.09473e40i			0.191356i
$696$	−5.41224e40	−	7.85289e40i	−0.327750	−	0.475549i
$697$	3.35910e40			0.199227
$698$	−2.10161e41			−1.22081
$699$	1.62197e41	−	1.11787e41i	0.922834	−	0.636020i
$700$	2.19391e39	+	4.73419e39i	0.0122264	+	0.0263830i
$701$		−	3.07719e41i		−	1.67974i	−0.542785	−	0.839872i	$-0.682630\pi$
$701$		−	3.07719e41i		−	1.67974i	0.542785	−	0.839872i	$-0.317370\pi$
$702$	3.29533e41	−	8.04792e40i	1.76202	−	0.430324i
$703$			1.33452e41i			0.698991i
$704$			8.62868e40i			0.442732i
$705$	1.07349e41	+	1.55758e41i	0.539580	+	0.782904i
$706$			3.42887e41i			1.68843i
$707$	1.35305e41	+	2.91972e41i	0.652730	+	1.40851i
$708$	−4.12734e39	−	5.98856e39i	−0.0195069	−	0.0283035i
$709$	−4.46581e40			−0.206790			−0.103395	−	0.994640i	$-0.532971\pi$
$709$	−4.46581e40			−0.206790			−0.103395	+	0.994640i	$0.532971\pi$
$710$	3.68152e41			1.67025
$711$	−1.07251e41	+	2.81591e41i	−0.476750	+	1.25173i
$712$		−	1.57652e41i		−	0.686656i
$713$	1.38574e41			0.591403
$714$	−2.32451e40	−	1.37260e40i	−0.0972094	−	0.0574011i
$715$	2.89649e41			1.18696
$716$			1.00623e40i			0.0404074i
$717$	−2.80421e41	+	1.93267e41i	−1.10353	+	0.760554i
$718$	−2.48742e41			−0.959277
$719$	6.81653e40			0.257629			0.128814	−	0.991669i	$-0.458883\pi$
$719$	6.81653e40			0.257629			0.128814	+	0.991669i	$0.458883\pi$
$720$	1.43477e41	−	3.76705e41i	0.531448	−	1.39534i
$721$	−1.41765e41	+	6.56965e40i	−0.514645	+	0.238496i
$722$		−	7.23153e39i		−	0.0257300i
$723$	−2.23975e41	+	1.54364e41i	−0.781076	+	0.538320i
$724$		−	1.67567e39i		−	0.00572769i
$725$			1.95840e41i			0.656145i
$726$	−2.01342e41	+	1.38765e41i	−0.661231	+	0.455722i
$727$			8.26628e40i			0.266110i	0.991109	+	0.133055i	$0.0424787\pi$
$727$			8.26628e40i			0.266110i	−0.991109	+	0.133055i	$0.957521\pi$
$728$	−2.35401e41	−	5.07967e41i	−0.742855	−	1.60299i
$729$	2.86867e41	−	1.49006e41i	0.887426	−	0.460951i
$730$	−6.92071e41			−2.09879
$731$	4.58487e40			0.136309
$732$	1.01237e40	−	6.97726e39i	0.0295071	−	0.0203364i
$733$			1.95437e41i			0.558469i	0.960223	+	0.279235i	$0.0900807\pi$
$733$			1.95437e41i			0.558469i	−0.960223	+	0.279235i	$0.909919\pi$
$734$	3.31967e41			0.930041
$735$	5.27561e41	+	5.26344e40i	1.44913	+	0.144578i
$736$	9.30443e39			0.0250589
$737$			1.15771e41i			0.305719i
$738$	−6.53448e41	−	2.48881e41i	−1.69197	−	0.644428i
$739$	5.29225e41			1.34368			0.671841	−	0.740696i	$-0.265504\pi$
$739$	5.29225e41			1.34368			0.671841	+	0.740696i	$0.265504\pi$
$740$	1.07446e40			0.0267504
$741$	−4.10920e41	−	5.96224e41i	−1.00321	−	1.45561i
$742$	−2.23093e41	−	4.81408e41i	−0.534109	−	1.15254i
$743$			4.92649e41i			1.15664i	0.815809	+	0.578322i	$0.196292\pi$
$743$			4.92649e41i			1.15664i	−0.815809	+	0.578322i	$0.803708\pi$
$744$	−2.97689e41	−	4.31932e41i	−0.685417	−	0.994506i
$745$		−	3.55745e41i		−	0.803291i
$746$		−	5.27676e40i		−	0.116857i
$747$	1.03476e41	−	2.71681e41i	0.224746	−	0.590080i
$748$		−	6.17785e38i		−	0.00131603i
$749$	−1.33160e41	+	6.17089e40i	−0.278220	+	0.128932i
$750$	−7.16340e40	+	4.93704e40i	−0.146802	+	0.101176i
$751$	−3.73723e41			−0.751226			−0.375613	−	0.926777i	$-0.622568\pi$
$751$	−3.73723e41			−0.751226			−0.375613	+	0.926777i	$0.622568\pi$
$752$	3.39504e41			0.669400
$753$	−6.65714e40	−	9.65917e40i	−0.128754	−	0.186815i
$754$			5.59656e41i			1.06178i
$755$	9.99645e41			1.86044
$756$	8.86275e39	+	1.11069e40i	0.0161809	+	0.0202781i
$757$	−3.70327e41			−0.663278			−0.331639	−	0.943406i	$-0.607602\pi$
$757$	−3.70327e41			−0.663278			−0.331639	+	0.943406i	$0.607602\pi$
$758$		−	1.68014e41i		−	0.295217i
$759$	7.23822e40	+	1.05023e41i	0.124774	+	0.181042i
$760$	−8.38711e41			−1.41845
$761$	−9.61317e41			−1.59510			−0.797552	−	0.603250i	$-0.793872\pi$
$761$	−9.61317e41			−1.59510			−0.797552	+	0.603250i	$0.793872\pi$
$762$	−1.62079e41	+	1.11706e41i	−0.263864	+	0.181856i
$763$	2.12373e41	+	4.58276e41i	0.339230	+	0.732017i
$764$			1.24754e40i			0.0195524i
$765$	3.75676e40	−	9.86355e40i	0.0577727	−	0.151685i
$766$			5.87224e41i			0.886108i
$767$		−	1.60245e42i		−	2.37274i
$768$	−3.03763e40	−	4.40745e40i	−0.0441364	−	0.0640398i
$769$		−	1.22108e41i		−	0.174106i	−0.996204	−	0.0870528i	$-0.972255\pi$
$769$		−	1.22108e41i		−	0.174106i	0.996204	−	0.0870528i	$-0.0277449\pi$
$770$	2.01749e41	+	4.35350e41i	0.282290	+	0.609148i
$771$	−3.00826e41	−	4.36483e41i	−0.413073	−	0.599348i
$772$	−3.00853e40			−0.0405419
$773$	1.73439e41			0.229374			0.114687	−	0.993402i	$-0.463414\pi$
$773$	1.73439e41			0.229374			0.114687	+	0.993402i	$0.463414\pi$
$774$	−8.91897e41	−	3.39700e41i	−1.15763	−	0.440912i
$775$			1.07718e42i			1.37218i
$776$	2.11313e40			0.0264199
$777$	2.93374e41	−	4.96832e41i	0.360012	−	0.609684i
$778$	−1.26513e42			−1.52381
$779$			1.49263e42i			1.76466i
$780$	−4.80038e40	+	3.30844e40i	−0.0557063	+	0.0383930i
$781$	4.52430e41			0.515361
$782$	4.87737e40			0.0545366
$783$	1.26531e41	+	5.18097e41i	0.138883	+	0.568677i
$784$	6.15086e41	−	7.25997e41i	0.662755	−	0.782262i
$785$		−	7.01910e41i		−	0.742458i
$786$	3.35468e41	−	2.31205e41i	0.348356	−	0.240088i
$787$		−	5.00187e41i		−	0.509916i	−0.966952	−	0.254958i	$-0.917938\pi$
$787$		−	5.00187e41i		−	0.509916i	0.966952	−	0.254958i	$-0.0820617\pi$
$788$		−	1.32503e40i		−	0.0132616i
$789$	8.19832e41	−	5.65031e41i	0.805580	−	0.555208i
$790$		−	2.04803e42i		−	1.97580i
$791$	7.08235e41	−	3.28209e41i	0.670840	−	0.310879i
$792$	1.71860e41	−	4.51227e41i	0.159831	−	0.419643i
$793$	2.70894e42			2.47365
$794$	1.00273e42			0.899054
$795$	1.70814e42	−	1.17726e42i	1.50383	−	1.03645i
$796$			2.40569e40i			0.0207970i
$797$	−2.15565e42			−1.82992			−0.914959	−	0.403546i	$-0.867777\pi$
$797$	−2.15565e42			−1.82992			−0.914959	+	0.403546i	$0.867777\pi$
$798$	6.09921e41	−	1.03291e42i	0.508431	−	0.861034i
$799$	8.88949e40			0.0727693
$800$			7.23261e40i			0.0581420i
$801$	−3.13784e41	+	8.23853e41i	−0.247719	+	0.650397i
$802$	−9.27108e41			−0.718790
$803$	−8.50502e41			−0.647590
$804$	−1.32237e40	−	1.91869e40i	−0.00988869	−	0.0143480i
$805$	−8.69116e41	+	4.02764e41i	−0.638319	+	0.295809i
$806$			3.07827e42i			2.22049i
$807$	1.07433e42	+	1.55880e42i	0.761154	+	1.10440i
$808$			2.20098e42i			1.53162i
$809$		−	2.89721e42i		−	1.98028i	−0.140075	−	0.990141i	$-0.544734\pi$
$809$		−	2.89721e42i		−	1.98028i	0.140075	−	0.990141i	$-0.455266\pi$
$810$	−1.46161e42	+	1.64042e42i	−0.981294	+	1.10134i
$811$		−	2.56710e42i		−	1.69294i	−0.532440	−	0.846468i	$-0.678725\pi$
$811$		−	2.56710e42i		−	1.69294i	0.532440	−	0.846468i	$-0.321275\pi$
$812$	−2.12705e40	+	9.85715e39i	−0.0137789	+	0.00638541i
$813$	−1.91654e42	+	1.32089e42i	−1.21957	+	0.840531i
$814$	5.22184e41			0.326414
$815$	2.36544e42			1.45253
$816$	−1.07497e41	−	1.55973e41i	−0.0648470	−	0.0940898i
$817$			2.03731e42i			1.20736i
$818$	1.06135e42			0.617924
$819$	2.19117e41	+	3.12305e42i	0.125331	+	1.78633i
$820$	1.20176e41			0.0675334
$821$			1.37843e42i			0.761040i	0.924773	+	0.380520i	$0.124255\pi$
$821$			1.37843e42i			0.761040i	−0.924773	+	0.380520i	$0.875745\pi$
$822$	−1.14400e42	−	1.65988e42i	−0.620559	−	0.900400i
$823$	8.44387e41			0.450033			0.225016	−	0.974355i	$-0.427756\pi$
$823$	8.44387e41			0.450033			0.225016	+	0.974355i	$0.427756\pi$
$824$	−1.06867e42			−0.559627
$825$	−8.16374e41	+	5.62648e41i	−0.420056	+	0.289504i
$826$	2.40852e42	−	1.11615e42i	1.21770	−	0.564302i
$827$			2.11848e41i			0.105243i	0.998615	+	0.0526216i	$0.0167577\pi$
$827$			2.11848e41i			0.105243i	−0.998615	+	0.0526216i	$0.983242\pi$
$828$	−2.39919e40	−	9.13788e39i	−0.0117118	−	0.00446073i
$829$			3.21127e42i			1.54041i	0.637796	+	0.770205i	$0.279846\pi$
$829$			3.21127e42i			1.54041i	−0.637796	+	0.770205i	$0.720154\pi$
$830$			1.97595e42i			0.931417i
$831$	1.57201e42	+	2.28091e42i	0.728183	+	1.05656i
$832$		−	3.82657e42i		−	1.74189i
$833$	1.61053e41	−	1.90093e41i	0.0720470	−	0.0850383i
$834$	−1.71794e41	−	2.49264e41i	−0.0755265	−	0.109585i
$835$	−8.24359e41			−0.356174
$836$	2.74516e40			0.0116567
$837$	6.95956e41	+	2.84968e42i	0.290444	+	1.18926i
$838$			1.66149e41i			0.0681489i
$839$	−2.48505e42			−1.00181			−0.500906	−	0.865502i	$-0.667000\pi$
$839$	−2.48505e42			−1.00181			−0.500906	+	0.865502i	$0.667000\pi$
$840$	3.12247e42	+	1.84378e42i	1.23723	+	0.730568i
$841$	1.68779e42			0.657318
$842$		−	2.62930e42i		−	1.00650i
$843$	−1.77178e42	+	1.22112e42i	−0.666668	+	0.459470i
$844$	−4.51159e40			−0.0166865
$845$	−8.83939e42			−3.21366
$846$	−1.72928e42	−	6.58636e41i	−0.618008	−	0.235383i
$847$	−9.48911e41	−	2.04763e42i	−0.333362	−	0.719355i
$848$		−	3.72321e42i		−	1.28581i
$849$	−2.43083e42	+	1.67534e42i	−0.825264	+	0.568775i
$850$			3.79132e41i			0.126537i
$851$			1.04247e42i			0.342046i
$852$	−7.49816e40	+	5.16776e40i	−0.0241869	+	0.0166697i
$853$		−	4.06963e42i		−	1.29061i	−0.763926	−	0.645304i	$-0.776731\pi$
$853$		−	4.06963e42i		−	1.29061i	0.763926	−	0.645304i	$-0.223269\pi$
$854$	1.88685e42	+	4.07159e42i	0.588299	+	1.26948i
$855$	4.38291e42	+	1.66934e42i	1.34355	+	0.511723i
$856$	−1.00380e42			−0.302537
$857$	−5.78254e39			−0.00171355			−0.000856774	−	1.00000i	$-0.500273\pi$
$857$	−5.78254e39			−0.00171355			−0.000856774		1.00000i	$0.500273\pi$
$858$	−2.33297e42	+	1.60789e42i	−0.679741	+	0.468480i
$859$			1.94307e42i			0.556657i	0.960486	+	0.278329i	$0.0897804\pi$
$859$			1.94307e42i			0.556657i	−0.960486	+	0.278329i	$0.910220\pi$
$860$	1.64030e41			0.0462057
$861$	3.28134e42	−	5.55698e42i	0.908877	−	1.53919i
$862$	3.88492e42			1.05810
$863$		−	3.43694e42i		−	0.920482i	−0.887794	−	0.460241i	$-0.847763\pi$
$863$		−	3.43694e42i		−	0.920482i	0.887794	−	0.460241i	$-0.152237\pi$
$864$	4.67294e40	+	1.91340e41i	0.0123067	+	0.0503913i
$865$	3.51354e42			0.909938
$866$	−4.04340e42			−1.02976
$867$	2.23769e42	+	3.24677e42i	0.560431	+	0.813158i
$868$	−1.16994e41	+	5.42172e40i	−0.0288156	+	0.0133537i
$869$		−	2.51687e42i		−	0.609640i
$870$	−2.05705e42	−	2.98467e42i	−0.490022	−	0.710997i
$871$		−	5.13411e42i		−	1.20282i
$872$			3.45462e42i			0.795997i
$873$	−1.10427e41	−	4.20589e40i	−0.0250248	−	0.00953128i
$874$			2.16728e42i			0.483058i
$875$	−3.37606e41	−	7.28513e41i	−0.0740106	−	0.159706i
$876$	1.40954e41	−	9.71463e40i	0.0303927	−	0.0209468i
$877$	−1.49480e42			−0.317021			−0.158511	−	0.987357i	$-0.550669\pi$
$877$	−1.49480e42			−0.317021			−0.158511	+	0.987357i	$0.550669\pi$
$878$	4.75513e42			0.991954
$879$	−2.61601e42	−	3.79570e42i	−0.536786	−	0.778849i
$880$			3.36700e42i			0.679585i
$881$	6.83529e42			1.35708			0.678541	−	0.734563i	$-0.262613\pi$
$881$	6.83529e42			1.35708			0.678541	+	0.734563i	$0.262613\pi$
$882$	−4.54140e42	+	2.50463e42i	−0.886942	+	0.489159i
$883$	−2.08582e42			−0.400725			−0.200363	−	0.979722i	$-0.564212\pi$
$883$	−2.08582e42			−0.400725			−0.200363	+	0.979722i	$0.564212\pi$
$884$			2.73969e40i			0.00517779i
$885$	5.88989e42	+	8.54594e42i	1.09504	+	1.58885i
$886$	1.49647e42			0.273703
$887$	2.03398e41			0.0365977			0.0182989	−	0.999833i	$-0.494175\pi$
$887$	2.03398e41			0.0365977			0.0182989	+	0.999833i	$0.494175\pi$
$888$	3.24935e42	−	2.23946e42i	0.575186	−	0.396420i
$889$	−7.63870e41	−	1.64834e42i	−0.133028	−	0.287059i
$890$		−	5.99193e42i		−	1.02662i
$891$	−1.79621e42	+	2.01595e42i	−0.302782	+	0.339823i
$892$		−	2.40988e41i		−	0.0399672i
$893$			3.95009e42i			0.644556i
$894$	1.97480e42	+	2.86534e42i	0.317051	+	0.460025i
$895$		−	1.43594e43i		−	2.26831i
$896$	6.05422e42	−	2.80564e42i	0.941005	−	0.436079i
$897$	−3.20994e42	−	4.65746e42i	−0.490915	−	0.712293i
$898$	5.33442e42			0.802750
$899$	−4.83970e42			−0.716644
$900$	7.10315e40	−	1.86496e41i	0.0103499	−	0.0271740i
$901$		−	9.74877e41i		−	0.139778i
$902$	5.84054e42			0.824058
$903$	4.47873e42	−	7.58477e42i	0.621845	−	1.05310i
$904$	5.33890e42			0.729473
$905$			2.39125e42i			0.321530i
$906$	−8.05160e42	+	5.54919e42i	−1.06543	+	0.734295i
$907$	−1.41709e43			−1.84540			−0.922700	−	0.385520i	$-0.874022\pi$
$907$	−1.41709e43			−1.84540			−0.922700	+	0.385520i	$0.874022\pi$
$908$	5.87118e40			0.00752456
$909$	4.38073e42	−	1.15018e43i	0.552549	−	1.45074i
$910$	−8.94697e42	−	1.93065e43i	−1.11065	−	2.39664i
$911$		−	4.06331e42i		−	0.496436i	−0.968704	−	0.248218i	$-0.920155\pi$
$911$		−	4.06331e42i		−	0.496436i	0.968704	−	0.248218i	$-0.0798449\pi$
$912$	6.93074e42	−	4.77669e42i	0.833402	−	0.574383i
$913$			2.42829e42i			0.287392i
$914$			3.67700e42i			0.428326i
$915$	−1.44469e43	+	9.95685e42i	−1.65641	+	1.14161i
$916$		−	2.62001e41i		−	0.0295678i
$917$	1.58104e42	+	3.41169e42i	0.175625	+	0.378978i
$918$	2.44955e41	+	1.00300e42i	0.0267835	+	0.109669i
$919$	−1.09037e43			−1.17355			−0.586773	−	0.809752i	$-0.699602\pi$
$919$	−1.09037e43			−1.17355			−0.586773	+	0.809752i	$0.699602\pi$
$920$	−6.55167e42			−0.694110
$921$	−5.77365e42	+	3.97922e42i	−0.602124	+	0.414986i
$922$			1.52542e43i			1.56600i
$923$	−2.00639e43			−2.02764
$924$	−1.02201e41	−	6.03483e40i	−0.0101674	−	0.00600373i
$925$	−8.10341e42			−0.793621
$926$		−	4.64811e42i		−	0.448143i
$927$	5.58462e42	+	2.12703e42i	0.530075	+	0.201892i
$928$	−3.24958e41			−0.0303656
$929$	1.03700e43			0.954006			0.477003	−	0.878902i	$-0.341723\pi$
$929$	1.03700e43			0.954006			0.477003	+	0.878902i	$0.341723\pi$
$930$	−1.13144e43	−	1.64166e43i	−1.02477	−	1.48689i
$931$	8.44689e42	+	7.15646e42i	0.753228	+	0.638157i
$932$		−	3.31181e41i		−	0.0290760i
$933$	−7.22403e42	−	1.04817e43i	−0.624447	−	0.906042i
$934$		−	4.33947e42i		−	0.369324i
$935$			8.81606e41i			0.0738765i
$936$	−7.62150e42	+	2.00106e43i	−0.628841	+	1.65105i
$937$			1.82929e42i			0.148614i	0.997235	+	0.0743070i	$0.0236745\pi$
$937$			1.82929e42i			0.148614i	−0.997235	+	0.0743070i	$0.976326\pi$
$938$	7.71669e42	−	3.57606e42i	0.617291	−	0.286064i
$939$	−1.59442e43	+	1.09888e43i	−1.25589	+	0.865566i
$940$	3.18034e41			0.0246672
$941$	1.14657e43			0.875693			0.437846	−	0.899050i	$-0.355741\pi$
$941$	1.14657e43			0.875693			0.437846	+	0.899050i	$0.355741\pi$
$942$	3.89642e42	+	5.65351e42i	0.293041	+	0.425187i
$943$			1.16598e43i			0.863521i
$944$	1.86275e43			1.35850
$945$	−1.26475e43	−	1.58500e43i	−0.908332	−	1.13833i
$946$	7.97180e42			0.563813
$947$			2.28165e42i			0.158918i	0.996838	+	0.0794592i	$0.0253193\pi$
$947$			2.28165e42i			0.158918i	−0.996838	+	0.0794592i	$0.974681\pi$
$948$	2.87482e41	+	4.17123e41i	0.0197193	+	0.0286117i
$949$	3.77173e43			2.54789
$950$	−1.68469e43			−1.12080
$951$	6.59232e42	−	4.54345e42i	0.431937	−	0.297693i
$952$	1.54610e42	−	7.16491e41i	0.0997705	−	0.0462355i
$953$			2.37993e43i			1.51257i	0.654240	+	0.756287i	$0.272989\pi$
$953$			2.37993e43i			1.51257i	−0.654240	+	0.756287i	$0.727011\pi$
$954$	−7.22301e42	+	1.89643e43i	−0.452134	+	1.18710i
$955$		−	1.78029e43i		−	1.09759i
$956$			5.72576e41i			0.0347691i
$957$	−2.52795e42	−	3.66793e42i	−0.151198	−	0.219381i
$958$			1.31238e43i			0.773143i
$959$	1.68809e43	−	7.82291e42i	0.979547	−	0.453940i
$960$	1.40648e43	+	2.04073e43i	0.803896	+	1.16641i
$961$	−8.85790e42			−0.498702
$962$	−2.31573e43			−1.28425
$963$	5.24564e42	+	1.99793e42i	0.286561	+	0.109144i
$964$			4.57321e41i			0.0246096i
$965$	4.29331e43			2.27586
$966$	4.76445e42	−	8.06866e42i	0.248797	−	0.421340i
$967$	−1.27159e43			−0.654127			−0.327063	−	0.945002i	$-0.606059\pi$
$967$	−1.27159e43			−0.654127			−0.327063	+	0.945002i	$0.606059\pi$
$968$		−	1.54357e43i		−	0.782229i
$969$	1.81473e42	−	1.25072e42i	0.0905977	−	0.0624402i
$970$	8.03145e41			0.0395006
$971$	−9.94012e42			−0.481629			−0.240814	−	0.970571i	$-0.577415\pi$
$971$	−9.94012e42			−0.481629			−0.240814	+	0.970571i	$0.577415\pi$
$972$	6.74209e40	−	5.39272e41i	0.00321835	−	0.0257423i
$973$	2.53500e42	−	1.17477e42i	0.119218	−	0.0552478i
$974$			3.95379e43i			1.83193i
$975$	3.62038e43	−	2.49518e43i	1.65267	−	1.13903i
$976$			3.14897e43i			1.41627i
$977$		−	1.18712e43i		−	0.526044i	−0.964790	−	0.263022i	$-0.915281\pi$
$977$		−	1.18712e43i		−	0.526044i	0.964790	−	0.263022i	$-0.0847193\pi$
$978$	−1.90523e43	+	1.31309e43i	−0.831830	+	0.573300i
$979$		−	7.36362e42i		−	0.316769i
$980$	5.76188e41	−	6.80085e41i	0.0244223	−	0.0288261i
$981$	6.87594e42	−	1.80531e43i	0.287165	−	0.753964i
$982$	2.59344e43			1.06724
$983$	−3.83176e43			−1.55372			−0.776859	−	0.629675i	$-0.783188\pi$
$983$	−3.83176e43			−1.55372			−0.776859	+	0.629675i	$0.783188\pi$
$984$	3.63434e43	−	2.50480e43i	1.45210	−	1.00079i
$985$			1.89087e43i			0.744452i
$986$	−1.70343e42			−0.0660857
$987$	8.68369e42	−	1.47059e43i	0.331975	−	0.562204i
$988$	−1.21740e42			−0.0458624
$989$			1.59146e43i			0.590813i
$990$	6.53196e42	−	1.71499e43i	0.238964	−	0.627411i
$991$	−1.46266e43			−0.527322			−0.263661	−	0.964615i	$-0.584930\pi$
$991$	−1.46266e43			−0.527322			−0.263661	+	0.964615i	$0.584930\pi$
$992$	−1.78736e42			−0.0635029
$993$	2.64799e43	+	3.84210e43i	0.927154	+	1.34525i
$994$	−1.39751e43	−	3.01566e43i	−0.482228	−	1.04059i
$995$		−	3.43302e43i		−	1.16746i
$996$	−2.77365e41	−	4.02443e41i	−0.00929590	−	0.0134879i
$997$			3.85113e43i			1.27206i	0.771663	+	0.636032i	$0.219425\pi$
$997$			3.85113e43i			1.27206i	−0.771663	+	0.636032i	$0.780575\pi$
$998$			1.51438e43i			0.492993i
$999$	−2.14377e43	+	5.23556e42i	−0.687826	+	0.167982i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.30.c.a.20.11	✓	76
3.2	odd	2	inner	21.30.c.a.20.66	yes	76
7.6	odd	2	inner	21.30.c.a.20.65	yes	76
21.20	even	2	inner	21.30.c.a.20.12	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.30.c.a.20.11	✓	76	1.1	even	1	trivial
21.30.c.a.20.12	yes	76	21.20	even	2	inner
21.30.c.a.20.65	yes	76	7.6	odd	2	inner
21.30.c.a.20.66	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)

\(f(q)\)	\(=\)	\(q-23469.1i q^{2} +(-4.70121e6 - 6.82122e6i) q^{3} -1.39279e7 q^{4} +1.98757e10 q^{5} +(-1.60088e11 + 1.10333e11i) q^{6} +(-7.54484e11 - 1.62808e12i) q^{7} -1.22730e13i q^{8} +(-2.44277e13 + 6.41359e13i) q^{9} +O(q^{10})\)	\(q-23469.1i q^{2} +(-4.70121e6 - 6.82122e6i) q^{3} -1.39279e7 q^{4} +1.98757e10 q^{5} +(-1.60088e11 + 1.10333e11i) q^{6} +(-7.54484e11 - 1.62808e12i) q^{7} -1.22730e13i q^{8} +(-2.44277e13 + 6.41359e13i) q^{9} -4.66464e14i q^{10} -5.73249e14i q^{11} +(6.54778e13 + 9.50050e13i) q^{12} +2.54219e16i q^{13} +(-3.82097e16 + 1.77071e16i) q^{14} +(-9.34397e16 - 1.35576e17i) q^{15} -2.95514e17 q^{16} -7.73767e16 q^{17} +(1.50521e18 + 5.73296e17i) q^{18} -3.43827e18i q^{19} -2.76826e17 q^{20} +(-7.55853e18 + 1.28005e19i) q^{21} -1.34536e19 q^{22} -2.68583e19i q^{23} +(-8.37168e19 + 5.76979e19i) q^{24} +2.08778e20 q^{25} +5.96629e20 q^{26} +(5.52325e20 - 1.34890e20i) q^{27} +(1.05084e19 + 2.26757e19i) q^{28} +9.38030e20i q^{29} +(-3.18185e21 + 2.19294e21i) q^{30} +5.15944e21i q^{31} +3.46426e20i q^{32} +(-3.91025e21 + 2.69496e21i) q^{33} +1.81596e21i q^{34} +(-1.49959e22 - 3.23593e22i) q^{35} +(3.40225e20 - 8.93276e20i) q^{36} -3.88136e22 q^{37} -8.06931e22 q^{38} +(1.73408e23 - 1.19514e23i) q^{39} -2.43934e23i q^{40} -4.34123e23 q^{41} +(3.00415e23 + 1.77392e23i) q^{42} -5.92539e23 q^{43} +7.98413e21i q^{44} +(-4.85516e23 + 1.27474e24i) q^{45} -6.30341e23 q^{46} -1.14886e24 q^{47} +(1.38927e24 + 2.01576e24i) q^{48} +(-2.08141e24 + 2.45673e24i) q^{49} -4.89983e24i q^{50} +(3.63764e23 + 5.27803e23i) q^{51} -3.54072e23i q^{52} +1.25991e25i q^{53} +(-3.16574e24 - 1.29626e25i) q^{54} -1.13937e25i q^{55} +(-1.99815e25 + 9.25979e24i) q^{56} +(-2.34532e25 + 1.61640e25i) q^{57} +2.20147e25 q^{58} -6.30342e25 q^{59} +(1.30141e24 + 1.88829e24i) q^{60} -1.06559e26i q^{61} +1.21087e26 q^{62} +(1.22849e26 - 8.61923e24i) q^{63} -1.50522e26 q^{64} +5.05277e26i q^{65} +(6.32483e25 + 9.17701e25i) q^{66} -2.01956e26 q^{67} +1.07769e24 q^{68} +(-1.83207e26 + 1.26267e26i) q^{69} +(-7.59443e26 + 3.51940e26i) q^{70} +7.89239e26i q^{71} +(7.87141e26 + 2.99801e26i) q^{72} -1.48365e27i q^{73} +9.10920e26i q^{74} +(-9.81508e26 - 1.42412e27i) q^{75} +4.78877e25i q^{76} +(-9.33297e26 + 4.32507e26i) q^{77} +(-2.80488e27 - 4.06974e27i) q^{78} +4.39054e27 q^{79} -5.87354e27 q^{80} +(-3.51671e27 - 3.13338e27i) q^{81} +1.01885e28i q^{82} -4.23602e27 q^{83} +(1.05274e26 - 1.78283e26i) q^{84} -1.53791e27 q^{85} +1.39064e28i q^{86} +(6.39851e27 - 4.40987e27i) q^{87} -7.03548e27 q^{88} +1.28454e28 q^{89} +(2.99171e28 + 1.13946e28i) q^{90} +(4.13890e28 - 1.91804e28i) q^{91} +3.74079e26i q^{92} +(3.51936e28 - 2.42556e28i) q^{93} +2.69627e28i q^{94} -6.83379e28i q^{95} +(2.36305e27 - 1.62862e27i) q^{96} +1.72177e27i q^{97} +(5.76572e28 + 4.88489e28i) q^{98} +(3.67658e28 + 1.40031e28i) 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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