LMFDB - Embedded newform 21.22.c.b.20.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,22,Mod(20,21)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 22, names="a")

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

chi := DirichletCharacter("21.20");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 22 $
Character orbit:	$[\chi]$	$=$	21.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$58.6902423003$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			20.4
Character	$\chi$	$=$	21.20
Dual form			21.22.c.b.20.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+247.072i q^{2} +(16209.6 - 100983. i) q^{3} +2.03611e6 q^{4} -3.48005e7 q^{5} +(2.49501e7 + 4.00494e6i) q^{6} +(7.14474e8 + 2.19256e8i) q^{7} +1.02121e9i q^{8} +(-9.93485e9 - 3.27379e9i) q^{9} +O(q^{10})$	\(q+247.072i q^{2} +(16209.6 - 100983. i) q^{3} +2.03611e6 q^{4} -3.48005e7 q^{5} +(2.49501e7 + 4.00494e6i) q^{6} +(7.14474e8 + 2.19256e8i) q^{7} +1.02121e9i q^{8} +(-9.93485e9 - 3.27379e9i) q^{9} -8.59823e9i q^{10} +9.21376e10i q^{11} +(3.30045e10 - 2.05613e11i) q^{12} -1.67572e11i q^{13} +(-5.41720e10 + 1.76527e11i) q^{14} +(-5.64102e11 + 3.51427e12i) q^{15} +4.01771e12 q^{16} +7.92508e12 q^{17} +(8.08863e11 - 2.45462e12i) q^{18} -3.32012e13i q^{19} -7.08576e13 q^{20} +(3.37225e13 - 6.85958e13i) q^{21} -2.27646e13 q^{22} -3.78679e14i q^{23} +(1.03125e14 + 1.65535e13i) q^{24} +7.34238e14 q^{25} +4.14025e13 q^{26} +(-4.91638e14 + 9.50186e14i) q^{27} +(1.45475e15 + 4.46428e14i) q^{28} +2.17759e15i q^{29} +(-8.68277e14 - 1.39374e14i) q^{30} -3.73514e15i q^{31} +3.13430e15i q^{32} +(9.30435e15 + 1.49351e15i) q^{33} +1.95807e15i q^{34} +(-2.48640e16 - 7.63021e15i) q^{35} +(-2.02284e16 - 6.66579e15i) q^{36} -1.35512e16 q^{37} +8.20309e15 q^{38} +(-1.69220e16 - 2.71628e15i) q^{39} -3.55387e16i q^{40} -6.54994e16 q^{41} +(1.69481e16 + 8.33188e15i) q^{42} +4.14672e15 q^{43} +1.87602e17i q^{44} +(3.45738e17 + 1.13930e17i) q^{45} +9.35610e16 q^{46} -4.66357e17 q^{47} +(6.51255e16 - 4.05721e17i) q^{48} +(4.62400e17 + 3.13305e17i) q^{49} +1.81410e17i q^{50} +(1.28462e17 - 8.00299e17i) q^{51} -3.41196e17i q^{52} -1.25598e18i q^{53} +(-2.34764e17 - 1.21470e17i) q^{54} -3.20643e18i q^{55} +(-2.23907e17 + 7.29630e17i) q^{56} +(-3.35276e18 - 5.38178e17i) q^{57} -5.38023e17 q^{58} +5.49943e17 q^{59} +(-1.14857e18 + 7.15542e18i) q^{60} -7.00101e18i q^{61} +9.22849e17 q^{62} +(-6.38039e18 - 4.51731e18i) q^{63} +7.65136e18 q^{64} +5.83161e18i q^{65} +(-3.69006e17 + 2.29884e18i) q^{66} -1.30709e19 q^{67} +1.61363e19 q^{68} +(-3.82402e19 - 6.13824e18i) q^{69} +(1.88521e18 - 6.14321e18i) q^{70} -3.38969e19i q^{71} +(3.34324e18 - 1.01456e19i) q^{72} -5.69462e19i q^{73} -3.34811e18i q^{74} +(1.19017e19 - 7.41457e19i) q^{75} -6.76012e19i q^{76} +(-2.02017e19 + 6.58299e19i) q^{77} +(6.71118e17 - 4.18095e18i) q^{78} -5.19511e19 q^{79} -1.39818e20 q^{80} +(8.79835e19 + 6.50493e19i) q^{81} -1.61831e19i q^{82} +1.77530e20 q^{83} +(6.86626e19 - 1.39668e20i) q^{84} -2.75797e20 q^{85} +1.02454e18i q^{86} +(2.19900e20 + 3.52979e19i) q^{87} -9.40921e19 q^{88} -4.40189e20 q^{89} +(-2.81488e19 + 8.54222e19i) q^{90} +(3.67412e19 - 1.19726e20i) q^{91} -7.71031e20i q^{92} +(-3.77186e20 - 6.05451e19i) q^{93} -1.15224e20i q^{94} +1.15542e21i q^{95} +(3.16512e20 + 5.08058e19i) q^{96} +5.59451e20i q^{97} +(-7.74089e19 + 1.14246e20i) q^{98} +(3.01639e20 - 9.15373e20i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 58720260 q^{4} + 1422287188 q^{7} + 10150644696 q^{9}+O(q^{10}) $ 52 * q - 58720260 * q^4 + 1422287188 * q^7 + 10150644696 * q^9	$ 52 q - 58720260 q^{4} + 1422287188 q^{7} + 10150644696 q^{9} - 687153165468 q^{15} + 36241782390404 q^{16} + 36759093002772 q^{18} + 79412641656180 q^{21} + 228880341648112 q^{22} + 45\!\cdots\!12 q^{25}+ \cdots + 15\!\cdots\!28 q^{99}+O(q^{100}) $ 52 * q - 58720260 * q^4 + 1422287188 * q^7 + 10150644696 * q^9 - 687153165468 * q^15 + 36241782390404 * q^16 + 36759093002772 * q^18 + 79412641656180 * q^21 + 228880341648112 * q^22 + 4502168959229812 * q^25 - 328465100861772 * q^28 - 2422487119598196 * q^30 + 94669723666911312 * q^36 - 111253244635261912 * q^37 - 198389110134084780 * q^39 - 125754675449474820 * q^42 + 808208758088766656 * q^43 - 1124214920076830456 * q^46 + 760563680048831596 * q^49 + 4341973540932052200 * q^51 - 13080454499124088812 * q^57 - 10814528487339424568 * q^58 + 13643758017961015644 * q^60 - 38182310822257441896 * q^63 - 30480555033993680900 * q^64 - 25547251957658589040 * q^67 + 73727169165159410040 * q^70 + 39846964674222889428 * q^72 + 45848199464273536260 * q^78 + 199210197493083963080 * q^79 + 235499606962845306588 * q^81 - 373919224753720758924 * q^84 - 570842672309470848672 * q^85 - 1060053674241923431168 * q^88 - 923077800435233893128 * q^91 - 2832166256981601869904 * q^93 + 1525182290356701596928 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			247.072i			0.170612i	0.996355	+	0.0853058i	$0.0271867\pi$
$2$			247.072i			0.170612i	−0.996355	+	0.0853058i	$0.972813\pi$
$3$	16209.6	−	100983.i	0.158489	−	0.987361i
$3$	16209.6	−	100983.i	0.158489	−	0.987361i
$4$	2.03611e6			0.970892
$5$	−3.48005e7			−1.59368			−0.796839	−	0.604192i	$-0.793496\pi$
$5$	−3.48005e7			−1.59368			−0.796839	+	0.604192i	$0.793496\pi$
$6$	2.49501e7	+	4.00494e6i	0.168455	+	0.0270401i
$7$	7.14474e8	+	2.19256e8i	0.955998	+	0.293374i
$7$	7.14474e8	+	2.19256e8i	0.955998	+	0.293374i
$8$			1.02121e9i			0.336257i
$9$	−9.93485e9	−	3.27379e9i	−0.949762	−	0.312972i
$10$		−	8.59823e9i		−	0.271900i
$11$			9.21376e10i			1.07106i	0.844516	+	0.535530i	$0.179888\pi$
$11$			9.21376e10i			1.07106i	−0.844516	+	0.535530i	$0.820112\pi$
$12$	3.30045e10	−	2.05613e11i	0.153876	−	0.958620i
$13$		−	1.67572e11i		−	0.337130i	−0.985691	−	0.168565i	$-0.946087\pi$
$13$		−	1.67572e11i		−	0.337130i	0.985691	−	0.168565i	$-0.0539133\pi$
$14$	−5.41720e10	+	1.76527e11i	−0.0500530	+	0.163104i
$15$	−5.64102e11	+	3.51427e12i	−0.252580	+	1.57353i
$16$	4.01771e12			0.913522
$17$	7.92508e12			0.953432			0.476716	−	0.879057i	$-0.341827\pi$
$17$	7.92508e12			0.953432			0.476716	+	0.879057i	$0.341827\pi$
$18$	8.08863e11	−	2.45462e12i	0.0533966	−	0.162041i
$19$		−	3.32012e13i		−	1.24234i	−0.783675	−	0.621171i	$-0.786657\pi$
$19$		−	3.32012e13i		−	1.24234i	0.783675	−	0.621171i	$-0.213343\pi$
$20$	−7.08576e13			−1.54729
$21$	3.37225e13	−	6.85958e13i	0.441181	−	0.897418i
$22$	−2.27646e13			−0.182735
$23$		−	3.78679e14i		−	1.90603i	−0.302928	−	0.953013i	$-0.597964\pi$
$23$		−	3.78679e14i		−	1.90603i	0.302928	−	0.953013i	$-0.402036\pi$
$24$	1.03125e14	+	1.65535e13i	0.332007	+	0.0532930i
$25$	7.34238e14			1.53981
$26$	4.14025e13			0.0575183
$27$	−4.91638e14	+	9.50186e14i	−0.459543	+	0.888156i
$28$	1.45475e15	+	4.46428e14i	0.928170	+	0.284834i
$29$			2.17759e15i			0.961165i	0.876950	+	0.480583i	$0.159575\pi$
$29$			2.17759e15i			0.961165i	−0.876950	+	0.480583i	$0.840425\pi$
$30$	−8.68277e14	−	1.39374e14i	−0.268463	−	0.0430932i
$31$		−	3.73514e15i		−	0.818482i	−0.912426	−	0.409241i	$-0.865794\pi$
$31$		−	3.73514e15i		−	0.818482i	0.912426	−	0.409241i	$-0.134206\pi$
$32$			3.13430e15i			0.492115i
$33$	9.30435e15	+	1.49351e15i	1.05752	+	0.169751i
$34$			1.95807e15i			0.162667i
$35$	−2.48640e16	−	7.63021e15i	−1.52355	−	0.467544i
$36$	−2.02284e16	−	6.66579e15i	−0.922116	−	0.303862i
$37$	−1.35512e16			−0.463296			−0.231648	−	0.972800i	$-0.574412\pi$
$37$	−1.35512e16			−0.463296			−0.231648	+	0.972800i	$0.574412\pi$
$38$	8.20309e15			0.211958
$39$	−1.69220e16	−	2.71628e15i	−0.332869	−	0.0534314i
$40$		−	3.55387e16i		−	0.535885i
$41$	−6.54994e16			−0.762092			−0.381046	−	0.924556i	$-0.624436\pi$
$41$	−6.54994e16			−0.762092			−0.381046	+	0.924556i	$0.624436\pi$
$42$	1.69481e16	+	8.33188e15i	0.153110	+	0.0752707i
$43$	4.14672e15			0.0292608			0.0146304	−	0.999893i	$-0.495343\pi$
$43$	4.14672e15			0.0292608			0.0146304	+	0.999893i	$0.495343\pi$
$44$			1.87602e17i			1.03988i
$45$	3.45738e17	+	1.13930e17i	1.51362	+	0.498776i
$46$	9.35610e16			0.325190
$47$	−4.66357e17			−1.29327			−0.646637	−	0.762798i	$-0.723825\pi$
$47$	−4.66357e17			−1.29327			−0.646637	+	0.762798i	$0.723825\pi$
$48$	6.51255e16	−	4.05721e17i	0.144783	−	0.901976i
$49$	4.62400e17	+	3.13305e17i	0.827863	+	0.560930i
$50$			1.81410e17i			0.262709i
$51$	1.28462e17	−	8.00299e17i	0.151108	−	0.941382i
$52$		−	3.41196e17i		−	0.327317i
$53$		−	1.25598e18i		−	0.986476i	−0.869894	−	0.493238i	$-0.835813\pi$
$53$		−	1.25598e18i		−	0.986476i	0.869894	−	0.493238i	$-0.164187\pi$
$54$	−2.34764e17	−	1.21470e17i	−0.151530	−	0.0784034i
$55$		−	3.20643e18i		−	1.70692i
$56$	−2.23907e17	+	7.29630e17i	−0.0986491	+	0.321461i
$57$	−3.35276e18	−	5.38178e17i	−1.22664	−	0.196898i
$58$	−5.38023e17			−0.163986
$59$	5.49943e17			0.140079			0.0700393	−	0.997544i	$-0.477688\pi$
$59$	5.49943e17			0.140079			0.0700393	+	0.997544i	$0.477688\pi$
$60$	−1.14857e18	+	7.15542e18i	−0.245228	+	1.52773i
$61$		−	7.00101e18i		−	1.25660i	−0.777971	−	0.628301i	$-0.783751\pi$
$61$		−	7.00101e18i		−	1.25660i	0.777971	−	0.628301i	$-0.216249\pi$
$62$	9.22849e17			0.139643
$63$	−6.38039e18	−	4.51731e18i	−0.816153	−	0.577836i
$64$	7.65136e18			0.829562
$65$			5.83161e18i			0.537277i
$66$	−3.69006e17	+	2.29884e18i	−0.0289615	+	0.180426i
$67$	−1.30709e19			−0.876032			−0.438016	−	0.898967i	$-0.644319\pi$
$67$	−1.30709e19			−0.876032			−0.438016	+	0.898967i	$0.644319\pi$
$68$	1.61363e19			0.925679
$69$	−3.82402e19	−	6.13824e18i	−1.88194	−	0.302084i
$70$	1.88521e18	−	6.14321e18i	0.0797684	−	0.259936i
$71$		−	3.38969e19i		−	1.23580i	−0.786258	−	0.617898i	$-0.787984\pi$
$71$		−	3.38969e19i		−	1.23580i	0.786258	−	0.617898i	$-0.212016\pi$
$72$	3.34324e18	−	1.01456e19i	0.105239	−	0.319364i
$73$		−	5.69462e19i		−	1.55087i	−0.631430	−	0.775433i	$-0.717532\pi$
$73$		−	5.69462e19i		−	1.55087i	0.631430	−	0.775433i	$-0.282468\pi$
$74$		−	3.34811e18i		−	0.0790436i
$75$	1.19017e19	−	7.41457e19i	0.244043	−	1.52035i
$76$		−	6.76012e19i		−	1.20618i
$77$	−2.02017e19	+	6.58299e19i	−0.314221	+	1.02393i
$78$	6.71118e17	−	4.18095e18i	0.00911602	−	0.0567913i
$79$	−5.19511e19			−0.617320			−0.308660	−	0.951172i	$-0.599881\pi$
$79$	−5.19511e19			−0.617320			−0.308660	+	0.951172i	$0.599881\pi$
$80$	−1.39818e20			−1.45586
$81$	8.79835e19	+	6.50493e19i	0.804098	+	0.594497i
$82$		−	1.61831e19i		−	0.130022i
$83$	1.77530e20			1.25589			0.627946	−	0.778257i	$-0.283896\pi$
$83$	1.77530e20			1.25589			0.627946	+	0.778257i	$0.283896\pi$
$84$	6.86626e19	−	1.39668e20i	0.428339	−	0.871296i
$85$	−2.75797e20			−1.51946
$86$			1.02454e18i			0.00499223i
$87$	2.19900e20	+	3.52979e19i	0.949017	+	0.152334i
$88$	−9.40921e19			−0.360151
$89$	−4.40189e20			−1.49639			−0.748194	−	0.663480i	$-0.769079\pi$
$89$	−4.40189e20			−1.49639			−0.748194	+	0.663480i	$0.769079\pi$
$90$	−2.81488e19	+	8.54222e19i	−0.0850970	+	0.258240i
$91$	3.67412e19	−	1.19726e20i	0.0989052	−	0.322296i
$92$		−	7.71031e20i		−	1.85055i
$93$	−3.77186e20	−	6.05451e19i	−0.808137	−	0.129720i
$94$		−	1.15224e20i		−	0.220648i
$95$			1.15542e21i			1.97989i
$96$	3.16512e20	+	5.08058e19i	0.485895	+	0.0779948i
$97$			5.59451e20i			0.770297i	0.922855	+	0.385149i	$0.125850\pi$
$97$			5.59451e20i			0.770297i	−0.922855	+	0.385149i	$0.874150\pi$
$98$	−7.74089e19	+	1.14246e20i	−0.0957012	+	0.141243i
$99$	3.01639e20	−	9.15373e20i	0.335211	−	1.01725i
$100$	1.49499e21			1.49499
$101$	7.90626e20			0.712191			0.356095	−	0.934450i	$-0.384108\pi$
$101$	7.90626e20			0.712191			0.356095	+	0.934450i	$0.384108\pi$
$102$	1.97732e20	+	3.17395e19i	0.160611	+	0.0257809i
$103$		−	3.92142e20i		−	0.287509i	−0.989613	−	0.143755i	$-0.954082\pi$
$103$		−	3.92142e20i		−	0.287509i	0.989613	−	0.143755i	$-0.0459176\pi$
$104$	1.71127e20			0.113362
$105$	−1.17356e21	+	2.38717e21i	−0.703100	+	1.43020i
$106$	3.10318e20			0.168304
$107$		−	1.59873e21i		−	0.785678i	−0.919607	−	0.392839i	$-0.871493\pi$
$107$		−	1.59873e21i		−	0.785678i	0.919607	−	0.392839i	$-0.128507\pi$
$108$	−1.00103e21	+	1.93468e21i	−0.446166	+	0.862303i
$109$	−6.51658e20			−0.263658			−0.131829	−	0.991272i	$-0.542085\pi$
$109$	−6.51658e20			−0.263658			−0.131829	+	0.991272i	$0.542085\pi$
$110$	7.92221e20			0.291221
$111$	−2.19659e20	+	1.36844e21i	−0.0734273	+	0.457440i
$112$	2.87055e21	+	8.80907e20i	0.873325	+	0.268004i
$113$		−	6.17950e21i		−	1.71250i	−0.516565	−	0.856248i	$-0.672789\pi$
$113$		−	6.17950e21i		−	1.71250i	0.516565	−	0.856248i	$-0.327211\pi$
$114$	1.32969e20	−	8.28374e20i	0.0335930	−	0.209279i
$115$			1.31782e22i			3.03759i
$116$			4.43382e21i			0.933187i
$117$	−5.48598e20	+	1.66481e21i	−0.105512	+	0.320194i
$118$			1.35876e20i			0.0238990i
$119$	5.66226e21	+	1.73762e21i	0.911479	+	0.279712i
$120$	−3.58881e21	−	5.76069e20i	−0.529112	−	0.0849319i
$121$	−1.08909e21			−0.147169
$122$	1.72975e21			0.214391
$123$	−1.06172e21	+	6.61434e21i	−0.120783	+	0.752459i
$124$		−	7.60514e21i		−	0.794657i
$125$	−8.95767e21			−0.860281
$126$	1.11610e21	−	1.57642e21i	0.0985855	−	0.139245i
$127$	1.92143e21			0.156202			0.0781008	−	0.996945i	$-0.475114\pi$
$127$	1.92143e21			0.156202			0.0781008	+	0.996945i	$0.475114\pi$
$128$			8.46355e21i			0.633648i
$129$	6.72167e19	−	4.18749e20i	0.00463751	−	0.0288910i
$130$	−1.44083e21			−0.0916657
$131$	−3.30217e21			−0.193843			−0.0969215	−	0.995292i	$-0.530900\pi$
$131$	−3.30217e21			−0.193843			−0.0969215	+	0.995292i	$0.530900\pi$
$132$	1.89447e22	+	3.04095e21i	1.02674	+	0.164810i
$133$	7.27956e21	−	2.37214e22i	0.364471	−	1.18768i
$134$		−	3.22946e21i		−	0.149461i
$135$	1.71092e22	−	3.30669e22i	0.732363	−	1.41543i
$136$			8.09319e21i			0.320598i
$137$		−	1.54231e22i		−	0.565725i	−0.959160	−	0.282863i	$-0.908716\pi$
$137$		−	1.54231e22i		−	0.565725i	0.959160	−	0.282863i	$-0.0912841\pi$
$138$	1.51659e21	−	9.44809e21i	0.0515391	−	0.321080i
$139$			1.70092e22i			0.535830i	0.963443	+	0.267915i	$0.0863347\pi$
$139$			1.70092e22i			0.535830i	−0.963443	+	0.267915i	$0.913665\pi$
$140$	−5.06259e22	−	1.55359e22i	−1.47920	−	0.453934i
$141$	−7.55945e21	+	4.70942e22i	−0.204970	+	1.27693i
$142$	8.37497e21			0.210841
$143$	1.54397e22			0.361086
$144$	−3.99154e22	−	1.31532e22i	−0.867629	−	0.285907i
$145$		−	7.57814e22i		−	1.53179i
$146$	1.40698e22			0.264596
$147$	3.91339e22	−	4.16160e22i	0.685047	−	0.728499i
$148$	−2.75916e22			−0.449810
$149$			6.09708e22i			0.926117i	0.886328	+	0.463059i	$0.153248\pi$
$149$			6.09708e22i			0.926117i	−0.886328	+	0.463059i	$0.846752\pi$
$150$	1.83193e22	+	2.94058e21i	0.259389	+	0.0416365i
$151$	−1.02653e23			−1.35554			−0.677770	−	0.735274i	$-0.737053\pi$
$151$	−1.02653e23			−1.35554			−0.677770	+	0.735274i	$0.737053\pi$
$152$	3.39055e22			0.417746
$153$	−7.87345e22	−	2.59451e22i	−0.905534	−	0.298397i
$154$	−1.62647e22	−	4.99128e21i	−0.174695	−	0.0536098i
$155$			1.29985e23i			1.30440i
$156$	−3.44550e22	−	5.53064e21i	−0.323180	−	0.0518761i
$157$		−	6.98052e22i		−	0.612268i	−0.951988	−	0.306134i	$-0.900964\pi$
$157$		−	6.98052e22i		−	0.612268i	0.951988	−	0.306134i	$-0.0990355\pi$
$158$		−	1.28357e22i		−	0.105322i
$159$	−1.26833e23	−	2.03589e22i	−0.974007	−	0.156346i
$160$		−	1.09075e23i		−	0.784272i
$161$	8.30276e22	−	2.70556e23i	0.559179	−	1.82216i
$162$	−1.60719e22	+	2.17383e22i	−0.101428	+	0.137188i
$163$	3.10704e23			1.83813			0.919066	−	0.394103i	$-0.128945\pi$
$163$	3.10704e23			1.83813			0.919066	+	0.394103i	$0.128945\pi$
$164$	−1.33364e23			−0.739908
$165$	−3.23796e23	−	5.19750e22i	−1.68535	−	0.270529i
$166$			4.38627e22i			0.214270i
$167$	2.26403e23			1.03839			0.519194	−	0.854656i	$-0.326232\pi$
$167$	2.26403e23			1.03839			0.519194	+	0.854656i	$0.326232\pi$
$168$	7.00509e22	+	3.44378e22i	0.301763	+	0.148350i
$169$	2.18984e23			0.886343
$170$		−	6.81417e22i		−	0.259238i
$171$	−1.08694e23	+	3.29849e23i	−0.388818	+	1.17993i
$172$	8.44317e21			0.0284091
$173$	−1.54465e23			−0.489041			−0.244521	−	0.969644i	$-0.578631\pi$
$173$	−1.54465e23			−0.489041			−0.244521	+	0.969644i	$0.578631\pi$
$174$	−8.72113e21	+	5.43312e22i	−0.0259900	+	0.161913i
$175$	5.24594e23	+	1.60986e23i	1.47205	+	0.451740i
$176$			3.70182e23i			0.978437i
$177$	8.91436e21	−	5.55350e22i	0.0222009	−	0.138308i
$178$		−	1.08758e23i		−	0.255301i
$179$			1.69966e23i			0.376188i	0.982151	+	0.188094i	$0.0602310\pi$
$179$			1.69966e23i			0.376188i	−0.982151	+	0.188094i	$0.939769\pi$
$180$	7.03959e23	+	2.31973e23i	1.46956	+	0.484257i
$181$			2.21194e23i			0.435660i	0.975987	+	0.217830i	$0.0698978\pi$
$181$			2.21194e23i			0.435660i	−0.975987	+	0.217830i	$0.930102\pi$
$182$	2.95810e22	+	9.07774e21i	0.0549874	+	0.0168744i
$183$	−7.06984e23	−	1.13484e23i	−1.24072	−	0.199157i
$184$	3.86712e23			0.640915
$185$	4.71587e23			0.738344
$186$	1.49590e22	−	9.31922e22i	0.0221318	−	0.137878i
$187$			7.30198e23i			1.02118i
$188$	−9.49552e23			−1.25563
$189$	−5.59596e23	+	5.71088e23i	−0.699884	+	0.714257i
$190$	−2.85472e23			−0.337793
$191$		−	1.22833e23i		−	0.137552i	−0.997632	−	0.0687758i	$-0.978091\pi$
$191$		−	1.22833e23i		−	0.137552i	0.997632	−	0.0687758i	$-0.0219093\pi$
$192$	1.24025e23	−	7.72658e23i	0.131476	−	0.819077i
$193$	−8.35000e23			−0.838175			−0.419087	−	0.907946i	$-0.637650\pi$
$193$	−8.35000e23			−0.838175			−0.419087	+	0.907946i	$0.637650\pi$
$194$	−1.38225e23			−0.131422
$195$	5.88894e23	+	9.45280e22i	0.530486	+	0.0851524i
$196$	9.41495e23	+	6.37923e23i	0.803766	+	0.544602i
$197$		−	1.49542e24i		−	1.21023i	−0.796138	−	0.605115i	$-0.793127\pi$
$197$		−	1.49542e24i		−	1.21023i	0.796138	−	0.605115i	$-0.206873\pi$
$198$	2.26163e23	+	7.45267e22i	0.173555	+	0.0571910i
$199$		−	3.32350e23i		−	0.241901i	−0.992659	−	0.120951i	$-0.961406\pi$
$199$		−	3.32350e23i		−	0.241901i	0.992659	−	0.120951i	$-0.0385942\pi$
$200$			7.49813e23i			0.517772i
$201$	−2.11874e23	+	1.31994e24i	−0.138841	+	0.864960i
$202$			1.95342e23i			0.121508i
$203$	−4.77450e23	+	1.55583e24i	−0.281981	+	0.918872i
$204$	2.61563e23	−	1.62950e24i	0.146710	−	0.913979i
$205$	2.27941e24			1.21453
$206$	9.68872e22			0.0490525
$207$	−1.23972e24	+	3.76212e24i	−0.596532	+	1.81027i
$208$		−	6.73258e23i		−	0.307976i
$209$	3.05908e24			1.33062
$210$	−5.89803e23	−	2.89954e23i	−0.244008	−	0.119957i
$211$	2.82664e24			1.11251			0.556256	−	0.831011i	$-0.312238\pi$
$211$	2.82664e24			1.11251			0.556256	+	0.831011i	$0.312238\pi$
$212$		−	2.55731e24i		−	0.957761i
$213$	−3.42301e24	−	5.49455e23i	−1.22018	−	0.195860i
$214$	3.95001e23			0.134046
$215$	−1.44308e23			−0.0466323
$216$	−9.70342e23	−	5.02067e23i	−0.298649	−	0.154525i
$217$	8.18951e23	−	2.66866e24i	0.240121	−	0.782467i
$218$		−	1.61006e23i		−	0.0449832i
$219$	−5.75060e24	−	9.23074e23i	−1.53126	−	0.245795i
$220$		−	6.52865e24i		−	1.65724i
$221$		−	1.32802e24i		−	0.321431i
$222$	−3.38103e23	−	5.42716e22i	−0.0780446	−	0.0125275i
$223$		−	4.24179e24i		−	0.934004i	−0.884256	−	0.467002i	$-0.845334\pi$
$223$		−	4.24179e24i		−	0.934004i	0.884256	−	0.467002i	$-0.154666\pi$
$224$	−6.87214e23	+	2.23938e24i	−0.144374	+	0.470461i
$225$	−7.29454e24	−	2.40374e24i	−1.46245	−	0.481916i
$226$	1.52678e24			0.292172
$227$	3.16057e23			0.0577422			0.0288711	−	0.999583i	$-0.490809\pi$
$227$	3.16057e23			0.0577422			0.0288711	+	0.999583i	$0.490809\pi$
$228$	−6.82659e24	−	1.09579e24i	−1.19093	−	0.191166i
$229$		−	3.56596e24i		−	0.594161i	−0.954853	−	0.297080i	$-0.903987\pi$
$229$		−	3.56596e24i		−	0.594161i	0.954853	−	0.297080i	$-0.0960129\pi$
$230$	−3.25597e24			−0.518249
$231$	6.32025e24	+	3.10711e24i	0.961188	+	0.472531i
$232$	−2.22379e24			−0.323199
$233$		−	1.60294e23i		−	0.0222679i	−0.999938	−	0.0111339i	$-0.996456\pi$
$233$		−	1.60294e23i		−	0.0222679i	0.999938	−	0.0111339i	$-0.00354412\pi$
$234$	−4.11328e23	−	1.35543e23i	−0.0546288	−	0.0180016i
$235$	1.62294e25			2.06106
$236$	1.11974e24			0.136001
$237$	−8.42107e23	+	5.24619e24i	−0.0978385	+	0.609518i
$238$	−4.29317e23	+	1.39899e24i	−0.0477222	+	0.155509i
$239$			7.82157e24i			0.831986i	0.909368	+	0.415993i	$0.136566\pi$
$239$			7.82157e24i			0.831986i	−0.909368	+	0.415993i	$0.863434\pi$
$240$	−2.26640e24	+	1.41193e25i	−0.230738	+	1.43746i
$241$			1.45971e25i			1.42261i	0.702882	+	0.711306i	$0.251896\pi$
$241$			1.45971e25i			1.42261i	−0.702882	+	0.711306i	$0.748104\pi$
$242$		−	2.69083e23i		−	0.0251088i
$243$	7.99506e24	−	7.83043e24i	0.714424	−	0.699713i
$244$		−	1.42548e25i		−	1.22002i
$245$	−1.60917e25	−	1.09032e25i	−1.31935	−	0.893941i
$246$	−1.63422e24	−	2.62321e23i	−0.128378	−	0.0206070i
$247$	−5.56361e24			−0.418831
$248$	3.81437e24			0.275220
$249$	2.87769e24	−	1.79276e25i	0.199045	−	1.24002i
$250$		−	2.21319e24i		−	0.146774i
$251$	1.07792e25			0.685508			0.342754	−	0.939425i	$-0.388640\pi$
$251$	1.07792e25			0.685508			0.342754	+	0.939425i	$0.388640\pi$
$252$	−1.29912e25	−	9.19773e24i	−0.792396	−	0.561016i
$253$	3.48906e25			2.04147
$254$			4.74731e23i			0.0266498i
$255$	−4.47055e24	+	2.78508e25i	−0.240818	+	1.50026i
$256$	1.39550e25			0.721454
$257$	−2.56886e25			−1.27480			−0.637401	−	0.770533i	$-0.719990\pi$
$257$	−2.56886e25			−1.27480			−0.637401	+	0.770533i	$0.719990\pi$
$258$	1.03461e23	+	1.66074e22i	0.00492913	+	0.000791214i
$259$	−9.68194e24	−	2.97117e24i	−0.442910	−	0.135919i
$260$			1.18738e25i			0.521637i
$261$	7.12899e24	−	2.16341e25i	0.300817	−	0.912878i
$262$		−	8.15873e23i		−	0.0330719i
$263$		−	1.48951e25i		−	0.580105i	−0.957011	−	0.290053i	$-0.906327\pi$
$263$		−	1.48951e25i		−	0.580105i	0.957011	−	0.290053i	$-0.0936728\pi$
$264$	−1.52520e24	+	9.50172e24i	−0.0570800	+	0.355599i
$265$			4.37088e25i			1.57212i
$266$	5.86090e24	+	1.79858e24i	0.202631	+	0.0621830i
$267$	−7.13529e24	+	4.44517e25i	−0.237161	+	1.47747i
$268$	−2.66138e25			−0.850532
$269$	5.79749e25			1.78173			0.890863	−	0.454273i	$-0.150101\pi$
$269$	5.79749e25			1.78173			0.890863	+	0.454273i	$0.150101\pi$
$270$	8.16992e24	+	4.22722e24i	0.241490	+	0.124950i
$271$			2.99675e25i			0.852066i	0.904708	+	0.426033i	$0.140089\pi$
$271$			2.99675e25i			0.852066i	−0.904708	+	0.426033i	$0.859911\pi$
$272$	3.18407e25			0.870982
$273$	−1.14948e25	−	5.65096e24i	−0.302547	−	0.148735i
$274$	3.81062e24			0.0965193
$275$			6.76509e25i			1.64923i
$276$	−7.78612e25	−	1.24981e25i	−1.82716	−	0.293291i
$277$	1.61099e25			0.363962			0.181981	−	0.983302i	$-0.441749\pi$
$277$	1.61099e25			0.363962			0.181981	+	0.983302i	$0.441749\pi$
$278$	−4.20249e24			−0.0914189
$279$	−1.22281e25	+	3.71080e25i	−0.256161	+	0.777363i
$280$	7.79207e24	−	2.53915e25i	0.157215	−	0.512305i
$281$		−	3.88973e25i		−	0.755967i	−0.925812	−	0.377983i	$-0.876618\pi$
$281$		−	3.88973e25i		−	0.755967i	0.925812	−	0.377983i	$-0.123382\pi$
$282$	−1.16357e25	−	1.86773e24i	−0.217859	−	0.0349702i
$283$			6.67261e25i			1.20376i	0.798588	+	0.601878i	$0.205581\pi$
$283$			6.67261e25i			1.20376i	−0.798588	+	0.601878i	$0.794419\pi$
$284$		−	6.90177e25i		−	1.19982i
$285$	1.16678e26	+	1.87289e25i	1.95487	+	0.313791i
$286$			3.81473e24i			0.0616056i
$287$	−4.67976e25	−	1.43611e25i	−0.728558	−	0.223578i
$288$	1.02611e25	−	3.11388e25i	0.154018	−	0.467392i
$289$	−6.28509e24			−0.0909671
$290$	1.87235e25			0.261341
$291$	5.64951e25	+	9.06847e24i	0.760561	+	0.122084i
$292$		−	1.15948e26i		−	1.50572i
$293$	−2.91436e25			−0.365118			−0.182559	−	0.983195i	$-0.558438\pi$
$293$	−2.91436e25			−0.365118			−0.182559	+	0.983195i	$0.558438\pi$
$294$	1.02822e25	+	9.66888e24i	0.124290	+	0.116877i
$295$	−1.91383e25			−0.223240
$296$		−	1.38386e25i		−	0.155786i
$297$	−8.75479e25	−	4.52983e25i	−0.951268	−	0.492198i
$298$	−1.50642e25			−0.158006
$299$	−6.34562e25			−0.642579
$300$	2.42331e25	−	1.50969e26i	0.236939	−	1.47609i
$301$	2.96272e24	+	9.09193e23i	0.0279732	+	0.00858436i
$302$		−	2.53626e25i		−	0.231271i
$303$	1.28157e25	−	7.98399e25i	0.112874	−	0.703189i
$304$		−	1.33393e26i		−	1.13491i
$305$			2.43639e26i			2.00262i
$306$	6.41030e24	−	1.94531e25i	0.0509100	−	0.154495i
$307$		−	1.50702e26i		−	1.15655i	−0.815842	−	0.578276i	$-0.803726\pi$
$307$		−	1.50702e26i		−	1.15655i	0.815842	−	0.578276i	$-0.196274\pi$
$308$	−4.11328e25	+	1.34037e26i	−0.305075	+	0.994126i
$309$	−3.95997e25	−	6.35646e24i	−0.283875	−	0.0455671i
$310$	−3.21156e25			−0.222545
$311$	7.43049e25			0.497775			0.248888	−	0.968532i	$-0.419935\pi$
$311$	7.43049e25			0.497775			0.248888	+	0.968532i	$0.419935\pi$
$312$	2.77390e24	−	1.72810e25i	0.0179667	−	0.111930i
$313$			2.26853e26i			1.42079i	0.703803	+	0.710395i	$0.251484\pi$
$313$			2.26853e26i			1.42079i	−0.703803	+	0.710395i	$0.748516\pi$
$314$	1.72469e25			0.104460
$315$	2.22041e26	+	1.57205e26i	1.30068	+	0.920884i
$316$	−1.05778e26			−0.599351
$317$		−	1.87990e26i		−	1.03042i	−0.857065	−	0.515209i	$-0.827714\pi$
$317$		−	1.87990e26i		−	1.03042i	0.857065	−	0.515209i	$-0.172286\pi$
$318$	5.03013e24	−	3.13369e25i	0.0266744	−	0.166177i
$319$	−2.00638e26			−1.02947
$320$	−2.66271e26			−1.32205
$321$	−1.61445e26	−	2.59147e25i	−0.775748	−	0.124521i
$322$	6.68469e25	+	2.05138e25i	0.310881	+	0.0954024i
$323$		−	2.63122e26i		−	1.18449i
$324$	1.79144e26	+	1.32447e26i	0.780692	+	0.577193i
$325$		−	1.23038e26i		−	0.519116i
$326$			7.67662e25i			0.313607i
$327$	−1.05631e25	+	6.58065e25i	−0.0417869	+	0.260326i
$328$		−	6.68889e25i		−	0.256259i
$329$	−3.33200e26	−	1.02251e26i	−1.23637	−	0.379413i
$330$	1.28416e25	−	8.00010e25i	0.0461553	−	0.287540i
$331$	−4.01134e26			−1.39667			−0.698337	−	0.715769i	$-0.746076\pi$
$331$	−4.01134e26			−1.39667			−0.698337	+	0.715769i	$0.746076\pi$
$332$	3.61470e26			1.21933
$333$	1.34629e26	+	4.43637e25i	0.440021	+	0.144998i
$334$			5.59379e25i			0.177161i
$335$	4.54874e26			1.39611
$336$	1.35487e26	−	2.75598e26i	0.403029	−	0.819811i
$337$	9.72732e25			0.280465			0.140233	−	0.990119i	$-0.455215\pi$
$337$	9.72732e25			0.280465			0.140233	+	0.990119i	$0.455215\pi$
$338$			5.41048e25i			0.151221i
$339$	−6.24025e26	−	1.00167e26i	−1.69085	−	0.271412i
$340$	−5.61552e26			−1.47523
$341$	3.44147e26			0.876643
$342$	−8.14965e25	−	2.68552e25i	−0.201310	−	0.0663368i
$343$	2.61678e26	+	3.25232e26i	0.626873	+	0.779121i
$344$			4.23469e24i			0.00983915i
$345$	1.33078e27	+	2.13614e26i	2.99920	+	0.481425i
$346$		−	3.81639e25i		−	0.0834361i
$347$			1.17581e26i			0.249390i	0.992195	+	0.124695i	$0.0397953\pi$
$347$			1.17581e26i			0.249390i	−0.992195	+	0.124695i	$0.960205\pi$
$348$	4.47741e26	+	7.18704e25i	0.921392	+	0.147900i
$349$			3.71476e26i			0.741761i	0.928681	+	0.370881i	$0.120944\pi$
$349$			3.71476e26i			0.741761i	−0.928681	+	0.370881i	$0.879056\pi$
$350$	−3.97751e25	+	1.29612e26i	−0.0770721	+	0.251150i
$351$	1.59225e26	+	8.23850e25i	0.299424	+	0.154926i
$352$	−2.88787e26			−0.527084
$353$	4.02575e26			0.713202			0.356601	−	0.934257i	$-0.383936\pi$
$353$	4.02575e26			0.713202			0.356601	+	0.934257i	$0.383936\pi$
$354$	1.37212e25	+	2.20249e24i	0.0235970	+	0.00378773i
$355$			1.17963e27i			1.96946i
$356$	−8.96272e26			−1.45283
$357$	2.67253e26	−	5.43627e26i	0.420636	−	0.855627i
$358$	−4.19939e25			−0.0641821
$359$		−	8.57792e26i		−	1.27318i	−0.771202	−	0.636591i	$-0.780344\pi$
$359$		−	8.57792e26i		−	1.27318i	0.771202	−	0.636591i	$-0.219656\pi$
$360$	−1.16346e26	+	3.53072e26i	−0.167717	+	0.508964i
$361$	−3.88111e26			−0.543414
$362$	−5.46508e25			−0.0743287
$363$	−1.76537e25	+	1.09980e26i	−0.0233247	+	0.145309i
$364$	7.48091e25	−	2.43775e26i	0.0960263	−	0.312914i
$365$			1.98175e27i			2.47158i
$366$	2.80386e25	−	1.74676e26i	0.0339786	−	0.211681i
$367$			1.01208e27i			1.19185i	0.803039	+	0.595927i	$0.203215\pi$
$367$			1.01208e27i			1.19185i	−0.803039	+	0.595927i	$0.796785\pi$
$368$		−	1.52142e27i		−	1.74120i
$369$	6.50727e26	+	2.14432e26i	0.723806	+	0.238513i
$370$			1.16516e26i			0.125970i
$371$	2.75381e26	−	8.97365e26i	0.289406	−	0.943069i
$372$	−7.67992e26	−	1.23276e26i	−0.784613	−	0.125944i
$373$	−8.85286e25			−0.0879308			−0.0439654	−	0.999033i	$-0.513999\pi$
$373$	−8.85286e25			−0.0879308			−0.0439654	+	0.999033i	$0.513999\pi$
$374$	−1.80411e26			−0.174226
$375$	−1.45200e26	+	9.04574e26i	−0.136345	+	0.849407i
$376$		−	4.76250e26i		−	0.434873i
$377$	3.64905e26			0.324038
$378$	−1.41100e26	−	1.38261e26i	−0.121861	−	0.119408i
$379$	−1.60854e26			−0.135120			−0.0675601	−	0.997715i	$-0.521521\pi$
$379$	−1.60854e26			−0.135120			−0.0675601	+	0.997715i	$0.521521\pi$
$380$			2.35256e27i			1.92226i
$381$	3.11456e25	−	1.94032e26i	0.0247562	−	0.154227i
$382$	3.03487e25			0.0234679
$383$	−2.47683e27			−1.86341			−0.931705	−	0.363216i	$-0.881679\pi$
$383$	−2.47683e27			−1.86341			−0.931705	+	0.363216i	$0.881679\pi$
$384$	8.54676e26	+	1.37191e26i	0.625639	+	0.100426i
$385$	7.03030e26	−	2.29091e27i	0.500767	−	1.63182i
$386$		−	2.06305e26i		−	0.143002i
$387$	−4.11971e25	−	1.35755e25i	−0.0277908	−	0.00915780i
$388$			1.13910e27i			0.747875i
$389$			1.99655e26i			0.127588i	0.997963	+	0.0637940i	$0.0203201\pi$
$389$			1.99655e26i			0.127588i	−0.997963	+	0.0637940i	$0.979680\pi$
$390$	−2.33552e25	+	1.45499e26i	−0.0145280	+	0.0905071i
$391$		−	3.00106e27i		−	1.81727i
$392$	−3.19951e26	+	4.72209e26i	−0.188617	+	0.278375i
$393$	−5.35268e25	+	3.33463e26i	−0.0307220	+	0.191393i
$394$	3.69477e26			0.206479
$395$	1.80793e27			0.983810
$396$	6.14170e26	−	1.86380e27i	0.325454	−	0.987642i
$397$			1.03765e26i			0.0535487i	0.999642	+	0.0267743i	$0.00852355\pi$
$397$			1.03765e26i			0.0535487i	−0.999642	+	0.0267743i	$0.991476\pi$
$398$	8.21143e25			0.0412712
$399$	−2.27746e27	−	1.11963e27i	−1.11490	−	0.548098i
$400$	2.94996e27			1.40665
$401$		−	2.10386e27i		−	0.977240i	−0.872497	−	0.488620i	$-0.837500\pi$
$401$		−	2.10386e27i		−	0.977240i	0.872497	−	0.488620i	$-0.162500\pi$
$402$	−3.26121e26	−	5.23482e25i	−0.147572	−	0.0236880i
$403$	−6.25906e26			−0.275935
$404$	1.60980e27			0.691460
$405$	−3.06187e27	−	2.26375e27i	−1.28147	−	0.947437i
$406$	−3.84403e26	−	1.17965e26i	−0.156770	−	0.0481092i
$407$		−	1.24857e27i		−	0.496217i
$408$	8.17276e26	+	1.31187e26i	0.316546	+	0.0508113i
$409$			1.90621e26i			0.0719576i	0.999353	+	0.0359788i	$0.0114549\pi$
$409$			1.90621e26i			0.0719576i	−0.999353	+	0.0359788i	$0.988545\pi$
$410$			5.63180e26i			0.207213i
$411$	−1.55747e27	−	2.50002e26i	−0.558575	−	0.0896612i
$412$		−	7.98442e26i		−	0.279140i
$413$	3.92920e26	+	1.20578e26i	0.133915	+	0.0410954i
$414$	−9.29515e26	−	3.06299e26i	−0.308854	−	0.101775i
$415$	−6.17814e27			−2.00149
$416$	5.25223e26			0.165907
$417$	1.71764e27	+	2.75712e26i	0.529058	+	0.0849232i
$418$			7.55813e26i			0.227020i
$419$	−2.23604e27			−0.654988			−0.327494	−	0.944853i	$-0.606204\pi$
$419$	−2.23604e27			−0.654988			−0.327494	+	0.944853i	$0.606204\pi$
$420$	−2.38949e27	+	4.86053e27i	−0.682634	+	1.38856i
$421$	9.55945e26			0.266361			0.133181	−	0.991092i	$-0.457481\pi$
$421$	9.55945e26			0.266361			0.133181	+	0.991092i	$0.457481\pi$
$422$			6.98383e26i			0.189807i
$423$	4.63318e27	+	1.52676e27i	1.22830	+	0.404758i
$424$	1.28262e27			0.331709
$425$	5.81889e27			1.46810
$426$	1.35755e26	−	8.45731e26i	0.0334160	−	0.208176i
$427$	1.53501e27	−	5.00204e27i	0.368654	−	1.20131i
$428$		−	3.25518e27i		−	0.762809i
$429$	2.50272e26	−	1.55915e27i	0.0572282	−	0.356523i
$430$		−	3.56545e25i		−	0.00795601i
$431$			8.11612e27i			1.76741i	0.468044	+	0.883705i	$0.344959\pi$
$431$			8.11612e27i			1.76741i	−0.468044	+	0.883705i	$0.655041\pi$
$432$	−1.97526e27	+	3.81757e27i	−0.419803	+	0.811350i
$433$		−	2.10911e27i		−	0.437499i	−0.975781	−	0.218749i	$-0.929802\pi$
$433$		−	2.10911e27i		−	0.437499i	0.975781	−	0.218749i	$-0.0701977\pi$
$434$	6.59351e26	+	2.02340e26i	0.133498	+	0.0409675i
$435$	−7.65264e27	−	1.22839e27i	−1.51243	−	0.242771i
$436$	−1.32685e27			−0.255984
$437$	−1.25726e28			−2.36794
$438$	2.28066e26	−	1.42081e27i	0.0419355	−	0.261252i
$439$			7.48107e27i			1.34303i	0.740991	+	0.671515i	$0.234356\pi$
$439$			7.48107e27i			1.34303i	−0.740991	+	0.671515i	$0.765644\pi$
$440$	3.27445e27			0.573965
$441$	−3.56818e27	−	4.62644e27i	−0.610718	−	0.791848i
$442$	3.28118e26			0.0548398
$443$			1.77997e27i			0.290518i	0.989394	+	0.145259i	$0.0464016\pi$
$443$			1.77997e27i			0.290518i	−0.989394	+	0.145259i	$0.953598\pi$
$444$	−4.47249e26	+	2.78629e27i	−0.0712899	+	0.444125i
$445$	1.53188e28			2.38476
$446$	1.04803e27			0.159352
$447$	6.15702e27	+	9.88312e26i	0.914412	+	0.146779i
$448$	5.46669e27	+	1.67760e27i	0.793059	+	0.243372i
$449$		−	6.70454e27i		−	0.950128i	−0.879951	−	0.475064i	$-0.842425\pi$
$449$		−	6.70454e27i		−	0.950128i	0.879951	−	0.475064i	$-0.157575\pi$
$450$	5.93898e26	−	1.80228e27i	0.0822205	−	0.249511i
$451$		−	6.03496e27i		−	0.816246i
$452$		−	1.25821e28i		−	1.66265i
$453$	−1.66396e27	+	1.03662e28i	−0.214838	+	1.33841i
$454$			7.80888e25i			0.00985150i
$455$	−1.27861e27	+	4.16653e27i	−0.157623	+	0.513635i
$456$	5.49595e26	−	3.42389e27i	0.0662082	−	0.412466i
$457$	4.82928e27			0.568542			0.284271	−	0.958744i	$-0.408249\pi$
$457$	4.82928e27			0.568542			0.284271	+	0.958744i	$0.408249\pi$
$458$	8.81049e26			0.101371
$459$	−3.89627e27	+	7.53030e27i	−0.438143	+	0.846796i
$460$			2.68323e28i			2.94917i
$461$	−1.23732e28			−1.32930			−0.664648	−	0.747157i	$-0.731418\pi$
$461$	−1.23732e28			−1.32930			−0.664648	+	0.747157i	$0.731418\pi$
$462$	−7.67680e26	+	1.56156e27i	−0.0806194	+	0.163990i
$463$	1.82176e28			1.87022			0.935108	−	0.354364i	$-0.115302\pi$
$463$	1.82176e28			1.87022			0.935108	+	0.354364i	$0.115302\pi$
$464$			8.74895e27i			0.878046i
$465$	1.31263e28	+	2.10700e27i	1.28791	+	0.206732i
$466$	3.96041e25			0.00379916
$467$	8.95927e27			0.840321			0.420161	−	0.907450i	$-0.361974\pi$
$467$	8.95927e27			0.840321			0.420161	+	0.907450i	$0.361974\pi$
$468$	−1.11700e27	+	3.38973e27i	−0.102441	+	0.310873i
$469$	−9.33882e27	−	2.86587e27i	−0.837485	−	0.257005i
$470$			4.00984e27i			0.351641i
$471$	−7.04915e27	−	1.13151e27i	−0.604529	−	0.0970377i
$472$			5.61609e26i			0.0471024i
$473$			3.82069e26i			0.0313401i
$474$	−1.29619e27	−	2.08061e26i	−0.103991	−	0.0166924i
$475$		−	2.43776e28i		−	1.91297i
$476$	1.15290e28	+	3.53798e27i	0.884947	+	0.271570i
$477$	−4.11182e27	+	1.24780e28i	−0.308739	+	0.936918i
$478$	−1.93249e27			−0.141947
$479$	3.71334e27			0.266834			0.133417	−	0.991060i	$-0.457405\pi$
$479$	3.71334e27			0.266834			0.133417	+	0.991060i	$0.457405\pi$
$480$	−1.10148e28	−	1.76807e27i	−0.774360	−	0.124298i
$481$			2.27080e27i			0.156191i
$482$	−3.60653e27			−0.242714
$483$	−2.59758e28	−	1.27700e28i	−1.71050	−	0.840903i
$484$	−2.21750e27			−0.142885
$485$		−	1.94692e28i		−	1.22761i
$486$	1.93468e27	+	1.97536e27i	0.119379	+	0.121889i
$487$	−1.08522e28			−0.655334			−0.327667	−	0.944793i	$-0.606262\pi$
$487$	−1.08522e28			−0.655334			−0.327667	+	0.944793i	$0.606262\pi$
$488$	7.14952e27			0.422541
$489$	5.03638e27	−	3.13759e28i	0.291324	−	1.81490i
$490$	2.69387e27	−	3.97582e27i	0.152517	−	0.225096i
$491$			1.43543e28i			0.795472i	0.917500	+	0.397736i	$0.130204\pi$
$491$			1.43543e28i			0.795472i	−0.917500	+	0.397736i	$0.869796\pi$
$492$	−2.16178e27	+	1.34675e28i	−0.117267	+	0.730556i
$493$			1.72576e28i			0.916406i
$494$		−	1.37461e27i		−	0.0714574i
$495$	−1.04972e28	+	3.18555e28i	−0.534219	+	1.62117i
$496$		−	1.50067e28i		−	0.747701i
$497$	7.43209e27	−	2.42184e28i	0.362551	−	1.18142i
$498$	4.42940e27	+	7.10997e26i	0.211561	+	0.0339594i
$499$	1.12880e28			0.527912			0.263956	−	0.964535i	$-0.414973\pi$
$499$	1.12880e28			0.527912			0.263956	+	0.964535i	$0.414973\pi$
$500$	−1.82388e28			−0.835239
$501$	3.66991e27	−	2.28629e28i	0.164573	−	1.02526i
$502$			2.66324e27i			0.116956i
$503$	1.02864e28			0.442386			0.221193	−	0.975230i	$-0.429005\pi$
$503$	1.02864e28			0.442386			0.221193	+	0.975230i	$0.429005\pi$
$504$	4.61314e27	−	6.51574e27i	0.194301	−	0.274437i
$505$	−2.75142e28			−1.13500
$506$			8.62049e27i			0.348298i
$507$	3.54964e27	−	2.21137e28i	0.140476	−	0.875141i
$508$	3.91224e27			0.151655
$509$	8.65416e27			0.328616			0.164308	−	0.986409i	$-0.447461\pi$
$509$	8.65416e27			0.328616			0.164308	+	0.986409i	$0.447461\pi$
$510$	−6.88116e27	−	1.10455e27i	−0.255962	−	0.0410864i
$511$	1.24858e28	−	4.06865e28i	0.454984	−	1.48262i
$512$			2.11972e28i			0.756736i
$513$	3.15473e28	+	1.63230e28i	1.10339	+	0.570909i
$514$		−	6.34693e27i		−	0.217496i
$515$			1.36467e28i			0.458197i
$516$	1.36860e26	−	8.52618e26i	0.00450252	−	0.0280500i
$517$		−	4.29690e28i		−	1.38517i
$518$	7.34093e26	−	2.39214e27i	0.0231894	−	0.0755655i
$519$	−2.50381e27	+	1.55983e28i	−0.0775076	+	0.482860i
$520$	−5.95531e27			−0.180663
$521$	−4.59585e28			−1.36637			−0.683187	−	0.730244i	$-0.739407\pi$
$521$	−4.59585e28			−1.36637			−0.683187	+	0.730244i	$0.739407\pi$
$522$	5.34518e27	+	1.76138e27i	0.155748	+	0.0513230i
$523$			5.26887e28i			1.50470i	0.658764	+	0.752349i	$0.271079\pi$
$523$			5.26887e28i			1.50470i	−0.658764	+	0.752349i	$0.728921\pi$
$524$	−6.72356e27			−0.188201
$525$	2.47603e28	−	5.03656e28i	0.679334	−	1.38185i
$526$	3.68015e27			0.0989728
$527$		−	2.96013e28i		−	0.780367i
$528$	3.73822e28	+	6.00051e27i	0.966070	+	0.155071i
$529$	−1.03926e29			−2.63294
$530$	−1.07992e28			−0.268223
$531$	−5.46360e27	−	1.80040e27i	−0.133041	−	0.0438406i
$532$	1.48220e28	−	4.82993e28i	0.353862	−	1.15310i
$533$			1.09759e28i			0.256924i
$534$	−1.09828e28	−	1.76293e27i	−0.252074	−	0.0404624i
$535$			5.56365e28i			1.25212i
$536$		−	1.33482e28i		−	0.294572i
$537$	1.71637e28	+	2.75508e27i	0.371433	+	0.0596217i
$538$			1.43240e28i			0.303983i
$539$	−2.88672e28	+	4.26044e28i	−0.600789	+	0.886691i
$540$	3.48363e28	−	6.73279e28i	0.711045	−	1.37423i
$541$	2.60992e28			0.522464			0.261232	−	0.965276i	$-0.415871\pi$
$541$	2.60992e28			0.522464			0.261232	+	0.965276i	$0.415871\pi$
$542$	−7.40413e27			−0.145372
$543$	2.23368e28	+	3.58546e27i	0.430153	+	0.0690473i
$544$			2.48396e28i			0.469198i
$545$	2.26780e28			0.420186
$546$	1.39619e27	−	2.84004e27i	0.0253760	−	0.0516180i
$547$	−8.15351e28			−1.45371			−0.726855	−	0.686791i	$-0.759019\pi$
$547$	−8.15351e28			−1.45371			−0.726855	+	0.686791i	$0.759019\pi$
$548$		−	3.14031e28i		−	0.549258i
$549$	−2.29199e28	+	6.95540e28i	−0.393280	+	1.19347i
$550$	−1.67147e28			−0.281377
$551$	7.22988e28			1.19410
$552$	6.26845e27	−	3.90514e28i	0.101578	−	0.632814i
$553$	−3.71177e28	−	1.13906e28i	−0.590157	−	0.181106i
$554$			3.98031e27i			0.0620961i
$555$	7.64424e27	−	4.76224e28i	0.117019	−	0.729012i
$556$			3.46325e28i			0.520233i
$557$			8.12529e28i			1.19773i	0.800850	+	0.598865i	$0.204382\pi$
$557$			8.12529e28i			1.19773i	−0.800850	+	0.598865i	$0.795618\pi$
$558$	−9.16836e27	−	3.02122e27i	−0.132627	−	0.0437041i
$559$		−	6.94876e26i		−	0.00986469i
$560$	−9.98966e28	−	3.06560e28i	−1.39180	−	0.427112i
$561$	7.37377e28	+	1.18362e28i	1.00828	+	0.161846i
$562$	9.61043e27			0.128977
$563$	1.36835e29			1.80243			0.901215	−	0.433372i	$-0.142676\pi$
$563$	1.36835e29			1.80243			0.901215	+	0.433372i	$0.142676\pi$
$564$	−1.53919e28	+	9.58888e28i	−0.199003	+	1.23976i
$565$			2.15050e29i			2.72917i
$566$	−1.64862e28			−0.205375
$567$	4.85995e28	+	6.57669e28i	0.594305	+	0.804239i
$568$	3.46159e28			0.415545
$569$			9.33152e28i			1.09970i	0.835264	+	0.549849i	$0.185315\pi$
$569$			9.33152e28i			1.09970i	−0.835264	+	0.549849i	$0.814685\pi$
$570$	−4.62738e27	+	2.88278e28i	−0.0535364	+	0.333523i
$571$	1.49938e29			1.70307			0.851536	−	0.524296i	$-0.175671\pi$
$571$	1.49938e29			1.70307			0.851536	+	0.524296i	$0.175671\pi$
$572$	3.14369e28			0.350576
$573$	−1.24041e28	−	1.99108e27i	−0.135813	−	0.0218004i
$574$	3.54824e27	−	1.15624e28i	0.0381450	−	0.124300i
$575$		−	2.78041e29i		−	2.93492i
$576$	−7.60151e28	−	2.50490e28i	−0.787887	−	0.259629i
$577$			6.52072e28i			0.663666i	0.943338	+	0.331833i	$0.107667\pi$
$577$			6.52072e28i			0.663666i	−0.943338	+	0.331833i	$0.892333\pi$
$578$		−	1.55287e27i		−	0.0155200i
$579$	−1.35350e28	+	8.43209e28i	−0.132841	+	0.827581i
$580$		−	1.54299e29i		−	1.48720i
$581$	1.26841e29	+	3.89245e28i	1.20063	+	0.368446i
$582$	−2.24057e27	+	1.39584e28i	−0.0208289	+	0.129761i
$583$	1.15723e29			1.05657
$584$	5.81542e28			0.521490
$585$	1.90915e28	−	5.79361e28i	0.168152	−	0.510285i
$586$		−	7.20057e27i		−	0.0622934i
$587$	−8.71061e28			−0.740199			−0.370099	−	0.928992i	$-0.620676\pi$
$587$	−8.71061e28			−0.740199			−0.370099	+	0.928992i	$0.620676\pi$
$588$	7.96807e28	−	8.47347e28i	0.665107	−	0.707293i
$589$	−1.24011e29			−1.01683
$590$		−	4.72854e27i		−	0.0380874i
$591$	−1.51012e29	−	2.42402e28i	−1.19493	−	0.191808i
$592$	−5.44447e28			−0.423231
$593$	−2.35881e29			−1.80143			−0.900716	−	0.434408i	$-0.856958\pi$
$593$	−2.35881e29			−1.80143			−0.900716	+	0.434408i	$0.856958\pi$
$594$	1.11920e28	−	2.16306e28i	0.0839747	−	0.162297i
$595$	−1.97049e29	−	6.04700e28i	−1.45260	−	0.445771i
$596$			1.24143e29i			0.899160i
$597$	−3.35617e28	−	5.38725e27i	−0.238844	−	0.0383387i
$598$		−	1.56783e28i		−	0.109631i
$599$		−	1.72970e29i		−	1.18848i	−0.804290	−	0.594238i	$-0.797454\pi$
$599$		−	1.72970e29i		−	1.18848i	0.804290	−	0.594238i	$-0.202546\pi$
$600$	7.57185e28	+	1.21542e28i	0.511227	+	0.0820611i
$601$		−	2.72534e28i		−	0.180817i	−0.995905	−	0.0904084i	$-0.971183\pi$
$601$		−	2.72534e28i		−	0.180817i	0.995905	−	0.0904084i	$-0.0288172\pi$
$602$	−2.24636e26	+	7.32006e26i	−0.00146459	+	0.00477256i
$603$	1.29857e29	+	4.27914e28i	0.832023	+	0.274173i
$604$	−2.09012e29			−1.31608
$605$	3.79008e28			0.234540
$606$	1.97262e28	+	3.16641e27i	0.119972	+	0.0192577i
$607$			2.01615e29i			1.20515i	0.798061	+	0.602576i	$0.205859\pi$
$607$			2.01615e29i			1.20515i	−0.798061	+	0.602576i	$0.794141\pi$
$608$	1.04063e29			0.611375
$609$	1.49374e29	+	7.34339e28i	0.862567	+	0.424048i
$610$	−6.01963e28			−0.341670
$611$			7.81486e28i			0.436002i
$612$	−1.60312e29	−	5.28269e28i	−0.879176	−	0.289711i
$613$	1.72405e29			0.929428			0.464714	−	0.885461i	$-0.346157\pi$
$613$	1.72405e29			0.929428			0.464714	+	0.885461i	$0.346157\pi$
$614$	3.72342e28			0.197321
$615$	3.69484e28	−	2.30182e29i	0.192489	−	1.19918i
$616$	−6.72264e28	−	2.06302e28i	−0.344304	−	0.105659i
$617$			2.50226e29i			1.25991i	0.776633	+	0.629954i	$0.216926\pi$
$617$			2.50226e29i			1.25991i	−0.776633	+	0.629954i	$0.783074\pi$
$618$	1.57050e27	−	9.78398e27i	0.00777427	−	0.0484325i
$619$		−	1.67096e29i		−	0.813233i	−0.913599	−	0.406616i	$-0.866709\pi$
$619$		−	1.67096e29i		−	0.813233i	0.913599	−	0.406616i	$-0.133291\pi$
$620$			2.64663e29i			1.26643i
$621$	3.59816e29	+	1.86173e29i	1.69285	+	0.875901i
$622$			1.83587e28i			0.0849263i
$623$	−3.14503e29	−	9.65140e28i	−1.43054	−	0.439001i
$624$	−6.79878e28	−	1.09132e28i	−0.304083	−	0.0488108i
$625$	−3.83803e28			−0.168798
$626$	−5.60492e28			−0.242403
$627$	4.95865e28	−	3.08916e29i	0.210889	−	1.31380i
$628$		−	1.42131e29i		−	0.594446i
$629$	−1.07394e29			−0.441721
$630$	−3.88409e28	+	5.48601e28i	−0.157114	+	0.221912i
$631$	1.18588e27			0.00471774			0.00235887	−	0.999997i	$-0.499249\pi$
$631$	1.18588e27			0.00471774			0.00235887	+	0.999997i	$0.499249\pi$
$632$		−	5.30532e28i		−	0.207578i
$633$	4.58187e28	−	2.85443e29i	0.176321	−	1.09845i
$634$	4.64472e28			0.175801
$635$	−6.68667e28			−0.248935
$636$	−2.58245e29	−	4.14530e28i	−0.945656	−	0.151795i
$637$	5.25013e28	−	7.74855e28i	0.189106	−	0.279098i
$638$		−	4.95721e28i		−	0.175639i
$639$	−1.10971e29	+	3.36760e29i	−0.386769	+	1.17371i
$640$		−	2.94536e29i		−	1.00983i
$641$		−	3.71900e29i		−	1.25434i	−0.778881	−	0.627172i	$-0.784212\pi$
$641$		−	3.71900e29i		−	1.25434i	0.778881	−	0.627172i	$-0.215788\pi$
$642$	6.40281e27	−	3.98885e28i	0.0212448	−	0.132352i
$643$		−	3.90743e29i		−	1.27549i	−0.770249	−	0.637743i	$-0.779868\pi$
$643$		−	3.90743e29i		−	1.27549i	0.770249	−	0.637743i	$-0.220132\pi$
$644$	1.69053e29	−	5.50882e29i	0.542902	−	1.76912i
$645$	−2.33917e27	+	1.45727e28i	−0.00739070	+	0.0460429i
$646$	6.50101e28			0.202088
$647$	3.08437e29			0.943347			0.471673	−	0.881773i	$-0.343650\pi$
$647$	3.08437e29			0.943347			0.471673	+	0.881773i	$0.343650\pi$
$648$	−6.64292e28	+	8.98499e28i	−0.199904	+	0.270384i
$649$			5.06704e28i			0.150033i
$650$	3.03993e28			0.0885672
$651$	−2.56215e29	−	1.25958e29i	−0.734520	−	0.361099i
$652$	6.32626e29			1.78463
$653$		−	8.04579e28i		−	0.223347i	−0.993745	−	0.111674i	$-0.964379\pi$
$653$		−	8.04579e28i		−	0.223347i	0.993745	−	0.111674i	$-0.0356211\pi$
$654$	−1.62589e28	−	2.60985e27i	−0.0444146	−	0.00712934i
$655$	1.14917e29			0.308923
$656$	−2.63158e29			−0.696188
$657$	−1.86430e29	+	5.65752e29i	−0.485377	+	1.47295i
$658$	2.52635e28	−	8.23243e28i	0.0647323	−	0.210939i
$659$			5.58260e29i			1.40780i	0.710301	+	0.703898i	$0.248559\pi$
$659$			5.58260e29i			1.40780i	−0.710301	+	0.703898i	$0.751441\pi$
$660$	−6.59283e29	−	1.05827e29i	−1.63629	−	0.262654i
$661$			2.91146e29i			0.711207i	0.934637	+	0.355603i	$0.115725\pi$
$661$			2.91146e29i			0.711207i	−0.934637	+	0.355603i	$0.884275\pi$
$662$		−	9.91090e28i		−	0.238289i
$663$	−1.34108e29	−	2.15267e28i	−0.317368	−	0.0509432i
$664$			1.81296e29i			0.422302i
$665$	−2.53332e29	+	8.25517e29i	−0.580849	+	1.89277i
$666$	−1.09610e28	+	3.32630e28i	−0.0247384	+	0.0750727i
$667$	8.24609e29			1.83201
$668$	4.60981e29			1.00816
$669$	−4.28350e29	−	6.87578e28i	−0.922199	−	0.148029i
$670$			1.12387e29i			0.238193i
$671$	6.45056e29			1.34589
$672$	2.15000e29	+	1.05697e29i	0.441633	+	0.217112i
$673$	−2.98874e29			−0.604408			−0.302204	−	0.953243i	$-0.597722\pi$
$673$	−2.98874e29			−0.604408			−0.302204	+	0.953243i	$0.597722\pi$
$674$			2.40335e28i			0.0478506i
$675$	−3.60979e29	+	6.97663e29i	−0.707608	+	1.36759i
$676$	4.45875e29			0.860543
$677$	2.07189e29			0.393719			0.196859	−	0.980432i	$-0.436926\pi$
$677$	2.07189e29			0.393719			0.196859	+	0.980432i	$0.436926\pi$
$678$	2.47485e28	−	1.54179e29i	0.0463060	−	0.288479i
$679$	−1.22663e29	+	3.99713e29i	−0.225985	+	0.736403i
$680$		−	2.81647e29i		−	0.510930i
$681$	5.12315e27	−	3.19164e28i	0.00915151	−	0.0570124i
$682$			8.50291e28i			0.149565i
$683$			5.00451e28i			0.0866851i	0.999060	+	0.0433426i	$0.0138007\pi$
$683$			5.00451e28i			0.0866851i	−0.999060	+	0.0433426i	$0.986199\pi$
$684$	−2.21312e29	+	6.71608e29i	−0.377500	+	1.14558i
$685$			5.36731e29i			0.901584i
$686$	−8.03558e28	+	6.46534e28i	−0.132927	+	0.106952i
$687$	−3.60102e29	−	5.78028e28i	−0.586651	−	0.0941679i
$688$	1.66603e28			0.0267304
$689$	−2.10468e29			−0.332571
$690$	−5.27780e28	+	3.28798e29i	−0.0821367	+	0.511698i
$691$		−	4.80820e29i		−	0.736993i	−0.929629	−	0.368496i	$-0.879873\pi$
$691$		−	4.80820e29i		−	0.736993i	0.929629	−	0.368496i	$-0.120127\pi$
$692$	−3.14507e29			−0.474806
$693$	4.16214e29	−	5.87874e29i	0.618897	−	0.874149i
$694$	−2.90511e28			−0.0425489
$695$		−	5.91927e29i		−	0.853941i
$696$	−3.60467e28	+	2.24565e29i	−0.0512234	+	0.319114i
$697$	−5.19088e29			−0.726603
$698$	−9.17814e28			−0.126553
$699$	−1.61869e28	−	2.59829e27i	−0.0219864	−	0.00352921i
$700$	1.06813e30	+	3.27785e29i	1.42920	+	0.438590i
$701$		−	1.10836e30i		−	1.46097i	−0.682931	−	0.730483i	$-0.739295\pi$
$701$		−	1.10836e30i		−	1.46097i	0.682931	−	0.730483i	$-0.260705\pi$
$702$	−2.03550e28	+	3.93401e28i	−0.0264321	+	0.0510852i
$703$			4.49915e29i			0.575572i
$704$			7.04978e29i			0.888510i
$705$	2.63073e29	−	1.63890e30i	0.326656	−	2.03501i
$706$			9.94650e28i			0.121681i
$707$	5.64881e29	+	1.73349e29i	0.680853	+	0.208938i
$708$	1.81506e28	−	1.13075e29i	0.0215547	−	0.134282i
$709$	3.69654e29			0.432523			0.216262	−	0.976335i	$-0.430614\pi$
$709$	3.69654e29			0.432523			0.216262	+	0.976335i	$0.430614\pi$
$710$	−2.91453e29			−0.336013
$711$	5.16127e29	+	1.70077e29i	0.586308	+	0.193204i
$712$		−	4.49527e29i		−	0.503171i
$713$	−1.41442e30			−1.56005
$714$	1.34315e29	+	6.60308e28i	0.145980	+	0.0717655i
$715$	−5.37310e29			−0.575455
$716$			3.46069e29i			0.365238i
$717$	7.89847e29	+	1.26785e29i	0.821471	+	0.131861i
$718$	2.11936e29			0.217220
$719$	5.12329e28			0.0517482			0.0258741	−	0.999665i	$-0.491763\pi$
$719$	5.12329e28			0.0517482			0.0258741	+	0.999665i	$0.491763\pi$
$720$	1.38908e30	+	4.57737e29i	1.38272	+	0.455643i
$721$	8.59793e28	−	2.80175e29i	0.0843478	−	0.274858i
$722$		−	9.58914e28i		−	0.0927127i
$723$	1.47406e30	+	2.36613e29i	1.40463	+	0.225468i
$724$			4.50374e29i			0.422979i
$725$			1.59887e30i			1.48001i
$726$	−2.71729e28	−	4.36173e27i	−0.0247914	−	0.00397946i
$727$			3.90953e29i			0.351571i	0.984428	+	0.175785i	$0.0562465\pi$
$727$			3.90953e29i			0.351571i	−0.984428	+	0.175785i	$0.943753\pi$
$728$	1.22266e29	+	3.75206e28i	0.108374	+	0.0332576i
$729$	−6.61145e29	−	9.34295e29i	−0.577641	−	0.816291i
$730$	−4.89636e29			−0.421681
$731$	3.28631e28			0.0278982
$732$	−1.43950e30	−	2.31065e29i	−1.20460	−	0.193360i
$733$		−	2.37201e30i		−	1.95670i	−0.206956	−	0.978350i	$-0.566356\pi$
$733$		−	2.37201e30i		−	1.95670i	0.206956	−	0.978350i	$-0.433644\pi$
$734$	−2.50058e29			−0.203344
$735$	−1.36188e30	+	1.44826e30i	−1.09174	+	1.16099i
$736$	1.18690e30			0.937984
$737$		−	1.20432e30i		−	0.938283i
$738$	−5.29801e28	+	1.60777e29i	−0.0406931	+	0.123490i
$739$	−2.08219e30			−1.57671			−0.788357	−	0.615217i	$-0.789068\pi$
$739$	−2.08219e30			−1.57671			−0.788357	+	0.615217i	$0.789068\pi$
$740$	9.60202e29			0.716852
$741$	−9.01839e28	+	5.61831e29i	−0.0663801	+	0.413537i
$742$	2.21714e29	+	6.80390e28i	0.160899	+	0.0493761i
$743$			3.31867e29i			0.237455i	0.992927	+	0.118728i	$0.0378815\pi$
$743$			3.31867e29i			0.237455i	−0.992927	+	0.118728i	$0.962118\pi$
$744$	6.18294e28	−	3.85187e29i	0.0436194	−	0.271742i
$745$		−	2.12181e30i		−	1.47593i
$746$		−	2.18730e28i		−	0.0150020i
$747$	−1.76373e30	−	5.81197e29i	−1.19280	−	0.393058i
$748$			1.48676e30i			0.991458i
$749$	3.50530e29	−	1.14225e30i	0.230498	−	0.751107i
$750$	−2.23495e29	−	3.58749e28i	−0.144919	−	0.0232620i
$751$	−1.43488e30			−0.917481			−0.458740	−	0.888570i	$-0.651699\pi$
$751$	−1.43488e30			−0.917481			−0.458740	+	0.888570i	$0.651699\pi$
$752$	−1.87369e30			−1.18144
$753$	1.74727e29	−	1.08852e30i	0.108645	−	0.676844i
$754$			9.01578e28i			0.0552846i
$755$	3.57236e30			2.16029
$756$	−1.13940e30	+	1.16280e30i	−0.679511	+	0.693466i
$757$	2.39650e29			0.140952			0.0704758	−	0.997513i	$-0.477548\pi$
$757$	2.39650e29			0.140952			0.0704758	+	0.997513i	$0.477548\pi$
$758$		−	3.97426e28i		−	0.0230531i
$759$	5.65562e29	−	3.52336e30i	0.323550	−	2.01567i
$760$	−1.17993e30			−0.665753
$761$	−1.91913e30			−1.06799			−0.533994	−	0.845488i	$-0.679310\pi$
$761$	−1.91913e30			−1.06799			−0.533994	+	0.845488i	$0.679310\pi$
$762$	4.79399e28	+	7.69521e27i	0.0263130	+	0.00422370i
$763$	−4.65592e29	−	1.42880e29i	−0.252057	−	0.0773505i
$764$		−	2.50102e29i		−	0.133548i
$765$	2.74000e30	+	9.02901e29i	1.44313	+	0.475549i
$766$		−	6.11955e29i		−	0.317919i
$767$		−	9.21553e28i		−	0.0472247i
$768$	2.26204e29	−	1.40922e30i	0.114343	−	0.712335i
$769$			3.84840e29i			0.191890i	0.995387	+	0.0959452i	$0.0305874\pi$
$769$			3.84840e29i			0.191890i	−0.995387	+	0.0959452i	$0.969413\pi$
$770$	5.66021e29	+	1.73699e29i	0.278407	+	0.0854367i
$771$	−4.16402e29	+	2.59412e30i	−0.202042	+	1.25869i
$772$	−1.70015e30			−0.813777
$773$	−8.12135e29			−0.383481			−0.191740	−	0.981446i	$-0.561413\pi$
$773$	−8.12135e29			−0.383481			−0.191740	+	0.981446i	$0.561413\pi$
$774$	3.35413e27	−	1.01786e28i	0.00156243	−	0.00474144i
$775$		−	2.74248e30i		−	1.26030i
$776$	−5.71318e29			−0.259018
$777$	−4.56979e29	+	9.29552e29i	−0.204397	+	0.415770i
$778$	−4.93292e28			−0.0217680
$779$			2.17466e30i			0.946778i
$780$	1.19905e30	+	1.92469e29i	0.515044	+	0.0826738i
$781$	3.12318e30			1.32361
$782$	7.41478e29			0.310047
$783$	−2.06912e30	−	1.07059e30i	−0.853664	−	0.441696i
$784$	1.85779e30	+	1.25877e30i	0.756272	+	0.512422i
$785$			2.42926e30i			0.975757i
$786$	−8.23894e28	−	1.32250e28i	−0.0326539	−	0.00524153i
$787$			1.17516e29i			0.0459580i	0.999736	+	0.0229790i	$0.00731508\pi$
$787$			1.17516e29i			0.0459580i	−0.999736	+	0.0229790i	$0.992685\pi$
$788$		−	3.04484e30i		−	1.17500i
$789$	−1.50415e30	−	2.41443e29i	−0.572773	−	0.0919403i
$790$			4.46688e29i			0.167849i
$791$	1.35489e30	−	4.41509e30i	0.502402	−	1.63714i
$792$	9.34791e29	+	3.08038e29i	0.342058	+	0.112717i
$793$	−1.17318e30			−0.423638
$794$	−2.56373e28			−0.00913603
$795$	4.41385e30	+	7.08502e29i	1.55225	+	0.249164i
$796$		−	6.76699e29i		−	0.234860i
$797$	−1.58304e30			−0.542223			−0.271112	−	0.962548i	$-0.587391\pi$
$797$	−1.58304e30			−0.542223			−0.271112	+	0.962548i	$0.587391\pi$
$798$	2.76629e29	−	5.62698e29i	0.0935119	−	0.190215i
$799$	−3.69591e30			−1.23305
$800$			2.30132e30i			0.757762i
$801$	4.37321e30	+	1.44109e30i	1.42121	+	0.468327i
$802$	5.19806e29			0.166729
$803$	5.24688e30			1.66107
$804$	−4.31398e29	+	2.68754e30i	−0.134800	+	0.839782i
$805$	−2.88940e30	+	9.41549e30i	−0.891151	+	2.90393i
$806$		−	1.54644e29i		−	0.0470777i
$807$	9.39749e29	−	5.85449e30i	0.282384	−	1.75921i
$808$			8.07397e29i			0.239479i
$809$		−	1.05288e30i		−	0.308262i	−0.988050	−	0.154131i	$-0.950742\pi$
$809$		−	1.05288e30i		−	0.308262i	0.988050	−	0.154131i	$-0.0492578\pi$
$810$	5.59309e29	−	7.56503e29i	0.161644	−	0.218634i
$811$			4.54432e30i			1.29643i	0.761456	+	0.648216i	$0.224485\pi$
$811$			4.54432e30i			1.29643i	−0.761456	+	0.648216i	$0.775515\pi$
$812$	−9.72140e29	+	3.16784e30i	−0.273773	+	0.892125i
$813$	3.02621e30	+	4.85761e29i	0.841296	+	0.135043i
$814$	3.08487e29			0.0846605
$815$	−1.08126e31			−2.92939
$816$	5.16125e29	−	3.21537e30i	0.138041	−	0.859973i
$817$		−	1.37676e29i		−	0.0363519i
$818$	−4.70972e28			−0.0122768
$819$	−7.56977e29	+	1.06918e30i	−0.194806	+	0.275150i
$820$	4.64113e30			1.17918
$821$		−	2.51589e30i		−	0.631085i	−0.948911	−	0.315542i	$-0.897814\pi$
$821$		−	2.51589e30i		−	0.631085i	0.948911	−	0.315542i	$-0.102186\pi$
$822$	6.17686e28	−	3.84808e29i	0.0152973	−	0.0952994i
$823$	−7.08678e30			−1.73281			−0.866404	−	0.499343i	$-0.833575\pi$
$823$	−7.08678e30			−1.73281			−0.866404	+	0.499343i	$0.833575\pi$
$824$	4.00460e29			0.0966771
$825$	6.83160e30	+	1.09659e30i	1.62838	+	0.261384i
$826$	−2.97915e28	+	9.70796e28i	−0.00701136	+	0.0228474i
$827$			4.19827e30i			0.975579i	0.872961	+	0.487789i	$0.162197\pi$
$827$			4.19827e30i			0.975579i	−0.872961	+	0.487789i	$0.837803\pi$
$828$	−2.52420e30	+	7.66008e30i	−0.579168	+	1.75758i
$829$		−	4.30255e30i		−	0.974773i	−0.873186	−	0.487387i	$-0.837950\pi$
$829$		−	4.30255e30i		−	0.974773i	0.873186	−	0.487387i	$-0.162050\pi$
$830$		−	1.52645e30i		−	0.341477i
$831$	2.61135e29	−	1.62683e30i	0.0576839	−	0.359361i
$832$		−	1.28216e30i		−	0.279670i
$833$	3.66455e30	+	2.48297e30i	0.789312	+	0.534809i
$834$	−6.81206e28	+	4.24381e29i	−0.0144889	+	0.0902635i
$835$	−7.87895e30			−1.65486
$836$	6.22862e30			1.29189
$837$	3.54908e30	+	1.83634e30i	0.726939	+	0.376127i
$838$		−	5.52464e29i		−	0.111749i
$839$	1.19493e30			0.238694			0.119347	−	0.992853i	$-0.461920\pi$
$839$	1.19493e30			0.238694			0.119347	+	0.992853i	$0.461920\pi$
$840$	−2.43781e30	−	1.19845e30i	−0.480913	−	0.236423i
$841$	3.90927e29			0.0761618
$842$			2.36187e29i			0.0454443i
$843$	−3.92797e30	−	6.30509e29i	−0.746412	−	0.119812i
$844$	5.75534e30			1.08013
$845$	−7.62075e30			−1.41255
$846$	−3.77219e29	+	1.14473e30i	−0.0690565	+	0.209563i
$847$	−7.78125e29	−	2.38789e29i	−0.140693	−	0.0431756i
$848$		−	5.04617e30i		−	0.901168i
$849$	6.73822e30	+	1.08160e30i	1.18854	+	0.190782i
$850$			1.43769e30i			0.250476i
$851$			5.13154e30i			0.883054i
$852$	−6.96962e30	−	1.11875e30i	−1.18466	−	0.190159i
$853$			1.04905e31i			1.76130i	0.473768	+	0.880650i	$0.342894\pi$
$853$			1.04905e31i			1.76130i	−0.473768	+	0.880650i	$0.657106\pi$
$854$	1.23586e30	+	3.79259e29i	0.204957	+	0.0628967i
$855$	3.78260e30	−	1.14789e31i	0.619650	−	1.88043i
$856$	1.63264e30			0.264190
$857$	8.27982e30			1.32350			0.661748	−	0.749727i	$-0.269815\pi$
$857$	8.27982e30			1.32350			0.661748	+	0.749727i	$0.269815\pi$
$858$	3.85223e29	+	6.18352e28i	0.0608269	+	0.00976380i
$859$		−	3.26719e30i		−	0.509620i	−0.966991	−	0.254810i	$-0.917987\pi$
$859$		−	3.26719e30i		−	0.509620i	0.966991	−	0.254810i	$-0.0820129\pi$
$860$	−2.93827e29			−0.0452749
$861$	−2.20880e30	+	4.49299e30i	−0.336220	+	0.683915i
$862$	−2.00527e30			−0.301541
$863$		−	3.79827e30i		−	0.564251i	−0.959377	−	0.282126i	$-0.908960\pi$
$863$		−	3.79827e30i		−	0.564251i	0.959377	−	0.282126i	$-0.0910395\pi$
$864$	−2.97817e30	−	1.54094e30i	−0.437074	−	0.226148i
$865$	5.37545e30			0.779374
$866$	5.21103e29			0.0746424
$867$	−1.01879e29	+	6.34689e29i	−0.0144173	+	0.0898173i
$868$	1.66747e30	−	5.43368e30i	0.233132	−	0.759690i
$869$		−	4.78665e30i		−	0.661187i
$870$	3.03500e29	−	1.89075e30i	0.0414196	−	0.258038i
$871$			2.19032e30i			0.295337i
$872$		−	6.65482e29i		−	0.0886570i
$873$	1.83153e30	−	5.55806e30i	0.241081	−	0.731600i
$874$		−	3.10634e30i		−	0.403998i
$875$	−6.40002e30	−	1.96402e30i	−0.822426	−	0.252384i
$876$	−1.17088e31	−	1.87948e30i	−1.48669	−	0.238641i
$877$	−2.66342e30			−0.334151			−0.167076	−	0.985944i	$-0.553432\pi$
$877$	−2.66342e30			−0.334151			−0.167076	+	0.985944i	$0.553432\pi$
$878$	−1.84836e30			−0.229137
$879$	−4.72406e29	+	2.94301e30i	−0.0578671	+	0.360503i
$880$		−	1.28825e31i		−	1.55931i
$881$	−4.93472e29			−0.0590222			−0.0295111	−	0.999564i	$-0.509395\pi$
$881$	−4.93472e29			−0.0590222			−0.0295111	+	0.999564i	$0.509395\pi$
$882$	1.14306e30	−	8.81597e29i	0.135098	−	0.104196i
$883$	−2.54602e30			−0.297355			−0.148677	−	0.988886i	$-0.547502\pi$
$883$	−2.54602e30			−0.297355			−0.148677	+	0.988886i	$0.547502\pi$
$884$		−	2.70400e30i		−	0.312074i
$885$	−3.10224e29	+	1.93265e30i	−0.0353811	+	0.220418i
$886$	−4.39781e29			−0.0495658
$887$	3.68852e30			0.410823			0.205411	−	0.978676i	$-0.434147\pi$
$887$	3.68852e30			0.410823			0.205411	+	0.978676i	$0.434147\pi$
$888$	−1.39747e30	−	2.24318e29i	−0.153817	−	0.0246904i
$889$	1.37281e30	+	4.21284e29i	0.149328	+	0.0458255i
$890$			3.78485e30i			0.406868i
$891$	−5.99349e30	+	8.10659e30i	−0.636742	+	0.861237i
$892$		−	8.63675e30i		−	0.906816i
$893$			1.54836e31i			1.60669i
$894$	−2.44184e29	+	1.52123e30i	−0.0250423	+	0.156009i
$895$		−	5.91490e30i		−	0.599523i
$896$	−1.85568e30	+	6.04698e30i	−0.185896	+	0.605766i
$897$	−1.02860e30	+	6.40801e30i	−0.101842	+	0.634457i
$898$	1.65650e30			0.162103
$899$	8.13362e30			0.786696
$900$	−1.48525e31	−	4.89428e30i	−1.41988	−	0.467889i
$901$		−	9.95374e30i		−	0.940538i
$902$	1.49107e30			0.139261
$903$	1.39838e29	−	2.84448e29i	0.0129093	−	0.0262592i
$904$	6.31059e30			0.575839
$905$		−	7.69765e30i		−	0.694301i
$906$	−2.56120e30	−	4.11118e29i	−0.228348	−	0.0366539i
$907$	1.14185e31			1.00631			0.503156	−	0.864196i	$-0.332172\pi$
$907$	1.14185e31			1.00631			0.503156	+	0.864196i	$0.332172\pi$
$908$	6.43525e29			0.0560614
$909$	−7.85475e30	−	2.58834e30i	−0.676412	−	0.222896i
$910$	−1.02943e30	−	3.15910e29i	−0.0876322	−	0.0268923i
$911$		−	6.68124e30i		−	0.562230i	−0.959674	−	0.281115i	$-0.909296\pi$
$911$		−	6.68124e30i		−	0.562230i	0.959674	−	0.281115i	$-0.0907043\pi$
$912$	−1.34704e31	−	2.16225e30i	−1.12056	−	0.179870i
$913$			1.63572e31i			1.34513i
$914$			1.19318e30i			0.0969998i
$915$	2.46034e31	+	3.94928e30i	1.97731	+	0.317393i
$916$		−	7.26068e30i		−	0.576866i
$917$	−2.35931e30	−	7.24019e29i	−0.185313	−	0.0568685i
$918$	−1.86053e30	−	9.62659e29i	−0.144473	−	0.0747523i
$919$	1.57690e31			1.21057			0.605287	−	0.796007i	$-0.293058\pi$
$919$	1.57690e31			1.21057			0.605287	+	0.796007i	$0.293058\pi$
$920$	−1.34578e31			−1.02141
$921$	−1.52183e31	−	2.44281e30i	−1.14193	−	0.183301i
$922$		−	3.05707e30i		−	0.226793i
$923$	−5.68018e30			−0.416624
$924$	1.28687e31	+	6.32641e30i	0.933210	+	0.458777i
$925$	−9.94977e30			−0.713387
$926$			4.50107e30i			0.319081i
$927$	−1.28379e30	+	3.89587e30i	−0.0899823	+	0.273066i
$928$	−6.82524e30			−0.473003
$929$	−2.75773e31			−1.88967			−0.944837	−	0.327542i	$-0.893780\pi$
$929$	−2.75773e31			−1.88967			−0.944837	+	0.327542i	$0.893780\pi$
$930$	−5.20581e29	+	3.24313e30i	−0.0352710	+	0.219732i
$931$	1.04021e31	−	1.53522e31i	0.696867	−	1.02849i
$932$		−	3.26375e29i		−	0.0216197i
$933$	1.20445e30	−	7.50355e30i	0.0788919	−	0.491484i
$934$			2.21359e30i			0.143369i
$935$		−	2.54112e31i		−	1.62744i
$936$	−1.70012e30	−	5.60235e29i	−0.107667	−	0.0354792i
$937$			1.35211e31i			0.846734i	0.905958	+	0.423367i	$0.139152\pi$
$937$			1.35211e31i			0.846734i	−0.905958	+	0.423367i	$0.860848\pi$
$938$	7.08077e29	−	2.30736e30i	0.0438481	−	0.142885i
$939$	2.29084e31	+	3.67720e30i	1.40283	+	0.225180i
$940$	3.30449e31			2.00107
$941$	2.76551e31			1.65609			0.828045	−	0.560661i	$-0.189453\pi$
$941$	2.76551e31			1.65609			0.828045	+	0.560661i	$0.189453\pi$
$942$	2.79566e29	−	1.74165e30i	0.0165558	−	0.103140i
$943$			2.48033e31i			1.45257i
$944$	2.20951e30			0.127965
$945$	1.94742e31	−	1.98742e31i	1.11539	−	1.13830i
$946$	−9.43986e28			−0.00534698
$947$			1.41750e31i			0.794049i	0.917808	+	0.397025i	$0.129957\pi$
$947$			1.41750e31i			0.794049i	−0.917808	+	0.397025i	$0.870043\pi$
$948$	−1.71462e30	+	1.06818e31i	−0.0949906	+	0.591776i
$949$	−9.54261e30			−0.522844
$950$	6.02302e30			0.326375
$951$	−1.89839e31	−	3.04725e30i	−1.01739	−	0.163310i
$952$	−1.77448e30	+	5.78237e30i	−0.0940552	+	0.306491i
$953$			1.97217e31i			1.03388i	0.856022	+	0.516939i	$0.172929\pi$
$953$			1.97217e31i			1.03388i	−0.856022	+	0.516939i	$0.827071\pi$
$954$	−3.08296e30	−	1.01592e30i	−0.159849	−	0.0526745i
$955$			4.27466e30i			0.219213i
$956$			1.59256e31i			0.807769i
$957$	−3.25227e30	+	2.02611e31i	−0.163159	+	1.01645i
$958$			9.17463e29i			0.0455251i
$959$	3.38160e30	−	1.10194e31i	0.165969	−	0.540832i
$960$	−4.31615e30	+	2.68889e31i	−0.209531	+	1.30534i
$961$	6.87425e30			0.330088
$962$	−5.61052e29			−0.0266480
$963$	−5.23390e30	+	1.58831e31i	−0.245895	+	0.746208i
$964$			2.97212e31i			1.38120i
$965$	2.90584e31			1.33578
$966$	3.15511e30	−	6.41789e30i	0.143468	−	0.291832i
$967$	−7.32432e29			−0.0329450			−0.0164725	−	0.999864i	$-0.505244\pi$
$967$	−7.32432e29			−0.0329450			−0.0164725	+	0.999864i	$0.505244\pi$
$968$		−	1.11219e30i		−	0.0494867i
$969$	−2.65709e31	−	4.26510e30i	−1.16952	−	0.187728i
$970$	4.81029e30			0.209444
$971$	−1.27667e31			−0.549893			−0.274947	−	0.961460i	$-0.588660\pi$
$971$	−1.27667e31			−0.549893			−0.274947	+	0.961460i	$0.588660\pi$
$972$	1.62788e31	−	1.59436e31i	0.693628	−	0.679346i
$973$	−3.72936e30	+	1.21526e31i	−0.157199	+	0.512253i
$974$		−	2.68127e30i		−	0.111808i
$975$	−1.24248e31	−	1.99440e30i	−0.512555	−	0.0822741i
$976$		−	2.81281e31i		−	1.14793i
$977$		−	2.34907e31i		−	0.948426i	−0.880410	−	0.474213i	$-0.842733\pi$
$977$		−	2.34907e31i		−	0.948426i	0.880410	−	0.474213i	$-0.157267\pi$
$978$	7.75210e30	+	1.24435e30i	0.309643	+	0.0497032i
$979$		−	4.05580e31i		−	1.60272i
$980$	−3.27645e31	−	2.22000e31i	−1.28094	−	0.867920i
$981$	6.47412e30	+	2.13339e30i	0.250413	+	0.0825176i
$982$	−3.54654e30			−0.135717
$983$	2.67503e31			1.01278			0.506392	−	0.862304i	$-0.330979\pi$
$983$	2.67503e31			1.01278			0.506392	+	0.862304i	$0.330979\pi$
$984$	−6.75465e30	−	1.08424e30i	−0.253020	−	0.0406142i
$985$			5.20414e31i			1.92872i
$986$	−4.26387e30			−0.156350
$987$	−1.57267e31	+	3.19901e31i	−0.570568	+	1.16061i
$988$	−1.13281e31			−0.406639
$989$		−	1.57028e30i		−	0.0557718i
$990$	−7.87059e30	−	2.59357e30i	−0.276591	−	0.0911440i
$991$	−3.65554e31			−1.27110			−0.635548	−	0.772062i	$-0.719226\pi$
$991$	−3.65554e31			−1.27110			−0.635548	+	0.772062i	$0.719226\pi$
$992$	1.17071e31			0.402787
$993$	−6.50222e30	+	4.05078e31i	−0.221358	+	1.37902i
$994$	5.98370e30	+	1.83626e30i	0.201564	+	0.0618554i
$995$			1.15659e31i			0.385512i
$996$	5.85929e30	−	3.65024e31i	0.193251	−	1.20392i
$997$			5.76581e29i			0.0188175i	0.999956	+	0.00940874i	$0.00299494\pi$
$997$			5.76581e29i			0.0188175i	−0.999956	+	0.00940874i	$0.997005\pi$
$998$			2.78895e30i			0.0900680i
$999$	6.66226e30	−	1.28761e31i	0.212904	−	0.411479i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.22.c.b.20.4	yes	52
3.2	odd	2	inner	21.22.c.b.20.49	yes	52
7.6	odd	2	inner	21.22.c.b.20.50	yes	52
21.20	even	2	inner	21.22.c.b.20.3	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.22.c.b.20.3	✓	52	21.20	even	2	inner
21.22.c.b.20.4	yes	52	1.1	even	1	trivial
21.22.c.b.20.49	yes	52	3.2	odd	2	inner
21.22.c.b.20.50	yes	52	7.6	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	21.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+247.072i q^{2} +(16209.6 - 100983. i) q^{3} +2.03611e6 q^{4} -3.48005e7 q^{5} +(2.49501e7 + 4.00494e6i) q^{6} +(7.14474e8 + 2.19256e8i) q^{7} +1.02121e9i q^{8} +(-9.93485e9 - 3.27379e9i) q^{9} +O(q^{10})\)	\(q+247.072i q^{2} +(16209.6 - 100983. i) q^{3} +2.03611e6 q^{4} -3.48005e7 q^{5} +(2.49501e7 + 4.00494e6i) q^{6} +(7.14474e8 + 2.19256e8i) q^{7} +1.02121e9i q^{8} +(-9.93485e9 - 3.27379e9i) q^{9} -8.59823e9i q^{10} +9.21376e10i q^{11} +(3.30045e10 - 2.05613e11i) q^{12} -1.67572e11i q^{13} +(-5.41720e10 + 1.76527e11i) q^{14} +(-5.64102e11 + 3.51427e12i) q^{15} +4.01771e12 q^{16} +7.92508e12 q^{17} +(8.08863e11 - 2.45462e12i) q^{18} -3.32012e13i q^{19} -7.08576e13 q^{20} +(3.37225e13 - 6.85958e13i) q^{21} -2.27646e13 q^{22} -3.78679e14i q^{23} +(1.03125e14 + 1.65535e13i) q^{24} +7.34238e14 q^{25} +4.14025e13 q^{26} +(-4.91638e14 + 9.50186e14i) q^{27} +(1.45475e15 + 4.46428e14i) q^{28} +2.17759e15i q^{29} +(-8.68277e14 - 1.39374e14i) q^{30} -3.73514e15i q^{31} +3.13430e15i q^{32} +(9.30435e15 + 1.49351e15i) q^{33} +1.95807e15i q^{34} +(-2.48640e16 - 7.63021e15i) q^{35} +(-2.02284e16 - 6.66579e15i) q^{36} -1.35512e16 q^{37} +8.20309e15 q^{38} +(-1.69220e16 - 2.71628e15i) q^{39} -3.55387e16i q^{40} -6.54994e16 q^{41} +(1.69481e16 + 8.33188e15i) q^{42} +4.14672e15 q^{43} +1.87602e17i q^{44} +(3.45738e17 + 1.13930e17i) q^{45} +9.35610e16 q^{46} -4.66357e17 q^{47} +(6.51255e16 - 4.05721e17i) q^{48} +(4.62400e17 + 3.13305e17i) q^{49} +1.81410e17i q^{50} +(1.28462e17 - 8.00299e17i) q^{51} -3.41196e17i q^{52} -1.25598e18i q^{53} +(-2.34764e17 - 1.21470e17i) q^{54} -3.20643e18i q^{55} +(-2.23907e17 + 7.29630e17i) q^{56} +(-3.35276e18 - 5.38178e17i) q^{57} -5.38023e17 q^{58} +5.49943e17 q^{59} +(-1.14857e18 + 7.15542e18i) q^{60} -7.00101e18i q^{61} +9.22849e17 q^{62} +(-6.38039e18 - 4.51731e18i) q^{63} +7.65136e18 q^{64} +5.83161e18i q^{65} +(-3.69006e17 + 2.29884e18i) q^{66} -1.30709e19 q^{67} +1.61363e19 q^{68} +(-3.82402e19 - 6.13824e18i) q^{69} +(1.88521e18 - 6.14321e18i) q^{70} -3.38969e19i q^{71} +(3.34324e18 - 1.01456e19i) q^{72} -5.69462e19i q^{73} -3.34811e18i q^{74} +(1.19017e19 - 7.41457e19i) q^{75} -6.76012e19i q^{76} +(-2.02017e19 + 6.58299e19i) q^{77} +(6.71118e17 - 4.18095e18i) q^{78} -5.19511e19 q^{79} -1.39818e20 q^{80} +(8.79835e19 + 6.50493e19i) q^{81} -1.61831e19i q^{82} +1.77530e20 q^{83} +(6.86626e19 - 1.39668e20i) q^{84} -2.75797e20 q^{85} +1.02454e18i q^{86} +(2.19900e20 + 3.52979e19i) q^{87} -9.40921e19 q^{88} -4.40189e20 q^{89} +(-2.81488e19 + 8.54222e19i) q^{90} +(3.67412e19 - 1.19726e20i) q^{91} -7.71031e20i q^{92} +(-3.77186e20 - 6.05451e19i) q^{93} -1.15224e20i q^{94} +1.15542e21i q^{95} +(3.16512e20 + 5.08058e19i) q^{96} +5.59451e20i q^{97} +(-7.74089e19 + 1.14246e20i) q^{98} +(3.01639e20 - 9.15373e20i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 58720260 q^{4} + 1422287188 q^{7} + 10150644696 q^{9}+O(q^{10}) \) 52 * q - 58720260 * q^4 + 1422287188 * q^7 + 10150644696 * q^9	\( 52 q - 58720260 q^{4} + 1422287188 q^{7} + 10150644696 q^{9} - 687153165468 q^{15} + 36241782390404 q^{16} + 36759093002772 q^{18} + 79412641656180 q^{21} + 228880341648112 q^{22} + 45\!\cdots\!12 q^{25}+ \cdots + 15\!\cdots\!28 q^{99}+O(q^{100}) \) 52 * q - 58720260 * q^4 + 1422287188 * q^7 + 10150644696 * q^9 - 687153165468 * q^15 + 36241782390404 * q^16 + 36759093002772 * q^18 + 79412641656180 * q^21 + 228880341648112 * q^22 + 4502168959229812 * q^25 - 328465100861772 * q^28 - 2422487119598196 * q^30 + 94669723666911312 * q^36 - 111253244635261912 * q^37 - 198389110134084780 * q^39 - 125754675449474820 * q^42 + 808208758088766656 * q^43 - 1124214920076830456 * q^46 + 760563680048831596 * q^49 + 4341973540932052200 * q^51 - 13080454499124088812 * q^57 - 10814528487339424568 * q^58 + 13643758017961015644 * q^60 - 38182310822257441896 * q^63 - 30480555033993680900 * q^64 - 25547251957658589040 * q^67 + 73727169165159410040 * q^70 + 39846964674222889428 * q^72 + 45848199464273536260 * q^78 + 199210197493083963080 * q^79 + 235499606962845306588 * q^81 - 373919224753720758924 * q^84 - 570842672309470848672 * q^85 - 1060053674241923431168 * q^88 - 923077800435233893128 * q^91 - 2832166256981601869904 * q^93 + 1525182290356701596928 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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