LMFDB - Embedded newform 21.22.c.b.20.47

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			20.47
Character	$\chi$	$=$	21.20
Dual form			21.22.c.b.20.48

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2329.72i q^{2} +(-52907.9 + 87527.8i) q^{3} -3.33046e6 q^{4} +3.45099e7 q^{5} +(2.03916e8 + 1.23261e8i) q^{6} +(4.88555e7 + 7.45761e8i) q^{7} +2.87327e9i q^{8} +(-4.86187e9 - 9.26181e9i) q^{9} +O(q^{10})$	\(q-2329.72i q^{2} +(-52907.9 + 87527.8i) q^{3} -3.33046e6 q^{4} +3.45099e7 q^{5} +(2.03916e8 + 1.23261e8i) q^{6} +(4.88555e7 + 7.45761e8i) q^{7} +2.87327e9i q^{8} +(-4.86187e9 - 9.26181e9i) q^{9} -8.03985e10i q^{10} +5.12942e9i q^{11} +(1.76208e11 - 2.91508e11i) q^{12} -3.88435e11i q^{13} +(1.73742e12 - 1.13820e11i) q^{14} +(-1.82584e12 + 3.02057e12i) q^{15} -2.90549e11 q^{16} +4.11275e12 q^{17} +(-2.15775e13 + 1.13268e13i) q^{18} -7.35621e11i q^{19} -1.14934e14 q^{20} +(-6.78596e13 - 3.51804e13i) q^{21} +1.19501e13 q^{22} +2.80126e14i q^{23} +(-2.51491e14 - 1.52019e14i) q^{24} +7.14095e14 q^{25} -9.04946e14 q^{26} +(1.06790e15 + 6.44740e13i) q^{27} +(-1.62712e14 - 2.48373e15i) q^{28} -2.85990e15i q^{29} +(7.03710e15 + 4.25371e15i) q^{30} +8.55595e15i q^{31} +6.70259e15i q^{32} +(-4.48967e14 - 2.71387e14i) q^{33} -9.58157e15i q^{34} +(1.68600e15 + 2.57361e16i) q^{35} +(1.61923e16 + 3.08461e16i) q^{36} -2.16290e16 q^{37} -1.71379e15 q^{38} +(3.39988e16 + 2.05513e16i) q^{39} +9.91564e16i q^{40} +8.87944e16 q^{41} +(-8.19606e16 + 1.58094e17i) q^{42} +2.16141e17 q^{43} -1.70833e16i q^{44} +(-1.67783e17 - 3.19624e17i) q^{45} +6.52616e17 q^{46} -1.24937e17 q^{47} +(1.53723e16 - 2.54311e16i) q^{48} +(-5.53772e17 + 7.28691e16i) q^{49} -1.66364e18i q^{50} +(-2.17597e17 + 3.59980e17i) q^{51} +1.29367e18i q^{52} -1.11914e18i q^{53} +(1.50207e17 - 2.48791e18i) q^{54} +1.77016e17i q^{55} +(-2.14278e18 + 1.40375e17i) q^{56} +(6.43872e16 + 3.89201e16i) q^{57} -6.66279e18 q^{58} -3.06749e18 q^{59} +(6.08091e18 - 1.00599e19i) q^{60} +8.59883e18i q^{61} +1.99330e19 q^{62} +(6.66957e18 - 4.07828e18i) q^{63} +1.50059e19 q^{64} -1.34048e19i q^{65} +(-6.32256e17 + 1.04597e18i) q^{66} +9.86518e18 q^{67} -1.36974e19 q^{68} +(-2.45188e19 - 1.48209e19i) q^{69} +(5.99581e19 - 3.92791e18i) q^{70} +2.59864e19i q^{71} +(2.66117e19 - 1.39695e19i) q^{72} +2.69585e18i q^{73} +5.03895e19i q^{74} +(-3.77812e19 + 6.25032e19i) q^{75} +2.44996e18i q^{76} +(-3.82532e18 + 2.50600e17i) q^{77} +(4.78788e19 - 7.92079e19i) q^{78} +5.09894e19 q^{79} -1.00268e19 q^{80} +(-6.21434e19 + 9.00595e19i) q^{81} -2.06866e20i q^{82} +1.71105e20 q^{83} +(2.26004e20 + 1.17167e20i) q^{84} +1.41930e20 q^{85} -5.03549e20i q^{86} +(2.50321e20 + 1.51311e20i) q^{87} -1.47382e19 q^{88} +3.53288e20 q^{89} +(-7.44636e20 + 3.90887e20i) q^{90} +(2.89679e20 - 1.89772e19i) q^{91} -9.32949e20i q^{92} +(-7.48884e20 - 4.52677e20i) q^{93} +2.91069e20i q^{94} -2.53862e19i q^{95} +(-5.86663e20 - 3.54620e20i) q^{96} -1.89705e20i q^{97} +(1.69765e20 + 1.29014e21i) q^{98} +(4.75077e19 - 2.49386e19i) 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 $

$2$		−	2329.72i		−	1.60875i	−0.594119	−	0.804377i	$-0.702499\pi$
$2$		−	2329.72i		−	1.60875i	0.594119	−	0.804377i	$-0.297501\pi$
$3$	−52907.9	+	87527.8i	−0.517305	+	0.855801i
$3$	−52907.9	+	87527.8i	−0.517305	+	0.855801i
$4$	−3.33046e6			−1.58809
$5$	3.45099e7			1.58037			0.790184	−	0.612869i	$-0.209985\pi$
$5$	3.45099e7			1.58037			0.790184	+	0.612869i	$0.209985\pi$
$6$	2.03916e8	+	1.23261e8i	1.37677	+	0.832217i
$7$	4.88555e7	+	7.45761e8i	0.0653709	+	0.997861i
$7$	4.88555e7	+	7.45761e8i	0.0653709	+	0.997861i
$8$			2.87327e9i			0.946090i
$9$	−4.86187e9	−	9.26181e9i	−0.464790	−	0.885421i
$10$		−	8.03985e10i		−	2.54242i
$11$			5.12942e9i			0.0596273i	0.999555	+	0.0298136i	$0.00949138\pi$
$11$			5.12942e9i			0.0596273i	−0.999555	+	0.0298136i	$0.990509\pi$
$12$	1.76208e11	−	2.91508e11i	0.821527	−	1.35909i
$13$		−	3.88435e11i		−	0.781471i	−0.920503	−	0.390736i	$-0.872221\pi$
$13$		−	3.88435e11i		−	0.781471i	0.920503	−	0.390736i	$-0.127779\pi$
$14$	1.73742e12	−	1.13820e11i	1.60531	−	0.105166i
$15$	−1.82584e12	+	3.02057e12i	−0.817533	+	1.35248i
$16$	−2.90549e11			−0.0660633
$17$	4.11275e12			0.494787			0.247394	−	0.968915i	$-0.420426\pi$
$17$	4.11275e12			0.494787			0.247394	+	0.968915i	$0.420426\pi$
$18$	−2.15775e13	+	1.13268e13i	−1.42442	+	0.747733i
$19$		−	7.35621e11i		−	0.0275259i	−0.999905	−	0.0137629i	$-0.995619\pi$
$19$		−	7.35621e11i		−	0.0275259i	0.999905	−	0.0137629i	$-0.00438102\pi$
$20$	−1.14934e14			−2.50977
$21$	−6.78596e13	−	3.51804e13i	−0.887787	−	0.460254i
$22$	1.19501e13			0.0959256
$23$			2.80126e14i			1.40997i	0.709220	+	0.704987i	$0.249047\pi$
$23$			2.80126e14i			1.40997i	−0.709220	+	0.704987i	$0.750953\pi$
$24$	−2.51491e14	−	1.52019e14i	−0.809664	−	0.489417i
$25$	7.14095e14			1.49757
$26$	−9.04946e14			−1.25719
$27$	1.06790e15	+	6.44740e13i	0.998182	+	0.0602649i
$28$	−1.62712e14	−	2.48373e15i	−0.103815	−	1.58469i
$29$		−	2.85990e15i		−	1.26233i	−0.775649	−	0.631164i	$-0.782577\pi$
$29$		−	2.85990e15i		−	1.26233i	0.775649	−	0.631164i	$-0.217423\pi$
$30$	7.03710e15	+	4.25371e15i	2.17581	+	1.31521i
$31$			8.55595e15i			1.87487i	0.348163	+	0.937434i	$0.386806\pi$
$31$			8.55595e15i			1.87487i	−0.348163	+	0.937434i	$0.613194\pi$
$32$			6.70259e15i			1.05237i
$33$	−4.48967e14	−	2.71387e14i	−0.0510291	−	0.0308455i
$34$		−	9.58157e15i		−	0.795991i
$35$	1.68600e15	+	2.57361e16i	0.103310	+	1.57699i
$36$	1.61923e16	+	3.08461e16i	0.738128	+	1.40613i
$37$	−2.16290e16			−0.739465			−0.369733	−	0.929138i	$-0.620551\pi$
$37$	−2.16290e16			−0.739465			−0.369733	+	0.929138i	$0.620551\pi$
$38$	−1.71379e15			−0.0442824
$39$	3.39988e16	+	2.05513e16i	0.668784	+	0.404259i
$40$			9.91564e16i			1.49517i
$41$	8.87944e16			1.03313			0.516565	−	0.856248i	$-0.327210\pi$
$41$	8.87944e16			1.03313			0.516565	+	0.856248i	$0.327210\pi$
$42$	−8.19606e16	+	1.58094e17i	−0.740436	+	1.42823i
$43$	2.16141e17			1.52517			0.762585	−	0.646888i	$-0.223930\pi$
$43$	2.16141e17			1.52517			0.762585	+	0.646888i	$0.223930\pi$
$44$		−	1.70833e16i		−	0.0946934i
$45$	−1.67783e17	−	3.19624e17i	−0.734540	−	1.39929i
$46$	6.52616e17			2.26830
$47$	−1.24937e17			−0.346469			−0.173235	−	0.984881i	$-0.555422\pi$
$47$	−1.24937e17			−0.346469			−0.173235	+	0.984881i	$0.555422\pi$
$48$	1.53723e16	−	2.54311e16i	0.0341749	−	0.0565370i
$49$	−5.53772e17	+	7.28691e16i	−0.991453	+	0.130462i
$50$		−	1.66364e18i		−	2.40921i
$51$	−2.17597e17	+	3.59980e17i	−0.255956	+	0.423439i
$52$			1.29367e18i			1.24105i
$53$		−	1.11914e18i		−	0.878997i	−0.898243	−	0.439499i	$-0.855156\pi$
$53$		−	1.11914e18i		−	0.878997i	0.898243	−	0.439499i	$-0.144844\pi$
$54$	1.50207e17	−	2.48791e18i	0.0969515	−	1.60583i
$55$			1.77016e17i			0.0942331i
$56$	−2.14278e18	+	1.40375e17i	−0.944066	+	0.0618467i
$57$	6.43872e16	+	3.89201e16i	0.0235567	+	0.0142393i
$58$	−6.66279e18			−2.03078
$59$	−3.06749e18			−0.781335			−0.390667	−	0.920532i	$-0.627756\pi$
$59$	−3.06749e18			−0.781335			−0.390667	+	0.920532i	$0.627756\pi$
$60$	6.08091e18	−	1.00599e19i	1.29832	−	2.14786i
$61$			8.59883e18i			1.54339i	0.635992	+	0.771696i	$0.280591\pi$
$61$			8.59883e18i			1.54339i	−0.635992	+	0.771696i	$0.719409\pi$
$62$	1.99330e19			3.01620
$63$	6.66957e18	−	4.07828e18i	0.853143	−	0.521677i
$64$	1.50059e19			1.62694
$65$		−	1.34048e19i		−	1.23501i
$66$	−6.32256e17	+	1.04597e18i	−0.0496228	+	0.0820932i
$67$	9.86518e18			0.661180			0.330590	−	0.943774i	$-0.392752\pi$
$67$	9.86518e18			0.661180			0.330590	+	0.943774i	$0.392752\pi$
$68$	−1.36974e19			−0.785766
$69$	−2.45188e19	−	1.48209e19i	−1.20666	−	0.729387i
$70$	5.99581e19	−	3.92791e18i	2.53699	−	0.166201i
$71$			2.59864e19i			0.947398i	0.880687	+	0.473699i	$0.157082\pi$
$71$			2.59864e19i			0.947398i	−0.880687	+	0.473699i	$0.842918\pi$
$72$	2.66117e19	−	1.39695e19i	0.837687	−	0.439733i
$73$			2.69585e18i			0.0734184i	0.999326	+	0.0367092i	$0.0116875\pi$
$73$			2.69585e18i			0.0734184i	−0.999326	+	0.0367092i	$0.988312\pi$
$74$			5.03895e19i			1.18962i
$75$	−3.77812e19	+	6.25032e19i	−0.774699	+	1.28162i
$76$			2.44996e18i			0.0437135i
$77$	−3.82532e18	+	2.50600e17i	−0.0594997	+	0.00389789i
$78$	4.78788e19	−	7.92079e19i	0.650354	−	1.07591i
$79$	5.09894e19			0.605892			0.302946	−	0.953008i	$-0.402030\pi$
$79$	5.09894e19			0.605892			0.302946	+	0.953008i	$0.402030\pi$
$80$	−1.00268e19			−0.104404
$81$	−6.21434e19	+	9.00595e19i	−0.567940	+	0.823070i
$82$		−	2.06866e20i		−	1.66205i
$83$	1.71105e20			1.21044			0.605220	−	0.796058i	$-0.293085\pi$
$83$	1.71105e20			1.21044			0.605220	+	0.796058i	$0.293085\pi$
$84$	2.26004e20	+	1.17167e20i	1.40988	+	0.730925i
$85$	1.41930e20			0.781946
$86$		−	5.03549e20i		−	2.45362i
$87$	2.50321e20	+	1.51311e20i	1.08030	+	0.653009i
$88$	−1.47382e19			−0.0564127
$89$	3.53288e20			1.20098			0.600488	−	0.799634i	$-0.294973\pi$
$89$	3.53288e20			1.20098			0.600488	+	0.799634i	$0.294973\pi$
$90$	−7.44636e20	+	3.90887e20i	−2.25112	+	1.18169i
$91$	2.89679e20	−	1.89772e19i	0.779800	−	0.0510855i
$92$		−	9.32949e20i		−	2.23916i
$93$	−7.48884e20	−	4.52677e20i	−1.60451	−	0.969879i
$94$			2.91069e20i			0.557384i
$95$		−	2.53862e19i		−	0.0435010i
$96$	−5.86663e20	−	3.54620e20i	−0.900618	−	0.544396i
$97$		−	1.89705e20i		−	0.261201i	−0.991435	−	0.130601i	$-0.958309\pi$
$97$		−	1.89705e20i		−	0.261201i	0.991435	−	0.130601i	$-0.0416905\pi$
$98$	1.69765e20	+	1.29014e21i	0.209881	+	1.59500i
$99$	4.75077e19	−	2.49386e19i	0.0527952	−	0.0277142i
$100$	−2.37827e21			−2.37827
$101$	1.79298e21			1.61511			0.807555	−	0.589792i	$-0.200790\pi$
$101$	1.79298e21			1.61511			0.807555	+	0.589792i	$0.200790\pi$
$102$	8.38653e20	+	5.06940e20i	0.681209	+	0.411770i
$103$		−	7.07965e20i		−	0.519064i	−0.965734	−	0.259532i	$-0.916432\pi$
$103$		−	7.07965e20i		−	0.519064i	0.965734	−	0.259532i	$-0.0835684\pi$
$104$	1.11608e21			0.739342
$105$	−2.34183e21	−	1.21407e21i	−1.40303	−	0.727372i
$106$	−2.60729e21			−1.41409
$107$			3.36740e21i			1.65487i	0.561559	+	0.827436i	$0.310202\pi$
$107$			3.36740e21i			1.65487i	−0.561559	+	0.827436i	$0.689798\pi$
$108$	−3.55659e21	−	2.14728e20i	−1.58520	−	0.0957061i
$109$	2.91696e21			1.18019			0.590096	−	0.807333i	$-0.299090\pi$
$109$	2.91696e21			1.18019			0.590096	+	0.807333i	$0.299090\pi$
$110$	4.12398e20			0.151598
$111$	1.14434e21	−	1.89314e21i	0.382529	−	0.632835i
$112$	−1.41949e19	−	2.16680e20i	−0.00431861	−	0.0659220i
$113$			1.25082e21i			0.346635i	0.984866	+	0.173318i	$0.0554487\pi$
$113$			1.25082e21i			0.346635i	−0.984866	+	0.173318i	$0.944551\pi$
$114$	9.06731e19	−	1.50005e20i	0.0229075	−	0.0378969i
$115$			9.66711e21i			2.22828i
$116$			9.52480e21i			2.00469i
$117$	−3.59761e21	+	1.88852e21i	−0.691931	+	0.363220i
$118$			7.14641e21i			1.25698i
$119$	2.00930e20	+	3.06713e21i	0.0323447	+	0.493729i
$120$	−8.67894e21	−	5.24615e21i	−1.27957	−	0.773460i
$121$	7.37394e21			0.996445
$122$	2.00329e22			2.48294
$123$	−4.69792e21	+	7.77198e21i	−0.534444	+	0.884154i
$124$		−	2.84953e22i		−	2.97746i
$125$	8.18774e21			0.786338
$126$	−9.50128e21	−	1.55383e22i	−0.839250	−	1.37250i
$127$	−1.42120e22			−1.15536			−0.577680	−	0.816263i	$-0.696042\pi$
$127$	−1.42120e22			−1.15536			−0.577680	+	0.816263i	$0.696042\pi$
$128$		−	2.09032e22i		−	1.56498i
$129$	−1.14355e22	+	1.89183e22i	−0.788978	+	1.30524i
$130$	−3.12296e22			−1.98683
$131$	−1.04676e22			−0.614470			−0.307235	−	0.951634i	$-0.599404\pi$
$131$	−1.04676e22			−0.614470			−0.307235	+	0.951634i	$0.599404\pi$
$132$	1.49527e21	+	9.03843e20i	0.0810387	+	0.0489854i
$133$	5.48597e20	−	3.59391e19i	0.0274670	−	0.00179939i
$134$		−	2.29831e22i		−	1.06368i
$135$	3.68530e22	+	2.22499e21i	1.57750	+	0.0952408i
$136$			1.18171e22i			0.468113i
$137$			1.22907e22i			0.450829i	0.974263	+	0.225414i	$0.0723736\pi$
$137$			1.22907e22i			0.450829i	−0.974263	+	0.225414i	$0.927626\pi$
$138$	−3.45285e22	+	5.71220e22i	−1.17340	+	1.94121i
$139$		−	1.09006e22i		−	0.343397i	−0.985150	−	0.171699i	$-0.945074\pi$
$139$		−	1.09006e22i		−	0.343397i	0.985150	−	0.171699i	$-0.0549255\pi$
$140$	−5.61516e21	−	8.57132e22i	−0.164066	−	2.50440i
$141$	6.61016e21	−	1.09355e22i	0.179230	−	0.296509i
$142$	6.05410e22			1.52413
$143$	1.99244e21			0.0465970
$144$	1.41261e21	+	2.69101e21i	0.0307056	+	0.0584938i
$145$		−	9.86950e22i		−	1.99495i
$146$	6.28058e21			0.118112
$147$	2.29208e22	−	5.23258e22i	0.401235	−	0.915975i
$148$	7.20345e22			1.17434
$149$			5.07250e22i			0.770488i	0.922815	+	0.385244i	$0.125883\pi$
$149$			5.07250e22i			0.770488i	−0.922815	+	0.385244i	$0.874117\pi$
$150$	1.45615e23	+	8.80199e22i	2.06181	+	1.24630i
$151$	1.27095e23			1.67831			0.839153	−	0.543896i	$-0.183051\pi$
$151$	1.27095e23			1.67831			0.839153	+	0.543896i	$0.183051\pi$
$152$	2.11364e21			0.0260419
$153$	−1.99956e22	−	3.80915e22i	−0.229972	−	0.438095i
$154$	5.83830e20	+	8.91194e21i	0.00627074	+	0.0957204i
$155$			2.95265e23i			2.96298i
$156$	−1.13232e23	−	6.84452e22i	−1.06209	−	0.641999i
$157$			6.04275e22i			0.530015i	0.964246	+	0.265008i	$0.0853745\pi$
$157$			6.04275e22i			0.530015i	−0.964246	+	0.265008i	$0.914626\pi$
$158$		−	1.18791e23i		−	0.974731i
$159$	9.79558e22	+	5.92113e22i	0.752247	+	0.454710i
$160$			2.31306e23i			1.66313i
$161$	−2.08907e23	+	1.36857e22i	−1.40696	+	0.0921712i
$162$	2.09814e23	+	1.44777e23i	1.32412	+	0.913675i
$163$	1.14916e22			0.0679844			0.0339922	−	0.999422i	$-0.489178\pi$
$163$	1.14916e22			0.0679844			0.0339922	+	0.999422i	$0.489178\pi$
$164$	−2.95727e23			−1.64070
$165$	−1.54938e22	−	9.36552e21i	−0.0806448	−	0.0487473i
$166$		−	3.98628e23i		−	1.94730i
$167$	8.08026e21			0.0370597			0.0185299	−	0.999828i	$-0.494101\pi$
$167$	8.08026e21			0.0370597			0.0185299	+	0.999828i	$0.494101\pi$
$168$	1.01083e23	−	1.94979e23i	0.435442	−	0.839926i
$169$	9.61829e22			0.389303
$170$		−	3.30659e23i		−	1.25796i
$171$	−6.81318e21	+	3.57649e21i	−0.0243720	+	0.0127938i
$172$	−7.19849e23			−2.42210
$173$	−2.56010e22			−0.0810536			−0.0405268	−	0.999178i	$-0.512904\pi$
$173$	−2.56010e22			−0.0810536			−0.0405268	+	0.999178i	$0.512904\pi$
$174$	3.52514e23	−	5.83179e23i	1.05053	−	1.73794i
$175$	3.48875e22	+	5.32544e23i	0.0978972	+	1.49436i
$176$		−	1.49035e21i		−	0.00393917i
$177$	1.62294e23	−	2.68491e23i	0.404189	−	0.668667i
$178$		−	8.23064e23i		−	1.93207i
$179$			3.91102e23i			0.865632i	0.901482	+	0.432816i	$0.142480\pi$
$179$			3.91102e23i			0.865632i	−0.901482	+	0.432816i	$0.857520\pi$
$180$	5.58794e23	+	1.06450e24i	1.16651	+	2.22220i
$181$		−	1.49908e23i		−	0.295257i	−0.989043	−	0.147628i	$-0.952836\pi$
$181$		−	1.49908e23i		−	0.295257i	0.989043	−	0.147628i	$-0.0471640\pi$
$182$	−4.42116e22	−	6.74873e23i	−0.0821839	−	1.25451i
$183$	−7.52636e23	−	4.54946e23i	−1.32084	−	0.798405i
$184$	−8.04879e23			−1.33396
$185$	−7.46413e23			−1.16863
$186$	−1.05461e24	+	1.74469e24i	−1.56030	+	2.58127i
$187$			2.10960e22i			0.0295028i
$188$	4.16099e23			0.550224
$189$	4.09055e21	+	7.99546e23i	0.00511602	+	0.999987i
$190$	−5.91428e22			−0.0699825
$191$		−	8.64251e23i		−	0.967808i	−0.875121	−	0.483904i	$-0.839218\pi$
$191$		−	8.64251e23i		−	0.967808i	0.875121	−	0.483904i	$-0.160782\pi$
$192$	−7.93928e23	+	1.31343e24i	−0.841625	+	1.39234i
$193$	−9.50930e23			−0.954546			−0.477273	−	0.878755i	$-0.658375\pi$
$193$	−9.50930e23			−0.954546			−0.477273	+	0.878755i	$0.658375\pi$
$194$	−4.41960e23			−0.420208
$195$	1.17330e24	+	7.09221e23i	1.05693	+	0.638879i
$196$	1.84432e24	−	2.42688e23i	1.57452	−	0.207185i
$197$			1.85803e24i			1.50368i	0.659343	+	0.751842i	$0.270834\pi$
$197$			1.85803e24i			1.50368i	−0.659343	+	0.751842i	$0.729166\pi$
$198$	−5.81000e22	−	1.10680e23i	−0.0445853	−	0.0849345i
$199$		−	1.75406e24i		−	1.27670i	−0.769747	−	0.638349i	$-0.779618\pi$
$199$		−	1.75406e24i		−	1.27670i	0.769747	−	0.638349i	$-0.220382\pi$
$200$			2.05179e24i			1.41683i
$201$	−5.21946e23	+	8.63477e23i	−0.342032	+	0.565838i
$202$		−	4.17716e24i		−	2.59831i
$203$	2.13280e24	−	1.39722e23i	1.25963	−	0.0825195i
$204$	7.24698e23	−	1.19890e24i	0.406481	−	0.672459i
$205$	3.06429e24			1.63273
$206$	−1.64936e24			−0.835047
$207$	2.59447e24	−	1.36194e24i	1.24842	−	0.655342i
$208$			1.12859e23i			0.0516265i
$209$	3.77331e21			0.00164129
$210$	−2.82845e24	+	5.45581e24i	−1.17016	+	2.25713i
$211$	−4.91382e24			−1.93399			−0.966993	−	0.254802i	$-0.917990\pi$
$211$	−4.91382e24			−1.93399			−0.966993	+	0.254802i	$0.917990\pi$
$212$			3.72725e24i			1.39593i
$213$	−2.27453e24	−	1.37488e24i	−0.810784	−	0.490094i
$214$	7.84511e24			2.66228
$215$	7.45900e24			2.41033
$216$	−1.85251e23	+	3.06836e24i	−0.0570160	+	0.944370i
$217$	−6.38069e24	+	4.18006e23i	−1.87086	+	0.122562i
$218$		−	6.79571e24i		−	1.89864i
$219$	−2.35961e23	−	1.42631e23i	−0.0628316	−	0.0379798i
$220$		−	5.89544e23i		−	0.149650i
$221$		−	1.59753e24i		−	0.386662i
$222$	−4.41048e24	−	2.66600e24i	−1.01808	−	0.615395i
$223$		−	6.16436e24i		−	1.35733i	−0.734446	−	0.678667i	$-0.762558\pi$
$223$		−	6.16436e24i		−	1.35733i	0.734446	−	0.678667i	$-0.237442\pi$
$224$	−4.99853e24	+	3.27459e23i	−1.05012	+	0.0687943i
$225$	−3.47184e24	−	6.61382e24i	−0.696054	−	1.32598i
$226$	2.91408e24			0.557651
$227$	−6.93449e24			−1.26690			−0.633451	−	0.773783i	$-0.718362\pi$
$227$	−6.93449e24			−1.26690			−0.633451	+	0.773783i	$0.718362\pi$
$228$	−2.14439e23	−	1.29622e23i	−0.0374101	−	0.0226132i
$229$			3.15897e24i			0.526349i	0.964748	+	0.263174i	$0.0847694\pi$
$229$			3.15897e24i			0.526349i	−0.964748	+	0.263174i	$0.915231\pi$
$230$	2.25217e25			3.58475
$231$	1.80455e23	−	3.48080e23i	0.0274437	−	0.0529363i
$232$	8.21729e24			1.19428
$233$		−	9.88048e24i		−	1.37259i	−0.727323	−	0.686295i	$-0.759236\pi$
$233$		−	9.88048e24i		−	1.37259i	0.727323	−	0.686295i	$-0.240764\pi$
$234$	4.39973e24	+	8.38144e24i	0.584332	+	1.11315i
$235$	−4.31157e24			−0.547549
$236$	1.02162e25			1.24083
$237$	−2.69774e24	+	4.46299e24i	−0.313431	+	0.518523i
$238$	7.14556e24	−	4.68113e23i	0.794288	−	0.0520346i
$239$			2.66821e24i			0.283820i	0.989880	+	0.141910i	$0.0453243\pi$
$239$			2.66821e24i			0.283820i	−0.989880	+	0.141910i	$0.954676\pi$
$240$	5.30498e23	−	8.77626e23i	0.0540089	−	0.0893493i
$241$			1.85809e25i			1.81087i	0.424487	+	0.905434i	$0.360455\pi$
$241$			1.85809e25i			1.81087i	−0.424487	+	0.905434i	$0.639545\pi$
$242$		−	1.71792e25i		−	1.60303i
$243$	−4.59483e24	−	1.02041e25i	−0.410586	−	0.911822i
$244$		−	2.86381e25i		−	2.45104i
$245$	−1.91106e25	+	2.51470e24i	−1.56686	+	0.206178i
$246$	1.81066e25	+	1.09449e25i	1.42239	+	0.859789i
$247$	−2.85741e23			−0.0215107
$248$	−2.45836e25			−1.77379
$249$	−9.05281e24	+	1.49765e25i	−0.626167	+	1.03590i
$250$		−	1.90752e25i		−	1.26502i
$251$	2.27896e25			1.44932			0.724658	−	0.689108i	$-0.241998\pi$
$251$	2.27896e25			1.44932			0.724658	+	0.689108i	$0.241998\pi$
$252$	−2.22127e25	+	1.35826e25i	−1.35487	+	0.828469i
$253$	−1.43688e24			−0.0840729
$254$			3.31102e25i			1.85869i
$255$	−7.50924e24	+	1.24229e25i	−0.404505	+	0.669190i
$256$	−1.72291e25			−0.890721
$257$	−6.00249e24			−0.297875			−0.148937	−	0.988847i	$-0.547585\pi$
$257$	−6.00249e24			−0.297875			−0.148937	+	0.988847i	$0.547585\pi$
$258$	4.40745e25	+	2.66417e25i	2.09981	+	1.26927i
$259$	−1.05669e24	−	1.61300e25i	−0.0483395	−	0.737883i
$260$			4.46443e25i			1.96131i
$261$	−2.64879e25	+	1.39045e25i	−1.11769	+	0.586718i
$262$			2.43867e25i			0.988531i
$263$		−	4.58439e23i		−	0.0178545i	−0.999960	−	0.00892723i	$-0.997158\pi$
$263$		−	4.58439e23i		−	0.0178545i	0.999960	−	0.00892723i	$-0.00284166\pi$
$264$	7.79768e23	−	1.29000e24i	0.0291826	−	0.0482781i
$265$		−	3.86214e25i		−	1.38914i
$266$	−8.37283e22	−	1.27808e24i	−0.00289478	−	0.0441876i
$267$	−1.86917e25	+	3.09225e25i	−0.621271	+	1.02780i
$268$	−3.28556e25			−1.05001
$269$	−2.23413e25			−0.686610			−0.343305	−	0.939224i	$-0.611547\pi$
$269$	−2.23413e25			−0.686610			−0.343305	+	0.939224i	$0.611547\pi$
$270$	5.18361e24	−	8.58574e25i	0.153219	−	2.53780i
$271$		−	3.04586e25i		−	0.866029i	−0.901387	−	0.433014i	$-0.857450\pi$
$271$		−	3.04586e25i		−	0.866029i	0.901387	−	0.433014i	$-0.142550\pi$
$272$	−1.19496e24			−0.0326873
$273$	−1.36653e25	+	2.63590e25i	−0.359676	+	0.693780i
$274$	2.86340e25			0.725273
$275$			3.66289e24i			0.0892958i
$276$	8.16590e25	+	4.93603e25i	1.91628	+	1.15833i
$277$	2.91712e25			0.659048			0.329524	−	0.944147i	$-0.393112\pi$
$277$	2.91712e25			0.659048			0.329524	+	0.944147i	$0.393112\pi$
$278$	−2.53955e25			−0.552441
$279$	7.92437e25	−	4.15979e25i	1.66005	−	0.871420i
$280$	−7.39469e25	+	4.84434e24i	−1.49197	+	0.0977406i
$281$		−	3.04913e25i		−	0.592598i	−0.955095	−	0.296299i	$-0.904248\pi$
$281$		−	3.04913e25i		−	0.592598i	0.955095	−	0.296299i	$-0.0957525\pi$
$282$	−2.54767e25	−	1.53999e25i	−0.477009	−	0.288338i
$283$			2.91776e25i			0.526370i	0.964745	+	0.263185i	$0.0847730\pi$
$283$			2.91776e25i			0.526370i	−0.964745	+	0.263185i	$0.915227\pi$
$284$		−	8.65466e25i		−	1.50455i
$285$	2.22200e24	+	1.34313e24i	0.0372282	+	0.0225033i
$286$		−	4.64185e24i		−	0.0749631i
$287$	4.33810e24	+	6.62194e25i	0.0675366	+	1.03092i
$288$	6.20782e25	−	3.25871e25i	0.931790	−	0.489131i
$289$	−5.21772e25			−0.755186
$290$	−2.29932e26			−3.20938
$291$	1.66044e25	+	1.00369e25i	0.223536	+	0.135121i
$292$		−	8.97842e24i		−	0.116595i
$293$	3.72338e25			0.466474			0.233237	−	0.972420i	$-0.425068\pi$
$293$	3.72338e25			0.466474			0.233237	+	0.972420i	$0.425068\pi$
$294$	−1.21905e26	−	5.33992e25i	−1.47358	−	0.645488i
$295$	−1.05859e26			−1.23480
$296$		−	6.21460e25i		−	0.699600i
$297$	−3.30714e23	+	5.47769e24i	−0.00359343	+	0.0595189i
$298$	1.18175e26			1.23953
$299$	1.08811e26			1.10185
$300$	1.25829e26	−	2.08164e26i	1.23029	−	2.03532i
$301$	1.05597e25	+	1.61189e26i	0.0997017	+	1.52191i
$302$		−	2.96097e26i		−	2.69998i
$303$	−9.48630e25	+	1.56936e26i	−0.835505	+	1.38221i
$304$			2.13734e23i			0.00181845i
$305$			2.96745e26i			2.43913i
$306$	−8.87427e25	+	4.65843e25i	−0.704787	+	0.369969i
$307$			2.05384e26i			1.57621i	0.615543	+	0.788104i	$0.288937\pi$
$307$			2.05384e26i			1.57621i	−0.615543	+	0.788104i	$0.711063\pi$
$308$	1.27401e25	−	8.34616e23i	0.0944908	−	0.00619019i
$309$	6.19666e25	+	3.74569e25i	0.444216	+	0.268515i
$310$	6.87886e26			4.76671
$311$	−1.16711e26			−0.781860			−0.390930	−	0.920421i	$-0.627846\pi$
$311$	−1.16711e26			−0.781860			−0.390930	+	0.920421i	$0.627846\pi$
$312$	−5.90494e25	+	9.76880e25i	−0.382465	+	0.632729i
$313$		−	1.15011e26i		−	0.720315i	−0.932891	−	0.360158i	$-0.882723\pi$
$313$		−	1.15011e26i		−	0.720315i	0.932891	−	0.360158i	$-0.117277\pi$
$314$	1.40779e26			0.852664
$315$	2.30166e26	−	1.40741e26i	1.34828	−	0.824442i
$316$	−1.69818e26			−0.962210
$317$			5.49826e25i			0.301372i	0.988582	+	0.150686i	$0.0481483\pi$
$317$			5.49826e25i			0.301372i	−0.988582	+	0.150686i	$0.951852\pi$
$318$	1.37946e26	−	2.28210e26i	0.731516	−	1.21018i
$319$	1.46696e25			0.0752692
$320$	5.17851e26			2.57116
$321$	−2.94741e26	−	1.78162e26i	−1.41624	−	0.856075i
$322$	3.18839e25	+	4.86695e26i	0.148281	+	2.26345i
$323$		−	3.02542e24i		−	0.0136194i
$324$	2.06966e26	−	2.99940e26i	0.901939	−	1.30711i
$325$		−	2.77379e26i		−	1.17030i
$326$		−	2.67722e25i		−	0.109370i
$327$	−1.54330e26	+	2.55315e26i	−0.610519	+	1.01001i
$328$			2.55131e26i			0.977434i
$329$	−6.10388e24	−	9.31733e25i	−0.0226490	−	0.345728i
$330$	−2.18191e25	+	3.60962e25i	−0.0784224	+	0.129738i
$331$	−2.90493e26			−1.01145			−0.505723	−	0.862696i	$-0.668774\pi$
$331$	−2.90493e26			−1.01145			−0.505723	+	0.862696i	$0.668774\pi$
$332$	−5.69859e26			−1.92229
$333$	1.05157e26	+	2.00323e26i	0.343696	+	0.654738i
$334$		−	1.88248e25i		−	0.0596200i
$335$	3.40446e26			1.04491
$336$	1.97166e25	+	1.02216e25i	0.0586501	+	0.0304059i
$337$	−5.05078e26			−1.45628			−0.728139	−	0.685429i	$-0.759615\pi$
$337$	−5.05078e26			−1.45628			−0.728139	+	0.685429i	$0.759615\pi$
$338$		−	2.24080e26i		−	0.626292i
$339$	−1.09482e26	−	6.61785e25i	−0.296651	−	0.179316i
$340$	−4.72694e26			−1.24180
$341$	−4.38871e25			−0.111793
$342$	8.33224e24	+	1.58728e25i	0.0205820	+	0.0392085i
$343$	−8.13977e25	−	4.09421e26i	−0.194995	−	0.980804i
$344$			6.21032e26i			1.44295i
$345$	−8.46141e26	−	5.11466e26i	−1.90696	−	1.15270i
$346$			5.96432e25i			0.130395i
$347$			2.27772e26i			0.483103i	0.970388	+	0.241552i	$0.0776563\pi$
$347$			2.27772e26i			0.483103i	−0.970388	+	0.241552i	$0.922344\pi$
$348$	−8.33685e26	−	5.03937e26i	−1.71562	−	1.03704i
$349$		−	4.01953e26i		−	0.802616i	−0.915943	−	0.401308i	$-0.868556\pi$
$349$		−	4.01953e26i		−	0.802616i	0.915943	−	0.401308i	$-0.131444\pi$
$350$	1.24068e27	−	8.12782e25i	2.40406	−	0.157492i
$351$	2.50439e25	−	4.14808e26i	0.0470953	−	0.780051i
$352$	−3.43804e25			−0.0627499
$353$	7.95291e26			1.40894			0.704469	−	0.709735i	$-0.251185\pi$
$353$	7.95291e26			1.40894			0.704469	+	0.709735i	$0.251185\pi$
$354$	−6.25509e26	−	3.78101e26i	−1.07572	−	0.650240i
$355$			8.96786e26i			1.49724i
$356$	−1.17661e27			−1.90725
$357$	−2.79089e26	−	1.44688e26i	−0.439266	−	0.227728i
$358$	9.11160e26			1.39259
$359$		−	1.22948e26i		−	0.182486i	−0.995829	−	0.0912429i	$-0.970916\pi$
$359$		−	1.22948e26i		−	0.182486i	0.995829	−	0.0912429i	$-0.0290840\pi$
$360$	9.18368e26	−	4.82086e26i	1.32386	−	0.694941i
$361$	7.13668e26			0.999242
$362$	−3.49245e26			−0.474996
$363$	−3.90139e26	+	6.45425e26i	−0.515466	+	0.852758i
$364$	−9.64767e26	+	6.32028e25i	−1.23839	+	0.0811282i
$365$			9.30334e25i			0.116028i
$366$	−1.05990e27	+	1.75344e27i	−1.28444	+	2.12490i
$367$			3.38582e26i			0.398722i	0.979926	+	0.199361i	$0.0638866\pi$
$367$			3.38582e26i			0.398722i	−0.979926	+	0.199361i	$0.936113\pi$
$368$		−	8.13904e25i		−	0.0931475i
$369$	−4.31707e26	−	8.22397e26i	−0.480189	−	0.914755i
$370$			1.73894e27i			1.88003i
$371$	8.34610e26	−	5.46761e25i	0.877117	−	0.0574608i
$372$	2.49413e27	+	1.50762e27i	2.54811	+	1.54025i
$373$	7.10009e26			0.705215			0.352607	−	0.935771i	$-0.385295\pi$
$373$	7.10009e26			0.705215			0.352607	+	0.935771i	$0.385295\pi$
$374$	4.91479e25			0.0474627
$375$	−4.33196e26	+	7.16655e26i	−0.406777	+	0.672949i
$376$		−	3.58979e26i		−	0.327791i
$377$	−1.11089e27			−0.986473
$378$	1.86272e27	−	9.52984e24i	1.60873	−	0.00823042i
$379$	−1.84776e27			−1.55215			−0.776073	−	0.630643i	$-0.782791\pi$
$379$	−1.84776e27			−1.55215			−0.776073	+	0.630643i	$0.782791\pi$
$380$			8.45478e25i			0.0690835i
$381$	7.51929e26	−	1.24395e27i	0.597674	−	0.988759i
$382$	−2.01347e27			−1.55697
$383$	−8.45726e26			−0.636272			−0.318136	−	0.948045i	$-0.603057\pi$
$383$	−8.45726e26			−0.636272			−0.318136	+	0.948045i	$0.603057\pi$
$384$	1.82961e27	+	1.10594e27i	1.33931	+	0.809570i
$385$	−1.32011e26	+	8.64819e24i	−0.0940315	+	0.00616010i
$386$			2.21540e27i			1.53563i
$387$	−1.05085e27	−	2.00186e27i	−0.708884	−	1.35042i
$388$			6.31805e26i			0.414810i
$389$			1.41617e26i			0.0904992i	0.998976	+	0.0452496i	$0.0144083\pi$
$389$			1.41617e26i			0.0904992i	−0.998976	+	0.0452496i	$0.985592\pi$
$390$	1.65229e27	−	2.73346e27i	1.02780	−	1.70033i
$391$			1.15209e27i			0.697637i
$392$	−2.09373e26	−	1.59114e27i	−0.123429	−	0.938004i
$393$	5.53821e26	−	9.16210e26i	0.317869	−	0.525864i
$394$	4.32869e27			2.41906
$395$	1.75964e27			0.957533
$396$	−1.58223e26	+	8.30570e25i	−0.0838435	+	0.0440126i
$397$		−	2.27686e27i		−	1.17500i	−0.809225	−	0.587498i	$-0.800113\pi$
$397$		−	2.27686e27i		−	1.17500i	0.809225	−	0.587498i	$-0.199887\pi$
$398$	−4.08648e27			−2.05389
$399$	−2.58794e25	+	4.99189e25i	−0.0126689	+	0.0244371i
$400$	−2.07480e26			−0.0989341
$401$		−	1.94142e27i		−	0.901784i	−0.892579	−	0.450892i	$-0.851106\pi$
$401$		−	1.94142e27i		−	0.901784i	0.892579	−	0.450892i	$-0.148894\pi$
$402$	2.01166e27	+	1.21599e27i	0.910294	+	0.550245i
$403$	3.32343e27			1.46516
$404$	−5.97147e27			−2.56494
$405$	−2.14456e27	+	3.10794e27i	−0.897555	+	1.30075i
$406$	−3.25514e26	−	4.96884e27i	−0.132754	−	2.02643i
$407$		−	1.10944e26i		−	0.0440923i
$408$	−1.03432e27	−	6.25215e26i	−0.400611	−	0.242157i
$409$			2.53930e27i			0.958560i	0.877662	+	0.479280i	$0.159102\pi$
$409$			2.53930e27i			0.958560i	−0.877662	+	0.479280i	$0.840898\pi$
$410$		−	7.13894e27i		−	2.62666i
$411$	−1.07578e27	−	6.50276e26i	−0.385820	−	0.233216i
$412$			2.35785e27i			0.824320i
$413$	−1.49864e26	−	2.28761e27i	−0.0510765	−	0.779663i
$414$	−3.17294e27	−	6.04441e27i	−1.05428	−	2.00840i
$415$	5.90482e27			1.91294
$416$	2.60352e27			0.822396
$417$	9.54109e26	+	5.76729e26i	0.293880	+	0.177641i
$418$		−	8.79076e24i		−	0.00264044i
$419$	4.21573e27			1.23488			0.617442	−	0.786617i	$-0.288169\pi$
$419$	4.21573e27			1.23488			0.617442	+	0.786617i	$0.288169\pi$
$420$	7.79937e27	+	4.04342e27i	2.22814	+	1.15513i
$421$	−4.62166e27			−1.28776			−0.643881	−	0.765126i	$-0.722677\pi$
$421$	−4.62166e27			−1.28776			−0.643881	+	0.765126i	$0.722677\pi$
$422$			1.14478e28i			3.11131i
$423$	6.07429e26	+	1.15715e27i	0.161036	+	0.306771i
$424$	3.21559e27			0.831610
$425$	2.93689e27			0.740976
$426$	−3.20310e27	+	5.29902e27i	−0.788441	+	1.30435i
$427$	−6.41267e27	+	4.20100e26i	−1.54009	+	0.100893i
$428$		−	1.12150e28i		−	2.62808i
$429$	−1.05416e26	+	1.74394e26i	−0.0241049	+	0.0398777i
$430$		−	1.73774e28i		−	3.87763i
$431$			6.44524e27i			1.40355i	0.712399	+	0.701775i	$0.247609\pi$
$431$			6.44524e27i			1.40355i	−0.712399	+	0.701775i	$0.752391\pi$
$432$	−3.10277e26	−	1.87329e25i	−0.0659432	−	0.00398130i
$433$		−	2.69544e27i		−	0.559122i	−0.960128	−	0.279561i	$-0.909811\pi$
$433$		−	2.69544e27i		−	0.559122i	0.960128	−	0.279561i	$-0.0901889\pi$
$434$	9.73838e26	+	1.48653e28i	0.197172	+	3.00975i
$435$	8.63855e27	+	5.22174e27i	1.70728	+	1.03200i
$436$	−9.71483e27			−1.87425
$437$	2.06066e26			0.0388108
$438$	−3.32292e26	+	5.49725e26i	−0.0611001	+	0.101081i
$439$		−	3.86249e27i		−	0.693409i	−0.937974	−	0.346704i	$-0.887301\pi$
$439$		−	3.86249e27i		−	0.693409i	0.937974	−	0.346704i	$-0.112699\pi$
$440$	−5.08615e26			−0.0891529
$441$	3.36727e27	+	4.77465e27i	0.576332	+	0.817216i
$442$	−3.72181e27			−0.622044
$443$		−	7.13537e27i		−	1.16460i	−0.812973	−	0.582301i	$-0.802153\pi$
$443$		−	7.13537e27i		−	1.16460i	0.812973	−	0.582301i	$-0.197847\pi$
$444$	−3.81119e27	+	6.30502e27i	−0.607490	+	1.00500i
$445$	1.21919e28			1.89798
$446$	−1.43613e28			−2.18362
$447$	−4.43984e27	−	2.68375e27i	−0.659384	−	0.398578i
$448$	7.33120e26	+	1.11908e28i	0.106354	+	1.62346i
$449$			1.43840e27i			0.203842i	0.994792	+	0.101921i	$0.0324989\pi$
$449$			1.43840e27i			0.203842i	−0.994792	+	0.101921i	$0.967501\pi$
$450$	−1.54084e28	+	8.08843e27i	−2.13317	+	1.11978i
$451$			4.55464e26i			0.0616027i
$452$		−	4.16583e27i		−	0.550488i
$453$	−6.72433e27	+	1.11244e28i	−0.868196	+	1.43630i
$454$			1.61554e28i			2.03813i
$455$	9.99680e27	−	6.54901e26i	1.23237	−	0.0807339i
$456$	−1.11828e26	+	1.85002e26i	−0.0134716	+	0.0222867i
$457$	4.29861e27			0.506067			0.253033	−	0.967458i	$-0.418572\pi$
$457$	4.29861e27			0.506067			0.253033	+	0.967458i	$0.418572\pi$
$458$	7.35954e27			0.846765
$459$	4.39199e27	+	2.65165e26i	0.493888	+	0.0298183i
$460$		−	3.21960e28i		−	3.53870i
$461$	−5.09154e26			−0.0547003			−0.0273501	−	0.999626i	$-0.508707\pi$
$461$	−5.09154e26			−0.0547003			−0.0273501	+	0.999626i	$0.508707\pi$
$462$	−8.10931e26	−	4.20410e26i	−0.0851615	−	0.0441502i
$463$	6.80934e27			0.699044			0.349522	−	0.936928i	$-0.386344\pi$
$463$	6.80934e27			0.699044			0.349522	+	0.936928i	$0.386344\pi$
$464$			8.30943e26i			0.0833936i
$465$	−2.58439e28	−	1.56218e28i	−2.53572	−	1.53277i
$466$	−2.30188e28			−2.20816
$467$	1.41874e28			1.33068			0.665342	−	0.746539i	$-0.268286\pi$
$467$	1.41874e28			1.33068			0.665342	+	0.746539i	$0.268286\pi$
$468$	1.19817e28	−	6.28965e27i	1.09885	−	0.576826i
$469$	4.81969e26	+	7.35706e27i	0.0432219	+	0.659766i
$470$			1.00448e28i			0.880872i
$471$	−5.28909e27	−	3.19709e27i	−0.453588	−	0.274180i
$472$		−	8.81374e27i		−	0.739213i
$473$			1.10868e27i			0.0909417i
$474$	1.03975e28	+	6.28498e27i	0.834175	+	0.504233i
$475$		−	5.25303e26i		−	0.0412218i
$476$	−6.69192e26	−	1.02149e28i	−0.0513662	−	0.784085i
$477$	−1.03653e28	+	5.44111e27i	−0.778282	+	0.408549i
$478$	6.21620e27			0.456596
$479$	5.73151e27			0.411857			0.205928	−	0.978567i	$-0.433979\pi$
$479$	5.73151e27			0.411857			0.205928	+	0.978567i	$0.433979\pi$
$480$	−2.02457e28	−	1.22379e28i	−1.42331	−	0.860347i
$481$			8.40144e27i			0.577871i
$482$	4.32883e28			2.91324
$483$	9.85494e27	−	1.90092e28i	0.648947	−	1.25176i
$484$	−2.45586e28			−1.58244
$485$		−	6.54669e27i		−	0.412794i
$486$	−2.37728e28	+	1.07047e28i	−1.46690	+	0.660531i
$487$	−1.45983e28			−0.881554			−0.440777	−	0.897617i	$-0.645297\pi$
$487$	−1.45983e28			−0.881554			−0.440777	+	0.897617i	$0.645297\pi$
$488$	−2.47068e28			−1.46019
$489$	−6.07994e26	+	1.00583e27i	−0.0351687	+	0.0581811i
$490$	5.85857e27	+	4.45225e28i	0.331690	+	2.52070i
$491$			5.53228e27i			0.306583i	0.988181	+	0.153292i	$0.0489874\pi$
$491$			5.53228e27i			0.306583i	−0.988181	+	0.153292i	$0.951013\pi$
$492$	1.56463e28	−	2.58843e28i	0.848744	−	1.40411i
$493$		−	1.17621e28i		−	0.624584i
$494$			6.65697e26i			0.0346054i
$495$	1.63949e27	−	8.60627e26i	0.0834359	−	0.0437986i
$496$		−	2.48593e27i		−	0.123860i
$497$	−1.93796e28	+	1.26958e27i	−0.945372	+	0.0619323i
$498$	3.48910e28	+	2.10905e28i	1.66650	+	1.00735i
$499$	−3.09444e27			−0.144719			−0.0723597	−	0.997379i	$-0.523053\pi$
$499$	−3.09444e27			−0.144719			−0.0723597	+	0.997379i	$0.523053\pi$
$500$	−2.72690e28			−1.24877
$501$	−4.27509e26	+	7.07247e26i	−0.0191712	+	0.0317157i
$502$		−	5.30936e28i		−	2.33159i
$503$	1.43502e28			0.617155			0.308577	−	0.951199i	$-0.400147\pi$
$503$	1.43502e28			0.617155			0.308577	+	0.951199i	$0.400147\pi$
$504$	1.17180e28	+	1.91635e28i	0.493553	+	0.807150i
$505$	6.18757e28			2.55247
$506$			3.34754e27i			0.135253i
$507$	−5.08883e27	+	8.41868e27i	−0.201388	+	0.333166i
$508$	4.73327e28			1.83482
$509$	−1.09072e28			−0.414167			−0.207084	−	0.978323i	$-0.566397\pi$
$509$	−1.09072e28			−0.414167			−0.207084	+	0.978323i	$0.566397\pi$
$510$	2.89418e28	+	1.74944e28i	1.07656	+	0.650749i
$511$	−2.01046e27	+	1.31707e26i	−0.0732614	+	0.00479943i
$512$		−	3.69820e27i		−	0.132025i
$513$	4.74284e25	−	7.85567e26i	0.00165885	−	0.0274758i
$514$			1.39841e28i			0.479207i
$515$		−	2.44318e28i		−	0.820313i
$516$	3.80857e28	−	6.30068e28i	1.25297	−	2.07284i
$517$		−	6.40856e26i		−	0.0206590i
$518$	−3.75785e28	+	2.46181e27i	−1.18707	+	0.0777663i
$519$	1.35449e27	−	2.24080e27i	0.0419295	−	0.0693658i
$520$	3.85158e28			1.16843
$521$	1.25296e28			0.372512			0.186256	−	0.982501i	$-0.440365\pi$
$521$	1.25296e28			0.372512			0.186256	+	0.982501i	$0.440365\pi$
$522$	3.23936e28	+	6.17095e28i	0.943885	+	1.79809i
$523$		−	6.04609e28i		−	1.72666i	−0.504639	−	0.863330i	$-0.668375\pi$
$523$		−	6.04609e28i		−	1.72666i	0.504639	−	0.863330i	$-0.331625\pi$
$524$	3.48621e28			0.975832
$525$	−4.84582e28	−	2.51221e28i	−1.32952	−	0.689261i
$526$	−1.06804e27			−0.0287234
$527$			3.51885e28i			0.927660i
$528$	1.30447e26	+	7.88512e25i	0.00337115	+	0.00203775i
$529$	−3.89989e28			−0.988026
$530$	−8.99771e28			−2.23478
$531$	1.49137e28	+	2.84105e28i	0.363157	+	0.691810i
$532$	−1.82708e27	+	1.19694e26i	−0.0436200	+	0.00285759i
$533$		−	3.44908e28i		−	0.807362i
$534$	7.20410e28	+	4.35466e28i	1.65347	+	0.999472i
$535$			1.16208e29i			2.61531i
$536$			2.83454e28i			0.625535i
$537$	−3.42323e28	−	2.06924e28i	−0.740809	−	0.447796i
$538$			5.20492e28i			1.10459i
$539$	−3.73776e26	−	2.84053e27i	−0.00777910	−	0.0591177i
$540$	−1.22738e29	−	7.41024e27i	−2.50520	−	0.151251i
$541$	−6.04828e28			−1.21077			−0.605384	−	0.795934i	$-0.706980\pi$
$541$	−6.04828e28			−1.21077			−0.605384	+	0.795934i	$0.706980\pi$
$542$	−7.09601e28			−1.39323
$543$	1.31211e28	+	7.93132e27i	0.252681	+	0.152738i
$544$			2.75661e28i			0.520699i
$545$	1.00664e29			1.86514
$546$	6.14093e28	+	3.18363e28i	1.11612	+	0.578629i
$547$	−3.93098e28			−0.700864			−0.350432	−	0.936588i	$-0.613965\pi$
$547$	−3.93098e28			−0.700864			−0.350432	+	0.936588i	$0.613965\pi$
$548$		−	4.09338e28i		−	0.715956i
$549$	7.96408e28	−	4.18064e28i	1.36655	−	0.717353i
$550$	8.53353e27			0.143655
$551$	−2.10380e27			−0.0347467
$552$	4.25844e28	−	7.04493e28i	0.690065	−	1.14161i
$553$	2.49111e27	+	3.80259e28i	0.0396077	+	0.604596i
$554$		−	6.79609e28i		−	1.06025i
$555$	3.94911e28	−	6.53319e28i	0.604537	−	1.00011i
$556$			3.63042e28i			0.545345i
$557$		−	4.25859e28i		−	0.627750i	−0.949464	−	0.313875i	$-0.898373\pi$
$557$		−	4.25859e28i		−	0.627750i	0.949464	−	0.313875i	$-0.101627\pi$
$558$	−9.69117e28	−	1.84616e29i	−1.40190	−	2.67061i
$559$		−	8.39566e28i		−	1.19188i
$560$	−4.89866e26	−	7.47761e27i	−0.00682500	−	0.104181i
$561$	−1.84649e27	−	1.11614e27i	−0.0252485	−	0.0152620i
$562$	−7.10364e28			−0.953344
$563$	−7.91241e28			−1.04225			−0.521123	−	0.853481i	$-0.674487\pi$
$563$	−7.91241e28			−1.04225			−0.521123	+	0.853481i	$0.674487\pi$
$564$	−2.20149e28	+	3.64202e28i	−0.284634	+	0.470882i
$565$			4.31658e28i			0.547812i
$566$	6.79757e28			0.846800
$567$	−7.01989e28	−	4.19442e28i	−0.858436	−	0.512920i
$568$	−7.46659e28			−0.896324
$569$		−	3.77975e28i		−	0.445435i	−0.974883	−	0.222718i	$-0.928507\pi$
$569$		−	3.77975e28i		−	0.445435i	0.974883	−	0.222718i	$-0.0714928\pi$
$570$	3.12912e27	−	5.17664e27i	0.0362023	−	0.0598911i
$571$	−1.16410e29			−1.32224			−0.661119	−	0.750281i	$-0.729918\pi$
$571$	−1.16410e29			−1.32224			−0.661119	+	0.750281i	$0.729918\pi$
$572$	−6.63576e27			−0.0740002
$573$	7.56459e28	+	4.57256e28i	0.828251	+	0.500652i
$574$	1.54273e29	−	1.01066e28i	1.65850	−	0.108650i
$575$			2.00037e29i			2.11153i
$576$	−7.29566e28	−	1.38982e29i	−0.756186	−	1.44053i
$577$			2.25293e28i			0.229299i	0.993406	+	0.114650i	$0.0365745\pi$
$577$			2.25293e28i			0.229299i	−0.993406	+	0.114650i	$0.963425\pi$
$578$			1.21559e29i			1.21491i
$579$	5.03117e28	−	8.32328e28i	0.493792	−	0.816901i
$580$			3.28700e29i			3.16815i
$581$	8.35943e27	+	1.27603e29i	0.0791275	+	1.20785i
$582$	2.33831e28	−	3.86838e28i	0.217376	−	0.359615i
$583$	5.74053e27			0.0524122
$584$	−7.74591e27			−0.0694604
$585$	−1.24153e29	+	6.51726e28i	−1.09351	+	0.574022i
$586$		−	8.67446e28i		−	0.750443i
$587$	−1.72478e29			−1.46566			−0.732830	−	0.680412i	$-0.761801\pi$
$587$	−1.72478e29			−1.46566			−0.732830	+	0.680412i	$0.761801\pi$
$588$	−7.63370e28	+	1.74269e29i	−0.637196	+	1.45465i
$589$	6.29394e27			0.0516074
$590$			2.46622e29i			1.98648i
$591$	−1.62629e29	−	9.83042e28i	−1.28685	−	0.777864i
$592$	6.28428e27			0.0488515
$593$	−1.84171e28			−0.140652			−0.0703261	−	0.997524i	$-0.522404\pi$
$593$	−1.84171e28			−0.140652			−0.0703261	+	0.997524i	$0.522404\pi$
$594$	1.27615e28	+	7.70472e26i	0.0957512	+	0.00578095i
$595$	6.93409e27	+	1.05846e29i	0.0511165	+	0.780274i
$596$		−	1.68938e29i		−	1.22360i
$597$	1.53529e29	+	9.28037e28i	1.09260	+	0.660443i
$598$		−	2.53499e29i		−	1.77261i
$599$		−	1.07610e29i		−	0.739389i	−0.929153	−	0.369694i	$-0.879462\pi$
$599$		−	1.07610e29i		−	0.739389i	0.929153	−	0.369694i	$-0.120538\pi$
$600$	−1.79589e29	−	1.08556e29i	−1.21253	−	0.732935i
$601$		−	1.62804e29i		−	1.08015i	−0.841617	−	0.540075i	$-0.818396\pi$
$601$		−	1.62804e29i		−	1.08015i	0.841617	−	0.540075i	$-0.181604\pi$
$602$	3.75527e29	−	2.46011e28i	2.44837	−	0.160395i
$603$	−4.79632e28	−	9.13695e28i	−0.307310	−	0.585422i
$604$	−4.23286e29			−2.66530
$605$	2.54474e29			1.57475
$606$	3.65617e29	+	2.21005e29i	2.22364	+	1.34412i
$607$		−	3.12917e27i		−	0.0187046i	−0.999956	−	0.00935228i	$-0.997023\pi$
$607$		−	3.12917e27i		−	0.0187046i	0.999956	−	0.00935228i	$-0.00297697\pi$
$608$	4.93057e27			0.0289674
$609$	−1.00613e29	+	1.94072e29i	−0.580992	+	1.12068i
$610$	6.91333e29			3.92396
$611$			4.85300e28i			0.270756i
$612$	6.65948e28	+	1.26862e29i	0.365216	+	0.695733i
$613$	2.18203e29			1.17632			0.588161	−	0.808744i	$-0.299852\pi$
$613$	2.18203e29			1.17632			0.588161	+	0.808744i	$0.299852\pi$
$614$	4.78488e29			2.53573
$615$	−1.62125e29	+	2.68210e29i	−0.844619	+	1.39729i
$616$	−7.20044e26	−	1.09912e28i	−0.00368775	−	0.0562921i
$617$			6.39451e28i			0.321968i	0.986957	+	0.160984i	$0.0514668\pi$
$617$			6.39451e28i			0.321968i	−0.986957	+	0.160984i	$0.948533\pi$
$618$	8.72643e28	−	1.44365e29i	0.431974	−	0.714634i
$619$		−	7.74911e28i		−	0.377138i	−0.982060	−	0.188569i	$-0.939615\pi$
$619$		−	7.74911e28i		−	0.377138i	0.982060	−	0.188569i	$-0.0603849\pi$
$620$		−	9.83369e29i		−	4.70548i
$621$	−1.80608e28	+	2.99146e29i	−0.0849720	+	1.40741i
$622$			2.71905e29i			1.25782i
$623$	1.72601e28	+	2.63468e29i	0.0785088	+	1.19841i
$624$	−9.87834e27	−	5.97115e27i	−0.0441820	−	0.0267067i
$625$	−5.79489e28			−0.254862
$626$	−2.67943e29			−1.15881
$627$	−1.99638e26	+	3.30269e26i	−0.000849050	+	0.00140462i
$628$		−	2.01252e29i		−	0.841711i
$629$	−8.89545e28			−0.365878
$630$	−3.27888e29	−	5.36223e29i	−1.32632	−	2.16905i
$631$	−6.62000e28			−0.263360			−0.131680	−	0.991292i	$-0.542037\pi$
$631$	−6.62000e28			−0.263360			−0.131680	+	0.991292i	$0.542037\pi$
$632$			1.46506e29i			0.573228i
$633$	2.59980e29	−	4.30096e29i	1.00046	−	1.65511i
$634$	1.28094e29			0.484834
$635$	−4.90456e29			−1.82590
$636$	−3.26238e29	−	1.97201e29i	−1.19463	−	0.722120i
$637$	2.83049e28	+	2.15104e29i	0.101952	+	0.774792i
$638$		−	3.41762e28i		−	0.121090i
$639$	2.40681e29	−	1.26342e29i	0.838846	−	0.440342i
$640$		−	7.21366e29i		−	2.47324i
$641$		−	5.35790e29i		−	1.80711i	−0.428469	−	0.903556i	$-0.640947\pi$
$641$		−	5.35790e29i		−	1.80711i	0.428469	−	0.903556i	$-0.359053\pi$
$642$	−4.15068e29	+	6.86665e29i	−1.37721	+	2.27838i
$643$		−	7.02568e27i		−	0.0229336i	−0.999934	−	0.0114668i	$-0.996350\pi$
$643$		−	7.02568e27i		−	0.0229336i	0.999934	−	0.0114668i	$-0.00365008\pi$
$644$	6.95757e29	−	4.55797e28i	2.23437	−	0.146376i
$645$	−3.94639e29	+	6.52869e29i	−1.24688	+	2.06276i
$646$	−7.04840e27			−0.0219103
$647$	−1.86087e29			−0.569141			−0.284571	−	0.958655i	$-0.591851\pi$
$647$	−1.86087e29			−0.569141			−0.284571	+	0.958655i	$0.591851\pi$
$648$	−2.58766e29	−	1.78555e29i	−0.778698	−	0.537322i
$649$		−	1.57344e28i		−	0.0465889i
$650$	−6.46218e29			−1.88273
$651$	3.01002e29	−	5.80604e29i	0.862916	−	1.66448i
$652$	−3.82722e28			−0.107965
$653$			1.68964e29i			0.469037i	0.972112	+	0.234518i	$0.0753513\pi$
$653$			1.68964e29i			0.469037i	−0.972112	+	0.234518i	$0.924649\pi$
$654$	5.94814e29	+	3.59547e29i	1.62486	+	0.982175i
$655$	−3.61237e29			−0.971089
$656$	−2.57992e28			−0.0682520
$657$	2.49684e28	−	1.31069e28i	0.0650062	−	0.0341242i
$658$	−2.17068e29	+	1.42204e28i	−0.556191	+	0.0364367i
$659$		−	1.52596e29i		−	0.384809i	−0.981316	−	0.192405i	$-0.938371\pi$
$659$		−	1.52596e29i		−	0.384809i	0.981316	−	0.192405i	$-0.0616286\pi$
$660$	5.16015e28	+	3.11915e28i	0.128071	+	0.0774150i
$661$			1.90403e29i			0.465112i	0.972583	+	0.232556i	$0.0747090\pi$
$661$			1.90403e29i			0.465112i	−0.972583	+	0.232556i	$0.925291\pi$
$662$			6.76770e29i			1.62717i
$663$	1.39829e29	+	8.45221e28i	0.330906	+	0.200022i
$664$			4.91632e29i			1.14518i
$665$	1.89320e28	−	1.24026e27i	0.0434080	−	0.00284370i
$666$	4.66698e29	−	2.44987e29i	1.05331	−	0.552923i
$667$	8.01133e29			1.77985
$668$	−2.69110e28			−0.0588541
$669$	5.39552e29	+	3.26143e29i	1.16161	+	0.702156i
$670$		−	7.93146e29i		−	1.68100i
$671$	−4.41070e28			−0.0920282
$672$	2.35800e29	−	4.54835e29i	0.484358	−	0.934280i
$673$	−9.33776e29			−1.88836			−0.944180	−	0.329431i	$-0.893143\pi$
$673$	−9.33776e29			−1.88836			−0.944180	+	0.329431i	$0.893143\pi$
$674$			1.17669e30i			2.34279i
$675$	7.62580e29	+	4.60405e28i	1.49484	+	0.0902507i
$676$	−3.20334e29			−0.618247
$677$	5.35876e29			1.01832			0.509159	−	0.860673i	$-0.329957\pi$
$677$	5.35876e29			1.01832			0.509159	+	0.860673i	$0.329957\pi$
$678$	−1.54178e29	+	2.55063e29i	−0.288476	+	0.477238i
$679$	1.41474e29	−	9.26813e27i	0.260642	−	0.0170749i
$680$			4.07805e29i			0.739791i
$681$	3.66889e29	−	6.06960e29i	0.655375	−	1.08422i
$682$			1.02245e29i			0.179848i
$683$			1.98799e29i			0.344347i	0.985067	+	0.172173i	$0.0550789\pi$
$683$			1.98799e29i			0.344347i	−0.985067	+	0.172173i	$0.944921\pi$
$684$	2.26911e28	−	1.19114e28i	0.0387049	−	0.0203176i
$685$			4.24152e29i			0.712476i
$686$	−9.53839e29	+	1.89634e29i	−1.57787	+	0.313699i
$687$	−2.76498e29	−	1.67135e29i	−0.450450	−	0.272283i
$688$	−6.27996e28			−0.100758
$689$	−4.34713e29			−0.686911
$690$	−1.19158e30	+	1.97128e30i	−1.85441	+	3.06783i
$691$			1.59235e29i			0.244073i	0.992526	+	0.122036i	$0.0389424\pi$
$691$			1.59235e29i			0.244073i	−0.992526	+	0.122036i	$0.961058\pi$
$692$	8.52631e28			0.128720
$693$	2.09192e28	+	3.42110e28i	0.0311062	+	0.0508706i
$694$	5.30645e29			0.777194
$695$		−	3.76180e29i		−	0.542694i
$696$	−4.34759e29	+	7.19241e29i	−0.617805	+	1.02206i
$697$	3.65189e29			0.511180
$698$	−9.36439e29			−1.29121
$699$	8.64816e29	+	5.22755e29i	1.17466	+	0.710048i
$700$	−1.16192e29	−	1.77362e30i	−0.155469	−	2.37318i
$701$		−	1.17219e30i		−	1.54511i	−0.634947	−	0.772556i	$-0.718978\pi$
$701$		−	1.17219e30i		−	1.54511i	0.634947	−	0.772556i	$-0.281022\pi$
$702$	−9.66389e29	−	5.83454e28i	−1.25491	−	0.0757648i
$703$			1.59107e28i			0.0203544i
$704$			7.69714e28i			0.0970100i
$705$	2.28116e29	−	3.77382e29i	0.283250	−	0.468593i
$706$		−	1.85281e30i		−	2.26663i
$707$	8.75972e28	+	1.33714e30i	0.105581	+	1.61166i
$708$	−5.40515e29	+	8.94198e29i	−0.641887	+	1.06190i
$709$	−1.06385e30			−1.24479			−0.622394	−	0.782704i	$-0.713840\pi$
$709$	−1.06385e30			−1.24479			−0.622394	+	0.782704i	$0.713840\pi$
$710$	2.08926e30			2.40869
$711$	−2.47904e29	−	4.72254e29i	−0.281613	−	0.536469i
$712$			1.01509e30i			1.13623i
$713$	−2.39674e30			−2.64351
$714$	−3.37083e29	+	6.50202e29i	−0.366358	+	0.706670i
$715$	6.87590e28			0.0736404
$716$		−	1.30255e30i		−	1.37470i
$717$	−2.33543e29	−	1.41169e29i	−0.242893	−	0.146821i
$718$	−2.86434e29			−0.293575
$719$	−6.67357e29			−0.674070			−0.337035	−	0.941492i	$-0.609424\pi$
$719$	−6.67357e29			−0.674070			−0.337035	+	0.941492i	$0.609424\pi$
$720$	4.87491e28	+	9.28666e28i	0.0485261	+	0.0924418i
$721$	5.27973e29	−	3.45880e28i	0.517954	−	0.0339317i
$722$		−	1.66265e30i		−	1.60753i
$723$	−1.62634e30	−	9.83073e29i	−1.54974	−	0.936772i
$724$			4.99263e29i			0.468894i
$725$		−	2.04224e30i		−	1.89042i
$726$	1.50366e30	+	9.08917e29i	1.37188	+	0.829258i
$727$		−	6.90567e29i		−	0.621004i	−0.950573	−	0.310502i	$-0.899503\pi$
$727$		−	6.90567e29i		−	0.621004i	0.950573	−	0.310502i	$-0.100497\pi$
$728$	5.45267e28	+	8.32329e29i	0.0483314	+	0.737760i
$729$	1.13625e30	+	1.37703e29i	0.992736	+	0.120311i
$730$	2.16742e29			0.186661
$731$	8.88933e29			0.754634
$732$	2.50663e30	+	1.51518e30i	2.09760	+	1.26794i
$733$		−	4.20731e29i		−	0.347066i	−0.984828	−	0.173533i	$-0.944482\pi$
$733$		−	4.20731e29i		−	0.347066i	0.984828	−	0.173533i	$-0.0555184\pi$
$734$	7.88802e29			0.641445
$735$	7.90995e29	−	1.80576e30i	0.634099	−	1.44758i
$736$	−1.87757e30			−1.48381
$737$			5.06026e28i			0.0394243i
$738$	−1.91596e30	+	1.00576e30i	−1.47162	+	0.772506i
$739$	1.25107e30			0.947357			0.473678	−	0.880698i	$-0.342926\pi$
$739$	1.25107e30			0.947357			0.473678	+	0.880698i	$0.342926\pi$
$740$	2.48590e30			1.85588
$741$	1.51179e28	−	2.50102e28i	0.0111276	−	0.0184089i
$742$	−1.27380e29	−	1.94441e30i	−0.0924403	−	1.41107i
$743$		−	2.36025e29i		−	0.168879i	−0.996429	−	0.0844395i	$-0.973090\pi$
$743$		−	2.36025e29i		−	0.168879i	0.996429	−	0.0844395i	$-0.0269100\pi$
$744$	1.30067e30	−	2.15175e30i	0.917593	−	1.51801i
$745$			1.75051e30i			1.21766i
$746$		−	1.65413e30i		−	1.13452i
$747$	−8.31891e29	−	1.58474e30i	−0.562601	−	1.07175i
$748$		−	7.02595e28i		−	0.0468531i
$749$	−2.51127e30	+	1.64516e29i	−1.65133	+	0.108180i
$750$	1.66961e30	+	1.00923e30i	1.08261	+	0.654404i
$751$	1.54560e30			0.988273			0.494137	−	0.869384i	$-0.335484\pi$
$751$	1.54560e30			0.988273			0.494137	+	0.869384i	$0.335484\pi$
$752$	3.63004e28			0.0228889
$753$	−1.20575e30	+	1.99473e30i	−0.749739	+	1.24033i
$754$			2.58806e30i			1.58699i
$755$	4.38604e30			2.65234
$756$	−1.36234e28	−	2.66286e30i	−0.00812470	−	1.58807i
$757$	1.15022e30			0.676510			0.338255	−	0.941055i	$-0.390163\pi$
$757$	1.15022e30			0.676510			0.338255	+	0.941055i	$0.390163\pi$
$758$			4.30476e30i			2.49702i
$759$	7.60224e28	−	1.25767e29i	0.0434914	−	0.0719496i
$760$	7.29415e28			0.0411559
$761$	−8.64030e28			−0.0480828			−0.0240414	−	0.999711i	$-0.507653\pi$
$761$	−8.64030e28			−0.0480828			−0.0240414	+	0.999711i	$0.507653\pi$
$762$	−2.89806e30	−	1.75179e30i	−1.59067	−	0.961511i
$763$	1.42510e29	+	2.17535e30i	0.0771501	+	1.17767i
$764$			2.87835e30i			1.53697i
$765$	−6.90048e29	−	1.31453e30i	−0.363441	−	0.692351i
$766$			1.97031e30i			1.02360i
$767$			1.19152e30i			0.610591i
$768$	9.11552e29	−	1.50802e30i	0.460775	−	0.762280i
$769$		−	2.41996e30i		−	1.20665i	−0.797494	−	0.603326i	$-0.793842\pi$
$769$		−	2.41996e30i		−	1.20665i	0.797494	−	0.603326i	$-0.206158\pi$
$770$	2.01479e28	+	3.07550e29i	0.00991008	+	0.151274i
$771$	3.17579e29	−	5.25384e29i	0.154092	−	0.254921i
$772$	3.16704e30			1.51590
$773$	1.59678e29			0.0753983			0.0376991	−	0.999289i	$-0.487997\pi$
$773$	1.59678e29			0.0753983			0.0376991	+	0.999289i	$0.487997\pi$
$774$	−4.66377e30	+	2.44819e30i	−2.17249	+	1.14042i
$775$			6.10977e30i			2.80774i
$776$	5.45074e29			0.247120
$777$	1.46773e30	+	7.60915e29i	0.656488	+	0.340342i
$778$	3.29929e29			0.145591
$779$		−	6.53190e28i		−	0.0284378i
$780$	−3.90762e30	−	2.36204e30i	−1.67849	−	1.01460i
$781$	−1.33295e29			−0.0564908
$782$	2.68405e30			1.12233
$783$	1.84389e29	−	3.05408e30i	0.0760742	−	1.26003i
$784$	1.60898e29	−	2.11721e28i	0.0654986	−	0.00861875i
$785$			2.08535e30i			0.837620i
$786$	−2.13452e30	−	1.29025e30i	−0.845985	−	0.511372i
$787$		−	3.10288e30i		−	1.21347i	−0.794903	−	0.606736i	$-0.792478\pi$
$787$		−	3.10288e30i		−	1.21347i	0.794903	−	0.606736i	$-0.207522\pi$
$788$		−	6.18809e30i		−	2.38798i
$789$	4.01262e28	+	2.42550e28i	0.0152799	+	0.00923621i
$790$		−	4.09947e30i		−	1.54043i
$791$	−9.32816e29	+	6.11097e28i	−0.345894	+	0.0226599i
$792$	7.16554e28	+	1.36503e29i	0.0262201	+	0.0499490i
$793$	3.34008e30			1.20612
$794$	−5.30446e30			−1.89028
$795$	3.38044e30	+	2.04337e30i	1.18883	+	0.718609i
$796$			5.84184e30i			2.02751i
$797$	2.95812e30			1.01322			0.506610	−	0.862175i	$-0.330898\pi$
$797$	2.95812e30			1.01322			0.506610	+	0.862175i	$0.330898\pi$
$798$	1.16297e29	+	6.02919e28i	0.0393133	+	0.0203811i
$799$	−5.13836e29			−0.171428
$800$			4.78629e30i			1.57599i
$801$	−1.71764e30	−	3.27209e30i	−0.558202	−	1.06337i
$802$	−4.52296e30			−1.45075
$803$	−1.38281e28			−0.00437774
$804$	1.73832e30	−	2.87578e30i	0.543177	−	0.898601i
$805$	−7.20935e30	+	4.72292e29i	−2.22351	+	0.145665i
$806$		−	7.74268e30i		−	2.35707i
$807$	1.18203e30	−	1.95549e30i	0.355187	−	0.587602i
$808$			5.15174e30i			1.52804i
$809$		−	2.66423e30i		−	0.780033i	−0.920808	−	0.390017i	$-0.872469\pi$
$809$		−	2.66423e30i		−	0.780033i	0.920808	−	0.390017i	$-0.127531\pi$
$810$	7.24065e30	+	4.99624e30i	2.09259	+	1.44394i
$811$		−	6.24009e29i		−	0.178021i	−0.996031	−	0.0890107i	$-0.971629\pi$
$811$		−	6.24009e29i		−	0.178021i	0.996031	−	0.0890107i	$-0.0283705\pi$
$812$	−7.10322e30	+	4.65339e29i	−2.00040	+	0.131048i
$813$	2.66597e30	+	1.61150e30i	0.741148	+	0.448001i
$814$	−2.58469e29			−0.0709336
$815$	3.96573e29			0.107440
$816$	6.32226e28	−	1.04592e29i	0.0169093	−	0.0279738i
$817$		−	1.58998e29i		−	0.0419816i
$818$	5.91587e30			1.54209
$819$	−1.58415e30	−	2.59069e30i	−0.407675	−	0.666707i
$820$	−1.02055e31			−2.59292
$821$			2.05593e30i			0.515711i	0.966184	+	0.257855i	$0.0830158\pi$
$821$			2.05593e30i			0.515711i	−0.966184	+	0.257855i	$0.916984\pi$
$822$	−1.51496e30	+	2.50627e30i	−0.375187	+	0.620689i
$823$	1.84157e30			0.450286			0.225143	−	0.974326i	$-0.427715\pi$
$823$	1.84157e30			0.450286			0.225143	+	0.974326i	$0.427715\pi$
$824$	2.03418e30			0.491081
$825$	−3.20605e29	−	1.93796e29i	−0.0764194	−	0.0461932i
$826$	−5.32951e30	+	3.49142e29i	−1.25429	+	0.0821696i
$827$			6.46545e30i			1.50242i	0.660065	+	0.751209i	$0.270529\pi$
$827$			6.46545e30i			1.50242i	−0.660065	+	0.751209i	$0.729471\pi$
$828$	−8.64080e30	+	4.53588e30i	−1.98260	+	1.04074i
$829$			2.82216e30i			0.639380i	0.947522	+	0.319690i	$0.103579\pi$
$829$			2.82216e30i			0.639380i	−0.947522	+	0.319690i	$0.896421\pi$
$830$		−	1.37566e31i		−	3.07745i
$831$	−1.54339e30	+	2.55329e30i	−0.340929	+	0.564014i
$832$		−	5.82880e30i		−	1.27141i
$833$	−2.27752e30	+	2.99692e29i	−0.490558	+	0.0645510i
$834$	1.34362e30	−	2.22281e30i	0.285781	−	0.472780i
$835$	2.78849e29			0.0585680
$836$	−1.25669e28			−0.00260652
$837$	−5.51636e29	+	9.13688e30i	−0.112989	+	1.87146i
$838$		−	9.82150e30i		−	1.98662i
$839$	−6.87817e30			−1.37395			−0.686977	−	0.726679i	$-0.741063\pi$
$839$	−6.87817e30			−1.37395			−0.686977	+	0.726679i	$0.741063\pi$
$840$	3.48836e30	−	6.72871e30i	0.688159	−	1.32739i
$841$	−3.04621e30			−0.593474
$842$			1.07672e31i			2.07169i
$843$	2.66884e30	+	1.61323e30i	0.507146	+	0.306554i
$844$	1.63653e31			3.07134
$845$	3.31926e30			0.615242
$846$	2.69583e30	−	1.41514e30i	0.493519	−	0.259066i
$847$	3.60258e29	+	5.49919e30i	0.0651385	+	0.994313i
$848$			3.25165e29i			0.0580694i
$849$	−2.55385e30	−	1.54372e30i	−0.450468	−	0.272294i
$850$		−	6.84215e30i		−	1.19205i
$851$		−	6.05883e30i		−	1.04263i
$852$	7.57523e30	+	4.57899e30i	1.28760	+	0.778313i
$853$			9.66484e30i			1.62267i	0.584583	+	0.811334i	$0.301258\pi$
$853$			9.66484e30i			1.62267i	−0.584583	+	0.811334i	$0.698742\pi$
$854$	9.78718e29	+	1.49398e31i	0.162312	+	2.47763i
$855$	−2.35122e29	+	1.23424e29i	−0.0385167	+	0.0202189i
$856$	−9.67546e30			−1.56566
$857$	9.77331e30			1.56222			0.781111	−	0.624392i	$-0.214653\pi$
$857$	9.77331e30			1.56222			0.781111	+	0.624392i	$0.214653\pi$
$858$	4.06291e29	+	2.45590e29i	0.0641535	+	0.0387788i
$859$			1.74488e30i			0.272168i	0.990697	+	0.136084i	$0.0434517\pi$
$859$			1.74488e30i			0.272168i	−0.990697	+	0.136084i	$0.956548\pi$
$860$	−2.48419e31			−3.82782
$861$	−6.02555e30	−	3.12382e30i	−0.917200	−	0.475503i
$862$	1.50156e31			2.25797
$863$		−	5.51035e30i		−	0.818589i	−0.912402	−	0.409295i	$-0.865775\pi$
$863$		−	5.51035e30i		−	0.818589i	0.912402	−	0.409295i	$-0.134225\pi$
$864$	−4.32143e29	+	7.15768e30i	−0.0634210	+	1.05046i
$865$	−8.83487e29			−0.128095
$866$	−6.27963e30			−0.899489
$867$	2.76059e30	−	4.56696e30i	0.390662	−	0.646289i
$868$	2.12507e31	−	1.39215e30i	2.97109	−	0.194639i
$869$			2.61546e29i			0.0361277i
$870$	1.21652e31	−	2.01254e31i	1.66023	−	2.74659i
$871$		−	3.83198e30i		−	0.516693i
$872$			8.38123e30i			1.11657i
$873$	−1.75701e30	+	9.22320e29i	−0.231273	+	0.121404i
$874$		−	4.80078e29i		−	0.0624370i
$875$	4.00017e29	+	6.10610e30i	0.0514036	+	0.784656i
$876$	7.85861e29	+	4.75029e29i	0.0997821	+	0.0603152i
$877$	−1.28183e30			−0.160818			−0.0804090	−	0.996762i	$-0.525623\pi$
$877$	−1.28183e30			−0.160818			−0.0804090	+	0.996762i	$0.525623\pi$
$878$	−8.99853e30			−1.11552
$879$	−1.96996e30	+	3.25900e30i	−0.241310	+	0.399209i
$880$		−	5.14318e28i		−	0.00622535i
$881$	5.77654e30			0.690909			0.345455	−	0.938435i	$-0.387725\pi$
$881$	5.77654e30			0.690909			0.345455	+	0.938435i	$0.387725\pi$
$882$	1.11236e31	−	7.84481e30i	1.31470	−	0.927176i
$883$	4.13098e30			0.482465			0.241232	−	0.970467i	$-0.422448\pi$
$883$	4.13098e30			0.482465			0.241232	+	0.970467i	$0.422448\pi$
$884$			5.32053e30i			0.614053i
$885$	5.60076e30	−	9.26558e30i	0.638767	−	1.05674i
$886$	−1.66234e31			−1.87356
$887$	−1.32995e31			−1.48128			−0.740641	−	0.671900i	$-0.765478\pi$
$887$	−1.32995e31			−1.48128			−0.740641	+	0.671900i	$0.765478\pi$
$888$	5.43950e30	+	3.28801e30i	0.598719	+	0.361907i
$889$	−6.94337e29	−	1.05988e31i	−0.0755269	−	1.15289i
$890$		−	2.84038e31i		−	3.05339i
$891$	−4.61953e29	−	3.18760e29i	−0.0490774	−	0.0338647i
$892$			2.05302e31i			2.15557i
$893$			9.19065e28i			0.00953687i
$894$	−6.25239e30	+	1.03436e31i	−0.641213	+	1.06079i
$895$			1.34969e31i			1.36802i
$896$	1.55888e31	−	1.02124e30i	1.56163	−	0.102304i
$897$	−5.75694e30	+	9.52396e30i	−0.569995	+	0.942967i
$898$	3.35109e30			0.327932
$899$	2.44692e31			2.36670
$900$	1.15628e31	+	2.20271e31i	1.10540	+	2.10577i
$901$		−	4.60274e30i		−	0.434916i
$902$	1.06110e30			0.0991036
$903$	−1.46672e31	−	7.60392e30i	−1.35403	−	0.701966i
$904$	−3.59396e30			−0.327948
$905$		−	5.17331e30i		−	0.466615i
$906$	2.59167e31	+	1.56658e31i	2.31065	+	1.39671i
$907$	−7.06118e30			−0.622302			−0.311151	−	0.950361i	$-0.600714\pi$
$907$	−7.06118e30			−0.622302			−0.311151	+	0.950361i	$0.600714\pi$
$908$	2.30951e31			2.01195
$909$	−8.71726e30	−	1.66063e31i	−0.750687	−	1.43005i
$910$	−1.52574e30	−	2.32898e31i	−0.129881	−	1.98258i
$911$		−	9.76514e30i		−	0.821742i	−0.911693	−	0.410871i	$-0.865225\pi$
$911$		−	9.76514e30i		−	0.821742i	0.911693	−	0.410871i	$-0.134775\pi$
$912$	−1.87077e28	−	1.13082e28i	−0.00155623	−	0.000940694i
$913$			8.77670e29i			0.0721752i
$914$		−	1.00146e31i		−	0.814137i
$915$	−2.59734e31	−	1.57001e31i	−2.08741	−	1.26177i
$916$		−	1.05208e31i		−	0.835888i
$917$	−5.11403e29	−	7.80636e30i	−0.0401684	−	0.613155i
$918$	6.17762e29	−	1.02321e31i	0.0479703	−	0.794544i
$919$	1.61670e30			0.124113			0.0620565	−	0.998073i	$-0.480234\pi$
$919$	1.61670e30			0.124113			0.0620565	+	0.998073i	$0.480234\pi$
$920$	−2.77763e31			−2.10815
$921$	−1.79768e31	−	1.08664e31i	−1.34892	−	0.815380i
$922$			1.18619e30i			0.0879993i
$923$	1.00940e31			0.740365
$924$	−6.00998e29	+	1.15927e30i	−0.0435830	+	0.0840676i
$925$	−1.54451e31			−1.10740
$926$		−	1.58639e31i		−	1.12459i
$927$	−6.55704e30	+	3.44204e30i	−0.459590	+	0.241256i
$928$	1.91688e31			1.32844
$929$	−4.32143e30			−0.296116			−0.148058	−	0.988979i	$-0.547302\pi$
$929$	−4.32143e30			−0.296116			−0.148058	+	0.988979i	$0.547302\pi$
$930$	−3.63946e31	+	6.02091e31i	−2.46584	+	4.07935i
$931$	5.36040e28	+	4.07366e29i	0.00359108	+	0.0272906i
$932$			3.29066e31i			2.17979i
$933$	6.17494e30	−	1.02155e31i	0.404460	−	0.669116i
$934$		−	3.30527e31i		−	2.14074i
$935$			7.28021e29i			0.0466253i
$936$	−5.42624e30	−	1.03369e31i	−0.343639	−	0.654629i
$937$			5.99725e30i			0.375566i	0.982210	+	0.187783i	$0.0601302\pi$
$937$			5.99725e30i			0.375566i	−0.982210	+	0.187783i	$0.939870\pi$
$938$	1.71399e31	−	1.12285e30i	1.06140	−	0.0695334i
$939$	1.00666e31	+	6.08497e30i	0.616446	+	0.372623i
$940$	1.43595e31			0.869556
$941$	7.31941e30			0.438314			0.219157	−	0.975690i	$-0.429669\pi$
$941$	7.31941e30			0.438314			0.219157	+	0.975690i	$0.429669\pi$
$942$	−7.44834e30	+	1.23221e31i	−0.441088	+	0.729711i
$943$			2.48736e31i			1.45669i
$944$	8.91257e29			0.0516175
$945$	1.41164e29	+	2.75922e31i	0.00808520	+	1.58035i
$946$	2.58291e30			0.146303
$947$			1.89558e31i			1.06186i	0.847416	+	0.530929i	$0.178157\pi$
$947$			1.89558e31i			1.06186i	−0.847416	+	0.530929i	$0.821843\pi$
$948$	8.98472e30	−	1.48638e31i	0.497756	−	0.823460i
$949$	1.04716e30			0.0573744
$950$	−1.22381e30			−0.0663157
$951$	−4.81251e30	−	2.90901e30i	−0.257915	−	0.155901i
$952$	−8.81269e30	+	5.77328e29i	−0.467112	+	0.0306010i
$953$			9.15410e30i			0.479888i	0.970787	+	0.239944i	$0.0771291\pi$
$953$			9.15410e30i			0.479888i	−0.970787	+	0.239944i	$0.922871\pi$
$954$	1.26763e31	+	2.41482e31i	0.657255	+	1.25206i
$955$		−	2.98252e31i		−	1.52949i
$956$		−	8.88638e30i		−	0.450731i
$957$	−7.76139e29	+	1.28400e30i	−0.0389372	+	0.0644155i
$958$		−	1.33528e31i		−	0.662576i
$959$	−9.16594e30	+	6.00470e29i	−0.449865	+	0.0294711i
$960$	−2.73984e31	+	4.53263e31i	−1.33008	+	2.20041i
$961$	−5.23789e31			−2.51513
$962$	1.95730e31			0.929652
$963$	3.11882e31	−	1.63718e31i	1.46526	−	0.769169i
$964$		−	6.18829e31i		−	2.87582i
$965$	−3.28165e31			−1.50853
$966$	−4.42863e31	−	2.29593e31i	−2.01377	−	1.04400i
$967$	2.08330e31			0.937074			0.468537	−	0.883444i	$-0.344781\pi$
$967$	2.08330e31			0.937074			0.468537	+	0.883444i	$0.344781\pi$
$968$			2.11874e31i			0.942726i
$969$	2.64808e29	+	1.60069e29i	0.0116555	+	0.00704541i
$970$	−1.52520e31			−0.664084
$971$	3.78036e31			1.62829			0.814144	−	0.580663i	$-0.197207\pi$
$971$	3.78036e31			1.62829			0.814144	+	0.580663i	$0.197207\pi$
$972$	1.53029e31	+	3.39845e31i	0.652046	+	1.44805i
$973$	8.12927e30	−	5.32557e29i	0.342663	−	0.0224482i
$974$			3.40101e31i			1.41820i
$975$	2.42784e31	+	1.46755e31i	1.00155	+	0.605405i
$976$		−	2.49838e30i		−	0.101961i
$977$			4.51470e31i			1.82279i	0.411535	+	0.911394i	$0.364993\pi$
$977$			4.51470e31i			1.82279i	−0.411535	+	0.911394i	$0.635007\pi$
$978$	2.34331e30	+	1.41646e30i	0.0935991	+	0.0565778i
$979$			1.81216e30i			0.0716109i
$980$	6.36472e31	−	8.37513e30i	2.48832	−	0.327429i
$981$	−1.41819e31	−	2.70163e31i	−0.548541	−	1.04497i
$982$	1.28887e31			0.493217
$983$	−6.86801e30			−0.260027			−0.130014	−	0.991512i	$-0.541502\pi$
$983$	−6.86801e30			−0.260027			−0.130014	+	0.991512i	$0.541502\pi$
$984$	−2.23310e31	−	1.34984e31i	−0.836489	−	0.505632i
$985$			6.41203e31i			2.37638i
$986$	−2.74024e31			−1.00480
$987$	8.47820e30	+	4.39534e30i	0.307591	+	0.159464i
$988$	9.51649e29			0.0341609
$989$			6.05467e31i			2.15045i
$990$	−2.00502e30	−	3.81955e30i	−0.0704612	−	0.134228i
$991$	−3.29436e31			−1.14551			−0.572754	−	0.819727i	$-0.694125\pi$
$991$	−3.29436e31			−1.14551			−0.572754	+	0.819727i	$0.694125\pi$
$992$	−5.73471e31			−1.97305
$993$	1.53694e31	−	2.54262e31i	0.523226	−	0.865596i
$994$	2.95776e30	+	4.51491e31i	0.0996338	+	1.52087i
$995$		−	6.05325e31i		−	2.01765i
$996$	3.01500e31	−	4.98785e31i	0.994408	−	1.64509i
$997$		−	1.34350e31i		−	0.438467i	−0.975672	−	0.219234i	$-0.929644\pi$
$997$		−	1.34350e31i		−	0.438467i	0.975672	−	0.219234i	$-0.0703557\pi$
$998$			7.20920e30i			0.232818i
$999$	−2.30975e31	−	1.39450e30i	−0.738121	−	0.0445638i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.22.c.b.20.47	yes	52
3.2	odd	2	inner	21.22.c.b.20.6	yes	52
7.6	odd	2	inner	21.22.c.b.20.5	✓	52
21.20	even	2	inner	21.22.c.b.20.48	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.22.c.b.20.5	✓	52	7.6	odd	2	inner
21.22.c.b.20.6	yes	52	3.2	odd	2	inner
21.22.c.b.20.47	yes	52	1.1	even	1	trivial
21.22.c.b.20.48	yes	52	21.20	even	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)

\(f(q)\)	\(=\)	\(q-2329.72i q^{2} +(-52907.9 + 87527.8i) q^{3} -3.33046e6 q^{4} +3.45099e7 q^{5} +(2.03916e8 + 1.23261e8i) q^{6} +(4.88555e7 + 7.45761e8i) q^{7} +2.87327e9i q^{8} +(-4.86187e9 - 9.26181e9i) q^{9} +O(q^{10})\)	\(q-2329.72i q^{2} +(-52907.9 + 87527.8i) q^{3} -3.33046e6 q^{4} +3.45099e7 q^{5} +(2.03916e8 + 1.23261e8i) q^{6} +(4.88555e7 + 7.45761e8i) q^{7} +2.87327e9i q^{8} +(-4.86187e9 - 9.26181e9i) q^{9} -8.03985e10i q^{10} +5.12942e9i q^{11} +(1.76208e11 - 2.91508e11i) q^{12} -3.88435e11i q^{13} +(1.73742e12 - 1.13820e11i) q^{14} +(-1.82584e12 + 3.02057e12i) q^{15} -2.90549e11 q^{16} +4.11275e12 q^{17} +(-2.15775e13 + 1.13268e13i) q^{18} -7.35621e11i q^{19} -1.14934e14 q^{20} +(-6.78596e13 - 3.51804e13i) q^{21} +1.19501e13 q^{22} +2.80126e14i q^{23} +(-2.51491e14 - 1.52019e14i) q^{24} +7.14095e14 q^{25} -9.04946e14 q^{26} +(1.06790e15 + 6.44740e13i) q^{27} +(-1.62712e14 - 2.48373e15i) q^{28} -2.85990e15i q^{29} +(7.03710e15 + 4.25371e15i) q^{30} +8.55595e15i q^{31} +6.70259e15i q^{32} +(-4.48967e14 - 2.71387e14i) q^{33} -9.58157e15i q^{34} +(1.68600e15 + 2.57361e16i) q^{35} +(1.61923e16 + 3.08461e16i) q^{36} -2.16290e16 q^{37} -1.71379e15 q^{38} +(3.39988e16 + 2.05513e16i) q^{39} +9.91564e16i q^{40} +8.87944e16 q^{41} +(-8.19606e16 + 1.58094e17i) q^{42} +2.16141e17 q^{43} -1.70833e16i q^{44} +(-1.67783e17 - 3.19624e17i) q^{45} +6.52616e17 q^{46} -1.24937e17 q^{47} +(1.53723e16 - 2.54311e16i) q^{48} +(-5.53772e17 + 7.28691e16i) q^{49} -1.66364e18i q^{50} +(-2.17597e17 + 3.59980e17i) q^{51} +1.29367e18i q^{52} -1.11914e18i q^{53} +(1.50207e17 - 2.48791e18i) q^{54} +1.77016e17i q^{55} +(-2.14278e18 + 1.40375e17i) q^{56} +(6.43872e16 + 3.89201e16i) q^{57} -6.66279e18 q^{58} -3.06749e18 q^{59} +(6.08091e18 - 1.00599e19i) q^{60} +8.59883e18i q^{61} +1.99330e19 q^{62} +(6.66957e18 - 4.07828e18i) q^{63} +1.50059e19 q^{64} -1.34048e19i q^{65} +(-6.32256e17 + 1.04597e18i) q^{66} +9.86518e18 q^{67} -1.36974e19 q^{68} +(-2.45188e19 - 1.48209e19i) q^{69} +(5.99581e19 - 3.92791e18i) q^{70} +2.59864e19i q^{71} +(2.66117e19 - 1.39695e19i) q^{72} +2.69585e18i q^{73} +5.03895e19i q^{74} +(-3.77812e19 + 6.25032e19i) q^{75} +2.44996e18i q^{76} +(-3.82532e18 + 2.50600e17i) q^{77} +(4.78788e19 - 7.92079e19i) q^{78} +5.09894e19 q^{79} -1.00268e19 q^{80} +(-6.21434e19 + 9.00595e19i) q^{81} -2.06866e20i q^{82} +1.71105e20 q^{83} +(2.26004e20 + 1.17167e20i) q^{84} +1.41930e20 q^{85} -5.03549e20i q^{86} +(2.50321e20 + 1.51311e20i) q^{87} -1.47382e19 q^{88} +3.53288e20 q^{89} +(-7.44636e20 + 3.90887e20i) q^{90} +(2.89679e20 - 1.89772e19i) q^{91} -9.32949e20i q^{92} +(-7.48884e20 - 4.52677e20i) q^{93} +2.91069e20i q^{94} -2.53862e19i q^{95} +(-5.86663e20 - 3.54620e20i) q^{96} -1.89705e20i q^{97} +(1.69765e20 + 1.29014e21i) q^{98} +(4.75077e19 - 2.49386e19i) 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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