LMFDB - Embedded newform 21.22.c.b.20.17

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			20.17
Character	$\chi$	$=$	21.20
Dual form			21.22.c.b.20.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2061.69i q^{2} +(-759.014 - 102273. i) q^{3} -2.15341e6 q^{4} +1.95223e7 q^{5} +(-2.10855e8 + 1.56485e6i) q^{6} +(-6.67328e8 - 3.36481e8i) q^{7} +1.15978e8i q^{8} +(-1.04592e10 + 1.55253e8i) q^{9} +O(q^{10})$	\(q-2061.69i q^{2} +(-759.014 - 102273. i) q^{3} -2.15341e6 q^{4} +1.95223e7 q^{5} +(-2.10855e8 + 1.56485e6i) q^{6} +(-6.67328e8 - 3.36481e8i) q^{7} +1.15978e8i q^{8} +(-1.04592e10 + 1.55253e8i) q^{9} -4.02489e10i q^{10} -1.09823e11i q^{11} +(1.63447e9 + 2.20235e11i) q^{12} -5.15271e11i q^{13} +(-6.93720e11 + 1.37582e12i) q^{14} +(-1.48177e10 - 1.99660e12i) q^{15} -4.27691e12 q^{16} +1.12356e13 q^{17} +(3.20084e11 + 2.15636e13i) q^{18} -4.21841e13i q^{19} -4.20394e13 q^{20} +(-3.39065e13 + 6.85050e13i) q^{21} -2.26421e14 q^{22} -2.30898e14i q^{23} +(1.18614e13 - 8.80291e10i) q^{24} -9.57173e13 q^{25} -1.06233e15 q^{26} +(2.38169e13 + 1.06958e15i) q^{27} +(1.43703e15 + 7.24581e14i) q^{28} +2.95496e15i q^{29} +(-4.11638e15 + 3.05495e13i) q^{30} +4.09546e15i q^{31} +9.06088e15i q^{32} +(-1.12319e16 + 8.33573e13i) q^{33} -2.31643e16i q^{34} +(-1.30278e16 - 6.56889e15i) q^{35} +(2.25229e16 - 3.34324e14i) q^{36} +2.53669e16 q^{37} -8.69705e16 q^{38} +(-5.26983e16 + 3.91098e14i) q^{39} +2.26416e15i q^{40} -1.05157e17 q^{41} +(1.41236e17 + 6.99046e16i) q^{42} +2.13460e17 q^{43} +2.36494e17i q^{44} +(-2.04188e17 + 3.03090e15i) q^{45} -4.76039e17 q^{46} +2.13141e17 q^{47} +(3.24623e15 + 4.37413e17i) q^{48} +(3.32106e17 + 4.49087e17i) q^{49} +1.97339e17i q^{50} +(-8.52799e15 - 1.14910e18i) q^{51} +1.10959e18i q^{52} -1.61549e18i q^{53} +(2.20513e18 - 4.91031e16i) q^{54} -2.14400e18i q^{55} +(3.90245e16 - 7.73954e16i) q^{56} +(-4.31430e18 + 3.20183e16i) q^{57} +6.09222e18 q^{58} +3.38337e18 q^{59} +(3.19085e16 + 4.29950e18i) q^{60} +5.43127e18i q^{61} +8.44356e18 q^{62} +(7.03195e18 + 3.41572e18i) q^{63} +9.71137e18 q^{64} -1.00593e19i q^{65} +(1.71857e17 + 2.31568e19i) q^{66} +1.42533e19 q^{67} -2.41948e19 q^{68} +(-2.36146e19 + 1.75255e17i) q^{69} +(-1.35430e19 + 2.68592e19i) q^{70} +2.98894e19i q^{71} +(-1.80060e16 - 1.21304e18i) q^{72} -3.08957e18i q^{73} -5.22987e19i q^{74} +(7.26508e16 + 9.78930e18i) q^{75} +9.08395e19i q^{76} +(-3.69534e19 + 7.32880e19i) q^{77} +(8.06322e17 + 1.08648e20i) q^{78} -6.07045e19 q^{79} -8.34951e19 q^{80} +(1.09371e20 - 3.24765e18i) q^{81} +2.16800e20i q^{82} +3.37951e19 q^{83} +(7.30144e19 - 1.47519e20i) q^{84} +2.19345e20 q^{85} -4.40088e20i q^{86} +(3.02213e20 - 2.24286e18i) q^{87} +1.27371e19 q^{88} -4.45786e18 q^{89} +(6.24877e18 + 4.20971e20i) q^{90} +(-1.73379e20 + 3.43855e20i) q^{91} +4.97216e20i q^{92} +(4.18855e20 - 3.10851e18i) q^{93} -4.39430e20i q^{94} -8.23530e20i q^{95} +(9.26683e20 - 6.87733e18i) q^{96} -8.29303e20i q^{97} +(9.25877e20 - 6.84700e20i) q^{98} +(1.70504e19 + 1.14866e21i) 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 $

$2$		−	2061.69i		−	1.42367i	−0.702349	−	0.711833i	$-0.747865\pi$
$2$		−	2061.69i		−	1.42367i	0.702349	−	0.711833i	$-0.252135\pi$
$3$	−759.014	−	102273.i	−0.00742124	−	0.999972i
$3$	−759.014	−	102273.i	−0.00742124	−	0.999972i
$4$	−2.15341e6			−1.02682
$5$	1.95223e7			0.894017			0.447008	−	0.894530i	$-0.352489\pi$
$5$	1.95223e7			0.894017			0.447008	+	0.894530i	$0.352489\pi$
$6$	−2.10855e8	+	1.56485e6i	−1.42363	+	0.0105654i
$7$	−6.67328e8	−	3.36481e8i	−0.892914	−	0.450227i
$7$	−6.67328e8	−	3.36481e8i	−0.892914	−	0.450227i
$8$			1.15978e8i			0.0381884i
$9$	−1.04592e10	+	1.55253e8i	−0.999890	+	0.0148421i
$10$		−	4.02489e10i		−	1.27278i
$11$		−	1.09823e11i		−	1.27665i	−0.769768	−	0.638323i	$-0.779628\pi$
$11$		−	1.09823e11i		−	1.27665i	0.769768	−	0.638323i	$-0.220372\pi$
$12$	1.63447e9	+	2.20235e11i	0.00762031	+	1.02680i
$13$		−	5.15271e11i		−	1.03665i	−0.855185	−	0.518323i	$-0.826557\pi$
$13$		−	5.15271e11i		−	1.03665i	0.855185	−	0.518323i	$-0.173443\pi$
$14$	−6.93720e11	+	1.37582e12i	−0.640973	+	1.27121i
$15$	−1.48177e10	−	1.99660e12i	−0.00663472	−	0.893992i
$16$	−4.27691e12			−0.972456
$17$	1.12356e13			1.35171			0.675855	−	0.737035i	$-0.263775\pi$
$17$	1.12356e13			1.35171			0.675855	+	0.737035i	$0.263775\pi$
$18$	3.20084e11	+	2.15636e13i	0.0211302	+	1.42351i
$19$		−	4.21841e13i		−	1.57847i	−0.614092	−	0.789235i	$-0.710478\pi$
$19$		−	4.21841e13i		−	1.57847i	0.614092	−	0.789235i	$-0.289522\pi$
$20$	−4.20394e13			−0.917998
$21$	−3.39065e13	+	6.85050e13i	−0.443588	+	0.896231i
$22$	−2.26421e14			−1.81752
$23$		−	2.30898e14i		−	1.16219i	−0.813836	−	0.581095i	$-0.802625\pi$
$23$		−	2.30898e14i		−	1.16219i	0.813836	−	0.581095i	$-0.197375\pi$
$24$	1.18614e13	−	8.80291e10i	0.0381873	−	0.000283405i
$25$	−9.57173e13			−0.200734
$26$	−1.06233e15			−1.47584
$27$	2.38169e13	+	1.06958e15i	0.0222621	+	0.999752i
$28$	1.43703e15	+	7.24581e14i	0.916866	+	0.462304i
$29$			2.95496e15i			1.30429i	0.758095	+	0.652144i	$0.226130\pi$
$29$			2.95496e15i			1.30429i	−0.758095	+	0.652144i	$0.773870\pi$
$30$	−4.11638e15	+	3.05495e13i	−1.27275	+	0.00944562i
$31$			4.09546e15i			0.897438i	0.893673	+	0.448719i	$0.148120\pi$
$31$			4.09546e15i			0.897438i	−0.893673	+	0.448719i	$0.851880\pi$
$32$			9.06088e15i			1.42264i
$33$	−1.12319e16	+	8.33573e13i	−1.27661	+	0.00947430i
$34$		−	2.31643e16i		−	1.92438i
$35$	−1.30278e16	−	6.56889e15i	−0.798280	−	0.402511i
$36$	2.25229e16	−	3.34324e14i	1.02671	−	0.0152402i
$37$	2.53669e16			0.867260			0.433630	−	0.901091i	$-0.357232\pi$
$37$	2.53669e16			0.867260			0.433630	+	0.901091i	$0.357232\pi$
$38$	−8.69705e16			−2.24721
$39$	−5.26983e16	+	3.91098e14i	−1.03662	+	0.00769320i
$40$			2.26416e15i			0.0341411i
$41$	−1.05157e17			−1.22351			−0.611753	−	0.791049i	$-0.709535\pi$
$41$	−1.05157e17			−1.22351			−0.611753	+	0.791049i	$0.709535\pi$
$42$	1.41236e17	+	6.99046e16i	1.27593	+	0.631521i
$43$	2.13460e17			1.50625			0.753127	−	0.657875i	$-0.228545\pi$
$43$	2.13460e17			1.50625			0.753127	+	0.657875i	$0.228545\pi$
$44$			2.36494e17i			1.31089i
$45$	−2.04188e17	+	3.03090e15i	−0.893918	+	0.0132691i
$46$	−4.76039e17			−1.65457
$47$	2.13141e17			0.591071			0.295535	−	0.955332i	$-0.404502\pi$
$47$	2.13141e17			0.591071			0.295535	+	0.955332i	$0.404502\pi$
$48$	3.24623e15	+	4.37413e17i	0.00721684	+	0.972430i
$49$	3.32106e17	+	4.49087e17i	0.594591	+	0.804028i
$50$			1.97339e17i			0.285778i
$51$	−8.52799e15	−	1.14910e18i	−0.0100314	−	1.35167i
$52$			1.10959e18i			1.06445i
$53$		−	1.61549e18i		−	1.26884i	−0.772987	−	0.634421i	$-0.781238\pi$
$53$		−	1.61549e18i		−	1.26884i	0.772987	−	0.634421i	$-0.218762\pi$
$54$	2.20513e18	−	4.91031e16i	1.42331	−	0.0316938i
$55$		−	2.14400e18i		−	1.14134i
$56$	3.90245e16	−	7.73954e16i	0.0171934	−	0.0340989i
$57$	−4.31430e18	+	3.20183e16i	−1.57843	+	0.0117142i
$58$	6.09222e18			1.85687
$59$	3.38337e18			0.861793			0.430896	−	0.902401i	$-0.358197\pi$
$59$	3.38337e18			0.861793			0.430896	+	0.902401i	$0.358197\pi$
$60$	3.19085e16	+	4.29950e18i	0.00681269	+	0.917973i
$61$			5.43127e18i			0.974851i	0.873165	+	0.487426i	$0.162064\pi$
$61$			5.43127e18i			0.974851i	−0.873165	+	0.487426i	$0.837936\pi$
$62$	8.44356e18			1.27765
$63$	7.03195e18	+	3.41572e18i	0.899498	+	0.436925i
$64$	9.71137e18			1.05291
$65$		−	1.00593e19i		−	0.926779i
$66$	1.71857e17	+	2.31568e19i	0.0134882	+	1.81747i
$67$	1.42533e19			0.955279			0.477640	−	0.878556i	$-0.341492\pi$
$67$	1.42533e19			0.955279			0.477640	+	0.878556i	$0.341492\pi$
$68$	−2.41948e19			−1.38797
$69$	−2.36146e19	+	1.75255e17i	−1.16216	+	0.00862489i
$70$	−1.35430e19	+	2.68592e19i	−0.573041	+	1.13648i
$71$			2.98894e19i			1.08969i	0.838536	+	0.544846i	$0.183412\pi$
$71$			2.98894e19i			1.08969i	−0.838536	+	0.544846i	$0.816588\pi$
$72$	−1.80060e16	−	1.21304e18i	−0.000566795	−	0.0381842i
$73$		−	3.08957e18i		−	0.0841411i	−0.999115	−	0.0420706i	$-0.986605\pi$
$73$		−	3.08957e18i		−	0.0841411i	0.999115	−	0.0420706i	$-0.0133954\pi$
$74$		−	5.22987e19i		−	1.23469i
$75$	7.26508e16	+	9.78930e18i	0.00148969	+	0.200728i
$76$			9.08395e19i			1.62081i
$77$	−3.69534e19	+	7.32880e19i	−0.574781	+	1.13994i
$78$	8.06322e17	+	1.08648e20i	0.0109525	+	1.47580i
$79$	−6.07045e19			−0.721335			−0.360667	−	0.932695i	$-0.617451\pi$
$79$	−6.07045e19			−0.721335			−0.360667	+	0.932695i	$0.617451\pi$
$80$	−8.34951e19			−0.869393
$81$	1.09371e20	−	3.24765e18i	0.999559	−	0.0296809i
$82$			2.16800e20i			1.74186i
$83$	3.37951e19			0.239075			0.119538	−	0.992830i	$-0.461859\pi$
$83$	3.37951e19			0.239075			0.119538	+	0.992830i	$0.461859\pi$
$84$	7.30144e19	−	1.47519e20i	0.455487	−	0.920271i
$85$	2.19345e20			1.20845
$86$		−	4.40088e20i		−	2.14440i
$87$	3.02213e20	−	2.24286e18i	1.30425	−	0.00967944i
$88$	1.27371e19			0.0487531
$89$	−4.45786e18			−0.0151542			−0.00757708	−	0.999971i	$-0.502412\pi$
$89$	−4.45786e18			−0.0151542			−0.00757708	+	0.999971i	$0.502412\pi$
$90$	6.24877e18	+	4.20971e20i	0.0188907	+	1.27264i
$91$	−1.73379e20	+	3.43855e20i	−0.466726	+	0.925636i
$92$			4.97216e20i			1.19336i
$93$	4.18855e20	−	3.10851e18i	0.897414	−	0.00666011i
$94$		−	4.39430e20i		−	0.841487i
$95$		−	8.23530e20i		−	1.41118i
$96$	9.26683e20	−	6.87733e18i	1.42260	−	0.0105578i
$97$		−	8.29303e20i		−	1.14185i	−0.821001	−	0.570926i	$-0.806584\pi$
$97$		−	8.29303e20i		−	1.14185i	0.821001	−	0.570926i	$-0.193416\pi$
$98$	9.25877e20	−	6.84700e20i	1.14467	−	0.846499i
$99$	1.70504e19	+	1.14866e21i	0.0189481	+	1.27651i
$100$	2.06118e20			0.206118
$101$	−1.30816e21			−1.17839			−0.589194	−	0.807992i	$-0.700555\pi$
$101$	−1.30816e21			−1.17839			−0.589194	+	0.807992i	$0.700555\pi$
$102$	−2.36909e21	+	1.75821e19i	−1.92433	+	0.0142813i
$103$		−	4.95812e20i		−	0.363518i	−0.983343	−	0.181759i	$-0.941821\pi$
$103$		−	4.95812e20i		−	0.363518i	0.983343	−	0.181759i	$-0.0581791\pi$
$104$	5.97602e19			0.0395878
$105$	−6.61932e20	+	1.33737e21i	−0.396575	+	0.801245i
$106$	−3.33064e21			−1.80641
$107$		−	2.59201e21i		−	1.27382i	−0.770940	−	0.636908i	$-0.780213\pi$
$107$		−	2.59201e21i		−	1.27382i	0.770940	−	0.636908i	$-0.219787\pi$
$108$	−5.12875e19	−	2.30323e21i	−0.0228593	−	1.02657i
$109$	1.17517e21			0.475469			0.237734	−	0.971330i	$-0.423595\pi$
$109$	1.17517e21			0.475469			0.237734	+	0.971330i	$0.423595\pi$
$110$	−4.42026e21			−1.62489
$111$	−1.92538e19	−	2.59435e21i	−0.00643615	−	0.867236i
$112$	2.85410e21	+	1.43910e21i	0.868320	+	0.437826i
$113$			2.57912e21i			0.714740i	0.933963	+	0.357370i	$0.116326\pi$
$113$			2.57912e21i			0.714740i	−0.933963	+	0.357370i	$0.883674\pi$
$114$	6.60118e19	+	8.89474e21i	0.0166771	+	2.24715i
$115$		−	4.50765e21i		−	1.03902i
$116$		−	6.36324e21i		−	1.33927i
$117$	7.99976e19	+	5.38932e21i	0.0153860	+	1.03653i
$118$		−	6.97545e21i		−	1.22690i
$119$	−7.49784e21	−	3.78058e21i	−1.20696	−	0.608576i
$120$	2.31562e20	−	1.71853e18i	0.0341401	−	0.000253369i
$121$	−4.66087e21			−0.629826
$122$	1.11976e22			1.38786
$123$	7.98154e19	+	1.07547e22i	0.00907994	+	1.22347i
$124$		−	8.81918e21i		−	0.921511i
$125$	−1.11776e22			−1.07348
$126$	7.04215e21	−	1.44977e22i	0.622035	−	1.28058i
$127$	1.10504e22			0.898337			0.449169	−	0.893447i	$-0.351720\pi$
$127$	1.10504e22			0.898337			0.449169	+	0.893447i	$0.351720\pi$
$128$		−	1.01979e21i		−	0.0763493i
$129$	−1.62019e20	−	2.18312e22i	−0.0111783	−	1.50621i
$130$	−2.07391e22			−1.31942
$131$	1.58647e22			0.931289			0.465644	−	0.884972i	$-0.345823\pi$
$131$	1.58647e22			0.931289			0.465644	+	0.884972i	$0.345823\pi$
$132$	2.41869e22	−	1.79502e20i	1.31085	−	0.00972844i
$133$	−1.41942e22	+	2.81506e22i	−0.710670	+	1.40944i
$134$		−	2.93859e22i		−	1.36000i
$135$	4.64961e20	+	2.08806e22i	0.0199027	+	0.893795i
$136$			1.30309e21i			0.0516196i
$137$		−	2.07157e21i		−	0.0759859i	−0.999278	−	0.0379929i	$-0.987904\pi$
$137$		−	2.07157e21i		−	0.0759859i	0.999278	−	0.0379929i	$-0.0120964\pi$
$138$	3.61320e20	+	4.86859e22i	0.0122790	+	1.65452i
$139$			2.47227e22i			0.778826i	0.921063	+	0.389413i	$0.127322\pi$
$139$			2.47227e22i			0.778826i	−0.921063	+	0.389413i	$0.872678\pi$
$140$	2.80541e22	+	1.41455e22i	0.819693	+	0.413308i
$141$	−1.61777e20	−	2.17986e22i	−0.00438648	−	0.591055i
$142$	6.16226e22			1.55136
$143$	−5.65887e22			−1.32343
$144$	4.47330e22	−	6.64005e20i	0.972349	−	0.0144333i
$145$			5.76877e22i			1.16606i
$146$	−6.36973e21			−0.119789
$147$	4.56774e22	−	3.43064e22i	0.799594	−	0.600542i
$148$	−5.46253e22			−0.890524
$149$			1.45149e22i			0.220474i	0.993905	+	0.110237i	$0.0351610\pi$
$149$			1.45149e22i			0.220474i	−0.993905	+	0.110237i	$0.964839\pi$
$150$	2.01825e22	−	1.49783e20i	0.285770	−	0.00212083i
$151$	−1.14495e23			−1.51192			−0.755959	−	0.654619i	$-0.772829\pi$
$151$	−1.14495e23			−1.51192			−0.755959	+	0.654619i	$0.772829\pi$
$152$	4.89243e21			0.0602792
$153$	−1.17516e23	+	1.74437e21i	−1.35156	+	0.0200622i
$154$	1.51097e23	+	7.61865e22i	1.62289	+	0.818296i
$155$			7.99527e22i			0.802325i
$156$	1.13481e23	−	8.42193e20i	1.06442	−	0.00789956i
$157$		−	1.16658e23i		−	1.02322i	−0.859219	−	0.511608i	$-0.829050\pi$
$157$		−	1.16658e23i		−	1.02322i	0.859219	−	0.511608i	$-0.170950\pi$
$158$			1.25154e23i			1.02694i
$159$	−1.65221e23	+	1.22618e21i	−1.26881	+	0.00941639i
$160$			1.76889e23i			1.27187i
$161$	−7.76927e22	+	1.54084e23i	−0.523249	+	1.03774i
$162$	−6.69565e21	−	2.25488e23i	−0.0422557	−	1.42304i
$163$	7.30065e22			0.431909			0.215954	−	0.976403i	$-0.430714\pi$
$163$	7.30065e22			0.431909			0.215954	+	0.976403i	$0.430714\pi$
$164$	2.26445e23			1.25633
$165$	−2.19273e23	+	1.62733e21i	−1.14131	+	0.00847019i
$166$		−	6.96750e22i		−	0.340363i
$167$	4.21191e22			0.193177			0.0965886	−	0.995324i	$-0.469207\pi$
$167$	4.21191e22			0.193177			0.0965886	+	0.995324i	$0.469207\pi$
$168$	−7.94509e21	−	3.93241e21i	−0.0342256	−	0.0169399i
$169$	−1.84396e22			−0.0746348
$170$		−	4.52221e23i		−	1.72043i
$171$	6.54923e21	+	4.41212e23i	0.0234278	+	1.57830i
$172$	−4.59666e23			−1.54666
$173$	1.09515e23			0.346729			0.173364	−	0.984858i	$-0.444536\pi$
$173$	1.09515e23			0.346729			0.173364	+	0.984858i	$0.444536\pi$
$174$	−4.62408e21	−	6.23070e23i	−0.0137803	−	1.85682i
$175$	6.38748e22	+	3.22071e22i	0.179238	+	0.0903758i
$176$			4.69703e23i			1.24148i
$177$	−2.56802e21	−	3.46027e23i	−0.00639557	−	0.861769i
$178$			9.19072e21i			0.0215744i
$179$			1.69301e22i			0.0374716i	0.999824	+	0.0187358i	$0.00596414\pi$
$179$			1.69301e22i			0.0374716i	−0.999824	+	0.0187358i	$0.994036\pi$
$180$	4.39699e23	−	6.52676e21i	0.917897	−	0.0136250i
$181$		−	2.60312e23i		−	0.512707i	−0.966583	−	0.256354i	$-0.917479\pi$
$181$		−	2.60312e23i		−	0.512707i	0.966583	−	0.256354i	$-0.0825212\pi$
$182$	7.08921e23	+	3.57454e23i	1.31780	+	0.664462i
$183$	5.55473e23	−	4.12241e21i	0.974824	−	0.00723461i
$184$	2.67791e22			0.0443822
$185$	4.95220e23			0.775345
$186$	−6.40878e21	−	8.63548e23i	−0.00948177	−	1.27762i
$187$		−	1.23393e24i		−	1.72565i
$188$	−4.58979e23			−0.606926
$189$	3.43999e23	−	7.21772e23i	0.430237	−	0.902716i
$190$	−1.69786e24			−2.00905
$191$			9.15056e23i			1.02470i	0.858776	+	0.512351i	$0.171225\pi$
$191$			9.15056e23i			1.02470i	−0.858776	+	0.512351i	$0.828775\pi$
$192$	−7.37107e21	−	9.93212e23i	−0.00781390	−	1.05288i
$193$	−4.03287e23			−0.404820			−0.202410	−	0.979301i	$-0.564877\pi$
$193$	−4.03287e23			−0.404820			−0.202410	+	0.979301i	$0.564877\pi$
$194$	−1.70976e24			−1.62562
$195$	−1.02879e24	+	7.63513e21i	−0.926753	+	0.00687785i
$196$	−7.15160e23	−	9.67066e23i	−0.610540	−	0.825596i
$197$		−	7.49247e23i		−	0.606359i	−0.952933	−	0.303179i	$-0.901952\pi$
$197$		−	7.49247e23i		−	0.606359i	0.952933	−	0.303179i	$-0.0980482\pi$
$198$	2.36818e24	−	3.51526e22i	1.81732	−	0.0269757i
$199$			1.86005e24i			1.35384i	0.736057	+	0.676919i	$0.236685\pi$
$199$			1.86005e24i			1.35384i	−0.736057	+	0.676919i	$0.763315\pi$
$200$		−	1.11011e22i		−	0.00766570i
$201$	−1.08185e22	−	1.45773e24i	−0.00708936	−	0.955253i
$202$			2.69703e24i			1.67763i
$203$	9.94291e23	−	1.97193e24i	0.587226	−	1.16462i
$204$	1.83642e22	+	2.47448e24i	0.0103004	+	1.38793i
$205$	−2.05290e24			−1.09384
$206$	−1.02221e24			−0.517528
$207$	3.58476e22	+	2.41500e24i	0.0172493	+	1.16206i
$208$			2.20377e24i			1.00809i
$209$	−4.63279e24			−2.01515
$210$	2.75725e24	+	1.36470e24i	1.14071	+	0.564591i
$211$	9.62999e23			0.379018			0.189509	−	0.981879i	$-0.439310\pi$
$211$	9.62999e23			0.379018			0.189509	+	0.981879i	$0.439310\pi$
$212$			3.47881e24i			1.30288i
$213$	3.05688e24	−	2.26865e22i	1.08966	−	0.00808688i
$214$	−5.34391e24			−1.81349
$215$	4.16723e24			1.34662
$216$	−1.24048e23	+	2.76224e21i	−0.0381789	+	0.000850154i
$217$	1.37805e24	−	2.73301e24i	0.404051	−	0.801335i
$218$		−	2.42283e24i		−	0.676908i
$219$	−3.15980e23	+	2.34503e21i	−0.0841388	+	0.000624432i
$220$			4.61690e24i			1.17196i
$221$		−	5.78939e24i		−	1.40124i
$222$	−5.34874e24	+	3.96954e22i	−1.23465	+	0.00916293i
$223$		−	9.70907e23i		−	0.213785i	−0.994271	−	0.106892i	$-0.965910\pi$
$223$		−	9.70907e23i		−	0.213785i	0.994271	−	0.106892i	$-0.0340900\pi$
$224$	3.04882e24	−	6.04657e24i	0.640512	−	1.27030i
$225$	1.00113e24	−	1.48604e22i	0.200712	−	0.00297931i
$226$	5.31734e24			1.01755
$227$	9.66778e24			1.76626			0.883131	−	0.469126i	$-0.155431\pi$
$227$	9.66778e24			1.76626			0.883131	+	0.469126i	$0.155431\pi$
$228$	9.29043e24	−	6.89485e22i	1.62077	−	0.0120284i
$229$			4.10875e24i			0.684600i	0.939591	+	0.342300i	$0.111206\pi$
$229$			4.10875e24i			0.684600i	−0.939591	+	0.342300i	$0.888794\pi$
$230$	−9.29337e24			−1.47921
$231$	7.52344e24	+	3.72371e24i	1.14417	+	0.566305i
$232$	−3.42711e23			−0.0498086
$233$		−	1.50807e24i		−	0.209501i	−0.994499	−	0.104750i	$-0.966596\pi$
$233$		−	1.50807e24i		−	0.209501i	0.994499	−	0.104750i	$-0.0334044\pi$
$234$	1.11111e25	−	1.64930e23i	1.47567	−	0.0219045i
$235$	4.16100e24			0.528427
$236$	−7.28576e24			−0.884910
$237$	4.60756e22	+	6.20844e24i	0.00535320	+	0.721315i
$238$	−7.79437e24	+	1.54582e25i	−0.866409	+	1.71831i
$239$		−	6.01108e24i		−	0.639402i	−0.947518	−	0.319701i	$-0.896417\pi$
$239$		−	6.01108e24i		−	0.639402i	0.947518	−	0.319701i	$-0.103583\pi$
$240$	6.33739e22	+	8.53929e24i	0.00645197	+	0.869369i
$241$			1.33812e24i			0.130411i	0.997872	+	0.0652057i	$0.0207704\pi$
$241$			1.33812e24i			0.130411i	−0.997872	+	0.0652057i	$0.979230\pi$
$242$			9.60926e24i			0.896661i
$243$	−4.15161e23	−	1.11832e25i	−0.0370980	−	0.999312i
$244$		−	1.16957e25i		−	1.00100i
$245$	6.48348e24	+	8.76720e24i	0.531574	+	0.718815i
$246$	2.21728e25	−	1.64554e23i	1.74182	−	0.0129268i
$247$	−2.17362e25			−1.63631
$248$	−4.74984e23			−0.0342717
$249$	−2.56510e22	−	3.45633e24i	−0.00177423	−	0.239068i
$250$			2.30447e25i			1.52827i
$251$	−2.97642e25			−1.89287			−0.946434	−	0.322897i	$-0.895343\pi$
$251$	−2.97642e25			−1.89287			−0.946434	+	0.322897i	$0.895343\pi$
$252$	−1.51427e25	−	7.35544e24i	−0.923626	−	0.448645i
$253$	−2.53579e25			−1.48371
$254$		−	2.27825e25i		−	1.27893i
$255$	−1.66486e23	−	2.24331e25i	−0.00896821	−	1.20842i
$256$	1.82637e25			0.944213
$257$	−9.49079e24			−0.470982			−0.235491	−	0.971877i	$-0.575670\pi$
$257$	−9.49079e24			−0.470982			−0.235491	+	0.971877i	$0.575670\pi$
$258$	−4.50092e25	+	3.34033e23i	−2.14434	+	0.0159141i
$259$	−1.69280e25	−	8.53549e24i	−0.774389	−	0.390464i
$260$			2.16617e25i			0.951639i
$261$	−4.58768e23	−	3.09066e25i	−0.0193583	−	1.30414i
$262$		−	3.27081e25i		−	1.32584i
$263$			2.22155e25i			0.865208i	0.901584	+	0.432604i	$0.142405\pi$
$263$			2.22155e25i			0.865208i	−0.901584	+	0.432604i	$0.857595\pi$
$264$	−9.66763e21	−	1.30266e24i	−0.000361808	−	0.0487517i
$265$		−	3.15381e25i		−	1.13437i
$266$	5.80378e25	+	2.92639e25i	2.00657	+	1.01176i
$267$	3.38358e21	+	4.55919e23i	0.000112463	+	0.0151537i
$268$	−3.06932e25			−0.980904
$269$	2.52837e25			0.777038			0.388519	−	0.921441i	$-0.372987\pi$
$269$	2.52837e25			0.777038			0.388519	+	0.921441i	$0.372987\pi$
$270$	4.30493e25	−	9.58604e23i	1.27247	−	0.0283348i
$271$		−	6.86265e24i		−	0.195126i	−0.995229	−	0.0975628i	$-0.968895\pi$
$271$		−	6.86265e24i		−	0.195126i	0.995229	−	0.0975628i	$-0.0311047\pi$
$272$	−4.80537e25			−1.31448
$273$	3.52986e25	+	1.74710e25i	0.929074	+	0.459844i
$274$	−4.27092e24			−0.108178
$275$			1.05120e25i			0.256266i
$276$	5.08518e25	−	3.77394e23i	1.19333	−	0.00885625i
$277$	−5.78389e24			−0.130672			−0.0653360	−	0.997863i	$-0.520812\pi$
$277$	−5.78389e24			−0.130672			−0.0653360	+	0.997863i	$0.520812\pi$
$278$	5.09705e25			1.10879
$279$	−6.35834e23	−	4.28352e25i	−0.0133199	−	0.897340i
$280$	7.61847e23	−	1.51094e24i	0.0153712	−	0.0304850i
$281$		−	2.45601e25i		−	0.477324i	−0.971103	−	0.238662i	$-0.923291\pi$
$281$		−	2.45601e25i		−	0.477324i	0.971103	−	0.238662i	$-0.0767089\pi$
$282$	−4.49419e25	+	3.33534e23i	−0.841464	+	0.00624488i
$283$		−	3.50073e25i		−	0.631541i	−0.948836	−	0.315770i	$-0.897737\pi$
$283$		−	3.50073e25i		−	0.631541i	0.948836	−	0.315770i	$-0.102263\pi$
$284$		−	6.43640e25i		−	1.11892i
$285$	−8.42250e25	+	6.25071e23i	−1.41114	+	0.0104727i
$286$			1.16668e26i			1.88412i
$287$	7.01739e25	+	3.53833e25i	1.09249	+	0.550856i
$288$	−1.40673e24	−	9.47695e25i	−0.0211150	−	1.42248i
$289$	5.71472e25			0.827118
$290$	1.18934e26			1.66007
$291$	−8.48154e25	+	6.29453e23i	−1.14182	+	0.00847397i
$292$			6.65310e24i			0.0863981i
$293$	−6.39934e25			−0.801724			−0.400862	−	0.916138i	$-0.631289\pi$
$293$	−6.39934e25			−0.801724			−0.400862	+	0.916138i	$0.631289\pi$
$294$	−7.07291e25	−	9.41725e25i	−0.854970	−	1.13835i
$295$	6.60511e25			0.770457
$296$			2.94201e24i			0.0331193i
$297$	1.17464e26	−	2.61565e24i	1.27633	−	0.0284208i
$298$	2.99252e25			0.313882
$299$	−1.18975e26			−1.20478
$300$	−1.56447e23	−	2.10803e25i	−0.00152965	−	0.206113i
$301$	−1.42448e26	−	7.18254e25i	−1.34496	−	0.678156i
$302$			2.36053e26i			2.15247i
$303$	9.92916e23	+	1.33790e26i	0.00874510	+	1.17835i
$304$			1.80418e26i			1.53499i
$305$			1.06031e26i			0.871533i
$306$	3.59634e24	+	2.42280e26i	0.0285618	+	1.92417i
$307$		−	3.28116e25i		−	0.251811i	−0.992042	−	0.125905i	$-0.959816\pi$
$307$		−	3.28116e25i		−	0.251811i	0.992042	−	0.125905i	$-0.0401836\pi$
$308$	7.95758e25	−	1.57819e26i	0.590199	−	1.17051i
$309$	−5.07082e25	+	3.76328e23i	−0.363508	+	0.00269776i
$310$	1.64838e26			1.14224
$311$	−2.76734e26			−1.85387			−0.926933	−	0.375228i	$-0.877564\pi$
$311$	−2.76734e26			−1.85387			−0.926933	+	0.375228i	$0.877564\pi$
$312$	−4.53588e22	−	6.11186e24i	−0.000293791	−	0.0395867i
$313$		−	1.79304e26i		−	1.12299i	−0.827481	−	0.561494i	$-0.810227\pi$
$313$		−	1.79304e26i		−	1.12299i	0.827481	−	0.561494i	$-0.189773\pi$
$314$	−2.40512e26			−1.45672
$315$	1.37280e26	+	6.66827e25i	0.804166	+	0.390618i
$316$	1.30722e26			0.740684
$317$			1.17639e26i			0.644808i	0.946602	+	0.322404i	$0.104491\pi$
$317$			1.17639e26i			0.644808i	−0.946602	+	0.322404i	$0.895509\pi$
$318$	2.52800e24	+	3.40635e26i	0.0134058	+	1.80636i
$319$	3.24523e26			1.66511
$320$	1.89588e26			0.941319
$321$	−2.65092e26	+	1.96737e24i	−1.27378	+	0.00945329i
$322$	3.17674e26	+	1.60178e26i	1.47739	+	0.744932i
$323$		−	4.73965e26i		−	2.13363i
$324$	−2.35520e26	+	6.99351e24i	−1.02637	+	0.0304770i
$325$			4.93204e25i			0.208090i
$326$		−	1.50517e26i		−	0.614893i
$327$	−8.91969e23	−	1.20188e26i	−0.00352857	−	0.475455i
$328$		−	1.21959e25i		−	0.0467237i
$329$	−1.42235e26	−	7.17180e25i	−0.527776	−	0.266116i
$330$	3.35504e24	+	4.52073e26i	0.0120587	+	1.62485i
$331$	1.90496e26			0.663271			0.331635	−	0.943408i	$-0.392400\pi$
$331$	1.90496e26			0.663271			0.331635	+	0.943408i	$0.392400\pi$
$332$	−7.27747e25			−0.245488
$333$	−2.65318e26	+	3.93830e24i	−0.867165	+	0.0128719i
$334$		−	8.68364e25i		−	0.275020i
$335$	2.78257e26			0.854036
$336$	1.45015e26	−	2.92990e26i	0.431370	−	0.871545i
$337$	−6.53084e26			−1.88302			−0.941510	−	0.336985i	$-0.890593\pi$
$337$	−6.53084e26			−1.88302			−0.941510	+	0.336985i	$0.890593\pi$
$338$			3.80167e25i			0.106255i
$339$	2.63775e26	−	1.95759e24i	0.714720	−	0.00530426i
$340$	−4.72339e26			−1.24087
$341$	4.49776e26			1.14571
$342$	9.09642e26	−	1.35025e25i	2.24696	−	0.0333533i
$343$	−7.05144e25	−	4.11436e26i	−0.168923	−	0.985629i
$344$			2.47567e25i			0.0575214i
$345$	−4.61011e26	+	3.42137e24i	−1.03899	+	0.00771080i
$346$		−	2.25786e26i		−	0.493626i
$347$		−	3.77882e26i		−	0.801487i	−0.916190	−	0.400744i	$-0.868752\pi$
$347$		−	3.77882e26i		−	0.801487i	0.916190	−	0.400744i	$-0.131248\pi$
$348$	−6.50788e26	+	4.82979e24i	−1.33924	+	0.00993908i
$349$		−	3.41611e26i		−	0.682126i	−0.940040	−	0.341063i	$-0.889213\pi$
$349$		−	3.41611e26i		−	0.682126i	0.940040	−	0.341063i	$-0.110787\pi$
$350$	6.64010e25	−	1.31690e26i	0.128665	−	0.255175i
$351$	5.51122e26	−	1.22722e25i	1.03639	−	0.0230779i
$352$	9.95094e26			1.81621
$353$	8.74403e25			0.154909			0.0774546	−	0.996996i	$-0.475321\pi$
$353$	8.74403e25			0.154909			0.0774546	+	0.996996i	$0.475321\pi$
$354$	−7.13400e26	+	5.29446e24i	−1.22687	+	0.00910516i
$355$			5.83509e26i			0.974204i
$356$	9.59959e24			0.0155606
$357$	−3.80960e26	+	7.69696e26i	−0.599602	+	1.21144i
$358$	3.49045e25			0.0533470
$359$		−	1.11054e27i		−	1.64832i	−0.566359	−	0.824159i	$-0.691648\pi$
$359$		−	1.11054e27i		−	1.64832i	0.566359	−	0.824159i	$-0.308352\pi$
$360$	−3.51518e23	−	2.36813e25i	−0.000506724	−	0.0341373i
$361$	−1.06529e27			−1.49156
$362$	−5.36683e26			−0.729924
$363$	3.53767e24	+	4.76681e26i	0.00467409	+	0.629808i
$364$	3.73356e26	−	7.40458e26i	0.479246	−	0.950465i
$365$		−	6.03155e25i		−	0.0752236i
$366$	−8.49913e24	−	1.14521e27i	−0.0102997	−	1.38782i
$367$		−	8.92501e26i		−	1.05103i	−0.850784	−	0.525515i	$-0.823873\pi$
$367$		−	8.92501e26i		−	1.05103i	0.850784	−	0.525515i	$-0.176127\pi$
$368$			9.87528e26i			1.13018i
$369$	1.09985e27	−	1.63259e25i	1.22337	−	0.0181594i
$370$		−	1.02099e27i		−	1.10383i
$371$	−5.43583e26	+	1.07806e27i	−0.571268	+	1.13297i
$372$	−9.01965e26	+	6.69388e24i	−0.921486	+	0.00683876i
$373$	1.74259e27			1.73082			0.865410	−	0.501064i	$-0.167058\pi$
$373$	1.74259e27			1.73082			0.865410	+	0.501064i	$0.167058\pi$
$374$	−2.54398e27			−2.45676
$375$	8.48394e24	+	1.14316e27i	0.00796653	+	1.07345i
$376$			2.47197e25i			0.0225720i
$377$	1.52261e27			1.35208
$378$	−1.48807e27	−	7.09219e26i	−1.28517	−	0.612514i
$379$	7.52589e25			0.0632188			0.0316094	−	0.999500i	$-0.489937\pi$
$379$	7.52589e25			0.0632188			0.0316094	+	0.999500i	$0.489937\pi$
$380$			1.77340e27i			1.44903i
$381$	−8.38742e24	−	1.13016e27i	−0.00666678	−	0.898312i
$382$	1.88656e27			1.45883
$383$	2.06634e26			0.155458			0.0777291	−	0.996975i	$-0.475233\pi$
$383$	2.06634e26			0.155458			0.0777291	+	0.996975i	$0.475233\pi$
$384$	−1.04297e26	+	7.74033e23i	−0.0763472	+	0.000566607i
$385$	−7.21416e26	+	1.43075e27i	−0.513864	+	1.01912i
$386$			8.31451e26i			0.576328i
$387$	−2.23262e27	+	3.31404e25i	−1.50609	+	0.0223559i
$388$			1.78583e27i			1.17248i
$389$		−	1.21725e27i		−	0.777871i	−0.921265	−	0.388936i	$-0.872843\pi$
$389$		−	1.21725e27i		−	0.777871i	0.921265	−	0.388936i	$-0.127157\pi$
$390$	1.57413e25	+	2.12105e27i	0.00979176	+	1.31939i
$391$		−	2.59428e27i		−	1.57094i
$392$	−5.20842e25	+	3.85171e25i	−0.0307045	+	0.0227065i
$393$	−1.20416e25	−	1.62254e27i	−0.00691132	−	0.931263i
$394$	−1.54471e27			−0.863252
$395$	−1.18509e27			−0.644885
$396$	−3.67165e25	−	2.47354e27i	−0.0194563	−	1.31075i
$397$			3.28608e27i			1.69581i	0.530148	+	0.847905i	$0.322136\pi$
$397$			3.28608e27i			1.69581i	−0.530148	+	0.847905i	$0.677864\pi$
$398$	3.83484e27			1.92741
$399$	2.88982e27	+	1.43031e27i	1.41467	+	0.700190i
$400$	4.09374e26			0.195205
$401$			1.23718e27i			0.574667i	0.957831	+	0.287333i	$0.0927688\pi$
$401$			1.23718e27i			0.574667i	−0.957831	+	0.287333i	$0.907231\pi$
$402$	−3.00538e27	+	2.23043e25i	−1.35996	+	0.0100929i
$403$	2.11027e27			0.930326
$404$	2.81701e27			1.21000
$405$	2.13517e27	−	6.34016e25i	0.893623	−	0.0265352i
$406$	−4.06550e27	−	2.04992e27i	−1.65802	−	0.836013i
$407$		−	2.78587e27i		−	1.10718i
$408$	1.33271e26	−	9.89061e23i	0.0516182	−	0.000383082i
$409$			2.84104e27i			1.07246i	0.844071	+	0.536232i	$0.180153\pi$
$409$			2.84104e27i			1.07246i	−0.844071	+	0.536232i	$0.819847\pi$
$410$			4.23244e27i			1.55726i
$411$	−2.11865e26	+	1.57235e24i	−0.0759838	+	0.000563910i
$412$			1.06768e27i			0.373269i
$413$	−2.25781e27	−	1.13844e27i	−0.769507	−	0.388003i
$414$	4.97898e27	−	7.39066e25i	1.65439	−	0.0245573i
$415$	6.59759e26			0.213737
$416$	4.66881e27			1.47478
$417$	2.52847e27	−	1.87649e25i	0.778805	−	0.00577986i
$418$			9.55137e27i			2.86890i
$419$	3.50430e27			1.02649			0.513244	−	0.858243i	$-0.328444\pi$
$419$	3.50430e27			1.02649			0.513244	+	0.858243i	$0.328444\pi$
$420$	1.42541e27	−	2.87991e27i	0.407213	−	0.822738i
$421$	−2.61126e27			−0.727593			−0.363797	−	0.931478i	$-0.618520\pi$
$421$	−2.61126e27			−0.727593			−0.363797	+	0.931478i	$0.618520\pi$
$422$		−	1.98540e27i		−	0.539595i
$423$	−2.22929e27	+	3.30909e25i	−0.591006	+	0.00877272i
$424$	1.87362e26			0.0484551
$425$	−1.07544e27			−0.271334
$426$	−4.67724e25	−	6.30233e27i	−0.0115130	−	1.55132i
$427$	1.82752e27	−	3.62444e27i	0.438904	−	0.870458i
$428$			5.58164e27i			1.30798i
$429$	4.29516e25	+	5.78750e27i	0.00982150	+	1.32339i
$430$		−	8.59153e27i		−	1.91713i
$431$		−	4.32301e27i		−	0.941401i	−0.882293	−	0.470701i	$-0.844001\pi$
$431$		−	4.32301e27i		−	0.941401i	0.882293	−	0.470701i	$-0.155999\pi$
$432$	−1.01863e26	−	4.57448e27i	−0.0216489	−	0.972215i
$433$			6.00077e27i			1.24475i	0.782717	+	0.622377i	$0.213833\pi$
$433$			6.00077e27i			1.24475i	−0.782717	+	0.622377i	$0.786167\pi$
$434$	−5.63462e27	−	2.84110e27i	−1.14083	−	0.575234i
$435$	5.89990e27	−	4.37858e25i	1.16602	−	0.00865358i
$436$	−2.53061e27			−0.488223
$437$	−9.74021e27			−1.83448
$438$	4.83472e24	+	6.51452e26i	0.000888982	+	0.119786i
$439$		−	3.42115e27i		−	0.614179i	−0.951681	−	0.307089i	$-0.900645\pi$
$439$		−	3.42115e27i		−	0.614179i	0.951681	−	0.307089i	$-0.0993550\pi$
$440$	2.48657e26			0.0435861
$441$	−3.54329e27	−	4.64553e27i	−0.606459	−	0.795115i
$442$	−1.19359e28			−1.99490
$443$			3.58900e27i			0.585780i	0.956146	+	0.292890i	$0.0946169\pi$
$443$			3.58900e27i			0.585780i	−0.956146	+	0.292890i	$0.905383\pi$
$444$	4.14613e25	+	5.58669e27i	0.00660879	+	0.890499i
$445$	−8.70277e25			−0.0135481
$446$	−2.00171e27			−0.304358
$447$	1.48448e27	−	1.10170e25i	0.220468	−	0.00163619i
$448$	−6.48067e27	−	3.26770e27i	−0.940157	−	0.474048i
$449$			4.67066e27i			0.661899i	0.943648	+	0.330950i	$0.107369\pi$
$449$			4.67066e27i			0.661899i	−0.943648	+	0.330950i	$0.892631\pi$
$450$	−3.06376e25	−	2.06401e27i	−0.00424154	−	0.285746i
$451$			1.15486e28i			1.56199i
$452$		−	5.55389e27i		−	0.733912i
$453$	8.69033e25	+	1.17097e28i	0.0112203	+	1.51188i
$454$		−	1.99319e28i		−	2.51457i
$455$	−3.38476e27	+	6.71283e27i	−0.417261	+	0.827534i
$456$	−3.71343e24	−	5.00364e26i	−0.000447347	−	0.0602775i
$457$	1.37696e27			0.162107			0.0810534	−	0.996710i	$-0.474172\pi$
$457$	1.37696e27			0.162107			0.0810534	+	0.996710i	$0.474172\pi$
$458$	8.47095e27			0.974641
$459$	2.67598e26	+	1.20174e28i	0.0300919	+	1.35137i
$460$			9.70680e27i			1.06689i
$461$	−1.09639e28			−1.17789			−0.588944	−	0.808174i	$-0.700456\pi$
$461$	−1.09639e28			−1.17789			−0.588944	+	0.808174i	$0.700456\pi$
$462$	7.67714e27	−	1.55110e28i	0.806229	−	1.62892i
$463$	5.06009e27			0.519467			0.259733	−	0.965680i	$-0.416365\pi$
$463$	5.06009e27			0.519467			0.259733	+	0.965680i	$0.416365\pi$
$464$		−	1.26381e28i		−	1.26836i
$465$	8.17701e27	−	6.06852e25i	0.802303	−	0.00595425i
$466$	−3.10918e27			−0.298259
$467$	−5.77790e27			−0.541930			−0.270965	−	0.962589i	$-0.587343\pi$
$467$	−5.77790e27			−0.541930			−0.270965	+	0.962589i	$0.587343\pi$
$468$	−1.72267e26	−	1.16054e28i	−0.0157987	−	1.06434i
$469$	−9.51163e27	−	4.79597e27i	−0.852982	−	0.430093i
$470$		−	8.57869e27i		−	0.752304i
$471$	−1.19309e28	+	8.85449e25i	−1.02319	+	0.00759354i
$472$			3.92397e26i			0.0329105i
$473$		−	2.34429e28i		−	1.92295i
$474$	1.27999e28	−	9.49935e25i	1.02691	−	0.00762117i
$475$			4.03775e27i			0.316852i
$476$	1.61459e28	+	8.14112e27i	1.23934	+	0.624901i
$477$	2.50810e26	+	1.68967e28i	0.0188323	+	1.26870i
$478$	−1.23930e28			−0.910295
$479$	9.85556e27			0.708204			0.354102	−	0.935207i	$-0.384787\pi$
$479$	9.85556e27			0.708204			0.354102	+	0.935207i	$0.384787\pi$
$480$	1.80910e28	−	1.34261e26i	1.27183	−	0.00943882i
$481$		−	1.30708e28i		−	0.899042i
$482$	2.75878e27			0.185662
$483$	1.58176e28	+	7.82892e27i	1.04159	+	0.515534i
$484$	1.00367e28			0.646720
$485$		−	1.61899e28i		−	1.02084i
$486$	−2.30563e28	+	8.55933e26i	−1.42269	+	0.0528152i
$487$	1.39895e27			0.0844786			0.0422393	−	0.999108i	$-0.486551\pi$
$487$	1.39895e27			0.0844786			0.0422393	+	0.999108i	$0.486551\pi$
$488$	−6.29909e26			−0.0372280
$489$	−5.54130e25	−	7.46660e27i	−0.00320530	−	0.431897i
$490$	1.80752e28	−	1.33669e28i	1.02335	−	0.756784i
$491$		−	1.11135e28i		−	0.615879i	−0.951406	−	0.307939i	$-0.900361\pi$
$491$		−	1.11135e28i		−	0.615879i	0.951406	−	0.307939i	$-0.0996394\pi$
$492$	−1.71875e26	−	2.31592e28i	−0.00932350	−	1.25629i
$493$			3.32009e28i			1.76302i
$494$			4.48134e28i			2.32956i
$495$	3.32863e26	+	2.24245e28i	0.0169399	+	1.14122i
$496$		−	1.75159e28i		−	0.872720i
$497$	1.00572e28	−	1.99460e28i	0.490609	−	0.973002i
$498$	−7.12588e27	+	5.28843e25i	−0.340354	+	0.00252592i
$499$	3.06648e28			1.43411			0.717057	−	0.697014i	$-0.245489\pi$
$499$	3.06648e28			1.43411			0.717057	+	0.697014i	$0.245489\pi$
$500$	2.40699e28			1.10227
$501$	−3.19690e25	−	4.30765e27i	−0.00143362	−	0.193172i
$502$			6.13645e28i			2.69481i
$503$	−3.08475e28			−1.32665			−0.663324	−	0.748332i	$-0.730855\pi$
$503$	−3.08475e28			−1.32665			−0.663324	+	0.748332i	$0.730855\pi$
$504$	−3.96149e26	+	8.15553e26i	−0.0166855	+	0.0343504i
$505$	−2.55384e28			−1.05350
$506$			5.22801e28i			2.11230i
$507$	1.39959e25	+	1.88588e27i	0.000553883	+	0.0746328i
$508$	−2.37960e28			−0.922434
$509$	−2.68589e28			−1.01988			−0.509942	−	0.860209i	$-0.670333\pi$
$509$	−2.68589e28			−1.01988			−0.509942	+	0.860209i	$0.670333\pi$
$510$	−4.62500e28	+	3.43242e26i	−1.72038	+	0.0127677i
$511$	−1.03958e27	+	2.06176e27i	−0.0378826	+	0.0751308i
$512$		−	3.97928e28i		−	1.42059i
$513$	4.51191e28	−	1.00470e27i	1.57808	−	0.0351400i
$514$			1.95670e28i			0.670521i
$515$		−	9.67939e27i		−	0.324991i
$516$	3.48893e26	+	4.70115e28i	0.0114781	+	1.54661i
$517$		−	2.34078e28i		−	0.754589i
$518$	−1.75975e28	+	3.49003e28i	−0.555890	+	1.10247i
$519$	−8.31235e25	−	1.12004e28i	−0.00257316	−	0.346719i
$520$	1.16666e27			0.0353922
$521$	5.78769e28			1.72071			0.860357	−	0.509691i	$-0.170240\pi$
$521$	5.78769e28			1.72071			0.860357	+	0.509691i	$0.170240\pi$
$522$	−6.37197e28	+	9.45837e26i	−1.85666	+	0.0275598i
$523$			3.94058e28i			1.12536i	0.826673	+	0.562682i	$0.190230\pi$
$523$			3.94058e28i			1.12536i	−0.826673	+	0.562682i	$0.809770\pi$
$524$	−3.41632e28			−0.956270
$525$	3.24544e27	−	6.55712e27i	0.0890431	−	0.179904i
$526$	4.58014e28			1.23177
$527$			4.60150e28i			1.21308i
$528$	4.80380e28	−	3.56512e26i	1.24145	−	0.00921335i
$529$	−1.38421e28			−0.350685
$530$	−6.50217e28			−1.61496
$531$	−3.53873e28	+	5.25279e26i	−0.861698	+	0.0127908i
$532$	3.05658e28	−	6.06197e28i	0.729733	−	1.44724i
$533$			5.41842e28i			1.26834i
$534$	9.39963e26	−	6.97589e24i	0.0215739	−	0.000160109i
$535$		−	5.06019e28i		−	1.13881i
$536$			1.65307e27i			0.0364806i
$537$	1.73149e27	−	1.28502e25i	0.0374706	−	0.000278086i
$538$		−	5.21272e28i		−	1.10624i
$539$	4.93201e28	−	3.64730e28i	1.02646	−	0.759083i
$540$	−1.00125e27	−	4.49644e28i	−0.0204366	−	0.917770i
$541$	3.13623e28			0.627822			0.313911	−	0.949452i	$-0.398361\pi$
$541$	3.13623e28			0.627822			0.313911	+	0.949452i	$0.398361\pi$
$542$	−1.41486e28			−0.277794
$543$	−2.66229e28	+	1.97581e26i	−0.512693	+	0.00380493i
$544$			1.01805e29i			1.92300i
$545$	2.29420e28			0.425077
$546$	3.60198e28	−	7.27748e28i	0.654664	−	1.32269i
$547$	−4.58701e27			−0.0817830			−0.0408915	−	0.999164i	$-0.513020\pi$
$547$	−4.58701e27			−0.0817830			−0.0408915	+	0.999164i	$0.513020\pi$
$548$			4.46092e27i			0.0780241i
$549$	−8.43223e26	−	5.68068e28i	−0.0144688	−	0.974744i
$550$	2.16724e28			0.364837
$551$	1.24653e29			2.05878
$552$	−2.03257e25	−	2.73878e27i	−0.000329371	−	0.0443809i
$553$	4.05098e28	+	2.04260e28i	0.644090	+	0.324764i
$554$			1.19246e28i			0.186033i
$555$	−3.75879e26	−	5.06477e28i	−0.00575403	−	0.775324i
$556$		−	5.32380e28i		−	0.799718i
$557$		−	5.57923e28i		−	0.822422i	−0.911540	−	0.411211i	$-0.865106\pi$
$557$		−	5.57923e28i		−	0.822422i	0.911540	−	0.411211i	$-0.134894\pi$
$558$	−8.83129e28	+	1.31089e27i	−1.27751	+	0.0189630i
$559$		−	1.09990e29i		−	1.56145i
$560$	5.57186e28	+	2.80945e28i	0.776293	+	0.391424i
$561$	−1.26198e29	+	9.36571e26i	−1.72561	+	0.0128065i
$562$	−5.06352e28			−0.679550
$563$	−5.51297e27			−0.0726185			−0.0363093	−	0.999341i	$-0.511560\pi$
$563$	−5.51297e27			−0.0726185			−0.0363093	+	0.999341i	$0.511560\pi$
$564$	3.48372e26	+	4.69412e28i	0.00450414	+	0.606909i
$565$			5.03503e28i			0.638989i
$566$	−7.21742e28			−0.899103
$567$	−7.40789e28	−	3.46340e28i	−0.905884	−	0.423526i
$568$	−3.46651e27			−0.0416136
$569$			4.19217e28i			0.494038i	0.969011	+	0.247019i	$0.0794509\pi$
$569$			4.19217e28i			0.494038i	−0.969011	+	0.247019i	$0.920549\pi$
$570$	1.28870e27	+	1.73646e29i	0.0149096	+	2.00899i
$571$	1.07694e29			1.22325			0.611623	−	0.791150i	$-0.290517\pi$
$571$	1.07694e29			1.22325			0.611623	+	0.791150i	$0.290517\pi$
$572$	1.21858e29			1.35893
$573$	9.35856e28	−	6.94541e26i	1.02467	−	0.00760456i
$574$	7.29493e28	−	1.44677e29i	0.784235	−	1.55534i
$575$			2.21009e28i			0.233291i
$576$	−1.01573e29	+	1.50772e27i	−1.05279	+	0.0156274i
$577$		−	1.13427e29i		−	1.15444i	−0.816590	−	0.577218i	$-0.804138\pi$
$577$		−	1.13427e29i		−	1.15444i	0.816590	−	0.577218i	$-0.195862\pi$
$578$		−	1.17820e29i		−	1.17754i
$579$	3.06100e26	+	4.12454e28i	0.00300427	+	0.404809i
$580$		−	1.24225e29i		−	1.19733i
$581$	−2.25524e28	−	1.13714e28i	−0.213473	−	0.107638i
$582$	1.29774e27	+	1.74863e29i	0.0120641	+	1.62557i
$583$	−1.77418e29			−1.61986
$584$	3.58323e26			0.00321321
$585$	1.56174e27	+	1.05212e29i	0.0137553	+	0.926677i
$586$			1.31934e29i			1.14139i
$587$	−1.89698e29			−1.61199			−0.805997	−	0.591920i	$-0.798370\pi$
$587$	−1.89698e29			−1.61199			−0.805997	+	0.591920i	$0.798370\pi$
$588$	−9.83620e28	+	7.38756e28i	−0.821042	+	0.616651i
$589$	1.72763e29			1.41658
$590$		−	1.36177e29i		−	1.09687i
$591$	−7.66278e28	+	5.68689e26i	−0.606342	+	0.00449994i
$592$	−1.08492e29			−0.843373
$593$	−2.34077e29			−1.78766			−0.893830	−	0.448407i	$-0.851992\pi$
$593$	−2.34077e29			−1.78766			−0.893830	+	0.448407i	$0.851992\pi$
$594$	−5.39265e27	−	2.42175e29i	−0.0404618	−	1.81707i
$595$	−1.46375e29	−	7.38055e28i	−1.07904	−	0.544077i
$596$		−	3.12565e28i		−	0.226388i
$597$	1.90233e29	−	1.41180e27i	1.35380	−	0.0100472i
$598$			2.45289e29i			1.71520i
$599$		−	1.27627e29i		−	0.876922i	−0.898750	−	0.438461i	$-0.855524\pi$
$599$		−	1.27627e29i		−	0.876922i	0.898750	−	0.438461i	$-0.144476\pi$
$600$	−1.13535e27	+	8.42591e24i	−0.00766549	+	5.68890e-5i
$601$		−	1.03497e29i		−	0.686666i	−0.939214	−	0.343333i	$-0.888444\pi$
$601$		−	1.03497e29i		−	0.686666i	0.939214	−	0.343333i	$-0.111556\pi$
$602$	−1.48082e29	+	2.93683e29i	−0.965468	+	1.91477i
$603$	−1.49078e29	+	2.21287e27i	−0.955174	+	0.0141783i
$604$	2.46554e29			1.55247
$605$	−9.09908e28			−0.563075
$606$	2.75833e29	−	2.04708e27i	1.67758	−	0.0124501i
$607$		−	7.57714e28i		−	0.452922i	−0.974020	−	0.226461i	$-0.927284\pi$
$607$		−	7.57714e28i		−	0.452922i	0.974020	−	0.226461i	$-0.0727156\pi$
$608$	3.82225e29			2.24560
$609$	−2.02430e29	−	1.00192e29i	−1.16894	−	0.578567i
$610$	2.18603e29			1.24077
$611$		−	1.09825e29i		−	0.612731i
$612$	2.53059e29	−	3.75633e27i	1.38781	−	0.0206003i
$613$	−8.06116e28			−0.434573			−0.217287	−	0.976108i	$-0.569721\pi$
$613$	−8.06116e28			−0.434573			−0.217287	+	0.976108i	$0.569721\pi$
$614$	−6.76473e28			−0.358495
$615$	1.55818e27	+	2.09956e29i	0.00811762	+	1.09381i
$616$	−8.49981e27	−	4.28579e27i	−0.0435323	−	0.0219500i
$617$			1.68400e29i			0.847905i	0.905684	+	0.423953i	$0.139358\pi$
$617$			1.68400e29i			0.847905i	−0.905684	+	0.423953i	$0.860642\pi$
$618$	7.75872e26	+	1.04545e29i	0.00384070	+	0.517514i
$619$			3.43525e29i			1.67188i	0.548817	+	0.835942i	$0.315078\pi$
$619$			3.43525e29i			1.67188i	−0.548817	+	0.835942i	$0.684922\pi$
$620$		−	1.72171e29i		−	0.823847i
$621$	2.46963e29	−	5.49927e27i	1.16190	−	0.0258728i
$622$			5.70539e29i			2.63928i
$623$	2.97485e27	+	1.49999e27i	0.0135314	+	0.00682281i
$624$	2.25386e29	−	1.67269e27i	1.00807	−	0.00748130i
$625$	−1.72570e29			−0.758972
$626$	−3.69670e29			−1.59876
$627$	3.51635e27	+	4.73810e29i	0.0149549	+	2.01509i
$628$			2.51212e29i			1.05066i
$629$	2.85013e29			1.17228
$630$	1.37479e29	−	2.83028e29i	0.556110	−	1.14486i
$631$	−2.86972e29			−1.14165			−0.570823	−	0.821073i	$-0.693376\pi$
$631$	−2.86972e29			−1.14165			−0.570823	+	0.821073i	$0.693376\pi$
$632$		−	7.04040e27i		−	0.0275466i
$633$	−7.30930e26	−	9.84888e28i	−0.00281279	−	0.379008i
$634$	2.42536e29			0.917990
$635$	2.15729e29			0.803128
$636$	3.55788e29	−	2.64046e27i	1.30284	−	0.00966898i
$637$	2.31401e29	−	1.71125e29i	0.833493	−	0.616380i
$638$		−	6.69066e29i		−	2.37057i
$639$	−4.64043e27	−	3.12619e29i	−0.0161733	−	1.08957i
$640$		−	1.99086e28i		−	0.0682576i
$641$			2.02581e29i			0.683265i	0.939834	+	0.341632i	$0.110980\pi$
$641$			2.02581e29i			0.683265i	−0.939834	+	0.341632i	$0.889020\pi$
$642$	4.05610e27	+	5.46538e29i	0.0134583	+	1.81344i
$643$		−	3.24332e29i		−	1.05870i	−0.848402	−	0.529352i	$-0.822435\pi$
$643$		−	3.24332e29i		−	1.05870i	0.848402	−	0.529352i	$-0.177565\pi$
$644$	1.67304e29	−	3.31806e29i	0.537285	−	1.06557i
$645$	−3.16299e27	−	4.26196e29i	−0.00999357	−	1.34658i
$646$	−9.77167e29			−3.03758
$647$	−3.72570e29			−1.13950			−0.569748	−	0.821819i	$-0.692959\pi$
$647$	−3.72570e29			−1.13950			−0.569748	+	0.821819i	$0.692959\pi$
$648$	3.76657e26	+	1.26846e28i	0.00113347	+	0.0381716i
$649$		−	3.71572e29i		−	1.10020i
$650$	1.01683e29			0.296250
$651$	−2.80559e29	−	1.38863e29i	−0.804312	−	0.398093i
$652$	−1.57213e29			−0.443494
$653$			5.73406e29i			1.59175i	0.605464	+	0.795873i	$0.292988\pi$
$653$			5.73406e29i			1.59175i	−0.605464	+	0.795873i	$0.707012\pi$
$654$	−2.47790e29	+	1.83896e27i	−0.676890	+	0.00502350i
$655$	3.09716e29			0.832588
$656$	4.49745e29			1.18981
$657$	4.79667e26	+	3.23145e28i	0.00124883	+	0.0841319i
$658$	−1.47860e29	+	2.93244e29i	−0.378860	+	0.751376i
$659$			3.15527e28i			0.0795682i	0.999208	+	0.0397841i	$0.0126670\pi$
$659$			3.15527e28i			0.0795682i	−0.999208	+	0.0397841i	$0.987333\pi$
$660$	4.72184e29	−	3.50429e27i	1.17193	−	0.00869739i
$661$			3.17504e29i			0.775594i	0.921745	+	0.387797i	$0.126764\pi$
$661$			3.17504e29i			0.775594i	−0.921745	+	0.387797i	$0.873236\pi$
$662$		−	3.92743e29i		−	0.944276i
$663$	−5.92098e29	+	4.39423e27i	−1.40121	+	0.0103990i
$664$			3.91950e27i			0.00912989i
$665$	−2.77103e29	+	5.49565e29i	−0.635351	+	1.26006i
$666$	8.11954e27	+	5.47002e29i	0.0183253	+	1.23455i
$667$	6.82294e29			1.51583
$668$	−9.06995e28			−0.198359
$669$	−9.92976e28	+	7.36932e26i	−0.213779	+	0.00158655i
$670$		−	5.73680e29i		−	1.21586i
$671$	5.96479e29			1.24454
$672$	−6.20716e29	−	3.07222e29i	−1.27501	−	0.631067i
$673$	3.93458e29			0.795684			0.397842	−	0.917454i	$-0.369759\pi$
$673$	3.93458e29			0.795684			0.397842	+	0.917454i	$0.369759\pi$
$674$			1.34645e30i			2.68079i
$675$	−2.27969e27	−	1.02377e29i	−0.00446876	−	0.200684i
$676$	3.97080e28			0.0766368
$677$	5.39053e29			1.02435			0.512177	−	0.858880i	$-0.328839\pi$
$677$	5.39053e29			1.02435			0.512177	+	0.858880i	$0.328839\pi$
$678$	−4.03594e27	−	5.43821e29i	−0.00755149	−	1.01752i
$679$	−2.79045e29	+	5.53417e29i	−0.514093	+	1.01958i
$680$			2.54392e28i			0.0461488i
$681$	−7.33798e27	−	9.88753e29i	−0.0131079	−	1.76621i
$682$		−	9.27298e29i		−	1.63111i
$683$		−	1.34724e29i		−	0.233360i	−0.993170	−	0.116680i	$-0.962775\pi$
$683$		−	1.34724e29i		−	0.233360i	0.993170	−	0.116680i	$-0.0372252\pi$
$684$	−1.41031e28	−	9.50109e29i	−0.0240562	−	1.62063i
$685$		−	4.04417e28i		−	0.0679327i
$686$	−8.48252e29	+	1.45379e29i	−1.40321	+	0.240490i
$687$	4.20214e29	−	3.11860e27i	0.684581	−	0.00508058i
$688$	−9.12950e29			−1.46477
$689$	−8.32416e29			−1.31534
$690$	7.05380e27	+	9.50461e29i	0.0109776	+	1.47917i
$691$			7.84599e29i			1.20262i	0.799016	+	0.601309i	$0.205354\pi$
$691$			7.84599e29i			1.20262i	−0.799016	+	0.601309i	$0.794646\pi$
$692$	−2.35830e29			−0.356029
$693$	3.75125e29	−	7.72271e29i	0.557798	−	1.14834i
$694$	−7.79075e29			−1.14105
$695$			4.82644e29i			0.696284i
$696$	2.60123e26	+	3.50501e28i	0.000369642	+	0.0498073i
$697$	−1.18150e30			−1.65383
$698$	−7.04295e29			−0.971120
$699$	−1.54235e29	+	1.14465e27i	−0.209495	+	0.00155476i
$700$	−1.37548e29	−	6.93550e28i	−0.184046	−	0.0928000i
$701$		−	7.51986e29i		−	0.991222i	−0.868545	−	0.495611i	$-0.834944\pi$
$701$		−	7.51986e29i		−	0.991222i	0.868545	−	0.495611i	$-0.165056\pi$
$702$	−2.53014e28	−	1.13624e30i	−0.0328552	−	1.47547i
$703$		−	1.07008e30i		−	1.36894i
$704$		−	1.06653e30i		−	1.34419i
$705$	−3.15826e27	−	4.25558e29i	−0.00392159	−	0.528413i
$706$		−	1.80275e29i		−	0.220539i
$707$	8.72975e29	+	4.40173e29i	1.05220	+	0.530542i
$708$	5.53000e27	+	7.45137e29i	0.00656713	+	0.884885i
$709$	1.55784e30			1.82279			0.911394	−	0.411534i	$-0.135007\pi$
$709$	1.55784e30			1.82279			0.911394	+	0.411534i	$0.135007\pi$
$710$	1.20301e30			1.38694
$711$	6.34921e29	−	9.42459e27i	0.721255	−	0.0107061i
$712$		−	5.17015e26i		−	0.000578713i
$713$	9.45631e29			1.04299
$714$	1.58687e30	+	7.85421e29i	1.72469	+	0.853633i
$715$	−1.10474e30			−1.18317
$716$		−	3.64573e28i		−	0.0384767i
$717$	−6.14771e29	+	4.56249e27i	−0.639385	+	0.00474516i
$718$	−2.28958e30			−2.34665
$719$	−1.78661e28			−0.0180459			−0.00902293	−	0.999959i	$-0.502872\pi$
$719$	−1.78661e28			−0.0180459			−0.00902293	+	0.999959i	$0.502872\pi$
$720$	8.73292e29	−	1.29629e28i	0.869297	−	0.0129036i
$721$	−1.66832e29	+	3.30869e29i	−0.163666	+	0.324591i
$722$			2.19629e30i			2.12349i
$723$	1.36853e29	−	1.01565e27i	0.130408	−	0.000967815i
$724$			5.60558e29i			0.526460i
$725$		−	2.82841e29i		−	0.261815i
$726$	9.82768e29	−	7.29356e27i	0.896637	−	0.00665434i
$727$			1.04360e30i			0.938475i	0.883072	+	0.469238i	$0.155471\pi$
$727$			1.04360e30i			0.938475i	−0.883072	+	0.469238i	$0.844529\pi$
$728$	−3.98796e28	−	2.01082e28i	−0.0353485	−	0.0178235i
$729$	−1.14343e30	+	5.09480e28i	−0.999009	+	0.0445132i
$730$	−1.24352e29			−0.107093
$731$	2.39836e30			2.03602
$732$	−1.19616e30	+	8.87723e27i	−1.00097	+	0.00742867i
$733$			2.13525e29i			0.176139i	0.996114	+	0.0880697i	$0.0280698\pi$
$733$			2.13525e29i			0.176139i	−0.996114	+	0.0880697i	$0.971930\pi$
$734$	−1.84006e30			−1.49632
$735$	8.91727e29	−	6.69739e29i	0.714850	−	0.536894i
$736$	2.09213e30			1.65338
$737$		−	1.56534e30i		−	1.21955i
$738$	−3.36590e28	−	2.26756e30i	−0.0258529	−	1.74167i
$739$	1.74393e30			1.32057			0.660287	−	0.751013i	$-0.270435\pi$
$739$	1.74393e30			1.32057			0.660287	+	0.751013i	$0.270435\pi$
$740$	−1.06641e30			−0.796143
$741$	1.64981e28	+	2.22303e30i	0.0121435	+	1.63627i
$742$	2.22263e30	+	1.12070e30i	1.61297	+	0.813294i
$743$		−	8.08005e28i		−	0.0578138i	−0.999582	−	0.0289069i	$-0.990797\pi$
$743$		−	8.08005e28i		−	0.0578138i	0.999582	−	0.0289069i	$-0.00920264\pi$
$744$	3.60519e26	+	4.85780e28i	0.000254339	+	0.0342708i
$745$			2.83364e29i			0.197108i
$746$		−	3.59267e30i		−	2.46411i
$747$	−3.53470e29	+	5.24681e27i	−0.239049	+	0.00354837i
$748$			2.65715e30i			1.77194i
$749$	−8.72162e29	+	1.72972e30i	−0.573506	+	1.13741i
$750$	2.35685e30	−	1.74912e28i	1.52823	−	0.0113417i
$751$	2.52556e30			1.61487			0.807437	−	0.589954i	$-0.200854\pi$
$751$	2.52556e30			1.61487			0.807437	+	0.589954i	$0.200854\pi$
$752$	−9.11585e29			−0.574791
$753$	2.25915e28	+	3.04408e30i	0.0140474	+	1.89282i
$754$		−	3.13914e30i		−	1.92492i
$755$	−2.23520e30			−1.35168
$756$	−7.40769e29	+	1.55427e30i	−0.441778	+	0.926930i
$757$	−1.56975e30			−0.923261			−0.461630	−	0.887072i	$-0.652735\pi$
$757$	−1.56975e30			−0.923261			−0.461630	+	0.887072i	$0.652735\pi$
$758$		−	1.55160e29i		−	0.0900025i
$759$	1.92470e28	+	2.59343e30i	0.0110109	+	1.48366i
$760$	9.55115e28			0.0538906
$761$	1.72012e30			0.957235			0.478618	−	0.878023i	$-0.341138\pi$
$761$	1.72012e30			0.957235			0.478618	+	0.878023i	$0.341138\pi$
$762$	−2.33004e30	+	1.72922e28i	−1.27890	+	0.00949126i
$763$	−7.84222e29	−	3.95422e29i	−0.424553	−	0.214069i
$764$		−	1.97049e30i		−	1.05219i
$765$	−2.29417e30	+	3.40541e28i	−1.20832	+	0.0179359i
$766$		−	4.26014e29i		−	0.221321i
$767$		−	1.74335e30i		−	0.893374i
$768$	−1.38624e28	−	1.86789e30i	−0.00700724	−	0.944187i
$769$		−	5.97512e29i		−	0.297934i	−0.988842	−	0.148967i	$-0.952405\pi$
$769$		−	5.97512e29i		−	0.297934i	0.988842	−	0.148967i	$-0.0475948\pi$
$770$	2.94976e30	+	1.48733e30i	1.45089	+	0.731570i
$771$	7.20364e27	+	9.70652e29i	0.00349527	+	0.470969i
$772$	8.68440e29			0.415679
$773$	−2.40153e30			−1.13397			−0.566987	−	0.823727i	$-0.691891\pi$
$773$	−2.40153e30			−1.13397			−0.566987	+	0.823727i	$0.691891\pi$
$774$	6.83252e28	+	4.60297e30i	0.0318274	+	2.14417i
$775$		−	3.92006e29i		−	0.180146i
$776$	9.61811e28			0.0436055
$777$	−8.60102e29	+	1.73776e30i	−0.384706	+	0.777265i
$778$	−2.50958e30			−1.10743
$779$			4.43594e30i			1.93127i
$780$	2.21541e30	−	1.64415e28i	0.951613	−	0.00706234i
$781$	3.28254e30			1.39115
$782$	−5.34859e30			−2.23650
$783$	−3.16056e30	+	7.03782e28i	−1.30396	+	0.0290362i
$784$	−1.42039e30	−	1.92070e30i	−0.578214	−	0.781883i
$785$		−	2.27743e30i		−	0.914773i
$786$	−3.34516e30	+	2.48259e28i	−1.32581	+	0.00983941i
$787$			1.42038e30i			0.555483i	0.960656	+	0.277741i	$0.0895858\pi$
$787$			1.42038e30i			0.555483i	−0.960656	+	0.277741i	$0.910414\pi$
$788$			1.61343e30i			0.622624i
$789$	2.27204e30	−	1.68619e28i	0.865184	−	0.00642092i
$790$			2.44329e30i			0.918101i
$791$	8.67826e29	−	1.72112e30i	0.321795	−	0.638201i
$792$	−1.33220e29	+	1.97748e27i	−0.0487477	+	0.000723597i
$793$	2.79858e30			1.01058
$794$	6.77487e30			2.41427
$795$	−3.22550e30	+	2.39379e28i	−1.13434	+	0.00841841i
$796$		−	4.00544e30i		−	1.39015i
$797$	−4.23430e30			−1.45034			−0.725170	−	0.688570i	$-0.758239\pi$
$797$	−4.23430e30			−1.45034			−0.725170	+	0.688570i	$0.758239\pi$
$798$	2.94886e30	−	5.95791e30i	0.996837	−	2.01402i
$799$	2.39477e30			0.798956
$800$		−	8.67283e29i		−	0.285572i
$801$	4.66257e28	−	6.92098e26i	0.0151525	−	0.000224919i
$802$	2.55067e30			0.818133
$803$	−3.39306e29			−0.107418
$804$	2.32965e28	+	3.13908e30i	0.00727952	+	0.980877i
$805$	−1.51674e30	+	3.00808e30i	−0.467794	+	0.927753i
$806$		−	4.35072e30i		−	1.32447i
$807$	−1.91907e28	−	2.58584e30i	−0.00576659	−	0.777017i
$808$		−	1.51719e29i		−	0.0450007i
$809$		−	4.80366e30i		−	1.40641i	−0.710986	−	0.703206i	$-0.751751\pi$
$809$		−	4.80366e30i		−	1.40641i	0.710986	−	0.703206i	$-0.248249\pi$
$810$	−1.30714e29	−	4.40205e30i	−0.0377773	−	1.27222i
$811$		−	8.54703e29i		−	0.243835i	−0.992540	−	0.121918i	$-0.961096\pi$
$811$		−	8.54703e29i		−	0.243835i	0.992540	−	0.121918i	$-0.0389043\pi$
$812$	−2.14111e30	+	4.24636e30i	−0.602977	+	1.19586i
$813$	−7.01864e29	+	5.20885e27i	−0.195120	+	0.00144807i
$814$	−5.74360e30			−1.57626
$815$	1.42525e30			0.386134
$816$	3.64734e28	+	4.91460e30i	0.00975506	+	1.31444i
$817$		−	9.00463e30i		−	2.37757i
$818$	5.85734e30			1.52683
$819$	1.76002e30	−	3.62336e30i	0.452936	−	0.932461i
$820$	4.42073e30			1.12318
$821$			6.10606e30i			1.53164i	0.643052	+	0.765822i	$0.277668\pi$
$821$			6.10606e30i			1.53164i	−0.643052	+	0.765822i	$0.722332\pi$
$822$	3.24169e27	+	4.36800e29i	0.000802819	+	0.108176i
$823$	2.44508e30			0.597854			0.298927	−	0.954276i	$-0.403371\pi$
$823$	2.44508e30			0.597854			0.298927	+	0.954276i	$0.403371\pi$
$824$	5.75034e28			0.0138822
$825$	1.07509e30	−	7.97874e27i	0.256259	−	0.00190181i
$826$	−2.34711e30	+	4.65491e30i	−0.552386	+	1.09552i
$827$			7.46910e28i			0.0173564i	0.999962	+	0.00867821i	$0.00276240\pi$
$827$			7.46910e28i			0.0173564i	−0.999962	+	0.00867821i	$0.997238\pi$
$828$	−7.71945e28	−	5.20048e30i	−0.0177120	−	1.19323i
$829$		−	5.33913e30i		−	1.20962i	−0.796371	−	0.604809i	$-0.793250\pi$
$829$		−	5.33913e30i		−	1.20962i	0.796371	−	0.604809i	$-0.206750\pi$
$830$		−	1.36022e30i		−	0.304290i
$831$	4.39006e27	+	5.91536e29i	0.000969749	+	0.130668i
$832$		−	5.00399e30i		−	1.09149i
$833$	3.73142e30	+	5.04577e30i	0.803714	+	1.08681i
$834$	−3.86873e28	−	5.21291e30i	−0.00822859	−	1.10876i
$835$	8.22261e29			0.172704
$836$	9.97628e30			2.06920
$837$	−4.38041e30	+	9.75412e28i	−0.897216	+	0.0199789i
$838$		−	7.22476e30i		−	1.46137i
$839$	−6.79091e30			−1.35652			−0.678262	−	0.734821i	$-0.737266\pi$
$839$	−6.79091e30			−1.35652			−0.678262	+	0.734821i	$0.737266\pi$
$840$	−1.55106e29	−	7.67696e28i	−0.0305983	−	0.0151446i
$841$	−3.59897e30			−0.701166
$842$			5.38361e30i			1.03585i
$843$	−2.51184e30	+	1.86415e28i	−0.477311	+	0.00354234i
$844$	−2.07373e30			−0.389185
$845$	−3.59984e29			−0.0667248
$846$	6.82231e28	+	4.59609e30i	0.0124894	+	0.841395i
$847$	3.11033e30	+	1.56830e30i	0.562380	+	0.283565i
$848$			6.90931e30i			1.23389i
$849$	−3.58031e30	+	2.65711e28i	−0.631524	+	0.00468682i
$850$			2.21723e30i			0.386289i
$851$		−	5.85716e30i		−	1.00792i
$852$	−6.58270e30	+	4.88532e28i	−1.11889	+	0.00830380i
$853$			5.44553e30i			0.914272i	0.889397	+	0.457136i	$0.151125\pi$
$853$			5.44553e30i			0.914272i	−0.889397	+	0.457136i	$0.848875\pi$
$854$	−7.47246e30	−	3.76778e30i	−1.23924	−	0.624853i
$855$	1.27856e29	+	8.61347e30i	0.0209448	+	1.41102i
$856$	3.00616e29			0.0486449
$857$	−8.68907e30			−1.38891			−0.694456	−	0.719535i	$-0.744355\pi$
$857$	−8.68907e30			−1.38891			−0.694456	+	0.719535i	$0.744355\pi$
$858$	1.19320e31	−	8.85528e28i	1.88407	−	0.0139825i
$859$			5.86174e30i			0.914321i	0.889384	+	0.457160i	$0.151133\pi$
$859$			5.86174e30i			0.914321i	−0.889384	+	0.457160i	$0.848867\pi$
$860$	−8.97374e30			−1.38274
$861$	3.56549e30	−	7.20376e30i	0.542733	−	1.09654i
$862$	−8.91270e30			−1.34024
$863$		−	2.61010e30i		−	0.387742i	−0.981027	−	0.193871i	$-0.937896\pi$
$863$		−	2.61010e30i		−	0.387742i	0.981027	−	0.193871i	$-0.0621044\pi$
$864$	−9.69130e30	+	2.15802e29i	−1.42229	+	0.0316710i
$865$	2.13799e30			0.309981
$866$	1.23717e31			1.77211
$867$	−4.33755e28	−	5.84462e30i	−0.00613824	−	0.827095i
$868$	−2.96749e30	+	5.88528e30i	−0.414889	+	0.822830i
$869$			6.66676e30i			0.920889i
$870$	−9.02726e28	−	1.21637e31i	−0.0123198	−	1.66003i
$871$		−	7.34432e30i		−	0.990286i
$872$			1.36294e29i			0.0181574i
$873$	1.28752e29	+	8.67385e30i	0.0169475	+	1.14173i
$874$			2.00813e31i			2.61169i
$875$	7.45910e30	+	3.76105e30i	0.958522	+	0.483308i
$876$	6.80433e29	−	5.04980e27i	0.0863957	−	0.000641182i
$877$	1.12364e30			0.140972			0.0704858	−	0.997513i	$-0.477545\pi$
$877$	1.12364e30			0.140972			0.0704858	+	0.997513i	$0.477545\pi$
$878$	−7.05334e30			−0.874385
$879$	4.85719e28	+	6.54480e30i	0.00594979	+	0.801702i
$880$			9.16969e30i			1.10991i
$881$	1.10064e31			1.31643			0.658216	−	0.752829i	$-0.271311\pi$
$881$	1.10064e31			1.31643			0.658216	+	0.752829i	$0.271311\pi$
$882$	−9.57763e30	+	7.30516e30i	−1.13198	+	0.863395i
$883$	1.30249e31			1.52120			0.760599	−	0.649222i	$-0.224906\pi$
$883$	1.30249e31			1.52120			0.760599	+	0.649222i	$0.224906\pi$
$884$			1.24669e31i			1.43883i
$885$	−5.01337e28	−	6.75524e30i	−0.00571775	−	0.770436i
$886$	7.39940e30			0.833955
$887$	3.68363e30			0.410277			0.205139	−	0.978733i	$-0.434235\pi$
$887$	3.68363e30			0.410277			0.205139	+	0.978733i	$0.434235\pi$
$888$	3.00888e29	−	2.23303e27i	0.0331184	−	0.000245786i
$889$	−7.37424e30	−	3.71826e30i	−0.802138	−	0.404456i
$890$			1.79424e29i			0.0192879i
$891$	−3.56667e29	−	1.20114e31i	−0.0378920	−	1.27608i
$892$			2.09076e30i			0.219519i
$893$		−	8.99117e30i		−	0.932987i
$894$	−2.27136e28	−	3.06054e30i	−0.00232939	−	0.313873i
$895$			3.30514e29i			0.0335002i
$896$	−3.43140e29	+	6.80532e29i	−0.0343745	+	0.0681734i
$897$	9.03036e28	+	1.21679e31i	0.00894096	+	1.20475i
$898$	9.62945e30			0.942323
$899$	−1.21019e31			−1.17052
$900$	−2.15583e30	+	3.20006e28i	−0.206096	+	0.00305922i
$901$		−	1.81510e31i		−	1.71511i
$902$	2.38097e31			2.22374
$903$	−7.23768e30	+	1.46231e31i	−0.668156	+	1.34995i
$904$	−2.99122e29			−0.0272948
$905$		−	5.08189e30i		−	0.458369i
$906$	2.41418e31	−	1.79167e29i	2.15241	−	0.0159740i
$907$	−7.33469e30			−0.646406			−0.323203	−	0.946330i	$-0.604760\pi$
$907$	−7.33469e30			−0.646406			−0.323203	+	0.946330i	$0.604760\pi$
$908$	−2.08186e31			−1.81364
$909$	1.36824e31	−	2.03097e29i	1.17826	−	0.0174897i
$910$	1.38398e31	+	6.97831e30i	1.17813	+	0.594040i
$911$		−	1.97607e31i		−	1.66287i	−0.555622	−	0.831435i	$-0.687520\pi$
$911$		−	1.97607e31i		−	1.66287i	0.555622	−	0.831435i	$-0.312480\pi$
$912$	1.84519e31	−	1.36940e29i	1.53495	−	0.0113916i
$913$		−	3.71149e30i		−	0.305214i
$914$		−	2.83886e30i		−	0.230786i
$915$	1.08441e31	−	8.04789e28i	0.871509	−	0.00646786i
$916$		−	8.84780e30i		−	0.702963i
$917$	−1.05870e31	−	5.33819e30i	−0.831561	−	0.419291i
$918$	2.47760e31	−	5.51703e29i	1.92391	−	0.0428408i
$919$	−2.29564e31			−1.76235			−0.881173	−	0.472793i	$-0.843246\pi$
$919$	−2.29564e31			−1.76235			−0.881173	+	0.472793i	$0.843246\pi$
$920$	5.22789e29			0.0396784
$921$	−3.35574e30	+	2.49045e28i	−0.251804	+	0.00186875i
$922$			2.26041e31i			1.67692i
$923$	1.54011e31			1.12963
$924$	−1.62010e31	−	8.01867e30i	−1.17486	−	0.581496i
$925$	−2.42805e30			−0.174088
$926$		−	1.04323e31i		−	0.739547i
$927$	7.69765e28	+	5.18580e30i	0.00539537	+	0.363478i
$928$	−2.67746e31			−1.85553
$929$	1.17358e31			0.804167			0.402083	−	0.915603i	$-0.368286\pi$
$929$	1.17358e31			0.804167			0.402083	+	0.915603i	$0.368286\pi$
$930$	−1.25114e29	−	1.68584e31i	−0.00847686	−	1.14221i
$931$	1.89443e31	−	1.40096e31i	1.26913	−	0.938544i
$932$			3.24750e30i			0.215120i
$933$	2.10045e29	+	2.83024e31i	0.0137580	+	1.85381i
$934$			1.19122e31i			0.771527i
$935$		−	2.40892e31i		−	1.54276i
$936$	−6.25044e29	+	9.27797e27i	−0.0395835	+	0.000587566i
$937$		−	1.34665e31i		−	0.843313i	−0.906756	−	0.421656i	$-0.861449\pi$
$937$		−	1.34665e31i		−	0.843313i	0.906756	−	0.421656i	$-0.138551\pi$
$938$	−9.88780e30	+	1.96100e31i	−0.612308	+	1.21436i
$939$	−1.83380e31	+	1.36095e29i	−1.12296	+	0.00833397i
$940$	−8.96033e30			−0.542602
$941$	−1.87253e31			−1.12134			−0.560671	−	0.828039i	$-0.689457\pi$
$941$	−1.87253e31			−1.12134			−0.560671	+	0.828039i	$0.689457\pi$
$942$	1.82552e29	+	2.45979e31i	0.0108107	+	1.45668i
$943$			2.42804e31i			1.42195i
$944$	−1.44703e31			−0.838056
$945$	6.71565e30	−	1.40906e31i	0.384640	−	0.807043i
$946$	−4.83319e31			−2.73764
$947$			2.57059e31i			1.43998i	0.693982	+	0.719992i	$0.255855\pi$
$947$			2.57059e31i			1.43998i	−0.693982	+	0.719992i	$0.744145\pi$
$948$	−9.92195e28	−	1.33693e31i	−0.00549679	−	0.740663i
$949$	−1.59197e30			−0.0872246
$950$	8.32458e30			0.451091
$951$	1.20313e31	−	8.92899e28i	0.644790	−	0.00478527i
$952$	4.38464e29	−	8.69585e29i	0.0232405	−	0.0460919i
$953$		−	2.74399e31i		−	1.43849i	−0.694756	−	0.719246i	$-0.744488\pi$
$953$		−	2.74399e31i		−	1.43849i	0.694756	−	0.719246i	$-0.255512\pi$
$954$	3.48358e31	−	5.17093e29i	1.80621	−	0.0268109i
$955$			1.78640e31i			0.916101i
$956$			1.29443e31i			0.656554i
$957$	−2.46318e29	−	3.31900e31i	−0.0123572	−	1.66507i
$958$		−	2.03191e31i		−	1.00825i
$959$	−6.97044e29	+	1.38241e30i	−0.0342109	+	0.0678489i
$960$	−1.43900e29	−	1.93898e31i	−0.00698575	−	0.941293i
$961$	4.05273e30			0.194604
$962$	−2.69480e31			−1.27994
$963$	4.02418e29	+	2.71103e31i	0.0189061	+	1.27367i
$964$		−	2.88151e30i		−	0.133910i
$965$	−7.87308e30			−0.361916
$966$	1.61408e31	−	3.26110e31i	0.733948	−	1.48288i
$967$	4.46138e30			0.200674			0.100337	−	0.994954i	$-0.468008\pi$
$967$	4.46138e30			0.200674			0.100337	+	0.994954i	$0.468008\pi$
$968$		−	5.40559e29i		−	0.0240520i
$969$	−4.84738e31	+	3.59746e29i	−2.13357	+	0.0158342i
$970$	−3.33785e31			−1.45333
$971$	2.17554e31			0.937054			0.468527	−	0.883449i	$-0.344785\pi$
$971$	2.17554e31			0.937054			0.468527	+	0.883449i	$0.344785\pi$
$972$	8.94011e29	+	2.40820e31i	0.0380932	+	1.02612i
$973$	8.31873e30	−	1.64981e31i	0.350649	−	0.695425i
$974$		−	2.88419e30i		−	0.120269i
$975$	5.04414e30	−	3.74349e28i	0.208084	−	0.00154429i
$976$		−	2.32291e31i		−	0.948000i
$977$			3.04944e31i			1.23120i	0.788060	+	0.615599i	$0.211086\pi$
$977$			3.04944e31i			1.23120i	−0.788060	+	0.615599i	$0.788914\pi$
$978$	−1.53938e31	+	1.14244e29i	−0.614876	+	0.00456327i
$979$			4.89576e29i			0.0193465i
$980$	−1.39616e31	−	1.88793e31i	−0.545833	−	0.738096i
$981$	−1.22913e31	+	1.82449e29i	−0.475416	+	0.00705694i
$982$	−2.29126e31			−0.876805
$983$	−2.98752e31			−1.13109			−0.565547	−	0.824716i	$-0.691335\pi$
$983$	−2.98752e31			−1.13109			−0.565547	+	0.824716i	$0.691335\pi$
$984$	−1.24731e30	+	9.25684e27i	−0.0467225	+	0.000346748i
$985$		−	1.46270e31i		−	0.542095i
$986$	6.84498e31			2.50995
$987$	−7.22686e30	+	1.46012e31i	−0.262192	+	0.529736i
$988$	4.68070e31			1.68021
$989$		−	4.92874e31i		−	1.75055i
$990$	4.62324e31	−	6.86260e29i	1.62471	−	0.0241168i
$991$	4.64507e30			0.161517			0.0807587	−	0.996734i	$-0.474266\pi$
$991$	4.64507e30			0.161517			0.0807587	+	0.996734i	$0.474266\pi$
$992$	−3.71084e31			−1.27673
$993$	−1.44589e29	−	1.94826e31i	−0.00492230	−	0.663253i
$994$	−4.11224e31	−	2.07348e31i	−1.38523	−	0.698464i
$995$			3.63124e31i			1.21035i
$996$	5.52370e28	+	7.44289e30i	0.00182183	+	0.245481i
$997$			4.49952e30i			0.146847i	0.997301	+	0.0734237i	$0.0233926\pi$
$997$			4.49952e30i			0.146847i	−0.997301	+	0.0734237i	$0.976607\pi$
$998$		−	6.32212e31i		−	2.04170i
$999$	6.04162e29	+	2.71319e31i	0.0193070	+	0.867045i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.22.c.b.20.17	✓	52
3.2	odd	2	inner	21.22.c.b.20.36	yes	52
7.6	odd	2	inner	21.22.c.b.20.35	yes	52
21.20	even	2	inner	21.22.c.b.20.18	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.22.c.b.20.17	✓	52	1.1	even	1	trivial
21.22.c.b.20.18	yes	52	21.20	even	2	inner
21.22.c.b.20.35	yes	52	7.6	odd	2	inner
21.22.c.b.20.36	yes	52	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2061.69i q^{2} +(-759.014 - 102273. i) q^{3} -2.15341e6 q^{4} +1.95223e7 q^{5} +(-2.10855e8 + 1.56485e6i) q^{6} +(-6.67328e8 - 3.36481e8i) q^{7} +1.15978e8i q^{8} +(-1.04592e10 + 1.55253e8i) q^{9} +O(q^{10})\)	\(q-2061.69i q^{2} +(-759.014 - 102273. i) q^{3} -2.15341e6 q^{4} +1.95223e7 q^{5} +(-2.10855e8 + 1.56485e6i) q^{6} +(-6.67328e8 - 3.36481e8i) q^{7} +1.15978e8i q^{8} +(-1.04592e10 + 1.55253e8i) q^{9} -4.02489e10i q^{10} -1.09823e11i q^{11} +(1.63447e9 + 2.20235e11i) q^{12} -5.15271e11i q^{13} +(-6.93720e11 + 1.37582e12i) q^{14} +(-1.48177e10 - 1.99660e12i) q^{15} -4.27691e12 q^{16} +1.12356e13 q^{17} +(3.20084e11 + 2.15636e13i) q^{18} -4.21841e13i q^{19} -4.20394e13 q^{20} +(-3.39065e13 + 6.85050e13i) q^{21} -2.26421e14 q^{22} -2.30898e14i q^{23} +(1.18614e13 - 8.80291e10i) q^{24} -9.57173e13 q^{25} -1.06233e15 q^{26} +(2.38169e13 + 1.06958e15i) q^{27} +(1.43703e15 + 7.24581e14i) q^{28} +2.95496e15i q^{29} +(-4.11638e15 + 3.05495e13i) q^{30} +4.09546e15i q^{31} +9.06088e15i q^{32} +(-1.12319e16 + 8.33573e13i) q^{33} -2.31643e16i q^{34} +(-1.30278e16 - 6.56889e15i) q^{35} +(2.25229e16 - 3.34324e14i) q^{36} +2.53669e16 q^{37} -8.69705e16 q^{38} +(-5.26983e16 + 3.91098e14i) q^{39} +2.26416e15i q^{40} -1.05157e17 q^{41} +(1.41236e17 + 6.99046e16i) q^{42} +2.13460e17 q^{43} +2.36494e17i q^{44} +(-2.04188e17 + 3.03090e15i) q^{45} -4.76039e17 q^{46} +2.13141e17 q^{47} +(3.24623e15 + 4.37413e17i) q^{48} +(3.32106e17 + 4.49087e17i) q^{49} +1.97339e17i q^{50} +(-8.52799e15 - 1.14910e18i) q^{51} +1.10959e18i q^{52} -1.61549e18i q^{53} +(2.20513e18 - 4.91031e16i) q^{54} -2.14400e18i q^{55} +(3.90245e16 - 7.73954e16i) q^{56} +(-4.31430e18 + 3.20183e16i) q^{57} +6.09222e18 q^{58} +3.38337e18 q^{59} +(3.19085e16 + 4.29950e18i) q^{60} +5.43127e18i q^{61} +8.44356e18 q^{62} +(7.03195e18 + 3.41572e18i) q^{63} +9.71137e18 q^{64} -1.00593e19i q^{65} +(1.71857e17 + 2.31568e19i) q^{66} +1.42533e19 q^{67} -2.41948e19 q^{68} +(-2.36146e19 + 1.75255e17i) q^{69} +(-1.35430e19 + 2.68592e19i) q^{70} +2.98894e19i q^{71} +(-1.80060e16 - 1.21304e18i) q^{72} -3.08957e18i q^{73} -5.22987e19i q^{74} +(7.26508e16 + 9.78930e18i) q^{75} +9.08395e19i q^{76} +(-3.69534e19 + 7.32880e19i) q^{77} +(8.06322e17 + 1.08648e20i) q^{78} -6.07045e19 q^{79} -8.34951e19 q^{80} +(1.09371e20 - 3.24765e18i) q^{81} +2.16800e20i q^{82} +3.37951e19 q^{83} +(7.30144e19 - 1.47519e20i) q^{84} +2.19345e20 q^{85} -4.40088e20i q^{86} +(3.02213e20 - 2.24286e18i) q^{87} +1.27371e19 q^{88} -4.45786e18 q^{89} +(6.24877e18 + 4.20971e20i) q^{90} +(-1.73379e20 + 3.43855e20i) q^{91} +4.97216e20i q^{92} +(4.18855e20 - 3.10851e18i) q^{93} -4.39430e20i q^{94} -8.23530e20i q^{95} +(9.26683e20 - 6.87733e18i) q^{96} -8.29303e20i q^{97} +(9.25877e20 - 6.84700e20i) q^{98} +(1.70504e19 + 1.14866e21i) 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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