LMFDB - Embedded newform 12.13.d.a.7.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,13,Mod(7,12)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(12, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 13, names="a")

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

chi := DirichletCharacter("12.7");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 13 $
Character orbit:	$[\chi]$	$=$	12.d (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:	$10.9679258073$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 1570 x^{10} - 4077 x^{9} + 1884069 x^{8} - 3551868 x^{7} + 881574992 x^{6} + \cdots + 104882177440000 $ x^12 - 3x^11 + 1570x^10 - 4077x^9 + 1884069x^8 - 3551868x^7 + 881574992x^6 + 2167220880x^5 + 304613421264x^4 + 27792635520x^3 + 5806366144000x^2 + 1120796928000*x + 104882177440000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{57}\cdot 3^{25} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			7.6
Root			$13.5291 - 23.4332i$ of defining polynomial
Character	$\chi$	$=$	12.7
Dual form			12.13.d.a.7.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-35.2919 + 53.3899i) q^{2} +420.888i q^{3} +(-1604.96 - 3768.46i) q^{4} +8409.28 q^{5} +(-22471.2 - 14854.0i) q^{6} -192052. i q^{7} +(257840. + 47307.4i) q^{8} -177147. q^{9} +O(q^{10})$	\(q+(-35.2919 + 53.3899i) q^{2} +420.888i q^{3} +(-1604.96 - 3768.46i) q^{4} +8409.28 q^{5} +(-22471.2 - 14854.0i) q^{6} -192052. i q^{7} +(257840. + 47307.4i) q^{8} -177147. q^{9} +(-296780. + 448971. i) q^{10} +748209. i q^{11} +(1.58610e6 - 675510. i) q^{12} +5.80736e6 q^{13} +(1.02537e7 + 6.77790e6i) q^{14} +3.53937e6i q^{15} +(-1.16254e7 + 1.20965e7i) q^{16} +2.57798e7 q^{17} +(6.25185e6 - 9.45786e6i) q^{18} +1.62006e7i q^{19} +(-1.34966e7 - 3.16901e7i) q^{20} +8.08326e7 q^{21} +(-3.99468e7 - 2.64057e7i) q^{22} -1.99788e8i q^{23} +(-1.99111e7 + 1.08522e8i) q^{24} -1.73425e8 q^{25} +(-2.04953e8 + 3.10054e8i) q^{26} -7.45591e7i q^{27} +(-7.23743e8 + 3.08237e8i) q^{28} +8.06751e8 q^{29} +(-1.88967e8 - 1.24911e8i) q^{30} -7.40990e8i q^{31} +(-2.35548e8 - 1.04759e9i) q^{32} -3.14913e8 q^{33} +(-9.09818e8 + 1.37638e9i) q^{34} -1.61502e9i q^{35} +(2.84314e8 + 6.67572e8i) q^{36} +4.40061e9 q^{37} +(-8.64947e8 - 5.71749e8i) q^{38} +2.44425e9i q^{39} +(2.16825e9 + 3.97821e8i) q^{40} +3.32788e9 q^{41} +(-2.85274e9 + 4.31565e9i) q^{42} +4.43899e9i q^{43} +(2.81960e9 - 1.20085e9i) q^{44} -1.48968e9 q^{45} +(1.06667e10 + 7.05091e9i) q^{46} -1.18788e10i q^{47} +(-5.09127e9 - 4.89300e9i) q^{48} -2.30429e10 q^{49} +(6.12048e9 - 9.25912e9i) q^{50} +1.08504e10i q^{51} +(-9.32060e9 - 2.18848e10i) q^{52} -1.52961e10 q^{53} +(3.98070e9 + 2.63133e9i) q^{54} +6.29190e9i q^{55} +(9.08550e9 - 4.95188e10i) q^{56} -6.81863e9 q^{57} +(-2.84718e10 + 4.30724e10i) q^{58} +2.87986e10i q^{59} +(1.33380e10 - 5.68056e9i) q^{60} -5.04818e10 q^{61} +(3.95614e10 + 2.61509e10i) q^{62} +3.40215e10i q^{63} +(6.42435e10 + 2.43955e10i) q^{64} +4.88357e10 q^{65} +(1.11139e10 - 1.68132e10i) q^{66} -7.04181e10i q^{67} +(-4.13756e10 - 9.71502e10i) q^{68} +8.40886e10 q^{69} +(8.62259e10 + 5.69972e10i) q^{70} +4.83964e10i q^{71} +(-4.56756e10 - 8.38036e9i) q^{72} +2.79013e10 q^{73} +(-1.55306e11 + 2.34948e11i) q^{74} -7.29924e10i q^{75} +(6.10513e10 - 2.60013e10i) q^{76} +1.43695e11 q^{77} +(-1.30498e11 - 8.62622e10i) q^{78} -4.03847e11i q^{79} +(-9.77613e10 + 1.01723e11i) q^{80} +3.13811e10 q^{81} +(-1.17447e11 + 1.77675e11i) q^{82} +3.84526e11i q^{83} +(-1.29733e11 - 3.04615e11i) q^{84} +2.16790e11 q^{85} +(-2.36997e11 - 1.56660e11i) q^{86} +3.39552e11i q^{87} +(-3.53958e10 + 1.92918e11i) q^{88} -4.78354e11 q^{89} +(5.25736e10 - 7.95338e10i) q^{90} -1.11532e12i q^{91} +(-7.52895e11 + 3.20653e11i) q^{92} +3.11874e11 q^{93} +(6.34210e11 + 4.19226e11i) q^{94} +1.36235e11i q^{95} +(4.40917e11 - 9.91393e10i) q^{96} -1.21562e12 q^{97} +(8.13227e11 - 1.23026e12i) q^{98} -1.32543e11i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 90 q^{2} - 4692 q^{4} - 10296 q^{5} - 48114 q^{6} - 648000 q^{8} - 2125764 q^{9}+O(q^{10}) $ 12 * q - 90 * q^2 - 4692 * q^4 - 10296 * q^5 - 48114 * q^6 - 648000 * q^8 - 2125764 * q^9	\( 12 q - 90 q^{2} - 4692 q^{4} - 10296 q^{5} - 48114 q^{6} - 648000 q^{8} - 2125764 q^{9} + 923028 q^{10} - 3018060 q^{12} + 2094840 q^{13} + 15389208 q^{14} - 61526928 q^{16} - 12097800 q^{17} + 15943230 q^{18} - 377644248 q^{20} - 75057840 q^{21} + 482545560 q^{22} - 332039088 q^{24} + 1058748132 q^{25} + 243358236 q^{26} - 185369520 q^{28} + 1997608680 q^{29} - 577761660 q^{30} + 1733536800 q^{32} + 322101360 q^{33} - 7816269348 q^{34} + 831173724 q^{36} - 960170280 q^{37} - 8280525240 q^{38} + 3985807104 q^{40} + 5806392696 q^{41} - 1390844520 q^{42} + 4989496464 q^{44} + 1823905512 q^{45} + 4149450240 q^{46} - 7791843600 q^{48} - 60479071668 q^{49} + 68552901522 q^{50} - 31090133640 q^{52} + 42482511720 q^{53} + 8523250758 q^{54} - 38053468224 q^{56} - 58319941680 q^{57} + 159666562500 q^{58} - 19968517224 q^{60} + 137368568088 q^{61} - 27876030840 q^{62} + 188355529344 q^{64} - 328250713392 q^{65} - 136719325224 q^{66} + 77938316280 q^{68} + 214339017024 q^{69} - 454939318704 q^{70} + 114791256000 q^{72} - 804477880680 q^{73} - 502785766548 q^{74} + 143972453808 q^{76} + 1383727360320 q^{77} - 72052158420 q^{78} - 417712547808 q^{80} + 376572715308 q^{81} + 460673773020 q^{82} + 28008331632 q^{84} + 1437981718224 q^{85} + 1255416205464 q^{86} + 47622991680 q^{88} - 1422946205928 q^{89} - 163511641116 q^{90} - 3462722444160 q^{92} + 1056734080560 q^{93} + 847910842896 q^{94} + 341032101984 q^{96} - 4056673857000 q^{97} + 1702751294790 q^{98}+O(q^{100}) \) 12 * q - 90 * q^2 - 4692 * q^4 - 10296 * q^5 - 48114 * q^6 - 648000 * q^8 - 2125764 * q^9 + 923028 * q^10 - 3018060 * q^12 + 2094840 * q^13 + 15389208 * q^14 - 61526928 * q^16 - 12097800 * q^17 + 15943230 * q^18 - 377644248 * q^20 - 75057840 * q^21 + 482545560 * q^22 - 332039088 * q^24 + 1058748132 * q^25 + 243358236 * q^26 - 185369520 * q^28 + 1997608680 * q^29 - 577761660 * q^30 + 1733536800 * q^32 + 322101360 * q^33 - 7816269348 * q^34 + 831173724 * q^36 - 960170280 * q^37 - 8280525240 * q^38 + 3985807104 * q^40 + 5806392696 * q^41 - 1390844520 * q^42 + 4989496464 * q^44 + 1823905512 * q^45 + 4149450240 * q^46 - 7791843600 * q^48 - 60479071668 * q^49 + 68552901522 * q^50 - 31090133640 * q^52 + 42482511720 * q^53 + 8523250758 * q^54 - 38053468224 * q^56 - 58319941680 * q^57 + 159666562500 * q^58 - 19968517224 * q^60 + 137368568088 * q^61 - 27876030840 * q^62 + 188355529344 * q^64 - 328250713392 * q^65 - 136719325224 * q^66 + 77938316280 * q^68 + 214339017024 * q^69 - 454939318704 * q^70 + 114791256000 * q^72 - 804477880680 * q^73 - 502785766548 * q^74 + 143972453808 * q^76 + 1383727360320 * q^77 - 72052158420 * q^78 - 417712547808 * q^80 + 376572715308 * q^81 + 460673773020 * q^82 + 28008331632 * q^84 + 1437981718224 * q^85 + 1255416205464 * q^86 + 47622991680 * q^88 - 1422946205928 * q^89 - 163511641116 * q^90 - 3462722444160 * q^92 + 1056734080560 * q^93 + 847910842896 * q^94 + 341032101984 * q^96 - 4056673857000 * q^97 + 1702751294790 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/12\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$1$	$-1$

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 $

$2$	−35.2919	+	53.3899i	−0.551436	+	0.834217i
$2$	−35.2919	+	53.3899i	−0.551436	+	0.834217i
$3$			420.888i			0.577350i
$3$			420.888i			0.577350i
$4$	−1604.96	−	3768.46i	−0.391837	−	0.920035i
$5$	8409.28			0.538194			0.269097	−	0.963113i	$-0.413275\pi$
$5$	8409.28			0.538194			0.269097	+	0.963113i	$0.413275\pi$
$6$	−22471.2	−	14854.0i	−0.481636	−	0.318372i
$7$		−	192052.i		−	1.63242i	−0.577756	−	0.816210i	$-0.696071\pi$
$7$		−	192052.i		−	1.63242i	0.577756	−	0.816210i	$-0.303929\pi$
$8$	257840.	+	47307.4i	0.983582	+	0.180463i
$9$	−177147.			−0.333333
$10$	−296780.	+	448971.i	−0.296780	+	0.448971i
$11$			748209.i			0.422345i	0.977449	+	0.211172i	$0.0677281\pi$
$11$			748209.i			0.422345i	−0.977449	+	0.211172i	$0.932272\pi$
$12$	1.58610e6	−	675510.i	0.531182	−	0.226227i
$13$	5.80736e6			1.20315			0.601573	−	0.798818i	$-0.294541\pi$
$13$	5.80736e6			1.20315			0.601573	+	0.798818i	$0.294541\pi$
$14$	1.02537e7	+	6.77790e6i	1.36179	+	0.900175i
$15$			3.53937e6i			0.310726i
$16$	−1.16254e7	+	1.20965e7i	−0.692928	+	0.721007i
$17$	2.57798e7			1.06804			0.534018	−	0.845473i	$-0.320681\pi$
$17$	2.57798e7			1.06804			0.534018	+	0.845473i	$0.320681\pi$
$18$	6.25185e6	−	9.45786e6i	0.183812	−	0.278072i
$19$			1.62006e7i			0.344357i	0.985066	+	0.172178i	$0.0550806\pi$
$19$			1.62006e7i			0.344357i	−0.985066	+	0.172178i	$0.944919\pi$
$20$	−1.34966e7	−	3.16901e7i	−0.210884	−	0.495157i
$21$	8.08326e7			0.942478
$22$	−3.99468e7	−	2.64057e7i	−0.352327	−	0.232896i
$23$		−	1.99788e8i		−	1.34959i	−0.738003	−	0.674797i	$-0.764231\pi$
$23$		−	1.99788e8i		−	1.34959i	0.738003	−	0.674797i	$-0.235769\pi$
$24$	−1.99111e7	+	1.08522e8i	−0.104191	+	0.567871i
$25$	−1.73425e8			−0.710347
$26$	−2.04953e8	+	3.10054e8i	−0.663458	+	1.00369i
$27$		−	7.45591e7i		−	0.192450i
$28$	−7.23743e8	+	3.08237e8i	−1.50188	+	0.639642i
$29$	8.06751e8			1.35629			0.678144	−	0.734929i	$-0.262785\pi$
$29$	8.06751e8			1.35629			0.678144	+	0.734929i	$0.262785\pi$
$30$	−1.88967e8	−	1.24911e8i	−0.259213	−	0.171346i
$31$		−	7.40990e8i		−	0.834915i	−0.908696	−	0.417457i	$-0.862921\pi$
$31$		−	7.40990e8i		−	0.834915i	0.908696	−	0.417457i	$-0.137079\pi$
$32$	−2.35548e8	−	1.04759e9i	−0.219371	−	0.975642i
$33$	−3.14913e8			−0.243841
$34$	−9.09818e8	+	1.37638e9i	−0.588954	+	0.890974i
$35$		−	1.61502e9i		−	0.878558i
$36$	2.84314e8	+	6.67572e8i	0.130612	+	0.306678i
$37$	4.40061e9			1.71515			0.857575	−	0.514358i	$-0.171970\pi$
$37$	4.40061e9			1.71515			0.857575	+	0.514358i	$0.171970\pi$
$38$	−8.64947e8	−	5.71749e8i	−0.287269	−	0.189891i
$39$			2.44425e9i			0.694637i
$40$	2.16825e9	+	3.97821e8i	0.529358	+	0.0971243i
$41$	3.32788e9			0.700590			0.350295	−	0.936639i	$-0.386081\pi$
$41$	3.32788e9			0.700590			0.350295	+	0.936639i	$0.386081\pi$
$42$	−2.85274e9	+	4.31565e9i	−0.519716	+	0.786231i
$43$			4.43899e9i			0.702220i	0.936334	+	0.351110i	$0.114196\pi$
$43$			4.43899e9i			0.702220i	−0.936334	+	0.351110i	$0.885804\pi$
$44$	2.81960e9	−	1.20085e9i	0.388572	−	0.165490i
$45$	−1.48968e9			−0.179398
$46$	1.06667e10	+	7.05091e9i	1.12585	+	0.744215i
$47$		−	1.18788e10i		−	1.10201i	−0.834501	−	0.551006i	$-0.814244\pi$
$47$		−	1.18788e10i		−	1.10201i	0.834501	−	0.551006i	$-0.185756\pi$
$48$	−5.09127e9	−	4.89300e9i	−0.416274	−	0.400062i
$49$	−2.30429e10			−1.66479
$50$	6.12048e9	−	9.25912e9i	0.391711	−	0.592584i
$51$			1.08504e10i			0.616631i
$52$	−9.32060e9	−	2.18848e10i	−0.471437	−	1.10694i
$53$	−1.52961e10			−0.690124			−0.345062	−	0.938580i	$-0.612142\pi$
$53$	−1.52961e10			−0.690124			−0.345062	+	0.938580i	$0.612142\pi$
$54$	3.98070e9	+	2.63133e9i	0.160545	+	0.106124i
$55$			6.29190e9i			0.227303i
$56$	9.08550e9	−	4.95188e10i	0.294592	−	1.60562i
$57$	−6.81863e9			−0.198815
$58$	−2.84718e10	+	4.30724e10i	−0.747905	+	1.13144i
$59$			2.87986e10i			0.682746i	0.939928	+	0.341373i	$0.110892\pi$
$59$			2.87986e10i			0.682746i	−0.939928	+	0.341373i	$0.889108\pi$
$60$	1.33380e10	−	5.68056e9i	0.285879	−	0.121754i
$61$	−5.04818e10			−0.979842			−0.489921	−	0.871767i	$-0.662974\pi$
$61$	−5.04818e10			−0.979842			−0.489921	+	0.871767i	$0.662974\pi$
$62$	3.95614e10	+	2.61509e10i	0.696500	+	0.460402i
$63$			3.40215e10i			0.544140i
$64$	6.42435e10	+	2.43955e10i	0.934866	+	0.355001i
$65$	4.88357e10			0.647526
$66$	1.11139e10	−	1.68132e10i	0.134463	−	0.203416i
$67$		−	7.04181e10i		−	0.778458i	−0.921141	−	0.389229i	$-0.872741\pi$
$67$		−	7.04181e10i		−	0.778458i	0.921141	−	0.389229i	$-0.127259\pi$
$68$	−4.13756e10	−	9.71502e10i	−0.418496	−	0.982631i
$69$	8.40886e10			0.779189
$70$	8.62259e10	+	5.69972e10i	0.732908	+	0.484469i
$71$			4.83964e10i			0.377801i	0.981996	+	0.188900i	$0.0604923\pi$
$71$			4.83964e10i			0.377801i	−0.981996	+	0.188900i	$0.939508\pi$
$72$	−4.56756e10	−	8.38036e9i	−0.327861	−	0.0601544i
$73$	2.79013e10			0.184369			0.0921844	−	0.995742i	$-0.470615\pi$
$73$	2.79013e10			0.184369			0.0921844	+	0.995742i	$0.470615\pi$
$74$	−1.55306e11	+	2.34948e11i	−0.945796	+	1.43081i
$75$		−	7.29924e10i		−	0.410119i
$76$	6.10513e10	−	2.60013e10i	0.316820	−	0.134932i
$77$	1.43695e11			0.689444
$78$	−1.30498e11	−	8.62622e10i	−0.579478	−	0.383048i
$79$		−	4.03847e11i		−	1.66132i	−0.556777	−	0.830662i	$-0.687962\pi$
$79$		−	4.03847e11i		−	1.66132i	0.556777	−	0.830662i	$-0.312038\pi$
$80$	−9.77613e10	+	1.01723e11i	−0.372930	+	0.388042i
$81$	3.13811e10			0.111111
$82$	−1.17447e11	+	1.77675e11i	−0.386331	+	0.584445i
$83$			3.84526e11i			1.17614i	0.808812	+	0.588068i	$0.200111\pi$
$83$			3.84526e11i			1.17614i	−0.808812	+	0.588068i	$0.799889\pi$
$84$	−1.29733e11	−	3.04615e11i	−0.369297	−	0.867112i
$85$	2.16790e11			0.574811
$86$	−2.36997e11	−	1.56660e11i	−0.585804	−	0.387229i
$87$			3.39552e11i			0.783053i
$88$	−3.53958e10	+	1.92918e11i	−0.0762177	+	0.415411i
$89$	−4.78354e11			−0.962519			−0.481259	−	0.876578i	$-0.659820\pi$
$89$	−4.78354e11			−0.962519			−0.481259	+	0.876578i	$0.659820\pi$
$90$	5.25736e10	−	7.95338e10i	0.0989265	−	0.149657i
$91$		−	1.11532e12i		−	1.96404i
$92$	−7.52895e11	+	3.20653e11i	−1.24167	+	0.528821i
$93$	3.11874e11			0.482038
$94$	6.34210e11	+	4.19226e11i	0.919318	+	0.607689i
$95$			1.36235e11i			0.185331i
$96$	4.40917e11	−	9.91393e10i	0.563287	−	0.126654i
$97$	−1.21562e12			−1.45938			−0.729691	−	0.683777i	$-0.760336\pi$
$97$	−1.21562e12			−1.45938			−0.729691	+	0.683777i	$0.760336\pi$
$98$	8.13227e11	−	1.23026e12i	0.918026	−	1.38880i
$99$		−	1.32543e11i		−	0.140782i
$100$	2.78340e11	+	6.53544e11i	0.278340	+	0.653544i
$101$	1.52254e12			1.43430			0.717151	−	0.696918i	$-0.245446\pi$
$101$	1.52254e12			1.43430			0.717151	+	0.696918i	$0.245446\pi$
$102$	−5.79303e11	−	3.82932e11i	−0.514404	−	0.340033i
$103$			1.02348e12i			0.857147i	0.903507	+	0.428574i	$0.140984\pi$
$103$			1.02348e12i			0.857147i	−0.903507	+	0.428574i	$0.859016\pi$
$104$	1.49737e12	+	2.74731e11i	1.18339	+	0.217124i
$105$	6.79744e11			0.507236
$106$	5.39830e11	−	8.16660e11i	0.380559	−	0.575713i
$107$			2.33951e12i			1.55891i	0.626456	+	0.779457i	$0.284505\pi$
$107$			2.33951e12i			1.55891i	−0.626456	+	0.779457i	$0.715495\pi$
$108$	−2.80973e11	+	1.19665e11i	−0.177061	+	0.0754090i
$109$	−3.01919e12			−1.80025			−0.900123	−	0.435637i	$-0.856523\pi$
$109$	−3.01919e12			−1.80025			−0.900123	+	0.435637i	$0.856523\pi$
$110$	−3.35924e11	−	2.22053e11i	−0.189620	−	0.125343i
$111$			1.85216e12i			0.990243i
$112$	2.32316e12	+	2.23269e12i	1.17699	+	1.13115i
$113$	−4.21569e11			−0.202487			−0.101244	−	0.994862i	$-0.532282\pi$
$113$	−4.21569e11			−0.202487			−0.101244	+	0.994862i	$0.532282\pi$
$114$	2.40643e11	−	3.64046e11i	0.109634	−	0.165855i
$115$		−	1.68008e12i		−	0.726343i
$116$	−1.29481e12	−	3.04021e12i	−0.531443	−	1.24783i
$117$	−1.02876e12			−0.401049
$118$	−1.53755e12	−	1.01636e12i	−0.569559	−	0.376491i
$119$		−	4.95107e12i		−	1.74348i
$120$	−1.67438e11	+	9.12591e11i	−0.0560747	+	0.305625i
$121$	2.57861e12			0.821625
$122$	1.78160e12	−	2.69522e12i	0.540320	−	0.817401i
$123$			1.40066e12i			0.404486i
$124$	−2.79239e12	+	1.18926e12i	−0.768151	+	0.327150i
$125$	−3.51142e12			−0.920499
$126$	−1.81641e12	−	1.20068e12i	−0.453931	−	0.300058i
$127$			1.97980e11i			0.0471846i	0.999722	+	0.0235923i	$0.00751035\pi$
$127$			1.97980e11i			0.0471846i	−0.999722	+	0.0235923i	$0.992490\pi$
$128$	−3.56975e12	+	2.56899e12i	−0.811667	+	0.584121i
$129$	−1.86832e12			−0.405427
$130$	−1.72351e12	+	2.60733e12i	−0.357069	+	0.540178i
$131$		−	2.26629e12i		−	0.448423i	−0.974541	−	0.224212i	$-0.928019\pi$
$131$		−	2.26629e12i		−	0.448423i	0.974541	−	0.224212i	$-0.0719807\pi$
$132$	5.05423e11	+	1.18674e12i	0.0955458	+	0.224342i
$133$	3.11136e12			0.562135
$134$	3.75961e12	+	2.48519e12i	0.649403	+	0.429270i
$135$		−	6.26988e11i		−	0.103575i
$136$	6.64707e12	+	1.21957e12i	1.05050	+	0.192741i
$137$	1.06046e13			1.60388			0.801939	−	0.597406i	$-0.203802\pi$
$137$	1.06046e13			1.60388			0.801939	+	0.597406i	$0.203802\pi$
$138$	−2.96765e12	+	4.48948e12i	−0.429673	+	0.650013i
$139$			1.02219e12i			0.141723i	0.997486	+	0.0708616i	$0.0225749\pi$
$139$			1.02219e12i			0.141723i	−0.997486	+	0.0708616i	$0.977425\pi$
$140$	−6.08615e12	+	2.59205e12i	−0.808304	+	0.344251i
$141$	4.99966e12			0.636247
$142$	−2.58388e12	−	1.70800e12i	−0.315168	−	0.208333i
$143$			4.34512e12i			0.508143i
$144$	2.05940e12	−	2.14286e12i	0.230976	−	0.240336i
$145$	6.78420e12			0.729946
$146$	−9.84691e11	+	1.48965e12i	−0.101668	+	0.153804i
$147$		−	9.69847e12i		−	0.961168i
$148$	−7.06281e12	−	1.65835e13i	−0.672059	−	1.57800i
$149$	4.63546e12			0.423619			0.211809	−	0.977311i	$-0.432064\pi$
$149$	4.63546e12			0.423619			0.211809	+	0.977311i	$0.432064\pi$
$150$	3.89706e12	+	2.57604e12i	0.342128	+	0.226154i
$151$			7.67283e12i			0.647283i	0.946180	+	0.323641i	$0.104907\pi$
$151$			7.67283e12i			0.647283i	−0.946180	+	0.323641i	$0.895093\pi$
$152$	−7.66407e11	+	4.17716e12i	−0.0621438	+	0.338703i
$153$	−4.56681e12			−0.356012
$154$	−5.07129e12	+	7.67189e12i	−0.380184	+	0.575146i
$155$		−	6.23119e12i		−	0.449346i
$156$	9.21106e12	−	3.92293e12i	0.639090	−	0.272184i
$157$	−6.58343e12			−0.439596			−0.219798	−	0.975545i	$-0.570540\pi$
$157$	−6.58343e12			−0.439596			−0.219798	+	0.975545i	$0.570540\pi$
$158$	2.15614e13	+	1.42525e13i	1.38590	+	0.916114i
$159$		−	6.43797e12i		−	0.398443i
$160$	−1.98079e12	−	8.80945e12i	−0.118064	−	0.525084i
$161$	−3.83699e13			−2.20310
$162$	−1.10750e12	+	1.67543e12i	−0.0612707	+	0.0926908i
$163$			3.43265e12i			0.183022i	0.995804	+	0.0915112i	$0.0291697\pi$
$163$			3.43265e12i			0.183022i	−0.995804	+	0.0915112i	$0.970830\pi$
$164$	−5.34112e12	−	1.25410e13i	−0.274517	−	0.644568i
$165$	−2.64819e12			−0.131234
$166$	−2.05298e13	−	1.35707e13i	−0.981153	−	0.648564i
$167$			2.48216e13i			1.14428i	0.820157	+	0.572139i	$0.193886\pi$
$167$			2.48216e13i			1.14428i	−0.820157	+	0.572139i	$0.806114\pi$
$168$	2.08419e13	+	3.82398e12i	0.927004	+	0.170083i
$169$	1.04273e13			0.447562
$170$	−7.65092e12	+	1.15744e13i	−0.316971	+	0.479517i
$171$		−	2.86988e12i		−	0.114786i
$172$	1.67282e13	−	7.12441e12i	0.646067	−	0.275156i
$173$	−2.52781e13			−0.942903			−0.471452	−	0.881892i	$-0.656270\pi$
$173$	−2.52781e13			−0.942903			−0.471452	+	0.881892i	$0.656270\pi$
$174$	−1.81287e13	−	1.19834e13i	−0.653236	−	0.431803i
$175$			3.33066e13i			1.15958i
$176$	−9.05071e12	−	8.69823e12i	−0.304513	−	0.292654i
$177$	−1.21210e13			−0.394184
$178$	1.68820e13	−	2.55393e13i	0.530767	−	0.802950i
$179$		−	3.68721e13i		−	1.12093i	−0.828177	−	0.560467i	$-0.810622\pi$
$179$		−	3.68721e13i		−	1.12093i	0.828177	−	0.560467i	$-0.189378\pi$
$180$	2.39088e12	+	5.61380e12i	0.0702947	+	0.165052i
$181$	5.27764e12			0.150096			0.0750479	−	0.997180i	$-0.476089\pi$
$181$	5.27764e12			0.150096			0.0750479	+	0.997180i	$0.476089\pi$
$182$	5.95467e13	+	3.93617e13i	1.63844	+	1.08304i
$183$		−	2.12472e13i		−	0.565712i
$184$	9.45146e12	−	5.15134e13i	0.243552	−	1.32744i
$185$	3.70059e13			0.923084
$186$	−1.10066e13	+	1.66509e13i	−0.265813	+	0.402125i
$187$			1.92887e13i			0.451080i
$188$	−4.47649e13	+	1.90651e13i	−1.01389	+	0.431809i
$189$	−1.43193e13			−0.314159
$190$	−7.27358e12	−	4.80800e12i	−0.154606	−	0.102198i
$191$			4.43177e13i			0.912803i	0.889774	+	0.456401i	$0.150862\pi$
$191$			4.43177e13i			0.912803i	−0.889774	+	0.456401i	$0.849138\pi$
$192$	−1.02678e13	+	2.70393e13i	−0.204960	+	0.539745i
$193$	3.90632e13			0.755831			0.377915	−	0.925840i	$-0.376641\pi$
$193$	3.90632e13			0.755831			0.377915	+	0.925840i	$0.376641\pi$
$194$	4.29017e13	−	6.49020e13i	0.804755	−	1.21744i
$195$			2.05544e13i			0.373849i
$196$	3.69830e13	+	8.68362e13i	0.652327	+	1.53167i
$197$	3.41818e13			0.584787			0.292394	−	0.956298i	$-0.405548\pi$
$197$	3.41818e13			0.584787			0.292394	+	0.956298i	$0.405548\pi$
$198$	7.07646e12	+	4.67770e12i	0.117442	+	0.0776320i
$199$		−	5.01748e12i		−	0.0807918i	−0.999184	−	0.0403959i	$-0.987138\pi$
$199$		−	5.01748e12i		−	0.0807918i	0.999184	−	0.0403959i	$-0.0128619\pi$
$200$	−4.47158e13	−	8.20426e12i	−0.698685	−	0.128192i
$201$	2.96381e13			0.449443
$202$	−5.37334e13	+	8.12883e13i	−0.790926	+	1.19652i
$203$		−	1.54939e14i		−	2.21403i
$204$	4.08894e13	−	1.74145e13i	0.567322	−	0.241619i
$205$	2.79851e13			0.377054
$206$	−5.46434e13	−	3.61205e13i	−0.715047	−	0.472662i
$207$			3.53919e13i			0.449865i
$208$	−6.75129e13	+	7.02486e13i	−0.833694	+	0.867477i
$209$	−1.21214e13			−0.145437
$210$	−2.39895e13	+	3.62915e13i	−0.279708	+	0.423145i
$211$		−	9.35524e13i		−	1.06013i	−0.847956	−	0.530066i	$-0.822167\pi$
$211$		−	9.35524e13i		−	1.06013i	0.847956	−	0.530066i	$-0.177833\pi$
$212$	2.45498e13	+	5.76430e13i	0.270416	+	0.634938i
$213$	−2.03695e13			−0.218123
$214$	−1.24906e14	−	8.25657e13i	−1.30047	−	0.859641i
$215$			3.73287e13i			0.377930i
$216$	3.52720e12	−	1.92243e13i	0.0347302	−	0.189290i
$217$	−1.42309e14			−1.36293
$218$	1.06553e14	−	1.61194e14i	0.992720	−	1.50180i
$219$			1.17433e13i			0.106445i
$220$	2.37108e13	−	1.00983e13i	0.209127	−	0.0890658i
$221$	1.49713e14			1.28500
$222$	−9.88869e13	−	6.53664e13i	−0.826077	−	0.546055i
$223$			1.78398e13i			0.145064i	0.997366	+	0.0725320i	$0.0231080\pi$
$223$			1.78398e13i			0.145064i	−0.997366	+	0.0725320i	$0.976892\pi$
$224$	−2.01192e14	+	4.52375e13i	−1.59266	+	0.358105i
$225$	3.07217e13			0.236782
$226$	1.48780e13	−	2.25075e13i	0.111659	−	0.168919i
$227$			1.36751e13i			0.0999485i	0.998751	+	0.0499742i	$0.0159139\pi$
$227$			1.36751e13i			0.0999485i	−0.998751	+	0.0499742i	$0.984086\pi$
$228$	1.09437e13	+	2.56958e13i	0.0779029	+	0.182916i
$229$	−9.88118e13			−0.685166			−0.342583	−	0.939488i	$-0.611302\pi$
$229$	−9.88118e13			−0.685166			−0.342583	+	0.939488i	$0.611302\pi$
$230$	8.96991e13	+	5.92931e13i	0.605928	+	0.400532i
$231$			6.04797e13i			0.398050i
$232$	2.08013e14	+	3.81653e13i	1.33402	+	0.244760i
$233$	−7.18845e13			−0.449262			−0.224631	−	0.974444i	$-0.572118\pi$
$233$	−7.18845e13			−0.449262			−0.224631	+	0.974444i	$0.572118\pi$
$234$	3.63068e13	−	5.49252e13i	0.221153	−	0.334562i
$235$		−	9.98924e13i		−	0.593096i
$236$	1.08526e14	−	4.62207e13i	0.628150	−	0.267525i
$237$	1.69974e14			0.959166
$238$	2.64337e14	+	1.74733e14i	1.45444	+	0.961419i
$239$			2.17724e14i			1.16820i	0.811680	+	0.584102i	$0.198553\pi$
$239$			2.17724e14i			1.16820i	−0.811680	+	0.584102i	$0.801447\pi$
$240$	−4.28139e13	−	4.11466e13i	−0.224036	−	0.215311i
$241$	−4.26407e13			−0.217632			−0.108816	−	0.994062i	$-0.534706\pi$
$241$	−4.26407e13			−0.217632			−0.108816	+	0.994062i	$0.534706\pi$
$242$	−9.10041e13	+	1.37672e14i	−0.453074	+	0.685414i
$243$			1.32079e13i			0.0641500i
$244$	8.10215e13	+	1.90239e14i	0.383938	+	0.901488i
$245$	−1.93774e14			−0.895981
$246$	−7.47814e13	−	4.94321e13i	−0.337429	−	0.223048i
$247$			9.40826e13i			0.414312i
$248$	3.50543e13	−	1.91057e14i	0.150671	−	0.821207i
$249$	−1.61843e14			−0.679042
$250$	1.23925e14	−	1.87475e14i	0.507596	−	0.767896i
$251$			2.51073e14i			1.00406i	0.864851	+	0.502028i	$0.167412\pi$
$251$			2.51073e14i			1.00406i	−0.864851	+	0.502028i	$0.832588\pi$
$252$	1.28209e14	−	5.46033e13i	0.500627	−	0.213214i
$253$	1.49484e14			0.569994
$254$	−1.05702e13	−	6.98710e12i	−0.0393622	−	0.0260193i
$255$			9.12442e13i			0.331867i
$256$	−1.11751e13	−	2.81253e14i	−0.0397018	−	0.999212i
$257$	2.52884e13			0.0877652			0.0438826	−	0.999037i	$-0.486027\pi$
$257$	2.52884e13			0.0877652			0.0438826	+	0.999037i	$0.486027\pi$
$258$	6.59365e13	−	9.97493e13i	0.223567	−	0.338214i
$259$		−	8.45147e14i		−	2.79984i
$260$	−7.83795e13	−	1.84036e14i	−0.253725	−	0.595747i
$261$	−1.42914e14			−0.452096
$262$	1.20997e14	+	7.99817e13i	0.374082	+	0.247277i
$263$			2.96423e14i			0.895730i	0.894101	+	0.447865i	$0.147816\pi$
$263$			2.96423e14i			0.895730i	−0.894101	+	0.447865i	$0.852184\pi$
$264$	−8.11971e13	−	1.48977e13i	−0.239837	−	0.0440043i
$265$	−1.28630e14			−0.371420
$266$	−1.09806e14	+	1.66115e14i	−0.309981	+	0.468943i
$267$		−	2.01334e14i		−	0.555711i
$268$	−2.65368e14	+	1.13018e14i	−0.716209	+	0.305029i
$269$	−2.90107e14			−0.765676			−0.382838	−	0.923816i	$-0.625053\pi$
$269$	−2.90107e14			−0.765676			−0.382838	+	0.923816i	$0.625053\pi$
$270$	3.34749e13	+	2.21276e13i	0.0864044	+	0.0571152i
$271$			4.86728e14i			1.22877i	0.789007	+	0.614384i	$0.210596\pi$
$271$			4.86728e14i			1.22877i	−0.789007	+	0.614384i	$0.789404\pi$
$272$	−2.99701e14	+	3.11845e14i	−0.740072	+	0.770062i
$273$	4.69424e14			1.13394
$274$	−3.74257e14	+	5.66179e14i	−0.884436	+	1.33798i
$275$		−	1.29758e14i		−	0.300011i
$276$	−1.34959e14	−	3.16885e14i	−0.305315	−	0.716881i
$277$	−2.87923e14			−0.637379			−0.318689	−	0.947859i	$-0.603243\pi$
$277$	−2.87923e14			−0.637379			−0.318689	+	0.947859i	$0.603243\pi$
$278$	−5.45744e13	−	3.60749e13i	−0.118228	−	0.0781513i
$279$			1.31264e14i			0.278305i
$280$	7.64025e13	−	4.16418e14i	0.158547	−	0.864134i
$281$	8.35003e14			1.69609			0.848047	−	0.529920i	$-0.177778\pi$
$281$	8.35003e14			1.69609			0.848047	+	0.529920i	$0.177778\pi$
$282$	−1.76448e14	+	2.66931e14i	−0.350850	+	0.530768i
$283$		−	5.74546e13i		−	0.111842i	−0.998435	−	0.0559212i	$-0.982190\pi$
$283$		−	5.74546e13i		−	0.111842i	0.998435	−	0.0559212i	$-0.0178096\pi$
$284$	1.82380e14	−	7.76744e13i	0.347590	−	0.148036i
$285$	−5.73398e13			−0.107001
$286$	−2.31986e14	−	1.53348e14i	−0.423901	−	0.280208i
$287$		−	6.39127e14i		−	1.14366i
$288$	4.17266e13	+	1.85577e14i	0.0731237	+	0.325214i
$289$	8.19760e13			0.140702
$290$	−2.39427e14	+	3.62208e14i	−0.402518	+	0.608933i
$291$		−	5.11642e14i		−	0.842574i
$292$	−4.47806e13	−	1.05145e14i	−0.0722425	−	0.169626i
$293$	2.19620e14			0.347109			0.173554	−	0.984824i	$-0.444475\pi$
$293$	2.19620e14			0.347109			0.173554	+	0.984824i	$0.444475\pi$
$294$	5.17801e14	+	3.42278e14i	0.801823	+	0.530023i
$295$			2.42176e14i			0.367450i
$296$	1.13465e15	+	2.08181e14i	1.68699	+	0.309522i
$297$	5.57858e13			0.0812803
$298$	−1.63594e14	+	2.47487e14i	−0.233599	+	0.353390i
$299$		−	1.16024e15i		−	1.62376i
$300$	−2.75069e14	+	1.17150e14i	−0.377324	+	0.160700i
$301$	8.52518e14			1.14632
$302$	−4.09652e14	−	2.70789e14i	−0.539975	−	0.356935i
$303$			6.40820e14i			0.828095i
$304$	−1.95970e14	−	1.88338e14i	−0.248284	−	0.238615i
$305$	−4.24516e14			−0.527345
$306$	1.61172e14	−	2.43822e14i	0.196318	−	0.296991i
$307$			9.85856e14i			1.17756i	0.808293	+	0.588781i	$0.200392\pi$
$307$			9.85856e14i			1.17756i	−0.808293	+	0.588781i	$0.799608\pi$
$308$	−2.30626e14	−	5.41511e14i	−0.270149	−	0.634312i
$309$	−4.30770e14			−0.494874
$310$	3.32683e14	+	2.19911e14i	0.374852	+	0.247786i
$311$			4.46244e14i			0.493185i	0.969119	+	0.246593i	$0.0793110\pi$
$311$			4.46244e14i			0.493185i	−0.969119	+	0.246593i	$0.920689\pi$
$312$	−1.15631e14	+	6.30225e14i	−0.125356	+	0.683232i
$313$	1.29474e15			1.37694			0.688471	−	0.725264i	$-0.258282\pi$
$313$	1.29474e15			1.37694			0.688471	+	0.725264i	$0.258282\pi$
$314$	2.32342e14	−	3.51489e14i	0.242409	−	0.366719i
$315$			2.86097e14i			0.292853i
$316$	−1.52188e15	+	6.48160e14i	−1.52848	+	0.650968i
$317$	2.35093e14			0.231678			0.115839	−	0.993268i	$-0.463044\pi$
$317$	2.35093e14			0.231678			0.115839	+	0.993268i	$0.463044\pi$
$318$	3.43723e14	+	2.27208e14i	0.332388	+	0.219716i
$319$			6.03619e14i			0.572821i
$320$	5.40242e14	+	2.05148e14i	0.503139	+	0.191059i
$321$	−9.84672e14			−0.900039
$322$	1.35415e15	−	2.04856e15i	1.21487	−	1.83787i
$323$			4.17648e14i			0.367786i
$324$	−5.03655e13	−	1.18258e14i	−0.0435374	−	0.102226i
$325$	−1.00714e15			−0.854652
$326$	−1.83269e14	−	1.21145e14i	−0.152680	−	0.100925i
$327$		−	1.27074e15i		−	1.03937i
$328$	8.58060e14	+	1.57433e14i	0.689088	+	0.126431i
$329$	−2.28136e15			−1.79895
$330$	9.34596e13	−	1.41387e14i	0.0723670	−	0.109477i
$331$			1.65323e14i			0.125709i	0.998023	+	0.0628544i	$0.0200204\pi$
$331$			1.65323e14i			0.125709i	−0.998023	+	0.0628544i	$0.979980\pi$
$332$	1.44907e15	−	6.17151e14i	1.08209	−	0.460853i
$333$	−7.79554e14			−0.571717
$334$	−1.32522e15	−	8.76002e14i	−0.954576	−	0.630996i
$335$		−	5.92165e14i		−	0.418962i
$336$	−9.39712e14	+	9.77791e14i	−0.653069	+	0.679533i
$337$	−1.71469e15			−1.17060			−0.585298	−	0.810819i	$-0.699022\pi$
$337$	−1.71469e15			−1.17060			−0.585298	+	0.810819i	$0.699022\pi$
$338$	−3.68000e14	+	5.56714e14i	−0.246802	+	0.373364i
$339$		−	1.77434e14i		−	0.116906i
$340$	−3.47939e14	−	8.16963e14i	−0.225232	−	0.528846i
$341$	5.54416e14			0.352622
$342$	1.53223e14	+	1.01284e14i	0.0957562	+	0.0632969i
$343$			1.76719e15i			1.08522i
$344$	−2.09997e14	+	1.14455e15i	−0.126725	+	0.690691i
$345$	7.07125e14			0.419355
$346$	8.92111e14	−	1.34959e15i	0.519951	−	0.786586i
$347$		−	1.54474e15i		−	0.884870i	−0.896801	−	0.442435i	$-0.854115\pi$
$347$		−	1.54474e15i		−	0.884870i	0.896801	−	0.442435i	$-0.145885\pi$
$348$	1.27959e15	−	5.44969e14i	0.720436	−	0.306829i
$349$	7.96922e14			0.441025			0.220513	−	0.975384i	$-0.429227\pi$
$349$	7.96922e14			0.441025			0.220513	+	0.975384i	$0.429227\pi$
$350$	−1.77824e15	−	1.17545e15i	−0.967345	−	0.639437i
$351$		−	4.32991e14i		−	0.231546i
$352$	7.83815e14	−	1.76239e14i	0.412057	−	0.0926502i
$353$	−5.85455e14			−0.302583			−0.151292	−	0.988489i	$-0.548343\pi$
$353$	−5.85455e14			−0.302583			−0.151292	+	0.988489i	$0.548343\pi$
$354$	4.27773e14	−	6.47139e14i	0.217367	−	0.328835i
$355$			4.06979e14i			0.203330i
$356$	7.67740e14	+	1.80266e15i	0.377150	+	0.885551i
$357$	2.08385e15			1.00660
$358$	1.96860e15	+	1.30129e15i	0.935103	+	0.618123i
$359$			2.30396e15i			1.07624i	0.842868	+	0.538120i	$0.180865\pi$
$359$			2.30396e15i			1.07624i	−0.842868	+	0.538120i	$0.819135\pi$
$360$	−3.84099e14	−	7.04728e13i	−0.176453	−	0.0323748i
$361$	1.95086e15			0.881418
$362$	−1.86258e14	+	2.81773e14i	−0.0827682	+	0.125213i
$363$			1.08531e15i			0.474365i
$364$	−4.20303e15	+	1.79004e15i	−1.80698	+	0.769583i
$365$	2.34630e14			0.0992262
$366$	1.13439e15	+	7.49854e14i	0.471927	+	0.311954i
$367$		−	3.94215e15i		−	1.61338i	−0.590975	−	0.806690i	$-0.701257\pi$
$367$		−	3.94215e15i		−	1.61338i	0.590975	−	0.806690i	$-0.298743\pi$
$368$	2.41674e15	+	2.32262e15i	0.973067	+	0.935171i
$369$	−5.89524e14			−0.233530
$370$	−1.30601e15	+	1.97574e15i	−0.509022	+	0.770052i
$371$			2.93766e15i			1.12657i
$372$	−5.00546e14	−	1.17529e15i	−0.188880	−	0.443492i
$373$	9.62006e14			0.357211			0.178605	−	0.983921i	$-0.442841\pi$
$373$	9.62006e14			0.357211			0.178605	+	0.983921i	$0.442841\pi$
$374$	−1.02982e15	−	6.80735e14i	−0.376298	−	0.248741i
$375$		−	1.47792e15i		−	0.531450i
$376$	5.61956e14	−	3.06284e15i	0.198873	−	1.08392i
$377$	4.68509e15			1.63181
$378$	5.05354e14	−	7.64504e14i	0.173239	−	0.262077i
$379$			7.38046e14i			0.249028i	0.992218	+	0.124514i	$0.0397372\pi$
$379$			7.38046e14i			0.249028i	−0.992218	+	0.124514i	$0.960263\pi$
$380$	5.13397e14	−	2.18653e14i	0.170511	−	0.0726194i
$381$	−8.33276e13			−0.0272420
$382$	−2.36612e15	−	1.56406e15i	−0.761476	−	0.503352i
$383$		−	6.59297e14i		−	0.208876i	−0.994531	−	0.104438i	$-0.966696\pi$
$383$		−	6.59297e14i		−	0.208876i	0.994531	−	0.104438i	$-0.0333044\pi$
$384$	−1.08126e15	−	1.50246e15i	−0.337242	−	0.468616i
$385$	1.20838e15			0.371054
$386$	−1.37862e15	+	2.08558e15i	−0.416792	+	0.630527i
$387$		−	7.86353e14i		−	0.234073i
$388$	1.95103e15	+	4.58103e15i	0.571839	+	1.34268i
$389$	−1.71529e15			−0.495040			−0.247520	−	0.968883i	$-0.579616\pi$
$389$	−1.71529e15			−0.495040			−0.247520	+	0.968883i	$0.579616\pi$
$390$	−1.09740e15	−	7.25403e14i	−0.311872	−	0.206154i
$391$		−	5.15050e15i		−	1.44142i
$392$	−5.94137e15	−	1.09010e15i	−1.63746	−	0.300434i
$393$	9.53856e14			0.258897
$394$	−1.20634e15	+	1.82496e15i	−0.322473	+	0.487839i
$395$		−	3.39606e15i		−	0.894114i
$396$	−4.99483e14	+	2.12727e14i	−0.129524	+	0.0551634i
$397$	−5.33258e15			−1.36205			−0.681027	−	0.732259i	$-0.738466\pi$
$397$	−5.33258e15			−1.36205			−0.681027	+	0.732259i	$0.738466\pi$
$398$	2.67883e14	+	1.77076e14i	0.0673979	+	0.0445515i
$399$			1.30954e15i			0.324549i
$400$	2.01613e15	−	2.09783e15i	0.492219	−	0.512165i
$401$	−3.28891e15			−0.791017			−0.395509	−	0.918462i	$-0.629432\pi$
$401$	−3.28891e15			−0.791017			−0.395509	+	0.918462i	$0.629432\pi$
$402$	−1.04599e15	+	1.58238e15i	−0.247839	+	0.374933i
$403$		−	4.30319e15i		−	1.00452i
$404$	−2.44362e15	−	5.73764e15i	−0.562012	−	1.31961i
$405$	2.63892e14			0.0597993
$406$	8.27215e15	+	5.46808e15i	1.84698	+	1.22090i
$407$			3.29258e15i			0.724385i
$408$	−5.13305e14	+	2.79767e15i	−0.111279	+	0.606507i
$409$	−3.11334e15			−0.665100			−0.332550	−	0.943086i	$-0.607909\pi$
$409$	−3.11334e15			−0.665100			−0.332550	+	0.943086i	$0.607909\pi$
$410$	−9.87646e14	+	1.49412e15i	−0.207921	+	0.314545i
$411$			4.46335e15i			0.925999i
$412$	3.85694e15	−	1.64265e15i	0.788605	−	0.335862i
$413$	5.53084e15			1.11453
$414$	−1.88957e15	−	1.24905e15i	−0.375285	−	0.248072i
$415$			3.23359e15i			0.632989i
$416$	−1.36791e15	−	6.08371e15i	−0.263935	−	1.17384i
$417$	−4.30226e14			−0.0818239
$418$	4.27788e14	−	6.47162e14i	0.0801994	−	0.121326i
$419$			5.08845e15i			0.940376i	0.882566	+	0.470188i	$0.155814\pi$
$419$			5.08845e15i			0.940376i	−0.882566	+	0.470188i	$0.844186\pi$
$420$	−1.09096e15	−	2.56159e15i	−0.198754	−	0.466675i
$421$	1.23557e15			0.221909			0.110954	−	0.993825i	$-0.464609\pi$
$421$	1.23557e15			0.221909			0.110954	+	0.993825i	$0.464609\pi$
$422$	4.99475e15	+	3.30164e15i	0.884381	+	0.584595i
$423$			2.10430e15i			0.367337i
$424$	−3.94396e15	−	7.23620e14i	−0.678793	−	0.124542i
$425$	−4.47085e15			−0.758677
$426$	7.18877e14	−	1.08752e15i	0.120281	−	0.181962i
$427$			9.69516e15i			1.59951i
$428$	8.81635e15	−	3.75483e15i	1.43425	−	0.610840i
$429$	−1.82881e15			−0.293376
$430$	−1.99297e15	−	1.31740e15i	−0.315276	−	0.208404i
$431$		−	1.01057e16i		−	1.57653i	−0.615336	−	0.788265i	$-0.710980\pi$
$431$		−	1.01057e16i		−	1.57653i	0.615336	−	0.788265i	$-0.289020\pi$
$432$	9.01903e14	+	8.66780e14i	0.138758	+	0.133354i
$433$	−2.25070e15			−0.341499			−0.170750	−	0.985314i	$-0.554619\pi$
$433$	−2.25070e15			−0.341499			−0.170750	+	0.985314i	$0.554619\pi$
$434$	5.02235e15	−	7.59786e15i	0.751569	−	1.13698i
$435$			2.85539e15i			0.421434i
$436$	4.84569e15	+	1.13777e16i	0.705402	+	1.65629i
$437$	3.23669e15			0.464742
$438$	−6.26976e14	−	4.14445e14i	−0.0887986	−	0.0586978i
$439$		−	1.26672e16i		−	1.76967i	−0.465903	−	0.884836i	$-0.654271\pi$
$439$		−	1.26672e16i		−	1.76967i	0.465903	−	0.884836i	$-0.345729\pi$
$440$	−2.97653e14	+	1.62230e15i	−0.0410199	+	0.223571i
$441$	4.08197e15			0.554931
$442$	−5.28364e15	+	7.99314e15i	−0.708598	+	1.07197i
$443$			8.26929e15i			1.09407i	0.837109	+	0.547036i	$0.184244\pi$
$443$			8.26929e15i			1.09407i	−0.837109	+	0.547036i	$0.815756\pi$
$444$	6.97981e15	−	2.97266e15i	0.911058	−	0.388013i
$445$	−4.02261e15			−0.518022
$446$	−9.52463e14	−	6.29599e14i	−0.121015	−	0.0799935i
$447$			1.95101e15i			0.244576i
$448$	4.68521e15	−	1.23381e16i	0.579510	−	1.52609i
$449$	−2.61387e13			−0.00319011			−0.00159506	−	0.999999i	$-0.500508\pi$
$449$	−2.61387e13			−0.00319011			−0.00159506	+	0.999999i	$0.500508\pi$
$450$	−1.08423e15	+	1.64023e15i	−0.130570	+	0.197528i
$451$			2.48995e15i			0.295891i
$452$	6.76603e14	+	1.58867e15i	0.0793420	+	0.186296i
$453$	−3.22941e15			−0.373709
$454$	−7.30113e14	−	4.82621e14i	−0.0833787	−	0.0551152i
$455$		−	9.37902e15i		−	1.05703i
$456$	−1.75812e15	−	3.22572e14i	−0.195550	−	0.0358787i
$457$	−1.61980e15			−0.177813			−0.0889067	−	0.996040i	$-0.528337\pi$
$457$	−1.61980e15			−0.177813			−0.0889067	+	0.996040i	$0.528337\pi$
$458$	3.48726e15	−	5.27555e15i	0.377825	−	0.571577i
$459$		−	1.92212e15i		−	0.205544i
$460$	−6.33131e15	+	2.69646e15i	−0.668261	+	0.284608i
$461$	6.13058e15			0.638698			0.319349	−	0.947637i	$-0.396536\pi$
$461$	6.13058e15			0.638698			0.319349	+	0.947637i	$0.396536\pi$
$462$	−3.22901e15	−	2.13445e15i	−0.332061	−	0.219499i
$463$			5.83824e15i			0.592647i	0.955088	+	0.296324i	$0.0957607\pi$
$463$			5.83824e15i			0.592647i	−0.955088	+	0.296324i	$0.904239\pi$
$464$	−9.37881e15	+	9.75886e15i	−0.939809	+	0.977892i
$465$	2.62264e15			0.259430
$466$	2.53694e15	−	3.83791e15i	0.247739	−	0.374782i
$467$			1.22182e16i			1.17789i	0.808172	+	0.588946i	$0.200457\pi$
$467$			1.22182e16i			1.17789i	−0.808172	+	0.588946i	$0.799543\pi$
$468$	1.65112e15	+	3.87683e15i	0.157146	+	0.368979i
$469$	−1.35240e16			−1.27077
$470$	5.33325e15	+	3.52539e15i	0.494771	+	0.327055i
$471$		−	2.77089e15i		−	0.253801i
$472$	−1.36239e15	+	7.42543e15i	−0.123211	+	0.671537i
$473$	−3.32129e15			−0.296579
$474$	−5.99872e15	+	9.07492e15i	−0.528918	+	0.800153i
$475$		−	2.80958e15i		−	0.244613i
$476$	−1.86579e16	+	7.94629e15i	−1.60407	+	0.683161i
$477$	2.70967e15			0.230041
$478$	−1.16243e16	−	7.68390e15i	−0.974537	−	0.644190i
$479$		−	1.85726e16i		−	1.53766i	−0.639455	−	0.768829i	$-0.720840\pi$
$479$		−	1.85726e16i		−	1.53766i	0.639455	−	0.768829i	$-0.279160\pi$
$480$	3.70780e15	−	8.33690e14i	0.303158	−	0.0681644i
$481$	2.55559e16			2.06358
$482$	1.50487e15	−	2.27658e15i	0.120010	−	0.181552i
$483$		−	1.61494e16i		−	1.27196i
$484$	−4.13858e15	−	9.71740e15i	−0.321943	−	0.755924i
$485$	−1.02225e16			−0.785430
$486$	−7.05170e14	−	4.66133e14i	−0.0535151	−	0.0353746i
$487$			9.11126e14i			0.0682975i	0.999417	+	0.0341488i	$0.0108720\pi$
$487$			9.11126e14i			0.0682975i	−0.999417	+	0.0341488i	$0.989128\pi$
$488$	−1.30162e16	−	2.38816e15i	−0.963754	−	0.176825i
$489$	−1.44476e15			−0.105668
$490$	6.83865e15	−	1.03456e16i	0.494076	−	0.747443i
$491$		−	9.34268e13i		−	0.00666780i	−0.999994	−	0.00333390i	$-0.998939\pi$
$491$		−	9.34268e13i		−	0.00666780i	0.999994	−	0.00333390i	$-0.00106121\pi$
$492$	5.27835e15	−	2.24802e15i	0.372141	−	0.158493i
$493$	2.07979e16			1.44856
$494$	−5.02306e15	−	3.32035e15i	−0.345626	−	0.228466i
$495$		−	1.11459e15i		−	0.0757678i
$496$	8.96338e15	+	8.61431e15i	0.601979	+	0.578536i
$497$	9.29464e15			0.616729
$498$	5.71173e15	−	8.64076e15i	0.374448	−	0.566469i
$499$		−	1.60263e15i		−	0.103808i	−0.998652	−	0.0519039i	$-0.983471\pi$
$499$		−	1.60263e15i		−	0.103808i	0.998652	−	0.0519039i	$-0.0165289\pi$
$500$	5.63571e15	+	1.32327e16i	0.360685	+	0.846891i
$501$	−1.04471e16			−0.660649
$502$	−1.34048e16	−	8.86085e15i	−0.837600	−	0.553672i
$503$			2.08437e16i			1.28696i	0.765461	+	0.643482i	$0.222511\pi$
$503$			2.08437e16i			1.28696i	−0.765461	+	0.643482i	$0.777489\pi$
$504$	−1.60947e15	+	8.77211e15i	−0.0981972	+	0.535206i
$505$	1.28035e16			0.771933
$506$	−5.27556e15	+	7.98091e15i	−0.314315	+	0.475499i
$507$			4.38874e15i			0.258400i
$508$	7.46082e14	−	3.17751e14i	0.0434114	−	0.0184886i
$509$	−1.02294e15			−0.0588223			−0.0294112	−	0.999567i	$-0.509363\pi$
$509$	−1.02294e15			−0.0588223			−0.0294112	+	0.999567i	$0.509363\pi$
$510$	−4.87152e15	−	3.22018e15i	−0.276849	−	0.183003i
$511$		−	5.35852e15i		−	0.300967i
$512$	1.54105e16	+	9.32932e15i	0.855453	+	0.517881i
$513$	1.20790e15			0.0662715
$514$	−8.92475e14	+	1.35014e15i	−0.0483969	+	0.0732152i
$515$			8.60672e15i			0.461312i
$516$	2.99858e15	+	7.04069e15i	0.158861	+	0.373007i
$517$	8.88785e15			0.465429
$518$	4.51223e16	+	2.98269e16i	2.33568	+	1.54393i
$519$		−	1.06392e16i		−	0.544385i
$520$	1.25918e16	+	2.31029e15i	0.636895	+	0.116855i
$521$	−2.99473e16			−1.49738			−0.748689	−	0.662921i	$-0.769317\pi$
$521$	−2.99473e16			−1.49738			−0.748689	+	0.662921i	$0.769317\pi$
$522$	5.04369e15	−	7.63014e15i	0.249302	−	0.377146i
$523$			3.07690e16i			1.50350i	0.659448	+	0.751750i	$0.270790\pi$
$523$			3.07690e16i			1.50350i	−0.659448	+	0.751750i	$0.729210\pi$
$524$	−8.54043e15	+	3.63731e15i	−0.412565	+	0.175709i
$525$	−1.40184e16			−0.669486
$526$	−1.58260e16	−	1.04613e16i	−0.747234	−	0.493938i
$527$		−	1.91026e16i		−	0.891720i
$528$	3.66099e15	−	3.80934e15i	0.168964	−	0.175811i
$529$	−1.80008e16			−0.821404
$530$	4.53958e15	−	6.86752e15i	0.204815	−	0.309845i
$531$		−	5.10159e15i		−	0.227582i
$532$	−4.99362e15	−	1.17250e16i	−0.220265	−	0.517184i
$533$	1.93262e16			0.842913
$534$	1.07492e16	+	7.10544e15i	0.463583	+	0.306439i
$535$			1.96736e16i			0.838998i
$536$	3.33129e15	−	1.81566e16i	0.140483	−	0.765677i
$537$	1.55191e16			0.647172
$538$	1.02384e16	−	1.54888e16i	0.422221	−	0.638740i
$539$		−	1.72409e16i		−	0.703116i
$540$	−2.36278e15	+	1.00629e15i	−0.0952930	+	0.0405847i
$541$	−9.46188e14			−0.0377393			−0.0188696	−	0.999822i	$-0.506007\pi$
$541$	−9.46188e14			−0.0377393			−0.0188696	+	0.999822i	$0.506007\pi$
$542$	−2.59863e16	−	1.71775e16i	−1.02506	−	0.677587i
$543$			2.22130e15i			0.0866579i
$544$	−6.07238e15	−	2.70066e16i	−0.234296	−	1.04202i
$545$	−2.53892e16			−0.968881
$546$	−1.65669e16	+	2.50625e16i	−0.625295	+	0.945951i
$547$			3.26129e15i			0.121749i	0.998145	+	0.0608746i	$0.0193890\pi$
$547$			3.26129e15i			0.121749i	−0.998145	+	0.0608746i	$0.980611\pi$
$548$	−1.70200e16	−	3.99631e16i	−0.628458	−	1.47562i
$549$	8.94270e15			0.326614
$550$	6.92776e15	+	4.57940e15i	0.250275	+	0.165437i
$551$			1.30698e16i			0.467047i
$552$	2.16814e16	+	3.97801e15i	0.766396	+	0.140615i
$553$	−7.75598e16			−2.71198
$554$	1.01613e16	−	1.53722e16i	0.351474	−	0.531712i
$555$			1.55754e16i			0.532943i
$556$	3.85207e15	−	1.64057e15i	0.130390	−	0.0555324i
$557$	−1.06541e16			−0.356768			−0.178384	−	0.983961i	$-0.557087\pi$
$557$	−1.06541e16			−0.356768			−0.178384	+	0.983961i	$0.557087\pi$
$558$	−7.00818e15	−	4.63256e15i	−0.232167	−	0.153467i
$559$			2.57788e16i			0.844873i
$560$	1.95361e16	+	1.87753e16i	0.633446	+	0.608777i
$561$	−8.11839e15			−0.260431
$562$	−2.94688e16	+	4.45807e16i	−0.935288	+	1.41491i
$563$		−	4.45857e16i		−	1.40006i	−0.714116	−	0.700028i	$-0.753171\pi$
$563$		−	4.45857e16i		−	1.40006i	0.714116	−	0.700028i	$-0.246829\pi$
$564$	−8.02427e15	−	1.88410e16i	−0.249305	−	0.585369i
$565$	−3.54509e15			−0.108978
$566$	3.06750e15	+	2.02768e15i	0.0933009	+	0.0616739i
$567$		−	6.02681e15i		−	0.181380i
$568$	−2.28950e15	+	1.24785e16i	−0.0681791	+	0.371598i
$569$	2.78386e16			0.820301			0.410150	−	0.912018i	$-0.365476\pi$
$569$	2.78386e16			0.820301			0.410150	+	0.912018i	$0.365476\pi$
$570$	2.02363e15	−	3.06137e15i	0.0590041	−	0.0892619i
$571$		−	3.48673e16i		−	1.00601i	−0.864284	−	0.503004i	$-0.832228\pi$
$571$		−	3.48673e16i		−	1.00601i	0.864284	−	0.503004i	$-0.167772\pi$
$572$	1.63744e16	−	6.97376e15i	0.467509	−	0.199109i
$573$	−1.86528e16			−0.527007
$574$	3.41229e16	+	2.25560e16i	0.954059	+	0.630654i
$575$			3.46482e16i			0.958681i
$576$	−1.13805e16	−	4.32158e15i	−0.311622	−	0.118334i
$577$	6.23408e16			1.68934			0.844671	−	0.535285i	$-0.179796\pi$
$577$	6.23408e16			1.68934			0.844671	+	0.535285i	$0.179796\pi$
$578$	−2.89309e15	+	4.37669e15i	−0.0775880	+	0.117376i
$579$			1.64413e16i			0.436379i
$580$	−1.08884e16	−	2.55660e16i	−0.286019	−	0.671575i
$581$	7.38492e16			1.91995
$582$	2.73165e16	+	1.80568e16i	0.702890	+	0.464626i
$583$		−	1.14447e16i		−	0.291470i
$584$	7.19408e15	+	1.31994e15i	0.181342	+	0.0332718i
$585$	−8.65110e15			−0.215842
$586$	−7.75080e15	+	1.17255e16i	−0.191408	+	0.289564i
$587$			6.86060e15i			0.167700i	0.996478	+	0.0838501i	$0.0267217\pi$
$587$			6.86060e15i			0.167700i	−0.996478	+	0.0838501i	$0.973278\pi$
$588$	−3.65483e16	+	1.55657e16i	−0.884308	+	0.376621i
$589$	1.20045e16			0.287509
$590$	−1.29297e16	−	8.54684e15i	−0.306533	−	0.202625i
$591$			1.43867e16i			0.337627i
$592$	−5.11588e16	+	5.32319e16i	−1.18848	+	1.23664i
$593$	−4.01477e16			−0.923278			−0.461639	−	0.887068i	$-0.652738\pi$
$593$	−4.01477e16			−0.923278			−0.461639	+	0.887068i	$0.652738\pi$
$594$	−1.96879e15	+	2.97840e15i	−0.0448209	+	0.0678054i
$595$		−	4.16350e16i		−	0.938332i
$596$	−7.43974e15	−	1.74685e16i	−0.165989	−	0.389744i
$597$	2.11180e15			0.0466451
$598$	6.19452e16	+	4.09472e16i	1.35457	+	0.895399i
$599$		−	2.96254e15i		−	0.0641362i	−0.999486	−	0.0320681i	$-0.989791\pi$
$599$		−	2.96254e15i		−	0.0641362i	0.999486	−	0.0320681i	$-0.0102093\pi$
$600$	3.45308e15	−	1.88204e16i	0.0740115	−	0.403386i
$601$	9.07584e16			1.92593			0.962964	−	0.269631i	$-0.0869019\pi$
$601$	9.07584e16			1.92593			0.962964	+	0.269631i	$0.0869019\pi$
$602$	−3.00870e16	+	4.55159e16i	−0.632120	+	0.956277i
$603$			1.24743e16i			0.259486i
$604$	2.89148e16	−	1.23146e16i	0.595523	−	0.253629i
$605$	2.16843e16			0.442194
$606$	−3.42133e16	−	2.26157e16i	−0.690811	−	0.456641i
$607$		−	6.47764e16i		−	1.29504i	−0.762047	−	0.647522i	$-0.775805\pi$
$607$		−	6.47764e16i		−	1.29504i	0.762047	−	0.647522i	$-0.224195\pi$
$608$	1.69715e16	−	3.81601e15i	0.335969	−	0.0755419i
$609$	6.52118e16			1.27827
$610$	1.49820e16	−	2.26649e16i	0.290797	−	0.439920i
$611$		−	6.89846e16i		−	1.32588i
$612$	7.32957e15	+	1.72099e16i	0.139499	+	0.327544i
$613$	−1.03068e17			−1.94251			−0.971254	−	0.238046i	$-0.923493\pi$
$613$	−1.03068e17			−1.94251			−0.971254	+	0.238046i	$0.923493\pi$
$614$	−5.26348e16	−	3.47927e16i	−0.982342	−	0.649350i
$615$			1.17786e16i			0.217692i
$616$	3.70504e16	+	6.79785e15i	0.678124	+	0.124419i
$617$	−3.80906e16			−0.690410			−0.345205	−	0.938527i	$-0.612191\pi$
$617$	−3.80906e16			−0.690410			−0.345205	+	0.938527i	$0.612191\pi$
$618$	1.52027e16	−	2.29988e16i	0.272891	−	0.412833i
$619$			3.54627e16i			0.630416i	0.949023	+	0.315208i	$0.102074\pi$
$619$			3.54627e16i			0.630416i	−0.949023	+	0.315208i	$0.897926\pi$
$620$	−2.34820e16	+	1.00008e16i	−0.413414	+	0.176070i
$621$	−1.48960e16			−0.259730
$622$	−2.38249e16	−	1.57488e16i	−0.411424	−	0.271960i
$623$			9.18690e16i			1.57123i
$624$	−2.95668e16	−	2.84154e16i	−0.500838	−	0.481333i
$625$	1.28114e16			0.214940
$626$	−4.56938e16	+	6.91259e16i	−0.759296	+	1.14867i
$627$		−	5.10177e15i		−	0.0839683i
$628$	1.05662e16	+	2.48094e16i	0.172250	+	0.404444i
$629$	1.13447e17			1.83184
$630$	−1.52747e16	−	1.00969e16i	−0.244303	−	0.161490i
$631$		−	2.41796e15i		−	0.0383065i	−0.999817	−	0.0191533i	$-0.993903\pi$
$631$		−	2.41796e15i		−	0.0383065i	0.999817	−	0.0191533i	$-0.00609704\pi$
$632$	1.91049e16	−	1.04128e17i	0.299808	−	1.63405i
$633$	3.93751e16			0.612068
$634$	−8.29689e15	+	1.25516e16i	−0.127756	+	0.193270i
$635$			1.66487e15i			0.0253944i
$636$	−2.42612e16	+	1.03327e16i	−0.366581	+	0.156125i
$637$	−1.33818e17			−2.00299
$638$	−3.22271e16	−	2.13029e16i	−0.477857	−	0.315874i
$639$		−	8.57327e15i		−	0.125934i
$640$	−3.00190e16	+	2.16034e16i	−0.436834	+	0.314370i
$641$	−7.32646e16			−1.05620			−0.528100	−	0.849182i	$-0.677095\pi$
$641$	−7.32646e16			−1.05620			−0.528100	+	0.849182i	$0.677095\pi$
$642$	3.47510e16	−	5.25715e16i	0.496314	−	0.750828i
$643$		−	5.58572e16i		−	0.790339i	−0.918608	−	0.395169i	$-0.870686\pi$
$643$		−	5.58572e16i		−	0.790339i	0.918608	−	0.395169i	$-0.129314\pi$
$644$	6.15822e16	+	1.44595e17i	0.863257	+	2.02693i
$645$	−1.57112e16			−0.218198
$646$	−2.22982e16	−	1.47396e16i	−0.306813	−	0.202810i
$647$			8.52631e16i			1.16235i	0.813780	+	0.581173i	$0.197406\pi$
$647$			8.52631e16i			1.16235i	−0.813780	+	0.581173i	$0.802594\pi$
$648$	8.09129e15	+	1.48456e15i	0.109287	+	0.0200515i
$649$	−2.15474e16			−0.288354
$650$	3.55438e16	−	5.37711e16i	0.471286	−	0.712965i
$651$		−	5.98962e16i		−	0.786889i
$652$	1.29358e16	−	5.50928e15i	0.168387	−	0.0717149i
$653$	−1.28375e17			−1.65577			−0.827887	−	0.560894i	$-0.810457\pi$
$653$	−1.28375e17			−1.65577			−0.827887	+	0.560894i	$0.810457\pi$
$654$	6.78448e16	+	4.48469e16i	0.867062	+	0.573147i
$655$		−	1.90579e16i		−	0.241339i
$656$	−3.86879e16	+	4.02556e16i	−0.485459	+	0.505130i
$657$	−4.94264e15			−0.0614563
$658$	8.05135e16	−	1.21802e17i	0.992004	−	1.50071i
$659$			9.03419e16i			1.10300i	0.834174	+	0.551501i	$0.185945\pi$
$659$			9.03419e16i			1.10300i	−0.834174	+	0.551501i	$0.814055\pi$
$660$	4.25025e15	+	9.97960e15i	0.0514222	+	0.120740i
$661$	3.76936e16			0.451917			0.225959	−	0.974137i	$-0.427449\pi$
$661$	3.76936e16			0.451917			0.225959	+	0.974137i	$0.427449\pi$
$662$	−8.82659e15	−	5.83457e15i	−0.104868	−	0.0693203i
$663$			6.30123e16i			0.741898i
$664$	−1.81909e16	+	9.91463e16i	−0.212249	+	1.15683i
$665$	2.61643e16			0.302538
$666$	2.75120e16	−	4.16203e16i	0.315265	−	0.476936i
$667$		−	1.61180e17i		−	1.83044i
$668$	9.35393e16	−	3.98378e16i	1.05277	−	0.448370i
$669$	−7.50855e15			−0.0837528
$670$	3.16156e16	+	2.08986e16i	0.349505	+	0.231030i
$671$		−	3.77710e16i		−	0.413831i
$672$	−1.90400e16	−	8.46792e16i	−0.206752	−	0.919520i
$673$	−5.56200e16			−0.598606			−0.299303	−	0.954158i	$-0.596754\pi$
$673$	−5.56200e16			−0.598606			−0.299303	+	0.954158i	$0.596754\pi$
$674$	6.05147e16	−	9.15472e16i	0.645508	−	0.976531i
$675$			1.29304e16i			0.136706i
$676$	−1.67355e16	−	3.92950e16i	−0.175371	−	0.411772i
$677$	7.87952e16			0.818404			0.409202	−	0.912444i	$-0.365807\pi$
$677$	7.87952e16			0.818404			0.409202	+	0.912444i	$0.365807\pi$
$678$	9.47316e15	+	6.26197e15i	0.0975252	+	0.0644663i
$679$			2.33464e17i			2.38232i
$680$	5.58970e16	+	1.02557e16i	0.565373	+	0.103732i
$681$	−5.75570e15			−0.0577053
$682$	−1.95664e16	+	2.96002e16i	−0.194448	+	0.294163i
$683$			5.12504e16i			0.504862i	0.967615	+	0.252431i	$0.0812301\pi$
$683$			5.12504e16i			0.504862i	−0.967615	+	0.252431i	$0.918770\pi$
$684$	−1.08150e16	+	4.60606e15i	−0.105607	+	0.0449772i
$685$	8.91771e16			0.863197
$686$	−9.43499e16	−	6.23673e16i	−0.905309	−	0.598429i
$687$		−	4.15887e16i		−	0.395581i
$688$	−5.36961e16	−	5.16050e16i	−0.506305	−	0.486588i
$689$	−8.88302e16			−0.830320
$690$	−2.49558e16	+	3.77533e16i	−0.231247	+	0.349833i
$691$			6.40379e16i			0.588259i	0.955766	+	0.294129i	$0.0950297\pi$
$691$			6.40379e16i			0.588259i	−0.955766	+	0.294129i	$0.904970\pi$
$692$	4.05704e16	+	9.52594e16i	0.369464	+	0.867504i
$693$	−2.54552e16			−0.229815
$694$	8.24737e16	+	5.45169e16i	0.738174	+	0.487949i
$695$			8.59585e15i			0.0762746i
$696$	−1.60633e16	+	8.75501e16i	−0.141312	+	0.770196i
$697$	8.57920e16			0.748256
$698$	−2.81249e16	+	4.25476e16i	−0.243197	+	0.367911i
$699$		−	3.02553e16i		−	0.259382i
$700$	1.25515e17	−	5.34559e16i	1.06686	−	0.454368i
$701$	1.93098e17			1.62731			0.813655	−	0.581348i	$-0.197474\pi$
$701$	1.93098e17			1.62731			0.813655	+	0.581348i	$0.197474\pi$
$702$	2.31174e16	+	1.52811e16i	0.193159	+	0.127683i
$703$			7.12924e16i			0.590624i
$704$	−1.82529e16	+	4.80676e16i	−0.149933	+	0.394836i
$705$	4.20436e16			0.342424
$706$	2.06618e16	−	3.12574e16i	0.166855	−	0.252420i
$707$		−	2.92408e17i		−	2.34138i
$708$	1.94538e16	+	4.56775e16i	0.154456	+	0.362663i
$709$	−1.93068e16			−0.151996			−0.0759980	−	0.997108i	$-0.524214\pi$
$709$	−1.93068e16			−0.151996			−0.0759980	+	0.997108i	$0.524214\pi$
$710$	−2.17286e16	−	1.43631e16i	−0.169621	−	0.112123i
$711$			7.15403e16i			0.553775i
$712$	−1.23339e17	−	2.26297e16i	−0.946716	−	0.173699i
$713$	−1.48041e17			−1.12680
$714$	−7.35430e16	+	1.11257e17i	−0.555076	+	0.839723i
$715$			3.65393e16i			0.273479i
$716$	−1.38951e17	+	5.91784e16i	−1.03130	+	0.439223i
$717$	−9.16375e16			−0.674463
$718$	−1.23008e17	−	8.13113e16i	−0.897818	−	0.593478i
$719$		−	2.21045e17i		−	1.59996i	−0.600029	−	0.799978i	$-0.704844\pi$
$719$		−	2.21045e17i		−	1.59996i	0.600029	−	0.799978i	$-0.295156\pi$
$720$	1.73181e16	−	1.80199e16i	0.124310	−	0.129347i
$721$	1.96562e17			1.39922
$722$	−6.88494e16	+	1.04156e17i	−0.486046	+	0.735294i
$723$		−	1.79470e16i		−	0.125650i
$724$	−8.47043e15	−	1.98886e16i	−0.0588131	−	0.138093i
$725$	−1.39911e17			−0.963435
$726$	−5.79445e16	−	3.83026e16i	−0.395724	−	0.261582i
$727$			1.20160e17i			0.813865i	0.913458	+	0.406932i	$0.133402\pi$
$727$			1.20160e17i			0.813865i	−0.913458	+	0.406932i	$0.866598\pi$
$728$	5.27627e16	−	2.87574e17i	0.354437	−	1.93179i
$729$	−5.55906e15			−0.0370370
$730$	−8.28054e15	+	1.25269e16i	−0.0547169	+	0.0827762i
$731$			1.14436e17i			0.749996i
$732$	−8.00693e16	+	3.41010e16i	−0.520475	+	0.221667i
$733$	−7.58459e16			−0.489000			−0.244500	−	0.969649i	$-0.578624\pi$
$733$	−7.58459e16			−0.489000			−0.244500	+	0.969649i	$0.578624\pi$
$734$	2.10471e17	+	1.39126e17i	1.34591	+	0.889676i
$735$		−	8.15572e16i		−	0.517295i
$736$	−2.09296e17	+	4.70597e16i	−1.31672	+	0.296062i
$737$	5.26875e16			0.328778
$738$	2.08054e16	−	3.14746e16i	0.128777	−	0.194815i
$739$		−	2.21632e17i		−	1.36071i	−0.732883	−	0.680355i	$-0.761826\pi$
$739$		−	2.21632e17i		−	1.36071i	0.732883	−	0.680355i	$-0.238174\pi$
$740$	−5.93932e16	−	1.39455e17i	−0.361698	−	0.849269i
$741$	−3.95983e16			−0.239203
$742$	−1.56842e17	−	1.03676e17i	−0.939805	−	0.621232i
$743$		−	2.29188e17i		−	1.36226i	−0.732165	−	0.681128i	$-0.761490\pi$
$743$		−	2.29188e17i		−	1.36226i	0.732165	−	0.681128i	$-0.238510\pi$
$744$	8.04136e16	+	1.47539e16i	0.474124	+	0.0869902i
$745$	3.89809e16			0.227989
$746$	−3.39510e16	+	5.13614e16i	−0.196979	+	0.297991i
$747$		−	6.81177e16i		−	0.392045i
$748$	7.26887e16	−	3.09576e16i	0.415009	−	0.176750i
$749$	4.49309e17			2.54480
$750$	7.89059e16	+	5.21585e16i	0.443345	+	0.293061i
$751$		−	1.69065e17i		−	0.942351i	−0.882039	−	0.471176i	$-0.843830\pi$
$751$		−	1.69065e17i		−	0.942351i	0.882039	−	0.471176i	$-0.156170\pi$
$752$	1.43692e17	+	1.38096e17i	0.794559	+	0.763615i
$753$	−1.05674e17			−0.579692
$754$	−1.65346e17	+	2.50137e17i	−0.899840	+	1.36129i
$755$			6.45230e16i			0.348364i
$756$	2.29819e16	+	5.39616e16i	0.123099	+	0.289037i
$757$	−5.99548e15			−0.0318602			−0.0159301	−	0.999873i	$-0.505071\pi$
$757$	−5.99548e15			−0.0318602			−0.0159301	+	0.999873i	$0.505071\pi$
$758$	−3.94042e16	−	2.60471e16i	−0.207744	−	0.137323i
$759$			6.29159e16i			0.329086i
$760$	−6.44493e15	+	3.51269e16i	−0.0334454	+	0.182288i
$761$	−2.35648e17			−1.21326			−0.606632	−	0.794983i	$-0.707480\pi$
$761$	−2.35648e17			−1.21326			−0.606632	+	0.794983i	$0.707480\pi$
$762$	2.94079e15	−	4.44885e15i	0.0150222	−	0.0227258i
$763$			5.79843e17i			2.93875i
$764$	1.67010e17	−	7.11283e16i	0.839810	−	0.357670i
$765$	−3.84036e16			−0.191604
$766$	3.51998e16	+	2.32678e16i	0.174248	+	0.115182i
$767$			1.67244e17i			0.821444i
$768$	1.18376e17	−	4.70345e15i	0.576895	−	0.0229218i
$769$	1.99155e17			0.963017			0.481508	−	0.876442i	$-0.340089\pi$
$769$	1.99155e17			0.963017			0.481508	+	0.876442i	$0.340089\pi$
$770$	−4.26459e16	+	6.45151e16i	−0.204613	+	0.309540i
$771$			1.06436e16i			0.0506712i
$772$	−6.26951e16	−	1.47208e17i	−0.296162	−	0.695390i
$773$	−7.95257e16			−0.372761			−0.186380	−	0.982478i	$-0.559676\pi$
$773$	−7.95257e16			−0.372761			−0.186380	+	0.982478i	$0.559676\pi$
$774$	4.19833e16	+	2.77519e16i	0.195268	+	0.129076i
$775$			1.28506e17i			0.593080i
$776$	−3.13436e17	−	5.75080e16i	−1.43542	−	0.263365i
$777$	3.55713e17			1.61649
$778$	6.05358e16	−	9.15792e16i	0.272983	−	0.412971i
$779$			5.39135e16i			0.241253i
$780$	7.74584e16	−	3.29890e16i	0.343954	−	0.146488i
$781$	−3.62106e16			−0.159562
$782$	2.74985e17	+	1.81771e17i	1.20245	+	0.794848i
$783$		−	6.01506e16i		−	0.261018i
$784$	2.67883e17	−	2.78738e17i	1.15358	−	1.20033i
$785$	−5.53619e16			−0.236588
$786$	−3.36634e16	+	5.09263e16i	−0.142765	+	0.215976i
$787$			5.38526e16i			0.226651i	0.993558	+	0.113326i	$0.0361503\pi$
$787$			5.38526e16i			0.226651i	−0.993558	+	0.113326i	$0.963850\pi$
$788$	−5.48606e16	−	1.28813e17i	−0.229141	−	0.538024i
$789$	−1.24761e17			−0.517150
$790$	1.81315e17	+	1.19854e17i	0.745886	+	0.493047i
$791$			8.09634e16i			0.330544i
$792$	6.27026e15	−	3.41749e16i	0.0254059	−	0.138470i
$793$	−2.93166e17			−1.17889
$794$	1.88197e17	−	2.84706e17i	0.751085	−	1.13625i
$795$		−	5.41387e16i		−	0.214440i
$796$	−1.89082e16	+	8.05287e15i	−0.0743312	+	0.0316572i
$797$	2.45587e16			0.0958198			0.0479099	−	0.998852i	$-0.484744\pi$
$797$	2.45587e16			0.0958198			0.0479099	+	0.998852i	$0.484744\pi$
$798$	−6.99160e16	−	4.62160e16i	−0.270744	−	0.178968i
$799$		−	3.06234e17i		−	1.17699i
$800$	4.08498e16	+	1.81677e17i	0.155830	+	0.693044i
$801$	8.47389e16			0.320840
$802$	1.16072e17	−	1.75595e17i	0.436195	−	0.659880i
$803$			2.08760e16i			0.0778672i
$804$	−4.75681e16	−	1.11690e17i	−0.176108	−	0.413503i
$805$	−3.22663e17			−1.18570
$806$	2.29747e17	+	1.51868e17i	0.837992	+	0.553931i
$807$		−	1.22103e17i		−	0.442063i
$808$	3.92572e17	+	7.20274e16i	1.41075	+	0.258839i
$809$	−4.48214e17			−1.59880			−0.799400	−	0.600799i	$-0.794849\pi$
$809$	−4.48214e17			−1.59880			−0.799400	+	0.600799i	$0.794849\pi$
$810$	−9.31326e15	+	1.40892e16i	−0.0329755	+	0.0498856i
$811$		−	2.88318e17i		−	1.01332i	−0.862146	−	0.506660i	$-0.830880\pi$
$811$		−	2.88318e17i		−	1.01332i	0.862146	−	0.506660i	$-0.169120\pi$
$812$	−5.83880e17	+	2.48671e17i	−2.03698	+	0.867538i
$813$	−2.04858e17			−0.709430
$814$	−1.75790e17	−	1.16201e17i	−0.604294	−	0.399452i
$815$			2.88661e16i			0.0985015i
$816$	−1.31252e17	−	1.26140e17i	−0.444595	−	0.427281i
$817$	−7.19141e16			−0.241814
$818$	1.09876e17	−	1.66221e17i	0.366760	−	0.554838i
$819$			1.97575e17i			0.654680i
$820$	−4.49150e16	−	1.05461e17i	−0.147743	−	0.346902i
$821$	3.50686e17			1.14514			0.572572	−	0.819855i	$-0.305946\pi$
$821$	3.50686e17			1.14514			0.572572	+	0.819855i	$0.305946\pi$
$822$	−2.38298e17	−	1.57520e17i	−0.772484	−	0.510629i
$823$		−	1.83144e17i		−	0.589377i	−0.955593	−	0.294689i	$-0.904784\pi$
$823$		−	1.83144e17i		−	0.589377i	0.955593	−	0.294689i	$-0.0952159\pi$
$824$	−4.84181e16	+	2.63894e17i	−0.154684	+	0.843074i
$825$	5.46136e16			0.173212
$826$	−1.95194e17	+	2.95291e17i	−0.614591	+	0.929759i
$827$			6.06407e17i			1.89553i	0.318968	+	0.947766i	$0.396664\pi$
$827$			6.06407e17i			1.89553i	−0.318968	+	0.947766i	$0.603336\pi$
$828$	1.33373e17	−	5.68027e16i	0.413891	−	0.176274i
$829$	3.25609e17			1.00316			0.501578	−	0.865112i	$-0.332753\pi$
$829$	3.25609e17			1.00316			0.501578	+	0.865112i	$0.332753\pi$
$830$	−1.72641e17	−	1.14120e17i	−0.528050	−	0.349053i
$831$		−	1.21183e17i		−	0.367991i
$832$	3.73085e17	+	1.41673e17i	1.12478	+	0.427118i
$833$	−5.94041e17			−1.77806
$834$	1.51835e16	−	2.29697e16i	0.0451207	−	0.0682589i
$835$			2.08732e17i			0.615843i
$836$	1.94544e16	+	4.56791e16i	0.0569877	+	0.133807i
$837$	−5.52476e16			−0.160679
$838$	−2.71672e17	−	1.79581e17i	−0.784478	−	0.518557i
$839$			2.58848e17i			0.742117i	0.928610	+	0.371058i	$0.121005\pi$
$839$			2.58848e17i			0.742117i	−0.928610	+	0.371058i	$0.878995\pi$
$840$	1.75265e17	+	3.21569e16i	0.498908	+	0.0915374i
$841$	2.97033e17			0.839515
$842$	−4.36056e16	+	6.59669e16i	−0.122369	+	0.185120i
$843$			3.51443e17i			0.979241i
$844$	−3.52549e17	+	1.50148e17i	−0.975359	+	0.415399i
$845$	8.76863e16			0.240875
$846$	−1.12348e17	−	7.42647e16i	−0.306439	−	0.202563i
$847$		−	4.95229e17i		−	1.34124i
$848$	1.77824e17	−	1.85030e17i	0.478206	−	0.497584i
$849$	2.41820e16			0.0645722
$850$	1.57785e17	−	2.38698e17i	0.418362	−	0.632901i
$851$		−	8.79190e17i		−	2.31476i
$852$	3.26923e16	+	7.67616e16i	0.0854687	+	0.200681i
$853$	6.77094e16			0.175774			0.0878870	−	0.996130i	$-0.471989\pi$
$853$	6.77094e16			0.175774			0.0878870	+	0.996130i	$0.471989\pi$
$854$	−5.17623e17	−	3.42161e17i	−1.33434	−	0.882029i
$855$		−	2.41337e16i		−	0.0617770i
$856$	−1.10676e17	+	6.03219e17i	−0.281327	+	1.53332i
$857$	5.69625e17			1.43782			0.718910	−	0.695103i	$-0.244641\pi$
$857$	5.69625e17			1.43782			0.718910	+	0.695103i	$0.244641\pi$
$858$	6.45422e16	−	9.76400e16i	0.161778	−	0.244740i
$859$		−	3.77313e16i		−	0.0939168i	−0.998897	−	0.0469584i	$-0.985047\pi$
$859$		−	3.77313e16i		−	0.0939168i	0.998897	−	0.0469584i	$-0.0149528\pi$
$860$	1.40672e17	−	5.99112e16i	0.347709	−	0.148087i
$861$	2.69001e17			0.660291
$862$	5.39542e17	+	3.56649e17i	1.31517	+	0.869355i
$863$			5.01665e16i			0.121437i	0.998155	+	0.0607183i	$0.0193391\pi$
$863$			5.01665e16i			0.121437i	−0.998155	+	0.0607183i	$0.980661\pi$
$864$	−7.81072e16	+	1.75622e16i	−0.187762	+	0.0422180i
$865$	−2.12570e17			−0.507465
$866$	7.94314e16	−	1.20164e17i	0.188315	−	0.284884i
$867$			3.45027e16i			0.0812342i
$868$	2.28401e17	+	5.36286e17i	0.534046	+	1.25394i
$869$	3.02162e17			0.701651
$870$	−1.52449e17	−	1.00772e17i	−0.351568	−	0.232394i
$871$		−	4.08943e17i		−	0.936599i
$872$	−7.78468e17	−	1.42830e17i	−1.77069	−	0.324878i
$873$	2.15344e17			0.486460
$874$	−1.14229e17	+	1.72806e17i	−0.256276	+	0.387696i
$875$			6.74378e17i			1.50264i
$876$	4.42543e16	−	1.88476e16i	0.0979335	−	0.0417092i
$877$	−3.64569e17			−0.801275			−0.400638	−	0.916237i	$-0.631211\pi$
$877$	−3.64569e17			−0.801275			−0.400638	+	0.916237i	$0.631211\pi$
$878$	6.76299e17	+	4.47049e17i	1.47629	+	0.975860i
$879$			9.24354e16i			0.200403i
$880$	−7.61099e16	−	7.31459e16i	−0.163887	−	0.157505i
$881$	7.83888e17			1.67648			0.838241	−	0.545300i	$-0.183584\pi$
$881$	7.83888e17			1.67648			0.838241	+	0.545300i	$0.183584\pi$
$882$	−1.44061e17	+	2.17936e17i	−0.306009	+	0.462933i
$883$			3.30429e16i			0.0697131i	0.999392	+	0.0348566i	$0.0110974\pi$
$883$			3.30429e16i			0.0697131i	−0.999392	+	0.0348566i	$0.988903\pi$
$884$	−2.40283e17	−	5.64186e17i	−0.503512	−	1.18225i
$885$	−1.01929e17			−0.212147
$886$	−4.41497e17	−	2.91839e17i	−0.912694	−	0.603311i
$887$		−	4.40353e17i		−	0.904189i	−0.891970	−	0.452094i	$-0.850677\pi$
$887$		−	4.40353e17i		−	0.904189i	0.891970	−	0.452094i	$-0.149323\pi$
$888$	−8.76210e16	+	4.77562e17i	−0.178702	+	0.973985i
$889$	3.80226e16			0.0770250
$890$	1.41966e17	−	2.14767e17i	0.285656	−	0.432143i
$891$			2.34796e16i			0.0469272i
$892$	6.72285e16	−	2.86322e16i	0.133464	−	0.0568414i
$893$	1.92444e17			0.379486
$894$	−1.04164e17	−	6.88549e16i	−0.204030	−	0.134868i
$895$		−	3.10068e17i		−	0.603280i
$896$	4.93381e17	+	6.85579e17i	0.953530	+	1.32498i
$897$	4.88333e17			0.937478
$898$	9.22484e14	−	1.39554e15i	0.00175914	−	0.00266125i
$899$		−	5.97795e17i		−	1.13238i
$900$	−4.93071e16	−	1.15773e17i	−0.0927801	−	0.217848i
$901$	−3.94332e17			−0.737077
$902$	−1.32938e17	−	8.78750e16i	−0.246837	−	0.163165i
$903$			3.58815e17i			0.661826i
$904$	−1.08697e17	−	1.99433e16i	−0.199163	−	0.0365416i
$905$	4.43812e16			0.0807807
$906$	1.13972e17	−	1.72418e17i	0.206077	−	0.311754i
$907$			6.33281e17i			1.13750i	0.822509	+	0.568752i	$0.192574\pi$
$907$			6.33281e17i			1.13750i	−0.822509	+	0.568752i	$0.807426\pi$
$908$	5.15342e16	−	2.19481e16i	0.0919561	−	0.0391635i
$909$	−2.69713e17			−0.478101
$910$	5.00745e17	+	3.31003e17i	0.881796	+	0.582887i
$911$		−	3.15684e17i		−	0.552258i	−0.961121	−	0.276129i	$-0.910948\pi$
$911$		−	3.15684e17i		−	0.552258i	0.961121	−	0.276129i	$-0.0890517\pi$
$912$	7.92694e16	−	8.24815e16i	0.137764	−	0.143347i
$913$	−2.87706e17			−0.496735
$914$	5.71659e16	−	8.64810e16i	0.0980527	−	0.148335i
$915$		−	1.78674e17i		−	0.304463i
$916$	1.58589e17	+	3.72369e17i	0.268473	+	0.630377i
$917$	−4.35247e17			−0.732014
$918$	1.02622e17	+	6.78352e16i	0.171468	+	0.113344i
$919$			8.76187e17i			1.45447i	0.686390	+	0.727234i	$0.259194\pi$
$919$			8.76187e17i			1.45447i	−0.686390	+	0.727234i	$0.740806\pi$
$920$	7.94800e16	−	4.33191e17i	0.131078	−	0.714418i
$921$	−4.14935e17			−0.679865
$922$	−2.16360e17	+	3.27311e17i	−0.352201	+	0.532813i
$923$			2.81055e17i			0.454550i
$924$	2.27916e17	−	9.70678e16i	0.366220	−	0.155971i
$925$	−7.63174e17			−1.21835
$926$	−3.11703e17	−	2.06043e17i	−0.494396	−	0.326807i
$927$		−	1.81306e17i		−	0.285716i
$928$	−1.90028e17	−	8.45142e17i	−0.297530	−	1.32325i
$929$	−9.68108e17			−1.50602			−0.753008	−	0.658011i	$-0.771398\pi$
$929$	−9.68108e17			−1.50602			−0.753008	+	0.658011i	$0.771398\pi$
$930$	−9.25578e16	+	1.40022e17i	−0.143059	+	0.216421i
$931$		−	3.73308e17i		−	0.573283i
$932$	1.15372e17	+	2.70894e17i	0.176037	+	0.413337i
$933$	−1.87819e17			−0.284741
$934$	−6.52328e17	−	4.31203e17i	−0.982618	−	0.649532i
$935$			1.62204e17i			0.242768i
$936$	−2.65255e17	−	4.86677e16i	−0.394464	−	0.0723746i
$937$	1.29269e18			1.91010			0.955050	−	0.296446i	$-0.0958014\pi$
$937$	1.29269e18			1.91010			0.955050	+	0.296446i	$0.0958014\pi$
$938$	4.77286e17	−	7.22043e17i	0.700748	−	1.06010i
$939$			5.44940e17i			0.794978i
$940$	−3.76441e17	+	1.60324e17i	−0.545669	+	0.232397i
$941$	−5.54035e16			−0.0797993			−0.0398997	−	0.999204i	$-0.512704\pi$
$941$	−5.54035e16			−0.0797993			−0.0398997	+	0.999204i	$0.512704\pi$
$942$	1.47937e17	+	9.77899e16i	0.211725	+	0.139955i
$943$		−	6.64871e17i		−	0.945513i
$944$	−3.48362e17	−	3.34795e17i	−0.492265	−	0.473094i
$945$	−1.20415e17			−0.169079
$946$	1.17215e17	−	1.77323e17i	0.163544	−	0.247411i
$947$			1.25165e18i			1.73533i	0.497149	+	0.867665i	$0.334380\pi$
$947$			1.25165e18i			1.73533i	−0.497149	+	0.867665i	$0.665620\pi$
$948$	−2.72803e17	−	6.40542e17i	−0.375836	−	0.882466i
$949$	1.62033e17			0.221823
$950$	1.50003e17	+	9.91554e16i	0.204060	+	0.134888i
$951$			9.89480e16i			0.133759i
$952$	2.34222e17	−	1.27659e18i	0.314635	−	1.71486i
$953$	−8.07216e17			−1.07754			−0.538769	−	0.842454i	$-0.681110\pi$
$953$	−8.07216e17			−1.07754			−0.538769	+	0.842454i	$0.681110\pi$
$954$	−9.56293e16	+	1.44669e17i	−0.126853	+	0.191904i
$955$			3.72680e17i			0.491265i
$956$	8.20485e17	−	3.49439e17i	1.07479	−	0.457746i
$957$	−2.54056e17			−0.330718
$958$	9.91589e17	+	6.55462e17i	1.28274	+	0.847920i
$959$		−	2.03664e18i		−	2.61820i
$960$	−8.63445e16	+	2.27381e17i	−0.110308	+	0.290488i
$961$	2.38597e17			0.302917
$962$	−9.01916e17	+	1.36443e18i	−1.13793	+	1.72147i
$963$		−	4.14437e17i		−	0.519638i
$964$	6.84367e16	+	1.60690e17i	0.0852761	+	0.200229i
$965$	3.28494e17			0.406783
$966$	8.62216e17	+	5.69944e17i	1.06109	+	0.701406i
$967$			9.22020e17i			1.12767i	0.825888	+	0.563834i	$0.190674\pi$
$967$			9.22020e17i			1.12767i	−0.825888	+	0.563834i	$0.809326\pi$
$968$	6.64869e17	+	1.21987e17i	0.808135	+	0.148273i
$969$	−1.75783e17			−0.212341
$970$	3.60772e17	−	5.45779e17i	0.433114	−	0.655219i
$971$			3.21154e17i			0.383176i	0.981475	+	0.191588i	$0.0613637\pi$
$971$			3.21154e17i			0.383176i	−0.981475	+	0.191588i	$0.938636\pi$
$972$	4.97736e16	−	2.11982e16i	0.0590203	−	0.0251363i
$973$	1.96313e17			0.231352
$974$	−4.86450e16	−	3.21554e16i	−0.0569750	−	0.0376617i
$975$		−	4.23893e17i		−	0.493433i
$976$	5.86871e17	−	6.10653e17i	0.678960	−	0.706473i
$977$	−1.05644e18			−1.21472			−0.607359	−	0.794427i	$-0.707771\pi$
$977$	−1.05644e18			−1.21472			−0.607359	+	0.794427i	$0.707771\pi$
$978$	5.09884e16	−	7.71358e16i	0.0582691	−	0.0881501i
$979$		−	3.57909e17i		−	0.406515i
$980$	3.11000e17	+	7.30230e17i	0.351078	+	0.824334i
$981$	5.34841e17			0.600082
$982$	4.98805e15	+	3.29721e15i	0.00556239	+	0.00367686i
$983$			1.65538e18i			1.83475i	0.398023	+	0.917375i	$0.369696\pi$
$983$			1.65538e18i			1.83475i	−0.398023	+	0.917375i	$0.630304\pi$
$984$	−6.62618e16	+	3.61147e17i	−0.0729949	+	0.397845i
$985$	2.87445e17			0.314729
$986$	−7.33997e17	+	1.11040e18i	−0.798790	+	1.20842i
$987$		−	9.60197e17i		−	1.03862i
$988$	3.54547e17	−	1.50999e17i	0.381181	−	0.162343i
$989$	8.86858e17			0.947712
$990$	5.95079e16	+	3.93361e16i	0.0632068	+	0.0417811i
$991$			1.47211e18i			1.55417i	0.629394	+	0.777087i	$0.283303\pi$
$991$			1.47211e18i			1.55417i	−0.629394	+	0.777087i	$0.716697\pi$
$992$	−7.76252e17	+	1.74539e17i	−0.814578	+	0.183156i
$993$	−6.95826e16			−0.0725780
$994$	−3.28026e17	+	4.96240e17i	−0.340087	+	0.514486i
$995$		−	4.21934e16i		−	0.0434816i
$996$	2.59751e17	+	6.09898e17i	0.266074	+	0.624742i
$997$	1.00149e18			1.01971			0.509855	−	0.860261i	$-0.329699\pi$
$997$	1.00149e18			1.01971			0.509855	+	0.860261i	$0.329699\pi$
$998$	8.55642e16	+	5.65598e16i	0.0865982	+	0.0572433i
$999$		−	3.28105e17i		−	0.330081i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.13.d.a.7.6	yes	12
3.2	odd	2		36.13.d.d.19.7		12
4.3	odd	2	inner	12.13.d.a.7.5	✓	12
8.3	odd	2		192.13.g.e.127.8		12
8.5	even	2		192.13.g.e.127.2		12
12.11	even	2		36.13.d.d.19.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.13.d.a.7.5	✓	12	4.3	odd	2	inner
12.13.d.a.7.6	yes	12	1.1	even	1	trivial
36.13.d.d.19.7		12	3.2	odd	2
36.13.d.d.19.8		12	12.11	even	2
192.13.g.e.127.2		12	8.5	even	2
192.13.g.e.127.8		12	8.3	odd	2

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:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	12.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-35.2919 + 53.3899i) q^{2} +420.888i q^{3} +(-1604.96 - 3768.46i) q^{4} +8409.28 q^{5} +(-22471.2 - 14854.0i) q^{6} -192052. i q^{7} +(257840. + 47307.4i) q^{8} -177147. q^{9} +O(q^{10})\)	\(q+(-35.2919 + 53.3899i) q^{2} +420.888i q^{3} +(-1604.96 - 3768.46i) q^{4} +8409.28 q^{5} +(-22471.2 - 14854.0i) q^{6} -192052. i q^{7} +(257840. + 47307.4i) q^{8} -177147. q^{9} +(-296780. + 448971. i) q^{10} +748209. i q^{11} +(1.58610e6 - 675510. i) q^{12} +5.80736e6 q^{13} +(1.02537e7 + 6.77790e6i) q^{14} +3.53937e6i q^{15} +(-1.16254e7 + 1.20965e7i) q^{16} +2.57798e7 q^{17} +(6.25185e6 - 9.45786e6i) q^{18} +1.62006e7i q^{19} +(-1.34966e7 - 3.16901e7i) q^{20} +8.08326e7 q^{21} +(-3.99468e7 - 2.64057e7i) q^{22} -1.99788e8i q^{23} +(-1.99111e7 + 1.08522e8i) q^{24} -1.73425e8 q^{25} +(-2.04953e8 + 3.10054e8i) q^{26} -7.45591e7i q^{27} +(-7.23743e8 + 3.08237e8i) q^{28} +8.06751e8 q^{29} +(-1.88967e8 - 1.24911e8i) q^{30} -7.40990e8i q^{31} +(-2.35548e8 - 1.04759e9i) q^{32} -3.14913e8 q^{33} +(-9.09818e8 + 1.37638e9i) q^{34} -1.61502e9i q^{35} +(2.84314e8 + 6.67572e8i) q^{36} +4.40061e9 q^{37} +(-8.64947e8 - 5.71749e8i) q^{38} +2.44425e9i q^{39} +(2.16825e9 + 3.97821e8i) q^{40} +3.32788e9 q^{41} +(-2.85274e9 + 4.31565e9i) q^{42} +4.43899e9i q^{43} +(2.81960e9 - 1.20085e9i) q^{44} -1.48968e9 q^{45} +(1.06667e10 + 7.05091e9i) q^{46} -1.18788e10i q^{47} +(-5.09127e9 - 4.89300e9i) q^{48} -2.30429e10 q^{49} +(6.12048e9 - 9.25912e9i) q^{50} +1.08504e10i q^{51} +(-9.32060e9 - 2.18848e10i) q^{52} -1.52961e10 q^{53} +(3.98070e9 + 2.63133e9i) q^{54} +6.29190e9i q^{55} +(9.08550e9 - 4.95188e10i) q^{56} -6.81863e9 q^{57} +(-2.84718e10 + 4.30724e10i) q^{58} +2.87986e10i q^{59} +(1.33380e10 - 5.68056e9i) q^{60} -5.04818e10 q^{61} +(3.95614e10 + 2.61509e10i) q^{62} +3.40215e10i q^{63} +(6.42435e10 + 2.43955e10i) q^{64} +4.88357e10 q^{65} +(1.11139e10 - 1.68132e10i) q^{66} -7.04181e10i q^{67} +(-4.13756e10 - 9.71502e10i) q^{68} +8.40886e10 q^{69} +(8.62259e10 + 5.69972e10i) q^{70} +4.83964e10i q^{71} +(-4.56756e10 - 8.38036e9i) q^{72} +2.79013e10 q^{73} +(-1.55306e11 + 2.34948e11i) q^{74} -7.29924e10i q^{75} +(6.10513e10 - 2.60013e10i) q^{76} +1.43695e11 q^{77} +(-1.30498e11 - 8.62622e10i) q^{78} -4.03847e11i q^{79} +(-9.77613e10 + 1.01723e11i) q^{80} +3.13811e10 q^{81} +(-1.17447e11 + 1.77675e11i) q^{82} +3.84526e11i q^{83} +(-1.29733e11 - 3.04615e11i) q^{84} +2.16790e11 q^{85} +(-2.36997e11 - 1.56660e11i) q^{86} +3.39552e11i q^{87} +(-3.53958e10 + 1.92918e11i) q^{88} -4.78354e11 q^{89} +(5.25736e10 - 7.95338e10i) q^{90} -1.11532e12i q^{91} +(-7.52895e11 + 3.20653e11i) q^{92} +3.11874e11 q^{93} +(6.34210e11 + 4.19226e11i) q^{94} +1.36235e11i q^{95} +(4.40917e11 - 9.91393e10i) q^{96} -1.21562e12 q^{97} +(8.13227e11 - 1.23026e12i) q^{98} -1.32543e11i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 90 q^{2} - 4692 q^{4} - 10296 q^{5} - 48114 q^{6} - 648000 q^{8} - 2125764 q^{9}+O(q^{10}) \) 12 * q - 90 * q^2 - 4692 * q^4 - 10296 * q^5 - 48114 * q^6 - 648000 * q^8 - 2125764 * q^9	\( 12 q - 90 q^{2} - 4692 q^{4} - 10296 q^{5} - 48114 q^{6} - 648000 q^{8} - 2125764 q^{9} + 923028 q^{10} - 3018060 q^{12} + 2094840 q^{13} + 15389208 q^{14} - 61526928 q^{16} - 12097800 q^{17} + 15943230 q^{18} - 377644248 q^{20} - 75057840 q^{21} + 482545560 q^{22} - 332039088 q^{24} + 1058748132 q^{25} + 243358236 q^{26} - 185369520 q^{28} + 1997608680 q^{29} - 577761660 q^{30} + 1733536800 q^{32} + 322101360 q^{33} - 7816269348 q^{34} + 831173724 q^{36} - 960170280 q^{37} - 8280525240 q^{38} + 3985807104 q^{40} + 5806392696 q^{41} - 1390844520 q^{42} + 4989496464 q^{44} + 1823905512 q^{45} + 4149450240 q^{46} - 7791843600 q^{48} - 60479071668 q^{49} + 68552901522 q^{50} - 31090133640 q^{52} + 42482511720 q^{53} + 8523250758 q^{54} - 38053468224 q^{56} - 58319941680 q^{57} + 159666562500 q^{58} - 19968517224 q^{60} + 137368568088 q^{61} - 27876030840 q^{62} + 188355529344 q^{64} - 328250713392 q^{65} - 136719325224 q^{66} + 77938316280 q^{68} + 214339017024 q^{69} - 454939318704 q^{70} + 114791256000 q^{72} - 804477880680 q^{73} - 502785766548 q^{74} + 143972453808 q^{76} + 1383727360320 q^{77} - 72052158420 q^{78} - 417712547808 q^{80} + 376572715308 q^{81} + 460673773020 q^{82} + 28008331632 q^{84} + 1437981718224 q^{85} + 1255416205464 q^{86} + 47622991680 q^{88} - 1422946205928 q^{89} - 163511641116 q^{90} - 3462722444160 q^{92} + 1056734080560 q^{93} + 847910842896 q^{94} + 341032101984 q^{96} - 4056673857000 q^{97} + 1702751294790 q^{98}+O(q^{100}) \) 12 * q - 90 * q^2 - 4692 * q^4 - 10296 * q^5 - 48114 * q^6 - 648000 * q^8 - 2125764 * q^9 + 923028 * q^10 - 3018060 * q^12 + 2094840 * q^13 + 15389208 * q^14 - 61526928 * q^16 - 12097800 * q^17 + 15943230 * q^18 - 377644248 * q^20 - 75057840 * q^21 + 482545560 * q^22 - 332039088 * q^24 + 1058748132 * q^25 + 243358236 * q^26 - 185369520 * q^28 + 1997608680 * q^29 - 577761660 * q^30 + 1733536800 * q^32 + 322101360 * q^33 - 7816269348 * q^34 + 831173724 * q^36 - 960170280 * q^37 - 8280525240 * q^38 + 3985807104 * q^40 + 5806392696 * q^41 - 1390844520 * q^42 + 4989496464 * q^44 + 1823905512 * q^45 + 4149450240 * q^46 - 7791843600 * q^48 - 60479071668 * q^49 + 68552901522 * q^50 - 31090133640 * q^52 + 42482511720 * q^53 + 8523250758 * q^54 - 38053468224 * q^56 - 58319941680 * q^57 + 159666562500 * q^58 - 19968517224 * q^60 + 137368568088 * q^61 - 27876030840 * q^62 + 188355529344 * q^64 - 328250713392 * q^65 - 136719325224 * q^66 + 77938316280 * q^68 + 214339017024 * q^69 - 454939318704 * q^70 + 114791256000 * q^72 - 804477880680 * q^73 - 502785766548 * q^74 + 143972453808 * q^76 + 1383727360320 * q^77 - 72052158420 * q^78 - 417712547808 * q^80 + 376572715308 * q^81 + 460673773020 * q^82 + 28008331632 * q^84 + 1437981718224 * q^85 + 1255416205464 * q^86 + 47622991680 * q^88 - 1422946205928 * q^89 - 163511641116 * q^90 - 3462722444160 * q^92 + 1056734080560 * q^93 + 847910842896 * q^94 + 341032101984 * q^96 - 4056673857000 * q^97 + 1702751294790 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more