LMFDB - Embedded newform 12.21.d.a.7.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,21,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, 21, names="a")

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

chi := DirichletCharacter("12.7");

S:= CuspForms(chi, 21);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 21 $
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:	$30.4216518123$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 8 x^{19} - 1800529 x^{18} + 10471600 x^{17} + 1401323871170 x^{16} - 8255926364216 x^{15} + \cdots + 17\!\cdots\!88 $ x^20 - 8x^19 - 1800529x^18 + 10471600x^17 + 1401323871170x^16 - 8255926364216x^15 - 618094244121155086x^14 + 4776792556997860420x^13 + 170108290172014159730219x^12 - 1822962046954348428067604x^11 - 30268361797163656482757584955x^10 + 429273525493411897272285527056x^9 + 3482282078039849041741632502870994x^8 - 60435809630459978311045044131417084x^7 - 250759366568586243949566404606021171194x^6 + 4820660604980619237148365440042241179296x^5 + 10477847059140453507669781324292395546888841x^4 - 190400851192787000531616700775511384585564956x^3 - 219026547432574645023476742933634147067753863733x^2 + 2495516610278349515190181419629668858430612303484*x + 1754305378275820584806685198344335887914554128464688
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{174}\cdot 3^{82}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			7.7
Root			$382.240 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	12.7
Dual form			12.21.d.a.7.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-146.341 - 1013.49i) q^{2} -34092.0i q^{3} +(-1.00574e6 + 296630. i) q^{4} +1.07961e7 q^{5} +(-3.45518e7 + 4.98905e6i) q^{6} -1.91267e8i q^{7} +(4.47813e8 + 9.75902e8i) q^{8} -1.16226e9 q^{9} +O(q^{10})$	\(q+(-146.341 - 1013.49i) q^{2} -34092.0i q^{3} +(-1.00574e6 + 296630. i) q^{4} +1.07961e7 q^{5} +(-3.45518e7 + 4.98905e6i) q^{6} -1.91267e8i q^{7} +(4.47813e8 + 9.75902e8i) q^{8} -1.16226e9 q^{9} +(-1.57992e9 - 1.09418e10i) q^{10} +4.63069e10i q^{11} +(1.01127e10 + 3.42878e10i) q^{12} +2.40605e11 q^{13} +(-1.93847e11 + 2.79902e10i) q^{14} -3.68062e11i q^{15} +(9.23533e11 - 5.96668e11i) q^{16} +2.93983e12 q^{17} +(1.70086e11 + 1.17794e12i) q^{18} +7.95667e12i q^{19} +(-1.08582e13 + 3.20246e12i) q^{20} -6.52066e12 q^{21} +(4.69316e13 - 6.77660e12i) q^{22} -3.00784e12i q^{23} +(3.32704e13 - 1.52668e13i) q^{24} +2.11894e13 q^{25} +(-3.52103e13 - 2.43850e14i) q^{26} +3.96238e13i q^{27} +(5.67355e13 + 1.92366e14i) q^{28} -3.33186e14 q^{29} +(-3.73027e14 + 5.38625e13i) q^{30} -6.82538e14i q^{31} +(-7.39867e14 - 8.48674e14i) q^{32} +1.57869e15 q^{33} +(-4.30218e14 - 2.97949e15i) q^{34} -2.06495e15i q^{35} +(1.16894e15 - 3.44761e14i) q^{36} -1.53400e15 q^{37} +(8.06400e15 - 1.16439e15i) q^{38} -8.20268e15i q^{39} +(4.83465e15 + 1.05360e16i) q^{40} +1.72703e16 q^{41} +(9.54240e14 + 6.60862e15i) q^{42} -2.59198e16i q^{43} +(-1.37360e16 - 4.65729e16i) q^{44} -1.25479e16 q^{45} +(-3.04842e15 + 4.40171e14i) q^{46} +3.90033e16i q^{47} +(-2.03416e16 - 3.14851e16i) q^{48} +4.32092e16 q^{49} +(-3.10087e15 - 2.14752e16i) q^{50} -1.00225e17i q^{51} +(-2.41987e17 + 7.13705e16i) q^{52} -7.34809e16 q^{53} +(4.01583e16 - 5.79858e15i) q^{54} +4.99936e17i q^{55} +(1.86658e17 - 8.56518e16i) q^{56} +2.71259e17 q^{57} +(4.87588e16 + 3.37681e17i) q^{58} +1.38469e17i q^{59} +(1.09178e17 + 3.70176e17i) q^{60} -2.55270e16 q^{61} +(-6.91745e17 + 9.98832e16i) q^{62} +2.22302e17i q^{63} +(-7.51849e17 + 8.74043e17i) q^{64} +2.59760e18 q^{65} +(-2.31027e17 - 1.59999e18i) q^{66} +1.07186e18i q^{67} +(-2.95672e18 + 8.72042e17i) q^{68} -1.02543e17 q^{69} +(-2.09280e18 + 3.02186e17i) q^{70} -3.16792e18i q^{71} +(-5.20475e17 - 1.13425e18i) q^{72} +3.57700e18 q^{73} +(2.24487e17 + 1.55470e18i) q^{74} -7.22387e17i q^{75} +(-2.36019e18 - 8.00238e18i) q^{76} +8.85698e18 q^{77} +(-8.31333e18 + 1.20039e18i) q^{78} -2.44971e18i q^{79} +(9.97060e18 - 6.44171e18i) q^{80} +1.35085e18 q^{81} +(-2.52735e18 - 1.75032e19i) q^{82} +6.12931e18i q^{83} +(6.55812e18 - 1.93422e18i) q^{84} +3.17389e19 q^{85} +(-2.62694e19 + 3.79312e18i) q^{86} +1.13590e19i q^{87} +(-4.51910e19 + 2.07368e19i) q^{88} +4.51744e19 q^{89} +(1.83628e18 + 1.27172e19i) q^{90} -4.60197e19i q^{91} +(8.92216e17 + 3.02512e18i) q^{92} -2.32691e19 q^{93} +(3.95295e19 - 5.70778e18i) q^{94} +8.59014e19i q^{95} +(-2.89330e19 + 2.52235e19i) q^{96} -5.96418e19 q^{97} +(-6.32328e18 - 4.37921e19i) q^{98} -5.38207e19i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 1254 q^{2} - 485524 q^{4} + 1476984 q^{5} - 36019890 q^{6} + 434160000 q^{8} - 23245229340 q^{9}+O(q^{10}) $ 20 * q + 1254 * q^2 - 485524 * q^4 + 1476984 * q^5 - 36019890 * q^6 + 434160000 * q^8 - 23245229340 * q^9	$ 20 q + 1254 q^{2} - 485524 q^{4} + 1476984 q^{5} - 36019890 q^{6} + 434160000 q^{8} - 23245229340 q^{9} + 3166779028 q^{10} + 35789598900 q^{12} - 197410187576 q^{13} + 1179712421976 q^{14} + 1592658749552 q^{16} + 4951946877000 q^{17} - 1457475879618 q^{18} - 20688414141528 q^{20} - 19078957703376 q^{21} + 54807260127768 q^{22} + 58196896476048 q^{24} + 513048947332092 q^{25} - 142319404376100 q^{26} - 10\!\cdots\!28 q^{28}+ \cdots + 30\!\cdots\!50 q^{98}+O(q^{100}) $ 20 * q + 1254 * q^2 - 485524 * q^4 + 1476984 * q^5 - 36019890 * q^6 + 434160000 * q^8 - 23245229340 * q^9 + 3166779028 * q^10 + 35789598900 * q^12 - 197410187576 * q^13 + 1179712421976 * q^14 + 1592658749552 * q^16 + 4951946877000 * q^17 - 1457475879618 * q^18 - 20688414141528 * q^20 - 19078957703376 * q^21 + 54807260127768 * q^22 + 58196896476048 * q^24 + 513048947332092 * q^25 - 142319404376100 * q^26 - 1064314324942128 * q^28 - 1120225678237608 * q^29 + 919562090032260 * q^30 + 926940361437984 * q^32 - 1250504741372400 * q^33 + 1615904447739868 * q^34 + 564305836503708 * q^36 + 13452822768639208 * q^37 + 30625874417040840 * q^38 - 42278345025251456 * q^40 + 26778887480335560 * q^41 + 34752013424992728 * q^42 - 160483087306778736 * q^44 - 1716641590575528 * q^45 + 312713467885194624 * q^46 - 170793646915261968 * q^48 - 198082137742572844 * q^49 + 575620844246091282 * q^50 - 896547684604982408 * q^52 + 241769380233802968 * q^53 + 41864530192578630 * q^54 - 2099928347597457216 * q^56 + 595468774322860464 * q^57 + 1656374273217670084 * q^58 + 94322711748139416 * q^60 + 430703667006221224 * q^61 + 1718273064332222664 * q^62 - 3197273374119743872 * q^64 - 1146808855391494992 * q^65 + 1921733716920631128 * q^66 + 4484111570418829944 * q^68 - 4519043719923504960 * q^69 - 12213680959006457904 * q^70 - 504607438512720000 * q^72 + 12562724768160620200 * q^73 - 22136012572796109780 * q^74 + 28495592855672115888 * q^76 + 19985445258493440192 * q^77 - 20625251537531633940 * q^78 + 49505459663687019552 * q^80 + 27017034353459841780 * q^81 - 50718250504081238180 * q^82 + 24536705912722373616 * q^84 - 15354475681609135696 * q^85 - 85391409389241086952 * q^86 + 66078172926918803520 * q^88 + 43679060294354361384 * q^89 - 3680625238748114076 * q^90 - 64869958570030809216 * q^92 - 50732545022865845424 * q^93 + 95503492747592513424 * q^94 - 89530085825201077920 * q^96 + 7230988441427384872 * q^97 + 304648861287114073350 * 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 $

$2$	−146.341	−	1013.49i	−0.142911	−	0.989736i
$2$	−146.341	−	1013.49i	−0.142911	−	0.989736i
$3$		−	34092.0i		−	0.577350i
$3$		−	34092.0i		−	0.577350i
$4$	−1.00574e6	+	296630.i	−0.959153	+	0.282888i
$5$	1.07961e7			1.10553			0.552763	−	0.833339i	$-0.313574\pi$
$5$	1.07961e7			1.10553			0.552763	+	0.833339i	$0.313574\pi$
$6$	−3.45518e7	+	4.98905e6i	−0.571424	+	0.0825097i
$7$		−	1.91267e8i		−	0.677110i	−0.940947	−	0.338555i	$-0.890062\pi$
$7$		−	1.91267e8i		−	0.677110i	0.940947	−	0.338555i	$-0.109938\pi$
$8$	4.47813e8	+	9.75902e8i	0.417058	+	0.908880i
$9$	−1.16226e9			−0.333333
$10$	−1.57992e9	−	1.09418e10i	−0.157992	−	1.09418i
$11$			4.63069e10i			1.78533i	0.450719	+	0.892666i	$0.351168\pi$
$11$			4.63069e10i			1.78533i	−0.450719	+	0.892666i	$0.648832\pi$
$12$	1.01127e10	+	3.42878e10i	0.163326	+	0.553767i
$13$	2.40605e11			1.74530			0.872651	−	0.488345i	$-0.162399\pi$
$13$	2.40605e11			1.74530			0.872651	+	0.488345i	$0.162399\pi$
$14$	−1.93847e11	+	2.79902e10i	−0.670160	+	0.0967665i
$15$		−	3.68062e11i		−	0.638275i
$16$	9.23533e11	−	5.96668e11i	0.839949	−	0.542666i
$17$	2.93983e12			1.45825			0.729127	−	0.684378i	$-0.239926\pi$
$17$	2.93983e12			1.45825			0.729127	+	0.684378i	$0.239926\pi$
$18$	1.70086e11	+	1.17794e12i	0.0476370	+	0.329912i
$19$			7.95667e12i			1.29776i	0.760889	+	0.648882i	$0.224763\pi$
$19$			7.95667e12i			1.29776i	−0.760889	+	0.648882i	$0.775237\pi$
$20$	−1.08582e13	+	3.20246e12i	−1.06037	+	0.312740i
$21$	−6.52066e12			−0.390930
$22$	4.69316e13	−	6.77660e12i	1.76701	−	0.255144i
$23$		−	3.00784e12i		−	0.0726067i	−0.999341	−	0.0363034i	$-0.988442\pi$
$23$		−	3.00784e12i		−	0.0726067i	0.999341	−	0.0363034i	$-0.0115583\pi$
$24$	3.32704e13	−	1.52668e13i	0.524742	−	0.240789i
$25$	2.11894e13			0.222187
$26$	−3.52103e13	−	2.43850e14i	−0.249423	−	1.72739i
$27$			3.96238e13i			0.192450i
$28$	5.67355e13	+	1.92366e14i	0.191547	+	0.649452i
$29$	−3.33186e14			−0.791967			−0.395983	−	0.918258i	$-0.629596\pi$
$29$	−3.33186e14			−0.791967			−0.395983	+	0.918258i	$0.629596\pi$
$30$	−3.73027e14	+	5.38625e13i	−0.631724	+	0.0912166i
$31$		−	6.82538e14i		−	0.832741i	−0.909195	−	0.416370i	$-0.863302\pi$
$31$		−	6.82538e14i		−	0.832741i	0.909195	−	0.416370i	$-0.136698\pi$
$32$	−7.39867e14	−	8.48674e14i	−0.657134	−	0.753774i
$33$	1.57869e15			1.03076
$34$	−4.30218e14	−	2.97949e15i	−0.208401	−	1.44329i
$35$		−	2.06495e15i		−	0.748563i
$36$	1.16894e15	−	3.44761e14i	0.319718	−	0.0942961i
$37$	−1.53400e15			−0.319013			−0.159507	−	0.987197i	$-0.550990\pi$
$37$	−1.53400e15			−0.319013			−0.159507	+	0.987197i	$0.550990\pi$
$38$	8.06400e15	−	1.16439e15i	1.28444	−	0.185465i
$39$		−	8.20268e15i		−	1.00765i
$40$	4.83465e15	+	1.05360e16i	0.461068	+	1.00479i
$41$	1.72703e16			1.28665			0.643325	−	0.765593i	$-0.277554\pi$
$41$	1.72703e16			1.28665			0.643325	+	0.765593i	$0.277554\pi$
$42$	9.54240e14	+	6.60862e15i	0.0558682	+	0.386917i
$43$		−	2.59198e16i		−	1.19935i	−0.800243	−	0.599676i	$-0.795296\pi$
$43$		−	2.59198e16i		−	1.19935i	0.800243	−	0.599676i	$-0.204704\pi$
$44$	−1.37360e16	−	4.65729e16i	−0.505049	−	1.71241i
$45$	−1.25479e16			−0.368509
$46$	−3.04842e15	+	4.40171e14i	−0.0718615	+	0.0103763i
$47$			3.90033e16i			0.741521i	0.928729	+	0.370760i	$0.120903\pi$
$47$			3.90033e16i			0.741521i	−0.928729	+	0.370760i	$0.879097\pi$
$48$	−2.03416e16	−	3.14851e16i	−0.313308	−	0.484944i
$49$	4.32092e16			0.541521
$50$	−3.10087e15	−	2.14752e16i	−0.0317529	−	0.219906i
$51$		−	1.00225e17i		−	0.841924i
$52$	−2.41987e17	+	7.13705e16i	−1.67401	+	0.493725i
$53$	−7.34809e16			−0.420161			−0.210080	−	0.977684i	$-0.567373\pi$
$53$	−7.34809e16			−0.420161			−0.210080	+	0.977684i	$0.567373\pi$
$54$	4.01583e16	−	5.79858e15i	0.190475	−	0.0275032i
$55$			4.99936e17i			1.97373i
$56$	1.86658e17	−	8.56518e16i	0.615412	−	0.282394i
$57$	2.71259e17			0.749264
$58$	4.87588e16	+	3.37681e17i	0.113181	+	0.783838i
$59$			1.38469e17i			0.270914i	0.990783	+	0.135457i	$0.0432502\pi$
$59$			1.38469e17i			0.270914i	−0.990783	+	0.135457i	$0.956750\pi$
$60$	1.09178e17	+	3.70176e17i	0.180561	+	0.612204i
$61$	−2.55270e16			−0.0357850			−0.0178925	−	0.999840i	$-0.505696\pi$
$61$	−2.55270e16			−0.0357850			−0.0178925	+	0.999840i	$0.505696\pi$
$62$	−6.91745e17	+	9.98832e16i	−0.824193	+	0.119008i
$63$			2.22302e17i			0.225703i
$64$	−7.51849e17	+	8.74043e17i	−0.652125	+	0.758111i
$65$	2.59760e18			1.92948
$66$	−2.31027e17	−	1.59999e18i	−0.147307	−	1.02018i
$67$			1.07186e18i			0.588015i	0.955803	+	0.294007i	$0.0949890\pi$
$67$			1.07186e18i			0.588015i	−0.955803	+	0.294007i	$0.905011\pi$
$68$	−2.95672e18	+	8.72042e17i	−1.39869	+	0.412523i
$69$	−1.02543e17			−0.0419195
$70$	−2.09280e18	+	3.02186e17i	−0.740879	+	0.106978i
$71$		−	3.16792e18i		−	0.973174i	−0.873632	−	0.486587i	$-0.838242\pi$
$71$		−	3.16792e18i		−	0.973174i	0.873632	−	0.486587i	$-0.161758\pi$
$72$	−5.20475e17	−	1.13425e18i	−0.139019	−	0.302960i
$73$	3.57700e18			0.832321			0.416160	−	0.909291i	$-0.363375\pi$
$73$	3.57700e18			0.832321			0.416160	+	0.909291i	$0.363375\pi$
$74$	2.24487e17	+	1.55470e18i	0.0455905	+	0.315739i
$75$		−	7.22387e17i		−	0.128280i
$76$	−2.36019e18	−	8.00238e18i	−0.367122	−	1.24475i
$77$	8.85698e18			1.20887
$78$	−8.31333e18	+	1.20039e18i	−0.997307	+	0.144004i
$79$		−	2.44971e18i		−	0.258728i	−0.991597	−	0.129364i	$-0.958706\pi$
$79$		−	2.44971e18i		−	0.258728i	0.991597	−	0.129364i	$-0.0412936\pi$
$80$	9.97060e18	−	6.44171e18i	0.928585	−	0.599931i
$81$	1.35085e18			0.111111
$82$	−2.52735e18	−	1.75032e19i	−0.183877	−	1.27344i
$83$			6.12931e18i			0.395030i	0.980300	+	0.197515i	$0.0632872\pi$
$83$			6.12931e18i			0.395030i	−0.980300	+	0.197515i	$0.936713\pi$
$84$	6.55812e18	−	1.93422e18i	0.374962	−	0.110589i
$85$	3.17389e19			1.61214
$86$	−2.62694e19	+	3.79312e18i	−1.18704	+	0.171401i
$87$			1.13590e19i			0.457242i
$88$	−4.51910e19	+	2.07368e19i	−1.62265	+	0.744587i
$89$	4.51744e19			1.44875			0.724373	−	0.689409i	$-0.242130\pi$
$89$	4.51744e19			1.44875			0.724373	+	0.689409i	$0.242130\pi$
$90$	1.83628e18	+	1.27172e19i	0.0526639	+	0.364726i
$91$		−	4.60197e19i		−	1.18176i
$92$	8.92216e17	+	3.02512e18i	0.0205396	+	0.0696410i
$93$	−2.32691e19			−0.480783
$94$	3.95295e19	−	5.70778e18i	0.733909	−	0.105971i
$95$			8.59014e19i			1.43471i
$96$	−2.89330e19	+	2.52235e19i	−0.435192	+	0.379396i
$97$	−5.96418e19			−0.808785			−0.404393	−	0.914585i	$-0.632517\pi$
$97$	−5.96418e19			−0.808785			−0.404393	+	0.914585i	$0.632517\pi$
$98$	−6.32328e18	−	4.37921e19i	−0.0773894	−	0.535963i
$99$		−	5.38207e19i		−	0.595111i
$100$	−2.13111e19	+	6.28540e18i	−0.213111	+	0.0628540i
$101$	−3.39089e19			−0.306973			−0.153486	−	0.988151i	$-0.549050\pi$
$101$	−3.39089e19			−0.306973			−0.153486	+	0.988151i	$0.549050\pi$
$102$	−1.01577e20	+	1.46670e19i	−0.833282	+	0.120320i
$103$			8.90853e19i			0.662878i	0.943477	+	0.331439i	$0.107534\pi$
$103$			8.90853e19i			0.662878i	−0.943477	+	0.331439i	$0.892466\pi$
$104$	1.07746e20	+	2.34807e20i	0.727892	+	1.58627i
$105$	−7.03981e19			−0.432183
$106$	1.07533e19	+	7.44721e19i	0.0600456	+	0.415848i
$107$			4.27182e19i			0.217157i	0.994088	+	0.108579i	$0.0346300\pi$
$107$			4.27182e19i			0.217157i	−0.994088	+	0.108579i	$0.965370\pi$
$108$	−1.17536e19	−	3.98514e19i	−0.0544419	−	0.184589i
$109$	−2.20332e20			−0.930705			−0.465352	−	0.885126i	$-0.654072\pi$
$109$	−2.20332e20			−0.930705			−0.465352	+	0.885126i	$0.654072\pi$
$110$	5.06680e20	−	7.31611e19i	1.95347	−	0.282068i
$111$			5.22972e19i			0.184182i
$112$	−1.14123e20	−	1.76641e20i	−0.367445	−	0.568738i
$113$	5.66517e20			1.66889			0.834447	−	0.551088i	$-0.185787\pi$
$113$	5.66517e20			1.66889			0.834447	+	0.551088i	$0.185787\pi$
$114$	−3.96962e19	−	2.74918e20i	−0.107078	−	0.741573i
$115$		−	3.24731e19i		−	0.0802686i
$116$	3.35100e20	−	9.88329e19i	0.759617	−	0.224038i
$117$	−2.79645e20			−0.581767
$118$	1.40336e20	−	2.02636e19i	0.268133	−	0.0387166i
$119$		−	5.62293e20i		−	0.987399i
$120$	3.59192e20	−	1.64823e20i	0.580116	−	0.266198i
$121$	−1.47158e21			−2.18741
$122$	3.73564e18	+	2.58713e19i	0.00511407	+	0.0354177i
$123$		−	5.88777e20i		−	0.742848i
$124$	2.02461e20	+	6.86459e20i	0.235573	+	0.798726i
$125$	−8.00837e20			−0.859892
$126$	2.25301e20	−	3.25319e19i	0.223387	−	0.0322555i
$127$			1.55027e20i			0.142027i	0.997475	+	0.0710134i	$0.0226233\pi$
$127$			1.55027e20i			0.142027i	−0.997475	+	0.0710134i	$0.977377\pi$
$128$	9.95859e20	+	6.34083e20i	0.843526	+	0.537089i
$129$	−8.83656e20			−0.692446
$130$	−3.80136e20	−	2.63264e21i	−0.275743	−	1.90967i
$131$		−	1.74629e21i		−	1.17328i	−0.809847	−	0.586641i	$-0.800450\pi$
$131$		−	1.74629e21i		−	1.17328i	0.809847	−	0.586641i	$-0.199550\pi$
$132$	−1.58776e21	+	4.68288e20i	−0.988658	+	0.291590i
$133$	1.52185e21			0.878729
$134$	1.08631e21	−	1.56856e20i	0.581979	−	0.0840338i
$135$			4.27784e20i			0.212758i
$136$	1.31649e21	+	2.86899e21i	0.608177	+	1.32538i
$137$	1.89259e21			0.812550			0.406275	−	0.913751i	$-0.366827\pi$
$137$	1.89259e21			0.812550			0.406275	+	0.913751i	$0.366827\pi$
$138$	1.50063e19	+	1.03927e20i	0.00599076	+	0.0414892i
$139$			8.14526e20i			0.302522i	0.988494	+	0.151261i	$0.0483334\pi$
$139$			8.14526e20i			0.302522i	−0.988494	+	0.151261i	$0.951667\pi$
$140$	6.12525e20	+	2.07681e21i	0.211760	+	0.717986i
$141$	1.32970e21			0.428117
$142$	−3.21065e21	+	4.63596e20i	−0.963185	+	0.139077i
$143$			1.11417e22i			3.11594i
$144$	−1.07339e21	+	6.93484e20i	−0.279983	+	0.180889i
$145$	−3.59713e21			−0.875540
$146$	−5.23462e20	−	3.62525e21i	−0.118948	−	0.823777i
$147$		−	1.47309e21i		−	0.312648i
$148$	1.54282e21	−	4.55031e20i	0.305983	−	0.0902451i
$149$	3.57345e21			0.662559			0.331280	−	0.943533i	$-0.392520\pi$
$149$	3.57345e21			0.662559			0.331280	+	0.943533i	$0.392520\pi$
$150$	−7.32132e20	+	1.05715e20i	−0.126963	+	0.0183326i
$151$		−	4.95119e21i		−	0.803416i	−0.915768	−	0.401708i	$-0.868417\pi$
$151$		−	4.95119e21i		−	0.803416i	0.915768	−	0.401708i	$-0.131583\pi$
$152$	−7.76494e21	+	3.56310e21i	−1.17951	+	0.541243i
$153$	−3.41685e21			−0.486085
$154$	−1.29614e21	−	8.97646e21i	−0.172760	−	1.19646i
$155$		−	7.36878e21i		−	0.920616i
$156$	2.43316e21	+	8.24980e21i	0.285052	+	0.966491i
$157$	1.09000e22			1.19792			0.598961	−	0.800778i	$-0.295581\pi$
$157$	1.09000e22			1.19792			0.598961	+	0.800778i	$0.295581\pi$
$158$	−2.48275e21	+	3.58492e20i	−0.256072	+	0.0369751i
$159$			2.50511e21i			0.242580i
$160$	−7.98771e21	−	9.16241e21i	−0.726478	−	0.833316i
$161$	−5.75301e20			−0.0491628
$162$	−1.97685e20	−	1.36907e21i	−0.0158790	−	0.109971i
$163$			2.02598e22i			1.53024i	0.643887	+	0.765120i	$0.277321\pi$
$163$			2.02598e22i			1.53024i	−0.643887	+	0.765120i	$0.722679\pi$
$164$	−1.73695e22	+	5.12288e21i	−1.23409	+	0.363978i
$165$	1.70438e22			1.13953
$166$	6.21199e21	−	8.96968e20i	0.390975	−	0.0564542i
$167$		−	3.04146e22i		−	1.80267i	−0.433119	−	0.901337i	$-0.642587\pi$
$167$		−	3.04146e22i		−	1.80267i	0.433119	−	0.901337i	$-0.357413\pi$
$168$	−2.92004e21	−	6.36353e21i	−0.163040	−	0.355308i
$169$	3.88856e22			2.04608
$170$	−4.64469e21	−	3.21670e22i	−0.230392	−	1.59559i
$171$		−	9.24774e21i		−	0.432588i
$172$	7.68858e21	+	2.60687e22i	0.339282	+	1.15036i
$173$	−1.71792e22			−0.715388			−0.357694	−	0.933839i	$-0.616437\pi$
$173$	−1.71792e22			−0.715388			−0.357694	+	0.933839i	$0.616437\pi$
$174$	1.15122e22	−	1.66228e21i	0.452549	−	0.0653450i
$175$		−	4.05283e21i		−	0.150445i
$176$	2.76298e22	+	4.27660e22i	0.968839	+	1.49959i
$177$	4.72067e21			0.156412
$178$	−6.61086e21	−	4.57837e22i	−0.207042	−	1.43387i
$179$		−	1.20931e22i		−	0.358104i	−0.983840	−	0.179052i	$-0.942697\pi$
$179$		−	1.20931e22i		−	0.358104i	0.983840	−	0.179052i	$-0.0573030\pi$
$180$	1.26200e22	−	3.72209e21i	0.353456	−	0.104247i
$181$	−5.69846e22			−1.50998			−0.754991	−	0.655736i	$-0.772359\pi$
$181$	−5.69846e22			−1.50998			−0.754991	+	0.655736i	$0.772359\pi$
$182$	−4.66405e22	+	6.73456e21i	−1.16963	+	0.168887i
$183$			8.70264e20i			0.0206605i
$184$	2.93536e21	−	1.34695e21i	0.0659908	−	0.0302812i
$185$	−1.65613e22			−0.352677
$186$	3.40521e21	+	2.35829e22i	0.0687092	+	0.475848i
$187$			1.36135e23i			2.60347i
$188$	−1.15696e22	−	3.92274e22i	−0.209767	−	0.711232i
$189$	7.57872e21			0.130310
$190$	8.70602e22	−	1.25709e22i	1.41998	−	0.205036i
$191$		−	1.90856e22i		−	0.295374i	−0.989034	−	0.147687i	$-0.952817\pi$
$191$		−	1.90856e22i		−	0.295374i	0.989034	−	0.147687i	$-0.0471829\pi$
$192$	2.97978e22	+	2.56320e22i	0.437696	+	0.376505i
$193$	−1.15093e23			−1.60500			−0.802500	−	0.596653i	$-0.796497\pi$
$193$	−1.15093e23			−1.60500			−0.802500	+	0.596653i	$0.796497\pi$
$194$	8.72803e21	+	6.04463e22i	0.115584	+	0.800484i
$195$		−	8.85574e22i		−	1.11398i
$196$	−4.34574e22	+	1.28171e22i	−0.519402	+	0.153190i
$197$	−4.40537e22			−0.500403			−0.250202	−	0.968194i	$-0.580497\pi$
$197$	−4.40537e22			−0.500403			−0.250202	+	0.968194i	$0.580497\pi$
$198$	−5.45467e22	+	7.87618e21i	−0.589002	+	0.0850479i
$199$			2.03521e22i			0.208968i	0.994527	+	0.104484i	$0.0333191\pi$
$199$			2.03521e22i			0.208968i	−0.994527	+	0.104484i	$0.966681\pi$
$200$	9.48887e21	+	2.06788e22i	0.0926648	+	0.201941i
$201$	3.65416e22			0.339490
$202$	4.96226e21	+	3.43663e22i	0.0438698	+	0.303822i
$203$			6.37275e22i			0.536249i
$204$	2.97296e22	+	1.00800e23i	0.238170	+	0.807533i
$205$	1.86452e23			1.42243
$206$	9.02869e22	−	1.30368e22i	0.656074	−	0.0947326i
$207$			3.49590e21i			0.0242022i
$208$	2.22206e23	−	1.43561e23i	1.46596	−	0.947116i
$209$	−3.68449e23			−2.31694
$210$	1.03021e22	+	7.13477e22i	0.0617637	+	0.427747i
$211$		−	5.93491e22i		−	0.339305i	−0.985504	−	0.169652i	$-0.945736\pi$
$211$		−	5.93491e22i		−	0.339305i	0.985504	−	0.169652i	$-0.0542645\pi$
$212$	7.39030e22	−	2.17966e22i	0.402998	−	0.118859i
$213$	−1.08001e23			−0.561862
$214$	4.32944e22	−	6.25141e21i	0.214928	−	0.0310342i
$215$		−	2.79834e23i		−	1.32591i
$216$	−3.86689e22	+	1.77440e22i	−0.174914	+	0.0802629i
$217$	−1.30547e23			−0.563858
$218$	3.22435e22	+	2.23304e23i	0.133008	+	0.921152i
$219$		−	1.21947e23i		−	0.480541i
$220$	−1.48296e23	−	5.02808e23i	−0.558345	−	1.89311i
$221$	7.07337e23			2.54509
$222$	5.30026e22	−	7.65321e21i	0.182292	−	0.0263217i
$223$			3.83956e23i			1.26250i	0.775578	+	0.631252i	$0.217459\pi$
$223$			3.83956e23i			1.26250i	−0.775578	+	0.631252i	$0.782541\pi$
$224$	−1.62323e23	+	1.41512e23i	−0.510388	+	0.444952i
$225$	−2.46276e22			−0.0740623
$226$	−8.29047e22	−	5.74159e23i	−0.238503	−	1.65176i
$227$		−	1.92172e23i		−	0.528970i	−0.964390	−	0.264485i	$-0.914798\pi$
$227$		−	1.92172e23i		−	0.528970i	0.964390	−	0.264485i	$-0.0852020\pi$
$228$	−2.72817e23	+	8.04634e22i	−0.718659	+	0.211958i
$229$	−3.53044e23			−0.890172			−0.445086	−	0.895488i	$-0.646827\pi$
$229$	−3.53044e23			−0.890172			−0.445086	+	0.895488i	$0.646827\pi$
$230$	−3.29112e22	+	4.75215e21i	−0.0794447	+	0.0114713i
$231$		−	3.01952e23i		−	0.697940i
$232$	−1.49205e23	−	3.25157e23i	−0.330296	−	0.719803i
$233$	6.59035e23			1.39749			0.698746	−	0.715370i	$-0.253742\pi$
$233$	6.59035e23			1.39749			0.698746	+	0.715370i	$0.253742\pi$
$234$	4.09236e22	+	2.83418e23i	0.0831409	+	0.575796i
$235$			4.21086e23i			0.819770i
$236$	−4.10739e22	−	1.39264e23i	−0.0766383	−	0.259848i
$237$	−8.35153e22			−0.149377
$238$	−5.69878e23	+	8.22864e22i	−0.977264	+	0.141110i
$239$		−	1.38342e22i		−	0.0227497i	−0.999935	−	0.0113749i	$-0.996379\pi$
$239$		−	1.38342e22i		−	0.0227497i	0.999935	−	0.0113749i	$-0.00362081\pi$
$240$	−2.19611e23	−	3.39917e23i	−0.346370	−	0.536119i
$241$	3.84170e23			0.581236			0.290618	−	0.956839i	$-0.406139\pi$
$241$	3.84170e23			0.581236			0.290618	+	0.956839i	$0.406139\pi$
$242$	2.15352e23	+	1.49143e24i	0.312605	+	2.16496i
$243$		−	4.60532e22i		−	0.0641500i
$244$	2.56736e22	−	7.57206e21i	0.0343233	−	0.0101232i
$245$	4.66493e23			0.598666
$246$	−5.96720e23	+	8.61622e22i	−0.735223	+	0.106161i
$247$			1.91441e24i			2.26499i
$248$	6.66090e23	−	3.05649e23i	0.756861	−	0.347301i
$249$	2.08960e23			0.228071
$250$	1.17195e23	+	8.11640e23i	0.122888	+	0.851066i
$251$		−	1.38623e23i		−	0.139668i	−0.997559	−	0.0698340i	$-0.977753\pi$
$251$		−	1.38623e23i		−	0.139668i	0.997559	−	0.0698340i	$-0.0222469\pi$
$252$	−6.59415e22	−	2.23579e23i	−0.0638489	−	0.216484i
$253$	1.39284e23			0.129627
$254$	1.57118e23	−	2.26868e22i	0.140569	−	0.0202972i
$255$		−	1.08204e24i		−	0.930768i
$256$	4.96901e23	−	1.10208e24i	0.411027	−	0.911623i
$257$	2.39752e23			0.190735			0.0953676	−	0.995442i	$-0.469597\pi$
$257$	2.39752e23			0.190735			0.0953676	+	0.995442i	$0.469597\pi$
$258$	1.29315e23	+	8.95575e23i	0.0989582	+	0.685338i
$259$			2.93404e23i			0.216007i
$260$	−2.61253e24	+	7.70526e23i	−1.85066	+	0.545826i
$261$	3.87249e23			0.263989
$262$	−1.76984e24	+	2.55553e23i	−1.16124	+	0.167675i
$263$		−	9.73850e23i		−	0.615084i	−0.951534	−	0.307542i	$-0.900493\pi$
$263$		−	9.73850e23i		−	0.615084i	0.951534	−	0.307542i	$-0.0995065\pi$
$264$	7.06959e23	+	1.54065e24i	0.429888	+	0.936839i
$265$	−7.93310e23			−0.464499
$266$	−2.22709e23	−	1.54238e24i	−0.125580	−	0.869710i
$267$		−	1.54008e24i		−	0.836433i
$268$	−3.17944e23	−	1.07801e24i	−0.166342	−	0.563996i
$269$	−1.37770e23			−0.0694433			−0.0347217	−	0.999397i	$-0.511054\pi$
$269$	−1.37770e23			−0.0694433			−0.0347217	+	0.999397i	$0.511054\pi$
$270$	4.33555e23	−	6.26023e22i	0.210575	−	0.0304055i
$271$			2.26479e24i			1.06007i	0.847975	+	0.530037i	$0.177822\pi$
$271$			2.26479e24i			1.06007i	−0.847975	+	0.530037i	$0.822178\pi$
$272$	2.71503e24	−	1.75410e24i	1.22486	−	0.791345i
$273$	−1.56890e24			−0.682290
$274$	−2.76963e23	−	1.91812e24i	−0.116122	−	0.804210i
$275$			9.81215e23i			0.396677i
$276$	1.03132e23	−	3.04174e22i	0.0402072	−	0.0118585i
$277$	−2.19671e24			−0.825990			−0.412995	−	0.910733i	$-0.635517\pi$
$277$	−2.19671e24			−0.825990			−0.412995	+	0.910733i	$0.635517\pi$
$278$	8.25514e23	−	1.19198e23i	0.299417	−	0.0432337i
$279$			7.93288e23i			0.277580i
$280$	2.01519e24	−	9.24709e23i	0.680354	−	0.312194i
$281$	−2.35803e24			−0.768222			−0.384111	−	0.923287i	$-0.625492\pi$
$281$	−2.35803e24			−0.768222			−0.384111	+	0.923287i	$0.625492\pi$
$282$	−1.94590e23	−	1.34764e24i	−0.0611827	−	0.423723i
$283$		−	5.72905e24i		−	1.73867i	−0.494219	−	0.869337i	$-0.664546\pi$
$283$		−	5.72905e24i		−	1.73867i	0.494219	−	0.869337i	$-0.335454\pi$
$284$	9.39699e23	+	3.18612e24i	0.275299	+	0.933423i
$285$	2.92855e24			0.828331
$286$	1.12919e25	−	1.63048e24i	3.08396	−	0.445303i
$287$		−	3.30323e24i		−	0.871205i
$288$	8.59919e23	+	9.86381e23i	0.219045	+	0.251258i
$289$	4.57838e24			1.12651
$290$	5.26407e23	+	3.64565e24i	0.125124	+	0.866553i
$291$			2.03330e24i			0.466952i
$292$	−3.59755e24	+	1.06105e24i	−0.798323	+	0.235454i
$293$	−8.31644e24			−1.78345			−0.891726	−	0.452576i	$-0.850505\pi$
$293$	−8.31644e24			−1.78345			−0.891726	+	0.452576i	$0.850505\pi$
$294$	−1.49296e24	+	2.15573e23i	−0.309438	+	0.0446808i
$295$			1.49493e24i			0.299502i
$296$	−6.86946e23	−	1.49704e24i	−0.133047	−	0.289945i
$297$	−1.83485e24			−0.343587
$298$	−5.22941e23	−	3.62165e24i	−0.0946870	−	0.655758i
$299$		−	7.23701e23i		−	0.126721i
$300$	2.14282e23	+	7.26537e23i	0.0362888	+	0.123040i
$301$	−4.95760e24			−0.812094
$302$	−5.01798e24	+	7.24562e23i	−0.795169	+	0.114817i
$303$			1.15602e24i			0.177231i
$304$	4.74749e24	+	7.34825e24i	0.704252	+	1.09005i
$305$	−2.75593e23			−0.0395612
$306$	5.00025e23	+	3.46294e24i	0.0694669	+	0.481095i
$307$			1.07096e25i			1.44009i	0.693927	+	0.720045i	$0.255879\pi$
$307$			1.07096e25i			1.44009i	−0.693927	+	0.720045i	$0.744121\pi$
$308$	−8.90786e24	+	2.62725e24i	−1.15949	+	0.341974i
$309$	3.03709e24			0.382713
$310$	−7.46818e24	+	1.07835e24i	−0.911167	+	0.131566i
$311$		−	7.26237e24i		−	0.857975i	−0.903311	−	0.428987i	$-0.858871\pi$
$311$		−	7.26237e24i		−	0.857975i	0.903311	−	0.428987i	$-0.141129\pi$
$312$	8.00502e24	−	3.67326e24i	0.915833	−	0.420249i
$313$	1.94087e24			0.215057			0.107528	−	0.994202i	$-0.465706\pi$
$313$	1.94087e24			0.215057			0.107528	+	0.994202i	$0.465706\pi$
$314$	−1.59511e24	−	1.10470e25i	−0.171196	−	1.18563i
$315$			2.40001e24i			0.249521i
$316$	7.26656e23	+	2.46378e24i	0.0731911	+	0.248160i
$317$	−2.82908e24			−0.276092			−0.138046	−	0.990426i	$-0.544082\pi$
$317$	−2.82908e24			−0.276092			−0.138046	+	0.990426i	$0.544082\pi$
$318$	2.53890e24	−	3.66599e23i	0.240090	−	0.0346673i
$319$		−	1.54288e25i		−	1.41392i
$320$	−8.11707e24	+	9.43630e24i	−0.720941	+	0.838111i
$321$	1.45635e24			0.125376
$322$	8.41901e22	+	5.83062e23i	0.00702590	+	0.0486582i
$323$			2.33913e25i			1.89247i
$324$	−1.35861e24	+	4.00703e23i	−0.106573	+	0.0314320i
$325$	5.09826e24			0.387783
$326$	2.05331e25	−	2.96484e24i	1.51453	−	0.218688i
$327$			7.51154e24i			0.537343i
$328$	7.73385e24	+	1.68541e25i	0.536608	+	1.16941i
$329$	7.46005e24			0.502091
$330$	−2.49421e24	−	1.72737e25i	−0.162852	−	1.12784i
$331$			1.73285e24i			0.109769i	0.998493	+	0.0548845i	$0.0174791\pi$
$331$			1.73285e24i			0.109769i	−0.998493	+	0.0548845i	$0.982521\pi$
$332$	−1.81813e24	−	6.16452e24i	−0.111749	−	0.378894i
$333$	1.78291e24			0.106338
$334$	−3.08249e25	+	4.45090e24i	−1.78417	+	0.257622i
$335$			1.15719e25i			0.650065i
$336$	−6.02205e24	+	3.89067e24i	−0.328361	+	0.212144i
$337$	3.04700e25			1.61277			0.806386	−	0.591390i	$-0.201421\pi$
$337$	3.04700e25			1.61277			0.806386	+	0.591390i	$0.201421\pi$
$338$	−5.69055e24	−	3.94101e25i	−0.292407	−	2.02507i
$339$		−	1.93137e25i		−	0.963537i
$340$	−3.19212e25	+	9.41469e24i	−1.54629	+	0.456055i
$341$	3.16062e25			1.48672
$342$	−9.37248e24	+	1.35332e24i	−0.428148	+	0.0618216i
$343$		−	2.35261e25i		−	1.04378i
$344$	2.52952e25	−	1.16072e25i	1.09007	−	0.500199i
$345$	−1.10707e24			−0.0463431
$346$	2.51402e24	+	1.74109e25i	0.102237	+	0.708045i
$347$		−	2.76615e25i		−	1.09290i	−0.837491	−	0.546451i	$-0.815978\pi$
$347$		−	2.76615e25i		−	1.09290i	0.837491	−	0.546451i	$-0.184022\pi$
$348$	−3.36941e24	−	1.14242e25i	−0.129348	−	0.438565i
$349$	−1.70171e25			−0.634793			−0.317397	−	0.948293i	$-0.602809\pi$
$349$	−1.70171e25			−0.634793			−0.317397	+	0.948293i	$0.602809\pi$
$350$	−4.10750e24	+	5.93094e23i	−0.148901	+	0.0215002i
$351$			9.53366e24i			0.335883i
$352$	3.92995e25	−	3.42610e25i	1.34574	−	1.17320i
$353$	3.25734e24			0.108422			0.0542108	−	0.998530i	$-0.482736\pi$
$353$	3.25734e24			0.108422			0.0542108	+	0.998530i	$0.482736\pi$
$354$	−6.90826e23	−	4.78434e24i	−0.0223530	−	0.154807i
$355$		−	3.42013e25i		−	1.07587i
$356$	−4.54339e25	+	1.34001e25i	−1.38957	+	0.409833i
$357$	−1.91697e25			−0.570075
$358$	−1.22563e25	+	1.76972e24i	−0.354428	+	0.0511770i
$359$			4.44193e25i			1.24919i	0.780951	+	0.624593i	$0.214735\pi$
$359$			4.44193e25i			1.24919i	−0.780951	+	0.624593i	$0.785265\pi$
$360$	−5.61913e24	−	1.22456e25i	−0.153689	−	0.334930i
$361$	−2.57187e25			−0.684191
$362$	8.33917e24	+	5.77532e25i	0.215793	+	1.49448i
$363$			5.01691e25i			1.26290i
$364$	1.36508e25	+	4.62841e25i	0.334306	+	1.13349i
$365$	3.86179e25			0.920152
$366$	8.82004e23	−	1.27355e23i	0.0204484	−	0.00295261i
$367$		−	7.53343e25i		−	1.69954i	−0.527150	−	0.849772i	$-0.676740\pi$
$367$		−	7.53343e25i		−	1.69954i	0.527150	−	0.849772i	$-0.323260\pi$
$368$	−1.79468e24	−	2.77784e24i	−0.0394012	−	0.0609859i
$369$	−2.00726e25			−0.428884
$370$	2.42360e24	+	1.67847e25i	0.0504015	+	0.349057i
$371$			1.40545e25i			0.284495i
$372$	2.34027e25	−	6.90229e24i	0.461145	−	0.136008i
$373$	−3.78754e25			−0.726556			−0.363278	−	0.931681i	$-0.618342\pi$
$373$	−3.78754e25			−0.726556			−0.363278	+	0.931681i	$0.618342\pi$
$374$	1.37971e26	−	1.99220e25i	2.57675	−	0.372064i
$375$			2.73021e25i			0.496459i
$376$	−3.80635e25	+	1.74662e25i	−0.673953	+	0.309257i
$377$	−8.01661e25			−1.38222
$378$	−1.10908e24	−	7.68095e24i	−0.0186227	−	0.128972i
$379$			4.90924e25i			0.802828i	0.915897	+	0.401414i	$0.131481\pi$
$379$			4.90924e25i			0.802828i	−0.915897	+	0.401414i	$0.868519\pi$
$380$	−2.54809e25	−	8.63949e25i	−0.405863	−	1.37611i
$381$	5.28518e24			0.0819992
$382$	−1.93431e25	+	2.79301e24i	−0.292342	+	0.0422122i
$383$			6.52213e25i			0.960288i	0.877190	+	0.480144i	$0.159416\pi$
$383$			6.52213e25i			0.960288i	−0.877190	+	0.480144i	$0.840584\pi$
$384$	2.16171e25	−	3.39508e25i	0.310088	−	0.487010i
$385$	9.56213e25			1.33643
$386$	1.68428e25	+	1.16645e26i	0.229372	+	1.58852i
$387$			3.01255e25i			0.399784i
$388$	5.99844e25	−	1.76915e25i	0.775749	−	0.228796i
$389$	−1.29988e25			−0.163836			−0.0819179	−	0.996639i	$-0.526105\pi$
$389$	−1.29988e25			−0.163836			−0.0819179	+	0.996639i	$0.526105\pi$
$390$	−8.97519e25	+	1.29596e25i	−1.10255	+	0.159200i
$391$		−	8.84256e24i		−	0.105879i
$392$	1.93496e25	+	4.21680e25i	0.225846	+	0.492178i
$393$	−5.95343e25			−0.677395
$394$	6.44686e24	+	4.46479e25i	0.0715131	+	0.495267i
$395$		−	2.64474e25i		−	0.286030i
$396$	1.59648e25	+	5.41299e25i	0.168350	+	0.570802i
$397$	−1.67468e26			−1.72198			−0.860989	−	0.508623i	$-0.830155\pi$
$397$	−1.67468e26			−1.72198			−0.860989	+	0.508623i	$0.830155\pi$
$398$	2.06267e25	−	2.97835e24i	0.206823	−	0.0298638i
$399$		−	5.18828e25i		−	0.507335i
$400$	1.95691e25	−	1.26430e25i	0.186625	−	0.120573i
$401$	−6.60499e25			−0.614368			−0.307184	−	0.951650i	$-0.599387\pi$
$401$	−6.60499e25			−0.614368			−0.307184	+	0.951650i	$0.599387\pi$
$402$	−5.34754e24	−	3.70346e25i	−0.0485169	−	0.336006i
$403$		−	1.64222e26i		−	1.45338i
$404$	3.41037e25	−	1.00584e25i	0.294434	−	0.0868390i
$405$	1.45840e25			0.122836
$406$	6.45871e25	−	9.32594e24i	0.530745	−	0.0766359i
$407$		−	7.10349e25i		−	0.569545i
$408$	9.78094e25	−	4.48819e25i	0.765207	−	0.351131i
$409$	4.92346e25			0.375870			0.187935	−	0.982181i	$-0.439821\pi$
$409$	4.92346e25			0.375870			0.187935	+	0.982181i	$0.439821\pi$
$410$	−2.72856e25	−	1.88968e26i	−0.203280	−	1.40782i
$411$		−	6.45220e25i		−	0.469126i
$412$	−2.64253e25	−	8.95970e25i	−0.187520	−	0.635801i
$413$	2.64845e25			0.183439
$414$	3.54306e24	−	5.11593e23i	0.0239538	−	0.00345877i
$415$			6.61729e25i			0.436716i
$416$	−1.78015e26	−	2.04195e26i	−1.14690	−	1.31556i
$417$	2.77688e25			0.174661
$418$	5.39192e25	+	3.73419e26i	0.331116	+	2.29316i
$419$			6.27242e25i			0.376092i	0.982160	+	0.188046i	$0.0602155\pi$
$419$			6.27242e25i			0.376092i	−0.982160	+	0.188046i	$0.939785\pi$
$420$	7.08025e25	−	2.08822e25i	0.414530	−	0.122259i
$421$	2.72495e25			0.155790			0.0778948	−	0.996962i	$-0.475180\pi$
$421$	2.72495e25			0.155790			0.0778948	+	0.996962i	$0.475180\pi$
$422$	−6.01497e25	+	8.68521e24i	−0.335822	+	0.0484904i
$423$		−	4.53321e25i		−	0.247174i
$424$	−3.29057e25	−	7.17101e25i	−0.175231	−	0.381876i
$425$	6.22932e25			0.324005
$426$	1.58049e25	+	1.09457e26i	0.0802963	+	0.556095i
$427$			4.88247e24i			0.0242304i
$428$	−1.26715e25	−	4.29636e25i	−0.0614313	−	0.208287i
$429$	3.79841e26			1.79899
$430$	−2.83608e26	+	4.09511e25i	−1.31230	+	0.189488i
$431$		−	1.71033e26i		−	0.773229i	−0.922241	−	0.386614i	$-0.873644\pi$
$431$		−	1.71033e26i		−	0.773229i	0.922241	−	0.386614i	$-0.126356\pi$
$432$	2.36422e25	+	3.65939e25i	0.104436	+	0.161648i
$433$	1.71657e26			0.740937			0.370469	−	0.928845i	$-0.379197\pi$
$433$	1.71657e26			0.740937			0.370469	+	0.928845i	$0.379197\pi$
$434$	1.91044e25	+	1.32308e26i	0.0805815	+	0.558070i
$435$			1.22633e26i			0.505493i
$436$	2.21597e26	−	6.53569e25i	0.892688	−	0.263285i
$437$	2.39324e25			0.0942264
$438$	−1.23592e26	+	1.78458e25i	−0.475608	+	0.0686746i
$439$			4.75235e26i			1.78757i	0.448497	+	0.893785i	$0.351960\pi$
$439$			4.75235e26i			1.78757i	−0.448497	+	0.893785i	$0.648040\pi$
$440$	−4.87889e26	+	2.23878e26i	−1.79388	+	0.823160i
$441$	−5.02204e25			−0.180507
$442$	−1.03512e26	−	7.16878e26i	−0.363722	−	2.51897i
$443$		−	9.74245e24i		−	0.0334681i	−0.999860	−	0.0167340i	$-0.994673\pi$
$443$		−	9.74245e24i		−	0.0334681i	0.999860	−	0.0167340i	$-0.00532686\pi$
$444$	−1.55129e25	−	5.25976e25i	−0.0521030	−	0.176659i
$445$	4.87709e26			1.60162
$446$	3.89135e26	−	5.61884e25i	1.24954	−	0.180426i
$447$		−	1.21826e26i		−	0.382529i
$448$	1.67176e26	+	1.43804e26i	0.513325	+	0.441561i
$449$	−4.31250e26			−1.29499			−0.647494	−	0.762071i	$-0.724183\pi$
$449$	−4.31250e26			−1.29499			−0.647494	+	0.762071i	$0.724183\pi$
$450$	3.60402e24	+	2.49598e25i	0.0105843	+	0.0733020i
$451$			7.99733e26i			2.29710i
$452$	−5.69772e26	+	1.68046e26i	−1.60072	+	0.472111i
$453$	−1.68796e26			−0.463852
$454$	−1.94764e26	+	2.81226e25i	−0.523541	+	0.0755957i
$455$		−	4.96836e26i		−	1.30647i
$456$	1.21473e26	+	2.64722e26i	0.312487	+	0.680991i
$457$	−4.25914e26			−1.07191			−0.535957	−	0.844245i	$-0.680049\pi$
$457$	−4.25914e26			−1.07191			−0.535957	+	0.844245i	$0.680049\pi$
$458$	5.16648e25	+	3.57806e26i	0.127215	+	0.881035i
$459$			1.16487e26i			0.280641i
$460$	9.63250e24	+	3.26597e25i	0.0227070	+	0.0769899i
$461$	1.06987e26			0.246786			0.123393	−	0.992358i	$-0.460622\pi$
$461$	1.06987e26			0.246786			0.123393	+	0.992358i	$0.460622\pi$
$462$	−3.06025e26	+	4.41879e25i	−0.690776	+	0.0997433i
$463$		−	8.35601e26i		−	1.84582i	−0.385018	−	0.922909i	$-0.625805\pi$
$463$		−	8.35601e26i		−	1.84582i	0.385018	−	0.922909i	$-0.374195\pi$
$464$	−3.07708e26	+	1.98801e26i	−0.665211	+	0.429774i
$465$	−2.51216e26			−0.531518
$466$	−9.64438e25	−	6.67925e26i	−0.199717	−	1.38315i
$467$			8.44915e26i			1.71255i	0.516518	+	0.856277i	$0.327228\pi$
$467$			8.44915e26i			1.71255i	−0.516518	+	0.856277i	$0.672772\pi$
$468$	2.81252e26	−	8.29512e25i	0.558004	−	0.164575i
$469$	2.05010e26			0.398151
$470$	4.26766e26	−	6.16221e25i	0.811356	−	0.117154i
$471$		−	3.71601e26i		−	0.691620i
$472$	−1.35132e26	+	6.20080e25i	−0.246228	+	0.112987i
$473$	1.20026e27			2.14124
$474$	1.22217e25	+	8.46419e25i	0.0213476	+	0.147843i
$475$			1.68597e26i			0.288346i
$476$	1.66793e26	+	5.65523e26i	0.279324	+	0.947067i
$477$	8.54040e25			0.140054
$478$	−1.40208e25	+	2.02451e24i	−0.0225162	+	0.00325119i
$479$		−	5.38762e26i		−	0.847309i	−0.905824	−	0.423655i	$-0.860747\pi$
$479$		−	5.38762e26i		−	0.847309i	0.905824	−	0.423655i	$-0.139253\pi$
$480$	−3.12364e26	+	2.72317e26i	−0.481115	+	0.419432i
$481$	−3.69088e26			−0.556774
$482$	−5.62197e25	−	3.89352e26i	−0.0830650	−	0.575270i
$483$			1.96131e25i			0.0283841i
$484$	1.48003e27	−	4.36515e26i	2.09806	−	0.618793i
$485$	−6.43901e26			−0.894133
$486$	−4.66744e25	+	6.73946e24i	−0.0634916	+	0.00916775i
$487$			4.96422e26i			0.661548i	0.943710	+	0.330774i	$0.107310\pi$
$487$			4.96422e26i			0.661548i	−0.943710	+	0.330774i	$0.892690\pi$
$488$	−1.14313e25	−	2.49118e25i	−0.0149244	−	0.0325243i
$489$	6.90697e26			0.883485
$490$	−6.82670e25	−	4.72786e26i	−0.0855559	−	0.592521i
$491$		−	1.47525e27i		−	1.81155i	−0.423757	−	0.905776i	$-0.639289\pi$
$491$		−	1.47525e27i		−	1.81155i	0.423757	−	0.905776i	$-0.360711\pi$
$492$	1.74649e26	+	5.92160e26i	0.210143	+	0.712505i
$493$	−9.79511e26			−1.15489
$494$	1.94024e27	−	2.80157e26i	2.24174	−	0.323692i
$495$		−	5.81057e26i		−	0.657910i
$496$	−4.07248e26	−	6.30346e26i	−0.451900	−	0.699459i
$497$	−6.05918e26			−0.658946
$498$	−3.05794e25	−	2.11779e26i	−0.0325938	−	0.225730i
$499$			7.80592e26i			0.815490i	0.913096	+	0.407745i	$0.133685\pi$
$499$			7.80592e26i			0.815490i	−0.913096	+	0.407745i	$0.866315\pi$
$500$	8.05438e26	−	2.37552e26i	0.824768	−	0.243253i
$501$	−1.03689e27			−1.04077
$502$	−1.40492e26	+	2.02861e25i	−0.138234	+	0.0199601i
$503$			1.18976e27i			1.14757i	0.819005	+	0.573786i	$0.194526\pi$
$503$			1.18976e27i			1.14757i	−0.819005	+	0.573786i	$0.805474\pi$
$504$	−2.16945e26	+	9.95497e25i	−0.205137	+	0.0941315i
$505$	−3.66086e26			−0.339366
$506$	−2.03829e25	−	1.41163e26i	−0.0185251	−	0.128297i
$507$		−	1.32569e27i		−	1.18130i
$508$	−4.59857e25	−	1.55918e26i	−0.0401777	−	0.136225i
$509$	−6.35580e26			−0.544493			−0.272247	−	0.962227i	$-0.587767\pi$
$509$	−6.35580e26			−0.544493			−0.272247	+	0.962227i	$0.587767\pi$
$510$	−1.09664e27	+	1.58347e26i	−0.921214	+	0.133017i
$511$		−	6.84163e26i		−	0.563573i
$512$	−1.18967e27	−	3.42324e26i	−0.961006	−	0.276527i
$513$	−3.15273e26			−0.249755
$514$	−3.50855e25	−	2.42986e26i	−0.0272582	−	0.188777i
$515$			9.61778e26i			0.732829i
$516$	8.88732e26	−	2.62119e26i	0.664162	−	0.195885i
$517$	−1.80612e27			−1.32386
$518$	2.97362e26	−	4.29370e25i	0.213790	−	0.0308698i
$519$			5.85672e26i			0.413029i
$520$	1.16324e27	+	2.53501e27i	0.804703	+	1.75366i
$521$	1.33512e27			0.906031			0.453016	−	0.891503i	$-0.350348\pi$
$521$	1.33512e27			0.906031			0.453016	+	0.891503i	$0.350348\pi$
$522$	−5.66704e25	−	3.92473e26i	−0.0377269	−	0.261279i
$523$			1.77267e27i			1.15774i	0.815419	+	0.578871i	$0.196507\pi$
$523$			1.77267e27i			1.15774i	−0.815419	+	0.578871i	$0.803493\pi$
$524$	5.18000e26	+	1.75632e27i	0.331908	+	1.12536i
$525$	−1.38169e26			−0.0868595
$526$	−9.86987e26	+	1.42514e26i	−0.608771	+	0.0879023i
$527$		−	2.00655e27i		−	1.21435i
$528$	1.45798e27	−	9.41955e26i	0.865787	−	0.559360i
$529$	1.70711e27			0.994728
$530$	1.16094e26	+	8.04011e26i	0.0663820	+	0.459731i
$531$		−	1.60937e26i		−	0.0903046i
$532$	−1.53059e27	+	4.51426e26i	−0.842836	+	0.248582i
$533$	4.15531e27			2.24559
$534$	−1.56086e27	+	2.25377e26i	−0.827848	+	0.119536i
$535$			4.61192e26i			0.240073i
$536$	−1.04603e27	+	4.79990e26i	−0.534435	+	0.245236i
$537$	−4.12279e26			−0.206751
$538$	2.01613e25	+	1.39628e26i	0.00992422	+	0.0687305i
$539$			2.00089e27i			0.966796i
$540$	−1.26893e26	−	4.30242e26i	−0.0601869	−	0.204068i
$541$	8.57341e26			0.399191			0.199596	−	0.979878i	$-0.436037\pi$
$541$	8.57341e26			0.399191			0.199596	+	0.979878i	$0.436037\pi$
$542$	2.29534e27	−	3.31432e26i	1.04919	−	0.151496i
$543$			1.94272e27i			0.871788i
$544$	−2.17508e27	−	2.49496e27i	−0.958268	−	1.09919i
$545$	−2.37873e27			−1.02892
$546$	2.29594e26	+	1.59007e27i	0.0975068	+	0.675287i
$547$			1.06428e27i			0.443794i	0.975070	+	0.221897i	$0.0712249\pi$
$547$			1.06428e27i			0.443794i	−0.975070	+	0.221897i	$0.928775\pi$
$548$	−1.90346e27	+	5.61398e26i	−0.779360	+	0.229861i
$549$	2.96690e25			0.0119283
$550$	9.94451e26	−	1.43592e26i	0.392605	−	0.0566895i
$551$		−	2.65105e27i		−	1.02779i
$552$	−4.59202e25	−	1.00072e26i	−0.0174829	−	0.0380998i
$553$	−4.68548e26			−0.175187
$554$	3.21468e26	+	2.22634e27i	0.118043	+	0.817511i
$555$			5.64608e26i			0.203618i
$556$	−2.41613e26	−	8.19205e26i	−0.0855799	−	0.290165i
$557$	−3.41193e27			−1.18699			−0.593497	−	0.804836i	$-0.702253\pi$
$557$	−3.41193e27			−1.18699			−0.593497	+	0.804836i	$0.702253\pi$
$558$	8.03988e26	−	1.16090e26i	0.274731	−	0.0396693i
$559$		−	6.23642e27i		−	2.09323i
$560$	−1.23209e27	−	1.90705e27i	−0.406220	−	0.628754i
$561$	4.64109e27			1.50311
$562$	3.45077e26	+	2.38984e27i	0.109787	+	0.760336i
$563$			2.48038e27i			0.775235i	0.921820	+	0.387618i	$0.126702\pi$
$563$			2.48038e27i			0.775235i	−0.921820	+	0.387618i	$0.873298\pi$
$564$	−1.33734e27	+	3.94429e26i	−0.410630	+	0.121109i
$565$	6.11621e27			1.84501
$566$	−5.80633e27	+	8.38394e26i	−1.72083	+	0.248476i
$567$		−	2.58373e26i		−	0.0752345i
$568$	3.09158e27	−	1.41863e27i	0.884498	−	0.405870i
$569$	6.57681e26			0.184881			0.0924405	−	0.995718i	$-0.470533\pi$
$569$	6.57681e26			0.184881			0.0924405	+	0.995718i	$0.470533\pi$
$570$	−4.28566e26	−	2.96805e27i	−0.118378	−	0.819828i
$571$		−	1.76246e27i		−	0.478365i	−0.970975	−	0.239182i	$-0.923121\pi$
$571$		−	1.76246e27i		−	0.478365i	0.970975	−	0.239182i	$-0.0768794\pi$
$572$	−3.30495e27	−	1.12057e28i	−0.881463	−	2.98867i
$573$	−6.50666e26			−0.170534
$574$	−3.34779e27	+	4.83398e26i	−0.862262	+	0.124505i
$575$		−	6.37344e25i		−	0.0161323i
$576$	8.73845e26	−	1.01587e27i	0.217375	−	0.252704i
$577$	1.23824e26			0.0302723			0.0151362	−	0.999885i	$-0.495182\pi$
$577$	1.23824e26			0.0302723			0.0151362	+	0.999885i	$0.495182\pi$
$578$	−6.70004e26	−	4.64014e27i	−0.160990	−	1.11494i
$579$			3.92374e27i			0.926647i
$580$	3.61779e27	−	1.06702e27i	0.839776	−	0.247680i
$581$	1.17233e27			0.267479
$582$	2.06073e27	−	2.97556e26i	0.462159	−	0.0667326i
$583$		−	3.40267e27i		−	0.750127i
$584$	1.60183e27	+	3.49081e27i	0.347126	+	0.756480i
$585$	−3.01909e27			−0.643158
$586$	1.21704e27	+	8.42862e27i	0.254875	+	1.76515i
$587$			5.22995e27i			1.07675i	0.842704	+	0.538377i	$0.180962\pi$
$587$			5.22995e27i			1.07675i	−0.842704	+	0.538377i	$0.819038\pi$
$588$	4.36961e26	+	1.48155e27i	0.0884443	+	0.299877i
$589$	5.43073e27			1.08070
$590$	1.51509e27	−	2.18769e26i	0.296428	−	0.0428022i
$591$			1.50188e27i			0.288908i
$592$	−1.41670e27	+	9.15290e26i	−0.267955	+	0.173118i
$593$	1.48959e27			0.277025			0.138513	−	0.990361i	$-0.455768\pi$
$593$	1.48959e27			0.277025			0.138513	+	0.990361i	$0.455768\pi$
$594$	2.68514e26	+	1.85961e27i	0.0491024	+	0.340061i
$595$		−	6.07059e27i		−	1.09160i
$596$	−3.59398e27	+	1.05999e27i	−0.635496	+	0.187430i
$597$	6.93844e26			0.120648
$598$	−7.33463e26	+	1.05907e26i	−0.125420	+	0.0181098i
$599$		−	2.24227e27i		−	0.377069i	−0.982067	−	0.188534i	$-0.939626\pi$
$599$		−	2.24227e27i		−	0.377069i	0.982067	−	0.188534i	$-0.0603737\pi$
$600$	7.04980e26	−	3.23494e26i	0.116591	−	0.0535000i
$601$	−4.22517e27			−0.687226			−0.343613	−	0.939111i	$-0.611651\pi$
$601$	−4.22517e27			−0.687226			−0.343613	+	0.939111i	$0.611651\pi$
$602$	7.25499e26	+	5.02447e27i	0.116057	+	0.803758i
$603$		−	1.24578e27i		−	0.196005i
$604$	1.46867e27	+	4.97964e27i	0.227277	+	0.770599i
$605$	−1.58874e28			−2.41824
$606$	1.17161e27	−	1.69173e26i	0.175412	−	0.0253282i
$607$		−	1.95058e27i		−	0.287260i	−0.989631	−	0.143630i	$-0.954122\pi$
$607$		−	1.95058e27i		−	0.287260i	0.989631	−	0.143630i	$-0.0458776\pi$
$608$	6.75262e27	−	5.88688e27i	0.978220	−	0.852804i
$609$	2.17260e27			0.309604
$610$	4.03305e25	+	2.79310e26i	0.00565373	+	0.0391551i
$611$			9.38438e27i			1.29418i
$612$	3.43648e27	−	1.01354e27i	0.466230	−	0.137508i
$613$	−8.10387e27			−1.08165			−0.540826	−	0.841134i	$-0.681888\pi$
$613$	−8.10387e27			−1.08165			−0.540826	+	0.841134i	$0.681888\pi$
$614$	1.08541e28	−	1.56725e27i	1.42531	−	0.205805i
$615$		−	6.35653e27i		−	0.821238i
$616$	3.96627e27	+	8.64355e27i	0.504168	+	1.09871i
$617$	4.80286e27			0.600688			0.300344	−	0.953831i	$-0.402899\pi$
$617$	4.80286e27			0.600688			0.300344	+	0.953831i	$0.402899\pi$
$618$	−4.44451e26	−	3.07806e27i	−0.0546939	−	0.378784i
$619$			1.27541e28i			1.54434i	0.635414	+	0.772172i	$0.280829\pi$
$619$			1.27541e28i			1.54434i	−0.635414	+	0.772172i	$0.719171\pi$
$620$	2.18580e27	+	7.41111e27i	0.260431	+	0.883012i
$621$	1.19182e26			0.0139732
$622$	−7.36033e27	+	1.06278e27i	−0.849168	+	0.122614i
$623$		−	8.64036e27i		−	0.980961i
$624$	−4.89428e27	−	7.57545e27i	−0.546818	−	0.846374i
$625$	−1.06667e28			−1.17282
$626$	−2.84028e26	−	1.96705e27i	−0.0307340	−	0.212849i
$627$			1.25612e28i			1.33769i
$628$	−1.09626e28	+	3.23325e27i	−1.14899	+	0.338878i
$629$	−4.50971e27			−0.465203
$630$	2.43238e27	−	3.51219e26i	0.246960	−	0.0356593i
$631$		−	9.27205e27i		−	0.926578i	−0.886207	−	0.463289i	$-0.846669\pi$
$631$		−	9.27205e27i		−	0.926578i	0.886207	−	0.463289i	$-0.153331\pi$
$632$	2.39068e27	−	1.09701e27i	0.235153	−	0.107905i
$633$	−2.02333e27			−0.195898
$634$	4.14011e26	+	2.86725e27i	0.0394565	+	0.273258i
$635$			1.67370e27i			0.157014i
$636$	−7.43089e26	−	2.51950e27i	−0.0686230	−	0.232671i
$637$	1.03963e28			0.945118
$638$	−1.56369e28	+	2.25787e27i	−1.39941	+	0.202065i
$639$			3.68195e27i			0.324391i
$640$	1.07514e28	+	6.84565e27i	0.932539	+	0.593766i
$641$	−4.38793e27			−0.374696			−0.187348	−	0.982294i	$-0.559989\pi$
$641$	−4.38793e27			−0.374696			−0.187348	+	0.982294i	$0.559989\pi$
$642$	−2.13123e26	−	1.47599e27i	−0.0179176	−	0.124089i
$643$			5.30800e27i			0.439361i	0.975572	+	0.219680i	$0.0705014\pi$
$643$			5.30800e27i			0.439361i	−0.975572	+	0.219680i	$0.929499\pi$
$644$	5.78606e26	−	1.70651e26i	0.0471546	−	0.0139076i
$645$	−9.54008e27			−0.765517
$646$	2.37068e28	−	3.42310e27i	1.87304	−	0.270455i
$647$		−	1.00606e28i		−	0.782678i	−0.920247	−	0.391339i	$-0.872012\pi$
$647$		−	1.00606e28i		−	0.782678i	0.920247	−	0.391339i	$-0.127988\pi$
$648$	6.04929e26	+	1.31830e27i	0.0463398	+	0.100987i
$649$	−6.41206e27			−0.483671
$650$	−7.46084e26	−	5.16703e27i	−0.0554184	−	0.383802i
$651$			4.45060e27i			0.325543i
$652$	−6.00967e27	−	2.03762e28i	−0.432887	−	1.46773i
$653$	2.32195e28			1.64711			0.823553	−	0.567239i	$-0.191988\pi$
$653$	2.32195e28			1.64711			0.823553	+	0.567239i	$0.191988\pi$
$654$	7.61286e27	−	1.09924e27i	0.531827	−	0.0767922i
$655$		−	1.88532e28i		−	1.29709i
$656$	1.59497e28	−	1.03046e28i	1.08072	−	0.698222i
$657$	−4.15741e27			−0.277440
$658$	−1.09171e27	−	7.56068e27i	−0.0717544	−	0.496938i
$659$			1.04185e28i			0.674451i	0.941424	+	0.337225i	$0.109488\pi$
$659$			1.04185e28i			0.674451i	−0.941424	+	0.337225i	$0.890512\pi$
$660$	−1.71417e28	+	5.05570e27i	−1.09299	+	0.322361i
$661$	5.33849e26			0.0335277			0.0167638	−	0.999859i	$-0.494664\pi$
$661$	5.33849e26			0.0335277			0.0167638	+	0.999859i	$0.494664\pi$
$662$	1.75622e27	−	2.53586e26i	0.108642	−	0.0156872i
$663$		−	2.41145e28i		−	1.46941i
$664$	−5.98160e27	+	2.74478e27i	−0.359035	+	0.164751i
$665$	1.64301e28			0.971458
$666$	−2.60913e26	−	1.80696e27i	−0.0151968	−	0.105246i
$667$			1.00217e27i			0.0575021i
$668$	9.02187e27	+	3.05893e28i	0.509955	+	1.72904i
$669$	1.30898e28			0.728907
$670$	1.17280e28	−	1.69344e27i	0.643393	−	0.0929015i
$671$		−	1.18208e27i		−	0.0638881i
$672$	4.82442e27	+	5.53392e27i	0.256893	+	0.294673i
$673$	−6.43508e27			−0.337600			−0.168800	−	0.985650i	$-0.553989\pi$
$673$	−6.43508e27			−0.337600			−0.168800	+	0.985650i	$0.553989\pi$
$674$	−4.45900e27	−	3.08810e28i	−0.230483	−	1.59622i
$675$			8.39603e26i			0.0427599i
$676$	−3.91090e28	+	1.15346e28i	−1.96250	+	0.578811i
$677$	1.77899e28			0.879604			0.439802	−	0.898095i	$-0.355049\pi$
$677$	1.77899e28			0.879604			0.439802	+	0.898095i	$0.355049\pi$
$678$	−1.95742e28	+	2.82638e27i	−0.953646	+	0.137700i
$679$			1.14075e28i			0.547637i
$680$	1.42131e28	+	3.09740e28i	0.672355	+	1.46524i
$681$	−6.55151e27			−0.305401
$682$	−4.62528e27	−	3.20326e28i	−0.212469	−	1.47146i
$683$			9.34406e27i			0.422989i	0.977379	+	0.211494i	$0.0678330\pi$
$683$			9.34406e27i			0.422989i	−0.977379	+	0.211494i	$0.932167\pi$
$684$	2.74315e27	+	9.30086e27i	0.122374	+	0.414918i
$685$	2.04327e28			0.898295
$686$	−2.38435e28	+	3.44283e27i	−1.03307	+	0.149168i
$687$			1.20360e28i			0.513941i
$688$	−1.54655e28	−	2.39378e28i	−0.650848	−	1.00739i
$689$	−1.76798e28			−0.733307
$690$	1.62010e26	+	1.12201e27i	0.00662294	+	0.0458674i
$691$		−	1.52991e28i		−	0.616431i	−0.951317	−	0.308215i	$-0.900268\pi$
$691$		−	1.52991e28i		−	0.616431i	0.951317	−	0.308215i	$-0.0997318\pi$
$692$	1.72779e28	−	5.09586e27i	0.686166	−	0.202375i
$693$	−1.02941e28			−0.402956
$694$	−2.80347e28	+	4.04801e27i	−1.08168	+	0.156188i
$695$			8.79375e27i			0.334446i
$696$	−1.10852e28	+	5.08669e27i	−0.415578	+	0.190697i
$697$	5.07717e28			1.87626
$698$	2.49030e27	+	1.72467e28i	0.0907190	+	0.628277i
$699$		−	2.24678e28i		−	0.806842i
$700$	1.20219e27	+	4.07611e27i	0.0425591	+	0.144300i
$701$	1.28504e28			0.448473			0.224236	−	0.974535i	$-0.428011\pi$
$701$	1.28504e28			0.448473			0.224236	+	0.974535i	$0.428011\pi$
$702$	9.66226e27	−	1.39516e27i	0.332436	−	0.0480014i
$703$		−	1.22056e28i		−	0.414004i
$704$	−4.04742e28	−	3.48158e28i	−1.35348	−	1.16426i
$705$	1.43556e28			0.473294
$706$	−4.76681e26	−	3.30127e27i	−0.0154946	−	0.107309i
$707$			6.48565e27i			0.207855i
$708$	−4.74779e27	+	1.40029e27i	−0.150023	+	0.0442472i
$709$	−6.18369e28			−1.92657			−0.963287	−	0.268475i	$-0.913480\pi$
$709$	−6.18369e28			−1.92657			−0.963287	+	0.268475i	$0.913480\pi$
$710$	−3.46627e28	+	5.00505e27i	−1.06483	+	0.153753i
$711$			2.84720e27i			0.0862426i
$712$	2.02297e28	+	4.40858e28i	0.604211	+	1.31674i
$713$	−2.05297e27			−0.0604626
$714$	2.80530e27	+	1.94282e28i	0.0814700	+	0.564224i
$715$			1.20287e29i			3.44475i
$716$	3.58719e27	+	1.21626e28i	0.101303	+	0.343476i
$717$	−4.71636e26			−0.0131346
$718$	4.50185e28	−	6.50036e27i	1.23636	−	0.178522i
$719$		−	3.50465e26i		−	0.00949196i	−0.999989	−	0.00474598i	$-0.998489\pi$
$719$		−	3.50465e26i		−	0.00949196i	0.999989	−	0.00474598i	$-0.00151070\pi$
$720$	−1.15884e28	+	7.48695e27i	−0.309528	+	0.199977i
$721$	1.70391e28			0.448842
$722$	3.76370e27	+	2.60656e28i	0.0977784	+	0.677168i
$723$		−	1.30971e28i		−	0.335577i
$724$	5.73119e28	−	1.69033e28i	1.44830	−	0.427156i
$725$	−7.06001e27			−0.175965
$726$	5.08458e28	−	7.34178e27i	1.24994	−	0.180483i
$727$			6.21932e28i			1.50799i	0.656879	+	0.753996i	$0.271876\pi$
$727$			6.21932e28i			1.50799i	−0.656879	+	0.753996i	$0.728124\pi$
$728$	4.49107e28	−	2.06082e28i	1.07408	−	0.492863i
$729$	−1.57004e27			−0.0370370
$730$	−5.65137e27	−	3.91388e28i	−0.131500	−	0.910707i
$731$		−	7.61998e28i		−	1.74896i
$732$	−2.58146e26	−	8.75264e26i	−0.00584460	−	0.0198166i
$733$	−4.05128e28			−0.904799			−0.452399	−	0.891815i	$-0.649432\pi$
$733$	−4.05128e28			−0.904799			−0.452399	+	0.891815i	$0.649432\pi$
$734$	−7.63505e28	+	1.10245e28i	−1.68210	+	0.242884i
$735$		−	1.59037e28i		−	0.345640i
$736$	−2.55268e27	+	2.22540e27i	−0.0547291	+	0.0477124i
$737$	−4.96343e28			−1.04980
$738$	2.93744e27	+	2.03433e28i	0.0612922	+	0.424481i
$739$			2.23933e28i			0.460971i	0.973076	+	0.230485i	$0.0740314\pi$
$739$			2.23933e28i			0.460971i	−0.973076	+	0.230485i	$0.925969\pi$
$740$	1.66565e28	−	4.91258e27i	0.338272	−	0.0997683i
$741$	6.52661e28			1.30769
$742$	1.42440e28	−	2.05674e27i	0.281575	−	0.0406575i
$743$		−	8.26305e28i		−	1.61158i	−0.592200	−	0.805791i	$-0.701741\pi$
$743$		−	8.26305e28i		−	1.61158i	0.592200	−	0.805791i	$-0.298259\pi$
$744$	−1.04202e28	−	2.27083e28i	−0.200514	−	0.436974i
$745$	3.85795e28			0.732476
$746$	5.54272e27	+	3.83863e28i	0.103833	+	0.719098i
$747$		−	7.12386e27i		−	0.131677i
$748$	−4.03816e28	−	1.36917e29i	−0.736491	−	2.49712i
$749$	8.17057e27			0.147040
$750$	2.76704e28	−	3.99541e27i	0.491363	−	0.0709495i
$751$		−	9.67448e28i		−	1.69523i	−0.530613	−	0.847614i	$-0.678038\pi$
$751$		−	9.67448e28i		−	1.69523i	0.530613	−	0.847614i	$-0.321962\pi$
$752$	2.32720e28	+	3.60209e28i	0.402398	+	0.622839i
$753$	−4.72591e27			−0.0806373
$754$	1.17316e28	+	8.12475e28i	0.197535	+	1.36803i
$755$		−	5.34538e28i		−	0.888197i
$756$	−7.62225e27	+	2.24807e27i	−0.124987	+	0.0368632i
$757$	−7.06674e28			−1.14356			−0.571782	−	0.820406i	$-0.693748\pi$
$757$	−7.06674e28			−1.14356			−0.571782	+	0.820406i	$0.693748\pi$
$758$	4.97546e28	−	7.18423e27i	0.794587	−	0.114733i
$759$		−	4.74846e27i		−	0.0748403i
$760$	−8.38314e28	+	3.84678e28i	−1.30398	+	0.598358i
$761$	−9.74736e28			−1.49638			−0.748188	−	0.663487i	$-0.769076\pi$
$761$	−9.74736e28			−1.49638			−0.748188	+	0.663487i	$0.769076\pi$
$762$	−7.73437e26	−	5.35647e27i	−0.0117186	−	0.0811575i
$763$			4.21422e28i			0.630190i
$764$	5.66136e27	+	1.91953e28i	0.0835579	+	0.283309i
$765$	−3.68889e28			−0.537379
$766$	6.61010e28	−	9.54454e27i	0.950431	−	0.137236i
$767$			3.33162e28i			0.472826i
$768$	−3.75722e28	−	1.69403e28i	−0.526326	−	0.237307i
$769$	−6.61207e28			−0.914270			−0.457135	−	0.889397i	$-0.651124\pi$
$769$	−6.61207e28			−0.914270			−0.457135	+	0.889397i	$0.651124\pi$
$770$	−1.39933e28	−	9.69112e28i	−0.190991	−	1.32272i
$771$		−	8.17361e27i		−	0.110121i
$772$	1.15754e29	−	3.41399e28i	1.53944	−	0.454035i
$773$	−6.67051e28			−0.875718			−0.437859	−	0.899044i	$-0.644263\pi$
$773$	−6.67051e28			−0.875718			−0.437859	+	0.899044i	$0.644263\pi$
$774$	3.05319e28	−	4.40860e27i	0.395680	−	0.0571335i
$775$		−	1.44626e28i		−	0.185024i
$776$	−2.67083e28	−	5.82046e28i	−0.337310	−	0.735089i
$777$	1.00027e28			0.124712
$778$	1.90226e27	+	1.31742e28i	0.0234139	+	0.162154i
$779$			1.37414e29i			1.66977i
$780$	2.62688e28	+	8.90661e28i	0.315133	+	1.06848i
$781$	1.46697e29			1.73744
$782$	−8.96183e27	+	1.29403e27i	−0.104792	+	0.0151313i
$783$		−	1.32021e28i		−	0.152414i
$784$	3.99051e28	−	2.57815e28i	0.454850	−	0.293865i
$785$	1.17678e29			1.32433
$786$	8.71230e27	+	6.03374e28i	0.0968071	+	0.670441i
$787$		−	5.62344e28i		−	0.616957i	−0.951231	−	0.308479i	$-0.900180\pi$
$787$		−	5.62344e28i		−	0.616957i	0.951231	−	0.308479i	$-0.0998198\pi$
$788$	4.43068e28	−	1.30676e28i	0.479963	−	0.141558i
$789$	−3.32005e28			−0.355119
$790$	−2.68042e28	+	3.87034e27i	−0.283094	+	0.0408769i
$791$		−	1.08356e29i		−	1.13003i
$792$	5.25238e28	−	2.41016e28i	0.540884	−	0.248196i
$793$	−6.14191e27			−0.0624556
$794$	2.45075e28	+	1.69727e29i	0.246090	+	1.70430i
$795$			2.70455e28i			0.268178i
$796$	−6.03705e27	−	2.04691e28i	−0.0591145	−	0.200432i
$797$	−5.01018e28			−0.484473			−0.242237	−	0.970217i	$-0.577881\pi$
$797$	−5.01018e28			−0.484473			−0.242237	+	0.970217i	$0.577881\pi$
$798$	−5.25827e28	+	7.59258e27i	−0.502127	+	0.0725037i
$799$			1.14663e29i			1.08133i
$800$	−1.56773e28	−	1.79829e28i	−0.146006	−	0.167479i
$801$	−5.25044e28			−0.482915
$802$	9.66580e27	+	6.69409e28i	0.0878000	+	0.608062i
$803$			1.65640e29i			1.48597i
$804$	−3.67516e28	+	1.08393e28i	−0.325623	+	0.0960378i
$805$	−6.21104e27			−0.0543507
$806$	−1.66437e29	+	2.40324e28i	−1.43847	+	0.207705i
$807$			4.69683e27i			0.0400931i
$808$	−1.51848e28	−	3.30918e28i	−0.128026	−	0.279002i
$809$	1.40927e29			1.17357			0.586785	−	0.809743i	$-0.300393\pi$
$809$	1.40927e29			1.17357			0.586785	+	0.809743i	$0.300393\pi$
$810$	−2.13423e27	−	1.47807e28i	−0.0175546	−	0.121575i
$811$			3.37450e28i			0.274158i	0.990560	+	0.137079i	$0.0437714\pi$
$811$			3.37450e28i			0.274158i	−0.990560	+	0.137079i	$0.956229\pi$
$812$	−1.89035e28	−	6.40936e28i	−0.151699	−	0.514345i
$813$	7.72113e28			0.612033
$814$	−7.19931e28	+	1.03953e28i	−0.563699	+	0.0813942i
$815$			2.18728e29i			1.69172i
$816$	−5.98008e28	−	9.25608e28i	−0.456883	−	0.707172i
$817$	2.06235e29			1.55648
$818$	−7.20504e27	−	4.98988e28i	−0.0537160	−	0.372012i
$819$			5.34869e28i			0.393921i
$820$	−1.87524e29	+	5.53074e28i	−1.36432	+	0.402387i
$821$	−8.76167e28			−0.629731			−0.314866	−	0.949136i	$-0.601959\pi$
$821$	−8.76167e28			−0.629731			−0.314866	+	0.949136i	$0.601959\pi$
$822$	−6.53924e28	+	9.44221e27i	−0.464311	+	0.0670433i
$823$		−	2.53850e29i		−	1.78065i	−0.455323	−	0.890326i	$-0.650476\pi$
$823$		−	2.53850e29i		−	1.78065i	0.455323	−	0.890326i	$-0.349524\pi$
$824$	−8.69385e28	+	3.98935e28i	−0.602476	+	0.276459i
$825$	3.34515e28			0.229022
$826$	−3.87576e27	−	2.68417e28i	−0.0262154	−	0.181556i
$827$		−	1.51545e29i		−	1.01271i	−0.862325	−	0.506356i	$-0.830992\pi$
$827$		−	1.51545e29i		−	1.01271i	0.862325	−	0.506356i	$-0.169008\pi$
$828$	−1.03699e27	−	3.51598e27i	−0.00684653	−	0.0232137i
$829$	−2.78405e29			−1.81607			−0.908033	−	0.418898i	$-0.862416\pi$
$829$	−2.78405e29			−1.81607			−0.908033	+	0.418898i	$0.862416\pi$
$830$	6.70655e28	−	9.68380e27i	0.432233	−	0.0624115i
$831$			7.48901e28i			0.476885i
$832$	−1.80898e29	+	2.10299e29i	−1.13815	+	1.32313i
$833$	1.27028e29			0.789676
$834$	−4.06371e27	−	2.81434e28i	−0.0249610	−	0.172868i
$835$		−	3.28360e29i		−	1.99290i
$836$	3.70566e29	−	1.09293e29i	2.22230	−	0.655435i
$837$	2.70447e28			0.160261
$838$	6.35703e28	−	9.17911e27i	0.372232	−	0.0537478i
$839$		−	6.37833e28i		−	0.369052i	−0.982828	−	0.184526i	$-0.940925\pi$
$839$		−	6.37833e28i		−	0.369052i	0.982828	−	0.184526i	$-0.0590749\pi$
$840$	−3.15251e28	−	6.87016e28i	−0.180245	−	0.392802i
$841$	−6.59816e28			−0.372789
$842$	−3.98772e27	−	2.76171e28i	−0.0222640	−	0.154190i
$843$			8.03899e28i			0.443533i
$844$	1.76047e28	+	5.96901e28i	0.0959853	+	0.325445i
$845$	4.19815e29			2.26199
$846$	−4.59436e28	+	6.63394e27i	−0.244636	+	0.0353238i
$847$			2.81465e29i			1.48112i
$848$	−6.78620e28	+	4.38437e28i	−0.352913	+	0.228007i
$849$	−1.95315e29			−1.00382
$850$	−9.11604e27	−	6.31335e28i	−0.0463039	−	0.320679i
$851$			4.61404e27i			0.0231625i
$852$	1.08621e29	−	3.20362e28i	0.538912	−	0.158944i
$853$	3.31227e29			1.62418			0.812092	−	0.583529i	$-0.198329\pi$
$853$	3.31227e29			1.62418			0.812092	+	0.583529i	$0.198329\pi$
$854$	4.94833e27	−	7.14504e26i	0.0239817	−	0.00346279i
$855$		−	9.98399e28i		−	0.478237i
$856$	−4.16887e28	+	1.91297e28i	−0.197370	+	0.0905673i
$857$	4.49894e28			0.210524			0.105262	−	0.994445i	$-0.466432\pi$
$857$	4.49894e28			0.210524			0.105262	+	0.994445i	$0.466432\pi$
$858$	−5.55863e28	−	3.84965e29i	−0.257096	−	1.78052i
$859$		−	1.71562e29i		−	0.784311i	−0.919899	−	0.392155i	$-0.871730\pi$
$859$		−	1.71562e29i		−	0.784311i	0.919899	−	0.392155i	$-0.128270\pi$
$860$	8.30070e28	+	2.81441e29i	0.375085	+	1.27175i
$861$	−1.12614e29			−0.502990
$862$	−1.73340e29	+	2.50292e28i	−0.765292	+	0.110503i
$863$		−	1.83899e29i		−	0.802550i	−0.915958	−	0.401275i	$-0.868567\pi$
$863$		−	1.83899e29i		−	0.802550i	0.915958	−	0.401275i	$-0.131433\pi$
$864$	3.36277e28	−	2.93163e28i	0.145064	−	0.126465i
$865$	−1.85469e29			−0.790879
$866$	−2.51204e28	−	1.73972e29i	−0.105888	−	0.733332i
$867$		−	1.56086e29i		−	0.650388i
$868$	1.31297e29	−	3.87241e28i	0.540826	−	0.159509i
$869$	1.13438e29			0.461915
$870$	1.24287e29	−	1.79462e28i	0.500304	−	0.0722405i
$871$			2.57893e29i			1.02626i
$872$	−9.86673e28	−	2.15022e29i	−0.388158	−	0.845899i
$873$	6.93193e28			0.269595
$874$	−3.50229e27	−	2.42553e28i	−0.0134660	−	0.0932592i
$875$			1.53174e29i			0.582242i
$876$	3.61731e28	+	1.22648e29i	0.135939	+	0.460912i
$877$	4.67952e28			0.173862			0.0869312	−	0.996214i	$-0.472294\pi$
$877$	4.67952e28			0.173862			0.0869312	+	0.996214i	$0.472294\pi$
$878$	4.81645e29	−	6.95462e28i	1.76922	−	0.255463i
$879$			2.83524e29i			1.02968i
$880$	2.98296e29	+	4.61708e29i	1.07108	+	1.65783i
$881$	−4.36430e29			−1.54937			−0.774686	−	0.632346i	$-0.782092\pi$
$881$	−4.36430e29			−1.54937			−0.774686	+	0.632346i	$0.782092\pi$
$882$	7.34930e27	+	5.08978e28i	0.0257965	+	0.178654i
$883$		−	4.10714e29i		−	1.42539i	−0.701476	−	0.712693i	$-0.747475\pi$
$883$		−	4.10714e29i		−	1.42539i	0.701476	−	0.712693i	$-0.252525\pi$
$884$	−7.11400e29	+	2.09817e29i	−2.44113	+	0.719977i
$885$	5.09650e28			0.172918
$886$	−9.87387e27	+	1.42572e27i	−0.0331246	+	0.00478296i
$887$			3.39600e29i			1.12650i	0.826287	+	0.563250i	$0.190449\pi$
$887$			3.39600e29i			1.12650i	−0.826287	+	0.563250i	$0.809551\pi$
$888$	−5.10369e28	+	2.34193e28i	−0.167400	+	0.0768148i
$889$	2.96516e28			0.0961679
$890$	−7.13718e28	−	4.94288e29i	−0.228890	−	1.58519i
$891$			6.25538e28i			0.198370i
$892$	−1.13893e29	−	3.86162e29i	−0.357147	−	1.21093i
$893$	−3.10337e29			−0.962319
$894$	−1.23469e29	+	1.78281e28i	−0.378602	+	0.0546676i
$895$		−	1.30559e29i		−	0.395893i
$896$	1.21279e29	−	1.90475e29i	0.363669	−	0.571160i
$897$	−2.46724e28			−0.0731622
$898$	6.31095e28	+	4.37067e29i	0.185068	+	1.28170i
$899$			2.27412e29i			0.659503i
$900$	2.47691e28	−	7.30528e27i	0.0710370	−	0.0209513i
$901$	−2.16021e29			−0.612701
$902$	8.10521e29	−	1.17034e29i	2.27352	−	0.328281i
$903$			1.69014e29i			0.468862i
$904$	2.53694e29	+	5.52866e29i	0.696026	+	1.51682i
$905$	−6.15214e29			−1.66932
$906$	2.47017e28	+	1.71073e29i	0.0662896	+	0.459091i
$907$		−	4.74910e29i		−	1.26049i	−0.776397	−	0.630244i	$-0.782955\pi$
$907$		−	4.74910e29i		−	1.26049i	0.776397	−	0.630244i	$-0.217045\pi$
$908$	5.70039e28	+	1.93276e29i	0.149639	+	0.507363i
$909$	3.94110e28			0.102324
$910$	−5.03538e29	+	7.27074e28i	−1.29306	+	0.186709i
$911$			5.13405e28i			0.130400i	0.997872	+	0.0651998i	$0.0207685\pi$
$911$			5.13405e28i			0.130400i	−0.997872	+	0.0651998i	$0.979232\pi$
$912$	2.50516e29	−	1.61851e29i	0.629343	−	0.406600i
$913$	−2.83829e29			−0.705260
$914$	6.23287e28	+	4.31659e29i	0.153188	+	1.06091i
$915$			9.39550e27i			0.0228407i
$916$	3.55072e29	−	1.04723e29i	0.853811	−	0.251819i
$917$	−3.34007e29			−0.794441
$918$	1.18059e29	−	1.70468e28i	0.277761	−	0.0401067i
$919$			1.46507e29i			0.340960i	0.985361	+	0.170480i	$0.0545318\pi$
$919$			1.46507e29i			0.340960i	−0.985361	+	0.170480i	$0.945468\pi$
$920$	3.16906e28	−	1.45419e28i	0.0729545	−	0.0334767i
$921$	3.65111e29			0.831436
$922$	−1.56565e28	−	1.08430e29i	−0.0352684	−	0.244253i
$923$		−	7.62216e29i		−	1.69848i
$924$	8.95679e28	+	3.03686e29i	0.197439	+	0.669431i
$925$	−3.25046e28			−0.0708805
$926$	−8.46873e29	+	1.22283e29i	−1.82687	+	0.263788i
$927$		−	1.03540e29i		−	0.220959i
$928$	2.46513e29	+	2.82766e29i	0.520428	+	0.596964i
$929$	−5.04980e28			−0.105467			−0.0527336	−	0.998609i	$-0.516793\pi$
$929$	−5.04980e28			−0.105467			−0.0527336	+	0.998609i	$0.516793\pi$
$930$	3.67632e28	+	2.54605e29i	0.0759598	+	0.526062i
$931$			3.43802e29i			0.702767i
$932$	−6.62821e29	+	1.95489e29i	−1.34041	+	0.395334i
$933$	−2.47588e29			−0.495352
$934$	8.56312e29	−	1.23646e29i	1.69497	−	0.244743i
$935$			1.46973e30i			2.87820i
$936$	−1.25229e29	−	2.72907e29i	−0.242631	−	0.528756i
$937$	2.12738e29			0.407802			0.203901	−	0.978992i	$-0.434638\pi$
$937$	2.12738e29			0.407802			0.203901	+	0.978992i	$0.434638\pi$
$938$	−3.00014e28	−	2.07776e29i	−0.0569001	−	0.394064i
$939$		−	6.61680e28i		−	0.124163i
$940$	−1.24907e29	−	4.23505e29i	−0.231903	−	0.786285i
$941$	8.76647e29			1.61038			0.805190	−	0.593017i	$-0.202063\pi$
$941$	8.76647e29			1.61038			0.805190	+	0.593017i	$0.202063\pi$
$942$	−3.76613e29	+	5.43804e28i	−0.684521	+	0.0988401i
$943$		−	5.19463e28i		−	0.0934195i
$944$	8.26198e28	+	1.27880e29i	0.147016	+	0.227554i
$945$	8.18210e28			0.144061
$946$	−1.75648e29	−	1.21646e30i	−0.306007	−	2.11926i
$947$		−	1.05902e30i		−	1.82559i	−0.408422	−	0.912793i	$-0.633921\pi$
$947$		−	1.05902e30i		−	1.82559i	0.408422	−	0.912793i	$-0.366079\pi$
$948$	8.39951e28	−	2.47731e28i	0.143275	−	0.0422569i
$949$	8.60643e29			1.45265
$950$	1.70871e29	−	2.46726e28i	0.285386	−	0.0412078i
$951$			9.64490e28i			0.159402i
$952$	5.48743e29	−	2.51802e29i	0.897427	−	0.411803i
$953$	5.99708e29			0.970534			0.485267	−	0.874366i	$-0.338722\pi$
$953$	5.99708e29			0.970534			0.485267	+	0.874366i	$0.338722\pi$
$954$	−1.24981e28	−	8.65560e28i	−0.0200152	−	0.138616i
$955$		−	2.06051e29i		−	0.326544i
$956$	4.10365e27	+	1.39137e28i	0.00643563	+	0.0218205i
$957$	−5.25999e29			−0.816329
$958$	−5.46030e29	+	7.88429e28i	−0.838612	+	0.121090i
$959$		−	3.61989e29i		−	0.550186i
$960$	3.21702e29	+	2.76727e29i	0.483884	+	0.416236i
$961$	2.05933e29			0.306543
$962$	5.40127e28	+	3.74067e29i	0.0795692	+	0.551059i
$963$		−	4.96497e28i		−	0.0723858i
$964$	−3.86377e29	+	1.13956e29i	−0.557494	+	0.164425i
$965$	−1.24256e30			−1.77437
$966$	1.98777e28	−	2.87020e27i	0.0280928	−	0.00405641i
$967$			2.59632e28i			0.0363157i	0.999835	+	0.0181578i	$0.00578014\pi$
$967$			2.59632e28i			0.0363157i	−0.999835	+	0.0181578i	$0.994220\pi$
$968$	−6.58992e29	−	1.43612e30i	−0.912277	−	1.98809i
$969$	7.97455e29			1.09262
$970$	9.42291e28	+	6.52587e29i	0.127781	+	0.884955i
$971$		−	1.17872e30i		−	1.58204i	−0.611788	−	0.791022i	$-0.709550\pi$
$971$		−	1.17872e30i		−	1.58204i	0.611788	−	0.791022i	$-0.290450\pi$
$972$	1.36607e28	+	4.63177e28i	0.0181473	+	0.0615297i
$973$	1.55792e29			0.204841
$974$	5.03118e29	−	7.26468e28i	0.654757	−	0.0945425i
$975$		−	1.73810e29i		−	0.223887i
$976$	−2.35750e28	+	1.52311e28i	−0.0300576	+	0.0194193i
$977$	1.95334e28			0.0246508			0.0123254	−	0.999924i	$-0.496077\pi$
$977$	1.95334e28			0.0246508			0.0123254	+	0.999924i	$0.496077\pi$
$978$	−1.01077e29	−	7.00014e29i	−0.126260	−	0.874416i
$979$			2.09189e30i			2.58649i
$980$	−4.69173e29	+	1.38376e29i	−0.574212	+	0.169355i
$981$	2.56083e29			0.310235
$982$	−1.49515e30	+	2.15889e29i	−1.79296	+	0.258891i
$983$		−	1.61206e29i		−	0.191358i	−0.995412	−	0.0956788i	$-0.969498\pi$
$983$		−	1.61206e29i		−	0.191358i	0.995412	−	0.0956788i	$-0.0305022\pi$
$984$	5.74589e29	−	2.63662e29i	0.675160	−	0.309811i
$985$	−4.75610e29			−0.553209
$986$	1.43343e29	+	9.92724e29i	0.165046	+	1.14303i
$987$		−	2.54328e29i		−	0.289883i
$988$	−5.67872e29	−	1.92541e30i	−0.640739	−	2.17247i
$989$	−7.79626e28			−0.0870810
$990$	−5.88895e29	+	8.50324e28i	−0.651157	+	0.0940226i
$991$			3.67391e29i			0.402153i	0.979575	+	0.201077i	$0.0644441\pi$
$991$			3.67391e29i			0.402153i	−0.979575	+	0.201077i	$0.935556\pi$
$992$	−5.79252e29	+	5.04987e29i	−0.627698	+	0.547222i
$993$	5.90761e28			0.0633752
$994$	8.86706e28	+	6.14091e29i	0.0941707	+	0.652183i
$995$			2.19725e29i			0.231019i
$996$	−2.10160e29	+	6.19838e28i	−0.218755	+	0.0645186i
$997$	4.62969e29			0.477090			0.238545	−	0.971131i	$-0.423330\pi$
$997$	4.62969e29			0.477090			0.238545	+	0.971131i	$0.423330\pi$
$998$	7.91122e29	−	1.14233e29i	0.807119	−	0.116543i
$999$		−	6.07830e28i		−	0.0613941i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.21.d.a.7.7	✓	20
3.2	odd	2		36.21.d.c.19.14		20
4.3	odd	2	inner	12.21.d.a.7.8	yes	20
12.11	even	2		36.21.d.c.19.13		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.21.d.a.7.7	✓	20	1.1	even	1	trivial
12.21.d.a.7.8	yes	20	4.3	odd	2	inner
36.21.d.c.19.13		20	12.11	even	2
36.21.d.c.19.14		20	3.2	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:	\( k \)	\(=\)	\( 21 \)
Character orbit:	\([\chi]\)	\(=\)	12.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-146.341 - 1013.49i) q^{2} -34092.0i q^{3} +(-1.00574e6 + 296630. i) q^{4} +1.07961e7 q^{5} +(-3.45518e7 + 4.98905e6i) q^{6} -1.91267e8i q^{7} +(4.47813e8 + 9.75902e8i) q^{8} -1.16226e9 q^{9} +O(q^{10})\)	\(q+(-146.341 - 1013.49i) q^{2} -34092.0i q^{3} +(-1.00574e6 + 296630. i) q^{4} +1.07961e7 q^{5} +(-3.45518e7 + 4.98905e6i) q^{6} -1.91267e8i q^{7} +(4.47813e8 + 9.75902e8i) q^{8} -1.16226e9 q^{9} +(-1.57992e9 - 1.09418e10i) q^{10} +4.63069e10i q^{11} +(1.01127e10 + 3.42878e10i) q^{12} +2.40605e11 q^{13} +(-1.93847e11 + 2.79902e10i) q^{14} -3.68062e11i q^{15} +(9.23533e11 - 5.96668e11i) q^{16} +2.93983e12 q^{17} +(1.70086e11 + 1.17794e12i) q^{18} +7.95667e12i q^{19} +(-1.08582e13 + 3.20246e12i) q^{20} -6.52066e12 q^{21} +(4.69316e13 - 6.77660e12i) q^{22} -3.00784e12i q^{23} +(3.32704e13 - 1.52668e13i) q^{24} +2.11894e13 q^{25} +(-3.52103e13 - 2.43850e14i) q^{26} +3.96238e13i q^{27} +(5.67355e13 + 1.92366e14i) q^{28} -3.33186e14 q^{29} +(-3.73027e14 + 5.38625e13i) q^{30} -6.82538e14i q^{31} +(-7.39867e14 - 8.48674e14i) q^{32} +1.57869e15 q^{33} +(-4.30218e14 - 2.97949e15i) q^{34} -2.06495e15i q^{35} +(1.16894e15 - 3.44761e14i) q^{36} -1.53400e15 q^{37} +(8.06400e15 - 1.16439e15i) q^{38} -8.20268e15i q^{39} +(4.83465e15 + 1.05360e16i) q^{40} +1.72703e16 q^{41} +(9.54240e14 + 6.60862e15i) q^{42} -2.59198e16i q^{43} +(-1.37360e16 - 4.65729e16i) q^{44} -1.25479e16 q^{45} +(-3.04842e15 + 4.40171e14i) q^{46} +3.90033e16i q^{47} +(-2.03416e16 - 3.14851e16i) q^{48} +4.32092e16 q^{49} +(-3.10087e15 - 2.14752e16i) q^{50} -1.00225e17i q^{51} +(-2.41987e17 + 7.13705e16i) q^{52} -7.34809e16 q^{53} +(4.01583e16 - 5.79858e15i) q^{54} +4.99936e17i q^{55} +(1.86658e17 - 8.56518e16i) q^{56} +2.71259e17 q^{57} +(4.87588e16 + 3.37681e17i) q^{58} +1.38469e17i q^{59} +(1.09178e17 + 3.70176e17i) q^{60} -2.55270e16 q^{61} +(-6.91745e17 + 9.98832e16i) q^{62} +2.22302e17i q^{63} +(-7.51849e17 + 8.74043e17i) q^{64} +2.59760e18 q^{65} +(-2.31027e17 - 1.59999e18i) q^{66} +1.07186e18i q^{67} +(-2.95672e18 + 8.72042e17i) q^{68} -1.02543e17 q^{69} +(-2.09280e18 + 3.02186e17i) q^{70} -3.16792e18i q^{71} +(-5.20475e17 - 1.13425e18i) q^{72} +3.57700e18 q^{73} +(2.24487e17 + 1.55470e18i) q^{74} -7.22387e17i q^{75} +(-2.36019e18 - 8.00238e18i) q^{76} +8.85698e18 q^{77} +(-8.31333e18 + 1.20039e18i) q^{78} -2.44971e18i q^{79} +(9.97060e18 - 6.44171e18i) q^{80} +1.35085e18 q^{81} +(-2.52735e18 - 1.75032e19i) q^{82} +6.12931e18i q^{83} +(6.55812e18 - 1.93422e18i) q^{84} +3.17389e19 q^{85} +(-2.62694e19 + 3.79312e18i) q^{86} +1.13590e19i q^{87} +(-4.51910e19 + 2.07368e19i) q^{88} +4.51744e19 q^{89} +(1.83628e18 + 1.27172e19i) q^{90} -4.60197e19i q^{91} +(8.92216e17 + 3.02512e18i) q^{92} -2.32691e19 q^{93} +(3.95295e19 - 5.70778e18i) q^{94} +8.59014e19i q^{95} +(-2.89330e19 + 2.52235e19i) q^{96} -5.96418e19 q^{97} +(-6.32328e18 - 4.37921e19i) q^{98} -5.38207e19i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 1254 q^{2} - 485524 q^{4} + 1476984 q^{5} - 36019890 q^{6} + 434160000 q^{8} - 23245229340 q^{9}+O(q^{10}) \) 20 * q + 1254 * q^2 - 485524 * q^4 + 1476984 * q^5 - 36019890 * q^6 + 434160000 * q^8 - 23245229340 * q^9	\( 20 q + 1254 q^{2} - 485524 q^{4} + 1476984 q^{5} - 36019890 q^{6} + 434160000 q^{8} - 23245229340 q^{9} + 3166779028 q^{10} + 35789598900 q^{12} - 197410187576 q^{13} + 1179712421976 q^{14} + 1592658749552 q^{16} + 4951946877000 q^{17} - 1457475879618 q^{18} - 20688414141528 q^{20} - 19078957703376 q^{21} + 54807260127768 q^{22} + 58196896476048 q^{24} + 513048947332092 q^{25} - 142319404376100 q^{26} - 10\!\cdots\!28 q^{28}+ \cdots + 30\!\cdots\!50 q^{98}+O(q^{100}) \) 20 * q + 1254 * q^2 - 485524 * q^4 + 1476984 * q^5 - 36019890 * q^6 + 434160000 * q^8 - 23245229340 * q^9 + 3166779028 * q^10 + 35789598900 * q^12 - 197410187576 * q^13 + 1179712421976 * q^14 + 1592658749552 * q^16 + 4951946877000 * q^17 - 1457475879618 * q^18 - 20688414141528 * q^20 - 19078957703376 * q^21 + 54807260127768 * q^22 + 58196896476048 * q^24 + 513048947332092 * q^25 - 142319404376100 * q^26 - 1064314324942128 * q^28 - 1120225678237608 * q^29 + 919562090032260 * q^30 + 926940361437984 * q^32 - 1250504741372400 * q^33 + 1615904447739868 * q^34 + 564305836503708 * q^36 + 13452822768639208 * q^37 + 30625874417040840 * q^38 - 42278345025251456 * q^40 + 26778887480335560 * q^41 + 34752013424992728 * q^42 - 160483087306778736 * q^44 - 1716641590575528 * q^45 + 312713467885194624 * q^46 - 170793646915261968 * q^48 - 198082137742572844 * q^49 + 575620844246091282 * q^50 - 896547684604982408 * q^52 + 241769380233802968 * q^53 + 41864530192578630 * q^54 - 2099928347597457216 * q^56 + 595468774322860464 * q^57 + 1656374273217670084 * q^58 + 94322711748139416 * q^60 + 430703667006221224 * q^61 + 1718273064332222664 * q^62 - 3197273374119743872 * q^64 - 1146808855391494992 * q^65 + 1921733716920631128 * q^66 + 4484111570418829944 * q^68 - 4519043719923504960 * q^69 - 12213680959006457904 * q^70 - 504607438512720000 * q^72 + 12562724768160620200 * q^73 - 22136012572796109780 * q^74 + 28495592855672115888 * q^76 + 19985445258493440192 * q^77 - 20625251537531633940 * q^78 + 49505459663687019552 * q^80 + 27017034353459841780 * q^81 - 50718250504081238180 * q^82 + 24536705912722373616 * q^84 - 15354475681609135696 * q^85 - 85391409389241086952 * q^86 + 66078172926918803520 * q^88 + 43679060294354361384 * q^89 - 3680625238748114076 * q^90 - 64869958570030809216 * q^92 - 50732545022865845424 * q^93 + 95503492747592513424 * q^94 - 89530085825201077920 * q^96 + 7230988441427384872 * q^97 + 304648861287114073350 * q^98

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