LMFDB - Embedded newform 8.15.d.b.3.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,15,Mod(3,8)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 15, names="a")

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

chi := DirichletCharacter("8.3");

S:= CuspForms(chi, 15);

N := Newforms(S);

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 15 $
Character orbit:	$[\chi]$	$=$	8.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:	$9.94631745215$
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} - x^{11} + 4349 x^{10} - 33891 x^{9} + 12151288 x^{8} - 474141530 x^{7} + 82897017850 x^{6} + \cdots + 37\!\cdots\!50 $ x^12 - x^11 + 4349x^10 - 33891x^9 + 12151288x^8 - 474141530x^7 + 82897017850x^6 - 1813403462870x^5 + 371618750972305x^4 - 24344904673267125x^3 + 1896685485375873305x^2 - 84437535339775221175x + 3788457560343891547750
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{66}\cdot 3^{6}\cdot 5^{2}\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.10
Root			$41.6607 + 39.1087i$ of defining polynomial
Character	$\chi$	$=$	8.3
Dual form			8.15.d.b.3.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(101.321 + 78.2175i) q^{2} +3476.15 q^{3} +(4148.05 + 15850.2i) q^{4} +78301.9i q^{5} +(352208. + 271895. i) q^{6} -1.22276e6i q^{7} +(-819477. + 1.93042e6i) q^{8} +7.30063e6 q^{9} +O(q^{10})$	\(q+(101.321 + 78.2175i) q^{2} +3476.15 q^{3} +(4148.05 + 15850.2i) q^{4} +78301.9i q^{5} +(352208. + 271895. i) q^{6} -1.22276e6i q^{7} +(-819477. + 1.93042e6i) q^{8} +7.30063e6 q^{9} +(-6.12457e6 + 7.93365e6i) q^{10} -1.24226e7 q^{11} +(1.44192e7 + 5.50977e7i) q^{12} +6.40552e6i q^{13} +(9.56408e7 - 1.23891e8i) q^{14} +2.72189e8i q^{15} +(-2.34023e8 + 1.31495e8i) q^{16} +5.71144e8 q^{17} +(7.39710e8 + 5.71037e8i) q^{18} -8.25863e8 q^{19} +(-1.24110e9 + 3.24800e8i) q^{20} -4.25048e9i q^{21} +(-1.25868e9 - 9.71665e8i) q^{22} -5.33718e9i q^{23} +(-2.84862e9 + 6.71041e9i) q^{24} -2.76666e7 q^{25} +(-5.01023e8 + 6.49016e8i) q^{26} +8.75175e9 q^{27} +(1.93809e10 - 5.07205e9i) q^{28} +1.07966e10i q^{29} +(-2.12899e10 + 2.75785e10i) q^{30} -3.45441e10i q^{31} +(-3.39967e10 - 4.98142e9i) q^{32} -4.31828e10 q^{33} +(5.78691e10 + 4.46734e10i) q^{34} +9.57440e10 q^{35} +(3.02834e10 + 1.15716e11i) q^{36} -2.16121e10i q^{37} +(-8.36776e10 - 6.45969e10i) q^{38} +2.22665e10i q^{39} +(-1.51155e11 - 6.41666e10i) q^{40} +1.16052e10 q^{41} +(3.32462e11 - 4.30664e11i) q^{42} -3.57933e11 q^{43} +(-5.15296e10 - 1.96901e11i) q^{44} +5.71653e11i q^{45} +(4.17461e11 - 5.40771e11i) q^{46} +8.17512e10i q^{47} +(-8.13498e11 + 4.57096e11i) q^{48} -8.16907e11 q^{49} +(-2.80322e9 - 2.16401e9i) q^{50} +1.98538e12 q^{51} +(-1.01529e11 + 2.65704e10i) q^{52} +7.30252e11i q^{53} +(8.86739e11 + 6.84540e11i) q^{54} -9.72713e11i q^{55} +(2.36043e12 + 1.00202e12i) q^{56} -2.87082e12 q^{57} +(-8.44485e11 + 1.09393e12i) q^{58} +2.62202e12 q^{59} +(-4.31425e12 + 1.12905e12i) q^{60} +4.54083e12i q^{61} +(2.70195e12 - 3.50006e12i) q^{62} -8.92688e12i q^{63} +(-3.05496e12 - 3.16386e12i) q^{64} -5.01564e11 q^{65} +(-4.37534e12 - 3.37765e12i) q^{66} -1.32990e12 q^{67} +(2.36913e12 + 9.05275e12i) q^{68} -1.85528e13i q^{69} +(9.70092e12 + 7.48886e12i) q^{70} +8.09853e12i q^{71} +(-5.98270e12 + 1.40932e13i) q^{72} +8.89986e12 q^{73} +(1.69045e12 - 2.18977e12i) q^{74} -9.61731e10 q^{75} +(-3.42572e12 - 1.30901e13i) q^{76} +1.51898e13i q^{77} +(-1.74163e12 + 2.25607e12i) q^{78} +1.21047e13i q^{79} +(-1.02963e13 - 1.83244e13i) q^{80} -4.49631e12 q^{81} +(1.17586e12 + 9.07730e11i) q^{82} -2.46085e13 q^{83} +(6.73709e13 - 1.76312e13i) q^{84} +4.47216e13i q^{85} +(-3.62663e13 - 2.79966e13i) q^{86} +3.75306e13i q^{87} +(1.01800e13 - 2.39808e13i) q^{88} +2.19758e13 q^{89} +(-4.47132e13 + 5.79207e13i) q^{90} +7.83238e12 q^{91} +(8.45955e13 - 2.21389e13i) q^{92} -1.20080e14i q^{93} +(-6.39437e12 + 8.28315e12i) q^{94} -6.46666e13i q^{95} +(-1.18178e14 - 1.73162e13i) q^{96} -1.90311e13 q^{97} +(-8.27702e13 - 6.38964e13i) q^{98} -9.06928e13 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 218 q^{2} - 3024 q^{3} - 30828 q^{4} + 518556 q^{6} - 1097608 q^{8} + 13188036 q^{9}+O(q^{10}) $ 12 * q + 218 * q^2 - 3024 * q^3 - 30828 * q^4 + 518556 * q^6 - 1097608 * q^8 + 13188036 * q^9	\( 12 q + 218 q^{2} - 3024 q^{3} - 30828 q^{4} + 518556 q^{6} - 1097608 q^{8} + 13188036 q^{9} - 14533440 q^{10} - 28256720 q^{11} + 34920024 q^{12} + 191568384 q^{14} - 185822448 q^{16} + 270339544 q^{17} + 1420811358 q^{18} - 2481505872 q^{19} - 1679371200 q^{20} + 3042383484 q^{22} + 7581335184 q^{24} - 15857276820 q^{25} - 2773507776 q^{26} - 16574868000 q^{27} + 25329333120 q^{28} + 42207767040 q^{30} + 38309251808 q^{32} - 136227597840 q^{33} + 350437044 q^{34} + 149949623040 q^{35} - 150590403492 q^{36} + 102789916636 q^{38} - 66999085440 q^{40} + 264287409880 q^{41} - 110343609600 q^{42} + 32253127344 q^{43} - 585547356392 q^{44} + 864780977664 q^{46} - 2387663418144 q^{48} - 646589230644 q^{49} - 388785556630 q^{50} + 4755867895776 q^{51} + 798005307840 q^{52} + 1305053764344 q^{54} - 1050155264256 q^{56} - 7479401742480 q^{57} + 389204742720 q^{58} + 1223083947184 q^{59} + 4350689397120 q^{60} + 9957296947200 q^{62} - 16809671099328 q^{64} - 8069319822720 q^{65} - 6067132925784 q^{66} - 9309378171216 q^{67} + 32301846360616 q^{68} + 35197935521280 q^{70} - 43695386222808 q^{72} + 3619334364696 q^{73} - 55499920147776 q^{74} + 9079078926000 q^{75} + 33532610502360 q^{76} + 92515055193600 q^{78} - 86826189154560 q^{80} + 56467107312444 q^{81} - 146233962574956 q^{82} - 18774355695824 q^{83} + 186893160787200 q^{84} + 96253393476220 q^{86} - 166888683024624 q^{88} + 54781416936088 q^{89} - 488020221650880 q^{90} + 36699395136768 q^{91} + 413167093560960 q^{92} + 496016398930944 q^{94} - 616114307580864 q^{96} + 73839238696536 q^{97} - 523654870565638 q^{98} - 223606851712368 q^{99}+O(q^{100}) \) 12 * q + 218 * q^2 - 3024 * q^3 - 30828 * q^4 + 518556 * q^6 - 1097608 * q^8 + 13188036 * q^9 - 14533440 * q^10 - 28256720 * q^11 + 34920024 * q^12 + 191568384 * q^14 - 185822448 * q^16 + 270339544 * q^17 + 1420811358 * q^18 - 2481505872 * q^19 - 1679371200 * q^20 + 3042383484 * q^22 + 7581335184 * q^24 - 15857276820 * q^25 - 2773507776 * q^26 - 16574868000 * q^27 + 25329333120 * q^28 + 42207767040 * q^30 + 38309251808 * q^32 - 136227597840 * q^33 + 350437044 * q^34 + 149949623040 * q^35 - 150590403492 * q^36 + 102789916636 * q^38 - 66999085440 * q^40 + 264287409880 * q^41 - 110343609600 * q^42 + 32253127344 * q^43 - 585547356392 * q^44 + 864780977664 * q^46 - 2387663418144 * q^48 - 646589230644 * q^49 - 388785556630 * q^50 + 4755867895776 * q^51 + 798005307840 * q^52 + 1305053764344 * q^54 - 1050155264256 * q^56 - 7479401742480 * q^57 + 389204742720 * q^58 + 1223083947184 * q^59 + 4350689397120 * q^60 + 9957296947200 * q^62 - 16809671099328 * q^64 - 8069319822720 * q^65 - 6067132925784 * q^66 - 9309378171216 * q^67 + 32301846360616 * q^68 + 35197935521280 * q^70 - 43695386222808 * q^72 + 3619334364696 * q^73 - 55499920147776 * q^74 + 9079078926000 * q^75 + 33532610502360 * q^76 + 92515055193600 * q^78 - 86826189154560 * q^80 + 56467107312444 * q^81 - 146233962574956 * q^82 - 18774355695824 * q^83 + 186893160787200 * q^84 + 96253393476220 * q^86 - 166888683024624 * q^88 + 54781416936088 * q^89 - 488020221650880 * q^90 + 36699395136768 * q^91 + 413167093560960 * q^92 + 496016398930944 * q^94 - 616114307580864 * q^96 + 73839238696536 * q^97 - 523654870565638 * q^98 - 223606851712368 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/8\mathbb{Z}\right)^\times$.

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

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 $

$2$	101.321	+	78.2175i	0.791573	+	0.611074i
$2$	101.321	+	78.2175i	0.791573	+	0.611074i
$3$	3476.15			1.58946			0.794729	−	0.606964i	$-0.207613\pi$
$3$	3476.15			1.58946			0.794729	+	0.606964i	$0.207613\pi$
$4$	4148.05	+	15850.2i	0.253177	+	0.967420i
$5$			78301.9i			1.00226i	0.865371	+	0.501132i	$0.167083\pi$
$5$			78301.9i			1.00226i	−0.865371	+	0.501132i	$0.832917\pi$
$6$	352208.	+	271895.i	1.25817	+	0.971277i
$7$		−	1.22276e6i		−	1.48475i	−0.669985	−	0.742375i	$-0.733699\pi$
$7$		−	1.22276e6i		−	1.48475i	0.669985	−	0.742375i	$-0.266301\pi$
$8$	−819477.	+	1.93042e6i	−0.390757	+	0.920494i
$9$	7.30063e6			1.52638
$10$	−6.12457e6	+	7.93365e6i	−0.612457	+	0.793365i
$11$	−1.24226e7			−0.637476			−0.318738	−	0.947843i	$-0.603259\pi$
$11$	−1.24226e7			−0.637476			−0.318738	+	0.947843i	$0.603259\pi$
$12$	1.44192e7	+	5.50977e7i	0.402414	+	1.53767i
$13$			6.40552e6i			0.102082i	0.998697	+	0.0510412i	$0.0162540\pi$
$13$			6.40552e6i			0.102082i	−0.998697	+	0.0510412i	$0.983746\pi$
$14$	9.56408e7	−	1.23891e8i	0.907292	−	1.17529i
$15$			2.72189e8i			1.59306i
$16$	−2.34023e8	+	1.31495e8i	−0.871803	+	0.489857i
$17$	5.71144e8			1.39188			0.695942	−	0.718098i	$-0.254987\pi$
$17$	5.71144e8			1.39188			0.695942	+	0.718098i	$0.254987\pi$
$18$	7.39710e8	+	5.71037e8i	1.20824	+	0.932731i
$19$	−8.25863e8			−0.923916			−0.461958	−	0.886902i	$-0.652853\pi$
$19$	−8.25863e8			−0.923916			−0.461958	+	0.886902i	$0.652853\pi$
$20$	−1.24110e9	+	3.24800e8i	−0.969610	+	0.253750i
$21$		−	4.25048e9i		−	2.35995i
$22$	−1.25868e9	−	9.71665e8i	−0.504609	−	0.389545i
$23$		−	5.33718e9i		−	1.56753i	−0.621054	−	0.783767i	$-0.713295\pi$
$23$		−	5.33718e9i		−	1.56753i	0.621054	−	0.783767i	$-0.286705\pi$
$24$	−2.84862e9	+	6.71041e9i	−0.621092	+	1.46309i
$25$	−2.76666e7			−0.00453289
$26$	−5.01023e8	+	6.49016e8i	−0.0623799	+	0.0808057i
$27$	8.75175e9			0.836659
$28$	1.93809e10	−	5.07205e9i	1.43638	−	0.375904i
$29$			1.07966e10i			0.625896i	0.949770	+	0.312948i	$0.101317\pi$
$29$			1.07966e10i			0.625896i	−0.949770	+	0.312948i	$0.898683\pi$
$30$	−2.12899e10	+	2.75785e10i	−0.973476	+	1.26102i
$31$		−	3.45441e10i		−	1.25557i	−0.778385	−	0.627787i	$-0.783961\pi$
$31$		−	3.45441e10i		−	1.25557i	0.778385	−	0.627787i	$-0.216039\pi$
$32$	−3.39967e10	−	4.98142e9i	−0.989435	−	0.144978i
$33$	−4.31828e10			−1.01324
$34$	5.78691e10	+	4.46734e10i	1.10178	+	0.850544i
$35$	9.57440e10			1.48811
$36$	3.02834e10	+	1.15716e11i	0.386444	+	1.47665i
$37$		−	2.16121e10i		−	0.227659i	−0.993500	−	0.113830i	$-0.963688\pi$
$37$		−	2.16121e10i		−	0.227659i	0.993500	−	0.113830i	$-0.0363118\pi$
$38$	−8.36776e10	−	6.45969e10i	−0.731348	−	0.564581i
$39$			2.22665e10i			0.162256i
$40$	−1.51155e11	−	6.41666e10i	−0.922578	−	0.391642i
$41$	1.16052e10			0.0595890			0.0297945	−	0.999556i	$-0.490515\pi$
$41$	1.16052e10			0.0595890			0.0297945	+	0.999556i	$0.490515\pi$
$42$	3.32462e11	−	4.30664e11i	1.44210	−	1.86807i
$43$	−3.57933e11			−1.31681			−0.658404	−	0.752665i	$-0.728768\pi$
$43$	−3.57933e11			−1.31681			−0.658404	+	0.752665i	$0.728768\pi$
$44$	−5.15296e10	−	1.96901e11i	−0.161394	−	0.616707i
$45$			5.71653e11i			1.52984i
$46$	4.17461e11	−	5.40771e11i	0.957880	−	1.24082i
$47$			8.17512e10i			0.161365i	0.996740	+	0.0806825i	$0.0257100\pi$
$47$			8.17512e10i			0.161365i	−0.996740	+	0.0806825i	$0.974290\pi$
$48$	−8.13498e11	+	4.57096e11i	−1.38569	+	0.778607i
$49$	−8.16907e11			−1.20448
$50$	−2.80322e9	−	2.16401e9i	−0.00358812	−	0.00276993i
$51$	1.98538e12			2.21234
$52$	−1.01529e11	+	2.65704e10i	−0.0987565	+	0.0258449i
$53$			7.30252e11i			0.621644i	0.950468	+	0.310822i	$0.100604\pi$
$53$			7.30252e11i			0.621644i	−0.950468	+	0.310822i	$0.899396\pi$
$54$	8.86739e11	+	6.84540e11i	0.662277	+	0.511261i
$55$		−	9.72713e11i		−	0.638919i
$56$	2.36043e12	+	1.00202e12i	1.36670	+	0.580177i
$57$	−2.87082e12			−1.46853
$58$	−8.44485e11	+	1.09393e12i	−0.382469	+	0.495442i
$59$	2.62202e12			1.05359			0.526796	−	0.849992i	$-0.323393\pi$
$59$	2.62202e12			1.05359			0.526796	+	0.849992i	$0.323393\pi$
$60$	−4.31425e12	+	1.12905e12i	−1.54116	+	0.403325i
$61$			4.54083e12i			1.44486i	0.691442	+	0.722432i	$0.256976\pi$
$61$			4.54083e12i			1.44486i	−0.691442	+	0.722432i	$0.743024\pi$
$62$	2.70195e12	−	3.50006e12i	0.767248	−	0.993879i
$63$		−	8.92688e12i		−	2.26629i
$64$	−3.05496e12	−	3.16386e12i	−0.694618	−	0.719379i
$65$	−5.01564e11			−0.102313
$66$	−4.37534e12	−	3.37765e12i	−0.802055	−	0.619166i
$67$	−1.32990e12			−0.219430			−0.109715	−	0.993963i	$-0.534994\pi$
$67$	−1.32990e12			−0.219430			−0.109715	+	0.993963i	$0.534994\pi$
$68$	2.36913e12	+	9.05275e12i	0.352393	+	1.34654i
$69$		−	1.85528e13i		−	2.49153i
$70$	9.70092e12	+	7.48886e12i	1.17795	+	0.909346i
$71$			8.09853e12i			0.890425i	0.895425	+	0.445213i	$0.146872\pi$
$71$			8.09853e12i			0.890425i	−0.895425	+	0.445213i	$0.853128\pi$
$72$	−5.98270e12	+	1.40932e13i	−0.596444	+	1.40502i
$73$	8.89986e12			0.805607			0.402803	−	0.915287i	$-0.368036\pi$
$73$	8.89986e12			0.805607			0.402803	+	0.915287i	$0.368036\pi$
$74$	1.69045e12	−	2.18977e12i	0.139117	−	0.180209i
$75$	−9.61731e10			−0.00720484
$76$	−3.42572e12	−	1.30901e13i	−0.233914	−	0.893815i
$77$			1.51898e13i			0.946492i
$78$	−1.74163e12	+	2.25607e12i	−0.0991503	+	0.128437i
$79$			1.21047e13i			0.630326i	0.949038	+	0.315163i	$0.102059\pi$
$79$			1.21047e13i			0.630326i	−0.949038	+	0.315163i	$0.897941\pi$
$80$	−1.02963e13	−	1.83244e13i	−0.490966	−	0.873777i
$81$	−4.49631e12			−0.196545
$82$	1.17586e12	+	9.07730e11i	0.0471690	+	0.0364133i
$83$	−2.46085e13			−0.906855			−0.453427	−	0.891293i	$-0.649799\pi$
$83$	−2.46085e13			−0.906855			−0.453427	+	0.891293i	$0.649799\pi$
$84$	6.73709e13	−	1.76312e13i	2.28306	−	0.597485i
$85$			4.47216e13i			1.39503i
$86$	−3.62663e13	−	2.79966e13i	−1.04235	−	0.804667i
$87$			3.75306e13i			0.994836i
$88$	1.01800e13	−	2.39808e13i	0.249098	−	0.586793i
$89$	2.19758e13			0.496838			0.248419	−	0.968653i	$-0.420089\pi$
$89$	2.19758e13			0.496838			0.248419	+	0.968653i	$0.420089\pi$
$90$	−4.47132e13	+	5.79207e13i	−0.934843	+	1.21098i
$91$	7.83238e12			0.151567
$92$	8.45955e13	−	2.21389e13i	1.51646	−	0.396864i
$93$		−	1.20080e14i		−	1.99568i
$94$	−6.39437e12	+	8.28315e12i	−0.0986059	+	0.127732i
$95$		−	6.46666e13i		−	0.926008i
$96$	−1.18178e14	−	1.73162e13i	−1.57267	−	0.230437i
$97$	−1.90311e13			−0.235538			−0.117769	−	0.993041i	$-0.537574\pi$
$97$	−1.90311e13			−0.235538			−0.117769	+	0.993041i	$0.537574\pi$
$98$	−8.27702e13	−	6.38964e13i	−0.953435	−	0.736027i
$99$	−9.06928e13			−0.973031
$100$	−1.14762e11	−	4.38521e11i	−0.00114762	−	0.00438521i
$101$		−	2.40430e13i		−	0.224253i	−0.993694	−	0.112127i	$-0.964234\pi$
$101$		−	2.40430e13i		−	0.224253i	0.993694	−	0.112127i	$-0.0357662\pi$
$102$	2.01161e14	+	1.55291e14i	1.75123	+	1.35190i
$103$			1.95579e14i			1.59024i	0.606455	+	0.795118i	$0.292591\pi$
$103$			1.95579e14i			1.59024i	−0.606455	+	0.795118i	$0.707409\pi$
$104$	−1.23653e13	−	5.24917e12i	−0.0939662	−	0.0398894i
$105$	3.32820e14			2.36529
$106$	−5.71184e13	+	7.39901e13i	−0.379870	+	0.492076i
$107$	−1.37882e14			−0.858659			−0.429329	−	0.903148i	$-0.641250\pi$
$107$	−1.37882e14			−0.858659			−0.429329	+	0.903148i	$0.641250\pi$
$108$	3.63027e13	+	1.38717e14i	0.211823	+	0.809401i
$109$		−	8.76085e13i		−	0.479249i	−0.970866	−	0.239624i	$-0.922976\pi$
$109$		−	8.76085e13i		−	0.479249i	0.970866	−	0.239624i	$-0.0770242\pi$
$110$	7.60832e13	−	9.85566e13i	0.390427	−	0.505751i
$111$		−	7.51270e13i		−	0.361855i
$112$	1.60786e14	+	2.86153e14i	0.727315	+	1.29441i
$113$	−2.71872e14			−1.15562			−0.577810	−	0.816171i	$-0.696093\pi$
$113$	−2.71872e14			−1.15562			−0.577810	+	0.816171i	$0.696093\pi$
$114$	−2.90875e14	−	2.24548e14i	−1.16245	−	0.897379i
$115$	4.17911e14			1.57108
$116$	−1.71129e14	+	4.47849e13i	−0.605504	+	0.158462i
$117$			4.67643e13i			0.155816i
$118$	2.65667e14	+	2.05088e14i	0.833996	+	0.643823i
$119$		−	6.98369e14i		−	2.06660i
$120$	−5.25437e14	−	2.23052e14i	−1.46640	−	0.622499i
$121$	−2.25429e14			−0.593624
$122$	−3.55173e14	+	4.60084e14i	−0.882919	+	1.14372i
$123$	4.03414e13			0.0947142
$124$	5.47531e14	−	1.43291e14i	1.21467	−	0.317882i
$125$			4.75750e14i			0.997721i
$126$	6.98238e14	−	9.04484e14i	1.38487	−	1.79394i
$127$			2.81166e14i			0.527640i	0.964572	+	0.263820i	$0.0849824\pi$
$127$			2.81166e14i			0.527640i	−0.964572	+	0.263820i	$0.915018\pi$
$128$	−6.20635e13	−	5.59518e14i	−0.110247	−	0.993904i
$129$	−1.24423e15			−2.09301
$130$	−5.08191e13	−	3.92311e13i	−0.0809886	−	0.0625211i
$131$	5.85233e14			0.883954			0.441977	−	0.897026i	$-0.354277\pi$
$131$	5.85233e14			0.883954			0.441977	+	0.897026i	$0.354277\pi$
$132$	−1.79124e14	−	6.84456e14i	−0.256529	−	0.980231i
$133$			1.00983e15i			1.37178i
$134$	−1.34747e14	−	1.04021e14i	−0.173695	−	0.134088i
$135$			6.85278e14i			0.838553i
$136$	−4.68039e14	+	1.10254e15i	−0.543888	+	1.28122i
$137$	1.12437e15			1.24127			0.620635	−	0.784099i	$-0.286875\pi$
$137$	1.12437e15			1.24127			0.620635	+	0.784099i	$0.286875\pi$
$138$	1.45116e15	−	1.87980e15i	1.52251	−	1.97223i
$139$	4.72495e14			0.471296			0.235648	−	0.971838i	$-0.424279\pi$
$139$	4.72495e14			0.471296			0.235648	+	0.971838i	$0.424279\pi$
$140$	3.97151e14	+	1.51756e15i	0.376755	+	1.43963i
$141$			2.84179e14i			0.256483i
$142$	−6.33446e14	+	8.20554e14i	−0.544116	+	0.704837i
$143$		−	7.95732e13i		−	0.0650750i
$144$	−1.70851e15	+	9.59996e14i	−1.33070	+	0.747708i
$145$	−8.45396e14			−0.627313
$146$	9.01746e14	+	6.96125e14i	0.637697	+	0.492285i
$147$	−2.83969e15			−1.91447
$148$	3.42557e14	−	8.96482e13i	0.220242	−	0.0576381i
$149$		−	2.88701e15i		−	1.77070i	−0.464927	−	0.885349i	$-0.653919\pi$
$149$		−	2.88701e15i		−	1.77070i	0.464927	−	0.885349i	$-0.346081\pi$
$150$	−9.74439e12	−	7.52242e12i	−0.00570316	−	0.00440269i
$151$		−	2.24622e15i		−	1.25492i	−0.778651	−	0.627458i	$-0.784096\pi$
$151$		−	2.24622e15i		−	1.25492i	0.778651	−	0.627458i	$-0.215904\pi$
$152$	6.76776e14	−	1.59426e15i	0.361027	−	0.850459i
$153$	4.16971e15			2.12454
$154$	−1.18811e15	+	1.53905e15i	−0.578377	+	0.749218i
$155$	2.70487e15			1.25842
$156$	−3.52929e14	+	9.23626e13i	−0.156969	+	0.0410794i
$157$			8.29076e14i			0.352612i	0.984335	+	0.176306i	$0.0564148\pi$
$157$			8.29076e14i			0.352612i	−0.984335	+	0.176306i	$0.943585\pi$
$158$	−9.46801e14	+	1.22647e15i	−0.385176	+	0.498949i
$159$			2.53846e15i			0.988077i
$160$	3.90055e14	−	2.66201e15i	0.145307	−	0.991675i
$161$	−6.52607e15			−2.32740
$162$	−4.55572e14	−	3.51690e14i	−0.155579	−	0.120103i
$163$	7.28616e14			0.238334			0.119167	−	0.992874i	$-0.461978\pi$
$163$	7.28616e14			0.238334			0.119167	+	0.992874i	$0.461978\pi$
$164$	4.81390e13	+	1.83945e14i	0.0150865	+	0.0576476i
$165$		−	3.38129e15i		−	1.01554i
$166$	−2.49336e15	−	1.92481e15i	−0.717842	−	0.554155i
$167$		−	2.61445e15i		−	0.721714i	−0.932621	−	0.360857i	$-0.882484\pi$
$167$		−	2.61445e15i		−	0.721714i	0.932621	−	0.360857i	$-0.117516\pi$
$168$	8.20518e15	+	3.48317e15i	2.17232	+	0.922167i
$169$	3.89635e15			0.989579
$170$	−3.49801e15	+	4.53126e15i	−0.852470	+	1.10427i
$171$	−6.02932e15			−1.41025
$172$	−1.48472e15	−	5.67331e15i	−0.333385	−	1.27391i
$173$		−	3.10555e14i		−	0.0669601i	−0.999439	−	0.0334801i	$-0.989341\pi$
$173$		−	3.10555e14i		−	0.0669601i	0.999439	−	0.0334801i	$-0.0106590\pi$
$174$	−2.93555e15	+	3.80266e15i	−0.607918	+	0.787485i
$175$			3.38294e13i			0.00673021i
$176$	2.90717e15	−	1.63351e15i	0.555753	−	0.312272i
$177$	9.11454e15			1.67464
$178$	2.22662e15	+	1.71889e15i	0.393284	+	0.303605i
$179$	3.32891e14			0.0565368			0.0282684	−	0.999600i	$-0.491001\pi$
$179$	3.32891e14			0.0565368			0.0282684	+	0.999600i	$0.491001\pi$
$180$	−9.06082e15	+	2.37124e15i	−1.47999	+	0.387319i
$181$			8.99764e15i			1.41377i	0.707328	+	0.706885i	$0.249900\pi$
$181$			8.99764e15i			1.41377i	−0.707328	+	0.706885i	$0.750100\pi$
$182$	7.93587e14	+	6.12629e14i	0.119976	+	0.0926185i
$183$			1.57846e16i			2.29655i
$184$	1.03030e16	+	4.37370e15i	1.44291	+	0.612525i
$185$	1.69227e15			0.228175
$186$	9.39239e15	−	1.21667e16i	1.21951	−	1.57973i
$187$	−7.09509e15			−0.887292
$188$	−1.29577e15	+	3.39108e14i	−0.156108	+	0.0408539i
$189$		−	1.07012e16i		−	1.24223i
$190$	5.05806e15	−	6.55211e15i	0.565859	−	0.733003i
$191$			3.86382e15i			0.416661i	0.978058	+	0.208330i	$0.0668030\pi$
$191$			3.86382e15i			0.416661i	−0.978058	+	0.208330i	$0.933197\pi$
$192$	−1.06195e16	−	1.09981e16i	−1.10407	−	1.14342i
$193$	−1.19858e16			−1.20161			−0.600807	−	0.799394i	$-0.705154\pi$
$193$	−1.19858e16			−1.20161			−0.600807	+	0.799394i	$0.705154\pi$
$194$	−1.92825e15	−	1.48856e15i	−0.186445	−	0.143931i
$195$	−1.74351e15			−0.162623
$196$	−3.38857e15	−	1.29481e16i	−0.304947	−	1.16524i
$197$			1.39191e15i			0.120878i	0.998172	+	0.0604389i	$0.0192500\pi$
$197$			1.39191e15i			0.120878i	−0.998172	+	0.0604389i	$0.980750\pi$
$198$	−9.18912e15	−	7.09376e15i	−0.770225	−	0.594594i
$199$		−	4.03176e15i		−	0.326229i	−0.986607	−	0.163115i	$-0.947846\pi$
$199$		−	4.03176e15i		−	0.326229i	0.986607	−	0.163115i	$-0.0521540\pi$
$200$	2.26721e13	−	5.34080e13i	0.00177126	−	0.00417250i
$201$	−4.62293e15			−0.348775
$202$	1.88058e15	−	2.43607e15i	0.137035	−	0.177513i
$203$	1.32016e16			0.929298
$204$	8.23545e15	+	3.14687e16i	0.560114	+	2.14026i
$205$			9.08709e14i			0.0597239i
$206$	−1.52977e16	+	1.98163e16i	−0.971752	+	1.25879i
$207$		−	3.89648e16i		−	2.39265i
$208$	−8.42293e14	−	1.49904e15i	−0.0500057	−	0.0889957i
$209$	1.02594e16			0.588974
$210$	3.37218e16	+	2.60324e16i	1.87230	+	1.44537i
$211$	2.07372e16			1.11371			0.556855	−	0.830609i	$-0.312008\pi$
$211$	2.07372e16			1.11371			0.556855	+	0.830609i	$0.312008\pi$
$212$	−1.15746e16	+	3.02912e15i	−0.601390	+	0.157386i
$213$			2.81517e16i			1.41529i
$214$	−1.39704e16	−	1.07848e16i	−0.679691	−	0.524704i
$215$		−	2.80268e16i		−	1.31979i
$216$	−7.17186e15	+	1.68945e16i	−0.326931	+	0.770140i
$217$	−4.22390e16			−1.86421
$218$	6.85252e15	−	8.87662e15i	0.292856	−	0.379360i
$219$	3.09372e16			1.28048
$220$	1.54177e16	−	4.03486e15i	0.618103	−	0.161760i
$221$			3.65847e15i			0.142087i
$222$	5.87624e15	−	7.61197e15i	0.221120	−	0.286435i
$223$			2.76017e16i			1.00647i	0.864149	+	0.503235i	$0.167857\pi$
$223$			2.76017e16i			1.00647i	−0.864149	+	0.503235i	$0.832143\pi$
$224$	−6.09106e15	+	4.15697e16i	−0.215257	+	1.46906i
$225$	−2.01983e14			−0.00691891
$226$	−2.75464e16	−	2.12651e16i	−0.914758	−	0.706170i
$227$	−2.32141e16			−0.747431			−0.373715	−	0.927543i	$-0.621916\pi$
$227$	−2.32141e16			−0.747431			−0.373715	+	0.927543i	$0.621916\pi$
$228$	−1.19083e16	−	4.55031e16i	−0.371797	−	1.42068i
$229$		−	4.67157e16i		−	1.41454i	−0.706945	−	0.707268i	$-0.749927\pi$
$229$		−	4.67157e16i		−	1.41454i	0.706945	−	0.707268i	$-0.250073\pi$
$230$	4.23434e16	+	3.26880e16i	1.24363	+	0.960048i
$231$			5.28020e16i			1.50441i
$232$	−2.08420e16	−	8.84759e15i	−0.576133	−	0.244573i
$233$	9.79623e15			0.262765			0.131382	−	0.991332i	$-0.458058\pi$
$233$	9.79623e15			0.262765			0.131382	+	0.991332i	$0.458058\pi$
$234$	−3.65778e15	+	4.73822e15i	−0.0952154	+	0.123340i
$235$	−6.40127e15			−0.161730
$236$	1.08763e16	+	4.15596e16i	0.266745	+	1.01927i
$237$			4.20778e16i			1.00188i
$238$	5.46247e16	−	7.07597e16i	1.26284	−	1.63586i
$239$		−	6.19469e16i		−	1.39070i	−0.718670	−	0.695351i	$-0.755249\pi$
$239$		−	6.19469e16i		−	1.39070i	0.718670	−	0.695351i	$-0.244751\pi$
$240$	−3.57914e16	−	6.36984e16i	−0.780370	−	1.38883i
$241$	7.73096e16			1.63725			0.818624	−	0.574330i	$-0.194738\pi$
$241$	7.73096e16			1.63725			0.818624	+	0.574330i	$0.194738\pi$
$242$	−2.28408e16	−	1.76325e16i	−0.469897	−	0.362748i
$243$	−5.74892e16			−1.14906
$244$	−7.19732e16	+	1.88356e16i	−1.39779	+	0.365806i
$245$		−	6.39653e16i		−	1.20721i
$246$	4.08745e15	+	3.15540e15i	0.0749732	+	0.0578774i
$247$		−	5.29008e15i		−	0.0943155i
$248$	6.66845e16	+	2.83081e16i	1.15575	+	0.490624i
$249$	−8.55426e16			−1.44141
$250$	−3.72120e16	+	4.82037e16i	−0.609681	+	0.789769i
$251$	−6.01638e15			−0.0958560			−0.0479280	−	0.998851i	$-0.515262\pi$
$251$	−6.01638e15			−0.0958560			−0.0479280	+	0.998851i	$0.515262\pi$
$252$	1.41493e17	−	3.70291e16i	2.19246	−	0.573773i
$253$			6.63017e16i			0.999266i
$254$	−2.19921e16	+	2.84882e16i	−0.322427	+	0.417666i
$255$			1.55459e17i			2.21735i
$256$	3.74758e16	−	6.15456e16i	0.520081	−	0.854117i
$257$	9.51315e16			1.28467			0.642337	−	0.766423i	$-0.277965\pi$
$257$	9.51315e16			1.28467			0.642337	+	0.766423i	$0.277965\pi$
$258$	−1.26067e17	−	9.73203e16i	−1.65677	−	1.27899i
$259$	−2.64264e16			−0.338017
$260$	−2.08051e15	−	7.94989e15i	−0.0259034	−	0.0989801i
$261$			7.88221e16i			0.955355i
$262$	5.92966e16	+	4.57754e16i	0.699714	+	0.540161i
$263$		−	2.88339e15i		−	0.0331294i	−0.999863	−	0.0165647i	$-0.994727\pi$
$263$		−	2.88339e15i		−	0.0331294i	0.999863	−	0.0165647i	$-0.00527294\pi$
$264$	3.53873e16	−	8.33607e16i	0.395932	−	0.932683i
$265$	−5.71801e16			−0.623051
$266$	−7.89862e16	+	1.02317e17i	−0.838262	+	1.08587i
$267$	7.63912e16			0.789704
$268$	−5.51649e15	−	2.10792e16i	−0.0555545	−	0.212281i
$269$		−	1.57898e17i		−	1.54921i	−0.632447	−	0.774603i	$-0.717949\pi$
$269$		−	1.57898e17i		−	1.54921i	0.632447	−	0.774603i	$-0.282051\pi$
$270$	−5.36007e16	+	6.94334e16i	−0.512418	+	0.663776i
$271$			2.91066e16i			0.271148i	0.990767	+	0.135574i	$0.0432878\pi$
$271$			2.91066e16i			0.271148i	−0.990767	+	0.135574i	$0.956712\pi$
$272$	−1.33661e17	+	7.51025e16i	−1.21345	+	0.681824i
$273$	2.72265e16			0.240909
$274$	1.13923e17	+	8.79456e16i	0.982557	+	0.758508i
$275$	3.43691e14			0.00288961
$276$	2.94066e17	−	7.69581e16i	2.41036	−	0.630798i
$277$			1.60748e16i			0.128466i	0.997935	+	0.0642330i	$0.0204601\pi$
$277$			1.60748e16i			0.128466i	−0.997935	+	0.0642330i	$0.979540\pi$
$278$	4.78739e16	+	3.69574e16i	0.373065	+	0.287997i
$279$		−	2.52194e17i		−	1.91648i
$280$	−7.84600e16	+	1.84826e17i	−0.581490	+	1.36980i
$281$	1.02347e17			0.739828			0.369914	−	0.929066i	$-0.379387\pi$
$281$	1.02347e17			0.739828			0.369914	+	0.929066i	$0.379387\pi$
$282$	−2.22278e16	+	2.87934e16i	−0.156730	+	0.203025i
$283$	−1.56843e17			−1.07885			−0.539423	−	0.842035i	$-0.681358\pi$
$283$	−1.56843e17			−1.07885			−0.539423	+	0.842035i	$0.681358\pi$
$284$	−1.28363e17	+	3.35931e16i	−0.861415	+	0.225435i
$285$		−	2.24791e17i		−	1.47185i
$286$	6.22401e15	−	8.06247e15i	0.0397657	−	0.0515117i
$287$		−	1.41903e16i		−	0.0884747i
$288$	−2.48197e17	−	3.63675e16i	−1.51025	−	0.221292i
$289$	1.57827e17			0.937340
$290$	−8.56567e16	−	6.61247e16i	−0.496564	−	0.383334i
$291$	−6.61547e16			−0.374378
$292$	3.69171e16	+	1.41065e17i	0.203961	+	0.779360i
$293$		−	2.71733e17i		−	1.46578i	−0.680347	−	0.732890i	$-0.738171\pi$
$293$		−	2.71733e17i		−	1.46578i	0.680347	−	0.732890i	$-0.261829\pi$
$294$	−2.87721e17	−	2.22113e17i	−1.51545	−	1.16989i
$295$			2.05309e17i			1.05598i
$296$	4.17204e16	+	1.77107e16i	0.209559	+	0.0889596i
$297$	−1.08720e17			−0.533350
$298$	2.25815e17	−	2.92516e17i	1.08203	−	1.40164i
$299$	3.41874e16			0.160018
$300$	−3.98931e14	−	1.52436e15i	−0.00182410	−	0.00697011i
$301$			4.37664e17i			1.95513i
$302$	1.75694e17	−	2.27591e17i	0.766846	−	0.993357i
$303$		−	8.35770e16i		−	0.356441i
$304$	1.93271e17	−	1.08597e17i	0.805473	−	0.452587i
$305$	−3.55556e17			−1.44813
$306$	4.22481e17	+	3.26144e17i	1.68173	+	1.29825i
$307$	1.65624e17			0.644397			0.322199	−	0.946672i	$-0.395578\pi$
$307$	1.65624e17			0.644397			0.322199	+	0.946672i	$0.395578\pi$
$308$	−2.40762e17	+	6.30081e16i	−0.915656	+	0.239630i
$309$			6.79861e17i			2.52761i
$310$	2.74061e17	+	2.11568e17i	0.996129	+	0.768985i
$311$			1.03818e17i			0.368934i	0.982839	+	0.184467i	$0.0590559\pi$
$311$			1.03818e17i			0.368934i	−0.982839	+	0.184467i	$0.940944\pi$
$312$	−4.29836e16	−	1.82469e16i	−0.149355	−	0.0634026i
$313$	6.36413e16			0.216236			0.108118	−	0.994138i	$-0.465518\pi$
$313$	6.36413e16			0.216236			0.108118	+	0.994138i	$0.465518\pi$
$314$	−6.48483e16	+	8.40032e16i	−0.215472	+	0.279118i
$315$	6.98991e17			2.27142
$316$	−1.91862e17	+	5.02110e16i	−0.609790	+	0.159584i
$317$		−	9.21049e16i		−	0.286331i	−0.989699	−	0.143165i	$-0.954272\pi$
$317$		−	9.21049e16i		−	0.286331i	0.989699	−	0.143165i	$-0.0457280\pi$
$318$	−1.98552e17	+	2.57200e17i	−0.603788	+	0.782135i
$319$		−	1.34122e17i		−	0.398993i
$320$	2.47736e17	−	2.39209e17i	0.721008	−	0.696190i
$321$	−4.79297e17			−1.36480
$322$	−6.61230e17	−	5.10453e17i	−1.84231	−	1.42221i
$323$	−4.71686e17			−1.28598
$324$	−1.86509e16	−	7.12674e16i	−0.0497605	−	0.190141i
$325$		−	1.77219e14i		−	0.000462728i
$326$	7.38244e16	+	5.69905e16i	0.188659	+	0.145640i
$327$		−	3.04540e17i		−	0.761746i
$328$	−9.51020e15	+	2.24029e16i	−0.0232848	+	0.0548513i
$329$	9.99617e16			0.239587
$330$	2.64476e17	−	3.42597e17i	0.620568	−	0.803871i
$331$	7.48431e17			1.71932			0.859658	−	0.510869i	$-0.170676\pi$
$331$	7.48431e17			1.71932			0.859658	+	0.510869i	$0.170676\pi$
$332$	−1.02077e17	−	3.90049e17i	−0.229595	−	0.877309i
$333$		−	1.57782e17i		−	0.347495i
$334$	2.04496e17	−	2.64900e17i	0.441020	−	0.571289i
$335$		−	1.04134e17i		−	0.219926i
$336$	5.58916e17	+	9.94708e17i	1.15604	+	2.05741i
$337$	−8.81200e17			−1.78511			−0.892555	−	0.450938i	$-0.851090\pi$
$337$	−8.81200e17			−1.78511			−0.892555	+	0.450938i	$0.851090\pi$
$338$	3.94783e17	+	3.04762e17i	0.783325	+	0.604706i
$339$	−9.45067e17			−1.83681
$340$	−7.08847e17	+	1.85508e17i	−1.34958	+	0.353191i
$341$			4.29128e17i			0.800398i
$342$	−6.10899e17	−	4.71598e17i	−1.11631	−	0.861765i
$343$			1.69576e17i			0.303603i
$344$	2.93318e17	−	6.90959e17i	0.514552	−	1.21211i
$345$	1.45272e18			2.49717
$346$	2.42909e16	−	3.14659e16i	0.0409176	−	0.0530039i
$347$	1.89663e17			0.313096			0.156548	−	0.987670i	$-0.449963\pi$
$347$	1.89663e17			0.313096			0.156548	+	0.987670i	$0.449963\pi$
$348$	−5.94869e17	+	1.55679e17i	−0.962424	+	0.251869i
$349$		−	2.47465e17i		−	0.392406i	−0.980563	−	0.196203i	$-0.937139\pi$
$349$		−	2.47465e17i		−	0.392406i	0.980563	−	0.196203i	$-0.0628611\pi$
$350$	−2.64605e15	+	3.42765e15i	−0.00411266	+	0.00532745i
$351$			5.60595e16i			0.0854081i
$352$	4.22328e17	+	6.18822e16i	0.630741	+	0.0924203i
$353$	8.64682e17			1.26600			0.633000	−	0.774152i	$-0.281824\pi$
$353$	8.64682e17			1.26600			0.633000	+	0.774152i	$0.281824\pi$
$354$	9.23498e17	+	7.12916e17i	1.32560	+	1.02333i
$355$	−6.34130e17			−0.892441
$356$	9.11568e16	+	3.48321e17i	0.125788	+	0.480651i
$357$		−	2.42763e18i		−	3.28477i
$358$	3.37290e16	+	2.60379e16i	0.0447530	+	0.0345482i
$359$			6.51784e17i			0.848091i	0.905641	+	0.424045i	$0.139390\pi$
$359$			6.51784e17i			0.848091i	−0.905641	+	0.424045i	$0.860610\pi$
$360$	−1.10353e18	−	4.68456e17i	−1.40820	−	0.597794i
$361$	−1.16958e17			−0.146379
$362$	−7.03773e17	+	9.11654e17i	−0.863918	+	1.11910i
$363$	−7.83623e17			−0.943542
$364$	3.24891e16	+	1.24145e17i	0.0383732	+	0.146629i
$365$			6.96876e17i			0.807431i
$366$	−1.23463e18	+	1.59932e18i	−1.40336	+	1.81789i
$367$		−	9.80258e17i		−	1.09315i	−0.837412	−	0.546573i	$-0.815932\pi$
$367$		−	9.80258e17i		−	1.09315i	0.837412	−	0.546573i	$-0.184068\pi$
$368$	7.01812e17	+	1.24902e18i	0.767868	+	1.36658i
$369$	8.47253e16			0.0909554
$370$	1.71463e17	+	1.32365e17i	0.180617	+	0.139432i
$371$	8.92919e17			0.922985
$372$	1.90330e18	−	4.98100e17i	1.93066	−	0.505261i
$373$		−	2.96658e17i		−	0.295321i	−0.989038	−	0.147660i	$-0.952826\pi$
$373$		−	2.96658e17i		−	0.295321i	0.989038	−	0.147660i	$-0.0471743\pi$
$374$	−7.18885e17	−	5.54960e17i	−0.702357	−	0.542201i
$375$			1.65378e18i			1.58584i
$376$	−1.57814e17	−	6.69933e16i	−0.148535	−	0.0630545i
$377$	−6.91579e16			−0.0638929
$378$	8.37025e17	−	1.08427e18i	0.759094	−	0.983316i
$379$	1.46559e18			1.30478			0.652389	−	0.757884i	$-0.273767\pi$
$379$	1.46559e18			1.30478			0.652389	+	0.757884i	$0.273767\pi$
$380$	1.02498e18	−	2.68240e17i	0.895839	−	0.234444i
$381$			9.77376e17i			0.838662i
$382$	−3.02218e17	+	3.91487e17i	−0.254611	+	0.329818i
$383$			4.12014e17i			0.340816i	0.985374	+	0.170408i	$0.0545086\pi$
$383$			4.12014e17i			0.340816i	−0.985374	+	0.170408i	$0.945491\pi$
$384$	−2.15742e17	−	1.94497e18i	−0.175233	−	1.57977i
$385$	−1.18939e18			−0.948635
$386$	−1.21442e18	−	9.37497e17i	−0.951166	−	0.734275i
$387$	−2.61313e18			−2.00995
$388$	−7.89418e16	−	3.01646e17i	−0.0596327	−	0.227864i
$389$			1.84541e18i			1.36913i	0.728950	+	0.684567i	$0.240009\pi$
$389$			1.84541e18i			1.36913i	−0.728950	+	0.684567i	$0.759991\pi$
$390$	−1.76655e17	−	1.36373e17i	−0.128728	−	0.0993747i
$391$		−	3.04830e18i		−	2.18183i
$392$	6.69437e17	−	1.57697e18i	0.470660	−	1.10872i
$393$	2.03435e18			1.40501
$394$	−1.08871e17	+	1.41030e17i	−0.0738653	+	0.0956837i
$395$	−9.47823e17			−0.631753
$396$	−3.76198e17	−	1.43750e18i	−0.246349	−	0.941329i
$397$		−	3.70137e17i		−	0.238138i	−0.992886	−	0.119069i	$-0.962009\pi$
$397$		−	3.70137e17i		−	0.238138i	0.992886	−	0.119069i	$-0.0379910\pi$
$398$	3.15354e17	−	4.08503e17i	0.199350	−	0.258234i
$399$			3.51031e18i			2.18039i
$400$	6.47461e15	−	3.63801e15i	0.00395179	−	0.00222047i
$401$	−7.04980e17			−0.422831			−0.211415	−	0.977396i	$-0.567807\pi$
$401$	−7.04980e17			−0.422831			−0.211415	+	0.977396i	$0.567807\pi$
$402$	−4.68402e17	−	3.61594e17i	−0.276081	−	0.213127i
$403$	2.21273e17			0.128172
$404$	3.81086e17	−	9.97316e16i	0.216947	−	0.0567758i
$405$		−	3.52069e17i		−	0.196989i
$406$	1.33761e18	+	1.03260e18i	0.735608	+	0.567870i
$407$			2.68479e17i			0.145127i
$408$	−1.62697e18	+	3.83261e18i	−0.864488	+	2.03645i
$409$	−2.58822e18			−1.35188			−0.675940	−	0.736957i	$-0.736262\pi$
$409$	−2.58822e18			−1.35188			−0.675940	+	0.736957i	$0.736262\pi$
$410$	−7.10769e16	+	9.20717e16i	−0.0364957	+	0.0472758i
$411$	3.90849e18			1.97295
$412$	−3.09997e18	+	8.11271e17i	−1.53843	+	0.402611i
$413$		−	3.20609e18i		−	1.56432i
$414$	3.04773e18	−	3.94797e18i	1.46209	−	1.89396i
$415$		−	1.92689e18i		−	0.908908i
$416$	3.19086e16	−	2.17767e17i	0.0147997	−	0.101004i
$417$	1.64246e18			0.749106
$418$	1.03949e18	+	8.02462e17i	0.466217	+	0.359907i
$419$	−3.91566e18			−1.72706			−0.863528	−	0.504300i	$-0.831751\pi$
$419$	−3.91566e18			−1.72706			−0.863528	+	0.504300i	$0.831751\pi$
$420$	1.38056e18	+	5.27527e18i	0.598837	+	2.28823i
$421$			2.55032e18i			1.08798i	0.839092	+	0.543989i	$0.183087\pi$
$421$			2.55032e18i			1.08798i	−0.839092	+	0.543989i	$0.816913\pi$
$422$	2.10112e18	+	1.62201e18i	0.881584	+	0.680560i
$423$			5.96835e17i			0.246304i
$424$	−1.40969e18	−	5.98424e17i	−0.572219	−	0.242912i
$425$	−1.58016e16			−0.00630926
$426$	−2.20195e18	+	2.85237e18i	−0.864850	+	1.12031i
$427$	5.55233e18			2.14526
$428$	−5.71941e17	−	2.18546e18i	−0.217393	−	0.830684i
$429$		−	2.76608e17i		−	0.103434i
$430$	2.19219e18	−	2.83972e18i	0.806489	−	1.04471i
$431$			2.11271e18i			0.764715i	0.924014	+	0.382357i	$0.124888\pi$
$431$			2.11271e18i			0.764715i	−0.924014	+	0.382357i	$0.875112\pi$
$432$	−2.04811e18	+	1.15081e18i	−0.729402	+	0.409843i
$433$	3.04735e18			1.06784			0.533920	−	0.845535i	$-0.320718\pi$
$433$	3.04735e18			1.06784			0.533920	+	0.845535i	$0.320718\pi$
$434$	−4.27971e18	−	3.30383e18i	−1.47566	−	1.13917i
$435$	−2.93872e18			−0.997088
$436$	1.38861e18	−	3.63405e17i	0.463635	−	0.121335i
$437$			4.40778e18i			1.44827i
$438$	3.13460e18	+	2.41983e18i	1.01359	+	0.782467i
$439$		−	5.46314e18i		−	1.73856i	−0.494317	−	0.869282i	$-0.664582\pi$
$439$		−	5.46314e18i		−	1.73856i	0.494317	−	0.869282i	$-0.335418\pi$
$440$	1.87774e18	+	7.97116e17i	0.588121	+	0.249662i
$441$	−5.96393e18			−1.83850
$442$	−2.86156e17	+	3.70681e17i	−0.0868255	+	0.112472i
$443$	2.92108e18			0.872403			0.436202	−	0.899849i	$-0.356323\pi$
$443$	2.92108e18			0.872403			0.436202	+	0.899849i	$0.356323\pi$
$444$	1.19078e18	−	3.11630e17i	0.350066	−	0.0916134i
$445$			1.72075e18i			0.497963i
$446$	−2.15893e18	+	2.79664e18i	−0.615028	+	0.796695i
$447$		−	1.00357e19i		−	2.81445i
$448$	−3.86863e18	+	3.73547e18i	−1.06810	+	1.03133i
$449$	−2.03315e18			−0.552644			−0.276322	−	0.961065i	$-0.589116\pi$
$449$	−2.03315e18			−0.552644			−0.276322	+	0.961065i	$0.589116\pi$
$450$	−2.04652e16	−	1.57986e16i	−0.00547683	−	0.00422797i
$451$	−1.44167e17			−0.0379865
$452$	−1.12774e18	−	4.30923e18i	−0.292576	−	1.11797i
$453$		−	7.80820e18i		−	1.99464i
$454$	−2.35209e18	−	1.81575e18i	−0.591646	−	0.456736i
$455$			6.13290e17i			0.151910i
$456$	2.35257e18	−	5.54187e18i	0.573837	−	1.35177i
$457$	−7.81286e18			−1.87671			−0.938353	−	0.345678i	$-0.887649\pi$
$457$	−7.81286e18			−1.87671			−0.938353	+	0.345678i	$0.887649\pi$
$458$	3.65398e18	−	4.73329e18i	0.864386	−	1.11971i
$459$	4.99851e18			1.16453
$460$	1.73352e18	+	6.62398e18i	0.397762	+	1.51990i
$461$		−	4.55572e17i		−	0.102956i	−0.998674	−	0.0514779i	$-0.983607\pi$
$461$		−	4.55572e17i		−	0.102956i	0.998674	−	0.0514779i	$-0.0163932\pi$
$462$	−4.13004e18	+	5.34997e18i	−0.919306	+	1.19085i
$463$			7.66287e18i			1.68006i	0.542541	+	0.840029i	$0.317462\pi$
$463$			7.66287e18i			1.68006i	−0.542541	+	0.840029i	$0.682538\pi$
$464$	−1.41970e18	−	2.52666e18i	−0.306599	−	0.545658i
$465$	9.40252e18			2.00020
$466$	9.92567e17	+	7.66236e17i	0.207998	+	0.160569i
$467$	8.71213e17			0.179848			0.0899241	−	0.995949i	$-0.471338\pi$
$467$	8.71213e17			0.179848			0.0899241	+	0.995949i	$0.471338\pi$
$468$	−7.41224e17	+	1.93981e17i	−0.150740	+	0.0394491i
$469$			1.62614e18i			0.325798i
$470$	−6.48586e17	−	5.00691e17i	−0.128021	−	0.0988292i
$471$			2.88199e18i			0.560462i
$472$	−2.14869e18	+	5.06159e18i	−0.411699	+	0.969825i
$473$	4.44646e18			0.839434
$474$	−3.29122e18	+	4.26338e18i	−0.612221	+	0.793060i
$475$	2.28488e16			0.00418801
$476$	1.10693e19	−	2.89687e18i	1.99927	−	0.523215i
$477$			5.33129e18i			0.948864i
$478$	4.84533e18	−	6.27655e18i	0.849822	−	1.10084i
$479$			9.96595e18i			1.72254i	0.508145	+	0.861271i	$0.330331\pi$
$479$			9.96595e18i			1.72254i	−0.508145	+	0.861271i	$0.669669\pi$
$480$	1.35589e18	−	9.25353e18i	0.230959	−	1.57623i
$481$	1.38437e17			0.0232400
$482$	7.83312e18	+	6.04696e18i	1.29600	+	1.00048i
$483$	−2.26856e19			−3.69930
$484$	−9.35090e17	−	3.57309e18i	−0.150292	−	0.574284i
$485$		−	1.49017e18i		−	0.236071i
$486$	−5.82488e18	−	4.49666e18i	−0.909564	−	0.702160i
$487$			6.28608e18i			0.967559i	0.875190	+	0.483779i	$0.160736\pi$
$487$			6.28608e18i			0.967559i	−0.875190	+	0.483779i	$0.839264\pi$
$488$	−8.76570e18	−	3.72111e18i	−1.32999	−	0.564591i
$489$	2.53278e18			0.378822
$490$	5.00321e18	−	6.48106e18i	0.737694	−	0.955594i
$491$	−8.40608e18			−1.22186			−0.610932	−	0.791683i	$-0.709205\pi$
$491$	−8.40608e18			−1.22186			−0.610932	+	0.791683i	$0.709205\pi$
$492$	1.67338e17	+	6.39420e17i	0.0239795	+	0.0916284i
$493$			6.16642e18i			0.871174i
$494$	4.13776e17	−	5.35998e17i	0.0576338	−	0.0746577i
$495$		−	7.10142e18i		−	0.975233i
$496$	4.54238e18	+	8.08411e18i	0.615051	+	1.09461i
$497$	9.90251e18			1.32206
$498$	−8.66729e18	−	6.69093e18i	−1.14098	−	0.880807i
$499$	1.12605e19			1.46169			0.730845	−	0.682543i	$-0.239126\pi$
$499$	1.12605e19			1.46169			0.730845	+	0.682543i	$0.239126\pi$
$500$	−7.54074e18	+	1.97344e18i	−0.965215	+	0.252600i
$501$		−	9.08821e18i		−	1.14713i
$502$	−6.09588e17	−	4.70586e17i	−0.0758770	−	0.0585751i
$503$			9.42941e18i			1.15747i	0.815517	+	0.578734i	$0.196453\pi$
$503$			9.42941e18i			1.15747i	−0.815517	+	0.578734i	$0.803547\pi$
$504$	1.72326e19	+	7.31537e18i	2.08611	+	0.885570i
$505$	1.88261e18			0.224761
$506$	−5.18595e18	+	6.71778e18i	−0.610625	+	0.790992i
$507$	1.35443e19			1.57290
$508$	−4.45655e18	+	1.16629e18i	−0.510449	+	0.133586i
$509$		−	1.61219e19i		−	1.82134i	−0.413131	−	0.910672i	$-0.635565\pi$
$509$		−	1.61219e19i		−	1.82134i	0.413131	−	0.910672i	$-0.364435\pi$
$510$	−1.21596e19	+	1.57513e19i	−1.35497	+	1.75520i
$511$		−	1.08823e19i		−	1.19612i
$512$	8.61104e18	−	3.30463e18i	0.933611	−	0.358289i
$513$	−7.22774e18			−0.773003
$514$	9.63886e18	+	7.44095e18i	1.01691	+	0.785031i
$515$	−1.53142e19			−1.59384
$516$	−5.16112e18	−	1.97213e19i	−0.529902	−	2.02482i
$517$		−	1.01556e18i		−	0.102866i
$518$	−2.67755e18	−	2.06700e18i	−0.267565	−	0.206554i
$519$		−	1.07954e18i		−	0.106430i
$520$	4.11020e17	−	9.68227e17i	0.0399797	−	0.0941789i
$521$	1.75596e17			0.0168520			0.00842599	−	0.999965i	$-0.497318\pi$
$521$	1.75596e17			0.0168520			0.00842599	+	0.999965i	$0.497318\pi$
$522$	−6.16527e18	+	7.98637e18i	−0.583792	+	0.756233i
$523$	−1.25789e18			−0.117525			−0.0587627	−	0.998272i	$-0.518716\pi$
$523$	−1.25789e18			−0.117525			−0.0587627	+	0.998272i	$0.518716\pi$
$524$	2.42757e18	+	9.27606e18i	0.223797	+	0.855154i
$525$			1.17596e17i			0.0106974i
$526$	2.25532e17	−	2.92149e17i	0.0202445	−	0.0262243i
$527$		−	1.97296e19i		−	1.74761i
$528$	1.01058e19	−	5.67832e18i	0.883347	−	0.496344i
$529$	−1.68927e19			−1.45717
$530$	−5.79356e18	−	4.47248e18i	−0.493190	−	0.380730i
$531$	1.91424e19			1.60818
$532$	−1.60060e19	+	4.18882e18i	−1.32709	+	0.347304i
$533$			7.43373e16i			0.00608298i
$534$	7.74006e18	+	5.97512e18i	0.625109	+	0.482568i
$535$		−	1.07964e19i		−	0.860603i
$536$	1.08982e18	−	2.56726e18i	0.0857437	−	0.201984i
$537$	1.15718e18			0.0898630
$538$	1.23503e19	−	1.59984e19i	0.946680	−	1.22631i
$539$	1.01481e19			0.767828
$540$	−1.08618e19	+	2.84257e18i	−0.811233	+	0.212302i
$541$			1.96944e19i			1.45199i	0.687702	+	0.725993i	$0.258620\pi$
$541$			1.96944e19i			1.45199i	−0.687702	+	0.725993i	$0.741380\pi$
$542$	−2.27664e18	+	2.94912e18i	−0.165691	+	0.214633i
$543$			3.12771e19i			2.24713i
$544$	−1.94170e19	−	2.84511e18i	−1.37718	−	0.201793i
$545$	6.85991e18			0.480333
$546$	2.75863e18	+	2.12959e18i	0.190697	+	0.147213i
$547$	−1.48813e19			−1.01562			−0.507809	−	0.861470i	$-0.669545\pi$
$547$	−1.48813e19			−1.01562			−0.507809	+	0.861470i	$0.669545\pi$
$548$	4.66396e18	+	1.78216e19i	0.314261	+	1.20083i
$549$			3.31509e19i			2.20541i
$550$	3.48232e16	+	2.68826e16i	0.00228734	+	0.00176577i
$551$		−	8.91653e18i		−	0.578275i
$552$	3.58147e19	+	1.52036e19i	2.29344	+	0.973584i
$553$	1.48011e19			0.935877
$554$	−1.25733e18	+	1.62872e18i	−0.0785022	+	0.101690i
$555$	5.88258e18			0.362675
$556$	1.95993e18	+	7.48915e18i	0.119321	+	0.455941i
$557$		−	3.26875e19i		−	1.96515i	−0.185877	−	0.982573i	$-0.559512\pi$
$557$		−	3.26875e19i		−	1.96515i	0.185877	−	0.982573i	$-0.440488\pi$
$558$	1.97260e19	−	2.55526e19i	1.17111	−	1.51704i
$559$		−	2.29275e18i		−	0.134423i
$560$	−2.24063e19	+	1.25899e19i	−1.29734	+	0.728961i
$561$	−2.46636e19			−1.41031
$562$	1.03699e19	+	8.00532e18i	0.585628	+	0.452090i
$563$	−4.43043e18			−0.247108			−0.123554	−	0.992338i	$-0.539429\pi$
$563$	−4.43043e18			−0.247108			−0.123554	+	0.992338i	$0.539429\pi$
$564$	−4.50430e18	+	1.17879e18i	−0.248127	+	0.0649356i
$565$		−	2.12881e19i		−	1.15824i
$566$	−1.58915e19	−	1.22679e19i	−0.853987	−	0.659255i
$567$			5.49788e18i			0.291819i
$568$	−1.56335e19	−	6.63656e18i	−0.819631	−	0.347940i
$569$	1.46295e19			0.757607			0.378803	−	0.925477i	$-0.376336\pi$
$569$	1.46295e19			0.757607			0.378803	+	0.925477i	$0.376336\pi$
$570$	1.75825e19	−	2.27761e19i	0.899410	−	1.16508i
$571$	2.65274e19			1.34043			0.670213	−	0.742169i	$-0.266203\pi$
$571$	2.65274e19			1.34043			0.670213	+	0.742169i	$0.266203\pi$
$572$	1.26125e18	−	3.30074e17i	0.0629549	−	0.0164755i
$573$			1.34312e19i			0.662265i
$574$	1.10993e18	−	1.43778e18i	0.0540646	−	0.0700342i
$575$			1.47662e17i			0.00710546i
$576$	−2.23031e19	−	2.30982e19i	−1.06025	−	1.09805i
$577$	−2.51473e19			−1.18103			−0.590515	−	0.807026i	$-0.701075\pi$
$577$	−2.51473e19			−1.18103			−0.590515	+	0.807026i	$0.701075\pi$
$578$	1.59913e19	+	1.23449e19i	0.741973	+	0.572784i
$579$	−4.16643e19			−1.90992
$580$	−3.50674e18	−	1.33997e19i	−0.158821	−	0.606875i
$581$			3.00901e19i			1.34645i
$582$	−6.70289e18	−	5.17446e18i	−0.296347	−	0.228772i
$583$		−	9.07163e18i		−	0.396283i
$584$	−7.29323e18	+	1.71804e19i	−0.314797	+	0.741556i
$585$	−3.66173e18			−0.156169
$586$	2.12543e19	−	2.75324e19i	0.895701	−	1.16027i
$587$	4.92032e18			0.204893			0.102446	−	0.994739i	$-0.467333\pi$
$587$	4.92032e18			0.204893			0.102446	+	0.994739i	$0.467333\pi$
$588$	−1.17792e19	−	4.50097e19i	−0.484701	−	1.85210i
$589$			2.85287e19i			1.16004i
$590$	−1.60588e19	+	2.08022e19i	−0.645280	+	0.835884i
$591$			4.83847e18i			0.192130i
$592$	2.84189e18	+	5.05773e18i	0.111521	+	0.198474i
$593$	−2.39619e19			−0.929264			−0.464632	−	0.885504i	$-0.653813\pi$
$593$	−2.39619e19			−0.929264			−0.464632	+	0.885504i	$0.653813\pi$
$594$	−1.10156e19	−	8.50377e18i	−0.422186	−	0.325916i
$595$	5.46836e19			2.07128
$596$	4.57597e19	−	1.19755e19i	1.71301	−	0.448300i
$597$		−	1.40150e19i		−	0.518528i
$598$	3.46392e18	+	2.67405e18i	0.126666	+	0.0977826i
$599$		−	6.06768e18i		−	0.219298i	−0.993970	−	0.109649i	$-0.965027\pi$
$599$		−	6.06768e18i		−	0.219298i	0.993970	−	0.109649i	$-0.0349727\pi$
$600$	7.88116e16	−	1.85654e17i	0.00281534	−	0.00663201i
$601$	−1.09470e19			−0.386522			−0.193261	−	0.981147i	$-0.561906\pi$
$601$	−1.09470e19			−0.386522			−0.193261	+	0.981147i	$0.561906\pi$
$602$	−3.42330e19	+	4.43448e19i	−1.19473	+	1.54763i
$603$	−9.70911e18			−0.334933
$604$	3.56031e19	−	9.31745e18i	1.21403	−	0.317716i
$605$		−	1.76515e19i		−	0.594968i
$606$	6.53718e18	−	8.46814e18i	0.217812	−	0.282150i
$607$			7.60119e18i			0.250358i	0.992134	+	0.125179i	$0.0399504\pi$
$607$			7.60119e18i			0.250358i	−0.992134	+	0.125179i	$0.960050\pi$
$608$	2.80766e19	+	4.11397e18i	0.914155	+	0.133948i
$609$	4.58908e19			1.47708
$610$	−3.60254e19	−	2.78107e19i	−1.14630	−	0.884917i
$611$	−5.23659e17			−0.0164725
$612$	1.72962e19	+	6.60907e19i	0.537885	+	2.05533i
$613$			8.67491e18i			0.266711i	0.991068	+	0.133356i	$0.0425753\pi$
$613$			8.67491e18i			0.266711i	−0.991068	+	0.133356i	$0.957425\pi$
$614$	1.67812e19	+	1.29547e19i	0.510088	+	0.393775i
$615$			3.15881e18i			0.0949286i
$616$	−2.93226e19	−	1.24477e19i	−0.871240	−	0.369849i
$617$	3.43504e19			1.00910			0.504551	−	0.863382i	$-0.331658\pi$
$617$	3.43504e19			1.00910			0.504551	+	0.863382i	$0.331658\pi$
$618$	−5.31770e19	+	6.88845e19i	−1.54456	+	2.00079i
$619$	−5.38020e19			−1.54513			−0.772563	−	0.634939i	$-0.781025\pi$
$619$	−5.38020e19			−1.54513			−0.772563	+	0.634939i	$0.781025\pi$
$620$	1.12199e19	+	4.28727e19i	0.318602	+	1.21742i
$621$		−	4.67097e19i		−	1.31149i
$622$	−8.12037e18	+	1.05190e19i	−0.225446	+	0.292039i
$623$		−	2.68710e19i		−	0.737680i
$624$	−2.92793e18	−	5.21087e18i	−0.0794821	−	0.141455i
$625$	−3.74210e19			−1.00451
$626$	6.44822e18	+	4.97786e18i	0.171167	+	0.132136i
$627$	3.56631e19			0.936151
$628$	−1.31410e19	+	3.43905e18i	−0.341124	+	0.0892732i
$629$		−	1.23436e19i		−	0.316875i
$630$	7.08228e19	+	5.46733e19i	1.79800	+	1.38801i
$631$		−	3.63162e19i		−	0.911790i	−0.890034	−	0.455895i	$-0.849319\pi$
$631$		−	3.63162e19i		−	0.911790i	0.890034	−	0.455895i	$-0.150681\pi$
$632$	−2.33672e19	−	9.91955e18i	−0.580211	−	0.246304i
$633$	7.20855e19			1.77020
$634$	7.20421e18	−	9.33219e18i	0.174969	−	0.226652i
$635$	−2.20159e19			−0.528834
$636$	−4.02351e19	+	1.05297e19i	−0.955885	+	0.250158i
$637$		−	5.23271e18i		−	0.122956i
$638$	1.04907e19	−	1.35894e19i	0.243815	−	0.315833i
$639$			5.91243e19i			1.35913i
$640$	4.38113e19	−	4.85969e18i	0.996154	−	0.110497i
$641$	3.52486e19			0.792749			0.396375	−	0.918089i	$-0.370268\pi$
$641$	3.52486e19			0.792749			0.396375	+	0.918089i	$0.370268\pi$
$642$	−4.85631e19	−	3.74894e19i	−1.08034	−	0.833996i
$643$	−2.71535e19			−0.597514			−0.298757	−	0.954329i	$-0.596572\pi$
$643$	−2.71535e19			−0.597514			−0.298757	+	0.954329i	$0.596572\pi$
$644$	−2.70705e19	−	1.03440e20i	−0.589243	−	2.25157i
$645$		−	9.74253e19i		−	2.09775i
$646$	−4.77919e19	−	3.68941e19i	−1.01795	−	0.785831i
$647$			5.30667e19i			1.11813i	0.829124	+	0.559065i	$0.188840\pi$
$647$			5.30667e19i			1.11813i	−0.829124	+	0.559065i	$0.811160\pi$
$648$	3.68462e18	−	8.67974e18i	0.0768012	−	0.180918i
$649$	−3.25724e19			−0.671640
$650$	1.38616e16	−	1.79560e16i	0.000282761	−	0.000366283i
$651$	−1.46829e20			−2.96309
$652$	3.02234e18	+	1.15487e19i	0.0603406	+	0.230569i
$653$			3.44437e19i			0.680327i	0.940366	+	0.340164i	$0.110482\pi$
$653$			3.44437e19i			0.680327i	−0.940366	+	0.340164i	$0.889518\pi$
$654$	2.38204e19	−	3.08564e19i	0.465483	−	0.602978i
$655$			4.58248e19i			0.885955i
$656$	−2.71588e18	+	1.52603e18i	−0.0519498	+	0.0291901i
$657$	6.49745e19			1.22966
$658$	1.01283e19	+	7.81875e18i	0.189650	+	0.146405i
$659$	7.52696e19			1.39451			0.697255	−	0.716823i	$-0.254405\pi$
$659$	7.52696e19			1.39451			0.697255	+	0.716823i	$0.254405\pi$
$660$	5.35942e19	−	1.40258e19i	0.982450	−	0.257110i
$661$		−	2.63651e19i		−	0.478211i	−0.970994	−	0.239106i	$-0.923146\pi$
$661$		−	2.63651e19i		−	0.478211i	0.970994	−	0.239106i	$-0.0768542\pi$
$662$	7.58321e19	+	5.85404e19i	1.36097	+	1.05063i
$663$			1.27174e19i			0.225841i
$664$	2.01661e19	−	4.75045e19i	0.354360	−	0.834754i
$665$	−7.90714e19			−1.37489
$666$	1.23413e19	−	1.59867e19i	0.212345	−	0.275068i
$667$	5.76235e19			0.981113
$668$	4.14396e19	−	1.08449e19i	0.698200	−	0.182721i
$669$			9.59474e19i			1.59974i
$670$	8.14507e18	−	1.05510e19i	0.134391	−	0.174088i
$671$		−	5.64090e19i		−	0.921066i
$672$	−2.11734e19	+	1.44502e20i	−0.342142	+	2.33502i
$673$	4.46266e18			0.0713656			0.0356828	−	0.999363i	$-0.488639\pi$
$673$	4.46266e18			0.0713656			0.0356828	+	0.999363i	$0.488639\pi$
$674$	−8.92844e19	−	6.89252e19i	−1.41305	−	1.09083i
$675$	−2.42131e17			−0.00379248
$676$	1.61622e19	+	6.17579e19i	0.250539	+	0.957339i
$677$			1.67194e19i			0.256507i	0.991741	+	0.128254i	$0.0409372\pi$
$677$			1.67194e19i			0.256507i	−0.991741	+	0.128254i	$0.959063\pi$
$678$	−9.57555e19	−	7.39207e19i	−1.45397	−	1.12243i
$679$			2.32703e19i			0.349715i
$680$	−8.63313e19	−	3.66483e19i	−1.28412	−	0.545120i
$681$	−8.06956e19			−1.18801
$682$	−3.35653e19	+	4.34798e19i	−0.489102	+	0.633574i
$683$	5.32780e19			0.768428			0.384214	−	0.923244i	$-0.374473\pi$
$683$	5.32780e19			0.768428			0.384214	+	0.923244i	$0.374473\pi$
$684$	−2.50099e19	−	9.55659e19i	−0.357042	−	1.36430i
$685$			8.80405e19i			1.24408i
$686$	−1.32638e19	+	1.71817e19i	−0.185524	+	0.240324i
$687$		−	1.62390e20i		−	2.24835i
$688$	8.37645e19	−	4.70664e19i	1.14800	−	0.645047i
$689$	−4.67764e18			−0.0634588
$690$	1.47192e20	+	1.13628e20i	1.97670	+	1.52596i
$691$	2.94841e19			0.391960			0.195980	−	0.980608i	$-0.437211\pi$
$691$	2.94841e19			0.391960			0.195980	+	0.980608i	$0.437211\pi$
$692$	4.92237e18	−	1.28820e18i	0.0647786	−	0.0169528i
$693$			1.10895e20i			1.44471i
$694$	1.92170e19	+	1.48350e19i	0.247838	+	0.191325i
$695$			3.69972e19i			0.472363i
$696$	−7.24497e19	−	3.07555e19i	−0.915740	−	0.388739i
$697$	6.62824e18			0.0829409
$698$	1.93561e19	−	2.50735e19i	0.239789	−	0.310618i
$699$	3.40531e19			0.417654
$700$	−5.36204e17	+	1.40326e17i	−0.00651094	+	0.00170393i
$701$		−	8.31673e19i		−	0.999830i	−0.866074	−	0.499915i	$-0.833365\pi$
$701$		−	8.31673e19i		−	0.999830i	0.866074	−	0.499915i	$-0.166635\pi$
$702$	−4.38483e18	+	5.68002e18i	−0.0521907	+	0.0676068i
$703$			1.78487e19i			0.210338i
$704$	3.79506e19	+	3.93034e19i	0.442802	+	0.458587i
$705$	−2.22518e19			−0.257064
$706$	8.76108e19	+	6.76332e19i	1.00213	+	0.773619i
$707$	−2.93987e19			−0.332960
$708$	3.78076e19	+	1.44467e20i	0.423981	+	1.62008i
$709$			1.32662e20i			1.47307i	0.676401	+	0.736534i	$0.263539\pi$
$709$			1.32662e20i			1.47307i	−0.676401	+	0.736534i	$0.736461\pi$
$710$	−6.42509e19	−	4.96000e19i	−0.706433	−	0.545348i
$711$			8.83721e19i			0.962117i
$712$	−1.80087e19	+	4.24225e19i	−0.194143	+	0.457336i
$713$	−1.84368e20			−1.96815
$714$	1.89883e20	−	2.45971e20i	2.00724	−	2.60014i
$715$	6.23073e18			0.0652224
$716$	1.38085e18	+	5.27640e18i	0.0143138	+	0.0546949i
$717$		−	2.15337e20i		−	2.21046i
$718$	−5.09809e19	+	6.60396e19i	−0.518246	+	0.671326i
$719$			8.31908e19i			0.837477i	0.908107	+	0.418739i	$0.137528\pi$
$719$			8.31908e19i			0.837477i	−0.908107	+	0.418739i	$0.862472\pi$
$720$	−7.51694e19	−	1.33780e20i	−0.749400	−	1.33371i
$721$	2.39145e20			2.36110
$722$	−1.18503e19	−	9.14813e18i	−0.115870	−	0.0894483i
$723$	2.68740e20			2.60234
$724$	−1.42615e20	+	3.73227e19i	−1.36771	+	0.357934i
$725$		−	2.98706e17i		−	0.00283712i
$726$	−7.93978e19	−	6.12930e19i	−0.746882	−	0.576574i
$727$		−	1.95774e20i		−	1.82396i	−0.410239	−	0.911978i	$-0.634555\pi$
$727$		−	1.95774e20i		−	1.82396i	0.410239	−	0.911978i	$-0.365445\pi$
$728$	−6.41845e18	+	1.51197e19i	−0.0592258	+	0.139516i
$729$	−1.78335e20			−1.62984
$730$	−5.45078e19	+	7.06084e19i	−0.493400	+	0.639141i
$731$	−2.04431e20			−1.83284
$732$	−2.50189e20	+	6.54754e19i	−2.22173	+	0.581434i
$733$		−	1.90170e20i		−	1.67269i	−0.548207	−	0.836343i	$-0.684689\pi$
$733$		−	1.90170e20i		−	1.67269i	0.548207	−	0.836343i	$-0.315311\pi$
$734$	7.66733e19	−	9.93211e19i	0.667993	−	0.865305i
$735$		−	2.22353e20i		−	1.91881i
$736$	−2.65868e19	+	1.81447e20i	−0.227259	+	1.55097i
$737$	1.65208e19			0.139881
$738$	8.58448e18	+	6.62700e18i	0.0719979	+	0.0555805i
$739$	−8.16899e19			−0.678668			−0.339334	−	0.940666i	$-0.610202\pi$
$739$	−8.16899e19			−0.678668			−0.339334	+	0.940666i	$0.610202\pi$
$740$	7.01962e18	+	2.68228e19i	0.0577686	+	0.220741i
$741$		−	1.83891e19i		−	0.149911i
$742$	9.04718e19	+	6.98419e19i	0.730610	+	0.564012i
$743$		−	2.00611e20i		−	1.60484i	−0.596757	−	0.802422i	$-0.703544\pi$
$743$		−	2.00611e20i		−	1.60484i	0.596757	−	0.802422i	$-0.296456\pi$
$744$	2.31805e20	+	9.84031e19i	1.83701	+	0.779827i
$745$	2.26058e20			1.77471
$746$	2.32038e19	−	3.00578e19i	0.180463	−	0.233768i
$747$	−1.79657e20			−1.38420
$748$	−2.94308e19	−	1.12459e20i	−0.224642	−	0.858384i
$749$			1.68596e20i			1.27489i
$750$	−1.29354e20	+	1.67563e20i	−0.969063	+	1.25531i
$751$			2.69203e20i			1.99803i	0.0444217	+	0.999013i	$0.485855\pi$
$751$			2.69203e20i			1.99803i	−0.0444217	+	0.999013i	$0.514145\pi$
$752$	−1.07499e19	−	1.91316e19i	−0.0790457	−	0.140678i
$753$	−2.09138e19			−0.152359
$754$	−7.00718e18	−	5.40936e18i	−0.0505759	−	0.0390433i
$755$	1.75884e20			1.25776
$756$	1.69617e20	−	4.43893e19i	1.20176	−	0.314504i
$757$		−	1.54483e20i		−	1.08445i	−0.840233	−	0.542225i	$-0.817582\pi$
$757$		−	1.54483e20i		−	1.08445i	0.840233	−	0.542225i	$-0.182418\pi$
$758$	1.48495e20	+	1.14634e20i	1.03283	+	0.797316i
$759$			2.30474e20i			1.58829i
$760$	1.24833e20	+	5.29928e19i	0.852385	+	0.361844i
$761$	1.86424e20			1.26128			0.630638	−	0.776077i	$-0.282793\pi$
$761$	1.86424e20			1.26128			0.630638	+	0.776077i	$0.282793\pi$
$762$	−7.64479e19	+	9.90291e19i	−0.512484	+	0.663862i
$763$	−1.07124e20			−0.711564
$764$	−6.12423e19	+	1.60273e19i	−0.403086	+	0.105489i
$765$			3.26496e20i			2.12935i
$766$	−3.22267e19	+	4.17458e19i	−0.208264	+	0.269781i
$767$			1.67954e19i			0.107553i
$768$	1.30271e20	−	2.13942e20i	0.826647	−	1.35758i
$769$	−2.62056e20			−1.64782			−0.823909	−	0.566723i	$-0.808211\pi$
$769$	−2.62056e20			−1.64782			−0.823909	+	0.566723i	$0.808211\pi$
$770$	−1.20511e20	−	9.30311e19i	−0.750914	−	0.579686i
$771$	3.30691e20			2.04194
$772$	−4.97176e19	−	1.89977e20i	−0.304221	−	1.16247i
$773$			1.05223e20i			0.638050i	0.947746	+	0.319025i	$0.103355\pi$
$773$			1.05223e20i			0.638050i	−0.947746	+	0.319025i	$0.896645\pi$
$774$	−2.64766e20	−	2.04393e20i	−1.59102	−	1.22823i
$775$			9.55717e17i			0.00569138i
$776$	1.55955e19	−	3.67378e19i	0.0920381	−	0.216811i
$777$	−9.18619e19			−0.537265
$778$	−1.44343e20	+	1.86980e20i	−0.836642	+	1.08377i
$779$	−9.58430e18			−0.0550552
$780$	−7.23217e18	−	2.76350e19i	−0.0411724	−	0.157325i
$781$		−	1.00605e20i		−	0.567625i
$782$	2.38430e20	−	3.08858e20i	1.33326	−	1.72708i
$783$			9.44893e19i			0.523661i
$784$	1.91175e20	−	1.07419e20i	1.05007	−	0.590023i
$785$	−6.49182e19			−0.353410
$786$	2.06124e20	+	1.59122e20i	1.11217	+	0.858564i
$787$	−1.84155e20			−0.984829			−0.492414	−	0.870361i	$-0.663886\pi$
$787$	−1.84155e20			−0.984829			−0.492414	+	0.870361i	$0.663886\pi$
$788$	−2.20620e19	+	5.77370e18i	−0.116940	+	0.0306035i
$789$		−	1.00231e19i		−	0.0526578i
$790$	−9.60347e19	−	7.41363e19i	−0.500079	−	0.386048i
$791$			3.32433e20i			1.71581i
$792$	7.43207e19	−	1.75075e20i	0.380219	−	0.895669i
$793$	−2.90864e19			−0.147495
$794$	2.89512e19	−	3.75028e19i	0.145520	−	0.188504i
$795$	−1.98766e20			−0.990314
$796$	6.39042e19	−	1.67239e19i	0.315600	−	0.0825937i
$797$		−	3.36728e19i		−	0.164843i	−0.996598	−	0.0824217i	$-0.973735\pi$
$797$		−	3.36728e19i		−	0.164843i	0.996598	−	0.0824217i	$-0.0262654\pi$
$798$	−2.74568e20	+	3.55669e20i	−1.33238	+	1.72594i
$799$			4.66917e19i			0.224601i
$800$	9.40573e17	+	1.37819e17i	0.00448500	+	0.000657172i
$801$	1.60437e20			0.758364
$802$	−7.14296e19	−	5.51418e19i	−0.334701	−	0.258381i
$803$	−1.10559e20			−0.513555
$804$	−1.91761e19	−	7.32744e19i	−0.0883017	−	0.337411i
$805$		−	5.11003e20i		−	2.33267i
$806$	2.24197e19	+	1.73074e19i	0.101457	+	0.0783225i
$807$		−	5.48875e20i		−	2.46240i
$808$	4.64130e19	+	1.97027e19i	0.206424	+	0.0876286i
$809$	4.38481e20			1.93335			0.966677	−	0.256001i	$-0.0824050\pi$
$809$	4.38481e20			1.93335			0.966677	+	0.256001i	$0.0824050\pi$
$810$	2.75380e19	−	3.56722e19i	0.120375	−	0.155932i
$811$	−3.31763e20			−1.43775			−0.718873	−	0.695141i	$-0.755342\pi$
$811$	−3.31763e20			−1.43775			−0.718873	+	0.695141i	$0.755342\pi$
$812$	5.47610e19	+	2.09249e20i	0.235277	+	0.899022i
$813$			1.01179e20i			0.430978i
$814$	−2.09998e19	+	2.72027e19i	−0.0886836	+	0.114879i
$815$			5.70520e19i			0.238873i
$816$	−4.64624e20	+	2.61067e20i	−1.92873	+	1.08373i
$817$	2.95603e20			1.21662
$818$	−2.62242e20	−	2.02444e20i	−1.07011	−	0.826098i
$819$	5.71813e19			0.231348
$820$	−1.44032e19	+	3.76937e18i	−0.0577781	+	0.0151207i
$821$			3.33157e20i			1.32510i	0.749020	+	0.662548i	$0.230525\pi$
$821$			3.33157e20i			1.32510i	−0.749020	+	0.662548i	$0.769475\pi$
$822$	3.96013e20	+	3.05712e20i	1.56173	+	1.20562i
$823$			6.00613e19i			0.234853i	0.993082	+	0.117426i	$0.0374644\pi$
$823$			6.00613e19i			0.234853i	−0.993082	+	0.117426i	$0.962536\pi$
$824$	−3.77549e20	−	1.60272e20i	−1.46380	−	0.621396i
$825$	1.19472e18			0.00459292
$826$	2.50773e20	−	3.24846e20i	0.955916	−	1.23827i
$827$	3.94219e18			0.0149004			0.00745022	−	0.999972i	$-0.497628\pi$
$827$	3.94219e18			0.0149004			0.00745022	+	0.999972i	$0.497628\pi$
$828$	6.17600e20	−	1.61628e20i	2.31470	−	0.605765i
$829$		−	3.29756e20i		−	1.22549i	−0.790280	−	0.612746i	$-0.790065\pi$
$829$		−	3.29756e20i		−	1.22549i	0.790280	−	0.612746i	$-0.209935\pi$
$830$	1.50716e20	−	1.95235e20i	0.555410	−	0.719467i
$831$			5.58785e19i			0.204191i
$832$	2.02662e19	−	1.95686e19i	0.0734359	−	0.0709082i
$833$	−4.66571e20			−1.67650
$834$	1.66417e20	+	1.28469e20i	0.592972	+	0.457759i
$835$	2.04716e20			0.723347
$836$	4.25564e19	+	1.62613e20i	0.149115	+	0.569786i
$837$		−	3.02321e20i		−	1.05049i
$838$	−3.96740e20	−	3.06273e20i	−1.36709	−	1.05536i
$839$			1.96300e20i			0.670789i	0.942078	+	0.335395i	$0.108870\pi$
$839$			1.96300e20i			0.670789i	−0.942078	+	0.335395i	$0.891130\pi$
$840$	−2.72739e20	+	6.42481e20i	−0.924254	+	2.17724i
$841$	1.80991e20			0.608255
$842$	−1.99480e20	+	2.58402e20i	−0.664836	+	0.861215i
$843$	3.55773e20			1.17593
$844$	8.60189e19	+	3.28689e20i	0.281966	+	1.07743i
$845$			3.05091e20i			0.991819i
$846$	−4.66829e19	+	6.04722e19i	−0.150510	+	0.194968i
$847$			2.75644e20i			0.881383i
$848$	−9.60244e19	−	1.70896e20i	−0.304516	−	0.541951i
$849$	−5.45209e20			−1.71478
$850$	−1.60104e18	−	1.23596e18i	−0.00499424	−	0.00385542i
$851$	−1.15348e20			−0.356864
$852$	−4.46210e20	+	1.16775e20i	−1.36918	+	0.358320i
$853$			3.16110e20i			0.962044i	0.876709	+	0.481022i	$0.159734\pi$
$853$			3.16110e20i			0.962044i	−0.876709	+	0.481022i	$0.840266\pi$
$854$	5.62570e20	+	4.34289e20i	1.69813	+	1.31091i
$855$		−	4.72107e20i		−	1.41344i
$856$	1.12991e20	−	2.66169e20i	0.335527	−	0.790390i
$857$	8.14488e19			0.239894			0.119947	−	0.992780i	$-0.461728\pi$
$857$	8.14488e19			0.239894			0.119947	+	0.992780i	$0.461728\pi$
$858$	2.16356e19	−	2.80263e19i	0.0632059	−	0.0818757i
$859$	4.12749e19			0.119601			0.0598003	−	0.998210i	$-0.480954\pi$
$859$	4.12749e19			0.119601			0.0598003	+	0.998210i	$0.480954\pi$
$860$	4.44231e20	−	1.16257e20i	1.27679	−	0.334140i
$861$		−	4.93276e19i		−	0.140627i
$862$	−1.65251e20	+	2.14063e20i	−0.467297	+	0.605328i
$863$		−	5.25561e20i		−	1.47417i	−0.675800	−	0.737085i	$-0.736202\pi$
$863$		−	5.25561e20i		−	1.47417i	0.675800	−	0.737085i	$-0.263798\pi$
$864$	−2.97531e20	−	4.35962e19i	−0.827820	−	0.121298i
$865$	2.43171e19			0.0671117
$866$	3.08761e20	+	2.38356e20i	0.845274	+	0.652530i
$867$	5.48631e20			1.48986
$868$	−1.75209e20	−	6.69497e20i	−0.471975	−	1.80348i
$869$		−	1.50372e20i		−	0.401818i
$870$	−2.97755e20	−	2.29859e20i	−0.789268	−	0.609294i
$871$		−	8.51870e18i		−	0.0223999i
$872$	1.69121e20	+	7.17932e19i	0.441145	+	0.187270i
$873$	−1.38939e20			−0.359520
$874$	−3.44765e20	+	4.46602e20i	−0.885001	+	1.14641i
$875$	5.81726e20			1.48137
$876$	1.28329e20	+	4.90361e20i	0.324188	+	1.23876i
$877$			1.53782e20i			0.385397i	0.981258	+	0.192698i	$0.0617239\pi$
$877$			1.53782e20i			0.385397i	−0.981258	+	0.192698i	$0.938276\pi$
$878$	4.27313e20	−	5.53533e20i	1.06239	−	1.37620i
$879$		−	9.44584e20i		−	2.32980i
$880$	1.27907e20	+	2.27637e20i	0.312979	+	0.557012i
$881$	−7.69020e20			−1.86684			−0.933418	−	0.358791i	$-0.883189\pi$
$881$	−7.69020e20			−1.86684			−0.933418	+	0.358791i	$0.883189\pi$
$882$	−6.04274e20	−	4.66484e20i	−1.45530	−	1.12346i
$883$	−4.89117e20			−1.16866			−0.584329	−	0.811517i	$-0.698642\pi$
$883$	−4.89117e20			−1.16866			−0.584329	+	0.811517i	$0.698642\pi$
$884$	−5.79875e19	+	1.51755e19i	−0.137458	+	0.0359731i
$885$			7.13685e20i			1.67843i
$886$	2.95968e20	+	2.28480e20i	0.690571	+	0.533103i
$887$			8.48449e19i			0.196409i	0.995166	+	0.0982043i	$0.0313099\pi$
$887$			8.48449e19i			0.196409i	−0.995166	+	0.0982043i	$0.968690\pi$
$888$	1.45026e20	+	6.15648e19i	0.333086	+	0.141398i
$889$	3.43798e20			0.783413
$890$	−1.34593e20	+	1.74349e20i	−0.304292	+	0.394174i
$891$	5.58559e19			0.125292
$892$	−4.37492e20	+	1.14493e20i	−0.973680	+	0.254815i
$893$		−	6.75153e19i		−	0.149088i
$894$	7.84965e20	−	1.01683e21i	1.71984	−	2.22785i
$895$			2.60660e19i			0.0566648i
$896$	−6.84154e20	+	7.58885e19i	−1.47570	+	0.163689i
$897$	1.18840e20			0.254341
$898$	−2.06002e20	−	1.59028e20i	−0.437458	−	0.337707i
$899$	3.72960e20			0.785858
$900$	−8.37837e17	−	3.20148e18i	−0.00175171	−	0.00669350i
$901$			4.17079e20i			0.865255i
$902$	−1.46072e19	−	1.12764e19i	−0.0300691	−	0.0232126i
$903$			1.52139e21i			3.10760i
$904$	2.22793e20	−	5.24826e20i	0.451567	−	1.06374i
$905$	−7.04532e20			−1.41697
$906$	6.10738e20	−	7.91138e20i	1.21887	−	1.57890i
$907$	−4.95417e20			−0.981115			−0.490558	−	0.871409i	$-0.663207\pi$
$907$	−4.95417e20			−0.981115			−0.490558	+	0.871409i	$0.663207\pi$
$908$	−9.62933e19	−	3.67948e20i	−0.189232	−	0.723080i
$909$		−	1.75529e20i		−	0.342296i
$910$	−4.79700e19	+	6.21394e19i	−0.0928282	+	0.120248i
$911$			1.16123e20i			0.222992i	0.993765	+	0.111496i	$0.0355642\pi$
$911$			1.16123e20i			0.222992i	−0.993765	+	0.111496i	$0.964436\pi$
$912$	6.71837e20	−	3.77498e20i	1.28027	−	0.719368i
$913$	3.05701e20			0.578098
$914$	−7.91609e20	−	6.11102e20i	−1.48555	−	1.14681i
$915$	−1.23596e21			−2.30175
$916$	7.40453e20	−	1.93779e20i	1.36845	−	0.358128i
$917$		−	7.15596e20i		−	1.31245i
$918$	5.06456e20	+	3.90971e20i	0.921813	+	0.711615i
$919$		−	3.68834e20i		−	0.666227i	−0.942887	−	0.333114i	$-0.891901\pi$
$919$		−	3.68834e20i		−	0.666227i	0.942887	−	0.333114i	$-0.108099\pi$
$920$	−3.42469e20	+	8.06742e20i	−0.613912	+	1.44617i
$921$	5.75732e20			1.02424
$922$	3.56337e19	−	4.61592e19i	0.0629136	−	0.0814971i
$923$	−5.18752e19			−0.0908967
$924$	−8.36922e20	+	2.19025e20i	−1.45540	+	0.380882i
$925$			5.97934e17i			0.00103196i
$926$	−5.99370e20	+	7.76413e20i	−1.02664	+	1.32989i
$927$			1.42785e21i			2.42730i
$928$	5.37825e19	−	3.67050e20i	0.0907414	−	0.619283i
$929$	6.92590e20			1.15975			0.579877	−	0.814704i	$-0.303100\pi$
$929$	6.92590e20			1.15975			0.579877	+	0.814704i	$0.303100\pi$
$930$	9.52676e20	+	7.35441e20i	1.58331	+	1.22227i
$931$	6.74653e20			1.11284
$932$	4.06352e19	+	1.55272e20i	0.0665260	+	0.254204i
$933$			3.60886e20i			0.586406i
$934$	8.82725e19	+	6.81441e19i	0.142363	+	0.109901i
$935$		−	5.55559e20i		−	0.889301i
$936$	−9.02745e19	−	3.83223e19i	−0.143428	−	0.0608864i
$937$	−2.59459e20			−0.409158			−0.204579	−	0.978850i	$-0.565583\pi$
$937$	−2.59459e20			−0.409158			−0.204579	+	0.978850i	$0.565583\pi$
$938$	−1.27193e20	+	1.64763e20i	−0.199087	+	0.257893i
$939$	2.21226e20			0.343699
$940$	−2.65528e19	−	1.01462e20i	−0.0409464	−	0.156461i
$941$		−	3.77809e20i		−	0.578289i	−0.957285	−	0.289145i	$-0.906629\pi$
$941$		−	3.77809e20i		−	0.578289i	0.957285	−	0.289145i	$-0.0933708\pi$
$942$	−2.25422e20	+	2.92007e20i	−0.342484	+	0.443647i
$943$		−	6.19391e19i		−	0.0934078i
$944$	−6.13613e20	+	3.44783e20i	−0.918525	+	0.516109i
$945$	8.37928e20			1.24504
$946$	4.50521e20	+	3.47791e20i	0.664473	+	0.512956i
$947$	2.20965e20			0.323499			0.161749	−	0.986832i	$-0.448286\pi$
$947$	2.20965e20			0.323499			0.161749	+	0.986832i	$0.448286\pi$
$948$	−6.66942e20	+	1.74541e20i	−0.969237	+	0.253652i
$949$			5.70082e19i			0.0822382i
$950$	2.31507e18	+	1.78717e18i	0.00331512	+	0.00255919i
$951$		−	3.20170e20i		−	0.455111i
$952$	1.34814e21	+	5.72297e20i	1.90229	+	0.807538i
$953$	4.64797e20			0.651048			0.325524	−	0.945534i	$-0.394459\pi$
$953$	4.64797e20			0.651048			0.325524	+	0.945534i	$0.394459\pi$
$954$	−4.17000e20	+	5.40174e20i	−0.579826	+	0.751096i
$955$	−3.02544e20			−0.417604
$956$	9.81871e20	−	2.56959e20i	1.34539	−	0.352094i
$957$		−	4.66228e20i		−	0.634184i
$958$	−7.79511e20	+	1.00976e21i	−1.05260	+	1.36352i
$959$		−	1.37483e21i		−	1.84298i
$960$	8.61168e20	−	8.31526e20i	1.14601	−	1.10657i
$961$	−4.36351e20			−0.576465
$962$	1.40266e19	+	1.08282e19i	0.0183962	+	0.0142014i
$963$	−1.00662e21			−1.31064
$964$	3.20684e20	+	1.22537e21i	0.414513	+	1.58391i
$965$		−	9.38509e20i		−	1.20433i
$966$	−2.29853e21	−	1.77441e21i	−2.92827	−	2.26055i
$967$			2.64237e20i			0.334201i	0.985940	+	0.167101i	$0.0534405\pi$
$967$			2.64237e20i			0.334201i	−0.985940	+	0.167101i	$0.946559\pi$
$968$	1.84734e20	−	4.35171e20i	0.231963	−	0.546428i
$969$	−1.63965e21			−2.04402
$970$	1.16557e20	−	1.50986e20i	0.144257	−	0.186868i
$971$	2.10301e20			0.258409			0.129204	−	0.991618i	$-0.458758\pi$
$971$	2.10301e20			0.258409			0.129204	+	0.991618i	$0.458758\pi$
$972$	−2.38468e20	−	9.11215e20i	−0.290915	−	1.11162i
$973$		−	5.77746e20i		−	0.699756i
$974$	−4.91682e20	+	6.36915e20i	−0.591250	+	0.765894i
$975$		−	6.16038e17i		−	0.000735487i
$976$	−5.97097e20	−	1.06266e21i	−0.707776	−	1.25964i
$977$	3.00312e20			0.353436			0.176718	−	0.984261i	$-0.443452\pi$
$977$	3.00312e20			0.353436			0.176718	+	0.984261i	$0.443452\pi$
$978$	2.56624e20	+	1.98107e20i	0.299865	+	0.231488i
$979$	−2.72997e20			−0.316722
$980$	1.01386e21	−	2.65331e20i	1.16788	−	0.305637i
$981$		−	6.39597e20i		−	0.731515i
$982$	−8.51716e20	−	6.57503e20i	−0.967196	−	0.746650i
$983$		−	9.92688e19i		−	0.111928i	−0.998433	−	0.0559639i	$-0.982177\pi$
$983$		−	9.92688e19i		−	0.111928i	0.998433	−	0.0559639i	$-0.0178232\pi$
$984$	−3.30589e19	+	7.78756e19i	−0.0370103	+	0.0871838i
$985$	−1.08989e20			−0.121151
$986$	−4.82322e20	+	6.24791e20i	−0.532352	+	0.689598i
$987$	3.47482e20			0.380813
$988$	8.38488e19	−	2.19435e19i	0.0912427	−	0.0238785i
$989$			1.91035e21i			2.06414i
$990$	5.55455e20	−	7.19525e20i	0.595940	−	0.771969i
$991$			1.04040e21i			1.10837i	0.832395	+	0.554183i	$0.186969\pi$
$991$			1.04040e21i			1.10837i	−0.832395	+	0.554183i	$0.813031\pi$
$992$	−1.72079e20	+	1.17439e21i	−0.182031	+	1.24231i
$993$	2.60166e21			2.73278
$994$	1.00334e21	+	7.74550e20i	1.04651	+	0.807876i
$995$	3.15694e20			0.326968
$996$	−3.54835e20	−	1.35587e21i	−0.364931	−	1.39445i
$997$			1.11429e21i			1.13798i	0.822345	+	0.568989i	$0.192665\pi$
$997$			1.11429e21i			1.13798i	−0.822345	+	0.568989i	$0.807335\pi$
$998$	1.14093e21	+	8.80771e20i	1.15703	+	0.893201i
$999$		−	1.89144e20i		−	0.190473i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.15.d.b.3.10	yes	12
3.2	odd	2		72.15.b.b.19.3		12
4.3	odd	2		32.15.d.b.15.2		12
8.3	odd	2	inner	8.15.d.b.3.9	✓	12
8.5	even	2		32.15.d.b.15.1		12
24.11	even	2		72.15.b.b.19.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.15.d.b.3.9	✓	12	8.3	odd	2	inner
8.15.d.b.3.10	yes	12	1.1	even	1	trivial
32.15.d.b.15.1		12	8.5	even	2
32.15.d.b.15.2		12	4.3	odd	2
72.15.b.b.19.3		12	3.2	odd	2
72.15.b.b.19.4		12	24.11	even	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:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 15 \)
Character orbit:	\([\chi]\)	\(=\)	8.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(101.321 + 78.2175i) q^{2} +3476.15 q^{3} +(4148.05 + 15850.2i) q^{4} +78301.9i q^{5} +(352208. + 271895. i) q^{6} -1.22276e6i q^{7} +(-819477. + 1.93042e6i) q^{8} +7.30063e6 q^{9} +O(q^{10})\)	\(q+(101.321 + 78.2175i) q^{2} +3476.15 q^{3} +(4148.05 + 15850.2i) q^{4} +78301.9i q^{5} +(352208. + 271895. i) q^{6} -1.22276e6i q^{7} +(-819477. + 1.93042e6i) q^{8} +7.30063e6 q^{9} +(-6.12457e6 + 7.93365e6i) q^{10} -1.24226e7 q^{11} +(1.44192e7 + 5.50977e7i) q^{12} +6.40552e6i q^{13} +(9.56408e7 - 1.23891e8i) q^{14} +2.72189e8i q^{15} +(-2.34023e8 + 1.31495e8i) q^{16} +5.71144e8 q^{17} +(7.39710e8 + 5.71037e8i) q^{18} -8.25863e8 q^{19} +(-1.24110e9 + 3.24800e8i) q^{20} -4.25048e9i q^{21} +(-1.25868e9 - 9.71665e8i) q^{22} -5.33718e9i q^{23} +(-2.84862e9 + 6.71041e9i) q^{24} -2.76666e7 q^{25} +(-5.01023e8 + 6.49016e8i) q^{26} +8.75175e9 q^{27} +(1.93809e10 - 5.07205e9i) q^{28} +1.07966e10i q^{29} +(-2.12899e10 + 2.75785e10i) q^{30} -3.45441e10i q^{31} +(-3.39967e10 - 4.98142e9i) q^{32} -4.31828e10 q^{33} +(5.78691e10 + 4.46734e10i) q^{34} +9.57440e10 q^{35} +(3.02834e10 + 1.15716e11i) q^{36} -2.16121e10i q^{37} +(-8.36776e10 - 6.45969e10i) q^{38} +2.22665e10i q^{39} +(-1.51155e11 - 6.41666e10i) q^{40} +1.16052e10 q^{41} +(3.32462e11 - 4.30664e11i) q^{42} -3.57933e11 q^{43} +(-5.15296e10 - 1.96901e11i) q^{44} +5.71653e11i q^{45} +(4.17461e11 - 5.40771e11i) q^{46} +8.17512e10i q^{47} +(-8.13498e11 + 4.57096e11i) q^{48} -8.16907e11 q^{49} +(-2.80322e9 - 2.16401e9i) q^{50} +1.98538e12 q^{51} +(-1.01529e11 + 2.65704e10i) q^{52} +7.30252e11i q^{53} +(8.86739e11 + 6.84540e11i) q^{54} -9.72713e11i q^{55} +(2.36043e12 + 1.00202e12i) q^{56} -2.87082e12 q^{57} +(-8.44485e11 + 1.09393e12i) q^{58} +2.62202e12 q^{59} +(-4.31425e12 + 1.12905e12i) q^{60} +4.54083e12i q^{61} +(2.70195e12 - 3.50006e12i) q^{62} -8.92688e12i q^{63} +(-3.05496e12 - 3.16386e12i) q^{64} -5.01564e11 q^{65} +(-4.37534e12 - 3.37765e12i) q^{66} -1.32990e12 q^{67} +(2.36913e12 + 9.05275e12i) q^{68} -1.85528e13i q^{69} +(9.70092e12 + 7.48886e12i) q^{70} +8.09853e12i q^{71} +(-5.98270e12 + 1.40932e13i) q^{72} +8.89986e12 q^{73} +(1.69045e12 - 2.18977e12i) q^{74} -9.61731e10 q^{75} +(-3.42572e12 - 1.30901e13i) q^{76} +1.51898e13i q^{77} +(-1.74163e12 + 2.25607e12i) q^{78} +1.21047e13i q^{79} +(-1.02963e13 - 1.83244e13i) q^{80} -4.49631e12 q^{81} +(1.17586e12 + 9.07730e11i) q^{82} -2.46085e13 q^{83} +(6.73709e13 - 1.76312e13i) q^{84} +4.47216e13i q^{85} +(-3.62663e13 - 2.79966e13i) q^{86} +3.75306e13i q^{87} +(1.01800e13 - 2.39808e13i) q^{88} +2.19758e13 q^{89} +(-4.47132e13 + 5.79207e13i) q^{90} +7.83238e12 q^{91} +(8.45955e13 - 2.21389e13i) q^{92} -1.20080e14i q^{93} +(-6.39437e12 + 8.28315e12i) q^{94} -6.46666e13i q^{95} +(-1.18178e14 - 1.73162e13i) q^{96} -1.90311e13 q^{97} +(-8.27702e13 - 6.38964e13i) q^{98} -9.06928e13 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 218 q^{2} - 3024 q^{3} - 30828 q^{4} + 518556 q^{6} - 1097608 q^{8} + 13188036 q^{9}+O(q^{10}) \) 12 * q + 218 * q^2 - 3024 * q^3 - 30828 * q^4 + 518556 * q^6 - 1097608 * q^8 + 13188036 * q^9	\( 12 q + 218 q^{2} - 3024 q^{3} - 30828 q^{4} + 518556 q^{6} - 1097608 q^{8} + 13188036 q^{9} - 14533440 q^{10} - 28256720 q^{11} + 34920024 q^{12} + 191568384 q^{14} - 185822448 q^{16} + 270339544 q^{17} + 1420811358 q^{18} - 2481505872 q^{19} - 1679371200 q^{20} + 3042383484 q^{22} + 7581335184 q^{24} - 15857276820 q^{25} - 2773507776 q^{26} - 16574868000 q^{27} + 25329333120 q^{28} + 42207767040 q^{30} + 38309251808 q^{32} - 136227597840 q^{33} + 350437044 q^{34} + 149949623040 q^{35} - 150590403492 q^{36} + 102789916636 q^{38} - 66999085440 q^{40} + 264287409880 q^{41} - 110343609600 q^{42} + 32253127344 q^{43} - 585547356392 q^{44} + 864780977664 q^{46} - 2387663418144 q^{48} - 646589230644 q^{49} - 388785556630 q^{50} + 4755867895776 q^{51} + 798005307840 q^{52} + 1305053764344 q^{54} - 1050155264256 q^{56} - 7479401742480 q^{57} + 389204742720 q^{58} + 1223083947184 q^{59} + 4350689397120 q^{60} + 9957296947200 q^{62} - 16809671099328 q^{64} - 8069319822720 q^{65} - 6067132925784 q^{66} - 9309378171216 q^{67} + 32301846360616 q^{68} + 35197935521280 q^{70} - 43695386222808 q^{72} + 3619334364696 q^{73} - 55499920147776 q^{74} + 9079078926000 q^{75} + 33532610502360 q^{76} + 92515055193600 q^{78} - 86826189154560 q^{80} + 56467107312444 q^{81} - 146233962574956 q^{82} - 18774355695824 q^{83} + 186893160787200 q^{84} + 96253393476220 q^{86} - 166888683024624 q^{88} + 54781416936088 q^{89} - 488020221650880 q^{90} + 36699395136768 q^{91} + 413167093560960 q^{92} + 496016398930944 q^{94} - 616114307580864 q^{96} + 73839238696536 q^{97} - 523654870565638 q^{98} - 223606851712368 q^{99}+O(q^{100}) \) 12 * q + 218 * q^2 - 3024 * q^3 - 30828 * q^4 + 518556 * q^6 - 1097608 * q^8 + 13188036 * q^9 - 14533440 * q^10 - 28256720 * q^11 + 34920024 * q^12 + 191568384 * q^14 - 185822448 * q^16 + 270339544 * q^17 + 1420811358 * q^18 - 2481505872 * q^19 - 1679371200 * q^20 + 3042383484 * q^22 + 7581335184 * q^24 - 15857276820 * q^25 - 2773507776 * q^26 - 16574868000 * q^27 + 25329333120 * q^28 + 42207767040 * q^30 + 38309251808 * q^32 - 136227597840 * q^33 + 350437044 * q^34 + 149949623040 * q^35 - 150590403492 * q^36 + 102789916636 * q^38 - 66999085440 * q^40 + 264287409880 * q^41 - 110343609600 * q^42 + 32253127344 * q^43 - 585547356392 * q^44 + 864780977664 * q^46 - 2387663418144 * q^48 - 646589230644 * q^49 - 388785556630 * q^50 + 4755867895776 * q^51 + 798005307840 * q^52 + 1305053764344 * q^54 - 1050155264256 * q^56 - 7479401742480 * q^57 + 389204742720 * q^58 + 1223083947184 * q^59 + 4350689397120 * q^60 + 9957296947200 * q^62 - 16809671099328 * q^64 - 8069319822720 * q^65 - 6067132925784 * q^66 - 9309378171216 * q^67 + 32301846360616 * q^68 + 35197935521280 * q^70 - 43695386222808 * q^72 + 3619334364696 * q^73 - 55499920147776 * q^74 + 9079078926000 * q^75 + 33532610502360 * q^76 + 92515055193600 * q^78 - 86826189154560 * q^80 + 56467107312444 * q^81 - 146233962574956 * q^82 - 18774355695824 * q^83 + 186893160787200 * q^84 + 96253393476220 * q^86 - 166888683024624 * q^88 + 54781416936088 * q^89 - 488020221650880 * q^90 + 36699395136768 * q^91 + 413167093560960 * q^92 + 496016398930944 * q^94 - 616114307580864 * q^96 + 73839238696536 * q^97 - 523654870565638 * q^98 - 223606851712368 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more