LMFDB - Embedded newform 8.17.d.b.3.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,17,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, 17, names="a")

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

chi := DirichletCharacter("8.3");

S:= CuspForms(chi, 17);

N := Newforms(S);

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 17 $
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:	$12.9859635085$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 7 x^{13} + 7894 x^{12} + 219192 x^{11} - 135772320 x^{10} + 11331786624 x^{9} + \cdots + 27\!\cdots\!20 $ x^14 - 7x^13 + 7894x^12 + 219192x^11 - 135772320x^10 + 11331786624x^9 - 652293490688x^8 + 465478371454976x^7 - 697940891942912x^6 + 5355071973862932480x^5 + 64434406660761845760x^4 - 122098039773726666915840x^3 + 21723325027733376807731200x^2 - 2811006993630615015868334080*x + 279841437428593117864520581120
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{91}\cdot 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.8
Root			$12.1331 - 125.704i$ of defining polynomial
Character	$\chi$	$=$	8.3
Dual form			8.17.d.b.3.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-48.2661 + 251.409i) q^{2} -8648.56 q^{3} +(-60876.8 - 24269.1i) q^{4} -474083. i q^{5} +(417432. - 2.17432e6i) q^{6} +5.25940e6i q^{7} +(9.03974e6 - 1.41336e7i) q^{8} +3.17508e7 q^{9} +O(q^{10})$	\(q+(-48.2661 + 251.409i) q^{2} -8648.56 q^{3} +(-60876.8 - 24269.1i) q^{4} -474083. i q^{5} +(417432. - 2.17432e6i) q^{6} +5.25940e6i q^{7} +(9.03974e6 - 1.41336e7i) q^{8} +3.17508e7 q^{9} +(1.19189e8 + 2.28822e7i) q^{10} -3.36346e8 q^{11} +(5.26496e8 + 2.09892e8i) q^{12} +2.31164e8i q^{13} +(-1.32226e9 - 2.53851e8i) q^{14} +4.10013e9i q^{15} +(3.11699e9 + 2.95484e9i) q^{16} +6.30324e9 q^{17} +(-1.53249e9 + 7.98244e9i) q^{18} +2.41335e10 q^{19} +(-1.15055e10 + 2.88606e10i) q^{20} -4.54862e10i q^{21} +(1.62341e10 - 8.45604e10i) q^{22} +8.96390e10i q^{23} +(-7.81807e10 + 1.22235e11i) q^{24} -7.21668e10 q^{25} +(-5.81166e10 - 1.11574e10i) q^{26} +9.76930e10 q^{27} +(1.27641e11 - 3.20175e11i) q^{28} -7.07610e11i q^{29} +(-1.03081e12 - 1.97898e11i) q^{30} -7.96218e11i q^{31} +(-8.93319e11 + 6.41020e11i) q^{32} +2.90891e12 q^{33} +(-3.04233e11 + 1.58469e12i) q^{34} +2.49339e12 q^{35} +(-1.93289e12 - 7.70563e11i) q^{36} +3.93345e12i q^{37} +(-1.16483e12 + 6.06737e12i) q^{38} -1.99923e12i q^{39} +(-6.70049e12 - 4.28559e12i) q^{40} -2.45944e12 q^{41} +(1.14356e13 + 2.19544e12i) q^{42} +7.81505e12 q^{43} +(2.04757e13 + 8.16281e12i) q^{44} -1.50525e13i q^{45} +(-2.25360e13 - 4.32653e12i) q^{46} +1.93668e13i q^{47} +(-2.69575e13 - 2.55551e13i) q^{48} +5.57169e12 q^{49} +(3.48321e12 - 1.81434e13i) q^{50} -5.45139e13 q^{51} +(5.61012e12 - 1.40725e13i) q^{52} -1.24133e14i q^{53} +(-4.71527e12 + 2.45609e13i) q^{54} +1.59456e14i q^{55} +(7.43341e13 + 4.75436e13i) q^{56} -2.08720e14 q^{57} +(1.77899e14 + 3.41536e13i) q^{58} +6.48211e13 q^{59} +(9.95064e13 - 2.49603e14i) q^{60} +1.48899e14i q^{61} +(2.00176e14 + 3.84304e13i) q^{62} +1.66990e14i q^{63} +(-1.18041e14 - 2.55528e14i) q^{64} +1.09591e14 q^{65} +(-1.40402e14 + 7.31326e14i) q^{66} -6.22826e13 q^{67} +(-3.83721e14 - 1.52974e14i) q^{68} -7.75248e14i q^{69} +(-1.20346e14 + 6.26860e14i) q^{70} +3.09209e14i q^{71} +(2.87019e14 - 4.48753e14i) q^{72} +7.83976e14 q^{73} +(-9.88904e14 - 1.89852e14i) q^{74} +6.24139e14 q^{75} +(-1.46917e15 - 5.85697e14i) q^{76} -1.76898e15i q^{77} +(5.02625e14 + 9.64952e13i) q^{78} +7.76963e14i q^{79} +(1.40084e15 - 1.47771e15i) q^{80} -2.21167e15 q^{81} +(1.18708e14 - 6.18325e14i) q^{82} +2.22709e15 q^{83} +(-1.10391e15 + 2.76905e15i) q^{84} -2.98826e15i q^{85} +(-3.77202e14 + 1.96477e15i) q^{86} +6.11981e15i q^{87} +(-3.04048e15 + 4.75378e15i) q^{88} +3.96120e15 q^{89} +(3.78434e15 + 7.26528e14i) q^{90} -1.21578e15 q^{91} +(2.17546e15 - 5.45693e15i) q^{92} +6.88614e15i q^{93} +(-4.86899e15 - 9.34762e14i) q^{94} -1.14413e16i q^{95} +(7.72592e15 - 5.54390e15i) q^{96} -1.69502e15 q^{97} +(-2.68924e14 + 1.40077e15i) q^{98} -1.06793e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 350 q^{2} + 11964 q^{3} - 54220 q^{4} + 4868124 q^{6} + 10899160 q^{8} + 86397354 q^{9}+O(q^{10}) $ 14 * q - 350 * q^2 + 11964 * q^3 - 54220 * q^4 + 4868124 * q^6 + 10899160 * q^8 + 86397354 * q^9	\( 14 q - 350 q^{2} + 11964 q^{3} - 54220 q^{4} + 4868124 q^{6} + 10899160 q^{8} + 86397354 q^{9} + 87155280 q^{10} - 49140292 q^{11} + 31616184 q^{12} - 2675193504 q^{14} + 9716374544 q^{16} - 9985136356 q^{17} - 7692086106 q^{18} + 62922133180 q^{19} + 31953450720 q^{20} - 51493048676 q^{22} + 54962419344 q^{24} - 429906632050 q^{25} - 518273679696 q^{26} + 655936606584 q^{27} + 102542376000 q^{28} - 364331826720 q^{30} + 95751080800 q^{32} + 4034287537464 q^{33} + 1015818512644 q^{34} - 3057653406720 q^{35} - 9569289445092 q^{36} + 9010383442844 q^{38} - 4027933291200 q^{40} + 8719629072668 q^{41} - 6653698130880 q^{42} + 16716309178300 q^{43} - 4351929975880 q^{44} + 21043605267744 q^{46} + 46562301973344 q^{48} - 104740771400434 q^{49} - 54483696687710 q^{50} + 40911296041848 q^{51} - 73249356722400 q^{52} - 18031398151752 q^{54} + 110873799752064 q^{56} - 310730528383176 q^{57} + 256627273576560 q^{58} + 347007330293180 q^{59} - 83822619107520 q^{60} + 346701622780800 q^{62} - 332173589517760 q^{64} + 220877370432000 q^{65} + 875905832132808 q^{66} - 614258765968196 q^{67} - 12\!\cdots\!76 q^{68}+ \cdots - 18\!\cdots\!92 q^{99}+O(q^{100}) \) 14 * q - 350 * q^2 + 11964 * q^3 - 54220 * q^4 + 4868124 * q^6 + 10899160 * q^8 + 86397354 * q^9 + 87155280 * q^10 - 49140292 * q^11 + 31616184 * q^12 - 2675193504 * q^14 + 9716374544 * q^16 - 9985136356 * q^17 - 7692086106 * q^18 + 62922133180 * q^19 + 31953450720 * q^20 - 51493048676 * q^22 + 54962419344 * q^24 - 429906632050 * q^25 - 518273679696 * q^26 + 655936606584 * q^27 + 102542376000 * q^28 - 364331826720 * q^30 + 95751080800 * q^32 + 4034287537464 * q^33 + 1015818512644 * q^34 - 3057653406720 * q^35 - 9569289445092 * q^36 + 9010383442844 * q^38 - 4027933291200 * q^40 + 8719629072668 * q^41 - 6653698130880 * q^42 + 16716309178300 * q^43 - 4351929975880 * q^44 + 21043605267744 * q^46 + 46562301973344 * q^48 - 104740771400434 * q^49 - 54483696687710 * q^50 + 40911296041848 * q^51 - 73249356722400 * q^52 - 18031398151752 * q^54 + 110873799752064 * q^56 - 310730528383176 * q^57 + 256627273576560 * q^58 + 347007330293180 * q^59 - 83822619107520 * q^60 + 346701622780800 * q^62 - 332173589517760 * q^64 + 220877370432000 * q^65 + 875905832132808 * q^66 - 614258765968196 * q^67 - 1235787871965976 * q^68 - 442172390987520 * q^70 - 1312232111609976 * q^72 - 542888518370276 * q^73 + 2394643836493776 * q^74 + 2861985572983740 * q^75 - 614792000883272 * q^76 - 4928152344599520 * q^78 + 6402194304908160 * q^80 - 5344304371237818 * q^81 + 4810720063300804 * q^82 + 7362421930746044 * q^83 - 9316784627856000 * q^84 - 8963192329247716 * q^86 + 3396904358318224 * q^88 - 408131327364580 * q^89 + 14680290550241520 * q^90 - 7162887702930432 * q^91 - 9213856910218560 * q^92 - 15838781433150144 * q^94 + 48917704300183104 * q^96 + 18372136634257180 * q^97 + 34005570793293730 * q^98 - 18934692015468492 * 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 $

$2$	−48.2661	+	251.409i	−0.188540	+	0.982066i
$2$	−48.2661	+	251.409i	−0.188540	+	0.982066i
$3$	−8648.56			−1.31818			−0.659088	−	0.752065i	$-0.729058\pi$
$3$	−8648.56			−1.31818			−0.659088	+	0.752065i	$0.729058\pi$
$4$	−60876.8	−	24269.1i	−0.928906	−	0.370316i
$5$		−	474083.i		−	1.21365i	−0.794835	−	0.606826i	$-0.792442\pi$
$5$		−	474083.i		−	1.21365i	0.794835	−	0.606826i	$-0.207558\pi$
$6$	417432.	−	2.17432e6i	0.248529	−	1.29454i
$7$			5.25940e6i			0.912329i	0.889895	+	0.456165i	$0.150777\pi$
$7$			5.25940e6i			0.912329i	−0.889895	+	0.456165i	$0.849223\pi$
$8$	9.03974e6	−	1.41336e7i	0.538811	−	0.842427i
$9$	3.17508e7			0.737590
$10$	1.19189e8	+	2.28822e7i	1.19189	+	0.228822i
$11$	−3.36346e8			−1.56908			−0.784540	−	0.620078i	$-0.787101\pi$
$11$	−3.36346e8			−1.56908			−0.784540	+	0.620078i	$0.787101\pi$
$12$	5.26496e8	+	2.09892e8i	1.22446	+	0.488143i
$13$			2.31164e8i			0.283382i	0.989911	+	0.141691i	$0.0452540\pi$
$13$			2.31164e8i			0.283382i	−0.989911	+	0.141691i	$0.954746\pi$
$14$	−1.32226e9	−	2.53851e8i	−0.895967	−	0.172010i
$15$			4.10013e9i			1.59981i
$16$	3.11699e9	+	2.95484e9i	0.725731	+	0.687978i
$17$	6.30324e9			0.903592			0.451796	−	0.892121i	$-0.350784\pi$
$17$	6.30324e9			0.903592			0.451796	+	0.892121i	$0.350784\pi$
$18$	−1.53249e9	+	7.98244e9i	−0.139065	+	0.724362i
$19$	2.41335e10			1.42099			0.710495	−	0.703702i	$-0.248471\pi$
$19$	2.41335e10			1.42099			0.710495	+	0.703702i	$0.248471\pi$
$20$	−1.15055e10	+	2.88606e10i	−0.449436	+	1.12737i
$21$		−	4.54862e10i		−	1.20261i
$22$	1.62341e10	−	8.45604e10i	0.295834	−	1.54094i
$23$			8.96390e10i			1.14465i	0.820025	+	0.572327i	$0.193959\pi$
$23$			8.96390e10i			1.14465i	−0.820025	+	0.572327i	$0.806041\pi$
$24$	−7.81807e10	+	1.22235e11i	−0.710248	+	1.11047i
$25$	−7.21668e10			−0.472952
$26$	−5.81166e10	−	1.11574e10i	−0.278300	−	0.0534288i
$27$	9.76930e10			0.345902
$28$	1.27641e11	−	3.20175e11i	0.337850	−	0.847468i
$29$		−	7.07610e11i		−	1.41452i	−0.706952	−	0.707261i	$-0.749930\pi$
$29$		−	7.07610e11i		−	1.41452i	0.706952	−	0.707261i	$-0.250070\pi$
$30$	−1.03081e12	−	1.97898e11i	−1.57112	−	0.301627i
$31$		−	7.96218e11i		−	0.933552i	−0.884376	−	0.466776i	$-0.845415\pi$
$31$		−	7.96218e11i		−	0.933552i	0.884376	−	0.466776i	$-0.154585\pi$
$32$	−8.93319e11	+	6.41020e11i	−0.812469	+	0.583005i
$33$	2.90891e12			2.06833
$34$	−3.04233e11	+	1.58469e12i	−0.170363	+	0.887386i
$35$	2.49339e12			1.10725
$36$	−1.93289e12	−	7.70563e11i	−0.685152	−	0.273142i
$37$			3.93345e12i			1.11985i	0.828543	+	0.559925i	$0.189170\pi$
$37$			3.93345e12i			1.11985i	−0.828543	+	0.559925i	$0.810830\pi$
$38$	−1.16483e12	+	6.06737e12i	−0.267913	+	1.39551i
$39$		−	1.99923e12i		−	0.373548i
$40$	−6.70049e12	−	4.28559e12i	−1.02241	−	0.653929i
$41$	−2.45944e12			−0.308010			−0.154005	−	0.988070i	$-0.549217\pi$
$41$	−2.45944e12			−0.308010			−0.154005	+	0.988070i	$0.549217\pi$
$42$	1.14356e13	+	2.19544e12i	1.18104	+	0.226740i
$43$	7.81505e12			0.668628			0.334314	−	0.942462i	$-0.391495\pi$
$43$	7.81505e12			0.668628			0.334314	+	0.942462i	$0.391495\pi$
$44$	2.04757e13	+	8.16281e12i	1.45753	+	0.581056i
$45$		−	1.50525e13i		−	0.895178i
$46$	−2.25360e13	−	4.32653e12i	−1.12413	−	0.215813i
$47$			1.93668e13i			0.813346i	0.913574	+	0.406673i	$0.133311\pi$
$47$			1.93668e13i			0.813346i	−0.913574	+	0.406673i	$0.866689\pi$
$48$	−2.69575e13	−	2.55551e13i	−0.956642	−	0.906877i
$49$	5.57169e12			0.167656
$50$	3.48321e12	−	1.81434e13i	0.0891703	−	0.464470i
$51$	−5.45139e13			−1.19109
$52$	5.61012e12	−	1.40725e13i	0.104941	−	0.263235i
$53$		−	1.24133e14i		−	1.99379i	−0.0787610	−	0.996894i	$-0.525096\pi$
$53$		−	1.24133e14i		−	1.99379i	0.0787610	−	0.996894i	$-0.474904\pi$
$54$	−4.71527e12	+	2.45609e13i	−0.0652163	+	0.339699i
$55$			1.59456e14i			1.90432i
$56$	7.43341e13	+	4.75436e13i	0.768571	+	0.491573i
$57$	−2.08720e14			−1.87312
$58$	1.77899e14	+	3.41536e13i	1.38915	+	0.266694i
$59$	6.48211e13			0.441469			0.220734	−	0.975334i	$-0.429155\pi$
$59$	6.48211e13			0.441469			0.220734	+	0.975334i	$0.429155\pi$
$60$	9.95064e13	−	2.49603e14i	0.592436	−	1.48607i
$61$			1.48899e14i			0.776698i	0.921512	+	0.388349i	$0.126955\pi$
$61$			1.48899e14i			0.776698i	−0.921512	+	0.388349i	$0.873045\pi$
$62$	2.00176e14	+	3.84304e13i	0.916810	+	0.176012i
$63$			1.66990e14i			0.672925i
$64$	−1.18041e14	−	2.55528e14i	−0.419366	−	0.907817i
$65$	1.09591e14			0.343928
$66$	−1.40402e14	+	7.31326e14i	−0.389961	+	2.03123i
$67$	−6.22826e13			−0.153380			−0.0766900	−	0.997055i	$-0.524435\pi$
$67$	−6.22826e13			−0.153380			−0.0766900	+	0.997055i	$0.524435\pi$
$68$	−3.83721e14	−	1.52974e14i	−0.839351	−	0.334615i
$69$		−	7.75248e14i		−	1.50886i
$70$	−1.20346e14	+	6.26860e14i	−0.208761	+	1.08739i
$71$			3.09209e14i			0.478835i	0.970917	+	0.239417i	$0.0769564\pi$
$71$			3.09209e14i			0.478835i	−0.970917	+	0.239417i	$0.923044\pi$
$72$	2.87019e14	−	4.48753e14i	0.397421	−	0.621366i
$73$	7.83976e14			0.972119			0.486060	−	0.873926i	$-0.338434\pi$
$73$	7.83976e14			0.972119			0.486060	+	0.873926i	$0.338434\pi$
$74$	−9.88904e14	−	1.89852e14i	−1.09977	−	0.211136i
$75$	6.24139e14			0.623435
$76$	−1.46917e15	−	5.85697e14i	−1.31997	−	0.526216i
$77$		−	1.76898e15i		−	1.43152i
$78$	5.02625e14	+	9.64952e13i	0.366849	+	0.0704286i
$79$			7.76963e14i			0.512134i	0.966659	+	0.256067i	$0.0824267\pi$
$79$			7.76963e14i			0.512134i	−0.966659	+	0.256067i	$0.917573\pi$
$80$	1.40084e15	−	1.47771e15i	0.834966	−	0.880786i
$81$	−2.21167e15			−1.19355
$82$	1.18708e14	−	6.18325e14i	0.0580721	−	0.302486i
$83$	2.22709e15			0.988811			0.494405	−	0.869231i	$-0.335386\pi$
$83$	2.22709e15			0.988811			0.494405	+	0.869231i	$0.335386\pi$
$84$	−1.10391e15	+	2.76905e15i	−0.445347	+	1.11711i
$85$		−	2.98826e15i		−	1.09665i
$86$	−3.77202e14	+	1.96477e15i	−0.126063	+	0.656636i
$87$			6.11981e15i			1.86459i
$88$	−3.04048e15	+	4.75378e15i	−0.845437	+	1.32184i
$89$	3.96120e15			1.00625			0.503126	−	0.864213i	$-0.332183\pi$
$89$	3.96120e15			1.00625			0.503126	+	0.864213i	$0.332183\pi$
$90$	3.78434e15	+	7.26528e14i	0.879124	+	0.168777i
$91$	−1.21578e15			−0.258538
$92$	2.17546e15	−	5.45693e15i	0.423884	−	1.06328i
$93$			6.88614e15i			1.23059i
$94$	−4.86899e15	−	9.34762e14i	−0.798759	−	0.153348i
$95$		−	1.14413e16i		−	1.72459i
$96$	7.72592e15	−	5.54390e15i	1.07098	−	0.768503i
$97$	−1.69502e15			−0.216273			−0.108136	−	0.994136i	$-0.534488\pi$
$97$	−1.69502e15			−0.216273			−0.108136	+	0.994136i	$0.534488\pi$
$98$	−2.68924e14	+	1.40077e15i	−0.0316097	+	0.164649i
$99$	−1.06793e16			−1.15734
$100$	4.39328e15	+	1.75142e15i	0.439328	+	0.175142i
$101$			1.04368e16i			0.963818i	0.876221	+	0.481909i	$0.160056\pi$
$101$			1.04368e16i			0.963818i	−0.876221	+	0.481909i	$0.839944\pi$
$102$	2.63118e15	−	1.37053e16i	0.224568	−	1.16973i
$103$		−	4.53431e15i		−	0.357942i	−0.983854	−	0.178971i	$-0.942723\pi$
$103$		−	4.53431e15i		−	0.357942i	0.983854	−	0.178971i	$-0.0572769\pi$
$104$	3.26717e15	+	2.08966e15i	0.238729	+	0.152689i
$105$	−2.15642e16			−1.45955
$106$	3.12080e16	+	5.99140e15i	1.95803	+	0.375908i
$107$	−1.56223e16			−0.909230			−0.454615	−	0.890688i	$-0.650223\pi$
$107$	−1.56223e16			−0.909230			−0.454615	+	0.890688i	$0.650223\pi$
$108$	−5.94724e15	−	2.37092e15i	−0.321311	−	0.128093i
$109$			1.70943e16i			0.857904i	0.903327	+	0.428952i	$0.141117\pi$
$109$			1.70943e16i			0.857904i	−0.903327	+	0.428952i	$0.858883\pi$
$110$	−4.00887e16	−	7.69633e15i	−1.87017	−	0.359039i
$111$		−	3.40187e16i		−	1.47616i
$112$	−1.55407e16	+	1.63935e16i	−0.627662	+	0.662106i
$113$	2.43112e16			0.914490			0.457245	−	0.889341i	$-0.348836\pi$
$113$	2.43112e16			0.914490			0.457245	+	0.889341i	$0.348836\pi$
$114$	1.00741e16	−	5.24740e16i	0.353157	−	1.83952i
$115$	4.24963e16			1.38921
$116$	−1.71730e16	+	4.30770e16i	−0.523821	+	1.31396i
$117$			7.33964e15i			0.209020i
$118$	−3.12866e15	+	1.62966e16i	−0.0832344	+	0.433552i
$119$			3.31512e16i			0.824373i
$120$	5.79496e16	+	3.70642e16i	1.34772	+	0.861994i
$121$	6.71791e16			1.46201
$122$	−3.74345e16	−	7.18677e15i	−0.762769	−	0.146438i
$123$	2.12706e16			0.406012
$124$	−1.93235e16	+	4.84712e16i	−0.345710	+	0.867182i
$125$		−	3.81263e16i		−	0.639653i
$126$	−4.19828e16	−	8.05997e15i	−0.660857	−	0.126873i
$127$		−	4.45125e16i		−	0.657736i	−0.944376	−	0.328868i	$-0.893333\pi$
$127$		−	4.45125e16i		−	0.657736i	0.944376	−	0.328868i	$-0.106667\pi$
$128$	6.99393e16	−	1.73432e16i	0.970603	−	0.240686i
$129$	−6.75890e16			−0.881370
$130$	−5.28952e15	+	2.75521e16i	−0.0648440	+	0.337760i
$131$	−9.09388e16			−1.04853			−0.524263	−	0.851557i	$-0.675659\pi$
$131$	−9.09388e16			−1.04853			−0.524263	+	0.851557i	$0.675659\pi$
$132$	−1.77085e17	−	7.05965e16i	−1.92128	−	0.765935i
$133$			1.26927e17i			1.29641i
$134$	3.00614e15	−	1.56584e16i	0.0289182	−	0.150629i
$135$		−	4.63146e16i		−	0.419805i
$136$	5.69796e16	−	8.90873e16i	0.486865	−	0.761210i
$137$	1.06993e17			0.862163			0.431082	−	0.902313i	$-0.358132\pi$
$137$	1.06993e17			0.862163			0.431082	+	0.902313i	$0.358132\pi$
$138$	1.94904e17	+	3.74182e16i	1.48180	+	0.284479i
$139$	1.29061e17			0.926138			0.463069	−	0.886322i	$-0.346748\pi$
$139$	1.29061e17			0.926138			0.463069	+	0.886322i	$0.346748\pi$
$140$	−1.51790e17	−	6.05122e16i	−1.02853	−	0.410033i
$141$		−	1.67495e17i		−	1.07213i
$142$	−7.77379e16	−	1.49243e16i	−0.470247	−	0.0902793i
$143$		−	7.77510e16i		−	0.444650i
$144$	9.89672e16	+	9.38188e16i	0.535292	+	0.507446i
$145$	−3.35466e17			−1.71674
$146$	−3.78395e16	+	1.97098e17i	−0.183283	+	0.954685i
$147$	−4.81871e16			−0.221000
$148$	9.54611e16	−	2.39456e17i	0.414699	−	1.04023i
$149$		−	9.98537e16i		−	0.411030i	−0.978654	−	0.205515i	$-0.934113\pi$
$149$		−	9.98537e16i		−	0.411030i	0.978654	−	0.205515i	$-0.0658870\pi$
$150$	−3.01248e16	+	1.56914e17i	−0.117542	+	0.612254i
$151$			4.89954e17i			1.81276i	0.422466	+	0.906379i	$0.361165\pi$
$151$			4.89954e17i			1.81276i	−0.422466	+	0.906379i	$0.638835\pi$
$152$	2.18160e17	−	3.41092e17i	0.765644	−	1.19708i
$153$	2.00133e17			0.666480
$154$	4.44737e17	+	8.53817e16i	1.40584	+	0.269898i
$155$	−3.77474e17			−1.13301
$156$	−4.85195e16	+	1.21707e17i	−0.138331	+	0.346991i
$157$			1.15854e17i			0.313844i	0.987611	+	0.156922i	$0.0501572\pi$
$157$			1.15854e17i			0.313844i	−0.987611	+	0.156922i	$0.949843\pi$
$158$	−1.95335e17	−	3.75010e16i	−0.502949	−	0.0965575i
$159$			1.07357e18i			2.62816i
$160$	3.03897e17	+	4.23507e17i	0.707565	+	0.986055i
$161$	−4.71447e17			−1.04430
$162$	1.06749e17	−	5.56034e17i	0.225032	−	1.17215i
$163$	2.02993e17			0.407362			0.203681	−	0.979037i	$-0.434709\pi$
$163$	2.02993e17			0.407362			0.203681	+	0.979037i	$0.434709\pi$
$164$	1.49723e17	+	5.96883e16i	0.286113	+	0.114061i
$165$		−	1.37907e18i		−	2.51023i
$166$	−1.07493e17	+	5.59910e17i	−0.186430	+	0.971077i
$167$		−	7.85356e17i		−	1.29818i	−0.760712	−	0.649090i	$-0.775150\pi$
$167$		−	7.85356e17i		−	1.29818i	0.760712	−	0.649090i	$-0.224850\pi$
$168$	−6.42883e17	−	4.11183e17i	−1.01311	−	0.647980i
$169$	6.11980e17			0.919694
$170$	7.51274e17	+	1.44232e17i	1.07698	+	0.206761i
$171$	7.66258e17			1.04811
$172$	−4.75755e17	−	1.89664e17i	−0.621092	−	0.247604i
$173$			2.26818e17i			0.282689i	0.989960	+	0.141345i	$0.0451425\pi$
$173$			2.26818e17i			0.282689i	−0.989960	+	0.141345i	$0.954857\pi$
$174$	−1.53857e18	−	2.95379e17i	−1.83115	−	0.351549i
$175$		−	3.79554e17i		−	0.431488i
$176$	−1.04839e18	−	9.93851e17i	−1.13873	−	1.07949i
$177$	−5.60609e17			−0.581934
$178$	−1.91192e17	+	9.95880e17i	−0.189718	+	0.988205i
$179$	8.41693e17			0.798600			0.399300	−	0.916820i	$-0.369253\pi$
$179$	8.41693e17			0.798600			0.399300	+	0.916820i	$0.369253\pi$
$180$	−3.65311e17	+	9.16350e17i	−0.331499	+	0.831536i
$181$			1.53160e18i			1.32958i	0.747029	+	0.664791i	$0.231480\pi$
$181$			1.53160e18i			1.32958i	−0.747029	+	0.664791i	$0.768520\pi$
$182$	5.86811e16	−	3.05658e17i	0.0487446	−	0.253901i
$183$		−	1.28776e18i		−	1.02383i
$184$	1.26692e18	+	8.10314e17i	0.964288	+	0.616752i
$185$	1.86478e18			1.35911
$186$	−1.73124e18	−	3.32367e17i	−1.20852	−	0.232014i
$187$	−2.12007e18			−1.41781
$188$	4.70015e17	−	1.17899e18i	0.301196	−	0.755522i
$189$			5.13806e17i			0.315577i
$190$	2.87644e18	+	5.52226e17i	1.69366	+	0.325153i
$191$		−	4.46054e17i		−	0.251838i	−0.992041	−	0.125919i	$-0.959812\pi$
$191$		−	4.46054e17i		−	0.251838i	0.992041	−	0.125919i	$-0.0401879\pi$
$192$	1.02089e18	+	2.20995e18i	0.552799	+	1.19666i
$193$	1.72057e17			0.0893743			0.0446872	−	0.999001i	$-0.485771\pi$
$193$	1.72057e17			0.0893743			0.0446872	+	0.999001i	$0.485771\pi$
$194$	8.18122e16	−	4.26144e17i	0.0407760	−	0.212394i
$195$	−9.47802e17			−0.453357
$196$	−3.39186e17	−	1.35220e17i	−0.155736	−	0.0620857i
$197$			2.09264e18i			0.922495i	0.887271	+	0.461248i	$0.152598\pi$
$197$			2.09264e18i			0.922495i	−0.887271	+	0.461248i	$0.847402\pi$
$198$	5.15448e17	−	2.68486e18i	0.218204	−	1.13658i
$199$		−	1.09178e18i		−	0.443926i	−0.975055	−	0.221963i	$-0.928754\pi$
$199$		−	1.09178e18i		−	0.443926i	0.975055	−	0.221963i	$-0.0712464\pi$
$200$	−6.52369e17	+	1.01998e18i	−0.254832	+	0.398428i
$201$	5.38655e17			0.202182
$202$	−2.62389e18	−	5.03742e17i	−0.946532	−	0.181718i
$203$	3.72160e18			1.29051
$204$	3.31863e18	+	1.32300e18i	1.10641	+	0.441082i
$205$			1.16598e18i			0.373817i
$206$	1.13996e18	+	2.18854e17i	0.351523	+	0.0674863i
$207$			2.84611e18i			0.844286i
$208$	−6.83052e17	+	7.20535e17i	−0.194961	+	0.205659i
$209$	−8.11720e18			−2.22965
$210$	1.04082e18	−	5.42144e18i	0.275183	−	1.43338i
$211$	−3.18194e18			−0.809903			−0.404951	−	0.914338i	$-0.632712\pi$
$211$	−3.18194e18			−0.809903			−0.404951	+	0.914338i	$0.632712\pi$
$212$	−3.01258e18	+	7.55679e18i	−0.738332	+	1.85204i
$213$		−	2.67421e18i		−	0.631189i
$214$	7.54027e17	−	3.92758e18i	0.171426	−	0.892924i
$215$		−	3.70498e18i		−	0.811482i
$216$	8.83120e17	−	1.38075e18i	0.186376	−	0.291397i
$217$	4.18763e18			0.851707
$218$	−4.29765e18	−	8.25074e17i	−0.842518	−	0.161749i
$219$	−6.78026e18			−1.28143
$220$	3.86985e18	−	9.70717e18i	0.705200	−	1.76893i
$221$			1.45708e18i			0.256062i
$222$	8.55259e18	+	1.64195e18i	1.44969	+	0.278315i
$223$		−	6.29937e18i		−	1.03005i	−0.857175	−	0.515025i	$-0.827783\pi$
$223$		−	6.29937e18i		−	1.03005i	0.857175	−	0.515025i	$-0.172217\pi$
$224$	−3.37138e18	−	4.69832e18i	−0.531892	−	0.741239i
$225$	−2.29136e18			−0.348845
$226$	−1.17341e18	+	6.11205e18i	−0.172418	+	0.898090i
$227$	1.18503e18			0.168083			0.0840416	−	0.996462i	$-0.473217\pi$
$227$	1.18503e18			0.168083			0.0840416	+	0.996462i	$0.473217\pi$
$228$	1.27062e19	+	5.06543e18i	1.73995	+	0.693646i
$229$			4.92313e18i			0.650964i	0.945548	+	0.325482i	$0.105527\pi$
$229$			4.92313e18i			0.650964i	−0.945548	+	0.325482i	$0.894473\pi$
$230$	−2.05113e18	+	1.06840e19i	−0.261922	+	1.36430i
$231$			1.52991e19i			1.88699i
$232$	−1.00011e19	−	6.39661e18i	−1.19163	−	0.762160i
$233$	1.53969e19			1.77249			0.886247	−	0.463213i	$-0.153304\pi$
$233$	1.53969e19			1.77249			0.886247	+	0.463213i	$0.153304\pi$
$234$	−1.84525e18	−	3.54256e17i	−0.205271	−	0.0394086i
$235$	9.18148e18			0.987120
$236$	−3.94610e18	−	1.57315e18i	−0.410083	−	0.163483i
$237$		−	6.71961e18i		−	0.675083i
$238$	−8.33451e18	−	1.60008e18i	−0.809588	−	0.155427i
$239$		−	1.04062e19i		−	0.977484i	−0.872428	−	0.488742i	$-0.837456\pi$
$239$		−	1.04062e19i		−	0.977484i	0.872428	−	0.488742i	$-0.162544\pi$
$240$	−1.21153e19	+	1.27801e19i	−1.10063	+	1.16103i
$241$	−2.15325e18			−0.189216			−0.0946079	−	0.995515i	$-0.530160\pi$
$241$	−2.15325e18			−0.189216			−0.0946079	+	0.995515i	$0.530160\pi$
$242$	−3.24248e18	+	1.68894e19i	−0.275647	+	1.43579i
$243$	1.49224e19			1.22741
$244$	3.61363e18	−	9.06447e18i	0.287624	−	0.721480i
$245$		−	2.64144e18i		−	0.203476i
$246$	−1.02665e18	+	5.34762e18i	−0.0765494	+	0.398731i
$247$			5.57878e18i			0.402683i
$248$	−1.12534e19	−	7.19761e18i	−0.786450	−	0.503008i
$249$	−1.92611e19			−1.30343
$250$	9.58528e18	+	1.84021e18i	0.628181	+	0.120600i
$251$	7.37436e18			0.468095			0.234048	−	0.972225i	$-0.424803\pi$
$251$	7.37436e18			0.468095			0.234048	+	0.972225i	$0.424803\pi$
$252$	4.05270e18	−	1.01658e19i	0.249195	−	0.625084i
$253$		−	3.01498e19i		−	1.79606i
$254$	1.11908e19	+	2.14844e18i	0.645940	+	0.124009i
$255$			2.58441e19i			1.44557i
$256$	9.84542e17	+	1.84205e19i	0.0533721	+	0.998575i
$257$	3.29749e19			1.73268			0.866341	−	0.499453i	$-0.166466\pi$
$257$	3.29749e19			1.73268			0.866341	+	0.499453i	$0.166466\pi$
$258$	3.26226e18	−	1.69925e19i	0.166173	−	0.865563i
$259$	−2.06876e19			−1.02167
$260$	−6.67153e18	−	2.65966e18i	−0.319476	−	0.127362i
$261$		−	2.24672e19i		−	1.04334i
$262$	4.38926e18	−	2.28628e19i	0.197689	−	1.02972i
$263$			2.54894e19i			1.11356i	0.830660	+	0.556780i	$0.187964\pi$
$263$			2.54894e19i			1.11356i	−0.830660	+	0.556780i	$0.812036\pi$
$264$	2.62958e19	−	4.11133e19i	1.11444	−	1.74241i
$265$	−5.88491e19			−2.41976
$266$	−3.19107e19	−	6.12630e18i	−1.27316	−	0.244425i
$267$	−3.42587e19			−1.32642
$268$	3.79156e18	+	1.51154e18i	0.142475	+	0.0567991i
$269$			1.11186e19i			0.405539i	0.979226	+	0.202770i	$0.0649943\pi$
$269$			1.11186e19i			0.405539i	−0.979226	+	0.202770i	$0.935006\pi$
$270$	1.16439e19	+	2.23543e18i	0.412276	+	0.0791499i
$271$		−	1.82277e19i		−	0.626582i	−0.949657	−	0.313291i	$-0.898569\pi$
$271$		−	1.82277e19i		−	0.626582i	0.949657	−	0.313291i	$-0.101431\pi$
$272$	1.96471e19	+	1.86251e19i	0.655765	+	0.621651i
$273$	1.05148e19			0.340799
$274$	−5.16412e18	+	2.68989e19i	−0.162552	+	0.846701i
$275$	2.42730e19			0.742100
$276$	−1.88146e19	+	4.71946e19i	−0.558755	+	1.40159i
$277$			2.42638e19i			0.700037i	0.936743	+	0.350019i	$0.113825\pi$
$277$			2.42638e19i			0.700037i	−0.936743	+	0.350019i	$0.886175\pi$
$278$	−6.22926e18	+	3.24470e19i	−0.174614	+	0.909528i
$279$		−	2.52806e19i		−	0.688579i
$280$	2.25396e19	−	3.52405e19i	0.596598	−	0.932778i
$281$	3.14664e19			0.809462			0.404731	−	0.914436i	$-0.367365\pi$
$281$	3.14664e19			0.809462			0.404731	+	0.914436i	$0.367365\pi$
$282$	4.21097e19	+	8.08434e18i	1.05291	+	0.202140i
$283$	−3.81352e18			−0.0926904			−0.0463452	−	0.998925i	$-0.514757\pi$
$283$	−3.81352e18			−0.0926904			−0.0463452	+	0.998925i	$0.514757\pi$
$284$	7.50422e18	−	1.88237e19i	0.177320	−	0.444792i
$285$			9.89505e19i			2.27331i
$286$	1.95473e19	+	3.75274e18i	0.436675	+	0.0838341i
$287$		−	1.29352e19i		−	0.281007i
$288$	−2.83636e19	+	2.03529e19i	−0.599269	+	0.430019i
$289$	−8.93041e18			−0.183522
$290$	1.61916e19	−	8.43391e19i	0.323673	−	1.68595i
$291$	1.46595e19			0.285086
$292$	−4.77259e19	−	1.90263e19i	−0.903007	−	0.359992i
$293$		−	2.83226e19i		−	0.521426i	−0.965416	−	0.260713i	$-0.916042\pi$
$293$		−	2.83226e19i		−	0.521426i	0.965416	−	0.260713i	$-0.0839576\pi$
$294$	2.32580e18	−	1.21147e19i	0.0416672	−	0.217036i
$295$		−	3.07306e19i		−	0.535790i
$296$	5.55937e19	+	3.55574e19i	0.943391	+	0.603387i
$297$	−3.28587e19			−0.542749
$298$	2.51041e19	+	4.81955e18i	0.403659	+	0.0774955i
$299$	−2.07213e19			−0.324375
$300$	−3.79956e19	−	1.51473e19i	−0.579112	−	0.230868i
$301$			4.11025e19i			0.610008i
$302$	−1.23179e20	−	2.36482e19i	−1.78025	−	0.341777i
$303$		−	9.02630e19i		−	1.27048i
$304$	7.52239e19	+	7.13106e19i	1.03126	+	0.977610i
$305$	7.05904e19			0.942642
$306$	−9.65965e18	+	5.03152e19i	−0.125658	+	0.654527i
$307$	−5.41392e19			−0.686128			−0.343064	−	0.939312i	$-0.611465\pi$
$307$	−5.41392e19			−0.686128			−0.343064	+	0.939312i	$0.611465\pi$
$308$	−4.29314e19	+	1.07690e20i	−0.530115	+	1.32974i
$309$			3.92152e19i			0.471831i
$310$	1.82192e19	−	9.49002e19i	0.213617	−	1.11269i
$311$		−	8.32696e19i		−	0.951488i	−0.879584	−	0.475744i	$-0.842179\pi$
$311$		−	8.32696e19i		−	0.951488i	0.879584	−	0.475744i	$-0.157821\pi$
$312$	−2.82563e19	−	1.80725e19i	−0.314687	−	0.201272i
$313$	9.41987e18			0.102256			0.0511281	−	0.998692i	$-0.483718\pi$
$313$	9.41987e18			0.102256			0.0511281	+	0.998692i	$0.483718\pi$
$314$	−2.91267e19	−	5.59183e18i	−0.308216	−	0.0591721i
$315$	7.91672e19			0.816697
$316$	1.88562e19	−	4.72990e19i	0.189652	−	0.475724i
$317$		−	1.91859e20i		−	1.88152i	−0.339076	−	0.940759i	$-0.610114\pi$
$317$		−	1.91859e20i		−	1.88152i	0.339076	−	0.940759i	$-0.389886\pi$
$318$	−2.69904e20	−	5.18170e19i	−2.58103	−	0.495513i
$319$			2.38002e20i			2.21950i
$320$	−1.21141e20	+	5.59613e19i	−1.10177	+	0.508965i
$321$	1.35110e20			1.19853
$322$	2.27549e19	−	1.18526e20i	0.196892	−	1.02557i
$323$	1.52119e20			1.28399
$324$	1.34640e20	+	5.36752e19i	1.10870	+	0.441992i
$325$		−	1.66823e19i		−	0.134026i
$326$	−9.79769e18	+	5.10343e19i	−0.0768039	+	0.400056i
$327$		−	1.47841e20i		−	1.13087i
$328$	−2.22327e19	+	3.47607e19i	−0.165959	+	0.259476i
$329$	−1.01858e20			−0.742039
$330$	3.46709e20	+	6.65621e19i	2.46521	+	0.473277i
$331$	−6.19336e19			−0.429836			−0.214918	−	0.976632i	$-0.568948\pi$
$331$	−6.19336e19			−0.429836			−0.214918	+	0.976632i	$0.568948\pi$
$332$	−1.35578e20	−	5.40494e19i	−0.918512	−	0.366173i
$333$			1.24890e20i			0.825990i
$334$	1.97445e20	+	3.79061e19i	1.27490	+	0.244758i
$335$			2.95271e19i			0.186150i
$336$	1.34405e20	−	1.41780e20i	0.827370	−	0.872773i
$337$	−1.88348e19			−0.113220			−0.0566100	−	0.998396i	$-0.518029\pi$
$337$	−1.88348e19			−0.113220			−0.0566100	+	0.998396i	$0.518029\pi$
$338$	−2.95379e19	+	1.53857e20i	−0.173399	+	0.903200i
$339$	−2.10257e20			−1.20546
$340$	−7.25222e19	+	1.81915e20i	−0.406106	+	1.01868i
$341$			2.67805e20i			1.46482i
$342$	−3.69843e19	+	1.92644e20i	−0.197610	+	1.02931i
$343$			2.04089e20i			1.06529i
$344$	7.06461e19	−	1.10455e20i	0.360264	−	0.563270i
$345$	−3.67532e20			−1.83123
$346$	−5.70241e19	−	1.09476e19i	−0.277619	−	0.0532981i
$347$	5.30770e18			0.0252505			0.0126253	−	0.999920i	$-0.495981\pi$
$347$	5.30770e18			0.0252505			0.0126253	+	0.999920i	$0.495981\pi$
$348$	1.48522e20	−	3.72554e20i	0.690489	−	1.73203i
$349$		−	1.88668e20i		−	0.857224i	−0.903489	−	0.428612i	$-0.859003\pi$
$349$		−	1.88668e20i		−	0.857224i	0.903489	−	0.428612i	$-0.140997\pi$
$350$	9.54232e19	+	1.83196e19i	0.423750	+	0.0813526i
$351$			2.25831e19i			0.0980226i
$352$	3.00465e20	−	2.15605e20i	1.27483	−	0.914781i
$353$	4.15743e19			0.172436			0.0862179	−	0.996276i	$-0.472522\pi$
$353$	4.15743e19			0.172436			0.0862179	+	0.996276i	$0.472522\pi$
$354$	2.70584e19	−	1.40942e20i	0.109718	−	0.571498i
$355$	1.46591e20			0.581139
$356$	−2.41145e20	−	9.61346e19i	−0.934713	−	0.372631i
$357$		−	2.86710e20i		−	1.08667i
$358$	−4.06253e19	+	2.11609e20i	−0.150568	+	0.784278i
$359$			5.04713e19i			0.182932i	0.995808	+	0.0914658i	$0.0291552\pi$
$359$			5.04713e19i			0.182932i	−0.995808	+	0.0914658i	$0.970845\pi$
$360$	−2.12746e20	−	1.36071e20i	−0.754122	−	0.482332i
$361$	2.93983e20			1.01921
$362$	−3.85056e20	−	7.39242e19i	−1.30574	−	0.250679i
$363$	−5.81003e20			−1.92719
$364$	7.40128e19	+	2.95059e19i	0.240157	+	0.0957409i
$365$		−	3.71669e20i		−	1.17982i
$366$	3.23754e20	+	6.21552e19i	1.00546	+	0.193032i
$367$			2.17545e19i			0.0661028i	0.999454	+	0.0330514i	$0.0105225\pi$
$367$			2.17545e19i			0.0661028i	−0.999454	+	0.0330514i	$0.989478\pi$
$368$	−2.64869e20	+	2.79404e20i	−0.787497	+	0.830712i
$369$	−7.80893e19			−0.227185
$370$	−9.00058e19	+	4.68822e20i	−0.256246	+	1.33473i
$371$	6.52862e20			1.81899
$372$	1.67120e20	−	4.19206e20i	0.455707	−	1.14310i
$373$		−	2.44842e20i		−	0.653453i	−0.945119	−	0.326727i	$-0.894054\pi$
$373$		−	2.44842e20i		−	0.653453i	0.945119	−	0.326727i	$-0.105946\pi$
$374$	1.02328e20	−	5.33004e20i	0.267313	−	1.39238i
$375$			3.29737e20i			0.843175i
$376$	2.73722e20	+	1.75071e20i	0.685185	+	0.438240i
$377$	1.63574e20			0.400851
$378$	−1.29175e20	−	2.47994e19i	−0.309917	−	0.0594987i
$379$	4.23969e19			0.0995911			0.0497956	−	0.998759i	$-0.484143\pi$
$379$	4.23969e19			0.0995911			0.0497956	+	0.998759i	$0.484143\pi$
$380$	−2.77669e20	+	6.96507e20i	−0.638643	+	1.60198i
$381$			3.84969e20i			0.867013i
$382$	1.12142e20	+	2.15293e19i	0.247321	+	0.0474814i
$383$			1.39034e20i			0.300284i	0.988664	+	0.150142i	$0.0479731\pi$
$383$			1.39034e20i			0.300284i	−0.988664	+	0.150142i	$0.952027\pi$
$384$	−6.04874e20	+	1.49994e20i	−1.27943	+	0.317266i
$385$	−8.38643e20			−1.73737
$386$	−8.30450e18	+	4.32565e19i	−0.0168506	+	0.0877714i
$387$	2.48135e20			0.493173
$388$	1.03187e20	+	4.11366e19i	0.200897	+	0.0800893i
$389$		−	4.58473e20i		−	0.874415i	−0.899361	−	0.437207i	$-0.855968\pi$
$389$		−	4.58473e20i		−	0.874415i	0.899361	−	0.437207i	$-0.144032\pi$
$390$	4.57467e19	−	2.38286e20i	0.0854758	−	0.445227i
$391$			5.65016e20i			1.03430i
$392$	5.03666e19	−	7.87479e19i	0.0903347	−	0.141238i
$393$	7.86490e20			1.38214
$394$	−5.26107e20	−	1.01003e20i	−0.905951	−	0.173927i
$395$	3.68345e20			0.621552
$396$	6.50120e20	+	2.59176e20i	1.07506	+	0.428582i
$397$			4.48116e20i			0.726217i	0.931747	+	0.363109i	$0.118285\pi$
$397$			4.48116e20i			0.726217i	−0.931747	+	0.363109i	$0.881715\pi$
$398$	2.74483e20	+	5.26960e19i	0.435964	+	0.0836976i
$399$		−	1.09774e21i		−	1.70890i
$400$	−2.24943e20	−	2.13242e20i	−0.343236	−	0.325381i
$401$	5.05309e20			0.755792			0.377896	−	0.925848i	$-0.376648\pi$
$401$	5.05309e20			0.755792			0.377896	+	0.925848i	$0.376648\pi$
$402$	−2.59988e19	+	1.35423e20i	−0.0381193	+	0.198556i
$403$	1.84057e20			0.264552
$404$	2.53290e20	−	6.35356e20i	0.356918	−	0.895296i
$405$			1.04852e21i			1.44856i
$406$	−1.79627e20	+	9.35643e20i	−0.243312	+	1.26737i
$407$		−	1.32300e21i		−	1.75713i
$408$	−4.92792e20	+	7.70477e20i	−0.641774	+	1.00341i
$409$	1.09683e21			1.40073			0.700364	−	0.713786i	$-0.253021\pi$
$409$	1.09683e21			1.40073			0.700364	+	0.713786i	$0.253021\pi$
$410$	−2.93137e20	−	5.62773e19i	−0.367113	−	0.0704794i
$411$	−9.25332e20			−1.13648
$412$	−1.10043e20	+	2.76034e20i	−0.132552	+	0.332495i
$413$			3.40920e20i			0.402765i
$414$	−7.15538e20	−	1.37371e20i	−0.829144	−	0.159181i
$415$		−	1.05583e21i		−	1.20007i
$416$	−1.48181e20	−	2.06503e20i	−0.165213	−	0.230239i
$417$	−1.11619e21			−1.22081
$418$	3.91786e20	−	2.04074e21i	0.420377	−	2.18966i
$419$	−1.44991e21			−1.52626			−0.763130	−	0.646246i	$-0.776338\pi$
$419$	−1.44991e21			−1.52626			−0.763130	+	0.646246i	$0.776338\pi$
$420$	1.31276e21	+	5.23344e20i	1.35579	+	0.540496i
$421$		−	4.39928e19i		−	0.0445785i	−0.999752	−	0.0222892i	$-0.992905\pi$
$421$		−	4.39928e19i		−	0.0445785i	0.999752	−	0.0222892i	$-0.00709547\pi$
$422$	1.53580e20	−	7.99969e20i	0.152699	−	0.795378i
$423$			6.14913e20i			0.599916i
$424$	−1.75444e21	−	1.12213e21i	−1.67962	−	1.07427i
$425$	−4.54884e20			−0.427356
$426$	6.72321e20	+	1.29074e20i	0.619869	+	0.119004i
$427$	−7.83118e20			−0.708605
$428$	9.51033e20	+	3.79138e20i	0.844589	+	0.336703i
$429$			6.72434e20i			0.586127i
$430$	9.31466e20	+	1.78825e20i	0.796928	+	0.152996i
$431$			3.88108e20i			0.325938i	0.986631	+	0.162969i	$0.0521071\pi$
$431$			3.88108e20i			0.325938i	−0.986631	+	0.162969i	$0.947893\pi$
$432$	3.04508e20	+	2.88668e20i	0.251032	+	0.237973i
$433$	−2.17182e21			−1.75760			−0.878800	−	0.477189i	$-0.841656\pi$
$433$	−2.17182e21			−1.75760			−0.878800	+	0.477189i	$0.841656\pi$
$434$	−2.02121e20	+	1.05281e21i	−0.160580	+	0.836432i
$435$	2.90130e21			2.26297
$436$	4.14862e20	−	1.04064e21i	0.317696	−	0.796911i
$437$			2.16330e21i			1.62654i
$438$	3.27257e20	−	1.70462e21i	0.241599	−	1.25844i
$439$		−	6.49148e19i		−	0.0470573i	−0.999723	−	0.0235287i	$-0.992510\pi$
$439$		−	6.49148e19i		−	0.0470573i	0.999723	−	0.0235287i	$-0.00749010\pi$
$440$	2.25369e21	+	1.44144e21i	1.60425	+	1.02607i
$441$	1.76906e20			0.123661
$442$	−3.66322e20	−	7.03276e19i	−0.251470	−	0.0482778i
$443$	−1.94688e21			−1.31253			−0.656266	−	0.754530i	$-0.727865\pi$
$443$	−1.94688e21			−1.31253			−0.656266	+	0.754530i	$0.727865\pi$
$444$	−8.25601e20	+	2.07095e21i	−0.546646	+	1.37121i
$445$		−	1.87794e21i		−	1.22124i
$446$	1.58372e21	+	3.04046e20i	1.01158	+	0.194205i
$447$			8.63591e20i			0.541811i
$448$	1.34392e21	−	6.20825e20i	0.828228	−	0.382600i
$449$	1.19607e21			0.724079			0.362040	−	0.932163i	$-0.382081\pi$
$449$	1.19607e21			0.724079			0.362040	+	0.932163i	$0.382081\pi$
$450$	1.10595e20	−	5.76067e20i	0.0657711	−	0.342589i
$451$	8.27223e20			0.483293
$452$	−1.47999e21	−	5.90010e20i	−0.849475	−	0.338651i
$453$		−	4.23740e21i		−	2.38954i
$454$	−5.71970e19	+	2.97928e20i	−0.0316903	+	0.165069i
$455$			5.76381e20i			0.313775i
$456$	−1.88677e21	+	2.94996e21i	−1.00925	+	1.57796i
$457$	1.21725e21			0.639811			0.319906	−	0.947449i	$-0.396349\pi$
$457$	1.21725e21			0.639811			0.319906	+	0.947449i	$0.396349\pi$
$458$	−1.23772e21	−	2.37620e20i	−0.639289	−	0.122733i
$459$	6.15782e20			0.312554
$460$	−2.58704e21	−	1.03135e21i	−1.29045	−	0.514448i
$461$			2.88773e21i			1.41563i	0.706400	+	0.707813i	$0.250318\pi$
$461$			2.88773e21i			1.41563i	−0.706400	+	0.707813i	$0.749682\pi$
$462$	−3.84633e21	−	7.38429e20i	−1.85315	−	0.355773i
$463$			2.98592e21i			1.41394i	0.707244	+	0.706969i	$0.249938\pi$
$463$			2.98592e21i			1.41394i	−0.707244	+	0.706969i	$0.750062\pi$
$464$	2.09088e21	−	2.20561e21i	0.973161	−	1.02656i
$465$	3.26460e21			1.49350
$466$	−7.43147e20	+	3.87091e21i	−0.334185	+	1.74071i
$467$	8.30551e20			0.367140			0.183570	−	0.983007i	$-0.441235\pi$
$467$	8.30551e20			0.367140			0.183570	+	0.983007i	$0.441235\pi$
$468$	1.78126e20	−	4.46814e20i	0.0774036	−	0.194160i
$469$		−	3.27569e20i		−	0.139933i
$470$	−4.43155e20	+	2.30830e21i	−0.186111	+	0.969416i
$471$		−	1.00197e21i		−	0.413702i
$472$	5.85966e20	−	9.16154e20i	0.237868	−	0.371905i
$473$	−2.62856e21			−1.04913
$474$	1.68937e21	+	3.24329e20i	0.662976	+	0.127280i
$475$	−1.74164e21			−0.672061
$476$	8.04549e20	−	2.01814e21i	0.305279	−	0.765765i
$477$		−	3.94131e21i		−	1.47060i
$478$	2.61621e21	+	5.02268e20i	0.959953	+	0.184294i
$479$		−	2.17430e21i		−	0.784578i	−0.919842	−	0.392289i	$-0.871683\pi$
$479$		−	2.17430e21i		−	0.784578i	0.919842	−	0.392289i	$-0.128317\pi$
$480$	−2.62827e21	−	3.66273e21i	−0.932696	−	1.29979i
$481$	−9.09270e20			−0.317346
$482$	1.03929e20	−	5.41345e20i	0.0356747	−	0.185822i
$483$	4.07734e21			1.37657
$484$	−4.08965e21	−	1.63037e21i	−1.35807	−	0.541408i
$485$			8.03581e20i			0.262480i
$486$	−7.20248e20	+	3.75163e21i	−0.231415	+	1.20540i
$487$		−	4.36632e21i		−	1.38001i	−0.723803	−	0.690007i	$-0.757607\pi$
$487$		−	4.36632e21i		−	1.38001i	0.723803	−	0.690007i	$-0.242393\pi$
$488$	2.10447e21	+	1.34601e21i	0.654312	+	0.418493i
$489$	−1.75560e21			−0.536975
$490$	6.64082e20	+	1.27492e20i	0.199827	+	0.0383632i
$491$	−3.60613e21			−1.06755			−0.533776	−	0.845626i	$-0.679227\pi$
$491$	−3.60613e21			−1.06755			−0.533776	+	0.845626i	$0.679227\pi$
$492$	−1.29489e21	−	5.16218e20i	−0.377147	−	0.150353i
$493$		−	4.46023e21i		−	1.27815i
$494$	−1.40255e21	−	2.69266e20i	−0.395462	−	0.0759218i
$495$			5.06287e21i			1.40461i
$496$	2.35270e21	−	2.48181e21i	0.642264	−	0.677508i
$497$	−1.62625e21			−0.436855
$498$	9.29660e20	−	4.84242e21i	0.245748	−	1.28005i
$499$	7.24429e21			1.88448			0.942240	−	0.334939i	$-0.108716\pi$
$499$	7.24429e21			1.88448			0.942240	+	0.334939i	$0.108716\pi$
$500$	−9.25289e20	+	2.32100e21i	−0.236874	+	0.594177i
$501$			6.79219e21i			1.71123i
$502$	−3.55932e20	+	1.85398e21i	−0.0882545	+	0.459700i
$503$			5.47680e21i			1.33654i	0.743917	+	0.668272i	$0.232966\pi$
$503$			5.47680e21i			1.33654i	−0.743917	+	0.668272i	$0.767034\pi$
$504$	2.36017e21	+	1.50955e21i	0.566890	+	0.362579i
$505$	4.94789e21			1.16974
$506$	7.57991e21	+	1.45521e21i	1.76384	+	0.338627i
$507$	−5.29274e21			−1.21232
$508$	−1.08028e21	+	2.70977e21i	−0.243571	+	0.610975i
$509$		−	3.97825e20i		−	0.0882977i	−0.999025	−	0.0441489i	$-0.985942\pi$
$509$		−	3.97825e20i		−	0.0882977i	0.999025	−	0.0441489i	$-0.0140576\pi$
$510$	−6.49744e21	−	1.24740e21i	−1.41965	−	0.272548i
$511$			4.12324e21i			0.886893i
$512$	−4.67858e21	−	6.41561e20i	−0.990729	−	0.135856i
$513$	2.35767e21			0.491524
$514$	−1.59157e21	+	8.29018e21i	−0.326679	+	1.70161i
$515$	−2.14964e21			−0.434418
$516$	4.11460e21	+	1.64032e21i	0.818709	+	0.326386i
$517$		−	6.51396e21i		−	1.27621i
$518$	9.98509e20	−	5.20104e21i	0.192625	−	1.00335i
$519$		−	1.96165e21i		−	0.372634i
$520$	9.90672e20	−	1.54891e21i	0.185312	−	0.289734i
$521$	−6.18484e21			−1.13927			−0.569635	−	0.821898i	$-0.692915\pi$
$521$	−6.18484e21			−1.13927			−0.569635	+	0.821898i	$0.692915\pi$
$522$	5.64845e21	+	1.08441e21i	1.02463	+	0.196711i
$523$	−5.41875e21			−0.968023			−0.484011	−	0.875062i	$-0.660821\pi$
$523$	−5.41875e21			−0.968023			−0.484011	+	0.875062i	$0.660821\pi$
$524$	5.53606e21	+	2.20700e21i	0.973981	+	0.388286i
$525$			3.28259e21i			0.568778i
$526$	−6.40826e21	−	1.23028e21i	−1.09359	−	0.209950i
$527$		−	5.01875e21i		−	0.843550i
$528$	9.06705e21	+	8.59538e21i	1.50105	+	1.42296i
$529$	−1.90255e21			−0.310234
$530$	2.84042e21	−	1.47952e22i	0.456221	−	2.37637i
$531$	2.05812e21			0.325623
$532$	3.08041e21	−	7.72693e21i	0.480082	−	1.20424i
$533$		−	5.68533e20i		−	0.0872847i
$534$	1.65353e21	−	8.61293e21i	0.250082	−	1.30263i
$535$			7.40625e21i			1.10349i
$536$	−5.63019e20	+	8.80277e20i	−0.0826427	+	0.129211i
$537$	−7.27943e21			−1.05270
$538$	−2.79532e21	−	5.36653e20i	−0.398266	−	0.0764602i
$539$	−1.87402e21			−0.263065
$540$	−1.12401e21	+	2.81948e21i	−0.155461	+	0.389959i
$541$			1.05445e22i			1.43697i	0.695540	+	0.718487i	$0.255165\pi$
$541$			1.05445e22i			1.43697i	−0.695540	+	0.718487i	$0.744835\pi$
$542$	4.58261e21	+	8.79781e20i	0.615344	+	0.118135i
$543$		−	1.32461e22i		−	1.75263i
$544$	−5.63080e21	+	4.04050e21i	−0.734140	+	0.526798i
$545$	8.10410e21			1.04120
$546$	−5.07507e20	+	2.64350e21i	−0.0642540	+	0.334687i
$547$	7.13870e21			0.890678			0.445339	−	0.895362i	$-0.353083\pi$
$547$	7.13870e21			0.890678			0.445339	+	0.895362i	$0.353083\pi$
$548$	−6.51337e21	−	2.59661e21i	−0.800868	−	0.319273i
$549$			4.72766e21i			0.572885i
$550$	−1.17157e21	+	6.10246e21i	−0.139915	+	0.728791i
$551$		−	1.70771e22i		−	2.01002i
$552$	−1.09570e22	−	7.00804e21i	−1.27110	−	0.812988i
$553$	−4.08635e21			−0.467234
$554$	−6.10014e21	−	1.17112e21i	−0.687482	−	0.131985i
$555$	−1.61277e22			−1.79155
$556$	−7.85680e21	−	3.13218e21i	−0.860295	−	0.342964i
$557$			1.07684e22i			1.16228i	0.813803	+	0.581141i	$0.197393\pi$
$557$			1.07684e22i			1.16228i	−0.813803	+	0.581141i	$0.802607\pi$
$558$	6.35577e21	+	1.22020e21i	0.676230	+	0.129824i
$559$			1.80656e21i			0.189477i
$560$	7.77188e21	+	7.36758e21i	0.803566	+	0.761764i
$561$	1.83356e22			1.86892
$562$	−1.51876e21	+	7.91093e21i	−0.152616	+	0.794944i
$563$	1.69449e22			1.67869			0.839346	−	0.543598i	$-0.182938\pi$
$563$	1.69449e22			1.67869			0.839346	+	0.543598i	$0.182938\pi$
$564$	−4.06495e21	+	1.01966e22i	−0.397029	+	0.995911i
$565$		−	1.15255e22i		−	1.10987i
$566$	1.84064e20	−	9.58753e20i	0.0174758	−	0.0910280i
$567$		−	1.16321e22i		−	1.08891i
$568$	4.37023e21	+	2.79517e21i	0.403383	+	0.258001i
$569$	−6.13631e21			−0.558482			−0.279241	−	0.960221i	$-0.590083\pi$
$569$	−6.13631e21			−0.558482			−0.279241	+	0.960221i	$0.590083\pi$
$570$	−2.48770e22	−	4.77596e21i	−2.23254	−	0.428609i
$571$	1.22205e22			1.08143			0.540715	−	0.841206i	$-0.318154\pi$
$571$	1.22205e22			1.08143			0.540715	+	0.841206i	$0.318154\pi$
$572$	−1.88694e21	+	4.73323e21i	−0.164661	+	0.413038i
$573$			3.85772e21i			0.331967i
$574$	3.25201e21	+	6.24330e20i	0.275967	+	0.0529809i
$575$		−	6.46896e21i		−	0.541367i
$576$	−3.74791e21	−	8.11322e21i	−0.309321	−	0.669597i
$577$	2.10546e22			1.71372			0.856860	−	0.515549i	$-0.172412\pi$
$577$	2.10546e22			1.71372			0.856860	+	0.515549i	$0.172412\pi$
$578$	4.31036e20	−	2.24518e21i	0.0346012	−	0.180231i
$579$	−1.48804e21			−0.117811
$580$	2.04221e22	+	8.14144e21i	1.59469	+	0.635737i
$581$			1.17132e22i			0.902121i
$582$	−7.07558e20	+	3.68553e21i	−0.0537499	+	0.279973i
$583$			4.17515e22i			3.12841i
$584$	7.08694e21	−	1.10804e22i	0.523788	−	0.818940i
$585$	3.47960e21			0.253678
$586$	7.12056e21	+	1.36702e21i	0.512075	+	0.0983095i
$587$	−2.17592e22			−1.54361			−0.771806	−	0.635857i	$-0.780647\pi$
$587$	−2.17592e22			−1.54361			−0.771806	+	0.635857i	$0.780647\pi$
$588$	2.93347e21	+	1.16946e21i	0.205288	+	0.0818399i
$589$		−	1.92155e22i		−	1.32657i
$590$	7.72594e21	+	1.48325e21i	0.526181	+	0.101018i
$591$		−	1.80983e22i		−	1.21601i
$592$	−1.16227e22	+	1.22605e22i	−0.770432	+	0.812710i
$593$	−2.51770e22			−1.64652			−0.823259	−	0.567666i	$-0.807847\pi$
$593$	−2.51770e22			−1.64652			−0.823259	+	0.567666i	$0.807847\pi$
$594$	1.58596e21	−	8.26096e21i	0.102330	−	0.533015i
$595$	1.57164e22			1.00050
$596$	−2.42336e21	+	6.07877e21i	−0.152211	+	0.381809i
$597$			9.44233e21i			0.585173i
$598$	1.00014e21	−	5.20951e21i	0.0611575	−	0.318557i
$599$			1.85387e22i			1.11857i	0.828974	+	0.559287i	$0.188925\pi$
$599$			1.85387e22i			1.11857i	−0.828974	+	0.559287i	$0.811075\pi$
$600$	5.64205e21	−	8.82132e21i	0.335913	−	0.525198i
$601$	−8.62532e21			−0.506733			−0.253367	−	0.967370i	$-0.581538\pi$
$601$	−8.62532e21			−0.506733			−0.253367	+	0.967370i	$0.581538\pi$
$602$	−1.03335e22	−	1.98386e21i	−0.599068	−	0.115011i
$603$	−1.97753e21			−0.113132
$604$	1.18907e22	−	2.98268e22i	0.671294	−	1.68388i
$605$		−	3.18485e22i		−	1.77438i
$606$	2.26929e22	+	4.35664e21i	1.24770	+	0.239536i
$607$			2.25482e22i			1.22350i	0.791053	+	0.611748i	$0.209533\pi$
$607$			2.25482e22i			1.22350i	−0.791053	+	0.611748i	$0.790467\pi$
$608$	−2.15589e22	+	1.54701e22i	−1.15451	+	0.828444i
$609$	−3.21865e22			−1.70112
$610$	−3.40712e21	+	1.77470e22i	−0.177725	+	0.925736i
$611$	−4.47690e21			−0.230488
$612$	−1.21835e22	−	4.85704e21i	−0.619097	−	0.246809i
$613$		−	3.52239e22i		−	1.76666i	−0.468751	−	0.883330i	$-0.655296\pi$
$613$		−	3.52239e22i		−	1.76666i	0.468751	−	0.883330i	$-0.344704\pi$
$614$	2.61309e21	−	1.36111e22i	0.129362	−	0.673822i
$615$		−	1.00840e22i		−	0.492758i
$616$	−2.50020e22	−	1.59911e22i	−1.20595	−	0.771317i
$617$	3.01062e22			1.43342			0.716712	−	0.697369i	$-0.245646\pi$
$617$	3.01062e22			1.43342			0.716712	+	0.697369i	$0.245646\pi$
$618$	−9.85905e21	−	1.89277e21i	−0.463369	−	0.0889589i
$619$	−3.97729e22			−1.84528			−0.922640	−	0.385662i	$-0.873973\pi$
$619$	−3.97729e22			−1.84528			−0.922640	+	0.385662i	$0.873973\pi$
$620$	2.29794e22	+	9.16093e21i	1.05246	+	0.419572i
$621$			8.75711e21i			0.395939i
$622$	2.09347e22	+	4.01910e21i	0.934423	+	0.179393i
$623$			2.08335e22i			0.918032i
$624$	5.90742e21	−	6.23159e21i	0.256993	−	0.271096i
$625$	−2.90868e22			−1.24927
$626$	−4.54661e20	+	2.36824e21i	−0.0192794	+	0.100422i
$627$	7.02021e22			2.93907
$628$	2.81167e21	−	7.05282e21i	0.116222	−	0.291532i
$629$			2.47935e22i			1.01189i
$630$	−3.82110e21	+	1.99033e22i	−0.153980	+	0.802050i
$631$		−	2.65496e22i		−	1.05639i	−0.849124	−	0.528194i	$-0.822869\pi$
$631$		−	2.65496e22i		−	1.05639i	0.849124	−	0.528194i	$-0.177131\pi$
$632$	1.09813e22	+	7.02354e21i	0.431435	+	0.275943i
$633$	2.75192e22			1.06760
$634$	4.82351e22	+	9.26030e21i	1.84777	+	0.354741i
$635$	−2.11026e22			−0.798263
$636$	2.60545e22	−	6.53553e22i	0.973252	−	2.44132i
$637$			1.28797e21i			0.0475107i
$638$	−5.98358e22	−	1.14874e22i	−2.17969	−	0.418464i
$639$			9.81766e21i			0.353184i
$640$	−8.22214e21	−	3.31570e22i	−0.292109	−	1.17797i
$641$	−1.08109e21			−0.0379315			−0.0189657	−	0.999820i	$-0.506037\pi$
$641$	−1.08109e21			−0.0379315			−0.0189657	+	0.999820i	$0.506037\pi$
$642$	−6.52124e21	+	3.39679e22i	−0.225970	+	1.17703i
$643$	−3.02703e22			−1.03593			−0.517963	−	0.855403i	$-0.673310\pi$
$643$	−3.02703e22			−1.03593			−0.517963	+	0.855403i	$0.673310\pi$
$644$	2.87002e22	+	1.14416e22i	0.970058	+	0.386722i
$645$			3.20428e22i			1.06968i
$646$	−7.34219e21	+	3.82440e22i	−0.242084	+	1.26097i
$647$		−	4.01656e21i		−	0.130804i	−0.997859	−	0.0654019i	$-0.979167\pi$
$647$		−	4.01656e21i		−	0.130804i	0.997859	−	0.0654019i	$-0.0208329\pi$
$648$	−1.99930e22	+	3.12589e22i	−0.643098	+	1.00548i
$649$	−2.18023e22			−0.692700
$650$	4.19409e21	+	8.05192e20i	0.131623	+	0.0252693i
$651$	−3.62169e22			−1.12270
$652$	−1.23576e22	−	4.92645e21i	−0.378401	−	0.150853i
$653$		−	1.20618e22i		−	0.364844i	−0.983220	−	0.182422i	$-0.941606\pi$
$653$		−	1.20618e22i		−	0.364844i	0.983220	−	0.182422i	$-0.0583937\pi$
$654$	3.71685e22	+	7.13570e21i	1.11059	+	0.213214i
$655$			4.31125e22i			1.27255i
$656$	−7.66605e21	−	7.26726e21i	−0.223533	−	0.211904i
$657$	2.48919e22			0.717026
$658$	4.91628e21	−	2.56079e22i	0.139904	−	0.728731i
$659$	3.87491e22			1.08938			0.544688	−	0.838638i	$-0.316648\pi$
$659$	3.87491e22			1.08938			0.544688	+	0.838638i	$0.316648\pi$
$660$	−3.34686e22	+	8.39530e22i	−0.929579	+	2.33177i
$661$		−	6.57212e22i		−	1.80341i	−0.432354	−	0.901704i	$-0.642317\pi$
$661$		−	6.57212e22i		−	1.80341i	0.432354	−	0.901704i	$-0.357683\pi$
$662$	2.98929e21	−	1.55706e22i	0.0810410	−	0.422127i
$663$		−	1.26016e22i		−	0.337535i
$664$	2.01323e22	−	3.14768e22i	0.532782	−	0.833001i
$665$	6.01742e22			1.57339
$666$	−3.13985e22	−	6.02797e21i	−0.811177	−	0.155732i
$667$	6.34295e22			1.61914
$668$	−1.90598e22	+	4.78099e22i	−0.480737	+	1.20589i
$669$			5.44805e22i			1.35779i
$670$	−7.42338e21	−	1.42516e21i	−0.182811	−	0.0350966i
$671$		−	5.00816e22i		−	1.21870i
$672$	2.91576e22	+	4.06337e22i	0.701128	+	0.977084i
$673$	−3.18312e22			−0.756366			−0.378183	−	0.925731i	$-0.623451\pi$
$673$	−3.18312e22			−0.756366			−0.378183	+	0.925731i	$0.623451\pi$
$674$	9.09085e20	−	4.73524e21i	0.0213464	−	0.111189i
$675$	−7.05020e21			−0.163595
$676$	−3.72554e22	−	1.48522e22i	−0.854309	−	0.340578i
$677$			3.11878e22i			0.706767i	0.935479	+	0.353383i	$0.114969\pi$
$677$			3.11878e22i			0.706767i	−0.935479	+	0.353383i	$0.885031\pi$
$678$	1.01483e22	−	5.28605e22i	0.227277	−	1.18384i
$679$		−	8.91479e21i		−	0.197312i
$680$	−4.22348e22	−	2.70131e22i	−0.923844	−	0.590885i
$681$	−1.02488e22			−0.221563
$682$	−6.73286e22	−	1.29259e22i	−1.43855	−	0.276176i
$683$	5.88382e22			1.24249			0.621246	−	0.783615i	$-0.286627\pi$
$683$	5.88382e22			1.24249			0.621246	+	0.783615i	$0.286627\pi$
$684$	−4.66473e22	−	1.85964e22i	−0.973594	−	0.388132i
$685$		−	5.07234e22i		−	1.04637i
$686$	−5.13097e22	−	9.85058e21i	−1.04618	−	0.200849i
$687$		−	4.25779e22i		−	0.858086i
$688$	2.43595e22	+	2.30923e22i	0.485244	+	0.460001i
$689$	2.86949e22			0.565004
$690$	1.77394e22	−	9.24008e22i	0.345259	−	1.79839i
$691$	1.30063e22			0.250224			0.125112	−	0.992143i	$-0.460071\pi$
$691$	1.30063e22			0.250224			0.125112	+	0.992143i	$0.460071\pi$
$692$	5.50466e21	−	1.38080e22i	0.104684	−	0.262591i
$693$		−	5.61666e22i		−	1.05587i
$694$	−2.56182e20	+	1.33440e21i	−0.00476073	+	0.0247977i
$695$		−	6.11855e22i		−	1.12401i
$696$	8.64948e22	+	5.53215e22i	1.57078	+	1.00466i
$697$	−1.55024e22			−0.278316
$698$	4.74328e22	+	9.10627e21i	0.841851	+	0.161621i
$699$	−1.33161e23			−2.33646
$700$	−9.21141e21	+	2.31060e22i	−0.159787	+	0.400812i
$701$			4.74005e22i			0.812904i	0.913672	+	0.406452i	$0.133234\pi$
$701$			4.74005e22i			0.812904i	−0.913672	+	0.406452i	$0.866766\pi$
$702$	−5.67758e21	−	1.09000e21i	−0.0962646	−	0.0184811i
$703$			9.49278e22i			1.59130i
$704$	3.97027e22	+	8.59458e22i	0.658020	+	1.42444i
$705$	−7.94066e22			−1.30120
$706$	−2.00663e21	+	1.04521e22i	−0.0325110	+	0.169343i
$707$	−5.48911e22			−0.879319
$708$	3.41281e22	+	1.36055e22i	0.540562	+	0.215500i
$709$			1.15634e23i			1.81098i	0.424364	+	0.905492i	$0.360498\pi$
$709$			1.15634e23i			1.81098i	−0.424364	+	0.905492i	$0.639502\pi$
$710$	−7.07538e21	+	3.68542e22i	−0.109568	+	0.570717i
$711$			2.46692e22i			0.377745i
$712$	3.58082e22	−	5.59859e22i	0.542179	−	0.847693i
$713$	7.13722e22			1.06859
$714$	7.20815e22	+	1.38384e22i	1.06718	+	0.204880i
$715$	−3.68604e22			−0.539650
$716$	−5.12395e22	−	2.04271e22i	−0.741824	−	0.295735i
$717$			8.99988e22i			1.28850i
$718$	−1.26889e22	−	2.43605e21i	−0.179651	−	0.0344898i
$719$		−	1.02086e23i		−	1.42933i	−0.699466	−	0.714666i	$-0.746579\pi$
$719$		−	1.02086e23i		−	1.42933i	0.699466	−	0.714666i	$-0.253421\pi$
$720$	4.44779e22	−	4.69186e22i	0.615863	−	0.649659i
$721$	2.38477e22			0.326561
$722$	−1.41894e22	+	7.39099e22i	−0.192162	+	1.00093i
$723$	1.86225e22			0.249420
$724$	3.71704e22	−	9.32385e22i	0.492366	−	1.23506i
$725$			5.10659e22i			0.669002i
$726$	2.80427e22	−	1.46069e23i	0.363352	−	1.89263i
$727$		−	3.78769e22i		−	0.485400i	−0.970101	−	0.242700i	$-0.921967\pi$
$727$		−	3.78769e22i		−	0.485400i	0.970101	−	0.242700i	$-0.0780330\pi$
$728$	−1.09903e22	+	1.71833e22i	−0.139303	+	0.217799i
$729$	−3.38522e22			−0.424391
$730$	9.34410e22	+	1.79390e22i	1.15866	+	0.222442i
$731$	4.92601e22			0.604166
$732$	−3.12527e22	+	7.83946e22i	−0.379140	+	0.951038i
$733$			1.64511e22i			0.197407i	0.995117	+	0.0987035i	$0.0314695\pi$
$733$			1.64511e22i			0.197407i	−0.995117	+	0.0987035i	$0.968530\pi$
$734$	−5.46926e21	−	1.05000e21i	−0.0649173	−	0.0124630i
$735$			2.28447e22i			0.268217i
$736$	−5.74605e22	−	8.00762e22i	−0.667339	−	0.929996i
$737$	2.09485e22			0.240665
$738$	3.76907e21	−	1.96323e22i	0.0428334	−	0.223111i
$739$	−5.53754e22			−0.622532			−0.311266	−	0.950323i	$-0.600753\pi$
$739$	−5.53754e22			−0.622532			−0.311266	+	0.950323i	$0.600753\pi$
$740$	−1.13522e23	−	4.52565e22i	−1.26248	−	0.503300i
$741$		−	4.82484e22i		−	0.530808i
$742$	−3.15111e22	+	1.64135e23i	−0.342952	+	1.78637i
$743$		−	1.39362e22i		−	0.150049i	−0.997182	−	0.0750247i	$-0.976096\pi$
$743$		−	1.39362e22i		−	0.150049i	0.997182	−	0.0750247i	$-0.0239036\pi$
$744$	9.73258e22	+	6.22489e22i	1.03668	+	0.663053i
$745$	−4.73389e22			−0.498848
$746$	6.15553e22	+	1.18176e22i	0.641734	+	0.123202i
$747$	7.07120e22			0.729337
$748$	1.29063e23	+	5.14521e22i	1.31701	+	0.525038i
$749$		−	8.21637e22i		−	0.829517i
$750$	−8.28988e22	−	1.59151e22i	−0.828053	−	0.158972i
$751$		−	2.00805e22i		−	0.198452i	−0.995065	−	0.0992261i	$-0.968363\pi$
$751$		−	2.00805e22i		−	0.198452i	0.995065	−	0.0992261i	$-0.0316367\pi$
$752$	−5.72259e22	+	6.03662e22i	−0.559564	+	0.590271i
$753$	−6.37775e22			−0.617032
$754$	−7.89507e21	+	4.11239e22i	−0.0755762	+	0.393662i
$755$	2.32279e23			2.20006
$756$	1.24696e22	−	3.12789e22i	0.116863	−	0.293141i
$757$		−	1.91749e23i		−	1.77814i	−0.457771	−	0.889070i	$-0.651352\pi$
$757$		−	1.91749e23i		−	1.77814i	0.457771	−	0.889070i	$-0.348648\pi$
$758$	−2.04634e21	+	1.06590e22i	−0.0187769	+	0.0978050i
$759$			2.60752e23i			2.36752i
$760$	−1.61706e23	−	1.03426e23i	−1.45284	−	0.929226i
$761$	−1.24960e23			−1.11095			−0.555473	−	0.831535i	$-0.687463\pi$
$761$	−1.24960e23			−1.11095			−0.555473	+	0.831535i	$0.687463\pi$
$762$	−9.67845e22	−	1.85809e22i	−0.851463	−	0.163466i
$763$	−8.99055e22			−0.782690
$764$	−1.08253e22	+	2.71543e22i	−0.0932596	+	0.233933i
$765$		−	9.48797e22i		−	0.808876i
$766$	−3.49545e22	−	6.71065e21i	−0.294898	−	0.0566154i
$767$			1.49843e22i			0.125105i
$768$	−8.51487e21	−	1.59310e23i	−0.0703539	−	1.31630i
$769$	1.20035e23			0.981517			0.490759	−	0.871296i	$-0.336720\pi$
$769$	1.20035e23			0.981517			0.490759	+	0.871296i	$0.336720\pi$
$770$	4.04780e22	−	2.10842e23i	0.327562	−	1.70621i
$771$	−2.85186e23			−2.28398
$772$	−1.04742e22	−	4.17565e21i	−0.0830203	−	0.0330968i
$773$			5.75530e22i			0.451474i	0.974188	+	0.225737i	$0.0724789\pi$
$773$			5.75530e22i			0.451474i	−0.974188	+	0.225737i	$0.927521\pi$
$774$	−1.19765e22	+	6.23832e22i	−0.0929827	+	0.484329i
$775$			5.74605e22i			0.441526i
$776$	−1.53226e22	+	2.39567e22i	−0.116530	+	0.182194i
$777$	1.78918e23			1.34674
$778$	1.15264e23	+	2.21287e22i	0.858732	+	0.164862i
$779$	−5.93548e22			−0.437680
$780$	5.76991e22	+	2.30023e22i	0.421126	+	0.167886i
$781$		−	1.04001e23i		−	0.751330i
$782$	−1.42050e23	−	2.72711e22i	−1.01575	−	0.195007i
$783$		−	6.91286e22i		−	0.489287i
$784$	1.73669e22	+	1.64635e22i	0.121673	+	0.115343i
$785$	5.49245e22			0.380898
$786$	−3.79608e22	+	1.97730e23i	−0.260588	+	1.35735i
$787$	2.25925e23			1.53520			0.767602	−	0.640927i	$-0.221450\pi$
$787$	2.25925e23			1.53520			0.767602	+	0.640927i	$0.221450\pi$
$788$	5.07863e22	−	1.27393e23i	0.341615	−	0.856911i
$789$		−	2.20447e23i		−	1.46787i
$790$	−1.77786e22	+	9.26051e22i	−0.117187	+	0.610405i
$791$			1.27862e23i			0.834316i
$792$	−9.65379e22	+	1.50936e23i	−0.623586	+	0.974973i
$793$	−3.44200e22			−0.220103
$794$	−1.12660e23	−	2.16288e22i	−0.713193	−	0.136921i
$795$	5.08960e23			3.18968
$796$	−2.64965e22	+	6.64640e22i	−0.164393	+	0.412365i
$797$		−	7.82765e22i		−	0.480801i	−0.970674	−	0.240400i	$-0.922721\pi$
$797$		−	7.82765e22i		−	0.480801i	0.970674	−	0.240400i	$-0.0772787\pi$
$798$	2.75981e23	+	5.29837e22i	1.67825	+	0.322195i
$799$			1.22074e23i			0.734933i
$800$	6.44680e22	−	4.62604e22i	0.384259	−	0.275733i
$801$	1.25771e23			0.742201
$802$	−2.43893e22	+	1.27039e23i	−0.142497	+	0.742237i
$803$	−2.63687e23			−1.52533
$804$	−3.27916e22	−	1.30727e22i	−0.187808	−	0.0748713i
$805$			2.23505e23i			1.26742i
$806$	−8.88371e21	+	4.62735e22i	−0.0498786	+	0.259808i
$807$		−	9.61601e22i		−	0.534573i
$808$	1.47509e23	+	9.43456e22i	0.811946	+	0.519315i
$809$	−3.31209e23			−1.80515			−0.902577	−	0.430528i	$-0.858327\pi$
$809$	−3.31209e23			−1.80515			−0.902577	+	0.430528i	$0.858327\pi$
$810$	−2.63606e23	−	5.06079e22i	−1.42258	−	0.273110i
$811$	3.39638e20			0.00181489			0.000907444	−	1.00000i	$-0.499711\pi$
$811$	3.39638e20			0.00181489			0.000907444		1.00000i	$0.499711\pi$
$812$	−2.26559e23	−	9.03197e22i	−1.19876	−	0.477897i
$813$			1.57643e23i			0.825945i
$814$	3.32614e23	+	6.38561e22i	1.72562	+	0.331289i
$815$		−	9.62356e22i		−	0.494396i
$816$	−1.69919e23	−	1.61080e23i	−0.864414	−	0.819446i
$817$	1.88604e23			0.950113
$818$	−5.29399e22	+	2.75753e23i	−0.264093	+	1.37561i
$819$	−3.86021e22			−0.190695
$820$	2.82972e22	−	7.09810e22i	0.138431	−	0.347241i
$821$			3.34837e23i			1.62214i	0.584950	+	0.811069i	$0.301114\pi$
$821$			3.34837e23i			1.62214i	−0.584950	+	0.811069i	$0.698886\pi$
$822$	4.46622e22	−	2.32637e23i	0.214272	−	1.11610i
$823$		−	1.56567e23i		−	0.743876i	−0.928258	−	0.371938i	$-0.878693\pi$
$823$		−	1.56567e23i		−	0.743876i	0.928258	−	0.371938i	$-0.121307\pi$
$824$	−6.40860e22	−	4.09890e22i	−0.301540	−	0.192863i
$825$	−2.09927e23			−0.978220
$826$	−8.57102e22	−	1.64549e22i	−0.395542	−	0.0759371i
$827$	−1.86174e22			−0.0850895			−0.0425447	−	0.999095i	$-0.513547\pi$
$827$	−1.86174e22			−0.0850895			−0.0425447	+	0.999095i	$0.513547\pi$
$828$	6.90725e22	−	1.73262e23i	0.312653	−	0.784262i
$829$			1.25534e23i			0.562762i	0.959596	+	0.281381i	$0.0907925\pi$
$829$			1.25534e23i			0.562762i	−0.959596	+	0.281381i	$0.909208\pi$
$830$	2.65444e23	+	5.09606e22i	1.17855	+	0.226261i
$831$		−	2.09847e23i		−	0.922773i
$832$	5.90687e22	−	2.72868e22i	0.257259	−	0.118841i
$833$	3.51197e22			0.151492
$834$	5.38741e22	−	2.80620e23i	0.230172	−	1.19892i
$835$	−3.72324e23			−1.57554
$836$	4.94149e23	+	1.96997e23i	2.07113	+	0.825675i
$837$		−	7.77850e22i		−	0.322918i
$838$	6.99815e22	−	3.64520e23i	0.287760	−	1.49889i
$839$		−	1.67036e21i		−	0.00680323i	−0.999994	−	0.00340162i	$-0.998917\pi$
$839$		−	1.67036e21i		−	0.00680323i	0.999994	−	0.00340162i	$-0.00108277\pi$
$840$	−1.94935e23	+	3.04780e23i	−0.786422	+	1.22957i
$841$	−2.50465e23			−1.00087
$842$	1.10602e22	+	2.12336e21i	0.0437790	+	0.00840481i
$843$	−2.72139e23			−1.06701
$844$	1.93706e23	+	7.72228e22i	0.752323	+	0.299920i
$845$		−	2.90129e23i		−	1.11619i
$846$	−1.54595e23	−	2.96795e22i	−0.589157	−	0.113108i
$847$			3.53322e23i			1.33384i
$848$	3.66792e23	−	3.86920e23i	1.37168	−	1.44695i
$849$	3.29815e22			0.122182
$850$	2.19555e22	−	1.14362e23i	0.0805735	−	0.419691i
$851$	−3.52591e23			−1.28184
$852$	−6.49007e22	+	1.62798e23i	−0.233740	+	0.586315i
$853$			1.56273e23i			0.557561i	0.960355	+	0.278780i	$0.0899302\pi$
$853$			1.56273e23i			0.557561i	−0.960355	+	0.278780i	$0.910070\pi$
$854$	3.77981e22	−	1.96883e23i	0.133600	−	0.695896i
$855$		−	3.63270e23i		−	1.27204i
$856$	−1.41221e23	+	2.20799e23i	−0.489903	+	0.765960i
$857$	2.71040e23			0.931510			0.465755	−	0.884914i	$-0.345783\pi$
$857$	2.71040e23			0.931510			0.465755	+	0.884914i	$0.345783\pi$
$858$	−1.69056e23	−	3.24558e22i	−0.575615	−	0.110508i
$859$	5.04189e23			1.70078			0.850390	−	0.526153i	$-0.176366\pi$
$859$	5.04189e23			1.70078			0.850390	+	0.526153i	$0.176366\pi$
$860$	−8.99165e22	+	2.25547e23i	−0.300505	+	0.753790i
$861$			1.11871e23i			0.370417i
$862$	−9.75739e22	−	1.87325e22i	−0.320092	−	0.0614522i
$863$		−	1.31327e23i		−	0.426842i	−0.976960	−	0.213421i	$-0.931539\pi$
$863$		−	1.31327e23i		−	0.426842i	0.976960	−	0.213421i	$-0.0684605\pi$
$864$	−8.72710e22	+	6.26232e22i	−0.281035	+	0.201663i
$865$	1.07531e23			0.343086
$866$	1.04825e23	−	5.46014e23i	0.331377	−	1.72608i
$867$	7.72352e22			0.241915
$868$	−2.54929e23	−	1.01630e23i	−0.791155	−	0.315401i
$869$		−	2.61328e23i		−	0.803579i
$870$	−1.40034e23	+	7.29411e23i	−0.426659	+	2.22238i
$871$		−	1.43975e22i		−	0.0434652i
$872$	2.41603e23	+	1.54528e23i	0.722721	+	0.462247i
$873$	−5.38184e22			−0.159521
$874$	−5.43873e23	−	1.04414e23i	−1.59737	−	0.306668i
$875$	2.00521e23			0.583574
$876$	4.12760e23	+	1.64550e23i	1.19032	+	0.474533i
$877$			3.32201e23i			0.949303i	0.880174	+	0.474651i	$0.157426\pi$
$877$			3.32201e23i			0.949303i	−0.880174	+	0.474651i	$0.842574\pi$
$878$	1.63201e22	+	3.13319e21i	0.0462134	+	0.00887217i
$879$			2.44950e23i			0.687332i
$880$	−4.71168e23	+	4.97023e23i	−1.31013	+	1.38202i
$881$	−2.02247e23			−0.557283			−0.278642	−	0.960395i	$-0.589884\pi$
$881$	−2.02247e23			−0.557283			−0.278642	+	0.960395i	$0.589884\pi$
$882$	−8.53856e21	+	4.44757e22i	−0.0233150	+	0.121443i
$883$	1.18519e23			0.320702			0.160351	−	0.987060i	$-0.448737\pi$
$883$	1.18519e23			0.320702			0.160351	+	0.987060i	$0.448737\pi$
$884$	3.53619e22	−	8.87022e22i	0.0948239	−	0.237857i
$885$			2.65775e23i			0.706266i
$886$	9.39684e22	−	4.89463e23i	0.247464	−	1.28899i
$887$			5.60601e22i			0.146307i	0.997321	+	0.0731535i	$0.0233063\pi$
$887$			5.60601e22i			0.146307i	−0.997321	+	0.0731535i	$0.976694\pi$
$888$	−4.80805e23	−	3.07520e23i	−1.24356	−	0.795371i
$889$	2.34109e23			0.600072
$890$	4.72130e23	+	9.06407e22i	1.19934	+	0.230252i
$891$	7.43888e23			1.87278
$892$	−1.52880e23	+	3.83485e23i	−0.381445	+	0.956819i
$893$			4.67389e23i			1.15576i
$894$	−2.17114e23	−	4.16822e22i	−0.532094	−	0.102153i
$895$		−	3.99032e23i		−	0.969223i
$896$	9.12150e22	+	3.67839e23i	0.219585	+	0.885509i
$897$	1.79209e23			0.427583
$898$	−5.77297e22	+	3.00703e23i	−0.136518	+	0.711093i
$899$	−5.63412e23			−1.32053
$900$	1.39490e23	+	5.56091e22i	0.324044	+	0.129183i
$901$		−	7.82437e23i		−	1.80157i
$902$	−3.99269e22	+	2.07971e23i	−0.0911199	+	0.474625i
$903$		−	3.55477e23i		−	0.804099i
$904$	2.19767e23	−	3.43605e23i	0.492737	−	0.770391i
$905$	7.26103e23			1.61365
$906$	1.06532e24	+	2.04523e23i	2.34668	+	0.450522i
$907$	1.94888e23			0.425527			0.212764	−	0.977104i	$-0.431754\pi$
$907$	1.94888e23			0.425527			0.212764	+	0.977104i	$0.431754\pi$
$908$	−7.21411e22	−	2.87597e22i	−0.156133	−	0.0622440i
$909$			3.31376e23i			0.710903i
$910$	−1.44907e23	−	2.78197e22i	−0.308148	−	0.0591590i
$911$			7.25398e23i			1.52908i	0.644578	+	0.764538i	$0.277033\pi$
$911$			7.25398e23i			1.52908i	−0.644578	+	0.764538i	$0.722967\pi$
$912$	−6.50578e23	−	6.16734e23i	−1.35938	−	1.28866i
$913$	−7.49074e23			−1.55152
$914$	−5.87522e22	+	3.06029e23i	−0.120630	+	0.628337i
$915$	−6.10505e23			−1.24257
$916$	1.19480e23	−	2.99704e23i	0.241063	−	0.604684i
$917$		−	4.78283e23i		−	0.956600i
$918$	−2.97214e22	+	1.54813e23i	−0.0589289	+	0.306949i
$919$		−	9.23297e23i		−	1.81475i	−0.420319	−	0.907376i	$-0.638082\pi$
$919$		−	9.23297e23i		−	1.81475i	0.420319	−	0.907376i	$-0.361918\pi$
$920$	3.84156e23	−	6.00625e23i	0.748523	−	1.17031i
$921$	4.68226e23			0.904437
$922$	−7.25999e23	−	1.39379e23i	−1.39024	−	0.266901i
$923$	−7.14780e22			−0.135693
$924$	3.71295e23	−	9.31360e23i	0.698785	−	1.75284i
$925$		−	2.83864e23i		−	0.529636i
$926$	−7.50687e23	−	1.44119e23i	−1.38858	−	0.266583i
$927$		−	1.43968e23i		−	0.264015i
$928$	4.53592e23	+	6.32121e23i	0.824673	+	1.14926i
$929$	−9.89953e23			−1.78439			−0.892193	−	0.451655i	$-0.850834\pi$
$929$	−9.89953e23			−1.78439			−0.892193	+	0.451655i	$0.850834\pi$
$930$	−1.57570e23	+	8.20750e23i	−0.281585	+	1.46672i
$931$	1.34464e23			0.238237
$932$	−9.37311e23	−	3.73667e23i	−1.64648	−	0.656384i
$933$			7.20162e23i			1.25423i
$934$	−4.00875e22	+	2.08808e23i	−0.0692203	+	0.360555i
$935$			1.00509e24i			1.72073i
$936$	1.03735e23	+	6.63485e22i	0.176084	+	0.112622i
$937$	5.77835e23			0.972495			0.486248	−	0.873821i	$-0.338365\pi$
$937$	5.77835e23			0.972495			0.486248	+	0.873821i	$0.338365\pi$
$938$	8.23537e22	+	1.58105e22i	0.137423	+	0.0263829i
$939$	−8.14683e22			−0.134792
$940$	−5.58939e23	−	2.22826e23i	−0.916941	−	0.365547i
$941$		−	6.92434e23i		−	1.12632i	−0.826348	−	0.563159i	$-0.809586\pi$
$941$		−	6.92434e23i		−	1.12632i	0.826348	−	0.563159i	$-0.190414\pi$
$942$	2.51904e23	+	4.83613e22i	0.406283	+	0.0779993i
$943$		−	2.20462e23i		−	0.352565i
$944$	2.02047e23	+	1.91536e23i	0.320388	+	0.303721i
$945$	2.43587e23			0.383001
$946$	1.26871e23	−	6.60844e23i	0.197803	−	1.03032i
$947$	4.84209e23			0.748570			0.374285	−	0.927314i	$-0.377888\pi$
$947$	4.84209e23			0.748570			0.374285	+	0.927314i	$0.377888\pi$
$948$	−1.63079e23	+	4.09068e23i	−0.249994	+	0.627088i
$949$			1.81227e23i			0.275481i
$950$	8.40620e22	−	4.37863e23i	0.126710	−	0.660008i
$951$			1.65931e24i			2.48017i
$952$	4.68545e23	+	2.99678e23i	0.694474	+	0.444181i
$953$	−8.84659e23			−1.30027			−0.650133	−	0.759820i	$-0.725287\pi$
$953$	−8.84659e23			−1.30027			−0.650133	+	0.759820i	$0.725287\pi$
$954$	9.90881e23	+	1.90232e23i	1.44422	+	0.277266i
$955$	−2.11467e23			−0.305643
$956$	−2.52549e23	+	6.33497e23i	−0.361978	+	0.907990i
$957$		−	2.05837e24i		−	2.92569i
$958$	5.46639e23	+	1.04945e23i	0.770507	+	0.147924i
$959$			5.62717e23i			0.786576i
$960$	1.04770e24	−	4.83985e23i	1.45233	−	0.670906i
$961$	9.34595e22			0.128480
$962$	4.38870e22	−	2.28599e23i	0.0598322	−	0.311654i
$963$	−4.96020e23			−0.670640
$964$	1.31083e23	+	5.22573e22i	0.175764	+	0.0700697i
$965$		−	8.15691e22i		−	0.108469i
$966$	−1.96797e23	+	1.02508e24i	−0.259539	+	1.35189i
$967$		−	5.65411e23i		−	0.739524i	−0.929126	−	0.369762i	$-0.879439\pi$
$967$		−	5.65411e23i		−	0.739524i	0.929126	−	0.369762i	$-0.120561\pi$
$968$	6.07282e23	−	9.49481e23i	0.787748	−	1.23164i
$969$	−1.31561e24			−1.69253
$970$	−2.02027e23	−	3.87858e22i	−0.257772	−	0.0494878i
$971$	9.92295e23			1.25570			0.627851	−	0.778333i	$-0.283935\pi$
$971$	9.92295e23			1.25570			0.627851	+	0.778333i	$0.283935\pi$
$972$	−9.08429e23	−	3.62153e23i	−1.14015	−	0.454530i
$973$			6.78781e23i			0.844943i
$974$	1.09773e24	+	2.10745e23i	1.35526	+	0.260187i
$975$			1.44278e23i			0.176670i
$976$	−4.39973e23	+	4.64116e23i	−0.534352	+	0.563674i
$977$	−3.56266e23			−0.429159			−0.214579	−	0.976707i	$-0.568838\pi$
$977$	−3.56266e23			−0.429159			−0.214579	+	0.976707i	$0.568838\pi$
$978$	8.47359e22	−	4.41373e23i	0.101241	−	0.527345i
$979$	−1.33233e24			−1.57889
$980$	−6.41054e22	+	1.60803e23i	−0.0753504	+	0.189010i
$981$			5.42757e23i			0.632781i
$982$	1.74054e23	−	9.06612e23i	0.201276	−	1.04841i
$983$			1.09368e24i			1.25448i	0.778828	+	0.627238i	$0.215815\pi$
$983$			1.09368e24i			1.25448i	−0.778828	+	0.627238i	$0.784185\pi$
$984$	1.92281e23	−	3.00630e23i	0.218764	−	0.342036i
$985$	9.92084e23			1.11959
$986$	1.12134e24	+	2.15278e23i	1.25523	+	0.240982i
$987$	8.80923e23			0.978139
$988$	1.35392e23	−	3.39618e23i	0.149120	−	0.374055i
$989$			7.00534e23i			0.765348i
$990$	−1.27285e24	−	2.44365e23i	−1.37942	−	0.264824i
$991$			4.56268e23i			0.490491i	0.969461	+	0.245245i	$0.0788686\pi$
$991$			4.56268e23i			0.490491i	−0.969461	+	0.245245i	$0.921131\pi$
$992$	5.10392e23	+	7.11277e23i	0.544265	+	0.758482i
$993$	5.35636e23			0.566599
$994$	7.84930e22	−	4.08855e23i	0.0823645	−	0.429020i
$995$	−5.17594e23			−0.538772
$996$	1.17256e24	+	4.67449e23i	1.21076	+	0.482681i
$997$		−	3.50687e23i		−	0.359218i	−0.983738	−	0.179609i	$-0.942517\pi$
$997$		−	3.50687e23i		−	0.359218i	0.983738	−	0.179609i	$-0.0574833\pi$
$998$	−3.49654e23	+	1.82128e24i	−0.355299	+	1.85068i
$999$			3.84271e23i			0.387359i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.17.d.b.3.8	yes	14
3.2	odd	2		72.17.b.b.19.7		14
4.3	odd	2		32.17.d.b.15.13		14
8.3	odd	2	inner	8.17.d.b.3.7	✓	14
8.5	even	2		32.17.d.b.15.14		14
24.11	even	2		72.17.b.b.19.8		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.17.d.b.3.7	✓	14	8.3	odd	2	inner
8.17.d.b.3.8	yes	14	1.1	even	1	trivial
32.17.d.b.15.13		14	4.3	odd	2
32.17.d.b.15.14		14	8.5	even	2
72.17.b.b.19.7		14	3.2	odd	2
72.17.b.b.19.8		14	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:	\( k \)	\(=\)	\( 17 \)
Character orbit:	\([\chi]\)	\(=\)	8.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-48.2661 + 251.409i) q^{2} -8648.56 q^{3} +(-60876.8 - 24269.1i) q^{4} -474083. i q^{5} +(417432. - 2.17432e6i) q^{6} +5.25940e6i q^{7} +(9.03974e6 - 1.41336e7i) q^{8} +3.17508e7 q^{9} +O(q^{10})\)	\(q+(-48.2661 + 251.409i) q^{2} -8648.56 q^{3} +(-60876.8 - 24269.1i) q^{4} -474083. i q^{5} +(417432. - 2.17432e6i) q^{6} +5.25940e6i q^{7} +(9.03974e6 - 1.41336e7i) q^{8} +3.17508e7 q^{9} +(1.19189e8 + 2.28822e7i) q^{10} -3.36346e8 q^{11} +(5.26496e8 + 2.09892e8i) q^{12} +2.31164e8i q^{13} +(-1.32226e9 - 2.53851e8i) q^{14} +4.10013e9i q^{15} +(3.11699e9 + 2.95484e9i) q^{16} +6.30324e9 q^{17} +(-1.53249e9 + 7.98244e9i) q^{18} +2.41335e10 q^{19} +(-1.15055e10 + 2.88606e10i) q^{20} -4.54862e10i q^{21} +(1.62341e10 - 8.45604e10i) q^{22} +8.96390e10i q^{23} +(-7.81807e10 + 1.22235e11i) q^{24} -7.21668e10 q^{25} +(-5.81166e10 - 1.11574e10i) q^{26} +9.76930e10 q^{27} +(1.27641e11 - 3.20175e11i) q^{28} -7.07610e11i q^{29} +(-1.03081e12 - 1.97898e11i) q^{30} -7.96218e11i q^{31} +(-8.93319e11 + 6.41020e11i) q^{32} +2.90891e12 q^{33} +(-3.04233e11 + 1.58469e12i) q^{34} +2.49339e12 q^{35} +(-1.93289e12 - 7.70563e11i) q^{36} +3.93345e12i q^{37} +(-1.16483e12 + 6.06737e12i) q^{38} -1.99923e12i q^{39} +(-6.70049e12 - 4.28559e12i) q^{40} -2.45944e12 q^{41} +(1.14356e13 + 2.19544e12i) q^{42} +7.81505e12 q^{43} +(2.04757e13 + 8.16281e12i) q^{44} -1.50525e13i q^{45} +(-2.25360e13 - 4.32653e12i) q^{46} +1.93668e13i q^{47} +(-2.69575e13 - 2.55551e13i) q^{48} +5.57169e12 q^{49} +(3.48321e12 - 1.81434e13i) q^{50} -5.45139e13 q^{51} +(5.61012e12 - 1.40725e13i) q^{52} -1.24133e14i q^{53} +(-4.71527e12 + 2.45609e13i) q^{54} +1.59456e14i q^{55} +(7.43341e13 + 4.75436e13i) q^{56} -2.08720e14 q^{57} +(1.77899e14 + 3.41536e13i) q^{58} +6.48211e13 q^{59} +(9.95064e13 - 2.49603e14i) q^{60} +1.48899e14i q^{61} +(2.00176e14 + 3.84304e13i) q^{62} +1.66990e14i q^{63} +(-1.18041e14 - 2.55528e14i) q^{64} +1.09591e14 q^{65} +(-1.40402e14 + 7.31326e14i) q^{66} -6.22826e13 q^{67} +(-3.83721e14 - 1.52974e14i) q^{68} -7.75248e14i q^{69} +(-1.20346e14 + 6.26860e14i) q^{70} +3.09209e14i q^{71} +(2.87019e14 - 4.48753e14i) q^{72} +7.83976e14 q^{73} +(-9.88904e14 - 1.89852e14i) q^{74} +6.24139e14 q^{75} +(-1.46917e15 - 5.85697e14i) q^{76} -1.76898e15i q^{77} +(5.02625e14 + 9.64952e13i) q^{78} +7.76963e14i q^{79} +(1.40084e15 - 1.47771e15i) q^{80} -2.21167e15 q^{81} +(1.18708e14 - 6.18325e14i) q^{82} +2.22709e15 q^{83} +(-1.10391e15 + 2.76905e15i) q^{84} -2.98826e15i q^{85} +(-3.77202e14 + 1.96477e15i) q^{86} +6.11981e15i q^{87} +(-3.04048e15 + 4.75378e15i) q^{88} +3.96120e15 q^{89} +(3.78434e15 + 7.26528e14i) q^{90} -1.21578e15 q^{91} +(2.17546e15 - 5.45693e15i) q^{92} +6.88614e15i q^{93} +(-4.86899e15 - 9.34762e14i) q^{94} -1.14413e16i q^{95} +(7.72592e15 - 5.54390e15i) q^{96} -1.69502e15 q^{97} +(-2.68924e14 + 1.40077e15i) q^{98} -1.06793e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 350 q^{2} + 11964 q^{3} - 54220 q^{4} + 4868124 q^{6} + 10899160 q^{8} + 86397354 q^{9}+O(q^{10}) \) 14 * q - 350 * q^2 + 11964 * q^3 - 54220 * q^4 + 4868124 * q^6 + 10899160 * q^8 + 86397354 * q^9	\( 14 q - 350 q^{2} + 11964 q^{3} - 54220 q^{4} + 4868124 q^{6} + 10899160 q^{8} + 86397354 q^{9} + 87155280 q^{10} - 49140292 q^{11} + 31616184 q^{12} - 2675193504 q^{14} + 9716374544 q^{16} - 9985136356 q^{17} - 7692086106 q^{18} + 62922133180 q^{19} + 31953450720 q^{20} - 51493048676 q^{22} + 54962419344 q^{24} - 429906632050 q^{25} - 518273679696 q^{26} + 655936606584 q^{27} + 102542376000 q^{28} - 364331826720 q^{30} + 95751080800 q^{32} + 4034287537464 q^{33} + 1015818512644 q^{34} - 3057653406720 q^{35} - 9569289445092 q^{36} + 9010383442844 q^{38} - 4027933291200 q^{40} + 8719629072668 q^{41} - 6653698130880 q^{42} + 16716309178300 q^{43} - 4351929975880 q^{44} + 21043605267744 q^{46} + 46562301973344 q^{48} - 104740771400434 q^{49} - 54483696687710 q^{50} + 40911296041848 q^{51} - 73249356722400 q^{52} - 18031398151752 q^{54} + 110873799752064 q^{56} - 310730528383176 q^{57} + 256627273576560 q^{58} + 347007330293180 q^{59} - 83822619107520 q^{60} + 346701622780800 q^{62} - 332173589517760 q^{64} + 220877370432000 q^{65} + 875905832132808 q^{66} - 614258765968196 q^{67} - 12\!\cdots\!76 q^{68}+ \cdots - 18\!\cdots\!92 q^{99}+O(q^{100}) \) 14 * q - 350 * q^2 + 11964 * q^3 - 54220 * q^4 + 4868124 * q^6 + 10899160 * q^8 + 86397354 * q^9 + 87155280 * q^10 - 49140292 * q^11 + 31616184 * q^12 - 2675193504 * q^14 + 9716374544 * q^16 - 9985136356 * q^17 - 7692086106 * q^18 + 62922133180 * q^19 + 31953450720 * q^20 - 51493048676 * q^22 + 54962419344 * q^24 - 429906632050 * q^25 - 518273679696 * q^26 + 655936606584 * q^27 + 102542376000 * q^28 - 364331826720 * q^30 + 95751080800 * q^32 + 4034287537464 * q^33 + 1015818512644 * q^34 - 3057653406720 * q^35 - 9569289445092 * q^36 + 9010383442844 * q^38 - 4027933291200 * q^40 + 8719629072668 * q^41 - 6653698130880 * q^42 + 16716309178300 * q^43 - 4351929975880 * q^44 + 21043605267744 * q^46 + 46562301973344 * q^48 - 104740771400434 * q^49 - 54483696687710 * q^50 + 40911296041848 * q^51 - 73249356722400 * q^52 - 18031398151752 * q^54 + 110873799752064 * q^56 - 310730528383176 * q^57 + 256627273576560 * q^58 + 347007330293180 * q^59 - 83822619107520 * q^60 + 346701622780800 * q^62 - 332173589517760 * q^64 + 220877370432000 * q^65 + 875905832132808 * q^66 - 614258765968196 * q^67 - 1235787871965976 * q^68 - 442172390987520 * q^70 - 1312232111609976 * q^72 - 542888518370276 * q^73 + 2394643836493776 * q^74 + 2861985572983740 * q^75 - 614792000883272 * q^76 - 4928152344599520 * q^78 + 6402194304908160 * q^80 - 5344304371237818 * q^81 + 4810720063300804 * q^82 + 7362421930746044 * q^83 - 9316784627856000 * q^84 - 8963192329247716 * q^86 + 3396904358318224 * q^88 - 408131327364580 * q^89 + 14680290550241520 * q^90 - 7162887702930432 * q^91 - 9213856910218560 * q^92 - 15838781433150144 * q^94 + 48917704300183104 * q^96 + 18372136634257180 * q^97 + 34005570793293730 * q^98 - 18934692015468492 * q^99

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