LMFDB - Embedded newform 10.26.b.a.9.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,26,Mod(9,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 26, names="a")

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

chi := DirichletCharacter("10.9");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	10.b (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:	$39.5996779952$
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} + 1406300109694 x^{10} + \cdots + 56\!\cdots\!01 $ x^12 + 1406300109694x^10 + 721371039010841274826815x^8 + 163583579306250445630287276512319780x^6 + 14727031184488621294308896513370084274619782815x^4 + 213559114414440049199738916498397853721503585895983619294*x^2 + 562442837480837791206109989109268286491448310078170789537309341601
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{90}\cdot 3^{8}\cdot 5^{29} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			9.9
Root			$58327.7i$ of defining polynomial
Character	$\chi$	$=$	10.9
Dual form			10.26.b.a.9.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+4096.00i q^{2} +116655. i q^{3} -1.67772e7 q^{4} +(5.03737e8 + 2.10410e8i) q^{5} -4.77821e8 q^{6} +1.34370e10i q^{7} -6.87195e10i q^{8} +8.33680e11 q^{9} +(-8.61839e11 + 2.06331e12i) q^{10} +4.67882e11 q^{11} -1.95715e12i q^{12} -9.38695e13i q^{13} -5.50381e13 q^{14} +(-2.45455e13 + 5.87637e13i) q^{15} +2.81475e14 q^{16} -6.14184e14i q^{17} +3.41475e15i q^{18} +1.66661e16 q^{19} +(-8.45130e15 - 3.53009e15i) q^{20} -1.56750e15 q^{21} +1.91644e15i q^{22} -1.60865e17i q^{23} +8.01650e15 q^{24} +(2.09479e17 + 2.11982e17i) q^{25} +3.84489e17 q^{26} +1.96094e17i q^{27} -2.25436e17i q^{28} +1.05009e18 q^{29} +(-2.40696e17 - 1.00538e17i) q^{30} -3.00725e18 q^{31} +1.15292e18i q^{32} +5.45810e16i q^{33} +2.51570e18 q^{34} +(-2.82729e18 + 6.76873e18i) q^{35} -1.39868e19 q^{36} +3.36937e19i q^{37} +6.82643e19i q^{38} +1.09504e19 q^{39} +(1.44593e19 - 3.46165e19i) q^{40} +5.09874e19 q^{41} -6.42050e18i q^{42} +2.92822e20i q^{43} -7.84976e18 q^{44} +(4.19955e20 + 1.75415e20i) q^{45} +6.58901e20 q^{46} +9.77356e20i q^{47} +3.28356e19i q^{48} +1.16051e21 q^{49} +(-8.68280e20 + 8.58024e20i) q^{50} +7.16479e19 q^{51} +1.57487e21i q^{52} +5.26216e21i q^{53} -8.03202e20 q^{54} +(2.35689e20 + 9.84470e19i) q^{55} +9.23387e20 q^{56} +1.94419e21i q^{57} +4.30117e21i q^{58} -4.10935e20 q^{59} +(4.11804e20 - 9.85891e20i) q^{60} -5.44766e21 q^{61} -1.23177e22i q^{62} +1.12022e22i q^{63} -4.72237e21 q^{64} +(1.97511e22 - 4.72855e22i) q^{65} -2.23564e20 q^{66} -6.32396e22i q^{67} +1.03043e22i q^{68} +1.87657e22 q^{69} +(-2.77247e22 - 1.15806e22i) q^{70} -1.81308e22 q^{71} -5.72901e22i q^{72} -3.48574e23i q^{73} -1.38010e23 q^{74} +(-2.47289e22 + 2.44368e22i) q^{75} -2.79610e23 q^{76} +6.28695e21i q^{77} +4.48528e22i q^{78} -3.43193e23 q^{79} +(1.41789e23 + 5.92251e22i) q^{80} +6.83492e23 q^{81} +2.08844e23i q^{82} +6.85739e23i q^{83} +2.62984e22 q^{84} +(1.29230e23 - 3.09387e23i) q^{85} -1.19940e24 q^{86} +1.22499e23i q^{87} -3.21526e22i q^{88} +4.29595e24 q^{89} +(-7.18498e23 + 1.72014e24i) q^{90} +1.26133e24 q^{91} +2.69886e24i q^{92} -3.50812e23i q^{93} -4.00325e24 q^{94} +(8.39532e24 + 3.50671e24i) q^{95} -1.34495e23 q^{96} +2.90151e24i q^{97} +4.75347e24i q^{98} +3.90064e23 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 201326592 q^{4} - 490295340 q^{5} - 6565199872 q^{6} - 1082937564236 q^{9} + 1636528619520 q^{10} + 19723089228624 q^{11} + 278591122243584 q^{14} - 449884766537680 q^{15} + 33\!\cdots\!72 q^{16}+ \cdots + 41\!\cdots\!28 q^{99}+O(q^{100}) $ 12 * q - 201326592 * q^4 - 490295340 * q^5 - 6565199872 * q^6 - 1082937564236 * q^9 + 1636528619520 * q^10 + 19723089228624 * q^11 + 278591122243584 * q^14 - 449884766537680 * q^15 + 3377699720527872 * q^16 - 4015312977833040 * q^19 + 8225790822973440 * q^20 - 56363420582029456 * q^21 + 110145776335716352 * q^24 - 1047554086248996900 * q^25 - 252210272532037632 * q^26 + 5852064063311009640 * q^29 - 3747916483574824960 * q^30 + 158585871554029824 * q^31 + 28121800210885115904 * q^34 - 42730948507221221040 * q^35 + 18168677429701246976 * q^36 - 249453273245123586912 * q^39 - 27456394139868856320 * q^40 + 206458603439752488024 * q^41 - 330898528175898230784 * q^44 + 957114913653485255020 * q^45 - 1111751773656740462592 * q^46 - 3432561496278055389084 * q^49 + 346631457781510963200 * q^50 - 3032451787323924027136 * q^51 + 6455741354411915345920 * q^54 - 7824754202169531625680 * q^55 - 4673983433563013382144 * q^56 + 24998150261761560337680 * q^59 + 7547813903312229498880 * q^60 + 7374571220622236593224 * q^61 - 56668397794435742564352 * q^64 + 20652620138653742557920 * q^65 + 56072959085731865952256 * q^66 - 370250651964757999709072 * q^69 + 157367128964587932549120 * q^70 + 149137752442507323299424 * q^71 + 27409492362780459270144 * q^74 + 1032897211530510645911200 * q^75 + 67365773136708124016640 * q^76 + 801700633747623249599040 * q^79 - 138005869407843165143040 * q^80 - 2864220237232227656687428 * q^81 + 945621281603553901674496 * q^84 + 2004099032091709203221760 * q^85 - 1363071174568488987328512 * q^86 - 5964345056120682049233480 * q^89 + 4840324611668628597309440 * q^90 - 14003423438242038482629536 * q^91 + 3325183945859356082110464 * q^94 + 18644670331946084490382800 * q^95 - 1847939481072001752236032 * q^96 + 4107440578564823447146928 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/10\mathbb{Z}\right)^\times$.

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

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 $

$2$			4096.00i			0.707107i
$2$			4096.00i			0.707107i
$3$			116655.i			0.126733i	0.997990	+	0.0633664i	$0.0201837\pi$
$3$			116655.i			0.126733i	−0.997990	+	0.0633664i	$0.979816\pi$
$4$	−1.67772e7			−0.500000
$5$	5.03737e8	+	2.10410e8i	0.922739	+	0.385426i
$5$	5.03737e8	+	2.10410e8i	0.922739	+	0.385426i
$6$	−4.77821e8			−0.0896137
$7$			1.34370e10i			0.366926i	0.983027	+	0.183463i	$0.0587307\pi$
$7$			1.34370e10i			0.366926i	−0.983027	+	0.183463i	$0.941269\pi$
$8$		−	6.87195e10i		−	0.353553i
$9$	8.33680e11			0.983939
$10$	−8.61839e11	+	2.06331e12i	−0.272537	+	0.652475i
$11$	4.67882e11			0.0449498			0.0224749	−	0.999747i	$-0.492845\pi$
$11$	4.67882e11			0.0449498			0.0224749	+	0.999747i	$0.492845\pi$
$12$		−	1.95715e12i		−	0.0633664i
$13$		−	9.38695e13i		−	1.11746i	−0.829349	−	0.558731i	$-0.811289\pi$
$13$		−	9.38695e13i		−	1.11746i	0.829349	−	0.558731i	$-0.188711\pi$
$14$	−5.50381e13			−0.259456
$15$	−2.45455e13	+	5.87637e13i	−0.0488462	+	0.116941i
$16$	2.81475e14			0.250000
$17$		−	6.14184e14i		−	0.255674i	−0.991795	−	0.127837i	$-0.959197\pi$
$17$		−	6.14184e14i		−	0.255674i	0.991795	−	0.127837i	$-0.0408035\pi$
$18$			3.41475e15i			0.695750i
$19$	1.66661e16			1.72748			0.863741	−	0.503936i	$-0.168115\pi$
$19$	1.66661e16			1.72748			0.863741	+	0.503936i	$0.168115\pi$
$20$	−8.45130e15	−	3.53009e15i	−0.461369	−	0.192713i
$21$	−1.56750e15			−0.0465016
$22$			1.91644e15i			0.0317843i
$23$		−	1.60865e17i		−	1.53060i	−0.643673	−	0.765301i	$-0.722590\pi$
$23$		−	1.60865e17i		−	1.53060i	0.643673	−	0.765301i	$-0.277410\pi$
$24$	8.01650e15			0.0448068
$25$	2.09479e17	+	2.11982e17i	0.702894	+	0.711295i
$26$	3.84489e17			0.790165
$27$			1.96094e17i			0.251430i
$28$		−	2.25436e17i		−	0.183463i
$29$	1.05009e18			0.551126			0.275563	−	0.961283i	$-0.411136\pi$
$29$	1.05009e18			0.551126			0.275563	+	0.961283i	$0.411136\pi$
$30$	−2.40696e17	−	1.00538e17i	−0.0826900	−	0.0345395i
$31$	−3.00725e18			−0.685722			−0.342861	−	0.939386i	$-0.611396\pi$
$31$	−3.00725e18			−0.685722			−0.342861	+	0.939386i	$0.611396\pi$
$32$			1.15292e18i			0.176777i
$33$			5.45810e16i			0.00569662i
$34$	2.51570e18			0.180789
$35$	−2.82729e18	+	6.76873e18i	−0.141423	+	0.338577i
$36$	−1.39868e19			−0.491969
$37$			3.36937e19i			0.841449i	0.907189	+	0.420724i	$0.138224\pi$
$37$			3.36937e19i			0.841449i	−0.907189	+	0.420724i	$0.861776\pi$
$38$			6.82643e19i			1.22151i
$39$	1.09504e19			0.141619
$40$	1.44593e19	−	3.46165e19i	0.136269	−	0.326237i
$41$	5.09874e19			0.352911			0.176455	−	0.984309i	$-0.443537\pi$
$41$	5.09874e19			0.352911			0.176455	+	0.984309i	$0.443537\pi$
$42$		−	6.42050e18i		−	0.0328816i
$43$			2.92822e20i			1.11750i	0.829335	+	0.558751i	$0.188719\pi$
$43$			2.92822e20i			1.11750i	−0.829335	+	0.558751i	$0.811281\pi$
$44$	−7.84976e18			−0.0224749
$45$	4.19955e20	+	1.75415e20i	0.907918	+	0.379236i
$46$	6.58901e20			1.08230
$47$			9.77356e20i			1.22696i	0.789711	+	0.613479i	$0.210230\pi$
$47$			9.77356e20i			1.22696i	−0.789711	+	0.613479i	$0.789770\pi$
$48$			3.28356e19i			0.0316832i
$49$	1.16051e21			0.865365
$50$	−8.68280e20	+	8.58024e20i	−0.502962	+	0.497021i
$51$	7.16479e19			0.0324023
$52$			1.57487e21i			0.558731i
$53$			5.26216e21i			1.47135i	0.677335	+	0.735675i	$0.263135\pi$
$53$			5.26216e21i			1.47135i	−0.677335	+	0.735675i	$0.736865\pi$
$54$	−8.03202e20			−0.177788
$55$	2.35689e20	+	9.84470e19i	0.0414769	+	0.0173248i
$56$	9.23387e20			0.129728
$57$			1.94419e21i			0.218929i
$58$			4.30117e21i			0.389705i
$59$	−4.10935e20			−0.0300693			−0.0150346	−	0.999887i	$-0.504786\pi$
$59$	−4.10935e20			−0.0300693			−0.0150346	+	0.999887i	$0.504786\pi$
$60$	4.11804e20	−	9.85891e20i	0.0244231	−	0.0584707i
$61$	−5.44766e21			−0.262777			−0.131388	−	0.991331i	$-0.541943\pi$
$61$	−5.44766e21			−0.262777			−0.131388	+	0.991331i	$0.541943\pi$
$62$		−	1.23177e22i		−	0.484879i
$63$			1.12022e22i			0.361032i
$64$	−4.72237e21			−0.125000
$65$	1.97511e22	−	4.72855e22i	0.430699	−	1.03113i
$66$	−2.23564e20			−0.00402812
$67$		−	6.32396e22i		−	0.944178i	−0.881551	−	0.472089i	$-0.843500\pi$
$67$		−	6.32396e22i		−	0.944178i	0.881551	−	0.472089i	$-0.156500\pi$
$68$			1.03043e22i			0.127837i
$69$	1.87657e22			0.193978
$70$	−2.77247e22	−	1.15806e22i	−0.239410	−	0.100001i
$71$	−1.81308e22			−0.131126			−0.0655628	−	0.997848i	$-0.520884\pi$
$71$	−1.81308e22			−0.131126			−0.0655628	+	0.997848i	$0.520884\pi$
$72$		−	5.72901e22i		−	0.347875i
$73$		−	3.48574e23i		−	1.78139i	−0.454603	−	0.890694i	$-0.650219\pi$
$73$		−	3.48574e23i		−	1.78139i	0.454603	−	0.890694i	$-0.349781\pi$
$74$	−1.38010e23			−0.594994
$75$	−2.47289e22	+	2.44368e22i	−0.0901445	+	0.0890797i
$76$	−2.79610e23			−0.863741
$77$			6.28695e21i			0.0164932i
$78$			4.48528e22i			0.100140i
$79$	−3.43193e23			−0.653432			−0.326716	−	0.945123i	$-0.605942\pi$
$79$	−3.43193e23			−0.653432			−0.326716	+	0.945123i	$0.605942\pi$
$80$	1.41789e23	+	5.92251e22i	0.230685	+	0.0963565i
$81$	6.83492e23			0.952074
$82$			2.08844e23i			0.249545i
$83$			6.85739e23i			0.704178i	0.935967	+	0.352089i	$0.114529\pi$
$83$			6.85739e23i			0.704178i	−0.935967	+	0.352089i	$0.885471\pi$
$84$	2.62984e22			0.0232508
$85$	1.29230e23	−	3.09387e23i	0.0985435	−	0.235920i
$86$	−1.19940e24			−0.790194
$87$			1.22499e23i			0.0698458i
$88$		−	3.21526e22i		−	0.0158922i
$89$	4.29595e24			1.84367			0.921837	−	0.387579i	$-0.126688\pi$
$89$	4.29595e24			1.84367			0.921837	+	0.387579i	$0.126688\pi$
$90$	−7.18498e23	+	1.72014e24i	−0.268160	+	0.641995i
$91$	1.26133e24			0.410025
$92$			2.69886e24i			0.765301i
$93$		−	3.50812e23i		−	0.0869035i
$94$	−4.00325e24			−0.867590
$95$	8.39532e24	+	3.50671e24i	1.59401	+	0.665816i
$96$	−1.34495e23			−0.0224034
$97$			2.90151e24i			0.424598i	0.977205	+	0.212299i	$0.0680951\pi$
$97$			2.90151e24i			0.424598i	−0.977205	+	0.212299i	$0.931905\pi$
$98$			4.75347e24i			0.611906i
$99$	3.90064e23			0.0442279
$100$	−3.51447e24	−	3.55648e24i	−0.351447	−	0.355648i
$101$	−8.46099e24			−0.747144			−0.373572	−	0.927601i	$-0.621867\pi$
$101$	−8.46099e24			−0.747144			−0.373572	+	0.927601i	$0.621867\pi$
$102$			2.93470e23i			0.0229119i
$103$		−	1.06290e25i		−	0.734562i	−0.930110	−	0.367281i	$-0.880289\pi$
$103$		−	1.06290e25i		−	0.734562i	0.930110	−	0.367281i	$-0.119711\pi$
$104$	−6.45066e24			−0.395082
$105$	−7.89610e23	−	3.29818e23i	−0.0429088	−	0.0179229i
$106$	−2.15538e25			−1.04040
$107$		−	2.28121e25i		−	0.979193i	−0.871949	−	0.489597i	$-0.837144\pi$
$107$		−	2.28121e25i		−	0.979193i	0.871949	−	0.489597i	$-0.162856\pi$
$108$		−	3.28991e24i		−	0.125715i
$109$	3.17871e25			1.08248			0.541240	−	0.840868i	$-0.317955\pi$
$109$	3.17871e25			1.08248			0.541240	+	0.840868i	$0.317955\pi$
$110$	−4.03239e23	+	9.65384e23i	−0.0122505	+	0.0293286i
$111$	−3.93056e24			−0.106639
$112$			3.78219e24i			0.0917314i
$113$			9.52597e24i			0.206742i	0.994643	+	0.103371i	$0.0329629\pi$
$113$			9.52597e24i			0.206742i	−0.994643	+	0.103371i	$0.967037\pi$
$114$	−7.96340e24			−0.154806
$115$	3.38475e25	−	8.10334e25i	0.589934	−	1.41235i
$116$	−1.76176e25			−0.275563
$117$		−	7.82571e25i		−	1.09951i
$118$		−	1.68319e24i		−	0.0212622i
$119$	8.25281e24			0.0938134
$120$	4.03821e24	+	1.68675e24i	0.0413450	+	0.0172697i
$121$	−1.08128e26			−0.997980
$122$		−	2.23136e25i		−	0.185811i
$123$			5.94796e24i			0.0447254i
$124$	5.04532e25			0.342861
$125$	6.09189e25	+	1.50860e26i	0.374435	+	0.927253i
$126$	−4.58842e25			−0.255289
$127$			2.95859e26i			1.49121i	0.666390	+	0.745604i	$0.267839\pi$
$127$			2.95859e26i			1.49121i	−0.666390	+	0.745604i	$0.732161\pi$
$128$		−	1.93428e25i		−	0.0883883i
$129$	−3.41593e25			−0.141624
$130$	1.93682e26	+	8.09004e25i	0.729115	+	0.304550i
$131$	−2.19768e26			−0.751749			−0.375874	−	0.926671i	$-0.622658\pi$
$131$	−2.19768e26			−0.751749			−0.375874	+	0.926671i	$0.622658\pi$
$132$		−	9.15717e23i		−	0.00284831i
$133$			2.23943e26i			0.633857i
$134$	2.59029e26			0.667635
$135$	−4.12601e25	+	9.87799e25i	−0.0969078	+	0.232004i
$136$	−4.22064e25			−0.0903945
$137$			3.42423e25i			0.0669200i	0.999440	+	0.0334600i	$0.0106526\pi$
$137$			3.42423e25i			0.0669200i	−0.999440	+	0.0334600i	$0.989347\pi$
$138$			7.68644e25i			0.137163i
$139$	2.79093e26			0.455055			0.227528	−	0.973772i	$-0.426936\pi$
$139$	2.79093e26			0.455055			0.227528	+	0.973772i	$0.426936\pi$
$140$	4.74340e25	−	1.13561e26i	0.0707114	−	0.169288i
$141$	−1.14014e26			−0.155496
$142$		−	7.42638e25i		−	0.0927199i
$143$		−	4.39198e25i		−	0.0502297i
$144$	2.34660e26			0.245985
$145$	5.28969e26	+	2.20949e26i	0.508546	+	0.212418i
$146$	1.42776e27			1.25963
$147$			1.35380e26i			0.109670i
$148$		−	5.65287e26i		−	0.420724i
$149$	−1.42906e27			−0.977739			−0.488870	−	0.872357i	$-0.662591\pi$
$149$	−1.42906e27			−0.977739			−0.488870	+	0.872357i	$0.662591\pi$
$150$	−1.00093e26	−	1.01290e26i	−0.0629889	−	0.0637418i
$151$	−2.51226e27			−1.45496			−0.727482	−	0.686127i	$-0.759310\pi$
$151$	−2.51226e27			−1.45496			−0.727482	+	0.686127i	$0.759310\pi$
$152$		−	1.14528e27i		−	0.610757i
$153$		−	5.12033e26i		−	0.251568i
$154$	−2.57513e25			−0.0116625
$155$	−1.51486e27	−	6.32755e26i	−0.632742	−	0.264295i
$156$	−1.83717e26			−0.0708096
$157$		−	3.34741e27i		−	1.19114i	−0.803302	−	0.595571i	$-0.796926\pi$
$157$		−	3.34741e27i		−	1.19114i	0.803302	−	0.595571i	$-0.203074\pi$
$158$		−	1.40572e27i		−	0.462046i
$159$	−6.13860e26			−0.186468
$160$	−2.42586e26	+	5.80769e26i	−0.0681343	+	0.163119i
$161$	2.16154e27			0.561617
$162$			2.79958e27i			0.673218i
$163$			8.42668e26i			0.187634i	0.995589	+	0.0938170i	$0.0299069\pi$
$163$			8.42668e26i			0.187634i	−0.995589	+	0.0938170i	$0.970093\pi$
$164$	−8.55426e26			−0.176455
$165$	−1.14844e25	+	2.74945e25i	−0.00219563	+	0.00525649i
$166$	−2.80879e27			−0.497929
$167$		−	3.08789e27i		−	0.507815i	−0.967229	−	0.253907i	$-0.918284\pi$
$167$		−	3.08789e27i		−	0.507815i	0.967229	−	0.253907i	$-0.0817159\pi$
$168$			1.07718e26i			0.0164408i
$169$	−1.75507e27			−0.248720
$170$	1.26725e27	+	5.29327e26i	0.166821	+	0.0696808i
$171$	1.38942e28			1.69974
$172$		−	4.91274e27i		−	0.558751i
$173$			9.76292e27i			1.03277i	0.856357	+	0.516385i	$0.172723\pi$
$173$			9.76292e27i			1.03277i	−0.856357	+	0.516385i	$0.827277\pi$
$174$	−5.01754e26			−0.0493885
$175$	−2.84842e27	+	2.81477e27i	−0.260992	+	0.257910i
$176$	1.31697e26			0.0112375
$177$		−	4.79378e25i		−	0.00381077i
$178$			1.75962e28i			1.30367i
$179$	1.48035e28			1.02259			0.511294	−	0.859406i	$-0.329166\pi$
$179$	1.48035e28			1.02259			0.511294	+	0.859406i	$0.329166\pi$
$180$	−7.04568e27	−	2.94297e27i	−0.453959	−	0.189618i
$181$	1.20192e28			0.722591			0.361295	−	0.932451i	$-0.382335\pi$
$181$	1.20192e28			0.722591			0.361295	+	0.932451i	$0.382335\pi$
$182$			5.16640e27i			0.289932i
$183$		−	6.35499e26i		−	0.0333025i
$184$	−1.10545e28			−0.541150
$185$	−7.08949e27	+	1.69728e28i	−0.324316	+	0.776437i
$186$	1.43693e27			0.0614501
$187$		−	2.87366e26i		−	0.0114925i
$188$		−	1.63973e28i		−	0.613479i
$189$	−2.63493e27			−0.0922563
$190$	−1.43635e28	+	3.43872e28i	−0.470803	+	1.12714i
$191$	8.66884e27			0.266099			0.133050	−	0.991109i	$-0.457523\pi$
$191$	8.66884e27			0.266099			0.133050	+	0.991109i	$0.457523\pi$
$192$		−	5.50890e26i		−	0.0158416i
$193$		−	1.60225e28i		−	0.431782i	−0.976417	−	0.215891i	$-0.930734\pi$
$193$		−	1.60225e28i		−	0.431782i	0.976417	−	0.215891i	$-0.0692657\pi$
$194$	−1.18846e28			−0.300236
$195$	5.51612e27	+	2.30407e27i	0.130677	+	0.0545837i
$196$	−1.94702e28			−0.432683
$197$		−	6.69730e28i		−	1.39660i	−0.715805	−	0.698300i	$-0.753940\pi$
$197$		−	6.69730e28i		−	1.39660i	0.715805	−	0.698300i	$-0.246060\pi$
$198$			1.59770e27i			0.0312738i
$199$	−1.81836e28			−0.334208			−0.167104	−	0.985939i	$-0.553442\pi$
$199$	−1.81836e28			−0.334208			−0.167104	+	0.985939i	$0.553442\pi$
$200$	1.45673e28	−	1.43953e28i	0.251481	−	0.248510i
$201$	7.37724e27			0.119658
$202$		−	3.46562e28i		−	0.528310i
$203$			1.41101e28i			0.202222i
$204$	−1.20205e27			−0.0162012
$205$	2.56842e28	+	1.07283e28i	0.325644	+	0.136021i
$206$	4.35365e28			0.519414
$207$		−	1.34110e29i		−	1.50602i
$208$		−	2.64219e28i		−	0.279365i
$209$	7.79776e27			0.0776500
$210$	1.35094e27	−	3.23424e27i	0.0126734	−	0.0303411i
$211$	−1.59042e29			−1.40598			−0.702992	−	0.711197i	$-0.748153\pi$
$211$	−1.59042e29			−1.40598			−0.702992	+	0.711197i	$0.748153\pi$
$212$		−	8.82844e28i		−	0.735675i
$213$		−	2.11506e27i		−	0.0166179i
$214$	9.34384e28			0.692394
$215$	−6.16127e28	+	1.47505e29i	−0.430715	+	1.03116i
$216$	1.34755e28			0.0888940
$217$		−	4.04085e28i		−	0.251609i
$218$			1.30200e29i			0.765428i
$219$	4.06630e28			0.225761
$220$	−3.95421e27	−	1.65167e27i	−0.0207385	−	0.00866241i
$221$	−5.76531e28			−0.285706
$222$		−	1.60996e28i		−	0.0754053i
$223$			3.74438e29i			1.65794i	0.559293	+	0.828970i	$0.311073\pi$
$223$			3.74438e29i			1.65794i	−0.559293	+	0.828970i	$0.688927\pi$
$224$	−1.54919e28			−0.0648639
$225$	1.74638e29	+	1.76726e29i	0.691604	+	0.699871i
$226$	−3.90184e28			−0.146189
$227$		−	3.09492e29i		−	1.09730i	−0.836052	−	0.548651i	$-0.815142\pi$
$227$		−	3.09492e29i		−	1.09730i	0.836052	−	0.548651i	$-0.184858\pi$
$228$		−	3.26181e28i		−	0.109464i
$229$	−4.36225e29			−1.38601			−0.693006	−	0.720932i	$-0.743714\pi$
$229$	−4.36225e29			−1.38601			−0.693006	+	0.720932i	$0.743714\pi$
$230$	3.31913e29	+	1.38639e29i	0.998679	+	0.417146i
$231$	−7.33407e26			−0.00209024
$232$		−	7.21616e28i		−	0.194853i
$233$			2.03884e29i			0.521715i	0.965377	+	0.260858i	$0.0840054\pi$
$233$			2.03884e29i			0.521715i	−0.965377	+	0.260858i	$0.915995\pi$
$234$	3.20541e29			0.777474
$235$	−2.05645e29	+	4.92330e29i	−0.472902	+	1.13216i
$236$	6.89435e27			0.0150346
$237$		−	4.00354e28i		−	0.0828113i
$238$			3.38035e28i			0.0663361i
$239$	7.19381e29			1.33963			0.669816	−	0.742527i	$-0.266373\pi$
$239$	7.19381e29			1.33963			0.669816	+	0.742527i	$0.266373\pi$
$240$	−6.90893e27	+	1.65405e28i	−0.0122115	+	0.0292353i
$241$	−5.94932e28			−0.0998285			−0.0499142	−	0.998754i	$-0.515895\pi$
$241$	−5.94932e28			−0.0998285			−0.0499142	+	0.998754i	$0.515895\pi$
$242$		−	4.42893e29i		−	0.705678i
$243$			2.45881e29i			0.372089i
$244$	9.13966e28			0.131388
$245$	5.84594e29	+	2.44184e29i	0.798506	+	0.333534i
$246$	−2.43628e28			−0.0316256
$247$		−	1.56444e30i		−	1.93039i
$248$			2.06656e29i			0.242439i
$249$	−7.99951e28			−0.0892425
$250$	−6.17922e29	+	2.49524e29i	−0.655667	+	0.264766i
$251$	−1.11692e30			−1.12745			−0.563727	−	0.825961i	$-0.690633\pi$
$251$	−1.11692e30			−1.12745			−0.563727	+	0.825961i	$0.690633\pi$
$252$		−	1.87942e29i		−	0.180516i
$253$		−	7.52656e28i		−	0.0688003i
$254$	−1.21184e30			−1.05444
$255$	3.60917e28	+	1.50754e28i	0.0298989	+	0.0124887i
$256$	7.92282e28			0.0625000
$257$		−	2.23332e30i		−	1.67798i	−0.544146	−	0.838991i	$-0.683146\pi$
$257$		−	2.23332e30i		−	1.67798i	0.544146	−	0.838991i	$-0.316854\pi$
$258$		−	1.39917e29i		−	0.100144i
$259$	−4.52744e29			−0.308749
$260$	−3.31368e29	+	7.93320e29i	−0.215349	+	0.515563i
$261$	8.75438e29			0.542275
$262$		−	9.00168e29i		−	0.531566i
$263$		−	1.67388e30i		−	0.942489i	−0.882003	−	0.471244i	$-0.843805\pi$
$263$		−	1.67388e30i		−	0.942489i	0.882003	−	0.471244i	$-0.156195\pi$
$264$	3.75078e27			0.00201406
$265$	−1.10721e30	+	2.65075e30i	−0.567096	+	1.35767i
$266$	−9.17270e29			−0.448205
$267$			5.01146e29i			0.233654i
$268$			1.06098e30i			0.472089i
$269$	1.51842e30			0.644895			0.322448	−	0.946587i	$-0.395494\pi$
$269$	1.51842e30			0.644895			0.322448	+	0.946587i	$0.395494\pi$
$270$	−4.04602e29	−	1.69002e29i	−0.164052	−	0.0685242i
$271$	3.73589e30			1.44637			0.723183	−	0.690657i	$-0.242678\pi$
$271$	3.73589e30			1.44637			0.723183	+	0.690657i	$0.242678\pi$
$272$		−	1.72877e29i		−	0.0639185i
$273$			1.47141e29i			0.0519637i
$274$	−1.40256e29			−0.0473196
$275$	9.80113e28	+	9.91828e28i	0.0315949	+	0.0319726i
$276$	−3.14837e29			−0.0969888
$277$		−	4.88475e30i		−	1.43829i	−0.694863	−	0.719143i	$-0.744535\pi$
$277$		−	4.88475e30i		−	1.43829i	0.694863	−	0.719143i	$-0.255465\pi$
$278$			1.14316e30i			0.321772i
$279$	−2.50708e30			−0.674708
$280$	4.65144e29	+	1.94290e29i	0.119705	+	0.0500005i
$281$	4.07868e30			1.00390			0.501950	−	0.864896i	$-0.332616\pi$
$281$	4.07868e30			1.00390			0.501950	+	0.864896i	$0.332616\pi$
$282$		−	4.67001e29i		−	0.109952i
$283$			8.77909e30i			1.97751i	0.149537	+	0.988756i	$0.452222\pi$
$283$			8.77909e30i			1.97751i	−0.149537	+	0.988756i	$0.547778\pi$
$284$	3.04184e29			0.0655628
$285$	−4.09077e29	+	9.79360e29i	−0.0843808	+	0.202014i
$286$	1.79896e29			0.0355177
$287$			6.85120e29i			0.129492i
$288$			9.61168e29i			0.173937i
$289$	5.39341e30			0.934631
$290$	−9.05008e29	+	2.16666e30i	−0.150203	+	0.359596i
$291$	−3.38477e29			−0.0538105
$292$			5.84809e30i			0.890694i
$293$			4.02063e30i			0.586744i	0.955998	+	0.293372i	$0.0947775\pi$
$293$			4.02063e30i			0.586744i	−0.955998	+	0.293372i	$0.905222\pi$
$294$	−5.54518e29			−0.0775486
$295$	−2.07003e29	−	8.64648e28i	−0.0277461	−	0.0115895i
$296$	2.31542e30			0.297497
$297$			9.17489e28i			0.0113017i
$298$		−	5.85344e30i		−	0.691366i
$299$	−1.51003e31			−1.71039
$300$	4.14882e29	−	4.09982e29i	0.0450722	−	0.0445399i
$301$	−3.93467e30			−0.410040
$302$		−	1.02902e31i		−	1.02882i
$303$		−	9.87021e29i		−	0.0946877i
$304$	4.69108e30			0.431870
$305$	−2.74419e30	−	1.14624e30i	−0.242474	−	0.101281i
$306$	2.09729e30			0.177885
$307$		−	3.20834e29i		−	0.0261247i	−0.999915	−	0.0130623i	$-0.995842\pi$
$307$		−	3.20834e29i		−	0.0261247i	0.999915	−	0.0130623i	$-0.00415799\pi$
$308$		−	1.05478e29i		−	0.00824662i
$309$	1.23993e30			0.0930932
$310$	2.59176e30	−	6.20487e30i	0.186885	−	0.447416i
$311$	−1.26721e31			−0.877692			−0.438846	−	0.898562i	$-0.644613\pi$
$311$	−1.26721e31			−0.877692			−0.438846	+	0.898562i	$0.644613\pi$
$312$		−	7.52505e29i		−	0.0500699i
$313$		−	2.76579e31i		−	1.76813i	−0.467361	−	0.884066i	$-0.654795\pi$
$313$		−	2.76579e31i		−	1.76813i	0.467361	−	0.884066i	$-0.345205\pi$
$314$	1.37110e31			0.842265
$315$	−2.35705e30	+	5.64296e30i	−0.139151	+	0.333139i
$316$	5.75783e30			0.326716
$317$			8.12742e30i			0.443315i	0.975125	+	0.221657i	$0.0711466\pi$
$317$			8.12742e30i			0.443315i	−0.975125	+	0.221657i	$0.928853\pi$
$318$		−	2.51437e30i		−	0.131853i
$319$	4.91318e29			0.0247730
$320$	−2.37883e30	−	9.93633e29i	−0.115342	−	0.0481783i
$321$	2.66116e30			0.124096
$322$			8.85368e30i			0.397123i
$323$		−	1.02360e31i		−	0.441672i
$324$	−1.14671e31			−0.476037
$325$	1.98987e31	−	1.96636e31i	0.794845	−	0.785456i
$326$	−3.45157e30			−0.132677
$327$			3.70814e30i			0.137186i
$328$		−	3.50383e30i		−	0.124773i
$329$	−1.31328e31			−0.450203
$330$	−1.12617e29	−	4.70400e28i	−0.00371690	−	0.00155254i
$331$	−3.24680e31			−1.03182			−0.515912	−	0.856642i	$-0.672547\pi$
$331$	−3.24680e31			−1.03182			−0.515912	+	0.856642i	$0.672547\pi$
$332$		−	1.15048e31i		−	0.352089i
$333$			2.80898e31i			0.827934i
$334$	1.26480e31			0.359079
$335$	1.33062e31	−	3.18561e31i	0.363911	−	0.871229i
$336$	−4.41213e29			−0.0116254
$337$			6.16105e31i			1.56416i	0.623178	+	0.782080i	$0.285841\pi$
$337$			6.16105e31i			1.56416i	−0.623178	+	0.782080i	$0.714159\pi$
$338$		−	7.18877e30i		−	0.175872i
$339$	−1.11126e30			−0.0262010
$340$	−2.16813e30	+	5.19065e30i	−0.0492717	+	0.117960i
$341$	−1.40704e30			−0.0308231
$342$			5.69106e31i			1.20189i
$343$			3.36139e31i			0.684451i
$344$	2.01226e31			0.395097
$345$	9.45299e30	+	3.94849e30i	0.178991	+	0.0747640i
$346$	−3.99889e31			−0.730279
$347$			8.34408e31i			1.46981i	0.678172	+	0.734903i	$0.262772\pi$
$347$			8.34408e31i			1.46981i	−0.678172	+	0.734903i	$0.737228\pi$
$348$		−	2.05519e30i		−	0.0349229i
$349$	1.07311e32			1.75924			0.879621	−	0.475676i	$-0.157796\pi$
$349$	1.07311e32			1.75924			0.879621	+	0.475676i	$0.157796\pi$
$350$	−1.15293e31	−	1.16671e31i	−0.182370	−	0.184550i
$351$	1.84073e31			0.280964
$352$			5.39431e29i			0.00794608i
$353$		−	1.05139e32i		−	1.49479i	−0.664381	−	0.747394i	$-0.731305\pi$
$353$		−	1.05139e32i		−	1.49479i	0.664381	−	0.747394i	$-0.268695\pi$
$354$	1.96353e29			0.00269462
$355$	−9.13316e30	−	3.81490e30i	−0.120995	−	0.0505393i
$356$	−7.20741e31			−0.921837
$357$			9.62736e29i			0.0118892i
$358$			6.06350e31i			0.723079i
$359$	−1.15543e32			−1.33064			−0.665321	−	0.746557i	$-0.731705\pi$
$359$	−1.15543e32			−1.33064			−0.665321	+	0.746557i	$0.731705\pi$
$360$	1.20544e31	−	2.88591e31i	0.134080	−	0.320998i
$361$	1.84682e32			1.98419
$362$			4.92305e31i			0.510949i
$363$		−	1.26137e31i		−	0.126477i
$364$	−2.11616e31			−0.205013
$365$	7.33433e31	−	1.75589e32i	0.686594	−	1.64376i
$366$	2.60300e30			0.0235484
$367$			5.65157e31i			0.494133i	0.968999	+	0.247066i	$0.0794666\pi$
$367$			5.65157e31i			0.494133i	−0.968999	+	0.247066i	$0.920533\pi$
$368$		−	4.52793e31i		−	0.382651i
$369$	4.25072e31			0.347242
$370$	−6.95205e31	−	2.90386e31i	−0.549024	−	0.229326i
$371$	−7.07079e31			−0.539876
$372$			5.88565e30i			0.0434518i
$373$		−	1.41123e31i		−	0.100748i	−0.998730	−	0.0503741i	$-0.983959\pi$
$373$		−	1.41123e31i		−	0.100748i	0.998730	−	0.0503741i	$-0.0160414\pi$
$374$	1.17705e30			0.00812643
$375$	−1.75986e31	+	7.10652e30i	−0.117513	+	0.0474533i
$376$	6.71634e31			0.433795
$377$		−	9.85713e31i		−	0.615862i
$378$		−	1.07927e31i		−	0.0652350i
$379$	−2.60316e32			−1.52234			−0.761169	−	0.648554i	$-0.775374\pi$
$379$	−2.60316e32			−1.52234			−0.761169	+	0.648554i	$0.775374\pi$
$380$	−1.40850e32	−	5.88328e31i	−0.797007	−	0.332908i
$381$	−3.45135e31			−0.188985
$382$			3.55076e31i			0.188161i
$383$		−	2.22460e32i		−	1.14095i	−0.821315	−	0.570475i	$-0.806759\pi$
$383$		−	2.22460e32i		−	1.14095i	0.821315	−	0.570475i	$-0.193241\pi$
$384$	2.25644e30			0.0112017
$385$	−1.32284e30	+	3.16697e30i	−0.00635692	+	0.0152190i
$386$	6.56283e31			0.305316
$387$			2.44120e32i			1.09955i
$388$		−	4.86793e31i		−	0.212299i
$389$	−2.83579e31			−0.119758			−0.0598789	−	0.998206i	$-0.519071\pi$
$389$	−2.83579e31			−0.119758			−0.0598789	+	0.998206i	$0.519071\pi$
$390$	−9.43747e30	+	2.25940e31i	−0.0385965	+	0.0924029i
$391$	−9.88004e31			−0.391335
$392$		−	7.97499e31i		−	0.305953i
$393$		−	2.56371e31i		−	0.0952713i
$394$	2.74322e32			0.987545
$395$	−1.72879e32	−	7.22113e31i	−0.602947	−	0.251850i
$396$	−6.54419e30			−0.0221139
$397$			1.97865e32i			0.647870i	0.946079	+	0.323935i	$0.105006\pi$
$397$			1.97865e32i			0.647870i	−0.946079	+	0.323935i	$0.894994\pi$
$398$		−	7.44802e31i		−	0.236321i
$399$	−2.61242e31			−0.0803306
$400$	5.89630e31	+	5.96678e31i	0.175723	+	0.177824i
$401$	5.91837e32			1.70961			0.854806	−	0.518947i	$-0.173676\pi$
$401$	5.91837e32			1.70961			0.854806	+	0.518947i	$0.173676\pi$
$402$			3.02172e31i			0.0846113i
$403$			2.82289e32i			0.766268i
$404$	1.41952e32			0.373572
$405$	3.44300e32	+	1.43814e32i	0.878516	+	0.366954i
$406$	−5.77949e31			−0.142993
$407$			1.57647e31i			0.0378229i
$408$		−	4.92361e30i		−	0.0114560i
$409$	−5.10098e32			−1.15110			−0.575549	−	0.817767i	$-0.695212\pi$
$409$	−5.10098e32			−1.15110			−0.575549	+	0.817767i	$0.695212\pi$
$410$	−4.39429e31	+	1.05203e32i	−0.0961813	+	0.230265i
$411$	−3.99455e30			−0.00848097
$412$			1.78326e32i			0.367281i
$413$		−	5.52175e30i		−	0.0110332i
$414$	5.49313e32			1.06492
$415$	−1.44286e32	+	3.45432e32i	−0.271409	+	0.649772i
$416$	1.08224e32			0.197541
$417$			3.25577e31i			0.0576704i
$418$			3.19396e31i			0.0549068i
$419$	−3.45646e32			−0.576709			−0.288354	−	0.957524i	$-0.593108\pi$
$419$	−3.45646e32			−0.576709			−0.288354	+	0.957524i	$0.593108\pi$
$420$	1.32475e31	+	5.53343e30i	0.0214544	+	0.00896146i
$421$	1.15256e31			0.0181191			0.00905955	−	0.999959i	$-0.497116\pi$
$421$	1.15256e31			0.0181191			0.00905955	+	0.999959i	$0.497116\pi$
$422$		−	6.51435e32i		−	0.994181i
$423$			8.14803e32i			1.20725i
$424$	3.61613e32			0.520201
$425$	1.30196e32	−	1.28658e32i	0.181860	−	0.179712i
$426$	8.66328e30			0.0117507
$427$		−	7.32004e31i		−	0.0964196i
$428$			3.82724e32i			0.489597i
$429$	5.12349e30			0.00636575
$430$	−6.04182e32	−	2.52366e32i	−0.729142	−	0.304561i
$431$	−1.12581e33			−1.31978			−0.659888	−	0.751364i	$-0.729396\pi$
$431$	−1.12581e33			−1.31978			−0.659888	+	0.751364i	$0.729396\pi$
$432$			5.51956e31i			0.0628576i
$433$			5.31109e32i			0.587604i	0.955866	+	0.293802i	$0.0949207\pi$
$433$			5.31109e32i			0.587604i	−0.955866	+	0.293802i	$0.905079\pi$
$434$	1.65513e32			0.177914
$435$	−2.57749e31	+	6.17071e31i	−0.0269204	+	0.0644495i
$436$	−5.33299e32			−0.541240
$437$		−	2.68098e33i		−	2.64409i
$438$			1.66556e32i			0.159637i
$439$	−7.89847e32			−0.735760			−0.367880	−	0.929873i	$-0.619916\pi$
$439$	−7.89847e32			−0.735760			−0.367880	+	0.929873i	$0.619916\pi$
$440$	6.76523e30	−	1.61965e31i	0.00612525	−	0.0146643i
$441$	9.67498e32			0.851467
$442$		−	2.36147e32i		−	0.202025i
$443$		−	1.82758e33i		−	1.51995i	−0.649953	−	0.759974i	$-0.725212\pi$
$443$		−	1.82758e33i		−	1.51995i	0.649953	−	0.759974i	$-0.274788\pi$
$444$	6.59438e31			0.0533196
$445$	2.16403e33	+	9.03910e32i	1.70123	+	0.710600i
$446$	−1.53370e33			−1.17234
$447$		−	1.66708e32i		−	0.123912i
$448$		−	6.34546e31i		−	0.0458657i
$449$	8.32692e31			0.0585336			0.0292668	−	0.999572i	$-0.490683\pi$
$449$	8.32692e31			0.0585336			0.0292668	+	0.999572i	$0.490683\pi$
$450$	−7.23868e32	+	7.15318e32i	−0.494883	+	0.489038i
$451$	2.38561e31			0.0158633
$452$		−	1.59819e32i		−	0.103371i
$453$		−	2.93069e32i		−	0.184392i
$454$	1.26768e33			0.775909
$455$	6.35378e32	+	2.65396e32i	0.378346	+	0.158034i
$456$	1.33604e32			0.0774030
$457$		−	2.02366e33i		−	1.14074i	−0.821389	−	0.570368i	$-0.806801\pi$
$457$		−	2.02366e33i		−	1.14074i	0.821389	−	0.570368i	$-0.193199\pi$
$458$		−	1.78678e33i		−	0.980058i
$459$	1.20438e32			0.0642842
$460$	−5.67867e32	+	1.35951e33i	−0.294967	+	0.706173i
$461$	−8.37646e32			−0.423447			−0.211724	−	0.977330i	$-0.567908\pi$
$461$	−8.37646e32			−0.423447			−0.211724	+	0.977330i	$0.567908\pi$
$462$		−	3.00404e30i		−	0.00147802i
$463$			3.37029e33i			1.61401i	0.590547	+	0.807003i	$0.298912\pi$
$463$			3.37029e33i			1.61401i	−0.590547	+	0.807003i	$0.701088\pi$
$464$	2.95574e32			0.137782
$465$	7.38143e31	−	1.76717e32i	0.0334949	−	0.0801892i
$466$	−8.35108e32			−0.368909
$467$		−	2.79564e33i		−	1.20232i	−0.799128	−	0.601161i	$-0.794705\pi$
$467$		−	2.79564e33i		−	1.20232i	0.799128	−	0.601161i	$-0.205295\pi$
$468$			1.31294e33i			0.549757i
$469$	8.49753e32			0.346443
$470$	−2.01659e33	−	8.42324e32i	−0.800559	−	0.334392i
$471$	3.90494e32			0.150957
$472$			2.82392e31i			0.0106311i
$473$			1.37006e32i			0.0502315i
$474$	1.63985e32			0.0585564
$475$	3.49119e33	+	3.53292e33i	1.21424	+	1.22875i
$476$	−1.38459e32			−0.0469067
$477$			4.38696e33i			1.44772i
$478$			2.94659e33i			0.947263i
$479$	−6.03192e33			−1.88913			−0.944565	−	0.328324i	$-0.893516\pi$
$479$	−6.03192e33			−1.88913			−0.944565	+	0.328324i	$0.893516\pi$
$480$	−6.77499e31	−	2.82990e31i	−0.0206725	−	0.00863486i
$481$	3.16281e33			0.940286
$482$		−	2.43684e32i		−	0.0705894i
$483$			2.52156e32i			0.0711754i
$484$	1.81409e33			0.498990
$485$	−6.10507e32	+	1.46160e33i	−0.163651	+	0.391793i
$486$	−1.00713e33			−0.263107
$487$		−	2.63729e33i		−	0.671500i	−0.941951	−	0.335750i	$-0.891010\pi$
$487$		−	2.63729e33i		−	0.671500i	0.941951	−	0.335750i	$-0.108990\pi$
$488$			3.74360e32i			0.0929056i
$489$	−9.83018e31			−0.0237794
$490$	−1.00018e33	+	2.39450e33i	−0.235844	+	0.564629i
$491$	4.59365e33			1.05594			0.527970	−	0.849263i	$-0.322953\pi$
$491$	4.59365e33			1.05594			0.527970	+	0.849263i	$0.322953\pi$
$492$		−	9.97902e31i		−	0.0223627i
$493$		−	6.44948e32i		−	0.140909i
$494$	6.40793e33			1.36499
$495$	1.96490e32	+	8.20733e31i	0.0408108	+	0.0170466i
$496$	−8.46465e32			−0.171430
$497$		−	2.43624e32i		−	0.0481134i
$498$		−	3.27660e32i		−	0.0631040i
$499$	−4.28804e33			−0.805382			−0.402691	−	0.915336i	$-0.631925\pi$
$499$	−4.28804e33			−0.805382			−0.402691	+	0.915336i	$0.631925\pi$
$500$	−1.02205e33	−	2.53101e33i	−0.187218	−	0.463626i
$501$	3.60219e32			0.0643569
$502$		−	4.57488e33i		−	0.797230i
$503$		−	1.27163e33i		−	0.216152i	−0.994143	−	0.108076i	$-0.965531\pi$
$503$		−	1.27163e33i		−	0.216152i	0.994143	−	0.108076i	$-0.0344690\pi$
$504$	7.69809e32			0.127644
$505$	−4.26211e33	−	1.78028e33i	−0.689418	−	0.287969i
$506$	3.08288e32			0.0486491
$507$		−	2.04739e32i		−	0.0315210i
$508$		−	4.96369e33i		−	0.745604i
$509$	−8.49642e33			−1.24527			−0.622635	−	0.782512i	$-0.713938\pi$
$509$	−8.49642e33			−1.24527			−0.622635	+	0.782512i	$0.713938\pi$
$510$	−6.17489e31	+	1.47832e32i	−0.00883085	+	0.0211417i
$511$	4.68380e33			0.653637
$512$			3.24519e32i			0.0441942i
$513$			3.26812e33i			0.434341i
$514$	9.14768e33			1.18651
$515$	2.23645e33	−	5.35424e33i	0.283119	−	0.677809i
$516$	5.73098e32			0.0708122
$517$			4.57287e32i			0.0551515i
$518$		−	1.85444e33i		−	0.218319i
$519$	−1.13890e33			−0.130886
$520$	−3.24944e33	−	1.35728e33i	−0.364558	−	0.152275i
$521$	−1.16997e34			−1.28146			−0.640730	−	0.767767i	$-0.721368\pi$
$521$	−1.16997e34			−1.28146			−0.640730	+	0.767767i	$0.721368\pi$
$522$			3.58580e33i			0.383446i
$523$		−	2.58251e33i		−	0.269631i	−0.990871	−	0.134816i	$-0.956956\pi$
$523$		−	2.58251e33i		−	0.269631i	0.990871	−	0.134816i	$-0.0430442\pi$
$524$	3.68709e33			0.375874
$525$	−3.28359e32	−	3.32283e32i	−0.0326856	−	0.0330763i
$526$	6.85619e33			0.666440
$527$			1.84700e33i			0.175321i
$528$			1.53632e31i			0.00142415i
$529$	−1.48316e34			−1.34274
$530$	−1.08575e34	−	4.53514e33i	−0.960019	−	0.400998i
$531$	−3.42588e32			−0.0295863
$532$		−	3.75714e33i		−	0.316929i
$533$		−	4.78616e33i		−	0.394364i
$534$	−2.05269e33			−0.165218
$535$	4.79989e33	−	1.14913e34i	0.377407	−	0.903539i
$536$	−4.34579e33			−0.333817
$537$			1.72691e33i			0.129596i
$538$			6.21946e33i			0.456010i
$539$	5.42984e32			0.0388980
$540$	6.92230e32	−	1.65725e33i	0.0484539	−	0.116002i
$541$	8.08434e33			0.552941			0.276470	−	0.961022i	$-0.410835\pi$
$541$	8.08434e33			0.552941			0.276470	+	0.961022i	$0.410835\pi$
$542$			1.53022e34i			1.02274i
$543$			1.40210e33i			0.0915760i
$544$	7.08106e32			0.0451972
$545$	1.60123e34	+	6.68832e33i	0.998846	+	0.417216i
$546$	−6.02689e32			−0.0367439
$547$			3.07411e34i			1.83180i	0.401408	+	0.915900i	$0.368521\pi$
$547$			3.07411e34i			1.83180i	−0.401408	+	0.915900i	$0.631479\pi$
$548$		−	5.74491e32i		−	0.0334600i
$549$	−4.54160e33			−0.258556
$550$	−4.06253e32	+	4.01454e32i	−0.0226080	+	0.0223410i
$551$	1.75009e34			0.952061
$552$		−	1.28957e33i		−	0.0685814i
$553$		−	4.61150e33i		−	0.239761i
$554$	2.00079e34			1.01702
$555$	−1.97997e33	−	8.27028e32i	−0.0984001	−	0.0411015i
$556$	−4.68240e33			−0.227528
$557$			2.42852e34i			1.15385i	0.816796	+	0.576927i	$0.195748\pi$
$557$			2.42852e34i			1.15385i	−0.816796	+	0.576927i	$0.804252\pi$
$558$		−	1.02690e34i		−	0.477091i
$559$	2.74871e34			1.24877
$560$	−7.95810e32	+	1.90523e33i	−0.0353557	+	0.0846442i
$561$	3.35228e31			0.00145648
$562$			1.67063e34i			0.709865i
$563$		−	2.54352e34i		−	1.05701i	−0.848929	−	0.528507i	$-0.822752\pi$
$563$		−	2.54352e34i		−	1.05701i	0.848929	−	0.528507i	$-0.177248\pi$
$564$	1.91284e33			0.0777480
$565$	−2.00436e33	+	4.79858e33i	−0.0796837	+	0.190769i
$566$	−3.59592e34			−1.39831
$567$			9.18411e33i			0.349341i
$568$			1.24594e33i			0.0463599i
$569$	−9.11823e33			−0.331900			−0.165950	−	0.986134i	$-0.553069\pi$
$569$	−9.11823e33			−0.331900			−0.165950	+	0.986134i	$0.553069\pi$
$570$	−4.01146e33	−	1.67558e33i	−0.142845	−	0.0596663i
$571$	−7.94351e33			−0.276733			−0.138366	−	0.990381i	$-0.544185\pi$
$571$	−7.94351e33			−0.276733			−0.138366	+	0.990381i	$0.544185\pi$
$572$			7.36853e32i			0.0251148i
$573$			1.01127e33i			0.0337236i
$574$	−2.80625e33			−0.0915646
$575$	3.41005e34	−	3.36977e34i	1.08871	−	1.07585i
$576$	−3.93694e33			−0.122992
$577$		−	3.99407e33i		−	0.122101i	−0.998135	−	0.0610503i	$-0.980555\pi$
$577$		−	3.99407e33i		−	0.122101i	0.998135	−	0.0610503i	$-0.0194450\pi$
$578$			2.20914e34i			0.660884i
$579$	1.86912e33			0.0547210
$580$	−8.87462e33	−	3.70691e33i	−0.254273	−	0.106209i
$581$	−9.21430e33			−0.258381
$582$		−	1.38640e33i		−	0.0380498i
$583$			2.46207e33i			0.0661369i
$584$	−2.39538e34			−0.629816
$585$	1.64661e34	−	3.94210e34i	0.423781	−	1.01456i
$586$	−1.64685e34			−0.414891
$587$			1.28546e34i			0.317017i	0.987358	+	0.158508i	$0.0506685\pi$
$587$			1.28546e34i			0.317017i	−0.987358	+	0.158508i	$0.949332\pi$
$588$		−	2.27131e33i		−	0.0548351i
$589$	−5.01190e34			−1.18457
$590$	3.54160e32	−	8.47885e32i	0.00819500	−	0.0196195i
$591$	7.81277e33			0.176995
$592$			9.48394e33i			0.210362i
$593$			1.35249e34i			0.293732i	0.989156	+	0.146866i	$0.0469186\pi$
$593$			1.35249e34i			0.293732i	−0.989156	+	0.146866i	$0.953081\pi$
$594$	−3.75804e32			−0.00799154
$595$	4.15725e33	+	1.73647e33i	0.0865653	+	0.0361581i
$596$	2.39757e34			0.488870
$597$		−	2.12122e33i		−	0.0423552i
$598$		−	6.18507e34i		−	1.20943i
$599$	4.11263e34			0.787561			0.393781	−	0.919204i	$-0.371167\pi$
$599$	4.11263e34			0.787561			0.393781	+	0.919204i	$0.371167\pi$
$600$	1.67929e33	+	1.69936e33i	0.0314944	+	0.0318709i
$601$	−8.66879e34			−1.59231			−0.796155	−	0.605092i	$-0.793136\pi$
$601$	−8.66879e34			−1.59231			−0.796155	+	0.605092i	$0.793136\pi$
$602$		−	1.61164e34i		−	0.289942i
$603$		−	5.27216e34i		−	0.929013i
$604$	4.21487e34			0.727482
$605$	−5.44681e34	−	2.27512e34i	−0.920874	−	0.384647i
$606$	4.04284e33			0.0669543
$607$		−	1.06263e35i		−	1.72394i	−0.506956	−	0.861972i	$-0.669229\pi$
$607$		−	1.06263e35i		−	1.72394i	0.506956	−	0.861972i	$-0.330771\pi$
$608$			1.92147e34i			0.305378i
$609$	−1.64602e33			−0.0256282
$610$	4.69500e33	−	1.12402e34i	0.0716165	−	0.171455i
$611$	9.17439e34			1.37108
$612$			8.59049e33i			0.125784i
$613$			3.14879e34i			0.451740i	0.974157	+	0.225870i	$0.0725224\pi$
$613$			3.14879e34i			0.451740i	−0.974157	+	0.225870i	$0.927478\pi$
$614$	1.31414e33			0.0184729
$615$	−1.25151e33	+	2.99621e33i	−0.0172383	+	0.0412698i
$616$	4.32036e32			0.00583124
$617$			1.34862e35i			1.78371i	0.452320	+	0.891856i	$0.350597\pi$
$617$			1.34862e35i			1.78371i	−0.452320	+	0.891856i	$0.649403\pi$
$618$			5.07877e33i			0.0658268i
$619$	−2.48732e34			−0.315936			−0.157968	−	0.987444i	$-0.550494\pi$
$619$	−2.48732e34			−0.315936			−0.157968	+	0.987444i	$0.550494\pi$
$620$	2.54152e34	+	1.06159e34i	0.316371	+	0.132148i
$621$	3.15446e34			0.384840
$622$		−	5.19048e34i		−	0.620622i
$623$			5.77248e34i			0.676491i
$624$	3.08226e33			0.0354048
$625$	−1.05528e33	+	8.88116e34i	−0.0118814	+	0.999929i
$626$	1.13287e35			1.25026
$627$			9.09651e32i			0.00984080i
$628$			5.61603e34i			0.595571i
$629$	2.06941e34			0.215137
$630$	−2.31136e34	−	9.65449e33i	−0.235565	−	0.0983948i
$631$	−9.95340e34			−0.994499			−0.497250	−	0.867607i	$-0.665657\pi$
$631$	−9.95340e34			−0.994499			−0.497250	+	0.867607i	$0.665657\pi$
$632$			2.35841e34i			0.231023i
$633$		−	1.85531e34i		−	0.178184i
$634$	−3.32899e34			−0.313471
$635$	−6.22516e34	+	1.49035e35i	−0.574750	+	1.37599i
$636$	1.02989e34			0.0932342
$637$		−	1.08937e35i		−	0.967013i
$638$			2.01244e33i			0.0175172i
$639$	−1.51153e34			−0.129020
$640$	4.06992e33	−	9.74369e33i	0.0340672	−	0.0815594i
$641$	2.11836e33			0.0173890			0.00869452	−	0.999962i	$-0.497232\pi$
$641$	2.11836e33			0.0173890			0.00869452	+	0.999962i	$0.497232\pi$
$642$			1.09001e34i			0.0877491i
$643$			5.48861e34i			0.433336i	0.976245	+	0.216668i	$0.0695190\pi$
$643$			5.48861e34i			0.433336i	−0.976245	+	0.216668i	$0.930481\pi$
$644$	−3.62647e34			−0.280809
$645$	−1.72073e34	−	7.18746e33i	−0.130682	−	0.0545857i
$646$	4.19268e34			0.312310
$647$			8.23657e34i			0.601787i	0.953658	+	0.300894i	$0.0972849\pi$
$647$			8.23657e34i			0.601787i	−0.953658	+	0.300894i	$0.902715\pi$
$648$		−	4.69692e34i		−	0.336609i
$649$	−1.92269e32			−0.00135161
$650$	8.05423e34	+	8.15050e34i	0.555402	+	0.562040i
$651$	4.71387e33			0.0318871
$652$		−	1.41376e34i		−	0.0938170i
$653$			2.06557e35i			1.34470i	0.740235	+	0.672349i	$0.234714\pi$
$653$			2.06557e35i			1.34470i	−0.740235	+	0.672349i	$0.765286\pi$
$654$	−1.51885e34			−0.0970050
$655$	−1.10705e35	−	4.62413e34i	−0.693667	−	0.289743i
$656$	1.43517e34			0.0882276
$657$		−	2.90599e35i		−	1.75278i
$658$		−	5.37919e34i		−	0.318341i
$659$	1.48751e35			0.863756			0.431878	−	0.901932i	$-0.357851\pi$
$659$	1.48751e35			0.863756			0.431878	+	0.901932i	$0.357851\pi$
$660$	1.92676e32	−	4.61280e32i	0.00109781	−	0.00262825i
$661$	1.93614e35			1.08248			0.541238	−	0.840869i	$-0.317956\pi$
$661$	1.93614e35			1.08248			0.541238	+	0.840869i	$0.317956\pi$
$662$		−	1.32989e35i		−	0.729610i
$663$		−	6.72555e33i		−	0.0362084i
$664$	4.71236e34			0.248965
$665$	−4.71198e34	+	1.12808e35i	−0.244305	+	0.584885i
$666$	−1.15056e35			−0.585438
$667$		−	1.68922e35i		−	0.843555i
$668$			5.18061e34i			0.253907i
$669$	−4.36802e34			−0.210116
$670$	1.30483e35	+	5.45023e34i	0.616052	+	0.257324i
$671$	−2.54886e33			−0.0118118
$672$		−	1.80721e33i		−	0.00822039i
$673$		−	2.68004e35i		−	1.19661i	−0.801268	−	0.598305i	$-0.795841\pi$
$673$		−	2.68004e35i		−	1.19661i	0.801268	−	0.598305i	$-0.204159\pi$
$674$	−2.52357e35			−1.10603
$675$	−4.15685e34	+	4.10775e34i	−0.178841	+	0.176729i
$676$	2.94452e34			0.124360
$677$		−	2.37470e35i		−	0.984578i	−0.870432	−	0.492289i	$-0.836160\pi$
$677$		−	2.37470e35i		−	0.984578i	0.870432	−	0.492289i	$-0.163840\pi$
$678$		−	4.55170e33i		−	0.0185269i
$679$	−3.89878e34			−0.155796
$680$	−2.12609e34	−	8.88064e33i	−0.0834105	−	0.0348404i
$681$	3.61039e34			0.139064
$682$		−	5.76322e33i		−	0.0217952i
$683$		−	2.30743e35i		−	0.856779i	−0.903594	−	0.428390i	$-0.859081\pi$
$683$		−	2.30743e35i		−	0.856779i	0.903594	−	0.428390i	$-0.140919\pi$
$684$	−2.33106e35			−0.849868
$685$	−7.20492e33	+	1.72491e34i	−0.0257927	+	0.0617497i
$686$	−1.37682e35			−0.483980
$687$		−	5.08880e34i		−	0.175653i
$688$			8.24222e34i			0.279376i
$689$	4.93957e35			1.64418
$690$	−1.61730e34	+	3.87194e34i	−0.0528662	+	0.126566i
$691$	−1.65717e35			−0.531974			−0.265987	−	0.963977i	$-0.585698\pi$
$691$	−1.65717e35			−0.531974			−0.265987	+	0.963977i	$0.585698\pi$
$692$		−	1.63795e35i		−	0.516385i
$693$			5.24131e33i			0.0162283i
$694$	−3.41774e35			−1.03931
$695$	1.40589e35	+	5.87239e34i	0.419897	+	0.175390i
$696$	8.41804e33			0.0246942
$697$		−	3.13156e34i		−	0.0902301i
$698$			4.39545e35i			1.24397i
$699$	−2.37842e34			−0.0661185
$700$	4.77885e34	−	4.72241e34i	0.130496	−	0.128955i
$701$	−4.91864e35			−1.31938			−0.659690	−	0.751538i	$-0.729312\pi$
$701$	−4.91864e35			−1.31938			−0.659690	+	0.751538i	$0.729312\pi$
$702$			7.53961e34i			0.198671i
$703$			5.61542e35i			1.45359i
$704$	−2.20951e33			−0.00561873
$705$	−5.74330e34	−	2.39897e34i	−0.143482	−	0.0599322i
$706$	4.30649e35			1.05697
$707$		−	1.13691e35i		−	0.274146i
$708$			8.04263e32i			0.00190538i
$709$	7.85100e35			1.82746			0.913728	−	0.406326i	$-0.133190\pi$
$709$	7.85100e35			1.82746			0.913728	+	0.406326i	$0.133190\pi$
$710$	1.56258e34	−	3.74094e34i	0.0357366	−	0.0855562i
$711$	−2.86114e35			−0.642937
$712$		−	2.95215e35i		−	0.651837i
$713$			4.83759e35i			1.04957i
$714$	−3.94337e33			−0.00840697
$715$	9.24117e33	−	2.21240e34i	0.0193598	−	0.0463489i
$716$	−2.48361e35			−0.511294
$717$			8.39197e34i			0.169775i
$718$		−	4.73262e35i		−	0.940906i
$719$	−2.69785e33			−0.00527118			−0.00263559	−	0.999997i	$-0.500839\pi$
$719$	−2.69785e33			−0.00527118			−0.00263559	+	0.999997i	$0.500839\pi$
$720$	1.18207e35	+	4.93748e34i	0.226980	+	0.0948089i
$721$	1.42823e35			0.269530
$722$			7.56456e35i			1.40304i
$723$		−	6.94021e33i		−	0.0126516i
$724$	−2.01648e35			−0.361295
$725$	2.19971e35	+	2.22600e35i	0.387383	+	0.392013i
$726$	5.16659e34			0.0894326
$727$			5.83647e35i			0.993048i	0.868023	+	0.496524i	$0.165391\pi$
$727$			5.83647e35i			0.993048i	−0.868023	+	0.496524i	$0.834609\pi$
$728$		−	8.66778e34i		−	0.144966i
$729$	5.50432e35			0.904918
$730$	7.19214e35	+	3.00414e35i	1.16231	+	0.485495i
$731$	1.79847e35			0.285717
$732$			1.06619e34i			0.0166512i
$733$		−	6.31572e35i		−	0.969668i	−0.874606	−	0.484834i	$-0.838880\pi$
$733$		−	6.31572e35i		−	0.969668i	0.874606	−	0.484834i	$-0.161120\pi$
$734$	−2.31488e35			−0.349405
$735$	−2.84854e34	+	6.81961e34i	−0.0422698	+	0.101197i
$736$	1.85464e35			0.270575
$737$		−	2.95887e34i		−	0.0424406i
$738$			1.74109e35i			0.245537i
$739$	−6.44973e35			−0.894305			−0.447153	−	0.894458i	$-0.647562\pi$
$739$	−6.44973e35			−0.894305			−0.447153	+	0.894458i	$0.647562\pi$
$740$	1.18942e35	−	2.84756e35i	0.162158	−	0.388219i
$741$	1.82500e35			0.244644
$742$		−	2.89620e35i		−	0.381750i
$743$		−	5.26299e35i		−	0.682138i	−0.940038	−	0.341069i	$-0.889211\pi$
$743$		−	5.26299e35i		−	0.682138i	0.940038	−	0.341069i	$-0.110789\pi$
$744$	−2.41076e34			−0.0307250
$745$	−7.19872e35	−	3.00689e35i	−0.902198	−	0.376846i
$746$	5.78040e34			0.0712398
$747$			5.71687e35i			0.692868i
$748$			4.82119e33i			0.00574625i
$749$	3.06527e35			0.359291
$750$	−2.91083e34	−	7.20839e34i	−0.0335545	−	0.0830946i
$751$	−1.61425e36			−1.83009			−0.915044	−	0.403355i	$-0.867844\pi$
$751$	−1.61425e36			−1.83009			−0.915044	+	0.403355i	$0.867844\pi$
$752$			2.75101e35i			0.306740i
$753$		−	1.30294e35i		−	0.142885i
$754$	4.03748e35			0.435481
$755$	−1.26552e36	−	5.28604e35i	−1.34255	−	0.560781i
$756$	4.42067e34			0.0461281
$757$			6.23656e35i			0.640098i	0.947401	+	0.320049i	$0.103699\pi$
$757$			6.23656e35i			0.640098i	−0.947401	+	0.320049i	$0.896301\pi$
$758$		−	1.06625e36i		−	1.07645i
$759$	8.78014e33			0.00871926
$760$	2.40979e35	−	5.76922e35i	0.235402	−	0.563569i
$761$	4.69451e35			0.451110			0.225555	−	0.974230i	$-0.427580\pi$
$761$	4.69451e35			0.451110			0.225555	+	0.974230i	$0.427580\pi$
$762$		−	1.41367e35i		−	0.133633i
$763$			4.27125e35i			0.397190i
$764$	−1.45439e35			−0.133050
$765$	1.07737e35	−	2.57930e35i	0.0969608	−	0.232131i
$766$	9.11195e35			0.806774
$767$			3.85743e34i			0.0336013i
$768$			9.24240e33i			0.00792081i
$769$	−1.07024e36			−0.902402			−0.451201	−	0.892422i	$-0.649004\pi$
$769$	−1.07024e36			−0.902402			−0.451201	+	0.892422i	$0.649004\pi$
$770$	−1.29719e34	−	5.41834e33i	−0.0107614	−	0.00449502i
$771$	2.60529e35			0.212655
$772$			2.68814e35i			0.215891i
$773$		−	1.40143e36i		−	1.10746i	−0.832695	−	0.553732i	$-0.813203\pi$
$773$		−	1.40143e36i		−	1.10746i	0.832695	−	0.553732i	$-0.186797\pi$
$774$	−9.99916e35			−0.777502
$775$	−6.29954e35	−	6.37484e35i	−0.481989	−	0.487751i
$776$	1.99390e35			0.150118
$777$		−	5.28151e34i		−	0.0391287i
$778$		−	1.16154e35i		−	0.0846816i
$779$	8.49760e35			0.609646
$780$	−9.25451e34	−	3.86559e34i	−0.0653387	−	0.0272919i
$781$	−8.48308e33			−0.00589407
$782$		−	4.04686e35i		−	0.276716i
$783$			2.05916e35i			0.138570i
$784$	3.26656e35			0.216341
$785$	7.04329e35	−	1.68622e36i	0.459097	−	1.09911i
$786$	1.05010e35			0.0673670
$787$			2.04262e36i			1.28974i	0.764292	+	0.644870i	$0.223089\pi$
$787$			2.04262e36i			1.28974i	−0.764292	+	0.644870i	$0.776911\pi$
$788$			1.12362e36i			0.698300i
$789$	1.95267e35			0.119444
$790$	2.95777e35	−	7.08113e35i	0.178085	−	0.426348i
$791$	−1.28001e35			−0.0758589
$792$		−	2.68050e34i		−	0.0156369i
$793$			5.11369e35i			0.293643i
$794$	−8.10456e35			−0.458114
$795$	−3.09224e35	−	1.29162e35i	−0.172062	−	0.0718698i
$796$	3.05071e35			0.167104
$797$			4.60347e35i			0.248231i	0.992268	+	0.124115i	$0.0396093\pi$
$797$			4.60347e35i			0.248231i	−0.992268	+	0.124115i	$0.960391\pi$
$798$		−	1.07005e35i		−	0.0568023i
$799$	6.00276e35			0.313701
$800$	−2.44399e35	+	2.41512e35i	−0.125740	+	0.124255i
$801$	3.58145e36			1.81406
$802$			2.42417e36i			1.20888i
$803$		−	1.63091e35i		−	0.0800731i
$804$	−1.23770e35			−0.0598292
$805$	1.08885e36	+	4.54810e35i	0.518226	+	0.216462i
$806$	−1.15625e36			−0.541833
$807$			1.77132e35i			0.0817294i
$808$			5.81435e35i			0.264155i
$809$	−2.81919e35			−0.126115			−0.0630576	−	0.998010i	$-0.520085\pi$
$809$	−2.81919e35			−0.126115			−0.0630576	+	0.998010i	$0.520085\pi$
$810$	−5.89060e35	+	1.41025e36i	−0.259476	+	0.621204i
$811$	8.66756e35			0.375955			0.187978	−	0.982173i	$-0.439807\pi$
$811$	8.66756e35			0.375955			0.187978	+	0.982173i	$0.439807\pi$
$812$		−	2.36728e35i		−	0.101111i
$813$			4.35812e35i			0.183302i
$814$	−6.45722e34			−0.0267449
$815$	−1.77306e35	+	4.24483e35i	−0.0723190	+	0.173137i
$816$	2.01671e34			0.00810058
$817$			4.88020e36i			1.93047i
$818$		−	2.08936e36i		−	0.813950i
$819$	1.05154e36			0.403440
$820$	−4.30910e35	−	1.79990e35i	−0.162822	−	0.0680105i
$821$	−2.61490e36			−0.973120			−0.486560	−	0.873647i	$-0.661748\pi$
$821$	−2.61490e36			−0.973120			−0.486560	+	0.873647i	$0.661748\pi$
$822$		−	1.63617e34i		−	0.00599695i
$823$			3.63703e35i			0.131295i	0.997843	+	0.0656477i	$0.0209113\pi$
$823$			3.63703e35i			0.131295i	−0.997843	+	0.0656477i	$0.979089\pi$
$824$	−7.30422e35			−0.259707
$825$	−1.15702e34	+	1.14335e34i	−0.00405198	+	0.00400412i
$826$	2.26171e34			0.00780165
$827$		−	3.87599e36i		−	1.31693i	−0.752610	−	0.658467i	$-0.771205\pi$
$827$		−	3.87599e36i		−	1.31693i	0.752610	−	0.658467i	$-0.228795\pi$
$828$			2.24998e36i			0.753009i
$829$	−1.44009e36			−0.474743			−0.237371	−	0.971419i	$-0.576286\pi$
$829$	−1.44009e36			−0.474743			−0.237371	+	0.971419i	$0.576286\pi$
$830$	−1.41489e36	−	5.90996e35i	−0.459458	−	0.191915i
$831$	5.69832e35			0.182278
$832$			4.43286e35i			0.139683i
$833$		−	7.12769e35i		−	0.221252i
$834$	−1.33356e35			−0.0407792
$835$	6.49722e35	−	1.55548e36i	0.195725	−	0.468580i
$836$	−1.30825e35			−0.0388250
$837$		−	5.89704e35i		−	0.172411i
$838$		−	1.41577e36i		−	0.407795i
$839$	2.94352e36			0.835300			0.417650	−	0.908608i	$-0.362854\pi$
$839$	2.94352e36			0.835300			0.417650	+	0.908608i	$0.362854\pi$
$840$	−2.26649e34	+	5.42616e34i	−0.00633671	+	0.0151705i
$841$	−2.52767e36			−0.696260
$842$			4.72088e34i			0.0128121i
$843$			4.75800e35i			0.127227i
$844$	2.66828e36			0.702992
$845$	−8.84095e35	−	3.69284e35i	−0.229504	−	0.0958632i
$846$	−3.33743e36			−0.853656
$847$		−	1.45292e36i		−	0.366184i
$848$			1.48117e36i			0.367837i
$849$	−1.02413e36			−0.250616
$850$	5.26985e35	+	5.33284e35i	0.127075	+	0.128594i
$851$	5.42013e36			1.28792
$852$			3.54848e34i			0.00830897i
$853$		−	1.60861e36i		−	0.371183i	−0.982627	−	0.185591i	$-0.940580\pi$
$853$		−	1.60861e36i		−	0.371183i	0.982627	−	0.185591i	$-0.0594201\pi$
$854$	2.99829e35			0.0681789
$855$	6.99901e36	+	2.92347e36i	1.56841	+	0.655123i
$856$	−1.56764e36			−0.346197
$857$		−	7.04998e36i		−	1.53436i	−0.641432	−	0.767180i	$-0.721659\pi$
$857$		−	7.04998e36i		−	1.53436i	0.641432	−	0.767180i	$-0.278341\pi$
$858$			2.09858e34i			0.00450127i
$859$	−6.59563e36			−1.39425			−0.697126	−	0.716948i	$-0.745538\pi$
$859$	−6.59563e36			−1.39425			−0.697126	+	0.716948i	$0.745538\pi$
$860$	1.03369e36	−	2.47473e36i	0.215357	−	0.515581i
$861$	−7.99230e34			−0.0164109
$862$		−	4.61133e36i		−	0.933222i
$863$		−	9.41312e36i		−	1.87758i	−0.344487	−	0.938791i	$-0.611947\pi$
$863$		−	9.41312e36i		−	1.87758i	0.344487	−	0.938791i	$-0.388053\pi$
$864$	−2.26081e35			−0.0444470
$865$	−2.05422e36	+	4.91795e36i	−0.398056	+	0.952977i
$866$	−2.17542e36			−0.415499
$867$			6.29170e35i			0.118448i
$868$			6.77942e35i			0.125805i
$869$	−1.60574e35			−0.0293716
$870$	−2.52752e35	−	1.05574e35i	−0.0455727	−	0.0190356i
$871$	−5.93627e36			−1.05508
$872$		−	2.18439e36i		−	0.382714i
$873$			2.41893e36i			0.417778i
$874$	1.09813e37			1.86965
$875$	−2.02711e36	+	8.18570e35i	−0.340233	+	0.137390i
$876$	−6.82212e35			−0.112880
$877$		−	4.23262e36i		−	0.690422i	−0.938525	−	0.345211i	$-0.887807\pi$
$877$		−	4.23262e36i		−	0.690422i	0.938525	−	0.345211i	$-0.112193\pi$
$878$		−	3.23521e36i		−	0.520261i
$879$	−4.69029e35			−0.0743598
$880$	6.63407e34	+	2.77104e34i	0.0103692	+	0.00433121i
$881$	−9.23339e36			−1.42286			−0.711431	−	0.702756i	$-0.751952\pi$
$881$	−9.23339e36			−1.42286			−0.711431	+	0.702756i	$0.751952\pi$
$882$			3.96287e36i			0.602078i
$883$			9.76831e36i			1.46322i	0.681721	+	0.731612i	$0.261232\pi$
$883$			9.76831e36i			1.46322i	−0.681721	+	0.731612i	$0.738768\pi$
$884$	9.67259e35			0.142853
$885$	1.00866e34	−	2.41481e34i	0.00146877	−	0.00351634i
$886$	7.48575e36			1.07477
$887$			1.62985e36i			0.230729i	0.993323	+	0.115365i	$0.0368036\pi$
$887$			1.62985e36i			0.230729i	−0.993323	+	0.115365i	$0.963196\pi$
$888$			2.70106e35i			0.0377027i
$889$	−3.97547e36			−0.547162
$890$	−3.70242e36	+	8.86386e36i	−0.502470	+	1.20295i
$891$	3.19794e35			0.0427955
$892$		−	6.28202e36i		−	0.828970i
$893$			1.62887e37i			2.11955i
$894$	6.82836e35			0.0876188
$895$	7.45706e36	+	3.11480e36i	0.943582	+	0.394132i
$896$	2.59910e35			0.0324320
$897$		−	1.76153e36i		−	0.216763i
$898$			3.41071e35i			0.0413895i
$899$	−3.15788e36			−0.377919
$900$	−2.92994e36	−	2.96496e36i	−0.345802	−	0.349935i
$901$	3.23194e36			0.376186
$902$			9.77145e34i			0.0112170i
$903$		−	4.59000e35i		−	0.0519656i
$904$	6.54619e35			0.0730943
$905$	6.05450e36	+	2.52895e36i	0.666763	+	0.278505i
$906$	1.20041e36			0.130385
$907$		−	4.47773e36i		−	0.479697i	−0.970810	−	0.239848i	$-0.922902\pi$
$907$		−	4.47773e36i		−	0.479697i	0.970810	−	0.239848i	$-0.0770977\pi$
$908$			5.19241e36i			0.548651i
$909$	−7.05376e36			−0.735144
$910$	−1.08706e36	+	2.60251e36i	−0.111747	+	0.267531i
$911$	9.15716e36			0.928498			0.464249	−	0.885705i	$-0.346324\pi$
$911$	9.15716e36			0.928498			0.464249	+	0.885705i	$0.346324\pi$
$912$			5.47241e35i			0.0547322i
$913$			3.20845e35i			0.0316527i
$914$	8.28891e36			0.806622
$915$	1.33715e35	−	3.20124e35i	0.0128356	−	0.0307295i
$916$	7.31864e36			0.693006
$917$		−	2.95303e36i		−	0.275836i
$918$			4.93313e35i			0.0454558i
$919$	−1.60416e36			−0.145816			−0.0729078	−	0.997339i	$-0.523228\pi$
$919$	−1.60416e36			−0.145816			−0.0729078	+	0.997339i	$0.523228\pi$
$920$	−5.56857e36	−	2.32598e36i	−0.499340	−	0.208573i
$921$	3.74270e34			0.00331085
$922$		−	3.43100e36i		−	0.299422i
$923$			1.70193e36i			0.146528i
$924$	1.23045e34			0.00104512
$925$	−7.14248e36	+	7.05812e36i	−0.598518	+	0.591449i
$926$	−1.38047e37			−1.14127
$927$		−	8.86121e36i		−	0.722764i
$928$			1.21067e36i			0.0974263i
$929$	8.64983e35			0.0686770			0.0343385	−	0.999410i	$-0.489068\pi$
$929$	8.64983e35			0.0686770			0.0343385	+	0.999410i	$0.489068\pi$
$930$	7.23832e35	+	3.02343e35i	0.0567024	+	0.0236845i
$931$	1.93412e37			1.49490
$932$		−	3.42060e36i		−	0.260858i
$933$		−	1.47826e36i		−	0.111232i
$934$	1.14510e37			0.850170
$935$	6.04646e34	−	1.44757e35i	0.00442951	−	0.0106046i
$936$	−5.37779e36			−0.388737
$937$			7.42933e36i			0.529913i	0.964260	+	0.264956i	$0.0853576\pi$
$937$			7.42933e36i			0.529913i	−0.964260	+	0.264956i	$0.914642\pi$
$938$			3.48059e36i			0.244972i
$939$	3.22644e36			0.224081
$940$	3.45016e36	−	8.25994e36i	0.236451	−	0.566081i
$941$	6.99775e36			0.473247			0.236623	−	0.971601i	$-0.423959\pi$
$941$	6.99775e36			0.473247			0.236623	+	0.971601i	$0.423959\pi$
$942$			1.59946e36i			0.106743i
$943$		−	8.20206e36i		−	0.540166i
$944$	−1.15668e35			−0.00751732
$945$	−1.32731e36	−	5.54414e35i	−0.0851284	−	0.0355580i
$946$	−5.61178e35			−0.0355190
$947$		−	9.94818e36i		−	0.621397i	−0.950509	−	0.310698i	$-0.899437\pi$
$947$		−	9.94818e36i		−	0.621397i	0.950509	−	0.310698i	$-0.100563\pi$
$948$			6.71682e35i			0.0414057i
$949$	−3.27204e37			−1.99063
$950$	−1.44708e37	+	1.42999e37i	−0.868857	+	0.858594i
$951$	−9.48108e35			−0.0561825
$952$		−	5.67129e35i		−	0.0331681i
$953$		−	1.89836e37i		−	1.09577i	−0.836555	−	0.547883i	$-0.815434\pi$
$953$		−	1.89836e37i		−	1.09577i	0.836555	−	0.547883i	$-0.184566\pi$
$954$	−1.79690e37			−1.02369
$955$	4.36682e36	+	1.82401e36i	0.245540	+	0.102562i
$956$	−1.20692e37			−0.669816
$957$			5.73149e34i			0.00313956i
$958$		−	2.47068e37i		−	1.33582i
$959$	−4.60115e35			−0.0245547
$960$	1.15913e35	−	2.77504e35i	0.00610577	−	0.0146177i
$961$	−1.01893e37			−0.529785
$962$			1.29549e37i			0.664883i
$963$		−	1.90180e37i		−	0.963466i
$964$	9.98131e35			0.0499142
$965$	3.37130e36	−	8.07114e36i	0.166420	−	0.398422i
$966$	−1.03283e36			−0.0503286
$967$		−	1.99094e37i		−	0.957693i	−0.877899	−	0.478846i	$-0.841055\pi$
$967$		−	1.99094e37i		−	0.957693i	0.877899	−	0.478846i	$-0.158945\pi$
$968$			7.43051e36i			0.352839i
$969$	1.19409e36			0.0559744
$970$	−5.98671e36	−	2.50064e36i	−0.277039	−	0.115719i
$971$	1.95878e37			0.894841			0.447421	−	0.894324i	$-0.352343\pi$
$971$	1.95878e37			0.894841			0.447421	+	0.894324i	$0.352343\pi$
$972$		−	4.12521e36i		−	0.186045i
$973$			3.75018e36i			0.166971i
$974$	1.08023e37			0.474822
$975$	2.29387e36	+	2.32129e36i	0.0995432	+	0.100733i
$976$	−1.53338e36			−0.0656942
$977$			2.97587e37i			1.25873i	0.777110	+	0.629365i	$0.216685\pi$
$977$			2.97587e37i			1.25873i	−0.777110	+	0.629365i	$0.783315\pi$
$978$		−	4.02644e35i		−	0.0168146i
$979$	2.01000e36			0.0828727
$980$	−9.80786e36	−	4.09672e36i	−0.399253	−	0.166767i
$981$	2.65003e37			1.06509
$982$			1.88156e37i			0.746663i
$983$			4.05260e37i			1.58787i	0.608004	+	0.793934i	$0.291970\pi$
$983$			4.05260e37i			1.58787i	−0.608004	+	0.793934i	$0.708030\pi$
$984$	4.08741e35			0.0158128
$985$	1.40918e37	−	3.37368e37i	0.538286	−	1.28870i
$986$	2.64171e36			0.0996376
$987$		−	1.53201e36i		−	0.0570555i
$988$			2.62469e37i			0.965197i
$989$	4.71047e37			1.71045
$990$	−3.36172e35	+	8.04821e35i	−0.0120537	+	0.0288576i
$991$	−3.58276e37			−1.26852			−0.634260	−	0.773120i	$-0.718695\pi$
$991$	−3.58276e37			−1.26852			−0.634260	+	0.773120i	$0.718695\pi$
$992$		−	3.46712e36i		−	0.121220i
$993$		−	3.78757e36i		−	0.130766i
$994$	9.97886e35			0.0340213
$995$	−9.15977e36	−	3.82602e36i	−0.308387	−	0.128813i
$996$	1.34210e36			0.0446213
$997$			9.64459e36i			0.316661i	0.987386	+	0.158330i	$0.0506111\pi$
$997$			9.64459e36i			0.316661i	−0.987386	+	0.158330i	$0.949389\pi$
$998$		−	1.75638e37i		−	0.569491i
$999$	−6.60714e36			−0.211566

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.26.b.a.9.9	yes	12
5.2	odd	4		50.26.a.k.1.3		6
5.3	odd	4		50.26.a.l.1.4		6
5.4	even	2	inner	10.26.b.a.9.4	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.26.b.a.9.4	✓	12	5.4	even	2	inner
10.26.b.a.9.9	yes	12	1.1	even	1	trivial
50.26.a.k.1.3		6	5.2	odd	4
50.26.a.l.1.4		6	5.3	odd	4

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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	10.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+4096.00i q^{2} +116655. i q^{3} -1.67772e7 q^{4} +(5.03737e8 + 2.10410e8i) q^{5} -4.77821e8 q^{6} +1.34370e10i q^{7} -6.87195e10i q^{8} +8.33680e11 q^{9} +(-8.61839e11 + 2.06331e12i) q^{10} +4.67882e11 q^{11} -1.95715e12i q^{12} -9.38695e13i q^{13} -5.50381e13 q^{14} +(-2.45455e13 + 5.87637e13i) q^{15} +2.81475e14 q^{16} -6.14184e14i q^{17} +3.41475e15i q^{18} +1.66661e16 q^{19} +(-8.45130e15 - 3.53009e15i) q^{20} -1.56750e15 q^{21} +1.91644e15i q^{22} -1.60865e17i q^{23} +8.01650e15 q^{24} +(2.09479e17 + 2.11982e17i) q^{25} +3.84489e17 q^{26} +1.96094e17i q^{27} -2.25436e17i q^{28} +1.05009e18 q^{29} +(-2.40696e17 - 1.00538e17i) q^{30} -3.00725e18 q^{31} +1.15292e18i q^{32} +5.45810e16i q^{33} +2.51570e18 q^{34} +(-2.82729e18 + 6.76873e18i) q^{35} -1.39868e19 q^{36} +3.36937e19i q^{37} +6.82643e19i q^{38} +1.09504e19 q^{39} +(1.44593e19 - 3.46165e19i) q^{40} +5.09874e19 q^{41} -6.42050e18i q^{42} +2.92822e20i q^{43} -7.84976e18 q^{44} +(4.19955e20 + 1.75415e20i) q^{45} +6.58901e20 q^{46} +9.77356e20i q^{47} +3.28356e19i q^{48} +1.16051e21 q^{49} +(-8.68280e20 + 8.58024e20i) q^{50} +7.16479e19 q^{51} +1.57487e21i q^{52} +5.26216e21i q^{53} -8.03202e20 q^{54} +(2.35689e20 + 9.84470e19i) q^{55} +9.23387e20 q^{56} +1.94419e21i q^{57} +4.30117e21i q^{58} -4.10935e20 q^{59} +(4.11804e20 - 9.85891e20i) q^{60} -5.44766e21 q^{61} -1.23177e22i q^{62} +1.12022e22i q^{63} -4.72237e21 q^{64} +(1.97511e22 - 4.72855e22i) q^{65} -2.23564e20 q^{66} -6.32396e22i q^{67} +1.03043e22i q^{68} +1.87657e22 q^{69} +(-2.77247e22 - 1.15806e22i) q^{70} -1.81308e22 q^{71} -5.72901e22i q^{72} -3.48574e23i q^{73} -1.38010e23 q^{74} +(-2.47289e22 + 2.44368e22i) q^{75} -2.79610e23 q^{76} +6.28695e21i q^{77} +4.48528e22i q^{78} -3.43193e23 q^{79} +(1.41789e23 + 5.92251e22i) q^{80} +6.83492e23 q^{81} +2.08844e23i q^{82} +6.85739e23i q^{83} +2.62984e22 q^{84} +(1.29230e23 - 3.09387e23i) q^{85} -1.19940e24 q^{86} +1.22499e23i q^{87} -3.21526e22i q^{88} +4.29595e24 q^{89} +(-7.18498e23 + 1.72014e24i) q^{90} +1.26133e24 q^{91} +2.69886e24i q^{92} -3.50812e23i q^{93} -4.00325e24 q^{94} +(8.39532e24 + 3.50671e24i) q^{95} -1.34495e23 q^{96} +2.90151e24i q^{97} +4.75347e24i q^{98} +3.90064e23 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 201326592 q^{4} - 490295340 q^{5} - 6565199872 q^{6} - 1082937564236 q^{9} + 1636528619520 q^{10} + 19723089228624 q^{11} + 278591122243584 q^{14} - 449884766537680 q^{15} + 33\!\cdots\!72 q^{16}+ \cdots + 41\!\cdots\!28 q^{99}+O(q^{100}) \) 12 * q - 201326592 * q^4 - 490295340 * q^5 - 6565199872 * q^6 - 1082937564236 * q^9 + 1636528619520 * q^10 + 19723089228624 * q^11 + 278591122243584 * q^14 - 449884766537680 * q^15 + 3377699720527872 * q^16 - 4015312977833040 * q^19 + 8225790822973440 * q^20 - 56363420582029456 * q^21 + 110145776335716352 * q^24 - 1047554086248996900 * q^25 - 252210272532037632 * q^26 + 5852064063311009640 * q^29 - 3747916483574824960 * q^30 + 158585871554029824 * q^31 + 28121800210885115904 * q^34 - 42730948507221221040 * q^35 + 18168677429701246976 * q^36 - 249453273245123586912 * q^39 - 27456394139868856320 * q^40 + 206458603439752488024 * q^41 - 330898528175898230784 * q^44 + 957114913653485255020 * q^45 - 1111751773656740462592 * q^46 - 3432561496278055389084 * q^49 + 346631457781510963200 * q^50 - 3032451787323924027136 * q^51 + 6455741354411915345920 * q^54 - 7824754202169531625680 * q^55 - 4673983433563013382144 * q^56 + 24998150261761560337680 * q^59 + 7547813903312229498880 * q^60 + 7374571220622236593224 * q^61 - 56668397794435742564352 * q^64 + 20652620138653742557920 * q^65 + 56072959085731865952256 * q^66 - 370250651964757999709072 * q^69 + 157367128964587932549120 * q^70 + 149137752442507323299424 * q^71 + 27409492362780459270144 * q^74 + 1032897211530510645911200 * q^75 + 67365773136708124016640 * q^76 + 801700633747623249599040 * q^79 - 138005869407843165143040 * q^80 - 2864220237232227656687428 * q^81 + 945621281603553901674496 * q^84 + 2004099032091709203221760 * q^85 - 1363071174568488987328512 * q^86 - 5964345056120682049233480 * q^89 + 4840324611668628597309440 * q^90 - 14003423438242038482629536 * q^91 + 3325183945859356082110464 * q^94 + 18644670331946084490382800 * q^95 - 1847939481072001752236032 * q^96 + 4107440578564823447146928 * q^99

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