LMFDB - Embedded newform 10.26.b.a.9.12

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			9.12
Root			$737346. i$ of defining polynomial
Character	$\chi$	$=$	10.9
Dual form			10.26.b.a.9.1

$q$-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} +1.47469e6i q^{3} -1.67772e7 q^{4} +(-2.33061e8 + 4.93666e8i) q^{5} -6.04034e9 q^{6} +3.57876e9i q^{7} -6.87195e10i q^{8} -1.32743e12 q^{9} +(-2.02205e12 - 9.54619e11i) q^{10} +1.08564e12 q^{11} -2.47412e13i q^{12} -2.13293e13i q^{13} -1.46586e13 q^{14} +(-7.28005e14 - 3.43694e14i) q^{15} +2.81475e14 q^{16} -3.79275e15i q^{17} -5.43715e15i q^{18} -6.90611e15 q^{19} +(3.91012e15 - 8.28233e15i) q^{20} -5.27758e15 q^{21} +4.44680e15i q^{22} +1.56245e17i q^{23} +1.01340e17 q^{24} +(-1.89388e17 - 2.30109e17i) q^{25} +8.73648e16 q^{26} -7.08060e17i q^{27} -6.00417e16i q^{28} -6.08503e17 q^{29} +(1.40777e18 - 2.98191e18i) q^{30} -3.42961e18 q^{31} +1.15292e18i q^{32} +1.60099e18i q^{33} +1.55351e19 q^{34} +(-1.76671e18 - 8.34071e17i) q^{35} +2.22706e19 q^{36} +7.61614e19i q^{37} -2.82874e19i q^{38} +3.14542e19 q^{39} +(3.39244e19 + 1.60158e19i) q^{40} +2.17158e20 q^{41} -2.16169e19i q^{42} -4.70339e20i q^{43} -1.82141e19 q^{44} +(3.09372e20 - 6.55306e20i) q^{45} -6.39979e20 q^{46} -6.53190e20i q^{47} +4.15089e20i q^{48} +1.32826e21 q^{49} +(9.42525e20 - 7.75734e20i) q^{50} +5.59313e21 q^{51} +3.57846e20i q^{52} +4.54358e21i q^{53} +2.90021e21 q^{54} +(-2.53021e20 + 5.35945e20i) q^{55} +2.45931e20 q^{56} -1.01844e22i q^{57} -2.49243e21i q^{58} -1.39811e22 q^{59} +(1.22139e22 + 5.76622e21i) q^{60} -4.30120e21 q^{61} -1.40477e22i q^{62} -4.75056e21i q^{63} -4.72237e21 q^{64} +(1.05295e22 + 4.97103e21i) q^{65} -6.55766e21 q^{66} +3.04650e22i q^{67} +6.36317e22i q^{68} -2.30413e23 q^{69} +(3.41635e21 - 7.23645e21i) q^{70} -4.08644e22 q^{71} +9.12202e22i q^{72} +1.14063e23i q^{73} -3.11957e23 q^{74} +(3.39339e23 - 2.79289e23i) q^{75} +1.15865e23 q^{76} +3.88526e21i q^{77} +1.28836e23i q^{78} -6.98160e23 q^{79} +(-6.56009e22 + 1.38955e23i) q^{80} -8.05452e22 q^{81} +8.89479e23i q^{82} -1.18110e24i q^{83} +8.85430e22 q^{84} +(1.87235e24 + 8.83942e23i) q^{85} +1.92651e24 q^{86} -8.97354e23i q^{87} -7.46049e22i q^{88} -2.79755e24 q^{89} +(2.68413e24 + 1.26719e24i) q^{90} +7.63325e22 q^{91} -2.62136e24i q^{92} -5.05762e24i q^{93} +2.67546e24 q^{94} +(1.60955e24 - 3.40931e24i) q^{95} -1.70020e24 q^{96} -1.06166e25i q^{97} +5.44056e24i q^{98} -1.44112e24 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
$3$			1.47469e6i			1.60209i	0.598607	+	0.801043i	$0.295721\pi$
$3$			1.47469e6i			1.60209i	−0.598607	+	0.801043i	$0.704279\pi$
$4$	−1.67772e7			−0.500000
$5$	−2.33061e8	+	4.93666e8i	−0.426918	+	0.904290i
$5$	−2.33061e8	+	4.93666e8i	−0.426918	+	0.904290i
$6$	−6.04034e9			−1.13285
$7$			3.57876e9i			0.0977254i	0.998806	+	0.0488627i	$0.0155597\pi$
$7$			3.57876e9i			0.0977254i	−0.998806	+	0.0488627i	$0.984440\pi$
$8$		−	6.87195e10i		−	0.353553i
$9$	−1.32743e12			−1.56668
$10$	−2.02205e12	−	9.54619e11i	−0.639430	−	0.301877i
$11$	1.08564e12			0.104299			0.0521493	−	0.998639i	$-0.483393\pi$
$11$	1.08564e12			0.104299			0.0521493	+	0.998639i	$0.483393\pi$
$12$		−	2.47412e13i		−	0.801043i
$13$		−	2.13293e13i		−	0.253913i	−0.991908	−	0.126956i	$-0.959479\pi$
$13$		−	2.13293e13i		−	0.253913i	0.991908	−	0.126956i	$-0.0405208\pi$
$14$	−1.46586e13			−0.0691023
$15$	−7.28005e14	−	3.43694e14i	−1.44875	−	0.683960i
$16$	2.81475e14			0.250000
$17$		−	3.79275e15i		−	1.57886i	−0.613844	−	0.789428i	$-0.710377\pi$
$17$		−	3.79275e15i		−	1.57886i	0.613844	−	0.789428i	$-0.289623\pi$
$18$		−	5.43715e15i		−	1.10781i
$19$	−6.90611e15			−0.715836			−0.357918	−	0.933753i	$-0.616513\pi$
$19$	−6.90611e15			−0.715836			−0.357918	+	0.933753i	$0.616513\pi$
$20$	3.91012e15	−	8.28233e15i	0.213459	−	0.452145i
$21$	−5.27758e15			−0.156564
$22$			4.44680e15i			0.0737503i
$23$			1.56245e17i			1.48665i	0.668932	+	0.743324i	$0.266752\pi$
$23$			1.56245e17i			1.48665i	−0.668932	+	0.743324i	$0.733248\pi$
$24$	1.01340e17			0.566423
$25$	−1.89388e17	−	2.30109e17i	−0.635481	−	0.772116i
$26$	8.73648e16			0.179544
$27$		−	7.08060e17i		−	0.907868i
$28$		−	6.00417e16i		−	0.0488627i
$29$	−6.08503e17			−0.319365			−0.159683	−	0.987168i	$-0.551047\pi$
$29$	−6.08503e17			−0.319365			−0.159683	+	0.987168i	$0.551047\pi$
$30$	1.40777e18	−	2.98191e18i	0.483633	−	1.02442i
$31$	−3.42961e18			−0.782030			−0.391015	−	0.920384i	$-0.627876\pi$
$31$	−3.42961e18			−0.782030			−0.391015	+	0.920384i	$0.627876\pi$
$32$			1.15292e18i			0.176777i
$33$			1.60099e18i			0.167095i
$34$	1.55351e19			1.11642
$35$	−1.76671e18	−	8.34071e17i	−0.0883721	−	0.0417208i
$36$	2.22706e19			0.783339
$37$			7.61614e19i			1.90201i	0.309173	+	0.951006i	$0.399948\pi$
$37$			7.61614e19i			1.90201i	−0.309173	+	0.951006i	$0.600052\pi$
$38$		−	2.82874e19i		−	0.506172i
$39$	3.14542e19			0.406790
$40$	3.39244e19	+	1.60158e19i	0.319715	+	0.150938i
$41$	2.17158e20			1.50306			0.751532	−	0.659696i	$-0.229315\pi$
$41$	2.17158e20			1.50306			0.751532	+	0.659696i	$0.229315\pi$
$42$		−	2.16169e19i		−	0.110708i
$43$		−	4.70339e20i		−	1.79496i	−0.441052	−	0.897481i	$-0.645395\pi$
$43$		−	4.70339e20i		−	1.79496i	0.441052	−	0.897481i	$-0.354605\pi$
$44$	−1.82141e19			−0.0521493
$45$	3.09372e20	−	6.55306e20i	0.668844	−	1.41673i
$46$	−6.39979e20			−1.05122
$47$		−	6.53190e20i		−	0.820004i	−0.912085	−	0.410002i	$-0.865528\pi$
$47$		−	6.53190e20i		−	0.820004i	0.912085	−	0.410002i	$-0.134472\pi$
$48$			4.15089e20i			0.400521i
$49$	1.32826e21			0.990450
$50$	9.42525e20	−	7.75734e20i	0.545969	−	0.449353i
$51$	5.59313e21			2.52946
$52$			3.57846e20i			0.126956i
$53$			4.54358e21i			1.27043i	0.772336	+	0.635214i	$0.219088\pi$
$53$			4.54358e21i			1.27043i	−0.772336	+	0.635214i	$0.780912\pi$
$54$	2.90021e21			0.641960
$55$	−2.53021e20	+	5.35945e20i	−0.0445270	+	0.0943162i
$56$	2.45931e20			0.0345512
$57$		−	1.01844e22i		−	1.14683i
$58$		−	2.49243e21i		−	0.225825i
$59$	−1.39811e22			−1.02303			−0.511517	−	0.859273i	$-0.670916\pi$
$59$	−1.39811e22			−1.02303			−0.511517	+	0.859273i	$0.670916\pi$
$60$	1.22139e22	+	5.76622e21i	0.724375	+	0.341980i
$61$	−4.30120e21			−0.207475			−0.103738	−	0.994605i	$-0.533080\pi$
$61$	−4.30120e21			−0.207475			−0.103738	+	0.994605i	$0.533080\pi$
$62$		−	1.40477e22i		−	0.552979i
$63$		−	4.75056e21i		−	0.153104i
$64$	−4.72237e21			−0.125000
$65$	1.05295e22	+	4.97103e21i	0.229611	+	0.108400i
$66$	−6.55766e21			−0.118154
$67$			3.04650e22i			0.454848i	0.973796	+	0.227424i	$0.0730303\pi$
$67$			3.04650e22i			0.454848i	−0.973796	+	0.227424i	$0.926970\pi$
$68$			6.36317e22i			0.789428i
$69$	−2.30413e23			−2.38174
$70$	3.41635e21	−	7.23645e21i	0.0295010	−	0.0624885i
$71$	−4.08644e22			−0.295540			−0.147770	−	0.989022i	$-0.547209\pi$
$71$	−4.08644e22			−0.295540			−0.147770	+	0.989022i	$0.547209\pi$
$72$			9.12202e22i			0.553905i
$73$			1.14063e23i			0.582918i	0.956583	+	0.291459i	$0.0941408\pi$
$73$			1.14063e23i			0.582918i	−0.956583	+	0.291459i	$0.905859\pi$
$74$	−3.11957e23			−1.34493
$75$	3.39339e23	−	2.79289e23i	1.23700	−	1.01810i
$76$	1.15865e23			0.357918
$77$			3.88526e21i			0.0101926i
$78$			1.28836e23i			0.287644i
$79$	−6.98160e23			−1.32928			−0.664640	−	0.747164i	$-0.731415\pi$
$79$	−6.98160e23			−1.32928			−0.664640	+	0.747164i	$0.731415\pi$
$80$	−6.56009e22	+	1.38955e23i	−0.106730	+	0.226073i
$81$	−8.05452e22			−0.112196
$82$			8.89479e23i			1.06283i
$83$		−	1.18110e24i		−	1.21286i	−0.795139	−	0.606428i	$-0.792602\pi$
$83$		−	1.18110e24i		−	1.21286i	0.795139	−	0.606428i	$-0.207398\pi$
$84$	8.85430e22			0.0782822
$85$	1.87235e24	+	8.83942e23i	1.42774	+	0.674042i
$86$	1.92651e24			1.26923
$87$		−	8.97354e23i		−	0.511650i
$88$		−	7.46049e22i		−	0.0368751i
$89$	−2.79755e24			−1.20061			−0.600307	−	0.799770i	$-0.704955\pi$
$89$	−2.79755e24			−1.20061			−0.600307	+	0.799770i	$0.704955\pi$
$90$	2.68413e24	+	1.26719e24i	1.00178	+	0.472944i
$91$	7.63325e22			0.0248137
$92$		−	2.62136e24i		−	0.743324i
$93$		−	5.05762e24i		−	1.25288i
$94$	2.67546e24			0.579831
$95$	1.60955e24	−	3.40931e24i	0.305603	−	0.647323i
$96$	−1.70020e24			−0.283211
$97$		−	1.06166e25i		−	1.55360i	−0.629750	−	0.776798i	$-0.716843\pi$
$97$		−	1.06166e25i		−	1.55360i	0.629750	−	0.776798i	$-0.283157\pi$
$98$			5.44056e24i			0.700354i
$99$	−1.44112e24			−0.163403
$100$	3.17741e24	+	3.86058e24i	0.317741	+	0.386058i
$101$	7.61024e24			0.672019			0.336009	−	0.941859i	$-0.390923\pi$
$101$	7.61024e24			0.672019			0.336009	+	0.941859i	$0.390923\pi$
$102$			2.29095e25i			1.78860i
$103$			1.50264e25i			1.03846i	0.854635	+	0.519229i	$0.173781\pi$
$103$			1.50264e25i			1.03846i	−0.854635	+	0.519229i	$0.826219\pi$
$104$	−1.46574e24			−0.0897718
$105$	1.23000e24	−	2.60536e24i	0.0668403	−	0.141580i
$106$	−1.86105e25			−0.898328
$107$			3.03661e24i			0.130344i	0.997874	+	0.0651721i	$0.0207596\pi$
$107$			3.03661e24i			0.130344i	−0.997874	+	0.0651721i	$0.979240\pi$
$108$			1.18793e25i			0.453934i
$109$	3.16922e25			1.07925			0.539625	−	0.841906i	$-0.318566\pi$
$109$	3.16922e25			1.07925			0.539625	+	0.841906i	$0.318566\pi$
$110$	−2.19523e24	−	1.03638e24i	−0.0666917	−	0.0314854i
$111$	−1.12315e26			−3.04719
$112$			1.00733e24i			0.0244314i
$113$		−	6.24206e25i		−	1.35471i	−0.735655	−	0.677357i	$-0.763125\pi$
$113$		−	6.24206e25i		−	1.35471i	0.735655	−	0.677357i	$-0.236875\pi$
$114$	4.17152e25			0.810931
$115$	−7.71328e25	−	3.64146e25i	−1.34436	−	0.634677i
$116$	1.02090e25			0.159683
$117$			2.83131e25i			0.397800i
$118$		−	5.72664e25i		−	0.723394i
$119$	1.35733e25			0.154294
$120$	−2.36184e25	+	5.00281e25i	−0.241816	+	0.512211i
$121$	−1.07168e26			−0.989122
$122$		−	1.76177e25i		−	0.146707i
$123$			3.20241e26i			2.40804i
$124$	5.75393e25			0.391015
$125$	1.57736e26	−	3.98650e25i	0.969516	−	0.245029i
$126$	1.94583e25			0.108261
$127$		−	1.67435e26i		−	0.843917i	−0.906615	−	0.421959i	$-0.861343\pi$
$127$		−	1.67435e26i		−	0.843917i	0.906615	−	0.421959i	$-0.138657\pi$
$128$		−	1.93428e25i		−	0.0883883i
$129$	6.93606e26			2.87568
$130$	−2.03613e25	+	4.31290e25i	−0.0766504	+	0.162359i
$131$	−1.90057e26			−0.650118			−0.325059	−	0.945694i	$-0.605384\pi$
$131$	−1.90057e26			−0.650118			−0.325059	+	0.945694i	$0.605384\pi$
$132$		−	2.68602e25i		−	0.0835477i
$133$		−	2.47153e25i		−	0.0699553i
$134$	−1.24785e26			−0.321626
$135$	3.49545e26	+	1.65021e26i	0.820976	+	0.387586i
$136$	−2.60636e26			−0.558210
$137$		−	3.51717e26i		−	0.687364i	−0.939086	−	0.343682i	$-0.888326\pi$
$137$		−	3.51717e26i		−	0.687364i	0.939086	−	0.343682i	$-0.111674\pi$
$138$		−	9.43773e26i		−	1.68414i
$139$	−3.91803e26			−0.638827			−0.319414	−	0.947615i	$-0.603486\pi$
$139$	−3.91803e26			−0.638827			−0.319414	+	0.947615i	$0.603486\pi$
$140$	2.96405e25	+	1.39934e25i	0.0441861	+	0.0208604i
$141$	9.63254e26			1.31372
$142$		−	1.67381e26i		−	0.208978i
$143$		−	2.31560e25i		−	0.0264828i
$144$	−3.73638e26			−0.391670
$145$	1.41818e26	−	3.00397e26i	0.136343	−	0.288799i
$146$	−4.67201e26			−0.412186
$147$			1.95878e27i			1.58679i
$148$		−	1.27778e27i		−	0.951006i
$149$	−1.80648e27			−1.23596			−0.617979	−	0.786194i	$-0.712048\pi$
$149$	−1.80648e27			−1.23596			−0.617979	+	0.786194i	$0.712048\pi$
$150$	1.14397e27	+	1.38993e27i	0.719902	+	0.874689i
$151$	−1.68416e26			−0.0975373			−0.0487687	−	0.998810i	$-0.515530\pi$
$151$	−1.68416e26			−0.0975373			−0.0487687	+	0.998810i	$0.515530\pi$
$152$			4.74584e26i			0.253086i
$153$			5.03460e27i			2.47356i
$154$	−1.59140e25			−0.00720728
$155$	7.99309e26	−	1.69308e27i	0.333863	−	0.707182i
$156$	−5.27713e26			−0.203395
$157$		−	1.56946e27i		−	0.558475i	−0.960222	−	0.279237i	$-0.909918\pi$
$157$		−	1.56946e27i		−	0.558475i	0.960222	−	0.279237i	$-0.0900817\pi$
$158$		−	2.85967e27i		−	0.939943i
$159$	−6.70039e27			−2.03533
$160$	−5.69158e26	−	2.68701e26i	−0.159857	−	0.0754692i
$161$	−5.59164e26			−0.145283
$162$		−	3.29913e26i		−	0.0793345i
$163$			5.35307e27i			1.19195i	0.803004	+	0.595974i	$0.203234\pi$
$163$			5.35307e27i			1.19195i	−0.803004	+	0.595974i	$0.796766\pi$
$164$	−3.64331e27			−0.751532
$165$	−7.90354e26	−	3.73129e26i	−0.151103	−	0.0713361i
$166$	4.83777e27			0.857618
$167$		−	1.01057e28i		−	1.66192i	−0.556334	−	0.830959i	$-0.687793\pi$
$167$		−	1.01057e28i		−	1.66192i	0.556334	−	0.830959i	$-0.312207\pi$
$168$			3.62672e26i			0.0553539i
$169$	6.60147e27			0.935528
$170$	−3.62063e27	+	7.66914e27i	−0.476620	+	1.00957i
$171$	9.16737e27			1.12148
$172$			7.89098e27i			0.897481i
$173$			8.66506e26i			0.0916633i	0.998949	+	0.0458316i	$0.0145938\pi$
$173$			8.66506e26i			0.0916633i	−0.998949	+	0.0458316i	$0.985406\pi$
$174$	3.67556e27			0.361791
$175$	8.23504e26	−	6.77776e26i	0.0754554	−	0.0621027i
$176$	3.05581e26			0.0260747
$177$		−	2.06178e28i		−	1.63899i
$178$		−	1.14588e28i		−	0.848962i
$179$	2.03208e28			1.40371			0.701856	−	0.712319i	$-0.252355\pi$
$179$	2.03208e28			1.40371			0.701856	+	0.712319i	$0.252355\pi$
$180$	−5.19041e27	+	1.09942e28i	−0.334422	+	0.708366i
$181$	−6.11555e27			−0.367666			−0.183833	−	0.982957i	$-0.558851\pi$
$181$	−6.11555e27			−0.367666			−0.183833	+	0.982957i	$0.558851\pi$
$182$			3.12658e26i			0.0175460i
$183$		−	6.34295e27i		−	0.332393i
$184$	1.07371e28			0.525609
$185$	−3.75982e28	−	1.77503e28i	−1.71997	−	0.812004i
$186$	2.07160e28			0.885919
$187$		−	4.11757e27i		−	0.164672i
$188$			1.09587e28i			0.410002i
$189$	2.53398e27			0.0887218
$190$	1.39645e28	+	6.59270e27i	0.457727	+	0.216094i
$191$	1.25038e28			0.383819			0.191909	−	0.981413i	$-0.438532\pi$
$191$	1.25038e28			0.383819			0.191909	+	0.981413i	$0.438532\pi$
$192$		−	6.96404e27i		−	0.200261i
$193$			4.00087e28i			1.07817i	0.842251	+	0.539086i	$0.181230\pi$
$193$			4.00087e28i			1.07817i	−0.842251	+	0.539086i	$0.818770\pi$
$194$	4.34855e28			1.09856
$195$	−7.33074e27	+	1.55278e28i	−0.173666	+	0.367856i
$196$	−2.22845e28			−0.495225
$197$			1.19953e28i			0.250141i	0.992148	+	0.125070i	$0.0399157\pi$
$197$			1.19953e28i			0.250141i	−0.992148	+	0.125070i	$0.960084\pi$
$198$		−	5.90281e27i		−	0.115543i
$199$	−3.34370e28			−0.614559			−0.307280	−	0.951619i	$-0.599419\pi$
$199$	−3.34370e28			−0.614559			−0.307280	+	0.951619i	$0.599419\pi$
$200$	−1.58129e28	+	1.30147e28i	−0.272984	+	0.224677i
$201$	−4.49265e28			−0.728705
$202$			3.11715e28i			0.475189i
$203$		−	2.17769e27i		−	0.0312101i
$204$	−9.38372e28			−1.26473
$205$	−5.06111e28	+	1.07203e29i	−0.641686	+	1.35921i
$206$	−6.15480e28			−0.734301
$207$		−	2.07404e29i		−	2.32910i
$208$		−	6.00366e27i		−	0.0634782i
$209$	−7.49757e27			−0.0746607
$210$	1.06715e28	+	5.03807e27i	0.100112	+	0.0472632i
$211$	6.92258e28			0.611980			0.305990	−	0.952035i	$-0.401013\pi$
$211$	6.92258e28			0.611980			0.305990	+	0.952035i	$0.401013\pi$
$212$		−	7.62287e28i		−	0.635214i
$213$		−	6.02624e28i		−	0.473480i
$214$	−1.24379e28			−0.0921672
$215$	2.32190e29	+	1.09618e29i	1.62317	+	0.766303i
$216$	−4.86575e28			−0.320980
$217$		−	1.22738e28i		−	0.0764242i
$218$			1.29811e29i			0.763144i
$219$	−1.68207e29			−0.933885
$220$	4.24499e27	−	8.99166e27i	0.0222635	−	0.0471581i
$221$	−8.08966e28			−0.400892
$222$		−	4.60040e29i		−	2.15469i
$223$			4.37006e29i			1.93498i	0.252908	+	0.967490i	$0.418613\pi$
$223$			4.37006e29i			1.93498i	−0.252908	+	0.967490i	$0.581387\pi$
$224$	−4.12603e27			−0.0172756
$225$	2.51399e29	+	3.05453e29i	0.995595	+	1.20966i
$226$	2.55675e29			0.957927
$227$			4.51616e28i			0.160120i	0.996790	+	0.0800600i	$0.0255112\pi$
$227$			4.51616e28i			0.160120i	−0.996790	+	0.0800600i	$0.974489\pi$
$228$			1.70866e29i			0.573415i
$229$	3.96675e29			1.26035			0.630175	−	0.776454i	$-0.282983\pi$
$229$	3.96675e29			1.26035			0.630175	+	0.776454i	$0.282983\pi$
$230$	1.49154e29	−	3.15936e29i	0.448785	−	0.950607i
$231$	−5.72957e27			−0.0163295
$232$			4.18160e28i			0.112913i
$233$		−	2.52711e29i		−	0.646658i	−0.946287	−	0.323329i	$-0.895198\pi$
$233$		−	2.52711e29i		−	0.646658i	0.946287	−	0.323329i	$-0.104802\pi$
$234$	−1.15971e29			−0.281287
$235$	3.22457e29	+	1.52233e29i	0.741522	+	0.350075i
$236$	2.34563e29			0.511517
$237$		−	1.02957e30i		−	2.12962i
$238$			5.55964e28i			0.109103i
$239$	−7.75729e29			−1.44456			−0.722281	−	0.691600i	$-0.756906\pi$
$239$	−7.75729e29			−1.44456			−0.722281	+	0.691600i	$0.756906\pi$
$240$	−2.04915e29	−	9.67411e28i	−0.362188	−	0.170990i
$241$	−1.98502e28			−0.0333082			−0.0166541	−	0.999861i	$-0.505301\pi$
$241$	−1.98502e28			−0.0333082			−0.0166541	+	0.999861i	$0.505301\pi$
$242$		−	4.38962e29i		−	0.699415i
$243$		−	7.18710e29i		−	1.08762i
$244$	7.21621e28			0.103738
$245$	−3.09566e29	+	6.55717e29i	−0.422841	+	0.895654i
$246$	−1.31171e30			−1.70274
$247$			1.47302e29i			0.181760i
$248$			2.35681e29i			0.276489i
$249$	1.74175e30			1.94310
$250$	1.63287e29	+	6.46086e29i	0.173261	+	0.685551i
$251$	−9.10004e29			−0.918590			−0.459295	−	0.888284i	$-0.651898\pi$
$251$	−9.10004e29			−0.918590			−0.459295	+	0.888284i	$0.651898\pi$
$252$			7.97011e28i			0.0765522i
$253$			1.69626e29i			0.155055i
$254$	6.85814e29			0.596740
$255$	−1.30354e30	+	2.76114e30i	−1.07987	+	2.28737i
$256$	7.92282e28			0.0625000
$257$		−	1.13259e30i		−	0.850961i	−0.904968	−	0.425480i	$-0.860105\pi$
$257$		−	1.13259e30i		−	0.850961i	0.904968	−	0.425480i	$-0.139895\pi$
$258$			2.84101e30i			2.03342i
$259$	−2.72563e29			−0.185875
$260$	−1.76656e29	−	8.34001e28i	−0.114805	−	0.0542000i
$261$	8.07744e29			0.500343
$262$		−	7.78473e29i		−	0.459703i
$263$			7.83926e29i			0.441396i	0.975342	+	0.220698i	$0.0708335\pi$
$263$			7.83926e29i			0.441396i	−0.975342	+	0.220698i	$0.929167\pi$
$264$	1.10019e29			0.0590771
$265$	−2.24301e30	−	1.05893e30i	−1.14884	−	0.542369i
$266$	1.01234e29			0.0494659
$267$		−	4.12553e30i		−	1.92349i
$268$		−	5.11118e29i		−	0.227424i
$269$	−2.21562e30			−0.941005			−0.470502	−	0.882399i	$-0.655927\pi$
$269$	−2.21562e30			−0.941005			−0.470502	+	0.882399i	$0.655927\pi$
$270$	−6.75927e29	+	1.43174e30i	−0.274065	+	0.580518i
$271$	−3.34900e29			−0.129658			−0.0648289	−	0.997896i	$-0.520650\pi$
$271$	−3.34900e29			−0.129658			−0.0648289	+	0.997896i	$0.520650\pi$
$272$		−	1.06756e30i		−	0.394714i
$273$			1.12567e29i			0.0397537i
$274$	1.44063e30			0.486040
$275$	−2.05608e29	−	2.49816e29i	−0.0662798	−	0.0805307i
$276$	3.86569e30			1.19087
$277$		−	3.78301e30i		−	1.11388i	−0.830552	−	0.556942i	$-0.811975\pi$
$277$		−	3.78301e30i		−	1.11388i	0.830552	−	0.556942i	$-0.188025\pi$
$278$		−	1.60483e30i		−	0.451719i
$279$	4.55256e30			1.22519
$280$	−5.73169e28	+	1.21408e29i	−0.0147505	+	0.0312443i
$281$	−2.06047e30			−0.507151			−0.253576	−	0.967316i	$-0.581607\pi$
$281$	−2.06047e30			−0.507151			−0.253576	+	0.967316i	$0.581607\pi$
$282$			3.94549e30i			0.928938i
$283$			1.40735e30i			0.317010i	0.987358	+	0.158505i	$0.0506673\pi$
$283$			1.40735e30i			0.317010i	−0.987358	+	0.158505i	$0.949333\pi$
$284$	6.85591e29			0.147770
$285$	5.02768e30	+	2.37359e30i	1.03707	+	0.489603i
$286$	9.48471e28			0.0187261
$287$			7.77157e29i			0.146888i
$288$		−	1.53042e30i		−	0.276952i
$289$	−8.61430e30			−1.49278
$290$	1.23043e30	+	5.80888e29i	0.204212	+	0.0964089i
$291$	1.56562e31			2.48899
$292$		−	1.91365e30i		−	0.291459i
$293$			3.14320e30i			0.458698i	0.973344	+	0.229349i	$0.0736598\pi$
$293$			3.14320e30i			0.458698i	−0.973344	+	0.229349i	$0.926340\pi$
$294$	−8.02315e30			−1.12203
$295$	3.25844e30	−	6.90196e30i	0.436752	−	0.925119i
$296$	5.23377e30			0.672463
$297$		−	7.68701e29i		−	0.0946894i
$298$		−	7.39933e30i		−	0.873955i
$299$	3.33260e30			0.377479
$300$	−5.69317e30	+	4.68570e30i	−0.618498	+	0.509048i
$301$	1.68323e30			0.175413
$302$		−	6.89831e29i		−	0.0689693i
$303$			1.12228e31i			1.07663i
$304$	−1.94390e30			−0.178959
$305$	1.00244e30	−	2.12335e30i	0.0885751	−	0.187618i
$306$	−2.06217e31			−1.74907
$307$		−	6.65869e29i		−	0.0542200i	−0.999632	−	0.0271100i	$-0.991370\pi$
$307$		−	6.65869e29i		−	0.0542200i	0.999632	−	0.0271100i	$-0.00863044\pi$
$308$		−	6.51839e28i		−	0.00509631i
$309$	−2.21593e31			−1.66370
$310$	6.93485e30	+	3.27397e30i	0.500053	+	0.236077i
$311$	−1.30158e31			−0.901497			−0.450749	−	0.892651i	$-0.648843\pi$
$311$	−1.30158e31			−0.901497			−0.450749	+	0.892651i	$0.648843\pi$
$312$		−	2.16151e30i		−	0.143822i
$313$			1.48840e31i			0.951514i	0.879577	+	0.475757i	$0.157826\pi$
$313$			1.48840e31i			0.951514i	−0.879577	+	0.475757i	$0.842174\pi$
$314$	6.42849e30			0.394901
$315$	2.34519e30	+	1.10717e30i	0.138451	+	0.0653631i
$316$	1.17132e31			0.664640
$317$			4.63362e30i			0.252743i	0.991983	+	0.126372i	$0.0403332\pi$
$317$			4.63362e30i			0.252743i	−0.991983	+	0.126372i	$0.959667\pi$
$318$		−	2.74448e31i		−	1.43920i
$319$	−6.60617e29			−0.0333093
$320$	1.10060e30	−	2.33127e30i	0.0533648	−	0.113036i
$321$	−4.47806e30			−0.208822
$322$		−	2.29034e30i		−	0.102731i
$323$			2.61931e31i			1.13020i
$324$	1.35132e30			0.0560980
$325$	−4.90806e30	+	4.03952e30i	−0.196050	+	0.161357i
$326$	−2.19262e31			−0.842835
$327$			4.67363e31i			1.72905i
$328$		−	1.49230e31i		−	0.531414i
$329$	2.33761e30			0.0801352
$330$	1.52834e30	−	3.23729e30i	0.0504422	−	0.106846i
$331$	−1.64006e31			−0.521207			−0.260604	−	0.965446i	$-0.583922\pi$
$331$	−1.64006e31			−0.521207			−0.260604	+	0.965446i	$0.583922\pi$
$332$			1.98155e31i			0.606428i
$333$		−	1.01099e32i		−	2.97984i
$334$	4.13928e31			1.17515
$335$	−1.50395e31	−	7.10021e30i	−0.411314	−	0.194183i
$336$	−1.48551e30			−0.0391411
$337$		−	8.69817e30i		−	0.220828i	−0.993886	−	0.110414i	$-0.964782\pi$
$337$		−	8.69817e30i		−	0.220828i	0.993886	−	0.110414i	$-0.0352177\pi$
$338$			2.70396e31i			0.661518i
$339$	9.20512e31			2.17037
$340$	−3.14128e31	−	1.48301e31i	−0.713872	−	0.337021i
$341$	−3.72333e30			−0.0815647
$342$			3.75495e31i			0.793009i
$343$			9.55290e30i			0.194518i
$344$	−3.23215e31			−0.634615
$345$	5.37004e31	−	1.13747e32i	1.01681	−	2.15378i
$346$	−3.54921e30			−0.0648157
$347$			8.06238e31i			1.42019i	0.704108	+	0.710093i	$0.251347\pi$
$347$			8.06238e31i			1.42019i	−0.704108	+	0.710093i	$0.748653\pi$
$348$			1.50551e31i			0.255825i
$349$	9.75945e31			1.59995			0.799977	−	0.600031i	$-0.204845\pi$
$349$	9.75945e31			1.59995			0.799977	+	0.600031i	$0.204845\pi$
$350$	2.77617e30	+	3.37307e30i	0.0439132	+	0.0533550i
$351$	−1.51024e31			−0.230519
$352$			1.25166e30i			0.0184376i
$353$			1.35792e31i			0.193060i	0.995330	+	0.0965298i	$0.0307743\pi$
$353$			1.35792e31i			0.193060i	−0.995330	+	0.0965298i	$0.969226\pi$
$354$	8.44503e31			1.15894
$355$	9.52390e30	−	2.01733e31i	0.126171	−	0.267253i
$356$	4.69351e31			0.600307
$357$			2.00165e31i			0.247193i
$358$			8.32340e31i			0.992574i
$359$	−1.23431e32			−1.42148			−0.710742	−	0.703453i	$-0.751641\pi$
$359$	−1.23431e32			−1.42148			−0.710742	+	0.703453i	$0.751641\pi$
$360$	−4.50323e31	−	2.12599e31i	−0.500891	−	0.236472i
$361$	−4.53822e31			−0.487579
$362$		−	2.50493e31i		−	0.259979i
$363$		−	1.58040e32i		−	1.58466i
$364$	−1.28065e30			−0.0124069
$365$	−5.63088e31	−	2.65836e31i	−0.527127	−	0.248859i
$366$	2.59807e31			0.235038
$367$			1.94163e31i			0.169762i	0.996391	+	0.0848811i	$0.0270510\pi$
$367$			1.94163e31i			0.169762i	−0.996391	+	0.0848811i	$0.972949\pi$
$368$			4.39791e31i			0.371662i
$369$	−2.88262e32			−2.35482
$370$	7.27050e31	−	1.54002e32i	0.574173	−	1.21620i
$371$	−1.62604e31			−0.124153
$372$			8.48527e31i			0.626439i
$373$		−	1.75681e32i		−	1.25420i	−0.778941	−	0.627098i	$-0.784243\pi$
$373$		−	1.75681e32i		−	1.25420i	0.778941	−	0.627098i	$-0.215757\pi$
$374$	1.68656e31			0.116441
$375$	5.87887e31	+	2.32612e32i	0.392557	+	1.55325i
$376$	−4.48869e31			−0.289915
$377$			1.29789e31i			0.0810909i
$378$			1.03792e31i			0.0627358i
$379$	−2.09100e32			−1.22283			−0.611413	−	0.791312i	$-0.709399\pi$
$379$	−2.09100e32			−1.22283			−0.611413	+	0.791312i	$0.709399\pi$
$380$	−2.70037e31	+	5.71987e31i	−0.152802	+	0.323662i
$381$	2.46915e32			1.35203
$382$			5.12157e31i			0.271401i
$383$			1.47981e32i			0.758966i	0.925199	+	0.379483i	$0.123898\pi$
$383$			1.47981e32i			0.758966i	−0.925199	+	0.379483i	$0.876102\pi$
$384$	2.85247e31			0.141606
$385$	−1.91802e30	−	9.05504e29i	−0.00921709	−	0.00435142i
$386$	−1.63876e32			−0.762383
$387$			6.24342e32i			2.81213i
$388$			1.78117e32i			0.776798i
$389$	−2.19739e32			−0.927978			−0.463989	−	0.885841i	$-0.653582\pi$
$389$	−2.19739e32			−0.927978			−0.463989	+	0.885841i	$0.653582\pi$
$390$	−6.36020e31	−	3.00267e31i	−0.260114	−	0.122801i
$391$	5.92598e32			2.34720
$392$		−	9.12774e31i		−	0.350177i
$393$		−	2.80275e32i		−	1.04155i
$394$	−4.91329e31			−0.176876
$395$	1.62714e32	−	3.44658e32i	0.567494	−	1.20206i
$396$	2.41779e31			0.0817013
$397$		−	1.95462e32i		−	0.640003i	−0.947417	−	0.320001i	$-0.896317\pi$
$397$		−	1.95462e32i		−	0.640003i	0.947417	−	0.320001i	$-0.103683\pi$
$398$		−	1.36958e32i		−	0.434559i
$399$	3.64475e31			0.112074
$400$	−5.33080e31	−	6.47698e31i	−0.158870	−	0.193029i
$401$	−4.71177e32			−1.36107			−0.680534	−	0.732717i	$-0.738252\pi$
$401$	−4.71177e32			−1.36107			−0.680534	+	0.732717i	$0.738252\pi$
$402$		−	1.84019e32i		−	0.515273i
$403$			7.31511e31i			0.198567i
$404$	−1.27679e32			−0.336009
$405$	1.87720e31	−	3.97624e31i	0.0478985	−	0.101458i
$406$	8.91980e30			0.0220689
$407$			8.26841e31i			0.198377i
$408$		−	3.84357e32i		−	0.894300i
$409$	4.32845e32			0.976767			0.488384	−	0.872629i	$-0.337587\pi$
$409$	4.32845e32			0.976767			0.488384	+	0.872629i	$0.337587\pi$
$410$	−4.39105e32	−	2.07303e32i	−0.961104	−	0.453741i
$411$	5.18675e32			1.10122
$412$		−	2.52101e32i		−	0.519229i
$413$		−	5.00349e31i		−	0.0999763i
$414$	8.49528e32			1.64692
$415$	5.83066e32	+	2.75268e32i	1.09677	+	0.517790i
$416$	2.45910e31			0.0448859
$417$		−	5.77790e32i		−	1.02346i
$418$		−	3.07101e31i		−	0.0527931i
$419$	−9.61858e31			−0.160485			−0.0802427	−	0.996775i	$-0.525570\pi$
$419$	−9.61858e31			−0.160485			−0.0802427	+	0.996775i	$0.525570\pi$
$420$	−2.06359e31	+	4.37106e31i	−0.0334201	+	0.0707899i
$421$	1.59673e31			0.0251018			0.0125509	−	0.999921i	$-0.496005\pi$
$421$	1.59673e31			0.0251018			0.0125509	+	0.999921i	$0.496005\pi$
$422$			2.83549e32i			0.432735i
$423$			8.67063e32i			1.28468i
$424$	3.12233e32			0.449164
$425$	−8.72744e32	+	7.18301e32i	−1.21906	+	1.00333i
$426$	2.46835e32			0.334801
$427$		−	1.53930e31i		−	0.0202756i
$428$		−	5.09458e31i		−	0.0651721i
$429$	3.41480e31			0.0424277
$430$	−4.48995e32	+	9.51051e32i	−0.541858	+	1.14775i
$431$	−7.11839e32			−0.834479			−0.417240	−	0.908796i	$-0.637002\pi$
$431$	−7.11839e32			−0.834479			−0.417240	+	0.908796i	$0.637002\pi$
$432$		−	1.99301e32i		−	0.226967i
$433$			9.69753e32i			1.07291i	0.843930	+	0.536454i	$0.180236\pi$
$433$			9.69753e32i			1.07291i	−0.843930	+	0.536454i	$0.819764\pi$
$434$	5.02733e31			0.0540401
$435$	4.42993e32	+	2.09138e32i	0.462680	+	0.218433i
$436$	−5.31708e32			−0.539625
$437$		−	1.07904e33i		−	1.06420i
$438$		−	6.88977e32i		−	0.660357i
$439$	6.89367e32			0.642161			0.321081	−	0.947052i	$-0.395954\pi$
$439$	6.89367e32			0.642161			0.321081	+	0.947052i	$0.395954\pi$
$440$	3.68298e31	+	1.73875e31i	0.0333458	+	0.0157427i
$441$	−1.76317e33			−1.55172
$442$		−	3.31353e32i		−	0.283473i
$443$			1.47442e33i			1.22624i	0.789990	+	0.613120i	$0.210086\pi$
$443$			1.47442e33i			1.22624i	−0.789990	+	0.613120i	$0.789914\pi$
$444$	1.88433e33			1.52359
$445$	6.52001e32	−	1.38106e33i	0.512564	−	1.08570i
$446$	−1.78998e33			−1.36824
$447$		−	2.66400e33i		−	1.98011i
$448$		−	1.69002e31i		−	0.0122157i
$449$	−2.43553e33			−1.71204			−0.856020	−	0.516942i	$-0.827070\pi$
$449$	−2.43553e33			−1.71204			−0.856020	+	0.516942i	$0.827070\pi$
$450$	−1.25113e33	+	1.02973e33i	−0.855358	+	0.703992i
$451$	2.35756e32			0.156768
$452$			1.04724e33i			0.677357i
$453$		−	2.48361e32i		−	0.156263i
$454$	−1.84982e32			−0.113222
$455$	−1.77902e31	+	3.76827e31i	−0.0105934	+	0.0224388i
$456$	−6.99866e32			−0.405466
$457$		−	1.75801e33i		−	0.990990i	−0.868611	−	0.495495i	$-0.834987\pi$
$457$		−	1.75801e33i		−	0.990990i	0.868611	−	0.495495i	$-0.165013\pi$
$458$			1.62478e33i			0.891201i
$459$	−2.68549e33			−1.43339
$460$	1.29407e33	+	6.10936e32i	0.672181	+	0.317339i
$461$	2.02960e33			1.02600			0.513002	−	0.858387i	$-0.328533\pi$
$461$	2.02960e33			1.02600			0.513002	+	0.858387i	$0.328533\pi$
$462$		−	2.34683e31i		−	0.0115467i
$463$		−	5.63047e32i		−	0.269639i	−0.990870	−	0.134819i	$-0.956955\pi$
$463$		−	5.63047e32i		−	0.269639i	0.990870	−	0.134819i	$-0.0430454\pi$
$464$	−1.71278e32			−0.0798413
$465$	2.49677e33	+	1.17873e33i	1.13297	+	0.534877i
$466$	1.03510e33			0.457256
$467$			3.35205e33i			1.44162i	0.693134	+	0.720808i	$0.256229\pi$
$467$			3.35205e33i			1.44162i	−0.693134	+	0.720808i	$0.743771\pi$
$468$		−	4.75016e32i		−	0.198900i
$469$	−1.09027e32			−0.0444502
$470$	−6.23547e32	+	1.32078e33i	−0.247540	+	0.524335i
$471$	2.31447e33			0.894725
$472$			9.60771e32i			0.361697i
$473$		−	5.10621e32i		−	0.187212i
$474$	4.21713e33			1.50587
$475$	1.30794e33	+	1.58915e33i	0.454900	+	0.552708i
$476$	−2.27723e32			−0.0771471
$477$		−	6.03128e33i		−	1.99035i
$478$		−	3.17739e33i		−	1.02146i
$479$	−3.28090e33			−1.02754			−0.513770	−	0.857928i	$-0.671752\pi$
$479$	−3.28090e33			−1.02754			−0.513770	+	0.857928i	$0.671752\pi$
$480$	3.96252e32	−	8.39333e32i	0.120908	−	0.256105i
$481$	1.62447e33			0.482945
$482$		−	8.13063e31i		−	0.0235525i
$483$		−	8.24595e32i		−	0.232756i
$484$	1.79799e33			0.494561
$485$	5.24104e33	+	2.47431e33i	1.40490	+	0.663259i
$486$	2.94384e33			0.769061
$487$		−	2.83575e33i		−	0.722032i	−0.932560	−	0.361016i	$-0.882430\pi$
$487$		−	2.83575e33i		−	0.722032i	0.932560	−	0.361016i	$-0.117570\pi$
$488$			2.95576e32i			0.0733536i
$489$	−7.89413e33			−1.90960
$490$	−2.68582e33	−	1.26798e33i	−0.633323	−	0.298994i
$491$	−6.18264e33			−1.42120			−0.710600	−	0.703596i	$-0.751576\pi$
$491$	−6.18264e33			−1.42120			−0.710600	+	0.703596i	$0.751576\pi$
$492$		−	5.37276e33i		−	1.20402i
$493$			2.30790e33i			0.504231i
$494$	−6.03351e32			−0.128524
$495$	3.35868e32	−	7.11429e32i	0.0697595	−	0.147763i
$496$	−9.65349e32			−0.195507
$497$		−	1.46244e32i		−	0.0288817i
$498$			7.13422e33i			1.37398i
$499$	2.73531e33			0.513748			0.256874	−	0.966445i	$-0.417307\pi$
$499$	2.73531e33			0.513748			0.256874	+	0.966445i	$0.417307\pi$
$500$	−2.64637e33	+	6.68824e32i	−0.484758	+	0.122514i
$501$	1.49028e34			2.66253
$502$		−	3.72738e33i		−	0.649542i
$503$		−	1.17377e33i		−	0.199519i	−0.995012	−	0.0997597i	$-0.968193\pi$
$503$		−	1.17377e33i		−	0.199519i	0.995012	−	0.0997597i	$-0.0318074\pi$
$504$	−3.26456e32			−0.0541306
$505$	−1.77365e33	+	3.75691e33i	−0.286897	+	0.607700i
$506$	−6.94790e32			−0.109641
$507$			9.73514e33i			1.49880i
$508$			2.80909e33i			0.421959i
$509$	4.20998e33			0.617031			0.308516	−	0.951219i	$-0.400168\pi$
$509$	4.20998e33			0.617031			0.308516	+	0.951219i	$0.400168\pi$
$510$	−1.13096e34	−	5.33931e33i	−1.61741	−	0.763586i
$511$	−4.08203e32			−0.0569659
$512$			3.24519e32i			0.0441942i
$513$			4.88994e33i			0.649885i
$514$	4.63910e33			0.601720
$515$	−7.41801e33	−	3.50207e33i	−0.939068	−	0.443337i
$516$	−1.16368e34			−1.43784
$517$		−	7.09131e32i		−	0.0855253i
$518$		−	1.11642e33i		−	0.131433i
$519$	−1.27783e33			−0.146852
$520$	3.41607e32	−	7.23585e32i	0.0383252	−	0.0811797i
$521$	−1.42619e34			−1.56208			−0.781042	−	0.624478i	$-0.785312\pi$
$521$	−1.42619e34			−1.56208			−0.781042	+	0.624478i	$0.785312\pi$
$522$			3.30852e33i			0.353796i
$523$		−	1.07993e34i		−	1.12752i	−0.825939	−	0.563760i	$-0.809354\pi$
$523$		−	1.07993e34i		−	1.12752i	0.825939	−	0.563760i	$-0.190646\pi$
$524$	3.18863e33			0.325059
$525$	9.99510e32	+	1.21442e33i	0.0994938	+	0.120886i
$526$	−3.21096e33			−0.312114
$527$			1.30076e34i			1.23471i
$528$			4.50639e32i			0.0417738i
$529$	−1.33667e34			−1.21012
$530$	4.33739e33	−	9.18737e33i	0.383513	−	0.812349i
$531$	1.85589e34			1.60276
$532$			4.14654e32i			0.0349777i
$533$		−	4.63183e33i		−	0.381647i
$534$	1.68982e34			1.36011
$535$	−1.49907e33	−	7.07715e32i	−0.117869	−	0.0556463i
$536$	2.09354e33			0.160813
$537$			2.99669e34i			2.24887i
$538$		−	9.07518e33i		−	0.665391i
$539$	1.44202e33			0.103303
$540$	−5.86439e33	−	2.76860e33i	−0.410488	−	0.193793i
$541$	−9.36097e32			−0.0640258			−0.0320129	−	0.999487i	$-0.510192\pi$
$541$	−9.36097e32			−0.0640258			−0.0320129	+	0.999487i	$0.510192\pi$
$542$		−	1.37175e33i		−	0.0916819i
$543$		−	9.01856e33i		−	0.589033i
$544$	4.37274e33			0.279105
$545$	−7.38623e33	+	1.56454e34i	−0.460751	+	0.975954i
$546$	−4.61074e32			−0.0281101
$547$		−	1.05246e34i		−	0.627137i	−0.949566	−	0.313568i	$-0.898475\pi$
$547$		−	1.05246e34i		−	0.627137i	0.949566	−	0.313568i	$-0.101525\pi$
$548$			5.90084e33i			0.343682i
$549$	5.70954e33			0.325047
$550$	1.02325e33	−	8.42171e32i	0.0569438	−	0.0468669i
$551$	4.20238e33			0.228613
$552$			1.58339e34i			0.842071i
$553$		−	2.49855e33i		−	0.129904i
$554$	1.54952e34			0.787635
$555$	2.61762e34	−	5.54458e34i	1.30090	−	2.75554i
$556$	6.57337e33			0.319414
$557$		−	9.65307e33i		−	0.458644i	−0.973351	−	0.229322i	$-0.926349\pi$
$557$		−	9.65307e33i		−	0.458644i	0.973351	−	0.229322i	$-0.0736509\pi$
$558$			1.86473e34i			0.866340i
$559$	−1.00320e34			−0.455764
$560$	−4.97285e32	−	2.34770e32i	−0.0220930	−	0.0104302i
$561$	6.07215e33			0.263819
$562$		−	8.43969e33i		−	0.358610i
$563$		−	4.08658e34i		−	1.69826i	−0.528180	−	0.849132i	$-0.677125\pi$
$563$		−	4.08658e34i		−	1.69826i	0.528180	−	0.849132i	$-0.322875\pi$
$564$	−1.61607e34			−0.656859
$565$	3.08149e34	+	1.45478e34i	1.22505	+	0.578352i
$566$	−5.76452e33			−0.224160
$567$		−	2.88252e32i		−	0.0109644i
$568$			2.80818e33i			0.104489i
$569$	−8.49519e33			−0.309221			−0.154611	−	0.987975i	$-0.549412\pi$
$569$	−8.49519e33			−0.309221			−0.154611	+	0.987975i	$0.549412\pi$
$570$	−9.72220e33	+	2.05934e34i	−0.346202	+	0.733317i
$571$	−2.91693e34			−1.01619			−0.508095	−	0.861301i	$-0.669650\pi$
$571$	−2.91693e34			−1.01619			−0.508095	+	0.861301i	$0.669650\pi$
$572$			3.88494e32i			0.0132414i
$573$			1.84393e34i			0.614910i
$574$	−3.18324e33			−0.103865
$575$	3.59533e34	−	2.95910e34i	1.14787	−	0.944737i
$576$	6.26861e33			0.195835
$577$			5.12659e33i			0.156722i	0.996925	+	0.0783611i	$0.0249687\pi$
$577$			5.12659e33i			0.156722i	−0.996925	+	0.0783611i	$0.975031\pi$
$578$		−	3.52842e34i		−	1.05556i
$579$	−5.90005e34			−1.72732
$580$	−2.37932e33	+	5.03982e33i	−0.0681714	+	0.144399i
$581$	4.22686e33			0.118527
$582$			6.41278e34i			1.75998i
$583$			4.93271e33i			0.132504i
$584$	7.83833e33			0.206093
$585$	−1.39772e34	−	6.59869e33i	−0.359727	−	0.169828i
$586$	−1.28746e34			−0.324349
$587$			6.37641e34i			1.57253i	0.617888	+	0.786266i	$0.287989\pi$
$587$			6.37641e34i			1.57253i	−0.617888	+	0.786266i	$0.712011\pi$
$588$		−	3.28628e34i		−	0.793393i
$589$	2.36852e34			0.559805
$590$	2.82704e34	+	1.33466e34i	0.654158	+	0.308830i
$591$	−1.76894e34			−0.400747
$592$			2.14375e34i			0.475503i
$593$			7.56532e34i			1.64302i	0.570192	+	0.821511i	$0.306869\pi$
$593$			7.56532e34i			1.64302i	−0.570192	+	0.821511i	$0.693131\pi$
$594$	3.14860e33			0.0669556
$595$	−3.16342e33	+	6.70069e33i	−0.0658711	+	0.139527i
$596$	3.03076e34			0.617979
$597$		−	4.93093e34i		−	0.984577i
$598$			1.36503e34i			0.266918i
$599$	−6.58590e34			−1.26119			−0.630594	−	0.776113i	$-0.717189\pi$
$599$	−6.58590e34			−1.26119			−0.630594	+	0.776113i	$0.717189\pi$
$600$	−1.91926e34	−	2.33192e34i	−0.359951	−	0.437344i
$601$	−3.63692e34			−0.668041			−0.334020	−	0.942566i	$-0.608405\pi$
$601$	−3.63692e34			−0.668041			−0.334020	+	0.942566i	$0.608405\pi$
$602$			6.89452e33i			0.124036i
$603$		−	4.04401e34i		−	0.712601i
$604$	2.82555e33			0.0487687
$605$	2.49768e34	−	5.29054e34i	0.422274	−	0.894453i
$606$	−4.59684e34			−0.761293
$607$			1.13535e35i			1.84193i	0.389650	+	0.920963i	$0.372596\pi$
$607$			1.13535e35i			1.84193i	−0.389650	+	0.920963i	$0.627404\pi$
$608$		−	7.96220e33i		−	0.126543i
$609$	3.21142e33			0.0500012
$610$	8.69726e33	+	4.10600e33i	0.132666	+	0.0626320i
$611$	−1.39321e34			−0.208210
$612$		−	8.44666e34i		−	1.23678i
$613$			8.49768e34i			1.21911i	0.792742	+	0.609557i	$0.208653\pi$
$613$			8.49768e34i			1.21911i	−0.792742	+	0.609557i	$0.791347\pi$
$614$	2.72740e33			0.0383393
$615$	−1.58092e35	−	7.46358e34i	−2.17757	−	1.02804i
$616$	2.66993e32			0.00360364
$617$		−	1.49456e35i		−	1.97674i	−0.152079	−	0.988368i	$-0.548597\pi$
$617$		−	1.49456e35i		−	1.97674i	0.152079	−	0.988368i	$-0.451403\pi$
$618$		−	9.07644e34i		−	1.17641i
$619$	5.75885e34			0.731481			0.365740	−	0.930717i	$-0.380816\pi$
$619$	5.75885e34			0.731481			0.365740	+	0.930717i	$0.380816\pi$
$620$	−1.34102e34	+	2.84052e34i	−0.166931	+	0.353591i
$621$	1.10631e35			1.34968
$622$		−	5.33125e34i		−	0.637455i
$623$		−	1.00118e34i		−	0.117330i
$624$	8.85356e33			0.101698
$625$	−1.70821e34	+	8.71597e34i	−0.192327	+	0.981331i
$626$	−6.09648e34			−0.672822
$627$		−	1.10566e34i		−	0.119613i
$628$			2.63311e34i			0.279237i
$629$	2.88861e35			3.00300
$630$	−4.53497e33	+	9.60588e33i	−0.0462187	+	0.0978995i
$631$	3.54832e34			0.354532			0.177266	−	0.984163i	$-0.443275\pi$
$631$	3.54832e34			0.354532			0.177266	+	0.984163i	$0.443275\pi$
$632$			4.79772e34i			0.469972i
$633$			1.02087e35i			0.980445i
$634$	−1.89793e34			−0.178716
$635$	8.26569e34	+	3.90226e34i	0.763146	+	0.360284i
$636$	1.12414e35			1.01767
$637$		−	2.83309e34i		−	0.251488i
$638$		−	2.70589e33i		−	0.0235533i
$639$	5.42446e34			0.463016
$640$	9.54888e33	+	4.50806e33i	0.0799287	+	0.0377346i
$641$	1.20958e35			0.992909			0.496454	−	0.868063i	$-0.334635\pi$
$641$	1.20958e35			0.992909			0.496454	+	0.868063i	$0.334635\pi$
$642$		−	1.83421e34i		−	0.147660i
$643$			4.32278e34i			0.341292i	0.985332	+	0.170646i	$0.0545855\pi$
$643$			4.32278e34i			0.341292i	−0.985332	+	0.170646i	$0.945415\pi$
$644$	9.38121e33			0.0726416
$645$	−1.61653e35	+	3.42409e35i	−1.22768	+	2.60045i
$646$	−1.07287e35			−0.799173
$647$		−	4.93254e34i		−	0.360385i	−0.983631	−	0.180193i	$-0.942328\pi$
$647$		−	4.93254e34i		−	0.360385i	0.983631	−	0.180193i	$-0.0576721\pi$
$648$			5.53503e33i			0.0396673i
$649$	−1.51784e34			−0.106701
$650$	−1.65459e34	−	2.01034e34i	−0.114097	−	0.138628i
$651$	1.81000e34			0.122438
$652$		−	8.98095e34i		−	0.595974i
$653$		−	2.81796e35i		−	1.83451i	−0.398301	−	0.917255i	$-0.630400\pi$
$653$		−	2.81796e35i		−	1.83451i	0.398301	−	0.917255i	$-0.369600\pi$
$654$	−1.91432e35			−1.22262
$655$	4.42949e34	−	9.38245e34i	0.277547	−	0.587896i
$656$	6.11245e34			0.375766
$657$		−	1.51410e35i		−	0.913246i
$658$			9.57486e33i			0.0566642i
$659$	1.27642e35			0.741185			0.370592	−	0.928796i	$-0.379155\pi$
$659$	1.27642e35			0.741185			0.370592	+	0.928796i	$0.379155\pi$
$660$	1.32599e34	+	6.26006e33i	0.0755514	+	0.0356681i
$661$	−3.04753e35			−1.70384			−0.851921	−	0.523671i	$-0.824562\pi$
$661$	−3.04753e35			−1.70384			−0.851921	+	0.523671i	$0.824562\pi$
$662$		−	6.71770e34i		−	0.368549i
$663$		−	1.19298e35i		−	0.642263i
$664$	−8.11643e34			−0.428809
$665$	1.22011e34	+	5.76018e33i	0.0632599	+	0.0298652i
$666$	4.14101e35			2.10707
$667$		−	9.50755e34i		−	0.474783i
$668$			1.69545e35i			0.830959i
$669$	−6.44450e35			−3.10001
$670$	2.90825e34	−	6.16019e34i	0.137308	−	0.290843i
$671$	−4.66957e33			−0.0216394
$672$		−	6.08463e33i		−	0.0276770i
$673$			2.27652e35i			1.01644i	0.861227	+	0.508221i	$0.169697\pi$
$673$			2.27652e35i			1.01644i	−0.861227	+	0.508221i	$0.830303\pi$
$674$	3.56277e34			0.156149
$675$	−1.62931e35	+	1.34098e35i	−0.700980	+	0.576933i
$676$	−1.10754e35			−0.467764
$677$		−	1.12736e35i		−	0.467416i	−0.972307	−	0.233708i	$-0.924914\pi$
$677$		−	1.12736e35i		−	0.467416i	0.972307	−	0.233708i	$-0.0750860\pi$
$678$			3.77042e35i			1.53468i
$679$	3.79942e34			0.151826
$680$	6.07440e34	−	1.28667e35i	0.238310	−	0.504783i
$681$	−6.65994e34			−0.256526
$682$		−	1.52508e34i		−	0.0576749i
$683$			1.62407e35i			0.603039i	0.953460	+	0.301520i	$0.0974939\pi$
$683$			1.62407e35i			0.603039i	−0.953460	+	0.301520i	$0.902506\pi$
$684$	−1.53803e35			−0.560742
$685$	1.73631e35	+	8.19717e34i	0.621576	+	0.293448i
$686$	−3.91287e34			−0.137545
$687$			5.84973e35i			2.01919i
$688$		−	1.32389e35i		−	0.448741i
$689$	9.69114e34			0.322578
$690$	4.65908e35	+	2.19957e35i	1.52295	+	0.718992i
$691$	−2.17749e35			−0.699006			−0.349503	−	0.936935i	$-0.613649\pi$
$691$	−2.17749e35			−0.699006			−0.349503	+	0.936935i	$0.613649\pi$
$692$		−	1.45376e34i		−	0.0458316i
$693$		−	5.15741e33i		−	0.0159686i
$694$	−3.30235e35			−1.00422
$695$	9.13142e34	−	1.93420e35i	0.272727	−	0.577685i
$696$	−6.16657e34			−0.180896
$697$		−	8.23625e35i		−	2.37312i
$698$			3.99747e35i			1.13134i
$699$	3.72671e35			1.03600
$700$	−1.38161e34	+	1.13712e34i	−0.0377277	+	0.0310513i
$701$	−1.31197e35			−0.351923			−0.175961	−	0.984397i	$-0.556303\pi$
$701$	−1.31197e35			−0.351923			−0.175961	+	0.984397i	$0.556303\pi$
$702$		−	6.18595e34i		−	0.163002i
$703$		−	5.25979e35i		−	1.36153i
$704$	−5.12681e33			−0.0130373
$705$	−2.24497e35	+	4.75525e35i	−0.560850	+	1.18798i
$706$	−5.56205e34			−0.136514
$707$			2.72353e34i			0.0656733i
$708$			3.45908e35i			0.819493i
$709$	−1.07011e35			−0.249088			−0.124544	−	0.992214i	$-0.539747\pi$
$709$	−1.07011e35			−0.249088			−0.124544	+	0.992214i	$0.539747\pi$
$710$	8.26300e34	+	3.90099e34i	0.188977	+	0.0892166i
$711$	9.26759e35			2.08256
$712$			1.92246e35i			0.424481i
$713$		−	5.35859e35i		−	1.16260i
$714$	−8.19876e34			−0.174792
$715$	1.14313e34	+	5.39677e33i	0.0239481	+	0.0113060i
$716$	−3.40927e35			−0.701856
$717$		−	1.14396e36i		−	2.31431i
$718$		−	5.05572e35i		−	1.00514i
$719$	7.33489e35			1.43312			0.716560	−	0.697526i	$-0.245716\pi$
$719$	7.33489e35			1.43312			0.716560	+	0.697526i	$0.245716\pi$
$720$	8.70805e34	−	1.84452e35i	0.167211	−	0.354183i
$721$	−5.37759e34			−0.101484
$722$		−	1.85885e35i		−	0.344771i
$723$		−	2.92729e34i		−	0.0533626i
$724$	1.02602e35			0.183833
$725$	1.15243e35	+	1.40022e35i	0.202951	+	0.246587i
$726$	6.47334e35			1.12052
$727$			1.00868e36i			1.71622i	0.513465	+	0.858111i	$0.328362\pi$
$727$			1.00868e36i			1.71622i	−0.513465	+	0.858111i	$0.671638\pi$
$728$		−	5.24553e33i		−	0.00877298i
$729$	9.91632e35			1.63026
$730$	1.08886e35	−	2.30641e35i	0.175970	−	0.372735i
$731$	−1.78388e36			−2.83399
$732$			1.06417e35i			0.166197i
$733$			1.19811e36i			1.83948i	0.392525	+	0.919741i	$0.371602\pi$
$733$			1.19811e36i			1.83948i	−0.392525	+	0.919741i	$0.628398\pi$
$734$	−7.95292e34			−0.120040
$735$	−9.66981e35	−	4.56515e35i	−1.43491	−	0.677428i
$736$	−1.80138e35			−0.262805
$737$			3.30741e34i			0.0474400i
$738$		−	1.18072e36i		−	1.66511i
$739$	7.47298e35			1.03619			0.518094	−	0.855324i	$-0.326642\pi$
$739$	7.47298e35			1.03619			0.518094	+	0.855324i	$0.326642\pi$
$740$	6.30794e35	+	2.97800e35i	0.859985	+	0.406002i
$741$	−2.17226e35			−0.291195
$742$		−	6.66026e34i		−	0.0877895i
$743$			1.09617e36i			1.42075i	0.703822	+	0.710376i	$0.251475\pi$
$743$			1.09617e36i			1.42075i	−0.703822	+	0.710376i	$0.748525\pi$
$744$	−3.47557e35			−0.442960
$745$	4.21019e35	−	8.91795e35i	0.527653	−	1.11766i
$746$	7.19590e35			0.886850
$747$			1.56782e36i			1.90015i
$748$			6.90814e34i			0.0823362i
$749$	−1.08673e34			−0.0127379
$750$	−9.52777e35	+	2.40798e35i	−1.09831	+	0.277580i
$751$	−4.75595e34			−0.0539186			−0.0269593	−	0.999637i	$-0.508582\pi$
$751$	−4.75595e34			−0.0539186			−0.0269593	+	0.999637i	$0.508582\pi$
$752$		−	1.83857e35i		−	0.205001i
$753$		−	1.34198e36i		−	1.47166i
$754$	−5.31617e34			−0.0573399
$755$	3.92512e34	−	8.31411e34i	0.0416405	−	0.0882021i
$756$	−4.25131e34			−0.0443609
$757$			1.35534e36i			1.39107i	0.718490	+	0.695537i	$0.244834\pi$
$757$			1.35534e36i			1.39107i	−0.718490	+	0.695537i	$0.755166\pi$
$758$		−	8.56475e35i		−	0.864669i
$759$	−2.50147e35			−0.248412
$760$	−2.34286e35	−	1.10607e35i	−0.228863	−	0.108047i
$761$	−4.04146e35			−0.388356			−0.194178	−	0.980966i	$-0.562204\pi$
$761$	−4.04146e35			−0.388356			−0.194178	+	0.980966i	$0.562204\pi$
$762$			1.01136e36i			0.956028i
$763$			1.13419e35i			0.105470i
$764$	−2.09779e35			−0.191909
$765$	−2.48541e36	−	1.17337e36i	−2.23682	−	1.05601i
$766$	−6.06132e35			−0.536670
$767$			2.98206e35i			0.259761i
$768$			1.16837e35i			0.100130i
$769$	1.59517e36			1.34502			0.672509	−	0.740089i	$-0.265217\pi$
$769$	1.59517e36			1.34502			0.672509	+	0.740089i	$0.265217\pi$
$770$	3.70894e33	−	7.85621e33i	0.00307692	−	0.00651747i
$771$	1.67023e36			1.36331
$772$		−	6.71234e35i		−	0.539086i
$773$			5.09562e35i			0.402674i	0.979522	+	0.201337i	$0.0645286\pi$
$773$			5.09562e35i			0.402674i	−0.979522	+	0.201337i	$0.935471\pi$
$774$	−2.55730e36			−1.98848
$775$	6.49527e35	+	7.89182e35i	0.496965	+	0.603818i
$776$	−7.29566e35			−0.549279
$777$		−	4.01947e35i		−	0.297787i
$778$		−	9.00052e35i		−	0.656180i
$779$	−1.49972e36			−1.07595
$780$	1.22989e35	−	2.60514e35i	0.0868331	−	0.183928i
$781$	−4.43642e34			−0.0308244
$782$			2.42728e36i			1.65972i
$783$			4.30856e35i			0.289941i
$784$	3.73872e35			0.247612
$785$	7.74787e35	+	3.65779e35i	0.505023	+	0.238423i
$786$	1.14801e36			0.736484
$787$			1.58597e36i			1.00141i	0.865619	+	0.500703i	$0.166925\pi$
$787$			1.58597e36i			1.00141i	−0.865619	+	0.500703i	$0.833075\pi$
$788$		−	2.01248e35i		−	0.125070i
$789$	−1.15605e36			−0.707154
$790$	1.41172e36	+	6.66477e35i	0.849981	+	0.401279i
$791$	2.23389e35			0.132390
$792$			9.90327e34i			0.0577715i
$793$			9.17416e34i			0.0526807i
$794$	8.00614e35			0.452550
$795$	1.56160e36	−	3.30775e36i	0.868922	−	1.84053i
$796$	5.60980e35			0.307280
$797$		−	1.54676e36i		−	0.834053i	−0.908894	−	0.417027i	$-0.863072\pi$
$797$		−	1.54676e36i		−	0.834053i	0.908894	−	0.417027i	$-0.136928\pi$
$798$			1.49289e35i			0.0792486i
$799$	−2.47738e36			−1.29467
$800$	2.65297e35	−	2.18350e35i	0.136492	−	0.112338i
$801$	3.71355e36			1.88098
$802$		−	1.92994e36i		−	0.962420i
$803$			1.23831e35i			0.0607976i
$804$	7.53742e35			0.364353
$805$	1.30319e35	−	2.76040e35i	0.0620241	−	0.131378i
$806$	−2.99627e35			−0.140408
$807$		−	3.26736e36i		−	1.50757i
$808$		−	5.22972e35i		−	0.237594i
$809$	−6.21020e35			−0.277811			−0.138905	−	0.990306i	$-0.544358\pi$
$809$	−6.21020e35			−0.277811			−0.138905	+	0.990306i	$0.544358\pi$
$810$	1.62867e35	+	7.68900e34i	0.0717414	+	0.0338694i
$811$	4.69897e35			0.203818			0.101909	−	0.994794i	$-0.467505\pi$
$811$	4.69897e35			0.203818			0.101909	+	0.994794i	$0.467505\pi$
$812$			3.65355e34i			0.0156050i
$813$		−	4.93874e35i		−	0.207723i
$814$	−3.38674e35			−0.140274
$815$	−2.64262e36	−	1.24759e36i	−1.07787	−	0.508865i
$816$	1.57433e36			0.632365
$817$			3.24821e36i			1.28490i
$818$			1.77293e36i			0.690679i
$819$	−1.01326e35			−0.0388752
$820$	8.49113e35	−	1.79858e36i	0.320843	−	0.679603i
$821$	−3.77384e36			−1.40441			−0.702205	−	0.711975i	$-0.747801\pi$
$821$	−3.77384e36			−1.40441			−0.702205	+	0.711975i	$0.747801\pi$
$822$			2.12449e36i			0.778677i
$823$		−	1.31964e36i		−	0.476385i	−0.971218	−	0.238192i	$-0.923445\pi$
$823$		−	1.31964e36i		−	0.476385i	0.971218	−	0.238192i	$-0.0765549\pi$
$824$	1.03260e36			0.367150
$825$	3.68402e35	−	3.03209e35i	0.129017	−	0.106186i
$826$	2.04943e35			0.0706939
$827$			2.35273e36i			0.799380i	0.916650	+	0.399690i	$0.130882\pi$
$827$			2.35273e36i			0.799380i	−0.916650	+	0.399690i	$0.869118\pi$
$828$			3.47966e36i			1.16455i
$829$	1.44960e36			0.477878			0.238939	−	0.971035i	$-0.423200\pi$
$829$	1.44960e36			0.477878			0.238939	+	0.971035i	$0.423200\pi$
$830$	−1.12750e36	+	2.38824e36i	−0.366133	+	0.775536i
$831$	5.57877e36			1.78454
$832$			1.00725e35i			0.0317391i
$833$		−	5.03776e36i		−	1.56378i
$834$	2.36663e36			0.723692
$835$	4.98882e36	+	2.35524e36i	1.50286	+	0.709503i
$836$	1.25788e35			0.0373304
$837$			2.42837e36i			0.709980i
$838$		−	3.93977e35i		−	0.113480i
$839$	6.60849e35			0.187533			0.0937665	−	0.995594i	$-0.470109\pi$
$839$	6.60849e35			0.187533			0.0937665	+	0.995594i	$0.470109\pi$
$840$	−1.79039e35	−	8.45248e34i	−0.0500560	−	0.0236316i
$841$	−3.26009e36			−0.898006
$842$			6.54019e34i			0.0177496i
$843$		−	3.03856e36i		−	0.812500i
$844$	−1.16142e36			−0.305990
$845$	−1.53855e36	+	3.25892e36i	−0.399394	+	0.845989i
$846$	−3.55149e36			−0.908408
$847$		−	3.83530e35i		−	0.0966623i
$848$			1.27890e36i			0.317607i
$849$	−2.07541e36			−0.507877
$850$	−2.94216e36	−	3.57476e36i	−0.709464	−	0.862005i
$851$	−1.18998e37			−2.82762
$852$			1.01104e36i			0.236740i
$853$		−	5.07169e35i		−	0.117028i	−0.998287	−	0.0585140i	$-0.981364\pi$
$853$		−	5.07169e35i		−	0.117028i	0.998287	−	0.0585140i	$-0.0186362\pi$
$854$	6.30496e34			0.0143370
$855$	−2.13656e36	+	4.52562e36i	−0.478783	+	1.01415i
$856$	2.08674e35			0.0460836
$857$		−	2.45792e36i		−	0.534943i	−0.963566	−	0.267471i	$-0.913812\pi$
$857$		−	2.45792e36i		−	0.534943i	0.963566	−	0.267471i	$-0.0861881\pi$
$858$			1.39870e35i			0.0300009i
$859$	7.15238e36			1.51194			0.755972	−	0.654603i	$-0.227164\pi$
$859$	7.15238e36			1.51194			0.755972	+	0.654603i	$0.227164\pi$
$860$	−3.89551e36	−	1.83908e36i	−0.811584	−	0.383151i
$861$	−1.14607e36			−0.235327
$862$		−	2.91569e36i		−	0.590066i
$863$		−	2.16205e36i		−	0.431252i	−0.976476	−	0.215626i	$-0.930821\pi$
$863$		−	2.16205e36i		−	0.431252i	0.976476	−	0.215626i	$-0.0691792\pi$
$864$	8.16337e35			0.160490
$865$	−4.27764e35	−	2.01949e35i	−0.0828902	−	0.0391327i
$866$	−3.97211e36			−0.758660
$867$		−	1.27034e37i		−	2.39157i
$868$			2.05919e35i			0.0382121i
$869$	−7.57953e35			−0.138642
$870$	−8.56631e35	+	1.81450e36i	−0.154455	+	0.327164i
$871$	6.49797e35			0.115492
$872$		−	2.17787e36i		−	0.381572i
$873$			1.40928e37i			2.43399i
$874$	4.41977e36			0.752500
$875$	1.42668e35	+	5.64499e35i	0.0239455	+	0.0947463i
$876$	2.82205e36			0.466943
$877$			6.84625e36i			1.11676i	0.829587	+	0.558378i	$0.188576\pi$
$877$			6.84625e36i			1.11676i	−0.829587	+	0.558378i	$0.811424\pi$
$878$			2.82365e36i			0.454077i
$879$	−4.63526e36			−0.734874
$880$	−7.12192e34	+	1.50855e35i	−0.0111318	+	0.0235791i
$881$	2.59663e36			0.400139			0.200069	−	0.979782i	$-0.435883\pi$
$881$	2.59663e36			0.400139			0.200069	+	0.979782i	$0.435883\pi$
$882$		−	7.22196e36i		−	1.09723i
$883$		−	1.13962e36i		−	0.170707i	−0.996351	−	0.0853533i	$-0.972798\pi$
$883$		−	1.13962e36i		−	0.170707i	0.996351	−	0.0853533i	$-0.0272019\pi$
$884$	1.35722e36			0.200446
$885$	1.01783e37	+	4.80520e36i	1.48212	+	0.699714i
$886$	−6.03924e36			−0.867083
$887$		−	2.38557e36i		−	0.337713i	−0.985641	−	0.168856i	$-0.945993\pi$
$887$		−	2.38557e36i		−	0.337713i	0.985641	−	0.168856i	$-0.0540074\pi$
$888$			7.71820e36i			1.07734i
$889$	5.99211e35			0.0824722
$890$	5.65680e36	+	2.67060e36i	0.767708	+	0.362437i
$891$	−8.74434e34			−0.0117019
$892$		−	7.33175e36i		−	0.967490i
$893$			4.51100e36i			0.586988i
$894$	1.09117e37			1.40015
$895$	−4.73599e36	+	1.00317e37i	−0.599271	+	1.26936i
$896$	6.92234e34			0.00863779
$897$			4.91456e36i			0.604754i
$898$		−	9.97593e36i		−	1.21060i
$899$	2.08693e36			0.249753
$900$	−4.21778e36	−	5.12465e36i	−0.497798	−	0.604829i
$901$	1.72327e37			2.00582
$902$			9.65657e35i			0.110851i
$903$			2.48225e36i			0.281027i
$904$	−4.28951e36			−0.478964
$905$	1.42530e36	−	3.01904e36i	0.156963	−	0.332477i
$906$	1.01729e36			0.110495
$907$		−	1.67063e37i		−	1.78974i	−0.446326	−	0.894870i	$-0.647268\pi$
$907$		−	1.67063e37i		−	1.78974i	0.446326	−	0.894870i	$-0.352732\pi$
$908$		−	7.57685e35i		−	0.0800600i
$909$	−1.01021e37			−1.05284
$910$	−1.54349e35	−	7.28685e34i	−0.0158666	−	0.00749070i
$911$	1.13215e37			1.14795			0.573976	−	0.818872i	$-0.305400\pi$
$911$	1.13215e37			1.14795			0.573976	+	0.818872i	$0.305400\pi$
$912$		−	2.86665e36i		−	0.286708i
$913$		−	1.28225e36i		−	0.126499i
$914$	7.20082e36			0.700736
$915$	3.13129e36	+	1.47829e36i	0.300580	+	0.141905i
$916$	−6.65510e36			−0.630175
$917$		−	6.80169e35i		−	0.0635331i
$918$		−	1.09998e37i		−	1.01356i
$919$	−1.76508e37			−1.60443			−0.802215	−	0.597035i	$-0.796345\pi$
$919$	−1.76508e37			−1.60443			−0.802215	+	0.597035i	$0.796345\pi$
$920$	−2.50240e36	+	5.30052e36i	−0.224392	+	0.475303i
$921$	9.81953e35			0.0868651
$922$			8.31325e36i			0.725495i
$923$			8.71609e35i			0.0750413i
$924$	9.61262e34			0.00816473
$925$	1.75254e37	−	1.44241e37i	1.46857	−	1.20869i
$926$	2.30624e36			0.190663
$927$		−	1.99465e37i		−	1.62693i
$928$		−	7.01556e35i		−	0.0564563i
$929$	−2.88984e36			−0.229445			−0.114722	−	0.993398i	$-0.536598\pi$
$929$	−2.88984e36			−0.229445			−0.114722	+	0.993398i	$0.536598\pi$
$930$	−4.82810e36	+	1.02268e37i	−0.378215	+	0.801128i
$931$	−9.17311e36			−0.708999
$932$			4.23978e36i			0.323329i
$933$		−	1.91942e37i		−	1.44428i
$934$	−1.37300e37			−1.01938
$935$	2.03270e36	+	9.59646e35i	0.148912	+	0.0703017i
$936$	1.94566e36			0.140644
$937$			1.29200e37i			0.921545i	0.887518	+	0.460772i	$0.152428\pi$
$937$			1.29200e37i			0.921545i	−0.887518	+	0.460772i	$0.847572\pi$
$938$		−	4.46575e35i		−	0.0314310i
$939$	−2.19493e37			−1.52441
$940$	−5.40993e36	−	2.55405e36i	−0.370761	−	0.175037i
$941$	2.06414e37			1.39595			0.697973	−	0.716124i	$-0.254086\pi$
$941$	2.06414e37			1.39595			0.697973	+	0.716124i	$0.254086\pi$
$942$			9.48005e36i			0.632666i
$943$			3.39299e37i			2.23453i
$944$	−3.93532e36			−0.255758
$945$	−5.90572e35	+	1.25094e36i	−0.0378770	+	0.0802303i
$946$	2.09150e36			0.132379
$947$			2.09426e36i			0.130815i	0.997859	+	0.0654073i	$0.0208347\pi$
$947$			2.09426e36i			0.130815i	−0.997859	+	0.0654073i	$0.979165\pi$
$948$			1.72734e37i			1.06481i
$949$	2.43288e36			0.148010
$950$	−6.50918e36	+	5.35730e36i	−0.390824	+	0.321663i
$951$	−6.83316e36			−0.404916
$952$		−	9.32753e35i		−	0.0545513i
$953$			1.70726e37i			0.985461i	0.870182	+	0.492731i	$0.164001\pi$
$953$			1.70726e37i			0.985461i	−0.870182	+	0.492731i	$0.835999\pi$
$954$	2.47041e37			1.40739
$955$	−2.91416e36	+	6.17271e36i	−0.163859	+	0.347083i
$956$	1.30146e37			0.722281
$957$		−	9.74207e35i		−	0.0533644i
$958$		−	1.34386e37i		−	0.726581i
$959$	1.25871e36			0.0671729
$960$	3.43791e36	+	1.62305e36i	0.181094	+	0.0854950i
$961$	−7.47058e36			−0.388429
$962$			6.65382e36i			0.341494i
$963$		−	4.03088e36i		−	0.204207i
$964$	3.33031e35			0.0166541
$965$	−1.97509e37	−	9.32447e36i	−0.974980	−	0.460291i
$966$	3.37754e36			0.164584
$967$		−	1.41585e37i		−	0.681063i	−0.940233	−	0.340532i	$-0.889393\pi$
$967$		−	1.41585e37i		−	0.681063i	0.940233	−	0.340532i	$-0.110607\pi$
$968$			7.36456e36i			0.349707i
$969$	−3.86268e37			−1.81068
$970$	−1.01348e37	+	2.14673e37i	−0.468995	+	0.993415i
$971$	−1.45645e37			−0.665357			−0.332678	−	0.943040i	$-0.607952\pi$
$971$	−1.45645e37			−0.665357			−0.332678	+	0.943040i	$0.607952\pi$
$972$			1.20580e37i			0.543808i
$973$		−	1.40217e36i		−	0.0624296i
$974$	1.16153e37			0.510554
$975$	−5.95705e36	−	7.23787e36i	−0.258508	−	0.314089i
$976$	−1.21068e36			−0.0518688
$977$			2.61043e36i			0.110415i	0.998475	+	0.0552077i	$0.0175821\pi$
$977$			2.61043e36i			0.110415i	−0.998475	+	0.0552077i	$0.982418\pi$
$978$		−	3.23343e37i		−	1.35029i
$979$	−3.03714e36			−0.125222
$980$	5.19366e36	−	1.10011e37i	0.211421	−	0.447827i
$981$	−4.20692e37			−1.69084
$982$		−	2.53241e37i		−	1.00494i
$983$		−	4.36771e37i		−	1.71133i	−0.517527	−	0.855667i	$-0.673147\pi$
$983$		−	4.36771e37i		−	1.71133i	0.517527	−	0.855667i	$-0.326853\pi$
$984$	2.20068e37			0.851370
$985$	−5.92168e36	−	2.79565e36i	−0.226200	−	0.106790i
$986$	−9.45314e36			−0.356545
$987$			3.44726e36i			0.128384i
$988$		−	2.47133e36i		−	0.0908800i
$989$	7.34881e37			2.66848
$990$	2.91401e36	+	1.37572e36i	0.104484	+	0.0493274i
$991$	5.30135e37			1.87701			0.938503	−	0.345271i	$-0.112213\pi$
$991$	5.30135e37			1.87701			0.938503	+	0.345271i	$0.112213\pi$
$992$		−	3.95407e36i		−	0.138245i
$993$		−	2.41859e37i		−	0.835019i
$994$	5.99015e35			0.0204225
$995$	7.79287e36	−	1.65067e37i	0.262367	−	0.555740i
$996$	−2.92218e37			−0.971549
$997$			4.76523e37i			1.56457i	0.622921	+	0.782284i	$0.285946\pi$
$997$			4.76523e37i			1.56457i	−0.622921	+	0.782284i	$0.714054\pi$
$998$			1.12038e37i			0.363275i
$999$	5.39268e37			1.72678

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.26.b.a.9.12	yes	12
5.2	odd	4		50.26.a.k.1.6		6
5.3	odd	4		50.26.a.l.1.1		6
5.4	even	2	inner	10.26.b.a.9.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.26.b.a.9.1	✓	12	5.4	even	2	inner
10.26.b.a.9.12	yes	12	1.1	even	1	trivial
50.26.a.k.1.6		6	5.2	odd	4
50.26.a.l.1.1		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} +1.47469e6i q^{3} -1.67772e7 q^{4} +(-2.33061e8 + 4.93666e8i) q^{5} -6.04034e9 q^{6} +3.57876e9i q^{7} -6.87195e10i q^{8} -1.32743e12 q^{9} +(-2.02205e12 - 9.54619e11i) q^{10} +1.08564e12 q^{11} -2.47412e13i q^{12} -2.13293e13i q^{13} -1.46586e13 q^{14} +(-7.28005e14 - 3.43694e14i) q^{15} +2.81475e14 q^{16} -3.79275e15i q^{17} -5.43715e15i q^{18} -6.90611e15 q^{19} +(3.91012e15 - 8.28233e15i) q^{20} -5.27758e15 q^{21} +4.44680e15i q^{22} +1.56245e17i q^{23} +1.01340e17 q^{24} +(-1.89388e17 - 2.30109e17i) q^{25} +8.73648e16 q^{26} -7.08060e17i q^{27} -6.00417e16i q^{28} -6.08503e17 q^{29} +(1.40777e18 - 2.98191e18i) q^{30} -3.42961e18 q^{31} +1.15292e18i q^{32} +1.60099e18i q^{33} +1.55351e19 q^{34} +(-1.76671e18 - 8.34071e17i) q^{35} +2.22706e19 q^{36} +7.61614e19i q^{37} -2.82874e19i q^{38} +3.14542e19 q^{39} +(3.39244e19 + 1.60158e19i) q^{40} +2.17158e20 q^{41} -2.16169e19i q^{42} -4.70339e20i q^{43} -1.82141e19 q^{44} +(3.09372e20 - 6.55306e20i) q^{45} -6.39979e20 q^{46} -6.53190e20i q^{47} +4.15089e20i q^{48} +1.32826e21 q^{49} +(9.42525e20 - 7.75734e20i) q^{50} +5.59313e21 q^{51} +3.57846e20i q^{52} +4.54358e21i q^{53} +2.90021e21 q^{54} +(-2.53021e20 + 5.35945e20i) q^{55} +2.45931e20 q^{56} -1.01844e22i q^{57} -2.49243e21i q^{58} -1.39811e22 q^{59} +(1.22139e22 + 5.76622e21i) q^{60} -4.30120e21 q^{61} -1.40477e22i q^{62} -4.75056e21i q^{63} -4.72237e21 q^{64} +(1.05295e22 + 4.97103e21i) q^{65} -6.55766e21 q^{66} +3.04650e22i q^{67} +6.36317e22i q^{68} -2.30413e23 q^{69} +(3.41635e21 - 7.23645e21i) q^{70} -4.08644e22 q^{71} +9.12202e22i q^{72} +1.14063e23i q^{73} -3.11957e23 q^{74} +(3.39339e23 - 2.79289e23i) q^{75} +1.15865e23 q^{76} +3.88526e21i q^{77} +1.28836e23i q^{78} -6.98160e23 q^{79} +(-6.56009e22 + 1.38955e23i) q^{80} -8.05452e22 q^{81} +8.89479e23i q^{82} -1.18110e24i q^{83} +8.85430e22 q^{84} +(1.87235e24 + 8.83942e23i) q^{85} +1.92651e24 q^{86} -8.97354e23i q^{87} -7.46049e22i q^{88} -2.79755e24 q^{89} +(2.68413e24 + 1.26719e24i) q^{90} +7.63325e22 q^{91} -2.62136e24i q^{92} -5.05762e24i q^{93} +2.67546e24 q^{94} +(1.60955e24 - 3.40931e24i) q^{95} -1.70020e24 q^{96} -1.06166e25i q^{97} +5.44056e24i q^{98} -1.44112e24 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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