LMFDB - Embedded newform 10.26.b.a.9.7

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			9.7
Root			$-543485. i$ of defining polynomial
Character	$\chi$	$=$	10.9
Dual form			10.26.b.a.9.6

$q$-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} -1.08697e6i q^{3} -1.67772e7 q^{4} +(-2.09490e8 - 5.04120e8i) q^{5} +4.45223e9 q^{6} -4.89841e10i q^{7} -6.87195e10i q^{8} -3.34213e11 q^{9} +(2.06488e12 - 8.58070e11i) q^{10} +1.14584e13 q^{11} +1.82363e13i q^{12} -1.28077e14i q^{13} +2.00639e14 q^{14} +(-5.47963e14 + 2.27709e14i) q^{15} +2.81475e14 q^{16} -3.78822e15i q^{17} -1.36894e15i q^{18} +1.02229e16 q^{19} +(3.51465e15 + 8.45774e15i) q^{20} -5.32442e16 q^{21} +4.69335e16i q^{22} +1.81999e17i q^{23} -7.46959e16 q^{24} +(-2.10251e17 + 2.11216e17i) q^{25} +5.24604e17 q^{26} -5.57697e17i q^{27} +8.21816e17i q^{28} -2.19149e18 q^{29} +(-9.32695e17 - 2.24446e18i) q^{30} +2.89689e18 q^{31} +1.15292e18i q^{32} -1.24549e19i q^{33} +1.55166e19 q^{34} +(-2.46939e19 + 1.02617e19i) q^{35} +5.60717e18 q^{36} -4.56681e19i q^{37} +4.18730e19i q^{38} -1.39216e20 q^{39} +(-3.46429e19 + 1.43960e19i) q^{40} -4.22120e18 q^{41} -2.18088e20i q^{42} -1.22773e19i q^{43} -1.92240e20 q^{44} +(7.00142e19 + 1.68484e20i) q^{45} -7.45466e20 q^{46} -4.60132e20i q^{47} -3.05955e20i q^{48} -1.05837e21 q^{49} +(-8.65141e20 - 8.61190e20i) q^{50} -4.11768e21 q^{51} +2.14878e21i q^{52} +2.54574e21i q^{53} +2.28433e21 q^{54} +(-2.40041e21 - 5.77640e21i) q^{55} -3.36616e21 q^{56} -1.11120e22i q^{57} -8.97634e21i q^{58} +2.20173e21 q^{59} +(9.19330e21 - 3.82032e21i) q^{60} +7.41676e21 q^{61} +1.18656e22i q^{62} +1.63711e22i q^{63} -4.72237e21 q^{64} +(-6.45663e22 + 2.68309e22i) q^{65} +5.10153e22 q^{66} +6.01134e22i q^{67} +6.35558e22i q^{68} +1.97827e23 q^{69} +(-4.20317e22 - 1.01146e23i) q^{70} +3.59036e22 q^{71} +2.29670e22i q^{72} +1.98356e23i q^{73} +1.87057e23 q^{74} +(2.29585e23 + 2.28537e23i) q^{75} -1.71512e23 q^{76} -5.61278e23i q^{77} -5.70229e23i q^{78} +7.84538e23 q^{79} +(-5.89661e22 - 1.41897e23i) q^{80} -8.89375e23 q^{81} -1.72901e22i q^{82} +4.60438e23i q^{83} +8.93289e23 q^{84} +(-1.90972e24 + 7.93593e23i) q^{85} +5.02877e22 q^{86} +2.38208e24i q^{87} -7.87413e23i q^{88} -5.94026e23 q^{89} +(-6.90109e23 + 2.86778e23i) q^{90} -6.27374e24 q^{91} -3.05343e24i q^{92} -3.14882e24i q^{93} +1.88470e24 q^{94} +(-2.14159e24 - 5.15357e24i) q^{95} +1.25319e24 q^{96} +8.71039e24i q^{97} -4.33508e24i q^{98} -3.82954e24 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
$3$		−	1.08697e6i		−	1.18087i	−0.807086	−	0.590434i	$-0.798957\pi$
$3$		−	1.08697e6i		−	1.18087i	0.807086	−	0.590434i	$-0.201043\pi$
$4$	−1.67772e7			−0.500000
$5$	−2.09490e8	−	5.04120e8i	−0.383740	−	0.923441i
$5$	−2.09490e8	−	5.04120e8i	−0.383740	−	0.923441i
$6$	4.45223e9			0.835000
$7$		−	4.89841e10i		−	1.33761i	−0.743438	−	0.668805i	$-0.766806\pi$
$7$		−	4.89841e10i		−	1.33761i	0.743438	−	0.668805i	$-0.233194\pi$
$8$		−	6.87195e10i		−	0.353553i
$9$	−3.34213e11			−0.394450
$10$	2.06488e12	−	8.58070e11i	0.652971	−	0.271345i
$11$	1.14584e13			1.10082			0.550408	−	0.834896i	$-0.314472\pi$
$11$	1.14584e13			1.10082			0.550408	+	0.834896i	$0.314472\pi$
$12$			1.82363e13i			0.590434i
$13$		−	1.28077e14i		−	1.52468i	−0.647174	−	0.762342i	$-0.724049\pi$
$13$		−	1.28077e14i		−	1.52468i	0.647174	−	0.762342i	$-0.275951\pi$
$14$	2.00639e14			0.945833
$15$	−5.47963e14	+	2.27709e14i	−1.09046	+	0.453147i
$16$	2.81475e14			0.250000
$17$		−	3.78822e15i		−	1.57697i	−0.615053	−	0.788486i	$-0.710866\pi$
$17$		−	3.78822e15i		−	1.57697i	0.615053	−	0.788486i	$-0.289134\pi$
$18$		−	1.36894e15i		−	0.278918i
$19$	1.02229e16			1.05963			0.529815	−	0.848113i	$-0.322261\pi$
$19$	1.02229e16			1.05963			0.529815	+	0.848113i	$0.322261\pi$
$20$	3.51465e15	+	8.45774e15i	0.191870	+	0.461720i
$21$	−5.32442e16			−1.57954
$22$			4.69335e16i			0.778394i
$23$			1.81999e17i			1.73169i	0.500312	+	0.865845i	$0.333218\pi$
$23$			1.81999e17i			1.73169i	−0.500312	+	0.865845i	$0.666782\pi$
$24$	−7.46959e16			−0.417500
$25$	−2.10251e17	+	2.11216e17i	−0.705487	+	0.708723i
$26$	5.24604e17			1.07811
$27$		−	5.57697e17i		−	0.715075i
$28$			8.21816e17i			0.668805i
$29$	−2.19149e18			−1.15018			−0.575088	−	0.818092i	$-0.695032\pi$
$29$	−2.19149e18			−1.15018			−0.575088	+	0.818092i	$0.695032\pi$
$30$	−9.32695e17	−	2.24446e18i	−0.320423	−	0.771073i
$31$	2.89689e18			0.660557			0.330278	−	0.943884i	$-0.392857\pi$
$31$	2.89689e18			0.660557			0.330278	+	0.943884i	$0.392857\pi$
$32$			1.15292e18i			0.176777i
$33$		−	1.24549e19i		−	1.29992i
$34$	1.55166e19			1.11509
$35$	−2.46939e19	+	1.02617e19i	−1.23520	+	0.513295i
$36$	5.60717e18			0.197225
$37$		−	4.56681e19i		−	1.14049i	−0.821475	−	0.570245i	$-0.806848\pi$
$37$		−	4.56681e19i		−	1.14049i	0.821475	−	0.570245i	$-0.193152\pi$
$38$			4.18730e19i			0.749271i
$39$	−1.39216e20			−1.80045
$40$	−3.46429e19	+	1.43960e19i	−0.326486	+	0.135673i
$41$	−4.22120e18			−0.0292172			−0.0146086	−	0.999893i	$-0.504650\pi$
$41$	−4.22120e18			−0.0292172			−0.0146086	+	0.999893i	$0.504650\pi$
$42$		−	2.18088e20i		−	1.11690i
$43$		−	1.22773e19i		−	0.0468540i	−0.999726	−	0.0234270i	$-0.992542\pi$
$43$		−	1.22773e19i		−	0.0468540i	0.999726	−	0.0234270i	$-0.00745772\pi$
$44$	−1.92240e20			−0.550408
$45$	7.00142e19	+	1.68484e20i	0.151367	+	0.364252i
$46$	−7.45466e20			−1.22449
$47$		−	4.60132e20i		−	0.577642i	−0.957383	−	0.288821i	$-0.906737\pi$
$47$		−	4.60132e20i		−	0.577642i	0.957383	−	0.288821i	$-0.0932633\pi$
$48$		−	3.05955e20i		−	0.295217i
$49$	−1.05837e21			−0.789199
$50$	−8.65141e20	−	8.61190e20i	−0.501143	−	0.498854i
$51$	−4.11768e21			−1.86220
$52$			2.14878e21i			0.762342i
$53$			2.54574e21i			0.711814i	0.934521	+	0.355907i	$0.115828\pi$
$53$			2.54574e21i			0.711814i	−0.934521	+	0.355907i	$0.884172\pi$
$54$	2.28433e21			0.505634
$55$	−2.40041e21	−	5.77640e21i	−0.422427	−	1.01654i
$56$	−3.36616e21			−0.472916
$57$		−	1.11120e22i		−	1.25128i
$58$		−	8.97634e21i		−	0.813297i
$59$	2.20173e21			0.161107			0.0805536	−	0.996750i	$-0.474331\pi$
$59$	2.20173e21			0.161107			0.0805536	+	0.996750i	$0.474331\pi$
$60$	9.19330e21	−	3.82032e21i	0.545231	−	0.226574i
$61$	7.41676e21			0.357760			0.178880	−	0.983871i	$-0.442753\pi$
$61$	7.41676e21			0.357760			0.178880	+	0.983871i	$0.442753\pi$
$62$			1.18656e22i			0.467084i
$63$			1.63711e22i			0.527620i
$64$	−4.72237e21			−0.125000
$65$	−6.45663e22	+	2.68309e22i	−1.40796	+	0.585083i
$66$	5.10153e22			0.919181
$67$			6.01134e22i			0.897503i	0.893656	+	0.448752i	$0.148131\pi$
$67$			6.01134e22i			0.897503i	−0.893656	+	0.448752i	$0.851869\pi$
$68$			6.35558e22i			0.788486i
$69$	1.97827e23			2.04490
$70$	−4.20317e22	−	1.01146e23i	−0.362954	−	0.873421i
$71$	3.59036e22			0.259662			0.129831	−	0.991536i	$-0.458557\pi$
$71$	3.59036e22			0.259662			0.129831	+	0.991536i	$0.458557\pi$
$72$			2.29670e22i			0.139459i
$73$			1.98356e23i			1.01370i	0.862034	+	0.506851i	$0.169190\pi$
$73$			1.98356e23i			1.01370i	−0.862034	+	0.506851i	$0.830810\pi$
$74$	1.87057e23			0.806448
$75$	2.29585e23	+	2.28537e23i	0.836909	+	0.833087i
$76$	−1.71512e23			−0.529815
$77$		−	5.61278e23i		−	1.47246i
$78$		−	5.70229e23i		−	1.27311i
$79$	7.84538e23			1.49374			0.746870	−	0.664970i	$-0.231556\pi$
$79$	7.84538e23			1.49374			0.746870	+	0.664970i	$0.231556\pi$
$80$	−5.89661e22	−	1.41897e23i	−0.0959351	−	0.230860i
$81$	−8.89375e23			−1.23886
$82$		−	1.72901e22i		−	0.0206597i
$83$			4.60438e23i			0.472819i	0.971654	+	0.236409i	$0.0759706\pi$
$83$			4.60438e23i			0.472819i	−0.971654	+	0.236409i	$0.924029\pi$
$84$	8.93289e23			0.789770
$85$	−1.90972e24	+	7.93593e23i	−1.45624	+	0.605148i
$86$	5.02877e22			0.0331308
$87$			2.38208e24i			1.35821i
$88$		−	7.87413e23i		−	0.389197i
$89$	−5.94026e23			−0.254936			−0.127468	−	0.991843i	$-0.540685\pi$
$89$	−5.94026e23			−0.254936			−0.127468	+	0.991843i	$0.540685\pi$
$90$	−6.90109e23	+	2.86778e23i	−0.257565	+	0.107032i
$91$	−6.27374e24			−2.03943
$92$		−	3.05343e24i		−	0.865845i
$93$		−	3.14882e24i		−	0.780031i
$94$	1.88470e24			0.408455
$95$	−2.14159e24	−	5.15357e24i	−0.406623	−	0.978505i
$96$	1.25319e24			0.208750
$97$			8.71039e24i			1.27465i	0.770595	+	0.637325i	$0.219959\pi$
$97$			8.71039e24i			1.27465i	−0.770595	+	0.637325i	$0.780041\pi$
$98$		−	4.33508e24i		−	0.558048i
$99$	−3.82954e24			−0.434217
$100$	3.52743e24	−	3.54362e24i	0.352743	−	0.354362i
$101$	7.81456e24			0.690061			0.345031	−	0.938591i	$-0.387869\pi$
$101$	7.81456e24			0.690061			0.345031	+	0.938591i	$0.387869\pi$
$102$		−	1.68660e25i		−	1.31677i
$103$			1.05677e25i			0.730321i	0.930945	+	0.365161i	$0.118986\pi$
$103$			1.05677e25i			0.730321i	−0.930945	+	0.365161i	$0.881014\pi$
$104$	−8.80140e24			−0.539057
$105$	1.11541e25	+	2.68415e25i	0.606134	+	1.45861i
$106$	−1.04274e25			−0.503328
$107$			4.46639e24i			0.191716i	0.995395	+	0.0958582i	$0.0305595\pi$
$107$			4.46639e24i			0.191716i	−0.995395	+	0.0958582i	$0.969440\pi$
$108$			9.35660e24i			0.357537i
$109$	4.49825e25			1.53184			0.765918	−	0.642939i	$-0.222285\pi$
$109$	4.49825e25			1.53184			0.765918	+	0.642939i	$0.222285\pi$
$110$	2.36601e25	−	9.83208e24i	0.718801	−	0.298701i
$111$	−4.96398e25			−1.34677
$112$		−	1.37878e25i		−	0.334402i
$113$			2.79039e25i			0.605598i	0.953054	+	0.302799i	$0.0979211\pi$
$113$			2.79039e25i			0.605598i	−0.953054	+	0.302799i	$0.902079\pi$
$114$	4.55146e25			0.884791
$115$	9.17492e25	−	3.81268e25i	1.59911	−	0.664519i
$116$	3.67671e25			0.575088
$117$			4.28051e25i			0.601412i
$118$			9.01830e24i			0.113920i
$119$	−1.85562e26			−2.10937
$120$	1.56480e25	+	3.76557e25i	0.160212	+	0.385537i
$121$	2.29472e25			0.211794
$122$			3.03790e25i			0.252974i
$123$			4.58832e24i			0.0345016i
$124$	−4.86017e25			−0.330278
$125$	1.50524e26	+	6.17444e25i	0.925188	+	0.379509i
$126$	−6.70561e25			−0.373084
$127$		−	1.91643e26i		−	0.965930i	−0.875640	−	0.482965i	$-0.839560\pi$
$127$		−	1.91643e26i		−	0.965930i	0.875640	−	0.482965i	$-0.160440\pi$
$128$		−	1.93428e25i		−	0.0883883i
$129$	−1.33450e25			−0.0553284
$130$	−1.09899e26	−	2.64464e26i	−0.413716	−	0.995575i
$131$	−2.22743e26			−0.761925			−0.380963	−	0.924590i	$-0.624407\pi$
$131$	−2.22743e26			−0.761925			−0.380963	+	0.924590i	$0.624407\pi$
$132$			2.08958e26i			0.649959i
$133$		−	5.00759e26i		−	1.41737i
$134$	−2.46224e26			−0.634631
$135$	−2.81146e26	+	1.16832e26i	−0.660329	+	0.274403i
$136$	−2.60325e26			−0.557543
$137$		−	3.59939e26i		−	0.703432i	−0.936107	−	0.351716i	$-0.885598\pi$
$137$		−	3.59939e26i		−	0.703432i	0.936107	−	0.351716i	$-0.114402\pi$
$138$			8.10299e26i			1.44596i
$139$	5.18148e26			0.844829			0.422414	−	0.906403i	$-0.361183\pi$
$139$	5.18148e26			0.844829			0.422414	+	0.906403i	$0.361183\pi$
$140$	4.14294e26	−	1.72162e26i	0.617602	−	0.256647i
$141$	−5.00149e26			−0.682119
$142$			1.47061e26i			0.183609i
$143$		−	1.46756e27i		−	1.67840i
$144$	−9.40727e25			−0.0986126
$145$	4.59094e26	+	1.10477e27i	0.441369	+	1.06212i
$146$	−8.12467e26			−0.716795
$147$			1.15042e27i			0.931940i
$148$			7.66184e26i			0.570245i
$149$	1.91990e27			1.31356			0.656780	−	0.754082i	$-0.271918\pi$
$149$	1.91990e27			1.31356			0.656780	+	0.754082i	$0.271918\pi$
$150$	−9.36086e26	+	9.40381e26i	−0.589081	+	0.591784i
$151$	−1.20411e27			−0.697356			−0.348678	−	0.937243i	$-0.613369\pi$
$151$	−1.20411e27			−0.697356			−0.348678	+	0.937243i	$0.613369\pi$
$152$		−	7.02512e26i		−	0.374636i
$153$			1.26607e27i			0.622037i
$154$	2.29899e27			1.04119
$155$	−6.06868e26	−	1.46038e27i	−0.253482	−	0.609985i
$156$	2.33566e27			0.900226
$157$		−	4.32983e27i		−	1.54073i	−0.637606	−	0.770363i	$-0.720075\pi$
$157$		−	4.32983e27i		−	1.54073i	0.637606	−	0.770363i	$-0.279925\pi$
$158$			3.21347e27i			1.05623i
$159$	2.76715e27			0.840559
$160$	5.81211e26	−	2.41525e26i	0.163243	−	0.0678364i
$161$	8.91503e27			2.31632
$162$		−	3.64288e27i		−	0.876006i
$163$		−	5.02220e27i		−	1.11828i	−0.829075	−	0.559138i	$-0.811132\pi$
$163$		−	5.02220e27i		−	1.11828i	0.829075	−	0.559138i	$-0.188868\pi$
$164$	7.08201e25			0.0146086
$165$	−6.27877e27	+	2.60917e27i	−1.20040	+	0.498831i
$166$	−1.88595e27			−0.334333
$167$			1.18728e28i			1.95253i	0.216580	+	0.976265i	$0.430510\pi$
$167$			1.18728e28i			1.95253i	−0.216580	+	0.976265i	$0.569490\pi$
$168$			3.65891e27i			0.558452i
$169$	−9.34736e27			−1.32466
$170$	−3.25056e27	−	7.82221e27i	−0.427904	−	1.02972i
$171$	−3.41663e27			−0.417971
$172$			2.05979e26i			0.0234270i
$173$			4.16222e27i			0.440300i	0.975466	+	0.220150i	$0.0706547\pi$
$173$			4.16222e27i			0.440300i	−0.975466	+	0.220150i	$0.929345\pi$
$174$	−9.75700e27			−0.960397
$175$	1.03462e28	+	1.02990e28i	0.947995	+	0.943665i
$176$	3.22524e27			0.275204
$177$		−	2.39322e27i		−	0.190246i
$178$		−	2.43313e27i		−	0.180267i
$179$	−1.09350e28			−0.755363			−0.377681	−	0.925936i	$-0.623279\pi$
$179$	−1.09350e28			−0.755363			−0.377681	+	0.925936i	$0.623279\pi$
$180$	−1.17464e27	−	2.82669e27i	−0.0756833	−	0.182126i
$181$	−8.64913e27			−0.519984			−0.259992	−	0.965611i	$-0.583720\pi$
$181$	−8.64913e27			−0.519984			−0.259992	+	0.965611i	$0.583720\pi$
$182$		−	2.56972e28i		−	1.44210i
$183$		−	8.06179e27i		−	0.422467i
$184$	1.25068e28			0.612245
$185$	−2.30222e28	+	9.56700e27i	−1.05318	+	0.437652i
$186$	1.28976e28			0.551565
$187$		−	4.34068e28i		−	1.73595i
$188$			7.71973e27i			0.288821i
$189$	−2.73183e28			−0.956490
$190$	2.11090e28	−	8.77196e27i	0.691908	−	0.287526i
$191$	1.76410e28			0.541511			0.270755	−	0.962648i	$-0.412727\pi$
$191$	1.76410e28			0.541511			0.270755	+	0.962648i	$0.412727\pi$
$192$			5.13307e27i			0.147609i
$193$			5.06807e27i			0.136577i	0.997666	+	0.0682883i	$0.0217538\pi$
$193$			5.06807e27i			0.136577i	−0.997666	+	0.0682883i	$0.978246\pi$
$194$	−3.56778e28			−0.901314
$195$	2.91643e28	+	7.01816e28i	0.690906	+	1.66261i
$196$	1.77565e28			0.394599
$197$		−	5.65172e27i		−	0.117856i	−0.998262	−	0.0589282i	$-0.981232\pi$
$197$		−	5.65172e27i		−	0.117856i	0.998262	−	0.0589282i	$-0.0187683\pi$
$198$		−	1.56858e28i		−	0.307038i
$199$	−2.19231e28			−0.402938			−0.201469	−	0.979495i	$-0.564572\pi$
$199$	−2.19231e28			−0.402938			−0.201469	+	0.979495i	$0.564572\pi$
$200$	1.45147e28	+	1.44484e28i	0.250572	+	0.249427i
$201$	6.53414e28			1.05983
$202$			3.20085e28i			0.487947i
$203$			1.07348e29i			1.53849i
$204$	6.90832e28			0.931098
$205$	8.84299e26	+	2.12799e27i	0.0112118	+	0.0269803i
$206$	−4.32852e28			−0.516415
$207$		−	6.08263e28i		−	0.683066i
$208$		−	3.60505e28i		−	0.381171i
$209$	1.17138e29			1.16646
$210$	−1.09943e29	+	4.56872e28i	−1.03139	+	0.428601i
$211$	9.10994e28			0.805350			0.402675	−	0.915343i	$-0.368080\pi$
$211$	9.10994e28			0.805350			0.402675	+	0.915343i	$0.368080\pi$
$212$		−	4.27105e28i		−	0.355907i
$213$		−	3.90261e28i		−	0.306627i
$214$	−1.82943e28			−0.135564
$215$	−6.18922e27	+	2.57196e27i	−0.0432669	+	0.0179798i
$216$	−3.83247e28			−0.252817
$217$		−	1.41901e29i		−	0.883567i
$218$			1.84248e29i			1.08317i
$219$	2.15607e29			1.19705
$220$	4.02722e28	+	9.69119e28i	0.211214	+	0.508269i
$221$	−4.85185e29			−2.40438
$222$		−	2.03325e29i		−	0.952309i
$223$		−	1.06006e29i		−	0.469374i	−0.972071	−	0.234687i	$-0.924594\pi$
$223$		−	1.06006e29i		−	0.469374i	0.972071	−	0.234687i	$-0.0754064\pi$
$224$	5.64748e28			0.236458
$225$	7.02688e28	−	7.05912e28i	0.278279	−	0.279556i
$226$	−1.14294e29			−0.428223
$227$		−	5.01045e29i		−	1.77645i	−0.459407	−	0.888226i	$-0.651938\pi$
$227$		−	5.01045e29i		−	1.77645i	0.459407	−	0.888226i	$-0.348062\pi$
$228$			1.86428e29i			0.625641i
$229$	3.20108e28			0.101708			0.0508538	−	0.998706i	$-0.483806\pi$
$229$	3.20108e28			0.101708			0.0508538	+	0.998706i	$0.483806\pi$
$230$	1.56167e29	+	3.75805e29i	0.469886	+	1.13074i
$231$	−6.10091e29			−1.73878
$232$			1.50598e29i			0.406648i
$233$			6.19627e29i			1.58556i	0.609510	+	0.792778i	$0.291366\pi$
$233$			6.19627e29i			1.58556i	−0.609510	+	0.792778i	$0.708634\pi$
$234$	−1.75330e29			−0.425263
$235$	−2.31962e29	+	9.63928e28i	−0.533418	+	0.221665i
$236$	−3.69390e28			−0.0805536
$237$		−	8.52768e29i		−	1.76391i
$238$		−	7.60064e29i		−	1.49155i
$239$	−2.16736e29			−0.403605			−0.201803	−	0.979426i	$-0.564680\pi$
$239$	−2.16736e29			−0.403605			−0.201803	+	0.979426i	$0.564680\pi$
$240$	−1.54238e29	+	6.40943e28i	−0.272616	+	0.113287i
$241$	7.46346e29			1.25236			0.626178	−	0.779681i	$-0.284619\pi$
$241$	7.46346e29			1.25236			0.626178	+	0.779681i	$0.284619\pi$
$242$			9.39918e28i			0.149761i
$243$			4.94192e29i			0.747855i
$244$	−1.24433e29			−0.178880
$245$	2.21718e29	+	5.33546e29i	0.302848	+	0.728779i
$246$	−1.87938e28			−0.0243963
$247$		−	1.30932e30i		−	1.61560i
$248$		−	1.99072e29i		−	0.233542i
$249$	5.00481e29			0.558337
$250$	−2.52905e29	+	6.16545e29i	−0.268354	+	0.654207i
$251$	7.46681e29			0.753726			0.376863	−	0.926269i	$-0.377003\pi$
$251$	7.46681e29			0.753726			0.376863	+	0.926269i	$0.377003\pi$
$252$		−	2.74662e29i		−	0.263810i
$253$			2.08541e30i			1.90627i
$254$	7.84968e29			0.683016
$255$	8.62611e29	+	2.07581e30i	0.714600	+	1.71963i
$256$	7.92282e28			0.0625000
$257$		−	2.03309e29i		−	0.152754i	−0.997079	−	0.0763769i	$-0.975665\pi$
$257$		−	2.03309e29i		−	0.152754i	0.997079	−	0.0763769i	$-0.0243352\pi$
$258$		−	5.46612e28i		−	0.0391231i
$259$	−2.23701e30			−1.52553
$260$	1.08324e30	−	4.50147e29i	0.703978	−	0.292542i
$261$	7.32424e29			0.453687
$262$		−	9.12354e29i		−	0.538763i
$263$		−	3.18718e30i		−	1.79457i	−0.441454	−	0.897284i	$-0.645537\pi$
$263$		−	3.18718e30i		−	1.79457i	0.441454	−	0.897284i	$-0.354463\pi$
$264$	−8.55894e29			−0.459590
$265$	1.28336e30	−	5.33307e29i	0.657318	−	0.273152i
$266$	2.05111e30			1.00223
$267$			6.45688e29i			0.301046i
$268$		−	1.00854e30i		−	0.448752i
$269$	−1.08398e29			−0.0460382			−0.0230191	−	0.999735i	$-0.507328\pi$
$269$	−1.08398e29			−0.0460382			−0.0230191	+	0.999735i	$0.507328\pi$
$270$	−4.78543e29	−	1.15158e30i	−0.194032	−	0.466923i
$271$	8.40525e29			0.325413			0.162706	−	0.986675i	$-0.447978\pi$
$271$	8.40525e29			0.325413			0.162706	+	0.986675i	$0.447978\pi$
$272$		−	1.06629e30i		−	0.394243i
$273$			6.81936e30i			2.40830i
$274$	1.47431e30			0.497402
$275$	−2.40914e30	+	2.42019e30i	−0.776610	+	0.780173i
$276$	−3.31898e30			−1.02245
$277$		−	5.28289e30i		−	1.55551i	−0.628564	−	0.777757i	$-0.716357\pi$
$277$		−	5.28289e30i		−	1.55551i	0.628564	−	0.777757i	$-0.283643\pi$
$278$			2.12233e30i			0.597384i
$279$	−9.68177e29			−0.260557
$280$	7.05176e29	+	1.69695e30i	0.181477	+	0.436710i
$281$	−5.89709e30			−1.45147			−0.725736	−	0.687973i	$-0.758501\pi$
$281$	−5.89709e30			−1.45147			−0.725736	+	0.687973i	$0.758501\pi$
$282$		−	2.04861e30i		−	0.482331i
$283$		−	1.58325e30i		−	0.356631i	−0.983973	−	0.178315i	$-0.942935\pi$
$283$		−	1.58325e30i		−	0.356631i	0.983973	−	0.178315i	$-0.0570648\pi$
$284$	−6.02362e29			−0.129831
$285$	−5.60177e30	+	2.32784e30i	−1.15549	+	0.480168i
$286$	6.01111e30			1.18680
$287$			2.06772e29i			0.0390812i
$288$		−	3.85322e29i		−	0.0697296i
$289$	−8.57999e30			−1.48684
$290$	−4.52515e30	+	1.88045e30i	−0.751032	+	0.312095i
$291$	9.46793e30			1.50519
$292$		−	3.32787e30i		−	0.506851i
$293$		−	4.96361e30i		−	0.724357i	−0.932109	−	0.362179i	$-0.882033\pi$
$293$		−	4.96361e30i		−	0.724357i	0.932109	−	0.362179i	$-0.117967\pi$
$294$	−4.71210e30			−0.658981
$295$	−4.61241e29	−	1.10994e30i	−0.0618233	−	0.148773i
$296$	−3.13829e30			−0.403224
$297$		−	6.39030e30i		−	0.787165i
$298$			7.86391e30i			0.928828i
$299$	2.33099e31			2.64028
$300$	−3.85180e30	−	3.83421e30i	−0.418455	−	0.416543i
$301$	−6.01391e29			−0.0626723
$302$		−	4.93203e30i		−	0.493105i
$303$		−	8.49419e30i		−	0.814871i
$304$	2.87749e30			0.264907
$305$	−1.55373e30	−	3.73894e30i	−0.137287	−	0.330370i
$306$	−5.18584e30			−0.439846
$307$			1.29347e31i			1.05323i	0.850102	+	0.526617i	$0.176540\pi$
$307$			1.29347e31i			1.05323i	−0.850102	+	0.526617i	$0.823460\pi$
$308$			9.41668e30i			0.736230i
$309$	1.14867e31			0.862413
$310$	5.98171e30	−	2.48573e30i	0.431325	−	0.179239i
$311$	−1.68637e30			−0.116801			−0.0584007	−	0.998293i	$-0.518600\pi$
$311$	−1.68637e30			−0.116801			−0.0584007	+	0.998293i	$0.518600\pi$
$312$			9.56685e30i			0.636556i
$313$		−	2.70375e30i		−	0.172847i	−0.996258	−	0.0864236i	$-0.972456\pi$
$313$		−	2.70375e30i		−	0.172847i	0.996258	−	0.0864236i	$-0.0275438\pi$
$314$	1.77350e31			1.08946
$315$	8.25302e30	−	3.42958e30i	0.487226	−	0.202469i
$316$	−1.31624e31			−0.746870
$317$			3.29106e31i			1.79513i	0.440887	+	0.897563i	$0.354664\pi$
$317$			3.29106e31i			1.79513i	−0.440887	+	0.897563i	$0.645336\pi$
$318$			1.13342e31i			0.594365i
$319$	−2.51109e31			−1.26613
$320$	9.89287e29	+	2.38064e30i	0.0479676	+	0.115430i
$321$	4.85483e30			0.226392
$322$			3.65160e31i			1.63789i
$323$		−	3.87266e31i		−	1.67100i
$324$	1.49212e31			0.619430
$325$	2.70520e31	+	2.69284e31i	1.08058	+	1.07564i
$326$	2.05709e31			0.790740
$327$		−	4.88946e31i		−	1.80890i
$328$			2.90079e29i			0.0103298i
$329$	−2.25391e31			−0.772659
$330$	−1.06872e31	−	2.57178e31i	−0.352727	−	0.848809i
$331$	−3.10367e31			−0.986337			−0.493168	−	0.869934i	$-0.664161\pi$
$331$	−3.10367e31			−0.986337			−0.493168	+	0.869934i	$0.664161\pi$
$332$		−	7.72486e30i		−	0.236409i
$333$			1.52629e31i			0.449867i
$334$	−4.86310e31			−1.38065
$335$	3.03044e31	−	1.25931e31i	0.828791	−	0.344408i
$336$	−1.49869e31			−0.394885
$337$			3.19922e31i			0.812214i	0.913825	+	0.406107i	$0.133114\pi$
$337$			3.19922e31i			0.812214i	−0.913825	+	0.406107i	$0.866886\pi$
$338$		−	3.82868e31i		−	0.936678i
$339$	3.03307e31			0.715132
$340$	3.20398e31	−	1.33143e31i	0.728120	−	0.302574i
$341$	3.31936e31			0.727151
$342$		−	1.39945e31i		−	0.295550i
$343$		−	1.38477e31i		−	0.281970i
$344$	−8.43688e29			−0.0165654
$345$	−4.14427e31	−	9.97285e31i	−0.784710	−	1.88834i
$346$	−1.70484e31			−0.311339
$347$			4.34215e31i			0.764867i	0.923983	+	0.382434i	$0.124914\pi$
$347$			4.34215e31i			0.764867i	−0.923983	+	0.382434i	$0.875086\pi$
$348$		−	3.99647e31i		−	0.679103i
$349$	−9.72186e31			−1.59379			−0.796896	−	0.604117i	$-0.793526\pi$
$349$	−9.72186e31			−1.59379			−0.796896	+	0.604117i	$0.793526\pi$
$350$	−4.21846e31	+	4.23781e31i	−0.667272	+	0.670334i
$351$	−7.14283e31			−1.09026
$352$			1.32106e31i			0.194598i
$353$			1.03434e32i			1.47055i	0.677767	+	0.735277i	$0.262948\pi$
$353$			1.03434e32i			1.47055i	−0.677767	+	0.735277i	$0.737052\pi$
$354$	9.80262e30			0.134524
$355$	−7.52143e30	−	1.80997e31i	−0.0996428	−	0.239783i
$356$	9.96611e30			0.127468
$357$			2.01701e32i			2.49089i
$358$		−	4.47897e31i		−	0.534122i
$359$	−4.33845e31			−0.499636			−0.249818	−	0.968293i	$-0.580371\pi$
$359$	−4.33845e31			−0.499636			−0.249818	+	0.968293i	$0.580371\pi$
$360$	1.15781e31	−	4.81134e30i	0.128782	−	0.0535162i
$361$	1.14311e31			0.122814
$362$		−	3.54268e31i		−	0.367684i
$363$		−	2.49429e31i		−	0.250100i
$364$	1.05256e32			1.01972
$365$	9.99954e31	−	4.15536e31i	0.936093	−	0.388998i
$366$	3.30211e31			0.298729
$367$		−	4.71466e31i		−	0.412216i	−0.978529	−	0.206108i	$-0.933920\pi$
$367$		−	4.71466e31i		−	0.412216i	0.978529	−	0.206108i	$-0.0660799\pi$
$368$			5.12281e31i			0.432922i
$369$	1.41078e30			0.0115247
$370$	−3.91864e31	−	9.42990e31i	−0.309467	−	0.744707i
$371$	1.24701e32			0.952129
$372$			5.28285e31i			0.390015i
$373$		−	9.92589e31i		−	0.708613i	−0.935129	−	0.354306i	$-0.884717\pi$
$373$		−	9.92589e31i		−	0.708613i	0.935129	−	0.354306i	$-0.115283\pi$
$374$	1.77794e32			1.22750
$375$	6.71143e31	−	1.63615e32i	0.448151	−	1.09253i
$376$	−3.16200e31			−0.204227
$377$			2.80680e32i			1.75365i
$378$		−	1.11896e32i		−	0.676341i
$379$	6.28833e31			0.367743			0.183872	−	0.982950i	$-0.441137\pi$
$379$	6.28833e31			0.367743			0.183872	+	0.982950i	$0.441137\pi$
$380$	3.59299e31	+	8.64626e31i	0.203311	+	0.489253i
$381$	−2.08310e32			−1.14064
$382$			7.22577e31i			0.382906i
$383$			4.95371e31i			0.254065i	0.991899	+	0.127033i	$0.0405453\pi$
$383$			4.95371e31i			0.254065i	−0.991899	+	0.127033i	$0.959455\pi$
$384$	−2.10250e31			−0.104375
$385$	−2.82951e32	+	1.17582e32i	−1.35973	+	0.565043i
$386$	−2.07588e31			−0.0965742
$387$			4.10323e30i			0.0184816i
$388$		−	1.46136e32i		−	0.637325i
$389$	4.10071e32			1.73177			0.865883	−	0.500246i	$-0.166757\pi$
$389$	4.10071e32			1.73177			0.865883	+	0.500246i	$0.166757\pi$
$390$	−2.87464e32	+	1.19457e32i	−1.17564	+	0.488544i
$391$	6.89451e32			2.73082
$392$			7.27306e31i			0.279024i
$393$			2.42114e32i			0.899734i
$394$	2.31495e31			0.0833370
$395$	−1.64353e32	−	3.95501e32i	−0.573209	−	1.37938i
$396$	6.42490e31			0.217108
$397$		−	1.81115e32i		−	0.593026i	−0.955029	−	0.296513i	$-0.904176\pi$
$397$		−	1.81115e32i		−	0.593026i	0.955029	−	0.296513i	$-0.0958239\pi$
$398$		−	8.97970e31i		−	0.284920i
$399$	−5.44310e32			−1.67373
$400$	−5.91805e31	+	5.94520e31i	−0.176372	+	0.177181i
$401$	1.30258e32			0.376271			0.188136	−	0.982143i	$-0.439756\pi$
$401$	1.30258e32			0.376271			0.188136	+	0.982143i	$0.439756\pi$
$402$			2.67638e32i			0.749415i
$403$		−	3.71025e32i		−	1.00714i
$404$	−1.31107e32			−0.345031
$405$	1.86315e32	+	4.48352e32i	0.475400	+	1.14401i
$406$	−4.39697e32			−1.08787
$407$		−	5.23282e32i		−	1.25547i
$408$			2.82965e32i			0.658385i
$409$	−8.59252e32			−1.93901			−0.969503	−	0.245081i	$-0.921186\pi$
$409$	−8.59252e32			−1.93901			−0.969503	+	0.245081i	$0.921186\pi$
$410$	−8.71627e30	+	3.62209e30i	−0.0190780	+	0.00792795i
$411$	−3.91243e32			−0.830661
$412$		−	1.77296e32i		−	0.365161i
$413$		−	1.07850e32i		−	0.215498i
$414$	2.49145e32			0.483000
$415$	2.32116e32	−	9.64569e31i	0.436620	−	0.181440i
$416$	1.47663e32			0.269529
$417$		−	5.63211e32i		−	0.997631i
$418$			4.79796e32i			0.824809i
$419$	4.67029e32			0.779235			0.389618	−	0.920977i	$-0.372607\pi$
$419$	4.67029e32			0.779235			0.389618	+	0.920977i	$0.372607\pi$
$420$	−1.87135e32	−	4.50325e32i	−0.303067	−	0.729306i
$421$	−7.42072e32			−1.16659			−0.583297	−	0.812259i	$-0.698238\pi$
$421$	−7.42072e32			−1.16659			−0.583297	+	0.812259i	$0.698238\pi$
$422$			3.73143e32i			0.569468i
$423$			1.53782e32i			0.227851i
$424$	1.74942e32			0.251664
$425$	8.00133e32	+	7.96479e32i	1.11764	+	1.11253i
$426$	1.59851e32			0.216818
$427$		−	3.63303e32i		−	0.478543i
$428$		−	7.49336e31i		−	0.0958582i
$429$	−1.59519e33			−1.98196
$430$	−1.05348e31	−	2.53511e31i	−0.0127136	−	0.0305943i
$431$	1.06420e33			1.24755			0.623774	−	0.781605i	$-0.285599\pi$
$431$	1.06420e33			1.24755			0.623774	+	0.781605i	$0.285599\pi$
$432$		−	1.56978e32i		−	0.178769i
$433$		−	9.20340e32i		−	1.01824i	−0.860696	−	0.509119i	$-0.829971\pi$
$433$		−	9.20340e32i		−	1.01824i	0.860696	−	0.509119i	$-0.170029\pi$
$434$	5.81227e32			0.624776
$435$	1.20085e33	−	4.99021e32i	1.25422	−	0.521199i
$436$	−7.54681e32			−0.765918
$437$			1.86055e33i			1.83495i
$438$			8.83127e32i			0.846441i
$439$	3.84917e32			0.358559			0.179279	−	0.983798i	$-0.442623\pi$
$439$	3.84917e32			0.358559			0.179279	+	0.983798i	$0.442623\pi$
$440$	−3.96951e32	+	1.64955e32i	−0.359400	+	0.149351i
$441$	3.53721e32			0.311300
$442$		−	1.98732e33i		−	1.70016i
$443$			8.53492e32i			0.709827i	0.934899	+	0.354914i	$0.115490\pi$
$443$			8.53492e32i			0.709827i	−0.934899	+	0.354914i	$0.884510\pi$
$444$	8.32818e32			0.673384
$445$	1.24442e32	+	2.99461e32i	0.0978292	+	0.235418i
$446$	4.34200e32			0.331897
$447$		−	2.08687e33i		−	1.55114i
$448$			2.31321e32i			0.167201i
$449$	−3.42652e32			−0.240865			−0.120432	−	0.992722i	$-0.538428\pi$
$449$	−3.42652e32			−0.240865			−0.120432	+	0.992722i	$0.538428\pi$
$450$	2.89142e32	+	2.87821e32i	0.197676	+	0.196773i
$451$	−4.83681e31			−0.0321627
$452$		−	4.68150e32i		−	0.302799i
$453$			1.30883e33i			0.823485i
$454$	2.05228e33			1.25614
$455$	1.31428e33	+	3.16272e33i	0.782613	+	1.88330i
$456$	−7.63609e32			−0.442395
$457$			4.52087e32i			0.254841i	0.991849	+	0.127421i	$0.0406698\pi$
$457$			4.52087e32i			0.254841i	−0.991849	+	0.127421i	$0.959330\pi$
$458$			1.31116e32i			0.0719181i
$459$	−2.11268e33			−1.12765
$460$	−1.53930e33	+	6.39662e32i	−0.799557	+	0.332260i
$461$	2.47159e33			1.24944			0.624718	−	0.780850i	$-0.285214\pi$
$461$	2.47159e33			1.24944			0.624718	+	0.780850i	$0.285214\pi$
$462$		−	2.49893e33i		−	1.22950i
$463$			1.72628e33i			0.826703i	0.910572	+	0.413351i	$0.135642\pi$
$463$			1.72628e33i			0.826703i	−0.910572	+	0.413351i	$0.864358\pi$
$464$	−6.16849e32			−0.287544
$465$	−1.58739e33	+	6.59646e32i	−0.720312	+	0.299329i
$466$	−2.53799e33			−1.12116
$467$		−	1.88292e33i		−	0.809787i	−0.914364	−	0.404893i	$-0.867309\pi$
$467$		−	1.88292e33i		−	0.809787i	0.914364	−	0.404893i	$-0.132691\pi$
$468$		−	7.18150e32i		−	0.300706i
$469$	2.94460e33			1.20051
$470$	−3.94825e32	−	9.50115e32i	−0.156741	−	0.377184i
$471$	−4.70639e33			−1.81939
$472$		−	1.51302e32i		−	0.0569600i
$473$		−	1.40678e32i		−	0.0515775i
$474$	3.49294e33			1.24727
$475$	−2.14938e33	+	2.15924e33i	−0.747554	+	0.750984i
$476$	3.11322e33			1.05469
$477$		−	8.50822e32i		−	0.280775i
$478$		−	8.87749e32i		−	0.285392i
$479$	−1.07303e33			−0.336061			−0.168030	−	0.985782i	$-0.553741\pi$
$479$	−1.07303e33			−0.336061			−0.168030	+	0.985782i	$0.553741\pi$
$480$	−2.62530e32	−	6.31759e32i	−0.0801058	−	0.192768i
$481$	−5.84904e33			−1.73889
$482$			3.05704e33i			0.885549i
$483$		−	9.69036e33i		−	2.73527i
$484$	−3.84991e32			−0.105897
$485$	4.39109e33	−	1.82474e33i	1.17706	−	0.489135i
$486$	−2.02421e33			−0.528814
$487$		−	6.26292e33i		−	1.59465i	−0.603552	−	0.797324i	$-0.706248\pi$
$487$		−	6.26292e33i		−	1.59465i	0.603552	−	0.797324i	$-0.293752\pi$
$488$		−	5.09676e32i		−	0.126487i
$489$	−5.45897e33			−1.32054
$490$	−2.18540e33	+	9.08155e32i	−0.515324	+	0.214146i
$491$	3.10431e33			0.713586			0.356793	−	0.934183i	$-0.383870\pi$
$491$	3.10431e33			0.713586			0.356793	+	0.934183i	$0.383870\pi$
$492$		−	7.69792e31i		−	0.0172508i
$493$			8.30184e33i			1.81379i
$494$	5.36298e33			1.14240
$495$	8.02249e32	+	1.93055e33i	0.166627	+	0.400974i
$496$	8.15401e32			0.165139
$497$		−	1.75870e33i		−	0.347326i
$498$			2.04997e33i			0.394804i
$499$	−7.12443e33			−1.33811			−0.669057	−	0.743211i	$-0.733302\pi$
$499$	−7.12443e33			−1.33811			−0.669057	+	0.743211i	$0.733302\pi$
$500$	−2.52537e33	−	1.03590e33i	−0.462594	−	0.189755i
$501$	1.29054e34			2.30568
$502$			3.05840e33i			0.532965i
$503$			1.03191e34i			1.75406i	0.480439	+	0.877028i	$0.340477\pi$
$503$			1.03191e34i			1.75406i	−0.480439	+	0.877028i	$0.659523\pi$
$504$	1.12501e33			0.186542
$505$	−1.63707e33	−	3.93948e33i	−0.264804	−	0.637231i
$506$	−8.54183e33			−1.34794
$507$			1.01603e34i			1.56425i
$508$			3.21523e33i			0.482965i
$509$	4.04421e32			0.0592736			0.0296368	−	0.999561i	$-0.490565\pi$
$509$	4.04421e32			0.0592736			0.0296368	+	0.999561i	$0.490565\pi$
$510$	−8.50250e33	+	3.53326e33i	−1.21596	+	0.505298i
$511$	9.71629e33			1.35594
$512$			3.24519e32i			0.0441942i
$513$		−	5.70128e33i		−	0.757714i
$514$	8.32753e32			0.108013
$515$	5.32738e33	−	2.21382e33i	0.674409	−	0.280254i
$516$	2.23892e32			0.0276642
$517$		−	5.27236e33i		−	0.635877i
$518$		−	9.16279e33i		−	1.07871i
$519$	4.52420e33			0.519936
$520$	1.84380e33	+	4.43696e33i	0.206858	+	0.497788i
$521$	9.14369e33			1.00150			0.500749	−	0.865593i	$-0.333058\pi$
$521$	9.14369e33			1.00150			0.500749	+	0.865593i	$0.333058\pi$
$522$			3.00001e33i			0.320805i
$523$		−	1.50595e33i		−	0.157231i	−0.996905	−	0.0786156i	$-0.974950\pi$
$523$		−	1.50595e33i		−	0.157231i	0.996905	−	0.0786156i	$-0.0250500\pi$
$524$	3.73700e33			0.380963
$525$	1.11947e34	−	1.12460e34i	1.11434	−	1.11946i
$526$	1.30547e34			1.26895
$527$		−	1.09740e34i		−	1.04168i
$528$		−	3.50574e33i		−	0.324979i
$529$	−2.20777e34			−1.99875
$530$	2.18443e33	+	5.25665e33i	0.193147	+	0.464794i
$531$	−7.35849e32			−0.0635487
$532$			8.40134e33i			0.708685i
$533$			5.40640e32i			0.0445470i
$534$	−2.64474e33			−0.212871
$535$	2.25160e33	−	9.35662e32i	0.177039	−	0.0735693i
$536$	4.13096e33			0.317315
$537$			1.18860e34i			0.891984i
$538$		−	4.43999e32i		−	0.0325539i
$539$	−1.21272e34			−0.868762
$540$	4.71685e33	−	1.96011e33i	0.330165	−	0.137202i
$541$	7.92779e32			0.0542234			0.0271117	−	0.999632i	$-0.491369\pi$
$541$	7.92779e32			0.0542234			0.0271117	+	0.999632i	$0.491369\pi$
$542$			3.44279e33i			0.230102i
$543$			9.40134e33i			0.614033i
$544$	4.36752e33			0.278772
$545$	−9.42336e33	−	2.26766e34i	−0.587827	−	1.41456i
$546$	−2.79321e34			−1.70293
$547$			2.56023e34i			1.52559i	0.646641	+	0.762794i	$0.276173\pi$
$547$			2.56023e34i			1.52559i	−0.646641	+	0.762794i	$0.723827\pi$
$548$			6.03878e33i			0.351716i
$549$	−2.47878e33			−0.141118
$550$	−9.91310e33	−	9.86783e33i	−0.551666	−	0.549146i
$551$	−2.24034e34			−1.21876
$552$		−	1.35946e34i		−	0.722981i
$553$		−	3.84298e34i		−	1.99804i
$554$	2.16387e34			1.09992
$555$	1.03990e34	+	2.50244e34i	0.516810	+	1.24366i
$556$	−8.69308e33			−0.422414
$557$			2.77017e34i			1.31618i	0.752938	+	0.658091i	$0.228636\pi$
$557$			2.77017e34i			1.31618i	−0.752938	+	0.658091i	$0.771364\pi$
$558$		−	3.96565e33i		−	0.184241i
$559$	−1.57244e33			−0.0714375
$560$	−6.95070e33	+	2.88840e33i	−0.308801	+	0.128324i
$561$	−4.71819e34			−2.04993
$562$		−	2.41545e34i		−	1.02635i
$563$			1.80222e33i			0.0748951i	0.999299	+	0.0374476i	$0.0119227\pi$
$563$			1.80222e33i			0.0748951i	−0.999299	+	0.0374476i	$0.988077\pi$
$564$	8.39110e33			0.341060
$565$	1.40669e34	−	5.84558e33i	0.559234	−	0.232393i
$566$	6.48499e33			0.252176
$567$			4.35652e34i			1.65711i
$568$		−	2.46728e33i		−	0.0918044i
$569$	2.00804e34			0.730920			0.365460	−	0.930827i	$-0.380912\pi$
$569$	2.00804e34			0.730920			0.365460	+	0.930827i	$0.380912\pi$
$570$	−9.53485e33	−	2.29449e34i	−0.339530	−	0.817052i
$571$	3.27237e34			1.14002			0.570008	−	0.821639i	$-0.306940\pi$
$571$	3.27237e34			1.14002			0.570008	+	0.821639i	$0.306940\pi$
$572$			2.46215e34i			0.839198i
$573$		−	1.91753e34i		−	0.639453i
$574$	−8.46937e32			−0.0276346
$575$	−3.84410e34	−	3.82655e34i	−1.22729	−	1.22168i
$576$	1.57828e33			0.0493063
$577$		−	1.86866e34i		−	0.571257i	−0.958340	−	0.285629i	$-0.907798\pi$
$577$		−	1.86866e34i		−	0.571257i	0.958340	−	0.285629i	$-0.0922024\pi$
$578$		−	3.51436e34i		−	1.05135i
$579$	5.50883e33			0.161279
$580$	−7.70232e33	−	1.85350e34i	−0.220684	−	0.531060i
$581$	2.25541e34			0.632447
$582$			3.87806e34i			1.06433i
$583$			2.91701e34i			0.783575i
$584$	1.36309e34			0.358398
$585$	2.15789e34	−	8.96723e33i	0.555369	−	0.230786i
$586$	2.03310e34			0.512198
$587$			2.44688e33i			0.0603443i	0.999545	+	0.0301721i	$0.00960555\pi$
$587$			2.44688e33i			0.0603443i	−0.999545	+	0.0301721i	$0.990394\pi$
$588$		−	1.93008e34i		−	0.465970i
$589$	2.96146e34			0.699945
$590$	4.54631e33	−	1.88924e33i	0.105198	−	0.0437157i
$591$	−6.14325e33			−0.139173
$592$		−	1.28544e34i		−	0.285122i
$593$			3.48844e34i			0.757613i	0.925476	+	0.378806i	$0.123665\pi$
$593$			3.48844e34i			0.757613i	−0.925476	+	0.378806i	$0.876335\pi$
$594$	2.61747e34			0.556610
$595$	3.88734e34	+	9.35458e34i	0.809451	+	1.94788i
$596$	−3.22106e34			−0.656780
$597$			2.38297e34i			0.475817i
$598$			9.54772e34i			1.86696i
$599$	−6.48903e34			−1.24264			−0.621319	−	0.783558i	$-0.713403\pi$
$599$	−6.48903e34			−1.24264			−0.621319	+	0.783558i	$0.713403\pi$
$600$	1.57049e34	−	1.57770e34i	0.294541	−	0.295892i
$601$	−2.18034e34			−0.400492			−0.200246	−	0.979746i	$-0.564174\pi$
$601$	−2.18034e34			−0.400492			−0.200246	+	0.979746i	$0.564174\pi$
$602$		−	2.46330e33i		−	0.0443160i
$603$		−	2.00907e34i		−	0.354020i
$604$	2.02016e34			0.348678
$605$	−4.80721e33	−	1.15682e34i	−0.0812738	−	0.195579i
$606$	3.47922e34			0.576201
$607$		−	7.37348e34i		−	1.19623i	−0.801411	−	0.598114i	$-0.795917\pi$
$607$		−	7.37348e34i		−	1.19623i	0.801411	−	0.598114i	$-0.204083\pi$
$608$			1.17862e34i			0.187318i
$609$	1.16684e35			1.81675
$610$	1.53147e34	−	6.36410e33i	0.233607	−	0.0970764i
$611$	−5.89324e34			−0.880722
$612$		−	2.12412e34i		−	0.311018i
$613$		−	1.05162e35i		−	1.50870i	−0.656473	−	0.754349i	$-0.727953\pi$
$613$		−	1.05162e35i		−	1.50870i	0.656473	−	0.754349i	$-0.272047\pi$
$614$	−5.29804e34			−0.744750
$615$	2.31306e33	−	9.61205e32i	0.0318602	−	0.0132397i
$616$	−3.85707e34			−0.520593
$617$			8.12769e34i			1.07499i	0.843268	+	0.537493i	$0.180628\pi$
$617$			8.12769e34i			1.07499i	−0.843268	+	0.537493i	$0.819372\pi$
$618$			4.70496e34i			0.609818i
$619$	−4.81305e34			−0.611346			−0.305673	−	0.952137i	$-0.598881\pi$
$619$	−4.81305e34			−0.611346			−0.305673	+	0.952137i	$0.598881\pi$
$620$	1.01815e34	+	2.45011e34i	0.126741	+	0.304993i
$621$	1.01500e35			1.23829
$622$		−	6.90737e33i		−	0.0825910i
$623$			2.90978e34i			0.341004i
$624$	−3.91858e34			−0.450113
$625$	−4.06568e32	−	8.88169e34i	−0.00457755	−	0.999990i
$626$	1.10746e34			0.122221
$627$		−	1.27325e35i		−	1.37743i
$628$			7.26425e34i			0.770363i
$629$	−1.73001e35			−1.79852
$630$	1.40476e34	+	3.38044e34i	0.143167	+	0.344521i
$631$	6.11675e34			0.611158			0.305579	−	0.952167i	$-0.401150\pi$
$631$	6.11675e34			0.611158			0.305579	+	0.952167i	$0.401150\pi$
$632$		−	5.39130e34i		−	0.528117i
$633$		−	9.90222e34i		−	0.951012i
$634$	−1.34802e35			−1.26935
$635$	−9.66110e34	+	4.01472e34i	−0.891979	+	0.370666i
$636$	−4.64250e34			−0.420279
$637$			1.35553e35i			1.20328i
$638$		−	1.02854e35i		−	0.895289i
$639$	−1.19995e34			−0.102424
$640$	−9.75111e33	+	4.05212e33i	−0.0816214	+	0.0339182i
$641$	9.15866e34			0.751807			0.375904	−	0.926659i	$-0.377332\pi$
$641$	9.15866e34			0.751807			0.375904	+	0.926659i	$0.377332\pi$
$642$			1.98854e34i			0.160083i
$643$			5.09730e34i			0.402442i	0.979546	+	0.201221i	$0.0644909\pi$
$643$			5.09730e34i			0.402442i	−0.979546	+	0.201221i	$0.935509\pi$
$644$	−1.49569e35			−1.15816
$645$	2.79564e33	+	6.72750e33i	0.0212317	+	0.0510925i
$646$	1.58624e35			1.18158
$647$		−	2.28658e35i		−	1.67064i	−0.549765	−	0.835320i	$-0.685283\pi$
$647$		−	2.28658e35i		−	1.67064i	0.549765	−	0.835320i	$-0.314717\pi$
$648$			6.11174e34i			0.438003i
$649$	2.52283e34			0.177349
$650$	−1.10299e35	+	1.10805e35i	−0.760595	+	0.764085i
$651$	−1.54242e35			−1.04338
$652$			8.42585e34i			0.559138i
$653$		−	1.93736e35i		−	1.26124i	−0.776093	−	0.630618i	$-0.782801\pi$
$653$		−	1.93736e35i		−	1.26124i	0.776093	−	0.630618i	$-0.217199\pi$
$654$	2.00272e35			1.27908
$655$	4.66623e34	+	1.12289e35i	0.292382	+	0.703593i
$656$	−1.18816e33			−0.00730429
$657$		−	6.62933e34i		−	0.399855i
$658$		−	9.23202e34i		−	0.546353i
$659$	2.14078e35			1.24310			0.621548	−	0.783376i	$-0.286504\pi$
$659$	2.14078e35			1.24310			0.621548	+	0.783376i	$0.286504\pi$
$660$	1.05340e35	−	4.37746e34i	0.600199	−	0.249416i
$661$	1.52863e35			0.854641			0.427320	−	0.904100i	$-0.359458\pi$
$661$	1.52863e35			0.854641			0.427320	+	0.904100i	$0.359458\pi$
$662$		−	1.27126e35i		−	0.697445i
$663$			5.27381e35i			2.83926i
$664$	3.16410e34			0.167167
$665$	−2.52443e35	+	1.04904e35i	−1.30886	+	0.543902i
$666$	−6.25168e34			−0.318104
$667$		−	3.98848e35i		−	1.99175i
$668$		−	1.99193e35i		−	0.976265i
$669$	−1.15225e35			−0.554268
$670$	5.15815e34	+	1.24127e35i	0.243534	+	0.586044i
$671$	8.49840e34			0.393827
$672$		−	6.13863e34i		−	0.279226i
$673$			2.04386e35i			0.912564i	0.889835	+	0.456282i	$0.150819\pi$
$673$			2.04386e35i			0.912564i	−0.889835	+	0.456282i	$0.849181\pi$
$674$	−1.31040e35			−0.574322
$675$	1.17795e35	+	1.17257e35i	0.506790	+	0.504475i
$676$	1.56823e35			0.662331
$677$			4.21908e34i			0.174928i	0.996168	+	0.0874640i	$0.0278763\pi$
$677$			4.21908e34i			0.174928i	−0.996168	+	0.0874640i	$0.972124\pi$
$678$			1.24235e35i			0.505675i
$679$	4.26671e35			1.70498
$680$	5.45353e34	+	1.31235e35i	0.213952	+	0.514858i
$681$	−5.44620e35			−2.09776
$682$			1.35961e35i			0.514173i
$683$			2.99380e35i			1.11164i	0.831303	+	0.555820i	$0.187595\pi$
$683$			2.99380e35i			1.11164i	−0.831303	+	0.555820i	$0.812405\pi$
$684$	5.73215e34			0.208986
$685$	−1.81453e35	+	7.54036e34i	−0.649578	+	0.269935i
$686$	5.67203e34			0.199383
$687$		−	3.47948e34i		−	0.120103i
$688$		−	3.45575e33i		−	0.0117135i
$689$	3.26052e35			1.08529
$690$	4.08488e35	−	1.69749e35i	1.33526	−	0.554874i
$691$	8.03613e34			0.257971			0.128986	−	0.991646i	$-0.458828\pi$
$691$	8.03613e34			0.257971			0.128986	+	0.991646i	$0.458828\pi$
$692$		−	6.98304e34i		−	0.220150i
$693$			1.87586e35i			0.580812i
$694$	−1.77854e35			−0.540843
$695$	−1.08547e35	−	2.61209e35i	−0.324195	−	0.780149i
$696$	1.63695e35			0.480198
$697$			1.59909e34i			0.0460746i
$698$		−	3.98207e35i		−	1.12698i
$699$	6.73516e35			1.87233
$700$	−1.73581e35	−	1.72788e35i	−0.473998	−	0.471833i
$701$	−4.53710e35			−1.21704			−0.608518	−	0.793540i	$-0.708235\pi$
$701$	−4.53710e35			−1.21704			−0.608518	+	0.793540i	$0.708235\pi$
$702$		−	2.92570e35i		−	0.770932i
$703$		−	4.66860e35i		−	1.20850i
$704$	−5.41106e34			−0.137602
$705$	1.04776e35	+	2.52135e35i	0.261757	+	0.629897i
$706$	−4.23667e35			−1.03984
$707$		−	3.82789e35i		−	0.923032i
$708$			4.01515e34i			0.0951232i
$709$	1.72814e35			0.402255			0.201128	−	0.979565i	$-0.435539\pi$
$709$	1.72814e35			0.402255			0.201128	+	0.979565i	$0.435539\pi$
$710$	7.41365e34	−	3.08078e34i	0.169552	−	0.0704581i
$711$	−2.62203e35			−0.589206
$712$			4.08212e34i			0.0901334i
$713$			5.27229e35i			1.14388i
$714$	−8.26166e35			−1.76133
$715$	−7.39825e35	+	3.07438e35i	−1.54990	+	0.644068i
$716$	1.83459e35			0.377681
$717$			2.35585e35i			0.476604i
$718$		−	1.77703e35i		−	0.353296i
$719$	−9.50282e35			−1.85670			−0.928349	−	0.371709i	$-0.878772\pi$
$719$	−9.50282e35			−1.85670			−0.928349	+	0.371709i	$0.878772\pi$
$720$	1.97073e34	+	4.74239e34i	0.0378416	+	0.0910629i
$721$	5.17647e35			0.976884
$722$			4.68219e34i			0.0868429i
$723$		−	8.11256e35i		−	1.47887i
$724$	1.45108e35			0.259992
$725$	4.60763e35	−	4.62877e35i	0.811433	−	0.815156i
$726$	1.02166e35			0.176848
$727$			1.71833e35i			0.292367i	0.989258	+	0.146183i	$0.0466989\pi$
$727$			1.71833e35i			0.292367i	−0.989258	+	0.146183i	$0.953301\pi$
$728$			4.31128e35i			0.721048i
$729$	−2.16385e35			−0.355741
$730$	1.70203e35	+	4.09581e35i	0.275063	+	0.661918i
$731$	−4.65090e34			−0.0738873
$732$			1.35254e35i			0.211233i
$733$			5.57098e35i			0.855327i	0.903938	+	0.427664i	$0.140663\pi$
$733$			5.57098e35i			0.855327i	−0.903938	+	0.427664i	$0.859337\pi$
$734$	1.93113e35			0.291481
$735$	5.79948e35	−	2.41000e35i	0.860592	−	0.357623i
$736$	−2.09830e35			−0.306122
$737$			6.88801e35i			0.987985i
$738$			5.77856e33i			0.00814921i
$739$	−6.81418e35			−0.944839			−0.472420	−	0.881374i	$-0.656619\pi$
$739$	−6.81418e35			−0.944839			−0.472420	+	0.881374i	$0.656619\pi$
$740$	3.86249e35	−	1.60508e35i	0.526588	−	0.218826i
$741$	−1.42319e36			−1.90781
$742$			5.10775e35i			0.673257i
$743$		−	7.94423e35i		−	1.02965i	−0.857294	−	0.514827i	$-0.827856\pi$
$743$		−	7.94423e35i		−	1.02965i	0.857294	−	0.514827i	$-0.172144\pi$
$744$	−2.16386e35			−0.275782
$745$	−4.02199e35	−	9.67861e35i	−0.504066	−	1.21300i
$746$	4.06564e35			0.501065
$747$		−	1.53884e35i		−	0.186503i
$748$			7.28246e35i			0.867977i
$749$	2.18782e35			0.256442
$750$	6.70166e35	+	2.74900e35i	0.772532	+	0.316890i
$751$	9.09984e35			1.03166			0.515828	−	0.856692i	$-0.327484\pi$
$751$	9.09984e35			1.03166			0.515828	+	0.856692i	$0.327484\pi$
$752$		−	1.29516e35i		−	0.144411i
$753$		−	8.11619e35i		−	0.890051i
$754$	−1.14966e36			−1.24002
$755$	2.52249e35	+	6.07016e35i	0.267604	+	0.643967i
$756$	4.58325e35			0.478245
$757$			9.30502e35i			0.955034i	0.878623	+	0.477517i	$0.158463\pi$
$757$			9.30502e35i			0.955034i	−0.878623	+	0.477517i	$0.841537\pi$
$758$			2.57570e35i			0.260034i
$759$	2.26677e36			2.25105
$760$	−3.54151e35	+	1.47169e35i	−0.345954	+	0.143763i
$761$	1.13441e36			1.09009			0.545045	−	0.838407i	$-0.316513\pi$
$761$	1.13441e36			1.09009			0.545045	+	0.838407i	$0.316513\pi$
$762$		−	8.53236e35i		−	0.806552i
$763$		−	2.20342e36i		−	2.04900i
$764$	−2.95967e35			−0.270755
$765$	6.38253e35	−	2.65229e35i	0.574414	−	0.238701i
$766$	−2.02904e35			−0.179651
$767$		−	2.81992e35i		−	0.245637i
$768$		−	8.61186e34i		−	0.0738043i
$769$	2.29001e36			1.93090			0.965448	−	0.260597i	$-0.0839193\pi$
$769$	2.29001e36			1.93090			0.965448	+	0.260597i	$0.0839193\pi$
$770$	−4.81615e35	−	1.15897e36i	−0.399546	−	0.961475i
$771$	−2.20990e35			−0.180382
$772$		−	8.50281e34i		−	0.0682883i
$773$			3.21550e35i			0.254100i	0.991896	+	0.127050i	$0.0405509\pi$
$773$			3.21550e35i			0.254100i	−0.991896	+	0.127050i	$0.959449\pi$
$774$	−1.68068e34			−0.0130684
$775$	−6.09074e35	+	6.11869e35i	−0.466014	+	0.468152i
$776$	5.98574e35			0.450657
$777$			2.43156e36i			1.80145i
$778$			1.67965e36i			1.22454i
$779$	−4.31529e34			−0.0309594
$780$	−4.89296e35	−	1.17745e36i	−0.345453	−	0.831305i
$781$	4.11397e35			0.285840
$782$			2.82399e36i			1.93098i
$783$			1.22219e36i			0.822461i
$784$	−2.97905e35			−0.197300
$785$	−2.18276e36	+	9.07055e35i	−1.42277	+	0.591239i
$786$	−9.91701e35			−0.636208
$787$		−	3.25977e35i		−	0.205827i	−0.994690	−	0.102914i	$-0.967183\pi$
$787$		−	3.25977e35i		−	0.205827i	0.994690	−	0.102914i	$-0.0328166\pi$
$788$			9.48202e34i			0.0589282i
$789$	−3.46437e36			−2.11915
$790$	1.61997e36	−	6.73188e35i	0.975370	−	0.405320i
$791$	1.36685e36			0.810054
$792$			2.63164e35i			0.153519i
$793$		−	9.49918e35i		−	0.545470i
$794$	7.41849e35			0.419333
$795$	−5.79688e35	−	1.39497e36i	−0.322556	−	0.776206i
$796$	3.67809e35			0.201469
$797$			8.54851e35i			0.460958i	0.973077	+	0.230479i	$0.0740293\pi$
$797$			8.54851e35i			0.460958i	−0.973077	+	0.230479i	$0.925971\pi$
$798$		−	2.22949e36i		−	1.18350i
$799$	−1.74308e36			−0.910925
$800$	−2.43515e35	−	2.42403e35i	−0.125286	−	0.124714i
$801$	1.98532e35			0.100559
$802$			5.33538e35i			0.266064i
$803$			2.27284e36i			1.11590i
$804$	−1.09625e36			−0.529917
$805$	−1.86761e36	−	4.49425e36i	−0.888867	−	2.13899i
$806$	1.51972e36			0.712156
$807$			1.17825e35i			0.0543651i
$808$		−	5.37013e35i		−	0.243973i
$809$	3.81958e36			1.70867			0.854336	−	0.519721i	$-0.173964\pi$
$809$	3.81958e36			1.70867			0.854336	+	0.519721i	$0.173964\pi$
$810$	−1.83645e36	+	7.63145e35i	−0.808940	+	0.336159i
$811$	−2.53614e36			−1.10005			−0.550025	−	0.835148i	$-0.685382\pi$
$811$	−2.53614e36			−1.10005			−0.550025	+	0.835148i	$0.685382\pi$
$812$		−	1.80100e36i		−	0.769243i
$813$		−	9.13625e35i		−	0.384270i
$814$	2.14336e36			0.887750
$815$	−2.53179e36	+	1.05210e36i	−1.03266	+	0.429128i
$816$	−1.15902e36			−0.465549
$817$		−	1.25509e35i		−	0.0496478i
$818$		−	3.51949e36i		−	1.37108i
$819$	2.09677e36			0.804455
$820$	−1.48361e34	−	3.57018e34i	−0.00560591	−	0.0134902i
$821$	−6.03536e35			−0.224602			−0.112301	−	0.993674i	$-0.535822\pi$
$821$	−6.03536e35			−0.224602			−0.112301	+	0.993674i	$0.535822\pi$
$822$		−	1.60253e36i		−	0.587366i
$823$		−	3.78844e36i		−	1.36761i	−0.729665	−	0.683804i	$-0.760324\pi$
$823$		−	3.78844e36i		−	1.36761i	0.729665	−	0.683804i	$-0.239676\pi$
$824$	7.26205e35			0.258208
$825$	2.63067e36	+	2.61866e36i	0.921282	+	0.917074i
$826$	4.41753e35			0.152380
$827$			3.11766e36i			1.05928i	0.848223	+	0.529639i	$0.177672\pi$
$827$			3.11766e36i			1.05928i	−0.848223	+	0.529639i	$0.822328\pi$
$828$			1.02050e36i			0.341533i
$829$	−5.42365e36			−1.78797			−0.893984	−	0.448099i	$-0.852101\pi$
$829$	−5.42365e36			−1.78797			−0.893984	+	0.448099i	$0.852101\pi$
$830$	3.95088e35	+	9.50747e35i	0.128297	+	0.308737i
$831$	−5.74233e36			−1.83686
$832$			6.04827e35i			0.190586i
$833$			4.00934e36i			1.24454i
$834$	2.30691e36			0.705432
$835$	5.98532e36	−	2.48723e36i	1.80305	−	0.749265i
$836$	−1.96525e36			−0.583228
$837$		−	1.61558e36i		−	0.472347i
$838$			1.91295e36i			0.551003i
$839$	3.97800e35			0.112886			0.0564431	−	0.998406i	$-0.482024\pi$
$839$	3.97800e35			0.112886			0.0564431	+	0.998406i	$0.482024\pi$
$840$	1.84453e36	−	7.66504e35i	0.515697	−	0.214301i
$841$	1.17226e36			0.322904
$842$		−	3.03953e36i		−	0.824907i
$843$			6.40996e36i			1.71400i
$844$	−1.52839e36			−0.402675
$845$	1.95818e36	+	4.71219e36i	0.508326	+	1.22325i
$846$	−6.29891e35			−0.161115
$847$		−	1.12405e36i		−	0.283297i
$848$			7.16563e35i			0.177953i
$849$	−1.72094e36			−0.421134
$850$	−3.26238e36	+	3.27734e36i	−0.786679	+	0.790288i
$851$	8.31153e36			1.97497
$852$			6.54749e35i			0.153313i
$853$		−	2.49788e36i		−	0.576379i	−0.957573	−	0.288189i	$-0.906947\pi$
$853$		−	2.49788e36i		−	0.576379i	0.957573	−	0.288189i	$-0.0930533\pi$
$854$	1.48809e36			0.338381
$855$	7.15748e35	+	1.72239e36i	0.160392	+	0.385972i
$856$	3.06928e35			0.0677820
$857$		−	5.58799e36i		−	1.21617i	−0.793871	−	0.608086i	$-0.791938\pi$
$857$		−	5.58799e36i		−	1.21617i	0.793871	−	0.608086i	$-0.208062\pi$
$858$		−	6.53389e36i		−	1.40146i
$859$	−4.00214e36			−0.846015			−0.423007	−	0.906126i	$-0.639026\pi$
$859$	−4.00214e36			−0.846015			−0.423007	+	0.906126i	$0.639026\pi$
$860$	1.03838e35	−	4.31504e34i	0.0216334	−	0.00898988i
$861$	2.24755e35			0.0461497
$862$			4.35896e36i			0.882149i
$863$		−	1.01320e36i		−	0.202097i	−0.994882	−	0.101048i	$-0.967780\pi$
$863$		−	1.01320e36i		−	0.202097i	0.994882	−	0.101048i	$-0.0322197\pi$
$864$	6.42981e35			0.126409
$865$	2.09826e36	−	8.71942e35i	0.406591	−	0.168961i
$866$	3.76971e36			0.720003
$867$			9.32618e36i			1.75576i
$868$			2.38071e36i			0.441783i
$869$	8.98952e36			1.64433
$870$	2.04399e36	+	4.91870e36i	0.368543	+	0.886870i
$871$	7.69915e36			1.36841
$872$		−	3.09117e36i		−	0.541586i
$873$		−	2.91113e36i		−	0.502786i
$874$	−7.62083e36			−1.29751
$875$	3.02449e36	−	7.37327e36i	0.507635	−	1.23754i
$876$	−3.61729e36			−0.598524
$877$		−	1.04808e37i		−	1.70962i	−0.518944	−	0.854808i	$-0.673675\pi$
$877$		−	1.04808e37i		−	1.70962i	0.518944	−	0.854808i	$-0.326325\pi$
$878$			1.57662e36i			0.253539i
$879$	−5.39529e36			−0.855370
$880$	−6.75656e35	−	1.62591e36i	−0.105607	−	0.254134i
$881$	−7.82632e36			−1.20603			−0.603016	−	0.797729i	$-0.706035\pi$
$881$	−7.82632e36			−1.20603			−0.603016	+	0.797729i	$0.706035\pi$
$882$			1.44884e36i			0.220122i
$883$			1.14075e37i			1.70876i	0.519651	+	0.854379i	$0.326062\pi$
$883$			1.14075e37i			1.70876i	−0.519651	+	0.854379i	$0.673938\pi$
$884$	8.14005e36			1.20219
$885$	−1.20647e36	+	5.01354e35i	−0.175681	+	0.0730052i
$886$	−3.49590e36			−0.501924
$887$		−	2.08825e35i		−	0.0295622i	−0.999891	−	0.0147811i	$-0.995295\pi$
$887$		−	2.08825e35i		−	0.0295622i	0.999891	−	0.0147811i	$-0.00470514\pi$
$888$			3.41122e36i			0.476155i
$889$	−9.38744e36			−1.29204
$890$	−1.22659e36	+	5.09716e35i	−0.166466	+	0.0691757i
$891$	−1.01908e37			−1.36375
$892$			1.77848e36i			0.234687i
$893$		−	4.70388e36i		−	0.612086i
$894$	8.54783e36			1.09682
$895$	2.29077e36	+	5.51255e36i	0.289863	+	0.697533i
$896$	−9.47490e35			−0.118229
$897$		−	2.53371e37i		−	3.11782i
$898$		−	1.40350e36i		−	0.170317i
$899$	−6.34849e36			−0.759756
$900$	−1.17891e36	+	1.18432e36i	−0.139140	+	0.139778i
$901$	9.64384e36			1.12251
$902$		−	1.98116e35i		−	0.0227425i
$903$			6.53693e35i			0.0740077i
$904$	1.91754e36			0.214111
$905$	1.81190e36	+	4.36020e36i	0.199539	+	0.480175i
$906$	−5.36097e36			−0.582292
$907$		−	1.26800e37i		−	1.35841i	−0.733950	−	0.679203i	$-0.762326\pi$
$907$		−	1.26800e37i		−	1.35841i	0.733950	−	0.679203i	$-0.237674\pi$
$908$			8.40614e36i			0.888226i
$909$	−2.61173e36			−0.272195
$910$	−1.29545e37	+	5.38331e36i	−1.33169	+	0.553391i
$911$	−9.78070e36			−0.991722			−0.495861	−	0.868402i	$-0.665148\pi$
$911$	−9.78070e36			−0.991722			−0.495861	+	0.868402i	$0.665148\pi$
$912$		−	3.12774e36i		−	0.312821i
$913$			5.27586e36i			0.520486i
$914$	−1.85175e36			−0.180200
$915$	−4.06411e36	+	1.68886e36i	−0.390123	+	0.162118i
$916$	−5.37053e35			−0.0508538
$917$			1.09108e37i			1.01916i
$918$		−	8.65354e36i		−	0.797370i
$919$	7.03823e36			0.639764			0.319882	−	0.947457i	$-0.396357\pi$
$919$	7.03823e36			0.639764			0.319882	+	0.947457i	$0.396357\pi$
$920$	−2.62006e36	−	6.30496e36i	−0.234943	−	0.565372i
$921$	1.40596e37			1.24373
$922$			1.01236e37i			0.883485i
$923$		−	4.59843e36i		−	0.395903i
$924$	1.02356e37			0.869391
$925$	9.64584e36	+	9.60178e36i	0.808292	+	0.804600i
$926$	−7.07085e36			−0.584567
$927$		−	3.53185e36i		−	0.288075i
$928$		−	2.52661e36i		−	0.203324i
$929$	−2.91517e36			−0.231455			−0.115728	−	0.993281i	$-0.536920\pi$
$929$	−2.91517e36			−0.231455			−0.115728	+	0.993281i	$0.536920\pi$
$930$	−2.70191e36	−	6.50194e36i	−0.211658	−	0.509338i
$931$	−1.08196e37			−0.836258
$932$		−	1.03956e37i		−	0.792778i
$933$			1.83303e36i			0.137927i
$934$	7.71244e36			0.572606
$935$	−2.18823e37	+	9.09328e36i	−1.60305	+	0.666156i
$936$	2.94154e36			0.212631
$937$		−	1.15106e37i		−	0.821016i	−0.911857	−	0.410508i	$-0.865351\pi$
$937$		−	1.15106e37i		−	0.821016i	0.911857	−	0.410508i	$-0.134649\pi$
$938$			1.20611e37i			0.848888i
$939$	−2.93889e36			−0.204110
$940$	3.89167e36	−	1.61720e36i	0.266709	−	0.110832i
$941$	1.44936e37			0.980179			0.490090	−	0.871672i	$-0.336964\pi$
$941$	1.44936e37			0.980179			0.490090	+	0.871672i	$0.336964\pi$
$942$		−	1.92774e37i		−	1.28651i
$943$		−	7.68253e35i		−	0.0505951i
$944$	6.19733e35			0.0402768
$945$	5.72290e36	+	1.37717e37i	0.367044	+	0.883262i
$946$	5.76215e35			0.0364708
$947$			2.53109e37i			1.58100i	0.612459	+	0.790502i	$0.290180\pi$
$947$			2.53109e37i			1.58100i	−0.612459	+	0.790502i	$0.709820\pi$
$948$			1.43071e37i			0.881956i
$949$	2.54049e37			1.54557
$950$	−8.84425e36	−	8.80385e36i	−0.531026	−	0.528601i
$951$	3.57728e37			2.11981
$952$			1.27518e37i			0.745775i
$953$		−	8.20660e36i		−	0.473698i	−0.971546	−	0.236849i	$-0.923885\pi$
$953$		−	8.20660e36i		−	0.473698i	0.971546	−	0.236849i	$-0.0761147\pi$
$954$	3.48496e36			0.198538
$955$	−3.69562e36	−	8.89320e36i	−0.207800	−	0.500053i
$956$	3.63622e36			0.201803
$957$			2.72948e37i			1.49513i
$958$		−	4.39513e36i		−	0.237631i
$959$	−1.76313e37			−0.940917
$960$	2.58768e36	−	1.07532e36i	0.136308	−	0.0566434i
$961$	−1.08408e37			−0.563665
$962$		−	2.39577e37i		−	1.22958i
$963$		−	1.49273e36i		−	0.0756226i
$964$	−1.25216e37			−0.626178
$965$	2.55492e36	−	1.06171e36i	0.126120	−	0.0524099i
$966$	3.96917e37			1.93413
$967$			2.92106e37i			1.40511i	0.711630	+	0.702555i	$0.247957\pi$
$967$			2.92106e37i			1.40511i	−0.711630	+	0.702555i	$0.752043\pi$
$968$		−	1.57692e36i		−	0.0748804i
$969$	−4.20946e37			−1.97324
$970$	7.47413e36	+	1.79859e37i	0.345871	+	0.832310i
$971$	9.97325e36			0.455613			0.227807	−	0.973706i	$-0.426845\pi$
$971$	9.97325e36			0.455613			0.227807	+	0.973706i	$0.426845\pi$
$972$		−	8.29117e36i		−	0.373928i
$973$		−	2.53810e37i		−	1.13005i
$974$	2.56529e37			1.12759
$975$	2.92703e37	−	2.94046e37i	1.27019	−	1.27602i
$976$	2.08763e36			0.0894399
$977$		−	3.07257e37i		−	1.29963i	−0.760092	−	0.649816i	$-0.774846\pi$
$977$		−	3.07257e37i		−	1.29963i	0.760092	−	0.649816i	$-0.225154\pi$
$978$		−	2.23600e37i		−	0.933760i
$979$	−6.80658e36			−0.280637
$980$	−3.71980e36	−	8.95141e36i	−0.151424	−	0.364389i
$981$	−1.50337e37			−0.604233
$982$			1.27153e37i			0.504582i
$983$		−	5.34152e36i		−	0.209289i	−0.994510	−	0.104644i	$-0.966630\pi$
$983$		−	5.34152e36i		−	0.209289i	0.994510	−	0.104644i	$-0.0333704\pi$
$984$	3.15307e35			0.0121982
$985$	−2.84915e36	+	1.18398e36i	−0.108833	+	0.0452263i
$986$	−3.40043e37			−1.28255
$987$			2.44993e37i			0.912409i
$988$			2.19667e37i			0.807800i
$989$	2.23445e36			0.0811365
$990$	−7.90753e36	+	3.28601e36i	−0.283531	+	0.117823i
$991$	−4.37784e36			−0.155003			−0.0775013	−	0.996992i	$-0.524694\pi$
$991$	−4.37784e36			−0.155003			−0.0775013	+	0.996992i	$0.524694\pi$
$992$			3.33988e36i			0.116771i
$993$			3.37359e37i			1.16473i
$994$	7.20365e36			0.245597
$995$	4.59266e36	+	1.10519e37i	0.154624	+	0.372090i
$996$	−8.39668e36			−0.279168
$997$			2.23560e37i			0.734015i	0.930218	+	0.367008i	$0.119618\pi$
$997$			2.23560e37i			0.734015i	−0.930218	+	0.367008i	$0.880382\pi$
$998$		−	2.91817e37i		−	0.946190i
$999$	−2.54690e37			−0.815535

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.26.b.a.9.7	yes	12
5.2	odd	4		50.26.a.k.1.1		6
5.3	odd	4		50.26.a.l.1.6		6
5.4	even	2	inner	10.26.b.a.9.6	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.26.b.a.9.6	✓	12	5.4	even	2	inner
10.26.b.a.9.7	yes	12	1.1	even	1	trivial
50.26.a.k.1.1		6	5.2	odd	4
50.26.a.l.1.6		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} -1.08697e6i q^{3} -1.67772e7 q^{4} +(-2.09490e8 - 5.04120e8i) q^{5} +4.45223e9 q^{6} -4.89841e10i q^{7} -6.87195e10i q^{8} -3.34213e11 q^{9} +(2.06488e12 - 8.58070e11i) q^{10} +1.14584e13 q^{11} +1.82363e13i q^{12} -1.28077e14i q^{13} +2.00639e14 q^{14} +(-5.47963e14 + 2.27709e14i) q^{15} +2.81475e14 q^{16} -3.78822e15i q^{17} -1.36894e15i q^{18} +1.02229e16 q^{19} +(3.51465e15 + 8.45774e15i) q^{20} -5.32442e16 q^{21} +4.69335e16i q^{22} +1.81999e17i q^{23} -7.46959e16 q^{24} +(-2.10251e17 + 2.11216e17i) q^{25} +5.24604e17 q^{26} -5.57697e17i q^{27} +8.21816e17i q^{28} -2.19149e18 q^{29} +(-9.32695e17 - 2.24446e18i) q^{30} +2.89689e18 q^{31} +1.15292e18i q^{32} -1.24549e19i q^{33} +1.55166e19 q^{34} +(-2.46939e19 + 1.02617e19i) q^{35} +5.60717e18 q^{36} -4.56681e19i q^{37} +4.18730e19i q^{38} -1.39216e20 q^{39} +(-3.46429e19 + 1.43960e19i) q^{40} -4.22120e18 q^{41} -2.18088e20i q^{42} -1.22773e19i q^{43} -1.92240e20 q^{44} +(7.00142e19 + 1.68484e20i) q^{45} -7.45466e20 q^{46} -4.60132e20i q^{47} -3.05955e20i q^{48} -1.05837e21 q^{49} +(-8.65141e20 - 8.61190e20i) q^{50} -4.11768e21 q^{51} +2.14878e21i q^{52} +2.54574e21i q^{53} +2.28433e21 q^{54} +(-2.40041e21 - 5.77640e21i) q^{55} -3.36616e21 q^{56} -1.11120e22i q^{57} -8.97634e21i q^{58} +2.20173e21 q^{59} +(9.19330e21 - 3.82032e21i) q^{60} +7.41676e21 q^{61} +1.18656e22i q^{62} +1.63711e22i q^{63} -4.72237e21 q^{64} +(-6.45663e22 + 2.68309e22i) q^{65} +5.10153e22 q^{66} +6.01134e22i q^{67} +6.35558e22i q^{68} +1.97827e23 q^{69} +(-4.20317e22 - 1.01146e23i) q^{70} +3.59036e22 q^{71} +2.29670e22i q^{72} +1.98356e23i q^{73} +1.87057e23 q^{74} +(2.29585e23 + 2.28537e23i) q^{75} -1.71512e23 q^{76} -5.61278e23i q^{77} -5.70229e23i q^{78} +7.84538e23 q^{79} +(-5.89661e22 - 1.41897e23i) q^{80} -8.89375e23 q^{81} -1.72901e22i q^{82} +4.60438e23i q^{83} +8.93289e23 q^{84} +(-1.90972e24 + 7.93593e23i) q^{85} +5.02877e22 q^{86} +2.38208e24i q^{87} -7.87413e23i q^{88} -5.94026e23 q^{89} +(-6.90109e23 + 2.86778e23i) q^{90} -6.27374e24 q^{91} -3.05343e24i q^{92} -3.14882e24i q^{93} +1.88470e24 q^{94} +(-2.14159e24 - 5.15357e24i) q^{95} +1.25319e24 q^{96} +8.71039e24i q^{97} -4.33508e24i q^{98} -3.82954e24 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more