LMFDB - Embedded newform 5.13.c.a.3.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,13,Mod(2,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 13, names="a")

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

chi := DirichletCharacter("5.2");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 13 $
Character orbit:	$[\chi]$	$=$	5.c (of order $4$, degree $2$, 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:	$4.56996908638$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 7950x^{8} + 16939113x^{6} + 4574579500x^{4} + 337520899536x^{2} + 6615595526400 $ x^10 + 7950x^8 + 16939113x^6 + 4574579500x^4 + 337520899536x^2 + 6615595526400
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{13}\cdot 3^{2}\cdot 5^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.3
Root			$62.7587i$ of defining polynomial
Character	$\chi$	$=$	5.3
Dual form			5.13.c.a.2.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.05147 - 3.05147i) q^{2} +(-299.721 - 299.721i) q^{3} +4077.38i q^{4} +(-15614.1 - 583.350i) q^{5} -1829.18 q^{6} +(-139850. + 139850. i) q^{7} +(24940.8 + 24940.8i) q^{8} -351775. i q^{9} +O(q^{10})$	\(q+(3.05147 - 3.05147i) q^{2} +(-299.721 - 299.721i) q^{3} +4077.38i q^{4} +(-15614.1 - 583.350i) q^{5} -1829.18 q^{6} +(-139850. + 139850. i) q^{7} +(24940.8 + 24940.8i) q^{8} -351775. i q^{9} +(-49426.1 + 45865.9i) q^{10} +1.90233e6 q^{11} +(1.22208e6 - 1.22208e6i) q^{12} +(-1.77028e6 - 1.77028e6i) q^{13} +853498. i q^{14} +(4.50504e6 + 4.85473e6i) q^{15} -1.65487e7 q^{16} +(-1.14267e7 + 1.14267e7i) q^{17} +(-1.07343e6 - 1.07343e6i) q^{18} +2.79430e7i q^{19} +(2.37854e6 - 6.36646e7i) q^{20} +8.38323e7 q^{21} +(5.80490e6 - 5.80490e6i) q^{22} +(-3.91216e7 - 3.91216e7i) q^{23} -1.49506e7i q^{24} +(2.43460e8 + 1.82170e7i) q^{25} -1.08039e7 q^{26} +(-2.64719e8 + 2.64719e8i) q^{27} +(-5.70223e8 - 5.70223e8i) q^{28} +8.54927e8i q^{29} +(2.85611e7 + 1.06705e6i) q^{30} +5.03000e8 q^{31} +(-1.52656e8 + 1.52656e8i) q^{32} +(-5.70168e8 - 5.70168e8i) q^{33} +6.97363e7i q^{34} +(2.26522e9 - 2.10206e9i) q^{35} +1.43432e9 q^{36} +(-1.34249e9 + 1.34249e9i) q^{37} +(8.52671e7 + 8.52671e7i) q^{38} +1.06118e9i q^{39} +(-3.74879e8 - 4.03978e8i) q^{40} -2.34687e9 q^{41} +(2.55812e8 - 2.55812e8i) q^{42} +(-4.61986e9 - 4.61986e9i) q^{43} +7.75651e9i q^{44} +(-2.05208e8 + 5.49265e9i) q^{45} -2.38757e8 q^{46} +(2.02672e8 - 2.02672e8i) q^{47} +(4.96001e9 + 4.96001e9i) q^{48} -2.52749e10i q^{49} +(7.98500e8 - 6.87323e8i) q^{50} +6.84963e9 q^{51} +(7.21811e9 - 7.21811e9i) q^{52} +(1.74618e10 + 1.74618e10i) q^{53} +1.61556e9i q^{54} +(-2.97031e10 - 1.10972e9i) q^{55} -6.97596e9 q^{56} +(8.37511e9 - 8.37511e9i) q^{57} +(2.60878e9 + 2.60878e9i) q^{58} +1.23184e10i q^{59} +(-1.97945e10 + 1.83688e10i) q^{60} -6.84075e10 q^{61} +(1.53489e9 - 1.53489e9i) q^{62} +(4.91959e10 + 4.91959e10i) q^{63} -6.68519e10i q^{64} +(2.66087e10 + 2.86741e10i) q^{65} -3.47970e9 q^{66} +(4.44857e10 - 4.44857e10i) q^{67} +(-4.65908e10 - 4.65908e10i) q^{68} +2.34512e10i q^{69} +(4.97888e8 - 1.33266e10i) q^{70} +2.05846e11 q^{71} +(8.77356e9 - 8.77356e9i) q^{72} +(-2.31849e10 - 2.31849e10i) q^{73} +8.19313e9i q^{74} +(-6.75102e10 - 7.84302e10i) q^{75} -1.13934e11 q^{76} +(-2.66041e11 + 2.66041e11i) q^{77} +(3.23817e9 + 3.23817e9i) q^{78} +7.81035e10i q^{79} +(2.58394e11 + 9.65369e9i) q^{80} -2.82638e10 q^{81} +(-7.16139e9 + 7.16139e9i) q^{82} +(-3.18989e11 - 3.18989e11i) q^{83} +3.41816e11i q^{84} +(1.85083e11 - 1.71751e11i) q^{85} -2.81948e10 q^{86} +(2.56240e11 - 2.56240e11i) q^{87} +(4.74456e10 + 4.74456e10i) q^{88} +9.33617e10i q^{89} +(1.61345e10 + 1.73869e10i) q^{90} +4.95149e11 q^{91} +(1.59514e11 - 1.59514e11i) q^{92} +(-1.50760e11 - 1.50760e11i) q^{93} -1.23689e9i q^{94} +(1.63005e10 - 4.36304e11i) q^{95} +9.15083e10 q^{96} +(-9.38946e11 + 9.38946e11i) q^{97} +(-7.71257e10 - 7.71257e10i) q^{98} -6.69191e11i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} + 318 q^{3} - 4250 q^{5} - 175080 q^{6} + 279598 q^{7} - 469980 q^{8}+O(q^{10}) $ 10 * q - 2 * q^2 + 318 * q^3 - 4250 * q^5 - 175080 * q^6 + 279598 * q^7 - 469980 * q^8	\( 10 q - 2 q^{2} + 318 q^{3} - 4250 q^{5} - 175080 q^{6} + 279598 q^{7} - 469980 q^{8} + 1552150 q^{10} + 312620 q^{11} - 2359992 q^{12} + 5290738 q^{13} - 5821650 q^{15} + 30547960 q^{16} - 41269502 q^{17} - 140573742 q^{18} + 334988100 q^{20} + 107493420 q^{21} - 155490544 q^{22} - 510099842 q^{23} + 942201250 q^{25} + 1475846420 q^{26} - 1993958640 q^{27} - 3562106488 q^{28} + 5922516000 q^{30} + 3077089820 q^{31} - 4623883832 q^{32} - 7503698004 q^{33} + 9330787150 q^{35} + 7760793660 q^{36} - 2599618502 q^{37} - 15310240920 q^{38} + 15901243500 q^{40} + 7412079020 q^{41} - 18593270064 q^{42} - 5784410402 q^{43} - 10510145100 q^{45} - 7382547880 q^{46} + 16053249598 q^{47} + 42572492208 q^{48} - 68314688750 q^{50} - 33139878180 q^{51} + 96763417228 q^{52} + 101763514618 q^{53} - 84180068500 q^{55} - 172002747600 q^{56} + 27733489920 q^{57} + 135238672320 q^{58} - 220124568600 q^{60} + 7731718220 q^{61} + 193287375176 q^{62} + 207465112158 q^{63} - 338075024150 q^{65} - 60815472960 q^{66} - 80010636002 q^{67} + 204699541412 q^{68} + 376969924200 q^{70} - 46557252580 q^{71} - 13986370620 q^{72} - 448527032342 q^{73} + 719724648750 q^{75} + 305095930800 q^{76} - 425580405844 q^{77} - 1690993241784 q^{78} + 873032236000 q^{80} + 1107831051810 q^{81} - 671946416464 q^{82} - 91118376722 q^{83} + 543768569650 q^{85} + 414117747320 q^{86} - 2078422804320 q^{87} - 1842434230560 q^{88} + 3098742811350 q^{90} + 2737742572220 q^{91} + 906853941448 q^{92} - 91295366484 q^{93} - 1044695070000 q^{95} - 3473259523680 q^{96} - 1409507601302 q^{97} - 1481746533298 q^{98}+O(q^{100}) \) 10 * q - 2 * q^2 + 318 * q^3 - 4250 * q^5 - 175080 * q^6 + 279598 * q^7 - 469980 * q^8 + 1552150 * q^10 + 312620 * q^11 - 2359992 * q^12 + 5290738 * q^13 - 5821650 * q^15 + 30547960 * q^16 - 41269502 * q^17 - 140573742 * q^18 + 334988100 * q^20 + 107493420 * q^21 - 155490544 * q^22 - 510099842 * q^23 + 942201250 * q^25 + 1475846420 * q^26 - 1993958640 * q^27 - 3562106488 * q^28 + 5922516000 * q^30 + 3077089820 * q^31 - 4623883832 * q^32 - 7503698004 * q^33 + 9330787150 * q^35 + 7760793660 * q^36 - 2599618502 * q^37 - 15310240920 * q^38 + 15901243500 * q^40 + 7412079020 * q^41 - 18593270064 * q^42 - 5784410402 * q^43 - 10510145100 * q^45 - 7382547880 * q^46 + 16053249598 * q^47 + 42572492208 * q^48 - 68314688750 * q^50 - 33139878180 * q^51 + 96763417228 * q^52 + 101763514618 * q^53 - 84180068500 * q^55 - 172002747600 * q^56 + 27733489920 * q^57 + 135238672320 * q^58 - 220124568600 * q^60 + 7731718220 * q^61 + 193287375176 * q^62 + 207465112158 * q^63 - 338075024150 * q^65 - 60815472960 * q^66 - 80010636002 * q^67 + 204699541412 * q^68 + 376969924200 * q^70 - 46557252580 * q^71 - 13986370620 * q^72 - 448527032342 * q^73 + 719724648750 * q^75 + 305095930800 * q^76 - 425580405844 * q^77 - 1690993241784 * q^78 + 873032236000 * q^80 + 1107831051810 * q^81 - 671946416464 * q^82 - 91118376722 * q^83 + 543768569650 * q^85 + 414117747320 * q^86 - 2078422804320 * q^87 - 1842434230560 * q^88 + 3098742811350 * q^90 + 2737742572220 * q^91 + 906853941448 * q^92 - 91295366484 * q^93 - 1044695070000 * q^95 - 3473259523680 * q^96 - 1409507601302 * q^97 - 1481746533298 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	3.05147	−	3.05147i	0.0476792	−	0.0476792i	−0.682865	−	0.730544i	$-0.739266\pi$
$2$	3.05147	−	3.05147i	0.0476792	−	0.0476792i	0.730544	+	0.682865i	$0.239266\pi$
$3$	−299.721	−	299.721i	−0.411141	−	0.411141i	0.470995	−	0.882136i	$-0.343895\pi$
$3$	−299.721	−	299.721i	−0.411141	−	0.411141i	−0.882136	+	0.470995i	$0.843895\pi$
$4$			4077.38i			0.995453i
$5$	−15614.1	−	583.350i	−0.999303	−	0.0373344i
$5$	−15614.1	−	583.350i	−0.999303	−	0.0373344i
$6$	−1829.18			−0.0392057
$7$	−139850.	+	139850.i	−1.18871	+	1.18871i	−0.211283	+	0.977425i	$0.567764\pi$
$7$	−139850.	+	139850.i	−1.18871	+	1.18871i	−0.977425	+	0.211283i	$0.932236\pi$
$8$	24940.8	+	24940.8i	0.0951417	+	0.0951417i
$9$		−	351775.i		−	0.661927i
$10$	−49426.1	+	45865.9i	−0.0494261	+	0.0458659i
$11$	1.90233e6			1.07381			0.536907	−	0.843641i	$-0.319593\pi$
$11$	1.90233e6			1.07381			0.536907	+	0.843641i	$0.319593\pi$
$12$	1.22208e6	−	1.22208e6i	0.409271	−	0.409271i
$13$	−1.77028e6	−	1.77028e6i	−0.366760	−	0.366760i	0.499534	−	0.866294i	$-0.333505\pi$
$13$	−1.77028e6	−	1.77028e6i	−0.366760	−	0.366760i	−0.866294	+	0.499534i	$0.833505\pi$
$14$			853498.i			0.113353i
$15$	4.50504e6	+	4.85473e6i	0.395504	+	0.426204i
$16$	−1.65487e7			−0.986381
$17$	−1.14267e7	+	1.14267e7i	−0.473398	+	0.473398i	−0.903012	−	0.429615i	$-0.858649\pi$
$17$	−1.14267e7	+	1.14267e7i	−0.473398	+	0.473398i	0.429615	+	0.903012i	$0.358649\pi$
$18$	−1.07343e6	−	1.07343e6i	−0.0315602	−	0.0315602i
$19$			2.79430e7i			0.593951i	0.954885	+	0.296976i	$0.0959780\pi$
$19$			2.79430e7i			0.593951i	−0.954885	+	0.296976i	$0.904022\pi$
$20$	2.37854e6	−	6.36646e7i	0.0371646	−	0.994759i
$21$	8.38323e7			0.977452
$22$	5.80490e6	−	5.80490e6i	0.0511986	−	0.0511986i
$23$	−3.91216e7	−	3.91216e7i	−0.264271	−	0.264271i	0.562516	−	0.826787i	$-0.309834\pi$
$23$	−3.91216e7	−	3.91216e7i	−0.264271	−	0.264271i	−0.826787	+	0.562516i	$0.809834\pi$
$24$		−	1.49506e7i		−	0.0782332i
$25$	2.43460e8	+	1.82170e7i	0.997212	+	0.0746167i
$26$	−1.08039e7			−0.0349737
$27$	−2.64719e8	+	2.64719e8i	−0.683286	+	0.683286i
$28$	−5.70223e8	−	5.70223e8i	−1.18330	−	1.18330i
$29$			8.54927e8i			1.43728i	0.695383	+	0.718639i	$0.255235\pi$
$29$			8.54927e8i			1.43728i	−0.695383	+	0.718639i	$0.744765\pi$
$30$	2.85611e7	+	1.06705e6i	0.0391784	+	0.00146372i
$31$	5.03000e8			0.566758			0.283379	−	0.959008i	$-0.408545\pi$
$31$	5.03000e8			0.566758			0.283379	+	0.959008i	$0.408545\pi$
$32$	−1.52656e8	+	1.52656e8i	−0.142172	+	0.142172i
$33$	−5.70168e8	−	5.70168e8i	−0.441489	−	0.441489i
$34$			6.97363e7i			0.0451425i
$35$	2.26522e9	−	2.10206e9i	1.23226	−	1.14350i
$36$	1.43432e9			0.658917
$37$	−1.34249e9	+	1.34249e9i	−0.523239	+	0.523239i	−0.918548	−	0.395309i	$-0.870638\pi$
$37$	−1.34249e9	+	1.34249e9i	−0.523239	+	0.523239i	0.395309	+	0.918548i	$0.370638\pi$
$38$	8.52671e7	+	8.52671e7i	0.0283191	+	0.0283191i
$39$			1.06118e9i			0.301580i
$40$	−3.74879e8	−	4.03978e8i	−0.0915233	−	0.0986274i
$41$	−2.34687e9			−0.494066			−0.247033	−	0.969007i	$-0.579456\pi$
$41$	−2.34687e9			−0.494066			−0.247033	+	0.969007i	$0.579456\pi$
$42$	2.55812e8	−	2.55812e8i	0.0466042	−	0.0466042i
$43$	−4.61986e9	−	4.61986e9i	−0.730833	−	0.730833i	0.239952	−	0.970785i	$-0.422868\pi$
$43$	−4.61986e9	−	4.61986e9i	−0.730833	−	0.730833i	−0.970785	+	0.239952i	$0.922868\pi$
$44$			7.75651e9i			1.06893i
$45$	−2.05208e8	+	5.49265e9i	−0.0247126	+	0.661465i
$46$	−2.38757e8			−0.0252005
$47$	2.02672e8	−	2.02672e8i	0.0188021	−	0.0188021i	−0.697643	−	0.716445i	$-0.745768\pi$
$47$	2.02672e8	−	2.02672e8i	0.0188021	−	0.0188021i	0.716445	+	0.697643i	$0.245768\pi$
$48$	4.96001e9	+	4.96001e9i	0.405541	+	0.405541i
$49$		−	2.52749e10i		−	1.82605i
$50$	7.98500e8	−	6.87323e8i	0.0511040	−	0.0439887i
$51$	6.84963e9			0.389266
$52$	7.21811e9	−	7.21811e9i	0.365093	−	0.365093i
$53$	1.74618e10	+	1.74618e10i	0.787833	+	0.787833i	0.981139	−	0.193306i	$-0.0619209\pi$
$53$	1.74618e10	+	1.74618e10i	0.787833	+	0.787833i	−0.193306	+	0.981139i	$0.561921\pi$
$54$			1.61556e9i			0.0651571i
$55$	−2.97031e10	−	1.10972e9i	−1.07307	−	0.0400902i
$56$	−6.97596e9			−0.226191
$57$	8.37511e9	−	8.37511e9i	0.244197	−	0.244197i
$58$	2.60878e9	+	2.60878e9i	0.0685283	+	0.0685283i
$59$			1.23184e10i			0.292039i	0.989282	+	0.146019i	$0.0466462\pi$
$59$			1.23184e10i			0.292039i	−0.989282	+	0.146019i	$0.953354\pi$
$60$	−1.97945e10	+	1.83688e10i	−0.424266	+	0.393706i
$61$	−6.84075e10			−1.32778			−0.663888	−	0.747832i	$-0.731095\pi$
$61$	−6.84075e10			−1.32778			−0.663888	+	0.747832i	$0.731095\pi$
$62$	1.53489e9	−	1.53489e9i	0.0270226	−	0.0270226i
$63$	4.91959e10	+	4.91959e10i	0.786838	+	0.786838i
$64$		−	6.68519e10i		−	0.972824i
$65$	2.66087e10	+	2.86741e10i	0.352812	+	0.380197i
$66$	−3.47970e9			−0.0420997
$67$	4.44857e10	−	4.44857e10i	0.491781	−	0.491781i	−0.417086	−	0.908867i	$-0.636949\pi$
$67$	4.44857e10	−	4.44857e10i	0.491781	−	0.491781i	0.908867	+	0.417086i	$0.136949\pi$
$68$	−4.65908e10	−	4.65908e10i	−0.471245	−	0.471245i
$69$			2.34512e10i			0.217305i
$70$	4.97888e8	−	1.33266e10i	0.00423198	−	0.113274i
$71$	2.05846e11			1.60691			0.803455	−	0.595365i	$-0.202993\pi$
$71$	2.05846e11			1.60691			0.803455	+	0.595365i	$0.202993\pi$
$72$	8.77356e9	−	8.77356e9i	0.0629768	−	0.0629768i
$73$	−2.31849e10	−	2.31849e10i	−0.153203	−	0.153203i	0.626344	−	0.779547i	$-0.284551\pi$
$73$	−2.31849e10	−	2.31849e10i	−0.153203	−	0.153203i	−0.779547	+	0.626344i	$0.784551\pi$
$74$			8.19313e9i			0.0498953i
$75$	−6.75102e10	−	7.84302e10i	−0.379316	−	0.440672i
$76$	−1.13934e11			−0.591251
$77$	−2.66041e11	+	2.66041e11i	−1.27645	+	1.27645i
$78$	3.23817e9	+	3.23817e9i	0.0143791	+	0.0143791i
$79$			7.81035e10i			0.321298i	0.987012	+	0.160649i	$0.0513587\pi$
$79$			7.81035e10i			0.321298i	−0.987012	+	0.160649i	$0.948641\pi$
$80$	2.58394e11	+	9.65369e9i	0.985693	+	0.0368259i
$81$	−2.82638e10			−0.100074
$82$	−7.16139e9	+	7.16139e9i	−0.0235567	+	0.0235567i
$83$	−3.18989e11	−	3.18989e11i	−0.975679	−	0.975679i	0.0240324	−	0.999711i	$-0.492350\pi$
$83$	−3.18989e11	−	3.18989e11i	−0.975679	−	0.975679i	−0.999711	+	0.0240324i	$0.992350\pi$
$84$			3.41816e11i			0.973008i
$85$	1.85083e11	−	1.71751e11i	0.490742	−	0.455394i
$86$	−2.81948e10			−0.0696911
$87$	2.56240e11	−	2.56240e11i	0.590923	−	0.590923i
$88$	4.74456e10	+	4.74456e10i	0.102165	+	0.102165i
$89$			9.33617e10i			0.187857i	0.995579	+	0.0939287i	$0.0299426\pi$
$89$			9.33617e10i			0.187857i	−0.995579	+	0.0939287i	$0.970057\pi$
$90$	1.61345e10	+	1.73869e10i	0.0303599	+	0.0327164i
$91$	4.95149e11			0.871942
$92$	1.59514e11	−	1.59514e11i	0.263070	−	0.263070i
$93$	−1.50760e11	−	1.50760e11i	−0.233017	−	0.233017i
$94$		−	1.23689e9i		−	0.00179294i
$95$	1.63005e10	−	4.36304e11i	0.0221748	−	0.593537i
$96$	9.15083e10			0.116905
$97$	−9.38946e11	+	9.38946e11i	−1.12722	+	1.12722i	−0.136597	+	0.990627i	$0.543617\pi$
$97$	−9.38946e11	+	9.38946e11i	−1.12722	+	1.12722i	−0.990627	+	0.136597i	$0.956383\pi$
$98$	−7.71257e10	−	7.71257e10i	−0.0870649	−	0.0870649i
$99$		−	6.69191e11i		−	0.710786i
$100$	−7.42774e10	+	9.92678e11i	−0.0742774	+	0.992678i
$101$	−8.68340e11			−0.818016			−0.409008	−	0.912531i	$-0.634125\pi$
$101$	−8.68340e11			−0.818016			−0.409008	+	0.912531i	$0.634125\pi$
$102$	2.09015e10	−	2.09015e10i	0.0185599	−	0.0185599i
$103$	1.18088e12	+	1.18088e12i	0.988971	+	0.988971i	0.999940	−	0.0109692i	$-0.00349168\pi$
$103$	1.18088e12	+	1.18088e12i	0.988971	+	0.988971i	−0.0109692	+	0.999940i	$0.503492\pi$
$104$		−	8.83046e10i		−	0.0697884i
$105$	−1.30897e12	−	4.89035e10i	−0.976771	−	0.0364926i
$106$	1.06568e11			0.0751266
$107$	8.07454e11	−	8.07454e11i	0.538041	−	0.538041i	−0.384912	−	0.922953i	$-0.625768\pi$
$107$	8.07454e11	−	8.07454e11i	0.538041	−	0.538041i	0.922953	+	0.384912i	$0.125768\pi$
$108$	−1.07936e12	−	1.07936e12i	−0.680179	−	0.680179i
$109$		−	3.31158e11i		−	0.197459i	−0.995114	−	0.0987293i	$-0.968522\pi$
$109$		−	3.31158e11i		−	0.197459i	0.995114	−	0.0987293i	$-0.0314778\pi$
$110$	−9.40246e10	+	8.72520e10i	−0.0530744	+	0.0492515i
$111$	8.04746e11			0.430250
$112$	2.31434e12	−	2.31434e12i	1.17252	−	1.17252i
$113$	2.49196e12	+	2.49196e12i	1.19694	+	1.19694i	0.975079	+	0.221858i	$0.0712121\pi$
$113$	2.49196e12	+	2.49196e12i	1.19694	+	1.19694i	0.221858	+	0.975079i	$0.428788\pi$
$114$		−	5.11128e10i		−	0.0232863i
$115$	5.88028e11	+	6.33671e11i	0.254221	+	0.273953i
$116$	−3.48586e12			−1.43074
$117$	−6.22741e11	+	6.22741e11i	−0.242768	+	0.242768i
$118$	3.75891e10	+	3.75891e10i	0.0139242	+	0.0139242i
$119$		−	3.19605e12i		−	1.12546i
$120$	−8.72143e9	+	2.33440e11i	−0.00292079	+	0.0781787i
$121$	4.80421e11			0.153077
$122$	−2.08743e11	+	2.08743e11i	−0.0633073	+	0.0633073i
$123$	7.03406e11	+	7.03406e11i	0.203131	+	0.203131i
$124$			2.05092e12i			0.564181i
$125$	−3.79078e12	−	4.26464e11i	−0.993731	−	0.111795i
$126$	3.00239e11			0.0750316
$127$	−4.08145e12	+	4.08145e12i	−0.972729	+	0.972729i	−0.999638	−	0.0269091i	$-0.991434\pi$
$127$	−4.08145e12	+	4.08145e12i	−0.972729	+	0.972729i	0.0269091	+	0.999638i	$0.491434\pi$
$128$	−8.29274e11	−	8.29274e11i	−0.188555	−	0.188555i
$129$			2.76934e12i			0.600950i
$130$	1.68694e11	+	6.30247e9i	0.0349493	+	0.00130572i
$131$	5.36726e12			1.06200			0.531000	−	0.847372i	$-0.321816\pi$
$131$	5.36726e12			1.06200			0.531000	+	0.847372i	$0.321816\pi$
$132$	2.32479e12	−	2.32479e12i	0.439481	−	0.439481i
$133$	−3.90783e12	−	3.90783e12i	−0.706035	−	0.706035i
$134$		−	2.71494e11i		−	0.0468955i
$135$	4.28777e12	−	3.97892e12i	0.708319	−	0.657299i
$136$	−5.69981e11			−0.0900797
$137$	1.07703e12	−	1.07703e12i	0.162894	−	0.162894i	−0.620954	−	0.783847i	$-0.713254\pi$
$137$	1.07703e12	−	1.07703e12i	0.162894	−	0.162894i	0.783847	+	0.620954i	$0.213254\pi$
$138$	7.15606e10	+	7.15606e10i	0.0103609	+	0.0103609i
$139$		−	3.35172e12i		−	0.464706i	−0.972632	−	0.232353i	$-0.925358\pi$
$139$		−	3.35172e12i		−	0.464706i	0.972632	−	0.232353i	$-0.0746425\pi$
$140$	8.57088e12	+	9.23615e12i	1.13830	+	1.22666i
$141$	−1.21490e11			−0.0154606
$142$	6.28132e11	−	6.28132e11i	0.0766162	−	0.0766162i
$143$	−3.36766e12	−	3.36766e12i	−0.393832	−	0.393832i
$144$			5.82143e12i			0.652912i
$145$	4.98721e11	−	1.33489e13i	0.0536599	−	1.43628i
$146$	−1.41496e11			−0.0146093
$147$	−7.57544e12	+	7.57544e12i	−0.750765	+	0.750765i
$148$	−5.47383e12	−	5.47383e12i	−0.520860	−	0.520860i
$149$			1.26933e13i			1.16000i	0.814617	+	0.579999i	$0.196947\pi$
$149$			1.26933e13i			1.16000i	−0.814617	+	0.579999i	$0.803053\pi$
$150$	−4.45333e11	−	3.33222e10i	−0.0390964	−	0.00292540i
$151$	−4.19633e11			−0.0354004			−0.0177002	−	0.999843i	$-0.505634\pi$
$151$	−4.19633e11			−0.0354004			−0.0177002	+	0.999843i	$0.505634\pi$
$152$	−6.96920e11	+	6.96920e11i	−0.0565095	+	0.0565095i
$153$	4.01962e12	+	4.01962e12i	0.313355	+	0.313355i
$154$			1.62363e12i			0.121720i
$155$	−7.85390e12	−	2.93425e11i	−0.566363	−	0.0211596i
$156$	−4.32684e12			−0.300209
$157$	−2.36946e12	+	2.36946e12i	−0.158216	+	0.158216i	−0.781776	−	0.623560i	$-0.785686\pi$
$157$	−2.36946e12	+	2.36946e12i	−0.158216	+	0.158216i	0.623560	+	0.781776i	$0.285686\pi$
$158$	2.38331e11	+	2.38331e11i	0.0153192	+	0.0153192i
$159$		−	1.04674e13i		−	0.647820i
$160$	2.47263e12	−	2.29453e12i	0.147380	−	0.136765i
$161$	1.09423e13			0.628283
$162$	−8.62463e10	+	8.62463e10i	−0.00477145	+	0.00477145i
$163$	4.04607e12	+	4.04607e12i	0.215728	+	0.215728i	0.806696	−	0.590967i	$-0.201254\pi$
$163$	4.04607e12	+	4.04607e12i	0.215728	+	0.215728i	−0.590967	+	0.806696i	$0.701254\pi$
$164$		−	9.56906e12i		−	0.491820i
$165$	8.57006e12	+	9.23528e12i	0.424698	+	0.457664i
$166$	−1.94677e12			−0.0930392
$167$	7.62914e12	−	7.62914e12i	0.351703	−	0.351703i	−0.509040	−	0.860743i	$-0.669999\pi$
$167$	7.62914e12	−	7.62914e12i	0.351703	−	0.351703i	0.860743	+	0.509040i	$0.169999\pi$
$168$	2.09085e12	+	2.09085e12i	0.0929965	+	0.0929965i
$169$		−	1.70303e13i		−	0.730974i
$170$	4.06806e10	−	1.08887e12i	0.00168537	−	0.0451110i
$171$	9.82964e12			0.393152
$172$	1.88369e13	−	1.88369e13i	0.727510	−	0.727510i
$173$	7.27661e12	+	7.27661e12i	0.271427	+	0.271427i	0.829674	−	0.558248i	$-0.188526\pi$
$173$	7.27661e12	+	7.27661e12i	0.271427	+	0.271427i	−0.558248	+	0.829674i	$0.688526\pi$
$174$		−	1.56382e12i		−	0.0563496i
$175$	−3.65956e13	+	3.15003e13i	−1.27409	+	1.09670i
$176$	−3.14811e13			−1.05919
$177$	3.69207e12	−	3.69207e12i	0.120069	−	0.120069i
$178$	2.84890e11	+	2.84890e11i	0.00895690	+	0.00895690i
$179$			2.95636e13i			0.898750i	0.893343	+	0.449375i	$0.148353\pi$
$179$			2.95636e13i			0.898750i	−0.893343	+	0.449375i	$0.851647\pi$
$180$	−2.23956e13	−	8.36710e11i	−0.658458	−	0.0246003i
$181$	−1.33490e13			−0.379644			−0.189822	−	0.981818i	$-0.560791\pi$
$181$	−1.33490e13			−0.379644			−0.189822	+	0.981818i	$0.560791\pi$
$182$	1.51093e12	−	1.51093e12i	0.0415735	−	0.0415735i
$183$	2.05032e13	+	2.05032e13i	0.545902	+	0.545902i
$184$		−	1.95145e12i		−	0.0502864i
$185$	2.17449e13	−	2.01786e13i	0.542409	−	0.503340i
$186$	−9.20079e11			−0.0222202
$187$	−2.17373e13	+	2.17373e13i	−0.508341	+	0.508341i
$188$	8.26368e11	+	8.26368e11i	0.0187166	+	0.0187166i
$189$		−	7.40420e13i		−	1.62445i
$190$	−1.28163e12	−	1.38111e12i	−0.0272421	−	0.0293567i
$191$	−3.72226e13			−0.766666			−0.383333	−	0.923610i	$-0.625224\pi$
$191$	−3.72226e13			−0.766666			−0.383333	+	0.923610i	$0.625224\pi$
$192$	−2.00370e13	+	2.00370e13i	−0.399967	+	0.399967i
$193$	4.09580e13	+	4.09580e13i	0.792491	+	0.792491i	0.981899	−	0.189407i	$-0.0606567\pi$
$193$	4.09580e13	+	4.09580e13i	0.792491	+	0.792491i	−0.189407	+	0.981899i	$0.560657\pi$
$194$			5.73033e12i			0.107490i
$195$	6.19041e11	−	1.65694e13i	0.0112593	−	0.301370i
$196$	1.03055e14			1.81775
$197$	6.17505e13	−	6.17505e13i	1.05644	−	1.05644i	0.0581268	−	0.998309i	$-0.481487\pi$
$197$	6.17505e13	−	6.17505e13i	1.05644	−	1.05644i	0.998309	−	0.0581268i	$-0.0185128\pi$
$198$	−2.04202e12	−	2.04202e12i	−0.0338898	−	0.0338898i
$199$			4.04506e13i			0.651339i	0.945484	+	0.325669i	$0.105590\pi$
$199$			4.04506e13i			0.651339i	−0.945484	+	0.325669i	$0.894410\pi$
$200$	5.61775e12	+	6.52644e12i	0.0877773	+	0.101976i
$201$	−2.66666e13			−0.404382
$202$	−2.64971e12	+	2.64971e12i	−0.0390024	+	0.0390024i
$203$	−1.19562e14	−	1.19562e14i	−1.70850	−	1.70850i
$204$			2.79285e13i			0.387496i
$205$	3.66442e13	+	1.36904e12i	0.493722	+	0.0184457i
$206$	7.20686e12			0.0943067
$207$	−1.37620e13	+	1.37620e13i	−0.174928	+	0.174928i
$208$	2.92959e13	+	2.92959e13i	0.361765	+	0.361765i
$209$			5.31567e13i			0.637793i
$210$	−4.14350e12	+	3.84505e12i	−0.0483116	+	0.0448317i
$211$	−9.82956e12			−0.111388			−0.0556941	−	0.998448i	$-0.517737\pi$
$211$	−9.82956e12			−0.111388			−0.0556941	+	0.998448i	$0.517737\pi$
$212$	−7.11984e13	+	7.11984e13i	−0.784251	+	0.784251i
$213$	−6.16964e13	−	6.16964e13i	−0.660666	−	0.660666i
$214$		−	4.92785e12i		−	0.0513068i
$215$	6.94400e13	+	7.48300e13i	0.703039	+	0.757609i
$216$	−1.32046e13			−0.130018
$217$	−7.03447e13	+	7.03447e13i	−0.673710	+	0.673710i
$218$	−1.01052e12	−	1.01052e12i	−0.00941467	−	0.00941467i
$219$			1.38980e13i			0.125976i
$220$	4.52476e12	−	1.21111e14i	0.0399079	−	1.06819i
$221$	4.04568e13			0.347247
$222$	2.45566e12	−	2.45566e12i	0.0205140	−	0.0205140i
$223$	−1.13933e13	−	1.13933e13i	−0.0926449	−	0.0926449i	0.659265	−	0.751910i	$-0.270867\pi$
$223$	−1.13933e13	−	1.13933e13i	−0.0926449	−	0.0926449i	−0.751910	+	0.659265i	$0.770867\pi$
$224$		−	4.26979e13i		−	0.338001i
$225$	6.40827e12	−	8.56432e13i	0.0493908	−	0.660082i
$226$	1.52083e13			0.114138
$227$	1.08283e14	−	1.08283e14i	0.791420	−	0.791420i	−0.190305	−	0.981725i	$-0.560948\pi$
$227$	1.08283e14	−	1.08283e14i	0.791420	−	0.791420i	0.981725	+	0.190305i	$0.0609478\pi$
$228$	3.41485e13	+	3.41485e13i	0.243087	+	0.243087i
$229$			1.33910e14i			0.928539i	0.885694	+	0.464270i	$0.153683\pi$
$229$			1.33910e14i			0.928539i	−0.885694	+	0.464270i	$0.846317\pi$
$230$	3.72798e12	+	1.39279e11i	0.0251829	+	0.000940845i
$231$	1.59476e14			1.04960
$232$	−2.13226e13	+	2.13226e13i	−0.136745	+	0.136745i
$233$	−1.49751e13	−	1.49751e13i	−0.0935909	−	0.0935909i	0.658761	−	0.752352i	$-0.271081\pi$
$233$	−1.49751e13	−	1.49751e13i	−0.0935909	−	0.0935909i	−0.752352	+	0.658761i	$0.771081\pi$
$234$			3.80055e12i			0.0231500i
$235$	−3.28276e12	+	3.04631e12i	−0.0194909	+	0.0180870i
$236$	−5.02266e13			−0.290711
$237$	2.34093e13	−	2.34093e13i	0.132099	−	0.132099i
$238$	−9.75264e12	−	9.75264e12i	−0.0536612	−	0.0536612i
$239$		−	6.21046e13i		−	0.333224i	−0.986023	−	0.166612i	$-0.946717\pi$
$239$		−	6.21046e13i		−	0.333224i	0.986023	−	0.166612i	$-0.0532827\pi$
$240$	−7.45527e13	−	8.03395e13i	−0.390118	−	0.420399i
$241$	−2.31557e14			−1.18183			−0.590917	−	0.806732i	$-0.701234\pi$
$241$	−2.31557e14			−1.18183			−0.590917	+	0.806732i	$0.701234\pi$
$242$	1.46599e12	−	1.46599e12i	0.00729860	−	0.00729860i
$243$	1.49154e14	+	1.49154e14i	0.724430	+	0.724430i
$244$		−	2.78923e14i		−	1.32174i
$245$	−1.47441e13	+	3.94646e14i	−0.0681746	+	1.82478i
$246$	4.29285e12			0.0193702
$247$	4.94669e13	−	4.94669e13i	0.217838	−	0.217838i
$248$	1.25452e13	+	1.25452e13i	0.0539223	+	0.0539223i
$249$			1.91216e14i			0.802282i
$250$	−1.28688e13	+	1.02661e13i	−0.0527106	+	0.0420500i
$251$	−3.54412e14			−1.41731			−0.708657	−	0.705553i	$-0.750699\pi$
$251$	−3.54412e14			−1.41731			−0.708657	+	0.705553i	$0.750699\pi$
$252$	−2.00590e14	+	2.00590e14i	−0.783260	+	0.783260i
$253$	−7.44221e13	−	7.44221e13i	−0.283778	−	0.283778i
$254$			2.49088e13i			0.0927579i
$255$	−1.06951e14	−	3.99573e12i	−0.388995	−	0.0145330i
$256$	2.68764e14			0.954843
$257$	3.35964e14	−	3.35964e14i	1.16599	−	1.16599i	0.182847	−	0.983141i	$-0.441469\pi$
$257$	3.35964e14	−	3.35964e14i	1.16599	−	1.16599i	0.983141	−	0.182847i	$-0.0585313\pi$
$258$	8.45057e12	+	8.45057e12i	0.0286529	+	0.0286529i
$259$		−	3.75495e14i		−	1.24396i
$260$	−1.16915e14	+	1.08494e14i	−0.378469	+	0.351208i
$261$	3.00742e14			0.951373
$262$	1.63780e13	−	1.63780e13i	0.0506354	−	0.0506354i
$263$	3.15945e14	+	3.15945e14i	0.954723	+	0.954723i	0.999018	−	0.0442950i	$-0.0141042\pi$
$263$	3.15945e14	+	3.15945e14i	0.954723	+	0.954723i	−0.0442950	+	0.999018i	$0.514104\pi$
$264$		−	2.84409e13i		−	0.0840079i
$265$	−2.62464e14	−	2.82837e14i	−0.757871	−	0.816697i
$266$	−2.38493e13			−0.0673264
$267$	2.79825e13	−	2.79825e13i	0.0772358	−	0.0772358i
$268$	1.81385e14	+	1.81385e14i	0.489545	+	0.489545i
$269$		−	3.14879e13i		−	0.0831056i	−0.999136	−	0.0415528i	$-0.986770\pi$
$269$		−	3.14879e13i		−	0.0831056i	0.999136	−	0.0415528i	$-0.0132305\pi$
$270$	9.42438e11	−	2.52256e13i	0.00243260	−	0.0651116i
$271$	−5.67808e13			−0.143346			−0.0716731	−	0.997428i	$-0.522834\pi$
$271$	−5.67808e13			−0.143346			−0.0716731	+	0.997428i	$0.522834\pi$
$272$	1.89097e14	−	1.89097e14i	0.466950	−	0.466950i
$273$	−1.48407e14	−	1.48407e14i	−0.358491	−	0.358491i
$274$		−	6.57306e12i		−	0.0155333i
$275$	4.63141e14	+	3.46546e13i	1.07082	+	0.0801245i
$276$	−9.56193e13			−0.216317
$277$	−5.75041e14	+	5.75041e14i	−1.27298	+	1.27298i	−0.328458	+	0.944519i	$0.606529\pi$
$277$	−5.75041e14	+	5.75041e14i	−1.27298	+	1.27298i	−0.944519	+	0.328458i	$0.893471\pi$
$278$	−1.02277e13	−	1.02277e13i	−0.0221568	−	0.0221568i
$279$		−	1.76943e14i		−	0.375152i
$280$	1.08923e14	+	4.06943e12i	0.226034	+	0.00844472i
$281$	−6.04282e14			−1.22744			−0.613722	−	0.789522i	$-0.710329\pi$
$281$	−6.04282e14			−1.22744			−0.613722	+	0.789522i	$0.710329\pi$
$282$	−3.70723e11	+	3.70723e11i	−0.000737149	+	0.000737149i
$283$	−2.84440e14	−	2.84440e14i	−0.553697	−	0.553697i	0.373809	−	0.927506i	$-0.378052\pi$
$283$	−2.84440e14	−	2.84440e14i	−0.553697	−	0.553697i	−0.927506	+	0.373809i	$0.878052\pi$
$284$			8.39310e14i			1.59960i
$285$	−1.35655e14	+	1.25884e14i	−0.253144	+	0.234910i
$286$	−2.05526e13			−0.0375553
$287$	3.28210e14	−	3.28210e14i	0.587301	−	0.587301i
$288$	5.37004e13	+	5.37004e13i	0.0941072	+	0.0941072i
$289$			3.21485e14i			0.551790i
$290$	−3.92120e13	−	4.22557e13i	−0.0659221	−	0.0710390i
$291$	5.62845e14			0.926895
$292$	9.45337e13	−	9.45337e13i	0.152507	−	0.152507i
$293$	−6.98235e14	−	6.98235e14i	−1.10356	−	1.10356i	−0.993978	−	0.109582i	$-0.965049\pi$
$293$	−6.98235e14	−	6.98235e14i	−1.10356	−	1.10356i	−0.109582	−	0.993978i	$-0.534951\pi$
$294$			4.62325e13i			0.0715918i
$295$	7.18591e12	−	1.92340e14i	0.0109031	−	0.291835i
$296$	−6.69656e13			−0.0995638
$297$	−5.03582e14	+	5.03582e14i	−0.733722	+	0.733722i
$298$	3.87333e13	+	3.87333e13i	0.0553079	+	0.0553079i
$299$			1.38513e14i			0.193848i
$300$	3.19790e14	−	2.75264e14i	0.438669	−	0.377592i
$301$	1.29218e15			1.73750
$302$	−1.28050e12	+	1.28050e12i	−0.00168786	+	0.00168786i
$303$	2.60260e14	+	2.60260e14i	0.336319	+	0.336319i
$304$		−	4.62420e14i		−	0.585862i
$305$	1.06812e15	+	3.99055e13i	1.32685	+	0.0495717i
$306$	2.45315e13			0.0298810
$307$	−2.44840e14	+	2.44840e14i	−0.292451	+	0.292451i	−0.838048	−	0.545597i	$-0.816303\pi$
$307$	−2.44840e14	+	2.44840e14i	−0.292451	+	0.292451i	0.545597	+	0.838048i	$0.316303\pi$
$308$	−1.08475e15	−	1.08475e15i	−1.27065	−	1.27065i
$309$		−	7.07872e14i		−	0.813212i
$310$	−2.48613e13	+	2.30706e13i	−0.0280126	+	0.0259949i
$311$	−2.41512e14			−0.266917			−0.133458	−	0.991054i	$-0.542608\pi$
$311$	−2.41512e14			−0.266917			−0.133458	+	0.991054i	$0.542608\pi$
$312$	−2.64668e13	+	2.64668e13i	−0.0286928	+	0.0286928i
$313$	1.08324e15	+	1.08324e15i	1.15202	+	1.15202i	0.986148	+	0.165868i	$0.0530425\pi$
$313$	1.08324e15	+	1.08324e15i	1.15202	+	1.15202i	0.165868	+	0.986148i	$0.446958\pi$
$314$			1.44607e13i			0.0150872i
$315$	−7.39451e14	−	7.96848e14i	−0.756913	−	0.815665i
$316$	−3.18458e14			−0.319837
$317$	−3.14941e14	+	3.14941e14i	−0.310366	+	0.310366i	−0.845051	−	0.534686i	$-0.820430\pi$
$317$	−3.14941e14	+	3.14941e14i	−0.310366	+	0.310366i	0.534686	+	0.845051i	$0.320430\pi$
$318$	−3.19409e13	−	3.19409e13i	−0.0308876	−	0.0308876i
$319$			1.62635e15i			1.54337i
$320$	−3.89980e13	+	1.04383e15i	−0.0363198	+	0.972145i
$321$	−4.84023e14			−0.442421
$322$	3.33902e13	−	3.33902e13i	0.0299560	−	0.0299560i
$323$	−3.19295e14	−	3.19295e14i	−0.281175	−	0.281175i
$324$		−	1.15242e14i		−	0.0996190i
$325$	−3.98744e14	−	4.63242e14i	−0.338371	−	0.393104i
$326$	2.46929e13			0.0205715
$327$	−9.92551e13	+	9.92551e13i	−0.0811832	+	0.0811832i
$328$	−5.85328e13	−	5.85328e13i	−0.0470063	−	0.0470063i
$329$			5.66874e13i			0.0447003i
$330$	5.43325e13	+	2.02988e12i	0.0420703	+	0.00157177i
$331$	−5.02118e14			−0.381802			−0.190901	−	0.981609i	$-0.561141\pi$
$331$	−5.02118e14			−0.381802			−0.190901	+	0.981609i	$0.561141\pi$
$332$	1.30064e15	−	1.30064e15i	0.971243	−	0.971243i
$333$	4.72254e14	+	4.72254e14i	0.346346	+	0.346346i
$334$		−	4.65602e13i		−	0.0335379i
$335$	−7.20555e14	+	6.68654e14i	−0.509798	+	0.473078i
$336$	−1.38732e15			−0.964140
$337$	4.60115e14	−	4.60115e14i	0.314114	−	0.314114i	−0.532387	−	0.846501i	$-0.678705\pi$
$337$	4.60115e14	−	4.60115e14i	0.314114	−	0.314114i	0.846501	+	0.532387i	$0.178705\pi$
$338$	−5.19674e13	−	5.19674e13i	−0.0348523	−	0.0348523i
$339$		−	1.49379e15i		−	0.984219i
$340$	7.00295e14	+	7.54653e14i	0.453323	+	0.488510i
$341$	9.56871e14			0.608593
$342$	2.99949e13	−	2.99949e13i	0.0187452	−	0.0187452i
$343$	1.59900e15	+	1.59900e15i	0.981937	+	0.981937i
$344$		−	2.30446e14i		−	0.139065i
$345$	1.36802e13	−	3.66169e14i	0.00811296	−	0.217154i
$346$	4.44087e13			0.0258828
$347$	6.91314e14	−	6.91314e14i	0.396003	−	0.396003i	−0.480818	−	0.876821i	$-0.659660\pi$
$347$	6.91314e14	−	6.91314e14i	0.396003	−	0.396003i	0.876821	+	0.480818i	$0.159660\pi$
$348$	1.04479e15	+	1.04479e15i	0.588237	+	0.588237i
$349$		−	2.73008e15i		−	1.51085i	−0.655233	−	0.755427i	$-0.727430\pi$
$349$		−	2.73008e15i		−	1.51085i	0.655233	−	0.755427i	$-0.272570\pi$
$350$	−1.55482e13	+	2.07793e14i	−0.00845806	+	0.113037i
$351$	9.37254e14			0.501204
$352$	−2.90401e14	+	2.90401e14i	−0.152666	+	0.152666i
$353$	−9.11536e14	−	9.11536e14i	−0.471114	−	0.471114i	0.431161	−	0.902275i	$-0.358104\pi$
$353$	−9.11536e14	−	9.11536e14i	−0.471114	−	0.471114i	−0.902275	+	0.431161i	$0.858104\pi$
$354$		−	2.25325e13i		−	0.0114496i
$355$	−3.21410e15	−	1.20080e14i	−1.60579	−	0.0599930i
$356$	−3.80671e14			−0.187003
$357$	−9.57924e14	+	9.57924e14i	−0.462724	+	0.462724i
$358$	9.02124e13	+	9.02124e13i	0.0428517	+	0.0428517i
$359$			8.63889e14i			0.403544i	0.979432	+	0.201772i	$0.0646701\pi$
$359$			8.63889e14i			0.403544i	−0.979432	+	0.201772i	$0.935330\pi$
$360$	−1.42109e14	+	1.31873e14i	−0.0652841	+	0.0605817i
$361$	1.43251e15			0.647222
$362$	−4.07341e13	+	4.07341e13i	−0.0181012	+	0.0181012i
$363$	−1.43993e14	−	1.43993e14i	−0.0629362	−	0.0629362i
$364$			2.01891e15i			0.867977i
$365$	3.48487e14	+	3.75537e14i	0.147377	+	0.158816i
$366$	1.25130e14			0.0520564
$367$	−9.26475e14	+	9.26475e14i	−0.379173	+	0.379173i	−0.870804	−	0.491631i	$-0.836401\pi$
$367$	−9.26475e14	+	9.26475e14i	−0.379173	+	0.379173i	0.491631	+	0.870804i	$0.336401\pi$
$368$	6.47413e14	+	6.47413e14i	0.260672	+	0.260672i
$369$			8.25569e14i			0.327036i
$370$	4.77946e12	−	1.27928e14i	0.00186281	−	0.0498605i
$371$	−4.88408e15			−1.87301
$372$	6.14705e14	−	6.14705e14i	0.231958	−	0.231958i
$373$	−1.95584e15	−	1.95584e15i	−0.726240	−	0.726240i	0.243629	−	0.969869i	$-0.421662\pi$
$373$	−1.95584e15	−	1.95584e15i	−0.726240	−	0.726240i	−0.969869	+	0.243629i	$0.921662\pi$
$374$			1.32661e14i			0.0484746i
$375$	1.00836e15	+	1.26400e15i	0.362600	+	0.454527i
$376$	1.01096e13			0.00357772
$377$	1.51346e15	−	1.51346e15i	0.527137	−	0.527137i
$378$	−2.25937e14	−	2.25937e14i	−0.0774527	−	0.0774527i
$379$		−	3.69819e15i		−	1.24783i	−0.781494	−	0.623913i	$-0.785542\pi$
$379$		−	3.69819e15i		−	1.24783i	0.781494	−	0.623913i	$-0.214458\pi$
$380$	1.77898e15	+	6.64634e13i	0.590839	+	0.0220740i
$381$	2.44659e15			0.799857
$382$	−1.13584e14	+	1.13584e14i	−0.0365541	+	0.0365541i
$383$	2.93071e15	+	2.93071e15i	0.928497	+	0.928497i	0.997609	−	0.0691121i	$-0.0220166\pi$
$383$	2.93071e15	+	2.93071e15i	0.928497	+	0.928497i	−0.0691121	+	0.997609i	$0.522017\pi$
$384$			4.97102e14i			0.155045i
$385$	4.30919e15	−	3.99880e15i	1.32322	−	1.22791i
$386$	2.49964e14			0.0755707
$387$	−1.62515e15	+	1.62515e15i	−0.483758	+	0.483758i
$388$	−3.82844e15	−	3.82844e15i	−1.12210	−	1.12210i
$389$			5.81707e15i			1.67883i	0.543491	+	0.839415i	$0.317102\pi$
$389$			5.81707e15i			1.67883i	−0.543491	+	0.839415i	$0.682898\pi$
$390$	−4.86721e13	−	5.24501e13i	−0.0138322	−	0.0149059i
$391$	8.94060e14			0.250211
$392$	6.30378e14	−	6.30378e14i	0.173734	−	0.173734i
$393$	−1.60868e15	−	1.60868e15i	−0.436632	−	0.436632i
$394$		−	3.76860e14i		−	0.100740i
$395$	4.55617e13	−	1.21952e15i	0.0119955	−	0.321074i
$396$	2.72855e15			0.707555
$397$	−3.51987e14	+	3.51987e14i	−0.0899050	+	0.0899050i	−0.750629	−	0.660724i	$-0.770249\pi$
$397$	−3.51987e14	+	3.51987e14i	−0.0899050	+	0.0899050i	0.660724	+	0.750629i	$0.270249\pi$
$398$	1.23434e14	+	1.23434e14i	0.0310553	+	0.0310553i
$399$			2.34252e15i			0.580559i
$400$	−4.02895e15	−	3.01468e14i	−0.983631	−	0.0736005i
$401$	1.33593e15			0.321306			0.160653	−	0.987011i	$-0.448640\pi$
$401$	1.33593e15			0.321306			0.160653	+	0.987011i	$0.448640\pi$
$402$	−8.13725e13	+	8.13725e13i	−0.0192806	+	0.0192806i
$403$	−8.90452e14	−	8.90452e14i	−0.207864	−	0.207864i
$404$		−	3.54055e15i		−	0.814296i
$405$	4.41315e14	+	1.64877e13i	0.100004	+	0.00373620i
$406$	−7.29678e14			−0.162920
$407$	−2.55385e15	+	2.55385e15i	−0.561862	+	0.561862i
$408$	1.70836e14	+	1.70836e14i	0.0370354	+	0.0370354i
$409$			4.54111e15i			0.970113i	0.874483	+	0.485056i	$0.161201\pi$
$409$			4.54111e15i			0.970113i	−0.874483	+	0.485056i	$0.838799\pi$
$410$	1.15996e14	−	1.07641e14i	0.0244198	−	0.0226608i
$411$	−6.45618e14			−0.133945
$412$	−4.81490e15	+	4.81490e15i	−0.984474	+	0.984474i
$413$	−1.72273e15	−	1.72273e15i	−0.347149	−	0.347149i
$414$			8.39888e13i			0.0166809i
$415$	4.79464e15	+	5.16681e15i	0.938572	+	1.01142i
$416$	5.40487e14			0.104286
$417$	−1.00458e15	+	1.00458e15i	−0.191060	+	0.191060i
$418$	1.62206e14	+	1.62206e14i	0.0304095	+	0.0304095i
$419$		−	6.60956e15i		−	1.22149i	−0.791829	−	0.610743i	$-0.790871\pi$
$419$		−	6.60956e15i		−	1.22149i	0.791829	−	0.610743i	$-0.209129\pi$
$420$	1.99398e14	−	5.33715e15i	0.0363267	−	0.972330i
$421$	−3.04516e15			−0.546913			−0.273456	−	0.961884i	$-0.588167\pi$
$421$	−3.04516e15			−0.546913			−0.273456	+	0.961884i	$0.588167\pi$
$422$	−2.99946e13	+	2.99946e13i	−0.00531091	+	0.00531091i
$423$	−7.12948e13	−	7.12948e13i	−0.0124456	−	0.0124456i
$424$			8.71024e14i			0.149912i
$425$	−2.99010e15	+	2.57378e15i	−0.507401	+	0.436754i
$426$	−3.76529e14			−0.0630001
$427$	9.56681e15	−	9.56681e15i	1.57834	−	1.57834i
$428$	3.29230e15	+	3.29230e15i	0.535595	+	0.535595i
$429$			2.01872e15i			0.323841i
$430$	4.40236e14	+	1.64474e13i	0.0696426	+	0.00260188i
$431$	4.31131e15			0.672583			0.336291	−	0.941758i	$-0.390827\pi$
$431$	4.31131e15			0.672583			0.336291	+	0.941758i	$0.390827\pi$
$432$	4.38076e15	−	4.38076e15i	0.673980	−	0.673980i
$433$	8.39595e14	+	8.39595e14i	0.127392	+	0.127392i	0.767928	−	0.640536i	$-0.221288\pi$
$433$	8.39595e14	+	8.39595e14i	0.127392	+	0.127392i	−0.640536	+	0.767928i	$0.721288\pi$
$434$			4.29310e14i			0.0642440i
$435$	−4.15043e15	+	3.85148e15i	−0.612573	+	0.568450i
$436$	1.35026e15			0.196561
$437$	1.09317e15	−	1.09317e15i	0.156964	−	0.156964i
$438$	4.24095e13	+	4.24095e13i	0.00600646	+	0.00600646i
$439$		−	6.03271e15i		−	0.842801i	−0.906875	−	0.421401i	$-0.861539\pi$
$439$		−	6.03271e15i		−	0.842801i	0.906875	−	0.421401i	$-0.138461\pi$
$440$	−7.13143e14	−	7.68498e14i	−0.0982790	−	0.105908i
$441$	−8.89109e15			−1.20871
$442$	1.23453e14	−	1.23453e14i	0.0165565	−	0.0165565i
$443$	−1.26831e14	−	1.26831e14i	−0.0167805	−	0.0167805i	0.698667	−	0.715447i	$-0.253777\pi$
$443$	−1.26831e14	−	1.26831e14i	−0.0167805	−	0.0167805i	−0.715447	+	0.698667i	$0.753777\pi$
$444$			3.28125e15i			0.428294i
$445$	5.44625e13	−	1.45776e15i	0.00701354	−	0.187727i
$446$	−6.95328e13			−0.00883447
$447$	3.80446e15	−	3.80446e15i	0.476923	−	0.476923i
$448$	9.34926e15	+	9.34926e15i	1.15640	+	1.15640i
$449$		−	1.85112e15i		−	0.225921i	−0.993599	−	0.112961i	$-0.963967\pi$
$449$		−	1.85112e15i		−	0.225921i	0.993599	−	0.112961i	$-0.0360334\pi$
$450$	−2.41783e14	−	2.80892e14i	−0.0291173	−	0.0338271i
$451$	−4.46451e15			−0.530535
$452$	−1.01607e16	+	1.01607e16i	−1.19149	+	1.19149i
$453$	1.25773e14	+	1.25773e14i	0.0145545	+	0.0145545i
$454$		−	6.60847e14i		−	0.0754686i
$455$	−7.73131e15	−	2.88845e14i	−0.871334	−	0.0325534i
$456$	4.17764e14			0.0464667
$457$	−5.70381e15	+	5.70381e15i	−0.626135	+	0.626135i	−0.947093	−	0.320958i	$-0.895995\pi$
$457$	−5.70381e15	+	5.70381e15i	−0.626135	+	0.626135i	0.320958	+	0.947093i	$0.395995\pi$
$458$	4.08623e14	+	4.08623e14i	0.0442720	+	0.0442720i
$459$		−	6.04971e15i		−	0.646931i
$460$	−2.58371e15	+	2.39761e15i	−0.272708	+	0.253065i
$461$	−2.93742e15			−0.306028			−0.153014	−	0.988224i	$-0.548898\pi$
$461$	−2.93742e15			−0.306028			−0.153014	+	0.988224i	$0.548898\pi$
$462$	4.86638e14	−	4.86638e14i	0.0500442	−	0.0500442i
$463$	6.57117e15	+	6.57117e15i	0.667047	+	0.667047i	0.957031	−	0.289984i	$-0.0936500\pi$
$463$	6.57117e15	+	6.57117e15i	0.667047	+	0.667047i	−0.289984	+	0.957031i	$0.593650\pi$
$464$		−	1.41479e16i		−	1.41770i
$465$	2.26604e15	+	2.44193e15i	0.224155	+	0.241554i
$466$	−9.13920e13			−0.00892469
$467$	6.77746e15	−	6.77746e15i	0.653380	−	0.653380i	−0.300425	−	0.953805i	$-0.597129\pi$
$467$	6.77746e15	−	6.77746e15i	0.653380	−	0.653380i	0.953805	+	0.300425i	$0.0971286\pi$
$468$	−2.53915e15	−	2.53915e15i	−0.241665	−	0.241665i
$469$			1.24427e16i			1.16917i
$470$	−7.21541e11	+	1.93130e13i	−6.69382e−5	+	0.00179169i
$471$	1.42035e15			0.130098
$472$	−3.07230e14	+	3.07230e14i	−0.0277851	+	0.0277851i
$473$	−8.78849e15	−	8.78849e15i	−0.784779	−	0.784779i
$474$		−	1.42866e14i		−	0.0125967i
$475$	−5.09036e14	+	6.80299e15i	−0.0443187	+	0.592296i
$476$	1.30315e16			1.12035
$477$	6.14263e15	−	6.14263e15i	0.521488	−	0.521488i
$478$	−1.89510e14	−	1.89510e14i	−0.0158879	−	0.0158879i
$479$			8.20020e15i			0.678909i	0.940623	+	0.339454i	$0.110242\pi$
$479$			8.20020e15i			0.678909i	−0.940623	+	0.339454i	$0.889758\pi$
$480$	−1.42882e15	−	5.33813e13i	−0.116824	−	0.00436458i
$481$	4.75317e15			0.383807
$482$	−7.06591e14	+	7.06591e14i	−0.0563489	+	0.0563489i
$483$	−3.27966e15	−	3.27966e15i	−0.258313	−	0.258313i
$484$			1.95886e15i			0.152381i
$485$	1.52085e16	−	1.41131e16i	1.16852	−	1.08435i
$486$	9.10276e14			0.0690805
$487$	1.23431e16	−	1.23431e16i	0.925234	−	0.925234i	−0.0721591	−	0.997393i	$-0.522989\pi$
$487$	1.23431e16	−	1.23431e16i	0.925234	−	0.925234i	0.997393	+	0.0721591i	$0.0229889\pi$
$488$	−1.70614e15	−	1.70614e15i	−0.126327	−	0.126327i
$489$		−	2.42539e15i		−	0.177389i
$490$	1.15926e15	+	1.24924e15i	0.0837536	+	0.0902547i
$491$	−2.83224e15			−0.202135			−0.101067	−	0.994880i	$-0.532226\pi$
$491$	−2.83224e15			−0.202135			−0.101067	+	0.994880i	$0.532226\pi$
$492$	−2.86805e15	+	2.86805e15i	−0.202207	+	0.202207i
$493$	−9.76896e15	−	9.76896e15i	−0.680404	−	0.680404i
$494$		−	3.01894e14i		−	0.0207727i
$495$	−3.90373e14	+	1.04488e16i	−0.0265368	+	0.710291i
$496$	−8.32401e15			−0.559039
$497$	−2.87876e16	+	2.87876e16i	−1.91015	+	1.91015i
$498$	5.83489e14	+	5.83489e14i	0.0382522	+	0.0382522i
$499$			5.35931e15i			0.347141i	0.984821	+	0.173570i	$0.0555304\pi$
$499$			5.35931e15i			0.347141i	−0.984821	+	0.173570i	$0.944470\pi$
$500$	1.73885e15	−	1.54565e16i	0.111287	−	0.989213i
$501$	−4.57323e15			−0.289199
$502$	−1.08148e15	+	1.08148e15i	−0.0675765	+	0.0675765i
$503$	1.79350e16	+	1.79350e16i	1.10737	+	1.10737i	0.993495	+	0.113879i	$0.0363276\pi$
$503$	1.79350e16	+	1.79350e16i	1.10737	+	1.10737i	0.113879	+	0.993495i	$0.463672\pi$
$504$			2.45397e15i			0.149722i
$505$	1.35584e16	+	5.06546e14i	0.817445	+	0.0305401i
$506$	−4.54194e14			−0.0270607
$507$	−5.10434e15	+	5.10434e15i	−0.300533	+	0.300533i
$508$	−1.66416e16	−	1.66416e16i	−0.968306	−	0.968306i
$509$			2.03516e16i			1.17029i	0.810930	+	0.585143i	$0.198961\pi$
$509$			2.03516e16i			1.17029i	−0.810930	+	0.585143i	$0.801039\pi$
$510$	−3.38551e14	+	3.14165e14i	−0.0192399	+	0.0178540i
$511$	6.48484e15			0.364228
$512$	4.21683e15	−	4.21683e15i	0.234081	−	0.234081i
$513$	−7.39703e15	−	7.39703e15i	−0.405838	−	0.405838i
$514$		−	2.05037e15i		−	0.111187i
$515$	−1.77496e16	−	1.91273e16i	−0.951359	−	1.02520i
$516$	−1.12917e16			−0.598218
$517$	3.85548e14	−	3.85548e14i	0.0201899	−	0.0201899i
$518$	−1.14581e15	−	1.14581e15i	−0.0593110	−	0.0593110i
$519$		−	4.36191e15i		−	0.223189i
$520$	−5.15124e13	+	1.37880e15i	−0.00260551	+	0.0697397i
$521$	3.47855e16			1.73929			0.869644	−	0.493679i	$-0.164348\pi$
$521$	3.47855e16			1.73929			0.869644	+	0.493679i	$0.164348\pi$
$522$	9.17705e14	−	9.17705e14i	0.0453607	−	0.0453607i
$523$	−7.33594e15	−	7.33594e15i	−0.358464	−	0.358464i	0.504782	−	0.863247i	$-0.331573\pi$
$523$	−7.33594e15	−	7.33594e15i	−0.358464	−	0.358464i	−0.863247	+	0.504782i	$0.831573\pi$
$524$			2.18843e16i			1.05717i
$525$	2.04098e16	+	1.52717e15i	0.974727	+	0.0729343i
$526$	1.92820e15			0.0910410
$527$	−5.74761e15	+	5.74761e15i	−0.268302	+	0.268302i
$528$	9.43556e15	+	9.43556e15i	0.435476	+	0.435476i
$529$		−	1.88536e16i		−	0.860321i
$530$	−1.66397e15	−	6.21667e13i	−0.0750742	−	0.00280480i
$531$	4.33329e15			0.193308
$532$	1.59337e16	−	1.59337e16i	0.702825	−	0.702825i
$533$	4.15461e15	+	4.15461e15i	0.181204	+	0.181204i
$534$		−	1.70776e14i		−	0.00736509i
$535$	−1.30787e16	+	1.21367e16i	−0.557753	+	0.517578i
$536$	2.21902e15			0.0935777
$537$	8.86084e15	−	8.86084e15i	0.369512	−	0.369512i
$538$	−9.60844e13	−	9.60844e13i	−0.00396241	−	0.00396241i
$539$		−	4.80812e16i		−	1.96084i
$540$	1.62236e16	+	1.74829e16i	0.654311	+	0.705099i
$541$	−3.26145e16			−1.30085			−0.650425	−	0.759571i	$-0.725409\pi$
$541$	−3.26145e16			−1.30085			−0.650425	+	0.759571i	$0.725409\pi$
$542$	−1.73265e14	+	1.73265e14i	−0.00683463	+	0.00683463i
$543$	4.00098e15	+	4.00098e15i	0.156087	+	0.156087i
$544$		−	3.48869e15i		−	0.134607i
$545$	−1.93181e14	+	5.17073e15i	−0.00737199	+	0.197321i
$546$	−9.05718e14			−0.0341851
$547$	−4.77595e15	+	4.77595e15i	−0.178294	+	0.178294i	−0.790612	−	0.612318i	$-0.790237\pi$
$547$	−4.77595e15	+	4.77595e15i	−0.178294	+	0.178294i	0.612318	+	0.790612i	$0.290237\pi$
$548$	4.39146e15	+	4.39146e15i	0.162153	+	0.162153i
$549$			2.40640e16i			0.878890i
$550$	1.51901e15	−	1.30751e15i	0.0548762	−	0.0472356i
$551$	−2.38892e16			−0.853673
$552$	−5.84892e14	+	5.84892e14i	−0.0206748	+	0.0206748i
$553$	−1.09228e16	−	1.09228e16i	−0.381930	−	0.381930i
$554$			3.50944e15i			0.121389i
$555$	−1.25654e16	−	4.69448e14i	−0.429950	−	0.0160631i
$556$	1.36662e16			0.462593
$557$	−1.16424e15	+	1.16424e15i	−0.0389864	+	0.0389864i	−0.726331	−	0.687345i	$-0.758776\pi$
$557$	−1.16424e15	+	1.16424e15i	−0.0389864	+	0.0389864i	0.687345	+	0.726331i	$0.258776\pi$
$558$	−5.39936e14	−	5.39936e14i	−0.0178870	−	0.0178870i
$559$			1.63569e16i			0.536081i
$560$	−3.74865e16	+	3.47863e16i	−1.21548	+	1.12793i
$561$	1.30302e16			0.417999
$562$	−1.84395e15	+	1.84395e15i	−0.0585236	+	0.0585236i
$563$	4.01583e16	+	4.01583e16i	1.26103	+	1.26103i	0.950595	+	0.310433i	$0.100474\pi$
$563$	4.01583e16	+	4.01583e16i	1.26103	+	1.26103i	0.310433	+	0.950595i	$0.399526\pi$
$564$		−	4.95361e14i		−	0.0153903i
$565$	−3.74561e16	−	4.03635e16i	−1.15142	−	1.24079i
$566$	−1.73592e15			−0.0527997
$567$	3.95271e15	−	3.95271e15i	0.118959	−	0.118959i
$568$	5.13396e15	+	5.13396e15i	0.152884	+	0.152884i
$569$		−	3.83937e16i		−	1.13132i	−0.824638	−	0.565661i	$-0.808621\pi$
$569$		−	3.83937e16i		−	1.13132i	0.824638	−	0.565661i	$-0.191379\pi$
$570$	−2.98166e13	+	7.98081e14i	−0.000869379	+	0.0232701i
$571$	−4.23164e16			−1.22093			−0.610467	−	0.792042i	$-0.709018\pi$
$571$	−4.23164e16			−1.22093			−0.610467	+	0.792042i	$0.709018\pi$
$572$	1.37312e16	−	1.37312e16i	0.392042	−	0.392042i
$573$	1.11564e16	+	1.11564e16i	0.315208	+	0.315208i
$574$		−	2.00305e15i		−	0.0560041i
$575$	−8.81187e15	−	1.02372e16i	−0.243815	−	0.283254i
$576$	−2.35168e16			−0.643938
$577$	1.14314e16	−	1.14314e16i	0.309775	−	0.309775i	−0.535047	−	0.844822i	$-0.679706\pi$
$577$	1.14314e16	−	1.14314e16i	0.309775	−	0.309775i	0.844822	+	0.535047i	$0.179706\pi$
$578$	9.81002e14	+	9.81002e14i	0.0263089	+	0.0263089i
$579$		−	2.45520e16i		−	0.651651i
$580$	5.44286e16	+	2.03347e15i	1.42975	+	0.0534159i
$581$	8.92214e16			2.31959
$582$	1.71750e15	−	1.71750e15i	0.0441936	−	0.0441936i
$583$	3.32181e16	+	3.32181e16i	0.845986	+	0.845986i
$584$		−	1.15650e15i		−	0.0291521i
$585$	1.00868e16	−	9.36027e15i	0.251663	−	0.233536i
$586$	−4.26129e15			−0.105234
$587$	−1.99599e16	+	1.99599e16i	−0.487900	+	0.487900i	−0.907643	−	0.419743i	$-0.862120\pi$
$587$	−1.99599e16	+	1.99599e16i	−0.487900	+	0.487900i	0.419743	+	0.907643i	$0.362120\pi$
$588$	−3.08879e16	−	3.08879e16i	−0.747352	−	0.747352i
$589$			1.40553e16i			0.336627i
$590$	−5.64993e14	−	6.08848e14i	−0.0133946	−	0.0144343i
$591$	−3.70159e16			−0.868687
$592$	2.22165e16	−	2.22165e16i	0.516113	−	0.516113i
$593$	−2.02903e16	−	2.02903e16i	−0.466618	−	0.466618i	0.434199	−	0.900817i	$-0.357031\pi$
$593$	−2.02903e16	−	2.02903e16i	−0.466618	−	0.466618i	−0.900817	+	0.434199i	$0.857031\pi$
$594$			3.07333e15i			0.0699666i
$595$	−1.86441e15	+	4.99034e16i	−0.0420185	+	1.12468i
$596$	−5.17554e16			−1.15472
$597$	1.21239e16	−	1.21239e16i	0.267792	−	0.267792i
$598$	4.22667e14	+	4.22667e14i	0.00924254	+	0.00924254i
$599$		−	9.11746e15i		−	0.197384i	−0.995118	−	0.0986922i	$-0.968534\pi$
$599$		−	9.11746e15i		−	0.197384i	0.995118	−	0.0986922i	$-0.0314659\pi$
$600$	2.72355e14	−	3.63987e15i	0.00583750	−	0.0780151i
$601$	6.78696e16			1.44022			0.720110	−	0.693860i	$-0.244092\pi$
$601$	6.78696e16			1.44022			0.720110	+	0.693860i	$0.244092\pi$
$602$	3.94305e15	−	3.94305e15i	0.0828424	−	0.0828424i
$603$	−1.56490e16	−	1.56490e16i	−0.325523	−	0.325523i
$604$		−	1.71100e15i		−	0.0352394i
$605$	−7.50135e15	−	2.80254e14i	−0.152970	−	0.00571504i
$606$	1.58835e15			0.0320709
$607$	−2.66447e16	+	2.66447e16i	−0.532696	+	0.532696i	−0.921374	−	0.388678i	$-0.872932\pi$
$607$	−2.66447e16	+	2.66447e16i	−0.532696	+	0.532696i	0.388678	+	0.921374i	$0.372932\pi$
$608$	−4.26565e15	−	4.26565e15i	−0.0844430	−	0.0844430i
$609$			7.16705e16i			1.40487i
$610$	3.38111e15	−	3.13757e15i	0.0656267	−	0.0608996i
$611$	−7.17571e14			−0.0137917
$612$	−1.63895e16	+	1.63895e16i	−0.311930	+	0.311930i
$613$	−4.12525e16	−	4.12525e16i	−0.777476	−	0.777476i	0.201925	−	0.979401i	$-0.435280\pi$
$613$	−4.12525e16	−	4.12525e16i	−0.777476	−	0.777476i	−0.979401	+	0.201925i	$0.935280\pi$
$614$			1.49425e15i			0.0278876i
$615$	−1.05727e16	−	1.13934e16i	−0.195405	−	0.210573i
$616$	−1.32706e16			−0.242888
$617$	−5.24556e16	+	5.24556e16i	−0.950781	+	0.950781i	−0.998844	−	0.0480633i	$-0.984695\pi$
$617$	−5.24556e16	+	5.24556e16i	−0.950781	+	0.950781i	0.0480633	+	0.998844i	$0.484695\pi$
$618$	−2.16005e15	−	2.16005e15i	−0.0387733	−	0.0387733i
$619$			5.51834e16i			0.980990i	0.871444	+	0.490495i	$0.163184\pi$
$619$			5.51834e16i			0.980990i	−0.871444	+	0.490495i	$0.836816\pi$
$620$	1.19640e15	−	3.20233e16i	0.0210634	−	0.563788i
$621$	2.07125e16			0.361145
$622$	−7.36965e14	+	7.36965e14i	−0.0127264	+	0.0127264i
$623$	−1.30567e16	−	1.30567e16i	−0.223308	−	0.223308i
$624$		−	1.75612e16i		−	0.297473i
$625$	5.89409e16	+	8.87021e15i	0.988865	+	0.148817i
$626$	6.61095e15			0.109854
$627$	1.59322e16	−	1.59322e16i	0.262223	−	0.262223i
$628$	−9.66117e15	−	9.66117e15i	−0.157497	−	0.157497i
$629$		−	3.06804e16i		−	0.495401i
$630$	−4.68797e15	−	1.75145e14i	−0.0749793	−	0.00280126i
$631$	4.66102e16			0.738422			0.369211	−	0.929346i	$-0.379628\pi$
$631$	4.66102e16			0.738422			0.369211	+	0.929346i	$0.379628\pi$
$632$	−1.94797e15	+	1.94797e15i	−0.0305688	+	0.0305688i
$633$	2.94613e15	+	2.94613e15i	0.0457962	+	0.0457962i
$634$			1.92207e15i			0.0295960i
$635$	6.61090e16	−	6.13472e16i	1.00837	−	0.935734i
$636$	4.26794e16			0.644875
$637$	−4.47438e16	+	4.47438e16i	−0.669724	+	0.669724i
$638$	4.96276e15	+	4.96276e15i	0.0735867	+	0.0735867i
$639$		−	7.24114e16i		−	1.06366i
$640$	1.24646e16	+	1.34321e16i	0.181384	+	0.195463i
$641$	−7.72188e16			−1.11320			−0.556602	−	0.830779i	$-0.687895\pi$
$641$	−7.72188e16			−1.11320			−0.556602	+	0.830779i	$0.687895\pi$
$642$	−1.47698e15	+	1.47698e15i	−0.0210943	+	0.0210943i
$643$	5.05512e16	+	5.05512e16i	0.715263	+	0.715263i	0.967631	−	0.252368i	$-0.0812094\pi$
$643$	5.05512e16	+	5.05512e16i	0.715263	+	0.715263i	−0.252368	+	0.967631i	$0.581209\pi$
$644$			4.46161e16i			0.625426i
$645$	1.61550e15	−	4.32408e16i	0.0224361	−	0.600532i
$646$	−1.94864e15			−0.0268124
$647$	9.11197e16	−	9.11197e16i	1.24219	−	1.24219i	0.283094	−	0.959092i	$-0.408639\pi$
$647$	9.11197e16	−	9.11197e16i	1.24219	−	1.24219i	0.959092	−	0.283094i	$-0.0913609\pi$
$648$	−7.04924e14	−	7.04924e14i	−0.00952121	−	0.00952121i
$649$			2.34335e16i			0.313595i
$650$	−2.63032e15	−	1.96815e14i	−0.0348762	−	0.00260962i
$651$	4.21676e16			0.553979
$652$	−1.64973e16	+	1.64973e16i	−0.214748	+	0.214748i
$653$	−6.59709e16	−	6.59709e16i	−0.850890	−	0.850890i	0.139353	−	0.990243i	$-0.455498\pi$
$653$	−6.59709e16	−	6.59709e16i	−0.850890	−	0.850890i	−0.990243	+	0.139353i	$0.955498\pi$
$654$			6.05748e14i			0.00774151i
$655$	−8.38050e16	−	3.13099e15i	−1.06126	−	0.0396491i
$656$	3.88376e16			0.487338
$657$	−8.15588e15	+	8.15588e15i	−0.101410	+	0.101410i
$658$	1.72980e14	+	1.72980e14i	0.00213128	+	0.00213128i
$659$			1.26567e17i			1.54528i	0.634842	+	0.772642i	$0.281065\pi$
$659$			1.26567e17i			1.54528i	−0.634842	+	0.772642i	$0.718935\pi$
$660$	−3.76557e16	+	3.49434e16i	−0.455583	+	0.422767i
$661$	−8.61105e16			−1.03240			−0.516199	−	0.856469i	$-0.672654\pi$
$661$	−8.61105e16			−1.03240			−0.516199	+	0.856469i	$0.672654\pi$
$662$	−1.53220e15	+	1.53220e15i	−0.0182040	+	0.0182040i
$663$	−1.21258e16	−	1.21258e16i	−0.142767	−	0.142767i
$664$		−	1.59117e16i		−	0.185655i
$665$	5.87377e16	+	6.32969e16i	0.679183	+	0.731902i
$666$	2.88214e15			0.0330270
$667$	3.34461e16	−	3.34461e16i	0.379831	−	0.379831i
$668$	3.11069e16	+	3.11069e16i	0.350104	+	0.350104i
$669$			6.82965e15i			0.0761801i
$670$	−1.58376e14	+	4.23913e15i	−0.00175081	+	0.0468628i
$671$	−1.30133e17			−1.42578
$672$	−1.27975e16	+	1.27975e16i	−0.138966	+	0.138966i
$673$	1.23431e16	+	1.23431e16i	0.132841	+	0.132841i	0.770401	−	0.637560i	$-0.220056\pi$
$673$	1.23431e16	+	1.23431e16i	0.132841	+	0.132841i	−0.637560	+	0.770401i	$0.720056\pi$
$674$		−	2.80806e15i		−	0.0299534i
$675$	−6.92708e16	+	5.96261e16i	−0.732365	+	0.630396i
$676$	6.94389e16			0.727650
$677$	−2.39813e16	+	2.39813e16i	−0.249081	+	0.249081i	−0.820593	−	0.571512i	$-0.806357\pi$
$677$	−2.39813e16	+	2.39813e16i	−0.249081	+	0.249081i	0.571512	+	0.820593i	$0.306357\pi$
$678$	−4.55826e15	−	4.55826e15i	−0.0469268	−	0.0469268i
$679$		−	2.62624e17i		−	2.67988i
$680$	8.89974e15	+	3.32498e14i	0.0900169	+	0.00336307i
$681$	−6.49097e16			−0.650769
$682$	2.91986e15	−	2.91986e15i	0.0290173	−	0.0290173i
$683$	2.29804e16	+	2.29804e16i	0.226378	+	0.226378i	0.811178	−	0.584800i	$-0.198827\pi$
$683$	2.29804e16	+	2.29804e16i	0.226378	+	0.226378i	−0.584800	+	0.811178i	$0.698827\pi$
$684$			4.00791e16i			0.391365i
$685$	−1.74452e16	+	1.61886e16i	−0.168862	+	0.156699i
$686$	9.75860e15			0.0936360
$687$	4.01357e16	−	4.01357e16i	0.381760	−	0.381760i
$688$	7.64528e16	+	7.64528e16i	0.720880	+	0.720880i
$689$		−	6.18247e16i		−	0.577892i
$690$	−1.07561e15	−	1.15910e15i	−0.00996691	−	0.0107405i
$691$	8.03477e16			0.738083			0.369042	−	0.929413i	$-0.379686\pi$
$691$	8.03477e16			0.738083			0.369042	+	0.929413i	$0.379686\pi$
$692$	−2.96695e16	+	2.96695e16i	−0.270193	+	0.270193i
$693$	9.35866e16	+	9.35866e16i	0.844918	+	0.844918i
$694$		−	4.21905e15i		−	0.0377622i
$695$	−1.95522e15	+	5.23340e16i	−0.0173495	+	0.464382i
$696$	1.27817e16			0.112443
$697$	2.68169e16	−	2.68169e16i	0.233890	−	0.233890i
$698$	−8.33075e15	−	8.33075e15i	−0.0720363	−	0.0720363i
$699$			8.97671e15i			0.0769580i
$700$	−1.28439e17	−	1.49214e17i	−1.09171	−	1.26830i
$701$	1.26706e17			1.06779			0.533897	−	0.845549i	$-0.320727\pi$
$701$	1.26706e17			1.06779			0.533897	+	0.845549i	$0.320727\pi$
$702$	2.86000e15	−	2.86000e15i	0.0238970	−	0.0238970i
$703$	−3.75131e16	−	3.75131e16i	−0.310779	−	0.310779i
$704$		−	1.27174e17i		−	1.04463i
$705$	1.89696e15	+	7.08712e13i	0.0154498	+	0.000577211i
$706$	−5.56305e15			−0.0449247
$707$	1.21438e17	−	1.21438e17i	0.972382	−	0.972382i
$708$	1.50540e16	+	1.50540e16i	0.119523	+	0.119523i
$709$			9.59720e16i			0.755557i	0.925896	+	0.377778i	$0.123312\pi$
$709$			9.59720e16i			0.755557i	−0.925896	+	0.377778i	$0.876688\pi$
$710$	−1.01741e16	+	9.44130e15i	−0.0794233	+	0.0737024i
$711$	2.74749e16			0.212676
$712$	−2.32852e15	+	2.32852e15i	−0.0178731	+	0.0178731i
$713$	−1.96782e16	−	1.96782e16i	−0.149778	−	0.149778i
$714$			5.84615e15i			0.0441246i
$715$	5.06184e16	+	5.45475e16i	0.378854	+	0.408261i
$716$	−1.20542e17			−0.894663
$717$	−1.86141e16	+	1.86141e16i	−0.137002	+	0.137002i
$718$	2.63613e15	+	2.63613e15i	0.0192407	+	0.0192407i
$719$			2.04601e17i			1.48093i	0.672094	+	0.740466i	$0.265395\pi$
$719$			2.04601e17i			1.48093i	−0.672094	+	0.740466i	$0.734605\pi$
$720$	3.39593e15	−	9.08964e16i	0.0243761	−	0.652457i
$721$	−3.30294e17			−2.35119
$722$	4.37125e15	−	4.37125e15i	0.0308590	−	0.0308590i
$723$	6.94027e16	+	6.94027e16i	0.485900	+	0.485900i
$724$		−	5.44289e16i		−	0.377918i
$725$	−1.55742e16	+	2.08140e17i	−0.107245	+	1.43327i
$726$	−8.78779e14			−0.00600150
$727$	−9.39165e16	+	9.39165e16i	−0.636115	+	0.636115i	−0.949595	−	0.313480i	$-0.898505\pi$
$727$	−9.39165e16	+	9.39165e16i	−0.636115	+	0.636115i	0.313480	+	0.949595i	$0.398505\pi$
$728$	1.23494e16	+	1.23494e16i	0.0829580	+	0.0829580i
$729$		−	7.43886e16i		−	0.495611i
$730$	2.20934e15	+	8.25418e13i	0.0145991	+	0.000545427i
$731$	1.05579e17			0.691949
$732$	−8.35992e16	+	8.35992e16i	−0.543420	+	0.543420i
$733$	−8.49174e16	−	8.49174e16i	−0.547485	−	0.547485i	0.378227	−	0.925713i	$-0.376534\pi$
$733$	−8.49174e16	−	8.49174e16i	−0.547485	−	0.547485i	−0.925713	+	0.378227i	$0.876534\pi$
$734$			5.65422e15i			0.0361573i
$735$	1.22703e17	−	1.13865e17i	0.778271	−	0.722212i
$736$	1.19443e16			0.0751437
$737$	8.46264e16	−	8.46264e16i	0.528081	−	0.528081i
$738$	2.51920e15	+	2.51920e15i	0.0155928	+	0.0155928i
$739$			2.76363e16i			0.169673i	0.996395	+	0.0848366i	$0.0270368\pi$
$739$			2.76363e16i			0.169673i	−0.996395	+	0.0848366i	$0.972963\pi$
$740$	8.22759e16	+	8.86622e16i	0.501051	+	0.539943i
$741$	−2.96526e16			−0.179124
$742$	−1.49036e16	+	1.49036e16i	−0.0893035	+	0.0893035i
$743$	−2.00496e17	−	2.00496e17i	−1.19172	−	1.19172i	−0.976585	−	0.215131i	$-0.930982\pi$
$743$	−2.00496e17	−	2.00496e17i	−1.19172	−	1.19172i	−0.215131	−	0.976585i	$-0.569018\pi$
$744$		−	7.52015e15i		−	0.0443393i
$745$	7.40464e15	−	1.98195e17i	0.0433078	−	1.15919i
$746$	−1.19364e16			−0.0692531
$747$	−1.12212e17	+	1.12212e17i	−0.645828	+	0.645828i
$748$	−8.86310e16	−	8.86310e16i	−0.506030	−	0.506030i
$749$			2.25846e17i			1.27915i
$750$	6.93404e15	+	7.80081e14i	0.0389600	+	0.00438300i
$751$	2.62797e17			1.46481			0.732403	−	0.680872i	$-0.238399\pi$
$751$	2.62797e17			1.46481			0.732403	+	0.680872i	$0.238399\pi$
$752$	−3.35396e15	+	3.35396e15i	−0.0185460	+	0.0185460i
$753$	1.06225e17	+	1.06225e17i	0.582715	+	0.582715i
$754$		−	9.23656e15i		−	0.0502669i
$755$	6.55219e15	+	2.44793e14i	0.0353757	+	0.00132165i
$756$	3.01897e17			1.61707
$757$	1.31218e17	−	1.31218e17i	0.697295	−	0.697295i	−0.266531	−	0.963826i	$-0.585878\pi$
$757$	1.31218e17	−	1.31218e17i	0.697295	−	0.697295i	0.963826	+	0.266531i	$0.0858775\pi$
$758$	−1.12849e16	−	1.12849e16i	−0.0594954	−	0.0594954i
$759$			4.46118e16i			0.233345i
$760$	1.12883e16	−	1.04752e16i	0.0585799	−	0.0543604i
$761$	3.33656e16			0.171787			0.0858936	−	0.996304i	$-0.472625\pi$
$761$	3.33656e16			0.171787			0.0858936	+	0.996304i	$0.472625\pi$
$762$	7.46571e15	−	7.46571e15i	0.0381365	−	0.0381365i
$763$	4.63125e16	+	4.63125e16i	0.234721	+	0.234721i
$764$		−	1.51770e17i		−	0.763180i
$765$	−6.04179e16	−	6.51076e16i	−0.301437	−	0.324835i
$766$	1.78860e16			0.0885400
$767$	2.18070e16	−	2.18070e16i	0.107108	−	0.107108i
$768$	−8.05545e16	−	8.05545e16i	−0.392575	−	0.392575i
$769$		−	9.17175e15i		−	0.0443501i	−0.999754	−	0.0221750i	$-0.992941\pi$
$769$		−	9.17175e15i		−	0.0443501i	0.999754	−	0.0221750i	$-0.00705911\pi$
$770$	9.47146e14	−	2.53516e16i	0.00454436	−	0.121636i
$771$	−2.01391e17			−0.958770
$772$	−1.67001e17	+	1.67001e17i	−0.788888	+	0.788888i
$773$	−1.24450e17	−	1.24450e17i	−0.583334	−	0.583334i	0.352484	−	0.935818i	$-0.385337\pi$
$773$	−1.24450e17	−	1.24450e17i	−0.583334	−	0.583334i	−0.935818	+	0.352484i	$0.885337\pi$
$774$			9.91821e15i			0.0461304i
$775$	1.22460e17	+	9.16314e15i	0.565178	+	0.0422896i
$776$	−4.68362e16			−0.214492
$777$	−1.12544e17	+	1.12544e17i	−0.511442	+	0.511442i
$778$	1.77506e16	+	1.77506e16i	0.0800453	+	0.0800453i
$779$		−	6.55784e16i		−	0.293451i
$780$	6.75598e16	+	2.52406e15i	0.300000	+	0.0112081i
$781$	3.91586e17			1.72552
$782$	2.72820e15	−	2.72820e15i	0.0119299	−	0.0119299i
$783$	−2.26315e17	−	2.26315e17i	−0.982071	−	0.982071i
$784$			4.18268e17i			1.80118i
$785$	3.83792e16	−	3.56147e16i	0.164013	−	0.152199i
$786$	−9.81770e15			−0.0416365
$787$	−1.69804e17	+	1.69804e17i	−0.714660	+	0.714660i	−0.967506	−	0.252847i	$-0.918633\pi$
$787$	−1.69804e17	+	1.69804e17i	−0.714660	+	0.714660i	0.252847	+	0.967506i	$0.418633\pi$
$788$	2.51780e17	+	2.51780e17i	1.05163	+	1.05163i
$789$		−	1.89391e17i		−	0.785051i
$790$	−3.58229e15	−	3.86035e15i	−0.0147366	−	0.0158805i
$791$	−6.97004e17			−2.84562
$792$	1.66902e16	−	1.66902e16i	0.0676254	−	0.0676254i
$793$	1.21100e17	+	1.21100e17i	0.486975	+	0.486975i
$794$			2.14816e15i			0.00857320i
$795$	−6.10613e15	+	1.63439e17i	−0.0241860	+	0.647369i
$796$	−1.64932e17			−0.648377
$797$	1.95317e17	−	1.95317e17i	0.762061	−	0.762061i	−0.214634	−	0.976695i	$-0.568856\pi$
$797$	1.95317e17	−	1.95317e17i	0.762061	−	0.762061i	0.976695	+	0.214634i	$0.0688557\pi$
$798$	7.14814e15	+	7.14814e15i	0.0276806	+	0.0276806i
$799$			4.63172e15i			0.0178017i
$800$	−3.99464e16	+	3.43846e16i	−0.152384	+	0.131167i
$801$	3.28423e16			0.124348
$802$	4.07656e15	−	4.07656e15i	0.0153196	−	0.0153196i
$803$	−4.41053e16	−	4.41053e16i	−0.164512	−	0.164512i
$804$		−	1.08730e17i		−	0.402544i
$805$	−1.70855e17	−	6.38321e15i	−0.627845	−	0.0234565i
$806$	−5.43438e15			−0.0198216
$807$	−9.43760e15	+	9.43760e15i	−0.0341681	+	0.0341681i
$808$	−2.16571e16	−	2.16571e16i	−0.0778274	−	0.0778274i
$809$			1.85574e17i			0.661950i	0.943640	+	0.330975i	$0.107378\pi$
$809$			1.85574e17i			0.661950i	−0.943640	+	0.330975i	$0.892622\pi$
$810$	1.39697e15	−	1.29635e15i	0.00494626	−	0.00458998i
$811$	3.08352e17			1.08373			0.541865	−	0.840466i	$-0.317718\pi$
$811$	3.08352e17			1.08373			0.541865	+	0.840466i	$0.317718\pi$
$812$	4.87498e17	−	4.87498e17i	1.70074	−	1.70074i
$813$	1.70184e16	+	1.70184e16i	0.0589354	+	0.0589354i
$814$			1.55860e16i			0.0535783i
$815$	−6.08155e16	−	6.55360e16i	−0.207524	−	0.223632i
$816$	−1.13353e17			−0.383964
$817$	1.29093e17	−	1.29093e17i	0.434079	−	0.434079i
$818$	1.38571e16	+	1.38571e16i	0.0462542	+	0.0462542i
$819$		−	1.74181e17i		−	0.577162i
$820$	−5.58211e15	+	1.49412e17i	−0.0183618	+	0.491477i
$821$	1.35732e17			0.443223			0.221611	−	0.975135i	$-0.428868\pi$
$821$	1.35732e17			0.443223			0.221611	+	0.975135i	$0.428868\pi$
$822$	−1.97009e15	+	1.97009e15i	−0.00638637	+	0.00638637i
$823$	2.99851e17	+	2.99851e17i	0.964954	+	0.964954i	0.999406	−	0.0344521i	$-0.0109686\pi$
$823$	2.99851e17	+	2.99851e17i	0.964954	+	0.964954i	−0.0344521	+	0.999406i	$0.510969\pi$
$824$			5.89044e16i			0.188185i
$825$	−1.28426e17	−	1.49200e17i	−0.407315	−	0.473200i
$826$	−1.05137e16			−0.0331036
$827$	−2.17032e17	+	2.17032e17i	−0.678408	+	0.678408i	−0.959640	−	0.281232i	$-0.909257\pi$
$827$	−2.17032e17	+	2.17032e17i	−0.678408	+	0.678408i	0.281232	+	0.959640i	$0.409257\pi$
$828$	−5.61129e16	−	5.61129e16i	−0.174133	−	0.174133i
$829$		−	6.19747e17i		−	1.90936i	−0.297637	−	0.954679i	$-0.596199\pi$
$829$		−	6.19747e17i		−	1.90936i	0.297637	−	0.954679i	$-0.403801\pi$
$830$	3.03971e16	+	1.13565e15i	0.0929744	+	0.00347356i
$831$	3.44704e17			1.04674
$832$	−1.18347e17	+	1.18347e17i	−0.356793	+	0.356793i
$833$	2.88808e17	+	2.88808e17i	0.864450	+	0.864450i
$834$			6.13090e15i			0.0182191i
$835$	−1.23573e17	+	1.14672e17i	−0.364589	+	0.338328i
$836$	−2.16740e17			−0.634894
$837$	−1.33154e17	+	1.33154e17i	−0.387258	+	0.387258i
$838$	−2.01689e16	−	2.01689e16i	−0.0582395	−	0.0582395i
$839$		−	3.98680e17i		−	1.14302i	−0.820596	−	0.571509i	$-0.806358\pi$
$839$		−	3.98680e17i		−	1.14302i	0.820596	−	0.571509i	$-0.193642\pi$
$840$	−3.14270e16	−	3.38664e16i	−0.0894597	−	0.0964036i
$841$	−3.77085e17			−1.06577
$842$	−9.29223e15	+	9.29223e15i	−0.0260764	+	0.0260764i
$843$	1.81116e17	+	1.81116e17i	0.504652	+	0.504652i
$844$		−	4.00788e16i		−	0.110882i
$845$	−9.93461e15	+	2.65913e17i	−0.0272905	+	0.730464i
$846$	−4.35108e14			−0.00118679
$847$	−6.71871e16	+	6.71871e16i	−0.181964	+	0.181964i
$848$	−2.88971e17	−	2.88971e17i	−0.777103	−	0.777103i
$849$			1.70506e17i			0.455295i
$850$	−1.27038e15	+	1.69780e16i	−0.00336838	+	0.0450166i
$851$	1.05041e17			0.276554
$852$	2.51559e17	−	2.51559e17i	0.657662	−	0.657662i
$853$	2.44226e17	+	2.44226e17i	0.634011	+	0.634011i	0.949072	−	0.315060i	$-0.102025\pi$
$853$	2.44226e17	+	2.44226e17i	0.634011	+	0.634011i	−0.315060	+	0.949072i	$0.602025\pi$
$854$		−	5.83857e16i		−	0.150508i
$855$	−1.53481e17	−	5.73412e15i	−0.392878	−	0.0146781i
$856$	4.02772e16			0.102380
$857$	−1.27540e17	+	1.27540e17i	−0.321929	+	0.321929i	−0.849507	−	0.527578i	$-0.823100\pi$
$857$	−1.27540e17	+	1.27540e17i	−0.321929	+	0.321929i	0.527578	+	0.849507i	$0.323100\pi$
$858$	6.16006e15	+	6.16006e15i	0.0154405	+	0.0154405i
$859$			6.86139e17i			1.70786i	0.520385	+	0.853932i	$0.325789\pi$
$859$			6.86139e17i			1.70786i	−0.520385	+	0.853932i	$0.674211\pi$
$860$	−3.05110e17	+	2.83133e17i	−0.754164	+	0.699842i
$861$	−1.96743e17			−0.482926
$862$	1.31558e16	−	1.31558e16i	0.0320682	−	0.0320682i
$863$	−4.15028e17	−	4.15028e17i	−1.00465	−	1.00465i	−0.999989	−	0.00465632i	$-0.998518\pi$
$863$	−4.15028e17	−	4.15028e17i	−1.00465	−	1.00465i	−0.00465632	−	0.999989i	$-0.501482\pi$
$864$		−	8.08216e16i		−	0.194288i
$865$	−1.09373e17	−	1.17863e17i	−0.261104	−	0.281371i
$866$	5.12400e15			0.0121479
$867$	9.63559e16	−	9.63559e16i	0.226863	−	0.226863i
$868$	−2.86822e17	−	2.86822e17i	−0.670647	−	0.670647i
$869$			1.48579e17i			0.345015i
$870$	−9.12252e14	+	2.44176e16i	−0.00210378	+	0.0563103i
$871$	−1.57504e17			−0.360731
$872$	8.25935e15	−	8.25935e15i	0.0187865	−	0.0187865i
$873$	3.30298e17	+	3.30298e17i	0.746140	+	0.746140i
$874$		−	6.67158e15i		−	0.0149679i
$875$	5.89784e17	−	4.70501e17i	1.31415	−	1.04836i
$876$	−5.66676e16			−0.125404
$877$	4.90704e17	−	4.90704e17i	1.07850	−	1.07850i	0.0818604	−	0.996644i	$-0.473914\pi$
$877$	4.90704e17	−	4.90704e17i	1.07850	−	1.07850i	0.996644	−	0.0818604i	$-0.0260862\pi$
$878$	−1.84086e16	−	1.84086e16i	−0.0401841	−	0.0401841i
$879$			4.18552e17i			0.907436i
$880$	4.91549e17	+	1.83645e16i	1.05845	+	0.0395442i
$881$	5.60698e17			1.19915			0.599575	−	0.800319i	$-0.295336\pi$
$881$	5.60698e17			1.19915			0.599575	+	0.800319i	$0.295336\pi$
$882$	−2.71309e16	+	2.71309e16i	−0.0576306	+	0.0576306i
$883$	−7.91439e16	−	7.91439e16i	−0.166976	−	0.166976i	0.618673	−	0.785649i	$-0.287671\pi$
$883$	−7.91439e16	−	7.91439e16i	−0.166976	−	0.166976i	−0.785649	+	0.618673i	$0.787671\pi$
$884$			1.64958e17i			0.345668i
$885$	−5.98022e16	+	5.54947e16i	−0.124468	+	0.115503i
$886$	−7.74044e14			−0.00160016
$887$	−5.11280e17	+	5.11280e17i	−1.04983	+	1.04983i	−0.0511332	+	0.998692i	$0.516283\pi$
$887$	−5.11280e17	+	5.11280e17i	−1.04983	+	1.04983i	−0.998692	+	0.0511332i	$0.983717\pi$
$888$	2.00710e16	+	2.00710e16i	0.0409347	+	0.0409347i
$889$		−	1.14158e18i		−	2.31258i
$890$	−4.28212e15	−	4.61450e15i	−0.00861626	−	0.00928506i
$891$	−5.37671e16			−0.107461
$892$	4.64549e16	−	4.64549e16i	0.0922237	−	0.0922237i
$893$	5.66324e15	+	5.66324e15i	0.0111675	+	0.0111675i
$894$		−	2.32184e16i		−	0.0454786i
$895$	1.72459e16	−	4.61609e17i	0.0335543	−	0.898123i
$896$	2.31948e17			0.448274
$897$	4.15152e16	−	4.15152e16i	0.0796989	−	0.0796989i
$898$	−5.64865e15	−	5.64865e15i	−0.0107718	−	0.0107718i
$899$			4.30028e17i			0.814589i
$900$	3.49199e17	+	2.61290e16i	0.657080	+	0.0491662i
$901$	−3.99061e17			−0.745916
$902$	−1.36233e16	+	1.36233e16i	−0.0252955	+	0.0252955i
$903$	−3.87294e17	−	3.87294e17i	−0.714355	−	0.714355i
$904$			1.24303e17i			0.227757i
$905$	2.08433e17	+	7.78713e15i	0.379380	+	0.0141738i
$906$	7.67586e14			0.00138790
$907$	−3.23458e17	+	3.23458e17i	−0.580997	+	0.580997i	−0.935177	−	0.354180i	$-0.884760\pi$
$907$	−3.23458e17	+	3.23458e17i	−0.580997	+	0.580997i	0.354180	+	0.935177i	$0.384760\pi$
$908$	4.41512e17	+	4.41512e17i	0.787821	+	0.787821i
$909$			3.05460e17i			0.541466i
$910$	−2.44733e16	+	2.27105e16i	−0.0430967	+	0.0399924i
$911$	8.58023e17			1.50103			0.750514	−	0.660855i	$-0.229806\pi$
$911$	8.58023e17			1.50103			0.750514	+	0.660855i	$0.229806\pi$
$912$	−1.38597e17	+	1.38597e17i	−0.240872	+	0.240872i
$913$	−6.06821e17	−	6.06821e17i	−1.04770	−	1.04770i
$914$			3.48100e16i			0.0597073i
$915$	−3.08178e17	−	3.32100e17i	−0.525141	−	0.565903i
$916$	−5.46002e17			−0.924318
$917$	−7.50613e17	+	7.50613e17i	−1.26241	+	1.26241i
$918$	−1.84605e16	−	1.84605e16i	−0.0308452	−	0.0308452i
$919$			6.38907e17i			1.06058i	0.847816	+	0.530291i	$0.177917\pi$
$919$			6.38907e17i			1.06058i	−0.847816	+	0.530291i	$0.822083\pi$
$920$	−1.13838e15	+	3.04702e16i	−0.00187741	+	0.0502514i
$921$	1.46768e17			0.240477
$922$	−8.96346e15	+	8.96346e15i	−0.0145912	+	0.0145912i
$923$	−3.64405e17	−	3.64405e17i	−0.589351	−	0.589351i
$924$			6.50246e17i			1.04483i
$925$	−3.51299e17	+	3.02386e17i	−0.560823	+	0.482738i
$926$	4.01035e16			0.0636086
$927$	4.15405e17	−	4.15405e17i	0.654626	−	0.654626i
$928$	−1.30509e17	−	1.30509e17i	−0.204340	−	0.204340i
$929$		−	6.27201e17i		−	0.975691i	−0.872930	−	0.487845i	$-0.837783\pi$
$929$		−	6.27201e17i		−	0.975691i	0.872930	−	0.487845i	$-0.162217\pi$
$930$	1.43662e16	+	5.36728e14i	0.0222047	+	0.000829576i
$931$	7.06257e17			1.08459
$932$	6.10591e16	−	6.10591e16i	0.0931654	−	0.0931654i
$933$	7.23862e16	+	7.23862e16i	0.109740	+	0.109740i
$934$		−	4.13625e16i		−	0.0623053i
$935$	3.52088e17	−	3.26727e17i	0.526965	−	0.489008i
$936$	−3.10633e16			−0.0461948
$937$	−1.73481e17	+	1.73481e17i	−0.256338	+	0.256338i	−0.823563	−	0.567225i	$-0.808017\pi$
$937$	−1.73481e17	+	1.73481e17i	−0.256338	+	0.256338i	0.567225	+	0.823563i	$0.308017\pi$
$938$	3.79685e16	+	3.79685e16i	0.0557450	+	0.0557450i
$939$		−	6.49340e17i		−	0.947281i
$940$	−1.24209e16	−	1.33851e16i	−0.0180048	−	0.0194023i
$941$	−8.37927e17			−1.20689			−0.603446	−	0.797404i	$-0.706206\pi$
$941$	−8.37927e17			−1.20689			−0.603446	+	0.797404i	$0.706206\pi$
$942$	4.33417e15	−	4.33417e15i	0.00620298	−	0.00620298i
$943$	9.18132e16	+	9.18132e16i	0.130568	+	0.130568i
$944$		−	2.03853e17i		−	0.288061i
$945$	−4.31924e16	+	1.15610e18i	−0.0606480	+	1.62332i
$946$	−5.36357e16			−0.0748353
$947$	5.21035e17	−	5.21035e17i	0.722382	−	0.722382i	−0.246708	−	0.969090i	$-0.579349\pi$
$947$	5.21035e17	−	5.21035e17i	0.722382	−	0.722382i	0.969090	+	0.246708i	$0.0793488\pi$
$948$	9.54486e16	+	9.54486e16i	0.131498	+	0.131498i
$949$			8.20877e16i			0.112378i
$950$	1.92058e16	+	2.23124e16i	0.0261271	+	0.0303533i
$951$	1.88789e17			0.255208
$952$	7.97120e16	−	7.97120e16i	0.107078	−	0.107078i
$953$	5.54390e17	+	5.54390e17i	0.740044	+	0.740044i	0.972586	−	0.232542i	$-0.0747044\pi$
$953$	5.54390e17	+	5.54390e17i	0.740044	+	0.740044i	−0.232542	+	0.972586i	$0.574704\pi$
$954$		−	3.74881e16i		−	0.0497283i
$955$	5.81197e17	+	2.17138e16i	0.766132	+	0.0286230i
$956$	2.53224e17			0.331709
$957$	4.87452e17	−	4.87452e17i	0.634542	−	0.634542i
$958$	2.50227e16	+	2.50227e16i	0.0323698	+	0.0323698i
$959$			3.01246e17i			0.387266i
$960$	3.24548e17	−	3.01171e17i	0.414621	−	0.384756i
$961$	−5.34654e17			−0.678785
$962$	1.45042e16	−	1.45042e16i	0.0182996	−	0.0182996i
$963$	−2.84042e17	−	2.84042e17i	−0.356144	−	0.356144i
$964$		−	9.44147e17i		−	1.17646i
$965$	−6.15629e17	−	6.63415e17i	−0.762352	−	0.821526i
$966$	−2.00155e16			−0.0246323
$967$	7.07457e17	−	7.07457e17i	0.865250	−	0.865250i	−0.126692	−	0.991942i	$-0.540436\pi$
$967$	7.07457e17	−	7.07457e17i	0.865250	−	0.865250i	0.991942	+	0.126692i	$0.0404361\pi$
$968$	1.19821e16	+	1.19821e16i	0.0145640	+	0.0145640i
$969$			1.91399e17i			0.231205i
$970$	3.34279e15	−	8.94740e16i	0.00401308	−	0.107415i
$971$	−9.86232e17			−1.17669			−0.588347	−	0.808608i	$-0.700221\pi$
$971$	−9.86232e17			−1.17669			−0.588347	+	0.808608i	$0.700221\pi$
$972$	−6.08156e17	+	6.08156e17i	−0.721136	+	0.721136i
$973$	4.68738e17	+	4.68738e17i	0.552400	+	0.552400i
$974$		−	7.53294e16i		−	0.0882289i
$975$	−1.93315e16	+	2.58356e17i	−0.0225029	+	0.300739i
$976$	1.13206e18			1.30969
$977$	−1.03914e17	+	1.03914e17i	−0.119483	+	0.119483i	−0.764320	−	0.644837i	$-0.776925\pi$
$977$	−1.03914e17	+	1.03914e17i	−0.119483	+	0.119483i	0.644837	+	0.764320i	$0.276925\pi$
$978$	−7.40100e15	−	7.40100e15i	−0.00845779	−	0.00845779i
$979$			1.77604e17i			0.201724i
$980$	−1.60912e18	−	6.01174e16i	−1.81648	−	0.0678646i
$981$	−1.16493e17			−0.130703
$982$	−8.64250e15	+	8.64250e15i	−0.00963763	+	0.00963763i
$983$	1.02512e18	+	1.02512e18i	1.13620	+	1.13620i	0.989125	+	0.147077i	$0.0469865\pi$
$983$	1.02512e18	+	1.02512e18i	1.13620	+	1.13620i	0.147077	+	0.989125i	$0.453014\pi$
$984$			3.50871e16i			0.0386524i
$985$	−1.00020e18	+	9.28157e17i	−1.09514	+	1.01626i
$986$	−5.96194e16			−0.0648823
$987$	1.69904e16	−	1.69904e16i	0.0183781	−	0.0183781i
$988$	2.01695e17	+	2.01695e17i	0.216847	+	0.216847i
$989$			3.61473e17i			0.386276i
$990$	3.06931e16	+	3.30755e16i	0.0326009	+	0.0351314i
$991$	−7.80402e17			−0.823903			−0.411952	−	0.911206i	$-0.635153\pi$
$991$	−7.80402e17			−0.823903			−0.411952	+	0.911206i	$0.635153\pi$
$992$	−7.67858e16	+	7.67858e16i	−0.0805769	+	0.0805769i
$993$	1.50496e17	+	1.50496e17i	0.156974	+	0.156974i
$994$			1.75689e17i			0.182149i
$995$	2.35969e16	−	6.31600e17i	0.0243173	−	0.650885i
$996$	−7.79658e17			−0.798635
$997$	−1.92699e17	+	1.92699e17i	−0.196204	+	0.196204i	−0.798371	−	0.602166i	$-0.794304\pi$
$997$	−1.92699e17	+	1.92699e17i	−0.196204	+	0.196204i	0.602166	+	0.798371i	$0.294304\pi$
$998$	1.63538e16	+	1.63538e16i	0.0165514	+	0.0165514i
$999$		−	7.10764e17i		−	0.715044i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.13.c.a.3.3	yes	10
3.2	odd	2		45.13.g.a.28.3		10
4.3	odd	2		80.13.p.c.33.3		10
5.2	odd	4	inner	5.13.c.a.2.3	✓	10
5.3	odd	4		25.13.c.b.7.3		10
5.4	even	2		25.13.c.b.18.3		10
15.2	even	4		45.13.g.a.37.3		10
20.7	even	4		80.13.p.c.17.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.13.c.a.2.3	✓	10	5.2	odd	4	inner
5.13.c.a.3.3	yes	10	1.1	even	1	trivial
25.13.c.b.7.3		10	5.3	odd	4
25.13.c.b.18.3		10	5.4	even	2
45.13.g.a.28.3		10	3.2	odd	2
45.13.g.a.37.3		10	15.2	even	4
80.13.p.c.17.3		10	20.7	even	4
80.13.p.c.33.3		10	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	5.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.05147 - 3.05147i) q^{2} +(-299.721 - 299.721i) q^{3} +4077.38i q^{4} +(-15614.1 - 583.350i) q^{5} -1829.18 q^{6} +(-139850. + 139850. i) q^{7} +(24940.8 + 24940.8i) q^{8} -351775. i q^{9} +O(q^{10})\)	\(q+(3.05147 - 3.05147i) q^{2} +(-299.721 - 299.721i) q^{3} +4077.38i q^{4} +(-15614.1 - 583.350i) q^{5} -1829.18 q^{6} +(-139850. + 139850. i) q^{7} +(24940.8 + 24940.8i) q^{8} -351775. i q^{9} +(-49426.1 + 45865.9i) q^{10} +1.90233e6 q^{11} +(1.22208e6 - 1.22208e6i) q^{12} +(-1.77028e6 - 1.77028e6i) q^{13} +853498. i q^{14} +(4.50504e6 + 4.85473e6i) q^{15} -1.65487e7 q^{16} +(-1.14267e7 + 1.14267e7i) q^{17} +(-1.07343e6 - 1.07343e6i) q^{18} +2.79430e7i q^{19} +(2.37854e6 - 6.36646e7i) q^{20} +8.38323e7 q^{21} +(5.80490e6 - 5.80490e6i) q^{22} +(-3.91216e7 - 3.91216e7i) q^{23} -1.49506e7i q^{24} +(2.43460e8 + 1.82170e7i) q^{25} -1.08039e7 q^{26} +(-2.64719e8 + 2.64719e8i) q^{27} +(-5.70223e8 - 5.70223e8i) q^{28} +8.54927e8i q^{29} +(2.85611e7 + 1.06705e6i) q^{30} +5.03000e8 q^{31} +(-1.52656e8 + 1.52656e8i) q^{32} +(-5.70168e8 - 5.70168e8i) q^{33} +6.97363e7i q^{34} +(2.26522e9 - 2.10206e9i) q^{35} +1.43432e9 q^{36} +(-1.34249e9 + 1.34249e9i) q^{37} +(8.52671e7 + 8.52671e7i) q^{38} +1.06118e9i q^{39} +(-3.74879e8 - 4.03978e8i) q^{40} -2.34687e9 q^{41} +(2.55812e8 - 2.55812e8i) q^{42} +(-4.61986e9 - 4.61986e9i) q^{43} +7.75651e9i q^{44} +(-2.05208e8 + 5.49265e9i) q^{45} -2.38757e8 q^{46} +(2.02672e8 - 2.02672e8i) q^{47} +(4.96001e9 + 4.96001e9i) q^{48} -2.52749e10i q^{49} +(7.98500e8 - 6.87323e8i) q^{50} +6.84963e9 q^{51} +(7.21811e9 - 7.21811e9i) q^{52} +(1.74618e10 + 1.74618e10i) q^{53} +1.61556e9i q^{54} +(-2.97031e10 - 1.10972e9i) q^{55} -6.97596e9 q^{56} +(8.37511e9 - 8.37511e9i) q^{57} +(2.60878e9 + 2.60878e9i) q^{58} +1.23184e10i q^{59} +(-1.97945e10 + 1.83688e10i) q^{60} -6.84075e10 q^{61} +(1.53489e9 - 1.53489e9i) q^{62} +(4.91959e10 + 4.91959e10i) q^{63} -6.68519e10i q^{64} +(2.66087e10 + 2.86741e10i) q^{65} -3.47970e9 q^{66} +(4.44857e10 - 4.44857e10i) q^{67} +(-4.65908e10 - 4.65908e10i) q^{68} +2.34512e10i q^{69} +(4.97888e8 - 1.33266e10i) q^{70} +2.05846e11 q^{71} +(8.77356e9 - 8.77356e9i) q^{72} +(-2.31849e10 - 2.31849e10i) q^{73} +8.19313e9i q^{74} +(-6.75102e10 - 7.84302e10i) q^{75} -1.13934e11 q^{76} +(-2.66041e11 + 2.66041e11i) q^{77} +(3.23817e9 + 3.23817e9i) q^{78} +7.81035e10i q^{79} +(2.58394e11 + 9.65369e9i) q^{80} -2.82638e10 q^{81} +(-7.16139e9 + 7.16139e9i) q^{82} +(-3.18989e11 - 3.18989e11i) q^{83} +3.41816e11i q^{84} +(1.85083e11 - 1.71751e11i) q^{85} -2.81948e10 q^{86} +(2.56240e11 - 2.56240e11i) q^{87} +(4.74456e10 + 4.74456e10i) q^{88} +9.33617e10i q^{89} +(1.61345e10 + 1.73869e10i) q^{90} +4.95149e11 q^{91} +(1.59514e11 - 1.59514e11i) q^{92} +(-1.50760e11 - 1.50760e11i) q^{93} -1.23689e9i q^{94} +(1.63005e10 - 4.36304e11i) q^{95} +9.15083e10 q^{96} +(-9.38946e11 + 9.38946e11i) q^{97} +(-7.71257e10 - 7.71257e10i) q^{98} -6.69191e11i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} + 318 q^{3} - 4250 q^{5} - 175080 q^{6} + 279598 q^{7} - 469980 q^{8}+O(q^{10}) \) 10 * q - 2 * q^2 + 318 * q^3 - 4250 * q^5 - 175080 * q^6 + 279598 * q^7 - 469980 * q^8	\( 10 q - 2 q^{2} + 318 q^{3} - 4250 q^{5} - 175080 q^{6} + 279598 q^{7} - 469980 q^{8} + 1552150 q^{10} + 312620 q^{11} - 2359992 q^{12} + 5290738 q^{13} - 5821650 q^{15} + 30547960 q^{16} - 41269502 q^{17} - 140573742 q^{18} + 334988100 q^{20} + 107493420 q^{21} - 155490544 q^{22} - 510099842 q^{23} + 942201250 q^{25} + 1475846420 q^{26} - 1993958640 q^{27} - 3562106488 q^{28} + 5922516000 q^{30} + 3077089820 q^{31} - 4623883832 q^{32} - 7503698004 q^{33} + 9330787150 q^{35} + 7760793660 q^{36} - 2599618502 q^{37} - 15310240920 q^{38} + 15901243500 q^{40} + 7412079020 q^{41} - 18593270064 q^{42} - 5784410402 q^{43} - 10510145100 q^{45} - 7382547880 q^{46} + 16053249598 q^{47} + 42572492208 q^{48} - 68314688750 q^{50} - 33139878180 q^{51} + 96763417228 q^{52} + 101763514618 q^{53} - 84180068500 q^{55} - 172002747600 q^{56} + 27733489920 q^{57} + 135238672320 q^{58} - 220124568600 q^{60} + 7731718220 q^{61} + 193287375176 q^{62} + 207465112158 q^{63} - 338075024150 q^{65} - 60815472960 q^{66} - 80010636002 q^{67} + 204699541412 q^{68} + 376969924200 q^{70} - 46557252580 q^{71} - 13986370620 q^{72} - 448527032342 q^{73} + 719724648750 q^{75} + 305095930800 q^{76} - 425580405844 q^{77} - 1690993241784 q^{78} + 873032236000 q^{80} + 1107831051810 q^{81} - 671946416464 q^{82} - 91118376722 q^{83} + 543768569650 q^{85} + 414117747320 q^{86} - 2078422804320 q^{87} - 1842434230560 q^{88} + 3098742811350 q^{90} + 2737742572220 q^{91} + 906853941448 q^{92} - 91295366484 q^{93} - 1044695070000 q^{95} - 3473259523680 q^{96} - 1409507601302 q^{97} - 1481746533298 q^{98}+O(q^{100}) \) 10 * q - 2 * q^2 + 318 * q^3 - 4250 * q^5 - 175080 * q^6 + 279598 * q^7 - 469980 * q^8 + 1552150 * q^10 + 312620 * q^11 - 2359992 * q^12 + 5290738 * q^13 - 5821650 * q^15 + 30547960 * q^16 - 41269502 * q^17 - 140573742 * q^18 + 334988100 * q^20 + 107493420 * q^21 - 155490544 * q^22 - 510099842 * q^23 + 942201250 * q^25 + 1475846420 * q^26 - 1993958640 * q^27 - 3562106488 * q^28 + 5922516000 * q^30 + 3077089820 * q^31 - 4623883832 * q^32 - 7503698004 * q^33 + 9330787150 * q^35 + 7760793660 * q^36 - 2599618502 * q^37 - 15310240920 * q^38 + 15901243500 * q^40 + 7412079020 * q^41 - 18593270064 * q^42 - 5784410402 * q^43 - 10510145100 * q^45 - 7382547880 * q^46 + 16053249598 * q^47 + 42572492208 * q^48 - 68314688750 * q^50 - 33139878180 * q^51 + 96763417228 * q^52 + 101763514618 * q^53 - 84180068500 * q^55 - 172002747600 * q^56 + 27733489920 * q^57 + 135238672320 * q^58 - 220124568600 * q^60 + 7731718220 * q^61 + 193287375176 * q^62 + 207465112158 * q^63 - 338075024150 * q^65 - 60815472960 * q^66 - 80010636002 * q^67 + 204699541412 * q^68 + 376969924200 * q^70 - 46557252580 * q^71 - 13986370620 * q^72 - 448527032342 * q^73 + 719724648750 * q^75 + 305095930800 * q^76 - 425580405844 * q^77 - 1690993241784 * q^78 + 873032236000 * q^80 + 1107831051810 * q^81 - 671946416464 * q^82 - 91118376722 * q^83 + 543768569650 * q^85 + 414117747320 * q^86 - 2078422804320 * q^87 - 1842434230560 * q^88 + 3098742811350 * q^90 + 2737742572220 * q^91 + 906853941448 * q^92 - 91295366484 * q^93 - 1044695070000 * q^95 - 3473259523680 * q^96 - 1409507601302 * q^97 - 1481746533298 * q^98

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