LMFDB - Embedded newform 10.15.c.b.3.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,15,Mod(3,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

N = Newforms(chi, 15, names="a")

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

chi := DirichletCharacter("10.3");

S:= CuspForms(chi, 15);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 15 $
Character orbit:	$[\chi]$	$=$	10.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:	$12.4328968152$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 513401x^{6} + 81983771116x^{4} + 4511941511282436x^{2} + 65023716741123799296 $ x^8 + 513401x^6 + 81983771116x^4 + 4511941511282436*x^2 + 65023716741123799296
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{4}\cdot 5^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.4
Root			$514.022i$ of defining polynomial
Character	$\chi$	$=$	10.3
Dual form			10.15.c.b.7.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(64.0000 - 64.0000i) q^{2} +(3060.13 + 3060.13i) q^{3} -8192.00i q^{4} +(20659.0 - 75344.0i) q^{5} +391697. q^{6} +(586054. - 586054. i) q^{7} +(-524288. - 524288. i) q^{8} +1.39459e7i q^{9} +O(q^{10})$	\(q+(64.0000 - 64.0000i) q^{2} +(3060.13 + 3060.13i) q^{3} -8192.00i q^{4} +(20659.0 - 75344.0i) q^{5} +391697. q^{6} +(586054. - 586054. i) q^{7} +(-524288. - 524288. i) q^{8} +1.39459e7i q^{9} +(-3.49984e6 - 6.14419e6i) q^{10} +1.03624e7 q^{11} +(2.50686e7 - 2.50686e7i) q^{12} +(2.36414e7 + 2.36414e7i) q^{13} -7.50150e7i q^{14} +(2.93782e8 - 1.67343e8i) q^{15} -6.71089e7 q^{16} +(-2.68064e8 + 2.68064e8i) q^{17} +(8.92536e8 + 8.92536e8i) q^{18} -4.55238e8i q^{19} +(-6.17218e8 - 1.69239e8i) q^{20} +3.58681e9 q^{21} +(6.63194e8 - 6.63194e8i) q^{22} +(-3.95873e7 - 3.95873e7i) q^{23} -3.20878e9i q^{24} +(-5.24992e9 - 3.11307e9i) q^{25} +3.02610e9 q^{26} +(-2.80397e10 + 2.80397e10i) q^{27} +(-4.80096e9 - 4.80096e9i) q^{28} -1.04495e10i q^{29} +(8.09208e9 - 2.95120e10i) q^{30} -1.10684e10 q^{31} +(-4.29497e9 + 4.29497e9i) q^{32} +(3.17103e10 + 3.17103e10i) q^{33} +3.43122e10i q^{34} +(-3.20484e10 - 5.62630e10i) q^{35} +1.14245e11 q^{36} +(-7.04363e9 + 7.04363e9i) q^{37} +(-2.91352e10 - 2.91352e10i) q^{38} +1.44692e11i q^{39} +(-5.03332e10 + 2.86707e10i) q^{40} -2.23620e10 q^{41} +(2.29556e11 - 2.29556e11i) q^{42} +(-2.16788e11 - 2.16788e11i) q^{43} -8.48888e10i q^{44} +(1.05074e12 + 2.88108e11i) q^{45} -5.06717e9 q^{46} +(-2.30554e11 + 2.30554e11i) q^{47} +(-2.05362e11 - 2.05362e11i) q^{48} -8.69642e9i q^{49} +(-5.35232e11 + 1.36759e11i) q^{50} -1.64062e12 q^{51} +(1.93670e11 - 1.93670e11i) q^{52} +(-3.91687e11 - 3.91687e11i) q^{53} +3.58908e12i q^{54} +(2.14077e11 - 7.80745e11i) q^{55} -6.14523e11 q^{56} +(1.39309e12 - 1.39309e12i) q^{57} +(-6.68767e11 - 6.68767e11i) q^{58} -4.44463e12i q^{59} +(-1.37088e12 - 2.40666e12i) q^{60} -2.34892e12 q^{61} +(-7.08377e11 + 7.08377e11i) q^{62} +(8.17304e12 + 8.17304e12i) q^{63} +5.49756e11i q^{64} +(2.26964e12 - 1.29283e12i) q^{65} +4.05892e12 q^{66} +(-5.17683e12 + 5.17683e12i) q^{67} +(2.19598e12 + 2.19598e12i) q^{68} -2.42285e11i q^{69} +(-5.65193e12 - 1.54974e12i) q^{70} +1.06495e13 q^{71} +(7.31165e12 - 7.31165e12i) q^{72} +(7.66256e11 + 7.66256e11i) q^{73} +9.01585e11i q^{74} +(-6.53907e12 - 2.55919e13i) q^{75} -3.72931e12 q^{76} +(6.07293e12 - 6.07293e12i) q^{77} +(9.26026e12 + 9.26026e12i) q^{78} +2.49923e13i q^{79} +(-1.38640e12 + 5.05625e12i) q^{80} -1.04908e14 q^{81} +(-1.43117e12 + 1.43117e12i) q^{82} +(2.02352e13 + 2.02352e13i) q^{83} -2.93831e13i q^{84} +(1.46591e13 + 2.57350e13i) q^{85} -2.77489e13 q^{86} +(3.19768e13 - 3.19768e13i) q^{87} +(-5.43288e12 - 5.43288e12i) q^{88} +5.70248e13i q^{89} +(8.56861e13 - 4.88083e13i) q^{90} +2.77103e13 q^{91} +(-3.24299e11 + 3.24299e11i) q^{92} +(-3.38708e13 - 3.38708e13i) q^{93} +2.95110e13i q^{94} +(-3.42995e13 - 9.40478e12i) q^{95} -2.62863e13 q^{96} +(1.04766e14 - 1.04766e14i) q^{97} +(-5.56571e11 - 5.56571e11i) q^{98} +1.44513e14i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 512 q^{2} + 1404 q^{3} - 100860 q^{5} + 179712 q^{6} + 1333276 q^{7} - 4194304 q^{8}+O(q^{10}) $ 8 * q + 512 * q^2 + 1404 * q^3 - 100860 * q^5 + 179712 * q^6 + 1333276 * q^7 - 4194304 * q^8	\( 8 q + 512 q^{2} + 1404 q^{3} - 100860 q^{5} + 179712 q^{6} + 1333276 q^{7} - 4194304 q^{8} - 9034240 q^{10} + 8181256 q^{11} + 11501568 q^{12} - 10529136 q^{13} + 721621020 q^{15} - 536870912 q^{16} - 1669855424 q^{17} + 2079049728 q^{18} - 330137600 q^{20} + 192520776 q^{21} + 523600384 q^{22} - 4778918036 q^{23} + 15448124800 q^{25} - 1347729408 q^{26} - 20842498800 q^{27} - 10922196992 q^{28} + 48428597760 q^{30} + 35788345016 q^{31} - 34359738368 q^{32} - 130209466872 q^{33} - 30069746420 q^{35} + 266118365184 q^{36} - 31454650344 q^{37} - 100622935040 q^{38} + 31750881280 q^{40} + 94198718056 q^{41} + 12321329664 q^{42} - 942463128516 q^{43} + 2927734430100 q^{45} - 611701508608 q^{46} - 1797815170164 q^{47} - 94220845056 q^{48} + 712475699200 q^{50} - 1982287069224 q^{51} - 86254682112 q^{52} + 540438256184 q^{53} + 788235527880 q^{55} - 1398041214976 q^{56} + 6485834218080 q^{57} - 841739223040 q^{58} + 287341117440 q^{60} - 19913995236984 q^{61} + 2290454081024 q^{62} + 25848827893644 q^{63} - 7034160749880 q^{65} - 16666811759616 q^{66} + 13553624120956 q^{67} + 13679455633408 q^{68} - 16955995571200 q^{70} - 51541518798664 q^{71} + 17031575371776 q^{72} + 44383738947944 q^{73} - 19405526378100 q^{75} - 12879735685120 q^{76} + 74886492270632 q^{77} + 66217996893696 q^{78} + 6768600023040 q^{80} - 322723412222112 q^{81} + 6028717955584 q^{82} + 134272999400364 q^{83} + 145335752004880 q^{85} - 120635280450048 q^{86} + 68423417580480 q^{87} - 4289334345728 q^{88} + 112569467389440 q^{90} - 234891728536584 q^{91} - 39148896550912 q^{92} + 66751748435208 q^{93} + 26760204832400 q^{95} - 12060268167168 q^{96} + 167451300858216 q^{97} + 78801761769472 q^{98}+O(q^{100}) \) 8 * q + 512 * q^2 + 1404 * q^3 - 100860 * q^5 + 179712 * q^6 + 1333276 * q^7 - 4194304 * q^8 - 9034240 * q^10 + 8181256 * q^11 + 11501568 * q^12 - 10529136 * q^13 + 721621020 * q^15 - 536870912 * q^16 - 1669855424 * q^17 + 2079049728 * q^18 - 330137600 * q^20 + 192520776 * q^21 + 523600384 * q^22 - 4778918036 * q^23 + 15448124800 * q^25 - 1347729408 * q^26 - 20842498800 * q^27 - 10922196992 * q^28 + 48428597760 * q^30 + 35788345016 * q^31 - 34359738368 * q^32 - 130209466872 * q^33 - 30069746420 * q^35 + 266118365184 * q^36 - 31454650344 * q^37 - 100622935040 * q^38 + 31750881280 * q^40 + 94198718056 * q^41 + 12321329664 * q^42 - 942463128516 * q^43 + 2927734430100 * q^45 - 611701508608 * q^46 - 1797815170164 * q^47 - 94220845056 * q^48 + 712475699200 * q^50 - 1982287069224 * q^51 - 86254682112 * q^52 + 540438256184 * q^53 + 788235527880 * q^55 - 1398041214976 * q^56 + 6485834218080 * q^57 - 841739223040 * q^58 + 287341117440 * q^60 - 19913995236984 * q^61 + 2290454081024 * q^62 + 25848827893644 * q^63 - 7034160749880 * q^65 - 16666811759616 * q^66 + 13553624120956 * q^67 + 13679455633408 * q^68 - 16955995571200 * q^70 - 51541518798664 * q^71 + 17031575371776 * q^72 + 44383738947944 * q^73 - 19405526378100 * q^75 - 12879735685120 * q^76 + 74886492270632 * q^77 + 66217996893696 * q^78 + 6768600023040 * q^80 - 322723412222112 * q^81 + 6028717955584 * q^82 + 134272999400364 * q^83 + 145335752004880 * q^85 - 120635280450048 * q^86 + 68423417580480 * q^87 - 4289334345728 * q^88 + 112569467389440 * q^90 - 234891728536584 * q^91 - 39148896550912 * q^92 + 66751748435208 * q^93 + 26760204832400 * q^95 - 12060268167168 * q^96 + 167451300858216 * q^97 + 78801761769472 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$7$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	64.0000	−	64.0000i	0.500000	−	0.500000i
$2$	64.0000	−	64.0000i	0.500000	−	0.500000i
$3$	3060.13	+	3060.13i	1.39924	+	1.39924i	0.802250	+	0.596988i	$0.203636\pi$
$3$	3060.13	+	3060.13i	1.39924	+	1.39924i	0.596988	+	0.802250i	$0.296364\pi$
$4$		−	8192.00i		−	0.500000i
$5$	20659.0	−	75344.0i	0.264436	−	0.964403i
$5$	20659.0	−	75344.0i	0.264436	−	0.964403i
$6$	391697.			1.39924
$7$	586054.	−	586054.i	0.711626	−	0.711626i	−0.255249	−	0.966875i	$-0.582158\pi$
$7$	586054.	−	586054.i	0.711626	−	0.711626i	0.966875	+	0.255249i	$0.0821576\pi$
$8$	−524288.	−	524288.i	−0.250000	−	0.250000i
$9$			1.39459e7i			2.91573i
$10$	−3.49984e6	−	6.14419e6i	−0.349984	−	0.614419i
$11$	1.03624e7			0.531755			0.265877	−	0.964007i	$-0.414338\pi$
$11$	1.03624e7			0.531755			0.265877	+	0.964007i	$0.414338\pi$
$12$	2.50686e7	−	2.50686e7i	0.699619	−	0.699619i
$13$	2.36414e7	+	2.36414e7i	0.376764	+	0.376764i	0.869933	−	0.493169i	$-0.164162\pi$
$13$	2.36414e7	+	2.36414e7i	0.376764	+	0.376764i	−0.493169	+	0.869933i	$0.664162\pi$
$14$		−	7.50150e7i		−	0.711626i
$15$	2.93782e8	−	1.67343e8i	1.71944	−	0.979422i
$16$	−6.71089e7			−0.250000
$17$	−2.68064e8	+	2.68064e8i	−0.653275	+	0.653275i	−0.953780	−	0.300505i	$-0.902845\pi$
$17$	−2.68064e8	+	2.68064e8i	−0.653275	+	0.653275i	0.300505	+	0.953780i	$0.402845\pi$
$18$	8.92536e8	+	8.92536e8i	1.45787	+	1.45787i
$19$		−	4.55238e8i		−	0.509288i	−0.967035	−	0.254644i	$-0.918042\pi$
$19$		−	4.55238e8i		−	0.509288i	0.967035	−	0.254644i	$-0.0819583\pi$
$20$	−6.17218e8	−	1.69239e8i	−0.482202	−	0.132218i
$21$	3.58681e9			1.99147
$22$	6.63194e8	−	6.63194e8i	0.265877	−	0.265877i
$23$	−3.95873e7	−	3.95873e7i	−0.0116268	−	0.0116268i	0.701269	−	0.712896i	$-0.252617\pi$
$23$	−3.95873e7	−	3.95873e7i	−0.0116268	−	0.0116268i	−0.712896	+	0.701269i	$0.752617\pi$
$24$		−	3.20878e9i		−	0.699619i
$25$	−5.24992e9	−	3.11307e9i	−0.860148	−	0.510045i
$26$	3.02610e9			0.376764
$27$	−2.80397e10	+	2.80397e10i	−2.68057	+	2.68057i
$28$	−4.80096e9	−	4.80096e9i	−0.355813	−	0.355813i
$29$		−	1.04495e10i		−	0.605772i	−0.953027	−	0.302886i	$-0.902050\pi$
$29$		−	1.04495e10i		−	0.605772i	0.953027	−	0.302886i	$-0.0979501\pi$
$30$	8.09208e9	−	2.95120e10i	0.370008	−	1.34943i
$31$	−1.10684e10			−0.402303			−0.201151	−	0.979560i	$-0.564468\pi$
$31$	−1.10684e10			−0.402303			−0.201151	+	0.979560i	$0.564468\pi$
$32$	−4.29497e9	+	4.29497e9i	−0.125000	+	0.125000i
$33$	3.17103e10	+	3.17103e10i	0.744052	+	0.744052i
$34$			3.43122e10i			0.653275i
$35$	−3.20484e10	−	5.62630e10i	−0.498115	−	0.874473i
$36$	1.14245e11			1.45787
$37$	−7.04363e9	+	7.04363e9i	−0.0741967	+	0.0741967i	−0.743231	−	0.669035i	$-0.766708\pi$
$37$	−7.04363e9	+	7.04363e9i	−0.0741967	+	0.0741967i	0.669035	+	0.743231i	$0.266708\pi$
$38$	−2.91352e10	−	2.91352e10i	−0.254644	−	0.254644i
$39$			1.44692e11i			1.05436i
$40$	−5.03332e10	+	2.86707e10i	−0.307210	+	0.174992i
$41$	−2.23620e10			−0.114821			−0.0574107	−	0.998351i	$-0.518284\pi$
$41$	−2.23620e10			−0.114821			−0.0574107	+	0.998351i	$0.518284\pi$
$42$	2.29556e11	−	2.29556e11i	0.995734	−	0.995734i
$43$	−2.16788e11	−	2.16788e11i	−0.797548	−	0.797548i	0.185160	−	0.982708i	$-0.440720\pi$
$43$	−2.16788e11	−	2.16788e11i	−0.797548	−	0.797548i	−0.982708	+	0.185160i	$0.940720\pi$
$44$		−	8.48888e10i		−	0.265877i
$45$	1.05074e12	+	2.88108e11i	2.81194	+	0.771024i
$46$	−5.06717e9			−0.0116268
$47$	−2.30554e11	+	2.30554e11i	−0.455081	+	0.455081i	−0.897037	−	0.441956i	$-0.854285\pi$
$47$	−2.30554e11	+	2.30554e11i	−0.455081	+	0.455081i	0.441956	+	0.897037i	$0.354285\pi$
$48$	−2.05362e11	−	2.05362e11i	−0.349810	−	0.349810i
$49$		−	8.69642e9i		−	0.0128224i
$50$	−5.35232e11	+	1.36759e11i	−0.685096	+	0.175051i
$51$	−1.64062e12			−1.82817
$52$	1.93670e11	−	1.93670e11i	0.188382	−	0.188382i
$53$	−3.91687e11	−	3.91687e11i	−0.333433	−	0.333433i	0.520456	−	0.853888i	$-0.325762\pi$
$53$	−3.91687e11	−	3.91687e11i	−0.333433	−	0.333433i	−0.853888	+	0.520456i	$0.825762\pi$
$54$			3.58908e12i			2.68057i
$55$	2.14077e11	−	7.80745e11i	0.140615	−	0.512826i
$56$	−6.14523e11			−0.355813
$57$	1.39309e12	−	1.39309e12i	0.712615	−	0.712615i
$58$	−6.68767e11	−	6.68767e11i	−0.302886	−	0.302886i
$59$		−	4.44463e12i		−	1.78596i	−0.450097	−	0.892979i	$-0.648611\pi$
$59$		−	4.44463e12i		−	1.78596i	0.450097	−	0.892979i	$-0.351389\pi$
$60$	−1.37088e12	−	2.40666e12i	−0.489711	−	0.859719i
$61$	−2.34892e12			−0.747409			−0.373705	−	0.927548i	$-0.621913\pi$
$61$	−2.34892e12			−0.747409			−0.373705	+	0.927548i	$0.621913\pi$
$62$	−7.08377e11	+	7.08377e11i	−0.201151	+	0.201151i
$63$	8.17304e12	+	8.17304e12i	2.07491	+	2.07491i
$64$			5.49756e11i			0.125000i
$65$	2.26964e12	−	1.29283e12i	0.462982	−	0.263723i
$66$	4.05892e12			0.744052
$67$	−5.17683e12	+	5.17683e12i	−0.854162	+	0.854162i	−0.990643	−	0.136481i	$-0.956421\pi$
$67$	−5.17683e12	+	5.17683e12i	−0.854162	+	0.854162i	0.136481	+	0.990643i	$0.456421\pi$
$68$	2.19598e12	+	2.19598e12i	0.326637	+	0.326637i
$69$		−	2.42285e11i		−	0.0325374i
$70$	−5.65193e12	−	1.54974e12i	−0.686294	−	0.188179i
$71$	1.06495e13			1.17091			0.585453	−	0.810706i	$-0.300917\pi$
$71$	1.06495e13			1.17091			0.585453	+	0.810706i	$0.300917\pi$
$72$	7.31165e12	−	7.31165e12i	0.728934	−	0.728934i
$73$	7.66256e11	+	7.66256e11i	0.0693607	+	0.0693607i	0.740936	−	0.671575i	$-0.234382\pi$
$73$	7.66256e11	+	7.66256e11i	0.0693607	+	0.0693607i	−0.671575	+	0.740936i	$0.734382\pi$
$74$			9.01585e11i			0.0741967i
$75$	−6.53907e12	−	2.55919e13i	−0.489877	−	1.91723i
$76$	−3.72931e12			−0.254644
$77$	6.07293e12	−	6.07293e12i	0.378410	−	0.378410i
$78$	9.26026e12	+	9.26026e12i	0.527182	+	0.527182i
$79$			2.49923e13i			1.30142i	0.759328	+	0.650708i	$0.225528\pi$
$79$			2.49923e13i			1.30142i	−0.759328	+	0.650708i	$0.774472\pi$
$80$	−1.38640e12	+	5.05625e12i	−0.0661089	+	0.241101i
$81$	−1.04908e14			−4.58577
$82$	−1.43117e12	+	1.43117e12i	−0.0574107	+	0.0574107i
$83$	2.02352e13	+	2.02352e13i	0.745695	+	0.745695i	0.973668	−	0.227972i	$-0.0732096\pi$
$83$	2.02352e13	+	2.02352e13i	0.745695	+	0.745695i	−0.227972	+	0.973668i	$0.573210\pi$
$84$		−	2.93831e13i		−	0.995734i
$85$	1.46591e13	+	2.57350e13i	0.457271	+	0.802770i
$86$	−2.77489e13			−0.797548
$87$	3.19768e13	−	3.19768e13i	0.847619	−	0.847619i
$88$	−5.43288e12	−	5.43288e12i	−0.132939	−	0.132939i
$89$			5.70248e13i			1.28924i	0.764503	+	0.644620i	$0.222984\pi$
$89$			5.70248e13i			1.28924i	−0.764503	+	0.644620i	$0.777016\pi$
$90$	8.56861e13	−	4.88083e13i	1.79148	−	1.02046i
$91$	2.77103e13			0.536230
$92$	−3.24299e11	+	3.24299e11i	−0.00581341	+	0.00581341i
$93$	−3.38708e13	−	3.38708e13i	−0.562917	−	0.562917i
$94$			2.95110e13i			0.455081i
$95$	−3.42995e13	−	9.40478e12i	−0.491159	−	0.134674i
$96$	−2.62863e13			−0.349810
$97$	1.04766e14	−	1.04766e14i	1.29664	−	1.29664i	0.366042	−	0.930598i	$-0.380713\pi$
$97$	1.04766e14	−	1.04766e14i	1.29664	−	1.29664i	0.930598	−	0.366042i	$-0.119287\pi$
$98$	−5.56571e11	−	5.56571e11i	−0.00641118	−	0.00641118i
$99$			1.44513e14i			1.55046i
$100$	−2.55023e13	+	4.30074e13i	−0.255023	+	0.430074i
$101$	1.07193e14			0.999809			0.499904	−	0.866081i	$-0.333368\pi$
$101$	1.07193e14			0.999809			0.499904	+	0.866081i	$0.333368\pi$
$102$	−1.05000e14	+	1.05000e14i	−0.914087	+	0.914087i
$103$	−3.67993e13	−	3.67993e13i	−0.299212	−	0.299212i	0.541493	−	0.840705i	$-0.317859\pi$
$103$	−3.67993e13	−	3.67993e13i	−0.299212	−	0.299212i	−0.840705	+	0.541493i	$0.817859\pi$
$104$		−	2.47898e13i		−	0.188382i
$105$	7.41000e13	−	2.70245e14i	0.526615	−	1.92058i
$106$	−5.01359e13			−0.333433
$107$	−3.45097e13	+	3.45097e13i	−0.214909	+	0.214909i	−0.806349	−	0.591440i	$-0.798560\pi$
$107$	−3.45097e13	+	3.45097e13i	−0.214909	+	0.214909i	0.591440	+	0.806349i	$0.298560\pi$
$108$	2.29701e14	+	2.29701e14i	1.34028	+	1.34028i
$109$		−	1.27768e14i		−	0.698935i	−0.936948	−	0.349468i	$-0.886362\pi$
$109$		−	1.27768e14i		−	0.698935i	0.936948	−	0.349468i	$-0.113638\pi$
$110$	−3.62667e13	−	6.36686e13i	−0.186106	−	0.326721i
$111$	−4.31089e13			−0.207638
$112$	−3.93294e13	+	3.93294e13i	−0.177906	+	0.177906i
$113$	1.09795e14	+	1.09795e14i	0.466697	+	0.466697i	0.900843	−	0.434146i	$-0.142950\pi$
$113$	1.09795e14	+	1.09795e14i	0.466697	+	0.466697i	−0.434146	+	0.900843i	$0.642950\pi$
$114$		−	1.78316e14i		−	0.712615i
$115$	−3.80050e12	+	2.16483e12i	−0.0142875	+	0.00813840i
$116$	−8.56022e13			−0.302886
$117$	−3.29699e14	+	3.29699e14i	−1.09854	+	1.09854i
$118$	−2.84456e14	−	2.84456e14i	−0.892979	−	0.892979i
$119$			3.14200e14i			0.929774i
$120$	−2.41763e14	−	6.62903e13i	−0.674715	−	0.185004i
$121$	−2.72371e14			−0.717237
$122$	−1.50331e14	+	1.50331e14i	−0.373705	+	0.373705i
$123$	−6.84306e13	−	6.84306e13i	−0.160662	−	0.160662i
$124$			9.06723e13i			0.201151i
$125$	−3.43009e14	+	3.31237e14i	−0.719343	+	0.694655i
$126$	1.04615e15			2.07491
$127$	5.92492e14	−	5.92492e14i	1.11188	−	1.11188i	0.118979	−	0.992897i	$-0.462038\pi$
$127$	5.92492e14	−	5.92492e14i	1.11188	−	1.11188i	0.992897	−	0.118979i	$-0.0379621\pi$
$128$	3.51844e13	+	3.51844e13i	0.0625000	+	0.0625000i
$129$		−	1.32680e15i		−	2.23192i
$130$	6.25162e13	−	2.27998e14i	0.0996298	−	0.363352i
$131$	1.40320e14			0.211943			0.105971	−	0.994369i	$-0.466205\pi$
$131$	1.40320e14			0.211943			0.105971	+	0.994369i	$0.466205\pi$
$132$	2.59771e14	−	2.59771e14i	0.372026	−	0.372026i
$133$	−2.66794e14	−	2.66794e14i	−0.362422	−	0.362422i
$134$			6.62634e14i			0.854162i
$135$	1.53335e15	+	2.69190e15i	1.87631	+	3.29399i
$136$	2.81085e14			0.326637
$137$	−1.45448e13	+	1.45448e13i	−0.0160570	+	0.0160570i	−0.715090	−	0.699033i	$-0.753614\pi$
$137$	−1.45448e13	+	1.45448e13i	−0.0160570	+	0.0160570i	0.699033	+	0.715090i	$0.253614\pi$
$138$	−1.55062e13	−	1.55062e13i	−0.0162687	−	0.0162687i
$139$		−	5.22402e14i		−	0.521076i	−0.965464	−	0.260538i	$-0.916100\pi$
$139$		−	5.22402e14i		−	0.521076i	0.965464	−	0.260538i	$-0.0838999\pi$
$140$	−4.60907e14	+	2.62540e14i	−0.437237	+	0.249058i
$141$	−1.41105e15			−1.27353
$142$	6.81570e14	−	6.81570e14i	0.585453	−	0.585453i
$143$	2.44981e14	+	2.44981e14i	0.200346	+	0.200346i
$144$		−	9.35891e14i		−	0.728934i
$145$	−7.87306e14	−	2.15876e14i	−0.584208	−	0.160188i
$146$	9.80807e13			0.0693607
$147$	2.66122e13	−	2.66122e13i	0.0179415	−	0.0179415i
$148$	5.77014e13	+	5.77014e13i	0.0370984	+	0.0370984i
$149$			2.39410e15i			1.46838i	0.678944	+	0.734190i	$0.262438\pi$
$149$			2.39410e15i			1.46838i	−0.678944	+	0.734190i	$0.737562\pi$
$150$	−2.05638e15	−	1.21938e15i	−1.20355	−	0.713675i
$151$	2.40402e15			1.34307			0.671537	−	0.740971i	$-0.265634\pi$
$151$	2.40402e15			1.34307			0.671537	+	0.740971i	$0.265634\pi$
$152$	−2.38676e14	+	2.38676e14i	−0.127322	+	0.127322i
$153$	−3.73838e15	−	3.73838e15i	−1.90478	−	1.90478i
$154$		−	7.77335e14i		−	0.378410i
$155$	−2.28662e14	+	8.33937e14i	−0.106383	+	0.387982i
$156$	1.18531e15			0.527182
$157$	−4.08435e14	+	4.08435e14i	−0.173710	+	0.173710i	−0.788607	−	0.614897i	$-0.789198\pi$
$157$	−4.08435e14	+	4.08435e14i	−0.173710	+	0.173710i	0.614897	+	0.788607i	$0.289198\pi$
$158$	1.59951e15	+	1.59951e15i	0.650708	+	0.650708i
$159$		−	2.39723e15i		−	0.933103i
$160$	2.34870e14	+	4.12330e14i	0.0874960	+	0.153605i
$161$	−4.64006e13			−0.0165479
$162$	−6.71410e15	+	6.71410e15i	−2.29289	+	2.29289i
$163$	4.24437e13	+	4.24437e13i	0.0138835	+	0.0138835i	0.714014	−	0.700131i	$-0.246875\pi$
$163$	4.24437e13	+	4.24437e13i	0.0138835	+	0.0138835i	−0.700131	+	0.714014i	$0.746875\pi$
$164$			1.83189e14i			0.0574107i
$165$	3.04429e15	−	1.73408e15i	0.914320	−	0.520812i
$166$	2.59011e15			0.745695
$167$	−2.32879e15	+	2.32879e15i	−0.642859	+	0.642859i	−0.951257	−	0.308399i	$-0.900207\pi$
$167$	−2.32879e15	+	2.32879e15i	−0.642859	+	0.642859i	0.308399	+	0.951257i	$0.400207\pi$
$168$	−1.88052e15	−	1.88052e15i	−0.497867	−	0.497867i
$169$		−	2.81955e15i		−	0.716098i
$170$	2.58522e15	+	7.08856e14i	0.630020	+	0.172749i
$171$	6.34869e15			1.48495
$172$	−1.77593e15	+	1.77593e15i	−0.398774	+	0.398774i
$173$	4.82698e15	+	4.82698e15i	1.04077	+	1.04077i	0.999133	+	0.0416327i	$0.0132559\pi$
$173$	4.82698e15	+	4.82698e15i	1.04077	+	1.04077i	0.0416327	+	0.999133i	$0.486744\pi$
$174$		−	4.09303e15i		−	0.847619i
$175$	−4.90117e15	+	1.25231e15i	−0.975064	+	0.249142i
$176$	−6.95409e14			−0.132939
$177$	1.36012e16	−	1.36012e16i	2.49898	−	2.49898i
$178$	3.64959e15	+	3.64959e15i	0.644620	+	0.644620i
$179$			6.64060e15i			1.12781i	0.825839	+	0.563905i	$0.190702\pi$
$179$			6.64060e15i			1.12781i	−0.825839	+	0.563905i	$0.809298\pi$
$180$	2.36018e15	−	8.60764e15i	0.385512	−	1.40597i
$181$	−8.41679e15			−1.32250			−0.661251	−	0.750165i	$-0.729974\pi$
$181$	−8.41679e15			−1.32250			−0.661251	+	0.750165i	$0.729974\pi$
$182$	1.77346e15	−	1.77346e15i	0.268115	−	0.268115i
$183$	−7.18800e15	−	7.18800e15i	−1.04580	−	1.04580i
$184$			4.15103e13i			0.00581341i
$185$	3.85181e14	+	6.76210e14i	0.0519353	+	0.0911758i
$186$	−4.33546e15			−0.562917
$187$	−2.77779e15	+	2.77779e15i	−0.347382	+	0.347382i
$188$	1.88870e15	+	1.88870e15i	0.227540	+	0.227540i
$189$			3.28656e16i			3.81512i
$190$	−2.79707e15	+	1.59326e15i	−0.312917	+	0.178243i
$191$	−8.40054e15			−0.905886			−0.452943	−	0.891539i	$-0.649626\pi$
$191$	−8.40054e15			−0.905886			−0.452943	+	0.891539i	$0.649626\pi$
$192$	−1.68233e15	+	1.68233e15i	−0.174905	+	0.174905i
$193$	−4.00836e15	−	4.00836e15i	−0.401852	−	0.401852i	0.477033	−	0.878885i	$-0.341712\pi$
$193$	−4.00836e15	−	4.00836e15i	−0.401852	−	0.401852i	−0.878885	+	0.477033i	$0.841712\pi$
$194$		−	1.34101e16i		−	1.29664i
$195$	1.09016e16	+	2.98919e15i	1.01683	+	0.278812i
$196$	−7.12410e13			−0.00641118
$197$	9.48744e15	−	9.48744e15i	0.823921	−	0.823921i	−0.162747	−	0.986668i	$-0.552035\pi$
$197$	9.48744e15	−	9.48744e15i	0.823921	−	0.823921i	0.986668	+	0.162747i	$0.0520355\pi$
$198$	9.24881e15	+	9.24881e15i	0.775228	+	0.775228i
$199$		−	1.99413e16i		−	1.61355i	−0.590858	−	0.806776i	$-0.701210\pi$
$199$		−	1.99413e16i		−	1.61355i	0.590858	−	0.806776i	$-0.298790\pi$
$200$	1.12033e15	+	4.38462e15i	0.0875256	+	0.342548i
$201$	−3.16836e16			−2.39035
$202$	6.86036e15	−	6.86036e15i	0.499904	−	0.499904i
$203$	−6.12397e15	−	6.12397e15i	−0.431083	−	0.431083i
$204$			1.34400e16i			0.914087i
$205$	−4.61976e14	+	1.68484e15i	−0.0303629	+	0.110734i
$206$	−4.71031e15			−0.299212
$207$	5.52079e14	−	5.52079e14i	0.0339007	−	0.0339007i
$208$	−1.58655e15	−	1.58655e15i	−0.0941910	−	0.0941910i
$209$		−	4.71736e15i		−	0.270816i
$210$	−1.25533e16	−	2.20381e16i	−0.696982	−	1.22360i
$211$	2.27715e15			0.122297			0.0611484	−	0.998129i	$-0.480524\pi$
$211$	2.27715e15			0.122297			0.0611484	+	0.998129i	$0.480524\pi$
$212$	−3.20870e15	+	3.20870e15i	−0.166716	+	0.166716i
$213$	3.25890e16	+	3.25890e16i	1.63838	+	1.63838i
$214$			4.41724e15i			0.214909i
$215$	−2.08123e16	+	1.18551e16i	−0.980058	+	0.558258i
$216$	2.94018e16			1.34028
$217$	−6.48668e15	+	6.48668e15i	−0.286289	+	0.286289i
$218$	−8.17716e15	−	8.17716e15i	−0.349468	−	0.349468i
$219$			4.68969e15i			0.194104i
$220$	−6.39586e15	−	1.75372e15i	−0.256413	−	0.0703075i
$221$	−1.26748e16			−0.492261
$222$	−2.75897e15	+	2.75897e15i	−0.103819	+	0.103819i
$223$	2.79864e16	+	2.79864e16i	1.02050	+	1.02050i	0.999785	+	0.0207154i	$0.00659438\pi$
$223$	2.79864e16	+	2.79864e16i	1.02050	+	1.02050i	0.0207154	+	0.999785i	$0.493406\pi$
$224$			5.03417e15i			0.177906i
$225$	4.34144e16	−	7.32148e16i	1.48716	−	2.50796i
$226$	1.40538e16			0.466697
$227$	2.12469e16	−	2.12469e16i	0.684092	−	0.684092i	−0.276827	−	0.960920i	$-0.589283\pi$
$227$	2.12469e16	−	2.12469e16i	0.684092	−	0.684092i	0.960920	+	0.276827i	$0.0892830\pi$
$228$	−1.14122e16	−	1.14122e16i	−0.356308	−	0.356308i
$229$		−	4.08944e16i		−	1.23827i	−0.785284	−	0.619136i	$-0.787483\pi$
$229$		−	4.08944e16i		−	1.23827i	0.785284	−	0.619136i	$-0.212517\pi$
$230$	−1.04683e14	+	3.81781e14i	−0.00307454	+	0.0112129i
$231$	3.71680e16			1.05897
$232$	−5.47854e15	+	5.47854e15i	−0.151443	+	0.151443i
$233$	4.88366e16	+	4.88366e16i	1.30995	+	1.30995i	0.921450	+	0.388498i	$0.127006\pi$
$233$	4.88366e16	+	4.88366e16i	1.30995	+	1.30995i	0.388498	+	0.921450i	$0.372994\pi$
$234$			4.22015e16i			1.09854i
$235$	1.26079e16	+	2.21339e16i	0.318542	+	0.559221i
$236$	−3.64104e16			−0.892979
$237$	−7.64797e16	+	7.64797e16i	−1.82099	+	1.82099i
$238$	2.01088e16	+	2.01088e16i	0.464887	+	0.464887i
$239$		−	5.63184e16i		−	1.26434i	−0.774829	−	0.632171i	$-0.782164\pi$
$239$		−	5.63184e16i		−	1.26434i	0.774829	−	0.632171i	$-0.217836\pi$
$240$	−1.97154e16	+	1.12302e16i	−0.429860	+	0.244855i
$241$	−1.76338e16			−0.373444			−0.186722	−	0.982413i	$-0.559786\pi$
$241$	−1.76338e16			−0.373444			−0.186722	+	0.982413i	$0.559786\pi$
$242$	−1.74317e16	+	1.74317e16i	−0.358618	+	0.358618i
$243$	−1.86919e17	−	1.86919e17i	−3.73602	−	3.73602i
$244$			1.92423e16i			0.373705i
$245$	−6.55223e14	−	1.79660e14i	−0.0123659	−	0.00339069i
$246$	−8.75911e15			−0.160662
$247$	1.07625e16	−	1.07625e16i	0.191881	−	0.191881i
$248$	5.80303e15	+	5.80303e15i	0.100576	+	0.100576i
$249$			1.23845e17i			2.08681i
$250$	−7.53409e14	+	4.31518e16i	−0.0123439	+	0.706999i
$251$	4.32260e16			0.688698			0.344349	−	0.938842i	$-0.388100\pi$
$251$	4.32260e16			0.688698			0.344349	+	0.938842i	$0.388100\pi$
$252$	6.69535e16	−	6.69535e16i	1.03746	−	1.03746i
$253$	−4.10219e14	−	4.10219e14i	−0.00618262	−	0.00618262i
$254$		−	7.58389e16i		−	1.11188i
$255$	−3.38937e16	+	1.23611e17i	−0.483434	+	1.76310i
$256$	4.50360e15			0.0625000
$257$	8.88626e16	−	8.88626e16i	1.20002	−	1.20002i	0.225856	−	0.974161i	$-0.427482\pi$
$257$	8.88626e16	−	8.88626e16i	1.20002	−	1.20002i	0.974161	−	0.225856i	$-0.0725178\pi$
$258$	−8.49154e16	−	8.49154e16i	−1.11596	−	1.11596i
$259$			8.25590e15i			0.105601i
$260$	−1.05908e16	−	1.85929e16i	−0.131861	−	0.231491i
$261$	1.45727e17			1.76627
$262$	8.98045e15	−	8.98045e15i	0.105971	−	0.105971i
$263$	2.29473e16	+	2.29473e16i	0.263658	+	0.263658i	0.826539	−	0.562880i	$-0.190307\pi$
$263$	2.29473e16	+	2.29473e16i	0.263658	+	0.263658i	−0.562880	+	0.826539i	$0.690307\pi$
$264$		−	3.32507e16i		−	0.372026i
$265$	−3.76031e16	+	2.14194e16i	−0.409735	+	0.233392i
$266$	−3.41497e16			−0.362422
$267$	−1.74504e17	+	1.74504e17i	−1.80395	+	1.80395i
$268$	4.24086e16	+	4.24086e16i	0.427081	+	0.427081i
$269$		−	2.42464e16i		−	0.237893i	−0.992901	−	0.118946i	$-0.962048\pi$
$269$		−	2.42464e16i		−	0.237893i	0.992901	−	0.118946i	$-0.0379517\pi$
$270$	2.70416e17	+	7.41470e16i	2.58515	+	0.708838i
$271$	−5.85971e16			−0.545873			−0.272936	−	0.962032i	$-0.587995\pi$
$271$	−5.85971e16			−0.545873			−0.272936	+	0.962032i	$0.587995\pi$
$272$	1.79895e16	−	1.79895e16i	0.163319	−	0.163319i
$273$	8.47971e16	+	8.47971e16i	0.750313	+	0.750313i
$274$			1.86173e15i			0.0160570i
$275$	−5.44018e16	−	3.22589e16i	−0.457388	−	0.271219i
$276$	−1.98480e15			−0.0162687
$277$	1.19537e17	−	1.19537e17i	0.955306	−	0.955306i	−0.0437366	−	0.999043i	$-0.513926\pi$
$277$	1.19537e17	−	1.19537e17i	0.955306	−	0.955306i	0.999043	+	0.0437366i	$0.0139262\pi$
$278$	−3.34337e16	−	3.34337e16i	−0.260538	−	0.260538i
$279$		−	1.54358e17i		−	1.17301i
$280$	−1.26954e16	+	4.63006e16i	−0.0940896	+	0.343147i
$281$	−6.52560e16			−0.471712			−0.235856	−	0.971788i	$-0.575789\pi$
$281$	−6.52560e16			−0.471712			−0.235856	+	0.971788i	$0.575789\pi$
$282$	−9.03075e16	+	9.03075e16i	−0.636766	+	0.636766i
$283$	4.60901e16	+	4.60901e16i	0.317031	+	0.317031i	0.847626	−	0.530594i	$-0.178031\pi$
$283$	4.60901e16	+	4.60901e16i	0.317031	+	0.317031i	−0.530594	+	0.847626i	$0.678031\pi$
$284$		−	8.72410e16i		−	0.585453i
$285$	−7.61811e16	−	1.33741e17i	−0.498808	−	0.875689i
$286$	3.13576e16			0.200346
$287$	−1.31053e16	+	1.31053e16i	−0.0817098	+	0.0817098i
$288$	−5.98971e16	−	5.98971e16i	−0.364467	−	0.364467i
$289$			2.46613e16i			0.146464i
$290$	−6.42037e16	+	3.65715e16i	−0.372198	+	0.212010i
$291$	6.41198e17			3.62862
$292$	6.27717e15	−	6.27717e15i	0.0346804	−	0.0346804i
$293$	−1.58311e17	−	1.58311e17i	−0.853961	−	0.853961i	0.136657	−	0.990618i	$-0.456364\pi$
$293$	−1.58311e17	−	1.58311e17i	−0.853961	−	0.853961i	−0.990618	+	0.136657i	$0.956364\pi$
$294$		−	3.40636e15i		−	0.0179415i
$295$	−3.34876e17	−	9.18217e16i	−1.72238	−	0.472271i
$296$	7.38578e15			0.0370984
$297$	−2.90559e17	+	2.90559e17i	−1.42541	+	1.42541i
$298$	1.53222e17	+	1.53222e17i	0.734190	+	0.734190i
$299$		−	1.87180e15i		−	0.00876113i
$300$	−2.09649e17	+	5.35680e16i	−0.958613	+	0.244938i
$301$	−2.54100e17			−1.13511
$302$	1.53858e17	−	1.53858e17i	0.671537	−	0.671537i
$303$	3.28025e17	+	3.28025e17i	1.39897	+	1.39897i
$304$			3.05505e16i			0.127322i
$305$	−4.85263e16	+	1.76977e17i	−0.197642	+	0.720804i
$306$	−4.78513e17			−1.90478
$307$	−2.01856e17	+	2.01856e17i	−0.785368	+	0.785368i	−0.980731	−	0.195363i	$-0.937411\pi$
$307$	−2.01856e17	+	2.01856e17i	−0.785368	+	0.785368i	0.195363	+	0.980731i	$0.437411\pi$
$308$	−4.97494e16	−	4.97494e16i	−0.189205	−	0.189205i
$309$		−	2.25222e17i		−	0.837338i
$310$	3.87376e16	+	6.80064e16i	0.140799	+	0.247183i
$311$	−9.34494e16			−0.332089			−0.166044	−	0.986118i	$-0.553099\pi$
$311$	−9.34494e16			−0.332089			−0.166044	+	0.986118i	$0.553099\pi$
$312$	7.58600e16	−	7.58600e16i	0.263591	−	0.263591i
$313$	−1.25988e17	−	1.25988e17i	−0.428073	−	0.428073i	0.459899	−	0.887971i	$-0.347886\pi$
$313$	−1.25988e17	−	1.25988e17i	−0.428073	−	0.428073i	−0.887971	+	0.459899i	$0.847886\pi$
$314$			5.22797e16i			0.173710i
$315$	7.84637e17	−	4.46942e17i	2.54973	−	1.45237i
$316$	2.04737e17			0.650708
$317$	3.25577e17	−	3.25577e17i	1.01214	−	1.01214i	0.0122106	−	0.999925i	$-0.496113\pi$
$317$	3.25577e17	−	3.25577e17i	1.01214	−	1.01214i	0.999925	−	0.0122106i	$-0.00388687\pi$
$318$	−1.53423e17	−	1.53423e17i	−0.466551	−	0.466551i
$319$		−	1.08282e17i		−	0.322122i
$320$	4.14208e16	+	1.13574e16i	0.120550	+	0.0330544i
$321$	−2.11209e17			−0.601418
$322$	−2.96964e15	+	2.96964e15i	−0.00827394	+	0.00827394i
$323$	1.22033e17	+	1.22033e17i	0.332705	+	0.332705i
$324$			8.59405e17i			2.29289i
$325$	−5.05182e16	−	1.97713e17i	−0.131906	−	0.516239i
$326$	5.43279e15			0.0138835
$327$	3.90988e17	−	3.90988e17i	0.977977	−	0.977977i
$328$	1.17241e16	+	1.17241e16i	0.0287053	+	0.0287053i
$329$			2.70235e17i			0.647694i
$330$	8.38534e16	−	3.05815e17i	0.196754	−	0.717566i
$331$	−4.33602e17			−0.996083			−0.498042	−	0.867153i	$-0.665947\pi$
$331$	−4.33602e17			−0.996083			−0.498042	+	0.867153i	$0.665947\pi$
$332$	1.65767e17	−	1.65767e17i	0.372848	−	0.372848i
$333$	−9.82296e16	−	9.82296e16i	−0.216338	−	0.216338i
$334$			2.98085e17i			0.642859i
$335$	2.83095e17	+	4.96991e17i	0.597886	+	1.04963i
$336$	−2.40707e17			−0.497867
$337$	2.49537e16	−	2.49537e16i	0.0505504	−	0.0505504i	−0.681380	−	0.731930i	$-0.738620\pi$
$337$	2.49537e16	−	2.49537e16i	0.0505504	−	0.0505504i	0.731930	+	0.681380i	$0.238620\pi$
$338$	−1.80451e17	−	1.80451e17i	−0.358049	−	0.358049i
$339$			6.71977e17i			1.30604i
$340$	2.10821e17	−	1.20087e17i	0.401385	−	0.228636i
$341$	−1.14695e17			−0.213926
$342$	4.06316e17	−	4.06316e17i	0.742474	−	0.742474i
$343$	3.92379e17	+	3.92379e17i	0.702501	+	0.702501i
$344$			2.27319e17i			0.398774i
$345$	−1.82547e16	−	5.00537e15i	−0.0313792	−	0.00860404i
$346$	6.17854e17			1.04077
$347$	−2.92646e17	+	2.92646e17i	−0.483099	+	0.483099i	−0.906120	−	0.423021i	$-0.860970\pi$
$347$	−2.92646e17	+	2.92646e17i	−0.483099	+	0.483099i	0.423021	+	0.906120i	$0.360970\pi$
$348$	−2.61954e17	−	2.61954e17i	−0.423809	−	0.423809i
$349$		−	9.77865e17i		−	1.55060i	−0.631591	−	0.775302i	$-0.717598\pi$
$349$		−	9.77865e17i		−	1.55060i	0.631591	−	0.775302i	$-0.282402\pi$
$350$	−2.33527e17	+	3.93823e17i	−0.362961	+	0.612103i
$351$	−1.32579e18			−2.01988
$352$	−4.45062e16	+	4.45062e16i	−0.0664694	+	0.0664694i
$353$	4.47238e17	+	4.47238e17i	0.654810	+	0.654810i	0.954147	−	0.299337i	$-0.0967656\pi$
$353$	4.47238e17	+	4.47238e17i	0.654810	+	0.654810i	−0.299337	+	0.954147i	$0.596766\pi$
$354$		−	1.74095e18i		−	2.49898i
$355$	2.20009e17	−	8.02379e17i	0.309629	−	1.12923i
$356$	4.67147e17			0.644620
$357$	−9.61494e17	+	9.61494e17i	−1.30098	+	1.30098i
$358$	4.24998e17	+	4.24998e17i	0.563905	+	0.563905i
$359$			1.30918e18i			1.70349i	0.523957	+	0.851745i	$0.324455\pi$
$359$			1.30918e18i			1.70349i	−0.523957	+	0.851745i	$0.675545\pi$
$360$	−3.99838e17	−	7.01941e17i	−0.510230	−	0.895742i
$361$	5.91765e17			0.740626
$362$	−5.38675e17	+	5.38675e17i	−0.661251	+	0.661251i
$363$	−8.33490e17	−	8.33490e17i	−1.00358	−	1.00358i
$364$		−	2.27002e17i		−	0.268115i
$365$	7.35629e16	−	4.19027e16i	0.0852332	−	0.0485503i
$366$	−9.20063e17			−1.04580
$367$	8.91792e16	−	8.91792e16i	0.0994491	−	0.0994491i	−0.655632	−	0.755081i	$-0.727598\pi$
$367$	8.91792e16	−	8.91792e16i	0.0994491	−	0.0994491i	0.755081	+	0.655632i	$0.227598\pi$
$368$	2.65666e15	+	2.65666e15i	0.00290670	+	0.00290670i
$369$		−	3.11857e17i		−	0.334789i
$370$	6.79290e16	+	1.86259e16i	0.0715556	+	0.0196202i
$371$	−4.59100e17			−0.474558
$372$	−2.77469e17	+	2.77469e17i	−0.281459	+	0.281459i
$373$	−5.50852e17	−	5.50852e17i	−0.548370	−	0.548370i	0.377599	−	0.925969i	$-0.376750\pi$
$373$	−5.50852e17	−	5.50852e17i	−0.548370	−	0.548370i	−0.925969	+	0.377599i	$0.876750\pi$
$374$			3.55557e17i			0.347382i
$375$	−2.06329e18	−	3.60239e16i	−1.97852	−	0.0345440i
$376$	2.41754e17			0.227540
$377$	2.47040e17	−	2.47040e17i	0.228233	−	0.228233i
$378$	2.10340e18	+	2.10340e18i	1.90756	+	1.90756i
$379$			7.64430e17i			0.680555i	0.940325	+	0.340277i	$0.110521\pi$
$379$			7.64430e17i			0.680555i	−0.940325	+	0.340277i	$0.889479\pi$
$380$	−7.70440e16	+	2.80981e17i	−0.0673369	+	0.245580i
$381$	3.62621e18			3.11156
$382$	−5.37635e17	+	5.37635e17i	−0.452943	+	0.452943i
$383$	6.47196e17	+	6.47196e17i	0.535359	+	0.535359i	0.922162	−	0.386804i	$-0.126421\pi$
$383$	6.47196e17	+	6.47196e17i	0.535359	+	0.535359i	−0.386804	+	0.922162i	$0.626421\pi$
$384$			2.15338e17i			0.174905i
$385$	−3.32098e17	−	5.83020e17i	−0.264875	−	0.465006i
$386$	−5.13070e17			−0.401852
$387$	3.02330e18	−	3.02330e18i	2.32544	−	2.32544i
$388$	−8.58246e17	−	8.58246e17i	−0.648320	−	0.648320i
$389$		−	1.21930e16i		−	0.00904617i	−0.999990	−	0.00452309i	$-0.998560\pi$
$389$		−	1.21930e16i		−	0.00904617i	0.999990	−	0.00452309i	$-0.00143975\pi$
$390$	8.89013e17	−	5.06397e17i	0.647822	−	0.369011i
$391$	2.12239e16			0.0151910
$392$	−4.55943e15	+	4.55943e15i	−0.00320559	+	0.00320559i
$393$	4.29397e17	+	4.29397e17i	0.296559	+	0.296559i
$394$		−	1.21439e18i		−	0.823921i
$395$	1.88302e18	+	5.16316e17i	1.25509	+	0.344141i
$396$	1.18385e18			0.775228
$397$	−2.50891e17	+	2.50891e17i	−0.161418	+	0.161418i	−0.783194	−	0.621777i	$-0.786411\pi$
$397$	−2.50891e17	+	2.50891e17i	−0.161418	+	0.161418i	0.621777	+	0.783194i	$0.286411\pi$
$398$	−1.27625e18	−	1.27625e18i	−0.806776	−	0.806776i
$399$		−	1.63285e18i		−	1.01423i
$400$	3.52316e17	+	2.08914e17i	0.215037	+	0.127511i
$401$	−1.75225e18			−1.05096			−0.525479	−	0.850807i	$-0.676114\pi$
$401$	−1.75225e18			−1.05096			−0.525479	+	0.850807i	$0.676114\pi$
$402$	−2.02775e18	+	2.02775e18i	−1.19518	+	1.19518i
$403$	−2.61672e17	−	2.61672e17i	−0.151573	−	0.151573i
$404$		−	8.78126e17i		−	0.499904i
$405$	−2.16729e18	+	7.90418e18i	−1.21264	+	4.42254i
$406$	−7.83868e17			−0.431083
$407$	−7.29889e16	+	7.29889e16i	−0.0394545	+	0.0394545i
$408$	8.60159e17	+	8.60159e17i	0.457044	+	0.457044i
$409$		−	2.02504e18i		−	1.05772i	−0.848710	−	0.528859i	$-0.822620\pi$
$409$		−	2.02504e18i		−	1.05772i	0.848710	−	0.528859i	$-0.177380\pi$
$410$	7.82632e16	+	1.37396e17i	0.0401856	+	0.0705485i
$411$	−8.90180e16			−0.0449350
$412$	−3.01460e17	+	3.01460e17i	−0.149606	+	0.149606i
$413$	−2.60479e18	−	2.60479e18i	−1.27093	−	1.27093i
$414$		−	7.06661e16i		−	0.0339007i
$415$	1.94264e18	−	1.10656e18i	0.916339	−	0.521963i
$416$	−2.03078e17			−0.0941910
$417$	1.59862e18	−	1.59862e18i	0.729109	−	0.729109i
$418$	−3.01911e17	−	3.01911e17i	−0.135408	−	0.135408i
$419$			1.82040e18i			0.802914i	0.915878	+	0.401457i	$0.131496\pi$
$419$			1.82040e18i			0.802914i	−0.915878	+	0.401457i	$0.868504\pi$
$420$	−2.21384e18	−	6.07027e17i	−0.960289	−	0.263307i
$421$	−4.82197e17			−0.205707			−0.102854	−	0.994696i	$-0.532797\pi$
$421$	−4.82197e17			−0.205707			−0.102854	+	0.994696i	$0.532797\pi$
$422$	1.45738e17	−	1.45738e17i	0.0611484	−	0.0611484i
$423$	−3.21528e18	−	3.21528e18i	−1.32689	−	1.32689i
$424$			4.10713e17i			0.166716i
$425$	2.24182e18	−	5.72814e17i	0.895112	−	0.228713i
$426$	4.17139e18			1.63838
$427$	−1.37659e18	+	1.37659e18i	−0.531876	+	0.531876i
$428$	2.82704e17	+	2.82704e17i	0.107455	+	0.107455i
$429$			1.49935e18i			0.560664i
$430$	−5.73266e17	+	2.09071e18i	−0.210900	+	0.769158i
$431$	−2.82159e17			−0.102130			−0.0510649	−	0.998695i	$-0.516262\pi$
$431$	−2.82159e17			−0.102130			−0.0510649	+	0.998695i	$0.516262\pi$
$432$	1.88171e18	−	1.88171e18i	0.670142	−	0.670142i
$433$	−9.73332e17	−	9.73332e17i	−0.341072	−	0.341072i	0.515698	−	0.856770i	$-0.327533\pi$
$433$	−9.73332e17	−	9.73332e17i	−0.341072	−	0.341072i	−0.856770	+	0.515698i	$0.827533\pi$
$434$			8.30295e17i			0.286289i
$435$	−1.74865e18	−	3.06987e18i	−0.593306	−	1.04159i
$436$	−1.04668e18			−0.349468
$437$	−1.80216e16	+	1.80216e16i	−0.00592140	+	0.00592140i
$438$	3.00140e17	+	3.00140e17i	0.0970522	+	0.0970522i
$439$			4.76034e18i			1.51491i	0.652889	+	0.757453i	$0.273557\pi$
$439$			4.76034e18i			1.51491i	−0.652889	+	0.757453i	$0.726443\pi$
$440$	−5.21573e17	+	2.97097e17i	−0.163360	+	0.0930528i
$441$	1.21279e17			0.0373866
$442$	−8.11187e17	+	8.11187e17i	−0.246130	+	0.246130i
$443$	5.74854e17	+	5.74854e17i	0.171685	+	0.171685i	0.787719	−	0.616035i	$-0.211262\pi$
$443$	5.74854e17	+	5.74854e17i	0.171685	+	0.171685i	−0.616035	+	0.787719i	$0.711262\pi$
$444$			3.53148e17i			0.103819i
$445$	4.29648e18	+	1.17808e18i	1.24335	+	0.340921i
$446$	3.58226e18			1.02050
$447$	−7.32627e18	+	7.32627e18i	−2.05461	+	2.05461i
$448$	3.22187e17	+	3.22187e17i	0.0889532	+	0.0889532i
$449$		−	1.86746e18i		−	0.507605i	−0.967256	−	0.253803i	$-0.918319\pi$
$449$		−	1.86746e18i		−	0.507605i	0.967256	−	0.253803i	$-0.0816814\pi$
$450$	−1.90722e18	−	7.46427e18i	−0.510403	−	1.99756i
$451$	−2.31723e17			−0.0610568
$452$	8.99444e17	−	8.99444e17i	0.233349	−	0.233349i
$453$	7.35664e18	+	7.35664e18i	1.87928	+	1.87928i
$454$		−	2.71960e18i		−	0.684092i
$455$	5.72467e17	−	2.08780e18i	0.141798	−	0.517142i
$456$	−1.46076e18			−0.356308
$457$	−8.48372e17	+	8.48372e17i	−0.203785	+	0.203785i	−0.801620	−	0.597834i	$-0.796028\pi$
$457$	−8.48372e17	+	8.48372e17i	−0.203785	+	0.203785i	0.597834	+	0.801620i	$0.296028\pi$
$458$	−2.61724e18	−	2.61724e18i	−0.619136	−	0.619136i
$459$		−	1.50329e19i		−	3.50230i
$460$	1.77343e16	+	3.11337e16i	0.00406920	+	0.00714374i
$461$	2.93163e18			0.662525			0.331262	−	0.943539i	$-0.392525\pi$
$461$	2.93163e18			0.662525			0.331262	+	0.943539i	$0.392525\pi$
$462$	2.37875e18	−	2.37875e18i	0.529486	−	0.529486i
$463$	2.21177e18	+	2.21177e18i	0.484924	+	0.484924i	0.906700	−	0.421776i	$-0.138593\pi$
$463$	2.21177e18	+	2.21177e18i	0.484924	+	0.484924i	−0.421776	+	0.906700i	$0.638593\pi$
$464$			7.01253e17i			0.151443i
$465$	−3.25170e18	+	1.85222e18i	−0.691735	+	0.394024i
$466$	6.25108e18			1.30995
$467$	3.42964e18	−	3.42964e18i	0.707996	−	0.707996i	−0.258118	−	0.966114i	$-0.583102\pi$
$467$	3.42964e18	−	3.42964e18i	0.707996	−	0.707996i	0.966114	+	0.258118i	$0.0831022\pi$
$468$	2.70090e18	+	2.70090e18i	0.549272	+	0.549272i
$469$			6.06781e18i			1.21569i
$470$	2.22347e18	+	6.09668e17i	0.438881	+	0.120339i
$471$	−2.49973e18			−0.486124
$472$	−2.33027e18	+	2.33027e18i	−0.446490	+	0.446490i
$473$	−2.24645e18	−	2.24645e18i	−0.424100	−	0.424100i
$474$			9.78941e18i			1.82099i
$475$	−1.41719e18	+	2.38997e18i	−0.259760	+	0.438063i
$476$	2.57393e18			0.464887
$477$	5.46241e18	−	5.46241e18i	0.972201	−	0.972201i
$478$	−3.60438e18	−	3.60438e18i	−0.632171	−	0.632171i
$479$			5.16000e18i			0.891869i	0.895065	+	0.445935i	$0.147129\pi$
$479$			5.16000e18i			0.891869i	−0.895065	+	0.445935i	$0.852871\pi$
$480$	−5.43050e17	+	1.98052e18i	−0.0925021	+	0.337357i
$481$	−3.33042e17			−0.0559093
$482$	−1.12856e18	+	1.12856e18i	−0.186722	+	0.186722i
$483$	−1.41992e17	−	1.41992e17i	−0.0231544	−	0.0231544i
$484$			2.23126e18i			0.358618i
$485$	−5.72914e18	−	1.00579e19i	−0.907606	−	1.59336i
$486$	−2.39256e19			−3.73602
$487$	−3.71490e18	+	3.71490e18i	−0.571801	+	0.571801i	−0.932631	−	0.360830i	$-0.882493\pi$
$487$	−3.71490e18	+	3.71490e18i	−0.571801	+	0.571801i	0.360830	+	0.932631i	$0.382493\pi$
$488$	1.23151e18	+	1.23151e18i	0.186852	+	0.186852i
$489$			2.59767e17i			0.0388527i
$490$	−5.34325e16	+	3.04361e16i	−0.00787830	+	0.00448762i
$491$	−6.47447e18			−0.941096			−0.470548	−	0.882374i	$-0.655944\pi$
$491$	−6.47447e18			−0.941096			−0.470548	+	0.882374i	$0.655944\pi$
$492$	−5.60583e17	+	5.60583e17i	−0.0803312	+	0.0803312i
$493$	2.80113e18	+	2.80113e18i	0.395735	+	0.395735i
$494$		−	1.37759e18i		−	0.191881i
$495$	1.08882e19	+	2.98549e18i	1.49527	+	0.409996i
$496$	7.42788e17			0.100576
$497$	6.24121e18	−	6.24121e18i	0.833247	−	0.833247i
$498$	7.92608e18	+	7.92608e18i	1.04341	+	1.04341i
$499$		−	1.70487e18i		−	0.221303i	−0.993859	−	0.110652i	$-0.964706\pi$
$499$		−	1.70487e18i		−	0.221303i	0.993859	−	0.110652i	$-0.0352938\pi$
$500$	2.71350e18	+	2.80993e18i	0.347328	+	0.359671i
$501$	−1.42528e19			−1.79902
$502$	2.76646e18	−	2.76646e18i	0.344349	−	0.344349i
$503$	−9.59671e18	−	9.59671e18i	−1.17800	−	1.17800i	−0.980252	−	0.197751i	$-0.936636\pi$
$503$	−9.59671e18	−	9.59671e18i	−1.17800	−	1.17800i	−0.197751	−	0.980252i	$-0.563364\pi$
$504$		−	8.57005e18i		−	1.03746i
$505$	2.21450e18	−	8.07635e18i	0.264385	−	0.964219i
$506$	−5.25081e16			−0.00618262
$507$	8.62819e18	−	8.62819e18i	1.00199	−	1.00199i
$508$	−4.85369e18	−	4.85369e18i	−0.555938	−	0.555938i
$509$			2.41377e18i			0.272691i	0.990661	+	0.136345i	$0.0435357\pi$
$509$			2.41377e18i			0.272691i	−0.990661	+	0.136345i	$0.956464\pi$
$510$	5.74192e18	+	1.00803e19i	0.639831	+	1.12327i
$511$	8.98135e17			0.0987178
$512$	2.88230e17	−	2.88230e17i	0.0312500	−	0.0312500i
$513$	1.27647e19	+	1.27647e19i	1.36518	+	1.36518i
$514$		−	1.13744e19i		−	1.20002i
$515$	−3.53285e18	+	2.01237e18i	−0.367684	+	0.209439i
$516$	−1.08692e19			−1.11596
$517$	−2.38910e18	+	2.38910e18i	−0.241991	+	0.241991i
$518$	5.28378e17	+	5.28378e17i	0.0528003	+	0.0528003i
$519$			2.95424e19i			2.91256i
$520$	−1.86776e18	−	5.12133e17i	−0.181676	−	0.0498149i
$521$	−7.60660e18			−0.730006			−0.365003	−	0.931006i	$-0.618932\pi$
$521$	−7.60660e18			−0.730006			−0.365003	+	0.931006i	$0.618932\pi$
$522$	9.32654e18	−	9.32654e18i	0.883135	−	0.883135i
$523$	9.47934e18	+	9.47934e18i	0.885658	+	0.885658i	0.994103	−	0.108444i	$-0.0345869\pi$
$523$	9.47934e18	+	9.47934e18i	0.885658	+	0.885658i	−0.108444	+	0.994103i	$0.534587\pi$
$524$		−	1.14950e18i		−	0.105971i
$525$	−1.88305e19	−	1.11660e19i	−1.71296	−	1.01574i
$526$	2.93726e18			0.263658
$527$	2.96704e18	−	2.96704e18i	0.262814	−	0.262814i
$528$	−2.12804e18	−	2.12804e18i	−0.186013	−	0.186013i
$529$		−	1.15897e19i		−	0.999730i
$530$	−1.03576e18	+	3.77744e18i	−0.0881714	+	0.321563i
$531$	6.19842e19			5.20738
$532$	−2.18558e18	+	2.18558e18i	−0.181211	+	0.181211i
$533$	−5.28667e17	−	5.28667e17i	−0.0432605	−	0.0432605i
$534$			2.23365e19i			1.80395i
$535$	1.88716e18	+	3.31304e18i	0.150429	+	0.264089i
$536$	5.42830e18			0.427081
$537$	−2.03211e19	+	2.03211e19i	−1.57808	+	1.57808i
$538$	−1.55177e18	−	1.55177e18i	−0.118946	−	0.118946i
$539$		−	9.01157e16i		−	0.00681835i
$540$	2.20520e19	−	1.25612e19i	1.64699	−	0.938156i
$541$	−5.61119e18			−0.413689			−0.206845	−	0.978374i	$-0.566319\pi$
$541$	−5.61119e18			−0.413689			−0.206845	+	0.978374i	$0.566319\pi$
$542$	−3.75022e18	+	3.75022e18i	−0.272936	+	0.272936i
$543$	−2.57565e19	−	2.57565e19i	−1.85050	−	1.85050i
$544$		−	2.30265e18i		−	0.163319i
$545$	−9.62656e18	−	2.63957e18i	−0.674056	−	0.184823i
$546$	1.08540e19			0.750313
$547$	−7.56675e17	+	7.56675e17i	−0.0516414	+	0.0516414i	−0.732456	−	0.680814i	$-0.761626\pi$
$547$	−7.56675e17	+	7.56675e17i	−0.0516414	+	0.0516414i	0.680814	+	0.732456i	$0.261626\pi$
$548$	1.19151e17	+	1.19151e17i	0.00802848	+	0.00802848i
$549$		−	3.27577e19i		−	2.17925i
$550$	−5.54628e18	+	1.41715e18i	−0.364303	+	0.0930844i
$551$	−4.75701e18			−0.308512
$552$	−1.27027e17	+	1.27027e17i	−0.00813434	+	0.00813434i
$553$	1.46468e19	+	1.46468e19i	0.926122	+	0.926122i
$554$		−	1.53007e19i		−	0.955306i
$555$	−8.90588e17	+	3.24800e18i	−0.0549068	+	0.200247i
$556$	−4.27952e18			−0.260538
$557$	−3.68902e18	+	3.68902e18i	−0.221781	+	0.221781i	−0.809248	−	0.587467i	$-0.800125\pi$
$557$	−3.68902e18	+	3.68902e18i	−0.221781	+	0.221781i	0.587467	+	0.809248i	$0.300125\pi$
$558$	−9.87894e18	−	9.87894e18i	−0.586504	−	0.586504i
$559$		−	1.02504e19i		−	0.600975i
$560$	2.15073e18	+	3.77575e18i	0.124529	+	0.218618i
$561$	−1.70008e19			−0.972141
$562$	−4.17639e18	+	4.17639e18i	−0.235856	+	0.235856i
$563$	1.63812e19	+	1.63812e19i	0.913665	+	0.913665i	0.996558	−	0.0828938i	$-0.0264162\pi$
$563$	1.63812e19	+	1.63812e19i	0.913665	+	0.913665i	−0.0828938	+	0.996558i	$0.526416\pi$
$564$			1.15594e19i			0.636766i
$565$	1.05407e19	−	6.00416e18i	0.573496	−	0.326673i
$566$	5.89953e18			0.317031
$567$	−6.14817e19	+	6.14817e19i	−3.26336	+	3.26336i
$568$	−5.58342e18	−	5.58342e18i	−0.292727	−	0.292727i
$569$			2.38811e19i			1.23671i	0.785898	+	0.618356i	$0.212201\pi$
$569$			2.38811e19i			1.23671i	−0.785898	+	0.618356i	$0.787799\pi$
$570$	−1.34350e19	−	3.68383e18i	−0.687249	−	0.188441i
$571$	−4.70733e18			−0.237860			−0.118930	−	0.992903i	$-0.537946\pi$
$571$	−4.70733e18			−0.237860			−0.118930	+	0.992903i	$0.537946\pi$
$572$	2.00689e18	−	2.00689e18i	0.100173	−	0.100173i
$573$	−2.57068e19	−	2.57068e19i	−1.26755	−	1.26755i
$574$			1.67748e18i			0.0817098i
$575$	8.45923e16	+	3.31068e17i	0.00407058	+	0.0159310i
$576$	−7.66682e18			−0.364467
$577$	1.78287e19	−	1.78287e19i	0.837317	−	0.837317i	−0.151188	−	0.988505i	$-0.548310\pi$
$577$	1.78287e19	−	1.78287e19i	0.837317	−	0.837317i	0.988505	+	0.151188i	$0.0483100\pi$
$578$	1.57832e18	+	1.57832e18i	0.0732320	+	0.0732320i
$579$		−	2.45323e19i		−	1.12457i
$580$	−1.76846e18	+	6.44961e18i	−0.0800938	+	0.292104i
$581$	2.37179e19			1.06131
$582$	4.10367e19	−	4.10367e19i	1.81431	−	1.81431i
$583$	−4.05882e18	−	4.05882e18i	−0.177304	−	0.177304i
$584$		−	8.03477e17i		−	0.0346804i
$585$	1.80296e19	+	3.16522e19i	0.768945	+	1.34993i
$586$	−2.02638e19			−0.853961
$587$	6.03375e18	−	6.03375e18i	0.251258	−	0.251258i	−0.570228	−	0.821486i	$-0.693145\pi$
$587$	6.03375e18	−	6.03375e18i	0.251258	−	0.251258i	0.821486	+	0.570228i	$0.193145\pi$
$588$	−2.18007e17	−	2.18007e17i	−0.00897076	−	0.00897076i
$589$			5.03876e18i			0.204888i
$590$	−2.73087e19	+	1.55555e19i	−1.09733	+	0.625057i
$591$	5.80657e19			2.30572
$592$	4.72690e17	−	4.72690e17i	0.0185492	−	0.0185492i
$593$	2.32554e19	+	2.32554e19i	0.901864	+	0.901864i	0.995597	−	0.0937335i	$-0.0298802\pi$
$593$	2.32554e19	+	2.32554e19i	0.901864	+	0.901864i	−0.0937335	+	0.995597i	$0.529880\pi$
$594$			3.71915e19i			1.42541i
$595$	2.36731e19	+	6.49107e18i	0.896678	+	0.245865i
$596$	1.96125e19			0.734190
$597$	6.10232e19	−	6.10232e19i	2.25774	−	2.25774i
$598$	−1.19795e17	−	1.19795e17i	−0.00438057	−	0.00438057i
$599$		−	1.39752e19i		−	0.505090i	−0.967585	−	0.252545i	$-0.918732\pi$
$599$		−	1.39752e19i		−	0.505090i	0.967585	−	0.252545i	$-0.0812676\pi$
$600$	−9.98916e18	+	1.68459e19i	−0.356837	+	0.601776i
$601$	−5.56800e19			−1.96597			−0.982987	−	0.183675i	$-0.941201\pi$
$601$	−5.56800e19			−1.96597			−0.982987	+	0.183675i	$0.941201\pi$
$602$	−1.62624e19	+	1.62624e19i	−0.567556	+	0.567556i
$603$	−7.21954e19	−	7.21954e19i	−2.49051	−	2.49051i
$604$		−	1.96938e19i		−	0.671537i
$605$	−5.62691e18	+	2.05215e19i	−0.189663	+	0.691705i
$606$	4.19872e19			1.39897
$607$	−3.16131e18	+	3.16131e18i	−0.104123	+	0.104123i	−0.757249	−	0.653126i	$-0.773457\pi$
$607$	−3.16131e18	+	3.16131e18i	−0.104123	+	0.104123i	0.653126	+	0.757249i	$0.273457\pi$
$608$	1.95523e18	+	1.95523e18i	0.0636610	+	0.0636610i
$609$		−	3.74803e19i		−	1.20637i
$610$	8.22083e18	+	1.44322e19i	0.261581	+	0.459223i
$611$	−1.09012e19			−0.342916
$612$	−3.06248e19	+	3.06248e19i	−0.952388	+	0.952388i
$613$	3.73864e19	+	3.73864e19i	1.14945	+	1.14945i	0.986661	+	0.162791i	$0.0520496\pi$
$613$	3.73864e19	+	3.73864e19i	1.14945	+	1.14945i	0.162791	+	0.986661i	$0.447950\pi$
$614$			2.58376e19i			0.785368i
$615$	−6.56954e18	+	3.74212e18i	−0.197428	+	0.112459i
$616$	−6.36793e18			−0.189205
$617$	−9.08675e18	+	9.08675e18i	−0.266939	+	0.266939i	−0.827866	−	0.560926i	$-0.810445\pi$
$617$	−9.08675e18	+	9.08675e18i	−0.266939	+	0.266939i	0.560926	+	0.827866i	$0.310445\pi$
$618$	−1.44142e19	−	1.44142e19i	−0.418669	−	0.418669i
$619$		−	1.94293e19i		−	0.557984i	−0.960293	−	0.278992i	$-0.910000\pi$
$619$		−	1.94293e19i		−	0.557984i	0.960293	−	0.278992i	$-0.0900003\pi$
$620$	6.83162e18	+	1.87320e18i	0.193991	+	0.0531916i
$621$	2.22003e18			0.0623330
$622$	−5.98076e18	+	5.98076e18i	−0.166044	+	0.166044i
$623$	3.34196e19	+	3.34196e19i	0.917456	+	0.917456i
$624$		−	9.71008e18i		−	0.263591i
$625$	1.78705e19	+	3.26867e19i	0.479708	+	0.877428i
$626$	−1.61264e19			−0.428073
$627$	1.44358e19	−	1.44358e19i	0.378937	−	0.378937i
$628$	3.34590e18	+	3.34590e18i	0.0868551	+	0.0868551i
$629$		−	3.77629e18i		−	0.0969417i
$630$	2.16124e19	−	7.88211e19i	0.548681	−	2.00105i
$631$	−2.54845e19			−0.639838			−0.319919	−	0.947445i	$-0.603656\pi$
$631$	−2.54845e19			−0.639838			−0.319919	+	0.947445i	$0.603656\pi$
$632$	1.31032e19	−	1.31032e19i	0.325354	−	0.325354i
$633$	6.96840e18	+	6.96840e18i	0.171122	+	0.171122i
$634$		−	4.16739e19i		−	1.01214i
$635$	−3.24004e19	−	5.68810e19i	−0.778277	−	1.36632i
$636$	−1.96381e19			−0.466551
$637$	2.05595e17	−	2.05595e17i	0.00483100	−	0.00483100i
$638$	−6.93003e18	−	6.93003e18i	−0.161061	−	0.161061i
$639$			1.48517e20i			3.41405i
$640$	3.37781e18	−	1.92406e18i	0.0768024	−	0.0437480i
$641$	2.90797e19			0.654008			0.327004	−	0.945023i	$-0.393961\pi$
$641$	2.90797e19			0.654008			0.327004	+	0.945023i	$0.393961\pi$
$642$	−1.35174e19	+	1.35174e19i	−0.300709	+	0.300709i
$643$	6.45652e18	+	6.45652e18i	0.142076	+	0.142076i	0.774568	−	0.632491i	$-0.217968\pi$
$643$	6.45652e18	+	6.45652e18i	0.142076	+	0.142076i	−0.632491	+	0.774568i	$0.717968\pi$
$644$			3.80114e17i			0.00827394i
$645$	−9.99667e19	−	2.74105e19i	−2.15247	−	0.590199i
$646$	1.56202e19			0.332705
$647$	−1.69207e19	+	1.69207e19i	−0.356525	+	0.356525i	−0.862530	−	0.506006i	$-0.831122\pi$
$647$	−1.69207e19	+	1.69207e19i	−0.356525	+	0.356525i	0.506006	+	0.862530i	$0.331122\pi$
$648$	5.50019e19	+	5.50019e19i	1.14644	+	1.14644i
$649$		−	4.60570e19i		−	0.949692i
$650$	−1.58868e19	−	9.42044e18i	−0.324073	−	0.192167i
$651$	−3.97002e19			−0.801173
$652$	3.47699e17	−	3.47699e17i	0.00694177	−	0.00694177i
$653$	1.71091e19	+	1.71091e19i	0.337937	+	0.337937i	0.855590	−	0.517653i	$-0.173194\pi$
$653$	1.71091e19	+	1.71091e19i	0.337937	+	0.337937i	−0.517653	+	0.855590i	$0.673194\pi$
$654$		−	5.00464e19i		−	0.977977i
$655$	2.89887e18	−	1.05722e19i	0.0560453	−	0.204399i
$656$	1.50069e18			0.0287053
$657$	−1.06861e19	+	1.06861e19i	−0.202237	+	0.202237i
$658$	1.72950e19	+	1.72950e19i	0.323847	+	0.323847i
$659$		−	5.14931e18i		−	0.0954007i	−0.998862	−	0.0477003i	$-0.984811\pi$
$659$		−	5.14931e18i		−	0.0954007i	0.998862	−	0.0477003i	$-0.0151893\pi$
$660$	−1.42056e19	−	2.49388e19i	−0.260406	−	0.457160i
$661$	−5.10674e19			−0.926261			−0.463131	−	0.886290i	$-0.653274\pi$
$661$	−5.10674e19			−0.926261			−0.463131	+	0.886290i	$0.653274\pi$
$662$	−2.77506e19	+	2.77506e19i	−0.498042	+	0.498042i
$663$	−3.87866e19	−	3.87866e19i	−0.688790	−	0.688790i
$664$		−	2.12182e19i		−	0.372848i
$665$	−2.56131e19	+	1.45896e19i	−0.445359	+	0.253684i
$666$	−1.25734e19			−0.216338
$667$	−4.13667e17	+	4.13667e17i	−0.00704320	+	0.00704320i
$668$	1.90775e19	+	1.90775e19i	0.321429	+	0.321429i
$669$			1.71284e20i			2.85585i
$670$	4.99255e19	+	1.36894e19i	0.823757	+	0.225871i
$671$	−2.43404e19			−0.397439
$672$	−1.54052e19	+	1.54052e19i	−0.248933	+	0.248933i
$673$	−5.24356e19	−	5.24356e19i	−0.838534	−	0.838534i	0.150132	−	0.988666i	$-0.452030\pi$
$673$	−5.24356e19	−	5.24356e19i	−0.838534	−	0.838534i	−0.988666	+	0.150132i	$0.952030\pi$
$674$		−	3.19407e18i		−	0.0505504i
$675$	2.34496e20	−	5.99168e19i	3.67290	−	0.938474i
$676$	−2.30977e19			−0.358049
$677$	−1.83304e19	+	1.83304e19i	−0.281223	+	0.281223i	−0.833597	−	0.552374i	$-0.813722\pi$
$677$	−1.83304e19	+	1.83304e19i	−0.281223	+	0.281223i	0.552374	+	0.833597i	$0.313722\pi$
$678$	4.30066e19	+	4.30066e19i	0.653020	+	0.653020i
$679$		−	1.22798e20i		−	1.84545i
$680$	5.80695e18	−	2.11781e19i	0.0863746	−	0.315010i
$681$	1.30037e20			1.91442
$682$	−7.34049e18	+	7.34049e18i	−0.106963	+	0.106963i
$683$	−4.69284e19	−	4.69284e19i	−0.676847	−	0.676847i	0.282439	−	0.959285i	$-0.408857\pi$
$683$	−4.69284e19	−	4.69284e19i	−0.676847	−	0.676847i	−0.959285	+	0.282439i	$0.908857\pi$
$684$		−	5.20085e19i		−	0.742474i
$685$	7.95381e17	+	1.39634e18i	0.0112394	+	0.0197314i
$686$	5.02245e19			0.702501
$687$	1.25142e20	−	1.25142e20i	1.73264	−	1.73264i
$688$	1.45484e19	+	1.45484e19i	0.199387	+	0.199387i
$689$		−	1.85200e19i		−	0.251251i
$690$	−1.48865e18	+	8.47958e17i	−0.0199916	+	0.0113876i
$691$	−5.94396e19			−0.790187			−0.395093	−	0.918641i	$-0.629288\pi$
$691$	−5.94396e19			−0.790187			−0.395093	+	0.918641i	$0.629288\pi$
$692$	3.95426e19	−	3.95426e19i	0.520383	−	0.520383i
$693$	8.46923e19	+	8.46923e19i	1.10334	+	1.10334i
$694$			3.74587e19i			0.483099i
$695$	−3.93598e19	−	1.07923e19i	−0.502527	−	0.137791i
$696$	−3.35301e19			−0.423809
$697$	5.99443e18	−	5.99443e18i	0.0750099	−	0.0750099i
$698$	−6.25833e19	−	6.25833e19i	−0.775302	−	0.775302i
$699$			2.98893e20i			3.66586i
$700$	1.02590e19	+	4.01504e19i	0.124571	+	0.487532i
$701$	2.70944e19			0.325726			0.162863	−	0.986649i	$-0.447927\pi$
$701$	2.70944e19			0.325726			0.162863	+	0.986649i	$0.447927\pi$
$702$	−8.48508e19	+	8.48508e19i	−1.00994	+	1.00994i
$703$	3.20653e18	+	3.20653e18i	0.0377875	+	0.0377875i
$704$			5.69679e18i			0.0664694i
$705$	−2.91510e19	+	1.06314e20i	−0.336767	+	1.22820i
$706$	5.72464e19			0.654810
$707$	6.28210e19	−	6.28210e19i	0.711490	−	0.711490i
$708$	−1.11421e20	−	1.11421e20i	−1.24949	−	1.24949i
$709$			3.74584e19i			0.415936i	0.978136	+	0.207968i	$0.0666849\pi$
$709$			3.74584e19i			0.415936i	−0.978136	+	0.207968i	$0.933315\pi$
$710$	−3.72717e19	−	6.54328e19i	−0.409798	−	0.719428i
$711$	−3.48539e20			−3.79459
$712$	2.98974e19	−	2.98974e19i	0.322310	−	0.322310i
$713$	4.38168e17	+	4.38168e17i	0.00467750	+	0.00467750i
$714$			1.23071e20i			1.30098i
$715$	2.35190e19	−	1.33968e19i	0.246193	−	0.140236i
$716$	5.43998e19			0.563905
$717$	1.72342e20	−	1.72342e20i	1.76912	−	1.76912i
$718$	8.37877e19	+	8.37877e19i	0.851745	+	0.851745i
$719$			6.23403e19i			0.627576i	0.949493	+	0.313788i	$0.101598\pi$
$719$			6.23403e19i			0.627576i	−0.949493	+	0.313788i	$0.898402\pi$
$720$	−7.05138e19	−	1.93346e19i	−0.702986	−	0.192756i
$721$	−4.31328e19			−0.425854
$722$	3.78730e19	−	3.78730e19i	0.370313	−	0.370313i
$723$	−5.39617e19	−	5.39617e19i	−0.522537	−	0.522537i
$724$			6.89503e19i			0.661251i
$725$	−3.25300e19	+	5.48590e19i	−0.308971	+	0.521053i
$726$	−1.06687e20			−1.00358
$727$	−9.12061e19	+	9.12061e19i	−0.849734	+	0.849734i	−0.990100	−	0.140366i	$-0.955172\pi$
$727$	−9.12061e19	+	9.12061e19i	−0.849734	+	0.849734i	0.140366	+	0.990100i	$0.455172\pi$
$728$	−1.45282e19	−	1.45282e19i	−0.134057	−	0.134057i
$729$		−	6.42223e20i		−	5.86939i
$730$	2.02625e18	−	7.38979e18i	0.0183414	−	0.0668917i
$731$	1.16226e20			1.04204
$732$	−5.88841e19	+	5.88841e19i	−0.522902	+	0.522902i
$733$	2.92997e19	+	2.92997e19i	0.257712	+	0.257712i	0.824123	−	0.566411i	$-0.191668\pi$
$733$	2.92997e19	+	2.92997e19i	0.257712	+	0.257712i	−0.566411	+	0.824123i	$0.691668\pi$
$734$		−	1.14149e19i		−	0.0994491i
$735$	−1.45529e18	−	2.55485e18i	−0.0125585	−	0.0220472i
$736$	3.40052e17			0.00290670
$737$	−5.36444e19	+	5.36444e19i	−0.454205	+	0.454205i
$738$	−1.99588e19	−	1.99588e19i	−0.167394	−	0.167394i
$739$		−	4.62584e19i		−	0.384308i	−0.981365	−	0.192154i	$-0.938453\pi$
$739$		−	4.62584e19i		−	0.384308i	0.981365	−	0.192154i	$-0.0615474\pi$
$740$	5.53951e18	−	3.15540e18i	0.0455879	−	0.0259677i
$741$	6.58691e19			0.536975
$742$	−2.93824e19	+	2.93824e19i	−0.237279	+	0.237279i
$743$	1.31916e19	+	1.31916e19i	0.105530	+	0.105530i	0.757900	−	0.652370i	$-0.226225\pi$
$743$	1.31916e19	+	1.31916e19i	0.105530	+	0.105530i	−0.652370	+	0.757900i	$0.726225\pi$
$744$			3.55161e19i			0.281459i
$745$	1.80381e20	+	4.94598e19i	1.41611	+	0.388292i
$746$	−7.05091e19			−0.548370
$747$	−2.82198e20	+	2.82198e20i	−2.17425	+	2.17425i
$748$	2.27556e19	+	2.27556e19i	0.173691	+	0.173691i
$749$			4.04491e19i			0.305870i
$750$	−1.34356e20	+	1.29745e20i	−1.00653	+	0.971988i
$751$	1.31467e20			0.975745			0.487873	−	0.872915i	$-0.337773\pi$
$751$	1.31467e20			0.975745			0.487873	+	0.872915i	$0.337773\pi$
$752$	1.54722e19	−	1.54722e19i	0.113770	−	0.113770i
$753$	1.32277e20	+	1.32277e20i	0.963653	+	0.963653i
$754$		−	3.16211e19i		−	0.228233i
$755$	4.96648e19	−	1.81129e20i	0.355157	−	1.29527i
$756$	2.69235e20			1.90756
$757$	−1.60168e20	+	1.60168e20i	−1.12436	+	1.12436i	−0.133281	+	0.991078i	$0.542551\pi$
$757$	−1.60168e20	+	1.60168e20i	−1.12436	+	1.12436i	−0.991078	+	0.133281i	$0.957449\pi$
$758$	4.89235e19	+	4.89235e19i	0.340277	+	0.340277i
$759$		−	2.51065e18i		−	0.0173019i
$760$	1.30520e19	+	2.29136e19i	0.0891213	+	0.156458i
$761$	−2.99090e19			−0.202353			−0.101177	−	0.994868i	$-0.532261\pi$
$761$	−2.99090e19			−0.202353			−0.101177	+	0.994868i	$0.532261\pi$
$762$	2.32077e20	−	2.32077e20i	1.55578	−	1.55578i
$763$	−7.48791e19	−	7.48791e19i	−0.497380	−	0.497380i
$764$			6.88172e19i			0.452943i
$765$	−3.58896e20	+	2.04433e20i	−2.34066	+	1.33328i
$766$	8.28411e19			0.535359
$767$	1.05077e20	−	1.05077e20i	0.672885	−	0.672885i
$768$	1.37816e19	+	1.37816e19i	0.0874524	+	0.0874524i
$769$		−	5.01739e19i		−	0.315496i	−0.987479	−	0.157748i	$-0.949577\pi$
$769$		−	5.01739e19i		−	0.315496i	0.987479	−	0.157748i	$-0.0504234\pi$
$770$	−5.85675e19	−	1.60590e19i	−0.364940	−	0.100065i
$771$	5.43863e20			3.35822
$772$	−3.28365e19	+	3.28365e19i	−0.200926	+	0.200926i
$773$	−2.16590e20	−	2.16590e20i	−1.31335	−	1.31335i	−0.918929	−	0.394423i	$-0.870945\pi$
$773$	−2.16590e20	−	2.16590e20i	−1.31335	−	1.31335i	−0.394423	−	0.918929i	$-0.629055\pi$
$774$		−	3.86983e20i		−	2.32544i
$775$	5.81083e19	+	3.44567e19i	0.346040	+	0.205193i
$776$	−1.09855e20			−0.648320
$777$	−2.52642e19	+	2.52642e19i	−0.147760	+	0.147760i
$778$	−7.80355e17	−	7.80355e17i	−0.00452309	−	0.00452309i
$779$			1.01800e19i			0.0584772i
$780$	2.44874e19	−	8.93062e19i	0.139406	−	0.508416i
$781$	1.10355e20			0.622635
$782$	1.35833e18	−	1.35833e18i	0.00759551	−	0.00759551i
$783$	2.93001e20	+	2.93001e20i	1.62381	+	1.62381i
$784$			5.83607e17i			0.00320559i
$785$	2.23353e19	+	3.92110e19i	0.121592	+	0.213462i
$786$	5.49628e19			0.296559
$787$	−1.41767e20	+	1.41767e20i	−0.758146	+	0.758146i	−0.975985	−	0.217839i	$-0.930099\pi$
$787$	−1.41767e20	+	1.41767e20i	−0.758146	+	0.758146i	0.217839	+	0.975985i	$0.430099\pi$
$788$	−7.77211e19	−	7.77211e19i	−0.411960	−	0.411960i
$789$			1.40444e20i			0.737842i
$790$	1.53557e20	−	8.74690e19i	0.799616	−	0.455475i
$791$	1.28692e20			0.664227
$792$	7.57663e19	−	7.57663e19i	0.387614	−	0.387614i
$793$	−5.55316e19	−	5.55316e19i	−0.281597	−	0.281597i
$794$			3.21140e19i			0.161418i
$795$	−1.80617e20	−	4.95244e19i	−0.899888	−	0.246746i
$796$	−1.63359e20			−0.806776
$797$	1.80332e20	−	1.80332e20i	0.882803	−	0.882803i	−0.111016	−	0.993819i	$-0.535410\pi$
$797$	1.80332e20	−	1.80332e20i	0.882803	−	0.882803i	0.993819	+	0.111016i	$0.0354104\pi$
$798$	−1.04503e20	−	1.04503e20i	−0.507115	−	0.507115i
$799$		−	1.23607e20i		−	0.594585i
$800$	3.59188e19	−	9.17773e18i	0.171274	−	0.0437628i
$801$	−7.95260e20			−3.75908
$802$	−1.12144e20	+	1.12144e20i	−0.525479	+	0.525479i
$803$	7.94025e18	+	7.94025e18i	0.0368829	+	0.0368829i
$804$			2.59552e20i			1.19518i
$805$	−9.58592e17	+	3.49601e18i	−0.00437585	+	0.0159588i
$806$	−3.34940e19			−0.151573
$807$	7.41972e19	−	7.41972e19i	0.332869	−	0.332869i
$808$	−5.62000e19	−	5.62000e19i	−0.249952	−	0.249952i
$809$			4.66147e19i			0.205534i	0.994705	+	0.102767i	$0.0327696\pi$
$809$			4.66147e19i			0.205534i	−0.994705	+	0.102767i	$0.967230\pi$
$810$	3.67160e20	+	6.44574e20i	1.60495	+	2.81759i
$811$	−3.34257e20			−1.44855			−0.724277	−	0.689510i	$-0.757826\pi$
$811$	−3.34257e20			−1.44855			−0.724277	+	0.689510i	$0.757826\pi$
$812$	−5.01675e19	+	5.01675e19i	−0.215541	+	0.215541i
$813$	−1.79315e20	−	1.79315e20i	−0.763806	−	0.763806i
$814$			9.34258e18i			0.0394545i
$815$	4.07472e18	−	2.32103e18i	0.0170606	−	0.00971802i
$816$	1.10100e20			0.457044
$817$	−9.86904e19	+	9.86904e19i	−0.406182	+	0.406182i
$818$	−1.29602e20	−	1.29602e20i	−0.528859	−	0.528859i
$819$			3.86444e20i			1.56350i
$820$	1.38022e19	+	3.78451e18i	0.0553671	+	0.0151814i
$821$	3.33093e20			1.32484			0.662420	−	0.749133i	$-0.269530\pi$
$821$	3.33093e20			1.32484			0.662420	+	0.749133i	$0.269530\pi$
$822$	−5.69715e18	+	5.69715e18i	−0.0224675	+	0.0224675i
$823$	−1.31310e20	−	1.31310e20i	−0.513449	−	0.513449i	0.402132	−	0.915582i	$-0.368269\pi$
$823$	−1.31310e20	−	1.31310e20i	−0.513449	−	0.513449i	−0.915582	+	0.402132i	$0.868269\pi$
$824$			3.85869e19i			0.149606i
$825$	−6.77604e19	−	2.65193e20i	−0.260494	−	1.01949i
$826$	−3.33414e20			−1.27093
$827$	9.99144e19	−	9.99144e19i	0.377650	−	0.377650i	−0.492604	−	0.870254i	$-0.663955\pi$
$827$	9.99144e19	−	9.99144e19i	0.377650	−	0.377650i	0.870254	+	0.492604i	$0.163955\pi$
$828$	−4.52263e18	−	4.52263e18i	−0.0169504	−	0.0169504i
$829$		−	3.19335e20i		−	1.18677i	−0.804920	−	0.593383i	$-0.797792\pi$
$829$		−	3.19335e20i		−	1.18677i	0.804920	−	0.593383i	$-0.202208\pi$
$830$	5.35091e19	−	1.95149e20i	0.197188	−	0.719151i
$831$	7.31596e20			2.67340
$832$	−1.29970e19	+	1.29970e19i	−0.0470955	+	0.0470955i
$833$	2.33120e18	+	2.33120e18i	0.00837652	+	0.00837652i
$834$		−	2.04623e20i		−	0.729109i
$835$	1.27350e20	+	2.23571e20i	0.449980	+	0.789970i
$836$	−3.86446e19			−0.135408
$837$	3.10355e20	−	3.10355e20i	1.07840	−	1.07840i
$838$	1.16506e20	+	1.16506e20i	0.401457	+	0.401457i
$839$			3.77429e20i			1.28974i	0.764293	+	0.644869i	$0.223088\pi$
$839$			3.77429e20i			1.28974i	−0.764293	+	0.644869i	$0.776912\pi$
$840$	−1.80536e20	+	1.02836e20i	−0.611798	+	0.348491i
$841$	1.88366e20			0.633041
$842$	−3.08606e19	+	3.08606e19i	−0.102854	+	0.102854i
$843$	−1.99692e20	−	1.99692e20i	−0.660037	−	0.660037i
$844$		−	1.86544e19i		−	0.0611484i
$845$	−2.12436e20	−	5.82491e19i	−0.690607	−	0.189362i
$846$	−4.11556e20			−1.32689
$847$	−1.59624e20	+	1.59624e20i	−0.510404	+	0.510404i
$848$	2.62857e19	+	2.62857e19i	0.0833581	+	0.0833581i
$849$			2.82084e20i			0.887205i
$850$	1.06816e20	−	1.80136e20i	0.333200	−	0.561913i
$851$	5.57677e17			0.00172534
$852$	2.66969e20	−	2.66969e20i	0.819189	−	0.819189i
$853$	9.80842e19	+	9.80842e19i	0.298508	+	0.298508i	0.840429	−	0.541921i	$-0.182303\pi$
$853$	9.80842e19	+	9.80842e19i	0.298508	+	0.298508i	−0.541921	+	0.840429i	$0.682303\pi$
$854$			1.76204e20i			0.531876i
$855$	1.31158e20	−	4.78336e20i	0.392673	−	1.43209i
$856$	3.61861e19			0.107455
$857$	−3.85045e20	+	3.85045e20i	−1.13408	+	1.13408i	−0.144594	+	0.989491i	$0.546187\pi$
$857$	−3.85045e20	+	3.85045e20i	−1.13408	+	1.13408i	−0.989491	+	0.144594i	$0.953813\pi$
$858$	9.59585e19	+	9.59585e19i	0.280332	+	0.280332i
$859$		−	2.31173e20i		−	0.669860i	−0.942243	−	0.334930i	$-0.891287\pi$
$859$		−	2.31173e20i		−	0.669860i	0.942243	−	0.334930i	$-0.108713\pi$
$860$	9.71167e19	+	1.70495e20i	0.279129	+	0.490029i
$861$	−8.02081e19			−0.228663
$862$	−1.80582e19	+	1.80582e19i	−0.0510649	+	0.0510649i
$863$	−2.25853e20	−	2.25853e20i	−0.633505	−	0.633505i	0.315441	−	0.948945i	$-0.397848\pi$
$863$	−2.25853e20	−	2.25853e20i	−0.633505	−	0.633505i	−0.948945	+	0.315441i	$0.897848\pi$
$864$		−	2.40859e20i		−	0.670142i
$865$	4.63405e20	−	2.63963e20i	1.27893	−	0.728502i
$866$	−1.24587e20			−0.341072
$867$	−7.54668e19	+	7.54668e19i	−0.204938	+	0.204938i
$868$	5.31389e19	+	5.31389e19i	0.143144	+	0.143144i
$869$			2.58980e20i			0.692035i
$870$	−3.08386e20	−	8.45581e19i	−0.817447	−	0.224141i
$871$	−2.44775e20			−0.643635
$872$	−6.69873e19	+	6.69873e19i	−0.174734	+	0.174734i
$873$	1.46106e21	+	1.46106e21i	3.78066	+	3.78066i
$874$			2.30677e18i			0.00592140i
$875$	−6.89904e18	+	3.95145e20i	−0.0175684	+	1.00624i
$876$	3.84179e19			0.0970522
$877$	3.98463e20	−	3.98463e20i	0.998599	−	0.998599i	−0.00140039	−	0.999999i	$-0.500446\pi$
$877$	3.98463e20	−	3.98463e20i	0.998599	−	0.998599i	0.999999	+	0.00140039i	$0.000445759\pi$
$878$	3.04661e20	+	3.04661e20i	0.757453	+	0.757453i
$879$		−	9.68907e20i		−	2.38979i
$880$	−1.43665e19	+	5.23949e19i	−0.0351537	+	0.128207i
$881$	5.84465e19			0.141882			0.0709410	−	0.997481i	$-0.477400\pi$
$881$	5.84465e19			0.141882			0.0709410	+	0.997481i	$0.477400\pi$
$882$	7.76186e18	−	7.76186e18i	0.0186933	−	0.0186933i
$883$	2.21727e20	+	2.21727e20i	0.529778	+	0.529778i	0.920506	−	0.390728i	$-0.127777\pi$
$883$	2.21727e20	+	2.21727e20i	0.529778	+	0.529778i	−0.390728	+	0.920506i	$0.627777\pi$
$884$			1.03832e20i			0.246130i
$885$	−7.43779e20	−	1.30575e21i	−1.74921	−	3.07085i
$886$	7.35813e19			0.171685
$887$	−2.90951e20	+	2.90951e20i	−0.673525	+	0.673525i	−0.958527	−	0.285002i	$-0.908006\pi$
$887$	−2.90951e20	+	2.90951e20i	−0.673525	+	0.673525i	0.285002	+	0.958527i	$0.408006\pi$
$888$	2.26015e19	+	2.26015e19i	0.0519094	+	0.0519094i
$889$		−	6.94465e20i		−	1.58248i
$890$	3.50371e20	−	1.99578e20i	0.792134	−	0.451213i
$891$	−1.08710e21			−2.43851
$892$	2.29265e20	−	2.29265e20i	0.510250	−	0.510250i
$893$	1.04957e20	+	1.04957e20i	0.231767	+	0.231767i
$894$			9.37762e20i			2.05461i
$895$	5.00330e20	+	1.37188e20i	1.08766	+	0.298233i
$896$	4.12399e19			0.0889532
$897$	5.72795e18	−	5.72795e18i	0.0122589	−	0.0122589i
$898$	−1.19517e20	−	1.19517e20i	−0.253803	−	0.253803i
$899$			1.15659e20i			0.243704i
$900$	−5.99775e20	−	3.55651e20i	−1.25398	−	0.743578i
$901$	2.09994e20			0.435646
$902$	−1.48303e19	+	1.48303e19i	−0.0305284	+	0.0305284i
$903$	−7.77579e20	−	7.77579e20i	−1.58829	−	1.58829i
$904$		−	1.15129e20i		−	0.233349i
$905$	−1.73883e20	+	6.34155e20i	−0.349717	+	1.27543i
$906$	9.41649e20			1.87928
$907$	−3.21482e20	+	3.21482e20i	−0.636656	+	0.636656i	−0.949729	−	0.313073i	$-0.898642\pi$
$907$	−3.21482e20	+	3.21482e20i	−0.636656	+	0.636656i	0.313073	+	0.949729i	$0.398642\pi$
$908$	−1.74055e20	−	1.74055e20i	−0.342046	−	0.342046i
$909$			1.49490e21i			2.91518i
$910$	−9.69814e19	−	1.70257e20i	−0.187672	−	0.329470i
$911$	−1.01526e20			−0.194961			−0.0974803	−	0.995237i	$-0.531078\pi$
$911$	−1.01526e20			−0.194961			−0.0974803	+	0.995237i	$0.531078\pi$
$912$	−9.34887e19	+	9.34887e19i	−0.178154	+	0.178154i
$913$	2.09685e20	+	2.09685e20i	0.396527	+	0.396527i
$914$			1.08592e20i			0.203785i
$915$	−6.90069e20	+	3.93075e20i	−1.28512	+	0.732029i
$916$	−3.35007e20			−0.619136
$917$	8.22349e19	−	8.22349e19i	0.150824	−	0.150824i
$918$	−9.62103e20	−	9.62103e20i	−1.75115	−	1.75115i
$919$			8.06021e19i			0.145592i	0.997347	+	0.0727960i	$0.0231922\pi$
$919$			8.06021e19i			0.145592i	−0.997347	+	0.0727960i	$0.976808\pi$
$920$	3.12755e18	+	8.57562e17i	0.00560647	+	0.00153727i
$921$	−1.23541e21			−2.19783
$922$	1.87624e20	−	1.87624e20i	0.331262	−	0.331262i
$923$	2.51770e20	+	2.51770e20i	0.441155	+	0.441155i
$924$		−	3.04480e20i		−	0.529486i
$925$	5.89058e19	−	1.50512e19i	0.101664	−	0.0259765i
$926$	2.83107e20			0.484924
$927$	5.13199e20	−	5.13199e20i	0.872423	−	0.872423i
$928$	4.48802e19	+	4.48802e19i	0.0757215	+	0.0757215i
$929$		−	2.57041e20i		−	0.430420i	−0.976568	−	0.215210i	$-0.930956\pi$
$929$		−	2.57041e20i		−	0.430420i	0.976568	−	0.215210i	$-0.0690436\pi$
$930$	−8.95664e19	+	3.26651e20i	−0.148855	+	0.542879i
$931$	−3.95894e18			−0.00653027
$932$	4.00069e20	−	4.00069e20i	0.654974	−	0.654974i
$933$	−2.85968e20	−	2.85968e20i	−0.464671	−	0.464671i
$934$		−	4.38994e20i		−	0.707996i
$935$	1.51903e20	+	2.66676e20i	0.243156	+	0.426877i
$936$	3.45715e20			0.549272
$937$	−5.54323e20	+	5.54323e20i	−0.874150	+	0.874150i	−0.992922	−	0.118772i	$-0.962104\pi$
$937$	−5.54323e20	+	5.54323e20i	−0.874150	+	0.874150i	0.118772	+	0.992922i	$0.462104\pi$
$938$	3.88340e20	+	3.88340e20i	0.607844	+	0.607844i
$939$		−	7.71078e20i		−	1.19795i
$940$	1.81321e20	−	1.03284e20i	0.279610	−	0.159271i
$941$	−5.68342e20			−0.869926			−0.434963	−	0.900448i	$-0.643238\pi$
$941$	−5.68342e20			−0.869926			−0.434963	+	0.900448i	$0.643238\pi$
$942$	−1.59983e20	+	1.59983e20i	−0.243062	+	0.243062i
$943$	8.85249e17	+	8.85249e17i	0.00133501	+	0.00133501i
$944$			2.98274e20i			0.446490i
$945$	2.47622e21	+	6.78971e20i	3.67932	+	1.00885i
$946$	−2.87545e20			−0.424100
$947$	8.78325e20	−	8.78325e20i	1.28589	−	1.28589i	0.348636	−	0.937258i	$-0.386645\pi$
$947$	8.78325e20	−	8.78325e20i	1.28589	−	1.28589i	0.937258	−	0.348636i	$-0.113355\pi$
$948$	6.26522e20	+	6.26522e20i	0.910496	+	0.910496i
$949$			3.62307e19i			0.0522652i
$950$	6.22578e19	+	2.43658e20i	0.0891515	+	0.348911i
$951$	1.99262e21			2.83244
$952$	1.64731e20	−	1.64731e20i	0.232444	−	0.232444i
$953$	−5.54354e20	−	5.54354e20i	−0.776492	−	0.776492i	0.202740	−	0.979233i	$-0.435015\pi$
$953$	−5.54354e20	−	5.54354e20i	−0.776492	−	0.776492i	−0.979233	+	0.202740i	$0.935015\pi$
$954$		−	6.99189e20i		−	0.972201i
$955$	−1.73547e20	+	6.32931e20i	−0.239549	+	0.873640i
$956$	−4.61360e20			−0.632171
$957$	3.31357e20	−	3.31357e20i	0.450726	−	0.450726i
$958$	3.30240e20	+	3.30240e20i	0.445935	+	0.445935i
$959$			1.70481e19i			0.0228531i
$960$	9.19980e19	+	1.61508e20i	0.122428	+	0.214930i
$961$	−6.34435e20			−0.838153
$962$	−2.13147e19	+	2.13147e19i	−0.0279546	+	0.0279546i
$963$	−4.81268e20	−	4.81268e20i	−0.626618	−	0.626618i
$964$			1.44456e20i			0.186722i
$965$	−3.84815e20	+	2.19197e20i	−0.493811	+	0.281283i
$966$	−1.81750e19			−0.0231544
$967$	−3.41310e20	+	3.41310e20i	−0.431682	+	0.431682i	−0.889200	−	0.457518i	$-0.848738\pi$
$967$	−3.41310e20	+	3.41310e20i	−0.431682	+	0.431682i	0.457518	+	0.889200i	$0.348738\pi$
$968$	1.42801e20	+	1.42801e20i	0.179309	+	0.179309i
$969$			7.46874e20i			0.931067i
$970$	−1.01037e21	−	2.77039e20i	−1.25048	−	0.342878i
$971$	−6.45633e19			−0.0793325			−0.0396663	−	0.999213i	$-0.512629\pi$
$971$	−6.45633e19			−0.0793325			−0.0396663	+	0.999213i	$0.512629\pi$
$972$	−1.53124e21	+	1.53124e21i	−1.86801	+	1.86801i
$973$	−3.06156e20	−	3.06156e20i	−0.370811	−	0.370811i
$974$			4.75508e20i			0.571801i
$975$	4.50435e20	−	7.59620e20i	0.537774	−	0.906909i
$976$	1.57633e20			0.186852
$977$	9.59487e20	−	9.59487e20i	1.12922	−	1.12922i	0.138911	−	0.990305i	$-0.455640\pi$
$977$	9.59487e20	−	9.59487e20i	1.12922	−	1.12922i	0.990305	−	0.138911i	$-0.0443602\pi$
$978$	1.66251e19	+	1.66251e19i	0.0194264	+	0.0194264i
$979$			5.90914e20i			0.685560i
$980$	−1.47177e18	+	5.36759e18i	−0.00169534	+	0.00618296i
$981$	1.78184e21			2.03791
$982$	−4.14366e20	+	4.14366e20i	−0.470548	+	0.470548i
$983$	−4.66356e20	−	4.66356e20i	−0.525827	−	0.525827i	0.393499	−	0.919325i	$-0.371265\pi$
$983$	−4.66356e20	−	4.66356e20i	−0.525827	−	0.525827i	−0.919325	+	0.393499i	$0.871265\pi$
$984$			7.17547e19i			0.0803312i
$985$	−5.18820e20	−	9.10823e20i	−0.576718	−	1.01247i
$986$	3.58545e20			0.395735
$987$	−8.26954e20	+	8.26954e20i	−0.906278	+	0.906278i
$988$	−8.81660e19	−	8.81660e19i	−0.0959407	−	0.0959407i
$989$			1.71641e19i			0.0185459i
$990$	8.87914e20	−	5.05771e20i	0.952631	−	0.542635i
$991$	7.67370e20			0.817503			0.408752	−	0.912646i	$-0.365964\pi$
$991$	7.67370e20			0.817503			0.408752	+	0.912646i	$0.365964\pi$
$992$	4.75384e19	−	4.75384e19i	0.0502878	−	0.0502878i
$993$	−1.32688e21	−	1.32688e21i	−1.39376	−	1.39376i
$994$		−	7.98875e20i		−	0.833247i
$995$	−1.50246e21	−	4.11969e20i	−1.55611	−	0.426681i
$996$	1.01454e21			1.04341
$997$	3.17020e20	−	3.17020e20i	0.323758	−	0.323758i	−0.526449	−	0.850207i	$-0.676477\pi$
$997$	3.17020e20	−	3.17020e20i	0.323758	−	0.323758i	0.850207	+	0.526449i	$0.176477\pi$
$998$	−1.09112e20	−	1.09112e20i	−0.110652	−	0.110652i
$999$		−	3.95003e20i		−	0.397779i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.15.c.b.3.4	✓	8
3.2	odd	2		90.15.g.b.73.2		8
4.3	odd	2		80.15.p.b.33.1		8
5.2	odd	4	inner	10.15.c.b.7.4	yes	8
5.3	odd	4		50.15.c.e.7.1		8
5.4	even	2		50.15.c.e.43.1		8
15.2	even	4		90.15.g.b.37.2		8
20.7	even	4		80.15.p.b.17.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.15.c.b.3.4	✓	8	1.1	even	1	trivial
10.15.c.b.7.4	yes	8	5.2	odd	4	inner
50.15.c.e.7.1		8	5.3	odd	4
50.15.c.e.43.1		8	5.4	even	2
80.15.p.b.17.1		8	20.7	even	4
80.15.p.b.33.1		8	4.3	odd	2
90.15.g.b.37.2		8	15.2	even	4
90.15.g.b.73.2		8	3.2	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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 15 \)
Character orbit:	\([\chi]\)	\(=\)	10.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(64.0000 - 64.0000i) q^{2} +(3060.13 + 3060.13i) q^{3} -8192.00i q^{4} +(20659.0 - 75344.0i) q^{5} +391697. q^{6} +(586054. - 586054. i) q^{7} +(-524288. - 524288. i) q^{8} +1.39459e7i q^{9} +O(q^{10})\)	\(q+(64.0000 - 64.0000i) q^{2} +(3060.13 + 3060.13i) q^{3} -8192.00i q^{4} +(20659.0 - 75344.0i) q^{5} +391697. q^{6} +(586054. - 586054. i) q^{7} +(-524288. - 524288. i) q^{8} +1.39459e7i q^{9} +(-3.49984e6 - 6.14419e6i) q^{10} +1.03624e7 q^{11} +(2.50686e7 - 2.50686e7i) q^{12} +(2.36414e7 + 2.36414e7i) q^{13} -7.50150e7i q^{14} +(2.93782e8 - 1.67343e8i) q^{15} -6.71089e7 q^{16} +(-2.68064e8 + 2.68064e8i) q^{17} +(8.92536e8 + 8.92536e8i) q^{18} -4.55238e8i q^{19} +(-6.17218e8 - 1.69239e8i) q^{20} +3.58681e9 q^{21} +(6.63194e8 - 6.63194e8i) q^{22} +(-3.95873e7 - 3.95873e7i) q^{23} -3.20878e9i q^{24} +(-5.24992e9 - 3.11307e9i) q^{25} +3.02610e9 q^{26} +(-2.80397e10 + 2.80397e10i) q^{27} +(-4.80096e9 - 4.80096e9i) q^{28} -1.04495e10i q^{29} +(8.09208e9 - 2.95120e10i) q^{30} -1.10684e10 q^{31} +(-4.29497e9 + 4.29497e9i) q^{32} +(3.17103e10 + 3.17103e10i) q^{33} +3.43122e10i q^{34} +(-3.20484e10 - 5.62630e10i) q^{35} +1.14245e11 q^{36} +(-7.04363e9 + 7.04363e9i) q^{37} +(-2.91352e10 - 2.91352e10i) q^{38} +1.44692e11i q^{39} +(-5.03332e10 + 2.86707e10i) q^{40} -2.23620e10 q^{41} +(2.29556e11 - 2.29556e11i) q^{42} +(-2.16788e11 - 2.16788e11i) q^{43} -8.48888e10i q^{44} +(1.05074e12 + 2.88108e11i) q^{45} -5.06717e9 q^{46} +(-2.30554e11 + 2.30554e11i) q^{47} +(-2.05362e11 - 2.05362e11i) q^{48} -8.69642e9i q^{49} +(-5.35232e11 + 1.36759e11i) q^{50} -1.64062e12 q^{51} +(1.93670e11 - 1.93670e11i) q^{52} +(-3.91687e11 - 3.91687e11i) q^{53} +3.58908e12i q^{54} +(2.14077e11 - 7.80745e11i) q^{55} -6.14523e11 q^{56} +(1.39309e12 - 1.39309e12i) q^{57} +(-6.68767e11 - 6.68767e11i) q^{58} -4.44463e12i q^{59} +(-1.37088e12 - 2.40666e12i) q^{60} -2.34892e12 q^{61} +(-7.08377e11 + 7.08377e11i) q^{62} +(8.17304e12 + 8.17304e12i) q^{63} +5.49756e11i q^{64} +(2.26964e12 - 1.29283e12i) q^{65} +4.05892e12 q^{66} +(-5.17683e12 + 5.17683e12i) q^{67} +(2.19598e12 + 2.19598e12i) q^{68} -2.42285e11i q^{69} +(-5.65193e12 - 1.54974e12i) q^{70} +1.06495e13 q^{71} +(7.31165e12 - 7.31165e12i) q^{72} +(7.66256e11 + 7.66256e11i) q^{73} +9.01585e11i q^{74} +(-6.53907e12 - 2.55919e13i) q^{75} -3.72931e12 q^{76} +(6.07293e12 - 6.07293e12i) q^{77} +(9.26026e12 + 9.26026e12i) q^{78} +2.49923e13i q^{79} +(-1.38640e12 + 5.05625e12i) q^{80} -1.04908e14 q^{81} +(-1.43117e12 + 1.43117e12i) q^{82} +(2.02352e13 + 2.02352e13i) q^{83} -2.93831e13i q^{84} +(1.46591e13 + 2.57350e13i) q^{85} -2.77489e13 q^{86} +(3.19768e13 - 3.19768e13i) q^{87} +(-5.43288e12 - 5.43288e12i) q^{88} +5.70248e13i q^{89} +(8.56861e13 - 4.88083e13i) q^{90} +2.77103e13 q^{91} +(-3.24299e11 + 3.24299e11i) q^{92} +(-3.38708e13 - 3.38708e13i) q^{93} +2.95110e13i q^{94} +(-3.42995e13 - 9.40478e12i) q^{95} -2.62863e13 q^{96} +(1.04766e14 - 1.04766e14i) q^{97} +(-5.56571e11 - 5.56571e11i) q^{98} +1.44513e14i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 512 q^{2} + 1404 q^{3} - 100860 q^{5} + 179712 q^{6} + 1333276 q^{7} - 4194304 q^{8}+O(q^{10}) \) 8 * q + 512 * q^2 + 1404 * q^3 - 100860 * q^5 + 179712 * q^6 + 1333276 * q^7 - 4194304 * q^8	\( 8 q + 512 q^{2} + 1404 q^{3} - 100860 q^{5} + 179712 q^{6} + 1333276 q^{7} - 4194304 q^{8} - 9034240 q^{10} + 8181256 q^{11} + 11501568 q^{12} - 10529136 q^{13} + 721621020 q^{15} - 536870912 q^{16} - 1669855424 q^{17} + 2079049728 q^{18} - 330137600 q^{20} + 192520776 q^{21} + 523600384 q^{22} - 4778918036 q^{23} + 15448124800 q^{25} - 1347729408 q^{26} - 20842498800 q^{27} - 10922196992 q^{28} + 48428597760 q^{30} + 35788345016 q^{31} - 34359738368 q^{32} - 130209466872 q^{33} - 30069746420 q^{35} + 266118365184 q^{36} - 31454650344 q^{37} - 100622935040 q^{38} + 31750881280 q^{40} + 94198718056 q^{41} + 12321329664 q^{42} - 942463128516 q^{43} + 2927734430100 q^{45} - 611701508608 q^{46} - 1797815170164 q^{47} - 94220845056 q^{48} + 712475699200 q^{50} - 1982287069224 q^{51} - 86254682112 q^{52} + 540438256184 q^{53} + 788235527880 q^{55} - 1398041214976 q^{56} + 6485834218080 q^{57} - 841739223040 q^{58} + 287341117440 q^{60} - 19913995236984 q^{61} + 2290454081024 q^{62} + 25848827893644 q^{63} - 7034160749880 q^{65} - 16666811759616 q^{66} + 13553624120956 q^{67} + 13679455633408 q^{68} - 16955995571200 q^{70} - 51541518798664 q^{71} + 17031575371776 q^{72} + 44383738947944 q^{73} - 19405526378100 q^{75} - 12879735685120 q^{76} + 74886492270632 q^{77} + 66217996893696 q^{78} + 6768600023040 q^{80} - 322723412222112 q^{81} + 6028717955584 q^{82} + 134272999400364 q^{83} + 145335752004880 q^{85} - 120635280450048 q^{86} + 68423417580480 q^{87} - 4289334345728 q^{88} + 112569467389440 q^{90} - 234891728536584 q^{91} - 39148896550912 q^{92} + 66751748435208 q^{93} + 26760204832400 q^{95} - 12060268167168 q^{96} + 167451300858216 q^{97} + 78801761769472 q^{98}+O(q^{100}) \) 8 * q + 512 * q^2 + 1404 * q^3 - 100860 * q^5 + 179712 * q^6 + 1333276 * q^7 - 4194304 * q^8 - 9034240 * q^10 + 8181256 * q^11 + 11501568 * q^12 - 10529136 * q^13 + 721621020 * q^15 - 536870912 * q^16 - 1669855424 * q^17 + 2079049728 * q^18 - 330137600 * q^20 + 192520776 * q^21 + 523600384 * q^22 - 4778918036 * q^23 + 15448124800 * q^25 - 1347729408 * q^26 - 20842498800 * q^27 - 10922196992 * q^28 + 48428597760 * q^30 + 35788345016 * q^31 - 34359738368 * q^32 - 130209466872 * q^33 - 30069746420 * q^35 + 266118365184 * q^36 - 31454650344 * q^37 - 100622935040 * q^38 + 31750881280 * q^40 + 94198718056 * q^41 + 12321329664 * q^42 - 942463128516 * q^43 + 2927734430100 * q^45 - 611701508608 * q^46 - 1797815170164 * q^47 - 94220845056 * q^48 + 712475699200 * q^50 - 1982287069224 * q^51 - 86254682112 * q^52 + 540438256184 * q^53 + 788235527880 * q^55 - 1398041214976 * q^56 + 6485834218080 * q^57 - 841739223040 * q^58 + 287341117440 * q^60 - 19913995236984 * q^61 + 2290454081024 * q^62 + 25848827893644 * q^63 - 7034160749880 * q^65 - 16666811759616 * q^66 + 13553624120956 * q^67 + 13679455633408 * q^68 - 16955995571200 * q^70 - 51541518798664 * q^71 + 17031575371776 * q^72 + 44383738947944 * q^73 - 19405526378100 * q^75 - 12879735685120 * q^76 + 74886492270632 * q^77 + 66217996893696 * q^78 + 6768600023040 * q^80 - 322723412222112 * q^81 + 6028717955584 * q^82 + 134272999400364 * q^83 + 145335752004880 * q^85 - 120635280450048 * q^86 + 68423417580480 * q^87 - 4289334345728 * q^88 + 112569467389440 * q^90 - 234891728536584 * q^91 - 39148896550912 * q^92 + 66751748435208 * q^93 + 26760204832400 * q^95 - 12060268167168 * q^96 + 167451300858216 * q^97 + 78801761769472 * q^98

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