LMFDB - Embedded newform 10.15.c.b.7.1

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			7.1
Root			$-148.763i$ of defining polynomial
Character	$\chi$	$=$	10.7
Dual form			10.15.c.b.3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(64.0000 + 64.0000i) q^{2} +(-2738.23 + 2738.23i) q^{3} +8192.00i q^{4} +(-76838.8 + 14117.8i) q^{5} -350493. q^{6} +(390848. + 390848. i) q^{7} +(-524288. + 524288. i) q^{8} -1.02128e7i q^{9} +O(q^{10})$	\(q+(64.0000 + 64.0000i) q^{2} +(-2738.23 + 2738.23i) q^{3} +8192.00i q^{4} +(-76838.8 + 14117.8i) q^{5} -350493. q^{6} +(390848. + 390848. i) q^{7} +(-524288. + 524288. i) q^{8} -1.02128e7i q^{9} +(-5.82123e6 - 4.01414e6i) q^{10} +2.58646e7 q^{11} +(-2.24316e7 - 2.24316e7i) q^{12} +(-4.31902e7 + 4.31902e7i) q^{13} +5.00286e7i q^{14} +(1.71744e8 - 2.49060e8i) q^{15} -6.71089e7 q^{16} +(-2.86750e8 - 2.86750e8i) q^{17} +(6.53621e8 - 6.53621e8i) q^{18} -9.14918e8i q^{19} +(-1.15653e8 - 6.29463e8i) q^{20} -2.14046e9 q^{21} +(1.65534e9 + 1.65534e9i) q^{22} +(-3.49403e9 + 3.49403e9i) q^{23} -2.87124e9i q^{24} +(5.70489e9 - 2.16960e9i) q^{25} -5.52835e9 q^{26} +(1.48682e10 + 1.48682e10i) q^{27} +(-3.20183e9 + 3.20183e9i) q^{28} +9.99929e9i q^{29} +(2.69315e10 - 4.94821e9i) q^{30} -2.36102e10 q^{31} +(-4.29497e9 - 4.29497e9i) q^{32} +(-7.08232e10 + 7.08232e10i) q^{33} -3.67039e10i q^{34} +(-3.55502e10 - 2.45144e10i) q^{35} +8.36635e10 q^{36} +(2.78948e10 + 2.78948e10i) q^{37} +(5.85547e10 - 5.85547e10i) q^{38} -2.36529e11i q^{39} +(3.28838e10 - 4.76875e10i) q^{40} +4.76492e10 q^{41} +(-1.36990e11 - 1.36990e11i) q^{42} +(6.06698e10 - 6.06698e10i) q^{43} +2.11883e11i q^{44} +(1.44183e11 + 7.84742e11i) q^{45} -4.47236e11 q^{46} +(-6.16788e11 - 6.16788e11i) q^{47} +(1.83759e11 - 1.83759e11i) q^{48} -3.72698e11i q^{49} +(5.03967e11 + 2.26259e11i) q^{50} +1.57037e12 q^{51} +(-3.53814e11 - 3.53814e11i) q^{52} +(-3.69698e11 + 3.69698e11i) q^{53} +1.90313e12i q^{54} +(-1.98741e12 + 3.65153e11i) q^{55} -4.09834e11 q^{56} +(2.50525e12 + 2.50525e12i) q^{57} +(-6.39955e11 + 6.39955e11i) q^{58} -1.87010e12i q^{59} +(2.04030e12 + 1.40693e12i) q^{60} -3.25369e12 q^{61} +(-1.51106e12 - 1.51106e12i) q^{62} +(3.99167e12 - 3.99167e12i) q^{63} -5.49756e11i q^{64} +(2.70893e12 - 3.92844e12i) q^{65} -9.06537e12 q^{66} +(5.83904e12 + 5.83904e12i) q^{67} +(2.34905e12 - 2.34905e12i) q^{68} -1.91349e13i q^{69} +(-7.06296e11 - 3.84414e12i) q^{70} -1.14270e13 q^{71} +(5.35446e12 + 5.35446e12i) q^{72} +(-3.16218e12 + 3.16218e12i) q^{73} +3.57054e12i q^{74} +(-9.68044e12 + 2.15621e13i) q^{75} +7.49501e12 q^{76} +(1.01091e13 + 1.01091e13i) q^{77} +(1.51379e13 - 1.51379e13i) q^{78} +2.36532e13i q^{79} +(5.15656e12 - 9.47433e11i) q^{80} -3.25774e13 q^{81} +(3.04955e12 + 3.04955e12i) q^{82} +(1.83109e13 - 1.83109e13i) q^{83} -1.75347e13i q^{84} +(2.60818e13 + 1.79852e13i) q^{85} +7.76573e12 q^{86} +(-2.73803e13 - 2.73803e13i) q^{87} +(-1.35605e13 + 1.35605e13i) q^{88} +6.00508e13i q^{89} +(-4.09957e13 + 5.94512e13i) q^{90} -3.37616e13 q^{91} +(-2.86231e13 - 2.86231e13i) q^{92} +(6.46502e13 - 6.46502e13i) q^{93} -7.89489e13i q^{94} +(1.29167e13 + 7.03012e13i) q^{95} +2.35212e13 q^{96} +(1.30900e12 + 1.30900e12i) q^{97} +(2.38527e13 - 2.38527e13i) q^{98} -2.64151e14i 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 $\left(\mathbb{Z}/10\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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
$3$	−2738.23	+	2738.23i	−1.25205	+	1.25205i	−0.297248	+	0.954800i	$0.596069\pi$
$3$	−2738.23	+	2738.23i	−1.25205	+	1.25205i	−0.954800	+	0.297248i	$0.903931\pi$
$4$			8192.00i			0.500000i
$5$	−76838.8	+	14117.8i	−0.983537	+	0.180708i
$5$	−76838.8	+	14117.8i	−0.983537	+	0.180708i
$6$	−350493.			−1.25205
$7$	390848.	+	390848.i	0.474594	+	0.474594i	0.903398	−	0.428804i	$-0.141065\pi$
$7$	390848.	+	390848.i	0.474594	+	0.474594i	−0.428804	+	0.903398i	$0.641065\pi$
$8$	−524288.	+	524288.i	−0.250000	+	0.250000i
$9$		−	1.02128e7i		−	2.13525i
$10$	−5.82123e6	−	4.01414e6i	−0.582123	−	0.401414i
$11$	2.58646e7			1.32726			0.663632	−	0.748059i	$-0.269014\pi$
$11$	2.58646e7			1.32726			0.663632	+	0.748059i	$0.269014\pi$
$12$	−2.24316e7	−	2.24316e7i	−0.626024	−	0.626024i
$13$	−4.31902e7	+	4.31902e7i	−0.688306	+	0.688306i	−0.961857	−	0.273551i	$-0.911802\pi$
$13$	−4.31902e7	+	4.31902e7i	−0.688306	+	0.688306i	0.273551	+	0.961857i	$0.411802\pi$
$14$			5.00286e7i			0.474594i
$15$	1.71744e8	−	2.49060e8i	1.00518	−	1.45769i
$16$	−6.71089e7			−0.250000
$17$	−2.86750e8	−	2.86750e8i	−0.698812	−	0.698812i	0.265342	−	0.964154i	$-0.414515\pi$
$17$	−2.86750e8	−	2.86750e8i	−0.698812	−	0.698812i	−0.964154	+	0.265342i	$0.914515\pi$
$18$	6.53621e8	−	6.53621e8i	1.06762	−	1.06762i
$19$		−	9.14918e8i		−	1.02354i	−0.859121	−	0.511772i	$-0.828989\pi$
$19$		−	9.14918e8i		−	1.02354i	0.859121	−	0.511772i	$-0.171011\pi$
$20$	−1.15653e8	−	6.29463e8i	−0.0903542	−	0.491768i
$21$	−2.14046e9			−1.18843
$22$	1.65534e9	+	1.65534e9i	0.663632	+	0.663632i
$23$	−3.49403e9	+	3.49403e9i	−1.02620	+	1.02620i	−0.0265531	+	0.999647i	$0.508453\pi$
$23$	−3.49403e9	+	3.49403e9i	−1.02620	+	1.02620i	−0.999647	+	0.0265531i	$0.991547\pi$
$24$		−	2.87124e9i		−	0.626024i
$25$	5.70489e9	−	2.16960e9i	0.934689	−	0.355467i
$26$	−5.52835e9			−0.688306
$27$	1.48682e10	+	1.48682e10i	1.42139	+	1.42139i
$28$	−3.20183e9	+	3.20183e9i	−0.237297	+	0.237297i
$29$			9.99929e9i			0.579673i	0.957076	+	0.289837i	$0.0936010\pi$
$29$			9.99929e9i			0.579673i	−0.957076	+	0.289837i	$0.906399\pi$
$30$	2.69315e10	−	4.94821e9i	1.23144	−	0.226256i
$31$	−2.36102e10			−0.858160			−0.429080	−	0.903266i	$-0.641162\pi$
$31$	−2.36102e10			−0.858160			−0.429080	+	0.903266i	$0.641162\pi$
$32$	−4.29497e9	−	4.29497e9i	−0.125000	−	0.125000i
$33$	−7.08232e10	+	7.08232e10i	−1.66180	+	1.66180i
$34$		−	3.67039e10i		−	0.698812i
$35$	−3.55502e10	−	2.45144e10i	−0.552543	−	0.381017i
$36$	8.36635e10			1.06762
$37$	2.78948e10	+	2.78948e10i	0.293840	+	0.293840i	0.838595	−	0.544755i	$-0.183377\pi$
$37$	2.78948e10	+	2.78948e10i	0.293840	+	0.293840i	−0.544755	+	0.838595i	$0.683377\pi$
$38$	5.85547e10	−	5.85547e10i	0.511772	−	0.511772i
$39$		−	2.36529e11i		−	1.72359i
$40$	3.28838e10	−	4.76875e10i	0.200707	−	0.291061i
$41$	4.76492e10			0.244663			0.122331	−	0.992489i	$-0.460963\pi$
$41$	4.76492e10			0.244663			0.122331	+	0.992489i	$0.460963\pi$
$42$	−1.36990e11	−	1.36990e11i	−0.594214	−	0.594214i
$43$	6.06698e10	−	6.06698e10i	0.223199	−	0.223199i	−0.586645	−	0.809844i	$-0.699552\pi$
$43$	6.06698e10	−	6.06698e10i	0.223199	−	0.223199i	0.809844	+	0.586645i	$0.199552\pi$
$44$			2.11883e11i			0.663632i
$45$	1.44183e11	+	7.84742e11i	0.385858	+	2.10010i
$46$	−4.47236e11			−1.02620
$47$	−6.16788e11	−	6.16788e11i	−1.21745	−	1.21745i	−0.968522	−	0.248928i	$-0.919922\pi$
$47$	−6.16788e11	−	6.16788e11i	−1.21745	−	1.21745i	−0.248928	−	0.968522i	$-0.580078\pi$
$48$	1.83759e11	−	1.83759e11i	0.313012	−	0.313012i
$49$		−	3.72698e11i		−	0.549522i
$50$	5.03967e11	+	2.26259e11i	0.645078	+	0.289611i
$51$	1.57037e12			1.74989
$52$	−3.53814e11	−	3.53814e11i	−0.344153	−	0.344153i
$53$	−3.69698e11	+	3.69698e11i	−0.314714	+	0.314714i	−0.846733	−	0.532019i	$-0.821434\pi$
$53$	−3.69698e11	+	3.69698e11i	−0.314714	+	0.314714i	0.532019	+	0.846733i	$0.321434\pi$
$54$			1.90313e12i			1.42139i
$55$	−1.98741e12	+	3.65153e11i	−1.30541	+	0.239848i
$56$	−4.09834e11			−0.237297
$57$	2.50525e12	+	2.50525e12i	1.28153	+	1.28153i
$58$	−6.39955e11	+	6.39955e11i	−0.289837	+	0.289837i
$59$		−	1.87010e12i		−	0.751450i	−0.926731	−	0.375725i	$-0.877394\pi$
$59$		−	1.87010e12i		−	0.751450i	0.926731	−	0.375725i	$-0.122606\pi$
$60$	2.04030e12	+	1.40693e12i	0.728845	+	0.502590i
$61$	−3.25369e12			−1.03530			−0.517651	−	0.855592i	$-0.673193\pi$
$61$	−3.25369e12			−1.03530			−0.517651	+	0.855592i	$0.673193\pi$
$62$	−1.51106e12	−	1.51106e12i	−0.429080	−	0.429080i
$63$	3.99167e12	−	3.99167e12i	1.01338	−	1.01338i
$64$		−	5.49756e11i		−	0.125000i
$65$	2.70893e12	−	3.92844e12i	0.552592	−	0.801357i
$66$	−9.06537e12			−1.66180
$67$	5.83904e12	+	5.83904e12i	0.963424	+	0.963424i	0.999354	−	0.0359302i	$-0.0114394\pi$
$67$	5.83904e12	+	5.83904e12i	0.963424	+	0.963424i	−0.0359302	+	0.999354i	$0.511439\pi$
$68$	2.34905e12	−	2.34905e12i	0.349406	−	0.349406i
$69$		−	1.91349e13i		−	2.56970i
$70$	−7.06296e11	−	3.84414e12i	−0.0857631	−	0.466780i
$71$	−1.14270e13			−1.25639			−0.628194	−	0.778057i	$-0.716205\pi$
$71$	−1.14270e13			−1.25639			−0.628194	+	0.778057i	$0.716205\pi$
$72$	5.35446e12	+	5.35446e12i	0.533812	+	0.533812i
$73$	−3.16218e12	+	3.16218e12i	−0.286237	+	0.286237i	−0.835590	−	0.549353i	$-0.814874\pi$
$73$	−3.16218e12	+	3.16218e12i	−0.286237	+	0.286237i	0.549353	+	0.835590i	$0.314874\pi$
$74$			3.57054e12i			0.293840i
$75$	−9.68044e12	+	2.15621e13i	−0.725214	+	1.61534i
$76$	7.49501e12			0.511772
$77$	1.01091e13	+	1.01091e13i	0.629911	+	0.629911i
$78$	1.51379e13	−	1.51379e13i	0.861793	−	0.861793i
$79$			2.36532e13i			1.23169i	0.787869	+	0.615843i	$0.211184\pi$
$79$			2.36532e13i			1.23169i	−0.787869	+	0.615843i	$0.788816\pi$
$80$	5.15656e12	−	9.47433e11i	0.245884	−	0.0451771i
$81$	−3.25774e13			−1.42404
$82$	3.04955e12	+	3.04955e12i	0.122331	+	0.122331i
$83$	1.83109e13	−	1.83109e13i	0.674783	−	0.674783i	−0.284032	−	0.958815i	$-0.591672\pi$
$83$	1.83109e13	−	1.83109e13i	0.674783	−	0.674783i	0.958815	+	0.284032i	$0.0916723\pi$
$84$		−	1.75347e13i		−	0.594214i
$85$	2.60818e13	+	1.79852e13i	0.813588	+	0.561026i
$86$	7.76573e12			0.223199
$87$	−2.73803e13	−	2.73803e13i	−0.725779	−	0.725779i
$88$	−1.35605e13	+	1.35605e13i	−0.331816	+	0.331816i
$89$			6.00508e13i			1.35765i	0.734299	+	0.678826i	$0.237511\pi$
$89$			6.00508e13i			1.35765i	−0.734299	+	0.678826i	$0.762489\pi$
$90$	−4.09957e13	+	5.94512e13i	−0.857119	+	1.24298i
$91$	−3.37616e13			−0.653332
$92$	−2.86231e13	−	2.86231e13i	−0.513100	−	0.513100i
$93$	6.46502e13	−	6.46502e13i	1.07446	−	1.07446i
$94$		−	7.89489e13i		−	1.21745i
$95$	1.29167e13	+	7.03012e13i	0.184963	+	1.00669i
$96$	2.35212e13			0.313012
$97$	1.30900e12	+	1.30900e12i	0.0162008	+	0.0162008i	0.715161	−	0.698960i	$-0.246353\pi$
$97$	1.30900e12	+	1.30900e12i	0.0162008	+	0.0162008i	−0.698960	+	0.715161i	$0.746353\pi$
$98$	2.38527e13	−	2.38527e13i	0.274761	−	0.274761i
$99$		−	2.64151e14i		−	2.83404i
$100$	1.77733e13	+	4.67344e13i	0.177733	+	0.467344i
$101$	−6.08529e13			−0.567586			−0.283793	−	0.958886i	$-0.591593\pi$
$101$	−6.08529e13			−0.567586			−0.283793	+	0.958886i	$0.591593\pi$
$102$	1.00504e14	+	1.00504e14i	0.874946	+	0.874946i
$103$	−2.07305e13	+	2.07305e13i	−0.168558	+	0.168558i	−0.786345	−	0.617787i	$-0.788029\pi$
$103$	−2.07305e13	+	2.07305e13i	−0.168558	+	0.168558i	0.617787	+	0.786345i	$0.288029\pi$
$104$		−	4.52882e13i		−	0.344153i
$105$	1.64471e14	−	3.02187e13i	1.16886	−	0.214759i
$106$	−4.73214e13			−0.314714
$107$	−3.67522e13	−	3.67522e13i	−0.228874	−	0.228874i	0.583348	−	0.812222i	$-0.301742\pi$
$107$	−3.67522e13	−	3.67522e13i	−0.228874	−	0.228874i	−0.812222	+	0.583348i	$0.801742\pi$
$108$	−1.21800e14	+	1.21800e14i	−0.710693	+	0.710693i
$109$			1.60641e14i			0.878763i	0.898301	+	0.439381i	$0.144802\pi$
$109$			1.60641e14i			0.878763i	−0.898301	+	0.439381i	$0.855198\pi$
$110$	−1.50564e14	−	1.03824e14i	−0.772630	−	0.532782i
$111$	−1.52765e14			−0.735804
$112$	−2.62294e13	−	2.62294e13i	−0.118648	−	0.118648i
$113$	−1.56665e14	+	1.56665e14i	−0.665923	+	0.665923i	−0.956770	−	0.290847i	$-0.906063\pi$
$113$	−1.56665e14	+	1.56665e14i	−0.665923	+	0.665923i	0.290847	+	0.956770i	$0.406063\pi$
$114$			3.20673e14i			1.28153i
$115$	2.19149e14	−	3.17806e14i	0.823863	−	1.19475i
$116$	−8.19142e13			−0.289837
$117$	4.41094e14	+	4.41094e14i	1.46971	+	1.46971i
$118$	1.19686e14	−	1.19686e14i	0.375725	−	0.375725i
$119$		−	2.24151e14i		−	0.663303i
$120$	4.05358e13	+	2.20623e14i	0.113128	+	0.615718i
$121$	2.89228e14			0.761629
$122$	−2.08236e14	−	2.08236e14i	−0.517651	−	0.517651i
$123$	−1.30474e14	+	1.30474e14i	−0.306330	+	0.306330i
$124$		−	1.93415e14i		−	0.429080i
$125$	−4.07727e14	+	2.47250e14i	−0.855065	+	0.518521i
$126$	5.10933e14			1.01338
$127$	6.99226e13	+	6.99226e13i	0.131217	+	0.131217i	0.769665	−	0.638448i	$-0.220423\pi$
$127$	6.99226e13	+	6.99226e13i	0.131217	+	0.131217i	−0.638448	+	0.769665i	$0.720423\pi$
$128$	3.51844e13	−	3.51844e13i	0.0625000	−	0.0625000i
$129$			3.32255e14i			0.558913i
$130$	4.24792e14	−	7.80484e13i	0.676975	−	0.124383i
$131$	−9.10870e14			−1.37581			−0.687903	−	0.725802i	$-0.741469\pi$
$131$	−9.10870e14			−1.37581			−0.687903	+	0.725802i	$0.741469\pi$
$132$	−5.80184e14	−	5.80184e14i	−0.830899	−	0.830899i
$133$	3.57594e14	−	3.57594e14i	0.485768	−	0.485768i
$134$			7.47397e14i			0.963424i
$135$	−1.35236e15	−	9.32548e14i	−1.65484	−	1.14113i
$136$	3.00679e14			0.349406
$137$	−8.64367e14	−	8.64367e14i	−0.954233	−	0.954233i	0.0447649	−	0.998998i	$-0.485746\pi$
$137$	−8.64367e14	−	8.64367e14i	−0.954233	−	0.954233i	−0.998998	+	0.0447649i	$0.985746\pi$
$138$	1.22464e15	−	1.22464e15i	1.28485	−	1.28485i
$139$			2.87503e14i			0.286774i	0.989667	+	0.143387i	$0.0457993\pi$
$139$			2.87503e14i			0.286774i	−0.989667	+	0.143387i	$0.954201\pi$
$140$	2.00822e14	−	2.91228e14i	0.190509	−	0.276272i
$141$	3.37781e15			3.04861
$142$	−7.31327e14	−	7.31327e14i	−0.628194	−	0.628194i
$143$	−1.11710e15	+	1.11710e15i	−0.913564	+	0.913564i
$144$			6.85371e14i			0.533812i
$145$	−1.41168e14	−	7.68334e14i	−0.104752	−	0.570130i
$146$	−4.04759e14			−0.286237
$147$	1.02053e15	+	1.02053e15i	0.688028	+	0.688028i
$148$	−2.28514e14	+	2.28514e14i	−0.146920	+	0.146920i
$149$			3.18002e14i			0.195041i	0.995234	+	0.0975206i	$0.0310912\pi$
$149$			3.18002e14i			0.195041i	−0.995234	+	0.0975206i	$0.968909\pi$
$150$	−1.99953e15	+	7.60429e14i	−1.17028	+	0.445062i
$151$	3.75936e14			0.210027			0.105014	−	0.994471i	$-0.466511\pi$
$151$	3.75936e14			0.210027			0.105014	+	0.994471i	$0.466511\pi$
$152$	4.79680e14	+	4.79680e14i	0.255886	+	0.255886i
$153$	−2.92852e15	+	2.92852e15i	−1.49214	+	1.49214i
$154$			1.29397e15i			0.629911i
$155$	1.81418e15	−	3.33326e14i	0.844032	−	0.155077i
$156$	1.93765e15			0.861793
$157$	2.17746e15	+	2.17746e15i	0.926088	+	0.926088i	0.997450	−	0.0713623i	$-0.0227347\pi$
$157$	2.17746e15	+	2.17746e15i	0.926088	+	0.926088i	−0.0713623	+	0.997450i	$0.522735\pi$
$158$	−1.51380e15	+	1.51380e15i	−0.615843	+	0.615843i
$159$		−	2.02464e15i		−	0.788074i
$160$	3.90656e14	+	2.69384e14i	0.145531	+	0.100354i
$161$	−2.73127e15			−0.974056
$162$	−2.08496e15	−	2.08496e15i	−0.712019	−	0.712019i
$163$	1.37234e15	−	1.37234e15i	0.448898	−	0.448898i	−0.446090	−	0.894988i	$-0.647184\pi$
$163$	1.37234e15	−	1.37234e15i	0.448898	−	0.448898i	0.894988	+	0.446090i	$0.147184\pi$
$164$			3.90342e14i			0.122331i
$165$	4.44210e15	−	6.44184e15i	1.33414	−	1.93474i
$166$	2.34380e15			0.674783
$167$	−1.95787e15	−	1.95787e15i	−0.540465	−	0.540465i	0.383200	−	0.923665i	$-0.374822\pi$
$167$	−1.95787e15	−	1.95787e15i	−0.540465	−	0.540465i	−0.923665	+	0.383200i	$0.874822\pi$
$168$	1.12222e15	−	1.12222e15i	0.297107	−	0.297107i
$169$			2.06589e14i			0.0524687i
$170$	5.18181e14	+	2.82029e15i	0.126281	+	0.687307i
$171$	−9.34390e15			−2.18552
$172$	4.97007e14	+	4.97007e14i	0.111600	+	0.111600i
$173$	−2.21333e15	+	2.21333e15i	−0.477226	+	0.477226i	−0.904243	−	0.427017i	$-0.859564\pi$
$173$	−2.21333e15	+	2.21333e15i	−0.477226	+	0.477226i	0.427017	+	0.904243i	$0.359564\pi$
$174$		−	3.50468e15i		−	0.725779i
$175$	3.07773e15	+	1.38176e15i	0.612300	+	0.274895i
$176$	−1.73574e15			−0.331816
$177$	5.12075e15	+	5.12075e15i	0.940851	+	0.940851i
$178$	−3.84325e15	+	3.84325e15i	−0.678826	+	0.678826i
$179$		−	5.21468e15i		−	0.885638i	−0.896611	−	0.442819i	$-0.853978\pi$
$179$		−	5.21468e15i		−	0.885638i	0.896611	−	0.442819i	$-0.146022\pi$
$180$	−6.42860e15	+	1.18115e15i	−1.05005	+	0.192929i
$181$	9.87054e15			1.55092			0.775462	−	0.631394i	$-0.217517\pi$
$181$	9.87054e15			1.55092			0.775462	+	0.631394i	$0.217517\pi$
$182$	−2.16074e15	−	2.16074e15i	−0.326666	−	0.326666i
$183$	8.90934e15	−	8.90934e15i	1.29625	−	1.29625i
$184$		−	3.66376e15i		−	0.513100i
$185$	−2.53722e15	−	1.74959e15i	−0.342102	−	0.235903i
$186$	8.27523e15			1.07446
$187$	−7.41666e15	−	7.41666e15i	−0.927507	−	0.927507i
$188$	5.05273e15	−	5.05273e15i	0.608725	−	0.608725i
$189$			1.16224e16i			1.34916i
$190$	−3.67261e15	+	5.32594e15i	−0.410865	+	0.595829i
$191$	−5.43402e15			−0.585987			−0.292994	−	0.956114i	$-0.594651\pi$
$191$	−5.43402e15			−0.585987			−0.292994	+	0.956114i	$0.594651\pi$
$192$	1.50536e15	+	1.50536e15i	0.156506	+	0.156506i
$193$	−9.76089e15	+	9.76089e15i	−0.978562	+	0.978562i	−0.999775	−	0.0212131i	$-0.993247\pi$
$193$	−9.76089e15	+	9.76089e15i	−0.978562	+	0.978562i	0.0212131	+	0.999775i	$0.493247\pi$
$194$			1.67552e14i			0.0162008i
$195$	3.33929e15	+	1.81746e16i	0.311466	+	1.69521i
$196$	3.05315e15			0.274761
$197$	−1.32529e15	−	1.32529e15i	−0.115093	−	0.115093i	0.647215	−	0.762308i	$-0.275934\pi$
$197$	−1.32529e15	−	1.32529e15i	−0.115093	−	0.115093i	−0.762308	+	0.647215i	$0.775934\pi$
$198$	1.69057e16	−	1.69057e16i	1.41702	−	1.41702i
$199$			1.35140e15i			0.109349i	0.998504	+	0.0546744i	$0.0174121\pi$
$199$			1.35140e15i			0.109349i	−0.998504	+	0.0546744i	$0.982588\pi$
$200$	−1.85351e15	+	4.12850e15i	−0.144806	+	0.322539i
$201$	−3.19772e16			−2.41251
$202$	−3.89459e15	−	3.89459e15i	−0.283793	−	0.283793i
$203$	−3.90820e15	+	3.90820e15i	−0.275109	+	0.275109i
$204$			1.28645e16i			0.874946i
$205$	−3.66130e15	+	6.72704e14i	−0.240635	+	0.0442127i
$206$	−2.65351e15			−0.168558
$207$	3.56840e16	+	3.56840e16i	2.19119	+	2.19119i
$208$	2.89845e15	−	2.89845e15i	0.172077	−	0.172077i
$209$		−	2.36640e16i		−	1.35851i
$210$	1.24601e16	+	8.59212e15i	0.691811	+	0.477052i
$211$	−7.46368e15			−0.400845			−0.200422	−	0.979710i	$-0.564231\pi$
$211$	−7.46368e15			−0.400845			−0.200422	+	0.979710i	$0.564231\pi$
$212$	−3.02857e15	−	3.02857e15i	−0.157357	−	0.157357i
$213$	3.12897e16	−	3.12897e16i	1.57306	−	1.57306i
$214$		−	4.70428e15i		−	0.228874i
$215$	−3.80527e15	+	5.51832e15i	−0.179191	+	0.259859i
$216$	−1.55904e16			−0.710693
$217$	−9.22802e15	−	9.22802e15i	−0.407277	−	0.407277i
$218$	−1.02810e16	+	1.02810e16i	−0.439381	+	0.439381i
$219$		−	1.73175e16i		−	0.716765i
$220$	−2.99133e15	−	1.62808e16i	−0.119924	−	0.652706i
$221$	2.47695e16			0.961993
$222$	−9.77695e15	−	9.77695e15i	−0.367902	−	0.367902i
$223$	1.25096e15	−	1.25096e15i	0.0456152	−	0.0456152i	−0.683931	−	0.729546i	$-0.739731\pi$
$223$	1.25096e15	−	1.25096e15i	0.0456152	−	0.0456152i	0.729546	+	0.683931i	$0.239731\pi$
$224$		−	3.35736e15i		−	0.118648i
$225$	−2.21577e16	−	5.82630e16i	−0.759010	−	1.99579i
$226$	−2.00532e16			−0.665923
$227$	3.98684e16	+	3.98684e16i	1.28365	+	1.28365i	0.938574	+	0.345079i	$0.112148\pi$
$227$	3.98684e16	+	3.98684e16i	1.28365	+	1.28365i	0.345079	+	0.938574i	$0.387852\pi$
$228$	−2.05230e16	+	2.05230e16i	−0.640764	+	0.640764i
$229$		−	1.48007e16i		−	0.448161i	−0.974571	−	0.224081i	$-0.928062\pi$
$229$		−	1.48007e16i		−	0.448161i	0.974571	−	0.224081i	$-0.0719379\pi$
$230$	3.43651e16	−	6.31401e15i	1.00931	−	0.185443i
$231$	−5.53623e16			−1.57736
$232$	−5.24251e15	−	5.24251e15i	−0.144918	−	0.144918i
$233$	−4.30267e16	+	4.30267e16i	−1.15411	+	1.15411i	−0.168388	+	0.985721i	$0.553856\pi$
$233$	−4.30267e16	+	4.30267e16i	−1.15411	+	1.15411i	−0.985721	+	0.168388i	$0.946144\pi$
$234$			5.64601e16i			1.46971i
$235$	5.61010e16	+	3.86855e16i	1.41741	+	0.977403i
$236$	1.53198e16			0.375725
$237$	−6.47678e16	−	6.47678e16i	−1.54213	−	1.54213i
$238$	1.43457e16	−	1.43457e16i	0.331652	−	0.331652i
$239$		−	5.45356e16i		−	1.22432i	−0.790734	−	0.612160i	$-0.790301\pi$
$239$		−	5.45356e16i		−	1.22432i	0.790734	−	0.612160i	$-0.209699\pi$
$240$	−1.15256e16	+	1.67141e16i	−0.251295	+	0.364423i
$241$	8.87225e16			1.87895			0.939473	−	0.342622i	$-0.111315\pi$
$241$	8.87225e16			1.87895			0.939473	+	0.342622i	$0.111315\pi$
$242$	1.85106e16	+	1.85106e16i	0.380814	+	0.380814i
$243$	1.80904e16	−	1.80904e16i	0.361579	−	0.361579i
$244$		−	2.66542e16i		−	0.517651i
$245$	5.26170e15	+	2.86377e16i	0.0993033	+	0.540475i
$246$	−1.67007e16			−0.306330
$247$	3.95155e16	+	3.95155e16i	0.704512	+	0.704512i
$248$	1.23786e16	−	1.23786e16i	0.214540	−	0.214540i
$249$			1.00279e17i			1.68972i
$250$	−4.19185e16	−	1.02705e16i	−0.686793	−	0.168272i
$251$	7.07067e16			1.12653			0.563267	−	0.826275i	$-0.309544\pi$
$251$	7.07067e16			1.12653			0.563267	+	0.826275i	$0.309544\pi$
$252$	3.26997e16	+	3.26997e16i	0.506688	+	0.506688i
$253$	−9.03718e16	+	9.03718e16i	−1.36204	+	1.36204i
$254$			8.95009e15i			0.131217i
$255$	−1.20665e17	+	2.21703e16i	−1.72108	+	0.316220i
$256$	4.50360e15			0.0625000
$257$	−6.40255e16	−	6.40255e16i	−0.864612	−	0.864612i	0.127258	−	0.991870i	$-0.459382\pi$
$257$	−6.40255e16	−	6.40255e16i	−0.864612	−	0.864612i	−0.991870	+	0.127258i	$0.959382\pi$
$258$	−2.12644e16	+	2.12644e16i	−0.279456	+	0.279456i
$259$			2.18053e16i			0.278909i
$260$	3.21818e16	+	2.21916e16i	0.400679	+	0.276296i
$261$	1.02121e17			1.23775
$262$	−5.82957e16	−	5.82957e16i	−0.687903	−	0.687903i
$263$	8.21414e16	−	8.21414e16i	0.943782	−	0.943782i	−0.0547197	−	0.998502i	$-0.517427\pi$
$263$	8.21414e16	−	8.21414e16i	0.943782	−	0.943782i	0.998502	+	0.0547197i	$0.0174265\pi$
$264$		−	7.42635e16i		−	0.830899i
$265$	2.31878e16	−	3.36265e16i	0.252661	−	0.366404i
$266$	4.57720e16			0.485768
$267$	−1.64433e17	−	1.64433e17i	−1.69985	−	1.69985i
$268$	−4.78334e16	+	4.78334e16i	−0.481712	+	0.481712i
$269$			1.39802e17i			1.37166i	0.727761	+	0.685830i	$0.240561\pi$
$269$			1.39802e17i			1.37166i	−0.727761	+	0.685830i	$0.759439\pi$
$270$	−2.68681e16	−	1.46234e17i	−0.256857	−	1.39799i
$271$	−5.23305e16			−0.487494			−0.243747	−	0.969839i	$-0.578377\pi$
$271$	−5.23305e16			−0.487494			−0.243747	+	0.969839i	$0.578377\pi$
$272$	1.92434e16	+	1.92434e16i	0.174703	+	0.174703i
$273$	9.24471e16	−	9.24471e16i	0.818003	−	0.818003i
$274$		−	1.10639e17i		−	0.954233i
$275$	1.47555e17	−	5.61158e16i	1.24058	−	0.471798i
$276$	1.56753e17			1.28485
$277$	−6.01815e16	−	6.01815e16i	−0.480955	−	0.480955i	0.424481	−	0.905437i	$-0.360456\pi$
$277$	−6.01815e16	−	6.01815e16i	−0.480955	−	0.480955i	−0.905437	+	0.424481i	$0.860456\pi$
$278$	−1.84002e16	+	1.84002e16i	−0.143387	+	0.143387i
$279$			2.41127e17i			1.83239i
$280$	3.14912e16	−	5.78598e15i	0.233390	−	0.0428815i
$281$	−5.68415e16			−0.410886			−0.205443	−	0.978669i	$-0.565864\pi$
$281$	−5.68415e16			−0.410886			−0.205443	+	0.978669i	$0.565864\pi$
$282$	2.16180e17	+	2.16180e17i	1.52431	+	1.52431i
$283$	−8.30468e16	+	8.30468e16i	−0.571239	+	0.571239i	−0.932475	−	0.361235i	$-0.882355\pi$
$283$	−8.30468e16	+	8.30468e16i	−0.571239	+	0.571239i	0.361235	+	0.932475i	$0.382355\pi$
$284$		−	9.36099e16i		−	0.628194i
$285$	−2.27870e17	−	1.57132e17i	−1.49201	−	1.02885i
$286$	−1.42989e17			−0.913564
$287$	1.86236e16	+	1.86236e16i	0.116115	+	0.116115i
$288$	−4.38638e16	+	4.38638e16i	−0.266906	+	0.266906i
$289$		−	3.92727e15i		−	0.0233241i
$290$	4.01386e16	−	5.82081e16i	0.232689	−	0.337441i
$291$	−7.16868e15			−0.0405684
$292$	−2.59045e16	−	2.59045e16i	−0.143119	−	0.143119i
$293$	−9.74311e16	+	9.74311e16i	−0.525562	+	0.525562i	−0.919246	−	0.393684i	$-0.871201\pi$
$293$	−9.74311e16	+	9.74311e16i	−0.525562	+	0.525562i	0.393684	+	0.919246i	$0.371201\pi$
$294$			1.30628e17i			0.688028i
$295$	2.64017e16	+	1.43696e17i	0.135793	+	0.739078i
$296$	−2.92498e16			−0.146920
$297$	3.84560e17	+	3.84560e17i	1.88655	+	1.88655i
$298$	−2.03521e16	+	2.03521e16i	−0.0975206	+	0.0975206i
$299$		−	3.01816e17i		−	1.41268i
$300$	−1.76637e17	−	7.93021e16i	−0.807669	−	0.362607i
$301$	4.74253e16			0.211858
$302$	2.40599e16	+	2.40599e16i	0.105014	+	0.105014i
$303$	1.66629e17	−	1.66629e17i	0.710645	−	0.710645i
$304$			6.13991e16i			0.255886i
$305$	2.50010e17	−	4.59351e16i	1.01826	−	0.187088i
$306$	−3.74851e17			−1.49214
$307$	−1.41363e17	−	1.41363e17i	−0.550006	−	0.550006i	0.376436	−	0.926443i	$-0.377149\pi$
$307$	−1.41363e17	−	1.41363e17i	−0.550006	−	0.550006i	−0.926443	+	0.376436i	$0.877149\pi$
$308$	−8.28141e16	+	8.28141e16i	−0.314955	+	0.314955i
$309$		−	1.13530e17i		−	0.422086i
$310$	1.37441e17	+	9.47748e16i	0.499555	+	0.344478i
$311$	4.77733e16			0.169771			0.0848854	−	0.996391i	$-0.472948\pi$
$311$	4.77733e16			0.169771			0.0848854	+	0.996391i	$0.472948\pi$
$312$	1.24010e17	+	1.24010e17i	0.430896	+	0.430896i
$313$	2.66266e17	−	2.66266e17i	0.904703	−	0.904703i	−0.0911355	−	0.995839i	$-0.529050\pi$
$313$	2.66266e17	−	2.66266e17i	0.904703	−	0.904703i	0.995839	+	0.0911355i	$0.0290496\pi$
$314$			2.78715e17i			0.926088i
$315$	−2.50361e17	+	3.63069e17i	−0.813566	+	1.17982i
$316$	−1.93767e17			−0.615843
$317$	−1.77217e17	−	1.77217e17i	−0.550921	−	0.550921i	0.375785	−	0.926707i	$-0.377373\pi$
$317$	−1.77217e17	−	1.77217e17i	−0.550921	−	0.550921i	−0.926707	+	0.375785i	$0.877373\pi$
$318$	1.29577e17	−	1.29577e17i	0.394037	−	0.394037i
$319$			2.58628e17i			0.769379i
$320$	7.76137e15	+	4.22426e16i	0.0225886	+	0.122942i
$321$	2.01272e17			0.573123
$322$	−1.74802e17	−	1.74802e17i	−0.487028	−	0.487028i
$323$	−2.62352e17	+	2.62352e17i	−0.715265	+	0.715265i
$324$		−	2.66874e17i		−	0.712019i
$325$	−1.52690e17	+	3.40101e17i	−0.398682	+	0.888022i
$326$	1.75659e17			0.448898
$327$	−4.39873e17	−	4.39873e17i	−1.10025	−	1.10025i
$328$	−2.49819e16	+	2.49819e16i	−0.0611657	+	0.0611657i
$329$		−	4.82141e17i		−	1.15559i
$330$	6.96573e17	−	1.27984e17i	1.63444	−	0.300301i
$331$	5.13674e17			1.18003			0.590013	−	0.807393i	$-0.299122\pi$
$331$	5.13674e17			1.18003			0.590013	+	0.807393i	$0.299122\pi$
$332$	1.50003e17	+	1.50003e17i	0.337391	+	0.337391i
$333$	2.84885e17	−	2.84885e17i	0.627422	−	0.627422i
$334$		−	2.50607e17i		−	0.540465i
$335$	−5.31099e17	−	3.66230e17i	−1.12166	−	0.773464i
$336$	1.43644e17			0.297107
$337$	2.13797e17	+	2.13797e17i	0.433103	+	0.433103i	0.889683	−	0.456579i	$-0.150926\pi$
$337$	2.13797e17	+	2.13797e17i	0.433103	+	0.433103i	−0.456579	+	0.889683i	$0.650926\pi$
$338$	−1.32217e16	+	1.32217e16i	−0.0262343	+	0.0262343i
$339$		−	8.57971e17i		−	1.66753i
$340$	−1.47335e17	+	2.13662e17i	−0.280513	+	0.406794i
$341$	−6.10670e17			−1.13901
$342$	−5.98010e17	−	5.98010e17i	−1.09276	−	1.09276i
$343$	4.10751e17	−	4.10751e17i	0.735393	−	0.735393i
$344$			6.36169e16i			0.111600i
$345$	2.70144e17	+	1.47031e18i	0.464367	+	2.52740i
$346$	−2.83307e17			−0.477226
$347$	2.60298e17	+	2.60298e17i	0.429699	+	0.429699i	0.888526	−	0.458827i	$-0.151730\pi$
$347$	2.60298e17	+	2.60298e17i	0.429699	+	0.429699i	−0.458827	+	0.888526i	$0.651730\pi$
$348$	2.24300e17	−	2.24300e17i	0.362889	−	0.362889i
$349$			6.48270e17i			1.02796i	0.857801	+	0.513982i	$0.171830\pi$
$349$			6.48270e17i			1.02796i	−0.857801	+	0.513982i	$0.828170\pi$
$350$	1.08542e17	+	2.85407e17i	0.168702	+	0.443597i
$351$	−1.28432e18			−1.95670
$352$	−1.11088e17	−	1.11088e17i	−0.165908	−	0.165908i
$353$	−4.05349e17	+	4.05349e17i	−0.593481	+	0.593481i	−0.938570	−	0.345089i	$-0.887849\pi$
$353$	−4.05349e17	+	4.05349e17i	−0.593481	+	0.593481i	0.345089	+	0.938570i	$0.387849\pi$
$354$			6.55456e17i			0.940851i
$355$	8.78036e17	−	1.61325e17i	1.23570	−	0.227040i
$356$	−4.91936e17			−0.678826
$357$	6.13777e17	+	6.13777e17i	0.830487	+	0.830487i
$358$	3.33740e17	−	3.33740e17i	0.442819	−	0.442819i
$359$			4.00926e17i			0.521678i	0.965382	+	0.260839i	$0.0839992\pi$
$359$			4.00926e17i			0.521678i	−0.965382	+	0.260839i	$0.916001\pi$
$360$	−4.87024e17	−	3.35837e17i	−0.621488	−	0.428560i
$361$	−3.80679e16			−0.0476440
$362$	6.31714e17	+	6.31714e17i	0.775462	+	0.775462i
$363$	−7.91974e17	+	7.91974e17i	−0.953596	+	0.953596i
$364$		−	2.76575e17i		−	0.326666i
$365$	1.98335e17	−	2.87621e17i	0.229799	−	0.333250i
$366$	1.14040e18			1.29625
$367$	6.57985e17	+	6.57985e17i	0.733759	+	0.733759i	0.971362	−	0.237603i	$-0.0763618\pi$
$367$	6.57985e17	+	6.57985e17i	0.733759	+	0.733759i	−0.237603	+	0.971362i	$0.576362\pi$
$368$	2.34481e17	−	2.34481e17i	0.256550	−	0.256550i
$369$		−	4.86633e17i		−	0.522416i
$370$	−5.04083e16	−	2.74356e17i	−0.0530994	−	0.289003i
$371$	−2.88992e17			−0.298723
$372$	5.29615e17	+	5.29615e17i	0.537229	+	0.537229i
$373$	−2.63316e16	+	2.63316e16i	−0.0262129	+	0.0262129i	−0.720092	−	0.693879i	$-0.755900\pi$
$373$	−2.63316e16	+	2.63316e16i	−0.0262129	+	0.0262129i	0.693879	+	0.720092i	$0.255900\pi$
$374$		−	9.49333e17i		−	0.927507i
$375$	4.39422e17	−	1.79348e18i	0.421369	−	1.71980i
$376$	6.46749e17			0.608725
$377$	−4.31871e17	−	4.31871e17i	−0.398993	−	0.398993i
$378$	−7.43835e17	+	7.43835e17i	−0.674581	+	0.674581i
$379$		−	4.53046e17i		−	0.403337i	−0.979454	−	0.201669i	$-0.935364\pi$
$379$		−	4.53046e17i		−	0.403337i	0.979454	−	0.201669i	$-0.0646364\pi$
$380$	−5.75907e17	+	1.05813e17i	−0.503347	+	0.0924816i
$381$	−3.82928e17			−0.328581
$382$	−3.47778e17	−	3.47778e17i	−0.292994	−	0.292994i
$383$	−9.71601e17	+	9.71601e17i	−0.803705	+	0.803705i	−0.983673	−	0.179968i	$-0.942401\pi$
$383$	−9.71601e17	+	9.71601e17i	−0.803705	+	0.803705i	0.179968	+	0.983673i	$0.442401\pi$
$384$			1.92686e17i			0.156506i
$385$	−9.19493e17	−	6.34055e17i	−0.733371	−	0.505710i
$386$	−1.24939e18			−0.978562
$387$	−6.19610e17	−	6.19610e17i	−0.476586	−	0.476586i
$388$	−1.07233e16	+	1.07233e16i	−0.00810041	+	0.00810041i
$389$			7.21780e17i			0.535497i	0.963489	+	0.267749i	$0.0862797\pi$
$389$			7.21780e17i			0.535497i	−0.963489	+	0.267749i	$0.913720\pi$
$390$	−9.49462e17	+	1.37689e18i	−0.691872	+	1.00334i
$391$	2.00382e18			1.43424
$392$	1.95401e17	+	1.95401e17i	0.137380	+	0.137380i
$393$	2.49417e18	−	2.49417e18i	1.72258	−	1.72258i
$394$		−	1.69637e17i		−	0.115093i
$395$	−3.33932e17	−	1.81748e18i	−0.222576	−	1.21141i
$396$	2.16392e18			1.41702
$397$	−2.20011e17	−	2.20011e17i	−0.141550	−	0.141550i	0.632781	−	0.774331i	$-0.281913\pi$
$397$	−2.20011e17	−	2.20011e17i	−0.141550	−	0.141550i	−0.774331	+	0.632781i	$0.781913\pi$
$398$	−8.64899e16	+	8.64899e16i	−0.0546744	+	0.0546744i
$399$			1.95835e18i			1.21641i
$400$	−3.82849e17	+	1.45599e17i	−0.233672	+	0.0888667i
$401$	−2.78349e18			−1.66947			−0.834736	−	0.550650i	$-0.814380\pi$
$401$	−2.78349e18			−1.66947			−0.834736	+	0.550650i	$0.814380\pi$
$402$	−2.04654e18	−	2.04654e18i	−1.20625	−	1.20625i
$403$	1.01973e18	−	1.01973e18i	0.590677	−	0.590677i
$404$		−	4.98507e17i		−	0.283793i
$405$	2.50321e18	−	4.59923e17i	1.40059	−	0.257336i
$406$	−5.00250e17			−0.275109
$407$	7.21488e17	+	7.21488e17i	0.390004	+	0.390004i
$408$	−8.23327e17	+	8.23327e17i	−0.437473	+	0.437473i
$409$			7.00247e17i			0.365753i	0.983136	+	0.182877i	$0.0585409\pi$
$409$			7.00247e17i			0.365753i	−0.983136	+	0.182877i	$0.941459\pi$
$410$	−2.77377e17	−	1.91270e17i	−0.142424	−	0.0982112i
$411$	4.73367e18			2.38949
$412$	−1.69825e17	−	1.69825e17i	−0.0842792	−	0.0842792i
$413$	7.30924e17	−	7.30924e17i	0.356633	−	0.356633i
$414$			4.56755e18i			2.19119i
$415$	−1.14848e18	+	1.66550e18i	−0.541734	+	0.785612i
$416$	3.71001e17			0.172077
$417$	−7.87250e17	−	7.87250e17i	−0.359054	−	0.359054i
$418$	1.51450e18	−	1.51450e18i	0.679257	−	0.679257i
$419$			2.39471e18i			1.05622i	0.849175	+	0.528111i	$0.177100\pi$
$419$			2.39471e18i			1.05622i	−0.849175	+	0.528111i	$0.822900\pi$
$420$	2.47552e17	+	1.34734e18i	0.107380	+	0.584431i
$421$	−1.56712e18			−0.668540			−0.334270	−	0.942477i	$-0.608490\pi$
$421$	−1.56712e18			−0.668540			−0.334270	+	0.942477i	$0.608490\pi$
$422$	−4.77676e17	−	4.77676e17i	−0.200422	−	0.200422i
$423$	−6.29915e18	+	6.29915e18i	−2.59956	+	2.59956i
$424$		−	3.87657e17i		−	0.157357i
$425$	−2.25800e18	−	1.01374e18i	−0.901576	−	0.404767i
$426$	4.00508e18			1.57306
$427$	−1.27170e18	−	1.27170e18i	−0.491348	−	0.491348i
$428$	3.01074e17	−	3.01074e17i	0.114437	−	0.114437i
$429$		−	6.11774e18i		−	2.28765i
$430$	−5.96709e17	+	1.09635e17i	−0.219525	+	0.0403340i
$431$	3.23068e18			1.16937			0.584686	−	0.811260i	$-0.301218\pi$
$431$	3.23068e18			1.16937			0.584686	+	0.811260i	$0.301218\pi$
$432$	−9.97788e17	−	9.97788e17i	−0.355347	−	0.355347i
$433$	−3.47325e18	+	3.47325e18i	−1.21709	+	1.21709i	−0.248438	+	0.968648i	$0.579917\pi$
$433$	−3.47325e18	+	3.47325e18i	−1.21709	+	1.21709i	−0.968648	+	0.248438i	$0.920083\pi$
$434$		−	1.18119e18i		−	0.407277i
$435$	2.49042e18	+	1.71732e18i	0.844984	+	0.582676i
$436$	−1.31597e18			−0.439381
$437$	3.19675e18	+	3.19675e18i	1.05036	+	1.05036i
$438$	1.10832e18	−	1.10832e18i	0.358383	−	0.358383i
$439$			2.30172e18i			0.732489i	0.930519	+	0.366245i	$0.119357\pi$
$439$			2.30172e18i			0.732489i	−0.930519	+	0.366245i	$0.880643\pi$
$440$	8.50528e17	−	1.23342e18i	0.266391	−	0.386315i
$441$	−3.80631e18			−1.17337
$442$	1.58525e18	+	1.58525e18i	0.480997	+	0.480997i
$443$	1.70852e18	−	1.70852e18i	0.510263	−	0.510263i	−0.404344	−	0.914607i	$-0.632500\pi$
$443$	1.70852e18	−	1.70852e18i	0.510263	−	0.510263i	0.914607	+	0.404344i	$0.132500\pi$
$444$		−	1.25145e18i		−	0.367902i
$445$	−8.47788e17	−	4.61423e18i	−0.245339	−	1.33530i
$446$	1.60123e17			0.0456152
$447$	−8.70763e17	−	8.70763e17i	−0.244201	−	0.244201i
$448$	2.14871e17	−	2.14871e17i	0.0593242	−	0.0593242i
$449$		−	2.17569e18i		−	0.591388i	−0.955283	−	0.295694i	$-0.904449\pi$
$449$		−	2.17569e18i		−	0.591388i	0.955283	−	0.295694i	$-0.0955509\pi$
$450$	2.31074e18	−	5.14693e18i	0.618392	−	1.37740i
$451$	1.23243e18			0.324732
$452$	−1.28340e18	−	1.28340e18i	−0.332961	−	0.332961i
$453$	−1.02940e18	+	1.02940e18i	−0.262964	+	0.262964i
$454$			5.10315e18i			1.28365i
$455$	2.59420e18	−	4.76642e17i	0.642576	−	0.118063i
$456$	−2.62695e18			−0.640764
$457$	1.29236e18	+	1.29236e18i	0.310435	+	0.310435i	0.845078	−	0.534643i	$-0.179554\pi$
$457$	1.29236e18	+	1.29236e18i	0.310435	+	0.310435i	−0.534643	+	0.845078i	$0.679554\pi$
$458$	9.47245e17	−	9.47245e17i	0.224081	−	0.224081i
$459$		−	8.52690e18i		−	1.98656i
$460$	2.60346e18	+	1.79527e18i	0.597375	+	0.411931i
$461$	3.77506e18			0.853135			0.426567	−	0.904456i	$-0.359723\pi$
$461$	3.77506e18			0.853135			0.426567	+	0.904456i	$0.359723\pi$
$462$	−3.54319e18	−	3.54319e18i	−0.788679	−	0.788679i
$463$	5.40083e17	−	5.40083e17i	0.118411	−	0.118411i	−0.645418	−	0.763830i	$-0.723317\pi$
$463$	5.40083e17	−	5.40083e17i	0.118411	−	0.118411i	0.763830	+	0.645418i	$0.223317\pi$
$464$		−	6.71041e17i		−	0.144918i
$465$	−4.05492e18	+	5.88037e18i	−0.862605	+	1.25093i
$466$	−5.50742e18			−1.15411
$467$	5.26588e18	+	5.26588e18i	1.08706	+	1.08706i	0.995830	+	0.0912289i	$0.0290795\pi$
$467$	5.26588e18	+	5.26588e18i	1.08706	+	1.08706i	0.0912289	+	0.995830i	$0.470920\pi$
$468$	−3.61344e18	+	3.61344e18i	−0.734853	+	0.734853i
$469$			4.56435e18i			0.914470i
$470$	1.11459e18	+	6.06634e18i	0.220003	+	1.19741i
$471$	−1.19248e19			−2.31901
$472$	9.80469e17	+	9.80469e17i	0.187862	+	0.187862i
$473$	1.56920e18	−	1.56920e18i	0.296245	−	0.296245i
$474$		−	8.29028e18i		−	1.54213i
$475$	−1.98500e18	−	5.21950e18i	−0.363836	−	0.956696i
$476$	1.83625e18			0.331652
$477$	3.77566e18	+	3.77566e18i	0.671993	+	0.671993i
$478$	3.49028e18	−	3.49028e18i	0.612160	−	0.612160i
$479$		−	6.76296e18i		−	1.16893i	−0.811419	−	0.584465i	$-0.801304\pi$
$479$		−	6.76296e18i		−	1.16893i	0.811419	−	0.584465i	$-0.198696\pi$
$480$	−1.80734e18	+	3.32069e17i	−0.307859	+	0.0565639i
$481$	−2.40957e18			−0.404504
$482$	5.67824e18	+	5.67824e18i	0.939473	+	0.939473i
$483$	7.47885e18	−	7.47885e18i	1.21957	−	1.21957i
$484$			2.36936e18i			0.380814i
$485$	−1.19062e17	−	8.21016e16i	−0.0188617	−	0.0130065i
$486$	2.31557e18			0.361579
$487$	−7.54039e18	−	7.54039e18i	−1.16062	−	1.16062i	−0.984340	−	0.176283i	$-0.943593\pi$
$487$	−7.54039e18	−	7.54039e18i	−1.16062	−	1.16062i	−0.176283	−	0.984340i	$-0.556407\pi$
$488$	1.70587e18	−	1.70587e18i	0.258826	−	0.258826i
$489$			7.51555e18i			1.12408i
$490$	−1.49606e18	+	2.16956e18i	−0.220586	+	0.319889i
$491$	−1.15594e18			−0.168021			−0.0840104	−	0.996465i	$-0.526773\pi$
$491$	−1.15594e18			−0.168021			−0.0840104	+	0.996465i	$0.526773\pi$
$492$	−1.06885e18	−	1.06885e18i	−0.153165	−	0.153165i
$493$	2.86729e18	−	2.86729e18i	0.405082	−	0.405082i
$494$			5.05798e18i			0.704512i
$495$	3.72924e18	+	2.02970e19i	0.512135	+	2.78738i
$496$	1.58446e18			0.214540
$497$	−4.46622e18	−	4.46622e18i	−0.596273	−	0.596273i
$498$	−6.41786e18	+	6.41786e18i	−0.844860	+	0.844860i
$499$			1.00572e19i			1.30549i	0.757576	+	0.652747i	$0.226384\pi$
$499$			1.00572e19i			1.30549i	−0.757576	+	0.652747i	$0.773616\pi$
$500$	−2.02547e18	−	3.34010e18i	−0.259260	−	0.427532i
$501$	1.07222e19			1.35338
$502$	4.52523e18	+	4.52523e18i	0.563267	+	0.563267i
$503$	−1.38272e18	+	1.38272e18i	−0.169730	+	0.169730i	−0.786861	−	0.617130i	$-0.788295\pi$
$503$	−1.38272e18	+	1.38272e18i	−0.169730	+	0.169730i	0.617130	+	0.786861i	$0.288295\pi$
$504$			4.18557e18i			0.506688i
$505$	4.67587e18	−	8.59112e17i	0.558242	−	0.102568i
$506$	−1.15676e19			−1.36204
$507$	−5.65688e17	−	5.65688e17i	−0.0656933	−	0.0656933i
$508$	−5.72806e17	+	5.72806e17i	−0.0656087	+	0.0656087i
$509$			1.02324e19i			1.15598i	0.816042	+	0.577992i	$0.196164\pi$
$509$			1.02324e19i			1.15598i	−0.816042	+	0.577992i	$0.803836\pi$
$510$	−9.14149e18	−	6.30369e18i	−1.01865	−	0.702431i
$511$	−2.47186e18			−0.271693
$512$	2.88230e17	+	2.88230e17i	0.0312500	+	0.0312500i
$513$	1.36032e19	−	1.36032e19i	1.45485	−	1.45485i
$514$		−	8.19527e18i		−	0.864612i
$515$	1.30024e18	−	1.88558e18i	0.135323	−	0.196243i
$516$	−2.72184e18			−0.279456
$517$	−1.59530e19	−	1.59530e19i	−1.61588	−	1.61588i
$518$	−1.39554e18	+	1.39554e18i	−0.139455	+	0.139455i
$519$		−	1.21212e19i		−	1.19502i
$520$	6.39372e17	+	3.47989e18i	0.0621914	+	0.338487i
$521$	9.66610e18			0.927656			0.463828	−	0.885925i	$-0.346475\pi$
$521$	9.66610e18			0.927656			0.463828	+	0.885925i	$0.346475\pi$
$522$	6.53575e18	+	6.53575e18i	0.618873	+	0.618873i
$523$	9.04084e18	−	9.04084e18i	0.844689	−	0.844689i	−0.144775	−	0.989465i	$-0.546246\pi$
$523$	9.04084e18	−	9.04084e18i	0.844689	−	0.844689i	0.989465	+	0.144775i	$0.0462459\pi$
$524$		−	7.46185e18i		−	0.687903i
$525$	−1.22111e19	+	4.64394e18i	−1.11081	+	0.422447i
$526$	1.05141e19			0.943782
$527$	6.77022e18	+	6.77022e18i	0.599693	+	0.599693i
$528$	4.75287e18	−	4.75287e18i	0.415449	−	0.415449i
$529$		−	1.28237e19i		−	1.10618i
$530$	3.63612e18	−	6.68076e17i	0.309533	−	0.0568715i
$531$	−1.90990e19			−1.60453
$532$	2.92941e18	+	2.92941e18i	0.242884	+	0.242884i
$533$	−2.05798e18	+	2.05798e18i	−0.168403	+	0.168403i
$534$		−	2.10474e19i		−	1.69985i
$535$	3.34286e18	+	2.30513e18i	0.266466	+	0.183747i
$536$	−6.12267e18			−0.481712
$537$	1.42790e19	+	1.42790e19i	1.10886	+	1.10886i
$538$	−8.94731e18	+	8.94731e18i	−0.685830	+	0.685830i
$539$		−	9.63970e18i		−	0.729360i
$540$	7.63943e18	−	1.10785e19i	0.570564	−	0.827421i
$541$	−2.05890e19			−1.51794			−0.758970	−	0.651126i	$-0.774297\pi$
$541$	−2.05890e19			−1.51794			−0.758970	+	0.651126i	$0.774297\pi$
$542$	−3.34915e18	−	3.34915e18i	−0.243747	−	0.243747i
$543$	−2.70278e19	+	2.70278e19i	−1.94183	+	1.94183i
$544$			2.46316e18i			0.174703i
$545$	−2.26791e18	−	1.23435e19i	−0.158800	−	0.864296i
$546$	1.18332e19			0.818003
$547$	−7.99634e18	−	7.99634e18i	−0.545733	−	0.545733i	0.379471	−	0.925204i	$-0.376106\pi$
$547$	−7.99634e18	−	7.99634e18i	−0.545733	−	0.545733i	−0.925204	+	0.379471i	$0.876106\pi$
$548$	7.08090e18	−	7.08090e18i	0.477116	−	0.477116i
$549$			3.32294e19i			2.21063i
$550$	1.30349e19	+	5.85209e18i	0.856188	+	0.384390i
$551$	9.14853e18			0.593321
$552$	1.00322e19	+	1.00322e19i	0.642426	+	0.642426i
$553$	−9.24480e18	+	9.24480e18i	−0.584550	+	0.584550i
$554$		−	7.70323e18i		−	0.480955i
$555$	1.17383e19	−	2.15671e18i	0.723691	−	0.132966i
$556$	−2.35523e18			−0.143387
$557$	−4.61244e18	−	4.61244e18i	−0.277296	−	0.277296i	0.554732	−	0.832029i	$-0.312821\pi$
$557$	−4.61244e18	−	4.61244e18i	−0.277296	−	0.277296i	−0.832029	+	0.554732i	$0.812821\pi$
$558$	−1.54321e19	+	1.54321e19i	−0.916193	+	0.916193i
$559$			5.24068e18i			0.307259i
$560$	2.38574e18	+	1.64513e18i	0.138136	+	0.0952543i
$561$	4.06171e19			2.32257
$562$	−3.63786e18	−	3.63786e18i	−0.205443	−	0.205443i
$563$	−8.44825e18	+	8.44825e18i	−0.471203	+	0.471203i	−0.902304	−	0.431101i	$-0.858125\pi$
$563$	−8.44825e18	+	8.44825e18i	−0.471203	+	0.471203i	0.431101	+	0.902304i	$0.358125\pi$
$564$			2.76711e19i			1.52431i
$565$	9.82620e18	−	1.42498e19i	0.534622	−	0.775297i
$566$	−1.06300e19			−0.571239
$567$	−1.27328e19	−	1.27328e19i	−0.675840	−	0.675840i
$568$	5.99103e18	−	5.99103e18i	0.314097	−	0.314097i
$569$			3.20525e19i			1.65988i	0.557854	+	0.829939i	$0.311625\pi$
$569$			3.20525e19i			1.65988i	−0.557854	+	0.829939i	$0.688375\pi$
$570$	−4.52721e18	−	2.46401e19i	−0.231583	−	1.26043i
$571$	1.71195e19			0.865045			0.432522	−	0.901623i	$-0.357624\pi$
$571$	1.71195e19			0.865045			0.432522	+	0.901623i	$0.357624\pi$
$572$	−9.15127e18	−	9.15127e18i	−0.456782	−	0.456782i
$573$	1.48796e19	−	1.48796e19i	0.733684	−	0.733684i
$574$			2.38382e18i			0.116115i
$575$	−1.23524e19	+	2.75137e19i	−0.594398	+	1.32396i
$576$	−5.61456e18			−0.266906
$577$	2.34153e19	+	2.34153e19i	1.09969	+	1.09969i	0.994447	+	0.105242i	$0.0335618\pi$
$577$	2.34153e19	+	2.34153e19i	1.09969	+	1.09969i	0.105242	+	0.994447i	$0.466438\pi$
$578$	2.51345e17	−	2.51345e17i	0.0116621	−	0.0116621i
$579$		−	5.34551e19i		−	2.45041i
$580$	6.29419e18	−	1.15645e18i	0.285065	−	0.0523759i
$581$	1.43136e19			0.640495
$582$	−4.58795e17	−	4.58795e17i	−0.0202842	−	0.0202842i
$583$	−9.56210e18	+	9.56210e18i	−0.417709	+	0.417709i
$584$		−	3.31578e18i		−	0.143119i
$585$	−4.01205e19	−	2.76658e19i	−1.71110	−	1.17992i
$586$	−1.24712e19			−0.525562
$587$	−2.82947e19	−	2.82947e19i	−1.17825	−	1.17825i	−0.980189	−	0.198063i	$-0.936535\pi$
$587$	−2.82947e19	−	2.82947e19i	−1.17825	−	1.17825i	−0.198063	−	0.980189i	$-0.563465\pi$
$588$	−8.36021e18	+	8.36021e18i	−0.344014	+	0.344014i
$589$			2.16014e19i			0.878366i
$590$	−7.50683e18	+	1.08863e19i	−0.301642	+	0.437436i
$591$	7.25790e18			0.288203
$592$	−1.87199e18	−	1.87199e18i	−0.0734601	−	0.0734601i
$593$	−2.61829e19	+	2.61829e19i	−1.01540	+	1.01540i	−0.0155160	+	0.999880i	$0.504939\pi$
$593$	−2.61829e19	+	2.61829e19i	−1.01540	+	1.01540i	−0.999880	+	0.0155160i	$0.995061\pi$
$594$			4.92237e19i			1.88655i
$595$	3.16453e18	+	1.72235e19i	0.119865	+	0.652383i
$596$	−2.60508e18			−0.0975206
$597$	−3.70045e18	−	3.70045e18i	−0.136910	−	0.136910i
$598$	1.93162e19	−	1.93162e19i	0.706340	−	0.706340i
$599$		−	3.02937e19i		−	1.09487i	−0.836847	−	0.547437i	$-0.815604\pi$
$599$		−	3.02937e19i		−	1.09487i	0.836847	−	0.547437i	$-0.184396\pi$
$600$	−6.22944e18	−	1.63801e19i	−0.222531	−	0.585138i
$601$	3.29522e19			1.16349			0.581746	−	0.813370i	$-0.302370\pi$
$601$	3.29522e19			1.16349			0.581746	+	0.813370i	$0.302370\pi$
$602$	3.03522e18	+	3.03522e18i	0.105929	+	0.105929i
$603$	5.96331e19	−	5.96331e19i	2.05715	−	2.05715i
$604$			3.07967e18i			0.105014i
$605$	−2.22240e19	+	4.08328e18i	−0.749090	+	0.137633i
$606$	2.13285e19			0.710645
$607$	−2.01165e19	−	2.01165e19i	−0.662571	−	0.662571i	0.293414	−	0.955985i	$-0.405209\pi$
$607$	−2.01165e19	−	2.01165e19i	−0.662571	−	0.662571i	−0.955985	+	0.293414i	$0.905209\pi$
$608$	−3.92954e18	+	3.92954e18i	−0.127943	+	0.127943i
$609$		−	2.14031e19i		−	0.688900i
$610$	1.89405e19	+	1.30608e19i	0.602673	+	0.415585i
$611$	5.32784e19			1.67596
$612$	−2.39905e19	−	2.39905e19i	−0.746069	−	0.746069i
$613$	1.45030e19	−	1.45030e19i	0.445897	−	0.445897i	−0.448091	−	0.893988i	$-0.647896\pi$
$613$	1.45030e19	−	1.45030e19i	0.445897	−	0.445897i	0.893988	+	0.448091i	$0.147896\pi$
$614$		−	1.80945e19i		−	0.550006i
$615$	8.18347e18	−	1.18675e19i	0.245930	−	0.356643i
$616$	−1.06002e19			−0.314955
$617$	1.32093e18	+	1.32093e18i	0.0388047	+	0.0388047i	0.726243	−	0.687438i	$-0.241265\pi$
$617$	1.32093e18	+	1.32093e18i	0.0388047	+	0.0388047i	−0.687438	+	0.726243i	$0.741265\pi$
$618$	7.26592e18	−	7.26592e18i	0.211043	−	0.211043i
$619$			3.22604e19i			0.926477i	0.886234	+	0.463239i	$0.153313\pi$
$619$			3.22604e19i			0.926477i	−0.886234	+	0.463239i	$0.846687\pi$
$620$	2.73060e18	+	1.48618e19i	0.0775384	+	0.422016i
$621$	−1.03900e20			−2.91725
$622$	3.05749e18	+	3.05749e18i	0.0848854	+	0.0848854i
$623$	−2.34707e19	+	2.34707e19i	−0.644333	+	0.644333i
$624$			1.58732e19i			0.430896i
$625$	2.78386e19	−	2.47546e19i	0.747287	−	0.664502i
$626$	3.40821e19			0.904703
$627$	6.47974e19	+	6.47974e19i	1.70092	+	1.70092i
$628$	−1.78377e19	+	1.78377e19i	−0.463044	+	0.463044i
$629$		−	1.59976e19i		−	0.410678i
$630$	−3.92595e19	+	7.21328e18i	−0.996692	+	0.183126i
$631$	−5.77137e19			−1.44902			−0.724509	−	0.689266i	$-0.757933\pi$
$631$	−5.77137e19			−1.44902			−0.724509	+	0.689266i	$0.757933\pi$
$632$	−1.24011e19	−	1.24011e19i	−0.307921	−	0.307921i
$633$	2.04373e19	−	2.04373e19i	0.501877	−	0.501877i
$634$		−	2.26837e19i		−	0.550921i
$635$	−6.35993e18	−	4.38561e18i	−0.152769	−	0.105345i
$636$	1.65858e19			0.394037
$637$	1.60969e19	+	1.60969e19i	0.378239	+	0.378239i
$638$	−1.65522e19	+	1.65522e19i	−0.384690	+	0.384690i
$639$			1.16702e20i			2.68270i
$640$	−2.20680e18	+	3.20025e18i	−0.0501768	+	0.0727653i
$641$	−2.57726e19			−0.579632			−0.289816	−	0.957082i	$-0.593594\pi$
$641$	−2.57726e19			−0.579632			−0.289816	+	0.957082i	$0.593594\pi$
$642$	1.28814e19	+	1.28814e19i	0.286561	+	0.286561i
$643$	−5.35402e19	+	5.35402e19i	−1.17816	+	1.17816i	−0.197945	+	0.980213i	$0.563427\pi$
$643$	−5.35402e19	+	5.35402e19i	−1.17816	+	1.17816i	−0.980213	+	0.197945i	$0.936573\pi$
$644$		−	2.23746e19i		−	0.487028i
$645$	−4.69073e18	−	2.55301e19i	−0.101000	−	0.549711i
$646$	−3.35811e19			−0.715265
$647$	2.01317e19	+	2.01317e19i	0.424180	+	0.424180i	0.886640	−	0.462460i	$-0.153033\pi$
$647$	2.01317e19	+	2.01317e19i	0.424180	+	0.424180i	−0.462460	+	0.886640i	$0.653033\pi$
$648$	1.70800e19	−	1.70800e19i	0.356010	−	0.356010i
$649$		−	4.83693e19i		−	0.997372i
$650$	−3.15386e19	+	1.19943e19i	−0.643352	+	0.244670i
$651$	5.05369e19			1.01986
$652$	1.12422e19	+	1.12422e19i	0.224449	+	0.224449i
$653$	1.99974e19	−	1.99974e19i	0.394985	−	0.394985i	−0.481475	−	0.876460i	$-0.659899\pi$
$653$	1.99974e19	−	1.99974e19i	0.394985	−	0.394985i	0.876460	+	0.481475i	$0.159899\pi$
$654$		−	5.63037e19i		−	1.10025i
$655$	6.99902e19	−	1.28595e19i	1.35316	−	0.248620i
$656$	−3.19768e18			−0.0611657
$657$	3.22948e19	+	3.22948e19i	0.611188	+	0.611188i
$658$	3.08570e19	−	3.08570e19i	0.577794	−	0.577794i
$659$		−	6.37504e19i		−	1.18110i	−0.807002	−	0.590548i	$-0.798912\pi$
$659$		−	6.37504e19i		−	1.18110i	0.807002	−	0.590548i	$-0.201088\pi$
$660$	5.27716e19	+	3.63897e19i	0.967370	+	0.667069i
$661$	−3.89116e19			−0.705779			−0.352889	−	0.935665i	$-0.614801\pi$
$661$	−3.89116e19			−0.705779			−0.352889	+	0.935665i	$0.614801\pi$
$662$	3.28752e19	+	3.28752e19i	0.590013	+	0.590013i
$663$	−6.78247e19	+	6.78247e19i	−1.20446	+	1.20446i
$664$			1.92004e19i			0.337391i
$665$	−2.24286e19	+	3.25256e19i	−0.389988	+	0.565553i
$666$	3.64653e19			0.627422
$667$	−3.49379e19	−	3.49379e19i	−0.594861	−	0.594861i
$668$	1.60388e19	−	1.60388e19i	0.270232	−	0.270232i
$669$			6.85083e18i			0.114225i
$670$	−1.05516e19	−	5.74291e19i	−0.174099	−	0.947563i
$671$	−8.41554e19			−1.37412
$672$	9.19322e18	+	9.19322e18i	0.148553	+	0.148553i
$673$	2.95436e19	−	2.95436e19i	0.472452	−	0.472452i	−0.430255	−	0.902707i	$-0.641576\pi$
$673$	2.95436e19	−	2.95436e19i	0.472452	−	0.472452i	0.902707	+	0.430255i	$0.141576\pi$
$674$			2.73660e19i			0.433103i
$675$	1.17079e20	+	5.25634e19i	1.83381	+	0.823298i
$676$	−1.69238e18			−0.0262343
$677$	−6.62167e19	−	6.62167e19i	−1.01589	−	1.01589i	−0.999872	−	0.0160179i	$-0.994901\pi$
$677$	−6.62167e19	−	6.62167e19i	−1.01589	−	1.01589i	−0.0160179	−	0.999872i	$-0.505099\pi$
$678$	5.49102e19	−	5.49102e19i	0.833767	−	0.833767i
$679$			1.02324e18i			0.0153776i
$680$	−2.31038e19	+	4.24494e18i	−0.343654	+	0.0631406i
$681$	−2.18338e20			−3.21439
$682$	−3.90829e19	−	3.90829e19i	−0.569503	−	0.569503i
$683$	−1.68519e19	+	1.68519e19i	−0.243054	+	0.243054i	−0.818112	−	0.575058i	$-0.804979\pi$
$683$	−1.68519e19	+	1.68519e19i	−0.243054	+	0.243054i	0.575058	+	0.818112i	$0.304979\pi$
$684$		−	7.65452e19i		−	1.09276i
$685$	7.86199e19	+	5.42139e19i	1.11096	+	0.766085i
$686$	5.25761e19			0.735393
$687$	4.05277e19	+	4.05277e19i	0.561119	+	0.561119i
$688$	−4.07148e18	+	4.07148e18i	−0.0557999	+	0.0557999i
$689$		−	3.19347e19i		−	0.433239i
$690$	−7.68103e19	+	1.11389e20i	−1.03152	+	1.49588i
$691$	2.00704e19			0.266814			0.133407	−	0.991061i	$-0.457408\pi$
$691$	2.00704e19			0.266814			0.133407	+	0.991061i	$0.457408\pi$
$692$	−1.81316e19	−	1.81316e19i	−0.238613	−	0.238613i
$693$	1.03243e20	−	1.03243e20i	1.34502	−	1.34502i
$694$			3.33181e19i			0.429699i
$695$	−4.05893e18	−	2.20914e19i	−0.0518224	−	0.282052i
$696$	2.87104e19			0.362889
$697$	−1.36634e19	−	1.36634e19i	−0.170973	−	0.170973i
$698$	−4.14892e19	+	4.14892e19i	−0.513982	+	0.513982i
$699$		−	2.35634e20i		−	2.89000i
$700$	−1.13194e19	+	2.52128e19i	−0.137448	+	0.306150i
$701$	1.46400e20			1.76001			0.880005	−	0.474965i	$-0.157539\pi$
$701$	1.46400e20			1.76001			0.880005	+	0.474965i	$0.157539\pi$
$702$	−8.21966e19	−	8.21966e19i	−0.978349	−	0.978349i
$703$	2.55215e19	−	2.55215e19i	0.300759	−	0.300759i
$704$		−	1.42192e19i		−	0.165908i
$705$	−2.59547e20	+	4.76875e19i	−2.99842	+	0.550910i
$706$	−5.18847e19			−0.593481
$707$	−2.37843e19	−	2.37843e19i	−0.269373	−	0.269373i
$708$	−4.19492e19	+	4.19492e19i	−0.470425	+	0.470425i
$709$			8.85163e19i			0.982878i	0.870912	+	0.491439i	$0.163529\pi$
$709$			8.85163e19i			0.982878i	−0.870912	+	0.491439i	$0.836471\pi$
$710$	6.65191e19	+	4.58696e19i	0.731371	+	0.504331i
$711$	2.41566e20			2.62996
$712$	−3.14839e19	−	3.14839e19i	−0.339413	−	0.339413i
$713$	8.24950e19	−	8.24950e19i	0.880645	−	0.880645i
$714$			7.85635e19i			0.830487i
$715$	7.00654e19	−	1.01607e20i	0.733435	−	1.06361i
$716$	4.27187e19			0.442819
$717$	1.49331e20	+	1.49331e20i	1.53291	+	1.53291i
$718$	−2.56592e19	+	2.56592e19i	−0.260839	+	0.260839i
$719$			1.46920e20i			1.47904i	0.673134	+	0.739520i	$0.264948\pi$
$719$			1.46920e20i			1.47904i	−0.673134	+	0.739520i	$0.735052\pi$
$720$	−9.67597e18	−	5.26631e19i	−0.0964644	−	0.525024i
$721$	−1.62050e19			−0.159993
$722$	−2.43634e18	−	2.43634e18i	−0.0238220	−	0.0238220i
$723$	−2.42943e20	+	2.42943e20i	−2.35253	+	2.35253i
$724$			8.08594e19i			0.775462i
$725$	2.16944e19	+	5.70448e19i	0.206055	+	0.541814i
$726$	−1.01373e20			−0.953596
$727$	−6.20201e19	−	6.20201e19i	−0.577818	−	0.577818i	0.356483	−	0.934302i	$-0.383976\pi$
$727$	−6.20201e19	−	6.20201e19i	−0.577818	−	0.577818i	−0.934302	+	0.356483i	$0.883976\pi$
$728$	1.77008e19	−	1.77008e19i	0.163333	−	0.163333i
$729$		−	5.67458e19i		−	0.518610i
$730$	3.11012e19	−	5.71432e18i	0.281525	−	0.0517255i
$731$	−3.47941e19			−0.311949
$732$	7.29853e19	+	7.29853e19i	0.648124	+	0.648124i
$733$	7.25212e19	−	7.25212e19i	0.637878	−	0.637878i	−0.312154	−	0.950032i	$-0.601050\pi$
$733$	7.25212e19	−	7.25212e19i	0.637878	−	0.637878i	0.950032	+	0.312154i	$0.101050\pi$
$734$			8.42221e19i			0.733759i
$735$	−9.28243e19	−	6.40088e19i	−0.801033	−	0.552368i
$736$	3.00135e19			0.256550
$737$	1.51024e20	+	1.51024e20i	1.27872	+	1.27872i
$738$	3.11445e19	−	3.11445e19i	0.261208	−	0.261208i
$739$			1.92493e20i			1.59920i	0.600533	+	0.799600i	$0.294955\pi$
$739$			1.92493e20i			1.59920i	−0.600533	+	0.799600i	$0.705045\pi$
$740$	1.43326e19	−	2.07849e19i	0.117952	−	0.171051i
$741$	−2.16405e20			−1.76417
$742$	−1.84955e19	−	1.84955e19i	−0.149361	−	0.149361i
$743$	1.27945e20	−	1.27945e20i	1.02354	−	1.02354i	0.0238197	−	0.999716i	$-0.492417\pi$
$743$	1.27945e20	−	1.27945e20i	1.02354	−	1.02354i	0.999716	−	0.0238197i	$-0.00758277\pi$
$744$			6.77907e19i			0.537229i
$745$	−4.48951e18	−	2.44349e19i	−0.0352456	−	0.191830i
$746$	−3.37045e18			−0.0262129
$747$	−1.87006e20	−	1.87006e20i	−1.44083	−	1.44083i
$748$	6.07573e19	−	6.07573e19i	0.463754	−	0.463754i
$749$		−	2.87291e19i		−	0.217244i
$750$	1.42906e20	−	8.66595e19i	1.07058	−	0.649213i
$751$	2.58067e19			0.191537			0.0957685	−	0.995404i	$-0.469469\pi$
$751$	2.58067e19			0.191537			0.0957685	+	0.995404i	$0.469469\pi$
$752$	4.13920e19	+	4.13920e19i	0.304362	+	0.304362i
$753$	−1.93611e20	+	1.93611e20i	−1.41047	+	1.41047i
$754$		−	5.52795e19i		−	0.398993i
$755$	−2.88865e19	+	5.30741e18i	−0.206570	+	0.0379537i
$756$	−9.52109e19			−0.674581
$757$	4.38442e19	+	4.38442e19i	0.307780	+	0.307780i	0.844048	−	0.536268i	$-0.180166\pi$
$757$	4.38442e19	+	4.38442e19i	0.307780	+	0.307780i	−0.536268	+	0.844048i	$0.680166\pi$
$758$	2.89950e19	−	2.89950e19i	0.201669	−	0.201669i
$759$		−	4.94918e20i		−	3.41068i
$760$	−4.36301e19	−	3.00860e19i	−0.297914	−	0.205433i
$761$	1.67230e20			1.13142			0.565709	−	0.824605i	$-0.308603\pi$
$761$	1.67230e20			1.13142			0.565709	+	0.824605i	$0.308603\pi$
$762$	−2.45074e19	−	2.45074e19i	−0.164291	−	0.164291i
$763$	−6.27864e19	+	6.27864e19i	−0.417055	+	0.417055i
$764$		−	4.45155e19i		−	0.292994i
$765$	1.83680e20	−	2.66369e20i	1.19793	−	1.73721i
$766$	−1.24365e20			−0.803705
$767$	8.07698e19	+	8.07698e19i	0.517228	+	0.517228i
$768$	−1.23319e19	+	1.23319e19i	−0.0782530	+	0.0782530i
$769$			2.44212e20i			1.53561i	0.640681	+	0.767807i	$0.278652\pi$
$769$			2.44212e20i			1.53561i	−0.640681	+	0.767807i	$0.721348\pi$
$770$	−1.82681e19	−	9.94271e19i	−0.113830	−	0.619540i
$771$	3.50633e20			2.16507
$772$	−7.99612e19	−	7.99612e19i	−0.489281	−	0.489281i
$773$	2.48602e19	−	2.48602e19i	0.150747	−	0.150747i	−0.627705	−	0.778451i	$-0.716005\pi$
$773$	2.48602e19	−	2.48602e19i	0.150747	−	0.150747i	0.778451	+	0.627705i	$0.216005\pi$
$774$		−	7.93101e19i		−	0.476586i
$775$	−1.34694e20	+	5.12247e19i	−0.802113	+	0.305048i
$776$	−1.37258e18			−0.00810041
$777$	−5.97078e19	−	5.97078e19i	−0.349208	−	0.349208i
$778$	−4.61939e19	+	4.61939e19i	−0.267749	+	0.267749i
$779$		−	4.35951e19i		−	0.250424i
$780$	−1.48887e20	+	2.73554e19i	−0.847605	+	0.155733i
$781$	−2.95555e20			−1.66756
$782$	1.28245e20	+	1.28245e20i	0.717121	+	0.717121i
$783$	−1.48671e20	+	1.48671e20i	−0.823939	+	0.823939i
$784$			2.50114e19i			0.137380i
$785$	−1.98054e20	−	1.36572e20i	−1.07819	−	0.743490i
$786$	3.19254e20			1.72258
$787$	−2.72600e19	−	2.72600e19i	−0.145781	−	0.145781i	0.630449	−	0.776231i	$-0.282871\pi$
$787$	−2.72600e19	−	2.72600e19i	−0.145781	−	0.145781i	−0.776231	+	0.630449i	$0.782871\pi$
$788$	1.08568e19	−	1.08568e19i	0.0575464	−	0.0575464i
$789$			4.49844e20i			2.36332i
$790$	9.49472e19	−	1.37691e20i	0.494416	−	0.716992i
$791$	−1.22465e20			−0.632085
$792$	1.38491e20	+	1.38491e20i	0.708510	+	0.708510i
$793$	1.40527e20	−	1.40527e20i	0.712605	−	0.712605i
$794$		−	2.81614e19i		−	0.141550i
$795$	2.85835e19	+	1.55571e20i	0.142412	+	0.775100i
$796$	−1.10707e19			−0.0546744
$797$	2.06223e19	+	2.06223e19i	0.100955	+	0.100955i	0.755780	−	0.654825i	$-0.227258\pi$
$797$	2.06223e19	+	2.06223e19i	0.100955	+	0.100955i	−0.654825	+	0.755780i	$0.727258\pi$
$798$	−1.25334e20	+	1.25334e20i	−0.608205	+	0.608205i
$799$			3.53727e20i			1.70154i
$800$	−3.38207e19	−	1.51840e19i	−0.161269	−	0.0724028i
$801$	6.13288e20			2.89893
$802$	−1.78143e20	−	1.78143e20i	−0.834736	−	0.834736i
$803$	−8.17885e19	+	8.17885e19i	−0.379912	+	0.379912i
$804$		−	2.61958e20i		−	1.20625i
$805$	2.09868e20	−	3.85597e19i	0.958020	−	0.176020i
$806$	1.30526e20			0.590677
$807$	−3.82809e20	−	3.82809e20i	−1.71739	−	1.71739i
$808$	3.19045e19	−	3.19045e19i	0.141897	−	0.141897i
$809$		−	3.75681e20i		−	1.65645i	−0.560393	−	0.828227i	$-0.689350\pi$
$809$		−	3.75681e20i		−	1.65645i	0.560393	−	0.828227i	$-0.310650\pi$
$810$	1.89641e20	+	1.30770e20i	0.828965	+	0.571629i
$811$	−2.20538e20			−0.955737			−0.477868	−	0.878432i	$-0.658590\pi$
$811$	−2.20538e20			−0.955737			−0.477868	+	0.878432i	$0.658590\pi$
$812$	−3.20160e19	−	3.20160e19i	−0.137555	−	0.137555i
$813$	1.43293e20	−	1.43293e20i	0.610366	−	0.610366i
$814$			9.23505e19i			0.390004i
$815$	−8.60743e19	+	1.24823e20i	−0.360388	+	0.522627i
$816$	−1.05386e20			−0.437473
$817$	−5.55079e19	−	5.55079e19i	−0.228455	−	0.228455i
$818$	−4.48158e19	+	4.48158e19i	−0.182877	+	0.182877i
$819$			3.44802e20i			1.39503i
$820$	−5.51079e18	−	2.99934e19i	−0.0221063	−	0.120318i
$821$	−1.52811e20			−0.607789			−0.303895	−	0.952706i	$-0.598287\pi$
$821$	−1.52811e20			−0.607789			−0.303895	+	0.952706i	$0.598287\pi$
$822$	3.02955e20	+	3.02955e20i	1.19475	+	1.19475i
$823$	1.61084e20	−	1.61084e20i	0.629874	−	0.629874i	−0.318162	−	0.948036i	$-0.603066\pi$
$823$	1.61084e20	−	1.61084e20i	0.629874	−	0.629874i	0.948036	+	0.318162i	$0.103066\pi$
$824$		−	2.17376e19i		−	0.0842792i
$825$	−2.50381e20	+	5.57697e20i	−0.962550	+	2.14398i
$826$	9.35582e19			0.356633
$827$	−8.74139e19	−	8.74139e19i	−0.330401	−	0.330401i	0.522337	−	0.852739i	$-0.325060\pi$
$827$	−8.74139e19	−	8.74139e19i	−0.330401	−	0.330401i	−0.852739	+	0.522337i	$0.825060\pi$
$828$	−2.92323e20	+	2.92323e20i	−1.09560	+	1.09560i
$829$			2.38503e20i			0.886363i	0.896432	+	0.443182i	$0.146150\pi$
$829$			2.38503e20i			0.886363i	−0.896432	+	0.443182i	$0.853850\pi$
$830$	−1.80095e20	+	3.30894e19i	−0.663673	+	0.121939i
$831$	3.29582e20			1.20436
$832$	2.37441e19	+	2.37441e19i	0.0860383	+	0.0860383i
$833$	−1.06871e20	+	1.06871e20i	−0.384012	+	0.384012i
$834$		−	1.00768e20i		−	0.359054i
$835$	1.78081e20	+	1.22799e20i	0.629234	+	0.433901i
$836$	1.93855e20			0.679257
$837$	−3.51042e20	−	3.51042e20i	−1.21978	−	1.21978i
$838$	−1.53262e20	+	1.53262e20i	−0.528111	+	0.528111i
$839$		−	2.84567e20i		−	0.972414i	−0.873844	−	0.486207i	$-0.838380\pi$
$839$		−	2.84567e20i		−	0.972414i	0.873844	−	0.486207i	$-0.161620\pi$
$840$	−7.03867e19	+	1.02073e20i	−0.238526	+	0.345905i
$841$	1.97572e20			0.663979
$842$	−1.00296e20	−	1.00296e20i	−0.334270	−	0.334270i
$843$	1.55645e20	−	1.55645e20i	0.514449	−	0.514449i
$844$		−	6.11425e19i		−	0.200422i
$845$	−2.91659e18	−	1.58740e19i	−0.00948153	−	0.0516048i
$846$	−8.06291e20			−2.59956
$847$	1.13044e20	+	1.13044e20i	0.361464	+	0.361464i
$848$	2.48100e19	−	2.48100e19i	0.0786785	−	0.0786785i
$849$		−	4.54802e20i		−	1.43044i
$850$	−7.96328e19	−	2.09392e20i	−0.248404	−	0.653172i
$851$	−1.94931e20			−0.603078
$852$	2.56325e20	+	2.56325e20i	0.786528	+	0.786528i
$853$	2.50777e20	−	2.50777e20i	0.763210	−	0.763210i	−0.213692	−	0.976901i	$-0.568549\pi$
$853$	2.50777e20	−	2.50777e20i	0.763210	−	0.763210i	0.976901	+	0.213692i	$0.0685487\pi$
$854$		−	1.62777e20i		−	0.491348i
$855$	7.17974e20	−	1.31916e20i	2.14954	−	0.394943i
$856$	3.85375e19			0.114437
$857$	3.97556e20	+	3.97556e20i	1.17093	+	1.17093i	0.981987	+	0.188946i	$0.0605071\pi$
$857$	3.97556e20	+	3.97556e20i	1.17093	+	1.17093i	0.188946	+	0.981987i	$0.439493\pi$
$858$	3.91535e20	−	3.91535e20i	1.14383	−	1.14383i
$859$		−	4.29840e20i		−	1.24553i	−0.782409	−	0.622765i	$-0.786009\pi$
$859$		−	4.29840e20i		−	1.24553i	0.782409	−	0.622765i	$-0.213991\pi$
$860$	−4.52061e19	−	3.11727e19i	−0.129929	−	0.0895954i
$861$	−1.01991e20			−0.290764
$862$	2.06763e20	+	2.06763e20i	0.584686	+	0.584686i
$863$	1.38671e20	−	1.38671e20i	0.388965	−	0.388965i	−0.485353	−	0.874318i	$-0.661309\pi$
$863$	1.38671e20	−	1.38671e20i	0.388965	−	0.388965i	0.874318	+	0.485353i	$0.161309\pi$
$864$		−	1.27717e20i		−	0.355347i
$865$	1.38822e20	−	2.01317e20i	0.383131	−	0.555608i
$866$	−4.44576e20			−1.21709
$867$	1.07538e19	+	1.07538e19i	0.0292029	+	0.0292029i
$868$	7.55959e19	−	7.55959e19i	0.203639	−	0.203639i
$869$			6.11780e20i			1.63477i
$870$	4.94786e19	+	2.69296e20i	0.131154	+	0.713830i
$871$	−5.04378e20			−1.32626
$872$	−8.42223e19	−	8.42223e19i	−0.219691	−	0.219691i
$873$	1.33686e19	−	1.33686e19i	0.0345928	−	0.0345928i
$874$			4.09184e20i			1.05036i
$875$	−2.55997e20	−	6.27220e19i	−0.651895	−	0.159722i
$876$	1.41865e20			0.358383
$877$	−4.38898e20	−	4.38898e20i	−1.09993	−	1.09993i	−0.994418	−	0.105516i	$-0.966351\pi$
$877$	−4.38898e20	−	4.38898e20i	−1.09993	−	1.09993i	−0.105516	−	0.994418i	$-0.533649\pi$
$878$	−1.47310e20	+	1.47310e20i	−0.366245	+	0.366245i
$879$		−	5.33577e20i		−	1.31606i
$880$	1.33373e20	−	2.45050e19i	0.326353	−	0.0599619i
$881$	−1.85321e20			−0.449877			−0.224939	−	0.974373i	$-0.572218\pi$
$881$	−1.85321e20			−0.449877			−0.224939	+	0.974373i	$0.572218\pi$
$882$	−2.43604e20	−	2.43604e20i	−0.586683	−	0.586683i
$883$	−2.58291e19	+	2.58291e19i	−0.0617142	+	0.0617142i	−0.737290	−	0.675576i	$-0.763895\pi$
$883$	−2.58291e19	+	2.58291e19i	−0.0617142	+	0.0617142i	0.675576	+	0.737290i	$0.263895\pi$
$884$			2.02912e20i			0.480997i
$885$	−4.65766e20	−	3.21178e20i	−1.09538	−	0.755342i
$886$	2.18691e20			0.510263
$887$	4.03432e20	+	4.03432e20i	0.933909	+	0.933909i	0.997947	−	0.0640382i	$-0.0203979\pi$
$887$	4.03432e20	+	4.03432e20i	0.933909	+	0.933909i	−0.0640382	+	0.997947i	$0.520398\pi$
$888$	8.00927e19	−	8.00927e19i	0.183951	−	0.183951i
$889$			5.46582e19i			0.124550i
$890$	2.41052e20	−	3.49569e20i	0.544981	−	0.790320i
$891$	−8.42603e20			−1.89007
$892$	1.02479e19	+	1.02479e19i	0.0228076	+	0.0228076i
$893$	−5.64310e20	+	5.64310e20i	−1.24611	+	1.24611i
$894$		−	1.11458e20i		−	0.244201i
$895$	7.36201e19	+	4.00690e20i	0.160042	+	0.871058i
$896$	2.75035e19			0.0593242
$897$	8.26442e20	+	8.26442e20i	1.76874	+	1.76874i
$898$	1.39244e20	−	1.39244e20i	0.295694	−	0.295694i
$899$		−	2.36086e20i		−	0.497453i
$900$	4.77291e20	−	1.81516e20i	0.997897	−	0.379505i
$901$	2.12022e20			0.439852
$902$	7.88753e19	+	7.88753e19i	0.162366	+	0.162366i
$903$	−1.29861e20	+	1.29861e20i	−0.265257	+	0.265257i
$904$		−	1.64276e20i		−	0.332961i
$905$	−7.58440e20	+	1.39351e20i	−1.52539	+	0.280265i
$906$	−1.31763e20			−0.262964
$907$	5.67712e20	+	5.67712e20i	1.12429	+	1.12429i	0.991090	+	0.133197i	$0.0425244\pi$
$907$	5.67712e20	+	5.67712e20i	1.12429	+	1.12429i	0.133197	+	0.991090i	$0.457476\pi$
$908$	−3.26602e20	+	3.26602e20i	−0.641826	+	0.641826i
$909$			6.21481e20i			1.21194i
$910$	1.96534e20	+	1.35524e20i	0.380319	+	0.262257i
$911$	3.35408e20			0.644087			0.322044	−	0.946725i	$-0.395630\pi$
$911$	3.35408e20			0.644087			0.322044	+	0.946725i	$0.395630\pi$
$912$	−1.68125e20	−	1.68125e20i	−0.320382	−	0.320382i
$913$	4.73605e20	−	4.73605e20i	0.895614	−	0.895614i
$914$			1.65422e20i			0.310435i
$915$	−5.58803e20	+	8.10364e20i	−1.04066	+	1.50915i
$916$	1.21247e20			0.224081
$917$	−3.56012e20	−	3.56012e20i	−0.652949	−	0.652949i
$918$	5.45722e20	−	5.45722e20i	0.993281	−	0.993281i
$919$		−	5.34031e20i		−	0.964624i	−0.875999	−	0.482312i	$-0.839797\pi$
$919$		−	5.34031e20i		−	0.964624i	0.875999	−	0.482312i	$-0.160203\pi$
$920$	5.17244e19	+	2.81519e20i	0.0927216	+	0.504653i
$921$	7.74170e20			1.37727
$922$	2.41604e20	+	2.41604e20i	0.426567	+	0.426567i
$923$	4.93534e20	−	4.93534e20i	0.864779	−	0.864779i
$924$		−	4.53528e20i		−	0.788679i
$925$	2.19657e20	+	9.86163e19i	0.379100	+	0.170199i
$926$	6.91307e19			0.118411
$927$	2.11718e20	+	2.11718e20i	0.359914	+	0.359914i
$928$	4.29466e19	−	4.29466e19i	0.0724591	−	0.0724591i
$929$		−	6.02030e20i		−	1.00811i	−0.863671	−	0.504055i	$-0.831841\pi$
$929$		−	6.02030e20i		−	1.00811i	0.863671	−	0.504055i	$-0.168159\pi$
$930$	−6.35859e20	+	1.16828e20i	−1.05677	+	0.194164i
$931$	−3.40988e20			−0.562460
$932$	−3.52475e20	−	3.52475e20i	−0.577055	−	0.577055i
$933$	−1.30814e20	+	1.30814e20i	−0.212561	+	0.212561i
$934$			6.74033e20i			1.08706i
$935$	6.74595e20	+	4.65180e20i	1.07985	+	0.744629i
$936$	−4.62521e20			−0.734853
$937$	−7.39887e20	−	7.39887e20i	−1.16678	−	1.16678i	−0.982960	−	0.183818i	$-0.941154\pi$
$937$	−7.39887e20	−	7.39887e20i	−1.16678	−	1.16678i	−0.183818	−	0.982960i	$-0.558846\pi$
$938$	−2.92119e20	+	2.92119e20i	−0.457235	+	0.457235i
$939$			1.45820e21i			2.26546i
$940$	−3.16912e20	+	4.59579e20i	−0.488702	+	0.708705i
$941$	−7.98651e20			−1.22245			−0.611223	−	0.791458i	$-0.709322\pi$
$941$	−7.98651e20			−1.22245			−0.611223	+	0.791458i	$0.709322\pi$
$942$	−7.63185e20	−	7.63185e20i	−1.15951	−	1.15951i
$943$	−1.66488e20	+	1.66488e20i	−0.251073	+	0.251073i
$944$			1.25500e20i			0.187862i
$945$	−1.64084e20	−	8.93053e20i	−0.243805	−	1.32695i
$946$	2.00858e20			0.296245
$947$	6.18338e19	+	6.18338e19i	0.0905265	+	0.0905265i	0.750920	−	0.660393i	$-0.229610\pi$
$947$	6.18338e19	+	6.18338e19i	0.0905265	+	0.0905265i	−0.660393	+	0.750920i	$0.729610\pi$
$948$	5.30578e20	−	5.30578e20i	0.771065	−	0.771065i
$949$		−	2.73150e20i		−	0.394038i
$950$	2.07008e20	−	4.61088e20i	0.296430	−	0.660266i
$951$	9.70519e20			1.37956
$952$	1.17520e20	+	1.17520e20i	0.165826	+	0.165826i
$953$	−4.04851e20	+	4.04851e20i	−0.567081	+	0.567081i	−0.931309	−	0.364229i	$-0.881333\pi$
$953$	−4.04851e20	+	4.04851e20i	−0.567081	+	0.567081i	0.364229	+	0.931309i	$0.381333\pi$
$954$			4.83285e20i			0.671993i
$955$	4.17544e20	−	7.67167e19i	0.576340	−	0.105893i
$956$	4.46756e20			0.612160
$957$	−7.08182e20	−	7.08182e20i	−0.963300	−	0.963300i
$958$	4.32830e20	−	4.32830e20i	0.584465	−	0.584465i
$959$		−	6.75673e20i		−	0.905745i
$960$	−1.36922e20	−	9.44175e19i	−0.182211	−	0.125647i
$961$	−1.99501e20			−0.263561
$962$	−1.54212e20	−	1.54212e20i	−0.202252	−	0.202252i
$963$	−3.75344e20	+	3.75344e20i	−0.488703	+	0.488703i
$964$			7.26815e20i			0.939473i
$965$	6.12212e20	−	8.87818e20i	0.785617	−	1.13929i
$966$	9.57293e20			1.21957
$967$	−9.34408e20	−	9.34408e20i	−1.18182	−	1.18182i	−0.979272	−	0.202548i	$-0.935078\pi$
$967$	−9.34408e20	−	9.34408e20i	−1.18182	−	1.18182i	−0.202548	−	0.979272i	$-0.564922\pi$
$968$	−1.51639e20	+	1.51639e20i	−0.190407	+	0.190407i
$969$		−	1.43676e21i		−	1.79109i
$970$	−2.36547e18	−	1.28745e19i	−0.00292763	−	0.0159341i
$971$	2.02598e20			0.248944			0.124472	−	0.992223i	$-0.460276\pi$
$971$	2.02598e20			0.248944			0.124472	+	0.992223i	$0.460276\pi$
$972$	1.48196e20	+	1.48196e20i	0.180789	+	0.180789i
$973$	−1.12370e20	+	1.12370e20i	−0.136101	+	0.136101i
$974$		−	9.65169e20i		−	1.16062i
$975$	−5.13173e20	−	1.34937e21i	−0.612677	−	1.61102i
$976$	2.18351e20			0.258826
$977$	4.52516e20	+	4.52516e20i	0.532564	+	0.532564i	0.921335	−	0.388771i	$-0.127100\pi$
$977$	4.52516e20	+	4.52516e20i	0.532564	+	0.532564i	−0.388771	+	0.921335i	$0.627100\pi$
$978$	−4.80995e20	+	4.80995e20i	−0.562042	+	0.562042i
$979$			1.55319e21i			1.80196i
$980$	−2.34600e20	+	4.31038e19i	−0.270237	+	0.0496516i
$981$	1.64060e21			1.87638
$982$	−7.39798e19	−	7.39798e19i	−0.0840104	−	0.0840104i
$983$	2.20832e20	−	2.20832e20i	0.248993	−	0.248993i	−0.571564	−	0.820557i	$-0.693663\pi$
$983$	2.20832e20	−	2.20832e20i	0.248993	−	0.248993i	0.820557	+	0.571564i	$0.193663\pi$
$984$		−	1.36812e20i		−	0.153165i
$985$	1.20544e20	+	8.31236e19i	0.133996	+	0.0923997i
$986$	3.67013e20			0.405082
$987$	1.32021e21	+	1.32021e21i	1.44685	+	1.44685i
$988$	−3.23711e20	+	3.23711e20i	−0.352256	+	0.352256i
$989$			4.23964e20i			0.458095i
$990$	−1.06034e21	+	1.53768e21i	−1.13762	+	1.64976i
$991$	2.99923e20			0.319517			0.159758	−	0.987156i	$-0.448928\pi$
$991$	2.99923e20			0.319517			0.159758	+	0.987156i	$0.448928\pi$
$992$	1.01405e20	+	1.01405e20i	0.107270	+	0.107270i
$993$	−1.40656e21	+	1.40656e21i	−1.47745	+	1.47745i
$994$		−	5.71676e20i		−	0.596273i
$995$	−1.90789e19	−	1.03840e20i	−0.0197602	−	0.107548i
$996$	−8.21486e20			−0.844860
$997$	−4.52310e20	−	4.52310e20i	−0.461924	−	0.461924i	0.437362	−	0.899286i	$-0.355913\pi$
$997$	−4.52310e20	−	4.52310e20i	−0.461924	−	0.461924i	−0.899286	+	0.437362i	$0.855913\pi$
$998$	−6.43664e20	+	6.43664e20i	−0.652747	+	0.652747i
$999$			8.29491e20i			0.835321i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.15.c.b.7.1	yes	8
3.2	odd	2		90.15.g.b.37.4		8
4.3	odd	2		80.15.p.b.17.4		8
5.2	odd	4		50.15.c.e.43.4		8
5.3	odd	4	inner	10.15.c.b.3.1	✓	8
5.4	even	2		50.15.c.e.7.4		8
15.8	even	4		90.15.g.b.73.4		8
20.3	even	4		80.15.p.b.33.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.15.c.b.3.1	✓	8	5.3	odd	4	inner
10.15.c.b.7.1	yes	8	1.1	even	1	trivial
50.15.c.e.7.4		8	5.4	even	2
50.15.c.e.43.4		8	5.2	odd	4
80.15.p.b.17.4		8	4.3	odd	2
80.15.p.b.33.4		8	20.3	even	4
90.15.g.b.37.4		8	3.2	odd	2
90.15.g.b.73.4		8	15.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 15 \)
Character orbit:	\([\chi]\)	\(=\)	10.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(64.0000 + 64.0000i) q^{2} +(-2738.23 + 2738.23i) q^{3} +8192.00i q^{4} +(-76838.8 + 14117.8i) q^{5} -350493. q^{6} +(390848. + 390848. i) q^{7} +(-524288. + 524288. i) q^{8} -1.02128e7i q^{9} +O(q^{10})\)	\(q+(64.0000 + 64.0000i) q^{2} +(-2738.23 + 2738.23i) q^{3} +8192.00i q^{4} +(-76838.8 + 14117.8i) q^{5} -350493. q^{6} +(390848. + 390848. i) q^{7} +(-524288. + 524288. i) q^{8} -1.02128e7i q^{9} +(-5.82123e6 - 4.01414e6i) q^{10} +2.58646e7 q^{11} +(-2.24316e7 - 2.24316e7i) q^{12} +(-4.31902e7 + 4.31902e7i) q^{13} +5.00286e7i q^{14} +(1.71744e8 - 2.49060e8i) q^{15} -6.71089e7 q^{16} +(-2.86750e8 - 2.86750e8i) q^{17} +(6.53621e8 - 6.53621e8i) q^{18} -9.14918e8i q^{19} +(-1.15653e8 - 6.29463e8i) q^{20} -2.14046e9 q^{21} +(1.65534e9 + 1.65534e9i) q^{22} +(-3.49403e9 + 3.49403e9i) q^{23} -2.87124e9i q^{24} +(5.70489e9 - 2.16960e9i) q^{25} -5.52835e9 q^{26} +(1.48682e10 + 1.48682e10i) q^{27} +(-3.20183e9 + 3.20183e9i) q^{28} +9.99929e9i q^{29} +(2.69315e10 - 4.94821e9i) q^{30} -2.36102e10 q^{31} +(-4.29497e9 - 4.29497e9i) q^{32} +(-7.08232e10 + 7.08232e10i) q^{33} -3.67039e10i q^{34} +(-3.55502e10 - 2.45144e10i) q^{35} +8.36635e10 q^{36} +(2.78948e10 + 2.78948e10i) q^{37} +(5.85547e10 - 5.85547e10i) q^{38} -2.36529e11i q^{39} +(3.28838e10 - 4.76875e10i) q^{40} +4.76492e10 q^{41} +(-1.36990e11 - 1.36990e11i) q^{42} +(6.06698e10 - 6.06698e10i) q^{43} +2.11883e11i q^{44} +(1.44183e11 + 7.84742e11i) q^{45} -4.47236e11 q^{46} +(-6.16788e11 - 6.16788e11i) q^{47} +(1.83759e11 - 1.83759e11i) q^{48} -3.72698e11i q^{49} +(5.03967e11 + 2.26259e11i) q^{50} +1.57037e12 q^{51} +(-3.53814e11 - 3.53814e11i) q^{52} +(-3.69698e11 + 3.69698e11i) q^{53} +1.90313e12i q^{54} +(-1.98741e12 + 3.65153e11i) q^{55} -4.09834e11 q^{56} +(2.50525e12 + 2.50525e12i) q^{57} +(-6.39955e11 + 6.39955e11i) q^{58} -1.87010e12i q^{59} +(2.04030e12 + 1.40693e12i) q^{60} -3.25369e12 q^{61} +(-1.51106e12 - 1.51106e12i) q^{62} +(3.99167e12 - 3.99167e12i) q^{63} -5.49756e11i q^{64} +(2.70893e12 - 3.92844e12i) q^{65} -9.06537e12 q^{66} +(5.83904e12 + 5.83904e12i) q^{67} +(2.34905e12 - 2.34905e12i) q^{68} -1.91349e13i q^{69} +(-7.06296e11 - 3.84414e12i) q^{70} -1.14270e13 q^{71} +(5.35446e12 + 5.35446e12i) q^{72} +(-3.16218e12 + 3.16218e12i) q^{73} +3.57054e12i q^{74} +(-9.68044e12 + 2.15621e13i) q^{75} +7.49501e12 q^{76} +(1.01091e13 + 1.01091e13i) q^{77} +(1.51379e13 - 1.51379e13i) q^{78} +2.36532e13i q^{79} +(5.15656e12 - 9.47433e11i) q^{80} -3.25774e13 q^{81} +(3.04955e12 + 3.04955e12i) q^{82} +(1.83109e13 - 1.83109e13i) q^{83} -1.75347e13i q^{84} +(2.60818e13 + 1.79852e13i) q^{85} +7.76573e12 q^{86} +(-2.73803e13 - 2.73803e13i) q^{87} +(-1.35605e13 + 1.35605e13i) q^{88} +6.00508e13i q^{89} +(-4.09957e13 + 5.94512e13i) q^{90} -3.37616e13 q^{91} +(-2.86231e13 - 2.86231e13i) q^{92} +(6.46502e13 - 6.46502e13i) q^{93} -7.89489e13i q^{94} +(1.29167e13 + 7.03012e13i) q^{95} +2.35212e13 q^{96} +(1.30900e12 + 1.30900e12i) q^{97} +(2.38527e13 - 2.38527e13i) q^{98} -2.64151e14i 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

Introduction

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