LMFDB - Embedded newform 91.10.e.a.53.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,10,Mod(53,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("91.53");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	91.e (of order $3$, 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:	$46.8682610909$
Analytic rank:	$0$
Dimension:	$70$
Relative dimension:	$35$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			53.5
Character	$\chi$	$=$	91.53
Dual form			91.10.e.a.79.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-17.8760 - 30.9621i) q^{2} +(96.3548 - 166.891i) q^{3} +(-383.101 + 663.550i) q^{4} +(-1261.17 - 2184.41i) q^{5} -6889.74 q^{6} +(-4557.75 - 4424.99i) q^{7} +9088.22 q^{8} +(-8726.99 - 15115.6i) q^{9} +O(q^{10})$	\(q+(-17.8760 - 30.9621i) q^{2} +(96.3548 - 166.891i) q^{3} +(-383.101 + 663.550i) q^{4} +(-1261.17 - 2184.41i) q^{5} -6889.74 q^{6} +(-4557.75 - 4424.99i) q^{7} +9088.22 q^{8} +(-8726.99 - 15115.6i) q^{9} +(-45089.4 + 78097.1i) q^{10} +(-18939.4 + 32804.0i) q^{11} +(73827.2 + 127873. i) q^{12} -28561.0 q^{13} +(-55532.8 + 220218. i) q^{14} -486080. q^{15} +(33686.9 + 58347.4i) q^{16} +(296645. - 513804. i) q^{17} +(-312007. + 540412. i) q^{18} +(-472339. - 818116. i) q^{19} +1.93263e6 q^{20} +(-1.17765e6 + 334280. i) q^{21} +1.35424e6 q^{22} +(385584. + 667852. i) q^{23} +(875694. - 1.51675e6i) q^{24} +(-2.20455e6 + 3.81839e6i) q^{25} +(510556. + 884309. i) q^{26} +429555. q^{27} +(4.68228e6 - 1.32908e6i) q^{28} -2.81286e6 q^{29} +(8.68915e6 + 1.50501e7i) q^{30} +(3.55500e6 - 6.15744e6i) q^{31} +(3.53096e6 - 6.11580e6i) q^{32} +(3.64981e6 + 6.32165e6i) q^{33} -2.12113e7 q^{34} +(-3.91791e6 + 1.55367e7i) q^{35} +1.33733e7 q^{36} +(-2.22234e6 - 3.84921e6i) q^{37} +(-1.68871e7 + 2.92492e7i) q^{38} +(-2.75199e6 + 4.76658e6i) q^{39} +(-1.14618e7 - 1.98524e7i) q^{40} -3.80270e6 q^{41} +(3.14017e7 + 3.04870e7i) q^{42} -2.86517e7 q^{43} +(-1.45114e7 - 2.51345e7i) q^{44} +(-2.20125e7 + 3.81267e7i) q^{45} +(1.37854e7 - 2.38770e7i) q^{46} +(1.13665e7 + 1.96874e7i) q^{47} +1.29836e7 q^{48} +(1.19253e6 + 4.03360e7i) q^{49} +1.57634e8 q^{50} +(-5.71663e7 - 9.90150e7i) q^{51} +(1.09417e7 - 1.89517e7i) q^{52} +(5.30751e7 - 9.19287e7i) q^{53} +(-7.67871e6 - 1.32999e7i) q^{54} +9.55435e7 q^{55} +(-4.14218e7 - 4.02153e7i) q^{56} -1.82049e8 q^{57} +(5.02827e7 + 8.70922e7i) q^{58} +(-1.28152e7 + 2.21966e7i) q^{59} +(1.86218e8 - 3.22539e8i) q^{60} +(-5.63333e7 - 9.75722e7i) q^{61} -2.54196e8 q^{62} +(-2.71109e7 + 1.07510e8i) q^{63} -2.17982e8 q^{64} +(3.60203e7 + 6.23891e7i) q^{65} +(1.30488e8 - 2.26011e8i) q^{66} +(1.05552e8 - 1.82822e8i) q^{67} +(2.27290e8 + 3.93678e8i) q^{68} +1.48612e8 q^{69} +(5.51085e8 - 1.56427e8i) q^{70} -6.89152e7 q^{71} +(-7.93128e7 - 1.37374e8i) q^{72} +(7.23465e7 - 1.25308e8i) q^{73} +(-7.94531e7 + 1.37617e8i) q^{74} +(4.24837e8 + 7.35840e8i) q^{75} +7.23815e8 q^{76} +(2.31479e8 - 6.57058e7i) q^{77} +1.96778e8 q^{78} +(-5.60139e7 - 9.70189e7i) q^{79} +(8.49700e7 - 1.47172e8i) q^{80} +(2.13163e8 - 3.69209e8i) q^{81} +(6.79770e7 + 1.17740e8i) q^{82} +1.58421e8 q^{83} +(2.29349e8 - 9.09496e8i) q^{84} -1.49648e9 q^{85} +(5.12178e8 + 8.87118e8i) q^{86} +(-2.71033e8 + 4.69443e8i) q^{87} +(-1.72126e8 + 2.98130e8i) q^{88} +(-4.13602e8 - 7.16380e8i) q^{89} +1.57398e9 q^{90} +(1.30174e8 + 1.26382e8i) q^{91} -5.90871e8 q^{92} +(-6.85083e8 - 1.18660e9i) q^{93} +(4.06375e8 - 7.03862e8i) q^{94} +(-1.19140e9 + 2.06357e9i) q^{95} +(-6.80449e8 - 1.17857e9i) q^{96} +9.78526e8 q^{97} +(1.22757e9 - 7.57968e8i) q^{98} +6.61136e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 70 q + 65 q^{2} - 8533 q^{4} - 2118 q^{5} + 17358 q^{6} - 8764 q^{7} - 106980 q^{8} - 215597 q^{9}+O(q^{10}) $ 70 * q + 65 * q^2 - 8533 * q^4 - 2118 * q^5 + 17358 * q^6 - 8764 * q^7 - 106980 * q^8 - 215597 * q^9	\( 70 q + 65 q^{2} - 8533 q^{4} - 2118 q^{5} + 17358 q^{6} - 8764 q^{7} - 106980 q^{8} - 215597 q^{9} + 16725 q^{10} + 117246 q^{11} + 79155 q^{12} - 1999270 q^{13} + 155800 q^{14} - 1075914 q^{15} - 1801693 q^{16} + 534494 q^{17} + 2034224 q^{18} - 1070554 q^{19} - 213462 q^{20} + 252483 q^{21} - 656508 q^{22} + 3982482 q^{23} - 8713082 q^{24} - 10791923 q^{25} - 1856465 q^{26} - 4695462 q^{27} + 43151747 q^{28} - 8248096 q^{29} + 7494360 q^{30} - 18116139 q^{31} + 23284165 q^{32} - 18685134 q^{33} - 35031796 q^{34} + 41739462 q^{35} + 69822756 q^{36} + 12174052 q^{37} - 86227130 q^{38} - 45752120 q^{40} - 14899440 q^{41} + 226294688 q^{42} - 100872292 q^{43} + 55709994 q^{44} - 128782765 q^{45} + 86862955 q^{46} - 15243502 q^{47} - 251600258 q^{48} + 168431298 q^{49} - 23415484 q^{50} + 89493887 q^{51} + 243711013 q^{52} + 42576150 q^{53} - 466420190 q^{54} - 72659096 q^{55} + 237491061 q^{56} - 533277320 q^{57} + 302514895 q^{58} + 40301350 q^{59} - 191686454 q^{60} + 9519912 q^{61} - 257610720 q^{62} - 292394291 q^{63} + 453888112 q^{64} + 60492198 q^{65} + 1445199979 q^{66} + 919692072 q^{67} - 220295462 q^{68} - 1381257496 q^{69} + 860352188 q^{70} - 811959580 q^{71} + 2266117080 q^{72} + 924540004 q^{73} - 727436321 q^{74} + 445426010 q^{75} + 649412196 q^{76} - 1151937348 q^{77} - 495761838 q^{78} + 1174788834 q^{79} + 2332520349 q^{80} - 800698791 q^{81} + 1124625342 q^{82} + 830514540 q^{83} + 1448184376 q^{84} - 1969339174 q^{85} + 1497823546 q^{86} + 721368044 q^{87} - 808482999 q^{88} - 1968216306 q^{89} + 777819470 q^{90} + 250308604 q^{91} - 4887921618 q^{92} + 853972744 q^{93} + 4664723138 q^{94} + 1357929150 q^{95} - 3736344295 q^{96} + 3467931764 q^{97} - 1557173329 q^{98} - 8781494080 q^{99}+O(q^{100}) \) 70 * q + 65 * q^2 - 8533 * q^4 - 2118 * q^5 + 17358 * q^6 - 8764 * q^7 - 106980 * q^8 - 215597 * q^9 + 16725 * q^10 + 117246 * q^11 + 79155 * q^12 - 1999270 * q^13 + 155800 * q^14 - 1075914 * q^15 - 1801693 * q^16 + 534494 * q^17 + 2034224 * q^18 - 1070554 * q^19 - 213462 * q^20 + 252483 * q^21 - 656508 * q^22 + 3982482 * q^23 - 8713082 * q^24 - 10791923 * q^25 - 1856465 * q^26 - 4695462 * q^27 + 43151747 * q^28 - 8248096 * q^29 + 7494360 * q^30 - 18116139 * q^31 + 23284165 * q^32 - 18685134 * q^33 - 35031796 * q^34 + 41739462 * q^35 + 69822756 * q^36 + 12174052 * q^37 - 86227130 * q^38 - 45752120 * q^40 - 14899440 * q^41 + 226294688 * q^42 - 100872292 * q^43 + 55709994 * q^44 - 128782765 * q^45 + 86862955 * q^46 - 15243502 * q^47 - 251600258 * q^48 + 168431298 * q^49 - 23415484 * q^50 + 89493887 * q^51 + 243711013 * q^52 + 42576150 * q^53 - 466420190 * q^54 - 72659096 * q^55 + 237491061 * q^56 - 533277320 * q^57 + 302514895 * q^58 + 40301350 * q^59 - 191686454 * q^60 + 9519912 * q^61 - 257610720 * q^62 - 292394291 * q^63 + 453888112 * q^64 + 60492198 * q^65 + 1445199979 * q^66 + 919692072 * q^67 - 220295462 * q^68 - 1381257496 * q^69 + 860352188 * q^70 - 811959580 * q^71 + 2266117080 * q^72 + 924540004 * q^73 - 727436321 * q^74 + 445426010 * q^75 + 649412196 * q^76 - 1151937348 * q^77 - 495761838 * q^78 + 1174788834 * q^79 + 2332520349 * q^80 - 800698791 * q^81 + 1124625342 * q^82 + 830514540 * q^83 + 1448184376 * q^84 - 1969339174 * q^85 + 1497823546 * q^86 + 721368044 * q^87 - 808482999 * q^88 - 1968216306 * q^89 + 777819470 * q^90 + 250308604 * q^91 - 4887921618 * q^92 + 853972744 * q^93 + 4664723138 * q^94 + 1357929150 * q^95 - 3736344295 * q^96 + 3467931764 * q^97 - 1557173329 * q^98 - 8781494080 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−17.8760	−	30.9621i	−0.790014	−	1.36834i	−0.925957	−	0.377628i	$-0.876740\pi$
$2$	−17.8760	−	30.9621i	−0.790014	−	1.36834i	0.135943	−	0.990717i	$-0.456593\pi$
$3$	96.3548	−	166.891i	0.686796	−	1.18957i	−0.286073	−	0.958208i	$-0.592350\pi$
$3$	96.3548	−	166.891i	0.686796	−	1.18957i	0.972869	−	0.231357i	$-0.0743167\pi$
$4$	−383.101	+	663.550i	−0.748244	+	1.29600i
$5$	−1261.17	−	2184.41i	−0.902421	−	1.56304i	−0.824342	−	0.566093i	$-0.808454\pi$
$5$	−1261.17	−	2184.41i	−0.902421	−	1.56304i	−0.0780796	−	0.996947i	$-0.524879\pi$
$6$	−6889.74			−2.17031
$7$	−4557.75	−	4424.99i	−0.717479	−	0.696580i
$7$	−4557.75	−	4424.99i	−0.717479	−	0.696580i
$8$	9088.22			0.784466
$9$	−8726.99	−	15115.6i	−0.443377	−	0.767951i
$10$	−45089.4	+	78097.1i	−1.42585	+	2.46965i
$11$	−18939.4	+	32804.0i	−0.390032	+	0.675554i	−0.992453	−	0.122624i	$-0.960869\pi$
$11$	−18939.4	+	32804.0i	−0.390032	+	0.675554i	0.602422	+	0.798178i	$0.294203\pi$
$12$	73827.2	+	127873.i	1.02778	+	1.78017i
$13$	−28561.0			−0.277350
$13$	−28561.0			−0.277350
$14$	−55532.8	+	220218.i	−0.386343	+	1.53207i
$15$	−486080.			−2.47912
$16$	33686.9	+	58347.4i	0.128505	+	0.222578i
$17$	296645.	−	513804.i	0.861424	−	1.49203i	−0.00913090	−	0.999958i	$-0.502906\pi$
$17$	296645.	−	513804.i	0.861424	−	1.49203i	0.870555	−	0.492072i	$-0.163760\pi$
$18$	−312007.	+	540412.i	−0.700548	+	1.21338i
$19$	−472339.	−	818116.i	−0.831501	−	1.44020i	−0.896847	−	0.442340i	$-0.854148\pi$
$19$	−472339.	−	818116.i	−0.831501	−	1.44020i	0.0653460	−	0.997863i	$-0.479185\pi$
$20$	1.93263e6			2.70093
$21$	−1.17765e6	+	334280.i	−1.32139	+	0.375080i
$22$	1.35424e6			1.23252
$23$	385584.	+	667852.i	0.287306	+	0.497628i	0.973166	−	0.230106i	$-0.0739071\pi$
$23$	385584.	+	667852.i	0.287306	+	0.497628i	−0.685860	+	0.727733i	$0.740574\pi$
$24$	875694.	−	1.51675e6i	0.538768	−	0.933173i
$25$	−2.20455e6	+	3.81839e6i	−1.12873	+	1.95502i
$26$	510556.	+	884309.i	0.219110	+	0.379510i
$27$	429555.			0.155554
$28$	4.68228e6	−	1.32908e6i	1.43962	−	0.408638i
$29$	−2.81286e6			−0.738512			−0.369256	−	0.929328i	$-0.620387\pi$
$29$	−2.81286e6			−0.738512			−0.369256	+	0.929328i	$0.620387\pi$
$30$	8.68915e6	+	1.50501e7i	1.95854	+	3.39229i
$31$	3.55500e6	−	6.15744e6i	0.691373	−	1.19749i	−0.280016	−	0.959995i	$-0.590340\pi$
$31$	3.55500e6	−	6.15744e6i	0.691373	−	1.19749i	0.971388	−	0.237497i	$-0.0763270\pi$
$32$	3.53096e6	−	6.11580e6i	0.595275	−	1.03105i
$33$	3.64981e6	+	6.32165e6i	0.535744	+	0.927936i
$34$	−2.12113e7			−2.72215
$35$	−3.91791e6	+	1.55367e7i	−0.441314	+	1.75006i
$36$	1.33733e7			1.32702
$37$	−2.22234e6	−	3.84921e6i	−0.194941	−	0.337648i	0.751940	−	0.659231i	$-0.229118\pi$
$37$	−2.22234e6	−	3.84921e6i	−0.194941	−	0.337648i	−0.946881	+	0.321583i	$0.895785\pi$
$38$	−1.68871e7	+	2.92492e7i	−1.31380	+	2.27556i
$39$	−2.75199e6	+	4.76658e6i	−0.190483	+	0.329926i
$40$	−1.14618e7	−	1.98524e7i	−0.707919	−	1.22615i
$41$	−3.80270e6			−0.210167			−0.105084	−	0.994463i	$-0.533511\pi$
$41$	−3.80270e6			−0.210167			−0.105084	+	0.994463i	$0.533511\pi$
$42$	3.14017e7	+	3.04870e7i	1.55715	+	1.51180i
$43$	−2.86517e7			−1.27804			−0.639018	−	0.769192i	$-0.720659\pi$
$43$	−2.86517e7			−1.27804			−0.639018	+	0.769192i	$0.720659\pi$
$44$	−1.45114e7	−	2.51345e7i	−0.583678	−	1.01096i
$45$	−2.20125e7	+	3.81267e7i	−0.800225	+	1.38603i
$46$	1.37854e7	−	2.38770e7i	0.453951	−	0.786266i
$47$	1.13665e7	+	1.96874e7i	0.339771	+	0.588501i	0.984390	−	0.176003i	$-0.0563170\pi$
$47$	1.13665e7	+	1.96874e7i	0.339771	+	0.588501i	−0.644618	+	0.764505i	$0.722984\pi$
$48$	1.29836e7			0.353028
$49$	1.19253e6	+	4.03360e7i	0.0295521	+	0.999563i
$50$	1.57634e8			3.56685
$51$	−5.71663e7	−	9.90150e7i	−1.18324	−	2.04944i
$52$	1.09417e7	−	1.89517e7i	0.207526	−	0.359445i
$53$	5.30751e7	−	9.19287e7i	0.923952	−	1.60033i	0.130713	−	0.991420i	$-0.458273\pi$
$53$	5.30751e7	−	9.19287e7i	0.923952	−	1.60033i	0.793238	−	0.608911i	$-0.208393\pi$
$54$	−7.67871e6	−	1.32999e7i	−0.122890	−	0.212852i
$55$	9.55435e7			1.40789
$56$	−4.14218e7	−	4.02153e7i	−0.562838	−	0.546443i
$57$	−1.82049e8			−2.28429
$58$	5.02827e7	+	8.70922e7i	0.583435	+	1.01054i
$59$	−1.28152e7	+	2.21966e7i	−0.137687	+	0.238480i	−0.926621	−	0.375998i	$-0.877300\pi$
$59$	−1.28152e7	+	2.21966e7i	−0.137687	+	0.238480i	0.788934	+	0.614478i	$0.210633\pi$
$60$	1.86218e8	−	3.22539e8i	1.85498	−	3.21293i
$61$	−5.63333e7	−	9.75722e7i	−0.520932	−	0.902281i	−0.999704	−	0.0243414i	$-0.992251\pi$
$61$	−5.63333e7	−	9.75722e7i	−0.520932	−	0.902281i	0.478772	−	0.877940i	$-0.341082\pi$
$62$	−2.54196e8			−2.18478
$63$	−2.71109e7	+	1.07510e8i	−0.216826	+	0.859836i
$64$	−2.17982e8			−1.62409
$65$	3.60203e7	+	6.23891e7i	0.250287	+	0.433509i
$66$	1.30488e8	−	2.26011e8i	0.846491	−	1.46616i
$67$	1.05552e8	−	1.82822e8i	0.639929	−	1.10839i	−0.345519	−	0.938412i	$-0.612297\pi$
$67$	1.05552e8	−	1.82822e8i	0.639929	−	1.10839i	0.985448	−	0.169977i	$-0.0543695\pi$
$68$	2.27290e8	+	3.93678e8i	1.28911	+	2.23281i
$69$	1.48612e8			0.789281
$70$	5.51085e8	−	1.56427e8i	2.74332	−	0.778700i
$71$	−6.89152e7			−0.321849			−0.160925	−	0.986967i	$-0.551448\pi$
$71$	−6.89152e7			−0.321849			−0.160925	+	0.986967i	$0.551448\pi$
$72$	−7.93128e7	−	1.37374e8i	−0.347814	−	0.602431i
$73$	7.23465e7	−	1.25308e8i	0.298170	−	0.516446i	−0.677547	−	0.735479i	$-0.736957\pi$
$73$	7.23465e7	−	1.25308e8i	0.298170	−	0.516446i	0.975717	+	0.219033i	$0.0702903\pi$
$74$	−7.94531e7	+	1.37617e8i	−0.308012	+	0.533493i
$75$	4.24837e8	+	7.35840e8i	1.55041	+	2.68539i
$76$	7.23815e8			2.48866
$77$	2.31479e8	−	6.57058e7i	0.750417	−	0.213008i
$78$	1.96778e8			0.601937
$79$	−5.60139e7	−	9.70189e7i	−0.161798	−	0.280243i	0.773715	−	0.633533i	$-0.218396\pi$
$79$	−5.60139e7	−	9.70189e7i	−0.161798	−	0.280243i	−0.935514	+	0.353291i	$0.885063\pi$
$80$	8.49700e7	−	1.47172e8i	0.231932	−	0.401718i
$81$	2.13163e8	−	3.69209e8i	0.550211	−	0.952993i
$82$	6.79770e7	+	1.17740e8i	0.166035	+	0.287581i
$83$	1.58421e8			0.366405			0.183202	−	0.983075i	$-0.441354\pi$
$83$	1.58421e8			0.366405			0.183202	+	0.983075i	$0.441354\pi$
$84$	2.29349e8	−	9.09496e8i	0.502620	−	1.99317i
$85$	−1.49648e9			−3.10947
$86$	5.12178e8	+	8.87118e8i	1.00967	+	1.74879i
$87$	−2.71033e8	+	4.69443e8i	−0.507207	+	0.878508i
$88$	−1.72126e8	+	2.98130e8i	−0.305966	+	0.529949i
$89$	−4.13602e8	−	7.16380e8i	−0.698760	−	1.21029i	−0.968897	−	0.247465i	$-0.920402\pi$
$89$	−4.13602e8	−	7.16380e8i	−0.698760	−	1.21029i	0.270137	−	0.962822i	$-0.412931\pi$
$90$	1.57398e9			2.52876
$91$	1.30174e8	+	1.26382e8i	0.198993	+	0.193197i
$92$	−5.90871e8			−0.859899
$93$	−6.85083e8	−	1.18660e9i	−0.949664	−	1.64487i
$94$	4.06375e8	−	7.03862e8i	0.536848	−	0.929848i
$95$	−1.19140e9	+	2.06357e9i	−1.50073	+	2.59934i
$96$	−6.80449e8	−	1.17857e9i	−0.817665	−	1.41624i
$97$	9.78526e8			1.12228			0.561138	−	0.827722i	$-0.310364\pi$
$97$	9.78526e8			1.12228			0.561138	+	0.827722i	$0.310364\pi$
$98$	1.22757e9	−	7.57968e8i	1.34440	−	0.830106i
$99$	6.61136e8			0.691724
$100$	−1.68913e9	−	2.92566e9i	−1.68913	−	2.92566i
$101$	−8.86642e7	+	1.53571e8i	−0.0847817	+	0.146846i	−0.905298	−	0.424777i	$-0.860353\pi$
$101$	−8.86642e7	+	1.53571e8i	−0.0847817	+	0.146846i	0.820516	+	0.571623i	$0.193686\pi$
$102$	−2.04381e9	+	3.53998e9i	−1.86956	+	3.23817i
$103$	−6.95803e7	−	1.20517e8i	−0.0609142	−	0.105506i	0.833960	−	0.551825i	$-0.186068\pi$
$103$	−6.95803e7	−	1.20517e8i	−0.0609142	−	0.105506i	−0.894874	+	0.446318i	$0.852735\pi$
$104$	−2.59569e8			−0.217572
$105$	2.21543e9	+	2.15090e9i	1.77871	+	1.72690i
$106$	−3.79508e9			−2.91974
$107$	2.45646e8	+	4.25470e8i	0.181168	+	0.313792i	0.942279	−	0.334830i	$-0.108679\pi$
$107$	2.45646e8	+	4.25470e8i	0.181168	+	0.313792i	−0.761110	+	0.648622i	$0.775346\pi$
$108$	−1.64563e8	+	2.85031e8i	−0.116393	+	0.201598i
$109$	7.67066e8	−	1.32860e9i	0.520491	−	0.901517i	−0.479225	−	0.877692i	$-0.659082\pi$
$109$	7.67066e8	−	1.32860e9i	0.520491	−	0.901517i	0.999716	−	0.0238252i	$-0.00758453\pi$
$110$	−1.70793e9	−	2.95823e9i	−1.11225	−	1.92648i
$111$	−8.56534e8			−0.535539
$112$	1.04650e8	−	4.14997e8i	0.0628434	−	0.249209i
$113$	−5.18792e8			−0.299323			−0.149662	−	0.988737i	$-0.547818\pi$
$113$	−5.18792e8			−0.299323			−0.149662	+	0.988737i	$0.547818\pi$
$114$	3.25430e9	+	5.63661e9i	1.80462	+	3.12569i
$115$	9.72576e8	−	1.68455e9i	0.518541	−	0.898140i
$116$	1.07761e9	−	1.86648e9i	0.552587	−	0.957110i
$117$	2.49251e8	+	4.31716e8i	0.122971	+	0.212991i
$118$	9.16338e8			0.435098
$119$	−3.62561e9	+	1.02914e9i	−1.65737	+	0.470449i
$120$	−4.41760e9			−1.94478
$121$	4.61570e8	+	7.99463e8i	0.195751	+	0.339050i
$122$	−2.01403e9	+	3.48840e9i	−0.823087	+	1.42563i
$123$	−3.66409e8	+	6.34638e8i	−0.144342	+	0.250008i
$124$	2.72385e9	+	4.71785e9i	1.03463	+	1.79203i
$125$	6.19481e9			2.26951
$126$	3.81336e9	−	1.08243e9i	1.34785	−	0.382590i
$127$	4.62118e9			1.57629			0.788145	−	0.615489i	$-0.211042\pi$
$127$	4.62118e9			1.57629			0.788145	+	0.615489i	$0.211042\pi$
$128$	2.08879e9	+	3.61789e9i	0.687780	+	1.19127i
$129$	−2.76073e9	+	4.78173e9i	−0.877750	+	1.52031i
$130$	1.28780e9	−	2.23053e9i	0.395460	−	0.684957i
$131$	2.23872e8	+	3.87757e8i	0.0664169	+	0.115037i	0.897322	−	0.441377i	$-0.145510\pi$
$131$	2.23872e8	+	3.87757e8i	0.0664169	+	0.115037i	−0.830905	+	0.556415i	$0.812177\pi$
$132$	−5.59298e9			−1.60347
$133$	−1.46735e9	+	5.81886e9i	−0.406632	+	1.61252i
$134$	−7.54741e9			−2.02221
$135$	−5.41743e8	−	9.38326e8i	−0.140375	−	0.243137i
$136$	2.69598e9	−	4.66957e9i	0.675757	−	1.17045i
$137$	−1.46219e9	+	2.53258e9i	−0.354618	+	0.614216i	−0.987053	−	0.160397i	$-0.948722\pi$
$137$	−1.46219e9	+	2.53258e9i	−0.354618	+	0.614216i	0.632434	+	0.774614i	$0.282056\pi$
$138$	−2.65658e9	−	4.60133e9i	−0.623543	−	1.08001i
$139$	1.95219e9			0.443563			0.221782	−	0.975096i	$-0.428813\pi$
$139$	1.95219e9			0.443563			0.221782	+	0.975096i	$0.428813\pi$
$140$	−8.80842e9	−	8.55185e9i	−1.93786	−	1.88141i
$141$	4.38087e9			0.933414
$142$	1.23193e9	+	2.13376e9i	0.254265	+	0.440400i
$143$	5.40929e8	−	9.36916e8i	0.108175	−	0.187365i
$144$	5.87970e8	−	1.01839e9i	0.113953	−	0.197372i
$145$	3.54751e9	+	6.14446e9i	0.666449	+	1.15432i
$146$	−5.17306e9			−0.942235
$147$	6.84663e9	+	3.68754e9i	1.20934	+	0.651342i
$148$	3.40553e9			0.583454
$149$	2.48750e9	+	4.30848e9i	0.413452	+	0.716120i	0.995265	−	0.0972027i	$-0.0309895\pi$
$149$	2.48750e9	+	4.30848e9i	0.413452	+	0.716120i	−0.581812	+	0.813323i	$0.697656\pi$
$150$	1.51888e10	−	2.63077e10i	2.44969	−	4.24300i
$151$	−2.99727e9	+	5.19142e9i	−0.469169	+	0.812625i	−0.999379	−	0.0352419i	$-0.988780\pi$
$151$	−2.99727e9	+	5.19142e9i	−0.469169	+	0.812625i	0.530210	+	0.847866i	$0.322113\pi$
$152$	−4.29273e9	−	7.43522e9i	−0.652284	−	1.12979i
$153$	−1.03553e10			−1.52774
$154$	−6.17230e9	−	5.99251e9i	−0.884308	−	0.858550i
$155$	−1.79339e10			−2.49564
$156$	−2.10858e9	−	3.65217e9i	−0.285055	−	0.493730i
$157$	3.91144e9	−	6.77481e9i	0.513793	−	0.889915i	−0.486079	−	0.873915i	$-0.661573\pi$
$157$	3.91144e9	−	6.77481e9i	0.513793	−	0.889915i	0.999872	−	0.0160002i	$-0.00509323\pi$
$158$	−2.00260e9	+	3.46861e9i	−0.255646	+	0.442791i
$159$	−1.02281e10	−	1.77155e10i	−1.26913	−	2.19820i
$160$	−1.78126e10			−2.14876
$161$	1.19784e9	−	4.75011e9i	0.140502	−	0.557169i
$162$	−1.52420e10			−1.73870
$163$	−1.59337e9	−	2.75979e9i	−0.176796	−	0.306219i	0.763985	−	0.645233i	$-0.223240\pi$
$163$	−1.59337e9	−	2.75979e9i	−0.176796	−	0.306219i	−0.940781	+	0.339014i	$0.889907\pi$
$164$	1.45682e9	−	2.52328e9i	0.157256	−	0.272376i
$165$	9.20607e9	−	1.59454e10i	0.966934	−	1.67478i
$166$	−2.83193e9	−	4.90504e9i	−0.289465	−	0.501368i
$167$	1.03902e8			0.0103371			0.00516854	−	0.999987i	$-0.498355\pi$
$167$	1.03902e8			0.0103371			0.00516854	+	0.999987i	$0.498355\pi$
$168$	−1.07028e10	+	3.03801e9i	−1.03658	+	0.294237i
$169$	8.15731e8			0.0769231
$170$	2.67511e10	+	4.63342e10i	2.45652	+	4.25482i
$171$	−8.24420e9	+	1.42794e10i	−0.737337	+	1.27711i
$172$	1.09765e10	−	1.90119e10i	0.956283	−	1.65633i
$173$	1.04797e10	+	1.81514e10i	0.889493	+	1.54065i	0.840476	+	0.541848i	$0.182275\pi$
$173$	1.04797e10	+	1.81514e10i	0.889493	+	1.54065i	0.0490164	+	0.998798i	$0.484391\pi$
$174$	1.93799e10			1.60280
$175$	2.69441e10	−	7.64815e9i	2.17166	−	0.616432i
$176$	−2.55204e9			−0.200485
$177$	2.46961e9	+	4.27750e9i	0.189125	+	0.327574i
$178$	−1.47871e10	+	2.56120e10i	−1.10406	+	1.91229i
$179$	−9.23791e8	+	1.60005e9i	−0.0672566	+	0.116492i	−0.897693	−	0.440622i	$-0.854758\pi$
$179$	−9.23791e8	+	1.60005e9i	−0.0672566	+	0.116492i	0.830436	+	0.557114i	$0.188091\pi$
$180$	−1.68660e10	−	2.92128e10i	−1.19753	−	2.07418i
$181$	1.54995e10			1.07341			0.536704	−	0.843771i	$-0.319669\pi$
$181$	1.54995e10			1.07341			0.536704	+	0.843771i	$0.319669\pi$
$182$	1.58607e9	−	6.28966e9i	0.107152	−	0.424919i
$183$	−2.17119e10			−1.43110
$184$	3.50428e9	+	6.06958e9i	0.225381	+	0.390372i
$185$	−5.60552e9	+	9.70904e9i	−0.351838	+	0.609401i
$186$	−2.44930e10	+	4.24232e10i	−1.50050	+	2.59893i
$187$	1.12366e10	+	1.94623e10i	0.671965	+	1.16388i
$188$	−1.74181e10			−1.01693
$189$	−1.95780e9	−	1.90078e9i	−0.111607	−	0.108356i
$190$	8.51899e10			4.74239
$191$	1.39846e10	+	2.42220e10i	0.760326	+	1.31692i	0.942683	+	0.333690i	$0.108294\pi$
$191$	1.39846e10	+	2.42220e10i	0.760326	+	1.31692i	−0.182357	+	0.983232i	$0.558373\pi$
$192$	−2.10036e10	+	3.63793e10i	−1.11542	+	1.93196i
$193$	5.66492e9	−	9.81193e9i	0.293891	−	0.509034i	−0.680835	−	0.732436i	$-0.738383\pi$
$193$	5.66492e9	−	9.81193e9i	0.293891	−	0.509034i	0.974726	+	0.223403i	$0.0717164\pi$
$194$	−1.74921e10	−	3.02972e10i	−0.886614	−	1.53566i
$195$	1.38829e10			0.687583
$196$	−2.72218e10	−	1.46615e10i	−1.31754	−	0.709618i
$197$	−2.57301e10			−1.21715			−0.608573	−	0.793498i	$-0.708258\pi$
$197$	−2.57301e10			−1.21715			−0.608573	+	0.793498i	$0.708258\pi$
$198$	−1.18185e10	−	2.04702e10i	−0.546471	−	0.946516i
$199$	1.27258e10	−	2.20417e10i	0.575236	−	0.996338i	−0.420780	−	0.907163i	$-0.638243\pi$
$199$	1.27258e10	−	2.20417e10i	0.575236	−	0.996338i	0.996016	−	0.0891756i	$-0.0284232\pi$
$200$	−2.00354e10	+	3.47024e10i	−0.885449	+	1.53364i
$201$	−2.03410e10	−	3.52316e10i	−0.879001	−	1.52247i
$202$	6.33984e9			0.267915
$203$	1.28203e10	+	1.24469e10i	0.529867	+	0.514433i
$204$	8.76019e10			3.54142
$205$	4.79586e9	+	8.30668e9i	0.189659	+	0.328500i
$206$	−2.48763e9	+	4.30870e9i	−0.0962461	+	0.166703i
$207$	6.72998e9	−	1.16567e10i	0.254769	−	0.441273i
$208$	−9.62132e8	−	1.66646e9i	−0.0356410	−	0.0617320i
$209$	3.57833e10			1.29725
$210$	2.69934e10	−	1.07044e11i	0.957790	−	3.79817i
$211$	−2.91262e10			−1.01161			−0.505805	−	0.862648i	$-0.668804\pi$
$211$	−2.91262e10			−1.01161			−0.505805	+	0.862648i	$0.668804\pi$
$212$	4.06662e10	+	7.04360e10i	1.38268	+	2.39488i
$213$	−6.64031e9	+	1.15013e10i	−0.221045	+	0.382861i
$214$	8.78231e9	−	1.52114e10i	0.286251	−	0.495801i
$215$	3.61348e10	+	6.25873e10i	1.15333	+	1.99762i
$216$	3.90389e9			0.122027
$217$	−4.34494e10	+	1.23332e10i	−1.33019	+	0.377579i
$218$	−5.48482e10			−1.64478
$219$	−1.39419e10	−	2.41480e10i	−0.409564	−	0.709386i
$220$	−3.66028e10	+	6.33979e10i	−1.05345	+	1.82462i
$221$	−8.47248e9	+	1.46748e10i	−0.238916	+	0.413815i
$222$	1.53114e10	+	2.65201e10i	0.423083	+	0.732802i
$223$	2.89795e10			0.784728			0.392364	−	0.919810i	$-0.371657\pi$
$223$	2.89795e10			0.784728			0.392364	+	0.919810i	$0.371657\pi$
$224$	−4.31556e10	+	1.22498e10i	−1.14530	+	0.325097i
$225$	7.69562e10			2.00181
$226$	9.27391e9	+	1.60629e10i	0.236469	+	0.409577i
$227$	−1.07977e9	+	1.87021e9i	−0.0269907	+	0.0467492i	−0.879205	−	0.476443i	$-0.841926\pi$
$227$	−1.07977e9	+	1.87021e9i	−0.0269907	+	0.0467492i	0.852215	+	0.523192i	$0.175259\pi$
$228$	6.97430e10	−	1.20798e11i	1.70920	−	2.96043i
$229$	−2.47748e10	−	4.29112e10i	−0.595319	−	1.03112i	−0.993502	−	0.113817i	$-0.963692\pi$
$229$	−2.47748e10	−	4.29112e10i	−0.595319	−	1.03112i	0.398182	−	0.917306i	$-0.369641\pi$
$230$	−6.95430e10			−1.63862
$231$	1.13383e10	−	4.49629e10i	0.261997	−	1.03896i
$232$	−2.55639e10			−0.579337
$233$	2.79028e10	+	4.83291e10i	0.620221	+	1.07425i	0.989444	+	0.144913i	$0.0462904\pi$
$233$	2.79028e10	+	4.83291e10i	0.620221	+	1.07425i	−0.369223	+	0.929341i	$0.620376\pi$
$234$	8.91123e9	−	1.54347e10i	0.194297	−	0.336532i
$235$	2.86702e10	−	4.96583e10i	0.613234	−	1.06215i
$236$	−9.81904e9	−	1.70071e10i	−0.206046	−	0.356883i
$237$	−2.15888e10			−0.444489
$238$	9.66757e10	+	9.38597e10i	1.95308	+	1.89619i
$239$	−2.78038e10			−0.551206			−0.275603	−	0.961272i	$-0.588877\pi$
$239$	−2.78038e10			−0.551206			−0.275603	+	0.961272i	$0.588877\pi$
$240$	−1.63745e10	−	2.83615e10i	−0.318580	−	0.551796i
$241$	−2.38879e10	+	4.13750e10i	−0.456143	+	0.790062i	−0.998753	−	0.0499222i	$-0.984103\pi$
$241$	−2.38879e10	+	4.13750e10i	−0.456143	+	0.790062i	0.542610	+	0.839984i	$0.317436\pi$
$242$	1.65020e10	−	2.85824e10i	0.309292	−	0.535709i
$243$	−3.68511e10	−	6.38279e10i	−0.677988	−	1.17431i
$244$	8.63254e10			1.55914
$245$	8.66065e10	−	5.34756e10i	1.53569	−	0.948218i
$246$	2.61996e10			0.456129
$247$	1.34905e10	+	2.33662e10i	0.230617	+	0.399440i
$248$	3.23086e10	−	5.59602e10i	0.542358	−	0.939392i
$249$	1.52646e10	−	2.64391e10i	0.251645	−	0.435862i
$250$	−1.10738e11	−	1.91804e11i	−1.79295	−	3.10547i
$251$	−5.46792e10			−0.869541			−0.434771	−	0.900541i	$-0.643171\pi$
$251$	−5.46792e10			−0.869541			−0.434771	+	0.900541i	$0.643171\pi$
$252$	−6.09520e10	−	5.91766e10i	−0.952107	−	0.924374i
$253$	−2.92110e10			−0.448233
$254$	−8.26081e10	−	1.43081e11i	−1.24529	−	2.15691i
$255$	−1.44193e11	+	2.49750e11i	−2.13557	+	3.69892i
$256$	1.88749e10	−	3.26923e10i	0.274666	−	0.475735i
$257$	2.57268e10	+	4.45601e10i	0.367863	+	0.637158i	0.989231	−	0.146361i	$-0.0467561\pi$
$257$	2.57268e10	+	4.45601e10i	0.367863	+	0.637158i	−0.621368	+	0.783519i	$0.713423\pi$
$258$	1.97403e11			2.77374
$259$	−6.90384e9	+	2.73776e10i	−0.0953327	+	0.378047i
$260$	−5.51977e10			−0.749102
$261$	2.45478e10	+	4.25181e10i	0.327439	+	0.567141i
$262$	8.00385e9	−	1.38631e10i	0.104941	−	0.181762i
$263$	2.32807e10	−	4.03233e10i	0.300051	−	0.519703i	−0.676096	−	0.736813i	$-0.736330\pi$
$263$	2.32807e10	−	4.03233e10i	0.300051	−	0.519703i	0.976147	+	0.217110i	$0.0696631\pi$
$264$	3.31703e10	+	5.74526e10i	0.420273	+	0.727934i
$265$	−2.67747e11			−3.33518
$266$	2.06395e11	−	5.85856e10i	2.52773	−	0.717503i
$267$	−1.59410e11			−1.91962
$268$	8.08745e10	+	1.40079e11i	0.957646	+	1.65869i
$269$	2.02694e10	−	3.51076e10i	0.236024	−	0.408805i	−0.723546	−	0.690276i	$-0.757489\pi$
$269$	2.02694e10	−	3.51076e10i	0.236024	−	0.408805i	0.959570	+	0.281471i	$0.0908224\pi$
$270$	−1.93684e10	+	3.35470e10i	−0.221797	+	0.384164i
$271$	4.57250e10	+	7.91979e10i	0.514981	+	0.891974i	0.999849	+	0.0173862i	$0.00553447\pi$
$271$	4.57250e10	+	7.91979e10i	0.514981	+	0.891974i	−0.484868	+	0.874588i	$0.661132\pi$
$272$	3.99722e10			0.442790
$273$	3.36350e10	−	9.54737e9i	0.366487	−	0.104028i
$274$	1.04552e11			1.12061
$275$	−8.35057e10	−	1.44636e11i	−0.880479	−	1.52504i
$276$	−5.69332e10	+	9.86113e10i	−0.590575	+	1.02291i
$277$	−3.27531e10	+	5.67300e10i	−0.334267	+	0.578967i	−0.983344	−	0.181756i	$-0.941822\pi$
$277$	−3.27531e10	+	5.67300e10i	−0.334267	+	0.578967i	0.649077	+	0.760723i	$0.275155\pi$
$278$	−3.48973e10	−	6.04439e10i	−0.350421	−	0.606947i
$279$	−1.24098e11			−1.22615
$280$	−3.56068e10	+	1.41201e11i	−0.346196	+	1.37286i
$281$	9.95778e10			0.952762			0.476381	−	0.879239i	$-0.341948\pi$
$281$	9.95778e10			0.952762			0.476381	+	0.879239i	$0.341948\pi$
$282$	−7.83123e10	−	1.35641e11i	−0.737410	−	1.27723i
$283$	−3.40044e10	+	5.88974e10i	−0.315135	+	0.545829i	−0.979466	−	0.201609i	$-0.935383\pi$
$283$	−3.40044e10	+	5.88974e10i	−0.315135	+	0.545829i	0.664331	+	0.747438i	$0.268716\pi$
$284$	2.64015e10	−	4.57287e10i	0.240822	−	0.417116i
$285$	2.29595e11	+	3.97670e11i	2.06139	+	3.57043i
$286$	−3.86785e10			−0.341840
$287$	1.73318e10	+	1.68269e10i	0.150791	+	0.146398i
$288$	−1.23258e11			−1.05572
$289$	−1.16703e11	−	2.02135e11i	−0.984102	−	1.70451i
$290$	1.26830e11	−	2.19676e11i	1.05301	−	1.82386i
$291$	9.42857e10	−	1.63308e11i	0.770775	−	1.33502i
$292$	5.54320e10	+	9.60111e10i	0.446209	+	0.772856i
$293$	−1.45475e11			−1.15315			−0.576573	−	0.817046i	$-0.695610\pi$
$293$	−1.45475e11			−1.15315			−0.576573	+	0.817046i	$0.695610\pi$
$294$	−8.21624e9	−	2.77905e11i	−0.0641372	−	2.16937i
$295$	6.46488e10			0.497005
$296$	−2.01972e10	−	3.49825e10i	−0.152925	−	0.264873i
$297$	−8.13552e9	+	1.40911e10i	−0.0606710	+	0.105085i
$298$	8.89331e10	−	1.54037e11i	0.653266	−	1.13149i
$299$	−1.10127e10	−	1.90745e10i	−0.0796842	−	0.138017i
$300$	−6.51023e11			−4.64035
$301$	1.30587e11	+	1.26784e11i	0.916964	+	0.890254i
$302$	2.14316e11			1.48260
$303$	1.70864e10	+	2.95946e10i	0.116455	+	0.201707i
$304$	3.18233e10	−	5.51196e10i	0.213705	−	0.370148i
$305$	−1.42092e11	+	2.46111e11i	−0.940201	+	1.62848i
$306$	1.85111e11	+	3.20621e11i	1.20694	+	2.09048i
$307$	−2.76272e11			−1.77507			−0.887533	−	0.460745i	$-0.847582\pi$
$307$	−2.76272e11			−1.77507			−0.887533	+	0.460745i	$0.847582\pi$
$308$	−4.50806e10	+	1.78770e11i	−0.285438	+	1.13192i
$309$	−2.68176e10			−0.167342
$310$	3.20586e11	+	5.55270e11i	1.97159	+	3.41489i
$311$	1.39423e11	−	2.41488e11i	0.845108	−	1.46377i	−0.0404188	−	0.999183i	$-0.512869\pi$
$311$	1.39423e11	−	2.41488e11i	0.845108	−	1.46377i	0.885527	−	0.464588i	$-0.153797\pi$
$312$	−2.50107e10	+	4.33198e10i	−0.149427	+	0.258816i
$313$	−8.02662e10	−	1.39025e11i	−0.472698	−	0.818736i	0.526814	−	0.849980i	$-0.323386\pi$
$313$	−8.02662e10	−	1.39025e11i	−0.472698	−	0.818736i	−0.999512	+	0.0312443i	$0.990053\pi$
$314$	−2.79683e11			−1.62361
$315$	2.69038e11	−	7.63670e10i	1.53963	−	0.437027i
$316$	8.58359e10			0.484258
$317$	6.31818e10	+	1.09434e11i	0.351419	+	0.608676i	0.986498	−	0.163771i	$-0.0523658\pi$
$317$	6.31818e10	+	1.09434e11i	0.351419	+	0.608676i	−0.635079	+	0.772447i	$0.719032\pi$
$318$	−3.65674e11	+	6.33365e11i	−2.00526	+	3.47322i
$319$	5.32740e10	−	9.22733e10i	0.288043	−	0.498905i
$320$	2.74913e11	+	4.76163e11i	1.46561	+	2.53852i
$321$	9.46765e10			0.497702
$322$	−1.68486e11	+	4.78251e10i	−0.873397	+	0.247916i
$323$	−5.60469e11			−2.86510
$324$	1.63326e11	+	2.82889e11i	0.823384	+	1.42614i
$325$	6.29641e10	−	1.09057e11i	0.313053	−	0.542224i
$326$	−5.69660e10	+	9.86680e10i	−0.279342	+	0.483835i
$327$	−1.47821e11	−	2.56033e11i	−0.714942	−	1.23832i
$328$	−3.45598e10			−0.164869
$329$	3.53107e10	−	1.40027e11i	0.166159	−	0.658915i
$330$	−6.58270e11			−3.05556
$331$	9.69717e10	+	1.67960e11i	0.444037	+	0.769095i	0.997985	−	0.0634570i	$-0.0202126\pi$
$331$	9.69717e10	+	1.67960e11i	0.444037	+	0.769095i	−0.553948	+	0.832552i	$0.686879\pi$
$332$	−6.06912e10	+	1.05120e11i	−0.274160	+	0.474859i
$333$	−3.87887e10	+	6.71840e10i	−0.172865	+	0.299411i
$334$	−1.85734e9	−	3.21701e9i	−0.00816644	−	0.0141447i
$335$	−5.32479e11			−2.30994
$336$	−5.91759e10	−	5.74522e10i	−0.253290	−	0.245912i
$337$	−4.92241e10			−0.207895			−0.103947	−	0.994583i	$-0.533147\pi$
$337$	−4.92241e10			−0.207895			−0.103947	+	0.994583i	$0.533147\pi$
$338$	−1.45820e10	−	2.52567e10i	−0.0607703	−	0.105257i
$339$	−4.99881e10	+	8.65819e10i	−0.205574	+	0.356064i
$340$	5.73304e11	−	9.92991e11i	2.32664	−	4.02986i
$341$	1.34659e11	+	2.33237e11i	0.539314	+	0.934120i
$342$	5.89492e11			2.33003
$343$	1.73051e11	−	1.89118e11i	0.675073	−	0.737751i
$344$	−2.60393e11			−1.00258
$345$	−1.87425e11	−	3.24629e11i	−0.712264	−	1.23368i
$346$	3.74671e11	−	6.48948e11i	1.40542	−	2.43426i
$347$	−1.25219e11	+	2.16886e11i	−0.463649	+	0.803063i	−0.999139	−	0.0414780i	$-0.986793\pi$
$347$	−1.25219e11	+	2.16886e11i	−0.463649	+	0.803063i	0.535491	+	0.844541i	$0.320127\pi$
$348$	−2.07666e11	−	3.59688e11i	−0.759029	−	1.31468i
$349$	4.18259e11			1.50914			0.754571	−	0.656218i	$-0.227845\pi$
$349$	4.18259e11			1.50914			0.754571	+	0.656218i	$0.227845\pi$
$350$	−7.18455e11	−	6.97528e11i	−2.55914	−	2.48459i
$351$	−1.22685e10			−0.0431430
$352$	1.33749e11	+	2.31659e11i	0.464352	+	0.804281i
$353$	1.41879e11	−	2.45741e11i	0.486330	−	0.842349i	−0.513546	−	0.858062i	$-0.671669\pi$
$353$	1.41879e11	−	2.45741e11i	0.486330	−	0.842349i	0.999877	+	0.0157132i	$0.00500187\pi$
$354$	8.82935e10	−	1.52929e11i	0.298823	−	0.517577i
$355$	8.69139e10	+	1.50539e11i	0.290444	+	0.503063i
$356$	6.33806e11			2.09137
$357$	−1.77591e11	+	7.04246e11i	−0.578646	+	2.29465i
$358$	6.60546e10			0.212535
$359$	1.08621e11	+	1.88137e11i	0.345134	+	0.597790i	0.985378	−	0.170382i	$-0.0545001\pi$
$359$	1.08621e11	+	1.88137e11i	0.345134	+	0.597790i	−0.640244	+	0.768172i	$0.721167\pi$
$360$	−2.00054e11	+	3.46504e11i	−0.627749	+	1.08729i
$361$	−2.84865e11	+	4.93401e11i	−0.882789	+	1.52904i
$362$	−2.77069e11	−	4.79898e11i	−0.848007	−	1.46879i
$363$	1.77898e11			0.537763
$364$	−1.33731e11	+	3.79598e10i	−0.399277	+	0.113336i
$365$	−3.64965e11			−1.07630
$366$	3.88122e11	+	6.72247e11i	1.13059	+	1.95823i
$367$	1.94573e11	−	3.37011e11i	0.559868	−	0.969720i	−0.437639	−	0.899151i	$-0.644185\pi$
$367$	1.94573e11	−	3.37011e11i	0.559868	−	0.969720i	0.997507	−	0.0705694i	$-0.0224816\pi$
$368$	−2.59783e10	+	4.49957e10i	−0.0738406	+	0.127896i
$369$	3.31861e10	+	5.74801e10i	0.0931833	+	0.161398i
$370$	4.00816e11			1.11183
$371$	−6.48687e11	+	1.84131e11i	−1.77768	+	0.504598i
$372$	1.04982e12			2.84232
$373$	1.69000e10	+	2.92716e10i	0.0452060	+	0.0782990i	0.887743	−	0.460339i	$-0.152272\pi$
$373$	1.69000e10	+	2.92716e10i	0.0452060	+	0.0782990i	−0.842537	+	0.538638i	$0.818939\pi$
$374$	4.01729e11	−	6.95816e11i	1.06172	−	1.83896i
$375$	5.96899e11	−	1.03386e12i	1.55869	−	2.69973i
$376$	1.03301e11	+	1.78923e11i	0.266539	+	0.461659i
$377$	8.03382e10			0.204826
$378$	−2.38544e10	+	9.45959e10i	−0.0600973	+	0.238319i
$379$	4.72727e11			1.17689			0.588443	−	0.808539i	$-0.299741\pi$
$379$	4.72727e11			1.17689			0.588443	+	0.808539i	$0.299741\pi$
$380$	−9.12855e11	−	1.58111e12i	−2.24582	−	3.88988i
$381$	4.45273e11	−	7.71235e11i	1.08259	−	1.87510i
$382$	4.99977e11	−	8.65985e11i	1.20134	−	2.08077i
$383$	−6.36802e10	−	1.10297e11i	−0.151220	−	0.261921i	0.780456	−	0.625211i	$-0.214987\pi$
$383$	−6.36802e10	−	1.10297e11i	−0.151220	−	0.261921i	−0.931676	+	0.363289i	$0.881654\pi$
$384$	8.05059e11			1.88946
$385$	−4.35463e11	−	4.22779e11i	−1.01013	−	0.980709i
$386$	−4.05064e11			−0.928712
$387$	2.50043e11	+	4.33088e11i	0.566652	+	0.981469i
$388$	−3.74874e11	+	6.49302e11i	−0.839737	+	1.45447i
$389$	7.70456e9	−	1.33447e10i	0.0170598	−	0.0295485i	−0.857369	−	0.514701i	$-0.827903\pi$
$389$	7.70456e9	−	1.33447e10i	0.0170598	−	0.0295485i	0.874429	+	0.485153i	$0.161236\pi$
$390$	−2.48171e11	−	4.29845e11i	−0.543200	−	0.940851i
$391$	4.57527e11			0.989968
$392$	1.08380e10	+	3.66582e11i	0.0231826	+	0.784123i
$393$	8.62845e10			0.182459
$394$	4.59950e11	+	7.96656e11i	0.961562	+	1.66547i
$395$	−1.41286e11	+	2.44715e11i	−0.292020	+	0.505794i
$396$	−2.53282e11	+	4.38697e11i	−0.517578	+	0.896472i
$397$	1.41399e11	+	2.44911e11i	0.285687	+	0.494824i	0.972775	−	0.231750i	$-0.0744450\pi$
$397$	1.41399e11	+	2.44911e11i	0.285687	+	0.494824i	−0.687089	+	0.726573i	$0.741112\pi$
$398$	−9.09944e11			−1.81778
$399$	8.29732e11	+	8.05563e11i	1.63893	+	1.59119i
$400$	−2.97058e11			−0.580191
$401$	2.41882e11	+	4.18952e11i	0.467147	+	0.809122i	0.999296	−	0.0375286i	$-0.0119485\pi$
$401$	2.41882e11	+	4.18952e11i	0.467147	+	0.809122i	−0.532149	+	0.846651i	$0.678615\pi$
$402$	−7.27229e11	+	1.25960e12i	−1.38885	+	2.40555i
$403$	−1.01534e11	+	1.75863e11i	−0.191752	+	0.332125i
$404$	−6.79347e10	−	1.17666e11i	−0.126875	−	0.219754i
$405$	−1.07534e12			−1.98609
$406$	1.56206e11	−	6.19444e11i	0.285319	−	1.13145i
$407$	1.68360e11			0.304133
$408$	−5.19540e11	−	8.99870e11i	−0.928215	−	1.60772i
$409$	−1.18935e11	+	2.06002e11i	−0.210162	+	0.364012i	−0.951765	−	0.306827i	$-0.900733\pi$
$409$	−1.18935e11	+	2.06002e11i	−0.210162	+	0.364012i	0.741603	+	0.670839i	$0.234066\pi$
$410$	1.71461e11	−	2.96980e11i	0.299667	−	0.519039i
$411$	2.81778e11	+	4.88053e11i	0.487100	+	0.843683i
$412$	1.06625e11			0.182315
$413$	1.56628e11	−	4.44593e10i	0.264908	−	0.0751948i
$414$	−4.81220e11			−0.805085
$415$	−1.99796e11	−	3.46057e11i	−0.330651	−	0.572705i
$416$	−1.00848e11	+	1.74673e11i	−0.165100	+	0.285961i
$417$	1.88103e11	−	3.25804e11i	0.304637	−	0.527647i
$418$	−6.39662e11	−	1.10793e12i	−1.02484	−	1.77508i
$419$	5.57689e11			0.883952			0.441976	−	0.897027i	$-0.354278\pi$
$419$	5.57689e11			0.883952			0.441976	+	0.897027i	$0.354278\pi$
$420$	−2.27596e12	+	6.46038e11i	−3.56897	+	1.01306i
$421$	1.01172e12			1.56960			0.784801	−	0.619747i	$-0.212765\pi$
$421$	1.01172e12			1.56960			0.784801	+	0.619747i	$0.212765\pi$
$422$	5.20659e11	+	9.01808e11i	0.799185	+	1.38423i
$423$	1.98391e11	−	3.43623e11i	0.301293	−	0.521856i
$424$	4.82358e11	−	8.35469e11i	0.724808	−	1.25541i
$425$	1.30794e12	+	2.26541e12i	1.94463	+	3.36819i
$426$	4.74808e11			0.698513
$427$	−1.75003e11	+	6.93984e11i	−0.254753	+	1.01024i
$428$	−3.76428e11			−0.542232
$429$	−1.04242e11	−	1.80553e11i	−0.148589	−	0.257363i
$430$	1.29189e12	−	2.23762e12i	1.82229	−	3.15630i
$431$	1.13004e11	−	1.95729e11i	0.157742	−	0.273217i	−0.776312	−	0.630349i	$-0.782912\pi$
$431$	1.13004e11	−	1.95729e11i	0.157742	−	0.273217i	0.934054	+	0.357132i	$0.116245\pi$
$432$	1.44704e10	+	2.50634e10i	0.0199895	+	0.0346229i
$433$	−5.54252e11			−0.757725			−0.378863	−	0.925453i	$-0.623685\pi$
$433$	−5.54252e11			−0.757725			−0.378863	+	0.925453i	$0.623685\pi$
$434$	1.15856e12	+	1.12482e12i	1.56753	+	1.52187i
$435$	1.36728e12			1.83086
$436$	5.87728e11	+	1.01797e12i	0.778909	+	1.34911i
$437$	3.64253e11	−	6.30905e11i	0.477790	−	0.827557i
$438$	−4.98449e11	+	8.63338e11i	−0.647123	+	1.12085i
$439$	−1.40988e11	−	2.44199e11i	−0.181173	−	0.313800i	0.761107	−	0.648626i	$-0.224656\pi$
$439$	−1.40988e11	−	2.44199e11i	−0.181173	−	0.313800i	−0.942280	+	0.334825i	$0.891323\pi$
$440$	8.68321e11			1.10444
$441$	5.99295e11	−	3.70037e11i	0.754513	−	0.465878i
$442$	6.05815e11			0.754988
$443$	−3.71744e11	−	6.43879e11i	−0.458592	−	0.794305i	0.540294	−	0.841476i	$-0.318313\pi$
$443$	−3.71744e11	−	6.43879e11i	−0.458592	−	0.794305i	−0.998887	+	0.0471707i	$0.984980\pi$
$444$	3.28139e11	−	5.68353e11i	0.400714	−	0.694057i
$445$	−1.04325e12	+	1.80696e12i	−1.26115	+	2.18438i
$446$	−5.18037e11	−	8.97266e11i	−0.619946	−	1.07378i
$447$	9.58731e11			1.13583
$448$	9.93506e11	+	9.64568e11i	1.16525	+	1.13131i
$449$	−3.82838e10			−0.0444536			−0.0222268	−	0.999753i	$-0.507076\pi$
$449$	−3.82838e10			−0.0444536			−0.0222268	+	0.999753i	$0.507076\pi$
$450$	−1.37567e12	−	2.38273e12i	−1.58146	−	2.73916i
$451$	7.20210e10	−	1.24744e11i	0.0819718	−	0.141979i
$452$	1.98750e11	−	3.44245e11i	0.223967	−	0.387922i
$453$	5.77602e11	+	1.00044e12i	0.644447	+	1.11621i
$454$	7.72075e10			0.0852920
$455$	1.11899e11	−	4.43743e11i	0.122399	−	0.485378i
$456$	−1.65450e12			−1.79194
$457$	−2.08611e11	−	3.61324e11i	−0.223725	−	0.387502i	0.732211	−	0.681077i	$-0.238488\pi$
$457$	−2.08611e11	−	3.61324e11i	−0.223725	−	0.387502i	−0.955936	+	0.293575i	$0.905155\pi$
$458$	−8.85746e11	+	1.53416e12i	−0.940621	+	1.62920i
$459$	1.27425e11	−	2.20707e11i	0.133998	−	0.232091i
$460$	7.45190e11	+	1.29071e12i	0.775991	+	1.34406i
$461$	−1.17515e12			−1.21182			−0.605911	−	0.795532i	$-0.707191\pi$
$461$	−1.17515e12			−1.21182			−0.605911	+	0.795532i	$0.707191\pi$
$462$	−1.59483e12	+	4.52696e11i	−1.62864	+	0.462294i
$463$	−5.32817e11			−0.538845			−0.269422	−	0.963022i	$-0.586833\pi$
$463$	−5.32817e11			−0.538845			−0.269422	+	0.963022i	$0.586833\pi$
$464$	−9.47567e10	−	1.64123e11i	−0.0949028	−	0.164376i
$465$	−1.72801e12	+	2.99301e12i	−1.71399	+	2.96872i
$466$	9.97580e11	−	1.72786e12i	0.979966	−	1.69735i
$467$	1.50317e11	+	2.60356e11i	0.146245	+	0.253304i	0.929837	−	0.367972i	$-0.119948\pi$
$467$	1.50317e11	+	2.60356e11i	0.146245	+	0.253304i	−0.783592	+	0.621276i	$0.786615\pi$
$468$	−3.81954e11			−0.368048
$469$	−1.29007e12	+	3.66189e11i	−1.23122	+	0.349484i
$470$	−2.05003e12			−1.93785
$471$	−7.53771e11	−	1.30557e12i	−0.705741	−	1.22238i
$472$	−1.16468e11	+	2.01728e11i	−0.108010	+	0.187080i
$473$	5.42648e11	−	9.39893e11i	0.498474	−	0.863383i
$474$	3.85921e11	+	6.68435e11i	0.351153	+	0.608214i
$475$	4.16518e12			3.75416
$476$	7.06090e11	−	2.80004e12i	0.630418	−	2.49996i
$477$	−1.85274e12			−1.63864
$478$	4.97020e11	+	8.60864e11i	0.435460	+	0.754239i
$479$	−6.41819e10	+	1.11166e11i	−0.0557061	+	0.0964858i	−0.892534	−	0.450981i	$-0.851074\pi$
$479$	−6.41819e10	+	1.11166e11i	−0.0557061	+	0.0964858i	0.836828	+	0.547467i	$0.184408\pi$
$480$	−1.71633e12	+	2.97277e12i	−1.47576	+	2.55608i
$481$	6.34724e10	+	1.09937e11i	0.0540669	+	0.0936467i
$482$	1.70808e12			1.44144
$483$	−6.77334e11	−	6.57605e11i	−0.566293	−	0.549798i
$484$	−7.07312e11			−0.585878
$485$	−1.23409e12	−	2.13751e12i	−1.01277	−	1.75416i
$486$	−1.31750e12	+	2.28197e12i	−1.07124	+	1.85544i
$487$	6.48321e11	−	1.12292e12i	0.522288	−	0.904629i	−0.477376	−	0.878699i	$-0.658412\pi$
$487$	6.48321e11	−	1.12292e12i	0.522288	−	0.904629i	0.999664	−	0.0259296i	$-0.00825458\pi$
$488$	−5.11970e11	−	8.86758e11i	−0.408653	−	0.707808i
$489$	−6.14115e11			−0.485690
$490$	−3.20389e12	−	1.72559e12i	−2.51070	−	1.35225i
$491$	−1.09743e12			−0.852137			−0.426068	−	0.904691i	$-0.640102\pi$
$491$	−1.09743e12			−0.852137			−0.426068	+	0.904691i	$0.640102\pi$
$492$	−2.80743e11	−	4.86261e11i	−0.216006	−	0.374133i
$493$	−8.34422e11	+	1.44526e12i	−0.636172	+	1.10188i
$494$	4.82311e11	−	8.35388e11i	0.364381	−	0.631127i
$495$	−8.33807e11	−	1.44420e12i	−0.624226	−	1.08119i
$496$	4.79028e11			0.355380
$497$	3.14098e11	+	3.04949e11i	0.230920	+	0.224194i
$498$	−1.09148e12			−0.795213
$499$	1.13392e11	+	1.96400e11i	0.0818707	+	0.141804i	0.904053	−	0.427419i	$-0.140577\pi$
$499$	1.13392e11	+	1.96400e11i	0.0818707	+	0.141804i	−0.822183	+	0.569224i	$0.807244\pi$
$500$	−2.37324e12	+	4.11057e12i	−1.69815	+	2.94128i
$501$	1.00114e10	−	1.73403e10i	0.00709947	−	0.0122966i
$502$	9.77444e11	+	1.69298e12i	0.686950	+	1.18983i
$503$	−1.37090e12			−0.954880			−0.477440	−	0.878664i	$-0.658435\pi$
$503$	−1.37090e12			−0.954880			−0.477440	+	0.878664i	$0.658435\pi$
$504$	−2.46390e11	+	9.77073e11i	−0.170093	+	0.674512i
$505$	4.47283e11			0.306035
$506$	5.22175e11	+	9.04433e11i	0.354110	+	0.613337i
$507$	7.85996e10	−	1.36138e11i	0.0528304	−	0.0915050i
$508$	−1.77038e12	+	3.06639e12i	−1.17945	+	2.04287i
$509$	−4.30579e11	−	7.45785e11i	−0.284330	−	0.492474i	0.688116	−	0.725600i	$-0.258438\pi$
$509$	−4.30579e11	−	7.45785e11i	−0.284330	−	0.492474i	−0.972447	+	0.233126i	$0.925105\pi$
$510$	1.03104e13			6.74852
$511$	−8.84223e11	+	2.50989e11i	−0.573677	+	0.162840i
$512$	7.89290e11			0.507600
$513$	−2.02896e11	−	3.51426e11i	−0.129344	−	0.224030i
$514$	9.19783e11	−	1.59311e12i	0.581234	−	1.00673i
$515$	−1.75505e11	+	3.03984e11i	−0.109941	+	0.190423i
$516$	−2.11528e12	−	3.66377e12i	−1.31354	−	2.27512i
$517$	−8.61100e11			−0.530086
$518$	9.71081e11	−	2.75644e11i	0.592613	−	0.168215i
$519$	4.03909e12			2.44360
$520$	3.27361e11	+	5.67006e11i	0.196341	+	0.340073i
$521$	4.08440e11	−	7.07439e11i	0.242862	−	0.420649i	−0.718667	−	0.695355i	$-0.755247\pi$
$521$	4.08440e11	−	7.07439e11i	0.242862	−	0.420649i	0.961528	+	0.274706i	$0.0885806\pi$
$522$	8.77632e11	−	1.52010e12i	0.517363	−	0.896099i
$523$	−8.37056e11	−	1.44982e12i	−0.489212	−	0.847339i	0.510711	−	0.859752i	$-0.329382\pi$
$523$	−8.37056e11	−	1.44982e12i	−0.489212	−	0.847339i	−0.999923	+	0.0124130i	$0.996049\pi$
$524$	−3.43062e11			−0.198784
$525$	1.31978e12	−	5.23368e12i	0.758203	−	3.00670i
$526$	−1.66466e12			−0.948177
$527$	−2.10915e12	−	3.65315e12i	−1.19113	−	2.06310i
$528$	−2.45902e11	+	4.25914e11i	−0.137692	+	0.238489i
$529$	6.03226e11	−	1.04482e12i	0.334911	−	0.580083i
$530$	4.78624e12	+	8.29002e12i	2.63484	+	4.56367i
$531$	4.47353e11			0.244188
$532$	−3.29897e12	−	3.20287e12i	−1.78556	−	1.73355i
$533$	1.08609e11			0.0582899
$534$	2.84961e12	+	4.93567e12i	1.51653	+	2.62670i
$535$	6.19603e11	−	1.07318e12i	0.326980	−	0.566346i
$536$	9.59284e11	−	1.66153e12i	0.502002	−	0.869493i
$537$	1.78023e11	+	3.08345e11i	0.0923831	+	0.160012i
$538$	−1.44934e12			−0.745848
$539$	−1.34577e12	−	7.24820e11i	−0.686786	−	0.369897i
$540$	8.30169e11			0.420140
$541$	−5.30898e11	−	9.19542e11i	−0.266454	−	0.461513i	0.701489	−	0.712680i	$-0.252519\pi$
$541$	−5.30898e11	−	9.19542e11i	−0.266454	−	0.461513i	−0.967944	+	0.251167i	$0.919186\pi$
$542$	1.63476e12	−	2.83148e12i	0.813685	−	1.40934i
$543$	1.49345e12	−	2.58674e12i	0.737212	−	1.27689i
$544$	−2.09488e12	−	3.62844e12i	−1.02557	−	1.77634i
$545$	−3.86961e12			−1.87881
$546$	−8.96864e11	−	8.70740e11i	−0.431877	−	0.419297i
$547$	−7.22252e11			−0.344942			−0.172471	−	0.985015i	$-0.555175\pi$
$547$	−7.22252e11			−0.344942			−0.172471	+	0.985015i	$0.555175\pi$
$548$	−1.12033e12	−	1.94047e12i	−0.530682	−	0.919168i
$549$	−9.83240e11	+	1.70302e12i	−0.461938	+	0.800101i
$550$	−2.98549e12	+	5.17103e12i	−1.39118	+	2.40960i
$551$	1.32863e12	+	2.30125e12i	0.614074	+	1.06361i
$552$	1.35061e12			0.619164
$553$	−1.74010e11	+	6.90048e11i	−0.0791247	+	0.313774i
$554$	2.34197e12			1.05630
$555$	1.08024e12	+	1.87102e12i	0.483282	+	0.837069i
$556$	−7.47886e11	+	1.29538e12i	−0.331894	+	0.574856i
$557$	−7.98159e11	+	1.38245e12i	−0.351351	+	0.608558i	−0.986486	−	0.163843i	$-0.947611\pi$
$557$	−7.98159e11	+	1.38245e12i	−0.351351	+	0.608558i	0.635136	+	0.772401i	$0.280944\pi$
$558$	2.21837e12	+	3.84233e12i	0.968679	+	1.67780i
$559$	8.18323e11			0.354463
$560$	−1.03851e12	+	2.94783e11i	−0.446235	+	0.126665i
$561$	4.33079e12			1.84601
$562$	−1.78005e12	−	3.08314e12i	−0.752695	−	1.30371i
$563$	1.99667e12	−	3.45833e12i	0.837564	−	1.45070i	−0.0543619	−	0.998521i	$-0.517312\pi$
$563$	1.99667e12	−	3.45833e12i	0.837564	−	1.45070i	0.891926	−	0.452182i	$-0.149354\pi$
$564$	−1.67832e12	+	2.90693e12i	−0.698422	+	1.20970i
$565$	6.54286e11	+	1.13326e12i	0.270115	+	0.467854i
$566$	2.43145e12			0.995844
$567$	−2.60529e12	+	7.39518e11i	−1.05860	+	0.300486i
$568$	−6.26316e11			−0.252480
$569$	3.93707e11	+	6.81921e11i	0.157459	+	0.272727i	0.933952	−	0.357399i	$-0.116336\pi$
$569$	3.93707e11	+	6.81921e11i	0.157459	+	0.272727i	−0.776493	+	0.630126i	$0.783003\pi$
$570$	8.20846e12	−	1.42175e13i	3.25705	−	5.64138i
$571$	−8.23097e11	+	1.42565e12i	−0.324033	+	0.561241i	−0.981316	−	0.192402i	$-0.938372\pi$
$571$	−8.23097e11	+	1.42565e12i	−0.324033	+	0.561241i	0.657283	+	0.753643i	$0.271705\pi$
$572$	4.14461e11	+	7.17867e11i	0.161883	+	0.280390i
$573$	5.38993e12			2.08875
$574$	2.11175e11	−	8.37425e11i	0.0811967	−	0.321990i
$575$	−3.40016e12			−1.29716
$576$	1.90232e12	+	3.29492e12i	0.720084	+	1.24722i
$577$	−2.61138e12	+	4.52305e12i	−0.980798	+	1.69879i	−0.321499	+	0.946910i	$0.604187\pi$
$577$	−2.61138e12	+	4.52305e12i	−0.980798	+	1.69879i	−0.659298	+	0.751882i	$0.729147\pi$
$578$	−4.17234e12	+	7.22671e12i	−1.55491	+	2.69318i
$579$	−1.09168e12	−	1.89085e12i	−0.403686	−	0.699205i
$580$	−5.43621e12			−1.99467
$581$	−7.22042e11	−	7.01011e11i	−0.262888	−	0.255230i
$582$	−6.74180e12			−2.43569
$583$	2.01042e12	+	3.48216e12i	0.720741	+	1.24836i
$584$	6.57501e11	−	1.13882e12i	0.233904	−	0.405134i
$585$	6.28698e11	−	1.08894e12i	0.221943	−	0.384416i
$586$	2.60051e12	+	4.50421e12i	0.911002	+	1.57790i
$587$	1.50102e12			0.521812			0.260906	−	0.965364i	$-0.415979\pi$
$587$	1.50102e12			0.521812			0.260906	+	0.965364i	$0.415979\pi$
$588$	−5.06982e12	+	3.13039e12i	−1.74902	+	1.07994i
$589$	−6.71667e12			−2.29951
$590$	−1.15566e12	−	2.00166e12i	−0.392641	−	0.680075i
$591$	−2.47921e12	+	4.29412e12i	−0.835931	+	1.44787i
$592$	1.49728e11	−	2.59336e11i	0.0501020	−	0.0867791i
$593$	−2.02404e12	−	3.50574e12i	−0.672160	−	1.16422i	−0.977290	−	0.211905i	$-0.932033\pi$
$593$	−2.02404e12	−	3.50574e12i	−0.672160	−	1.16422i	0.305130	−	0.952311i	$-0.401300\pi$
$594$	5.81722e11			0.191724
$595$	6.82059e12	+	6.62192e12i	2.23098	+	2.16599i
$596$	−3.81186e12			−1.23745
$597$	−2.45238e12	−	4.24765e12i	−0.790140	−	1.36856i
$598$	−3.93725e11	+	6.81951e11i	−0.125903	+	0.218071i
$599$	−6.25024e11	+	1.08257e12i	−0.198370	+	0.343587i	−0.948000	−	0.318270i	$-0.896898\pi$
$599$	−6.25024e11	+	1.08257e12i	−0.198370	+	0.343587i	0.749630	+	0.661857i	$0.230231\pi$
$600$	3.86102e12	+	6.68748e12i	1.21625	+	2.10660i
$601$	−2.24452e12			−0.701759			−0.350879	−	0.936421i	$-0.614117\pi$
$601$	−2.24452e12			−0.701759			−0.350879	+	0.936421i	$0.614117\pi$
$602$	1.59111e12	−	6.30964e12i	0.493760	−	1.95804i
$603$	−3.68462e12			−1.13492
$604$	−2.29651e12	−	3.97768e12i	−0.702106	−	1.21608i
$605$	1.16424e12	−	2.01652e12i	0.353299	−	0.611933i
$606$	6.10874e11	−	1.05806e12i	0.184003	−	0.318702i
$607$	1.88152e12	+	3.25889e12i	0.562549	+	0.974363i	0.997273	+	0.0737995i	$0.0235125\pi$
$607$	1.88152e12	+	3.25889e12i	0.562549	+	0.974363i	−0.434724	+	0.900564i	$0.643154\pi$
$608$	−6.67124e12			−1.97989
$609$	3.31258e12	−	9.40284e11i	0.975862	−	0.277001i
$610$	1.01601e13			2.97109
$611$	−3.24639e11	−	5.62291e11i	−0.0942356	−	0.163221i
$612$	3.96711e12	−	6.87124e12i	1.14312	−	1.97995i
$613$	1.19344e12	−	2.06709e12i	0.341372	−	0.591273i	−0.643316	−	0.765601i	$-0.722442\pi$
$613$	1.19344e12	−	2.06709e12i	0.341372	−	0.591273i	0.984688	+	0.174328i	$0.0557752\pi$
$614$	4.93863e12	+	8.55397e12i	1.40233	+	2.42890i
$615$	1.84842e12			0.521029
$616$	2.10373e12	−	5.97149e11i	0.588677	−	0.167097i
$617$	4.82886e12			1.34141			0.670705	−	0.741725i	$-0.265992\pi$
$617$	4.82886e12			1.34141			0.670705	+	0.741725i	$0.265992\pi$
$618$	4.79390e11	+	8.30328e11i	0.132203	+	0.228982i
$619$	−2.45935e12	+	4.25972e12i	−0.673306	+	1.16620i	0.303655	+	0.952782i	$0.401793\pi$
$619$	−2.45935e12	+	4.25972e12i	−0.673306	+	1.16620i	−0.976961	+	0.213418i	$0.931540\pi$
$620$	6.87049e12	−	1.19000e13i	1.86735	−	3.23434i
$621$	1.65630e11	+	2.86879e11i	0.0446916	+	0.0774081i
$622$	−9.96928e12			−2.67059
$623$	−1.28488e12	+	5.09527e12i	−0.341717	+	1.35510i
$624$	−3.70824e11			−0.0979123
$625$	−3.50696e12	−	6.07423e12i	−0.919328	−	1.59232i
$626$	−2.86967e12	+	4.97042e12i	−0.746875	+	1.29363i
$627$	3.44790e12	−	5.97193e12i	0.890944	−	1.54316i
$628$	2.99695e12	+	5.19087e12i	0.768885	+	1.33175i
$629$	−2.63699e12			−0.671708
$630$	−7.17379e12	−	6.96483e12i	−1.81433	−	1.76148i
$631$	−2.52088e12			−0.633025			−0.316512	−	0.948588i	$-0.602512\pi$
$631$	−2.52088e12			−0.633025			−0.316512	+	0.948588i	$0.602512\pi$
$632$	−5.09066e11	−	8.81729e11i	−0.126925	−	0.219841i
$633$	−2.80645e12	+	4.86091e12i	−0.694769	+	1.20337i
$634$	2.25887e12	−	3.91248e12i	0.555252	−	0.961725i
$635$	−5.82810e12	−	1.00946e13i	−1.42248	−	2.46380i
$636$	1.56735e13			3.79848
$637$	−3.40599e10	−	1.15204e12i	−0.00819627	−	0.277229i
$638$	−3.80930e12			−0.910232
$639$	6.01422e11	+	1.04169e12i	0.142700	+	0.247164i
$640$	5.26864e12	−	9.12556e12i	1.24133	−	2.15005i
$641$	3.10736e12	−	5.38211e12i	0.726994	−	1.25919i	−0.231155	−	0.972917i	$-0.574250\pi$
$641$	3.10736e12	−	5.38211e12i	0.726994	−	1.25919i	0.958148	−	0.286273i	$-0.0924164\pi$
$642$	−1.69243e12	−	2.93138e12i	−0.393192	−	0.681028i
$643$	−2.37867e12			−0.548762			−0.274381	−	0.961621i	$-0.588473\pi$
$643$	−2.37867e12			−0.548762			−0.274381	+	0.961621i	$0.588473\pi$
$644$	2.69304e12	+	2.61460e12i	0.616959	+	0.598989i
$645$	1.39270e13			3.16840
$646$	1.00189e13	+	1.73533e13i	2.26347	+	3.92044i
$647$	1.23810e12	−	2.14445e12i	0.277771	−	0.481113i	−0.693059	−	0.720880i	$-0.743738\pi$
$647$	1.23810e12	−	2.14445e12i	0.277771	−	0.481113i	0.970830	+	0.239767i	$0.0770710\pi$
$648$	1.93727e12	−	3.35545e12i	0.431621	−	0.747590i
$649$	−4.85426e11	−	8.40782e11i	−0.107404	−	0.186030i
$650$	−4.50218e12			−0.989265
$651$	−2.12825e12	+	8.43970e12i	−0.464417	+	1.84167i
$652$	2.44168e12			0.529146
$653$	6.54424e11	+	1.13350e12i	0.140848	+	0.243955i	0.927816	−	0.373038i	$-0.121684\pi$
$653$	6.54424e11	+	1.13350e12i	0.140848	+	0.243955i	−0.786968	+	0.616993i	$0.788351\pi$
$654$	−5.28489e12	+	9.15369e12i	−1.12963	+	1.95658i
$655$	5.64682e11	−	9.78057e11i	0.119872	−	0.207624i
$656$	−1.28101e11	−	2.21878e11i	−0.0270076	−	0.0467786i
$657$	−2.52547e12			−0.528807
$658$	−4.96674e12	+	1.40982e12i	−1.03289	+	0.293189i
$659$	−5.97580e11			−0.123428			−0.0617138	−	0.998094i	$-0.519657\pi$
$659$	−5.97580e11			−0.123428			−0.0617138	+	0.998094i	$0.519657\pi$
$660$	7.05371e12	+	1.22174e13i	1.44701	+	2.50629i
$661$	8.22956e11	−	1.42540e12i	0.167676	−	0.290423i	−0.769927	−	0.638132i	$-0.779707\pi$
$661$	8.22956e11	−	1.42540e12i	0.167676	−	0.290423i	0.937602	+	0.347710i	$0.113041\pi$
$662$	3.46693e12	−	6.00490e12i	0.701591	−	1.21519i
$663$	1.63273e12	+	2.82797e12i	0.328173	+	0.568412i
$664$	1.43976e12			0.287432
$665$	1.45614e13	−	4.13329e12i	2.88739	−	0.819593i
$666$	2.77355e12			0.546262
$667$	−1.08460e12	−	1.87858e12i	−0.212179	−	0.367504i
$668$	−3.98048e10	+	6.89440e10i	−0.00773466	+	0.0133968i
$669$	2.79231e12	−	4.83643e12i	0.538948	−	0.933485i
$670$	9.51859e12	+	1.64867e13i	1.82489	+	3.16080i
$671$	4.26768e12			0.812720
$672$	−2.11386e12	+	8.38262e12i	−0.399865	+	1.58569i
$673$	−2.44650e12			−0.459703			−0.229851	−	0.973226i	$-0.573824\pi$
$673$	−2.44650e12			−0.459703			−0.229851	+	0.973226i	$0.573824\pi$
$674$	8.79929e11	+	1.52408e12i	0.164240	+	0.284471i
$675$	−9.46974e11	+	1.64021e12i	−0.175578	+	0.304111i
$676$	−3.12507e11	+	5.41279e11i	−0.0575572	+	0.0996921i
$677$	−2.97431e12	−	5.15165e12i	−0.544173	−	0.942535i	−0.998658	−	0.0517808i	$-0.983510\pi$
$677$	−2.97431e12	−	5.15165e12i	−0.544173	−	0.942535i	0.454486	−	0.890754i	$-0.349823\pi$
$678$	3.57434e12			0.649625
$679$	−4.45988e12	−	4.32997e12i	−0.805210	−	0.781755i
$680$	−1.36004e13			−2.43927
$681$	2.08081e11	+	3.60407e11i	0.0370741	+	0.0642143i
$682$	4.81434e12	−	8.33867e12i	0.852132	−	1.47594i
$683$	−2.92497e12	+	5.06619e12i	−0.514313	+	0.890817i	0.485549	+	0.874210i	$0.338620\pi$
$683$	−2.92497e12	+	5.06619e12i	−0.514313	+	0.890817i	−0.999862	+	0.0166071i	$0.994714\pi$
$684$	−6.31672e12	−	1.09409e13i	−1.10342	−	1.91117i
$685$	7.37629e12			1.28006
$686$	−8.94895e12	−	1.97735e12i	−1.54281	−	0.340899i
$687$	−9.54867e12			−1.63545
$688$	−9.65189e11	−	1.67176e12i	−0.164234	−	0.284462i
$689$	−1.51588e12	+	2.62558e12i	−0.256258	+	0.443852i
$690$	−6.70080e12	+	1.16061e13i	−1.12540	+	1.94925i
$691$	−4.19682e12	−	7.26911e12i	−0.700276	−	1.21291i	−0.968369	−	0.249521i	$-0.919727\pi$
$691$	−4.19682e12	−	7.26911e12i	−0.700276	−	1.21291i	0.268093	−	0.963393i	$-0.413606\pi$
$692$	−1.60592e13			−2.66223
$693$	−3.01329e12	−	2.92552e12i	−0.496297	−	0.481841i
$694$	8.95368e12			1.46516
$695$	−2.46205e12	−	4.26439e12i	−0.400281	−	0.693307i
$696$	−2.46321e12	+	4.26640e12i	−0.397886	+	0.689160i
$697$	−1.12805e12	+	1.95384e12i	−0.181043	+	0.313576i
$698$	−7.47678e12	−	1.29502e13i	−1.19224	−	2.06503i
$699$	1.07543e13			1.70386
$700$	−5.24738e12	+	2.08088e13i	−0.826041	+	3.27571i
$701$	8.97194e12			1.40332			0.701658	−	0.712514i	$-0.252444\pi$
$701$	8.97194e12			1.40332			0.701658	+	0.712514i	$0.252444\pi$
$702$	2.19312e11	+	3.79859e11i	0.0340835	+	0.0590344i
$703$	−2.09940e12	+	3.63627e12i	−0.324188	+	0.561509i
$704$	4.12845e12	−	7.15069e12i	0.633447	−	1.09716i
$705$	−5.52503e12	−	9.56963e12i	−0.842333	−	1.45896i
$706$	−1.01449e13			−1.53683
$707$	1.08366e12	−	3.07599e11i	0.163119	−	0.0463018i
$708$	−3.78445e12			−0.566047
$709$	−6.61522e12	−	1.14579e13i	−0.983188	−	1.70293i	−0.649728	−	0.760167i	$-0.725117\pi$
$709$	−6.61522e12	−	1.14579e13i	−0.983188	−	1.70293i	−0.333460	−	0.942764i	$-0.608216\pi$
$710$	3.10734e12	−	5.38207e12i	0.458909	−	0.794854i
$711$	−9.77664e11	+	1.69336e12i	−0.143475	+	0.248506i
$712$	−3.75891e12	−	6.51062e12i	−0.548153	−	0.949429i
$713$	5.48301e12			0.794541
$714$	2.49795e13	−	7.09050e12i	3.59702	−	1.02102i
$715$	−2.72882e12			−0.390479
$716$	−7.07810e11	−	1.22596e12i	−0.100649	−	0.174329i
$717$	−2.67903e12	+	4.64022e12i	−0.378566	+	0.655695i
$718$	3.88340e12	−	6.72625e12i	0.545322	−	0.944525i
$719$	4.24564e12	+	7.35367e12i	0.592466	+	1.02618i	0.993899	+	0.110293i	$0.0351789\pi$
$719$	4.24564e12	+	7.35367e12i	0.592466	+	1.02618i	−0.401433	+	0.915888i	$0.631488\pi$
$720$	−2.96613e12			−0.411333
$721$	−2.16155e11	+	8.57176e11i	−0.0297891	+	0.118130i
$722$	2.03690e13			2.78966
$723$	4.60342e12	+	7.97336e12i	0.626554	+	1.08522i
$724$	−5.93788e12	+	1.02847e13i	−0.803171	+	1.39113i
$725$	6.20109e12	−	1.07406e13i	0.833580	−	1.44380i
$726$	−3.18010e12	−	5.50809e12i	−0.424841	−	0.735845i
$727$	−8.37329e12			−1.11171			−0.555855	−	0.831279i	$-0.687609\pi$
$727$	−8.37329e12			−1.11171			−0.555855	+	0.831279i	$0.687609\pi$
$728$	1.18305e12	+	1.14859e12i	0.156103	+	0.151556i
$729$	−5.81173e12			−0.762135
$730$	6.52411e12	+	1.13001e13i	0.850293	+	1.47275i
$731$	−8.49940e12	+	1.47214e13i	−1.10093	+	1.90687i
$732$	8.31787e12	−	1.44070e13i	1.07081	−	1.85470i
$733$	−4.65351e12	−	8.06011e12i	−0.595405	−	1.03127i	−0.993490	−	0.113923i	$-0.963658\pi$
$733$	−4.65351e12	−	8.06011e12i	−0.595405	−	1.03127i	0.398084	−	0.917349i	$-0.369675\pi$
$734$	−1.39127e13			−1.76922
$735$	−5.79666e11	−	1.96065e13i	−0.0732630	−	2.47803i
$736$	5.44593e12			0.684103
$737$	3.99820e12	+	6.92509e12i	0.499185	+	0.864613i
$738$	1.18647e12	−	2.05502e12i	0.147232	−	0.255014i
$739$	6.32115e12	−	1.09486e13i	0.779644	−	1.35038i	−0.152503	−	0.988303i	$-0.548733\pi$
$739$	6.32115e12	−	1.09486e13i	0.779644	−	1.35038i	0.932147	−	0.362080i	$-0.117933\pi$
$740$	−4.29496e12	−	7.43909e12i	−0.526522	−	0.911962i
$741$	5.19949e12			0.633547
$742$	1.72970e13	+	1.67932e13i	2.09485	+	2.03383i
$743$	3.36045e12			0.404527			0.202264	−	0.979331i	$-0.435170\pi$
$743$	3.36045e12			0.404527			0.202264	+	0.979331i	$0.435170\pi$
$744$	−6.22618e12	−	1.07841e13i	−0.744978	−	1.29034i
$745$	6.27434e12	−	1.08675e13i	0.746216	−	1.29248i
$746$	6.04206e11	−	1.04652e12i	0.0714267	−	0.123715i
$747$	−1.38254e12	−	2.39462e12i	−0.162455	−	0.281381i
$748$	−1.72190e13			−2.01118
$749$	7.63112e11	−	3.02617e12i	0.0885973	−	0.351338i
$750$	−4.26806e13			−4.92555
$751$	−1.79160e12	−	3.10313e12i	−0.205523	−	0.355976i	0.744776	−	0.667314i	$-0.232556\pi$
$751$	−1.79160e12	−	3.10313e12i	−0.205523	−	0.355976i	−0.950299	+	0.311338i	$0.899223\pi$
$752$	−7.65805e11	+	1.32641e12i	−0.0873249	+	0.151251i
$753$	−5.26860e12	+	9.12548e12i	−0.597197	+	1.03438i
$754$	−1.43612e12	−	2.48744e12i	−0.161816	−	0.280273i
$755$	1.51203e13			1.69355
$756$	2.01130e12	−	5.70912e11i	0.223938	−	0.0635654i
$757$	−4.74472e12			−0.525145			−0.262572	−	0.964912i	$-0.584571\pi$
$757$	−4.74472e12			−0.525145			−0.262572	+	0.964912i	$0.584571\pi$
$758$	−8.45046e12	−	1.46366e13i	−0.929756	−	1.61039i
$759$	−2.81462e12	+	4.87506e12i	−0.307844	+	0.533202i
$760$	−1.08277e13	+	1.87542e13i	−1.17727	+	2.03909i
$761$	−1.42317e12	−	2.46500e12i	−0.153825	−	0.266432i	0.778806	−	0.627265i	$-0.215826\pi$
$761$	−1.42317e12	−	2.46500e12i	−0.153825	−	0.266432i	−0.932630	+	0.360833i	$0.882492\pi$
$762$	−3.18387e13			−3.42104
$763$	−9.37512e12	+	2.66115e12i	−1.00142	+	0.284256i
$764$	−2.14301e13			−2.27564
$765$	1.30598e13	+	2.26202e13i	1.37867	+	2.38792i
$766$	−2.27669e12	+	3.94335e12i	−0.238932	+	0.413843i
$767$	3.66015e11	−	6.33957e11i	0.0381874	−	0.0661425i
$768$	−3.63737e12	−	6.30012e12i	−0.377279	−	0.653466i
$769$	3.36608e12			0.347101			0.173551	−	0.984825i	$-0.444476\pi$
$769$	3.36608e12			0.347101			0.173551	+	0.984825i	$0.444476\pi$
$770$	−5.30580e12	+	2.10404e13i	−0.543929	+	2.15698i
$771$	9.91560e12			1.01059
$772$	4.34048e12	+	7.51792e12i	0.439804	+	0.761763i
$773$	−6.86253e12	+	1.18863e13i	−0.691316	+	1.19740i	0.280090	+	0.959974i	$0.409636\pi$
$773$	−6.86253e12	+	1.18863e13i	−0.691316	+	1.19740i	−0.971407	+	0.237421i	$0.923698\pi$
$774$	8.93954e12	−	1.54837e13i	0.895325	−	1.55075i
$775$	1.56743e13	+	2.71488e13i	1.56074	+	2.70329i
$776$	8.89306e12			0.880387
$777$	3.90387e12	+	3.79015e12i	0.384238	+	0.373046i
$778$	−5.50906e11			−0.0539100
$779$	1.79617e12	+	3.11105e12i	0.174754	+	0.302683i
$780$	−5.31856e12	+	9.21202e12i	−0.514480	+	0.891106i
$781$	1.30521e12	−	2.26070e12i	0.125531	−	0.217427i
$782$	−8.17873e12	−	1.41660e13i	−0.782088	−	1.35462i
$783$	−1.20828e12			−0.114879
$784$	−2.31333e12	+	1.42838e12i	−0.218683	+	0.135027i
$785$	−1.97320e13			−1.85463
$786$	−1.54242e12	−	2.67155e12i	−0.144145	−	0.249667i
$787$	−1.27123e12	+	2.20184e12i	−0.118124	+	0.204597i	−0.919024	−	0.394201i	$-0.871021\pi$
$787$	−1.27123e12	+	2.20184e12i	−0.118124	+	0.204597i	0.800900	+	0.598798i	$0.204355\pi$
$788$	9.85721e12	−	1.70732e13i	0.910722	−	1.57742i
$789$	−4.48641e12	−	7.77069e12i	−0.412147	−	0.713860i
$790$	1.01025e13			0.922800
$791$	2.36452e12	+	2.29565e12i	0.214758	+	0.208502i
$792$	6.00855e12			0.542634
$793$	1.60894e12	+	2.78676e12i	0.144481	+	0.250248i
$794$	5.05530e12	−	8.75604e12i	0.451393	−	0.781835i
$795$	−2.57987e13	+	4.46847e13i	−2.29058	+	3.96741i
$796$	9.75054e12	+	1.68884e13i	0.860834	+	1.49101i
$797$	−6.53297e11			−0.0573520			−0.0286760	−	0.999589i	$-0.509129\pi$
$797$	−6.53297e11			−0.0573520			−0.0286760	+	0.999589i	$0.509129\pi$
$798$	1.01097e13	−	4.00905e13i	0.882519	−	3.49968i
$799$	1.34873e13			1.17075
$800$	1.55683e13	+	2.69651e13i	1.34381	+	2.32754i
$801$	−7.21900e12	+	1.25037e13i	−0.619628	+	1.07323i
$802$	8.64775e12	−	1.49783e13i	0.738105	−	1.27844i
$803$	2.74040e12	+	4.74651e12i	0.232592	+	0.402861i
$804$	3.11706e13			2.63083
$805$	−1.18869e13	+	3.37412e12i	−0.997669	+	0.283191i
$806$	7.26011e12			0.605948
$807$	−3.90610e12	−	6.76557e12i	−0.324200	−	0.561531i
$808$	−8.05800e11	+	1.39569e12i	−0.0665084	+	0.115196i
$809$	−1.10340e13	+	1.91114e13i	−0.905659	+	1.56865i	−0.0856280	+	0.996327i	$0.527290\pi$
$809$	−1.10340e13	+	1.91114e13i	−0.905659	+	1.56865i	−0.820031	+	0.572320i	$0.806044\pi$
$810$	1.92228e13	+	3.32948e13i	1.56904	+	2.71765i
$811$	−5.34958e12			−0.434236			−0.217118	−	0.976145i	$-0.569666\pi$
$811$	−5.34958e12			−0.434236			−0.217118	+	0.976145i	$0.569666\pi$
$812$	−1.31706e13	+	3.73851e12i	−1.06317	+	0.301784i
$813$	1.76233e13			1.41475
$814$	−3.00959e12	−	5.21277e12i	−0.240269	−	0.416158i
$815$	−4.01902e12	+	6.96115e12i	−0.319089	+	0.552678i
$816$	3.85151e12	−	6.67102e12i	0.304107	−	0.526728i
$817$	1.35333e13	+	2.34404e13i	1.06269	+	1.84063i
$818$	8.50432e12			0.664125
$819$	7.74314e11	−	3.07059e12i	0.0601367	−	0.238476i
$820$	−7.34920e12			−0.567646
$821$	−2.47414e12	−	4.28534e12i	−0.190055	−	0.329186i	0.755213	−	0.655480i	$-0.227533\pi$
$821$	−2.47414e12	−	4.28534e12i	−0.190055	−	0.329186i	−0.945268	+	0.326294i	$0.894200\pi$
$822$	1.00741e13	−	1.74489e13i	0.769632	−	1.33304i
$823$	−9.37832e12	+	1.62437e13i	−0.712567	+	1.23420i	0.251323	+	0.967903i	$0.419134\pi$
$823$	−9.37832e12	+	1.62437e13i	−0.712567	+	1.23420i	−0.963890	+	0.266299i	$0.914199\pi$
$824$	−6.32361e11	−	1.09528e12i	−0.0477851	−	0.0827662i
$825$	−3.21847e13			−2.41884
$826$	−4.17644e12	−	4.05479e12i	−0.312173	−	0.303080i
$827$	−1.14171e13			−0.848749			−0.424375	−	0.905487i	$-0.639506\pi$
$827$	−1.14171e13			−0.848749			−0.424375	+	0.905487i	$0.639506\pi$
$828$	5.15652e12	+	8.93136e12i	0.381259	+	0.660360i
$829$	8.32377e11	−	1.44172e12i	0.0612103	−	0.106019i	−0.833796	−	0.552072i	$-0.813837\pi$
$829$	8.32377e11	−	1.44172e12i	0.0612103	−	0.106019i	0.895007	+	0.446053i	$0.147171\pi$
$830$	−7.14310e12	+	1.23722e13i	−0.522438	+	0.904890i
$831$	6.31183e12	+	1.09324e13i	0.459146	+	0.795264i
$832$	6.22578e12			0.450442
$833$	2.10786e13	+	1.13527e13i	1.51684	+	0.816955i
$834$	−1.34501e13			−0.962671
$835$	−1.31038e11	−	2.26964e11i	−0.00932841	−	0.0161573i
$836$	−1.37086e13	+	2.37441e13i	−0.970658	+	1.68123i
$837$	1.52707e12	−	2.64496e12i	0.107546	−	0.186275i
$838$	−9.96923e12	−	1.72672e13i	−0.698334	−	1.20955i
$839$	3.66205e12			0.255150			0.127575	−	0.991829i	$-0.459281\pi$
$839$	3.66205e12			0.255150			0.127575	+	0.991829i	$0.459281\pi$
$840$	2.01343e13	+	1.95478e13i	1.39534	+	1.35470i
$841$	−6.59495e12			−0.454600
$842$	−1.80854e13	−	3.13249e13i	−1.24001	−	2.14776i
$843$	9.59480e12	−	1.66187e13i	0.654353	−	1.13337i
$844$	1.11583e13	−	1.93267e13i	0.756931	−	1.31104i
$845$	−1.02878e12	−	1.78189e12i	−0.0694170	−	0.120234i
$846$	−1.41857e13			−0.952104
$847$	1.43390e12	−	5.68619e12i	0.0957287	−	0.379618i
$848$	7.15174e12			0.474931
$849$	6.55298e12	+	1.13501e13i	0.432866	+	0.749747i
$850$	4.67613e13	−	8.09929e13i	3.07257	−	5.32184i
$851$	1.71380e12	−	2.96839e12i	0.112015	−	0.194016i
$852$	−5.08782e12	−	8.81236e12i	−0.330791	−	0.572946i
$853$	3.06326e13			1.98113			0.990565	−	0.137046i	$-0.0437608\pi$
$853$	3.06326e13			1.98113			0.990565	+	0.137046i	$0.0437608\pi$
$854$	2.46155e13	−	6.98718e12i	1.58361	−	0.449513i
$855$	4.15894e13			2.66155
$856$	2.23248e12	+	3.86677e12i	0.142120	+	0.246159i
$857$	4.52400e12	−	7.83580e12i	0.286490	−	0.496214i	−0.686480	−	0.727149i	$-0.740845\pi$
$857$	4.52400e12	−	7.83580e12i	0.286490	−	0.496214i	0.972969	+	0.230934i	$0.0741783\pi$
$858$	−3.72686e12	+	6.45511e12i	−0.234774	+	0.406641i
$859$	−5.69443e12	−	9.86304e12i	−0.356846	−	0.618075i	0.630586	−	0.776119i	$-0.282815\pi$
$859$	−5.69443e12	−	9.86304e12i	−0.356846	−	0.618075i	−0.987432	+	0.158044i	$0.949481\pi$
$860$	−5.53731e13			−3.45188
$861$	4.47827e12	−	1.27117e12i	0.277713	−	0.0788294i
$862$	−8.08024e12			−0.498473
$863$	1.60543e13	+	2.78068e13i	0.985240	+	1.70649i	0.640866	+	0.767653i	$0.278575\pi$
$863$	1.60543e13	+	2.78068e13i	0.985240	+	1.70649i	0.344374	+	0.938833i	$0.388091\pi$
$864$	1.51674e12	−	2.62707e12i	0.0925975	−	0.160384i
$865$	2.64335e13	−	4.57841e13i	1.60539	−	2.78062i
$866$	9.90780e12	+	1.71608e13i	0.598614	+	1.03683i
$867$	−4.49794e13			−2.70351
$868$	8.46180e12	−	3.35558e13i	0.505969	−	2.00645i
$869$	4.24348e12			0.252426
$870$	−2.44414e13	−	4.23337e13i	−1.44640	−	2.50524i
$871$	−3.01468e12	+	5.22158e12i	−0.177484	+	0.307412i
$872$	6.97127e12	−	1.20746e13i	0.408308	−	0.707209i
$873$	−8.53959e12	−	1.47910e13i	−0.497591	−	0.861853i
$874$	−2.60455e13			−1.50984
$875$	−2.82344e13	−	2.74120e13i	−1.62833	−	1.58090i
$876$	2.13646e13			1.22582
$877$	−9.32190e11	−	1.61460e12i	−0.0532116	−	0.0921651i	0.838193	−	0.545374i	$-0.183612\pi$
$877$	−9.32190e11	−	1.61460e12i	−0.0532116	−	0.0921651i	−0.891404	+	0.453209i	$0.850279\pi$
$878$	−5.04061e12	+	8.73059e12i	−0.286258	+	0.495813i
$879$	−1.40172e13	+	2.42785e13i	−0.791976	+	1.37174i
$880$	3.21857e12	+	5.57472e12i	0.180922	+	0.313365i
$881$	−2.82798e13			−1.58156			−0.790780	−	0.612101i	$-0.790325\pi$
$881$	−2.82798e13			−1.58156			−0.790780	+	0.612101i	$0.790325\pi$
$882$	−2.21701e13	−	1.19406e13i	−1.23356	−	0.664384i
$883$	2.47105e13			1.36791			0.683956	−	0.729524i	$-0.260258\pi$
$883$	2.47105e13			1.36791			0.683956	+	0.729524i	$0.260258\pi$
$884$	−6.49163e12	−	1.12438e13i	−0.357535	−	0.619269i
$885$	6.22922e12	−	1.07893e13i	0.341341	−	0.591220i
$886$	−1.32906e13	+	2.30199e13i	−0.724589	+	1.25502i
$887$	8.13471e12	+	1.40897e13i	0.441251	+	0.764270i	0.997783	−	0.0665570i	$-0.0212014\pi$
$887$	8.13471e12	+	1.40897e13i	0.441251	+	0.764270i	−0.556531	+	0.830827i	$0.687868\pi$
$888$	−7.78437e12			−0.420112
$889$	−2.10622e13	−	2.04487e13i	−1.13096	−	1.09801i
$890$	7.45963e13			3.98531
$891$	8.07437e12	+	1.39852e13i	0.429199	+	0.743395i
$892$	−1.11021e13	+	1.92294e13i	−0.587168	+	1.01700i
$893$	1.07377e13	−	1.85982e13i	0.565041	−	0.978679i
$894$	−1.71383e13	−	2.96843e13i	−0.897321	−	1.55421i
$895$	4.66024e12			0.242775
$896$	6.48894e12	−	2.57323e13i	0.336347	−	1.33380i
$897$	−4.24449e12			−0.218907
$898$	6.84361e11	+	1.18535e12i	0.0351190	+	0.0608278i
$899$	−9.99973e12	+	1.73200e13i	−0.510587	+	0.884363i
$900$	−2.94820e13	+	5.10644e13i	−1.49784	+	2.59434i
$901$	−3.14889e13	−	5.45404e13i	−1.59183	−	2.75713i
$902$	−5.14978e12			−0.259036
$903$	3.37418e13	−	9.57770e12i	1.68878	−	0.479365i
$904$	−4.71489e12			−0.234809
$905$	−1.95476e13	−	3.38574e13i	−0.968666	−	1.67778i
$906$	2.06504e13	−	3.57676e13i	1.01824	−	1.76365i
$907$	−1.29437e13	+	2.24192e13i	−0.635076	+	1.09998i	0.351423	+	0.936217i	$0.385698\pi$
$907$	−1.29437e13	+	2.24192e13i	−0.635076	+	1.09998i	−0.986499	+	0.163767i	$0.947635\pi$
$908$	−8.27319e11	−	1.43296e12i	−0.0403912	−	0.0699596i
$909$	3.09509e12			0.150361
$910$	−1.57395e13	+	4.46771e12i	−0.760861	+	0.215972i
$911$	2.76947e13			1.33218			0.666092	−	0.745870i	$-0.267966\pi$
$911$	2.76947e13			1.33218			0.666092	+	0.745870i	$0.267966\pi$
$912$	−6.13266e12	−	1.06221e13i	−0.293543	−	0.508432i
$913$	−3.00040e12	+	5.19685e12i	−0.142909	+	0.247526i
$914$	−7.45824e12	+	1.29181e13i	−0.353491	+	0.612265i
$915$	2.73825e13	+	4.74279e13i	1.29145	+	2.23686i
$916$	3.79650e13			1.78178
$917$	6.95471e11	−	2.75793e12i	0.0324801	−	0.128802i
$918$	−9.11141e12			−0.423441
$919$	−2.00897e12	−	3.47963e12i	−0.0929080	−	0.160921i	0.815826	−	0.578298i	$-0.196283\pi$
$919$	−2.00897e12	−	3.47963e12i	−0.0929080	−	0.160921i	−0.908734	+	0.417377i	$0.862950\pi$
$920$	8.83899e12	−	1.53096e13i	0.406778	−	0.704560i
$921$	−2.66201e13	+	4.61074e13i	−1.21911	+	2.11156i
$922$	2.10069e13	+	3.63851e13i	0.957357	+	1.65819i
$923$	1.96829e12			0.0892649
$924$	2.54914e13	+	2.47489e13i	1.15046	+	1.11695i
$925$	1.95971e13			0.880143
$926$	9.52463e12	+	1.64971e13i	0.425695	+	0.737325i
$927$	−1.21445e12	+	2.10349e12i	−0.0540159	+	0.0935583i
$928$	−9.93210e12	+	1.72029e13i	−0.439618	+	0.761440i
$929$	−2.39897e12	−	4.15513e12i	−0.105670	−	0.183027i	0.808342	−	0.588714i	$-0.200366\pi$
$929$	−2.39897e12	−	4.15513e12i	−0.105670	−	0.183027i	−0.914012	+	0.405687i	$0.867032\pi$
$930$	1.23560e14			5.41632
$931$	3.24362e13	−	2.00279e13i	1.41500	−	0.873699i
$932$	−4.27584e13			−1.85631
$933$	−2.68681e13	−	4.65370e13i	−1.16083	−	2.01062i
$934$	5.37412e12	−	9.30824e12i	0.231071	−	0.400227i
$935$	2.83425e13	−	4.90907e13i	1.21279	−	2.10062i
$936$	2.26525e12	+	3.92353e12i	0.0964662	+	0.167084i
$937$	−3.77577e13			−1.60021			−0.800106	−	0.599859i	$-0.795223\pi$
$937$	−3.77577e13			−1.60021			−0.800106	+	0.599859i	$0.795223\pi$
$938$	3.43992e13	+	3.33972e13i	1.45089	+	1.40863i
$939$	−3.09361e13			−1.29859
$940$	2.19672e13	+	3.80483e13i	0.917697	+	1.58950i
$941$	−2.22589e13	+	3.85535e13i	−0.925444	+	1.60292i	−0.134597	+	0.990900i	$0.542974\pi$
$941$	−2.22589e13	+	3.85535e13i	−0.925444	+	1.60292i	−0.790846	+	0.612015i	$0.790359\pi$
$942$	−2.69488e13	+	4.66767e13i	−1.11509	+	1.93139i
$943$	−1.46626e12	−	2.53964e12i	−0.0603822	−	0.104585i
$944$	−1.72682e12			−0.0707739
$945$	−1.68296e12	+	6.67386e12i	−0.0686483	+	0.272229i
$946$	−3.88014e13			−1.57521
$947$	1.43990e13	+	2.49398e13i	0.581778	+	1.00767i	0.995269	+	0.0971607i	$0.0309761\pi$
$947$	1.43990e13	+	2.49398e13i	0.581778	+	1.00767i	−0.413491	+	0.910508i	$0.635691\pi$
$948$	8.27070e12	−	1.43253e13i	0.332586	−	0.576057i
$949$	−2.06629e12	+	3.57892e12i	−0.0826976	+	0.143236i
$950$	−7.44567e13	−	1.28963e14i	−2.96584	−	5.13698i
$951$	2.43515e13			0.965413
$952$	−3.29504e13	+	9.35304e12i	−1.30015	+	0.369051i
$953$	2.06289e12			0.0810137			0.0405068	−	0.999179i	$-0.487103\pi$
$953$	2.06289e12			0.0810137			0.0405068	+	0.999179i	$0.487103\pi$
$954$	3.31196e13	+	5.73648e13i	1.29454	+	2.24222i
$955$	3.52740e13	−	6.10963e13i	1.37227	−	2.37684i
$956$	1.06517e13	−	1.84492e13i	0.412436	−	0.714361i
$957$	−1.02664e13	−	1.77819e13i	−0.395653	−	0.685292i
$958$	4.58926e12			0.176034
$959$	1.78710e13	−	5.07271e12i	0.682282	−	0.193667i
$960$	1.05957e14			4.02631
$961$	−1.20563e13	−	2.08821e13i	−0.455992	−	0.789802i
$962$	2.26926e12	−	3.93048e12i	0.0854273	−	0.147964i
$963$	4.28749e12	−	7.42615e12i	0.160652	−	0.278257i
$964$	−1.83029e13	−	3.17016e13i	−0.682612	−	1.18232i
$965$	−2.85778e13			−1.06085
$966$	−8.25281e12	+	3.27270e13i	−0.304933	+	1.20923i
$967$	4.68920e13			1.72456			0.862282	−	0.506428i	$-0.169035\pi$
$967$	4.68920e13			1.72456			0.862282	+	0.506428i	$0.169035\pi$
$968$	4.19485e12	+	7.26570e12i	0.153560	+	0.265973i
$969$	−5.40038e13	+	9.35374e13i	−1.96774	+	3.40822i
$970$	−4.41211e13	+	7.64201e13i	−1.60020	+	2.77163i
$971$	1.72103e13	+	2.98092e13i	0.621302	+	1.07613i	0.989244	+	0.146277i	$0.0467292\pi$
$971$	1.72103e13	+	2.98092e13i	0.621302	+	1.07613i	−0.367942	+	0.929849i	$0.619938\pi$
$972$	5.64707e13			2.02920
$973$	−8.89759e12	−	8.63842e12i	−0.318247	−	0.308977i
$974$	−4.63575e13			−1.65046
$975$	−1.21338e13	−	2.10163e13i	−0.430007	−	0.744794i
$976$	3.79539e12	−	6.57381e12i	0.133885	−	0.231896i
$977$	2.31914e12	−	4.01687e12i	0.0814332	−	0.141046i	−0.822433	−	0.568863i	$-0.807384\pi$
$977$	2.31914e12	−	4.01687e12i	0.0814332	−	0.141046i	0.903866	+	0.427816i	$0.140717\pi$
$978$	1.09779e13	+	1.90143e13i	0.383702	+	0.664592i
$979$	3.13336e13			1.09015
$980$	2.30472e12	+	7.79543e13i	0.0798179	+	2.69975i
$981$	−2.67767e13			−0.923095
$982$	1.96176e13	+	3.39787e13i	0.673200	+	1.16602i
$983$	6.68552e12	−	1.15797e13i	0.228373	−	0.395553i	−0.728953	−	0.684564i	$-0.759993\pi$
$983$	6.68552e12	−	1.15797e13i	0.228373	−	0.395553i	0.957326	+	0.289010i	$0.0933261\pi$
$984$	−3.33000e12	+	5.76773e12i	−0.113231	+	0.196122i
$985$	3.24500e13	+	5.62051e13i	1.09838	+	1.90245i
$986$	5.96644e13			2.01034
$987$	−1.99669e13	−	1.93853e13i	−0.669705	−	0.650198i
$988$	−2.06729e13			−0.690231
$989$	−1.10477e13	−	1.91351e13i	−0.367187	−	0.635986i
$990$	−2.98102e13	+	5.16328e13i	−0.986295	+	1.70831i
$991$	−9.12360e12	+	1.58025e13i	−0.300493	+	0.520469i	−0.976248	−	0.216657i	$-0.930485\pi$
$991$	−9.12360e12	+	1.58025e13i	−0.300493	+	0.520469i	0.675755	+	0.737127i	$0.263818\pi$
$992$	−2.51051e13	−	4.34833e13i	−0.823114	−	1.42567i
$993$	3.73748e13			1.21985
$994$	3.82705e12	−	1.51764e13i	0.124344	−	0.493094i
$995$	−6.41977e13			−2.07642
$996$	1.16958e13	+	2.02577e13i	0.376584	+	0.652263i
$997$	−2.19400e12	+	3.80012e12i	−0.0703249	+	0.121806i	−0.899044	−	0.437859i	$-0.855737\pi$
$997$	−2.19400e12	+	3.80012e12i	−0.0703249	+	0.121806i	0.828719	+	0.559665i	$0.189070\pi$
$998$	4.05397e12	−	7.02168e12i	0.129358	−	0.224055i
$999$	−9.54619e11	−	1.65345e12i	−0.0303239	−	0.0525225i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.e.a.53.5	✓	70
7.2	even	3	inner	91.10.e.a.79.5	yes	70

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.e.a.53.5	✓	70	1.1	even	1	trivial
91.10.e.a.79.5	yes	70	7.2	even	3	inner

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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	91.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-17.8760 - 30.9621i) q^{2} +(96.3548 - 166.891i) q^{3} +(-383.101 + 663.550i) q^{4} +(-1261.17 - 2184.41i) q^{5} -6889.74 q^{6} +(-4557.75 - 4424.99i) q^{7} +9088.22 q^{8} +(-8726.99 - 15115.6i) q^{9} +O(q^{10})\)	\(q+(-17.8760 - 30.9621i) q^{2} +(96.3548 - 166.891i) q^{3} +(-383.101 + 663.550i) q^{4} +(-1261.17 - 2184.41i) q^{5} -6889.74 q^{6} +(-4557.75 - 4424.99i) q^{7} +9088.22 q^{8} +(-8726.99 - 15115.6i) q^{9} +(-45089.4 + 78097.1i) q^{10} +(-18939.4 + 32804.0i) q^{11} +(73827.2 + 127873. i) q^{12} -28561.0 q^{13} +(-55532.8 + 220218. i) q^{14} -486080. q^{15} +(33686.9 + 58347.4i) q^{16} +(296645. - 513804. i) q^{17} +(-312007. + 540412. i) q^{18} +(-472339. - 818116. i) q^{19} +1.93263e6 q^{20} +(-1.17765e6 + 334280. i) q^{21} +1.35424e6 q^{22} +(385584. + 667852. i) q^{23} +(875694. - 1.51675e6i) q^{24} +(-2.20455e6 + 3.81839e6i) q^{25} +(510556. + 884309. i) q^{26} +429555. q^{27} +(4.68228e6 - 1.32908e6i) q^{28} -2.81286e6 q^{29} +(8.68915e6 + 1.50501e7i) q^{30} +(3.55500e6 - 6.15744e6i) q^{31} +(3.53096e6 - 6.11580e6i) q^{32} +(3.64981e6 + 6.32165e6i) q^{33} -2.12113e7 q^{34} +(-3.91791e6 + 1.55367e7i) q^{35} +1.33733e7 q^{36} +(-2.22234e6 - 3.84921e6i) q^{37} +(-1.68871e7 + 2.92492e7i) q^{38} +(-2.75199e6 + 4.76658e6i) q^{39} +(-1.14618e7 - 1.98524e7i) q^{40} -3.80270e6 q^{41} +(3.14017e7 + 3.04870e7i) q^{42} -2.86517e7 q^{43} +(-1.45114e7 - 2.51345e7i) q^{44} +(-2.20125e7 + 3.81267e7i) q^{45} +(1.37854e7 - 2.38770e7i) q^{46} +(1.13665e7 + 1.96874e7i) q^{47} +1.29836e7 q^{48} +(1.19253e6 + 4.03360e7i) q^{49} +1.57634e8 q^{50} +(-5.71663e7 - 9.90150e7i) q^{51} +(1.09417e7 - 1.89517e7i) q^{52} +(5.30751e7 - 9.19287e7i) q^{53} +(-7.67871e6 - 1.32999e7i) q^{54} +9.55435e7 q^{55} +(-4.14218e7 - 4.02153e7i) q^{56} -1.82049e8 q^{57} +(5.02827e7 + 8.70922e7i) q^{58} +(-1.28152e7 + 2.21966e7i) q^{59} +(1.86218e8 - 3.22539e8i) q^{60} +(-5.63333e7 - 9.75722e7i) q^{61} -2.54196e8 q^{62} +(-2.71109e7 + 1.07510e8i) q^{63} -2.17982e8 q^{64} +(3.60203e7 + 6.23891e7i) q^{65} +(1.30488e8 - 2.26011e8i) q^{66} +(1.05552e8 - 1.82822e8i) q^{67} +(2.27290e8 + 3.93678e8i) q^{68} +1.48612e8 q^{69} +(5.51085e8 - 1.56427e8i) q^{70} -6.89152e7 q^{71} +(-7.93128e7 - 1.37374e8i) q^{72} +(7.23465e7 - 1.25308e8i) q^{73} +(-7.94531e7 + 1.37617e8i) q^{74} +(4.24837e8 + 7.35840e8i) q^{75} +7.23815e8 q^{76} +(2.31479e8 - 6.57058e7i) q^{77} +1.96778e8 q^{78} +(-5.60139e7 - 9.70189e7i) q^{79} +(8.49700e7 - 1.47172e8i) q^{80} +(2.13163e8 - 3.69209e8i) q^{81} +(6.79770e7 + 1.17740e8i) q^{82} +1.58421e8 q^{83} +(2.29349e8 - 9.09496e8i) q^{84} -1.49648e9 q^{85} +(5.12178e8 + 8.87118e8i) q^{86} +(-2.71033e8 + 4.69443e8i) q^{87} +(-1.72126e8 + 2.98130e8i) q^{88} +(-4.13602e8 - 7.16380e8i) q^{89} +1.57398e9 q^{90} +(1.30174e8 + 1.26382e8i) q^{91} -5.90871e8 q^{92} +(-6.85083e8 - 1.18660e9i) q^{93} +(4.06375e8 - 7.03862e8i) q^{94} +(-1.19140e9 + 2.06357e9i) q^{95} +(-6.80449e8 - 1.17857e9i) q^{96} +9.78526e8 q^{97} +(1.22757e9 - 7.57968e8i) q^{98} +6.61136e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q + 65 q^{2} - 8533 q^{4} - 2118 q^{5} + 17358 q^{6} - 8764 q^{7} - 106980 q^{8} - 215597 q^{9}+O(q^{10}) \) 70 * q + 65 * q^2 - 8533 * q^4 - 2118 * q^5 + 17358 * q^6 - 8764 * q^7 - 106980 * q^8 - 215597 * q^9	\( 70 q + 65 q^{2} - 8533 q^{4} - 2118 q^{5} + 17358 q^{6} - 8764 q^{7} - 106980 q^{8} - 215597 q^{9} + 16725 q^{10} + 117246 q^{11} + 79155 q^{12} - 1999270 q^{13} + 155800 q^{14} - 1075914 q^{15} - 1801693 q^{16} + 534494 q^{17} + 2034224 q^{18} - 1070554 q^{19} - 213462 q^{20} + 252483 q^{21} - 656508 q^{22} + 3982482 q^{23} - 8713082 q^{24} - 10791923 q^{25} - 1856465 q^{26} - 4695462 q^{27} + 43151747 q^{28} - 8248096 q^{29} + 7494360 q^{30} - 18116139 q^{31} + 23284165 q^{32} - 18685134 q^{33} - 35031796 q^{34} + 41739462 q^{35} + 69822756 q^{36} + 12174052 q^{37} - 86227130 q^{38} - 45752120 q^{40} - 14899440 q^{41} + 226294688 q^{42} - 100872292 q^{43} + 55709994 q^{44} - 128782765 q^{45} + 86862955 q^{46} - 15243502 q^{47} - 251600258 q^{48} + 168431298 q^{49} - 23415484 q^{50} + 89493887 q^{51} + 243711013 q^{52} + 42576150 q^{53} - 466420190 q^{54} - 72659096 q^{55} + 237491061 q^{56} - 533277320 q^{57} + 302514895 q^{58} + 40301350 q^{59} - 191686454 q^{60} + 9519912 q^{61} - 257610720 q^{62} - 292394291 q^{63} + 453888112 q^{64} + 60492198 q^{65} + 1445199979 q^{66} + 919692072 q^{67} - 220295462 q^{68} - 1381257496 q^{69} + 860352188 q^{70} - 811959580 q^{71} + 2266117080 q^{72} + 924540004 q^{73} - 727436321 q^{74} + 445426010 q^{75} + 649412196 q^{76} - 1151937348 q^{77} - 495761838 q^{78} + 1174788834 q^{79} + 2332520349 q^{80} - 800698791 q^{81} + 1124625342 q^{82} + 830514540 q^{83} + 1448184376 q^{84} - 1969339174 q^{85} + 1497823546 q^{86} + 721368044 q^{87} - 808482999 q^{88} - 1968216306 q^{89} + 777819470 q^{90} + 250308604 q^{91} - 4887921618 q^{92} + 853972744 q^{93} + 4664723138 q^{94} + 1357929150 q^{95} - 3736344295 q^{96} + 3467931764 q^{97} - 1557173329 q^{98} - 8781494080 q^{99}+O(q^{100}) \) 70 * q + 65 * q^2 - 8533 * q^4 - 2118 * q^5 + 17358 * q^6 - 8764 * q^7 - 106980 * q^8 - 215597 * q^9 + 16725 * q^10 + 117246 * q^11 + 79155 * q^12 - 1999270 * q^13 + 155800 * q^14 - 1075914 * q^15 - 1801693 * q^16 + 534494 * q^17 + 2034224 * q^18 - 1070554 * q^19 - 213462 * q^20 + 252483 * q^21 - 656508 * q^22 + 3982482 * q^23 - 8713082 * q^24 - 10791923 * q^25 - 1856465 * q^26 - 4695462 * q^27 + 43151747 * q^28 - 8248096 * q^29 + 7494360 * q^30 - 18116139 * q^31 + 23284165 * q^32 - 18685134 * q^33 - 35031796 * q^34 + 41739462 * q^35 + 69822756 * q^36 + 12174052 * q^37 - 86227130 * q^38 - 45752120 * q^40 - 14899440 * q^41 + 226294688 * q^42 - 100872292 * q^43 + 55709994 * q^44 - 128782765 * q^45 + 86862955 * q^46 - 15243502 * q^47 - 251600258 * q^48 + 168431298 * q^49 - 23415484 * q^50 + 89493887 * q^51 + 243711013 * q^52 + 42576150 * q^53 - 466420190 * q^54 - 72659096 * q^55 + 237491061 * q^56 - 533277320 * q^57 + 302514895 * q^58 + 40301350 * q^59 - 191686454 * q^60 + 9519912 * q^61 - 257610720 * q^62 - 292394291 * q^63 + 453888112 * q^64 + 60492198 * q^65 + 1445199979 * q^66 + 919692072 * q^67 - 220295462 * q^68 - 1381257496 * q^69 + 860352188 * q^70 - 811959580 * q^71 + 2266117080 * q^72 + 924540004 * q^73 - 727436321 * q^74 + 445426010 * q^75 + 649412196 * q^76 - 1151937348 * q^77 - 495761838 * q^78 + 1174788834 * q^79 + 2332520349 * q^80 - 800698791 * q^81 + 1124625342 * q^82 + 830514540 * q^83 + 1448184376 * q^84 - 1969339174 * q^85 + 1497823546 * q^86 + 721368044 * q^87 - 808482999 * q^88 - 1968216306 * q^89 + 777819470 * q^90 + 250308604 * q^91 - 4887921618 * q^92 + 853972744 * q^93 + 4664723138 * q^94 + 1357929150 * q^95 - 3736344295 * q^96 + 3467931764 * q^97 - 1557173329 * q^98 - 8781494080 * q^99

Introduction

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