LMFDB - Embedded newform 37.10.c.a.10.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,10,Mod(10,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("37.10");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	37.c (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:	$19.0563259381$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$27$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			10.16
Character	$\chi$	$=$	37.10
Dual form			37.10.c.a.26.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.95661 - 6.85305i) q^{2} +(96.3161 + 166.824i) q^{3} +(224.690 + 389.175i) q^{4} +(891.239 + 1543.67i) q^{5} +1524.34 q^{6} +(2975.14 + 5153.10i) q^{7} +7607.62 q^{8} +(-8712.07 + 15089.8i) q^{9} +O(q^{10})$	\(q+(3.95661 - 6.85305i) q^{2} +(96.3161 + 166.824i) q^{3} +(224.690 + 389.175i) q^{4} +(891.239 + 1543.67i) q^{5} +1524.34 q^{6} +(2975.14 + 5153.10i) q^{7} +7607.62 q^{8} +(-8712.07 + 15089.8i) q^{9} +14105.1 q^{10} +37000.8 q^{11} +(-43282.6 + 74967.7i) q^{12} +(-90357.4 - 156504. i) q^{13} +47085.9 q^{14} +(-171681. + 297361. i) q^{15} +(-84941.2 + 147122. i) q^{16} +(216709. - 375350. i) q^{17} +(68940.6 + 119409. i) q^{18} +(-401112. - 694746. i) q^{19} +(-400506. + 693696. i) q^{20} +(-573108. + 992653. i) q^{21} +(146398. - 253568. i) q^{22} +1.19895e6 q^{23} +(732736. + 1.26914e6i) q^{24} +(-612051. + 1.06010e6i) q^{25} -1.43004e6 q^{26} +435127. q^{27} +(-1.33697e6 + 2.31571e6i) q^{28} -905715. q^{29} +(1.35855e6 + 2.35308e6i) q^{30} +5.39652e6 q^{31} +(2.61971e6 + 4.53747e6i) q^{32} +(3.56377e6 + 6.17263e6i) q^{33} +(-1.71486e6 - 2.97023e6i) q^{34} +(-5.30313e6 + 9.18529e6i) q^{35} -7.83008e6 q^{36} +(-9.21443e6 + 6.71238e6i) q^{37} -6.34817e6 q^{38} +(1.74057e7 - 3.01476e7i) q^{39} +(6.78021e6 + 1.17437e7i) q^{40} +(-1.09305e7 - 1.89323e7i) q^{41} +(4.53513e6 + 7.85508e6i) q^{42} -1.70341e7 q^{43} +(8.31372e6 + 1.43998e7i) q^{44} -3.10582e7 q^{45} +(4.74376e6 - 8.21644e6i) q^{46} -4.69094e6 q^{47} -3.27248e7 q^{48} +(2.47384e6 - 4.28481e6i) q^{49} +(4.84330e6 + 8.38883e6i) q^{50} +8.34901e7 q^{51} +(4.06049e7 - 7.03298e7i) q^{52} +(1.09963e7 - 1.90461e7i) q^{53} +(1.72163e6 - 2.98195e6i) q^{54} +(3.29765e7 + 5.71170e7i) q^{55} +(2.26338e7 + 3.92028e7i) q^{56} +(7.72670e7 - 1.33830e8i) q^{57} +(-3.58356e6 + 6.20691e6i) q^{58} +(-3.36319e7 + 5.82522e7i) q^{59} -1.54301e8 q^{60} +(-4.28221e7 - 7.41701e7i) q^{61} +(2.13519e7 - 3.69826e7i) q^{62} -1.03679e8 q^{63} -4.55191e7 q^{64} +(1.61060e8 - 2.78964e8i) q^{65} +5.64018e7 q^{66} +(1.21654e7 + 2.10712e7i) q^{67} +1.94769e8 q^{68} +(1.15478e8 + 2.00013e8i) q^{69} +(4.19648e7 + 7.26852e7i) q^{70} +(-1.62959e8 - 2.82252e8i) q^{71} +(-6.62781e7 + 1.14797e8i) q^{72} -3.27141e8 q^{73} +(9.54241e6 + 8.97052e7i) q^{74} -2.35801e8 q^{75} +(1.80252e8 - 3.12205e8i) q^{76} +(1.10083e8 + 1.90669e8i) q^{77} +(-1.37735e8 - 2.38565e8i) q^{78} +(2.90732e8 + 5.03562e8i) q^{79} -3.02811e8 q^{80} +(2.13390e8 + 3.69601e8i) q^{81} -1.72992e8 q^{82} +(-2.39873e8 + 4.15472e8i) q^{83} -5.15088e8 q^{84} +7.72557e8 q^{85} +(-6.73972e7 + 1.16735e8i) q^{86} +(-8.72350e7 - 1.51095e8i) q^{87} +2.81488e8 q^{88} +(-5.22428e8 + 9.04871e8i) q^{89} +(-1.22885e8 + 2.12843e8i) q^{90} +(5.37653e8 - 9.31242e8i) q^{91} +(2.69392e8 + 4.66600e8i) q^{92} +(5.19771e8 + 9.00271e8i) q^{93} +(-1.85602e7 + 3.21473e7i) q^{94} +(7.14972e8 - 1.23837e9i) q^{95} +(-5.04640e8 + 8.74062e8i) q^{96} -5.79454e8 q^{97} +(-1.95760e7 - 3.39067e7i) q^{98} +(-3.22354e8 + 5.58333e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 32 q^{2} + 73 q^{3} - 6486 q^{4} + 2729 q^{5} + 1020 q^{6} + 4231 q^{7} - 7848 q^{8} - 140840 q^{9}+O(q^{10}) $ 54 * q + 32 * q^2 + 73 * q^3 - 6486 * q^4 + 2729 * q^5 + 1020 * q^6 + 4231 * q^7 - 7848 * q^8 - 140840 * q^9	\( 54 q + 32 q^{2} + 73 q^{3} - 6486 q^{4} + 2729 q^{5} + 1020 q^{6} + 4231 q^{7} - 7848 q^{8} - 140840 q^{9} - 82404 q^{10} - 108196 q^{11} + 45492 q^{12} - 29827 q^{13} - 504992 q^{14} + 87135 q^{15} - 1561814 q^{16} + 116991 q^{17} + 1767678 q^{18} - 599677 q^{19} + 4122556 q^{20} - 221017 q^{21} - 257914 q^{22} + 1752736 q^{23} + 1149408 q^{24} - 6037260 q^{25} - 16731604 q^{26} - 1916582 q^{27} + 1917318 q^{28} - 11336100 q^{29} - 20390006 q^{30} + 14447580 q^{31} - 873740 q^{32} - 4494200 q^{33} + 13736524 q^{34} - 8546699 q^{35} + 61692836 q^{36} - 1919410 q^{37} - 85447920 q^{38} - 14035313 q^{39} + 3210182 q^{40} + 28676571 q^{41} - 101904850 q^{42} + 56602028 q^{43} + 153011074 q^{44} + 104234980 q^{45} + 99535572 q^{46} - 147509100 q^{47} - 203670880 q^{48} - 201857540 q^{49} - 91421384 q^{50} + 328228338 q^{51} - 69374156 q^{52} + 59137361 q^{53} + 201615042 q^{54} - 219079762 q^{55} + 202573590 q^{56} - 5989161 q^{57} - 157098688 q^{58} + 137993791 q^{59} + 413427232 q^{60} - 244884419 q^{61} + 109345558 q^{62} - 995908592 q^{63} + 184008092 q^{64} + 248745395 q^{65} + 1965122248 q^{66} - 130143913 q^{67} + 667610796 q^{68} + 246927272 q^{69} - 291173360 q^{70} + 473387559 q^{71} + 366188748 q^{72} + 923638972 q^{73} - 885443390 q^{74} - 2185997392 q^{75} - 337459826 q^{76} - 586609928 q^{77} - 261025842 q^{78} + 563110723 q^{79} - 4210381784 q^{80} + 713813329 q^{81} + 3458576264 q^{82} - 663594441 q^{83} - 2635249016 q^{84} - 1417287750 q^{85} - 2269028474 q^{86} + 314944482 q^{87} - 7714172 q^{88} + 655027619 q^{89} + 588021376 q^{90} - 1833870961 q^{91} - 2384055268 q^{92} - 90092600 q^{93} - 1449940302 q^{94} + 2787158841 q^{95} + 2383567424 q^{96} - 2751583248 q^{97} + 4970876154 q^{98} + 2668760954 q^{99}+O(q^{100}) \) 54 * q + 32 * q^2 + 73 * q^3 - 6486 * q^4 + 2729 * q^5 + 1020 * q^6 + 4231 * q^7 - 7848 * q^8 - 140840 * q^9 - 82404 * q^10 - 108196 * q^11 + 45492 * q^12 - 29827 * q^13 - 504992 * q^14 + 87135 * q^15 - 1561814 * q^16 + 116991 * q^17 + 1767678 * q^18 - 599677 * q^19 + 4122556 * q^20 - 221017 * q^21 - 257914 * q^22 + 1752736 * q^23 + 1149408 * q^24 - 6037260 * q^25 - 16731604 * q^26 - 1916582 * q^27 + 1917318 * q^28 - 11336100 * q^29 - 20390006 * q^30 + 14447580 * q^31 - 873740 * q^32 - 4494200 * q^33 + 13736524 * q^34 - 8546699 * q^35 + 61692836 * q^36 - 1919410 * q^37 - 85447920 * q^38 - 14035313 * q^39 + 3210182 * q^40 + 28676571 * q^41 - 101904850 * q^42 + 56602028 * q^43 + 153011074 * q^44 + 104234980 * q^45 + 99535572 * q^46 - 147509100 * q^47 - 203670880 * q^48 - 201857540 * q^49 - 91421384 * q^50 + 328228338 * q^51 - 69374156 * q^52 + 59137361 * q^53 + 201615042 * q^54 - 219079762 * q^55 + 202573590 * q^56 - 5989161 * q^57 - 157098688 * q^58 + 137993791 * q^59 + 413427232 * q^60 - 244884419 * q^61 + 109345558 * q^62 - 995908592 * q^63 + 184008092 * q^64 + 248745395 * q^65 + 1965122248 * q^66 - 130143913 * q^67 + 667610796 * q^68 + 246927272 * q^69 - 291173360 * q^70 + 473387559 * q^71 + 366188748 * q^72 + 923638972 * q^73 - 885443390 * q^74 - 2185997392 * q^75 - 337459826 * q^76 - 586609928 * q^77 - 261025842 * q^78 + 563110723 * q^79 - 4210381784 * q^80 + 713813329 * q^81 + 3458576264 * q^82 - 663594441 * q^83 - 2635249016 * q^84 - 1417287750 * q^85 - 2269028474 * q^86 + 314944482 * q^87 - 7714172 * q^88 + 655027619 * q^89 + 588021376 * q^90 - 1833870961 * q^91 - 2384055268 * q^92 - 90092600 * q^93 - 1449940302 * q^94 + 2787158841 * q^95 + 2383567424 * q^96 - 2751583248 * q^97 + 4970876154 * q^98 + 2668760954 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

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

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 $

$2$	3.95661	−	6.85305i	0.174859	−	0.302865i	−0.765253	−	0.643729i	$-0.777386\pi$
$2$	3.95661	−	6.85305i	0.174859	−	0.302865i	0.940113	+	0.340864i	$0.110720\pi$
$3$	96.3161	+	166.824i	0.686520	+	1.18909i	0.972957	+	0.230988i	$0.0741959\pi$
$3$	96.3161	+	166.824i	0.686520	+	1.18909i	−0.286437	+	0.958099i	$0.592471\pi$
$4$	224.690	+	389.175i	0.438849	+	0.760108i
$5$	891.239	+	1543.67i	0.637719	+	1.10456i	0.985932	+	0.167146i	$0.0534551\pi$
$5$	891.239	+	1543.67i	0.637719	+	1.10456i	−0.348213	+	0.937415i	$0.613212\pi$
$6$	1524.34			0.480177
$7$	2975.14	+	5153.10i	0.468346	+	0.811199i	0.999346	−	0.0361730i	$-0.0115167\pi$
$7$	2975.14	+	5153.10i	0.468346	+	0.811199i	−0.531000	+	0.847372i	$0.678183\pi$
$8$	7607.62			0.656665
$9$	−8712.07	+	15089.8i	−0.442619	+	0.766639i
$10$	14105.1			0.446044
$11$	37000.8			0.761980			0.380990	−	0.924579i	$-0.375583\pi$
$11$	37000.8			0.761980			0.380990	+	0.924579i	$0.375583\pi$
$12$	−43282.6	+	74967.7i	−0.602557	+	1.04366i
$13$	−90357.4	−	156504.i	−0.877443	−	1.51978i	−0.854138	−	0.520047i	$-0.825914\pi$
$13$	−90357.4	−	156504.i	−0.877443	−	1.51978i	−0.0233049	−	0.999728i	$-0.507419\pi$
$14$	47085.9			0.327578
$15$	−171681.	+	297361.i	−0.875613	+	1.51661i
$16$	−84941.2	+	147122.i	−0.324025	+	0.561227i
$17$	216709.	−	375350.i	0.629298	−	1.08998i	−0.358395	−	0.933570i	$-0.616676\pi$
$17$	216709.	−	375350.i	0.629298	−	1.08998i	0.987693	−	0.156406i	$-0.0499907\pi$
$18$	68940.6	+	119409.i	0.154792	+	0.268108i
$19$	−401112.	−	694746.i	−0.706113	−	1.22302i	−0.966289	−	0.257462i	$-0.917114\pi$
$19$	−401112.	−	694746.i	−0.706113	−	1.22302i	0.260176	−	0.965561i	$-0.416219\pi$
$20$	−400506.	+	693696.i	−0.559724	+	0.969470i
$21$	−573108.	+	992653.i	−0.643058	+	1.11381i
$22$	146398.	−	253568.i	0.133239	−	0.230777i
$23$	1.19895e6			0.893356			0.446678	−	0.894695i	$-0.352607\pi$
$23$	1.19895e6			0.893356			0.446678	+	0.894695i	$0.352607\pi$
$24$	732736.	+	1.26914e6i	0.450814	+	0.780832i
$25$	−612051.	+	1.06010e6i	−0.313370	+	0.542773i
$26$	−1.43004e6			−0.613715
$27$	435127.			0.157572
$28$	−1.33697e6	+	2.31571e6i	−0.411066	+	0.711987i
$29$	−905715.			−0.237794			−0.118897	−	0.992907i	$-0.537936\pi$
$29$	−905715.			−0.237794			−0.118897	+	0.992907i	$0.537936\pi$
$30$	1.35855e6	+	2.35308e6i	0.306218	+	0.530385i
$31$	5.39652e6			1.04951			0.524754	−	0.851254i	$-0.324157\pi$
$31$	5.39652e6			1.04951			0.524754	+	0.851254i	$0.324157\pi$
$32$	2.61971e6	+	4.53747e6i	0.441650	+	0.764960i
$33$	3.56377e6	+	6.17263e6i	0.523115	+	0.906061i
$34$	−1.71486e6	−	2.97023e6i	−0.220077	−	0.381184i
$35$	−5.30313e6	+	9.18529e6i	−0.597346	+	1.03463i
$36$	−7.83008e6			−0.776971
$37$	−9.21443e6	+	6.71238e6i	−0.808278	+	0.588802i
$37$	−9.21443e6	+	6.71238e6i	−0.808278	+	0.588802i
$38$	−6.34817e6			−0.493881
$39$	1.74057e7	−	3.01476e7i	1.20476	−	2.08671i
$40$	6.78021e6	+	1.17437e7i	0.418767	+	0.725326i
$41$	−1.09305e7	−	1.89323e7i	−0.604108	−	1.04635i	−0.992192	−	0.124721i	$-0.960196\pi$
$41$	−1.09305e7	−	1.89323e7i	−0.604108	−	1.04635i	0.388084	−	0.921624i	$-0.373137\pi$
$42$	4.53513e6	+	7.85508e6i	0.224889	+	0.389519i
$43$	−1.70341e7			−0.759820			−0.379910	−	0.925023i	$-0.624045\pi$
$43$	−1.70341e7			−0.759820			−0.379910	+	0.925023i	$0.624045\pi$
$44$	8.31372e6	+	1.43998e7i	0.334394	+	0.579187i
$45$	−3.10582e7			−1.12907
$46$	4.74376e6	−	8.21644e6i	0.156211	−	0.270566i
$47$	−4.69094e6			−0.140223			−0.0701116	−	0.997539i	$-0.522336\pi$
$47$	−4.69094e6			−0.140223			−0.0701116	+	0.997539i	$0.522336\pi$
$48$	−3.27248e7			−0.889798
$49$	2.47384e6	−	4.28481e6i	0.0613040	−	0.106182i
$50$	4.84330e6	+	8.38883e6i	0.109591	+	0.189818i
$51$	8.34901e7			1.72810
$52$	4.06049e7	−	7.03298e7i	0.770129	−	1.33390i
$53$	1.09963e7	−	1.90461e7i	0.191427	−	0.331562i	−0.754296	−	0.656534i	$-0.772022\pi$
$53$	1.09963e7	−	1.90461e7i	0.191427	−	0.331562i	0.945723	+	0.324973i	$0.105355\pi$
$54$	1.72163e6	−	2.98195e6i	0.0275529	−	0.0477230i
$55$	3.29765e7	+	5.71170e7i	0.485929	+	0.841654i
$56$	2.26338e7	+	3.92028e7i	0.307546	+	0.532686i
$57$	7.72670e7	−	1.33830e8i	0.969521	−	1.67926i
$58$	−3.58356e6	+	6.20691e6i	−0.0415804	+	0.0720194i
$59$	−3.36319e7	+	5.82522e7i	−0.361341	+	0.625862i	−0.988182	−	0.153286i	$-0.951014\pi$
$59$	−3.36319e7	+	5.82522e7i	−0.361341	+	0.625862i	0.626840	+	0.779148i	$0.284348\pi$
$60$	−1.54301e8			−1.53705
$61$	−4.28221e7	−	7.41701e7i	−0.395990	−	0.685875i	0.597237	−	0.802065i	$-0.296265\pi$
$61$	−4.28221e7	−	7.41701e7i	−0.395990	−	0.685875i	−0.993227	+	0.116190i	$0.962932\pi$
$62$	2.13519e7	−	3.69826e7i	0.183516	−	0.317859i
$63$	−1.03679e8			−0.829196
$64$	−4.55191e7			−0.339144
$65$	1.61060e8	−	2.78964e8i	1.11912	−	1.93838i
$66$	5.64018e7			0.365885
$67$	1.21654e7	+	2.10712e7i	0.0737550	+	0.127747i	0.900544	−	0.434764i	$-0.143168\pi$
$67$	1.21654e7	+	2.10712e7i	0.0737550	+	0.127747i	−0.826789	+	0.562512i	$0.809835\pi$
$68$	1.94769e8			1.10467
$69$	1.15478e8	+	2.00013e8i	0.613306	+	1.06228i
$70$	4.19648e7	+	7.26852e7i	0.208903	+	0.361830i
$71$	−1.62959e8	−	2.82252e8i	−0.761052	−	1.31818i	−0.942309	−	0.334745i	$-0.891350\pi$
$71$	−1.62959e8	−	2.82252e8i	−0.761052	−	1.31818i	0.181256	−	0.983436i	$-0.441984\pi$
$72$	−6.62781e7	+	1.14797e8i	−0.290653	+	0.503425i
$73$	−3.27141e8			−1.34829			−0.674144	−	0.738600i	$-0.735487\pi$
$73$	−3.27141e8			−1.34829			−0.674144	+	0.738600i	$0.735487\pi$
$74$	9.54241e6	+	8.97052e7i	0.0369927	+	0.347756i
$75$	−2.35801e8			−0.860540
$76$	1.80252e8	−	3.12205e8i	0.619753	−	1.07344i
$77$	1.10083e8	+	1.90669e8i	0.356870	+	0.618118i
$78$	−1.37735e8	−	2.38565e8i	−0.421328	−	0.729761i
$79$	2.90732e8	+	5.03562e8i	0.839790	+	1.45456i	0.890070	+	0.455824i	$0.150655\pi$
$79$	2.90732e8	+	5.03562e8i	0.839790	+	1.45456i	−0.0502802	+	0.998735i	$0.516011\pi$
$80$	−3.02811e8			−0.826547
$81$	2.13390e8	+	3.69601e8i	0.550796	+	0.954006i
$82$	−1.72992e8			−0.422535
$83$	−2.39873e8	+	4.15472e8i	−0.554791	+	0.960926i	0.443129	+	0.896458i	$0.353868\pi$
$83$	−2.39873e8	+	4.15472e8i	−0.554791	+	0.960926i	−0.997920	+	0.0644681i	$0.979465\pi$
$84$	−5.15088e8			−1.12882
$85$	7.72557e8			1.60526
$86$	−6.73972e7	+	1.16735e8i	−0.132861	+	0.230123i
$87$	−8.72350e7	−	1.51095e8i	−0.163250	−	0.282758i
$88$	2.81488e8			0.500366
$89$	−5.22428e8	+	9.04871e8i	−0.882614	+	1.52873i	−0.0341908	+	0.999415i	$0.510885\pi$
$89$	−5.22428e8	+	9.04871e8i	−0.882614	+	1.52873i	−0.848424	+	0.529318i	$0.822448\pi$
$90$	−1.22885e8	+	2.12843e8i	−0.197427	+	0.341954i
$91$	5.37653e8	−	9.31242e8i	0.821894	−	1.42356i
$92$	2.69392e8	+	4.66600e8i	0.392048	+	0.679047i
$93$	5.19771e8	+	9.00271e8i	0.720509	+	1.24796i
$94$	−1.85602e7	+	3.21473e7i	−0.0245193	+	0.0424687i
$95$	7.14972e8	−	1.23837e9i	0.900602	−	1.55989i
$96$	−5.04640e8	+	8.74062e8i	−0.606403	+	1.05032i
$97$	−5.79454e8			−0.664578			−0.332289	−	0.943178i	$-0.607821\pi$
$97$	−5.79454e8			−0.664578			−0.332289	+	0.943178i	$0.607821\pi$
$98$	−1.95760e7	−	3.39067e7i	−0.0214391	−	0.0371337i
$99$	−3.22354e8	+	5.58333e8i	−0.337267	+	0.584164i
$100$	−5.50088e8			−0.550088
$101$	−4.04788e8			−0.387063			−0.193531	−	0.981094i	$-0.561994\pi$
$101$	−4.04788e8			−0.387063			−0.193531	+	0.981094i	$0.561994\pi$
$102$	3.30338e8	−	5.72162e8i	0.302174	−	0.523381i
$103$	1.47349e9			1.28997			0.644985	−	0.764195i	$-0.276864\pi$
$103$	1.47349e9			1.28997			0.644985	+	0.764195i	$0.276864\pi$
$104$	−6.87405e8	−	1.19062e9i	−0.576186	−	0.997983i
$105$	−2.04311e9			−1.64036
$106$	−8.70158e7	−	1.50716e8i	−0.0669456	−	0.115953i
$107$	2.98248e8	+	5.16580e8i	0.219963	+	0.380987i	0.954796	−	0.297260i	$-0.0960729\pi$
$107$	2.98248e8	+	5.16580e8i	0.219963	+	0.380987i	−0.734833	+	0.678248i	$0.762740\pi$
$108$	9.77689e7	+	1.69341e8i	0.0691503	+	0.119772i
$109$	1.36415e9	−	2.36278e9i	0.925643	−	1.60326i	0.135118	−	0.990829i	$-0.456859\pi$
$109$	1.36415e9	−	2.36278e9i	0.925643	−	1.60326i	0.790524	−	0.612431i	$-0.209808\pi$
$110$	5.21901e8			0.339876
$111$	−2.00729e9	−	8.90680e8i	−1.25504	−	0.556889i
$112$	−1.01085e9			−0.607023
$113$	6.21293e8	−	1.07611e9i	0.358462	−	0.620875i	−0.629242	−	0.777209i	$-0.716635\pi$
$113$	6.21293e8	−	1.07611e9i	0.358462	−	0.620875i	0.987704	+	0.156335i	$0.0499679\pi$
$114$	−6.11431e8	−	1.05903e9i	−0.339059	−	0.587267i
$115$	1.06855e9	+	1.85078e9i	0.569710	+	0.986766i
$116$	−2.03506e8	−	3.52482e8i	−0.104356	−	0.180749i
$117$	3.14880e9			1.55349
$118$	2.66137e8	+	4.60963e8i	0.126368	+	0.218875i
$119$	2.57896e9			1.17892
$120$	−1.30609e9	+	2.26221e9i	−0.574984	+	0.995902i
$121$	−9.88890e8			−0.419386
$122$	−6.77722e8			−0.276970
$123$	2.10557e9	−	3.64696e9i	0.829464	−	1.43667i
$124$	1.21255e9	+	2.10019e9i	0.460575	+	0.797740i
$125$	1.29947e9			0.476069
$126$	−4.10216e8	+	7.10515e8i	−0.144992	+	0.251134i
$127$	−1.65769e8	+	2.87121e8i	−0.0565442	+	0.0979374i	−0.892912	−	0.450231i	$-0.851342\pi$
$127$	−1.65769e8	+	2.87121e8i	−0.0565442	+	0.0979374i	0.836368	+	0.548169i	$0.184675\pi$
$128$	−1.52139e9	+	2.63513e9i	−0.500952	+	0.867675i
$129$	−1.64066e9	−	2.84170e9i	−0.521632	−	0.903493i
$130$	−1.27450e9	−	2.20751e9i	−0.391378	−	0.677886i
$131$	4.36948e8	−	7.56816e8i	0.129631	−	0.224528i	−0.793903	−	0.608045i	$-0.791954\pi$
$131$	4.36948e8	−	7.56816e8i	0.129631	−	0.224528i	0.923534	+	0.383517i	$0.125287\pi$
$132$	−1.60149e9	+	2.77386e9i	−0.459136	+	0.795247i
$133$	2.38673e9	−	4.13394e9i	0.661410	−	1.14560i
$134$	1.92536e8			0.0515869
$135$	3.87802e8	+	6.71693e8i	0.100487	+	0.174048i
$136$	1.64864e9	−	2.85552e9i	0.413238	−	0.715749i
$137$	2.30253e9			0.558422			0.279211	−	0.960230i	$-0.409927\pi$
$137$	2.30253e9			0.558422			0.279211	+	0.960230i	$0.409927\pi$
$138$	1.82760e9			0.428969
$139$	−1.45546e9	+	2.52093e9i	−0.330700	+	0.572789i	−0.982649	−	0.185473i	$-0.940618\pi$
$139$	−1.45546e9	+	2.52093e9i	−0.330700	+	0.572789i	0.651949	+	0.758263i	$0.273952\pi$
$140$	−4.76625e9			−1.04858
$141$	−4.51813e8	−	7.82563e8i	−0.0962660	−	0.166738i
$142$	−2.57905e9			−0.532308
$143$	−3.34329e9	−	5.79076e9i	−0.668594	−	1.15804i
$144$	−1.48003e9	−	2.56348e9i	−0.286839	−	0.496820i
$145$	−8.07209e8	−	1.39813e9i	−0.151646	−	0.262658i
$146$	−1.29437e9	+	2.24192e9i	−0.235760	+	0.408349i
$147$	9.53081e8			0.168346
$148$	−4.68269e9	−	2.07782e9i	−0.802264	−	0.355983i
$149$	−5.23061e9			−0.869389			−0.434694	−	0.900578i	$-0.643144\pi$
$149$	−5.23061e9			−0.869389			−0.434694	+	0.900578i	$0.643144\pi$
$150$	−9.32974e8	+	1.61596e9i	−0.150473	+	0.260627i
$151$	2.74267e9	+	4.75044e9i	0.429316	+	0.743597i	0.996813	−	0.0797787i	$-0.0254214\pi$
$151$	2.74267e9	+	4.75044e9i	0.429316	+	0.743597i	−0.567497	+	0.823376i	$0.692088\pi$
$152$	−3.05150e9	−	5.28536e9i	−0.463679	−	0.803116i
$153$	3.77596e9	+	6.54016e9i	0.557079	+	0.964888i
$154$	1.74222e9			0.249608
$155$	4.80959e9	+	8.33045e9i	0.669291	+	1.15925i
$156$	1.56436e10			2.11484
$157$	−3.19022e9	+	5.52562e9i	−0.419056	+	0.725827i	−0.995845	−	0.0910668i	$-0.970972\pi$
$157$	−3.19022e9	+	5.52562e9i	−0.419056	+	0.725827i	0.576789	+	0.816893i	$0.304306\pi$
$158$	4.60125e9			0.587380
$159$	4.23647e9			0.525674
$160$	−4.66957e9	+	8.08794e9i	−0.563297	+	0.975658i
$161$	3.56704e9	+	6.17829e9i	0.418400	+	0.724689i
$162$	3.37720e9			0.385246
$163$	4.58501e7	−	7.94147e7i	0.00508740	−	0.00881164i	−0.863470	−	0.504399i	$-0.831714\pi$
$163$	4.58501e7	−	7.94147e7i	0.00508740	−	0.00881164i	0.868558	+	0.495588i	$0.165047\pi$
$164$	4.91198e9	−	8.50779e9i	0.530224	−	0.918374i
$165$	−6.35234e9	+	1.10026e10i	−0.667200	+	1.15562i
$166$	1.89816e9	+	3.28772e9i	0.194020	+	0.336053i
$167$	−1.99091e9	−	3.44836e9i	−0.198074	−	0.343074i	0.749830	−	0.661631i	$-0.230135\pi$
$167$	−1.99091e9	−	3.44836e9i	−0.198074	−	0.343074i	−0.947904	+	0.318556i	$0.896802\pi$
$168$	−4.35999e9	+	7.55172e9i	−0.422273	+	0.731399i
$169$	−1.10267e10	+	1.90988e10i	−1.03981	+	1.80101i
$170$	3.05671e9	−	5.29437e9i	0.280694	−	0.486177i
$171$	1.39781e10			1.25016
$172$	−3.82740e9	−	6.62925e9i	−0.333446	−	0.577546i
$173$	−6.75639e8	+	1.17024e9i	−0.0573465	+	0.0993271i	−0.893273	−	0.449514i	$-0.851597\pi$
$173$	−6.75639e8	+	1.17024e9i	−0.0573465	+	0.0993271i	0.835927	+	0.548841i	$0.184931\pi$
$174$	−1.38062e9			−0.114183
$175$	−7.28376e9			−0.587063
$176$	−3.14289e9	+	5.44364e9i	−0.246901	+	0.427644i
$177$	−1.29572e10			−0.992272
$178$	4.13408e9	+	7.16044e9i	0.308666	+	0.534626i
$179$	1.60426e9			0.116798			0.0583990	−	0.998293i	$-0.481400\pi$
$179$	1.60426e9			0.116798			0.0583990	+	0.998293i	$0.481400\pi$
$180$	−6.97847e9	−	1.20871e10i	−0.495489	−	0.858212i
$181$	−9.64211e9	−	1.67006e10i	−0.667757	−	1.15659i	−0.978530	−	0.206105i	$-0.933921\pi$
$181$	−9.64211e9	−	1.67006e10i	−0.667757	−	1.15659i	0.310773	−	0.950484i	$-0.399412\pi$
$182$	−4.25456e9	−	7.36912e9i	−0.287431	−	0.497845i
$183$	8.24892e9	−	1.42876e10i	0.543710	−	0.941733i
$184$	9.12112e9			0.586635
$185$	−1.85740e10	−	8.24170e9i	−1.16582	−	0.517302i
$186$	8.22613e9			0.503950
$187$	8.01839e9	−	1.38883e10i	0.479512	−	0.830540i
$188$	−1.05401e9	−	1.82560e9i	−0.0615367	−	0.106585i
$189$	1.29457e9	+	2.24225e9i	0.0737983	+	0.127822i
$190$	−5.65773e9	−	9.79948e9i	−0.314957	−	0.545522i
$191$	−3.48188e10			−1.89306			−0.946529	−	0.322619i	$-0.895437\pi$
$191$	−3.48188e10			−1.89306			−0.946529	+	0.322619i	$0.895437\pi$
$192$	−4.38422e9	−	7.59369e9i	−0.232829	−	0.403271i
$193$	−1.31917e10			−0.684373			−0.342186	−	0.939632i	$-0.611167\pi$
$193$	−1.31917e10			−0.684373			−0.342186	+	0.939632i	$0.611167\pi$
$194$	−2.29267e9	+	3.97103e9i	−0.116208	+	0.201277i
$195$	6.20507e10			3.07320
$196$	2.22339e9			0.107613
$197$	−1.31619e10	+	2.27970e10i	−0.622616	+	1.07840i	0.366381	+	0.930465i	$0.380597\pi$
$197$	−1.31619e10	+	2.27970e10i	−0.622616	+	1.07840i	−0.988997	+	0.147937i	$0.952737\pi$
$198$	2.55085e9	+	4.41821e9i	0.117948	+	0.204293i
$199$	1.86311e10			0.842170			0.421085	−	0.907021i	$-0.361649\pi$
$199$	1.86311e10			0.842170			0.421085	+	0.907021i	$0.361649\pi$
$200$	−4.65625e9	+	8.06486e9i	−0.205779	+	0.356420i
$201$	−2.34346e9	+	4.05899e9i	−0.101269	+	0.175402i
$202$	−1.60159e9	+	2.77403e9i	−0.0676814	+	0.117228i
$203$	−2.69463e9	−	4.66724e9i	−0.111370	−	0.192898i
$204$	1.87594e10	+	3.24923e10i	0.758375	+	1.31354i
$205$	1.94834e10	−	3.37463e10i	0.770501	−	1.33455i
$206$	5.83002e9	−	1.00979e10i	0.225563	−	0.390687i
$207$	−1.04453e10	+	1.80918e10i	−0.395416	+	0.684881i
$208$	3.07003e10			1.13725
$209$	−1.48414e10	−	2.57061e10i	−0.538044	−	0.931919i
$210$	−8.08377e9	+	1.40015e10i	−0.286832	+	0.496807i
$211$	3.57256e10			1.24082			0.620409	−	0.784278i	$-0.286966\pi$
$211$	3.57256e10			1.24082			0.620409	+	0.784278i	$0.286966\pi$
$212$	9.88302e9			0.336030
$213$	3.13911e10	−	5.43709e10i	1.04496	−	1.80992i
$214$	4.72020e9			0.153850
$215$	−1.51814e10	−	2.62950e10i	−0.484552	−	0.839268i
$216$	3.31028e9			0.103472
$217$	1.60554e10	+	2.78088e10i	0.491533	+	0.851360i
$218$	−1.07948e10	−	1.86972e10i	−0.323714	−	0.560689i
$219$	−3.15090e10	−	5.45751e10i	−0.925626	−	1.60323i
$220$	−1.48190e10	+	2.56673e10i	−0.426499	+	0.738717i
$221$	−7.83249e10			−2.20869
$222$	−1.40459e10	+	1.02320e10i	−0.388116	+	0.282729i
$223$	1.11165e10			0.301021			0.150510	−	0.988608i	$-0.451908\pi$
$223$	1.11165e10			0.301021			0.150510	+	0.988608i	$0.451908\pi$
$224$	−1.55880e10	+	2.69992e10i	−0.413690	+	0.716532i
$225$	−1.06645e10	−	1.84714e10i	−0.277407	−	0.480484i
$226$	−4.91643e9	−	8.51550e9i	−0.125361	−	0.217131i
$227$	−2.41011e10	−	4.17443e10i	−0.602449	−	1.04347i	−0.992449	−	0.122658i	$-0.960858\pi$
$227$	−2.41011e10	−	4.17443e10i	−0.602449	−	1.04347i	0.390000	−	0.920815i	$-0.372475\pi$
$228$	6.94446e10			1.70189
$229$	3.30814e10	+	5.72986e10i	0.794921	+	1.37684i	0.922889	+	0.385066i	$0.125821\pi$
$229$	3.30814e10	+	5.72986e10i	0.794921	+	1.37684i	−0.127968	+	0.991778i	$0.540846\pi$
$230$	1.69113e10			0.398476
$231$	−2.12055e10	+	3.67289e10i	−0.489997	+	0.848700i
$232$	−6.89034e9			−0.156151
$233$	5.83414e10			1.29681			0.648403	−	0.761297i	$-0.275437\pi$
$233$	5.83414e10			1.29681			0.648403	+	0.761297i	$0.275437\pi$
$234$	1.24586e10	−	2.15789e10i	0.271642	−	0.470498i
$235$	−4.18075e9	−	7.24127e9i	−0.0894229	−	0.154885i
$236$	−3.02271e10			−0.634297
$237$	−5.60043e10	+	9.70023e10i	−1.15307	+	1.99717i
$238$	1.02039e10	−	1.76737e10i	0.206144	−	0.357052i
$239$	2.86998e10	−	4.97095e10i	0.568969	−	0.985483i	−0.427700	−	0.903921i	$-0.640676\pi$
$239$	2.86998e10	−	4.97095e10i	0.568969	−	0.985483i	0.996668	−	0.0815617i	$-0.0259908\pi$
$240$	−2.91656e10	−	5.05163e10i	−0.567441	−	0.982836i
$241$	2.98189e10	+	5.16478e10i	0.569396	+	0.986223i	0.996626	+	0.0820798i	$0.0261562\pi$
$241$	2.98189e10	+	5.16478e10i	0.569396	+	0.986223i	−0.427230	+	0.904143i	$0.640510\pi$
$242$	−3.91265e9	+	6.77691e9i	−0.0733334	+	0.127017i
$243$	−3.68234e10	+	6.37800e10i	−0.677478	+	1.17343i
$244$	1.92435e10	−	3.33306e10i	0.347559	−	0.601990i
$245$	8.81912e9			0.156379
$246$	−1.66619e10	−	2.88592e10i	−0.290079	−	0.502431i
$247$	−7.24868e10	+	1.25551e11i	−1.23915	+	2.14626i
$248$	4.10546e10			0.689175
$249$	−9.24144e10			−1.52350
$250$	5.14148e9	−	8.90531e9i	0.0832450	−	0.144185i
$251$	−4.56656e10			−0.726202			−0.363101	−	0.931750i	$-0.618282\pi$
$251$	−4.56656e10			−0.726202			−0.363101	+	0.931750i	$0.618282\pi$
$252$	−2.32956e10	−	4.03492e10i	−0.363891	−	0.630278i
$253$	4.43619e10			0.680719
$254$	1.31177e9	+	2.27205e9i	0.0197745	+	0.0342505i
$255$	7.44096e10	+	1.28881e11i	1.10204	+	1.90879i
$256$	3.86219e8	+	6.68951e8i	0.00562023	+	0.00973452i
$257$	1.88744e10	−	3.26914e10i	0.269882	−	0.467449i	−0.698949	−	0.715171i	$-0.746349\pi$
$257$	1.88744e10	−	3.26914e10i	0.269882	−	0.467449i	0.968831	+	0.247722i	$0.0796821\pi$
$258$	−2.59658e10			−0.364848
$259$	−6.20038e10	−	2.75126e10i	−0.856189	−	0.379911i
$260$	1.44755e11			1.96450
$261$	7.89066e9	−	1.36670e10i	0.105252	−	0.182302i
$262$	−3.45767e9	−	5.98885e9i	−0.0453343	−	0.0785214i
$263$	−8.11756e9	−	1.40600e10i	−0.104622	−	0.181211i	0.808961	−	0.587862i	$-0.200030\pi$
$263$	−8.11756e9	−	1.40600e10i	−0.104622	−	0.181211i	−0.913584	+	0.406650i	$0.866697\pi$
$264$	2.71118e10	+	4.69590e10i	0.343511	+	0.594979i
$265$	3.92012e10			0.488307
$266$	−1.88867e10	−	3.27127e10i	−0.231307	−	0.400636i
$267$	−2.01273e11			−2.42373
$268$	−5.46692e9	+	9.46898e9i	−0.0647346	+	0.112124i
$269$	−1.31411e11			−1.53020			−0.765099	−	0.643913i	$-0.777310\pi$
$269$	−1.31411e11			−1.53020			−0.765099	+	0.643913i	$0.777310\pi$
$270$	6.13753e9			0.0702840
$271$	3.07898e10	−	5.33295e10i	0.346773	−	0.600628i	−0.638902	−	0.769288i	$-0.720611\pi$
$271$	3.07898e10	−	5.33295e10i	0.346773	−	0.600628i	0.985674	+	0.168661i	$0.0539442\pi$
$272$	3.68150e10	+	6.37654e10i	0.407816	+	0.706358i
$273$	2.07138e11			2.25699
$274$	9.11021e9	−	1.57793e10i	0.0976452	−	0.169126i
$275$	−2.26464e10	+	3.92247e10i	−0.238782	+	0.413582i
$276$	−5.18935e10	+	8.98822e10i	−0.538297	+	0.932358i
$277$	8.76845e10	+	1.51874e11i	0.894878	+	1.54997i	0.833956	+	0.551831i	$0.186071\pi$
$277$	8.76845e10	+	1.51874e11i	0.894878	+	1.54997i	0.0609218	+	0.998143i	$0.480596\pi$
$278$	1.15174e10	+	1.99487e10i	0.115652	+	0.200315i
$279$	−4.70149e10	+	8.14321e10i	−0.464533	+	0.804594i
$280$	−4.03442e10	+	6.98782e10i	−0.392256	+	0.679408i
$281$	8.07874e10	−	1.39928e11i	0.772974	−	1.33883i	−0.162952	−	0.986634i	$-0.552102\pi$
$281$	8.07874e10	−	1.39928e11i	0.772974	−	1.33883i	0.935926	−	0.352197i	$-0.114565\pi$
$282$	−7.15059e9			−0.0673319
$283$	2.23274e10	+	3.86723e10i	0.206919	+	0.358394i	0.950742	−	0.309982i	$-0.100323\pi$
$283$	2.23274e10	+	3.86723e10i	0.206919	+	0.358394i	−0.743824	+	0.668376i	$0.766990\pi$
$284$	7.32305e10	−	1.26839e11i	0.667973	−	1.15696i
$285$	2.75453e11			2.47313
$286$	−5.29124e10			−0.467639
$287$	6.50399e10	−	1.12652e11i	0.565863	−	0.980103i
$288$	−9.12924e10			−0.781931
$289$	−3.46314e10	−	5.99833e10i	−0.292031	−	0.505813i
$290$	−1.27752e10			−0.106066
$291$	−5.58107e10	−	9.66670e10i	−0.456246	−	0.790242i
$292$	−7.35055e10	−	1.27315e11i	−0.591694	−	1.02484i
$293$	−2.27419e10	−	3.93901e10i	−0.180269	−	0.312236i	0.761703	−	0.647927i	$-0.224364\pi$
$293$	−2.27419e10	−	3.93901e10i	−0.180269	−	0.312236i	−0.941972	+	0.335691i	$0.891030\pi$
$294$	3.77097e9	−	6.53151e9i	0.0294368	−	0.0509860i
$295$	−1.19896e11			−0.921737
$296$	−7.00998e10	+	5.10653e10i	−0.530767	+	0.386645i
$297$	1.61000e10			0.120067
$298$	−2.06955e10	+	3.58456e10i	−0.152020	+	0.263307i
$299$	−1.08334e11	−	1.87639e11i	−0.783868	−	1.35770i
$300$	−5.29824e10	−	9.17681e10i	−0.377647	−	0.654103i
$301$	−5.06789e10	−	8.77784e10i	−0.355859	−	0.616366i
$302$	4.34067e10			0.300279
$303$	−3.89876e10	−	6.75285e10i	−0.265726	−	0.460251i
$304$	1.36284e11			0.915192
$305$	7.63295e10	−	1.32207e11i	0.505060	−	0.874790i
$306$	5.97601e10			0.389641
$307$	−3.69234e10			−0.237235			−0.118618	−	0.992940i	$-0.537846\pi$
$307$	−3.69234e10			−0.237235			−0.118618	+	0.992940i	$0.537846\pi$
$308$	−4.94690e10	+	8.56829e10i	−0.313224	+	0.542520i
$309$	1.41921e11	+	2.45814e11i	0.885590	+	1.53389i
$310$	7.61186e10			0.468127
$311$	−1.06839e11	+	1.85051e11i	−0.647604	+	1.12168i	0.336090	+	0.941830i	$0.390895\pi$
$311$	−1.06839e11	+	1.85051e11i	−0.647604	+	1.12168i	−0.983694	+	0.179852i	$0.942438\pi$
$312$	1.32416e11	−	2.29352e11i	0.791126	−	1.37027i
$313$	5.48615e10	−	9.50229e10i	0.323086	−	0.559601i	−0.658037	−	0.752985i	$-0.728613\pi$
$313$	5.48615e10	−	9.50229e10i	0.323086	−	0.559601i	0.981123	+	0.193384i	$0.0619464\pi$
$314$	2.52449e10	+	4.37255e10i	0.146552	+	0.253835i
$315$	−9.24025e10	−	1.60046e11i	−0.528794	−	0.915898i
$316$	−1.30649e11	+	2.26291e11i	−0.737081	+	1.27666i
$317$	8.70787e10	−	1.50825e11i	0.484335	−	0.838892i	−0.515504	−	0.856887i	$-0.672395\pi$
$317$	8.70787e10	−	1.50825e11i	0.484335	−	0.838892i	0.999838	+	0.0179954i	$0.00572843\pi$
$318$	1.67620e10	−	2.90327e10i	0.0919189	−	0.159208i
$319$	−3.35122e10			−0.181194
$320$	−4.05684e10	−	7.02665e10i	−0.216278	−	0.374605i
$321$	−5.74521e10	+	9.95099e10i	−0.302018	+	0.523111i
$322$	5.64535e10			0.292644
$323$	−3.47697e11			−1.77742
$324$	−9.58932e10	+	1.66092e11i	−0.483432	+	0.837328i
$325$	2.21213e11			1.09986
$326$	−3.62822e8	−	6.28426e8i	−0.00177916	−	0.00308159i
$327$	5.25559e11			2.54189
$328$	−8.31554e10	−	1.44029e11i	−0.396696	−	0.687098i
$329$	−1.39562e10	−	2.41729e10i	−0.0656730	−	0.113749i
$330$	5.02675e10	+	8.70658e10i	0.233332	+	0.404143i
$331$	−1.10382e11	+	1.91187e11i	−0.505441	+	0.875450i	0.494539	+	0.869155i	$0.335337\pi$
$331$	−1.10382e11	+	1.91187e11i	−0.505441	+	0.875450i	−0.999980	+	0.00629444i	$0.997996\pi$
$332$	−2.15588e11			−0.973877
$333$	−2.10115e10	−	1.97522e11i	−0.0936392	−	0.880272i
$334$	−3.15090e10			−0.138540
$335$	−2.16846e10	+	3.75589e10i	−0.0940699	+	0.162934i
$336$	−9.73610e10	−	1.68634e11i	−0.416733	−	0.721803i
$337$	−3.48926e10	−	6.04358e10i	−0.147367	−	0.255247i	0.782887	−	0.622164i	$-0.213746\pi$
$337$	−3.48926e10	−	6.04358e10i	−0.147367	−	0.255247i	−0.930253	+	0.366918i	$0.880413\pi$
$338$	8.72565e10	+	1.51133e11i	0.363641	+	0.629844i
$339$	2.39362e11			0.984366
$340$	1.73586e11	+	3.00660e11i	0.704466	+	1.22017i
$341$	1.99675e11			0.799705
$342$	5.53057e10	−	9.57923e10i	0.218601	−	0.378628i
$343$	2.69556e11			1.05154
$344$	−1.29589e11			−0.498947
$345$	−2.05837e11	+	3.56519e11i	−0.782234	+	1.35487i
$346$	5.34648e9	+	9.26037e9i	0.0200551	+	0.0347365i
$347$	−1.70262e11			−0.630426			−0.315213	−	0.949021i	$-0.602076\pi$
$347$	−1.70262e11			−0.630426			−0.315213	+	0.949021i	$0.602076\pi$
$348$	3.92017e10	−	6.78994e10i	0.143284	−	0.248176i
$349$	−5.29093e10	+	9.16416e10i	−0.190905	+	0.330657i	−0.945550	−	0.325475i	$-0.894476\pi$
$349$	−5.29093e10	+	9.16416e10i	−0.190905	+	0.330657i	0.754645	+	0.656133i	$0.227809\pi$
$350$	−2.88190e10	+	4.99160e10i	−0.102653	+	0.177801i
$351$	−3.93170e10	−	6.80990e10i	−0.138260	−	0.239474i
$352$	9.69312e10	+	1.67890e11i	0.336528	+	0.582884i
$353$	−7.20507e10	+	1.24796e11i	−0.246975	+	0.427772i	−0.962685	−	0.270625i	$-0.912770\pi$
$353$	−7.20507e10	+	1.24796e11i	−0.246975	+	0.427772i	0.715710	+	0.698397i	$0.246103\pi$
$354$	−5.12665e10	+	8.87962e10i	−0.173508	+	0.300524i
$355$	2.90470e11	−	5.03109e11i	0.970675	−	1.68126i
$356$	−4.69538e11			−1.54934
$357$	2.48395e11	+	4.30233e11i	0.809350	+	1.40183i
$358$	6.34743e9	−	1.09941e10i	0.0204232	−	0.0353740i
$359$	−1.38656e11			−0.440567			−0.220284	−	0.975436i	$-0.570698\pi$
$359$	−1.38656e11			−0.440567			−0.220284	+	0.975436i	$0.570698\pi$
$360$	−2.36279e11			−0.741418
$361$	−1.60437e11	+	2.77885e11i	−0.497190	+	0.861158i
$362$	−1.52600e11			−0.467053
$363$	−9.52460e10	−	1.64971e11i	−0.287917	−	0.498687i
$364$	4.83222e11			1.44275
$365$	−2.91561e11	−	5.04999e11i	−0.859828	−	1.48927i
$366$	−6.52755e10	−	1.13061e11i	−0.190145	−	0.329341i
$367$	−1.46367e11	−	2.53516e11i	−0.421160	−	0.729470i	0.574893	−	0.818228i	$-0.305044\pi$
$367$	−1.46367e11	−	2.53516e11i	−0.421160	−	0.729470i	−0.996053	+	0.0887580i	$0.971710\pi$
$368$	−1.01840e11	+	1.76392e11i	−0.289469	+	0.501376i
$369$	3.80911e11			1.06956
$370$	−1.29971e11	+	9.46791e10i	−0.360527	+	0.262631i
$371$	1.30862e11			0.358617
$372$	−2.33575e11	+	4.04564e11i	−0.632388	+	1.09533i
$373$	−6.13170e10	−	1.06204e11i	−0.164018	−	0.284087i	0.772288	−	0.635272i	$-0.219112\pi$
$373$	−6.13170e10	−	1.06204e11i	−0.164018	−	0.284087i	−0.936306	+	0.351185i	$0.885779\pi$
$374$	−6.34513e10	−	1.09901e11i	−0.167694	−	0.290455i
$375$	1.25160e11	+	2.16783e11i	0.326831	+	0.566088i
$376$	−3.56869e10			−0.0920796
$377$	8.18381e10	+	1.41748e11i	0.208651	+	0.361393i
$378$	2.04884e10			0.0516172
$379$	−4.86540e10	+	8.42712e10i	−0.121127	+	0.209799i	−0.920213	−	0.391419i	$-0.871984\pi$
$379$	−4.86540e10	+	8.42712e10i	−0.121127	+	0.209799i	0.799085	+	0.601218i	$0.205318\pi$
$380$	6.42590e11			1.58091
$381$	−6.38651e10			−0.155275
$382$	−1.37764e11	+	2.38615e11i	−0.331018	+	0.573341i
$383$	−4.18771e10	−	7.25333e10i	−0.0994449	−	0.172244i	0.812010	−	0.583643i	$-0.198373\pi$
$383$	−4.18771e10	−	7.25333e10i	−0.0994449	−	0.172244i	−0.911455	+	0.411400i	$0.865040\pi$
$384$	−5.86138e11			−1.37565
$385$	−1.96220e11	+	3.39863e11i	−0.455166	+	0.788370i
$386$	−5.21944e10	+	9.04033e10i	−0.119669	+	0.207272i
$387$	1.48402e11	−	2.57040e11i	0.336311	−	0.582508i
$388$	−1.30198e11	−	2.25509e11i	−0.291649	−	0.505151i
$389$	3.48196e11	+	6.03093e11i	0.770993	+	1.33540i	0.937019	+	0.349278i	$0.113573\pi$
$389$	3.48196e11	+	6.03093e11i	0.770993	+	1.33540i	−0.166026	+	0.986121i	$0.553094\pi$
$390$	2.45510e11	−	4.25237e11i	0.537377	−	0.930765i
$391$	2.59822e11	−	4.50025e11i	0.562187	−	0.973736i
$392$	1.88200e10	−	3.25972e10i	0.0402562	−	0.0697258i
$393$	1.68340e11			0.355977
$394$	1.04153e11	+	1.80398e11i	0.217740	+	0.377137i
$395$	−5.18223e11	+	8.97589e11i	−1.07110	+	1.85520i
$396$	−2.89719e11			−0.592037
$397$	3.60413e11			0.728187			0.364094	−	0.931362i	$-0.381379\pi$
$397$	3.60413e11			0.728187			0.364094	+	0.931362i	$0.381379\pi$
$398$	7.37160e10	−	1.27680e11i	0.147261	−	0.255064i
$399$	9.19522e11			1.81628
$400$	−1.03977e11	−	1.80093e11i	−0.203079	−	0.351744i
$401$	3.63670e11			0.702358			0.351179	−	0.936308i	$-0.385781\pi$
$401$	3.63670e11			0.702358			0.351179	+	0.936308i	$0.385781\pi$
$402$	1.85443e10	+	3.21196e10i	0.0354155	+	0.0613414i
$403$	−4.87615e11	−	8.44575e11i	−0.920884	−	1.59502i
$404$	−9.09520e10	−	1.57533e11i	−0.169862	−	0.294209i
$405$	−3.80362e11	+	6.58806e11i	−0.702505	+	1.21677i
$406$	−4.26465e10			−0.0778961
$407$	−3.40941e11	+	2.48363e11i	−0.615892	+	0.448655i
$408$	6.35161e11			1.13478
$409$	2.70956e11	−	4.69309e11i	0.478788	−	0.829286i	−0.520916	−	0.853608i	$-0.674409\pi$
$409$	2.70956e11	−	4.69309e11i	0.478788	−	0.829286i	0.999704	+	0.0243224i	$0.00774281\pi$
$410$	−1.54177e11	−	2.67042e11i	−0.269458	−	0.466716i
$411$	2.21771e11	+	3.84118e11i	0.383368	+	0.664013i
$412$	3.31079e11	+	5.73446e11i	0.566102	+	0.980517i
$413$	−4.00239e11			−0.676931
$414$	8.26560e10	+	1.43164e11i	0.138284	+	0.239515i
$415$	−8.55135e11			−1.41520
$416$	4.73420e11	−	8.19988e11i	0.775045	−	1.34242i
$417$	−5.60738e11			−0.908129
$418$	−2.34887e11			−0.376327
$419$	3.09430e11	−	5.35949e11i	0.490455	−	0.849493i	−0.509484	−	0.860480i	$-0.670164\pi$
$419$	3.09430e11	−	5.35949e11i	0.490455	−	0.849493i	0.999940	+	0.0109865i	$0.00349719\pi$
$420$	−4.59067e11	−	7.95127e11i	−0.719870	−	1.24685i
$421$	−5.47777e11			−0.849835			−0.424917	−	0.905232i	$-0.639697\pi$
$421$	−5.47777e11			−0.849835			−0.424917	+	0.905232i	$0.639697\pi$
$422$	1.41352e11	−	2.44829e11i	0.216968	−	0.375800i
$423$	4.08678e10	−	7.07852e10i	0.0620655	−	0.107501i
$424$	8.36554e10	−	1.44895e11i	0.125704	−	0.217725i
$425$	2.65274e11	+	4.59467e11i	0.394406	+	0.683132i
$426$	−2.48404e11	−	4.30249e11i	−0.365440	−	0.632960i
$427$	2.54804e11	−	4.41334e11i	0.370921	−	0.642453i
$428$	−1.34027e11	+	2.32141e11i	−0.193061	+	0.334392i
$429$	6.44026e11	−	1.11549e12i	0.918006	−	1.59003i
$430$	−2.40268e11			−0.338913
$431$	5.07485e11	+	8.78989e11i	0.708395	+	1.22698i	0.965452	+	0.260580i	$0.0839136\pi$
$431$	5.07485e11	+	8.78989e11i	0.708395	+	1.22698i	−0.257058	+	0.966396i	$0.582753\pi$
$432$	−3.69602e10	+	6.40170e10i	−0.0510573	+	0.0884338i
$433$	6.19726e11			0.847235			0.423618	−	0.905841i	$-0.360760\pi$
$433$	6.19726e11			0.847235			0.423618	+	0.905841i	$0.360760\pi$
$434$	2.54100e11			0.343796
$435$	1.55494e11	−	2.69324e11i	0.208216	−	0.360640i
$436$	1.22605e12			1.62487
$437$	−4.80911e11	−	8.32962e11i	−0.630810	−	1.09259i
$438$	−4.98675e11			−0.647417
$439$	−1.24736e10	−	2.16049e10i	−0.0160288	−	0.0277628i	0.857900	−	0.513817i	$-0.171769\pi$
$439$	−1.24736e10	−	2.16049e10i	−0.0160288	−	0.0277628i	−0.873929	+	0.486054i	$0.838436\pi$
$440$	2.50873e11	+	4.34525e11i	0.319093	+	0.552685i
$441$	4.31045e10	+	7.46592e10i	0.0542687	+	0.0939961i
$442$	−3.09901e11	+	5.36765e11i	−0.386210	+	0.668935i
$443$	−6.13793e11			−0.757190			−0.378595	−	0.925562i	$-0.623593\pi$
$443$	−6.13793e11			−0.757190			−0.378595	+	0.925562i	$0.623593\pi$
$444$	−1.04387e11	−	9.81314e11i	−0.127475	−	1.19835i
$445$	−1.86243e12			−2.25144
$446$	4.39837e10	−	7.61820e10i	0.0526363	−	0.0911687i
$447$	−5.03792e11	−	8.72593e11i	−0.596853	−	1.03378i
$448$	−1.35426e11	−	2.34564e11i	−0.158837	−	0.275113i
$449$	5.80333e11	+	1.00517e12i	0.673858	+	1.16716i	0.976801	+	0.214148i	$0.0686974\pi$
$449$	5.80333e11	+	1.00517e12i	0.673858	+	1.16716i	−0.302943	+	0.953009i	$0.597969\pi$
$450$	−1.68781e11			−0.194029
$451$	−4.04439e11	−	7.00508e11i	−0.460318	−	0.797294i
$452$	5.58394e11			0.629243
$453$	−5.28326e11	+	9.15088e11i	−0.589468	+	1.02099i
$454$	−3.81435e11			−0.421375
$455$	1.91671e12			2.09655
$456$	5.87818e11	−	1.01813e12i	0.636650	−	1.10271i
$457$	8.82477e11	+	1.52849e12i	0.946412	+	1.63923i	0.752899	+	0.658136i	$0.228655\pi$
$457$	8.82477e11	+	1.52849e12i	0.946412	+	1.63923i	0.193513	+	0.981098i	$0.438012\pi$
$458$	5.23561e11			0.555997
$459$	9.42958e10	−	1.63325e11i	0.0991597	−	0.171750i
$460$	−4.80185e11	+	8.31705e11i	−0.500032	+	0.866082i
$461$	8.13969e11	−	1.40984e12i	0.839371	−	1.45383i	−0.0510513	−	0.998696i	$-0.516257\pi$
$461$	8.13969e11	−	1.40984e12i	0.839371	−	1.45383i	0.890422	−	0.455136i	$-0.150409\pi$
$462$	1.67803e11	+	2.90644e11i	0.171361	+	0.296806i
$463$	−9.13923e11	−	1.58296e12i	−0.924262	−	1.60087i	−0.792744	−	0.609555i	$-0.791348\pi$
$463$	−9.13923e11	−	1.58296e12i	−0.924262	−	1.60087i	−0.131518	−	0.991314i	$-0.541985\pi$
$464$	7.69325e10	−	1.33251e11i	0.0770511	−	0.133456i
$465$	−9.26481e11	+	1.60471e12i	−0.918964	+	1.59169i
$466$	2.30834e11	−	3.99816e11i	0.226758	−	0.392757i
$467$	1.31008e11			0.127459			0.0637296	−	0.997967i	$-0.479700\pi$
$467$	1.31008e11			0.127459			0.0637296	+	0.997967i	$0.479700\pi$
$468$	7.07506e11	+	1.22544e12i	0.681748	+	1.18082i
$469$	−7.23879e10	+	1.25380e11i	−0.0690857	+	0.119660i
$470$	−6.61664e10			−0.0625456
$471$	−1.22908e12			−1.15076
$472$	−2.55859e11	+	4.43161e11i	−0.237280	+	0.410981i
$473$	−6.30275e11			−0.578968
$474$	4.43174e11	+	7.67600e11i	0.403248	+	0.698446i
$475$	9.82003e11			0.885099
$476$	5.79467e11	+	1.00367e12i	0.517366	+	0.896104i
$477$	1.91601e11	+	3.31862e11i	0.169459	+	0.293511i
$478$	−2.27108e11	−	3.93362e11i	−0.198979	−	0.344641i
$479$	−7.42362e11	+	1.28581e12i	−0.644326	+	1.11601i	0.340130	+	0.940378i	$0.389529\pi$
$479$	−7.42362e11	+	1.28581e12i	−0.644326	+	1.11601i	−0.984457	+	0.175628i	$0.943805\pi$
$480$	−1.79902e12			−1.54686
$481$	1.88310e12	+	8.35577e11i	1.60406	+	0.711760i
$482$	4.71926e11			0.398256
$483$	−6.87126e11	+	1.19014e12i	−0.574479	+	0.995027i
$484$	−2.22194e11	−	3.84852e11i	−0.184047	−	0.318779i
$485$	−5.16432e11	−	8.94486e11i	−0.423814	−	0.734067i
$486$	2.91391e11	+	5.04705e11i	0.236926	+	0.410369i
$487$	2.49441e11			0.200950			0.100475	−	0.994940i	$-0.467964\pi$
$487$	2.49441e11			0.200950			0.100475	+	0.994940i	$0.467964\pi$
$488$	−3.25774e11	−	5.64258e11i	−0.260033	−	0.450390i
$489$	1.76644e10			0.0139704
$490$	3.48938e10	−	6.04379e10i	0.0273443	−	0.0473616i
$491$	−7.78093e10			−0.0604178			−0.0302089	−	0.999544i	$-0.509617\pi$
$491$	−7.78093e10			−0.0604178			−0.0302089	+	0.999544i	$0.509617\pi$
$492$	1.89241e12			1.45604
$493$	−1.96276e11	+	3.39961e11i	−0.149643	+	0.259190i
$494$	5.73604e11	+	9.93511e11i	0.433352	+	0.750588i
$495$	−1.14918e12			−0.860326
$496$	−4.58386e11	+	7.93949e11i	−0.340067	+	0.589013i
$497$	9.69650e11	−	1.67948e12i	0.712872	−	1.23473i
$498$	−3.65648e11	+	6.33320e11i	−0.266398	+	0.461415i
$499$	5.72794e11	+	9.92108e11i	0.413567	+	0.716319i	0.995277	−	0.0970773i	$-0.0309494\pi$
$499$	5.72794e11	+	9.92108e11i	0.413567	+	0.716319i	−0.581710	+	0.813396i	$0.697616\pi$
$500$	2.91978e11	+	5.05720e11i	0.208922	+	0.361864i
$501$	3.83514e11	−	6.64265e11i	0.271964	−	0.471055i
$502$	−1.80681e11	+	3.12949e11i	−0.126983	+	0.219941i
$503$	−1.66740e11	+	2.88803e11i	−0.116141	+	0.201162i	−0.918235	−	0.396036i	$-0.870386\pi$
$503$	−1.66740e11	+	2.88803e11i	−0.116141	+	0.201162i	0.802094	+	0.597197i	$0.203719\pi$
$504$	−7.88748e11			−0.544504
$505$	−3.60763e11	−	6.24859e11i	−0.246837	−	0.427534i
$506$	1.75523e11	−	3.04014e11i	0.119030	−	0.206166i
$507$	−4.24819e12			−2.85540
$508$	−1.48987e11			−0.0992573
$509$	−5.09653e11	+	8.82745e11i	−0.336546	+	0.582915i	−0.983781	−	0.179376i	$-0.942592\pi$
$509$	−5.09653e11	+	8.82745e11i	−0.336546	+	0.582915i	0.647235	+	0.762291i	$0.275925\pi$
$510$	1.17764e12			0.770809
$511$	−9.73293e11	−	1.68579e12i	−0.631465	−	1.09373i
$512$	−1.55179e12			−0.997973
$513$	−1.74535e11	−	3.02303e11i	−0.111264	−	0.192714i
$514$	−1.49357e11	−	2.58694e11i	−0.0943825	−	0.163475i
$515$	1.31323e12	+	2.27458e12i	0.822638	+	1.42485i
$516$	7.37280e11	−	1.27701e12i	0.457835	−	0.792993i
$517$	−1.73569e11			−0.106847
$518$	−4.33870e11	+	3.16059e11i	−0.264774	+	0.192879i
$519$	−2.60300e11			−0.157478
$520$	1.22528e12	−	2.12225e12i	0.734889	−	1.27286i
$521$	9.01156e11	+	1.56085e12i	0.535834	+	0.928092i	0.999122	+	0.0418842i	$0.0133361\pi$
$521$	9.01156e11	+	1.56085e12i	0.535834	+	0.928092i	−0.463288	+	0.886208i	$0.653331\pi$
$522$	−6.24405e10	−	1.08150e11i	−0.0368086	−	0.0637544i
$523$	−1.57796e12	−	2.73312e12i	−0.922231	−	1.59735i	−0.795955	−	0.605356i	$-0.793031\pi$
$523$	−1.57796e12	−	2.73312e12i	−0.922231	−	1.59735i	−0.126276	−	0.991995i	$-0.540302\pi$
$524$	3.92712e11			0.227554
$525$	−7.01543e11	−	1.21511e12i	−0.403030	−	0.698069i
$526$	−1.28472e11			−0.0731767
$527$	1.16947e12	−	2.02559e12i	0.660453	−	1.14394i
$528$	−1.21084e12			−0.678009
$529$	−3.63681e11			−0.201916
$530$	1.55104e11	−	2.68648e11i	0.0853849	−	0.147891i
$531$	−5.86008e11	−	1.01500e12i	−0.319873	−	0.554037i
$532$	2.14510e12			1.16104
$533$	−1.97531e12	+	3.42134e12i	−1.06014	+	1.83622i
$534$	−7.96357e11	+	1.37933e12i	−0.423811	+	0.734062i
$535$	−5.31620e11	+	9.20793e11i	−0.280549	+	0.485926i
$536$	9.25501e10	+	1.60301e11i	0.0484323	+	0.0838872i
$537$	1.54516e11	+	2.67629e11i	0.0801842	+	0.138883i
$538$	−5.19943e11	+	9.00568e11i	−0.267569	+	0.463443i
$539$	9.15339e10	−	1.58541e11i	0.0467124	−	0.0809083i
$540$	−1.74271e11	+	3.01846e11i	−0.0881969	+	0.152761i
$541$	1.32775e12			0.666390			0.333195	−	0.942858i	$-0.391873\pi$
$541$	1.32775e12			0.666390			0.333195	+	0.942858i	$0.391873\pi$
$542$	−2.43646e11	−	4.22008e11i	−0.121273	−	0.210050i
$543$	1.85738e12	−	3.21708e12i	0.916857	−	1.58804i
$544$	2.27085e12			1.11172
$545$	4.86314e12			2.36120
$546$	8.19566e11	−	1.41953e12i	0.394654	−	0.683561i
$547$	−1.50706e12			−0.719761			−0.359880	−	0.932998i	$-0.617182\pi$
$547$	−1.50706e12			−0.719761			−0.359880	+	0.932998i	$0.617182\pi$
$548$	5.17356e11	+	8.96088e11i	0.245063	+	0.424461i
$549$	1.49228e12			0.701091
$550$	1.79206e11	+	3.10393e11i	0.0835064	+	0.144637i
$551$	3.63293e11	+	6.29242e11i	0.167909	+	0.290827i
$552$	8.78511e11	+	1.52163e12i	0.402737	+	0.697561i
$553$	−1.72994e12	+	2.99634e12i	−0.786625	+	1.36247i
$554$	1.38773e12			0.625910
$555$	−4.14055e11	−	3.89240e12i	−0.185242	−	1.74140i
$556$	−1.30811e12			−0.580509
$557$	−6.70908e11	+	1.16205e12i	−0.295335	+	0.511535i	−0.975063	−	0.221929i	$-0.928765\pi$
$557$	−6.70908e11	+	1.16205e12i	−0.295335	+	0.511535i	0.679728	+	0.733464i	$0.262098\pi$
$558$	3.72039e11	+	6.44390e11i	0.162456	+	0.281381i
$559$	1.53916e12	+	2.66590e12i	0.666699	+	1.15476i
$560$	−9.00908e11	−	1.56042e12i	−0.387110	−	0.670494i
$561$	3.08920e12			1.31678
$562$	−6.39288e11	−	1.10728e12i	−0.270323	−	0.468213i
$563$	2.68265e12			1.12532			0.562660	−	0.826688i	$-0.309778\pi$
$563$	2.68265e12			1.12532			0.562660	+	0.826688i	$0.309778\pi$
$564$	2.03036e11	−	3.51669e11i	0.0844924	−	0.146345i
$565$	2.21488e12			0.914392
$566$	3.53364e11			0.144727
$567$	−1.26973e12	+	2.19924e12i	−0.515926	+	0.893610i
$568$	−1.23973e12	−	2.14727e12i	−0.499756	−	0.865603i
$569$	−1.25819e12			−0.503200			−0.251600	−	0.967831i	$-0.580957\pi$
$569$	−1.25819e12			−0.503200			−0.251600	+	0.967831i	$0.580957\pi$
$570$	1.08986e12	−	1.88770e12i	0.432449	−	0.749023i
$571$	−6.76749e11	+	1.17216e12i	−0.266419	+	0.461451i	−0.967934	−	0.251203i	$-0.919174\pi$
$571$	−6.76749e11	+	1.17216e12i	−0.266419	+	0.461451i	0.701515	+	0.712654i	$0.252507\pi$
$572$	1.50241e12	−	2.60226e12i	0.586823	−	1.01641i
$573$	−3.35361e12	−	5.80863e12i	−1.29962	−	2.25101i
$574$	−5.14675e11	−	8.91443e11i	−0.197893	−	0.342760i
$575$	−7.33816e11	+	1.27101e12i	−0.279951	+	0.484889i
$576$	3.96566e11	−	6.86872e11i	0.150112	−	0.260001i
$577$	−1.53772e11	+	2.66342e11i	−0.0577547	+	0.100034i	−0.893457	−	0.449148i	$-0.851727\pi$
$577$	−1.53772e11	+	2.66342e11i	−0.0577547	+	0.100034i	0.835703	+	0.549182i	$0.185061\pi$
$578$	−5.48091e11			−0.204257
$579$	−1.27057e12	−	2.20070e12i	−0.469836	−	0.813779i
$580$	3.62744e11	−	6.28292e11i	0.133099	−	0.230534i
$581$	−2.85462e12			−1.03934
$582$	−8.83285e11			−0.319115
$583$	4.06870e11	−	7.04720e11i	0.145864	−	0.252643i
$584$	−2.48877e12			−0.885373
$585$	2.80634e12	+	4.86072e12i	0.990691	+	1.71593i
$586$	−3.59923e11			−0.126087
$587$	−2.08495e12	−	3.61125e12i	−0.724811	−	1.25541i	−0.959052	−	0.283231i	$-0.908594\pi$
$587$	−2.08495e12	−	3.61125e12i	−0.724811	−	1.25541i	0.234240	−	0.972179i	$-0.424740\pi$
$588$	2.14148e11	+	3.70916e11i	0.0738783	+	0.127961i
$589$	−2.16461e12	−	3.74921e12i	−0.741071	−	1.28357i
$590$	−4.74383e11	+	8.21655e11i	−0.161174	+	0.279162i
$591$	−5.07080e12			−1.70975
$592$	−2.04858e11	−	1.92581e12i	−0.0685497	−	0.644414i
$593$	−8.04659e11			−0.267218			−0.133609	−	0.991034i	$-0.542657\pi$
$593$	−8.04659e11			−0.267218			−0.133609	+	0.991034i	$0.542657\pi$
$594$	6.37016e10	−	1.10334e11i	0.0209948	−	0.0363640i
$595$	2.29847e12	+	3.98106e12i	0.751817	+	1.30219i
$596$	−1.17527e12	−	2.03562e12i	−0.381530	−	0.660829i
$597$	1.79447e12	+	3.10812e12i	0.578166	+	1.00141i
$598$	−1.71454e12			−0.548266
$599$	2.13745e12	+	3.70218e12i	0.678384	+	1.17500i	0.975467	+	0.220145i	$0.0706529\pi$
$599$	2.13745e12	+	3.70218e12i	0.678384	+	1.17500i	−0.297083	+	0.954852i	$0.596014\pi$
$600$	−1.79389e12			−0.565086
$601$	8.42230e11	−	1.45878e12i	0.263327	−	0.456096i	−0.703797	−	0.710401i	$-0.748513\pi$
$601$	8.42230e11	−	1.45878e12i	0.263327	−	0.456096i	0.967124	+	0.254305i	$0.0818468\pi$
$602$	−8.02066e11			−0.248901
$603$	−4.23945e11			−0.130582
$604$	−1.23250e12	+	2.13476e12i	−0.376809	+	0.652653i
$605$	−8.81337e11	−	1.52652e12i	−0.267450	−	0.463237i
$606$	−6.17035e11			−0.185859
$607$	2.36835e12	−	4.10210e12i	0.708103	−	1.22647i	−0.257457	−	0.966290i	$-0.582885\pi$
$607$	2.36835e12	−	4.10210e12i	0.708103	−	1.22647i	0.965560	−	0.260181i	$-0.0837822\pi$
$608$	2.10159e12	−	3.64006e12i	0.623709	−	1.08030i
$609$	5.19073e11	−	8.99061e11i	0.152915	−	0.264857i
$610$	−6.04012e11	−	1.04618e12i	−0.176629	−	0.305930i
$611$	4.23861e11	+	7.34150e11i	0.123038	+	0.213108i
$612$	−1.69685e12	+	2.93902e12i	−0.488946	+	0.846880i
$613$	1.73897e12	−	3.01199e12i	0.497417	−	0.861552i	−0.502578	−	0.864532i	$-0.667615\pi$
$613$	1.73897e12	−	3.01199e12i	0.497417	−	0.861552i	0.999996	+	0.00297958i	$0.000948432\pi$
$614$	−1.46092e11	+	2.53038e11i	−0.0414827	+	0.0718502i
$615$	7.50628e12			2.11586
$616$	8.37467e11	+	1.45053e12i	0.234344	+	0.405896i
$617$	−1.37966e12	+	2.38964e12i	−0.383255	+	0.663818i	−0.991525	−	0.129912i	$-0.958530\pi$
$617$	−1.37966e12	+	2.38964e12i	−0.383255	+	0.663818i	0.608270	+	0.793730i	$0.291864\pi$
$618$	2.24610e12			0.619414
$619$	2.29837e12			0.629234			0.314617	−	0.949219i	$-0.398124\pi$
$619$	2.29837e12			0.629234			0.314617	+	0.949219i	$0.398124\pi$
$620$	−2.16134e12	+	3.74355e12i	−0.587435	+	1.01747i
$621$	5.21694e11			0.140768
$622$	8.45443e11	+	1.46435e12i	0.226479	+	0.392273i
$623$	−6.21719e12			−1.65348
$624$	2.95693e12	+	5.12155e12i	0.780747	+	1.35229i
$625$	2.35355e12	+	4.07646e12i	0.616968	+	1.06862i
$626$	−4.34131e11	−	7.51937e11i	−0.112989	−	0.195703i
$627$	2.85894e12	−	4.95183e12i	0.738756	−	1.27956i
$628$	−2.86725e12			−0.735609
$629$	5.22650e11	+	4.91327e12i	0.133132	+	1.25153i
$630$	−1.46240e12			−0.369858
$631$	−3.45268e12	+	5.98021e12i	−0.867009	+	1.50170i	−0.00197053	+	0.999998i	$0.500627\pi$
$631$	−3.45268e12	+	5.98021e12i	−0.867009	+	1.50170i	−0.865038	+	0.501706i	$0.832706\pi$
$632$	2.21178e12	+	3.83091e12i	0.551461	+	0.955158i
$633$	3.44095e12	+	5.95990e12i	0.851847	+	1.47544i
$634$	−6.89073e11	−	1.19351e12i	−0.169381	−	0.293376i
$635$	−5.90961e11			−0.144237
$636$	9.51894e11	+	1.64873e12i	0.230691	+	0.399569i
$637$	−8.94118e11			−0.215163
$638$	−1.32595e11	+	2.29661e11i	−0.0316835	+	0.0548774i
$639$	5.67883e12			1.34743
$640$	−5.42369e12			−1.27787
$641$	2.78699e11	−	4.82721e11i	0.0652040	−	0.112937i	−0.831580	−	0.555404i	$-0.812564\pi$
$641$	2.78699e11	−	4.82721e11i	0.0652040	−	0.112937i	0.896784	+	0.442468i	$0.145897\pi$
$642$	4.54631e11	+	7.87444e11i	0.105621	+	0.182941i
$643$	−1.30021e12			−0.299960			−0.149980	−	0.988689i	$-0.547921\pi$
$643$	−1.30021e12			−0.299960			−0.149980	+	0.988689i	$0.547921\pi$
$644$	−1.60296e12	+	2.77641e12i	−0.367228	+	0.636058i
$645$	2.92443e12	−	5.06527e12i	0.665309	−	1.15235i
$646$	−1.37570e12	+	2.38279e12i	−0.310798	+	0.538318i
$647$	−2.35538e12	−	4.07964e12i	−0.528436	−	0.915278i	−0.999450	−	0.0331523i	$-0.989445\pi$
$647$	−2.35538e12	−	4.07964e12i	−0.528436	−	0.915278i	0.471014	−	0.882125i	$-0.343888\pi$
$648$	1.62339e12	+	2.81179e12i	0.361688	+	0.626462i
$649$	−1.24441e12	+	2.15538e12i	−0.275335	+	0.476894i
$650$	8.75255e11	−	1.51599e12i	0.192320	−	0.333108i
$651$	−3.09279e12	+	5.35687e12i	−0.674895	+	1.16895i
$652$	4.12083e10			0.00893040
$653$	−2.98464e12	−	5.16954e12i	−0.642365	−	1.11261i	−0.984903	−	0.173105i	$-0.944620\pi$
$653$	−2.98464e12	−	5.16954e12i	−0.642365	−	1.11261i	0.342538	−	0.939504i	$-0.388713\pi$
$654$	2.07943e12	−	3.60168e12i	0.444472	−	0.769849i
$655$	1.55770e12			0.330672
$656$	3.71381e12			0.782983
$657$	2.85008e12	−	4.93648e12i	0.596778	−	1.03365i
$658$	−2.20877e11			−0.0459341
$659$	3.98880e12	+	6.90881e12i	0.823869	+	1.42698i	0.902781	+	0.430101i	$0.141522\pi$
$659$	3.98880e12	+	6.90881e12i	0.823869	+	1.42698i	−0.0789116	+	0.996882i	$0.525144\pi$
$660$	−5.70924e12			−1.17120
$661$	−1.57999e12	−	2.73662e12i	−0.321919	−	0.557581i	0.658965	−	0.752174i	$-0.270995\pi$
$661$	−1.57999e12	−	2.73662e12i	−0.321919	−	0.557581i	−0.980884	+	0.194593i	$0.937661\pi$
$662$	8.73474e11	+	1.51290e12i	0.176762	+	0.306161i
$663$	−7.54395e12	−	1.30665e13i	−1.51631	−	2.62633i
$664$	−1.82486e12	+	3.16075e12i	−0.364312	+	0.631006i
$665$	8.50858e12			1.68717
$666$	−1.43676e12	−	6.37526e11i	−0.282977	−	0.125564i
$667$	−1.08590e12			−0.212435
$668$	8.94678e11	−	1.54963e12i	0.173849	−	0.301116i
$669$	1.07070e12	+	1.85451e12i	0.206657	+	0.357940i
$670$	1.71595e11	+	2.97212e11i	0.0328980	+	0.0569809i
$671$	−1.58445e12	−	2.74435e12i	−0.301737	−	0.522623i
$672$	−6.00551e12			−1.13603
$673$	1.20451e12	+	2.08627e12i	0.226330	+	0.392014i	0.956718	−	0.291018i	$-0.0939940\pi$
$673$	1.20451e12	+	2.08627e12i	0.226330	+	0.392014i	−0.730388	+	0.683033i	$0.760661\pi$
$674$	−5.52226e11			−0.103074
$675$	−2.66320e11	+	4.61280e11i	−0.0493784	+	0.0855259i
$676$	−9.91036e12			−1.82528
$677$	1.14882e12			0.210185			0.105092	−	0.994462i	$-0.466486\pi$
$677$	1.14882e12			0.210185			0.105092	+	0.994462i	$0.466486\pi$
$678$	9.47062e11	−	1.64036e12i	0.172125	−	0.298130i
$679$	−1.72396e12	−	2.98598e12i	−0.311253	−	0.539105i
$680$	5.87732e12			1.05412
$681$	4.64265e12	−	8.04130e12i	0.827187	−	1.43273i
$682$	7.90037e11	−	1.36838e12i	0.139836	−	0.242202i
$683$	−8.19494e11	+	1.41940e12i	−0.144096	+	0.249582i	−0.929035	−	0.369991i	$-0.879361\pi$
$683$	−8.19494e11	+	1.41940e12i	−0.144096	+	0.249582i	0.784939	+	0.619573i	$0.212694\pi$
$684$	3.14074e12	+	5.43991e12i	0.548629	+	0.950254i
$685$	2.05210e12	+	3.55435e12i	0.356116	+	0.616811i
$686$	1.06653e12	−	1.84728e12i	0.183871	−	0.318474i
$687$	−6.37254e12	+	1.10376e13i	−1.09146	+	1.89046i
$688$	1.44690e12	−	2.50610e12i	0.246201	−	0.426432i
$689$	−3.97438e12			−0.671866
$690$	1.62883e12	+	2.82122e12i	0.273561	+	0.473822i
$691$	5.16668e12	−	8.94895e12i	0.862105	−	1.49321i	−0.00778780	−	0.999970i	$-0.502479\pi$
$691$	5.16668e12	−	8.94895e12i	0.862105	−	1.49321i	0.869893	−	0.493240i	$-0.164188\pi$
$692$	−6.07239e11			−0.100666
$693$	−3.83619e12			−0.631831
$694$	−6.73659e11	+	1.16681e12i	−0.110236	+	0.190934i
$695$	−5.18866e12			−0.843574
$696$	−6.63650e11	−	1.14948e12i	−0.107201	−	0.185677i
$697$	−9.47497e12			−1.52065
$698$	4.18683e11	+	7.25180e11i	0.0667630	+	0.115637i
$699$	5.61921e12	+	9.73276e12i	0.890283	+	1.54202i
$700$	−1.63659e12	−	2.83466e12i	−0.257632	−	0.446231i
$701$	5.59514e12	−	9.69107e12i	0.875145	−	1.51580i	0.0185375	−	0.999828i	$-0.494099\pi$
$701$	5.59514e12	−	9.69107e12i	0.875145	−	1.51580i	0.856608	−	0.515968i	$-0.172568\pi$
$702$	−6.22248e11			−0.0967044
$703$	8.35941e12	+	3.70927e12i	1.29085	+	0.572782i
$704$	−1.68424e12			−0.258421
$705$	8.05347e11	−	1.39490e12i	0.122781	−	0.212663i
$706$	5.70153e11	+	9.87534e11i	0.0863715	+	0.149600i
$707$	−1.20430e12	−	2.08591e12i	−0.181279	−	0.313985i
$708$	−2.91136e12	−	5.04262e12i	−0.435457	−	0.754234i
$709$	4.43413e12			0.659023			0.329511	−	0.944152i	$-0.393116\pi$
$709$	4.43413e12			0.659023			0.329511	+	0.944152i	$0.393116\pi$
$710$	−2.29855e12	−	3.98121e12i	−0.339463	−	0.587966i
$711$	−1.01315e13			−1.48683
$712$	−3.97443e12	+	6.88391e12i	−0.579582	+	1.00387i
$713$	6.47013e12			0.937584
$714$	3.93121e12			0.566088
$715$	5.95935e12	−	1.03219e13i	0.852750	−	1.47701i
$716$	3.60462e11	+	6.24338e11i	0.0512567	+	0.0887792i
$717$	1.10570e13			1.56243
$718$	−5.48606e11	+	9.50213e11i	−0.0770372	+	0.133432i
$719$	3.14519e12	−	5.44763e12i	0.438901	−	0.760199i	−0.558704	−	0.829367i	$-0.688701\pi$
$719$	3.14519e12	−	5.44763e12i	0.438901	−	0.760199i	0.997605	+	0.0691682i	$0.0220345\pi$
$720$	2.63812e12	−	4.56935e12i	0.365845	−	0.633663i
$721$	4.38384e12	+	7.59304e12i	0.604152	+	1.04642i
$722$	1.26957e12	+	2.19897e12i	0.173876	+	0.301163i
$723$	−5.74407e12	+	9.94903e12i	−0.781804	+	1.35412i
$724$	4.33298e12	−	7.50494e12i	0.586088	−	1.01513i
$725$	5.54344e11	−	9.60152e11i	0.0745175	−	0.129068i
$726$	−1.50741e12			−0.201379
$727$	−1.46020e12	−	2.52915e12i	−0.193869	−	0.335791i	0.752660	−	0.658409i	$-0.228770\pi$
$727$	−1.46020e12	−	2.52915e12i	−0.193869	−	0.335791i	−0.946529	+	0.322618i	$0.895437\pi$
$728$	4.09026e12	−	7.08453e12i	0.539709	−	0.934803i
$729$	−5.78644e12			−0.758818
$730$	−4.61437e12			−0.601395
$731$	−3.69144e12	+	6.39375e12i	−0.478153	+	0.828186i
$732$	7.41382e12			0.954425
$733$	2.00768e12	+	3.47740e12i	0.256878	+	0.444925i	0.965404	−	0.260759i	$-0.0839729\pi$
$733$	2.00768e12	+	3.47740e12i	0.256878	+	0.444925i	−0.708526	+	0.705685i	$0.750640\pi$
$734$	−2.31647e12			−0.294575
$735$	8.49423e11	+	1.47124e12i	0.107357	+	0.185948i
$736$	3.14089e12	+	5.44018e12i	0.394550	+	0.683381i
$737$	4.50131e11	+	7.79650e11i	0.0561999	+	0.0973410i
$738$	1.50712e12	−	2.61040e12i	0.187022	−	0.323932i
$739$	1.22695e13			1.51331			0.756656	−	0.653814i	$-0.226832\pi$
$739$	1.22695e13			1.51331			0.756656	+	0.653814i	$0.226832\pi$
$740$	−9.65926e11	−	9.08036e12i	−0.118413	−	1.11317i
$741$	−2.79266e13			−3.40280
$742$	5.17769e11	−	8.96803e11i	0.0627074	−	0.108612i
$743$	−7.61984e12	−	1.31980e13i	−0.917268	−	1.58876i	−0.803546	−	0.595243i	$-0.797056\pi$
$743$	−7.61984e12	−	1.31980e13i	−0.917268	−	1.58876i	−0.113722	−	0.993513i	$-0.536277\pi$
$744$	3.95422e12	+	6.84891e12i	0.473133	+	0.819490i
$745$	−4.66172e12	−	8.07434e12i	−0.554425	−	0.960293i
$746$	−9.70430e11			−0.114720
$747$	−4.17958e12	−	7.23924e12i	−0.491122	−	0.850649i
$748$	7.20662e12			0.841733
$749$	−1.77466e12	+	3.07380e12i	−0.206038	+	0.356868i
$750$	1.98083e12			0.228597
$751$	−2.82024e12			−0.323524			−0.161762	−	0.986830i	$-0.551718\pi$
$751$	−2.82024e12			−0.323524			−0.161762	+	0.986830i	$0.551718\pi$
$752$	3.98454e11	−	6.90143e11i	0.0454358	−	0.0786971i
$753$	−4.39833e12	−	7.61813e12i	−0.498552	−	0.863518i
$754$	1.29521e12			0.145938
$755$	−4.88875e12	+	8.46756e12i	−0.547566	+	0.948411i
$756$	−5.81753e11	+	1.00763e12i	−0.0647725	+	0.112189i
$757$	−1.44951e12	+	2.51062e12i	−0.160431	+	0.277875i	−0.935023	−	0.354586i	$-0.884622\pi$
$757$	−1.44951e12	+	2.51062e12i	−0.160431	+	0.277875i	0.774592	+	0.632461i	$0.217955\pi$
$758$	3.85010e11	+	6.66857e11i	0.0423604	+	0.0733704i
$759$	4.27277e12	+	7.40065e12i	0.467327	+	0.809435i
$760$	5.43924e12	−	9.42104e12i	0.591394	−	1.02432i
$761$	−3.44713e12	+	5.97060e12i	−0.372586	+	0.645338i	−0.989963	−	0.141330i	$-0.954862\pi$
$761$	−3.44713e12	+	5.97060e12i	−0.372586	+	0.645338i	0.617377	+	0.786668i	$0.288196\pi$
$762$	−2.52689e11	+	4.37670e11i	−0.0271512	+	0.0470273i
$763$	1.62342e13			1.73408
$764$	−7.82346e12	−	1.35506e13i	−0.830766	−	1.43893i
$765$	−6.73057e12	+	1.16577e13i	−0.710519	+	1.23065i
$766$	−6.62766e11			−0.0695554
$767$	1.21556e13			1.26823
$768$	−7.43982e10	+	1.28862e11i	−0.00771680	+	0.0133659i
$769$	1.90360e13			1.96294			0.981472	−	0.191604i	$-0.0613690\pi$
$769$	1.90360e13			1.96294			0.981472	+	0.191604i	$0.0613690\pi$
$770$	1.55273e12	+	2.68941e12i	0.159180	+	0.275707i
$771$	7.27162e12			0.741117
$772$	−2.96405e12	−	5.13388e12i	−0.300336	−	0.520197i
$773$	4.83637e12	+	8.37684e12i	0.487205	+	0.843864i	0.999892	−	0.0147120i	$-0.00468315\pi$
$773$	4.83637e12	+	8.37684e12i	0.487205	+	0.843864i	−0.512687	+	0.858576i	$0.671350\pi$
$774$	−1.17434e12	−	2.03402e12i	−0.117614	−	0.203714i
$775$	−3.30295e12	+	5.72087e12i	−0.328885	+	0.569645i
$776$	−4.40826e12			−0.436405
$777$	−1.38220e12	−	1.29937e13i	−0.136043	−	1.27890i
$778$	5.51070e12			0.539261
$779$	−8.76873e12	+	1.51879e13i	−0.853136	+	1.47767i
$780$	1.39422e13	+	2.41486e13i	1.34867	+	2.33597i
$781$	−6.02959e12	−	1.04436e13i	−0.579907	−	1.00443i
$782$	−2.05603e12	−	3.56115e12i	−0.196607	−	0.340533i
$783$	−3.94101e11			−0.0374697
$784$	4.20261e11	+	7.27914e11i	0.0397280	+	0.0688110i
$785$	−1.13730e13			−1.06896
$786$	6.66058e11	−	1.15365e12i	0.0622458	−	0.107813i
$787$	−1.25274e13			−1.16405			−0.582027	−	0.813169i	$-0.697740\pi$
$787$	−1.25274e13			−1.16405			−0.582027	+	0.813169i	$0.697740\pi$
$788$	−1.18294e13			−1.09294
$789$	1.56370e12	−	2.70841e12i	0.143651	−	0.248810i
$790$	4.10081e12	+	7.10282e12i	0.374583	+	0.648797i
$791$	7.39374e12			0.671537
$792$	−2.45234e12	+	4.24758e12i	−0.221471	+	0.383600i
$793$	−7.73860e12	+	1.34036e13i	−0.694917	+	1.20363i
$794$	1.42601e12	−	2.46993e12i	0.127330	−	0.220542i
$795$	3.77570e12	+	6.53971e12i	0.335232	+	0.580639i
$796$	4.18623e12	+	7.25077e12i	0.369585	+	0.640140i
$797$	4.54919e12	−	7.87943e12i	0.399367	−	0.691723i	−0.594281	−	0.804257i	$-0.702563\pi$
$797$	4.54919e12	−	7.87943e12i	0.399367	−	0.691723i	0.993648	+	0.112534i	$0.0358967\pi$
$798$	3.63819e12	−	6.30153e12i	0.317594	−	0.550089i
$799$	−1.01657e12	+	1.76075e12i	−0.0882421	+	0.152840i
$800$	−6.41358e12			−0.553600
$801$	−9.10286e12	−	1.57666e13i	−0.781324	−	1.35329i
$802$	1.43890e12	−	2.49225e12i	0.122814	−	0.212719i
$803$	−1.21045e13			−1.02737
$804$	−2.10621e12			−0.177766
$805$	−6.35817e12	+	1.10127e13i	−0.533642	+	0.924296i
$806$	−7.71722e12			−0.644099
$807$	−1.26570e13	−	2.19226e13i	−1.05051	−	1.81954i
$808$	−3.07947e12			−0.254170
$809$	9.86819e12	+	1.70922e13i	0.809971	+	1.40291i	0.912884	+	0.408220i	$0.133850\pi$
$809$	9.86819e12	+	1.70922e13i	0.809971	+	1.40291i	−0.102913	+	0.994690i	$0.532816\pi$
$810$	3.00989e12	+	5.21328e12i	0.245679	+	0.425528i
$811$	−1.25455e12	−	2.17295e12i	−0.101835	−	0.176383i	0.810606	−	0.585592i	$-0.199138\pi$
$811$	−1.25455e12	−	2.17295e12i	−0.101835	−	0.176383i	−0.912441	+	0.409209i	$0.865805\pi$
$812$	1.21092e12	−	2.09737e12i	0.0977490	−	0.169306i
$813$	1.18622e13			0.952265
$814$	3.53077e11	+	3.31916e12i	0.0281877	+	0.264983i
$815$	1.63454e11			0.0129773
$816$	−7.09175e12	+	1.22833e13i	−0.559948	+	0.969858i
$817$	6.83257e12	+	1.18344e13i	0.536519	+	0.929278i
$818$	−2.14413e12	−	3.71375e12i	−0.167441	−	0.290016i
$819$	9.36814e12	+	1.62261e13i	0.727572	+	1.26019i
$820$	1.75110e13			1.35253
$821$	−1.11904e13	−	1.93823e13i	−0.859607	−	1.48888i	−0.872305	−	0.488963i	$-0.837375\pi$
$821$	−1.11904e13	−	1.93823e13i	−0.859607	−	1.48888i	0.0126981	−	0.999919i	$-0.495958\pi$
$822$	3.50984e12			0.268141
$823$	1.05403e13	−	1.82564e13i	0.800857	−	1.38713i	−0.118195	−	0.992990i	$-0.537711\pi$
$823$	1.05403e13	−	1.82564e13i	0.800857	−	1.38713i	0.919053	−	0.394135i	$-0.128956\pi$
$824$	1.12097e13			0.847078
$825$	−8.72484e12			−0.655714
$826$	−1.58359e12	+	2.74286e12i	−0.118368	+	0.205019i
$827$	5.18073e12	+	8.97329e12i	0.385138	+	0.667079i	0.991788	−	0.127890i	$-0.0408205\pi$
$827$	5.18073e12	+	8.97329e12i	0.385138	+	0.667079i	−0.606650	+	0.794969i	$0.707487\pi$
$828$	−9.38784e12			−0.694112
$829$	6.71986e11	−	1.16391e12i	0.0494157	−	0.0855905i	−0.840260	−	0.542184i	$-0.817597\pi$
$829$	6.71986e11	−	1.16391e12i	0.0494157	−	0.0855905i	0.889675	+	0.456594i	$0.150931\pi$
$830$	−3.38344e12	+	5.86028e12i	−0.247461	+	0.428615i
$831$	−1.68908e13	+	2.92558e13i	−1.22870	+	2.12818i
$832$	4.11299e12	+	7.12390e12i	0.297579	+	0.515422i
$833$	−1.07220e12	−	1.85711e12i	−0.0771569	−	0.133640i
$834$	−2.21862e12	+	3.84276e12i	−0.158795	+	0.275040i
$835$	3.54876e12	−	6.14662e12i	0.252631	−	0.437570i
$836$	6.66946e12	−	1.15518e13i	0.472240	−	0.817943i
$837$	2.34817e12			0.165373
$838$	−2.44859e12	−	4.24108e12i	−0.171521	−	0.297083i
$839$	7.88763e12	−	1.36618e13i	0.549564	−	0.951872i	−0.448741	−	0.893662i	$-0.648127\pi$
$839$	7.88763e12	−	1.36618e13i	0.549564	−	0.951872i	0.998304	−	0.0582100i	$-0.0185393\pi$
$840$	−1.55432e13			−1.07717
$841$	−1.36868e13			−0.943454
$842$	−2.16734e12	+	3.75394e12i	−0.148601	+	0.257385i
$843$	3.11245e13			2.12265
$844$	8.02720e12	+	1.39035e13i	0.544532	+	0.943156i
$845$	−3.93096e13			−2.65243
$846$	−3.23396e11	−	5.60139e11i	−0.0217054	−	0.0375949i
$847$	−2.94209e12	−	5.09585e12i	−0.196418	−	0.340206i
$848$	1.86807e12	+	3.23559e12i	0.124054	+	0.214868i
$849$	−4.30098e12	+	7.44952e12i	−0.284108	+	0.492089i
$850$	4.19834e12			0.275862
$851$	−1.10476e13	+	8.04779e12i	−0.722079	+	0.526009i
$852$	2.82131e13			1.83431
$853$	2.65362e12	−	4.59620e12i	0.171620	−	0.297254i	−0.767366	−	0.641209i	$-0.778433\pi$
$853$	2.65362e12	−	4.59620e12i	0.171620	−	0.297254i	0.938986	+	0.343954i	$0.111767\pi$
$854$	−2.01632e12	−	3.49237e12i	−0.129718	−	0.224678i
$855$	1.24578e13	+	2.15775e13i	0.797248	+	1.38087i
$856$	2.26895e12	+	3.92994e12i	0.144442	+	0.250181i
$857$	−5.17714e12			−0.327851			−0.163925	−	0.986473i	$-0.552416\pi$
$857$	−5.17714e12			−0.327851			−0.163925	+	0.986473i	$0.552416\pi$
$858$	−5.09632e12	−	8.82708e12i	−0.321043	−	0.556064i
$859$	−6.88316e12			−0.431339			−0.215669	−	0.976466i	$-0.569193\pi$
$859$	−6.88316e12			−0.431339			−0.215669	+	0.976466i	$0.569193\pi$
$860$	6.82225e12	−	1.18165e13i	0.425290	−	0.736623i
$861$	2.50575e13			1.55390
$862$	8.03168e12			0.495477
$863$	4.32546e12	−	7.49192e12i	0.265451	−	0.459774i	−0.702231	−	0.711949i	$-0.747813\pi$
$863$	4.32546e12	−	7.49192e12i	0.265451	−	0.459774i	0.967682	+	0.252175i	$0.0811459\pi$
$864$	1.13991e12	+	1.97438e12i	0.0695917	+	0.120536i
$865$	−2.40862e12			−0.146284
$866$	2.45201e12	−	4.24701e12i	0.148147	−	0.256598i
$867$	6.67111e12	−	1.15547e13i	0.400970	−	0.694501i
$868$	−7.21500e12	+	1.24967e13i	−0.431417	+	0.747237i
$869$	1.07573e13	+	1.86322e13i	0.639903	+	1.10835i
$870$	−1.23046e12	−	2.13122e12i	−0.0728167	−	0.126122i
$871$	2.19848e12	−	3.80787e12i	0.129432	−	0.224182i
$872$	1.03779e13	−	1.79751e13i	0.607837	−	1.05280i
$873$	5.04825e12	−	8.74382e12i	0.294155	−	0.509492i
$874$	−7.61111e12			−0.441211
$875$	3.86610e12	+	6.69628e12i	0.222965	+	0.386187i
$876$	1.41595e13	−	2.45250e13i	0.812420	−	1.40715i
$877$	−3.35122e13			−1.91295			−0.956477	−	0.291808i	$-0.905743\pi$
$877$	−3.35122e13			−1.91295			−0.956477	+	0.291808i	$0.905743\pi$
$878$	−1.97413e11			−0.0112112
$879$	4.38082e12	−	7.58780e12i	0.247517	−	0.428712i
$880$	−1.12043e13			−0.629812
$881$	−3.71470e12	−	6.43405e12i	−0.207746	−	0.359826i	0.743258	−	0.669004i	$-0.233279\pi$
$881$	−3.71470e12	−	6.43405e12i	−0.207746	−	0.359826i	−0.951004	+	0.309178i	$0.899946\pi$
$882$	6.82191e11			0.0379575
$883$	−1.19579e13	−	2.07116e13i	−0.661958	−	1.14655i	−0.980100	−	0.198502i	$-0.936392\pi$
$883$	−1.19579e13	−	2.07116e13i	−0.661958	−	1.14655i	0.318142	−	0.948043i	$-0.396941\pi$
$884$	−1.75989e13	−	3.04821e13i	−0.969281	−	1.67884i
$885$	−1.15479e13	−	2.00016e13i	−0.632791	−	1.09603i
$886$	−2.42854e12	+	4.20635e12i	−0.132402	+	0.229326i
$887$	−1.86483e13			−1.01154			−0.505771	−	0.862668i	$-0.668792\pi$
$887$	−1.86483e13			−1.01154			−0.505771	+	0.862668i	$0.668792\pi$
$888$	−1.52707e13	−	6.77595e12i	−0.824138	−	0.365689i
$889$	−1.97275e12			−0.105929
$890$	−7.36891e12	+	1.27633e13i	−0.393685	+	0.681882i
$891$	7.89558e12	+	1.36755e13i	0.419695	+	0.726934i
$892$	2.49778e12	+	4.32627e12i	0.132103	+	0.228808i
$893$	1.88159e12	+	3.25901e12i	0.0990133	+	0.171496i
$894$	−7.97323e12			−0.417460
$895$	1.42978e12	+	2.47645e12i	0.0744843	+	0.129011i
$896$	−1.81054e13			−0.938476
$897$	2.08685e13	−	3.61454e13i	1.07628	−	1.86418i
$898$	9.18460e12			0.471321
$899$	−4.88771e12			−0.249567
$900$	4.79241e12	−	8.30070e12i	0.243480	−	0.421719i
$901$	−4.76597e12	−	8.25490e12i	−0.240929	−	0.417302i
$902$	−6.40082e12			−0.321963
$903$	9.76238e12	−	1.69089e13i	0.488608	−	0.846295i
$904$	4.72656e12	−	8.18664e12i	0.235390	−	0.407707i
$905$	1.71868e13	−	2.97685e13i	0.851682	−	1.47516i
$906$	4.18076e12	+	7.24129e12i	0.206148	+	0.357058i
$907$	1.09338e13	+	1.89378e13i	0.536459	+	0.929174i	0.999091	+	0.0426241i	$0.0135718\pi$
$907$	1.09338e13	+	1.89378e13i	0.536459	+	0.929174i	−0.462632	+	0.886550i	$0.653095\pi$
$908$	1.08306e13	−	1.87591e13i	0.528768	−	0.915853i
$909$	3.52654e12	−	6.10815e12i	0.171321	−	0.296737i
$910$	7.58367e12	−	1.31353e13i	0.366600	−	0.634970i
$911$	2.90416e13			1.39697			0.698487	−	0.715622i	$-0.253857\pi$
$911$	2.90416e13			1.39697			0.698487	+	0.715622i	$0.253857\pi$
$912$	1.31263e13	+	2.27354e13i	0.628298	+	1.08824i
$913$	−8.87547e12	+	1.53728e13i	−0.422740	+	0.732207i
$914$	1.39665e13			0.661955
$915$	2.94070e13			1.38694
$916$	−1.48661e13	+	2.57489e13i	−0.697700	+	1.20845i
$917$	5.19993e12			0.242849
$918$	−7.46184e11	−	1.29243e12i	−0.0346780	−	0.0600640i
$919$	5.91243e12			0.273430			0.136715	−	0.990610i	$-0.456346\pi$
$919$	5.91243e12			0.273430			0.136715	+	0.990610i	$0.456346\pi$
$920$	8.12910e12	+	1.40800e13i	0.374108	+	0.647974i
$921$	−3.55632e12	−	6.15972e12i	−0.162867	−	0.282093i
$922$	−6.44111e12	−	1.11563e13i	−0.293543	−	0.508432i
$923$	−2.94490e13	+	5.10072e13i	−1.33556	+	2.31326i
$924$	−1.90587e13			−0.860139
$925$	−1.47612e12	−	1.38766e13i	−0.0662956	−	0.623224i
$926$	−1.44641e13			−0.646462
$927$	−1.28372e13	+	2.22346e13i	−0.570966	+	0.988941i
$928$	−2.37271e12	−	4.10965e12i	−0.105022	−	0.181903i
$929$	3.03573e12	+	5.25805e12i	0.133719	+	0.231608i	0.925107	−	0.379706i	$-0.123975\pi$
$929$	3.03573e12	+	5.25805e12i	0.133719	+	0.231608i	−0.791388	+	0.611314i	$0.790641\pi$
$930$	7.33145e12	+	1.26984e13i	0.321378	+	0.556643i
$931$	−3.96914e12			−0.173150
$932$	1.31088e13	+	2.27050e13i	0.569102	+	0.985713i
$933$	−4.11614e13			−1.77837
$934$	5.18347e11	−	8.97803e11i	0.0222874	−	0.0386029i
$935$	2.85852e13			1.22318
$936$	2.39549e13			1.02012
$937$	−1.64259e13	+	2.84505e13i	−0.696146	+	1.20576i	0.273646	+	0.961830i	$0.411770\pi$
$937$	−1.64259e13	+	2.84505e13i	−0.696146	+	1.20576i	−0.969793	+	0.243931i	$0.921563\pi$
$938$	5.72822e11	+	9.92156e11i	0.0241605	+	0.0418473i
$939$	2.11362e13			0.887220
$940$	1.87875e12	−	3.25409e12i	0.0784863	−	0.135942i
$941$	1.55670e13	−	2.69628e13i	0.647218	−	1.12101i	−0.336567	−	0.941660i	$-0.609266\pi$
$941$	1.55670e13	−	2.69628e13i	0.647218	−	1.12101i	0.983785	−	0.179354i	$-0.0574008\pi$
$942$	−4.86298e12	+	8.42293e12i	−0.201221	+	0.348525i
$943$	−1.31051e13	−	2.26988e13i	−0.539683	−	0.934758i
$944$	−5.71347e12	−	9.89602e12i	−0.234167	−	0.405589i
$945$	−2.30754e12	+	3.99677e12i	−0.0941251	+	0.163029i
$946$	−2.49375e12	+	4.31930e12i	−0.101238	+	0.175349i
$947$	4.22768e12	−	7.32256e12i	0.170816	−	0.295861i	−0.767890	−	0.640582i	$-0.778693\pi$
$947$	4.22768e12	−	7.32256e12i	0.170816	−	0.295861i	0.938705	+	0.344721i	$0.112026\pi$
$948$	−5.03345e13			−2.02408
$949$	2.95596e13	+	5.11988e13i	1.18304	+	2.04909i
$950$	3.88540e12	−	6.72972e12i	0.154768	−	0.268065i
$951$	3.35483e13			1.33002
$952$	1.96197e13			0.774153
$953$	−9.35687e12	+	1.62066e13i	−0.367462	+	0.636463i	−0.989168	−	0.146788i	$-0.953107\pi$
$953$	−9.35687e12	+	1.62066e13i	−0.367462	+	0.636463i	0.621706	+	0.783251i	$0.286440\pi$
$954$	3.03235e12			0.118526
$955$	−3.10319e13	−	5.37488e13i	−1.20724	−	2.09100i
$956$	2.57943e13			0.998764
$957$	−3.22776e12	−	5.59065e12i	−0.124394	−	0.215456i
$958$	5.87447e12	+	1.01749e13i	0.225333	+	0.390288i
$959$	6.85036e12	+	1.18652e13i	0.261535	+	0.452991i
$960$	7.81478e12	−	1.35356e13i	0.296959	−	0.514347i
$961$	2.68278e12			0.101468
$962$	1.31770e13	−	9.59895e12i	0.496052	−	0.361357i
$963$	−1.03934e13			−0.389440
$964$	−1.34000e13	+	2.32095e13i	−0.499757	+	0.865605i
$965$	−1.17570e13	−	2.03636e13i	−0.436437	−	0.755932i
$966$	5.43738e12	+	9.41782e12i	0.200906	+	0.347979i
$967$	−3.55100e11	−	6.15051e11i	−0.0130596	−	0.0226200i	0.859422	−	0.511267i	$-0.170824\pi$
$967$	−3.55100e11	−	6.15051e11i	−0.0130596	−	0.0226200i	−0.872481	+	0.488647i	$0.837490\pi$
$968$	−7.52310e12			−0.275396
$969$	−3.34888e13	−	5.80044e13i	−1.22023	−	2.11351i
$970$	−8.17328e12			−0.296431
$971$	1.10110e13	−	1.90716e13i	0.397504	−	0.688496i	−0.595914	−	0.803049i	$-0.703210\pi$
$971$	1.10110e13	−	1.90716e13i	0.397504	−	0.688496i	0.993417	+	0.114552i	$0.0365433\pi$
$972$	−3.30955e13			−1.18924
$973$	−1.73208e13			−0.619528
$974$	9.86942e11	−	1.70943e12i	0.0351379	−	0.0608607i
$975$	2.13064e13	+	3.69038e13i	0.755074	+	1.30783i
$976$	1.45494e13			0.513242
$977$	−2.29097e13	+	3.96807e13i	−0.804440	+	1.39333i	0.112229	+	0.993682i	$0.464201\pi$
$977$	−2.29097e13	+	3.96807e13i	−0.804440	+	1.39333i	−0.916669	+	0.399648i	$0.869132\pi$
$978$	6.98912e10	−	1.21055e11i	0.00244285	−	0.00423115i
$979$	−1.93302e13	+	3.34809e13i	−0.672535	+	1.16486i
$980$	1.98157e12	+	3.43218e12i	0.0686266	+	0.118865i
$981$	2.37692e13	+	4.11694e13i	0.819415	+	1.41927i
$982$	−3.07861e11	+	5.33231e11i	−0.0105646	+	0.0182984i
$983$	−1.48172e13	+	2.56641e13i	−0.506144	+	0.876668i	0.493830	+	0.869558i	$0.335596\pi$
$983$	−1.48172e13	+	2.56641e13i	−0.506144	+	0.876668i	−0.999975	+	0.00710960i	$0.997737\pi$
$984$	1.60184e13	−	2.77447e13i	0.544680	−	0.943413i
$985$	−4.69215e13			−1.58821
$986$	1.55318e12	+	2.69018e12i	0.0523329	+	0.0906433i
$987$	2.68842e12	−	4.65648e12i	0.0901716	−	0.156182i
$988$	−6.51484e13			−2.17519
$989$	−2.04230e13			−0.678790
$990$	−4.54684e12	+	7.87536e12i	−0.150436	+	0.260563i
$991$	5.54939e13			1.82774			0.913869	−	0.406010i	$-0.133080\pi$
$991$	5.54939e13			1.82774			0.913869	+	0.406010i	$0.133080\pi$
$992$	1.41373e13	+	2.44865e13i	0.463515	+	0.802832i
$993$	−4.25261e13			−1.38798
$994$	−7.67305e12	−	1.32901e13i	−0.249304	−	0.431807i
$995$	1.66048e13	+	2.87603e13i	0.537068	+	0.930228i
$996$	−2.07646e13	−	3.59654e13i	−0.668586	−	1.15802i
$997$	7.52968e12	−	1.30418e13i	0.241350	−	0.418031i	−0.719749	−	0.694235i	$-0.755743\pi$
$997$	7.52968e12	−	1.30418e13i	0.241350	−	0.418031i	0.961099	+	0.276203i	$0.0890763\pi$
$998$	9.06529e12			0.289264
$999$	−4.00945e12	+	2.92074e12i	−0.127362	+	0.0927787i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.10.c.a.10.16	✓	54
37.26	even	3	inner	37.10.c.a.26.16	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.10.c.a.10.16	✓	54	1.1	even	1	trivial
37.10.c.a.26.16	yes	54	37.26	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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	37.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.95661 - 6.85305i) q^{2} +(96.3161 + 166.824i) q^{3} +(224.690 + 389.175i) q^{4} +(891.239 + 1543.67i) q^{5} +1524.34 q^{6} +(2975.14 + 5153.10i) q^{7} +7607.62 q^{8} +(-8712.07 + 15089.8i) q^{9} +O(q^{10})\)	\(q+(3.95661 - 6.85305i) q^{2} +(96.3161 + 166.824i) q^{3} +(224.690 + 389.175i) q^{4} +(891.239 + 1543.67i) q^{5} +1524.34 q^{6} +(2975.14 + 5153.10i) q^{7} +7607.62 q^{8} +(-8712.07 + 15089.8i) q^{9} +14105.1 q^{10} +37000.8 q^{11} +(-43282.6 + 74967.7i) q^{12} +(-90357.4 - 156504. i) q^{13} +47085.9 q^{14} +(-171681. + 297361. i) q^{15} +(-84941.2 + 147122. i) q^{16} +(216709. - 375350. i) q^{17} +(68940.6 + 119409. i) q^{18} +(-401112. - 694746. i) q^{19} +(-400506. + 693696. i) q^{20} +(-573108. + 992653. i) q^{21} +(146398. - 253568. i) q^{22} +1.19895e6 q^{23} +(732736. + 1.26914e6i) q^{24} +(-612051. + 1.06010e6i) q^{25} -1.43004e6 q^{26} +435127. q^{27} +(-1.33697e6 + 2.31571e6i) q^{28} -905715. q^{29} +(1.35855e6 + 2.35308e6i) q^{30} +5.39652e6 q^{31} +(2.61971e6 + 4.53747e6i) q^{32} +(3.56377e6 + 6.17263e6i) q^{33} +(-1.71486e6 - 2.97023e6i) q^{34} +(-5.30313e6 + 9.18529e6i) q^{35} -7.83008e6 q^{36} +(-9.21443e6 + 6.71238e6i) q^{37} -6.34817e6 q^{38} +(1.74057e7 - 3.01476e7i) q^{39} +(6.78021e6 + 1.17437e7i) q^{40} +(-1.09305e7 - 1.89323e7i) q^{41} +(4.53513e6 + 7.85508e6i) q^{42} -1.70341e7 q^{43} +(8.31372e6 + 1.43998e7i) q^{44} -3.10582e7 q^{45} +(4.74376e6 - 8.21644e6i) q^{46} -4.69094e6 q^{47} -3.27248e7 q^{48} +(2.47384e6 - 4.28481e6i) q^{49} +(4.84330e6 + 8.38883e6i) q^{50} +8.34901e7 q^{51} +(4.06049e7 - 7.03298e7i) q^{52} +(1.09963e7 - 1.90461e7i) q^{53} +(1.72163e6 - 2.98195e6i) q^{54} +(3.29765e7 + 5.71170e7i) q^{55} +(2.26338e7 + 3.92028e7i) q^{56} +(7.72670e7 - 1.33830e8i) q^{57} +(-3.58356e6 + 6.20691e6i) q^{58} +(-3.36319e7 + 5.82522e7i) q^{59} -1.54301e8 q^{60} +(-4.28221e7 - 7.41701e7i) q^{61} +(2.13519e7 - 3.69826e7i) q^{62} -1.03679e8 q^{63} -4.55191e7 q^{64} +(1.61060e8 - 2.78964e8i) q^{65} +5.64018e7 q^{66} +(1.21654e7 + 2.10712e7i) q^{67} +1.94769e8 q^{68} +(1.15478e8 + 2.00013e8i) q^{69} +(4.19648e7 + 7.26852e7i) q^{70} +(-1.62959e8 - 2.82252e8i) q^{71} +(-6.62781e7 + 1.14797e8i) q^{72} -3.27141e8 q^{73} +(9.54241e6 + 8.97052e7i) q^{74} -2.35801e8 q^{75} +(1.80252e8 - 3.12205e8i) q^{76} +(1.10083e8 + 1.90669e8i) q^{77} +(-1.37735e8 - 2.38565e8i) q^{78} +(2.90732e8 + 5.03562e8i) q^{79} -3.02811e8 q^{80} +(2.13390e8 + 3.69601e8i) q^{81} -1.72992e8 q^{82} +(-2.39873e8 + 4.15472e8i) q^{83} -5.15088e8 q^{84} +7.72557e8 q^{85} +(-6.73972e7 + 1.16735e8i) q^{86} +(-8.72350e7 - 1.51095e8i) q^{87} +2.81488e8 q^{88} +(-5.22428e8 + 9.04871e8i) q^{89} +(-1.22885e8 + 2.12843e8i) q^{90} +(5.37653e8 - 9.31242e8i) q^{91} +(2.69392e8 + 4.66600e8i) q^{92} +(5.19771e8 + 9.00271e8i) q^{93} +(-1.85602e7 + 3.21473e7i) q^{94} +(7.14972e8 - 1.23837e9i) q^{95} +(-5.04640e8 + 8.74062e8i) q^{96} -5.79454e8 q^{97} +(-1.95760e7 - 3.39067e7i) q^{98} +(-3.22354e8 + 5.58333e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 32 q^{2} + 73 q^{3} - 6486 q^{4} + 2729 q^{5} + 1020 q^{6} + 4231 q^{7} - 7848 q^{8} - 140840 q^{9}+O(q^{10}) \) 54 * q + 32 * q^2 + 73 * q^3 - 6486 * q^4 + 2729 * q^5 + 1020 * q^6 + 4231 * q^7 - 7848 * q^8 - 140840 * q^9	\( 54 q + 32 q^{2} + 73 q^{3} - 6486 q^{4} + 2729 q^{5} + 1020 q^{6} + 4231 q^{7} - 7848 q^{8} - 140840 q^{9} - 82404 q^{10} - 108196 q^{11} + 45492 q^{12} - 29827 q^{13} - 504992 q^{14} + 87135 q^{15} - 1561814 q^{16} + 116991 q^{17} + 1767678 q^{18} - 599677 q^{19} + 4122556 q^{20} - 221017 q^{21} - 257914 q^{22} + 1752736 q^{23} + 1149408 q^{24} - 6037260 q^{25} - 16731604 q^{26} - 1916582 q^{27} + 1917318 q^{28} - 11336100 q^{29} - 20390006 q^{30} + 14447580 q^{31} - 873740 q^{32} - 4494200 q^{33} + 13736524 q^{34} - 8546699 q^{35} + 61692836 q^{36} - 1919410 q^{37} - 85447920 q^{38} - 14035313 q^{39} + 3210182 q^{40} + 28676571 q^{41} - 101904850 q^{42} + 56602028 q^{43} + 153011074 q^{44} + 104234980 q^{45} + 99535572 q^{46} - 147509100 q^{47} - 203670880 q^{48} - 201857540 q^{49} - 91421384 q^{50} + 328228338 q^{51} - 69374156 q^{52} + 59137361 q^{53} + 201615042 q^{54} - 219079762 q^{55} + 202573590 q^{56} - 5989161 q^{57} - 157098688 q^{58} + 137993791 q^{59} + 413427232 q^{60} - 244884419 q^{61} + 109345558 q^{62} - 995908592 q^{63} + 184008092 q^{64} + 248745395 q^{65} + 1965122248 q^{66} - 130143913 q^{67} + 667610796 q^{68} + 246927272 q^{69} - 291173360 q^{70} + 473387559 q^{71} + 366188748 q^{72} + 923638972 q^{73} - 885443390 q^{74} - 2185997392 q^{75} - 337459826 q^{76} - 586609928 q^{77} - 261025842 q^{78} + 563110723 q^{79} - 4210381784 q^{80} + 713813329 q^{81} + 3458576264 q^{82} - 663594441 q^{83} - 2635249016 q^{84} - 1417287750 q^{85} - 2269028474 q^{86} + 314944482 q^{87} - 7714172 q^{88} + 655027619 q^{89} + 588021376 q^{90} - 1833870961 q^{91} - 2384055268 q^{92} - 90092600 q^{93} - 1449940302 q^{94} + 2787158841 q^{95} + 2383567424 q^{96} - 2751583248 q^{97} + 4970876154 q^{98} + 2668760954 q^{99}+O(q^{100}) \) 54 * q + 32 * q^2 + 73 * q^3 - 6486 * q^4 + 2729 * q^5 + 1020 * q^6 + 4231 * q^7 - 7848 * q^8 - 140840 * q^9 - 82404 * q^10 - 108196 * q^11 + 45492 * q^12 - 29827 * q^13 - 504992 * q^14 + 87135 * q^15 - 1561814 * q^16 + 116991 * q^17 + 1767678 * q^18 - 599677 * q^19 + 4122556 * q^20 - 221017 * q^21 - 257914 * q^22 + 1752736 * q^23 + 1149408 * q^24 - 6037260 * q^25 - 16731604 * q^26 - 1916582 * q^27 + 1917318 * q^28 - 11336100 * q^29 - 20390006 * q^30 + 14447580 * q^31 - 873740 * q^32 - 4494200 * q^33 + 13736524 * q^34 - 8546699 * q^35 + 61692836 * q^36 - 1919410 * q^37 - 85447920 * q^38 - 14035313 * q^39 + 3210182 * q^40 + 28676571 * q^41 - 101904850 * q^42 + 56602028 * q^43 + 153011074 * q^44 + 104234980 * q^45 + 99535572 * q^46 - 147509100 * q^47 - 203670880 * q^48 - 201857540 * q^49 - 91421384 * q^50 + 328228338 * q^51 - 69374156 * q^52 + 59137361 * q^53 + 201615042 * q^54 - 219079762 * q^55 + 202573590 * q^56 - 5989161 * q^57 - 157098688 * q^58 + 137993791 * q^59 + 413427232 * q^60 - 244884419 * q^61 + 109345558 * q^62 - 995908592 * q^63 + 184008092 * q^64 + 248745395 * q^65 + 1965122248 * q^66 - 130143913 * q^67 + 667610796 * q^68 + 246927272 * q^69 - 291173360 * q^70 + 473387559 * q^71 + 366188748 * q^72 + 923638972 * q^73 - 885443390 * q^74 - 2185997392 * q^75 - 337459826 * q^76 - 586609928 * q^77 - 261025842 * q^78 + 563110723 * q^79 - 4210381784 * q^80 + 713813329 * q^81 + 3458576264 * q^82 - 663594441 * q^83 - 2635249016 * q^84 - 1417287750 * q^85 - 2269028474 * q^86 + 314944482 * q^87 - 7714172 * q^88 + 655027619 * q^89 + 588021376 * q^90 - 1833870961 * q^91 - 2384055268 * q^92 - 90092600 * q^93 - 1449940302 * q^94 + 2787158841 * q^95 + 2383567424 * q^96 - 2751583248 * q^97 + 4970876154 * q^98 + 2668760954 * q^99

Introduction

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