LMFDB - Embedded newform 91.8.e.b.53.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,8,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, 8, names="a")

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

chi := DirichletCharacter("91.53");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
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:	$28.4270373191$
Analytic rank:	$0$
Dimension:	$58$
Relative dimension:	$29$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			53.9
Character	$\chi$	$=$	91.53
Dual form			91.8.e.b.79.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.25043 - 10.8261i) q^{2} +(2.85376 - 4.94285i) q^{3} +(-14.1357 + 24.4837i) q^{4} +(-229.621 - 397.716i) q^{5} -71.3488 q^{6} +(873.653 + 245.508i) q^{7} -1246.69 q^{8} +(1077.21 + 1865.79i) q^{9} +O(q^{10})$	\(q+(-6.25043 - 10.8261i) q^{2} +(2.85376 - 4.94285i) q^{3} +(-14.1357 + 24.4837i) q^{4} +(-229.621 - 397.716i) q^{5} -71.3488 q^{6} +(873.653 + 245.508i) q^{7} -1246.69 q^{8} +(1077.21 + 1865.79i) q^{9} +(-2870.46 + 4971.78i) q^{10} +(-1443.53 + 2500.26i) q^{11} +(80.6796 + 139.741i) q^{12} -2197.00 q^{13} +(-2802.82 - 10992.7i) q^{14} -2621.13 q^{15} +(9601.73 + 16630.7i) q^{16} +(-12678.5 + 21959.9i) q^{17} +(13466.1 - 23323.9i) q^{18} +(-25887.7 - 44838.8i) q^{19} +12983.4 q^{20} +(3706.70 - 3617.71i) q^{21} +36090.6 q^{22} +(54033.4 + 93588.5i) q^{23} +(-3557.76 + 6162.22i) q^{24} +(-66389.3 + 114990. i) q^{25} +(13732.2 + 23784.8i) q^{26} +24778.7 q^{27} +(-18360.6 + 17919.8i) q^{28} -132430. q^{29} +(16383.2 + 28376.5i) q^{30} +(-13657.7 + 23655.9i) q^{31} +(40241.5 - 69700.3i) q^{32} +(8238.95 + 14270.3i) q^{33} +316985. q^{34} +(-102967. - 403839. i) q^{35} -60908.5 q^{36} +(93989.7 + 162795. i) q^{37} +(-323619. + 560524. i) q^{38} +(-6269.70 + 10859.4i) q^{39} +(286267. + 495829. i) q^{40} +80065.0 q^{41} +(-62334.1 - 17516.7i) q^{42} +1.03787e6 q^{43} +(-40810.5 - 70685.9i) q^{44} +(494701. - 856848. i) q^{45} +(675463. - 1.16994e6i) q^{46} +(-359358. - 622427. i) q^{47} +109604. q^{48} +(702995. + 428977. i) q^{49} +1.65985e6 q^{50} +(72363.0 + 125336. i) q^{51} +(31056.1 - 53790.7i) q^{52} +(104730. - 181398. i) q^{53} +(-154878. - 268256. i) q^{54} +1.32586e6 q^{55} +(-1.08918e6 - 306073. i) q^{56} -295509. q^{57} +(827745. + 1.43370e6i) q^{58} +(-722809. + 1.25194e6i) q^{59} +(37051.5 - 64175.1i) q^{60} +(-923534. - 1.59961e6i) q^{61} +341467. q^{62} +(483044. + 1.89451e6i) q^{63} +1.45194e6 q^{64} +(504478. + 873781. i) q^{65} +(102994. - 178391. i) q^{66} +(525579. - 910330. i) q^{67} +(-358440. - 620836. i) q^{68} +616792. q^{69} +(-3.72840e6 + 3.63889e6i) q^{70} -989653. q^{71} +(-1.34295e6 - 2.32606e6i) q^{72} +(-2.02831e6 + 3.51313e6i) q^{73} +(1.17495e6 - 2.03508e6i) q^{74} +(378918. + 656305. i) q^{75} +1.46376e6 q^{76} +(-1.87498e6 + 1.82996e6i) q^{77} +156753. q^{78} +(968043. + 1.67670e6i) q^{79} +(4.40952e6 - 7.63752e6i) q^{80} +(-2.28515e6 + 3.95800e6i) q^{81} +(-500440. - 866788. i) q^{82} -5.21053e6 q^{83} +(36178.4 + 141893. i) q^{84} +1.16451e7 q^{85} +(-6.48710e6 - 1.12360e7i) q^{86} +(-377923. + 654582. i) q^{87} +(1.79964e6 - 3.11706e6i) q^{88} +(2.14374e6 + 3.71307e6i) q^{89} -1.23684e7 q^{90} +(-1.91941e6 - 539381. i) q^{91} -3.05519e6 q^{92} +(77951.8 + 135016. i) q^{93} +(-4.49229e6 + 7.78087e6i) q^{94} +(-1.18887e7 + 2.05919e7i) q^{95} +(-229679. - 397816. i) q^{96} +4.56137e6 q^{97} +(250117. - 1.02920e7i) q^{98} -6.21994e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 58 q - 31 q^{2} - 1893 q^{4} + 48 q^{5} - 4602 q^{6} + 85 q^{7} + 11436 q^{8} - 25535 q^{9}+O(q^{10}) $ 58 * q - 31 * q^2 - 1893 * q^4 + 48 * q^5 - 4602 * q^6 + 85 * q^7 + 11436 * q^8 - 25535 * q^9	\( 58 q - 31 q^{2} - 1893 q^{4} + 48 q^{5} - 4602 q^{6} + 85 q^{7} + 11436 q^{8} - 25535 q^{9} + 3029 q^{10} - 15843 q^{11} + 10995 q^{12} - 127426 q^{13} - 65720 q^{14} + 115668 q^{15} - 154909 q^{16} + 43475 q^{17} - 67288 q^{18} + 64641 q^{19} + 40146 q^{20} - 321354 q^{21} + 170964 q^{22} - 96894 q^{23} + 501382 q^{24} - 637413 q^{25} + 68107 q^{26} + 156816 q^{27} - 877133 q^{28} + 155846 q^{29} - 335448 q^{30} + 393806 q^{31} - 1827215 q^{32} + 299052 q^{33} - 38692 q^{34} - 133704 q^{35} + 5417220 q^{36} - 597180 q^{37} - 502034 q^{38} + 1223016 q^{40} - 1436280 q^{41} - 2542432 q^{42} + 3496372 q^{43} - 2679210 q^{44} - 2509582 q^{45} + 2358719 q^{46} + 2368643 q^{47} - 843698 q^{48} + 995403 q^{49} + 3451796 q^{50} - 2396956 q^{51} + 4158921 q^{52} - 1919163 q^{53} - 4029674 q^{54} + 6075808 q^{55} + 3653181 q^{56} + 11452960 q^{57} - 4051049 q^{58} + 48733 q^{59} - 2792030 q^{60} + 1417921 q^{61} - 10244784 q^{62} + 7636291 q^{63} + 30707792 q^{64} - 105456 q^{65} - 22397813 q^{66} - 7025007 q^{67} + 5107354 q^{68} - 19729612 q^{69} - 13744304 q^{70} + 29267486 q^{71} - 7267524 q^{72} - 2417490 q^{73} + 2601511 q^{74} + 17567528 q^{75} - 19814476 q^{76} - 824982 q^{77} + 10110594 q^{78} - 7837082 q^{79} - 7428483 q^{80} - 24976533 q^{81} - 11520562 q^{82} - 38573688 q^{83} - 14286428 q^{84} + 41189436 q^{85} + 17943598 q^{86} - 37502020 q^{87} - 2949879 q^{88} + 15969588 q^{89} - 114635026 q^{90} - 186745 q^{91} + 83440638 q^{92} - 14525204 q^{93} - 30315990 q^{94} - 8678760 q^{95} + 23478593 q^{96} - 14169276 q^{97} + 14221151 q^{98} + 83443706 q^{99}+O(q^{100}) \) 58 * q - 31 * q^2 - 1893 * q^4 + 48 * q^5 - 4602 * q^6 + 85 * q^7 + 11436 * q^8 - 25535 * q^9 + 3029 * q^10 - 15843 * q^11 + 10995 * q^12 - 127426 * q^13 - 65720 * q^14 + 115668 * q^15 - 154909 * q^16 + 43475 * q^17 - 67288 * q^18 + 64641 * q^19 + 40146 * q^20 - 321354 * q^21 + 170964 * q^22 - 96894 * q^23 + 501382 * q^24 - 637413 * q^25 + 68107 * q^26 + 156816 * q^27 - 877133 * q^28 + 155846 * q^29 - 335448 * q^30 + 393806 * q^31 - 1827215 * q^32 + 299052 * q^33 - 38692 * q^34 - 133704 * q^35 + 5417220 * q^36 - 597180 * q^37 - 502034 * q^38 + 1223016 * q^40 - 1436280 * q^41 - 2542432 * q^42 + 3496372 * q^43 - 2679210 * q^44 - 2509582 * q^45 + 2358719 * q^46 + 2368643 * q^47 - 843698 * q^48 + 995403 * q^49 + 3451796 * q^50 - 2396956 * q^51 + 4158921 * q^52 - 1919163 * q^53 - 4029674 * q^54 + 6075808 * q^55 + 3653181 * q^56 + 11452960 * q^57 - 4051049 * q^58 + 48733 * q^59 - 2792030 * q^60 + 1417921 * q^61 - 10244784 * q^62 + 7636291 * q^63 + 30707792 * q^64 - 105456 * q^65 - 22397813 * q^66 - 7025007 * q^67 + 5107354 * q^68 - 19729612 * q^69 - 13744304 * q^70 + 29267486 * q^71 - 7267524 * q^72 - 2417490 * q^73 + 2601511 * q^74 + 17567528 * q^75 - 19814476 * q^76 - 824982 * q^77 + 10110594 * q^78 - 7837082 * q^79 - 7428483 * q^80 - 24976533 * q^81 - 11520562 * q^82 - 38573688 * q^83 - 14286428 * q^84 + 41189436 * q^85 + 17943598 * q^86 - 37502020 * q^87 - 2949879 * q^88 + 15969588 * q^89 - 114635026 * q^90 - 186745 * q^91 + 83440638 * q^92 - 14525204 * q^93 - 30315990 * q^94 - 8678760 * q^95 + 23478593 * q^96 - 14169276 * q^97 + 14221151 * q^98 + 83443706 * 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 $

$2$	−6.25043	−	10.8261i	−0.552465	−	0.956897i	−0.998096	−	0.0616806i	$-0.980354\pi$
$2$	−6.25043	−	10.8261i	−0.552465	−	0.956897i	0.445631	−	0.895217i	$-0.352979\pi$
$3$	2.85376	−	4.94285i	0.0610229	−	0.105695i	−0.833900	−	0.551916i	$-0.813897\pi$
$3$	2.85376	−	4.94285i	0.0610229	−	0.105695i	0.894923	+	0.446221i	$0.147230\pi$
$4$	−14.1357	+	24.4837i	−0.110435	+	0.191279i
$5$	−229.621	−	397.716i	−0.821518	−	1.42291i	−0.904552	−	0.426364i	$-0.859794\pi$
$5$	−229.621	−	397.716i	−0.821518	−	1.42291i	0.0830341	−	0.996547i	$-0.473539\pi$
$6$	−71.3488			−0.134852
$7$	873.653	+	245.508i	0.962710	+	0.270534i
$7$	873.653	+	245.508i	0.962710	+	0.270534i
$8$	−1246.69			−0.860884
$9$	1077.21	+	1865.79i	0.492552	+	0.853126i
$10$	−2870.46	+	4971.78i	−0.907719	+	1.57222i
$11$	−1443.53	+	2500.26i	−0.327002	+	0.566384i	−0.981916	−	0.189320i	$-0.939372\pi$
$11$	−1443.53	+	2500.26i	−0.327002	+	0.566384i	0.654913	+	0.755704i	$0.272705\pi$
$12$	80.6796	+	139.741i	0.0134781	+	0.0233448i
$13$	−2197.00			−0.277350
$13$	−2197.00			−0.277350
$14$	−2802.82	−	10992.7i	−0.272990	−	1.07068i
$15$	−2621.13			−0.200525
$16$	9601.73	+	16630.7i	0.586043	+	1.01506i
$17$	−12678.5	+	21959.9i	−0.625890	+	1.08407i	0.362478	+	0.931993i	$0.381931\pi$
$17$	−12678.5	+	21959.9i	−0.625890	+	1.08407i	−0.988368	+	0.152082i	$0.951402\pi$
$18$	13466.1	−	23323.9i	0.544236	−	0.942644i
$19$	−25887.7	−	44838.8i	−0.865877	−	1.49974i	−0.866174	−	0.499743i	$-0.833428\pi$
$19$	−25887.7	−	44838.8i	−0.865877	−	1.49974i	0.000296803	−	1.00000i	$-0.499906\pi$
$20$	12983.4			0.362897
$21$	3706.70	−	3617.71i	0.0873414	−	0.0852446i
$22$	36090.6			0.722629
$23$	54033.4	+	93588.5i	0.926008	+	1.60389i	0.789933	+	0.613194i	$0.210115\pi$
$23$	54033.4	+	93588.5i	0.926008	+	1.60389i	0.136075	+	0.990699i	$0.456551\pi$
$24$	−3557.76	+	6162.22i	−0.0525336	+	0.0909908i
$25$	−66389.3	+	114990.i	−0.849783	+	1.47187i
$26$	13732.2	+	23784.8i	0.153226	+	0.265396i
$27$	24778.7			0.242274
$28$	−18360.6	+	17919.8i	−0.158065	+	0.154270i
$29$	−132430.			−1.00831			−0.504155	−	0.863613i	$-0.668196\pi$
$29$	−132430.			−1.00831			−0.504155	+	0.863613i	$0.668196\pi$
$30$	16383.2	+	28376.5i	0.110783	+	0.191882i
$31$	−13657.7	+	23655.9i	−0.0823404	+	0.142618i	−0.904255	−	0.426993i	$-0.859573\pi$
$31$	−13657.7	+	23655.9i	−0.0823404	+	0.142618i	0.821914	+	0.569611i	$0.192906\pi$
$32$	40241.5	−	69700.3i	0.217095	−	0.376019i
$33$	8238.95	+	14270.3i	0.0399092	+	0.0691248i
$34$	316985.			1.38313
$35$	−102967.	−	403839.i	−0.405937	−	1.59210i
$36$	−60908.5			−0.217580
$37$	93989.7	+	162795.i	0.305052	+	0.528366i	0.977273	−	0.211985i	$-0.0679927\pi$
$37$	93989.7	+	162795.i	0.305052	+	0.528366i	−0.672221	+	0.740351i	$0.734659\pi$
$38$	−323619.	+	560524.i	−0.956733	+	1.65711i
$39$	−6269.70	+	10859.4i	−0.0169247	+	0.0293144i
$40$	286267.	+	495829.i	0.707231	+	1.22496i
$41$	80065.0			0.181426			0.0907129	−	0.995877i	$-0.471085\pi$
$41$	80065.0			0.181426			0.0907129	+	0.995877i	$0.471085\pi$
$42$	−62334.1	−	17516.7i	−0.129823	−	0.0364821i
$43$	1.03787e6			1.99068			0.995340	−	0.0964258i	$-0.0307410\pi$
$43$	1.03787e6			1.99068			0.995340	+	0.0964258i	$0.0307410\pi$
$44$	−40810.5	−	70685.9i	−0.0722250	−	0.125097i
$45$	494701.	−	856848.i	0.809281	−	1.40172i
$46$	675463.	−	1.16994e6i	1.02317	−	1.77219i
$47$	−359358.	−	622427.i	−0.504877	−	0.874472i	−0.999984	−	0.00564038i	$-0.998205\pi$
$47$	−359358.	−	622427.i	−0.504877	−	0.874472i	0.495107	−	0.868832i	$-0.335129\pi$
$48$	109604.			0.143048
$49$	702995.	+	428977.i	0.853622	+	0.520893i
$50$	1.65985e6			1.87790
$51$	72363.0	+	125336.i	0.0763872	+	0.132307i
$52$	31056.1	−	53790.7i	0.0306292	−	0.0530513i
$53$	104730.	−	181398.i	0.0966289	−	0.167366i	−0.813658	−	0.581343i	$-0.802527\pi$
$53$	104730.	−	181398.i	0.0966289	−	0.167366i	0.910287	+	0.413977i	$0.135861\pi$
$54$	−154878.	−	268256.i	−0.133848	−	0.231831i
$55$	1.32586e6			1.07455
$56$	−1.08918e6	−	306073.i	−0.828782	−	0.232899i
$57$	−295509.			−0.211353
$58$	827745.	+	1.43370e6i	0.557055	+	0.964848i
$59$	−722809.	+	1.25194e6i	−0.458186	+	0.793601i	−0.998865	−	0.0476277i	$-0.984834\pi$
$59$	−722809.	+	1.25194e6i	−0.458186	+	0.793601i	0.540679	+	0.841229i	$0.318167\pi$
$60$	37051.5	−	64175.1i	0.0221450	−	0.0383563i
$61$	−923534.	−	1.59961e6i	−0.520953	−	0.902317i	−0.999703	−	0.0243655i	$-0.992243\pi$
$61$	−923534.	−	1.59961e6i	−0.520953	−	0.902317i	0.478750	−	0.877951i	$-0.341090\pi$
$62$	341467.			0.181961
$63$	483044.	+	1.89451e6i	0.243385	+	0.954565i
$64$	1.45194e6			0.692338
$65$	504478.	+	873781.i	0.227848	+	0.394644i
$66$	102994.	−	178391.i	0.0440969	−	0.0763780i
$67$	525579.	−	910330.i	0.213489	−	0.369774i	−0.739315	−	0.673360i	$-0.764850\pi$
$67$	525579.	−	910330.i	0.213489	−	0.369774i	0.952804	+	0.303585i	$0.0981838\pi$
$68$	−358440.	−	620836.i	−0.138240	−	0.239440i
$69$	616792.			0.226030
$70$	−3.72840e6	+	3.63889e6i	−1.29921	+	1.26802i
$71$	−989653.			−0.328155			−0.164077	−	0.986447i	$-0.552465\pi$
$71$	−989653.			−0.328155			−0.164077	+	0.986447i	$0.552465\pi$
$72$	−1.34295e6	−	2.32606e6i	−0.424030	−	0.734442i
$73$	−2.02831e6	+	3.51313e6i	−0.610244	+	1.05697i	0.380955	+	0.924593i	$0.375595\pi$
$73$	−2.02831e6	+	3.51313e6i	−0.610244	+	1.05697i	−0.991199	+	0.132380i	$0.957738\pi$
$74$	1.17495e6	−	2.03508e6i	0.337061	−	0.583808i
$75$	378918.	+	656305.i	0.103712	+	0.179635i
$76$	1.46376e6			0.382493
$77$	−1.87498e6	+	1.82996e6i	−0.468035	+	0.456799i
$78$	156753.			0.0374012
$79$	968043.	+	1.67670e6i	0.220902	+	0.382614i	0.955082	−	0.296341i	$-0.0957665\pi$
$79$	968043.	+	1.67670e6i	0.220902	+	0.382614i	−0.734180	+	0.678955i	$0.762433\pi$
$80$	4.40952e6	−	7.63752e6i	0.962890	−	1.66777i
$81$	−2.28515e6	+	3.95800e6i	−0.477768	+	0.827519i
$82$	−500440.	−	866788.i	−0.100231	−	0.173606i
$83$	−5.21053e6			−1.00025			−0.500125	−	0.865953i	$-0.666713\pi$
$83$	−5.21053e6			−1.00025			−0.500125	+	0.865953i	$0.666713\pi$
$84$	36178.4	+	141893.i	0.00665996	+	0.0261206i
$85$	1.16451e7			2.05672
$86$	−6.48710e6	−	1.12360e7i	−1.09978	−	1.90488i
$87$	−377923.	+	654582.i	−0.0615299	+	0.106573i
$88$	1.79964e6	−	3.11706e6i	0.281511	−	0.487591i
$89$	2.14374e6	+	3.71307e6i	0.322335	+	0.558301i	0.980969	−	0.194162i	$-0.0621988\pi$
$89$	2.14374e6	+	3.71307e6i	0.322335	+	0.558301i	−0.658634	+	0.752463i	$0.728865\pi$
$90$	−1.23684e7			−1.78840
$91$	−1.91941e6	−	539381.i	−0.267008	−	0.0750327i
$92$	−3.05519e6			−0.409055
$93$	77951.8	+	135016.i	0.0100493	+	0.0174059i
$94$	−4.49229e6	+	7.78087e6i	−0.557853	+	0.966230i
$95$	−1.18887e7	+	2.05919e7i	−1.42267	+	2.46413i
$96$	−229679.	−	397816.i	−0.0264955	−	0.0458915i
$97$	4.56137e6			0.507451			0.253726	−	0.967276i	$-0.418344\pi$
$97$	4.56137e6			0.507451			0.253726	+	0.967276i	$0.418344\pi$
$98$	250117.	−	1.02920e7i	0.0268443	−	1.10460i
$99$	−6.21994e6			−0.644263
$100$	−1.87692e6	−	3.25091e6i	−0.187692	−	0.325091i
$101$	−6.71248e6	+	1.16264e7i	−0.648274	+	1.12284i	0.335261	+	0.942125i	$0.391175\pi$
$101$	−6.71248e6	+	1.16264e7i	−0.648274	+	1.12284i	−0.983535	+	0.180718i	$0.942158\pi$
$102$	904599.	−	1.56681e6i	0.0844025	−	0.146189i
$103$	−1.68930e6	−	2.92595e6i	−0.152327	−	0.263838i	0.779756	−	0.626084i	$-0.215343\pi$
$103$	−1.68930e6	−	2.92595e6i	−0.152327	−	0.263838i	−0.932082	+	0.362246i	$0.882010\pi$
$104$	2.73898e6			0.238766
$105$	−2.28996e6	−	643509.i	−0.193048	−	0.0542490i
$106$	−2.61844e6			−0.213536
$107$	−8.06011e6	−	1.39605e7i	−0.636059	−	1.10169i	−0.986290	−	0.165024i	$-0.947230\pi$
$107$	−8.06011e6	−	1.39605e7i	−0.636059	−	1.10169i	0.350230	−	0.936664i	$-0.386103\pi$
$108$	−350264.	+	606676.i	−0.0267555	+	0.0463419i
$109$	−3.18595e6	+	5.51822e6i	−0.235638	+	0.408138i	−0.959458	−	0.281852i	$-0.909051\pi$
$109$	−3.18595e6	+	5.51822e6i	−0.235638	+	0.408138i	0.723820	+	0.689989i	$0.242385\pi$
$110$	−8.28718e6	−	1.43538e7i	−0.593652	−	1.02824i
$111$	1.07290e6			0.0744607
$112$	4.30561e6	+	1.68867e7i	0.289582	+	1.13575i
$113$	1.46552e7			0.955473			0.477737	−	0.878503i	$-0.341457\pi$
$113$	1.46552e7			0.955473			0.477737	+	0.878503i	$0.341457\pi$
$114$	1.84706e6	+	3.19920e6i	0.116765	+	0.202243i
$115$	2.48144e7	−	4.29798e7i	1.52146	−	2.63525i
$116$	1.87199e6	−	3.24238e6i	0.111353	−	0.192868i
$117$	−2.36664e6	−	4.09913e6i	−0.136609	−	0.236615i
$118$	1.80715e7			1.01253
$119$	−1.64680e7	+	1.60726e7i	−0.895831	+	0.874324i
$120$	3.26775e6			0.172629
$121$	5.57604e6	+	9.65799e6i	0.286139	+	0.495608i
$122$	−1.15450e7	+	1.99965e7i	−0.575616	+	0.996997i
$123$	228486.	−	395749.i	0.0110711	−	0.0191757i
$124$	−386123.	−	668785.i	−0.0181865	−	0.0315000i
$125$	2.50992e7			1.14941
$126$	1.74909e7	−	1.70710e7i	0.778959	−	0.760259i
$127$	−4.28835e7			−1.85771			−0.928853	−	0.370448i	$-0.879204\pi$
$127$	−4.28835e7			−1.85771			−0.928853	+	0.370448i	$0.879204\pi$
$128$	−1.42261e7	−	2.46404e7i	−0.599587	−	1.03852i
$129$	2.96182e6	−	5.13001e6i	0.121477	−	0.210404i
$130$	6.30640e6	−	1.09230e7i	0.251756	−	0.436054i
$131$	1.16745e7	+	2.02208e7i	0.453720	+	0.785866i	0.998614	−	0.0526389i	$-0.0167632\pi$
$131$	1.16745e7	+	2.02208e7i	0.453720	+	0.785866i	−0.544893	+	0.838505i	$0.683430\pi$
$132$	−465853.			−0.0176295
$133$	−1.16086e7	−	4.55292e7i	−0.427857	−	1.67807i
$134$	−1.31404e7			−0.471782
$135$	−5.68972e6	−	9.85489e6i	−0.199032	−	0.344734i
$136$	1.58063e7	−	2.73772e7i	0.538819	−	0.933262i
$137$	−1.05404e7	+	1.82565e7i	−0.350216	+	0.606592i	−0.986287	−	0.165038i	$-0.947225\pi$
$137$	−1.05404e7	+	1.82565e7i	−0.350216	+	0.606592i	0.636071	+	0.771630i	$0.280559\pi$
$138$	−3.85521e6	−	6.67743e6i	−0.124874	−	0.216288i
$139$	−4.63774e6			−0.146472			−0.0732360	−	0.997315i	$-0.523333\pi$
$139$	−4.63774e6			−0.146472			−0.0732360	+	0.997315i	$0.523333\pi$
$140$	1.13430e7	+	3.18753e6i	0.349365	+	0.0981762i
$141$	−4.10209e6			−0.123236
$142$	6.18575e6	+	1.07140e7i	0.181294	+	0.314010i
$143$	3.17143e6	−	5.49308e6i	0.0906941	−	0.157087i
$144$	−2.06862e7	+	3.58296e7i	−0.577314	+	0.999937i
$145$	3.04088e7	+	5.26695e7i	0.828344	+	1.43473i
$146$	5.07111e7			1.34855
$147$	4.12655e6	−	2.25060e6i	0.107146	−	0.0584370i
$148$	−5.31444e6			−0.134754
$149$	−9.41646e6	−	1.63098e7i	−0.233204	−	0.403921i	0.725545	−	0.688174i	$-0.241588\pi$
$149$	−9.41646e6	−	1.63098e7i	−0.233204	−	0.403921i	−0.958749	+	0.284254i	$0.908254\pi$
$150$	4.73679e6	−	8.20437e6i	0.114595	−	0.198484i
$151$	−8.89282e6	+	1.54028e7i	−0.210194	+	0.364066i	−0.951775	−	0.306797i	$-0.900743\pi$
$151$	−8.89282e6	+	1.54028e7i	−0.210194	+	0.364066i	0.741581	+	0.670863i	$0.234076\pi$
$152$	3.22740e7	+	5.59003e7i	0.745420	+	1.29110i
$153$	−5.46299e7			−1.23314
$154$	3.15307e7	+	8.86054e6i	0.695682	+	0.195496i
$155$	1.25444e7			0.270576
$156$	−177253.	−	307011.i	−0.00373816	−	0.00647468i
$157$	−1.34184e7	+	2.32414e7i	−0.276728	+	0.479307i	−0.970570	−	0.240821i	$-0.922583\pi$
$157$	−1.34184e7	+	2.32414e7i	−0.276728	+	0.479307i	0.693842	+	0.720128i	$0.255917\pi$
$158$	1.21014e7	−	2.09602e7i	0.244081	−	0.422761i
$159$	−597750.	−	1.03533e6i	−0.0117931	−	0.0204263i
$160$	−3.69612e7			−0.713389
$161$	2.42297e7	+	9.50295e7i	0.457569	+	1.79460i
$162$	5.71327e7			1.05580
$163$	2.49419e7	+	4.32006e7i	0.451099	+	0.781327i	0.998455	−	0.0555734i	$-0.0176987\pi$
$163$	2.49419e7	+	4.32006e7i	0.451099	+	0.781327i	−0.547355	+	0.836900i	$0.684365\pi$
$164$	−1.13177e6	+	1.96029e6i	−0.0200358	+	0.0347030i
$165$	3.78367e6	−	6.55352e6i	0.0655722	−	0.113574i
$166$	3.25681e7	+	5.64095e7i	0.552603	+	0.957137i
$167$	−2.03218e7			−0.337640			−0.168820	−	0.985647i	$-0.553996\pi$
$167$	−2.03218e7			−0.337640			−0.168820	+	0.985647i	$0.553996\pi$
$168$	−4.62112e6	+	4.51018e6i	−0.0751908	+	0.0733857i
$169$	4.82681e6			0.0769231
$170$	−7.27866e7	−	1.26070e8i	−1.13627	−	1.96807i
$171$	5.57731e7	−	9.66019e7i	0.852980	−	1.47740i
$172$	−1.46709e7	+	2.54108e7i	−0.219841	+	0.380776i
$173$	5.74778e6	+	9.95545e6i	0.0843993	+	0.146184i	0.905135	−	0.425124i	$-0.139770\pi$
$173$	5.74778e6	+	9.95545e6i	0.0843993	+	0.146184i	−0.820736	+	0.571308i	$0.806436\pi$
$174$	9.44873e6			0.135972
$175$	−8.62320e7	+	8.41619e7i	−1.21629	+	1.18709i
$176$	−5.54414e7			−0.766550
$177$	4.12544e6	+	7.14548e6i	0.0559196	+	0.0968556i
$178$	2.67986e7	−	4.64166e7i	0.356158	−	0.616884i
$179$	−4.61959e7	+	8.00137e7i	−0.602030	+	1.04275i	0.390483	+	0.920610i	$0.372308\pi$
$179$	−4.61959e7	+	8.00137e7i	−0.602030	+	1.04275i	−0.992513	+	0.122136i	$0.961025\pi$
$180$	1.39859e7	+	2.42243e7i	0.178746	+	0.309597i
$181$	1.32179e8			1.65686			0.828431	−	0.560091i	$-0.189234\pi$
$181$	1.32179e8			1.65686			0.828431	+	0.560091i	$0.189234\pi$
$182$	6.15779e6	+	2.41511e7i	0.0757138	+	0.296952i
$183$	−1.05422e7			−0.127160
$184$	−6.73630e7	−	1.16676e8i	−0.797185	−	1.38077i
$185$	4.31641e7	−	7.47624e7i	0.501212	−	0.868124i
$186$	974464.	−	1.68782e6i	0.0111038	−	0.0192323i
$187$	−3.66037e7	−	6.33994e7i	−0.409335	−	0.708989i
$188$	2.03191e7			0.223024
$189$	2.16480e7	+	6.08338e6i	0.233239	+	0.0655433i
$190$	2.97239e8			3.14389
$191$	−2.85660e7	−	4.94777e7i	−0.296642	−	0.513798i	0.678724	−	0.734394i	$-0.262533\pi$
$191$	−2.85660e7	−	4.94777e7i	−0.296642	−	0.513798i	−0.975365	+	0.220595i	$0.929200\pi$
$192$	4.14347e6	−	7.17671e6i	0.0422484	−	0.0731764i
$193$	−5.54284e7	+	9.60049e7i	−0.554986	+	0.961264i	0.442919	+	0.896562i	$0.353943\pi$
$193$	−5.54284e7	+	9.60049e7i	−0.554986	+	0.961264i	−0.997905	+	0.0647022i	$0.979390\pi$
$194$	−2.85105e7	−	4.93817e7i	−0.280349	−	0.485579i
$195$	5.75863e6			0.0556157
$196$	−2.04403e7	+	1.11480e7i	−0.193906	+	0.105755i
$197$	4.01917e7			0.374546			0.187273	−	0.982308i	$-0.440035\pi$
$197$	4.01917e7			0.374546			0.187273	+	0.982308i	$0.440035\pi$
$198$	3.88773e7	+	6.73374e7i	0.355933	+	0.616493i
$199$	2.52172e6	−	4.36774e6i	0.0226835	−	0.0392890i	−0.854461	−	0.519516i	$-0.826112\pi$
$199$	2.52172e6	−	4.36774e6i	0.0226835	−	0.0392890i	0.877144	+	0.480227i	$0.159446\pi$
$200$	8.27671e7	−	1.43357e8i	0.731564	−	1.26711i
$201$	−2.99975e6	−	5.19572e6i	−0.0260555	−	0.0451294i
$202$	1.67824e8			1.43259
$203$	−1.15698e8	−	3.25126e7i	−0.970710	−	0.272782i
$204$	−4.09160e6			−0.0337433
$205$	−1.83846e7	−	3.18431e7i	−0.149045	−	0.258153i
$206$	−2.11177e7	+	3.65769e7i	−0.168311	+	0.291522i
$207$	−1.16411e8	+	2.01629e8i	−0.912215	+	1.58000i
$208$	−2.10950e7	−	3.65376e7i	−0.162539	−	0.281526i
$209$	1.49479e8			1.13257
$210$	7.34656e6	+	2.88134e7i	0.0547414	+	0.214698i
$211$	4.39224e6			0.0321883			0.0160941	−	0.999870i	$-0.494877\pi$
$211$	4.39224e6			0.0321883			0.0160941	+	0.999870i	$0.494877\pi$
$212$	2.96087e6	+	5.12838e6i	0.0213424	+	0.0369662i
$213$	−2.82423e6	+	4.89171e6i	−0.0200249	+	0.0346842i
$214$	−1.00758e8	+	1.74518e8i	−0.702801	+	1.21729i
$215$	−2.38316e8	−	4.12775e8i	−1.63538	−	2.83256i
$216$	−3.08915e7			−0.208569
$217$	−1.77398e7	+	1.73140e7i	−0.117853	+	0.115024i
$218$	7.96542e7			0.520728
$219$	1.15766e7	+	2.00512e7i	0.0744776	+	0.128999i
$220$	−1.87419e7	+	3.24619e7i	−0.118668	+	0.205539i
$221$	2.78548e7	−	4.82459e7i	0.173591	−	0.300668i
$222$	−6.70605e6	−	1.16152e7i	−0.0411369	−	0.0712512i
$223$	3.74081e7			0.225891			0.112945	−	0.993601i	$-0.463971\pi$
$223$	3.74081e7			0.225891			0.112945	+	0.993601i	$0.463971\pi$
$224$	5.22691e7	−	5.10143e7i	0.310725	−	0.303266i
$225$	−2.86061e8			−1.67425
$226$	−9.16015e7	−	1.58659e8i	−0.527866	−	0.914290i
$227$	−7.49312e7	+	1.29785e8i	−0.425179	+	0.736432i	−0.996437	−	0.0843383i	$-0.973122\pi$
$227$	−7.49312e7	+	1.29785e8i	−0.425179	+	0.736432i	0.571258	+	0.820771i	$0.306456\pi$
$228$	4.17722e6	−	7.23516e6i	0.0233408	−	0.0404274i
$229$	−7.90919e7	−	1.36991e8i	−0.435219	−	0.753822i	0.562094	−	0.827073i	$-0.309996\pi$
$229$	−7.90919e7	−	1.36991e8i	−0.435219	−	0.753822i	−0.997314	+	0.0732515i	$0.976662\pi$
$230$	−6.20403e8			−3.36222
$231$	3.69451e6	+	1.44900e7i	0.0197204	+	0.0773439i
$232$	1.65100e8			0.868037
$233$	5.39973e7	+	9.35261e7i	0.279657	+	0.484381i	0.971300	−	0.237859i	$-0.0764458\pi$
$233$	5.39973e7	+	9.35261e7i	0.279657	+	0.484381i	−0.691642	+	0.722240i	$0.743112\pi$
$234$	−2.95850e7	+	5.12427e7i	−0.150944	+	0.261442i
$235$	−1.65033e8	+	2.85845e8i	−0.829530	+	1.43679i
$236$	−2.04348e7	−	3.53941e7i	−0.101200	−	0.175283i
$237$	1.10502e7			0.0539203
$238$	2.76935e8	+	7.78224e7i	1.33155	+	0.374184i
$239$	3.03676e8			1.43886			0.719430	−	0.694565i	$-0.244403\pi$
$239$	3.03676e8			1.43886			0.719430	+	0.694565i	$0.244403\pi$
$240$	−2.51674e7	−	4.35912e7i	−0.117517	−	0.203545i
$241$	3.82699e6	−	6.62853e6i	0.0176115	−	0.0305041i	−0.857085	−	0.515174i	$-0.827727\pi$
$241$	3.82699e6	−	6.62853e6i	0.0176115	−	0.0305041i	0.874697	+	0.484670i	$0.161060\pi$
$242$	6.97053e7	−	1.20733e8i	0.316164	−	0.547612i
$243$	4.01381e7	+	6.95212e7i	0.179446	+	0.310810i
$244$	5.22191e7			0.230126
$245$	9.18851e6	−	3.78094e8i	0.0399175	−	1.64255i
$246$	−5.71254e6			−0.0244656
$247$	5.68753e7	+	9.85109e7i	0.240151	+	0.415954i
$248$	1.70270e7	−	2.94917e7i	0.0708855	−	0.122777i
$249$	−1.48696e7	+	2.57549e7i	−0.0610381	+	0.105721i
$250$	−1.56881e8	−	2.71726e8i	−0.635009	−	1.09987i
$251$	2.24744e8			0.897079			0.448539	−	0.893763i	$-0.351944\pi$
$251$	2.24744e8			0.897079			0.448539	+	0.893763i	$0.351944\pi$
$252$	−5.32129e7	−	1.49535e7i	−0.209467	−	0.0588629i
$253$	−3.11995e8			−1.21123
$254$	2.68040e8	+	4.64259e8i	1.02632	+	1.77763i
$255$	3.32321e7	−	5.75598e7i	0.125507	−	0.217384i
$256$	−8.49149e7	+	1.47077e8i	−0.316333	+	0.547904i
$257$	−1.56736e8	−	2.71474e8i	−0.575973	−	0.997615i	−0.995935	−	0.0900731i	$-0.971290\pi$
$257$	−1.56736e8	−	2.71474e8i	−0.575973	−	0.997615i	0.419962	−	0.907542i	$-0.362043\pi$
$258$	−7.40505e7			−0.268447
$259$	4.21469e7	+	1.65302e8i	0.150736	+	0.591191i
$260$	−2.85246e7			−0.100650
$261$	−1.42655e8	−	2.47086e8i	−0.496645	−	0.860215i
$262$	1.45941e8	−	2.52777e8i	0.501329	−	0.868327i
$263$	1.10171e7	−	1.90821e7i	0.0373440	−	0.0646816i	−0.846749	−	0.531992i	$-0.821444\pi$
$263$	1.10171e7	−	1.90821e7i	0.0373440	−	0.0646816i	0.884093	+	0.467310i	$0.154777\pi$
$264$	−1.02714e7	−	1.77907e7i	−0.0343572	−	0.0595084i
$265$	−9.61932e7			−0.317529
$266$	−4.20343e8	+	4.10252e8i	−1.36936	+	1.33649i
$267$	2.44709e7			0.0786793
$268$	1.48588e7	+	2.57363e7i	0.0471534	+	0.0816721i
$269$	−2.96420e8	+	5.13415e8i	−0.928485	+	1.60818i	−0.142627	+	0.989776i	$0.545555\pi$
$269$	−2.96420e8	+	5.13415e8i	−0.928485	+	1.60818i	−0.785858	+	0.618407i	$0.787778\pi$
$270$	−7.11264e7	+	1.23195e8i	−0.219916	+	0.380906i
$271$	1.42862e8	+	2.47445e8i	0.436039	+	0.755242i	0.997380	−	0.0723431i	$-0.0230477\pi$
$271$	1.42862e8	+	2.47445e8i	0.436039	+	0.755242i	−0.561341	+	0.827585i	$0.689714\pi$
$272$	−4.86944e8			−1.46720
$273$	−8.14362e6	+	7.94812e6i	−0.0242241	+	0.0236426i
$274$	2.63529e8			0.773928
$275$	−1.91669e8	−	3.31981e8i	−0.555762	−	0.962607i
$276$	−8.71878e6	+	1.51014e7i	−0.0249617	+	0.0432349i
$277$	1.92524e8	−	3.33461e8i	0.544258	−	0.942682i	−0.454396	−	0.890800i	$-0.650145\pi$
$277$	1.92524e8	−	3.33461e8i	0.544258	−	0.942682i	0.998653	−	0.0518820i	$-0.0165220\pi$
$278$	2.89879e7	+	5.02084e7i	0.0809206	+	0.140159i
$279$	−5.88492e7			−0.162228
$280$	1.28368e8	+	5.03463e8i	0.349465	+	1.37061i
$281$	−3.03188e8			−0.815154			−0.407577	−	0.913171i	$-0.633626\pi$
$281$	−3.03188e8			−0.815154			−0.407577	+	0.913171i	$0.633626\pi$
$282$	2.56398e7	+	4.44094e7i	0.0680836	+	0.117924i
$283$	−3.52954e8	+	6.11334e8i	−0.925689	+	1.60334i	−0.135240	+	0.990813i	$0.543180\pi$
$283$	−3.52954e8	+	6.11334e8i	−0.925689	+	1.60334i	−0.790449	+	0.612527i	$0.790153\pi$
$284$	1.39894e7	−	2.42304e7i	0.0362398	−	0.0627691i
$285$	6.78551e7	+	1.17529e8i	0.173630	+	0.300737i
$286$	−7.92912e7			−0.200421
$287$	6.99490e7	+	1.96566e7i	0.174661	+	0.0490819i
$288$	1.73395e8			0.427722
$289$	−1.16322e8	−	2.01475e8i	−0.283478	−	0.490998i
$290$	3.80135e8	−	6.58414e8i	0.915262	−	1.58528i
$291$	1.30170e7	−	2.25462e7i	0.0309661	−	0.0536349i
$292$	−5.73430e7	−	9.93209e7i	−0.134785	−	0.233454i
$293$	−4.74524e8			−1.10210			−0.551050	−	0.834472i	$-0.685773\pi$
$293$	−4.74524e8			−1.10210			−0.551050	+	0.834472i	$0.685773\pi$
$294$	−5.01578e7	−	3.06070e7i	−0.115113	−	0.0702434i
$295$	6.63889e8			1.50563
$296$	−1.17176e8	−	2.02955e8i	−0.262615	−	0.454862i
$297$	−3.57688e7	+	6.19533e7i	−0.0792240	+	0.137220i
$298$	−1.17714e8	+	2.03886e8i	−0.257674	+	0.446304i
$299$	−1.18711e8	−	2.05614e8i	−0.256828	−	0.444840i
$300$	−2.14250e7			−0.0458139
$301$	9.06734e8	+	2.54804e8i	1.91645	+	0.538548i
$302$	2.22336e8			0.464499
$303$	3.83116e7	+	6.63576e7i	0.0791190	+	0.137038i
$304$	4.97134e8	−	8.61061e8i	1.01488	−	1.75783i
$305$	−4.24126e8	+	7.34607e8i	−0.855944	+	1.48254i
$306$	3.41461e8	+	5.91427e8i	0.681264	+	1.17998i
$307$	5.92147e8			1.16801			0.584003	−	0.811752i	$-0.301486\pi$
$307$	5.92147e8			1.16801			0.584003	+	0.811752i	$0.301486\pi$
$308$	−1.83003e7	−	7.17742e7i	−0.0356886	−	0.139972i
$309$	−1.92834e7			−0.0371817
$310$	−7.84081e7	−	1.35807e8i	−0.149484	−	0.258914i
$311$	1.39482e8	−	2.41591e8i	0.262941	−	0.455427i	−0.704081	−	0.710119i	$-0.748641\pi$
$311$	1.39482e8	−	2.41591e8i	0.262941	−	0.455427i	0.967022	+	0.254693i	$0.0819743\pi$
$312$	7.81639e6	−	1.35384e7i	0.0145702	−	0.0252363i
$313$	−1.03626e7	−	1.79486e7i	−0.0191013	−	0.0330845i	0.856317	−	0.516451i	$-0.172747\pi$
$313$	−1.03626e7	−	1.79486e7i	−0.0191013	−	0.0330845i	−0.875418	+	0.483367i	$0.839414\pi$
$314$	3.35484e8			0.611530
$315$	6.42560e8	−	6.27134e8i	1.15832	−	1.13051i
$316$	−5.47358e7			−0.0975814
$317$	3.60836e8	+	6.24986e8i	0.636212	+	1.10195i	0.986257	+	0.165219i	$0.0528330\pi$
$317$	3.60836e8	+	6.24986e8i	0.636212	+	1.10195i	−0.350045	+	0.936733i	$0.613834\pi$
$318$	−7.47238e6	+	1.29425e7i	−0.0130306	+	0.0225696i
$319$	1.91166e8	−	3.31110e8i	0.329719	−	0.571090i
$320$	−3.33396e8	−	5.77458e8i	−0.568768	−	0.985134i
$321$	−9.20063e7			−0.155257
$322$	8.77349e8	−	8.56287e8i	1.46446	−	1.42930i
$323$	1.31287e9			2.16778
$324$	−6.46043e7	−	1.11898e8i	−0.105525	−	0.182774i
$325$	1.45857e8	−	2.52632e8i	0.235687	−	0.408222i
$326$	3.11795e8	−	5.40044e8i	0.498433	−	0.863311i
$327$	1.81838e7	+	3.14953e7i	0.0287587	+	0.0498114i
$328$	−9.98165e7			−0.156187
$329$	−1.61144e8	−	6.32010e8i	−0.249475	−	0.978450i
$330$	−9.45983e7			−0.144905
$331$	6.34543e8	+	1.09906e9i	0.961753	+	1.66580i	0.718098	+	0.695942i	$0.245013\pi$
$331$	6.34543e8	+	1.09906e9i	0.961753	+	1.66580i	0.243655	+	0.969862i	$0.421654\pi$
$332$	7.36545e7	−	1.27573e8i	0.110463	−	0.191327i
$333$	−2.02494e8	+	3.50730e8i	−0.300509	+	0.520496i
$334$	1.27020e8	+	2.20005e8i	0.186534	+	0.323087i
$335$	−4.82736e8			−0.701541
$336$	9.57558e7	+	2.69087e7i	0.137714	+	0.0386994i
$337$	−1.06090e9			−1.50998			−0.754989	−	0.655738i	$-0.772358\pi$
$337$	−1.06090e9			−1.50998			−0.754989	+	0.655738i	$0.772358\pi$
$338$	−3.01696e7	−	5.22553e7i	−0.0424973	−	0.0736075i
$339$	4.18225e7	−	7.24387e7i	0.0583057	−	0.100988i
$340$	−1.64611e8	+	2.85114e8i	−0.227134	+	0.393408i
$341$	−3.94307e7	−	6.82959e7i	−0.0538510	−	0.0932726i
$342$	−1.39442e9			−1.88497
$343$	5.08856e8	+	5.47368e8i	0.680872	+	0.732403i
$344$	−1.29390e9			−1.71374
$345$	−1.41629e8	−	2.45308e8i	−0.185688	−	0.321621i
$346$	7.18522e7	−	1.24452e8i	0.0932553	−	0.161523i
$347$	−5.52930e7	+	9.57703e7i	−0.0710423	+	0.123049i	−0.899358	−	0.437212i	$-0.855966\pi$
$347$	−5.52930e7	+	9.57703e7i	−0.0710423	+	0.123049i	0.828316	+	0.560261i	$0.189299\pi$
$348$	−1.06844e7	−	1.85059e7i	−0.0135901	−	0.0235388i
$349$	7.04233e8			0.886804			0.443402	−	0.896323i	$-0.353771\pi$
$349$	7.04233e8			0.886804			0.443402	+	0.896323i	$0.353771\pi$
$350$	1.45013e9	+	4.07505e8i	1.80787	+	0.508037i
$351$	−5.44389e7			−0.0671946
$352$	1.16179e8	+	2.01229e8i	0.141981	+	0.245918i
$353$	2.87404e8	−	4.97799e8i	0.347762	−	0.602341i	−0.638090	−	0.769962i	$-0.720275\pi$
$353$	2.87404e8	−	4.97799e8i	0.347762	−	0.602341i	0.985852	+	0.167621i	$0.0536085\pi$
$354$	5.15716e7	−	8.93246e7i	0.0617872	−	0.107019i
$355$	2.27245e8	+	3.93600e8i	0.269585	+	0.466935i
$356$	−1.21213e8			−0.142388
$357$	3.24490e7	+	1.27266e8i	0.0377453	+	0.148038i
$358$	1.15498e9			1.33040
$359$	−8.94065e7	−	1.54857e8i	−0.101985	−	0.176644i	0.810517	−	0.585715i	$-0.199186\pi$
$359$	−8.94065e7	−	1.54857e8i	−0.101985	−	0.176644i	−0.912503	+	0.409071i	$0.865853\pi$
$360$	−6.16741e8	+	1.06823e9i	−0.696697	+	1.20671i
$361$	−8.93412e8	+	1.54744e9i	−0.999486	+	1.73116i
$362$	−8.26174e8	−	1.43097e9i	−0.915359	−	1.58545i
$363$	6.36507e7			0.0698441
$364$	4.03383e7	−	3.93699e7i	0.0438392	−	0.0427868i
$365$	1.86297e9			2.00530
$366$	6.58930e7	+	1.14130e8i	0.0702515	+	0.121679i
$367$	1.74750e8	−	3.02676e8i	0.184538	−	0.319629i	−0.758883	−	0.651227i	$-0.774254\pi$
$367$	1.74750e8	−	3.02676e8i	0.184538	−	0.319629i	0.943421	+	0.331598i	$0.107588\pi$
$368$	−1.03763e9	+	1.79722e9i	−1.08536	+	1.87990i
$369$	8.62470e7	+	1.49384e8i	0.0893617	+	0.154779i
$370$	−1.07918e9			−1.10761
$371$	1.36033e8	−	1.32767e8i	0.138304	−	0.134984i
$372$	−4.40761e6			−0.00443918
$373$	−8.27984e8	−	1.43411e9i	−0.826116	−	1.43087i	−0.901064	−	0.433687i	$-0.857212\pi$
$373$	−8.27984e8	−	1.43411e9i	−0.826116	−	1.43087i	0.0749479	−	0.997187i	$-0.476121\pi$
$374$	−4.57577e8	+	7.92547e8i	−0.452286	+	0.783383i
$375$	7.16271e7	−	1.24062e8i	0.0701403	−	0.121487i
$376$	4.48010e8	+	7.75976e8i	0.434640	+	0.752819i
$377$	2.90949e8			0.279655
$378$	−6.94503e7	−	2.72386e8i	−0.0661383	−	0.259396i
$379$	−1.64557e9			−1.55267			−0.776334	−	0.630321i	$-0.782923\pi$
$379$	−1.64557e9			−1.55267			−0.776334	+	0.630321i	$0.782923\pi$
$380$	−3.36111e8	−	5.82161e8i	−0.314224	−	0.544253i
$381$	−1.22379e8	+	2.11967e8i	−0.113363	+	0.196350i
$382$	−3.57099e8	+	6.18514e8i	−0.327768	+	0.567711i
$383$	−9.83182e8	−	1.70292e9i	−0.894207	−	1.54881i	−0.834783	−	0.550580i	$-0.814407\pi$
$383$	−9.83182e8	−	1.70292e9i	−0.894207	−	1.54881i	−0.0594246	−	0.998233i	$-0.518927\pi$
$384$	−1.62392e8			−0.146354
$385$	1.15834e9	+	3.25509e8i	1.03448	+	0.290703i
$386$	1.38581e9			1.22644
$387$	1.11800e9	+	1.93644e9i	0.980514	+	1.69830i
$388$	−6.44781e7	+	1.11679e8i	−0.0560404	+	0.0970649i
$389$	7.63179e8	−	1.32186e9i	0.657359	−	1.13858i	−0.323937	−	0.946079i	$-0.605007\pi$
$389$	7.63179e8	−	1.32186e9i	0.657359	−	1.13858i	0.981297	−	0.192501i	$-0.0616600\pi$
$390$	−3.59939e7	−	6.23432e7i	−0.0307257	−	0.0532186i
$391$	−2.74026e9			−2.31832
$392$	−8.76419e8	−	5.34803e8i	−0.734870	−	0.448428i
$393$	1.33264e8			0.110749
$394$	−2.51215e8	−	4.35118e8i	−0.206923	−	0.358402i
$395$	4.44567e8	−	7.70012e8i	0.362950	−	0.628648i
$396$	8.79231e7	−	1.52287e8i	0.0711492	−	0.123234i
$397$	−6.91452e8	−	1.19763e9i	−0.554619	−	0.960629i	−0.997933	−	0.0642623i	$-0.979531\pi$
$397$	−6.91452e8	−	1.19763e9i	−0.554619	−	0.960629i	0.443314	−	0.896367i	$-0.353803\pi$
$398$	−6.30473e7			−0.0501274
$399$	−2.58172e8	−	7.25498e7i	−0.203472	−	0.0571783i
$400$	−2.54981e9			−1.99204
$401$	8.42121e8	+	1.45860e9i	0.652182	+	1.12961i	0.982592	+	0.185775i	$0.0594797\pi$
$401$	8.42121e8	+	1.45860e9i	0.652182	+	1.12961i	−0.330410	+	0.943838i	$0.607187\pi$
$402$	−3.74994e7	+	6.49509e7i	−0.0287895	+	0.0498648i
$403$	3.00061e7	−	5.19720e7i	0.0228371	−	0.0395551i
$404$	−1.89771e8	−	3.28693e8i	−0.143184	−	0.248002i
$405$	2.09888e9			1.56998
$406$	3.71178e8	+	1.45577e9i	0.275258	+	1.07957i
$407$	−5.42707e8			−0.399011
$408$	−9.02144e7	−	1.56256e8i	−0.0657605	−	0.113901i
$409$	−6.03339e7	+	1.04501e8i	−0.0436043	+	0.0755249i	−0.887004	−	0.461762i	$-0.847217\pi$
$409$	−6.03339e7	+	1.04501e8i	−0.0436043	+	0.0755249i	0.843400	+	0.537287i	$0.180551\pi$
$410$	−2.29823e8	+	3.98066e8i	−0.164684	+	0.285241i
$411$	6.01596e7	+	1.04199e8i	0.0427424	+	0.0740319i
$412$	9.55177e7			0.0672889
$413$	−9.38846e8	+	9.16307e8i	−0.655797	+	0.640053i
$414$	2.91047e9			2.01587
$415$	1.19645e9	+	2.07231e9i	0.821724	+	1.42327i
$416$	−8.84106e7	+	1.53132e8i	−0.0602112	+	0.104289i
$417$	−1.32350e7	+	2.29237e7i	−0.00893814	+	0.0154813i
$418$	−9.34305e8	−	1.61826e9i	−0.625708	−	1.08376i
$419$	−1.98627e9			−1.31913			−0.659567	−	0.751646i	$-0.729260\pi$
$419$	−1.98627e9			−1.31913			−0.659567	+	0.751646i	$0.729260\pi$
$420$	4.81256e7	−	4.69703e7i	0.0316960	−	0.0309350i
$421$	−2.06657e9			−1.34978			−0.674888	−	0.737920i	$-0.735808\pi$
$421$	−2.06657e9			−1.34978			−0.674888	+	0.737920i	$0.735808\pi$
$422$	−2.74534e7	−	4.75507e7i	−0.0177829	−	0.0308009i
$423$	7.74211e8	−	1.34097e9i	0.497357	−	0.861447i
$424$	−1.30567e8	+	2.26148e8i	−0.0831862	+	0.144083i
$425$	−1.68344e9	−	2.91580e9i	−1.06374	−	1.84245i
$426$	7.06105e7			0.0442523
$427$	−4.14131e8	−	1.62424e9i	−0.257419	−	1.00961i
$428$	4.55741e8			0.280973
$429$	−1.81010e7	−	3.13518e7i	−0.0110688	−	0.0191718i
$430$	−2.97915e9	+	5.16004e9i	−1.80698	+	3.12978i
$431$	8.31152e8	−	1.43960e9i	0.500046	−	0.866105i	−0.499954	−	0.866052i	$-0.666650\pi$
$431$	8.31152e8	−	1.43960e9i	0.500046	−	0.866105i	1.00000		5.29583e-5i	$-1.68571e-5\pi$
$432$	2.37919e8	+	4.12087e8i	0.141983	+	0.245921i
$433$	−3.28803e9			−1.94638			−0.973192	−	0.229995i	$-0.926129\pi$
$433$	−3.28803e9			−1.94638			−0.973192	+	0.229995i	$0.926129\pi$
$434$	2.98324e8	+	8.38329e7i	0.175176	+	0.0492267i
$435$	3.47117e8			0.202192
$436$	−9.00711e7	−	1.56008e8i	−0.0520455	−	0.0901454i
$437$	2.79760e9	−	4.84559e9i	1.60362	−	2.77755i
$438$	1.44717e8	−	2.50657e8i	0.0822925	−	0.142535i
$439$	1.12628e8	+	1.95077e8i	0.0635358	+	0.110047i	0.896044	−	0.443966i	$-0.146429\pi$
$439$	1.12628e8	+	1.95077e8i	0.0635358	+	0.110047i	−0.832508	+	0.554013i	$0.813096\pi$
$440$	−1.65294e9			−0.925065
$441$	−4.31057e7	+	1.77374e9i	−0.0239331	+	0.984814i
$442$	−6.96417e8			−0.383611
$443$	−9.38389e8	−	1.62534e9i	−0.512826	−	0.888240i	−0.999889	−	0.0148737i	$-0.995265\pi$
$443$	−9.38389e8	−	1.62534e9i	−0.512826	−	0.888240i	0.487064	−	0.873366i	$-0.338068\pi$
$444$	−1.51661e7	+	2.62685e7i	−0.00822307	+	0.0142428i
$445$	9.84498e8	−	1.70520e9i	0.529608	−	0.917308i
$446$	−2.33817e8	−	4.04982e8i	−0.124797	−	0.216154i
$447$	−1.07489e8			−0.0569230
$448$	1.26849e9	+	3.56462e8i	0.666520	+	0.187301i
$449$	1.87988e9			0.980092			0.490046	−	0.871697i	$-0.336980\pi$
$449$	1.87988e9			0.980092			0.490046	+	0.871697i	$0.336980\pi$
$450$	1.78801e9	+	3.09692e9i	0.924965	+	1.60209i
$451$	−1.15576e8	+	2.00184e8i	−0.0593266	+	0.102757i
$452$	−2.07162e8	+	3.58815e8i	−0.105518	+	0.182762i
$453$	5.07559e7	+	8.79117e7i	0.0256533	+	0.0444327i
$454$	1.87341e9			0.939587
$455$	2.26218e8	+	8.87234e8i	0.112587	+	0.441569i
$456$	3.68409e8			0.181951
$457$	−4.95098e8	−	8.57536e8i	−0.242653	−	0.420287i	0.718816	−	0.695200i	$-0.244684\pi$
$457$	−4.95098e8	−	8.57536e8i	−0.242653	−	0.420287i	−0.961469	+	0.274913i	$0.911351\pi$
$458$	−9.88717e8	+	1.71251e9i	−0.480887	+	0.832920i
$459$	−3.14158e8	+	5.44138e8i	−0.151637	+	0.262642i
$460$	7.01537e8	+	1.21510e9i	0.336046	+	0.582048i
$461$	−2.15806e9			−1.02591			−0.512956	−	0.858415i	$-0.671449\pi$
$461$	−2.15806e9			−1.02591			−0.512956	+	0.858415i	$0.671449\pi$
$462$	1.33777e8	−	1.30566e8i	0.0631154	−	0.0616002i
$463$	−3.06302e9			−1.43422			−0.717111	−	0.696959i	$-0.754536\pi$
$463$	−3.06302e9			−1.43422			−0.717111	+	0.696959i	$0.754536\pi$
$464$	−1.27156e9	−	2.20240e9i	−0.590913	−	1.02349i
$465$	3.57987e7	−	6.20053e7i	0.0165113	−	0.0285985i
$466$	6.75012e8	−	1.16916e9i	0.309002	−	0.535207i
$467$	−2.19859e8	−	3.80807e8i	−0.0998932	−	0.173020i	0.811747	−	0.584009i	$-0.198517\pi$
$467$	−2.19859e8	−	3.80807e8i	−0.0998932	−	0.173020i	−0.911640	+	0.410989i	$0.865183\pi$
$468$	1.33816e8			0.0603459
$469$	6.82667e8	−	6.66278e8i	0.305565	−	0.298229i
$470$	4.12610e9			1.83315
$471$	7.65859e7	+	1.32651e8i	0.0337735	+	0.0584974i
$472$	9.01121e8	−	1.56079e9i	0.394445	−	0.683198i
$473$	−1.49819e9	+	2.59494e9i	−0.650957	+	1.12749i
$474$	−6.90687e7	−	1.19631e8i	−0.0297891	−	0.0515962i
$475$	6.87467e9			2.94323
$476$	−1.60732e8	−	6.30395e8i	−0.0683089	−	0.267910i
$477$	4.51267e8			0.190379
$478$	−1.89811e9	−	3.28762e9i	−0.794920	−	1.37684i
$479$	−1.75759e9	+	3.04423e9i	−0.730706	+	1.26562i	0.225876	+	0.974156i	$0.427476\pi$
$479$	−1.75759e9	+	3.04423e9i	−0.730706	+	1.26562i	−0.956582	+	0.291464i	$0.905858\pi$
$480$	−1.05478e8	+	1.82694e8i	−0.0435330	+	0.0754014i
$481$	−2.06495e8	−	3.57661e8i	−0.0846063	−	0.146542i
$482$	−9.56812e7			−0.0389190
$483$	5.38862e8	+	1.51427e8i	0.217602	+	0.0611490i
$484$	−3.15285e8			−0.126399
$485$	−1.04739e9	−	1.81413e9i	−0.416880	−	0.722058i
$486$	5.01760e8	−	8.69074e8i	0.198276	−	0.343423i
$487$	1.82642e9	−	3.16345e9i	0.716555	−	1.24111i	−0.245802	−	0.969320i	$-0.579051\pi$
$487$	1.82642e9	−	3.16345e9i	0.716555	−	1.24111i	0.962357	−	0.271789i	$-0.0876154\pi$
$488$	1.15136e9	+	1.99422e9i	0.448480	+	0.776790i
$489$	2.84712e8			0.110109
$490$	−4.15070e9	+	2.26378e9i	−1.59381	+	0.869255i
$491$	2.83885e9			1.08232			0.541161	−	0.840919i	$-0.317985\pi$
$491$	2.83885e9			1.08232			0.541161	+	0.840919i	$0.317985\pi$
$492$	6.45961e6	+	1.11884e7i	0.00244528	+	0.00423535i
$493$	1.67902e9	−	2.90815e9i	0.631091	−	1.09308i
$494$	7.10990e8	−	1.23147e9i	0.265350	−	0.459600i
$495$	1.42823e9	+	2.47377e9i	0.529273	+	0.916728i
$496$	−5.24552e8			−0.193020
$497$	−8.64613e8	−	2.42968e8i	−0.315918	−	0.0887771i
$498$	3.71765e8			0.134886
$499$	−1.85683e8	−	3.21613e8i	−0.0668992	−	0.115873i	0.830636	−	0.556816i	$-0.187977\pi$
$499$	−1.85683e8	−	3.21613e8i	−0.0668992	−	0.115873i	−0.897535	+	0.440943i	$0.854644\pi$
$500$	−3.54795e8	+	6.14523e8i	−0.126935	+	0.219858i
$501$	−5.79933e7	+	1.00447e8i	−0.0206037	+	0.0356867i
$502$	−1.40475e9	−	2.43309e9i	−0.495604	−	0.858412i
$503$	3.62419e9			1.26976			0.634882	−	0.772609i	$-0.281049\pi$
$503$	3.62419e9			1.26976			0.634882	+	0.772609i	$0.281049\pi$
$504$	−6.02207e8	−	2.36188e9i	−0.209527	−	0.821770i
$505$	6.16531e9			2.13027
$506$	1.95010e9	+	3.37767e9i	0.669160	+	1.15902i
$507$	1.37745e7	−	2.38582e7i	0.00469407	−	0.00813036i
$508$	6.06188e8	−	1.04995e9i	0.205156	−	0.355341i
$509$	1.30730e9	+	2.26431e9i	0.439404	+	0.761070i	0.997644	−	0.0686098i	$-0.0218564\pi$
$509$	1.30730e9	+	2.26431e9i	0.439404	+	0.761070i	−0.558240	+	0.829680i	$0.688523\pi$
$510$	−8.30860e8			−0.277353
$511$	−2.63454e9	+	2.57129e9i	−0.873435	+	0.852467i
$512$	−1.51887e9			−0.500123
$513$	−6.41465e8	−	1.11105e9i	−0.209779	−	0.363348i
$514$	−1.95933e9	+	3.39366e9i	−0.636410	+	1.10229i
$515$	−7.75798e8	+	1.34372e9i	−0.250279	+	0.433495i
$516$	8.37346e7	+	1.45033e8i	0.0268306	+	0.0464720i
$517$	2.07497e9			0.660383
$518$	1.52613e9	−	1.48949e9i	0.482433	−	0.470851i
$519$	6.56111e7			0.0206012
$520$	−6.28929e8	−	1.08934e9i	−0.196151	−	0.339743i
$521$	1.25088e9	−	2.16659e9i	0.387512	−	0.671190i	−0.604603	−	0.796527i	$-0.706668\pi$
$521$	1.25088e9	−	2.16659e9i	0.387512	−	0.671190i	0.992114	+	0.125338i	$0.0400014\pi$
$522$	−1.78331e9	+	3.08879e9i	−0.548758	+	0.950477i
$523$	−1.96779e9	−	3.40832e9i	−0.601483	−	1.04180i	−0.992597	−	0.121457i	$-0.961243\pi$
$523$	−1.96779e9	−	3.40832e9i	−0.601483	−	1.04180i	0.391114	−	0.920342i	$-0.372090\pi$
$524$	−6.60107e8			−0.200426
$525$	1.69914e8	+	6.66409e8i	0.0512475	+	0.200994i
$526$	−2.75445e8			−0.0825249
$527$	−3.46321e8	−	5.99845e8i	−0.103072	−	0.178526i
$528$	−1.58216e8	+	2.74039e8i	−0.0467770	+	0.0810202i
$529$	−4.13680e9	+	7.16514e9i	−1.21498	+	2.10441i
$530$	6.01249e8	+	1.04139e9i	0.175424	+	0.303843i
$531$	−3.11448e9			−0.902722
$532$	1.27882e9	+	3.59365e8i	0.368230	+	0.103477i
$533$	−1.75903e8			−0.0503185
$534$	−1.52954e8	−	2.64923e8i	−0.0434675	−	0.0752880i
$535$	−3.70154e9	+	6.41126e9i	−1.04507	+	1.81011i
$536$	−6.55236e8	+	1.13490e9i	−0.183790	+	0.318333i
$537$	2.63664e8	+	4.56679e8i	0.0734752	+	0.127263i
$538$	7.41101e9			2.05182
$539$	−2.08735e9	+	1.13843e9i	−0.574162	+	0.313145i
$540$	3.21713e8			0.0879204
$541$	1.55684e9	+	2.69652e9i	0.422720	+	0.732172i	0.996204	−	0.0870443i	$-0.0277422\pi$
$541$	1.55684e9	+	2.69652e9i	0.422720	+	0.732172i	−0.573485	+	0.819216i	$0.694409\pi$
$542$	1.78590e9	−	3.09327e9i	0.481792	−	0.834489i
$543$	3.77206e8	−	6.53340e8i	0.101106	−	0.175122i
$544$	1.02041e9	+	1.76740e9i	0.271755	+	0.470694i
$545$	2.92625e9			0.774324
$546$	1.36948e8	+	3.84842e7i	0.0360065	+	0.0101183i
$547$	−2.45534e9			−0.641441			−0.320721	−	0.947174i	$-0.603925\pi$
$547$	−2.45534e9			−0.641441			−0.320721	+	0.947174i	$0.603925\pi$
$548$	−2.97992e8	−	5.16138e8i	−0.0773523	−	0.133978i
$549$	1.98968e9	−	3.44623e9i	0.513193	−	0.888876i
$550$	−2.39603e9	+	4.15005e9i	−0.614078	+	1.06361i
$551$	3.42831e9	+	5.93801e9i	0.873072	+	1.51220i
$552$	−7.68951e8			−0.194586
$553$	4.34090e8	+	1.70252e9i	0.109155	+	0.428108i
$554$	−4.81342e9			−1.20273
$555$	−2.46359e8	−	4.26707e8i	−0.0611708	−	0.105951i
$556$	6.55576e7	−	1.13549e8i	0.0161756	−	0.0280170i
$557$	1.20110e9	−	2.08036e9i	0.294500	−	0.510089i	−0.680369	−	0.732870i	$-0.738180\pi$
$557$	1.20110e9	−	2.08036e9i	0.294500	−	0.510089i	0.974868	+	0.222781i	$0.0715136\pi$
$558$	3.67832e8	+	6.37104e8i	0.0896252	+	0.155235i
$559$	−2.28019e9			−0.552115
$560$	5.72746e9	−	5.58996e9i	1.37817	−	1.34509i
$561$	−4.17832e8			−0.0999152
$562$	1.89505e9	+	3.28233e9i	0.450344	+	0.780019i
$563$	1.00983e9	−	1.74908e9i	0.238489	−	0.413075i	−0.721792	−	0.692110i	$-0.756681\pi$
$563$	1.00983e9	−	1.74908e9i	0.238489	−	0.413075i	0.960281	+	0.279035i	$0.0900145\pi$
$564$	5.79858e7	−	1.00434e8i	0.0136096	−	0.0235725i
$565$	−3.36515e9	−	5.82862e9i	−0.784938	−	1.35955i
$566$	8.82444e9			2.04564
$567$	−2.96815e9	+	2.89689e9i	−0.683825	+	0.667408i
$568$	1.23379e9			0.282503
$569$	−3.64850e9	−	6.31940e9i	−0.830275	−	1.43808i	−0.897820	−	0.440362i	$-0.854850\pi$
$569$	−3.64850e9	−	6.31940e9i	−0.830275	−	1.43808i	0.0675451	−	0.997716i	$-0.478483\pi$
$570$	8.48247e8	−	1.46921e9i	0.191849	−	0.332293i
$571$	2.38335e9	−	4.12809e9i	0.535749	−	0.927945i	−0.463377	−	0.886161i	$-0.653362\pi$
$571$	2.38335e9	−	4.12809e9i	0.535749	−	0.927945i	0.999127	−	0.0417841i	$-0.0133042\pi$
$572$	8.96607e7	+	1.55297e8i	0.0200316	+	0.0346958i
$573$	−3.26081e8			−0.0724077
$574$	−2.24408e8	−	8.80134e8i	−0.0495275	−	0.194248i
$575$	−1.43489e10			−3.14762
$576$	1.56404e9	+	2.70900e9i	0.341013	+	0.590651i
$577$	3.57808e9	−	6.19742e9i	0.775416	−	1.34306i	−0.159144	−	0.987255i	$-0.550873\pi$
$577$	3.57808e9	−	6.19742e9i	0.775416	−	1.34306i	0.934560	−	0.355805i	$-0.115793\pi$
$578$	−1.45412e9	+	2.51861e9i	−0.313223	+	0.542518i
$579$	3.16358e8	+	5.47949e8i	0.0677337	+	0.117318i
$580$	−1.71939e9			−0.365913
$581$	−4.55220e9	−	1.27923e9i	−0.962952	−	0.270602i
$582$	−3.25448e8			−0.0684308
$583$	3.02362e8	+	5.23707e8i	0.0631957	+	0.109458i
$584$	2.52867e9	−	4.37979e9i	0.525349	−	0.909931i
$585$	−1.08686e9	+	1.88250e9i	−0.224454	+	0.388766i
$586$	2.96598e9	+	5.13722e9i	0.608872	+	1.05460i
$587$	5.05006e9			1.03054			0.515268	−	0.857029i	$-0.327692\pi$
$587$	5.05006e9			1.03054			0.515268	+	0.857029i	$0.327692\pi$
$588$	−3.22847e6	+	1.32847e8i	−0.000654902	+	0.0269483i
$589$	1.41427e9			0.285187
$590$	−4.14959e9	−	7.18730e9i	−0.831808	−	1.44073i
$591$	1.14697e8	−	1.98662e8i	0.0228558	−	0.0395875i
$592$	−1.80493e9	+	3.12623e9i	−0.357548	+	0.619291i
$593$	1.60683e9	+	2.78311e9i	0.316430	+	0.548074i	0.979741	−	0.200271i	$-0.0641823\pi$
$593$	1.60683e9	+	2.78311e9i	0.316430	+	0.548074i	−0.663310	+	0.748345i	$0.730849\pi$
$594$	8.94281e8			0.175074
$595$	1.01737e10	+	2.85895e9i	1.98003	+	0.556414i
$596$	5.32432e8			0.103015
$597$	−1.43927e7	−	2.49289e7i	−0.00276843	−	0.00479506i
$598$	−1.48399e9	+	2.57035e9i	−0.283777	+	0.491517i
$599$	−4.44347e8	+	7.69631e8i	−0.0844750	+	0.146315i	−0.905167	−	0.425055i	$-0.860255\pi$
$599$	−4.44347e8	+	7.69631e8i	−0.0844750	+	0.146315i	0.820692	+	0.571370i	$0.193588\pi$
$600$	−4.72394e8	−	8.18210e8i	−0.0892843	−	0.154645i
$601$	−3.61488e9			−0.679255			−0.339628	−	0.940560i	$-0.610301\pi$
$601$	−3.61488e9			−0.679255			−0.339628	+	0.940560i	$0.610301\pi$
$602$	−2.90895e9	−	1.14090e10i	−0.543436	−	2.13137i
$603$	2.26464e9			0.420619
$604$	−2.51412e8	−	4.35459e8i	−0.0464255	−	0.0804114i
$605$	2.56076e9	−	4.43536e9i	0.470137	−	0.814301i
$606$	4.78927e8	−	8.29527e8i	0.0874210	−	0.151418i
$607$	3.59436e9	+	6.22562e9i	0.652321	+	1.12985i	0.982558	+	0.185955i	$0.0595380\pi$
$607$	3.59436e9	+	6.22562e9i	0.652321	+	1.12985i	−0.330237	+	0.943898i	$0.607129\pi$
$608$	−4.16704e9			−0.751909
$609$	−4.90879e8	+	4.79094e8i	−0.0880671	+	0.0859529i
$610$	1.06039e10			1.89152
$611$	7.89511e8	+	1.36747e9i	0.140028	+	0.242535i
$612$	7.72232e8	−	1.33754e9i	0.136181	−	0.235873i
$613$	−2.22811e8	+	3.85920e8i	−0.0390684	+	0.0676684i	−0.884898	−	0.465784i	$-0.845772\pi$
$613$	−2.22811e8	+	3.85920e8i	−0.0390684	+	0.0676684i	0.845830	+	0.533452i	$0.179106\pi$
$614$	−3.70117e9	−	6.41061e9i	−0.645282	−	1.11766i
$615$	−2.09861e8			−0.0363805
$616$	2.33752e9	−	2.28140e9i	0.402924	−	0.393251i
$617$	−4.24160e9			−0.726996			−0.363498	−	0.931595i	$-0.618418\pi$
$617$	−4.24160e9			−0.726996			−0.363498	+	0.931595i	$0.618418\pi$
$618$	1.20530e8	+	2.08763e8i	0.0205416	+	0.0355791i
$619$	−2.31838e9	+	4.01555e9i	−0.392887	+	0.680500i	−0.992829	−	0.119543i	$-0.961857\pi$
$619$	−2.31838e9	+	4.01555e9i	−0.392887	+	0.680500i	0.599942	+	0.800043i	$0.295190\pi$
$620$	−1.77324e8	+	3.07134e8i	−0.0298811	+	0.0517556i
$621$	1.33888e9	+	2.31901e9i	0.224347	+	0.388581i
$622$	−3.48730e9			−0.581062
$623$	9.61298e8	+	3.77024e9i	0.159276	+	0.624685i
$624$	−2.40800e8			−0.0396744
$625$	−5.76652e8	−	9.98790e8i	−0.0944786	−	0.163642i
$626$	−1.29541e8	+	2.24372e8i	−0.0211056	+	0.0365560i
$627$	4.26575e8	−	7.38850e8i	0.0691129	−	0.119707i
$628$	−3.79358e8	−	6.57067e8i	−0.0611210	−	0.105865i
$629$	−4.76661e9			−0.763717
$630$	−1.08057e10	−	3.03654e9i	−1.72171	−	0.483823i
$631$	5.16298e8			0.0818083			0.0409042	−	0.999163i	$-0.486976\pi$
$631$	5.16298e8			0.0818083			0.0409042	+	0.999163i	$0.486976\pi$
$632$	−1.20685e9	−	2.09033e9i	−0.190171	−	0.329386i
$633$	1.25344e7	−	2.17102e7i	0.00196422	−	0.00340213i
$634$	4.51075e9	−	7.81285e9i	0.702970	−	1.21758i
$635$	9.84696e9	+	1.70554e10i	1.52614	+	2.64335i
$636$	3.37984e7			0.00520950
$637$	−1.54448e9	−	9.42463e8i	−0.236752	−	0.144470i
$638$	−4.77949e9			−0.728633
$639$	−1.06607e9	−	1.84648e9i	−0.161633	−	0.279957i
$640$	−6.53325e9	+	1.13159e10i	−0.985143	+	1.70632i
$641$	2.74168e9	−	4.74873e9i	0.411163	−	0.712154i	−0.583855	−	0.811858i	$-0.698456\pi$
$641$	2.74168e9	−	4.74873e9i	0.411163	−	0.712154i	0.995017	+	0.0997038i	$0.0317895\pi$
$642$	5.75079e8	+	9.96066e8i	0.0857739	+	0.148565i
$643$	1.88292e9			0.279315			0.139657	−	0.990200i	$-0.455400\pi$
$643$	1.88292e9			0.279315			0.139657	+	0.990200i	$0.455400\pi$
$644$	−2.66918e9	−	7.50075e8i	−0.393801	−	0.110663i
$645$	−2.72038e9			−0.399182
$646$	−8.20603e9	−	1.42133e10i	−1.19762	−	2.07434i
$647$	−1.14731e9	+	1.98719e9i	−0.166539	+	0.288453i	−0.937201	−	0.348791i	$-0.886592\pi$
$647$	−1.14731e9	+	1.98719e9i	−0.166539	+	0.288453i	0.770662	+	0.637244i	$0.219926\pi$
$648$	2.84888e9	−	4.93441e9i	0.411303	−	0.712398i
$649$	−2.08679e9	−	3.61443e9i	−0.299655	−	0.519018i
$650$	−3.64668e9			−0.520836
$651$	3.49551e7	+	1.37095e8i	0.00496567	+	0.0194755i
$652$	−1.41028e9			−0.199269
$653$	2.08182e9	+	3.60581e9i	0.292581	+	0.506765i	0.974419	−	0.224738i	$-0.0721525\pi$
$653$	2.08182e9	+	3.60581e9i	0.292581	+	0.506765i	−0.681838	+	0.731503i	$0.738819\pi$
$654$	2.27314e8	−	3.93719e8i	0.0317763	−	0.0550382i
$655$	5.36142e9	−	9.28625e9i	0.745478	−	1.29121i
$656$	7.68763e8	+	1.33154e9i	0.106323	+	0.184158i
$657$	−8.73966e9			−1.20231
$658$	−5.83497e9	+	5.69489e9i	−0.798450	+	0.779282i
$659$	−8.58615e9			−1.16869			−0.584346	−	0.811505i	$-0.698649\pi$
$659$	−8.58615e9			−1.16869			−0.584346	+	0.811505i	$0.698649\pi$
$660$	1.06970e8	+	1.85277e8i	0.0144829	+	0.0250852i
$661$	−2.62631e9	+	4.54891e9i	−0.353705	+	0.612635i	−0.986895	−	0.161361i	$-0.948412\pi$
$661$	−2.62631e9	+	4.54891e9i	−0.353705	+	0.612635i	0.633190	+	0.773996i	$0.281745\pi$
$662$	7.93234e9	−	1.37392e10i	1.06267	−	1.84060i
$663$	−1.58981e8	−	2.75364e8i	−0.0211860	−	0.0366952i
$664$	6.49594e9			0.861100
$665$	−1.54421e10	+	1.50714e10i	−2.03625	+	1.98736i
$666$	5.06269e9			0.664082
$667$	−7.15564e9	−	1.23939e10i	−0.933702	−	1.61722i
$668$	2.87262e8	−	4.97552e8i	0.0372873	−	0.0645834i
$669$	1.06754e8	−	1.84903e8i	0.0137845	−	0.0238755i
$670$	3.01731e9	+	5.22613e9i	0.387577	+	0.671303i
$671$	5.33258e9			0.681411
$672$	−1.02993e8	−	4.03941e8i	−0.0130922	−	0.0513482i
$673$	−2.03248e9			−0.257024			−0.128512	−	0.991708i	$-0.541020\pi$
$673$	−2.03248e9			−0.257024			−0.128512	+	0.991708i	$0.541020\pi$
$674$	6.63109e9	+	1.14854e10i	0.834209	+	1.44489i
$675$	−1.64504e9	+	2.84930e9i	−0.205880	+	0.356594i
$676$	−6.82303e7	+	1.18178e8i	−0.00849500	+	0.0147138i
$677$	−2.21829e9	−	3.84219e9i	−0.274763	−	0.475903i	0.695313	−	0.718707i	$-0.255266\pi$
$677$	−2.21829e9	−	3.84219e9i	−0.274763	−	0.475903i	−0.970075	+	0.242805i	$0.921933\pi$
$678$	−1.04563e9			−0.128847
$679$	3.98506e9	+	1.11985e9i	0.488529	+	0.137283i
$680$	−1.45178e10			−1.77060
$681$	4.27671e8	+	7.40748e8i	0.0518913	+	0.0898784i
$682$	−4.92917e8	+	8.53757e8i	−0.0595016	+	0.103060i
$683$	−2.33991e9	+	4.05285e9i	−0.281013	+	0.486729i	−0.971635	−	0.236487i	$-0.924004\pi$
$683$	−2.33991e9	+	4.05285e9i	−0.281013	+	0.486729i	0.690621	+	0.723217i	$0.257337\pi$
$684$	1.57678e9	+	2.73107e9i	0.188398	+	0.326314i
$685$	9.68122e9			1.15083
$686$	2.74527e9	−	8.93019e9i	0.324677	−	1.05615i
$687$	−9.02836e8			−0.106233
$688$	9.96531e9	+	1.72604e10i	1.16662	+	2.02065i
$689$	−2.30092e8	+	3.98532e8i	−0.0268000	+	0.0464190i
$690$	−1.77048e9	+	3.06656e9i	−0.205172	+	0.355369i
$691$	−2.47618e9	−	4.28887e9i	−0.285502	−	0.494504i	0.687229	−	0.726441i	$-0.258827\pi$
$691$	−2.47618e9	−	4.28887e9i	−0.285502	−	0.494504i	−0.972731	+	0.231937i	$0.925494\pi$
$692$	−3.24995e8			−0.0372826
$693$	−5.43407e9	−	1.52705e9i	−0.620238	−	0.174295i
$694$	1.38242e9			0.156994
$695$	1.06492e9	+	1.84450e9i	0.120329	+	0.208416i
$696$	4.71154e8	−	8.16063e8i	0.0529701	−	0.0917469i
$697$	−1.01511e9	+	1.75822e9i	−0.113553	+	0.196679i
$698$	−4.40176e9	−	7.62407e9i	−0.489928	−	0.848580i
$699$	6.16381e8			0.0682620
$700$	−8.41647e8	−	3.30097e9i	−0.0927442	−	0.363746i
$701$	9.24389e8			0.101354			0.0506771	−	0.998715i	$-0.483862\pi$
$701$	9.24389e8			0.101354			0.0506771	+	0.998715i	$0.483862\pi$
$702$	3.40266e8	+	5.89358e8i	0.0371227	+	0.0642983i
$703$	4.86636e9	−	8.42878e9i	0.528276	−	0.915000i
$704$	−2.09591e9	+	3.63022e9i	−0.226396	+	0.392129i
$705$	9.41926e8	+	1.63146e9i	0.101241	+	0.175354i
$706$	−7.18560e9			−0.768505
$707$	−8.71874e9	+	8.50943e9i	−0.927867	+	0.905592i
$708$	−2.33264e8			−0.0247019
$709$	1.48793e9	+	2.57718e9i	0.156791	+	0.271570i	0.933710	−	0.358031i	$-0.116552\pi$
$709$	1.48793e9	+	2.57718e9i	0.156791	+	0.271570i	−0.776919	+	0.629601i	$0.783218\pi$
$710$	2.84076e9	−	4.92034e9i	0.297872	−	0.515930i
$711$	−2.08558e9	+	3.61232e9i	−0.217612	+	0.376915i
$712$	−2.67259e9	−	4.62906e9i	−0.277493	−	0.480632i
$713$	−2.95190e9			−0.304991
$714$	1.17497e9	−	1.14676e9i	0.120804	−	0.117904i
$715$	−2.91291e9			−0.298027
$716$	−1.30602e9	−	2.26210e9i	−0.132970	−	0.230312i
$717$	8.66619e8	−	1.50103e9i	0.0878033	−	0.152080i
$718$	−1.11766e9	+	1.93584e9i	−0.112687	+	0.195179i
$719$	5.55011e9	+	9.61306e9i	0.556865	+	0.964519i	0.997756	+	0.0669580i	$0.0213293\pi$
$719$	5.55011e9	+	9.61306e9i	0.556865	+	0.964519i	−0.440891	+	0.897561i	$0.645337\pi$
$720$	1.90000e10			1.89709
$721$	−7.57517e8	−	2.97100e9i	−0.0752694	−	0.295209i
$722$	2.23368e10			2.20872
$723$	−2.18426e7	−	3.78324e7i	−0.00214941	−	0.00372289i
$724$	−1.86844e9	+	3.23623e9i	−0.182976	+	0.316923i
$725$	8.79194e9	−	1.52281e10i	0.856844	−	1.48410i
$726$	−3.97844e8	−	6.89086e8i	−0.0385864	−	0.0668337i
$727$	1.86609e10			1.80120			0.900602	−	0.434645i	$-0.143126\pi$
$727$	1.86609e10			1.80120			0.900602	+	0.434645i	$0.143126\pi$
$728$	2.39292e9	+	6.72443e8i	0.229863	+	0.0645945i
$729$	−9.53707e9			−0.911735
$730$	−1.16443e10	−	2.01686e10i	−1.10786	−	1.91887i
$731$	−1.31586e10	+	2.27914e10i	−1.24595	+	2.15804i
$732$	1.49021e8	−	2.58111e8i	0.0140429	−	0.0243231i
$733$	−6.32499e8	−	1.09552e9i	−0.0593193	−	0.102744i	0.834841	−	0.550492i	$-0.185560\pi$
$733$	−6.32499e8	−	1.09552e9i	−0.0593193	−	0.102744i	−0.894160	+	0.447748i	$0.852226\pi$
$734$	−4.36904e9			−0.407803
$735$	−1.84264e9	−	1.12441e9i	−0.171173	−	0.104452i
$736$	8.69754e9			0.804126
$737$	1.51738e9	+	2.62817e9i	0.139623	+	0.241834i
$738$	1.07816e9	−	1.86743e9i	0.0987385	−	0.171020i
$739$	−6.49149e9	+	1.12436e10i	−0.591683	+	1.02482i	0.402323	+	0.915498i	$0.368203\pi$
$739$	−6.49149e9	+	1.12436e10i	−0.591683	+	1.02482i	−0.994006	+	0.109327i	$0.965130\pi$
$740$	1.22031e9	+	2.11363e9i	0.110703	+	0.191743i
$741$	6.49233e8			0.0586188
$742$	−2.28760e9	−	6.42847e8i	−0.205574	−	0.0577689i
$743$	−3.54641e9			−0.317196			−0.158598	−	0.987343i	$-0.550697\pi$
$743$	−3.54641e9			−0.317196			−0.158598	+	0.987343i	$0.550697\pi$
$744$	−9.71819e7	−	1.68324e8i	−0.00865128	−	0.0149845i
$745$	−4.32444e9	+	7.49014e9i	−0.383162	+	0.663656i
$746$	−1.03505e10	+	1.79276e10i	−0.912800	+	1.58102i
$747$	−5.61285e9	−	9.72174e9i	−0.492676	−	0.853340i
$748$	2.06967e9			0.180820
$749$	−3.61432e9	−	1.41755e10i	−0.314297	−	1.23268i
$750$	−1.79080e9			−0.155000
$751$	8.75852e9	+	1.51702e10i	0.754555	+	1.30693i	0.945595	+	0.325346i	$0.105481\pi$
$751$	8.75852e9	+	1.51702e10i	0.754555	+	1.30693i	−0.191040	+	0.981582i	$0.561186\pi$
$752$	6.90093e9	−	1.19528e10i	0.591759	−	1.02496i
$753$	6.41365e8	−	1.11088e9i	0.0547423	−	0.0948164i
$754$	−1.81856e9	−	3.14983e9i	−0.154499	−	0.267601i
$755$	8.16792e9			0.690712
$756$	−4.54953e8	+	4.44031e8i	−0.0382949	+	0.0373755i
$757$	−8.45110e9			−0.708073			−0.354036	−	0.935232i	$-0.615191\pi$
$757$	−8.45110e9			−0.708073			−0.354036	+	0.935232i	$0.615191\pi$
$758$	1.02855e10	+	1.78150e10i	0.857795	+	1.48574i
$759$	−8.90356e8	+	1.54214e9i	−0.0739125	+	0.128020i
$760$	1.48216e10	−	2.56718e10i	1.22475	−	2.12133i
$761$	5.93374e9	+	1.02775e10i	0.488070	+	0.845363i	0.999906	−	0.0137208i	$-0.00436760\pi$
$761$	5.93374e9	+	1.02775e10i	0.488070	+	0.845363i	−0.511835	+	0.859083i	$0.671034\pi$
$762$	3.05969e9			0.250515
$763$	−4.13818e9	+	4.03884e9i	−0.337267	+	0.329170i
$764$	1.61520e9			0.131039
$765$	1.25442e10	+	2.17272e10i	1.01304	+	1.75464i
$766$	−1.22906e10	+	2.12880e10i	−0.988036	+	1.71133i
$767$	1.58801e9	−	2.75052e9i	0.127078	−	0.220105i
$768$	4.84653e8	+	8.39444e8i	0.0386071	+	0.0668694i
$769$	1.77855e10			1.41034			0.705171	−	0.709037i	$-0.250870\pi$
$769$	1.77855e10			1.41034			0.705171	+	0.709037i	$0.250870\pi$
$770$	−3.71614e9	−	1.45748e10i	−0.293342	−	1.15050i
$771$	−1.78914e9			−0.140590
$772$	−1.56704e9	−	2.71419e9i	−0.122580	−	0.212314i
$773$	3.27177e9	−	5.66688e9i	0.254774	−	0.441282i	−0.710060	−	0.704141i	$-0.751332\pi$
$773$	3.27177e9	−	5.66688e9i	0.254774	−	0.441282i	0.964834	+	0.262860i	$0.0846656\pi$
$774$	1.39760e10	−	2.42071e10i	1.08340	−	1.87650i
$775$	−1.81346e9	−	3.14100e9i	−0.139943	−	0.242388i
$776$	−5.68663e9			−0.436857
$777$	9.37338e8	+	2.63404e8i	0.0716840	+	0.0201442i
$778$	−1.90808e10			−1.45267
$779$	−2.07270e9	−	3.59002e9i	−0.157092	−	0.272092i
$780$	−8.14021e7	+	1.40993e8i	−0.00614193	+	0.0106381i
$781$	1.42859e9	−	2.47439e9i	0.107307	−	0.185862i
$782$	1.71278e10	+	2.96662e10i	1.28079	+	2.21839i
$783$	−3.28145e9			−0.244287
$784$	−3.84222e8	+	1.58102e10i	−0.0284758	+	1.17174i
$785$	1.23246e10			0.909348
$786$	−8.32960e8	−	1.44273e9i	−0.0611850	−	0.105976i
$787$	2.71102e9	−	4.69563e9i	0.198254	−	0.343386i	−0.749708	−	0.661768i	$-0.769806\pi$
$787$	2.71102e9	−	4.69563e9i	0.198254	−	0.343386i	0.947962	+	0.318382i	$0.103140\pi$
$788$	−5.68138e8	+	9.84043e8i	−0.0413630	+	0.0716428i
$789$	−6.28800e7	−	1.08911e8i	−0.00455767	−	0.00789411i
$790$	−1.11149e10			−0.802069
$791$	1.28036e10	+	3.59798e9i	0.919844	+	0.258488i
$792$	7.75436e9			0.554635
$793$	2.02900e9	+	3.51434e9i	0.144486	+	0.250258i
$794$	−8.64374e9	+	1.49714e10i	−0.612815	+	1.06143i
$795$	−2.74512e8	+	4.75469e8i	−0.0193765	+	0.0335612i
$796$	7.12924e7	+	1.23482e8i	0.00501011	+	0.00867777i
$797$	−1.85911e10			−1.30077			−0.650384	−	0.759605i	$-0.725392\pi$
$797$	−1.85911e10			−1.30077			−0.650384	+	0.759605i	$0.725392\pi$
$798$	8.28258e8	+	3.24845e9i	0.0576973	+	0.226291i
$799$	1.82246e10			1.26399
$800$	5.34321e9	+	9.25471e9i	0.368967	+	0.639069i
$801$	−4.61853e9	+	7.99953e9i	−0.317534	+	0.549985i
$802$	1.05272e10	−	1.82337e10i	0.720616	−	1.24814i
$803$	−5.85583e9	−	1.01426e10i	−0.399102	−	0.691265i
$804$	1.69614e8			0.0115097
$805$	3.22311e10	−	3.14573e10i	2.17765	−	2.12538i
$806$	−7.50203e8			−0.0504668
$807$	1.69182e9	+	2.93032e9i	0.113318	+	0.196272i
$808$	8.36841e9	−	1.44945e10i	0.558088	−	0.966637i
$809$	9.60492e9	−	1.66362e10i	0.637784	−	1.10468i	−0.348133	−	0.937445i	$-0.613184\pi$
$809$	9.60492e9	−	1.66362e10i	0.637784	−	1.10468i	0.985918	−	0.167230i	$-0.0534823\pi$
$810$	−1.31189e10	−	2.27226e10i	−0.867359	−	1.50231i
$811$	4.04424e9			0.266234			0.133117	−	0.991100i	$-0.457501\pi$
$811$	4.04424e9			0.266234			0.133117	+	0.991100i	$0.457501\pi$
$812$	2.43150e9	−	2.37313e9i	0.159378	−	0.155552i
$813$	1.63078e9			0.106433
$814$	3.39215e9	+	5.87538e9i	0.220440	+	0.381813i
$815$	1.14544e10	−	1.98395e10i	0.741172	−	1.28375i
$816$	−1.38962e9	+	2.40689e9i	−0.0895325	+	0.155075i
$817$	−2.68680e10	−	4.65367e10i	−1.72368	−	2.98551i
$818$	1.50845e9			0.0963595
$819$	−1.06125e9	−	4.16225e9i	−0.0675030	−	0.264749i
$820$	1.03952e9			0.0658390
$821$	−4.01662e9	−	6.95699e9i	−0.253314	−	0.438753i	0.711122	−	0.703069i	$-0.248187\pi$
$821$	−4.01662e9	−	6.95699e9i	−0.253314	−	0.438753i	−0.964436	+	0.264316i	$0.914854\pi$
$822$	7.52046e8	−	1.30258e9i	0.0472273	−	0.0818001i
$823$	4.66122e9	−	8.07347e9i	0.291474	−	0.504848i	−0.682684	−	0.730713i	$-0.739188\pi$
$823$	4.66122e9	−	8.07347e9i	0.291474	−	0.504848i	0.974159	+	0.225865i	$0.0725209\pi$
$824$	2.10604e9	+	3.64777e9i	0.131136	+	0.227134i
$825$	−2.18791e9			−0.135657
$826$	1.57882e10	+	4.43669e9i	0.974770	+	0.273923i
$827$	1.57442e10			0.967949			0.483974	−	0.875082i	$-0.339193\pi$
$827$	1.57442e10			0.967949			0.483974	+	0.875082i	$0.339193\pi$
$828$	−3.29109e9	−	5.70034e9i	−0.201481	−	0.348975i
$829$	6.22844e9	−	1.07880e10i	0.379698	−	0.657657i	−0.611320	−	0.791384i	$-0.709361\pi$
$829$	6.22844e9	−	1.07880e10i	0.379698	−	0.657657i	0.991018	+	0.133727i	$0.0426945\pi$
$830$	1.49566e10	−	2.59056e10i	0.907947	−	1.57261i
$831$	−1.09883e9	−	1.90323e9i	−0.0664243	−	0.115050i
$832$	−3.18991e9			−0.192020
$833$	−1.83332e10	+	9.99888e9i	−1.09896	+	0.599368i
$834$	3.30897e8			0.0197520
$835$	4.66631e9	+	8.08228e9i	0.277377	+	0.480431i
$836$	−2.11298e9	+	3.65979e9i	−0.125076	+	0.216638i
$837$	−3.38422e8	+	5.86163e8i	−0.0199489	+	0.0345525i
$838$	1.24150e10	+	2.15034e10i	0.728775	+	1.26228i
$839$	3.29282e9			0.192487			0.0962435	−	0.995358i	$-0.469317\pi$
$839$	3.29282e9			0.192487			0.0962435	+	0.995358i	$0.469317\pi$
$840$	2.85488e9	+	8.02258e8i	0.166192	+	0.0467021i
$841$	2.87855e8			0.0166874
$842$	1.29169e10	+	2.23728e10i	0.745704	+	1.29160i
$843$	−8.65224e8	+	1.49861e9i	−0.0497430	+	0.0861575i
$844$	−6.20874e7	+	1.07538e8i	−0.00355471	+	0.00615695i
$845$	−1.10834e9	−	1.91970e9i	−0.0631937	−	0.109455i
$846$	−1.93566e10			−1.09909
$847$	2.50041e9	+	9.80669e9i	0.141390	+	0.554537i
$848$	4.02237e9			0.226515
$849$	2.01449e9	+	3.48919e9i	0.112976	+	0.195681i
$850$	−2.10444e10	+	3.64500e10i	−1.17536	+	2.03578i
$851$	−1.01572e10	+	1.75927e10i	−0.564962	+	0.978542i
$852$	−7.98448e7	−	1.38295e8i	−0.00442291	−	0.00766070i
$853$	−3.25486e10			−1.79560			−0.897802	−	0.440399i	$-0.854837\pi$
$853$	−3.25486e10			−1.79560			−0.897802	+	0.440399i	$0.854837\pi$
$854$	−1.49956e10	+	1.46356e10i	−0.823874	+	0.804095i
$855$	−5.12268e10			−2.80295
$856$	1.00485e10	+	1.74045e10i	0.547573	+	0.948425i
$857$	6.40055e9	−	1.10861e10i	0.347364	−	0.601652i	−0.638417	−	0.769691i	$-0.720410\pi$
$857$	6.40055e9	−	1.10861e10i	0.347364	−	0.601652i	0.985780	+	0.168039i	$0.0537436\pi$
$858$	−2.26278e8	+	3.91924e8i	−0.0122303	+	0.0211835i
$859$	1.63824e10	+	2.83751e10i	0.881862	+	1.52743i	0.849268	+	0.527962i	$0.177044\pi$
$859$	1.63824e10	+	2.83751e10i	0.881862	+	1.52743i	0.0325943	+	0.999469i	$0.489623\pi$
$860$	1.34750e10			0.722413
$861$	2.96777e8	−	2.89652e8i	0.0158460	−	0.0154656i
$862$	−2.07802e10			−1.10503
$863$	2.36467e9	+	4.09573e9i	0.125237	+	0.216917i	0.921826	−	0.387605i	$-0.126697\pi$
$863$	2.36467e9	+	4.09573e9i	0.125237	+	0.216917i	−0.796588	+	0.604522i	$0.793364\pi$
$864$	9.97134e8	−	1.72709e9i	0.0525963	−	0.0910995i
$865$	2.63963e9	−	4.57197e9i	0.138671	−	0.240185i
$866$	2.05516e10	+	3.55964e10i	1.07531	+	1.86249i
$867$	−1.32782e9			−0.0691945
$868$	−1.73145e8	−	6.79082e8i	−0.00898653	−	0.0352455i
$869$	−5.58959e9			−0.288942
$870$	−2.16963e9	−	3.75791e9i	−0.111704	−	0.193477i
$871$	−1.15470e9	+	1.99999e9i	−0.0592113	+	0.102557i
$872$	3.97190e9	−	6.87953e9i	0.202857	−	0.351359i
$873$	4.91357e9	+	8.51055e9i	0.249946	+	0.432920i
$874$	−6.99448e10			−3.54377
$875$	2.19280e10	+	6.16206e9i	1.10655	+	0.310955i
$876$	−6.54571e8			−0.0328998
$877$	−1.56577e10	−	2.71199e10i	−0.783842	−	1.35765i	−0.929688	−	0.368347i	$-0.879924\pi$
$877$	−1.56577e10	−	2.71199e10i	−0.783842	−	1.35765i	0.145846	−	0.989307i	$-0.453409\pi$
$878$	1.40794e9	−	2.43862e9i	0.0702026	−	0.121595i
$879$	−1.35417e9	+	2.34550e9i	−0.0672533	+	0.116486i
$880$	1.27305e10	+	2.20499e10i	0.629734	+	1.09073i
$881$	−4.97610e9			−0.245174			−0.122587	−	0.992458i	$-0.539119\pi$
$881$	−4.97610e9			−0.245174			−0.122587	+	0.992458i	$0.539119\pi$
$882$	1.94720e10	−	1.06200e10i	0.955588	−	0.521174i
$883$	7.10838e9			0.347463			0.173731	−	0.984793i	$-0.444418\pi$
$883$	7.10838e9			0.347463			0.173731	+	0.984793i	$0.444418\pi$
$884$	7.87493e8	+	1.36398e9i	0.0383410	+	0.0664086i
$885$	1.89458e9	−	3.28151e9i	0.0918779	−	0.159137i
$886$	−1.17307e10	+	2.03181e10i	−0.566636	+	0.981443i
$887$	−8.28022e9	−	1.43418e10i	−0.398391	−	0.690033i	0.595137	−	0.803625i	$-0.297098\pi$
$887$	−8.28022e9	−	1.43418e10i	−0.398391	−	0.690033i	−0.993528	+	0.113591i	$0.963765\pi$
$888$	−1.33757e9			−0.0641020
$889$	−3.74653e10	−	1.05282e10i	−1.78843	−	0.502574i
$890$	−2.46141e10			−1.17036
$891$	−6.59735e9	−	1.14270e10i	−0.312462	−	0.541201i
$892$	−5.28789e8	+	9.15890e8i	−0.0249463	+	0.0432082i
$893$	−1.86059e10	+	3.22264e10i	−0.874322	+	1.51437i
$894$	6.71853e8	+	1.16368e9i	0.0314480	+	0.0544695i
$895$	4.24303e10			1.97831
$896$	−6.37929e9	−	2.50198e10i	−0.296275	−	1.16200i
$897$	−1.35509e9			−0.0626896
$898$	−1.17500e10	−	2.03516e10i	−0.541467	−	0.937848i
$899$	1.80870e9	−	3.13275e9i	0.0830246	−	0.143803i
$900$	4.04367e9	−	7.00385e9i	0.184896	−	0.320249i
$901$	2.65566e9	+	4.59973e9i	0.120958	+	0.209506i
$902$	2.88960e9			0.131104
$903$	3.84706e9	−	3.75470e9i	0.173869	−	0.169695i
$904$	−1.82706e10			−0.822552
$905$	−3.03510e10	−	5.25695e10i	−1.36114	−	2.35757i
$906$	6.34492e8	−	1.09897e9i	0.0283451	−	0.0490951i
$907$	2.32507e9	−	4.02714e9i	0.103469	−	0.179214i	−0.809643	−	0.586923i	$-0.800339\pi$
$907$	2.32507e9	−	4.02714e9i	0.103469	−	0.179214i	0.913112	+	0.407710i	$0.133672\pi$
$908$	−2.11841e9	−	3.66919e9i	−0.0939094	−	0.162656i
$909$	−2.89231e10			−1.27723
$910$	8.19129e9	−	7.99464e9i	0.360336	−	0.351685i
$911$	−1.70510e9			−0.0747200			−0.0373600	−	0.999302i	$-0.511895\pi$
$911$	−1.70510e9			−0.0747200			−0.0373600	+	0.999302i	$0.511895\pi$
$912$	−2.83740e9	−	4.91452e9i	−0.123862	−	0.214535i
$913$	7.52155e9	−	1.30277e10i	0.327084	−	0.566526i
$914$	−6.18915e9	+	1.07199e10i	−0.268114	+	0.464387i
$915$	2.42070e9	+	4.19278e9i	0.104464	+	0.180937i
$916$	4.47207e9			0.192254
$917$	5.23507e9	+	2.05321e10i	0.224197	+	0.879309i
$918$	7.85450e9			0.335096
$919$	−1.42968e9	−	2.47628e9i	−0.0607623	−	0.105243i	0.834044	−	0.551698i	$-0.186020\pi$
$919$	−1.42968e9	−	2.47628e9i	−0.0607623	−	0.105243i	−0.894806	+	0.446454i	$0.852687\pi$
$920$	−3.09360e10	+	5.35826e10i	−1.30980	+	2.26865i
$921$	1.68984e9	−	2.92689e9i	0.0712750	−	0.123452i
$922$	1.34888e10	+	2.33633e10i	0.566780	+	0.981692i
$923$	2.17427e9			0.0910137
$924$	−4.06994e8	−	1.14371e8i	−0.0169721	−	0.00476939i
$925$	−2.49596e10			−1.03691
$926$	1.91452e10	+	3.31604e10i	0.792357	+	1.37240i
$927$	3.63947e9	−	6.30375e9i	0.150058	−	0.259908i
$928$	−5.32919e9	+	9.23042e9i	−0.218899	+	0.379144i
$929$	5.07345e9	+	8.78747e9i	0.207610	+	0.359591i	0.950961	−	0.309310i	$-0.100098\pi$
$929$	5.07345e9	+	8.78747e9i	0.207610	+	0.359591i	−0.743351	+	0.668901i	$0.766765\pi$
$930$	−8.95030e8			−0.0364878
$931$	1.03592e9	−	4.26267e10i	0.0420730	−	1.73124i
$932$	−3.05316e9			−0.123536
$933$	−7.96097e8	−	1.37888e9i	−0.0320908	−	0.0555829i
$934$	−2.74843e9	+	4.76042e9i	−0.110375	+	0.191175i
$935$	−1.68100e10	+	2.91157e10i	−0.672552	+	1.16489i
$936$	2.95047e9	+	5.11036e9i	0.117605	+	0.203698i
$937$	1.99993e10			0.794192			0.397096	−	0.917777i	$-0.370018\pi$
$937$	1.99993e10			0.794192			0.397096	+	0.917777i	$0.370018\pi$
$938$	−1.14801e10	−	3.22607e9i	−0.454189	−	0.127633i
$939$	−1.18289e8			−0.00466247
$940$	−4.66570e9	−	8.08123e9i	−0.183218	−	0.317344i
$941$	1.83468e10	−	3.17776e10i	0.717788	−	1.24325i	−0.244086	−	0.969754i	$-0.578488\pi$
$941$	1.83468e10	−	3.17776e10i	0.717788	−	1.24325i	0.961874	−	0.273492i	$-0.0881787\pi$
$942$	9.57390e8	−	1.65825e9i	0.0373173	−	0.0646355i
$943$	4.32618e9	+	7.49317e9i	0.168002	+	0.290988i
$944$	−2.77609e10			−1.07407
$945$	−2.55139e9	−	1.00066e10i	−0.0983479	−	0.385724i
$946$	3.74572e10			1.43852
$947$	1.73761e10	+	3.00963e10i	0.664855	+	1.15156i	0.979324	+	0.202296i	$0.0648402\pi$
$947$	1.73761e10	+	3.00963e10i	0.664855	+	1.15156i	−0.314469	+	0.949268i	$0.601826\pi$
$948$	−1.56203e8	+	2.70551e8i	−0.00595469	+	0.0103138i
$949$	4.45619e9	−	7.71834e9i	0.169251	−	0.293152i
$950$	−4.29696e10	−	7.44256e10i	−1.62603	−	2.81637i
$951$	4.11895e9			0.155294
$952$	2.05305e10	−	2.00376e10i	0.771206	−	0.752692i
$953$	3.81638e9			0.142832			0.0714162	−	0.997447i	$-0.477248\pi$
$953$	3.81638e9			0.142832			0.0714162	+	0.997447i	$0.477248\pi$
$954$	−2.82061e9	−	4.88544e9i	−0.105178	−	0.182173i
$955$	−1.31187e10	+	2.27223e10i	−0.487393	+	0.844189i
$956$	−4.29268e9	+	7.43513e9i	−0.158901	+	0.275224i
$957$	−1.09108e9	−	1.88981e9i	−0.0402408	−	0.0696991i
$958$	4.39427e10			1.61476
$959$	−1.36908e10	+	1.33621e10i	−0.501261	+	0.489227i
$960$	−3.80572e9			−0.138831
$961$	1.33832e10	+	2.31804e10i	0.486440	+	0.842539i
$962$	−2.58137e9	+	4.47106e9i	−0.0934840	+	0.161919i
$963$	1.73649e10	−	3.00769e10i	0.626585	−	1.08528i
$964$	1.08194e8	+	1.87398e8i	0.00388986	+	0.00673744i
$965$	5.09102e10			1.82372
$966$	−1.72876e9	−	6.78024e9i	−0.0617041	−	0.242005i
$967$	2.99587e10			1.06544			0.532721	−	0.846291i	$-0.321170\pi$
$967$	2.99587e10			1.06544			0.532721	+	0.846291i	$0.321170\pi$
$968$	−6.95162e9	−	1.20406e10i	−0.246333	−	0.426661i
$969$	3.74662e9	−	6.48934e9i	0.132284	−	0.229122i
$970$	−1.30932e10	+	2.26782e10i	−0.460624	+	0.797824i
$971$	−1.35364e10	−	2.34457e10i	−0.474500	−	0.821858i	0.525074	−	0.851057i	$-0.324038\pi$
$971$	−1.35364e10	−	2.34457e10i	−0.474500	−	0.821858i	−0.999574	+	0.0291989i	$0.990704\pi$
$972$	−2.26952e9			−0.0792686
$973$	−4.05177e9	−	1.13860e9i	−0.141010	−	0.0396257i
$974$	−4.56636e10			−1.58349
$975$	−8.32482e8	−	1.44190e9i	−0.0287646	−	0.0498218i
$976$	1.77350e10	−	3.07180e10i	0.610602	−	1.05759i
$977$	1.37428e10	−	2.38031e10i	0.471458	−	0.816589i	−0.528009	−	0.849239i	$-0.677061\pi$
$977$	1.37428e10	−	2.38031e10i	0.471458	−	0.816589i	0.999467	+	0.0326499i	$0.0103946\pi$
$978$	−1.77957e9	−	3.08231e9i	−0.0608316	−	0.105363i
$979$	−1.23782e10			−0.421617
$980$	9.12727e9	+	5.56959e9i	0.309777	+	0.189031i
$981$	−1.37278e10			−0.464257
$982$	−1.77440e10	−	3.07335e10i	−0.597945	−	1.03567i
$983$	−2.00984e10	+	3.48114e10i	−0.674876	+	1.16892i	0.301629	+	0.953425i	$0.402470\pi$
$983$	−2.00984e10	+	3.48114e10i	−0.674876	+	1.16892i	−0.976505	+	0.215494i	$0.930864\pi$
$984$	−2.84852e8	+	4.93378e8i	−0.00953095	+	0.0165081i
$985$	−9.22887e9	−	1.59849e10i	−0.307696	−	0.532945i
$986$	−4.19784e10			−1.39462
$987$	−3.58380e9	−	1.00709e9i	−0.118641	−	0.0333396i
$988$	−3.21589e9			−0.106084
$989$	5.60794e10	+	9.71323e10i	1.84339	+	3.19284i
$990$	1.78541e10	−	3.09242e10i	0.584810	−	1.01292i
$991$	1.75432e9	−	3.03858e9i	0.0572600	−	0.0991773i	−0.835974	−	0.548768i	$-0.815097\pi$
$991$	1.75432e9	−	3.03858e9i	0.0572600	−	0.0991773i	0.893235	+	0.449591i	$0.148430\pi$
$992$	1.09922e9	+	1.90390e9i	0.0357513	+	0.0619232i
$993$	7.24333e9			0.234756
$994$	2.77382e9	+	1.08790e10i	0.0895830	+	0.351347i
$995$	−2.31616e9			−0.0745397
$996$	−4.20384e8	−	7.28126e8i	−0.0134815	−	0.0233506i
$997$	2.34863e10	−	4.06794e10i	0.750553	−	1.30000i	−0.197002	−	0.980403i	$-0.563121\pi$
$997$	2.34863e10	−	4.06794e10i	0.750553	−	1.30000i	0.947555	−	0.319593i	$-0.103546\pi$
$998$	−2.32120e9	+	4.02044e9i	−0.0739189	+	0.128031i
$999$	2.32895e9	+	4.03385e9i	0.0739061	+	0.128009i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.e.b.53.9	✓	58
7.2	even	3	inner	91.8.e.b.79.9	yes	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.e.b.53.9	✓	58	1.1	even	1	trivial
91.8.e.b.79.9	yes	58	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:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	91.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.25043 - 10.8261i) q^{2} +(2.85376 - 4.94285i) q^{3} +(-14.1357 + 24.4837i) q^{4} +(-229.621 - 397.716i) q^{5} -71.3488 q^{6} +(873.653 + 245.508i) q^{7} -1246.69 q^{8} +(1077.21 + 1865.79i) q^{9} +O(q^{10})\)	\(q+(-6.25043 - 10.8261i) q^{2} +(2.85376 - 4.94285i) q^{3} +(-14.1357 + 24.4837i) q^{4} +(-229.621 - 397.716i) q^{5} -71.3488 q^{6} +(873.653 + 245.508i) q^{7} -1246.69 q^{8} +(1077.21 + 1865.79i) q^{9} +(-2870.46 + 4971.78i) q^{10} +(-1443.53 + 2500.26i) q^{11} +(80.6796 + 139.741i) q^{12} -2197.00 q^{13} +(-2802.82 - 10992.7i) q^{14} -2621.13 q^{15} +(9601.73 + 16630.7i) q^{16} +(-12678.5 + 21959.9i) q^{17} +(13466.1 - 23323.9i) q^{18} +(-25887.7 - 44838.8i) q^{19} +12983.4 q^{20} +(3706.70 - 3617.71i) q^{21} +36090.6 q^{22} +(54033.4 + 93588.5i) q^{23} +(-3557.76 + 6162.22i) q^{24} +(-66389.3 + 114990. i) q^{25} +(13732.2 + 23784.8i) q^{26} +24778.7 q^{27} +(-18360.6 + 17919.8i) q^{28} -132430. q^{29} +(16383.2 + 28376.5i) q^{30} +(-13657.7 + 23655.9i) q^{31} +(40241.5 - 69700.3i) q^{32} +(8238.95 + 14270.3i) q^{33} +316985. q^{34} +(-102967. - 403839. i) q^{35} -60908.5 q^{36} +(93989.7 + 162795. i) q^{37} +(-323619. + 560524. i) q^{38} +(-6269.70 + 10859.4i) q^{39} +(286267. + 495829. i) q^{40} +80065.0 q^{41} +(-62334.1 - 17516.7i) q^{42} +1.03787e6 q^{43} +(-40810.5 - 70685.9i) q^{44} +(494701. - 856848. i) q^{45} +(675463. - 1.16994e6i) q^{46} +(-359358. - 622427. i) q^{47} +109604. q^{48} +(702995. + 428977. i) q^{49} +1.65985e6 q^{50} +(72363.0 + 125336. i) q^{51} +(31056.1 - 53790.7i) q^{52} +(104730. - 181398. i) q^{53} +(-154878. - 268256. i) q^{54} +1.32586e6 q^{55} +(-1.08918e6 - 306073. i) q^{56} -295509. q^{57} +(827745. + 1.43370e6i) q^{58} +(-722809. + 1.25194e6i) q^{59} +(37051.5 - 64175.1i) q^{60} +(-923534. - 1.59961e6i) q^{61} +341467. q^{62} +(483044. + 1.89451e6i) q^{63} +1.45194e6 q^{64} +(504478. + 873781. i) q^{65} +(102994. - 178391. i) q^{66} +(525579. - 910330. i) q^{67} +(-358440. - 620836. i) q^{68} +616792. q^{69} +(-3.72840e6 + 3.63889e6i) q^{70} -989653. q^{71} +(-1.34295e6 - 2.32606e6i) q^{72} +(-2.02831e6 + 3.51313e6i) q^{73} +(1.17495e6 - 2.03508e6i) q^{74} +(378918. + 656305. i) q^{75} +1.46376e6 q^{76} +(-1.87498e6 + 1.82996e6i) q^{77} +156753. q^{78} +(968043. + 1.67670e6i) q^{79} +(4.40952e6 - 7.63752e6i) q^{80} +(-2.28515e6 + 3.95800e6i) q^{81} +(-500440. - 866788. i) q^{82} -5.21053e6 q^{83} +(36178.4 + 141893. i) q^{84} +1.16451e7 q^{85} +(-6.48710e6 - 1.12360e7i) q^{86} +(-377923. + 654582. i) q^{87} +(1.79964e6 - 3.11706e6i) q^{88} +(2.14374e6 + 3.71307e6i) q^{89} -1.23684e7 q^{90} +(-1.91941e6 - 539381. i) q^{91} -3.05519e6 q^{92} +(77951.8 + 135016. i) q^{93} +(-4.49229e6 + 7.78087e6i) q^{94} +(-1.18887e7 + 2.05919e7i) q^{95} +(-229679. - 397816. i) q^{96} +4.56137e6 q^{97} +(250117. - 1.02920e7i) q^{98} -6.21994e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 58 q - 31 q^{2} - 1893 q^{4} + 48 q^{5} - 4602 q^{6} + 85 q^{7} + 11436 q^{8} - 25535 q^{9}+O(q^{10}) \) 58 * q - 31 * q^2 - 1893 * q^4 + 48 * q^5 - 4602 * q^6 + 85 * q^7 + 11436 * q^8 - 25535 * q^9	\( 58 q - 31 q^{2} - 1893 q^{4} + 48 q^{5} - 4602 q^{6} + 85 q^{7} + 11436 q^{8} - 25535 q^{9} + 3029 q^{10} - 15843 q^{11} + 10995 q^{12} - 127426 q^{13} - 65720 q^{14} + 115668 q^{15} - 154909 q^{16} + 43475 q^{17} - 67288 q^{18} + 64641 q^{19} + 40146 q^{20} - 321354 q^{21} + 170964 q^{22} - 96894 q^{23} + 501382 q^{24} - 637413 q^{25} + 68107 q^{26} + 156816 q^{27} - 877133 q^{28} + 155846 q^{29} - 335448 q^{30} + 393806 q^{31} - 1827215 q^{32} + 299052 q^{33} - 38692 q^{34} - 133704 q^{35} + 5417220 q^{36} - 597180 q^{37} - 502034 q^{38} + 1223016 q^{40} - 1436280 q^{41} - 2542432 q^{42} + 3496372 q^{43} - 2679210 q^{44} - 2509582 q^{45} + 2358719 q^{46} + 2368643 q^{47} - 843698 q^{48} + 995403 q^{49} + 3451796 q^{50} - 2396956 q^{51} + 4158921 q^{52} - 1919163 q^{53} - 4029674 q^{54} + 6075808 q^{55} + 3653181 q^{56} + 11452960 q^{57} - 4051049 q^{58} + 48733 q^{59} - 2792030 q^{60} + 1417921 q^{61} - 10244784 q^{62} + 7636291 q^{63} + 30707792 q^{64} - 105456 q^{65} - 22397813 q^{66} - 7025007 q^{67} + 5107354 q^{68} - 19729612 q^{69} - 13744304 q^{70} + 29267486 q^{71} - 7267524 q^{72} - 2417490 q^{73} + 2601511 q^{74} + 17567528 q^{75} - 19814476 q^{76} - 824982 q^{77} + 10110594 q^{78} - 7837082 q^{79} - 7428483 q^{80} - 24976533 q^{81} - 11520562 q^{82} - 38573688 q^{83} - 14286428 q^{84} + 41189436 q^{85} + 17943598 q^{86} - 37502020 q^{87} - 2949879 q^{88} + 15969588 q^{89} - 114635026 q^{90} - 186745 q^{91} + 83440638 q^{92} - 14525204 q^{93} - 30315990 q^{94} - 8678760 q^{95} + 23478593 q^{96} - 14169276 q^{97} + 14221151 q^{98} + 83443706 q^{99}+O(q^{100}) \) 58 * q - 31 * q^2 - 1893 * q^4 + 48 * q^5 - 4602 * q^6 + 85 * q^7 + 11436 * q^8 - 25535 * q^9 + 3029 * q^10 - 15843 * q^11 + 10995 * q^12 - 127426 * q^13 - 65720 * q^14 + 115668 * q^15 - 154909 * q^16 + 43475 * q^17 - 67288 * q^18 + 64641 * q^19 + 40146 * q^20 - 321354 * q^21 + 170964 * q^22 - 96894 * q^23 + 501382 * q^24 - 637413 * q^25 + 68107 * q^26 + 156816 * q^27 - 877133 * q^28 + 155846 * q^29 - 335448 * q^30 + 393806 * q^31 - 1827215 * q^32 + 299052 * q^33 - 38692 * q^34 - 133704 * q^35 + 5417220 * q^36 - 597180 * q^37 - 502034 * q^38 + 1223016 * q^40 - 1436280 * q^41 - 2542432 * q^42 + 3496372 * q^43 - 2679210 * q^44 - 2509582 * q^45 + 2358719 * q^46 + 2368643 * q^47 - 843698 * q^48 + 995403 * q^49 + 3451796 * q^50 - 2396956 * q^51 + 4158921 * q^52 - 1919163 * q^53 - 4029674 * q^54 + 6075808 * q^55 + 3653181 * q^56 + 11452960 * q^57 - 4051049 * q^58 + 48733 * q^59 - 2792030 * q^60 + 1417921 * q^61 - 10244784 * q^62 + 7636291 * q^63 + 30707792 * q^64 - 105456 * q^65 - 22397813 * q^66 - 7025007 * q^67 + 5107354 * q^68 - 19729612 * q^69 - 13744304 * q^70 + 29267486 * q^71 - 7267524 * q^72 - 2417490 * q^73 + 2601511 * q^74 + 17567528 * q^75 - 19814476 * q^76 - 824982 * q^77 + 10110594 * q^78 - 7837082 * q^79 - 7428483 * q^80 - 24976533 * q^81 - 11520562 * q^82 - 38573688 * q^83 - 14286428 * q^84 + 41189436 * q^85 + 17943598 * q^86 - 37502020 * q^87 - 2949879 * q^88 + 15969588 * q^89 - 114635026 * q^90 - 186745 * q^91 + 83440638 * q^92 - 14525204 * q^93 - 30315990 * q^94 - 8678760 * q^95 + 23478593 * q^96 - 14169276 * q^97 + 14221151 * q^98 + 83443706 * q^99

Introduction

L-functions

Modular forms

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