LMFDB - Embedded newform 76.8.f.a.27.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,8,Mod(27,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("76.27");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	76.f (of order $6$, 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:	$23.7412619368$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$68$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			27.16
Character	$\chi$	$=$	76.27
Dual form			76.8.f.a.31.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-8.08949 + 7.90950i) q^{2} +(43.0241 - 74.5200i) q^{3} +(2.87975 - 127.968i) q^{4} +(-29.6094 + 51.2850i) q^{5} +(241.372 + 943.128i) q^{6} +1634.91i q^{7} +(988.864 + 1057.97i) q^{8} +(-2608.65 - 4518.32i) q^{9} +O(q^{10})$	\(q+(-8.08949 + 7.90950i) q^{2} +(43.0241 - 74.5200i) q^{3} +(2.87975 - 127.968i) q^{4} +(-29.6094 + 51.2850i) q^{5} +(241.372 + 943.128i) q^{6} +1634.91i q^{7} +(988.864 + 1057.97i) q^{8} +(-2608.65 - 4518.32i) q^{9} +(-166.114 - 649.066i) q^{10} -2666.21i q^{11} +(-9412.25 - 5720.30i) q^{12} +(-7336.20 + 4235.56i) q^{13} +(-12931.3 - 13225.6i) q^{14} +(2547.84 + 4412.99i) q^{15} +(-16367.4 - 737.029i) q^{16} +(1288.71 - 2232.11i) q^{17} +(56840.3 + 15917.8i) q^{18} +(-29888.7 + 732.515i) q^{19} +(6477.56 + 3936.74i) q^{20} +(121834. + 70340.7i) q^{21} +(21088.4 + 21568.3i) q^{22} +(-59079.7 + 34109.7i) q^{23} +(121385. - 28171.8i) q^{24} +(37309.1 + 64621.2i) q^{25} +(25845.0 - 92289.2i) q^{26} -260753. q^{27} +(209216. + 4708.14i) q^{28} +(-134287. + 77530.7i) q^{29} +(-55515.3 - 15546.7i) q^{30} +65344.0 q^{31} +(138234. - 123496. i) q^{32} +(-198686. - 114711. i) q^{33} +(7229.85 + 28249.6i) q^{34} +(-83846.6 - 48408.8i) q^{35} +(-585711. + 320812. i) q^{36} +264441. i q^{37} +(235991. - 242330. i) q^{38} +728925. i q^{39} +(-83537.7 + 19388.0i) q^{40} +(547020. + 315822. i) q^{41} +(-1.54193e6 + 394623. i) q^{42} +(-189982. - 109686. i) q^{43} +(-341188. - 7678.01i) q^{44} +308963. q^{45} +(208134. - 743220. i) q^{46} +(14898.6 - 8601.71i) q^{47} +(-759117. + 1.18799e6i) q^{48} -1.84940e6 q^{49} +(-812932. - 227657. i) q^{50} +(-110891. - 192069. i) q^{51} +(520888. + 950994. i) q^{52} +(1.28664e6 - 742840. i) q^{53} +(2.10936e6 - 2.06242e6i) q^{54} +(136737. + 78944.9i) q^{55} +(-1.72969e6 + 1.61671e6i) q^{56} +(-1.23135e6 + 2.25882e6i) q^{57} +(473085. - 1.68933e6i) q^{58} +(-955553. + 1.65507e6i) q^{59} +(572057. - 313333. i) q^{60} +(473882. + 820787. i) q^{61} +(-528600. + 516838. i) q^{62} +(7.38706e6 - 4.26492e6i) q^{63} +(-141450. + 2.09238e6i) q^{64} -501650. i q^{65} +(2.51458e6 - 643549. i) q^{66} +(-1.77345e6 - 3.07171e6i) q^{67} +(-281926. - 171341. i) q^{68} +5.87016e6i q^{69} +(1.06117e6 - 271581. i) q^{70} +(-646442. + 1.11967e6i) q^{71} +(2.20065e6 - 7.22788e6i) q^{72} +(2.29276e6 - 3.97118e6i) q^{73} +(-2.09160e6 - 2.13919e6i) q^{74} +6.42076e6 q^{75} +(7666.20 + 3.82690e6i) q^{76} +4.35902e6 q^{77} +(-5.76543e6 - 5.89664e6i) q^{78} +(-328330. + 568685. i) q^{79} +(522428. - 817580. i) q^{80} +(-5.51354e6 + 9.54973e6i) q^{81} +(-6.92311e6 + 1.77181e6i) q^{82} +2.78336e6i q^{83} +(9.35218e6 - 1.53882e7i) q^{84} +(76315.8 + 132183. i) q^{85} +(2.40442e6 - 615357. i) q^{86} +1.33428e7i q^{87} +(2.82077e6 - 2.63652e6i) q^{88} +(-7.04611e6 + 4.06807e6i) q^{89} +(-2.49935e6 + 2.44374e6i) q^{90} +(-6.92477e6 - 1.19941e7i) q^{91} +(4.19480e6 + 7.65851e6i) q^{92} +(2.81137e6 - 4.86943e6i) q^{93} +(-52486.9 + 187424. i) q^{94} +(847421. - 1.55453e6i) q^{95} +(-3.25553e6 - 1.56145e7i) q^{96} +(-1.14343e7 - 6.60157e6i) q^{97} +(1.49607e7 - 1.46278e7i) q^{98} +(-1.20468e7 + 6.95521e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 3 q^{2} - 27 q^{4} - 2 q^{5} + 309 q^{6} - 45540 q^{9}+O(q^{10}) $ 136 * q - 3 * q^2 - 27 * q^4 - 2 * q^5 + 309 * q^6 - 45540 * q^9	$ 136 q - 3 q^{2} - 27 q^{4} - 2 q^{5} + 309 q^{6} - 45540 q^{9} - 19464 q^{10} - 10602 q^{13} + 13602 q^{14} + 6525 q^{16} - 23974 q^{17} - 91316 q^{20} + 54264 q^{21} + 381 q^{22} - 51631 q^{24} - 937502 q^{25} + 172188 q^{26} - 165428 q^{28} - 6 q^{29} - 454352 q^{30} + 573507 q^{32} - 182106 q^{33} - 629706 q^{34} - 277130 q^{36} - 759906 q^{38} - 627504 q^{40} - 1873020 q^{41} + 332080 q^{42} - 358069 q^{44} + 321240 q^{45} - 7221687 q^{48} - 15750664 q^{49} + 2848050 q^{52} - 1027650 q^{53} + 4352085 q^{54} - 137426 q^{57} + 10387724 q^{58} + 1607094 q^{60} + 5318582 q^{61} + 3394376 q^{62} - 1319538 q^{64} + 2439607 q^{66} - 87756 q^{68} - 17825238 q^{70} + 26155014 q^{72} + 299212 q^{73} + 1895842 q^{74} + 29672379 q^{76} + 907280 q^{77} + 7456734 q^{78} + 5489562 q^{80} - 11065208 q^{81} + 1288975 q^{82} + 6118214 q^{85} + 16831518 q^{86} - 17728542 q^{89} + 52167894 q^{90} + 10184840 q^{92} - 3299132 q^{93} - 68841730 q^{96} - 9435888 q^{97} - 35100021 q^{98}+O(q^{100}) $ 136 * q - 3 * q^2 - 27 * q^4 - 2 * q^5 + 309 * q^6 - 45540 * q^9 - 19464 * q^10 - 10602 * q^13 + 13602 * q^14 + 6525 * q^16 - 23974 * q^17 - 91316 * q^20 + 54264 * q^21 + 381 * q^22 - 51631 * q^24 - 937502 * q^25 + 172188 * q^26 - 165428 * q^28 - 6 * q^29 - 454352 * q^30 + 573507 * q^32 - 182106 * q^33 - 629706 * q^34 - 277130 * q^36 - 759906 * q^38 - 627504 * q^40 - 1873020 * q^41 + 332080 * q^42 - 358069 * q^44 + 321240 * q^45 - 7221687 * q^48 - 15750664 * q^49 + 2848050 * q^52 - 1027650 * q^53 + 4352085 * q^54 - 137426 * q^57 + 10387724 * q^58 + 1607094 * q^60 + 5318582 * q^61 + 3394376 * q^62 - 1319538 * q^64 + 2439607 * q^66 - 87756 * q^68 - 17825238 * q^70 + 26155014 * q^72 + 299212 * q^73 + 1895842 * q^74 + 29672379 * q^76 + 907280 * q^77 + 7456734 * q^78 + 5489562 * q^80 - 11065208 * q^81 + 1288975 * q^82 + 6118214 * q^85 + 16831518 * q^86 - 17728542 * q^89 + 52167894 * q^90 + 10184840 * q^92 - 3299132 * q^93 - 68841730 * q^96 - 9435888 * q^97 - 35100021 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−8.08949	+	7.90950i	−0.715017	+	0.699107i
$2$	−8.08949	+	7.90950i	−0.715017	+	0.699107i
$3$	43.0241	−	74.5200i	0.920000	−	1.59349i	0.120589	−	0.992703i	$-0.461522\pi$
$3$	43.0241	−	74.5200i	0.920000	−	1.59349i	0.799411	−	0.600784i	$-0.205145\pi$
$4$	2.87975	−	127.968i	0.0224980	−	0.999747i
$5$	−29.6094	+	51.2850i	−0.105934	+	0.183483i	−0.914119	−	0.405445i	$-0.867117\pi$
$5$	−29.6094	+	51.2850i	−0.105934	+	0.183483i	0.808185	+	0.588928i	$0.200450\pi$
$6$	241.372	+	943.128i	0.456203	+	1.78255i
$7$			1634.91i			1.80157i	0.434264	+	0.900786i	$0.357009\pi$
$7$			1634.91i			1.80157i	−0.434264	+	0.900786i	$0.642991\pi$
$8$	988.864	+	1057.97i	0.682844	+	0.730564i
$9$	−2608.65	−	4518.32i	−1.19280	−	2.06599i
$10$	−166.114	−	649.066i	−0.0525297	−	0.205253i
$11$		−	2666.21i		−	0.603976i	−0.953312	−	0.301988i	$-0.902350\pi$
$11$		−	2666.21i		−	0.603976i	0.953312	−	0.301988i	$-0.0976502\pi$
$12$	−9412.25	−	5720.30i	−1.57239	−	0.955617i
$13$	−7336.20	+	4235.56i	−0.926125	+	0.534699i	−0.885584	−	0.464479i	$-0.846242\pi$
$13$	−7336.20	+	4235.56i	−0.926125	+	0.534699i	−0.0405412	+	0.999178i	$0.512908\pi$
$14$	−12931.3	−	13225.6i	−1.25949	−	1.28815i
$15$	2547.84	+	4412.99i	0.194918	+	0.337609i
$16$	−16367.4	−	737.029i	−0.998988	−	0.0449847i
$17$	1288.71	−	2232.11i	0.0636184	−	0.110190i	−0.832462	−	0.554082i	$-0.813069\pi$
$17$	1288.71	−	2232.11i	0.0636184	−	0.110190i	0.896080	+	0.443892i	$0.146403\pi$
$18$	56840.3	+	15917.8i	2.29722	+	0.643323i
$19$	−29888.7	+	732.515i	−0.999700	+	0.0245007i
$19$	−29888.7	+	732.515i	−0.999700	+	0.0245007i
$20$	6477.56	+	3936.74i	0.181053	+	0.110035i
$21$	121834.	+	70340.7i	2.87078	+	1.65745i
$22$	21088.4	+	21568.3i	0.422244	+	0.431853i
$23$	−59079.7	+	34109.7i	−1.01249	+	0.584561i	−0.911920	−	0.410369i	$-0.865400\pi$
$23$	−59079.7	+	34109.7i	−1.01249	+	0.584561i	−0.100570	+	0.994930i	$0.532067\pi$
$24$	121385.	−	28171.8i	1.79236	−	0.415983i
$25$	37309.1	+	64621.2i	0.477556	+	0.827151i
$26$	25845.0	−	92289.2i	0.288383	−	1.02978i
$27$	−260753.			−2.54950
$28$	209216.	+	4708.14i	1.80112	+	0.0405318i
$29$	−134287.	+	77530.7i	−1.02245	+	0.590310i	−0.914812	−	0.403880i	$-0.867661\pi$
$29$	−134287.	+	77530.7i	−1.02245	+	0.590310i	−0.107636	+	0.994190i	$0.534328\pi$
$30$	−55515.3	−	15546.7i	−0.375395	−	0.105127i
$31$	65344.0			0.393949			0.196974	−	0.980409i	$-0.436888\pi$
$31$	65344.0			0.393949			0.196974	+	0.980409i	$0.436888\pi$
$32$	138234.	−	123496.i	0.745742	−	0.666235i
$33$	−198686.	−	114711.i	−0.962428	−	0.555658i
$34$	7229.85	+	28249.6i	0.0315466	+	0.123264i
$35$	−83846.6	−	48408.8i	−0.330558	−	0.190848i
$36$	−585711.	+	320812.i	−2.09230	+	1.14602i
$37$			264441.i			0.858268i	0.903241	+	0.429134i	$0.141181\pi$
$37$			264441.i			0.858268i	−0.903241	+	0.429134i	$0.858819\pi$
$38$	235991.	−	242330.i	0.697674	−	0.716416i
$39$			728925.i			1.96769i
$40$	−83537.7	+	19388.0i	−0.206382	+	0.0478986i
$41$	547020.	+	315822.i	1.23954	+	0.715648i	0.969000	−	0.247062i	$-0.0794650\pi$
$41$	547020.	+	315822.i	1.23954	+	0.715648i	0.270538	+	0.962709i	$0.412798\pi$
$42$	−1.54193e6	+	394623.i	−3.21139	+	0.821882i
$43$	−189982.	−	109686.i	−0.364395	−	0.210384i	0.306612	−	0.951835i	$-0.400805\pi$
$43$	−189982.	−	109686.i	−0.364395	−	0.210384i	−0.671007	+	0.741451i	$0.734138\pi$
$44$	−341188.	−	7678.01i	−0.603823	−	0.0135883i
$45$	308963.			0.505432
$46$	208134.	−	743220.i	0.315276	−	1.12581i
$47$	14898.6	−	8601.71i	0.0209316	−	0.0120849i	−0.489498	−	0.872005i	$-0.662820\pi$
$47$	14898.6	−	8601.71i	0.0209316	−	0.0120849i	0.510429	+	0.859920i	$0.329487\pi$
$48$	−759117.	+	1.18799e6i	−0.990751	+	1.55049i
$49$	−1.84940e6			−2.24566
$50$	−812932.	−	227657.i	−0.919728	−	0.257564i
$51$	−110891.	−	192069.i	−0.117058	−	0.202750i
$52$	520888.	+	950994.i	0.513727	+	0.937920i
$53$	1.28664e6	−	742840.i	1.18711	−	0.685378i	0.229460	−	0.973318i	$-0.426304\pi$
$53$	1.28664e6	−	742840.i	1.18711	−	0.685378i	0.957648	+	0.287941i	$0.0929705\pi$
$54$	2.10936e6	−	2.06242e6i	1.82294	−	1.78238i
$55$	136737.	+	78944.9i	0.110819	+	0.0639815i
$56$	−1.72969e6	+	1.61671e6i	−1.31616	+	1.23019i
$57$	−1.23135e6	+	2.25882e6i	−0.880682	+	1.61555i
$58$	473085.	−	1.68933e6i	0.318377	−	1.13688i
$59$	−955553.	+	1.65507e6i	−0.605721	+	1.04914i	0.386216	+	0.922408i	$0.373782\pi$
$59$	−955553.	+	1.65507e6i	−0.605721	+	1.04914i	−0.991937	+	0.126731i	$0.959551\pi$
$60$	572057.	−	313333.i	0.341908	−	0.187274i
$61$	473882.	+	820787.i	0.267310	+	0.462995i	0.968166	−	0.250308i	$-0.0805318\pi$
$61$	473882.	+	820787.i	0.267310	+	0.462995i	−0.700856	+	0.713303i	$0.747199\pi$
$62$	−528600.	+	516838.i	−0.281680	+	0.275412i
$63$	7.38706e6	−	4.26492e6i	3.72203	−	2.14891i
$64$	−141450.	+	2.09238e6i	−0.0674486	+	0.997723i
$65$		−	501650.i		−	0.226571i
$66$	2.51458e6	−	643549.i	1.07662	−	0.275535i
$67$	−1.77345e6	−	3.07171e6i	−0.720372	−	1.24772i	−0.960851	−	0.277067i	$-0.910638\pi$
$67$	−1.77345e6	−	3.07171e6i	−0.720372	−	1.24772i	0.240478	−	0.970655i	$-0.422696\pi$
$68$	−281926.	−	171341.i	−0.108731	−	0.0660814i
$69$			5.87016e6i			2.15119i
$70$	1.06117e6	−	271581.i	0.369777	−	0.0946360i
$71$	−646442.	+	1.11967e6i	−0.214351	+	0.371267i	−0.953072	−	0.302745i	$-0.902097\pi$
$71$	−646442.	+	1.11967e6i	−0.214351	+	0.371267i	0.738721	+	0.674012i	$0.235430\pi$
$72$	2.20065e6	−	7.22788e6i	0.694843	−	2.28217i
$73$	2.29276e6	−	3.97118e6i	0.689809	−	1.19478i	−0.282091	−	0.959388i	$-0.591028\pi$
$73$	2.29276e6	−	3.97118e6i	0.689809	−	1.19478i	0.971900	−	0.235396i	$-0.0756387\pi$
$74$	−2.09160e6	−	2.13919e6i	−0.600021	−	0.613676i
$75$	6.42076e6			1.75741
$76$	7666.20	+	3.82690e6i	0.00200324	+	0.999998i
$77$	4.35902e6			1.08811
$78$	−5.76543e6	−	5.89664e6i	−1.37563	−	1.40693i
$79$	−328330.	+	568685.i	−0.0749232	+	0.129771i	−0.901053	−	0.433709i	$-0.857204\pi$
$79$	−328330.	+	568685.i	−0.0749232	+	0.129771i	0.826130	+	0.563480i	$0.190538\pi$
$80$	522428.	−	817580.i	0.114081	−	0.178532i
$81$	−5.51354e6	+	9.54973e6i	−1.15274	+	1.99661i
$82$	−6.92311e6	+	1.77181e6i	−1.38661	+	0.354870i
$83$			2.78336e6i			0.534313i	0.963653	+	0.267156i	$0.0860840\pi$
$83$			2.78336e6i			0.534313i	−0.963653	+	0.267156i	$0.913916\pi$
$84$	9.35218e6	−	1.53882e7i	1.72161	−	2.83276i
$85$	76315.8	+	132183.i	0.0134787	+	0.0233458i
$86$	2.40442e6	−	615357.i	0.407630	−	0.104324i
$87$			1.33428e7i			2.17234i
$88$	2.82077e6	−	2.63652e6i	0.441243	−	0.412421i
$89$	−7.04611e6	+	4.06807e6i	−1.05946	+	0.611679i	−0.925283	−	0.379278i	$-0.876172\pi$
$89$	−7.04611e6	+	4.06807e6i	−1.05946	+	0.611679i	−0.134177	+	0.990957i	$0.542839\pi$
$90$	−2.49935e6	+	2.44374e6i	−0.361392	+	0.353351i
$91$	−6.92477e6	−	1.19941e7i	−0.963298	−	1.66848i
$92$	4.19480e6	+	7.65851e6i	0.561634	+	1.02539i
$93$	2.81137e6	−	4.86943e6i	0.362433	−	0.627752i
$94$	−52486.9	+	187424.i	−0.00651783	+	0.0232743i
$95$	847421.	−	1.55453e6i	0.101407	−	0.186023i
$96$	−3.25553e6	−	1.56145e7i	−0.375554	−	1.80127i
$97$	−1.14343e7	−	6.60157e6i	−1.27206	−	0.734423i	−0.296683	−	0.954976i	$-0.595880\pi$
$97$	−1.14343e7	−	6.60157e6i	−1.27206	−	0.734423i	−0.975375	+	0.220553i	$0.929214\pi$
$98$	1.49607e7	−	1.46278e7i	1.60568	−	1.56996i
$99$	−1.20468e7	+	6.95521e6i	−1.24781	+	0.720423i
$100$	8.37686e6	−	4.58826e6i	0.837686	−	0.458826i
$101$	−16298.4	−	28229.7i	−0.00157406	−	0.00272635i	0.865237	−	0.501363i	$-0.167168\pi$
$101$	−16298.4	−	28229.7i	−0.00157406	−	0.00272635i	−0.866811	+	0.498636i	$0.833834\pi$
$102$	2.41622e6	+	676648.i	0.225443	+	0.0631338i
$103$	−1.09557e7			−0.987892			−0.493946	−	0.869493i	$-0.664446\pi$
$103$	−1.09557e7			−0.987892			−0.493946	+	0.869493i	$0.664446\pi$
$104$	−1.17356e7	−	3.57310e6i	−1.02303	−	0.311478i
$105$	−7.21485e6	+	4.16550e6i	−0.608226	+	0.351159i
$106$	−4.53275e6	+	1.61858e7i	−0.369650	+	1.31997i
$107$	−3.08903e6			−0.243769			−0.121884	−	0.992544i	$-0.538894\pi$
$107$	−3.08903e6			−0.243769			−0.121884	+	0.992544i	$0.538894\pi$
$108$	−750902.	+	3.33679e7i	−0.0573588	+	2.54886i
$109$	5.26238e6	+	3.03824e6i	0.389215	+	0.224713i	0.681820	−	0.731520i	$-0.261189\pi$
$109$	5.26238e6	+	3.03824e6i	0.389215	+	0.224713i	−0.292605	+	0.956233i	$0.594522\pi$
$110$	−1.73054e6	+	442893.i	−0.123968	+	0.0317267i
$111$	1.97061e7	+	1.13773e7i	1.36764	+	0.789606i
$112$	1.20498e6	−	2.67593e7i	0.0810431	−	1.79975i
$113$			1.13855e7i			0.742296i	0.928574	+	0.371148i	$0.121036\pi$
$113$			1.13855e7i			0.742296i	−0.928574	+	0.371148i	$0.878964\pi$
$114$	−7.90516e6	−	2.80121e7i	−0.499740	−	1.77084i
$115$		−	4.03987e6i		−	0.247700i
$116$	9.53470e6	+	1.74077e7i	0.567158	+	1.03547i
$117$	3.82752e7	+	2.20982e7i	2.20936	+	1.27558i
$118$	−5.36080e6	−	2.09466e7i	−0.300360	−	1.17362i
$119$	3.64930e6	+	2.10692e6i	0.198516	+	0.114613i
$120$	−2.14934e6	+	7.05938e6i	−0.113546	+	0.372934i
$121$	1.23785e7			0.635213
$122$	−1.03255e7	−	2.89159e6i	−0.514814	−	0.144171i
$123$	4.70702e7	−	2.71760e7i	2.28075	−	1.31679i
$124$	188174.	−	8.36191e6i	0.00886307	−	0.393849i
$125$	−9.04527e6			−0.414225
$126$	−2.60242e7	+	9.29290e7i	−1.15899	+	4.13861i
$127$	−1.38974e7	−	2.40710e7i	−0.602033	−	1.04275i	−0.992513	−	0.122140i	$-0.961024\pi$
$127$	−1.38974e7	−	2.40710e7i	−0.602033	−	1.04275i	0.390480	−	0.920611i	$-0.372309\pi$
$128$	−1.54054e7	−	1.80451e7i	−0.649288	−	0.760542i
$129$	−1.63476e7	+	9.43831e6i	−0.670488	+	0.387106i
$130$	3.96780e6	+	4.05809e6i	0.158397	+	0.162002i
$131$	5.79630e6	+	3.34650e6i	0.225269	+	0.130059i	0.608388	−	0.793640i	$-0.291817\pi$
$131$	5.79630e6	+	3.34650e6i	0.225269	+	0.130059i	−0.383119	+	0.923699i	$0.625150\pi$
$132$	−1.52515e7	+	2.50950e7i	−0.577170	+	0.949683i
$133$	−1.19760e6	−	4.88654e7i	−0.0441398	−	1.80103i
$134$	3.86419e7	+	1.08214e7i	1.38737	+	0.388524i
$135$	7.72074e6	−	1.33727e7i	0.270079	−	0.467791i
$136$	3.63586e6	−	843835.i	0.123943	−	0.0287654i
$137$	−4.48102e6	−	7.76135e6i	−0.148886	−	0.257879i	0.781930	−	0.623367i	$-0.214236\pi$
$137$	−4.48102e6	−	7.76135e6i	−0.148886	−	0.257879i	−0.930816	+	0.365488i	$0.880902\pi$
$138$	−4.64300e7	−	4.74866e7i	−1.50391	−	1.53813i
$139$	2.28447e7	−	1.31894e7i	0.721496	−	0.416556i	−0.0938072	−	0.995590i	$-0.529904\pi$
$139$	2.28447e7	−	1.31894e7i	0.721496	−	0.416556i	0.815303	+	0.579035i	$0.196570\pi$
$140$	−6.43622e6	+	1.05902e7i	−0.198236	+	0.326180i
$141$		−	1.48032e6i		−	0.0444723i
$142$	−3.62664e6	−	1.41706e7i	−0.106291	−	0.415316i
$143$	1.12929e7	+	1.95598e7i	0.322945	+	0.559357i
$144$	3.93668e7	+	7.58759e7i	1.09865	+	2.11756i
$145$		−	9.18255e6i		−	0.250136i
$146$	1.28627e7	+	5.02594e7i	0.342057	+	1.33654i
$147$	−7.95687e7	+	1.37817e8i	−2.06601	+	3.57843i
$148$	3.38399e7	+	761524.i	0.858050	+	0.0193093i
$149$	1.58956e7	−	2.75320e7i	0.393663	−	0.681845i	−0.599266	−	0.800550i	$-0.704541\pi$
$149$	1.58956e7	−	2.75320e7i	0.393663	−	0.681845i	0.992930	+	0.118705i	$0.0378742\pi$
$150$	−5.19407e7	+	5.07850e7i	−1.25657	+	1.22862i
$151$	−7.83494e7			−1.85189			−0.925947	−	0.377653i	$-0.876731\pi$
$151$	−7.83494e7			−1.85189			−0.925947	+	0.377653i	$0.876731\pi$
$152$	−3.03308e7	−	3.08970e7i	−0.700538	−	0.713615i
$153$	−1.34472e7			−0.303536
$154$	−3.52622e7	+	3.44776e7i	−0.778014	+	0.760703i
$155$	−1.93480e6	+	3.35117e6i	−0.0417325	+	0.0722829i
$156$	9.32788e7	+	2.09912e6i	1.96719	+	0.0442692i
$157$	−1.92101e7	+	3.32728e7i	−0.396169	+	0.686184i	−0.993250	−	0.115997i	$-0.962994\pi$
$157$	−1.92101e7	+	3.32728e7i	−0.396169	+	0.686184i	0.597081	+	0.802181i	$0.296327\pi$
$158$	−1.84199e6	−	7.19730e6i	−0.0371524	−	0.145168i
$159$		−	1.27840e8i		−	2.52219i
$160$	2.24047e6	+	1.07460e7i	0.0432433	+	0.207408i
$161$	−5.57663e7	−	9.65901e7i	−1.05313	−	1.82407i
$162$	−3.09318e7	−	1.20862e8i	−0.571614	−	2.23350i
$163$		−	2.87610e7i		−	0.520173i	−0.965585	−	0.260087i	$-0.916249\pi$
$163$		−	2.87610e7i		−	0.520173i	0.965585	−	0.260087i	$-0.0837511\pi$
$164$	4.19903e7	−	6.90914e7i	0.743354	−	1.22312i
$165$	1.17659e7	−	6.79307e6i	0.203907	−	0.117726i
$166$	−2.20150e7	−	2.25159e7i	−0.373542	−	0.382043i
$167$	−5.68377e7	−	9.84458e7i	−0.944341	−	1.63565i	−0.757065	−	0.653340i	$-0.773367\pi$
$167$	−5.68377e7	−	9.84458e7i	−0.944341	−	1.63565i	−0.187277	−	0.982307i	$-0.559966\pi$
$168$	4.60585e7	+	1.98454e8i	0.749424	+	3.22907i
$169$	4.50567e6	−	7.80405e6i	0.0718052	−	0.124370i
$170$	−1.66285e6	−	465672.i	−0.0259587	−	0.00726958i
$171$	8.12790e7	+	1.33136e8i	1.24306	+	2.03615i
$172$	−1.45834e7	+	2.39957e7i	−0.218529	+	0.359570i
$173$	6.41414e7	+	3.70321e7i	0.941840	+	0.543772i	0.890537	−	0.454911i	$-0.150329\pi$
$173$	6.41414e7	+	3.70321e7i	0.941840	+	0.543772i	0.0513037	+	0.998683i	$0.483662\pi$
$174$	−1.05535e8	−	1.07936e8i	−1.51870	−	1.55326i
$175$	−1.05650e8	+	6.09971e7i	−1.49017	+	0.860351i
$176$	−1.96507e6	+	4.36389e7i	−0.0271697	+	0.603365i
$177$	8.22237e7	+	1.42416e8i	1.11453	+	1.93042i
$178$	2.48230e7	−	8.86398e7i	0.329902	−	1.17804i
$179$	1.00224e7			0.130613			0.0653063	−	0.997865i	$-0.479198\pi$
$179$	1.00224e7			0.130613			0.0653063	+	0.997865i	$0.479198\pi$
$180$	889736.	−	3.95373e7i	0.0113712	−	0.505304i
$181$	6.03100e7	−	3.48200e7i	0.755987	−	0.436469i	−0.0718664	−	0.997414i	$-0.522896\pi$
$181$	6.03100e7	−	3.48200e7i	0.755987	−	0.436469i	0.827853	+	0.560945i	$0.189562\pi$
$182$	1.50885e8	+	4.22544e7i	1.85522	+	0.519543i
$183$	8.15534e7			0.983701
$184$	−9.45088e7	−	2.87747e7i	−1.11843	−	0.340525i
$185$	−1.35619e7	−	7.82995e6i	−0.157477	−	0.0909197i
$186$	1.57722e7	+	6.16277e7i	0.179720	+	0.702233i
$187$	−5.95126e6	−	3.43596e6i	−0.0665523	−	0.0384240i
$188$	−1.05784e6	−	1.93131e6i	−0.0116109	−	0.0211982i
$189$		−	4.26308e8i		−	4.59311i
$190$	5.44037e6	+	1.92781e7i	0.0575428	+	0.203904i
$191$			1.13023e8i			1.17368i	0.809703	+	0.586840i	$0.199628\pi$
$191$			1.13023e8i			1.17368i	−0.809703	+	0.586840i	$0.800372\pi$
$192$	1.49838e8	+	1.00564e8i	1.52781	+	1.02538i
$193$	−1.22910e7	−	7.09623e6i	−0.123066	−	0.0710522i	0.437203	−	0.899363i	$-0.355969\pi$
$193$	−1.22910e7	−	7.09623e6i	−0.123066	−	0.0710522i	−0.560269	+	0.828311i	$0.689302\pi$
$194$	1.44712e8	−	3.70359e7i	1.42298	−	0.364180i
$195$	−3.73830e7	−	2.15831e7i	−0.361038	−	0.208445i
$196$	−5.32580e6	+	2.36663e8i	−0.0505229	+	2.24509i
$197$	6.31973e7			0.588934			0.294467	−	0.955662i	$-0.404858\pi$
$197$	6.31973e7			0.588934			0.294467	+	0.955662i	$0.404858\pi$
$198$	4.24401e7	−	1.51548e8i	0.388551	−	1.38747i
$199$	−1.86301e7	+	1.07561e7i	−0.167583	+	0.0967540i	−0.581446	−	0.813585i	$-0.697513\pi$
$199$	−1.86301e7	+	1.07561e7i	−0.167583	+	0.0967540i	0.413863	+	0.910339i	$0.364179\pi$
$200$	−3.14737e7	+	1.03373e8i	−0.278191	+	0.913701i
$201$	−3.05205e8			−2.65097
$202$	355128.	+	99451.5i	0.00303149	+	0.000848949i
$203$	−1.26756e8	−	2.19548e8i	−1.06349	−	1.84201i
$204$	−2.48979e7	+	1.36373e7i	−0.205333	+	0.112467i
$205$	−3.23939e7	+	1.87026e7i	−0.262618	+	0.151623i
$206$	8.86259e7	−	8.66540e7i	0.706359	−	0.690642i
$207$	3.08237e8	+	1.77961e8i	2.41540	+	1.39453i
$208$	1.23196e8	−	6.39182e7i	0.949241	−	0.492496i
$209$	1.95304e6	+	7.96895e7i	0.0147978	+	0.603795i
$210$	2.54175e7	−	9.07626e7i	0.189394	−	0.676300i
$211$	1.41621e7	−	2.45296e7i	0.103786	−	0.179763i	−0.809455	−	0.587181i	$-0.800238\pi$
$211$	1.41621e7	−	2.45296e7i	0.103786	−	0.179763i	0.913242	+	0.407418i	$0.133571\pi$
$212$	−9.13543e7	−	1.66787e8i	−0.658496	−	1.20223i
$213$	5.56252e7	+	9.63457e7i	0.394406	+	0.683131i
$214$	2.49886e7	−	2.44326e7i	0.174299	−	0.170421i
$215$	1.12505e7	−	6.49549e6i	0.0772037	−	0.0445736i
$216$	−2.57849e8	−	2.75869e8i	−1.74091	−	1.86258i
$217$			1.06832e8i			0.709727i
$218$	−6.66009e7	+	1.70450e7i	−0.435394	+	0.111429i
$219$	−1.97288e8	−	3.41713e8i	−1.26925	−	2.19840i
$220$	1.04962e7	−	1.72705e7i	0.0664586	−	0.109352i
$221$			2.18336e7i			0.136067i
$222$	−2.49402e8	+	6.38287e7i	−1.52990	+	0.391544i
$223$	−6.97549e7	+	1.20819e8i	−0.421219	+	0.729572i	−0.996059	−	0.0886936i	$-0.971731\pi$
$223$	−6.97549e7	+	1.20819e8i	−0.421219	+	0.729572i	0.574840	+	0.818266i	$0.305064\pi$
$224$	2.01905e8	+	2.26000e8i	1.20027	+	1.34351i
$225$	1.94653e8	−	3.37149e8i	1.13926	−	1.97325i
$226$	−9.00535e7	−	9.21028e7i	−0.518945	−	0.530754i
$227$	2.62502e8			1.48951			0.744754	−	0.667339i	$-0.232567\pi$
$227$	2.62502e8			1.48951			0.744754	+	0.667339i	$0.232567\pi$
$228$	2.85510e8	+	1.64078e8i	1.59533	+	0.916806i
$229$	−1.78555e8			−0.982533			−0.491267	−	0.871009i	$-0.663466\pi$
$229$	−1.78555e8			−0.982533			−0.491267	+	0.871009i	$0.663466\pi$
$230$	3.19533e7	+	3.26805e7i	0.173169	+	0.177109i
$231$	1.87543e8	−	3.24834e8i	1.00106	−	1.73388i
$232$	−2.14817e8	−	6.54044e7i	−1.12943	−	0.343874i
$233$	−1.26779e8	+	2.19587e8i	−0.656599	+	1.13726i	0.324891	+	0.945752i	$0.394672\pi$
$233$	−1.26779e8	+	2.19587e8i	−0.656599	+	1.13726i	−0.981490	+	0.191512i	$0.938661\pi$
$234$	−4.84413e8	+	1.23974e8i	−2.47150	+	0.632524i
$235$			1.01877e6i			0.00512079i
$236$	2.09043e8	+	1.27046e8i	1.03525	+	0.629171i
$237$	2.82523e7	+	4.89344e7i	0.137859	+	0.238778i
$238$	−4.61857e7	+	1.18202e7i	−0.222069	+	0.0568335i
$239$			1.79084e8i			0.848526i	0.905539	+	0.424263i	$0.139467\pi$
$239$			1.79084e8i			0.848526i	−0.905539	+	0.424263i	$0.860533\pi$
$240$	−3.84491e7	−	7.41071e7i	−0.179534	−	0.346035i
$241$	1.20171e8	−	6.93808e7i	0.553019	−	0.319286i	−0.197320	−	0.980339i	$-0.563224\pi$
$241$	1.20171e8	−	6.93808e7i	0.553019	−	0.319286i	0.750339	+	0.661053i	$0.229890\pi$
$242$	−1.00136e8	+	9.79077e7i	−0.454188	+	0.444082i
$243$	1.89297e8	+	3.27873e8i	0.846297	+	1.46583i
$244$	1.06399e8	−	5.82778e7i	0.468892	−	0.256826i
$245$	5.47596e7	−	9.48464e7i	0.237891	−	0.412040i
$246$	−1.65825e8	+	5.92141e8i	−0.710196	+	2.53602i
$247$	2.16167e8	−	1.31969e8i	0.912747	−	0.557229i
$248$	6.46163e7	+	6.91320e7i	0.269005	+	0.287805i
$249$	2.07416e8	+	1.19752e8i	0.851420	+	0.491568i
$250$	7.31717e7	−	7.15436e7i	0.296178	−	0.289588i
$251$	1.80066e8	−	1.03961e8i	0.718745	−	0.414968i	−0.0955456	−	0.995425i	$-0.530460\pi$
$251$	1.80066e8	−	1.03961e8i	0.718745	−	0.414968i	0.814291	+	0.580457i	$0.197126\pi$
$252$	−5.24499e8	−	9.57586e8i	−2.06463	−	3.76943i
$253$	9.09435e7	+	1.57519e8i	0.353061	+	0.611520i
$254$	3.02812e8	+	8.48006e7i	1.15946	+	0.324699i
$255$	1.31337e7			0.0496016
$256$	2.67349e8	+	2.41265e7i	0.995953	+	0.0898783i
$257$	−4.52085e8	+	2.61011e8i	−1.66132	+	0.959166i	−0.689240	+	0.724533i	$0.742055\pi$
$257$	−4.52085e8	+	2.61011e8i	−1.66132	+	0.959166i	−0.972084	+	0.234632i	$0.924611\pi$
$258$	5.75917e7	−	2.05653e8i	0.208781	−	0.745530i
$259$	−4.32338e8			−1.54623
$260$	−6.41949e7	−	1.44463e6i	−0.226514	−	0.00509740i
$261$	7.00617e8	+	4.04501e8i	2.43915	+	1.40824i
$262$	−7.33582e7	+	1.87744e7i	−0.251996	+	0.0644927i
$263$	1.94202e6	+	1.12123e6i	0.00658278	+	0.00380057i	0.503288	−	0.864119i	$-0.332124\pi$
$263$	1.94202e6	+	1.12123e6i	0.00658278	+	0.00380057i	−0.496705	+	0.867919i	$0.665457\pi$
$264$	−7.51120e7	−	3.23638e8i	−0.251244	−	1.08254i
$265$			8.79803e7i			0.290419i
$266$	3.96189e8	+	3.85824e8i	1.29067	+	1.25691i
$267$			7.00102e8i			2.25098i
$268$	−3.98186e8	+	2.18098e8i	−1.26361	+	0.692119i
$269$	4.22102e7	+	2.43701e7i	0.132216	+	0.0763350i	0.564649	−	0.825331i	$-0.309011\pi$
$269$	4.22102e7	+	2.43701e7i	0.132216	+	0.0763350i	−0.432433	+	0.901666i	$0.642345\pi$
$270$	4.33146e7	+	1.69246e8i	0.133925	+	0.523292i
$271$	−3.62214e8	−	2.09124e8i	−1.10553	−	0.638281i	−0.167865	−	0.985810i	$-0.553687\pi$
$271$	−3.62214e8	−	2.09124e8i	−1.10553	−	0.638281i	−0.937669	+	0.347529i	$0.887021\pi$
$272$	−2.27379e7	+	3.55840e7i	−0.0685109	+	0.107217i
$273$	−1.19173e9			−3.54494
$274$	9.76376e7	+	2.73428e7i	0.286741	+	0.0803001i
$275$	1.72294e8	−	9.94737e7i	0.499579	−	0.288432i
$276$	7.51190e8	+	1.69046e7i	2.15064	+	0.0483975i
$277$	6.98664e7			0.197510			0.0987551	−	0.995112i	$-0.468514\pi$
$277$	6.98664e7			0.197510			0.0987551	+	0.995112i	$0.468514\pi$
$278$	−8.04806e7	+	2.87386e8i	−0.224664	+	0.802247i
$279$	−1.70460e8	−	2.95245e8i	−0.469902	−	0.813894i
$280$	−3.16977e7	−	1.36577e8i	−0.0862928	−	0.371813i
$281$	2.28616e8	−	1.31992e8i	0.614660	−	0.354874i	−0.160127	−	0.987096i	$-0.551190\pi$
$281$	2.28616e8	−	1.31992e8i	0.614660	−	0.354874i	0.774787	+	0.632222i	$0.217857\pi$
$282$	1.17086e7	+	1.19751e7i	0.0310909	+	0.0317985i
$283$	−2.53639e8	−	1.46438e8i	−0.665217	−	0.384063i	0.129045	−	0.991639i	$-0.458809\pi$
$283$	−2.53639e8	−	1.46438e8i	−0.665217	−	0.384063i	−0.794262	+	0.607576i	$0.792142\pi$
$284$	1.41420e8	+	8.59480e7i	0.366350	+	0.222649i
$285$	−7.93843e7	−	1.30032e8i	−0.203132	−	0.332732i
$286$	−2.46062e8	−	6.89082e7i	−0.621962	−	0.174177i
$287$	−5.16342e8	+	8.94330e8i	−1.28929	+	2.23312i
$288$	−9.18597e8	−	3.02426e8i	−2.26596	−	0.746011i
$289$	2.01848e8	+	3.49611e8i	0.491905	+	0.852005i
$290$	7.26294e7	+	7.42822e7i	0.174872	+	0.178851i
$291$	−9.83898e8	+	5.68054e8i	−2.34059	+	1.35134i
$292$	−5.01579e8	−	3.04835e8i	−1.17896	−	0.716514i
$293$			2.13589e8i			0.496068i	0.968751	+	0.248034i	$0.0797845\pi$
$293$			2.13589e8i			0.496068i	−0.968751	+	0.248034i	$0.920216\pi$
$294$	−4.46393e8	−	1.74422e9i	−1.02448	−	4.00300i
$295$	−5.65868e7	−	9.80111e7i	−0.128333	−	0.222279i
$296$	−2.79771e8	+	2.61496e8i	−0.627020	+	0.586063i
$297$			6.95221e8i			1.53984i
$298$	8.91768e7	+	3.48446e8i	0.195207	+	0.762744i
$299$	2.88947e8	−	5.00471e8i	0.625128	−	1.08275i
$300$	1.84902e7	−	8.21650e8i	0.0395382	−	1.75696i
$301$	1.79327e8	−	3.10604e8i	0.379021	−	0.656484i
$302$	6.33807e8	−	6.19704e8i	1.32414	−	1.29467i
$303$	−2.80490e6			−0.00579253
$304$	4.89741e8	+	1.00395e7i	0.999790	+	0.0204953i
$305$	−5.61255e7			−0.113269
$306$	1.08781e8	−	1.06360e8i	0.217034	−	0.212204i
$307$	3.01821e8	−	5.22769e8i	0.595340	−	1.03116i	−0.398159	−	0.917317i	$-0.630351\pi$
$307$	3.01821e8	−	5.22769e8i	0.595340	−	1.03116i	0.993499	−	0.113843i	$-0.0363160\pi$
$308$	1.25529e7	−	5.57813e8i	0.0244802	−	1.08783i
$309$	−4.71359e8	+	8.16418e8i	−0.908860	+	1.57419i
$310$	−1.08545e7	−	4.24125e7i	−0.0206940	−	0.0808590i
$311$		−	1.40133e8i		−	0.264167i	−0.991239	−	0.132084i	$-0.957833\pi$
$311$		−	1.40133e8i		−	0.264167i	0.991239	−	0.132084i	$-0.0421667\pi$
$312$	−7.71181e8	+	7.20808e8i	−1.43752	+	1.34363i
$313$	7.56803e7	+	1.31082e8i	0.139501	+	0.241623i	0.927308	−	0.374299i	$-0.122117\pi$
$313$	7.56803e7	+	1.31082e8i	0.139501	+	0.241623i	−0.787807	+	0.615923i	$0.788783\pi$
$314$	−1.07772e8	−	4.21102e8i	−0.196449	−	0.767598i
$315$			5.05128e8i			0.910572i
$316$	7.18277e7	+	4.36533e7i	0.128052	+	0.0778238i
$317$	8.34537e8	−	4.81820e8i	1.47143	−	0.849528i	0.471941	−	0.881630i	$-0.343554\pi$
$317$	8.34537e8	−	4.81820e8i	1.47143	−	0.849528i	0.999485	+	0.0321025i	$0.0102203\pi$
$318$	1.01115e9	+	1.03416e9i	1.76328	+	1.80341i
$319$	2.06713e8	+	3.58037e8i	0.356533	+	0.617534i
$320$	−1.03119e8	−	6.92083e7i	−0.175920	−	0.118068i
$321$	−1.32903e8	+	2.30194e8i	−0.224267	+	0.388442i
$322$	1.21510e9	+	3.40281e8i	2.02823	+	0.567993i
$323$	−3.68827e7	+	6.76588e7i	−0.0608996	+	0.111716i
$324$	1.20618e9	+	7.33055e8i	1.97017	+	1.19737i
$325$	−5.47414e8	−	3.16050e8i	−0.884553	−	0.510697i
$326$	2.27485e8	+	2.32662e8i	0.363657	+	0.371933i
$327$	4.52819e8	−	2.61435e8i	0.716156	−	0.413473i
$328$	2.06798e8	+	8.91036e8i	0.323584	+	1.39424i
$329$	1.40630e7	+	2.43579e7i	0.0217718	+	0.0377098i
$330$	−4.14508e7	+	1.48015e8i	−0.0634941	+	0.226729i
$331$	9.52388e8			1.44350			0.721749	−	0.692155i	$-0.243339\pi$
$331$	9.52388e8			1.44350			0.721749	+	0.692155i	$0.243339\pi$
$332$	3.56180e8	+	8.01537e6i	0.534178	+	0.0120210i
$333$	1.19483e9	−	6.89835e8i	1.77317	−	1.02374i
$334$	1.23845e9	+	3.46819e8i	1.81871	+	0.509319i
$335$	2.10043e8			0.305247
$336$	−1.94226e9	−	1.24109e9i	−2.79331	−	1.78491i
$337$	−7.61206e8	−	4.39483e8i	−1.08342	−	0.625514i	−0.151604	−	0.988441i	$-0.548444\pi$
$337$	−7.61206e8	−	4.39483e8i	−1.08342	−	0.625514i	−0.931817	+	0.362927i	$0.881777\pi$
$338$	2.52775e7	+	9.87684e7i	0.0356062	+	0.139126i
$339$	8.48447e8	+	4.89851e8i	1.18284	+	0.682913i
$340$	1.71349e7	−	9.38529e6i	0.0236431	−	0.0129501i
$341$		−	1.74221e8i		−	0.237936i
$342$	−1.71054e9	−	4.34126e8i	−2.31229	−	0.586846i
$343$		−	1.67718e9i		−	2.24414i
$344$	−7.18216e7	−	3.09460e8i	−0.0951263	−	0.409874i
$345$	−3.01051e8	−	1.73812e8i	−0.394706	−	0.227884i
$346$	−8.11777e8	+	2.07756e8i	−1.05359	+	0.269642i
$347$	−2.85064e8	−	1.64582e8i	−0.366259	−	0.211460i	0.305564	−	0.952172i	$-0.401155\pi$
$347$	−2.85064e8	−	1.64582e8i	−0.366259	−	0.211460i	−0.671823	+	0.740712i	$0.734488\pi$
$348$	1.70744e9	+	3.84238e7i	2.17179	+	0.0488734i
$349$	−3.54448e8			−0.446337			−0.223169	−	0.974780i	$-0.571640\pi$
$349$	−3.54448e8			−0.446337			−0.223169	+	0.974780i	$0.571640\pi$
$350$	3.72199e8	−	1.32907e9i	0.464020	−	1.65696i
$351$	1.91294e9	−	1.10443e9i	2.36116	−	1.36322i
$352$	−3.29266e8	−	3.68560e8i	−0.402390	−	0.450410i
$353$	4.64217e7			0.0561706			0.0280853	−	0.999606i	$-0.491059\pi$
$353$	4.64217e7			0.0561706			0.0280853	+	0.999606i	$0.491059\pi$
$354$	−1.79158e9	−	5.01722e8i	−2.14647	−	0.601107i
$355$	−3.82816e7	−	6.63056e7i	−0.0454141	−	0.0786595i
$356$	5.00291e8	+	9.13389e8i	0.587689	+	1.07295i
$357$	3.14016e8	−	1.81297e8i	0.365269	−	0.210888i
$358$	−8.10759e7	+	7.92719e7i	−0.0933902	+	0.0913122i
$359$	−7.86326e8	−	4.53985e8i	−0.896958	−	0.517859i	−0.0207457	−	0.999785i	$-0.506604\pi$
$359$	−7.86326e8	−	4.53985e8i	−0.896958	−	0.517859i	−0.876212	+	0.481926i	$0.839937\pi$
$360$	3.05522e8	+	3.26874e8i	0.345131	+	0.369251i
$361$	8.92799e8	−	4.37879e7i	0.998799	−	0.0489867i
$362$	−2.12469e8	+	7.58697e8i	−0.235404	+	0.840598i
$363$	5.32575e8	−	9.22446e8i	0.584396	−	1.01220i
$364$	−1.55479e9	+	8.51606e8i	−1.68973	+	0.925516i
$365$	1.35775e8	+	2.35169e8i	0.146148	+	0.253136i
$366$	−6.59726e8	+	6.45046e8i	−0.703363	+	0.687713i
$367$	−3.98729e8	+	2.30206e8i	−0.421063	+	0.243101i	−0.695532	−	0.718495i	$-0.744831\pi$
$367$	−3.98729e8	+	2.30206e8i	−0.421063	+	0.243101i	0.274469	+	0.961596i	$0.411498\pi$
$368$	9.92121e8	−	5.14744e8i	1.03776	−	0.538423i
$369$		−	3.29548e9i		−	3.41450i
$370$	1.71640e8	−	4.39272e7i	0.176162	−	0.0450846i
$371$	1.21448e9	+	2.10354e9i	1.23476	+	2.13866i
$372$	−6.15034e8	−	3.73787e8i	−0.619439	−	0.376464i
$373$			1.94054e9i			1.93616i	0.250636	+	0.968081i	$0.419360\pi$
$373$			1.94054e9i			1.93616i	−0.250636	+	0.968081i	$0.580640\pi$
$374$	7.53194e7	−	1.92763e7i	0.0744485	−	0.0190534i
$375$	−3.89165e8	+	6.74054e8i	−0.381087	+	0.660063i
$376$	2.38330e7	+	7.25635e6i	0.0231218	+	0.00703981i
$377$	6.56771e8	−	1.13756e9i	0.631276	−	1.09340i
$378$	3.37188e9	+	3.44862e9i	3.21108	+	3.28415i
$379$	−1.26620e9			−1.19472			−0.597358	−	0.801975i	$-0.703783\pi$
$379$	−1.26620e9			−1.19472			−0.597358	+	0.801975i	$0.703783\pi$
$380$	−1.96490e8	−	1.12919e8i	−0.183695	−	0.105566i
$381$	−2.39169e9			−2.21548
$382$	−8.93954e8	−	9.14297e8i	−0.820528	−	0.839200i
$383$	1.43747e8	−	2.48977e8i	0.130738	−	0.226445i	−0.793223	−	0.608931i	$-0.791599\pi$
$383$	1.43747e8	−	2.48977e8i	0.130738	−	0.226445i	0.923961	+	0.382486i	$0.124932\pi$
$384$	−2.00752e9	+	3.71636e8i	−1.80926	+	0.334934i
$385$	−1.29068e8	+	2.23552e8i	−0.115267	+	0.199649i
$386$	1.55556e8	−	3.98110e7i	0.137667	−	0.0352328i
$387$			1.14453e9i			1.00378i
$388$	−8.77715e8	+	1.44420e9i	−0.762856	+	1.25521i
$389$	−5.12031e8	−	8.86863e8i	−0.441034	−	0.763894i	0.556732	−	0.830692i	$-0.312055\pi$
$389$	−5.12031e8	−	8.86863e8i	−0.441034	−	0.763894i	−0.997767	+	0.0667980i	$0.978722\pi$
$390$	4.73120e8	−	1.21084e8i	0.403874	−	0.103362i
$391$			1.75829e8i			0.148756i
$392$	−1.82880e9	−	1.95661e9i	−1.53343	−	1.64060i
$393$	4.98762e8	−	2.87960e8i	0.414495	−	0.239309i
$394$	−5.11234e8	+	4.99859e8i	−0.421098	+	0.411728i
$395$	−1.94434e7	−	3.36769e7i	−0.0158738	−	0.0274943i
$396$	8.55350e8	+	1.56163e9i	0.692167	+	1.26370i
$397$	−1.90515e8	+	3.29981e8i	−0.152813	+	0.264681i	−0.932261	−	0.361787i	$-0.882167\pi$
$397$	−1.90515e8	+	3.29981e8i	−0.152813	+	0.264681i	0.779447	+	0.626468i	$0.215500\pi$
$398$	6.56328e7	−	2.34366e8i	0.0521831	−	0.186339i
$399$	−3.69298e9	−	2.01315e9i	−2.91053	−	1.58661i
$400$	−5.63025e8	−	1.08518e9i	−0.439863	−	0.847797i
$401$	9.06756e8	+	5.23516e8i	0.702239	+	0.405438i	0.808181	−	0.588934i	$-0.200452\pi$
$401$	9.06756e8	+	5.23516e8i	0.702239	+	0.405438i	−0.105942	+	0.994372i	$0.533786\pi$
$402$	2.46895e9	−	2.41401e9i	1.89549	−	1.85331i
$403$	−4.79377e8	+	2.76768e8i	−0.364846	+	0.210644i
$404$	−3.65942e6	+	2.00437e6i	−0.00276107	+	0.00151232i
$405$	−3.26505e8	−	5.65524e8i	−0.244229	−	0.423018i
$406$	2.76190e9	+	7.73453e8i	2.04817	+	0.573579i
$407$	7.05055e8			0.518373
$408$	9.35471e7	−	3.07249e8i	0.0681898	−	0.223965i
$409$	−2.20333e8	+	1.27209e8i	−0.159238	+	0.0919363i	−0.577502	−	0.816390i	$-0.695972\pi$
$409$	−2.20333e8	+	1.27209e8i	−0.159238	+	0.0919363i	0.418263	+	0.908326i	$0.362639\pi$
$410$	1.14122e8	−	4.07514e8i	0.0817759	−	0.292011i
$411$	−7.71168e8			−0.547902
$412$	−3.15496e7	+	1.40197e9i	−0.0222256	+	0.987642i
$413$	−2.70589e9	−	1.56225e9i	−1.89010	−	1.09125i
$414$	−3.90106e9	+	9.98387e8i	−2.70197	+	0.691509i
$415$	−1.42745e8	−	8.24136e7i	−0.0980373	−	0.0566019i
$416$	−4.91036e8	+	1.49149e9i	−0.334416	+	1.01576i
$417$		−	2.26985e9i		−	1.53293i
$418$	−6.46103e8	−	6.29200e8i	−0.432698	−	0.421378i
$419$			2.39950e9i			1.59357i	0.604261	+	0.796786i	$0.293468\pi$
$419$			2.39950e9i			1.59357i	−0.604261	+	0.796786i	$0.706532\pi$
$420$	5.12272e8	+	9.35263e8i	0.337387	+	0.615972i
$421$	−4.60285e8	−	2.65746e8i	−0.300635	−	0.173572i	0.342093	−	0.939666i	$-0.388864\pi$
$421$	−4.60285e8	−	2.65746e8i	−0.300635	−	0.173572i	−0.642728	+	0.766094i	$0.722198\pi$
$422$	7.94518e7	+	3.10447e8i	0.0514648	+	0.201092i
$423$	−7.77305e7	−	4.48778e7i	−0.0499345	−	0.0288297i
$424$	2.05821e9	+	6.26656e8i	1.31132	+	0.399253i
$425$	1.92322e8			0.121525
$426$	−1.21203e9	−	3.39420e8i	−0.759588	−	0.212718i
$427$	−1.34192e9	+	7.74755e8i	−0.834118	+	0.481578i
$428$	−8.89562e6	+	3.95295e8i	−0.00548432	+	0.243707i
$429$	1.94347e9			1.18844
$430$	−3.96349e7	+	1.41531e8i	−0.0240402	+	0.0858445i
$431$	5.45978e8	+	9.45661e8i	0.328477	+	0.568938i	0.982210	−	0.187787i	$-0.0601315\pi$
$431$	5.45978e8	+	9.45661e8i	0.328477	+	0.568938i	−0.653733	+	0.756725i	$0.726798\pi$
$432$	4.26785e9	+	1.92182e8i	2.54692	+	0.114689i
$433$	1.58798e9	−	9.16822e8i	0.940022	−	0.542722i	0.0500548	−	0.998746i	$-0.484060\pi$
$433$	1.58798e9	−	9.16822e8i	0.940022	−	0.542722i	0.889967	+	0.456024i	$0.150727\pi$
$434$	−8.44985e8	−	8.64214e8i	−0.496175	−	0.507466i
$435$	−6.84284e8	−	3.95072e8i	−0.398588	−	0.230125i
$436$	4.03950e8	−	6.64665e8i	0.233413	−	0.384061i
$437$	1.74083e9	−	1.06277e9i	0.997864	−	0.609193i
$438$	4.29874e9	+	1.20384e9i	2.44445	+	0.684554i
$439$	−9.00299e8	+	1.55936e9i	−0.507880	+	0.879674i	0.492079	+	0.870551i	$0.336237\pi$
$439$	−9.00299e8	+	1.55936e9i	−0.507880	+	0.879674i	−0.999958	+	0.00912280i	$0.997096\pi$
$440$	5.16925e7	+	2.22729e8i	0.0289296	+	0.124650i
$441$	4.82444e9	+	8.35617e9i	2.67862	+	4.63951i
$442$	−1.72693e8	−	1.76623e8i	−0.0951253	−	0.0972900i
$443$	1.04525e9	−	6.03475e8i	0.571224	−	0.329796i	−0.186414	−	0.982471i	$-0.559687\pi$
$443$	1.04525e9	−	6.03475e8i	0.571224	−	0.329796i	0.757638	+	0.652675i	$0.226353\pi$
$444$	1.51268e9	−	2.48898e9i	0.820176	−	1.34953i
$445$		−	4.81813e8i		−	0.259190i
$446$	−3.91336e8	−	1.52909e9i	−0.208871	−	0.816133i
$447$	−1.36779e9	−	2.36908e9i	−0.724341	−	1.25459i
$448$	−3.42085e9	−	2.31258e8i	−1.79747	−	0.121513i
$449$		−	1.79538e9i		−	0.936039i	−0.883718	−	0.468019i	$-0.844968\pi$
$449$		−	1.79538e9i		−	0.936039i	0.883718	−	0.468019i	$-0.155032\pi$
$450$	1.09203e9	+	4.26697e9i	0.564927	+	2.20737i
$451$	8.42048e8	−	1.45847e9i	0.432234	−	0.748651i
$452$	1.45697e9	+	3.27874e7i	0.742108	+	0.0167002i
$453$	−3.37091e9	+	5.83860e9i	−1.70374	+	2.95097i
$454$	−2.12351e9	+	2.07626e9i	−1.06502	+	1.04133i
$455$	8.20154e8			0.408184
$456$	−3.60740e9	+	9.30937e8i	−1.78163	+	0.459773i
$457$	3.42415e9			1.67821			0.839104	−	0.543971i	$-0.183080\pi$
$457$	3.42415e9			1.67821			0.839104	+	0.543971i	$0.183080\pi$
$458$	1.44442e9	−	1.41228e9i	0.702528	−	0.686896i
$459$	−3.36034e8	+	5.82028e8i	−0.162195	+	0.280931i
$460$	−5.16973e8	−	1.16338e7i	−0.247637	−	0.00557275i
$461$	−1.82646e9	+	3.16351e9i	−0.868272	+	1.50389i	−0.00451098	+	0.999990i	$0.501436\pi$
$461$	−1.82646e9	+	3.16351e9i	−0.868272	+	1.50389i	−0.863761	+	0.503902i	$0.831897\pi$
$462$	1.05215e9	+	4.11111e9i	0.496397	+	1.93960i
$463$		−	1.42527e9i		−	0.667363i	−0.942686	−	0.333682i	$-0.891709\pi$
$463$		−	1.42527e9i		−	0.667363i	0.942686	−	0.333682i	$-0.108291\pi$
$464$	2.25507e9	−	1.17000e9i	1.04797	−	0.543718i
$465$	1.66486e8	+	2.88362e8i	0.0767878	+	0.133000i
$466$	−7.11248e8	−	2.77910e9i	−0.325590	−	1.27220i
$467$		−	3.97091e6i		−	0.00180418i	−1.00000		0.000902092i	$-0.999713\pi$
$467$		−	3.97091e6i		−	0.00180418i	1.00000		0.000902092i	$-0.000287145\pi$
$468$	2.93808e9	−	4.83435e9i	1.32496	−	2.18011i
$469$	5.02197e9	−	2.89944e9i	2.24786	−	1.29780i
$470$	−8.05793e6	−	8.24130e6i	−0.00357998	−	0.00366145i
$471$	1.65299e9	+	2.86307e9i	0.728951	+	1.26258i
$472$	−2.69592e9	+	6.25688e8i	−1.18008	+	0.273880i
$473$	−2.92446e8	+	5.06532e8i	−0.127067	+	0.220086i
$474$	−6.15593e8	−	1.72393e8i	−0.265503	−	0.0743525i
$475$	−1.16246e9	−	1.90411e9i	−0.497678	−	0.815203i
$476$	2.80127e8	−	4.60925e8i	0.119050	−	0.195887i
$477$	−6.71278e9	−	3.87563e9i	−2.83197	−	1.63504i
$478$	−1.41647e9	−	1.44870e9i	−0.593211	−	0.606710i
$479$	1.51771e9	−	8.76252e8i	0.630980	−	0.364296i	−0.150152	−	0.988663i	$-0.547976\pi$
$479$	1.51771e9	−	8.76252e8i	0.630980	−	0.364296i	0.781131	+	0.624367i	$0.214643\pi$
$480$	8.97183e8	+	2.95376e8i	0.370285	+	0.121908i
$481$	−1.12006e9	−	1.93999e9i	−0.458915	−	0.794863i
$482$	−4.23356e8	+	1.51175e9i	−0.172203	+	0.614914i
$483$	−9.59720e9			−3.87551
$484$	3.56470e7	−	1.58405e9i	0.0142910	−	0.635052i
$485$	6.77124e8	−	3.90938e8i	0.269508	−	0.155601i
$486$	−4.12463e9	−	1.15508e9i	−1.62989	−	0.456440i
$487$	3.65869e9			1.43541			0.717703	−	0.696349i	$-0.245194\pi$
$487$	3.65869e9			1.43541			0.717703	+	0.696349i	$0.245194\pi$
$488$	−3.99764e8	+	1.31300e9i	−0.155716	+	0.511440i
$489$	−2.14327e9	−	1.23742e9i	−0.828889	−	0.478559i
$490$	3.07210e8	+	1.20038e9i	0.117964	+	0.460927i
$491$	4.05199e8	+	2.33942e8i	0.154484	+	0.0891913i	0.575249	−	0.817978i	$-0.304905\pi$
$491$	4.05199e8	+	2.33942e8i	0.154484	+	0.0891913i	−0.420765	+	0.907170i	$0.638238\pi$
$492$	−3.34209e9	−	6.10171e9i	−1.26515	−	2.30980i
$493$			3.99657e8i			0.150218i
$494$	−7.04871e8	+	2.77734e9i	−0.263066	+	1.03654i
$495$		−	8.23760e8i		−	0.305269i
$496$	−1.06951e9	−	4.81604e7i	−0.393550	−	0.0177217i
$497$	−1.83056e9	−	1.05688e9i	−0.668863	−	0.386168i
$498$	−2.62506e9	+	6.71825e8i	−0.952439	+	0.243755i
$499$	1.92005e9	+	1.10854e9i	0.691769	+	0.399393i	0.804274	−	0.594258i	$-0.202554\pi$
$499$	1.92005e9	+	1.10854e9i	0.691769	+	0.399393i	−0.112506	+	0.993651i	$0.535888\pi$
$500$	−2.60481e7	+	1.15750e9i	−0.00931926	+	0.414120i
$501$	−9.78158e9			−3.47518
$502$	−6.34364e8	+	2.26523e9i	−0.223808	+	0.799189i
$503$	−1.36360e9	+	7.87278e8i	−0.477750	+	0.275829i	−0.719478	−	0.694515i	$-0.755619\pi$
$503$	−1.36360e9	+	7.87278e8i	−0.477750	+	0.275829i	0.241728	+	0.970344i	$0.422286\pi$
$504$	1.18170e10	+	3.59786e9i	4.11148	+	1.25181i
$505$	1.93035e6			0.000666984
$506$	−1.98158e9	−	5.54929e8i	−0.679962	−	0.190419i
$507$	−3.87705e8	−	6.71525e8i	−0.132122	−	0.228841i
$508$	−3.12033e9	+	1.70910e9i	−1.05603	+	0.578420i
$509$	2.05689e9	−	1.18755e9i	0.691352	−	0.399153i	−0.112766	−	0.993622i	$-0.535971\pi$
$509$	2.05689e9	−	1.18755e9i	0.691352	−	0.399153i	0.804118	+	0.594469i	$0.202638\pi$
$510$	−1.06245e8	+	1.03881e8i	−0.0354660	+	0.0346768i
$511$	6.49253e9	+	3.74846e9i	2.15249	+	1.24274i
$512$	−2.35355e9	+	1.91942e9i	−0.774958	+	0.632013i
$513$	7.79356e9	−	1.91005e8i	2.54874	−	0.0624647i
$514$	1.59267e9	−	5.68722e9i	0.517315	−	1.84726i
$515$	3.24392e8	−	5.61863e8i	0.104651	−	0.181261i
$516$	1.16072e9	+	2.11915e9i	0.371924	+	0.679027i
$517$	−2.29339e7	−	3.97228e7i	−0.00729897	−	0.0126422i
$518$	3.49739e9	−	3.41958e9i	1.10558	−	1.08098i
$519$	5.51926e9	−	3.18655e9i	1.73299	−	1.00054i
$520$	5.30731e8	−	4.96063e8i	0.165525	−	0.154713i
$521$		−	1.42916e9i		−	0.442740i	−0.975190	−	0.221370i	$-0.928947\pi$
$521$		−	1.42916e9i		−	0.442740i	0.975190	−	0.221370i	$-0.0710529\pi$
$522$	−8.86703e9	+	2.26932e9i	−2.72855	+	0.698310i
$523$	1.40534e9	+	2.43412e9i	0.429561	+	0.744022i	0.996834	−	0.0795079i	$-0.0253349\pi$
$523$	1.40534e9	+	2.43412e9i	0.429561	+	0.744022i	−0.567273	+	0.823530i	$0.692002\pi$
$524$	4.44935e8	−	7.32102e8i	0.135094	−	0.222286i
$525$			1.04974e10i			3.16609i
$526$	−2.45783e7	+	6.29027e6i	−0.00736381	+	0.00188460i
$527$	8.42092e7	−	1.45855e8i	0.0250624	−	0.0434093i
$528$	3.16743e9	+	2.02396e9i	0.936457	+	0.598390i
$529$	6.24527e8	−	1.08171e9i	0.183424	−	0.317700i
$530$	−6.95880e8	−	7.11716e8i	−0.203034	−	0.207654i
$531$	9.97083e9			2.89002
$532$	−6.25664e9	+	1.25336e7i	−1.80157	+	0.00360898i
$533$	−5.35074e9			−1.53062
$534$	−5.53745e9	−	5.66347e9i	−1.57368	−	1.60949i
$535$	9.14643e7	−	1.58421e8i	0.0258234	−	0.0447274i
$536$	1.49607e9	−	4.91375e9i	0.419639	−	1.37828i
$537$	4.31204e8	−	7.46868e8i	0.120164	−	0.208129i
$538$	−5.34214e8	+	1.36720e8i	−0.147903	+	0.0378524i
$539$			4.93088e9i			1.35632i
$540$	−1.68904e9	−	1.02651e9i	−0.461596	−	0.280535i
$541$	3.09682e9	+	5.36384e9i	0.840863	+	1.45642i	0.889166	+	0.457584i	$0.151285\pi$
$541$	3.09682e9	+	5.36384e9i	0.840863	+	1.45642i	−0.0483037	+	0.998833i	$0.515382\pi$
$542$	4.58419e9	−	1.17322e9i	1.23670	−	0.316506i
$543$		−	5.99240e9i		−	1.60621i
$544$	−9.75131e7	−	4.67702e8i	−0.0259697	−	0.124558i
$545$	−3.11632e8	+	1.79921e8i	−0.0824622	+	0.0476096i
$546$	9.64048e9	−	9.42598e9i	2.53469	−	2.47829i
$547$	−1.52976e9	−	2.64962e9i	−0.399639	−	0.692195i	0.594042	−	0.804434i	$-0.297531\pi$
$547$	−1.52976e9	−	2.64962e9i	−0.399639	−	0.692195i	−0.993681	+	0.112239i	$0.964198\pi$
$548$	−1.00611e9	+	5.51075e8i	−0.261163	+	0.143047i
$549$	2.47239e9	−	4.28230e9i	0.637695	−	1.10452i
$550$	−6.06980e8	+	2.16745e9i	−0.155563	+	0.555494i
$551$	3.95687e9	−	2.41566e9i	1.00768	−	0.615184i
$552$	−6.21045e9	+	5.80478e9i	−1.57158	+	1.46892i
$553$	−9.29750e8	−	5.36792e8i	−0.233791	−	0.134979i
$554$	−5.65184e8	+	5.52608e8i	−0.141223	+	0.138081i
$555$	−1.16698e9	+	6.73754e8i	−0.289759	+	0.167292i
$556$	−1.62203e9	−	2.96136e9i	−0.400218	−	0.730685i
$557$	3.79308e8	+	6.56980e8i	0.0930033	+	0.161086i	0.908774	−	0.417290i	$-0.137020\pi$
$557$	3.79308e8	+	6.56980e8i	0.0930033	+	0.161086i	−0.815770	+	0.578376i	$0.803687\pi$
$558$	3.71417e9	+	1.04013e9i	0.904987	+	0.253436i
$559$	1.85833e9			0.449968
$560$	1.33667e9	+	8.54125e8i	0.321638	+	0.205524i
$561$	−5.12096e8	+	2.95659e8i	−0.122456	+	0.0707002i
$562$	−8.05402e8	+	2.87599e9i	−0.191397	+	0.683454i
$563$	3.62267e9			0.855558			0.427779	−	0.903883i	$-0.359296\pi$
$563$	3.62267e9			0.855558			0.427779	+	0.903883i	$0.359296\pi$
$564$	−1.89434e8	−	4.26296e6i	−0.0444611	−	0.00100054i
$565$	−5.83905e8	−	3.37118e8i	−0.136199	−	0.0786343i
$566$	3.21006e9	−	8.21543e8i	0.744143	−	0.190446i
$567$	−1.56130e10	−	9.01416e9i	−3.59704	−	2.07675i
$568$	−1.82382e9	+	4.23285e8i	−0.417602	+	0.0969200i
$569$			4.57763e9i			1.04171i	0.853644	+	0.520856i	$0.174387\pi$
$569$			4.57763e9i			1.04171i	−0.853644	+	0.520856i	$0.825613\pi$
$570$	1.67067e9	+	4.24005e8i	0.377858	+	0.0958979i
$571$			8.10152e9i			1.82113i	0.413369	+	0.910563i	$0.364352\pi$
$571$			8.10152e9i			1.82113i	−0.413369	+	0.910563i	$0.635648\pi$
$572$	2.53555e9	−	1.38880e9i	0.566481	−	0.310279i
$573$	8.42246e9	+	4.86271e9i	1.87024	+	1.07978i
$574$	−2.89676e9	−	1.13187e10i	−0.639324	−	2.49807i
$575$	−4.40842e9	−	2.54520e9i	−0.967041	−	0.558322i
$576$	9.82302e9	−	4.81917e9i	2.14174	−	1.05074i
$577$	8.28646e8			0.179578			0.0897891	−	0.995961i	$-0.471381\pi$
$577$	8.28646e8			0.179578			0.0897891	+	0.995961i	$0.471381\pi$
$578$	−4.39809e9	−	1.23166e9i	−0.947364	−	0.265303i
$579$	−1.05762e9	+	6.10619e8i	−0.226441	+	0.130736i
$580$	−1.17507e9	−	2.64434e7i	−0.250072	−	0.00562756i
$581$	−4.55055e9			−0.962603
$582$	3.46622e9	−	1.23774e10i	0.728828	−	2.60255i
$583$	−1.98057e9	−	3.43044e9i	−0.413952	−	0.716985i
$584$	6.46861e9	−	1.50128e9i	1.34390	−	0.311901i
$585$	−2.26662e9	+	1.30863e9i	−0.468093	+	0.270254i
$586$	−1.68938e9	−	1.72782e9i	−0.346805	−	0.354697i
$587$	2.59685e9	+	1.49929e9i	0.529924	+	0.305952i	0.740986	−	0.671521i	$-0.234359\pi$
$587$	2.59685e9	+	1.49929e9i	0.529924	+	0.305952i	−0.211061	+	0.977473i	$0.567692\pi$
$588$	1.74070e10	+	1.05791e10i	3.53104	+	2.14599i
$589$	−1.95305e9	+	4.78654e7i	−0.393830	+	0.00965203i
$590$	1.23298e9	+	3.45288e8i	0.247157	+	0.0692148i
$591$	2.71901e9	−	4.70946e9i	0.541819	−	0.938458i
$592$	1.94901e8	−	4.32822e9i	0.0386089	−	0.857399i
$593$	3.68866e9	+	6.38894e9i	0.726402	+	1.25817i	0.958394	+	0.285448i	$0.0921423\pi$
$593$	3.68866e9	+	6.38894e9i	0.726402	+	1.25817i	−0.231992	+	0.972718i	$0.574524\pi$
$594$	−5.49885e9	−	5.62399e9i	−1.07651	−	1.10101i
$595$	−2.16107e8	+	1.24770e8i	−0.0420591	+	0.0242828i
$596$	−3.47743e9	−	2.11341e9i	−0.672816	−	0.408904i
$597$			1.85109e9i			0.356055i
$598$	1.62104e9	+	6.33398e9i	0.309984	+	1.21122i
$599$	2.92212e9	+	5.06126e9i	0.555525	+	0.962198i	0.997862	+	0.0653493i	$0.0208162\pi$
$599$	2.92212e9	+	5.06126e9i	0.555525	+	0.962198i	−0.442337	+	0.896849i	$0.645851\pi$
$600$	6.34926e9	+	6.79297e9i	1.20003	+	1.28390i
$601$		−	3.88882e9i		−	0.730731i	−0.930864	−	0.365365i	$-0.880944\pi$
$601$		−	3.88882e9i		−	0.730731i	0.930864	−	0.365365i	$-0.119056\pi$
$602$	1.00605e9	+	3.93102e9i	0.187946	+	0.734374i
$603$	−9.25263e9	+	1.60260e10i	−1.71852	+	2.97656i
$604$	−2.25627e8	+	1.00262e10i	−0.0416640	+	1.85143i
$605$	−3.66520e8	+	6.34832e8i	−0.0672906	+	0.116551i
$606$	2.26902e7	−	2.21854e7i	0.00414176	−	0.00404960i
$607$	−9.75760e9			−1.77085			−0.885426	−	0.464780i	$-0.846134\pi$
$607$	−9.75760e9			−1.77085			−0.885426	+	0.464780i	$0.846134\pi$
$608$	−4.04116e9	+	3.79239e9i	−0.729195	+	0.684306i
$609$	−2.18143e10			−3.91363
$610$	4.54026e8	−	4.43924e8i	0.0809891	−	0.0791871i
$611$	−7.28661e7	+	1.26208e8i	−0.0129235	+	0.0223842i
$612$	−3.87244e7	+	1.72080e9i	−0.00682897	+	0.303459i
$613$	4.65941e9	−	8.07033e9i	0.816994	−	1.41508i	−0.0908931	−	0.995861i	$-0.528972\pi$
$613$	4.65941e9	−	8.07033e9i	0.816994	−	1.41508i	0.907887	−	0.419215i	$-0.137695\pi$
$614$	1.69326e9	+	6.61619e9i	0.295213	+	1.15350i
$615$			3.21866e9i			0.557972i
$616$	4.31047e9	+	4.61171e9i	0.743006	+	0.794931i
$617$	3.55983e9	+	6.16581e9i	0.610143	+	1.05680i	0.991216	+	0.132254i	$0.0422213\pi$
$617$	3.55983e9	+	6.16581e9i	0.610143	+	1.05680i	−0.381073	+	0.924545i	$0.624445\pi$
$618$	−2.64440e9	−	1.03326e10i	−0.450679	−	1.76096i
$619$			2.74304e9i			0.464852i	0.972614	+	0.232426i	$0.0746664\pi$
$619$			2.74304e9i			0.464852i	−0.972614	+	0.232426i	$0.925334\pi$
$620$	4.23269e8	+	2.57242e8i	0.0713257	+	0.0433482i
$621$	1.54052e10	−	8.89419e9i	2.58135	−	1.49034i
$622$	1.10838e9	+	1.13360e9i	0.184681	+	0.188884i
$623$	−6.65095e9	−	1.15198e10i	−1.10198	−	1.90869i
$624$	5.37239e8	−	1.19306e10i	0.0885160	−	1.96570i
$625$	−2.64695e9	+	4.58464e9i	−0.433675	+	0.751148i
$626$	−1.64901e9	−	4.61795e8i	−0.268666	−	0.0752383i
$627$	6.02249e9	+	3.28303e9i	0.975753	+	0.531911i
$628$	4.20252e9	+	2.55408e9i	0.677098	+	0.411506i
$629$	5.90260e8	+	3.40787e8i	0.0945728	+	0.0546016i
$630$	−3.99530e9	−	4.08623e9i	−0.636587	−	0.651074i
$631$	−5.35900e9	+	3.09402e9i	−0.849144	+	0.490253i	−0.860362	−	0.509684i	$-0.829762\pi$
$631$	−5.35900e9	+	3.09402e9i	−0.849144	+	0.490253i	0.0112183	+	0.999937i	$0.496429\pi$
$632$	−9.26326e8	+	2.14988e8i	−0.145967	+	0.0338770i
$633$	−1.21863e9	−	2.11073e9i	−0.190967	−	0.330764i
$634$	−2.94003e9	+	1.04984e10i	−0.458183	+	1.63611i
$635$	1.64597e9			0.255103
$636$	−1.63594e10	−	3.68148e8i	−2.52155	−	0.0567443i
$637$	1.35676e10	−	7.83323e9i	2.07976	−	1.20075i
$638$	−4.50410e9	−	1.26134e9i	−0.686650	−	0.192292i
$639$	6.74537e9			1.02271
$640$	1.38159e9	−	2.55762e8i	0.208328	−	0.0385661i
$641$	−6.47032e8	−	3.73564e8i	−0.0970337	−	0.0560224i	0.450698	−	0.892677i	$-0.351175\pi$
$641$	−6.47032e8	−	3.73564e8i	−0.0970337	−	0.0560224i	−0.547732	+	0.836654i	$0.684509\pi$
$642$	−7.45605e8	−	2.91335e9i	−0.111208	−	0.434530i
$643$	−4.56518e9	−	2.63571e9i	−0.677203	−	0.390984i	0.121597	−	0.992580i	$-0.461198\pi$
$643$	−4.56518e9	−	2.63571e9i	−0.677203	−	0.390984i	−0.798801	+	0.601596i	$0.794532\pi$
$644$	−1.25210e10	+	6.85813e9i	−1.84730	+	1.01182i
$645$		−	1.11785e9i		−	0.164031i
$646$	−2.36784e8	−	8.39049e8i	−0.0345572	−	0.122454i
$647$			3.40875e9i			0.494800i	0.968913	+	0.247400i	$0.0795763\pi$
$647$			3.40875e9i			0.494800i	−0.968913	+	0.247400i	$0.920424\pi$
$648$	−1.55555e10	+	3.61022e9i	−2.24580	+	0.521220i
$649$	4.41275e9	+	2.54770e9i	0.633655	+	0.365841i
$650$	6.92809e9	−	1.77309e9i	0.989503	−	0.253241i
$651$	7.96110e9	+	4.59634e9i	1.13094	+	0.652949i
$652$	−3.68048e9	−	8.28246e7i	−0.520042	−	0.0117029i
$653$	−4.66330e9			−0.655386			−0.327693	−	0.944784i	$-0.606271\pi$
$653$	−4.66330e9			−0.655386			−0.327693	+	0.944784i	$0.606271\pi$
$654$	−1.59526e9	+	5.69645e9i	−0.223002	+	0.796310i
$655$	−3.43250e8	+	1.98176e8i	−0.0477273	+	0.0275553i
$656$	−8.72054e9	−	5.57236e9i	−1.20609	−	0.770683i
$657$	−2.39241e10			−3.29122
$658$	−3.06422e8	−	8.58115e7i	−0.0419304	−	0.0117423i
$659$	2.09186e9	+	3.62321e9i	0.284730	+	0.493167i	0.972544	−	0.232720i	$-0.0747627\pi$
$659$	2.09186e9	+	3.62321e9i	0.284730	+	0.493167i	−0.687814	+	0.725887i	$0.741429\pi$
$660$	−8.35410e8	−	1.52522e9i	−0.113109	−	0.206504i
$661$	2.94686e7	−	1.70137e7i	0.00396875	−	0.00229136i	−0.498014	−	0.867169i	$-0.665937\pi$
$661$	2.94686e7	−	1.70137e7i	0.00396875	−	0.00229136i	0.501983	+	0.864877i	$0.332604\pi$
$662$	−7.70434e9	+	7.53291e9i	−1.03212	+	1.00916i
$663$	1.62704e9	+	9.39371e8i	0.216821	+	0.125181i
$664$	−2.94471e9	+	2.75236e9i	−0.390350	+	0.364852i
$665$	2.54153e9	+	1.38546e9i	0.335134	+	0.182691i
$666$	−4.20931e9	+	1.50309e10i	−0.552143	+	1.97163i
$667$	5.28909e9	−	9.16097e9i	0.690145	−	1.19537i
$668$	−1.27616e10	+	6.98989e9i	−1.65648	+	0.907303i
$669$	6.00229e9	+	1.03963e10i	0.775042	+	1.34241i
$670$	−1.69914e9	+	1.66134e9i	−0.218257	+	0.213401i
$671$	2.18839e9	−	1.26347e9i	0.279638	−	0.161449i
$672$	2.55283e10	−	5.32250e9i	3.24511	−	0.676586i
$673$		−	1.11803e10i		−	1.41384i	−0.707293	−	0.706920i	$-0.750084\pi$
$673$		−	1.11803e10i		−	1.41384i	0.707293	−	0.706920i	$-0.249916\pi$
$674$	9.63386e9	−	2.46557e9i	1.21197	−	0.310175i
$675$	−9.72844e9	−	1.68502e10i	−1.21753	−	2.10883i
$676$	−9.85691e8	−	5.99054e8i	−0.122723	−	0.0745852i
$677$			4.19169e9i			0.519193i	0.965717	+	0.259597i	$0.0835896\pi$
$677$			4.19169e9i			0.519193i	−0.965717	+	0.259597i	$0.916410\pi$
$678$	−1.07380e10	+	2.74814e9i	−1.32318	+	0.338638i
$679$	1.07930e10	−	1.86940e10i	1.32312	−	2.29170i
$680$	−6.43796e7	+	2.11451e8i	−0.00785176	+	0.0257886i
$681$	1.12939e10	−	1.95617e10i	1.37035	−	2.37351i
$682$	1.37800e9	+	1.40936e9i	0.166342	+	0.170128i
$683$	−1.45467e10			−1.74700			−0.873500	−	0.486824i	$-0.838155\pi$
$683$	−1.45467e10			−1.74700			−0.873500	+	0.486824i	$0.838155\pi$
$684$	1.72711e10	−	1.00177e10i	2.06360	−	1.19694i
$685$	5.30722e8			0.0630885
$686$	1.32657e10	+	1.35676e10i	1.56890	+	1.60460i
$687$	−7.68217e9	+	1.33059e10i	−0.903931	+	1.56565i
$688$	3.02867e9	+	1.93530e9i	0.354562	+	0.226563i
$689$	−6.29269e9	+	1.08993e10i	−0.732941	+	1.26949i
$690$	3.81012e9	−	9.75113e8i	0.441536	−	0.113001i
$691$			5.16891e9i			0.595971i	0.954570	+	0.297986i	$0.0963148\pi$
$691$			5.16891e9i			0.595971i	−0.954570	+	0.297986i	$0.903685\pi$
$692$	4.92362e9	−	8.10138e9i	0.564824	−	0.929368i
$693$	−1.13712e10	−	1.96954e10i	−1.29789	−	2.24802i
$694$	3.60778e9	−	9.23328e8i	0.409715	−	0.104857i
$695$			1.56212e9i			0.176510i
$696$	−1.41162e10	+	1.31942e10i	−1.58704	+	1.48337i
$697$	1.40990e9	−	8.14005e8i	0.157715	−	0.0910568i
$698$	2.86730e9	−	2.80350e9i	0.319139	−	0.312038i
$699$	1.09091e10	+	1.88951e10i	1.20814	+	2.09256i
$700$	7.50140e9	+	1.36954e10i	0.826608	+	1.50915i
$701$	2.84302e8	−	4.92425e8i	0.0311722	−	0.0539918i	−0.850018	−	0.526753i	$-0.823409\pi$
$701$	2.84302e8	−	4.92425e8i	0.0311722	−	0.0539918i	0.881191	+	0.472761i	$0.156743\pi$
$702$	−6.73916e9	+	2.40647e10i	−0.735235	+	2.62543i
$703$	−1.93707e8	−	7.90380e9i	−0.0210282	−	0.858010i
$704$	5.57871e9	+	3.77135e8i	0.602601	+	0.0407373i
$705$	7.59185e7	+	4.38316e7i	0.00815991	+	0.00471113i
$706$	−3.75528e8	+	3.67172e8i	−0.0401629	+	0.0392693i
$707$	4.61531e7	−	2.66465e7i	0.00491171	−	0.00283578i
$708$	1.84614e10	−	1.01118e10i	1.95500	−	1.07081i
$709$	4.56500e9	+	7.90682e9i	0.481038	+	0.833182i	0.999763	−	0.0217588i	$-0.00692659\pi$
$709$	4.56500e9	+	7.90682e9i	0.481038	+	0.833182i	−0.518725	+	0.854941i	$0.673593\pi$
$710$	8.34122e8	+	2.33591e8i	0.0874632	+	0.0244935i
$711$	3.42600e9			0.357474
$712$	−1.12715e10	−	3.43181e9i	−1.17032	−	0.356322i
$713$	−3.86050e9	+	2.22886e9i	−0.398869	+	0.230287i
$714$	−1.10626e9	+	3.95031e9i	−0.113740	+	0.406151i
$715$	−1.33750e9			−0.136843
$716$	2.88619e7	−	1.28254e9i	0.00293853	−	0.130580i
$717$	1.33454e10	+	7.70496e9i	1.35212	+	0.780644i
$718$	9.95177e9	−	2.54693e9i	1.00338	−	0.256792i
$719$	1.36554e10	+	7.88394e9i	1.37010	+	0.791028i	0.990940	−	0.134302i	$-0.0428794\pi$
$719$	1.36554e10	+	7.88394e9i	1.37010	+	0.791028i	0.379161	+	0.925331i	$0.376213\pi$
$720$	−5.05693e9	−	2.27715e8i	−0.504920	−	0.0227367i
$721$		−	1.79116e10i		−	1.77976i
$722$	−6.87595e9	+	7.41581e9i	−0.679911	+	0.733294i
$723$		−	1.19402e10i		−	1.17497i
$724$	−4.28215e9	−	7.81799e9i	−0.419350	−	0.765615i
$725$	−1.00202e10	−	5.78519e9i	−0.976552	−	0.563813i
$726$	2.98783e9	+	1.16745e10i	0.289786	+	1.13230i
$727$	−6.18156e9	−	3.56892e9i	−0.596661	−	0.344482i	0.171066	−	0.985260i	$-0.445279\pi$
$727$	−6.18156e9	−	3.56892e9i	−0.596661	−	0.344482i	−0.767727	+	0.640777i	$0.778612\pi$
$728$	5.84170e9	−	1.91867e10i	0.561151	−	1.84306i
$729$	8.46121e9			0.808884
$730$	−2.95841e9	−	8.28485e8i	−0.281468	−	0.0788233i
$731$	−4.89662e8	+	2.82707e8i	−0.0463645	+	0.0267686i
$732$	2.34853e8	−	1.04362e10i	0.0221314	−	0.983452i
$733$	1.12377e10			1.05393			0.526967	−	0.849885i	$-0.323329\pi$
$733$	1.12377e10			1.05393			0.526967	+	0.849885i	$0.323329\pi$
$734$	1.40470e9	−	5.01600e9i	0.131113	−	0.468189i
$735$	−4.71197e9	−	8.16137e9i	−0.437720	−	0.758154i
$736$	−3.95440e9	+	1.20112e10i	−0.365601	+	1.11049i
$737$	−8.18980e9	+	4.72839e9i	−0.753594	+	0.435088i
$738$	2.60656e10	+	2.66588e10i	2.38710	+	2.44142i
$739$	−5.03507e9	−	2.90700e9i	−0.458934	−	0.264966i	0.252662	−	0.967555i	$-0.418694\pi$
$739$	−5.03507e9	−	2.90700e9i	−0.458934	−	0.264966i	−0.711596	+	0.702589i	$0.752027\pi$
$740$	−1.04103e9	+	1.71293e9i	−0.0944396	+	0.155392i
$741$	−5.33949e8	−	2.17866e10i	−0.0482099	−	1.96710i
$742$	−2.64625e10	−	7.41065e9i	−2.37803	−	0.665951i
$743$	−8.95580e9	+	1.55119e10i	−0.801020	+	1.38741i	0.117926	+	0.993022i	$0.462376\pi$
$743$	−8.95580e9	+	1.55119e10i	−0.801020	+	1.38741i	−0.918945	+	0.394385i	$0.870958\pi$
$744$	7.93177e9	−	1.84086e9i	0.706098	−	0.163876i
$745$	9.41319e8	+	1.63041e9i	0.0834046	+	0.144461i
$746$	−1.53487e10	−	1.56980e10i	−1.35359	−	1.38439i
$747$	1.25761e10	−	7.26082e9i	1.10389	−	0.637328i
$748$	−4.56830e8	+	7.51674e8i	−0.0399116	+	0.0656710i
$749$		−	5.05029e9i		−	0.439167i
$750$	−2.18328e9	−	8.53085e9i	−0.188971	−	0.738377i
$751$	−7.40447e9	−	1.28249e10i	−0.637902	−	1.10488i	−0.985892	−	0.167381i	$-0.946469\pi$
$751$	−7.40447e9	−	1.28249e10i	−0.637902	−	1.10488i	0.347990	−	0.937498i	$-0.386864\pi$
$752$	−2.50191e8	+	1.29807e8i	−0.0214541	+	0.0111310i
$753$		−	1.78914e10i		−	1.52708i
$754$	3.68459e9	+	1.43970e10i	0.313033	+	1.22313i
$755$	2.31988e9	−	4.01815e9i	0.196178	−	0.339791i
$756$	−5.45536e10	−	1.22766e9i	−4.59195	−	0.103336i
$757$	−1.07261e9	+	1.85782e9i	−0.0898686	+	0.155657i	−0.907455	−	0.420148i	$-0.861978\pi$
$757$	−1.07261e9	+	1.85782e9i	−0.0898686	+	0.155657i	0.817587	+	0.575805i	$0.195311\pi$
$758$	1.02429e10	−	1.00150e10i	0.854242	−	0.835235i
$759$	1.56511e10			1.29926
$760$	2.48263e9	−	6.40675e8i	0.205147	−	0.0529408i
$761$	−8.32694e9			−0.684919			−0.342459	−	0.939533i	$-0.611260\pi$
$761$	−8.32694e9			−0.684919			−0.342459	+	0.939533i	$0.611260\pi$
$762$	1.93476e10	−	1.89171e10i	1.58411	−	1.54886i
$763$	−4.96726e9	+	8.60354e9i	−0.404837	+	0.701199i
$764$	1.44633e10	+	3.25477e8i	1.17338	+	0.0264055i
$765$	3.98163e8	−	6.89638e8i	0.0321548	−	0.0556937i
$766$	8.06442e8	+	3.15106e9i	0.0648295	+	0.253312i
$767$		−	1.61892e10i		−	1.29551i
$768$	1.33004e10	−	1.88848e10i	1.05950	−	1.50435i
$769$	8.03709e9	+	1.39207e10i	0.637319	+	1.10387i	0.986019	+	0.166634i	$0.0532900\pi$
$769$	8.03709e9	+	1.39207e10i	0.637319	+	1.10387i	−0.348700	+	0.937234i	$0.613377\pi$
$770$	−7.24092e8	−	2.82929e9i	−0.0571579	−	0.223336i
$771$			4.49192e10i			3.52973i
$772$	−9.43483e8	+	1.55242e9i	−0.0738029	+	0.121436i
$773$	5.21749e9	−	3.01232e9i	0.406288	−	0.234570i	−0.282906	−	0.959148i	$-0.591298\pi$
$773$	5.21749e9	−	3.01232e9i	0.406288	−	0.234570i	0.689193	+	0.724577i	$0.257965\pi$
$774$	−9.05268e9	−	9.25869e9i	−0.701752	−	0.717722i
$775$	2.43792e9	+	4.22261e9i	0.188133	+	0.325855i
$776$	−4.32265e9	−	1.86252e10i	−0.332074	−	1.43082i
$777$	−1.86010e10	+	3.22178e10i	−1.42253	+	2.46390i
$778$	1.11567e10	+	3.12437e9i	0.849391	+	0.237867i
$779$	−1.65811e10	−	9.03882e9i	−1.25670	−	0.685063i
$780$	−2.86959e9	+	4.72165e9i	−0.216515	+	0.356257i
$781$	2.98527e9	+	1.72355e9i	0.224236	+	0.129463i
$782$	−1.39072e9	−	1.42237e9i	−0.103996	−	0.106363i
$783$	3.50157e10	−	2.02163e10i	2.60673	−	1.50500i
$784$	3.02698e10	+	1.36306e9i	2.24339	+	0.101020i
$785$	−1.13760e9	−	1.97038e9i	−0.0839354	−	0.145380i
$786$	−1.75711e9	+	6.27441e9i	−0.129068	+	0.460886i
$787$	7.30940e8			0.0534528			0.0267264	−	0.999643i	$-0.491492\pi$
$787$	7.30940e8			0.0534528			0.0267264	+	0.999643i	$0.491492\pi$
$788$	1.81992e8	−	8.08720e9i	0.0132499	−	0.588785i
$789$	1.67108e8	−	9.64798e7i	0.0121123	−	0.00699305i
$790$	4.23654e8	+	1.18642e8i	0.0305715	+	0.00856135i
$791$	−1.86143e10			−1.33730
$792$	−1.92710e10	−	5.86738e9i	−1.37837	−	0.419668i
$793$	−6.95298e9	−	4.01431e9i	−0.495125	−	0.285861i
$794$	−1.06882e9	−	4.17625e9i	−0.0757760	−	0.296084i
$795$	6.55629e9	+	3.78528e9i	0.462779	+	0.267185i
$796$	1.32278e9	+	2.41503e9i	0.0929593	+	0.169717i
$797$		−	2.29283e9i		−	0.160424i	−0.996778	−	0.0802119i	$-0.974440\pi$
$797$		−	2.29283e9i		−	0.160424i	0.996778	−	0.0802119i	$-0.0255597\pi$
$798$	4.57973e10	−	1.29242e10i	3.19029	−	0.900316i
$799$		−	4.43403e7i		−	0.00307528i
$800$	1.31378e10	+	4.32531e9i	0.907211	+	0.298677i
$801$	3.67617e10	+	2.12244e10i	2.52745	+	1.45922i
$802$	−1.14759e10	+	2.93701e9i	−0.785558	+	0.201046i
$803$	−1.05880e10	−	6.11298e9i	−0.721621	−	0.416628i
$804$	−8.78913e8	+	3.90563e10i	−0.0596416	+	2.65030i
$805$	6.60484e9			0.446248
$806$	1.68882e9	−	6.03054e9i	0.113608	−	0.405680i
$807$	3.63211e9	−	2.09700e9i	0.243278	−	0.140456i
$808$	1.37493e7	−	4.51585e7i	0.000916937	−	0.00301162i
$809$	−9.42087e8			−0.0625563			−0.0312782	−	0.999511i	$-0.509958\pi$
$809$	−9.42087e8			−0.0625563			−0.0312782	+	0.999511i	$0.509958\pi$
$810$	7.11427e9	+	1.99231e9i	0.470363	+	0.131722i
$811$	−4.26754e9	−	7.39160e9i	−0.280934	−	0.486592i	0.690681	−	0.723160i	$-0.257311\pi$
$811$	−4.26754e9	−	7.39160e9i	−0.280934	−	0.486592i	−0.971615	+	0.236567i	$0.923978\pi$
$812$	−2.84600e10	+	1.55884e10i	−1.86547	+	1.02178i
$813$	−3.11679e10	+	1.79948e10i	−2.03418	+	1.17444i
$814$	−5.70353e9	+	5.57663e9i	−0.370645	+	0.362398i
$815$	1.47501e9	+	8.51598e8i	0.0954429	+	0.0551040i
$816$	1.67344e9	+	3.22540e9i	0.107819	+	0.207811i
$817$	5.75866e9	+	3.13921e9i	0.369441	+	0.201393i
$818$	7.76220e8	−	2.77178e9i	0.0495847	−	0.177061i
$819$	−3.61287e10	+	6.25767e10i	−2.29804	+	3.98033i
$820$	2.30004e9	+	4.19923e9i	0.145676	+	0.265963i
$821$	−1.58364e10	−	2.74295e10i	−0.998750	−	1.72989i	−0.542663	−	0.839950i	$-0.682584\pi$
$821$	−1.58364e10	−	2.74295e10i	−0.998750	−	1.72989i	−0.456087	−	0.889935i	$-0.650749\pi$
$822$	6.23836e9	−	6.09955e9i	0.391759	−	0.383042i
$823$	−6.20729e9	+	3.58378e9i	−0.388152	+	0.224100i	−0.681359	−	0.731949i	$-0.738611\pi$
$823$	−6.20729e9	+	3.58378e9i	−0.388152	+	0.224100i	0.293207	+	0.956049i	$0.405278\pi$
$824$	−1.08337e10	−	1.15908e10i	−0.674576	−	0.721718i
$825$		−	1.71191e10i		−	1.06143i
$826$	3.42458e10	−	8.76445e9i	2.11435	−	0.541121i
$827$	−4.79041e9	−	8.29724e9i	−0.294513	−	0.510111i	0.680359	−	0.732879i	$-0.261824\pi$
$827$	−4.79041e9	−	8.29724e9i	−0.294513	−	0.510111i	−0.974871	+	0.222768i	$0.928491\pi$
$828$	2.36608e10	−	3.89319e10i	1.44852	−	2.38341i
$829$		−	9.66556e9i		−	0.589232i	−0.955616	−	0.294616i	$-0.904808\pi$
$829$		−	9.66556e9i		−	0.589232i	0.955616	−	0.294616i	$-0.0951917\pi$
$830$	1.80658e9	−	4.62353e8i	0.109669	−	0.0280673i
$831$	3.00594e9	−	5.20645e9i	0.181709	−	0.314730i
$832$	−7.82468e9	−	1.59492e10i	−0.471015	−	0.960081i
$833$	−2.38333e9	+	4.12805e9i	−0.142865	+	0.247450i
$834$	1.79534e10	+	1.83619e10i	1.07168	+	1.09607i
$835$	6.73173e9			0.400151
$836$	1.02033e10	−	2.04397e7i	0.603975	−	0.00120991i
$837$	−1.70386e10			−1.00437
$838$	−1.89788e10	−	1.94107e10i	−1.11408	−	1.13943i
$839$	1.38441e10	−	2.39787e10i	0.809279	−	1.40171i	−0.104085	−	0.994568i	$-0.533191\pi$
$839$	1.38441e10	−	2.39787e10i	0.809279	−	1.40171i	0.913364	−	0.407144i	$-0.133475\pi$
$840$	−1.15415e10	−	3.51399e9i	−0.671868	−	0.204561i
$841$	3.39707e9	−	5.88389e9i	0.196933	−	0.341098i
$842$	5.82539e9	−	1.49088e9i	0.336304	−	0.0860694i
$843$		−	2.27153e10i		−	1.30594i
$844$	−3.09820e9	−	1.88293e9i	−0.177383	−	0.107804i
$845$	2.66821e8	+	4.62147e8i	0.0152132	+	0.0263501i
$846$	9.83761e8	−	2.51771e8i	0.0558590	−	0.0142958i
$847$			2.02378e10i			1.14438i
$848$	−2.16064e10	+	1.12101e10i	−1.21674	+	0.631282i
$849$	−2.18252e10	+	1.26008e10i	−1.22400	+	0.706676i
$850$	−1.55579e9	+	1.52117e9i	−0.0868927	+	0.0849593i
$851$	−9.02000e9	−	1.56231e10i	−0.501710	−	0.868987i
$852$	1.24893e10	−	6.84077e9i	0.691831	−	0.378937i
$853$	9.46104e9	−	1.63870e10i	0.521936	−	0.904020i	−0.477738	−	0.878502i	$-0.658543\pi$
$853$	9.46104e9	−	1.63870e10i	0.521936	−	0.904020i	0.999674	−	0.0255176i	$-0.00812340\pi$
$854$	4.72749e9	−	1.68812e10i	0.259734	−	0.927475i
$855$	−9.23451e9	+	2.26320e8i	−0.505280	+	0.0123834i
$856$	−3.05462e9	−	3.26810e9i	−0.166456	−	0.178089i
$857$	1.63969e10	+	9.46673e9i	0.889872	+	0.513768i	0.873901	−	0.486104i	$-0.161583\pi$
$857$	1.63969e10	+	9.46673e9i	0.889872	+	0.513768i	0.0159716	+	0.999872i	$0.494916\pi$
$858$	−1.57217e10	+	1.53718e10i	−0.849753	+	0.830846i
$859$	−3.91572e9	+	2.26074e9i	−0.210783	+	0.121696i	−0.601675	−	0.798741i	$-0.705500\pi$
$859$	−3.91572e9	+	2.26074e9i	−0.210783	+	0.121696i	0.390892	+	0.920436i	$0.372167\pi$
$860$	−7.98814e8	−	1.45841e9i	−0.0428253	−	0.0781869i
$861$	4.44303e10	+	7.69556e10i	2.37229	+	4.10893i
$862$	−1.18964e10	−	3.33151e9i	−0.632615	−	0.177160i
$863$	−7.22292e9			−0.382538			−0.191269	−	0.981538i	$-0.561260\pi$
$863$	−7.22292e9			−0.382538			−0.191269	+	0.981538i	$0.561260\pi$
$864$	−3.60448e10	+	3.22019e10i	−1.90127	+	1.69857i
$865$	−3.79838e9	+	2.19300e9i	−0.199546	+	0.115208i
$866$	−5.59437e9	+	1.99768e10i	−0.292711	+	1.04523i
$867$	3.47373e10			1.81021
$868$	1.36710e10	+	3.07648e8i	0.709547	+	0.0159675i
$869$	1.51623e9	+	8.75397e8i	0.0783784	+	0.0452518i
$870$	8.66033e9	−	2.21641e9i	0.445879	−	0.114113i
$871$	2.60208e10	+	1.50231e10i	1.33431	+	0.770364i
$872$	1.98941e9	+	8.57185e9i	0.101606	+	0.437791i
$873$			6.88849e10i			3.50408i
$874$	−5.67645e9	+	2.23664e10i	−0.287598	+	1.13320i
$875$		−	1.47882e10i		−	0.746257i
$876$	−4.42963e10	+	2.42624e10i	−2.22640	+	1.21947i
$877$	−4.22703e9	−	2.44048e9i	−0.211610	−	0.122173i	0.390449	−	0.920624i	$-0.372320\pi$
$877$	−4.22703e9	−	2.44048e9i	−0.211610	−	0.122173i	−0.602060	+	0.798451i	$0.705653\pi$
$878$	−5.05082e9	−	1.97354e10i	−0.251844	−	0.984044i
$879$	1.59166e10	+	9.18946e9i	0.790478	+	0.456383i
$880$	−2.17984e9	−	1.39290e9i	−0.107829	−	0.0689019i
$881$	−1.98014e10			−0.975621			−0.487810	−	0.872950i	$-0.662204\pi$
$881$	−1.98014e10			−0.975621			−0.487810	+	0.872950i	$0.662204\pi$
$882$	−1.05120e11	−	2.94383e10i	−5.15878	−	1.44468i
$883$	−2.02247e9	+	1.16767e9i	−0.0988596	+	0.0570766i	−0.548615	−	0.836075i	$-0.684845\pi$
$883$	−2.02247e9	+	1.16767e9i	−0.0988596	+	0.0570766i	0.449755	+	0.893152i	$0.351511\pi$
$884$	2.79399e9	+	6.28752e7i	0.136032	+	0.00306123i
$885$	−9.73839e9			−0.472265
$886$	−3.68235e9	+	1.31492e10i	−0.177872	+	0.635157i
$887$	3.37675e9	+	5.84871e9i	0.162468	+	0.281402i	0.935753	−	0.352656i	$-0.114721\pi$
$887$	3.37675e9	+	5.84871e9i	0.162468	+	0.281402i	−0.773286	+	0.634058i	$0.781388\pi$
$888$	7.44979e9	+	3.20992e10i	0.357025	+	1.53833i
$889$	3.93539e10	−	2.27210e10i	1.87859	−	1.08460i
$890$	3.81090e9	+	3.89763e9i	0.181202	+	0.185325i
$891$	2.54616e10	+	1.47002e10i	1.20591	+	0.696230i
$892$	1.52600e10	+	9.27429e9i	0.719911	+	0.437526i
$893$	−4.38999e8	+	2.68007e8i	−0.0206292	+	0.0125941i
$894$	2.98030e10	+	8.34613e9i	1.39501	+	0.390665i
$895$	−2.96757e8	+	5.13998e8i	−0.0138363	+	0.0239652i
$896$	2.95021e10	−	2.51865e10i	1.37017	−	1.16974i
$897$	−2.48634e10	−	4.30647e10i	−1.15024	−	1.99227i
$898$	1.42005e10	+	1.45237e10i	0.654391	+	0.669283i
$899$	−8.77485e9	+	5.06616e9i	−0.402792	+	0.232552i
$900$	−4.25836e10	−	2.58802e10i	−1.94712	−	1.18336i
$901$		−	3.82921e9i		−	0.174411i
$902$	4.72402e9	+	1.84585e10i	0.214333	+	0.837476i
$903$	−1.54308e10	−	2.67269e10i	−0.697399	−	1.20793i
$904$	−1.20455e10	+	1.12587e10i	−0.542295	+	0.506872i
$905$			4.12400e9i			0.184947i
$906$	−1.89114e10	−	7.38935e10i	−0.844839	−	3.30109i
$907$	9.34164e9	−	1.61802e10i	0.415717	−	0.720043i	−0.579787	−	0.814768i	$-0.696864\pi$
$907$	9.34164e9	−	1.61802e10i	0.415717	−	0.720043i	0.995503	+	0.0947257i	$0.0301974\pi$
$908$	7.55941e8	−	3.35918e10i	0.0335110	−	1.48913i
$909$	−8.50339e7	+	1.47283e8i	−0.00375507	+	0.00650398i
$910$	−6.63463e9	+	6.48701e9i	−0.291858	+	0.285364i
$911$	−2.62145e10			−1.14875			−0.574377	−	0.818591i	$-0.694756\pi$
$911$	−2.62145e10			−1.14875			−0.574377	+	0.818591i	$0.694756\pi$
$912$	2.18188e10	−	3.60635e10i	0.952466	−	1.57430i
$913$	7.42101e9			0.322712
$914$	−2.76996e10	+	2.70833e10i	−1.19995	+	1.17325i
$915$	−2.41475e9	+	4.18247e9i	−0.104207	+	0.180492i
$916$	−5.14193e8	+	2.28492e10i	−0.0221051	+	0.982285i
$917$	−5.47123e9	+	9.47645e9i	−0.234311	+	0.405838i
$918$	−1.88520e9	−	7.36617e9i	−0.0804283	−	0.314262i
$919$			1.07297e10i			0.456021i	0.973659	+	0.228011i	$0.0732221\pi$
$919$			1.07297e10i			0.456021i	−0.973659	+	0.228011i	$0.926778\pi$
$920$	4.27406e9	−	3.99488e9i	0.180960	−	0.169140i
$921$	−2.59712e10	−	4.49834e10i	−1.09543	−	1.89733i
$922$	−1.02467e10	−	4.00376e10i	−0.430552	−	1.68232i
$923$		−	1.09522e10i		−	0.458453i
$924$	−4.10282e10	−	2.49349e10i	−1.71092	−	1.03981i
$925$	−1.70885e10	+	9.86605e9i	−0.709917	+	0.409871i
$926$	1.12731e10	+	1.15297e10i	0.466559	+	0.477176i
$927$	2.85796e10	+	4.95013e10i	1.17836	+	2.04097i
$928$	−8.98827e9	+	2.73012e10i	−0.369197	+	1.12141i
$929$	−2.93276e9	+	5.07970e9i	−0.120011	+	0.207866i	−0.919772	−	0.392453i	$-0.871626\pi$
$929$	−2.93276e9	+	5.07970e9i	−0.120011	+	0.207866i	0.799761	+	0.600319i	$0.204960\pi$
$930$	−3.62759e9	−	1.01588e9i	−0.147886	−	0.0414146i
$931$	5.52761e10	−	1.35471e9i	2.24499	−	0.0550203i
$932$	2.77349e10	+	1.68559e10i	1.12220	+	0.682019i
$933$	−1.04427e10	−	6.02910e9i	−0.420947	−	0.243034i
$934$	3.14079e7	+	3.21226e7i	0.00126132	+	0.00129002i
$935$	3.52427e8	−	2.03474e8i	0.0141003	−	0.00814081i
$936$	1.44697e10	+	6.23462e10i	0.576760	+	2.48510i
$937$	2.91399e9	+	5.04718e9i	0.115718	+	0.200429i	0.918066	−	0.396427i	$-0.129750\pi$
$937$	2.91399e9	+	5.04718e9i	0.115718	+	0.200429i	−0.802349	+	0.596855i	$0.796417\pi$
$938$	−1.76921e10	+	6.31762e10i	−0.699954	+	2.49945i
$939$	1.30243e10			0.513364
$940$	1.30369e8	+	2.93379e6i	0.00511950	+	0.000115208i
$941$	−8.25356e9	+	4.76520e9i	−0.322907	+	0.186431i	−0.652688	−	0.757627i	$-0.726359\pi$
$941$	−8.25356e9	+	4.76520e9i	−0.322907	+	0.186431i	0.329780	+	0.944058i	$0.393025\pi$
$942$	−3.60173e10	−	1.00864e10i	−1.40389	−	0.393151i
$943$	−4.30904e10			−1.67336
$944$	1.68598e10	−	2.63849e10i	0.652303	−	1.02083i
$945$	2.18632e10	+	1.26227e10i	0.842758	+	0.486567i
$946$	−1.64067e9	−	6.41068e9i	−0.0630089	−	0.246199i
$947$	−2.58582e10	−	1.49292e10i	−0.989403	−	0.571232i	−0.0843074	−	0.996440i	$-0.526868\pi$
$947$	−2.58582e10	−	1.49292e10i	−0.989403	−	0.571232i	−0.905096	+	0.425208i	$0.860201\pi$
$948$	6.34337e9	−	3.47446e9i	0.241819	−	0.132452i
$949$			3.88445e10i			1.47536i
$950$	2.44643e10	+	6.20888e9i	0.925762	+	0.234953i
$951$		−	8.29196e10i		−	3.12626i
$952$	1.37960e9	+	5.94431e9i	0.0518230	+	0.223291i
$953$	1.26103e10	+	7.28058e9i	0.471956	+	0.272484i	0.717058	−	0.697013i	$-0.245488\pi$
$953$	1.26103e10	+	7.28058e9i	0.471956	+	0.272484i	−0.245102	+	0.969497i	$0.578821\pi$
$954$	8.49572e10	−	2.17429e10i	3.16797	−	0.810770i
$955$	−5.79638e9	−	3.34654e9i	−0.215350	−	0.124332i
$956$	2.29170e10	+	5.15718e8i	0.848311	+	0.0190902i
$957$	3.55746e10			1.31204
$958$	−5.34681e9	+	1.90928e10i	−0.196479	+	0.701600i
$959$	1.26891e10	−	7.32608e9i	0.464587	−	0.268229i
$960$	−9.59403e9	+	4.70682e9i	−0.349987	+	0.171703i
$961$	−2.32428e10			−0.844804
$962$	2.44051e10	+	6.83448e9i	0.883826	+	0.247510i
$963$	8.05820e9	+	1.39572e10i	0.290768	+	0.503624i
$964$	−8.53243e9	−	1.55778e10i	−0.306763	−	0.560063i
$965$	7.27861e8	−	4.20231e8i	0.0260737	−	0.0150537i
$966$	7.76364e10	−	7.59090e10i	2.77106	−	2.70940i
$967$	−2.19431e10	−	1.26688e10i	−0.780377	−	0.450551i	0.0561870	−	0.998420i	$-0.482106\pi$
$967$	−2.19431e10	−	1.26688e10i	−0.780377	−	0.450551i	−0.836564	+	0.547869i	$0.815439\pi$
$968$	1.22407e10	+	1.30961e10i	0.433751	+	0.464064i
$969$	3.45508e9	+	5.65946e9i	0.121990	+	0.199821i
$970$	−2.38547e9	+	8.51819e9i	−0.0839213	+	0.299672i
$971$	−2.09301e10	+	3.62520e10i	−0.733675	+	1.27076i	0.221627	+	0.975132i	$0.428863\pi$
$971$	−2.09301e10	+	3.62520e10i	−0.733675	+	1.27076i	−0.955302	+	0.295632i	$0.904470\pi$
$972$	4.25022e10	−	2.32797e10i	1.48450	−	0.813104i
$973$	2.15635e10	+	3.73491e10i	0.750455	+	1.29983i
$974$	−2.95970e10	+	2.89384e10i	−1.02634	+	1.00350i
$975$	−4.71040e10	+	2.71955e10i	−1.62758	+	0.939683i
$976$	−7.15127e9	−	1.37834e10i	−0.246212	−	0.474551i
$977$			3.97668e10i			1.36424i	0.731242	+	0.682118i	$0.238941\pi$
$977$			3.97668e10i			1.36424i	−0.731242	+	0.682118i	$0.761059\pi$
$978$	2.71253e10	−	6.94212e9i	0.927234	−	0.237304i
$979$	1.08463e10	+	1.87864e10i	0.369440	+	0.639888i
$980$	−1.19796e10	−	7.28059e9i	−0.406584	−	0.247101i
$981$		−	3.17029e10i		−	1.07215i
$982$	−5.12821e9	+	1.31245e9i	−0.172813	+	0.0442275i
$983$	−6.24100e9	+	1.08097e10i	−0.209564	+	0.362976i	−0.951577	−	0.307409i	$-0.900538\pi$
$983$	−6.24100e9	+	1.08097e10i	−0.209564	+	0.362976i	0.742013	+	0.670385i	$0.233871\pi$
$984$	7.52973e10	+	2.29255e10i	2.51940	+	0.767072i
$985$	−1.87124e9	+	3.24107e9i	−0.0623881	+	0.108059i
$986$	−3.16109e9	−	3.23302e9i	−0.105019	−	0.107409i
$987$	2.42020e9			0.0801201
$988$	−1.62653e10	−	2.80424e10i	−0.536553	−	0.925052i
$989$	1.49654e10			0.491929
$990$	6.51552e9	+	6.66380e9i	0.213416	+	0.218272i
$991$	−3.25599e9	+	5.63954e9i	−0.106274	+	0.184071i	−0.914258	−	0.405133i	$-0.867225\pi$
$991$	−3.25599e9	+	5.63954e9i	−0.106274	+	0.184071i	0.807984	+	0.589204i	$0.200559\pi$
$992$	9.03273e9	−	8.06971e9i	0.293784	−	0.262462i
$993$	4.09757e10	−	7.09720e10i	1.32802	−	2.30019i
$994$	2.31677e10	−	5.92924e9i	0.748222	−	0.191490i
$995$		−	1.27393e9i		−	0.0409981i
$996$	1.59216e10	−	2.61976e10i	0.510599	−	0.840146i
$997$	1.32158e10	+	2.28905e10i	0.422339	+	0.731512i	0.996168	−	0.0874630i	$-0.0278760\pi$
$997$	1.32158e10	+	2.28905e10i	0.422339	+	0.731512i	−0.573829	+	0.818975i	$0.694543\pi$
$998$	−2.43002e10	+	6.21909e9i	−0.773845	+	0.198048i
$999$		−	6.89537e10i		−	2.18816i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.8.f.a.27.16	✓	136
4.3	odd	2	inner	76.8.f.a.27.40	yes	136
19.12	odd	6	inner	76.8.f.a.31.40	yes	136
76.31	even	6	inner	76.8.f.a.31.16	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.8.f.a.27.16	✓	136	1.1	even	1	trivial
76.8.f.a.27.40	yes	136	4.3	odd	2	inner
76.8.f.a.31.16	yes	136	76.31	even	6	inner
76.8.f.a.31.40	yes	136	19.12	odd	6	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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	76.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-8.08949 + 7.90950i) q^{2} +(43.0241 - 74.5200i) q^{3} +(2.87975 - 127.968i) q^{4} +(-29.6094 + 51.2850i) q^{5} +(241.372 + 943.128i) q^{6} +1634.91i q^{7} +(988.864 + 1057.97i) q^{8} +(-2608.65 - 4518.32i) q^{9} +O(q^{10})\)	\(q+(-8.08949 + 7.90950i) q^{2} +(43.0241 - 74.5200i) q^{3} +(2.87975 - 127.968i) q^{4} +(-29.6094 + 51.2850i) q^{5} +(241.372 + 943.128i) q^{6} +1634.91i q^{7} +(988.864 + 1057.97i) q^{8} +(-2608.65 - 4518.32i) q^{9} +(-166.114 - 649.066i) q^{10} -2666.21i q^{11} +(-9412.25 - 5720.30i) q^{12} +(-7336.20 + 4235.56i) q^{13} +(-12931.3 - 13225.6i) q^{14} +(2547.84 + 4412.99i) q^{15} +(-16367.4 - 737.029i) q^{16} +(1288.71 - 2232.11i) q^{17} +(56840.3 + 15917.8i) q^{18} +(-29888.7 + 732.515i) q^{19} +(6477.56 + 3936.74i) q^{20} +(121834. + 70340.7i) q^{21} +(21088.4 + 21568.3i) q^{22} +(-59079.7 + 34109.7i) q^{23} +(121385. - 28171.8i) q^{24} +(37309.1 + 64621.2i) q^{25} +(25845.0 - 92289.2i) q^{26} -260753. q^{27} +(209216. + 4708.14i) q^{28} +(-134287. + 77530.7i) q^{29} +(-55515.3 - 15546.7i) q^{30} +65344.0 q^{31} +(138234. - 123496. i) q^{32} +(-198686. - 114711. i) q^{33} +(7229.85 + 28249.6i) q^{34} +(-83846.6 - 48408.8i) q^{35} +(-585711. + 320812. i) q^{36} +264441. i q^{37} +(235991. - 242330. i) q^{38} +728925. i q^{39} +(-83537.7 + 19388.0i) q^{40} +(547020. + 315822. i) q^{41} +(-1.54193e6 + 394623. i) q^{42} +(-189982. - 109686. i) q^{43} +(-341188. - 7678.01i) q^{44} +308963. q^{45} +(208134. - 743220. i) q^{46} +(14898.6 - 8601.71i) q^{47} +(-759117. + 1.18799e6i) q^{48} -1.84940e6 q^{49} +(-812932. - 227657. i) q^{50} +(-110891. - 192069. i) q^{51} +(520888. + 950994. i) q^{52} +(1.28664e6 - 742840. i) q^{53} +(2.10936e6 - 2.06242e6i) q^{54} +(136737. + 78944.9i) q^{55} +(-1.72969e6 + 1.61671e6i) q^{56} +(-1.23135e6 + 2.25882e6i) q^{57} +(473085. - 1.68933e6i) q^{58} +(-955553. + 1.65507e6i) q^{59} +(572057. - 313333. i) q^{60} +(473882. + 820787. i) q^{61} +(-528600. + 516838. i) q^{62} +(7.38706e6 - 4.26492e6i) q^{63} +(-141450. + 2.09238e6i) q^{64} -501650. i q^{65} +(2.51458e6 - 643549. i) q^{66} +(-1.77345e6 - 3.07171e6i) q^{67} +(-281926. - 171341. i) q^{68} +5.87016e6i q^{69} +(1.06117e6 - 271581. i) q^{70} +(-646442. + 1.11967e6i) q^{71} +(2.20065e6 - 7.22788e6i) q^{72} +(2.29276e6 - 3.97118e6i) q^{73} +(-2.09160e6 - 2.13919e6i) q^{74} +6.42076e6 q^{75} +(7666.20 + 3.82690e6i) q^{76} +4.35902e6 q^{77} +(-5.76543e6 - 5.89664e6i) q^{78} +(-328330. + 568685. i) q^{79} +(522428. - 817580. i) q^{80} +(-5.51354e6 + 9.54973e6i) q^{81} +(-6.92311e6 + 1.77181e6i) q^{82} +2.78336e6i q^{83} +(9.35218e6 - 1.53882e7i) q^{84} +(76315.8 + 132183. i) q^{85} +(2.40442e6 - 615357. i) q^{86} +1.33428e7i q^{87} +(2.82077e6 - 2.63652e6i) q^{88} +(-7.04611e6 + 4.06807e6i) q^{89} +(-2.49935e6 + 2.44374e6i) q^{90} +(-6.92477e6 - 1.19941e7i) q^{91} +(4.19480e6 + 7.65851e6i) q^{92} +(2.81137e6 - 4.86943e6i) q^{93} +(-52486.9 + 187424. i) q^{94} +(847421. - 1.55453e6i) q^{95} +(-3.25553e6 - 1.56145e7i) q^{96} +(-1.14343e7 - 6.60157e6i) q^{97} +(1.49607e7 - 1.46278e7i) q^{98} +(-1.20468e7 + 6.95521e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 3 q^{2} - 27 q^{4} - 2 q^{5} + 309 q^{6} - 45540 q^{9}+O(q^{10}) \) 136 * q - 3 * q^2 - 27 * q^4 - 2 * q^5 + 309 * q^6 - 45540 * q^9	\( 136 q - 3 q^{2} - 27 q^{4} - 2 q^{5} + 309 q^{6} - 45540 q^{9} - 19464 q^{10} - 10602 q^{13} + 13602 q^{14} + 6525 q^{16} - 23974 q^{17} - 91316 q^{20} + 54264 q^{21} + 381 q^{22} - 51631 q^{24} - 937502 q^{25} + 172188 q^{26} - 165428 q^{28} - 6 q^{29} - 454352 q^{30} + 573507 q^{32} - 182106 q^{33} - 629706 q^{34} - 277130 q^{36} - 759906 q^{38} - 627504 q^{40} - 1873020 q^{41} + 332080 q^{42} - 358069 q^{44} + 321240 q^{45} - 7221687 q^{48} - 15750664 q^{49} + 2848050 q^{52} - 1027650 q^{53} + 4352085 q^{54} - 137426 q^{57} + 10387724 q^{58} + 1607094 q^{60} + 5318582 q^{61} + 3394376 q^{62} - 1319538 q^{64} + 2439607 q^{66} - 87756 q^{68} - 17825238 q^{70} + 26155014 q^{72} + 299212 q^{73} + 1895842 q^{74} + 29672379 q^{76} + 907280 q^{77} + 7456734 q^{78} + 5489562 q^{80} - 11065208 q^{81} + 1288975 q^{82} + 6118214 q^{85} + 16831518 q^{86} - 17728542 q^{89} + 52167894 q^{90} + 10184840 q^{92} - 3299132 q^{93} - 68841730 q^{96} - 9435888 q^{97} - 35100021 q^{98}+O(q^{100}) \) 136 * q - 3 * q^2 - 27 * q^4 - 2 * q^5 + 309 * q^6 - 45540 * q^9 - 19464 * q^10 - 10602 * q^13 + 13602 * q^14 + 6525 * q^16 - 23974 * q^17 - 91316 * q^20 + 54264 * q^21 + 381 * q^22 - 51631 * q^24 - 937502 * q^25 + 172188 * q^26 - 165428 * q^28 - 6 * q^29 - 454352 * q^30 + 573507 * q^32 - 182106 * q^33 - 629706 * q^34 - 277130 * q^36 - 759906 * q^38 - 627504 * q^40 - 1873020 * q^41 + 332080 * q^42 - 358069 * q^44 + 321240 * q^45 - 7221687 * q^48 - 15750664 * q^49 + 2848050 * q^52 - 1027650 * q^53 + 4352085 * q^54 - 137426 * q^57 + 10387724 * q^58 + 1607094 * q^60 + 5318582 * q^61 + 3394376 * q^62 - 1319538 * q^64 + 2439607 * q^66 - 87756 * q^68 - 17825238 * q^70 + 26155014 * q^72 + 299212 * q^73 + 1895842 * q^74 + 29672379 * q^76 + 907280 * q^77 + 7456734 * q^78 + 5489562 * q^80 - 11065208 * q^81 + 1288975 * q^82 + 6118214 * q^85 + 16831518 * q^86 - 17728542 * q^89 + 52167894 * q^90 + 10184840 * q^92 - 3299132 * q^93 - 68841730 * q^96 - 9435888 * q^97 - 35100021 * q^98

Introduction

L-functions

Modular forms

Varieties

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