LMFDB - Embedded newform 76.8.f.a.27.12

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			27.12
Character	$\chi$	$=$	76.27
Dual form			76.8.f.a.31.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-9.80808 + 5.63929i) q^{2} +(-43.2012 + 74.8267i) q^{3} +(64.3967 - 110.621i) q^{4} +(243.358 - 421.508i) q^{5} +(1.75099 - 977.530i) q^{6} -413.429i q^{7} +(-7.78194 + 1448.13i) q^{8} +(-2639.19 - 4571.21i) q^{9} +O(q^{10})$	\(q+(-9.80808 + 5.63929i) q^{2} +(-43.2012 + 74.8267i) q^{3} +(64.3967 - 110.621i) q^{4} +(243.358 - 421.508i) q^{5} +(1.75099 - 977.530i) q^{6} -413.429i q^{7} +(-7.78194 + 1448.13i) q^{8} +(-2639.19 - 4571.21i) q^{9} +(-9.86356 + 5506.55i) q^{10} -1916.28i q^{11} +(5495.41 + 9597.57i) q^{12} +(691.822 - 399.424i) q^{13} +(2331.45 + 4054.94i) q^{14} +(21026.7 + 36419.3i) q^{15} +(-8090.13 - 14247.3i) q^{16} +(-9120.65 + 15797.4i) q^{17} +(51663.8 + 29951.6i) q^{18} +(-38.9218 + 29897.7i) q^{19} +(-30956.3 - 54064.2i) q^{20} +(30935.5 + 17860.6i) q^{21} +(10806.4 + 18795.0i) q^{22} +(-32849.4 + 18965.6i) q^{23} +(-108023. - 63143.4i) q^{24} +(-79383.3 - 137496. i) q^{25} +(-4532.98 + 7818.97i) q^{26} +267103. q^{27} +(-45734.0 - 26623.4i) q^{28} +(64614.9 - 37305.4i) q^{29} +(-411610. - 238627. i) q^{30} -304086. q^{31} +(159693. + 94115.9i) q^{32} +(143389. + 82785.5i) q^{33} +(369.670 - 206376. i) q^{34} +(-174263. - 100611. i) q^{35} +(-675628. - 2420.44i) q^{36} +567936. i q^{37} +(-168220. - 293458. i) q^{38} +69022.3i q^{39} +(608506. + 355695. i) q^{40} +(-25084.8 - 14482.7i) q^{41} +(-404139. - 723.911i) q^{42} +(434045. + 250596. i) q^{43} +(-211981. - 123402. i) q^{44} -2.56907e6 q^{45} +(215237. - 371264. i) q^{46} +(347865. - 200840. i) q^{47} +(1.41558e6 + 10142.8i) q^{48} +652620. q^{49} +(1.55398e6 + 900905. i) q^{50} +(-788046. - 1.36494e6i) q^{51} +(366.317 - 102252. i) q^{52} +(-694500. + 400970. i) q^{53} +(-2.61976e6 + 1.50627e6i) q^{54} +(-807725. - 466341. i) q^{55} +(598700. + 3217.28i) q^{56} +(-2.23546e6 - 1.29453e6i) q^{57} +(-423372. + 730277. i) q^{58} +(-858505. + 1.48697e6i) q^{59} +(5.38280e6 + 19283.8i) q^{60} +(266897. + 462279. i) q^{61} +(2.98250e6 - 1.71483e6i) q^{62} +(-1.88987e6 + 1.09112e6i) q^{63} +(-2.09703e6 - 22538.6i) q^{64} -388811. i q^{65} +(-1.87322e6 - 3355.39i) q^{66} +(-1.42385e6 - 2.46618e6i) q^{67} +(1.16019e6 + 2.02624e6i) q^{68} -3.27735e6i q^{69} +(2.27656e6 + 4077.88i) q^{70} +(-824367. + 1.42785e6i) q^{71} +(6.64026e6 - 3.78633e6i) q^{72} +(872964. - 1.51202e6i) q^{73} +(-3.20276e6 - 5.57036e6i) q^{74} +1.37178e7 q^{75} +(3.30481e6 + 1.92962e6i) q^{76} -792243. q^{77} +(-389237. - 676976. i) q^{78} +(-2.36128e6 + 4.08986e6i) q^{79} +(-7.97414e6 - 57135.4i) q^{80} +(-5.76725e6 + 9.98917e6i) q^{81} +(327706. + 587.001i) q^{82} +8.30847e6i q^{83} +(3.96791e6 - 2.27196e6i) q^{84} +(4.43916e6 + 7.68885e6i) q^{85} +(-5.67034e6 - 10156.9i) q^{86} +6.44656e6i q^{87} +(2.77503e6 + 14912.4i) q^{88} +(-5.75343e6 + 3.32174e6i) q^{89} +(2.51976e7 - 1.44877e7i) q^{90} +(-165133. - 286019. i) q^{91} +(-17393.6 + 4.85516e6i) q^{92} +(1.31369e7 - 2.27537e7i) q^{93} +(-2.27929e6 + 3.93157e6i) q^{94} +(1.25926e7 + 7.29223e6i) q^{95} +(-1.39413e7 + 7.88340e6i) q^{96} +(-3.90194e6 - 2.25279e6i) q^{97} +(-6.40095e6 + 3.68032e6i) q^{98} +(-8.75970e6 + 5.05742e6i) 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 $

$2$	−9.80808	+	5.63929i	−0.866920	+	0.498448i
$2$	−9.80808	+	5.63929i	−0.866920	+	0.498448i
$3$	−43.2012	+	74.8267i	−0.923786	+	1.60004i	−0.130285	+	0.991477i	$0.541589\pi$
$3$	−43.2012	+	74.8267i	−0.923786	+	1.60004i	−0.793502	+	0.608568i	$0.791744\pi$
$4$	64.3967	−	110.621i	0.503099	−	0.864229i
$5$	243.358	−	421.508i	0.870663	−	1.50803i	0.00935014	−	0.999956i	$-0.497024\pi$
$5$	243.358	−	421.508i	0.870663	−	1.50803i	0.861312	−	0.508076i	$-0.169643\pi$
$6$	1.75099	−	977.530i	0.00330944	−	1.84757i
$7$		−	413.429i		−	0.455572i	−0.973711	−	0.227786i	$-0.926851\pi$
$7$		−	413.429i		−	0.455572i	0.973711	−	0.227786i	$-0.0731487\pi$
$8$	−7.78194	+	1448.13i	−0.00537369	+	0.999986i
$9$	−2639.19	−	4571.21i	−1.20676	−	2.09017i
$10$	−9.86356	+	5506.55i	−0.00311913	+	1.74132i
$11$		−	1916.28i		−	0.434094i	−0.976161	−	0.217047i	$-0.930358\pi$
$11$		−	1916.28i		−	0.434094i	0.976161	−	0.217047i	$-0.0696425\pi$
$12$	5495.41	+	9597.57i	0.918048	+	1.60334i
$13$	691.822	−	399.424i	0.0873359	−	0.0504234i	−0.455696	−	0.890135i	$-0.650610\pi$
$13$	691.822	−	399.424i	0.0873359	−	0.0504234i	0.543032	+	0.839712i	$0.317276\pi$
$14$	2331.45	+	4054.94i	0.227079	+	0.394945i
$15$	21026.7	+	36419.3i	1.60861	+	2.78620i
$16$	−8090.13	−	14247.3i	−0.493782	−	0.869586i
$17$	−9120.65	+	15797.4i	−0.450251	+	0.779858i	−0.998401	−	0.0565222i	$-0.981999\pi$
$17$	−9120.65	+	15797.4i	−0.450251	+	0.779858i	0.548150	+	0.836380i	$0.315332\pi$
$18$	51663.8	+	29951.6i	2.08801	+	1.21050i
$19$	−38.9218	+	29897.7i	−0.00130183	+	0.999999i
$19$	−38.9218	+	29897.7i	−0.00130183	+	0.999999i
$20$	−30956.3	−	54064.2i	−0.865255	−	1.51114i
$21$	30935.5	+	17860.6i	0.728936	+	0.420851i
$22$	10806.4	+	18795.0i	0.216373	+	0.376325i
$23$	−32849.4	+	18965.6i	−0.562963	+	0.325027i	−0.754334	−	0.656491i	$-0.772040\pi$
$23$	−32849.4	+	18965.6i	−0.562963	+	0.325027i	0.191371	+	0.981518i	$0.438707\pi$
$24$	−108023.	−	63143.4i	−1.59506	−	0.932371i
$25$	−79383.3	−	137496.i	−1.01611	−	1.75995i
$26$	−4532.98	+	7818.97i	−0.0505797	+	0.0872454i
$27$	267103.			2.61159
$28$	−45734.0	−	26623.4i	−0.393719	−	0.229198i
$29$	64614.9	−	37305.4i	0.491971	−	0.284040i	−0.233421	−	0.972376i	$-0.574992\pi$
$29$	64614.9	−	37305.4i	0.491971	−	0.284040i	0.725392	+	0.688336i	$0.241659\pi$
$30$	−411610.	−	238627.i	−2.78331	−	1.61360i
$31$	−304086.			−1.83329			−0.916643	−	0.399706i	$-0.869112\pi$
$31$	−304086.			−1.83329			−0.916643	+	0.399706i	$0.869112\pi$
$32$	159693.	+	94115.9i	0.861513	+	0.507736i
$33$	143389.	+	82785.5i	0.694570	+	0.401010i
$34$	369.670	−	206376.i	0.00161301	−	0.900501i
$35$	−174263.	−	100611.i	−0.687018	−	0.396650i
$36$	−675628.	−	2420.44i	−2.41351	−	0.00864639i
$37$			567936.i			1.84329i	0.388034	+	0.921645i	$0.373154\pi$
$37$			567936.i			1.84329i	−0.388034	+	0.921645i	$0.626846\pi$
$38$	−168220.	−	293458.i	−0.497319	−	0.867568i
$39$			69022.3i			0.186322i
$40$	608506.	+	355695.i	1.50333	+	0.878754i
$41$	−25084.8	−	14482.7i	−0.0568417	−	0.0328176i	0.471310	−	0.881968i	$-0.343781\pi$
$41$	−25084.8	−	14482.7i	−0.0568417	−	0.0328176i	−0.528152	+	0.849150i	$0.677115\pi$
$42$	−404139.	−	723.911i	−0.841702	−	0.00150769i
$43$	434045.	+	250596.i	0.832522	+	0.480657i	0.854715	−	0.519097i	$-0.173732\pi$
$43$	434045.	+	250596.i	0.832522	+	0.480657i	−0.0221936	+	0.999754i	$0.507065\pi$
$44$	−211981.	−	123402.i	−0.375157	−	0.218392i
$45$	−2.56907e6			−4.20273
$46$	215237.	−	371264.i	0.326035	−	0.562380i
$47$	347865.	−	200840.i	0.488729	−	0.282168i	−0.235318	−	0.971918i	$-0.575613\pi$
$47$	347865.	−	200840.i	0.488729	−	0.282168i	0.724047	+	0.689751i	$0.242280\pi$
$48$	1.41558e6	+	10142.8i	1.84753	+	0.0132377i
$49$	652620.			0.792454
$50$	1.55398e6	+	900905.i	1.75813	+	1.01926i
$51$	−788046.	−	1.36494e6i	−0.831871	−	1.44084i
$52$	366.317	−	102252.i	0.000361281	−	0.100846i
$53$	−694500.	+	400970.i	−0.640777	+	0.369953i	−0.784914	−	0.619605i	$-0.787293\pi$
$53$	−694500.	+	400970.i	−0.640777	+	0.369953i	0.144137	+	0.989558i	$0.453959\pi$
$54$	−2.61976e6	+	1.50627e6i	−2.26404	+	1.30174i
$55$	−807725.	−	466341.i	−0.654628	−	0.377949i
$56$	598700.	+	3217.28i	0.455566	+	0.00244811i
$57$	−2.23546e6	−	1.29453e6i	−1.59884	−	0.925869i
$58$	−423372.	+	730277.i	−0.284921	+	0.491462i
$59$	−858505.	+	1.48697e6i	−0.544203	+	0.942587i	0.454454	+	0.890770i	$0.349834\pi$
$59$	−858505.	+	1.48697e6i	−0.544203	+	0.942587i	−0.998657	+	0.0518165i	$0.983499\pi$
$60$	5.38280e6	+	19283.8i	3.21720	+	0.0115256i
$61$	266897.	+	462279.i	0.150553	+	0.260765i	0.931431	−	0.363918i	$-0.118561\pi$
$61$	266897.	+	462279.i	0.150553	+	0.260765i	−0.780878	+	0.624684i	$0.785228\pi$
$62$	2.98250e6	−	1.71483e6i	1.58931	−	0.913798i
$63$	−1.88987e6	+	1.09112e6i	−0.952225	+	0.549767i
$64$	−2.09703e6	−	22538.6i	−0.999942	−	0.0107472i
$65$		−	388811.i		−	0.175607i
$66$	−1.87322e6	−	3355.39i	−0.802019	−	0.00143661i
$67$	−1.42385e6	−	2.46618e6i	−0.578366	−	1.00176i	−0.995667	−	0.0929913i	$-0.970357\pi$
$67$	−1.42385e6	−	2.46618e6i	−0.578366	−	1.00176i	0.417301	−	0.908769i	$-0.362976\pi$
$68$	1.16019e6	+	2.02624e6i	0.447454	+	0.781466i
$69$		−	3.27735e6i		−	1.20102i
$70$	2.27656e6	+	4077.88i	0.793298	+	0.00142099i
$71$	−824367.	+	1.42785e6i	−0.273348	+	0.473453i	−0.969717	−	0.244231i	$-0.921465\pi$
$71$	−824367.	+	1.42785e6i	−0.273348	+	0.473453i	0.696369	+	0.717684i	$0.254798\pi$
$72$	6.64026e6	−	3.78633e6i	2.09663	−	1.19551i
$73$	872964.	−	1.51202e6i	0.262643	−	0.454912i	−0.704300	−	0.709902i	$-0.748739\pi$
$73$	872964.	−	1.51202e6i	0.262643	−	0.454912i	0.966944	+	0.254991i	$0.0820724\pi$
$74$	−3.20276e6	−	5.57036e6i	−0.918784	−	1.59798i
$75$	1.37178e7			3.75466
$76$	3.30481e6	+	1.92962e6i	0.863573	+	0.504224i
$77$	−792243.			−0.197761
$78$	−389237.	−	676976.i	−0.0928717	−	0.161526i
$79$	−2.36128e6	+	4.08986e6i	−0.538832	+	0.933285i	0.460135	+	0.887849i	$0.347801\pi$
$79$	−2.36128e6	+	4.08986e6i	−0.538832	+	0.933285i	−0.998967	+	0.0454358i	$0.985532\pi$
$80$	−7.97414e6	−	57135.4i	−1.74128	−	0.0124764i
$81$	−5.76725e6	+	9.98917e6i	−1.20579	+	2.08849i
$82$	327706.	+	587.001i	0.0656350	+	0.000117568i
$83$			8.30847e6i			1.59495i	0.603350	+	0.797477i	$0.293832\pi$
$83$			8.30847e6i			1.59495i	−0.603350	+	0.797477i	$0.706168\pi$
$84$	3.96791e6	−	2.27196e6i	0.730439	−	0.418237i
$85$	4.43916e6	+	7.68885e6i	0.784033	+	1.35799i
$86$	−5.67034e6	−	10156.9i	−0.961312	−	0.00172194i
$87$			6.44656e6i			1.04957i
$88$	2.77503e6	+	14912.4i	0.434088	+	0.00233269i
$89$	−5.75343e6	+	3.32174e6i	−0.865091	+	0.499460i	−0.865714	−	0.500539i	$-0.833135\pi$
$89$	−5.75343e6	+	3.32174e6i	−0.865091	+	0.499460i	0.000623066		1.00000i	$0.499802\pi$
$90$	2.51976e7	−	1.44877e7i	3.64343	−	2.09484i
$91$	−165133.	−	286019.i	−0.0229715	−	0.0397878i
$92$	−17393.6	+	4.85516e6i	−0.00232880	+	0.650050i
$93$	1.31369e7	−	2.27537e7i	1.69357	−	2.93334i
$94$	−2.27929e6	+	3.93157e6i	−0.283043	+	0.488223i
$95$	1.25926e7	+	7.29223e6i	1.50690	+	0.872625i
$96$	−1.39413e7	+	7.88340e6i	−1.60825	+	0.909419i
$97$	−3.90194e6	−	2.25279e6i	−0.434090	−	0.250622i	0.266998	−	0.963697i	$-0.413968\pi$
$97$	−3.90194e6	−	2.25279e6i	−0.434090	−	0.250622i	−0.701087	+	0.713075i	$0.747302\pi$
$98$	−6.40095e6	+	3.68032e6i	−0.686994	+	0.394997i
$99$	−8.75970e6	+	5.05742e6i	−0.907332	+	0.523848i
$100$	−2.03220e7	−	72803.5i	−2.03220	−	0.00728035i
$101$	−5.07409e6	−	8.78858e6i	−0.490042	−	0.848777i	0.509893	−	0.860238i	$-0.329685\pi$
$101$	−5.07409e6	−	8.78858e6i	−0.490042	−	0.848777i	−0.999934	+	0.0114609i	$0.996352\pi$
$102$	1.54265e7	+	8.94337e6i	1.43935	+	0.834451i
$103$	−5.51288e6			−0.497105			−0.248553	−	0.968618i	$-0.579955\pi$
$103$	−5.51288e6			−0.497105			−0.248553	+	0.968618i	$0.579955\pi$
$104$	573035.	+	1.00496e6i	0.0499533	+	0.0876056i
$105$	1.50568e7	−	8.69303e6i	1.26931	−	0.732839i
$106$	4.55052e6	−	7.84924e6i	0.371100	−	0.640113i
$107$	8.18333e6			0.645783			0.322892	−	0.946436i	$-0.395345\pi$
$107$	8.18333e6			0.645783			0.322892	+	0.946436i	$0.395345\pi$
$108$	1.72005e7	−	2.95472e7i	1.31389	−	2.25701i
$109$	−2.15545e7	−	1.24445e7i	−1.59421	−	0.920416i	−0.992574	−	0.121644i	$-0.961183\pi$
$109$	−2.15545e7	−	1.24445e7i	−1.59421	−	0.920416i	−0.601634	−	0.798772i	$-0.705483\pi$
$110$	1.05521e7	+	18901.3i	0.755898	+	0.00135400i
$111$	−4.24968e7	−	2.45355e7i	−2.94935	−	1.70281i
$112$	−5.89024e6	+	3.34469e6i	−0.396159	+	0.224953i
$113$			2.90319e7i			1.89278i	0.323026	+	0.946390i	$0.395300\pi$
$113$			2.90319e7i			1.89278i	−0.323026	+	0.946390i	$0.604700\pi$
$114$	2.92258e7	+	90397.9i	1.84756	+	0.00571467i
$115$			1.84617e7i			1.13196i
$116$	34213.3	−	9.55013e6i	0.00203513	−	0.568076i
$117$	−3.65170e6	−	2.10831e6i	−0.210787	−	0.121698i
$118$	34796.2	−	1.94257e7i	0.00194959	−	1.08840i
$119$	6.53111e6	+	3.77074e6i	0.355281	+	0.205122i
$120$	−5.29036e7	+	3.01660e7i	−2.79480	+	1.59362i
$121$	1.58151e7			0.811562
$122$	−5.22468e6	−	3.02896e6i	−0.260495	−	0.151020i
$123$	2.16739e6	−	1.25134e6i	0.105019	−	0.0606328i
$124$	−1.95821e7	+	3.36384e7i	−0.922325	+	1.58438i
$125$	−3.92495e7			−1.79742
$126$	1.23828e7	−	2.13593e7i	0.551472	−	0.951239i
$127$	−1.20852e7	−	2.09322e7i	−0.523530	−	0.906780i	−0.999625	−	0.0273862i	$-0.991282\pi$
$127$	−1.20852e7	−	2.09322e7i	−0.523530	−	0.906780i	0.476095	−	0.879394i	$-0.342052\pi$
$128$	2.06949e7	−	1.16047e7i	0.872227	−	0.489102i
$129$	−3.75026e7	+	2.16521e7i	−1.53814	+	0.888048i
$130$	2.19262e6	+	3.81349e6i	0.0875310	+	0.152237i
$131$	7.96267e6	+	4.59725e6i	0.309463	+	0.178669i	0.646686	−	0.762756i	$-0.276154\pi$
$131$	7.96267e6	+	4.59725e6i	0.309463	+	0.178669i	−0.337223	+	0.941425i	$0.609488\pi$
$132$	1.83916e7	−	1.05307e7i	0.696002	−	0.398519i
$133$	1.23605e7	+	16091.4i	0.455572	+	0.000593079i
$134$	2.78728e7	+	1.61590e7i	1.00072	+	0.580160i
$135$	6.50015e7	−	1.12586e8i	2.27381	−	3.93836i
$136$	−2.28058e7	−	1.33309e7i	−0.777427	−	0.454435i
$137$	1.55572e7	+	2.69459e7i	0.516904	+	0.895303i	0.999807	+	0.0196298i	$0.00624877\pi$
$137$	1.55572e7	+	2.69459e7i	0.516904	+	0.895303i	−0.482904	+	0.875673i	$0.660418\pi$
$138$	1.84819e7	+	3.21445e7i	0.598647	+	1.04119i
$139$	5.98413e6	−	3.45494e6i	0.188995	−	0.109116i	−0.402517	−	0.915412i	$-0.631865\pi$
$139$	5.98413e6	−	3.45494e6i	0.188995	−	0.109116i	0.591512	+	0.806296i	$0.298531\pi$
$140$	−2.23517e7	+	1.27982e7i	−0.688434	+	0.394186i
$141$			3.47061e7i			1.04265i
$142$	33412.5	−	1.86533e7i	0.000979265	−	0.546696i
$143$	−765406.	−	1.32572e6i	−0.0218885	−	0.0379120i
$144$	−4.37760e7	+	7.45830e7i	−1.22171	+	2.08147i
$145$		−	3.63142e7i		−	0.989211i
$146$	−35382.2	+	1.97529e7i	−0.000940914	+	0.525286i
$147$	−2.81940e7	+	4.88334e7i	−0.732058	+	1.26796i
$148$	6.28258e7	+	3.65732e7i	1.59302	+	0.927358i
$149$	−2.24795e7	+	3.89357e7i	−0.556718	+	0.964263i	0.441050	+	0.897483i	$0.354606\pi$
$149$	−2.24795e7	+	3.89357e7i	−0.556718	+	0.964263i	−0.997768	+	0.0667809i	$0.978727\pi$
$150$	−1.34545e8	+	7.73589e7i	−3.25499	+	1.87150i
$151$	1.73600e7			0.410328			0.205164	−	0.978728i	$-0.434227\pi$
$151$	1.73600e7			0.410328			0.205164	+	0.978728i	$0.434227\pi$
$152$	−4.32955e7	−	289026.i	−0.999978	−	0.00667550i
$153$	9.62845e7			2.17338
$154$	7.77038e6	−	4.46769e6i	0.171443	−	0.0985737i
$155$	−7.40016e7	+	1.28175e8i	−1.59617	+	2.76465i
$156$	7.63534e6	+	4.44481e6i	0.161025	+	0.0937383i
$157$	1.46673e7	−	2.54046e7i	0.302484	−	0.523918i	−0.674214	−	0.738536i	$-0.735517\pi$
$157$	1.46673e7	−	2.54046e7i	0.302484	−	0.523918i	0.976698	+	0.214618i	$0.0688507\pi$
$158$	95705.5	−	5.34297e7i	0.00193035	−	1.07766i
$159$		−	6.92896e7i		−	1.36703i
$160$	7.85331e7	−	4.44081e7i	1.51577	−	0.857122i
$161$	7.84092e6	+	1.35809e7i	0.148073	+	0.256470i
$162$	233753.	−	1.30498e8i	0.00431971	−	2.41157i
$163$		−	6.38105e7i		−	1.15408i	−0.816716	−	0.577040i	$-0.804208\pi$
$163$		−	6.38105e7i		−	1.15408i	0.816716	−	0.577040i	$-0.195792\pi$
$164$	−3.21747e6	+	1.84227e6i	−0.0569589	+	0.0326137i
$165$	6.97894e7	−	4.02930e7i	1.20947	−	0.698289i
$166$	−4.68539e7	−	8.14901e7i	−0.795001	−	1.38270i
$167$	4.92575e6	+	8.53165e6i	0.0818398	+	0.141751i	0.904040	−	0.427447i	$-0.140587\pi$
$167$	4.92575e6	+	8.53165e6i	0.0818398	+	0.141751i	−0.822200	+	0.569198i	$0.807254\pi$
$168$	−2.61053e7	+	4.46597e7i	−0.424762	+	0.726664i
$169$	−3.10552e7	+	5.37891e7i	−0.494915	+	0.857218i
$170$	−8.68993e7	−	5.03791e7i	−1.35658	−	0.786465i
$171$	1.36771e8	−	7.87277e7i	2.09174	−	1.20404i
$172$	5.56724e7	−	3.18771e7i	0.834238	−	0.477671i
$173$	−7.02394e7	−	4.05527e7i	−1.03138	−	0.595468i	−0.114001	−	0.993481i	$-0.536367\pi$
$173$	−7.02394e7	−	4.05527e7i	−1.03138	−	0.595468i	−0.917380	+	0.398012i	$0.869700\pi$
$174$	−3.63540e7	−	6.32283e7i	−0.523155	−	0.909891i
$175$	−5.68448e7	+	3.28193e7i	−0.801784	+	0.462910i
$176$	−2.73018e7	+	1.55029e7i	−0.377482	+	0.214348i
$177$	−7.41769e7	−	1.28478e8i	−1.00545	−	1.74150i
$178$	3.76978e7	−	6.50252e7i	0.501009	−	0.864195i
$179$	−8.72386e7			−1.13690			−0.568451	−	0.822717i	$-0.692457\pi$
$179$	−8.72386e7			−1.13690			−0.568451	+	0.822717i	$0.692457\pi$
$180$	−1.65439e8	+	2.84193e8i	−2.11439	+	3.63212i
$181$	9.64787e7	−	5.57020e7i	1.20936	−	0.698225i	0.246742	−	0.969081i	$-0.420640\pi$
$181$	9.64787e7	−	5.57020e7i	1.20936	−	0.698225i	0.962620	+	0.270856i	$0.0873066\pi$
$182$	3.23258e6	+	1.87406e6i	0.0397466	+	0.0230427i
$183$	−4.61211e7			−0.556315
$184$	−2.72091e7	−	4.77179e7i	−0.321997	−	0.564702i
$185$	2.39390e8	+	1.38212e8i	2.77974	+	1.60488i
$186$	−532452.	+	2.97253e8i	−0.00606716	+	3.38712i
$187$	3.02723e7	+	1.74777e7i	0.338532	+	0.195451i
$188$	184193.	−	5.14147e7i	0.00202172	−	0.564332i
$189$		−	1.10428e8i		−	1.18977i
$190$	−1.64632e8	−	509222.i	−1.74132	−	0.00538604i
$191$			9.06186e7i			0.941024i	0.882394	+	0.470512i	$0.155931\pi$
$191$			9.06186e7i			0.941024i	−0.882394	+	0.470512i	$0.844069\pi$
$192$	9.22808e7	−	1.55940e8i	0.940929	−	1.59002i
$193$	−1.40053e6	−	808598.i	−0.0140231	−	0.00809622i	0.492972	−	0.870045i	$-0.335910\pi$
$193$	−1.40053e6	−	808598.i	−0.0140231	−	0.00809622i	−0.506995	+	0.861949i	$0.669244\pi$
$194$	5.09747e7	+	91308.0i	0.501243	+	0.000897848i
$195$	2.90935e7	+	1.67971e7i	0.280979	+	0.162223i
$196$	4.20266e7	−	7.21936e7i	0.398683	−	0.684861i
$197$	5.08215e7			0.473604			0.236802	−	0.971558i	$-0.423901\pi$
$197$	5.08215e7			0.473604			0.236802	+	0.971558i	$0.423901\pi$
$198$	5.73956e7	−	9.90021e7i	0.525473	−	0.906392i
$199$	−7.39799e7	+	4.27123e7i	−0.665469	+	0.384209i	−0.794358	−	0.607450i	$-0.792192\pi$
$199$	−7.39799e7	+	4.27123e7i	−0.665469	+	0.384209i	0.128889	+	0.991659i	$0.458859\pi$
$200$	1.99730e8	−	1.13888e8i	1.76538	−	1.00663i
$201$	2.46048e8			2.13715
$202$	9.93284e7	+	5.75847e7i	0.847898	+	0.491561i
$203$	−1.54231e7	−	2.67136e7i	−0.129401	−	0.224128i
$204$	−2.01739e8	−	722728.i	−1.66373	−	0.00596031i
$205$	−1.22092e7	+	7.04896e6i	−0.0989799	+	0.0571461i
$206$	5.40708e7	−	3.10888e7i	0.430950	−	0.247781i
$207$	1.73392e8	+	1.00108e8i	1.35873	+	0.784461i
$208$	−1.12876e7	−	6.62520e6i	−0.0869724	−	0.0510478i
$209$	5.72922e7	+	74584.9i	0.434094	+	0.000565118i
$210$	−9.86554e7	+	1.70171e8i	−0.735112	+	1.26800i
$211$	5.55623e7	−	9.62368e7i	0.407185	−	0.705265i	−0.587388	−	0.809305i	$-0.699844\pi$
$211$	5.55623e7	−	9.62368e7i	0.407185	−	0.705265i	0.994573	+	0.104040i	$0.0331771\pi$
$212$	−367735.	+	1.02648e8i	−0.00265069	+	0.739901i
$213$	−7.12273e7	−	1.23369e8i	−0.505031	−	0.874740i
$214$	−8.02627e7	+	4.61482e7i	−0.559842	+	0.321889i
$215$	2.11256e8	−	1.21969e8i	1.44969	−	0.836979i
$216$	−2.07858e6	+	3.86800e8i	−0.0140339	+	2.61155i
$217$			1.25718e8i			0.835195i
$218$	2.81586e8	+	504389.i	1.84083	+	0.00329737i
$219$	7.54262e7	+	1.30642e8i	0.485253	+	0.840483i
$220$	−1.03602e8	+	5.93208e7i	−0.655977	+	0.375602i
$221$			1.45720e7i			0.0908127i
$222$	5.55175e8	+	994453.i	3.40561	+	0.00610027i
$223$	9.69384e6	−	1.67902e7i	0.0585368	−	0.101389i	−0.835272	−	0.549837i	$-0.814690\pi$
$223$	9.69384e6	−	1.67902e7i	0.0585368	−	0.101389i	0.893809	+	0.448448i	$0.148023\pi$
$224$	3.89102e7	−	6.60217e7i	0.231311	−	0.392481i
$225$	−4.19015e8	+	7.25756e8i	−2.45240	+	4.24768i
$226$	−1.63719e8	−	2.84747e8i	−0.943452	−	1.64089i
$227$	−1.59952e8			−0.907611			−0.453806	−	0.891101i	$-0.649934\pi$
$227$	−1.59952e8			−0.907611			−0.453806	+	0.891101i	$0.649934\pi$
$228$	−2.87159e8	+	1.63926e8i	−1.60454	+	0.915960i
$229$	−7.75275e7			−0.426611			−0.213305	−	0.976986i	$-0.568423\pi$
$229$	−7.75275e7			−0.426611			−0.213305	+	0.976986i	$0.568423\pi$
$230$	−1.04111e8	−	1.81074e8i	−0.564221	−	0.981314i
$231$	3.42259e7	−	5.92810e7i	0.182689	−	0.316427i
$232$	5.35204e7	+	9.38613e7i	0.281392	+	0.493490i
$233$	−3.09953e7	+	5.36854e7i	−0.160528	+	0.278042i	−0.935058	−	0.354495i	$-0.884653\pi$
$233$	−3.09953e7	+	5.36854e7i	−0.160528	+	0.278042i	0.774530	+	0.632537i	$0.217986\pi$
$234$	4.77055e7	+	85452.1i	0.243396	+	0.000435981i
$235$		−	1.95504e8i		−	0.982692i
$236$	1.09206e8	+	1.90725e8i	0.540822	+	0.944530i
$237$	−2.04021e8	−	3.53374e8i	−0.995532	−	1.72431i
$238$	−8.53219e7	−	152832.i	−0.410243	−	0.000734845i
$239$			3.28960e8i			1.55866i	0.626617	+	0.779328i	$0.284439\pi$
$239$			3.28960e8i			1.55866i	−0.626617	+	0.779328i	$0.715561\pi$
$240$	3.48768e8	−	5.94210e8i	1.62853	−	2.77460i
$241$	1.73579e8	−	1.00216e8i	0.798799	−	0.461187i	−0.0442523	−	0.999020i	$-0.514091\pi$
$241$	1.73579e8	−	1.00216e8i	0.798799	−	0.461187i	0.843051	+	0.537834i	$0.180757\pi$
$242$	−1.55115e8	+	8.91858e7i	−0.703559	+	0.404522i
$243$	−2.06228e8	−	3.57197e8i	−0.921987	−	1.59693i
$244$	6.83252e7	+	244775.i	0.301104	+	0.00107870i
$245$	1.58820e8	−	2.75084e8i	0.689960	−	1.19505i
$246$	−1.42012e7	+	2.44958e7i	−0.0608209	+	0.104910i
$247$	1.19149e7	+	2.06994e7i	0.0503097	+	0.0874014i
$248$	2.36638e6	−	4.40357e8i	0.00985152	−	1.83326i
$249$	−6.21696e8	−	3.58936e8i	−2.55200	−	1.47340i
$250$	3.84962e8	−	2.21340e8i	1.55822	−	0.895920i
$251$	−6.06885e7	+	3.50385e7i	−0.242241	+	0.139858i	−0.616206	−	0.787585i	$-0.711331\pi$
$251$	−6.06885e7	+	3.50385e7i	−0.242241	+	0.139858i	0.373965	+	0.927443i	$0.377998\pi$
$252$	−1.00068e6	+	2.79324e8i	−0.00393905	+	1.09953i
$253$	3.63434e7	+	6.29485e7i	0.141092	+	0.244379i
$254$	2.36576e8	+	1.37153e8i	0.905841	+	0.525153i
$255$	−7.67108e8			−2.89712
$256$	−1.37535e8	+	2.30525e8i	−0.512358	+	0.858772i
$257$	1.30623e8	−	7.54154e7i	0.480015	−	0.277137i	−0.240408	−	0.970672i	$-0.577281\pi$
$257$	1.30623e8	−	7.54154e7i	0.480015	−	0.277137i	0.720423	+	0.693535i	$0.243948\pi$
$258$	2.45725e8	−	4.23854e8i	0.890802	−	1.53655i
$259$	2.34801e8			0.839752
$260$	−4.30108e7	−	2.50382e7i	−0.151765	−	0.0883478i
$261$	−3.41062e8	−	1.96912e8i	−1.18738	−	0.685537i
$262$	−1.04024e8	−	186332.i	−0.357337	−	0.000640077i
$263$	−1.04466e8	−	6.03137e7i	−0.354105	−	0.204442i	0.312387	−	0.949955i	$-0.398871\pi$
$263$	−1.04466e8	−	6.03137e7i	−0.354105	−	0.204442i	−0.666492	+	0.745513i	$0.732205\pi$
$264$	−1.21000e8	+	2.07002e8i	−0.404737	+	0.692405i
$265$			3.90316e8i			1.28842i
$266$	−1.21324e8	+	6.95469e7i	−0.395240	+	0.226565i
$267$		−	5.74013e8i		−	1.84558i
$268$	−3.64504e8	−	1.30583e6i	−1.15673	−	0.00414396i
$269$	1.98554e8	+	1.14635e8i	0.621936	+	0.359075i	0.777622	−	0.628732i	$-0.216426\pi$
$269$	1.98554e8	+	1.14635e8i	0.621936	+	0.359075i	−0.155686	+	0.987807i	$0.549759\pi$
$270$	−2.63458e6	+	1.47081e9i	−0.00814589	+	4.54762i
$271$	−3.77935e8	−	2.18201e8i	−1.15352	−	0.665984i	−0.203776	−	0.979018i	$-0.565321\pi$
$271$	−3.77935e8	−	2.18201e8i	−1.15352	−	0.665984i	−0.949742	+	0.313034i	$0.898655\pi$
$272$	2.98858e8	+	2.14134e6i	0.900479	+	0.00645201i
$273$	2.85358e7			0.0848830
$274$	−3.04542e8	−	1.76555e8i	−0.894376	−	0.518506i
$275$	−2.63480e8	+	1.52120e8i	−0.763983	+	0.441086i
$276$	−3.62545e8	−	2.11051e8i	−1.03796	−	0.604233i
$277$	−4.73034e8			−1.33725			−0.668626	−	0.743598i	$-0.733117\pi$
$277$	−4.73034e8			−1.33725			−0.668626	+	0.743598i	$0.733117\pi$
$278$	−3.92094e7	+	6.76326e7i	−0.109454	+	0.188799i
$279$	8.02540e8	+	1.39004e9i	2.21234	+	3.83189i
$280$	1.47054e8	−	2.51574e8i	0.400336	−	0.684876i
$281$	4.30403e8	−	2.48493e8i	1.15719	−	0.668101i	0.206557	−	0.978435i	$-0.433774\pi$
$281$	4.30403e8	−	2.48493e8i	1.15719	−	0.668101i	0.950628	+	0.310333i	$0.100441\pi$
$282$	−1.95718e8	−	3.40400e8i	−0.519707	−	0.903895i
$283$	−9.64436e7	−	5.56818e7i	−0.252942	−	0.146036i	0.368169	−	0.929759i	$-0.379985\pi$
$283$	−9.64436e7	−	5.56818e7i	−0.252942	−	0.146036i	−0.621111	+	0.783723i	$0.713318\pi$
$284$	1.04864e8	+	1.83141e8i	0.271651	+	0.474430i
$285$	−1.08967e9	+	6.27231e8i	−2.78829	+	1.60498i
$286$	1.49833e7	+	8.68644e6i	0.0378727	+	0.0219564i
$287$	−5.98757e6	+	1.03708e7i	−0.0149508	+	0.0258955i
$288$	8.76281e6	−	9.78381e8i	0.0216157	−	2.41343i
$289$	3.87967e7	+	6.71979e7i	0.0945481	+	0.163762i
$290$	2.04787e8	+	3.56173e8i	0.493070	+	0.857567i
$291$	3.37137e8	−	1.94646e8i	0.802013	−	0.463042i
$292$	−1.11045e8	−	1.93937e8i	−0.261012	−	0.455850i
$293$			3.51864e8i			0.817219i	0.912709	+	0.408609i	$0.133986\pi$
$293$			3.51864e8i			0.817219i	−0.912709	+	0.408609i	$0.866014\pi$
$294$	1.14273e6	−	6.37956e8i	0.00262258	−	1.46411i
$295$	4.17847e8	+	7.23733e8i	0.947634	+	1.64135i
$296$	−8.22448e8	−	4.41965e6i	−1.84326	−	0.00990528i
$297$		−	5.11843e8i		−	1.13368i
$298$	911120.	−	5.08653e8i	0.00199443	−	1.11343i
$299$	−1.51506e7	+	2.62417e7i	−0.0327779	+	0.0567730i
$300$	8.83383e8	−	1.51748e9i	1.88897	−	3.24489i
$301$	1.03604e8	−	1.79447e8i	0.218974	−	0.379274i
$302$	−1.70268e8	+	9.78982e7i	−0.355721	+	0.204527i
$303$	8.76827e8			1.81078
$304$	4.26276e8	−	2.41321e8i	0.870228	−	0.492650i
$305$	2.59806e8			0.524323
$306$	−9.44366e8	+	5.42977e8i	−1.88415	+	1.08332i
$307$	−2.31234e8	+	4.00509e8i	−0.456107	+	0.790001i	−0.998751	−	0.0499618i	$-0.984090\pi$
$307$	−2.31234e8	+	4.00509e8i	−0.456107	+	0.790001i	0.542644	+	0.839963i	$0.317423\pi$
$308$	−5.10179e7	+	8.76390e7i	−0.0994935	+	0.170911i
$309$	2.38163e8	−	4.12511e8i	0.459219	−	0.795391i
$310$	2.99937e6	−	1.67446e9i	0.00571826	−	3.19234i
$311$			1.01720e8i			0.191755i	0.995393	+	0.0958775i	$0.0305657\pi$
$311$			1.01720e8i			0.191755i	−0.995393	+	0.0958775i	$0.969434\pi$
$312$	−9.99536e7	−	537128.i	−0.186319	−	0.00100124i
$313$	3.07297e8	+	5.32254e8i	0.566439	+	0.981101i	0.996914	+	0.0784988i	$0.0250127\pi$
$313$	3.07297e8	+	5.32254e8i	0.566439	+	0.981101i	−0.430475	+	0.902602i	$0.641654\pi$
$314$	−594484.	+	3.31884e8i	−0.00108364	+	0.604968i
$315$			1.06213e9i			1.91465i
$316$	3.00367e8	+	5.24582e8i	0.535485	+	0.935209i
$317$	−5.72338e8	+	3.30439e8i	−1.00913	+	0.582619i	−0.910935	−	0.412549i	$-0.864639\pi$
$317$	−5.72338e8	+	3.30439e8i	−1.00913	+	0.582619i	−0.0981899	+	0.995168i	$0.531305\pi$
$318$	3.90744e8	+	6.79597e8i	0.681393	+	1.18510i
$319$	−7.14875e7	−	1.23820e8i	−0.123300	−	0.213562i
$320$	−5.19829e8	+	8.78430e8i	−0.886820	+	1.49859i
$321$	−3.53530e8	+	6.12331e8i	−0.596566	+	1.03328i
$322$	−1.53491e8	−	8.89850e7i	−0.256205	−	0.148532i
$323$	−4.71951e8	−	2.73301e8i	−0.779271	−	0.451266i
$324$	7.33623e8	+	1.28125e9i	1.19830	+	2.09279i
$325$	−1.09838e8	−	6.34152e7i	−0.177485	−	0.102471i
$326$	3.59846e8	+	6.25858e8i	0.575248	+	1.00049i
$327$	1.86236e9	−	1.07523e9i	2.94541	−	1.70054i
$328$	2.11681e7	−	3.62134e7i	0.0331225	−	0.0566645i
$329$	−8.30330e7	−	1.43817e8i	−0.128548	−	0.222651i
$330$	−4.57276e8	+	7.88760e8i	−0.700454	+	1.20822i
$331$	4.86323e8			0.737101			0.368550	−	0.929608i	$-0.379854\pi$
$331$	4.86323e8			0.737101			0.368550	+	0.929608i	$0.379854\pi$
$332$	9.19094e8	+	5.35038e8i	1.37840	+	0.802420i
$333$	2.59616e9	−	1.49889e9i	3.85280	−	2.22441i
$334$	−9.64246e7	−	5.59013e7i	−0.141604	−	0.0820936i
$335$	−1.38602e9			−2.01425
$336$	4.19330e6	−	5.85242e8i	0.00603072	−	0.841681i
$337$	2.11047e8	+	1.21848e8i	0.300382	+	0.173426i	0.642614	−	0.766190i	$-0.277850\pi$
$337$	2.11047e8	+	1.21848e8i	0.300382	+	0.173426i	−0.342233	+	0.939615i	$0.611183\pi$
$338$	1.25870e6	−	7.02697e8i	0.00177302	−	0.989828i
$339$	−2.17236e9	−	1.25421e9i	−3.02853	−	1.74852i
$340$	1.13642e9	+	4.07121e6i	1.56806	+	0.00561756i
$341$			5.82713e8i			0.795819i
$342$	−8.97494e8	+	1.54346e9i	−1.21322	+	2.08643i
$343$		−	6.10288e8i		−	0.816592i
$344$	−3.66275e8	+	6.26606e8i	−0.485123	+	0.829927i
$345$	−1.38143e9	−	7.97568e8i	−1.81118	−	1.04568i
$346$	9.17602e8	+	1.64365e6i	1.19093	+	0.00213325i
$347$	1.98440e8	+	1.14570e8i	0.254963	+	0.147203i	0.622035	−	0.782990i	$-0.286306\pi$
$347$	1.98440e8	+	1.14570e8i	0.254963	+	0.147203i	−0.367072	+	0.930193i	$0.619640\pi$
$348$	7.13127e8	+	4.15137e8i	0.907067	+	0.528037i
$349$	−7.49621e7			−0.0943958			−0.0471979	−	0.998886i	$-0.515029\pi$
$349$	−7.49621e7			−0.0943958			−0.0471979	+	0.998886i	$0.515029\pi$
$350$	3.72460e8	−	6.42459e8i	0.464346	−	0.800953i
$351$	1.84787e8	−	1.06687e8i	0.228085	−	0.131685i
$352$	1.80352e8	−	3.06016e8i	0.220405	−	0.373978i
$353$	1.50851e9			1.82531			0.912654	−	0.408733i	$-0.134029\pi$
$353$	1.50851e9			1.82531			0.912654	+	0.408733i	$0.134029\pi$
$354$	1.45206e9	+	8.41818e8i	1.73969	+	1.00857i
$355$	4.01232e8	+	6.94955e8i	0.475989	+	0.824436i
$356$	−3.04641e6	+	8.50361e8i	−0.00357861	+	0.998914i
$357$	−5.64304e8	+	3.25801e8i	−0.656408	+	0.378978i
$358$	8.55643e8	−	4.91964e8i	0.985603	−	0.566687i
$359$	−4.90463e8	−	2.83169e8i	−0.559469	−	0.323009i	0.193463	−	0.981107i	$-0.438028\pi$
$359$	−4.90463e8	−	2.83169e8i	−0.559469	−	0.323009i	−0.752932	+	0.658098i	$0.771361\pi$
$360$	1.99923e7	−	3.72035e9i	0.0225842	−	4.20267i
$361$	−8.93869e8	−	2.32734e6i	−0.999997	−	0.00260366i
$362$	−6.32150e8	+	1.09040e9i	−0.700391	+	1.20811i
$363$	−6.83230e8	+	1.18339e9i	−0.749710	+	1.29854i
$364$	−4.22738e7	−	151446.i	−0.0459427	−	0.000164590i
$365$	−4.24885e8	−	7.35923e8i	−0.457348	−	0.792149i
$366$	4.52359e8	−	2.60090e8i	0.482281	−	0.277294i
$367$	−1.11733e9	+	6.45089e8i	−1.17991	+	0.681222i	−0.955994	−	0.293386i	$-0.905218\pi$
$367$	−1.11733e9	+	6.45089e8i	−1.17991	+	0.681222i	−0.223917	+	0.974608i	$0.571884\pi$
$368$	5.35964e8	+	3.14581e8i	0.560620	+	0.329052i
$369$			1.52890e8i			0.158412i
$370$	−3.12737e9	−	5.60187e6i	−3.20976	−	0.00574946i
$371$	1.65772e8	+	2.87126e8i	0.168540	+	0.291920i
$372$	−1.67108e9	−	2.91848e9i	−1.68305	−	2.93939i
$373$		−	5.36356e8i		−	0.535146i	−0.963538	−	0.267573i	$-0.913778\pi$
$373$		−	5.36356e8i		−	0.535146i	0.963538	−	0.267573i	$-0.0862216\pi$
$374$	−3.95474e8	−	708390.i	−0.390902	−	0.000700200i
$375$	1.69563e9	−	2.93691e9i	1.66043	−	2.87595i
$376$	2.88136e8	+	5.05318e8i	0.279538	+	0.490238i
$377$	2.98013e7	−	5.16174e7i	0.0286445	−	0.0496137i
$378$	6.22735e8	+	1.08308e9i	0.593037	+	1.03143i
$379$	−1.50929e8			−0.142408			−0.0712041	−	0.997462i	$-0.522684\pi$
$379$	−1.50929e8			−0.142408			−0.0712041	+	0.997462i	$0.522684\pi$
$380$	1.61760e9	−	9.23416e8i	1.51227	−	0.863287i
$381$	2.08838e9			1.93452
$382$	−5.11025e8	−	8.88794e8i	−0.469051	−	0.815792i
$383$	1.25438e8	−	2.17265e8i	0.114087	−	0.197604i	−0.803328	−	0.595537i	$-0.796939\pi$
$383$	1.25438e8	−	2.17265e8i	0.114087	−	0.197604i	0.917414	+	0.397934i	$0.130273\pi$
$384$	−2.57040e7	+	2.04987e9i	−0.0231655	+	1.84743i
$385$	−1.92798e8	+	3.33937e8i	−0.172183	+	0.298230i
$386$	1.82965e7	+	32773.4i	0.0161924	+	2.90045e-5i
$387$		−	2.64548e9i		−	2.32015i
$388$	−5.00478e8	+	2.86566e8i	−0.434985	+	0.249065i
$389$	6.89401e7	+	1.19408e8i	0.0593811	+	0.102851i	0.894188	−	0.447692i	$-0.147754\pi$
$389$	6.89401e7	+	1.19408e8i	0.0593811	+	0.102851i	−0.834807	+	0.550543i	$0.814421\pi$
$390$	−3.80075e8	−	680806.i	−0.324446	−	0.000581162i
$391$		−	6.91915e8i		−	0.585375i
$392$	−5.07865e6	+	9.45081e8i	−0.00425841	+	0.792442i
$393$	−6.87994e8	+	3.97214e8i	−0.571756	+	0.330104i
$394$	−4.98461e8	+	2.86597e8i	−0.410577	+	0.236067i
$395$	1.14927e9	+	1.99060e9i	0.938282	+	1.62515i
$396$	−4.63822e6	+	1.29469e9i	−0.00375335	+	1.04769i
$397$	1.47723e8	−	2.55863e8i	0.118490	−	0.205230i	−0.800680	−	0.599093i	$-0.795528\pi$
$397$	1.47723e8	−	2.55863e8i	0.118490	−	0.205230i	0.919169	+	0.393863i	$0.128861\pi$
$398$	4.84733e8	−	8.36120e8i	0.385400	−	0.664780i
$399$	−5.35195e8	+	9.24204e8i	−0.421800	+	0.728388i
$400$	−1.31672e9	+	2.24336e9i	−1.02869	+	1.75262i
$401$	−7.35552e8	−	4.24671e8i	−0.569650	−	0.328888i	0.187359	−	0.982291i	$-0.440007\pi$
$401$	−7.35552e8	−	4.24671e8i	−0.569650	−	0.328888i	−0.757010	+	0.653404i	$0.773340\pi$
$402$	−2.41326e9	+	1.38754e9i	−1.85274	+	1.06526i
$403$	−2.10373e8	+	1.21459e8i	−0.160112	+	0.0924405i
$404$	−1.29896e9	−	4.65351e6i	−0.980077	−	0.00351112i
$405$	2.80701e9	+	4.86188e9i	2.09967	+	3.63674i
$406$	3.01917e8	+	1.75034e8i	0.223896	+	0.129802i
$407$	1.08832e9			0.800161
$408$	1.98274e9	−	1.13057e9i	1.44529	−	0.824117i
$409$	1.27703e9	−	7.37292e8i	0.922929	−	0.532853i	0.0383609	−	0.999264i	$-0.487786\pi$
$409$	1.27703e9	−	7.37292e8i	0.922929	−	0.532853i	0.884568	+	0.466410i	$0.154453\pi$
$410$	7.99971e7	−	1.37988e8i	0.0573233	−	0.0988774i
$411$	−2.68836e9			−1.91003
$412$	−3.55012e8	+	6.09842e8i	−0.250093	+	0.429613i
$413$	6.14757e8	+	3.54930e8i	0.429416	+	0.247924i
$414$	−2.26517e9	−	4.05748e6i	−1.56892	−	0.00281031i
$415$	3.50209e9	+	2.02193e9i	2.40524	+	1.38867i
$416$	1.48071e8	+	1.32619e6i	0.100843	+	0.000903192i
$417$			5.97030e8i			0.403200i
$418$	−5.62347e8	+	3.22356e8i	−0.376606	+	0.215883i
$419$		−	8.24990e8i		−	0.547898i	−0.961744	−	0.273949i	$-0.911670\pi$
$419$		−	8.24990e8i		−	0.547898i	0.961744	−	0.273949i	$-0.0883300\pi$
$420$	7.97249e6	−	2.22540e9i	0.00525075	−	1.46567i
$421$	−1.62644e9	−	9.39027e8i	−1.06231	−	0.613325i	−0.136240	−	0.990676i	$-0.543502\pi$
$421$	−1.62644e9	−	9.39027e8i	−1.06231	−	0.613325i	−0.926070	+	0.377351i	$0.876835\pi$
$422$	−2.25200e6	+	1.25723e9i	−0.00145873	+	0.814369i
$423$	−1.83616e9	−	1.06011e9i	−1.17956	−	0.681019i
$424$	−5.75254e8	−	1.00885e9i	−0.366504	−	0.642756i
$425$	2.89611e9			1.83001
$426$	1.39432e9	+	8.08344e8i	0.873834	+	0.506597i
$427$	1.91119e8	−	1.10343e8i	0.118797	−	0.0685878i
$428$	5.26979e8	−	9.05250e8i	0.324893	−	0.558104i
$429$	1.32266e8			0.0808812
$430$	−1.38420e9	+	2.38762e9i	−0.839575	+	1.44819i
$431$	1.80632e8	+	3.12863e8i	0.108673	+	0.188228i	0.915233	−	0.402925i	$-0.132006\pi$
$431$	1.80632e8	+	3.12863e8i	0.108673	+	0.188228i	−0.806560	+	0.591153i	$0.798673\pi$
$432$	−2.16089e9	−	3.80549e9i	−1.28956	−	2.27100i
$433$	1.44200e9	−	8.32539e8i	0.853606	−	0.492830i	−0.00826003	−	0.999966i	$-0.502629\pi$
$433$	1.44200e9	−	8.32539e8i	0.853606	−	0.492830i	0.861866	+	0.507136i	$0.169296\pi$
$434$	−7.08960e8	−	1.23305e9i	−0.416301	−	0.724047i
$435$	2.71727e9	+	1.56882e9i	1.58278	+	0.913820i
$436$	−2.76466e9	+	1.58300e9i	−1.59749	+	0.914699i
$437$	−5.65749e8	−	9.82858e8i	−0.324294	−	0.563386i
$438$	−1.47652e9	−	8.55997e8i	−0.839612	−	0.486758i
$439$	4.65081e8	−	8.05544e8i	0.262363	−	0.454426i	−0.704506	−	0.709698i	$-0.748831\pi$
$439$	4.65081e8	−	8.05544e8i	0.262363	−	0.454426i	0.966869	+	0.255271i	$0.0821648\pi$
$440$	6.81609e8	−	1.16607e9i	0.381462	−	0.652587i
$441$	−1.72239e9	−	2.98326e9i	−0.956304	−	1.65637i
$442$	−8.21759e7	−	1.42923e8i	−0.0452654	−	0.0787273i
$443$	3.12402e7	−	1.80365e7i	0.0170726	−	0.00985689i	−0.491439	−	0.870912i	$-0.663529\pi$
$443$	3.12402e7	−	1.80365e7i	0.0170726	−	0.00985689i	0.508512	+	0.861055i	$0.330196\pi$
$444$	−5.45081e9	+	3.12104e9i	−2.95543	+	1.69223i
$445$			3.23349e9i			1.73945i
$446$	−392902.	+	2.19346e8i	−0.000209707	+	0.117073i
$447$	−1.94229e9	−	3.36414e9i	−1.02858	−	1.78155i
$448$	−9.31809e6	+	8.66972e8i	−0.00489614	+	0.455546i
$449$			2.29991e8i			0.119908i	0.998201	+	0.0599540i	$0.0190954\pi$
$449$			2.29991e8i			0.119908i	−0.998201	+	0.0599540i	$0.980905\pi$
$450$	1.69832e7	−	9.48122e9i	0.00878567	−	4.90479i
$451$	−2.77529e7	+	4.80694e7i	−0.0142459	+	0.0246746i
$452$	3.21154e9	+	1.86956e9i	1.63579	+	0.952256i
$453$	−7.49974e8	+	1.29899e9i	−0.379055	+	0.656543i
$454$	1.56882e9	−	9.02018e8i	0.786826	−	0.452397i
$455$	−1.60746e8			−0.0800017
$456$	1.89205e9	−	3.22717e9i	0.934447	−	1.59384i
$457$	−2.49069e8			−0.122071			−0.0610355	−	0.998136i	$-0.519440\pi$
$457$	−2.49069e8			−0.122071			−0.0610355	+	0.998136i	$0.519440\pi$
$458$	7.60396e8	−	4.37201e8i	0.369837	−	0.212643i
$459$	−2.43615e9	+	4.21954e9i	−1.17587	+	2.03667i
$460$	2.04226e9	+	1.18887e9i	0.978268	+	0.569486i
$461$	−1.19623e9	+	2.07193e9i	−0.568671	+	0.984966i	0.428027	+	0.903766i	$0.359209\pi$
$461$	−1.19623e9	+	2.07193e9i	−0.568671	+	0.984966i	−0.996698	+	0.0812006i	$0.974125\pi$
$462$	−1.38721e6	+	7.74442e8i	−0.000654480	+	0.365378i
$463$			3.23004e8i			0.151243i	0.997137	+	0.0756214i	$0.0240940\pi$
$463$			3.23004e8i			0.151243i	−0.997137	+	0.0756214i	$0.975906\pi$
$464$	−1.05424e9	−	6.18782e8i	−0.489923	−	0.287557i
$465$	−6.39392e9	−	1.10746e10i	−2.94905	−	5.10790i
$466$	1.25627e6	−	7.01342e8i	0.000575087	−	0.321055i
$467$		−	1.24638e9i		−	0.566295i	−0.959076	−	0.283148i	$-0.908621\pi$
$467$		−	1.24638e9i		−	0.566295i	0.959076	−	0.283148i	$-0.0913787\pi$
$468$	−4.68381e8	+	2.68187e8i	−0.211222	+	0.120942i
$469$	−1.01959e9	+	5.88661e8i	−0.456374	+	0.263488i
$470$	1.10250e9	+	1.91752e9i	0.489821	+	0.851915i
$471$	1.26729e9	+	2.19502e9i	0.558862	+	0.967977i
$472$	−2.14666e9	−	1.25480e9i	−0.939649	−	0.549260i
$473$	4.80212e8	−	8.31751e8i	0.208650	−	0.361393i
$474$	3.99383e9	+	2.31539e9i	1.72253	+	0.998619i
$475$	4.11390e9	−	2.36802e9i	1.76127	−	1.01381i
$476$	8.37706e8	−	4.79656e8i	0.356014	−	0.203848i
$477$	3.66584e9	+	2.11647e9i	1.54653	+	0.892890i
$478$	−1.85510e9	−	3.22646e9i	−0.776909	−	1.35123i
$479$	3.28053e8	−	1.89402e8i	0.136386	−	0.0787425i	−0.430254	−	0.902708i	$-0.641576\pi$
$479$	3.28053e8	−	1.89402e8i	0.136386	−	0.0787425i	0.566641	+	0.823965i	$0.308243\pi$
$480$	−6.98142e7	+	7.79486e9i	−0.0288137	+	3.21710i
$481$	2.26847e8	+	3.92911e8i	0.0929449	+	0.160985i
$482$	−1.13733e9	+	1.96179e9i	−0.462617	+	0.797971i
$483$	−1.35495e9			−0.547152
$484$	1.01844e9	−	1.74948e9i	0.408296	−	0.701375i
$485$	−1.89913e9	+	1.09647e9i	−0.755892	+	0.436414i
$486$	4.03703e9	+	2.34043e9i	1.59527	+	0.924846i
$487$	−2.72552e9			−1.06930			−0.534648	−	0.845075i	$-0.679556\pi$
$487$	−2.72552e9			−1.06930			−0.534648	+	0.845075i	$0.679556\pi$
$488$	−6.71519e8	+	3.82905e8i	−0.261571	+	0.149150i
$489$	4.77473e9	+	2.75669e9i	1.84658	+	1.06612i
$490$	−6.43715e6	+	3.59368e9i	−0.00247177	+	1.37992i
$491$	−1.29852e9	−	7.49703e8i	−0.495068	−	0.285828i	0.231607	−	0.972810i	$-0.425602\pi$
$491$	−1.29852e9	−	7.49703e8i	−0.495068	−	0.285828i	−0.726675	+	0.686982i	$0.758935\pi$
$492$	1.14762e6	−	3.20341e8i	0.000434431	−	0.121265i
$493$			1.36100e9i			0.511557i
$494$	−2.33592e8	−	1.35830e8i	−0.0871795	−	0.0506933i
$495$			4.92304e9i			1.82438i
$496$	2.46009e9	+	4.33240e9i	0.905244	+	1.59420i
$497$	5.90312e8	+	3.40817e8i	0.215692	+	0.124530i
$498$	8.12178e9	+	1.45481e7i	2.94679	+	0.00527841i
$499$	−1.22271e9	−	7.05933e8i	−0.440527	−	0.254338i	0.263294	−	0.964716i	$-0.415191\pi$
$499$	−1.22271e9	−	7.05933e8i	−0.440527	−	0.254338i	−0.703821	+	0.710377i	$0.748524\pi$
$500$	−2.52754e9	+	4.34183e9i	−0.904281	+	1.55338i
$501$	−8.51193e8			−0.302410
$502$	3.97645e8	−	6.85901e8i	0.140292	−	0.241990i
$503$	−3.50049e9	+	2.02101e9i	−1.22643	+	0.708077i	−0.966280	−	0.257493i	$-0.917104\pi$
$503$	−3.50049e9	+	2.02101e9i	−1.22643	+	0.708077i	−0.260145	+	0.965570i	$0.583770\pi$
$504$	−1.56538e9	−	2.74527e9i	−0.544643	−	0.955166i
$505$	−4.93927e9			−1.70664
$506$	−7.11444e8	−	4.12453e8i	−0.244126	−	0.141530i
$507$	−2.68324e9	−	4.64751e9i	−0.914391	−	1.58377i
$508$	−3.09379e9	−	1.10835e7i	−1.04705	−	0.00375106i
$509$	−2.30909e9	+	1.33316e9i	−0.776120	+	0.448093i	−0.835054	−	0.550169i	$-0.814563\pi$
$509$	−2.30909e9	+	1.33316e9i	−0.776120	+	0.448093i	0.0589332	+	0.998262i	$0.481230\pi$
$510$	7.52386e9	−	4.32595e9i	2.51157	−	1.44406i
$511$	−6.25112e8	−	3.60908e8i	−0.207245	−	0.119653i
$512$	4.89579e7	−	3.03661e9i	0.0161205	−	0.999870i
$513$	−1.03961e7	+	7.98574e9i	−0.00339985	+	2.61159i
$514$	−8.55874e8	+	1.47630e9i	−0.277996	+	0.479518i
$515$	−1.34160e9	+	2.32372e9i	−0.432811	+	0.749651i
$516$	−1.98574e7	+	5.54291e9i	−0.00636282	+	1.77608i
$517$	−3.84865e8	−	6.66606e8i	−0.122487	−	0.212154i
$518$	−2.30295e9	+	1.32411e9i	−0.727997	+	0.418573i
$519$	6.06885e9	−	3.50385e9i	1.90555	−	1.10017i
$520$	5.63051e8	+	3.02571e6i	0.175605	+	0.000943659i
$521$		−	5.78099e9i		−	1.79089i	−0.445168	−	0.895447i	$-0.646856\pi$
$521$		−	5.78099e9i		−	1.79089i	0.445168	−	0.895447i	$-0.353144\pi$
$522$	4.45561e9	+	7.98107e6i	1.37107	+	0.00245592i
$523$	−1.23670e9	−	2.14203e9i	−0.378015	−	0.654741i	0.612759	−	0.790270i	$-0.290060\pi$
$523$	−1.23670e9	−	2.14203e9i	−0.378015	−	0.654741i	−0.990773	+	0.135530i	$0.956726\pi$
$524$	1.02132e9	−	5.84793e8i	0.310101	−	0.177559i
$525$		−	5.67134e9i		−	1.71052i
$526$	1.36474e9	+	2.44458e6i	0.408884	+	0.000732410i
$527$	2.77346e9	−	4.80378e9i	0.825439	−	1.42970i
$528$	1.94363e7	−	2.71264e9i	0.00574640	−	0.802000i
$529$	−9.83024e8	+	1.70265e9i	−0.288715	+	0.500069i
$530$	−2.20111e9	−	3.82825e9i	−0.642208	−	1.11695i
$531$	9.06303e9			2.62689
$532$	7.97759e8	−	1.36630e9i	0.229710	−	0.393420i
$533$	−2.31390e7			−0.00661909
$534$	3.23703e9	+	5.62997e9i	0.919925	+	1.59997i
$535$	1.99148e9	−	3.44934e9i	0.562259	−	0.973862i
$536$	3.58244e9	−	2.04274e9i	1.00485	−	0.572975i
$537$	3.76881e9	−	6.52778e9i	1.05025	−	1.81909i
$538$	−2.59389e9	−	4.64629e6i	−0.718149	−	0.00128638i
$539$		−	1.25060e9i		−	0.344000i
$540$	−8.26851e9	−	1.44407e10i	−2.25969	−	3.94648i
$541$	1.31206e8	+	2.27256e8i	0.0356258	+	0.0617057i	0.883289	−	0.468830i	$-0.155324\pi$
$541$	1.31206e8	+	2.27256e8i	0.0356258	+	0.0617057i	−0.847663	+	0.530535i	$0.821991\pi$
$542$	4.93731e9	+	8.84392e6i	1.33197	+	0.00238587i
$543$			9.62557e9i			2.58004i
$544$	−2.94330e9	+	1.66435e9i	−0.783859	+	0.443248i
$545$	−1.04909e10	+	6.05692e9i	−2.77603	+	1.60274i
$546$	−2.79881e8	+	1.60922e8i	−0.0735868	+	0.0423098i
$547$	−2.07203e9	−	3.58886e9i	−0.541303	−	0.937564i	−0.998830	−	0.0483680i	$-0.984598\pi$
$547$	−2.07203e9	−	3.58886e9i	−0.541303	−	0.937564i	0.457527	−	0.889196i	$-0.348735\pi$
$548$	3.98262e9	+	1.42677e7i	1.03380	+	0.00370359i
$549$	1.40878e9	−	2.44009e9i	0.363363	−	0.629364i
$550$	1.72638e9	−	2.97785e9i	0.442454	−	0.763192i
$551$	1.11283e9	+	1.93329e9i	0.283399	+	0.492341i
$552$	4.74604e9	+	2.55041e7i	1.20100	+	0.00645392i
$553$	1.69087e9	+	9.76222e8i	0.425179	+	0.245477i
$554$	4.63956e9	−	2.66758e9i	1.15929	−	0.666551i
$555$	−2.06838e10	+	1.19418e10i	−5.13577	+	2.96514i
$556$	3.16857e6	−	8.84459e8i	0.000781811	−	0.218231i
$557$	−3.42003e8	−	5.92367e8i	−0.0838566	−	0.145244i	0.821047	−	0.570861i	$-0.193390\pi$
$557$	−3.42003e8	−	5.92367e8i	−0.0838566	−	0.145244i	−0.904903	+	0.425617i	$0.860057\pi$
$558$	−1.57102e10	−	9.10786e9i	−3.82792	−	2.21920i
$559$	4.00376e8			0.0969453
$560$	−2.36214e7	+	3.29674e9i	−0.00568391	+	0.793279i
$561$	−2.61560e9	+	1.51012e9i	−0.625462	+	0.361110i
$562$	−2.82010e9	+	4.86441e9i	−0.670173	+	1.15599i
$563$	1.59650e9			0.377042			0.188521	−	0.982069i	$-0.439631\pi$
$563$	1.59650e9			0.377042			0.188521	+	0.982069i	$0.439631\pi$
$564$	3.83923e9	+	2.23496e9i	0.901089	+	0.524557i
$565$	1.22372e10	+	7.06512e9i	2.85437	+	1.64797i
$566$	1.25993e9	+	2.25684e6i	0.292072	+	0.000523171i
$567$	4.12981e9	+	2.38435e9i	0.951457	+	0.549324i
$568$	−2.06130e9	−	1.20491e9i	−0.471978	−	0.275889i
$569$			2.26995e9i			0.516564i	0.966070	+	0.258282i	$0.0831563\pi$
$569$			2.26995e9i			0.516564i	−0.966070	+	0.258282i	$0.916844\pi$
$570$	7.15042e9	−	1.22969e10i	1.61722	−	2.78121i
$571$		−	3.25189e9i		−	0.730986i	−0.930814	−	0.365493i	$-0.880900\pi$
$571$		−	3.25189e9i		−	0.730986i	0.930814	−	0.365493i	$-0.119100\pi$
$572$	−1.95943e8	−	701964.i	−0.0437767	−	0.000156830i
$573$	−6.78069e9	−	3.91483e9i	−1.50568	−	0.869305i
$574$	242683.	−	1.35483e8i	5.35608e−5	−	0.0299015i
$575$	5.21539e9	+	3.01111e9i	1.14406	+	0.660524i
$576$	5.43143e9	+	9.64545e9i	1.18423	+	2.10302i
$577$	4.32411e9			0.937090			0.468545	−	0.883440i	$-0.344778\pi$
$577$	4.32411e9			0.937090			0.468545	+	0.883440i	$0.344778\pi$
$578$	−7.59470e8	−	4.40296e8i	−0.163593	−	0.0948413i
$579$	1.21009e8	−	6.98649e7i	0.0259086	−	0.0149584i
$580$	−4.01713e9	−	2.33852e9i	−0.854905	−	0.497671i
$581$	3.43496e9			0.726616
$582$	−2.20900e9	+	3.81032e9i	−0.464478	+	0.801182i
$583$	7.68370e8	+	1.33086e9i	0.160594	+	0.278158i
$584$	2.18281e9	+	1.27594e9i	0.453494	+	0.265084i
$585$	−1.77734e9	+	1.02615e9i	−0.367049	+	0.211916i
$586$	−1.98427e9	−	3.45111e9i	−0.407341	−	0.708463i
$587$	5.75221e9	+	3.32104e9i	1.17382	+	0.677705i	0.954577	−	0.297965i	$-0.0963080\pi$
$587$	5.75221e9	+	3.32104e9i	1.17382	+	0.677705i	0.219243	+	0.975670i	$0.429641\pi$
$588$	3.58641e9	+	6.26356e9i	0.727511	+	1.27058i
$589$	1.18356e7	−	9.09146e9i	0.00238663	−	1.83329i
$590$	−8.17962e9	−	4.74206e9i	−1.63965	−	0.950572i
$591$	−2.19555e9	+	3.80280e9i	−0.437509	+	0.757788i
$592$	8.09155e9	−	4.59468e9i	1.60290	−	0.910184i
$593$	−1.63173e9	−	2.82623e9i	−0.321333	−	0.556566i	0.659430	−	0.751766i	$-0.270798\pi$
$593$	−1.63173e9	−	2.82623e9i	−0.321333	−	0.556566i	−0.980763	+	0.195200i	$0.937464\pi$
$594$	2.88643e9	+	5.02019e9i	0.565078	+	0.982806i
$595$	3.17879e9	−	1.83528e9i	0.618661	−	0.357184i
$596$	2.85951e9	+	4.99404e9i	0.553260	+	0.966252i
$597$		−	7.38089e9i		−	1.41971i
$598$	614072.	−	3.42819e8i	0.000117426	−	0.0655557i
$599$	−1.51031e9	−	2.61593e9i	−0.287126	−	0.497316i	0.685997	−	0.727605i	$-0.259366\pi$
$599$	−1.51031e9	−	2.61593e9i	−0.287126	−	0.497316i	−0.973122	+	0.230288i	$0.926033\pi$
$600$	−1.06751e8	+	1.98652e10i	−0.0201764	+	3.75461i
$601$		−	5.66704e9i		−	1.06487i	−0.846472	−	0.532434i	$-0.821277\pi$
$601$		−	5.66704e9i		−	1.06487i	0.846472	−	0.532434i	$-0.178723\pi$
$602$	−4.19917e6	+	2.34428e9i	−0.000784469	+	0.437947i
$603$	−7.51563e9	+	1.30175e10i	−1.39590	+	2.41777i
$604$	1.11793e9	−	1.92039e9i	0.206436	−	0.354617i
$605$	3.84871e9	−	6.66617e9i	0.706597	−	1.22386i
$606$	−8.59998e9	+	4.94468e9i	−1.56980	+	0.902577i
$607$	9.10387e9			1.65221			0.826106	−	0.563515i	$-0.190551\pi$
$607$	9.10387e9			1.65221			0.826106	+	0.563515i	$0.190551\pi$
$608$	−2.82006e9	+	4.77079e9i	−0.508857	+	0.860851i
$609$	2.66519e9			0.478154
$610$	−2.54819e9	+	1.46512e9i	−0.454546	+	0.261348i
$611$	1.60440e8	−	2.77891e8i	0.0284557	−	0.0492868i
$612$	6.20041e9	−	1.06511e10i	1.09343	−	1.87830i
$613$	−2.50217e9	+	4.33389e9i	−0.438738	+	0.759916i	−0.997592	−	0.0693494i	$-0.977908\pi$
$613$	−2.50217e9	+	4.33389e9i	−0.438738	+	0.759916i	0.558855	+	0.829266i	$0.311241\pi$
$614$	9.37217e6	−	5.23222e9i	0.00163400	−	0.912213i
$615$		−	1.21809e9i		−	0.211163i
$616$	6.16519e6	−	1.14727e9i	0.00106271	−	0.197758i
$617$	4.07251e8	+	7.05379e8i	0.0698013	+	0.120899i	0.898814	−	0.438331i	$-0.144430\pi$
$617$	4.07251e8	+	7.05379e8i	0.0698013	+	0.120899i	−0.829012	+	0.559230i	$0.811097\pi$
$618$	−9.65302e6	+	5.38901e9i	−0.00164514	+	0.918437i
$619$		−	8.63972e9i		−	1.46414i	−0.681229	−	0.732070i	$-0.738554\pi$
$619$		−	8.63972e9i		−	1.46414i	0.681229	−	0.732070i	$-0.261446\pi$
$620$	9.41337e9	+	1.64402e10i	1.58626	+	2.77036i
$621$	−8.77416e9	+	5.06576e9i	−1.47023	+	0.848837i
$622$	−5.73631e8	−	9.97682e8i	−0.0955799	−	0.166236i
$623$	1.37330e9	+	2.37863e9i	0.227540	+	0.394111i
$624$	9.83381e8	−	5.58400e8i	0.162023	−	0.0920024i
$625$	−3.34985e9	+	5.80211e9i	−0.548839	+	0.950617i
$626$	−6.01553e9	−	3.48745e9i	−0.980085	−	0.568196i
$627$	−2.48067e9	+	4.28376e9i	−0.401914	+	0.694047i
$628$	−1.86576e9	−	3.25849e9i	−0.300605	−	0.524998i
$629$	−8.97194e9	−	5.17995e9i	−1.43750	−	0.829943i
$630$	−5.98964e9	−	1.04174e10i	−0.954352	−	1.65985i
$631$	7.09918e9	−	4.09871e9i	1.12488	−	0.649449i	0.182236	−	0.983255i	$-0.441666\pi$
$631$	7.09918e9	−	4.09871e9i	1.12488	−	0.649449i	0.942642	+	0.333806i	$0.108333\pi$
$632$	−5.90430e9	−	3.45128e9i	−0.930376	−	0.543840i
$633$	4.80072e9	+	8.31509e9i	0.752304	+	1.30303i
$634$	3.75009e9	−	6.46856e9i	0.584425	−	1.00808i
$635$	−1.17641e10			−1.82327
$636$	−7.66490e9	−	4.46202e9i	−1.18143	−	0.687752i
$637$	4.51497e8	−	2.60672e8i	0.0692097	−	0.0399582i
$638$	1.39941e9	+	8.11297e8i	0.213341	+	0.123682i
$639$	8.70265e9			1.31947
$640$	1.44794e8	−	1.15472e10i	0.0218334	−	1.74119i
$641$	4.13155e9	+	2.38535e9i	0.619598	+	0.357725i	0.776712	−	0.629856i	$-0.216886\pi$
$641$	4.13155e9	+	2.38535e9i	0.619598	+	0.357725i	−0.157115	+	0.987580i	$0.550219\pi$
$642$	1.43290e7	−	7.99945e9i	0.00213718	−	1.19313i
$643$	7.20987e9	+	4.16262e9i	1.06952	+	0.617488i	0.928050	−	0.372455i	$-0.121484\pi$
$643$	7.20987e9	+	4.16262e9i	1.06952	+	0.617488i	0.141470	+	0.989943i	$0.454817\pi$
$644$	2.00726e9	+	7.19101e6i	0.296145	+	0.00106094i
$645$			2.10768e10i			3.09276i
$646$	6.17016e9	+	1.90848e7i	0.900498	+	0.00278531i
$647$		−	7.21197e9i		−	1.04686i	−0.852069	−	0.523430i	$-0.824652\pi$
$647$		−	7.21197e9i		−	1.04686i	0.852069	−	0.523430i	$-0.175348\pi$
$648$	−1.44208e10	−	8.42948e9i	−2.08198	−	1.21699i
$649$	2.84945e9	+	1.64513e9i	0.409171	+	0.236235i
$650$	1.43492e9	+	2.57029e6i	0.204942	+	0.000367101i
$651$	−9.40705e9	−	5.43116e9i	−1.33635	−	0.771541i
$652$	−7.05880e9	−	4.10919e9i	−0.997388	−	0.580617i
$653$	1.74372e9			0.245065			0.122533	−	0.992464i	$-0.460898\pi$
$653$	1.74372e9			0.245065			0.122533	+	0.992464i	$0.460898\pi$
$654$	−1.22026e10	+	2.10484e10i	−1.70581	+	2.94236i
$655$	3.87555e9	−	2.23755e9i	0.538876	−	0.311120i
$656$	−3.40024e6	+	4.74557e8i	−0.000470269	+	0.0656335i
$657$	−9.21567e9			−1.26779
$658$	1.62542e9	+	9.42324e8i	0.222421	+	0.128946i
$659$	−3.98796e9	−	6.90735e9i	−0.542815	−	0.940183i	−0.998741	−	0.0501651i	$-0.984025\pi$
$659$	−3.98796e9	−	6.90735e9i	−0.542815	−	0.940183i	0.455926	−	0.890018i	$-0.349308\pi$
$660$	3.69532e7	−	1.03149e10i	0.00500320	−	1.39657i
$661$	−6.63184e9	+	3.82890e9i	−0.893160	+	0.515666i	−0.874975	−	0.484169i	$-0.839122\pi$
$661$	−6.63184e9	+	3.82890e9i	−0.893160	+	0.515666i	−0.0181851	+	0.999835i	$0.505789\pi$
$662$	−4.76989e9	+	2.74252e9i	−0.639007	+	0.367406i
$663$	−1.09038e9	−	6.29529e8i	−0.145304	−	0.0838916i
$664$	−1.20318e10	−	6.46561e7i	−1.59493	−	0.00857079i
$665$	3.01482e9	−	5.20615e9i	0.397544	−	0.686501i
$666$	−1.70106e10	+	2.93417e10i	−2.23131	+	3.84881i
$667$	−1.41504e9	+	2.45092e9i	−0.184641	+	0.319808i
$668$	1.26098e9	+	4.51747e6i	0.163679	+	0.000586378i
$669$	8.37572e8	+	1.45072e9i	0.108151	+	0.187323i
$670$	1.35942e10	−	7.81618e9i	1.74619	−	1.00400i
$671$	8.85855e8	−	5.11449e8i	0.113197	−	0.0653542i
$672$	3.25922e9	+	5.76374e9i	0.414306	+	0.732676i
$673$			9.13055e9i			1.15463i	0.816520	+	0.577317i	$0.195900\pi$
$673$			9.13055e9i			1.15463i	−0.816520	+	0.577317i	$0.804100\pi$
$674$	−2.75710e9	−	4.93863e6i	−0.346851	−	0.000621293i
$675$	−2.12035e10	−	3.67255e10i	−2.65365	−	4.59626i
$676$	3.95037e9	+	6.89921e9i	0.491841	+	0.858985i
$677$		−	1.04821e10i		−	1.29834i	−0.760643	−	0.649171i	$-0.775116\pi$
$677$		−	1.04821e10i		−	1.29834i	0.760643	−	0.649171i	$-0.224884\pi$
$678$	2.83795e10	+	5.08346e7i	3.49704	+	0.00626405i
$679$	−9.31366e8	+	1.61317e9i	−0.114176	+	0.197759i
$680$	−1.11690e10	+	6.36866e9i	−1.36218	+	0.776725i
$681$	6.91013e9	−	1.19687e10i	0.838439	−	1.45222i
$682$	−3.28609e9	−	5.71529e9i	−0.396674	−	0.689911i
$683$	−1.75406e9			−0.210655			−0.105327	−	0.994438i	$-0.533589\pi$
$683$	−1.75406e9			−0.210655			−0.105327	+	0.994438i	$0.533589\pi$
$684$	9.86620e7	−	2.01996e10i	0.0117884	−	2.41350i
$685$	1.51439e10			1.80019
$686$	3.44159e9	+	5.98575e9i	0.407029	+	0.707920i
$687$	3.34928e9	−	5.80113e9i	0.394097	−	0.682596i
$688$	5.88348e7	−	8.21133e9i	0.00688771	−	0.961289i
$689$	−3.20314e8	+	5.54800e8i	−0.0373086	+	0.0646203i
$690$	1.80469e10	+	3.23263e7i	2.09137	+	0.00374614i
$691$		−	3.99510e9i		−	0.460632i	−0.973116	−	0.230316i	$-0.926024\pi$
$691$		−	3.99510e9i		−	0.460632i	0.973116	−	0.230316i	$-0.0739760\pi$
$692$	−9.00918e9	+	5.15851e9i	−1.03351	+	0.591770i
$693$	2.09088e9	+	3.62151e9i	0.238651	+	0.413355i
$694$	−2.59241e9	−	4.64363e6i	−0.294405	−	0.000527351i
$695$		−	3.36314e9i		−	0.380013i
$696$	−9.33548e9	−	5.01667e7i	−1.04955	−	0.00564006i
$697$	4.57579e8	−	2.64184e8i	0.0511861	−	0.0295523i
$698$	7.35234e8	−	4.22733e8i	0.0818335	−	0.0470514i
$699$	−2.67807e9	−	4.63855e9i	−0.296587	−	0.513703i
$700$	−3.00990e7	+	8.40170e9i	−0.00331673	+	0.925814i
$701$	3.63726e9	−	6.29992e9i	0.398805	−	0.690751i	−0.594773	−	0.803893i	$-0.702758\pi$
$701$	3.63726e9	−	6.29992e9i	0.398805	−	0.690751i	0.993579	+	0.113142i	$0.0360915\pi$
$702$	−1.21077e9	+	2.08847e9i	−0.132094	+	0.227849i
$703$	−1.69800e10	−	2.21051e7i	−1.84329	−	0.00239966i
$704$	−4.31902e7	+	4.01849e9i	−0.00466531	+	0.434069i
$705$	1.46289e10	+	8.44600e9i	1.57235	+	0.907798i
$706$	−1.47956e10	+	8.50692e9i	−1.58240	+	0.909821i
$707$	−3.63345e9	+	2.09777e9i	−0.386679	+	0.223249i
$708$	−1.89892e10	−	6.80286e7i	−2.01090	−	0.00720402i
$709$	2.53356e9	+	4.38826e9i	0.266974	+	0.462413i	0.968079	−	0.250645i	$-0.0806427\pi$
$709$	2.53356e9	+	4.38826e9i	0.266974	+	0.462413i	−0.701105	+	0.713058i	$0.747309\pi$
$710$	−7.85437e9	−	4.55350e9i	−0.823582	−	0.477465i
$711$	2.49275e10			2.60097
$712$	−4.76556e9	−	8.35758e9i	−0.494804	−	0.867762i
$713$	9.98904e9	−	5.76717e9i	1.03207	−	0.595868i
$714$	3.69745e9	−	6.37775e9i	0.380153	−	0.655728i
$715$	−7.45070e8			−0.0762300
$716$	−5.61788e9	+	9.65044e9i	−0.571975	+	0.982543i
$717$	−2.46150e10	−	1.42115e10i	−2.49392	−	1.43986i
$718$	6.40737e9	+	1.14772e7i	0.646018	+	0.00115717i
$719$	−1.43690e8	−	8.29594e7i	−0.0144170	−	0.00832366i	0.492774	−	0.870157i	$-0.335983\pi$
$719$	−1.43690e8	−	8.29594e7i	−0.0144170	−	0.00832366i	−0.507191	+	0.861834i	$0.669316\pi$
$720$	2.07841e10	+	3.66022e10i	2.07523	+	3.65464i
$721$			2.27918e9i			0.226467i
$722$	8.78026e9	−	5.01796e9i	0.868214	−	0.496189i
$723$			1.73178e10i			1.70415i
$724$	5.10850e7	−	1.42596e10i	0.00500275	−	1.39644i
$725$	−1.02587e10	−	5.92286e9i	−0.999791	−	0.577229i
$726$	2.76921e7	−	1.54597e10i	0.00268582	−	1.49942i
$727$	−1.12409e10	−	6.48991e9i	−1.08500	−	0.626424i	−0.152758	−	0.988264i	$-0.548815\pi$
$727$	−1.12409e10	−	6.48991e9i	−1.08500	−	0.626424i	−0.932240	+	0.361840i	$0.882149\pi$
$728$	4.15479e8	−	2.36909e8i	0.0399107	−	0.0227574i
$729$	1.04112e10			0.995300
$730$	8.31739e9	+	4.82193e9i	0.791329	+	0.458766i
$731$	−7.91755e9	+	4.57120e9i	−0.749687	+	0.432832i
$732$	−2.97005e9	+	5.10197e9i	−0.279882	+	0.480783i
$733$	7.63967e9			0.716491			0.358245	−	0.933627i	$-0.383375\pi$
$733$	7.63967e9			0.716491			0.358245	+	0.933627i	$0.383375\pi$
$734$	7.32098e9	−	1.26280e10i	0.683334	−	1.17869i
$735$	1.37224e10	+	2.37680e10i	1.27475	+	2.20793i
$736$	−7.03079e9	−	6.29709e7i	−0.650028	−	0.00582194i
$737$	−4.72589e9	+	2.72849e9i	−0.434858	+	0.251065i
$738$	−8.62194e8	−	1.49956e9i	−0.0789602	−	0.137331i
$739$	1.58197e10	+	9.13350e9i	1.44192	+	0.832495i	0.997978	−	0.0635585i	$-0.0202450\pi$
$739$	1.58197e10	+	9.13350e9i	1.44192	+	0.832495i	0.443946	+	0.896054i	$0.353578\pi$
$740$	3.07050e10	−	1.75812e10i	2.78547	−	1.59491i
$741$	−2.06361e9	−	2.68647e6i	−0.186322	−	0.000242560i
$742$	−3.24510e9	−	1.88132e9i	−0.291618	−	0.169063i
$743$	−7.89225e9	+	1.36698e10i	−0.705895	+	1.22265i	0.260472	+	0.965481i	$0.416122\pi$
$743$	−7.89225e9	+	1.36698e10i	−0.705895	+	1.22265i	−0.966368	+	0.257165i	$0.917212\pi$
$744$	3.28482e10	+	1.92010e10i	2.92420	+	1.70930i
$745$	1.09411e10	+	1.89506e10i	0.969427	+	1.67910i
$746$	3.02467e9	+	5.26062e9i	0.266742	+	0.463928i
$747$	3.79798e10	−	2.19276e10i	3.33373	−	1.92473i
$748$	3.88284e9	−	2.22325e9i	0.339230	−	0.194237i
$749$		−	3.38322e9i		−	0.294201i
$750$	−6.87257e7	+	3.83676e10i	−0.00594846	+	3.32086i
$751$	−2.92188e9	−	5.06085e9i	−0.251723	−	0.435997i	0.712277	−	0.701898i	$-0.247664\pi$
$751$	−2.92188e9	−	5.06085e9i	−0.251723	−	0.435997i	−0.964000	+	0.265901i	$0.914330\pi$
$752$	−5.67570e9	−	3.33131e9i	−0.486695	−	0.285662i
$753$		−	6.05483e9i		−	0.516796i
$754$	−1.20788e6	+	6.74326e8i	−0.000102618	+	0.0572889i
$755$	4.22469e9	−	7.31738e9i	0.357257	−	0.618787i
$756$	−1.22157e10	−	7.11119e9i	−1.02823	−	0.598571i
$757$	−1.09194e10	+	1.89130e10i	−0.914880	+	1.58462i	−0.107803	+	0.994172i	$0.534382\pi$
$757$	−1.09194e10	+	1.89130e10i	−0.914880	+	1.58462i	−0.807077	+	0.590446i	$0.798952\pi$
$758$	1.48032e9	−	8.51133e8i	0.123457	−	0.0709831i
$759$	−6.28031e9			−0.521356
$760$	−1.06581e10	+	1.81791e10i	−0.880710	+	1.50219i
$761$	−1.59753e10			−1.31402			−0.657010	−	0.753882i	$-0.728179\pi$
$761$	−1.59753e10			−1.31402			−0.657010	+	0.753882i	$0.728179\pi$
$762$	−2.04830e10	+	1.17770e10i	−1.67707	+	0.964256i
$763$	−5.14491e9	+	8.91124e9i	−0.419316	+	0.726277i
$764$	1.00243e10	+	5.83554e9i	0.813260	+	0.473428i
$765$	2.34316e10	−	4.05847e10i	1.89228	−	3.27753i
$766$	−5.08415e6	+	2.83834e9i	−0.000408713	+	0.228173i
$767$			1.37163e9i			0.109762i
$768$	−1.13077e10	−	2.02503e10i	−0.900764	−	1.61312i
$769$	4.48524e9	+	7.76866e9i	0.355667	+	0.616033i	0.987232	−	0.159290i	$-0.0509205\pi$
$769$	4.48524e9	+	7.76866e9i	0.355667	+	0.616033i	−0.631565	+	0.775323i	$0.717587\pi$
$770$	7.81434e6	−	4.36252e9i	0.000616843	−	0.344366i
$771$			1.30322e10i			1.02406i
$772$	−1.79638e8	+	1.02858e8i	−0.0140520	+	0.00804593i
$773$	6.91864e9	−	3.99448e9i	0.538756	−	0.311051i	−0.205818	−	0.978590i	$-0.565986\pi$
$773$	6.91864e9	−	3.99448e9i	0.538756	−	0.311051i	0.744575	+	0.667539i	$0.232652\pi$
$774$	1.49187e10	+	2.59471e10i	1.15648	+	2.01139i
$775$	2.41394e10	+	4.18106e10i	1.86281	+	3.22649i
$776$	3.29270e9	−	5.63300e9i	0.252951	−	0.432737i
$777$	−1.01437e10	+	1.75694e10i	−0.775751	+	1.34364i
$778$	−1.34954e9	−	7.82386e8i	−0.102744	−	0.0595652i
$779$	4.33976e8	−	7.49413e8i	0.0328915	−	0.0567989i
$780$	3.73164e9	−	2.13668e9i	0.281559	−	0.161216i
$781$	2.73615e9	+	1.57972e9i	0.205523	+	0.118659i
$782$	3.90191e9	+	6.78635e9i	0.291779	+	0.507473i
$783$	1.72588e10	−	9.96438e9i	1.28483	−	0.741795i
$784$	−5.27978e9	−	9.29807e9i	−0.391300	−	0.689107i
$785$	−7.13882e9	−	1.23648e10i	−0.526723	−	0.912312i
$786$	4.50789e9	−	7.77570e9i	0.331127	−	0.571164i
$787$	−8.31534e9			−0.608091			−0.304046	−	0.952657i	$-0.598338\pi$
$787$	−8.31534e9			−0.608091			−0.304046	+	0.952657i	$0.598338\pi$
$788$	3.27274e9	−	5.62194e9i	0.238270	−	0.409302i
$789$	9.02615e9	−	5.21125e9i	0.654234	−	0.377722i
$790$	−2.24977e10	−	1.30429e10i	−1.62347	−	0.941192i
$791$	1.20026e10			0.862298
$792$	−7.25565e9	−	1.27246e10i	−0.518965	−	0.910134i
$793$	3.69291e8	+	2.13210e8i	0.0262974	+	0.0151828i
$794$	−5.98737e6	+	3.34258e9i	−0.000424487	+	0.236979i
$795$	−2.92061e10	−	1.68621e10i	−2.06152	−	1.19022i
$796$	−3.91720e7	+	1.09343e10i	−0.00275284	+	0.768413i
$797$		−	1.03920e10i		−	0.727101i	−0.931574	−	0.363551i	$-0.881564\pi$
$797$		−	1.03920e10i		−	0.727101i	0.931574	−	0.363551i	$-0.118436\pi$
$798$	3.73730e7	−	1.20828e10i	0.00260345	−	0.841699i
$799$			7.32717e9i			0.508185i
$800$	2.63574e8	−	2.94284e10i	0.0182007	−	2.03213i
$801$	3.03688e10	+	1.75334e10i	2.08792	+	1.20546i
$802$	9.60920e9	+	1.72124e7i	0.657774	+	0.00117823i
$803$	−2.89745e9	−	1.67284e9i	−0.197474	−	0.114012i
$804$	1.58447e10	−	2.72182e10i	1.07520	−	1.84698i
$805$	7.63259e9			0.515687
$806$	1.37841e9	−	2.37764e9i	0.0927272	−	0.159946i
$807$	−1.71555e10	+	9.90476e9i	−1.14907	+	0.663417i
$808$	1.27665e10	−	7.27956e9i	0.851398	−	0.485474i
$809$	1.46686e10			0.974025			0.487013	−	0.873395i	$-0.338087\pi$
$809$	1.46686e10			0.974025			0.487013	+	0.873395i	$0.338087\pi$
$810$	−5.49489e10	−	3.18561e10i	−3.63297	−	2.10618i
$811$	−3.65013e9	−	6.32221e9i	−0.240290	−	0.416194i	0.720507	−	0.693448i	$-0.243909\pi$
$811$	−3.65013e9	−	6.32221e9i	−0.240290	−	0.416194i	−0.960797	+	0.277253i	$0.910576\pi$
$812$	−3.94830e9	−	1.41448e7i	−0.258800	−	0.000927148i
$813$	3.26545e10	−	1.88531e10i	2.13121	−	1.23045i
$814$	−1.06744e10	+	6.13738e9i	−0.693675	+	0.398839i
$815$	−2.68966e10	−	1.55288e10i	−1.74039	−	1.00481i
$816$	−1.30713e10	+	2.22700e10i	−0.842174	+	1.43485i
$817$	−7.50914e9	+	1.29672e10i	−0.481740	+	0.831895i
$818$	−8.36737e9	+	1.44329e10i	−0.534506	+	0.921973i
$819$	−8.71635e8	+	1.50972e9i	−0.0554423	+	0.0960288i
$820$	−6.46469e6	+	1.80452e9i	−0.000409448	+	0.114291i
$821$	−5.49437e9	−	9.51653e9i	−0.346511	−	0.600174i	0.639116	−	0.769110i	$-0.279300\pi$
$821$	−5.49437e9	−	9.51653e9i	−0.346511	−	0.600174i	−0.985627	+	0.168936i	$0.945967\pi$
$822$	2.63676e10	−	1.51605e10i	1.65585	−	0.952052i
$823$	−2.11775e10	+	1.22268e10i	−1.32427	+	0.764566i	−0.984406	−	0.175910i	$-0.943713\pi$
$823$	−2.11775e10	+	1.22268e10i	−1.32427	+	0.764566i	−0.339860	+	0.940476i	$0.610380\pi$
$824$	4.29009e7	−	7.98339e9i	0.00267129	−	0.497098i
$825$		−	2.62872e10i		−	1.62988i
$826$	−8.03114e9	−	1.43857e7i	−0.495847	−	0.000888181i
$827$	1.57747e10	+	2.73225e10i	0.969820	+	1.67978i	0.696065	+	0.717979i	$0.254932\pi$
$827$	1.57747e10	+	2.73225e10i	0.969820	+	1.67978i	0.273755	+	0.961799i	$0.411734\pi$
$828$	2.22399e10	−	1.27342e10i	1.36153	−	0.779588i
$829$		−	1.79367e9i		−	0.109346i	−0.998504	−	0.0546728i	$-0.982588\pi$
$829$		−	1.79367e9i		−	0.109346i	0.998504	−	0.0546728i	$-0.0174116\pi$
$830$	−4.57510e10	−	8.19511e7i	−2.77733	−	0.00497487i
$831$	2.04357e10	−	3.53956e10i	1.23534	−	2.13966i
$832$	−1.45977e9	+	8.22011e8i	−0.0878727	+	0.0494819i
$833$	−5.95232e9	+	1.03097e10i	−0.356803	+	0.618001i
$834$	−3.36683e9	−	5.85572e9i	−0.200974	−	0.349542i
$835$	4.79487e9			0.285019
$836$	3.69768e9	−	6.33293e9i	0.218881	−	0.374872i
$837$	−8.12221e10			−4.78779
$838$	4.65236e9	+	8.09157e9i	0.273099	+	0.474984i
$839$	−3.40219e9	+	5.89276e9i	−0.198880	+	0.344470i	−0.948166	−	0.317777i	$-0.897064\pi$
$839$	−3.40219e9	+	5.89276e9i	−0.198880	+	0.344470i	0.749286	+	0.662247i	$0.230397\pi$
$840$	1.24715e10	+	2.18719e10i	0.726008	+	1.27323i
$841$	−5.84155e9	+	1.01179e10i	−0.338643	+	0.586547i
$842$	2.12477e10	+	3.80598e7i	1.22665	+	0.00219722i
$843$			4.29408e10i			2.46873i
$844$	−7.06780e9	−	1.23437e10i	−0.404656	−	0.706719i
$845$	1.51150e10	+	2.61800e10i	0.861808	+	1.49270i
$846$	2.39875e10	+	4.29674e7i	1.36204	+	0.00243974i
$847$		−	6.53839e9i		−	0.369725i
$848$	1.13313e10	+	6.65085e9i	0.638110	+	0.374534i
$849$	8.33296e9	−	4.81104e9i	0.467329	−	0.269812i
$850$	−2.84053e10	+	1.63320e10i	−1.58647	+	0.912166i
$851$	−1.07713e10	−	1.86564e10i	−0.599119	−	1.03770i
$852$	−1.82341e10	−	6.53235e7i	−1.01006	−	0.00361852i
$853$	−9.37010e9	+	1.62295e10i	−0.516919	+	0.895330i	0.482888	+	0.875682i	$0.339588\pi$
$853$	−9.37010e9	+	1.62295e10i	−0.516919	+	0.895330i	−0.999807	+	0.0196478i	$0.993746\pi$
$854$	−1.25226e9	+	2.16003e9i	−0.0688004	+	0.118674i
$855$	9.99927e7	−	7.68091e10i	0.00547126	−	4.20273i
$856$	−6.36822e7	+	1.18506e10i	−0.00347024	+	0.645774i
$857$	−3.08513e10	−	1.78120e10i	−1.67433	−	0.966675i	−0.965169	−	0.261627i	$-0.915741\pi$
$857$	−3.08513e10	−	1.78120e10i	−1.67433	−	0.966675i	−0.709160	−	0.705047i	$-0.750926\pi$
$858$	−1.29727e9	+	7.45886e8i	−0.0701175	+	0.0403151i
$859$	1.21600e10	−	7.02061e9i	0.654575	−	0.377919i	−0.135632	−	0.990759i	$-0.543306\pi$
$859$	1.21600e10	−	7.02061e9i	0.654575	−	0.377919i	0.790207	+	0.612840i	$0.209973\pi$
$860$	1.11859e8	−	3.12239e10i	0.00599691	−	1.67395i
$861$	−5.17340e8	−	8.96060e8i	−0.0276226	−	0.0478438i
$862$	−3.53598e9	−	2.04995e9i	−0.188033	−	0.109010i
$863$	2.05488e10			1.08830			0.544151	−	0.838988i	$-0.316852\pi$
$863$	2.05488e10			1.08830			0.544151	+	0.838988i	$0.316852\pi$
$864$	4.26545e10	+	2.51386e10i	2.24992	+	1.32600i
$865$	−3.41866e10	+	1.97376e10i	−1.79597	+	1.03690i
$866$	−9.44831e9	+	1.62975e10i	−0.494358	+	0.852722i
$867$	−6.70427e9			−0.349369
$868$	1.39071e10	+	8.09581e9i	0.721799	+	0.420186i
$869$	7.83731e9	+	4.52487e9i	0.405133	+	0.233904i
$870$	−3.54983e10	−	6.35860e7i	−1.82764	−	0.00327374i
$871$	−1.97010e9	−	1.13744e9i	−0.101024	−	0.0583264i
$872$	1.81890e10	−	3.11169e10i	0.928970	−	1.58924i
$873$			2.37821e10i			1.20976i
$874$	1.10915e10	+	6.44953e9i	0.561955	+	0.326767i
$875$			1.62269e10i			0.818854i
$876$	1.93090e10	+	6.91744e7i	0.970499	+	0.00347681i
$877$	1.24973e10	+	7.21532e9i	0.625630	+	0.361208i	0.779058	−	0.626952i	$-0.215698\pi$
$877$	1.24973e10	+	7.21532e9i	0.625630	+	0.361208i	−0.153427	+	0.988160i	$0.549031\pi$
$878$	−1.88503e7	+	1.05236e10i	−0.000939911	+	0.524726i
$879$	−2.63288e10	−	1.52010e10i	−1.30759	−	0.754935i
$880$	−1.09487e8	+	1.52807e10i	−0.00541594	+	0.755880i
$881$	−2.08816e10			−1.02884			−0.514419	−	0.857539i	$-0.671992\pi$
$881$	−2.08816e10			−1.02884			−0.514419	+	0.857539i	$0.671992\pi$
$882$	3.37168e10	+	1.95470e10i	1.65465	+	0.959269i
$883$	−5.06479e9	+	2.92416e9i	−0.247570	+	0.142935i	−0.618651	−	0.785666i	$-0.712321\pi$
$883$	−5.06479e9	+	2.92416e9i	−0.247570	+	0.142935i	0.371081	+	0.928601i	$0.378987\pi$
$884$	1.61197e9	+	9.38390e8i	0.0784830	+	0.0456878i
$885$	−7.22060e10			−3.50165
$886$	−2.04693e8	+	3.53076e8i	−0.00988746	+	0.0170550i
$887$	1.82273e9	+	3.15706e9i	0.0876980	+	0.151897i	0.906538	−	0.422125i	$-0.138716\pi$
$887$	1.82273e9	+	3.15706e9i	0.0876980	+	0.151897i	−0.818840	+	0.574022i	$0.805382\pi$
$888$	3.58615e10	−	6.13501e10i	1.71863	−	2.94015i
$889$	−8.65397e9	+	4.99637e9i	−0.413104	+	0.238506i
$890$	−1.82346e10	−	3.17143e10i	−0.867023	−	1.50796i
$891$	1.91420e10	+	1.10516e10i	0.906600	+	0.523426i
$892$	−1.23310e9	−	2.15358e9i	−0.0581732	−	0.101598i
$893$	5.99111e9	+	1.04082e10i	0.281531	+	0.489096i
$894$	3.80214e10	+	2.20426e10i	1.77970	+	1.03177i
$895$	−2.12302e10	+	3.67717e10i	−0.989858	+	1.71448i
$896$	−4.79772e9	−	8.55588e9i	−0.222821	−	0.397362i
$897$	−1.30905e9	−	2.26734e9i	−0.0605596	−	0.104892i
$898$	−1.29698e9	−	2.25577e9i	−0.0597679	−	0.103951i
$899$	−1.96485e10	+	1.13441e10i	−0.901924	+	0.520726i
$900$	5.33008e10	+	9.30883e10i	2.43717	+	4.25644i
$901$		−	1.46284e10i		−	0.666286i
$902$	1.12486e6	−	6.27975e8i	5.10357e−5	−	0.0284918i
$903$	8.95160e9	+	1.55046e10i	0.404570	+	0.700736i
$904$	−4.20420e10	−	2.25924e8i	−1.89275	−	0.0101712i
$905$		−	5.42220e10i		−	2.43168i
$906$	3.03973e7	−	1.69699e10i	0.00135796	−	0.758109i
$907$	1.50761e10	−	2.61127e10i	0.670911	−	1.16205i	−0.306735	−	0.951795i	$-0.599237\pi$
$907$	1.50761e10	−	2.61127e10i	0.670911	−	1.16205i	0.977646	−	0.210257i	$-0.0674301\pi$
$908$	−1.03004e10	+	1.76941e10i	−0.456619	+	0.784384i
$909$	−2.67829e10	+	4.63894e10i	−1.18273	+	2.04854i
$910$	1.57661e9	−	9.06492e8i	0.0693550	−	0.0398767i
$911$	8.88198e8			0.0389220			0.0194610	−	0.999811i	$-0.493805\pi$
$911$	8.88198e8			0.0389220			0.0194610	+	0.999811i	$0.493805\pi$
$912$	−3.58342e8	+	4.23222e10i	−0.0156428	+	1.84751i
$913$	1.59213e10			0.692360
$914$	2.44289e9	−	1.40457e9i	0.105826	−	0.0608461i
$915$	−1.12239e10	+	1.94404e10i	−0.484363	+	0.838941i
$916$	−4.99252e9	+	8.57619e9i	−0.214628	+	0.368689i
$917$	1.90063e9	−	3.29200e9i	0.0813965	−	0.140983i
$918$	9.87399e7	−	5.51237e10i	0.00421253	−	2.35174i
$919$		−	2.76635e10i		−	1.17572i	−0.808964	−	0.587858i	$-0.799972\pi$
$919$		−	2.76635e10i		−	1.17572i	0.808964	−	0.587858i	$-0.200028\pi$
$920$	−2.67350e10	−	1.43668e8i	−1.13194	−	0.00608278i
$921$	−1.99792e10	−	3.46049e10i	−0.842692	−	1.45958i
$922$	4.84845e7	−	2.70675e10i	0.00203725	−	1.13734i
$923$			1.31709e9i			0.0551326i
$924$	−4.35370e9	−	7.60361e9i	−0.181554	−	0.317079i
$925$	7.80890e10	−	4.50847e10i	3.24410	−	1.87298i
$926$	−1.82152e9	−	3.16805e9i	−0.0753867	−	0.131115i
$927$	1.45495e10	+	2.52005e10i	0.599888	+	1.03904i
$928$	1.38296e10	+	1.23864e8i	0.568057	+	0.00508777i
$929$	−1.04097e10	+	1.80301e10i	−0.425973	+	0.737807i	−0.996511	−	0.0834644i	$-0.973401\pi$
$929$	−1.04097e10	+	1.80301e10i	−0.425973	+	0.737807i	0.570538	+	0.821271i	$0.306735\pi$
$930$	1.25165e11	+	7.25633e10i	5.10261	+	2.95819i
$931$	−2.54011e7	+	1.95118e10i	−0.00103164	+	0.792453i
$932$	3.94275e9	+	6.88590e9i	0.159531	+	0.278615i
$933$	−7.61140e9	−	4.39445e9i	−0.306817	−	0.177141i
$934$	7.02873e9	+	1.22246e10i	0.282269	+	0.490933i
$935$	1.47340e10	−	8.50666e9i	0.589494	−	0.340344i
$936$	3.08153e9	−	5.27174e9i	0.122829	−	0.210130i
$937$	−1.00559e10	−	1.74174e10i	−0.399331	−	0.691662i	0.594312	−	0.804234i	$-0.297424\pi$
$937$	−1.00559e10	−	1.74174e10i	−0.399331	−	0.691662i	−0.993644	+	0.112572i	$0.964091\pi$
$938$	6.68059e9	−	1.15234e10i	0.264305	−	0.455901i
$939$	−5.31024e10			−2.09307
$940$	−2.16269e10	−	1.25898e10i	−0.849271	−	0.494392i
$941$	−4.37794e10	+	2.52760e10i	−1.71280	+	0.988884i	−0.782055	+	0.623210i	$0.785828\pi$
$941$	−4.37794e10	+	2.52760e10i	−1.71280	+	0.988884i	−0.930743	+	0.365674i	$0.880838\pi$
$942$	−2.48081e10	−	1.43823e10i	−0.966974	−	0.560595i
$943$	1.09869e9			0.0426664
$944$	2.81308e10	+	2.01559e8i	1.08838	+	0.00779832i
$945$	−4.65462e10	−	2.68735e10i	−1.79421	−	1.03589i
$946$	−1.94635e7	+	1.08659e10i	−0.000747485	+	0.417300i
$947$	−1.58998e10	−	9.17973e9i	−0.608367	−	0.351241i	0.163959	−	0.986467i	$-0.447573\pi$
$947$	−1.58998e10	−	9.17973e9i	−0.608367	−	0.351241i	−0.772326	+	0.635226i	$0.780907\pi$
$948$	−5.22290e10	−	1.87110e8i	−1.99105	−	0.00713293i
$949$		−	1.39473e9i		−	0.0529735i
$950$	−2.69954e10	+	4.64253e10i	−1.02155	+	1.75680i
$951$		−	5.71015e10i		−	2.15286i
$952$	−5.51136e9	+	9.42858e9i	−0.207028	+	0.354174i
$953$	2.48246e10	+	1.43325e10i	0.929089	+	0.536410i	0.886523	−	0.462684i	$-0.153114\pi$
$953$	2.48246e10	+	1.43325e10i	0.929089	+	0.536410i	0.0425656	+	0.999094i	$0.486447\pi$
$954$	−4.78902e10	−	8.57830e7i	−1.78578	−	0.00319876i
$955$	3.81964e10	+	2.20527e10i	1.41909	+	0.819314i
$956$	3.63899e10	+	2.11839e10i	1.34703	+	0.784158i
$957$	1.23534e10			0.455611
$958$	−2.14948e9	+	3.70765e9i	−0.0789867	+	0.136245i
$959$	1.11402e10	−	6.43179e9i	0.407875	−	0.235487i
$960$	−4.32728e10	−	7.68463e10i	−1.57858	−	2.80333i
$961$	6.49556e10			2.36094
$962$	−4.44068e9	−	2.57444e9i	−0.160819	−	0.0932331i
$963$	−2.15974e10	−	3.74077e10i	−0.779307	−	1.34980i
$964$	9.19092e7	−	2.56551e10i	0.00330438	−	0.922367i
$965$	−6.81661e8	+	3.93557e8i	−0.0244187	+	0.0140982i
$966$	1.32894e10	−	7.64096e9i	0.474337	−	0.272727i
$967$	4.23942e10	+	2.44763e10i	1.50770	+	0.870469i	0.999960	+	0.00895670i	$0.00285104\pi$
$967$	4.23942e10	+	2.44763e10i	1.50770	+	0.870469i	0.507737	+	0.861512i	$0.330482\pi$
$968$	−1.23072e8	+	2.29023e10i	−0.00436109	+	0.811551i
$969$	4.08391e10	−	2.35076e10i	1.44193	−	0.829995i
$970$	1.24436e10	−	2.14640e10i	0.437768	−	0.755109i
$971$	5.79292e8	−	1.00336e9i	0.0203063	−	0.0351715i	−0.855694	−	0.517483i	$-0.826869\pi$
$971$	5.79292e8	−	1.00336e9i	0.0203063	−	0.0351715i	0.876000	+	0.482311i	$0.160203\pi$
$972$	−5.27939e10	−	1.89134e8i	−1.84396	−	0.00660599i
$973$	−1.42837e9	−	2.47401e9i	−0.0497103	−	0.0861007i
$974$	2.67321e10	−	1.53700e10i	0.926994	−	0.532988i
$975$	9.49029e9	−	5.47922e9i	0.327917	−	0.189323i
$976$	4.42700e9	−	7.54246e9i	0.152417	−	0.259680i
$977$			2.07265e10i			0.711041i	0.934668	+	0.355521i	$0.115696\pi$
$977$			2.07265e10i			0.711041i	−0.934668	+	0.355521i	$0.884304\pi$
$978$	−6.23767e10	−	1.11732e8i	−2.13224	−	0.00381936i
$979$	6.36538e9	+	1.10252e10i	0.216813	+	0.375531i
$980$	−2.02027e10	−	3.52834e10i	−0.685674	−	1.19751i
$981$			1.31373e11i			4.44289i
$982$	1.69638e10	+	3.03863e7i	0.571654	+	0.00102397i
$983$	9.65011e9	−	1.67145e10i	0.324037	−	0.561249i	−0.657280	−	0.753647i	$-0.728293\pi$
$983$	9.65011e9	−	1.67145e10i	0.324037	−	0.561249i	0.981317	+	0.192398i	$0.0616264\pi$
$984$	1.79524e9	+	3.14840e9i	0.0600676	+	0.105343i
$985$	1.23678e10	−	2.14217e10i	0.412350	−	0.714210i
$986$	−7.67508e9	−	1.33488e10i	−0.254984	−	0.443479i
$987$	1.43485e10			0.475003
$988$	3.05708e9	+	1.49318e7i	0.100846	+	0.000492565i
$989$	−1.90108e10			−0.624905
$990$	−2.77625e10	−	4.82856e10i	−0.909359	−	1.58159i
$991$	2.75969e9	−	4.77991e9i	0.0900745	−	0.156014i	−0.817468	−	0.575974i	$-0.804623\pi$
$991$	2.75969e9	−	4.77991e9i	0.0900745	−	0.156014i	0.907542	+	0.419961i	$0.137956\pi$
$992$	−4.85605e10	−	2.86193e10i	−1.57940	−	0.930826i
$993$	−2.10097e10	+	3.63899e10i	−0.680924	+	1.17939i
$994$	−7.71180e9	−	1.38137e7i	−0.249060	−	0.000446126i
$995$			4.15775e10i			1.33806i
$996$	−7.97411e10	+	4.56584e10i	−2.55726	+	1.46424i
$997$	8.24632e9	+	1.42830e10i	0.263528	+	0.456444i	0.967177	−	0.254104i	$-0.0817804\pi$
$997$	8.24632e9	+	1.42830e10i	0.263528	+	0.456444i	−0.703649	+	0.710548i	$0.748447\pi$
$998$	1.59734e10	+	2.86123e7i	0.508676	+	0.000911161i
$999$			1.51697e11i			4.81392i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.8.f.a.27.12	✓	136
4.3	odd	2	inner	76.8.f.a.27.35	yes	136
19.12	odd	6	inner	76.8.f.a.31.35	yes	136
76.31	even	6	inner	76.8.f.a.31.12	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.8.f.a.27.12	✓	136	1.1	even	1	trivial
76.8.f.a.27.35	yes	136	4.3	odd	2	inner
76.8.f.a.31.12	yes	136	76.31	even	6	inner
76.8.f.a.31.35	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)

\(f(q)\)	\(=\)	\(q+(-9.80808 + 5.63929i) q^{2} +(-43.2012 + 74.8267i) q^{3} +(64.3967 - 110.621i) q^{4} +(243.358 - 421.508i) q^{5} +(1.75099 - 977.530i) q^{6} -413.429i q^{7} +(-7.78194 + 1448.13i) q^{8} +(-2639.19 - 4571.21i) q^{9} +O(q^{10})\)	\(q+(-9.80808 + 5.63929i) q^{2} +(-43.2012 + 74.8267i) q^{3} +(64.3967 - 110.621i) q^{4} +(243.358 - 421.508i) q^{5} +(1.75099 - 977.530i) q^{6} -413.429i q^{7} +(-7.78194 + 1448.13i) q^{8} +(-2639.19 - 4571.21i) q^{9} +(-9.86356 + 5506.55i) q^{10} -1916.28i q^{11} +(5495.41 + 9597.57i) q^{12} +(691.822 - 399.424i) q^{13} +(2331.45 + 4054.94i) q^{14} +(21026.7 + 36419.3i) q^{15} +(-8090.13 - 14247.3i) q^{16} +(-9120.65 + 15797.4i) q^{17} +(51663.8 + 29951.6i) q^{18} +(-38.9218 + 29897.7i) q^{19} +(-30956.3 - 54064.2i) q^{20} +(30935.5 + 17860.6i) q^{21} +(10806.4 + 18795.0i) q^{22} +(-32849.4 + 18965.6i) q^{23} +(-108023. - 63143.4i) q^{24} +(-79383.3 - 137496. i) q^{25} +(-4532.98 + 7818.97i) q^{26} +267103. q^{27} +(-45734.0 - 26623.4i) q^{28} +(64614.9 - 37305.4i) q^{29} +(-411610. - 238627. i) q^{30} -304086. q^{31} +(159693. + 94115.9i) q^{32} +(143389. + 82785.5i) q^{33} +(369.670 - 206376. i) q^{34} +(-174263. - 100611. i) q^{35} +(-675628. - 2420.44i) q^{36} +567936. i q^{37} +(-168220. - 293458. i) q^{38} +69022.3i q^{39} +(608506. + 355695. i) q^{40} +(-25084.8 - 14482.7i) q^{41} +(-404139. - 723.911i) q^{42} +(434045. + 250596. i) q^{43} +(-211981. - 123402. i) q^{44} -2.56907e6 q^{45} +(215237. - 371264. i) q^{46} +(347865. - 200840. i) q^{47} +(1.41558e6 + 10142.8i) q^{48} +652620. q^{49} +(1.55398e6 + 900905. i) q^{50} +(-788046. - 1.36494e6i) q^{51} +(366.317 - 102252. i) q^{52} +(-694500. + 400970. i) q^{53} +(-2.61976e6 + 1.50627e6i) q^{54} +(-807725. - 466341. i) q^{55} +(598700. + 3217.28i) q^{56} +(-2.23546e6 - 1.29453e6i) q^{57} +(-423372. + 730277. i) q^{58} +(-858505. + 1.48697e6i) q^{59} +(5.38280e6 + 19283.8i) q^{60} +(266897. + 462279. i) q^{61} +(2.98250e6 - 1.71483e6i) q^{62} +(-1.88987e6 + 1.09112e6i) q^{63} +(-2.09703e6 - 22538.6i) q^{64} -388811. i q^{65} +(-1.87322e6 - 3355.39i) q^{66} +(-1.42385e6 - 2.46618e6i) q^{67} +(1.16019e6 + 2.02624e6i) q^{68} -3.27735e6i q^{69} +(2.27656e6 + 4077.88i) q^{70} +(-824367. + 1.42785e6i) q^{71} +(6.64026e6 - 3.78633e6i) q^{72} +(872964. - 1.51202e6i) q^{73} +(-3.20276e6 - 5.57036e6i) q^{74} +1.37178e7 q^{75} +(3.30481e6 + 1.92962e6i) q^{76} -792243. q^{77} +(-389237. - 676976. i) q^{78} +(-2.36128e6 + 4.08986e6i) q^{79} +(-7.97414e6 - 57135.4i) q^{80} +(-5.76725e6 + 9.98917e6i) q^{81} +(327706. + 587.001i) q^{82} +8.30847e6i q^{83} +(3.96791e6 - 2.27196e6i) q^{84} +(4.43916e6 + 7.68885e6i) q^{85} +(-5.67034e6 - 10156.9i) q^{86} +6.44656e6i q^{87} +(2.77503e6 + 14912.4i) q^{88} +(-5.75343e6 + 3.32174e6i) q^{89} +(2.51976e7 - 1.44877e7i) q^{90} +(-165133. - 286019. i) q^{91} +(-17393.6 + 4.85516e6i) q^{92} +(1.31369e7 - 2.27537e7i) q^{93} +(-2.27929e6 + 3.93157e6i) q^{94} +(1.25926e7 + 7.29223e6i) q^{95} +(-1.39413e7 + 7.88340e6i) q^{96} +(-3.90194e6 - 2.25279e6i) q^{97} +(-6.40095e6 + 3.68032e6i) q^{98} +(-8.75970e6 + 5.05742e6i) 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

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