LMFDB - Embedded newform 76.8.d.a.75.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,8,Mod(75,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("76.75");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	76.d (of order $2$, degree $1$, 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:	$68$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			75.10
Character	$\chi$	$=$	76.75
Dual form			76.8.d.a.75.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-10.6582 + 3.79499i) q^{2} +60.8414 q^{3} +(99.1961 - 80.8959i) q^{4} -369.508 q^{5} +(-648.462 + 230.893i) q^{6} +900.474i q^{7} +(-750.256 + 1238.66i) q^{8} +1514.68 q^{9} +O(q^{10})$	\(q+(-10.6582 + 3.79499i) q^{2} +60.8414 q^{3} +(99.1961 - 80.8959i) q^{4} -369.508 q^{5} +(-648.462 + 230.893i) q^{6} +900.474i q^{7} +(-750.256 + 1238.66i) q^{8} +1514.68 q^{9} +(3938.30 - 1402.28i) q^{10} -3232.87i q^{11} +(6035.23 - 4921.82i) q^{12} -5364.16i q^{13} +(-3417.29 - 9597.47i) q^{14} -22481.4 q^{15} +(3295.72 - 16049.1i) q^{16} +23614.0 q^{17} +(-16143.8 + 5748.20i) q^{18} +(-20597.8 + 21670.3i) q^{19} +(-36653.7 + 29891.6i) q^{20} +54786.1i q^{21} +(12268.7 + 34456.7i) q^{22} -105104. i q^{23} +(-45646.6 + 75361.6i) q^{24} +58410.8 q^{25} +(20357.0 + 57172.5i) q^{26} -40905.0 q^{27} +(72844.6 + 89323.5i) q^{28} -120148. i q^{29} +(239612. - 85316.6i) q^{30} -225020. q^{31} +(25779.7 + 183562. i) q^{32} -196693. i q^{33} +(-251684. + 89615.1i) q^{34} -332732. i q^{35} +(150250. - 122531. i) q^{36} -410326. i q^{37} +(137297. - 309136. i) q^{38} -326363. i q^{39} +(277225. - 457693. i) q^{40} -158707. i q^{41} +(-207913. - 583924. i) q^{42} +424031. i q^{43} +(-261526. - 320688. i) q^{44} -559685. q^{45} +(398869. + 1.12022e6i) q^{46} -1.01067e6i q^{47} +(200516. - 976450. i) q^{48} +12689.3 q^{49} +(-622556. + 221669. i) q^{50} +1.43671e6 q^{51} +(-433939. - 532104. i) q^{52} -928458. i q^{53} +(435975. - 155234. i) q^{54} +1.19457e6i q^{55} +(-1.11538e6 - 675586. i) q^{56} +(-1.25320e6 + 1.31845e6i) q^{57} +(455962. + 1.28057e6i) q^{58} +378976. q^{59} +(-2.23006e6 + 1.81865e6i) q^{60} +1.27562e6 q^{61} +(2.39831e6 - 853948. i) q^{62} +1.36393e6i q^{63} +(-971384. - 1.85862e6i) q^{64} +1.98210e6i q^{65} +(746447. + 2.09640e6i) q^{66} -630550. q^{67} +(2.34242e6 - 1.91028e6i) q^{68} -6.39469e6i q^{69} +(1.26272e6 + 3.54634e6i) q^{70} -3.25263e6 q^{71} +(-1.13640e6 + 1.87617e6i) q^{72} -4.59002e6 q^{73} +(1.55719e6 + 4.37335e6i) q^{74} +3.55380e6 q^{75} +(-290176. + 3.81589e6i) q^{76} +2.91112e6 q^{77} +(1.23855e6 + 3.47846e6i) q^{78} +2.29205e6 q^{79} +(-1.21779e6 + 5.93026e6i) q^{80} -5.80132e6 q^{81} +(602292. + 1.69154e6i) q^{82} +3.91292e6i q^{83} +(4.43197e6 + 5.43457e6i) q^{84} -8.72557e6 q^{85} +(-1.60919e6 - 4.51942e6i) q^{86} -7.31000e6i q^{87} +(4.00442e6 + 2.42548e6i) q^{88} -7.89968e6i q^{89} +(5.96526e6 - 2.12400e6i) q^{90} +4.83029e6 q^{91} +(-8.50249e6 - 1.04259e7i) q^{92} -1.36905e7 q^{93} +(3.83549e6 + 1.07720e7i) q^{94} +(7.61103e6 - 8.00736e6i) q^{95} +(1.56847e6 + 1.11682e7i) q^{96} -1.92523e6i q^{97} +(-135245. + 48155.7i) q^{98} -4.89677e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 54 q^{4} - 4 q^{5} - 150 q^{6} + 48888 q^{9}+O(q^{10}) $ 68 * q - 54 * q^4 - 4 * q^5 - 150 * q^6 + 48888 * q^9	$ 68 q - 54 q^{4} - 4 q^{5} - 150 q^{6} + 48888 q^{9} + 13050 q^{16} + 23968 q^{17} - 79660 q^{20} - 232154 q^{24} + 937496 q^{25} - 391242 q^{26} - 37666 q^{28} - 468496 q^{30} - 1128652 q^{36} - 530466 q^{38} + 651806 q^{42} + 1433776 q^{44} - 321252 q^{45} - 4014380 q^{49} + 1697586 q^{54} + 137420 q^{57} + 2227894 q^{58} - 3042164 q^{61} + 2261524 q^{62} + 9825150 q^{64} - 749476 q^{66} - 11176962 q^{68} + 598424 q^{73} - 6195964 q^{74} - 1714536 q^{76} - 2556764 q^{77} + 16623216 q^{80} + 43726748 q^{81} - 20460388 q^{82} + 27222844 q^{85} - 61733582 q^{92} + 17778200 q^{93} - 36370886 q^{96}+O(q^{100}) $ 68 * q - 54 * q^4 - 4 * q^5 - 150 * q^6 + 48888 * q^9 + 13050 * q^16 + 23968 * q^17 - 79660 * q^20 - 232154 * q^24 + 937496 * q^25 - 391242 * q^26 - 37666 * q^28 - 468496 * q^30 - 1128652 * q^36 - 530466 * q^38 + 651806 * q^42 + 1433776 * q^44 - 321252 * q^45 - 4014380 * q^49 + 1697586 * q^54 + 137420 * q^57 + 2227894 * q^58 - 3042164 * q^61 + 2261524 * q^62 + 9825150 * q^64 - 749476 * q^66 - 11176962 * q^68 + 598424 * q^73 - 6195964 * q^74 - 1714536 * q^76 - 2556764 * q^77 + 16623216 * q^80 + 43726748 * q^81 - 20460388 * q^82 + 27222844 * q^85 - 61733582 * q^92 + 17778200 * q^93 - 36370886 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$	$39$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−10.6582	+	3.79499i	−0.942064	+	0.335433i
$2$	−10.6582	+	3.79499i	−0.942064	+	0.335433i
$3$	60.8414			1.30099			0.650497	−	0.759509i	$-0.274561\pi$
$3$	60.8414			1.30099			0.650497	+	0.759509i	$0.274561\pi$
$4$	99.1961	−	80.8959i	0.774969	−	0.631999i
$5$	−369.508			−1.32199			−0.660995	−	0.750390i	$-0.729866\pi$
$5$	−369.508			−1.32199			−0.660995	+	0.750390i	$0.729866\pi$
$6$	−648.462	+	230.893i	−1.22562	+	0.436396i
$7$			900.474i			0.992266i	0.868247	+	0.496133i	$0.165247\pi$
$7$			900.474i			0.992266i	−0.868247	+	0.496133i	$0.834753\pi$
$8$	−750.256	+	1238.66i	−0.518077	+	0.855334i
$9$	1514.68			0.692583
$10$	3938.30	−	1402.28i	1.24540	−	0.443439i
$11$		−	3232.87i		−	0.732343i	−0.930547	−	0.366171i	$-0.880668\pi$
$11$		−	3232.87i		−	0.732343i	0.930547	−	0.366171i	$-0.119332\pi$
$12$	6035.23	−	4921.82i	1.00823	−	0.822226i
$13$		−	5364.16i		−	0.677174i	−0.940935	−	0.338587i	$-0.890051\pi$
$13$		−	5364.16i		−	0.677174i	0.940935	−	0.338587i	$-0.109949\pi$
$14$	−3417.29	−	9597.47i	−0.332839	−	0.934778i
$15$	−22481.4			−1.71990
$16$	3295.72	−	16049.1i	0.201155	−	0.979559i
$17$	23614.0			1.16573			0.582867	−	0.812568i	$-0.301931\pi$
$17$	23614.0			1.16573			0.582867	+	0.812568i	$0.301931\pi$
$18$	−16143.8	+	5748.20i	−0.652458	+	0.232315i
$19$	−20597.8	+	21670.3i	−0.688942	+	0.724817i
$19$	−20597.8	+	21670.3i	−0.688942	+	0.724817i
$20$	−36653.7	+	29891.6i	−1.02450	+	0.835496i
$21$			54786.1i			1.29093i
$22$	12268.7	+	34456.7i	0.245652	+	0.689914i
$23$		−	105104.i		−	1.80124i	−0.434604	−	0.900622i	$-0.643112\pi$
$23$		−	105104.i		−	1.80124i	0.434604	−	0.900622i	$-0.356888\pi$
$24$	−45646.6	+	75361.6i	−0.674015	+	1.11278i
$25$	58410.8			0.747658
$26$	20357.0	+	57172.5i	0.227147	+	0.637941i
$27$	−40905.0			−0.399947
$28$	72844.6	+	89323.5i	0.627111	+	0.768976i
$29$		−	120148.i		−	0.914797i	−0.889262	−	0.457399i	$-0.848781\pi$
$29$		−	120148.i		−	0.914797i	0.889262	−	0.457399i	$-0.151219\pi$
$30$	239612.	−	85316.6i	1.62026	−	0.576911i
$31$	−225020.			−1.35661			−0.678304	−	0.734781i	$-0.737285\pi$
$31$	−225020.			−1.35661			−0.678304	+	0.734781i	$0.737285\pi$
$32$	25779.7	+	183562.i	0.139076	+	0.990282i
$33$		−	196693.i		−	0.952773i
$34$	−251684.	+	89615.1i	−1.09820	+	0.391025i
$35$		−	332732.i		−	1.31177i
$36$	150250.	−	122531.i	0.536731	−	0.437712i
$37$		−	410326.i		−	1.33175i	−0.746063	−	0.665876i	$-0.768058\pi$
$37$		−	410326.i		−	1.33175i	0.746063	−	0.665876i	$-0.231942\pi$
$38$	137297.	−	309136.i	0.405900	−	0.913918i
$39$		−	326363.i		−	0.880999i
$40$	277225.	−	457693.i	0.684893	−	1.13074i
$41$		−	158707.i		−	0.359627i	−0.983701	−	0.179814i	$-0.942451\pi$
$41$		−	158707.i		−	0.359627i	0.983701	−	0.179814i	$-0.0575495\pi$
$42$	−207913.	−	583924.i	−0.433021	−	1.21614i
$43$			424031.i			0.813313i	0.913581	+	0.406657i	$0.133305\pi$
$43$			424031.i			0.813313i	−0.913581	+	0.406657i	$0.866695\pi$
$44$	−261526.	−	320688.i	−0.462840	−	0.567543i
$45$	−559685.			−0.915588
$46$	398869.	+	1.12022e6i	0.604197	+	1.69689i
$47$		−	1.01067e6i		−	1.41993i	−0.704237	−	0.709965i	$-0.748711\pi$
$47$		−	1.01067e6i		−	1.41993i	0.704237	−	0.709965i	$-0.251289\pi$
$48$	200516.	−	976450.i	0.261701	−	1.27440i
$49$	12689.3			0.0154081
$50$	−622556.	+	221669.i	−0.704342	+	0.250789i
$51$	1.43671e6			1.51661
$52$	−433939.	−	532104.i	−0.427973	−	0.524789i
$53$		−	928458.i		−	0.856637i	−0.903628	−	0.428318i	$-0.859106\pi$
$53$		−	928458.i		−	0.856637i	0.903628	−	0.428318i	$-0.140894\pi$
$54$	435975.	−	155234.i	0.376776	−	0.134156i
$55$			1.19457e6i			0.968150i
$56$	−1.11538e6	−	675586.i	−0.848719	−	0.514070i
$57$	−1.25320e6	+	1.31845e6i	−0.896308	+	0.942982i
$58$	455962.	+	1.28057e6i	0.306853	+	0.861797i
$59$	378976.			0.240231			0.120116	−	0.992760i	$-0.461673\pi$
$59$	378976.			0.240231			0.120116	+	0.992760i	$0.461673\pi$
$60$	−2.23006e6	+	1.81865e6i	−1.33287	+	1.08698i
$61$	1.27562e6			0.719557			0.359779	−	0.933038i	$-0.382852\pi$
$61$	1.27562e6			0.719557			0.359779	+	0.933038i	$0.382852\pi$
$62$	2.39831e6	−	853948.i	1.27801	−	0.455052i
$63$			1.36393e6i			0.687227i
$64$	−971384.	−	1.85862e6i	−0.463192	−	0.886258i
$65$			1.98210e6i			0.895218i
$66$	746447.	+	2.09640e6i	0.319591	+	0.897573i
$67$	−630550.			−0.256128			−0.128064	−	0.991766i	$-0.540876\pi$
$67$	−630550.			−0.256128			−0.128064	+	0.991766i	$0.540876\pi$
$68$	2.34242e6	−	1.91028e6i	0.903407	−	0.736742i
$69$		−	6.39469e6i		−	2.34341i
$70$	1.26272e6	+	3.54634e6i	0.440010	+	1.23577i
$71$	−3.25263e6			−1.07853			−0.539263	−	0.842137i	$-0.681297\pi$
$71$	−3.25263e6			−1.07853			−0.539263	+	0.842137i	$0.681297\pi$
$72$	−1.13640e6	+	1.87617e6i	−0.358812	+	0.592390i
$73$	−4.59002e6			−1.38097			−0.690485	−	0.723347i	$-0.742603\pi$
$73$	−4.59002e6			−1.38097			−0.690485	+	0.723347i	$0.742603\pi$
$74$	1.55719e6	+	4.37335e6i	0.446714	+	1.25460i
$75$	3.55380e6			0.972698
$76$	−290176.	+	3.81589e6i	−0.0758253	+	0.997121i
$77$	2.91112e6			0.726679
$78$	1.23855e6	+	3.47846e6i	0.295516	+	0.829957i
$79$	2.29205e6			0.523034			0.261517	−	0.965199i	$-0.415777\pi$
$79$	2.29205e6			0.523034			0.261517	+	0.965199i	$0.415777\pi$
$80$	−1.21779e6	+	5.93026e6i	−0.265925	+	1.29497i
$81$	−5.80132e6			−1.21291
$82$	602292.	+	1.69154e6i	0.120631	+	0.338792i
$83$			3.91292e6i			0.751151i	0.926792	+	0.375575i	$0.122555\pi$
$83$			3.91292e6i			0.751151i	−0.926792	+	0.375575i	$0.877445\pi$
$84$	4.43197e6	+	5.43457e6i	0.815867	+	1.00043i
$85$	−8.72557e6			−1.54109
$86$	−1.60919e6	−	4.51942e6i	−0.272812	−	0.766193i
$87$		−	7.31000e6i		−	1.19014i
$88$	4.00442e6	+	2.42548e6i	0.626397	+	0.379410i
$89$		−	7.89968e6i		−	1.18780i	−0.804537	−	0.593902i	$-0.797587\pi$
$89$		−	7.89968e6i		−	1.18780i	0.804537	−	0.593902i	$-0.202413\pi$
$90$	5.96526e6	−	2.12400e6i	0.862543	−	0.307119i
$91$	4.83029e6			0.671937
$92$	−8.50249e6	−	1.04259e7i	−1.13838	−	1.39591i
$93$	−1.36905e7			−1.76494
$94$	3.83549e6	+	1.07720e7i	0.476292	+	1.33767i
$95$	7.61103e6	−	8.00736e6i	0.910774	−	0.958201i
$96$	1.56847e6	+	1.11682e7i	0.180937	+	1.28835i
$97$		−	1.92523e6i		−	0.214181i	−0.994249	−	0.107091i	$-0.965846\pi$
$97$		−	1.92523e6i		−	0.214181i	0.994249	−	0.107091i	$-0.0341535\pi$
$98$	−135245.	+	48155.7i	−0.0145155	+	0.00516840i
$99$		−	4.89677e6i		−	0.507208i
$100$	5.79412e6	−	4.72519e6i	0.579412	−	0.472519i
$101$	1.77438e7			1.71365			0.856826	−	0.515606i	$-0.172433\pi$
$101$	1.77438e7			1.71365			0.856826	+	0.515606i	$0.172433\pi$
$102$	−1.53128e7	+	5.45231e6i	−1.42874	+	0.508721i
$103$	−1.03513e7			−0.933394			−0.466697	−	0.884417i	$-0.654556\pi$
$103$	−1.03513e7			−0.933394			−0.466697	+	0.884417i	$0.654556\pi$
$104$	6.64435e6	+	4.02450e6i	0.579210	+	0.350829i
$105$		−	2.02439e7i		−	1.70660i
$106$	3.52349e6	+	9.89572e6i	0.287344	+	0.807007i
$107$	1.38767e6			0.109508			0.0547538	−	0.998500i	$-0.482563\pi$
$107$	1.38767e6			0.109508			0.0547538	+	0.998500i	$0.482563\pi$
$108$	−4.05761e6	+	3.30904e6i	−0.309947	+	0.252766i
$109$			1.00958e7i			0.746701i	0.927690	+	0.373351i	$0.121791\pi$
$109$			1.00958e7i			0.746701i	−0.927690	+	0.373351i	$0.878209\pi$
$110$	−4.53339e6	−	1.27320e7i	−0.324749	−	0.912059i
$111$		−	2.49648e7i		−	1.73260i
$112$	1.44518e7	+	2.96771e6i	0.971984	+	0.199599i
$113$			2.52682e7i			1.64740i	0.567022	+	0.823702i	$0.308095\pi$
$113$			2.52682e7i			1.64740i	−0.567022	+	0.823702i	$0.691905\pi$
$114$	8.35335e6	−	1.88083e7i	0.528073	−	1.18900i
$115$			3.88368e7i			2.38123i
$116$	−9.71950e6	−	1.19182e7i	−0.578151	−	0.708940i
$117$		−	8.12499e6i		−	0.468999i
$118$	−4.03922e6	+	1.43821e6i	−0.226313	+	0.0805816i
$119$			2.12638e7i			1.15672i
$120$	1.68668e7	−	2.78467e7i	0.891041	−	1.47109i
$121$	9.03570e6			0.463674
$122$	−1.35958e7	+	4.84095e6i	−0.677869	+	0.241363i
$123$		−	9.65596e6i		−	0.467873i
$124$	−2.23211e7	+	1.82032e7i	−1.05133	+	0.857375i
$125$	7.28454e6			0.333593
$126$	−5.17610e6	−	1.45371e7i	−0.230519	−	0.647411i
$127$	−1.91469e7			−0.829441			−0.414720	−	0.909949i	$-0.636121\pi$
$127$	−1.91469e7			−0.829441			−0.414720	+	0.909949i	$0.636121\pi$
$128$	1.74067e7	+	1.61232e7i	0.733637	+	0.679542i
$129$			2.57986e7i			1.05812i
$130$	−7.52205e6	−	2.11257e7i	−0.300286	−	0.843352i
$131$		−	1.61614e6i		−	0.0628102i	−0.999507	−	0.0314051i	$-0.990002\pi$
$131$		−	1.61614e6i		−	0.0628102i	0.999507	−	0.0314051i	$-0.00999819\pi$
$132$	−1.59116e7	−	1.95111e7i	−0.602151	−	0.738369i
$133$	−1.95136e7	−	1.85478e7i	−0.719211	−	0.683613i
$134$	6.72055e6	−	2.39293e6i	0.241289	−	0.0859139i
$135$	1.51147e7			0.528726
$136$	−1.77166e7	+	2.92497e7i	−0.603940	+	0.997091i
$137$	1.49847e7			0.497883			0.248942	−	0.968519i	$-0.419917\pi$
$137$	1.49847e7			0.497883			0.248942	+	0.968519i	$0.419917\pi$
$138$	2.42678e7	+	6.81561e7i	0.786056	+	2.20764i
$139$			9.54397e6i			0.301424i	0.988578	+	0.150712i	$0.0481566\pi$
$139$			9.54397e6i			0.301424i	−0.988578	+	0.150712i	$0.951843\pi$
$140$	−2.69166e7	−	3.30057e7i	−0.829035	−	1.01658i
$141$		−	6.14906e7i		−	1.84732i
$142$	3.46673e7	−	1.23437e7i	1.01604	−	0.361774i
$143$	−1.73417e7			−0.495923
$144$	4.99196e6	−	2.43092e7i	0.139316	−	0.678426i
$145$			4.43957e7i			1.20935i
$146$	4.89215e7	−	1.74191e7i	1.30096	−	0.463223i
$147$	772033.			0.0200459
$148$	−3.31937e7	−	4.07027e7i	−0.841666	−	1.03207i
$149$	−6.91385e7			−1.71225			−0.856127	−	0.516766i	$-0.827136\pi$
$149$	−6.91385e7			−1.71225			−0.856127	+	0.516766i	$0.827136\pi$
$150$	−3.78772e7	+	1.34866e7i	−0.916344	+	0.326275i
$151$	−3.10969e7			−0.735018			−0.367509	−	0.930020i	$-0.619789\pi$
$151$	−3.10969e7			−0.735018			−0.367509	+	0.930020i	$0.619789\pi$
$152$	−1.13885e7	−	4.17718e7i	−0.263035	−	0.964786i
$153$	3.57677e7			0.807367
$154$	−3.10274e7	+	1.10477e7i	−0.684578	+	0.243752i
$155$	8.31465e7			1.79342
$156$	−2.64014e7	−	3.23740e7i	−0.556790	−	0.682747i
$157$	5.84457e7			1.20532			0.602662	−	0.797997i	$-0.294107\pi$
$157$	5.84457e7			1.20532			0.602662	+	0.797997i	$0.294107\pi$
$158$	−2.44293e7	+	8.69833e6i	−0.492732	+	0.175443i
$159$		−	5.64887e7i		−	1.11448i
$160$	−9.52578e6	−	6.78277e7i	−0.183857	−	1.30914i
$161$	9.46436e7			1.78731
$162$	6.18318e7	−	2.20160e7i	1.14264	−	0.406851i
$163$		−	4.12418e7i		−	0.745901i	−0.927851	−	0.372950i	$-0.878346\pi$
$163$		−	4.12418e7i		−	0.745901i	0.927851	−	0.372950i	$-0.121654\pi$
$164$	−1.28387e7	−	1.57431e7i	−0.227284	−	0.278700i
$165$			7.26794e7i			1.25956i
$166$	−1.48495e7	−	4.17048e7i	−0.251961	−	0.707632i
$167$	−8.29338e7			−1.37792			−0.688960	−	0.724799i	$-0.741932\pi$
$167$	−8.29338e7			−1.37792			−0.688960	+	0.724799i	$0.741932\pi$
$168$	−6.78612e7	−	4.11036e7i	−1.10418	−	0.668802i
$169$	3.39743e7			0.541435
$170$	9.29992e7	−	3.31135e7i	1.45180	−	0.516932i
$171$	−3.11990e7	+	3.28236e7i	−0.477149	+	0.501996i
$172$	3.43024e7	+	4.20622e7i	0.514013	+	0.630293i
$173$			4.16331e7i			0.611333i	0.952139	+	0.305666i	$0.0988792\pi$
$173$			4.16331e7i			0.611333i	−0.952139	+	0.305666i	$0.901121\pi$
$174$	2.77414e7	+	7.79117e7i	0.399214	+	1.12119i
$175$			5.25974e7i			0.741876i
$176$	−5.18847e7	−	1.06546e7i	−0.717373	−	0.147314i
$177$	2.30574e7			0.312539
$178$	2.99792e7	+	8.41967e7i	0.398429	+	1.11899i
$179$	−1.17861e8			−1.53597			−0.767985	−	0.640468i	$-0.778740\pi$
$179$	−1.17861e8			−1.53597			−0.767985	+	0.640468i	$0.778740\pi$
$180$	−5.55186e7	+	4.52762e7i	−0.709553	+	0.578651i
$181$		−	1.37664e7i		−	0.172562i	−0.996271	−	0.0862809i	$-0.972502\pi$
$181$		−	1.37664e7i		−	0.172562i	0.996271	−	0.0862809i	$-0.0274982\pi$
$182$	−5.14824e7	+	1.83309e7i	−0.633008	+	0.225390i
$183$	7.76103e7			0.936139
$184$	1.30188e8	+	7.88550e7i	1.54066	+	0.933183i
$185$			1.51619e8i			1.76056i
$186$	1.45917e8	−	5.19554e7i	1.66269	−	0.592019i
$187$		−	7.63412e7i		−	0.853716i
$188$	−8.17590e7	−	1.00255e8i	−0.897394	−	1.10040i
$189$		−	3.68339e7i		−	0.396854i
$190$	−5.07323e7	+	1.14228e8i	−0.536595	+	1.20819i
$191$			7.90121e7i			0.820497i	0.911974	+	0.410248i	$0.134558\pi$
$191$			7.90121e7i			0.820497i	−0.911974	+	0.410248i	$0.865442\pi$
$192$	−5.91004e7	−	1.13081e8i	−0.602609	−	1.15302i
$193$			1.31658e7i			0.131825i	0.997825	+	0.0659125i	$0.0209958\pi$
$193$			1.31658e7i			0.131825i	−0.997825	+	0.0659125i	$0.979004\pi$
$194$	7.30623e6	+	2.05196e7i	0.0718435	+	0.201773i
$195$			1.20594e8i			1.16467i
$196$	1.25872e6	−	1.02651e6i	0.0119408	−	0.00973793i
$197$	−5.10395e7			−0.475636			−0.237818	−	0.971310i	$-0.576432\pi$
$197$	−5.10395e7			−0.475636			−0.237818	+	0.971310i	$0.576432\pi$
$198$	1.85832e7	+	5.21909e7i	0.170134	+	0.477822i
$199$			1.19998e8i			1.07941i	0.841853	+	0.539707i	$0.181465\pi$
$199$			1.19998e8i			1.07941i	−0.841853	+	0.539707i	$0.818535\pi$
$200$	−4.38231e7	+	7.23509e7i	−0.387345	+	0.639497i
$201$	−3.83635e7			−0.333221
$202$	−1.89118e8	+	6.73377e7i	−1.61437	+	0.574815i
$203$	1.08190e8			0.907722
$204$	1.42516e8	−	1.16224e8i	1.17533	−	0.958496i
$205$			5.86434e7i			0.475424i
$206$	1.10327e8	−	3.92831e7i	0.879317	−	0.313091i
$207$		−	1.59199e8i		−	1.24751i
$208$	−8.60900e7	−	1.76788e7i	−0.663332	−	0.136217i
$209$	7.00575e7	+	6.65900e7i	0.530814	+	0.504541i
$210$	7.68254e7	+	2.15764e8i	0.572450	+	1.60773i
$211$	9.42091e7			0.690406			0.345203	−	0.938528i	$-0.387810\pi$
$211$	9.42091e7			0.690406			0.345203	+	0.938528i	$0.387810\pi$
$212$	−7.51084e7	−	9.20994e7i	−0.541393	−	0.663867i
$213$	−1.97895e8			−1.40316
$214$	−1.47902e7	+	5.26621e6i	−0.103163	+	0.0367325i
$215$		−	1.56683e8i		−	1.07519i
$216$	3.06892e7	−	5.06672e7i	0.207204	−	0.342088i
$217$		−	2.02624e8i		−	1.34612i
$218$	−3.83134e7	−	1.07603e8i	−0.250468	−	0.703440i
$219$	−2.79263e8			−1.79663
$220$	9.66358e7	+	1.18497e8i	0.611870	+	0.750286i
$221$		−	1.26670e8i		−	0.789404i
$222$	9.47414e7	+	2.66081e8i	0.581171	+	1.63222i
$223$	1.32658e8			0.801061			0.400531	−	0.916283i	$-0.368826\pi$
$223$	1.32658e8			0.801061			0.400531	+	0.916283i	$0.368826\pi$
$224$	−1.65293e8	+	2.32139e7i	−0.982623	+	0.138001i
$225$	8.84736e7			0.517815
$226$	−9.58927e7	−	2.69315e8i	−0.552594	−	1.55196i
$227$	2.46219e8			1.39711			0.698557	−	0.715554i	$-0.253826\pi$
$227$	2.46219e8			1.39711			0.698557	+	0.715554i	$0.253826\pi$
$228$	−1.76547e7	+	2.32164e8i	−0.0986481	+	1.29725i
$229$	−1.64506e7			−0.0905230			−0.0452615	−	0.998975i	$-0.514412\pi$
$229$	−1.64506e7			−0.0905230			−0.0452615	+	0.998975i	$0.514412\pi$
$230$	−1.47385e8	−	4.13932e8i	−0.798742	−	2.24327i
$231$	1.77117e8			0.945404
$232$	1.48822e8	+	9.01420e7i	0.782457	+	0.473936i
$233$	−1.06735e8			−0.552793			−0.276396	−	0.961044i	$-0.589140\pi$
$233$	−1.06735e8			−0.552793			−0.276396	+	0.961044i	$0.589140\pi$
$234$	3.08343e7	+	8.65981e7i	0.157318	+	0.441827i
$235$			3.73450e8i			1.87713i
$236$	3.75929e7	−	3.06576e7i	0.186172	−	0.151826i
$237$	1.39452e8			0.680464
$238$	−8.06961e7	−	2.26635e8i	−0.388001	−	1.08970i
$239$			2.96610e8i			1.40538i	0.711497	+	0.702689i	$0.248018\pi$
$239$			2.96610e8i			1.40538i	−0.711497	+	0.702689i	$0.751982\pi$
$240$	−7.40922e7	+	3.60806e8i	−0.345966	+	1.68474i
$241$			2.21139e8i			1.01767i	0.860865	+	0.508833i	$0.169923\pi$
$241$			2.21139e8i			1.01767i	−0.860865	+	0.508833i	$0.830077\pi$
$242$	−9.63047e7	+	3.42904e7i	−0.436811	+	0.155532i
$243$	−2.63501e8			−1.17804
$244$	1.26536e8	−	1.03192e8i	0.557635	−	0.454759i
$245$	−4.68878e6			−0.0203694
$246$	3.66443e7	+	1.02916e8i	0.156940	+	0.440766i
$247$	1.16243e8	+	1.10490e8i	0.490827	+	0.466533i
$248$	1.68822e8	−	2.78722e8i	0.702828	−	1.16035i
$249$			2.38067e8i			0.977242i
$250$	−7.76404e7	+	2.76448e7i	−0.314266	+	0.111898i
$251$		−	2.28457e8i		−	0.911899i	−0.890006	−	0.455949i	$-0.849300\pi$
$251$		−	2.28457e8i		−	0.911899i	0.890006	−	0.455949i	$-0.150700\pi$
$252$	1.10336e8	+	1.35296e8i	0.434327	+	0.532580i
$253$	−3.39788e8			−1.31913
$254$	2.04072e8	−	7.26623e7i	0.781386	−	0.278222i
$255$	−5.30876e8			−2.00494
$256$	−2.46712e8	−	1.05787e8i	−0.919074	−	0.394086i
$257$		−	5.14468e8i		−	1.89057i	−0.326245	−	0.945285i	$-0.605784\pi$
$257$		−	5.14468e8i		−	1.89057i	0.326245	−	0.945285i	$-0.394216\pi$
$258$	−9.79057e7	−	2.74968e8i	−0.354927	−	0.996812i
$259$	3.69488e8			1.32145
$260$	1.60344e8	+	1.96616e8i	0.565777	+	0.693766i
$261$		−	1.81986e8i		−	0.633573i
$262$	6.13324e6	+	1.72252e7i	0.0210686	+	0.0591712i
$263$		−	2.55978e8i		−	0.867677i	−0.900991	−	0.433838i	$-0.857159\pi$
$263$		−	2.55978e8i		−	0.867677i	0.900991	−	0.433838i	$-0.142841\pi$
$264$	2.43634e8	+	1.47570e8i	0.814939	+	0.493610i
$265$			3.43072e8i			1.13247i
$266$	2.78369e8	+	1.23632e8i	0.906849	+	0.402760i
$267$		−	4.80628e8i		−	1.54532i
$268$	−6.25480e7	+	5.10089e7i	−0.198492	+	0.161873i
$269$		−	3.79678e8i		−	1.18928i	−0.803994	−	0.594638i	$-0.797296\pi$
$269$		−	3.79678e8i		−	1.18928i	0.803994	−	0.594638i	$-0.202704\pi$
$270$	−1.61096e8	+	5.73601e7i	−0.498094	+	0.177352i
$271$		−	3.90853e8i		−	1.19295i	−0.802633	−	0.596474i	$-0.796568\pi$
$271$		−	3.90853e8i		−	1.19295i	0.802633	−	0.596474i	$-0.203432\pi$
$272$	7.78252e7	−	3.78984e8i	0.234493	−	1.14190i
$273$	2.93882e8			0.874185
$274$	−1.59711e8	+	5.68670e7i	−0.469038	+	0.167006i
$275$		−	1.88835e8i		−	0.547542i
$276$	−5.17304e8	−	6.34328e8i	−1.48103	−	1.81607i
$277$	−3.80865e8			−1.07669			−0.538347	−	0.842723i	$-0.680951\pi$
$277$	−3.80865e8			−1.07669			−0.538347	+	0.842723i	$0.680951\pi$
$278$	−3.62193e7	−	1.01722e8i	−0.101107	−	0.283960i
$279$	−3.40833e8			−0.939564
$280$	4.12140e8	+	2.49634e8i	1.12200	+	0.679596i
$281$		−	3.58785e8i		−	0.964632i	−0.875997	−	0.482316i	$-0.839796\pi$
$281$		−	3.58785e8i		−	0.964632i	0.875997	−	0.482316i	$-0.160204\pi$
$282$	2.33356e8	+	6.55382e8i	0.619652	+	1.74029i
$283$			1.72632e7i			0.0452760i	0.999744	+	0.0226380i	$0.00720652\pi$
$283$			1.72632e7i			0.0452760i	−0.999744	+	0.0226380i	$0.992793\pi$
$284$	−3.22648e8	+	2.63125e8i	−0.835825	+	0.681628i
$285$	4.63066e8	−	4.87179e8i	1.18491	−	1.24661i
$286$	1.84832e8	−	6.58115e7i	0.467192	−	0.166349i
$287$	1.42912e8			0.356846
$288$	3.90479e7	+	2.78038e8i	0.0963218	+	0.685852i
$289$	1.47284e8			0.358934
$290$	−1.68481e8	−	4.73180e8i	−0.405657	−	1.13929i
$291$		−	1.17134e8i		−	0.278648i
$292$	−4.55312e8	+	3.71313e8i	−1.07021	+	0.872772i
$293$		−	6.69401e8i		−	1.55471i	−0.629061	−	0.777356i	$-0.716560\pi$
$293$		−	6.69401e8i		−	1.55471i	0.629061	−	0.777356i	$-0.283440\pi$
$294$	−8.22851e6	+	2.92986e6i	−0.0188845	+	0.00672405i
$295$	−1.40035e8			−0.317584
$296$	5.08253e8	+	3.07850e8i	1.13909	+	0.689950i
$297$			1.32241e8i			0.292898i
$298$	7.36895e8	−	2.62380e8i	1.61305	−	0.574346i
$299$	−5.63796e8			−1.21976
$300$	3.52523e8	−	2.87487e8i	0.753811	−	0.614744i
$301$	−3.81829e8			−0.807023
$302$	3.31438e8	−	1.18013e8i	0.692434	−	0.246549i
$303$	1.07956e9			2.22945
$304$	2.79905e8	+	4.01995e8i	0.571417	+	0.820660i
$305$	−4.71349e8			−0.951248
$306$	−3.81221e8	+	1.35738e8i	−0.760591	+	0.270818i
$307$	4.81907e8			0.950558			0.475279	−	0.879835i	$-0.342347\pi$
$307$	4.81907e8			0.950558			0.475279	+	0.879835i	$0.342347\pi$
$308$	2.88772e8	−	2.35497e8i	0.563154	−	0.459260i
$309$	−6.29788e8			−1.21434
$310$	−8.86195e8	+	3.15540e8i	−1.68952	+	0.601574i
$311$		−	3.77639e8i		−	0.711893i	−0.934506	−	0.355947i	$-0.884158\pi$
$311$		−	3.77639e8i		−	0.711893i	0.934506	−	0.355947i	$-0.115842\pi$
$312$	4.04252e8	+	2.44856e8i	0.753548	+	0.456425i
$313$	−3.97642e8			−0.732972			−0.366486	−	0.930424i	$-0.619439\pi$
$313$	−3.97642e8			−0.732972			−0.366486	+	0.930424i	$0.619439\pi$
$314$	−6.22928e8	+	2.21801e8i	−1.13549	+	0.404306i
$315$		−	5.03982e8i		−	0.908507i
$316$	2.27363e8	−	1.85418e8i	0.405335	−	0.330557i
$317$			8.58523e8i			1.51372i	0.653579	+	0.756859i	$0.273267\pi$
$317$			8.58523e8i			1.51372i	−0.653579	+	0.756859i	$0.726733\pi$
$318$	2.14374e8	+	6.02070e8i	0.373833	+	1.04991i
$319$	−3.88424e8			−0.669945
$320$	3.58934e8	+	6.86773e8i	0.612335	+	1.17162i
$321$	8.44281e7			0.142469
$322$	−1.00873e9	+	3.59172e8i	−1.68376	+	0.599524i
$323$	−4.86397e8	+	5.11724e8i	−0.803122	+	0.844943i
$324$	−5.75468e8	+	4.69303e8i	−0.939969	+	0.766559i
$325$		−	3.13325e8i		−	0.506295i
$326$	1.56512e8	+	4.39565e8i	0.250200	+	0.702686i
$327$			6.14241e8i			0.971453i
$328$	1.96583e8	+	1.19071e8i	0.307601	+	0.186315i
$329$	9.10082e8			1.40895
$330$	−2.75818e8	−	7.74634e8i	−0.422497	−	1.18658i
$331$	−8.07137e8			−1.22335			−0.611673	−	0.791111i	$-0.709503\pi$
$331$	−8.07137e8			−1.22335			−0.611673	+	0.791111i	$0.709503\pi$
$332$	3.16539e8	+	3.88146e8i	0.474727	+	0.582119i
$333$		−	6.21513e8i		−	0.922349i
$334$	8.83928e8	−	3.14733e8i	1.29809	−	0.462200i
$335$	2.32993e8			0.338599
$336$	8.79268e8	+	1.80560e8i	1.26454	+	0.259677i
$337$		−	5.23508e8i		−	0.745107i	−0.928011	−	0.372553i	$-0.878482\pi$
$337$		−	5.23508e8i		−	0.745107i	0.928011	−	0.372553i	$-0.121518\pi$
$338$	−3.62106e8	+	1.28932e8i	−0.510067	+	0.181615i
$339$			1.53736e9i			2.14326i
$340$	−8.65542e8	+	7.05862e8i	−1.19430	+	0.973966i
$341$			7.27460e8i			0.993502i
$342$	2.07961e8	−	4.68242e8i	0.281119	−	0.632964i
$343$			7.53006e8i			1.00755i
$344$	−5.25228e8	−	3.18132e8i	−0.695655	−	0.421359i
$345$			2.36288e9i			3.09796i
$346$	−1.57997e8	−	4.43736e8i	−0.205061	−	0.575914i
$347$		−	5.50494e8i		−	0.707293i	−0.935379	−	0.353647i	$-0.884942\pi$
$347$		−	5.50494e8i		−	0.707293i	0.935379	−	0.353647i	$-0.115058\pi$
$348$	−5.91349e8	−	7.25123e8i	−0.752170	−	0.922326i
$349$	1.06602e9			1.34238			0.671192	−	0.741284i	$-0.265783\pi$
$349$	1.06602e9			1.34238			0.671192	+	0.741284i	$0.265783\pi$
$350$	−1.99607e8	−	5.60596e8i	−0.248850	−	0.698895i
$351$			2.19421e8i			0.270834i
$352$	5.93434e8	−	8.33424e7i	0.725225	−	0.101851i
$353$	−1.07052e9			−1.29534			−0.647671	−	0.761920i	$-0.724257\pi$
$353$	−1.07052e9			−1.29534			−0.647671	+	0.761920i	$0.724257\pi$
$354$	−2.45752e8	+	8.75028e7i	−0.294432	+	0.104836i
$355$	1.20187e9			1.42580
$356$	−6.39052e8	−	7.83618e8i	−0.750691	−	0.920511i
$357$			1.29372e9i			1.50488i
$358$	1.25619e9	−	4.47280e8i	1.44698	−	0.515215i
$359$			3.42540e8i			0.390734i	0.980730	+	0.195367i	$0.0625898\pi$
$359$			3.42540e8i			0.390734i	−0.980730	+	0.195367i	$0.937410\pi$
$360$	4.19907e8	−	6.93257e8i	0.474345	−	0.783133i
$361$	−4.53359e7	−	8.92721e8i	−0.0507186	−	0.998713i
$362$	5.22433e7	+	1.46725e8i	0.0578829	+	0.162564i
$363$	5.49745e8			0.603237
$364$	4.79146e8	−	3.90751e8i	0.520730	−	0.424663i
$365$	1.69605e9			1.82563
$366$	−8.27189e8	+	2.94530e8i	−0.881903	+	0.314012i
$367$			8.40065e8i			0.887118i	0.896245	+	0.443559i	$0.146284\pi$
$367$			8.40065e8i			0.887118i	−0.896245	+	0.443559i	$0.853716\pi$
$368$	−1.68683e9	−	3.46394e8i	−1.76443	−	0.362329i
$369$		−	2.40390e8i		−	0.249072i
$370$	−5.75392e8	−	1.61599e9i	−0.590551	−	1.65856i
$371$	8.36052e8			0.850011
$372$	−1.35805e9	+	1.10751e9i	−1.36777	+	1.11544i
$373$			1.51282e9i			1.50940i	0.656069	+	0.754701i	$0.272218\pi$
$373$			1.51282e9i			1.50940i	−0.656069	+	0.754701i	$0.727782\pi$
$374$	2.89714e8	+	8.13663e8i	0.286365	+	0.804255i
$375$	4.43202e8			0.434003
$376$	1.25187e9	+	7.58261e8i	1.21451	+	0.735634i
$377$	−6.44495e8			−0.619477
$378$	1.39784e8	+	3.92584e8i	0.133118	+	0.373862i
$379$	1.08588e9			1.02458			0.512289	−	0.858813i	$-0.328798\pi$
$379$	1.08588e9			1.02458			0.512289	+	0.858813i	$0.328798\pi$
$380$	1.07222e8	−	1.41000e9i	0.100240	−	1.31818i
$381$	−1.16492e9			−1.07910
$382$	−2.99850e8	−	8.42130e8i	−0.275222	−	0.772961i
$383$	−6.95995e8			−0.633010			−0.316505	−	0.948591i	$-0.602509\pi$
$383$	−6.95995e8			−0.633010			−0.316505	+	0.948591i	$0.602509\pi$
$384$	1.05905e9	+	9.80958e8i	0.954456	+	0.884079i
$385$	−1.07568e9			−0.960662
$386$	−4.99642e7	−	1.40325e8i	−0.0442184	−	0.124188i
$387$			6.42271e8i			0.563287i
$388$	−1.55743e8	−	1.90975e8i	−0.135362	−	0.165984i
$389$	1.41264e9			1.21677			0.608384	−	0.793642i	$-0.291818\pi$
$389$	1.41264e9			1.21677			0.608384	+	0.793642i	$0.291818\pi$
$390$	−4.57652e8	−	1.28532e9i	−0.390670	−	1.09720i
$391$		−	2.48193e9i		−	2.09977i
$392$	−9.52020e6	+	1.57176e7i	−0.00798260	+	0.0131791i
$393$		−	9.83284e7i		−	0.0817156i
$394$	5.43991e8	−	1.93695e8i	0.448080	−	0.159544i
$395$	−8.46931e8			−0.691446
$396$	−3.96128e8	−	4.85740e8i	−0.320555	−	0.393071i
$397$	−2.05349e8			−0.164712			−0.0823560	−	0.996603i	$-0.526244\pi$
$397$	−2.05349e8			−0.164712			−0.0823560	+	0.996603i	$0.526244\pi$
$398$	−4.55391e8	−	1.27897e9i	−0.362071	−	1.01688i
$399$	−1.18723e9	−	1.12847e9i	−0.935689	−	0.889376i
$400$	1.92506e8	−	9.37441e8i	0.150395	−	0.732376i
$401$		−	1.73190e9i		−	1.34128i	−0.741785	−	0.670638i	$-0.766020\pi$
$401$		−	1.73190e9i		−	1.34128i	0.741785	−	0.670638i	$-0.233980\pi$
$402$	4.08888e8	−	1.45589e8i	0.313916	−	0.111773i
$403$			1.20704e9i			0.918660i
$404$	1.76012e9	−	1.43540e9i	1.32803	−	1.08303i
$405$	2.14363e9			1.60346
$406$	−1.15312e9	+	4.10582e8i	−0.855132	+	0.304480i
$407$	−1.32653e9			−0.975298
$408$	−1.07790e9	+	1.77959e9i	−0.785722	+	1.29721i
$409$			2.33740e8i			0.168928i	0.996427	+	0.0844638i	$0.0269177\pi$
$409$			2.33740e8i			0.168928i	−0.996427	+	0.0844638i	$0.973082\pi$
$410$	−2.22551e8	−	6.25036e8i	−0.159473	−	0.447880i
$411$	9.11693e8			0.647743
$412$	−1.02681e9	+	8.37378e8i	−0.723352	+	0.589904i
$413$			3.41258e8i			0.238373i
$414$	6.04159e8	+	1.69678e9i	0.418456	+	1.17523i
$415$		−	1.44585e9i		−	0.993014i
$416$	9.84659e8	−	1.38286e8i	0.670593	−	0.0941787i
$417$			5.80669e8i			0.392150i
$418$	−9.99398e8	−	4.43864e8i	−0.669301	−	0.297258i
$419$		−	1.67546e9i		−	1.11272i	−0.830942	−	0.556359i	$-0.812198\pi$
$419$		−	1.67546e9i		−	1.11272i	0.830942	−	0.556359i	$-0.187802\pi$
$420$	−1.63765e9	−	2.00811e9i	−1.07857	−	1.32256i
$421$		−	1.89877e9i		−	1.24018i	−0.784531	−	0.620090i	$-0.787096\pi$
$421$		−	1.89877e9i		−	1.24018i	0.784531	−	0.620090i	$-0.212904\pi$
$422$	−1.00410e9	+	3.57523e8i	−0.650406	+	0.231585i
$423$		−	1.53084e9i		−	0.983420i
$424$	1.15004e9	+	6.96581e8i	0.732710	+	0.443804i
$425$	1.37932e9			0.871570
$426$	2.10921e9	−	7.51009e8i	1.32186	−	0.470665i
$427$			1.14866e9i			0.713992i
$428$	1.37652e8	−	1.12257e8i	0.0848650	−	0.0692087i
$429$	−1.05509e9			−0.645193
$430$	5.94609e8	+	1.66996e9i	0.360655	+	1.01290i
$431$	−1.61906e9			−0.974076			−0.487038	−	0.873381i	$-0.661923\pi$
$431$	−1.61906e9			−0.974076			−0.487038	+	0.873381i	$0.661923\pi$
$432$	−1.34811e8	+	6.56488e8i	−0.0804513	+	0.391772i
$433$		−	2.51329e9i		−	1.48777i	−0.668310	−	0.743883i	$-0.732982\pi$
$433$		−	2.51329e9i		−	1.48777i	0.668310	−	0.743883i	$-0.267018\pi$
$434$	7.68958e8	+	2.15962e9i	0.451532	+	1.26813i
$435$			2.70110e9i			1.57336i
$436$	8.16706e8	+	1.00146e9i	0.471914	+	0.578670i
$437$	2.27764e9	+	2.16491e9i	1.30557	+	1.24095i
$438$	2.97645e9	−	1.05980e9i	1.69254	−	0.602650i
$439$	−1.19139e9			−0.672091			−0.336046	−	0.941846i	$-0.609090\pi$
$439$	−1.19139e9			−0.672091			−0.336046	+	0.941846i	$0.609090\pi$
$440$	−1.47966e9	−	8.96234e8i	−0.828091	−	0.501576i
$441$	1.92202e7			0.0106714
$442$	4.80710e8	+	1.35007e9i	0.264792	+	0.743669i
$443$			1.87376e9i			1.02400i	0.858985	+	0.512001i	$0.171095\pi$
$443$			1.87376e9i			1.02400i	−0.858985	+	0.512001i	$0.828905\pi$
$444$	−2.01955e9	−	2.47641e9i	−1.09500	−	1.34271i
$445$			2.91899e9i			1.57027i
$446$	−1.41390e9	+	5.03435e8i	−0.754651	+	0.268702i
$447$	−4.20649e9			−2.22763
$448$	1.67364e9	−	8.74706e8i	0.879404	−	0.459610i
$449$			2.57932e9i			1.34475i	0.740209	+	0.672376i	$0.234726\pi$
$449$			2.57932e9i			1.34475i	−0.740209	+	0.672376i	$0.765274\pi$
$450$	−9.42973e8	+	3.35757e8i	−0.487815	+	0.173692i
$451$	−5.13080e8			−0.263370
$452$	2.04410e9	+	2.50651e9i	1.04116	+	1.27669i
$453$	−1.89198e9			−0.956254
$454$	−2.62427e9	+	9.34401e8i	−1.31617	+	0.468638i
$455$	−1.78483e9			−0.888294
$456$	−6.92892e8	−	2.54146e9i	−0.342207	−	1.25518i
$457$	1.23984e9			0.607659			0.303829	−	0.952726i	$-0.401735\pi$
$457$	1.23984e9			0.607659			0.303829	+	0.952726i	$0.401735\pi$
$458$	1.75335e8	−	6.24301e7i	0.0852784	−	0.0303644i
$459$	−9.65931e8			−0.466232
$460$	3.14173e9	+	3.85245e9i	1.50493	+	1.84538i
$461$	3.24338e8			0.154186			0.0770929	−	0.997024i	$-0.475436\pi$
$461$	3.24338e8			0.154186			0.0770929	+	0.997024i	$0.475436\pi$
$462$	−1.88775e9	+	6.72156e8i	−0.890631	+	0.317120i
$463$		−	2.93118e9i		−	1.37249i	−0.727372	−	0.686244i	$-0.759258\pi$
$463$		−	2.93118e9i		−	1.37249i	0.727372	−	0.686244i	$-0.240742\pi$
$464$	−1.92827e9	−	3.95975e8i	−0.896098	−	0.184016i
$465$	5.05875e9			2.33323
$466$	1.13761e9	−	4.05059e8i	0.520766	−	0.185425i
$467$			6.96072e8i			0.316261i	0.987418	+	0.158130i	$0.0505466\pi$
$467$			6.96072e8i			0.316261i	−0.987418	+	0.158130i	$0.949453\pi$
$468$	−6.57278e8	−	8.05967e8i	−0.296407	−	0.363460i
$469$		−	5.67794e8i		−	0.254147i
$470$	−1.41724e9	−	3.98032e9i	−0.629653	−	1.76838i
$471$	3.55592e9			1.56812
$472$	−2.84329e8	+	4.69421e8i	−0.124458	+	0.205478i
$473$	1.37084e9			0.595624
$474$	−1.48631e9	+	5.29219e8i	−0.641040	+	0.228250i
$475$	−1.20313e9	+	1.26578e9i	−0.515093	+	0.541915i
$476$	1.72016e9	+	2.10929e9i	0.731044	+	0.896420i
$477$		−	1.40632e9i		−	0.593292i
$478$	−1.12563e9	−	3.16134e9i	−0.471410	−	1.32396i
$479$		−	4.16753e9i		−	1.73262i	−0.499503	−	0.866312i	$-0.666484\pi$
$479$		−	4.16753e9i		−	1.73262i	0.499503	−	0.866312i	$-0.333516\pi$
$480$	−5.79562e8	−	4.12673e9i	−0.239197	−	1.70319i
$481$	−2.20106e9			−0.901828
$482$	−8.39220e8	−	2.35695e9i	−0.341359	−	0.958707i
$483$	5.75825e9			2.32528
$484$	8.96306e8	−	7.30951e8i	0.359333	−	0.293042i
$485$			7.11387e8i			0.283146i
$486$	2.80846e9	−	9.99986e8i	1.10979	−	0.395154i
$487$	2.96002e9			1.16130			0.580649	−	0.814154i	$-0.302799\pi$
$487$	2.96002e9			1.16130			0.580649	+	0.814154i	$0.302799\pi$
$488$	−9.57038e8	+	1.58005e9i	−0.372786	+	0.615462i
$489$		−	2.50921e9i		−	0.970412i
$490$	4.99741e7	−	1.77939e7i	0.0191893	−	0.00683257i
$491$		−	2.11377e9i		−	0.805883i	−0.915226	−	0.402941i	$-0.867988\pi$
$491$		−	2.11377e9i		−	0.805883i	0.915226	−	0.402941i	$-0.132012\pi$
$492$	−7.81127e8	−	9.57833e8i	−0.295695	−	0.362587i
$493$		−	2.83719e9i		−	1.06641i
$494$	−1.65826e9	−	7.36484e8i	−0.618881	−	0.274865i
$495$			1.80939e9i			0.670524i
$496$	−7.41602e8	+	3.61136e9i	−0.272888	+	1.32888i
$497$		−	2.92891e9i		−	1.07019i
$498$	−9.03464e8	−	2.53738e9i	−0.327799	−	0.920625i
$499$			1.82088e9i			0.656040i	0.944671	+	0.328020i	$0.106381\pi$
$499$			1.82088e9i			0.656040i	−0.944671	+	0.328020i	$0.893619\pi$
$500$	7.22598e8	−	5.89289e8i	0.258525	−	0.210831i
$501$	−5.04581e9			−1.79266
$502$	8.66993e8	+	2.43495e9i	0.305881	+	0.859067i
$503$			4.32970e9i			1.51694i	0.651706	+	0.758472i	$0.274054\pi$
$503$			4.32970e9i			1.51694i	−0.651706	+	0.758472i	$0.725946\pi$
$504$	−1.68944e9	−	1.02330e9i	−0.587808	−	0.356037i
$505$	−6.55648e9			−2.26543
$506$	3.62154e9	−	1.28949e9i	1.24270	−	0.442479i
$507$	2.06704e9			0.704404
$508$	−1.89930e9	+	1.54890e9i	−0.642791	+	0.524206i
$509$			3.27361e9i			1.10031i	0.835063	+	0.550155i	$0.185431\pi$
$509$			3.27361e9i			1.10031i	−0.835063	+	0.550155i	$0.814569\pi$
$510$	5.65820e9	−	2.01467e9i	1.88879	−	0.672525i
$511$		−	4.13319e9i		−	1.37029i
$512$	3.03097e9	+	1.91229e8i	0.998016	+	0.0629665i
$513$	8.42551e8	−	8.86425e8i	0.275540	−	0.289889i
$514$	1.95240e9	+	5.48333e9i	0.634160	+	1.78104i
$515$	3.82489e9			1.23394
$516$	2.08700e9	+	2.55912e9i	0.668728	+	0.820007i
$517$	−3.26737e9			−1.03988
$518$	−3.93809e9	+	1.40220e9i	−1.24489	+	0.443259i
$519$			2.53302e9i			0.795339i
$520$	−2.45514e9	−	1.48708e9i	−0.765710	−	0.463792i
$521$		−	2.05962e9i		−	0.638049i	−0.947746	−	0.319025i	$-0.896645\pi$
$521$		−	2.05962e9i		−	0.638049i	0.947746	−	0.319025i	$-0.103355\pi$
$522$	6.90636e8	+	1.93965e9i	0.212521	+	0.596866i
$523$	3.74662e9			1.14521			0.572603	−	0.819833i	$-0.305934\pi$
$523$	3.74662e9			1.14521			0.572603	+	0.819833i	$0.305934\pi$
$524$	−1.30739e8	−	1.60315e8i	−0.0396959	−	0.0486759i
$525$			3.20010e9i			0.965175i
$526$	9.71435e8	+	2.72828e9i	0.291047	+	0.817407i
$527$	−5.31362e9			−1.58144
$528$	−3.15674e9	−	6.48243e8i	−0.933297	−	0.191655i
$529$	−7.64206e9			−2.24448
$530$	−1.30196e9	−	3.65654e9i	−0.379866	−	1.06685i
$531$	5.74027e8			0.166380
$532$	−3.43611e9	−	2.61296e8i	−0.989409	−	0.0752388i
$533$	−8.51330e8			−0.243530
$534$	1.82398e9	+	5.12265e9i	0.518353	+	1.45579i
$535$	−5.12756e8			−0.144768
$536$	4.73074e8	−	7.81034e8i	0.132694	−	0.219075i
$537$	−7.17080e9			−1.99829
$538$	1.44087e9	+	4.04670e9i	0.398922	+	1.12037i
$539$		−	4.10228e7i		−	0.0112840i
$540$	1.49932e9	−	1.22272e9i	0.409747	−	0.334155i
$541$	6.51079e9			1.76784			0.883921	−	0.467636i	$-0.154894\pi$
$541$	6.51079e9			1.76784			0.883921	+	0.467636i	$0.154894\pi$
$542$	1.48329e9	+	4.16581e9i	0.400154	+	1.12383i
$543$		−	8.37566e8i		−	0.224502i
$544$	6.08762e8	+	4.33465e9i	0.162126	+	1.15440i
$545$		−	3.73046e9i		−	0.987131i
$546$	−3.13226e9	+	1.11528e9i	−0.823538	+	0.293231i
$547$	3.70155e9			0.967003			0.483501	−	0.875344i	$-0.339365\pi$
$547$	3.70155e9			0.967003			0.483501	+	0.875344i	$0.339365\pi$
$548$	1.48643e9	−	1.21220e9i	0.385844	−	0.314662i
$549$	1.93215e9			0.498353
$550$	7.16626e8	+	2.01265e9i	0.183664	+	0.515820i
$551$	2.60366e9	+	2.47479e9i	0.663060	+	0.630242i
$552$	7.92081e9	+	4.79765e9i	2.00439	+	1.21407i
$553$			2.06393e9i			0.518989i
$554$	4.05935e9	−	1.44538e9i	1.01431	−	0.361159i
$555$			9.22469e9i			2.29048i
$556$	7.72068e8	+	9.46724e8i	0.190499	+	0.233594i
$557$	3.42488e9			0.839755			0.419877	−	0.907581i	$-0.362073\pi$
$557$	3.42488e9			0.839755			0.419877	+	0.907581i	$0.362073\pi$
$558$	3.63268e9	−	1.29346e9i	0.885130	−	0.315161i
$559$	2.27457e9			0.550755
$560$	−5.34005e9	−	1.09659e9i	−1.28495	−	0.263868i
$561$		−	4.64471e9i		−	1.11068i
$562$	1.36158e9	+	3.82401e9i	0.323570	+	0.908745i
$563$	−6.35215e9			−1.50017			−0.750087	−	0.661339i	$-0.769988\pi$
$563$	−6.35215e9			−1.50017			−0.750087	+	0.661339i	$0.769988\pi$
$564$	−4.97434e9	−	6.09963e9i	−1.16750	−	1.43162i
$565$		−	9.33680e9i		−	2.17785i
$566$	−6.55137e7	−	1.83995e8i	−0.0151871	−	0.0426529i
$567$		−	5.22394e9i		−	1.20353i
$568$	2.44031e9	−	4.02889e9i	0.558760	−	0.922500i
$569$			5.71881e9i			1.30141i	0.759333	+	0.650703i	$0.225526\pi$
$569$			5.71881e9i			1.30141i	−0.759333	+	0.650703i	$0.774474\pi$
$570$	−3.08663e9	+	6.94980e9i	−0.698107	+	1.57185i
$571$			1.20341e8i			0.0270513i	0.999909	+	0.0135257i	$0.00430549\pi$
$571$			1.20341e8i			0.0270513i	−0.999909	+	0.0135257i	$0.995695\pi$
$572$	−1.72022e9	+	1.40287e9i	−0.384325	+	0.313423i
$573$			4.80721e9i			1.06746i
$574$	−1.52319e9	+	5.42348e8i	−0.336172	+	0.119698i
$575$		−	6.13922e9i		−	1.34671i
$576$	−1.47133e9	−	2.81521e9i	−0.320799	−	0.613807i
$577$	6.52598e9			1.41426			0.707132	−	0.707082i	$-0.249989\pi$
$577$	6.52598e9			1.41426			0.707132	+	0.707082i	$0.249989\pi$
$578$	−1.56979e9	+	5.58943e8i	−0.338139	+	0.120398i
$579$			8.01028e8i			0.171503i
$580$	3.59143e9	+	4.40388e9i	0.764310	+	0.937211i
$581$	−3.52348e9			−0.745342
$582$	4.44522e8	+	1.24844e9i	0.0934679	+	0.262505i
$583$	−3.00159e9			−0.627351
$584$	3.44369e9	−	5.68545e9i	0.715449	−	1.18119i
$585$			3.00224e9i			0.620013i
$586$	2.54037e9	+	7.13464e9i	0.521502	+	1.46464i
$587$		−	2.62866e9i		−	0.536414i	−0.963361	−	0.268207i	$-0.913569\pi$
$587$		−	2.62866e9i		−	0.536414i	0.963361	−	0.268207i	$-0.0864312\pi$
$588$	7.65826e7	−	6.24543e7i	0.0155349	−	0.0126690i
$589$	4.63490e9	−	4.87625e9i	0.934624	−	0.983293i
$590$	1.49252e9	−	5.31430e8i	0.299184	−	0.106528i
$591$	−3.10532e9			−0.618799
$592$	−6.58537e9	−	1.35232e9i	−1.30453	−	0.267888i
$593$	3.92698e8			0.0773335			0.0386667	−	0.999252i	$-0.487689\pi$
$593$	3.92698e8			0.0773335			0.0386667	+	0.999252i	$0.487689\pi$
$594$	−5.01852e8	−	1.40945e9i	−0.0982478	−	0.275929i
$595$		−	7.85715e9i		−	1.52917i
$596$	−6.85827e9	+	5.59302e9i	−1.32694	+	1.08214i
$597$			7.30085e9i			1.40431i
$598$	6.00907e9	−	2.13960e9i	1.14909	−	0.409146i
$599$	7.99242e7			0.0151944			0.00759721	−	0.999971i	$-0.497582\pi$
$599$	7.99242e7			0.0151944			0.00759721	+	0.999971i	$0.497582\pi$
$600$	−2.66626e9	+	4.40193e9i	−0.503933	+	0.831982i
$601$		−	3.24899e9i		−	0.610504i	−0.952272	−	0.305252i	$-0.901259\pi$
$601$		−	3.24899e9i		−	0.610504i	0.952272	−	0.305252i	$-0.0987407\pi$
$602$	4.06962e9	−	1.44904e9i	0.760268	−	0.270702i
$603$	−9.55080e8			−0.177390
$604$	−3.08469e9	+	2.51561e9i	−0.569616	+	0.464531i
$605$	−3.33876e9			−0.612973
$606$	−1.15062e10	+	4.09692e9i	−2.10028	+	0.747831i
$607$	−9.80387e9			−1.77925			−0.889625	−	0.456691i	$-0.849034\pi$
$607$	−9.80387e9			−1.77925			−0.889625	+	0.456691i	$0.849034\pi$
$608$	−4.50886e9	−	3.22232e9i	−0.813588	−	0.581442i
$609$	6.58246e9			1.18094
$610$	5.02375e9	−	1.78877e9i	0.896136	−	0.319080i
$611$	−5.42140e9			−0.961540
$612$	3.54801e9	−	2.89346e9i	0.625685	−	0.510255i
$613$	−5.76734e9			−1.01126			−0.505631	−	0.862750i	$-0.668740\pi$
$613$	−5.76734e9			−1.01126			−0.505631	+	0.862750i	$0.668740\pi$
$614$	−5.13628e9	+	1.82883e9i	−0.895487	+	0.318849i
$615$			3.56795e9i			0.618523i
$616$	−2.18408e9	+	3.60587e9i	−0.376476	+	0.621553i
$617$	−2.60935e8			−0.0447233			−0.0223617	−	0.999750i	$-0.507119\pi$
$617$	−2.60935e8			−0.0447233			−0.0223617	+	0.999750i	$0.507119\pi$
$618$	6.71243e9	−	2.39004e9i	1.14399	−	0.407330i
$619$		−	1.98611e9i		−	0.336579i	−0.985738	−	0.168289i	$-0.946176\pi$
$619$		−	1.98611e9i		−	0.336579i	0.985738	−	0.168289i	$-0.0538243\pi$
$620$	8.24780e9	−	6.72621e9i	1.38985	−	1.13344i
$621$			4.29928e9i			0.720402i
$622$	1.43314e9	+	4.02496e9i	0.238793	+	0.670649i
$623$	7.11346e9			1.17862
$624$	−5.23784e9	−	1.07560e9i	−0.862991	−	0.177217i
$625$	−7.25504e9			−1.18867
$626$	4.23817e9	−	1.50905e9i	0.690507	−	0.245863i
$627$	4.26240e9	+	4.05143e9i	0.690585	+	0.656405i
$628$	5.79758e9	−	4.72802e9i	0.934089	−	0.761763i
$629$		−	9.68946e9i		−	1.55247i
$630$	1.91261e9	+	5.37156e9i	0.304743	+	0.855872i
$631$		−	7.15571e9i		−	1.13384i	−0.823775	−	0.566918i	$-0.808136\pi$
$631$		−	7.15571e9i		−	1.13384i	0.823775	−	0.566918i	$-0.191864\pi$
$632$	−1.71963e9	+	2.83907e9i	−0.270972	+	0.447369i
$633$	5.73182e9			0.898213
$634$	−3.25809e9	−	9.15035e9i	−0.507751	−	1.42602i
$635$	7.07492e9			1.09651
$636$	−4.56970e9	−	5.60346e9i	−0.704349	−	0.863687i
$637$		−	6.80673e7i		−	0.0104340i
$638$	4.13992e9	−	1.47407e9i	0.631131	−	0.224722i
$639$	−4.92670e9			−0.746969
$640$	−6.43190e9	−	5.95764e9i	−0.969861	−	0.898348i
$641$			9.03856e9i			1.35549i	0.735298	+	0.677744i	$0.237042\pi$
$641$			9.03856e9i			1.35549i	−0.735298	+	0.677744i	$0.762958\pi$
$642$	−8.99855e8	+	3.20404e8i	−0.134215	+	0.0477887i
$643$			1.08619e10i			1.61127i	0.592412	+	0.805635i	$0.298176\pi$
$643$			1.08619e10i			1.61127i	−0.592412	+	0.805635i	$0.701824\pi$
$644$	9.38827e9	−	7.65627e9i	1.38511	−	1.12958i
$645$		−	9.53279e9i		−	1.39882i
$646$	3.24214e9	−	7.29995e9i	0.473171	−	1.06538i
$647$			1.12360e10i			1.63097i	0.578776	+	0.815486i	$0.303530\pi$
$647$			1.12360e10i			1.63097i	−0.578776	+	0.815486i	$0.696470\pi$
$648$	4.35247e9	−	7.18584e9i	0.628382	−	1.03744i
$649$		−	1.22518e9i		−	0.175932i
$650$	1.18907e9	+	3.33949e9i	0.169828	+	0.476962i
$651$		−	1.23280e10i		−	1.75129i
$652$	−3.33629e9	−	4.09103e9i	−0.471409	−	0.578050i
$653$	8.26847e9			1.16206			0.581030	−	0.813882i	$-0.302650\pi$
$653$	8.26847e9			1.16206			0.581030	+	0.813882i	$0.302650\pi$
$654$	−2.33104e9	−	6.54673e9i	−0.325857	−	0.915171i
$655$			5.97176e8i			0.0830344i
$656$	−2.54710e9	−	5.23054e8i	−0.352276	−	0.0723407i
$657$	−6.95240e9			−0.956437
$658$	−9.69988e9	+	3.45376e9i	−1.32732	+	0.472608i
$659$	3.59078e9			0.488754			0.244377	−	0.969680i	$-0.421417\pi$
$659$	3.59078e9			0.488754			0.244377	+	0.969680i	$0.421417\pi$
$660$	5.87946e9	+	7.20951e9i	0.796038	+	0.976117i
$661$			1.83820e9i			0.247564i	0.992309	+	0.123782i	$0.0395024\pi$
$661$			1.83820e9i			0.247564i	−0.992309	+	0.123782i	$0.960498\pi$
$662$	8.60266e9	−	3.06308e9i	1.15247	−	0.410351i
$663$		−	7.70676e9i		−	1.02701i
$664$	−4.84676e9	−	2.93569e9i	−0.642485	−	0.389154i
$665$	7.21042e9	+	6.85354e9i	0.950790	+	0.903730i
$666$	2.35864e9	+	6.62423e9i	0.309386	+	0.868912i
$667$	−1.26281e10			−1.64777
$668$	−8.22671e9	+	6.70900e9i	−1.06785	+	0.870844i
$669$	8.07109e9			1.04218
$670$	−2.48329e9	+	8.84206e8i	−0.318982	+	0.113577i
$671$		−	4.12390e9i		−	0.526962i
$672$	−1.00567e10	+	1.41237e9i	−1.27839	+	0.179538i
$673$			2.97955e9i			0.376789i	0.982093	+	0.188394i	$0.0603283\pi$
$673$			2.97955e9i			0.376789i	−0.982093	+	0.188394i	$0.939672\pi$
$674$	1.98671e9	+	5.57967e9i	0.249934	+	0.701938i
$675$	−2.38929e9			−0.299024
$676$	3.37011e9	−	2.74838e9i	0.419596	−	0.342187i
$677$		−	1.45268e10i		−	1.79932i	−0.436588	−	0.899662i	$-0.643813\pi$
$677$		−	1.45268e10i		−	1.79932i	0.436588	−	0.899662i	$-0.356187\pi$
$678$	−5.83425e9	−	1.63855e10i	−0.718921	−	2.01909i
$679$	1.73362e9			0.212525
$680$	6.54641e9	−	1.08080e10i	0.798403	−	1.31814i
$681$	1.49803e10			1.81764
$682$	−2.76071e9	−	7.75344e9i	−0.333254	−	0.935943i
$683$	7.01872e9			0.842919			0.421459	−	0.906847i	$-0.361518\pi$
$683$	7.01872e9			0.842919			0.421459	+	0.906847i	$0.361518\pi$
$684$	−4.39524e8	+	5.77984e9i	−0.0525153	+	0.690589i
$685$	−5.53698e9			−0.658197
$686$	−2.85765e9	−	8.02571e9i	−0.337967	−	0.949181i
$687$	−1.00088e9			−0.117770
$688$	6.80532e9	+	1.39749e9i	0.796689	+	0.163602i
$689$	−4.98040e9			−0.580092
$690$	−8.96713e9	−	2.51842e10i	−1.03916	−	2.91848i
$691$			9.33187e8i			0.107596i	0.998552	+	0.0537980i	$0.0171327\pi$
$691$			9.33187e8i			0.107596i	−0.998552	+	0.0537980i	$0.982867\pi$
$692$	3.36795e9	+	4.12984e9i	0.386362	+	0.473764i
$693$	4.40941e9			0.503285
$694$	2.08912e9	+	5.86730e9i	0.237250	+	0.666315i
$695$		−	3.52657e9i		−	0.398479i
$696$	9.05457e9	+	5.48437e9i	1.01797	+	0.616587i
$697$		−	3.74771e9i		−	0.419229i
$698$	−1.13619e10	+	4.04554e9i	−1.26461	+	0.450280i
$699$	−6.49393e9			−0.719179
$700$	4.25491e9	+	5.21746e9i	0.468865	+	0.574931i
$701$	−1.25226e10			−1.37304			−0.686518	−	0.727112i	$-0.740862\pi$
$701$	−1.25226e10			−1.37304			−0.686518	+	0.727112i	$0.740862\pi$
$702$	−8.32701e8	−	2.33864e9i	−0.0908467	−	0.255143i
$703$	8.89191e9	+	8.45180e9i	0.965276	+	0.917499i
$704$	−6.00868e9	+	3.14036e9i	−0.649044	+	0.339215i
$705$			2.27212e10i			2.44214i
$706$	1.14099e10	−	4.06263e9i	1.22029	−	0.434501i
$707$			1.59779e10i			1.70040i
$708$	2.28721e9	−	1.86525e9i	0.242208	−	0.197525i
$709$	3.07952e9			0.324504			0.162252	−	0.986749i	$-0.448124\pi$
$709$	3.07952e9			0.324504			0.162252	+	0.986749i	$0.448124\pi$
$710$	−1.28098e10	+	4.56110e9i	−1.34320	+	0.478261i
$711$	3.47173e9			0.362245
$712$	9.78499e9	+	5.92679e9i	1.01597	+	0.615374i
$713$			2.36505e10i			2.44358i
$714$	−4.90967e9	−	1.37888e10i	−0.504787	−	1.41769i
$715$	6.40787e9			0.655606
$716$	−1.16913e10	+	9.53443e9i	−1.19033	+	0.970731i
$717$			1.80462e10i			1.82839i
$718$	−1.29994e9	−	3.65088e9i	−0.131065	−	0.368096i
$719$		−	1.36676e10i		−	1.37133i	−0.727917	−	0.685665i	$-0.759511\pi$
$719$		−	1.36676e10i		−	1.37133i	0.727917	−	0.685665i	$-0.240489\pi$
$720$	−1.84457e9	+	8.98245e9i	−0.184175	+	0.896873i
$721$		−	9.32109e9i		−	0.926175i
$722$	3.87107e9	+	9.34279e9i	0.382782	+	0.923839i
$723$			1.34544e10i			1.32398i
$724$	−1.11364e9	−	1.36557e9i	−0.109059	−	0.133730i
$725$		−	7.01796e9i		−	0.683956i
$726$	−5.85931e9	+	2.08628e9i	−0.568288	+	0.202346i
$727$			7.60566e9i			0.734119i	0.930198	+	0.367059i	$0.119635\pi$
$727$			7.60566e9i			0.734119i	−0.930198	+	0.367059i	$0.880365\pi$
$728$	−3.62396e9	+	5.98307e9i	−0.348115	+	0.574730i
$729$	−3.34432e9			−0.319713
$730$	−1.80769e10	+	6.43648e9i	−1.71986	+	0.612376i
$731$			1.00131e10i			0.948106i
$732$	7.69863e9	−	6.27835e9i	0.725479	−	0.591639i
$733$	−6.23188e9			−0.584460			−0.292230	−	0.956348i	$-0.594397\pi$
$733$	−6.23188e9			−0.584460			−0.292230	+	0.956348i	$0.594397\pi$
$734$	−3.18804e9	−	8.95361e9i	−0.297569	−	0.835722i
$735$	−2.85272e8			−0.0265005
$736$	1.92932e10	−	2.70955e9i	1.78374	−	0.250510i
$737$			2.03849e9i			0.187574i
$738$	9.12279e8	+	2.56214e9i	0.0835469	+	0.234642i
$739$		−	6.71548e8i		−	0.0612098i	−0.999532	−	0.0306049i	$-0.990257\pi$
$739$		−	6.71548e8i		−	0.0612098i	0.999532	−	0.0306049i	$-0.00974337\pi$
$740$	1.22653e10	+	1.50400e10i	1.11267	+	1.36438i
$741$	7.07241e9	+	6.72236e9i	0.638563	+	0.606957i
$742$	−8.91084e9	+	3.17281e9i	−0.800765	+	0.285122i
$743$	1.12976e10			1.01048			0.505239	−	0.862980i	$-0.331404\pi$
$743$	1.12976e10			1.01048			0.505239	+	0.862980i	$0.331404\pi$
$744$	1.02714e10	−	1.69578e10i	0.914375	−	1.50961i
$745$	2.55472e10			2.26358
$746$	−5.74112e9	−	1.61239e10i	−0.506303	−	1.42195i
$747$			5.92681e9i			0.520234i
$748$	−6.17569e9	−	7.57275e9i	−0.539548	−	0.661604i
$749$			1.24956e9i			0.108661i
$750$	−4.72375e9	+	1.68195e9i	−0.408858	+	0.145579i
$751$	−1.84554e10			−1.58995			−0.794977	−	0.606639i	$-0.792517\pi$
$751$	−1.84554e10			−1.58995			−0.794977	+	0.606639i	$0.792517\pi$
$752$	−1.62204e10	−	3.33088e9i	−1.39091	−	0.285626i
$753$		−	1.38997e10i		−	1.18637i
$754$	6.86919e9	−	2.44586e9i	0.583587	−	0.207793i
$755$	1.14905e10			0.971687
$756$	−2.97971e9	−	3.65377e9i	−0.250811	−	0.307550i
$757$	−8.06853e9			−0.676019			−0.338010	−	0.941143i	$-0.609754\pi$
$757$	−8.06853e9			−0.676019			−0.338010	+	0.941143i	$0.609754\pi$
$758$	−1.15736e10	+	4.12091e9i	−0.965219	+	0.343678i
$759$	−2.06732e10			−1.71618
$760$	4.20814e9	+	1.54350e10i	0.347730	+	1.27544i
$761$	9.65979e9			0.794550			0.397275	−	0.917700i	$-0.369956\pi$
$761$	9.65979e9			0.794550			0.397275	+	0.917700i	$0.369956\pi$
$762$	1.24160e10	−	4.42088e9i	1.01658	−	0.361965i
$763$	−9.09098e9			−0.740926
$764$	6.39175e9	+	7.83769e9i	0.518553	+	0.635860i
$765$	−1.32164e10			−1.06733
$766$	7.41808e9	−	2.64129e9i	0.596336	−	0.212332i
$767$		−	2.03289e9i		−	0.162678i
$768$	−1.50103e10	−	6.43621e9i	−1.19571	−	0.512703i
$769$	2.54906e9			0.202133			0.101067	−	0.994880i	$-0.467774\pi$
$769$	2.54906e9			0.202133			0.101067	+	0.994880i	$0.467774\pi$
$770$	1.14649e10	−	4.08220e9i	0.905005	−	0.322238i
$771$		−	3.13010e10i		−	2.45962i
$772$	1.06506e9	+	1.30600e9i	0.0833132	+	0.102160i
$773$			1.24498e10i			0.969466i	0.874662	+	0.484733i	$0.161083\pi$
$773$			1.24498e10i			0.969466i	−0.874662	+	0.484733i	$0.838917\pi$
$774$	−2.43741e9	−	6.84548e9i	−0.188945	−	0.530653i
$775$	−1.31436e10			−1.01428
$776$	2.38470e9	+	1.44442e9i	0.183197	+	0.110962i
$777$	2.24802e10			1.71920
$778$	−1.50563e10	+	5.36096e9i	−1.14627	+	0.408145i
$779$	3.43924e9	+	3.26901e9i	0.260664	+	0.247762i
$780$	9.75553e9	+	1.19624e10i	0.736071	+	0.902585i
$781$			1.05153e10i			0.789851i
$782$	9.41892e9	+	2.64530e10i	0.704332	+	1.97812i
$783$			4.91466e9i			0.365871i
$784$	4.18202e7	−	2.03651e8i	0.00309942	−	0.0150932i
$785$	−2.15961e10			−1.59343
$786$	3.73155e8	+	1.04801e9i	0.0274101	+	0.0769813i
$787$	1.99582e10			1.45952			0.729761	−	0.683702i	$-0.239631\pi$
$787$	1.99582e10			1.45952			0.729761	+	0.683702i	$0.239631\pi$
$788$	−5.06292e9	+	4.12889e9i	−0.368603	+	0.300601i
$789$		−	1.55741e10i		−	1.12884i
$790$	9.02679e9	−	3.21410e9i	0.651386	−	0.231934i
$791$	−2.27534e10			−1.63466
$792$	6.06541e9	+	3.67383e9i	0.433832	+	0.262773i
$793$		−	6.84261e9i		−	0.487265i
$794$	2.18866e9	−	7.79297e8i	0.155169	−	0.0552499i
$795$			2.08730e10i			1.47333i
$796$	9.70734e9	+	1.19033e10i	0.682188	+	0.836513i
$797$			1.48130e10i			1.03643i	0.855252	+	0.518213i	$0.173403\pi$
$797$			1.48130e10i			1.03643i	−0.855252	+	0.518213i	$0.826597\pi$
$798$	1.69364e10	+	7.52198e9i	1.17980	+	0.523989i
$799$		−	2.38660e10i		−	1.65526i
$800$	1.50581e9	+	1.07220e10i	0.103981	+	0.740392i
$801$		−	1.19655e10i		−	0.822653i
$802$	6.57256e9	+	1.84590e10i	0.449908	+	1.26357i
$803$			1.48389e10i			1.01134i
$804$	−3.80551e9	+	3.10345e9i	−0.258236	+	0.210595i
$805$	−3.49715e10			−2.36281
$806$	−4.58072e9	−	1.28649e10i	−0.308149	−	0.865437i
$807$		−	2.31001e10i		−	1.54724i
$808$	−1.33124e10	+	2.19785e10i	−0.887804	+	1.46574i
$809$	−3.70712e9			−0.246160			−0.123080	−	0.992397i	$-0.539277\pi$
$809$	−3.70712e9			−0.246160			−0.123080	+	0.992397i	$0.539277\pi$
$810$	−2.28473e10	+	8.13506e9i	−1.51056	+	0.537853i
$811$	2.26249e10			1.48941			0.744703	−	0.667396i	$-0.232591\pi$
$811$	2.26249e10			1.48941			0.744703	+	0.667396i	$0.232591\pi$
$812$	1.07321e10	−	8.75216e9i	0.703457	−	0.573679i
$813$		−	2.37801e10i		−	1.55202i
$814$	1.41385e10	−	5.03418e9i	0.918794	−	0.327147i
$815$			1.52392e10i			0.986074i
$816$	4.73500e9	−	2.30579e10i	0.305073	−	1.48561i
$817$	−9.18890e9	−	8.73409e9i	−0.589503	−	0.560326i
$818$	−8.87040e8	−	2.49125e9i	−0.0566639	−	0.159141i
$819$	7.31634e9			0.465372
$820$	4.74401e9	+	5.81720e9i	0.300467	+	0.368439i
$821$	1.79900e10			1.13457			0.567284	−	0.823522i	$-0.307994\pi$
$821$	1.79900e10			1.13457			0.567284	+	0.823522i	$0.307994\pi$
$822$	−9.71704e9	+	3.45987e9i	−0.610215	+	0.217274i
$823$		−	9.79458e9i		−	0.612472i	−0.951956	−	0.306236i	$-0.900930\pi$
$823$		−	9.79458e9i		−	0.612472i	0.951956	−	0.306236i	$-0.0990697\pi$
$824$	7.76613e9	−	1.28217e10i	0.483570	−	0.798363i
$825$		−	1.14890e10i		−	0.712348i
$826$	−1.29507e9	−	3.63721e9i	−0.0799584	−	0.224563i
$827$	2.06423e10			1.26908			0.634541	−	0.772889i	$-0.281189\pi$
$827$	2.06423e10			1.26908			0.634541	+	0.772889i	$0.281189\pi$
$828$	−1.28785e10	−	1.57919e10i	−0.788425	−	0.966782i
$829$		−	5.36331e9i		−	0.326958i	−0.986547	−	0.163479i	$-0.947728\pi$
$829$		−	5.36331e9i		−	0.326958i	0.986547	−	0.163479i	$-0.0522716\pi$
$830$	5.48700e9	+	1.54102e10i	0.333090	+	0.935483i
$831$	−2.31724e10			−1.40077
$832$	−9.96993e9	+	5.21066e9i	−0.600151	+	0.313662i
$833$	2.99645e8			0.0179618
$834$	−2.20363e9	−	6.18891e9i	−0.131540	−	0.369431i
$835$	3.06447e10			1.82160
$836$	1.23363e10	+	9.38102e8i	0.730234	+	0.0555301i
$837$	9.20442e9			0.542572
$838$	6.35835e9	+	1.78574e10i	0.373242	+	1.04825i
$839$	1.19553e10			0.698865			0.349433	−	0.936961i	$-0.386374\pi$
$839$	1.19553e10			0.698865			0.349433	+	0.936961i	$0.386374\pi$
$840$	2.50752e10	+	1.51881e10i	1.45971	+	0.884150i
$841$	2.81425e9			0.163146
$842$	7.20581e9	+	2.02375e10i	0.415997	+	1.16833i
$843$		−	2.18290e10i		−	1.25498i
$844$	9.34517e9	−	7.62113e9i	0.535043	−	0.436336i
$845$	−1.25537e10			−0.715772
$846$	5.80953e9	+	1.63161e10i	0.329871	+	0.926444i
$847$			8.13642e9i			0.460088i
$848$	−1.49009e10	−	3.05994e9i	−0.839127	−	0.172316i
$849$			1.05032e9i			0.0589038i
$850$	−1.47011e10	+	5.23449e9i	−0.821075	+	0.292353i
$851$	−4.31270e10			−2.39881
$852$	−1.96304e10	+	1.60089e10i	−1.08740	+	0.886793i
$853$	−2.36359e10			−1.30392			−0.651961	−	0.758253i	$-0.726053\pi$
$853$	−2.36359e10			−1.30392			−0.651961	+	0.758253i	$0.726053\pi$
$854$	−4.35915e9	−	1.22427e10i	−0.239497	−	0.672626i
$855$	1.15283e10	−	1.21286e10i	0.630787	−	0.663634i
$856$	−1.04111e9	+	1.71885e9i	−0.0567334	+	0.0936656i
$857$			2.34604e10i			1.27322i	0.771186	+	0.636610i	$0.219664\pi$
$857$			2.34604e10i			1.27322i	−0.771186	+	0.636610i	$0.780336\pi$
$858$	1.12454e10	−	4.00406e9i	0.607813	−	0.216419i
$859$			1.98290e9i			0.106739i	0.998575	+	0.0533697i	$0.0169962\pi$
$859$			1.98290e9i			0.106739i	−0.998575	+	0.0533697i	$0.983004\pi$
$860$	−1.26750e10	−	1.55423e10i	−0.679521	−	0.833241i
$861$	8.69494e9			0.464254
$862$	1.72563e10	−	6.14433e9i	0.917642	−	0.326737i
$863$	−1.96538e9			−0.104090			−0.0520449	−	0.998645i	$-0.516574\pi$
$863$	−1.96538e9			−0.104090			−0.0520449	+	0.998645i	$0.516574\pi$
$864$	−1.05452e9	−	7.50861e9i	−0.0556231	−	0.396061i
$865$		−	1.53837e10i		−	0.808176i
$866$	9.53791e9	+	2.67872e10i	0.499046	+	1.40157i
$867$	8.96099e9			0.466970
$868$	−1.63915e10	−	2.00995e10i	−0.850744	−	1.04320i
$869$		−	7.40992e9i		−	0.383040i
$870$	−1.02506e10	−	2.87890e10i	−0.527757	−	1.48221i
$871$			3.38237e9i			0.173443i
$872$	−1.25052e10	−	7.57441e9i	−0.638679	−	0.386849i
$873$		−	2.91611e9i		−	0.148338i
$874$	−3.24915e10	−	1.44305e10i	−1.64619	−	0.731124i
$875$			6.55954e9i			0.331013i
$876$	−2.77018e10	+	2.25912e10i	−1.39234	+	1.13547i
$877$		−	8.18145e9i		−	0.409573i	−0.978807	−	0.204787i	$-0.934350\pi$
$877$		−	8.18145e9i		−	0.409573i	0.978807	−	0.204787i	$-0.0656501\pi$
$878$	1.26981e10	−	4.52132e9i	0.633153	−	0.225442i
$879$		−	4.07273e10i		−	2.02267i
$880$	1.91718e10	+	3.93697e9i	0.948360	+	0.194748i
$881$	−2.72108e10			−1.34068			−0.670341	−	0.742053i	$-0.733852\pi$
$881$	−2.72108e10			−1.34068			−0.670341	+	0.742053i	$0.733852\pi$
$882$	−2.04853e8	+	7.29404e7i	−0.0100532	+	0.00357955i
$883$			1.44329e10i			0.705491i	0.935719	+	0.352745i	$0.114752\pi$
$883$			1.44329e10i			0.705491i	−0.935719	+	0.352745i	$0.885248\pi$
$884$	−1.02470e10	−	1.25651e10i	−0.498903	−	0.611764i
$885$	−8.51990e9			−0.413174
$886$	−7.11090e9	−	1.99710e10i	−0.343484	−	0.964675i
$887$	−1.02589e10			−0.493591			−0.246796	−	0.969068i	$-0.579378\pi$
$887$	−1.02589e10			−0.493591			−0.246796	+	0.969068i	$0.579378\pi$
$888$	3.09228e10	+	1.87300e10i	1.48195	+	0.897621i
$889$		−	1.72413e10i		−	0.823026i
$890$	−1.10776e10	−	3.11113e10i	−0.526719	−	1.47929i
$891$			1.87549e10i			0.888267i
$892$	1.31591e10	−	1.07315e10i	0.620798	−	0.506270i
$893$	2.19016e10	+	2.08175e10i	1.02919	+	0.978249i
$894$	4.48337e10	−	1.59636e10i	2.09857	−	0.747221i
$895$	4.35503e10			2.03054
$896$	−1.45185e10	+	1.56743e10i	−0.674286	+	0.727963i
$897$	−3.43021e10			−1.58689
$898$	−9.78849e9	−	2.74910e10i	−0.451075	−	1.26684i
$899$			2.70357e10i			1.24102i
$900$	8.77624e9	−	7.15715e9i	0.401291	−	0.327259i
$901$		−	2.19246e10i		−	0.998610i
$902$	5.46852e9	−	1.94713e9i	0.248112	−	0.0883431i
$903$	−2.32310e10			−1.04993
$904$	−3.12986e10	−	1.89576e10i	−1.40908	−	0.853483i
$905$			5.08678e9i			0.228125i
$906$	2.01652e10	−	7.18005e9i	0.900852	−	0.320759i
$907$	9.34499e9			0.415866			0.207933	−	0.978143i	$-0.433326\pi$
$907$	9.34499e9			0.415866			0.207933	+	0.978143i	$0.433326\pi$
$908$	2.44240e10	−	1.99181e10i	1.08272	−	0.882975i
$909$	2.68762e10			1.18685
$910$	1.90231e10	−	6.77341e9i	0.836830	−	0.297963i
$911$	1.93476e10			0.847838			0.423919	−	0.905700i	$-0.360654\pi$
$911$	1.93476e10			0.847838			0.423919	+	0.905700i	$0.360654\pi$
$912$	1.70298e10	+	2.44579e10i	0.743410	+	1.06767i
$913$	1.26500e10			0.550100
$914$	−1.32145e10	+	4.70519e9i	−0.572454	+	0.203829i
$915$	−2.86776e10			−1.23757
$916$	−1.63184e9	+	1.33079e9i	−0.0701525	+	0.0572104i
$917$	1.45529e9			0.0623244
$918$	1.02951e10	−	3.66570e9i	0.439220	−	0.156390i
$919$		−	4.42797e10i		−	1.88192i	−0.338520	−	0.940959i	$-0.609926\pi$
$919$		−	4.42797e10i		−	1.88192i	0.338520	−	0.940959i	$-0.390074\pi$
$920$	−4.81054e10	−	2.91375e10i	−2.03674	−	1.23366i
$921$	2.93199e10			1.23667
$922$	−3.45687e9	+	1.23086e9i	−0.145253	+	0.0517190i
$923$			1.74477e10i			0.730350i
$924$	1.75693e10	−	1.43280e10i	0.732659	−	0.597494i
$925$		−	2.39675e10i		−	0.995695i
$926$	1.11238e10	+	3.12412e10i	0.460378	+	1.29297i
$927$	−1.56789e10			−0.646453
$928$	2.20547e10	−	3.09739e9i	0.905907	−	0.127226i
$929$	1.92421e10			0.787404			0.393702	−	0.919238i	$-0.371194\pi$
$929$	1.92421e10			0.787404			0.393702	+	0.919238i	$0.371194\pi$
$930$	−5.39174e10	+	1.91979e10i	−2.19805	+	0.782643i
$931$	−2.61370e8	+	2.74981e8i	−0.0106153	+	0.0111681i
$932$	−1.05877e10	+	8.63444e9i	−0.428397	+	0.349364i
$933$		−	2.29761e10i		−	0.926168i
$934$	−2.64159e9	−	7.41890e9i	−0.106084	−	0.297938i
$935$			2.82086e10i			1.12860i
$936$	1.00641e10	+	6.09582e9i	0.401151	+	0.242978i
$937$	−3.28295e10			−1.30369			−0.651846	−	0.758351i	$-0.726005\pi$
$937$	−3.28295e10			−1.30369			−0.651846	+	0.758351i	$0.726005\pi$
$938$	2.15477e9	+	6.05168e9i	0.0852494	+	0.239423i
$939$	−2.41931e10			−0.953592
$940$	3.02106e10	+	3.70448e10i	1.18635	+	1.45472i
$941$		−	1.35755e10i		−	0.531120i	−0.964094	−	0.265560i	$-0.914443\pi$
$941$		−	1.35755e10i		−	0.531120i	0.964094	−	0.265560i	$-0.0855569\pi$
$942$	−3.78998e10	+	1.34947e10i	−1.47727	+	0.525999i
$943$	−1.66808e10			−0.647776
$944$	1.24900e9	−	6.08223e9i	0.0483237	−	0.235321i
$945$			1.36104e10i			0.524637i
$946$	−1.46107e10	+	5.20232e9i	−0.561116	+	0.199792i
$947$		−	2.04863e10i		−	0.783861i	−0.919995	−	0.391930i	$-0.871807\pi$
$947$		−	2.04863e10i		−	0.783861i	0.919995	−	0.391930i	$-0.128193\pi$
$948$	1.38331e10	−	1.12811e10i	0.527338	−	0.430052i
$949$			2.46216e10i			0.935157i
$950$	8.01963e9	−	1.80569e10i	0.303474	−	0.683298i
$951$			5.22338e10i			1.96934i
$952$	−2.63386e10	−	1.59533e10i	−0.989379	−	0.599269i
$953$		−	1.52016e9i		−	0.0568939i	−0.999595	−	0.0284469i	$-0.990944\pi$
$953$		−	1.52016e9i		−	0.0568939i	0.999595	−	0.0284469i	$-0.00905616\pi$
$954$	5.33696e9	+	1.49888e10i	0.199010	+	0.558919i
$955$		−	2.91956e10i		−	1.08469i
$956$	2.39945e10	+	2.94226e10i	0.888198	+	1.08913i
$957$	−2.36323e10			−0.871594
$958$	1.58157e10	+	4.44185e10i	0.581179	+	1.63224i
$959$			1.34934e10i			0.494033i
$960$	2.18380e10	+	4.17843e10i	0.796644	+	1.52428i
$961$	2.31213e10			0.840387
$962$	2.34594e10	−	8.35300e9i	0.849579	−	0.302503i
$963$	2.10188e9			0.0758431
$964$	1.78892e10	+	2.19361e10i	0.643164	+	0.788660i
$965$		−	4.86487e9i		−	0.174271i
$966$	−6.13728e10	+	2.18525e10i	−2.19056	+	0.779976i
$967$		−	3.63192e10i		−	1.29165i	−0.763487	−	0.645823i	$-0.776514\pi$
$967$		−	3.63192e10i		−	1.29165i	0.763487	−	0.645823i	$-0.223486\pi$
$968$	−6.77909e9	+	1.11921e10i	−0.240219	+	0.396596i
$969$	−2.95931e10	+	3.11340e10i	−1.04486	+	1.09926i
$970$	−2.69971e9	−	7.58213e9i	−0.0949764	−	0.266741i
$971$	9.10590e9			0.319195			0.159597	−	0.987182i	$-0.448980\pi$
$971$	9.10590e9			0.319195			0.159597	+	0.987182i	$0.448980\pi$
$972$	−2.61383e10	+	2.13162e10i	−0.912947	+	0.744522i
$973$	−8.59410e9			−0.299092
$974$	−3.15486e10	+	1.12333e10i	−1.09402	+	0.389538i
$975$		−	1.90631e10i		−	0.658686i
$976$	4.20407e9	−	2.04725e10i	0.144742	−	0.704849i
$977$			9.72996e9i			0.333795i	0.985974	+	0.166898i	$0.0533749\pi$
$977$			9.72996e9i			0.333795i	−0.985974	+	0.166898i	$0.946625\pi$
$978$	9.52244e9	+	2.67438e10i	0.325508	+	0.914190i
$979$	−2.55387e10			−0.869879
$980$	−4.65108e8	+	3.79303e8i	−0.0157857	+	0.0128734i
$981$			1.52919e10i			0.517152i
$982$	8.02173e9	+	2.25290e10i	0.270320	+	0.759193i
$983$	−1.13261e9			−0.0380315			−0.0190158	−	0.999819i	$-0.506053\pi$
$983$	−1.13261e9			−0.0380315			−0.0190158	+	0.999819i	$0.506053\pi$
$984$	1.19604e10	+	7.24444e9i	0.400187	+	0.242394i
$985$	1.88595e10			0.628786
$986$	1.07671e10	+	3.02394e10i	0.357709	+	1.00463i
$987$	5.53707e10			1.83303
$988$	2.04690e10	+	1.55655e9i	0.675225	+	0.0513469i
$989$	4.45674e10			1.46498
$990$	−6.86663e9	−	1.92849e10i	−0.224916	−	0.631677i
$991$	2.02590e10			0.661242			0.330621	−	0.943764i	$-0.392742\pi$
$991$	2.02590e10			0.661242			0.330621	+	0.943764i	$0.392742\pi$
$992$	−5.80094e9	−	4.13052e10i	−0.188672	−	1.34342i
$993$	−4.91074e10			−1.59156
$994$	1.11152e10	+	3.12170e10i	0.358976	+	1.00818i
$995$		−	4.43401e10i		−	1.42697i
$996$	1.92587e10	+	2.36153e10i	0.617616	+	0.757333i
$997$	−1.02253e10			−0.326772			−0.163386	−	0.986562i	$-0.552242\pi$
$997$	−1.02253e10			−0.326772			−0.163386	+	0.986562i	$0.552242\pi$
$998$	−6.91024e9	−	1.94074e10i	−0.220057	−	0.618031i
$999$			1.67844e10i			0.532631i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.8.d.a.75.10	yes	68
4.3	odd	2	inner	76.8.d.a.75.60	yes	68
19.18	odd	2	inner	76.8.d.a.75.59	yes	68
76.75	even	2	inner	76.8.d.a.75.9	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.8.d.a.75.9	✓	68	76.75	even	2	inner
76.8.d.a.75.10	yes	68	1.1	even	1	trivial
76.8.d.a.75.59	yes	68	19.18	odd	2	inner
76.8.d.a.75.60	yes	68	4.3	odd	2	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.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-10.6582 + 3.79499i) q^{2} +60.8414 q^{3} +(99.1961 - 80.8959i) q^{4} -369.508 q^{5} +(-648.462 + 230.893i) q^{6} +900.474i q^{7} +(-750.256 + 1238.66i) q^{8} +1514.68 q^{9} +O(q^{10})\)	\(q+(-10.6582 + 3.79499i) q^{2} +60.8414 q^{3} +(99.1961 - 80.8959i) q^{4} -369.508 q^{5} +(-648.462 + 230.893i) q^{6} +900.474i q^{7} +(-750.256 + 1238.66i) q^{8} +1514.68 q^{9} +(3938.30 - 1402.28i) q^{10} -3232.87i q^{11} +(6035.23 - 4921.82i) q^{12} -5364.16i q^{13} +(-3417.29 - 9597.47i) q^{14} -22481.4 q^{15} +(3295.72 - 16049.1i) q^{16} +23614.0 q^{17} +(-16143.8 + 5748.20i) q^{18} +(-20597.8 + 21670.3i) q^{19} +(-36653.7 + 29891.6i) q^{20} +54786.1i q^{21} +(12268.7 + 34456.7i) q^{22} -105104. i q^{23} +(-45646.6 + 75361.6i) q^{24} +58410.8 q^{25} +(20357.0 + 57172.5i) q^{26} -40905.0 q^{27} +(72844.6 + 89323.5i) q^{28} -120148. i q^{29} +(239612. - 85316.6i) q^{30} -225020. q^{31} +(25779.7 + 183562. i) q^{32} -196693. i q^{33} +(-251684. + 89615.1i) q^{34} -332732. i q^{35} +(150250. - 122531. i) q^{36} -410326. i q^{37} +(137297. - 309136. i) q^{38} -326363. i q^{39} +(277225. - 457693. i) q^{40} -158707. i q^{41} +(-207913. - 583924. i) q^{42} +424031. i q^{43} +(-261526. - 320688. i) q^{44} -559685. q^{45} +(398869. + 1.12022e6i) q^{46} -1.01067e6i q^{47} +(200516. - 976450. i) q^{48} +12689.3 q^{49} +(-622556. + 221669. i) q^{50} +1.43671e6 q^{51} +(-433939. - 532104. i) q^{52} -928458. i q^{53} +(435975. - 155234. i) q^{54} +1.19457e6i q^{55} +(-1.11538e6 - 675586. i) q^{56} +(-1.25320e6 + 1.31845e6i) q^{57} +(455962. + 1.28057e6i) q^{58} +378976. q^{59} +(-2.23006e6 + 1.81865e6i) q^{60} +1.27562e6 q^{61} +(2.39831e6 - 853948. i) q^{62} +1.36393e6i q^{63} +(-971384. - 1.85862e6i) q^{64} +1.98210e6i q^{65} +(746447. + 2.09640e6i) q^{66} -630550. q^{67} +(2.34242e6 - 1.91028e6i) q^{68} -6.39469e6i q^{69} +(1.26272e6 + 3.54634e6i) q^{70} -3.25263e6 q^{71} +(-1.13640e6 + 1.87617e6i) q^{72} -4.59002e6 q^{73} +(1.55719e6 + 4.37335e6i) q^{74} +3.55380e6 q^{75} +(-290176. + 3.81589e6i) q^{76} +2.91112e6 q^{77} +(1.23855e6 + 3.47846e6i) q^{78} +2.29205e6 q^{79} +(-1.21779e6 + 5.93026e6i) q^{80} -5.80132e6 q^{81} +(602292. + 1.69154e6i) q^{82} +3.91292e6i q^{83} +(4.43197e6 + 5.43457e6i) q^{84} -8.72557e6 q^{85} +(-1.60919e6 - 4.51942e6i) q^{86} -7.31000e6i q^{87} +(4.00442e6 + 2.42548e6i) q^{88} -7.89968e6i q^{89} +(5.96526e6 - 2.12400e6i) q^{90} +4.83029e6 q^{91} +(-8.50249e6 - 1.04259e7i) q^{92} -1.36905e7 q^{93} +(3.83549e6 + 1.07720e7i) q^{94} +(7.61103e6 - 8.00736e6i) q^{95} +(1.56847e6 + 1.11682e7i) q^{96} -1.92523e6i q^{97} +(-135245. + 48155.7i) q^{98} -4.89677e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 54 q^{4} - 4 q^{5} - 150 q^{6} + 48888 q^{9}+O(q^{10}) \) 68 * q - 54 * q^4 - 4 * q^5 - 150 * q^6 + 48888 * q^9	\( 68 q - 54 q^{4} - 4 q^{5} - 150 q^{6} + 48888 q^{9} + 13050 q^{16} + 23968 q^{17} - 79660 q^{20} - 232154 q^{24} + 937496 q^{25} - 391242 q^{26} - 37666 q^{28} - 468496 q^{30} - 1128652 q^{36} - 530466 q^{38} + 651806 q^{42} + 1433776 q^{44} - 321252 q^{45} - 4014380 q^{49} + 1697586 q^{54} + 137420 q^{57} + 2227894 q^{58} - 3042164 q^{61} + 2261524 q^{62} + 9825150 q^{64} - 749476 q^{66} - 11176962 q^{68} + 598424 q^{73} - 6195964 q^{74} - 1714536 q^{76} - 2556764 q^{77} + 16623216 q^{80} + 43726748 q^{81} - 20460388 q^{82} + 27222844 q^{85} - 61733582 q^{92} + 17778200 q^{93} - 36370886 q^{96}+O(q^{100}) \) 68 * q - 54 * q^4 - 4 * q^5 - 150 * q^6 + 48888 * q^9 + 13050 * q^16 + 23968 * q^17 - 79660 * q^20 - 232154 * q^24 + 937496 * q^25 - 391242 * q^26 - 37666 * q^28 - 468496 * q^30 - 1128652 * q^36 - 530466 * q^38 + 651806 * q^42 + 1433776 * q^44 - 321252 * q^45 - 4014380 * q^49 + 1697586 * q^54 + 137420 * q^57 + 2227894 * q^58 - 3042164 * q^61 + 2261524 * q^62 + 9825150 * q^64 - 749476 * q^66 - 11176962 * q^68 + 598424 * q^73 - 6195964 * q^74 - 1714536 * q^76 - 2556764 * q^77 + 16623216 * q^80 + 43726748 * q^81 - 20460388 * q^82 + 27222844 * q^85 - 61733582 * q^92 + 17778200 * q^93 - 36370886 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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