LMFDB - Embedded newform 84.9.h.e.83.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,9,Mod(83,84)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(84, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("84.83");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	84.h (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:	$34.2198032451$
Analytic rank:	$0$
Dimension:	$120$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			83.7
Character	$\chi$	$=$	84.83
Dual form			84.9.h.e.83.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-15.5666 + 3.69894i) q^{2} +(-6.21954 + 80.7609i) q^{3} +(228.636 - 115.160i) q^{4} -832.715 q^{5} +(-201.913 - 1280.17i) q^{6} +(-1274.55 - 2034.78i) q^{7} +(-3133.10 + 2638.35i) q^{8} +(-6483.63 - 1004.59i) q^{9} +O(q^{10})$	\(q+(-15.5666 + 3.69894i) q^{2} +(-6.21954 + 80.7609i) q^{3} +(228.636 - 115.160i) q^{4} -832.715 q^{5} +(-201.913 - 1280.17i) q^{6} +(-1274.55 - 2034.78i) q^{7} +(-3133.10 + 2638.35i) q^{8} +(-6483.63 - 1004.59i) q^{9} +(12962.5 - 3080.16i) q^{10} -21523.4 q^{11} +(7878.38 + 19181.1i) q^{12} -5471.22i q^{13} +(27366.9 + 26960.0i) q^{14} +(5179.10 - 67250.8i) q^{15} +(39012.6 - 52659.2i) q^{16} +47343.9 q^{17} +(104644. - 8344.56i) q^{18} -40407.1 q^{19} +(-190388. + 95895.1i) q^{20} +(172258. - 90278.4i) q^{21} +(335046. - 79613.8i) q^{22} -344738. q^{23} +(-193589. - 269441. i) q^{24} +302790. q^{25} +(20237.7 + 85168.1i) q^{26} +(121457. - 517376. i) q^{27} +(-525732. - 318446. i) q^{28} -636232. i q^{29} +(168136. + 1.06602e6i) q^{30} -722235. q^{31} +(-412508. + 964027. i) q^{32} +(133866. - 1.73825e6i) q^{33} +(-736982. + 175122. i) q^{34} +(1.06134e6 + 1.69439e6i) q^{35} +(-1.59808e6 + 516967. i) q^{36} -608509. q^{37} +(629000. - 149463. i) q^{38} +(441861. + 34028.5i) q^{39} +(2.60898e6 - 2.19699e6i) q^{40} +3.60092e6 q^{41} +(-2.34752e6 + 2.04250e6i) q^{42} +356105. i q^{43} +(-4.92102e6 + 2.47863e6i) q^{44} +(5.39902e6 + 836538. i) q^{45} +(5.36638e6 - 1.27516e6i) q^{46} +8.67897e6i q^{47} +(4.01016e6 + 3.47820e6i) q^{48} +(-2.51584e6 + 5.18686e6i) q^{49} +(-4.71340e6 + 1.12000e6i) q^{50} +(-294457. + 3.82353e6i) q^{51} +(-630064. - 1.25092e6i) q^{52} +9.75148e6i q^{53} +(23077.5 + 8.50302e6i) q^{54} +1.79229e7 q^{55} +(9.36175e6 + 3.01246e6i) q^{56} +(251314. - 3.26331e6i) q^{57} +(2.35338e6 + 9.90395e6i) q^{58} -1.64808e7i q^{59} +(-6.56045e6 - 1.59724e7i) q^{60} +9.78423e6i q^{61} +(1.12427e7 - 2.67150e6i) q^{62} +(6.21960e6 + 1.44732e7i) q^{63} +(2.85546e6 - 1.65324e7i) q^{64} +4.55597e6i q^{65} +(4.34585e6 + 2.75537e7i) q^{66} -1.94657e7i q^{67} +(1.08245e7 - 5.45210e6i) q^{68} +(2.14411e6 - 2.78413e7i) q^{69} +(-2.27888e7 - 2.24500e7i) q^{70} -3.48589e7 q^{71} +(2.29644e7 - 1.39586e7i) q^{72} +1.79616e7i q^{73} +(9.47239e6 - 2.25084e6i) q^{74} +(-1.88321e6 + 2.44536e7i) q^{75} +(-9.23851e6 + 4.65326e6i) q^{76} +(2.74327e7 + 4.37954e7i) q^{77} +(-7.00412e6 + 1.10471e6i) q^{78} +6.97623e7i q^{79} +(-3.24864e7 + 4.38501e7i) q^{80} +(4.10283e7 + 1.30268e7i) q^{81} +(-5.60539e7 + 1.33196e7i) q^{82} -2.94298e7i q^{83} +(2.89878e7 - 4.04780e7i) q^{84} -3.94240e7 q^{85} +(-1.31721e6 - 5.54333e6i) q^{86} +(5.13827e7 + 3.95707e6i) q^{87} +(6.74351e7 - 5.67863e7i) q^{88} -8.61585e7 q^{89} +(-8.71385e7 + 6.94864e6i) q^{90} +(-1.11327e7 + 6.97335e6i) q^{91} +(-7.88194e7 + 3.96999e7i) q^{92} +(4.49196e6 - 5.83283e7i) q^{93} +(-3.21030e7 - 1.35102e8i) q^{94} +3.36476e7 q^{95} +(-7.52901e7 - 3.93103e7i) q^{96} +3.96417e6i q^{97} +(1.99771e7 - 9.00475e7i) q^{98} +(1.39550e8 + 2.16222e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 1028 q^{4} - 26248 q^{9}+O(q^{10}) $ 120 * q - 1028 * q^4 - 26248 * q^9	$ 120 q - 1028 q^{4} - 26248 q^{9} - 373500 q^{16} - 289340 q^{18} - 620200 q^{21} - 640592 q^{22} + 9327272 q^{25} + 54500 q^{28} - 1299380 q^{30} - 11227168 q^{36} - 8553936 q^{37} - 8996308 q^{42} - 26738344 q^{46} - 13574664 q^{49} - 50788176 q^{57} - 18533288 q^{58} - 24117668 q^{60} - 99498308 q^{64} + 10779752 q^{70} + 76835716 q^{72} - 13132860 q^{78} + 23514872 q^{81} - 171096188 q^{84} - 88829152 q^{85} + 184844592 q^{88} + 626423664 q^{93}+O(q^{100}) $ 120 * q - 1028 * q^4 - 26248 * q^9 - 373500 * q^16 - 289340 * q^18 - 620200 * q^21 - 640592 * q^22 + 9327272 * q^25 + 54500 * q^28 - 1299380 * q^30 - 11227168 * q^36 - 8553936 * q^37 - 8996308 * q^42 - 26738344 * q^46 - 13574664 * q^49 - 50788176 * q^57 - 18533288 * q^58 - 24117668 * q^60 - 99498308 * q^64 + 10779752 * q^70 + 76835716 * q^72 - 13132860 * q^78 + 23514872 * q^81 - 171096188 * q^84 - 88829152 * q^85 + 184844592 * q^88 + 626423664 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−15.5666	+	3.69894i	−0.972910	+	0.231184i
$2$	−15.5666	+	3.69894i	−0.972910	+	0.231184i
$3$	−6.21954	+	80.7609i	−0.0767844	+	0.997048i
$3$	−6.21954	+	80.7609i	−0.0767844	+	0.997048i
$4$	228.636	−	115.160i	0.893108	−	0.449842i
$5$	−832.715			−1.33234			−0.666172	−	0.745798i	$-0.732069\pi$
$5$	−832.715			−1.33234			−0.666172	+	0.745798i	$0.732069\pi$
$6$	−201.913	−	1280.17i	−0.155797	−	0.987789i
$7$	−1274.55	−	2034.78i	−0.530842	−	0.847471i
$7$	−1274.55	−	2034.78i	−0.530842	−	0.847471i
$8$	−3133.10	+	2638.35i	−0.764918	+	0.644128i
$9$	−6483.63	−	1004.59i	−0.988208	−	0.153115i
$10$	12962.5	−	3080.16i	1.29625	−	0.308016i
$11$	−21523.4			−1.47008			−0.735039	−	0.678025i	$-0.762836\pi$
$11$	−21523.4			−1.47008			−0.735039	+	0.678025i	$0.762836\pi$
$12$	7878.38	+	19181.1i	0.379937	+	0.925012i
$13$		−	5471.22i		−	0.191563i	−0.995402	−	0.0957814i	$-0.969465\pi$
$13$		−	5471.22i		−	0.191563i	0.995402	−	0.0957814i	$-0.0305350\pi$
$14$	27366.9	+	26960.0i	0.712383	+	0.701791i
$15$	5179.10	−	67250.8i	0.102303	−	1.32841i
$16$	39012.6	−	52659.2i	0.595284	−	0.803515i
$17$	47343.9			0.566850			0.283425	−	0.958994i	$-0.408529\pi$
$17$	47343.9			0.566850			0.283425	+	0.958994i	$0.408529\pi$
$18$	104644.	−	8344.56i	0.996836	−	0.0794901i
$19$	−40407.1			−0.310058			−0.155029	−	0.987910i	$-0.549547\pi$
$19$	−40407.1			−0.310058			−0.155029	+	0.987910i	$0.549547\pi$
$20$	−190388.	+	95895.1i	−1.18993	+	0.599345i
$21$	172258.	−	90278.4i	0.885729	−	0.464202i
$22$	335046.	−	79613.8i	1.43025	−	0.339858i
$23$	−344738.			−1.23191			−0.615953	−	0.787783i	$-0.711229\pi$
$23$	−344738.			−1.23191			−0.615953	+	0.787783i	$0.711229\pi$
$24$	−193589.	−	269441.i	−0.583493	−	0.812119i
$25$	302790.			0.775143
$26$	20237.7	+	85168.1i	0.0442862	+	0.186373i
$27$	121457.	−	517376.i	0.228542	−	0.973534i
$28$	−525732.	−	318446.i	−0.855327	−	0.518088i
$29$		−	636232.i		−	0.899547i	−0.893143	−	0.449773i	$-0.851505\pi$
$29$		−	636232.i		−	0.899547i	0.893143	−	0.449773i	$-0.148495\pi$
$30$	168136.	+	1.06602e6i	0.207575	+	1.31608i
$31$	−722235.			−0.782045			−0.391022	−	0.920381i	$-0.627878\pi$
$31$	−722235.			−0.782045			−0.391022	+	0.920381i	$0.627878\pi$
$32$	−412508.	+	964027.i	−0.393399	+	0.919368i
$33$	133866.	−	1.73825e6i	0.112879	−	1.46574i
$34$	−736982.	+	175122.i	−0.551494	+	0.131047i
$35$	1.06134e6	+	1.69439e6i	0.707264	+	1.12912i
$36$	−1.59808e6	+	516967.i	−0.951455	+	0.307789i
$37$	−608509.			−0.324683			−0.162342	−	0.986735i	$-0.551905\pi$
$37$	−608509.			−0.324683			−0.162342	+	0.986735i	$0.551905\pi$
$38$	629000.	−	149463.i	0.301659	−	0.0716804i
$39$	441861.	+	34028.5i	0.190997	+	0.0147090i
$40$	2.60898e6	−	2.19699e6i	1.01913	−	0.858200i
$41$	3.60092e6			1.27432			0.637159	−	0.770733i	$-0.280110\pi$
$41$	3.60092e6			1.27432			0.637159	+	0.770733i	$0.280110\pi$
$42$	−2.34752e6	+	2.04250e6i	−0.754419	+	0.656393i
$43$			356105.i			0.104161i	0.998643	+	0.0520804i	$0.0165852\pi$
$43$			356105.i			0.104161i	−0.998643	+	0.0520804i	$0.983415\pi$
$44$	−4.92102e6	+	2.47863e6i	−1.31294	+	0.661303i
$45$	5.39902e6	+	836538.i	1.31663	+	0.204003i
$46$	5.36638e6	−	1.27516e6i	1.19853	−	0.284797i
$47$			8.67897e6i			1.77859i	0.457331	+	0.889297i	$0.348806\pi$
$47$			8.67897e6i			1.77859i	−0.457331	+	0.889297i	$0.651194\pi$
$48$	4.01016e6	+	3.47820e6i	0.755434	+	0.655224i
$49$	−2.51584e6	+	5.18686e6i	−0.436414	+	0.899746i
$50$	−4.71340e6	+	1.12000e6i	−0.754144	+	0.179200i
$51$	−294457.	+	3.82353e6i	−0.0435253	+	0.565177i
$52$	−630064.	−	1.25092e6i	−0.0861730	−	0.171086i
$53$			9.75148e6i			1.23585i	0.786236	+	0.617927i	$0.212027\pi$
$53$			9.75148e6i			1.23585i	−0.786236	+	0.617927i	$0.787973\pi$
$54$	23077.5	+	8.50302e6i	0.00271403	+	0.999996i
$55$	1.79229e7			1.95865
$56$	9.36175e6	+	3.01246e6i	0.951930	+	0.306316i
$57$	251314.	−	3.26331e6i	0.0238076	−	0.309143i
$58$	2.35338e6	+	9.90395e6i	0.207961	+	0.875178i
$59$		−	1.64808e7i		−	1.36010i	−0.733165	−	0.680051i	$-0.761958\pi$
$59$		−	1.64808e7i		−	1.36010i	0.733165	−	0.680051i	$-0.238042\pi$
$60$	−6.56045e6	−	1.59724e7i	−0.506207	−	1.23244i
$61$			9.78423e6i			0.706655i	0.935500	+	0.353327i	$0.114950\pi$
$61$			9.78423e6i			0.706655i	−0.935500	+	0.353327i	$0.885050\pi$
$62$	1.12427e7	−	2.67150e6i	0.760859	−	0.180796i
$63$	6.21960e6	+	1.44732e7i	0.394821	+	0.918758i
$64$	2.85546e6	−	1.65324e7i	0.170198	−	0.985410i
$65$			4.55597e6i			0.255228i
$66$	4.34585e6	+	2.75537e7i	0.229034	+	1.45213i
$67$		−	1.94657e7i		−	0.965987i	−0.875624	−	0.482994i	$-0.839549\pi$
$67$		−	1.94657e7i		−	0.965987i	0.875624	−	0.482994i	$-0.160451\pi$
$68$	1.08245e7	−	5.45210e6i	0.506259	−	0.254993i
$69$	2.14411e6	−	2.78413e7i	0.0945912	−	1.22827i
$70$	−2.27888e7	−	2.24500e7i	−0.949139	−	0.935028i
$71$	−3.48589e7			−1.37177			−0.685884	−	0.727711i	$-0.740584\pi$
$71$	−3.48589e7			−1.37177			−0.685884	+	0.727711i	$0.740584\pi$
$72$	2.29644e7	−	1.39586e7i	0.854524	−	0.519412i
$73$			1.79616e7i			0.632490i	0.948678	+	0.316245i	$0.102422\pi$
$73$			1.79616e7i			0.632490i	−0.948678	+	0.316245i	$0.897578\pi$
$74$	9.47239e6	−	2.25084e6i	0.315888	−	0.0750615i
$75$	−1.88321e6	+	2.44536e7i	−0.0595189	+	0.772854i
$76$	−9.23851e6	+	4.65326e6i	−0.276916	+	0.139477i
$77$	2.74327e7	+	4.37954e7i	0.780379	+	1.24585i
$78$	−7.00412e6	+	1.10471e6i	−0.189224	+	0.0298449i
$79$			6.97623e7i			1.79107i	0.444991	+	0.895535i	$0.353207\pi$
$79$			6.97623e7i			1.79107i	−0.444991	+	0.895535i	$0.646793\pi$
$80$	−3.24864e7	+	4.38501e7i	−0.793124	+	1.07056i
$81$	4.10283e7	+	1.30268e7i	0.953111	+	0.302620i
$82$	−5.60539e7	+	1.33196e7i	−1.23980	+	0.294601i
$83$		−	2.94298e7i		−	0.620119i	−0.950717	−	0.310060i	$-0.899651\pi$
$83$		−	2.94298e7i		−	0.620119i	0.950717	−	0.310060i	$-0.100349\pi$
$84$	2.89878e7	−	4.04780e7i	0.582235	−	0.813021i
$85$	−3.94240e7			−0.755240
$86$	−1.31721e6	−	5.54333e6i	−0.0240803	−	0.101339i
$87$	5.13827e7	+	3.95707e6i	0.896891	+	0.0690711i
$88$	6.74351e7	−	5.67863e7i	1.12449	−	0.946918i
$89$	−8.61585e7			−1.37321			−0.686607	−	0.727029i	$-0.740901\pi$
$89$	−8.61585e7			−1.37321			−0.686607	+	0.727029i	$0.740901\pi$
$90$	−8.71385e7	+	6.94864e6i	−1.32813	+	0.105908i
$91$	−1.11327e7	+	6.97335e6i	−0.162344	+	0.101689i
$92$	−7.88194e7	+	3.96999e7i	−1.10023	+	0.554163i
$93$	4.49196e6	−	5.83283e7i	0.0600488	−	0.779736i
$94$	−3.21030e7	−	1.35102e8i	−0.411182	−	1.73041i
$95$	3.36476e7			0.413105
$96$	−7.52901e7	−	3.93103e7i	−0.886447	−	0.462830i
$97$			3.96417e6i			0.0447781i	0.999749	+	0.0223891i	$0.00712725\pi$
$97$			3.96417e6i			0.0447781i	−0.999749	+	0.0223891i	$0.992873\pi$
$98$	1.99771e7	−	9.00475e7i	0.216585	−	0.976264i
$99$	1.39550e8	+	2.16222e7i	1.45274	+	0.225092i
$100$	6.92286e7	−	3.48692e7i	0.692286	−	0.348692i
$101$	−4.58959e7			−0.441051			−0.220525	−	0.975381i	$-0.570777\pi$
$101$	−4.58959e7			−0.441051			−0.220525	+	0.975381i	$0.570777\pi$
$102$	−9.55934e6	−	6.06085e7i	−0.0883135	−	0.559929i
$103$	1.97474e8			1.75454			0.877268	−	0.480002i	$-0.159364\pi$
$103$	1.97474e8			1.75454			0.877268	+	0.480002i	$0.159364\pi$
$104$	1.44350e7	+	1.71419e7i	0.123391	+	0.146530i
$105$	−1.43442e8	+	7.51763e7i	−1.18010	+	0.618477i
$106$	−3.60701e7	−	1.51797e8i	−0.285709	−	1.20237i
$107$	2.50178e7			0.190860			0.0954298	−	0.995436i	$-0.469577\pi$
$107$	2.50178e7			0.190860			0.0954298	+	0.995436i	$0.469577\pi$
$108$	−3.18114e7	−	1.32277e8i	−0.233823	−	0.972279i
$109$	−3.15623e7			−0.223595			−0.111798	−	0.993731i	$-0.535661\pi$
$109$	−3.15623e7			−0.223595			−0.111798	+	0.993731i	$0.535661\pi$
$110$	−2.78998e8	+	6.62957e7i	−1.90559	+	0.452808i
$111$	3.78464e6	−	4.91437e7i	0.0249306	−	0.323725i
$112$	−1.56873e8	−	1.22651e7i	−0.996958	−	0.0779469i
$113$		−	3.15849e8i		−	1.93716i	−0.248705	−	0.968579i	$-0.580005\pi$
$113$		−	3.15849e8i		−	1.93716i	0.248705	−	0.968579i	$-0.419995\pi$
$114$	8.15871e6	+	5.17282e7i	0.0483061	+	0.306272i
$115$	2.87069e8			1.64132
$116$	−7.32682e7	−	1.45465e8i	−0.404654	−	0.803392i
$117$	−5.49634e6	+	3.54734e7i	−0.0293312	+	0.189304i
$118$	6.09617e7	+	2.56550e8i	0.314433	+	1.32326i
$119$	−6.03422e7	−	9.63343e7i	−0.300908	−	0.480389i
$120$	1.61204e8	+	2.24368e8i	0.777413	+	1.08202i
$121$	2.48898e8			1.16113
$122$	−3.61913e7	−	1.52307e8i	−0.163367	−	0.687512i
$123$	−2.23960e7	+	2.90813e8i	−0.0978477	+	1.27055i
$124$	−1.65129e8	+	8.31722e7i	−0.698450	+	0.351796i
$125$	7.31415e7			0.299588
$126$	−1.50353e8	−	2.02291e8i	−0.596527	−	0.802593i
$127$		−	2.12861e7i		−	0.0818240i	−0.999163	−	0.0409120i	$-0.986974\pi$
$127$		−	2.12861e7i		−	0.0818240i	0.999163	−	0.0409120i	$-0.0130263\pi$
$128$	1.67028e7	+	2.67915e8i	0.0622229	+	0.998062i
$129$	−2.87594e7	−	2.21481e6i	−0.103853	−	0.00799793i
$130$	−1.68523e7	−	7.09208e7i	−0.0590045	−	0.248314i
$131$		−	8.53248e7i		−	0.289728i	−0.989452	−	0.144864i	$-0.953726\pi$
$131$		−	8.53248e7i		−	0.289728i	0.989452	−	0.144864i	$-0.0462744\pi$
$132$	−1.69570e8	−	4.12842e8i	−0.558537	−	1.35984i
$133$	5.15009e7	+	8.22195e7i	0.164592	+	0.262765i
$134$	7.20026e7	+	3.03014e8i	0.223321	+	0.939819i
$135$	−1.01139e8	+	4.30827e8i	−0.304497	+	1.29708i
$136$	−1.48333e8	+	1.24910e8i	−0.433594	+	0.365124i
$137$			1.83312e8i			0.520366i	0.965559	+	0.260183i	$0.0837829\pi$
$137$			1.83312e8i			0.520366i	−0.965559	+	0.260183i	$0.916217\pi$
$138$	6.96070e7	+	4.41325e8i	0.191927	+	1.21686i
$139$	5.58558e8			1.49627			0.748134	−	0.663548i	$-0.230950\pi$
$139$	5.58558e8			1.49627			0.748134	+	0.663548i	$0.230950\pi$
$140$	4.37785e8	+	2.65175e8i	1.13959	+	0.690272i
$141$	−7.00921e8	−	5.39792e7i	−1.77334	−	0.136568i
$142$	5.42633e8	−	1.28941e8i	1.33461	−	0.317130i
$143$			1.17759e8i			0.281612i
$144$	−3.05844e8	+	3.02231e8i	−0.711296	+	0.702893i
$145$			5.29800e8i			1.19851i
$146$	−6.64389e7	−	2.79600e8i	−0.146221	−	0.615356i
$147$	−4.03248e8	−	2.35441e8i	−0.863580	−	0.504212i
$148$	−1.39127e8	+	7.00756e7i	−0.289977	+	0.146056i
$149$		−	4.05038e8i		−	0.821770i	−0.911687	−	0.410885i	$-0.865220\pi$
$149$		−	4.05038e8i		−	0.821770i	0.911687	−	0.410885i	$-0.134780\pi$
$150$	−6.11372e7	−	3.87624e8i	−0.120765	−	0.765677i
$151$			7.97971e7i			0.153490i	0.997051	+	0.0767449i	$0.0244527\pi$
$151$			7.97971e7i			0.153490i	−0.997051	+	0.0767449i	$0.975547\pi$
$152$	1.26600e8	−	1.06608e8i	0.237169	−	0.199717i
$153$	−3.06961e8	−	4.75612e7i	−0.560166	−	0.0867935i
$154$	−5.89029e8	−	5.80271e8i	−1.04726	−	1.03169i
$155$	6.01416e8			1.04195
$156$	1.04944e8	−	4.31044e7i	0.177198	−	0.0727818i
$157$		−	1.00933e9i		−	1.66125i	−0.556829	−	0.830627i	$-0.687982\pi$
$157$		−	1.00933e9i		−	1.66125i	0.556829	−	0.830627i	$-0.312018\pi$
$158$	−2.58047e8	−	1.08596e9i	−0.414066	−	1.74255i
$159$	−7.87538e8	−	6.06497e7i	−1.23221	−	0.0948943i
$160$	3.43502e8	−	8.02760e8i	0.524142	−	1.22492i
$161$	4.39386e8	+	7.01465e8i	0.653947	+	1.04401i
$162$	−6.86855e8	−	5.10211e7i	−0.997252	−	0.0740781i
$163$		−	7.30955e8i		−	1.03548i	−0.855539	−	0.517738i	$-0.826774\pi$
$163$		−	7.30955e8i		−	1.03548i	0.855539	−	0.517738i	$-0.173226\pi$
$164$	8.23298e8	−	4.14680e8i	1.13810	−	0.573241i
$165$	−1.11472e8	+	1.44747e9i	−0.150394	+	1.95287i
$166$	1.08859e8	+	4.58121e8i	0.143361	+	0.603320i
$167$			1.05412e9i			1.35526i	0.735402	+	0.677632i	$0.236994\pi$
$167$			1.05412e9i			1.35526i	−0.735402	+	0.677632i	$0.763006\pi$
$168$	−3.01515e8	+	7.37327e8i	−0.378505	+	0.925599i
$169$	7.85796e8			0.963304
$170$	6.13696e8	−	1.45827e8i	0.734781	−	0.174599i
$171$	2.61985e8	+	4.05926e7i	0.306402	+	0.0474747i
$172$	4.10089e7	+	8.14183e7i	0.0468559	+	0.0930269i
$173$	4.46938e8			0.498957			0.249479	−	0.968380i	$-0.419741\pi$
$173$	4.46938e8			0.498957			0.249479	+	0.968380i	$0.419741\pi$
$174$	−8.14488e8	+	1.28463e8i	−0.888562	+	0.140147i
$175$	−3.85921e8	−	6.16111e8i	−0.411478	−	0.656911i
$176$	−8.39683e8	+	1.13340e9i	−0.875114	+	1.18123i
$177$	1.33101e9	+	1.02503e8i	1.35609	+	0.104435i
$178$	1.34119e9	−	3.18695e8i	1.33601	−	0.317465i
$179$	8.12408e8			0.791338			0.395669	−	0.918393i	$-0.370513\pi$
$179$	8.12408e8			0.791338			0.395669	+	0.918393i	$0.370513\pi$
$180$	1.33074e9	−	4.30487e8i	1.26767	−	0.410081i
$181$			4.69854e8i			0.437773i	0.975750	+	0.218886i	$0.0702424\pi$
$181$			4.69854e8i			0.437773i	−0.975750	+	0.218886i	$0.929758\pi$
$182$	1.47504e8	−	1.49730e8i	0.134437	−	0.136466i
$183$	−7.90183e8	−	6.08534e7i	−0.704569	−	0.0542601i
$184$	1.08010e9	−	9.09539e8i	0.942307	−	0.793505i
$185$	5.06715e8			0.432590
$186$	1.45828e8	+	9.24586e8i	0.121840	+	0.772495i
$187$	−1.01900e9			−0.833314
$188$	9.99466e8	+	1.98432e9i	0.800086	+	1.58848i
$189$	−1.20755e9	+	4.12284e8i	−0.946362	+	0.323109i
$190$	−5.23778e8	+	1.24461e8i	−0.401914	+	0.0955031i
$191$	−1.24092e9			−0.932415			−0.466207	−	0.884675i	$-0.654380\pi$
$191$	−1.24092e9			−0.932415			−0.466207	+	0.884675i	$0.654380\pi$
$192$	1.31741e9	+	3.33433e8i	0.969432	+	0.245360i
$193$	3.50922e8			0.252919			0.126459	−	0.991972i	$-0.459639\pi$
$193$	3.50922e8			0.252919			0.126459	+	0.991972i	$0.459639\pi$
$194$	−1.46632e7	−	6.17085e7i	−0.0103520	−	0.0435651i
$195$	−3.67944e8	−	2.83360e7i	−0.254474	−	0.0195975i
$196$	2.21048e7	+	1.47562e9i	0.0149783	+	0.999888i
$197$		−	2.21755e9i		−	1.47234i	−0.676797	−	0.736169i	$-0.736633\pi$
$197$		−	2.21755e9i		−	1.47234i	0.676797	−	0.736169i	$-0.263367\pi$
$198$	−2.25229e9	+	1.79603e8i	−1.46543	+	0.116857i
$199$	5.92738e8			0.377964			0.188982	−	0.981981i	$-0.439481\pi$
$199$	5.92738e8			0.377964			0.188982	+	0.981981i	$0.439481\pi$
$200$	−9.48673e8	+	7.98866e8i	−0.592920	+	0.499291i
$201$	1.57207e9	+	1.21068e8i	0.963135	+	0.0741728i
$202$	7.14442e8	−	1.69766e8i	0.429103	−	0.101964i
$203$	−1.29459e9	+	8.10910e8i	−0.762340	+	0.477517i
$204$	3.72993e8	+	9.08106e8i	0.215368	+	0.524344i
$205$	−2.99854e9			−1.69783
$206$	−3.07400e9	+	7.30446e8i	−1.70701	+	0.405620i
$207$	2.23515e9	+	3.46320e8i	1.21738	+	0.188624i
$208$	−2.88110e8	−	2.13446e8i	−0.153924	−	0.114034i
$209$	8.69699e8			0.455810
$210$	1.95482e9	−	1.70082e9i	1.00515	−	0.874542i
$211$		−	4.59046e8i		−	0.231594i	−0.993273	−	0.115797i	$-0.963058\pi$
$211$		−	4.59046e8i		−	0.231594i	0.993273	−	0.115797i	$-0.0369421\pi$
$212$	1.12298e9	+	2.22954e9i	0.555939	+	1.10375i
$213$	2.16806e8	−	2.81524e9i	0.105330	−	1.36772i
$214$	−3.89441e8	+	9.25393e7i	−0.185689	+	0.0441236i
$215$		−	2.96534e8i		−	0.138778i
$216$	9.84481e8	+	1.94144e9i	0.452264	+	0.891884i
$217$	9.20525e8	+	1.46959e9i	0.415142	+	0.662760i
$218$	4.91317e8	−	1.16747e8i	0.217538	−	0.0516916i
$219$	−1.45059e9	−	1.11713e8i	−0.630623	−	0.0485654i
$220$	4.09781e9	−	2.06399e9i	1.74929	−	0.881083i
$221$		−	2.59029e8i		−	0.108587i
$222$	1.22866e8	+	7.78997e8i	0.0505846	+	0.320719i
$223$	−3.58169e9			−1.44833			−0.724167	−	0.689625i	$-0.757775\pi$
$223$	−3.58169e9			−1.44833			−0.724167	+	0.689625i	$0.757775\pi$
$224$	2.48734e9	−	3.89339e8i	0.987970	−	0.154645i
$225$	−1.96318e9	−	3.04180e8i	−0.766002	−	0.118686i
$226$	1.16830e9	+	4.91668e9i	0.447840	+	1.88468i
$227$		−	4.66119e9i		−	1.75547i	−0.479147	−	0.877735i	$-0.659054\pi$
$227$		−	4.66119e9i		−	1.75547i	0.479147	−	0.877735i	$-0.340946\pi$
$228$	−3.18342e8	−	7.75051e8i	−0.117803	−	0.286808i
$229$			1.97646e9i			0.718696i	0.933204	+	0.359348i	$0.117001\pi$
$229$			1.97646e9i			0.718696i	−0.933204	+	0.359348i	$0.882999\pi$
$230$	−4.46867e9	+	1.06185e9i	−1.59686	+	0.379447i
$231$	−3.70757e9	+	1.94310e9i	−1.30209	+	0.682413i
$232$	1.67860e9	+	1.99338e9i	0.579423	+	0.688079i
$233$		−	2.54034e9i		−	0.861922i	−0.902371	−	0.430961i	$-0.858175\pi$
$233$		−	2.54034e9i		−	0.861922i	0.902371	−	0.430961i	$-0.141825\pi$
$234$	−4.56549e7	−	5.72530e8i	−0.0152273	−	0.190957i
$235$		−	7.22711e9i		−	2.36970i
$236$	−1.89793e9	−	3.76811e9i	−0.611831	−	1.21472i
$237$	−5.63407e9	−	4.33889e8i	−1.78578	−	0.137526i
$238$	1.29566e9	+	1.27639e9i	0.403814	+	0.397811i
$239$	2.64828e9			0.811658			0.405829	−	0.913949i	$-0.366983\pi$
$239$	2.64828e9			0.811658			0.405829	+	0.913949i	$0.366983\pi$
$240$	−3.33932e9	−	2.89635e9i	−1.00650	−	0.872985i
$241$		−	1.61164e8i		−	0.0477750i	−0.999715	−	0.0238875i	$-0.992396\pi$
$241$		−	1.61164e8i		−	0.0477750i	0.999715	−	0.0238875i	$-0.00760435\pi$
$242$	−3.87449e9	+	9.20660e8i	−1.12967	+	0.268434i
$243$	−1.30723e9	+	3.23246e9i	−0.374911	+	0.927061i
$244$	1.12675e9	+	2.23702e9i	0.317883	+	0.631119i
$245$	2.09498e9	−	4.31918e9i	0.581454	−	1.19877i
$246$	−7.27071e8	−	4.60980e9i	−0.198535	−	1.25876i
$247$			2.21076e8i			0.0593956i
$248$	2.26284e9	−	1.90551e9i	0.598200	−	0.503737i
$249$	2.37678e9	+	1.83040e8i	0.618288	+	0.0476155i
$250$	−1.13856e9	+	2.70546e8i	−0.291472	+	0.0692598i
$251$			4.99267e9i			1.25788i	0.777456	+	0.628938i	$0.216510\pi$
$251$			4.99267e9i			1.25788i	−0.777456	+	0.628938i	$0.783490\pi$
$252$	3.08875e9	+	2.59283e9i	0.765914	+	0.642943i
$253$	7.41994e9			1.81100
$254$	7.87359e7	+	3.31351e8i	0.0189164	+	0.0796074i
$255$	2.45199e8	−	3.18392e9i	0.0579907	−	0.753010i
$256$	−1.25101e9	−	4.10874e9i	−0.291273	−	0.956640i
$257$	−6.97349e9			−1.59852			−0.799260	−	0.600986i	$-0.794775\pi$
$257$	−6.97349e9			−1.59852			−0.799260	+	0.600986i	$0.794775\pi$
$258$	4.55877e8	−	7.19022e7i	0.102889	−	0.0162279i
$259$	7.75575e8	+	1.23818e9i	0.172355	+	0.275160i
$260$	5.24664e8	+	1.04166e9i	0.114812	+	0.227946i
$261$	−6.39153e8	+	4.12510e9i	−0.137734	+	0.888939i
$262$	3.15611e8	+	1.32821e9i	0.0669804	+	0.281879i
$263$	7.74654e9			1.61914			0.809570	−	0.587023i	$-0.199700\pi$
$263$	7.74654e9			1.61914			0.809570	+	0.587023i	$0.199700\pi$
$264$	4.16669e9	+	5.79930e9i	0.857780	+	1.19388i
$265$		−	8.12021e9i		−	1.64658i
$266$	−1.10582e9	−	1.08938e9i	−0.220880	−	0.217596i
$267$	5.35866e8	−	6.95823e9i	0.105441	−	1.36916i
$268$	−2.24166e9	−	4.45056e9i	−0.434542	−	0.862731i
$269$	2.81721e9			0.538035			0.269017	−	0.963135i	$-0.413301\pi$
$269$	2.81721e9			0.538035			0.269017	+	0.963135i	$0.413301\pi$
$270$	−1.92170e7	−	7.08060e9i	−0.00361602	−	1.33234i
$271$	−1.86840e9			−0.346412			−0.173206	−	0.984886i	$-0.555413\pi$
$271$	−1.86840e9			−0.346412			−0.173206	+	0.984886i	$0.555413\pi$
$272$	1.84701e9	−	2.49309e9i	0.337437	−	0.455473i
$273$	−4.93934e8	−	9.42459e8i	−0.0889238	−	0.169673i
$274$	−6.78060e8	−	2.85354e9i	−0.120300	−	0.506269i
$275$	−6.51708e9			−1.13952
$276$	−2.71598e9	−	6.61244e9i	−0.468047	−	1.13953i
$277$	−3.96381e9			−0.673276			−0.336638	−	0.941634i	$-0.609290\pi$
$277$	−3.96381e9			−0.673276			−0.336638	+	0.941634i	$0.609290\pi$
$278$	−8.69483e9	+	2.06607e9i	−1.45573	+	0.345913i
$279$	4.68271e9	+	7.25550e8i	0.772823	+	0.119743i
$280$	−7.79568e9	−	2.50852e9i	−1.26830	−	0.408118i
$281$			9.56712e9i			1.53446i	0.641371	+	0.767231i	$0.278366\pi$
$281$			9.56712e9i			1.53446i	−0.641371	+	0.767231i	$0.721634\pi$
$282$	1.11106e10	−	1.75239e9i	1.75688	−	0.277099i
$283$	−7.33520e9			−1.14358			−0.571790	−	0.820400i	$-0.693751\pi$
$283$	−7.33520e9			−1.14358			−0.571790	+	0.820400i	$0.693751\pi$
$284$	−7.96999e9	+	4.01434e9i	−1.22514	+	0.617079i
$285$	−2.09273e8	+	2.71741e9i	−0.0317200	+	0.411885i
$286$	−4.35585e8	−	1.83311e9i	−0.0651042	−	0.273983i
$287$	−4.58955e9	−	7.32706e9i	−0.676461	−	1.07995i
$288$	3.64301e9	−	5.83600e9i	0.529529	−	0.848292i
$289$	−4.73431e9			−0.678681
$290$	−1.95970e9	−	8.24717e9i	−0.277075	−	1.16604i
$291$	−3.20150e8	−	2.46553e7i	−0.0446459	−	0.00343826i
$292$	2.06845e9	+	4.10666e9i	0.284521	+	0.564882i
$293$	6.39313e8			0.0867447			0.0433724	−	0.999059i	$-0.486190\pi$
$293$	6.39313e8			0.0867447			0.0433724	+	0.999059i	$0.486190\pi$
$294$	7.14806e9	+	2.17342e9i	0.956751	+	0.290908i
$295$			1.37239e10i			1.81212i
$296$	1.90652e9	−	1.60546e9i	0.248356	−	0.209138i
$297$	−2.61416e9	+	1.11357e10i	−0.335975	+	1.43117i
$298$	1.49821e9	+	6.30504e9i	0.189980	+	0.799508i
$299$			1.88614e9i			0.235987i
$300$	2.38549e9	+	5.80783e9i	0.294505	+	0.717016i
$301$	7.24595e8	−	4.53874e8i	0.0882733	−	0.0552929i
$302$	−2.95165e8	−	1.24217e9i	−0.0354843	−	0.149332i
$303$	2.85452e8	−	3.70660e9i	0.0338658	−	0.439749i
$304$	−1.57638e9	+	2.12780e9i	−0.184573	+	0.249137i
$305$		−	8.14748e9i		−	0.941508i
$306$	4.95425e9	−	3.95064e8i	0.565057	−	0.0450590i
$307$	1.09245e10			1.22984			0.614920	−	0.788589i	$-0.289188\pi$
$307$	1.09245e10			1.22984			0.614920	+	0.788589i	$0.289188\pi$
$308$	1.13155e10	+	6.85405e9i	1.25740	+	0.761630i
$309$	−1.22820e9	+	1.59482e10i	−0.134721	+	1.74936i
$310$	−9.36198e9	+	2.22460e9i	−1.01373	+	0.240883i
$311$			6.67172e9i			0.713175i	0.934262	+	0.356588i	$0.116060\pi$
$311$			6.67172e9i			0.713175i	−0.934262	+	0.356588i	$0.883940\pi$
$312$	−1.47417e9	+	1.05917e9i	−0.155572	+	0.111775i
$313$		−	3.31702e9i		−	0.345597i	−0.984957	−	0.172799i	$-0.944719\pi$
$313$		−	3.31702e9i		−	0.345597i	0.984957	−	0.172799i	$-0.0552810\pi$
$314$	3.73346e9	+	1.57119e10i	0.384055	+	1.61625i
$315$	−5.17916e9	−	1.20520e10i	−0.526038	−	1.22410i
$316$	8.03380e9	+	1.59502e10i	0.805699	+	1.59962i
$317$		−	9.64683e9i		−	0.955317i	−0.878546	−	0.477659i	$-0.841486\pi$
$317$		−	9.64683e9i		−	0.955317i	0.878546	−	0.477659i	$-0.158514\pi$
$318$	1.24836e10	−	1.96895e9i	1.22076	−	0.192542i
$319$			1.36939e10i			1.32240i
$320$	−2.37778e9	+	1.37668e10i	−0.226763	+	1.31291i
$321$	−1.55599e8	+	2.02046e9i	−0.0146550	+	0.190296i
$322$	−9.43441e9	−	9.29414e9i	−0.877589	−	0.864541i
$323$	−1.91303e9			−0.175757
$324$	1.08807e10	−	1.74641e9i	0.987363	−	0.158477i
$325$		−	1.65663e9i		−	0.148488i
$326$	2.70376e9	+	1.13785e10i	0.239385	+	1.00743i
$327$	1.96303e8	−	2.54900e9i	0.0171686	−	0.222935i
$328$	−1.12820e10	+	9.50047e9i	−0.974748	+	0.820823i
$329$	1.76598e10	−	1.10618e10i	1.50731	−	0.944151i
$330$	−3.61886e9	−	2.29444e10i	−0.305152	−	1.93473i
$331$			6.76015e9i			0.563176i	0.959535	+	0.281588i	$0.0908611\pi$
$331$			6.76015e9i			0.563176i	−0.959535	+	0.281588i	$0.909139\pi$
$332$	−3.38912e9	−	6.72870e9i	−0.278956	−	0.553833i
$333$	3.94535e9	+	6.11302e8i	0.320855	+	0.0497140i
$334$	−3.89912e9	−	1.64090e10i	−0.313315	−	1.31855i
$335$			1.62094e10i			1.28703i
$336$	1.96622e9	−	1.25929e10i	0.154268	−	0.988029i
$337$	−6.35536e9			−0.492743			−0.246372	−	0.969175i	$-0.579238\pi$
$337$	−6.35536e9			−0.492743			−0.246372	+	0.969175i	$0.579238\pi$
$338$	−1.22321e10	+	2.90661e9i	−0.937208	+	0.222700i
$339$	2.55082e10	+	1.96443e9i	1.93144	+	0.148744i
$340$	−9.01373e9	+	4.54005e9i	−0.674511	+	0.339739i
$341$	1.55450e10			1.14967
$342$	−4.22835e9	+	3.37179e8i	−0.309077	+	0.0246466i
$343$	1.37607e10	−	1.49173e9i	0.994175	−	0.107774i
$344$	−9.39529e8	−	1.11571e9i	−0.0670929	−	0.0796745i
$345$	−1.78543e9	+	2.31839e10i	−0.126028	+	1.63648i
$346$	−6.95729e9	+	1.65320e9i	−0.485440	+	0.115351i
$347$	1.87277e10			1.29172			0.645858	−	0.763458i	$-0.276500\pi$
$347$	1.87277e10			1.29172			0.645858	+	0.763458i	$0.276500\pi$
$348$	1.22036e10	−	5.01248e9i	0.832092	−	0.341771i
$349$			1.56501e10i			1.05491i	0.849584	+	0.527454i	$0.176853\pi$
$349$			1.56501e10i			1.05491i	−0.849584	+	0.527454i	$0.823147\pi$
$350$	8.28642e9	+	8.16322e9i	0.552198	+	0.543988i
$351$	−2.83068e9	−	6.64517e8i	−0.186493	−	0.0437802i
$352$	8.87859e9	−	2.07492e10i	0.578327	−	1.35154i
$353$	1.76719e10			1.13811			0.569054	−	0.822300i	$-0.307310\pi$
$353$	1.76719e10			1.13811			0.569054	+	0.822300i	$0.307310\pi$
$354$	−2.10984e10	+	3.32769e9i	−1.34349	+	0.211900i
$355$	2.90276e10			1.82767
$356$	−1.96989e10	+	9.92197e9i	−1.22643	+	0.617729i
$357$	8.15534e9	−	4.27413e9i	0.502076	−	0.263133i
$358$	−1.26464e10	+	3.00505e9i	−0.769901	+	0.182945i
$359$	−9.36438e9			−0.563769			−0.281885	−	0.959448i	$-0.590960\pi$
$359$	−9.36438e9			−0.563769			−0.281885	+	0.959448i	$0.590960\pi$
$360$	−1.91228e10	+	1.16235e10i	−1.13852	+	0.692036i
$361$	−1.53508e10			−0.903864
$362$	−1.73796e9	−	7.31401e9i	−0.101206	−	0.425913i
$363$	−1.54803e9	+	2.01013e10i	−0.0891566	+	1.15770i
$364$	−1.74229e9	+	2.87640e9i	−0.0992464	+	0.163849i
$365$		−	1.49569e10i		−	0.842695i
$366$	1.25255e10	−	1.97556e9i	0.698026	−	0.110095i
$367$	−2.50460e10			−1.38062			−0.690310	−	0.723514i	$-0.742526\pi$
$367$	−2.50460e10			−1.38062			−0.690310	+	0.723514i	$0.742526\pi$
$368$	−1.34491e10	+	1.81536e10i	−0.733335	+	0.989856i
$369$	−2.33470e10	−	3.61744e9i	−1.25929	−	0.195118i
$370$	−7.88780e9	+	1.87431e9i	−0.420871	+	0.100008i
$371$	1.98421e10	−	1.24288e10i	1.04735	−	0.656043i
$372$	−5.69004e9	−	1.38532e10i	−0.297128	−	0.723401i
$373$	2.85841e10			1.47669			0.738346	−	0.674423i	$-0.235607\pi$
$373$	2.85841e10			1.47669			0.738346	+	0.674423i	$0.235607\pi$
$374$	1.58624e10	−	3.76923e9i	0.810740	−	0.192649i
$375$	−4.54906e8	+	5.90697e9i	−0.0230037	+	0.298703i
$376$	−2.28981e10	−	2.71921e10i	−1.14564	−	1.36048i
$377$	−3.48097e9			−0.172320
$378$	1.72724e10	−	1.08845e10i	0.846027	−	0.533140i
$379$			9.55511e8i			0.0463104i	0.999732	+	0.0231552i	$0.00737120\pi$
$379$			9.55511e8i			0.0463104i	−0.999732	+	0.0231552i	$0.992629\pi$
$380$	7.69305e9	−	3.87485e9i	0.368947	−	0.185832i
$381$	1.71908e9	+	1.32389e8i	0.0815824	+	0.00628280i
$382$	1.93168e10	−	4.59008e9i	0.907156	−	0.215559i
$383$			1.74316e10i			0.810105i	0.914293	+	0.405052i	$0.132747\pi$
$383$			1.74316e10i			0.810105i	−0.914293	+	0.405052i	$0.867253\pi$
$384$	−2.17410e10	−	3.17373e8i	−0.999893	−	0.0145964i
$385$	−2.28436e10	−	3.64691e10i	−1.03973	−	1.65990i
$386$	−5.46265e9	+	1.29804e9i	−0.246067	+	0.0584707i
$387$	3.57740e8	−	2.30886e9i	0.0159486	−	0.102933i
$388$	4.56512e8	+	9.06351e8i	0.0201431	+	0.0399917i
$389$		−	1.99435e10i		−	0.870968i	−0.900196	−	0.435484i	$-0.856577\pi$
$389$		−	1.99435e10i		−	0.870968i	0.900196	−	0.435484i	$-0.143423\pi$
$390$	5.83244e9	−	9.19909e8i	0.252111	−	0.0397637i
$391$	−1.63212e10			−0.698307
$392$	−5.80234e9	−	2.28886e10i	−0.245730	−	0.969338i
$393$	6.89091e9	+	5.30681e8i	0.288872	+	0.0222466i
$394$	8.20257e9	+	3.45196e10i	0.340381	+	1.43245i
$395$		−	5.80922e10i		−	2.38632i
$396$	3.43961e10	−	1.11269e10i	1.39871	−	0.452474i
$397$			3.72310e10i			1.49880i	0.662119	+	0.749399i	$0.269657\pi$
$397$			3.72310e10i			1.49880i	−0.662119	+	0.749399i	$0.730343\pi$
$398$	−9.22690e9	+	2.19250e9i	−0.367725	+	0.0873792i
$399$	−6.96043e9	+	3.64789e9i	−0.274628	+	0.143930i
$400$	1.18126e10	−	1.59447e10i	0.461430	−	0.622839i
$401$		−	2.99431e10i		−	1.15803i	−0.815318	−	0.579013i	$-0.803438\pi$
$401$		−	2.99431e10i		−	1.15803i	0.815318	−	0.579013i	$-0.196562\pi$
$402$	−2.49195e10	+	3.93038e9i	−0.954192	+	0.150498i
$403$			3.95151e9i			0.149811i
$404$	−1.04935e10	+	5.28536e9i	−0.393906	+	0.198403i
$405$	−3.41649e10	−	1.08476e10i	−1.26987	−	0.403194i
$406$	1.71528e10	−	1.74117e10i	0.631294	−	0.640821i
$407$	1.30972e10			0.477310
$408$	−9.16525e9	−	1.27564e10i	−0.330753	−	0.460350i
$409$			2.59409e10i			0.927027i	0.886090	+	0.463513i	$0.153411\pi$
$409$			2.59409e10i			0.927027i	−0.886090	+	0.463513i	$0.846589\pi$
$410$	4.66769e10	−	1.10914e10i	1.65184	−	0.392511i
$411$	−1.48044e10	−	1.14012e9i	−0.518830	−	0.0399560i
$412$	4.51497e10	−	2.27411e10i	1.56699	−	0.789264i
$413$	−3.35349e10	+	2.10057e10i	−1.15265	+	0.721999i
$414$	−3.60747e10	+	2.87669e9i	−1.22801	+	0.0979244i
$415$			2.45067e10i			0.826212i
$416$	5.27441e9	+	2.25692e9i	0.176117	+	0.0753605i
$417$	−3.47397e9	+	4.51097e10i	−0.114890	+	1.49185i
$418$	−1.35382e10	+	3.21696e9i	−0.443462	+	0.105376i
$419$			4.07500e10i			1.32212i	0.750332	+	0.661061i	$0.229893\pi$
$419$			4.07500e10i			1.32212i	−0.750332	+	0.661061i	$0.770107\pi$
$420$	−2.41386e10	+	3.37066e10i	−0.775737	+	1.08322i
$421$	−3.73286e10			−1.18827			−0.594133	−	0.804367i	$-0.702505\pi$
$421$	−3.73286e10			−1.18827			−0.594133	+	0.804367i	$0.702505\pi$
$422$	1.69798e9	+	7.14577e9i	0.0535407	+	0.225320i
$423$	8.71881e9	−	5.62713e10i	0.272330	−	1.75762i
$424$	−2.57278e10	−	3.05524e10i	−0.796048	−	0.945327i
$425$	1.43353e10			0.439390
$426$	7.03846e9	+	4.46255e10i	0.213717	+	1.35502i
$427$	1.99087e10	−	1.24705e10i	0.598869	−	0.375122i
$428$	5.71996e9	−	2.88104e9i	0.170458	−	0.0858566i
$429$	−9.51035e9	−	7.32409e8i	−0.280781	−	0.0216234i
$430$	1.09686e9	+	4.61602e9i	0.0320832	+	0.135019i
$431$	−5.08358e10			−1.47320			−0.736598	−	0.676331i	$-0.763569\pi$
$431$	−5.08358e10			−1.47320			−0.736598	+	0.676331i	$0.763569\pi$
$432$	−2.25062e10	−	2.65800e10i	−0.646202	−	0.763167i
$433$		−	1.37944e10i		−	0.392420i	−0.980562	−	0.196210i	$-0.937137\pi$
$433$		−	1.37944e10i		−	0.392420i	0.980562	−	0.196210i	$-0.0628635\pi$
$434$	−1.97653e10	−	1.94715e10i	−0.557115	−	0.548832i
$435$	−4.27871e10	−	3.29511e9i	−1.19497	−	0.0920266i
$436$	−7.21627e9	+	3.63470e9i	−0.199695	+	0.100583i
$437$	1.39299e10			0.381963
$438$	2.29940e10	−	3.62668e9i	0.624767	−	0.0985400i
$439$	2.78711e10			0.750407			0.375203	−	0.926943i	$-0.377573\pi$
$439$	2.78711e10			0.750407			0.375203	+	0.926943i	$0.377573\pi$
$440$	−5.61542e10	+	4.72868e10i	−1.49821	+	1.26162i
$441$	2.15225e10	−	3.11023e10i	0.569033	−	0.822315i
$442$	9.58133e8	+	4.03219e9i	0.0251036	+	0.105646i
$443$	2.17717e10			0.565298			0.282649	−	0.959223i	$-0.408787\pi$
$443$	2.17717e10			0.565298			0.282649	+	0.959223i	$0.408787\pi$
$444$	−4.79406e9	−	1.16718e10i	−0.123359	−	0.300336i
$445$	7.17455e10			1.82959
$446$	5.57546e10	−	1.32485e10i	1.40910	−	0.334831i
$447$	3.27112e10	+	2.51915e9i	0.819344	+	0.0630991i
$448$	−3.72793e10	+	1.52612e10i	−0.925455	+	0.378858i
$449$		−	8.21673e9i		−	0.202169i	−0.994878	−	0.101084i	$-0.967769\pi$
$449$		−	8.21673e9i		−	0.202169i	0.994878	−	0.101084i	$-0.0322312\pi$
$450$	3.16851e10	−	2.52665e9i	0.772690	−	0.0616162i
$451$	−7.75040e10			−1.87335
$452$	−3.63730e10	−	7.22143e10i	−0.871415	−	1.73009i
$453$	−6.44449e9	−	4.96301e8i	−0.153037	−	0.0117856i
$454$	1.72415e10	+	7.25587e10i	0.405836	+	1.70791i
$455$	9.27039e9	−	5.80682e9i	0.216298	−	0.135485i
$456$	7.82236e9	+	1.08874e10i	0.180917	+	0.251804i
$457$	1.45452e10			0.333468			0.166734	−	0.986002i	$-0.446678\pi$
$457$	1.45452e10			0.333468			0.166734	+	0.986002i	$0.446678\pi$
$458$	−7.31079e9	−	3.07666e10i	−0.166151	−	0.699226i
$459$	5.75024e9	−	2.44946e10i	0.129549	−	0.551848i
$460$	6.56341e10	−	3.30587e10i	1.46588	−	0.738337i
$461$	−8.33762e10			−1.84603			−0.923015	−	0.384765i	$-0.874283\pi$
$461$	−8.33762e10			−1.84603			−0.923015	+	0.384765i	$0.874283\pi$
$462$	5.05267e10	−	4.39615e10i	1.10906	−	0.964949i
$463$		−	4.32089e10i		−	0.940262i	−0.882597	−	0.470131i	$-0.844207\pi$
$463$		−	4.32089e10i		−	0.940262i	0.882597	−	0.470131i	$-0.155793\pi$
$464$	−3.35035e10	−	2.48210e10i	−0.722799	−	0.535486i
$465$	−3.74053e9	+	4.85709e10i	−0.0800057	+	1.03888i
$466$	9.39656e9	+	3.95443e10i	0.199262	+	0.838572i
$467$			6.39557e9i			0.134466i	0.997737	+	0.0672328i	$0.0214170\pi$
$467$			6.39557e9i			0.134466i	−0.997737	+	0.0672328i	$0.978583\pi$
$468$	2.82844e9	+	8.74344e9i	0.0589609	+	0.182263i
$469$	−3.96084e10	+	2.48101e10i	−0.818646	+	0.512786i
$470$	2.67326e10	+	1.12501e11i	0.547836	+	2.30550i
$471$	8.15147e10	+	6.27759e9i	1.65635	+	0.127558i
$472$	4.34822e10	+	5.16362e10i	0.876080	+	1.04037i
$473$		−	7.66460e9i		−	0.153125i
$474$	8.93080e10	−	1.40859e10i	1.76920	−	0.279043i
$475$	−1.22349e10			−0.240339
$476$	−2.48902e10	−	1.50765e10i	−0.484842	−	0.293679i
$477$	9.79624e9	−	6.32250e10i	0.189228	−	1.22128i
$478$	−4.12247e10	+	9.79584e9i	−0.789670	+	0.187642i
$479$			3.89446e10i			0.739785i	0.929075	+	0.369892i	$0.120605\pi$
$479$			3.89446e10i			0.739785i	−0.929075	+	0.369892i	$0.879395\pi$
$480$	6.26952e10	+	3.27343e10i	1.18105	+	0.616649i
$481$			3.32929e9i			0.0621972i
$482$	5.96137e8	+	2.50877e9i	0.0110448	+	0.0464808i
$483$	−5.93837e10	+	3.11224e10i	−1.09114	+	0.571853i
$484$	5.69071e10	−	2.86630e10i	1.03701	−	0.522325i
$485$		−	3.30103e9i		−	0.0596599i
$486$	8.39243e9	−	5.51537e10i	0.150433	−	0.988620i
$487$		−	5.76291e10i		−	1.02453i	−0.858827	−	0.512266i	$-0.828806\pi$
$487$		−	5.76291e10i		−	1.02453i	0.858827	−	0.512266i	$-0.171194\pi$
$488$	−2.58142e10	−	3.06550e10i	−0.455176	−	0.540533i
$489$	5.90326e10	+	4.54620e9i	1.03242	+	0.0795085i
$490$	−1.66353e10	+	7.49839e10i	−0.288566	+	1.30072i
$491$	7.63273e10			1.31327			0.656635	−	0.754209i	$-0.271979\pi$
$491$	7.63273e10			1.31327			0.656635	+	0.754209i	$0.271979\pi$
$492$	2.83694e10	+	6.90694e10i	0.484160	+	1.17876i
$493$		−	3.01217e10i		−	0.509908i
$494$	−8.17748e8	−	3.44140e9i	−0.0137313	−	0.0577866i
$495$	−1.16205e11	−	1.80052e10i	−1.93556	−	0.299900i
$496$	−2.81762e10	+	3.80323e10i	−0.465539	+	0.628385i
$497$	4.44295e10	+	7.09302e10i	0.728191	+	1.16253i
$498$	−3.76753e10	+	5.94225e9i	−0.612547	+	0.0966126i
$499$		−	5.67945e10i		−	0.916019i	−0.888947	−	0.458009i	$-0.848563\pi$
$499$		−	5.67945e10i		−	0.916019i	0.888947	−	0.458009i	$-0.151437\pi$
$500$	1.67228e10	−	8.42294e9i	0.267564	−	0.134767i
$501$	−8.51315e10	−	6.55613e9i	−1.35126	−	0.104063i
$502$	−1.84676e10	−	7.77187e10i	−0.290800	−	1.22380i
$503$			1.38011e10i			0.215597i	0.994173	+	0.107798i	$0.0343801\pi$
$503$			1.38011e10i			0.215597i	−0.994173	+	0.107798i	$0.965620\pi$
$504$	−5.76719e10	−	2.89364e10i	−0.893803	−	0.448459i
$505$	3.82183e10			0.587632
$506$	−1.15503e11	+	2.74459e10i	−1.76194	+	0.418673i
$507$	−4.88729e9	+	6.34616e10i	−0.0739667	+	0.960460i
$508$	−2.45129e9	−	4.86675e9i	−0.0368079	−	0.0730776i
$509$	3.84988e10			0.573557			0.286778	−	0.957997i	$-0.407416\pi$
$509$	3.84988e10			0.573557			0.286778	+	0.957997i	$0.407416\pi$
$510$	7.96021e9	+	5.04696e10i	0.117664	+	0.746018i
$511$	3.65479e10	−	2.28930e10i	0.536017	−	0.335752i
$512$	3.46719e10	+	5.93315e10i	0.504542	+	0.863387i
$513$	−4.90772e9	+	2.09057e10i	−0.0708615	+	0.301852i
$514$	1.08553e11	−	2.57945e10i	1.55522	−	0.369552i
$515$	−1.64440e11			−2.33765
$516$	−6.83047e9	+	2.80553e9i	−0.0963500	+	0.0395746i
$517$		−	1.86801e11i		−	2.61467i
$518$	−1.66530e10	−	1.64054e10i	−0.231299	−	0.227860i
$519$	−2.77975e9	+	3.60951e10i	−0.0383121	+	0.497484i
$520$	−1.20202e10	−	1.42743e10i	−0.164399	−	0.195228i
$521$	6.06110e10			0.822623			0.411311	−	0.911495i	$-0.365071\pi$
$521$	6.06110e10			0.822623			0.411311	+	0.911495i	$0.365071\pi$
$522$	−5.30908e9	−	6.65778e10i	−0.0715051	−	0.896700i
$523$	−6.98690e10			−0.933851			−0.466925	−	0.884297i	$-0.654638\pi$
$523$	−6.98690e10			−0.933851			−0.466925	+	0.884297i	$0.654638\pi$
$524$	−9.82597e9	−	1.95083e10i	−0.130332	−	0.258758i
$525$	5.21579e10	−	2.73354e10i	0.686567	−	0.359823i
$526$	−1.20587e11	+	2.86540e10i	−1.57528	+	0.374319i
$527$	−3.41934e10			−0.443302
$528$	−8.63123e10	−	7.48628e10i	−1.11055	−	0.963231i
$529$	4.05333e10			0.517594
$530$	3.00362e10	+	1.26404e11i	0.380663	+	1.60198i
$531$	−1.65565e10	+	1.06856e11i	−0.208253	+	1.34406i
$532$	2.12433e10	+	1.28675e10i	0.265201	+	0.160638i
$533$		−	1.97014e10i		−	0.244112i
$534$	1.73965e10	+	1.10298e11i	0.213942	+	1.35645i
$535$	−2.08327e10			−0.254291
$536$	5.13574e10	+	6.09881e10i	0.622219	+	0.738901i
$537$	−5.05280e9	+	6.56108e10i	−0.0607624	+	0.789002i
$538$	−4.38543e10	+	1.04207e10i	−0.523460	+	0.124385i
$539$	5.41495e10	−	1.11639e11i	0.641563	−	1.32270i
$540$	2.64899e10	+	1.10150e11i	0.311533	+	1.29541i
$541$	−4.55917e10			−0.532227			−0.266114	−	0.963942i	$-0.585740\pi$
$541$	−4.55917e10			−0.532227			−0.266114	+	0.963942i	$0.585740\pi$
$542$	2.90846e10	−	6.91110e9i	0.337028	−	0.0800848i
$543$	−3.79458e10	−	2.92227e9i	−0.436480	−	0.0336141i
$544$	−1.95298e10	+	4.56408e10i	−0.222998	+	0.521144i
$545$	2.62824e10			0.297906
$546$	1.11749e10	+	1.28438e10i	0.125740	+	0.144519i
$547$		−	5.48441e10i		−	0.612605i	−0.951934	−	0.306303i	$-0.900908\pi$
$547$		−	5.48441e10i		−	0.612605i	0.951934	−	0.306303i	$-0.0990920\pi$
$548$	2.11101e10	+	4.19117e10i	0.234082	+	0.464743i
$549$	9.82914e9	−	6.34374e10i	0.108200	−	0.698322i
$550$	1.01448e11	−	2.41063e10i	1.10865	−	0.263439i
$551$			2.57083e10i			0.278912i
$552$	6.67374e10	+	9.28867e10i	0.718808	+	1.00045i
$553$	1.41951e11	−	8.89156e10i	1.51788	−	0.950775i
$554$	6.17028e10	−	1.46619e10i	0.655037	−	0.155651i
$555$	−3.15153e9	+	4.09227e10i	−0.0332162	+	0.431313i
$556$	1.27706e11	−	6.43233e10i	1.33633	−	0.673084i
$557$			6.51327e10i			0.676672i	0.941025	+	0.338336i	$0.109864\pi$
$557$			6.51327e10i			0.676672i	−0.941025	+	0.338336i	$0.890136\pi$
$558$	−7.55774e10	+	6.02673e9i	−0.779570	+	0.0621648i
$559$	1.94833e9			0.0199533
$560$	1.30631e11	+	1.02133e10i	1.32829	+	0.103852i
$561$	6.33772e9	−	8.22955e10i	0.0639855	−	0.830854i
$562$	−3.53882e10	−	1.48927e11i	−0.354743	−	1.49289i
$563$		−	4.06657e10i		−	0.404757i	−0.979307	−	0.202379i	$-0.935133\pi$
$563$		−	4.06657e10i		−	0.404757i	0.979307	−	0.202379i	$-0.0648672\pi$
$564$	−1.66472e11	+	6.83762e10i	−1.64522	+	0.675754i
$565$			2.63012e11i			2.58096i
$566$	1.14184e11	−	2.71325e10i	1.11260	−	0.264377i
$567$	−2.57860e10	−	1.00087e11i	−0.249490	−	0.968377i
$568$	1.09217e11	−	9.19700e10i	1.04929	−	0.883594i
$569$			5.29330e10i			0.504984i	0.967599	+	0.252492i	$0.0812501\pi$
$569$			5.29330e10i			0.504984i	−0.967599	+	0.252492i	$0.918750\pi$
$570$	−6.79389e9	−	4.30748e10i	−0.0643604	−	0.408060i
$571$			1.47872e11i			1.39104i	0.718505	+	0.695522i	$0.244827\pi$
$571$			1.47872e11i			1.39104i	−0.718505	+	0.695522i	$0.755173\pi$
$572$	1.35611e10	+	2.69240e10i	0.126681	+	0.251510i
$573$	7.71793e9	−	1.00218e11i	0.0715949	−	0.929662i
$574$	9.85459e10	+	9.70807e10i	0.907801	+	0.894304i
$575$	−1.04383e11			−0.954903
$576$	−3.51221e10	+	1.04322e11i	−0.319073	+	0.947730i
$577$			8.90098e10i			0.803035i	0.915851	+	0.401518i	$0.131517\pi$
$577$			8.90098e10i			0.803035i	−0.915851	+	0.401518i	$0.868483\pi$
$578$	7.36970e10	−	1.75119e10i	0.660295	−	0.156900i
$579$	−2.18257e9	+	2.83408e10i	−0.0194202	+	0.252172i
$580$	6.10116e10	+	1.21131e11i	0.539138	+	1.07040i
$581$	−5.98831e10	+	3.75098e10i	−0.525533	+	0.329185i
$582$	5.07483e9	−	8.00417e8i	0.0442313	−	0.00697629i
$583$		−	2.09885e11i		−	1.81680i
$584$	−4.73890e10	−	5.62756e10i	−0.407404	−	0.483803i
$585$	4.57689e9	−	2.95393e10i	0.0390793	−	0.252218i
$586$	−9.95190e9	+	2.36478e9i	−0.0843948	+	0.0200540i
$587$		−	3.70494e10i		−	0.312053i	−0.987753	−	0.156027i	$-0.950131\pi$
$587$		−	3.70494e10i		−	0.312053i	0.987753	−	0.156027i	$-0.0498685\pi$
$588$	−1.19310e11	−	7.39249e9i	−0.998086	−	0.0618417i
$589$	2.91834e10			0.242479
$590$	−5.07637e10	−	2.13633e11i	−0.418934	−	1.76303i
$591$	1.79091e11	+	1.37921e10i	1.46799	+	0.113053i
$592$	−2.37395e10	+	3.20436e10i	−0.193279	+	0.260888i
$593$	−5.33990e10			−0.431832			−0.215916	−	0.976412i	$-0.569274\pi$
$593$	−5.33990e10			−0.431832			−0.215916	+	0.976412i	$0.569274\pi$
$594$	−4.96707e8	−	1.83014e11i	−0.00398983	−	1.47007i
$595$	5.02479e10	+	8.02191e10i	0.400913	+	0.640044i
$596$	−4.66440e10	−	9.26061e10i	−0.369667	−	0.733930i
$597$	−3.68656e9	+	4.78700e10i	−0.0290218	+	0.376848i
$598$	−6.97671e9	−	2.93607e10i	−0.0545564	−	0.229595i
$599$	8.25610e10			0.641309			0.320655	−	0.947196i	$-0.396097\pi$
$599$	8.25610e10			0.641309			0.320655	+	0.947196i	$0.396097\pi$
$600$	−5.86168e10	−	8.15842e10i	−0.452290	−	0.629508i
$601$			2.03611e10i			0.156064i	0.996951	+	0.0780322i	$0.0248637\pi$
$601$			2.03611e10i			0.156064i	−0.996951	+	0.0780322i	$0.975136\pi$
$602$	−9.60060e9	+	9.74549e9i	−0.0730991	+	0.0742024i
$603$	−1.95551e10	+	1.26209e11i	−0.147908	+	0.954597i
$604$	9.18940e9	+	1.82445e10i	0.0690462	+	0.137083i
$605$	−2.07262e11			−1.54702
$606$	9.26698e9	+	5.87548e10i	0.0687144	+	0.435665i
$607$	9.85859e10			0.726206			0.363103	−	0.931749i	$-0.381717\pi$
$607$	9.85859e10			0.726206			0.363103	+	0.931749i	$0.381717\pi$
$608$	1.66683e10	−	3.89536e10i	0.121976	−	0.285058i
$609$	−5.74381e10	−	1.09596e11i	−0.417571	−	0.796755i
$610$	3.01370e10	+	1.26828e11i	0.217661	+	0.916002i
$611$	4.74846e10			0.340712
$612$	−7.56593e10	+	2.44752e10i	−0.539332	+	0.174470i
$613$	−1.45318e11			−1.02915			−0.514575	−	0.857445i	$-0.672050\pi$
$613$	−1.45318e11			−1.02915			−0.514575	+	0.857445i	$0.672050\pi$
$614$	−1.70057e11	+	4.04091e10i	−1.19652	+	0.284319i
$615$	1.86495e10	−	2.42165e11i	0.130367	−	1.69282i
$616$	−2.01497e11	−	6.48384e10i	−1.39941	−	0.450308i
$617$			1.79664e11i			1.23971i	0.784717	+	0.619854i	$0.212808\pi$
$617$			1.79664e11i			1.23971i	−0.784717	+	0.619854i	$0.787192\pi$
$618$	−3.98726e10	−	2.52802e11i	−0.273351	−	1.73311i
$619$	1.06225e11			0.723545			0.361772	−	0.932266i	$-0.382172\pi$
$619$	1.06225e11			0.723545			0.361772	+	0.932266i	$0.382172\pi$
$620$	1.37505e11	−	6.92588e10i	0.930577	−	0.468714i
$621$	−4.18708e10	+	1.78359e11i	−0.281543	+	1.19930i
$622$	−2.46783e10	−	1.03856e11i	−0.164875	−	0.693856i
$623$	1.09813e11	+	1.75313e11i	0.728959	+	1.16376i
$624$	1.90300e10	−	2.19405e10i	0.125517	−	0.144713i
$625$	−1.79183e11			−1.17430
$626$	1.22694e10	+	5.16345e10i	0.0798965	+	0.336235i
$627$	−5.40912e9	+	7.02376e10i	−0.0349991	+	0.454464i
$628$	−1.16234e11	−	2.30770e11i	−0.747302	−	1.48368i
$629$	−2.88092e10			−0.184047
$630$	1.25201e11	+	1.68451e11i	0.794780	+	1.06933i
$631$			1.17969e11i			0.744133i	0.928206	+	0.372067i	$0.121351\pi$
$631$			1.17969e11i			0.744133i	−0.928206	+	0.372067i	$0.878649\pi$
$632$	−1.84057e11	−	2.18573e11i	−1.15368	−	1.37002i
$633$	3.70730e10	+	2.85506e9i	0.230910	+	0.0177828i
$634$	3.56830e10	+	1.50168e11i	0.220854	+	0.929438i
$635$			1.77252e10i			0.109018i
$636$	−1.87044e11	+	7.68258e10i	−1.14318	+	0.469547i
$637$	2.83784e10	+	1.37647e10i	0.172358	+	0.0836007i
$638$	−5.06529e10	−	2.13167e11i	−0.305718	−	1.28658i
$639$	2.26012e11	+	3.50189e10i	1.35559	+	0.210039i
$640$	−1.39087e10	−	2.23097e11i	−0.0829024	−	1.32976i
$641$			3.85284e10i			0.228217i	0.993468	+	0.114109i	$0.0364012\pi$
$641$			3.85284e10i			0.228217i	−0.993468	+	0.114109i	$0.963599\pi$
$642$	−5.05141e9	−	3.20271e10i	−0.0297353	−	0.188529i
$643$	1.63615e11			0.957151			0.478575	−	0.878046i	$-0.341153\pi$
$643$	1.63615e11			0.957151			0.478575	+	0.878046i	$0.341153\pi$
$644$	1.81240e11	+	1.09780e11i	1.05368	+	0.638236i
$645$	2.39484e10	+	1.84431e9i	0.138368	+	0.0106560i
$646$	2.97793e10	−	7.07618e9i	0.170995	−	0.0406321i
$647$			6.10413e10i			0.348343i	0.984715	+	0.174171i	$0.0557247\pi$
$647$			6.10413e10i			0.348343i	−0.984715	+	0.174171i	$0.944275\pi$
$648$	−1.62915e11	+	6.74327e10i	−0.923978	+	0.382446i
$649$			3.54724e11i			1.99946i
$650$	6.12778e9	+	2.57881e10i	0.0343281	+	0.144466i
$651$	−1.24410e11	+	6.52022e10i	−0.692680	+	0.363027i
$652$	−8.41765e10	−	1.67122e11i	−0.465801	−	0.924793i
$653$		−	2.38679e11i		−	1.31269i	−0.754462	−	0.656344i	$-0.772102\pi$
$653$		−	2.38679e11i		−	1.31269i	0.754462	−	0.656344i	$-0.227898\pi$
$654$	6.37283e9	+	4.04053e10i	0.0348355	+	0.220865i
$655$			7.10513e10i			0.386017i
$656$	1.40481e11	−	1.89621e11i	0.758581	−	1.02393i
$657$	1.80441e10	−	1.16456e11i	0.0968440	−	0.625032i
$658$	−2.33985e11	+	2.37516e11i	−1.24820	+	1.26704i
$659$	3.13540e10			0.166246			0.0831231	−	0.996539i	$-0.473511\pi$
$659$	3.13540e10			0.166246			0.0831231	+	0.996539i	$0.473511\pi$
$660$	1.41203e11	+	3.43780e11i	0.744164	+	1.81178i
$661$		−	2.94027e11i		−	1.54021i	−0.637915	−	0.770107i	$-0.720203\pi$
$661$		−	2.94027e11i		−	1.54021i	0.637915	−	0.770107i	$-0.279797\pi$
$662$	−2.50054e10	−	1.05232e11i	−0.130197	−	0.547920i
$663$	2.09194e10	+	1.61104e9i	0.108267	+	0.00833782i
$664$	7.76461e10	+	9.22066e10i	0.399436	+	0.474340i
$665$	−4.28856e10	−	6.84655e10i	−0.219293	−	0.350094i
$666$	−6.36767e10	+	5.07774e9i	−0.323656	+	0.0258091i
$667$			2.19333e11i			1.10816i
$668$	1.21392e11	+	2.41009e11i	0.609654	+	1.21040i
$669$	2.22765e10	−	2.89260e11i	0.111209	−	1.44406i
$670$	−5.99576e10	−	2.52325e11i	−0.297540	−	1.25216i
$671$		−	2.10590e11i		−	1.03884i
$672$	1.59732e10	+	2.03302e11i	0.0783277	+	0.996928i
$673$	5.02950e9			0.0245168			0.0122584	−	0.999925i	$-0.496098\pi$
$673$	5.02950e9			0.0245168			0.0122584	+	0.999925i	$0.496098\pi$
$674$	9.89312e10	−	2.35081e10i	0.479395	−	0.113914i
$675$	3.67759e10	−	1.56656e11i	0.177153	−	0.754628i
$676$	1.79661e11	−	9.04920e10i	0.860334	−	0.433334i
$677$	−2.65705e11			−1.26487			−0.632434	−	0.774614i	$-0.717944\pi$
$677$	−2.65705e11			−1.26487			−0.632434	+	0.774614i	$0.717944\pi$
$678$	−4.04341e11	+	6.37739e10i	−1.91350	+	0.301803i
$679$	8.06621e9	−	5.05254e9i	0.0379481	−	0.0237701i
$680$	1.23519e11	−	1.04014e11i	0.577697	−	0.486471i
$681$	3.76442e11	+	2.89904e10i	1.75029	+	0.134793i
$682$	−2.41981e11	+	5.74998e10i	−1.11852	+	0.265784i
$683$	1.19864e11			0.550815			0.275407	−	0.961328i	$-0.411187\pi$
$683$	1.19864e11			0.550815			0.275407	+	0.961328i	$0.411187\pi$
$684$	6.45737e10	−	2.08892e10i	0.295006	−	0.0954325i
$685$		−	1.52647e11i		−	0.693307i
$686$	−2.08688e11	+	7.41210e10i	−0.942328	+	0.334692i
$687$	−1.59620e11	−	1.22926e10i	−0.716574	−	0.0551846i
$688$	1.87522e10	+	1.38926e10i	0.0836948	+	0.0620053i
$689$	5.33525e10			0.236744
$690$	−5.79628e10	−	3.67498e11i	−0.255713	−	1.62128i
$691$	−2.63859e11			−1.15734			−0.578669	−	0.815563i	$-0.696428\pi$
$691$	−2.63859e11			−1.15734			−0.578669	+	0.815563i	$0.696428\pi$
$692$	1.02186e11	−	5.14692e10i	0.445623	−	0.224452i
$693$	−1.33867e11	−	3.11512e11i	−0.580418	−	1.35065i
$694$	−2.91526e11	+	6.92727e10i	−1.25672	+	0.298624i
$695$	−4.65120e11			−1.99355
$696$	−1.71427e11	+	1.23167e11i	−0.730538	+	0.524879i
$697$	1.70481e11			0.722347
$698$	−5.78887e10	−	2.43618e11i	−0.243878	−	1.02633i
$699$	2.05160e11	+	1.57997e10i	0.859377	+	0.0661822i
$700$	−1.59186e11	−	9.64223e10i	−0.663000	−	0.401592i
$701$			3.15034e11i			1.30462i	0.757951	+	0.652312i	$0.226201\pi$
$701$			3.15034e11i			1.30462i	−0.757951	+	0.652312i	$0.773799\pi$
$702$	4.65219e10	−	1.26262e8i	0.191562	−	0.000519907i
$703$	2.45881e10			0.100671
$704$	−6.14592e10	+	3.55834e11i	−0.250205	+	1.44863i
$705$	5.83668e11	+	4.49493e10i	2.36270	+	0.181956i
$706$	−2.75090e11	+	6.53671e10i	−1.10728	+	0.263112i
$707$	5.84967e10	+	9.33880e10i	0.234128	+	0.373778i
$708$	3.16120e11	−	1.29842e11i	1.25811	−	0.516753i
$709$	−2.42824e11			−0.960962			−0.480481	−	0.877005i	$-0.659538\pi$
$709$	−2.42824e11			−0.960962			−0.480481	+	0.877005i	$0.659538\pi$
$710$	−4.51859e11	+	1.07371e11i	−1.77816	+	0.422527i
$711$	7.00826e10	−	4.52313e11i	0.274240	−	1.76995i
$712$	2.69943e11	−	2.27316e11i	1.05040	−	0.884525i
$713$	2.48982e11			0.963406
$714$	−1.11141e11	+	9.66997e10i	−0.427643	+	0.372077i
$715$		−	9.80601e10i		−	0.375205i
$716$	1.85745e11	−	9.35565e10i	0.706751	−	0.355977i
$717$	−1.64711e10	+	2.13878e11i	−0.0623227	+	0.809261i
$718$	1.45771e11	−	3.46383e10i	0.548497	−	0.130334i
$719$		−	2.59119e11i		−	0.969580i	−0.874631	−	0.484790i	$-0.838896\pi$
$719$		−	2.59119e11i		−	0.969580i	0.874631	−	0.484790i	$-0.161104\pi$
$720$	2.54681e11	−	2.51673e11i	0.947691	−	0.936496i
$721$	−2.51691e11	−	4.01817e11i	−0.931380	−	1.48692i
$722$	2.38960e11	−	5.67818e10i	0.879378	−	0.208959i
$723$	1.30158e10	+	1.00237e9i	0.0476339	+	0.00366837i
$724$	5.41082e10	+	1.07425e11i	0.196928	+	0.390978i
$725$		−	1.92645e11i		−	0.697277i
$726$	−5.02558e10	−	3.18633e11i	−0.180900	−	1.14695i
$727$	2.28566e11			0.818226			0.409113	−	0.912484i	$-0.365838\pi$
$727$	2.28566e11			0.818226			0.409113	+	0.912484i	$0.365838\pi$
$728$	1.64818e10	−	5.12202e10i	0.0586787	−	0.182354i
$729$	−2.52926e11	−	1.25678e11i	−0.895537	−	0.444988i
$730$	5.53247e10	+	2.32828e11i	0.194817	+	0.819866i
$731$			1.68594e10i			0.0590436i
$732$	−1.87672e11	+	7.70838e10i	−0.653664	+	0.268484i
$733$			4.29467e11i			1.48770i	0.668349	+	0.743848i	$0.267001\pi$
$733$			4.29467e11i			1.48770i	−0.668349	+	0.743848i	$0.732999\pi$
$734$	3.89880e11	−	9.26437e10i	1.34322	−	0.319177i
$735$	3.35791e11	+	1.96056e11i	1.15059	+	0.671785i
$736$	1.42207e11	−	3.32337e11i	0.484630	−	1.13258i
$737$			4.18969e11i			1.42008i
$738$	3.76814e11	−	3.00480e10i	1.27028	−	0.101296i
$739$			1.65192e11i			0.553873i	0.960888	+	0.276937i	$0.0893192\pi$
$739$			1.65192e11i			0.553873i	−0.960888	+	0.276937i	$0.910681\pi$
$740$	1.15853e11	−	5.83530e10i	0.386350	−	0.194597i
$741$	−1.78543e10	−	1.37499e9i	−0.0592203	−	0.00456066i
$742$	−2.62900e11	+	2.66868e11i	−0.867311	+	0.880401i
$743$	4.22331e11			1.38579			0.692895	−	0.721038i	$-0.256335\pi$
$743$	4.22331e11			1.38579			0.692895	+	0.721038i	$0.256335\pi$
$744$	1.39817e11	+	1.94600e11i	0.456317	+	0.635113i
$745$			3.37281e11i			1.09488i
$746$	−4.44957e11	+	1.05731e11i	−1.43669	+	0.341387i
$747$	−2.95649e10	+	1.90812e11i	−0.0949498	+	0.612807i
$748$	−2.32980e11	+	1.17348e11i	−0.744240	+	0.374860i
$749$	−3.18864e10	−	5.09056e10i	−0.101316	−	0.161748i
$750$	−1.47682e10	−	9.36339e10i	−0.0466748	−	0.295929i
$751$			4.01114e11i			1.26098i	0.776197	+	0.630490i	$0.217146\pi$
$751$			4.01114e11i			1.26098i	−0.776197	+	0.630490i	$0.782854\pi$
$752$	4.57027e11	+	3.38589e11i	1.42913	+	1.05877i
$753$	−4.03212e11	−	3.10521e10i	−1.25416	−	0.0965852i
$754$	5.41867e10	−	1.28759e10i	0.167651	−	0.0398375i
$755$		−	6.64483e10i		−	0.204501i
$756$	−2.28610e11	+	2.33324e11i	−0.699855	+	0.714285i
$757$	5.06472e10			0.154231			0.0771156	−	0.997022i	$-0.475429\pi$
$757$	5.06472e10			0.154231			0.0771156	+	0.997022i	$0.475429\pi$
$758$	−3.53438e9	−	1.48740e10i	−0.0107062	−	0.0450559i
$759$	−4.61486e10	+	5.99241e11i	−0.139056	+	1.80565i
$760$	−1.05421e11	+	8.87742e10i	−0.315991	+	0.266092i
$761$	4.69072e11			1.39862			0.699312	−	0.714816i	$-0.253490\pi$
$761$	4.69072e11			1.39862			0.699312	+	0.714816i	$0.253490\pi$
$762$	−2.72499e10	+	4.29793e9i	−0.0808248	+	0.0127479i
$763$	4.02278e10	+	6.42223e10i	0.118694	+	0.189491i
$764$	−2.83718e11	+	1.42903e11i	−0.832747	+	0.419439i
$765$	2.55611e11	+	3.96050e10i	0.746335	+	0.115639i
$766$	−6.44783e10	−	2.71350e11i	−0.187283	−	0.788159i
$767$	−9.01704e10			−0.260545
$768$	3.39606e11	−	7.54781e10i	0.976181	−	0.216958i
$769$		−	6.42328e11i		−	1.83676i	−0.395703	−	0.918379i	$-0.629499\pi$
$769$		−	6.42328e11i		−	1.83676i	0.395703	−	0.918379i	$-0.370501\pi$
$770$	4.90494e11	+	4.83201e11i	1.39531	+	1.37456i
$771$	4.33719e10	−	5.63185e11i	0.122741	−	1.59380i
$772$	8.02333e10	−	4.04120e10i	0.225884	−	0.113774i
$773$	−4.16910e11			−1.16768			−0.583841	−	0.811868i	$-0.698451\pi$
$773$	−4.16910e11			−1.16768			−0.583841	+	0.811868i	$0.698451\pi$
$774$	2.97154e9	+	3.72642e10i	0.00827976	+	0.103831i
$775$	−2.18685e11			−0.606196
$776$	−1.04589e10	−	1.24202e10i	−0.0288428	−	0.0342516i
$777$	−1.04820e11	+	5.49352e10i	−0.287581	+	0.150719i
$778$	7.37697e10	+	3.10451e11i	0.201354	+	0.847374i
$779$	−1.45503e11			−0.395113
$780$	−8.73884e10	+	3.58937e10i	−0.236089	+	0.0969705i
$781$	7.50283e11			2.01661
$782$	2.54066e11	−	6.03713e10i	0.679390	−	0.161437i
$783$	−3.29171e11	−	7.72747e10i	−0.875739	−	0.205585i
$784$	1.74986e11	+	3.34835e11i	0.463169	+	0.886270i
$785$			8.40488e11i			2.21336i
$786$	−1.09231e11	+	1.72282e10i	−0.286190	+	0.0451387i
$787$	−1.69568e11			−0.442022			−0.221011	−	0.975271i	$-0.570936\pi$
$787$	−1.69568e11			−0.442022			−0.221011	+	0.975271i	$0.570936\pi$
$788$	−2.55372e11	−	5.07010e11i	−0.662320	−	1.31496i
$789$	−4.81799e10	+	6.25617e11i	−0.124325	+	1.61436i
$790$	2.14879e11	+	9.04295e11i	0.551679	+	2.32168i
$791$	−6.42682e11	+	4.02565e11i	−1.64169	+	1.02832i
$792$	−4.94271e11	+	3.00437e11i	−1.25622	+	0.763576i
$793$	5.35317e10			0.135369
$794$	−1.37715e11	−	5.79559e11i	−0.346498	−	1.45820i
$795$	6.55795e11	+	5.05039e10i	1.64172	+	0.126432i
$796$	1.35521e11	−	6.82595e10i	0.337563	−	0.170024i
$797$	−1.02744e11			−0.254638			−0.127319	−	0.991862i	$-0.540637\pi$
$797$	−1.02744e11			−0.254638			−0.127319	+	0.991862i	$0.540637\pi$
$798$	9.48566e10	−	8.25313e10i	0.233914	−	0.203520i
$799$			4.10896e11i			1.00820i
$800$	−1.24903e11	+	2.91898e11i	−0.304940	+	0.712641i
$801$	5.58620e11	+	8.65540e10i	1.35702	+	0.210260i
$802$	1.10758e11	+	4.66110e11i	0.267717	+	1.12666i
$803$		−	3.86595e11i		−	0.929810i
$804$	3.73373e11	−	1.53358e11i	0.893550	−	0.367014i
$805$	−3.65884e11	−	5.84121e11i	−0.871283	−	1.39097i
$806$	−1.46164e10	−	6.15114e10i	−0.0346338	−	0.145752i
$807$	−1.75218e10	+	2.27520e11i	−0.0413127	+	0.536446i
$808$	1.43797e11	−	1.21089e11i	0.337368	−	0.284093i
$809$			4.57004e11i			1.06690i	0.845830	+	0.533452i	$0.179106\pi$
$809$			4.57004e11i			1.06690i	−0.845830	+	0.533452i	$0.820894\pi$
$810$	5.71955e11	+	4.24861e10i	1.32868	+	0.0986976i
$811$	−3.99179e11			−0.922751			−0.461375	−	0.887205i	$-0.652644\pi$
$811$	−3.99179e11			−0.922751			−0.461375	+	0.887205i	$0.652644\pi$
$812$	−2.02606e11	+	3.34488e11i	−0.466045	+	0.769406i
$813$	1.16206e10	−	1.50894e11i	0.0265990	−	0.345389i
$814$	−2.03878e11	+	4.84457e10i	−0.464379	+	0.110346i
$815$			6.08678e11i			1.37961i
$816$	1.89857e11	+	1.64672e11i	0.428218	+	0.371414i
$817$		−	1.43892e10i		−	0.0322959i
$818$	−9.59539e10	−	4.03811e11i	−0.214314	−	0.901914i
$819$	7.91859e10	−	3.40288e10i	0.176000	−	0.0756330i
$820$	−6.85573e11	+	3.45310e11i	−1.51635	+	0.763755i
$821$		−	1.96111e11i		−	0.431648i	−0.976432	−	0.215824i	$-0.930756\pi$
$821$		−	1.96111e11i		−	0.431648i	0.976432	−	0.215824i	$-0.0692437\pi$
$822$	2.34672e11	−	3.70131e10i	0.514012	−	0.0810714i
$823$		−	3.85386e11i		−	0.840032i	−0.907517	−	0.420016i	$-0.862024\pi$
$823$		−	3.85386e11i		−	0.840032i	0.907517	−	0.420016i	$-0.137976\pi$
$824$	−6.18708e11	+	5.21006e11i	−1.34208	+	1.13015i
$825$	4.05332e10	−	5.26325e11i	0.0874974	−	1.13616i
$826$	4.44324e11	−	4.51030e11i	0.954507	−	0.968913i
$827$	−3.47492e11			−0.742886			−0.371443	−	0.928456i	$-0.621137\pi$
$827$	−3.47492e11			−0.742886			−0.371443	+	0.928456i	$0.621137\pi$
$828$	5.50918e11	−	1.78218e11i	1.17210	−	0.379167i
$829$			7.10193e11i			1.50369i	0.659340	+	0.751845i	$0.270836\pi$
$829$			7.10193e11i			1.50369i	−0.659340	+	0.751845i	$0.729164\pi$
$830$	−9.06487e10	−	3.81484e11i	−0.191007	−	0.803830i
$831$	2.46530e10	−	3.20120e11i	0.0516971	−	0.671289i
$832$	−9.04526e10	−	1.56228e10i	−0.188768	−	0.0326037i
$833$	−1.19110e11	+	2.45566e11i	−0.247382	+	0.510021i
$834$	−1.12780e11	−	7.15052e11i	−0.233114	−	1.47800i
$835$		−	8.77781e11i		−	1.80568i
$836$	1.98844e11	−	1.00154e11i	0.407088	−	0.205042i
$837$	−8.77203e10	+	3.73667e11i	−0.178730	+	0.761347i
$838$	−1.50732e11	−	6.34337e11i	−0.305653	−	1.28631i
$839$		−	7.87654e11i		−	1.58960i	−0.606871	−	0.794800i	$-0.707576\pi$
$839$		−	7.87654e11i		−	1.58960i	0.606871	−	0.794800i	$-0.292424\pi$
$840$	2.51076e11	−	6.13984e11i	0.504299	−	1.23322i
$841$	9.54551e10			0.190816
$842$	5.81078e11	−	1.38076e11i	1.15608	−	0.274708i
$843$	−7.72649e11	−	5.95031e10i	−1.52993	−	0.117823i
$844$	−5.28636e10	−	1.04954e11i	−0.104181	−	0.206838i
$845$	−6.54345e11			−1.28345
$846$	7.24221e10	+	9.08200e11i	0.141381	+	1.77297i
$847$	−3.17234e11	−	5.06453e11i	−0.616376	−	0.984024i
$848$	5.13505e11	+	3.80430e11i	0.993027	+	0.735684i
$849$	4.56216e10	−	5.92397e11i	0.0878091	−	1.14020i
$850$	−2.23151e11	+	5.30253e10i	−0.427487	+	0.101580i
$851$	2.09776e11			0.399979
$852$	−2.74632e11	−	6.68631e11i	−0.521185	−	1.26890i
$853$		−	5.66334e11i		−	1.06974i	−0.844936	−	0.534868i	$-0.820361\pi$
$853$		−	5.66334e11i		−	1.06974i	0.844936	−	0.534868i	$-0.179639\pi$
$854$	−2.63783e11	+	2.67764e11i	−0.495924	+	0.503409i
$855$	−2.18159e11	−	3.38021e10i	−0.408233	−	0.0632527i
$856$	−7.83833e10	+	6.60056e10i	−0.145992	+	0.122938i
$857$	1.31191e10			0.0243210			0.0121605	−	0.999926i	$-0.496129\pi$
$857$	1.31191e10			0.0243210			0.0121605	+	0.999926i	$0.496129\pi$
$858$	1.50753e11	−	2.37771e10i	0.278173	−	0.0438743i
$859$	−5.29121e10			−0.0971812			−0.0485906	−	0.998819i	$-0.515473\pi$
$859$	−5.29121e10			−0.0971812			−0.0485906	+	0.998819i	$0.515473\pi$
$860$	−3.41488e10	−	6.77983e10i	−0.0624282	−	0.123944i
$861$	6.20285e11	−	3.25085e11i	1.12870	−	0.591540i
$862$	7.91338e11	−	1.88038e11i	1.43329	−	0.340579i
$863$	8.03730e10			0.144900			0.0724498	−	0.997372i	$-0.476918\pi$
$863$	8.03730e10			0.144900			0.0724498	+	0.997372i	$0.476918\pi$
$864$	4.48663e11	+	3.30509e11i	0.805128	+	0.593101i
$865$	−3.72173e11			−0.664783
$866$	5.10247e10	+	2.14732e11i	0.0907212	+	0.381790i
$867$	2.94452e10	−	3.82347e11i	0.0521121	−	0.676677i
$868$	3.79702e11	+	2.29993e11i	0.668904	+	0.405168i
$869$		−	1.50152e12i		−	2.63301i
$870$	6.78237e11	−	1.06973e11i	1.18387	−	0.186724i
$871$	−1.06501e11			−0.185047
$872$	9.88880e10	−	8.32723e10i	0.171032	−	0.144024i
$873$	3.98237e9	−	2.57022e10i	0.00685622	−	0.0442501i
$874$	−2.16840e11	+	5.15257e10i	−0.371616	+	0.0883036i
$875$	−9.32225e10	−	1.48827e11i	−0.159034	−	0.253892i
$876$	−3.44522e11	+	1.41508e11i	−0.585061	+	0.240306i
$877$	2.83488e11			0.479221			0.239611	−	0.970869i	$-0.422980\pi$
$877$	2.83488e11			0.479221			0.239611	+	0.970869i	$0.422980\pi$
$878$	−4.33858e11	+	1.03094e11i	−0.730078	+	0.173482i
$879$	−3.97623e9	+	5.16315e10i	−0.00666064	+	0.0864886i
$880$	6.99217e11	−	9.43804e11i	1.16595	−	1.57381i
$881$	4.31008e11			0.715454			0.357727	−	0.933826i	$-0.383552\pi$
$881$	4.31008e11			0.715454			0.357727	+	0.933826i	$0.383552\pi$
$882$	−2.19985e11	+	5.63766e11i	−0.363512	+	0.931589i
$883$		−	4.79070e11i		−	0.788055i	−0.919099	−	0.394027i	$-0.871081\pi$
$883$		−	4.79070e11i		−	0.788055i	0.919099	−	0.394027i	$-0.128919\pi$
$884$	−2.98297e10	−	5.92233e10i	−0.0488472	−	0.0969803i
$885$	−1.10835e12	−	8.53560e10i	−1.80677	−	0.139143i
$886$	−3.38911e11	+	8.05323e10i	−0.549985	+	0.130688i
$887$			2.60766e11i			0.421266i	0.977565	+	0.210633i	$0.0675525\pi$
$887$			2.60766e11i			0.421266i	−0.977565	+	0.210633i	$0.932447\pi$
$888$	1.17800e11	+	1.63957e11i	0.189450	+	0.263681i
$889$	−4.33124e10	+	2.71302e10i	−0.0693434	+	0.0434356i
$890$	−1.11683e12	+	2.65382e11i	−1.78003	+	0.422972i
$891$	−8.83069e11	−	2.80381e11i	−1.40115	−	0.444875i
$892$	−8.18902e11	+	4.12466e11i	−1.29352	+	0.651521i
$893$		−	3.50692e11i		−	0.551468i
$894$	−5.18519e11	+	8.17823e10i	−0.811736	+	0.128029i
$895$	−6.76505e11			−1.05434
$896$	5.23860e11	−	3.75458e11i	0.812798	−	0.582545i
$897$	−1.52326e11	−	1.17309e10i	−0.235291	−	0.0181202i
$898$	3.03932e10	+	1.27906e11i	0.0467381	+	0.196692i
$899$			4.59509e11i			0.703485i
$900$	−4.83882e11	+	1.56533e11i	−0.737513	+	0.238580i
$901$			4.61673e11i			0.700544i
$902$	1.20647e12	−	2.86683e11i	1.82260	−	0.433087i
$903$	3.21486e10	+	6.13418e10i	0.0483517	+	0.0922583i
$904$	8.33318e11	+	9.89586e11i	1.24778	+	1.48177i
$905$		−	3.91255e11i		−	0.583264i
$906$	1.02154e11	−	1.61121e10i	0.151616	−	0.0239132i
$907$			3.67039e11i			0.542354i	0.962530	+	0.271177i	$0.0874128\pi$
$907$			3.67039e11i			0.542354i	−0.962530	+	0.271177i	$0.912587\pi$
$908$	−5.36781e11	−	1.06571e12i	−0.789684	−	1.56782i
$909$	2.97573e11	+	4.61066e10i	0.435850	+	0.0675317i
$910$	−1.22829e11	+	1.24683e11i	−0.179116	+	0.181820i
$911$	9.05942e11			1.31531			0.657653	−	0.753321i	$-0.271549\pi$
$911$	9.05942e11			1.31531			0.657653	+	0.753321i	$0.271549\pi$
$912$	−1.62039e11	−	1.40544e11i	−0.234229	−	0.203158i
$913$			6.33430e11i			0.911623i
$914$	−2.26418e11	+	5.38017e10i	−0.324434	+	0.0770923i
$915$	6.57998e11	+	5.06736e10i	0.938728	+	0.0722931i
$916$	2.27608e11	+	4.51888e11i	0.323300	+	0.641873i
$917$	−1.73617e11	+	1.08751e11i	−0.245536	+	0.153800i
$918$	1.09258e9	+	4.02566e11i	0.00153845	+	0.566848i
$919$			2.36440e11i			0.331482i	0.986169	+	0.165741i	$0.0530016\pi$
$919$			2.36440e11i			0.331482i	−0.986169	+	0.165741i	$0.946998\pi$
$920$	−8.99416e11	+	7.57387e11i	−1.25548	+	1.05722i
$921$	−6.79454e10	+	8.82273e11i	−0.0944326	+	1.22621i
$922$	1.29788e12	−	3.08404e11i	1.79602	−	0.426772i
$923$			1.90721e11i			0.262780i
$924$	−6.23916e11	+	8.71224e11i	−0.855930	+	1.19520i
$925$	−1.84250e11			−0.251676
$926$	1.59827e11	+	6.72614e11i	0.217373	+	0.914791i
$927$	−1.28035e12	−	1.98381e11i	−1.73385	−	0.268646i
$928$	6.13345e11	+	2.62451e11i	0.827014	+	0.353880i
$929$	7.44978e11			1.00019			0.500093	−	0.865972i	$-0.333299\pi$
$929$	7.44978e11			1.00019			0.500093	+	0.865972i	$0.333299\pi$
$930$	−1.21434e11	−	7.69917e11i	−0.162333	−	1.02923i
$931$	1.01658e11	−	2.09586e11i	0.135314	−	0.278974i
$932$	−2.92544e11	−	5.80812e11i	−0.387729	−	0.769789i
$933$	−5.38814e11	−	4.14950e10i	−0.711070	−	0.0547608i
$934$	−2.36568e10	−	9.95570e10i	−0.0310863	−	0.130823i
$935$	8.48539e11			1.11026
$936$	−7.63706e10	−	1.25643e11i	−0.0995000	−	0.163695i
$937$		−	4.15186e11i		−	0.538622i	−0.963053	−	0.269311i	$-0.913204\pi$
$937$		−	4.15186e11i		−	0.538622i	0.963053	−	0.269311i	$-0.0867960\pi$
$938$	5.24796e11	−	5.32717e11i	0.677921	−	0.688153i
$939$	2.67885e11	+	2.06303e10i	0.344577	+	0.0265365i
$940$	−8.32271e11	−	1.65238e12i	−1.06599	−	2.11640i
$941$	2.93919e11			0.374861			0.187430	−	0.982278i	$-0.439984\pi$
$941$	2.93919e11			0.374861			0.187430	+	0.982278i	$0.439984\pi$
$942$	−1.29212e12	+	2.03797e11i	−1.64097	+	0.258818i
$943$	−1.24137e12			−1.56984
$944$	−8.67868e11	−	6.42960e11i	−1.09286	−	0.809647i
$945$	1.00554e12	−	3.43315e11i	1.26088	−	0.430493i
$946$	2.83509e10	+	1.19311e11i	0.0353999	+	0.148976i
$947$	4.72894e11			0.587982			0.293991	−	0.955808i	$-0.405016\pi$
$947$	4.72894e11			0.587982			0.293991	+	0.955808i	$0.405016\pi$
$948$	−1.33812e12	+	5.49614e11i	−1.65676	+	0.680494i
$949$	9.82719e10			0.121162
$950$	1.90455e11	−	4.52561e10i	0.233829	−	0.0555626i
$951$	7.79086e11	+	5.99988e10i	0.952497	+	0.0733535i
$952$	4.43222e11	+	1.42622e11i	0.539602	+	0.173635i
$953$		−	1.49141e12i		−	1.80811i	−0.427420	−	0.904053i	$-0.640577\pi$
$953$		−	1.49141e12i		−	1.80811i	0.427420	−	0.904053i	$-0.359423\pi$
$954$	8.13718e10	+	1.02043e12i	0.0982382	+	1.23194i
$955$	1.03333e12			1.24230
$956$	6.05492e11	−	3.04975e11i	0.724898	−	0.365118i
$957$	−1.10593e12	−	8.51696e10i	−1.31850	−	0.101540i
$958$	−1.44054e11	−	6.06234e11i	−0.171026	−	0.719744i
$959$	3.72999e11	−	2.33641e11i	0.440995	−	0.276232i
$960$	−1.09703e12	−	2.77655e11i	−1.29162	−	0.326904i
$961$	−3.31268e11			−0.388406
$962$	−1.23148e10	−	5.18255e10i	−0.0143790	−	0.0605123i
$963$	−1.62206e11	−	2.51326e10i	−0.188609	−	0.0292235i
$964$	−1.85596e10	−	3.68479e10i	−0.0214912	−	0.0426682i
$965$	−2.92218e11			−0.336975
$966$	8.09280e11	−	7.04126e11i	0.929374	−	0.808615i
$967$			9.62442e11i			1.10070i	0.834934	+	0.550349i	$0.185505\pi$
$967$			9.62442e11i			1.10070i	−0.834934	+	0.550349i	$0.814495\pi$
$968$	−7.79824e11	+	6.56681e11i	−0.888169	+	0.747916i
$969$	1.18982e10	−	1.54498e11i	0.0134954	−	0.175238i
$970$	1.22103e10	+	5.13857e10i	0.0137924	+	0.0580437i
$971$			9.08241e11i			1.02170i	0.859669	+	0.510851i	$0.170669\pi$
$971$			9.08241e11i			1.02170i	−0.859669	+	0.510851i	$0.829331\pi$
$972$	7.33689e10	+	8.89596e11i	0.0821953	+	0.996616i
$973$	−7.11911e11	−	1.13654e12i	−0.794281	−	1.26804i
$974$	2.13167e11	+	8.97087e11i	0.236855	+	0.996778i
$975$	1.33791e11	+	1.03035e10i	0.148050	+	0.0114016i
$976$	5.15229e11	+	3.81708e11i	0.567808	+	0.420661i
$977$			3.46212e11i			0.379983i	0.981786	+	0.189991i	$0.0608460\pi$
$977$			3.46212e11i			0.379983i	−0.981786	+	0.189991i	$0.939154\pi$
$978$	−9.35750e11	+	1.47589e11i	−1.02283	+	0.161324i
$979$	1.85442e12			2.01873
$980$	−1.84070e10	−	1.22877e12i	−0.0199563	−	1.33220i
$981$	2.04638e11	+	3.17072e10i	0.220959	+	0.0342359i
$982$	−1.18815e12	+	2.82330e11i	−1.27769	+	0.303607i
$983$		−	9.48672e11i		−	1.01602i	−0.861351	−	0.508010i	$-0.830381\pi$
$983$		−	9.48672e11i		−	1.01602i	0.861351	−	0.508010i	$-0.169619\pi$
$984$	−6.97097e11	−	9.70236e11i	−0.743554	−	1.03490i
$985$			1.84659e12i			1.96166i
$986$	1.11418e11	+	4.68892e11i	0.117882	+	0.496095i
$987$	7.83524e11	+	1.49502e12i	0.825626	+	1.57535i
$988$	2.54591e10	+	5.05459e10i	0.0267186	+	0.0530467i
$989$		−	1.22763e11i		−	0.128316i
$990$	1.87552e12	−	1.49558e11i	1.95245	−	0.155693i
$991$			1.72781e11i			0.179144i	0.995980	+	0.0895719i	$0.0285499\pi$
$991$			1.72781e11i			0.179144i	−0.995980	+	0.0895719i	$0.971450\pi$
$992$	2.97928e11	−	6.96254e11i	0.307655	−	0.718987i
$993$	−5.45955e11	−	4.20450e10i	−0.561513	−	0.0432431i
$994$	−9.53980e11	−	9.39797e11i	−0.977223	−	0.962694i
$995$	−4.93582e11			−0.503579
$996$	5.64495e11	−	2.31859e11i	0.573618	−	0.235606i
$997$			6.51571e11i			0.659449i	0.944077	+	0.329724i	$0.106956\pi$
$997$			6.51571e11i			0.659449i	−0.944077	+	0.329724i	$0.893044\pi$
$998$	2.10080e11	+	8.84096e11i	0.211769	+	0.891204i
$999$	−7.39075e10	+	3.14828e11i	−0.0742039	+	0.316090i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.9.h.e.83.7	yes	120
3.2	odd	2	inner	84.9.h.e.83.113	yes	120
4.3	odd	2	inner	84.9.h.e.83.116	yes	120
7.6	odd	2	inner	84.9.h.e.83.8	yes	120
12.11	even	2	inner	84.9.h.e.83.6	yes	120
21.20	even	2	inner	84.9.h.e.83.114	yes	120
28.27	even	2	inner	84.9.h.e.83.115	yes	120
84.83	odd	2	inner	84.9.h.e.83.5	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.9.h.e.83.5	✓	120	84.83	odd	2	inner
84.9.h.e.83.6	yes	120	12.11	even	2	inner
84.9.h.e.83.7	yes	120	1.1	even	1	trivial
84.9.h.e.83.8	yes	120	7.6	odd	2	inner
84.9.h.e.83.113	yes	120	3.2	odd	2	inner
84.9.h.e.83.114	yes	120	21.20	even	2	inner
84.9.h.e.83.115	yes	120	28.27	even	2	inner
84.9.h.e.83.116	yes	120	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:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	84.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-15.5666 + 3.69894i) q^{2} +(-6.21954 + 80.7609i) q^{3} +(228.636 - 115.160i) q^{4} -832.715 q^{5} +(-201.913 - 1280.17i) q^{6} +(-1274.55 - 2034.78i) q^{7} +(-3133.10 + 2638.35i) q^{8} +(-6483.63 - 1004.59i) q^{9} +O(q^{10})\)	\(q+(-15.5666 + 3.69894i) q^{2} +(-6.21954 + 80.7609i) q^{3} +(228.636 - 115.160i) q^{4} -832.715 q^{5} +(-201.913 - 1280.17i) q^{6} +(-1274.55 - 2034.78i) q^{7} +(-3133.10 + 2638.35i) q^{8} +(-6483.63 - 1004.59i) q^{9} +(12962.5 - 3080.16i) q^{10} -21523.4 q^{11} +(7878.38 + 19181.1i) q^{12} -5471.22i q^{13} +(27366.9 + 26960.0i) q^{14} +(5179.10 - 67250.8i) q^{15} +(39012.6 - 52659.2i) q^{16} +47343.9 q^{17} +(104644. - 8344.56i) q^{18} -40407.1 q^{19} +(-190388. + 95895.1i) q^{20} +(172258. - 90278.4i) q^{21} +(335046. - 79613.8i) q^{22} -344738. q^{23} +(-193589. - 269441. i) q^{24} +302790. q^{25} +(20237.7 + 85168.1i) q^{26} +(121457. - 517376. i) q^{27} +(-525732. - 318446. i) q^{28} -636232. i q^{29} +(168136. + 1.06602e6i) q^{30} -722235. q^{31} +(-412508. + 964027. i) q^{32} +(133866. - 1.73825e6i) q^{33} +(-736982. + 175122. i) q^{34} +(1.06134e6 + 1.69439e6i) q^{35} +(-1.59808e6 + 516967. i) q^{36} -608509. q^{37} +(629000. - 149463. i) q^{38} +(441861. + 34028.5i) q^{39} +(2.60898e6 - 2.19699e6i) q^{40} +3.60092e6 q^{41} +(-2.34752e6 + 2.04250e6i) q^{42} +356105. i q^{43} +(-4.92102e6 + 2.47863e6i) q^{44} +(5.39902e6 + 836538. i) q^{45} +(5.36638e6 - 1.27516e6i) q^{46} +8.67897e6i q^{47} +(4.01016e6 + 3.47820e6i) q^{48} +(-2.51584e6 + 5.18686e6i) q^{49} +(-4.71340e6 + 1.12000e6i) q^{50} +(-294457. + 3.82353e6i) q^{51} +(-630064. - 1.25092e6i) q^{52} +9.75148e6i q^{53} +(23077.5 + 8.50302e6i) q^{54} +1.79229e7 q^{55} +(9.36175e6 + 3.01246e6i) q^{56} +(251314. - 3.26331e6i) q^{57} +(2.35338e6 + 9.90395e6i) q^{58} -1.64808e7i q^{59} +(-6.56045e6 - 1.59724e7i) q^{60} +9.78423e6i q^{61} +(1.12427e7 - 2.67150e6i) q^{62} +(6.21960e6 + 1.44732e7i) q^{63} +(2.85546e6 - 1.65324e7i) q^{64} +4.55597e6i q^{65} +(4.34585e6 + 2.75537e7i) q^{66} -1.94657e7i q^{67} +(1.08245e7 - 5.45210e6i) q^{68} +(2.14411e6 - 2.78413e7i) q^{69} +(-2.27888e7 - 2.24500e7i) q^{70} -3.48589e7 q^{71} +(2.29644e7 - 1.39586e7i) q^{72} +1.79616e7i q^{73} +(9.47239e6 - 2.25084e6i) q^{74} +(-1.88321e6 + 2.44536e7i) q^{75} +(-9.23851e6 + 4.65326e6i) q^{76} +(2.74327e7 + 4.37954e7i) q^{77} +(-7.00412e6 + 1.10471e6i) q^{78} +6.97623e7i q^{79} +(-3.24864e7 + 4.38501e7i) q^{80} +(4.10283e7 + 1.30268e7i) q^{81} +(-5.60539e7 + 1.33196e7i) q^{82} -2.94298e7i q^{83} +(2.89878e7 - 4.04780e7i) q^{84} -3.94240e7 q^{85} +(-1.31721e6 - 5.54333e6i) q^{86} +(5.13827e7 + 3.95707e6i) q^{87} +(6.74351e7 - 5.67863e7i) q^{88} -8.61585e7 q^{89} +(-8.71385e7 + 6.94864e6i) q^{90} +(-1.11327e7 + 6.97335e6i) q^{91} +(-7.88194e7 + 3.96999e7i) q^{92} +(4.49196e6 - 5.83283e7i) q^{93} +(-3.21030e7 - 1.35102e8i) q^{94} +3.36476e7 q^{95} +(-7.52901e7 - 3.93103e7i) q^{96} +3.96417e6i q^{97} +(1.99771e7 - 9.00475e7i) q^{98} +(1.39550e8 + 2.16222e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 1028 q^{4} - 26248 q^{9}+O(q^{10}) \) 120 * q - 1028 * q^4 - 26248 * q^9	\( 120 q - 1028 q^{4} - 26248 q^{9} - 373500 q^{16} - 289340 q^{18} - 620200 q^{21} - 640592 q^{22} + 9327272 q^{25} + 54500 q^{28} - 1299380 q^{30} - 11227168 q^{36} - 8553936 q^{37} - 8996308 q^{42} - 26738344 q^{46} - 13574664 q^{49} - 50788176 q^{57} - 18533288 q^{58} - 24117668 q^{60} - 99498308 q^{64} + 10779752 q^{70} + 76835716 q^{72} - 13132860 q^{78} + 23514872 q^{81} - 171096188 q^{84} - 88829152 q^{85} + 184844592 q^{88} + 626423664 q^{93}+O(q^{100}) \) 120 * q - 1028 * q^4 - 26248 * q^9 - 373500 * q^16 - 289340 * q^18 - 620200 * q^21 - 640592 * q^22 + 9327272 * q^25 + 54500 * q^28 - 1299380 * q^30 - 11227168 * q^36 - 8553936 * q^37 - 8996308 * q^42 - 26738344 * q^46 - 13574664 * q^49 - 50788176 * q^57 - 18533288 * q^58 - 24117668 * q^60 - 99498308 * q^64 + 10779752 * q^70 + 76835716 * q^72 - 13132860 * q^78 + 23514872 * q^81 - 171096188 * q^84 - 88829152 * q^85 + 184844592 * q^88 + 626423664 * q^93

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