LMFDB - Embedded newform 76.8.d.a.75.7

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			75.7
Character	$\chi$	$=$	76.75
Dual form			76.8.d.a.75.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-10.7294 - 3.58884i) q^{2} +80.7260 q^{3} +(102.240 + 77.0123i) q^{4} +174.727 q^{5} +(-866.143 - 289.713i) q^{6} +433.835i q^{7} +(-820.594 - 1193.22i) q^{8} +4329.69 q^{9} +O(q^{10})$	\(q+(-10.7294 - 3.58884i) q^{2} +80.7260 q^{3} +(102.240 + 77.0123i) q^{4} +174.727 q^{5} +(-866.143 - 289.713i) q^{6} +433.835i q^{7} +(-820.594 - 1193.22i) q^{8} +4329.69 q^{9} +(-1874.71 - 627.067i) q^{10} -7055.30i q^{11} +(8253.46 + 6216.90i) q^{12} -13221.1i q^{13} +(1556.96 - 4654.79i) q^{14} +14105.0 q^{15} +(4522.20 + 15747.5i) q^{16} -8082.65 q^{17} +(-46455.1 - 15538.6i) q^{18} +(29600.4 + 4205.43i) q^{19} +(17864.1 + 13456.1i) q^{20} +35021.8i q^{21} +(-25320.4 + 75699.2i) q^{22} +65065.7i q^{23} +(-66243.3 - 96324.1i) q^{24} -47595.6 q^{25} +(-47448.5 + 141855. i) q^{26} +172971. q^{27} +(-33410.6 + 44355.4i) q^{28} -146291. i q^{29} +(-151338. - 50620.6i) q^{30} +326080. q^{31} +(7994.87 - 185191. i) q^{32} -569546. i q^{33} +(86722.1 + 29007.4i) q^{34} +75802.5i q^{35} +(442670. + 333440. i) q^{36} +463428. i q^{37} +(-302503. - 151353. i) q^{38} -1.06729e6i q^{39} +(-143380. - 208488. i) q^{40} -8839.46i q^{41} +(125688. - 375763. i) q^{42} +273637. i q^{43} +(543345. - 721337. i) q^{44} +756513. q^{45} +(233511. - 698117. i) q^{46} +344078. i q^{47} +(365060. + 1.27124e6i) q^{48} +635331. q^{49} +(510673. + 170813. i) q^{50} -652481. q^{51} +(1.01819e6 - 1.35173e6i) q^{52} -755502. i q^{53} +(-1.85588e6 - 620767. i) q^{54} -1.23275e6i q^{55} +(517661. - 356002. i) q^{56} +(2.38953e6 + 339487. i) q^{57} +(-525016. + 1.56962e6i) q^{58} -1.11517e6 q^{59} +(1.44210e6 + 1.08626e6i) q^{60} -146512. q^{61} +(-3.49864e6 - 1.17025e6i) q^{62} +1.87837e6i q^{63} +(-750403. + 1.95830e6i) q^{64} -2.31008e6i q^{65} +(-2.04401e6 + 6.11090e6i) q^{66} -1.89197e6 q^{67} +(-826374. - 622464. i) q^{68} +5.25250e6i q^{69} +(272043. - 813316. i) q^{70} +1.38358e6 q^{71} +(-3.55292e6 - 5.16628e6i) q^{72} -3.48753e6 q^{73} +(1.66317e6 - 4.97231e6i) q^{74} -3.84220e6 q^{75} +(2.70249e6 + 2.70956e6i) q^{76} +3.06083e6 q^{77} +(-3.83033e6 + 1.14514e7i) q^{78} +2.19880e6 q^{79} +(790150. + 2.75152e6i) q^{80} +4.49425e6 q^{81} +(-31723.4 + 94842.1i) q^{82} +6.41987e6i q^{83} +(-2.69711e6 + 3.58064e6i) q^{84} -1.41226e6 q^{85} +(982040. - 2.93596e6i) q^{86} -1.18095e7i q^{87} +(-8.41853e6 + 5.78954e6i) q^{88} -4.43104e6i q^{89} +(-8.11694e6 - 2.71501e6i) q^{90} +5.73578e6 q^{91} +(-5.01086e6 + 6.65235e6i) q^{92} +2.63231e7 q^{93} +(1.23484e6 - 3.69176e6i) q^{94} +(5.17199e6 + 734800. i) q^{95} +(645395. - 1.49498e7i) q^{96} -4.19353e6i q^{97} +(-6.81672e6 - 2.28010e6i) q^{98} -3.05473e7i 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 $

$2$	−10.7294	−	3.58884i	−0.948355	−	0.317212i
$2$	−10.7294	−	3.58884i	−0.948355	−	0.317212i
$3$	80.7260			1.72619			0.863096	−	0.505039i	$-0.168522\pi$
$3$	80.7260			1.72619			0.863096	+	0.505039i	$0.168522\pi$
$4$	102.240	+	77.0123i	0.798753	+	0.601659i
$5$	174.727			0.625121			0.312561	−	0.949898i	$-0.398813\pi$
$5$	174.727			0.625121			0.312561	+	0.949898i	$0.398813\pi$
$6$	−866.143	−	289.713i	−1.63704	−	0.547569i
$7$			433.835i			0.478059i	0.971012	+	0.239029i	$0.0768292\pi$
$7$			433.835i			0.478059i	−0.971012	+	0.239029i	$0.923171\pi$
$8$	−820.594	−	1193.22i	−0.566648	−	0.823960i
$9$	4329.69			1.97974
$10$	−1874.71	−	627.067i	−0.592837	−	0.198296i
$11$		−	7055.30i		−	1.59824i	−0.601174	−	0.799118i	$-0.705300\pi$
$11$		−	7055.30i		−	1.59824i	0.601174	−	0.799118i	$-0.294700\pi$
$12$	8253.46	+	6216.90i	1.37880	+	1.03858i
$13$		−	13221.1i		−	1.66904i	−0.550979	−	0.834519i	$-0.685745\pi$
$13$		−	13221.1i		−	1.66904i	0.550979	−	0.834519i	$-0.314255\pi$
$14$	1556.96	−	4654.79i	0.151646	−	0.453369i
$15$	14105.0			1.07908
$16$	4522.20	+	15747.5i	0.276013	+	0.961154i
$17$	−8082.65			−0.399009			−0.199505	−	0.979897i	$-0.563933\pi$
$17$	−8082.65			−0.399009			−0.199505	+	0.979897i	$0.563933\pi$
$18$	−46455.1	−	15538.6i	−1.87750	−	0.627998i
$19$	29600.4	+	4205.43i	0.990058	+	0.140661i
$19$	29600.4	+	4205.43i	0.990058	+	0.140661i
$20$	17864.1	+	13456.1i	0.499318	+	0.376110i
$21$			35021.8i			0.825221i
$22$	−25320.4	+	75699.2i	−0.506980	+	1.51569i
$23$			65065.7i			1.11508i	0.830151	+	0.557538i	$0.188254\pi$
$23$			65065.7i			1.11508i	−0.830151	+	0.557538i	$0.811746\pi$
$24$	−66243.3	−	96324.1i	−0.978144	−	1.42231i
$25$	−47595.6			−0.609224
$26$	−47448.5	+	141855.i	−0.529439	+	1.58284i
$27$	172971.			1.69122
$28$	−33410.6	+	44355.4i	−0.287628	+	0.381851i
$29$		−	146291.i		−	1.11385i	−0.830564	−	0.556923i	$-0.811982\pi$
$29$		−	146291.i		−	1.11385i	0.830564	−	0.556923i	$-0.188018\pi$
$30$	−151338.	−	50620.6i	−1.02335	−	0.342297i
$31$	326080.			1.96588			0.982942	−	0.183913i	$-0.0588766\pi$
$31$	326080.			1.96588			0.982942	+	0.183913i	$0.0588766\pi$
$32$	7994.87	−	185191.i	0.0431307	−	0.999069i
$33$		−	569546.i		−	2.75886i
$34$	86722.1	+	29007.4i	0.378402	+	0.126570i
$35$			75802.5i			0.298844i
$36$	442670.	+	333440.i	1.58133	+	1.19113i
$37$			463428.i			1.50410i	0.659107	+	0.752049i	$0.270935\pi$
$37$			463428.i			1.50410i	−0.659107	+	0.752049i	$0.729065\pi$
$38$	−302503.	−	151353.i	−0.894307	−	0.447454i
$39$		−	1.06729e6i		−	2.88108i
$40$	−143380.	−	208488.i	−0.354224	−	0.515075i
$41$		−	8839.46i		−	0.0200301i	−0.999950	−	0.0100150i	$-0.996812\pi$
$41$		−	8839.46i		−	0.0200301i	0.999950	−	0.0100150i	$-0.00318793\pi$
$42$	125688.	−	375763.i	0.261770	−	0.782602i
$43$			273637.i			0.524850i	0.964952	+	0.262425i	$0.0845222\pi$
$43$			273637.i			0.524850i	−0.964952	+	0.262425i	$0.915478\pi$
$44$	543345.	−	721337.i	0.961593	−	1.27660i
$45$	756513.			1.23758
$46$	233511.	−	698117.i	0.353716	−	1.05749i
$47$			344078.i			0.483409i	0.970350	+	0.241704i	$0.0777065\pi$
$47$			344078.i			0.483409i	−0.970350	+	0.241704i	$0.922294\pi$
$48$	365060.	+	1.27124e6i	0.476452	+	1.65914i
$49$	635331.			0.771460
$50$	510673.	+	170813.i	0.577760	+	0.193253i
$51$	−652481.			−0.688767
$52$	1.01819e6	−	1.35173e6i	1.00419	−	1.33315i
$53$		−	755502.i		−	0.697060i	−0.937298	−	0.348530i	$-0.886681\pi$
$53$		−	755502.i		−	0.697060i	0.937298	−	0.348530i	$-0.113319\pi$
$54$	−1.85588e6	−	620767.i	−1.60388	−	0.536476i
$55$		−	1.23275e6i		−	0.999091i
$56$	517661.	−	356002.i	0.393901	−	0.270891i
$57$	2.38953e6	+	339487.i	1.70903	+	0.242807i
$58$	−525016.	+	1.56962e6i	−0.353325	+	1.05632i
$59$	−1.11517e6			−0.706903			−0.353451	−	0.935453i	$-0.614992\pi$
$59$	−1.11517e6			−0.706903			−0.353451	+	0.935453i	$0.614992\pi$
$60$	1.44210e6	+	1.08626e6i	0.861918	+	0.649238i
$61$	−146512.			−0.0826453			−0.0413227	−	0.999146i	$-0.513157\pi$
$61$	−146512.			−0.0826453			−0.0413227	+	0.999146i	$0.513157\pi$
$62$	−3.49864e6	−	1.17025e6i	−1.86436	−	0.623602i
$63$			1.87837e6i			0.946432i
$64$	−750403.	+	1.95830e6i	−0.357820	+	0.933791i
$65$		−	2.31008e6i		−	1.04335i
$66$	−2.04401e6	+	6.11090e6i	−0.875144	+	2.61638i
$67$	−1.89197e6			−0.768516			−0.384258	−	0.923226i	$-0.625543\pi$
$67$	−1.89197e6			−0.768516			−0.384258	+	0.923226i	$0.625543\pi$
$68$	−826374.	−	622464.i	−0.318710	−	0.240067i
$69$			5.25250e6i			1.92484i
$70$	272043.	−	813316.i	0.0947970	−	0.283411i
$71$	1.38358e6			0.458774			0.229387	−	0.973335i	$-0.426328\pi$
$71$	1.38358e6			0.458774			0.229387	+	0.973335i	$0.426328\pi$
$72$	−3.55292e6	−	5.16628e6i	−1.12182	−	1.63123i
$73$	−3.48753e6			−1.04927			−0.524636	−	0.851326i	$-0.675799\pi$
$73$	−3.48753e6			−1.04927			−0.524636	+	0.851326i	$0.675799\pi$
$74$	1.66317e6	−	4.97231e6i	0.477118	−	1.42642i
$75$	−3.84220e6			−1.05164
$76$	2.70249e6	+	2.70956e6i	0.706182	+	0.708030i
$77$	3.06083e6			0.764050
$78$	−3.83033e6	+	1.14514e7i	−0.913914	+	2.73229i
$79$	2.19880e6			0.501755			0.250877	−	0.968019i	$-0.419281\pi$
$79$	2.19880e6			0.501755			0.250877	+	0.968019i	$0.419281\pi$
$80$	790150.	+	2.75152e6i	0.172542	+	0.600838i
$81$	4.49425e6			0.939635
$82$	−31723.4	+	94842.1i	−0.00635377	+	0.0189956i
$83$			6.41987e6i			1.23240i	0.787588	+	0.616202i	$0.211329\pi$
$83$			6.41987e6i			1.23240i	−0.787588	+	0.616202i	$0.788671\pi$
$84$	−2.69711e6	+	3.58064e6i	−0.496502	+	0.659148i
$85$	−1.41226e6			−0.249429
$86$	982040.	−	2.93596e6i	0.166489	−	0.497744i
$87$		−	1.18095e7i		−	1.92271i
$88$	−8.41853e6	+	5.78954e6i	−1.31688	+	0.905637i
$89$		−	4.43104e6i		−	0.666255i	−0.942882	−	0.333127i	$-0.891896\pi$
$89$		−	4.43104e6i		−	0.666255i	0.942882	−	0.333127i	$-0.108104\pi$
$90$	−8.11694e6	−	2.71501e6i	−1.17366	−	0.392575i
$91$	5.73578e6			0.797898
$92$	−5.01086e6	+	6.65235e6i	−0.670896	+	0.890671i
$93$	2.63231e7			3.39350
$94$	1.23484e6	−	3.69176e6i	0.153343	−	0.458443i
$95$	5.17199e6	+	734800.i	0.618906	+	0.0879299i
$96$	645395.	−	1.49498e7i	0.0744519	−	1.72459i
$97$		−	4.19353e6i		−	0.466529i	−0.972413	−	0.233265i	$-0.925059\pi$
$97$		−	4.19353e6i		−	0.466529i	0.972413	−	0.233265i	$-0.0749408\pi$
$98$	−6.81672e6	−	2.28010e6i	−0.731618	−	0.244716i
$99$		−	3.05473e7i		−	3.16409i
$100$	−4.86619e6	−	3.66545e6i	−0.486619	−	0.366545i
$101$	5.11194e6			0.493697			0.246849	−	0.969054i	$-0.420605\pi$
$101$	5.11194e6			0.493697			0.246849	+	0.969054i	$0.420605\pi$
$102$	7.00073e6	+	2.34165e6i	0.653195	+	0.218485i
$103$	−1.13980e7			−1.02778			−0.513890	−	0.857856i	$-0.671796\pi$
$103$	−1.13980e7			−1.02778			−0.513890	+	0.857856i	$0.671796\pi$
$104$	−1.57757e7	+	1.08492e7i	−1.37522	+	0.945757i
$105$			6.11923e6i			0.515863i
$106$	−2.71138e6	+	8.10609e6i	−0.221116	+	0.661060i
$107$	2.72402e6			0.214965			0.107482	−	0.994207i	$-0.465721\pi$
$107$	2.72402e6			0.214965			0.107482	+	0.994207i	$0.465721\pi$
$108$	1.76847e7	+	1.33209e7i	1.35087	+	1.01754i
$109$			1.47134e7i			1.08823i	0.839010	+	0.544116i	$0.183135\pi$
$109$			1.47134e7i			1.08823i	−0.839010	+	0.544116i	$0.816865\pi$
$110$	−4.42414e6	+	1.32267e7i	−0.316924	+	0.947493i
$111$			3.74107e7i			2.59636i
$112$	−6.83183e6	+	1.96189e6i	−0.459488	+	0.131951i
$113$			1.40186e7i			0.913965i	0.889476	+	0.456982i	$0.151070\pi$
$113$			1.40186e7i			0.913965i	−0.889476	+	0.456982i	$0.848930\pi$
$114$	−2.44198e7	−	1.22181e7i	−1.54375	−	0.772392i
$115$			1.13687e7i			0.697058i
$116$	1.12662e7	−	1.49569e7i	0.670156	−	0.889689i
$117$		−	5.72434e7i		−	3.30426i
$118$	1.19651e7	+	4.00217e6i	0.670394	+	0.224238i
$119$		−	3.50654e6i		−	0.190750i
$120$	−1.15745e7	−	1.68304e7i	−0.611458	−	0.889118i
$121$	−3.02901e7			−1.55436
$122$	1.57199e6	+	525808.i	0.0783771	+	0.0262161i
$123$		−	713574.i		−	0.0345757i
$124$	3.33385e7	+	2.51122e7i	1.57026	+	1.18279i
$125$	−2.19667e7			−1.00596
$126$	6.74118e6	−	2.01538e7i	0.300220	−	0.897554i
$127$	−7.40303e6			−0.320698			−0.160349	−	0.987060i	$-0.551262\pi$
$127$	−7.40303e6			−0.320698			−0.160349	+	0.987060i	$0.551262\pi$
$128$	1.50794e7	−	1.83183e7i	0.635550	−	0.772060i
$129$			2.20896e7i			0.905992i
$130$	−8.29052e6	+	2.47858e7i	−0.330963	+	0.989467i
$131$		−	3.18761e7i		−	1.23884i	−0.785060	−	0.619420i	$-0.787368\pi$
$131$		−	3.18761e7i		−	1.23884i	0.785060	−	0.619420i	$-0.212632\pi$
$132$	4.38621e7	−	5.82307e7i	1.65989	−	2.20365i
$133$	−1.82446e6	+	1.28417e7i	−0.0672440	+	0.473306i
$134$	2.02997e7	+	6.78999e6i	0.728826	+	0.243782i
$135$	3.02227e7			1.05722
$136$	6.63258e6	+	9.64440e6i	0.226098	+	0.328767i
$137$	1.64641e7			0.547037			0.273519	−	0.961867i	$-0.411812\pi$
$137$	1.64641e7			0.547037			0.273519	+	0.961867i	$0.411812\pi$
$138$	1.88504e7	−	5.63562e7i	0.610581	−	1.82543i
$139$			4.28056e7i			1.35191i	0.736942	+	0.675956i	$0.236269\pi$
$139$			4.28056e7i			1.35191i	−0.736942	+	0.675956i	$0.763731\pi$
$140$	−5.83772e6	+	7.75008e6i	−0.179802	+	0.238703i
$141$			2.77761e7i			0.834457i
$142$	−1.48450e7	−	4.96544e6i	−0.435081	−	0.145529i
$143$	−9.32789e7			−2.66752
$144$	1.95798e7	+	6.81821e7i	0.546435	+	1.90284i
$145$		−	2.55610e7i		−	0.696289i
$146$	3.74192e7	+	1.25162e7i	0.995083	+	0.332842i
$147$	5.12877e7			1.33169
$148$	−3.56897e7	+	4.73811e7i	−0.904954	+	1.20140i
$149$	4.68180e6			0.115947			0.0579737	−	0.998318i	$-0.481536\pi$
$149$	4.68180e6			0.115947			0.0579737	+	0.998318i	$0.481536\pi$
$150$	4.12246e7	+	1.37891e7i	0.997325	+	0.333592i
$151$	−4.47017e7			−1.05659			−0.528293	−	0.849062i	$-0.677168\pi$
$151$	−4.47017e7			−1.05659			−0.528293	+	0.849062i	$0.677168\pi$
$152$	−1.92719e7	−	3.87708e7i	−0.445116	−	0.895473i
$153$	−3.49954e7			−0.789935
$154$	−3.28409e7	−	1.09848e7i	−0.724591	−	0.242366i
$155$	5.69749e7			1.22892
$156$	8.21944e7	−	1.09120e8i	1.73343	−	2.30127i
$157$	2.85143e7			0.588050			0.294025	−	0.955798i	$-0.405005\pi$
$157$	2.85143e7			0.588050			0.294025	+	0.955798i	$0.405005\pi$
$158$	−2.35918e7	−	7.89116e6i	−0.475841	−	0.159163i
$159$		−	6.09887e7i		−	1.20326i
$160$	1.39692e6	−	3.23579e7i	0.0269619	−	0.624539i
$161$	−2.82278e7			−0.533072
$162$	−4.82206e7	−	1.61291e7i	−0.891108	−	0.298063i
$163$			7.89964e7i			1.42873i	0.699772	+	0.714366i	$0.253285\pi$
$163$			7.89964e7i			1.42873i	−0.699772	+	0.714366i	$0.746715\pi$
$164$	680747.	−	903750.i	0.0120513	−	0.0159991i
$165$		−	9.95149e7i		−	1.72462i
$166$	2.30399e7	−	6.88814e7i	0.390933	−	1.16876i
$167$	7.63814e7			1.26905			0.634527	−	0.772901i	$-0.281195\pi$
$167$	7.63814e7			1.26905			0.634527	+	0.772901i	$0.281195\pi$
$168$	4.17887e7	−	2.87386e7i	0.679949	−	0.467610i
$169$	−1.12049e8			−1.78569
$170$	1.51527e7	+	5.06836e6i	0.236547	+	0.0791218i
$171$	1.28161e8	+	1.82082e7i	1.96006	+	0.278472i
$172$	−2.10734e7	+	2.79768e7i	−0.315781	+	0.419226i
$173$		−	2.99108e7i		−	0.439205i	−0.975589	−	0.219602i	$-0.929524\pi$
$173$		−	2.99108e7i		−	0.439205i	0.975589	−	0.219602i	$-0.0704760\pi$
$174$	−4.23825e7	+	1.26709e8i	−0.609908	+	1.82342i
$175$		−	2.06486e7i		−	0.291245i
$176$	1.11104e8	−	3.19055e7i	1.53615	−	0.441135i
$177$	−9.00234e7			−1.22025
$178$	−1.59023e7	+	4.75424e7i	−0.211344	+	0.631846i
$179$	−1.26680e8			−1.65090			−0.825450	−	0.564475i	$-0.809079\pi$
$179$	−1.26680e8			−1.65090			−0.825450	+	0.564475i	$0.809079\pi$
$180$	7.73462e7	+	5.82608e7i	0.988520	+	0.744600i
$181$			9.93035e7i			1.24477i	0.782711	+	0.622386i	$0.213837\pi$
$181$			9.93035e7i			1.24477i	−0.782711	+	0.622386i	$0.786163\pi$
$182$	−6.15415e7	−	2.05848e7i	−0.756690	−	0.253103i
$183$	−1.18273e7			−0.142662
$184$	7.76378e7	−	5.33925e7i	0.918779	−	0.631856i
$185$			8.09733e7i			0.940244i
$186$	−2.82432e8	−	9.44696e7i	−3.21824	−	1.07646i
$187$			5.70255e7i			0.637711i
$188$	−2.64983e7	+	3.51787e7i	−0.290847	+	0.386124i
$189$			7.50409e7i			0.808504i
$190$	−5.28553e7	−	2.64454e7i	−0.559050	−	0.279713i
$191$		−	4.68737e7i		−	0.486757i	−0.969931	−	0.243379i	$-0.921744\pi$
$191$		−	4.68737e7i		−	0.486757i	0.969931	−	0.243379i	$-0.0782557\pi$
$192$	−6.05771e7	+	1.58086e8i	−0.617666	+	1.61190i
$193$			1.09605e7i			0.109744i	0.998493	+	0.0548719i	$0.0174750\pi$
$193$			1.09605e7i			0.109744i	−0.998493	+	0.0548719i	$0.982525\pi$
$194$	−1.50499e7	+	4.49941e7i	−0.147989	+	0.442435i
$195$		−	1.86484e8i		−	1.80103i
$196$	6.49565e7	+	4.89283e7i	0.616206	+	0.464156i
$197$	1.59826e8			1.48941			0.744707	−	0.667391i	$-0.232589\pi$
$197$	1.59826e8			1.48941			0.744707	+	0.667391i	$0.232589\pi$
$198$	−1.09629e8	+	3.27754e8i	−1.00369	+	3.00068i
$199$			1.96697e7i			0.176934i	0.996079	+	0.0884670i	$0.0281968\pi$
$199$			1.96697e7i			0.176934i	−0.996079	+	0.0884670i	$0.971803\pi$
$200$	3.90567e7	+	5.67921e7i	0.345215	+	0.501976i
$201$	−1.52731e8			−1.32661
$202$	−5.48481e7	−	1.83459e7i	−0.468200	−	0.156607i
$203$	6.34662e7			0.532484
$204$	−6.67099e7	−	5.02491e7i	−0.550155	−	0.414402i
$205$		−	1.54449e6i		−	0.0125212i
$206$	1.22294e8	+	4.09058e7i	0.974699	+	0.326024i
$207$			2.81715e8i			2.20756i
$208$	2.08200e8	−	5.97886e7i	1.60420	−	0.460677i
$209$	2.96705e7	−	2.08840e8i	0.224809	−	1.58235i
$210$	2.19610e7	−	6.56558e7i	0.163638	−	0.489221i
$211$	−1.54487e8			−1.13215			−0.566073	−	0.824355i	$-0.691538\pi$
$211$	−1.54487e8			−1.13215			−0.566073	+	0.824355i	$0.691538\pi$
$212$	5.81830e7	−	7.72428e7i	0.419392	−	0.556779i
$213$	1.11691e8			0.791932
$214$	−2.92271e7	−	9.77608e6i	−0.203863	−	0.0681893i
$215$			4.78117e7i			0.328095i
$216$	−1.41939e8	−	2.06393e8i	−0.958328	−	1.39350i
$217$			1.41465e8i			0.939808i
$218$	5.28043e7	−	1.57867e8i	0.345200	−	1.03203i
$219$	−2.81535e8			−1.81125
$220$	9.49368e7	−	1.26037e8i	0.601112	−	0.798027i
$221$			1.06862e8i			0.665962i
$222$	1.34261e8	−	4.01395e8i	0.823598	−	2.46227i
$223$	−6.17231e6			−0.0372718			−0.0186359	−	0.999826i	$-0.505932\pi$
$223$	−6.17231e6			−0.0372718			−0.0186359	+	0.999826i	$0.505932\pi$
$224$	8.03424e7	+	3.46845e6i	0.477614	+	0.0206190i
$225$	−2.06074e8			−1.20611
$226$	5.03105e7	−	1.50411e8i	0.289920	−	0.866763i
$227$	−1.57676e8			−0.894696			−0.447348	−	0.894360i	$-0.647631\pi$
$227$	−1.57676e8			−0.894696			−0.447348	+	0.894360i	$0.647631\pi$
$228$	2.18161e8	+	2.18732e8i	1.21901	+	1.22220i
$229$	−2.90105e7			−0.159636			−0.0798180	−	0.996809i	$-0.525434\pi$
$229$	−2.90105e7			−0.159636			−0.0798180	+	0.996809i	$0.525434\pi$
$230$	4.08005e7	−	1.21980e8i	0.221115	−	0.661058i
$231$	2.47089e8			1.31890
$232$	−1.74558e8	+	1.20046e8i	−0.917765	+	0.631159i
$233$	−1.43879e8			−0.745161			−0.372581	−	0.928000i	$-0.621527\pi$
$233$	−1.43879e8			−0.745161			−0.372581	+	0.928000i	$0.621527\pi$
$234$	−2.05438e8	+	6.14188e8i	−1.04815	+	3.13362i
$235$			6.01196e7i			0.302189i
$236$	−1.14016e8	−	8.58819e7i	−0.564641	−	0.425314i
$237$	1.77501e8			0.866125
$238$	−1.25844e7	+	3.76231e7i	−0.0605081	+	0.180898i
$239$			1.39635e7i			0.0661611i	0.999453	+	0.0330805i	$0.0105318\pi$
$239$			1.39635e7i			0.0661611i	−0.999453	+	0.0330805i	$0.989468\pi$
$240$	6.37857e7	+	2.22119e8i	0.297841	+	1.03716i
$241$		−	2.16373e8i		−	0.995735i	−0.867253	−	0.497868i	$-0.834117\pi$
$241$		−	2.16373e8i		−	0.995735i	0.867253	−	0.497868i	$-0.165883\pi$
$242$	3.24994e8	+	1.08706e8i	1.47408	+	0.493061i
$243$	−1.54855e7			−0.0692313
$244$	−1.49794e7	−	1.12832e7i	−0.0660132	−	0.0497243i
$245$	1.11009e8			0.482256
$246$	−2.56091e6	+	7.65623e6i	−0.0109678	+	0.0327901i
$247$	5.56004e7	−	3.91351e8i	0.234768	−	1.65244i
$248$	−2.67579e8	−	3.89086e8i	−1.11396	−	1.61981i
$249$			5.18251e8i			2.12737i
$250$	2.35690e8	+	7.88352e7i	0.954007	+	0.319102i
$251$			1.63195e8i			0.651400i	0.945473	+	0.325700i	$0.105600\pi$
$251$			1.63195e8i			0.651400i	−0.945473	+	0.325700i	$0.894400\pi$
$252$	−1.44658e8	+	1.92045e8i	−0.569429	+	0.755966i
$253$	4.59058e8			1.78216
$254$	7.94301e7	+	2.65683e7i	0.304135	+	0.101729i
$255$	−1.14006e8			−0.430563
$256$	−2.27535e8	+	1.42427e8i	−0.847633	+	0.530583i
$257$			9.85814e7i			0.362267i	0.983458	+	0.181134i	$0.0579767\pi$
$257$			9.85814e7i			0.362267i	−0.983458	+	0.181134i	$0.942023\pi$
$258$	7.92762e7	−	2.37009e8i	0.287392	−	0.859202i
$259$	−2.01051e8			−0.719047
$260$	1.77905e8	−	2.36184e8i	0.627741	−	0.833380i
$261$		−	6.33397e8i		−	2.20513i
$262$	−1.14398e8	+	3.42011e8i	−0.392975	+	1.17486i
$263$		−	4.55390e8i		−	1.54361i	−0.635858	−	0.771806i	$-0.719353\pi$
$263$		−	4.55390e8i		−	1.54361i	0.635858	−	0.771806i	$-0.280647\pi$
$264$	−6.79595e8	+	4.67366e8i	−2.27319	+	1.56330i
$265$		−	1.32006e8i		−	0.435747i
$266$	6.56622e7	−	1.31236e8i	0.213909	−	0.427531i
$267$		−	3.57700e8i		−	1.15008i
$268$	−1.93436e8	−	1.45705e8i	−0.613855	−	0.462385i
$269$		−	3.77037e8i		−	1.18100i	−0.807037	−	0.590502i	$-0.798930\pi$
$269$		−	3.77037e8i		−	1.18100i	0.807037	−	0.590502i	$-0.201070\pi$
$270$	−3.24272e8	−	1.08465e8i	−1.00262	−	0.335362i
$271$			4.60513e8i			1.40556i	0.711407	+	0.702781i	$0.248058\pi$
$271$			4.60513e8i			1.40556i	−0.711407	+	0.702781i	$0.751942\pi$
$272$	−3.65514e7	−	1.27282e8i	−0.110132	−	0.383509i
$273$	4.63027e8			1.37733
$274$	−1.76650e8	−	5.90872e7i	−0.518785	−	0.173527i
$275$			3.35801e8i			0.973683i
$276$	−4.04507e8	+	5.37018e8i	−1.15810	+	1.53747i
$277$	3.38368e8			0.956554			0.478277	−	0.878209i	$-0.341261\pi$
$277$	3.38368e8			0.956554			0.478277	+	0.878209i	$0.341261\pi$
$278$	1.53622e8	−	4.59278e8i	0.428843	−	1.28209i
$279$	1.41183e9			3.89194
$280$	9.04491e7	−	6.22031e7i	0.246236	−	0.169340i
$281$			2.95018e8i			0.793189i	0.917994	+	0.396595i	$0.129808\pi$
$281$			2.95018e8i			0.793189i	−0.917994	+	0.396595i	$0.870192\pi$
$282$	9.96840e7	−	2.98021e8i	0.264700	−	0.791361i
$283$		−	4.30443e8i		−	1.12892i	−0.825460	−	0.564460i	$-0.809084\pi$
$283$		−	4.30443e8i		−	1.12892i	0.825460	−	0.564460i	$-0.190916\pi$
$284$	1.41457e8	+	1.06552e8i	0.366447	+	0.276025i
$285$	4.17514e8	+	5.93175e7i	1.06835	+	0.151784i
$286$	1.00083e9	+	3.34763e8i	2.52975	+	0.846168i
$287$	3.83486e6			0.00957554
$288$	3.46154e7	−	8.01822e8i	0.0853877	−	1.97790i
$289$	−3.45009e8			−0.840792
$290$	−9.17344e7	+	2.74254e8i	−0.220871	+	0.660329i
$291$		−	3.38527e8i		−	0.805319i
$292$	−3.56567e8	−	2.68583e8i	−0.838110	−	0.631304i
$293$			2.13205e8i			0.495178i	0.968865	+	0.247589i	$0.0796382\pi$
$293$			2.13205e8i			0.495178i	−0.968865	+	0.247589i	$0.920362\pi$
$294$	−5.50287e8	−	1.84064e8i	−1.26291	−	0.422428i
$295$	−1.94850e8			−0.441900
$296$	5.52972e8	−	3.80286e8i	1.23932	−	0.852295i
$297$		−	1.22036e9i		−	2.70297i
$298$	−5.02330e7	−	1.68023e7i	−0.109959	−	0.0367799i
$299$	8.60241e8			1.86111
$300$	−3.92829e8	−	2.95897e8i	−0.839999	−	0.632727i
$301$	−1.18713e8			−0.250909
$302$	4.79623e8	+	1.60427e8i	1.00202	+	0.335162i
$303$	4.12667e8			0.852217
$304$	6.76341e7	+	4.85152e8i	0.138073	+	0.990422i
$305$	−2.55995e7			−0.0516633
$306$	3.75480e8	+	1.25593e8i	0.749138	+	0.250577i
$307$	−4.51286e8			−0.890159			−0.445080	−	0.895491i	$-0.646825\pi$
$307$	−4.51286e8			−0.890159			−0.445080	+	0.895491i	$0.646825\pi$
$308$	3.12941e8	+	2.35722e8i	0.610288	+	0.459698i
$309$	−9.20119e8			−1.77415
$310$	−6.11306e8	−	2.04474e8i	−1.16545	−	0.389827i
$311$		−	7.11517e8i		−	1.34129i	−0.741776	−	0.670647i	$-0.766016\pi$
$311$		−	7.11517e8i		−	1.34129i	0.741776	−	0.670647i	$-0.233984\pi$
$312$	−1.27351e9	+	8.75810e8i	−2.37390	+	1.63256i
$313$	8.66058e8			1.59640			0.798200	−	0.602392i	$-0.205786\pi$
$313$	8.66058e8			1.59640			0.798200	+	0.602392i	$0.205786\pi$
$314$	−3.05942e8	−	1.02333e8i	−0.557680	−	0.186537i
$315$			3.28202e8i			0.591635i
$316$	2.24806e8	+	1.69335e8i	0.400778	+	0.301885i
$317$		−	8.57033e6i		−	0.0151109i	−0.999971	−	0.00755544i	$-0.997595\pi$
$317$		−	8.57033e6i		−	0.0151109i	0.999971	−	0.00755544i	$-0.00240500\pi$
$318$	−2.18879e8	+	6.54373e8i	−0.381688	+	1.14112i
$319$	−1.03213e9			−1.78019
$320$	−1.31115e8	+	3.42167e8i	−0.223681	+	0.583732i
$321$	2.19899e8			0.371070
$322$	3.02867e8	+	1.01305e8i	0.505541	+	0.169097i
$323$	−2.39250e8	−	3.39910e7i	−0.395042	−	0.0561249i
$324$	4.59494e8	+	3.46112e8i	0.750537	+	0.565340i
$325$			6.29267e8i			1.01682i
$326$	2.83506e8	−	8.47585e8i	0.453211	−	1.35494i
$327$			1.18776e9i			1.87850i
$328$	−1.05474e7	+	7.25361e6i	−0.0165040	+	0.0113500i
$329$	−1.49273e8			−0.231098
$330$	−3.57143e8	+	1.06774e9i	−0.547071	+	1.63556i
$331$	−3.67354e8			−0.556785			−0.278392	−	0.960467i	$-0.589802\pi$
$331$	−3.67354e8			−0.556785			−0.278392	+	0.960467i	$0.589802\pi$
$332$	−4.94409e8	+	6.56370e8i	−0.741487	+	0.984386i
$333$			2.00650e9i			2.97773i
$334$	−8.19527e8	−	2.74121e8i	−1.20351	−	0.402559i
$335$	−3.30578e8			−0.480416
$336$	−5.51507e8	+	1.58376e8i	−0.793164	+	0.227772i
$337$			6.30434e8i			0.897294i	0.893709	+	0.448647i	$0.148094\pi$
$337$			6.30434e8i			0.897294i	−0.893709	+	0.448647i	$0.851906\pi$
$338$	1.20222e9	+	4.02128e8i	1.69347	+	0.566442i
$339$			1.13166e9i			1.57768i
$340$	−1.44390e8	−	1.08761e8i	−0.199232	−	0.150071i
$341$		−	2.30059e9i		−	3.14195i
$342$	−1.30974e9	−	6.55313e8i	−1.77050	−	0.885844i
$343$			6.32910e8i			0.846862i
$344$	3.26510e8	−	2.24545e8i	0.432455	−	0.297405i
$345$			9.17751e8i			1.20326i
$346$	−1.07345e8	+	3.20925e8i	−0.139321	+	0.416522i
$347$			3.17451e8i			0.407872i	0.978984	+	0.203936i	$0.0653734\pi$
$347$			3.17451e8i			0.407872i	−0.978984	+	0.203936i	$0.934627\pi$
$348$	9.09478e8	−	1.20741e9i	1.15682	−	1.53577i
$349$	−2.73637e7			−0.0344576			−0.0172288	−	0.999852i	$-0.505484\pi$
$349$	−2.73637e7			−0.0344576			−0.0172288	+	0.999852i	$0.505484\pi$
$350$	−7.41046e7	+	2.21547e8i	−0.0923862	+	0.276203i
$351$		−	2.28687e9i		−	2.82272i
$352$	−1.30658e9	−	5.64062e7i	−1.59675	−	0.0689331i
$353$	−1.23682e9			−1.49656			−0.748279	−	0.663384i	$-0.769120\pi$
$353$	−1.23682e9			−1.49656			−0.748279	+	0.663384i	$0.769120\pi$
$354$	9.65898e8	+	3.23080e8i	1.15723	+	0.387078i
$355$	2.41748e8			0.286789
$356$	3.41244e8	−	4.53031e8i	0.400858	−	0.532173i
$357$		−	2.83069e8i		−	0.329271i
$358$	1.35920e9	+	4.54633e8i	1.56564	+	0.523685i
$359$			6.80582e8i			0.776336i	0.921589	+	0.388168i	$0.126892\pi$
$359$			6.80582e8i			0.776336i	−0.921589	+	0.388168i	$0.873108\pi$
$360$	−6.20790e8	−	9.02688e8i	−0.701271	−	1.01971i
$361$	8.58501e8	+	2.48965e8i	0.960429	+	0.278524i
$362$	3.56385e8	−	1.06547e9i	0.394856	−	1.18049i
$363$	−2.44520e9			−2.68312
$364$	5.86428e8	+	4.41726e8i	0.637324	+	0.480062i
$365$	−6.09365e8			−0.655922
$366$	1.26900e8	+	4.24464e7i	0.135294	+	0.0452540i
$367$		−	4.24684e8i		−	0.448471i	−0.974535	−	0.224236i	$-0.928011\pi$
$367$		−	4.24684e8i		−	0.448471i	0.974535	−	0.224236i	$-0.0719885\pi$
$368$	−1.02463e9	+	2.94240e8i	−1.07176	+	0.307776i
$369$		−	3.82721e7i		−	0.0396543i
$370$	2.90600e8	−	8.68795e8i	0.298257	−	0.891685i
$371$	3.27763e8			0.333235
$372$	2.69129e9	+	2.02721e9i	2.71057	+	2.04173i
$373$			1.76392e9i			1.75994i	0.475030	+	0.879970i	$0.342437\pi$
$373$			1.76392e9i			1.75994i	−0.475030	+	0.879970i	$0.657563\pi$
$374$	2.04656e8	−	6.11850e8i	0.202289	−	0.604776i
$375$	−1.77329e9			−1.73648
$376$	4.10561e8	−	2.82349e8i	0.398310	−	0.273923i
$377$	−1.93413e9			−1.85905
$378$	2.69310e8	−	8.05145e8i	0.256467	−	0.766748i
$379$	1.01165e9			0.954538			0.477269	−	0.878757i	$-0.341627\pi$
$379$	1.01165e9			0.954538			0.477269	+	0.878757i	$0.341627\pi$
$380$	4.72197e8	+	4.73433e8i	0.441449	+	0.442605i
$381$	−5.97617e8			−0.553587
$382$	−1.68222e8	+	5.02927e8i	−0.154405	+	0.461618i
$383$	−6.12574e8			−0.557138			−0.278569	−	0.960416i	$-0.589860\pi$
$383$	−6.12574e8			−0.557138			−0.278569	+	0.960416i	$0.589860\pi$
$384$	1.21730e9	−	1.47877e9i	1.09708	−	1.33272i
$385$	5.34809e8			0.477624
$386$	3.93355e7	−	1.17600e8i	0.0348120	−	0.104076i
$387$			1.18476e9i			1.03907i
$388$	3.22954e8	−	4.28748e8i	0.280691	−	0.372642i
$389$	1.28709e9			1.10863			0.554314	−	0.832308i	$-0.312981\pi$
$389$	1.28709e9			1.10863			0.554314	+	0.832308i	$0.312981\pi$
$390$	−6.69261e8	+	2.00086e9i	−0.571307	+	1.70801i
$391$		−	5.25904e8i		−	0.444926i
$392$	−5.21348e8	−	7.58090e8i	−0.437146	−	0.635652i
$393$		−	2.57323e9i		−	2.13848i
$394$	−1.71484e9	−	5.73590e8i	−1.41249	−	0.472460i
$395$	3.84189e8			0.313657
$396$	2.35252e9	−	3.12317e9i	1.90371	−	2.52733i
$397$	−1.78398e8			−0.143094			−0.0715472	−	0.997437i	$-0.522794\pi$
$397$	−1.78398e8			−0.143094			−0.0715472	+	0.997437i	$0.522794\pi$
$398$	7.05913e7	−	2.11044e8i	0.0561256	−	0.167796i
$399$	−1.47281e8	+	1.03666e9i	−0.116076	+	0.817017i
$400$	−2.15237e8	−	7.49514e8i	−0.168154	−	0.585558i
$401$			8.12800e8i			0.629475i	0.949179	+	0.314737i	$0.101916\pi$
$401$			8.12800e8i			0.629475i	−0.949179	+	0.314737i	$0.898084\pi$
$402$	1.63872e9	+	5.48129e8i	1.25809	+	0.420816i
$403$		−	4.31114e9i		−	3.28114i
$404$	5.22647e8	+	3.93682e8i	0.394342	+	0.297037i
$405$	7.85265e8			0.587386
$406$	−6.80955e8	−	2.27770e8i	−0.504984	−	0.168910i
$407$	3.26962e9			2.40391
$408$	5.35422e8	+	7.78554e8i	0.390288	+	0.567516i
$409$		−	1.90940e9i		−	1.37996i	−0.723829	−	0.689979i	$-0.757620\pi$
$409$		−	1.90940e9i		−	1.37996i	0.723829	−	0.689979i	$-0.242380\pi$
$410$	−5.54293e6	+	1.65714e7i	−0.00397188	+	0.0118745i
$411$	1.32908e9			0.944292
$412$	−1.16534e9	−	8.77789e8i	−0.820942	−	0.618372i
$413$		−	4.83800e8i		−	0.337941i
$414$	1.01103e9	−	3.02263e9i	0.700266	−	2.09355i
$415$			1.12172e9i			0.770402i
$416$	−2.44844e9	−	1.05701e8i	−1.66749	−	0.0719868i
$417$			3.45552e9i			2.33366i
$418$	−1.06784e9	+	2.13425e9i	−0.715138	+	1.42931i
$419$			2.87932e9i			1.91223i	0.292989	+	0.956116i	$0.405350\pi$
$419$			2.87932e9i			1.91223i	−0.292989	+	0.956116i	$0.594650\pi$
$420$	−4.71256e8	+	6.25633e8i	−0.310374	+	0.412047i
$421$			8.50916e6i			0.00555775i	0.999996	+	0.00277888i	$0.000884545\pi$
$421$			8.50916e6i			0.00555775i	−0.999996	+	0.00277888i	$0.999115\pi$
$422$	1.65755e9	+	5.54428e8i	1.07368	+	0.359130i
$423$			1.48975e9i			0.957025i
$424$	−9.01481e8	+	6.19961e8i	−0.574349	+	0.394988i
$425$	3.84699e8			0.243086
$426$	−1.19837e9	−	4.00840e8i	−0.751033	−	0.251210i
$427$		−	6.35619e7i		−	0.0395093i
$428$	2.78505e8	+	2.09783e8i	0.171704	+	0.129335i
$429$	−7.53004e9			−4.60465
$430$	1.71589e8	−	5.12991e8i	0.104076	−	0.311150i
$431$	2.75091e9			1.65503			0.827516	−	0.561442i	$-0.189753\pi$
$431$	2.75091e9			1.65503			0.827516	+	0.561442i	$0.189753\pi$
$432$	7.82212e8	+	2.72387e9i	0.466800	+	1.62553i
$433$		−	2.82061e9i		−	1.66969i	−0.550489	−	0.834843i	$-0.685559\pi$
$433$		−	2.82061e9i		−	1.66969i	0.550489	−	0.834843i	$-0.314441\pi$
$434$	5.07695e8	−	1.51783e9i	0.298118	−	0.891271i
$435$		−	2.06344e9i		−	1.20193i
$436$	−1.13312e9	+	1.50431e9i	−0.654745	+	0.869229i
$437$	−2.73629e8	+	1.92597e9i	−0.156847	+	1.10399i
$438$	3.02070e9	+	1.01038e9i	1.71770	+	0.574549i
$439$	1.24929e9			0.704753			0.352377	−	0.935858i	$-0.385374\pi$
$439$	1.24929e9			0.704753			0.352377	+	0.935858i	$0.385374\pi$
$440$	−1.47094e9	+	1.01159e9i	−0.823211	+	0.566133i
$441$	2.75079e9			1.52729
$442$	3.83510e8	−	1.14656e9i	0.211251	−	0.631568i
$443$		−	1.03219e8i		−	0.0564087i	−0.999602	−	0.0282044i	$-0.991021\pi$
$443$		−	1.03219e8i		−	0.0564087i	0.999602	−	0.0282044i	$-0.00897892\pi$
$444$	−2.88109e9	+	3.82489e9i	−1.56213	+	2.07385i
$445$		−	7.74220e8i		−	0.416490i
$446$	6.62252e7	+	2.21514e7i	0.0353469	+	0.0118231i
$447$	3.77944e8			0.200148
$448$	−8.49579e8	−	3.25551e8i	−0.446407	−	0.171059i
$449$		−	2.40138e9i		−	1.25198i	−0.779829	−	0.625992i	$-0.784694\pi$
$449$		−	2.40138e9i		−	1.25198i	0.779829	−	0.625992i	$-0.215306\pi$
$450$	2.21106e9	+	7.39569e8i	1.14382	+	0.382591i
$451$	−6.23650e7			−0.0320128
$452$	−1.07960e9	+	1.43327e9i	−0.549895	+	0.730032i
$453$	−3.60859e9			−1.82387
$454$	1.69177e9	+	5.65875e8i	0.848489	+	0.283808i
$455$	1.00219e9			0.498783
$456$	−1.55575e9	−	3.12982e9i	−0.768355	−	1.54576i
$457$	−3.27255e9			−1.60391			−0.801954	−	0.597385i	$-0.796206\pi$
$457$	−3.27255e9			−1.60391			−0.801954	+	0.597385i	$0.796206\pi$
$458$	3.11265e8	+	1.04114e8i	0.151391	+	0.0506384i
$459$	−1.39807e9			−0.674813
$460$	−8.75531e8	+	1.16234e9i	−0.419391	+	0.556777i
$461$	−2.43333e9			−1.15677			−0.578386	−	0.815763i	$-0.696317\pi$
$461$	−2.43333e9			−1.15677			−0.578386	+	0.815763i	$0.696317\pi$
$462$	−2.65112e9	−	8.86763e8i	−1.25078	−	0.418370i
$463$			1.71546e9i			0.803243i	0.915806	+	0.401621i	$0.131553\pi$
$463$			1.71546e9i			0.803243i	−0.915806	+	0.401621i	$0.868447\pi$
$464$	2.30373e9	−	6.61559e8i	1.07058	−	0.307437i
$465$	4.59935e9			2.12135
$466$	1.54373e9	+	5.16358e8i	0.706677	+	0.236374i
$467$			2.93745e9i			1.33463i	0.744776	+	0.667315i	$0.232556\pi$
$467$			2.93745e9i			1.33463i	−0.744776	+	0.667315i	$0.767444\pi$
$468$	4.40845e9	−	5.85259e9i	1.98804	−	2.63929i
$469$		−	8.20803e8i		−	0.367396i
$470$	2.15760e8	−	6.45048e8i	0.0958580	−	0.286582i
$471$	2.30185e9			1.01509
$472$	9.15103e8	+	1.33065e9i	0.400565	+	0.582459i
$473$	1.93059e9			0.838834
$474$	−1.90448e9	−	6.37022e8i	−0.821394	−	0.274745i
$475$	−1.40885e9	−	2.00160e8i	−0.603167	−	0.0856938i
$476$	2.70046e8	−	3.58510e8i	0.114766	−	0.152362i
$477$		−	3.27109e9i		−	1.38000i
$478$	5.01129e7	−	1.49820e8i	0.0209871	−	0.0627442i
$479$		−	1.10272e9i		−	0.458448i	−0.973374	−	0.229224i	$-0.926381\pi$
$479$		−	1.10272e9i		−	0.458448i	0.973374	−	0.229224i	$-0.0736189\pi$
$480$	1.12768e8	−	2.61212e9i	0.0465415	−	1.07808i
$481$	6.12704e9			2.51040
$482$	−7.76529e8	+	2.32156e9i	−0.315859	+	0.944310i
$483$	−2.27872e9			−0.920185
$484$	−3.09687e9	−	2.33271e9i	−1.24155	−	0.935194i
$485$		−	7.32722e8i		−	0.291637i
$486$	1.66150e8	+	5.55749e7i	0.0656558	+	0.0219610i
$487$	1.23453e9			0.484339			0.242169	−	0.970234i	$-0.422141\pi$
$487$	1.23453e9			0.484339			0.242169	+	0.970234i	$0.422141\pi$
$488$	1.20227e8	+	1.74821e8i	0.0468308	+	0.0680964i
$489$			6.37707e9i			2.46627i
$490$	−1.19106e9	−	3.98394e8i	−0.457350	−	0.152977i
$491$		−	2.40544e9i		−	0.917084i	−0.888673	−	0.458542i	$-0.848372\pi$
$491$		−	2.40544e9i		−	0.917084i	0.888673	−	0.458542i	$-0.151628\pi$
$492$	5.49540e7	−	7.29561e7i	0.0208028	−	0.0276175i
$493$			1.18242e9i			0.444435i
$494$	−2.00106e9	+	3.99942e9i	−0.746818	+	1.49263i
$495$		−	5.33743e9i		−	1.97794i
$496$	1.47460e9	+	5.13496e9i	0.542611	+	1.88952i
$497$			6.00243e8i			0.219321i
$498$	1.85992e9	−	5.56053e9i	0.674826	−	2.01750i
$499$			3.18232e9i			1.14655i	0.819364	+	0.573273i	$0.194327\pi$
$499$			3.18232e9i			1.14655i	−0.819364	+	0.573273i	$0.805673\pi$
$500$	−2.24589e9	−	1.69171e9i	−0.803514	−	0.605244i
$501$	6.16597e9			2.19063
$502$	5.85680e8	−	1.75098e9i	0.206632	−	0.617758i
$503$		−	1.18862e9i		−	0.416442i	−0.978082	−	0.208221i	$-0.933233\pi$
$503$		−	1.18862e9i		−	0.416442i	0.978082	−	0.208221i	$-0.0667674\pi$
$504$	2.24131e9	−	1.54138e9i	0.779822	−	0.536294i
$505$	8.93192e8			0.308621
$506$	−4.92542e9	−	1.64749e9i	−1.69012	−	0.565321i
$507$	−9.04530e9			−3.08244
$508$	−7.56888e8	−	5.70124e8i	−0.256159	−	0.192951i
$509$			1.58013e9i			0.531105i	0.964096	+	0.265552i	$0.0855543\pi$
$509$			1.58013e9i			0.531105i	−0.964096	+	0.265552i	$0.914446\pi$
$510$	1.22321e9	+	4.09149e8i	0.408326	+	0.136580i
$511$		−	1.51301e9i		−	0.501614i
$512$	2.95246e9	−	7.11573e8i	0.972164	−	0.234301i
$513$	5.12003e9	+	7.27418e8i	1.67441	+	0.237888i
$514$	3.53793e8	−	1.05772e9i	0.114916	−	0.343558i
$515$	−1.99154e9			−0.642487
$516$	−1.70117e9	+	2.25845e9i	−0.545098	+	0.723664i
$517$	2.42757e9			0.772602
$518$	2.15716e9	+	7.21541e8i	0.681912	+	0.228090i
$519$		−	2.41458e9i		−	0.758152i
$520$	−2.75644e9	+	1.89564e9i	−0.859680	+	0.591213i
$521$		−	2.79877e8i		−	0.0867033i	−0.999060	−	0.0433517i	$-0.986196\pi$
$521$		−	2.79877e8i		−	0.0867033i	0.999060	−	0.0433517i	$-0.0138036\pi$
$522$	−2.27316e9	+	6.79597e9i	−0.699493	+	2.09124i
$523$	−3.46973e9			−1.06057			−0.530285	−	0.847819i	$-0.677915\pi$
$523$	−3.46973e9			−1.06057			−0.530285	+	0.847819i	$0.677915\pi$
$524$	2.45485e9	−	3.25902e9i	0.745359	−	0.989527i
$525$		−	1.66688e9i		−	0.502744i
$526$	−1.63432e9	+	4.88606e9i	−0.489652	+	1.46389i
$527$	−2.63559e9			−0.784406
$528$	8.96896e9	−	2.57561e9i	2.65169	−	0.761484i
$529$	−8.28722e8			−0.243396
$530$	−4.73750e8	+	1.41635e9i	−0.138224	+	0.413243i
$531$	−4.82835e9			−1.39948
$532$	−1.17550e9	+	1.17243e9i	−0.338480	+	0.337596i
$533$	−1.16867e8			−0.0334309
$534$	−1.28373e9	+	3.83791e9i	−0.364820	+	1.09069i
$535$	4.75959e8			0.134379
$536$	1.55254e9	+	2.25754e9i	0.435478	+	0.633227i
$537$	−1.02263e10			−2.84977
$538$	−1.35313e9	+	4.04538e9i	−0.374628	+	1.12001i
$539$		−	4.48245e9i		−	1.23298i
$540$	3.08998e9	+	2.32752e9i	0.844457	+	0.636085i
$541$	8.61411e8			0.233894			0.116947	−	0.993138i	$-0.462689\pi$
$541$	8.61411e8			0.233894			0.116947	+	0.993138i	$0.462689\pi$
$542$	1.65271e9	−	4.94104e9i	0.445861	−	1.33297i
$543$			8.01638e9i			2.14872i
$544$	−6.46198e7	+	1.49684e9i	−0.0172095	+	0.398638i
$545$			2.57083e9i			0.680277i
$546$	−4.96800e9	−	1.66173e9i	−1.30619	−	0.436904i
$547$	6.55615e9			1.71275			0.856374	−	0.516356i	$-0.172712\pi$
$547$	6.55615e9			1.71275			0.856374	+	0.516356i	$0.172712\pi$
$548$	1.68330e9	+	1.26794e9i	0.436948	+	0.329130i
$549$	−6.34352e8			−0.163616
$550$	1.20514e9	−	3.60295e9i	0.308864	−	0.923397i
$551$	6.15217e8	−	4.33029e9i	0.156674	−	1.10277i
$552$	6.26739e9	−	4.31017e9i	1.58599	−	1.09071i
$553$			9.53917e8i			0.239868i
$554$	−3.63048e9	−	1.21435e9i	−0.907153	−	0.303430i
$555$			6.53665e9i			1.62304i
$556$	−3.29656e9	+	4.37646e9i	−0.813390	+	1.07984i
$557$	1.45384e9			0.356470			0.178235	−	0.983988i	$-0.442961\pi$
$557$	1.45384e9			0.356470			0.178235	+	0.983988i	$0.442961\pi$
$558$	−1.51481e10	−	5.06682e9i	−3.69094	−	1.23457i
$559$	3.61779e9			0.875995
$560$	−1.19370e9	+	3.42794e8i	−0.287236	+	0.0824851i
$561$			4.60345e9i			1.10081i
$562$	1.05877e9	−	3.16537e9i	0.251609	−	0.752225i
$563$	3.88281e9			0.916995			0.458497	−	0.888696i	$-0.348388\pi$
$563$	3.88281e9			0.916995			0.458497	+	0.888696i	$0.348388\pi$
$564$	−2.13910e9	+	2.83984e9i	−0.502058	+	0.666525i
$565$			2.44942e9i			0.571339i
$566$	−1.54479e9	+	4.61840e9i	−0.358107	+	1.07062i
$567$			1.94976e9i			0.449201i
$568$	−1.13535e9	−	1.65091e9i	−0.259963	−	0.378011i
$569$		−	5.01129e9i		−	1.14040i	−0.821506	−	0.570200i	$-0.806866\pi$
$569$		−	5.01129e9i		−	1.14040i	0.821506	−	0.570200i	$-0.193134\pi$
$570$	−4.26680e9	−	2.13483e9i	−0.965028	−	0.482839i
$571$		−	1.00894e9i		−	0.226799i	−0.993549	−	0.113399i	$-0.963826\pi$
$571$		−	1.00894e9i		−	0.226799i	0.993549	−	0.113399i	$-0.0361739\pi$
$572$	−9.53687e9	−	7.18362e9i	−2.13069	−	1.60494i
$573$		−	3.78393e9i		−	0.840236i
$574$	−4.11458e7	−	1.37627e7i	−0.00908101	−	0.00303747i
$575$		−	3.09684e9i		−	0.679331i
$576$	−3.24902e9	+	8.47885e9i	−0.708391	+	1.84866i
$577$	4.04131e9			0.875805			0.437902	−	0.899023i	$-0.355722\pi$
$577$	4.04131e9			0.875805			0.437902	+	0.899023i	$0.355722\pi$
$578$	3.70175e9	+	1.23818e9i	0.797369	+	0.266709i
$579$			8.84798e8i			0.189439i
$580$	1.96851e9	−	2.61337e9i	0.418929	−	0.556163i
$581$	−2.78516e9			−0.589161
$582$	−1.21492e9	+	3.63220e9i	−0.255457	+	0.763728i
$583$	−5.33029e9			−1.11407
$584$	2.86185e9	+	4.16140e9i	0.594568	+	0.864559i
$585$		−	1.00019e10i		−	2.06557i
$586$	7.65160e8	−	2.28757e9i	0.157076	−	0.469604i
$587$			5.50071e9i			1.12250i	0.827647	+	0.561249i	$0.189679\pi$
$587$			5.50071e9i			1.12250i	−0.827647	+	0.561249i	$0.810321\pi$
$588$	5.24368e9	+	3.94979e9i	1.06369	+	0.801222i
$589$	9.65211e9	+	1.37131e9i	1.94634	+	0.276523i
$590$	2.09063e9	+	6.99287e8i	0.419078	+	0.140176i
$591$	1.29021e10			2.57102
$592$	−7.29785e9	+	2.09572e9i	−1.44567	+	0.415152i
$593$	1.50668e9			0.296709			0.148354	−	0.988934i	$-0.452602\pi$
$593$	1.50668e9			0.296709			0.148354	+	0.988934i	$0.452602\pi$
$594$	−4.37969e9	+	1.30938e10i	−0.857415	+	2.56338i
$595$		−	6.12685e8i		−	0.119242i
$596$	4.78670e8	+	3.60557e8i	0.0926134	+	0.0697608i
$597$			1.58785e9i			0.305422i
$598$	−9.22988e9	−	3.08727e9i	−1.76499	−	0.590365i
$599$	8.12364e8			0.154439			0.0772195	−	0.997014i	$-0.475396\pi$
$599$	8.12364e8			0.154439			0.0772195	+	0.997014i	$0.475396\pi$
$600$	3.15289e9	+	4.58460e9i	0.595908	+	0.866507i
$601$		−	1.65521e9i		−	0.311023i	−0.987834	−	0.155512i	$-0.950297\pi$
$601$		−	1.65521e9i		−	0.311023i	0.987834	−	0.155512i	$-0.0497026\pi$
$602$	1.27372e9	+	4.26043e8i	0.237951	+	0.0795913i
$603$	−8.19166e9			−1.52146
$604$	−4.57032e9	−	3.44258e9i	−0.843952	−	0.635704i
$605$	−5.29248e9			−0.971663
$606$	−4.42767e9	−	1.48100e9i	−0.808204	−	0.270333i
$607$	2.76198e9			0.501256			0.250628	−	0.968083i	$-0.419363\pi$
$607$	2.76198e9			0.501256			0.250628	+	0.968083i	$0.419363\pi$
$608$	1.01546e9	−	5.44812e9i	0.183232	−	0.983070i
$609$	5.12338e9			0.919170
$610$	2.74668e8	+	9.18727e7i	0.0489952	+	0.0163882i
$611$	4.54910e9			0.806828
$612$	−3.57795e9	−	2.69508e9i	−0.630963	−	0.475271i
$613$	−2.58095e8			−0.0452551			−0.0226275	−	0.999744i	$-0.507203\pi$
$613$	−2.58095e8			−0.0452551			−0.0226275	+	0.999744i	$0.507203\pi$
$614$	4.84203e9	+	1.61959e9i	0.844187	+	0.282369i
$615$		−	1.24680e8i		−	0.0216140i
$616$	−2.51170e9	−	3.65225e9i	−0.432948	−	0.629547i
$617$	7.52149e9			1.28916			0.644578	−	0.764538i	$-0.277033\pi$
$617$	7.52149e9			1.28916			0.644578	+	0.764538i	$0.277033\pi$
$618$	9.87233e9	+	3.30216e9i	1.68252	+	0.562780i
$619$		−	4.82597e9i		−	0.817837i	−0.912571	−	0.408919i	$-0.865906\pi$
$619$		−	4.82597e9i		−	0.817837i	0.912571	−	0.408919i	$-0.134094\pi$
$620$	5.82513e9	+	4.38777e9i	0.981601	+	0.739388i
$621$			1.12545e10i			1.88584i
$622$	−2.55352e9	+	7.63416e9i	−0.425475	+	1.27202i
$623$	1.92234e9			0.318509
$624$	1.68072e10	−	4.82650e9i	2.76916	−	0.795218i
$625$	−1.19769e8			−0.0196230
$626$	−9.29229e9	−	3.10815e9i	−1.51395	−	0.506397i
$627$	2.39519e9	−	1.68588e10i	0.388063	−	2.73143i
$628$	2.91532e9	+	2.19595e9i	0.469707	+	0.353806i
$629$		−	3.74573e9i		−	0.600149i
$630$	1.17786e9	−	3.52141e9i	0.187674	−	0.561080i
$631$		−	4.83003e9i		−	0.765328i	−0.923888	−	0.382664i	$-0.875007\pi$
$631$		−	4.83003e9i		−	0.765328i	0.923888	−	0.382664i	$-0.124993\pi$
$632$	−1.80432e9	−	2.62366e9i	−0.284318	−	0.413426i
$633$	−1.24711e10			−1.95430
$634$	−3.07576e7	+	9.19545e7i	−0.00479335	+	0.0143305i
$635$	−1.29351e9			−0.200475
$636$	4.69688e9	−	6.23551e9i	0.723952	−	0.961108i
$637$		−	8.39978e9i		−	1.28760i
$638$	1.10741e10	+	3.70415e9i	1.68825	+	0.564698i
$639$	5.99046e9			0.908254
$640$	2.63478e9	−	3.20070e9i	0.397296	−	0.482631i
$641$		−	1.16510e10i		−	1.74727i	−0.486584	−	0.873634i	$-0.661757\pi$
$641$		−	1.16510e10i		−	1.74727i	0.486584	−	0.873634i	$-0.338243\pi$
$642$	−2.35939e9	−	7.89184e8i	−0.351906	−	0.117708i
$643$			6.75964e9i			1.00273i	0.865235	+	0.501367i	$0.167169\pi$
$643$			6.75964e9i			1.00273i	−0.865235	+	0.501367i	$0.832831\pi$
$644$	−2.88602e9	−	2.17389e9i	−0.425793	−	0.320727i
$645$			3.85965e9i			0.566355i
$646$	2.44502e9	+	1.22333e9i	0.356837	+	0.178538i
$647$			3.07191e9i			0.445906i	0.974829	+	0.222953i	$0.0715696\pi$
$647$			3.07191e9i			0.445906i	−0.974829	+	0.222953i	$0.928430\pi$
$648$	−3.68795e9	−	5.36263e9i	−0.532443	−	0.774222i
$649$			7.86787e9i			1.12980i
$650$	2.25834e9	−	6.75166e9i	0.322547	−	0.964304i
$651$			1.14199e10i			1.62229i
$652$	−6.08370e9	+	8.07663e9i	−0.859609	+	1.14120i
$653$	−4.48572e9			−0.630428			−0.315214	−	0.949021i	$-0.602076\pi$
$653$	−4.48572e9			−0.630428			−0.315214	+	0.949021i	$0.602076\pi$
$654$	4.26268e9	−	1.27439e10i	0.595882	−	1.78148i
$655$		−	5.56960e9i		−	0.774425i
$656$	1.39200e8	−	3.99738e7i	0.0192520	−	0.00552856i
$657$	−1.51000e10			−2.07729
$658$	1.60161e9	+	5.35717e8i	0.219163	+	0.0733070i
$659$	−2.84984e9			−0.387902			−0.193951	−	0.981011i	$-0.562130\pi$
$659$	−2.84984e9			−0.387902			−0.193951	+	0.981011i	$0.562130\pi$
$660$	7.66388e9	−	1.01744e10i	1.03764	−	1.37755i
$661$			4.65454e9i			0.626862i	0.949611	+	0.313431i	$0.101478\pi$
$661$			4.65454e9i			0.626862i	−0.949611	+	0.313431i	$0.898522\pi$
$662$	3.94150e9	+	1.31838e9i	0.528029	+	0.176619i
$663$			8.62652e9i			1.14958i
$664$	7.66033e9	−	5.26811e9i	1.01545	−	0.698339i
$665$	−3.18782e8	+	2.24379e9i	−0.0420356	+	0.295873i
$666$	7.20102e9	−	2.15286e10i	0.944570	−	2.82394i
$667$	9.51855e9			1.24202
$668$	7.80927e9	+	5.88231e9i	1.01366	+	0.763537i
$669$	−4.98266e8			−0.0643383
$670$	3.54691e9	+	1.18639e9i	0.455604	+	0.152394i
$671$			1.03368e9i			0.132087i
$672$	6.48572e9	+	2.79995e8i	0.824453	+	0.0355924i
$673$		−	1.41820e10i		−	1.79344i	−0.442603	−	0.896718i	$-0.645945\pi$
$673$		−	1.41820e10i		−	1.79344i	0.442603	−	0.896718i	$-0.354055\pi$
$674$	2.26253e9	−	6.76418e9i	0.284632	−	0.850953i
$675$	−8.23267e9			−1.03033
$676$	−1.14560e10	−	8.62918e9i	−1.42633	−	1.07438i
$677$			2.87259e9i			0.355807i	0.984048	+	0.177903i	$0.0569314\pi$
$677$			2.87259e9i			0.355807i	−0.984048	+	0.177903i	$0.943069\pi$
$678$	4.06137e9	−	1.21421e10i	0.500459	−	1.49620i
$679$	1.81930e9			0.223028
$680$	1.15889e9	+	1.68513e9i	0.141338	+	0.205520i
$681$	−1.27286e10			−1.54442
$682$	−8.25646e9	+	2.46840e10i	−0.996663	+	2.97968i
$683$	−1.43911e10			−1.72830			−0.864152	−	0.503231i	$-0.832145\pi$
$683$	−1.43911e10			−1.72830			−0.864152	+	0.503231i	$0.832145\pi$
$684$	1.17010e10	+	1.17316e10i	1.39806	+	1.40172i
$685$	2.87672e9			0.341964
$686$	2.27141e9	−	6.79075e9i	0.268635	−	0.803125i
$687$	−2.34190e9			−0.275562
$688$	−4.30911e9	+	1.23744e9i	−0.504462	+	0.144866i
$689$	−9.98858e9			−1.16342
$690$	3.29367e9	−	9.84693e9i	0.381687	−	1.14111i
$691$		−	1.89341e9i		−	0.218309i	−0.994025	−	0.109154i	$-0.965186\pi$
$691$		−	1.89341e9i		−	0.218309i	0.994025	−	0.109154i	$-0.0348143\pi$
$692$	2.30350e9	−	3.05809e9i	0.264251	−	0.350816i
$693$	1.32525e10			1.51262
$694$	1.13928e9	−	3.40606e9i	0.129382	−	0.386807i
$695$			7.47927e9i			0.845109i
$696$	−1.40914e10	+	9.69082e9i	−1.58424	+	1.08950i
$697$			7.14463e7i			0.00799217i
$698$	2.93596e8	+	9.82039e7i	0.0326780	+	0.0109304i
$699$	−1.16147e10			−1.28629
$700$	1.59020e9	−	2.11112e9i	0.175230	−	0.232633i
$701$	−7.23446e9			−0.793219			−0.396610	−	0.917987i	$-0.629813\pi$
$701$	−7.23446e9			−0.793219			−0.396610	+	0.917987i	$0.629813\pi$
$702$	−8.20723e9	+	2.45368e10i	−0.895399	+	2.67694i
$703$	−1.94891e9	+	1.37177e10i	−0.211567	+	1.48914i
$704$	1.38164e10	+	5.29432e9i	1.49242	+	0.571881i
$705$			4.85322e9i			0.521637i
$706$	1.32703e10	+	4.43874e9i	1.41927	+	0.474726i
$707$			2.21774e9i			0.236016i
$708$	−9.20403e9	−	6.93291e9i	−0.974679	−	0.734174i
$709$	1.10926e10			1.16888			0.584440	−	0.811437i	$-0.301314\pi$
$709$	1.10926e10			1.16888			0.584440	+	0.811437i	$0.301314\pi$
$710$	−2.59381e9	−	8.67594e8i	−0.271978	−	0.0909730i
$711$	9.52014e9			0.993344
$712$	−5.28721e9	+	3.63608e9i	−0.548967	+	0.377532i
$713$			2.12166e10i			2.19211i
$714$	−1.01589e9	+	3.03716e9i	−0.104449	+	0.312265i
$715$	−1.62983e10			−1.66752
$716$	−1.29518e10	−	9.75588e9i	−1.31866	−	0.993278i
$717$			1.12722e9i			0.114207i
$718$	2.44250e9	−	7.30224e9i	0.246263	−	0.736242i
$719$		−	4.22446e9i		−	0.423858i	−0.977285	−	0.211929i	$-0.932025\pi$
$719$		−	4.22446e9i		−	0.423858i	0.977285	−	0.211929i	$-0.0679745\pi$
$720$	3.42111e9	+	1.19132e10i	0.341588	+	1.18950i
$721$		−	4.94486e9i		−	0.491339i
$722$	−8.31771e9	−	5.75227e9i	−0.822476	−	0.568799i
$723$		−	1.74670e10i		−	1.71883i
$724$	−7.64760e9	+	1.01528e10i	−0.748928	+	0.994265i
$725$			6.96282e9i			0.678582i
$726$	2.62355e10	+	8.77543e9i	2.54455	+	0.851119i
$727$		−	1.07254e10i		−	1.03525i	−0.855608	−	0.517624i	$-0.826816\pi$
$727$		−	1.07254e10i		−	1.03525i	0.855608	−	0.517624i	$-0.173184\pi$
$728$	−4.70674e9	−	6.84405e9i	−0.452127	−	0.657436i
$729$	−1.10790e10			−1.05914
$730$	6.53813e9	+	2.18692e9i	0.622047	+	0.208066i
$731$		−	2.21171e9i		−	0.209420i
$732$	−1.20923e9	−	9.10849e8i	−0.113952	−	0.0858337i
$733$	−1.43068e10			−1.34177			−0.670887	−	0.741560i	$-0.734086\pi$
$733$	−1.43068e10			−1.34177			−0.670887	+	0.741560i	$0.734086\pi$
$734$	−1.52412e9	+	4.55661e9i	−0.142260	+	0.425310i
$735$	8.96133e9			0.832467
$736$	1.20496e10	+	5.20192e8i	1.11404	+	0.0480941i
$737$			1.33484e10i			1.22827i
$738$	−1.37353e8	+	4.10638e8i	−0.0125788	+	0.0376064i
$739$		−	9.22564e8i		−	0.0840893i	−0.999116	−	0.0420447i	$-0.986613\pi$
$739$		−	9.22564e8i		−	0.0840893i	0.999116	−	0.0420447i	$-0.0133872\pi$
$740$	−6.23594e9	+	8.27874e9i	−0.565706	+	0.751023i
$741$	4.48840e9	−	3.15922e10i	0.405255	−	2.85244i
$742$	−3.51670e9	−	1.17629e9i	−0.316025	−	0.105706i
$743$	−6.09352e9			−0.545014			−0.272507	−	0.962154i	$-0.587853\pi$
$743$	−6.09352e9			−0.545014			−0.272507	+	0.962154i	$0.587853\pi$
$744$	−2.16006e10	−	3.14093e10i	−1.92292	−	2.79611i
$745$	8.18036e8			0.0724812
$746$	6.33043e9	−	1.89258e10i	0.558274	−	1.66905i
$747$			2.77961e10i			2.43984i
$748$	−4.39167e9	+	5.83031e9i	−0.383684	+	0.509374i
$749$			1.18177e9i			0.102766i
$750$	1.90263e10	+	6.36405e9i	1.64680	+	0.550832i
$751$	1.55373e10			1.33855			0.669277	−	0.743013i	$-0.266604\pi$
$751$	1.55373e10			1.33855			0.669277	+	0.743013i	$0.266604\pi$
$752$	−5.41839e9	+	1.55599e9i	−0.464630	+	0.133427i
$753$			1.31741e10i			1.12444i
$754$	2.07521e10	+	6.94130e9i	1.76304	+	0.589714i
$755$	−7.81058e9			−0.660494
$756$	−5.77908e9	+	7.67222e9i	−0.486443	+	0.645795i
$757$	2.15314e10			1.80400			0.902000	−	0.431736i	$-0.142099\pi$
$757$	2.15314e10			1.80400			0.902000	+	0.431736i	$0.142099\pi$
$758$	−1.08544e10	−	3.63065e9i	−0.905241	−	0.302791i
$759$	3.70579e10			3.07635
$760$	−3.36732e9	−	6.77430e9i	−0.278251	−	0.559779i
$761$	−1.65643e10			−1.36247			−0.681235	−	0.732065i	$-0.738557\pi$
$761$	−1.65643e10			−1.36247			−0.681235	+	0.732065i	$0.738557\pi$
$762$	6.41208e9	+	2.14475e9i	0.524996	+	0.175604i
$763$	−6.38320e9			−0.520239
$764$	3.60985e9	−	4.79238e9i	0.292862	−	0.388799i
$765$	−6.11463e9			−0.493805
$766$	6.57255e9	+	2.19843e9i	0.528364	+	0.176731i
$767$			1.47438e10i			1.17985i
$768$	−1.83680e10	+	1.14976e10i	−1.46318	+	0.915888i
$769$	1.63976e10			1.30029			0.650143	−	0.759812i	$-0.274709\pi$
$769$	1.63976e10			1.30029			0.650143	+	0.759812i	$0.274709\pi$
$770$	−5.73818e9	−	1.91935e9i	−0.452957	−	0.151508i
$771$			7.95809e9i			0.625343i
$772$	−8.44094e8	+	1.12061e9i	−0.0660283	+	0.0876582i
$773$			1.82410e10i			1.42044i	0.703982	+	0.710218i	$0.251403\pi$
$773$			1.82410e10i			1.42044i	−0.703982	+	0.710218i	$0.748597\pi$
$774$	4.25193e9	−	1.27118e10i	0.329605	−	0.985405i
$775$	−1.55200e10			−1.19766
$776$	−5.00381e9	+	3.44119e9i	−0.384401	+	0.264358i
$777$	−1.62301e10			−1.24121
$778$	−1.38097e10	−	4.61917e9i	−1.05137	−	0.351670i
$779$	3.71737e7	−	2.61652e8i	0.00281744	−	0.0198309i
$780$	1.43615e10	−	1.90662e10i	1.08360	−	1.43857i
$781$		−	9.76154e9i		−	0.733229i
$782$	−1.88739e9	+	5.64264e9i	−0.141136	+	0.421947i
$783$		−	2.53042e10i		−	1.88376i
$784$	2.87309e9	+	1.00049e10i	0.212933	+	0.741492i
$785$	4.98221e9			0.367603
$786$	−9.23491e9	+	2.76092e10i	−0.678350	+	2.02803i
$787$	−1.46967e10			−1.07475			−0.537375	−	0.843344i	$-0.680584\pi$
$787$	−1.46967e10			−1.07475			−0.537375	+	0.843344i	$0.680584\pi$
$788$	1.63407e10	+	1.23086e10i	1.18967	+	0.896119i
$789$		−	3.67618e10i		−	2.66457i
$790$	−4.12212e9	−	1.37880e9i	−0.297458	−	0.0994958i
$791$	−6.08174e9			−0.436929
$792$	−3.64497e10	+	2.50669e10i	−2.60709	+	1.79293i
$793$			1.93705e9i			0.137938i
$794$	1.91410e9	+	6.40241e8i	0.135704	+	0.0453912i
$795$		−	1.06564e10i		−	0.752183i
$796$	−1.51481e9	+	2.01103e9i	−0.106454	+	0.141327i
$797$		−	8.62812e8i		−	0.0603687i	−0.999544	−	0.0301844i	$-0.990391\pi$
$797$		−	8.62812e8i		−	0.0603687i	0.999544	−	0.0301844i	$-0.00960944\pi$
$798$	5.30065e9	−	1.05942e10i	0.369249	−	0.738001i
$799$		−	2.78107e9i		−	0.192885i
$800$	−3.80521e8	+	8.81429e9i	−0.0262763	+	0.608657i
$801$		−	1.91850e10i		−	1.31901i
$802$	2.91701e9	−	8.72086e9i	0.199677	−	0.596965i
$803$			2.46056e10i			1.67699i
$804$	−1.56153e10	−	1.17622e10i	−1.05963	−	0.798165i
$805$	−4.93214e9			−0.333235
$806$	−1.54720e10	+	4.62560e10i	−1.04082	+	3.11168i
$807$		−	3.04367e10i		−	2.03864i
$808$	−4.19483e9	−	6.09968e9i	−0.279753	−	0.406787i
$809$	8.14906e9			0.541112			0.270556	−	0.962704i	$-0.412792\pi$
$809$	8.14906e9			0.541112			0.270556	+	0.962704i	$0.412792\pi$
$810$	−8.42543e9	−	2.81819e9i	−0.557050	−	0.186326i
$811$	1.52110e10			1.00135			0.500674	−	0.865636i	$-0.333085\pi$
$811$	1.52110e10			1.00135			0.500674	+	0.865636i	$0.333085\pi$
$812$	6.48881e9	+	4.88768e9i	0.425323	+	0.320374i
$813$			3.71754e10i			2.42627i
$814$	−3.50811e10	−	1.17342e10i	−2.27975	−	0.762547i
$815$			1.38028e10i			0.893131i
$816$	−2.95065e9	−	1.02750e10i	−0.190109	−	0.662011i
$817$	−1.15076e9	+	8.09978e9i	−0.0738257	+	0.519632i
$818$	−6.85254e9	+	2.04868e10i	−0.437739	+	1.30869i
$819$	2.48342e10			1.57963
$820$	1.18945e8	−	1.57909e8i	0.00753349	−	0.0100014i
$821$	1.45595e9			0.0918220			0.0459110	−	0.998946i	$-0.485381\pi$
$821$	1.45595e9			0.0918220			0.0459110	+	0.998946i	$0.485381\pi$
$822$	−1.42603e10	−	4.76987e9i	−0.895523	−	0.299541i
$823$		−	1.91146e10i		−	1.19527i	−0.801769	−	0.597634i	$-0.796108\pi$
$823$		−	1.91146e10i		−	1.19527i	0.801769	−	0.597634i	$-0.203892\pi$
$824$	9.35316e9	+	1.36004e10i	0.582389	+	0.846849i
$825$			2.71079e10i			1.68076i
$826$	−1.73628e9	+	5.19089e9i	−0.107199	+	0.320488i
$827$	−1.15133e10			−0.707833			−0.353917	−	0.935277i	$-0.615150\pi$
$827$	−1.15133e10			−0.707833			−0.353917	+	0.935277i	$0.615150\pi$
$828$	−2.16955e10	+	2.88026e10i	−1.32820	+	1.76330i
$829$		−	1.23591e10i		−	0.753432i	−0.926329	−	0.376716i	$-0.877053\pi$
$829$		−	1.23591e10i		−	0.753432i	0.926329	−	0.376716i	$-0.122947\pi$
$830$	4.02569e9	−	1.20354e10i	0.244381	−	0.730614i
$831$	2.73151e10			1.65120
$832$	2.58909e10	+	9.92116e9i	1.55853	+	0.597215i
$833$	−5.13516e9			−0.307820
$834$	1.24013e10	−	3.70757e10i	0.740265	−	2.21314i
$835$	1.33459e10			0.793312
$836$	1.91168e10	−	1.90669e10i	1.13160	−	1.12865i
$837$	5.64025e10			3.32475
$838$	1.03334e10	−	3.08934e10i	0.606583	−	1.81347i
$839$	−2.27531e10			−1.33007			−0.665033	−	0.746814i	$-0.731582\pi$
$839$	−2.27531e10			−1.33007			−0.665033	+	0.746814i	$0.731582\pi$
$840$	7.30160e9	−	5.02141e9i	0.425051	−	0.292313i
$841$	−4.15127e9			−0.240655
$842$	3.05380e7	−	9.12982e7i	0.00176299	−	0.00527072i
$843$			2.38157e10i			1.36920i
$844$	−1.57948e10	−	1.18974e10i	−0.904305	−	0.681165i
$845$	−1.95780e10			−1.11627
$846$	5.34649e9	−	1.59842e10i	0.303580	−	0.907599i
$847$		−	1.31409e10i		−	0.743075i
$848$	1.18973e10	−	3.41654e9i	0.669982	−	0.192398i
$849$		−	3.47480e10i		−	1.94873i
$850$	−4.12759e9	−	1.38062e9i	−0.230532	−	0.0771097i
$851$	−3.01533e10			−1.67719
$852$	1.14193e10	+	8.60155e9i	0.632559	+	0.476473i
$853$	2.60035e10			1.43453			0.717267	−	0.696799i	$-0.245393\pi$
$853$	2.60035e10			1.43453			0.717267	+	0.696799i	$0.245393\pi$
$854$	−2.28114e8	+	6.81982e8i	−0.0125328	+	0.0374688i
$855$	2.23931e10	+	3.18146e9i	1.22527	+	0.174079i
$856$	−2.23531e9	−	3.25036e9i	−0.121809	−	0.177122i
$857$			9.24773e9i			0.501883i	0.968002	+	0.250941i	$0.0807401\pi$
$857$			9.24773e9i			0.501883i	−0.968002	+	0.250941i	$0.919260\pi$
$858$	8.07928e10	+	2.70241e10i	4.36684	+	1.46065i
$859$		−	2.91694e10i		−	1.57019i	−0.619376	−	0.785094i	$-0.712614\pi$
$859$		−	2.91694e10i		−	1.57019i	0.619376	−	0.785094i	$-0.287386\pi$
$860$	−3.68209e9	+	4.88829e9i	−0.197401	+	0.262067i
$861$	3.09573e8			0.0165292
$862$	−2.95157e10	−	9.87259e9i	−1.56956	−	0.524996i
$863$	−1.50970e10			−0.799563			−0.399781	−	0.916611i	$-0.630914\pi$
$863$	−1.50970e10			−0.799563			−0.399781	+	0.916611i	$0.630914\pi$
$864$	1.38288e9	−	3.20328e10i	0.0729437	−	1.68965i
$865$		−	5.22622e9i		−	0.274556i
$866$	−1.01227e10	+	3.02634e10i	−0.529644	+	1.58345i
$867$	−2.78512e10			−1.45137
$868$	−1.08945e10	+	1.44634e10i	−0.565444	+	0.750675i
$869$		−	1.55132e10i		−	0.801922i
$870$	−7.40535e9	+	2.21395e10i	−0.381266	+	1.13986i
$871$			2.50140e10i			1.28268i
$872$	1.75564e10	−	1.20738e10i	0.896660	−	0.616645i
$873$		−	1.81567e10i		−	0.923607i
$874$	9.84790e9	−	1.96825e10i	0.498946	−	0.997221i
$875$		−	9.52993e9i		−	0.480908i
$876$	−2.87842e10	−	2.16816e10i	−1.44674	−	1.08975i
$877$			1.45517e10i			0.728478i	0.931305	+	0.364239i	$0.118671\pi$
$877$			1.45517e10i			0.728478i	−0.931305	+	0.364239i	$0.881329\pi$
$878$	−1.34041e10	−	4.48350e9i	−0.668356	−	0.223556i
$879$			1.72112e10i			0.854772i
$880$	1.94128e10	−	5.57474e9i	0.960280	−	0.275763i
$881$	−1.42245e10			−0.700844			−0.350422	−	0.936592i	$-0.613962\pi$
$881$	−1.42245e10			−0.700844			−0.350422	+	0.936592i	$0.613962\pi$
$882$	−2.95143e10	−	9.87214e9i	−1.44841	−	0.484475i
$883$			2.45682e10i			1.20091i	0.799659	+	0.600455i	$0.205014\pi$
$883$			2.45682e10i			1.20091i	−0.799659	+	0.600455i	$0.794986\pi$
$884$	−8.22967e9	+	1.09256e10i	−0.400682	+	0.531939i
$885$	−1.57295e10			−0.762804
$886$	−3.70437e8	+	1.10748e9i	−0.0178935	+	0.0534955i
$887$	1.81878e10			0.875078			0.437539	−	0.899199i	$-0.355850\pi$
$887$	1.81878e10			0.875078			0.437539	+	0.899199i	$0.355850\pi$
$888$	4.46393e10	−	3.06990e10i	2.13930	−	1.47122i
$889$		−	3.21169e9i		−	0.153312i
$890$	−2.77855e9	+	8.30692e9i	−0.132116	+	0.394980i
$891$		−	3.17082e10i		−	1.50176i
$892$	−6.31059e8	−	4.75344e8i	−0.0297710	−	0.0224249i
$893$	−1.44700e9	+	1.01849e10i	−0.0679966	+	0.478603i
$894$	−4.05511e9	−	1.35638e9i	−0.189811	−	0.0634892i
$895$	−2.21343e10			−1.03201
$896$	7.94713e9	+	6.54197e9i	0.369090	+	0.303830i
$897$	6.94439e10			3.21263
$898$	−8.61818e9	+	2.57654e10i	−0.397144	+	1.18733i
$899$		−	4.77026e10i		−	2.18969i
$900$	−2.10691e10	−	1.58703e10i	−0.963381	−	0.725664i
$901$			6.10646e9i			0.278133i
$902$	6.69140e8	+	2.23818e8i	0.0303594	+	0.0101548i
$903$	−9.58325e9			−0.433117
$904$	1.67273e10	−	1.15036e10i	0.753070	−	0.517896i
$905$			1.73510e10i			0.778133i
$906$	3.87181e10	+	1.29507e10i	1.72968	+	0.578554i
$907$	−1.57710e9			−0.0701835			−0.0350917	−	0.999384i	$-0.511172\pi$
$907$	−1.57710e9			−0.0701835			−0.0350917	+	0.999384i	$0.511172\pi$
$908$	−1.61209e10	−	1.21430e10i	−0.714642	−	0.538302i
$909$	2.21331e10			0.977393
$910$	−1.07529e10	−	3.59671e9i	−0.473023	−	0.158220i
$911$	1.43356e10			0.628206			0.314103	−	0.949389i	$-0.398296\pi$
$911$	1.43356e10			0.628206			0.314103	+	0.949389i	$0.398296\pi$
$912$	5.45984e9	+	3.91644e10i	0.238340	+	1.70966i
$913$	4.52941e10			1.96967
$914$	3.51125e10	+	1.17447e10i	1.52107	+	0.508779i
$915$	−2.06655e9			−0.0891809
$916$	−2.96604e9	−	2.23416e9i	−0.127510	−	0.0960464i
$917$	1.38289e10			0.592238
$918$	1.50004e10	+	5.01744e9i	0.639962	+	0.214059i
$919$			1.23378e10i			0.524366i	0.965018	+	0.262183i	$0.0844425\pi$
$919$			1.23378e10i			0.524366i	−0.965018	+	0.262183i	$0.915558\pi$
$920$	1.35654e10	−	9.32910e9i	0.574348	−	0.394987i
$921$	−3.64305e10			−1.53659
$922$	2.61082e10	+	8.73283e9i	1.09703	+	0.366942i
$923$		−	1.82924e10i		−	0.765712i
$924$	2.52625e10	+	1.90289e10i	1.05347	+	0.793527i
$925$		−	2.20571e10i		−	0.916332i
$926$	6.15651e9	−	1.84059e10i	0.254798	−	0.761759i
$927$	−4.93500e10			−2.03474
$928$	−2.70919e10	−	1.16958e9i	−1.11281	−	0.0480410i
$929$	−8.54133e9			−0.349519			−0.174759	−	0.984611i	$-0.555915\pi$
$929$	−8.54133e9			−0.349519			−0.174759	+	0.984611i	$0.555915\pi$
$930$	−4.93484e10	−	1.65064e10i	−2.01179	−	0.672916i
$931$	1.88061e10	+	2.67184e9i	0.763790	+	0.108514i
$932$	−1.47102e10	−	1.10804e10i	−0.595200	−	0.448333i
$933$		−	5.74380e10i		−	2.31533i
$934$	1.05420e10	−	3.15170e10i	0.423360	−	1.26570i
$935$			9.96388e9i			0.398646i
$936$	−6.83040e10	+	4.69736e10i	−2.72258	+	1.87236i
$937$	−1.66665e10			−0.661845			−0.330923	−	0.943658i	$-0.607360\pi$
$937$	−1.66665e10			−0.661845			−0.330923	+	0.943658i	$0.607360\pi$
$938$	−2.94573e9	+	8.80673e9i	−0.116542	+	0.348421i
$939$	6.99134e10			2.75569
$940$	−4.62995e9	+	6.14666e9i	−0.181815	+	0.241375i
$941$			1.68442e10i			0.659002i	0.944155	+	0.329501i	$0.106881\pi$
$941$			1.68442e10i			0.659002i	−0.944155	+	0.329501i	$0.893119\pi$
$942$	−2.46975e10	−	8.26098e9i	−0.962664	−	0.321998i
$943$	5.75146e8			0.0223350
$944$	−5.04303e9	−	1.75612e10i	−0.195115	−	0.679442i
$945$			1.31117e10i			0.505413i
$946$	−2.07141e10	−	6.92859e9i	−0.795513	−	0.266088i
$947$			2.75201e10i			1.05299i	0.850178	+	0.526496i	$0.176494\pi$
$947$			2.75201e10i			1.05299i	−0.850178	+	0.526496i	$0.823506\pi$
$948$	1.81477e10	+	1.36697e10i	0.691820	+	0.521112i
$949$			4.61091e10i			1.75128i
$950$	1.43978e10	+	7.20374e9i	0.544833	+	0.272600i
$951$		−	6.91849e8i		−	0.0260843i
$952$	−4.18407e9	+	2.87744e9i	−0.157170	+	0.108088i
$953$		−	3.86077e10i		−	1.44494i	−0.691403	−	0.722469i	$-0.743007\pi$
$953$		−	3.86077e10i		−	1.44494i	0.691403	−	0.722469i	$-0.256993\pi$
$954$	−1.17394e10	+	3.50969e10i	−0.437752	+	1.30873i
$955$		−	8.19008e9i		−	0.304282i
$956$	−1.07536e9	+	1.42764e9i	−0.0398064	+	0.0528464i
$957$	−8.33197e10			−3.07295
$958$	−3.95748e9	+	1.18315e10i	−0.145425	+	0.434772i
$959$			7.14271e9i			0.261516i
$960$	−1.05844e10	+	2.76218e10i	−0.386116	+	1.00763i
$961$	7.88155e10			2.86470
$962$	−6.57395e10	−	2.19890e10i	−2.38075	−	0.796328i
$963$	1.17942e10			0.425574
$964$	1.66634e10	−	2.21221e10i	0.599093	−	0.795347i
$965$			1.91509e9i			0.0686032i
$966$	2.44493e10	+	8.17795e9i	0.872662	+	0.291894i
$967$		−	2.47913e10i		−	0.881671i	−0.897588	−	0.440835i	$-0.854682\pi$
$967$		−	2.47913e10i		−	0.881671i	0.897588	−	0.440835i	$-0.145318\pi$
$968$	2.48558e10	+	3.61427e10i	0.880774	+	1.28073i
$969$	−1.93137e10	−	2.74396e9i	−0.681919	−	0.0968823i
$970$	−2.62962e9	+	7.86167e9i	−0.0925108	+	0.276576i
$971$	3.25480e10			1.14093			0.570463	−	0.821324i	$-0.306764\pi$
$971$	3.25480e10			1.14093			0.570463	+	0.821324i	$0.306764\pi$
$972$	−1.58324e9	−	1.19257e9i	−0.0552987	−	0.0416536i
$973$	−1.85705e10			−0.646293
$974$	−1.32457e10	−	4.43052e9i	−0.459325	−	0.153638i
$975$			5.07982e10i			1.75522i
$976$	−6.62557e8	−	2.30720e9i	−0.0228112	−	0.0794349i
$977$		−	3.46262e10i		−	1.18788i	−0.804508	−	0.593942i	$-0.797571\pi$
$977$		−	3.46262e10i		−	1.18788i	0.804508	−	0.593942i	$-0.202429\pi$
$978$	2.28863e10	−	6.84222e10i	0.782329	−	2.33890i
$979$	−3.12623e10			−1.06483
$980$	1.13496e10	+	8.54907e9i	0.385204	+	0.290154i
$981$			6.37047e10i			2.15442i
$982$	−8.63274e9	+	2.58089e10i	−0.290910	+	0.869721i
$983$	5.75995e9			0.193411			0.0967056	−	0.995313i	$-0.469169\pi$
$983$	5.75995e9			0.193411			0.0967056	+	0.995313i	$0.469169\pi$
$984$	−8.51452e8	+	5.85555e8i	−0.0284890	+	0.0195923i
$985$	2.79259e10			0.931065
$986$	4.24353e9	−	1.26867e10i	0.140980	−	0.421482i
$987$	−1.20502e10			−0.398919
$988$	3.58234e10	−	3.57300e10i	1.18173	−	1.17865i
$989$	−1.78044e10			−0.585248
$990$	−1.91552e10	+	5.72674e10i	−0.627427	+	1.87579i
$991$	−3.66915e9			−0.119759			−0.0598795	−	0.998206i	$-0.519072\pi$
$991$	−3.66915e9			−0.119759			−0.0598795	+	0.998206i	$0.519072\pi$
$992$	2.60697e9	−	6.03872e10i	0.0847900	−	1.96406i
$993$	−2.96551e10			−0.961118
$994$	2.15418e9	−	6.44025e9i	0.0695712	−	0.207994i
$995$			3.43682e9i			0.110605i
$996$	−3.99117e10	+	5.29862e10i	−1.27995	+	1.69924i
$997$	−4.51347e10			−1.44237			−0.721186	−	0.692741i	$-0.756403\pi$
$997$	−4.51347e10			−1.44237			−0.721186	+	0.692741i	$0.756403\pi$
$998$	1.14208e10	−	3.41444e10i	0.363698	−	1.08733i
$999$			8.01598e10i			2.54377i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.8.d.a.75.7	✓	68
4.3	odd	2	inner	76.8.d.a.75.61	yes	68
19.18	odd	2	inner	76.8.d.a.75.62	yes	68
76.75	even	2	inner	76.8.d.a.75.8	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.8.d.a.75.7	✓	68	1.1	even	1	trivial
76.8.d.a.75.8	yes	68	76.75	even	2	inner
76.8.d.a.75.61	yes	68	4.3	odd	2	inner
76.8.d.a.75.62	yes	68	19.18	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)

\(f(q)\)	\(=\)	\(q+(-10.7294 - 3.58884i) q^{2} +80.7260 q^{3} +(102.240 + 77.0123i) q^{4} +174.727 q^{5} +(-866.143 - 289.713i) q^{6} +433.835i q^{7} +(-820.594 - 1193.22i) q^{8} +4329.69 q^{9} +O(q^{10})\)	\(q+(-10.7294 - 3.58884i) q^{2} +80.7260 q^{3} +(102.240 + 77.0123i) q^{4} +174.727 q^{5} +(-866.143 - 289.713i) q^{6} +433.835i q^{7} +(-820.594 - 1193.22i) q^{8} +4329.69 q^{9} +(-1874.71 - 627.067i) q^{10} -7055.30i q^{11} +(8253.46 + 6216.90i) q^{12} -13221.1i q^{13} +(1556.96 - 4654.79i) q^{14} +14105.0 q^{15} +(4522.20 + 15747.5i) q^{16} -8082.65 q^{17} +(-46455.1 - 15538.6i) q^{18} +(29600.4 + 4205.43i) q^{19} +(17864.1 + 13456.1i) q^{20} +35021.8i q^{21} +(-25320.4 + 75699.2i) q^{22} +65065.7i q^{23} +(-66243.3 - 96324.1i) q^{24} -47595.6 q^{25} +(-47448.5 + 141855. i) q^{26} +172971. q^{27} +(-33410.6 + 44355.4i) q^{28} -146291. i q^{29} +(-151338. - 50620.6i) q^{30} +326080. q^{31} +(7994.87 - 185191. i) q^{32} -569546. i q^{33} +(86722.1 + 29007.4i) q^{34} +75802.5i q^{35} +(442670. + 333440. i) q^{36} +463428. i q^{37} +(-302503. - 151353. i) q^{38} -1.06729e6i q^{39} +(-143380. - 208488. i) q^{40} -8839.46i q^{41} +(125688. - 375763. i) q^{42} +273637. i q^{43} +(543345. - 721337. i) q^{44} +756513. q^{45} +(233511. - 698117. i) q^{46} +344078. i q^{47} +(365060. + 1.27124e6i) q^{48} +635331. q^{49} +(510673. + 170813. i) q^{50} -652481. q^{51} +(1.01819e6 - 1.35173e6i) q^{52} -755502. i q^{53} +(-1.85588e6 - 620767. i) q^{54} -1.23275e6i q^{55} +(517661. - 356002. i) q^{56} +(2.38953e6 + 339487. i) q^{57} +(-525016. + 1.56962e6i) q^{58} -1.11517e6 q^{59} +(1.44210e6 + 1.08626e6i) q^{60} -146512. q^{61} +(-3.49864e6 - 1.17025e6i) q^{62} +1.87837e6i q^{63} +(-750403. + 1.95830e6i) q^{64} -2.31008e6i q^{65} +(-2.04401e6 + 6.11090e6i) q^{66} -1.89197e6 q^{67} +(-826374. - 622464. i) q^{68} +5.25250e6i q^{69} +(272043. - 813316. i) q^{70} +1.38358e6 q^{71} +(-3.55292e6 - 5.16628e6i) q^{72} -3.48753e6 q^{73} +(1.66317e6 - 4.97231e6i) q^{74} -3.84220e6 q^{75} +(2.70249e6 + 2.70956e6i) q^{76} +3.06083e6 q^{77} +(-3.83033e6 + 1.14514e7i) q^{78} +2.19880e6 q^{79} +(790150. + 2.75152e6i) q^{80} +4.49425e6 q^{81} +(-31723.4 + 94842.1i) q^{82} +6.41987e6i q^{83} +(-2.69711e6 + 3.58064e6i) q^{84} -1.41226e6 q^{85} +(982040. - 2.93596e6i) q^{86} -1.18095e7i q^{87} +(-8.41853e6 + 5.78954e6i) q^{88} -4.43104e6i q^{89} +(-8.11694e6 - 2.71501e6i) q^{90} +5.73578e6 q^{91} +(-5.01086e6 + 6.65235e6i) q^{92} +2.63231e7 q^{93} +(1.23484e6 - 3.69176e6i) q^{94} +(5.17199e6 + 734800. i) q^{95} +(645395. - 1.49498e7i) q^{96} -4.19353e6i q^{97} +(-6.81672e6 - 2.28010e6i) q^{98} -3.05473e7i 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

Related objects

Downloads

Learn more