LMFDB - Embedded newform 100.9.j.b.91.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [100,9,Mod(11,100)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(100, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 8])) N = Newforms(chi, 9, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("100.11"); S:= CuspForms(chi, 9); N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	100.j (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [464] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$40.7378610061$
Analytic rank:	$0$
Dimension:	$464$
Relative dimension:	$116$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			91.13
Character	$\chi$	$=$	100.91
Dual form			100.9.j.b.11.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-15.1733 - 5.07641i) q^{2} +(66.9566 - 21.7555i) q^{3} +(204.460 + 154.052i) q^{4} +(-7.73474 - 624.952i) q^{5} +(-1126.40 - 9.79525i) q^{6} +539.637i q^{7} +(-2320.31 - 3375.41i) q^{8} +(-1298.07 + 943.105i) q^{9} +(-3055.15 + 9521.87i) q^{10} +(-3618.94 + 4981.05i) q^{11} +(17041.4 + 5866.67i) q^{12} +(2340.29 - 1700.32i) q^{13} +(2739.42 - 8188.10i) q^{14} +(-14114.1 - 41676.4i) q^{15} +(18071.9 + 62995.0i) q^{16} +(-39654.3 + 122043. i) q^{17} +(24483.7 - 7720.51i) q^{18} +(218786. + 71087.9i) q^{19} +(94693.7 - 128969. i) q^{20} +(11740.1 + 36132.3i) q^{21} +(80197.3 - 57207.9i) q^{22} +(135470. - 186458. i) q^{23} +(-228794. - 175526. i) q^{24} +(-390505. + 9667.69i) q^{25} +(-44141.4 + 13919.2i) q^{26} +(-337901. + 465080. i) q^{27} +(-83132.2 + 110334. i) q^{28} +(227566. + 700375. i) q^{29} +(2590.81 + 704019. i) q^{30} +(-1.05782e6 - 343705. i) q^{31} +(45577.1 - 1.04759e6i) q^{32} +(-133947. + 412246. i) q^{33} +(1.22123e6 - 1.65050e6i) q^{34} +(337247. - 4173.96i) q^{35} +(-410692. - 7143.38i) q^{36} +(-1.73367e6 + 1.25958e6i) q^{37} +(-2.95884e6 - 2.18929e6i) q^{38} +(119706. - 164762. i) q^{39} +(-2.09152e6 + 1.47619e6i) q^{40} +(2.70407e6 - 1.96462e6i) q^{41} +(5285.88 - 607845. i) q^{42} +3.01287e6i q^{43} +(-1.50727e6 + 460920. i) q^{44} +(599436. + 803939. i) q^{45} +(-3.00206e6 + 2.14149e6i) q^{46} +(2.28936e6 - 743857. i) q^{47} +(2.58052e6 + 3.82477e6i) q^{48} +5.47359e6 q^{49} +(5.97435e6 + 1.83567e6i) q^{50} +9.03432e6i q^{51} +(740433. + 12878.7i) q^{52} +(-3.42085e6 - 1.05283e7i) q^{53} +(7.48802e6 - 5.34150e6i) q^{54} +(3.14091e6 + 2.22314e6i) q^{55} +(1.82150e6 - 1.25213e6i) q^{56} +1.61957e7 q^{57} +(102460. - 1.17822e7i) q^{58} +(7.70792e6 + 1.06090e7i) q^{59} +(3.53458e6 - 1.06955e7i) q^{60} +(1.03807e7 + 7.54199e6i) q^{61} +(1.43058e7 + 1.05851e7i) q^{62} +(-508935. - 700489. i) q^{63} +(-6.00953e6 + 1.56640e7i) q^{64} +(-1.08072e6 - 1.44942e6i) q^{65} +(4.12515e6 - 5.57518e6i) q^{66} +(2.51604e7 + 8.17511e6i) q^{67} +(-2.69088e7 + 1.88442e7i) q^{68} +(5.01410e6 - 1.54318e7i) q^{69} +(-5.13836e6 - 1.64867e6i) q^{70} +(6.65726e6 - 2.16308e6i) q^{71} +(6.19530e6 + 2.19323e6i) q^{72} +(4.14409e7 + 3.01085e7i) q^{73} +(3.26997e7 - 1.03113e7i) q^{74} +(-2.59366e7 + 9.14297e6i) q^{75} +(3.37818e7 + 4.82391e7i) q^{76} +(-2.68796e6 - 1.95292e6i) q^{77} +(-2.65274e6 + 1.89231e6i) q^{78} +(-5.38806e7 + 1.75069e7i) q^{79} +(3.92291e7 - 1.17813e7i) q^{80} +(-9.25355e6 + 2.84795e7i) q^{81} +(-5.10029e7 + 1.60829e7i) q^{82} +(-5.49796e7 - 1.78640e7i) q^{83} +(-3.16587e6 + 9.19620e6i) q^{84} +(7.65780e7 + 2.38381e7i) q^{85} +(1.52946e7 - 4.57153e7i) q^{86} +(3.04740e7 + 4.19439e7i) q^{87} +(2.52101e7 + 657823. i) q^{88} +(2.82158e7 + 2.05000e7i) q^{89} +(-5.01432e6 - 1.52414e7i) q^{90} +(917555. + 1.26291e6i) q^{91} +(5.64224e7 - 1.72538e7i) q^{92} -7.83052e7 q^{93} +(-3.85133e7 - 334916. i) q^{94} +(4.27343e7 - 1.37281e8i) q^{95} +(-1.97391e7 - 7.11343e7i) q^{96} +(-9.23936e6 - 2.84358e7i) q^{97} +(-8.30527e7 - 2.77862e7i) q^{98} -9.87881e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 464 q + 29 q^{2} + 509 q^{4} - 1230 q^{5} - 515 q^{6} + 21284 q^{8} + 262434 q^{9} + 3445 q^{10} - 35805 q^{12} - 29522 q^{13} - 33705 q^{14} - 63391 q^{16} - 319922 q^{17} - 569696 q^{18} + 1244935 q^{20}+ \cdots + 209675864 q^{98}+O(q^{100}) $ 464 * q + 29 * q^2 + 509 * q^4 - 1230 * q^5 - 515 * q^6 + 21284 * q^8 + 262434 * q^9 + 3445 * q^10 - 35805 * q^12 - 29522 * q^13 - 33705 * q^14 - 63391 * q^16 - 319922 * q^17 - 569696 * q^18 + 1244935 * q^20 + 39360 * q^21 + 140220 * q^22 + 989900 * q^24 - 431710 * q^25 - 855842 * q^26 - 2358605 * q^28 - 2884562 * q^29 + 7229675 * q^30 - 7078666 * q^32 - 1866570 * q^33 + 1448973 * q^34 + 777029 * q^36 - 7317972 * q^37 + 4012465 * q^38 - 4154830 * q^40 + 1687438 * q^41 - 21337315 * q^42 + 510580 * q^44 + 2596050 * q^45 + 1721385 * q^46 + 41153690 * q^48 - 396068336 * q^49 - 60015715 * q^50 - 8419912 * q^52 + 26717388 * q^53 - 13729145 * q^54 + 7138890 * q^56 - 19745300 * q^57 - 41444182 * q^58 + 96768050 * q^60 + 26136558 * q^61 - 87505940 * q^62 + 19616924 * q^64 + 22030140 * q^65 - 69968200 * q^66 + 276958 * q^68 - 73697610 * q^69 + 39639840 * q^70 - 145994351 * q^72 - 39004722 * q^73 + 4922908 * q^74 - 19181080 * q^76 + 111211200 * q^77 - 197089615 * q^78 - 395680960 * q^80 - 539852286 * q^81 + 186999258 * q^82 - 377672700 * q^84 - 283475540 * q^85 - 340843785 * q^86 - 29231040 * q^88 - 206040612 * q^89 + 351285695 * q^90 + 43044280 * q^92 + 241823660 * q^93 - 442380075 * q^94 - 474931550 * q^96 + 2388718 * q^97 + 209675864 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−15.1733	−	5.07641i	−0.948333	−	0.317275i
$2$	−15.1733	−	5.07641i	−0.948333	−	0.317275i
$3$	66.9566	−	21.7555i	0.826625	−	0.268587i	0.135002	−	0.990845i	$-0.456896\pi$
$3$	66.9566	−	21.7555i	0.826625	−	0.268587i	0.691623	+	0.722259i	$0.256896\pi$
$4$	204.460	+	154.052i	0.798673	+	0.601766i
$5$	−7.73474	−	624.952i	−0.0123756	−	0.999923i
$5$	−7.73474	−	624.952i	−0.0123756	−	0.999923i
$6$	−1126.40	−	9.79525i	−0.869132	−	0.00755806i
$7$			539.637i			0.224755i	0.993666	+	0.112378i	$0.0358466\pi$
$7$			539.637i			0.224755i	−0.993666	+	0.112378i	$0.964153\pi$
$8$	−2320.31	−	3375.41i	−0.566482	−	0.824074i
$9$	−1298.07	+	943.105i	−0.197847	+	0.143744i
$10$	−3055.15	+	9521.87i	−0.305515	+	0.952187i
$11$	−3618.94	+	4981.05i	−0.247179	+	0.340212i	−0.914521	−	0.404539i	$-0.867432\pi$
$11$	−3618.94	+	4981.05i	−0.247179	+	0.340212i	0.667342	+	0.744751i	$0.267432\pi$
$12$	17041.4	+	5866.67i	0.821829	+	0.282922i
$13$	2340.29	−	1700.32i	0.0819399	−	0.0595328i	−0.546061	−	0.837745i	$-0.683873\pi$
$13$	2340.29	−	1700.32i	0.0819399	−	0.0595328i	0.628001	+	0.778213i	$0.283873\pi$
$14$	2739.42	−	8188.10i	0.0713093	−	0.213143i
$15$	−14114.1	−	41676.4i	−0.278796	−	0.823238i
$16$	18071.9	+	62995.0i	0.275756	+	0.961228i
$17$	−39654.3	+	122043.i	−0.474783	+	1.46123i	0.371468	+	0.928446i	$0.378854\pi$
$17$	−39654.3	+	122043.i	−0.474783	+	1.46123i	−0.846251	+	0.532785i	$0.821146\pi$
$18$	24483.7	−	7720.51i	0.233231	−	0.0735454i
$19$	218786.	+	71087.9i	1.67882	+	0.545483i	0.984683	−	0.174355i	$-0.0557842\pi$
$19$	218786.	+	71087.9i	1.67882	+	0.545483i	0.694142	+	0.719839i	$0.255784\pi$
$20$	94693.7	−	128969.i	0.591836	−	0.806059i
$21$	11740.1	+	36132.3i	0.0603663	+	0.185788i
$22$	80197.3	−	57207.9i	0.342349	−	0.244211i
$23$	135470.	−	186458.i	0.484095	−	0.666299i	−0.495191	−	0.868784i	$-0.664902\pi$
$23$	135470.	−	186458.i	0.484095	−	0.666299i	0.979285	+	0.202485i	$0.0649017\pi$
$24$	−228794.	−	175526.i	−0.689604	−	0.529050i
$25$	−390505.	+	9667.69i	−0.999694	+	0.0247493i
$26$	−44141.4	+	13919.2i	−0.0965947	+	0.0304594i
$27$	−337901.	+	465080.i	−0.635820	+	0.875131i
$28$	−83132.2	+	110334.i	−0.135250	+	0.179506i
$29$	227566.	+	700375.i	0.321747	+	0.990235i	0.972888	+	0.231278i	$0.0742908\pi$
$29$	227566.	+	700375.i	0.321747	+	0.990235i	−0.651141	+	0.758957i	$0.725709\pi$
$30$	2590.81	+	704019.i	0.00319853	+	0.869159i
$31$	−1.05782e6	−	343705.i	−1.14542	−	0.372168i	−0.326001	−	0.945369i	$-0.605701\pi$
$31$	−1.05782e6	−	343705.i	−1.14542	−	0.372168i	−0.819414	+	0.573201i	$0.805701\pi$
$32$	45577.1	−	1.04759e6i	0.0434657	−	0.999055i
$33$	−133947.	+	412246.i	−0.112948	+	0.347617i
$34$	1.22123e6	−	1.65050e6i	0.913865	−	1.23510i
$35$	337247.	−	4173.96i	0.224738	−	0.00278148i
$36$	−410692.	−	7143.38i	−0.244515	−	0.00425298i
$37$	−1.73367e6	+	1.25958e6i	−0.925037	+	0.672079i	−0.944773	−	0.327727i	$-0.893718\pi$
$37$	−1.73367e6	+	1.25958e6i	−0.925037	+	0.672079i	0.0197357	+	0.999805i	$0.493718\pi$
$38$	−2.95884e6	−	2.18929e6i	−1.41902	−	1.04995i
$39$	119706.	−	164762.i	0.0517439	−	0.0712193i
$40$	−2.09152e6	+	1.47619e6i	−0.817000	+	0.576637i
$41$	2.70407e6	−	1.96462e6i	0.956933	−	0.695253i	0.00449687	−	0.999990i	$-0.498569\pi$
$41$	2.70407e6	−	1.96462e6i	0.956933	−	0.695253i	0.952437	+	0.304737i	$0.0985686\pi$
$42$	5285.88	−	607845.i	0.00169871	−	0.195342i
$43$			3.01287e6i			0.881266i	0.897687	+	0.440633i	$0.145246\pi$
$43$			3.01287e6i			0.881266i	−0.897687	+	0.440633i	$0.854754\pi$
$44$	−1.50727e6	+	460920.i	−0.402143	+	0.122975i
$45$	599436.	+	803939.i	0.146182	+	0.196053i
$46$	−3.00206e6	+	2.14149e6i	−0.670484	+	0.478283i
$47$	2.28936e6	−	743857.i	0.469161	−	0.152440i	−0.0648891	−	0.997892i	$-0.520669\pi$
$47$	2.28936e6	−	743857.i	0.469161	−	0.152440i	0.534050	+	0.845453i	$0.320669\pi$
$48$	2.58052e6	+	3.82477e6i	0.486120	+	0.720511i
$49$	5.47359e6			0.949485
$50$	5.97435e6	+	1.83567e6i	0.955895	+	0.293708i
$51$			9.03432e6i			1.33541i
$52$	740433.	+	12878.7i	0.101268	+	0.00176141i
$53$	−3.42085e6	−	1.05283e7i	−0.433542	−	1.33430i	−0.894574	−	0.446921i	$-0.852521\pi$
$53$	−3.42085e6	−	1.05283e7i	−0.433542	−	1.33430i	0.461032	−	0.887384i	$-0.347479\pi$
$54$	7.48802e6	−	5.34150e6i	0.880627	−	0.628186i
$55$	3.14091e6	+	2.22314e6i	0.343245	+	0.242950i
$56$	1.82150e6	−	1.25213e6i	0.185215	−	0.127320i
$57$	1.61957e7			1.53427
$58$	102460.	−	1.17822e7i	0.00905400	−	1.04116i
$59$	7.70792e6	+	1.06090e7i	0.636106	+	0.875524i	0.998400	−	0.0565392i	$-0.0180066\pi$
$59$	7.70792e6	+	1.06090e7i	0.636106	+	0.875524i	−0.362295	+	0.932064i	$0.618007\pi$
$60$	3.53458e6	−	1.06955e7i	0.272730	−	0.825267i
$61$	1.03807e7	+	7.54199e6i	0.749731	+	0.544711i	0.895743	−	0.444571i	$-0.146644\pi$
$61$	1.03807e7	+	7.54199e6i	0.749731	+	0.544711i	−0.146013	+	0.989283i	$0.546644\pi$
$62$	1.43058e7	+	1.05851e7i	0.968156	+	0.716352i
$63$	−508935.	−	700489.i	−0.0323073	−	0.0444671i
$64$	−6.00953e6	+	1.56640e7i	−0.358196	+	0.933647i
$65$	−1.08072e6	−	1.44942e6i	−0.0605423	−	0.0811969i
$66$	4.12515e6	−	5.57518e6i	0.217402	−	0.293821i
$67$	2.51604e7	+	8.17511e6i	1.24859	+	0.405690i	0.857414	−	0.514627i	$-0.172070\pi$
$67$	2.51604e7	+	8.17511e6i	1.24859	+	0.405690i	0.391172	+	0.920317i	$0.372070\pi$
$68$	−2.69088e7	+	1.88442e7i	−1.25851	+	0.881337i
$69$	5.01410e6	−	1.54318e7i	0.221206	−	0.680801i
$70$	−5.13836e6	−	1.64867e6i	−0.214009	−	0.0686661i
$71$	6.65726e6	−	2.16308e6i	0.261976	−	0.0851213i	−0.175084	−	0.984554i	$-0.556020\pi$
$71$	6.65726e6	−	2.16308e6i	0.261976	−	0.0851213i	0.437060	+	0.899432i	$0.356020\pi$
$72$	6.19530e6	+	2.19323e6i	0.230533	+	0.0816119i
$73$	4.14409e7	+	3.01085e7i	1.45928	+	1.06023i	0.983551	+	0.180632i	$0.0578142\pi$
$73$	4.14409e7	+	3.01085e7i	1.45928	+	1.06023i	0.475725	+	0.879594i	$0.342186\pi$
$74$	3.26997e7	−	1.03113e7i	1.09048	−	0.343863i
$75$	−2.59366e7	+	9.14297e6i	−0.819725	+	0.288963i
$76$	3.37818e7	+	4.82391e7i	1.01258	+	1.44592i
$77$	−2.68796e6	−	1.95292e6i	−0.0764645	−	0.0555547i
$78$	−2.65274e6	+	1.89231e6i	−0.0716666	+	0.0511226i
$79$	−5.38806e7	+	1.75069e7i	−1.38333	+	0.449470i	−0.903761	−	0.428037i	$-0.859205\pi$
$79$	−5.38806e7	+	1.75069e7i	−1.38333	+	0.449470i	−0.479564	+	0.877507i	$0.659205\pi$
$80$	3.92291e7	−	1.17813e7i	0.957742	−	0.287630i
$81$	−9.25355e6	+	2.84795e7i	−0.214965	+	0.661595i
$82$	−5.10029e7	+	1.60829e7i	−1.12808	+	0.355720i
$83$	−5.49796e7	−	1.78640e7i	−1.15848	−	0.376414i	−0.334150	−	0.942520i	$-0.608449\pi$
$83$	−5.49796e7	−	1.78640e7i	−1.15848	−	0.376414i	−0.824332	+	0.566106i	$0.808449\pi$
$84$	−3.16587e6	+	9.19620e6i	−0.0635882	+	0.184710i
$85$	7.65780e7	+	2.38381e7i	1.46699	+	0.456663i
$86$	1.52946e7	−	4.57153e7i	0.279604	−	0.835734i
$87$	3.04740e7	+	4.19439e7i	0.531928	+	0.732136i
$88$	2.52101e7	+	657823.i	0.420383	+	0.0109693i
$89$	2.82158e7	+	2.05000e7i	0.449710	+	0.326734i	0.789481	−	0.613774i	$-0.210350\pi$
$89$	2.82158e7	+	2.05000e7i	0.449710	+	0.326734i	−0.339771	+	0.940508i	$0.610350\pi$
$90$	−5.01432e6	−	1.52414e7i	−0.0764262	−	0.232303i
$91$	917555.	+	1.26291e6i	0.0133803	+	0.0184164i
$92$	5.64224e7	−	1.72538e7i	0.787589	−	0.240843i
$93$	−7.83052e7			−1.04679
$94$	−3.85133e7	−	334916.i	−0.493286	−	0.00428967i
$95$	4.27343e7	−	1.37281e8i	0.524665	−	1.68545i
$96$	−1.97391e7	−	7.11343e7i	−0.232403	−	0.837518i
$97$	−9.23936e6	−	2.84358e7i	−0.104365	−	0.321202i	0.885216	−	0.465180i	$-0.154011\pi$
$97$	−9.23936e6	−	2.84358e7i	−0.104365	−	0.321202i	−0.989581	+	0.143978i	$0.954011\pi$
$98$	−8.30527e7	−	2.77862e7i	−0.900428	−	0.301248i
$99$		−	9.87881e6i		−	0.102840i
$100$	−8.13321e7	−	5.81815e7i	−0.813321	−	0.581815i
$101$	1.29415e8			1.24365			0.621826	−	0.783155i	$-0.286391\pi$
$101$	1.29415e8			1.24365			0.621826	+	0.783155i	$0.286391\pi$
$102$	4.58619e7	−	1.37081e8i	0.423693	−	1.26641i
$103$	−6.38086e7	+	2.07327e7i	−0.566931	+	0.184207i	−0.578437	−	0.815727i	$-0.696337\pi$
$103$	−6.38086e7	+	2.07327e7i	−0.566931	+	0.184207i	0.0115064	+	0.999934i	$0.496337\pi$
$104$	−1.11695e7	−	3.95415e6i	−0.0954770	−	0.0338003i
$105$	2.24901e7	−	7.61647e6i	0.185027	−	0.0626609i
$106$	−1.54021e6	+	1.77115e8i	−0.0121999	+	1.40292i
$107$			3.63646e6i			0.0277424i	0.999904	+	0.0138712i	$0.00441548\pi$
$107$			3.63646e6i			0.0277424i	−0.999904	+	0.0138712i	$0.995585\pi$
$108$	−1.40734e8	+	4.30361e7i	−1.03444	+	0.316328i
$109$	−3.37170e7	+	2.44968e7i	−0.238859	+	0.173542i	−0.700775	−	0.713382i	$-0.747162\pi$
$109$	−3.37170e7	+	2.44968e7i	−0.238859	+	0.173542i	0.461916	+	0.886924i	$0.347162\pi$
$110$	−3.63725e7	−	4.96770e7i	−0.248429	−	0.339300i
$111$	−8.86777e7	+	1.22054e8i	−0.584147	+	0.804010i
$112$	−3.39945e7	+	9.75228e6i	−0.216041	+	0.0619775i
$113$	1.04031e8	−	7.55829e7i	0.638041	−	0.463564i	−0.221136	−	0.975243i	$-0.570976\pi$
$113$	1.04031e8	−	7.55829e7i	0.638041	−	0.463564i	0.859177	+	0.511679i	$0.170976\pi$
$114$	−2.45743e8	−	8.22161e7i	−1.45500	−	0.486786i
$115$	−1.17575e8	−	8.32198e7i	−0.672239	−	0.475812i
$116$	−6.13661e7	+	1.78256e8i	−0.338919	+	0.984490i
$117$	−1.43428e6	+	4.41427e6i	−0.00765406	+	0.0235568i
$118$	−6.30991e7	−	2.00103e8i	−0.325458	−	1.03211i
$119$	−6.58592e7	−	2.13989e7i	−0.328419	−	0.106710i
$120$	−1.07926e8	+	1.44343e8i	−0.520476	+	0.696098i
$121$	5.45264e7	+	1.67815e8i	0.254370	+	0.782870i
$122$	−1.19223e8	−	1.67134e8i	−0.538171	−	0.754439i
$123$	1.38314e8	−	1.90373e8i	0.604289	−	0.831733i
$124$	−1.63333e8	−	2.33233e8i	−0.690854	−	0.986512i
$125$	9.06230e6	+	2.43972e8i	0.0371192	+	0.999311i
$126$	4.16627e6	+	1.32123e7i	0.0165297	+	0.0524200i
$127$	−8.07030e7	+	1.11078e8i	−0.310223	+	0.426986i	−0.935451	−	0.353457i	$-0.885006\pi$
$127$	−8.07030e7	+	1.11078e8i	−0.310223	+	0.426986i	0.625227	+	0.780443i	$0.285006\pi$
$128$	1.70701e8	−	2.07168e8i	0.635912	−	0.771762i
$129$	6.55467e7	+	2.01732e8i	0.236696	+	0.728477i
$130$	9.04028e6	+	2.74786e7i	0.0316525	+	0.0962103i
$131$	2.87458e8	+	9.34006e7i	0.976087	+	0.317150i	0.753271	−	0.657711i	$-0.228475\pi$
$131$	2.87458e8	+	9.34006e7i	0.976087	+	0.317150i	0.222816	+	0.974860i	$0.428475\pi$
$132$	−9.08942e7	+	6.36532e7i	−0.299392	+	0.209664i
$133$	−3.83617e7	+	1.18065e8i	−0.122600	+	0.377325i
$134$	−3.40267e8	−	2.51768e8i	−1.05536	−	0.780876i
$135$	2.93267e8	+	2.07574e8i	0.882932	+	0.624941i
$136$	5.03957e8	−	1.49329e8i	1.47312	−	0.436505i
$137$	−1.87550e8	+	1.36263e8i	−0.532396	+	0.386808i	−0.821253	−	0.570564i	$-0.806725\pi$
$137$	−1.87550e8	+	1.36263e8i	−0.532396	+	0.386808i	0.288857	+	0.957372i	$0.406725\pi$
$138$	−1.54419e8	+	2.08698e8i	−0.425778	+	0.575443i
$139$	−1.29325e8	+	1.78001e8i	−0.346437	+	0.476830i	−0.946308	−	0.323267i	$-0.895219\pi$
$139$	−1.29325e8	+	1.78001e8i	−0.346437	+	0.476830i	0.599871	+	0.800097i	$0.295219\pi$
$140$	6.95967e7	+	5.11003e7i	0.181166	+	0.133018i
$141$	1.37105e8	−	9.96123e7i	0.346877	−	0.252021i
$142$	−1.11994e8	−	973907.i	−0.275448	−	0.00239532i
$143$			1.78104e7i			0.0425922i
$144$	−8.28696e7	−	6.47284e7i	−0.192728	−	0.150538i
$145$	4.35940e8	−	1.47635e8i	0.986178	−	0.333977i
$146$	−4.75953e8	−	6.67218e8i	−1.04750	−	1.46844i
$147$	3.66493e8	−	1.19081e8i	0.784868	−	0.255019i
$148$	−5.48508e8	−	9.54048e6i	−1.14324	−	0.0198849i
$149$	−3.01581e7			−0.0611869			−0.0305935	−	0.999532i	$-0.509740\pi$
$149$	−3.01581e7			−0.0611869			−0.0305935	+	0.999532i	$0.509740\pi$
$150$	4.39958e8	−	7.06454e6i	0.869053	−	0.0139546i
$151$			3.98894e8i			0.767272i	0.923484	+	0.383636i	$0.125328\pi$
$151$			3.98894e8i			0.767272i	−0.923484	+	0.383636i	$0.874672\pi$
$152$	−2.67701e8	−	9.03438e8i	−0.501506	−	1.69248i
$153$	−6.36256e7	−	1.95820e8i	−0.116109	−	0.357347i
$154$	3.08715e7	+	4.32775e7i	0.0548877	+	0.0769447i
$155$	−2.06617e8	+	6.63742e8i	−0.357964	+	1.14993i
$156$	4.98571e7	−	1.52462e7i	0.0841837	−	0.0257432i
$157$	−1.05338e8			−0.173376			−0.0866879	−	0.996236i	$-0.527628\pi$
$157$	−1.05338e8			−0.173376			−0.0866879	+	0.996236i	$0.527628\pi$
$158$	9.06421e8	+	7.88233e6i	1.45446	+	0.0126481i
$159$	−4.58098e8	−	6.30517e8i	−0.716753	−	0.986526i
$160$	−6.55043e8	−	2.03807e7i	−0.999516	−	0.0310985i
$161$	1.00620e8	+	7.31044e7i	0.149754	+	0.108803i
$162$	2.84981e8	−	3.85154e8i	0.413767	−	0.559209i
$163$	−4.60251e8	−	6.33482e8i	−0.651996	−	0.897395i	0.347188	−	0.937796i	$-0.387137\pi$
$163$	−4.60251e8	−	6.33482e8i	−0.651996	−	0.897395i	−0.999184	+	0.0404007i	$0.987137\pi$
$164$	8.55527e8	+	1.48806e7i	1.18266	+	0.0205706i
$165$	2.58670e8	+	8.05218e7i	0.348988	+	0.108637i
$166$	7.43539e8	+	5.50155e8i	0.979200	+	0.724523i
$167$	1.28104e9	+	4.16236e8i	1.64702	+	0.535148i	0.978091	−	0.208180i	$-0.0667539\pi$
$167$	1.28104e9	+	4.16236e8i	1.64702	+	0.535148i	0.668927	+	0.743328i	$0.266754\pi$
$168$	9.47205e7	−	1.23466e8i	0.118907	−	0.154992i
$169$	−2.49489e8	+	7.67848e8i	−0.305847	+	0.941300i
$170$	−1.04093e9	−	7.50444e8i	−1.24631	−	0.898510i
$171$	−3.51044e8	+	1.14061e8i	−0.410560	+	0.133399i
$172$	−4.64139e8	+	6.16013e8i	−0.530316	+	0.703843i
$173$	1.65812e8	+	1.20470e8i	0.185111	+	0.134491i	0.676482	−	0.736460i	$-0.263504\pi$
$173$	1.65812e8	+	1.20470e8i	0.185111	+	0.134491i	−0.491370	+	0.870951i	$0.663504\pi$
$174$	−2.49468e8	−	7.91128e8i	−0.272156	−	0.863077i
$175$	−5.21704e6	−	2.10731e8i	−0.00556253	−	0.224686i
$176$	−3.79183e8	−	1.37958e8i	−0.395183	−	0.143780i
$177$	7.46902e8	+	5.42656e8i	0.760975	+	0.552881i
$178$	−3.24062e8	−	4.54289e8i	−0.322811	−	0.452535i
$179$	−1.47939e9	+	4.80683e8i	−1.44102	+	0.468216i	−0.922216	−	0.386676i	$-0.873623\pi$
$179$	−1.47939e9	+	4.80683e8i	−1.44102	+	0.468216i	−0.518806	+	0.854892i	$0.673623\pi$
$180$	−1.28767e6	+	2.56718e8i	−0.00122664	+	0.244549i
$181$	2.40647e8	−	7.40634e8i	0.224215	−	0.690064i	−0.774155	−	0.632996i	$-0.781825\pi$
$181$	2.40647e8	−	7.40634e8i	0.224215	−	0.690064i	0.998370	−	0.0570677i	$-0.0181751\pi$
$182$	−7.51134e6	−	2.38204e7i	−0.00684592	−	0.0217102i
$183$	8.59134e8	+	2.79149e8i	0.766049	+	0.248904i
$184$	−9.43703e8	−	2.46246e7i	−0.823311	−	0.0214831i
$185$	8.00589e8	+	1.07372e9i	0.683475	+	0.916649i
$186$	1.18815e9	+	3.97509e8i	0.992704	+	0.332120i
$187$	−4.64398e8	−	6.39189e8i	−0.379773	−	0.522712i
$188$	5.82675e8	+	2.00591e8i	0.466439	+	0.160576i
$189$	−2.50975e8	−	1.82344e8i	−0.196690	−	0.142904i
$190$	−1.34531e9	+	1.86607e9i	−1.03231	+	1.43190i
$191$	−1.18237e9	−	1.62739e9i	−0.888422	−	1.22281i	−0.974016	−	0.226478i	$-0.927279\pi$
$191$	−1.18237e9	−	1.62739e9i	−0.888422	−	1.22281i	0.0855942	−	0.996330i	$-0.472721\pi$
$192$	−6.15992e7	+	1.17955e9i	−0.0453284	+	0.867982i
$193$	5.96776e8			0.430112			0.215056	−	0.976602i	$-0.431007\pi$
$193$	5.96776e8			0.430112			0.215056	+	0.976602i	$0.431007\pi$
$194$	−4.15995e6	+	4.78369e8i	−0.00293684	+	0.337719i
$195$	−1.03894e8	−	7.35364e7i	−0.0718542	−	0.0508585i
$196$	1.11913e9	+	8.43218e8i	0.758328	+	0.571368i
$197$	−5.04184e8	−	1.55172e9i	−0.334753	−	1.03026i	−0.966844	−	0.255369i	$-0.917803\pi$
$197$	−5.04184e8	−	1.55172e9i	−0.334753	−	1.03026i	0.632091	−	0.774894i	$-0.282197\pi$
$198$	−5.01489e7	+	1.49895e8i	−0.0326288	+	0.0975271i
$199$		−	3.43759e8i		−	0.219200i	−0.993976	−	0.109600i	$-0.965043\pi$
$199$		−	3.43759e8i		−	0.219200i	0.993976	−	0.109600i	$-0.0349571\pi$
$200$	9.38726e8	+	1.29568e9i	0.586704	+	0.809801i
$201$	1.86251e9			1.14108
$202$	−1.96366e9	−	6.56963e8i	−1.17940	−	0.394580i
$203$	−3.77948e8	+	1.22803e8i	−0.222561	+	0.0723143i
$204$	−1.39176e9	+	1.84716e9i	−0.803604	+	1.06656i
$205$	−1.24871e9	−	1.67472e9i	−0.707042	−	0.948256i
$206$	1.07344e9	+	9.33472e6i	0.596084	+	0.00518361i
$207$			3.69798e8i			0.201411i
$208$	1.49405e8	+	1.16698e8i	0.0798200	+	0.0623464i
$209$	−1.14587e9	+	8.32521e8i	−0.600550	+	0.436325i
$210$	−3.79915e8	+	1.39810e6i	−0.195348	+	0.000718887i
$211$	−2.22947e9	+	3.06860e9i	−1.12479	+	1.54814i	−0.327187	+	0.944959i	$0.606101\pi$
$211$	−2.22947e9	+	3.06860e9i	−1.12479	+	1.54814i	−0.797603	+	0.603182i	$0.793899\pi$
$212$	9.22479e8	−	2.67961e9i	0.456681	−	1.32656i
$213$	3.98689e8	−	2.89664e8i	0.193694	−	0.140727i
$214$	1.84602e7	−	5.51773e7i	0.00880198	−	0.0263090i
$215$	1.88290e9	−	2.33038e7i	0.881199	−	0.0109062i
$216$	2.35387e9	+	6.14209e7i	1.08135	+	0.0282164i
$217$	1.85476e8	−	5.70837e8i	0.0836467	−	0.257438i
$218$	6.35955e8	−	2.00537e8i	0.281579	−	0.0887910i
$219$	3.42977e9	+	1.11440e9i	1.49104	+	0.484467i
$220$	2.99712e8	+	9.38407e8i	0.127942	+	0.400590i
$221$	1.14710e8	+	3.53041e8i	0.0480875	+	0.147998i
$222$	1.96513e9	−	1.40181e9i	0.809059	−	0.577134i
$223$	1.04648e9	−	1.44036e9i	0.423167	−	0.582439i	−0.543201	−	0.839603i	$-0.682788\pi$
$223$	1.04648e9	−	1.44036e9i	0.423167	−	0.582439i	0.966368	+	0.257164i	$0.0827879\pi$
$224$	5.65316e8	+	2.45951e7i	0.224543	+	0.00976915i
$225$	4.97787e8	−	3.80837e8i	0.194229	−	0.148597i
$226$	−1.96218e9	+	6.18741e8i	−0.752153	+	0.237178i
$227$	1.64338e9	−	2.26192e9i	0.618919	−	0.851870i	−0.378354	−	0.925661i	$-0.623510\pi$
$227$	1.64338e9	−	2.26192e9i	0.618919	−	0.851870i	0.997274	+	0.0737913i	$0.0235099\pi$
$228$	3.31138e9	+	2.49499e9i	1.22538	+	0.923270i
$229$	2.98197e8	+	9.17755e8i	0.108433	+	0.333722i	0.990521	−	0.137363i	$-0.0438626\pi$
$229$	2.98197e8	+	9.17755e8i	0.108433	+	0.333722i	−0.882088	+	0.471085i	$0.843863\pi$
$230$	1.36155e9	+	1.85958e9i	0.486544	+	0.664513i
$231$	−2.22464e8	−	7.22828e7i	−0.0781287	−	0.0253856i
$232$	1.83603e9	−	2.39321e9i	0.633763	−	0.826094i
$233$	8.46546e8	−	2.60540e9i	0.287228	−	0.883997i	−0.698494	−	0.715616i	$-0.746146\pi$
$233$	8.46546e8	−	2.60540e9i	0.287228	−	0.883997i	0.985722	−	0.168381i	$-0.0538539\pi$
$234$	4.41715e7	−	5.96982e7i	0.0147326	−	0.0199112i
$235$	−4.82582e8	−	1.42498e9i	−0.158234	−	0.467238i
$236$	−5.83822e7	+	3.35655e9i	−0.0188206	+	1.08204i
$237$	−3.22679e9	+	2.34440e9i	−1.02277	+	0.743086i
$238$	8.90674e8	+	6.59021e8i	0.277594	+	0.205396i
$239$	−2.97325e9	+	4.09233e9i	−0.911254	+	1.25423i	0.0554821	+	0.998460i	$0.482330\pi$
$239$	−2.97325e9	+	4.09233e9i	−0.911254	+	1.25423i	−0.966737	+	0.255774i	$0.917670\pi$
$240$	2.37034e9	−	1.64229e9i	0.714439	−	0.494999i
$241$	8.91706e8	−	6.47863e8i	0.264334	−	0.192050i	−0.447721	−	0.894173i	$-0.647764\pi$
$241$	8.91706e8	−	6.47863e8i	0.264334	−	0.192050i	0.712056	+	0.702123i	$0.247764\pi$
$242$	2.45501e7	−	2.82311e9i	0.00715800	−	0.823127i
$243$		−	1.66352e9i		−	0.477093i
$244$	9.60572e8	+	3.14120e9i	0.271001	+	0.886208i
$245$	−4.23368e7	−	3.42073e9i	−0.0117504	−	0.949412i
$246$	−3.06509e9	+	2.18645e9i	−0.836956	+	0.597034i
$247$	6.32894e8	−	2.05640e8i	0.170037	−	0.0552483i
$248$	1.29432e9	+	4.36806e9i	0.342164	+	1.15473i
$249$	−4.06989e9			−1.05873
$250$	1.10100e9	−	3.74788e9i	0.281855	−	0.959457i
$251$			4.01460e9i			1.01146i	0.862692	+	0.505729i	$0.168776\pi$
$251$			4.01460e9i			1.01146i	−0.862692	+	0.505729i	$0.831224\pi$
$252$	3.85483e6	−	2.21625e8i	0.000955880	−	0.0549561i
$253$	4.38499e8	+	1.34956e9i	0.107025	+	0.329390i
$254$	1.78841e9	−	1.27574e9i	0.429667	−	0.306499i
$255$	5.64602e9	−	6.98781e7i	1.33531	−	0.0165265i
$256$	−3.64178e9	+	2.27688e9i	−0.847918	+	0.530128i
$257$	−5.60682e8			−0.128524			−0.0642619	−	0.997933i	$-0.520469\pi$
$257$	−5.60682e8			−0.128524			−0.0642619	+	0.997933i	$0.520469\pi$
$258$	2.95119e7	−	3.39369e9i	0.00666067	−	0.765937i
$259$	−6.79718e8	−	9.35552e8i	−0.151053	−	0.207907i
$260$	2.32154e6	−	4.62835e8i	0.000508022	−	0.101282i
$261$	−9.55924e8	−	6.94519e8i	−0.205997	−	0.149666i
$262$	−3.88755e9	−	2.87645e9i	−0.825032	−	0.610452i
$263$	−2.03531e9	−	2.80136e9i	−0.425409	−	0.585525i	0.541483	−	0.840712i	$-0.317863\pi$
$263$	−2.03531e9	−	2.80136e9i	−0.425409	−	0.585525i	−0.966892	+	0.255186i	$0.917863\pi$
$264$	1.70230e9	−	5.04414e8i	0.350445	−	0.103842i
$265$	−6.55323e9	+	2.21930e9i	−1.32884	+	0.450021i
$266$	1.18142e9	−	1.59670e9i	0.235982	−	0.318931i
$267$	2.33523e9	+	7.58761e8i	0.459498	+	0.149300i
$268$	3.88491e9	+	5.54750e9i	0.753081	+	1.07537i
$269$	−1.55613e8	+	4.78926e8i	−0.0297191	+	0.0914660i	−0.964816	−	0.262927i	$-0.915312\pi$
$269$	−1.55613e8	+	4.78926e8i	−0.0297191	+	0.0914660i	0.935097	+	0.354392i	$0.115312\pi$
$270$	−3.39610e9	−	4.63834e9i	−0.639036	−	0.872785i
$271$	−6.81481e9	+	2.21427e9i	−1.26350	+	0.410538i	−0.862742	−	0.505644i	$-0.831255\pi$
$271$	−6.81481e9	+	2.21427e9i	−1.26350	+	0.410538i	−0.400763	+	0.916182i	$0.631255\pi$
$272$	−8.40476e9	−	2.92465e8i	−1.53550	−	0.0534317i
$273$	8.89115e7	+	6.45980e7i	0.0160069	+	0.0116297i
$274$	3.53749e9	−	1.11548e9i	0.627614	−	0.197907i
$275$	1.36506e9	−	1.98011e9i	0.238683	−	0.346226i
$276$	3.40248e9	−	2.38276e9i	0.586354	−	0.410623i
$277$	−6.94768e9	−	5.04778e9i	−1.18011	−	0.857397i	−0.187922	−	0.982184i	$-0.560175\pi$
$277$	−6.94768e9	−	5.04778e9i	−1.18011	−	0.857397i	−0.992183	+	0.124787i	$0.960175\pi$
$278$	2.86590e9	−	2.04436e9i	0.479824	−	0.342278i
$279$	1.69727e9	−	5.51477e8i	0.280114	−	0.0910145i
$280$	−7.96608e8	−	1.12866e9i	−0.129602	−	0.183625i
$281$	−2.71712e9	+	8.36245e9i	−0.435797	+	1.34125i	0.456471	+	0.889738i	$0.349113\pi$
$281$	−2.71712e9	+	8.36245e9i	−0.435797	+	1.34125i	−0.892268	+	0.451507i	$0.850887\pi$
$282$	−2.58601e9	+	8.15452e8i	−0.408915	+	0.128944i
$283$	−1.26089e9	−	4.09687e8i	−0.196576	−	0.0638714i	0.209074	−	0.977900i	$-0.432955\pi$
$283$	−1.26089e9	−	4.09687e8i	−0.196576	−	0.0638714i	−0.405650	+	0.914028i	$0.632955\pi$
$284$	1.69437e9	+	5.83302e8i	0.260456	+	0.0896644i
$285$	−1.25270e8	−	1.01216e10i	−0.0189875	−	1.53415i
$286$	9.04130e7	−	2.70244e8i	0.0135135	−	0.0403916i
$287$	1.06018e9	+	1.45921e9i	0.156262	+	0.215076i
$288$	9.28821e8	+	1.40283e9i	0.135009	+	0.203908i
$289$	−7.67863e9	−	5.57885e9i	−1.10076	−	0.799748i
$290$	−7.36412e9	+	2.71002e7i	−1.04119	+	0.00383161i
$291$	−1.23727e9	−	1.70296e9i	−0.172541	−	0.237483i
$292$	3.83472e9	+	1.25400e10i	0.527476	+	1.72492i
$293$	9.51666e8			0.129126			0.0645630	−	0.997914i	$-0.479435\pi$
$293$	9.51666e8			0.129126			0.0645630	+	0.997914i	$0.479435\pi$
$294$	−6.16543e9	−	5.36152e7i	−0.825228	−	0.00717627i
$295$	6.57053e9	−	4.89914e9i	0.867585	−	0.646892i
$296$	8.27426e9	+	2.92921e9i	1.07786	+	0.381578i
$297$	−1.09374e9	−	3.36620e9i	−0.140569	−	0.432628i
$298$	4.57599e8	+	1.53095e8i	0.0580256	+	0.0194131i
$299$		−	6.66706e8i		−	0.0834161i
$300$	−6.71149e9	−	2.12621e9i	−0.828579	−	0.262496i
$301$	−1.62586e9			−0.198069
$302$	2.02495e9	−	6.05255e9i	0.243437	−	0.727630i
$303$	8.66519e9	−	2.81549e9i	1.02803	−	0.334028i
$304$	−5.24300e8	+	1.50671e10i	−0.0613882	+	1.76415i
$305$	4.63309e9	−	6.54575e9i	0.535391	−	0.756415i
$306$	−2.86469e7	+	3.29422e9i	−0.00326732	+	0.375723i
$307$		−	1.03098e10i		−	1.16064i	−0.814389	−	0.580319i	$-0.802928\pi$
$307$		−	1.03098e10i		−	1.16064i	0.814389	−	0.580319i	$-0.197072\pi$
$308$	−2.48730e8	−	8.13380e8i	−0.0276392	−	0.0903838i
$309$	−3.82136e9	+	2.77638e9i	−0.419164	+	0.304540i
$310$	6.50450e9	−	9.02231e9i	0.704315	−	0.976947i
$311$	7.85698e9	−	1.08142e10i	0.839874	−	1.15599i	−0.146130	−	0.989265i	$-0.546682\pi$
$311$	7.85698e9	−	1.08142e10i	0.839874	−	1.15599i	0.986004	−	0.166722i	$-0.0533181\pi$
$312$	−8.33894e8	−	2.17593e7i	−0.0880020	−	0.00229629i
$313$	4.85076e7	−	3.52429e7i	0.00505397	−	0.00367193i	−0.585255	−	0.810849i	$-0.699006\pi$
$313$	4.85076e7	−	3.52429e7i	0.00505397	−	0.00367193i	0.590309	+	0.807177i	$0.299006\pi$
$314$	1.59834e9	+	5.34741e8i	0.164418	+	0.0550079i
$315$	−4.33836e8	+	3.23478e8i	−0.0440639	+	0.0328551i
$316$	−1.37134e10	−	4.72096e9i	−1.37530	−	0.473459i
$317$	−6.03850e9	+	1.85846e10i	−0.597987	+	1.84042i	−0.0587304	+	0.998274i	$0.518705\pi$
$317$	−6.03850e9	+	1.85846e10i	−0.597987	+	1.84042i	−0.539257	+	0.842141i	$0.681295\pi$
$318$	3.75011e9	+	1.18925e10i	0.366720	+	1.16296i
$319$	−4.31215e9	−	1.40110e9i	−0.416419	−	0.135303i
$320$	9.83573e9	+	3.63451e9i	0.938008	+	0.346614i
$321$	7.91132e7	+	2.43485e8i	0.00745124	+	0.0229326i
$322$	−1.15563e9	−	1.62002e9i	−0.107497	−	0.150695i
$323$	−1.73516e10	+	2.38825e10i	−1.59415	+	2.19416i
$324$	−6.27931e9	+	4.39739e9i	−0.569812	+	0.399039i
$325$	−8.97456e8	+	6.86608e8i	−0.0804414	+	0.0615426i
$326$	3.76774e9	+	1.19485e10i	0.333588	+	1.05789i
$327$	−1.72463e9	+	2.37375e9i	−0.150836	+	0.207608i
$328$	−1.29057e10	−	4.56879e9i	−1.11503	−	0.394735i
$329$	4.01413e8	+	1.23542e9i	0.0342616	+	0.105446i
$330$	−3.51613e9	−	2.53490e9i	−0.296489	−	0.213750i
$331$	−1.23005e10	−	3.99669e9i	−1.02474	−	0.332957i	−0.252029	−	0.967720i	$-0.581098\pi$
$331$	−1.23005e10	−	3.99669e9i	−1.02474	−	0.332957i	−0.772707	+	0.634762i	$0.781098\pi$
$332$	−8.48916e9	−	1.21222e10i	−0.698735	−	0.997766i
$333$	1.06251e9	−	3.27006e9i	0.0864083	−	0.265937i
$334$	−1.73247e10	−	1.28188e10i	−1.39213	−	1.03006i
$335$	4.91445e9	−	1.57873e10i	0.390207	−	1.25351i
$336$	−2.06399e9	+	1.39255e9i	−0.161939	+	0.109258i
$337$	−4.92192e9	+	3.57599e9i	−0.381606	+	0.277253i	−0.762007	−	0.647569i	$-0.775786\pi$
$337$	−4.92192e9	+	3.57599e9i	−0.381606	+	0.277253i	0.380401	+	0.924822i	$0.375786\pi$
$338$	7.68348e9	−	1.03843e10i	0.588696	−	0.795629i
$339$	5.32121e9	−	7.32402e9i	0.402913	−	0.554563i
$340$	1.19848e10	+	1.66709e10i	0.896844	+	1.24751i
$341$	5.54019e9	−	4.02518e9i	0.409739	−	0.297692i
$342$	5.90552e9	+	5.13551e7i	0.431672	+	0.00375387i
$343$			6.06466e9i			0.438157i
$344$	1.01697e10	−	6.99081e9i	0.726229	−	0.499222i
$345$	−9.68292e9	−	3.01421e9i	−0.683487	−	0.212763i
$346$	−1.90437e9	−	2.66966e9i	−0.132876	−	0.186274i
$347$	−1.59869e10	+	5.19445e9i	−1.10267	+	0.358279i	−0.803129	−	0.595805i	$-0.796833\pi$
$347$	−1.59869e10	+	5.19445e9i	−1.10267	+	0.358279i	−0.299540	+	0.954084i	$0.596833\pi$
$348$	−2.30820e8	+	1.32704e10i	−0.0157382	+	0.904833i
$349$	9.90906e9			0.667930			0.333965	−	0.942586i	$-0.391613\pi$
$349$	9.90906e9			0.667930			0.333965	+	0.942586i	$0.391613\pi$
$350$	−9.90598e8	+	3.22398e9i	−0.0660124	+	0.214842i
$351$			1.66296e9i			0.109560i
$352$	5.05313e9	+	4.01817e9i	0.329147	+	0.261733i
$353$	−4.23838e9	−	1.30444e10i	−0.272961	−	0.840088i	−0.989752	−	0.142800i	$-0.954390\pi$
$353$	−4.23838e9	−	1.30444e10i	−0.272961	−	0.840088i	0.716790	−	0.697289i	$-0.245610\pi$
$354$	−8.57825e9	−	1.20255e10i	−0.546243	−	0.765754i
$355$	−1.40331e9	−	4.14374e9i	−0.0883569	−	0.260903i
$356$	2.61095e9	+	8.53814e9i	0.162554	+	0.531574i
$357$	−4.87525e9			−0.300140
$358$	2.48874e10	+	2.16424e8i	1.51512	+	0.0131757i
$359$	−1.13620e10	−	1.56384e10i	−0.684031	−	0.941488i	0.315943	−	0.948778i	$-0.397679\pi$
$359$	−1.13620e10	−	1.56384e10i	−0.684031	−	0.941488i	−0.999973	+	0.00729062i	$0.997679\pi$
$360$	1.32274e9	−	3.88873e9i	0.0787527	−	0.231525i
$361$	2.90739e10	+	2.11234e10i	1.71188	+	1.24376i
$362$	−7.41117e9	+	1.00163e10i	−0.431571	+	0.583273i
$363$	7.30181e9	+	1.00501e10i	0.420537	+	0.578820i
$364$	−6.94985e6	+	3.99565e8i	−0.000395886	+	0.0227605i
$365$	1.84959e10	−	2.61314e10i	1.04209	−	1.47228i
$366$	−1.16188e10	−	8.59694e9i	−0.647498	−	0.479093i
$367$	−1.22415e10	−	3.97750e9i	−0.674792	−	0.219253i	−0.0484780	−	0.998824i	$-0.515437\pi$
$367$	−1.22415e10	−	3.97750e9i	−0.674792	−	0.219253i	−0.626314	+	0.779571i	$0.715437\pi$
$368$	1.41941e10	+	5.16426e9i	0.773957	+	0.281590i
$369$	−1.65723e9	+	5.10044e9i	−0.0893877	+	0.275107i
$370$	−6.69698e9	−	2.03560e10i	−0.357332	−	1.08614i
$371$	5.68146e9	−	1.84602e9i	0.299892	−	0.0974408i
$372$	−1.60103e10	−	1.20631e10i	−0.836041	−	0.629922i
$373$	1.38694e10	+	1.00767e10i	0.716512	+	0.520576i	0.885268	−	0.465082i	$-0.153975\pi$
$373$	1.38694e10	+	1.00767e10i	0.716512	+	0.520576i	−0.168756	+	0.985658i	$0.553975\pi$
$374$	3.80168e9	+	1.20561e10i	0.194307	+	0.616198i
$375$	5.91453e9	+	1.61384e10i	0.299085	+	0.816086i
$376$	−7.82284e9	−	6.00153e9i	−0.391393	−	0.300269i
$377$	1.72343e9	+	1.25214e9i	0.0853154	+	0.0619853i
$378$	2.88247e9	+	4.04081e9i	0.141188	+	0.197925i
$379$	−6.33685e9	+	2.05897e9i	−0.307126	+	0.0997914i	−0.458525	−	0.888681i	$-0.651622\pi$
$379$	−6.33685e9	+	2.05897e9i	−0.307126	+	0.0997914i	0.151399	+	0.988473i	$0.451622\pi$
$380$	2.98858e10	−	2.14851e10i	1.43328	−	1.03039i
$381$	−2.98704e9	+	9.19315e9i	−0.141756	+	0.436279i
$382$	9.67917e9	+	3.06951e10i	0.454553	+	1.44150i
$383$	2.75702e10	+	8.95811e9i	1.28128	+	0.416314i	0.869032	−	0.494756i	$-0.164743\pi$
$383$	2.75702e10	+	8.95811e9i	1.28128	+	0.416314i	0.412251	+	0.911070i	$0.364743\pi$
$384$	6.92253e9	−	1.75850e10i	0.318376	−	0.808755i
$385$	−1.19969e9	+	1.69495e9i	−0.0546042	+	0.0771462i
$386$	−9.05508e9	−	3.02948e9i	−0.407890	−	0.136464i
$387$	−2.84146e9	−	3.91093e9i	−0.126677	−	0.174356i
$388$	2.49152e9	−	7.23733e9i	0.109935	−	0.319339i
$389$	−2.30268e9	−	1.67299e9i	−0.100562	−	0.0730627i	0.536368	−	0.843984i	$-0.319796\pi$
$389$	−2.30268e9	−	1.67299e9i	−0.100562	−	0.0730627i	−0.636930	+	0.770922i	$0.719796\pi$
$390$	1.20312e9	+	1.64320e9i	0.0520056	+	0.0710284i
$391$	1.73840e10	+	2.39270e10i	0.743777	+	1.02372i
$392$	−1.27004e10	−	1.84756e10i	−0.537866	−	0.782446i
$393$	2.12792e10			0.892040
$394$	−2.27005e8	+	2.61042e10i	−0.00941999	+	1.08324i
$395$	1.13577e10	+	3.35374e10i	0.466555	+	1.37766i
$396$	1.52185e9	−	2.01982e9i	0.0618859	−	0.0821359i
$397$	9.54450e9	+	2.93750e10i	0.384230	+	1.18254i	0.937037	+	0.349229i	$0.113557\pi$
$397$	9.54450e9	+	2.93750e10i	0.384230	+	1.18254i	−0.552807	+	0.833309i	$0.686443\pi$
$398$	−1.74506e9	+	5.21597e9i	−0.0695469	+	0.207875i
$399$			8.73982e9i			0.344835i
$400$	−7.66620e9	−	2.44252e10i	−0.299461	−	0.954109i
$401$	3.30843e10			1.27951			0.639757	−	0.768577i	$-0.279035\pi$
$401$	3.30843e10			1.27951			0.639757	+	0.768577i	$0.279035\pi$
$402$	−2.82605e10	−	9.45486e9i	−1.08212	−	0.362035i
$403$	−3.06000e9	+	9.94253e8i	−0.116011	+	0.0376944i
$404$	2.64602e10	+	1.99366e10i	0.993271	+	0.748387i
$405$	1.78699e10	+	5.56274e9i	0.664205	+	0.206761i
$406$	6.35813e9	+	5.52910e7i	0.234005	+	0.00203493i
$407$		−	1.31939e10i		−	0.480833i
$408$	3.04945e10	−	2.09624e10i	1.10048	−	0.756486i
$409$	8.68831e9	−	6.31243e9i	0.310486	−	0.225581i	−0.421619	−	0.906773i	$-0.638538\pi$
$409$	8.68831e9	−	6.31243e9i	0.310486	−	0.225581i	0.732105	+	0.681192i	$0.238538\pi$
$410$	1.04455e10	+	3.17500e10i	0.369653	+	1.12359i
$411$	−9.59324e9	+	1.32040e10i	−0.336200	+	0.462740i
$412$	−1.62402e10	−	5.59084e9i	−0.563642	−	0.194039i
$413$	−5.72504e9	+	4.15948e9i	−0.196779	+	0.142968i
$414$	1.87725e9	−	5.61107e9i	0.0639028	−	0.191005i
$415$	−1.07389e10	+	3.44978e10i	−0.362048	+	1.16305i
$416$	−1.67456e9	−	2.52914e9i	−0.0559150	−	0.0844501i
$417$	−4.78668e9	+	1.47319e10i	−0.158303	+	0.487208i
$418$	2.16128e10	−	6.81523e9i	0.707957	−	0.223242i
$419$	1.66981e10	+	5.42556e9i	0.541767	+	0.176031i	0.567101	−	0.823648i	$-0.308065\pi$
$419$	1.66981e10	+	5.42556e9i	0.541767	+	0.176031i	−0.0253342	+	0.999679i	$0.508065\pi$
$420$	5.77167e9	+	1.90739e9i	0.185483	+	0.0612974i
$421$	7.26131e9	+	2.23480e10i	0.231146	+	0.711394i	0.997609	+	0.0691063i	$0.0220147\pi$
$421$	7.26131e9	+	2.23480e10i	0.231146	+	0.711394i	−0.766463	+	0.642288i	$0.777985\pi$
$422$	4.94060e10	−	3.52432e10i	1.55786	−	1.11129i
$423$	−2.27022e9	+	3.12468e9i	−0.0709097	+	0.0975988i
$424$	−2.75999e10	+	3.59757e10i	−0.853972	+	1.11313i
$425$	1.43053e10	−	4.80420e10i	0.438473	−	1.47253i
$426$	−7.51990e9	+	2.37127e9i	−0.228335	+	0.0720016i
$427$	−4.06994e9	+	5.60179e9i	−0.122427	+	0.168506i
$428$	−5.60205e8	+	7.43512e8i	−0.0166944	+	0.0221571i
$429$	3.87475e8	+	1.19253e9i	0.0114397	+	0.0352078i
$430$	−2.86882e10	−	9.20478e9i	−0.839131	−	0.269240i
$431$	1.60330e10	+	5.20943e9i	0.464628	+	0.150967i	0.531970	−	0.846763i	$-0.321452\pi$
$431$	1.60330e10	+	5.20943e9i	0.464628	+	0.150967i	−0.0673420	+	0.997730i	$0.521452\pi$
$432$	−3.54043e10	−	1.28812e10i	−1.01653	−	0.369845i
$433$	−6.84251e9	+	2.10591e10i	−0.194654	+	0.599084i	0.805326	+	0.592832i	$0.201990\pi$
$433$	−6.84251e9	+	2.10591e10i	−0.194654	+	0.599084i	−0.999980	+	0.00625206i	$0.998010\pi$
$434$	−5.71209e9	+	7.71994e9i	−0.161004	+	0.217598i
$435$	2.59772e10	−	1.93692e10i	0.725497	−	0.540948i
$436$	−1.06676e10	−	1.85546e8i	−0.295202	−	0.00513460i
$437$	4.28938e10	−	3.11641e10i	1.17617	−	0.854534i
$438$	−4.63839e10	−	3.43200e10i	−1.26029	−	0.932506i
$439$	6.77965e9	−	9.33139e9i	0.182536	−	0.251240i	−0.707937	−	0.706276i	$-0.750374\pi$
$439$	6.77965e9	−	9.33139e9i	0.182536	−	0.251240i	0.890473	+	0.455036i	$0.150374\pi$
$440$	2.16114e8	−	1.57602e10i	0.00576596	−	0.420486i
$441$	−7.10512e9	+	5.16218e9i	−0.187853	+	0.136483i
$442$	5.16473e7	−	5.93913e9i	0.00135319	−	0.155609i
$443$			2.58965e10i			0.672399i	0.941791	+	0.336199i	$0.109142\pi$
$443$			2.58965e10i			0.672399i	−0.941791	+	0.336199i	$0.890858\pi$
$444$	−3.69338e10	+	1.12943e10i	−0.950368	+	0.290621i
$445$	1.25933e10	−	1.77921e10i	0.321143	−	0.453719i
$446$	−2.31904e10	+	1.65426e10i	−0.586097	+	0.418086i
$447$	−2.01928e9	+	6.56105e8i	−0.0505786	+	0.0164340i
$448$	−8.45287e9	−	3.24296e9i	−0.209842	−	0.0805063i
$449$	−3.90008e10			−0.959595			−0.479797	−	0.877379i	$-0.659290\pi$
$449$	−3.90008e10			−0.959595			−0.479797	+	0.877379i	$0.659290\pi$
$450$	−9.48637e9	+	3.25160e9i	−0.231340	+	0.0792952i
$451$			2.05789e10i			0.497412i
$452$	3.29139e10	+	5.72488e8i	0.788543	+	0.0137155i
$453$	8.67815e9	+	2.67086e10i	0.206079	+	0.634247i
$454$	−3.64179e10	+	2.59784e10i	−0.857219	+	0.611488i
$455$	7.82159e8	−	5.83196e8i	0.0182494	−	0.0136072i
$456$	−3.75791e10	−	5.46672e10i	−0.869135	−	1.26435i
$457$	−1.74974e10			−0.401152			−0.200576	−	0.979678i	$-0.564281\pi$
$457$	−1.74974e10			−0.401152			−0.200576	+	0.979678i	$0.564281\pi$
$458$	1.34261e8	−	1.54392e10i	0.00305132	−	0.350883i
$459$	−4.33608e10	−	5.96810e10i	−0.976892	−	1.34458i
$460$	−1.12192e10	−	3.51278e10i	−0.250572	−	0.784549i
$461$	3.03914e10	+	2.20807e10i	0.672896	+	0.488887i	0.870993	−	0.491295i	$-0.163476\pi$
$461$	3.03914e10	+	2.20807e10i	0.672896	+	0.488887i	−0.198098	+	0.980182i	$0.563476\pi$
$462$	3.00858e9	+	2.22609e9i	0.0660379	+	0.0488623i
$463$	−2.48603e10	−	3.42172e10i	−0.540981	−	0.744597i	0.447773	−	0.894147i	$-0.352217\pi$
$463$	−2.48603e10	−	3.42172e10i	−0.540981	−	0.744597i	−0.988754	+	0.149551i	$0.952217\pi$
$464$	−4.00076e10	+	2.69926e10i	−0.863118	+	0.582335i
$465$	6.05671e8	+	4.89370e10i	0.0129546	+	1.04671i
$466$	−2.60710e10	+	3.52352e10i	−0.552859	+	0.747194i
$467$	−1.40212e10	−	4.55578e9i	−0.294794	−	0.0957845i	0.157886	−	0.987457i	$-0.449532\pi$
$467$	−1.40212e10	−	4.55578e9i	−0.294794	−	0.0957845i	−0.452680	+	0.891673i	$0.649532\pi$
$468$	−9.73282e8	+	6.81589e8i	−0.0202887	+	0.0142082i
$469$	−4.41160e9	+	1.35775e10i	−0.0911810	+	0.280626i
$470$	8.85841e7	+	2.40715e10i	0.00181537	+	0.493302i
$471$	−7.05311e9	+	2.29169e9i	−0.143317	+	0.0465664i
$472$	1.79251e10	−	5.06337e10i	0.361154	−	1.02017i
$473$	−1.50073e10	−	1.09034e10i	−0.299818	−	0.217830i
$474$	6.08624e10	−	1.91919e10i	1.20569	−	0.380193i
$475$	−8.61244e10	−	2.56451e10i	−1.69181	−	0.503766i
$476$	−1.01690e10	−	1.45210e10i	−0.198085	−	0.282858i
$477$	1.43698e10	+	1.04403e10i	0.277573	+	0.201669i
$478$	6.58884e10	−	4.70008e10i	1.26211	−	0.900313i
$479$	5.86324e10	−	1.90508e10i	1.11377	−	0.361886i	0.306383	−	0.951908i	$-0.400881\pi$
$479$	5.86324e10	−	1.90508e10i	1.11377	−	0.361886i	0.807387	+	0.590022i	$0.200881\pi$
$480$	−4.43029e10	+	1.28862e10i	−0.834578	+	0.242750i
$481$	−1.91559e9	+	5.89557e9i	−0.0357867	+	0.110140i
$482$	−1.68190e10	+	5.30357e9i	−0.311610	+	0.0982608i
$483$	8.32758e9	+	2.70579e9i	0.153014	+	0.0497171i
$484$	−1.47038e10	+	4.27114e10i	−0.267946	+	0.778328i
$485$	−1.76996e10	+	5.99410e9i	−0.319886	+	0.108332i
$486$	−8.44472e9	+	2.52412e10i	−0.151370	+	0.452444i
$487$	−3.24022e10	−	4.45978e10i	−0.576048	−	0.792863i	0.417207	−	0.908812i	$-0.363009\pi$
$487$	−3.24022e10	−	4.45978e10i	−0.576048	−	0.792863i	−0.993255	+	0.115949i	$0.963009\pi$
$488$	1.37092e9	−	5.25387e10i	0.0241732	−	0.926403i
$489$	−4.45986e10	−	3.24028e10i	−0.779984	−	0.566692i
$490$	−1.67226e10	+	5.21189e10i	−0.290082	+	0.904088i
$491$	−1.98955e10	−	2.73839e10i	−0.342318	−	0.471160i	0.602799	−	0.797893i	$-0.294052\pi$
$491$	−1.98955e10	−	2.73839e10i	−0.342318	−	0.471160i	−0.945117	+	0.326733i	$0.894052\pi$
$492$	5.76069e10	−	1.76161e10i	0.983138	−	0.300642i
$493$	−9.45001e10			−1.59972
$494$	−1.06470e10	−	9.25876e7i	−0.178781	−	0.00155469i
$495$	−6.17379e9	+	7.64101e7i	−0.102833	+	0.00127271i
$496$	2.53495e9	−	7.28485e10i	0.0418835	−	1.20363i
$497$	1.16728e9	+	3.59251e9i	0.0191315	+	0.0588806i
$498$	6.17538e10	+	2.06604e10i	1.00403	+	0.335909i
$499$		−	5.90692e9i		−	0.0952706i	−0.998865	−	0.0476353i	$-0.984831\pi$
$499$		−	5.90692e9i		−	0.0952706i	0.998865	−	0.0476353i	$-0.0151685\pi$
$500$	−3.57316e10	+	5.12787e10i	−0.571705	+	0.820459i
$501$	9.48298e10			1.50520
$502$	2.03798e10	−	6.09149e10i	0.320911	−	0.959199i
$503$	−1.69479e10	+	5.50671e9i	−0.264755	+	0.0860241i	−0.438386	−	0.898787i	$-0.644450\pi$
$503$	−1.69479e10	+	5.50671e9i	−0.264755	+	0.0860241i	0.173631	+	0.984811i	$0.444450\pi$
$504$	−1.18355e9	+	3.34321e9i	−0.0183427	+	0.0518134i
$505$	−1.00099e9	−	8.08781e10i	−0.0153909	−	1.24356i
$506$	1.97431e8	−	2.27033e10i	0.00301171	−	0.346328i
$507$			5.68402e10i			0.860249i
$508$	−3.36124e10	+	1.02786e10i	−0.504713	+	0.154340i
$509$	5.45699e9	−	3.96473e9i	0.0812984	−	0.0590667i	−0.546394	−	0.837529i	$-0.684000\pi$
$509$	5.45699e9	−	3.96473e9i	0.0812984	−	0.0590667i	0.627692	+	0.778462i	$0.284000\pi$
$510$	−8.60236e10	−	2.76012e10i	−1.27156	−	0.407988i
$511$	−1.62477e10	+	2.23630e10i	−0.238291	+	0.327980i
$512$	6.68163e10	−	1.60607e10i	0.972305	−	0.233715i
$513$	−1.06990e11	+	7.77325e10i	−1.54480	+	1.12236i
$514$	8.50741e9	+	2.84625e9i	0.121883	+	0.0407775i
$515$	1.34505e10	+	3.97170e10i	0.191209	+	0.564608i
$516$	−1.76755e10	+	5.13437e10i	−0.249330	+	0.724250i
$517$	−4.57986e9	+	1.40954e10i	−0.0641048	+	0.197294i
$518$	5.56435e9	+	1.76460e10i	0.0772850	+	0.245091i
$519$	1.37231e10	+	4.45891e9i	0.189140	+	0.0614554i
$520$	−2.38476e9	+	7.01096e9i	−0.0326161	+	0.0958880i
$521$	−2.09956e10	−	6.46179e10i	−0.284956	−	0.877005i	−0.986412	−	0.164292i	$-0.947466\pi$
$521$	−2.09956e10	−	6.46179e10i	−0.284956	−	0.877005i	0.701456	−	0.712713i	$-0.252534\pi$
$522$	1.09789e10	+	1.53908e10i	0.147869	+	0.207291i
$523$	6.20610e10	−	8.54196e10i	0.829491	−	1.14170i	−0.158526	−	0.987355i	$-0.550674\pi$
$523$	6.20610e10	−	8.54196e10i	0.829491	−	1.14170i	0.988018	−	0.154342i	$-0.0493257\pi$
$524$	4.43851e10	+	6.33801e10i	0.588724	+	0.840675i
$525$	−4.93389e9	−	1.39964e10i	−0.0649459	−	0.184237i
$526$	1.66615e10	+	5.28380e10i	0.217657	+	0.690245i
$527$	8.38939e10	−	1.15470e11i	1.08765	−	1.49702i
$528$	−2.83901e10	−	9.87908e8i	−0.365285	−	0.0127110i
$529$	7.78489e9	+	2.39594e10i	0.0994099	+	0.305952i
$530$	1.10700e11	−	4.07381e8i	1.40296	−	0.00516294i
$531$	−2.00109e10	−	6.50194e9i	−0.251703	−	0.0817833i
$532$	−2.60316e10	+	1.82299e10i	−0.324978	+	0.227582i
$533$	2.98781e9	−	9.19554e9i	0.0370207	−	0.113938i
$534$	−3.15814e10	−	2.33675e10i	−0.388388	−	0.287374i
$535$	2.27262e9	−	2.81271e7i	0.0277403	−	0.000343328i
$536$	−3.07857e10	−	1.03895e11i	−0.372983	−	1.25874i
$537$	−8.85974e10	+	6.43698e10i	−1.06543	+	0.774079i
$538$	4.79239e9	−	6.47695e9i	0.0572035	−	0.0773111i
$539$	−1.98086e10	+	2.72642e10i	−0.234693	+	0.323027i
$540$	2.79841e10	+	8.76190e10i	0.329106	+	1.03044i
$541$	7.18788e10	−	5.22230e10i	0.839096	−	0.609639i	−0.0830219	−	0.996548i	$-0.526457\pi$
$541$	7.18788e10	−	5.22230e10i	0.839096	−	0.609639i	0.922118	+	0.386909i	$0.126457\pi$
$542$	1.14644e11	+	9.96956e8i	1.32848	+	0.0115526i
$543$		−	5.48257e10i		−	0.630645i
$544$	1.26044e11	+	4.71037e10i	1.43921	+	0.537847i
$545$	1.55701e10	+	2.08820e10i	0.176484	+	0.236693i
$546$	−1.02116e9	−	1.43152e9i	−0.0114901	−	0.0161074i
$547$	−2.02094e10	+	6.56643e9i	−0.225738	+	0.0733466i	−0.419702	−	0.907662i	$-0.637865\pi$
$547$	−2.02094e10	+	6.56643e9i	−0.225738	+	0.0733466i	0.193964	+	0.981009i	$0.437865\pi$
$548$	−5.93381e10	−	1.03210e9i	−0.657978	−	0.0114446i
$549$	−2.05877e10			−0.226631
$550$	−3.07644e10	+	2.31153e10i	−0.336200	+	0.252609i
$551$			1.69409e11i			1.83794i
$552$	−6.37229e10	+	1.88820e10i	−0.686340	+	0.203372i
$553$	−9.44737e9	−	2.90760e10i	−0.101021	−	0.310910i
$554$	7.97949e10	+	1.11861e11i	0.847102	+	1.18752i
$555$	7.69640e10	+	5.44752e10i	0.811177	+	0.574152i
$556$	−5.38633e10	+	1.64713e10i	−0.563630	+	0.172357i
$557$	1.04832e10			0.108911			0.0544557	−	0.998516i	$-0.482658\pi$
$557$	1.04832e10			0.108911			0.0544557	+	0.998516i	$0.482658\pi$
$558$	−2.85528e10	−	2.48298e8i	−0.294518	−	0.00256116i
$559$	5.12284e9	+	7.05099e9i	0.0524643	+	0.0722109i
$560$	6.35765e9	+	2.11695e10i	0.0646464	+	0.215257i
$561$	−4.50004e10	−	3.26947e10i	−0.454323	−	0.330085i
$562$	8.36790e10	−	1.13093e11i	0.838825	−	1.13368i
$563$	−9.61648e10	−	1.32360e11i	−0.957156	−	1.31741i	−0.948275	−	0.317451i	$-0.897173\pi$
$563$	−9.61648e10	−	1.32360e11i	−0.957156	−	1.31741i	−0.00888128	−	0.999961i	$-0.502827\pi$
$564$	4.33779e10	+	7.54495e8i	0.428699	+	0.00745658i
$565$	−4.80403e10	−	6.44297e10i	−0.471424	−	0.632255i
$566$	1.70521e10	+	1.26171e10i	0.166155	+	0.122940i
$567$	−1.53686e10	−	4.99356e9i	−0.148697	−	0.0483146i
$568$	−2.27482e10	−	1.74520e10i	−0.218551	−	0.167668i
$569$	3.56889e10	−	1.09839e11i	0.340474	−	1.04787i	−0.623488	−	0.781833i	$-0.714285\pi$
$569$	3.56889e10	−	1.09839e11i	0.340474	−	1.04787i	0.963962	−	0.266039i	$-0.0857150\pi$
$570$	−4.94804e10	+	1.54214e11i	−0.468742	+	1.46091i
$571$	1.95923e11	−	6.36593e10i	1.84307	−	0.598849i	0.845137	−	0.534549i	$-0.179519\pi$
$571$	1.95923e11	−	6.36593e10i	1.84307	−	0.598849i	0.997931	−	0.0642996i	$-0.0204813\pi$
$572$	−2.74373e9	+	3.64152e9i	−0.0256306	+	0.0340172i
$573$	−1.14572e11	−	8.32415e10i	−1.06282	−	0.772185i
$574$	−8.67892e9	−	2.75231e10i	−0.0799499	−	0.253542i
$575$	−5.10990e10	+	7.41225e10i	−0.467456	+	0.678076i
$576$	−6.97199e9	−	2.60006e10i	−0.0633384	−	0.236208i
$577$	1.59202e11	+	1.15667e11i	1.43630	+	1.04353i	0.988799	+	0.149252i	$0.0476866\pi$
$577$	1.59202e11	+	1.15667e11i	1.43630	+	1.04353i	0.447503	+	0.894282i	$0.352313\pi$
$578$	8.81899e10	+	1.23630e11i	0.790146	+	1.10767i
$579$	3.99581e10	−	1.29832e10i	0.355542	−	0.115522i
$580$	1.11876e11	+	3.69721e10i	0.988609	+	0.326710i
$581$	9.64006e9	−	2.96690e10i	0.0846009	−	0.260375i
$582$	1.01286e10	+	3.21205e10i	0.0882793	+	0.279956i
$583$	6.48219e10	+	2.10619e10i	0.561109	+	0.182315i
$584$	5.47289e9	−	2.09741e11i	0.0470506	−	1.80315i
$585$	2.76980e9	+	8.62216e8i	0.0236497	+	0.00736194i
$586$	−1.44399e10	−	4.83104e9i	−0.122455	−	0.0409685i
$587$	2.90213e10	+	3.99444e10i	0.244436	+	0.336437i	0.913553	−	0.406720i	$-0.133328\pi$
$587$	2.90213e10	+	3.99444e10i	0.244436	+	0.336437i	−0.669117	+	0.743157i	$0.733328\pi$
$588$	9.32779e10	+	3.21118e10i	0.780314	+	0.268630i
$589$	−2.07002e11	−	1.50396e11i	−1.71994	−	1.24961i
$590$	−1.24567e11	+	4.09816e10i	−1.02800	+	0.338206i
$591$	−6.75169e10	−	9.29291e10i	−0.553430	−	0.761731i
$592$	−1.10678e11	−	8.64494e10i	−0.901105	−	0.703842i
$593$	−8.77555e10			−0.709669			−0.354834	−	0.934929i	$-0.615463\pi$
$593$	−8.77555e10			−0.709669			−0.354834	+	0.934929i	$0.615463\pi$
$594$	−4.92450e8	+	5.66288e10i	−0.00395563	+	0.454874i
$595$	−1.28639e10	+	4.13244e10i	−0.102637	+	0.329715i
$596$	−6.16613e9	−	4.64591e9i	−0.0488683	−	0.0368202i
$597$	−7.47865e9	−	2.30169e10i	−0.0588743	−	0.181197i
$598$	−3.38447e9	+	1.01162e10i	−0.0264659	+	0.0791062i
$599$		−	4.10745e10i		−	0.319055i	−0.987194	−	0.159527i	$-0.949003\pi$
$599$		−	4.10745e10i		−	0.319055i	0.987194	−	0.159527i	$-0.0509970\pi$
$600$	9.10422e10	+	6.63320e10i	0.702486	+	0.511821i
$601$	1.11309e11			0.853165			0.426582	−	0.904449i	$-0.359717\pi$
$601$	1.11309e11			0.853165			0.426582	+	0.904449i	$0.359717\pi$
$602$	2.46697e10	+	8.25352e9i	0.187836	+	0.0628425i
$603$	−4.03701e10	+	1.31170e10i	−0.305345	+	0.0992125i
$604$	−6.14504e10	+	8.15579e10i	−0.461718	+	0.612799i
$605$	1.04455e11	−	3.53744e10i	0.779662	−	0.264039i
$606$	−1.45772e11	−	1.26765e9i	−1.08090	−	0.00939960i
$607$			1.62599e11i			1.19774i	0.800847	+	0.598869i	$0.204383\pi$
$607$			1.62599e11i			1.19774i	−0.800847	+	0.598869i	$0.795617\pi$
$608$	8.44423e10	−	2.25957e11i	0.617939	−	1.65353i
$609$	−2.26345e10	+	1.64449e10i	−0.164551	+	0.119554i
$610$	−1.03528e11	+	7.58014e10i	−0.747721	+	0.547467i
$611$	4.09295e9	−	5.63347e9i	0.0293678	−	0.0404214i
$612$	1.71575e10	−	4.98390e10i	0.122306	−	0.355274i
$613$	−1.16342e11	+	8.45273e10i	−0.823937	+	0.598625i	−0.917837	−	0.396956i	$-0.870066\pi$
$613$	−1.16342e11	+	8.45273e10i	−0.823937	+	0.598625i	0.0939006	+	0.995582i	$0.470066\pi$
$614$	−5.23368e10	+	1.56434e11i	−0.368242	+	1.10067i
$615$	−1.20044e11	−	8.49670e10i	−0.839148	−	0.593950i
$616$	−3.54986e8	+	1.36043e10i	−0.00246540	+	0.0944832i
$617$	−1.97506e10	+	6.07860e10i	−0.136282	+	0.419434i	−0.995787	−	0.0916937i	$-0.970772\pi$
$617$	−1.97506e10	+	6.07860e10i	−0.136282	+	0.419434i	0.859505	+	0.511127i	$0.170772\pi$
$618$	7.20768e10	−	2.27282e10i	0.494130	−	0.155815i
$619$	3.76130e10	+	1.22212e10i	0.256198	+	0.0832437i	0.434300	−	0.900768i	$-0.356996\pi$
$619$	3.76130e10	+	1.22212e10i	0.256198	+	0.0832437i	−0.178102	+	0.984012i	$0.556996\pi$
$620$	−1.44496e11	+	1.03879e11i	−0.977887	+	0.703010i
$621$	4.09426e10	+	1.26008e11i	0.275302	+	0.847293i
$622$	−1.74114e11	+	1.24202e11i	−1.16325	+	0.829790i
$623$	−1.10626e10	+	1.52263e10i	−0.0734351	+	0.101075i
$624$	1.25425e10	+	4.56334e9i	0.0827266	+	0.0300985i
$625$	1.52401e11	−	7.55057e9i	0.998775	−	0.0494834i
$626$	−9.14930e8	+	2.88507e8i	−0.00595786	+	0.00187871i
$627$	−5.86115e10	+	8.06717e10i	−0.379238	+	0.521977i
$628$	−2.15375e10	−	1.62276e10i	−0.138470	−	0.104332i
$629$	−8.49765e10	−	2.61531e11i	−0.542870	−	1.67078i
$630$	8.22484e9	−	2.70591e9i	0.0522114	−	0.0171772i
$631$	9.45954e10	+	3.07359e10i	0.596695	+	0.193878i	0.591766	−	0.806110i	$-0.298431\pi$
$631$	9.45954e10	+	3.07359e10i	0.596695	+	0.193878i	0.00492939	+	0.999988i	$0.498431\pi$
$632$	1.84113e11	+	1.41248e11i	1.15403	+	0.885346i
$633$	−8.25187e10	+	2.53967e11i	−0.513970	+	1.58184i
$634$	1.85967e11	−	2.51336e11i	1.15101	−	1.55560i
$635$	7.00427e10	+	4.95763e10i	0.430793	+	0.304916i
$636$	3.46977e9	−	1.99487e11i	0.0212067	−	1.21923i
$637$	1.28098e10	−	9.30684e9i	0.0778007	−	0.0565255i
$638$	5.83171e10	+	4.31496e10i	0.351976	+	0.260432i
$639$	−6.60161e9	+	9.08633e9i	−0.0395955	+	0.0544986i
$640$	−1.30791e11	−	1.05078e11i	−0.779572	−	0.626312i
$641$	−1.15873e11	+	8.41865e10i	−0.686356	+	0.498667i	−0.875460	−	0.483290i	$-0.839442\pi$
$641$	−1.15873e11	+	8.41865e10i	−0.686356	+	0.498667i	0.189104	+	0.981957i	$0.439442\pi$
$642$	3.56201e7	−	4.09609e9i	0.000209679	−	0.0241118i
$643$		−	1.23307e11i		−	0.721347i	−0.932692	−	0.360674i	$-0.882547\pi$
$643$		−	1.23307e11i		−	0.721347i	0.932692	−	0.360674i	$-0.117453\pi$
$644$	9.31082e9	+	3.04476e10i	0.0541308	+	0.177015i
$645$	1.25566e11	−	4.25239e10i	0.725492	−	0.245694i
$646$	3.84519e11	−	2.74293e11i	2.20794	−	1.57501i
$647$	−2.57289e11	+	8.35982e10i	−1.46826	+	0.477067i	−0.930583	−	0.366082i	$-0.880699\pi$
$647$	−2.57289e11	+	8.35982e10i	−1.46826	+	0.477067i	−0.537680	+	0.843149i	$0.680699\pi$
$648$	1.17601e11	−	3.48468e10i	0.666977	−	0.197635i
$649$	−8.07387e10			−0.455096
$650$	1.71029e10	−	5.86228e9i	0.0958112	−	0.0328408i
$651$		−	4.22564e10i		−	0.235271i
$652$	3.48609e9	−	2.00424e11i	0.0192907	−	1.10907i
$653$	4.66801e9	+	1.43666e10i	0.0256731	+	0.0790138i	0.963072	−	0.269243i	$-0.0867736\pi$
$653$	4.66801e9	+	1.43666e10i	0.0256731	+	0.0790138i	−0.937399	+	0.348257i	$0.886774\pi$
$654$	3.82186e10	−	2.72628e10i	0.208912	−	0.149025i
$655$	5.61475e10	−	1.80370e11i	0.305046	−	0.979937i
$656$	1.72629e11	+	1.34838e11i	0.932176	+	0.728111i
$657$	−8.21888e10			−0.441114
$658$	1.80733e8	−	2.07832e10i	0.000964126	−	0.110869i
$659$	1.08184e11	+	1.48903e11i	0.573618	+	0.789518i	0.992978	−	0.118302i	$-0.0377452\pi$
$659$	1.08184e11	+	1.48903e11i	0.573618	+	0.789518i	−0.419359	+	0.907820i	$0.637745\pi$
$660$	4.04832e10	+	5.63122e10i	0.213353	+	0.296775i
$661$	−1.57084e11	−	1.14128e11i	−0.822859	−	0.597842i	0.0946712	−	0.995509i	$-0.469820\pi$
$661$	−1.57084e11	−	1.14128e11i	−0.822859	−	0.597842i	−0.917530	+	0.397667i	$0.869820\pi$
$662$	1.66351e11	+	1.23086e11i	0.866153	+	0.640878i
$663$	1.53612e10	+	2.11429e10i	0.0795007	+	0.109423i
$664$	6.72717e10	+	2.27028e11i	0.346067	+	1.16791i
$665$	7.40818e10	+	2.30610e10i	0.378813	+	0.117921i
$666$	−3.27220e10	+	4.42240e10i	−0.166319	+	0.224782i
$667$	1.61419e11	+	5.24481e10i	0.815549	+	0.264988i
$668$	1.97800e11	+	2.82451e11i	0.993393	+	1.41853i
$669$	3.87331e10	−	1.19208e11i	0.193365	−	0.595116i
$670$	−1.54711e11	+	2.14598e11i	−0.767755	+	1.06494i
$671$	−7.51340e10	+	2.44125e10i	−0.370635	+	0.120427i
$672$	3.83867e10	−	1.06519e10i	0.188237	−	0.0522338i
$673$	−1.32891e11	−	9.65509e10i	−0.647791	−	0.470648i	0.214727	−	0.976674i	$-0.431114\pi$
$673$	−1.32891e11	−	9.65509e10i	−0.647791	−	0.470648i	−0.862518	+	0.506026i	$0.831114\pi$
$674$	9.28352e10	−	2.92740e10i	0.449855	−	0.141854i
$675$	1.27456e11	−	1.84883e11i	0.613966	−	0.890599i
$676$	−1.69299e11	+	1.18560e11i	−0.810714	+	0.567742i
$677$	2.13372e11	+	1.55024e11i	1.01574	+	0.737979i	0.965406	−	0.260753i	$-0.0839708\pi$
$677$	2.13372e11	+	1.55024e11i	1.01574	+	0.737979i	0.0503360	+	0.998732i	$0.483971\pi$
$678$	−1.17920e11	+	8.41172e10i	−0.558045	+	0.398076i
$679$	1.53450e10	−	4.98590e9i	0.0721919	−	0.0234566i
$680$	−9.72217e10	−	3.13794e11i	−0.454703	−	1.46760i
$681$	6.08259e10	−	1.87203e11i	0.282813	−	0.870410i
$682$	−1.04497e11	+	3.29512e10i	−0.483019	+	0.152312i
$683$	6.03128e10	+	1.95968e10i	0.277157	+	0.0900539i	0.444298	−	0.895879i	$-0.353453\pi$
$683$	6.03128e10	+	1.95968e10i	0.277157	+	0.0900539i	−0.167140	+	0.985933i	$0.553453\pi$
$684$	−8.93458e10	−	3.07581e10i	−0.408178	−	0.140519i
$685$	8.66085e10	+	1.16156e11i	0.393367	+	0.527568i
$686$	3.07867e10	−	9.20211e10i	0.139016	−	0.415519i
$687$	3.99325e10	+	5.49624e10i	0.179267	+	0.246739i
$688$	−1.89796e11	+	5.44484e10i	−0.847098	+	0.243014i
$689$	−2.59072e10	−	1.88227e10i	−0.114959	−	0.0835228i
$690$	1.31621e11	+	9.48901e10i	0.580669	+	0.418624i
$691$	−1.18650e10	−	1.63307e10i	−0.0520420	−	0.0716297i	0.782203	−	0.623024i	$-0.214096\pi$
$691$	−1.18650e10	−	1.63307e10i	−0.0520420	−	0.0716297i	−0.834245	+	0.551394i	$0.814096\pi$
$692$	1.53434e10	+	5.01750e10i	0.0669110	+	0.218808i
$693$	5.33098e9			0.0231139
$694$	2.68943e11	+	2.33876e9i	1.15937	+	0.0100820i
$695$	1.12242e11	+	7.94454e10i	0.481081	+	0.340510i
$696$	7.08685e10	−	2.00185e11i	0.302007	−	0.853090i
$697$	1.32541e11	+	4.07919e11i	0.561589	+	1.72839i
$698$	−1.50353e11	−	5.03024e10i	−0.633420	−	0.211918i
$699$		−	1.92866e11i		−	0.807880i
$700$	3.13969e10	−	4.38898e10i	0.130766	−	0.182798i
$701$	2.53912e11			1.05151			0.525753	−	0.850637i	$-0.323784\pi$
$701$	2.53912e11			1.05151			0.525753	+	0.850637i	$0.323784\pi$
$702$	8.44186e9	−	2.52326e10i	0.0347608	−	0.103900i
$703$	−4.68844e11	+	1.52337e11i	−1.91958	+	0.623710i
$704$	−5.62750e10	−	8.66209e10i	−0.229100	−	0.352640i
$705$	−6.33134e10	−	8.49133e10i	−0.256294	−	0.343731i
$706$	−1.90830e9	+	2.19443e11i	−0.00768116	+	0.883288i
$707$			6.98371e10i			0.279517i
$708$	6.91144e10	+	2.26013e11i	0.275065	+	0.899500i
$709$	3.01136e11	−	2.18788e11i	1.19173	−	0.865841i	0.198283	−	0.980145i	$-0.436464\pi$
$709$	3.01136e11	−	2.18788e11i	1.19173	−	0.865841i	0.993446	+	0.114304i	$0.0364636\pi$
$710$	2.57595e8	+	6.99981e10i	0.00101369	+	0.275456i
$711$	5.34302e10	−	7.35403e10i	0.209078	−	0.287771i
$712$	3.72633e9	−	1.42806e11i	0.0144998	−	0.555683i
$713$	−2.07388e11	+	1.50676e11i	−0.802465	+	0.583025i
$714$	7.39739e10	+	2.47488e10i	0.284633	+	0.0952272i
$715$	1.11307e10	−	1.37759e8i	0.0425890	−	0.000527104i
$716$	−3.76526e11	−	1.29623e11i	−1.43266	−	0.493206i
$717$	−1.10048e11	+	3.38693e11i	−0.416395	+	1.28153i
$718$	9.30120e10	+	2.94965e11i	0.349978	+	1.10987i
$719$	1.24036e11	+	4.03018e10i	0.464122	+	0.150802i	0.531738	−	0.846909i	$-0.321539\pi$
$719$	1.24036e11	+	4.03018e10i	0.464122	+	0.150802i	−0.0676156	+	0.997711i	$0.521539\pi$
$720$	−3.98112e10	+	5.22902e10i	−0.148141	+	0.194577i
$721$	−1.11881e10	−	3.44335e10i	−0.0414015	−	0.127421i
$722$	−3.33916e11	−	4.68103e11i	−1.22882	−	1.72263i
$723$	4.56111e10	−	6.27782e10i	0.166923	−	0.229750i
$724$	1.63299e11	−	1.14358e11i	0.594331	−	0.416210i
$725$	−9.56365e10	−	2.71300e11i	−0.346156	−	0.981969i
$726$	−5.97745e10	−	1.89560e11i	−0.215164	−	0.682340i
$727$	−1.20806e11	+	1.66275e11i	−0.432464	+	0.595235i	−0.968517	−	0.248949i	$-0.919915\pi$
$727$	−1.20806e11	+	1.66275e11i	−0.432464	+	0.595235i	0.536053	+	0.844184i	$0.319915\pi$
$728$	2.13381e9	−	6.02745e9i	0.00759678	−	0.0214589i
$729$	−9.69033e10	−	2.98238e11i	−0.343106	−	1.05597i
$730$	−4.13298e11	+	3.02608e11i	−1.45536	+	1.06559i
$731$	−3.67701e11	−	1.19473e11i	−1.28773	−	0.418410i
$732$	1.32655e11	+	1.89426e11i	0.462040	+	0.659775i
$733$	8.67121e10	−	2.66872e11i	0.300375	−	0.924459i	−0.680988	−	0.732295i	$-0.738449\pi$
$733$	8.67121e10	−	2.66872e11i	0.300375	−	0.924459i	0.981363	−	0.192164i	$-0.0615506\pi$
$734$	1.65553e11	+	1.22495e11i	0.570364	+	0.422020i
$735$	−7.72546e10	−	2.28120e11i	−0.264713	−	0.781652i
$736$	−1.89156e11	−	1.50414e11i	−0.644628	−	0.512599i
$737$	−1.31775e11	+	9.57400e10i	−0.446645	+	0.324507i
$738$	5.10376e10	−	6.89779e10i	0.172054	−	0.232533i
$739$	−2.71817e11	+	3.74123e11i	−0.911377	+	1.25440i	0.0553171	+	0.998469i	$0.482383\pi$
$739$	−2.71817e11	+	3.74123e11i	−0.911377	+	1.25440i	−0.966694	+	0.255934i	$0.917617\pi$
$740$	−1.71978e9	+	3.42865e11i	−0.00573516	+	1.14339i
$741$	3.79026e10	−	2.75379e10i	0.125718	−	0.0913393i
$742$	−9.55779e10	−	8.31156e8i	−0.315313	−	0.00274200i
$743$		−	5.12783e11i		−	1.68259i	−0.540576	−	0.841295i	$-0.681794\pi$
$743$		−	5.12783e11i		−	1.68259i	0.540576	−	0.841295i	$-0.318206\pi$
$744$	1.81692e11	+	2.64312e11i	0.592987	+	0.862631i
$745$	2.33265e8	+	1.88474e10i	0.000757224	+	0.0611822i
$746$	−1.59292e11	−	2.23305e11i	−0.514326	−	0.721012i
$747$	8.82151e10	−	2.86628e10i	0.283309	−	0.0920528i
$748$	3.51749e9	−	2.02230e11i	0.0112364	−	0.646010i
$749$	−1.96237e9			−0.00623525
$750$	−7.81796e9	−	2.74898e11i	−0.0247086	−	0.868814i
$751$			1.05588e11i			0.331935i	0.986131	+	0.165967i	$0.0530747\pi$
$751$			1.05588e11i			0.331935i	−0.986131	+	0.165967i	$0.946925\pi$
$752$	8.82323e10	+	1.30775e11i	0.275903	+	0.408934i
$753$	8.73398e10	+	2.68804e11i	0.271664	+	0.836097i
$754$	−1.97938e10	−	2.77480e10i	−0.0612411	−	0.0858512i
$755$	2.49290e11	−	3.08534e9i	0.767214	−	0.00949545i
$756$	−2.32239e10	−	7.59452e10i	−0.0710964	−	0.232495i
$757$	5.62221e11			1.71208			0.856038	−	0.516912i	$-0.172919\pi$
$757$	5.62221e11			1.71208			0.856038	+	0.516912i	$0.172919\pi$
$758$	1.06603e11	+	9.27034e8i	0.322919	+	0.00280814i
$759$	5.87208e10	+	8.08223e10i	0.176940	+	0.243537i
$760$	−5.62535e11	+	1.74288e11i	−1.68615	+	0.522413i
$761$	5.19399e11	+	3.77365e11i	1.54868	+	1.12518i	0.944583	+	0.328274i	$0.106467\pi$
$761$	5.19399e11	+	3.77365e11i	1.54868	+	1.12518i	0.604099	+	0.796909i	$0.293533\pi$
$762$	9.19915e10	−	1.24327e11i	0.272852	−	0.368763i
$763$	−1.32194e10	−	1.81949e10i	−0.0390044	−	0.0536849i
$764$	8.95563e9	−	5.14883e11i	0.0262859	−	1.51125i
$765$	−1.21886e11	+	4.12776e10i	−0.355883	+	0.120523i
$766$	−3.72857e11	−	2.75882e11i	−1.08300	−	0.801324i
$767$	3.60775e10	+	1.17223e10i	0.104245	+	0.0338712i
$768$	−1.94306e11	+	2.31681e11i	−0.558525	+	0.665956i
$769$	5.09267e10	−	1.56736e11i	0.145626	−	0.448192i	−0.851465	−	0.524412i	$-0.824285\pi$
$769$	5.09267e10	−	1.56736e11i	0.145626	−	0.448192i	0.997091	+	0.0762200i	$0.0242851\pi$
$770$	2.68076e10	−	1.96280e10i	0.0762596	−	0.0558357i
$771$	−3.75414e10	+	1.21979e10i	−0.106241	+	0.0345198i
$772$	1.22017e11	+	9.19345e10i	0.343519	+	0.258827i
$773$	−1.88201e11	−	1.36736e11i	−0.527114	−	0.382971i	0.292163	−	0.956368i	$-0.405625\pi$
$773$	−1.88201e11	−	1.36736e11i	−0.527114	−	0.382971i	−0.819277	+	0.573398i	$0.805625\pi$
$774$	2.32609e10	+	7.37663e10i	0.0648131	+	0.205539i
$775$	4.16405e11	+	1.23992e11i	1.15428	+	0.343706i
$776$	−7.45443e10	+	9.71665e10i	−0.205574	+	0.267960i
$777$	−6.58651e10	−	4.78538e10i	−0.180705	−	0.131290i
$778$	2.64465e10	+	3.70742e10i	0.0721855	+	0.101194i
$779$	7.31272e11	−	2.37605e11i	1.98577	−	0.645216i
$780$	−9.91377e9	−	3.10403e10i	−0.0267831	−	0.0838587i
$781$	−1.33179e10	+	4.09882e10i	−0.0357957	+	0.110168i
$782$	−1.42310e11	−	4.51301e11i	−0.380547	−	1.20681i
$783$	−4.02625e11	−	1.30821e11i	−1.07116	−	0.348040i
$784$	9.89183e10	+	3.44809e11i	0.261826	+	0.912671i
$785$	8.14766e8	+	6.58315e10i	0.00214563	+	0.173362i
$786$	−3.22876e11	−	1.08022e11i	−0.845951	−	0.283022i
$787$	−2.32649e11	−	3.20213e11i	−0.606459	−	0.834719i	0.389821	−	0.920890i	$-0.372537\pi$
$787$	−2.32649e11	−	3.20213e11i	−0.606459	−	0.834719i	−0.996280	+	0.0861713i	$0.972537\pi$
$788$	1.35960e11	−	3.94935e11i	0.352619	−	1.02429i
$789$	−1.97222e11	−	1.43290e11i	−0.508918	−	0.369751i
$790$	−2.08485e9	−	5.66531e11i	−0.00535263	−	1.45450i
$791$	4.07873e10	+	5.61389e10i	0.104188	+	0.143403i
$792$	−3.33450e10	+	2.29219e10i	−0.0847481	+	0.0582573i
$793$	3.71175e10			0.0938611
$794$	4.29733e9	−	4.94168e11i	0.0108123	−	1.24335i
$795$	−3.90500e11	+	2.91166e11i	−0.977580	+	0.728907i
$796$	5.29567e10	−	7.02850e10i	0.131907	−	0.175069i
$797$	7.39191e10	+	2.27500e11i	0.183199	+	0.563829i	0.999913	−	0.0132143i	$-0.00420636\pi$
$797$	7.39191e10	+	2.27500e11i	0.183199	+	0.563829i	−0.816714	+	0.577043i	$0.804206\pi$
$798$	4.43669e10	−	1.32612e11i	0.109408	−	0.327018i
$799$			3.08898e11i			0.757928i
$800$	−7.67039e9	+	4.09528e11i	−0.0187265	+	0.999825i
$801$	−5.59599e10			−0.135940
$802$	−5.02000e11	−	1.67950e11i	−1.21341	−	0.405958i
$803$	−2.99944e11	+	9.74578e10i	−0.721404	+	0.234398i
$804$	3.80809e11	+	2.86924e11i	0.911346	+	0.686661i
$805$	4.49085e10	−	6.34479e10i	0.106941	−	0.151089i
$806$	5.14776e10	+	4.47655e8i	0.121977	+	0.00106073i
$807$			3.54527e10i			0.0835902i
$808$	−3.00283e11	−	4.36828e11i	−0.704507	−	1.02486i
$809$	−2.47358e11	+	1.79716e11i	−0.577473	+	0.419559i	−0.837812	−	0.545958i	$-0.816166\pi$
$809$	−2.47358e11	+	1.79716e11i	−0.577473	+	0.419559i	0.260339	+	0.965517i	$0.416166\pi$
$810$	−2.42907e11	−	1.75120e11i	−0.564287	−	0.406814i
$811$	−8.33416e10	+	1.14710e11i	−0.192654	+	0.265166i	−0.894406	−	0.447256i	$-0.852401\pi$
$811$	−8.33416e10	+	1.14710e11i	−0.192654	+	0.265166i	0.701752	+	0.712421i	$0.252401\pi$
$812$	−9.61934e10	−	3.31154e10i	−0.221269	−	0.0761739i
$813$	−4.08124e11	+	2.96520e11i	−0.934180	+	0.678721i
$814$	−6.69774e10	+	2.00195e11i	−0.152556	+	0.455990i
$815$	−3.92336e11	+	2.92535e11i	−0.889257	+	0.663051i
$816$	−5.69117e11	+	1.63267e11i	−1.28363	+	0.368247i
$817$	−2.14179e11	+	6.59175e11i	−0.480716	+	1.47949i
$818$	−1.63875e11	+	5.16752e10i	−0.366016	+	0.115417i
$819$	−2.38211e9	−	7.73993e8i	−0.00529451	−	0.00172029i
$820$	2.68240e9	−	5.34779e11i	0.00593292	−	1.18282i
$821$	−1.36136e11	−	4.18984e11i	−0.299641	−	0.922200i	−0.981623	−	0.190831i	$-0.938882\pi$
$821$	−1.36136e11	−	4.18984e11i	−0.299641	−	0.922200i	0.681982	−	0.731369i	$-0.261118\pi$
$822$	2.12590e11	−	1.51649e11i	0.465646	−	0.332164i
$823$	4.55133e11	−	6.26437e11i	0.992062	−	1.36546i	0.0619911	−	0.998077i	$-0.480255\pi$
$823$	4.55133e11	−	6.26437e11i	0.992062	−	1.36546i	0.930071	−	0.367380i	$-0.119745\pi$
$824$	2.18037e11	+	1.67274e11i	0.472957	+	0.362843i
$825$	4.83215e10	−	1.62279e11i	0.104310	−	0.350306i
$826$	1.07983e11	−	3.40506e10i	0.231972	−	0.0731484i
$827$	1.38911e11	−	1.91195e11i	0.296971	−	0.408746i	−0.634292	−	0.773094i	$-0.718708\pi$
$827$	1.38911e11	−	1.91195e11i	0.296971	−	0.408746i	0.931263	+	0.364348i	$0.118708\pi$
$828$	−5.69682e10	+	7.56090e10i	−0.121202	+	0.160861i
$829$	1.68272e11	+	5.17889e11i	0.356283	+	1.09653i	0.955262	+	0.295761i	$0.0955733\pi$
$829$	1.68272e11	+	5.17889e11i	0.356283	+	1.09653i	−0.598979	+	0.800765i	$0.704427\pi$
$830$	3.38069e11	−	4.68932e11i	0.712350	−	0.988092i
$831$	−5.75010e11	−	1.86832e11i	−1.20579	−	0.391785i
$832$	1.25697e10	+	4.68763e10i	0.0262321	+	0.0978273i
$833$	−2.17052e11	+	6.68016e11i	−0.450799	+	1.38742i
$834$	1.47415e11	−	1.99233e11i	0.304704	−	0.411810i
$835$	2.50219e11	−	8.03811e11i	0.514725	−	1.65351i
$836$	−3.62536e11	−	6.30577e9i	−0.742208	−	0.0129096i
$837$	5.17287e11	−	3.75831e11i	1.05397	−	0.765757i
$838$	−2.25824e11	−	1.67090e11i	−0.457925	−	0.338825i
$839$	−2.14818e10	+	2.95672e10i	−0.0433534	+	0.0596708i	−0.830143	−	0.557550i	$-0.811741\pi$
$839$	−2.14818e10	+	2.95672e10i	−0.0433534	+	0.0596708i	0.786790	+	0.617221i	$0.211741\pi$
$840$	−7.78928e10	−	5.82408e10i	−0.156452	−	0.116980i
$841$	−3.40307e10	+	2.47247e10i	−0.0680278	+	0.0494251i
$842$	3.26935e9	−	3.75955e11i	0.00650448	−	0.747976i
$843$			6.19034e11i			1.22576i
$844$	−9.28562e11	+	2.83952e11i	−1.82996	+	0.559598i
$845$	4.81798e11	+	1.49979e11i	0.945013	+	0.294174i
$846$	5.03089e10	−	3.58873e10i	0.0982118	−	0.0700583i
$847$	−9.05593e10	+	2.94245e10i	−0.175954	+	0.0571710i
$848$	6.01409e11	−	4.05763e11i	1.16302	−	0.784674i
$849$	−9.33377e10			−0.179650
$850$	−4.60940e11	+	6.56337e11i	−0.883017	+	1.25734i
$851$			4.93891e11i			0.941701i
$852$	1.26139e11	+	2.19401e9i	0.239383	+	0.00416371i
$853$	1.74054e11	+	5.35685e11i	0.328768	+	1.01184i	0.969711	+	0.244255i	$0.0785433\pi$
$853$	1.74054e11	+	5.35685e11i	0.328768	+	1.01184i	−0.640944	+	0.767588i	$0.721457\pi$
$854$	9.01915e10	−	6.43372e10i	0.169564	−	0.120957i
$855$	7.39979e10	+	2.18503e11i	0.138470	+	0.408878i
$856$	1.22745e10	−	8.43773e9i	0.0228618	−	0.0157156i
$857$	4.99444e10			0.0925898			0.0462949	−	0.998928i	$-0.485259\pi$
$857$	4.99444e10			0.0925898			0.0462949	+	0.998928i	$0.485259\pi$
$858$	1.74458e8	−	2.00616e10i	0.000321915	−	0.0370183i
$859$	3.09106e11	+	4.25448e11i	0.567721	+	0.781401i	0.992282	−	0.123998i	$-0.0395718\pi$
$859$	3.09106e11	+	4.25448e11i	0.567721	+	0.781401i	−0.424562	+	0.905399i	$0.639572\pi$
$860$	3.88568e11	+	2.85300e11i	0.710352	+	0.521565i
$861$	1.02732e11	+	7.46393e10i	0.186936	+	0.135817i
$862$	−2.16829e11	−	1.60434e11i	−0.392724	−	0.290582i
$863$	4.15097e11	+	5.71332e11i	0.748353	+	1.03002i	0.998094	+	0.0617073i	$0.0196545\pi$
$863$	4.15097e11	+	5.71332e11i	0.748353	+	1.03002i	−0.249741	+	0.968313i	$0.580345\pi$
$864$	4.71811e11	+	3.75177e11i	0.846667	+	0.673257i
$865$	7.40053e10	−	1.04557e11i	0.132190	−	0.186761i
$866$	2.10728e11	−	2.84801e11i	0.374672	−	0.506372i
$867$	−6.35506e11	−	2.06488e11i	−1.12472	−	0.365443i
$868$	1.25861e11	−	8.81404e10i	0.221724	−	0.155273i
$869$	1.07788e11	−	3.31739e11i	0.189014	−	0.581724i
$870$	−4.92487e11	+	1.62025e11i	−0.859643	+	0.282817i
$871$	7.27829e10	−	2.36486e10i	0.126461	−	0.0410897i
$872$	1.60921e11	+	5.69682e10i	0.278321	+	0.0985296i
$873$	3.88113e10	+	2.81981e10i	0.0668192	+	0.0485470i
$874$	−8.09043e11	+	2.55118e11i	−1.38652	+	0.437215i
$875$	−1.31657e11	+	4.89035e9i	−0.224600	+	0.00834273i
$876$	5.29575e11	+	7.56213e11i	0.899314	+	1.28419i
$877$	−4.92463e11	−	3.57795e11i	−0.832482	−	0.604834i	0.0877781	−	0.996140i	$-0.472023\pi$
$877$	−4.92463e11	−	3.57795e11i	−0.832482	−	0.604834i	−0.920261	+	0.391306i	$0.872023\pi$
$878$	−1.50240e11	+	1.07172e11i	−0.252818	+	0.180345i
$879$	6.37203e10	−	2.07040e10i	0.106739	−	0.0346815i
$880$	−8.32845e10	+	2.38038e11i	−0.138878	+	0.396932i
$881$	−2.85302e11	+	8.78070e11i	−0.473589	+	1.45756i	0.374262	+	0.927323i	$0.377896\pi$
$881$	−2.85302e11	+	8.78070e11i	−0.473589	+	1.45756i	−0.847851	+	0.530234i	$0.822104\pi$
$882$	1.34014e11	−	4.22589e10i	0.221450	−	0.0698303i
$883$	5.55241e11	+	1.80409e11i	0.913354	+	0.296767i	0.727738	−	0.685856i	$-0.240572\pi$
$883$	5.55241e11	+	1.80409e11i	0.913354	+	0.296767i	0.185616	+	0.982622i	$0.440572\pi$
$884$	−3.09331e10	+	8.98542e10i	−0.0506541	+	0.147140i
$885$	3.33357e11	−	4.70975e11i	0.543421	−	0.767759i
$886$	1.31461e11	−	3.92937e11i	0.213336	−	0.637658i
$887$	3.93732e11	+	5.41926e11i	0.636073	+	0.875479i	0.998398	−	0.0565727i	$-0.0180173\pi$
$887$	3.93732e11	+	5.41926e11i	0.636073	+	0.875479i	−0.362326	+	0.932051i	$0.618017\pi$
$888$	6.17743e11	+	1.61191e10i	0.993472	+	0.0259233i
$889$	−5.99419e10	−	4.35503e10i	−0.0959673	−	0.0697244i
$890$	−2.81402e11	+	2.06037e11i	−0.448505	+	0.328386i
$891$	−1.08370e11	−	1.49158e11i	−0.171948	−	0.236666i
$892$	4.35853e11	−	1.33283e11i	0.688464	−	0.210531i
$893$	5.53758e11			0.870792
$894$	3.39699e10	+	2.95406e8i	0.0531795	+	0.000462455i
$895$	3.11846e11	+	9.20830e11i	0.486014	+	1.43512i
$896$	1.11796e11	+	9.21168e10i	0.173457	+	0.142925i
$897$	−1.45045e10	−	4.46404e10i	−0.0224044	−	0.0689538i
$898$	5.91772e11	+	1.97984e11i	0.910016	+	0.304456i
$899$		−	8.19082e11i		−	1.25397i
$900$	1.60446e11	−	1.18091e9i	0.244546	−	0.00179990i
$901$	1.42056e12			2.15556
$902$	1.04467e11	−	3.12251e11i	0.157817	−	0.471713i
$903$	−1.08862e11	+	3.53714e10i	−0.163729	+	0.0531988i
$904$	−4.96507e11	−	1.75771e11i	−0.743450	−	0.263192i
$905$	−4.64722e11	−	1.44664e11i	−0.692786	−	0.215658i
$906$	3.90727e9	−	4.49312e11i	0.00579909	−	0.666861i
$907$			1.27954e11i			0.189071i	0.995521	+	0.0945357i	$0.0301367\pi$
$907$			1.27954e11i			0.189071i	−0.995521	+	0.0945357i	$0.969863\pi$
$908$	6.84458e11	−	2.09306e11i	1.00694	−	0.307920i
$909$	−1.67990e11	+	1.22052e11i	−0.246053	+	0.178768i
$910$	−1.48285e10	+	4.87847e9i	−0.0216238	+	0.00711407i
$911$	3.64912e11	−	5.02258e11i	0.529803	−	0.729211i	−0.457297	−	0.889314i	$-0.651183\pi$
$911$	3.64912e11	−	5.02258e11i	0.529803	−	0.729211i	0.987100	+	0.160103i	$0.0511825\pi$
$912$	2.92688e11	+	1.02025e12i	0.423083	+	1.47478i
$913$	2.87949e11	−	2.09207e11i	0.414413	−	0.301088i
$914$	2.65494e11	+	8.88239e10i	0.380425	+	0.127276i
$915$	1.67810e11	−	5.39076e11i	0.239405	−	0.769070i
$916$	−8.04127e10	+	2.33582e11i	−0.114220	+	0.331786i
$917$	−5.04025e10	+	1.55123e11i	−0.0712811	+	0.219381i
$918$	3.54963e11	+	1.12568e12i	0.499818	+	1.58505i
$919$	−1.16838e12	−	3.79628e11i	−1.63802	−	0.532227i	−0.661929	−	0.749567i	$-0.730262\pi$
$919$	−1.16838e12	−	3.79628e11i	−1.63802	−	0.532227i	−0.976096	+	0.217340i	$0.930262\pi$
$920$	−8.08989e9	+	5.89960e11i	−0.0112925	+	0.823514i
$921$	−2.24295e11	−	6.90310e11i	−0.311732	−	0.959413i
$922$	−3.49049e11	−	4.89317e11i	−0.483017	−	0.677121i
$923$	1.19020e10	−	1.63817e10i	0.0163988	−	0.0225710i
$924$	−3.43496e10	−	4.90499e10i	−0.0471231	−	0.0672900i
$925$	6.64829e11	−	5.08635e11i	0.908120	−	0.694767i
$926$	2.03513e11	+	6.45391e11i	0.276788	+	0.877766i
$927$	6.32751e10	−	8.70907e10i	0.0856868	−	0.117938i
$928$	7.44074e11	−	2.06473e11i	1.00328	−	0.278402i
$929$	−2.84655e11	−	8.76078e11i	−0.382170	−	1.17620i	−0.938513	−	0.345244i	$-0.887796\pi$
$929$	−2.84655e11	−	8.76078e11i	−0.382170	−	1.17620i	0.556343	−	0.830953i	$-0.312204\pi$
$930$	2.39234e11	−	7.45612e11i	0.319810	−	0.996739i
$931$	1.19755e12	+	3.89106e11i	1.59402	+	0.517928i
$932$	5.74452e11	−	4.02289e11i	0.761361	−	0.533180i
$933$	2.90808e11	−	8.95015e11i	0.383778	−	1.18115i
$934$	1.89622e11	+	1.40304e11i	0.249173	+	0.184367i
$935$	−3.95870e11	+	2.95170e11i	−0.517972	+	0.386212i
$936$	1.82280e10	−	5.40120e9i	0.0237484	−	0.00703698i
$937$	5.69339e11	−	4.13649e11i	0.738606	−	0.536629i	−0.153668	−	0.988123i	$-0.549109\pi$
$937$	5.69339e11	−	4.13649e11i	0.738606	−	0.536629i	0.892274	+	0.451494i	$0.149109\pi$
$938$	1.35864e11	−	1.83621e11i	0.175506	−	0.237198i
$939$	2.48118e9	−	3.41505e9i	0.00319151	−	0.00439274i
$940$	1.20853e11	−	3.65695e11i	0.154791	−	0.468390i
$941$	2.53092e11	−	1.83882e11i	0.322790	−	0.234520i	−0.414575	−	0.910015i	$-0.636070\pi$
$941$	2.53092e11	−	1.83882e11i	0.322790	−	0.234520i	0.737365	+	0.675495i	$0.236070\pi$
$942$	1.18653e11	+	1.03182e9i	0.150686	+	0.00131038i
$943$		−	7.70340e11i		−	0.974172i
$944$	−5.29020e11	+	6.77287e11i	−0.666169	+	0.852873i
$945$	−1.12015e11	+	1.58258e11i	−0.140459	+	0.198444i
$946$	1.72360e11	+	2.41624e11i	0.215215	+	0.301701i
$947$	2.90253e11	−	9.43088e10i	0.360891	−	0.117261i	−0.122958	−	0.992412i	$-0.539238\pi$
$947$	2.90253e11	−	9.43088e10i	0.360891	−	0.117261i	0.483850	+	0.875151i	$0.339238\pi$
$948$	−1.02091e12	−	1.77572e10i	−1.26402	−	0.0219858i
$949$	1.48178e11			0.182691
$950$	1.17661e12	+	8.26323e11i	1.44457	+	1.01451i
$951$			1.37573e12i			1.68194i
$952$	8.05837e10	+	2.71954e11i	0.0981068	+	0.331091i
$953$	−4.20496e11	−	1.29415e12i	−0.509789	−	1.56897i	−0.792568	−	0.609784i	$-0.791256\pi$
$953$	−4.20496e11	−	1.29415e12i	−0.509789	−	1.56897i	0.282779	−	0.959185i	$-0.408744\pi$
$954$	−1.65039e11	−	2.31361e11i	−0.199247	−	0.279317i
$955$	−1.00790e12	+	7.51511e11i	−1.21172	+	0.903487i
$956$	−1.23834e12	+	3.78683e11i	−1.48255	+	0.453360i
$957$	−3.19209e11			−0.380563
$958$	−9.86359e11	−	8.57748e9i	−1.17104	−	0.0101835i
$959$	−7.35326e10	−	1.01209e11i	−0.0869372	−	0.119659i
$960$	7.37638e11	+	2.93731e10i	0.868477	+	0.0345831i
$961$	3.10836e11	+	2.25836e11i	0.364450	+	0.264789i
$962$	5.89942e10	−	7.97312e10i	0.0688825	−	0.0930953i
$963$	−3.42957e9	−	4.72040e9i	−0.00398781	−	0.00548875i
$964$	2.82123e11	+	4.90711e9i	0.326686	+	0.00568222i
$965$	−4.61591e9	−	3.72956e11i	−0.00532289	−	0.430079i
$966$	−1.12621e11	−	8.33301e10i	−0.129334	−	0.0956959i
$967$	−1.11243e12	−	3.61450e11i	−1.27223	−	0.413373i	−0.406394	−	0.913698i	$-0.633214\pi$
$967$	−1.11243e12	−	3.61450e11i	−1.27223	−	0.413373i	−0.865838	+	0.500325i	$0.833214\pi$
$968$	4.39926e11	−	5.73432e11i	0.501047	−	0.653102i
$969$	−6.42231e11	+	1.97658e12i	−0.728444	+	2.24192i
$970$	2.98990e11	−	1.10029e9i	0.337730	−	0.00124286i
$971$	1.11450e12	−	3.62123e11i	1.25373	−	0.407361i	0.394473	−	0.918908i	$-0.370927\pi$
$971$	1.11450e12	−	3.62123e11i	1.25373	−	0.407361i	0.859256	+	0.511547i	$0.170927\pi$
$972$	2.56269e11	−	3.40124e11i	0.287099	−	0.381041i
$973$	−9.60560e10	−	6.97888e10i	−0.107170	−	0.0778636i
$974$	2.65253e11	+	8.41185e11i	0.294730	+	0.934664i
$975$	−4.51531e10	+	6.54976e10i	−0.0499654	+	0.0724781i
$976$	−2.87509e11	+	7.90228e11i	−0.316849	+	0.870869i
$977$	−1.03882e12	−	7.54746e11i	−1.14015	−	0.828367i	−0.153009	−	0.988225i	$-0.548896\pi$
$977$	−1.03882e12	−	7.54746e11i	−1.14015	−	0.828367i	−0.987140	+	0.159858i	$0.948896\pi$
$978$	5.12220e11	+	7.18059e11i	0.559888	+	0.784883i
$979$	−2.04223e11	+	6.63561e10i	−0.222318	+	0.0722354i
$980$	5.18315e11	−	7.05926e11i	0.561939	−	0.765341i
$981$	2.06640e10	−	6.35973e10i	0.0223120	−	0.0686693i
$982$	1.62870e11	+	5.16502e11i	0.175144	+	0.555426i
$983$	1.18434e12	+	3.84814e11i	1.26841	+	0.412133i	0.864486	−	0.502657i	$-0.167644\pi$
$983$	1.18434e12	+	3.84814e11i	1.26841	+	0.412133i	0.403929	+	0.914790i	$0.367644\pi$
$984$	−9.63516e11	−	2.51416e10i	−1.02773	−	0.0268171i
$985$	−9.65850e11	+	3.27093e11i	−1.02604	+	0.347477i
$986$	1.43388e12	+	4.79721e11i	1.51707	+	0.507553i
$987$	5.37545e10	+	7.39867e10i	0.0566430	+	0.0779624i
$988$	1.61081e11	+	5.54535e10i	0.169050	+	0.0581971i
$989$	5.61774e11	+	4.08153e11i	0.587187	+	0.426616i
$990$	9.40648e10	+	3.01813e10i	0.0979234	+	0.0314193i
$991$	−3.23321e11	−	4.45014e11i	−0.335228	−	0.461401i	0.607812	−	0.794081i	$-0.292047\pi$
$991$	−3.23321e11	−	4.45014e11i	−0.335228	−	0.461401i	−0.943040	+	0.332680i	$0.892047\pi$
$992$	−4.08272e11	+	1.09249e12i	−0.421603	+	1.12816i
$993$	−9.10553e11			−0.936501
$994$	5.25557e8	−	6.04359e10i	0.000538362	−	0.0619084i
$995$	−2.14833e11	+	2.65888e9i	−0.219184	+	0.00271273i
$996$	−8.32130e11	−	6.26975e11i	−0.845578	−	0.637107i
$997$	−7.85296e10	−	2.41689e11i	−0.0794790	−	0.244611i	0.903420	−	0.428757i	$-0.141048\pi$
$997$	−7.85296e10	−	2.41689e11i	−0.0794790	−	0.244611i	−0.982899	+	0.184145i	$0.941048\pi$
$998$	−2.99859e10	+	8.96277e10i	−0.0302270	+	0.0903483i
$999$		−	1.23191e12i		−	1.23685i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.9.j.b.91.13	yes	464
4.3	odd	2	inner	100.9.j.b.91.33	yes	464
25.11	even	5	inner	100.9.j.b.11.33	yes	464
100.11	odd	10	inner	100.9.j.b.11.13	✓	464

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.9.j.b.11.13	✓	464	100.11	odd	10	inner
100.9.j.b.11.33	yes	464	25.11	even	5	inner
100.9.j.b.91.13	yes	464	1.1	even	1	trivial
100.9.j.b.91.33	yes	464	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	100.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-15.1733 - 5.07641i) q^{2} +(66.9566 - 21.7555i) q^{3} +(204.460 + 154.052i) q^{4} +(-7.73474 - 624.952i) q^{5} +(-1126.40 - 9.79525i) q^{6} +539.637i q^{7} +(-2320.31 - 3375.41i) q^{8} +(-1298.07 + 943.105i) q^{9} +(-3055.15 + 9521.87i) q^{10} +(-3618.94 + 4981.05i) q^{11} +(17041.4 + 5866.67i) q^{12} +(2340.29 - 1700.32i) q^{13} +(2739.42 - 8188.10i) q^{14} +(-14114.1 - 41676.4i) q^{15} +(18071.9 + 62995.0i) q^{16} +(-39654.3 + 122043. i) q^{17} +(24483.7 - 7720.51i) q^{18} +(218786. + 71087.9i) q^{19} +(94693.7 - 128969. i) q^{20} +(11740.1 + 36132.3i) q^{21} +(80197.3 - 57207.9i) q^{22} +(135470. - 186458. i) q^{23} +(-228794. - 175526. i) q^{24} +(-390505. + 9667.69i) q^{25} +(-44141.4 + 13919.2i) q^{26} +(-337901. + 465080. i) q^{27} +(-83132.2 + 110334. i) q^{28} +(227566. + 700375. i) q^{29} +(2590.81 + 704019. i) q^{30} +(-1.05782e6 - 343705. i) q^{31} +(45577.1 - 1.04759e6i) q^{32} +(-133947. + 412246. i) q^{33} +(1.22123e6 - 1.65050e6i) q^{34} +(337247. - 4173.96i) q^{35} +(-410692. - 7143.38i) q^{36} +(-1.73367e6 + 1.25958e6i) q^{37} +(-2.95884e6 - 2.18929e6i) q^{38} +(119706. - 164762. i) q^{39} +(-2.09152e6 + 1.47619e6i) q^{40} +(2.70407e6 - 1.96462e6i) q^{41} +(5285.88 - 607845. i) q^{42} +3.01287e6i q^{43} +(-1.50727e6 + 460920. i) q^{44} +(599436. + 803939. i) q^{45} +(-3.00206e6 + 2.14149e6i) q^{46} +(2.28936e6 - 743857. i) q^{47} +(2.58052e6 + 3.82477e6i) q^{48} +5.47359e6 q^{49} +(5.97435e6 + 1.83567e6i) q^{50} +9.03432e6i q^{51} +(740433. + 12878.7i) q^{52} +(-3.42085e6 - 1.05283e7i) q^{53} +(7.48802e6 - 5.34150e6i) q^{54} +(3.14091e6 + 2.22314e6i) q^{55} +(1.82150e6 - 1.25213e6i) q^{56} +1.61957e7 q^{57} +(102460. - 1.17822e7i) q^{58} +(7.70792e6 + 1.06090e7i) q^{59} +(3.53458e6 - 1.06955e7i) q^{60} +(1.03807e7 + 7.54199e6i) q^{61} +(1.43058e7 + 1.05851e7i) q^{62} +(-508935. - 700489. i) q^{63} +(-6.00953e6 + 1.56640e7i) q^{64} +(-1.08072e6 - 1.44942e6i) q^{65} +(4.12515e6 - 5.57518e6i) q^{66} +(2.51604e7 + 8.17511e6i) q^{67} +(-2.69088e7 + 1.88442e7i) q^{68} +(5.01410e6 - 1.54318e7i) q^{69} +(-5.13836e6 - 1.64867e6i) q^{70} +(6.65726e6 - 2.16308e6i) q^{71} +(6.19530e6 + 2.19323e6i) q^{72} +(4.14409e7 + 3.01085e7i) q^{73} +(3.26997e7 - 1.03113e7i) q^{74} +(-2.59366e7 + 9.14297e6i) q^{75} +(3.37818e7 + 4.82391e7i) q^{76} +(-2.68796e6 - 1.95292e6i) q^{77} +(-2.65274e6 + 1.89231e6i) q^{78} +(-5.38806e7 + 1.75069e7i) q^{79} +(3.92291e7 - 1.17813e7i) q^{80} +(-9.25355e6 + 2.84795e7i) q^{81} +(-5.10029e7 + 1.60829e7i) q^{82} +(-5.49796e7 - 1.78640e7i) q^{83} +(-3.16587e6 + 9.19620e6i) q^{84} +(7.65780e7 + 2.38381e7i) q^{85} +(1.52946e7 - 4.57153e7i) q^{86} +(3.04740e7 + 4.19439e7i) q^{87} +(2.52101e7 + 657823. i) q^{88} +(2.82158e7 + 2.05000e7i) q^{89} +(-5.01432e6 - 1.52414e7i) q^{90} +(917555. + 1.26291e6i) q^{91} +(5.64224e7 - 1.72538e7i) q^{92} -7.83052e7 q^{93} +(-3.85133e7 - 334916. i) q^{94} +(4.27343e7 - 1.37281e8i) q^{95} +(-1.97391e7 - 7.11343e7i) q^{96} +(-9.23936e6 - 2.84358e7i) q^{97} +(-8.30527e7 - 2.77862e7i) q^{98} -9.87881e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 464 q + 29 q^{2} + 509 q^{4} - 1230 q^{5} - 515 q^{6} + 21284 q^{8} + 262434 q^{9} + 3445 q^{10} - 35805 q^{12} - 29522 q^{13} - 33705 q^{14} - 63391 q^{16} - 319922 q^{17} - 569696 q^{18} + 1244935 q^{20}+ \cdots + 209675864 q^{98}+O(q^{100}) \) 464 * q + 29 * q^2 + 509 * q^4 - 1230 * q^5 - 515 * q^6 + 21284 * q^8 + 262434 * q^9 + 3445 * q^10 - 35805 * q^12 - 29522 * q^13 - 33705 * q^14 - 63391 * q^16 - 319922 * q^17 - 569696 * q^18 + 1244935 * q^20 + 39360 * q^21 + 140220 * q^22 + 989900 * q^24 - 431710 * q^25 - 855842 * q^26 - 2358605 * q^28 - 2884562 * q^29 + 7229675 * q^30 - 7078666 * q^32 - 1866570 * q^33 + 1448973 * q^34 + 777029 * q^36 - 7317972 * q^37 + 4012465 * q^38 - 4154830 * q^40 + 1687438 * q^41 - 21337315 * q^42 + 510580 * q^44 + 2596050 * q^45 + 1721385 * q^46 + 41153690 * q^48 - 396068336 * q^49 - 60015715 * q^50 - 8419912 * q^52 + 26717388 * q^53 - 13729145 * q^54 + 7138890 * q^56 - 19745300 * q^57 - 41444182 * q^58 + 96768050 * q^60 + 26136558 * q^61 - 87505940 * q^62 + 19616924 * q^64 + 22030140 * q^65 - 69968200 * q^66 + 276958 * q^68 - 73697610 * q^69 + 39639840 * q^70 - 145994351 * q^72 - 39004722 * q^73 + 4922908 * q^74 - 19181080 * q^76 + 111211200 * q^77 - 197089615 * q^78 - 395680960 * q^80 - 539852286 * q^81 + 186999258 * q^82 - 377672700 * q^84 - 283475540 * q^85 - 340843785 * q^86 - 29231040 * q^88 - 206040612 * q^89 + 351285695 * q^90 + 43044280 * q^92 + 241823660 * q^93 - 442380075 * q^94 - 474931550 * q^96 + 2388718 * q^97 + 209675864 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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