LMFDB - Embedded newform 31.8.g.a.7.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [31,8,Mod(7,31)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(31, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([28])) N = Newforms(chi, 8, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("31.7"); S:= CuspForms(chi, 8); N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	31.g (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$9.68393579001$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$18$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			7.6
Character	$\chi$	$=$	31.7
Dual form			31.8.g.a.9.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.14721 - 9.68611i) q^{2} +(14.5381 - 3.09018i) q^{3} +(19.6383 - 14.2681i) q^{4} +(-175.802 + 304.498i) q^{5} +(-75.6864 - 131.093i) q^{6} +(-506.982 - 225.723i) q^{7} +(-1254.66 - 911.567i) q^{8} +(-1796.12 + 799.682i) q^{9} +(3502.68 + 744.518i) q^{10} +(419.058 + 3987.07i) q^{11} +(241.414 - 268.117i) q^{12} +(-2684.23 - 2981.13i) q^{13} +(-590.799 + 5621.08i) q^{14} +(-1614.88 + 4970.09i) q^{15} +(-3920.70 + 12066.7i) q^{16} +(-2550.63 + 24267.7i) q^{17} +(13398.6 + 14880.6i) q^{18} +(-2699.59 + 2998.20i) q^{19} +(892.142 + 8488.16i) q^{20} +(-8068.09 - 1714.93i) q^{21} +(37300.4 - 16607.2i) q^{22} +(15056.1 + 10938.9i) q^{23} +(-21057.4 - 9375.35i) q^{24} +(-22750.0 - 39404.2i) q^{25} +(-20427.8 + 35382.0i) q^{26} +(-49938.3 + 36282.3i) q^{27} +(-13176.9 + 2800.83i) q^{28} +(-66747.4 - 205427. i) q^{29} +53223.2 q^{30} +(-41904.5 - 160489. i) q^{31} -69290.3 q^{32} +(18413.1 + 56669.6i) q^{33} +(243087. - 51669.7i) q^{34} +(157860. - 114692. i) q^{35} +(-23862.7 + 41331.5i) q^{36} +(-22467.8 - 38915.3i) q^{37} +(37537.1 + 16712.6i) q^{38} +(-48235.9 - 35045.4i) q^{39} +(498142. - 221787. i) q^{40} +(-16068.0 - 3415.36i) q^{41} +(8781.01 + 83545.7i) q^{42} +(-450640. + 500486. i) q^{43} +(65117.4 + 72320.2i) q^{44} +(72259.0 - 687498. i) q^{45} +(58570.6 - 180262. i) q^{46} +(-290156. + 893007. i) q^{47} +(-19711.5 + 187543. i) q^{48} +(-344978. - 383137. i) q^{49} +(-310074. + 344372. i) q^{50} +(37909.9 + 360689. i) q^{51} +(-95248.6 - 20245.7i) q^{52} +(1.51918e6 - 676380. i) q^{53} +(508601. + 369520. i) q^{54} +(-1.28772e6 - 573332. i) q^{55} +(430330. + 745354. i) q^{56} +(-29982.1 + 51930.5i) q^{57} +(-1.77972e6 + 1.29305e6i) q^{58} +(-107971. + 22950.0i) q^{59} +(39200.0 + 120645. i) q^{60} -2.68815e6 q^{61} +(-1.42263e6 + 910983. i) q^{62} +1.09110e6 q^{63} +(719921. + 2.21569e6i) q^{64} +(1.37964e6 - 293251. i) q^{65} +(490959. - 356702. i) q^{66} +(874224. - 1.51420e6i) q^{67} +(296162. + 512968. i) q^{68} +(252690. + 112505. i) q^{69} +(-1.60774e6 - 1.16809e6i) q^{70} +(3.97025e6 - 1.76767e6i) q^{71} +(2.98249e6 + 633947. i) q^{72} +(3217.45 + 30612.0i) q^{73} +(-306227. + 340100. i) q^{74} +(-452509. - 502562. i) q^{75} +(-10236.9 + 97397.6i) q^{76} +(687518. - 2.11596e6i) q^{77} +(-187646. + 577513. i) q^{78} +(33066.6 - 314608. i) q^{79} +(-2.98501e6 - 3.31519e6i) q^{80} +(2.26327e6 - 2.51361e6i) q^{81} +(17487.8 + 166385. i) q^{82} +(-528958. - 112433. i) q^{83} +(-182912. + 81437.8i) q^{84} +(-6.94104e6 - 5.04296e6i) q^{85} +(6.26602e6 + 2.78981e6i) q^{86} +(-1.60519e6 - 2.78027e6i) q^{87} +(3.10870e6 - 5.38443e6i) q^{88} +(-6.53660e6 + 4.74912e6i) q^{89} +(-6.88660e6 + 1.46379e6i) q^{90} +(687943. + 2.11727e6i) q^{91} +451752. q^{92} +(-1.10515e6 - 2.20372e6i) q^{93} +9.56295e6 q^{94} +(-438352. - 1.34911e6i) q^{95} +(-1.00735e6 + 214119. i) q^{96} +(249640. - 181374. i) q^{97} +(-2.62539e6 + 4.54731e6i) q^{98} +(-3.94107e6 - 6.82613e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 6 q^{2} - 8 q^{3} - 2362 q^{4} - 75 q^{5} - 1637 q^{6} + 5518 q^{7} + 3401 q^{8} + 14542 q^{9} - 5312 q^{10} + 1361 q^{11} - 18281 q^{12} + 22457 q^{13} + 28470 q^{14} - 86918 q^{15} - 155730 q^{16}+ \cdots - 102755966 q^{99}+O(q^{100}) $ 144 * q - 6 * q^2 - 8 * q^3 - 2362 * q^4 - 75 * q^5 - 1637 * q^6 + 5518 * q^7 + 3401 * q^8 + 14542 * q^9 - 5312 * q^10 + 1361 * q^11 - 18281 * q^12 + 22457 * q^13 + 28470 * q^14 - 86918 * q^15 - 155730 * q^16 + 51582 * q^17 - 24915 * q^18 + 206748 * q^19 + 53815 * q^20 - 28547 * q^21 + 471441 * q^22 - 10235 * q^23 + 69278 * q^24 - 974301 * q^25 - 279651 * q^26 - 948323 * q^27 + 550632 * q^28 - 32990 * q^29 + 2457990 * q^30 + 899715 * q^31 - 1048518 * q^32 + 780887 * q^33 - 1741528 * q^34 + 40023 * q^35 - 2118881 * q^36 - 787972 * q^37 + 580274 * q^38 + 2541281 * q^39 + 2341817 * q^40 + 1129504 * q^41 - 4390379 * q^42 + 481927 * q^43 - 3123681 * q^44 - 1715971 * q^45 + 2065430 * q^46 - 3123106 * q^47 + 1041890 * q^48 + 76766 * q^49 + 7537425 * q^50 + 6145978 * q^51 + 3260257 * q^52 + 141486 * q^53 - 8979668 * q^54 - 8182779 * q^55 - 5240874 * q^56 - 5487037 * q^57 + 5315215 * q^58 + 7471552 * q^59 + 8590679 * q^60 + 10667852 * q^61 + 27020951 * q^62 - 23783686 * q^63 - 3962521 * q^64 + 935148 * q^65 + 3015728 * q^66 - 17382495 * q^67 - 29462568 * q^68 - 26986306 * q^69 - 31811186 * q^70 - 6186650 * q^71 + 35811589 * q^72 + 6470154 * q^73 + 55339663 * q^74 + 17367737 * q^75 + 2919592 * q^76 + 31865334 * q^77 - 7291717 * q^78 + 4223078 * q^79 + 77431338 * q^80 - 5164601 * q^81 - 19477394 * q^82 - 28867780 * q^83 - 76561164 * q^84 - 45198987 * q^85 - 60993764 * q^86 + 18253055 * q^87 - 45197061 * q^88 - 8429459 * q^89 + 83458809 * q^90 - 53128088 * q^91 + 77469728 * q^92 + 41662009 * q^93 - 16867972 * q^94 - 12744274 * q^95 + 119555444 * q^96 + 20643027 * q^97 + 49624796 * q^98 - 102755966 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{14}{15}\right)$

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 $

$2$	−3.14721	−	9.68611i	−0.278177	−	0.856140i	−0.988361	−	0.152124i	$-0.951389\pi$
$2$	−3.14721	−	9.68611i	−0.278177	−	0.856140i	0.710185	−	0.704015i	$-0.248611\pi$
$3$	14.5381	−	3.09018i	0.310874	−	0.0660783i	−0.0498328	−	0.998758i	$-0.515869\pi$
$3$	14.5381	−	3.09018i	0.310874	−	0.0660783i	0.360707	+	0.932679i	$0.382535\pi$
$4$	19.6383	−	14.2681i	0.153424	−	0.111469i
$5$	−175.802	+	304.498i	−0.628967	+	1.08940i	0.358792	+	0.933418i	$0.383189\pi$
$5$	−175.802	+	304.498i	−0.628967	+	1.08940i	−0.987759	+	0.155986i	$0.950145\pi$
$6$	−75.6864	−	131.093i	−0.143050	−	0.247770i
$7$	−506.982	−	225.723i	−0.558662	−	0.248732i	0.107926	−	0.994159i	$-0.465579\pi$
$7$	−506.982	−	225.723i	−0.558662	−	0.248732i	−0.666588	+	0.745427i	$0.732246\pi$
$8$	−1254.66	−	911.567i	−0.866388	−	0.629468i
$9$	−1796.12	+	799.682i	−0.821269	+	0.365653i
$10$	3502.68	+	744.518i	1.10765	+	0.235437i
$11$	419.058	+	3987.07i	0.0949292	+	0.903191i	0.933543	+	0.358465i	$0.116700\pi$
$11$	419.058	+	3987.07i	0.0949292	+	0.903191i	−0.838614	+	0.544726i	$0.816634\pi$
$12$	241.414	−	268.117i	0.0403299	−	0.0447909i
$13$	−2684.23	−	2981.13i	−0.338858	−	0.376340i	0.549498	−	0.835495i	$-0.314819\pi$
$13$	−2684.23	−	2981.13i	−0.338858	−	0.376340i	−0.888356	+	0.459155i	$0.848152\pi$
$14$	−590.799	+	5621.08i	−0.0575429	+	0.547484i
$15$	−1614.88	+	4970.09i	−0.123544	+	0.380228i
$16$	−3920.70	+	12066.7i	−0.239301	+	0.736491i
$17$	−2550.63	+	24267.7i	−0.125915	+	1.19800i	0.730940	+	0.682442i	$0.239082\pi$
$17$	−2550.63	+	24267.7i	−0.125915	+	1.19800i	−0.856855	+	0.515558i	$0.827585\pi$
$18$	13398.6	+	14880.6i	0.541508	+	0.601405i
$19$	−2699.59	+	2998.20i	−0.0902944	+	0.100282i	−0.786599	−	0.617465i	$-0.788160\pi$
$19$	−2699.59	+	2998.20i	−0.0902944	+	0.100282i	0.696304	+	0.717747i	$0.254826\pi$
$20$	892.142	+	8488.16i	0.0249361	+	0.237251i
$21$	−8068.09	−	1714.93i	−0.190109	−	0.0404090i
$22$	37300.4	−	16607.2i	0.746851	−	0.332519i
$23$	15056.1	+	10938.9i	0.258027	+	0.187467i	0.709277	−	0.704930i	$-0.249022\pi$
$23$	15056.1	+	10938.9i	0.258027	+	0.187467i	−0.451250	+	0.892398i	$0.649022\pi$
$24$	−21057.4	−	9375.35i	−0.310932	−	0.138436i
$25$	−22750.0	−	39404.2i	−0.291200	−	0.504374i
$26$	−20427.8	+	35382.0i	−0.227937	+	0.394798i
$27$	−49938.3	+	36282.3i	−0.488271	+	0.354749i
$28$	−13176.9	+	2800.83i	−0.113438	+	0.0241120i
$29$	−66747.4	−	205427.i	−0.508208	−	1.56410i	−0.795310	−	0.606202i	$-0.792692\pi$
$29$	−66747.4	−	205427.i	−0.508208	−	1.56410i	0.287103	−	0.957900i	$-0.407308\pi$
$30$	53223.2			0.359896
$31$	−41904.5	−	160489.i	−0.252636	−	0.967561i
$31$	−41904.5	−	160489.i	−0.252636	−	0.967561i
$32$	−69290.3			−0.373807
$33$	18413.1	+	56669.6i	0.0891924	+	0.274506i
$34$	243087.	−	51669.7i	1.06068	−	0.225455i
$35$	157860.	−	114692.i	0.622350	−	0.452164i
$36$	−23862.7	+	41331.5i	−0.0852436	+	0.147646i
$37$	−22467.8	−	38915.3i	−0.0729212	−	0.126303i	0.827259	−	0.561820i	$-0.189899\pi$
$37$	−22467.8	−	38915.3i	−0.0729212	−	0.126303i	−0.900180	+	0.435517i	$0.856565\pi$
$38$	37537.1	+	16712.6i	0.110973	+	0.0494085i
$39$	−48235.9	−	35045.4i	−0.130210	−	0.0946030i
$40$	498142.	−	221787.i	1.23067	−	0.547932i
$41$	−16068.0	−	3415.36i	−0.0364098	−	0.00773914i	0.189671	−	0.981848i	$-0.439258\pi$
$41$	−16068.0	−	3415.36i	−0.0364098	−	0.00773914i	−0.226081	+	0.974109i	$0.572591\pi$
$42$	8781.01	+	83545.7i	0.0182882	+	0.174001i
$43$	−450640.	+	500486.i	−0.864351	+	0.959959i	−0.999524	−	0.0308633i	$-0.990174\pi$
$43$	−450640.	+	500486.i	−0.864351	+	0.959959i	0.135173	+	0.990822i	$0.456841\pi$
$44$	65117.4	+	72320.2i	0.115242	+	0.127990i
$45$	72259.0	−	687498.i	0.118208	−	1.12468i
$46$	58570.6	−	180262.i	0.0887212	−	0.273056i
$47$	−290156.	+	893007.i	−0.407651	+	1.25462i	0.511011	+	0.859574i	$0.329271\pi$
$47$	−290156.	+	893007.i	−0.407651	+	1.25462i	−0.918661	+	0.395046i	$0.870729\pi$
$48$	−19711.5	+	187543.i	−0.0257262	+	0.244769i
$49$	−344978.	−	383137.i	−0.418895	−	0.465230i
$50$	−310074.	+	344372.i	−0.350809	+	0.389613i
$51$	37909.9	+	360689.i	0.0400182	+	0.380747i
$52$	−95248.6	−	20245.7i	−0.0939392	−	0.0199674i
$53$	1.51918e6	−	676380.i	1.40166	−	0.624059i	0.439923	−	0.898036i	$-0.355006\pi$
$53$	1.51918e6	−	676380.i	1.40166	−	0.624059i	0.961736	+	0.273977i	$0.0883392\pi$
$54$	508601.	+	369520.i	0.439540	+	0.319345i
$55$	−1.28772e6	−	573332.i	−1.04365	−	0.464662i
$56$	430330.	+	745354.i	0.327449	+	0.567158i
$57$	−29982.1	+	51930.5i	−0.0214437	+	0.0371416i
$58$	−1.77972e6	+	1.29305e6i	−1.19772	+	0.870193i
$59$	−107971.	+	22950.0i	−0.0684426	+	0.0145479i	−0.242006	−	0.970275i	$-0.577805\pi$
$59$	−107971.	+	22950.0i	−0.0684426	+	0.0145479i	0.173563	+	0.984823i	$0.444472\pi$
$60$	39200.0	+	120645.i	0.0234292	+	0.0721076i
$61$	−2.68815e6			−1.51635			−0.758175	−	0.652051i	$-0.773909\pi$
$61$	−2.68815e6			−1.51635			−0.758175	+	0.652051i	$0.773909\pi$
$62$	−1.42263e6	+	910983.i	−0.758090	+	0.485444i
$63$	1.09110e6			0.549761
$64$	719921.	+	2.21569e6i	0.343285	+	1.05652i
$65$	1.37964e6	−	293251.i	0.623116	−	0.132447i
$66$	490959.	−	356702.i	0.210204	−	0.152722i
$67$	874224.	−	1.51420e6i	0.355109	−	0.615066i	−0.632028	−	0.774946i	$-0.717777\pi$
$67$	874224.	−	1.51420e6i	0.355109	−	0.615066i	0.987137	+	0.159880i	$0.0511106\pi$
$68$	296162.	+	512968.i	0.114222	+	0.197838i
$69$	252690.	+	112505.i	0.0926013	+	0.0412287i
$70$	−1.60774e6	−	1.16809e6i	−0.560239	−	0.407037i
$71$	3.97025e6	−	1.76767e6i	1.31648	−	0.586134i	0.376199	−	0.926539i	$-0.377231\pi$
$71$	3.97025e6	−	1.76767e6i	1.31648	−	0.586134i	0.940279	+	0.340405i	$0.110564\pi$
$72$	2.98249e6	+	633947.i	0.941704	+	0.200165i
$73$	3217.45	+	30612.0i	0.000968015	+	0.00921005i	0.994995	−	0.0999223i	$-0.0318594\pi$
$73$	3217.45	+	30612.0i	0.000968015	+	0.00921005i	−0.994027	+	0.109132i	$0.965193\pi$
$74$	−306227.	+	340100.i	−0.0878482	+	0.0975653i
$75$	−452509.	−	502562.i	−0.123855	−	0.137555i
$76$	−10236.9	+	97397.6i	−0.00267498	+	0.0254508i
$77$	687518.	−	2.11596e6i	0.171619	−	0.528190i
$78$	−187646.	+	577513.i	−0.0447721	+	0.137794i
$79$	33066.6	−	314608.i	0.00754562	−	0.0717917i	−0.990101	−	0.140356i	$-0.955175\pi$
$79$	33066.6	−	314608.i	0.00754562	−	0.0717917i	0.997647	+	0.0685645i	$0.0218419\pi$
$80$	−2.98501e6	−	3.31519e6i	−0.651824	−	0.723924i
$81$	2.26327e6	−	2.51361e6i	0.473193	−	0.525534i
$82$	17487.8	+	166385.i	0.00350257	+	0.0333247i
$83$	−528958.	−	112433.i	−0.101542	−	0.0215835i	0.156860	−	0.987621i	$-0.449863\pi$
$83$	−528958.	−	112433.i	−0.101542	−	0.0215835i	−0.258403	+	0.966037i	$0.583196\pi$
$84$	−182912.	+	81437.8i	−0.0336717	+	0.0149916i
$85$	−6.94104e6	−	5.04296e6i	−1.22591	−	0.890675i
$86$	6.26602e6	+	2.78981e6i	1.06230	+	0.472967i
$87$	−1.60519e6	−	2.78027e6i	−0.261342	−	0.452657i
$88$	3.10870e6	−	5.38443e6i	0.486284	−	0.842269i
$89$	−6.53660e6	+	4.74912e6i	−0.982850	+	0.714082i	−0.958344	−	0.285617i	$-0.907801\pi$
$89$	−6.53660e6	+	4.74912e6i	−0.982850	+	0.714082i	−0.0245062	+	0.999700i	$0.507801\pi$
$90$	−6.88660e6	+	1.46379e6i	−0.995763	+	0.211656i
$91$	687943.	+	2.11727e6i	0.0956990	+	0.294531i
$92$	451752.			0.0604843
$93$	−1.10515e6	−	2.20372e6i	−0.142473	−	0.284096i
$94$	9.56295e6			1.18753
$95$	−438352.	−	1.34911e6i	−0.0524555	−	0.161441i
$96$	−1.00735e6	+	214119.i	−0.116207	+	0.0247006i
$97$	249640.	−	181374.i	0.0277724	−	0.0201778i	−0.573812	−	0.818987i	$-0.694536\pi$
$97$	249640.	−	181374.i	0.0277724	−	0.0201778i	0.601585	+	0.798809i	$0.294536\pi$
$98$	−2.62539e6	+	4.54731e6i	−0.281775	+	0.488049i
$99$	−3.94107e6	−	6.82613e6i	−0.408217	−	0.707052i
$100$	−1.00899e6	−	449233.i	−0.100899	−	0.0449233i
$101$	1.24339e7	+	9.03376e6i	1.20083	+	0.872456i	0.994366	−	0.105997i	$-0.0338035\pi$
$101$	1.24339e7	+	9.03376e6i	1.20083	+	0.872456i	0.206467	+	0.978454i	$0.433804\pi$
$102$	3.37436e6	−	1.50236e6i	0.314841	−	0.140176i
$103$	2.89619e6	+	615603.i	0.261154	+	0.0555099i	0.336628	−	0.941638i	$-0.390714\pi$
$103$	2.89619e6	+	615603.i	0.261154	+	0.0555099i	−0.0754740	+	0.997148i	$0.524047\pi$
$104$	650298.	+	6.18717e6i	0.0566886	+	0.539356i
$105$	1.94058e6	−	2.15523e6i	0.163594	−	0.181690i
$106$	−1.13327e7	−	1.25862e7i	−0.924190	−	1.02642i
$107$	−2.36004e6	+	2.24543e7i	−0.186241	+	1.77197i	0.358662	+	0.933468i	$0.383233\pi$
$107$	−2.36004e6	+	2.24543e7i	−0.186241	+	1.77197i	−0.544903	+	0.838499i	$0.683434\pi$
$108$	−463025.	+	1.42505e6i	−0.0353689	+	0.108854i
$109$	−4.01766e6	+	1.23651e7i	−0.297154	+	0.914545i	0.685336	+	0.728227i	$0.259655\pi$
$109$	−4.01766e6	+	1.23651e7i	−0.297154	+	0.914545i	−0.982490	+	0.186318i	$0.940345\pi$
$110$	−1.50062e6	+	1.42774e7i	−0.107497	+	1.02277i
$111$	−446895.	−	496327.i	−0.0310152	−	0.0344459i
$112$	4.71145e6	−	5.23259e6i	0.316877	−	0.351928i
$113$	641562.	+	6.10406e6i	0.0418277	+	0.397964i	0.995326	+	0.0965673i	$0.0307863\pi$
$113$	641562.	+	6.10406e6i	0.0418277	+	0.397964i	−0.953499	+	0.301397i	$0.902547\pi$
$114$	597365.	+	126974.i	0.0377635	+	0.00802689i
$115$	−5.97775e6	+	2.66146e6i	−0.366518	+	0.163184i
$116$	−4.24185e6	−	3.08189e6i	−0.252321	−	0.183322i
$117$	7.20514e6	+	3.20793e6i	0.415903	+	0.185172i
$118$	562105.	+	973594.i	0.0314942	+	0.0545495i
$119$	6.77089e6	−	1.17275e7i	0.368325	−	0.637958i
$120$	6.55670e6	−	4.76372e6i	0.346378	−	0.251659i
$121$	3.34020e6	−	709981.i	0.171405	−	0.0364332i
$122$	8.46017e6	+	2.60377e7i	0.421813	+	1.29821i
$123$	−244153.			−0.0118302
$124$	−3.11280e6	−	2.55383e6i	−0.146614	−	0.120286i
$125$	−1.14711e7			−0.525313
$126$	−3.43393e6	−	1.05686e7i	−0.152931	−	0.470672i
$127$	−6.76972e6	+	1.43895e6i	−0.293263	+	0.0623350i	−0.352194	−	0.935927i	$-0.614564\pi$
$127$	−6.76972e6	+	1.43895e6i	−0.293263	+	0.0623350i	0.0589307	+	0.998262i	$0.481231\pi$
$128$	1.20204e7	−	8.73331e6i	0.506621	−	0.368081i
$129$	−5.00487e6	+	8.66870e6i	−0.205272	+	0.355541i
$130$	−7.18248e6	−	1.24404e7i	−0.286730	−	0.496631i
$131$	−2.77406e7	−	1.23509e7i	−1.07812	−	0.480009i	−0.210681	−	0.977555i	$-0.567568\pi$
$131$	−2.77406e7	−	1.23509e7i	−1.07812	−	0.480009i	−0.867438	+	0.497545i	$0.834235\pi$
$132$	1.17017e6	+	850177.i	0.0442832	+	0.0321737i
$133$	2.04541e6	−	910674.i	0.0753875	−	0.0335647i
$134$	−1.74181e7	−	3.70233e6i	−0.625365	−	0.132926i
$135$	−2.26863e6	−	2.15846e7i	−0.0793589	−	0.755050i
$136$	2.53218e7	−	2.81227e7i	0.863193	−	0.958673i
$137$	−2.34526e6	−	2.60467e6i	−0.0779235	−	0.0865428i	0.702922	−	0.711267i	$-0.251878\pi$
$137$	−2.34526e6	−	2.60467e6i	−0.0779235	−	0.0865428i	−0.780846	+	0.624724i	$0.785212\pi$
$138$	294467.	−	2.80166e6i	0.00953805	−	0.0907485i
$139$	−978701.	+	3.01213e6i	−0.0309100	+	0.0951311i	−0.965321	−	0.261065i	$-0.915926\pi$
$139$	−978701.	+	3.01213e6i	−0.0309100	+	0.0951311i	0.934411	+	0.356196i	$0.115926\pi$
$140$	1.46367e6	−	4.50472e6i	0.0450812	−	0.138746i
$141$	−1.45877e6	+	1.38793e7i	−0.0438249	+	0.416966i
$142$	−2.96171e7	−	3.28931e7i	−0.868026	−	0.964041i
$143$	1.07612e7	−	1.19515e7i	0.307739	−	0.341779i
$144$	−2.60747e6	−	2.48085e7i	−0.0727698	−	0.692358i
$145$	7.42864e7	+	1.57901e7i	2.02358	+	0.430126i
$146$	286385.	−	127507.i	0.00761581	−	0.00339078i
$147$	−6.19930e6	−	4.50406e6i	−0.160965	−	0.116948i
$148$	−996475.	−	443659.i	−0.0252668	−	0.0112495i
$149$	2.51695e7	+	4.35949e7i	0.623337	+	1.07965i	0.988860	+	0.148849i	$0.0475569\pi$
$149$	2.51695e7	+	4.35949e7i	0.623337	+	1.07965i	−0.365523	+	0.930802i	$0.619110\pi$
$150$	−3.44373e6	+	5.96472e6i	−0.0833125	+	0.144301i
$151$	−6.45763e6	+	4.69174e6i	−0.152635	+	0.110896i	−0.661482	−	0.749961i	$-0.730072\pi$
$151$	−6.45763e6	+	4.69174e6i	−0.152635	+	0.110896i	0.508847	+	0.860857i	$0.330072\pi$
$152$	6.12015e6	−	1.30088e6i	0.141354	−	0.0300458i
$153$	−1.48252e7	−	4.56272e7i	−0.334642	−	1.02992i
$154$	−2.26592e7			−0.499945
$155$	5.62353e7	+	1.54544e7i	1.21296	+	0.333343i
$156$	−1.44730e6			−0.0305227
$157$	1.72907e7	+	5.32152e7i	0.356585	+	1.09746i	0.955085	+	0.296332i	$0.0957636\pi$
$157$	1.72907e7	+	5.32152e7i	0.356585	+	1.09746i	−0.598500	+	0.801123i	$0.704236\pi$
$158$	−3.15139e6	+	669849.i	−0.0635628	+	0.0135107i
$159$	1.99959e7	−	1.45278e7i	0.394503	−	0.286623i
$160$	1.21814e7	−	2.10987e7i	0.235113	−	0.407227i
$161$	−5.16400e6	−	8.94431e6i	−0.0975204	−	0.168910i
$162$	−3.14701e7	−	1.40114e7i	−0.581562	−	0.258928i
$163$	−884592.	−	642694.i	−0.0159988	−	0.0116238i	0.579757	−	0.814789i	$-0.303147\pi$
$163$	−884592.	−	642694.i	−0.0159988	−	0.0116238i	−0.595756	+	0.803166i	$0.703147\pi$
$164$	−364278.	+	162187.i	−0.00644882	+	0.00287120i
$165$	−2.04928e7	−	4.35588e6i	−0.355147	−	0.0754888i
$166$	575697.	+	5.47739e6i	0.00976823	+	0.0929385i
$167$	−6.52273e7	+	7.24423e7i	−1.08373	+	1.20361i	−0.105864	+	0.994381i	$0.533761\pi$
$167$	−6.52273e7	+	7.24423e7i	−1.08373	+	1.20361i	−0.977867	+	0.209226i	$0.932906\pi$
$168$	8.55948e6	+	9.50626e6i	0.139272	+	0.154678i
$169$	4.87691e6	−	4.64007e7i	0.0777215	−	0.739471i
$170$	−2.70018e7	+	8.31029e7i	−0.421523	+	1.29731i
$171$	2.45117e6	−	7.54394e6i	0.0374876	−	0.115375i
$172$	−1.70883e6	+	1.62585e7i	−0.0256065	+	0.243629i
$173$	4.46303e7	+	4.95670e7i	0.655343	+	0.727833i	0.975614	−	0.219494i	$-0.0704405\pi$
$173$	4.46303e7	+	4.95670e7i	0.655343	+	0.727833i	−0.320271	+	0.947326i	$0.603774\pi$
$174$	−2.18781e7	+	2.42981e7i	−0.314839	+	0.349664i
$175$	2.63942e6	+	2.51124e7i	0.0372285	+	0.354205i
$176$	−4.97537e7	−	1.05755e7i	−0.687909	−	0.146220i
$177$	−1.49878e6	+	667301.i	−0.0203157	+	0.00904515i
$178$	6.65726e7	+	4.83678e7i	0.884760	+	0.642816i
$179$	−6.04929e7	−	2.69332e7i	−0.788349	−	0.350996i	−0.0272481	−	0.999629i	$-0.508674\pi$
$179$	−6.04929e7	−	2.69332e7i	−0.788349	−	0.350996i	−0.761101	+	0.648633i	$0.775341\pi$
$180$	−8.39022e6	−	1.45323e7i	−0.107231	−	0.185729i
$181$	4.92215e7	−	8.52541e7i	0.616992	−	1.06866i	−0.373040	−	0.927815i	$-0.621684\pi$
$181$	4.92215e7	−	8.52541e7i	0.616992	−	1.06866i	0.990032	−	0.140846i	$-0.0449822\pi$
$182$	1.83430e7	−	1.33270e7i	0.225539	−	0.163863i
$183$	−3.90807e7	+	8.30686e6i	−0.471394	+	0.100198i
$184$	−8.91880e6	−	2.74492e7i	−0.105547	−	0.324839i
$185$	1.57995e7			0.183460
$186$	−1.78673e7	+	1.76402e7i	−0.203593	+	0.201005i
$187$	−9.78258e7			−1.09398
$188$	7.04331e6	+	2.16771e7i	0.0773080	+	0.237930i
$189$	3.35075e7	−	7.12225e6i	0.361016	−	0.0767363i
$190$	−1.16880e7	+	8.49186e6i	−0.123624	+	0.0898184i
$191$	4.90706e7	−	8.49928e7i	0.509571	−	0.882603i	−0.490368	−	0.871516i	$-0.663137\pi$
$191$	4.90706e7	−	8.49928e7i	0.509571	−	0.882603i	0.999939	−	0.0110871i	$-0.00352921\pi$
$192$	1.73132e7	+	2.99873e7i	0.176532	+	0.305762i
$193$	−1.17527e8	−	5.23266e7i	−1.17676	−	0.523928i	−0.277239	−	0.960801i	$-0.589419\pi$
$193$	−1.17527e8	−	5.23266e7i	−1.17676	−	0.523928i	−0.899523	+	0.436873i	$0.856086\pi$
$194$	−2.54248e6	−	1.84722e6i	−0.0250007	−	0.0181640i
$195$	1.91512e7	−	8.52666e6i	0.184959	−	0.0823489i
$196$	−1.22414e7	−	2.60199e6i	−0.116128	−	0.0246837i
$197$	1.48607e7	+	1.41390e8i	0.138486	+	1.31761i	0.814260	+	0.580500i	$0.197143\pi$
$197$	1.48607e7	+	1.41390e8i	0.138486	+	1.31761i	−0.675774	+	0.737109i	$0.736190\pi$
$198$	−5.37153e7	+	5.96569e7i	−0.491779	+	0.546176i
$199$	1.38624e8	+	1.53958e8i	1.24696	+	1.38489i	0.893263	+	0.449534i	$0.148410\pi$
$199$	1.38624e8	+	1.53958e8i	1.24696	+	1.38489i	0.353700	+	0.935359i	$0.384923\pi$
$200$	−7.37592e6	+	7.01772e7i	−0.0651945	+	0.620284i
$201$	8.03045e6	−	2.47152e7i	0.0697515	−	0.214673i
$202$	4.83699e7	−	1.48867e8i	0.412901	−	1.27078i
$203$	−1.25299e7	+	1.19214e8i	−0.105127	+	1.00021i
$204$	5.89081e6	+	6.54241e6i	0.0485814	+	0.0539551i
$205$	3.86475e6	−	4.29224e6i	0.0313316	−	0.0347973i
$206$	−3.15210e6	−	2.99902e7i	−0.0251226	−	0.239026i
$207$	−3.57901e7	−	7.60742e6i	−0.280457	−	0.0596130i
$208$	4.64964e7	−	2.07015e7i	0.358260	−	0.159507i
$209$	−1.30853e7	−	9.50706e6i	−0.0991455	−	0.0720334i
$210$	−2.69832e7	−	1.20137e7i	−0.201060	−	0.0895177i
$211$	−1.22900e8	−	2.12869e8i	−0.900664	−	1.56000i	−0.826635	−	0.562739i	$-0.809748\pi$
$211$	−1.22900e8	−	2.12869e8i	−0.900664	−	1.56000i	−0.0740289	−	0.997256i	$-0.523586\pi$
$212$	2.01834e7	−	3.49586e7i	0.145485	−	0.251988i
$213$	5.22577e7	−	3.79674e7i	0.370528	−	0.269205i
$214$	2.24922e8	−	4.78087e7i	1.56886	−	0.333471i
$215$	−7.31736e7	−	2.25205e8i	−0.502134	−	1.54541i
$216$	9.57295e7			0.646335
$217$	−1.49812e7	+	9.08236e7i	−0.0995259	+	0.603378i
$218$	1.32414e8			0.865639
$219$	141372.	+	435099.i	0.000909515	+	0.00279920i
$220$	−3.34691e7	+	7.11407e6i	−0.211916	+	0.0450442i
$221$	7.91916e7	−	5.75361e7i	0.493522	−	0.358565i
$222$	−3.40101e6	+	5.89072e6i	−0.0208628	+	0.0361354i
$223$	−3.32063e7	−	5.75149e7i	−0.200518	−	0.347307i	0.748178	−	0.663499i	$-0.230929\pi$
$223$	−3.32063e7	−	5.75149e7i	−0.200518	−	0.347307i	−0.948695	+	0.316192i	$0.897596\pi$
$224$	3.51289e7	+	1.56404e7i	0.208832	+	0.0929780i
$225$	7.23725e7	+	5.25817e7i	0.423579	+	0.307748i
$226$	5.71055e7	−	2.54250e7i	0.329077	−	0.146515i
$227$	−1.20336e8	−	2.55782e7i	−0.682817	−	0.145137i	−0.146573	−	0.989200i	$-0.546824\pi$
$227$	−1.20336e8	−	2.55782e7i	−0.682817	−	0.145137i	−0.536245	+	0.844063i	$0.680158\pi$
$228$	152150.	+	1.44761e6i	0.000850161	+	0.00808874i
$229$	−4.26531e7	+	4.73711e7i	−0.234707	+	0.260669i	−0.848980	−	0.528425i	$-0.822783\pi$
$229$	−4.26531e7	+	4.73711e7i	−0.234707	+	0.260669i	0.614273	+	0.789094i	$0.289449\pi$
$230$	4.45925e7	+	4.95249e7i	0.241665	+	0.268396i
$231$	3.45653e6	−	3.28867e7i	0.0184501	−	0.175541i
$232$	−1.03515e8	+	3.18587e8i	−0.544247	+	1.67502i
$233$	6.17808e7	−	1.90142e8i	0.319969	−	0.984763i	−0.653692	−	0.756761i	$-0.726781\pi$
$233$	6.17808e7	−	1.90142e8i	0.319969	−	0.984763i	0.973661	−	0.228002i	$-0.0732193\pi$
$234$	8.39634e6	−	7.98858e7i	0.0428385	−	0.407581i
$235$	−2.20909e8	−	2.45344e8i	−1.11039	−	1.23321i
$236$	−1.79292e6	+	1.99124e6i	−0.00887911	+	0.00986125i
$237$	−491467.	−	4.67599e6i	−0.00239814	−	0.0228168i
$238$	−1.34904e8	−	2.86746e7i	−0.648640	−	0.137873i
$239$	−2.56116e8	+	1.14030e8i	−1.21351	+	0.540291i	−0.910823	−	0.412798i	$-0.864552\pi$
$239$	−2.56116e8	+	1.14030e8i	−1.21351	+	0.540291i	−0.302691	+	0.953089i	$0.597885\pi$
$240$	−5.36410e7	−	3.89724e7i	−0.250471	−	0.181978i
$241$	−3.51354e7	−	1.56433e7i	−0.161691	−	0.0719893i	0.324295	−	0.945956i	$-0.394873\pi$
$241$	−3.51354e7	−	1.56433e7i	−0.161691	−	0.0719893i	−0.485986	+	0.873967i	$0.661539\pi$
$242$	−1.73893e7	−	3.01191e7i	−0.0788728	−	0.136612i
$243$	9.26348e7	−	1.60448e8i	0.414145	−	0.717320i
$244$	−5.27907e7	+	3.83547e7i	−0.232645	+	0.169026i
$245$	1.77312e8	−	3.76889e7i	0.770295	−	0.163731i
$246$	768400.	+	2.36489e6i	0.00329090	+	0.0101283i
$247$	1.61844e7			0.0683371
$248$	−9.37201e7	+	2.39558e8i	−0.390168	+	0.997310i
$249$	−8.03750e6			−0.0329931
$250$	3.61018e7	+	1.11110e8i	0.146130	+	0.449741i
$251$	6.32151e7	−	1.34368e7i	0.252327	−	0.0536337i	−0.0800117	−	0.996794i	$-0.525496\pi$
$251$	6.32151e7	−	1.34368e7i	0.252327	−	0.0536337i	0.332338	+	0.943160i	$0.392162\pi$
$252$	2.14274e7	−	1.55679e7i	0.0843467	−	0.0612815i
$253$	−3.73047e7	+	6.46137e7i	−0.144824	+	0.250843i
$254$	3.52435e7	+	6.10436e7i	0.134946	+	0.233734i
$255$	−1.16493e8	−	5.18662e7i	−0.439958	−	0.195882i
$256$	1.18829e8	+	8.63344e7i	0.442673	+	0.321621i
$257$	−1.25012e8	+	5.56587e7i	−0.459393	+	0.204535i	−0.623366	−	0.781930i	$-0.714235\pi$
$257$	−1.25012e8	+	5.56587e7i	−0.459393	+	0.204535i	0.163974	+	0.986465i	$0.447569\pi$
$258$	9.97174e7	+	2.11956e7i	0.361495	+	0.0768381i
$259$	2.60667e6	+	2.48008e7i	0.00932260	+	0.0886987i
$260$	2.29096e7	−	2.54437e7i	0.0808373	−	0.0897789i
$261$	2.84163e8	+	3.15594e8i	0.989293	+	1.09872i
$262$	−3.23269e7	+	3.07570e8i	−0.111048	+	1.05655i
$263$	8.25486e7	−	2.54058e8i	0.279811	−	0.861169i	−0.708095	−	0.706117i	$-0.750445\pi$
$263$	8.25486e7	−	2.54058e8i	0.279811	−	0.861169i	0.987906	−	0.155053i	$-0.0495547\pi$
$264$	2.85559e7	−	8.78861e7i	0.0955174	−	0.293972i
$265$	−6.11175e7	+	5.81494e8i	−0.201746	+	1.91949i
$266$	−1.52582e7	−	1.69460e7i	−0.0497071	−	0.0552053i
$267$	−8.03545e7	+	8.92427e7i	−0.258357	+	0.286935i
$268$	−4.43643e6	−	4.22098e7i	−0.0140787	−	0.133950i
$269$	5.75039e8	+	1.22228e8i	1.80121	+	0.382859i	0.981735	−	0.190255i	$-0.0609314\pi$
$269$	5.75039e8	+	1.22228e8i	1.80121	+	0.382859i	0.819476	+	0.573114i	$0.194265\pi$
$270$	−2.01931e8	+	8.99054e7i	−0.624352	+	0.277979i
$271$	−3.30785e8	−	2.40329e8i	−1.00961	−	0.733524i	−0.0454822	−	0.998965i	$-0.514482\pi$
$271$	−3.30785e8	−	2.40329e8i	−1.00961	−	0.733524i	−0.964127	+	0.265441i	$0.914482\pi$
$272$	−2.82830e8	−	1.25924e8i	−0.852185	−	0.379417i
$273$	1.65442e7	+	2.86553e7i	0.0492125	+	0.0852385i
$274$	−1.78481e7	+	3.09139e7i	−0.0524162	+	0.0907876i
$275$	1.47574e8	−	1.07219e8i	0.427902	−	0.310889i
$276$	6.56764e6	−	1.39599e6i	0.0188030	−	0.00399670i
$277$	8.44304e7	+	2.59850e8i	0.238682	+	0.734588i	0.996612	+	0.0822515i	$0.0262111\pi$
$277$	8.44304e7	+	2.59850e8i	0.238682	+	0.734588i	−0.757930	+	0.652336i	$0.773789\pi$
$278$	3.22560e7			0.0900439
$279$	2.03605e8	+	2.54746e8i	0.561273	+	0.702252i
$280$	−3.02611e8			−0.823819
$281$	−4.70524e7	−	1.44812e8i	−0.126506	−	0.389344i	0.867667	−	0.497146i	$-0.165619\pi$
$281$	−4.70524e7	−	1.44812e8i	−0.126506	−	0.389344i	−0.994172	+	0.107802i	$0.965619\pi$
$282$	1.39027e8	−	2.95512e7i	0.369172	−	0.0784699i
$283$	8.33376e6	−	6.05483e6i	0.0218569	−	0.0158800i	−0.576803	−	0.816883i	$-0.695700\pi$
$283$	8.33376e6	−	6.05483e6i	0.0218569	−	0.0158800i	0.598660	+	0.801003i	$0.295700\pi$
$284$	5.27478e7	−	9.13618e7i	0.136644	−	0.236674i
$285$	−1.05418e7	−	1.82590e7i	−0.0269748	−	0.0467217i
$286$	−1.49631e8	−	6.66200e7i	−0.378216	−	0.168393i
$287$	7.37525e6	+	5.35843e6i	0.0184158	+	0.0133798i
$288$	1.24453e8	−	5.54103e7i	0.306996	−	0.136684i
$289$	−1.81042e8	−	3.84816e7i	−0.441201	−	0.0937802i
$290$	−8.08505e7	−	7.69241e8i	−0.194666	−	1.85212i
$291$	3.06882e6	−	3.40827e6i	0.00730040	−	0.00810791i
$292$	499959.	+	555261.i	0.00117515	+	0.00130514i
$293$	−7.99143e7	+	7.60334e8i	−0.185604	+	1.76591i	0.364874	+	0.931057i	$0.381112\pi$
$293$	−7.99143e7	+	7.60334e8i	−0.185604	+	1.76591i	−0.550478	+	0.834850i	$0.685554\pi$
$294$	−2.41163e7	+	7.42224e7i	−0.0553471	+	0.170341i
$295$	1.19933e7	−	3.69117e7i	0.0271996	−	0.0837118i
$296$	−7.28441e6	+	6.93065e7i	−0.0163258	+	0.155329i
$297$	−1.65587e8	−	1.83903e8i	−0.366758	−	0.407326i
$298$	3.43051e8	−	3.80997e8i	0.750935	−	0.833997i
$299$	−7.80363e6	−	7.42466e7i	−0.0168829	−	0.160630i
$300$	−1.60571e7	−	3.41304e6i	−0.0343354	−	0.00729822i
$301$	3.41437e8	−	1.52018e8i	0.721653	−	0.321300i
$302$	6.57682e7	+	4.77834e7i	0.137402	+	0.0998281i
$303$	2.08682e8	+	9.29111e7i	0.430958	+	0.191875i
$304$	−2.55940e7	−	4.43302e7i	−0.0522494	−	0.0904986i
$305$	4.72582e8	−	8.18536e8i	0.953735	−	1.65192i
$306$	−3.95293e8	+	2.87197e8i	−0.788667	+	0.573000i
$307$	−1.61106e8	+	3.42441e7i	−0.317780	+	0.0675463i	−0.364041	−	0.931383i	$-0.618603\pi$
$307$	−1.61106e8	+	3.42441e7i	−0.317780	+	0.0675463i	0.0462601	+	0.998929i	$0.485270\pi$
$308$	−1.66890e7	−	5.13635e7i	−0.0325464	−	0.100167i
$309$	4.40075e7			0.0848539
$310$	−2.72913e7	−	5.93340e8i	−0.0520306	−	1.13120i
$311$	−8.75763e8			−1.65092			−0.825459	−	0.564462i	$-0.809084\pi$
$311$	−8.75763e8			−1.65092			−0.825459	+	0.564462i	$0.809084\pi$
$312$	2.85736e7	+	8.79404e7i	0.0532628	+	0.163926i
$313$	4.21762e8	−	8.96482e7i	0.777431	−	0.165248i	0.197926	−	0.980217i	$-0.436579\pi$
$313$	4.21762e8	−	8.96482e7i	0.777431	−	0.165248i	0.579505	+	0.814969i	$0.303246\pi$
$314$	4.61031e8	−	3.34959e8i	0.840381	−	0.610573i
$315$	−1.91818e8	+	3.32239e8i	−0.345782	+	0.598912i
$316$	−3.83947e6	−	6.65016e6i	−0.00684489	−	0.0118557i
$317$	−8.37466e8	−	3.72864e8i	−1.47659	−	0.657420i	−0.498744	−	0.866749i	$-0.666205\pi$
$317$	−8.37466e8	−	3.72864e8i	−1.47659	−	0.657420i	−0.977845	+	0.209330i	$0.932872\pi$
$318$	−2.03649e8	−	1.47960e8i	−0.355131	−	0.258018i
$319$	7.91082e8	−	3.52213e8i	1.36444	−	0.607488i
$320$	−8.01235e8	−	1.70308e8i	−1.36689	−	0.290542i
$321$	3.50771e7	+	3.33736e8i	0.0591910	+	0.563165i
$322$	−7.03834e7	+	7.81687e7i	−0.117483	+	0.130478i
$323$	−6.58737e7	−	7.31602e7i	−0.108769	−	0.120800i
$324$	8.58234e6	−	8.16555e7i	0.0140184	−	0.133376i
$325$	−5.64030e7	+	1.73591e8i	−0.0911403	+	0.280501i
$326$	−3.44121e6	+	1.05909e7i	−0.00550110	+	0.0169306i
$327$	−2.01990e7	+	1.92181e8i	−0.0319458	+	0.303944i
$328$	1.70466e7	+	1.89322e7i	0.0266735	+	0.0296239i
$329$	3.48675e8	−	3.87243e8i	0.539804	−	0.599513i
$330$	2.23036e7	+	2.12205e8i	0.0341646	+	0.325055i
$331$	2.47669e8	+	5.26437e7i	0.375382	+	0.0797900i	0.391739	−	0.920076i	$-0.371874\pi$
$331$	2.47669e8	+	5.26437e7i	0.375382	+	0.0797900i	−0.0163570	+	0.999866i	$0.505207\pi$
$332$	−1.19920e7	+	5.33920e6i	−0.0179850	+	0.00800742i
$333$	7.14746e7	+	5.19293e7i	0.106071	+	0.0770651i
$334$	9.06968e8	+	4.03808e8i	1.33192	+	0.593011i
$335$	3.07380e8	+	5.32398e8i	0.446703	+	0.773713i
$336$	5.23260e7	−	9.06313e7i	0.0752541	−	0.130344i
$337$	−3.13121e8	+	2.27495e8i	−0.445663	+	0.323793i	−0.787881	−	0.615827i	$-0.788822\pi$
$337$	−3.13121e8	+	2.27495e8i	−0.445663	+	0.323793i	0.342218	+	0.939621i	$0.388822\pi$
$338$	−4.64791e8	+	9.87944e7i	−0.654711	+	0.139163i
$339$	2.81897e7	+	8.67591e7i	0.0393000	+	0.120953i
$340$	−2.08263e8			−0.287367
$341$	6.22320e8	−	2.34330e8i	0.849910	−	0.320028i
$342$	−8.07858e7			−0.109205
$343$	2.29646e8	+	7.06778e8i	0.307277	+	0.945700i
$344$	1.02163e9	−	2.17154e8i	1.35313	−	0.287616i
$345$	−7.86809e7	+	5.71650e7i	−0.103158	+	0.0749486i
$346$	3.39651e8	−	5.88292e8i	0.440825	−	0.763531i
$347$	−1.22565e8	−	2.12289e8i	−0.157476	−	0.272757i	0.776482	−	0.630140i	$-0.217002\pi$
$347$	−1.22565e8	−	2.12289e8i	−0.157476	−	0.272757i	−0.933958	+	0.357383i	$0.883669\pi$
$348$	−7.11922e7	−	3.16968e7i	−0.0905535	−	0.0403170i
$349$	−2.74868e8	−	1.99703e8i	−0.346127	−	0.251476i	0.401115	−	0.916028i	$-0.368623\pi$
$349$	−2.74868e8	−	1.99703e8i	−0.346127	−	0.251476i	−0.747242	+	0.664552i	$0.768623\pi$
$350$	2.34935e8	−	1.04600e8i	0.292893	−	0.130404i
$351$	2.42208e8	+	5.14829e7i	0.298960	+	0.0635460i
$352$	−2.90367e7	−	2.76266e8i	−0.0354852	−	0.337619i
$353$	−1.95169e7	+	2.16757e7i	−0.0236156	+	0.0262278i	−0.754837	−	0.655913i	$-0.772284\pi$
$353$	−1.95169e7	+	2.16757e7i	−0.0236156	+	0.0262278i	0.731221	+	0.682140i	$0.238951\pi$
$354$	1.11805e7	+	1.24172e7i	0.0133953	+	0.0148770i
$355$	−1.59726e8	+	1.51969e9i	−0.189486	+	1.80284i
$356$	−6.06071e7	+	1.86529e8i	−0.0711948	+	0.219115i
$357$	6.21960e7	−	1.91420e8i	0.0723475	−	0.222663i
$358$	−7.04940e7	+	6.70705e8i	−0.0812010	+	0.772576i
$359$	−8.58631e8	−	9.53606e8i	−0.979435	−	1.08777i	−0.996128	−	0.0879126i	$-0.971980\pi$
$359$	−8.58631e8	−	9.53606e8i	−0.979435	−	1.08777i	0.0166927	−	0.999861i	$-0.494686\pi$
$360$	−7.17361e8	+	7.96711e8i	−0.810362	+	0.899999i
$361$	9.17336e7	+	8.72787e8i	0.102625	+	0.976412i
$362$	−9.80691e8	−	2.08452e8i	−1.08656	−	0.230955i
$363$	4.63663e7	−	2.06436e7i	0.0508779	−	0.0226523i
$364$	4.37194e7	+	3.17640e7i	0.0475137	+	0.0345207i
$365$	−9.88692e6	−	4.40194e6i	−0.0106423	−	0.00473826i
$366$	2.03456e8	+	3.52397e8i	0.216914	+	0.375706i
$367$	−5.43659e8	+	9.41645e8i	−0.574110	+	0.994388i	0.422027	+	0.906583i	$0.361319\pi$
$367$	−5.43659e8	+	9.41645e8i	−0.574110	+	0.994388i	−0.996138	+	0.0878052i	$0.972015\pi$
$368$	−1.91026e8	+	1.38789e8i	−0.199814	+	0.145173i
$369$	3.15912e7	−	6.71491e6i	0.0327321	−	0.00695741i
$370$	−4.97243e7	−	1.53036e8i	−0.0510344	−	0.157068i
$371$	−9.22868e8			−0.938277
$372$	−5.31460e7	−	2.75088e7i	−0.0535267	−	0.0277059i
$373$	2.06145e8			0.205679			0.102840	−	0.994698i	$-0.467207\pi$
$373$	2.06145e8			0.205679			0.102840	+	0.994698i	$0.467207\pi$
$374$	3.07878e8	+	9.47552e8i	0.304318	+	0.936596i
$375$	−1.66768e8	+	3.54476e7i	−0.163306	+	0.0347118i
$376$	1.17808e9	−	8.55927e8i	1.14293	−	0.830385i
$377$	−4.33241e8	+	7.50396e8i	−0.416423	+	0.721267i
$378$	−1.74442e8	−	3.02143e8i	−0.166123	−	0.287734i
$379$	−2.51159e8	−	1.11823e8i	−0.236980	−	0.105510i	0.284811	−	0.958584i	$-0.408069\pi$
$379$	−2.51159e8	−	1.11823e8i	−0.236980	−	0.105510i	−0.521791	+	0.853074i	$0.674736\pi$
$380$	−2.78577e7	−	2.02398e7i	−0.0260437	−	0.0189218i
$381$	−9.39725e7	+	4.18393e7i	−0.0870489	+	0.0387567i
$382$	−9.77685e8	−	2.07813e8i	−0.897382	−	0.190744i
$383$	−2.01368e8	−	1.91588e9i	−0.183144	−	1.74250i	−0.571150	−	0.820846i	$-0.693503\pi$
$383$	−2.01368e8	−	1.91588e9i	−0.183144	−	1.74250i	0.388006	−	0.921657i	$-0.373164\pi$
$384$	1.47766e8	−	1.64111e8i	0.133173	−	0.147904i
$385$	5.23439e8	+	5.81338e8i	0.467470	+	0.519177i
$386$	−1.36958e8	+	1.30307e9i	−0.121208	+	1.15322i
$387$	4.09171e8	−	1.25930e9i	0.358853	−	1.10444i
$388$	2.31465e6	−	7.12376e6i	0.00201175	−	0.00619153i
$389$	8.80265e7	−	8.37516e8i	0.0758211	−	0.721389i	−0.888898	−	0.458106i	$-0.848528\pi$
$389$	8.80265e7	−	8.37516e8i	0.0758211	−	0.721389i	0.964719	−	0.263283i	$-0.0848053\pi$
$390$	−1.42863e8	−	1.58665e8i	−0.121953	−	0.135443i
$391$	−3.03864e8	+	3.37475e8i	−0.257075	+	0.285511i
$392$	8.35767e7	+	7.95179e8i	0.0700784	+	0.666751i
$393$	−4.41464e8	−	9.38360e7i	−0.366877	−	0.0779822i
$394$	1.32275e9	−	5.88926e8i	1.08953	−	0.485092i
$395$	8.99841e7	+	6.53773e7i	0.0734642	+	0.0533749i
$396$	−1.74791e8	−	7.78222e7i	−0.141445	−	0.0629753i
$397$	−8.56575e8	−	1.48363e9i	−0.687066	−	1.19003i	−0.972783	−	0.231719i	$-0.925565\pi$
$397$	−8.56575e8	−	1.48363e9i	−0.687066	−	1.19003i	0.285716	−	0.958314i	$-0.407768\pi$
$398$	1.05497e9	−	1.82727e9i	0.838786	−	1.45282i
$399$	2.69223e7	−	1.95602e7i	0.0212181	−	0.0154159i
$400$	5.64673e8	−	1.20025e8i	0.441151	−	0.0937696i
$401$	5.62980e8	+	1.73267e9i	0.436001	+	1.34187i	0.892057	+	0.451923i	$0.149262\pi$
$401$	5.62980e8	+	1.73267e9i	0.436001	+	1.34187i	−0.456056	+	0.889951i	$0.650738\pi$
$402$	−2.64668e8			−0.203193
$403$	−3.65957e8	+	5.55711e8i	−0.278524	+	0.422942i
$404$	3.73075e8			0.281489
$405$	3.67503e8	+	1.13106e9i	0.274896	+	0.846042i
$406$	1.19416e9	−	2.53826e8i	0.885565	−	0.188233i
$407$	1.45743e8	−	1.05888e8i	0.107154	−	0.0778516i
$408$	2.81228e8	−	4.87100e8i	0.204997	−	0.355065i
$409$	8.76981e7	+	1.51898e8i	0.0633810	+	0.109779i	0.895975	−	0.444105i	$-0.146478\pi$
$409$	8.76981e7	+	1.51898e8i	0.0633810	+	0.109779i	−0.832594	+	0.553884i	$0.813145\pi$
$410$	−5.37383e7	−	2.39258e7i	−0.0385070	−	0.0171444i
$411$	−4.21446e7	−	3.06198e7i	−0.0299430	−	0.0217549i
$412$	6.56596e7	−	2.92335e7i	0.0462549	−	0.0205940i
$413$	5.99198e7	+	1.27364e7i	0.0418548	+	0.00889652i
$414$	3.89526e7	+	3.70609e8i	0.0269796	+	0.256693i
$415$	1.27227e8	−	1.41300e8i	0.0873800	−	0.0970454i
$416$	1.85991e8	+	2.06564e8i	0.126667	+	0.140678i
$417$	−4.92047e6	+	4.68152e7i	−0.00332300	+	0.0316163i
$418$	−5.09041e7	+	1.56667e8i	−0.0340907	+	0.104920i
$419$	6.48725e8	−	1.99657e9i	0.430836	−	1.32598i	−0.466458	−	0.884543i	$-0.654470\pi$
$419$	6.48725e8	−	1.99657e9i	0.430836	−	1.32598i	0.897294	−	0.441433i	$-0.145530\pi$
$420$	7.35869e6	−	7.00133e7i	0.00484650	−	0.0461113i
$421$	−1.49512e9	−	1.66050e9i	−0.976538	−	1.08456i	−0.996402	−	0.0847526i	$-0.972990\pi$
$421$	−1.49512e9	−	1.66050e9i	−0.976538	−	1.08456i	0.0198640	−	0.999803i	$-0.493677\pi$
$422$	−1.67508e9	+	1.86036e9i	−1.08503	+	1.20505i
$423$	−1.92969e8	−	1.83598e9i	−0.123964	−	1.17944i
$424$	−2.52262e9	−	5.36200e8i	−1.60721	−	0.341622i
$425$	1.01427e9	−	4.51584e8i	0.640906	−	0.285350i
$426$	−5.32222e8	−	3.86682e8i	−0.333549	−	0.242337i
$427$	1.36284e9	+	6.06777e8i	0.847127	+	0.377165i
$428$	2.74032e8	+	4.74637e8i	0.168946	+	0.292623i
$429$	1.19515e8	−	2.07006e8i	0.0730839	−	0.126585i
$430$	−1.95107e9	+	1.41754e9i	−1.18340	+	0.859794i
$431$	1.95350e9	−	4.15230e8i	1.17529	−	0.249815i	0.421434	−	0.906859i	$-0.361527\pi$
$431$	1.95350e9	−	4.15230e8i	1.17529	−	0.249815i	0.753852	+	0.657045i	$0.228194\pi$
$432$	−2.42014e8	−	7.44841e8i	−0.144426	−	0.444499i
$433$	3.02039e9			1.78795			0.893975	−	0.448116i	$-0.147905\pi$
$433$	3.02039e9			1.78795			0.893975	+	0.448116i	$0.147905\pi$
$434$	9.26877e8	−	1.40732e8i	0.544262	−	0.0826377i
$435$	1.12878e9			0.657502
$436$	9.75259e7	+	3.00154e8i	0.0563530	+	0.173437i
$437$	−7.34423e7	+	1.56106e7i	−0.0420980	+	0.00894820i
$438$	3.76949e6	−	2.73870e6i	0.00214350	−	0.00155734i
$439$	−7.11399e7	+	1.23218e8i	−0.0401317	+	0.0695102i	−0.885394	−	0.464842i	$-0.846111\pi$
$439$	−7.11399e7	+	1.23218e8i	−0.0401317	+	0.0695102i	0.845262	+	0.534352i	$0.179444\pi$
$440$	1.09303e9	+	1.89319e9i	0.611714	+	1.05952i
$441$	9.26009e8	+	4.12286e8i	0.514138	+	0.228909i
$442$	−8.06534e8	−	5.85981e8i	−0.444268	−	0.322779i
$443$	−2.77207e9	+	1.23421e9i	−1.51493	+	0.674488i	−0.984842	−	0.173456i	$-0.944506\pi$
$443$	−2.77207e9	+	1.23421e9i	−1.51493	+	0.674488i	−0.530084	+	0.847945i	$0.677840\pi$
$444$	−1.58579e7	−	3.37070e6i	−0.00859814	−	0.00182759i
$445$	−2.96949e8	−	2.82528e9i	−0.159743	−	1.51985i
$446$	−4.52589e8	+	5.02651e8i	−0.241564	+	0.268284i
$447$	5.00634e8	+	5.56010e8i	0.265121	+	0.294447i
$448$	1.35145e8	−	1.28582e9i	0.0710111	−	0.675625i
$449$	−2.01934e8	+	6.21490e8i	−0.105280	+	0.324020i	−0.989796	−	0.142490i	$-0.954489\pi$
$449$	−2.01934e8	+	6.21490e8i	−0.105280	+	0.324020i	0.884516	+	0.466510i	$0.154489\pi$
$450$	2.81541e8	−	8.66494e8i	0.145646	−	0.448251i
$451$	6.88385e6	−	6.54955e7i	0.00353357	−	0.0336197i
$452$	9.96923e7	+	1.10719e8i	0.0507782	+	0.0563949i
$453$	−7.93836e7	+	8.81644e7i	−0.0401224	+	0.0445605i
$454$	1.30969e8	+	1.24609e9i	0.0656860	+	0.624961i
$455$	−7.65645e8	−	1.62743e8i	−0.381055	−	0.0809958i
$456$	8.49556e7	−	3.78247e7i	0.0419580	−	0.0186809i
$457$	−2.64667e9	−	1.92292e9i	−1.29716	−	0.942441i	−0.297235	−	0.954804i	$-0.596064\pi$
$457$	−2.64667e9	−	1.92292e9i	−1.29716	−	0.942441i	−0.999924	+	0.0123637i	$0.996064\pi$
$458$	5.93080e8	+	2.64056e8i	0.288459	+	0.128430i
$459$	−7.53112e8	−	1.30443e9i	−0.363509	−	0.629616i
$460$	−7.94188e7	+	1.37557e8i	−0.0380427	+	0.0658919i
$461$	−7.93356e8	+	5.76407e8i	−0.377151	+	0.274016i	−0.760170	−	0.649724i	$-0.774884\pi$
$461$	−7.93356e8	+	5.76407e8i	−0.377151	+	0.274016i	0.383019	+	0.923740i	$0.374884\pi$
$462$	−3.29423e8	+	7.00210e7i	−0.155420	+	0.0330355i
$463$	6.34159e8	+	1.95174e9i	0.296937	+	0.913879i	0.982564	+	0.185926i	$0.0595283\pi$
$463$	6.34159e8	+	1.95174e9i	0.296937	+	0.913879i	−0.685627	+	0.727953i	$0.740472\pi$
$464$	2.74052e9			1.27356
$465$	8.65314e8	+	5.09010e7i	0.399106	+	0.0234769i
$466$	−2.03617e9			−0.932103
$467$	−1.13033e9	−	3.47880e9i	−0.513566	−	1.58059i	−0.785876	−	0.618384i	$-0.787788\pi$
$467$	−1.13033e9	−	3.47880e9i	−0.513566	−	1.58059i	0.272310	−	0.962209i	$-0.412212\pi$
$468$	1.87268e8	−	3.98050e7i	0.0844505	−	0.0179505i
$469$	−7.85005e8	+	5.70340e8i	−0.351372	+	0.255287i
$470$	−1.68118e9	+	2.91189e9i	−0.746917	+	1.29370i
$471$	4.15818e8	+	7.20219e8i	0.183371	+	0.317608i
$472$	1.56388e8	+	6.96285e7i	0.0684553	+	0.0304783i
$473$	−2.18432e9	−	1.58700e9i	−0.949078	−	0.689546i
$474$	−4.37454e7	+	1.94767e7i	−0.0188672	+	0.00840024i
$475$	1.79558e8	+	3.81661e7i	0.0768734	+	0.0163399i
$476$	−3.43603e7	−	3.26916e8i	−0.0146027	−	0.138935i
$477$	−2.18773e9	+	2.42972e9i	−0.922951	+	1.02504i
$478$	1.91056e9	+	2.12190e9i	0.800136	+	0.888641i
$479$	−4.34453e8	+	4.13355e9i	−0.180621	+	1.71850i	0.410455	+	0.911881i	$0.365370\pi$
$479$	−4.34453e8	+	4.13355e9i	−0.180621	+	1.71850i	−0.591076	+	0.806616i	$0.701297\pi$
$480$	1.11896e8	−	3.44379e8i	0.0461815	−	0.142132i
$481$	−5.57032e7	+	1.71437e8i	−0.0228230	+	0.0702419i
$482$	−4.09442e7	+	3.89558e8i	−0.0166543	+	0.158456i
$483$	−1.02714e8	−	1.14076e8i	−0.0414779	−	0.0460659i
$484$	5.54657e7	−	6.16010e7i	0.0222365	−	0.0246961i
$485$	1.13408e7	+	1.07901e8i	0.00451386	+	0.0429465i
$486$	−1.84566e9	−	3.92307e8i	−0.729331	−	0.155024i
$487$	6.76461e7	−	3.01180e7i	0.0265394	−	0.0118161i	−0.393424	−	0.919357i	$-0.628710\pi$
$487$	6.76461e7	−	3.01180e7i	0.0265394	−	0.0118161i	0.419963	+	0.907541i	$0.362043\pi$
$488$	3.37273e9	+	2.45043e9i	1.31375	+	0.954493i
$489$	−1.48464e7	−	6.61002e6i	−0.00574168	−	0.00255636i
$490$	−9.23097e8	−	1.59885e9i	−0.354455	−	0.613934i
$491$	−9.24343e8	+	1.60101e9i	−0.352410	+	0.610392i	−0.986671	−	0.162727i	$-0.947971\pi$
$491$	−9.24343e8	+	1.60101e9i	−0.352410	+	0.610392i	0.634261	+	0.773119i	$0.281304\pi$
$492$	−4.79474e6	+	3.48359e6i	−0.00181505	+	0.00131871i
$493$	5.15549e9	−	1.09583e9i	1.93778	−	0.411889i
$494$	−5.09356e7	−	1.56764e8i	−0.0190098	−	0.0585061i
$495$	2.77139e9			1.02702
$496$	2.10086e9	+	1.23580e8i	0.773057	+	0.0454741i
$497$	−2.41185e9			−0.881257
$498$	2.52957e7	+	7.78521e7i	0.00917791	+	0.0282467i
$499$	4.59152e9	−	9.75957e8i	1.65426	−	0.351624i	0.716148	−	0.697949i	$-0.245904\pi$
$499$	4.59152e9	−	9.75957e8i	1.65426	−	0.351624i	0.938115	+	0.346324i	$0.112570\pi$
$500$	−2.25272e8	+	1.63670e8i	−0.0805958	+	0.0585562i
$501$	−7.24424e8	+	1.25474e9i	−0.257372	+	0.445781i
$502$	−3.29101e8	−	5.70020e8i	−0.116109	−	0.201107i
$503$	1.87661e9	+	8.35519e8i	0.657484	+	0.292731i	0.708231	−	0.705981i	$-0.249493\pi$
$503$	1.87661e9	+	8.35519e8i	0.657484	+	0.292731i	−0.0507467	+	0.998712i	$0.516160\pi$
$504$	−1.36897e9	−	9.94614e8i	−0.476307	−	0.346057i
$505$	−4.93666e9	+	2.19794e9i	−1.70574	+	0.759445i
$506$	7.43261e8	+	1.57985e8i	0.255044	+	0.0542112i
$507$	−7.24852e7	−	6.89650e8i	−0.0247014	−	0.235018i
$508$	−1.12415e8	+	1.24849e8i	−0.0380452	+	0.0422535i
$509$	−5.04752e8	−	5.60584e8i	−0.169655	−	0.188421i	0.652322	−	0.757942i	$-0.273795\pi$
$509$	−5.04752e8	−	5.60584e8i	−0.169655	−	0.188421i	−0.821976	+	0.569522i	$0.807128\pi$
$510$	−1.35753e8	+	1.29160e9i	−0.0453162	+	0.431155i
$511$	5.27864e6	−	1.62460e7i	0.00175004	−	0.00538608i
$512$	1.04996e9	−	3.23145e9i	0.345723	−	1.06403i
$513$	2.60315e7	−	2.47673e8i	0.00851310	−	0.0809967i
$514$	9.32554e8	+	1.03571e9i	0.302903	+	0.336408i
$515$	−6.96604e8	+	7.73657e8i	−0.224730	+	0.249588i
$516$	2.53983e7	+	2.41648e8i	0.00813823	+	0.0774301i
$517$	−3.68207e9	−	7.82649e8i	−1.17186	−	0.249087i
$518$	2.32020e8	−	1.03302e8i	0.0733451	−	0.0326553i
$519$	8.02013e8	+	5.82697e8i	0.251823	+	0.182960i
$520$	−1.99830e9	−	8.89702e8i	−0.623232	−	0.277481i
$521$	2.59477e9	+	4.49428e9i	0.803836	+	1.39228i	0.917074	+	0.398716i	$0.130544\pi$
$521$	2.59477e9	+	4.49428e9i	0.803836	+	1.39228i	−0.113239	+	0.993568i	$0.536123\pi$
$522$	2.16256e9	−	3.74567e9i	0.665461	−	1.15261i
$523$	−6.39798e8	+	4.64840e8i	−0.195563	+	0.142085i	−0.681258	−	0.732044i	$-0.738567\pi$
$523$	−6.39798e8	+	4.64840e8i	−0.195563	+	0.142085i	0.485695	+	0.874129i	$0.338567\pi$
$524$	−7.21002e8	+	1.53254e8i	−0.218916	+	0.0465320i
$525$	1.15974e8	+	3.56931e8i	0.0349786	+	0.107653i
$526$	−2.72064e9			−0.815118
$527$	4.00157e9	−	6.07576e8i	1.19095	−	0.180827i
$528$	−7.56006e8			−0.223515
$529$	−9.45123e8	−	2.90879e9i	−0.277583	−	0.854313i
$530$	5.82477e9	−	1.23809e9i	1.69947	−	0.361233i
$531$	1.75576e8	−	1.27564e8i	0.0508903	−	0.0369740i
$532$	2.71748e7	−	4.70681e7i	0.00782484	−	0.0135530i
$533$	3.29485e7	+	5.70684e7i	0.00942519	+	0.0163249i
$534$	1.11731e9	+	4.97457e8i	0.317525	+	0.141371i
$535$	−6.42237e9	−	4.66612e9i	−1.81325	−	1.31740i
$536$	−2.47715e9	+	1.10290e9i	−0.694826	+	0.309357i
$537$	−9.62683e8	−	2.04624e8i	−0.268271	−	0.0570227i
$538$	−6.25851e8	−	5.95457e9i	−0.173274	−	1.64859i
$539$	1.38303e9	−	1.53601e9i	0.380426	−	0.422506i
$540$	−3.52522e8	−	3.91516e8i	−0.0963404	−	0.106997i
$541$	3.89408e8	−	3.70497e9i	0.105734	−	1.00599i	−0.805077	−	0.593170i	$-0.797876\pi$
$541$	3.89408e8	−	3.70497e9i	0.105734	−	1.00599i	0.910812	−	0.412822i	$-0.135457\pi$
$542$	−1.28681e9	+	3.96039e9i	−0.347149	+	1.06842i
$543$	4.52138e8	−	1.39154e9i	0.121191	−	0.372989i
$544$	1.76734e8	−	1.68151e9i	0.0470679	−	0.447821i
$545$	−3.05883e9	−	3.39718e9i	−0.809408	−	0.898939i
$546$	2.25491e8	−	2.50433e8i	0.0592863	−	0.0658441i
$547$	5.94110e8	+	5.65258e9i	0.155207	+	1.47670i	0.743873	+	0.668321i	$0.232987\pi$
$547$	5.94110e8	+	5.65258e9i	0.155207	+	1.47670i	−0.588666	+	0.808376i	$0.700347\pi$
$548$	−8.32204e7	−	1.76891e7i	−0.0216022	−	0.00459169i
$549$	4.82823e9	−	2.14967e9i	1.24533	−	0.554457i
$550$	−1.50298e9	−	1.09198e9i	−0.385197	−	0.279862i
$551$	7.96104e8	+	3.54448e8i	0.202740	+	0.0902656i
$552$	−2.14486e8	−	3.71500e8i	−0.0542765	−	0.0940096i
$553$	−8.77783e7	+	1.52036e8i	−0.0220724	+	0.0382305i
$554$	2.25122e9	−	1.63561e9i	0.562514	−	0.408690i
$555$	2.29695e8	−	4.88232e7i	0.0570330	−	0.0121227i
$556$	2.37573e7	+	7.31173e7i	0.00586185	+	0.0180409i
$557$	2.52388e9			0.618836			0.309418	−	0.950926i	$-0.399866\pi$
$557$	2.52388e9			0.618836			0.309418	+	0.950926i	$0.399866\pi$
$558$	1.82671e9	−	2.77388e9i	0.445092	−	0.675878i
$559$	2.70164e9			0.654162
$560$	7.65031e8	+	2.35452e9i	0.184086	+	0.566558i
$561$	−1.42220e9	+	3.02299e8i	−0.340089	+	0.0722881i
$562$	−1.25459e9	+	9.11510e8i	−0.298142	+	0.216613i
$563$	−2.70477e9	+	4.68480e9i	−0.638779	+	1.10640i	0.346921	+	0.937894i	$0.387227\pi$
$563$	−2.70477e9	+	4.68480e9i	−0.638779	+	1.10640i	−0.985701	+	0.168504i	$0.946106\pi$
$564$	1.69383e8	+	2.93380e8i	0.0397551	+	0.0688578i
$565$	−1.97146e9	−	8.77750e8i	−0.459852	−	0.204739i
$566$	−8.48758e7	−	6.16659e7i	−0.0196755	−	0.0142951i
$567$	−1.71481e9	+	7.63485e8i	−0.395072	+	0.175897i
$568$	−6.59268e9	−	1.40132e9i	−1.50953	−	0.320861i
$569$	−4.19112e8	−	3.98758e9i	−0.0953755	−	0.907437i	−0.932681	−	0.360702i	$-0.882537\pi$
$569$	−4.19112e8	−	3.98758e9i	−0.0953755	−	0.907437i	0.837306	−	0.546735i	$-0.184130\pi$
$570$	−1.43681e8	+	1.59574e8i	−0.0324966	+	0.0360911i
$571$	3.69313e9	+	4.10164e9i	0.830173	+	0.922001i	0.997961	−	0.0638225i	$-0.0203291\pi$
$571$	3.69313e9	+	4.10164e9i	0.830173	+	0.922001i	−0.167788	+	0.985823i	$0.553662\pi$
$572$	4.08064e7	−	3.88247e8i	0.00911680	−	0.0867406i
$573$	4.50753e8	−	1.38727e9i	0.100091	−	0.308050i
$574$	2.86909e7	−	8.83016e7i	0.00633218	−	0.0194884i
$575$	8.85116e7	−	8.42132e8i	0.0194161	−	0.184732i
$576$	−3.06491e9	−	3.40392e9i	−0.668250	−	0.742166i
$577$	−8.49779e8	+	9.43775e8i	−0.184158	+	0.204528i	−0.828154	−	0.560501i	$-0.810609\pi$
$577$	−8.49779e8	+	9.43775e8i	−0.184158	+	0.204528i	0.643996	+	0.765029i	$0.277275\pi$
$578$	1.97039e8	+	1.87470e9i	0.0424429	+	0.403817i
$579$	−1.87033e9	−	3.97551e8i	−0.400445	−	0.0851172i
$580$	1.68415e9	−	7.49833e8i	0.358413	−	0.159576i
$581$	2.42793e8	+	1.76399e8i	0.0513594	+	0.0373148i
$582$	−4.26712e7	−	1.89984e7i	−0.00897231	−	0.00399473i
$583$	3.33340e9	+	5.77362e9i	0.696703	+	1.20672i
$584$	2.38681e7	−	4.13407e7i	0.00495875	−	0.00858881i
$585$	−2.24348e9	+	1.62999e9i	−0.463316	+	0.336619i
$586$	7.61619e9	−	1.61887e9i	1.56349	−	0.332331i
$587$	1.18228e9	+	3.63869e9i	0.241261	+	0.742526i	0.996229	+	0.0867639i	$0.0276526\pi$
$587$	1.18228e9	+	3.63869e9i	0.241261	+	0.742526i	−0.754968	+	0.655762i	$0.772347\pi$
$588$	−1.86008e8			−0.0377321
$589$	5.94303e8	+	3.07616e8i	0.119841	+	0.0620306i
$590$	−3.95276e8			−0.0792353
$591$	6.52967e8	+	2.00962e9i	0.130117	+	0.400460i
$592$	5.57668e8	−	1.18536e8i	0.110471	−	0.0234814i
$593$	−3.16707e9	+	2.30101e9i	−0.623686	+	0.453134i	−0.854207	−	0.519933i	$-0.825957\pi$
$593$	−3.16707e9	+	2.30101e9i	−0.623686	+	0.453134i	0.230521	+	0.973067i	$0.425957\pi$
$594$	−1.26017e9	+	2.18268e9i	−0.246704	+	0.427304i
$595$	2.38067e9	+	4.12344e9i	0.463329	+	0.802509i
$596$	1.11630e9	+	4.97009e8i	0.215983	+	0.0961618i
$597$	2.49110e9	+	1.80989e9i	0.479160	+	0.348130i
$598$	−6.94601e8	+	3.09256e8i	−0.132826	+	0.0591377i
$599$	−4.62595e9	−	9.83277e8i	−0.879442	−	0.186931i	−0.254002	−	0.967204i	$-0.581747\pi$
$599$	−4.62595e9	−	9.83277e8i	−0.879442	−	0.186931i	−0.625440	+	0.780272i	$0.715080\pi$
$600$	1.09628e8	+	1.04304e9i	0.0207201	+	0.197138i
$601$	2.31076e9	−	2.56635e9i	0.434204	−	0.482232i	−0.485840	−	0.874048i	$-0.661486\pi$
$601$	2.31076e9	−	2.56635e9i	0.434204	−	0.482232i	0.920044	+	0.391816i	$0.128153\pi$
$602$	−2.54703e9	−	2.82877e9i	−0.475825	−	0.528457i
$603$	−3.59328e8	+	3.41878e9i	−0.0667392	+	0.634981i
$604$	−5.98748e7	+	1.84276e8i	−0.0110564	+	0.0340282i
$605$	−3.71025e8	+	1.14190e9i	−0.0681176	+	0.209644i
$606$	2.43182e8	−	2.31373e9i	0.0443893	−	0.422336i
$607$	5.05989e9	+	5.61958e9i	0.918291	+	1.01987i	0.999731	+	0.0231877i	$0.00738154\pi$
$607$	5.05989e9	+	5.61958e9i	0.918291	+	1.01987i	−0.0814397	+	0.996678i	$0.525952\pi$
$608$	1.87056e8	−	2.07747e8i	0.0337527	−	0.0374862i
$609$	1.86231e8	+	1.77187e9i	0.0334112	+	0.317887i
$610$	−9.41574e9	−	2.00138e9i	−1.67958	−	0.357005i
$611$	3.44102e9	−	1.53204e9i	0.610299	−	0.271723i
$612$	−9.42153e8	−	6.84514e8i	−0.166147	−	0.120713i
$613$	5.41986e9	+	2.41308e9i	0.950334	+	0.423116i	0.822554	−	0.568687i	$-0.192548\pi$
$613$	5.41986e9	+	2.41308e9i	0.950334	+	0.423116i	0.127779	+	0.991803i	$0.459215\pi$
$614$	8.38726e8	+	1.45272e9i	0.146228	+	0.253275i
$615$	4.29225e7	−	7.43439e7i	0.00744084	−	0.0128879i
$616$	−2.79145e9	+	2.02810e9i	−0.481168	+	0.349589i
$617$	−8.01699e9	+	1.70406e9i	−1.37408	+	0.292071i	−0.835032	−	0.550202i	$-0.814551\pi$
$617$	−8.01699e9	+	1.70406e9i	−1.37408	+	0.292071i	−0.539052	+	0.842272i	$0.681217\pi$
$618$	−1.38501e8	−	4.26261e8i	−0.0236044	−	0.0726468i
$619$	4.31673e9			0.731540			0.365770	−	0.930705i	$-0.380806\pi$
$619$	4.31673e9			0.731540			0.365770	+	0.930705i	$0.380806\pi$
$620$	1.32487e9	−	4.98871e8i	0.223256	−	0.0840654i
$621$	−1.14876e9			−0.192491
$622$	2.75621e9	+	8.48274e9i	0.459247	+	1.41342i
$623$	4.38592e9	−	9.32257e8i	0.726696	−	0.154464i
$624$	6.12000e8	−	4.44644e8i	0.100834	−	0.0732599i
$625$	3.79398e9	−	6.57136e9i	0.621605	−	1.07665i
$626$	−2.19571e9	−	3.80309e9i	−0.357739	−	0.619621i
$627$	−2.19615e8	−	9.77789e7i	−0.0355816	−	0.0158420i
$628$	1.09884e9	+	7.98351e8i	0.177041	+	0.128628i
$629$	1.00169e9	−	4.45981e8i	0.160493	−	0.0714561i
$630$	3.82179e9	+	8.12347e8i	0.608941	+	0.129434i
$631$	−7.28731e8	−	6.93341e9i	−0.115469	−	1.09861i	−0.886792	−	0.462168i	$-0.847072\pi$
$631$	−7.28731e8	−	6.93341e9i	−0.115469	−	1.09861i	0.771323	−	0.636443i	$-0.219595\pi$
$632$	−3.28273e8	+	3.64584e8i	−0.0517280	+	0.0574498i
$633$	−2.44454e9	−	2.71493e9i	−0.383075	−	0.425448i
$634$	−9.75921e8	+	9.28527e9i	−0.152091	+	1.44705i
$635$	7.51972e8	−	2.31433e9i	0.116545	−	0.358689i
$636$	1.85400e8	−	5.70604e8i	0.0285766	−	0.0879498i
$637$	−2.16184e8	+	2.05685e9i	−0.0331387	+	0.315294i
$638$	−5.90127e9	−	6.55403e9i	−0.899649	−	0.999162i
$639$	−5.71746e9	+	6.34988e9i	−0.866862	+	0.962747i
$640$	5.46069e8	+	5.19550e9i	0.0823413	+	0.783425i
$641$	−9.85083e9	−	2.09386e9i	−1.47730	−	0.314010i	−0.602355	−	0.798228i	$-0.705771\pi$
$641$	−9.85083e9	−	2.09386e9i	−1.47730	−	0.314010i	−0.874948	+	0.484218i	$0.839104\pi$
$642$	3.12221e9	−	1.39010e9i	0.465682	−	0.207335i
$643$	−6.37055e9	−	4.62848e9i	−0.945015	−	0.686593i	0.00460796	−	0.999989i	$-0.498533\pi$
$643$	−6.37055e9	−	4.62848e9i	−0.945015	−	0.686593i	−0.949622	+	0.313396i	$0.898533\pi$
$644$	−2.29030e8	−	1.01971e8i	−0.0337903	−	0.0150444i
$645$	−1.75973e9	−	3.04794e9i	−0.258219	−	0.447248i
$646$	−5.01319e8	+	8.68311e8i	−0.0731645	+	0.126725i
$647$	−6.98471e9	+	5.07469e9i	−1.01387	+	0.736621i	−0.965018	−	0.262184i	$-0.915557\pi$
$647$	−6.98471e9	+	5.07469e9i	−1.01387	+	0.736621i	−0.0488547	+	0.998806i	$0.515557\pi$
$648$	−5.13097e9	+	1.09062e9i	−0.740775	+	0.157457i
$649$	−1.36750e8	−	4.20872e8i	−0.0196368	−	0.0604357i
$650$	1.85893e9			0.265501
$651$	6.28630e7	+	1.36670e9i	0.00893021	+	0.194151i
$652$	−2.65419e7			−0.00375029
$653$	2.11812e8	+	6.51891e8i	0.0297684	+	0.0916176i	0.964837	−	0.262850i	$-0.0846623\pi$
$653$	2.11812e8	+	6.51891e8i	0.0297684	+	0.0916176i	−0.935068	+	0.354467i	$0.884662\pi$
$654$	1.92506e9	−	4.09183e8i	0.269105	−	0.0572000i
$655$	8.63768e9	−	6.27564e9i	1.20103	−	0.872596i
$656$	1.04210e8	−	1.80497e8i	0.0144127	−	0.0249635i
$657$	−3.02588e7	−	5.24098e7i	−0.00416268	−	0.00720997i
$658$	−4.84824e9	−	2.15857e9i	−0.663427	−	0.295377i
$659$	−1.33501e9	−	9.69942e8i	−0.181713	−	0.132022i	0.493210	−	0.869910i	$-0.335823\pi$
$659$	−1.33501e9	−	9.69942e8i	−0.181713	−	0.132022i	−0.674923	+	0.737888i	$0.735823\pi$
$660$	−4.64594e8	+	2.06851e8i	−0.0629028	+	0.0280061i
$661$	8.31994e9	+	1.76846e9i	1.12051	+	0.238171i	0.730682	−	0.682717i	$-0.239202\pi$
$661$	8.31994e9	+	1.76846e9i	1.12051	+	0.238171i	0.389825	+	0.920889i	$0.372535\pi$
$662$	−2.69554e8	−	2.56463e9i	−0.0361112	−	0.343575i
$663$	9.73502e8	−	1.08118e9i	0.129730	−	0.144080i
$664$	5.61173e8	+	6.23246e8i	0.0743890	+	0.0826174i
$665$	−8.22882e7	+	7.82920e8i	−0.0108508	+	0.103238i
$666$	2.78048e8	−	8.55743e8i	0.0364720	−	0.112249i
$667$	1.24219e9	−	3.82307e9i	0.162087	−	0.498852i
$668$	−2.47343e8	+	2.35331e9i	−0.0321057	+	0.305465i
$669$	−6.60488e8	−	7.33547e8i	−0.0852852	−	0.0947188i
$670$	4.18948e9	−	4.65289e9i	0.538144	−	0.597669i
$671$	−1.12649e9	−	1.07179e10i	−0.143946	−	1.36955i
$672$	5.59041e8	+	1.18828e8i	0.0710642	+	0.0151052i
$673$	4.72676e9	−	2.10449e9i	0.597738	−	0.266130i	−0.0854855	−	0.996339i	$-0.527244\pi$
$673$	4.72676e9	−	2.10449e9i	0.597738	−	0.266130i	0.683224	+	0.730209i	$0.260577\pi$
$674$	3.18900e9	+	2.31695e9i	0.401185	+	0.291478i
$675$	2.56577e9	+	1.14236e9i	0.321111	+	0.142968i
$676$	−5.66274e8	−	9.80815e8i	−0.0705039	−	0.122116i
$677$	3.32858e9	−	5.76527e9i	0.412286	−	0.714100i	−0.582853	−	0.812577i	$-0.698064\pi$
$677$	3.32858e9	−	5.76527e9i	0.412286	−	0.714100i	0.995139	+	0.0984773i	$0.0313972\pi$
$678$	7.51640e8	−	5.46098e8i	0.0926202	−	0.0672925i
$679$	−1.67503e8	+	3.56039e7i	−0.0205342	+	0.00436469i
$680$	4.11168e9	+	1.26544e10i	0.501462	+	1.54334i
$681$	−1.82850e9			−0.221861
$682$	−4.22832e9	−	5.29037e9i	−0.510414	−	0.638618i
$683$	1.23322e10			1.48105			0.740524	−	0.672030i	$-0.234577\pi$
$683$	1.23322e10			1.48105			0.740524	+	0.672030i	$0.234577\pi$
$684$	−5.95005e7	−	1.83124e8i	−0.00710925	−	0.0218800i
$685$	1.20542e9	−	2.56219e8i	0.143291	−	0.0304575i
$686$	6.12319e9	−	4.44876e9i	0.724174	−	0.526143i
$687$	−4.73712e8	+	8.20493e8i	−0.0557398	+	0.0965442i
$688$	−4.27238e9	−	7.39998e9i	−0.500162	−	0.866306i
$689$	−6.09419e9	−	2.71331e9i	−0.709821	−	0.316033i
$690$	8.01332e8	+	5.82202e8i	0.0928626	+	0.0674686i
$691$	3.44135e9	−	1.53219e9i	0.396785	−	0.176660i	−0.198637	−	0.980073i	$-0.563652\pi$
$691$	3.44135e9	−	1.53219e9i	0.396785	−	0.176660i	0.595422	+	0.803413i	$0.296985\pi$
$692$	1.58369e9	+	3.36624e8i	0.181676	+	0.0386165i
$693$	4.57236e8	+	4.35031e9i	0.0521884	+	0.496540i
$694$	−1.67052e9	+	1.85530e9i	−0.189712	+	0.210696i
$695$	−7.45130e8	−	8.27551e8i	−0.0841948	−	0.0935078i
$696$	−5.20428e8	+	4.95154e9i	−0.0585098	+	0.556683i
$697$	1.23866e8	−	3.81221e8i	0.0138560	−	0.0426444i
$698$	−1.06928e9	+	3.29091e9i	−0.119014	+	0.366288i
$699$	3.10606e8	−	2.95522e9i	0.0343985	−	0.327280i
$700$	4.10139e8	+	4.55505e8i	0.0451947	+	0.0501938i
$701$	1.21571e9	−	1.35018e9i	0.133296	−	0.148040i	−0.672801	−	0.739823i	$-0.734909\pi$
$701$	1.21571e9	−	1.35018e9i	0.133296	−	0.148040i	0.806097	+	0.591783i	$0.201576\pi$
$702$	−2.63610e8	−	2.50808e9i	−0.0287596	−	0.273629i
$703$	1.77330e8	+	3.76926e7i	0.0192503	+	0.00409178i
$704$	−8.53242e9	+	3.79888e9i	−0.921654	+	0.410347i
$705$	−3.96976e9	−	2.88420e9i	−0.426680	−	0.310001i
$706$	2.71377e8	+	1.20825e8i	0.0290240	+	0.0129223i
$707$	−4.26463e9	−	7.38656e9i	−0.453852	−	0.786094i
$708$	−1.99125e7	+	3.44894e7i	−0.00210867	+	0.00365232i
$709$	−9.31229e9	+	6.76577e9i	−0.981284	+	0.712944i	−0.957995	−	0.286784i	$-0.907414\pi$
$709$	−9.31229e9	+	6.76577e9i	−0.981284	+	0.712944i	−0.0232887	+	0.999729i	$0.507414\pi$
$710$	1.52226e10	−	3.23566e9i	1.59619	−	0.339281i
$711$	1.92195e8	+	5.91514e8i	0.0200539	+	0.0617194i
$712$	1.25304e10			1.30102
$713$	1.12465e9	−	2.87472e9i	0.116199	−	0.297017i
$714$	−2.04986e9			−0.210756
$715$	1.74736e9	+	5.37783e9i	0.178777	+	0.550220i
$716$	−1.57226e9	+	3.34195e8i	−0.160077	+	0.0340254i
$717$	−3.37108e9	+	2.44923e9i	−0.341548	+	0.248149i
$718$	−6.53445e9	+	1.13180e10i	−0.658830	+	1.14113i
$719$	−3.13260e9	−	5.42582e9i	−0.314307	−	0.544395i	0.664983	−	0.746858i	$-0.268439\pi$
$719$	−3.13260e9	−	5.42582e9i	−0.314307	−	0.544395i	−0.979290	+	0.202463i	$0.935105\pi$
$720$	8.01251e9	+	3.56740e9i	0.800028	+	0.356195i
$721$	−1.32936e9	−	9.65834e8i	−0.132089	−	0.0959686i
$722$	8.16521e9	−	3.63539e9i	0.807397	−	0.359476i
$723$	−5.59143e8	−	1.18850e8i	−0.0550224	−	0.0116954i
$724$	−2.49784e8	−	2.37654e9i	−0.0244613	−	0.232734i
$725$	−6.57619e9	+	7.30360e9i	−0.640902	+	0.711793i
$726$	−3.45881e8	−	3.84139e8i	−0.0335466	−	0.0372572i
$727$	2.17893e7	−	2.07312e8i	0.00210317	−	0.0200103i	−0.993420	−	0.114528i	$-0.963464\pi$
$727$	2.17893e7	−	2.07312e8i	0.00210317	−	0.0200103i	0.995523	+	0.0945180i	$0.0301310\pi$
$728$	1.06690e9	−	3.28357e9i	0.102486	−	0.315418i
$729$	−1.43497e9	+	4.41638e9i	−0.137182	+	0.422202i
$730$	−1.15215e7	+	1.09620e8i	−0.00109617	+	0.0104294i
$731$	−1.09962e10	−	1.22125e10i	−1.04120	−	1.15636i
$732$	−6.48956e8	+	7.20739e8i	−0.0611542	+	0.0679187i
$733$	7.89468e8	+	7.51129e9i	0.0740408	+	0.704451i	0.967080	+	0.254472i	$0.0819017\pi$
$733$	7.89468e8	+	7.51129e9i	0.0740408	+	0.704451i	−0.893039	+	0.449979i	$0.851432\pi$
$734$	1.08319e10	+	2.30239e9i	1.01104	+	0.214903i
$735$	2.46132e9	−	1.09585e9i	0.228646	−	0.101800i
$736$	−1.04324e9	−	7.57959e8i	−0.0964522	−	0.0700766i
$737$	6.40358e9	+	2.85106e9i	0.589232	+	0.262343i
$738$	−1.64465e8	−	2.84862e8i	−0.0150618	−	0.0260878i
$739$	−6.34470e9	+	1.09893e10i	−0.578303	+	1.00165i	0.417371	+	0.908736i	$0.362951\pi$
$739$	−6.34470e9	+	1.09893e10i	−0.578303	+	1.00165i	−0.995674	+	0.0929137i	$0.970382\pi$
$740$	3.10275e8	−	2.25428e8i	0.0281472	−	0.0204502i
$741$	2.35291e8	−	5.00126e7i	0.0212442	−	0.00451560i
$742$	2.90446e9	+	8.93901e9i	0.261007	+	0.803296i
$743$	−1.62883e10			−1.45685			−0.728426	−	0.685125i	$-0.759748\pi$
$743$	−1.62883e10			−1.45685			−0.728426	+	0.685125i	$0.759748\pi$
$744$	−6.22239e8	+	3.77234e9i	−0.0553927	+	0.335819i
$745$	−1.76994e10			−1.56823
$746$	−6.48780e8	−	1.99674e9i	−0.0572152	−	0.176090i
$747$	1.03998e9	−	2.21055e8i	0.0912857	−	0.0194034i
$748$	−1.92113e9	+	1.39578e9i	−0.167842	+	0.121945i
$749$	6.26493e9	−	1.08512e10i	0.544791	−	0.943606i
$750$	8.68203e8	+	1.50377e9i	0.0751461	+	0.130157i
$751$	−9.54439e9	−	4.24944e9i	−0.822258	−	0.366093i	−0.0479093	−	0.998852i	$-0.515256\pi$
$751$	−9.54439e9	−	4.24944e9i	−0.822258	−	0.366093i	−0.774349	+	0.632759i	$0.781923\pi$
$752$	−9.63801e9	−	7.00243e9i	−0.826466	−	0.600463i
$753$	8.77508e8	−	3.90692e8i	0.0748977	−	0.0333466i
$754$	8.63192e9	+	1.83477e9i	0.733344	+	0.155877i
$755$	−2.93362e8	−	2.79115e9i	−0.0248078	−	0.236031i
$756$	5.56411e8	−	6.17956e8i	0.0468348	−	0.0520154i
$757$	1.06109e10	+	1.17847e10i	0.889034	+	0.987373i	0.999979	−	0.00645384i	$-0.00205433\pi$
$757$	1.06109e10	+	1.17847e10i	0.889034	+	0.987373i	−0.110945	+	0.993827i	$0.535388\pi$
$758$	−2.92682e8	+	2.78468e9i	−0.0244092	+	0.232238i
$759$	−3.42674e8	+	1.05464e9i	−0.0284469	+	0.0875505i
$760$	−6.79819e8	+	2.09227e9i	−0.0561753	+	0.172890i
$761$	−7.18889e8	+	6.83977e9i	−0.0591310	+	0.562594i	0.924345	+	0.381557i	$0.124612\pi$
$761$	−7.18889e8	+	6.83977e9i	−0.0591310	+	0.562594i	−0.983476	+	0.181037i	$0.942055\pi$
$762$	7.01011e8	+	7.78552e8i	0.0573961	+	0.0637448i
$763$	4.82797e9	−	5.36200e9i	0.393485	−	0.437009i
$764$	−2.49019e8	−	2.36926e9i	−0.0202025	−	0.192214i
$765$	1.64997e10	+	3.50711e9i	1.33248	+	0.283227i
$766$	−1.79237e10	+	7.98016e9i	−1.44088	+	0.641521i
$767$	3.58237e8	+	2.60274e8i	0.0286673	+	0.0208280i
$768$	1.99434e9	+	8.87938e8i	0.158868	+	0.0707324i
$769$	6.74171e8	+	1.16770e9i	0.0534599	+	0.0925952i	0.891517	−	0.452987i	$-0.149642\pi$
$769$	6.74171e8	+	1.16770e9i	0.0534599	+	0.0925952i	−0.838057	+	0.545583i	$0.816308\pi$
$770$	3.98353e9	−	6.89968e9i	0.314449	−	0.544642i
$771$	−1.64544e9	+	1.19548e9i	−0.129298	+	0.0939405i
$772$	−3.05464e9	+	6.49283e8i	−0.238946	+	0.0507895i
$773$	−3.61152e9	−	1.11151e10i	−0.281230	−	0.865536i	−0.987503	−	0.157597i	$-0.949625\pi$
$773$	−3.61152e9	−	1.11151e10i	−0.281230	−	0.865536i	0.706274	−	0.707939i	$-0.250375\pi$
$774$	−1.34855e10			−1.04538
$775$	−5.37060e9	+	5.30233e9i	−0.414445	+	0.409177i
$776$	−4.78549e8			−0.0367630
$777$	1.14535e8	+	3.52503e8i	0.00875921	+	0.0269581i
$778$	−8.38932e9	+	1.78320e9i	−0.638701	+	0.135760i
$779$	5.36170e7	−	3.89550e7i	0.00406370	−	0.00295245i
$780$	2.54438e8	−	4.40700e8i	0.0191978	−	0.0332515i
$781$	8.71159e9	+	1.50889e10i	0.654363	+	1.13339i
$782$	4.22514e9	+	1.88115e9i	0.315949	+	0.140670i
$783$	1.07866e10	+	7.83694e9i	0.803007	+	0.583419i
$784$	5.97575e9	−	2.66057e9i	0.442880	−	0.197183i
$785$	−1.92436e10	−	4.09036e9i	−1.41985	−	0.301799i
$786$	4.80472e8	+	4.57139e9i	0.0352931	+	0.335791i
$787$	−8.12978e8	+	9.02904e8i	−0.0594521	+	0.0660283i	−0.772137	−	0.635456i	$-0.780812\pi$
$787$	−8.12978e8	+	9.02904e8i	−0.0594521	+	0.0660283i	0.712685	+	0.701484i	$0.247479\pi$
$788$	2.30920e9	+	2.56462e9i	0.168120	+	0.186716i
$789$	4.15018e8	−	3.94863e9i	0.0300813	−	0.286205i
$790$	3.50053e8	−	1.07735e9i	0.0252603	−	0.0777433i
$791$	1.05256e9	−	3.23946e9i	0.0756190	−	0.232731i
$792$	−1.27776e9	+	1.21570e10i	−0.0913924	+	0.869541i
$793$	7.21560e9	+	8.01374e9i	0.513827	+	0.570662i
$794$	−1.16748e10	+	1.29662e10i	−0.827709	+	0.919264i
$795$	9.08385e8	+	8.64271e9i	0.0641188	+	0.610049i
$796$	4.91903e9	+	1.04557e9i	0.345687	+	0.0734781i
$797$	1.61059e10	−	7.17082e9i	1.12689	−	0.501724i	0.243284	−	0.969955i	$-0.421775\pi$
$797$	1.61059e10	−	7.17082e9i	1.12689	−	0.501724i	0.883606	+	0.468231i	$0.155108\pi$
$798$	−2.74192e8	−	1.99212e8i	−0.0191005	−	0.0138773i
$799$	−2.09311e10	−	9.31913e9i	−1.45171	−	0.646341i
$800$	1.57636e9	+	2.73033e9i	0.108853	+	0.188539i
$801$	7.94271e9	−	1.37572e10i	0.546078	−	0.945835i
$802$	1.50111e10	−	1.09062e10i	1.02755	−	0.746556i
$803$	−1.20704e8	+	2.56564e7i	−0.00822654	+	0.00174861i
$804$	−1.94933e8	−	5.99943e8i	−0.0132279	−	0.0407112i
$805$	3.63136e9			0.245349
$806$	6.53442e9	+	1.79577e9i	0.439577	+	0.120803i
$807$	8.73771e9			0.585248
$808$	−7.36550e9	−	2.26687e10i	−0.491204	−	1.51177i
$809$	8.65718e9	−	1.84014e9i	0.574852	−	0.122189i	0.0886933	−	0.996059i	$-0.471731\pi$
$809$	8.65718e9	−	1.84014e9i	0.574852	−	0.122189i	0.486159	+	0.873870i	$0.338398\pi$
$810$	9.79894e9	−	7.11935e9i	0.647860	−	0.470698i
$811$	8.54811e9	−	1.48058e10i	0.562726	−	0.974671i	−0.434531	−	0.900657i	$-0.643086\pi$
$811$	8.54811e9	−	1.48058e10i	0.562726	−	0.974671i	0.997257	−	0.0740138i	$-0.0235809\pi$
$812$	1.45489e9	+	2.51994e9i	0.0953639	+	0.165175i
$813$	−5.55166e9	−	2.47176e9i	−0.362331	−	0.161320i
$814$	−1.48433e9	−	1.07843e9i	−0.0964595	−	0.0700819i
$815$	3.51211e8	−	1.56369e8i	0.0227257	−	0.0101181i
$816$	−4.50095e9	−	9.56705e8i	−0.289993	−	0.0616400i
$817$	−2.84015e8	−	2.70222e9i	−0.0182206	−	0.173358i
$818$	1.19529e9	−	1.32751e9i	0.0763551	−	0.0848009i
$819$	−2.92877e9	−	3.25273e9i	−0.186291	−	0.206897i
$820$	1.46552e7	−	1.39435e8i	0.000928202	−	0.00883126i
$821$	2.71727e9	−	8.36291e9i	0.171369	−	0.527420i	−0.828080	−	0.560610i	$-0.810567\pi$
$821$	2.71727e9	−	8.36291e9i	0.171369	−	0.527420i	0.999449	+	0.0331902i	$0.0105667\pi$
$822$	−1.63949e8	+	5.04584e8i	−0.0102958	+	0.0316871i
$823$	−1.98720e9	+	1.89070e10i	−0.124263	+	1.18229i	0.737633	+	0.675202i	$0.235943\pi$
$823$	−1.98720e9	+	1.89070e10i	−0.124263	+	1.18229i	−0.861896	+	0.507084i	$0.830723\pi$
$824$	−3.07258e9	−	3.41244e9i	−0.191319	−	0.212481i
$825$	1.81412e9	−	2.01479e9i	0.112481	−	0.124922i
$826$	−6.52145e7	−	6.20474e8i	−0.00402637	−	0.0383084i
$827$	1.53656e10	+	3.26605e9i	0.944667	+	0.200795i	0.654398	−	0.756150i	$-0.272922\pi$
$827$	1.53656e10	+	3.26605e9i	0.944667	+	0.200795i	0.290269	+	0.956945i	$0.406255\pi$
$828$	−8.11399e8	+	3.61258e8i	−0.0496739	+	0.0221163i
$829$	1.45274e10	+	1.05548e10i	0.885618	+	0.643439i	0.934732	−	0.355354i	$-0.115640\pi$
$829$	1.45274e10	+	1.05548e10i	0.885618	+	0.643439i	−0.0491141	+	0.998793i	$0.515640\pi$
$830$	−1.76906e9	−	7.87637e8i	−0.107391	−	0.0478138i
$831$	2.03044e9	+	3.51683e9i	0.122740	+	0.212593i
$832$	4.67284e9	−	8.09359e9i	0.281286	−	0.487202i
$833$	1.01778e10	−	7.39457e9i	0.610091	−	0.443257i
$834$	4.68943e8	−	9.96769e7i	0.0279923	−	0.00594995i
$835$	−1.05914e10	−	3.25970e10i	−0.629581	−	1.93765i
$836$	−3.92621e8			−0.0232408
$837$	7.91554e9	+	6.49414e9i	0.466596	+	0.382810i
$838$	−2.13807e10			−1.25507
$839$	8.91689e8	+	2.74434e9i	0.0521251	+	0.160424i	0.973730	−	0.227704i	$-0.0731218\pi$
$839$	8.91689e8	+	2.74434e9i	0.0521251	+	0.160424i	−0.921605	+	0.388128i	$0.873122\pi$
$840$	−4.39940e9	+	9.35122e8i	−0.256104	+	0.0544366i
$841$	−2.37897e10	+	1.72842e10i	−1.37912	+	1.00199i
$842$	−1.13783e10	+	1.97079e10i	−0.656881	+	1.13775i
$843$	−1.13155e9	−	1.95990e9i	−0.0650545	−	0.112678i
$844$	−5.45077e9	−	2.42684e9i	−0.312075	−	0.138945i
$845$	1.32715e10	+	9.64233e9i	0.756698	+	0.549773i
$846$	−1.71762e10	+	7.64732e9i	−0.975281	+	0.434223i
$847$	−1.85368e9	−	3.94011e8i	−0.104820	−	0.0222801i
$848$	2.20543e9	+	2.09833e10i	0.124196	+	1.18165i
$849$	1.02447e8	−	1.13779e8i	0.00574542	−	0.00638093i
$850$	−7.56623e9	−	8.40315e9i	−0.422584	−	0.469327i
$851$	8.74135e7	−	8.31684e8i	0.00486211	−	0.0462599i
$852$	4.84530e8	−	1.49123e9i	0.0268400	−	0.0826050i
$853$	9.10030e9	−	2.80078e10i	0.502035	−	1.54511i	−0.303664	−	0.952779i	$-0.598210\pi$
$853$	9.10030e9	−	2.80078e10i	0.502035	−	1.54511i	0.805699	−	0.592326i	$-0.201790\pi$
$854$	1.58816e9	−	1.51103e10i	0.0872551	−	0.830177i
$855$	1.86619e9	+	2.07261e9i	0.102111	+	0.113406i
$856$	2.34296e10	−	2.60212e10i	1.27675	−	1.41798i
$857$	−1.44510e9	−	1.37492e10i	−0.0784269	−	0.746182i	−0.961101	−	0.276197i	$-0.910926\pi$
$857$	−1.44510e9	−	1.37492e10i	−0.0784269	−	0.746182i	0.882674	−	0.469985i	$-0.155741\pi$
$858$	−2.38122e9	−	5.06144e8i	−0.128705	−	0.0273570i
$859$	−1.65201e10	+	7.35521e9i	−0.889275	+	0.395931i	−0.799946	−	0.600071i	$-0.795139\pi$
$859$	−1.65201e10	+	7.35521e9i	−0.889275	+	0.395931i	−0.0893286	+	0.996002i	$0.528472\pi$
$860$	−4.65024e9	−	3.37860e9i	−0.249305	−	0.181131i
$861$	1.23781e8	+	5.51108e7i	0.00660911	+	0.00294256i
$862$	−1.01700e10	−	1.76150e10i	−0.540813	−	0.936716i
$863$	−9.00434e9	+	1.55960e10i	−0.476885	+	0.825989i	−0.999649	−	0.0264881i	$-0.991568\pi$
$863$	−9.00434e9	+	1.55960e10i	−0.476885	+	0.825989i	0.522764	+	0.852478i	$0.324901\pi$
$864$	3.46024e9	−	2.51401e9i	0.182519	−	0.132608i
$865$	−2.29391e10	+	4.87586e9i	−1.20509	+	0.256150i
$866$	−9.50580e9	−	2.92558e10i	−0.497366	−	1.53074i
$867$	−2.75093e9			−0.143355
$868$	1.00167e9	+	1.99737e9i	0.0519884	+	0.103667i
$869$	1.26822e9			0.0655580
$870$	−3.55251e9	−	1.09335e10i	−0.182902	−	0.562913i
$871$	−6.86065e9	+	1.45828e9i	−0.351805	+	0.0747784i
$872$	1.63124e10	−	1.18517e10i	0.833127	−	0.605302i
$873$	−3.03341e8	+	5.25402e8i	−0.0154305	+	0.0267265i
$874$	3.82345e8	+	6.62240e8i	0.0193716	+	0.0335526i
$875$	5.81561e9	+	2.58928e9i	0.293472	+	0.130662i
$876$	8.98433e6	+	6.52750e6i	0.000451566	+	0.000328082i
$877$	2.56451e10	−	1.14179e10i	1.28383	−	0.571596i	0.352510	−	0.935808i	$-0.385328\pi$
$877$	2.56451e10	−	1.14179e10i	1.28383	−	0.571596i	0.931316	+	0.364212i	$0.118662\pi$
$878$	1.41740e9	+	3.01277e8i	0.0706741	+	0.0150222i
$879$	1.18776e9	+	1.13008e10i	0.0589886	+	0.561239i
$880$	1.19670e10	−	1.32907e10i	0.591965	−	0.657443i
$881$	9.88368e9	+	1.09769e10i	0.486971	+	0.540836i	0.935684	−	0.352840i	$-0.114784\pi$
$881$	9.88368e9	+	1.09769e10i	0.486971	+	0.540836i	−0.448713	+	0.893676i	$0.648117\pi$
$882$	1.07910e9	−	1.02670e10i	0.0529569	−	0.503851i
$883$	−9.26660e9	+	2.85197e10i	−0.452958	+	1.39406i	0.420558	+	0.907266i	$0.361834\pi$
$883$	−9.26660e9	+	2.85197e10i	−0.452958	+	1.39406i	−0.873516	+	0.486795i	$0.838166\pi$
$884$	7.34261e8	−	2.25982e9i	0.0357493	−	0.110025i
$885$	6.02971e7	−	5.73689e8i	0.00292412	−	0.0278211i
$886$	2.06789e10	+	2.29663e10i	0.998873	+	1.10936i
$887$	−6.31120e9	+	7.00930e9i	−0.303654	+	0.337242i	−0.875589	−	0.483057i	$-0.839526\pi$
$887$	−6.31120e9	+	7.00930e9i	−0.303654	+	0.337242i	0.571935	+	0.820299i	$0.306193\pi$
$888$	1.08268e8	+	1.03010e9i	0.00518864	+	0.0493666i
$889$	3.75693e9	+	7.98559e8i	0.179340	+	0.0381198i
$890$	−2.64315e10	+	1.17680e10i	−1.25677	+	0.559551i
$891$	1.09704e10	+	7.97046e9i	0.519577	+	0.377495i
$892$	−1.47274e9	−	6.55706e8i	−0.0694783	−	0.0309337i
$893$	−1.89411e9	−	3.28070e9i	−0.0890074	−	0.154165i
$894$	3.80998e9	−	6.59908e9i	0.178337	−	0.308889i
$895$	1.88358e10	−	1.36850e10i	0.878222	−	0.638066i
$896$	−8.06541e9	+	1.71436e9i	−0.374583	+	0.0796201i
$897$	−3.42885e8	−	1.05529e9i	−0.0158626	−	0.0488202i
$898$	6.65535e9			0.306693
$899$	−3.01717e10	+	1.93205e10i	−1.38497	+	0.886870i
$900$	2.17151e9			0.0992918
$901$	1.25393e10	+	3.85920e10i	0.571133	+	1.75777i
$902$	−6.56061e8	+	1.39450e8i	−0.0297661	+	0.00632697i
$903$	4.49410e9	−	3.26516e9i	0.203112	−	0.147570i
$904$	4.75931e9	−	8.24337e9i	0.214267	−	0.371121i
$905$	1.73064e10	+	2.99756e10i	0.776136	+	1.34431i
$906$	1.10381e9	+	4.91447e8i	0.0493111	+	0.0219547i
$907$	1.86198e10	+	1.35281e10i	0.828609	+	0.602019i	0.919165	−	0.393872i	$-0.128865\pi$
$907$	1.86198e10	+	1.35281e10i	0.828609	+	0.602019i	−0.0905568	+	0.995891i	$0.528865\pi$
$908$	−2.72814e9	+	1.21465e9i	−0.120939	+	0.0538455i
$909$	−2.95569e10	−	6.28250e9i	−1.30522	−	0.277434i
$910$	8.33300e8	+	7.92832e9i	0.0366569	+	0.348768i
$911$	−1.35980e10	+	1.51021e10i	−0.595882	+	0.661794i	−0.963352	−	0.268241i	$-0.913558\pi$
$911$	−1.35980e10	+	1.51021e10i	−0.595882	+	0.661794i	0.367470	+	0.930036i	$0.380224\pi$
$912$	−5.09078e8	−	5.65388e8i	−0.0222230	−	0.0246811i
$913$	2.26616e8	−	2.15611e9i	0.00985469	−	0.0937611i
$914$	−1.02960e10	+	3.16878e10i	−0.446022	+	1.37271i
$915$	4.34104e9	−	1.33603e10i	0.187335	−	0.576559i
$916$	−1.61741e8	+	1.53886e9i	−0.00695323	+	0.0661555i
$917$	1.12761e10	+	1.25234e10i	0.482910	+	0.536326i
$918$	−1.02646e10	+	1.14000e10i	−0.437920	+	0.486359i
$919$	−3.57284e9	−	3.39933e10i	−0.151848	−	1.44474i	−0.759486	−	0.650524i	$-0.774550\pi$
$919$	−3.57284e9	−	3.39933e10i	−0.151848	−	1.44474i	0.607638	−	0.794214i	$-0.292117\pi$
$920$	9.92616e9	+	2.10987e9i	0.420266	+	0.0893303i
$921$	−2.23636e9	+	9.95692e8i	−0.0943263	+	0.0419968i
$922$	8.08000e9	+	5.87046e9i	0.339510	+	0.246669i
$923$	−1.59267e10	−	7.09103e9i	−0.666684	−	0.296827i
$924$	−4.01349e8	−	6.95157e8i	−0.0167367	−	0.0289889i
$925$	−1.02228e9	+	1.77065e9i	−0.0424693	+	0.0735590i
$926$	1.69090e10	−	1.22851e10i	0.699807	−	0.508440i
$927$	−5.69417e9	+	1.21033e9i	−0.234775	+	0.0499029i
$928$	4.62495e9	+	1.42341e10i	0.189972	+	0.584673i
$929$	−1.77475e10			−0.726245			−0.363123	−	0.931741i	$-0.618289\pi$
$929$	−1.77475e10			−0.726245			−0.363123	+	0.931741i	$0.618289\pi$
$930$	−2.23029e9	−	8.54172e9i	−0.0909224	−	0.348221i
$931$	2.08002e9			0.0844782
$932$	−1.49968e9	−	4.61555e9i	−0.0606798	−	0.186753i
$933$	−1.27320e10	+	2.70626e9i	−0.513227	+	0.109090i
$934$	−3.01386e10	+	2.18970e10i	−1.21035	+	0.879368i
$935$	1.71979e10	−	2.97877e10i	0.688075	−	1.19178i
$936$	−6.11578e9	−	1.05928e10i	−0.243774	−	0.422228i
$937$	6.77178e9	+	3.01499e9i	0.268914	+	0.119728i	0.536764	−	0.843732i	$-0.319646\pi$
$937$	6.77178e9	+	3.01499e9i	0.268914	+	0.119728i	−0.267850	+	0.963461i	$0.586313\pi$
$938$	7.99495e9	+	5.80867e9i	0.316305	+	0.229809i
$939$	5.85460e9	−	2.60664e9i	0.230764	−	0.102743i
$940$	−7.83885e9	−	1.66620e9i	−0.307826	−	0.0654304i
$941$	4.23400e9	+	4.02838e10i	0.165648	+	1.57604i	0.689535	+	0.724252i	$0.257815\pi$
$941$	4.23400e9	+	4.02838e10i	0.165648	+	1.57604i	−0.523887	+	0.851788i	$0.675518\pi$
$942$	5.66745e9	−	6.29434e9i	0.220907	−	0.245342i
$943$	−2.04561e8	−	2.27188e8i	−0.00794385	−	0.00882254i
$944$	1.46393e8	−	1.39284e9i	0.00566393	−	0.0538887i
$945$	−3.72198e9	+	1.14551e10i	−0.143470	+	0.441557i
$946$	−8.49736e9	+	2.61522e10i	−0.326336	+	1.00436i
$947$	1.54302e9	−	1.46809e10i	0.0590401	−	0.561729i	−0.924518	−	0.381138i	$-0.875532\pi$
$947$	1.54302e9	−	1.46809e10i	0.0590401	−	0.561729i	0.983558	−	0.180591i	$-0.0578011\pi$
$948$	−7.63689e7	−	8.48163e7i	−0.00291130	−	0.00323333i
$949$	8.26222e7	−	9.17612e7i	0.00313809	−	0.00348520i
$950$	−1.95424e8	−	1.85933e9i	−0.00739511	−	0.0703598i
$951$	−1.33274e10	−	2.83283e9i	−0.502474	−	0.106804i
$952$	−1.91856e10	+	8.54198e9i	−0.720686	+	0.320870i
$953$	2.23224e9	+	1.62182e9i	0.0835441	+	0.0606984i	0.628773	−	0.777589i	$-0.283557\pi$
$953$	2.23224e9	+	1.62182e9i	0.0835441	+	0.0606984i	−0.545229	+	0.838287i	$0.683557\pi$
$954$	3.04197e10	+	1.35437e10i	1.13432	+	0.505032i
$955$	1.72534e10	+	2.98838e10i	0.641007	+	1.11026i
$956$	−3.40270e9	+	5.89365e9i	−0.125957	+	0.218163i
$957$	1.04125e10	−	7.56510e9i	0.384027	−	0.279012i
$958$	4.14053e10	−	8.80098e9i	1.52152	−	0.323409i
$959$	6.01068e8	+	1.84990e9i	0.0220069	+	0.0677302i
$960$	−1.21748e10			−0.444131
$961$	−2.40006e10	+	1.34504e10i	−0.872350	+	0.488881i
$962$	1.83587e9			0.0664857
$963$	−1.37174e10	−	4.22177e10i	−0.494970	−	1.52336i
$964$	−9.13198e8	+	1.94106e8i	−0.0328319	+	0.00697863i
$965$	3.65948e10	−	2.65877e10i	1.31091	−	0.952435i
$966$	−7.81689e8	+	1.35392e9i	−0.0279006	+	0.0483253i
$967$	−2.08168e10	−	3.60558e10i	−0.740323	−	1.28228i	−0.952348	−	0.305013i	$-0.901339\pi$
$967$	−2.08168e10	−	3.60558e10i	−0.740323	−	1.28228i	0.212025	−	0.977264i	$-0.431994\pi$
$968$	−4.83802e9	−	2.15403e9i	−0.171437	−	0.0763286i
$969$	−1.18376e9	−	8.60051e8i	−0.0417956	−	0.0303663i
$970$	1.00945e9	−	4.49434e8i	0.0355126	−	0.0158112i
$971$	4.57003e10	+	9.71390e9i	1.60196	+	0.340507i	0.920316	−	0.391176i	$-0.127932\pi$
$971$	4.57003e10	+	9.71390e9i	1.60196	+	0.340507i	0.681645	+	0.731683i	$0.261265\pi$
$972$	−4.70094e8	−	4.47265e9i	−0.0164192	−	0.156219i
$973$	1.17609e9	−	1.30618e9i	0.0409304	−	0.0454578i
$974$	−5.04622e8	−	5.60440e8i	−0.0174989	−	0.0194345i
$975$	−2.83569e8	+	2.69798e9i	−0.00979812	+	0.0932229i
$976$	1.05394e10	−	3.24370e10i	0.362863	−	1.11678i
$977$	−1.17154e10	+	3.60564e10i	−0.401909	+	1.23695i	0.521540	+	0.853227i	$0.325358\pi$
$977$	−1.17154e10	+	3.60564e10i	−0.401909	+	1.23695i	−0.923449	+	0.383722i	$0.874642\pi$
$978$	−1.73009e7	+	1.64607e8i	−0.000591400	+	0.00562680i
$979$	−2.16743e10	−	2.40718e10i	−0.738254	−	0.819914i
$980$	2.94436e9	−	3.27004e9i	0.0999309	−	0.110985i
$981$	−2.67196e9	−	2.54220e10i	−0.0903625	−	0.859742i
$982$	1.84167e10	+	3.91458e9i	0.620613	+	0.131915i
$983$	1.03730e10	−	4.61836e9i	0.348311	−	0.155078i	−0.225122	−	0.974331i	$-0.572278\pi$
$983$	1.03730e10	−	4.61836e9i	0.348311	−	0.155078i	0.573433	+	0.819253i	$0.305611\pi$
$984$	3.06330e8	+	2.22562e8i	0.0102496	+	0.00744676i
$985$	−4.56654e10	−	2.03316e10i	−1.52251	−	0.677866i
$986$	−2.68398e10	−	4.64878e10i	−0.891681	−	1.54444i
$987$	3.87244e9	−	6.70727e9i	0.128196	−	0.222042i
$988$	3.17833e8	−	2.30920e8i	0.0104846	−	0.00761748i
$989$	−1.22596e10	+	2.60586e9i	−0.402986	+	0.0856574i
$990$	−8.72213e9	−	2.68440e10i	−0.285693	−	0.879272i
$991$	4.65807e9			0.152037			0.0760183	−	0.997106i	$-0.475779\pi$
$991$	4.65807e9			0.152037			0.0760183	+	0.997106i	$0.475779\pi$
$992$	2.90358e9	+	1.11203e10i	0.0944370	+	0.361682i
$993$	3.76333e9			0.121969
$994$	7.59059e9	+	2.33614e10i	0.245145	+	0.754479i
$995$	−7.12502e10	+	1.51447e10i	−2.29301	+	0.487394i
$996$	−1.57843e8	+	1.14680e8i	−0.00506194	+	0.00367772i
$997$	2.30309e10	−	3.98907e10i	0.736000	−	1.27479i	−0.218283	−	0.975886i	$-0.570045\pi$
$997$	2.30309e10	−	3.98907e10i	0.736000	−	1.27479i	0.954283	−	0.298905i	$-0.0966212\pi$
$998$	−2.39037e10	−	4.14024e10i	−0.761217	−	1.31847i
$999$	2.53394e9	+	1.12818e9i	0.0804113	+	0.0358014i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.8.g.a.7.6	✓	144
31.9	even	15	inner	31.8.g.a.9.6	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.8.g.a.7.6	✓	144	1.1	even	1	trivial
31.8.g.a.9.6	yes	144	31.9	even	15	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:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	31.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.14721 - 9.68611i) q^{2} +(14.5381 - 3.09018i) q^{3} +(19.6383 - 14.2681i) q^{4} +(-175.802 + 304.498i) q^{5} +(-75.6864 - 131.093i) q^{6} +(-506.982 - 225.723i) q^{7} +(-1254.66 - 911.567i) q^{8} +(-1796.12 + 799.682i) q^{9} +(3502.68 + 744.518i) q^{10} +(419.058 + 3987.07i) q^{11} +(241.414 - 268.117i) q^{12} +(-2684.23 - 2981.13i) q^{13} +(-590.799 + 5621.08i) q^{14} +(-1614.88 + 4970.09i) q^{15} +(-3920.70 + 12066.7i) q^{16} +(-2550.63 + 24267.7i) q^{17} +(13398.6 + 14880.6i) q^{18} +(-2699.59 + 2998.20i) q^{19} +(892.142 + 8488.16i) q^{20} +(-8068.09 - 1714.93i) q^{21} +(37300.4 - 16607.2i) q^{22} +(15056.1 + 10938.9i) q^{23} +(-21057.4 - 9375.35i) q^{24} +(-22750.0 - 39404.2i) q^{25} +(-20427.8 + 35382.0i) q^{26} +(-49938.3 + 36282.3i) q^{27} +(-13176.9 + 2800.83i) q^{28} +(-66747.4 - 205427. i) q^{29} +53223.2 q^{30} +(-41904.5 - 160489. i) q^{31} -69290.3 q^{32} +(18413.1 + 56669.6i) q^{33} +(243087. - 51669.7i) q^{34} +(157860. - 114692. i) q^{35} +(-23862.7 + 41331.5i) q^{36} +(-22467.8 - 38915.3i) q^{37} +(37537.1 + 16712.6i) q^{38} +(-48235.9 - 35045.4i) q^{39} +(498142. - 221787. i) q^{40} +(-16068.0 - 3415.36i) q^{41} +(8781.01 + 83545.7i) q^{42} +(-450640. + 500486. i) q^{43} +(65117.4 + 72320.2i) q^{44} +(72259.0 - 687498. i) q^{45} +(58570.6 - 180262. i) q^{46} +(-290156. + 893007. i) q^{47} +(-19711.5 + 187543. i) q^{48} +(-344978. - 383137. i) q^{49} +(-310074. + 344372. i) q^{50} +(37909.9 + 360689. i) q^{51} +(-95248.6 - 20245.7i) q^{52} +(1.51918e6 - 676380. i) q^{53} +(508601. + 369520. i) q^{54} +(-1.28772e6 - 573332. i) q^{55} +(430330. + 745354. i) q^{56} +(-29982.1 + 51930.5i) q^{57} +(-1.77972e6 + 1.29305e6i) q^{58} +(-107971. + 22950.0i) q^{59} +(39200.0 + 120645. i) q^{60} -2.68815e6 q^{61} +(-1.42263e6 + 910983. i) q^{62} +1.09110e6 q^{63} +(719921. + 2.21569e6i) q^{64} +(1.37964e6 - 293251. i) q^{65} +(490959. - 356702. i) q^{66} +(874224. - 1.51420e6i) q^{67} +(296162. + 512968. i) q^{68} +(252690. + 112505. i) q^{69} +(-1.60774e6 - 1.16809e6i) q^{70} +(3.97025e6 - 1.76767e6i) q^{71} +(2.98249e6 + 633947. i) q^{72} +(3217.45 + 30612.0i) q^{73} +(-306227. + 340100. i) q^{74} +(-452509. - 502562. i) q^{75} +(-10236.9 + 97397.6i) q^{76} +(687518. - 2.11596e6i) q^{77} +(-187646. + 577513. i) q^{78} +(33066.6 - 314608. i) q^{79} +(-2.98501e6 - 3.31519e6i) q^{80} +(2.26327e6 - 2.51361e6i) q^{81} +(17487.8 + 166385. i) q^{82} +(-528958. - 112433. i) q^{83} +(-182912. + 81437.8i) q^{84} +(-6.94104e6 - 5.04296e6i) q^{85} +(6.26602e6 + 2.78981e6i) q^{86} +(-1.60519e6 - 2.78027e6i) q^{87} +(3.10870e6 - 5.38443e6i) q^{88} +(-6.53660e6 + 4.74912e6i) q^{89} +(-6.88660e6 + 1.46379e6i) q^{90} +(687943. + 2.11727e6i) q^{91} +451752. q^{92} +(-1.10515e6 - 2.20372e6i) q^{93} +9.56295e6 q^{94} +(-438352. - 1.34911e6i) q^{95} +(-1.00735e6 + 214119. i) q^{96} +(249640. - 181374. i) q^{97} +(-2.62539e6 + 4.54731e6i) q^{98} +(-3.94107e6 - 6.82613e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 6 q^{2} - 8 q^{3} - 2362 q^{4} - 75 q^{5} - 1637 q^{6} + 5518 q^{7} + 3401 q^{8} + 14542 q^{9} - 5312 q^{10} + 1361 q^{11} - 18281 q^{12} + 22457 q^{13} + 28470 q^{14} - 86918 q^{15} - 155730 q^{16}+ \cdots - 102755966 q^{99}+O(q^{100}) \) 144 * q - 6 * q^2 - 8 * q^3 - 2362 * q^4 - 75 * q^5 - 1637 * q^6 + 5518 * q^7 + 3401 * q^8 + 14542 * q^9 - 5312 * q^10 + 1361 * q^11 - 18281 * q^12 + 22457 * q^13 + 28470 * q^14 - 86918 * q^15 - 155730 * q^16 + 51582 * q^17 - 24915 * q^18 + 206748 * q^19 + 53815 * q^20 - 28547 * q^21 + 471441 * q^22 - 10235 * q^23 + 69278 * q^24 - 974301 * q^25 - 279651 * q^26 - 948323 * q^27 + 550632 * q^28 - 32990 * q^29 + 2457990 * q^30 + 899715 * q^31 - 1048518 * q^32 + 780887 * q^33 - 1741528 * q^34 + 40023 * q^35 - 2118881 * q^36 - 787972 * q^37 + 580274 * q^38 + 2541281 * q^39 + 2341817 * q^40 + 1129504 * q^41 - 4390379 * q^42 + 481927 * q^43 - 3123681 * q^44 - 1715971 * q^45 + 2065430 * q^46 - 3123106 * q^47 + 1041890 * q^48 + 76766 * q^49 + 7537425 * q^50 + 6145978 * q^51 + 3260257 * q^52 + 141486 * q^53 - 8979668 * q^54 - 8182779 * q^55 - 5240874 * q^56 - 5487037 * q^57 + 5315215 * q^58 + 7471552 * q^59 + 8590679 * q^60 + 10667852 * q^61 + 27020951 * q^62 - 23783686 * q^63 - 3962521 * q^64 + 935148 * q^65 + 3015728 * q^66 - 17382495 * q^67 - 29462568 * q^68 - 26986306 * q^69 - 31811186 * q^70 - 6186650 * q^71 + 35811589 * q^72 + 6470154 * q^73 + 55339663 * q^74 + 17367737 * q^75 + 2919592 * q^76 + 31865334 * q^77 - 7291717 * q^78 + 4223078 * q^79 + 77431338 * q^80 - 5164601 * q^81 - 19477394 * q^82 - 28867780 * q^83 - 76561164 * q^84 - 45198987 * q^85 - 60993764 * q^86 + 18253055 * q^87 - 45197061 * q^88 - 8429459 * q^89 + 83458809 * q^90 - 53128088 * q^91 + 77469728 * q^92 + 41662009 * q^93 - 16867972 * q^94 - 12744274 * q^95 + 119555444 * q^96 + 20643027 * q^97 + 49624796 * q^98 - 102755966 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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