LMFDB - Embedded newform 18.9.d.a.11.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [18,9,Mod(5,18)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(18, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5])) N = Newforms(chi, 9, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("18.5"); S:= CuspForms(chi, 9); N := Newforms(S);

Level:	$N$	$=$	$18 = 2 \cdot 3^{2}$
Weight:	$k$	$=$	$9$
Character orbit:	$[\chi]$	$=$	18.d (of order $6$ , degree $2$ , 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:	$7.33281498110$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{16} - 8 x^{15} + 5476 x^{14} - 38192 x^{13} + 11414542 x^{12} - 67991120 x^{11} + \cdots + 19\!\cdots\!29$ x^16 - 8x^15 + 5476x^14 - 38192x^13 + 11414542x^12 - 67991120x^11 + 11330952892x^10 - 56032421816x^9 + 5575009041895x^8 - 21964587980304x^7 + 1366797007396500x^6 - 4023749554164360x^5 + 166750774096111110x^4 - 326820812596206264x^3 + 9443577280676906808x^2 - 9280833855293027160*x + 190324219382219227329
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$2^{28}\cdot 3^{22}$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.6
Root			$0.500000 + 11.5235i$ of defining polynomial
Character	$\chi$	$=$	18.11
Dual form			18.9.d.a.5.6

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(9.79796 + 5.65685i) q^{2} +(7.38176 + 80.6629i) q^{3} +(64.0000 + 110.851i) q^{4} +(935.250 - 539.967i) q^{5} +(-383.972 + 832.090i) q^{6} +(-2056.09 + 3561.25i) q^{7} +1448.15i q^{8} +(-6452.02 + 1190.87i) q^{9} +12218.1 q^{10} +(8419.53 + 4861.02i) q^{11} +(-8469.15 + 5980.71i) q^{12} +(-4116.02 - 7129.16i) q^{13} +(-40291.0 + 23262.0i) q^{14} +(50459.1 + 71454.1i) q^{15} +(-8192.00 + 14189.0i) q^{16} -87809.9i q^{17} +(-69953.2 - 24830.0i) q^{18} +123643. q^{19} +(119712. + 69115.7i) q^{20} +(-302439. - 139562. i) q^{21} +(54996.1 + 95256.1i) q^{22} +(92029.4 - 53133.2i) q^{23} +(-116812. + 10689.9i) q^{24} +(387816. - 671717. i) q^{25} -93134.9i q^{26} +(-143686. - 511648. i) q^{27} -526359. q^{28} +(430885. + 248772. i) q^{29} +(90190.8 + 985544. i) q^{30} +(-577977. - 1.00109e6i) q^{31} +(-160530. + 92681.9i) q^{32} +(-329953. + 715027. i) q^{33} +(496728. - 860358. i) q^{34} +4.44088e6i q^{35} +(-544939. - 638999. i) q^{36} +1.20145e6 q^{37} +(1.21145e6 + 699428. i) q^{38} +(544675. - 384636. i) q^{39} +(781955. + 1.35439e6i) q^{40} +(1.53952e6 - 888843. i) q^{41} +(-2.17380e6 - 3.07827e6i) q^{42} +(-528726. + 915780. i) q^{43} +1.24442e6i q^{44} +(-5.39122e6 + 4.59764e6i) q^{45} +1.20227e6 q^{46} +(-3.80689e6 - 2.19791e6i) q^{47} +(-1.20499e6 - 556051. i) q^{48} +(-5.57261e6 - 9.65205e6i) q^{49} +(7.59961e6 - 4.38763e6i) q^{50} +(7.08301e6 - 648192. i) q^{51} +(526851. - 912532. i) q^{52} +1.04810e6i q^{53} +(1.48649e6 - 5.82592e6i) q^{54} +1.04991e7 q^{55} +(-5.15724e6 - 2.97754e6i) q^{56} +(912700. + 9.97337e6i) q^{57} +(2.81453e6 + 4.87491e6i) q^{58} +(-8.70048e6 + 5.02323e6i) q^{59} +(-4.69139e6 + 1.01665e7i) q^{60} +(-4.15770e6 + 7.20135e6i) q^{61} -1.30781e7i q^{62} +(9.02495e6 - 2.54258e7i) q^{63} -2.09715e6 q^{64} +(-7.69902e6 - 4.44503e6i) q^{65} +(-7.27767e6 + 5.13931e6i) q^{66} +(6.19183e6 + 1.07246e7i) q^{67} +(9.73384e6 - 5.61983e6i) q^{68} +(4.96522e6 + 7.03114e6i) q^{69} +(-2.51214e7 + 4.35116e7i) q^{70} -1.69579e7i q^{71} +(-1.72456e6 - 9.34352e6i) q^{72} -2.42736e7 q^{73} +(1.17718e7 + 6.79644e6i) q^{74} +(5.70454e7 + 2.63239e7i) q^{75} +(7.91313e6 + 1.37059e7i) q^{76} +(-3.46226e7 + 1.99894e7i) q^{77} +(7.51254e6 - 687500. i) q^{78} +(6.39004e6 - 1.10679e7i) q^{79} +1.76936e7i q^{80} +(4.02104e7 - 1.53670e7i) q^{81} +2.01122e7 q^{82} +(-2.79188e7 - 1.61189e7i) q^{83} +(-3.88546e6 - 4.24577e7i) q^{84} +(-4.74144e7 - 8.21242e7i) q^{85} +(-1.03609e7 + 5.98185e6i) q^{86} +(-1.68860e7 + 3.65928e7i) q^{87} +(-7.03950e6 + 1.21928e7i) q^{88} +2.10088e7i q^{89} +(-7.88311e7 + 1.45501e7i) q^{90} +3.38516e7 q^{91} +(1.17798e7 + 6.80105e6i) q^{92} +(7.64841e7 - 5.40111e7i) q^{93} +(-2.48665e7 - 4.30700e7i) q^{94} +(1.15637e8 - 6.67629e7i) q^{95} +(-8.66099e6 - 1.22646e7i) q^{96} +(-4.46651e7 + 7.73622e7i) q^{97} -1.26094e8i q^{98} +(-6.01118e7 - 2.13368e7i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$16 q + 126 q^{3} + 1024 q^{4} - 882 q^{5} + 384 q^{6} - 1846 q^{7} - 28662 q^{9} + 45756 q^{11} + 5376 q^{12} - 3370 q^{13} - 94464 q^{14} + 128754 q^{15} - 131072 q^{16} - 236544 q^{18} + 362180 q^{19}+ \cdots + 366888330 q^{99}+O(q^{100})$ 16 * q + 126 * q^3 + 1024 * q^4 - 882 * q^5 + 384 * q^6 - 1846 * q^7 - 28662 * q^9 + 45756 * q^11 + 5376 * q^12 - 3370 * q^13 - 94464 * q^14 + 128754 * q^15 - 131072 * q^16 - 236544 * q^18 + 362180 * q^19 - 112896 * q^20 - 299166 * q^21 - 61824 * q^22 + 1311138 * q^23 - 147456 * q^24 + 963394 * q^25 - 208656 * q^27 - 472576 * q^28 - 2851290 * q^29 - 1253376 * q^30 + 542438 * q^31 + 3875796 * q^33 + 220416 * q^34 - 3655680 * q^36 + 3343328 * q^37 - 1314432 * q^38 - 5896002 * q^39 + 9218592 * q^41 + 14237952 * q^42 + 339512 * q^43 - 32740578 * q^45 + 7417344 * q^46 - 34980606 * q^47 - 1376256 * q^48 - 2364654 * q^49 + 27744768 * q^50 + 50877810 * q^51 + 431360 * q^52 - 5648256 * q^54 - 4584276 * q^55 - 12091392 * q^56 - 34049898 * q^57 - 7852800 * q^58 + 93924216 * q^59 + 18604800 * q^60 - 841954 * q^61 - 14043234 * q^63 - 33554432 * q^64 - 126568134 * q^65 - 35179776 * q^66 + 29946644 * q^67 - 5476608 * q^68 + 70499610 * q^69 - 34359552 * q^70 - 11894784 * q^72 - 7547764 * q^73 + 35124480 * q^74 + 114494910 * q^75 + 23179520 * q^76 + 9309294 * q^77 + 23014656 * q^78 + 33813002 * q^79 - 46018134 * q^81 - 137346048 * q^82 + 114200226 * q^83 - 15040512 * q^84 - 125696772 * q^85 - 171379584 * q^86 - 159599970 * q^87 + 7913472 * q^88 + 129745152 * q^90 + 268578316 * q^91 + 167825664 * q^92 + 120711534 * q^93 - 11832576 * q^94 - 143949240 * q^95 - 25165824 * q^96 - 89415484 * q^97 + 366888330 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/18\mathbb{Z}\right)^\times$ .

$n$	$11$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	9.79796	+	5.65685i	0.612372	+	0.353553i
$2$	9.79796	+	5.65685i	0.612372	+	0.353553i
$3$	7.38176	+	80.6629i	0.0911329	+	0.995839i
$3$	7.38176	+	80.6629i	0.0911329	+	0.995839i
$4$	64.0000	+	110.851i	0.250000	+	0.433013i
$5$	935.250	−	539.967i	1.49640	−	0.863947i	0.496408	−	0.868089i	$-0.334652\pi$
$5$	935.250	−	539.967i	1.49640	−	0.863947i	0.999991	+	0.00414227i	$0.00131853\pi$
$6$	−383.972	+	832.090i	−0.296275	+	0.642045i
$7$	−2056.09	+	3561.25i	−0.856347	+	1.48324i	0.0190419	+	0.999819i	$0.493938\pi$
$7$	−2056.09	+	3561.25i	−0.856347	+	1.48324i	−0.875389	+	0.483419i	$0.839395\pi$
$8$			1448.15i			0.353553i
$9$	−6452.02	+	1190.87i	−0.983390	+	0.181507i
$10$	12218.1			1.22181
$11$	8419.53	+	4861.02i	0.575065	+	0.332014i	0.759170	−	0.650893i	$-0.225605\pi$
$11$	8419.53	+	4861.02i	0.575065	+	0.332014i	−0.184105	+	0.982907i	$0.558939\pi$
$12$	−8469.15	+	5980.71i	−0.408428	+	0.288421i
$13$	−4116.02	−	7129.16i	−0.144113	−	0.249612i	0.784928	−	0.619586i	$-0.212700\pi$
$13$	−4116.02	−	7129.16i	−0.144113	−	0.249612i	−0.929042	+	0.369975i	$0.879366\pi$
$14$	−40291.0	+	23262.0i	−1.04881	+	0.605529i
$15$	50459.1	+	71454.1i	0.996723	+	1.41144i
$16$	−8192.00	+	14189.0i	−0.125000	+	0.216506i
$17$		−	87809.9i		−	1.05135i	−0.850685	−	0.525676i	$-0.823813\pi$
$17$		−	87809.9i		−	1.05135i	0.850685	−	0.525676i	$-0.176187\pi$
$18$	−69953.2	−	24830.0i	−0.666373	−	0.236531i
$19$	123643.			0.948754			0.474377	−	0.880322i	$-0.342673\pi$
$19$	123643.			0.948754			0.474377	+	0.880322i	$0.342673\pi$
$20$	119712.	+	69115.7i	0.748200	+	0.431973i
$21$	−302439.	−	139562.i	−1.55511	−	0.717612i
$22$	54996.1	+	95256.1i	0.234769	+	0.406632i
$23$	92029.4	−	53133.2i	0.328863	−	0.189869i	−0.326473	−	0.945206i	$-0.605860\pi$
$23$	92029.4	−	53133.2i	0.328863	−	0.189869i	0.655336	+	0.755337i	$0.272527\pi$
$24$	−116812.	+	10689.9i	−0.352082	+	0.0322203i
$25$	387816.	−	671717.i	0.992808	−	1.71959i
$26$		−	93134.9i		−	0.203807i
$27$	−143686.	−	511648.i	−0.270371	−	0.962756i
$28$	−526359.			−0.856347
$29$	430885.	+	248772.i	0.609213	+	0.351729i	0.772657	−	0.634823i	$-0.218927\pi$
$29$	430885.	+	248772.i	0.609213	+	0.351729i	−0.163444	+	0.986553i	$0.552260\pi$
$30$	90190.8	+	985544.i	0.111347	+	1.21672i
$31$	−577977.	−	1.00109e6i	−0.625841	−	1.08399i	−0.988378	−	0.152019i	$-0.951422\pi$
$31$	−577977.	−	1.00109e6i	−0.625841	−	1.08399i	0.362536	−	0.931970i	$-0.381911\pi$
$32$	−160530.	+	92681.9i	−0.153093	+	0.0883883i
$33$	−329953.	+	715027.i	−0.278225	+	0.602929i
$34$	496728.	−	860358.i	0.371709	−	0.643819i
$35$			4.44088e6i			2.95935i
$36$	−544939.	−	638999.i	−0.324442	−	0.380443i
$37$	1.20145e6			0.641061			0.320531	−	0.947238i	$-0.396139\pi$
$37$	1.20145e6			0.641061			0.320531	+	0.947238i	$0.396139\pi$
$38$	1.21145e6	+	699428.i	0.580991	+	0.335435i
$39$	544675.	−	384636.i	0.235439	−	0.166261i
$40$	781955.	+	1.35439e6i	0.305451	+	0.529057i
$41$	1.53952e6	−	888843.i	0.544816	−	0.314550i	−0.202212	−	0.979342i	$-0.564813\pi$
$41$	1.53952e6	−	888843.i	0.544816	−	0.314550i	0.747029	+	0.664792i	$0.231480\pi$
$42$	−2.17380e6	−	3.07827e6i	−0.698590	−	0.989259i
$43$	−528726.	+	915780.i	−0.154652	+	0.267866i	−0.932932	−	0.360052i	$-0.882759\pi$
$43$	−528726.	+	915780.i	−0.154652	+	0.267866i	0.778280	+	0.627917i	$0.216092\pi$
$44$			1.24442e6i			0.332014i
$45$	−5.39122e6	+	4.59764e6i	−1.31473	+	1.12120i
$46$	1.20227e6			0.268516
$47$	−3.80689e6	−	2.19791e6i	−0.780151	−	0.450420i	0.0563327	−	0.998412i	$-0.482059\pi$
$47$	−3.80689e6	−	2.19791e6i	−0.780151	−	0.450420i	−0.836484	+	0.547992i	$0.815393\pi$
$48$	−1.20499e6	−	556051.i	−0.226997	−	0.104749i
$49$	−5.57261e6	−	9.65205e6i	−0.966662	−	1.67431i
$50$	7.59961e6	−	4.38763e6i	1.21594	−	0.702021i
$51$	7.08301e6	−	648192.i	1.04698	−	0.0958127i
$52$	526851.	−	912532.i	0.0720567	−	0.124806i
$53$			1.04810e6i			0.132831i	0.997792	+	0.0664157i	$0.0211563\pi$
$53$			1.04810e6i			0.132831i	−0.997792	+	0.0664157i	$0.978844\pi$
$54$	1.48649e6	−	5.82592e6i	0.174818	−	0.685156i
$55$	1.04991e7			1.14737
$56$	−5.15724e6	−	2.97754e6i	−0.524404	−	0.302765i
$57$	912700.	+	9.97337e6i	0.0864627	+	0.944806i
$58$	2.81453e6	+	4.87491e6i	0.248710	+	0.430779i
$59$	−8.70048e6	+	5.02323e6i	−0.718018	+	0.414548i	−0.814023	−	0.580833i	$-0.802727\pi$
$59$	−8.70048e6	+	5.02323e6i	−0.718018	+	0.414548i	0.0960047	+	0.995381i	$0.469394\pi$
$60$	−4.69139e6	+	1.01665e7i	−0.361990	+	0.784453i
$61$	−4.15770e6	+	7.20135e6i	−0.300285	+	0.520109i	−0.976200	−	0.216870i	$-0.930415\pi$
$61$	−4.15770e6	+	7.20135e6i	−0.300285	+	0.520109i	0.675915	+	0.736979i	$0.263749\pi$
$62$		−	1.30781e7i		−	0.885073i
$63$	9.02495e6	−	2.54258e7i	0.572905	−	1.61403i
$64$	−2.09715e6			−0.125000
$65$	−7.69902e6	−	4.44503e6i	−0.431302	−	0.249013i
$66$	−7.27767e6	+	5.13931e6i	−0.383545	+	0.270850i
$67$	6.19183e6	+	1.07246e7i	0.307270	+	0.532207i	0.977764	−	0.209708i	$-0.0672513\pi$
$67$	6.19183e6	+	1.07246e7i	0.307270	+	0.532207i	−0.670494	+	0.741915i	$0.733918\pi$
$68$	9.73384e6	−	5.61983e6i	0.455248	−	0.262838i
$69$	4.96522e6	+	7.03114e6i	0.219049	+	0.310191i
$70$	−2.51214e7	+	4.35116e7i	−1.04629	+	1.81223i
$71$		−	1.69579e7i		−	0.667328i	−0.942692	−	0.333664i	$-0.891715\pi$
$71$		−	1.69579e7i		−	0.667328i	0.942692	−	0.333664i	$-0.108285\pi$
$72$	−1.72456e6	−	9.34352e6i	−0.0641725	−	0.347681i
$73$	−2.42736e7			−0.854757			−0.427378	−	0.904073i	$-0.640563\pi$
$73$	−2.42736e7			−0.854757			−0.427378	+	0.904073i	$0.640563\pi$
$74$	1.17718e7	+	6.79644e6i	0.392568	+	0.226649i
$75$	5.70454e7	+	2.63239e7i	1.80292	+	0.831965i
$76$	7.91313e6	+	1.37059e7i	0.237189	+	0.410823i
$77$	−3.46226e7	+	1.99894e7i	−0.984911	+	0.568639i
$78$	7.51254e6	−	687500.i	0.202959	−	0.0185735i
$79$	6.39004e6	−	1.10679e7i	0.164057	−	0.284155i	−0.772263	−	0.635303i	$-0.780875\pi$
$79$	6.39004e6	−	1.10679e7i	0.164057	−	0.284155i	0.936320	+	0.351148i	$0.114209\pi$
$80$			1.76936e7i			0.431973i
$81$	4.02104e7	−	1.53670e7i	0.934110	−	0.356985i
$82$	2.01122e7			0.444841
$83$	−2.79188e7	−	1.61189e7i	−0.588281	−	0.339644i	0.176136	−	0.984366i	$-0.443640\pi$
$83$	−2.79188e7	−	1.61189e7i	−0.588281	−	0.339644i	−0.764418	+	0.644722i	$0.776973\pi$
$84$	−3.88546e6	−	4.24577e7i	−0.0780414	−	0.852784i
$85$	−4.74144e7	−	8.21242e7i	−0.908312	−	1.57324i
$86$	−1.03609e7	+	5.98185e6i	−0.189410	+	0.109356i
$87$	−1.68860e7	+	3.65928e7i	−0.294746	+	0.638732i
$88$	−7.03950e6	+	1.21928e7i	−0.117385	+	0.203316i
$89$			2.10088e7i			0.334843i	0.985885	+	0.167422i	$0.0535441\pi$
$89$			2.10088e7i			0.334843i	−0.985885	+	0.167422i	$0.946456\pi$
$90$	−7.88311e7	+	1.45501e7i	−1.20151	+	0.221767i
$91$	3.38516e7			0.493644
$92$	1.17798e7	+	6.80105e6i	0.164432	+	0.0949346i
$93$	7.64841e7	−	5.40111e7i	1.02244	−	0.722024i
$94$	−2.48665e7	−	4.30700e7i	−0.318495	−	0.551650i
$95$	1.15637e8	−	6.67629e7i	1.41972	−	0.819673i
$96$	−8.66099e6	−	1.22646e7i	−0.101972	−	0.144401i
$97$	−4.46651e7	+	7.73622e7i	−0.504523	+	0.873860i	0.495463	+	0.868629i	$0.334998\pi$
$97$	−4.46651e7	+	7.73622e7i	−0.504523	+	0.873860i	−0.999986	+	0.00523116i	$0.998335\pi$
$98$		−	1.26094e8i		−	1.36707i
$99$	−6.01118e7	−	2.13368e7i	−0.625776	−	0.222121i
$100$	9.92808e7			0.992808
$101$	−3.08430e7	−	1.78072e7i	−0.296395	−	0.171124i	0.344427	−	0.938813i	$-0.388073\pi$
$101$	−3.08430e7	−	1.78072e7i	−0.296395	−	0.171124i	−0.640822	+	0.767689i	$0.721406\pi$
$102$	7.30657e7	+	3.37166e7i	0.675014	+	0.311489i
$103$	−4.35300e6	−	7.53962e6i	−0.0386759	−	0.0669886i	0.846040	−	0.533120i	$-0.178981\pi$
$103$	−4.35300e6	−	7.53962e6i	−0.0386759	−	0.0669886i	−0.884715	+	0.466132i	$0.845647\pi$
$104$	1.03241e7	−	5.96064e6i	0.0882510	−	0.0509518i
$105$	−3.58215e8	+	3.27815e7i	−2.94704	+	0.269694i
$106$	−5.92897e6	+	1.02693e7i	−0.0469630	+	0.0813422i
$107$			2.34341e8i			1.78778i	0.448290	+	0.893888i	$0.352033\pi$
$107$			2.34341e8i			1.78778i	−0.448290	+	0.893888i	$0.647967\pi$
$108$	4.75209e7	−	4.86733e7i	0.349293	−	0.357763i
$109$	2.66492e8			1.88789			0.943947	−	0.330098i	$-0.107082\pi$
$109$	2.66492e8			1.88789			0.943947	+	0.330098i	$0.107082\pi$
$110$	1.02870e8	+	5.93921e7i	0.702617	+	0.405656i
$111$	8.86883e6	+	9.69126e7i	0.0584217	+	0.638393i
$112$	−3.36870e7	−	5.83476e7i	−0.214087	−	0.370809i
$113$	−2.47560e8	+	1.42929e8i	−1.51833	+	0.876610i	−0.518565	+	0.855038i	$0.673534\pi$
$113$	−2.47560e8	+	1.42929e8i	−1.51833	+	0.876610i	−0.999767	+	0.0215714i	$0.993133\pi$
$114$	−4.74753e7	+	1.02882e8i	−0.281092	+	0.609142i
$115$	5.73803e7	−	9.93856e7i	0.328074	−	0.568241i
$116$			6.36855e7i			0.351729i
$117$	3.50465e7	+	4.10958e7i	0.187026	+	0.219308i
$118$	−1.13663e8			−0.586259
$119$	3.12713e8	+	1.80545e8i	1.55940	+	0.900322i
$120$	−1.03477e8	+	7.30726e7i	−0.499019	+	0.352395i
$121$	−5.99205e7	−	1.03785e8i	−0.279534	−	0.484166i
$122$	−8.14740e7	+	4.70390e7i	−0.367773	+	0.212334i
$123$	8.30610e7	+	1.17621e8i	0.362892	+	0.513883i
$124$	7.39811e7	−	1.28139e8i	0.312921	−	0.541994i
$125$		−	4.15781e8i		−	1.70304i
$126$	2.32256e8	−	1.98068e8i	0.921478	−	0.785837i
$127$	−8.18752e7			−0.314730			−0.157365	−	0.987541i	$-0.550300\pi$
$127$	−8.18752e7			−0.314730			−0.157365	+	0.987541i	$0.550300\pi$
$128$	−2.05478e7	−	1.18633e7i	−0.0765466	−	0.0441942i
$129$	−7.77724e7	−	3.58885e7i	−0.280845	−	0.129597i
$130$	−5.02898e7	−	8.71044e7i	−0.176078	−	0.304977i
$131$	3.27800e8	−	1.89256e8i	1.11308	−	0.642634i	0.173451	−	0.984843i	$-0.444508\pi$
$131$	3.27800e8	−	1.89256e8i	1.11308	−	0.642634i	0.939624	+	0.342208i	$0.111175\pi$
$132$	−1.00379e8	+	9.18601e6i	−0.330632	+	0.0302574i
$133$	−2.54220e8	+	4.40322e8i	−0.812463	+	1.40723i
$134$			1.40105e8i			0.434545i
$135$	−4.10656e8	−	4.00933e8i	−1.23635	−	1.20708i
$136$	1.27162e8			0.371709
$137$	8.36881e7	+	4.83174e7i	0.237565	+	0.137158i	0.614057	−	0.789262i	$-0.289537\pi$
$137$	8.36881e7	+	4.83174e7i	0.237565	+	0.137158i	−0.376492	+	0.926420i	$0.622870\pi$
$138$	8.87485e6	+	9.69784e7i	0.0244706	+	0.267398i
$139$	−2.13230e8	−	3.69325e8i	−0.571200	−	0.989348i	−0.996443	−	0.0842686i	$-0.973145\pi$
$139$	−2.13230e8	−	3.69325e8i	−0.571200	−	0.989348i	0.425243	−	0.905079i	$-0.360189\pi$
$140$	−4.92277e8	+	2.84216e8i	−1.28144	+	0.739839i
$141$	1.49188e8	−	3.23299e8i	0.377449	−	0.817953i
$142$	9.59286e7	−	1.66153e8i	0.235936	−	0.408653i
$143$		−	8.00322e7i		−	0.191391i
$144$	3.59577e7	−	1.01303e8i	0.0836262	−	0.235599i
$145$	5.37313e8			1.21550
$146$	−2.37832e8	−	1.37312e8i	−0.523429	−	0.302202i
$147$	7.37427e8	−	5.20752e8i	1.57925	−	1.11522i
$148$	7.68929e7	+	1.33182e8i	0.160265	+	0.277588i
$149$	3.73436e8	−	2.15603e8i	0.757653	−	0.437431i	−0.0707992	−	0.997491i	$-0.522555\pi$
$149$	3.73436e8	−	2.15603e8i	0.757653	−	0.437431i	0.828453	+	0.560059i	$0.189222\pi$
$150$	4.10018e8	+	5.80618e8i	0.809912	+	1.14690i
$151$	−4.20280e8	+	7.27947e8i	−0.808409	+	1.40021i	0.105556	+	0.994413i	$0.466338\pi$
$151$	−4.20280e8	+	7.27947e8i	−0.808409	+	1.40021i	−0.913965	+	0.405793i	$0.866996\pi$
$152$			1.79054e8i			0.335435i
$153$	1.04570e8	+	5.66551e8i	0.190828	+	1.03389i
$154$	−4.52308e8			−0.804176
$155$	−1.08111e9	−	6.24177e8i	−1.87302	−	1.08139i
$156$	7.74966e7	+	3.57612e7i	0.130853	+	0.0603829i
$157$	2.10919e8	+	3.65323e8i	0.347150	+	0.601282i	0.985742	−	0.168264i	$-0.0538160\pi$
$157$	2.10919e8	+	3.65323e8i	0.347150	+	0.601282i	−0.638592	+	0.769546i	$0.720483\pi$
$158$	1.25219e8	−	7.22951e7i	0.200928	−	0.116006i
$159$	−8.45431e7	+	7.73685e6i	−0.132279	+	0.0121053i
$160$	−1.00090e8	+	1.73361e8i	−0.152726	+	0.264529i
$161$			4.36987e8i			0.650376i
$162$	4.80909e8	+	7.68988e7i	0.698237	+	0.111650i
$163$	−5.50818e8			−0.780293			−0.390146	−	0.920753i	$-0.627576\pi$
$163$	−5.50818e8			−0.780293			−0.390146	+	0.920753i	$0.627576\pi$
$164$	1.97059e8	+	1.13772e8i	0.272408	+	0.157275i
$165$	7.75022e7	+	8.46892e8i	0.104563	+	1.14259i
$166$	−1.82365e8	−	3.15866e8i	−0.240165	−	0.415978i
$167$	5.25550e8	−	3.03427e8i	0.675691	−	0.390111i	−0.122538	−	0.992464i	$-0.539103\pi$
$167$	5.25550e8	−	3.03427e8i	0.675691	−	0.390111i	0.798230	+	0.602353i	$0.205770\pi$
$168$	2.02107e8	−	4.37978e8i	0.253714	−	0.549813i
$169$	3.73982e8	−	6.47756e8i	0.458463	−	0.794081i
$170$		−	1.07287e9i		−	1.28455i
$171$	−7.97744e8	+	1.47242e8i	−0.932995	+	0.172206i
$172$	−1.35354e8			−0.154652
$173$	−8.26617e8	−	4.77248e8i	−0.922826	−	0.532794i	−0.0382907	−	0.999267i	$-0.512191\pi$
$173$	−8.26617e8	−	4.77248e8i	−0.922826	−	0.532794i	−0.884536	+	0.466473i	$0.845525\pi$
$174$	−3.72448e8	+	2.63014e8i	−0.406321	+	0.286933i
$175$	1.59477e9	+	2.76222e9i	1.70038	+	2.94514i
$176$	−1.37946e8	+	7.96429e7i	−0.143766	+	0.0830035i
$177$	−4.69413e8	−	6.64726e8i	−0.478258	−	0.677251i
$178$	−1.18844e8	+	2.05844e8i	−0.118385	+	0.205049i
$179$			9.44019e8i			0.919536i	0.888039	+	0.459768i	$0.152067\pi$
$179$			9.44019e8i			0.919536i	−0.888039	+	0.459768i	$0.847933\pi$
$180$	−8.54692e8	−	3.03375e8i	−0.814178	−	0.288994i
$181$	−8.68230e8			−0.808948			−0.404474	−	0.914550i	$-0.632545\pi$
$181$	−8.68230e8			−0.808948			−0.404474	+	0.914550i	$0.632545\pi$
$182$	3.31677e8	+	1.91494e8i	0.302294	+	0.174530i
$183$	−6.11573e8	−	2.82214e8i	−0.545311	−	0.251637i
$184$	7.69451e7	+	1.33273e8i	0.0671289	+	0.116271i
$185$	1.12366e9	−	6.48744e8i	0.959284	−	0.553843i
$186$	1.05492e9	−	9.65397e7i	0.881390	−	0.0806593i
$187$	4.26845e8	−	7.39318e8i	0.349063	−	0.604595i
$188$		−	5.62665e8i		−	0.450420i
$189$	2.11754e9	+	5.40291e8i	1.65953	+	0.423429i
$190$	1.51067e9			1.15919
$191$	−6.09956e7	−	3.52159e7i	−0.0458316	−	0.0264609i	0.476909	−	0.878953i	$-0.341757\pi$
$191$	−6.09956e7	−	3.52159e7i	−0.0458316	−	0.0264609i	−0.522741	+	0.852492i	$0.675090\pi$
$192$	−1.54807e7	−	1.69162e8i	−0.0113916	−	0.124480i
$193$	−1.36871e9	−	2.37068e9i	−0.986467	−	1.70861i	−0.635225	−	0.772327i	$-0.719093\pi$
$193$	−1.36871e9	−	2.37068e9i	−0.986467	−	1.70861i	−0.351242	−	0.936285i	$-0.614241\pi$
$194$	−8.75254e8	+	5.05328e8i	−0.617913	+	0.356752i
$195$	3.01717e8	−	6.53838e8i	0.208671	−	0.452201i
$196$	7.13294e8	−	1.23546e9i	0.483331	−	0.837154i
$197$			5.47276e8i			0.363364i	0.983357	+	0.181682i	$0.0581541\pi$
$197$			5.47276e8i			0.363364i	−0.983357	+	0.181682i	$0.941846\pi$
$198$	−4.68274e8	−	5.49101e8i	−0.304676	−	0.357266i
$199$	−2.66467e9			−1.69915			−0.849574	−	0.527469i	$-0.823141\pi$
$199$	−2.66467e9			−1.69915			−0.849574	+	0.527469i	$0.823141\pi$
$200$	9.72749e8	+	5.61617e8i	0.607968	+	0.351011i
$201$	−8.19368e8	+	5.78617e8i	−0.501990	+	0.354493i
$202$	−2.01465e8	−	3.48948e8i	−0.121003	−	0.209583i
$203$	−1.77188e9	+	1.02299e9i	−1.04340	+	0.602405i
$204$	5.25165e8	+	7.43676e8i	0.303232	+	0.429401i
$205$	9.59891e8	−	1.66258e9i	0.543509	−	0.941385i
$206$		−	9.84972e7i		−	0.0546959i
$207$	−5.30501e8	+	4.52411e8i	−0.288938	+	0.246406i
$208$	1.34874e8			0.0720567
$209$	1.04101e9	+	6.01029e8i	0.545595	+	0.315000i
$210$	−3.69521e9	−	1.70518e9i	−1.90004	−	0.876782i
$211$	−9.39137e8	−	1.62663e9i	−0.473804	−	0.820653i	0.525746	−	0.850642i	$-0.323786\pi$
$211$	−9.39137e8	−	1.62663e9i	−0.473804	−	0.820653i	−0.999550	+	0.0299884i	$0.990453\pi$
$212$	−1.16184e8	+	6.70786e7i	−0.0575176	+	0.0332078i
$213$	1.36788e9	−	1.25179e8i	0.664551	−	0.0608155i
$214$	−1.32563e9	+	2.29606e9i	−0.632074	+	1.09478i
$215$			1.14198e9i			0.534446i
$216$	7.40946e8	−	2.08080e8i	0.340386	−	0.0955906i
$217$	4.75349e9			2.14375
$218$	2.61107e9	+	1.50750e9i	1.15609	+	0.667471i
$219$	−1.79182e8	−	1.95798e9i	−0.0778964	−	0.851200i
$220$	6.71945e8	+	1.16384e9i	0.286842	+	0.496826i
$221$	−6.26011e8	+	3.61427e8i	−0.262430	+	0.151514i
$222$	−4.61324e8	+	9.99716e8i	−0.189930	+	0.411590i
$223$	1.45052e9	−	2.51237e9i	0.586548	−	1.01593i	−0.408132	−	0.912923i	$-0.633820\pi$
$223$	1.45052e9	−	2.51237e9i	0.586548	−	1.01593i	0.994680	−	0.103009i	$-0.0328470\pi$
$224$		−	7.62249e8i		−	0.302765i
$225$	−1.70227e9	+	4.79577e9i	−0.664198	+	1.87123i
$226$	−3.23411e9			−1.23971
$227$	3.60966e9	+	2.08404e9i	1.35945	+	0.784877i	0.989549	−	0.144195i	$-0.0460594\pi$
$227$	3.60966e9	+	2.08404e9i	1.35945	+	0.784877i	0.369898	+	0.929072i	$0.379393\pi$
$228$	−1.04715e9	+	7.39470e8i	−0.387497	+	0.273641i
$229$	1.80018e9	+	3.11801e9i	0.654599	+	1.13380i	0.981994	+	0.188911i	$0.0604957\pi$
$229$	1.80018e9	+	3.11801e9i	0.654599	+	1.13380i	−0.327396	+	0.944887i	$0.606171\pi$
$230$	1.12442e9	−	6.49184e8i	0.401807	−	0.231983i
$231$	−1.86798e9	−	2.64520e9i	−0.656030	−	0.928991i
$232$	−3.60260e8	+	6.23988e8i	−0.124355	+	0.215389i
$233$			2.86365e9i			0.971618i	0.874065	+	0.485809i	$0.161475\pi$
$233$			2.86365e9i			0.971618i	−0.874065	+	0.485809i	$0.838525\pi$
$234$	1.10912e8	+	6.00908e8i	0.0369925	+	0.200422i
$235$	−4.74719e9			−1.55656
$236$	−1.11366e9	−	6.42973e8i	−0.359009	−	0.207274i
$237$	9.39937e8	+	4.33739e8i	0.297924	+	0.137479i
$238$	2.04263e9	+	3.53795e9i	0.636624	+	1.10266i
$239$	1.21500e9	−	7.01479e8i	0.372378	−	0.214992i	−0.302119	−	0.953270i	$-0.597694\pi$
$239$	1.21500e9	−	7.01479e8i	0.372378	−	0.214992i	0.674497	+	0.738278i	$0.264361\pi$
$240$	−1.42722e9	+	1.30610e8i	−0.430176	+	0.0393670i
$241$	2.21808e9	−	3.84182e9i	0.657519	−	1.13886i	−0.323737	−	0.946147i	$-0.604939\pi$
$241$	2.21808e9	−	3.84182e9i	0.657519	−	1.13886i	0.981256	−	0.192709i	$-0.0617273\pi$
$242$		−	1.35585e9i		−	0.395320i
$243$	1.53637e9	+	3.13005e9i	0.440627	+	0.897690i
$244$	−1.06437e9			−0.300285
$245$	−1.04236e10	−	6.01805e9i	−2.89303	−	1.67029i
$246$	1.48464e8	+	1.62231e9i	0.0405396	+	0.442990i
$247$	−5.08916e8	−	8.81468e8i	−0.136728	−	0.236820i
$248$	1.44973e9	−	8.37001e8i	0.383248	−	0.221268i
$249$	1.09411e9	−	2.37100e9i	0.284619	−	0.616786i
$250$	2.35201e9	−	4.07381e9i	0.602116	−	1.04290i
$251$		−	2.42084e9i		−	0.609916i	−0.952366	−	0.304958i	$-0.901357\pi$
$251$		−	2.42084e9i		−	0.609916i	0.952366	−	0.304958i	$-0.0986425\pi$
$252$	3.39608e9	−	6.26825e8i	0.842123	−	0.155433i
$253$	1.03313e9			0.252157
$254$	−8.02210e8	−	4.63156e8i	−0.192732	−	0.111274i
$255$	6.27438e9	−	4.43081e9i	1.48392	−	1.04791i
$256$	−1.34218e8	−	2.32472e8i	−0.0312500	−	0.0541266i
$257$	−2.08915e9	+	1.20617e9i	−0.478891	+	0.276488i	−0.719954	−	0.694022i	$-0.755837\pi$
$257$	−2.08915e9	+	1.20617e9i	−0.478891	+	0.276488i	0.241063	+	0.970509i	$0.422504\pi$
$258$	−5.58995e8	−	7.91581e8i	−0.126162	−	0.178656i
$259$	−2.47029e9	+	4.27867e9i	−0.548971	+	0.950846i
$260$		−	1.13793e9i		−	0.249013i
$261$	−3.07633e9	−	1.09195e9i	−0.662935	−	0.235310i
$262$	4.28237e9			0.908822
$263$	5.65030e9	+	3.26220e9i	1.18100	+	0.681849i	0.956245	−	0.292567i	$-0.0945096\pi$
$263$	5.65030e9	+	3.26220e9i	1.18100	+	0.681849i	0.224752	+	0.974416i	$0.427843\pi$
$264$	−1.03547e9	−	4.77823e8i	−0.213168	−	0.0983674i
$265$	5.65941e8	+	9.80238e8i	0.114759	+	0.198769i
$266$	−4.98168e9	+	2.87617e9i	−0.995060	+	0.574498i
$267$	−1.69463e9	+	1.55082e8i	−0.333450	+	0.0305152i
$268$	−7.92554e8	+	1.37274e9i	−0.153635	+	0.266103i
$269$		−	6.64127e9i		−	1.26836i	−0.773186	−	0.634180i	$-0.781338\pi$
$269$		−	6.64127e9i		−	1.26836i	0.773186	−	0.634180i	$-0.218662\pi$
$270$	−1.75557e9	−	6.25134e9i	−0.330341	−	1.17630i
$271$	−2.72229e9			−0.504728			−0.252364	−	0.967632i	$-0.581208\pi$
$271$	−2.72229e9			−0.504728			−0.252364	+	0.967632i	$0.581208\pi$
$272$	1.24593e9	+	7.19339e8i	0.227624	+	0.131419i
$273$	2.49885e8	+	2.73057e9i	0.0449872	+	0.491590i
$274$	5.46649e8	+	9.46823e8i	0.0969853	+	0.167983i
$275$	6.53045e9	−	3.77036e9i	1.14186	−	0.659252i
$276$	−4.61637e8	+	1.00039e9i	−0.0795544	+	0.172399i
$277$	−5.00946e9	+	8.67663e9i	−0.850886	+	1.47378i	0.0295233	+	0.999564i	$0.490601\pi$
$277$	−5.00946e9	+	8.67663e9i	−0.850886	+	1.47378i	−0.880410	+	0.474214i	$0.842732\pi$
$278$		−	4.82484e9i		−	0.807799i
$279$	4.92128e9	+	5.77073e9i	0.812198	+	0.952388i
$280$	−6.43108e9			−1.04629
$281$	−6.83019e9	−	3.94341e9i	−1.09549	−	0.632480i	−0.160456	−	0.987043i	$-0.551296\pi$
$281$	−6.83019e9	−	3.94341e9i	−1.09549	−	0.632480i	−0.935032	+	0.354563i	$0.884630\pi$
$282$	3.29060e9	−	2.32374e9i	0.520329	−	0.367444i
$283$	4.86855e8	+	8.43258e8i	0.0759021	+	0.131466i	0.901478	−	0.432824i	$-0.142483\pi$
$283$	4.86855e8	+	8.43258e8i	0.0759021	+	0.131466i	−0.825576	+	0.564291i	$0.809150\pi$
$284$	1.87981e9	−	1.08531e9i	0.288962	−	0.166832i
$285$	6.23889e9	+	8.83477e9i	0.945645	+	1.33911i
$286$	4.52730e8	−	7.84152e8i	0.0676668	−	0.117202i
$287$			7.31016e9i			1.07746i
$288$	9.25369e8	−	7.89155e8i	0.134507	−	0.114708i
$289$	−7.34822e8			−0.105339
$290$	5.26458e9	+	3.03950e9i	0.744340	+	0.429745i
$291$	−6.56997e9	−	3.03175e9i	−0.916203	−	0.422787i
$292$	−1.55351e9	−	2.69076e9i	−0.213689	−	0.370121i
$293$	−4.59420e9	+	2.65246e9i	−0.623361	+	0.359898i	−0.778176	−	0.628046i	$-0.783855\pi$
$293$	−4.59420e9	+	2.65246e9i	−0.623361	+	0.359898i	0.154815	+	0.987943i	$0.450522\pi$
$294$	1.01711e10	−	9.30795e8i	1.36138	−	0.124585i
$295$	−5.42475e9	+	9.39595e9i	−0.716295	+	1.24066i
$296$			1.73989e9i			0.226649i
$297$	1.27736e9	−	5.00630e9i	0.164167	−	0.643414i
$298$	4.87854e9			0.618621
$299$	−7.57590e8	−	4.37395e8i	−0.0947871	−	0.0547254i
$300$	7.32868e8	+	8.00828e9i	0.0904775	+	0.988677i
$301$	−2.17422e9	−	3.76585e9i	−0.264872	−	0.458772i
$302$	−8.23578e9	+	4.75493e9i	−0.990095	+	0.571632i
$303$	1.20871e9	−	2.61933e9i	0.143400	−	0.310756i
$304$	−1.01288e9	+	1.75436e9i	−0.118594	+	0.205411i
$305$			8.98008e9i			1.03772i
$306$	−2.18032e9	+	6.14258e9i	−0.248677	+	0.700592i
$307$	1.34241e10			1.51124			0.755618	−	0.655013i	$-0.227337\pi$
$307$	1.34241e10			1.51124			0.755618	+	0.655013i	$0.227337\pi$
$308$	−4.43169e9	−	2.55864e9i	−0.492455	−	0.284319i
$309$	5.76035e8	−	4.06782e8i	0.0631852	−	0.0446198i
$310$	−7.06176e9	−	1.22313e10i	−0.764656	−	1.32442i
$311$	1.98291e9	−	1.14483e9i	0.211964	−	0.122377i	−0.390260	−	0.920705i	$-0.627615\pi$
$311$	1.98291e9	−	1.14483e9i	0.211964	−	0.122377i	0.602224	+	0.798327i	$0.294282\pi$
$312$	5.57013e8	+	7.88774e8i	0.0587823	+	0.0832404i
$313$	8.94161e9	−	1.54873e10i	0.931619	−	1.61361i	0.151065	−	0.988524i	$-0.451730\pi$
$313$	8.94161e9	−	1.54873e10i	0.931619	−	1.61361i	0.780555	−	0.625088i	$-0.214937\pi$
$314$			4.77256e9i			0.490945i
$315$	−5.28851e9	−	2.86527e10i	−0.537144	−	2.91020i
$316$	1.63585e9			0.164057
$317$	5.77404e9	+	3.33364e9i	0.571798	+	0.330128i	0.757867	−	0.652409i	$-0.226242\pi$
$317$	5.77404e9	+	3.33364e9i	0.571798	+	0.330128i	−0.186069	+	0.982537i	$0.559575\pi$
$318$	−8.72116e8	−	4.02442e8i	−0.0852836	−	0.0393546i
$319$	2.41856e9	+	4.18908e9i	0.233558	+	0.404535i
$320$	−1.96136e9	+	1.13239e9i	−0.187050	+	0.107993i
$321$	−1.89026e10	+	1.72985e9i	−1.78034	+	0.162925i
$322$	−2.47197e9	+	4.28158e9i	−0.229943	+	0.398272i
$323$		−	1.08570e10i		−	0.997474i
$324$	4.27692e9	+	3.47388e9i	0.388106	+	0.315235i
$325$	−6.38503e9			−0.572308
$326$	−5.39689e9	−	3.11590e9i	−0.477830	−	0.275875i
$327$	1.96718e9	+	2.14960e10i	0.172049	+	1.88004i
$328$	1.28718e9	+	2.22946e9i	0.111210	+	0.192622i
$329$	1.56546e10	−	9.03820e9i	1.33616	−	0.771433i
$330$	−4.03138e9	+	8.73623e9i	−0.339937	+	0.736662i
$331$	−7.84292e9	+	1.35843e10i	−0.653380	+	1.13169i	0.328918	+	0.944359i	$0.393316\pi$
$331$	−7.84292e9	+	1.35843e10i	−0.653380	+	1.13169i	−0.982297	+	0.187328i	$0.940017\pi$
$332$		−	4.12645e9i		−	0.339644i
$333$	−7.75179e9	+	1.43077e9i	−0.630413	+	0.116357i
$334$	6.86576e9			0.551700
$335$	1.15818e10	+	6.68676e9i	0.919597	+	0.530929i
$336$	4.45782e9	−	3.14800e9i	0.349756	−	0.246989i
$337$	−1.29188e9	−	2.23761e9i	−0.100162	−	0.173486i	0.811589	−	0.584229i	$-0.198603\pi$
$337$	−1.29188e9	−	2.23761e9i	−0.100162	−	0.173486i	−0.911751	+	0.410743i	$0.865270\pi$
$338$	7.32852e9	−	4.23112e9i	0.561500	−	0.324182i
$339$	−1.33565e10	−	1.89139e10i	−1.01133	−	1.43213i
$340$	6.06905e9	−	1.05119e10i	0.454156	−	0.786621i
$341$		−	1.12382e10i		−	0.831152i
$342$	−8.64919e9	−	3.07005e9i	−0.632224	−	0.224409i
$343$	2.21253e10			1.59850
$344$	−1.32619e9	−	7.65677e8i	−0.0947049	−	0.0546779i
$345$	8.44030e9	+	3.89482e9i	0.595774	+	0.274923i
$346$	−5.39944e9	−	9.35211e9i	−0.376742	−	0.652537i
$347$	1.45626e10	−	8.40775e9i	1.00444	−	0.579912i	0.0948784	−	0.995489i	$-0.469754\pi$
$347$	1.45626e10	−	8.40775e9i	1.00444	−	0.579912i	0.909558	+	0.415577i	$0.136420\pi$
$348$	−5.13706e9	+	4.70111e8i	−0.350266	+	0.0320541i
$349$	1.22366e10	−	2.11945e10i	0.824822	−	1.42863i	−0.0772336	−	0.997013i	$-0.524609\pi$
$349$	1.22366e10	−	2.11945e10i	0.824822	−	1.42863i	0.902055	−	0.431620i	$-0.142058\pi$
$350$			3.60855e10i			2.40470i
$351$	−3.05620e9	+	3.13032e9i	−0.201351	+	0.206234i
$352$	−1.80211e9			−0.117385
$353$	−9.05088e9	−	5.22553e9i	−0.582897	−	0.336536i	0.179387	−	0.983779i	$-0.442589\pi$
$353$	−9.05088e9	−	5.22553e9i	−0.582897	−	0.336536i	−0.762284	+	0.647243i	$0.775922\pi$
$354$	−8.39031e8	−	9.16836e9i	−0.0534275	−	0.583820i
$355$	−9.15672e9	−	1.58599e10i	−0.576536	−	0.998590i
$356$	−2.32885e9	+	1.34456e9i	−0.144991	+	0.0837108i
$357$	−1.22549e10	+	2.65571e10i	−0.754463	+	1.63496i
$358$	−5.34018e9	+	9.24946e9i	−0.325105	+	0.563098i
$359$			2.37497e10i			1.42982i	0.699219	+	0.714908i	$0.253531\pi$
$359$			2.37497e10i			1.42982i	−0.699219	+	0.714908i	$0.746469\pi$
$360$	−6.65809e9	−	7.80732e9i	−0.396405	−	0.464828i
$361$	−1.69607e9			−0.0998656
$362$	−8.50688e9	−	4.91145e9i	−0.495377	−	0.286006i
$363$	7.92931e9	−	5.59948e9i	0.456677	−	0.322494i
$364$	2.16651e9	+	3.75250e9i	0.123411	+	0.213754i
$365$	−2.27019e10	+	1.31069e10i	−1.27906	+	0.738464i
$366$	−4.39573e9	−	6.22470e9i	−0.244966	−	0.346892i
$367$	−5.17433e9	+	8.96220e9i	−0.285226	+	0.494027i	−0.972664	−	0.232217i	$-0.925402\pi$
$367$	−5.17433e9	+	8.96220e9i	−0.285226	+	0.494027i	0.687438	+	0.726243i	$0.258735\pi$
$368$			1.74107e9i			0.0949346i
$369$	−8.87452e9	+	7.56820e9i	−0.478674	+	0.408213i
$370$	1.46794e10			0.783252
$371$	−3.73256e9	−	2.15499e9i	−0.197020	−	0.113750i
$372$	1.08822e10	+	5.02164e9i	0.568256	+	0.262225i
$373$	4.02672e9	+	6.97448e9i	0.208025	+	0.360310i	0.951092	−	0.308907i	$-0.0999631\pi$
$373$	4.02672e9	+	6.97448e9i	0.208025	+	0.360310i	−0.743067	+	0.669217i	$0.766630\pi$
$374$	8.36443e9	−	4.82920e9i	0.427513	−	0.246825i
$375$	3.35382e10	−	3.06920e9i	1.69595	−	0.155203i
$376$	3.18291e9	−	5.51296e9i	0.159248	−	0.275825i
$377$		−	4.09580e9i		−	0.202756i
$378$	1.76912e10	+	1.72724e10i	0.866544	+	0.846028i
$379$	−2.63218e10			−1.27573			−0.637864	−	0.770149i	$-0.720182\pi$
$379$	−2.63218e10			−1.27573			−0.637864	+	0.770149i	$0.720182\pi$
$380$	1.48015e10	+	8.54565e9i	0.709858	+	0.409837i
$381$	−6.04383e8	−	6.60429e9i	−0.0286822	−	0.313420i
$382$	−3.98422e8	−	6.90087e8i	−0.0187107	−	0.0324079i
$383$	−2.64941e10	+	1.52964e10i	−1.23127	+	0.710876i	−0.967295	−	0.253653i	$-0.918368\pi$
$383$	−2.64941e10	+	1.52964e10i	−1.23127	+	0.710876i	−0.263978	+	0.964529i	$0.585035\pi$
$384$	8.05248e8	−	1.74502e9i	0.0370344	−	0.0802556i
$385$	−2.15872e10	+	3.73901e10i	−0.982547	+	1.70182i
$386$		−	3.09704e10i		−	1.39508i
$387$	2.32077e9	−	6.53827e9i	0.103464	−	0.291487i
$388$	−1.14343e10			−0.504523
$389$	3.76791e10	+	2.17540e10i	1.64552	+	0.950039i	0.978824	+	0.204704i	$0.0656233\pi$
$389$	3.76791e10	+	2.17540e10i	1.64552	+	0.950039i	0.666691	+	0.745334i	$0.267710\pi$
$390$	6.65487e9	−	4.69951e9i	0.287661	−	0.203139i
$391$	−4.66562e9	−	8.08109e9i	−0.199619	−	0.345751i
$392$	1.39777e10	−	8.07001e9i	0.591957	−	0.341767i
$393$	1.76857e10	+	2.50443e10i	0.741398	+	1.04988i
$394$	−3.09586e9	+	5.36219e9i	−0.128468	+	0.222514i
$395$		−	1.38016e10i		−	0.566947i
$396$	−1.48194e9	−	8.02902e9i	−0.0602629	−	0.326499i
$397$	4.31419e10			1.73675			0.868375	−	0.495908i	$-0.165165\pi$
$397$	4.31419e10			1.73675			0.868375	+	0.495908i	$0.165165\pi$
$398$	−2.61083e10	−	1.50737e10i	−1.04051	−	0.600740i
$399$	−3.73943e10	−	1.72558e10i	−1.47541	−	0.680838i
$400$	6.35397e9	+	1.10054e10i	0.248202	+	0.429899i
$401$	−1.57455e10	+	9.09069e9i	−0.608948	+	0.351576i	−0.772554	−	0.634950i	$-0.781021\pi$
$401$	−1.57455e10	+	9.09069e9i	−0.608948	+	0.351576i	0.163606	+	0.986526i	$0.447688\pi$
$402$	−1.13013e10	+	1.03422e9i	−0.432737	+	0.0396013i
$403$	−4.75794e9	+	8.24099e9i	−0.180384	+	0.312434i
$404$		−	4.55864e9i		−	0.171124i
$405$	2.93091e10	−	3.60843e10i	1.08939	−	1.34121i
$406$	−2.31477e10			−0.851930
$407$	1.01157e10	+	5.84028e9i	0.368652	+	0.212841i
$408$	9.38682e8	+	1.02573e10i	0.0338749	+	0.370162i
$409$	3.23724e9	+	5.60707e9i	0.115686	+	0.200374i	0.918054	−	0.396456i	$-0.129760\pi$
$409$	3.23724e9	+	5.60707e9i	0.115686	+	0.200374i	−0.802368	+	0.596830i	$0.796427\pi$
$410$	1.88099e10	−	1.08599e10i	0.665659	−	0.384319i
$411$	−3.27965e9	+	7.10720e9i	−0.114937	+	0.249076i
$412$	5.57184e8	−	9.65071e8i	0.0193379	−	0.0334943i
$413$		−	4.13128e10i		−	1.41999i
$414$	−7.75705e9	+	1.43174e9i	−0.264055	+	0.0487375i
$415$	−3.48148e10			−1.17374
$416$	1.32149e9	+	7.62961e8i	0.0441255	+	0.0254759i
$417$	2.82168e10	−	1.99260e10i	0.933176	−	0.658985i
$418$	6.79986e9	+	1.17777e10i	0.222738	+	0.385794i
$419$	−3.28096e10	+	1.89427e10i	−1.06450	+	0.614589i	−0.926673	−	0.375868i	$-0.877345\pi$
$419$	−3.28096e10	+	1.89427e10i	−1.06450	+	0.614589i	−0.137826	+	0.990456i	$0.544011\pi$
$420$	−2.65596e10	−	3.76105e10i	−0.853541	−	1.20868i
$421$	2.38781e10	−	4.13581e10i	0.760102	−	1.31654i	−0.182696	−	0.983170i	$-0.558482\pi$
$421$	2.38781e10	−	4.13581e10i	0.760102	−	1.31654i	0.942798	−	0.333366i	$-0.108184\pi$
$422$		−	2.12502e10i		−	0.670061i
$423$	2.71795e10	+	9.64744e9i	0.848947	+	0.301336i
$424$	−1.51782e9			−0.0469630
$425$	−5.89834e10	−	3.40541e10i	−1.80790	−	1.04379i
$426$	1.41105e10	+	6.51138e9i	0.428454	+	0.197713i
$427$	−1.70972e10	−	2.96133e10i	−0.514297	−	0.890789i
$428$	−2.59770e10	+	1.49978e10i	−0.774130	+	0.446944i
$429$	6.45563e9	−	5.90779e8i	0.190594	−	0.0174420i
$430$	−6.46000e9	+	1.11890e10i	−0.188955	+	0.327280i
$431$		−	2.73395e10i		−	0.792285i	−0.918189	−	0.396143i	$-0.870349\pi$
$431$		−	2.73395e10i		−	0.792285i	0.918189	−	0.396143i	$-0.129651\pi$
$432$	8.43683e9	+	2.15266e9i	0.242239	+	0.0618075i
$433$	−6.96958e9			−0.198269			−0.0991345	−	0.995074i	$-0.531607\pi$
$433$	−6.96958e9			−0.198269			−0.0991345	+	0.995074i	$0.531607\pi$
$434$	4.65745e10	+	2.68898e10i	1.31277	+	0.757930i
$435$	3.96632e9	+	4.33413e10i	0.110772	+	1.21044i
$436$	1.70555e10	+	2.95409e10i	0.471973	+	0.817482i
$437$	1.13788e10	−	6.56953e9i	0.312010	−	0.180139i
$438$	9.32038e9	−	2.01978e10i	0.253243	−	0.548792i
$439$	4.26214e9	−	7.38223e9i	0.114754	−	0.198760i	−0.802927	−	0.596077i	$-0.796725\pi$
$439$	4.26214e9	−	7.38223e9i	0.114754	−	0.198760i	0.917682	+	0.397317i	$0.130059\pi$
$440$			1.52044e10i			0.405656i
$441$	4.74489e10	+	5.56389e10i	1.25450	+	1.47104i
$442$	−8.17817e9			−0.214273
$443$	−1.77214e10	−	1.02315e10i	−0.460134	−	0.265658i	0.251967	−	0.967736i	$-0.418923\pi$
$443$	−1.77214e10	−	1.02315e10i	−0.460134	−	0.265658i	−0.712101	+	0.702077i	$0.752256\pi$
$444$	−1.01753e10	+	7.18553e9i	−0.261827	+	0.184896i
$445$	1.13441e10	+	1.96485e10i	0.289287	+	0.501060i
$446$	2.84242e10	−	1.64107e10i	0.718372	−	0.414752i
$447$	2.01478e10	+	2.85309e10i	0.504658	+	0.714636i
$448$	4.31193e9	−	7.46849e9i	0.107043	−	0.185405i
$449$			1.52992e10i			0.376430i	0.982128	+	0.188215i	$0.0602702\pi$
$449$			1.52992e10i			0.376430i	−0.982128	+	0.188215i	$0.939730\pi$
$450$	−4.38077e10	+	3.73592e10i	−1.06832	+	0.911062i
$451$	1.72827e10			0.417740
$452$	−3.16877e10	−	1.82949e10i	−0.759166	−	0.438305i
$453$	−6.18207e10	−	2.85275e10i	−1.46805	−	0.677440i
$454$	2.35782e10	+	4.08386e10i	0.554992	+	0.961274i
$455$	3.16597e10	−	1.82788e10i	0.738689	−	0.426483i
$456$	−1.44430e10	+	1.32173e9i	−0.334039	+	0.0305692i
$457$	−1.20106e10	+	2.08029e10i	−0.275359	+	0.476935i	−0.970226	−	0.242203i	$-0.922130\pi$
$457$	−1.20106e10	+	2.08029e10i	−0.275359	+	0.476935i	0.694867	+	0.719138i	$0.255463\pi$
$458$			4.07335e10i			0.925742i
$459$	−4.49278e10	+	1.26171e10i	−1.01219	+	0.284255i
$460$	1.46894e10			0.328074
$461$	4.96796e10	+	2.86825e10i	1.09995	+	0.635058i	0.936209	−	0.351445i	$-0.114310\pi$
$461$	4.96796e10	+	2.86825e10i	1.09995	+	0.635058i	0.163744	+	0.986503i	$0.447643\pi$
$462$	−3.33883e9	−	3.64845e10i	−0.0732869	−	0.800830i
$463$	3.03202e10	+	5.25162e10i	0.659795	+	1.14280i	0.980669	+	0.195676i	$0.0626900\pi$
$463$	3.03202e10	+	5.25162e10i	0.659795	+	1.14280i	−0.320874	+	0.947122i	$0.603977\pi$
$464$	−7.05962e9	+	4.07587e9i	−0.152303	+	0.0879324i
$465$	4.23675e10	−	9.18128e10i	0.906194	−	1.96377i
$466$	−1.61992e10	+	2.80579e10i	−0.343519	+	0.594992i
$467$			1.01091e10i			0.212543i	0.994337	+	0.106271i	$0.0338912\pi$
$467$			1.01091e10i			0.212543i	−0.994337	+	0.106271i	$0.966109\pi$
$468$	−2.31254e9	+	6.51509e9i	−0.0482066	+	0.135812i
$469$	−5.09238e10			−1.05252
$470$	−4.65128e10	−	2.68542e10i	−0.953193	−	0.550326i
$471$	−2.79111e10	+	1.97101e10i	−0.567143	+	0.400502i
$472$	−7.27441e9	−	1.25996e10i	−0.146565	−	0.253858i
$473$	−8.90324e9	+	5.14029e9i	−0.177870	+	0.102693i
$474$	6.75587e9	+	9.56684e9i	0.133834	+	0.189520i
$475$	4.79505e10	−	8.30528e10i	0.941931	−	1.63147i
$476$			4.62195e10i			0.900322i
$477$	−1.24815e9	−	6.76238e9i	−0.0241099	−	0.130625i
$478$	1.58727e10			0.304045
$479$	1.87971e10	+	1.08525e10i	0.357067	+	0.206153i	0.667793	−	0.744347i	$-0.267239\pi$
$479$	1.87971e10	+	1.08525e10i	0.357067	+	0.206153i	−0.310727	+	0.950499i	$0.600572\pi$
$480$	−1.47227e10	−	6.79386e9i	−0.277346	−	0.127983i
$481$	−4.94520e9	−	8.56534e9i	−0.0923855	−	0.160016i
$482$	4.34652e10	−	2.50947e10i	0.805293	−	0.464936i
$483$	−3.52486e10	+	3.22573e9i	−0.647670	+	0.0592706i
$484$	7.66982e9	−	1.32845e10i	0.139767	−	0.242083i
$485$			9.64707e10i			1.74353i
$486$	−2.65293e9	+	3.93592e10i	−0.0475533	+	0.705506i
$487$	−5.82792e9			−0.103609			−0.0518045	−	0.998657i	$-0.516497\pi$
$487$	−5.82792e9			−0.103609			−0.0518045	+	0.998657i	$0.516497\pi$
$488$	−1.04287e10	−	6.02100e9i	−0.183886	−	0.106167i
$489$	−4.06601e9	−	4.44306e10i	−0.0711103	−	0.777046i
$490$	−6.80865e10	−	1.17929e11i	−1.18107	−	2.04568i
$491$	−2.15718e10	+	1.24545e10i	−0.371159	+	0.214288i	−0.673964	−	0.738764i	$-0.735410\pi$
$491$	−2.15718e10	+	1.24545e10i	−0.371159	+	0.214288i	0.302806	+	0.953052i	$0.402077\pi$
$492$	−7.72253e9	+	1.67352e10i	−0.131795	+	0.285607i
$493$	2.18446e10	−	3.78360e10i	0.369791	−	0.640497i
$494$		−	1.15154e10i		−	0.193363i
$495$	−6.77407e10	+	1.25031e10i	−1.12831	+	0.208256i
$496$	1.89392e10			0.312921
$497$	6.03915e10	+	3.48670e10i	0.989806	+	0.571465i
$498$	2.41325e10	−	1.70417e10i	0.392360	−	0.277075i
$499$	−8.19755e9	−	1.41986e10i	−0.132215	−	0.229004i	0.792315	−	0.610112i	$-0.208876\pi$
$499$	−8.19755e9	−	1.41986e10i	−0.132215	−	0.229004i	−0.924530	+	0.381109i	$0.875542\pi$
$500$	4.60899e10	−	2.66100e10i	0.737438	−	0.425760i
$501$	2.83548e10	+	4.01526e10i	0.450065	+	0.637328i
$502$	1.36943e10	−	2.37192e10i	0.215638	−	0.373496i
$503$		−	4.61285e10i		−	0.720606i	−0.932835	−	0.360303i	$-0.882673\pi$
$503$		−	4.61285e10i		−	0.720606i	0.932835	−	0.360303i	$-0.117327\pi$
$504$	3.68205e10	+	1.30695e10i	0.570647	+	0.202552i
$505$	−3.84612e10			−0.591367
$506$	1.01225e10	+	5.84424e9i	0.154414	+	0.0891509i
$507$	5.50105e10	+	2.53849e10i	0.832557	+	0.384188i
$508$	−5.24001e9	−	9.07597e9i	−0.0786824	−	0.136282i
$509$	−6.69443e9	+	3.86503e9i	−0.0997339	+	0.0575814i	−0.549037	−	0.835798i	$-0.685006\pi$
$509$	−6.69443e9	+	3.86503e9i	−0.0997339	+	0.0575814i	0.449303	+	0.893379i	$0.351672\pi$
$510$	8.65405e10	−	7.91964e9i	1.27920	−	0.117064i
$511$	4.99087e10	−	8.64444e10i	0.731969	−	1.26781i
$512$		−	3.03700e9i		−	0.0441942i
$513$	−1.77657e10	−	6.32615e10i	−0.256516	−	0.913419i
$514$	−2.72925e10			−0.391013
$515$	−8.14229e9	−	4.70095e9i	−0.115749	−	0.0668278i
$516$	−9.99150e8	−	1.09180e10i	−0.0140939	−	0.154009i
$517$	−2.13681e10	−	3.70107e10i	−0.299092	−	0.518042i
$518$	−4.84077e10	+	2.79482e10i	−0.672349	+	0.388181i
$519$	3.23943e10	−	7.02003e10i	0.446477	−	0.967541i
$520$	6.43709e9	−	1.11494e10i	0.0880392	−	0.152488i
$521$			3.97902e10i			0.540039i	0.962855	+	0.270019i	$0.0870301\pi$
$521$			3.97902e10i			0.540039i	−0.962855	+	0.270019i	$0.912970\pi$
$522$	−2.39648e10	−	2.81013e10i	−0.322769	−	0.378481i
$523$	−3.49978e10			−0.467772			−0.233886	−	0.972264i	$-0.575144\pi$
$523$	−3.49978e10			−0.467772			−0.233886	+	0.972264i	$0.575144\pi$
$524$	4.19585e10	+	2.42247e10i	0.556538	+	0.321317i
$525$	−2.11037e11	+	1.49029e11i	−2.77792	+	1.96170i
$526$	3.69076e10	+	6.39259e10i	0.482140	+	0.835091i
$527$	−8.79053e10	+	5.07521e10i	−1.13965	+	0.657979i
$528$	−7.44251e9	−	1.05392e10i	−0.0957599	−	0.135604i
$529$	−3.35092e10	+	5.80397e10i	−0.427899	+	0.741143i
$530$			1.28058e10i			0.162294i
$531$	5.01537e10	−	4.27711e10i	0.630848	−	0.537988i
$532$	−6.50804e10			−0.812463
$533$	−1.26734e10	−	7.31699e9i	−0.157031	−	0.0906617i
$534$	−1.74812e10	−	8.06681e9i	−0.214984	−	0.0992057i
$535$	1.26536e11	+	2.19167e11i	1.54454	+	2.67523i
$536$	−1.55308e10	+	8.96673e9i	−0.188163	+	0.108636i
$537$	−7.61474e10	+	6.96853e9i	−0.915709	+	0.0838000i
$538$	3.75687e10	−	6.50709e10i	0.448433	−	0.776708i
$539$		−	1.08354e11i		−	1.28378i
$540$	1.81620e10	−	7.11814e10i	0.213593	−	0.837127i
$541$	2.34001e10			0.273168			0.136584	−	0.990629i	$-0.456388\pi$
$541$	2.34001e10			0.273168			0.136584	+	0.990629i	$0.456388\pi$
$542$	−2.66729e10	−	1.53996e10i	−0.309081	−	0.178448i
$543$	−6.40907e9	−	7.00340e10i	−0.0737218	−	0.805582i
$544$	8.13839e9	+	1.40961e10i	0.0929272	+	0.160955i
$545$	2.49236e11	−	1.43897e11i	2.82504	−	1.63104i
$546$	−1.29981e10	+	2.81676e10i	−0.146254	+	0.316942i
$547$	−1.16091e10	+	2.01075e10i	−0.129673	+	0.224600i	−0.923550	−	0.383478i	$-0.874726\pi$
$547$	−1.16091e10	+	2.01075e10i	−0.129673	+	0.224600i	0.793877	+	0.608078i	$0.208059\pi$
$548$			1.23692e10i			0.137158i
$549$	1.82497e10	−	5.14145e10i	0.200894	−	0.565974i
$550$	8.53134e10			0.932324
$551$	5.32757e10	+	3.07588e10i	0.577994	+	0.333705i
$552$	−1.01822e10	+	7.19040e9i	−0.109669	+	0.0774456i
$553$	2.62770e10	+	4.55131e10i	0.280980	+	0.486671i
$554$	−9.81649e10	+	5.66755e10i	−1.04212	+	0.601667i
$555$	6.06242e10	+	8.58486e10i	0.638960	+	0.904819i
$556$	2.72934e10	−	4.72735e10i	0.285600	−	0.494674i
$557$		−	3.65617e10i		−	0.379844i	−0.981799	−	0.189922i	$-0.939176\pi$
$557$		−	3.65617e10i		−	0.379844i	0.981799	−	0.189922i	$-0.0608236\pi$
$558$	1.55744e10	+	8.43804e10i	0.160647	+	0.870372i
$559$	8.70499e9			0.0891499
$560$	−6.30115e10	−	3.63797e10i	−0.640719	−	0.369919i
$561$	6.27864e10	+	2.89731e10i	0.633891	+	0.292512i
$562$	−4.46146e10	−	7.72748e10i	−0.447231	−	0.774627i
$563$	−1.15433e11	+	6.66450e10i	−1.14893	+	0.663337i	−0.948627	−	0.316397i	$-0.897527\pi$
$563$	−1.15433e11	+	6.66450e10i	−1.14893	+	0.663337i	−0.200306	+	0.979733i	$0.564194\pi$
$564$	4.53862e10	−	4.15346e9i	0.448546	−	0.0410481i
$565$	−1.54354e11	+	2.67348e11i	−1.51469	+	2.62352i
$566$			1.10163e10i			0.107342i
$567$	−2.79503e10	+	1.74795e11i	−0.270430	+	1.69121i
$568$	2.45577e10			0.235936
$569$	−1.42643e11	−	8.23549e10i	−1.36082	−	0.785670i	−0.371087	−	0.928598i	$-0.621015\pi$
$569$	−1.42643e11	−	8.23549e10i	−1.36082	−	0.785670i	−0.989733	+	0.142928i	$0.954348\pi$
$570$	1.11514e10	+	1.21855e11i	0.105641	+	1.15437i
$571$	−6.84597e10	−	1.18576e11i	−0.644007	−	1.11545i	−0.984530	−	0.175216i	$-0.943937\pi$
$571$	−6.84597e10	−	1.18576e11i	−0.644007	−	1.11545i	0.340523	−	0.940236i	$-0.389396\pi$
$572$	8.87167e9	−	5.12206e9i	0.0828745	−	0.0478476i
$573$	2.39036e9	−	5.18004e9i	0.0221740	−	0.0480524i
$574$	−4.13525e10	+	7.16247e10i	−0.380938	+	0.659804i
$575$		−	8.24235e10i		−	0.754015i
$576$	1.35309e10	−	2.49743e9i	0.122924	−	0.0226884i
$577$	−1.01555e11			−0.916218			−0.458109	−	0.888896i	$-0.651473\pi$
$577$	−1.01555e11			−0.916218			−0.458109	+	0.888896i	$0.651473\pi$
$578$	−7.19976e9	−	4.15678e9i	−0.0645070	−	0.0372431i
$579$	1.81122e11	−	1.27904e11i	1.61160	−	1.13807i
$580$	3.43881e10	+	5.95619e10i	0.303876	+	0.526328i
$581$	1.14807e11	−	6.62840e10i	1.00755	−	0.581707i
$582$	−4.72222e10	−	6.68703e10i	−0.411580	−	0.582829i
$583$	−5.09485e9	+	8.82453e9i	−0.0441018	+	0.0763866i
$584$		−	3.51519e10i		−	0.302202i
$585$	5.49677e10	+	1.95109e10i	0.469336	+	0.166592i
$586$	−6.00184e10			−0.508972
$587$	−3.25669e10	−	1.88025e10i	−0.274299	−	0.158367i	0.356541	−	0.934280i	$-0.383956\pi$
$587$	−3.25669e10	−	1.88025e10i	−0.274299	−	0.158367i	−0.630840	+	0.775913i	$0.717289\pi$
$588$	1.04921e11	+	4.84165e10i	0.877717	+	0.405027i
$589$	−7.14626e10	−	1.23777e11i	−0.593769	−	1.02844i
$590$	−1.06303e11	+	6.13741e10i	−0.877278	+	0.506497i
$591$	−4.41449e10	+	4.03986e9i	−0.361852	+	0.0331144i
$592$	−9.84229e9	+	1.70474e10i	−0.0801326	+	0.138794i
$593$			1.30215e11i			1.05304i	0.850163	+	0.526519i	$0.176503\pi$
$593$			1.30215e11i			1.05304i	−0.850163	+	0.526519i	$0.823497\pi$
$594$	4.08354e10	−	4.18256e10i	0.328013	−	0.335967i
$595$	3.89953e11			3.11132
$596$	4.77998e10	+	2.75972e10i	0.378827	+	0.218716i
$597$	−1.96700e10	−	2.14940e11i	−0.154848	−	1.69208i
$598$	−4.94856e9	−	8.57115e9i	−0.0386967	−	0.0670246i
$599$	1.13848e11	−	6.57304e10i	0.884341	−	0.510575i	0.0122537	−	0.999925i	$-0.496099\pi$
$599$	1.13848e11	−	6.57304e10i	0.884341	−	0.510575i	0.872087	+	0.489350i	$0.162766\pi$
$600$	−3.81211e10	+	8.26106e10i	−0.294144	+	0.637427i
$601$	2.15092e10	−	3.72550e10i	0.164864	−	0.285553i	−0.771743	−	0.635935i	$-0.780615\pi$
$601$	2.15092e10	−	3.72550e10i	0.164864	−	0.285553i	0.936607	+	0.350382i	$0.113948\pi$
$602$		−	4.91969e10i		−	0.374586i
$603$	−5.27213e10	−	6.18214e10i	−0.398765	−	0.467595i
$604$	−1.07592e11			−0.808409
$605$	−1.12081e11	−	6.47102e10i	−0.836588	−	0.483004i
$606$	2.66600e10	−	1.88266e10i	0.197683	−	0.139599i
$607$	−1.29606e10	−	2.24485e10i	−0.0954710	−	0.165361i	0.814334	−	0.580396i	$-0.197102\pi$
$607$	−1.29606e10	−	2.24485e10i	−0.0954710	−	0.165361i	−0.909805	+	0.415036i	$0.863769\pi$
$608$	−1.98483e10	+	1.14594e10i	−0.145248	+	0.0838588i
$609$	−9.55972e10	−	1.35373e11i	−0.694986	−	0.984156i
$610$	−5.07990e10	+	8.79865e10i	−0.366890	+	0.635472i
$611$			3.61866e10i			0.259646i
$612$	−5.61104e10	+	4.78510e10i	−0.399980	+	0.341103i
$613$	1.28485e11			0.909933			0.454967	−	0.890508i	$-0.349651\pi$
$613$	1.28485e11			0.909933			0.454967	+	0.890508i	$0.349651\pi$
$614$	1.31529e11	+	7.59383e10i	0.925439	+	0.534303i
$615$	1.41194e11	+	6.51549e10i	0.986999	+	0.455456i
$616$	−2.89477e10	−	5.01389e10i	−0.201044	−	0.348219i
$617$	−1.02289e11	+	5.90563e10i	−0.705808	+	0.407498i	−0.809507	−	0.587110i	$-0.800265\pi$
$617$	−1.02289e11	+	5.90563e10i	−0.705808	+	0.407498i	0.103699	+	0.994609i	$0.466932\pi$
$618$	7.94507e9	−	7.27083e8i	0.0544683	−	0.00498460i
$619$	−6.40218e10	+	1.10889e11i	−0.436079	+	0.755312i	−0.997383	−	0.0722982i	$-0.976967\pi$
$619$	−6.40218e10	+	1.10889e11i	−0.436079	+	0.755312i	0.561304	+	0.827610i	$0.310300\pi$
$620$		−	1.59789e11i		−	1.08139i
$621$	−4.04089e10	−	3.94521e10i	−0.271713	−	0.265280i
$622$	2.59046e10			0.173068
$623$	−7.48177e10	−	4.31960e10i	−0.496652	−	0.286742i
$624$	9.95606e8	+	1.08793e10i	0.00656673	+	0.0717568i
$625$	−7.30176e10	−	1.26470e11i	−0.478528	−	0.828835i
$626$	1.75219e11	−	1.01163e11i	1.14100	−	0.658754i
$627$	−4.07962e10	+	8.84077e10i	−0.263967	+	0.572032i
$628$	−2.69977e10	+	4.67613e10i	−0.173575	+	0.300641i
$629$		−	1.05499e11i		−	0.673980i
$630$	1.10267e11	−	3.10654e11i	0.699978	−	1.97203i
$631$	−2.40613e11			−1.51775			−0.758877	−	0.651233i	$-0.774252\pi$
$631$	−2.40613e11			−1.51775			−0.758877	+	0.651233i	$0.774252\pi$
$632$	1.60280e10	+	9.25377e9i	0.100464	+	0.0580030i
$633$	1.24277e11	−	8.77610e10i	0.774059	−	0.546621i
$634$	3.77159e10	+	6.53258e10i	0.233436	+	0.404322i
$635$	−7.65738e10	+	4.42099e10i	−0.470961	+	0.271910i
$636$	−6.26840e9	−	8.87655e9i	−0.0383114	−	0.0542520i
$637$	−4.58740e10	+	7.94561e10i	−0.278618	+	0.482580i
$638$			5.47259e10i			0.330301i
$639$	2.01947e10	+	1.09413e11i	0.121125	+	0.656244i
$640$	−2.56231e10			−0.152726
$641$	1.87111e11	+	1.08029e11i	1.10833	+	0.639893i	0.938396	−	0.345563i	$-0.112312\pi$
$641$	1.87111e11	+	1.08029e11i	1.10833	+	0.639893i	0.169932	+	0.985456i	$0.445645\pi$
$642$	−1.94993e11	−	8.99804e10i	−1.14783	−	0.529673i
$643$	−1.85669e10	−	3.21588e10i	−0.108616	−	0.188129i	0.806594	−	0.591106i	$-0.201309\pi$
$643$	−1.85669e10	−	3.21588e10i	−0.108616	−	0.188129i	−0.915210	+	0.402977i	$0.867975\pi$
$644$	−4.84405e10	+	2.79671e10i	−0.281621	+	0.162594i
$645$	−9.21153e10	+	8.42981e9i	−0.532222	+	0.0487056i
$646$	6.14167e10	−	1.06377e11i	0.352660	−	0.610825i
$647$			5.88598e10i			0.335894i	0.985796	+	0.167947i	$0.0537137\pi$
$647$			5.88598e10i			0.335894i	−0.985796	+	0.167947i	$0.946286\pi$
$648$	2.22538e10	+	5.82309e10i	0.126213	+	0.330258i
$649$	−9.76719e10			−0.550543
$650$	−6.25603e10	−	3.61192e10i	−0.350465	−	0.202341i
$651$	3.50892e10	+	3.83431e11i	0.195366	+	2.13483i
$652$	−3.52523e10	−	6.10588e10i	−0.195073	−	0.337877i
$653$	−1.48938e11	+	8.59893e10i	−0.819129	+	0.472925i	−0.850116	−	0.526595i	$-0.823468\pi$
$653$	−1.48938e11	+	8.59893e10i	−0.819129	+	0.472925i	0.0309867	+	0.999520i	$0.490135\pi$
$654$	−1.02325e11	+	2.21745e11i	−0.559335	+	1.21211i
$655$	2.04384e11	−	3.54003e11i	1.11040	−	1.92328i
$656$			2.91256e10i			0.157275i
$657$	1.56614e11	−	2.89067e10i	0.840559	−	0.155145i
$658$	2.04511e11			1.09097
$659$	2.34850e11	+	1.35591e11i	1.24523	+	0.718934i	0.970154	−	0.242489i	$-0.0779639\pi$
$659$	2.34850e11	+	1.35591e11i	1.24523	+	0.718934i	0.275075	+	0.961423i	$0.411297\pi$
$660$	−8.89189e10	+	6.27923e10i	−0.468617	+	0.330926i
$661$	1.21597e11	+	2.10613e11i	0.636968	+	1.10326i	0.986095	+	0.166185i	$0.0531451\pi$
$661$	1.21597e11	+	2.10613e11i	0.636968	+	1.10326i	−0.349126	+	0.937076i	$0.613522\pi$
$662$	−1.53689e11	+	8.87325e10i	−0.800223	+	0.462009i
$663$	−3.37749e10	−	4.78279e10i	−0.174799	−	0.247530i
$664$	2.33427e10	−	4.04308e10i	0.120082	−	0.207989i
$665$			5.49082e11i			2.80770i
$666$	−8.40454e10	−	2.98321e10i	−0.427186	−	0.151631i
$667$	5.28721e10			0.267130
$668$	6.72704e10	+	3.88386e10i	0.337846	+	0.195055i
$669$	2.13363e11	+	9.84574e10i	1.06516	+	0.491523i
$670$	7.56521e10	+	1.31033e11i	0.375424	+	0.650253i
$671$	−7.00118e10	+	4.04213e10i	−0.345367	+	0.199398i
$672$	6.14853e10	−	5.62674e9i	0.301505	−	0.0275918i
$673$	1.44609e10	−	2.50471e10i	0.0704914	−	0.122095i	−0.828625	−	0.559804i	$-0.810877\pi$
$673$	1.44609e10	−	2.50471e10i	0.0704914	−	0.122095i	0.899117	+	0.437709i	$0.144210\pi$
$674$		−	2.92320e10i		−	0.141651i
$675$	−3.99406e11	−	1.01909e11i	−1.92398	−	0.490904i
$676$	9.57394e10			0.458463
$677$	1.58076e11	+	9.12654e10i	0.752509	+	0.434462i	0.826600	−	0.562790i	$-0.190272\pi$
$677$	1.58076e11	+	9.12654e10i	0.752509	+	0.434462i	−0.0740905	+	0.997252i	$0.523605\pi$
$678$	−2.38734e10	−	2.60873e11i	−0.112979	−	1.23455i
$679$	−1.83671e11	−	3.18127e11i	−0.864095	−	1.49666i
$680$	1.18929e11	−	6.86634e10i	0.556225	−	0.321137i
$681$	−1.41459e11	+	3.06549e11i	−0.657721	+	1.42532i
$682$	6.35730e10	−	1.10112e11i	0.293857	−	0.508974i
$683$		−	3.71514e11i		−	1.70723i	−0.520903	−	0.853616i	$-0.674405\pi$
$683$		−	3.71514e11i		−	1.70723i	0.520903	−	0.853616i	$-0.325595\pi$
$684$	−6.73776e10	−	7.90075e10i	−0.307816	−	0.360947i
$685$	1.04359e11			0.473989
$686$	2.16783e11	+	1.25159e11i	0.978876	+	0.565155i
$687$	−2.38219e11	+	1.68225e11i	−1.06942	+	0.755201i
$688$	−8.66264e9	−	1.50041e10i	−0.0386631	−	0.0669665i
$689$	7.47209e9	−	4.31401e9i	0.0331562	−	0.0191428i
$690$	6.06653e10	+	8.59069e10i	0.267636	+	0.378993i
$691$	−9.88238e10	+	1.71168e11i	−0.433460	+	0.750775i	−0.997169	−	0.0751987i	$-0.976041\pi$
$691$	−9.88238e10	+	1.71168e11i	−0.433460	+	0.750775i	0.563708	+	0.825974i	$0.309374\pi$
$692$		−	1.22175e11i		−	0.532794i
$693$	1.99581e11	−	1.70203e11i	0.865339	−	0.737962i
$694$	1.90246e11			0.820119
$695$	−3.98846e11	−	2.30274e11i	−1.70949	−	0.986973i
$696$	−5.29921e10	−	2.44535e10i	−0.225826	−	0.104209i
$697$	−7.80492e10	−	1.35185e11i	−0.330702	−	0.572793i
$698$	2.39788e11	−	1.38442e11i	1.01020	−	0.583237i
$699$	−2.30990e11	+	2.11388e10i	−0.967575	+	0.0885464i
$700$	−2.04130e11	+	3.53564e11i	−0.850189	+	1.47257i
$701$		−	6.70096e10i		−	0.277501i	−0.990327	−	0.138751i	$-0.955691\pi$
$701$		−	6.70096e10i		−	0.277501i	0.990327	−	0.138751i	$-0.0443087\pi$
$702$	−4.76523e10	+	1.33822e10i	−0.196217	+	0.0551035i
$703$	1.48551e11			0.608209
$704$	−1.76570e10	−	1.01943e10i	−0.0718831	−	0.0415017i
$705$	−3.50426e10	−	3.82922e11i	−0.141854	−	1.55008i
$706$	−5.91201e10	−	1.02399e11i	−0.237967	−	0.412170i
$707$	1.26832e11	−	7.32264e10i	0.507634	−	0.293083i
$708$	4.36433e10	−	9.45775e10i	0.173694	−	0.376405i
$709$	5.70291e10	−	9.87774e10i	0.225690	−	0.390906i	−0.730836	−	0.682553i	$-0.760870\pi$
$709$	5.70291e10	−	9.87774e10i	0.225690	−	0.390906i	0.956526	+	0.291647i	$0.0942031\pi$
$710$		−	2.07193e11i		−	0.815345i
$711$	−2.80483e10	+	7.90198e10i	−0.109756	+	0.309213i
$712$	−3.04240e10			−0.118385
$713$	−1.06382e11	−	6.14196e10i	−0.411632	−	0.237656i
$714$	−2.70303e11	+	1.90881e11i	−1.04006	+	0.734464i
$715$	−4.32147e10	−	7.48501e10i	−0.165351	−	0.286397i
$716$	−1.04646e11	+	6.04172e10i	−0.398171	+	0.229884i
$717$	6.55522e10	+	9.28271e10i	0.248034	+	0.351235i
$718$	−1.34348e11	+	2.32698e11i	−0.505516	+	0.875580i
$719$			2.31072e11i			0.864633i	0.901722	+	0.432317i	$0.142304\pi$
$719$			2.31072e11i			0.864633i	−0.901722	+	0.432317i	$0.857696\pi$
$720$	−2.10708e10	−	1.14160e11i	−0.0784063	−	0.424798i
$721$	3.58007e10			0.132480
$722$	−1.66181e10	−	9.59444e9i	−0.0611549	−	0.0353078i
$723$	3.26266e11	+	1.50557e11i	1.19404	+	0.550995i
$724$	−5.55667e10	−	9.62444e10i	−0.202237	−	0.350285i
$725$	3.34208e11	−	1.92955e11i	1.20966	−	0.698400i
$726$	1.09367e11	−	1.00085e10i	0.393675	−	0.0360267i
$727$	1.70637e11	−	2.95551e11i	0.610850	−	1.05802i	−0.380248	−	0.924885i	$-0.624161\pi$
$727$	1.70637e11	−	2.95551e11i	0.610850	−	1.05802i	0.991097	−	0.133138i	$-0.0425055\pi$
$728$			4.90224e10i			0.174530i
$729$	−2.41138e11	+	1.47034e11i	−0.853799	+	0.520603i
$730$	−2.96576e11			−1.04435
$731$	8.04145e10	+	4.64274e10i	0.281621	+	0.162594i
$732$	−7.85694e9	−	8.58554e10i	−0.0273659	−	0.299036i
$733$	2.07203e11	+	3.58887e11i	0.717763	+	1.24320i	0.961884	+	0.273457i	$0.0881670\pi$
$733$	2.07203e11	+	3.58887e11i	0.717763	+	1.24320i	−0.244122	+	0.969745i	$0.578500\pi$
$734$	−1.01396e11	+	5.85408e10i	−0.349330	+	0.201685i
$735$	4.08489e11	−	8.85220e11i	1.39969	−	3.03320i
$736$	−9.84897e9	+	1.70589e10i	−0.0335645	+	0.0581353i
$737$			1.20394e11i			0.408071i
$738$	−1.29764e11	+	2.39510e10i	−0.437452	+	0.0807418i
$739$	2.71838e11			0.911449			0.455725	−	0.890121i	$-0.349380\pi$
$739$	2.71838e11			0.911449			0.455725	+	0.890121i	$0.349380\pi$
$740$	1.43828e11	+	8.30392e10i	0.479642	+	0.276921i
$741$	6.73451e10	−	4.75574e10i	0.223374	−	0.157741i
$742$	−2.43810e10	−	4.22291e10i	−0.0804332	−	0.139314i
$743$	−2.96676e11	+	1.71286e11i	−0.973479	+	0.562039i	−0.900295	−	0.435280i	$-0.856649\pi$
$743$	−2.96676e11	+	1.71286e11i	−0.973479	+	0.562039i	−0.0731842	+	0.997318i	$0.523316\pi$
$744$	7.82165e10	+	1.10761e11i	0.255274	+	0.361488i
$745$	2.32837e11	−	4.03286e11i	0.755835	−	1.30914i
$746$			9.11142e10i			0.294192i
$747$	1.99328e11	+	7.07521e10i	0.640157	+	0.227225i
$748$	1.09272e11			0.349063
$749$	−8.34547e11	−	4.81826e11i	−2.65170	−	1.53096i
$750$	3.45967e11	+	1.59649e11i	1.09343	+	0.504568i
$751$	−5.25839e10	−	9.10780e10i	−0.165308	−	0.286321i	0.771457	−	0.636282i	$-0.219528\pi$
$751$	−5.25839e10	−	9.10780e10i	−0.165308	−	0.286321i	−0.936765	+	0.349960i	$0.886195\pi$
$752$	6.23721e10	−	3.60105e10i	0.195038	−	0.112605i
$753$	1.95272e11	−	1.78700e10i	0.607378	−	0.0555834i
$754$	2.31693e10	−	4.01304e10i	0.0716849	−	0.124162i
$755$			9.07750e11i			2.79369i
$756$	7.56306e10	+	2.69311e11i	0.231532	+	0.824454i
$757$	−4.23531e11			−1.28974			−0.644869	−	0.764293i	$-0.723088\pi$
$757$	−4.23531e11			−1.28974			−0.644869	+	0.764293i	$0.723088\pi$
$758$	−2.57900e11	−	1.48898e11i	−0.781221	−	0.451038i
$759$	7.62628e9	+	8.33349e10i	0.0229798	+	0.251108i
$760$	9.66830e10	+	1.67460e11i	0.289798	+	0.501945i
$761$	4.62418e11	−	2.66977e11i	1.37878	−	0.796041i	0.386770	−	0.922176i	$-0.373591\pi$
$761$	4.62418e11	−	2.66977e11i	1.37878	−	0.796041i	0.992013	+	0.126135i	$0.0402574\pi$
$762$	3.14378e10	−	6.81275e10i	0.0932465	−	0.202070i
$763$	−5.47931e11	+	9.49044e11i	−1.61669	+	2.80019i
$764$		−	9.01526e9i		−	0.0264609i
$765$	4.03718e11	+	4.73403e11i	1.17878	+	1.38224i
$766$	−3.46118e11			−1.00533
$767$	7.16228e10	+	4.13514e10i	0.206952	+	0.119484i
$768$	1.77611e10	−	1.25424e10i	0.0510535	−	0.0360527i
$769$	−5.66789e10	−	9.81707e10i	−0.162075	−	0.280722i	0.773538	−	0.633750i	$-0.218485\pi$
$769$	−5.66789e10	−	9.81707e10i	−0.162075	−	0.280722i	−0.935613	+	0.353028i	$0.885152\pi$
$770$	−4.23021e11	+	2.44231e11i	−1.20337	+	0.694766i
$771$	−1.12715e11	−	1.59613e11i	−0.318980	−	0.451701i
$772$	1.75195e11	−	3.03447e11i	0.493234	−	0.854306i
$773$		−	2.83942e11i		−	0.795265i	−0.917545	−	0.397632i	$-0.869832\pi$
$773$		−	2.83942e11i		−	0.795265i	0.917545	−	0.397632i	$-0.130168\pi$
$774$	5.97249e10	−	5.09334e10i	0.166415	−	0.141919i
$775$	−8.96595e11			−2.48536
$776$	−1.12032e11	−	6.46820e10i	−0.308956	−	0.178376i
$777$	−3.63365e11	−	1.67677e11i	−0.996918	−	0.460033i
$778$	2.46119e11	+	4.26290e11i	0.671779	+	1.16355i
$779$	1.90350e11	−	1.09899e11i	0.516897	−	0.298430i
$780$	9.17886e10	−	8.39991e9i	0.247976	−	0.0226932i
$781$	8.24328e10	−	1.42778e11i	0.221562	−	0.383757i
$782$		−	1.05571e11i		−	0.282304i
$783$	6.53712e10	−	2.56207e11i	0.173916	−	0.681621i
$784$	1.82603e11			0.483331
$785$	3.94524e11	+	2.27779e11i	1.03895	+	0.599839i
$786$	3.16114e10	+	3.45428e11i	0.0828236	+	0.905040i
$787$	3.25568e11	+	5.63900e11i	0.848678	+	1.46995i	0.882389	+	0.470521i	$0.155934\pi$
$787$	3.25568e11	+	5.63900e11i	0.848678	+	1.46995i	−0.0337110	+	0.999432i	$0.510733\pi$
$788$	−6.06662e10	+	3.50257e10i	−0.157341	+	0.0908409i
$789$	−2.21430e11	+	4.79851e11i	−0.571384	+	1.23822i
$790$	7.80739e10	−	1.35228e11i	0.200446	−	0.347183i
$791$		−	1.17550e12i		−	3.00273i
$792$	3.08990e10	−	8.70512e10i	0.0785315	−	0.221245i
$793$	6.84528e10			0.173100
$794$	4.22703e11	+	2.44047e11i	1.06354	+	0.614034i
$795$	−7.48913e10	+	5.28863e10i	−0.187483	+	0.132396i
$796$	−1.70539e11	−	2.95382e11i	−0.424787	−	0.735753i
$797$	4.16469e11	−	2.40448e11i	1.03216	−	0.595921i	0.114561	−	0.993416i	$-0.463454\pi$
$797$	4.16469e11	−	2.40448e11i	1.03216	−	0.595921i	0.917604	+	0.397496i	$0.130121\pi$
$798$	−2.68774e11	−	3.80606e11i	−0.662790	−	0.938564i
$799$	−1.92998e11	+	3.34283e11i	−0.473550	+	0.820213i
$800$			1.43774e11i			0.351011i
$801$	−2.50188e10	−	1.35549e11i	−0.0607765	−	0.329281i
$802$	−2.05699e11			−0.497204
$803$	−2.04372e11	−	1.17994e11i	−0.491541	−	0.283791i
$804$	−1.16580e11	−	5.37965e10i	−0.278997	−	0.128745i
$805$	2.35958e11	+	4.08692e11i	0.561890	+	0.973223i
$806$	−9.32361e10	+	5.38299e10i	−0.220925	+	0.127551i
$807$	5.35705e11	−	4.90243e10i	1.26308	−	0.115589i
$808$	2.57876e10	−	4.46654e10i	0.0605013	−	0.104791i
$809$			1.97505e11i			0.461089i	0.973062	+	0.230545i	$0.0740508\pi$
$809$			1.97505e11i			0.461089i	−0.973062	+	0.230545i	$0.925949\pi$
$810$	4.91293e11	−	1.87755e11i	1.14130	−	0.436166i
$811$	−1.30697e11			−0.302121			−0.151061	−	0.988524i	$-0.548269\pi$
$811$	−1.30697e11			−0.302121			−0.151061	+	0.988524i	$0.548269\pi$
$812$	−2.26800e11	−	1.30943e11i	−0.521698	−	0.301203i
$813$	−2.00953e10	−	2.19588e11i	−0.0459973	−	0.502627i
$814$	6.60752e10	+	1.14446e11i	0.150501	+	0.260676i
$815$	−5.15152e11	+	2.97423e11i	−1.16763	+	0.674131i
$816$	−4.88268e10	+	1.05810e11i	−0.110128	+	0.238654i
$817$	−6.53730e10	+	1.13229e11i	−0.146727	+	0.254139i
$818$			7.32504e10i			0.163605i
$819$	−2.18411e11	+	4.03129e10i	−0.485445	+	0.0896001i
$820$	2.45732e11			0.543509
$821$	2.25465e10	+	1.30172e10i	0.0496256	+	0.0286514i	0.524608	−	0.851344i	$-0.324212\pi$
$821$	2.25465e10	+	1.30172e10i	0.0496256	+	0.0286514i	−0.474982	+	0.879996i	$0.657545\pi$
$822$	−7.23383e10	+	5.10835e10i	−0.158446	+	0.111891i
$823$	1.02310e11	+	1.77206e11i	0.223007	+	0.386260i	0.955720	−	0.294278i	$-0.0950792\pi$
$823$	1.02310e11	+	1.77206e11i	0.223007	+	0.386260i	−0.732712	+	0.680539i	$0.761746\pi$
$824$	1.09185e10	−	6.30382e9i	0.0236840	−	0.0136740i
$825$	3.52334e11	+	4.98933e11i	0.760570	+	1.07703i
$826$	2.33701e11	−	4.04781e11i	0.502042	−	0.869562i
$827$		−	2.31574e11i		−	0.495072i	−0.968879	−	0.247536i	$-0.920379\pi$
$827$		−	2.31574e11i		−	0.495072i	0.968879	−	0.247536i	$-0.0796208\pi$
$828$	−8.41024e10	−	2.98523e10i	−0.178932	−	0.0635122i
$829$	7.98205e11			1.69004			0.845019	−	0.534736i	$-0.179589\pi$
$829$	7.98205e11			1.69004			0.845019	+	0.534736i	$0.179589\pi$
$830$	−3.41114e11	−	1.96942e11i	−0.718765	−	0.414979i
$831$	−7.36861e11	−	3.40029e11i	−1.54519	−	0.713036i
$832$	8.63192e9	+	1.49509e10i	0.0180142	+	0.0312015i
$833$	−8.47545e11	+	4.89331e11i	−1.76029	+	1.01630i
$834$	3.89185e11	−	3.56158e10i	0.804438	−	0.0736171i
$835$	3.27681e11	−	5.67559e11i	0.674070	−	1.16752i
$836$			1.53863e11i			0.315000i
$837$	−4.29156e11	+	4.39563e11i	−0.874407	+	0.895612i
$838$	−4.28623e11			−0.869160
$839$	5.56790e11	+	3.21463e11i	1.12368	+	0.648758i	0.942338	−	0.334662i	$-0.108622\pi$
$839$	5.56790e11	+	3.21463e11i	1.12368	+	0.648758i	0.181343	+	0.983420i	$0.441955\pi$
$840$	−4.74727e10	−	5.18750e11i	−0.0953514	−	1.04194i
$841$	−1.26349e11	−	2.18842e11i	−0.252573	−	0.437469i
$842$	4.67914e11	−	2.70150e11i	0.930931	−	0.537473i
$843$	2.67669e11	−	5.80053e11i	0.530014	−	1.14857i
$844$	1.20210e11	−	2.08209e11i	0.236902	−	0.410327i
$845$		−	8.07752e11i		−	1.58435i
$846$	2.11730e11	+	2.48276e11i	0.413334	+	0.484678i
$847$	4.92808e11			0.957511
$848$	−1.48715e10	−	8.58606e9i	−0.0287588	−	0.0166039i
$849$	−6.44258e10	+	4.54959e10i	−0.124002	+	0.0875672i
$850$	−3.85278e11	−	6.67321e11i	−0.738071	−	1.27838i
$851$	1.10569e11	−	6.38370e10i	0.210821	−	0.121718i
$852$	1.01420e11	+	1.43619e11i	0.192472	+	0.272555i
$853$	9.75384e10	−	1.68942e11i	0.184238	−	0.319110i	−0.759081	−	0.650996i	$-0.774352\pi$
$853$	9.75384e10	−	1.68942e11i	0.184238	−	0.319110i	0.943320	+	0.331886i	$0.107685\pi$
$854$		−	3.86866e11i		−	0.727326i
$855$	−6.66584e11	+	5.68464e11i	−1.24736	+	1.06375i
$856$	−3.39362e11			−0.632074
$857$	−3.84904e10	−	2.22224e10i	−0.0713557	−	0.0411972i	0.463898	−	0.885889i	$-0.346451\pi$
$857$	−3.84904e10	−	2.22224e10i	−0.0713557	−	0.0411972i	−0.535253	+	0.844692i	$0.679784\pi$
$858$	6.65940e10	+	3.07301e10i	0.122881	+	0.0567042i
$859$	−1.25294e11	−	2.17015e11i	−0.230122	−	0.398582i	0.727722	−	0.685872i	$-0.240579\pi$
$859$	−1.25294e11	−	2.17015e11i	−0.230122	−	0.398582i	−0.957844	+	0.287290i	$0.907246\pi$
$860$	−1.26590e11	+	7.30866e10i	−0.231422	+	0.133611i
$861$	−5.89659e11	+	5.39619e10i	−1.07297	+	0.0981916i
$862$	1.54656e11	−	2.67871e11i	0.280115	−	0.485174i
$863$			3.91558e11i			0.705915i	0.935639	+	0.352958i	$0.114824\pi$
$863$			3.91558e11i			0.705915i	−0.935639	+	0.352958i	$0.885176\pi$
$864$	7.04864e10	+	6.88176e10i	0.126488	+	0.123494i
$865$	−1.03079e12			−1.84122
$866$	−6.82876e10	−	3.94259e10i	−0.121415	−	0.0700987i
$867$	−5.42428e9	−	5.92729e10i	−0.00959988	−	0.104901i
$868$	3.04224e11	+	5.26931e11i	0.535937	+	0.928271i
$869$	1.07602e11	−	6.21242e10i	0.188687	−	0.108939i
$870$	−2.06313e11	+	4.47093e11i	−0.360123	+	0.780406i
$871$	5.09714e10	−	8.82851e10i	0.0885633	−	0.153396i
$872$			3.85921e11i			0.667471i
$873$	1.96052e11	−	5.52333e11i	0.337531	−	0.950920i
$874$	1.48651e11			0.254755
$875$	1.48070e12	+	8.54884e11i	2.52601	+	1.45839i
$876$	2.05577e11	−	1.45173e11i	0.349106	−	0.246530i
$877$	3.99055e10	+	6.91184e10i	0.0674582	+	0.116841i	0.897782	−	0.440441i	$-0.145178\pi$
$877$	3.99055e10	+	6.91184e10i	0.0674582	+	0.116841i	−0.830324	+	0.557282i	$0.811844\pi$
$878$	8.35204e10	−	4.82206e10i	0.140545	−	0.0811436i
$879$	−2.47869e11	−	3.51002e11i	−0.415209	−	0.587968i
$880$	−8.60090e10	+	1.48972e11i	−0.143421	+	0.248413i
$881$			5.84453e11i			0.970166i	0.874468	+	0.485083i	$0.161211\pi$
$881$			5.84453e11i			0.970166i	−0.874468	+	0.485083i	$0.838789\pi$
$882$	1.50161e11	+	8.13560e11i	0.248132	+	1.34436i
$883$	7.52384e10			0.123765			0.0618823	−	0.998083i	$-0.480290\pi$
$883$	7.52384e10			0.123765			0.0618823	+	0.998083i	$0.480290\pi$
$884$	−8.01294e10	−	4.62627e10i	−0.131215	−	0.0757569i
$885$	−7.97949e11	−	3.68218e11i	−1.30077	−	0.600249i
$886$	−1.15756e11	−	2.00495e11i	−0.187849	−	0.325364i
$887$	6.05896e11	−	3.49814e11i	0.978822	−	0.565123i	0.0769076	−	0.997038i	$-0.475495\pi$
$887$	6.05896e11	−	3.49814e11i	0.978822	−	0.565123i	0.901914	+	0.431915i	$0.142162\pi$
$888$	−1.40344e11	+	1.28434e10i	−0.225706	+	0.0206552i
$889$	1.68343e11	−	2.91578e11i	0.269518	−	0.466819i
$890$			2.56687e11i			0.409113i
$891$	4.13252e11	+	6.60802e10i	0.655698	+	0.104848i
$892$	3.71333e11			0.586548
$893$	−4.70694e11	−	2.71755e11i	−0.740172	−	0.427338i
$894$	3.60122e10	+	3.93518e11i	0.0563768	+	0.616047i
$895$	5.09739e11	+	8.82894e11i	0.794430	+	1.37599i
$896$	8.44963e10	−	4.87840e10i	0.131101	−	0.0756911i
$897$	2.96892e10	−	6.43382e10i	0.0458594	−	0.0993800i
$898$	−8.65455e10	+	1.49901e11i	−0.133088	+	0.230515i
$899$		−	5.75137e11i		−	0.880507i
$900$	−6.40562e11	+	1.18230e11i	−0.976317	+	0.180202i
$901$	9.20338e10			0.139652
$902$	1.69335e11	+	9.77658e10i	0.255812	+	0.147693i
$903$	2.87715e11	−	2.03177e11i	0.432725	−	0.305579i
$904$	−2.06983e11	−	3.58505e11i	−0.309928	−	0.536812i
$905$	−8.12012e11	+	4.68815e11i	−1.21051	+	0.698888i
$906$	−4.44341e11	−	6.29222e11i	−0.659483	−	0.933881i
$907$	−5.79947e10	+	1.00450e11i	−0.0856958	+	0.148429i	−0.905687	−	0.423946i	$-0.860645\pi$
$907$	−5.79947e10	+	1.00450e11i	−0.0856958	+	0.148429i	0.819992	+	0.572375i	$0.193978\pi$
$908$			5.33513e11i			0.784877i
$909$	2.20205e11	+	7.81624e10i	0.322532	+	0.114483i
$910$	4.13601e11			0.603137
$911$	9.81176e11	+	5.66482e11i	1.42454	+	0.822456i	0.996682	−	0.0813913i	$-0.0259363\pi$
$911$	9.81176e11	+	5.66482e11i	1.42454	+	0.822456i	0.427854	+	0.903848i	$0.359270\pi$
$912$	−1.48989e11	−	6.87516e10i	−0.215364	−	0.0993810i
$913$	−1.56709e11	−	2.71428e11i	−0.225533	−	0.390635i
$914$	−2.35358e11	+	1.35884e11i	−0.337244	+	0.194708i
$915$	−7.24360e11	+	6.62889e10i	−1.03340	+	0.0945706i
$916$	−2.30424e11	+	3.99105e11i	−0.327299	+	0.566899i
$917$			1.55651e12i			2.20127i
$918$	−5.11573e11	−	1.30528e11i	−0.720340	−	0.183795i
$919$	−3.06256e11			−0.429361			−0.214680	−	0.976684i	$-0.568871\pi$
$919$	−3.06256e11			−0.429361			−0.214680	+	0.976684i	$0.568871\pi$
$920$	1.43926e11	+	8.30956e10i	0.200903	+	0.115992i
$921$	9.90936e10	+	1.08283e12i	0.137723	+	1.50495i
$922$	3.24506e11	+	5.62060e11i	0.449054	+	0.777784i
$923$	−1.20896e11	+	6.97992e10i	−0.166573	+	0.0961709i
$924$	1.73674e11	−	3.76361e11i	0.238257	−	0.516317i
$925$	4.65942e11	−	8.07035e11i	0.636451	−	1.10237i
$926$			6.86069e11i			0.933090i
$927$	3.70644e10	+	4.34619e10i	0.0501923	+	0.0588559i
$928$	−9.22265e10			−0.124355
$929$	−8.75115e11	−	5.05248e11i	−1.17490	−	0.678331i	−0.220074	−	0.975483i	$-0.570630\pi$
$929$	−8.75115e11	−	5.05248e11i	−1.17490	−	0.678331i	−0.954830	+	0.297152i	$0.903963\pi$
$930$	9.34486e11	−	6.59911e11i	1.24923	−	0.882173i
$931$	−6.89012e11	−	1.19340e12i	−0.917124	−	1.58851i
$932$	−3.17439e11	+	1.83273e11i	−0.420723	+	0.242905i
$933$	1.06983e11	+	1.51496e11i	0.141185	+	0.199929i
$934$	−5.71858e10	+	9.90488e10i	−0.0751452	+	0.130155i
$935$		−	9.21929e11i		−	1.20629i
$936$	−5.95131e10	+	5.07528e10i	−0.0775370	+	0.0661236i
$937$	−3.80033e11			−0.493018			−0.246509	−	0.969141i	$-0.579283\pi$
$937$	−3.80033e11			−0.493018			−0.246509	+	0.969141i	$0.579283\pi$
$938$	−4.98950e11	−	2.88069e11i	−0.644533	−	0.372121i
$939$	1.31526e12	+	6.06933e11i	1.69180	+	0.780689i
$940$	−3.03820e11	−	5.26232e11i	−0.389139	−	0.674009i
$941$	4.20722e11	−	2.42904e11i	0.536583	−	0.309796i	−0.207110	−	0.978318i	$-0.566406\pi$
$941$	4.20722e11	−	2.42904e11i	0.536583	−	0.309796i	0.743693	+	0.668521i	$0.233072\pi$
$942$	−3.84969e11	+	3.52299e10i	−0.488902	+	0.0447412i
$943$	9.44541e10	−	1.63599e11i	0.119447	−	0.206888i
$944$		−	1.64601e11i		−	0.207274i
$945$	2.27217e12	−	6.38094e11i	2.84914	−	0.800124i
$946$	−1.16311e11			−0.145231
$947$	4.64773e9	+	2.68337e9i	0.00577885	+	0.00333642i	0.502887	−	0.864352i	$-0.332271\pi$
$947$	4.64773e9	+	2.68337e9i	0.00577885	+	0.00333642i	−0.497108	+	0.867689i	$0.665605\pi$
$948$	1.20755e10	+	1.31953e11i	0.0149510	+	0.163375i
$949$	9.99106e10	+	1.73050e11i	0.123182	+	0.213357i
$950$	9.39635e11	−	5.42498e11i	1.15363	−	0.666046i
$951$	−2.26279e11	+	4.90359e11i	−0.276644	+	0.599504i
$952$	−2.61457e11	+	4.52857e11i	−0.318312	+	0.551332i
$953$		−	2.87948e11i		−	0.349094i	−0.984649	−	0.174547i	$-0.944154\pi$
$953$		−	2.87948e11i		−	0.349094i	0.984649	−	0.174547i	$-0.0558462\pi$
$954$	2.60244e10	−	7.33182e10i	0.0314187	−	0.0885152i
$955$	−7.60616e10			−0.0914433
$956$	1.55520e11	+	8.97893e10i	0.186189	+	0.107496i
$957$	−3.20050e11	+	2.26011e11i	−0.381566	+	0.269453i
$958$	1.22782e11	+	2.12665e11i	0.145772	+	0.252484i
$959$	−3.44141e11	+	1.98690e11i	−0.406876	+	0.234910i
$960$	−1.05820e11	−	1.49850e11i	−0.124590	−	0.176430i
$961$	−2.41670e11	+	4.18585e11i	−0.283354	+	0.490784i
$962$		−	1.11897e11i		−	0.130653i
$963$	−2.79069e11	−	1.51197e12i	−0.324494	−	1.75808i
$964$	5.67827e11			0.657519
$965$	−2.56017e12	−	1.47812e12i	−2.95230	−	1.70451i
$966$	−3.63612e11	−	1.67791e11i	−0.417570	−	0.192690i
$967$	−4.51417e11	−	7.81877e11i	−0.516264	−	0.894195i	−0.999822	−	0.0188827i	$-0.993989\pi$
$967$	−4.51417e11	−	7.81877e11i	−0.516264	−	0.894195i	0.483558	−	0.875312i	$-0.339344\pi$
$968$	1.50297e11	−	8.67741e10i	0.171179	−	0.0988300i
$969$	8.75761e11	−	8.01441e10i	0.993323	−	0.0909027i
$970$	−5.45721e11	+	9.45216e11i	−0.616429	+	1.06769i
$971$		−	8.08040e11i		−	0.908983i	−0.890751	−	0.454492i	$-0.849821\pi$
$971$		−	8.08040e11i		−	0.908983i	0.890751	−	0.454492i	$-0.150179\pi$
$972$	−2.48642e11	+	3.70632e11i	−0.278554	+	0.415220i
$973$	1.75368e12			1.95658
$974$	−5.71017e10	−	3.29677e10i	−0.0634473	−	0.0366313i
$975$	−4.71328e10	−	5.15035e11i	−0.0521561	−	0.569926i
$976$	−6.81198e10	−	1.17987e11i	−0.0750713	−	0.130027i
$977$	1.39658e12	−	8.06317e11i	1.53281	−	0.884968i	0.533579	−	0.845750i	$-0.320847\pi$
$977$	1.39658e12	−	8.06317e11i	1.53281	−	0.884968i	0.999231	−	0.0392176i	$-0.0124866\pi$
$978$	2.11499e11	−	4.58330e11i	0.231181	−	0.500983i
$979$	−1.02124e11	+	1.76884e11i	−0.111173	+	0.192557i
$980$		−	1.54062e12i		−	1.67029i
$981$	−1.71941e12	+	3.17357e11i	−1.85653	+	0.342666i
$982$	−2.81812e11			−0.303050
$983$	1.24469e12	+	7.18625e11i	1.33306	+	0.769641i	0.985767	−	0.168117i	$-0.0537687\pi$
$983$	1.24469e12	+	7.18625e11i	1.33306	+	0.769641i	0.347290	+	0.937758i	$0.387102\pi$
$984$	−1.70333e11	+	1.20285e11i	−0.181685	+	0.128302i
$985$	2.95511e11	+	5.11840e11i	0.313927	+	0.543737i
$986$	4.28065e11	−	2.47143e11i	0.452900	−	0.261482i
$987$	8.44606e11	+	1.19603e12i	0.889991	+	1.26030i
$988$	6.51412e10	−	1.12828e11i	0.0683641	−	0.118410i
$989$			1.12372e11i			0.117455i
$990$	−7.34449e11	−	2.60694e11i	−0.764576	−	0.271388i
$991$	−1.11953e12			−1.16075			−0.580377	−	0.814348i	$-0.697095\pi$
$991$	−1.11953e12			−1.16075			−0.580377	+	0.814348i	$0.697095\pi$
$992$	1.85565e11	+	1.07136e11i	0.191624	+	0.110634i
$993$	−1.15365e12	−	5.32356e11i	−1.18652	−	0.547527i
$994$	3.94476e11	+	6.83252e11i	0.404087	+	0.699899i
$995$	−2.49213e12	+	1.43883e12i	−2.54261	+	1.46797i
$996$	3.32852e11	−	3.04605e10i	0.338231	−	0.0309528i
$997$	−4.45668e11	+	7.71920e11i	−0.451057	+	0.781253i	−0.998452	−	0.0556212i	$-0.982286\pi$
$997$	−4.45668e11	+	7.71920e11i	−0.451057	+	0.781253i	0.547395	+	0.836874i	$0.315619\pi$
$998$		−	1.85489e11i		−	0.186981i
$999$	−1.72632e11	−	6.14721e11i	−0.173324	−	0.617186i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.9.d.a.11.6	yes	16
3.2	odd	2		54.9.d.a.35.1		16
4.3	odd	2		144.9.q.b.65.5		16
9.2	odd	6		162.9.b.c.161.9		16
9.4	even	3		54.9.d.a.17.1		16
9.5	odd	6	inner	18.9.d.a.5.6	✓	16
9.7	even	3		162.9.b.c.161.8		16
12.11	even	2		432.9.q.c.305.1		16
36.23	even	6		144.9.q.b.113.5		16
36.31	odd	6		432.9.q.c.17.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.9.d.a.5.6	✓	16	9.5	odd	6	inner
18.9.d.a.11.6	yes	16	1.1	even	1	trivial
54.9.d.a.17.1		16	9.4	even	3
54.9.d.a.35.1		16	3.2	odd	2
144.9.q.b.65.5		16	4.3	odd	2
144.9.q.b.113.5		16	36.23	even	6
162.9.b.c.161.8		16	9.7	even	3
162.9.b.c.161.9		16	9.2	odd	6
432.9.q.c.17.1		16	36.31	odd	6
432.9.q.c.305.1		16	12.11	even	2

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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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	18.9.d.a.11.6

Level	$18$
Weight	$9$
Character	18.11
Analytic conductor	$7.333$
Analytic rank	$0$
Dimension	$16$
Inner twists	$2$