LMFDB - Embedded newform 18.11.d.a.11.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [18,11,Mod(5,18)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(18, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("18.5");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$N$	$=$	$18 = 2 \cdot 3^{2}$
Weight:	$k$	$=$	$11$
Character orbit:	$[\chi]$	$=$	18.d (of order $6$ , degree $2$ , minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$11.4364305481$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{20} - 10 x^{19} + 63819 x^{18} - 574086 x^{17} + 1685636151 x^{16} - 13472077884 x^{15} + \cdots + 42\!\cdots\!17$ x^20 - 10x^19 + 63819x^18 - 574086x^17 + 1685636151x^16 - 13472077884x^15 + 23849722149866x^14 - 166712339223788x^13 + 195479019402402405x^12 - 1170707468814910094x^11 + 938326637750627487341x^10 - 4680905675328128110986x^9 + 2551316542474577226379677x^8 - 10177193606819996156162676x^7 + 3644946427174260203987635170x^6 - 10899238750832113741944409252x^5 + 2446510322689300614446071763767x^4 - 4874867111497712925857039900178x^3 + 623192578601325527612865828822963x^2 - 620756959890572838693596656972206*x + 42080692026395342189225080891718217
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$2^{46}\cdot 3^{37}$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.8
Root			$0.500000 + 106.731i$ of defining polynomial
Character	$\chi$	$=$	18.11
Dual form			18.11.d.a.5.8

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(19.5959 + 11.3137i) q^{2} +(1.63905 - 242.994i) q^{3} +(256.000 + 443.405i) q^{4} +(-1947.00 + 1124.10i) q^{5} +(2781.29 - 4743.16i) q^{6} +(14864.4 - 25746.0i) q^{7} +11585.2i q^{8} +(-59043.6 - 796.560i) q^{9} -50871.1 q^{10} +(-139666. - 80636.1i) q^{11} +(108165. - 61479.8i) q^{12} +(-249281. - 431767. i) q^{13} +(582564. - 336344. i) q^{14} +(269960. + 474954. i) q^{15} +(-131072. + 227023. i) q^{16} -1.34561e6i q^{17} +(-1.14800e6 - 683612. i) q^{18} +4.27615e6 q^{19} +(-996867. - 575541. i) q^{20} +(-6.23176e6 - 3.65417e6i) q^{21} +(-1.82459e6 - 3.16028e6i) q^{22} +(-3.03804e6 + 1.75401e6i) q^{23} +(2.81515e6 + 18988.8i) q^{24} +(-2.35559e6 + 4.08001e6i) q^{25} -1.12812e7i q^{26} +(-290335. + 1.43460e7i) q^{27} +1.52212e7 q^{28} +(1.44144e7 + 8.32218e6i) q^{29} +(-83380.3 + 1.23614e7i) q^{30} +(5.30867e6 + 9.19489e6i) q^{31} +(-5.13695e6 + 2.96582e6i) q^{32} +(-1.98231e7 + 3.38059e7i) q^{33} +(1.52238e7 - 2.63684e7i) q^{34} +6.68367e7i q^{35} +(-1.47620e7 - 2.63842e7i) q^{36} -3.61380e6 q^{37} +(8.37950e7 + 4.83791e7i) q^{38} +(-1.05326e8 + 5.98661e7i) q^{39} +(-1.30230e7 - 2.25565e7i) q^{40} +(1.48901e7 - 8.59682e6i) q^{41} +(-8.07748e7 - 1.42111e8i) q^{42} +(7.92855e7 - 1.37327e8i) q^{43} -8.25714e7i q^{44} +(1.15854e8 - 6.48203e7i) q^{45} -7.93776e7 q^{46} +(1.61474e8 + 9.32273e7i) q^{47} +(5.49506e7 + 3.22219e7i) q^{48} +(-3.00665e8 - 5.20767e8i) q^{49} +(-9.23200e7 + 5.33010e7i) q^{50} +(-3.26975e8 - 2.20552e6i) q^{51} +(1.27632e8 - 2.21065e8i) q^{52} +6.84291e8i q^{53} +(-1.67995e8 + 2.77838e8i) q^{54} +3.62574e8 q^{55} +(2.98273e8 + 1.72208e8i) q^{56} +(7.00882e6 - 1.03908e9i) q^{57} +(1.88309e8 + 3.26161e8i) q^{58} +(1.08798e8 - 6.28147e7i) q^{59} +(-1.41487e8 + 2.41290e8i) q^{60} +(3.64774e8 - 6.31807e8i) q^{61} +2.40243e8i q^{62} +(-8.98158e8 + 1.50829e9i) q^{63} -1.34218e8 q^{64} +(9.70702e8 + 5.60435e8i) q^{65} +(-7.70921e8 + 4.38185e8i) q^{66} +(-1.98462e8 - 3.43746e8i) q^{67} +(5.96649e8 - 3.44476e8i) q^{68} +(4.21236e8 + 7.41102e8i) q^{69} +(-7.56171e8 + 1.30973e9i) q^{70} -2.21535e9i q^{71} +(9.22834e6 - 6.84034e8i) q^{72} +6.41670e8 q^{73} +(-7.08157e7 - 4.08854e7i) q^{74} +(9.87558e8 + 5.79084e8i) q^{75} +(1.09469e9 + 1.89607e9i) q^{76} +(-4.15211e9 + 2.39722e9i) q^{77} +(-2.74126e9 - 1.84904e7i) q^{78} +(1.46673e9 - 2.54045e9i) q^{79} -5.89354e8i q^{80} +(3.48552e9 + 9.40636e7i) q^{81} +3.89048e8 q^{82} +(-1.18456e9 - 6.83904e8i) q^{83} +(2.49483e7 - 3.69866e9i) q^{84} +(1.51260e9 + 2.61991e9i) q^{85} +(3.10735e9 - 1.79403e9i) q^{86} +(2.04587e9 - 3.48899e9i) q^{87} +(9.34189e8 - 1.61806e9i) q^{88} -6.25559e9i q^{89} +(3.00362e9 + 4.05219e7i) q^{90} -1.48217e10 q^{91} +(-1.55548e9 - 8.98055e8i) q^{92} +(2.24301e9 - 1.27491e9i) q^{93} +(2.10949e9 + 3.65375e9i) q^{94} +(-8.32568e9 + 4.80683e9i) q^{95} +(7.12258e8 + 1.25311e9i) q^{96} +(-3.15546e9 + 5.46542e9i) q^{97} -1.36065e10i q^{98} +(8.18215e9 + 4.87230e9i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$20 q - 84 q^{3} + 5120 q^{4} - 9918 q^{5} + 12864 q^{6} + 12238 q^{7} + 79248 q^{9} - 327582 q^{11} + 9216 q^{12} - 280550 q^{13} + 175680 q^{14} - 2685042 q^{15} - 2621440 q^{16} + 3925632 q^{18} - 2966240 q^{19}+ \cdots + 41160676842 q^{99}+O(q^{100})$ 20 * q - 84 * q^3 + 5120 * q^4 - 9918 * q^5 + 12864 * q^6 + 12238 * q^7 + 79248 * q^9 - 327582 * q^11 + 9216 * q^12 - 280550 * q^13 + 175680 * q^14 - 2685042 * q^15 - 2621440 * q^16 + 3925632 * q^18 - 2966240 * q^19 - 5078016 * q^20 - 11895726 * q^21 + 3473472 * q^22 + 10446606 * q^23 + 2752512 * q^24 + 9609944 * q^25 + 2340576 * q^27 + 12531712 * q^28 + 32440806 * q^29 + 37556352 * q^30 - 40069958 * q^31 - 35367930 * q^33 + 30746496 * q^34 - 32695296 * q^36 - 127390400 * q^37 + 370567296 * q^38 + 153125550 * q^39 - 245419398 * q^41 - 344505600 * q^42 - 86593094 * q^43 + 394622766 * q^45 - 366913920 * q^46 + 1094979330 * q^47 + 26738688 * q^48 - 598072056 * q^49 - 456606720 * q^50 - 2329772724 * q^51 + 143641600 * q^52 + 1623484224 * q^54 - 262510308 * q^55 + 89948160 * q^56 + 311135772 * q^57 + 249515904 * q^58 - 2125085130 * q^59 - 2357738496 * q^60 + 312021586 * q^61 + 5475513858 * q^63 - 2684354560 * q^64 + 13076821350 * q^65 + 2185467264 * q^66 - 1200881210 * q^67 - 2610487296 * q^68 - 11765922354 * q^69 + 1138681152 * q^70 + 1554382848 * q^72 + 5213376328 * q^73 + 9118122624 * q^74 + 13244996208 * q^75 - 759357440 * q^76 - 33678720774 * q^77 - 14572366080 * q^78 - 3396212726 * q^79 + 14546869128 * q^81 + 3667214592 * q^82 + 16739541378 * q^83 + 1518514176 * q^84 + 7141101588 * q^85 - 11512304064 * q^86 - 32778228834 * q^87 - 1778417664 * q^88 + 16769410560 * q^90 - 10426841884 * q^91 + 5348662272 * q^92 - 4843832814 * q^93 + 6416128320 * q^94 - 26494427340 * q^95 - 1962934272 * q^96 + 6721893598 * q^97 + 41160676842 * 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

)

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

$2$	19.5959	+	11.3137i	0.612372	+	0.353553i
$2$	19.5959	+	11.3137i	0.612372	+	0.353553i
$3$	1.63905	−	242.994i	0.00674506	−	0.999977i
$3$	1.63905	−	242.994i	0.00674506	−	0.999977i
$4$	256.000	+	443.405i	0.250000	+	0.433013i
$5$	−1947.00	+	1124.10i	−0.623042	+	0.359713i	−0.778052	−	0.628200i	$-0.783792\pi$
$5$	−1947.00	+	1124.10i	−0.623042	+	0.359713i	0.155011	+	0.987913i	$0.450459\pi$
$6$	2781.29	−	4743.16i	0.357676	−	0.609974i
$7$	14864.4	−	25746.0i	0.884419	−	1.53186i	0.0380412	−	0.999276i	$-0.487888\pi$
$7$	14864.4	−	25746.0i	0.884419	−	1.53186i	0.846378	−	0.532583i	$-0.178778\pi$
$8$			11585.2i			0.353553i
$9$	−59043.6	−	796.560i	−0.999909	−	0.0134898i
$10$	−50871.1			−0.508711
$11$	−139666.	−	80636.1i	−0.867215	−	0.500687i	−0.000793402	−	1.00000i	$-0.500253\pi$
$11$	−139666.	−	80636.1i	−0.867215	−	0.500687i	−0.866422	+	0.499313i	$0.833586\pi$
$12$	108165.	−	61479.8i	0.434689	−	0.247074i
$13$	−249281.	−	431767.i	−0.671385	−	1.16287i	−0.977511	−	0.210883i	$-0.932366\pi$
$13$	−249281.	−	431767.i	−0.671385	−	1.16287i	0.306126	−	0.951991i	$-0.400967\pi$
$14$	582564.	−	336344.i	1.08319	−	0.625379i
$15$	269960.	+	474954.i	0.355503	+	0.625454i
$16$	−131072.	+	227023.i	−0.125000	+	0.216506i
$17$		−	1.34561e6i		−	0.947707i	−0.880604	−	0.473853i	$-0.842863\pi$
$17$		−	1.34561e6i		−	0.947707i	0.880604	−	0.473853i	$-0.157137\pi$
$18$	−1.14800e6	−	683612.i	−0.607547	−	0.361782i
$19$	4.27615e6			1.72697			0.863485	−	0.504375i	$-0.168277\pi$
$19$	4.27615e6			1.72697			0.863485	+	0.504375i	$0.168277\pi$
$20$	−996867.	−	575541.i	−0.311521	−	0.179857i
$21$	−6.23176e6	−	3.65417e6i	−1.52586	−	0.894732i
$22$	−1.82459e6	−	3.16028e6i	−0.354039	−	0.613214i
$23$	−3.03804e6	+	1.75401e6i	−0.472013	+	0.272517i	−0.717082	−	0.696989i	$-0.754523\pi$
$23$	−3.03804e6	+	1.75401e6i	−0.472013	+	0.272517i	0.245069	+	0.969506i	$0.421189\pi$
$24$	2.81515e6	+	18988.8i	0.353545	+	0.00238474i
$25$	−2.35559e6	+	4.08001e6i	−0.241213	+	0.417793i
$26$		−	1.12812e7i		−	0.949482i
$27$	−290335.	+	1.43460e7i	−0.0202339	+	0.999795i
$28$	1.52212e7			0.884419
$29$	1.44144e7	+	8.32218e6i	0.702761	+	0.405739i	0.808375	−	0.588668i	$-0.200347\pi$
$29$	1.44144e7	+	8.32218e6i	0.702761	+	0.405739i	−0.105614	+	0.994407i	$0.533681\pi$
$30$	−83380.3	+	1.23614e7i	−0.00343129	+	0.508700i
$31$	5.30867e6	+	9.19489e6i	0.185429	+	0.321172i	0.943721	−	0.330743i	$-0.107299\pi$
$31$	5.30867e6	+	9.19489e6i	0.185429	+	0.321172i	−0.758292	+	0.651915i	$0.773966\pi$
$32$	−5.13695e6	+	2.96582e6i	−0.153093	+	0.0883883i
$33$	−1.98231e7	+	3.38059e7i	−0.506525	+	0.863818i
$34$	1.52238e7	−	2.63684e7i	0.335065	−	0.580350i
$35$			6.68367e7i			1.27255i
$36$	−1.47620e7	−	2.63842e7i	−0.244136	−	0.436346i
$37$	−3.61380e6			−0.0521141			−0.0260570	−	0.999660i	$-0.508295\pi$
$37$	−3.61380e6			−0.0521141			−0.0260570	+	0.999660i	$0.508295\pi$
$38$	8.37950e7	+	4.83791e7i	1.05755	+	0.610576i
$39$	−1.05326e8	+	5.98661e7i	−1.16738	+	0.663527i
$40$	−1.30230e7	−	2.25565e7i	−0.127178	−	0.220278i
$41$	1.48901e7	−	8.59682e6i	0.128523	−	0.0742025i	−0.434360	−	0.900739i	$-0.643026\pi$
$41$	1.48901e7	−	8.59682e6i	0.128523	−	0.0742025i	0.562883	+	0.826537i	$0.309692\pi$
$42$	−8.07748e7	−	1.42111e8i	−0.618058	−	1.08738i
$43$	7.92855e7	−	1.37327e8i	0.539326	−	0.934141i	−0.459614	−	0.888119i	$-0.652012\pi$
$43$	7.92855e7	−	1.37327e8i	0.539326	−	0.934141i	0.998940	−	0.0460220i	$-0.0146544\pi$
$44$		−	8.25714e7i		−	0.500687i
$45$	1.15854e8	−	6.48203e7i	0.627837	−	0.351276i
$46$	−7.93776e7			−0.385397
$47$	1.61474e8	+	9.32273e7i	0.704068	+	0.406494i	0.808861	−	0.588000i	$-0.200085\pi$
$47$	1.61474e8	+	9.32273e7i	0.704068	+	0.406494i	−0.104793	+	0.994494i	$0.533418\pi$
$48$	5.49506e7	+	3.22219e7i	0.215658	+	0.126458i
$49$	−3.00665e8	−	5.20767e8i	−1.06439	−	1.84359i
$50$	−9.23200e7	+	5.33010e7i	−0.295424	+	0.170563i
$51$	−3.26975e8	−	2.20552e6i	−0.947685	−	0.00639234i
$52$	1.27632e8	−	2.21065e8i	0.335693	−	0.581437i
$53$			6.84291e8i			1.63630i	0.575008	+	0.818148i	$0.304999\pi$
$53$			6.84291e8i			1.63630i	−0.575008	+	0.818148i	$0.695001\pi$
$54$	−1.67995e8	+	2.77838e8i	−0.365872	+	0.605093i
$55$	3.62574e8			0.720415
$56$	2.98273e8	+	1.72208e8i	0.541594	+	0.312689i
$57$	7.00882e6	−	1.03908e9i	0.0116485	−	1.72693i
$58$	1.88309e8	+	3.26161e8i	0.286901	+	0.496927i
$59$	1.08798e8	−	6.28147e7i	0.152182	−	0.0878620i	−0.421976	−	0.906607i	$-0.638663\pi$
$59$	1.08798e8	−	6.28147e7i	0.152182	−	0.0878620i	0.574157	+	0.818745i	$0.305330\pi$
$60$	−1.41487e8	+	2.41290e8i	−0.181954	+	0.310301i
$61$	3.64774e8	−	6.31807e8i	0.431892	−	0.748058i	−0.565145	−	0.824992i	$-0.691180\pi$
$61$	3.64774e8	−	6.31807e8i	0.431892	−	0.748058i	0.997036	+	0.0769336i	$0.0245129\pi$
$62$			2.40243e8i			0.262236i
$63$	−8.98158e8	+	1.50829e9i	−0.905003	+	1.51979i
$64$	−1.34218e8			−0.125000
$65$	9.70702e8	+	5.60435e8i	0.836602	+	0.483012i
$66$	−7.70921e8	+	4.38185e8i	−0.615588	+	0.349895i
$67$	−1.98462e8	−	3.43746e8i	−0.146995	−	0.254603i	0.783120	−	0.621870i	$-0.213627\pi$
$67$	−1.98462e8	−	3.43746e8i	−0.146995	−	0.254603i	−0.930116	+	0.367267i	$0.880294\pi$
$68$	5.96649e8	−	3.44476e8i	0.410369	−	0.236927i
$69$	4.21236e8	+	7.41102e8i	0.269327	+	0.473841i
$70$	−7.56171e8	+	1.30973e9i	−0.449914	+	0.779274i
$71$		−	2.21535e9i		−	1.22786i	−0.789359	−	0.613932i	$-0.789587\pi$
$71$		−	2.21535e9i		−	1.22786i	0.789359	−	0.613932i	$-0.210413\pi$
$72$	9.22834e6	−	6.84034e8i	0.00476937	−	0.353521i
$73$	6.41670e8			0.309526			0.154763	−	0.987952i	$-0.450539\pi$
$73$	6.41670e8			0.309526			0.154763	+	0.987952i	$0.450539\pi$
$74$	−7.08157e7	−	4.08854e7i	−0.0319132	−	0.0184251i
$75$	9.87558e8	+	5.79084e8i	0.416156	+	0.244025i
$76$	1.09469e9	+	1.89607e9i	0.431742	+	0.747800i
$77$	−4.15211e9	+	2.39722e9i	−1.53396	+	0.885634i
$78$	−2.74126e9	−	1.84904e7i	−0.949461	−	0.00640431i
$79$	1.46673e9	−	2.54045e9i	0.476666	−	0.825610i	−0.522976	−	0.852347i	$-0.675178\pi$
$79$	1.46673e9	−	2.54045e9i	0.476666	−	0.825610i	0.999643	+	0.0267371i	$0.00851168\pi$
$80$		−	5.89354e8i		−	0.179857i
$81$	3.48552e9	+	9.40636e7i	0.999636	+	0.0269772i
$82$	3.89048e8			0.104938
$83$	−1.18456e9	−	6.83904e8i	−0.300722	−	0.173622i	0.342045	−	0.939684i	$-0.388880\pi$
$83$	−1.18456e9	−	6.83904e8i	−0.300722	−	0.173622i	−0.642767	+	0.766062i	$0.722214\pi$
$84$	2.49483e7	−	3.69866e9i	0.00596546	−	0.884399i
$85$	1.51260e9	+	2.61991e9i	0.340903	+	0.590461i
$86$	3.10735e9	−	1.79403e9i	0.660537	−	0.381361i
$87$	2.04587e9	−	3.48899e9i	0.410470	−	0.700008i
$88$	9.34189e8	−	1.61806e9i	0.177020	−	0.306607i
$89$		−	6.25559e9i		−	1.12026i	−0.828405	−	0.560129i	$-0.810751\pi$
$89$		−	6.25559e9i		−	1.12026i	0.828405	−	0.560129i	$-0.189249\pi$
$90$	3.00362e9	+	4.05219e7i	0.508665	+	0.00686242i
$91$	−1.48217e10			−2.37514
$92$	−1.55548e9	−	8.98055e8i	−0.236007	−	0.136259i
$93$	2.24301e9	−	1.27491e9i	0.322416	−	0.183258i
$94$	2.10949e9	+	3.65375e9i	0.287435	+	0.497851i
$95$	−8.32568e9	+	4.80683e9i	−1.07597	+	0.621214i
$96$	7.12258e8	+	1.25311e9i	0.0873537	+	0.153686i
$97$	−3.15546e9	+	5.46542e9i	−0.367455	+	0.636451i	−0.989167	−	0.146795i	$-0.953104\pi$
$97$	−3.15546e9	+	5.46542e9i	−0.367455	+	0.636451i	0.621712	+	0.783246i	$0.286438\pi$
$98$		−	1.36065e10i		−	1.50528i
$99$	8.18215e9	+	4.87230e9i	0.860382	+	0.512340i
$100$	−2.41213e9			−0.241213
$101$	1.05143e8	+	6.07044e7i	0.0100040	+	0.00577582i	0.504994	−	0.863123i	$-0.331495\pi$
$101$	1.05143e8	+	6.07044e7i	0.0100040	+	0.00577582i	−0.494990	+	0.868899i	$0.664828\pi$
$102$	−6.38243e9	−	3.74252e9i	−0.578076	−	0.338972i
$103$	−3.79283e8	−	6.56937e8i	−0.0327173	−	0.0566680i	0.849203	−	0.528066i	$-0.177083\pi$
$103$	−3.79283e8	−	6.56937e8i	−0.0327173	−	0.0566680i	−0.881920	+	0.471398i	$0.843749\pi$
$104$	5.00212e9	−	2.88798e9i	0.411138	−	0.237371i
$105$	1.62409e10	+	1.09549e8i	1.27252	+	0.00858342i
$106$	−7.74187e9	+	1.34093e10i	−0.578518	+	1.00202i
$107$			2.72307e10i			1.94151i	0.240075	+	0.970754i	$0.422828\pi$
$107$			2.72307e10i			1.94151i	−0.240075	+	0.970754i	$0.577172\pi$
$108$	−6.43540e9	+	3.54383e9i	−0.437983	+	0.241187i
$109$	1.43218e10			0.930818			0.465409	−	0.885096i	$-0.345907\pi$
$109$	1.43218e10			0.930818			0.465409	+	0.885096i	$0.345907\pi$
$110$	7.10496e9	+	4.10205e9i	0.441162	+	0.254705i
$111$	−5.92319e6	+	8.78133e8i	−0.000351513	+	0.0521129i
$112$	3.89662e9	+	6.74915e9i	0.221105	+	0.382965i
$113$	−7.03582e9	+	4.06213e9i	−0.381876	+	0.220476i	−0.678634	−	0.734477i	$-0.737428\pi$
$113$	−7.03582e9	+	4.06213e9i	−0.381876	+	0.220476i	0.296758	+	0.954953i	$0.404094\pi$
$114$	1.18932e10	−	2.02824e10i	0.617695	−	1.05341i
$115$	3.94339e9	−	6.83014e9i	0.196056	−	0.339579i
$116$			8.52191e9i			0.405739i
$117$	1.43745e10	+	2.56916e10i	0.655637	+	1.17182i
$118$	2.84267e9			0.124256
$119$	−3.46440e10	−	2.00017e10i	−1.45175	−	0.838170i
$120$	−5.50245e9	+	3.12755e9i	−0.221131	+	0.125689i
$121$	3.56599e7	+	6.17647e7i	0.00137484	+	0.00238130i
$122$	1.42962e10	−	8.25390e9i	0.528957	−	0.305394i
$123$	−2.06457e9	−	3.63231e9i	−0.0733339	−	0.129020i
$124$	−2.71804e9	+	4.70778e9i	−0.0927144	+	0.160586i
$125$		−	3.25469e10i		−	1.06650i
$126$	−3.46646e10	+	1.93949e10i	−1.09153	+	0.610710i
$127$	−4.79236e10			−1.45054			−0.725272	−	0.688462i	$-0.758286\pi$
$127$	−4.79236e10			−1.45054			−0.725272	+	0.688462i	$0.758286\pi$
$128$	−2.63012e9	−	1.51850e9i	−0.0765466	−	0.0441942i
$129$	−3.32396e10	−	1.94910e10i	−0.930482	−	0.545615i
$130$	1.26812e10	+	2.19645e10i	0.341541	+	0.591567i
$131$	3.39307e10	−	1.95899e10i	0.879500	−	0.507780i	0.00900673	−	0.999959i	$-0.497133\pi$
$131$	3.39307e10	−	1.95899e10i	0.879500	−	0.507780i	0.870494	+	0.492180i	$0.163800\pi$
$132$	−2.00644e10	−	1.35339e8i	−0.500676	−	0.00337716i
$133$	6.35625e10	−	1.10093e11i	1.52737	−	2.64547i
$134$		−	8.98136e9i		−	0.207883i
$135$	−1.55611e10	−	2.82580e10i	−0.347033	−	0.630192i
$136$	1.55892e10			0.335065
$137$	5.27689e10	+	3.04661e10i	1.09339	+	0.631269i	0.934477	−	0.356024i	$-0.115868\pi$
$137$	5.27689e10	+	3.04661e10i	1.09339	+	0.631269i	0.158913	+	0.987293i	$0.449201\pi$
$138$	−1.30104e8	+	1.92883e10i	−0.00259953	+	0.385389i
$139$	1.76691e10	+	3.06038e10i	0.340518	+	0.589795i	0.984529	−	0.175221i	$-0.0560641\pi$
$139$	1.76691e10	+	3.06038e10i	0.340518	+	0.589795i	−0.644011	+	0.765017i	$0.722731\pi$
$140$	−2.96357e10	+	1.71102e10i	−0.551030	+	0.318137i
$141$	2.29184e10	−	3.90846e10i	0.411234	−	0.701310i
$142$	2.50638e10	−	4.34118e10i	0.434115	−	0.751910i
$143$			8.04041e10i			1.34462i
$144$	7.91980e9	−	1.32999e10i	0.127909	−	0.214800i
$145$	−3.74200e10			−0.583799
$146$	1.25741e10	+	7.25967e9i	0.189545	+	0.109434i
$147$	−1.27036e11	+	7.22064e10i	−1.85072	+	1.05194i
$148$	−9.25132e8	−	1.60238e9i	−0.0130285	−	0.0225661i
$149$	3.30466e10	−	1.90795e10i	0.449983	−	0.259798i	−0.257840	−	0.966188i	$-0.583011\pi$
$149$	3.30466e10	−	1.90795e10i	0.449983	−	0.259798i	0.707823	+	0.706390i	$0.249677\pi$
$150$	1.28005e10	+	2.25206e10i	0.168567	+	0.296568i
$151$	3.67685e10	−	6.36850e10i	0.468373	−	0.811245i	−0.530974	−	0.847388i	$-0.678174\pi$
$151$	3.67685e10	−	6.36850e10i	0.468373	−	0.811245i	0.999347	+	0.0361428i	$0.0115071\pi$
$152$			4.95402e10i			0.610576i
$153$	−1.07186e9	+	7.94496e10i	−0.0127844	+	0.947621i
$154$	−1.08486e11			−1.25248
$155$	−2.06720e10	−	1.19350e10i	−0.231060	−	0.133402i
$156$	−5.35083e10	−	3.13761e10i	−0.579159	−	0.339607i
$157$	1.62940e10	+	2.82220e10i	0.170816	+	0.295863i	0.938706	−	0.344720i	$-0.112026\pi$
$157$	1.62940e10	+	2.82220e10i	0.170816	+	0.295863i	−0.767889	+	0.640583i	$0.778693\pi$
$158$	5.74838e10	−	3.31883e10i	0.583795	−	0.337054i
$159$	1.66279e11	+	1.12159e9i	1.63626	+	0.0110369i
$160$	6.66778e9	−	1.15489e10i	0.0635889	−	0.110139i
$161$			1.04290e11i			0.964077i
$162$	6.72377e10	+	4.12774e10i	0.602612	+	0.369945i
$163$	−2.26873e10			−0.197171			−0.0985857	−	0.995129i	$-0.531432\pi$
$163$	−2.26873e10			−0.197171			−0.0985857	+	0.995129i	$0.531432\pi$
$164$	7.62375e9	+	4.40157e9i	0.0642613	+	0.0371013i
$165$	5.94276e8	−	8.81034e10i	0.00485924	−	0.720398i
$166$	−1.54750e10	−	2.68035e10i	−0.122769	−	0.212643i
$167$	−1.28548e11	+	7.42170e10i	−0.989649	+	0.571374i	−0.905170	−	0.425051i	$-0.860256\pi$
$167$	−1.28548e11	+	7.42170e10i	−0.989649	+	0.571374i	−0.0844800	+	0.996425i	$0.526923\pi$
$168$	4.23345e10	−	7.21964e10i	0.316335	−	0.539472i
$169$	−5.53525e10	+	9.58734e10i	−0.401517	+	0.695448i
$170$			6.84526e10i			0.482109i
$171$	−2.52479e11	−	3.40621e9i	−1.72681	−	0.0232965i
$172$	8.11884e10			0.539326
$173$	1.93325e11	+	1.11616e11i	1.24755	+	0.720271i	0.970619	−	0.240620i	$-0.0773507\pi$
$173$	1.93325e11	+	1.11616e11i	1.24755	+	0.720271i	0.276927	+	0.960891i	$0.410684\pi$
$174$	7.95640e10	−	4.52235e10i	0.498851	−	0.283543i
$175$	7.00291e10	+	1.21294e11i	0.426666	+	0.739008i
$176$	3.66126e10	−	2.11383e10i	0.216804	−	0.125172i
$177$	−1.50853e10	−	2.65403e10i	−0.0868336	−	0.152771i
$178$	7.07739e10	−	1.22584e11i	0.396071	−	0.686015i
$179$		−	3.46223e11i		−	1.88404i	−0.335550	−	0.942022i	$-0.608922\pi$
$179$		−	3.46223e11i		−	1.88404i	0.335550	−	0.942022i	$-0.391078\pi$
$180$	5.84002e10	+	3.47761e10i	0.309066	+	0.184043i
$181$	−4.03335e10			−0.207622			−0.103811	−	0.994597i	$-0.533104\pi$
$181$	−4.03335e10			−0.207622			−0.103811	+	0.994597i	$0.533104\pi$
$182$	−2.90444e11	−	1.67688e11i	−1.45447	−	0.839740i
$183$	−1.52928e11	−	8.96737e10i	−0.745128	−	0.436928i
$184$	−2.03207e10	−	3.51964e10i	−0.0963493	−	0.166882i
$185$	7.03608e9	−	4.06228e9i	0.0324692	−	0.0187461i
$186$	5.83777e10	+	3.93770e8i	0.262230	+	0.00176880i
$187$	−1.08505e11	+	1.87936e11i	−0.474505	+	0.821866i
$188$			9.54648e10i			0.406494i
$189$	3.65035e11	+	2.20720e11i	1.51365	+	0.915234i
$190$	−2.17532e11			−0.878529
$191$	−7.65392e10	−	4.41899e10i	−0.301104	−	0.173843i	0.341835	−	0.939760i	$-0.388952\pi$
$191$	−7.65392e10	−	4.41899e10i	−0.301104	−	0.173843i	−0.642939	+	0.765918i	$0.722285\pi$
$192$	−2.19989e8	+	3.26142e10i	−0.000843132	+	0.124997i
$193$	9.21581e10	+	1.59622e11i	0.344149	+	0.596084i	0.985199	−	0.171415i	$-0.0548340\pi$
$193$	9.21581e10	+	1.59622e11i	0.344149	+	0.596084i	−0.641050	+	0.767500i	$0.721501\pi$
$194$	−1.23668e11	+	7.14000e10i	−0.450039	+	0.259830i
$195$	1.37774e11	−	2.34957e11i	0.488644	−	0.833325i
$196$	1.53941e11	−	2.66633e11i	0.532197	−	0.921793i
$197$		−	5.62698e11i		−	1.89646i	−0.317580	−	0.948231i	$-0.602870\pi$
$197$		−	5.62698e11i		−	1.89646i	0.317580	−	0.948231i	$-0.397130\pi$
$198$	1.05213e11	+	1.88048e11i	0.345735	+	0.617934i
$199$	−2.24708e11			−0.720034			−0.360017	−	0.932946i	$-0.617229\pi$
$199$	−2.24708e11			−0.720034			−0.360017	+	0.932946i	$0.617229\pi$
$200$	−4.72679e10	−	2.72901e10i	−0.147712	−	0.0852816i
$201$	−8.38537e10	+	4.76617e10i	−0.255589	+	0.145275i
$202$	1.37358e9	+	2.37912e9i	0.00408412	+	0.00707390i
$203$	4.28525e11	−	2.47409e11i	1.24307	−	0.717687i
$204$	−8.27278e10	−	1.45547e11i	−0.234153	−	0.411958i
$205$	−1.93274e10	+	3.34761e10i	−0.0533832	+	0.0924625i
$206$		−	1.71644e10i		−	0.0462692i
$207$	1.80774e11	−	1.01143e11i	0.475647	−	0.266125i
$208$	1.30695e11			0.335693
$209$	−5.97232e11	−	3.44812e11i	−1.49765	−	0.864671i
$210$	3.17017e11	+	1.85892e11i	0.776222	+	0.455160i
$211$	3.10097e11	+	5.37104e11i	0.741456	+	1.28424i	0.951832	+	0.306619i	$0.0991977\pi$
$211$	3.10097e11	+	5.37104e11i	0.741456	+	1.28424i	−0.210376	+	0.977620i	$0.567469\pi$
$212$	−3.03418e11	+	1.75179e11i	−0.708537	+	0.409074i
$213$	−5.38317e11	−	3.63106e9i	−1.22784	−	0.00828201i
$214$	−3.08080e11	+	5.33610e11i	−0.686427	+	1.18893i
$215$			3.56501e11i			0.776011i
$216$	−1.66201e11	−	3.36360e9i	−0.353481	−	0.00715378i
$217$	3.15642e11			0.655987
$218$	2.80649e11	+	1.62033e11i	0.570007	+	0.329094i
$219$	1.05173e9	−	1.55922e11i	0.00208777	−	0.309519i
$220$	9.28188e10	+	1.60767e11i	0.180104	+	0.311949i
$221$	−5.80989e11	+	3.35434e11i	−1.10206	+	0.636277i
$222$	−1.00510e10	+	1.71408e10i	−0.0186399	+	0.0317882i
$223$	1.17304e11	−	2.03177e11i	0.212711	−	0.368426i	−0.739851	−	0.672771i	$-0.765104\pi$
$223$	1.17304e11	−	2.03177e11i	0.212711	−	0.368426i	0.952562	+	0.304344i	$0.0984374\pi$
$224$			1.76341e11i			0.312689i
$225$	1.42333e11	−	2.39022e11i	0.246827	−	0.414501i
$226$	−1.83831e11			−0.311800
$227$	8.93353e11	+	5.15778e11i	1.48216	+	0.855723i	0.999795	−	0.0202491i	$-0.00644594\pi$
$227$	8.93353e11	+	5.15778e11i	1.48216	+	0.855723i	0.482361	+	0.875972i	$0.339779\pi$
$228$	4.62528e11	−	2.62897e11i	0.750695	−	0.426689i
$229$	4.81204e10	+	8.33469e10i	0.0764102	+	0.132346i	0.901699	−	0.432365i	$-0.142321\pi$
$229$	4.81204e10	+	8.33469e10i	0.0764102	+	0.132346i	−0.825288	+	0.564711i	$0.808987\pi$
$230$	1.54549e11	−	8.92286e10i	0.240119	−	0.138633i
$231$	5.75706e11	+	1.01287e12i	0.875267	+	1.53990i
$232$	−9.64144e10	+	1.66995e11i	−0.143450	+	0.248463i
$233$		−	7.14740e11i		−	1.04080i	−0.853922	−	0.520401i	$-0.825782\pi$
$233$		−	7.14740e11i		−	1.04080i	0.853922	−	0.520401i	$-0.174218\pi$
$234$	−8.98612e9	+	6.66080e11i	−0.0128083	+	0.949396i
$235$	−4.19189e11			−0.584885
$236$	5.57047e10	+	3.21611e10i	0.0760908	+	0.0439310i
$237$	−6.14911e11	−	3.60571e11i	−0.822376	−	0.482224i
$238$	−4.52587e11	−	7.83904e11i	−0.592676	−	1.02654i
$239$	8.12115e10	−	4.68875e10i	0.104142	−	0.0601267i	−0.447024	−	0.894522i	$-0.647516\pi$
$239$	8.12115e10	−	4.68875e10i	0.104142	−	0.0601267i	0.551167	+	0.834395i	$0.314183\pi$
$240$	−1.43210e11	−	9.65981e8i	−0.179853	−	0.00121314i
$241$	1.55897e10	−	2.70022e10i	0.0191758	−	0.0332135i	−0.856278	−	0.516515i	$-0.827229\pi$
$241$	1.55897e10	−	2.70022e10i	0.0191758	−	0.0332135i	0.875454	+	0.483301i	$0.160562\pi$
$242$			1.61378e9i			0.00194432i
$243$	2.85699e10	−	8.46807e11i	0.0337192	−	0.999431i
$244$	3.73529e11			0.431892
$245$	1.17079e12	+	6.75958e11i	1.32632	+	0.765754i
$246$	6.37668e8	−	9.45364e10i	0.000707814	−	0.104936i
$247$	−1.06596e12	−	1.84630e12i	−1.15946	−	2.00825i
$248$	−1.06525e11	+	6.15022e10i	−0.113552	+	0.0655590i
$249$	−1.68126e11	+	2.86720e11i	−0.175646	+	0.299544i
$250$	3.68226e11	−	6.37786e11i	0.377063	−	0.653093i
$251$			5.40360e11i			0.542394i	0.962524	+	0.271197i	$0.0874195\pi$
$251$			5.40360e11i			0.542394i	−0.962524	+	0.271197i	$0.912581\pi$
$252$	−8.98714e11	−	1.21246e10i	−0.884339	−	0.0119306i
$253$	5.65747e11			0.545783
$254$	−9.39108e11	−	5.42194e11i	−0.888274	−	0.512845i
$255$	6.39102e11	−	3.63260e11i	0.592747	−	0.336912i
$256$	−3.43597e10	−	5.95128e10i	−0.0312500	−	0.0541266i
$257$	−1.43387e12	+	8.27848e11i	−1.27893	+	0.738388i	−0.976651	−	0.214833i	$-0.931079\pi$
$257$	−1.43387e12	+	8.27848e11i	−1.27893	+	0.738388i	−0.302275	+	0.953221i	$0.597746\pi$
$258$	−4.30846e11	−	7.58008e11i	−0.376897	−	0.663095i
$259$	−5.37170e10	+	9.30406e10i	−0.0460907	+	0.0798314i
$260$			5.73885e11i			0.483012i
$261$	−8.44451e11	−	5.02853e11i	−0.697223	−	0.415182i
$262$	8.86537e11			0.718109
$263$	5.11270e11	+	2.95182e11i	0.406323	+	0.234591i	0.689209	−	0.724563i	$-0.257958\pi$
$263$	5.11270e11	+	2.95182e11i	0.406323	+	0.234591i	−0.282886	+	0.959154i	$0.591292\pi$
$264$	−3.91649e11	−	2.29655e11i	−0.305406	−	0.179084i
$265$	−7.69214e11	−	1.33232e12i	−0.588597	−	1.01948i
$266$	2.49113e12	−	1.43826e12i	1.87063	−	1.08001i
$267$	−1.52007e12	−	1.02532e10i	−1.12023	−	0.00755621i
$268$	1.01612e11	−	1.75998e11i	0.0734976	−	0.127302i
$269$			6.19166e11i			0.439588i	0.975546	+	0.219794i	$0.0705385\pi$
$269$			6.19166e11i			0.439588i	−0.975546	+	0.219794i	$0.929462\pi$
$270$	1.47697e10	−	7.29796e11i	0.0102932	−	0.508607i
$271$	1.40389e12			0.960474			0.480237	−	0.877139i	$-0.340551\pi$
$271$	1.40389e12			0.960474			0.480237	+	0.877139i	$0.340551\pi$
$272$	3.05485e11	+	1.76372e11i	0.205185	+	0.118463i
$273$	−2.42934e10	+	3.60158e12i	−0.0160205	+	2.37509i
$274$	6.89370e11	+	1.19402e12i	0.446375	+	0.773143i
$275$	6.57992e11	−	3.79892e11i	0.418367	−	0.241544i
$276$	−2.20772e11	+	3.76500e11i	−0.137847	+	0.235082i
$277$	2.94962e11	−	5.10889e11i	0.180870	−	0.313276i	−0.761307	−	0.648392i	$-0.775442\pi$
$277$	2.94962e11	−	5.10889e11i	0.180870	−	0.313276i	0.942177	+	0.335115i	$0.108775\pi$
$278$			7.99613e11i			0.481566i
$279$	−3.06119e11	−	5.47128e11i	−0.181079	−	0.323644i
$280$	−7.74319e11			−0.449914
$281$	−1.37349e12	−	7.92985e11i	−0.783960	−	0.452620i	0.0538718	−	0.998548i	$-0.482844\pi$
$281$	−1.37349e12	−	7.92985e11i	−0.783960	−	0.452620i	−0.837832	+	0.545928i	$0.816177\pi$
$282$	8.91299e11	−	5.06607e11i	0.499779	−	0.284070i
$283$	1.28404e12	+	2.22403e12i	0.707371	+	1.22520i	0.965829	+	0.259181i	$0.0834525\pi$
$283$	1.28404e12	+	2.22403e12i	0.707371	+	1.22520i	−0.258457	+	0.966023i	$0.583214\pi$
$284$	9.82296e11	−	5.67129e11i	0.531680	−	0.306966i
$285$	1.15439e12	+	2.03097e12i	0.613942	+	1.08014i
$286$	−9.09669e11	+	1.57559e12i	−0.475393	+	0.823406i
$287$		−	5.11147e11i		−	0.262504i
$288$	3.05667e11	−	1.71021e11i	0.154272	−	0.0863151i
$289$	2.05332e11			0.101851
$290$	−7.33278e11	−	4.23358e11i	−0.357502	−	0.206404i
$291$	1.32290e12	+	7.75718e11i	0.633958	+	0.371740i
$292$	1.64267e11	+	2.84520e11i	0.0773815	+	0.134029i
$293$	−2.29745e12	+	1.32644e12i	−1.06392	+	0.614254i	−0.926514	−	0.376261i	$-0.877210\pi$
$293$	−2.29745e12	+	1.32644e12i	−1.06392	+	0.614254i	−0.137406	+	0.990515i	$0.543876\pi$
$294$	−3.30632e12	−	2.23018e10i	−1.50525	−	0.0101532i
$295$	−1.41220e11	+	2.44601e11i	−0.0632103	+	0.109483i
$296$		−	4.18667e10i		−	0.0184251i
$297$	1.19735e12	−	1.98023e12i	0.518132	−	0.856907i
$298$	8.63439e11			0.367410
$299$	1.51465e12	+	8.74483e11i	0.633806	+	0.365928i
$300$	−3.95360e9	+	5.86134e11i	−0.00162699	+	0.241207i
$301$	−2.35707e12	−	4.08256e12i	−0.953981	−	1.65234i
$302$	1.44103e12	−	8.31977e11i	0.573637	−	0.331190i
$303$	1.49232e10	−	2.54497e10i	0.00584316	−	0.00996482i
$304$	−5.60483e11	+	9.70785e11i	−0.215871	+	0.373900i
$305$			1.64018e12i			0.621429i
$306$	−9.19874e11	+	1.54476e12i	−0.342863	+	0.575777i
$307$	1.92040e12			0.704206			0.352103	−	0.935961i	$-0.385467\pi$
$307$	1.92040e12			0.704206			0.352103	+	0.935961i	$0.385467\pi$
$308$	−2.12588e12	−	1.22738e12i	−0.766982	−	0.442817i
$309$	−1.60254e11	+	9.10869e10i	−0.0568874	+	0.0323343i
$310$	−2.70058e11	−	4.67754e11i	−0.0943298	−	0.163384i
$311$	−1.30530e12	+	7.53618e11i	−0.448652	+	0.259030i	−0.707261	−	0.706953i	$-0.750069\pi$
$311$	−1.30530e12	+	7.53618e11i	−0.448652	+	0.259030i	0.258609	+	0.965982i	$0.416736\pi$
$312$	−6.93564e11	−	1.22022e12i	−0.234592	−	0.412730i
$313$	−1.90318e12	+	3.29641e12i	−0.633517	+	1.09728i	0.353310	+	0.935506i	$0.385056\pi$
$313$	−1.90318e12	+	3.29641e12i	−0.633517	+	1.09728i	−0.986827	+	0.161778i	$0.948277\pi$
$314$			7.37382e11i			0.241571i
$315$	5.32394e10	−	3.94628e12i	0.0171664	−	1.27243i
$316$	1.50193e12			0.476666
$317$	−2.81750e12	−	1.62669e12i	−0.880173	−	0.508168i	−0.00945758	−	0.999955i	$-0.503010\pi$
$317$	−2.81750e12	−	1.62669e12i	−0.880173	−	0.508168i	−0.870715	+	0.491787i	$0.836344\pi$
$318$	3.24570e12	+	1.90321e12i	0.998097	+	0.585263i
$319$	−1.34214e12	−	2.32465e12i	−0.406297	−	0.703726i
$320$	2.61323e11	−	1.50875e11i	0.0778802	−	0.0449642i
$321$	6.61690e12	+	4.46324e10i	1.94146	+	0.0130956i
$322$	−1.17990e12	+	2.04365e12i	−0.340853	+	0.590374i
$323$		−	5.75402e12i		−	1.63666i
$324$	8.50584e11	+	1.56958e12i	0.238228	+	0.439599i
$325$	2.34882e12			0.647787
$326$	−4.44578e11	−	2.56677e11i	−0.120742	−	0.0697106i
$327$	2.34741e10	−	3.48012e12i	0.00627842	−	0.930797i
$328$	9.95962e10	+	1.72506e11i	0.0262345	+	0.0454396i
$329$	4.80045e12	−	2.77154e12i	1.24538	−	0.719022i
$330$	1.00842e12	−	1.71974e12i	0.257675	−	0.439434i
$331$	−2.55875e12	+	4.43188e12i	−0.644002	+	1.11544i	0.340529	+	0.940234i	$0.389394\pi$
$331$	−2.55875e12	+	4.43188e12i	−0.644002	+	1.11544i	−0.984531	+	0.175210i	$0.943940\pi$
$332$		−	7.00318e11i		−	0.173622i
$333$	2.13372e11	+	2.87861e9i	0.0521093	+	0.000703009i
$334$	−3.35868e12			−0.808045
$335$	7.72813e11	+	4.46184e11i	0.183168	+	0.105752i
$336$	1.64639e12	−	9.35795e11i	0.384447	−	0.218517i
$337$	−3.31588e11	−	5.74327e11i	−0.0762868	−	0.132133i	0.825358	−	0.564609i	$-0.190973\pi$
$337$	−3.31588e11	−	5.74327e11i	−0.0762868	−	0.132133i	−0.901645	+	0.432477i	$0.857640\pi$
$338$	−2.16937e12	+	1.25248e12i	−0.491756	+	0.283915i
$339$	9.75543e11	+	1.71632e12i	0.217895	+	0.383354i
$340$	−7.74453e11	+	1.34139e12i	−0.170451	+	0.295230i
$341$		−	1.71228e12i		−	0.371367i
$342$	−4.90903e12	−	2.92322e12i	−1.04922	−	0.624787i
$343$	−9.47920e12			−1.99665
$344$	1.59096e12	+	9.18542e11i	0.330269	+	0.190681i
$345$	−1.65322e12	−	9.69416e11i	−0.338249	−	0.198342i
$346$	2.52558e12	+	4.37444e12i	0.509309	+	0.882149i
$347$	−7.91407e12	+	4.56919e12i	−1.57309	+	0.908222i	−0.577298	+	0.816533i	$0.695893\pi$
$347$	−7.91407e12	+	4.56919e12i	−1.57309	+	0.908222i	−0.995788	+	0.0916881i	$0.970774\pi$
$348$	2.07078e12	+	1.39678e10i	0.405730	+	0.00273673i
$349$	3.19348e12	−	5.53126e12i	0.616789	−	1.06831i	−0.373279	−	0.927719i	$-0.621767\pi$
$349$	3.19348e12	−	5.53126e12i	0.616789	−	1.06831i	0.990068	−	0.140590i	$-0.0449000\pi$
$350$			3.16916e12i			0.603397i
$351$	6.26649e12	−	3.45082e12i	1.17622	−	0.647718i
$352$	9.56609e11			0.177020
$353$	−5.64691e12	−	3.26024e12i	−1.03024	−	0.594807i	−0.113184	−	0.993574i	$-0.536105\pi$
$353$	−5.64691e12	−	3.26024e12i	−1.03024	−	0.594807i	−0.917052	+	0.398767i	$0.869438\pi$
$354$	4.65927e9	−	6.90753e11i	0.000838112	−	0.124253i
$355$	2.49028e12	+	4.31329e12i	0.441679	+	0.765010i
$356$	2.77376e12	−	1.60143e12i	0.485086	−	0.280065i
$357$	−4.91709e12	+	8.38551e12i	−0.847943	+	1.44607i
$358$	3.91707e12	−	6.78457e12i	0.666110	−	1.15374i
$359$			1.81592e12i			0.304526i	0.988340	+	0.152263i	$0.0486560\pi$
$359$			1.81592e12i			0.304526i	−0.988340	+	0.152263i	$0.951344\pi$
$360$	7.50958e11	+	1.34219e12i	0.124195	+	0.221974i
$361$	1.21544e13			1.98242
$362$	−7.90373e11	−	4.56322e11i	−0.127142	−	0.0734055i
$363$	1.50669e10	−	8.56392e9i	0.00239052	−	0.00135875i
$364$	−3.79435e12	−	6.57200e12i	−0.593786	−	1.02847i
$365$	−1.24933e12	+	7.21304e11i	−0.192848	+	0.111341i
$366$	−1.98222e12	−	3.48742e12i	−0.301819	−	0.531005i
$367$	−3.64687e12	+	6.31657e12i	−0.547760	+	0.948748i	0.450668	+	0.892692i	$0.351186\pi$
$367$	−3.64687e12	+	6.31657e12i	−0.547760	+	0.948748i	−0.998428	+	0.0560561i	$0.982147\pi$
$368$		−	9.19608e11i		−	0.136259i
$369$	−8.86015e11	+	4.95727e11i	−0.129512	+	0.0724620i
$370$	1.83838e11			0.0265110
$371$	1.76177e13	+	1.01716e13i	2.50657	+	1.44717i
$372$	1.13951e12	+	6.68185e11i	0.159957	+	0.0937955i
$373$	4.64863e12	+	8.05166e12i	0.643844	+	1.11517i	0.984567	+	0.175007i	$0.0559947\pi$
$373$	4.64863e12	+	8.05166e12i	0.643844	+	1.11517i	−0.340724	+	0.940164i	$0.610672\pi$
$374$	−4.25250e12	+	2.45518e12i	−0.581147	+	0.335525i
$375$	−7.90871e12	−	5.33459e10i	−1.06647	−	0.00719358i
$376$	−1.08006e12	+	1.87072e12i	−0.143717	+	0.248926i
$377$		−	8.29823e12i		−	1.08963i
$378$	4.65604e12	+	8.45510e12i	0.603334	+	1.09562i
$379$	−1.18896e13			−1.52045			−0.760224	−	0.649661i	$-0.774911\pi$
$379$	−1.18896e13			−1.52045			−0.760224	+	0.649661i	$0.774911\pi$
$380$	−4.26275e12	−	2.46110e12i	−0.537987	−	0.310607i
$381$	−7.85492e10	+	1.16452e13i	−0.00978401	+	1.45051i
$382$	−9.99903e11	−	1.73188e12i	−0.122925	−	0.212913i
$383$	7.13023e12	−	4.11664e12i	0.865186	−	0.499515i	−0.000559502	−	1.00000i	$-0.500178\pi$
$383$	7.13023e12	−	4.11664e12i	0.865186	−	0.499515i	0.865746	+	0.500484i	$0.166845\pi$
$384$	−3.73298e11	+	6.36616e11i	−0.0447095	+	0.0762467i
$385$	5.38945e12	−	9.33480e12i	0.637149	−	1.10357i
$386$			4.17060e12i			0.486701i
$387$	−4.79069e12	+	8.04510e12i	−0.551879	+	0.926780i
$388$	−3.23119e12			−0.367455
$389$	3.37542e12	+	1.94880e12i	0.378948	+	0.218786i	0.677360	−	0.735651i	$-0.263124\pi$
$389$	3.37542e12	+	1.94880e12i	0.378948	+	0.218786i	−0.298412	+	0.954437i	$0.596457\pi$
$390$	5.35803e12	−	3.04546e12i	0.593857	−	0.337543i
$391$	2.36021e12	+	4.08801e12i	0.258266	+	0.447330i
$392$	6.03321e12	−	3.48328e12i	0.651806	−	0.376320i
$393$	−4.70462e12	−	8.27708e12i	−0.501836	−	0.882905i
$394$	6.36620e12	−	1.10266e13i	0.670501	−	1.16134i
$395$			6.59502e12i			0.685853i
$396$	−6.57731e10	+	4.87532e12i	−0.00675417	+	0.500641i
$397$	3.90898e11			0.0396380			0.0198190	−	0.999804i	$-0.493691\pi$
$397$	3.90898e11			0.0396380			0.0198190	+	0.999804i	$0.493691\pi$
$398$	−4.40336e12	−	2.54228e12i	−0.440929	−	0.254571i
$399$	−2.66479e13	−	1.56258e13i	−2.63511	−	1.54517i
$400$	−6.17505e11	−	1.06955e12i	−0.0603032	−	0.104448i
$401$	−2.92962e12	+	1.69141e12i	−0.282546	+	0.163128i	−0.634575	−	0.772861i	$-0.718825\pi$
$401$	−2.92962e12	+	1.69141e12i	−0.282546	+	0.163128i	0.352030	+	0.935989i	$0.385492\pi$
$402$	−2.18242e12	−	1.47209e10i	−0.207878	−	0.00140218i
$403$	2.64670e12	−	4.58422e12i	0.248988	−	0.431261i
$404$			6.21613e10i			0.00577582i
$405$	−6.89205e12	+	3.73494e12i	−0.632519	+	0.342774i
$406$	1.11964e13			1.01496
$407$	5.04724e11	+	2.91403e11i	0.0451941	+	0.0260928i
$408$	2.55515e10	−	3.78809e12i	0.00226003	−	0.335057i
$409$	2.96970e12	+	5.14368e12i	0.259476	+	0.449425i	0.966102	−	0.258162i	$-0.0831170\pi$
$409$	2.96970e12	+	5.14368e12i	0.259476	+	0.449425i	−0.706626	+	0.707587i	$0.749784\pi$
$410$	−7.57478e11	+	4.37330e11i	−0.0653809	+	0.0377477i
$411$	7.48959e12	−	1.27726e13i	0.638630	−	1.08911i
$412$	1.94193e11	−	3.36352e11i	0.0163586	−	0.0283340i
$413$		−	3.73482e12i		−	0.310827i
$414$	4.68674e12	+	6.32290e10i	0.385362	+	0.00519894i
$415$	3.07512e12			0.249817
$416$	2.56109e12	+	1.47864e12i	0.205569	+	0.118685i
$417$	7.46551e12	−	4.24333e12i	0.592079	−	0.336532i
$418$	−7.80221e12	−	1.35138e13i	−0.611415	−	1.05900i
$419$	2.82956e12	−	1.63365e12i	0.219104	−	0.126500i	−0.386432	−	0.922318i	$-0.626292\pi$
$419$	2.82956e12	−	1.63365e12i	0.219104	−	0.126500i	0.605535	+	0.795819i	$0.292959\pi$
$420$	4.10911e12	+	7.22936e12i	0.314413	+	0.553163i
$421$	9.53634e12	−	1.65174e13i	0.721060	−	1.24891i	−0.239516	−	0.970892i	$-0.576989\pi$
$421$	9.53634e12	−	1.65174e13i	0.721060	−	1.24891i	0.960575	−	0.278020i	$-0.0896780\pi$
$422$			1.40334e13i			1.04858i
$423$	−9.45978e12	−	5.63310e12i	−0.698520	−	0.415955i
$424$	−7.92768e12			−0.578518
$425$	5.49009e12	+	3.16971e12i	0.395945	+	0.228599i
$426$	−1.05077e13	−	6.16152e12i	−0.748964	−	0.439177i
$427$	−1.08443e13	−	1.87829e13i	−0.763947	−	1.32319i
$428$	−1.20742e13	+	6.97105e12i	−0.840698	+	0.485377i
$429$	1.95378e13	+	1.31786e11i	1.34459	+	0.00906951i
$430$	−4.03335e12	+	6.98596e12i	−0.274361	+	0.475208i
$431$		−	1.15810e13i		−	0.778681i	−0.921094	−	0.389340i	$-0.872703\pi$
$431$		−	1.15810e13i		−	0.778681i	0.921094	−	0.389340i	$-0.127297\pi$
$432$	−3.21882e12	−	1.94627e12i	−0.213933	−	0.129355i
$433$	−9.49725e12			−0.623963			−0.311981	−	0.950088i	$-0.600993\pi$
$433$	−9.49725e12			−0.623963			−0.311981	+	0.950088i	$0.600993\pi$
$434$	6.18529e12	+	3.57108e12i	0.401709	+	0.231927i
$435$	−6.13332e10	+	9.09284e12i	−0.00393776	+	0.583786i
$436$	3.66638e12	+	6.35036e12i	0.232705	+	0.403056i
$437$	−1.29911e13	+	7.50042e12i	−0.815153	+	0.470629i
$438$	1.78467e12	−	3.04354e12i	0.110710	−	0.188803i
$439$	−1.00399e13	+	1.73896e13i	−0.615754	+	1.06652i	0.374498	+	0.927228i	$0.377815\pi$
$439$	−1.00399e13	+	1.73896e13i	−0.615754	+	1.06652i	−0.990252	+	0.139290i	$0.955518\pi$
$440$			4.20050e12i			0.254705i
$441$	1.73375e13	+	3.09875e13i	1.03943	+	1.85778i
$442$	−1.51800e13			−0.899831
$443$	5.44483e12	+	3.14358e12i	0.319129	+	0.184249i	0.651004	−	0.759074i	$-0.274348\pi$
$443$	5.44483e12	+	3.14358e12i	0.319129	+	0.184249i	−0.331875	+	0.943323i	$0.607681\pi$
$444$	−3.90885e11	+	2.22176e11i	−0.0226534	+	0.0128760i
$445$	7.03193e12	+	1.21797e13i	0.402972	+	0.697968i
$446$	4.59737e12	−	2.65430e12i	0.260517	−	0.150409i
$447$	−4.58205e12	−	8.06142e12i	−0.256757	−	0.451725i
$448$	−1.99507e12	+	3.45556e12i	−0.110552	+	0.191482i
$449$		−	4.03044e12i		−	0.220862i	−0.993884	−	0.110431i	$-0.964777\pi$
$449$		−	4.03044e12i		−	0.220862i	0.993884	−	0.110431i	$-0.0352231\pi$
$450$	5.49337e12	−	3.07355e12i	0.297698	−	0.166562i
$451$	−2.77286e12			−0.148609
$452$	−3.60234e12	−	2.07981e12i	−0.190938	−	0.110238i
$453$	−1.54148e13	−	9.03893e12i	−0.808068	−	0.473834i
$454$	1.16707e13	+	2.02143e13i	0.605088	+	1.04804i
$455$	2.88579e13	−	1.66611e13i	1.47981	−	0.854371i
$456$	1.20380e13	+	8.11988e10i	0.610562	+	0.00411837i
$457$	5.10969e12	−	8.85024e12i	0.256338	−	0.443991i	−0.708920	−	0.705289i	$-0.750817\pi$
$457$	5.10969e12	−	8.85024e12i	0.256338	−	0.443991i	0.965258	+	0.261298i	$0.0841506\pi$
$458$			2.17768e12i			0.108060i
$459$	1.93041e13	+	3.90677e11i	0.947513	+	0.0191759i
$460$	4.03803e12			0.196056
$461$	−9.69960e11	−	5.60007e11i	−0.0465853	−	0.0268961i	0.476526	−	0.879160i	$-0.341896\pi$
$461$	−9.69960e11	−	5.60007e11i	−0.0465853	−	0.0268961i	−0.523112	+	0.852264i	$0.675229\pi$
$462$	−1.77814e11	+	2.63615e13i	−0.00844802	+	1.25245i
$463$	1.43746e13	+	2.48975e13i	0.675602	+	1.17018i	0.976293	+	0.216455i	$0.0694495\pi$
$463$	1.43746e13	+	2.48975e13i	0.675602	+	1.17018i	−0.300691	+	0.953722i	$0.597217\pi$
$464$	−3.77866e12	+	2.18161e12i	−0.175690	+	0.101435i
$465$	−2.93402e12	+	5.00362e12i	−0.134958	+	0.230155i
$466$	8.08636e12	−	1.40060e13i	0.367979	−	0.637359i
$467$			2.33221e13i			1.04998i	0.851107	+	0.524992i	$0.175932\pi$
$467$			2.33221e13i			1.04998i	−0.851107	+	0.524992i	$0.824068\pi$
$468$	−7.71193e12	+	1.29508e13i	−0.343506	+	0.576856i
$469$	−1.18001e13			−0.520021
$470$	−8.21439e12	−	4.74258e12i	−0.358167	−	0.206788i
$471$	6.88451e12	−	3.91309e12i	0.297008	−	0.168817i
$472$	7.27723e11	+	1.26045e12i	0.0310639	+	0.0538043i
$473$	−2.21470e13	+	1.27866e13i	−0.935424	+	0.540067i
$474$	−7.97035e12	−	1.40226e13i	−0.333109	−	0.586055i
$475$	−1.00729e13	+	1.74467e13i	−0.416567	+	0.721515i
$476$		−	2.04817e13i		−	0.838170i
$477$	5.45079e11	−	4.04030e13i	0.0220733	−	1.63615i
$478$	2.12188e12			0.0850320
$479$	−4.02408e13	−	2.32330e13i	−1.59584	−	0.921358i	−0.992277	−	0.124042i	$-0.960414\pi$
$479$	−4.02408e13	−	2.32330e13i	−1.59584	−	0.921358i	−0.603562	−	0.797316i	$-0.706252\pi$
$480$	−2.79540e12	−	1.63916e12i	−0.109708	−	0.0643304i
$481$	9.00850e11	+	1.56032e12i	0.0349886	+	0.0606021i
$482$	6.10990e11	−	3.52755e11i	0.0234855	−	0.0135593i
$483$	2.53418e13	+	1.70936e11i	0.964055	+	0.00650276i
$484$	−1.82579e10	+	3.16235e10i	−0.000687421	+	0.00119065i
$485$		−	1.41883e13i		−	0.528714i
$486$	1.01404e13	−	1.62707e13i	0.374001	−	0.600103i
$487$	−2.47240e13			−0.902555			−0.451278	−	0.892384i	$-0.649032\pi$
$487$	−2.47240e13			−0.902555			−0.451278	+	0.892384i	$0.649032\pi$
$488$	7.31964e12	+	4.22599e12i	0.264479	+	0.152697i
$489$	−3.71855e10	+	5.51288e12i	−0.00132993	+	0.197167i
$490$	1.52952e13	+	2.64920e13i	0.541470	+	0.937853i
$491$	1.29872e13	−	7.49815e12i	0.455101	−	0.262753i	−0.254881	−	0.966972i	$-0.582036\pi$
$491$	1.29872e13	−	7.49815e12i	0.455101	−	0.262753i	0.709982	+	0.704220i	$0.248703\pi$
$492$	1.08205e12	−	1.84531e12i	0.0375339	−	0.0640095i
$493$	1.11984e13	−	1.93962e13i	0.384522	−	0.666011i
$494$		−	4.82399e13i		−	1.63973i
$495$	−2.14077e13	−	2.88812e11i	−0.720349	−	0.00971826i
$496$	−2.78327e12			−0.0927144
$497$	−5.70362e13	−	3.29299e13i	−1.88091	−	1.08595i
$498$	−6.53846e12	+	3.71640e12i	−0.213466	+	0.121332i
$499$	1.08896e13	+	1.88614e13i	0.351974	+	0.609636i	0.986595	−	0.163187i	$-0.0521773\pi$
$499$	1.08896e13	+	1.88614e13i	0.351974	+	0.609636i	−0.634621	+	0.772823i	$0.718844\pi$
$500$	1.44314e13	−	8.33200e12i	0.461806	−	0.266624i
$501$	1.78236e13	+	3.13580e13i	0.564686	+	0.993481i
$502$	−6.11348e12	+	1.05889e13i	−0.191765	+	0.332147i
$503$			1.63134e13i			0.506647i	0.967382	+	0.253323i	$0.0815237\pi$
$503$			1.63134e13i			0.506647i	−0.967382	+	0.253323i	$0.918476\pi$
$504$	−1.74739e13	−	1.04054e13i	−0.537327	−	0.319967i
$505$	−2.72952e11			−0.00831055
$506$	1.10863e13	+	6.40070e12i	0.334222	+	0.192963i
$507$	2.32060e13	+	1.36075e13i	0.692724	+	0.406199i
$508$	−1.22685e13	−	2.12496e13i	−0.362636	−	0.628104i
$509$	5.37118e12	−	3.10105e12i	0.157210	−	0.0907654i	−0.419331	−	0.907833i	$-0.637735\pi$
$509$	5.37118e12	−	3.10105e12i	0.157210	−	0.0907654i	0.576541	+	0.817068i	$0.304402\pi$
$510$	1.66336e13	+	1.12197e11i	0.482098	+	0.00325186i
$511$	9.53806e12	−	1.65204e13i	0.273751	−	0.474150i
$512$		−	1.55494e12i		−	0.0441942i
$513$	−1.24152e12	+	6.13455e13i	−0.0349434	+	1.72662i
$514$	−3.74641e13			−1.04424
$515$	1.47693e12	+	8.52706e11i	0.0407684	+	0.0235377i
$516$	1.33072e11	−	1.97283e13i	0.00363779	−	0.539314i
$517$	−1.50350e13	−	2.60414e13i	−0.407052	−	0.705035i
$518$	−2.10527e12	+	1.21548e12i	−0.0564493	+	0.0325910i
$519$	2.74389e13	−	4.67939e13i	0.728670	−	1.24266i
$520$	−6.49277e12	+	1.12458e13i	−0.170771	+	0.295784i
$521$			3.48571e13i			0.908035i	0.890993	+	0.454018i	$0.150010\pi$
$521$			3.48571e13i			0.908035i	−0.890993	+	0.454018i	$0.849990\pi$
$522$	−1.08587e13	−	1.94077e13i	−0.280171	−	0.500752i
$523$	6.31789e13			1.61459			0.807297	−	0.590146i	$-0.200930\pi$
$523$	6.31789e13			1.61459			0.807297	+	0.590146i	$0.200930\pi$
$524$	1.73725e13	+	1.00300e13i	0.439750	+	0.253890i
$525$	2.95886e13	−	1.68179e13i	0.741869	−	0.421672i
$526$	6.67920e12	+	1.15687e13i	0.165881	+	0.287314i
$527$	1.23727e13	−	7.14339e12i	0.304377	−	0.175732i
$528$	−5.07648e12	−	8.93130e12i	−0.123707	−	0.217643i
$529$	−1.45601e13	+	2.52189e13i	−0.351469	+	0.608762i
$530$		−	3.48107e13i		−	0.832402i
$531$	−6.47388e12	+	3.62214e12i	−0.153353	+	0.0858011i
$532$	6.50880e13			1.52737
$533$	−7.42364e12	−	4.28604e12i	−0.172576	−	0.0996370i
$534$	−2.96712e13	−	1.73986e13i	−0.683328	−	0.400689i
$535$	−3.06101e13	−	5.30182e13i	−0.698386	−	1.20964i
$536$	3.98238e12	−	2.29923e12i	0.0900158	−	0.0519706i
$537$	−8.41304e13	−	5.67477e11i	−1.88400	−	0.0127080i
$538$	−7.00506e12	+	1.21331e13i	−0.155418	+	0.269191i
$539$			9.69779e13i			2.13171i
$540$	8.54612e12	−	1.41339e13i	0.186123	−	0.307818i
$541$	7.35259e12			0.158655			0.0793275	−	0.996849i	$-0.474723\pi$
$541$	7.35259e12			0.158655			0.0793275	+	0.996849i	$0.474723\pi$
$542$	2.75104e13	+	1.58832e13i	0.588168	+	0.339579i
$543$	−6.61087e10	+	9.80083e12i	−0.00140042	+	0.207617i
$544$	3.99083e12	+	6.91233e12i	0.0837663	+	0.145087i
$545$	−2.78846e13	+	1.60992e13i	−0.579939	+	0.334828i
$546$	−4.12233e13	+	7.03015e13i	−0.849532	+	1.44878i
$547$	−1.54898e13	+	2.68292e13i	−0.316308	+	0.547861i	−0.979715	−	0.200398i	$-0.935777\pi$
$547$	−1.54898e13	+	2.68292e13i	−0.316308	+	0.547861i	0.663407	+	0.748259i	$0.269110\pi$
$548$			3.11973e13i			0.631269i
$549$	−2.20409e13	+	3.70136e13i	−0.441944	+	0.742164i
$550$	1.71919e13			0.341595
$551$	6.16382e13	+	3.55869e13i	1.21365	+	0.700699i
$552$	−8.58584e12	+	4.88012e12i	−0.167528	+	0.0952215i
$553$	−4.36042e13	−	7.55247e13i	−0.843146	−	1.46037i
$554$	1.15601e13	−	6.67422e12i	0.221520	−	0.127894i
$555$	−9.75580e11	−	1.71639e12i	−0.0185267	−	0.0325949i
$556$	−9.04658e12	+	1.56691e13i	−0.170259	+	0.294898i
$557$		−	4.75936e13i		−	0.887713i	−0.896098	−	0.443856i	$-0.853610\pi$
$557$		−	4.75936e13i		−	0.887713i	0.896098	−	0.443856i	$-0.146390\pi$
$558$	1.91368e11	−	1.41848e13i	0.00353751	−	0.262212i
$559$	−7.90574e13			−1.44838
$560$	−1.51735e13	−	8.76042e12i	−0.275515	−	0.159069i
$561$	4.54895e13	+	2.66741e13i	0.818647	+	0.480037i
$562$	−1.79432e13	−	3.10785e13i	−0.320050	−	0.554344i
$563$	2.30402e13	−	1.33023e13i	0.407328	−	0.235171i	−0.282313	−	0.959322i	$-0.591102\pi$
$563$	2.30402e13	−	1.33023e13i	0.407328	−	0.235171i	0.689641	+	0.724152i	$0.257768\pi$
$564$	2.31974e13	+	1.56471e11i	0.406485	+	0.00274182i
$565$	9.13251e12	−	1.58180e13i	0.158616	−	0.274732i
$566$			5.81092e13i			1.00037i
$567$	5.42320e13	−	8.83397e13i	0.925422	−	1.50744i
$568$	2.56653e13			0.434115
$569$	5.19930e13	+	3.00182e13i	0.871734	+	0.503296i	0.867924	−	0.496697i	$-0.165454\pi$
$569$	5.19930e13	+	3.00182e13i	0.871734	+	0.503296i	0.00380969	+	0.999993i	$0.498787\pi$
$570$	−3.56546e11	+	5.28592e13i	−0.00592573	+	0.878509i
$571$	1.88388e13	+	3.26298e13i	0.310366	+	0.537569i	0.978442	−	0.206524i	$-0.0662152\pi$
$571$	1.88388e13	+	3.26298e13i	0.310366	+	0.537569i	−0.668076	+	0.744093i	$0.732882\pi$
$572$	−3.56516e13	+	2.05835e13i	−0.582236	+	0.336154i
$573$	−1.08634e13	+	1.85262e13i	−0.175870	+	0.299925i
$574$	5.78297e12	−	1.00164e13i	0.0928093	−	0.160750i
$575$		−	1.65270e13i		−	0.262938i
$576$	7.92470e12	+	1.06912e11i	0.124989	+	0.00168623i
$577$	5.84772e13			0.914339			0.457170	−	0.889379i	$-0.348863\pi$
$577$	5.84772e13			0.914339			0.457170	+	0.889379i	$0.348863\pi$
$578$	4.02367e12	+	2.32307e12i	0.0623710	+	0.0360099i
$579$	3.89384e13	−	2.21323e13i	0.598392	−	0.340121i
$580$	−9.57951e12	−	1.65922e13i	−0.145950	−	0.252792i
$581$	−3.52155e13	+	2.03317e13i	−0.531929	+	0.307109i
$582$	1.71471e13	+	3.01678e13i	0.256789	+	0.451781i
$583$	5.51786e13	−	9.55721e13i	0.819272	−	1.41902i
$584$			7.43390e12i			0.109434i
$585$	−5.68673e13	−	3.38633e13i	−0.830010	−	0.494254i
$586$	−6.00276e13			−0.868686
$587$	2.13867e13	+	1.23476e13i	0.306869	+	0.177171i	0.645525	−	0.763739i	$-0.276639\pi$
$587$	2.13867e13	+	1.23476e13i	0.306869	+	0.177171i	−0.338655	+	0.940910i	$0.609972\pi$
$588$	−6.45380e13	−	3.78437e13i	−0.918182	−	0.538403i
$589$	2.27007e13	+	3.93187e13i	0.320230	+	0.554655i
$590$	−5.53469e12	+	3.19546e12i	−0.0774165	+	0.0446964i
$591$	−1.36733e14	−	9.22290e11i	−1.89642	−	0.0127918i
$592$	4.73668e11	−	8.20416e11i	0.00651426	−	0.0112830i
$593$			1.80785e13i			0.246540i	0.992373	+	0.123270i	$0.0393382\pi$
$593$			1.80785e13i			0.246540i	−0.992373	+	0.123270i	$0.960662\pi$
$594$	4.58670e13	−	2.52579e13i	0.620252	−	0.341559i
$595$	8.99360e13			1.20600
$596$	1.69199e13	+	9.76870e12i	0.224991	+	0.129899i
$597$	−3.68308e11	+	5.46028e13i	−0.00485668	+	0.720018i
$598$	1.97873e13	+	3.42726e13i	0.258750	+	0.448168i
$599$	−3.34483e13	+	1.93114e13i	−0.433750	+	0.250426i	−0.700943	−	0.713217i	$-0.747237\pi$
$599$	−3.34483e13	+	1.93114e13i	−0.433750	+	0.250426i	0.267193	+	0.963643i	$0.413904\pi$
$600$	−6.70882e12	+	1.14411e13i	−0.0862760	+	0.147133i
$601$	8.70929e12	−	1.50849e13i	0.111074	−	0.192385i	−0.805130	−	0.593099i	$-0.797904\pi$
$601$	8.70929e12	−	1.50849e13i	0.111074	−	0.192385i	0.916203	+	0.400714i	$0.131238\pi$
$602$		−	1.06669e14i		−	1.34913i
$603$	1.14441e13	+	2.04541e13i	0.143547	+	0.256563i
$604$	3.76510e13			0.468373
$605$	−1.38860e11	−	8.01708e10i	−0.00171317	−	0.000989098i
$606$	5.80364e11	−	3.29874e11i	0.00710129	−	0.00403631i
$607$	−7.76902e13	−	1.34563e14i	−0.942807	−	1.63299i	−0.760083	−	0.649826i	$-0.774842\pi$
$607$	−7.76902e13	−	1.34563e14i	−0.942807	−	1.63299i	−0.182724	−	0.983164i	$-0.558492\pi$
$608$	−2.19664e13	+	1.26823e13i	−0.264387	+	0.152644i
$609$	−5.94166e13	−	1.04535e14i	−0.709286	−	1.24788i
$610$	−1.85565e13	+	3.21408e13i	−0.219708	+	0.380546i
$611$		−	9.29591e13i		−	1.09166i
$612$	−3.55027e13	+	1.98638e13i	−0.413528	+	0.231369i
$613$	5.61031e13			0.648164			0.324082	−	0.946029i	$-0.394945\pi$
$613$	5.61031e13			0.648164			0.324082	+	0.946029i	$0.394945\pi$
$614$	3.76320e13	+	2.17268e13i	0.431236	+	0.248974i
$615$	8.10283e12	+	4.75133e12i	0.0921003	+	0.0540057i
$616$	−2.77724e13	−	4.81032e13i	−0.313119	−	0.542338i
$617$	1.31202e14	−	7.57492e13i	1.46728	−	0.847135i	0.467951	−	0.883754i	$-0.344992\pi$
$617$	1.31202e14	−	7.57492e13i	1.46728	−	0.847135i	0.999329	+	0.0366198i	$0.0116591\pi$
$618$	−4.17085e12	−	2.81333e10i	−0.0462682	−	0.000312089i
$619$	−4.34646e13	+	7.52829e13i	−0.478280	+	0.828405i	−0.999690	−	0.0249011i	$-0.992073\pi$
$619$	−4.34646e13	+	7.52829e13i	−0.478280	+	0.828405i	0.521410	+	0.853306i	$0.325406\pi$
$620$		−	1.22214e13i		−	0.133402i
$621$	−2.42810e13	−	4.40929e13i	−0.262911	−	0.477431i
$622$	−3.41049e13			−0.366323
$623$	−1.61056e14	−	9.29858e13i	−1.71608	−	0.990778i
$624$	2.14215e11	−	3.17581e13i	0.00226427	−	0.335685i
$625$	1.35822e13	+	2.35251e13i	0.142420	+	0.246679i
$626$	−7.45892e13	+	4.30641e13i	−0.775897	+	0.447965i
$627$	−8.47663e13	+	1.44559e14i	−0.874753	+	1.49179i
$628$	−8.34253e12	+	1.44497e13i	−0.0854082	+	0.147931i
$629$			4.86276e12i			0.0493889i
$630$	4.56903e13	−	7.67286e13i	0.460385	−	0.773134i
$631$	3.41250e13			0.341135			0.170568	−	0.985346i	$-0.445440\pi$
$631$	3.41250e13			0.341135			0.170568	+	0.985346i	$0.445440\pi$
$632$	2.94317e13	+	1.69924e13i	0.291897	+	0.168527i
$633$	1.31022e14	−	7.44715e13i	1.28921	−	0.732777i
$634$	−3.68077e13	−	6.37528e13i	−0.359329	−	0.622376i
$635$	9.33076e13	−	5.38711e13i	0.903750	−	0.521780i
$636$	4.20701e13	+	7.40161e13i	0.404285	+	0.711280i
$637$	−1.49900e14	+	2.59634e14i	−1.42924	+	2.47551i
$638$		−	6.07381e13i		−	0.574590i
$639$	−1.76466e12	+	1.30802e14i	−0.0165636	+	1.22775i
$640$	6.82781e12			0.0635889
$641$	−2.58178e13	−	1.49059e13i	−0.238577	−	0.137743i	0.375945	−	0.926642i	$-0.377318\pi$
$641$	−2.58178e13	−	1.49059e13i	−0.238577	−	0.137743i	−0.614523	+	0.788899i	$0.710651\pi$
$642$	1.29159e14	+	7.57363e13i	1.18427	+	0.694431i
$643$	7.83827e13	+	1.35763e14i	0.713125	+	1.23517i	0.963678	+	0.267065i	$0.0860539\pi$
$643$	7.83827e13	+	1.35763e14i	0.713125	+	1.23517i	−0.250554	+	0.968103i	$0.580613\pi$
$644$	−4.62425e13	+	2.66981e13i	−0.417458	+	0.241019i
$645$	8.66277e13	+	5.84322e11i	0.775994	+	0.00523424i
$646$	6.50993e13	−	1.12755e14i	0.578647	−	1.00225i
$647$		−	8.18632e13i		−	0.722050i	−0.932556	−	0.361025i	$-0.882427\pi$
$647$		−	8.18632e13i		−	0.722050i	0.932556	−	0.361025i	$-0.117573\pi$
$648$	−1.08975e12	+	4.03805e13i	−0.00953787	+	0.353425i
$649$	−2.02605e13			−0.175965
$650$	4.60272e13	+	2.65738e13i	0.396687	+	0.229027i
$651$	5.17352e11	−	7.66991e13i	0.00442467	−	0.655972i
$652$	−5.80794e12	−	1.00596e13i	−0.0492929	−	0.0853778i
$653$	−4.65107e13	+	2.68529e13i	−0.391730	+	0.226165i	−0.682909	−	0.730503i	$-0.739286\pi$
$653$	−4.65107e13	+	2.68529e13i	−0.391730	+	0.226165i	0.291180	+	0.956668i	$0.405952\pi$
$654$	3.98330e13	−	6.79305e13i	0.332931	−	0.567775i
$655$	−4.40421e13	+	7.62832e13i	−0.365310	+	0.632736i
$656$			4.50721e12i			0.0371013i
$657$	−3.78865e13	−	5.11128e11i	−0.309498	−	0.00417545i
$658$	1.25426e14			1.01685
$659$	3.33191e13	+	1.92368e13i	0.268081	+	0.154777i	0.628015	−	0.778201i	$-0.283867\pi$
$659$	3.33191e13	+	1.92368e13i	0.268081	+	0.154777i	−0.359934	+	0.932978i	$0.617201\pi$
$660$	3.92176e13	−	2.22910e13i	0.313157	−	0.177996i
$661$	2.14777e12	+	3.72005e12i	0.0170208	+	0.0294809i	0.874410	−	0.485187i	$-0.161249\pi$
$661$	2.14777e12	+	3.72005e12i	0.0170208	+	0.0294809i	−0.857390	+	0.514668i	$0.827915\pi$
$662$	−1.00282e14	+	5.78978e13i	−0.788738	+	0.455378i
$663$	8.05564e13	+	1.41727e14i	0.628829	+	1.10633i
$664$	7.92319e12	−	1.37234e13i	0.0613847	−	0.106321i
$665$			2.85803e14i			2.19765i
$666$	4.14865e12	+	2.47043e12i	0.0316618	+	0.0188539i
$667$	−5.83888e13			−0.442283
$668$	−6.58163e13	−	3.79991e13i	−0.494825	−	0.285687i
$669$	−4.91787e13	−	2.88373e13i	−0.366983	−	0.215191i
$670$	1.00960e13	+	1.74868e13i	0.0747781	+	0.129520i
$671$	−1.01893e14	+	5.88279e13i	−0.749086	+	0.432485i
$672$	4.28499e13	+	2.89032e11i	0.312682	+	0.00210911i
$673$	−2.41842e13	+	4.18883e13i	−0.175169	+	0.303401i	−0.940220	−	0.340569i	$-0.889380\pi$
$673$	−2.41842e13	+	4.18883e13i	−0.175169	+	0.303401i	0.765051	+	0.643970i	$0.222714\pi$
$674$		−	1.50060e13i		−	0.107886i
$675$	−5.78478e13	−	3.49778e13i	−0.412827	−	0.249617i
$676$	−5.66810e13			−0.401517
$677$	−3.90974e13	−	2.25729e13i	−0.274919	−	0.158724i	0.356202	−	0.934409i	$-0.384071\pi$
$677$	−3.90974e13	−	2.25729e13i	−0.274919	−	0.158724i	−0.631121	+	0.775684i	$0.717405\pi$
$678$	−3.01308e11	+	4.46699e13i	−0.00210311	+	0.311793i
$679$	9.38083e13	+	1.62481e14i	0.649969	+	1.12578i
$680$	−3.03522e13	+	1.75239e13i	−0.208759	+	0.120527i
$681$	1.26795e14	−	2.16235e14i	0.865701	−	1.47635i
$682$	1.93723e13	−	3.35538e13i	0.131298	−	0.227415i
$683$			4.47211e13i			0.300891i	0.988618	+	0.150445i	$0.0480708\pi$
$683$			4.47211e13i			0.300891i	−0.988618	+	0.150445i	$0.951929\pi$
$684$	−6.31244e13	−	1.12823e14i	−0.421615	−	0.753556i
$685$	−1.36988e14			−0.908303
$686$	−1.85754e14	−	1.07245e14i	−1.22269	−	0.705921i
$687$	2.03317e13	−	1.15564e13i	0.132859	−	0.0755158i
$688$	2.07842e13	+	3.59993e13i	0.134832	+	0.233535i
$689$	2.95454e14	−	1.70581e14i	1.90280	−	1.09858i
$690$	−2.14288e13	−	3.77007e13i	−0.137010	−	0.241048i
$691$	−4.53194e13	+	7.84956e13i	−0.287670	+	0.498259i	−0.973253	−	0.229736i	$-0.926214\pi$
$691$	−4.53194e13	+	7.84956e13i	−0.287670	+	0.498259i	0.685583	+	0.727994i	$0.259547\pi$
$692$			1.14295e14i			0.720271i
$693$	2.47065e14	−	1.38233e14i	1.54577	−	0.864861i
$694$	−2.06778e14			−1.28442
$695$	−6.88037e13	−	3.97238e13i	−0.424314	−	0.244978i
$696$	4.04207e13	+	2.37019e13i	0.247490	+	0.145123i
$697$	−1.15680e13	−	2.00363e13i	−0.0703222	−	0.121802i
$698$	1.25158e14	−	7.22601e13i	0.755409	−	0.436135i
$699$	−1.73678e14	−	1.17149e12i	−1.04078	−	0.00702027i
$700$	−3.58549e13	+	6.21025e13i	−0.213333	+	0.369504i
$701$		−	3.09162e14i		−	1.82640i	−0.407512	−	0.913200i	$-0.633604\pi$
$701$		−	3.09162e14i		−	1.82640i	0.407512	−	0.913200i	$-0.366396\pi$
$702$	1.61839e14	+	3.27532e12i	0.949288	+	0.0192118i
$703$	−1.54531e13			−0.0899994
$704$	1.87456e13	+	1.08228e13i	0.108402	+	0.0625859i
$705$	−6.87071e11	+	1.01861e14i	−0.00394508	+	0.584872i
$706$	−7.37709e13	−	1.27775e14i	−0.420592	−	0.728487i
$707$	3.12579e12	−	1.80467e12i	0.0176955	−	0.0102165i
$708$	7.90628e12	−	1.34832e13i	0.0444433	−	0.0757927i
$709$	1.68200e14	−	2.91330e14i	0.938845	−	1.62613i	0.171214	−	0.985234i	$-0.445231\pi$
$709$	1.68200e14	−	2.91330e14i	0.938845	−	1.62613i	0.767630	−	0.640893i	$-0.221436\pi$
$710$			1.12697e14i			0.624628i
$711$	−8.86246e13	+	1.48829e14i	−0.487760	+	0.819105i
$712$	7.24725e13			0.396071
$713$	−3.22559e13	−	1.86230e13i	−0.175050	−	0.101065i
$714$	−1.91226e14	+	1.08691e14i	−1.03052	+	0.585738i
$715$	−9.03826e13	−	1.56547e14i	−0.483676	−	0.837752i
$716$	1.53517e14	−	8.86332e13i	0.815815	−	0.471011i
$717$	−1.12603e13	−	1.98108e13i	−0.0594229	−	0.104546i
$718$	−2.05448e13	+	3.55846e13i	−0.107666	+	0.186483i
$719$		−	2.55650e13i		−	0.133046i	−0.997785	−	0.0665230i	$-0.978809\pi$
$719$		−	2.55650e13i		−	0.133046i	0.997785	−	0.0665230i	$-0.0211906\pi$
$720$	−4.69456e11	+	3.47976e13i	−0.00242623	+	0.179840i
$721$	−2.25513e13			−0.115743
$722$	2.38176e14	+	1.37511e14i	1.21398	+	0.700893i
$723$	−6.53584e12	−	3.83248e12i	−0.0330834	−	0.0193994i
$724$	−1.03254e13	−	1.78841e13i	−0.0519055	−	0.0899030i
$725$	−6.79091e13	+	3.92073e13i	−0.339030	+	0.195739i
$726$	3.92140e11	+	2.64507e9i	0.00194428	+	1.31146e-5i
$727$	1.58613e14	−	2.74726e14i	0.781030	−	1.35278i	−0.150312	−	0.988639i	$-0.548028\pi$
$727$	1.58613e14	−	2.74726e14i	0.781030	−	1.35278i	0.931342	−	0.364145i	$-0.118639\pi$
$728$		−	1.71713e14i		−	0.839740i
$729$	−2.05723e14	−	8.33028e12i	−0.999181	−	0.0404596i
$730$	−3.26425e13			−0.157459
$731$	−1.84788e14	−	1.06687e14i	−0.885292	−	0.511123i
$732$	6.12232e11	−	9.07654e13i	0.00291313	−	0.431882i
$733$	8.88330e13	+	1.53863e14i	0.419811	+	0.727135i	0.995920	−	0.0902383i	$-0.0287629\pi$
$733$	8.88330e13	+	1.53863e14i	0.419811	+	0.727135i	−0.576109	+	0.817373i	$0.695430\pi$
$734$	−1.42928e14	+	8.25193e13i	−0.670866	+	0.387325i
$735$	1.66173e14	−	2.83388e14i	0.774682	−	1.32113i
$736$	1.04042e13	−	1.80206e13i	0.0481747	−	0.0834410i
$737$			6.40128e13i			0.294394i
$738$	−2.29708e13	−	3.09900e11i	−0.104929	−	0.00141560i
$739$	1.16517e14			0.528651			0.264325	−	0.964434i	$-0.414851\pi$
$739$	1.16517e14			0.528651			0.264325	+	0.964434i	$0.414851\pi$
$740$	3.60247e12	+	2.07989e12i	0.0162346	+	0.00937306i
$741$	−4.50388e14	+	2.55997e14i	−2.01602	+	1.14589i
$742$	2.30157e14	+	3.98644e14i	1.02330	+	1.77242i
$743$	−3.44601e14	+	1.98955e14i	−1.52185	+	0.878642i	−0.522185	+	0.852832i	$0.674883\pi$
$743$	−3.44601e14	+	1.98955e14i	−1.52185	+	0.878642i	−0.999667	+	0.0258092i	$0.991784\pi$
$744$	1.47701e13	+	2.59858e13i	0.0647916	+	0.113991i
$745$	−4.28947e13	+	7.42957e13i	−0.186905	+	0.323730i
$746$			2.10373e14i			0.910533i
$747$	6.93958e13	+	4.13238e13i	0.298353	+	0.177663i
$748$	−1.11109e14			−0.474505
$749$	7.01079e14	+	4.04768e14i	2.97412	+	1.71711i
$750$	−1.54375e14	−	9.05222e13i	−0.650535	−	0.381460i
$751$	−1.69746e14	−	2.94008e14i	−0.710557	−	1.23072i	−0.964648	−	0.263540i	$-0.915110\pi$
$751$	−1.69746e14	−	2.94008e14i	−0.710557	−	1.23072i	0.254092	−	0.967180i	$-0.418223\pi$
$752$	−4.23296e13	+	2.44390e13i	−0.176017	+	0.101623i
$753$	1.31305e14	+	8.85677e11i	0.542381	+	0.00365848i
$754$	9.38838e13	−	1.62611e14i	0.385242	−	0.667259i
$755$			1.65327e14i			0.673919i
$756$	−4.41924e12	+	2.18363e14i	−0.0178953	+	0.884238i
$757$	1.77949e14			0.715839			0.357919	−	0.933753i	$-0.383486\pi$
$757$	1.77949e14			0.715839			0.357919	+	0.933753i	$0.383486\pi$
$758$	−2.32988e14	−	1.34516e14i	−0.931080	−	0.537559i
$759$	9.27288e11	−	1.37473e14i	0.00368134	−	0.545770i
$760$	−5.56883e13	−	9.64550e13i	−0.219632	−	0.380414i
$761$	2.28145e14	−	1.31719e14i	0.893896	−	0.516091i	0.0186809	−	0.999825i	$-0.494053\pi$
$761$	2.28145e14	−	1.31719e14i	0.893896	−	0.516091i	0.875215	+	0.483735i	$0.160720\pi$
$762$	−1.33289e14	+	2.27309e14i	−0.518825	+	0.884794i
$763$	2.12885e14	−	3.68728e14i	0.823234	−	1.42588i
$764$		−	4.52505e13i		−	0.173843i
$765$	−8.72227e13	−	1.55894e14i	−0.332907	−	0.595006i
$766$	1.86298e14			0.706421
$767$	−5.42426e13	−	3.13170e13i	−0.204345	−	0.117979i
$768$	−1.45176e13	+	8.25168e12i	−0.0543361	+	0.0308842i
$769$	7.35366e13	+	1.27369e14i	0.273446	+	0.473623i	0.969742	−	0.244132i	$-0.0785031\pi$
$769$	7.35366e13	+	1.27369e14i	0.273446	+	0.473623i	−0.696296	+	0.717755i	$0.745170\pi$
$770$	2.11222e14	−	1.21949e14i	0.780345	−	0.450532i
$771$	1.98812e14	+	3.49780e14i	0.729745	+	1.28388i
$772$	−4.71849e13	+	8.17267e13i	−0.172075	+	0.298042i
$773$		−	8.04772e13i		−	0.291592i	−0.989315	−	0.145796i	$-0.953426\pi$
$773$		−	8.04772e13i		−	0.291592i	0.989315	−	0.145796i	$-0.0465743\pi$
$774$	−1.84898e14	+	1.03451e14i	−0.665622	+	0.372416i
$775$	−5.00203e13			−0.178911
$776$	−6.33182e13	−	3.65568e13i	−0.225019	−	0.129915i
$777$	2.25203e13	+	1.32054e13i	0.0795187	+	0.0466281i
$778$	4.40963e13	+	7.63770e13i	0.154705	+	0.267957i
$779$	6.36724e13	−	3.67613e13i	0.221954	−	0.128145i
$780$	1.39451e14	+	9.40626e11i	0.483001	+	0.00325795i
$781$	−1.78637e14	+	3.09408e14i	−0.614775	+	1.06482i
$782$			1.06811e14i			0.365244i
$783$	−1.23575e14	+	2.04373e14i	−0.419876	+	0.694407i
$784$	1.57635e14			0.532197
$785$	−6.34490e13	−	3.66323e13i	−0.212851	−	0.122890i
$786$	1.45308e12	−	2.15424e14i	0.00484369	−	0.718093i
$787$	7.76520e13	+	1.34497e14i	0.257205	+	0.445492i	0.965492	−	0.260433i	$-0.0838652\pi$
$787$	7.76520e13	+	1.34497e14i	0.257205	+	0.445492i	−0.708287	+	0.705924i	$0.750532\pi$
$788$	2.49503e14	−	1.44051e14i	0.821192	−	0.474116i
$789$	7.25656e13	−	1.23752e14i	0.237326	−	0.404732i
$790$	−7.46142e13	+	1.29236e14i	−0.242486	+	0.419997i
$791$			2.41525e14i			0.779973i
$792$	−5.64468e13	+	9.47921e13i	−0.181140	+	0.304191i
$793$	−3.63725e14			−1.15986
$794$	7.66001e12	+	4.42251e12i	0.0242732	+	0.0140141i
$795$	−3.25007e14	+	1.84731e14i	−1.02343	+	0.581707i
$796$	−5.75253e13	−	9.96367e13i	−0.180009	−	0.311784i
$797$	−3.08113e14	+	1.77889e14i	−0.958117	+	0.553169i	−0.895593	−	0.444874i	$-0.853248\pi$
$797$	−3.08113e14	+	1.77889e14i	−0.958117	+	0.553169i	−0.0625243	+	0.998043i	$0.519915\pi$
$798$	−3.45405e14	−	6.07689e14i	−1.06737	−	1.87787i
$799$	1.25447e14	−	2.17281e14i	0.385237	−	0.667250i
$800$		−	2.79451e13i		−	0.0852816i
$801$	−4.98295e12	+	3.69353e14i	−0.0151121	+	1.12016i
$802$	−7.65447e13			−0.230698
$803$	−8.96194e13	−	5.17418e13i	−0.268426	−	0.154976i
$804$	−4.26000e13	−	2.49797e13i	−0.126803	−	0.0743546i
$805$	−1.17232e14	−	2.03052e14i	−0.346791	−	0.600660i
$806$	1.03729e14	−	5.98880e13i	0.304947	−	0.176061i
$807$	1.50454e14	+	1.01484e12i	0.439578	+	0.00296505i
$808$	−7.03275e11	+	1.21811e12i	−0.00204206	+	0.00353695i
$809$			1.56806e14i			0.452503i	0.974069	+	0.226251i	$0.0726471\pi$
$809$			1.56806e14i			0.452503i	−0.974069	+	0.226251i	$0.927353\pi$
$810$	−1.77312e14	−	4.78512e12i	−0.508526	−	0.0137236i
$811$	−2.21265e14			−0.630680			−0.315340	−	0.948979i	$-0.602118\pi$
$811$	−2.21265e14			−0.630680			−0.315340	+	0.948979i	$0.602118\pi$
$812$	2.19405e14	+	1.26673e14i	0.621535	+	0.358843i
$813$	2.30104e12	−	3.41137e14i	0.00647845	−	0.960452i
$814$	6.59369e12	+	1.14206e13i	0.0184504	+	0.0319571i
$815$	4.41722e13	−	2.55028e13i	0.122846	−	0.0709252i
$816$	4.33580e13	−	7.39420e13i	0.119845	−	0.204381i
$817$	3.39037e14	−	5.87229e14i	0.931400	−	1.61323i
$818$			1.34393e14i			0.366954i
$819$	8.75125e14	+	1.18063e13i	2.37493	+	0.0320403i
$820$	−1.97913e13			−0.0533832
$821$	8.17415e13	+	4.71935e13i	0.219143	+	0.126522i	0.605553	−	0.795805i	$-0.292952\pi$
$821$	8.17415e13	+	4.71935e13i	0.219143	+	0.126522i	−0.386411	+	0.922327i	$0.626285\pi$
$822$	2.91271e14	−	1.65556e14i	0.776137	−	0.441150i
$823$	2.34392e14	+	4.05978e14i	0.620788	+	1.07524i	0.989339	+	0.145629i	$0.0465204\pi$
$823$	2.34392e14	+	4.05978e14i	0.620788	+	1.07524i	−0.368552	+	0.929607i	$0.620146\pi$
$824$	7.61077e12	−	4.39408e12i	0.0200352	−	0.0115673i
$825$	−9.12332e13	−	1.60511e14i	−0.238717	−	0.419987i
$826$	4.22547e13	−	7.31872e13i	0.109894	−	0.190342i
$827$		−	1.29770e14i		−	0.335465i	−0.985833	−	0.167732i	$-0.946356\pi$
$827$		−	1.29770e14i		−	0.335465i	0.985833	−	0.167732i	$-0.0536444\pi$
$828$	9.11256e13	+	5.42634e13i	0.234147	+	0.139430i
$829$	−5.69843e14			−1.45540			−0.727701	−	0.685895i	$-0.759411\pi$
$829$	−5.69843e14			−1.45540			−0.727701	+	0.685895i	$0.759411\pi$
$830$	6.02597e13	+	3.47910e13i	0.152981	+	0.0883235i
$831$	−1.23660e14	−	7.25114e13i	−0.312049	−	0.182979i
$832$	3.34579e13	+	5.79508e13i	0.0839232	+	0.145359i
$833$	−7.00749e14	+	4.04577e14i	−1.74718	+	1.00873i
$834$	1.94301e14	+	1.31060e12i	0.481555	+	0.00324819i
$835$	1.66855e14	−	2.89002e14i	0.411062	−	0.711980i
$836$		−	3.53088e14i		−	0.864671i
$837$	−1.33451e14	+	7.34884e13i	−0.324858	+	0.178892i
$838$	7.39306e13			0.178897
$839$	−8.08840e13	−	4.66984e13i	−0.194560	−	0.112329i	0.399556	−	0.916709i	$-0.369164\pi$
$839$	−8.08840e13	−	4.66984e13i	−0.194560	−	0.112329i	−0.594115	+	0.804380i	$0.702498\pi$
$840$	−1.26915e12	+	1.88155e14i	−0.00303470	+	0.449904i
$841$	−7.18364e13	−	1.24424e14i	−0.170752	−	0.295750i
$842$	3.73747e14	−	2.15783e14i	0.883114	−	0.509866i
$843$	−1.94942e14	+	3.32451e14i	−0.457897	+	0.780889i
$844$	−1.58770e14	+	2.74997e14i	−0.370728	+	0.642120i
$845$		−	2.48888e14i		−	0.577724i
$846$	−1.21642e14	−	2.17411e14i	−0.280692	−	0.501683i
$847$	2.12025e12			0.00486375
$848$	−1.55350e14	−	8.96914e13i	−0.354268	−	0.204537i
$849$	5.42531e14	−	3.08370e14i	1.22995	−	0.699091i
$850$	7.17223e13	+	1.24227e14i	0.161644	+	0.279976i
$851$	1.09789e13	−	6.33865e12i	0.0245985	−	0.0142020i
$852$	−1.36199e14	−	2.39622e14i	−0.303373	−	0.533739i
$853$	−2.26582e14	+	3.92452e14i	−0.501743	+	0.869044i	0.498255	+	0.867030i	$0.333974\pi$
$853$	−2.26582e14	+	3.92452e14i	−0.501743	+	0.869044i	−0.999998	+	0.00201360i	$0.999359\pi$
$854$		−	4.90758e14i		−	1.08038i
$855$	4.95407e14	−	2.77181e14i	1.08426	−	0.606643i
$856$	−3.15474e14			−0.686427
$857$	3.24360e14	+	1.87269e14i	0.701654	+	0.405100i	0.807963	−	0.589233i	$-0.200570\pi$
$857$	3.24360e14	+	1.87269e14i	0.701654	+	0.405100i	−0.106309	+	0.994333i	$0.533903\pi$
$858$	3.81369e14	+	2.23627e14i	0.820180	+	0.480937i
$859$	8.30172e13	+	1.43790e14i	0.177502	+	0.307442i	0.941024	−	0.338339i	$-0.109865\pi$
$859$	8.30172e13	+	1.43790e14i	0.177502	+	0.307442i	−0.763523	+	0.645781i	$0.776532\pi$
$860$	−1.58074e14	+	9.12642e13i	−0.336023	+	0.194003i
$861$	−1.24206e14	−	8.37796e11i	−0.262498	−	0.00177061i
$862$	1.31024e14	−	2.26940e14i	0.275305	−	0.476843i
$863$		−	3.99274e14i		−	0.834097i	−0.908884	−	0.417048i	$-0.863065\pi$
$863$		−	3.99274e14i		−	0.834097i	0.908884	−	0.417048i	$-0.136935\pi$
$864$	−4.10561e13	−	7.45556e13i	−0.0852726	−	0.154850i
$865$	−5.01872e14			−1.03636
$866$	−1.86107e14	−	1.07449e14i	−0.382098	−	0.220604i
$867$	3.36549e11	−	4.98945e13i	0.000686994	−	0.101849i
$868$	8.08042e13	+	1.39957e14i	0.163997	+	0.284051i
$869$	−4.09704e14	+	2.36543e14i	−0.826745	+	0.477321i
$870$	−1.04076e14	+	1.77489e14i	−0.208811	+	0.356102i
$871$	−9.89455e13	+	1.71379e14i	−0.197381	+	0.341874i
$872$			1.65921e14i			0.329094i
$873$	1.90663e14	−	3.20185e14i	0.376007	−	0.631436i
$874$	−3.39430e14			−0.665569
$875$	−8.37950e14	−	4.83791e14i	−1.63372	−	0.943230i
$876$	6.94059e13	−	3.94498e13i	0.134548	−	0.0764757i
$877$	−8.18187e12	−	1.41714e13i	−0.0157708	−	0.0273159i	0.858032	−	0.513596i	$-0.171687\pi$
$877$	−8.18187e12	−	1.41714e13i	−0.0157708	−	0.0273159i	−0.873803	+	0.486280i	$0.838354\pi$
$878$	−3.93483e14	+	2.27177e14i	−0.754142	+	0.435404i
$879$	3.18551e14	+	5.60443e14i	0.607064	+	1.06804i
$880$	−4.75232e13	+	8.23127e13i	−0.0900519	+	0.155974i
$881$		−	3.83618e14i		−	0.722803i	−0.932410	−	0.361401i	$-0.882298\pi$
$881$		−	3.83618e14i		−	0.722803i	0.932410	−	0.361401i	$-0.117702\pi$
$882$	−1.08384e13	+	8.03380e14i	−0.0203060	+	1.50514i
$883$	7.74044e14			1.44199			0.720995	−	0.692940i	$-0.243685\pi$
$883$	7.74044e14			1.44199			0.720995	+	0.692940i	$0.243685\pi$
$884$	−2.97466e14	−	1.71742e14i	−0.551032	−	0.318138i
$885$	5.92052e13	+	3.47167e13i	0.109055	+	0.0639473i
$886$	7.11310e13	+	1.23203e14i	0.130284	+	0.225658i
$887$	7.58295e14	−	4.37802e14i	1.38108	−	0.797369i	0.388796	−	0.921324i	$-0.372891\pi$
$887$	7.58295e14	−	4.37802e14i	1.38108	−	0.797369i	0.992288	+	0.123954i	$0.0395576\pi$
$888$	−1.01734e13	−	6.86216e10i	−0.0184247	−	0.000124278i
$889$	−7.12358e14	+	1.23384e15i	−1.28289	+	2.22203i
$890$			3.18229e14i			0.569888i
$891$	−4.79223e14	−	2.94196e14i	−0.853392	−	0.523900i
$892$	1.20120e14			0.212711
$893$	6.90489e14	+	3.98654e14i	1.21590	+	0.702003i
$894$	1.41522e12	−	2.09811e14i	0.00247820	−	0.367401i
$895$	3.89191e14	+	6.74099e14i	0.677716	+	1.17384i
$896$	−7.81905e13	+	4.51433e13i	−0.135398	+	0.0781723i
$897$	2.14977e14	−	3.66618e14i	0.370195	−	0.631323i
$898$	4.55993e13	−	7.89803e13i	0.0780866	−	0.135250i
$899$			1.76719e14i			0.300943i
$900$	1.42421e14	+	1.92140e12i	0.241191	+	0.00325392i
$901$	9.20788e14			1.55073
$902$	−5.43367e13	−	3.13713e13i	−0.0910040	−	0.0525412i
$903$	−9.95904e14	+	5.66063e14i	−1.65874	+	0.942814i
$904$	−4.70607e13	−	8.15116e13i	−0.0779501	−	0.135014i
$905$	7.85296e13	−	4.53391e13i	0.129357	−	0.0746844i
$906$	−1.99804e14	−	3.51525e14i	−0.327313	−	0.575858i
$907$	−8.39634e13	+	1.45429e14i	−0.136790	+	0.236927i	−0.926280	−	0.376837i	$-0.877012\pi$
$907$	−8.39634e13	+	1.45429e14i	−0.136790	+	0.236927i	0.789490	+	0.613763i	$0.210345\pi$
$908$			5.28156e14i			0.855723i
$909$	−6.15968e12	−	3.66796e12i	−0.00992518	−	0.00591024i
$910$	7.53995e14			1.20826
$911$	3.24184e14	+	1.87168e14i	0.516654	+	0.298291i	0.735565	−	0.677454i	$-0.236917\pi$
$911$	3.24184e14	+	1.87168e14i	0.516654	+	0.298291i	−0.218910	+	0.975745i	$0.570250\pi$
$912$	2.34977e14	+	1.37785e14i	0.372435	+	0.218388i
$913$	1.10295e14	+	1.91036e14i	0.173861	+	0.301135i
$914$	2.00258e14	−	1.15619e14i	0.313949	−	0.181259i
$915$	3.98554e14	+	2.68833e12i	0.621414	+	0.00419157i
$916$	−2.46376e13	+	4.26736e13i	−0.0382051	+	0.0661732i
$917$		−	1.16477e15i		−	1.79636i
$918$	3.73861e14	+	2.26056e14i	0.573451	+	0.346739i
$919$	9.39489e14			1.43322			0.716612	−	0.697472i	$-0.245692\pi$
$919$	9.39489e14			1.43322			0.716612	+	0.697472i	$0.245692\pi$
$920$	7.91288e13	+	4.56851e13i	0.120059	+	0.0693163i
$921$	3.14763e12	−	4.66646e14i	0.00474991	−	0.704190i
$922$	−1.26715e13	−	2.19477e13i	−0.0190184	−	0.0329408i
$923$	−9.56513e14	+	5.52243e14i	−1.42785	+	0.824370i
$924$	−3.01730e14	+	5.14565e14i	−0.447980	+	0.763977i
$925$	8.51264e12	−	1.47443e13i	0.0125706	−	0.0217729i
$926$			6.50520e14i			0.955446i
$927$	2.18709e13	+	3.90901e13i	0.0319499	+	0.0571042i
$928$	−9.87283e13			−0.143450
$929$	−3.50968e14	−	2.02631e14i	−0.507211	−	0.292839i	0.224475	−	0.974480i	$-0.427933\pi$
$929$	−3.50968e14	−	2.02631e14i	−0.507211	−	0.292839i	−0.731687	+	0.681641i	$0.761267\pi$
$930$	−1.14104e14	+	6.48560e13i	−0.164016	+	0.0932256i
$931$	−1.28569e15	−	2.22688e15i	−1.83818	−	3.18382i
$932$	3.16919e14	−	1.82973e14i	0.450681	−	0.260201i
$933$	1.80986e14	+	3.18417e14i	0.255997	+	0.450389i
$934$	−2.63859e14	+	4.57018e14i	−0.371226	+	0.642982i
$935$		−	4.87882e14i		−	0.682742i
$936$	−2.97644e14	+	1.66532e14i	−0.414303	+	0.231803i
$937$	−8.09182e14			−1.12034			−0.560168	−	0.828379i	$-0.689264\pi$
$937$	−8.09182e14			−1.12034			−0.560168	+	0.828379i	$0.689264\pi$
$938$	−2.31234e14	−	1.33503e14i	−0.318447	−	0.183855i
$939$	7.97889e14	+	4.67866e14i	1.09299	+	0.640904i
$940$	−1.07312e14	−	1.85870e14i	−0.146221	−	0.253263i
$941$	2.92643e14	−	1.68958e14i	0.396635	−	0.228997i	−0.288396	−	0.957511i	$-0.593122\pi$
$941$	2.92643e14	−	1.68958e14i	0.396635	−	0.228997i	0.685031	+	0.728514i	$0.259789\pi$
$942$	1.79180e14	+	1.20861e12i	0.241565	+	0.00162941i
$943$	−3.01579e13	+	5.22350e13i	−0.0404429	+	0.0700491i
$944$			3.29330e13i			0.0439310i
$945$	−9.58837e14	−	1.94050e13i	−1.27229	−	0.0257487i
$946$	−5.78654e14			−0.763771
$947$	6.70987e14	+	3.87394e14i	0.880976	+	0.508632i	0.870980	−	0.491318i	$-0.163485\pi$
$947$	6.70987e14	+	3.87394e14i	0.880976	+	0.508632i	0.00999585	+	0.999950i	$0.496818\pi$
$948$	2.46174e12	−	3.64961e14i	0.00321514	−	0.476655i
$949$	−1.59956e14	−	2.77052e14i	−0.207811	−	0.359940i
$950$	−3.94774e14	+	2.27923e14i	−0.510188	+	0.294557i
$951$	−3.99894e14	+	6.81971e14i	−0.514093	+	0.876725i
$952$	2.31725e14	−	4.01359e14i	0.296338	−	0.513272i
$953$			9.36729e13i			0.119165i	0.998223	+	0.0595826i	$0.0189770\pi$
$953$			9.36729e13i			0.119165i	−0.998223	+	0.0595826i	$0.981023\pi$
$954$	4.67790e14	−	7.85568e14i	0.591982	−	0.994127i
$955$	1.98696e14			0.250134
$956$	4.15803e13	+	2.40064e13i	0.0520712	+	0.0300633i
$957$	−5.67076e14	+	3.22321e14i	−0.706451	+	0.401541i
$958$	−5.25704e14	−	9.10545e14i	−0.651499	−	1.12843i
$959$	1.56876e15	−	9.05723e14i	1.93403	−	1.11661i
$960$	−3.62334e13	−	6.37472e13i	−0.0444378	−	0.0781817i
$961$	3.53450e14	−	6.12194e14i	0.431232	−	0.746916i
$962$			4.07678e13i			0.0494814i
$963$	2.16909e13	−	1.60780e15i	0.0261906	−	1.94133i
$964$	1.59639e13			0.0191758
$965$	−3.58865e14	−	2.07191e14i	−0.428839	−	0.247590i
$966$	4.94662e14	+	2.90059e14i	0.588062	+	0.344827i
$967$	1.78686e14	+	3.09493e14i	0.211329	+	0.366032i	0.952131	−	0.305692i	$-0.0988877\pi$
$967$	1.78686e14	+	3.09493e14i	0.211329	+	0.366032i	−0.740802	+	0.671723i	$0.765554\pi$
$968$	−7.15559e11	+	4.13128e11i	−0.000841916	+	0.000486080i
$969$	−1.39820e15	−	9.43112e12i	−1.63662	−	0.0110394i
$970$	1.60522e14	−	2.78032e14i	0.186929	−	0.323770i
$971$			4.85967e14i			0.563002i	0.959561	+	0.281501i	$0.0908324\pi$
$971$			4.85967e14i			0.563002i	−0.959561	+	0.281501i	$0.909168\pi$
$972$	3.82792e14	−	2.04115e14i	0.441196	−	0.235257i
$973$	1.05057e15			1.20464
$974$	−4.84489e14	−	2.79720e14i	−0.552700	−	0.319101i
$975$	3.84983e12	−	5.70749e14i	0.00436936	−	0.647772i
$976$	9.56233e13	+	1.65624e14i	0.107973	+	0.187015i
$977$	−1.17797e15	+	6.80104e14i	−1.32331	+	0.764016i	−0.984256	−	0.176750i	$-0.943442\pi$
$977$	−1.17797e15	+	6.80104e14i	−1.32331	+	0.764016i	−0.339058	+	0.940765i	$0.610108\pi$
$978$	−6.30998e13	+	1.07609e14i	−0.0705235	+	0.120269i
$979$	−5.04427e14	+	8.73692e14i	−0.560899	+	0.971505i
$980$			6.92181e14i			0.765754i
$981$	−8.45611e14	−	1.14082e13i	−0.930734	−	0.0125566i
$982$	3.39328e14			0.371588
$983$	4.11477e14	+	2.37566e14i	0.448309	+	0.258831i	0.707116	−	0.707098i	$-0.249996\pi$
$983$	4.11477e14	+	2.37566e14i	0.448309	+	0.258831i	−0.258807	+	0.965929i	$0.583329\pi$
$984$	4.20812e13	−	2.39186e13i	0.0456155	−	0.0259275i
$985$	6.32531e14	+	1.09558e15i	0.682183	+	1.18158i
$986$	4.38885e14	−	2.53391e14i	0.470941	−	0.271898i
$987$	−6.65601e14	−	1.17103e15i	−0.710605	−	1.25020i
$988$	5.45772e14	−	9.45305e14i	0.579731	−	1.00412i
$989$			5.56272e14i			0.587903i
$990$	−4.16235e14	−	2.47860e14i	−0.437686	−	0.260633i
$991$	−8.99597e14			−0.941195			−0.470597	−	0.882348i	$-0.655962\pi$
$991$	−8.99597e14			−0.941195			−0.470597	+	0.882348i	$0.655962\pi$
$992$	−5.45408e13	−	3.14891e13i	−0.0567758	−	0.0327795i
$993$	1.07273e15	+	6.29025e14i	1.11107	+	0.651511i
$994$	−7.45118e14	−	1.29058e15i	−0.767880	−	1.33001i
$995$	4.37508e14	−	2.52595e14i	0.448611	−	0.259006i
$996$	−1.70173e14	−	1.14786e12i	−0.173618	−	0.00117109i
$997$	7.57151e14	−	1.31142e15i	0.768611	−	1.33127i	−0.169705	−	0.985495i	$-0.554282\pi$
$997$	7.57151e14	−	1.31142e15i	0.768611	−	1.33127i	0.938316	−	0.345778i	$-0.112385\pi$
$998$			4.92808e14i			0.497766i
$999$	1.04921e12	−	5.18434e13i	0.00105447	−	0.0521034i

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	18.11.d.a.11.8	yes	20
3.2	odd	2		54.11.d.a.35.4		20
9.2	odd	6		162.11.b.c.161.17		20
9.4	even	3		54.11.d.a.17.4		20
9.5	odd	6	inner	18.11.d.a.5.8	✓	20
9.7	even	3		162.11.b.c.161.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.11.d.a.5.8	✓	20	9.5	odd	6	inner
18.11.d.a.11.8	yes	20	1.1	even	1	trivial
54.11.d.a.17.4		20	9.4	even	3
54.11.d.a.35.4		20	3.2	odd	2
162.11.b.c.161.4		20	9.7	even	3
162.11.b.c.161.17		20	9.2	odd	6

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Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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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	18.11.d.a.11.8

Level	$18$
Weight	$11$
Character	18.11
Analytic conductor	$11.436$
Analytic rank	$0$
Dimension	$20$
Inner twists	$2$