LMFDB - Embedded newform 18.11.d.a.11.3

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			11.3
Root			$0.500000 - 66.6144i$ of defining polynomial
Character	$\chi$	$=$	18.11
Dual form			18.11.d.a.5.3

$q$ -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} +(16.6955 + 242.426i) q^{3} +(256.000 + 443.405i) q^{4} +(2723.51 - 1572.42i) q^{5} +(2415.57 - 4939.44i) q^{6} +(-1768.70 + 3063.49i) q^{7} -11585.2i q^{8} +(-58491.5 + 8094.85i) q^{9} -71159.5 q^{10} +(101896. + 58830.0i) q^{11} +(-103219. + 69463.9i) q^{12} +(140036. + 242550. i) q^{13} +(69318.8 - 40021.2i) q^{14} +(426665. + 633996. i) q^{15} +(-131072. + 227023. i) q^{16} +2.62588e6i q^{17} +(1.23778e6 + 503130. i) q^{18} -1.16270e6 q^{19} +(1.39444e6 + 805078. i) q^{20} +(-772198. - 377633. i) q^{21} +(-1.33117e6 - 2.30565e6i) q^{22} +(-6.93397e6 + 4.00333e6i) q^{23} +(2.80856e6 - 193422. i) q^{24} +(62187.6 - 107712. i) q^{25} -6.33732e6i q^{26} +(-2.93895e6 - 1.40447e7i) q^{27} -1.81115e6 q^{28} +(2.58924e7 + 1.49490e7i) q^{29} +(-1.18805e6 - 1.72509e7i) q^{30} +(-9.71127e6 - 1.68204e7i) q^{31} +(5.13695e6 - 2.96582e6i) q^{32} +(-1.25607e7 + 2.56845e7i) q^{33} +(2.97084e7 - 5.14565e7i) q^{34} +1.11246e7i q^{35} +(-1.85631e7 - 2.38632e7i) q^{36} -2.58918e7 q^{37} +(2.27842e7 + 1.31544e7i) q^{38} +(-5.64624e7 + 3.79979e7i) q^{39} +(-1.82168e7 - 3.15525e7i) q^{40} +(-3.60572e7 + 2.08176e7i) q^{41} +(1.08595e7 + 1.61365e7i) q^{42} +(9.70076e7 - 1.68022e8i) q^{43} +6.02419e7i q^{44} +(-1.46574e8 + 1.14020e8i) q^{45} +1.81170e8 q^{46} +(2.63103e8 + 1.51902e8i) q^{47} +(-5.72246e7 - 2.79850e7i) q^{48} +(1.34981e8 + 2.33794e8i) q^{49} +(-2.43725e6 + 1.40714e6i) q^{50} +(-6.36581e8 + 4.38404e7i) q^{51} +(-7.16985e7 + 1.24186e8i) q^{52} +2.93367e8i q^{53} +(-1.01306e8 + 3.08469e8i) q^{54} +3.70021e8 q^{55} +(3.54912e7 + 2.04909e7i) q^{56} +(-1.94119e7 - 2.81868e8i) q^{57} +(-3.38257e8 - 5.85878e8i) q^{58} +(4.61741e8 - 2.66586e8i) q^{59} +(-1.71891e8 + 3.51489e8i) q^{60} +(5.88708e8 - 1.01967e9i) q^{61} +4.39482e8i q^{62} +(7.86558e7 - 1.93505e8i) q^{63} -1.34218e8 q^{64} +(7.62780e8 + 4.40391e8i) q^{65} +(5.36726e8 - 3.61204e8i) q^{66} +(-9.91277e8 - 1.71694e9i) q^{67} +(-1.16433e9 + 6.72225e8i) q^{68} +(-1.08628e9 - 1.61414e9i) q^{69} +(1.25860e8 - 2.17996e8i) q^{70} -1.40331e9i q^{71} +(9.37807e7 + 6.77638e8i) q^{72} -6.62520e7 q^{73} +(5.07374e8 + 2.92933e8i) q^{74} +(2.71504e7 + 1.32776e7i) q^{75} +(-2.97651e8 - 5.15547e8i) q^{76} +(-3.60450e8 + 2.08106e8i) q^{77} +(1.53633e9 - 1.05805e8i) q^{78} +(-2.94881e9 + 5.10750e9i) q^{79} +8.24400e8i q^{80} +(3.35573e9 - 9.46960e8i) q^{81} +9.42098e8 q^{82} +(2.24450e9 + 1.29586e9i) q^{83} +(-3.02381e7 - 4.39070e8i) q^{84} +(4.12898e9 + 7.15160e9i) q^{85} +(-3.80191e9 + 2.19503e9i) q^{86} +(-3.19173e9 + 6.52657e9i) q^{87} +(6.81559e8 - 1.18050e9i) q^{88} -8.23594e9i q^{89} +(4.16223e9 - 5.76026e8i) q^{90} -9.90731e8 q^{91} +(-3.55019e9 - 2.04971e9i) q^{92} +(3.91557e9 - 2.63509e9i) q^{93} +(-3.43716e9 - 5.95333e9i) q^{94} +(-3.16662e9 + 1.82825e9i) q^{95} +(8.04755e8 + 1.19581e9i) q^{96} +(-6.95568e9 + 1.20476e10i) q^{97} -6.10854e9i q^{98} +(-6.43630e9 - 2.61622e9i) 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
$3$	16.6955	+	242.426i	0.0687058	+	0.997637i
$3$	16.6955	+	242.426i	0.0687058	+	0.997637i
$4$	256.000	+	443.405i	0.250000	+	0.433013i
$5$	2723.51	−	1572.42i	0.871523	−	0.503174i	0.00366883	−	0.999993i	$-0.498832\pi$
$5$	2723.51	−	1572.42i	0.871523	−	0.503174i	0.867854	+	0.496819i	$0.165499\pi$
$6$	2415.57	−	4939.44i	0.310644	−	0.635217i
$7$	−1768.70	+	3063.49i	−0.105236	+	0.182274i	−0.913835	−	0.406086i	$-0.866893\pi$
$7$	−1768.70	+	3063.49i	−0.105236	+	0.182274i	0.808598	+	0.588361i	$0.200227\pi$
$8$		−	11585.2i		−	0.353553i
$9$	−58491.5	+	8094.85i	−0.990559	+	0.137087i
$10$	−71159.5			−0.711595
$11$	101896.	+	58830.0i	0.632697	+	0.365288i	0.781796	−	0.623534i	$-0.214304\pi$
$11$	101896.	+	58830.0i	0.632697	+	0.365288i	−0.149099	+	0.988822i	$0.547637\pi$
$12$	−103219.	+	69463.9i	−0.414813	+	0.279160i
$13$	140036.	+	242550.i	0.377158	+	0.653257i	0.990648	−	0.136446i	$-0.0435680\pi$
$13$	140036.	+	242550.i	0.377158	+	0.653257i	−0.613489	+	0.789703i	$0.710235\pi$
$14$	69318.8	−	40021.2i	0.128887	−	0.0744132i
$15$	426665.	+	633996.i	0.561864	+	0.834892i
$16$	−131072.	+	227023.i	−0.125000	+	0.216506i
$17$			2.62588e6i			1.84940i	0.380701	+	0.924698i	$0.375683\pi$
$17$			2.62588e6i			1.84940i	−0.380701	+	0.924698i	$0.624317\pi$
$18$	1.23778e6	+	503130.i	0.655059	+	0.266267i
$19$	−1.16270e6			−0.469569			−0.234785	−	0.972047i	$-0.575438\pi$
$19$	−1.16270e6			−0.469569			−0.234785	+	0.972047i	$0.575438\pi$
$20$	1.39444e6	+	805078.i	0.435761	+	0.251587i
$21$	−772198.	−	377633.i	−0.189074	−	0.0924642i
$22$	−1.33117e6	−	2.30565e6i	−0.258298	−	0.447384i
$23$	−6.93397e6	+	4.00333e6i	−1.07732	+	0.621988i	−0.930171	−	0.367127i	$-0.880342\pi$
$23$	−6.93397e6	+	4.00333e6i	−1.07732	+	0.621988i	−0.147144	+	0.989115i	$0.547008\pi$
$24$	2.80856e6	−	193422.i	0.352718	−	0.0242912i
$25$	62187.6	−	107712.i	0.00636801	−	0.0110297i
$26$		−	6.33732e6i		−	0.533382i
$27$	−2.93895e6	−	1.40447e7i	−0.204820	−	0.978800i
$28$	−1.81115e6			−0.105236
$29$	2.58924e7	+	1.49490e7i	1.26236	+	0.728823i	0.973530	−	0.228558i	$-0.0734012\pi$
$29$	2.58924e7	+	1.49490e7i	1.26236	+	0.728823i	0.288828	+	0.957381i	$0.406734\pi$
$30$	−1.18805e6	−	1.72509e7i	−0.0488908	−	0.709914i
$31$	−9.71127e6	−	1.68204e7i	−0.339209	−	0.587528i	0.645075	−	0.764119i	$-0.276826\pi$
$31$	−9.71127e6	−	1.68204e7i	−0.339209	−	0.587528i	−0.984284	+	0.176592i	$0.943493\pi$
$32$	5.13695e6	−	2.96582e6i	0.153093	−	0.0883883i
$33$	−1.25607e7	+	2.56845e7i	−0.320955	+	0.656299i
$34$	2.97084e7	−	5.14565e7i	0.653860	−	1.13252i
$35$			1.11246e7i			0.211808i
$36$	−1.85631e7	−	2.38632e7i	−0.307000	−	0.394653i
$37$	−2.58918e7			−0.373383			−0.186691	−	0.982419i	$-0.559776\pi$
$37$	−2.58918e7			−0.373383			−0.186691	+	0.982419i	$0.559776\pi$
$38$	2.27842e7	+	1.31544e7i	0.287551	+	0.166018i
$39$	−5.64624e7	+	3.79979e7i	−0.625801	+	0.421150i
$40$	−1.82168e7	−	3.15525e7i	−0.177899	−	0.308130i
$41$	−3.60572e7	+	2.08176e7i	−0.311224	+	0.179685i	−0.647474	−	0.762088i	$-0.724175\pi$
$41$	−3.60572e7	+	2.08176e7i	−0.311224	+	0.179685i	0.336250	+	0.941773i	$0.390841\pi$
$42$	1.08595e7	+	1.61365e7i	0.0830927	+	0.123470i
$43$	9.70076e7	−	1.68022e8i	0.659878	−	1.14294i	−0.320769	−	0.947157i	$-0.603941\pi$
$43$	9.70076e7	−	1.68022e8i	0.659878	−	1.14294i	0.980647	−	0.195785i	$-0.0627254\pi$
$44$			6.02419e7i			0.365288i
$45$	−1.46574e8	+	1.14020e8i	−0.794316	+	0.617898i
$46$	1.81170e8			0.879624
$47$	2.63103e8	+	1.51902e8i	1.14719	+	0.662331i	0.948201	−	0.317670i	$-0.102900\pi$
$47$	2.63103e8	+	1.51902e8i	1.14719	+	0.662331i	0.198990	+	0.980001i	$0.436234\pi$
$48$	−5.72246e7	−	2.79850e7i	−0.224583	−	0.109829i
$49$	1.34981e8	+	2.33794e8i	0.477851	+	0.827662i
$50$	−2.43725e6	+	1.40714e6i	−0.00779919	+	0.00450286i
$51$	−6.36581e8	+	4.38404e7i	−1.84503	+	0.127064i
$52$	−7.16985e7	+	1.24186e8i	−0.188579	+	0.326629i
$53$			2.93367e8i			0.701508i	0.936468	+	0.350754i	$0.114075\pi$
$53$			2.93367e8i			0.701508i	−0.936468	+	0.350754i	$0.885925\pi$
$54$	−1.01306e8	+	3.08469e8i	−0.220632	+	0.671805i
$55$	3.70021e8			0.735213
$56$	3.54912e7	+	2.04909e7i	0.0644437	+	0.0372066i
$57$	−1.94119e7	−	2.81868e8i	−0.0322621	−	0.468460i
$58$	−3.38257e8	−	5.85878e8i	−0.515356	−	0.892622i
$59$	4.61741e8	−	2.66586e8i	0.645860	−	0.372888i	−0.141008	−	0.990008i	$-0.545034\pi$
$59$	4.61741e8	−	2.66586e8i	0.645860	−	0.372888i	0.786868	+	0.617121i	$0.211701\pi$
$60$	−1.71891e8	+	3.51489e8i	−0.221053	+	0.452017i
$61$	5.88708e8	−	1.01967e9i	0.697029	−	1.20729i	−0.272463	−	0.962166i	$-0.587838\pi$
$61$	5.88708e8	−	1.01967e9i	0.697029	−	1.20729i	0.969492	−	0.245124i	$-0.0788286\pi$
$62$			4.39482e8i			0.479714i
$63$	7.86558e7	−	1.93505e8i	0.0792552	−	0.194980i
$64$	−1.34218e8			−0.125000
$65$	7.62780e8	+	4.40391e8i	0.657404	+	0.379552i
$66$	5.36726e8	−	3.61204e8i	0.428581	−	0.288425i
$67$	−9.91277e8	−	1.71694e9i	−0.734211	−	1.27169i	−0.955069	−	0.296385i	$-0.904219\pi$
$67$	−9.91277e8	−	1.71694e9i	−0.734211	−	1.27169i	0.220857	−	0.975306i	$-0.429115\pi$
$68$	−1.16433e9	+	6.72225e8i	−0.800812	+	0.462349i
$69$	−1.08628e9	−	1.61414e9i	−0.694536	−	1.03204i
$70$	1.25860e8	−	2.17996e8i	0.0748856	−	0.129706i
$71$		−	1.40331e9i		−	0.777787i	−0.921283	−	0.388894i	$-0.872857\pi$
$71$		−	1.40331e9i		−	0.777787i	0.921283	−	0.388894i	$-0.127143\pi$
$72$	9.37807e7	+	6.77638e8i	0.0484676	+	0.350215i
$73$	−6.62520e7			−0.0319584			−0.0159792	−	0.999872i	$-0.505087\pi$
$73$	−6.62520e7			−0.0319584			−0.0159792	+	0.999872i	$0.505087\pi$
$74$	5.07374e8	+	2.92933e8i	0.228649	+	0.132011i
$75$	2.71504e7	+	1.32776e7i	0.0114412	+	0.00559516i
$76$	−2.97651e8	−	5.15547e8i	−0.117392	−	0.203329i
$77$	−3.60450e8	+	2.08106e8i	−0.133165	+	0.0768830i
$78$	1.53633e9	−	1.05805e8i	0.532122	−	0.0366465i
$79$	−2.94881e9	+	5.10750e9i	−0.958323	+	1.65986i	−0.231749	+	0.972776i	$0.574445\pi$
$79$	−2.94881e9	+	5.10750e9i	−0.958323	+	1.65986i	−0.726574	+	0.687089i	$0.758888\pi$
$80$			8.24400e8i			0.251587i
$81$	3.35573e9	−	9.46960e8i	0.962414	−	0.271585i
$82$	9.42098e8			0.254113
$83$	2.24450e9	+	1.29586e9i	0.569809	+	0.328979i	0.757073	−	0.653330i	$-0.226629\pi$
$83$	2.24450e9	+	1.29586e9i	0.569809	+	0.328979i	−0.187264	+	0.982310i	$0.559962\pi$
$84$	−3.02381e7	−	4.39070e8i	−0.00723034	−	0.104988i
$85$	4.12898e9	+	7.15160e9i	0.930568	+	1.61179i
$86$	−3.80191e9	+	2.19503e9i	−0.808182	+	0.466604i
$87$	−3.19173e9	+	6.52657e9i	−0.640369	+	1.30945i
$88$	6.81559e8	−	1.18050e9i	0.129149	−	0.223692i
$89$		−	8.23594e9i		−	1.47490i	−0.675401	−	0.737451i	$-0.736029\pi$
$89$		−	8.23594e9i		−	1.47490i	0.675401	−	0.737451i	$-0.263971\pi$
$90$	4.16223e9	−	5.76026e8i	0.704877	−	0.0975504i
$91$	−9.90731e8			−0.158763
$92$	−3.55019e9	−	2.04971e9i	−0.538658	−	0.310994i
$93$	3.91557e9	−	2.63509e9i	0.562834	−	0.378774i
$94$	−3.43716e9	−	5.95333e9i	−0.468339	−	0.811187i
$95$	−3.16662e9	+	1.82825e9i	−0.409240	+	0.236275i
$96$	8.04755e8	+	1.19581e9i	0.0986979	+	0.146659i
$97$	−6.95568e9	+	1.20476e10i	−0.809992	+	1.40295i	0.102877	+	0.994694i	$0.467195\pi$
$97$	−6.95568e9	+	1.20476e10i	−0.809992	+	1.40295i	−0.912869	+	0.408253i	$0.866138\pi$
$98$		−	6.10854e9i		−	0.675783i
$99$	−6.43630e9	−	2.61622e9i	−0.676800	−	0.275105i
$100$	6.36801e7			0.00636801
$101$	−6.11084e9	−	3.52810e9i	−0.581426	−	0.335686i	0.180274	−	0.983616i	$-0.442302\pi$
$101$	−6.11084e9	−	3.52810e9i	−0.581426	−	0.335686i	−0.761700	+	0.647930i	$0.775635\pi$
$102$	1.29704e10	+	6.34300e9i	1.17477	+	0.574505i
$103$	1.11688e9	+	1.93449e9i	0.0963431	+	0.166871i	0.910168	−	0.414239i	$-0.135952\pi$
$103$	1.11688e9	+	1.93449e9i	0.0963431	+	0.166871i	−0.813825	+	0.581110i	$0.802619\pi$
$104$	2.81000e9	−	1.62235e9i	0.230961	−	0.133346i
$105$	−2.69688e9	+	1.85731e8i	−0.211308	+	0.0145525i
$106$	3.31907e9	−	5.74880e9i	0.248020	−	0.429584i
$107$		−	1.41199e10i		−	1.00673i	−0.864074	−	0.503365i	$-0.832095\pi$
$107$		−	1.41199e10i		−	1.00673i	0.864074	−	0.503365i	$-0.167905\pi$
$108$	5.47512e9	−	4.89859e9i	0.372628	−	0.333390i
$109$	1.76266e10			1.14561			0.572804	−	0.819692i	$-0.305855\pi$
$109$	1.76266e10			1.14561			0.572804	+	0.819692i	$0.305855\pi$
$110$	−7.25091e9	−	4.18631e9i	−0.450224	−	0.259937i
$111$	−4.32277e8	−	6.27685e9i	−0.0256536	−	0.372500i
$112$	−4.63655e8	−	8.03075e8i	−0.0263090	−	0.0455686i
$113$	2.44862e10	−	1.41371e10i	1.32901	−	0.767306i	0.343867	−	0.939019i	$-0.388263\pi$
$113$	2.44862e10	−	1.41371e10i	1.32901	−	0.767306i	0.985147	+	0.171712i	$0.0549299\pi$
$114$	−2.80858e9	+	5.74309e9i	−0.145869	+	0.298278i
$115$	−1.25898e10	+	2.18062e10i	−0.625937	+	1.08415i
$116$			1.53078e10i			0.728823i
$117$	−1.01543e10	−	1.30535e10i	−0.463150	−	0.595386i
$118$	−1.20643e10			−0.527343
$119$	−8.04434e9	−	4.64440e9i	−0.337098	−	0.194623i
$120$	7.34500e9	−	4.94302e9i	0.295179	−	0.198649i
$121$	−6.04678e9	−	1.04733e10i	−0.233130	−	0.403792i
$122$	−2.30726e10	+	1.33209e10i	−0.853683	+	0.492874i
$123$	−5.64872e9	−	8.39363e9i	−0.200643	−	0.298143i
$124$	4.97217e9	−	8.61205e9i	0.169605	−	0.293764i
$125$			3.03202e10i			0.993531i
$126$	−3.73060e9	+	2.90203e9i	−0.117470	+	0.0913795i
$127$	4.94881e9			0.149790			0.0748948	−	0.997191i	$-0.476138\pi$
$127$	4.94881e9			0.149790			0.0748948	+	0.997191i	$0.476138\pi$
$128$	2.63012e9	+	1.51850e9i	0.0765466	+	0.0441942i
$129$	4.23525e10	+	2.07119e10i	1.18558	+	0.579792i
$130$	−9.96491e9	−	1.72597e10i	−0.268384	−	0.464855i
$131$	1.82913e9	−	1.05605e9i	0.0474119	−	0.0273733i	−0.476107	−	0.879388i	$-0.657952\pi$
$131$	1.82913e9	−	1.05605e9i	0.0474119	−	0.0273733i	0.523519	+	0.852014i	$0.324619\pi$
$132$	−1.46042e10	+	1.00577e9i	−0.364425	+	0.0250974i
$133$	2.05647e9	−	3.56192e9i	0.0494157	−	0.0855905i
$134$			4.48601e10i			1.03833i
$135$	−3.00884e10	−	3.36296e10i	−0.671012	−	0.749986i
$136$	3.04214e10			0.653860
$137$	7.00520e10	+	4.04446e10i	1.45150	+	0.838025i	0.998567	−	0.0535178i	$-0.0170434\pi$
$137$	7.00520e10	+	4.04446e10i	1.45150	+	0.838025i	0.452936	+	0.891543i	$0.350377\pi$
$138$	3.02473e9	+	4.39203e10i	0.0604353	+	0.877546i
$139$	−4.37910e10	−	7.58482e10i	−0.843938	−	1.46174i	−0.886540	−	0.462651i	$-0.846898\pi$
$139$	−4.37910e10	−	7.58482e10i	−0.843938	−	1.46174i	0.0426027	−	0.999092i	$-0.486435\pi$
$140$	−4.93269e9	+	2.84789e9i	−0.0917157	+	0.0529521i
$141$	−3.24324e10	+	6.63189e10i	−0.581947	+	1.18999i
$142$	−1.58766e10	+	2.74991e10i	−0.274989	+	0.476295i
$143$			3.29533e10i			0.551085i
$144$	5.82888e9	−	1.43399e10i	0.0941397	−	0.231598i
$145$	9.40243e10			1.46690
$146$	1.29827e9	+	7.49555e8i	0.0195704	+	0.0112990i
$147$	−5.44241e10	+	3.66262e10i	−0.792875	+	0.533587i
$148$	−6.62831e9	−	1.14806e10i	−0.0933456	−	0.161679i
$149$	4.46548e10	−	2.57814e10i	0.608046	−	0.351056i	−0.164154	−	0.986435i	$-0.552490\pi$
$149$	4.46548e10	−	2.57814e10i	0.608046	−	0.351056i	0.772200	+	0.635379i	$0.219156\pi$
$150$	−3.81819e8	−	5.67358e8i	−0.00502807	−	0.00747138i
$151$	−1.30802e10	+	2.26555e10i	−0.166621	+	0.288596i	−0.937230	−	0.348713i	$-0.886619\pi$
$151$	−1.30802e10	+	2.26555e10i	−0.166621	+	0.288596i	0.770609	+	0.637308i	$0.219952\pi$
$152$			1.34702e10i			0.166018i
$153$	−2.12561e10	−	1.53592e11i	−0.253528	−	1.83194i
$154$	9.41779e9			0.108729
$155$	−5.28975e10	−	3.05404e10i	−0.591257	−	0.341362i
$156$	−3.13028e10	−	1.53082e10i	−0.338813	−	0.165692i
$157$	−3.82190e10	−	6.61973e10i	−0.400665	−	0.693972i	0.593141	−	0.805099i	$-0.297888\pi$
$157$	−3.82190e10	−	6.61973e10i	−0.400665	−	0.693972i	−0.993806	+	0.111126i	$0.964554\pi$
$158$	1.15569e11	−	6.67240e10i	1.17370	−	0.677637i
$159$	−7.11198e10	+	4.89792e9i	−0.699850	+	0.0481977i
$160$	9.32702e9	−	1.61549e10i	0.0889494	−	0.154065i
$161$		−	2.83228e10i		−	0.261823i
$162$	−7.64723e10	−	1.94092e10i	−0.685376	−	0.173953i
$163$	1.41500e11			1.22976			0.614878	−	0.788622i	$-0.289205\pi$
$163$	1.41500e11			1.22976			0.614878	+	0.788622i	$0.289205\pi$
$164$	−1.84613e10	−	1.06586e10i	−0.155612	−	0.0898425i
$165$	6.17770e9	+	8.97027e10i	0.0505134	+	0.733476i
$166$	−2.93220e10	−	5.07872e10i	−0.232623	−	0.402916i
$167$	−1.53375e11	+	8.85509e10i	−1.18079	+	0.681727i	−0.956196	−	0.292726i	$-0.905438\pi$
$167$	−1.53375e11	+	8.85509e10i	−1.18079	+	0.681727i	−0.224590	+	0.974453i	$0.572104\pi$
$168$	−4.37497e9	+	8.94609e9i	−0.0326910	+	0.0668478i
$169$	2.97090e10	−	5.14574e10i	0.215503	−	0.373263i
$170$		−	1.86856e11i		−	1.31602i
$171$	6.80081e10	−	9.41188e9i	0.465136	−	0.0643718i
$172$	9.93358e10			0.659878
$173$	2.11541e10	+	1.22133e10i	0.136510	+	0.0788140i	0.566700	−	0.823925i	$-0.308220\pi$
$173$	2.11541e10	+	1.22133e10i	0.136510	+	0.0788140i	−0.430190	+	0.902738i	$0.641553\pi$
$174$	1.36385e11	−	9.17838e10i	0.855105	−	0.575466i
$175$	2.19983e8	+	3.81022e8i	0.00134029	+	0.00232145i
$176$	−2.67116e10	+	1.54219e10i	−0.158174	+	0.0913220i
$177$	7.23364e10	+	1.07487e11i	0.416381	+	0.618714i
$178$	−9.31790e10	+	1.61391e11i	−0.521456	+	0.903189i
$179$			7.03466e10i			0.382805i	0.981512	+	0.191403i	$0.0613036\pi$
$179$			7.03466e10i			0.382805i	−0.981512	+	0.191403i	$0.938696\pi$
$180$	−8.80797e10	−	3.58025e10i	−0.466137	−	0.189475i
$181$	−2.06743e11			−1.06424			−0.532118	−	0.846670i	$-0.678604\pi$
$181$	−2.06743e11			−1.06424			−0.532118	+	0.846670i	$0.678604\pi$
$182$	1.94143e10	+	1.12088e10i	0.0972219	+	0.0561311i
$183$	2.57024e11	+	1.25694e11i	1.25233	+	0.612434i
$184$	4.63795e10	+	8.03317e10i	0.219906	+	0.380889i
$185$	−7.05166e10	+	4.07128e10i	−0.325411	+	0.187876i
$186$	−1.06542e11	+	7.33738e9i	−0.478581	+	0.0329592i
$187$	−1.54480e11	+	2.67568e11i	−0.675562	+	1.17011i
$188$			1.55548e11i			0.662331i
$189$	4.82239e10	+	1.58375e10i	0.199965	+	0.0656717i
$190$	8.27372e10			0.334143
$191$	−1.41671e11	−	8.17939e10i	−0.557333	−	0.321776i	0.194741	−	0.980855i	$-0.437613\pi$
$191$	−1.41671e11	−	8.17939e10i	−0.557333	−	0.321776i	−0.752074	+	0.659078i	$0.770947\pi$
$192$	−2.24083e9	−	3.25378e10i	−0.00858823	−	0.124705i
$193$	−3.61307e9	−	6.25802e9i	−0.0134924	−	0.0233695i	0.859200	−	0.511639i	$-0.170962\pi$
$193$	−3.61307e9	−	6.25802e9i	−0.0134924	−	0.0233695i	−0.872693	+	0.488270i	$0.837628\pi$
$194$	2.72606e11	−	1.57389e11i	0.992034	−	0.572751i
$195$	−9.40271e10	+	1.92270e11i	−0.333488	+	0.681928i
$196$	−6.91103e10	+	1.19702e11i	−0.238925	+	0.413831i
$197$		−	4.99975e10i		−	0.168507i	−0.996444	−	0.0842534i	$-0.973149\pi$
$197$		−	4.99975e10i		−	0.168507i	0.996444	−	0.0842534i	$-0.0268505\pi$
$198$	9.65261e10	+	1.24086e11i	0.317189	+	0.407751i
$199$	−1.03391e11			−0.331298			−0.165649	−	0.986185i	$-0.552972\pi$
$199$	−1.03391e11			−0.331298			−0.165649	+	0.986185i	$0.552972\pi$
$200$	−1.24787e9	−	7.20458e8i	−0.00389959	−	0.00225143i
$201$	3.99681e11	−	2.68976e11i	1.21824	−	0.819849i
$202$	7.98317e10	+	1.38273e11i	0.237366	+	0.411130i
$203$	−9.15921e10	+	5.28807e10i	−0.265692	+	0.153397i
$204$	−1.82404e11	−	2.71040e11i	−0.516277	−	0.767154i
$205$	−6.54680e10	+	1.13394e11i	−0.180826	+	0.313199i
$206$		−	5.05442e10i		−	0.136250i
$207$	3.73172e11	−	2.90290e11i	0.981878	−	0.763802i
$208$	−7.34193e10			−0.188579
$209$	−1.18475e11	−	6.84016e10i	−0.297095	−	0.171528i
$210$	5.49492e10	+	2.68722e10i	0.134544	+	0.0657971i
$211$	−2.37979e11	−	4.12191e11i	−0.569018	−	0.985567i	−0.996663	−	0.0816210i	$-0.973990\pi$
$211$	−2.37979e11	−	4.12191e11i	−0.569018	−	0.985567i	0.427646	−	0.903946i	$-0.359343\pi$
$212$	−1.30081e11	+	7.51020e10i	−0.303762	+	0.175377i
$213$	3.40198e11	−	2.34289e10i	0.775949	−	0.0534385i
$214$	−1.59749e11	+	2.76693e11i	−0.355933	+	0.616494i
$215$		−	6.10146e11i		−	1.32813i
$216$	−1.62711e11	+	3.40484e10i	−0.346058	+	0.0724149i
$217$	6.87055e10			0.142788
$218$	−3.45410e11	−	1.99422e11i	−0.701539	−	0.405034i
$219$	−1.10611e9	−	1.60612e10i	−0.00219573	−	0.0318828i
$220$	9.47255e10	+	1.64069e11i	0.183803	+	0.318357i
$221$	−6.36906e11	+	3.67718e11i	−1.20813	+	0.697515i
$222$	−6.25435e10	+	1.27891e11i	−0.115989	+	0.237179i
$223$	4.15323e11	−	7.19360e11i	0.753116	−	1.30443i	−0.193190	−	0.981161i	$-0.561883\pi$
$223$	4.15323e11	−	7.19360e11i	0.753116	−	1.30443i	0.946306	−	0.323273i	$-0.104783\pi$
$224$			2.09826e10i			0.0372066i
$225$	−2.76553e9	+	6.80364e9i	−0.00479586	+	0.0117986i
$226$	−6.39773e11			−1.08514
$227$	5.22102e11	+	3.01436e11i	0.866216	+	0.500110i	0.866089	−	0.499890i	$-0.166626\pi$
$227$	5.22102e11	+	3.01436e11i	0.866216	+	0.500110i	0.000126854		1.00000i	$0.499960\pi$
$228$	1.20012e11	−	8.07656e10i	0.194783	−	0.131085i
$229$	1.61816e11	+	2.80274e11i	0.256948	+	0.445047i	0.965423	−	0.260689i	$-0.0839498\pi$
$229$	1.61816e11	+	2.80274e11i	0.256948	+	0.445047i	−0.708475	+	0.705736i	$0.750616\pi$
$230$	4.93418e11	−	2.84875e11i	0.766613	−	0.442604i
$231$	−5.64681e10	−	8.39079e10i	−0.0858506	−	0.127568i
$232$	1.73188e11	−	2.99970e11i	0.257678	−	0.446311i
$233$		−	4.11909e11i		−	0.599822i	−0.953967	−	0.299911i	$-0.903043\pi$
$233$		−	4.11909e11i		−	0.599822i	0.953967	−	0.299911i	$-0.0969569\pi$
$234$	5.12996e10	+	3.70679e11i	0.0731197	+	0.528347i
$235$	9.55416e11			1.33307
$236$	2.36411e11	+	1.36492e11i	0.322930	+	0.186444i
$237$	−1.28742e12	−	6.29596e11i	−1.72178	−	0.842016i
$238$	1.05091e11	+	1.82023e11i	0.137620	+	0.238364i
$239$	2.69167e10	−	1.55403e10i	0.0345169	−	0.0199283i	−0.482642	−	0.875818i	$-0.660323\pi$
$239$	2.69167e10	−	1.55403e10i	0.0345169	−	0.0199283i	0.517159	+	0.855889i	$0.326990\pi$
$240$	−1.99856e11	+	1.37638e10i	−0.250992	+	0.0172855i
$241$	−2.57545e11	+	4.46081e11i	−0.316787	+	0.548692i	−0.979816	−	0.199902i	$-0.935937\pi$
$241$	−2.57545e11	+	4.46081e11i	−0.316787	+	0.548692i	0.663028	+	0.748594i	$0.269271\pi$
$242$			2.73646e11i			0.329695i
$243$	2.85593e11	+	7.97706e11i	0.337067	+	0.941481i
$244$	6.02837e11			0.697029
$245$	7.35244e11	+	4.24493e11i	0.832916	+	0.480884i
$246$	1.57288e10	+	2.28389e11i	0.0174590	+	0.253512i
$247$	−1.62820e11	−	2.82013e11i	−0.177102	−	0.306749i
$248$	−1.94869e11	+	1.12507e11i	−0.207722	+	0.119929i
$249$	−2.76677e11	+	5.65760e11i	−0.289053	+	0.591065i
$250$	3.43033e11	−	5.94151e11i	0.351266	−	0.608411i
$251$		−	2.39065e11i		−	0.239965i	−0.992776	−	0.119982i	$-0.961716\pi$
$251$		−	2.39065e11i		−	0.239965i	0.992776	−	0.119982i	$-0.0382838\pi$
$252$	1.05937e11	−	1.46610e10i	0.104243	−	0.0144265i
$253$	−9.42063e11			−0.908819
$254$	−9.69764e10	−	5.59893e10i	−0.0917271	−	0.0529586i
$255$	−1.66480e12	+	1.12037e12i	−1.54405	+	1.03911i
$256$	−3.43597e10	−	5.95128e10i	−0.0312500	−	0.0541266i
$257$	−9.90187e10	+	5.71685e10i	−0.0883185	+	0.0509907i	−0.543509	−	0.839403i	$-0.682905\pi$
$257$	−9.90187e10	+	5.71685e10i	−0.0883185	+	0.0509907i	0.455190	+	0.890394i	$0.349571\pi$
$258$	−5.95607e11	−	8.85033e11i	−0.521028	−	0.774214i
$259$	4.57950e10	−	7.93192e10i	0.0392934	−	0.0680581i
$260$			4.50960e11i			0.379552i
$261$	−1.63550e12	−	6.64794e11i	−1.35035	−	0.548889i
$262$	−4.77913e10			−0.0387117
$263$	1.25016e12	+	7.21777e11i	0.993540	+	0.573620i	0.906330	−	0.422570i	$-0.138872\pi$
$263$	1.25016e12	+	7.21777e11i	0.993540	+	0.573620i	0.0872091	+	0.996190i	$0.472205\pi$
$264$	2.97561e11	+	1.45519e11i	0.232037	+	0.113475i
$265$	4.61296e11	+	7.98988e11i	0.352980	+	0.611380i
$266$	−8.05970e10	+	4.65327e10i	−0.0605216	+	0.0349422i
$267$	1.99660e12	−	1.37503e11i	1.47142	−	0.101334i
$268$	5.07534e11	−	8.79074e11i	0.367106	−	0.635846i
$269$			1.88424e12i			1.33775i	0.743374	+	0.668876i	$0.233224\pi$
$269$			1.88424e12i			1.33775i	−0.743374	+	0.668876i	$0.766776\pi$
$270$	2.09134e11	+	9.99415e11i	0.145749	+	0.696509i
$271$	3.02894e11			0.207226			0.103613	−	0.994618i	$-0.466960\pi$
$271$	3.02894e11			0.207226			0.103613	+	0.994618i	$0.466960\pi$
$272$	−5.96136e11	−	3.44179e11i	−0.400406	−	0.231175i
$273$	−1.65408e10	−	2.40179e11i	−0.0109079	−	0.158388i
$274$	−9.15156e11	−	1.58510e12i	−0.592573	−	1.02637i
$275$	1.26734e10	−	7.31699e9i	0.00805804	−	0.00465231i
$276$	4.37629e11	−	8.94879e11i	0.273250	−	0.558752i
$277$	1.02245e12	−	1.77093e12i	0.626962	−	1.08593i	−0.361196	−	0.932490i	$-0.617631\pi$
$277$	1.02245e12	−	1.77093e12i	0.626962	−	1.08593i	0.988158	−	0.153440i	$-0.0490352\pi$
$278$			1.98175e12i			1.19351i
$279$	7.04186e11	+	9.05240e11i	0.416549	+	0.535480i
$280$	1.28881e11			0.0748856
$281$	−1.09764e11	−	6.33724e10i	−0.0626512	−	0.0361717i	0.468347	−	0.883545i	$-0.344850\pi$
$281$	−1.09764e11	−	6.33724e10i	−0.0626512	−	0.0361717i	−0.530998	+	0.847373i	$0.678183\pi$
$282$	1.38586e12	−	9.32650e11i	0.777092	−	0.522965i
$283$	1.15329e12	+	1.99756e12i	0.635343	+	1.10045i	0.986442	+	0.164108i	$0.0524745\pi$
$283$	1.15329e12	+	1.99756e12i	0.635343	+	1.10045i	−0.351100	+	0.936338i	$0.614192\pi$
$284$	6.22233e11	−	3.59246e11i	0.336792	−	0.194447i
$285$	−4.96084e11	−	7.37148e11i	−0.263834	−	0.392040i
$286$	3.72824e11	−	6.45750e11i	0.194838	−	0.337469i
$287$		−	1.47281e11i		−	0.0756375i
$288$	−2.76460e11	+	2.15058e11i	−0.139531	+	0.108541i
$289$	−4.87925e12			−2.42027
$290$	−1.84249e12	−	1.06376e12i	−0.898288	−	0.518627i
$291$	−3.03677e12	−	1.48509e12i	−1.45528	−	0.711687i
$292$	−1.69605e10	−	2.93764e10i	−0.00798959	−	0.0138384i
$293$	2.38700e12	−	1.37814e12i	1.10539	−	0.638196i	0.167757	−	0.985828i	$-0.446347\pi$
$293$	2.38700e12	−	1.37814e12i	1.10539	−	0.638196i	0.937631	+	0.347632i	$0.113014\pi$
$294$	1.48087e12	−	1.01985e11i	0.674186	−	0.0464302i
$295$	8.38371e11	−	1.45210e12i	0.375255	−	0.649960i
$296$			2.99963e11i			0.132011i
$297$	5.26781e11	−	1.60400e12i	0.227954	−	0.694102i
$298$	−1.16673e12			−0.496467
$299$	−1.94201e12	−	1.12122e12i	−0.812637	−	0.469176i
$300$	1.06317e9	+	1.54377e10i	0.000437519	+	0.00635296i
$301$	3.43156e11	+	5.94363e11i	0.138886	+	0.240558i
$302$	5.12636e11	−	2.95971e11i	0.204068	−	0.117819i
$303$	7.53278e11	−	1.54033e12i	0.294946	−	0.603115i
$304$	1.52397e11	−	2.63960e11i	0.0586962	−	0.101665i
$305$		−	3.70278e12i		−	1.40291i
$306$	−1.32116e12	+	3.25025e12i	−0.492434	+	1.21146i
$307$	1.87362e12			0.687051			0.343525	−	0.939143i	$-0.388379\pi$
$307$	1.87362e12			0.687051			0.343525	+	0.939143i	$0.388379\pi$
$308$	−1.84550e11	−	1.06550e11i	−0.0665826	−	0.0384415i
$309$	−4.50324e11	+	3.03058e11i	−0.159858	+	0.107580i
$310$	6.91050e11	+	1.19693e12i	0.241380	+	0.418082i
$311$	−1.14997e12	+	6.63936e11i	−0.395262	+	0.228205i	−0.684438	−	0.729071i	$-0.739952\pi$
$311$	−1.14997e12	+	6.63936e11i	−0.395262	+	0.228205i	0.289176	+	0.957276i	$0.406619\pi$
$312$	4.40214e11	+	6.54130e11i	0.148899	+	0.221254i
$313$	−1.81903e12	+	3.15065e12i	−0.605505	+	1.04877i	0.386466	+	0.922304i	$0.373696\pi$
$313$	−1.81903e12	+	3.15065e12i	−0.605505	+	1.04877i	−0.991971	+	0.126462i	$0.959638\pi$
$314$			1.72960e12i			0.566626i
$315$	−9.00517e10	−	6.50693e11i	−0.0290362	−	0.209809i
$316$	−3.01959e12			−0.958323
$317$	3.63475e12	+	2.09852e12i	1.13548	+	0.655568i	0.945306	−	0.326183i	$-0.105763\pi$
$317$	3.63475e12	+	2.09852e12i	1.13548	+	0.655568i	0.190170	+	0.981751i	$0.439096\pi$
$318$	1.44907e12	+	7.08649e11i	0.445609	+	0.217919i
$319$	1.75890e12	+	3.04650e12i	0.532460	+	0.922248i
$320$	−3.65543e11	+	2.11046e11i	−0.108940	+	0.0628967i
$321$	3.42303e12	−	2.35739e11i	1.00435	−	0.0691683i
$322$	−3.20436e11	+	5.55012e11i	−0.0925683	+	0.160333i
$323$		−	3.05311e12i		−	0.868420i
$324$	1.27895e12	+	1.24553e12i	0.358204	+	0.348841i
$325$	3.48341e10			0.00960699
$326$	−2.77283e12	−	1.60089e12i	−0.753069	−	0.434784i
$327$	2.94285e11	+	4.27315e12i	0.0787100	+	1.14290i
$328$	2.41177e11	+	4.17731e11i	0.0635282	+	0.110034i
$329$	−9.30702e11	+	5.37341e11i	−0.241452	+	0.139402i
$330$	8.93813e11	−	1.82770e12i	0.228390	−	0.467020i
$331$	1.36972e11	−	2.37242e11i	0.0344740	−	0.0597107i	−0.848274	−	0.529558i	$-0.822358\pi$
$331$	1.36972e11	−	2.37242e11i	0.0344740	−	0.0597107i	0.882748	+	0.469847i	$0.155691\pi$
$332$			1.32696e12i			0.328979i
$333$	1.51445e12	−	2.09590e11i	0.369857	−	0.0511859i
$334$	4.00736e12			0.964108
$335$	−5.39950e12	−	3.11741e12i	−1.27976	−	0.738872i
$336$	1.86945e11	−	1.25810e11i	0.0436533	−	0.0293777i
$337$	2.70652e12	+	4.68783e12i	0.622676	+	1.07851i	0.988985	+	0.148013i	$0.0472877\pi$
$337$	2.70652e12	+	4.68783e12i	0.622676	+	1.07851i	−0.366310	+	0.930493i	$0.619379\pi$
$338$	−1.16435e12	+	6.72237e11i	−0.263937	+	0.152384i
$339$	3.83601e12	+	5.70006e12i	0.856804	+	1.27315i
$340$	−2.11404e12	+	3.66162e12i	−0.465284	+	0.805896i
$341$		−	2.28526e12i		−	0.495636i
$342$	−1.43916e12	−	5.84989e11i	−0.307595	−	0.125031i
$343$	−1.95420e12			−0.411621
$344$	−1.94658e12	−	1.12386e12i	−0.404091	−	0.233302i
$345$	−5.49658e12	−	2.68803e12i	−1.12460	−	0.549970i
$346$	−2.76356e11	−	4.78662e11i	−0.0557299	−	0.0965270i
$347$	−2.92142e12	+	1.68668e12i	−0.580693	+	0.335263i	−0.761409	−	0.648272i	$-0.775492\pi$
$347$	−2.92142e12	+	1.68668e12i	−0.580693	+	0.335263i	0.180716	+	0.983535i	$0.442159\pi$
$348$	−3.71100e12	+	2.55571e11i	−0.727101	+	0.0500744i
$349$	−1.81649e11	+	3.14625e11i	−0.0350838	+	0.0607668i	−0.883034	−	0.469309i	$-0.844503\pi$
$349$	−1.81649e11	+	3.14625e11i	−0.0350838	+	0.0607668i	0.847950	+	0.530076i	$0.177836\pi$
$350$		−	9.95529e9i		−	0.00189546i
$351$	2.99498e12	−	2.67961e12i	0.562158	−	0.502963i
$352$	6.97917e11			0.129149
$353$	5.17336e12	+	2.98684e12i	0.943842	+	0.544927i	0.891163	−	0.453684i	$-0.149891\pi$
$353$	5.17336e12	+	2.98684e12i	0.943842	+	0.544927i	0.0526793	+	0.998611i	$0.483224\pi$
$354$	−2.01420e11	−	2.92470e12i	−0.0362315	−	0.526097i
$355$	−2.20659e12	−	3.82192e12i	−0.391362	−	0.677859i
$356$	3.65186e12	−	2.10840e12i	0.638651	−	0.368725i
$357$	9.91619e11	−	2.02770e12i	0.171003	−	0.349673i
$358$	7.95881e11	−	1.37851e12i	0.135342	−	0.234419i
$359$		−	7.66652e12i		−	1.28566i	−0.766009	−	0.642830i	$-0.777760\pi$
$359$		−	7.66652e12i		−	1.28566i	0.766009	−	0.642830i	$-0.222240\pi$
$360$	1.32094e12	+	1.69809e12i	0.218460	+	0.280833i
$361$	−4.77919e12			−0.779505
$362$	4.05132e12	+	2.33903e12i	0.651708	+	0.376264i
$363$	2.43805e12	−	1.64075e12i	0.386821	−	0.260322i
$364$	−2.53627e11	−	4.39295e11i	−0.0396907	−	0.0687463i
$365$	−1.80438e11	+	1.04176e11i	−0.0278524	+	0.0160806i
$366$	−3.61455e12	−	5.37098e12i	−0.550362	−	0.817802i
$367$	1.22538e12	−	2.12241e12i	0.184051	−	0.318786i	−0.759205	−	0.650851i	$-0.774412\pi$
$367$	1.22538e12	−	2.12241e12i	0.184051	−	0.318786i	0.943256	+	0.332065i	$0.107745\pi$
$368$		−	2.09890e12i		−	0.310994i
$369$	1.94052e12	−	1.50953e12i	0.283653	−	0.220653i
$370$	1.84245e12			0.265697
$371$	−8.98727e11	−	5.18880e11i	−0.127867	−	0.0738240i
$372$	2.17080e12	+	1.06160e12i	0.304722	+	0.149021i
$373$	−3.72849e12	−	6.45793e12i	−0.516403	−	0.894436i	−0.999819	−	0.0190449i	$-0.993937\pi$
$373$	−3.72849e12	−	6.45793e12i	−0.516403	−	0.894436i	0.483416	−	0.875391i	$-0.339396\pi$
$374$	6.05437e12	−	3.49549e12i	0.827391	−	0.477695i
$375$	−7.35039e12	+	5.06211e11i	−0.991183	+	0.0682614i
$376$	1.75982e12	−	3.04811e12i	0.234169	−	0.405593i
$377$			8.37360e12i			1.09953i
$378$	−7.65810e11	−	8.55942e11i	−0.0992344	−	0.110914i
$379$	7.23632e12			0.925383			0.462691	−	0.886519i	$-0.346884\pi$
$379$	7.23632e12			0.925383			0.462691	+	0.886519i	$0.346884\pi$
$380$	−1.62131e12	−	9.36065e11i	−0.204620	−	0.118138i
$381$	8.26229e10	+	1.19972e12i	0.0102914	+	0.149436i
$382$	1.85078e12	+	3.20565e12i	0.227530	+	0.394094i
$383$	−1.24591e13	+	7.19325e12i	−1.51179	+	0.872833i	−0.511886	+	0.859054i	$0.671053\pi$
$383$	−1.24591e13	+	7.19325e12i	−1.51179	+	0.872833i	−0.999905	+	0.0137793i	$0.995614\pi$
$384$	−3.24212e11	+	6.62961e11i	−0.0388305	+	0.0794021i
$385$	−6.54458e11	+	1.13356e12i	−0.0773710	+	0.134011i
$386$			1.63509e11i			0.0190812i
$387$	−4.31401e12	+	1.06131e13i	−0.496966	+	1.22261i
$388$	−7.12261e12			−0.809992
$389$	1.40723e13	+	8.12466e12i	1.57986	+	0.912131i	0.994878	+	0.101083i	$0.0322308\pi$
$389$	1.40723e13	+	8.12466e12i	1.57986	+	0.912131i	0.584980	+	0.811048i	$0.301103\pi$
$390$	4.01783e12	−	2.70391e12i	0.445317	−	0.299688i
$391$	−1.05123e13	−	1.82078e13i	−1.15030	−	1.99238i
$392$	2.70856e12	−	1.56379e12i	0.292623	−	0.168946i
$393$	2.86551e11	+	4.25797e11i	0.0305661	+	0.0454192i
$394$	−5.65657e11	+	9.79747e11i	−0.0595761	+	0.103189i
$395$			1.85471e13i			1.92881i
$396$	−4.87649e11	−	3.52364e12i	−0.0500762	−	0.361839i
$397$	1.08192e13			1.09709			0.548545	−	0.836121i	$-0.315182\pi$
$397$	1.08192e13			1.09709			0.548545	+	0.836121i	$0.315182\pi$
$398$	2.02605e12	+	1.16974e12i	0.202878	+	0.117132i
$399$	8.97834e11	+	4.39074e11i	0.0887834	+	0.0434183i
$400$	1.63021e10	+	2.82361e10i	0.00159200	+	0.00275743i
$401$	−2.64167e12	+	1.52517e12i	−0.254775	+	0.147094i	−0.621949	−	0.783058i	$-0.713659\pi$
$401$	−2.64167e12	+	1.52517e12i	−0.254775	+	0.147094i	0.367174	+	0.930152i	$0.380325\pi$
$402$	−1.08752e13	+	7.48962e11i	−1.03588	+	0.0713394i
$403$	2.71986e12	−	4.71093e12i	0.255871	−	0.443182i
$404$		−	3.61277e12i		−	0.335686i
$405$	7.65035e12	−	7.85567e12i	0.702111	−	0.720955i
$406$	2.39311e12			0.216936
$407$	−2.63829e12	−	1.52322e12i	−0.236238	−	0.136392i
$408$	5.07901e11	+	7.37494e12i	0.0449240	+	0.652315i
$409$	1.15785e12	+	2.00545e12i	0.101166	+	0.175225i	0.912165	−	0.409822i	$-0.134409\pi$
$409$	1.15785e12	+	2.00545e12i	0.101166	+	0.175225i	−0.810999	+	0.585047i	$0.801076\pi$
$410$	2.56581e12	−	1.48137e12i	0.221465	−	0.127863i
$411$	−8.63525e12	+	1.76577e13i	−0.736318	+	1.50565i
$412$	−5.71843e11	+	9.90461e11i	−0.0481716	+	0.0834356i
$413$			1.88605e12i			0.156965i
$414$	−1.05969e13	+	1.46654e12i	−0.871320	+	0.120585i
$415$	8.15055e12			0.662135
$416$	1.43872e12	+	8.30645e11i	0.115481	+	0.0666728i
$417$	1.76564e13	−	1.18824e13i	1.40031	−	0.942374i
$418$	1.54775e12	+	2.68078e12i	0.121289	+	0.210078i
$419$	−6.22872e11	+	3.59615e11i	−0.0482312	+	0.0278463i	−0.523922	−	0.851766i	$-0.675532\pi$
$419$	−6.22872e11	+	3.59615e11i	−0.0482312	+	0.0278463i	0.475690	+	0.879613i	$0.342198\pi$
$420$	−7.72756e11	−	1.14826e12i	−0.0591284	−	0.0878609i
$421$	−5.82520e12	+	1.00895e13i	−0.440453	+	0.762888i	−0.997723	−	0.0674438i	$-0.978516\pi$
$421$	−5.82520e12	+	1.00895e13i	−0.440453	+	0.762888i	0.557270	+	0.830332i	$0.311849\pi$
$422$			1.07697e13i			0.804712i
$423$	−1.66189e13	−	6.75522e12i	−1.22716	−	0.498813i
$424$	3.39873e12			0.248020
$425$	2.82839e11	+	1.63297e11i	0.0203983	+	0.0117770i
$426$	−6.93155e12	−	3.38979e12i	−0.494063	−	0.241615i
$427$	2.08250e12	+	3.60700e12i	0.146705	+	0.254101i
$428$	6.26084e12	−	3.61470e12i	0.435927	−	0.251683i
$429$	−7.98873e12	+	5.50172e11i	−0.549783	+	0.0378628i
$430$	−6.90302e12	+	1.19564e13i	−0.469566	+	0.813312i
$431$		−	2.09437e13i		−	1.40821i	−0.710096	−	0.704105i	$-0.751348\pi$
$431$		−	2.09437e13i		−	1.40821i	0.710096	−	0.704105i	$-0.248652\pi$
$432$	3.57369e12	+	1.17366e12i	0.237519	+	0.0780051i
$433$	3.14275e12			0.206477			0.103238	−	0.994657i	$-0.467080\pi$
$433$	3.14275e12			0.206477			0.103238	+	0.994657i	$0.467080\pi$
$434$	−1.34635e12	−	7.77314e11i	−0.0874396	−	0.0504833i
$435$	1.56978e12	+	2.27939e13i	0.100784	+	1.46343i
$436$	4.51241e12	+	7.81573e12i	0.286402	+	0.496063i
$437$	8.06213e12	−	4.65467e12i	0.505874	−	0.292067i
$438$	−1.60036e11	+	3.27248e11i	−0.00992768	+	0.0203005i
$439$	1.06716e13	−	1.84837e13i	0.654494	−	1.13362i	−0.327526	−	0.944842i	$-0.606215\pi$
$439$	1.06716e13	−	1.84837e13i	0.654494	−	1.13362i	0.982020	−	0.188775i	$-0.0604516\pi$
$440$		−	4.28679e12i		−	0.259937i
$441$	−9.78777e12	−	1.25823e13i	−0.586801	−	0.754341i
$442$	1.66410e13			0.986435
$443$	−4.73121e12	−	2.73157e12i	−0.277303	−	0.160101i	0.354899	−	0.934905i	$-0.384515\pi$
$443$	−4.73121e12	−	2.73157e12i	−0.277303	−	0.160101i	−0.632202	+	0.774804i	$0.717849\pi$
$444$	2.67252e12	−	1.79855e12i	0.154884	−	0.104233i
$445$	−1.29503e13	−	2.24307e13i	−0.742132	−	1.28541i
$446$	−1.62773e13	+	9.39769e12i	−0.922374	+	0.532533i
$447$	6.99562e12	+	1.03950e13i	0.392002	+	0.582490i
$448$	2.37392e11	−	4.11174e11i	0.0131545	−	0.0227843i
$449$		−	1.40422e13i		−	0.769489i	−0.923023	−	0.384744i	$-0.874290\pi$
$449$		−	1.40422e13i		−	0.769489i	0.923023	−	0.384744i	$-0.125710\pi$
$450$	1.31168e11	−	1.02035e11i	0.00710827	−	0.00552952i
$451$	−4.89880e12			−0.262547
$452$	1.25369e13	+	7.23821e12i	0.664507	+	0.383653i
$453$	−5.71067e12	−	2.79273e12i	−0.299361	−	0.146399i
$454$	−6.82071e12	−	1.18138e13i	−0.353631	−	0.612507i
$455$	−2.69826e12	+	1.55784e12i	−0.138365	+	0.0798853i
$456$	−3.26551e12	+	2.24891e11i	−0.165626	+	0.0114064i
$457$	−1.17027e13	+	2.02696e13i	−0.587089	+	1.01687i	0.407523	+	0.913195i	$0.366393\pi$
$457$	−1.17027e13	+	2.02696e13i	−0.587089	+	1.01687i	−0.994611	+	0.103672i	$0.966941\pi$
$458$		−	7.32297e12i		−	0.363379i
$459$	3.68797e13	−	7.71732e12i	1.81019	−	0.378794i
$460$	−1.28920e13			−0.625937
$461$	−3.27632e12	−	1.89158e12i	−0.157355	−	0.0908491i	0.419255	−	0.907869i	$-0.362291\pi$
$461$	−3.27632e12	−	1.89158e12i	−0.157355	−	0.0908491i	−0.576610	+	0.817020i	$0.695625\pi$
$462$	1.57235e11	+	2.28311e12i	0.00747031	+	0.108472i
$463$	8.38498e12	+	1.45232e13i	0.394092	+	0.682587i	0.992985	−	0.118242i	$-0.0377259\pi$
$463$	8.38498e12	+	1.45232e13i	0.394092	+	0.682587i	−0.598893	+	0.800829i	$0.704393\pi$
$464$	−6.78754e12	+	3.91879e12i	−0.315590	+	0.182206i
$465$	6.52062e12	−	1.33336e13i	0.299933	−	0.613314i
$466$	−4.66022e12	+	8.07174e12i	−0.212069	+	0.367314i
$467$		−	1.13848e13i		−	0.512557i	−0.966603	−	0.256278i	$-0.917504\pi$
$467$		−	1.13848e13i		−	0.512557i	0.966603	−	0.256278i	$-0.0824964\pi$
$468$	3.18849e12	−	7.84419e12i	0.142022	−	0.349397i
$469$	7.01311e12			0.309062
$470$	−1.87223e13	−	1.08093e13i	−0.816336	−	0.471312i
$471$	1.54099e13	−	1.03705e13i	0.664805	−	0.447398i
$472$	−3.08847e12	−	5.34938e12i	−0.131836	−	0.228346i
$473$	1.97695e13	−	1.14139e13i	0.835006	−	0.482091i
$474$	1.81051e13	+	2.69030e13i	0.756676	+	1.12437i
$475$	−7.23055e10	+	1.25237e11i	−0.00299022	+	0.00517922i
$476$		−	4.75587e12i		−	0.194623i
$477$	−2.37476e12	−	1.71595e13i	−0.0961675	−	0.694885i
$478$	−7.03275e11			−0.0281829
$479$	−3.35729e13	−	1.93833e13i	−1.33141	−	0.768688i	−0.345891	−	0.938275i	$-0.612423\pi$
$479$	−3.35729e13	−	1.93833e13i	−1.33141	−	0.768688i	−0.985515	+	0.169587i	$0.945757\pi$
$480$	4.07208e12	+	1.99140e12i	0.159812	+	0.0781541i
$481$	−3.62579e12	−	6.28006e12i	−0.140824	−	0.243915i
$482$	1.00937e13	−	5.82758e12i	0.387984	−	0.224002i
$483$	6.86619e12	−	4.72864e11i	0.261204	−	0.0179887i
$484$	3.09595e12	−	5.36235e12i	0.116565	−	0.201896i
$485$			4.37489e13i			1.63027i
$486$	3.42855e12	−	1.88629e13i	0.126453	−	0.695708i
$487$	−7.72957e12			−0.282170			−0.141085	−	0.989997i	$-0.545059\pi$
$487$	−7.72957e12			−0.282170			−0.141085	+	0.989997i	$0.545059\pi$
$488$	−1.18132e13	−	6.82033e12i	−0.426842	−	0.246437i
$489$	2.36242e12	+	3.43033e13i	0.0844914	+	1.22685i
$490$	−9.60519e12	−	1.66367e13i	−0.340036	−	0.588960i
$491$	−1.27649e12	+	7.36980e11i	−0.0447310	+	0.0258255i	−0.522199	−	0.852824i	$-0.674888\pi$
$491$	−1.27649e12	+	7.36980e11i	−0.0447310	+	0.0258255i	0.477468	+	0.878649i	$0.341555\pi$
$492$	2.27570e12	−	4.65344e12i	0.0789388	−	0.161417i
$493$	−3.92542e13	+	6.79903e13i	−1.34788	+	2.33460i
$494$			7.36840e12i			0.250460i
$495$	−2.16431e13	+	2.99527e12i	−0.728272	+	0.100788i
$496$	5.09150e12			0.169605
$497$	4.29901e12	+	2.48203e12i	0.141771	+	0.0818514i
$498$	1.18226e13	−	7.95633e12i	0.385981	−	0.259756i
$499$	2.22627e13	+	3.85601e13i	0.719573	+	1.24634i	0.961169	+	0.275960i	$0.0889957\pi$
$499$	2.22627e13	+	3.85601e13i	0.719573	+	1.24634i	−0.241596	+	0.970377i	$0.577671\pi$
$500$	−1.34441e13	+	7.76196e12i	−0.430212	+	0.248383i
$501$	−2.40277e13	−	3.57036e13i	−0.761243	−	1.13116i
$502$	−2.70471e12	+	4.68470e12i	−0.0848403	+	0.146948i
$503$			2.40535e12i			0.0747031i	0.999302	+	0.0373516i	$0.0118921\pi$
$503$			2.40535e12i			0.0747031i	−0.999302	+	0.0373516i	$0.988108\pi$
$504$	−2.24181e12	−	9.11246e11i	−0.0689359	−	0.0280210i
$505$	−2.21906e13			−0.675634
$506$	1.84606e13	+	1.06582e13i	0.556536	+	0.321316i
$507$	1.29706e13	+	6.34311e12i	0.387187	+	0.189349i
$508$	1.26689e12	+	2.19433e12i	0.0374474	+	0.0648608i
$509$	−7.54088e12	+	4.35373e12i	−0.220716	+	0.127430i	−0.606282	−	0.795250i	$-0.707340\pi$
$509$	−7.54088e12	+	4.35373e12i	−0.220716	+	0.127430i	0.385566	+	0.922680i	$0.374006\pi$
$510$	4.52988e13	−	3.11966e12i	1.31291	−	0.0904184i
$511$	1.17180e11	−	2.02962e11i	0.00336318	−	0.00582519i
$512$			1.55494e12i			0.0441942i
$513$	3.41711e12	+	1.63298e13i	0.0961773	+	0.459614i
$514$	2.58715e12			0.0721118
$515$	6.08367e12	+	3.51241e12i	0.167930	+	0.0969547i
$516$	1.65846e12	+	2.40816e13i	0.0453375	+	0.658319i
$517$	1.78728e13	+	3.09566e13i	0.483883	+	0.838110i
$518$	−1.79479e12	+	1.03622e12i	−0.0481243	+	0.0277846i
$519$	−2.60764e12	+	5.33220e12i	−0.0692487	+	0.141602i
$520$	5.10203e12	−	8.83698e12i	0.134192	−	0.232427i
$521$			2.30229e12i			0.0599751i	0.999550	+	0.0299876i	$0.00954677\pi$
$521$			2.30229e12i			0.0599751i	−0.999550	+	0.0299876i	$0.990453\pi$
$522$	2.45278e13	+	3.15308e13i	0.632857	+	0.813546i
$523$	4.59297e13			1.17378			0.586888	−	0.809668i	$-0.300353\pi$
$523$	4.59297e13			1.17378			0.586888	+	0.809668i	$0.300353\pi$
$524$	9.36514e11	+	5.40697e11i	0.0237060	+	0.0136866i
$525$	−8.86968e10	+	5.96909e10i	−0.00222388	+	0.00149662i
$526$	−1.63320e13	−	2.82878e13i	−0.405611	−	0.702539i
$527$	4.41684e13	−	2.55006e13i	1.08657	−	0.627332i
$528$	−4.18464e12	−	6.21809e12i	−0.101974	−	0.151526i
$529$	1.13401e13	−	1.96416e13i	0.273739	−	0.474130i
$530$		−	2.08759e13i		−	0.499190i
$531$	−2.48500e13	+	1.93308e13i	−0.588645	+	0.457906i
$532$	2.10583e12			0.0494157
$533$	−1.00986e13	−	5.83044e12i	−0.234761	−	0.135539i
$534$	−4.06810e13	−	1.98945e13i	−0.936882	−	0.458170i
$535$	−2.22024e13	−	3.84557e13i	−0.506561	−	0.877389i
$536$	−1.98912e13	+	1.14842e13i	−0.449611	+	0.259583i
$537$	−1.70538e13	+	1.17447e12i	−0.381901	+	0.0263009i
$538$	2.13178e13	−	3.69235e13i	0.472967	−	0.819203i
$539$			3.17637e13i			0.698212i
$540$	7.20891e12	−	2.19505e13i	0.157000	−	0.478053i
$541$	−7.70812e13			−1.66327			−0.831633	−	0.555325i	$-0.812594\pi$
$541$	−7.70812e13			−1.66327			−0.831633	+	0.555325i	$0.812594\pi$
$542$	−5.93548e12	−	3.42685e12i	−0.126899	−	0.0732654i
$543$	−3.45168e12	−	5.01198e13i	−0.0731192	−	1.06172i
$544$	7.78789e12	+	1.34890e13i	0.163465	+	0.283130i
$545$	4.80062e13	−	2.77164e13i	0.998424	−	0.576440i
$546$	−2.39318e12	+	4.89366e12i	−0.0493188	+	0.100849i
$547$	2.26279e13	−	3.91927e13i	0.462070	−	0.800329i	−0.536994	−	0.843586i	$-0.680440\pi$
$547$	2.26279e13	−	3.91927e13i	0.462070	−	0.800329i	0.999064	+	0.0432573i	$0.0137735\pi$
$548$			4.14152e13i			0.838025i
$549$	−2.61804e13	+	6.44077e13i	−0.524945	+	1.29145i
$550$	−3.31129e11			−0.00657936
$551$	−3.01051e13	−	1.73812e13i	−0.592765	−	0.342233i
$552$	−1.87001e13	+	1.25848e13i	−0.364880	+	0.245556i
$553$	−1.04312e13	−	1.80673e13i	−0.201701	−	0.349356i
$554$	−4.00715e13	+	2.31353e13i	−0.767868	+	0.443329i
$555$	−1.10471e13	−	1.64153e13i	−0.209790	−	0.311734i
$556$	2.24210e13	−	3.88343e13i	0.421969	−	0.730872i
$557$		−	5.21515e13i		−	0.972726i	−0.873757	−	0.486363i	$-0.838323\pi$
$557$		−	5.21515e13i		−	0.972726i	0.873757	−	0.486363i	$-0.161677\pi$
$558$	−3.55754e12	−	2.57060e13i	−0.0657626	−	0.475185i
$559$	5.43383e13			0.995513
$560$	−2.52554e12	−	1.45812e12i	−0.0458579	−	0.0264761i
$561$	−6.74445e13	−	3.29828e13i	−1.21376	−	0.593573i
$562$	1.43395e12	+	2.48368e12i	0.0255772	+	0.0443011i
$563$	2.40413e13	−	1.38803e13i	0.425027	−	0.245390i	−0.272199	−	0.962241i	$-0.587751\pi$
$563$	2.40413e13	−	1.38803e13i	0.425027	−	0.245390i	0.697226	+	0.716851i	$0.254417\pi$
$564$	−3.77089e13	+	2.59695e12i	−0.660766	+	0.0455060i
$565$	4.44590e13	−	7.70052e13i	0.772177	−	1.33745i
$566$		−	5.21921e13i		−	0.898510i
$567$	−3.03430e12	+	1.19551e13i	−0.0517777	+	0.204004i
$568$	−1.62576e13			−0.274989
$569$	4.66989e13	+	2.69616e13i	0.782971	+	0.452048i	0.837482	−	0.546465i	$-0.184027\pi$
$569$	4.66989e13	+	2.69616e13i	0.782971	+	0.452048i	−0.0545115	+	0.998513i	$0.517360\pi$
$570$	1.38134e12	+	2.00576e13i	0.0229576	+	0.333354i
$571$	4.63585e13	+	8.02953e13i	0.763746	+	1.32285i	0.940907	+	0.338665i	$0.109975\pi$
$571$	4.63585e13	+	8.02953e13i	0.763746	+	1.32285i	−0.177161	+	0.984182i	$0.556691\pi$
$572$	−1.46117e13	+	8.43605e12i	−0.238627	+	0.137771i
$573$	1.74637e13	−	3.57103e13i	0.282724	−	0.578124i
$574$	−1.66629e12	+	2.88610e12i	−0.0267419	+	0.0463183i
$575$			9.95830e11i			0.0158433i
$576$	7.85060e12	−	1.08647e12i	0.123820	−	0.0171359i
$577$	2.32522e13			0.363568			0.181784	−	0.983338i	$-0.441813\pi$
$577$	2.32522e13			0.363568			0.181784	+	0.983338i	$0.441813\pi$
$578$	9.56133e13	+	5.52024e13i	1.48211	+	0.855694i
$579$	1.45678e12	−	9.80382e11i	0.0223873	−	0.0150662i
$580$	2.40702e13	+	4.16908e13i	0.366725	+	0.635186i
$581$	−7.93971e12	+	4.58400e12i	−0.119929	+	0.0692410i
$582$	4.27064e13	+	6.34590e13i	0.639556	+	0.950338i
$583$	−1.72588e13	+	2.98931e13i	−0.256252	+	0.443842i
$584$			7.67545e11i			0.0112990i
$585$	−4.81810e13	−	1.95846e13i	−0.703229	−	0.285848i
$586$	−6.23674e13			−0.902546
$587$	5.83410e13	+	3.36832e13i	0.837112	+	0.483307i	0.856282	−	0.516509i	$-0.172769\pi$
$587$	5.83410e13	+	3.36832e13i	0.837112	+	0.483307i	−0.0191695	+	0.999816i	$0.506102\pi$
$588$	−3.01728e13	−	1.47556e13i	−0.429268	−	0.209928i
$589$	1.12913e13	+	1.95571e13i	0.159282	+	0.275885i
$590$	−3.28573e13	+	1.89702e13i	−0.459591	+	0.265345i
$591$	1.21207e13	−	8.34734e11i	0.168109	−	0.0115774i
$592$	3.39369e12	−	5.87805e12i	0.0466728	−	0.0808397i
$593$			8.07690e13i			1.10147i	0.834681	+	0.550733i	$0.185652\pi$
$593$			8.07690e13i			1.10147i	−0.834681	+	0.550733i	$0.814348\pi$
$594$	−2.84700e13	+	2.54721e13i	−0.384995	+	0.344455i
$595$	−2.92118e13			−0.391718
$596$	2.28632e13	+	1.32001e13i	0.304023	+	0.175528i
$597$	−1.72617e12	−	2.50647e13i	−0.0227621	−	0.330515i
$598$	2.53704e13	+	4.39428e13i	0.331758	+	0.574621i
$599$	−3.96524e13	+	2.28933e13i	−0.514204	+	0.296876i	−0.734560	−	0.678544i	$-0.762611\pi$
$599$	−3.96524e13	+	2.28933e13i	−0.514204	+	0.296876i	0.220356	+	0.975419i	$0.429278\pi$
$600$	1.53824e11	−	3.14544e11i	0.00197819	−	0.00404507i
$601$	5.34626e13	−	9.25999e13i	0.681833	−	1.18097i	−0.292588	−	0.956238i	$-0.594517\pi$
$601$	5.34626e13	−	9.25999e13i	0.681833	−	1.18097i	0.974421	−	0.224730i	$-0.0721501\pi$
$602$		−	1.55295e13i		−	0.196415i
$603$	7.18797e13	+	9.24023e13i	0.901612	+	1.15903i
$604$	−1.33941e13			−0.166621
$605$	−3.29369e13	−	1.90161e13i	−0.406356	−	0.234609i
$606$	−3.21880e13	+	2.16618e13i	−0.393850	+	0.265052i
$607$	−7.71330e13	−	1.33598e14i	−0.936046	−	1.62128i	−0.772759	−	0.634700i	$-0.781124\pi$
$607$	−7.71330e13	−	1.33598e14i	−0.936046	−	1.62128i	−0.163287	−	0.986579i	$-0.552210\pi$
$608$	−5.97273e12	+	3.44836e12i	−0.0718878	+	0.0415045i
$609$	−1.43488e13	−	2.13214e13i	−0.171289	−	0.254524i
$610$	−4.18922e13	+	7.25594e13i	−0.496003	+	0.859102i
$611$			8.50873e13i			0.999215i
$612$	6.26617e13	−	4.87445e13i	0.729870	−	0.567765i
$613$	−8.26123e13			−0.954426			−0.477213	−	0.878788i	$-0.658353\pi$
$613$	−8.26123e13			−0.954426			−0.477213	+	0.878788i	$0.658353\pi$
$614$	−3.67152e13	−	2.11976e13i	−0.420731	−	0.242909i
$615$	−2.85826e13	−	1.39780e13i	−0.324883	−	0.158880i
$616$	2.41095e12	+	4.17589e12i	0.0271822	+	0.0470810i
$617$	−1.12347e14	+	6.48637e13i	−1.25643	+	0.725398i	−0.972378	−	0.233413i	$-0.925011\pi$
$617$	−1.12347e14	+	6.48637e13i	−1.25643	+	0.725398i	−0.284048	+	0.958810i	$0.591677\pi$
$618$	1.22532e13	−	8.43862e11i	0.135928	−	0.00936115i
$619$	1.93661e13	−	3.35430e13i	0.213102	−	0.369104i	−0.739581	−	0.673067i	$-0.764977\pi$
$619$	1.93661e13	−	3.35430e13i	0.213102	−	0.369104i	0.952684	+	0.303963i	$0.0983098\pi$
$620$		−	3.12733e13i		−	0.341362i
$621$	7.66042e13	+	8.56200e13i	0.829458	+	0.927080i
$622$	3.00463e13			0.322730
$623$	2.52307e13	+	1.45669e13i	0.268837	+	0.155213i
$624$	−1.22577e12	−	1.77987e13i	−0.0129565	−	0.188133i
$625$	4.82833e13	+	8.36291e13i	0.506287	+	0.876915i
$626$	7.12911e13	−	4.11599e13i	0.741589	−	0.428157i
$627$	1.46043e13	−	2.98634e13i	0.150710	−	0.308178i
$628$	1.95682e13	−	3.38930e13i	0.200333	−	0.346986i
$629$		−	6.79888e13i		−	0.690532i
$630$	−5.59711e12	+	1.37698e13i	−0.0563976	+	0.138747i
$631$	−9.48250e13			−0.947930			−0.473965	−	0.880544i	$-0.657178\pi$
$631$	−9.48250e13			−0.947930			−0.473965	+	0.880544i	$0.657178\pi$
$632$	5.91715e13	+	3.41627e13i	0.586851	+	0.338818i
$633$	9.59526e13	−	6.45739e13i	0.944144	−	0.635387i
$634$	−4.74842e13	−	8.22450e13i	−0.463556	−	0.802903i
$635$	1.34781e13	−	7.78159e12i	0.130545	−	0.0753702i
$636$	−2.03784e13	−	3.02810e13i	−0.195833	−	0.290994i
$637$	−3.78045e13	+	6.54792e13i	−0.360451	+	0.624319i
$638$		−	7.95986e13i		−	0.753012i
$639$	1.13596e13	+	8.20815e13i	0.106624	+	0.770444i
$640$	9.55087e12			0.0889494
$641$	−5.99175e13	−	3.45934e13i	−0.553686	−	0.319671i	0.196921	−	0.980419i	$-0.436906\pi$
$641$	−5.99175e13	−	3.45934e13i	−0.553686	−	0.319671i	−0.750607	+	0.660749i	$0.770239\pi$
$642$	−6.97446e13	−	3.41077e13i	−0.639492	−	0.312735i
$643$	3.32919e13	+	5.76632e13i	0.302889	+	0.524619i	0.976789	−	0.214203i	$-0.0687155\pi$
$643$	3.32919e13	+	5.76632e13i	0.302889	+	0.524619i	−0.673900	+	0.738823i	$0.735382\pi$
$644$	1.25585e13	−	7.25065e12i	0.113373	−	0.0654557i
$645$	1.47915e14	−	1.01867e13i	1.32500	−	0.0912505i
$646$	−3.45420e13	+	5.98285e13i	−0.307033	+	0.531796i
$647$		−	5.45437e13i		−	0.481087i	−0.970638	−	0.240543i	$-0.922674\pi$
$647$		−	5.45437e13i		−	0.481087i	0.970638	−	0.240543i	$-0.0773256\pi$
$648$	−1.09708e13	−	3.88769e13i	−0.0960199	−	0.340265i
$649$	6.27331e13			0.544845
$650$	−6.82605e11	−	3.94102e11i	−0.00588306	−	0.00339658i
$651$	1.14707e12	+	1.66560e13i	0.00981039	+	0.142451i
$652$	3.62240e13	+	6.27419e13i	0.307439	+	0.532500i
$653$	8.64389e12	−	4.99055e12i	0.0728020	−	0.0420323i	−0.463157	−	0.886276i	$-0.653283\pi$
$653$	8.64389e12	−	4.99055e12i	0.0728020	−	0.0420323i	0.535959	+	0.844244i	$0.319950\pi$
$654$	4.25783e13	−	8.70657e13i	0.355877	−	0.727710i
$655$	3.32110e12	−	5.75231e12i	0.0275471	−	0.0477129i
$656$		−	1.09144e13i		−	0.0898425i
$657$	3.87518e12	−	5.36299e11i	0.0316566	−	0.00438107i
$658$	2.43173e13			0.197145
$659$	−1.46706e14	−	8.47006e13i	−1.18038	−	0.681490i	−0.224274	−	0.974526i	$-0.572001\pi$
$659$	−1.46706e14	−	8.47006e13i	−1.18038	−	0.681490i	−0.956101	+	0.293036i	$0.905334\pi$
$660$	−3.81931e13	+	2.57031e13i	−0.304976	+	0.205242i
$661$	1.91393e13	+	3.31503e13i	0.151677	+	0.262712i	0.931844	−	0.362859i	$-0.118199\pi$
$661$	1.91393e13	+	3.31503e13i	0.151677	+	0.262712i	−0.780167	+	0.625571i	$0.784866\pi$
$662$	−5.36818e12	+	3.09932e12i	−0.0422219	+	0.0243768i
$663$	−9.97778e13	−	1.48263e14i	−0.778873	−	1.15735i
$664$	1.50129e13	−	2.60031e13i	0.116312	−	0.201458i
$665$		−	1.29345e13i		−	0.0994587i
$666$	−3.20483e13	−	1.30270e13i	−0.244587	−	0.0994195i
$667$	−2.39383e14			−1.81328
$668$	−7.85278e13	−	4.53381e13i	−0.590393	−	0.340864i
$669$	1.81326e14	+	8.86749e13i	1.35310	+	0.661714i
$670$	7.05388e13	+	1.22177e14i	0.522461	+	0.904930i
$671$	1.19975e14	−	6.92674e13i	0.882017	−	0.509233i
$672$	−5.08673e12	+	3.50316e11i	−0.0371187	+	0.00255631i
$673$	−1.82599e13	+	3.16270e13i	−0.132258	+	0.229078i	−0.924547	−	0.381069i	$-0.875556\pi$
$673$	−1.82599e13	+	3.16270e13i	−0.132258	+	0.229078i	0.792289	+	0.610146i	$0.208889\pi$
$674$		−	1.22483e14i		−	0.880596i
$675$	−1.69555e12	−	5.56846e11i	−0.0121002	−	0.00397390i
$676$	3.04220e13			0.215503
$677$	−1.17109e14	−	6.76128e13i	−0.823466	−	0.475429i	0.0281439	−	0.999604i	$-0.491040\pi$
$677$	−1.17109e14	−	6.76128e13i	−0.823466	−	0.475429i	−0.851610	+	0.524175i	$0.824374\pi$
$678$	−1.06813e13	−	1.55098e14i	−0.0745551	−	1.08257i
$679$	−2.46051e13	−	4.26172e13i	−0.170481	−	0.295282i
$680$	8.28530e13	−	4.78352e13i	0.569854	−	0.329006i
$681$	−6.43590e13	+	1.31604e14i	−0.439414	+	0.898529i
$682$	−2.58547e13	+	4.47817e13i	−0.175234	+	0.303514i
$683$			6.56579e13i			0.441757i	0.975301	+	0.220879i	$0.0708925\pi$
$683$			6.56579e13i			0.441757i	−0.975301	+	0.220879i	$0.929108\pi$
$684$	2.15833e13	+	2.77457e13i	0.144158	+	0.185317i
$685$	2.54383e14			1.68669
$686$	3.82943e13	+	2.21092e13i	0.252065	+	0.145530i
$687$	−6.52441e13	+	4.39078e13i	−0.426341	+	0.286918i
$688$	2.54300e13	+	4.40460e13i	0.164969	+	0.285736i
$689$	−7.11562e13	+	4.10820e13i	−0.458265	+	0.264579i
$690$	7.72990e13	+	1.14861e14i	0.494229	+	0.734392i
$691$	−9.81955e13	+	1.70080e14i	−0.623306	+	1.07960i	0.365560	+	0.930788i	$0.380878\pi$
$691$	−9.81955e13	+	1.70080e14i	−0.623306	+	1.07960i	−0.988866	+	0.148810i	$0.952456\pi$
$692$			1.25064e13i			0.0788140i
$693$	1.93987e13	−	1.50902e13i	0.121368	−	0.0944124i
$694$	7.63306e13			0.474134
$695$	−2.38530e14	−	1.37715e14i	−1.47102	−	0.849295i
$696$	7.56119e13	+	3.69770e13i	0.462960	+	0.226405i
$697$	−5.46646e13	−	9.46818e13i	−0.332309	−	0.575576i
$698$	7.11916e12	−	4.11025e12i	0.0429686	−	0.0248080i
$699$	9.98574e13	−	6.87704e12i	0.598404	−	0.0412112i
$700$	−1.12631e11	+	1.95083e11i	−0.000670145	+	0.00116073i
$701$			5.99806e13i			0.354340i	0.984180	+	0.177170i	$0.0566943\pi$
$701$			5.99806e13i			0.354340i	−0.984180	+	0.177170i	$0.943306\pi$
$702$	−8.90057e13	+	1.86250e13i	−0.522074	+	0.109247i
$703$	3.01044e13			0.175329
$704$	−1.36763e13	−	7.89602e12i	−0.0790871	−	0.0456610i
$705$	1.59512e13	+	2.31618e14i	0.0915898	+	1.32992i
$706$	−6.75845e13	−	1.17060e14i	−0.385322	−	0.667397i
$707$	2.16165e13	−	1.24803e13i	0.122374	−	0.0706527i
$708$	−2.91422e13	+	5.95910e13i	−0.163816	+	0.334977i
$709$	1.16327e14	−	2.01484e14i	0.649304	−	1.12463i	−0.333985	−	0.942578i	$-0.608394\pi$
$709$	1.16327e14	−	2.01484e14i	0.649304	−	1.12463i	0.983289	−	0.182049i	$-0.0582731\pi$
$710$			9.98586e13i			0.553470i
$711$	1.31136e14	−	3.22615e14i	0.721730	−	1.77557i
$712$	−9.54153e13			−0.521456
$713$	1.34675e14	+	7.77549e13i	0.730871	+	0.421968i
$714$	−4.23725e13	+	2.85157e13i	−0.228346	+	0.153671i
$715$	5.18164e13	+	8.97486e13i	0.277292	+	0.480283i
$716$	−3.11920e13	+	1.80087e13i	−0.165759	+	0.0957013i
$717$	4.21677e12	+	6.26584e12i	0.0222527	+	0.0330661i
$718$	−8.67368e13	+	1.50232e14i	−0.454549	+	0.787302i
$719$			1.83519e14i			0.955074i	0.878612	+	0.477537i	$0.158470\pi$
$719$			1.83519e14i			0.955074i	−0.878612	+	0.477537i	$0.841530\pi$
$720$	−6.67339e12	−	4.82204e13i	−0.0344893	−	0.249212i
$721$	−7.90173e12			−0.0405551
$722$	9.36527e13	+	5.40704e13i	0.477347	+	0.275597i
$723$	−1.12441e14	−	5.49880e13i	−0.569160	−	0.278340i
$724$	−5.29262e13	−	9.16708e13i	−0.266059	−	0.460827i
$725$	3.22037e12	−	1.85928e12i	0.0160774	−	0.00928230i
$726$	−6.63389e13	+	4.56866e12i	−0.328916	+	0.0226520i
$727$	−2.15624e13	+	3.73472e13i	−0.106176	+	0.183902i	−0.914218	−	0.405223i	$-0.867194\pi$
$727$	−2.15624e13	+	3.73472e13i	−0.106176	+	0.183902i	0.808042	+	0.589125i	$0.200527\pi$
$728$			1.14779e13i			0.0561311i
$729$	−1.88616e14	+	8.25532e13i	−0.916097	+	0.400956i
$730$	4.71446e12			0.0227414
$731$	4.41206e14	+	2.54730e14i	2.11375	+	1.22038i
$732$	1.00647e13	+	1.46143e14i	0.0478900	+	0.695382i
$733$	−1.69315e12	−	2.93263e12i	−0.00800159	−	0.0138592i	0.861997	−	0.506914i	$-0.169214\pi$
$733$	−1.69315e12	−	2.93263e12i	−0.00800159	−	0.0138592i	−0.869998	+	0.493054i	$0.835880\pi$
$734$	−4.80247e13	+	2.77271e13i	−0.225416	+	0.130144i
$735$	−9.06328e13	+	1.85329e14i	−0.422522	+	0.863987i
$736$	−2.37463e13	+	4.11298e13i	−0.109953	+	0.190444i
$737$		−	2.33267e14i		−	1.07279i
$738$	−5.51047e13	+	7.62614e12i	−0.251714	+	0.0348356i
$739$	1.10782e14			0.502627			0.251314	−	0.967906i	$-0.419137\pi$
$739$	1.10782e14			0.502627			0.251314	+	0.967906i	$0.419137\pi$
$740$	−3.61045e13	−	2.08449e13i	−0.162706	−	0.0939382i
$741$	6.56488e13	−	4.41801e13i	0.293857	−	0.197759i
$742$	1.17409e13	+	2.03359e13i	0.0522014	+	0.0904155i
$743$	−8.04222e13	+	4.64318e13i	−0.355167	+	0.205056i	−0.666958	−	0.745095i	$-0.732404\pi$
$743$	−8.04222e13	+	4.64318e13i	−0.355167	+	0.205056i	0.311792	+	0.950150i	$0.399071\pi$
$744$	−3.05281e13	−	4.53628e13i	−0.133917	−	0.198992i
$745$	8.10784e13	−	1.40432e14i	0.353284	−	0.611906i
$746$			1.68732e14i			0.730304i
$747$	−1.41774e14	−	5.76281e13i	−0.609528	−	0.247760i
$748$	−1.58188e14			−0.675562
$749$	4.32562e13	+	2.49740e13i	0.183501	+	0.105945i
$750$	1.49765e14	+	7.32405e13i	0.631107	+	0.308635i
$751$	−8.69923e13	−	1.50675e14i	−0.364151	−	0.630727i	0.624489	−	0.781034i	$-0.285307\pi$
$751$	−8.69923e13	−	1.50675e14i	−0.364151	−	0.630727i	−0.988639	+	0.150306i	$0.951974\pi$
$752$	−6.89708e13	+	3.98203e13i	−0.286798	+	0.165583i
$753$	5.79555e13	−	3.99131e12i	0.239398	−	0.0164870i
$754$	9.47365e13	−	1.64088e14i	0.388741	−	0.673319i
$755$			8.22701e13i			0.335357i
$756$	5.32288e12	+	2.54371e13i	0.0215545	+	0.103005i
$757$	3.09896e13			0.124663			0.0623314	−	0.998056i	$-0.480146\pi$
$757$	3.09896e13			0.124663			0.0623314	+	0.998056i	$0.480146\pi$
$758$	−1.41802e14	−	8.18696e13i	−0.566679	−	0.327172i
$759$	−1.57282e13	−	2.28380e14i	−0.0624412	−	0.906672i
$760$	2.11807e13	+	3.66861e13i	0.0835358	+	0.144688i
$761$	2.06720e14	−	1.19350e14i	0.809951	−	0.467626i	−0.0369878	−	0.999316i	$-0.511776\pi$
$761$	2.06720e14	−	1.19350e14i	0.809951	−	0.467626i	0.846939	+	0.531690i	$0.178443\pi$
$762$	1.19542e13	−	2.44443e13i	0.0465313	−	0.0951489i
$763$	−3.11763e13	+	5.39989e13i	−0.120560	+	0.208815i
$764$		−	8.37570e13i		−	0.321776i
$765$	−2.99401e14	−	3.84885e14i	−1.14274	−	1.46901i
$766$	3.25529e14			1.23437
$767$	1.29321e14	+	7.46635e13i	0.487183	+	0.281275i
$768$	1.38538e13	−	9.32328e12i	0.0518516	−	0.0348950i
$769$	−9.67736e13	−	1.67617e14i	−0.359853	−	0.623284i	0.628083	−	0.778146i	$-0.283840\pi$
$769$	−9.67736e13	−	1.67617e14i	−0.359853	−	0.623284i	−0.987936	+	0.154863i	$0.950506\pi$
$770$	2.56494e13	−	1.48087e13i	0.0947598	−	0.0547096i
$771$	−1.55123e13	−	2.30502e13i	−0.0569382	−	0.0846065i
$772$	1.84989e12	−	3.20411e12i	0.00674621	−	0.0116848i
$773$			3.34106e11i			0.00121056i	1.00000		0.000605280i	$0.000192667\pi$
$773$			3.34106e11i			0.00121056i	−1.00000		0.000605280i	$0.999807\pi$
$774$	2.04611e14	−	1.59167e14i	0.736587	−	0.572990i
$775$	−2.41568e12			−0.00864035
$776$	1.39574e14	+	8.05832e13i	0.496017	+	0.286375i
$777$	1.99936e13	+	9.77761e12i	0.0705970	+	0.0345245i
$778$	−1.83840e14	−	3.18420e14i	−0.644974	−	1.11713i
$779$	4.19237e13	−	2.42046e13i	0.146141	−	0.0843746i
$780$	−1.09324e14	+	7.52902e12i	−0.378655	+	0.0260775i
$781$	8.25565e13	−	1.42992e14i	0.284116	−	0.492104i
$782$			4.75731e14i			1.62677i
$783$	1.33858e14	−	4.07586e14i	0.454815	−	1.38487i
$784$	−7.07689e13			−0.238925
$785$	−2.08180e14	−	1.20193e14i	−0.698378	−	0.403209i
$786$	−7.97900e11	−	1.15858e13i	−0.00265972	−	0.0386202i
$787$	−2.15809e14	−	3.73792e14i	−0.714818	−	1.23810i	−0.963030	−	0.269395i	$-0.913176\pi$
$787$	−2.15809e14	−	3.73792e14i	−0.714818	−	1.23810i	0.248212	−	0.968706i	$-0.420157\pi$
$788$	2.21692e13	−	1.27994e13i	0.0729656	−	0.0421267i
$789$	−1.54105e14	+	3.15120e14i	−0.504003	+	1.03060i
$790$	2.09836e14	−	3.63447e14i	0.681938	−	1.18115i
$791$			1.00018e14i			0.322994i
$792$	−3.03095e13	+	7.45661e13i	−0.0972642	+	0.239285i
$793$	3.29762e14			1.05156
$794$	−2.12012e14	−	1.22405e14i	−0.671828	−	0.387880i
$795$	−1.85994e14	+	1.25170e14i	−0.585683	+	0.394152i
$796$	−2.64682e13	−	4.58442e13i	−0.0828245	−	0.143456i
$797$	−9.68562e13	+	5.59200e13i	−0.301187	+	0.173890i	−0.642976	−	0.765886i	$-0.722300\pi$
$797$	−9.68562e13	+	5.59200e13i	−0.301187	+	0.173890i	0.341789	+	0.939777i	$0.388967\pi$
$798$	−1.26263e13	−	1.87619e13i	−0.0390178	−	0.0579779i
$799$	−3.98877e14	+	6.90876e14i	−1.22491	+	2.12161i
$800$		−	7.37749e11i		−	0.00225143i
$801$	6.66687e13	+	4.81733e14i	0.202190	+	1.46098i
$802$	6.90212e13			0.208023
$803$	−6.75084e12	−	3.89760e12i	−0.0202200	−	0.0116740i
$804$	2.21584e14	+	1.08363e14i	0.659565	+	0.322552i
$805$	−4.45354e13	−	7.71375e13i	−0.131742	−	0.228185i
$806$	−1.06596e14	+	6.15434e13i	−0.313377	+	0.180928i
$807$	−4.56789e14	+	3.14584e13i	−1.33459	+	0.0919114i
$808$	−4.08738e13	+	7.07955e13i	−0.118683	+	0.205565i
$809$		−	3.04434e14i		−	0.878517i	−0.898361	−	0.439258i	$-0.855241\pi$
$809$		−	3.04434e14i		−	0.878517i	0.898361	−	0.439258i	$-0.144759\pi$
$810$	−2.38792e14	+	6.73852e13i	−0.684850	+	0.193259i
$811$	3.89680e14			1.11072			0.555358	−	0.831611i	$-0.312581\pi$
$811$	3.89680e14			1.11072			0.555358	+	0.831611i	$0.312581\pi$
$812$	−4.68951e13	−	2.70749e13i	−0.132846	−	0.0766985i
$813$	5.05697e12	+	7.34292e13i	0.0142376	+	0.206736i
$814$	3.44664e13	+	5.96976e13i	0.0964438	+	0.167046i
$815$	3.85377e14	−	2.22497e14i	1.07176	−	0.618781i
$816$	7.34851e13	−	1.50265e14i	0.203118	−	0.415343i
$817$	−1.12791e14	+	1.95359e14i	−0.309858	+	0.536690i
$818$		−	5.23982e13i		−	0.143070i
$819$	5.79493e13	−	8.01981e12i	0.157264	−	0.0217643i
$820$	−6.70393e13			−0.180826
$821$	4.29902e14	+	2.48204e14i	1.15253	+	0.665416i	0.949504	−	0.313756i	$-0.101587\pi$
$821$	4.29902e14	+	2.48204e14i	1.15253	+	0.665416i	0.203031	+	0.979172i	$0.434921\pi$
$822$	3.68989e14	−	2.48321e14i	0.983229	−	0.661691i
$823$	2.56346e14	+	4.44004e14i	0.678933	+	1.17595i	0.975303	+	0.220873i	$0.0708907\pi$
$823$	2.56346e14	+	4.44004e14i	0.678933	+	1.17595i	−0.296370	+	0.955073i	$0.595776\pi$
$824$	2.24116e13	−	1.29393e13i	0.0589979	−	0.0340624i
$825$	1.98542e12	+	2.95020e12i	0.00519495	+	0.00771936i
$826$	2.13382e13	−	3.69589e13i	0.0554955	−	0.0961211i
$827$		−	1.98057e14i		−	0.511990i	−0.966678	−	0.255995i	$-0.917597\pi$
$827$		−	1.98057e14i		−	0.511990i	0.966678	−	0.255995i	$-0.0824031\pi$
$828$	2.24248e14	+	9.11521e13i	0.576206	+	0.234215i
$829$	−1.98572e12			−0.00507160			−0.00253580	−	0.999997i	$-0.500807\pi$
$829$	−1.98572e12			−0.00507160			−0.00253580	+	0.999997i	$0.500807\pi$
$830$	−1.59718e14	−	9.22130e13i	−0.405473	−	0.234100i
$831$	4.46389e14	+	2.18301e14i	1.12644	+	0.550871i
$832$	−1.87953e13	−	3.25545e13i	−0.0471448	−	0.0816571i
$833$	−6.13915e14	+	3.54444e14i	−1.53067	+	0.883736i
$834$	−4.80428e14	+	3.30864e13i	−1.19069	+	0.0820010i
$835$	−2.78478e14	+	4.82338e14i	−0.686055	+	1.18828i
$836$		−	7.00432e13i		−	0.171528i
$837$	−2.07697e14	+	1.85826e14i	−0.505595	+	0.452355i
$838$	1.62743e13			0.0393806
$839$	2.17488e14	+	1.25567e14i	0.523150	+	0.302041i	0.738222	−	0.674557i	$-0.235666\pi$
$839$	2.17488e14	+	1.25567e14i	0.523150	+	0.302041i	−0.215073	+	0.976598i	$0.568999\pi$
$840$	2.15173e12	+	3.12440e13i	0.00514508	+	0.0747086i
$841$	2.36591e14	+	4.09788e14i	0.562365	+	0.974045i
$842$	2.28300e14	−	1.31809e14i	0.539443	−	0.311448i
$843$	1.35305e13	−	2.76677e13i	0.0317817	−	0.0649884i
$844$	1.21845e14	−	2.11042e14i	0.284509	−	0.492784i
$845$		−	1.86860e14i		−	0.433743i
$846$	2.49236e14	+	3.20396e14i	0.575120	+	0.739325i
$847$	4.27799e13			0.0981347
$848$	−6.66012e13	−	3.84522e13i	−0.151881	−	0.0876884i
$849$	−4.65006e14	+	3.12939e14i	−1.05419	+	0.709448i
$850$	−3.69499e12	−	6.39991e12i	−0.00832758	−	0.0144238i
$851$	1.79533e14	−	1.03654e14i	0.402251	−	0.232240i
$852$	9.74791e13	+	1.44848e14i	0.217127	+	0.322636i
$853$	−1.51848e14	+	2.63008e14i	−0.336250	+	0.582403i	−0.983724	−	0.179685i	$-0.942492\pi$
$853$	−1.51848e14	+	2.63008e14i	−0.336250	+	0.582403i	0.647474	+	0.762088i	$0.275825\pi$
$854$		−	9.42433e13i		−	0.207473i
$855$	1.70421e14	−	1.32571e14i	0.372986	−	0.290146i
$856$	−1.63583e14			−0.355933
$857$	−3.93597e14	−	2.27243e14i	−0.851427	−	0.491572i	0.00970495	−	0.999953i	$-0.496911\pi$
$857$	−3.93597e14	−	2.27243e14i	−0.851427	−	0.491572i	−0.861132	+	0.508381i	$0.830244\pi$
$858$	1.62771e14	+	7.96010e13i	0.350058	+	0.171192i
$859$	7.72817e13	+	1.33856e14i	0.165238	+	0.286201i	0.936740	−	0.350026i	$-0.113827\pi$
$859$	7.72817e13	+	1.33856e14i	0.165238	+	0.286201i	−0.771502	+	0.636227i	$0.780494\pi$
$860$	2.70542e14	−	1.56197e14i	0.575099	−	0.332033i
$861$	3.57047e13	−	2.45893e12i	0.0754587	−	0.00519673i
$862$	−2.36951e14	+	4.10411e14i	−0.497878	+	0.862349i
$863$		−	9.37665e13i		−	0.195882i	−0.995192	−	0.0979408i	$-0.968774\pi$
$863$		−	9.37665e13i		−	0.195882i	0.995192	−	0.0979408i	$-0.0312256\pi$
$864$	−5.67513e13	−	6.34306e13i	−0.117871	−	0.131744i
$865$	7.68178e13			0.158629
$866$	−6.15852e13	−	3.55562e13i	−0.126441	−	0.0730005i
$867$	−8.14615e13	−	1.18286e15i	−0.166287	−	2.41455i
$868$	1.75886e13	+	3.04644e13i	0.0356971	+	0.0618292i
$869$	−6.00948e14	+	3.46957e14i	−1.21266	+	0.700127i
$870$	2.27122e14	−	4.64428e14i	0.455684	−	0.931798i
$871$	2.77629e14	−	4.80868e14i	0.553828	−	0.959258i
$872$		−	2.04208e14i		−	0.405034i
$873$	3.09325e14	−	7.60987e14i	0.610019	−	1.50074i
$874$	−2.10646e14			−0.413045
$875$	−9.28854e13	−	5.36274e13i	−0.181095	−	0.104555i
$876$	6.83844e12	−	4.60212e12i	0.0132567	−	0.00892149i
$877$	−2.56886e14	−	4.44939e14i	−0.495156	−	0.857635i	0.504828	−	0.863220i	$-0.331556\pi$
$877$	−2.56886e14	−	4.44939e14i	−0.495156	−	0.857635i	−0.999984	+	0.00558431i	$0.998222\pi$
$878$	−4.18238e14	+	2.41470e14i	−0.801588	+	0.462797i
$879$	3.73948e14	+	5.55662e14i	0.712635	+	1.05893i
$880$	−4.84994e13	+	8.40035e13i	−0.0919017	+	0.159178i
$881$		−	8.03330e14i		−	1.51361i	−0.653640	−	0.756806i	$-0.726759\pi$
$881$		−	8.03330e14i		−	1.51361i	0.653640	−	0.756806i	$-0.273241\pi$
$882$	4.94477e13	+	3.57298e14i	0.0926410	+	0.669403i
$883$	−7.28134e14			−1.35646			−0.678232	−	0.734848i	$-0.737253\pi$
$883$	−7.28134e14			−1.35646			−0.678232	+	0.734848i	$0.737253\pi$
$884$	−3.26096e14	−	1.88272e14i	−0.604066	−	0.348758i
$885$	3.66024e14	+	1.78999e14i	0.674206	+	0.329712i
$886$	6.18083e13	+	1.07055e14i	0.113208	+	0.196083i
$887$	4.70560e13	−	2.71678e13i	0.0857032	−	0.0494808i	−0.456536	−	0.889705i	$-0.650910\pi$
$887$	4.70560e13	−	2.71678e13i	0.0857032	−	0.0494808i	0.542239	+	0.840224i	$0.317577\pi$
$888$	−7.27187e13	+	5.00804e12i	−0.131699	+	0.00906990i
$889$	−8.75298e12	+	1.51606e13i	−0.0157633	+	0.0273028i
$890$			5.86066e14i			1.04953i
$891$	3.97647e14	+	1.00926e14i	0.708124	+	0.179727i
$892$	4.25291e14			0.753116
$893$	−3.05909e14	−	1.76617e14i	−0.538686	−	0.311010i
$894$	−1.94792e13	−	2.82847e14i	−0.0341102	−	0.495294i
$895$	1.10614e14	+	1.91589e14i	0.192618	+	0.333623i
$896$	−9.30381e12	+	5.37156e12i	−0.0161109	+	0.00930165i
$897$	2.39390e14	−	4.89514e14i	0.412234	−	0.842952i
$898$	−1.58869e14	+	2.75169e14i	−0.272055	+	0.471214i
$899$		−	5.80695e14i		−	0.988894i
$900$	−3.72475e12	+	5.15481e11i	−0.00630789	+	0.000872971i
$901$	−7.70347e14			−1.29737
$902$	9.59965e13	+	5.54236e13i	0.160777	+	0.0928244i
$903$	−1.38360e14	+	9.31130e13i	−0.230447	+	0.155086i
$904$	−1.63782e14	−	2.83679e14i	−0.271284	−	0.469877i
$905$	−5.63066e14	+	3.25086e14i	−0.927505	+	0.535496i
$906$	8.03097e13	+	1.19335e14i	0.131561	+	0.195491i
$907$	5.46173e14	−	9.45999e14i	0.889802	−	1.54118i	0.0496935	−	0.998765i	$-0.484176\pi$
$907$	5.46173e14	−	9.45999e14i	0.889802	−	1.54118i	0.840109	−	0.542418i	$-0.182491\pi$
$908$			3.08670e14i			0.500110i
$909$	3.85992e14	+	1.56897e14i	0.621955	+	0.252811i
$910$	7.04999e13			0.112975
$911$	7.31673e14	+	4.22432e14i	1.16607	+	0.673232i	0.952752	−	0.303751i	$-0.0982390\pi$
$911$	7.31673e14	+	4.22432e14i	1.16607	+	0.673232i	0.213320	+	0.976982i	$0.431572\pi$
$912$	6.65351e13	+	3.25381e13i	0.105457	+	0.0515725i
$913$	1.52471e14	+	2.64088e14i	0.240344	+	0.416288i
$914$	4.58649e14	−	2.64801e14i	0.719034	−	0.415134i
$915$	8.97650e14	−	6.18199e13i	1.39959	−	0.0963879i
$916$	−8.28500e13	+	1.43500e14i	−0.128474	+	0.222523i
$917$			7.47135e12i			0.0115226i
$918$	−8.10003e14	−	2.66018e14i	−1.24243	−	0.408036i
$919$	−1.79863e14			−0.274387			−0.137194	−	0.990544i	$-0.543808\pi$
$919$	−1.79863e14			−0.274387			−0.137194	+	0.990544i	$0.543808\pi$
$920$	2.52630e14	+	1.45856e14i	0.383306	+	0.221302i
$921$	3.12810e13	+	4.54213e14i	0.0472044	+	0.685427i
$922$	4.28016e13	+	7.41346e13i	0.0642400	+	0.111267i
$923$	3.40372e14	−	1.96514e14i	0.508095	−	0.293349i
$924$	2.27493e13	−	4.65186e13i	0.0337760	−	0.0690665i
$925$	−1.61015e12	+	2.78886e12i	−0.00237770	+	0.00411830i
$926$		−	3.79461e14i		−	0.557330i
$927$	−8.09875e13	−	1.04111e14i	−0.118309	−	0.152088i
$928$	1.77344e14			0.257678
$929$	7.27829e14	+	4.20212e14i	1.05184	+	0.607282i	0.923165	−	0.384405i	$-0.125593\pi$
$929$	7.27829e14	+	4.20212e14i	1.05184	+	0.607282i	0.128678	+	0.991686i	$0.458927\pi$
$930$	−2.78630e14	+	1.87512e14i	−0.400510	+	0.269534i
$931$	−1.56942e14	−	2.71832e14i	−0.224384	−	0.388644i
$932$	1.82643e14	−	1.05449e14i	0.259730	−	0.149955i
$933$	−1.80155e14	−	2.67698e14i	−0.254822	−	0.378649i
$934$	−1.28805e14	+	2.23096e14i	−0.181216	+	0.313876i
$935$			9.71631e14i			1.35970i
$936$	−1.51228e14	+	1.17640e14i	−0.210501	+	0.163748i
$937$	3.29089e14			0.455633			0.227816	−	0.973704i	$-0.426841\pi$
$937$	3.29089e14			0.455633			0.227816	+	0.973704i	$0.426841\pi$
$938$	−1.37428e14	−	7.93442e13i	−0.189261	−	0.109270i
$939$	−7.94168e14	−	3.88378e14i	−1.08789	−	0.532018i
$940$	2.44587e14	+	4.23636e14i	0.333268	+	0.577237i
$941$	−4.44757e13	+	2.56781e13i	−0.0602802	+	0.0348028i	−0.529837	−	0.848099i	$-0.677747\pi$
$941$	−4.44757e13	+	2.56781e13i	−0.0602802	+	0.0348028i	0.469557	+	0.882902i	$0.344414\pi$
$942$	−4.19299e14	+	2.88765e13i	−0.565287	+	0.0389305i
$943$	1.66680e14	−	2.88698e14i	0.223524	−	0.387155i
$944$			1.39768e14i			0.186444i
$945$	1.56241e14	−	3.26945e13i	0.207318	−	0.0433826i
$946$	−5.16535e14			−0.681779
$947$	−6.88773e14	−	3.97663e14i	−0.904329	−	0.522114i	−0.0257265	−	0.999669i	$-0.508190\pi$
$947$	−6.88773e14	−	3.97663e14i	−0.904329	−	0.522114i	−0.878602	+	0.477555i	$0.841523\pi$
$948$	−5.04135e13	−	7.32025e14i	−0.0658424	−	0.956058i
$949$	−9.27767e12	−	1.60694e13i	−0.0120534	−	0.0208770i
$950$	2.83379e12	−	1.63609e12i	0.00366226	−	0.00211441i
$951$	−4.48052e14	+	9.16193e14i	−0.576005	+	1.17783i
$952$	−5.38065e13	+	9.31956e13i	−0.0688098	+	0.119182i
$953$		−	4.74655e14i		−	0.603828i	−0.953335	−	0.301914i	$-0.902374\pi$
$953$		−	4.74655e14i		−	0.603828i	0.953335	−	0.301914i	$-0.0976256\pi$
$954$	−1.47602e14	+	3.63124e14i	−0.186788	+	0.459529i
$955$	−5.14457e14			−0.647638
$956$	1.37813e13	+	7.95665e12i	0.0172584	+	0.00996416i
$957$	−7.09184e14	+	4.77265e14i	−0.883486	+	0.594566i
$958$	4.38594e14	+	7.59667e14i	0.543545	+	0.941447i
$959$	−2.47803e14	+	1.43069e14i	−0.305501	+	0.176381i
$960$	−5.72660e13	−	8.50936e13i	−0.0702330	−	0.104362i
$961$	2.21197e14	−	3.83124e14i	0.269874	−	0.467436i
$962$			1.64085e14i			0.199156i
$963$	1.14299e14	+	8.25896e14i	0.138010	+	0.997226i
$964$	−2.63726e14			−0.316787
$965$	−1.96805e13	−	1.13625e13i	−0.0235179	−	0.0135781i
$966$	−1.39899e14	−	6.84158e13i	−0.166314	−	0.0813338i
$967$	4.91651e13	+	8.51564e13i	0.0581466	+	0.100713i	0.893633	−	0.448798i	$-0.148148\pi$
$967$	4.91651e13	+	8.51564e13i	0.0581466	+	0.100713i	−0.835487	+	0.549510i	$0.814814\pi$
$968$	−1.21336e14	+	7.00534e13i	−0.142762	+	0.0824238i
$969$	7.40152e14	−	5.09732e13i	0.866368	−	0.0596655i
$970$	4.94963e14	−	8.57301e14i	0.576387	−	0.998331i
$971$			1.48879e15i			1.72479i	0.506232	+	0.862397i	$0.331038\pi$
$971$			1.48879e15i			1.72479i	−0.506232	+	0.862397i	$0.668962\pi$
$972$	−2.80595e14	+	3.30846e14i	−0.323406	+	0.381325i
$973$	3.09813e14			0.355251
$974$	1.51468e14	+	8.74501e13i	0.172793	+	0.0997621i
$975$	5.81573e11	+	8.44467e12i	0.000660056	+	0.00958429i
$976$	1.54326e14	+	2.67301e14i	0.174257	+	0.301823i
$977$	3.56664e14	−	2.05920e14i	0.400670	−	0.231327i	−0.286103	−	0.958199i	$-0.592360\pi$
$977$	3.56664e14	−	2.05920e14i	0.400670	−	0.231327i	0.686773	+	0.726872i	$0.259027\pi$
$978$	3.41804e14	−	6.98932e14i	0.382017	−	0.781161i
$979$	4.84520e14	−	8.39213e14i	0.538764	−	0.933166i
$980$			4.34681e14i			0.480884i
$981$	−1.03101e15	+	1.42685e14i	−1.13479	+	0.157048i
$982$	3.33519e13			0.0365227
$983$	−8.10894e13	−	4.68170e13i	−0.0883479	−	0.0510077i	0.455175	−	0.890402i	$-0.349577\pi$
$983$	−8.10894e13	−	4.68170e13i	−0.0883479	−	0.0510077i	−0.543523	+	0.839394i	$0.682910\pi$
$984$	−9.72422e13	+	6.54418e13i	−0.105409	+	0.0709381i
$985$	−7.86170e13	−	1.36169e14i	−0.0847882	−	0.146857i
$986$	1.53845e15	−	8.88222e14i	1.65081	−	0.953097i
$987$	−1.45804e14	−	2.16655e14i	−0.155662	−	0.231304i
$988$	8.33639e13	−	1.44390e14i	0.0885510	−	0.153375i
$989$			1.55341e15i			1.64175i
$990$	4.58004e14	+	1.86169e14i	0.481608	+	0.195763i
$991$	1.26533e14			0.132384			0.0661918	−	0.997807i	$-0.478915\pi$
$991$	1.26533e14			0.132384			0.0661918	+	0.997807i	$0.478915\pi$
$992$	−9.97727e13	−	5.76038e13i	−0.103861	−	0.0599643i
$993$	5.98005e13	+	2.92447e13i	0.0619382	+	0.0302901i
$994$	−5.61620e13	−	9.72755e13i	−0.0578777	−	0.100247i
$995$	−2.81587e14	+	1.62574e14i	−0.288734	+	0.166700i
$996$	−3.21690e14	+	2.21543e13i	−0.328202	+	0.0226028i
$997$	7.43844e14	−	1.28838e15i	0.755103	−	1.30788i	−0.190220	−	0.981742i	$-0.560920\pi$
$997$	7.43844e14	−	1.28838e15i	0.755103	−	1.30788i	0.945323	−	0.326136i	$-0.105747\pi$
$998$		−	1.00749e15i		−	1.01763i
$999$	7.60947e13	+	3.63643e14i	0.0764763	+	0.365467i

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.11.3	yes	20
3.2	odd	2		54.11.d.a.35.7		20
9.2	odd	6		162.11.b.c.161.3		20
9.4	even	3		54.11.d.a.17.7		20
9.5	odd	6	inner	18.11.d.a.5.3	✓	20
9.7	even	3		162.11.b.c.161.18		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.11.d.a.5.3	✓	20	9.5	odd	6	inner
18.11.d.a.11.3	yes	20	1.1	even	1	trivial
54.11.d.a.17.7		20	9.4	even	3
54.11.d.a.35.7		20	3.2	odd	2
162.11.b.c.161.3		20	9.2	odd	6
162.11.b.c.161.18		20	9.7	even	3

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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

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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.11.3

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