LMFDB - Embedded newform 19.10.c.a.11.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [19,10,Mod(7,19)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(19, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 10, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("19.7"); S:= CuspForms(chi, 10); N := Newforms(S);

Level:	$ N $	$=$	$ 19 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	19.c (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$9.78568088711$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			11.5
Character	$\chi$	$=$	19.11
Dual form			19.10.c.a.7.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-6.82378 + 11.8191i) q^{2} +(-35.4198 + 61.3488i) q^{3} +(162.872 + 282.103i) q^{4} +(-572.036 + 990.795i) q^{5} +(-483.393 - 837.262i) q^{6} +5106.36 q^{7} -11433.2 q^{8} +(7332.38 + 12700.1i) q^{9} +(-7806.89 - 13521.9i) q^{10} -43281.6 q^{11} -23075.6 q^{12} +(-85931.4 - 148838. i) q^{13} +(-34844.7 + 60352.7i) q^{14} +(-40522.8 - 70187.5i) q^{15} +(-5373.08 + 9306.45i) q^{16} +(-33106.4 + 57341.9i) q^{17} -200138. q^{18} +(-343633. - 452332. i) q^{19} -372675. q^{20} +(-180866. + 313269. i) q^{21} +(295344. - 511552. i) q^{22} +(971304. + 1.68235e6i) q^{23} +(404960. - 701411. i) q^{24} +(322113. + 557915. i) q^{25} +2.34551e6 q^{26} -2.43318e6 q^{27} +(831683. + 1.44052e6i) q^{28} +(630053. + 1.09128e6i) q^{29} +1.10607e6 q^{30} +8.70857e6 q^{31} +(-3.00022e6 - 5.19653e6i) q^{32} +(1.53303e6 - 2.65528e6i) q^{33} +(-451821. - 782577. i) q^{34} +(-2.92102e6 + 5.05935e6i) q^{35} +(-2.38848e6 + 4.13697e6i) q^{36} -1.42377e7 q^{37} +(7.69105e6 - 974836. i) q^{38} +1.21747e7 q^{39} +(6.54018e6 - 1.13279e7i) q^{40} +(-6.40554e6 + 1.10947e7i) q^{41} +(-2.46838e6 - 4.27536e6i) q^{42} +(-1.02374e7 + 1.77317e7i) q^{43} +(-7.04937e6 - 1.22099e7i) q^{44} -1.67775e7 q^{45} -2.65119e7 q^{46} +(-4.32647e6 - 7.49367e6i) q^{47} +(-380627. - 659265. i) q^{48} -1.42787e7 q^{49} -8.79210e6 q^{50} +(-2.34524e6 - 4.06208e6i) q^{51} +(2.79917e7 - 4.84830e7i) q^{52} +(2.84863e7 + 4.93398e7i) q^{53} +(1.66035e7 - 2.87581e7i) q^{54} +(2.47586e7 - 4.28832e7i) q^{55} -5.83818e7 q^{56} +(3.99214e7 - 5.06002e6i) q^{57} -1.71974e7 q^{58} +(5.66593e6 - 9.81368e6i) q^{59} +(1.32000e7 - 2.28632e7i) q^{60} +(6.44706e7 + 1.11666e8i) q^{61} +(-5.94254e7 + 1.02928e8i) q^{62} +(3.74417e7 + 6.48510e7i) q^{63} +7.63893e7 q^{64} +1.96623e8 q^{65} +(2.09221e7 + 3.62381e7i) q^{66} +(5.22515e7 + 9.05022e7i) q^{67} -2.15684e7 q^{68} -1.37613e8 q^{69} +(-3.98648e7 - 6.90478e7i) q^{70} +(-1.04127e8 + 1.80354e8i) q^{71} +(-8.38323e7 - 1.45202e8i) q^{72} +(2.13095e8 - 3.69091e8i) q^{73} +(9.71547e7 - 1.68277e8i) q^{74} -4.56366e7 q^{75} +(7.16357e7 - 1.70612e8i) q^{76} -2.21012e8 q^{77} +(-8.30774e7 + 1.43894e8i) q^{78} +(-1.70770e8 + 2.95782e8i) q^{79} +(-6.14719e6 - 1.06472e7i) q^{80} +(-5.81406e7 + 1.00702e8i) q^{81} +(-8.74200e7 - 1.51416e8i) q^{82} -4.42595e8 q^{83} -1.17832e8 q^{84} +(-3.78761e7 - 6.56033e7i) q^{85} +(-1.39715e8 - 2.41994e8i) q^{86} -8.92653e7 q^{87} +4.94846e8 q^{88} +(2.72449e8 + 4.71895e8i) q^{89} +(1.14486e8 - 1.98296e8i) q^{90} +(-4.38796e8 - 7.60018e8i) q^{91} +(-3.16397e8 + 5.48015e8i) q^{92} +(-3.08456e8 + 5.34261e8i) q^{93} +1.18092e8 q^{94} +(6.44738e8 - 8.17202e7i) q^{95} +4.25068e8 q^{96} +(1.75163e8 - 3.03391e8i) q^{97} +(9.74349e7 - 1.68762e8i) q^{98} +(-3.17357e8 - 5.49679e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 15 q^{2} - 74 q^{3} - 2987 q^{4} - 285 q^{5} - 535 q^{6} - 2676 q^{7} - 24270 q^{8} - 57928 q^{9} + 41180 q^{10} - 114810 q^{11} + 235458 q^{12} + 98671 q^{13} - 148290 q^{14} + 428251 q^{15} - 279203 q^{16}+ \cdots - 736622698 q^{99}+O(q^{100}) $ 28 * q + 15 * q^2 - 74 * q^3 - 2987 * q^4 - 285 * q^5 - 535 * q^6 - 2676 * q^7 - 24270 * q^8 - 57928 * q^9 + 41180 * q^10 - 114810 * q^11 + 235458 * q^12 + 98671 * q^13 - 148290 * q^14 + 428251 * q^15 - 279203 * q^16 + 466251 * q^17 + 734964 * q^18 + 387157 * q^19 - 3343620 * q^20 + 689090 * q^21 - 1689395 * q^22 - 3087747 * q^23 - 234183 * q^24 - 3260823 * q^25 + 9033144 * q^26 + 4216540 * q^27 - 703814 * q^28 + 7831383 * q^29 - 11859224 * q^30 - 9265632 * q^31 + 11470815 * q^32 + 22791973 * q^33 + 13457096 * q^34 - 13222428 * q^35 + 7355018 * q^36 + 27205020 * q^37 - 67677738 * q^38 - 20775702 * q^39 - 16500258 * q^40 + 20419440 * q^41 - 10220798 * q^42 + 27415427 * q^43 + 41775405 * q^44 - 85982588 * q^45 - 137234708 * q^46 - 90906681 * q^47 + 33057375 * q^48 + 229824892 * q^49 + 44406714 * q^50 + 134429123 * q^51 + 66195006 * q^52 + 47827863 * q^53 - 130507669 * q^54 - 157712310 * q^55 + 382459116 * q^56 - 162912873 * q^57 - 344026048 * q^58 + 255540 * q^59 + 287916794 * q^60 + 304035459 * q^61 + 693626280 * q^62 - 122148024 * q^63 - 908491514 * q^64 - 1424960190 * q^65 - 611099417 * q^66 + 165758480 * q^67 + 357518508 * q^68 + 271237278 * q^69 + 1167527028 * q^70 + 685508589 * q^71 + 142349670 * q^72 - 602867050 * q^73 - 82104492 * q^74 + 1900274774 * q^75 - 1298297525 * q^76 - 491994756 * q^77 - 911449840 * q^78 + 78162339 * q^79 + 227607150 * q^80 + 1230916118 * q^81 + 360208019 * q^82 + 413839926 * q^83 - 467304924 * q^84 - 1440537237 * q^85 + 936824310 * q^86 - 678876318 * q^87 - 1646777694 * q^88 + 1256827551 * q^89 + 1879090924 * q^90 + 537759588 * q^91 - 677003592 * q^92 - 492493440 * q^93 - 848375184 * q^94 - 2034458607 * q^95 - 6041588930 * q^96 + 2109813492 * q^97 + 2689941591 * q^98 - 736622698 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/19\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−6.82378	+	11.8191i	−0.301571	+	0.522337i	−0.976492	−	0.215553i	$-0.930844\pi$
$2$	−6.82378	+	11.8191i	−0.301571	+	0.522337i	0.674921	+	0.737890i	$0.264178\pi$
$3$	−35.4198	+	61.3488i	−0.252464	+	0.437281i	−0.964204	−	0.265163i	$-0.914574\pi$
$3$	−35.4198	+	61.3488i	−0.252464	+	0.437281i	0.711739	+	0.702444i	$0.247908\pi$
$4$	162.872	+	282.103i	0.318109	+	0.550982i
$5$	−572.036	+	990.795i	−0.409316	+	0.708955i	−0.994813	−	0.101719i	$-0.967566\pi$
$5$	−572.036	+	990.795i	−0.409316	+	0.708955i	0.585498	+	0.810674i	$0.300899\pi$
$6$	−483.393	−	837.262i	−0.152272	−	0.263743i
$7$	5106.36			0.803841			0.401920	−	0.915675i	$-0.368343\pi$
$7$	5106.36			0.803841			0.401920	+	0.915675i	$0.368343\pi$
$8$	−11433.2			−0.986873
$9$	7332.38	+	12700.1i	0.372523	+	0.645230i
$10$	−7806.89	−	13521.9i	−0.246876	−	0.427601i
$11$	−43281.6			−0.891326			−0.445663	−	0.895201i	$-0.647032\pi$
$11$	−43281.6			−0.891326			−0.445663	+	0.895201i	$0.647032\pi$
$12$	−23075.6			−0.321245
$13$	−85931.4	−	148838.i	−0.834463	−	1.44533i	−0.894467	−	0.447134i	$-0.852445\pi$
$13$	−85931.4	−	148838.i	−0.834463	−	1.44533i	0.0600045	−	0.998198i	$-0.480888\pi$
$14$	−34844.7	+	60352.7i	−0.242415	+	0.419876i
$15$	−40522.8	−	70187.5i	−0.206675	−	0.357972i
$16$	−5373.08	+	9306.45i	−0.0204967	+	0.0355013i
$17$	−33106.4	+	57341.9i	−0.0961372	+	0.166515i	−0.910083	−	0.414427i	$-0.863982\pi$
$17$	−33106.4	+	57341.9i	−0.0961372	+	0.166515i	0.813945	+	0.580941i	$0.197315\pi$
$18$	−200138.			−0.449370
$19$	−343633.	−	452332.i	−0.604928	−	0.796280i
$19$	−343633.	−	452332.i	−0.604928	−	0.796280i
$20$	−372675.			−0.520829
$21$	−180866.	+	313269.i	−0.202941	+	0.351504i
$22$	295344.	−	511552.i	0.268798	−	0.465573i
$23$	971304.	+	1.68235e6i	0.723736	+	1.25355i	0.959492	+	0.281735i	$0.0909098\pi$
$23$	971304.	+	1.68235e6i	0.723736	+	1.25355i	−0.235757	+	0.971812i	$0.575757\pi$
$24$	404960.	−	701411.i	0.249150	−	0.431541i
$25$	322113.	+	557915.i	0.164922	+	0.285653i
$26$	2.34551e6			1.00660
$27$	−2.43318e6			−0.881124
$28$	831683.	+	1.44052e6i	0.255709	+	0.442902i
$29$	630053.	+	1.09128e6i	0.165419	+	0.286514i	0.936804	−	0.349854i	$-0.113769\pi$
$29$	630053.	+	1.09128e6i	0.165419	+	0.286514i	−0.771385	+	0.636369i	$0.780436\pi$
$30$	1.10607e6			0.249309
$31$	8.70857e6			1.69363			0.846817	−	0.531885i	$-0.178516\pi$
$31$	8.70857e6			1.69363			0.846817	+	0.531885i	$0.178516\pi$
$32$	−3.00022e6	−	5.19653e6i	−0.505799	−	0.876070i
$33$	1.53303e6	−	2.65528e6i	0.225028	−	0.389760i
$34$	−451821.	−	782577.i	−0.0579844	−	0.100432i
$35$	−2.92102e6	+	5.05935e6i	−0.329024	+	0.569887i
$36$	−2.38848e6	+	4.13697e6i	−0.237006	+	0.410507i
$37$	−1.42377e7			−1.24891			−0.624455	−	0.781061i	$-0.714679\pi$
$37$	−1.42377e7			−1.24891			−0.624455	+	0.781061i	$0.714679\pi$
$38$	7.69105e6	−	974836.i	0.598355	−	0.0758412i
$39$	1.21747e7			0.842688
$40$	6.54018e6	−	1.13279e7i	0.403943	−	0.699649i
$41$	−6.40554e6	+	1.10947e7i	−0.354020	+	0.613181i	−0.986950	−	0.161028i	$-0.948519\pi$
$41$	−6.40554e6	+	1.10947e7i	−0.354020	+	0.613181i	0.632929	+	0.774209i	$0.281852\pi$
$42$	−2.46838e6	−	4.27536e6i	−0.122402	−	0.212007i
$43$	−1.02374e7	+	1.77317e7i	−0.456647	+	0.790936i	−0.998781	−	0.0493557i	$-0.984283\pi$
$43$	−1.02374e7	+	1.77317e7i	−0.456647	+	0.790936i	0.542134	+	0.840292i	$0.317617\pi$
$44$	−7.04937e6	−	1.22099e7i	−0.283539	−	0.491104i
$45$	−1.67775e7			−0.609919
$46$	−2.65119e7			−0.873032
$47$	−4.32647e6	−	7.49367e6i	−0.129328	−	0.224003i	0.794088	−	0.607803i	$-0.207949\pi$
$47$	−4.32647e6	−	7.49367e6i	−0.129328	−	0.224003i	−0.923417	+	0.383799i	$0.874615\pi$
$48$	−380627.	−	659265.i	−0.0103494	−	0.0179256i
$49$	−1.42787e7			−0.353840
$50$	−8.79210e6			−0.198943
$51$	−2.34524e6	−	4.06208e6i	−0.0485424	−	0.0840780i
$52$	2.79917e7	−	4.84830e7i	0.530901	−	0.919547i
$53$	2.84863e7	+	4.93398e7i	0.495901	+	0.858926i	0.999989	−	0.00472648i	$-0.00150449\pi$
$53$	2.84863e7	+	4.93398e7i	0.495901	+	0.858926i	−0.504088	+	0.863652i	$0.668171\pi$
$54$	1.66035e7	−	2.87581e7i	0.265722	−	0.460244i
$55$	2.47586e7	−	4.28832e7i	0.364834	−	0.631910i
$56$	−5.83818e7			−0.793289
$57$	3.99214e7	−	5.06002e6i	0.500921	−	0.0634915i
$58$	−1.71974e7			−0.199543
$59$	5.66593e6	−	9.81368e6i	0.0608747	−	0.105438i	−0.833982	−	0.551792i	$-0.813944\pi$
$59$	5.66593e6	−	9.81368e6i	0.0608747	−	0.105438i	0.894857	+	0.446354i	$0.147278\pi$
$60$	1.32000e7	−	2.28632e7i	0.131491	−	0.227748i
$61$	6.44706e7	+	1.11666e8i	0.596180	+	1.03261i	0.993379	+	0.114882i	$0.0366489\pi$
$61$	6.44706e7	+	1.11666e8i	0.596180	+	1.03261i	−0.397199	+	0.917732i	$0.630018\pi$
$62$	−5.94254e7	+	1.02928e8i	−0.510751	+	0.884647i
$63$	3.74417e7	+	6.48510e7i	0.299450	+	0.518662i
$64$	7.63893e7			0.569145
$65$	1.96623e8			1.36623
$66$	2.09221e7	+	3.62381e7i	0.135724	+	0.235081i
$67$	5.22515e7	+	9.05022e7i	0.316783	+	0.548684i	0.979815	−	0.199907i	$-0.0640640\pi$
$67$	5.22515e7	+	9.05022e7i	0.316783	+	0.548684i	−0.663032	+	0.748591i	$0.730731\pi$
$68$	−2.15684e7			−0.122329
$69$	−1.37613e8			−0.730870
$70$	−3.98648e7	−	6.90478e7i	−0.198449	−	0.343723i
$71$	−1.04127e8	+	1.80354e8i	−0.486298	+	0.842292i	−0.999876	−	0.0157506i	$-0.994986\pi$
$71$	−1.04127e8	+	1.80354e8i	−0.486298	+	0.842292i	0.513578	+	0.858043i	$0.328320\pi$
$72$	−8.38323e7	−	1.45202e8i	−0.367634	−	0.636760i
$73$	2.13095e8	−	3.69091e8i	0.878253	−	1.52118i	0.0249965	−	0.999688i	$-0.492043\pi$
$73$	2.13095e8	−	3.69091e8i	0.878253	−	1.52118i	0.853257	−	0.521491i	$-0.174624\pi$
$74$	9.71547e7	−	1.68277e8i	0.376636	−	0.652352i
$75$	−4.56366e7			−0.166547
$76$	7.16357e7	−	1.70612e8i	0.246302	−	0.586609i
$77$	−2.21012e8			−0.716484
$78$	−8.30774e7	+	1.43894e8i	−0.254131	+	0.440167i
$79$	−1.70770e8	+	2.95782e8i	−0.493275	+	0.854378i	−0.999970	−	0.00774780i	$-0.997534\pi$
$79$	−1.70770e8	+	2.95782e8i	−0.493275	+	0.854378i	0.506695	+	0.862126i	$0.330867\pi$
$80$	−6.14719e6	−	1.06472e7i	−0.0167792	−	0.0290625i
$81$	−5.81406e7	+	1.00702e8i	−0.150071	+	0.259931i
$82$	−8.74200e7	−	1.51416e8i	−0.213525	−	0.369836i
$83$	−4.42595e8			−1.02366			−0.511830	−	0.859087i	$-0.671032\pi$
$83$	−4.42595e8			−1.02366			−0.511830	+	0.859087i	$0.671032\pi$
$84$	−1.17832e8			−0.258230
$85$	−3.78761e7	−	6.56033e7i	−0.0787009	−	0.136314i
$86$	−1.39715e8	−	2.41994e8i	−0.275424	−	0.477048i
$87$	−8.92653e7			−0.167050
$88$	4.94846e8			0.879626
$89$	2.72449e8	+	4.71895e8i	0.460288	+	0.797242i	0.998975	−	0.0452640i	$-0.0144129\pi$
$89$	2.72449e8	+	4.71895e8i	0.460288	+	0.797242i	−0.538687	+	0.842506i	$0.681080\pi$
$90$	1.14486e8	−	1.98296e8i	0.183934	−	0.318583i
$91$	−4.38796e8	−	7.60018e8i	−0.670775	−	1.16182i
$92$	−3.16397e8	+	5.48015e8i	−0.460454	+	0.797530i
$93$	−3.08456e8	+	5.34261e8i	−0.427582	+	0.740594i
$94$	1.18092e8			0.156007
$95$	6.44738e8	−	8.17202e7i	0.812133	−	0.102937i
$96$	4.25068e8			0.510785
$97$	1.75163e8	−	3.03391e8i	0.200895	−	0.347961i	−0.747922	−	0.663787i	$-0.768948\pi$
$97$	1.75163e8	−	3.03391e8i	0.200895	−	0.347961i	0.948817	+	0.315826i	$0.102282\pi$
$98$	9.74349e7	−	1.68762e8i	0.106708	−	0.184824i
$99$	−3.17357e8	−	5.49679e8i	−0.332040	−	0.575110i
$100$	−1.04926e8	+	1.81738e8i	−0.104926	+	0.181738i
$101$	5.34624e8	+	9.25997e8i	0.511214	+	0.885448i	0.999916	+	0.0129974i	$0.00413731\pi$
$101$	5.34624e8	+	9.25997e8i	0.511214	+	0.885448i	−0.488702	+	0.872451i	$0.662529\pi$
$102$	6.40136e7			0.0585560
$103$	1.95401e8			0.171064			0.0855320	−	0.996335i	$-0.472741\pi$
$103$	1.95401e8			0.171064			0.0855320	+	0.996335i	$0.472741\pi$
$104$	9.82468e8	+	1.70168e9i	0.823509	+	1.42636i
$105$	−2.06924e8	−	3.58402e8i	−0.166134	−	0.287752i
$106$	−7.77538e8			−0.598198
$107$	8.54437e8			0.630163			0.315082	−	0.949065i	$-0.397968\pi$
$107$	8.54437e8			0.630163			0.315082	+	0.949065i	$0.397968\pi$
$108$	−3.96297e8	−	6.86406e8i	−0.280294	−	0.485483i
$109$	4.39585e8	−	7.61383e8i	0.298279	−	0.516635i	−0.677463	−	0.735557i	$-0.736921\pi$
$109$	4.39585e8	−	7.61383e8i	0.298279	−	0.516635i	0.975742	+	0.218922i	$0.0702540\pi$
$110$	3.37895e8	+	5.85252e8i	0.220047	+	0.381132i
$111$	5.04295e8	−	8.73465e8i	0.315305	−	0.546125i
$112$	−2.74369e7	+	4.75221e7i	−0.0164761	+	0.0285374i
$113$	1.80190e9			1.03963			0.519815	−	0.854279i	$-0.326001\pi$
$113$	1.80190e9			1.03963			0.519815	+	0.854279i	$0.326001\pi$
$114$	−2.12610e8	+	5.06365e8i	−0.117899	+	0.280797i
$115$	−2.22248e9			−1.18494
$116$	−2.05236e8	+	3.55479e8i	−0.105243	+	0.182286i
$117$	1.26016e9	−	2.18267e9i	0.621714	−	1.07684i
$118$	7.73261e7	+	1.33933e8i	0.0367162	+	0.0635942i
$119$	−1.69053e8	+	2.92808e8i	−0.0772790	+	0.133851i
$120$	4.63303e8	+	8.02465e8i	0.203962	+	0.353273i
$121$	−4.84647e8			−0.205538
$122$	−1.75973e9			−0.719163
$123$	−4.53765e8	−	7.85945e8i	−0.178755	−	0.309613i
$124$	1.41838e9	+	2.45671e9i	0.538761	+	0.933161i
$125$	−2.97155e9			−1.08865
$126$	−1.02198e9			−0.361222
$127$	−1.93485e8	−	3.35126e8i	−0.0659981	−	0.114312i	0.831138	−	0.556066i	$-0.187690\pi$
$127$	−1.93485e8	−	3.35126e8i	−0.0659981	−	0.114312i	−0.897136	+	0.441754i	$0.854356\pi$
$128$	1.01485e9	−	1.75777e9i	0.334161	−	0.578785i
$129$	−7.25212e8	−	1.25610e9i	−0.230574	−	0.399367i
$130$	−1.34171e9	+	2.32392e9i	−0.412017	+	0.713634i
$131$	−1.75053e9	+	3.03200e9i	−0.519336	+	0.899516i	0.480412	+	0.877043i	$0.340487\pi$
$131$	−1.75053e9	+	3.03200e9i	−0.519336	+	0.899516i	−0.999747	+	0.0224727i	$0.992846\pi$
$132$	9.98748e8			0.286334
$133$	−1.75471e9	−	2.30977e9i	−0.486266	−	0.640082i
$134$	−1.42621e9			−0.382131
$135$	1.39187e9	−	2.41078e9i	0.360658	−	0.624678i
$136$	3.78511e8	−	6.55600e8i	0.0948752	−	0.164329i
$137$	−2.56092e8	−	4.43565e8i	−0.0621089	−	0.107576i	0.833299	−	0.552823i	$-0.186449\pi$
$137$	−2.56092e8	−	4.43565e8i	−0.0621089	−	0.107576i	−0.895408	+	0.445247i	$0.853116\pi$
$138$	9.39044e8	−	1.62647e9i	0.220409	−	0.381760i
$139$	−1.88234e8	−	3.26030e8i	−0.0427692	−	0.0740784i	0.843848	−	0.536582i	$-0.180285\pi$
$139$	−1.88234e8	−	3.26030e8i	−0.0427692	−	0.0740784i	−0.886618	+	0.462503i	$0.846951\pi$
$140$	−1.90301e9			−0.418663
$141$	6.12971e8			0.130603
$142$	−1.42108e9	−	2.46139e9i	−0.293307	−	0.508022i
$143$	3.71925e9	+	6.44194e9i	0.743778	+	1.28826i
$144$	−1.57590e8			−0.0305420
$145$	−1.44165e9			−0.270835
$146$	2.90822e9	+	5.03719e9i	0.529712	+	0.917488i
$147$	5.05749e8	−	8.75983e8i	0.0893320	−	0.154728i
$148$	−2.31892e9	−	4.01648e9i	−0.397290	−	0.688127i
$149$	4.41322e9	−	7.64392e9i	0.733529	−	1.27051i	−0.221836	−	0.975084i	$-0.571205\pi$
$149$	4.41322e9	−	7.64392e9i	0.733529	−	1.27051i	0.955366	−	0.295426i	$-0.0954616\pi$
$150$	3.11414e8	−	5.39385e8i	0.0502259	−	0.0869938i
$151$	−3.19127e8			−0.0499537			−0.0249768	−	0.999688i	$-0.507951\pi$
$151$	−3.19127e8			−0.0499537			−0.0249768	+	0.999688i	$0.507951\pi$
$152$	3.92882e9	+	5.17158e9i	0.596988	+	0.785827i
$153$	−9.70994e8			−0.143253
$154$	1.50813e9	−	2.61216e9i	0.216071	−	0.374246i
$155$	−4.98162e9	+	8.62841e9i	−0.693230	+	1.20071i
$156$	1.98292e9	+	3.43451e9i	0.268067	+	0.464306i
$157$	3.12435e9	−	5.41154e9i	0.410404	−	0.710841i	−0.584530	−	0.811372i	$-0.698721\pi$
$157$	3.12435e9	−	5.41154e9i	0.410404	−	0.710841i	0.994934	+	0.100531i	$0.0320543\pi$
$158$	−2.33059e9	−	4.03670e9i	−0.297515	−	0.515312i
$159$	−4.03592e9			−0.500789
$160$	6.86493e9			0.828126
$161$	4.95982e9	+	8.59067e9i	0.581768	+	1.00765i
$162$	−7.93477e8	−	1.37434e9i	−0.0905142	−	0.156775i
$163$	1.13939e10			1.26423			0.632115	−	0.774874i	$-0.282187\pi$
$163$	1.13939e10			1.26423			0.632115	+	0.774874i	$0.282187\pi$
$164$	−4.17313e9			−0.450469
$165$	1.75389e9	+	3.03783e9i	0.184215	+	0.319070i
$166$	3.02017e9	−	5.23110e9i	0.308706	−	0.534695i
$167$	3.82644e9	+	6.62758e9i	0.380689	+	0.659373i	0.991161	−	0.132665i	$-0.0423535\pi$
$167$	3.82644e9	+	6.62758e9i	0.380689	+	0.659373i	−0.610472	+	0.792038i	$0.709020\pi$
$168$	2.06787e9	−	3.58166e9i	0.200277	−	0.346890i
$169$	−9.46617e9	+	1.63959e10i	−0.892656	+	1.54613i
$170$	1.03383e9			0.0949357
$171$	3.22499e9	−	7.68083e9i	0.288433	−	0.686951i
$172$	−6.66953e9			−0.581055
$173$	3.43263e8	−	5.94548e8i	0.0291353	−	0.0504638i	−0.851090	−	0.525020i	$-0.824058\pi$
$173$	3.43263e8	−	5.94548e8i	0.0291353	−	0.0504638i	0.880225	+	0.474556i	$0.157391\pi$
$174$	6.09127e8	−	1.05504e9i	0.0503774	−	0.0872563i
$175$	1.64482e9	+	2.84891e9i	0.132571	+	0.229619i
$176$	2.32556e8	−	4.02798e8i	0.0182692	−	0.0316432i
$177$	4.01372e8	+	6.95196e8i	0.0307374	+	0.0532387i
$178$	−7.43652e9			−0.555238
$179$	−1.89262e10			−1.37793			−0.688963	−	0.724796i	$-0.741934\pi$
$179$	−1.89262e10			−1.37793			−0.688963	+	0.724796i	$0.741934\pi$
$180$	−2.73259e9	−	4.73299e9i	−0.194021	−	0.336054i
$181$	−1.00284e9	−	1.73697e9i	−0.0694511	−	0.120293i	0.829209	−	0.558939i	$-0.188791\pi$
$181$	−1.00284e9	−	1.73697e9i	−0.0694511	−	0.120293i	−0.898660	+	0.438646i	$0.855458\pi$
$182$	1.19770e10			0.809146
$183$	−9.13414e9			−0.602057
$184$	−1.11051e10	−	1.92346e10i	−0.714235	−	1.23709i
$185$	8.14446e9	−	1.41066e10i	0.511198	−	0.885421i
$186$	−4.20967e9	−	7.29136e9i	−0.257893	−	0.446684i
$187$	1.43290e9	−	2.48185e9i	0.0856896	−	0.148419i
$188$	1.40932e9	−	2.44102e9i	0.0822811	−	0.142515i
$189$	−1.24247e10			−0.708284
$190$	−3.43369e9	+	8.17789e9i	−0.191148	+	0.455250i
$191$	−2.79879e10			−1.52167			−0.760834	−	0.648947i	$-0.775210\pi$
$191$	−2.79879e10			−1.52167			−0.760834	+	0.648947i	$0.775210\pi$
$192$	−2.70569e9	+	4.68640e9i	−0.143689	+	0.248876i
$193$	7.98131e9	−	1.38240e10i	0.414063	−	0.717178i	−0.581267	−	0.813713i	$-0.697443\pi$
$193$	7.98131e9	−	1.38240e10i	0.414063	−	0.717178i	0.995330	+	0.0965351i	$0.0307760\pi$
$194$	2.39055e9	+	4.14055e9i	0.121169	+	0.209870i
$195$	−6.96436e9	+	1.20626e10i	−0.344925	+	0.597428i
$196$	−2.32561e9	−	4.02807e9i	−0.112560	−	0.194959i
$197$	4.10111e10			1.94001			0.970004	−	0.243090i	$-0.0781609\pi$
$197$	4.10111e10			1.94001			0.970004	+	0.243090i	$0.0781609\pi$
$198$	8.66231e9			0.400535
$199$	1.70068e10	+	2.94567e10i	0.768749	+	1.33151i	0.938242	+	0.345981i	$0.112454\pi$
$199$	1.70068e10	+	2.94567e10i	0.768749	+	1.33151i	−0.169492	+	0.985531i	$0.554213\pi$
$200$	−3.68277e9	−	6.37874e9i	−0.162757	−	0.281903i
$201$	−7.40294e9			−0.319906
$202$	−1.45926e10			−0.616670
$203$	3.21727e9	+	5.57248e9i	0.132971	+	0.230312i
$204$	7.63948e8	−	1.32320e9i	0.0308836	−	0.0534920i
$205$	−7.32839e9	−	1.26932e10i	−0.289812	−	0.501969i
$206$	−1.33337e9	+	2.30947e9i	−0.0515880	+	0.0893530i
$207$	−1.42439e10	+	2.46712e10i	−0.539217	+	0.933951i
$208$	1.84687e9			0.0684148
$209$	1.48730e10	+	1.95777e10i	0.539188	+	0.709745i
$210$	5.64801e9			0.200405
$211$	1.39287e10	−	2.41251e10i	0.483769	−	0.837913i	−0.516057	−	0.856554i	$-0.672601\pi$
$211$	1.39287e10	−	2.41251e10i	0.483769	−	0.837913i	0.999826	+	0.0186415i	$0.00593411\pi$
$212$	−9.27925e9	+	1.60721e10i	−0.315502	+	0.546465i
$213$	−7.37633e9	−	1.27762e10i	−0.245546	−	0.425297i
$214$	−5.83049e9	+	1.00987e10i	−0.190039	+	0.329158i
$215$	−1.17123e10	−	2.02863e10i	−0.373826	−	0.647485i
$216$	2.78189e10			0.869558
$217$	4.44691e10			1.36141
$218$	5.99926e9	+	1.03910e10i	0.179905	+	0.311605i
$219$	1.50955e10	+	2.61462e10i	0.443455	+	0.768087i
$220$	1.61300e10			0.464228
$221$	1.13795e10			0.320892
$222$	6.88240e9	+	1.19207e10i	0.190174	+	0.329391i
$223$	1.35472e10	−	2.34644e10i	0.366840	−	0.635386i	−0.622229	−	0.782835i	$-0.713773\pi$
$223$	1.35472e10	−	2.34644e10i	0.366840	−	0.635386i	0.989070	+	0.147449i	$0.0471062\pi$
$224$	−1.53202e10	−	2.65353e10i	−0.406582	−	0.704221i
$225$	−4.72370e9	+	8.18169e9i	−0.122874	+	0.212825i
$226$	−1.22958e10	+	2.12969e10i	−0.313523	+	0.543037i
$227$	−6.78995e10			−1.69727			−0.848634	−	0.528981i	$-0.822574\pi$
$227$	−6.78995e10			−1.69727			−0.848634	+	0.528981i	$0.822574\pi$
$228$	7.92953e9	+	1.04378e10i	0.194330	+	0.255801i
$229$	1.31038e10			0.314875			0.157437	−	0.987529i	$-0.449677\pi$
$229$	1.31038e10			0.314875			0.157437	+	0.987529i	$0.449677\pi$
$230$	1.51657e10	−	2.62678e10i	0.357345	−	0.618940i
$231$	7.82818e9	−	1.35588e10i	0.180887	−	0.313305i
$232$	−7.20350e9	−	1.24768e10i	−0.163248	−	0.282753i
$233$	2.93355e10	−	5.08106e10i	0.652067	−	1.12941i	−0.330554	−	0.943787i	$-0.607236\pi$
$233$	2.93355e10	−	5.08106e10i	0.652067	−	1.12941i	0.982621	−	0.185625i	$-0.0594311\pi$
$234$	1.71982e10	+	2.97881e10i	0.374982	+	0.649488i
$235$	9.89959e9			0.211744
$236$	3.69129e9			0.0774593
$237$	−1.20973e10	−	2.09531e10i	−0.249069	−	0.431400i
$238$	−2.30716e9	−	3.99612e9i	−0.0466103	−	0.0807313i
$239$	−7.29833e10			−1.44688			−0.723441	−	0.690387i	$-0.757440\pi$
$239$	−7.29833e10			−1.44688			−0.723441	+	0.690387i	$0.757440\pi$
$240$	8.70928e8			0.0169446
$241$	3.55136e10	+	6.15114e10i	0.678139	+	1.17457i	0.975541	+	0.219818i	$0.0705465\pi$
$241$	3.55136e10	+	6.15114e10i	0.678139	+	1.17457i	−0.297402	+	0.954752i	$0.596120\pi$
$242$	3.30713e9	−	5.72811e9i	0.0619843	−	0.107360i
$243$	−2.80648e10	−	4.86096e10i	−0.516337	−	0.894322i
$244$	−2.10009e10	+	3.63747e10i	−0.379301	+	0.656969i
$245$	8.16794e9	−	1.41473e10i	0.144832	−	0.250857i
$246$	1.23856e10			0.215630
$247$	−3.77951e10	+	9.00150e10i	−0.646098	+	1.53879i
$248$	−9.95665e10			−1.67140
$249$	1.56766e10	−	2.71527e10i	0.258438	−	0.447627i
$250$	2.02772e10	−	3.51212e10i	0.328306	−	0.568643i
$251$	3.70915e10	+	6.42444e10i	0.589852	+	1.02165i	0.994251	+	0.107071i	$0.0341471\pi$
$251$	3.70915e10	+	6.42444e10i	0.589852	+	1.02165i	−0.404400	+	0.914582i	$0.632520\pi$
$252$	−1.21964e10	+	2.11248e10i	−0.190515	+	0.329982i
$253$	−4.20396e10	−	7.28148e10i	−0.645084	−	1.11732i
$254$	5.28121e9			0.0796125
$255$	5.36625e9			0.0794767
$256$	3.34059e10	+	5.78607e10i	0.486119	+	0.841983i
$257$	−4.83532e10	−	8.37503e10i	−0.691396	−	1.19753i	−0.971381	−	0.237528i	$-0.923663\pi$
$257$	−4.83532e10	−	8.37503e10i	−0.691396	−	1.19753i	0.279985	−	0.960004i	$-0.409670\pi$
$258$	1.97947e10			0.278139
$259$	−7.27026e10			−1.00392
$260$	3.20245e10	+	5.54680e10i	0.434612	+	0.752770i
$261$	−9.23957e9	+	1.60034e10i	−0.123245	+	0.213467i
$262$	−2.38904e10	−	4.13794e10i	−0.313233	−	0.542536i
$263$	5.06675e10	−	8.77588e10i	0.653024	−	1.13107i	−0.329362	−	0.944204i	$-0.606834\pi$
$263$	5.06675e10	−	8.77588e10i	0.653024	−	1.13107i	0.982385	−	0.186866i	$-0.0598331\pi$
$264$	−1.75273e10	+	3.03582e10i	−0.222074	+	0.384644i
$265$	−6.51808e10			−0.811920
$266$	3.92732e10	−	4.97786e9i	0.480982	−	0.0609643i
$267$	−3.86003e10			−0.464825
$268$	−1.70206e10	+	2.94805e10i	−0.201543	+	0.349083i
$269$	6.74584e10	−	1.16841e11i	0.785509	−	1.36054i	−0.143186	−	0.989696i	$-0.545735\pi$
$269$	6.74584e10	−	1.16841e11i	0.785509	−	1.36054i	0.928695	−	0.370845i	$-0.120932\pi$
$270$	1.89956e10	+	3.29013e10i	0.217528	+	0.376770i
$271$	−1.66855e10	+	2.89001e10i	−0.187922	+	0.325490i	−0.944557	−	0.328347i	$-0.893508\pi$
$271$	−1.66855e10	+	2.89001e10i	−0.187922	+	0.325490i	0.756636	+	0.653837i	$0.226842\pi$
$272$	−3.55766e8	−	6.16206e8i	−0.00394099	−	0.00682599i
$273$	6.21683e10			0.677387
$274$	6.99007e9			0.0749211
$275$	−1.39416e10	−	2.41475e10i	−0.146999	−	0.254610i
$276$	−2.24134e10	−	3.88211e10i	−0.232497	−	0.402696i
$277$	1.08796e11			1.11034			0.555168	−	0.831738i	$-0.312654\pi$
$277$	1.08796e11			1.11034			0.555168	+	0.831738i	$0.312654\pi$
$278$	5.13786e9			0.0515918
$279$	6.38546e10	+	1.10599e11i	0.630918	+	1.09278i
$280$	3.33965e10	−	5.78444e10i	0.324705	−	0.562406i
$281$	−1.58945e10	−	2.75301e10i	−0.152079	−	0.263408i	0.779913	−	0.625888i	$-0.215263\pi$
$281$	−1.58945e10	−	2.75301e10i	−0.152079	−	0.263408i	−0.931992	+	0.362480i	$0.881930\pi$
$282$	−4.18278e9	+	7.24478e9i	−0.0393862	+	0.0682189i
$283$	−5.42987e10	+	9.40481e10i	−0.503211	+	0.871587i	0.496782	+	0.867875i	$0.334515\pi$
$283$	−5.42987e10	+	9.40481e10i	−0.503211	+	0.871587i	−0.999993	+	0.00371190i	$0.998818\pi$
$284$	−6.78377e10			−0.618783
$285$	−1.78230e10	+	4.24485e10i	−0.160022	+	0.381119i
$286$	−1.01517e11			−0.897209
$287$	−3.27090e10	+	5.66536e10i	−0.284576	+	0.492900i
$288$	4.39975e10	−	7.62059e10i	0.376844	−	0.652713i
$289$	5.71019e10	+	9.89033e10i	0.481515	+	0.834009i
$290$	9.83751e9	−	1.70391e10i	0.0816759	−	0.141467i
$291$	1.24085e10	+	2.14921e10i	0.101438	+	0.175695i
$292$	1.38829e11			1.11752
$293$	1.14354e9			0.00906459			0.00453229	−	0.999990i	$-0.498557\pi$
$293$	1.14354e9			0.00906459			0.00453229	+	0.999990i	$0.498557\pi$
$294$	6.90224e9	+	1.19550e10i	0.0538800	+	0.0933228i
$295$	6.48223e9	+	1.12276e10i	0.0498340	+	0.0863149i
$296$	1.62782e11			1.23252
$297$	1.05312e11			0.785369
$298$	6.02297e10	+	1.04321e11i	0.442423	+	0.766299i
$299$	1.66931e11	−	2.89133e11i	1.20786	−	2.09208i
$300$	−7.43293e9	−	1.28742e10i	−0.0529803	−	0.0917645i
$301$	−5.22757e10	+	9.05442e10i	−0.367072	+	0.635787i
$302$	2.17765e9	−	3.77181e9i	0.0150646	−	0.0260926i
$303$	−7.57451e10			−0.516253
$304$	6.05597e9	−	7.67591e8i	0.0406680	−	0.00515464i
$305$	−1.47518e11			−0.976103
$306$	6.62585e9	−	1.14763e10i	0.0432011	−	0.0748266i
$307$	−5.91264e10	+	1.02410e11i	−0.379891	+	0.657990i	−0.991046	−	0.133520i	$-0.957372\pi$
$307$	−5.91264e10	+	1.02410e11i	−0.379891	+	0.657990i	0.611155	+	0.791511i	$0.290705\pi$
$308$	−3.59966e10	−	6.23479e10i	−0.227920	−	0.394770i
$309$	−6.92105e9	+	1.19876e10i	−0.0431875	+	0.0748030i
$310$	−6.79869e10	−	1.17757e11i	−0.418117	−	0.724200i
$311$	4.73648e10			0.287101			0.143550	−	0.989643i	$-0.454148\pi$
$311$	4.73648e10			0.287101			0.143550	+	0.989643i	$0.454148\pi$
$312$	−1.39195e11			−0.831627
$313$	−3.49844e10	−	6.05947e10i	−0.206027	−	0.356850i	0.744432	−	0.667698i	$-0.232720\pi$
$313$	−3.49844e10	−	6.05947e10i	−0.206027	−	0.356850i	−0.950460	+	0.310848i	$0.899387\pi$
$314$	4.26398e10	+	7.38543e10i	0.247532	+	0.428738i
$315$	−8.56721e10			−0.490277
$316$	−1.11255e11			−0.627662
$317$	1.33199e11	+	2.30707e11i	0.740857	+	1.28320i	0.952106	+	0.305769i	$0.0989136\pi$
$317$	1.33199e11	+	2.30707e11i	0.740857	+	1.28320i	−0.211249	+	0.977432i	$0.567753\pi$
$318$	2.75402e10	−	4.77011e10i	0.151024	−	0.261581i
$319$	−2.72697e10	−	4.72325e10i	−0.147442	−	0.255378i
$320$	−4.36974e10	+	7.56862e10i	−0.232960	+	0.403498i
$321$	−3.02640e10	+	5.24187e10i	−0.159094	+	0.275558i
$322$	−1.35379e11			−0.701778
$323$	3.73140e10	−	4.72953e9i	0.190748	−	0.0241772i
$324$	−3.78779e10			−0.190956
$325$	5.53592e10	−	9.58849e10i	0.275242	−	0.476733i
$326$	−7.77491e10	+	1.34665e11i	−0.381256	+	0.660354i
$327$	3.11400e10	+	5.39360e10i	0.150610	+	0.260864i
$328$	7.32356e10	−	1.26848e11i	0.349373	−	0.605132i
$329$	−2.20925e10	−	3.82654e10i	−0.103959	−	0.180063i
$330$	−4.78727e10			−0.222216
$331$	2.73481e11			1.25228			0.626140	−	0.779710i	$-0.284634\pi$
$331$	2.73481e11			1.25228			0.626140	+	0.779710i	$0.284634\pi$
$332$	−7.20864e10	−	1.24857e11i	−0.325636	−	0.564018i
$333$	−1.04396e11	−	1.80819e11i	−0.465248	−	0.805834i
$334$	−1.04443e11			−0.459219
$335$	−1.19559e11			−0.518657
$336$	−1.94362e9	−	3.36644e9i	−0.00831924	−	0.0144093i
$337$	1.13432e11	−	1.96470e11i	0.479073	−	0.829778i	−0.520639	−	0.853777i	$-0.674306\pi$
$337$	1.13432e11	−	1.96470e11i	0.479073	−	0.829778i	0.999712	+	0.0239987i	$0.00763975\pi$
$338$	−1.29190e11	−	2.23764e11i	−0.538399	−	0.932534i
$339$	−6.38230e10	+	1.10545e11i	−0.262469	+	0.454610i
$340$	1.23379e10	−	2.13699e10i	0.0500710	−	0.0867255i
$341$	−3.76921e11			−1.50958
$342$	6.87741e10	+	9.05288e10i	0.271836	+	0.357824i
$343$	−2.78972e11			−1.08827
$344$	1.17046e11	−	2.02729e11i	0.450653	−	0.780554i
$345$	7.87198e10	−	1.36347e11i	0.299156	−	0.518154i
$346$	4.68470e9	+	8.11414e9i	0.0175727	+	0.0304369i
$347$	−9.98437e10	+	1.72934e11i	−0.369690	+	0.640322i	−0.989517	−	0.144416i	$-0.953870\pi$
$347$	−9.98437e10	+	1.72934e11i	−0.369690	+	0.640322i	0.619827	+	0.784739i	$0.287203\pi$
$348$	−1.45388e10	−	2.51820e10i	−0.0531401	−	0.0920414i
$349$	3.95278e11			1.42622			0.713112	−	0.701050i	$-0.247285\pi$
$349$	3.95278e11			1.42622			0.713112	+	0.701050i	$0.247285\pi$
$350$	−4.48956e10			−0.159918
$351$	2.09087e11	+	3.62149e11i	0.735265	+	1.27352i
$352$	1.29854e11	+	2.24914e11i	0.450832	+	0.780864i
$353$	3.08549e11			1.05764			0.528820	−	0.848734i	$-0.322635\pi$
$353$	3.08549e11			1.05764			0.528820	+	0.848734i	$0.322635\pi$
$354$	−1.09555e10			−0.0370781
$355$	−1.19129e11	−	2.06338e11i	−0.398098	−	0.689526i
$356$	−8.87485e10	+	1.53717e11i	−0.292844	+	0.507220i
$357$	−1.19756e10	−	2.07424e10i	−0.0390204	−	0.0675853i
$358$	1.29149e11	−	2.23692e11i	0.415543	−	0.719742i
$359$	−1.36553e11	+	2.36517e11i	−0.433887	+	0.751515i	−0.997204	−	0.0747263i	$-0.976192\pi$
$359$	−1.36553e11	+	2.36517e11i	−0.433887	+	0.751515i	0.563317	+	0.826241i	$0.309525\pi$
$360$	1.91820e11			0.601912
$361$	−8.65201e10	+	3.10872e11i	−0.268123	+	0.963385i
$362$	2.73727e10			0.0837778
$363$	1.71661e10	−	2.97325e10i	0.0518909	−	0.0898777i
$364$	1.42935e11	−	2.47571e11i	0.426760	−	0.739170i
$365$	2.43796e11	+	4.22266e11i	0.718965	+	1.24528i
$366$	6.23293e10	−	1.07958e11i	0.181563	−	0.314477i
$367$	1.88107e10	+	3.25810e10i	0.0541261	+	0.0937492i	0.891819	−	0.452392i	$-0.149429\pi$
$367$	1.88107e10	+	3.25810e10i	0.0541261	+	0.0937492i	−0.837693	+	0.546142i	$0.816096\pi$
$368$	−2.08756e10			−0.0593367
$369$	−1.87871e11			−0.527524
$370$	1.11152e11	+	1.92521e11i	0.308326	+	0.534035i
$371$	1.45461e11	+	2.51946e11i	0.398626	+	0.690440i
$372$	−2.00955e11			−0.544072
$373$	−4.38382e11			−1.17263			−0.586317	−	0.810081i	$-0.699423\pi$
$373$	−4.38382e11			−1.17263			−0.586317	+	0.810081i	$0.699423\pi$
$374$	1.95556e10	+	3.38712e10i	0.0516831	+	0.0895177i
$375$	1.05252e11	−	1.82301e11i	0.274846	−	0.476046i
$376$	4.94653e10	+	8.56764e10i	0.127631	+	0.221063i
$377$	1.08283e11	−	1.87551e11i	0.276072	−	0.478171i
$378$	8.47833e10	−	1.46849e11i	0.213598	−	0.369963i
$379$	5.40365e11			1.34527			0.672637	−	0.739973i	$-0.265162\pi$
$379$	5.40365e11			1.34527			0.672637	+	0.739973i	$0.265162\pi$
$380$	1.28063e11	+	1.68572e11i	0.315064	+	0.414725i
$381$	2.74128e10			0.0666487
$382$	1.90983e11	−	3.30792e11i	0.458891	−	0.794823i
$383$	7.14550e10	−	1.23764e11i	0.169683	−	0.293899i	−0.768625	−	0.639699i	$-0.779059\pi$
$383$	7.14550e10	−	1.23764e11i	0.169683	−	0.293899i	0.938308	+	0.345800i	$0.112392\pi$
$384$	7.18914e10	+	1.24520e11i	0.168728	+	0.292245i
$385$	1.26426e11	−	2.18977e11i	0.293268	−	0.507955i
$386$	1.08925e11	+	1.88664e11i	0.249739	+	0.432561i
$387$	−3.00258e11			−0.680448
$388$	1.14117e11			0.255627
$389$	−1.94173e10	−	3.36318e10i	−0.0429949	−	0.0744693i	0.843727	−	0.536772i	$-0.180357\pi$
$389$	−1.94173e10	−	3.36318e10i	−0.0429949	−	0.0744693i	−0.886722	+	0.462303i	$0.847023\pi$
$390$	−9.50465e10	−	1.64625e11i	−0.208039	−	0.360335i
$391$	−1.28625e11			−0.278312
$392$	1.63251e11			0.349196
$393$	−1.24007e11	−	2.14786e11i	−0.262227	−	0.454191i
$394$	−2.79851e11	+	4.84716e11i	−0.585051	+	1.01334i
$395$	−1.95373e11	−	3.38396e11i	−0.403810	−	0.699420i
$396$	1.03377e11	−	1.79055e11i	0.211250	−	0.365896i
$397$	−2.91608e11	+	5.05080e11i	−0.589172	+	1.02048i	0.405169	+	0.914242i	$0.367213\pi$
$397$	−2.91608e11	+	5.05080e11i	−0.589172	+	1.02048i	−0.994341	+	0.106235i	$0.966121\pi$
$398$	−4.64204e11			−0.927331
$399$	2.03853e11	−	2.58383e10i	0.402661	−	0.0510370i
$400$	−6.92295e9			−0.0135214
$401$	−3.16256e11	+	5.47772e11i	−0.610786	+	1.05791i	0.380322	+	0.924854i	$0.375813\pi$
$401$	−3.16256e11	+	5.47772e11i	−0.610786	+	1.05791i	−0.991108	+	0.133059i	$0.957520\pi$
$402$	5.05160e10	−	8.74963e10i	0.0964744	−	0.167098i
$403$	−7.48340e11	−	1.29616e12i	−1.41327	−	2.44786i
$404$	−1.74151e11	+	3.01638e11i	−0.325244	+	0.563339i
$405$	−6.65170e10	−	1.15211e11i	−0.122853	−	0.212787i
$406$	−8.78159e10			−0.160401
$407$	6.16230e11			1.11319
$408$	2.68135e10	+	4.64424e10i	0.0479052	+	0.0829743i
$409$	−2.70410e11	−	4.68364e11i	−0.477824	−	0.827616i	0.521853	−	0.853036i	$-0.325241\pi$
$409$	−2.70410e11	−	4.68364e11i	−0.477824	−	0.827616i	−0.999677	+	0.0254197i	$0.991908\pi$
$410$	2.00029e11			0.349596
$411$	3.62829e10			0.0627212
$412$	3.18253e10	+	5.51230e10i	0.0544171	+	0.0942531i
$413$	2.89323e10	−	5.01121e10i	0.0489336	−	0.0847555i
$414$	−1.94395e11	−	3.36702e11i	−0.325225	−	0.563306i
$415$	2.53180e11	−	4.38521e11i	0.419000	−	0.725729i
$416$	−5.15626e11	+	8.93091e11i	−0.844141	+	1.46210i
$417$	2.66688e10			0.0431908
$418$	−3.32881e11	+	4.21925e10i	−0.533330	+	0.0675993i
$419$	3.14473e11			0.498449			0.249225	−	0.968446i	$-0.419824\pi$
$419$	3.14473e11			0.498449			0.249225	+	0.968446i	$0.419824\pi$
$420$	6.74041e10	−	1.16747e11i	0.105698	−	0.183073i
$421$	−4.51454e11	+	7.81941e11i	−0.700396	+	1.21312i	0.267931	+	0.963438i	$0.413660\pi$
$421$	−4.51454e11	+	7.81941e11i	−0.700396	+	1.21312i	−0.968327	+	0.249684i	$0.919673\pi$
$422$	1.90092e11	+	3.29249e11i	0.291782	+	0.505381i
$423$	6.34467e10	−	1.09893e11i	0.0963557	−	0.166893i
$424$	−3.25689e11	−	5.64110e11i	−0.489392	−	0.847651i
$425$	−4.26559e10			−0.0634204
$426$	2.01338e11			0.296198
$427$	3.29210e11	+	5.70208e11i	0.479234	+	0.830057i
$428$	1.39164e11	+	2.41039e11i	0.200461	+	0.347208i
$429$	−5.26940e11			−0.751110
$430$	3.19689e11			0.450940
$431$	−2.37341e11	−	4.11087e11i	−0.331303	−	0.573833i	0.651465	−	0.758679i	$-0.274155\pi$
$431$	−2.37341e11	−	4.11087e11i	−0.331303	−	0.573833i	−0.982768	+	0.184845i	$0.940822\pi$
$432$	1.30737e10	−	2.26443e10i	0.0180601	−	0.0312810i
$433$	2.93540e11	+	5.08426e11i	0.401302	+	0.695076i	0.993883	−	0.110435i	$-0.0352243\pi$
$433$	2.93540e11	+	5.08426e11i	0.401302	+	0.695076i	−0.592581	+	0.805511i	$0.701891\pi$
$434$	−3.03447e11	+	5.25586e11i	−0.410563	+	0.711115i
$435$	5.10629e10	−	8.84436e10i	0.0683761	−	0.118431i
$436$	2.86384e11			0.379542
$437$	4.27207e11	−	1.01746e12i	0.560366	−	1.33460i
$438$	−4.12034e11			−0.534934
$439$	2.74474e11	−	4.75402e11i	0.352704	−	0.610901i	−0.634018	−	0.773318i	$-0.718596\pi$
$439$	2.74474e11	−	4.75402e11i	0.352704	−	0.610901i	0.986722	+	0.162417i	$0.0519290\pi$
$440$	−2.83070e11	+	4.90291e11i	−0.360045	+	0.623616i
$441$	−1.04697e11	−	1.81341e11i	−0.131814	−	0.228308i
$442$	−7.76513e10	+	1.34496e11i	−0.0967717	+	0.167614i
$443$	2.38442e10	+	4.12994e10i	0.0294148	+	0.0509480i	0.880358	−	0.474310i	$-0.157302\pi$
$443$	2.38442e10	+	4.12994e10i	0.0294148	+	0.0509480i	−0.850943	+	0.525258i	$0.823969\pi$
$444$	3.28542e11			0.401206
$445$	−6.23401e11			−0.753612
$446$	1.84886e11	+	3.20232e11i	0.221257	+	0.383228i
$447$	3.12631e11	+	5.41492e11i	0.370380	+	0.641517i
$448$	3.90071e11			0.457502
$449$	−7.69861e10			−0.0893930			−0.0446965	−	0.999001i	$-0.514232\pi$
$449$	−7.69861e10			−0.0893930			−0.0446965	+	0.999001i	$0.514232\pi$
$450$	−6.44670e10	−	1.11660e11i	−0.0741108	−	0.128364i
$451$	2.77242e11	−	4.80198e11i	0.315548	−	0.546545i
$452$	2.93480e11	+	5.08322e11i	0.330716	+	0.572817i
$453$	1.13034e10	−	1.95781e10i	0.0126115	−	0.0218438i
$454$	4.63331e11	−	8.02513e11i	0.511847	−	0.886545i
$455$	1.00403e12			1.09823
$456$	−4.56428e11	+	5.78520e10i	−0.494346	+	0.0626580i
$457$	1.11586e10			0.0119671			0.00598353	−	0.999982i	$-0.498095\pi$
$457$	1.11586e10			0.0119671			0.00598353	+	0.999982i	$0.498095\pi$
$458$	−8.94175e10	+	1.54876e11i	−0.0949572	+	0.164471i
$459$	8.05537e10	−	1.39523e11i	0.0847088	−	0.146720i
$460$	−3.61980e11	−	6.26968e11i	−0.376942	−	0.652883i
$461$	3.76950e11	−	6.52896e11i	0.388713	−	0.673271i	−0.603563	−	0.797315i	$-0.706253\pi$
$461$	3.76950e11	−	6.52896e11i	0.388713	−	0.673271i	0.992277	+	0.124044i	$0.0395863\pi$
$462$	1.06836e11	+	1.85045e11i	0.109101	+	0.188968i
$463$	−4.94597e11			−0.500193			−0.250096	−	0.968221i	$-0.580462\pi$
$463$	−4.94597e11			−0.500193			−0.250096	+	0.968221i	$0.580462\pi$
$464$	−1.35413e10			−0.0135622
$465$	−3.52895e11	−	6.11233e11i	−0.350032	−	0.606273i
$466$	4.00358e11	+	6.93441e11i	0.393289	+	0.681197i
$467$	−5.65296e10			−0.0549984			−0.0274992	−	0.999622i	$-0.508754\pi$
$467$	−5.65296e10			−0.0549984			−0.0274992	+	0.999622i	$0.508754\pi$
$468$	8.20982e11			0.791092
$469$	2.66815e11	+	4.62136e11i	0.254643	+	0.441055i
$470$	−6.75526e10	+	1.17005e11i	−0.0638560	+	0.110602i
$471$	2.21328e11	+	3.83351e11i	0.207225	+	0.358924i
$472$	−6.47795e10	+	1.12201e11i	−0.0600757	+	0.104054i
$473$	4.43091e11	−	7.67456e11i	0.407022	−	0.704982i
$474$	3.30196e11			0.300448
$475$	1.41674e11	−	3.37420e11i	0.127694	−	0.304123i
$476$	−1.10136e11			−0.0983327
$477$	−4.17745e11	+	7.23556e11i	−0.369470	+	0.639940i
$478$	4.98022e11	−	8.62599e11i	0.436338	−	0.755759i
$479$	6.86516e11	+	1.18908e12i	0.595856	+	1.03205i	0.993425	+	0.114481i	$0.0365204\pi$
$479$	6.86516e11	+	1.18908e12i	0.595856	+	1.03205i	−0.397570	+	0.917572i	$0.630146\pi$
$480$	−2.43154e11	+	4.21156e11i	−0.209072	+	0.362124i
$481$	1.22346e12	+	2.11910e12i	1.04217	+	1.80509i
$482$	−9.69349e11			−0.818029
$483$	−7.02703e11			−0.587503
$484$	−7.89354e10	−	1.36720e11i	−0.0653835	−	0.113247i
$485$	2.00399e11	+	3.47101e11i	0.164459	+	0.284852i
$486$	7.66032e11			0.622850
$487$	−1.48901e12			−1.19955			−0.599775	−	0.800168i	$-0.704743\pi$
$487$	−1.48901e12			−1.19955			−0.599775	+	0.800168i	$0.704743\pi$
$488$	−7.37103e11	−	1.27670e12i	−0.588354	−	1.01906i
$489$	−4.03568e11	+	6.98999e11i	−0.319173	+	0.552824i
$490$	1.11473e11	+	1.93076e11i	0.0873545	+	0.151302i
$491$	2.93341e11	−	5.08081e11i	0.227775	−	0.394518i	−0.729374	−	0.684116i	$-0.760188\pi$
$491$	2.93341e11	−	5.08081e11i	0.227775	−	0.394518i	0.957148	+	0.289598i	$0.0935217\pi$
$492$	1.47811e11	−	2.56017e11i	0.113727	−	0.196982i
$493$	−8.34350e10			−0.0636117
$494$	−8.05995e11	−	1.06095e12i	−0.608921	−	0.801535i
$495$	7.26159e11			0.543636
$496$	−4.67919e10	+	8.10459e10i	−0.0347139	+	0.0601262i
$497$	−5.31711e11	+	9.20951e11i	−0.390906	+	0.677069i
$498$	2.13948e11	+	3.70568e11i	0.155875	+	0.269983i
$499$	−7.81422e11	+	1.35346e12i	−0.564200	+	0.977223i	0.432924	+	0.901431i	$0.357482\pi$
$499$	−7.81422e11	+	1.35346e12i	−0.564200	+	0.977223i	−0.997124	+	0.0757923i	$0.975851\pi$
$500$	−4.83983e11	−	8.38283e11i	−0.346310	−	0.599827i
$501$	−5.42126e11			−0.384442
$502$	−1.01242e12			−0.711529
$503$	−1.01499e12	−	1.75801e12i	−0.706978	−	1.22452i	−0.965973	−	0.258643i	$-0.916725\pi$
$503$	−1.01499e12	−	1.75801e12i	−0.706978	−	1.22452i	0.258995	−	0.965879i	$-0.416609\pi$
$504$	−4.28078e11	−	7.41452e11i	−0.295519	−	0.511854i
$505$	−1.22330e12			−0.836991
$506$	1.14748e12			0.778156
$507$	−6.70579e11	−	1.16148e12i	−0.450728	−	0.780683i
$508$	6.30267e10	−	1.09165e11i	0.0419892	−	0.0727275i
$509$	2.14056e11	+	3.70756e11i	0.141351	+	0.244826i	0.928005	−	0.372567i	$-0.121522\pi$
$509$	2.14056e11	+	3.70756e11i	0.141351	+	0.244826i	−0.786655	+	0.617393i	$0.788189\pi$
$510$	−3.66181e10	+	6.34244e10i	−0.0239679	+	0.0415136i
$511$	1.08814e12	−	1.88471e12i	0.705976	−	1.22279i
$512$	1.27387e11			0.0819241
$513$	8.36121e11	+	1.10060e12i	0.533017	+	0.701622i
$514$	1.31981e12			0.834020
$515$	−1.11776e11	+	1.93602e11i	−0.0700191	+	0.121277i
$516$	2.36233e11	−	4.09168e11i	0.146696	−	0.254085i
$517$	1.87257e11	+	3.24338e11i	0.115274	+	0.199660i
$518$	4.96107e11	−	8.59282e11i	0.302755	−	0.524387i
$519$	2.43166e10	+	4.21175e10i	0.0147112	+	0.0254806i
$520$	−2.24803e12			−1.34830
$521$	−1.62846e12			−0.968295			−0.484148	−	0.874986i	$-0.660870\pi$
$521$	−1.62846e12			−0.968295			−0.484148	+	0.874986i	$0.660870\pi$
$522$	−1.26098e11	−	2.18407e11i	−0.0743344	−	0.128751i
$523$	−6.52934e10	−	1.13092e11i	−0.0381603	−	0.0660956i	0.846314	−	0.532684i	$-0.178816\pi$
$523$	−6.52934e10	−	1.13092e11i	−0.0381603	−	0.0660956i	−0.884475	+	0.466588i	$0.845483\pi$
$524$	−1.14045e12			−0.660822
$525$	−2.33037e11			−0.133878
$526$	6.91488e11	+	1.19769e12i	0.393866	+	0.682197i
$527$	−2.88309e11	+	4.99366e11i	−0.162821	+	0.282014i
$528$	1.64741e10	+	2.85341e10i	0.00922466	+	0.0159776i
$529$	−9.86287e11	+	1.70830e12i	−0.547586	+	0.948447i
$530$	4.44780e11	−	7.70381e11i	0.244852	−	0.424096i
$531$	1.66179e11			0.0907091
$532$	3.65797e11	−	8.71206e11i	0.197988	−	0.471540i
$533$	2.20175e12			1.18167
$534$	2.63400e11	−	4.56222e11i	0.140178	−	0.242795i
$535$	−4.88769e11	+	8.46572e11i	−0.257936	+	0.446758i
$536$	−5.97399e11	−	1.03473e12i	−0.312625	−	0.541482i
$537$	6.70363e11	−	1.16110e12i	0.347877	−	0.602541i
$538$	9.20643e11	+	1.59460e12i	0.473774	+	0.820601i
$539$	6.18007e11			0.315387
$540$	9.06784e11			0.458915
$541$	−1.78586e12	−	3.09320e12i	−0.896313	−	1.55246i	−0.832171	−	0.554519i	$-0.812902\pi$
$541$	−1.78586e12	−	3.09320e12i	−0.896313	−	1.55246i	−0.0641425	−	0.997941i	$-0.520431\pi$
$542$	−2.27716e11	−	3.94416e11i	−0.113344	−	0.196317i
$543$	1.42082e11			0.0701357
$544$	3.97306e11			0.194504
$545$	5.02916e11	+	8.71076e11i	0.244181	+	0.422933i
$546$	−4.24223e11	+	7.34775e11i	−0.204281	+	0.353824i
$547$	1.42423e12	+	2.46685e12i	0.680203	+	1.17815i	0.974919	+	0.222561i	$0.0714417\pi$
$547$	1.42423e12	+	2.46685e12i	0.680203	+	1.17815i	−0.294716	+	0.955585i	$0.595225\pi$
$548$	8.34206e10	−	1.44489e11i	0.0395149	−	0.0684418i
$549$	−9.45446e11	+	1.63756e12i	−0.444182	+	0.769346i
$550$	3.80537e11			0.177323
$551$	2.77115e11	−	6.59994e11i	0.128079	−	0.305041i
$552$	1.57336e12			0.721276
$553$	−8.72012e11	+	1.51037e12i	−0.396515	+	0.686784i
$554$	−7.42401e11	+	1.28588e12i	−0.334845	+	0.579969i
$555$	5.76950e11	+	9.99306e11i	0.258119	+	0.447075i
$556$	6.13160e10	−	1.06202e11i	0.0272105	−	0.0471301i
$557$	−9.76409e11	−	1.69119e12i	−0.429817	−	0.744464i	0.567040	−	0.823690i	$-0.308088\pi$
$557$	−9.76409e11	−	1.69119e12i	−0.429817	−	0.744464i	−0.996857	+	0.0792260i	$0.974755\pi$
$558$	−1.74292e12			−0.761067
$559$	3.51885e12			1.52422
$560$	−3.13897e10	−	5.43686e10i	−0.0134878	−	0.0233616i
$561$	1.01506e11	+	1.75813e11i	0.0432671	+	0.0749409i
$562$	4.33843e11			0.183450
$563$	4.09942e12			1.71963			0.859814	−	0.510607i	$-0.170579\pi$
$563$	4.09942e12			1.71963			0.859814	+	0.510607i	$0.170579\pi$
$564$	9.98358e10	+	1.72921e11i	0.0415461	+	0.0719600i
$565$	−1.03075e12	+	1.78532e12i	−0.425537	+	0.737051i
$566$	−7.41044e11	−	1.28353e12i	−0.303508	−	0.525692i
$567$	−2.96887e11	+	5.14223e11i	−0.120633	+	0.208943i
$568$	1.19050e12	−	2.06201e12i	0.479914	−	0.831236i
$569$	3.23614e12			1.29426			0.647131	−	0.762379i	$-0.275969\pi$
$569$	3.23614e12			1.29426			0.647131	+	0.762379i	$0.275969\pi$
$570$	−3.80084e11	−	5.00312e11i	−0.150814	−	0.198520i
$571$	1.11045e12			0.437156			0.218578	−	0.975819i	$-0.429858\pi$
$571$	1.11045e12			0.437156			0.218578	+	0.975819i	$0.429858\pi$
$572$	−1.21152e12	+	2.09842e12i	−0.473206	+	0.819617i
$573$	9.91324e11	−	1.71702e12i	0.384167	−	0.665396i
$574$	−4.46398e11	−	7.73183e11i	−0.171640	−	0.297289i
$575$	−6.25738e11	+	1.08381e12i	−0.238719	+	0.413474i
$576$	5.60116e11	+	9.70149e11i	0.212020	+	0.367229i
$577$	1.88194e12			0.706830			0.353415	−	0.935467i	$-0.385020\pi$
$577$	1.88194e12			0.706830			0.353415	+	0.935467i	$0.385020\pi$
$578$	−1.55860e12			−0.580845
$579$	5.65392e11	+	9.79288e11i	0.209072	+	0.362124i
$580$	−2.34805e11	−	4.06693e11i	−0.0861550	−	0.149225i
$581$	−2.26005e12			−0.822859
$582$	−3.38691e11			−0.122363
$583$	−1.23294e12	−	2.13551e12i	−0.442010	−	0.765583i
$584$	−2.43635e12	+	4.21988e12i	−0.866725	+	1.50121i
$585$	1.44172e12	+	2.49713e12i	0.508954	+	0.881535i
$586$	−7.80328e9	+	1.35157e10i	−0.00273362	+	0.00473477i
$587$	2.34129e12	−	4.05523e12i	0.813923	−	1.40976i	−0.0961764	−	0.995364i	$-0.530661\pi$
$587$	2.34129e12	−	4.05523e12i	0.813923	−	1.40976i	0.910099	−	0.414391i	$-0.136005\pi$
$588$	3.29490e11			0.113669
$589$	−2.99255e12	−	3.93916e12i	−1.02453	−	1.34861i
$590$	−1.76933e11			−0.0601140
$591$	−1.45260e12	+	2.51598e12i	−0.489783	+	0.848329i
$592$	7.65002e10	−	1.32502e11i	0.0255985	−	0.0443379i
$593$	−2.68604e12	−	4.65236e12i	−0.892004	−	1.54500i	−0.837470	−	0.546484i	$-0.815966\pi$
$593$	−2.68604e12	−	4.65236e12i	−0.892004	−	1.54500i	−0.0545337	−	0.998512i	$-0.517367\pi$
$594$	−7.18626e11	+	1.24470e12i	−0.236845	+	0.410227i
$595$	−1.93409e11	−	3.34994e11i	−0.0632630	−	0.109575i
$596$	2.87516e12			0.933370
$597$	−2.40951e12			−0.776327
$598$	2.27820e12	+	3.94596e12i	0.728512	+	1.26182i
$599$	−2.89117e12	−	5.00765e12i	−0.917599	−	1.58933i	−0.803052	−	0.595909i	$-0.796792\pi$
$599$	−2.89117e12	−	5.00765e12i	−0.917599	−	1.58933i	−0.114547	−	0.993418i	$-0.536542\pi$
$600$	5.21771e11			0.164361
$601$	3.45916e12			1.08152			0.540761	−	0.841176i	$-0.318136\pi$
$601$	3.45916e12			1.08152			0.540761	+	0.841176i	$0.318136\pi$
$602$	−7.13436e11	−	1.23571e12i	−0.221397	−	0.383470i
$603$	−7.66255e11	+	1.32719e12i	−0.236018	+	0.408795i
$604$	−5.19769e10	−	9.00266e10i	−0.0158907	−	0.0275236i
$605$	2.77235e11	−	4.80186e11i	0.0841297	−	0.145717i
$606$	5.16868e11	−	8.95241e11i	0.155687	−	0.269658i
$607$	−4.84715e12			−1.44923			−0.724616	−	0.689153i	$-0.757983\pi$
$607$	−4.84715e12			−1.44923			−0.724616	+	0.689153i	$0.757983\pi$
$608$	−1.31958e12	+	3.14280e12i	−0.391625	+	0.932717i
$609$	−4.55820e11			−0.134281
$610$	1.00663e12	−	1.74353e12i	0.294365	−	0.509855i
$611$	−7.43560e11	+	1.28788e12i	−0.215839	+	0.373845i
$612$	−1.58148e11	−	2.73920e11i	−0.0455703	−	0.0789300i
$613$	−2.04595e12	+	3.54368e12i	−0.585224	+	1.01364i	0.409624	+	0.912255i	$0.365660\pi$
$613$	−2.04595e12	+	3.54368e12i	−0.585224	+	1.01364i	−0.994847	+	0.101383i	$0.967673\pi$
$614$	−8.06932e11	−	1.39765e12i	−0.229128	−	0.396862i
$615$	1.03828e12			0.292669
$616$	2.52686e12			0.707079
$617$	−6.19098e11	−	1.07231e12i	−0.171979	−	0.297877i	0.767132	−	0.641489i	$-0.221683\pi$
$617$	−6.19098e11	−	1.07231e12i	−0.171979	−	0.297877i	−0.939112	+	0.343612i	$0.888350\pi$
$618$	−9.44554e10	−	1.63602e11i	−0.0260483	−	0.0451169i
$619$	−9.16613e9			−0.00250945			−0.00125472	−	0.999999i	$-0.500399\pi$
$619$	−9.16613e9			−0.00250945			−0.00125472	+	0.999999i	$0.500399\pi$
$620$	−3.24546e12			−0.882092
$621$	−2.36336e12	−	4.09345e12i	−0.637701	−	1.10453i
$622$	−3.23207e11	+	5.59811e11i	−0.0865814	+	0.149963i
$623$	1.39122e12	+	2.40966e12i	0.369998	+	0.640855i
$624$	−6.54156e10	+	1.13303e11i	−0.0172723	+	0.0299165i
$625$	1.07071e12	−	1.85452e12i	0.280680	−	0.486152i
$626$	9.54903e11			0.248528
$627$	−1.72787e12	+	2.19006e11i	−0.446484	+	0.0565916i
$628$	2.03548e12			0.522214
$629$	4.71358e11	−	8.16415e11i	0.120067	−	0.207962i
$630$	5.84607e11	−	1.01257e12i	0.147854	−	0.256090i
$631$	−6.79747e11	−	1.17736e12i	−0.170693	−	0.295648i	0.767970	−	0.640486i	$-0.221267\pi$
$631$	−6.79747e11	−	1.17736e12i	−0.170693	−	0.295648i	−0.938662	+	0.344838i	$0.887934\pi$
$632$	1.95244e12	−	3.38172e12i	0.486800	−	0.843163i
$633$	9.86700e11	+	1.70901e12i	0.244269	+	0.423086i
$634$	−3.63568e12			−0.893685
$635$	4.42722e11			0.108056
$636$	−6.57338e11	−	1.13854e12i	−0.159306	−	0.275926i
$637$	1.22699e12	+	2.12521e12i	0.295266	+	0.511416i
$638$	7.44330e11			0.177858
$639$	−3.05400e12			−0.724629
$640$	1.16106e12	+	2.01101e12i	0.273555	+	0.473811i
$641$	−3.06055e11	+	5.30103e11i	−0.0716042	+	0.124022i	−0.899605	−	0.436706i	$-0.856145\pi$
$641$	−3.06055e11	+	5.30103e11i	−0.0716042	+	0.124022i	0.828000	+	0.560728i	$0.189479\pi$
$642$	−4.13029e11	−	7.15388e11i	−0.0959562	−	0.166201i
$643$	−8.33175e11	+	1.44310e12i	−0.192215	+	0.332926i	−0.945984	−	0.324213i	$-0.894900\pi$
$643$	−8.33175e11	+	1.44310e12i	−0.192215	+	0.332926i	0.753769	+	0.657139i	$0.228234\pi$
$644$	−1.61563e12	+	2.79836e12i	−0.370132	+	0.641087i
$645$	1.65939e12			0.377511
$646$	−1.98724e11	+	4.73293e11i	−0.0448956	+	0.106926i
$647$	6.55308e12			1.47020			0.735100	−	0.677959i	$-0.237135\pi$
$647$	6.55308e12			1.47020			0.735100	+	0.677959i	$0.237135\pi$
$648$	6.64731e11	−	1.15135e12i	0.148101	−	0.256519i
$649$	−2.45231e11	+	4.24752e11i	−0.0542593	+	0.0939798i
$650$	7.55518e11	+	1.30860e12i	0.166010	+	0.287538i
$651$	−1.57508e12	+	2.72813e12i	−0.343708	+	0.595319i
$652$	1.85574e12	+	3.21424e12i	0.402164	+	0.696568i
$653$	−1.30273e12			−0.280379			−0.140189	−	0.990125i	$-0.544771\pi$
$653$	−1.30273e12			−0.280379			−0.140189	+	0.990125i	$0.544771\pi$
$654$	−8.49969e11			−0.181678
$655$	−2.00273e12	−	3.46883e12i	−0.425144	−	0.736371i
$656$	−6.88350e10	−	1.19226e11i	−0.0145125	−	0.0251364i
$657$	6.24996e12			1.30868
$658$	6.03018e11			0.125405
$659$	3.40720e11	+	5.90144e11i	0.0703741	+	0.121892i	0.899065	−	0.437815i	$-0.144247\pi$
$659$	3.40720e11	+	5.90144e11i	0.0703741	+	0.121892i	−0.828691	+	0.559706i	$0.810914\pi$
$660$	−5.71320e11	+	9.89555e11i	−0.117201	+	0.202998i
$661$	3.81427e11	+	6.60651e11i	0.0777150	+	0.134606i	0.902264	−	0.431185i	$-0.141904\pi$
$661$	3.81427e11	+	6.60651e11i	0.0777150	+	0.134606i	−0.824549	+	0.565791i	$0.808571\pi$
$662$	−1.86618e12	+	3.23231e12i	−0.377652	+	0.654112i
$663$	−4.03060e11	+	6.98120e11i	−0.0810137	+	0.140320i
$664$	5.06027e12			1.01022
$665$	3.29226e12	−	4.17293e11i	0.652826	−	0.0827453i
$666$	2.84950e12			0.561222
$667$	−1.22395e12	+	2.11994e12i	−0.239439	+	0.414721i
$668$	−1.24644e12	+	2.15889e12i	−0.242201	+	0.419505i
$669$	9.59676e11	+	1.66221e12i	0.185228	+	0.320825i
$670$	8.15843e11	−	1.41308e12i	0.156412	−	0.270913i
$671$	−2.79039e12	−	4.83310e12i	−0.531391	−	0.920396i
$672$	2.17055e12			0.410590
$673$	2.67918e12			0.503425			0.251713	−	0.967802i	$-0.419006\pi$
$673$	2.67918e12			0.503425			0.251713	+	0.967802i	$0.419006\pi$
$674$	1.54807e12	+	2.68134e12i	0.288949	+	0.500475i
$675$	−7.83758e11	−	1.35751e12i	−0.145316	−	0.251696i
$676$	−6.16710e12			−1.13585
$677$	2.12102e12			0.388057			0.194029	−	0.980996i	$-0.437845\pi$
$677$	2.12102e12			0.388057			0.194029	+	0.980996i	$0.437845\pi$
$678$	−8.71029e11	−	1.50867e12i	−0.158307	−	0.274195i
$679$	8.94445e11	−	1.54922e12i	0.161488	−	0.279705i
$680$	4.33043e11	+	7.50053e11i	0.0776678	+	0.134525i
$681$	2.40498e12	−	4.16556e12i	0.428500	−	0.742183i
$682$	2.57203e12	−	4.45488e12i	0.455246	−	0.788509i
$683$	−5.10179e12			−0.897077			−0.448539	−	0.893763i	$-0.648055\pi$
$683$	−5.10179e12			−0.897077			−0.448539	+	0.893763i	$0.648055\pi$
$684$	2.69204e12	−	3.41215e11i	0.470251	−	0.0596040i
$685$	5.85976e11			0.101689
$686$	1.90365e12	−	3.29721e12i	0.328192	−	0.568445i
$687$	−4.64134e11	+	8.03904e11i	−0.0794947	+	0.137689i
$688$	−1.10013e11	−	1.90547e11i	−0.0187195	−	0.0324231i
$689$	4.89574e12	−	8.47967e12i	0.827622	−	1.43348i
$690$	1.07433e12	+	1.86080e12i	0.180434	+	0.312521i
$691$	−3.99404e12			−0.666441			−0.333220	−	0.942849i	$-0.608135\pi$
$691$	−3.99404e12			−0.666441			−0.333220	+	0.942849i	$0.608135\pi$
$692$	2.23632e11			0.0370728
$693$	−1.62054e12	−	2.80686e12i	−0.266907	−	0.462297i
$694$	−1.36262e12	−	2.36013e12i	−0.222976	−	0.386206i
$695$	4.30706e11			0.0700243
$696$	1.02058e12			0.164857
$697$	−4.24128e11	−	7.34612e11i	−0.0680691	−	0.117899i
$698$	−2.69729e12	+	4.67184e12i	−0.430108	+	0.744970i
$699$	2.07811e12	+	3.59940e12i	0.329247	+	0.570273i
$700$	−5.35791e11	+	9.28017e11i	−0.0843440	+	0.146088i
$701$	−2.52383e12	+	4.37139e12i	−0.394756	+	0.683737i	−0.993070	−	0.117525i	$-0.962504\pi$
$701$	−2.52383e12	+	4.37139e12i	−0.394756	+	0.683737i	0.598314	+	0.801261i	$0.295837\pi$
$702$	−5.70704e12			−0.886940
$703$	4.89254e12	+	6.44015e12i	0.755501	+	0.994482i
$704$	−3.30626e12			−0.507294
$705$	−3.50641e11	+	6.07328e11i	−0.0534579	+	0.0925918i
$706$	−2.10547e12	+	3.64678e12i	−0.318954	+	0.552445i
$707$	2.72998e12	+	4.72847e12i	0.410934	+	0.711759i
$708$	−1.30744e11	+	2.26456e11i	−0.0195557	+	0.0338715i
$709$	−4.30997e12	−	7.46509e12i	−0.640570	−	1.10950i	−0.985306	−	0.170800i	$-0.945365\pi$
$709$	−4.30997e12	−	7.46509e12i	−0.640570	−	1.10950i	0.344736	−	0.938700i	$-0.387968\pi$
$710$	3.25164e12			0.480220
$711$	−5.00860e12			−0.735026
$712$	−3.11495e12	−	5.39525e12i	−0.454246	−	0.786777i
$713$	8.45867e12	+	1.46508e13i	1.22574	+	2.12305i
$714$	3.26876e11			0.0470697
$715$	−8.51018e12			−1.21776
$716$	−3.08256e12	−	5.33915e12i	−0.438331	−	0.759212i
$717$	2.58505e12	−	4.47744e12i	0.365286	−	0.632694i
$718$	−1.86362e12	−	3.22788e12i	−0.261696	−	0.453271i
$719$	−9.59884e11	+	1.66257e12i	−0.133949	+	0.232006i	−0.925195	−	0.379491i	$-0.876099\pi$
$719$	−9.59884e11	+	1.66257e12i	−0.133949	+	0.232006i	0.791247	+	0.611497i	$0.209432\pi$
$720$	9.01471e10	−	1.56139e11i	0.0125013	−	0.0216529i
$721$	9.97785e11			0.137508
$722$	−3.08385e12	−	3.14392e12i	−0.422353	−	0.430580i
$723$	−5.03154e12			−0.684823
$724$	3.26670e11	−	5.65809e11i	0.0441861	−	0.0765326i
$725$	−4.05896e11	+	7.03032e11i	−0.0545624	+	0.0945049i
$726$	2.34275e11	+	4.05777e11i	0.0312976	+	0.0542091i
$727$	−3.29839e12	+	5.71298e12i	−0.437923	+	0.758504i	−0.997529	−	0.0702543i	$-0.977619\pi$
$727$	−3.29839e12	+	5.71298e12i	−0.437923	+	0.758504i	0.559607	+	0.828758i	$0.310952\pi$
$728$	5.01683e12	+	8.68941e12i	0.661970	+	1.14657i
$729$	1.68743e12			0.221285
$730$	−6.65443e12			−0.867277
$731$	−6.77845e11	−	1.17406e12i	−0.0878016	−	0.152077i
$732$	−1.48770e12	−	2.57676e12i	−0.191520	−	0.331722i
$733$	2.18940e12			0.280128			0.140064	−	0.990142i	$-0.455269\pi$
$733$	2.18940e12			0.280128			0.140064	+	0.990142i	$0.455269\pi$
$734$	−5.13439e11			−0.0652915
$735$	5.78613e11	+	1.00219e12i	0.0731300	+	0.126665i
$736$	5.82825e12	−	1.00948e13i	0.732130	−	1.26809i
$737$	−2.26153e12	−	3.91708e12i	−0.282357	−	0.489056i
$738$	1.28199e12	−	2.22048e12i	0.159086	−	0.275545i
$739$	−2.50013e12	+	4.33036e12i	−0.308364	+	0.534102i	−0.978005	−	0.208583i	$-0.933115\pi$
$739$	−2.50013e12	+	4.33036e12i	−0.308364	+	0.534102i	0.669641	+	0.742685i	$0.266448\pi$
$740$	5.30602e12			0.650468
$741$	−4.18363e12	−	5.50699e12i	−0.509766	−	0.671016i
$742$	−3.97039e12			−0.480856
$743$	−2.43670e12	+	4.22050e12i	−0.293328	+	0.508059i	−0.974595	−	0.223977i	$-0.928096\pi$
$743$	−2.43670e12	+	4.22050e12i	−0.293328	+	0.508059i	0.681267	+	0.732035i	$0.261429\pi$
$744$	3.52662e12	−	6.10829e12i	0.421969	−	0.730872i
$745$	5.04904e12	+	8.74519e12i	0.600490	+	1.04008i
$746$	2.99142e12	−	5.18129e12i	0.353633	−	0.612510i
$747$	−3.24528e12	−	5.62099e12i	−0.381337	−	0.660495i
$748$	9.33516e11			0.109035
$749$	4.36306e12			0.506551
$750$	1.43643e12	+	2.48797e12i	0.165771	+	0.287124i
$751$	−1.48299e12	−	2.56861e12i	−0.170121	−	0.294659i	0.768341	−	0.640041i	$-0.221083\pi$
$751$	−1.48299e12	−	2.56861e12i	−0.170121	−	0.294659i	−0.938462	+	0.345382i	$0.887749\pi$
$752$	9.29860e10			0.0106032
$753$	−5.25509e12			−0.595666
$754$	1.47779e12	+	2.55961e12i	0.166511	+	0.288405i
$755$	1.82552e11	−	3.16190e11i	0.0204468	−	0.0354149i
$756$	−2.02363e12	−	3.50504e12i	−0.225312	−	0.390251i
$757$	4.81110e12	−	8.33307e12i	0.532492	−	0.922303i	−0.466788	−	0.884369i	$-0.654589\pi$
$757$	4.81110e12	−	8.33307e12i	0.532492	−	0.922303i	0.999280	−	0.0379340i	$-0.0120777\pi$
$758$	−3.68733e12	+	6.38664e12i	−0.405696	+	0.702686i
$759$	5.95614e12			0.651443
$760$	−7.37140e12	+	9.34321e11i	−0.801473	+	0.101586i
$761$	−1.58309e13			−1.71110			−0.855551	−	0.517719i	$-0.826781\pi$
$761$	−1.58309e13			−1.71110			−0.855551	+	0.517719i	$0.826781\pi$
$762$	−1.87059e11	+	3.23996e11i	−0.0200993	+	0.0348131i
$763$	2.24468e12	−	3.88789e12i	0.239769	−	0.415292i
$764$	−4.55844e12	−	7.89545e12i	−0.484057	−	0.838411i
$765$	5.55443e11	−	9.62056e11i	0.0586359	−	0.101560i
$766$	9.75186e11	+	1.68907e12i	0.102343	+	0.177263i
$767$	−1.94753e12			−0.203191
$768$	−4.73291e12			−0.490911
$769$	5.90692e12	+	1.02311e13i	0.609106	+	1.05500i	0.991388	+	0.130956i	$0.0418048\pi$
$769$	5.90692e12	+	1.02311e13i	0.609106	+	1.05500i	−0.382282	+	0.924046i	$0.624862\pi$
$770$	1.72541e12	+	2.98850e12i	0.176883	+	0.306369i
$771$	6.85064e12			0.698211
$772$	5.19973e12			0.526869
$773$	8.44076e12	+	1.46198e13i	0.850303	+	1.47277i	0.880935	+	0.473238i	$0.156915\pi$
$773$	8.44076e12	+	1.46198e13i	0.850303	+	1.47277i	−0.0306313	+	0.999531i	$0.509752\pi$
$774$	2.04889e12	−	3.54878e12i	0.205203	−	0.355423i
$775$	2.80514e12	+	4.85865e12i	0.279317	+	0.483791i
$776$	−2.00267e12	+	3.46872e12i	−0.198258	+	0.343393i
$777$	2.57511e12	−	4.46022e12i	0.253455	−	0.438997i
$778$	5.29999e11			0.0518641
$779$	7.21965e12	−	9.15086e11i	0.702421	−	0.0890315i
$780$	−4.53719e12			−0.438896
$781$	4.50680e12	−	7.80601e12i	0.433450	−	0.750757i
$782$	8.77712e11	−	1.52024e12i	0.0839308	−	0.145372i
$783$	−1.53303e12	−	2.65529e12i	−0.145755	−	0.252455i
$784$	7.67208e10	−	1.32884e11i	0.00725255	−	0.0125618i
$785$	3.57448e12	+	6.19119e12i	0.335970	+	0.581916i
$786$	3.38477e12			0.316321
$787$	−2.35359e12			−0.218698			−0.109349	−	0.994003i	$-0.534877\pi$
$787$	−2.35359e12			−0.218698			−0.109349	+	0.994003i	$0.534877\pi$
$788$	6.67956e12	+	1.15693e13i	0.617135	+	1.06891i
$789$	3.58927e12	+	6.21679e12i	0.329730	+	0.571110i
$790$	5.33273e12			0.487111
$791$	9.20116e12			0.835697
$792$	3.62840e12	+	6.28457e12i	0.327681	+	0.567561i
$793$	1.10801e13	−	1.91913e13i	0.994980	−	1.72336i
$794$	−3.97974e12	−	6.89311e12i	−0.355355	−	0.615493i
$795$	2.30869e12	−	3.99877e12i	0.204981	−	0.355037i
$796$	−5.53988e12	+	9.59535e12i	−0.489093	+	0.847133i
$797$	−6.75552e12			−0.593057			−0.296528	−	0.955024i	$-0.595829\pi$
$797$	−6.75552e12			−0.593057			−0.296528	+	0.955024i	$0.595829\pi$
$798$	−1.08566e12	+	2.58568e12i	−0.0947724	+	0.225716i
$799$	5.72935e11			0.0497331
$800$	1.93282e12	−	3.34774e12i	0.166834	−	0.288966i
$801$	−3.99539e12	+	6.92022e12i	−0.342936	+	0.593983i
$802$	−4.31613e12	−	7.47575e12i	−0.368391	−	0.638073i
$803$	−9.22309e12	+	1.59749e13i	−0.782810	+	1.35587i
$804$	−1.20573e12	−	2.08839e12i	−0.101765	−	0.176262i
$805$	−1.13488e13			−0.952507
$806$	2.04260e13			1.70481
$807$	4.77873e12	+	8.27700e12i	0.396626	+	0.686976i
$808$	−6.11245e12	−	1.05871e13i	−0.504503	−	0.873825i
$809$	−9.11978e12			−0.748541			−0.374271	−	0.927319i	$-0.622107\pi$
$809$	−9.11978e12			−0.748541			−0.374271	+	0.927319i	$0.622107\pi$
$810$	1.81559e12			0.148196
$811$	1.56575e12	+	2.71196e12i	0.127095	+	0.220135i	0.922550	−	0.385878i	$-0.126101\pi$
$811$	1.56575e12	+	2.71196e12i	0.127095	+	0.220135i	−0.795455	+	0.606013i	$0.792768\pi$
$812$	−1.04801e12	+	1.81520e12i	−0.0845984	+	0.146529i
$813$	−1.18199e12	−	2.04727e12i	−0.0948870	−	0.164349i
$814$	−4.20502e12	+	7.28330e12i	−0.335705	+	0.581458i
$815$	−6.51769e12	+	1.12890e13i	−0.517469	+	0.896283i
$816$	5.04047e10			0.00397983
$817$	1.15385e13	−	1.46250e12i	0.906046	−	0.114841i
$818$	7.38088e12			0.576392
$819$	6.43485e12	−	1.11455e13i	0.499759	−	0.865608i
$820$	2.38718e12	−	4.13472e12i	0.184384	−	0.319362i
$821$	−2.85959e12	−	4.95295e12i	−0.219664	−	0.380469i	0.735041	−	0.678022i	$-0.237163\pi$
$821$	−2.85959e12	−	4.95295e12i	−0.219664	−	0.380469i	−0.954705	+	0.297553i	$0.903829\pi$
$822$	−2.47587e11	+	4.28833e11i	−0.0189149	+	0.0327616i
$823$	1.25360e12	+	2.17131e12i	0.0952492	+	0.164976i	0.909713	−	0.415239i	$-0.136302\pi$
$823$	1.25360e12	+	2.17131e12i	0.0952492	+	0.164976i	−0.814463	+	0.580215i	$0.802969\pi$
$824$	−2.23405e12			−0.168818
$825$	1.97523e12			0.148448
$826$	3.94855e11	+	6.83909e11i	0.0295139	+	0.0511196i
$827$	1.25294e12	+	2.17015e12i	0.0931441	+	0.161330i	0.908833	−	0.417161i	$-0.136975\pi$
$827$	1.25294e12	+	2.17015e12i	0.0931441	+	0.161330i	−0.815688	+	0.578491i	$0.803642\pi$
$828$	−9.27976e12			−0.686120
$829$	−8.75659e12			−0.643932			−0.321966	−	0.946751i	$-0.604344\pi$
$829$	−8.75659e12			−0.643932			−0.321966	+	0.946751i	$0.604344\pi$
$830$	3.45530e12	+	5.98475e12i	0.252717	+	0.437718i
$831$	−3.85353e12	+	6.67451e12i	−0.280320	+	0.485529i
$832$	−6.56424e12	−	1.13696e13i	−0.474930	−	0.822603i
$833$	4.72717e11	−	8.18770e11i	0.0340172	−	0.0589195i
$834$	−1.81982e11	+	3.15202e11i	−0.0130251	+	0.0225601i
$835$	−8.75543e12			−0.623288
$836$	−3.10051e12	+	7.38437e12i	−0.219536	+	0.522860i
$837$	−2.11895e13			−1.49230
$838$	−2.14590e12	+	3.71680e12i	−0.150318	+	0.260358i
$839$	9.20278e12	−	1.59397e13i	0.641195	−	1.11058i	−0.343971	−	0.938980i	$-0.611772\pi$
$839$	9.20278e12	−	1.59397e13i	0.641195	−	1.11058i	0.985166	−	0.171603i	$-0.0548945\pi$
$840$	2.36579e12	+	4.09767e12i	0.163953	+	0.283975i
$841$	6.45964e12	−	1.11884e13i	0.445273	−	0.771235i
$842$	−6.16124e12	−	1.06716e13i	−0.422439	−	0.731686i
$843$	2.25192e12			0.153578
$844$	9.07435e12			0.615566
$845$	−1.08300e13	−	1.87581e13i	−0.730756	−	1.26571i
$846$	8.65893e11	+	1.49977e12i	0.0581162	+	0.100660i
$847$	−2.47478e12			−0.165220
$848$	−6.12238e11			−0.0406573
$849$	−3.84649e12	−	6.66232e12i	−0.254086	−	0.440089i
$850$	2.91075e11	−	5.04156e11i	0.0191258	−	0.0331268i
$851$	−1.38291e13	−	2.39527e13i	−0.903881	−	1.56557i
$852$	2.40280e12	−	4.16176e12i	0.156221	−	0.270582i
$853$	−5.80741e12	+	1.00587e13i	−0.375588	+	0.650537i	−0.990415	−	0.138125i	$-0.955893\pi$
$853$	−5.80741e12	+	1.00587e13i	−0.375588	+	0.650537i	0.614827	+	0.788662i	$0.289226\pi$
$854$	−8.98582e12			−0.578093
$855$	5.76532e12	+	7.58901e12i	0.368957	+	0.485666i
$856$	−9.76892e12			−0.621891
$857$	−7.45617e11	+	1.29145e12i	−0.0472174	+	0.0817830i	−0.888668	−	0.458551i	$-0.848369\pi$
$857$	−7.45617e11	+	1.29145e12i	−0.0472174	+	0.0817830i	0.841451	+	0.540334i	$0.181702\pi$
$858$	3.59573e12	−	6.22798e12i	0.226513	−	0.392333i
$859$	6.80974e12	+	1.17948e13i	0.426738	+	0.739131i	0.996581	−	0.0826221i	$-0.0263294\pi$
$859$	6.80974e12	+	1.17948e13i	0.426738	+	0.739131i	−0.569843	+	0.821753i	$0.692996\pi$
$860$	3.81521e12	−	6.60814e12i	0.237835	−	0.411942i
$861$	−2.31709e12	−	4.01331e12i	−0.143691	−	0.248879i
$862$	6.47825e12			0.399646
$863$	−1.79553e13			−1.10190			−0.550951	−	0.834538i	$-0.685735\pi$
$863$	−1.79553e13			−1.10190			−0.550951	+	0.834538i	$0.685735\pi$
$864$	7.30007e12	+	1.26441e13i	0.445672	+	0.771926i
$865$	3.92717e11	+	6.80206e11i	0.0238510	+	0.0413112i
$866$	−8.01221e12			−0.484085
$867$	−8.09014e12			−0.486262
$868$	7.24277e12	+	1.25448e13i	0.433078	+	0.750113i
$869$	7.39120e12	−	1.28019e13i	0.439669	−	0.761529i
$870$	6.96885e11	+	1.20704e12i	0.0412405	+	0.0714307i
$871$	8.98008e12	−	1.55540e13i	0.528687	−	0.915713i
$872$	−5.02584e12	+	8.70501e12i	−0.294364	+	0.509853i
$873$	5.13745e12			0.299353
$874$	9.11036e12	+	1.19922e13i	0.528122	+	0.695178i
$875$	−1.51738e13			−0.875102
$876$	−4.91728e12	+	8.51698e12i	−0.282135	+	0.488671i
$877$	−8.28872e12	+	1.43565e13i	−0.473140	+	0.819502i	−0.999527	−	0.0307428i	$-0.990213\pi$
$877$	−8.28872e12	+	1.43565e13i	−0.473140	+	0.819502i	0.526388	+	0.850245i	$0.323546\pi$
$878$	3.74589e12	+	6.48808e12i	0.212731	+	0.368460i
$879$	−4.05040e10	+	7.01550e10i	−0.00228849	+	0.00396377i
$880$	2.66060e11	+	4.60830e11i	0.0149558	+	0.0259041i
$881$	2.93493e13			1.64137			0.820685	−	0.571381i	$-0.193592\pi$
$881$	2.93493e13			1.64137			0.820685	+	0.571381i	$0.193592\pi$
$882$	2.85772e12			0.159005
$883$	5.96712e12	+	1.03354e13i	0.330325	+	0.572140i	0.982576	−	0.185864i	$-0.0595083\pi$
$883$	5.96712e12	+	1.03354e13i	0.330325	+	0.572140i	−0.652250	+	0.758004i	$0.726175\pi$
$884$	1.85340e12	+	3.21019e12i	0.102079	+	0.176805i
$885$	−9.18396e11			−0.0503252
$886$	−6.50831e11			−0.0354827
$887$	−2.26672e12	−	3.92607e12i	−0.122954	−	0.212962i	0.797978	−	0.602687i	$-0.205903\pi$
$887$	−2.26672e12	−	3.92607e12i	−0.122954	−	0.212962i	−0.920931	+	0.389725i	$0.872570\pi$
$888$	−5.76569e12	+	9.98646e12i	−0.311166	+	0.538956i
$889$	−9.88005e11	−	1.71128e12i	−0.0530519	−	0.0918887i
$890$	4.25395e12	−	7.36806e12i	0.227268	−	0.393639i
$891$	2.51642e12	−	4.35857e12i	0.133762	−	0.231683i
$892$	8.82583e12			0.466781
$893$	−1.90290e12	+	4.53208e12i	−0.100135	+	0.238487i
$894$	−8.53329e12			−0.446784
$895$	1.08265e13	−	1.87520e13i	0.564007	−	0.976888i
$896$	5.18218e12	−	8.97579e12i	0.268613	−	0.465251i
$897$	1.18253e13	+	2.04821e13i	0.609884	+	1.05635i
$898$	5.25336e11	−	9.09909e11i	0.0269584	−	0.0466933i
$899$	5.48686e12	+	9.50352e12i	0.280159	+	0.485250i
$900$	−3.07744e12			−0.156350
$901$	−3.77232e12			−0.190698
$902$	3.78368e12	+	6.55353e12i	0.190320	+	0.329644i
$903$	−3.70319e12	−	6.41411e12i	−0.185345	−	0.321027i
$904$	−2.06015e13			−1.02598
$905$	2.29465e12			0.113710
$906$	1.54264e11	+	2.67193e11i	0.00760655	+	0.0131749i
$907$	7.86445e12	−	1.36216e13i	0.385865	−	0.668338i	−0.606024	−	0.795446i	$-0.707236\pi$
$907$	7.86445e12	−	1.36216e13i	0.385865	−	0.668338i	0.991889	+	0.127109i	$0.0405697\pi$
$908$	−1.10589e13	−	1.91546e13i	−0.539917	−	0.935163i
$909$	−7.84014e12	+	1.35795e13i	−0.380878	+	0.659701i
$910$	−6.85128e12	+	1.18668e13i	−0.331196	+	0.573648i
$911$	−2.24271e13			−1.07880			−0.539398	−	0.842051i	$-0.681348\pi$
$911$	−2.24271e13			−1.07880			−0.539398	+	0.842051i	$0.681348\pi$
$912$	−1.67410e11	+	3.98715e11i	−0.00801319	+	0.0190847i
$913$	1.91563e13			0.912414
$914$	−7.61439e10	+	1.31885e11i	−0.00360892	+	0.00625083i
$915$	5.22505e12	−	9.05006e12i	0.246431	−	0.426831i
$916$	2.13424e12	+	3.69662e12i	0.100165	+	0.173490i
$917$	−8.93882e12	+	1.54825e13i	−0.417463	+	0.723067i
$918$	1.09936e12	+	1.90415e12i	0.0510915	+	0.0884931i
$919$	2.94625e13			1.36254			0.681270	−	0.732032i	$-0.261428\pi$
$919$	2.94625e13			1.36254			0.681270	+	0.732032i	$0.261428\pi$
$920$	2.54100e13			1.16939
$921$	−4.18849e12	−	7.25468e12i	−0.191818	−	0.332238i
$922$	5.14445e12	+	8.91044e12i	0.234450	+	0.406079i
$923$	3.57912e13			1.62319
$924$	5.09996e12			0.230167
$925$	−4.58613e12	−	7.94341e12i	−0.205972	−	0.356754i
$926$	3.37502e12	−	5.84571e12i	0.150844	−	0.261269i
$927$	1.43275e12	+	2.48160e12i	0.0637253	+	0.110376i
$928$	3.78059e12	−	6.54818e12i	0.167338	−	0.289838i
$929$	1.33285e13	−	2.30856e13i	0.587097	−	1.01688i	−0.407513	−	0.913199i	$-0.633604\pi$
$929$	1.33285e13	−	2.30856e13i	0.587097	−	1.01688i	0.994610	−	0.103683i	$-0.0330626\pi$
$930$	9.63232e12			0.422238
$931$	4.90665e12	+	6.45872e12i	0.214048	+	0.281756i
$932$	1.91117e13			0.829714
$933$	−1.67765e12	+	2.90578e12i	−0.0724827	+	0.125544i
$934$	3.85746e11	−	6.68131e11i	0.0165859	−	0.0287277i
$935$	1.63934e12	+	2.83942e12i	0.0701482	+	0.121500i
$936$	−1.44077e13	+	2.49548e13i	−0.613553	+	1.06270i
$937$	−2.47205e12	−	4.28172e12i	−0.104768	−	0.181464i	0.808875	−	0.587980i	$-0.200077\pi$
$937$	−2.47205e12	−	4.28172e12i	−0.104768	−	0.181464i	−0.913643	+	0.406516i	$0.866743\pi$
$938$	−7.28274e12			−0.307172
$939$	4.95655e12			0.208058
$940$	1.61237e12	+	2.79270e12i	0.0673579	+	0.116667i
$941$	−9.26449e11	−	1.60466e12i	−0.0385184	−	0.0667158i	0.846124	−	0.532987i	$-0.178930\pi$
$941$	−9.26449e11	−	1.60466e12i	−0.0385184	−	0.0667158i	−0.884642	+	0.466271i	$0.845597\pi$
$942$	−6.04117e12			−0.249972
$943$	−2.48869e13			−1.02487
$944$	6.08870e10	+	1.05459e11i	0.00249546	+	0.00432226i
$945$	7.10736e12	−	1.23103e13i	0.289911	−	0.502141i
$946$	6.04711e12	+	1.04739e13i	0.245492	+	0.425205i
$947$	−7.05670e12	+	1.22226e13i	−0.285119	+	0.493841i	−0.972638	−	0.232326i	$-0.925367\pi$
$947$	−7.05670e12	+	1.22226e13i	−0.285119	+	0.493841i	0.687519	+	0.726167i	$0.258700\pi$
$948$	3.94061e12	−	6.82534e12i	0.158462	−	0.274465i
$949$	−7.32461e13			−2.93148
$950$	3.02126e12	+	3.97695e12i	0.120346	+	0.158414i
$951$	−1.88715e13			−0.748160
$952$	1.93281e12	−	3.34773e12i	0.0762646	−	0.132094i
$953$	−1.22295e13	+	2.11821e13i	−0.480275	+	0.831861i	−0.999744	−	0.0226283i	$-0.992797\pi$
$953$	−1.22295e13	+	2.11821e13i	−0.480275	+	0.831861i	0.519469	+	0.854490i	$0.326130\pi$
$954$	−5.70120e12	−	9.87477e12i	−0.222843	−	0.385975i
$955$	1.60101e13	−	2.77302e13i	0.622842	−	1.07879i
$956$	−1.18869e13	−	2.05888e13i	−0.460267	−	0.797205i
$957$	3.86355e12			0.148896
$958$	−1.87386e13			−0.718772
$959$	−1.30770e12	−	2.26500e12i	−0.0499257	−	0.0864738i
$960$	−3.09551e12	−	5.36157e12i	−0.117628	−	0.203738i
$961$	4.93996e13			1.86839
$962$	−3.33946e13			−1.25715
$963$	6.26506e12	+	1.08514e13i	0.234751	+	0.406600i
$964$	−1.15684e13	+	2.00370e13i	−0.431445	+	0.747284i
$965$	9.13119e12	+	1.58157e13i	0.338965	+	0.587104i
$966$	4.79509e12	−	8.30535e12i	0.177174	−	0.306874i
$967$	−1.12890e13	+	1.95531e13i	−0.415180	+	0.719112i	−0.995447	−	0.0953137i	$-0.969615\pi$
$967$	−1.12890e13	+	1.95531e13i	−0.415180	+	0.719112i	0.580268	+	0.814426i	$0.302948\pi$
$968$	5.54105e12			0.202840
$969$	−1.03150e12	+	2.45669e12i	−0.0375849	+	0.0895145i
$970$	−5.46992e12			−0.198385
$971$	1.48353e13	−	2.56955e13i	0.535561	−	0.927619i	−0.463575	−	0.886058i	$-0.653433\pi$
$971$	1.48353e13	−	2.56955e13i	0.535561	−	0.927619i	0.999136	−	0.0415616i	$-0.0132333\pi$
$972$	9.14194e12	−	1.58343e13i	0.328504	−	0.568985i
$973$	−9.61188e11	−	1.66483e12i	−0.0343796	−	0.0595472i
$974$	1.01607e13	−	1.75989e13i	0.361750	−	0.626570i
$975$	3.92162e12	+	6.79244e12i	0.138978	+	0.240716i
$976$	−1.38562e12			−0.0488788
$977$	−6.62018e12			−0.232458			−0.116229	−	0.993222i	$-0.537081\pi$
$977$	−6.62018e12			−0.232458			−0.116229	+	0.993222i	$0.537081\pi$
$978$	−5.50771e12	−	9.53964e12i	−0.192507	−	0.333432i
$979$	−1.17920e13	−	2.04244e13i	−0.410267	−	0.710602i
$980$	5.32132e12			0.184290
$981$	1.28928e13			0.444464
$982$	4.00339e12	+	6.93407e12i	0.137381	+	0.237950i
$983$	2.45411e13	−	4.25065e13i	0.838308	−	1.45199i	−0.0530009	−	0.998594i	$-0.516879\pi$
$983$	2.45411e13	−	4.25065e13i	0.838308	−	1.45199i	0.891309	−	0.453397i	$-0.149788\pi$
$984$	5.18797e12	+	8.98583e12i	0.176409	+	0.305549i
$985$	−2.34598e13	+	4.06336e13i	−0.794075	+	1.37538i
$986$	5.69342e11	−	9.86130e11i	0.0191835	−	0.0332268i
$987$	3.13005e12			0.104984
$988$	−3.15492e13	+	3.99885e12i	−1.05337	+	0.133515i
$989$	−3.97745e13			−1.32197
$990$	−4.95515e12	+	8.58257e12i	−0.163945	+	0.283961i
$991$	−2.60638e13	+	4.51438e13i	−0.858432	+	1.48685i	0.0149919	+	0.999888i	$0.495228\pi$
$991$	−2.60638e13	+	4.51438e13i	−0.858432	+	1.48685i	−0.873424	+	0.486960i	$0.838106\pi$
$992$	−2.61276e13	−	4.52544e13i	−0.856638	−	1.48374i
$993$	−9.68665e12	+	1.67778e13i	−0.316156	+	0.547599i
$994$	−7.25656e12	−	1.25687e13i	−0.235772	−	0.408369i
$995$	−3.89141e13			−1.25864
$996$	1.02131e13			0.328846
$997$	3.37464e12	+	5.84504e12i	0.108168	+	0.187353i	0.915028	−	0.403390i	$-0.132168\pi$
$997$	3.37464e12	+	5.84504e12i	0.108168	+	0.187353i	−0.806860	+	0.590743i	$0.798835\pi$
$998$	−1.06645e13	−	1.84715e13i	−0.340293	−	0.589405i
$999$	3.46428e13			1.10045

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.10.c.a.11.5	yes	28
19.7	even	3	inner	19.10.c.a.7.5	✓	28
19.8	odd	6		361.10.a.f.1.5		14
19.11	even	3		361.10.a.e.1.10		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.10.c.a.7.5	✓	28	19.7	even	3	inner
19.10.c.a.11.5	yes	28	1.1	even	1	trivial
361.10.a.e.1.10		14	19.11	even	3
361.10.a.f.1.5		14	19.8	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	19.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.82378 + 11.8191i) q^{2} +(-35.4198 + 61.3488i) q^{3} +(162.872 + 282.103i) q^{4} +(-572.036 + 990.795i) q^{5} +(-483.393 - 837.262i) q^{6} +5106.36 q^{7} -11433.2 q^{8} +(7332.38 + 12700.1i) q^{9} +(-7806.89 - 13521.9i) q^{10} -43281.6 q^{11} -23075.6 q^{12} +(-85931.4 - 148838. i) q^{13} +(-34844.7 + 60352.7i) q^{14} +(-40522.8 - 70187.5i) q^{15} +(-5373.08 + 9306.45i) q^{16} +(-33106.4 + 57341.9i) q^{17} -200138. q^{18} +(-343633. - 452332. i) q^{19} -372675. q^{20} +(-180866. + 313269. i) q^{21} +(295344. - 511552. i) q^{22} +(971304. + 1.68235e6i) q^{23} +(404960. - 701411. i) q^{24} +(322113. + 557915. i) q^{25} +2.34551e6 q^{26} -2.43318e6 q^{27} +(831683. + 1.44052e6i) q^{28} +(630053. + 1.09128e6i) q^{29} +1.10607e6 q^{30} +8.70857e6 q^{31} +(-3.00022e6 - 5.19653e6i) q^{32} +(1.53303e6 - 2.65528e6i) q^{33} +(-451821. - 782577. i) q^{34} +(-2.92102e6 + 5.05935e6i) q^{35} +(-2.38848e6 + 4.13697e6i) q^{36} -1.42377e7 q^{37} +(7.69105e6 - 974836. i) q^{38} +1.21747e7 q^{39} +(6.54018e6 - 1.13279e7i) q^{40} +(-6.40554e6 + 1.10947e7i) q^{41} +(-2.46838e6 - 4.27536e6i) q^{42} +(-1.02374e7 + 1.77317e7i) q^{43} +(-7.04937e6 - 1.22099e7i) q^{44} -1.67775e7 q^{45} -2.65119e7 q^{46} +(-4.32647e6 - 7.49367e6i) q^{47} +(-380627. - 659265. i) q^{48} -1.42787e7 q^{49} -8.79210e6 q^{50} +(-2.34524e6 - 4.06208e6i) q^{51} +(2.79917e7 - 4.84830e7i) q^{52} +(2.84863e7 + 4.93398e7i) q^{53} +(1.66035e7 - 2.87581e7i) q^{54} +(2.47586e7 - 4.28832e7i) q^{55} -5.83818e7 q^{56} +(3.99214e7 - 5.06002e6i) q^{57} -1.71974e7 q^{58} +(5.66593e6 - 9.81368e6i) q^{59} +(1.32000e7 - 2.28632e7i) q^{60} +(6.44706e7 + 1.11666e8i) q^{61} +(-5.94254e7 + 1.02928e8i) q^{62} +(3.74417e7 + 6.48510e7i) q^{63} +7.63893e7 q^{64} +1.96623e8 q^{65} +(2.09221e7 + 3.62381e7i) q^{66} +(5.22515e7 + 9.05022e7i) q^{67} -2.15684e7 q^{68} -1.37613e8 q^{69} +(-3.98648e7 - 6.90478e7i) q^{70} +(-1.04127e8 + 1.80354e8i) q^{71} +(-8.38323e7 - 1.45202e8i) q^{72} +(2.13095e8 - 3.69091e8i) q^{73} +(9.71547e7 - 1.68277e8i) q^{74} -4.56366e7 q^{75} +(7.16357e7 - 1.70612e8i) q^{76} -2.21012e8 q^{77} +(-8.30774e7 + 1.43894e8i) q^{78} +(-1.70770e8 + 2.95782e8i) q^{79} +(-6.14719e6 - 1.06472e7i) q^{80} +(-5.81406e7 + 1.00702e8i) q^{81} +(-8.74200e7 - 1.51416e8i) q^{82} -4.42595e8 q^{83} -1.17832e8 q^{84} +(-3.78761e7 - 6.56033e7i) q^{85} +(-1.39715e8 - 2.41994e8i) q^{86} -8.92653e7 q^{87} +4.94846e8 q^{88} +(2.72449e8 + 4.71895e8i) q^{89} +(1.14486e8 - 1.98296e8i) q^{90} +(-4.38796e8 - 7.60018e8i) q^{91} +(-3.16397e8 + 5.48015e8i) q^{92} +(-3.08456e8 + 5.34261e8i) q^{93} +1.18092e8 q^{94} +(6.44738e8 - 8.17202e7i) q^{95} +4.25068e8 q^{96} +(1.75163e8 - 3.03391e8i) q^{97} +(9.74349e7 - 1.68762e8i) q^{98} +(-3.17357e8 - 5.49679e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 15 q^{2} - 74 q^{3} - 2987 q^{4} - 285 q^{5} - 535 q^{6} - 2676 q^{7} - 24270 q^{8} - 57928 q^{9} + 41180 q^{10} - 114810 q^{11} + 235458 q^{12} + 98671 q^{13} - 148290 q^{14} + 428251 q^{15} - 279203 q^{16}+ \cdots - 736622698 q^{99}+O(q^{100}) \) 28 * q + 15 * q^2 - 74 * q^3 - 2987 * q^4 - 285 * q^5 - 535 * q^6 - 2676 * q^7 - 24270 * q^8 - 57928 * q^9 + 41180 * q^10 - 114810 * q^11 + 235458 * q^12 + 98671 * q^13 - 148290 * q^14 + 428251 * q^15 - 279203 * q^16 + 466251 * q^17 + 734964 * q^18 + 387157 * q^19 - 3343620 * q^20 + 689090 * q^21 - 1689395 * q^22 - 3087747 * q^23 - 234183 * q^24 - 3260823 * q^25 + 9033144 * q^26 + 4216540 * q^27 - 703814 * q^28 + 7831383 * q^29 - 11859224 * q^30 - 9265632 * q^31 + 11470815 * q^32 + 22791973 * q^33 + 13457096 * q^34 - 13222428 * q^35 + 7355018 * q^36 + 27205020 * q^37 - 67677738 * q^38 - 20775702 * q^39 - 16500258 * q^40 + 20419440 * q^41 - 10220798 * q^42 + 27415427 * q^43 + 41775405 * q^44 - 85982588 * q^45 - 137234708 * q^46 - 90906681 * q^47 + 33057375 * q^48 + 229824892 * q^49 + 44406714 * q^50 + 134429123 * q^51 + 66195006 * q^52 + 47827863 * q^53 - 130507669 * q^54 - 157712310 * q^55 + 382459116 * q^56 - 162912873 * q^57 - 344026048 * q^58 + 255540 * q^59 + 287916794 * q^60 + 304035459 * q^61 + 693626280 * q^62 - 122148024 * q^63 - 908491514 * q^64 - 1424960190 * q^65 - 611099417 * q^66 + 165758480 * q^67 + 357518508 * q^68 + 271237278 * q^69 + 1167527028 * q^70 + 685508589 * q^71 + 142349670 * q^72 - 602867050 * q^73 - 82104492 * q^74 + 1900274774 * q^75 - 1298297525 * q^76 - 491994756 * q^77 - 911449840 * q^78 + 78162339 * q^79 + 227607150 * q^80 + 1230916118 * q^81 + 360208019 * q^82 + 413839926 * q^83 - 467304924 * q^84 - 1440537237 * q^85 + 936824310 * q^86 - 678876318 * q^87 - 1646777694 * q^88 + 1256827551 * q^89 + 1879090924 * q^90 + 537759588 * q^91 - 677003592 * q^92 - 492493440 * q^93 - 848375184 * q^94 - 2034458607 * q^95 - 6041588930 * q^96 + 2109813492 * q^97 + 2689941591 * q^98 - 736622698 * q^99

Introduction

L-functions

Modular forms

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Database

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