LMFDB - Embedded newform 19.10.c.a.7.14

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			7.14
Character	$\chi$	$=$	19.7
Dual form			19.10.c.a.11.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(20.1948 + 34.9785i) q^{2} +(-65.0904 - 112.740i) q^{3} +(-559.662 + 969.363i) q^{4} +(886.813 + 1536.00i) q^{5} +(2628.98 - 4553.53i) q^{6} -9612.95 q^{7} -24529.6 q^{8} +(1367.97 - 2369.40i) q^{9} +(-35818.1 + 62038.7i) q^{10} -50797.0 q^{11} +145715. q^{12} +(10711.5 - 18552.8i) q^{13} +(-194132. - 336246. i) q^{14} +(115446. - 199958. i) q^{15} +(-208824. - 361694. i) q^{16} +(232247. + 402264. i) q^{17} +110504. q^{18} +(51766.0 + 565692. i) q^{19} -1.98526e6 q^{20} +(625711. + 1.08376e6i) q^{21} +(-1.02584e6 - 1.77680e6i) q^{22} +(-53546.5 + 92745.2i) q^{23} +(1.59664e6 + 2.76547e6i) q^{24} +(-596311. + 1.03284e6i) q^{25} +865267. q^{26} -2.91852e6 q^{27} +(5.38000e6 - 9.31844e6i) q^{28} +(-2.23926e6 + 3.87851e6i) q^{29} +9.32565e6 q^{30} +8.18175e6 q^{31} +(2.15476e6 - 3.73215e6i) q^{32} +(3.30640e6 + 5.72685e6i) q^{33} +(-9.38039e6 + 1.62473e7i) q^{34} +(-8.52489e6 - 1.47655e7i) q^{35} +(1.53120e6 + 2.65212e6i) q^{36} +1.82843e7 q^{37} +(-1.87416e7 + 1.32348e7i) q^{38} -2.78886e6 q^{39} +(-2.17532e7 - 3.76776e7i) q^{40} +(-1.30188e6 - 2.25491e6i) q^{41} +(-2.52722e7 + 4.37728e7i) q^{42} +(-5.31678e6 - 9.20894e6i) q^{43} +(2.84291e7 - 4.92407e7i) q^{44} +4.85254e6 q^{45} -4.32545e6 q^{46} +(-2.72958e7 + 4.72776e7i) q^{47} +(-2.71849e7 + 4.70857e7i) q^{48} +5.20552e7 q^{49} -4.81696e7 q^{50} +(3.02342e7 - 5.23671e7i) q^{51} +(1.19896e7 + 2.07666e7i) q^{52} +(9.49201e6 - 1.64406e7i) q^{53} +(-5.89390e7 - 1.02085e8i) q^{54} +(-4.50474e7 - 7.80244e7i) q^{55} +2.35802e8 q^{56} +(6.04067e7 - 4.26573e7i) q^{57} -1.80886e8 q^{58} +(-2.18524e7 - 3.78494e7i) q^{59} +(1.29222e8 + 2.23818e8i) q^{60} +(9.96836e6 - 1.72657e7i) q^{61} +(1.65229e8 + 2.86185e8i) q^{62} +(-1.31503e7 + 2.27769e7i) q^{63} -3.97761e7 q^{64} +3.79963e7 q^{65} +(-1.33544e8 + 2.31305e8i) q^{66} +(4.48849e7 - 7.77429e7i) q^{67} -5.19920e8 q^{68} +1.39415e7 q^{69} +(3.44317e8 - 5.96375e8i) q^{70} +(1.37746e7 + 2.38584e7i) q^{71} +(-3.35558e7 + 5.81204e7i) q^{72} +(-1.41458e8 - 2.45013e8i) q^{73} +(3.69248e8 + 6.39557e8i) q^{74} +1.55257e8 q^{75} +(-5.77333e8 - 2.66417e8i) q^{76} +4.88309e8 q^{77} +(-5.63206e7 - 9.75501e7i) q^{78} +(4.77492e6 + 8.27041e6i) q^{79} +(3.70376e8 - 6.41510e8i) q^{80} +(1.63042e8 + 2.82397e8i) q^{81} +(5.25823e7 - 9.10752e7i) q^{82} -6.70013e8 q^{83} -1.40075e9 q^{84} +(-4.11920e8 + 7.13466e8i) q^{85} +(2.14743e8 - 3.71946e8i) q^{86} +5.83017e8 q^{87} +1.24603e9 q^{88} +(2.72155e8 - 4.71386e8i) q^{89} +(9.79963e7 + 1.69734e8i) q^{90} +(-1.02969e8 + 1.78348e8i) q^{91} +(-5.99359e7 - 1.03812e8i) q^{92} +(-5.32553e8 - 9.22410e8i) q^{93} -2.20493e9 q^{94} +(-8.23000e8 + 5.81176e8i) q^{95} -5.61017e8 q^{96} +(5.17944e8 + 8.97106e8i) q^{97} +(1.05125e9 + 1.82081e9i) q^{98} +(-6.94889e7 + 1.20358e8i) 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 $\left(\mathbb{Z}/19\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	20.1948	+	34.9785i	0.892494	+	1.54584i	0.836876	+	0.547392i	$0.184379\pi$
$2$	20.1948	+	34.9785i	0.892494	+	1.54584i	0.0556175	+	0.998452i	$0.482287\pi$
$3$	−65.0904	−	112.740i	−0.463950	−	0.803586i	0.535203	−	0.844723i	$-0.320235\pi$
$3$	−65.0904	−	112.740i	−0.463950	−	0.803586i	−0.999153	+	0.0411379i	$0.986902\pi$
$4$	−559.662	+	969.363i	−1.09309	+	1.89329i
$5$	886.813	+	1536.00i	0.634552	+	1.09908i	0.986610	+	0.163097i	$0.0521485\pi$
$5$	886.813	+	1536.00i	0.634552	+	1.09908i	−0.352058	+	0.935978i	$0.614518\pi$
$6$	2628.98	−	4553.53i	0.828145	−	1.43439i
$7$	−9612.95			−1.51327			−0.756633	−	0.653839i	$-0.773157\pi$
$7$	−9612.95			−1.51327			−0.756633	+	0.653839i	$0.773157\pi$
$8$	−24529.6			−2.11732
$9$	1367.97	−	2369.40i	0.0695002	−	0.120378i
$10$	−35818.1	+	62038.7i	−1.13267	+	1.96184i
$11$	−50797.0			−1.04609			−0.523047	−	0.852304i	$-0.675205\pi$
$11$	−50797.0			−1.04609			−0.523047	+	0.852304i	$0.675205\pi$
$12$	145715.			2.02856
$13$	10711.5	−	18552.8i	0.104017	−	0.180163i	−0.809319	−	0.587369i	$-0.800164\pi$
$13$	10711.5	−	18552.8i	0.104017	−	0.180163i	0.913336	+	0.407206i	$0.133497\pi$
$14$	−194132.	−	336246.i	−1.35058	−	2.33927i
$15$	115446.	−	199958.i	0.588801	−	1.01983i
$16$	−208824.	−	361694.i	−0.796601	−	1.37975i
$17$	232247.	+	402264.i	0.674421	+	1.16813i	0.976638	+	0.214892i	$0.0689398\pi$
$17$	232247.	+	402264.i	0.674421	+	1.16813i	−0.302217	+	0.953239i	$0.597727\pi$
$18$	110504.			0.248114
$19$	51766.0	+	565692.i	0.0911284	+	0.995839i
$19$	51766.0	+	565692.i	0.0911284	+	0.995839i
$20$	−1.98526e6			−2.77449
$21$	625711.	+	1.08376e6i	0.702081	+	1.21604i
$22$	−1.02584e6	−	1.77680e6i	−0.933632	−	1.61710i
$23$	−53546.5	+	92745.2i	−0.0398984	+	0.0691061i	−0.885285	−	0.465049i	$-0.846037\pi$
$23$	−53546.5	+	92745.2i	−0.0398984	+	0.0691061i	0.845387	+	0.534155i	$0.179370\pi$
$24$	1.59664e6	+	2.76547e6i	0.982329	+	1.70144i
$25$	−596311.	+	1.03284e6i	−0.305311	+	0.528815i
$26$	865267.			0.371338
$27$	−2.91852e6			−1.05688
$28$	5.38000e6	−	9.31844e6i	1.65414	−	2.86505i
$29$	−2.23926e6	+	3.87851e6i	−0.587913	+	1.01830i	0.406592	+	0.913610i	$0.366717\pi$
$29$	−2.23926e6	+	3.87851e6i	−0.587913	+	1.01830i	−0.994505	+	0.104686i	$0.966616\pi$
$30$	9.32565e6			2.10200
$31$	8.18175e6			1.59118			0.795588	−	0.605838i	$-0.207162\pi$
$31$	8.18175e6			1.59118			0.795588	+	0.605838i	$0.207162\pi$
$32$	2.15476e6	−	3.73215e6i	0.363265	−	0.629194i
$33$	3.30640e6	+	5.72685e6i	0.485336	+	0.840626i
$34$	−9.38039e6	+	1.62473e7i	−1.20383	+	2.08510i
$35$	−8.52489e6	−	1.47655e7i	−0.960246	−	1.66319i
$36$	1.53120e6	+	2.65212e6i	0.151940	+	0.263168i
$37$	1.82843e7			1.60388			0.801938	−	0.597408i	$-0.203803\pi$
$37$	1.82843e7			1.60388			0.801938	+	0.597408i	$0.203803\pi$
$38$	−1.87416e7	+	1.32348e7i	−1.45808	+	1.02965i
$39$	−2.78886e6			−0.193035
$40$	−2.17532e7	−	3.76776e7i	−1.34355	−	2.32709i
$41$	−1.30188e6	−	2.25491e6i	−0.0719519	−	0.124624i	0.827805	−	0.561016i	$-0.189589\pi$
$41$	−1.30188e6	−	2.25491e6i	−0.0719519	−	0.124624i	−0.899757	+	0.436392i	$0.856256\pi$
$42$	−2.52722e7	+	4.37728e7i	−1.25320	+	2.17061i
$43$	−5.31678e6	−	9.20894e6i	−0.237160	−	0.410773i	0.722738	−	0.691122i	$-0.242883\pi$
$43$	−5.31678e6	−	9.20894e6i	−0.237160	−	0.410773i	−0.959898	+	0.280349i	$0.909550\pi$
$44$	2.84291e7	−	4.92407e7i	1.14348	−	1.98056i
$45$	4.85254e6			0.176406
$46$	−4.32545e6			−0.142436
$47$	−2.72958e7	+	4.72776e7i	−0.815934	+	1.41324i	0.0927218	+	0.995692i	$0.470443\pi$
$47$	−2.72958e7	+	4.72776e7i	−0.815934	+	1.41324i	−0.908655	+	0.417547i	$0.862890\pi$
$48$	−2.71849e7	+	4.70857e7i	−0.739167	+	1.28027i
$49$	5.20552e7			1.28998
$50$	−4.81696e7			−1.08995
$51$	3.02342e7	−	5.23671e7i	0.625795	−	1.08391i
$52$	1.19896e7	+	2.07666e7i	0.227400	+	0.393868i
$53$	9.49201e6	−	1.64406e7i	0.165241	−	0.286205i	−0.771500	−	0.636229i	$-0.780493\pi$
$53$	9.49201e6	−	1.64406e7i	0.165241	−	0.286205i	0.936741	+	0.350024i	$0.113827\pi$
$54$	−5.89390e7	−	1.02085e8i	−0.943258	−	1.63377i
$55$	−4.50474e7	−	7.80244e7i	−0.663801	−	1.14974i
$56$	2.35802e8			3.20406
$57$	6.04067e7	−	4.26573e7i	0.757963	−	0.535249i
$58$	−1.80886e8			−2.09884
$59$	−2.18524e7	−	3.78494e7i	−0.234782	−	0.406654i	0.724427	−	0.689351i	$-0.242104\pi$
$59$	−2.18524e7	−	3.78494e7i	−0.234782	−	0.406654i	−0.959209	+	0.282697i	$0.908771\pi$
$60$	1.29222e8	+	2.23818e8i	1.28722	+	2.22954i
$61$	9.96836e6	−	1.72657e7i	0.0921806	−	0.159661i	−0.816248	−	0.577702i	$-0.803950\pi$
$61$	9.96836e6	−	1.72657e7i	0.0921806	−	0.159661i	0.908428	+	0.418040i	$0.137283\pi$
$62$	1.65229e8	+	2.86185e8i	1.42012	+	2.45971i
$63$	−1.31503e7	+	2.27769e7i	−0.105172	+	0.182164i
$64$	−3.97761e7			−0.296355
$65$	3.79963e7			0.264017
$66$	−1.33544e8	+	2.31305e8i	−0.866318	+	1.50051i
$67$	4.48849e7	−	7.77429e7i	0.272122	−	0.471329i	−0.697283	−	0.716796i	$-0.745608\pi$
$67$	4.48849e7	−	7.77429e7i	0.272122	−	0.471329i	0.969405	+	0.245467i	$0.0789413\pi$
$68$	−5.19920e8			−2.94881
$69$	1.39415e7			0.0740436
$70$	3.44317e8	−	5.96375e8i	1.71403	−	2.96878i
$71$	1.37746e7	+	2.38584e7i	0.0643306	+	0.111424i	0.896397	−	0.443252i	$-0.146175\pi$
$71$	1.37746e7	+	2.38584e7i	0.0643306	+	0.111424i	−0.832066	+	0.554676i	$0.812842\pi$
$72$	−3.35558e7	+	5.81204e7i	−0.147154	+	0.254878i
$73$	−1.41458e8	−	2.45013e8i	−0.583009	−	1.00980i	−0.995120	−	0.0986683i	$-0.968542\pi$
$73$	−1.41458e8	−	2.45013e8i	−0.583009	−	1.00980i	0.412111	−	0.911134i	$-0.364792\pi$
$74$	3.69248e8	+	6.39557e8i	1.43145	+	2.47934i
$75$	1.55257e8			0.566597
$76$	−5.77333e8	−	2.66417e8i	−1.98502	−	0.916010i
$77$	4.88309e8			1.58302
$78$	−5.63206e7	−	9.75501e7i	−0.172283	−	0.298402i
$79$	4.77492e6	+	8.27041e6i	0.0137925	+	0.0238894i	0.872839	−	0.488008i	$-0.162276\pi$
$79$	4.77492e6	+	8.27041e6i	0.0137925	+	0.0238894i	−0.859047	+	0.511897i	$0.828943\pi$
$80$	3.70376e8	−	6.41510e8i	1.01097	−	1.75105i
$81$	1.63042e8	+	2.82397e8i	0.420839	+	0.728915i
$82$	5.25823e7	−	9.10752e7i	0.128433	−	0.222453i
$83$	−6.70013e8			−1.54964			−0.774821	−	0.632180i	$-0.782160\pi$
$83$	−6.70013e8			−1.54964			−0.774821	+	0.632180i	$0.782160\pi$
$84$	−1.40075e9			−3.06975
$85$	−4.11920e8	+	7.13466e8i	−0.855909	+	1.48248i
$86$	2.14743e8	−	3.71946e8i	0.423327	−	0.733224i
$87$	5.83017e8			1.09105
$88$	1.24603e9			2.21491
$89$	2.72155e8	−	4.71386e8i	0.459791	−	0.796382i	−0.539158	−	0.842204i	$-0.681258\pi$
$89$	2.72155e8	−	4.71386e8i	0.459791	−	0.796382i	0.998950	+	0.0458226i	$0.0145909\pi$
$90$	9.79963e7	+	1.69734e8i	0.157441	+	0.272696i
$91$	−1.02969e8	+	1.78348e8i	−0.157406	+	0.272635i
$92$	−5.99359e7	−	1.03812e8i	−0.0872251	−	0.151078i
$93$	−5.32553e8	−	9.22410e8i	−0.738227	−	1.27865i
$94$	−2.20493e9			−2.91286
$95$	−8.23000e8	+	5.81176e8i	−1.03668	+	0.732068i
$96$	−5.61017e8			−0.674148
$97$	5.17944e8	+	8.97106e8i	0.594033	+	1.02889i	0.993683	+	0.112227i	$0.0357983\pi$
$97$	5.17944e8	+	8.97106e8i	0.594033	+	1.02889i	−0.399650	+	0.916668i	$0.630868\pi$
$98$	1.05125e9	+	1.82081e9i	1.15130	+	1.99410i
$99$	−6.94889e7	+	1.20358e8i	−0.0727038	+	0.125927i
$100$	−6.67465e8	−	1.15608e9i	−0.667465	−	1.15608i
$101$	1.18708e8	−	2.05608e8i	0.113510	−	0.196605i	−0.803673	−	0.595071i	$-0.797124\pi$
$101$	1.18708e8	−	2.05608e8i	0.113510	−	0.196605i	0.917183	+	0.398466i	$0.130457\pi$
$102$	2.44230e9			2.23407
$103$	1.52038e9			1.33102			0.665509	−	0.746389i	$-0.268214\pi$
$103$	1.52038e9			1.33102			0.665509	+	0.746389i	$0.268214\pi$
$104$	−2.62749e8	+	4.55094e8i	−0.220237	+	0.381462i
$105$	−1.10978e9	+	1.92219e9i	−0.891013	+	1.54328i
$106$	7.66758e8			0.589905
$107$	8.05083e8			0.593764			0.296882	−	0.954914i	$-0.404053\pi$
$107$	8.05083e8			0.593764			0.296882	+	0.954914i	$0.404053\pi$
$108$	1.63338e9	−	2.82910e9i	1.15526	−	2.00098i
$109$	7.73779e8	+	1.34022e9i	0.525046	+	0.909407i	0.999575	+	0.0291667i	$0.00928537\pi$
$109$	7.73779e8	+	1.34022e9i	0.525046	+	0.909407i	−0.474528	+	0.880240i	$0.657381\pi$
$110$	1.81945e9	−	3.15138e9i	1.18488	−	2.05226i
$111$	−1.19013e9	−	2.06137e9i	−0.744118	−	1.28885i
$112$	2.00742e9	+	3.47695e9i	1.20547	+	2.08794i
$113$	−2.08633e9			−1.20373			−0.601865	−	0.798598i	$-0.705576\pi$
$113$	−2.08633e9			−1.20373			−0.601865	+	0.798598i	$0.705576\pi$
$114$	2.71199e9	+	1.25148e9i	1.50389	+	0.693986i
$115$	−1.89943e8			−0.101270
$116$	−2.50646e9	−	4.34131e9i	−1.28528	−	2.22618i
$117$	−2.93061e7	−	5.07596e7i	−0.0144584	−	0.0250427i
$118$	8.82609e8	−	1.52872e9i	0.419083	−	0.725872i
$119$	−2.23258e9	−	3.86695e9i	−1.02058	−	1.76769i
$120$	−2.83185e9	+	4.90490e9i	−1.24668	+	2.15931i
$121$	2.22385e8			0.0943131
$122$	8.05237e8			0.329082
$123$	−1.69479e8	+	2.93547e8i	−0.0667642	+	0.115639i
$124$	−4.57901e9	+	7.93108e9i	−1.73930	+	3.01255i
$125$	1.34885e9			0.494160
$126$	−1.06227e9			−0.375463
$127$	−2.18891e9	+	3.79130e9i	−0.746640	+	1.29322i	0.202785	+	0.979223i	$0.435001\pi$
$127$	−2.18891e9	+	3.79130e9i	−0.746640	+	1.29322i	−0.949425	+	0.313995i	$0.898333\pi$
$128$	−1.90651e9	−	3.30217e9i	−0.627760	−	1.08731i
$129$	−6.92144e8	+	1.19883e9i	−0.220061	+	0.381156i
$130$	7.67329e8	+	1.32905e9i	0.235633	+	0.408129i
$131$	2.82212e9	+	4.88805e9i	0.837249	+	1.45016i	0.892186	+	0.451667i	$0.149171\pi$
$131$	2.82212e9	+	4.88805e9i	0.837249	+	1.45016i	−0.0549378	+	0.998490i	$0.517496\pi$
$132$	−7.40186e9			−2.12206
$133$	−4.97624e8	−	5.43797e9i	−0.137902	−	1.50697i
$134$	3.62577e9			0.971468
$135$	−2.58818e9	−	4.48286e9i	−0.670644	−	1.16159i
$136$	−5.69694e9	−	9.86739e9i	−1.42796	−	2.47330i
$137$	−1.16693e7	+	2.02118e7i	−0.00283010	+	0.00490188i	−0.867437	−	0.497547i	$-0.834234\pi$
$137$	−1.16693e7	+	2.02118e7i	−0.00283010	+	0.00490188i	0.864607	+	0.502449i	$0.167568\pi$
$138$	2.81545e8	+	4.87651e8i	0.0660834	+	0.114460i
$139$	1.90508e9	−	3.29969e9i	0.432858	−	0.749733i	−0.564260	−	0.825597i	$-0.690838\pi$
$139$	1.90508e9	−	3.29969e9i	0.432858	−	0.749733i	0.997118	+	0.0758647i	$0.0241717\pi$
$140$	1.90842e10			4.19854
$141$	7.10677e9			1.51421
$142$	−5.56353e8	+	9.63632e8i	−0.114829	+	0.198890i
$143$	−5.44111e8	+	9.42428e8i	−0.108812	+	0.188467i
$144$	−1.14266e9			−0.221456
$145$	−7.94321e9			−1.49225
$146$	5.71345e9	−	9.89599e9i	1.04066	−	1.80248i
$147$	−3.38829e9	−	5.86870e9i	−0.598485	−	1.03661i
$148$	−1.02330e10	+	1.77241e10i	−1.75318	+	3.03660i
$149$	1.26151e9	+	2.18501e9i	0.209678	+	0.363174i	0.951613	−	0.307298i	$-0.0994250\pi$
$149$	1.26151e9	+	2.18501e9i	0.209678	+	0.363174i	−0.741935	+	0.670472i	$0.766092\pi$
$150$	3.13538e9	+	5.43064e9i	0.505684	+	0.875871i
$151$	−1.86229e9			−0.291508			−0.145754	−	0.989321i	$-0.546561\pi$
$151$	−1.86229e9			−0.291508			−0.145754	+	0.989321i	$0.546561\pi$
$152$	−1.26980e9	−	1.38762e10i	−0.192948	−	2.10851i
$153$	1.27083e9			0.187489
$154$	9.86131e9	+	1.70803e10i	1.41283	+	2.44710i
$155$	7.25568e9	+	1.25672e10i	1.00968	+	1.74882i
$156$	1.56082e9	−	2.70342e9i	0.211005	−	0.365471i
$157$	−1.57941e9	−	2.73562e9i	−0.207466	−	0.359342i	0.743450	−	0.668792i	$-0.233188\pi$
$157$	−1.57941e9	−	2.73562e9i	−0.207466	−	0.359342i	−0.950916	+	0.309450i	$0.899855\pi$
$158$	−1.92857e8	+	3.34039e8i	−0.0246195	+	0.0426422i
$159$	−2.47136e9			−0.306654
$160$	7.64347e9			0.922042
$161$	5.14740e8	−	8.91555e8i	0.0603770	−	0.104576i
$162$	−6.58520e9	+	1.14059e10i	−0.751193	+	1.30110i
$163$	1.36849e10			1.51844			0.759218	−	0.650837i	$-0.225582\pi$
$163$	1.36849e10			1.51844			0.759218	+	0.650837i	$0.225582\pi$
$164$	2.91444e9			0.314600
$165$	−5.86431e9	+	1.01573e10i	−0.615941	+	1.06684i
$166$	−1.35308e10	−	2.34360e10i	−1.38305	−	2.39551i
$167$	1.31551e9	−	2.27853e9i	0.130879	−	0.226689i	−0.793137	−	0.609044i	$-0.791553\pi$
$167$	1.31551e9	−	2.27853e9i	0.130879	−	0.226689i	0.924016	+	0.382355i	$0.124887\pi$
$168$	−1.53484e10	−	2.65843e10i	−1.48653	−	2.57474i
$169$	5.07278e9	+	8.78631e9i	0.478361	+	0.828545i
$170$	−3.32746e10			−3.05557
$171$	1.41117e9	+	6.51198e8i	0.126210	+	0.0582412i
$172$	1.19024e10			1.03695
$173$	−4.83278e9	−	8.37062e9i	−0.410194	−	0.710477i	0.584717	−	0.811238i	$-0.301206\pi$
$173$	−4.83278e9	−	8.37062e9i	−0.410194	−	0.710477i	−0.994911	+	0.100761i	$0.967872\pi$
$174$	1.17739e10	+	2.03931e10i	0.973756	+	1.68659i
$175$	5.73231e9	−	9.92865e9i	0.462017	−	0.800237i
$176$	1.06076e10	+	1.83730e10i	0.833320	+	1.44335i
$177$	−2.84476e9	+	4.92727e9i	−0.217854	+	0.377334i
$178$	2.19845e10			1.64144
$179$	−2.66812e9			−0.194252			−0.0971261	−	0.995272i	$-0.530965\pi$
$179$	−2.66812e9			−0.194252			−0.0971261	+	0.995272i	$0.530965\pi$
$180$	−2.71578e9	+	4.70388e9i	−0.192827	+	0.333987i
$181$	−5.47400e9	+	9.48124e9i	−0.379097	+	0.656616i	−0.990931	−	0.134370i	$-0.957099\pi$
$181$	−5.47400e9	+	9.48124e9i	−0.379097	+	0.656616i	0.611834	+	0.790986i	$0.290432\pi$
$182$	−8.31776e9			−0.561934
$183$	−2.59538e9			−0.171069
$184$	1.31347e9	−	2.27500e9i	0.0844776	−	0.146319i
$185$	1.62147e10	+	2.80848e10i	1.01774	+	1.76278i
$186$	2.15096e10	−	3.72558e10i	1.31773	−	2.28237i
$187$	−1.17975e10	−	2.04338e10i	−0.705507	−	1.22197i
$188$	−3.05528e10	−	5.29190e10i	−1.78378	−	3.08959i
$189$	2.80556e10			1.59934
$190$	−3.69490e10	−	1.70505e10i	−2.05689	−	0.949175i
$191$	6.71373e8			0.0365018			0.0182509	−	0.999833i	$-0.494190\pi$
$191$	6.71373e8			0.0365018			0.0182509	+	0.999833i	$0.494190\pi$
$192$	2.58905e9	+	4.48436e9i	0.137494	+	0.238147i
$193$	−2.62154e9	−	4.54064e9i	−0.136003	−	0.235564i	0.789977	−	0.613136i	$-0.210092\pi$
$193$	−2.62154e9	−	4.54064e9i	−0.136003	−	0.235564i	−0.925980	+	0.377572i	$0.876759\pi$
$194$	−2.09196e10	+	3.62338e10i	−1.06034	+	1.83656i
$195$	−2.47320e9	−	4.28370e9i	−0.122491	−	0.212160i
$196$	−2.91333e10	+	5.04604e10i	−1.41006	+	2.44229i
$197$	−5.28793e9			−0.250143			−0.125071	−	0.992148i	$-0.539916\pi$
$197$	−5.28793e9			−0.250143			−0.125071	+	0.992148i	$0.539916\pi$
$198$	−5.61326e9			−0.259551
$199$	1.30903e10	−	2.26731e10i	0.591712	−	1.02488i	−0.402289	−	0.915513i	$-0.631785\pi$
$199$	1.30903e10	−	2.26731e10i	0.591712	−	1.02488i	0.994002	−	0.109363i	$-0.0348812\pi$
$200$	1.46273e10	−	2.53352e10i	0.646440	−	1.11967i
$201$	−1.16863e10			−0.505004
$202$	9.58915e9			0.405228
$203$	2.15259e10	−	3.72839e10i	0.889670	−	1.54095i
$204$	3.38418e10	+	5.86158e10i	1.36810	+	2.36962i
$205$	2.30904e9	−	3.99937e9i	0.0913144	−	0.158161i
$206$	3.07038e10	+	5.31805e10i	1.18793	+	2.05755i
$207$	1.46500e8	+	2.53746e8i	0.00554590	+	0.00960578i
$208$	−8.94727e9			−0.331441
$209$	−2.62956e9	−	2.87355e10i	−0.0953288	−	1.04174i
$210$	−8.96470e10			−3.18089
$211$	−5.33480e9	−	9.24015e9i	−0.185288	−	0.320928i	0.758386	−	0.651806i	$-0.225988\pi$
$211$	−5.33480e9	−	9.24015e9i	−0.185288	−	0.320928i	−0.943674	+	0.330878i	$0.892655\pi$
$212$	1.06246e10	+	1.84024e10i	0.361246	+	0.625696i
$213$	1.79319e9	−	3.10590e9i	0.0596924	−	0.103390i
$214$	1.62585e10	+	2.81606e10i	0.529931	+	0.917867i
$215$	9.42998e9	−	1.63332e10i	0.300980	−	0.521313i
$216$	7.15901e10			2.23775
$217$	−7.86507e10			−2.40787
$218$	−3.12527e10	+	5.41312e10i	−0.937201	+	1.62328i
$219$	−1.84152e10	+	3.18960e10i	−0.540975	+	0.936996i
$220$	1.00845e11			2.90238
$221$	9.95086e9			0.280605
$222$	4.80690e10	−	8.32580e10i	1.32824	−	2.30058i
$223$	7.32651e9	+	1.26899e10i	0.198392	+	0.343626i	0.948007	−	0.318248i	$-0.103095\pi$
$223$	7.32651e9	+	1.26899e10i	0.198392	+	0.343626i	−0.749615	+	0.661874i	$0.769761\pi$
$224$	−2.07136e10	+	3.58770e10i	−0.549717	+	0.952138i
$225$	1.63147e9	+	2.82580e9i	0.0424384	+	0.0735055i
$226$	−4.21330e10	−	7.29765e10i	−1.07432	−	1.86078i
$227$	1.69607e10			0.423961			0.211981	−	0.977274i	$-0.432009\pi$
$227$	1.69607e10			0.423961			0.211981	+	0.977274i	$0.432009\pi$
$228$	7.54306e9	+	8.24296e10i	0.184859	+	2.02012i
$229$	4.78651e10			1.15016			0.575081	−	0.818096i	$-0.304970\pi$
$229$	4.78651e10			1.15016			0.575081	+	0.818096i	$0.304970\pi$
$230$	−3.83586e9	−	6.64391e9i	−0.0903832	−	0.156548i
$231$	−3.17842e10	−	5.50519e10i	−0.734442	−	1.27209i
$232$	5.49281e10	−	9.51383e10i	1.24480	−	2.15605i
$233$	2.70690e10	+	4.68849e10i	0.601687	+	1.04215i	0.992566	+	0.121711i	$0.0388380\pi$
$233$	2.70690e10	+	4.68849e10i	0.601687	+	1.04215i	−0.390878	+	0.920442i	$0.627829\pi$
$234$	1.18366e9	−	2.05016e9i	0.0258081	−	0.0447009i
$235$	−9.68249e10			−2.07101
$236$	4.89198e10			1.02655
$237$	6.21603e8	−	1.07665e9i	0.0127981	−	0.0221670i
$238$	9.01732e10	−	1.56185e11i	1.82172	−	3.15531i
$239$	2.11901e10			0.420090			0.210045	−	0.977692i	$-0.432639\pi$
$239$	2.11901e10			0.420090			0.210045	+	0.977692i	$0.432639\pi$
$240$	−9.64317e10			−1.87616
$241$	−2.39847e10	+	4.15426e10i	−0.457991	+	0.793263i	−0.998855	−	0.0478467i	$-0.984764\pi$
$241$	−2.39847e10	+	4.15426e10i	−0.457991	+	0.793263i	0.540864	+	0.841110i	$0.318097\pi$
$242$	4.49103e9	+	7.77870e9i	0.0841738	+	0.145793i
$243$	−7.49768e9	+	1.29864e10i	−0.137943	+	0.238924i
$244$	1.11578e10	+	1.93259e10i	0.201523	+	0.349049i
$245$	4.61632e10	+	7.99570e10i	0.818556	+	1.41778i
$246$	−1.36904e10			−0.238346
$247$	1.10497e10	+	5.09900e9i	0.188892	+	0.0871664i
$248$	−2.00695e11			−3.36902
$249$	4.36114e10	+	7.55372e10i	0.718957	+	1.24527i
$250$	2.72397e10	+	4.71806e10i	0.441035	+	0.763895i
$251$	−2.18218e10	+	3.77965e10i	−0.347024	+	0.601063i	−0.985719	−	0.168396i	$-0.946141\pi$
$251$	−2.18218e10	+	3.77965e10i	−0.347024	+	0.601063i	0.638695	+	0.769460i	$0.279474\pi$
$252$	−1.47194e10	−	2.54947e10i	−0.229926	−	0.398243i
$253$	2.72000e9	−	4.71118e9i	0.0417375	−	0.0722915i
$254$	−1.76819e11			−2.66549
$255$	1.07248e11			1.58840
$256$	6.68205e10	−	1.15737e11i	0.972367	−	1.68419i
$257$	−1.33468e10	+	2.31174e10i	−0.190844	+	0.330552i	−0.945530	−	0.325534i	$-0.894456\pi$
$257$	−1.33468e10	+	2.31174e10i	−0.190844	+	0.330552i	0.754686	+	0.656086i	$0.227789\pi$
$258$	−5.59109e10			−0.785611
$259$	−1.75766e11			−2.42709
$260$	−2.12651e10	+	3.68322e10i	−0.288594	+	0.499860i
$261$	6.12649e9	+	1.06114e10i	0.0817202	+	0.141544i
$262$	−1.13984e11	+	1.97427e11i	−1.49448	+	2.58851i
$263$	−2.86247e10	−	4.95795e10i	−0.368927	−	0.639001i	0.620471	−	0.784229i	$-0.286942\pi$
$263$	−2.86247e10	−	4.95795e10i	−0.368927	−	0.639001i	−0.989398	+	0.145229i	$0.953608\pi$
$264$	−8.11046e10	−	1.40477e11i	−1.02761	−	1.77987i
$265$	3.36705e10			0.419415
$266$	1.80163e11	−	1.27225e11i	2.20647	−	1.55814i
$267$	−7.08586e10			−0.853281
$268$	5.02407e10	+	8.70195e10i	0.594907	+	1.03041i
$269$	−9.55047e9	−	1.65419e10i	−0.111209	−	0.192619i	0.805049	−	0.593208i	$-0.202139\pi$
$269$	−9.55047e9	−	1.65419e10i	−0.111209	−	0.192619i	−0.916258	+	0.400589i	$0.868806\pi$
$270$	1.04536e11	−	1.81061e11i	1.19709	−	2.07342i
$271$	1.03308e10	+	1.78934e10i	0.116351	+	0.201526i	0.918319	−	0.395841i	$-0.129547\pi$
$271$	1.03308e10	+	1.78934e10i	0.116351	+	0.201526i	−0.801968	+	0.597367i	$0.796214\pi$
$272$	9.69978e10	−	1.68005e11i	1.07449	−	1.86107i
$273$	2.68092e10			0.292114
$274$	−9.42637e8			−0.0101034
$275$	3.02908e10	−	5.24652e10i	0.319384	−	0.553190i
$276$	−7.80250e9	+	1.35143e10i	−0.0809363	+	0.140186i
$277$	−2.89600e10			−0.295556			−0.147778	−	0.989021i	$-0.547212\pi$
$277$	−2.89600e10			−0.295556			−0.147778	+	0.989021i	$0.547212\pi$
$278$	1.53891e11			1.54529
$279$	1.11924e10	−	1.93858e10i	0.110587	−	0.191543i
$280$	2.09112e11	+	3.62193e11i	2.03314	+	3.52151i
$281$	−6.15871e10	+	1.06672e11i	−0.589266	+	1.02064i	0.405063	+	0.914289i	$0.367250\pi$
$281$	−6.15871e10	+	1.06672e11i	−0.589266	+	1.02064i	−0.994329	+	0.106349i	$0.966084\pi$
$282$	1.43520e11	+	2.48584e11i	1.35142	+	2.34073i
$283$	−5.91112e10	−	1.02384e11i	−0.547811	−	0.948836i	−0.998424	−	0.0561169i	$-0.982128\pi$
$283$	−5.91112e10	−	1.02384e11i	−0.547811	−	0.948836i	0.450613	−	0.892719i	$-0.351205\pi$
$284$	−3.08366e10			−0.281277
$285$	1.19091e11	+	5.49559e10i	1.06925	+	0.493415i
$286$	−4.39529e10			−0.388455
$287$	1.25149e10	+	2.16764e10i	0.108882	+	0.188590i
$288$	−5.89530e9	−	1.02110e10i	−0.0504940	−	0.0874582i
$289$	−4.85838e10	+	8.41496e10i	−0.409686	+	0.709597i
$290$	−1.60412e11	−	2.77841e11i	−1.33182	−	2.30678i
$291$	6.74264e10	−	1.16786e11i	0.551203	−	0.954712i
$292$	3.16675e11			2.54913
$293$	−1.53730e11			−1.21858			−0.609290	−	0.792948i	$-0.708545\pi$
$293$	−1.53730e11			−1.21858			−0.609290	+	0.792948i	$0.708545\pi$
$294$	1.36852e11	−	2.37035e11i	1.06829	−	1.85033i
$295$	3.87579e10	−	6.71307e10i	0.297962	−	0.516086i
$296$	−4.48507e11			−3.39591
$297$	1.48252e11			1.10560
$298$	−5.09521e10	+	8.82516e10i	−0.374273	+	0.648260i
$299$	1.14713e9	+	1.98688e9i	0.00830024	+	0.0143764i
$300$	−8.68912e10	+	1.50500e11i	−0.619341	+	1.07273i
$301$	5.11100e10	+	8.85251e10i	0.358886	+	0.621609i
$302$	−3.76086e10	−	6.51400e10i	−0.260169	−	0.450627i
$303$	−3.09070e10			−0.210652
$304$	1.93798e11	−	1.36854e11i	1.30142	−	0.919021i
$305$	3.53603e10			0.233973
$306$	2.56642e10	+	4.44518e10i	0.167333	+	0.289830i
$307$	−8.36357e10	−	1.44861e11i	−0.537365	−	0.930743i	−0.999045	−	0.0436965i	$-0.986087\pi$
$307$	−8.36357e10	−	1.44861e11i	−0.537365	−	0.930743i	0.461680	−	0.887046i	$-0.347247\pi$
$308$	−2.73288e11	+	4.73348e11i	−1.73038	+	2.99711i
$309$	−9.89621e10	−	1.71407e11i	−0.617527	−	1.06959i
$310$	−2.93054e11	+	5.07585e11i	−1.80227	+	3.12163i
$311$	2.16624e11			1.31306			0.656531	−	0.754299i	$-0.272023\pi$
$311$	2.16624e11			1.31306			0.656531	+	0.754299i	$0.272023\pi$
$312$	6.84097e10			0.408716
$313$	1.67473e10	−	2.90072e10i	0.0986270	−	0.170827i	−0.812490	−	0.582976i	$-0.801888\pi$
$313$	1.67473e10	−	2.90072e10i	0.0986270	−	0.170827i	0.911117	+	0.412149i	$0.135222\pi$
$314$	6.37919e10	−	1.10491e11i	0.370324	−	0.641420i
$315$	−4.66472e10			−0.266949
$316$	−1.06894e10			−0.0603059
$317$	−1.02219e11	+	1.77048e11i	−0.568543	+	0.984746i	0.428167	+	0.903700i	$0.359159\pi$
$317$	−1.02219e11	+	1.77048e11i	−0.568543	+	0.984746i	−0.996710	+	0.0810461i	$0.974174\pi$
$318$	−4.99086e10	−	8.64442e10i	−0.273686	−	0.474039i
$319$	1.13748e11	−	1.97017e11i	0.615013	−	1.06523i
$320$	−3.52740e10	−	6.10963e10i	−0.188053	−	0.325717i
$321$	−5.24032e10	−	9.07650e10i	−0.275477	−	0.477140i
$322$	4.15803e10			0.215544
$323$	−2.15535e11	+	1.52204e11i	−1.10181	+	0.778064i
$324$	−3.64993e11			−1.84006
$325$	1.27748e10	+	2.21265e10i	0.0635152	+	0.110012i
$326$	2.76363e11	+	4.78676e11i	1.35519	+	2.34726i
$327$	1.00731e11	−	1.74472e11i	0.487191	−	0.843839i
$328$	3.19345e10	+	5.53122e10i	0.152345	+	0.263869i
$329$	2.62393e11	−	4.54478e11i	1.23473	−	2.13861i
$330$	−4.73715e11			−2.19889
$331$	2.97146e11			1.36064			0.680320	−	0.732915i	$-0.261841\pi$
$331$	2.97146e11			1.36064			0.680320	+	0.732915i	$0.261841\pi$
$332$	3.74981e11	−	6.49485e11i	1.69390	−	2.93392i
$333$	2.50124e10	−	4.33228e10i	0.111470	−	0.193071i
$334$	1.06266e11			0.467235
$335$	1.59218e11			0.690701
$336$	2.61327e11	−	4.52632e11i	1.11856	−	1.93740i
$337$	−1.26873e11	−	2.19750e11i	−0.535838	−	0.928099i	−0.999122	−	0.0418894i	$-0.986662\pi$
$337$	−1.26873e11	−	2.19750e11i	−0.535838	−	0.928099i	0.463284	−	0.886210i	$-0.346671\pi$
$338$	−2.04888e11	+	3.54876e11i	−0.853868	+	1.47894i
$339$	1.35800e11	+	2.35212e11i	0.558471	+	0.967300i
$340$	−4.61072e11	−	7.98600e11i	−1.87117	−	3.24096i
$341$	−4.15608e11			−1.66452
$342$	5.72035e9	+	6.25112e10i	0.0226102	+	0.247082i
$343$	−1.12487e11			−0.438811
$344$	1.30419e11	+	2.25892e11i	0.502142	+	0.869736i
$345$	1.23635e10	+	2.14141e10i	0.0469844	+	0.0813795i
$346$	1.95194e11	−	3.38086e11i	0.732191	−	1.26819i
$347$	2.20830e11	+	3.82489e11i	0.817666	+	1.41624i	0.907398	+	0.420273i	$0.138066\pi$
$347$	2.20830e11	+	3.82489e11i	0.817666	+	1.41624i	−0.0897321	+	0.995966i	$0.528601\pi$
$348$	−3.26293e11	+	5.65155e11i	−1.19262	+	2.06567i
$349$	−5.67673e10			−0.204825			−0.102413	−	0.994742i	$-0.532656\pi$
$349$	−5.67673e10			−0.204825			−0.102413	+	0.994742i	$0.532656\pi$
$350$	4.63052e11			1.64939
$351$	−3.12617e10	+	5.41468e10i	−0.109934	+	0.190410i
$352$	−1.09455e11	+	1.89582e11i	−0.380009	+	0.658196i
$353$	1.62704e11			0.557713			0.278857	−	0.960333i	$-0.410045\pi$
$353$	1.62704e11			0.557713			0.278857	+	0.960333i	$0.410045\pi$
$354$	−2.29798e11			−0.777734
$355$	−2.44311e10	+	4.23158e10i	−0.0816422	+	0.141408i
$356$	3.04629e11	+	5.27633e11i	1.00519	+	1.74103i
$357$	−2.90640e11	+	5.03402e11i	−0.946995	+	1.64024i
$358$	−5.38822e10	−	9.33266e10i	−0.173369	−	0.300284i
$359$	1.58715e11	+	2.74903e11i	0.504306	+	0.873484i	0.999988	+	0.00497930i	$0.00158497\pi$
$359$	1.58715e11	+	2.74903e11i	0.504306	+	0.873484i	−0.495682	+	0.868504i	$0.665082\pi$
$360$	−1.19031e11			−0.373507
$361$	−3.17328e11	+	5.85673e10i	−0.983391	+	0.181498i
$362$	−4.42186e11			−1.35337
$363$	−1.44752e10	−	2.50717e10i	−0.0437566	−	0.0757886i
$364$	−1.15256e11	−	1.99629e11i	−0.344117	−	0.596028i
$365$	2.50894e11	−	4.34561e11i	0.739899	−	1.28154i
$366$	−5.24132e10	−	9.07824e10i	−0.152678	−	0.264446i
$367$	8.54809e10	−	1.48057e11i	0.245964	−	0.426022i	−0.716438	−	0.697651i	$-0.754229\pi$
$367$	8.54809e10	−	1.48057e11i	0.245964	−	0.426022i	0.962402	+	0.271628i	$0.0875621\pi$
$368$	4.47272e10			0.127133
$369$	−7.12372e9			−0.0200027
$370$	−6.54908e11	+	1.13433e12i	−1.81666	+	3.14654i
$371$	−9.12462e10	+	1.58043e11i	−0.250053	+	0.433105i
$372$	1.19220e12			3.22779
$373$	−2.39356e11			−0.640257			−0.320129	−	0.947374i	$-0.603726\pi$
$373$	−2.39356e11			−0.640257			−0.320129	+	0.947374i	$0.603726\pi$
$374$	4.76496e11	−	8.25315e11i	1.25932	−	2.18121i
$375$	−8.77971e10	−	1.52069e11i	−0.229266	−	0.397100i
$376$	6.69554e11	−	1.15970e12i	1.72759	−	2.99227i
$377$	4.79716e10	+	8.30892e10i	0.122306	+	0.211840i
$378$	5.66577e11	+	9.81340e11i	1.42740	+	2.47233i
$379$	−1.72464e10			−0.0429361			−0.0214680	−	0.999770i	$-0.506834\pi$
$379$	−1.72464e10			−0.0429361			−0.0214680	+	0.999770i	$0.506834\pi$
$380$	−1.02769e11	−	1.12305e12i	−0.252834	−	2.76294i
$381$	5.69908e11			1.38562
$382$	1.35583e10	+	2.34836e10i	0.0325776	+	0.0564260i
$383$	1.45871e11	+	2.52656e11i	0.346398	+	0.599979i	0.985607	−	0.169055i	$-0.0540714\pi$
$383$	1.45871e11	+	2.52656e11i	0.346398	+	0.599979i	−0.639209	+	0.769033i	$0.720738\pi$
$384$	−2.48191e11	+	4.29879e11i	−0.582499	+	1.00892i
$385$	4.33038e11	+	7.50045e11i	1.00451	+	1.73986i
$386$	1.05883e11	−	1.83395e11i	0.242764	−	0.420479i
$387$	−2.90929e10			−0.0659306
$388$	−1.15950e12			−2.59732
$389$	9.67889e10	−	1.67643e11i	0.214315	−	0.371204i	−0.738746	−	0.673984i	$-0.764581\pi$
$389$	9.67889e10	−	1.67643e11i	0.214315	−	0.371204i	0.953060	+	0.302780i	$0.0979148\pi$
$390$	9.98916e10	−	1.73017e11i	0.218644	−	0.378703i
$391$	−4.97441e10			−0.107633
$392$	−1.27689e12			−2.73129
$393$	3.67386e11	−	6.36331e11i	0.776884	−	1.34560i
$394$	−1.06789e11	−	1.84964e11i	−0.223251	−	0.386682i
$395$	−8.46892e9	+	1.46686e10i	−0.0175042	+	0.0303181i
$396$	−7.77806e10	−	1.34720e11i	−0.158944	−	0.275298i
$397$	−2.96749e11	−	5.13984e11i	−0.599559	−	1.03847i	−0.992886	−	0.119068i	$-0.962009\pi$
$397$	−2.96749e11	−	5.13984e11i	−0.599559	−	1.03847i	0.393327	−	0.919399i	$-0.371324\pi$
$398$	1.05743e12			2.11240
$399$	−5.80686e11	+	4.10062e11i	−1.14700	+	0.809975i
$400$	4.98097e11			0.972845
$401$	5.35857e10	+	9.28131e10i	0.103490	+	0.179250i	0.913120	−	0.407690i	$-0.133666\pi$
$401$	5.35857e10	+	9.28131e10i	0.103490	+	0.179250i	−0.809630	+	0.586940i	$0.800332\pi$
$402$	−2.36003e11	−	4.08769e11i	−0.450713	−	0.780658i
$403$	8.76387e10	−	1.51795e11i	0.165510	−	0.286671i
$404$	1.32873e11	+	2.30142e11i	0.248153	+	0.429814i
$405$	−2.89175e11	+	5.00866e11i	−0.534088	+	0.925068i
$406$	1.73885e12			3.17610
$407$	−9.28787e11			−1.67780
$408$	−7.41632e11	+	1.28454e12i	−1.32501	+	2.29498i
$409$	1.90481e10	−	3.29923e10i	0.0336587	−	0.0582986i	−0.848705	−	0.528866i	$-0.822617\pi$
$409$	1.90481e10	−	3.29923e10i	0.0336587	−	0.0582986i	0.882364	+	0.470567i	$0.155951\pi$
$410$	1.86523e11			0.325990
$411$	3.03824e9			0.00525211
$412$	−8.50898e11	+	1.47380e12i	−1.45492	+	2.52000i
$413$	2.10066e11	+	3.63844e11i	0.355287	+	0.615376i
$414$	−5.91710e9	+	1.02487e10i	−0.00989936	+	0.0171462i
$415$	−5.94176e11	−	1.02914e12i	−0.983328	−	1.70317i
$416$	−4.61613e10	−	7.99538e10i	−0.0755716	−	0.130894i
$417$	−4.96009e11			−0.803299
$418$	9.52019e11	−	6.72286e11i	1.52529	−	1.07711i
$419$	2.80944e10			0.0445305			0.0222652	−	0.999752i	$-0.492912\pi$
$419$	2.80944e10			0.0445305			0.0222652	+	0.999752i	$0.492912\pi$
$420$	−1.24220e12	−	2.15155e12i	−1.94791	−	3.37389i
$421$	−2.98259e11	−	5.16600e11i	−0.462727	−	0.801466i	0.536369	−	0.843984i	$-0.319796\pi$
$421$	−2.98259e11	−	5.16600e11i	−0.462727	−	0.801466i	−0.999096	+	0.0425175i	$0.986462\pi$
$422$	2.15471e11	−	3.73206e11i	0.330737	−	0.572853i
$423$	7.46797e10	+	1.29349e11i	0.113415	+	0.196441i
$424$	−2.32835e11	+	4.03283e11i	−0.349867	+	0.605987i
$425$	−5.53967e11			−0.823633
$426$	1.44853e11			0.213100
$427$	−9.58253e10	+	1.65974e11i	−0.139494	+	0.241610i
$428$	−4.50575e11	+	7.80418e11i	−0.649037	+	1.12417i
$429$	1.41666e11			0.201933
$430$	7.61748e11			1.07449
$431$	3.88948e11	−	6.73678e11i	0.542931	−	0.940383i	−0.455803	−	0.890080i	$-0.650648\pi$
$431$	3.88948e11	−	6.73678e11i	0.542931	−	0.940383i	0.998734	−	0.0503028i	$-0.0160186\pi$
$432$	6.09457e11	+	1.05561e12i	0.841911	+	1.45823i
$433$	−9.59002e10	+	1.66104e11i	−0.131106	+	0.227083i	−0.924103	−	0.382143i	$-0.875186\pi$
$433$	−9.59002e10	+	1.66104e11i	−0.131106	+	0.227083i	0.792997	+	0.609226i	$0.208520\pi$
$434$	−1.58834e12	−	2.75108e12i	−2.14901	−	3.72220i
$435$	5.17027e11	+	8.95517e11i	0.692328	+	1.19915i
$436$	−1.73222e12			−2.29569
$437$	−5.52372e10	−	2.54898e10i	−0.0724544	−	0.0334349i
$438$	−1.48756e12			−1.93127
$439$	4.57087e11	+	7.91697e11i	0.587365	+	1.01735i	0.994576	+	0.104012i	$0.0331681\pi$
$439$	4.57087e11	+	7.91697e11i	0.587365	+	1.01735i	−0.407211	+	0.913334i	$0.633499\pi$
$440$	1.10500e12	+	1.91391e12i	1.40548	+	2.43436i
$441$	7.12101e10	−	1.23339e11i	0.0896536	−	0.155285i
$442$	2.00956e11	+	3.48066e11i	0.250438	+	0.433772i
$443$	−5.69226e11	+	9.85928e11i	−0.702211	+	1.21627i	0.265478	+	0.964117i	$0.414470\pi$
$443$	−5.69226e11	+	9.85928e11i	−0.702211	+	1.21627i	−0.967689	+	0.252148i	$0.918863\pi$
$444$	2.66429e12			3.25355
$445$	9.65401e11			1.16704
$446$	−2.95915e11	+	5.12540e11i	−0.354128	+	0.613368i
$447$	1.64225e11	−	2.84446e11i	0.194561	−	0.336989i
$448$	3.82366e11			0.448465
$449$	8.78278e11			1.01982			0.509910	−	0.860228i	$-0.329679\pi$
$449$	8.78278e11			1.01982			0.509910	+	0.860228i	$0.329679\pi$
$450$	−6.58947e10	+	1.14133e11i	−0.0757520	+	0.131206i
$451$	6.61314e10	+	1.14543e11i	0.0752684	+	0.130369i
$452$	1.16764e12	−	2.02241e12i	1.31579	−	2.27901i
$453$	1.21217e11	+	2.09954e11i	0.135245	+	0.234252i
$454$	3.42517e11	+	5.93258e11i	0.378383	+	0.655378i
$455$	−3.65257e11			−0.399528
$456$	−1.48175e12	+	1.04637e12i	−1.60485	+	1.13329i
$457$	7.14022e11			0.765753			0.382877	−	0.923800i	$-0.374933\pi$
$457$	7.14022e11			0.765753			0.382877	+	0.923800i	$0.374933\pi$
$458$	9.66627e11	+	1.67425e12i	1.02651	+	1.77797i
$459$	−6.77818e11	−	1.17402e12i	−0.712781	−	1.23457i
$460$	1.06304e11	−	1.84124e11i	0.110698	−	0.191734i
$461$	−7.55181e11	−	1.30801e12i	−0.778748	−	1.34883i	−0.932664	−	0.360747i	$-0.882522\pi$
$461$	−7.55181e11	−	1.30801e12i	−0.778748	−	1.34883i	0.153916	−	0.988084i	$-0.450812\pi$
$462$	1.28375e12	−	2.22353e12i	1.31097	−	2.27067i
$463$	−6.77202e11			−0.684863			−0.342432	−	0.939543i	$-0.611251\pi$
$463$	−6.77202e11			−0.684863			−0.342432	+	0.939543i	$0.611251\pi$
$464$	1.87045e12			1.87333
$465$	9.44550e11	−	1.63601e12i	0.936886	−	1.62273i
$466$	−1.09331e12	+	1.89367e12i	−1.07400	+	1.86023i
$467$	−2.81510e11			−0.273884			−0.136942	−	0.990579i	$-0.543727\pi$
$467$	−2.81510e11			−0.273884			−0.136942	+	0.990579i	$0.543727\pi$
$468$	6.56059e10			0.0632174
$469$	−4.31476e11	+	7.47339e11i	−0.411793	+	0.713246i
$470$	−1.95536e12	−	3.38679e12i	−1.84836	−	3.20146i
$471$	−2.05609e11	+	3.56126e11i	−0.192508	+	0.333433i
$472$	5.36030e11	+	9.28431e11i	0.497107	+	0.861015i
$473$	2.70077e11	+	4.67786e11i	0.248091	+	0.429707i
$474$	5.02127e10			0.0456889
$475$	−6.15139e11	−	2.83863e11i	−0.554437	−	0.255851i
$476$	4.99797e12			4.46233
$477$	−2.59696e10	−	4.49807e10i	−0.0229685	−	0.0397826i
$478$	4.27930e11	+	7.41197e11i	0.374928	+	0.649394i
$479$	−4.54492e11	+	7.87203e11i	−0.394472	+	0.683246i	−0.993034	−	0.117831i	$-0.962406\pi$
$479$	−4.54492e11	+	7.87203e11i	−0.394472	+	0.683246i	0.598561	+	0.801077i	$0.295739\pi$
$480$	−4.97517e11	−	8.61724e11i	−0.427781	−	0.740939i
$481$	1.95852e11	−	3.39226e11i	0.166830	−	0.288959i
$482$	−1.93746e12			−1.63502
$483$	−1.34019e11			−0.112048
$484$	−1.24461e11	+	2.15572e11i	−0.103093	+	0.178562i
$485$	−9.18639e11	+	1.59113e12i	−0.753889	+	1.30577i
$486$	−6.05657e11			−0.492452
$487$	1.95171e12			1.57230			0.786148	−	0.618038i	$-0.212072\pi$
$487$	1.95171e12			1.57230			0.786148	+	0.618038i	$0.212072\pi$
$488$	−2.44520e11	+	4.23521e11i	−0.195175	+	0.338054i
$489$	−8.90754e11	−	1.54283e12i	−0.704478	−	1.22019i
$490$	−1.86452e12	+	3.22944e12i	−1.46111	+	2.53072i
$491$	7.36472e11	+	1.27561e12i	0.571860	+	0.990490i	0.996375	+	0.0850694i	$0.0271112\pi$
$491$	7.36472e11	+	1.27561e12i	0.571860	+	0.990490i	−0.424515	+	0.905421i	$0.639555\pi$
$492$	−1.89702e11	−	3.28574e11i	−0.145959	−	0.252808i
$493$	−2.08025e12			−1.58600
$494$	4.47914e10	+	4.89475e11i	0.0338395	+	0.369793i
$495$	−2.46494e11			−0.184537
$496$	−1.70855e12	−	2.95929e12i	−1.26753	−	2.19543i
$497$	−1.32415e11	−	2.29349e11i	−0.0973494	−	0.168614i
$498$	−1.76145e12	+	3.05092e12i	−1.28333	+	2.22279i
$499$	7.85741e11	+	1.36094e12i	0.567319	+	0.982625i	0.996830	+	0.0795634i	$0.0253526\pi$
$499$	7.85741e11	+	1.36094e12i	0.567319	+	0.982625i	−0.429511	+	0.903062i	$0.641314\pi$
$500$	−7.54899e11	+	1.30752e12i	−0.540162	+	0.935587i
$501$	−3.42508e11			−0.242885
$502$	−1.76275e12			−1.23887
$503$	8.94182e11	−	1.54877e12i	0.622831	−	1.07877i	−0.366125	−	0.930565i	$-0.619316\pi$
$503$	8.94182e11	−	1.54877e12i	0.622831	−	1.07877i	0.988956	−	0.148209i	$-0.0473508\pi$
$504$	3.22571e11	−	5.58709e11i	0.222683	−	0.385698i
$505$	4.21087e11			0.288112
$506$	2.19720e11			0.149002
$507$	6.60379e11	−	1.14381e12i	0.443871	−	0.768808i
$508$	−2.45010e12	−	4.24370e12i	−1.63229	−	2.82721i
$509$	7.92691e11	−	1.37298e12i	0.523448	−	0.906639i	−0.476179	−	0.879348i	$-0.657979\pi$
$509$	7.92691e11	−	1.37298e12i	0.523448	−	0.906639i	0.999628	−	0.0272908i	$-0.00868801\pi$
$510$	2.16586e12	+	3.75138e12i	1.41763	+	2.45541i
$511$	1.35983e12	+	2.35530e12i	0.882249	+	1.52810i
$512$	3.44545e12			2.21580
$513$	−1.51080e11	−	1.65098e12i	−0.0963117	−	1.05248i
$514$	−1.07815e12			−0.681308
$515$	1.34829e12	+	2.33531e12i	0.844600	+	1.46289i
$516$	−7.74733e11	−	1.34188e12i	−0.481092	−	0.833276i
$517$	1.38654e12	−	2.40156e12i	0.853544	−	1.47838i
$518$	−3.54956e12	−	6.14803e12i	−2.16616	−	3.75190i
$519$	−6.29135e11	+	1.08969e12i	−0.380619	+	0.659252i
$520$	−9.32035e11			−0.559007
$521$	−4.70053e11			−0.279497			−0.139748	−	0.990187i	$-0.544629\pi$
$521$	−4.70053e11			−0.279497			−0.139748	+	0.990187i	$0.544629\pi$
$522$	−2.47447e11	+	4.28591e11i	−0.145870	+	0.252653i
$523$	1.42037e12	−	2.46015e12i	0.830125	−	1.43782i	−0.0678130	−	0.997698i	$-0.521602\pi$
$523$	1.42037e12	−	2.46015e12i	0.830125	−	1.43782i	0.897938	−	0.440121i	$-0.145065\pi$
$524$	−6.31773e12			−3.66075
$525$	−1.49247e12			−0.857412
$526$	1.15614e12	−	2.00250e12i	0.658530	−	1.14061i
$527$	1.90019e12	+	3.29123e12i	1.07312	+	1.85870i
$528$	1.38091e12	−	2.39181e12i	0.773238	−	1.33929i
$529$	8.94842e11	+	1.54991e12i	0.496816	+	0.860511i
$530$	6.79971e11	+	1.17774e12i	0.374325	+	0.648350i
$531$	−1.19574e11			−0.0652695
$532$	5.54987e12	+	2.56105e12i	3.00387	+	1.38617i
$533$	−5.57801e10			−0.0299369
$534$	−1.43098e12	−	2.47853e12i	−0.761548	−	1.31904i
$535$	7.13958e11	+	1.23661e12i	0.376774	+	0.652591i
$536$	−1.10101e12	+	1.90700e12i	−0.576168	+	0.997952i
$537$	1.73669e11	+	3.00803e11i	0.0901234	+	0.156098i
$538$	3.85740e11	−	6.68121e11i	0.198506	−	0.343823i
$539$	−2.64425e12			−1.34944
$540$	5.79402e12			2.93230
$541$	1.27759e12	−	2.21286e12i	0.641217	−	1.11062i	−0.343944	−	0.938990i	$-0.611763\pi$
$541$	1.27759e12	−	2.21286e12i	0.641217	−	1.11062i	0.985161	−	0.171631i	$-0.0549036\pi$
$542$	−4.17256e11	+	7.22708e11i	−0.207685	+	0.359721i
$543$	1.42522e12			0.703529
$544$	2.00175e12			0.979974
$545$	−1.37239e12	+	2.37706e12i	−0.666338	+	1.15413i
$546$	5.41407e11	+	9.37744e11i	0.260709	+	0.451562i
$547$	−1.47878e12	+	2.56132e12i	−0.706254	+	1.22327i	0.259983	+	0.965613i	$0.416283\pi$
$547$	−1.47878e12	+	2.56132e12i	−0.706254	+	1.22327i	−0.966237	+	0.257655i	$0.917050\pi$
$548$	−1.30617e10	−	2.26236e10i	−0.00618711	−	0.0107164i
$549$	−2.72729e10	−	4.72380e10i	−0.0128131	−	0.0221930i
$550$	2.44687e12			1.14019
$551$	−2.30996e12	−	1.06596e12i	−1.06763	−	0.492672i
$552$	−3.41978e11			−0.156774
$553$	−4.59011e10	−	7.95030e10i	−0.0208718	−	0.0361510i
$554$	−5.84843e11	−	1.01298e12i	−0.263782	−	0.456884i
$555$	2.11085e12	−	3.65610e12i	0.944363	−	1.63568i
$556$	2.13240e12	+	3.69342e12i	0.946306	+	1.63905i
$557$	1.58540e12	−	2.74599e12i	0.697894	−	1.20879i	−0.271301	−	0.962495i	$-0.587454\pi$
$557$	1.58540e12	−	2.74599e12i	0.697894	−	1.20879i	0.969195	−	0.246294i	$-0.0792129\pi$
$558$	9.04115e11			0.394793
$559$	−2.27803e11			−0.0986747
$560$	−3.56040e12	+	6.16680e12i	−1.52987	+	2.64980i
$561$	−1.53580e12	+	2.66009e12i	−0.654641	+	1.13387i
$562$	−4.97496e12			−2.10366
$563$	−2.44299e12			−1.02479			−0.512393	−	0.858751i	$-0.671241\pi$
$563$	−2.44299e12			−1.02479			−0.512393	+	0.858751i	$0.671241\pi$
$564$	−3.97739e12	+	6.88904e12i	−1.65517	+	2.86684i
$565$	−1.85018e12	−	3.20461e12i	−0.763829	−	1.32299i
$566$	2.38748e12	−	4.13524e12i	0.977835	−	1.69366i
$567$	−1.56731e12	−	2.71466e12i	−0.636842	−	1.10304i
$568$	−3.37887e11	−	5.85237e11i	−0.136208	−	0.235920i
$569$	1.82279e12			0.729007			0.364503	−	0.931202i	$-0.381239\pi$
$569$	1.82279e12			0.729007			0.364503	+	0.931202i	$0.381239\pi$
$570$	4.82752e11	+	5.27545e12i	0.191552	+	2.09326i
$571$	1.27674e12			0.502621			0.251310	−	0.967907i	$-0.419139\pi$
$571$	1.27674e12			0.502621			0.251310	+	0.967907i	$0.419139\pi$
$572$	−6.09037e11	−	1.05488e12i	−0.237882	−	0.412024i
$573$	−4.37000e10	−	7.56906e10i	−0.0169350	−	0.0293323i
$574$	−5.05471e11	+	8.75502e11i	−0.194354	+	0.336630i
$575$	−6.38607e10	−	1.10610e11i	−0.0243629	−	0.0421977i
$576$	−5.44127e10	+	9.42455e10i	−0.0205968	+	0.0356746i
$577$	−3.78237e12			−1.42060			−0.710301	−	0.703898i	$-0.751441\pi$
$577$	−3.78237e12			−1.42060			−0.710301	+	0.703898i	$0.751441\pi$
$578$	−3.92457e12			−1.46257
$579$	−3.41275e11	+	5.91105e11i	−0.126197	+	0.218580i
$580$	4.44551e12	−	7.69986e12i	1.63116	−	2.82525i
$581$	6.44080e12			2.34502
$582$	5.44666e12			1.96778
$583$	−4.82165e11	+	8.35135e11i	−0.172857	+	0.299398i
$584$	3.46992e12	+	6.01007e12i	1.23442	+	2.13807i
$585$	5.19780e10	−	9.00285e10i	0.0183492	−	0.0317818i
$586$	−3.10455e12	−	5.37723e12i	−1.08757	−	1.88373i
$587$	−1.92576e12	−	3.33551e12i	−0.669468	−	1.15955i	−0.978053	−	0.208356i	$-0.933189\pi$
$587$	−1.92576e12	−	3.33551e12i	−0.669468	−	1.15955i	0.308585	−	0.951197i	$-0.400145\pi$
$588$	7.58520e12			2.61679
$589$	4.23536e11	+	4.62835e12i	0.145001	+	1.58456i
$590$	3.13084e12			1.06372
$591$	3.44194e11	+	5.96161e11i	0.116054	+	0.201011i
$592$	−3.81820e12	−	6.61332e12i	−1.27765	−	2.21295i
$593$	−1.97807e12	+	3.42612e12i	−0.656894	+	1.13777i	0.324521	+	0.945878i	$0.394797\pi$
$593$	−1.97807e12	+	3.42612e12i	−0.656894	+	1.13777i	−0.981415	+	0.191895i	$0.938537\pi$
$594$	2.99392e12	+	5.18562e12i	0.986737	+	1.70908i
$595$	3.95977e12	−	6.85851e12i	1.29522	−	2.24338i
$596$	−2.82408e12			−0.916789
$597$	−3.40821e12			−1.09810
$598$	−4.63320e10	+	8.02494e10i	−0.0148158	+	0.0256618i
$599$	1.08071e12	−	1.87184e12i	0.342994	−	0.594083i	−0.641993	−	0.766710i	$-0.721892\pi$
$599$	1.08071e12	−	1.87184e12i	0.342994	−	0.594083i	0.984987	+	0.172627i	$0.0552255\pi$
$600$	−3.80838e12			−1.19966
$601$	3.76890e12			1.17836			0.589181	−	0.808001i	$-0.299450\pi$
$601$	3.76890e12			1.17836			0.589181	+	0.808001i	$0.299450\pi$
$602$	−2.06431e12	+	3.57550e12i	−0.640607	+	1.10956i
$603$	−1.22803e11	−	2.12700e11i	−0.0378251	−	0.0655149i
$604$	1.04225e12	−	1.80524e12i	0.318645	−	0.551909i
$605$	1.97214e11	+	3.41585e11i	0.0598465	+	0.103657i
$606$	−6.24162e11	−	1.08108e12i	−0.188005	−	0.325635i
$607$	−4.08291e11			−0.122073			−0.0610366	−	0.998136i	$-0.519441\pi$
$607$	−4.08291e11			−0.122073			−0.0610366	+	0.998136i	$0.519441\pi$
$608$	2.22279e12	+	1.02573e12i	0.659679	+	0.304416i
$609$	−5.60452e12			−1.65105
$610$	7.14094e11	+	1.23685e12i	0.208820	+	0.361686i
$611$	5.84757e11	+	1.01283e12i	0.169742	+	0.294002i
$612$	−7.11237e11	+	1.23190e12i	−0.204943	+	0.354971i
$613$	−3.13774e12	−	5.43473e12i	−0.897522	−	1.55455i	−0.830652	−	0.556792i	$-0.812032\pi$
$613$	−3.13774e12	−	5.43473e12i	−0.897522	−	1.55455i	−0.0668701	−	0.997762i	$-0.521301\pi$
$614$	3.37802e12	−	5.85090e12i	0.959189	−	1.66136i
$615$	−6.01186e11			−0.169461
$616$	−1.19780e13			−3.35175
$617$	1.96080e12	−	3.39621e12i	0.544691	−	0.943433i	−0.453935	−	0.891035i	$-0.649980\pi$
$617$	1.96080e12	−	3.39621e12i	0.544691	−	0.943433i	0.998626	−	0.0523982i	$-0.0166865\pi$
$618$	3.99704e12	−	6.92308e12i	1.10228	−	1.90920i
$619$	4.37972e12			1.19905			0.599527	−	0.800354i	$-0.295355\pi$
$619$	4.37972e12			1.19905			0.599527	+	0.800354i	$0.295355\pi$
$620$	−1.62429e13			−4.41470
$621$	1.56276e11	−	2.70679e11i	0.0421678	−	0.0730368i
$622$	4.37469e12	+	7.57719e12i	1.17190	+	2.02979i
$623$	−2.61621e12	+	4.53141e12i	−0.695787	+	1.20514i
$624$	5.82382e11	+	1.00871e12i	0.153772	+	0.266341i
$625$	2.36084e12	+	4.08910e12i	0.618881	+	1.07193i
$626$	1.35284e12			0.352096
$627$	−3.06848e12	+	2.16686e12i	−0.792901	+	0.559921i
$628$	3.53575e12			0.907116
$629$	4.24648e12	+	7.35512e12i	1.08169	+	1.87354i
$630$	−9.42033e11	−	1.63165e12i	−0.238250	−	0.412662i
$631$	9.59848e11	−	1.66251e12i	0.241030	−	0.417475i	−0.719978	−	0.693997i	$-0.755848\pi$
$631$	9.59848e11	−	1.66251e12i	0.241030	−	0.417475i	0.961008	+	0.276521i	$0.0891816\pi$
$632$	−1.17127e11	−	2.02870e11i	−0.0292032	−	0.0505814i
$633$	−6.94489e11	+	1.20289e12i	−0.171929	+	0.297790i
$634$	−8.25715e12			−2.02968
$635$	−7.76461e12			−1.89513
$636$	1.38312e12	−	2.39564e12i	0.335200	−	0.580584i
$637$	5.57588e11	−	9.65772e11i	0.134180	−	0.232406i
$638$	9.18845e12			2.19558
$639$	7.53733e10			0.0178840
$640$	3.38143e12	−	5.85681e12i	0.796692	−	1.37991i
$641$	1.58816e12	+	2.75077e12i	0.371563	+	0.643566i	0.989806	−	0.142421i	$-0.0454887\pi$
$641$	1.58816e12	+	2.75077e12i	0.371563	+	0.643566i	−0.618243	+	0.785987i	$0.712155\pi$
$642$	2.11655e12	−	3.66597e12i	0.491723	−	0.851689i
$643$	−7.04197e11	−	1.21971e12i	−0.162459	−	0.281388i	0.773291	−	0.634052i	$-0.218609\pi$
$643$	−7.04197e11	−	1.21971e12i	−0.162459	−	0.281388i	−0.935750	+	0.352664i	$0.885276\pi$
$644$	5.76161e11	+	9.97939e11i	0.131995	+	0.228622i
$645$	−2.45521e12			−0.558559
$646$	−9.67657e12	−	4.46536e12i	−2.18613	−	1.00881i
$647$	−2.75462e12			−0.618005			−0.309003	−	0.951061i	$-0.599995\pi$
$647$	−2.75462e12			−0.618005			−0.309003	+	0.951061i	$0.599995\pi$
$648$	−3.99935e12	−	6.92708e12i	−0.891050	−	1.54334i
$649$	1.11003e12	+	1.92264e12i	0.245604	+	0.425398i
$650$	−5.15968e11	+	8.93683e11i	−0.113374	+	0.196369i
$651$	5.11941e12	+	8.86708e12i	1.11713	+	1.93493i
$652$	−7.65890e12	+	1.32656e13i	−1.65979	+	2.87483i
$653$	−6.16480e12			−1.32681			−0.663406	−	0.748260i	$-0.730890\pi$
$653$	−6.16480e12			−1.32681			−0.663406	+	0.748260i	$0.730890\pi$
$654$	8.13700e12			1.73926
$655$	−5.00538e12	+	8.66957e12i	−1.06255	+	1.84040i
$656$	−5.43726e11	+	9.41762e11i	−0.114634	+	0.198552i
$657$	−7.74045e11			−0.162077
$658$	2.11959e13			4.40794
$659$	5.88249e11	−	1.01888e12i	0.121500	−	0.210445i	−0.798859	−	0.601518i	$-0.794563\pi$
$659$	5.88249e11	−	1.01888e12i	0.121500	−	0.210445i	0.920359	+	0.391073i	$0.127896\pi$
$660$	−6.56406e12	−	1.13693e13i	−1.34656	−	2.33231i
$661$	−2.49247e12	+	4.31709e12i	−0.507837	+	0.879599i	0.492122	+	0.870526i	$0.336221\pi$
$661$	−2.49247e12	+	4.31709e12i	−0.507837	+	0.879599i	−0.999959	+	0.00907283i	$0.997112\pi$
$662$	6.00080e12	+	1.03937e13i	1.21436	+	2.10334i
$663$	−6.47706e11	−	1.12186e12i	−0.130187	−	0.225490i
$664$	1.64351e13			3.28108
$665$	7.91145e12	−	5.58682e12i	1.56877	−	1.10781i
$666$	2.02049e12			0.397944
$667$	−2.39809e11	−	4.15361e11i	−0.0469136	−	0.0812568i
$668$	1.47248e12	+	2.55041e12i	0.286125	+	0.495583i
$669$	9.53771e11	−	1.65198e12i	0.184088	−	0.318850i
$670$	3.21538e12	+	5.56920e12i	0.616447	+	1.06772i
$671$	−5.06362e11	+	8.77045e11i	−0.0964295	+	0.167021i
$672$	5.39302e12			1.02017
$673$	8.79480e12			1.65256			0.826282	−	0.563257i	$-0.190452\pi$
$673$	8.79480e12			1.65256			0.826282	+	0.563257i	$0.190452\pi$
$674$	5.12435e12	−	8.87563e12i	0.956465	−	1.65665i
$675$	1.74034e12	−	3.01436e12i	0.322677	−	0.558893i
$676$	−1.13562e13			−2.09157
$677$	−9.07801e12			−1.66089			−0.830446	−	0.557099i	$-0.811914\pi$
$677$	−9.07801e12			−1.66089			−0.830446	+	0.557099i	$0.811914\pi$
$678$	−5.48491e12	+	9.50014e12i	−0.996864	+	1.72662i
$679$	−4.97897e12	−	8.62383e12i	−0.898930	−	1.55699i
$680$	1.01042e13	−	1.75010e13i	1.81223	−	3.13887i
$681$	−1.10398e12	−	1.91214e12i	−0.196697	−	0.340689i
$682$	−8.39313e12	−	1.45373e13i	−1.48557	−	2.57309i
$683$	3.54139e12			0.622702			0.311351	−	0.950295i	$-0.399218\pi$
$683$	3.54139e12			0.622702			0.311351	+	0.950295i	$0.399218\pi$
$684$	−1.42102e12	+	1.00348e12i	−0.248227	+	0.175290i
$685$	−4.13939e10			−0.00718338
$686$	−2.27165e12	−	3.93461e12i	−0.391636	−	0.678333i
$687$	−3.11556e12	−	5.39631e12i	−0.533618	−	0.924254i
$688$	−2.22055e12	+	3.84610e12i	−0.377843	+	0.654444i
$689$	−2.03347e11	−	3.52208e11i	−0.0343757	−	0.0595405i
$690$	−4.99356e11	+	8.64910e11i	−0.0838666	+	0.145261i
$691$	3.84132e12			0.640957			0.320479	−	0.947256i	$-0.396156\pi$
$691$	3.84132e12			0.640957			0.320479	+	0.947256i	$0.396156\pi$
$692$	1.08189e13			1.79352
$693$	6.67993e11	−	1.15700e12i	0.110020	−	0.190561i
$694$	−8.91925e12	+	1.54486e13i	−1.45952	+	2.52797i
$695$	6.75778e12			1.09868
$696$	−1.43012e13			−2.31010
$697$	6.04715e11	−	1.04740e12i	0.0970517	−	0.168098i
$698$	−1.14641e12	−	1.98563e12i	−0.182805	−	0.316628i
$699$	3.52387e12	−	6.10352e12i	0.558306	−	0.967014i
$700$	6.41631e12	+	1.11134e13i	1.01005	+	1.74946i
$701$	4.86085e12	+	8.41924e12i	0.760293	+	1.31687i	0.942699	+	0.333643i	$0.108278\pi$
$701$	4.86085e12	+	8.41924e12i	0.760293	+	1.31687i	−0.182406	+	0.983223i	$0.558389\pi$
$702$	−2.52530e12			−0.392460
$703$	9.46505e11	+	1.03433e13i	0.146158	+	1.59720i
$704$	2.02051e12			0.310016
$705$	6.30238e12	+	1.09160e13i	0.960845	+	1.66423i
$706$	3.28577e12	+	5.69112e12i	0.497756	+	0.862138i
$707$	−1.14113e12	+	1.97650e12i	−0.171771	+	0.297516i
$708$	−3.18421e12	−	5.51521e12i	−0.476268	−	0.824921i
$709$	−1.04515e12	+	1.81024e12i	−0.155335	+	0.269048i	−0.933181	−	0.359407i	$-0.882979\pi$
$709$	−1.04515e12	+	1.81024e12i	−0.155335	+	0.269048i	0.777846	+	0.628455i	$0.216312\pi$
$710$	−1.97352e12			−0.291460
$711$	2.61278e10			0.00383434
$712$	−6.67585e12	+	1.15629e13i	−0.973523	+	1.68619i
$713$	−4.38104e11	+	7.58818e11i	−0.0634855	+	0.109960i
$714$	−2.34777e13			−3.38075
$715$	−1.93010e12			−0.276186
$716$	1.49324e12	−	2.58637e12i	0.212335	−	0.367775i
$717$	−1.37927e12	−	2.38897e12i	−0.194901	−	0.337578i
$718$	−6.41046e12	+	1.11032e13i	−0.900180	+	1.55916i
$719$	−2.14349e12	−	3.71264e12i	−0.299117	−	0.518086i	0.676817	−	0.736151i	$-0.263359\pi$
$719$	−2.14349e12	−	3.71264e12i	−0.299117	−	0.518086i	−0.975934	+	0.218065i	$0.930026\pi$
$720$	−1.01333e12	−	1.75514e12i	−0.140525	−	0.243397i
$721$	−1.46153e13			−2.01419
$722$	−8.45698e12	−	9.91690e12i	−1.15824	−	1.35818i
$723$	6.24469e12			0.849940
$724$	−6.12717e12	−	1.06126e13i	−0.828775	−	1.43548i
$725$	−2.67059e12	−	4.62560e12i	−0.358993	−	0.621794i
$726$	5.84646e11	−	1.01264e12i	0.0781049	−	0.135282i
$727$	−4.32997e12	−	7.49973e12i	−0.574884	−	0.995728i	−0.996054	−	0.0887464i	$-0.971714\pi$
$727$	−4.32997e12	−	7.49973e12i	−0.574884	−	0.995728i	0.421170	−	0.906982i	$-0.361619\pi$
$728$	2.52579e12	−	4.37479e12i	0.333277	−	0.577253i
$729$	8.37041e12			1.09767
$730$	2.02670e13			2.64142
$731$	2.46962e12	−	4.27751e12i	0.319891	−	0.554067i
$732$	1.45253e12	−	2.51586e12i	0.186994	−	0.323882i
$733$	3.40841e12			0.436098			0.218049	−	0.975938i	$-0.430031\pi$
$733$	3.40841e12			0.436098			0.218049	+	0.975938i	$0.430031\pi$
$734$	6.90509e12			0.878085
$735$	6.00956e12	−	1.04089e13i	0.759539	−	1.31556i
$736$	2.30759e11	+	3.99687e11i	0.0289874	+	0.0502077i
$737$	−2.28002e12	+	3.94910e12i	−0.284665	+	0.493055i
$738$	−1.43862e11	−	2.49177e11i	−0.0178523	−	0.0309210i
$739$	−4.23820e12	−	7.34077e12i	−0.522734	−	0.905402i	−0.999650	−	0.0264533i	$-0.991579\pi$
$739$	−4.23820e12	−	7.34077e12i	−0.522734	−	0.905402i	0.476916	−	0.878949i	$-0.341755\pi$
$740$	−3.62991e13			−4.44993
$741$	−1.44368e11	−	1.57764e12i	−0.0175910	−	0.192232i
$742$	−7.37080e12			−0.892683
$743$	−5.48983e12	−	9.50866e12i	−0.660860	−	1.14464i	−0.980390	−	0.197066i	$-0.936859\pi$
$743$	−5.48983e12	−	9.50866e12i	−0.660860	−	1.14464i	0.319531	−	0.947576i	$-0.396475\pi$
$744$	1.30633e13	+	2.26263e13i	1.56306	+	2.70730i
$745$	−2.23745e12	+	3.87538e12i	−0.266103	+	0.460905i
$746$	−4.83375e12	−	8.37231e12i	−0.571426	−	0.989738i
$747$	−9.16559e11	+	1.58753e12i	−0.107700	+	0.186543i
$748$	2.64104e13			3.08473
$749$	−7.73922e12			−0.898523
$750$	3.54609e12	−	6.14201e12i	0.409237	−	0.708818i
$751$	3.94958e12	−	6.84087e12i	0.453076	−	0.784751i	−0.545499	−	0.838111i	$-0.683660\pi$
$751$	3.94958e12	−	6.84087e12i	0.453076	−	0.784751i	0.998575	+	0.0533604i	$0.0169932\pi$
$752$	2.28001e13			2.59990
$753$	5.68157e12			0.644008
$754$	−1.93756e12	+	3.35595e12i	−0.218315	+	0.378132i
$755$	−1.65150e12	−	2.86049e12i	−0.184977	−	0.320390i
$756$	−1.57016e13	+	2.71960e13i	−1.74822	+	3.02801i
$757$	−2.12118e12	−	3.67399e12i	−0.234771	−	0.406636i	0.724435	−	0.689343i	$-0.242101\pi$
$757$	−2.12118e12	−	3.67399e12i	−0.234771	−	0.406636i	−0.959206	+	0.282707i	$0.908768\pi$
$758$	−3.48288e11	−	6.03253e11i	−0.0383202	−	0.0663725i
$759$	−7.08184e11			−0.0774565
$760$	2.01879e13	−	1.42560e13i	2.19497	−	1.55002i
$761$	1.64007e13			1.77268			0.886342	−	0.463031i	$-0.153238\pi$
$761$	1.64007e13			1.77268			0.886342	+	0.463031i	$0.153238\pi$
$762$	1.15092e13	+	1.99345e13i	1.23665	+	2.14195i
$763$	−7.43830e12	−	1.28835e13i	−0.794535	−	1.37618i
$764$	−3.75742e11	+	6.50804e11i	−0.0398997	+	0.0691083i
$765$	1.12699e12	+	1.95200e12i	0.118972	+	0.206065i
$766$	−5.89169e12	+	1.02047e13i	−0.618316	+	1.07095i
$767$	−9.36285e11			−0.0976853
$768$	−1.73975e13			−1.80452
$769$	6.71890e12	−	1.16375e13i	0.692835	−	1.20003i	−0.278070	−	0.960561i	$-0.589695\pi$
$769$	6.71890e12	−	1.16375e13i	0.692835	−	1.20003i	0.970905	−	0.239464i	$-0.0769718\pi$
$770$	−1.74903e13	+	3.02940e13i	−1.79303	+	3.10562i
$771$	3.47500e12			0.354169
$772$	5.86871e12			0.594655
$773$	−3.31689e12	+	5.74502e12i	−0.334136	+	0.578740i	−0.983318	−	0.181892i	$-0.941778\pi$
$773$	−3.31689e12	+	5.74502e12i	−0.334136	+	0.578740i	0.649183	+	0.760633i	$0.275111\pi$
$774$	−5.87525e11	−	1.01762e12i	−0.0588427	−	0.101918i
$775$	−4.87887e12	+	8.45044e12i	−0.485804	+	0.841437i
$776$	−1.27050e13	−	2.20057e13i	−1.25775	−	2.17850i
$777$	1.14407e13	+	1.98158e13i	1.12605	+	1.95037i
$778$	7.81854e12			0.765099
$779$	1.20820e12	−	8.53189e11i	0.117549	−	0.0830093i
$780$	5.53662e12			0.535573
$781$	−6.99710e11	−	1.21193e12i	−0.0672959	−	0.116560i
$782$	−1.00457e12	−	1.73997e12i	−0.0960620	−	0.166384i
$783$	6.53532e12	−	1.13195e13i	0.621353	−	1.07622i
$784$	−1.08704e13	−	1.88281e13i	−1.02760	−	1.77985i
$785$	2.80128e12	−	4.85197e12i	0.263296	−	0.456042i
$786$	2.96772e13			2.77345
$787$	−3.85149e12			−0.357884			−0.178942	−	0.983860i	$-0.557267\pi$
$787$	−3.85149e12			−0.357884			−0.178942	+	0.983860i	$0.557267\pi$
$788$	2.95946e12	−	5.12593e12i	0.273429	−	0.473592i
$789$	−3.72639e12	+	6.45430e12i	−0.342328	+	0.592929i
$790$	−6.84113e11			−0.0624894
$791$	2.00558e13			1.82157
$792$	1.70454e12	−	2.95234e12i	0.153937	−	0.266626i
$793$	−2.13552e11	−	3.69883e11i	−0.0191767	−	0.0332150i
$794$	1.19856e13	−	2.07596e13i	1.07021	−	1.85365i
$795$	−2.19163e12	−	3.79601e12i	−0.194588	−	0.337036i
$796$	1.46523e13	+	2.53785e13i	1.29359	+	2.24056i
$797$	−8.96871e12			−0.787349			−0.393675	−	0.919250i	$-0.628796\pi$
$797$	−8.96871e12			−0.787349			−0.393675	+	0.919250i	$0.628796\pi$
$798$	−2.60702e13	−	1.20304e13i	−2.27579	−	1.05019i
$799$	−2.53575e13			−2.20113
$800$	2.56981e12	+	4.45104e12i	0.221818	+	0.384200i
$801$	−7.44600e11	−	1.28969e12i	−0.0639112	−	0.110697i
$802$	−2.16431e12	+	3.74869e12i	−0.184729	+	0.319959i
$803$	7.18565e12	+	1.24459e13i	0.609883	+	1.05635i
$804$	6.54038e12	−	1.13283e13i	0.552015	−	0.956118i
$805$	1.82591e12			0.153249
$806$	7.07939e12			0.590865
$807$	−1.24329e12	+	2.15344e12i	−0.103191	+	0.178732i
$808$	−2.91186e12	+	5.04349e12i	−0.240336	+	0.416275i
$809$	7.19472e12			0.590535			0.295268	−	0.955415i	$-0.404591\pi$
$809$	7.19472e12			0.590535			0.295268	+	0.955415i	$0.404591\pi$
$810$	−2.33594e13			−1.90668
$811$	−6.61755e12	+	1.14619e13i	−0.537160	+	0.930388i	0.461896	+	0.886934i	$0.347169\pi$
$811$	−6.61755e12	+	1.14619e13i	−0.537160	+	0.930388i	−0.999055	+	0.0434538i	$0.986164\pi$
$812$	2.40944e13	+	4.17328e13i	1.94498	+	3.36880i
$813$	1.34487e12	−	2.32938e12i	0.107962	−	0.186996i
$814$	−1.87567e13	−	3.24875e13i	−1.49743	−	2.59362i
$815$	1.21359e13	+	2.10200e13i	0.963525	+	1.66887i
$816$	−2.52545e13			−1.99404
$817$	4.93420e12	−	3.48438e12i	0.387452	−	0.273606i
$818$	1.53869e12			0.120161
$819$	2.81718e11	+	4.87949e11i	0.0218794	+	0.0378963i
$820$	2.58456e12	+	4.47660e12i	0.199630	+	0.345769i
$821$	2.84310e12	−	4.92440e12i	0.218398	−	0.378276i	−0.735921	−	0.677068i	$-0.763250\pi$
$821$	2.84310e12	−	4.92440e12i	0.218398	−	0.378276i	0.954318	+	0.298792i	$0.0965836\pi$
$822$	6.13567e10	+	1.06273e11i	0.00468747	+	0.00811894i
$823$	−1.17891e13	+	2.04193e13i	−0.895739	+	1.55147i	−0.0628526	+	0.998023i	$0.520020\pi$
$823$	−1.17891e13	+	2.04193e13i	−0.895739	+	1.55147i	−0.832887	+	0.553443i	$0.813314\pi$
$824$	−3.72943e13			−2.81819
$825$	−7.88656e12			−0.592714
$826$	−8.48448e12	+	1.46955e13i	−0.634184	+	1.09844i
$827$	−4.91407e11	+	8.51141e11i	−0.0365314	+	0.0632742i	−0.883713	−	0.468029i	$-0.844964\pi$
$827$	−4.91407e11	+	8.51141e11i	−0.0365314	+	0.0632742i	0.847182	+	0.531303i	$0.178298\pi$
$828$	−3.27963e11			−0.0242487
$829$	−8.04163e12			−0.591356			−0.295678	−	0.955288i	$-0.595546\pi$
$829$	−8.04163e12			−0.591356			−0.295678	+	0.955288i	$0.595546\pi$
$830$	2.39985e13	−	4.15667e13i	1.75523	−	3.04014i
$831$	1.88502e12	+	3.26495e12i	0.137123	+	0.237505i
$832$	−4.26062e11	+	7.37960e11i	−0.0308260	+	0.0533922i
$833$	1.20897e13	+	2.09399e13i	0.869986	+	1.50686i
$834$	−1.00168e13	−	1.73496e13i	−0.716939	−	1.24178i
$835$	4.66644e12			0.332198
$836$	2.93268e13	+	1.35332e13i	2.07652	+	0.958232i
$837$	−2.38786e13			−1.68168
$838$	5.67362e11	+	9.82700e11i	0.0397432	+	0.0688372i
$839$	−2.64237e12	−	4.57673e12i	−0.184105	−	0.318879i	0.759170	−	0.650893i	$-0.225605\pi$
$839$	−2.64237e12	−	4.57673e12i	−0.184105	−	0.318879i	−0.943275	+	0.332014i	$0.892272\pi$
$840$	2.72224e13	−	4.71506e13i	1.88655	−	3.26761i
$841$	−2.77499e12	−	4.80642e12i	−0.191284	−	0.331314i
$842$	1.20466e13	−	2.08653e13i	0.825961	−	1.43061i
$843$	1.60349e13			1.09356
$844$	1.19427e13			0.810146
$845$	−8.99721e12	+	1.55836e13i	−0.607089	+	1.05151i
$846$	−3.01629e12	+	5.22436e12i	−0.202445	+	0.350644i
$847$	−2.13778e12			−0.142721
$848$	−7.92865e12			−0.526523
$849$	−7.69514e12	+	1.33284e13i	−0.508314	+	0.880426i
$850$	−1.11873e13	−	1.93769e13i	−0.735087	−	1.27321i
$851$	−9.79060e11	+	1.69578e12i	−0.0639921	+	0.110838i
$852$	2.00717e12	+	3.47651e12i	0.130498	+	0.226030i
$853$	−8.08954e12	−	1.40115e13i	−0.523182	−	0.906179i	−0.999636	−	0.0269789i	$-0.991411\pi$
$853$	−8.08954e12	−	1.40115e13i	−0.523182	−	0.906179i	0.476454	−	0.879200i	$-0.341922\pi$
$854$	−7.74070e12			−0.497989
$855$	2.51197e11	+	2.74505e12i	0.0160756	+	0.175672i
$856$	−1.97484e13			−1.25719
$857$	−3.93975e12	−	6.82385e12i	−0.249491	−	0.432131i	0.713894	−	0.700254i	$-0.246930\pi$
$857$	−3.93975e12	−	6.82385e12i	−0.249491	−	0.432131i	−0.963385	+	0.268123i	$0.913597\pi$
$858$	2.86091e12	+	4.95525e12i	0.180224	+	0.312157i
$859$	9.95166e12	−	1.72368e13i	0.623629	−	1.08016i	−0.365175	−	0.930939i	$-0.618991\pi$
$859$	9.95166e12	−	1.72368e13i	0.623629	−	1.08016i	0.988804	−	0.149219i	$-0.0476758\pi$
$860$	1.05552e13	+	1.82822e13i	0.657997	+	1.13968i
$861$	1.62920e12	−	2.82185e12i	0.101032	−	0.174993i
$862$	3.14190e13			1.93825
$863$	−6.88670e12			−0.422632			−0.211316	−	0.977418i	$-0.567775\pi$
$863$	−6.88670e12			−0.422632			−0.211316	+	0.977418i	$0.567775\pi$
$864$	−6.28870e12	+	1.08923e13i	−0.383927	+	0.664982i
$865$	8.57154e12	−	1.48463e13i	0.520579	−	0.901669i
$866$	−7.74675e12			−0.468047
$867$	1.26494e13			0.760296
$868$	4.40178e13	−	7.62411e13i	2.63202	−	4.55880i
$869$	−2.42552e11	−	4.20112e11i	−0.0144283	−	0.0249905i
$870$	−2.08825e13	+	3.61696e13i	−1.23580	+	2.14046i
$871$	−9.61568e11	−	1.66548e12i	−0.0566107	−	0.0980526i
$872$	−1.89805e13	−	3.28752e13i	−1.11169	−	1.92550i
$873$	2.83414e12			0.165142
$874$	−2.23911e11	−	2.44687e12i	−0.0129800	−	0.141844i
$875$	−1.29664e13			−0.747796
$876$	−2.06125e13	−	3.57020e13i	−1.18267	−	2.04844i
$877$	1.35689e13	+	2.35020e13i	0.774542	+	1.34155i	0.935051	+	0.354512i	$0.115353\pi$
$877$	1.35689e13	+	2.35020e13i	0.774542	+	1.34155i	−0.160509	+	0.987034i	$0.551314\pi$
$878$	−1.84616e13	+	3.19764e13i	−1.04844	+	1.81595i
$879$	1.00063e13	+	1.73315e13i	0.565360	+	0.979232i
$880$	−1.88140e13	+	3.25868e13i	−1.05757	+	1.83176i
$881$	−5.73268e12			−0.320602			−0.160301	−	0.987068i	$-0.551246\pi$
$881$	−5.73268e12			−0.320602			−0.160301	+	0.987068i	$0.551246\pi$
$882$	5.75230e12			0.320061
$883$	−1.57296e13	+	2.72444e13i	−0.870750	+	1.50818i	−0.00952737	+	0.999955i	$0.503033\pi$
$883$	−1.57296e13	+	2.72444e13i	−0.870750	+	1.50818i	−0.861222	+	0.508228i	$0.830301\pi$
$884$	−5.56912e12	+	9.64600e12i	−0.306727	+	0.531266i
$885$	−1.00911e13			−0.552959
$886$	−4.59816e13			−2.50688
$887$	1.39606e13	−	2.41804e13i	0.757263	−	1.31162i	−0.186979	−	0.982364i	$-0.559870\pi$
$887$	1.39606e13	−	2.41804e13i	0.757263	−	1.31162i	0.944242	−	0.329254i	$-0.106797\pi$
$888$	2.91935e13	+	5.05646e13i	1.57553	+	2.72890i
$889$	2.10419e13	−	3.64456e13i	1.12987	−	1.95698i
$890$	1.94961e13	+	3.37682e13i	1.04158	+	1.80407i
$891$	−8.28203e12	−	1.43449e13i	−0.440237	−	0.762514i
$892$	−1.64015e13			−0.867443
$893$	−2.81576e13	−	1.29936e13i	−1.48171	−	0.683753i
$894$	1.32660e13			0.694577
$895$	−2.36612e12	−	4.09824e12i	−0.123263	−	0.213498i
$896$	1.83272e13	+	3.17436e13i	0.949969	+	1.64539i
$897$	1.49334e11	−	2.58654e11i	0.00770180	−	0.0133399i
$898$	1.77367e13	+	3.07208e13i	0.910183	+	1.57648i
$899$	−1.83211e13	+	3.17330e13i	−0.935474	+	1.62029i
$900$	−3.65230e12			−0.185556
$901$	8.81798e12			0.445767
$902$	−2.67102e12	+	4.62635e12i	−0.134353	+	0.232707i
$903$	6.65354e12	−	1.15243e13i	0.333010	−	0.576791i
$904$	5.11768e13			2.54868
$905$	−1.94176e13			−0.962227
$906$	−4.89592e12	+	8.47999e12i	−0.241411	+	0.418137i
$907$	−4.77136e12	−	8.26423e12i	−0.234104	−	0.405480i	0.724908	−	0.688846i	$-0.241882\pi$
$907$	−4.77136e12	−	8.26423e12i	−0.234104	−	0.405480i	−0.959012	+	0.283366i	$0.908549\pi$
$908$	−9.49223e12	+	1.64410e13i	−0.463428	+	0.802681i
$909$	−3.24779e11	−	5.62533e11i	−0.0157779	−	0.0273282i
$910$	−7.37630e12	−	1.27761e13i	−0.356576	−	0.617608i
$911$	2.01303e13			0.968315			0.484158	−	0.874981i	$-0.339126\pi$
$911$	2.01303e13			0.968315			0.484158	+	0.874981i	$0.339126\pi$
$912$	−2.80433e13	−	1.29409e13i	−1.34231	−	0.619422i
$913$	3.40346e13			1.62107
$914$	1.44196e13	+	2.49754e13i	0.683430	+	1.18374i
$915$	−2.30161e12	−	3.98651e12i	−0.108552	−	0.188018i
$916$	−2.67883e13	+	4.63986e13i	−1.25723	+	2.17759i
$917$	−2.71289e13	−	4.69886e13i	−1.26698	−	2.19447i
$918$	2.73768e13	−	4.74181e13i	1.27231	−	2.20370i
$919$	−2.20807e13			−1.02116			−0.510580	−	0.859830i	$-0.670569\pi$
$919$	−2.20807e13			−1.02116			−0.510580	+	0.859830i	$0.670569\pi$
$920$	4.65922e12			0.214421
$921$	−1.08878e13	+	1.88582e13i	−0.498621	+	0.863637i
$922$	3.05015e13	−	5.28302e13i	1.39006	−	2.40765i
$923$	5.90188e11			0.0267659
$924$	7.11537e13			3.21125
$925$	−1.09031e13	+	1.88848e13i	−0.489681	+	0.848152i
$926$	−1.36760e13	−	2.36875e13i	−0.611236	−	1.05869i
$927$	2.07984e12	−	3.60238e12i	0.0925061	−	0.160225i
$928$	9.65012e12	+	1.67145e13i	0.427137	+	0.739823i
$929$	−7.97806e11	−	1.38184e12i	−0.0351420	−	0.0608678i	0.847919	−	0.530125i	$-0.177855\pi$
$929$	−7.97806e11	−	1.38184e12i	−0.0351420	−	0.0608678i	−0.883061	+	0.469257i	$0.844522\pi$
$930$	7.63001e13			3.34466
$931$	2.69469e12	+	2.94472e13i	0.117553	+	1.28461i
$932$	−6.05980e13			−2.63079
$933$	−1.41002e13	−	2.44222e13i	−0.609196	−	1.05516i
$934$	−5.68504e12	−	9.84677e12i	−0.244440	−	0.423383i
$935$	2.09243e13	−	3.62419e13i	0.895362	−	1.55081i
$936$	7.18866e11	+	1.24511e12i	0.0306130	+	0.0530234i
$937$	−5.55677e12	+	9.62460e12i	−0.235502	+	0.407901i	−0.959418	−	0.281986i	$-0.909007\pi$
$937$	−5.55677e12	+	9.62460e12i	−0.235502	+	0.407901i	0.723917	+	0.689887i	$0.242340\pi$
$938$	−3.48543e13			−1.47009
$939$	−4.36036e12			−0.183032
$940$	5.41892e13	−	9.38585e13i	2.26380	−	3.92101i
$941$	1.21592e13	−	2.10603e13i	0.505535	−	0.875613i	−0.494444	−	0.869209i	$-0.664628\pi$
$941$	1.21592e13	−	2.10603e13i	0.505535	−	0.875613i	0.999979	−	0.00640365i	$-0.00203836\pi$
$942$	−1.66090e13			−0.687248
$943$	2.78844e11			0.0114831
$944$	−9.12661e12	+	1.58077e13i	−0.374055	+	0.647882i
$945$	2.48800e13	+	4.30935e13i	1.01486	+	1.75780i
$946$	−1.09083e13	+	1.88937e13i	−0.442840	+	0.767022i
$947$	1.50050e12	+	2.59894e12i	0.0606262	+	0.105008i	0.894745	−	0.446576i	$-0.147357\pi$
$947$	1.50050e12	+	2.59894e12i	0.0606262	+	0.105008i	−0.834119	+	0.551584i	$0.814024\pi$
$948$	6.95775e11	+	1.20512e12i	0.0279790	+	0.0484610i
$949$	−6.06092e12			−0.242572
$950$	−2.49355e12	−	2.72492e13i	−0.0993257	−	1.08542i
$951$	2.66138e13			1.05510
$952$	5.47644e13	+	9.48547e13i	2.16089	+	3.74276i
$953$	−1.07585e13	−	1.86343e13i	−0.422509	−	0.731806i	0.573676	−	0.819083i	$-0.305517\pi$
$953$	−1.07585e13	−	1.86343e13i	−0.422509	−	0.731806i	−0.996184	+	0.0872764i	$0.972184\pi$
$954$	1.04890e12	−	1.81676e12i	0.0409985	−	0.0710115i
$955$	5.95382e11	+	1.03123e12i	0.0231622	+	0.0401182i
$956$	−1.18593e13	+	2.05409e13i	−0.459196	+	0.795351i
$957$	−2.96155e13			−1.14134
$958$	−3.67136e13			−1.40826
$959$	1.12176e11	−	1.94295e11i	0.00428270	−	0.00741785i
$960$	−4.59200e12	+	7.95357e12i	−0.174494	+	0.302233i
$961$	4.05014e13			1.53184
$962$	1.58208e13			0.595580
$963$	1.10133e12	−	1.90756e12i	0.0412667	−	0.0714761i
$964$	−2.68466e13	−	4.64997e13i	−1.00125	−	1.73422i
$965$	4.64963e12	−	8.05340e12i	0.172602	−	0.298955i
$966$	−2.70648e12	−	4.68776e12i	−0.100002	−	0.173208i
$967$	−8.55455e12	−	1.48169e13i	−0.314614	−	0.544927i	0.664741	−	0.747074i	$-0.268542\pi$
$967$	−8.55455e12	−	1.48169e13i	−0.314614	−	0.544927i	−0.979355	+	0.202146i	$0.935208\pi$
$968$	−5.45502e12			−0.199691
$969$	3.11888e13	+	1.43924e13i	1.13643	+	0.524417i
$970$	−7.42070e13			−2.69136
$971$	6.13592e12	+	1.06277e13i	0.221510	+	0.383666i	0.955267	−	0.295746i	$-0.0955682\pi$
$971$	6.13592e12	+	1.06277e13i	0.221510	+	0.383666i	−0.733757	+	0.679412i	$0.762235\pi$
$972$	−8.39233e12	−	1.45359e13i	−0.301567	−	0.522330i
$973$	−1.83134e13	+	3.17197e13i	−0.655030	+	1.13455i
$974$	3.94144e13	+	6.82678e13i	1.40326	+	2.43053i
$975$	1.66303e12	−	2.88045e12i	0.0589358	−	0.102080i
$976$	−8.32654e12			−0.293725
$977$	1.53208e13			0.537969			0.268984	−	0.963145i	$-0.413312\pi$
$977$	1.53208e13			0.537969			0.268984	+	0.963145i	$0.413312\pi$
$978$	3.59772e13	−	6.23144e13i	1.25749	−	2.17803i
$979$	−1.38246e13	+	2.39450e13i	−0.480985	+	0.833090i
$980$	−1.03343e14			−3.57902
$981$	4.23403e12			0.145963
$982$	−2.97459e13	+	5.15213e13i	−1.02076	+	1.76801i
$983$	2.81825e13	+	4.88136e13i	0.962696	+	1.66744i	0.715681	+	0.698428i	$0.246117\pi$
$983$	2.81825e13	+	4.88136e13i	0.962696	+	1.66744i	0.247016	+	0.969011i	$0.420550\pi$
$984$	4.15726e12	−	7.20059e12i	0.141361	−	0.244844i
$985$	−4.68941e12	−	8.12229e12i	−0.158728	−	0.274926i
$986$	−4.20103e13	−	7.27639e13i	−1.41550	−	2.45171i
$987$	−6.83170e13			−2.29140
$988$	−1.11269e13	+	7.85745e12i	−0.371507	+	0.262346i
$989$	1.13878e12			0.0378492
$990$	−4.97791e12	−	8.62200e12i	−0.164698	−	0.285266i
$991$	2.27808e12	+	3.94575e12i	0.0750304	+	0.129956i	0.901099	−	0.433612i	$-0.142761\pi$
$991$	2.27808e12	+	3.94575e12i	0.0750304	+	0.129956i	−0.826069	+	0.563569i	$0.809428\pi$
$992$	1.76297e13	−	3.05355e13i	0.578019	−	1.00116i
$993$	−1.93413e13	−	3.35002e13i	−0.631269	−	1.09339i
$994$	5.34819e12	−	9.26334e12i	0.173767	−	0.300974i
$995$	4.64346e13			1.50189
$996$	−9.76306e13			−3.14354
$997$	1.51242e13	−	2.61959e13i	0.484781	−	0.839665i	−0.515067	−	0.857150i	$-0.672233\pi$
$997$	1.51242e13	−	2.61959e13i	0.484781	−	0.839665i	0.999847	+	0.0174856i	$0.00556614\pi$
$998$	−3.17358e13	+	5.49681e13i	−1.01266	+	1.75397i
$999$	−5.33630e13			−1.69510

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.10.c.a.7.14	✓	28
19.7	even	3		361.10.a.e.1.1		14
19.11	even	3	inner	19.10.c.a.11.14	yes	28
19.12	odd	6		361.10.a.f.1.14		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.10.c.a.7.14	✓	28	1.1	even	1	trivial
19.10.c.a.11.14	yes	28	19.11	even	3	inner
361.10.a.e.1.1		14	19.7	even	3
361.10.a.f.1.14		14	19.12	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+(20.1948 + 34.9785i) q^{2} +(-65.0904 - 112.740i) q^{3} +(-559.662 + 969.363i) q^{4} +(886.813 + 1536.00i) q^{5} +(2628.98 - 4553.53i) q^{6} -9612.95 q^{7} -24529.6 q^{8} +(1367.97 - 2369.40i) q^{9} +(-35818.1 + 62038.7i) q^{10} -50797.0 q^{11} +145715. q^{12} +(10711.5 - 18552.8i) q^{13} +(-194132. - 336246. i) q^{14} +(115446. - 199958. i) q^{15} +(-208824. - 361694. i) q^{16} +(232247. + 402264. i) q^{17} +110504. q^{18} +(51766.0 + 565692. i) q^{19} -1.98526e6 q^{20} +(625711. + 1.08376e6i) q^{21} +(-1.02584e6 - 1.77680e6i) q^{22} +(-53546.5 + 92745.2i) q^{23} +(1.59664e6 + 2.76547e6i) q^{24} +(-596311. + 1.03284e6i) q^{25} +865267. q^{26} -2.91852e6 q^{27} +(5.38000e6 - 9.31844e6i) q^{28} +(-2.23926e6 + 3.87851e6i) q^{29} +9.32565e6 q^{30} +8.18175e6 q^{31} +(2.15476e6 - 3.73215e6i) q^{32} +(3.30640e6 + 5.72685e6i) q^{33} +(-9.38039e6 + 1.62473e7i) q^{34} +(-8.52489e6 - 1.47655e7i) q^{35} +(1.53120e6 + 2.65212e6i) q^{36} +1.82843e7 q^{37} +(-1.87416e7 + 1.32348e7i) q^{38} -2.78886e6 q^{39} +(-2.17532e7 - 3.76776e7i) q^{40} +(-1.30188e6 - 2.25491e6i) q^{41} +(-2.52722e7 + 4.37728e7i) q^{42} +(-5.31678e6 - 9.20894e6i) q^{43} +(2.84291e7 - 4.92407e7i) q^{44} +4.85254e6 q^{45} -4.32545e6 q^{46} +(-2.72958e7 + 4.72776e7i) q^{47} +(-2.71849e7 + 4.70857e7i) q^{48} +5.20552e7 q^{49} -4.81696e7 q^{50} +(3.02342e7 - 5.23671e7i) q^{51} +(1.19896e7 + 2.07666e7i) q^{52} +(9.49201e6 - 1.64406e7i) q^{53} +(-5.89390e7 - 1.02085e8i) q^{54} +(-4.50474e7 - 7.80244e7i) q^{55} +2.35802e8 q^{56} +(6.04067e7 - 4.26573e7i) q^{57} -1.80886e8 q^{58} +(-2.18524e7 - 3.78494e7i) q^{59} +(1.29222e8 + 2.23818e8i) q^{60} +(9.96836e6 - 1.72657e7i) q^{61} +(1.65229e8 + 2.86185e8i) q^{62} +(-1.31503e7 + 2.27769e7i) q^{63} -3.97761e7 q^{64} +3.79963e7 q^{65} +(-1.33544e8 + 2.31305e8i) q^{66} +(4.48849e7 - 7.77429e7i) q^{67} -5.19920e8 q^{68} +1.39415e7 q^{69} +(3.44317e8 - 5.96375e8i) q^{70} +(1.37746e7 + 2.38584e7i) q^{71} +(-3.35558e7 + 5.81204e7i) q^{72} +(-1.41458e8 - 2.45013e8i) q^{73} +(3.69248e8 + 6.39557e8i) q^{74} +1.55257e8 q^{75} +(-5.77333e8 - 2.66417e8i) q^{76} +4.88309e8 q^{77} +(-5.63206e7 - 9.75501e7i) q^{78} +(4.77492e6 + 8.27041e6i) q^{79} +(3.70376e8 - 6.41510e8i) q^{80} +(1.63042e8 + 2.82397e8i) q^{81} +(5.25823e7 - 9.10752e7i) q^{82} -6.70013e8 q^{83} -1.40075e9 q^{84} +(-4.11920e8 + 7.13466e8i) q^{85} +(2.14743e8 - 3.71946e8i) q^{86} +5.83017e8 q^{87} +1.24603e9 q^{88} +(2.72155e8 - 4.71386e8i) q^{89} +(9.79963e7 + 1.69734e8i) q^{90} +(-1.02969e8 + 1.78348e8i) q^{91} +(-5.99359e7 - 1.03812e8i) q^{92} +(-5.32553e8 - 9.22410e8i) q^{93} -2.20493e9 q^{94} +(-8.23000e8 + 5.81176e8i) q^{95} -5.61017e8 q^{96} +(5.17944e8 + 8.97106e8i) q^{97} +(1.05125e9 + 1.82081e9i) q^{98} +(-6.94889e7 + 1.20358e8i) 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

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