LMFDB - Embedded newform 19.10.c.a.11.3

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			11.3
Character	$\chi$	$=$	19.11
Dual form			19.10.c.a.7.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-16.3218 + 28.2702i) q^{2} +(-65.4143 + 113.301i) q^{3} +(-276.801 - 479.434i) q^{4} +(-805.880 + 1395.83i) q^{5} +(-2135.35 - 3698.54i) q^{6} -7030.62 q^{7} +1358.05 q^{8} +(1283.45 + 2223.00i) q^{9} +(-26306.8 - 45564.7i) q^{10} +48122.3 q^{11} +72427.0 q^{12} +(78134.7 + 135333. i) q^{13} +(114752. - 198757. i) q^{14} +(-105432. - 182614. i) q^{15} +(119556. - 207078. i) q^{16} +(115035. - 199247. i) q^{17} -83792.6 q^{18} +(-351240. + 446451. i) q^{19} +892274. q^{20} +(459903. - 796575. i) q^{21} +(-785442. + 1.36043e6i) q^{22} +(-252892. - 438021. i) q^{23} +(-88835.7 + 153868. i) q^{24} +(-322324. - 558281. i) q^{25} -5.10119e6 q^{26} -2.91092e6 q^{27} +(1.94608e6 + 3.37071e6i) q^{28} +(-523657. - 907001. i) q^{29} +6.88336e6 q^{30} +1.56771e6 q^{31} +(4.25041e6 + 7.36192e6i) q^{32} +(-3.14789e6 + 5.45230e6i) q^{33} +(3.75516e6 + 6.50412e6i) q^{34} +(5.66584e6 - 9.81352e6i) q^{35} +(710519. - 1.23066e6i) q^{36} -1.01626e7 q^{37} +(-6.88838e6 - 1.72165e7i) q^{38} -2.04445e7 q^{39} +(-1.09442e6 + 1.89560e6i) q^{40} +(1.04812e7 - 1.81540e7i) q^{41} +(1.50129e7 + 2.60030e7i) q^{42} +(196251. - 339917. i) q^{43} +(-1.33203e7 - 2.30715e7i) q^{44} -4.13722e6 q^{45} +1.65106e7 q^{46} +(-2.38877e7 - 4.13748e7i) q^{47} +(1.56414e7 + 2.70917e7i) q^{48} +9.07597e6 q^{49} +2.10436e7 q^{50} +(1.50499e7 + 2.60672e7i) q^{51} +(4.32556e7 - 7.49208e7i) q^{52} +(4.25064e7 + 7.36232e7i) q^{53} +(4.75114e7 - 8.22922e7i) q^{54} +(-3.87808e7 + 6.71704e7i) q^{55} -9.54791e6 q^{56} +(-2.76072e7 - 6.90000e7i) q^{57} +3.41881e7 q^{58} +(-6.47865e7 + 1.12214e8i) q^{59} +(-5.83675e7 + 1.01095e8i) q^{60} +(5.02645e6 + 8.70606e6i) q^{61} +(-2.55878e7 + 4.43194e7i) q^{62} +(-9.02343e6 - 1.56290e7i) q^{63} -1.55071e8 q^{64} -2.51869e8 q^{65} +(-1.02758e8 - 1.77982e8i) q^{66} +(1.06302e8 + 1.84121e8i) q^{67} -1.27367e8 q^{68} +6.61709e7 q^{69} +(1.84953e8 + 3.20348e8i) q^{70} +(1.78505e8 - 3.09180e8i) q^{71} +(1.74298e6 + 3.01893e6i) q^{72} +(-1.52816e8 + 2.64685e8i) q^{73} +(1.65871e8 - 2.87297e8i) q^{74} +8.43383e7 q^{75} +(3.11267e8 + 4.48180e7i) q^{76} -3.38330e8 q^{77} +(3.33691e8 - 5.77969e8i) q^{78} +(2.42805e8 - 4.20551e8i) q^{79} +(1.92696e8 + 3.33760e8i) q^{80} +(1.65154e8 - 2.86055e8i) q^{81} +(3.42145e8 + 5.92612e8i) q^{82} -4.81884e8 q^{83} -5.09206e8 q^{84} +(1.85409e8 + 3.21138e8i) q^{85} +(6.40634e6 + 1.10961e7i) q^{86} +1.37019e8 q^{87} +6.53524e7 q^{88} +(-3.82057e8 - 6.61742e8i) q^{89} +(6.75268e7 - 1.16960e8i) q^{90} +(-5.49335e8 - 9.51477e8i) q^{91} +(-1.40001e8 + 2.42490e8i) q^{92} +(-1.02550e8 + 1.77623e8i) q^{93} +1.55956e9 q^{94} +(-3.40110e8 - 8.50055e8i) q^{95} -1.11215e9 q^{96} +(-5.47630e8 + 9.48522e8i) q^{97} +(-1.48136e8 + 2.56579e8i) q^{98} +(6.17625e7 + 1.06976e8i) 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 $

$2$	−16.3218	+	28.2702i	−0.721328	+	1.24938i	0.239140	+	0.970985i	$0.423134\pi$
$2$	−16.3218	+	28.2702i	−0.721328	+	1.24938i	−0.960468	+	0.278391i	$0.910199\pi$
$3$	−65.4143	+	113.301i	−0.466259	+	0.807584i	−0.999257	−	0.0385325i	$-0.987732\pi$
$3$	−65.4143	+	113.301i	−0.466259	+	0.807584i	0.532999	+	0.846116i	$0.321065\pi$
$4$	−276.801	−	479.434i	−0.540627	−	0.936394i
$5$	−805.880	+	1395.83i	−0.576641	+	0.998772i	0.419220	+	0.907885i	$0.362304\pi$
$5$	−805.880	+	1395.83i	−0.576641	+	0.998772i	−0.995861	+	0.0908869i	$0.971030\pi$
$6$	−2135.35	−	3698.54i	−0.672650	−	1.16506i
$7$	−7030.62			−1.10676			−0.553378	−	0.832930i	$-0.686662\pi$
$7$	−7030.62			−1.10676			−0.553378	+	0.832930i	$0.686662\pi$
$8$	1358.05			0.117222
$9$	1283.45	+	2223.00i	0.0652059	+	0.112940i
$10$	−26306.8	−	45564.7i	−0.831894	−	1.44088i
$11$	48122.3			0.991013			0.495507	−	0.868604i	$-0.334982\pi$
$11$	48122.3			0.991013			0.495507	+	0.868604i	$0.334982\pi$
$12$	72427.0			1.00829
$13$	78134.7	+	135333.i	0.758750	+	1.31419i	0.943488	+	0.331406i	$0.107523\pi$
$13$	78134.7	+	135333.i	0.758750	+	1.31419i	−0.184738	+	0.982788i	$0.559144\pi$
$14$	114752.	−	198757.i	0.798334	−	1.38276i
$15$	−105432.	−	182614.i	−0.537728	−	0.931372i
$16$	119556.	−	207078.i	0.456072	−	0.789939i
$17$	115035.	−	199247.i	0.334049	−	0.578590i	−0.649253	−	0.760573i	$-0.724918\pi$
$17$	115035.	−	199247.i	0.334049	−	0.578590i	0.983302	+	0.181983i	$0.0582515\pi$
$18$	−83792.6			−0.188139
$19$	−351240.	+	446451.i	−0.618319	+	0.785927i
$19$	−351240.	+	446451.i	−0.618319	+	0.785927i
$20$	892274.			1.24699
$21$	459903.	−	796575.i	0.516035	−	0.893799i
$22$	−785442.	+	1.36043e6i	−0.714845	+	1.23815i
$23$	−252892.	−	438021.i	−0.188434	−	0.326377i	0.756294	−	0.654232i	$-0.227008\pi$
$23$	−252892.	−	438021.i	−0.188434	−	0.326377i	−0.944728	+	0.327854i	$0.893675\pi$
$24$	−88835.7	+	153868.i	−0.0546559	+	0.0946667i
$25$	−322324.	−	558281.i	−0.165030	−	0.285840i
$26$	−5.10119e6			−2.18923
$27$	−2.91092e6			−1.05413
$28$	1.94608e6	+	3.37071e6i	0.598343	+	1.03636i
$29$	−523657.	−	907001.i	−0.137485	−	0.238131i	0.789059	−	0.614318i	$-0.210569\pi$
$29$	−523657.	−	907001.i	−0.137485	−	0.238131i	−0.926544	+	0.376186i	$0.877235\pi$
$30$	6.88336e6			1.55151
$31$	1.56771e6			0.304886			0.152443	−	0.988312i	$-0.451286\pi$
$31$	1.56771e6			0.304886			0.152443	+	0.988312i	$0.451286\pi$
$32$	4.25041e6	+	7.36192e6i	0.716565	+	1.24113i
$33$	−3.14789e6	+	5.45230e6i	−0.462068	+	0.800326i
$34$	3.75516e6	+	6.50412e6i	0.481918	+	0.834706i
$35$	5.66584e6	−	9.81352e6i	0.638201	−	1.10540i
$36$	710519.	−	1.23066e6i	0.0705042	−	0.122117i
$37$	−1.01626e7			−0.891448			−0.445724	−	0.895171i	$-0.647054\pi$
$37$	−1.01626e7			−0.891448			−0.445724	+	0.895171i	$0.647054\pi$
$38$	−6.88838e6	−	1.72165e7i	−0.535909	−	1.33942i
$39$	−2.04445e7			−1.41510
$40$	−1.09442e6	+	1.89560e6i	−0.0675951	+	0.117078i
$41$	1.04812e7	−	1.81540e7i	0.579275	−	1.00333i	−0.416287	−	0.909233i	$-0.636669\pi$
$41$	1.04812e7	−	1.81540e7i	0.579275	−	1.00333i	0.995563	−	0.0941013i	$-0.0299977\pi$
$42$	1.50129e7	+	2.60030e7i	0.744461	+	1.28944i
$43$	196251.	−	339917.i	0.00875395	−	0.0151623i	−0.861615	−	0.507562i	$-0.830547\pi$
$43$	196251.	−	339917.i	0.00875395	−	0.0151623i	0.870369	+	0.492400i	$0.163880\pi$
$44$	−1.33203e7	−	2.30715e7i	−0.535769	−	0.927979i
$45$	−4.13722e6			−0.150402
$46$	1.65106e7			0.543691
$47$	−2.38877e7	−	4.13748e7i	−0.714060	−	1.23679i	−0.963321	−	0.268351i	$-0.913521\pi$
$47$	−2.38877e7	−	4.13748e7i	−0.714060	−	1.23679i	0.249261	−	0.968436i	$-0.419812\pi$
$48$	1.56414e7	+	2.70917e7i	0.425295	+	0.736632i
$49$	9.07597e6			0.224911
$50$	2.10436e7			0.476162
$51$	1.50499e7	+	2.60672e7i	0.311507	+	0.539545i
$52$	4.32556e7	−	7.49208e7i	0.820402	−	1.42098i
$53$	4.25064e7	+	7.36232e7i	0.739968	+	1.28166i	0.952509	+	0.304509i	$0.0984925\pi$
$53$	4.25064e7	+	7.36232e7i	0.739968	+	1.28166i	−0.212542	+	0.977152i	$0.568174\pi$
$54$	4.75114e7	−	8.22922e7i	0.760372	−	1.31700i
$55$	−3.87808e7	+	6.71704e7i	−0.571459	+	0.989796i
$56$	−9.54791e6			−0.129737
$57$	−2.76072e7	−	6.90000e7i	−0.346406	−	0.865789i
$58$	3.41881e7			0.396688
$59$	−6.47865e7	+	1.12214e8i	−0.696066	+	1.20562i	0.273754	+	0.961800i	$0.411735\pi$
$59$	−6.47865e7	+	1.12214e8i	−0.696066	+	1.20562i	−0.969820	+	0.243822i	$0.921599\pi$
$60$	−5.83675e7	+	1.01095e8i	−0.581420	+	1.00705i
$61$	5.02645e6	+	8.70606e6i	0.0464812	+	0.0805077i	0.888330	−	0.459206i	$-0.151866\pi$
$61$	5.02645e6	+	8.70606e6i	0.0464812	+	0.0805077i	−0.841849	+	0.539713i	$0.818533\pi$
$62$	−2.55878e7	+	4.43194e7i	−0.219923	+	0.380917i
$63$	−9.02343e6	−	1.56290e7i	−0.0721671	−	0.124997i
$64$	−1.55071e8			−1.15537
$65$	−2.51869e8			−1.75011
$66$	−1.02758e8	−	1.77982e8i	−0.666605	−	1.15459i
$67$	1.06302e8	+	1.84121e8i	0.644476	+	1.11626i	0.984422	+	0.175820i	$0.0562576\pi$
$67$	1.06302e8	+	1.84121e8i	0.644476	+	1.11626i	−0.339947	+	0.940445i	$0.610409\pi$
$68$	−1.27367e8			−0.722384
$69$	6.61709e7			0.351436
$70$	1.84953e8	+	3.20348e8i	0.920705	+	1.59471i
$71$	1.78505e8	−	3.09180e8i	0.833658	−	1.44394i	−0.0614611	−	0.998109i	$-0.519576\pi$
$71$	1.78505e8	−	3.09180e8i	0.833658	−	1.44394i	0.895119	−	0.445828i	$-0.147091\pi$
$72$	1.74298e6	+	3.01893e6i	0.00764358	+	0.0132391i
$73$	−1.52816e8	+	2.64685e8i	−0.629818	+	1.09088i	0.357769	+	0.933810i	$0.383537\pi$
$73$	−1.52816e8	+	2.64685e8i	−0.629818	+	1.09088i	−0.987588	+	0.157068i	$0.949796\pi$
$74$	1.65871e8	−	2.87297e8i	0.643026	−	1.11375i
$75$	8.43383e7			0.307786
$76$	3.11267e8	+	4.48180e7i	1.07022	+	0.154096i
$77$	−3.38330e8			−1.09681
$78$	3.33691e8	−	5.77969e8i	1.02075	−	1.76799i
$79$	2.42805e8	−	4.20551e8i	0.701351	−	1.21478i	−0.266641	−	0.963796i	$-0.585914\pi$
$79$	2.42805e8	−	4.20551e8i	0.701351	−	1.21478i	0.967992	−	0.250980i	$-0.0807529\pi$
$80$	1.92696e8	+	3.33760e8i	0.525979	+	0.911023i
$81$	1.65154e8	−	2.86055e8i	0.426290	−	0.738357i
$82$	3.42145e8	+	5.92612e8i	0.835695	+	1.44747i
$83$	−4.81884e8			−1.11453			−0.557264	−	0.830335i	$-0.688149\pi$
$83$	−4.81884e8			−1.11453			−0.557264	+	0.830335i	$0.688149\pi$
$84$	−5.09206e8			−1.11593
$85$	1.85409e8	+	3.21138e8i	0.385253	+	0.667278i
$86$	6.40634e6	+	1.10961e7i	0.0126289	+	0.0218740i
$87$	1.37019e8			0.256415
$88$	6.53524e7			0.116169
$89$	−3.82057e8	−	6.61742e8i	−0.645465	−	1.11798i	−0.984194	−	0.177094i	$-0.943330\pi$
$89$	−3.82057e8	−	6.61742e8i	−0.645465	−	1.11798i	0.338729	−	0.940884i	$-0.390003\pi$
$90$	6.75268e7	−	1.16960e8i	0.108489	−	0.187908i
$91$	−5.49335e8	−	9.51477e8i	−0.839752	−	1.45449i
$92$	−1.40001e8	+	2.42490e8i	−0.203745	+	0.352897i
$93$	−1.02550e8	+	1.77623e8i	−0.142156	+	0.246221i
$94$	1.55956e9			2.06028
$95$	−3.40110e8	−	8.50055e8i	−0.428414	−	1.07076i
$96$	−1.11215e9			−1.33642
$97$	−5.47630e8	+	9.48522e8i	−0.628079	+	1.08786i	0.359858	+	0.933007i	$0.382825\pi$
$97$	−5.47630e8	+	9.48522e8i	−0.628079	+	1.08786i	−0.987937	+	0.154857i	$0.950508\pi$
$98$	−1.48136e8	+	2.56579e8i	−0.162235	+	0.280998i
$99$	6.17625e7	+	1.06976e8i	0.0646199	+	0.111925i
$100$	−1.78439e8	+	3.09066e8i	−0.178439	+	0.309066i
$101$	8.69150e8	+	1.50541e9i	0.831091	+	1.43949i	0.897174	+	0.441678i	$0.145616\pi$
$101$	8.69150e8	+	1.50541e9i	0.831091	+	1.43949i	−0.0660829	+	0.997814i	$0.521050\pi$
$102$	−9.82564e8			−0.898793
$103$	1.30106e9			1.13901			0.569506	−	0.821987i	$-0.307135\pi$
$103$	1.30106e9			1.13901			0.569506	+	0.821987i	$0.307135\pi$
$104$	1.06111e8	+	1.83789e8i	0.0889424	+	0.154053i
$105$	7.41253e8	+	1.28389e9i	0.595134	+	1.03080i
$106$	−2.77512e9			−2.13504
$107$	4.91003e8			0.362124			0.181062	−	0.983472i	$-0.442047\pi$
$107$	4.91003e8			0.362124			0.181062	+	0.983472i	$0.442047\pi$
$108$	8.05746e8	+	1.39559e9i	0.569891	+	0.987079i
$109$	4.49904e8	−	7.79257e8i	0.305282	−	0.528764i	−0.672042	−	0.740513i	$-0.734583\pi$
$109$	4.49904e8	−	7.79257e8i	0.305282	−	0.528764i	0.977324	+	0.211749i	$0.0679160\pi$
$110$	−1.26594e9	−	2.19268e9i	−0.824418	−	1.42793i
$111$	6.64777e8	−	1.15143e9i	0.415645	−	0.719918i
$112$	−8.40556e8	+	1.45588e9i	−0.504760	+	0.874271i
$113$	9.19161e8			0.530321			0.265160	−	0.964204i	$-0.414575\pi$
$113$	9.19161e8			0.530321			0.265160	+	0.964204i	$0.414575\pi$
$114$	2.40124e9	+	3.45744e8i	1.33157	+	0.191727i
$115$	8.15202e8			0.434635
$116$	−2.89898e8	+	5.02118e8i	−0.148656	+	0.257481i
$117$	−2.00564e8	+	3.47386e8i	−0.0989500	+	0.171386i
$118$	−2.11486e9	−	3.66305e9i	−1.00418	−	1.73930i
$119$	−8.08768e8	+	1.40083e9i	−0.369711	+	0.640359i
$120$	−1.43182e8	−	2.47998e8i	−0.0630336	−	0.109177i
$121$	−4.21905e7			−0.0178929
$122$	−3.28162e8			−0.134113
$123$	1.37124e9	+	2.37507e9i	0.540184	+	0.935627i
$124$	−4.33943e8	−	7.51612e8i	−0.164830	−	0.285493i
$125$	−2.10895e9			−0.772630
$126$	5.89114e8			0.208224
$127$	5.95269e6	+	1.03104e7i	0.00203047	+	0.00351688i	0.867039	−	0.498241i	$-0.166020\pi$
$127$	5.95269e6	+	1.03104e7i	0.00203047	+	0.00351688i	−0.865008	+	0.501757i	$0.832687\pi$
$128$	3.54829e8	−	6.14581e8i	0.116835	−	0.202365i
$129$	2.56753e7	+	4.44708e7i	0.00816321	+	0.0141391i
$130$	4.11095e9	−	7.12037e9i	1.26240	−	2.18654i
$131$	−2.62021e9	+	4.53833e9i	−0.777347	+	1.34640i	0.156119	+	0.987738i	$0.450102\pi$
$131$	−2.62021e9	+	4.53833e9i	−0.777347	+	1.34640i	−0.933466	+	0.358666i	$0.883232\pi$
$132$	3.48535e9			0.999227
$133$	2.46943e9	−	3.13883e9i	0.684329	−	0.869831i
$134$	−6.94018e9			−1.85951
$135$	2.34585e9	−	4.06314e9i	0.607854	−	1.05283i
$136$	1.56223e8	−	2.70587e8i	0.0391580	−	0.0678236i
$137$	−3.02410e8	−	5.23790e8i	−0.0733423	−	0.127033i	0.827022	−	0.562170i	$-0.190033\pi$
$137$	−3.02410e8	−	5.23790e8i	−0.0733423	−	0.127033i	−0.900364	+	0.435137i	$0.856700\pi$
$138$	−1.08003e9	+	1.87066e9i	−0.253501	+	0.439076i
$139$	−2.92300e9	−	5.06279e9i	−0.664144	−	1.15033i	−0.979517	−	0.201363i	$-0.935463\pi$
$139$	−2.92300e9	−	5.06279e9i	−0.664144	−	1.15033i	0.315373	−	0.948968i	$-0.397871\pi$
$140$	−6.27324e9			−1.38012
$141$	6.25039e9			1.33175
$142$	5.82704e9	+	1.00927e10i	1.20268	+	2.08310i
$143$	3.76002e9	+	6.51255e9i	0.751932	+	1.30238i
$144$	6.13778e8			0.118954
$145$	1.68802e9			0.317118
$146$	−4.98845e9	−	8.64025e9i	−0.908611	−	1.57376i
$147$	−5.93698e8	+	1.02831e9i	−0.104867	+	0.181634i
$148$	2.81301e9	+	4.87228e9i	0.481941	+	0.834746i
$149$	3.22931e9	−	5.59332e9i	0.536749	−	0.929676i	−0.462328	−	0.886709i	$-0.652986\pi$
$149$	3.22931e9	−	5.59332e9i	0.536749	−	0.929676i	0.999077	−	0.0429668i	$-0.0136810\pi$
$150$	−1.37655e9	+	2.38426e9i	−0.222015	+	0.384541i
$151$	−4.43584e9			−0.694352			−0.347176	−	0.937800i	$-0.612859\pi$
$151$	−4.43584e9			−0.694352			−0.347176	+	0.937800i	$0.612859\pi$
$152$	−4.77000e8	+	6.06301e8i	−0.0724807	+	0.0921282i
$153$	5.90566e8			0.0871279
$154$	5.52214e9	−	9.56463e9i	0.791160	−	1.37033i
$155$	−1.26339e9	+	2.18825e9i	−0.175810	+	0.304512i
$156$	5.65906e9	+	9.80178e9i	0.765039	+	1.32509i
$157$	−2.19534e9	+	3.80244e9i	−0.288372	+	0.499475i	−0.973421	−	0.229022i	$-0.926447\pi$
$157$	−2.19534e9	+	3.80244e9i	−0.288372	+	0.499475i	0.685049	+	0.728497i	$0.259781\pi$
$158$	7.92602e9	+	1.37283e10i	1.01181	+	1.75250i
$159$	−1.11221e10			−1.38006
$160$	−1.37013e10			−1.65280
$161$	1.77799e9	+	3.07956e9i	0.208551	+	0.361220i
$162$	5.39120e9	+	9.33784e9i	0.614990	+	1.06519i
$163$	−5.99931e9			−0.665667			−0.332834	−	0.942986i	$-0.608005\pi$
$163$	−5.99931e9			−0.665667			−0.332834	+	0.942986i	$0.608005\pi$
$164$	−1.16049e10			−1.25269
$165$	−5.07364e9	−	8.78780e9i	−0.532895	−	0.923002i
$166$	7.86521e9	−	1.36229e10i	0.803940	−	1.39247i
$167$	−8.56849e9	−	1.48411e10i	−0.852472	−	1.47652i	−0.878971	−	0.476876i	$-0.841769\pi$
$167$	−8.56849e9	−	1.48411e10i	−0.852472	−	1.47652i	0.0264987	−	0.999649i	$-0.491564\pi$
$168$	6.24570e8	−	1.08179e9i	0.0604908	−	0.104773i
$169$	−6.90782e9	+	1.19647e10i	−0.651404	+	1.12827i
$170$	−1.21048e10			−1.11157
$171$	−1.44326e9	−	2.07808e8i	−0.129081	−	0.0185858i
$172$	−2.17290e8			−0.0189305
$173$	−2.58738e8	+	4.48147e8i	−0.0219610	+	0.0380376i	−0.876797	−	0.480861i	$-0.840324\pi$
$173$	−2.58738e8	+	4.48147e8i	−0.0219610	+	0.0380376i	0.854836	+	0.518898i	$0.173658\pi$
$174$	−2.23639e9	+	3.87354e9i	−0.184959	+	0.320358i
$175$	2.26613e9	+	3.92506e9i	0.182648	+	0.316355i
$176$	5.75333e9	−	9.96506e9i	0.451973	−	0.782840i
$177$	−8.47592e9	−	1.46807e10i	−0.649094	−	1.12426i
$178$	2.49434e10			1.86237
$179$	7.49018e9			0.545323			0.272661	−	0.962110i	$-0.412096\pi$
$179$	7.49018e9			0.545323			0.272661	+	0.962110i	$0.412096\pi$
$180$	1.14519e9	+	1.98352e9i	0.0813112	+	0.140835i
$181$	1.12325e10	+	1.94553e10i	0.777901	+	1.34736i	0.933150	+	0.359488i	$0.117049\pi$
$181$	1.12325e10	+	1.94553e10i	0.777901	+	1.34736i	−0.155249	+	0.987875i	$0.549618\pi$
$182$	3.58645e10			2.42295
$183$	−1.31521e9			−0.0866890
$184$	−3.43439e8	−	5.94854e8i	−0.0220887	−	0.0382587i
$185$	8.18982e9	−	1.41852e10i	0.514045	−	0.890353i
$186$	−3.34761e9	−	5.79824e9i	−0.205082	−	0.355212i
$187$	5.53576e9	−	9.58821e9i	0.331047	−	0.573391i
$188$	−1.32243e10	+	2.29052e10i	−0.772080	+	1.33728i
$189$	2.04656e10			1.16666
$190$	2.95824e10	+	4.25944e9i	1.64681	+	0.237116i
$191$	−1.25284e10			−0.681153			−0.340576	−	0.940217i	$-0.610622\pi$
$191$	−1.25284e10			−0.681153			−0.340576	+	0.940217i	$0.610622\pi$
$192$	1.01439e10	−	1.75697e10i	0.538701	−	0.933058i
$193$	−1.76120e10	+	3.05049e10i	−0.913696	+	1.58257i	−0.104896	+	0.994483i	$0.533451\pi$
$193$	−1.76120e10	+	3.05049e10i	−0.913696	+	1.58257i	−0.808800	+	0.588084i	$0.799882\pi$
$194$	−1.78766e10	−	3.09632e10i	−0.906101	−	1.56941i
$195$	1.64758e10	−	2.85370e10i	0.816002	−	1.41336i
$196$	−2.51224e9	−	4.35133e9i	−0.121593	−	0.210605i
$197$	−4.20800e9			−0.199057			−0.0995285	−	0.995035i	$-0.531733\pi$
$197$	−4.20800e9			−0.199057			−0.0995285	+	0.995035i	$0.531733\pi$
$198$	−4.03229e9			−0.186448
$199$	−1.38589e10	−	2.40043e10i	−0.626456	−	1.08505i	−0.988257	−	0.152798i	$-0.951172\pi$
$199$	−1.38589e10	−	2.40043e10i	−0.626456	−	1.08505i	0.361802	−	0.932255i	$-0.382162\pi$
$200$	−4.37731e8	−	7.58172e8i	−0.0193452	−	0.0335068i
$201$	−2.78148e10			−1.20197
$202$	−5.67443e10			−2.39796
$203$	3.68163e9	+	6.37677e9i	0.152163	+	0.263554i
$204$	8.33165e9	−	1.44308e10i	0.336818	−	0.583386i
$205$	1.68932e10	+	2.92600e10i	0.668068	+	1.15713i
$206$	−2.12355e10	+	3.67810e10i	−0.821601	+	1.42305i
$207$	6.49147e8	−	1.12436e9i	0.0245740	−	0.0425635i
$208$	3.73660e10			1.38418
$209$	−1.69025e10	+	2.14842e10i	−0.612762	+	0.778864i
$210$	−4.83943e10			−1.71715
$211$	−1.33462e10	+	2.31163e10i	−0.463539	+	0.802873i	−0.999134	−	0.0416015i	$-0.986754\pi$
$211$	−1.33462e10	+	2.31163e10i	−0.463539	+	0.802873i	0.535595	+	0.844475i	$0.320087\pi$
$212$	2.35316e10	−	4.07580e10i	0.800093	−	1.38580i
$213$	2.33535e10	+	4.04495e10i	0.777400	+	1.34650i
$214$	−8.01404e9	+	1.38807e10i	−0.261210	+	0.452429i
$215$	3.16310e8	+	5.47865e8i	0.0100958	+	0.0174864i
$216$	−3.95317e9			−0.123567
$217$	−1.10220e10			−0.337435
$218$	1.46865e10	+	2.54377e10i	0.440416	+	0.762824i
$219$	−1.99927e10	−	3.46283e10i	−0.587316	−	1.01726i
$220$	4.29383e10			1.23578
$221$	3.59530e10			1.01384
$222$	2.17007e10	+	3.75867e10i	0.599633	+	1.03859i
$223$	6.01371e9	−	1.04161e10i	0.162844	−	0.282054i	−0.773044	−	0.634353i	$-0.781267\pi$
$223$	6.01371e9	−	1.04161e10i	0.162844	−	0.282054i	0.935887	+	0.352299i	$0.114600\pi$
$224$	−2.98830e10	−	5.17589e10i	−0.793064	−	1.37363i
$225$	8.27371e8	−	1.43305e9i	0.0215218	−	0.0372769i
$226$	−1.50024e10	+	2.59848e10i	−0.382535	+	0.662570i
$227$	−2.62916e10			−0.657204			−0.328602	−	0.944468i	$-0.606577\pi$
$227$	−2.62916e10			−0.657204			−0.328602	+	0.944468i	$0.606577\pi$
$228$	−2.54392e10	+	3.23351e10i	−0.623444	+	0.792442i
$229$	−4.02994e10			−0.968365			−0.484182	−	0.874967i	$-0.660883\pi$
$229$	−4.02994e10			−0.968365			−0.484182	+	0.874967i	$0.660883\pi$
$230$	−1.33056e10	+	2.30459e10i	−0.313514	+	0.543023i
$231$	2.21316e10	−	3.83330e10i	0.511397	−	0.885766i
$232$	−7.11151e8	−	1.23175e9i	−0.0161163	−	0.0279143i
$233$	2.39214e10	−	4.14332e10i	0.531723	−	0.920972i	−0.467591	−	0.883945i	$-0.654878\pi$
$233$	2.39214e10	−	4.14332e10i	0.531723	−	0.920972i	0.999314	−	0.0370269i	$-0.0117887\pi$
$234$	−6.54711e9	−	1.13399e10i	−0.142751	−	0.247252i
$235$	7.70026e10			1.64702
$236$	7.17319e10			1.50525
$237$	3.17658e10	+	5.50200e10i	0.654022	+	1.13280i
$238$	−2.64011e10	−	4.57280e10i	−0.533366	−	0.923817i
$239$	4.06787e10			0.806447			0.403224	−	0.915101i	$-0.367890\pi$
$239$	4.06787e10			0.806447			0.403224	+	0.915101i	$0.367890\pi$
$240$	−5.04204e10			−0.980969
$241$	4.78076e10	+	8.28052e10i	0.912894	+	1.58118i	0.809956	+	0.586490i	$0.199491\pi$
$241$	4.78076e10	+	8.28052e10i	0.912894	+	1.58118i	0.102938	+	0.994688i	$0.467176\pi$
$242$	6.88624e8	−	1.19273e9i	0.0129066	−	0.0223550i
$243$	−7.04102e9	−	1.21954e10i	−0.129541	−	0.224372i
$244$	2.78265e9	−	4.81970e9i	0.0502580	−	0.0870493i
$245$	−7.31415e9	+	1.26685e10i	−0.129693	+	0.224635i
$246$	−8.95246e10			−1.55860
$247$	−8.78637e10	−	1.26511e10i	−1.50201	−	0.216268i
$248$	2.12902e9			0.0357394
$249$	3.15221e10	−	5.45979e10i	0.519659	−	0.900075i
$250$	3.44219e10	−	5.96204e10i	0.557320	−	0.965306i
$251$	−3.13763e10	−	5.43453e10i	−0.498965	−	0.864232i	0.501035	−	0.865427i	$-0.332953\pi$
$251$	−3.13763e10	−	5.43453e10i	−0.498965	−	0.864232i	−0.999999	+	0.00119519i	$0.999620\pi$
$252$	−4.99539e9	+	8.65227e9i	−0.0780310	+	0.135154i
$253$	−1.21697e10	−	2.10786e10i	−0.186741	−	0.323444i
$254$	−3.88634e8			−0.00585853
$255$	−4.85136e10			−0.718510
$256$	−2.81153e10	−	4.86972e10i	−0.409132	−	0.708638i
$257$	9.43795e9	+	1.63470e10i	0.134952	+	0.233743i	0.925579	−	0.378554i	$-0.123579\pi$
$257$	9.43795e9	+	1.63470e10i	0.134952	+	0.233743i	−0.790627	+	0.612298i	$0.790245\pi$
$258$	−1.67626e9			−0.0235534
$259$	7.14491e10			0.986616
$260$	6.97176e10	+	1.20754e11i	0.946155	+	1.63879i
$261$	1.34417e9	−	2.32818e9i	0.0179297	−	0.0310551i
$262$	−8.55329e10	−	1.48147e11i	−1.12144	−	1.94240i
$263$	2.23262e10	−	3.86701e10i	0.287749	−	0.498396i	−0.685523	−	0.728051i	$-0.740426\pi$
$263$	2.23262e10	−	3.86701e10i	0.287749	−	0.498396i	0.973272	+	0.229655i	$0.0737598\pi$
$264$	−4.27498e9	+	7.40448e9i	−0.0541647	+	0.0938160i
$265$	−1.37020e11			−1.70678
$266$	4.84295e10	+	1.21042e11i	0.593121	+	1.48242i
$267$	9.99678e10			1.20381
$268$	5.88493e10	−	1.01930e11i	0.696842	−	1.20697i
$269$	3.77771e10	−	6.54318e10i	0.439889	−	0.761910i	−0.557791	−	0.829981i	$-0.688351\pi$
$269$	3.77771e10	−	6.54318e10i	0.439889	−	0.761910i	0.997680	+	0.0680710i	$0.0216844\pi$
$270$	7.65770e10	+	1.32635e11i	0.876923	+	1.51888i
$271$	−4.61304e10	+	7.99001e10i	−0.519547	+	0.899882i	0.480195	+	0.877162i	$0.340566\pi$
$271$	−4.61304e10	+	7.99001e10i	−0.519547	+	0.899882i	−0.999742	+	0.0227202i	$0.992767\pi$
$272$	−2.75064e10	−	4.76425e10i	−0.304701	−	0.527757i
$273$	1.43737e11			1.56617
$274$	1.97435e10			0.211615
$275$	−1.55110e10	−	2.68658e10i	−0.163547	−	0.283271i
$276$	−1.83162e10	−	3.17246e10i	−0.189996	−	0.329083i
$277$	−1.50355e11			−1.53447			−0.767235	−	0.641367i	$-0.778368\pi$
$277$	−1.50355e11			−1.53447			−0.767235	+	0.641367i	$0.778368\pi$
$278$	1.90834e11			1.91626
$279$	2.01207e9	+	3.48501e9i	0.0198804	+	0.0344338i
$280$	7.69447e9	−	1.33272e10i	0.0748114	−	0.129577i
$281$	5.70263e10	+	9.87725e10i	0.545629	+	0.945056i	0.998567	+	0.0535147i	$0.0170424\pi$
$281$	5.70263e10	+	9.87725e10i	0.545629	+	0.945056i	−0.452938	+	0.891542i	$0.649624\pi$
$282$	−1.02018e11	+	1.76700e11i	−0.960625	+	1.66385i
$283$	1.22126e10	−	2.11528e10i	0.113180	−	0.196033i	−0.803871	−	0.594804i	$-0.797230\pi$
$283$	1.22126e10	−	2.11528e10i	0.113180	−	0.196033i	0.917051	+	0.398771i	$0.130563\pi$
$284$	−1.97642e11			−1.80279
$285$	1.18560e11	+	1.70710e10i	1.06448	+	0.153270i
$286$	−2.45481e11			−2.16956
$287$	−7.36895e10	+	1.27634e11i	−0.641117	+	1.11045i
$288$	−1.09104e10	+	1.88973e10i	−0.0934486	+	0.161858i
$289$	3.28278e10	+	5.68594e10i	0.276822	+	0.479470i
$290$	−2.75515e10	+	4.77206e10i	−0.228746	+	0.396200i
$291$	−7.16456e10	−	1.24094e11i	−0.585694	−	1.01445i
$292$	1.69198e11			1.36199
$293$	1.60725e11			1.27403			0.637016	−	0.770851i	$-0.280168\pi$
$293$	1.60725e11			1.27403			0.637016	+	0.770851i	$0.280168\pi$
$294$	−1.93804e10	−	3.35679e10i	−0.151286	−	0.262036i
$295$	−1.04420e11	−	1.80861e11i	−0.802761	−	1.39042i
$296$	−1.38013e10			−0.104497
$297$	−1.40080e11			−1.04466
$298$	1.05416e11	+	1.82586e11i	0.774343	+	1.34120i
$299$	3.95193e10	−	6.84494e10i	0.285949	−	0.495278i
$300$	−2.33449e10	−	4.04346e10i	−0.166398	−	0.288209i
$301$	−1.37977e9	+	2.38983e9i	−0.00968850	+	0.0167810i
$302$	7.24008e10	−	1.25402e11i	0.500855	−	0.867507i
$303$	−2.27419e11			−1.55001
$304$	5.04571e10	+	1.26110e11i	0.338837	+	0.846873i
$305$	−1.62029e10			−0.107212
$306$	−9.63910e9	+	1.66954e10i	−0.0628478	+	0.108856i
$307$	1.19384e10	−	2.06779e10i	0.0767050	−	0.132857i	−0.825121	−	0.564955i	$-0.808893\pi$
$307$	1.19384e10	−	2.06779e10i	0.0767050	−	0.132857i	0.901826	+	0.432098i	$0.142227\pi$
$308$	9.36500e10	+	1.62207e11i	0.592966	+	1.02705i
$309$	−8.51076e10	+	1.47411e11i	−0.531074	+	0.919847i
$310$	−4.12414e10	−	7.14322e10i	−0.253633	−	0.439305i
$311$	1.23217e11			0.746875			0.373438	−	0.927655i	$-0.378179\pi$
$311$	1.23217e11			0.746875			0.373438	+	0.927655i	$0.378179\pi$
$312$	−2.77646e10			−0.165881
$313$	1.89427e10	+	3.28098e10i	0.111556	+	0.193221i	0.916398	−	0.400269i	$-0.131083\pi$
$313$	1.89427e10	+	3.28098e10i	0.111556	+	0.193221i	−0.804842	+	0.593489i	$0.797750\pi$
$314$	−7.16637e10	−	1.24125e11i	−0.416022	−	0.720571i
$315$	2.90872e10			0.166458
$316$	−2.68835e11			−1.51668
$317$	−7.32334e9	−	1.26844e10i	−0.0407326	−	0.0705510i	0.844940	−	0.534861i	$-0.179636\pi$
$317$	−7.32334e9	−	1.26844e10i	−0.0407326	−	0.0705510i	−0.885673	+	0.464310i	$0.846303\pi$
$318$	1.81532e11	−	3.14423e11i	0.995479	−	1.72422i
$319$	−2.51996e10	−	4.36470e10i	−0.136250	−	0.235991i
$320$	1.24969e11	−	2.16452e11i	0.666234	−	1.15395i
$321$	−3.21186e10	+	5.56310e10i	−0.168843	+	0.292445i
$322$	−1.16080e11			−0.601734
$323$	4.85490e10	+	1.21341e11i	0.248181	+	0.620292i
$324$	−1.82859e11			−0.921857
$325$	5.03693e10	−	8.72422e10i	0.250433	−	0.433762i
$326$	9.79194e10	−	1.69601e11i	0.480164	−	0.831669i
$327$	5.88603e10	+	1.01949e11i	0.284681	+	0.493081i
$328$	1.42340e10	−	2.46540e10i	0.0679040	−	0.117613i
$329$	1.67945e11	+	2.90890e11i	0.790291	+	1.36882i
$330$	3.31243e11			1.53757
$331$	3.83806e10			0.175746			0.0878730	−	0.996132i	$-0.471993\pi$
$331$	3.83806e10			0.175746			0.0878730	+	0.996132i	$0.471993\pi$
$332$	1.33386e11	+	2.31031e11i	0.602545	+	1.04364i
$333$	−1.30431e10	−	2.25914e10i	−0.0581276	−	0.100680i
$334$	5.59412e11			2.45965
$335$	−3.42668e11			−1.48652
$336$	−1.09969e11	−	1.90471e11i	−0.470698	−	0.815272i
$337$	5.25904e10	−	9.10893e10i	0.222112	−	0.384709i	−0.733337	−	0.679865i	$-0.762038\pi$
$337$	5.25904e10	−	9.10893e10i	0.222112	−	0.384709i	0.955449	+	0.295156i	$0.0953716\pi$
$338$	−2.25496e11	−	3.90570e11i	−0.939752	−	1.62770i
$339$	−6.01263e10	+	1.04142e11i	−0.247267	+	0.428278i
$340$	1.02643e11	−	1.77783e11i	0.416556	−	0.721497i
$341$	7.54417e10			0.302146
$342$	2.94313e10	−	3.74093e10i	0.116330	−	0.147864i
$343$	2.19901e11			0.857835
$344$	2.66518e8	−	4.61623e8i	0.00102616	−	0.00177736i
$345$	−5.33258e10	+	9.23631e10i	−0.202652	+	0.351004i
$346$	−8.44612e9	−	1.46291e10i	−0.0316822	−	0.0548751i
$347$	5.92691e10	−	1.02657e11i	0.219455	−	0.380108i	−0.735186	−	0.677865i	$-0.762905\pi$
$347$	5.92691e10	−	1.02657e11i	0.219455	−	0.380108i	0.954642	+	0.297758i	$0.0962387\pi$
$348$	−3.79269e10	−	6.56913e10i	−0.138625	−	0.240105i
$349$	−3.34182e11			−1.20578			−0.602890	−	0.797824i	$-0.705984\pi$
$349$	−3.34182e11			−1.20578			−0.602890	+	0.797824i	$0.705984\pi$
$350$	−1.47949e11			−0.526996
$351$	−2.27444e11	−	3.93945e11i	−0.799820	−	1.38533i
$352$	2.04539e11	+	3.54273e11i	0.710126	+	1.22997i
$353$	1.08334e11			0.371345			0.185673	−	0.982612i	$-0.440554\pi$
$353$	1.08334e11			0.371345			0.185673	+	0.982612i	$0.440554\pi$
$354$	5.53369e11			1.87284
$355$	2.87707e11	+	4.98324e11i	0.961442	+	1.66527i
$356$	−2.11507e11	+	3.66342e11i	−0.697912	+	1.20882i
$357$	−1.05810e11	−	1.83268e11i	−0.344762	−	0.597146i
$358$	−1.22253e11	+	2.11749e11i	−0.393356	+	0.681313i
$359$	−2.44436e11	+	4.23376e11i	−0.776677	+	1.34524i	0.157170	+	0.987572i	$0.449763\pi$
$359$	−2.44436e11	+	4.23376e11i	−0.776677	+	1.34524i	−0.933847	+	0.357672i	$0.883571\pi$
$360$	−5.61854e9			−0.0176304
$361$	−7.59491e10	−	3.13623e11i	−0.235364	−	0.971907i
$362$	−7.33340e11			−2.24449
$363$	2.75986e9	−	4.78022e9i	0.00834271	−	0.0144500i
$364$	−3.04113e11	+	5.26740e11i	−0.907986	+	1.57268i
$365$	−2.46302e11	−	4.26608e11i	−0.726358	−	1.25809i
$366$	2.14665e10	−	3.71811e10i	0.0625311	−	0.108307i
$367$	6.75013e10	+	1.16916e11i	0.194229	+	0.336415i	0.946648	−	0.322270i	$-0.104446\pi$
$367$	6.75013e10	+	1.16916e11i	0.194229	+	0.336415i	−0.752418	+	0.658686i	$0.771113\pi$
$368$	−1.20939e11			−0.343758
$369$	5.38085e10			0.151089
$370$	2.67345e11	+	4.63055e11i	0.741590	+	1.28447i
$371$	−2.98846e11	−	5.17617e11i	−0.818964	−	1.41849i
$372$	1.13544e11			0.307413
$373$	−4.44023e11			−1.18773			−0.593863	−	0.804566i	$-0.702398\pi$
$373$	−4.44023e11			−1.18773			−0.593863	+	0.804566i	$0.702398\pi$
$374$	1.80707e11	+	3.12993e11i	0.477587	+	0.827205i
$375$	1.37956e11	−	2.38946e11i	0.360246	−	0.623964i
$376$	−3.24407e10	−	5.61889e10i	−0.0837037	−	0.144979i
$377$	8.18316e10	−	1.41736e11i	0.208634	−	0.361365i
$378$	−3.34035e11	+	5.78565e11i	−0.841547	+	1.45760i
$379$	1.29215e11			0.321688			0.160844	−	0.986980i	$-0.448578\pi$
$379$	1.29215e11			0.321688			0.160844	+	0.986980i	$0.448578\pi$
$380$	−3.13402e11	+	3.98357e11i	−0.771038	+	0.980045i
$381$	−1.55756e9			−0.00378689
$382$	2.04485e11	−	3.54179e11i	0.491334	−	0.851016i
$383$	1.16507e11	−	2.01796e11i	0.276667	−	0.479201i	−0.693887	−	0.720083i	$-0.744103\pi$
$383$	1.16507e11	−	2.01796e11i	0.276667	−	0.479201i	0.970554	+	0.240882i	$0.0774368\pi$
$384$	4.64217e10	+	8.04048e10i	0.108951	+	0.188708i
$385$	2.72653e11	−	4.72249e11i	0.632466	−	1.09546i
$386$	−5.74919e11	−	9.95790e11i	−1.31815	−	2.28310i
$387$	1.00751e9			0.00228324
$388$	6.06338e11			1.35823
$389$	1.89079e11	+	3.27494e11i	0.418668	+	0.725155i	0.995806	−	0.0914923i	$-0.0291637\pi$
$389$	1.89079e11	+	3.27494e11i	0.418668	+	0.725155i	−0.577138	+	0.816647i	$0.695830\pi$
$390$	5.37829e11	+	9.31548e11i	1.17721	+	2.03899i
$391$	−1.16366e11			−0.251785
$392$	1.23256e10			0.0263646
$393$	−3.42798e11	−	5.93743e11i	−0.724889	−	1.25555i
$394$	6.86820e10	−	1.18961e11i	0.143585	−	0.248697i
$395$	3.91343e11	+	6.77827e11i	0.808856	+	1.40098i
$396$	3.41918e10	−	5.92220e10i	0.0698706	−	0.121019i
$397$	−1.35176e11	+	2.34131e11i	−0.273112	+	0.473044i	−0.969657	−	0.244469i	$-0.921386\pi$
$397$	−1.35176e11	+	2.34131e11i	−0.273112	+	0.473044i	0.696545	+	0.717513i	$0.254720\pi$
$398$	9.04809e11			1.80752
$399$	1.94095e11	+	4.85113e11i	0.383387	+	0.958218i
$400$	−1.54143e11			−0.301061
$401$	−5.26340e10	+	9.11648e10i	−0.101652	+	0.176067i	−0.912366	−	0.409377i	$-0.865746\pi$
$401$	−5.26340e10	+	9.11648e10i	−0.101652	+	0.176067i	0.810713	+	0.585443i	$0.199080\pi$
$402$	4.53987e11	−	7.86328e11i	0.867014	−	1.50171i
$403$	1.22492e11	+	2.12163e11i	0.231332	+	0.400680i
$404$	4.81163e11	−	8.33400e11i	0.898621	−	1.55646i
$405$	2.66188e11	+	4.61051e11i	0.491633	+	0.851534i
$406$	−2.40363e11			−0.439037
$407$	−4.89046e11			−0.883436
$408$	2.04385e10	+	3.54004e10i	0.0365155	+	0.0632467i
$409$	3.94346e11	+	6.83028e11i	0.696823	+	1.20693i	0.969562	+	0.244845i	$0.0787372\pi$
$409$	3.94346e11	+	6.83028e11i	0.696823	+	1.20693i	−0.272739	+	0.962088i	$0.587929\pi$
$410$	−1.10291e12			−1.92758
$411$	7.91278e10			0.136786
$412$	−3.60134e11	−	6.23770e11i	−0.615781	−	1.06656i
$413$	4.55489e11	−	7.88930e11i	0.770376	−	1.33433i
$414$	2.11905e10	+	3.67030e10i	0.0354519	+	0.0614044i
$415$	3.88341e11	−	6.72626e11i	0.642683	−	1.11316i
$416$	−6.64209e11	+	1.15044e12i	−1.08739	+	1.88341i
$417$	7.64824e11			1.23865
$418$	−3.31485e11	−	8.28497e11i	−0.531093	−	1.32739i
$419$	−1.55327e10			−0.0246198			−0.0123099	−	0.999924i	$-0.503918\pi$
$419$	−1.55327e10			−0.0246198			−0.0123099	+	0.999924i	$0.503918\pi$
$420$	4.10359e11	−	7.10763e11i	0.643491	−	1.11456i
$421$	3.49813e10	−	6.05894e10i	0.0542708	−	0.0939998i	−0.837614	−	0.546263i	$-0.816050\pi$
$421$	3.49813e10	−	6.05894e10i	0.0542708	−	0.0939998i	0.891885	+	0.452263i	$0.149383\pi$
$422$	−4.35667e11	−	7.54598e11i	−0.668727	−	1.15827i
$423$	6.13173e10	−	1.06205e11i	0.0931218	−	0.161292i
$424$	5.77257e10	+	9.99838e10i	0.0867406	+	0.150239i
$425$	−1.48314e11			−0.220512
$426$	−1.52469e12			−2.24304
$427$	−3.53390e10	−	6.12090e10i	−0.0514433	−	0.0891025i
$428$	−1.35910e11	−	2.35403e11i	−0.195774	−	0.339091i
$429$	−9.83837e11			−1.40238
$430$	−2.06510e10			−0.0291295
$431$	−1.00132e11	−	1.73433e11i	−0.139773	−	0.242094i	0.787638	−	0.616139i	$-0.211304\pi$
$431$	−1.00132e11	−	1.73433e11i	−0.139773	−	0.242094i	−0.927411	+	0.374045i	$0.877971\pi$
$432$	−3.48019e11	+	6.02787e11i	−0.480758	+	0.832697i
$433$	2.90449e11	+	5.03072e11i	0.397077	+	0.687757i	0.993364	−	0.115014i	$-0.0366914\pi$
$433$	2.90449e11	+	5.03072e11i	0.397077	+	0.687757i	−0.596287	+	0.802771i	$0.703358\pi$
$434$	1.79898e11	−	3.11592e11i	0.243401	−	0.421583i
$435$	−1.10421e11	+	1.91254e11i	−0.147859	+	0.256100i
$436$	−4.98136e11			−0.660175
$437$	2.84381e11	+	4.09468e10i	0.373021	+	0.0537097i
$438$	1.30526e12			1.69459
$439$	−5.28991e11	+	9.16240e11i	−0.679764	+	1.17739i	0.295288	+	0.955408i	$0.404584\pi$
$439$	−5.28991e11	+	9.16240e11i	−0.679764	+	1.17739i	−0.975052	+	0.221977i	$0.928749\pi$
$440$	−5.26662e10	+	9.12205e10i	−0.0669877	+	0.116026i
$441$	1.16485e10	+	2.01758e10i	0.0146655	+	0.0254014i
$442$	−5.86816e11	+	1.01640e12i	−0.731311	+	1.26667i
$443$	2.95490e11	+	5.11804e11i	0.364524	+	0.631374i	0.988700	−	0.149910i	$-0.0478984\pi$
$443$	2.95490e11	+	5.11804e11i	0.364524	+	0.631374i	−0.624176	+	0.781284i	$0.714565\pi$
$444$	−7.36044e11			−0.898836
$445$	1.23157e12			1.48881
$446$	1.96309e11	+	3.40017e11i	0.234927	+	0.406906i
$447$	4.22485e11	+	7.31766e11i	0.500527	+	0.866939i
$448$	1.09025e12			1.27871
$449$	−3.98165e11			−0.462333			−0.231166	−	0.972914i	$-0.574254\pi$
$449$	−3.98165e11			−0.462333			−0.231166	+	0.972914i	$0.574254\pi$
$450$	2.70083e10	+	4.67798e10i	0.0310486	+	0.0537777i
$451$	5.04381e11	−	8.73614e11i	0.574070	−	0.994318i
$452$	−2.54425e11	−	4.40677e11i	−0.286706	−	0.496589i
$453$	2.90167e11	−	5.02584e11i	0.323747	−	0.560747i
$454$	4.29125e11	−	7.43267e11i	0.474059	−	0.821095i
$455$	1.77079e12			1.93694
$456$	−3.74918e10	−	9.37053e10i	−0.0406064	−	0.101490i
$457$	−1.18858e12			−1.27469			−0.637345	−	0.770578i	$-0.719967\pi$
$457$	−1.18858e12			−1.27469			−0.637345	+	0.770578i	$0.719967\pi$
$458$	6.57758e11	−	1.13927e12i	0.698508	−	1.20985i
$459$	−3.34858e11	+	5.79992e11i	−0.352131	+	0.609908i
$460$	−2.25649e11	−	3.90835e11i	−0.234976	−	0.406990i
$461$	−9.14723e11	+	1.58435e12i	−0.943269	+	1.63379i	−0.184089	+	0.982910i	$0.558933\pi$
$461$	−9.14723e11	+	1.58435e12i	−0.943269	+	1.63379i	−0.759180	+	0.650880i	$0.774400\pi$
$462$	7.22454e11	+	1.25133e12i	0.737770	+	1.27786i
$463$	−1.55322e11			−0.157079			−0.0785396	−	0.996911i	$-0.525026\pi$
$463$	−1.55322e11			−0.157079			−0.0785396	+	0.996911i	$0.525026\pi$
$464$	−2.50426e11			−0.250812
$465$	−1.65287e11	−	2.86285e11i	−0.163946	−	0.283962i
$466$	7.80881e11	+	1.35253e12i	0.767094	+	1.32864i
$467$	8.82959e11			0.859043			0.429521	−	0.903057i	$-0.358682\pi$
$467$	8.82959e11			0.859043			0.429521	+	0.903057i	$0.358682\pi$
$468$	2.22065e11			0.213980
$469$	−7.47372e11	−	1.29449e12i	−0.713278	−	1.23543i
$470$	−1.25682e12	+	2.17688e12i	−1.18804	+	2.05775i
$471$	−2.87213e11	−	4.97468e11i	−0.268912	−	0.465769i
$472$	−8.79832e10	+	1.52391e11i	−0.0815944	+	0.141326i
$473$	9.44406e9	−	1.63576e10i	0.00867528	−	0.0150260i
$474$	−2.07390e12			−1.88706
$475$	3.62458e11	+	5.21887e10i	0.326690	+	0.0470387i
$476$	8.95472e11			0.799504
$477$	−1.09109e11	+	1.88983e11i	−0.0965005	+	0.167144i
$478$	−6.63948e11	+	1.14999e12i	−0.581713	+	1.00756i
$479$	2.09687e11	+	3.63188e11i	0.181996	+	0.315226i	0.942560	−	0.334037i	$-0.108411\pi$
$479$	2.09687e11	+	3.63188e11i	0.181996	+	0.315226i	−0.760564	+	0.649262i	$0.775078\pi$
$480$	8.96259e11	−	1.55237e12i	0.770634	−	1.33478i
$481$	−7.94050e11	−	1.37533e12i	−0.676386	−	1.17154i
$482$	−3.12122e12			−2.63398
$483$	−4.65222e11			−0.388954
$484$	1.16784e10	+	2.02275e10i	0.00967338	+	0.0167548i
$485$	−8.82648e11	−	1.52879e12i	−0.724352	−	1.25461i
$486$	4.59688e11			0.373766
$487$	4.61007e11			0.371387			0.185694	−	0.982608i	$-0.440547\pi$
$487$	4.61007e11			0.371387			0.185694	+	0.982608i	$0.440547\pi$
$488$	6.82615e9	+	1.18232e10i	0.00544863	+	0.00943730i
$489$	3.92441e11	−	6.79727e11i	0.310373	−	0.537582i
$490$	−2.38760e11	−	4.13544e11i	−0.187102	−	0.324070i
$491$	−9.99585e11	+	1.73133e12i	−0.776163	+	1.34435i	0.157975	+	0.987443i	$0.449503\pi$
$491$	−9.99585e11	+	1.73133e12i	−0.776163	+	1.34435i	−0.934138	+	0.356911i	$0.883830\pi$
$492$	7.59124e11	−	1.31484e12i	0.584077	−	1.01165i
$493$	−2.40956e11			−0.183707
$494$	1.79174e12	−	2.27743e12i	1.35364	−	1.72058i
$495$	−1.99093e11			−0.149050
$496$	1.87430e11	−	3.24638e11i	0.139050	−	0.240841i
$497$	−1.25500e12	+	2.17372e12i	−0.922656	+	1.59809i
$498$	1.02899e12	+	1.78227e12i	0.749688	+	1.29850i
$499$	2.45234e11	−	4.24757e11i	0.177063	−	0.306682i	−0.763810	−	0.645441i	$-0.776674\pi$
$499$	2.45234e11	−	4.24757e11i	0.177063	−	0.306682i	0.940873	+	0.338759i	$0.110007\pi$
$500$	5.83761e11	+	1.01110e12i	0.417705	+	0.723486i
$501$	2.24201e12			1.58989
$502$	2.04847e12			1.43967
$503$	4.85003e11	+	8.40050e11i	0.337822	+	0.585125i	0.984023	−	0.178042i	$-0.0569764\pi$
$503$	4.85003e11	+	8.40050e11i	0.337822	+	0.585125i	−0.646201	+	0.763168i	$0.723643\pi$
$504$	−1.22542e10	−	2.12250e10i	−0.00845958	−	0.0146524i
$505$	−2.80172e12			−1.91696
$506$	7.94527e11			0.538805
$507$	−9.03740e11	−	1.56532e12i	−0.607446	−	1.05213i
$508$	3.29542e9	−	5.70784e9i	0.00219545	−	0.00380264i
$509$	−1.46124e11	−	2.53094e11i	−0.0964919	−	0.167129i	0.813738	−	0.581231i	$-0.197429\pi$
$509$	−1.46124e11	−	2.53094e11i	−0.0964919	−	0.167129i	−0.910230	+	0.414102i	$0.864096\pi$
$510$	7.91829e11	−	1.37149e12i	0.518281	−	0.897689i
$511$	1.07439e12	−	1.86090e12i	0.697056	−	1.20734i
$512$	2.19891e12			1.41414
$513$	1.02243e12	−	1.29958e12i	0.651787	−	0.828468i
$514$	−6.16177e11			−0.389378
$515$	−1.04849e12	+	1.81605e12i	−0.656801	+	1.13761i
$516$	1.42139e10	−	2.46192e10i	0.00882651	−	0.0152880i
$517$	−1.14953e12	−	1.99105e12i	−0.707643	−	1.22567i
$518$	−1.16618e12	+	2.01988e12i	−0.711673	+	1.23265i
$519$	−3.38503e10	−	5.86304e10i	−0.0204790	−	0.0354707i
$520$	−3.42050e11			−0.205151
$521$	1.17680e11			0.0699735			0.0349868	−	0.999388i	$-0.488861\pi$
$521$	1.17680e11			0.0699735			0.0349868	+	0.999388i	$0.488861\pi$
$522$	4.38786e10	+	7.59999e10i	0.0258664	+	0.0448019i
$523$	−1.00706e12	−	1.74427e12i	−0.588567	−	1.01943i	−0.994420	−	0.105490i	$-0.966359\pi$
$523$	−1.00706e12	−	1.74427e12i	−0.588567	−	1.01943i	0.405853	−	0.913938i	$-0.366974\pi$
$524$	2.90111e12			1.68102
$525$	−5.92950e11			−0.340644
$526$	7.28806e11	+	1.26233e12i	0.415123	+	0.719013i
$527$	1.80342e11	−	3.12361e11i	0.101847	−	0.176404i
$528$	7.52700e11	+	1.30371e12i	0.421473	+	0.730012i
$529$	7.72668e11	−	1.33830e12i	0.428985	−	0.743024i
$530$	2.23641e12	−	3.87358e12i	1.23115	−	2.13241i
$531$	−3.32600e11			−0.181550
$532$	−2.18840e12	−	3.15098e11i	−1.18447	−	0.170547i
$533$	3.27579e12			1.75810
$534$	−1.63165e12	+	2.82611e12i	−0.868345	+	1.50402i
$535$	−3.95690e11	+	6.85355e11i	−0.208815	+	0.361679i
$536$	1.44364e11	+	2.50045e11i	0.0755469	+	0.130851i
$537$	−4.89965e11	+	8.48644e11i	−0.254261	+	0.440394i
$538$	1.23318e12	+	2.13593e12i	0.634608	+	1.09917i
$539$	4.36757e11			0.222890
$540$	−2.59734e12			−1.31449
$541$	−1.34208e12	−	2.32456e12i	−0.673584	−	1.16668i	−0.976881	−	0.213786i	$-0.931421\pi$
$541$	−1.34208e12	−	2.32456e12i	−0.673584	−	1.16668i	0.303297	−	0.952896i	$-0.401913\pi$
$542$	−1.50586e12	−	2.60822e12i	−0.749528	−	1.29822i
$543$	−2.93907e12			−1.45081
$544$	1.95579e12			0.957472
$545$	7.25138e11	+	1.25598e12i	0.352076	+	0.609814i
$546$	−2.34605e12	+	4.06348e12i	−1.12972	+	1.95673i
$547$	1.78143e12	+	3.08552e12i	0.850795	+	1.47362i	0.880492	+	0.474061i	$0.157212\pi$
$547$	1.78143e12	+	3.08552e12i	0.850795	+	1.47362i	−0.0296975	+	0.999559i	$0.509454\pi$
$548$	−1.67415e11	+	2.89972e11i	−0.0793016	+	0.137354i
$549$	−1.29024e10	+	2.23476e10i	−0.00606169	+	0.0104992i
$550$	1.01267e12			0.471883
$551$	5.88860e11	+	8.47875e10i	0.272164	+	0.0391877i
$552$	8.98633e10			0.0411961
$553$	−1.70707e12	+	2.95673e12i	−0.776225	+	1.34446i
$554$	2.45406e12	−	4.25055e12i	1.10686	−	1.91713i
$555$	1.07146e12	+	1.85583e12i	0.479356	+	0.830269i
$556$	−1.61818e12	+	2.80277e12i	−0.718109	+	1.24380i
$557$	−3.87035e11	−	6.70365e11i	−0.170374	−	0.295096i	0.768177	−	0.640238i	$-0.221164\pi$
$557$	−3.87035e11	−	6.70365e11i	−0.170374	−	0.295096i	−0.938551	+	0.345142i	$0.887831\pi$
$558$	−1.31362e11			−0.0573610
$559$	6.13361e10			0.0265683
$560$	−1.35477e12	−	2.34654e12i	−0.582131	−	1.00828i
$561$	7.24235e11	+	1.25441e12i	0.308707	+	0.534696i
$562$	−3.72309e12			−1.57431
$563$	−1.18409e12			−0.496703			−0.248352	−	0.968670i	$-0.579889\pi$
$563$	−1.18409e12			−0.496703			−0.248352	+	0.968670i	$0.579889\pi$
$564$	−1.73012e12	−	2.99665e12i	−0.719978	−	1.24704i
$565$	−7.40734e11	+	1.28299e12i	−0.305805	+	0.529669i
$566$	3.98663e11	+	6.90504e11i	0.163279	+	0.282808i
$567$	−1.16113e12	+	2.01114e12i	−0.471800	+	0.817182i
$568$	2.42418e11	−	4.19881e11i	0.0977232	−	0.169262i
$569$	−3.83096e12			−1.53215			−0.766077	−	0.642749i	$-0.777794\pi$
$569$	−3.83096e12			−1.53215			−0.766077	+	0.642749i	$0.777794\pi$
$570$	−2.41771e12	+	3.07308e12i	−0.959328	+	1.21938i
$571$	2.67721e12			1.05395			0.526975	−	0.849881i	$-0.323326\pi$
$571$	2.67721e12			1.05395			0.526975	+	0.849881i	$0.323326\pi$
$572$	2.08156e12	−	3.60536e12i	0.813029	−	1.40821i
$573$	8.19534e11	−	1.41947e12i	0.317593	−	0.550088i
$574$	−2.40549e12	−	4.16643e12i	−0.924911	−	1.60199i
$575$	−1.63026e11	+	2.82369e11i	−0.0621945	+	0.107724i
$576$	−1.99026e11	−	3.44723e11i	−0.0753369	−	0.130487i
$577$	3.47372e12			1.30468			0.652339	−	0.757927i	$-0.273788\pi$
$577$	3.47372e12			1.30468			0.652339	+	0.757927i	$0.273788\pi$
$578$	−2.14323e12			−0.798718
$579$	−2.30416e12	−	3.99092e12i	−0.852037	−	1.47577i
$580$	−4.67246e11	−	8.09293e11i	−0.171443	−	0.296948i
$581$	3.38794e12			1.23351
$582$	4.67753e12			1.68991
$583$	2.04551e12	+	3.54292e12i	0.733318	+	1.27014i
$584$	−2.07531e11	+	3.59454e11i	−0.0738287	+	0.127875i
$585$	−3.23261e11	−	5.59904e11i	−0.114117	−	0.197657i
$586$	−2.62333e12	+	4.54373e12i	−0.918995	+	1.59175i
$587$	−2.30317e12	+	3.98920e12i	−0.800670	+	1.38680i	0.118505	+	0.992953i	$0.462190\pi$
$587$	−2.30317e12	+	3.98920e12i	−0.800670	+	1.38680i	−0.919175	+	0.393848i	$0.871144\pi$
$588$	6.57345e11			0.226775
$589$	−5.50641e11	+	6.99905e11i	−0.188517	+	0.239618i
$590$	6.81731e12			2.31621
$591$	2.75263e11	−	4.76769e11i	0.0928120	−	0.160755i
$592$	−1.21500e12	+	2.10444e12i	−0.406564	+	0.704189i
$593$	2.78033e11	+	4.81568e11i	0.0923317	+	0.159923i	0.908492	−	0.417903i	$-0.137235\pi$
$593$	2.78033e11	+	4.81568e11i	0.0923317	+	0.159923i	−0.816160	+	0.577826i	$0.803901\pi$
$594$	2.28636e12	−	3.96009e12i	0.753539	−	1.30517i
$595$	−1.30354e12	−	2.25780e12i	−0.426381	−	0.738514i
$596$	−3.57550e12			−1.16072
$597$	3.62628e12			1.16836
$598$	1.29005e12	+	2.23443e12i	0.412526	+	0.714515i
$599$	1.17591e12	+	2.03673e12i	0.373210	+	0.646418i	0.990057	−	0.140664i	$-0.0449239\pi$
$599$	1.17591e12	+	2.03673e12i	0.373210	+	0.646418i	−0.616848	+	0.787083i	$0.711591\pi$
$600$	1.14535e11			0.0360794
$601$	2.41731e12			0.755782			0.377891	−	0.925850i	$-0.376649\pi$
$601$	2.41731e12			0.755782			0.377891	+	0.925850i	$0.376649\pi$
$602$	−4.50405e10	−	7.80125e10i	−0.0139772	−	0.0242092i
$603$	−2.72867e11	+	4.72620e11i	−0.0840472	+	0.145574i
$604$	1.22785e12	+	2.12669e12i	0.375385	+	0.650187i
$605$	3.40005e10	−	5.88906e10i	0.0103178	−	0.0178709i
$606$	3.71189e12	−	6.42918e12i	1.11807	−	1.93655i
$607$	2.87814e12			0.860525			0.430262	−	0.902704i	$-0.358421\pi$
$607$	2.87814e12			0.860525			0.430262	+	0.902704i	$0.358421\pi$
$608$	−4.77965e12	−	6.88201e11i	−1.41850	−	0.204244i
$609$	−9.63325e11			−0.283789
$610$	2.64460e11	−	4.58057e11i	0.0773348	−	0.133948i
$611$	3.73292e12	−	6.46561e12i	1.08359	−	1.87683i
$612$	−1.63469e11	−	2.83137e11i	−0.0471037	−	0.0815860i
$613$	2.33944e12	−	4.05202e12i	0.669174	−	1.15904i	−0.308961	−	0.951075i	$-0.599981\pi$
$613$	2.33944e12	−	4.05202e12i	0.669174	−	1.15904i	0.978135	−	0.207969i	$-0.0666853\pi$
$614$	3.89712e11	+	6.75001e11i	0.110659	+	0.191667i
$615$	−4.42024e12			−1.24597
$616$	−4.59468e11			−0.128571
$617$	−2.32552e12	−	4.02791e12i	−0.646005	−	1.11891i	−0.984068	−	0.177791i	$-0.943105\pi$
$617$	−2.32552e12	−	4.02791e12i	−0.646005	−	1.11891i	0.338063	−	0.941123i	$-0.390228\pi$
$618$	−2.77821e12	−	4.81201e12i	−0.766157	−	1.32702i
$619$	−1.45440e12			−0.398178			−0.199089	−	0.979981i	$-0.563798\pi$
$619$	−1.45440e12			−0.398178			−0.199089	+	0.979981i	$0.563798\pi$
$620$	1.39883e12			0.380190
$621$	7.36148e11	+	1.27505e12i	0.198634	+	0.344044i
$622$	−2.01112e12	+	3.48336e12i	−0.538742	+	0.933128i
$623$	2.68609e12	+	4.65245e12i	0.714373	+	1.23733i
$624$	−2.44427e12	+	4.23360e12i	−0.645385	+	1.11784i
$625$	2.32910e12	−	4.03412e12i	0.610560	−	1.05752i
$626$	−1.23672e12			−0.321874
$627$	−1.32852e12	−	3.32044e12i	−0.343293	−	0.858009i
$628$	2.43069e12			0.623608
$629$	−1.16905e12	+	2.02486e12i	−0.297787	+	0.515783i
$630$	−4.74755e11	+	8.22300e11i	−0.120071	+	0.207969i
$631$	−5.52544e11	−	9.57035e11i	−0.138751	−	0.240323i	0.788273	−	0.615325i	$-0.210975\pi$
$631$	−5.52544e11	−	9.57035e11i	−0.138751	−	0.240323i	−0.927024	+	0.375002i	$0.877642\pi$
$632$	3.29741e11	−	5.71127e11i	0.0822140	−	0.142399i
$633$	−1.74606e12	−	3.02427e12i	−0.432258	−	0.748693i
$634$	4.78120e11			0.117526
$635$	−1.91886e10			−0.00468341
$636$	3.07861e12	+	5.33231e12i	0.746101	+	1.29228i
$637$	7.09148e11	+	1.22828e12i	0.170651	+	0.295577i
$638$	1.64521e12			0.393123
$639$	9.16407e11			0.217438
$640$	5.71899e11	+	9.90558e11i	0.134744	+	0.233383i
$641$	−2.26763e12	+	3.92765e12i	−0.530532	+	0.918908i	0.468833	+	0.883287i	$0.344674\pi$
$641$	−2.26763e12	+	3.92765e12i	−0.530532	+	0.918908i	−0.999365	+	0.0356216i	$0.988659\pi$
$642$	−1.04847e12	−	1.81600e12i	−0.243583	−	0.421898i
$643$	−1.27514e11	+	2.20861e11i	−0.0294177	+	0.0509530i	−0.880359	−	0.474307i	$-0.842699\pi$
$643$	−1.27514e11	+	2.20861e11i	−0.0294177	+	0.0509530i	0.850942	+	0.525260i	$0.176032\pi$
$644$	9.84297e11	−	1.70485e12i	0.225496	−	0.390571i
$645$	−8.27647e10			−0.0188290
$646$	−4.22273e12	−	6.08013e11i	−0.953997	−	0.137362i
$647$	−4.53998e11			−0.101856			−0.0509278	−	0.998702i	$-0.516218\pi$
$647$	−4.53998e11			−0.101856			−0.0509278	+	0.998702i	$0.516218\pi$
$648$	2.24287e11	−	3.88476e11i	0.0499707	−	0.0865518i
$649$	−3.11768e12	+	5.39998e12i	−0.689811	+	1.19479i
$650$	1.64423e12	+	2.84790e12i	0.361288	+	0.625769i
$651$	7.20993e11	−	1.24880e12i	0.157332	−	0.272507i
$652$	1.66062e12	+	2.87627e12i	0.359878	+	0.623327i
$653$	6.55393e12			1.41056			0.705281	−	0.708928i	$-0.250821\pi$
$653$	6.55393e12			1.41056			0.705281	+	0.708928i	$0.250821\pi$
$654$	−3.84282e12			−0.821392
$655$	−4.22315e12	−	7.31471e12i	−0.896500	−	1.55278i
$656$	−2.50620e12	−	4.34086e12i	−0.528382	−	0.915185i
$657$	−7.84524e11			−0.164271
$658$	−1.09647e13			−2.28023
$659$	−1.53456e12	−	2.65794e12i	−0.316956	−	0.548985i	0.662895	−	0.748712i	$-0.269328\pi$
$659$	−1.53456e12	−	2.65794e12i	−0.316956	−	0.548985i	−0.979851	+	0.199728i	$0.935994\pi$
$660$	−2.80878e12	+	4.86495e12i	−0.576195	+	0.998000i
$661$	9.26411e11	+	1.60459e12i	0.188754	+	0.326932i	0.944835	−	0.327546i	$-0.106222\pi$
$661$	9.26411e11	+	1.60459e12i	0.188754	+	0.326932i	−0.756081	+	0.654478i	$0.772888\pi$
$662$	−6.26440e11	+	1.08503e12i	−0.126771	+	0.219573i
$663$	−2.35184e12	+	4.07350e12i	−0.472712	+	0.818760i
$664$	−6.54421e11			−0.130648
$665$	2.39119e12	+	5.97641e12i	0.474150	+	1.18507i
$666$	8.51548e11			0.167716
$667$	−2.64857e11	+	4.58746e11i	−0.0518138	+	0.0897441i
$668$	−4.74353e12	+	8.21604e12i	−0.921739	+	1.59650i
$669$	7.86765e11	+	1.36272e12i	0.151855	+	0.263020i
$670$	5.59295e12	−	9.68728e12i	1.07227	−	1.85723i
$671$	2.41884e11	+	4.18956e11i	0.0460634	+	0.0797842i
$672$	7.81910e12			1.47909
$673$	−3.06193e12			−0.575344			−0.287672	−	0.957729i	$-0.592881\pi$
$673$	−3.06193e12			−0.575344			−0.287672	+	0.957729i	$0.592881\pi$
$674$	1.71674e12	+	2.97348e12i	0.320431	+	0.555003i
$675$	9.38259e11	+	1.62511e12i	0.173963	+	0.301312i
$676$	7.64837e12			1.40867
$677$	3.93792e11			0.0720474			0.0360237	−	0.999351i	$-0.488531\pi$
$677$	3.93792e11			0.0720474			0.0360237	+	0.999351i	$0.488531\pi$
$678$	−1.96274e12	−	3.39956e12i	−0.356721	−	0.617858i
$679$	3.85017e12	−	6.66870e12i	0.695131	−	1.20400i
$680$	2.51794e11	+	4.36121e11i	0.0451602	+	0.0782198i
$681$	1.71984e12	−	2.97886e12i	0.306427	−	0.530747i
$682$	−1.23134e12	+	2.13275e12i	−0.217946	+	0.377494i
$683$	3.18438e11			0.0559927			0.0279963	−	0.999608i	$-0.491087\pi$
$683$	3.18438e11			0.0559927			0.0279963	+	0.999608i	$0.491087\pi$
$684$	2.99865e11	+	7.49467e11i	0.0523809	+	0.130918i
$685$	9.74827e11			0.169169
$686$	−3.58918e12	+	6.21664e12i	−0.618780	+	1.07176i
$687$	2.63616e12	−	4.56596e12i	0.451508	−	0.782035i
$688$	−4.69262e10	−	8.12785e10i	−0.00798486	−	0.0138302i
$689$	−6.64245e12	+	1.15051e13i	−1.12290	+	1.94492i
$690$	−1.74075e12	−	3.01506e12i	−0.292358	−	0.506378i
$691$	5.23744e12			0.873912			0.436956	−	0.899483i	$-0.356057\pi$
$691$	5.23744e12			0.873912			0.436956	+	0.899483i	$0.356057\pi$
$692$	2.86476e11			0.0474909
$693$	−4.34228e11	−	7.52105e11i	−0.0715185	−	0.123874i
$694$	1.93476e12	+	3.35109e12i	0.316598	+	0.548364i
$695$	9.42235e12			1.53189
$696$	1.86078e11			0.0300575
$697$	−2.41142e12	−	4.17670e12i	−0.387013	−	0.670326i
$698$	5.45444e12	−	9.44736e12i	0.869762	−	1.50647i
$699$	3.12961e12	+	5.42064e12i	0.495841	+	0.858822i
$700$	1.25454e12	−	2.17292e12i	0.197489	−	0.342061i
$701$	3.41785e11	−	5.91989e11i	0.0534592	−	0.0925940i	−0.838057	−	0.545582i	$-0.816309\pi$
$701$	3.41785e11	−	5.91989e11i	0.0534592	−	0.0925940i	0.891517	+	0.452988i	$0.149642\pi$
$702$	1.48492e13			2.30773
$703$	3.56950e12	−	4.53709e12i	0.551199	−	0.700613i
$704$	−7.46238e12			−1.14499
$705$	−5.03707e12	+	8.72446e12i	−0.767939	+	1.33011i
$706$	−1.76820e12	+	3.06261e12i	−0.267862	+	0.463950i
$707$	−6.11066e12	−	1.05840e13i	−0.919816	−	1.59317i
$708$	−4.69229e12	+	8.12729e12i	−0.701835	+	1.21561i
$709$	1.05510e12	+	1.82749e12i	0.156814	+	0.271610i	0.933718	−	0.358009i	$-0.116544\pi$
$709$	1.05510e12	+	1.82749e12i	0.156814	+	0.271610i	−0.776904	+	0.629619i	$0.783211\pi$
$710$	−1.87836e13			−2.77406
$711$	1.24651e12			0.182929
$712$	−5.18851e11	−	8.98676e11i	−0.0756629	−	0.131052i
$713$	−3.96461e11	−	6.86690e11i	−0.0574509	−	0.0995079i
$714$	6.90803e12			0.994746
$715$	−1.21205e13			−1.73438
$716$	−2.07329e12	−	3.59105e12i	−0.294816	−	0.510637i
$717$	−2.66096e12	+	4.60893e12i	−0.376013	+	0.651274i
$718$	−7.97927e12	−	1.38205e13i	−1.12048	−	1.94072i
$719$	5.06196e12	−	8.76757e12i	0.706380	−	1.22349i	−0.259811	−	0.965660i	$-0.583660\pi$
$719$	5.06196e12	−	8.76757e12i	0.706380	−	1.22349i	0.966191	−	0.257827i	$-0.0830065\pi$
$720$	−4.94631e11	+	8.56727e11i	−0.0685939	+	0.118808i
$721$	−9.14722e12			−1.26061
$722$	1.01058e13	+	2.97179e12i	1.38405	+	0.407005i
$723$	−1.25092e13			−1.70258
$724$	6.21836e12	−	1.07705e13i	0.841109	−	1.45684i
$725$	−3.37574e11	+	5.84696e11i	−0.0453783	+	0.0785975i
$726$	9.00917e10	+	1.56043e11i	0.0120357	+	0.0208464i
$727$	−3.40184e12	+	5.89215e12i	−0.451657	+	0.782293i	−0.998489	−	0.0549496i	$-0.982500\pi$
$727$	−3.40184e12	+	5.89215e12i	−0.451657	+	0.782293i	0.546832	+	0.837242i	$0.315834\pi$
$728$	−7.46023e11	−	1.29215e12i	−0.0984376	−	0.170499i
$729$	8.34377e12			1.09418
$730$	1.60804e13			2.09577
$731$	−4.51516e10	−	7.82048e10i	−0.00584850	−	0.0101299i
$732$	3.64050e11	+	6.30554e11i	0.0468664	+	0.0811750i
$733$	−7.70482e12			−0.985813			−0.492906	−	0.870082i	$-0.664066\pi$
$733$	−7.70482e12			−0.985813			−0.492906	+	0.870082i	$0.664066\pi$
$734$	−4.40697e12			−0.560412
$735$	−9.56899e11	−	1.65740e12i	−0.120941	−	0.209476i
$736$	2.14979e12	−	3.72354e12i	0.270051	−	0.467741i
$737$	5.11552e12	+	8.86034e12i	0.638684	+	1.10623i
$738$	−8.78250e11	+	1.52117e12i	−0.108984	+	0.188767i
$739$	−2.01780e12	+	3.49493e12i	−0.248873	+	0.431061i	−0.963213	−	0.268738i	$-0.913393\pi$
$739$	−2.01780e12	+	3.49493e12i	−0.248873	+	0.431061i	0.714340	+	0.699798i	$0.246727\pi$
$740$	−9.06780e12			−1.11163
$741$	7.18092e12	−	9.12746e12i	0.874980	−	1.11216i
$742$	1.95108e13			2.36297
$743$	6.06131e12	−	1.04985e13i	0.729654	−	1.26380i	−0.227375	−	0.973807i	$-0.573014\pi$
$743$	6.06131e12	−	1.04985e13i	0.729654	−	1.26380i	0.957029	−	0.289991i	$-0.0936522\pi$
$744$	−1.39268e11	+	2.41220e11i	−0.0166638	+	0.0288626i
$745$	5.20487e12	+	9.01509e12i	0.619023	+	1.07218i
$746$	7.24725e12	−	1.25526e13i	0.856739	−	1.48392i
$747$	−6.18473e11	−	1.07123e12i	−0.0726738	−	0.125875i
$748$	−6.12922e12			−0.715892
$749$	−3.45205e12			−0.400783
$750$	4.50336e12	+	7.80005e12i	0.519710	+	0.900164i
$751$	−3.81355e11	−	6.60527e11i	−0.0437472	−	0.0757724i	0.843323	−	0.537408i	$-0.180596\pi$
$751$	−3.81355e11	−	6.60527e11i	−0.0437472	−	0.0757724i	−0.887070	+	0.461635i	$0.847263\pi$
$752$	−1.14237e13			−1.30265
$753$	8.20983e12			0.930586
$754$	2.67127e12	+	4.62678e12i	0.300987	+	0.521324i
$755$	3.57476e12	−	6.19166e12i	0.400392	−	0.693499i
$756$	−5.66489e12	−	9.81188e12i	−0.630730	−	1.09246i
$757$	−8.71768e11	+	1.50995e12i	−0.0964871	+	0.167121i	−0.910228	−	0.414107i	$-0.864094\pi$
$757$	−8.71768e11	+	1.50995e12i	−0.0964871	+	0.167121i	0.813741	+	0.581227i	$0.197427\pi$
$758$	−2.10901e12	+	3.65292e12i	−0.232043	+	0.401909i
$759$	3.18430e12			0.348278
$760$	−4.61886e11	−	1.15442e12i	−0.0502197	−	0.125517i
$761$	2.20854e12			0.238712			0.119356	−	0.992852i	$-0.461917\pi$
$761$	2.20854e12			0.238712			0.119356	+	0.992852i	$0.461917\pi$
$762$	2.54222e10	−	4.40325e10i	0.00273159	−	0.00473126i
$763$	−3.16311e12	+	5.47866e12i	−0.337873	+	0.585213i
$764$	3.46787e12	+	6.00652e12i	0.368250	+	0.637827i
$765$	−4.75926e11	+	8.24328e11i	−0.0502415	+	0.0870209i
$766$	3.80320e12	+	6.58734e12i	0.399135	+	0.691322i
$767$	−2.02483e13			−2.11256
$768$	7.35658e12			0.763045
$769$	9.15604e12	+	1.58587e13i	0.944146	+	1.63531i	0.757452	+	0.652891i	$0.226444\pi$
$769$	9.15604e12	+	1.58587e13i	0.944146	+	1.63531i	0.186694	+	0.982418i	$0.440223\pi$
$770$	8.90037e12	+	1.54159e13i	0.912431	+	1.58038i
$771$	−2.46951e12			−0.251690
$772$	1.95001e13			1.97587
$773$	−4.15767e12	−	7.20129e12i	−0.418834	−	0.725442i	0.576988	−	0.816752i	$-0.304228\pi$
$773$	−4.15767e12	−	7.20129e12i	−0.418834	−	0.725442i	−0.995822	+	0.0913104i	$0.970894\pi$
$774$	−1.64444e10	+	2.84825e10i	−0.00164696	+	0.00285262i
$775$	−5.05309e11	−	8.75222e11i	−0.0503153	−	0.0871486i
$776$	−7.43707e11	+	1.28814e12i	−0.0736248	+	0.127522i
$777$	−4.67379e12	+	8.09525e12i	−0.460018	+	0.796775i
$778$	−1.23444e13			−1.20799
$779$	4.42346e12	+	1.10558e13i	0.430371	+	1.07565i
$780$	−1.82421e13			−1.76461
$781$	8.59007e12	−	1.48784e13i	0.826166	−	1.43096i
$782$	1.89930e12	−	3.28968e12i	0.181620	−	0.314574i
$783$	1.52432e12	+	2.64021e12i	0.144927	+	0.251021i
$784$	1.08509e12	−	1.87943e12i	0.102576	−	0.177666i
$785$	−3.53836e12	−	6.12862e12i	−0.332574	−	0.576036i
$786$	2.23803e13			2.09153
$787$	−1.77310e13			−1.64758			−0.823789	−	0.566897i	$-0.808144\pi$
$787$	−1.77310e13			−1.64758			−0.823789	+	0.566897i	$0.808144\pi$
$788$	1.16478e12	+	2.01745e12i	0.107616	+	0.186396i
$789$	2.92090e12	+	5.05915e12i	0.268331	+	0.464763i
$790$	−2.55497e13			−2.33380
$791$	−6.46227e12			−0.586936
$792$	8.38764e10	+	1.45278e11i	0.00757489	+	0.0131201i
$793$	−7.85480e11	+	1.36049e12i	−0.0705352	+	0.122171i
$794$	−4.41261e12	−	7.64287e12i	−0.394007	−	0.682439i
$795$	8.96308e12	−	1.55245e13i	0.795802	−	1.37837i
$796$	−7.67233e12	+	1.32889e13i	−0.677358	+	1.17322i
$797$	−3.57434e12			−0.313786			−0.156893	−	0.987616i	$-0.550148\pi$
$797$	−3.57434e12			−0.313786			−0.156893	+	0.987616i	$0.550148\pi$
$798$	−1.68822e13	−	2.43079e12i	−1.47372	−	0.212195i
$799$	−1.09917e13			−0.954124
$800$	2.74001e12	−	4.74584e12i	0.236509	−	0.409646i
$801$	9.80699e11	−	1.69862e12i	0.0841763	−	0.145798i
$802$	−1.71816e12	−	2.97594e12i	−0.146649	−	0.254004i
$803$	−7.35385e12	+	1.27372e13i	−0.624158	+	1.08107i
$804$	7.69916e12	+	1.33353e13i	0.649817	+	1.12552i
$805$	−5.73137e12			−0.481036
$806$	−7.99718e12			−0.667466
$807$	4.94232e12	+	8.56035e12i	0.410204	+	0.710494i
$808$	1.18035e12	+	2.04442e12i	0.0974223	+	0.168740i
$809$	2.27933e12			0.187085			0.0935426	−	0.995615i	$-0.470181\pi$
$809$	2.27933e12			0.187085			0.0935426	+	0.995615i	$0.470181\pi$
$810$	−1.73787e13			−1.41851
$811$	5.09906e12	+	8.83183e12i	0.413901	+	0.716897i	0.995312	−	0.0967122i	$-0.0308327\pi$
$811$	5.09906e12	+	8.83183e12i	0.413901	+	0.716897i	−0.581411	+	0.813610i	$0.697499\pi$
$812$	2.03816e12	−	3.53020e12i	0.164527	−	0.284968i
$813$	−6.03517e12	−	1.04532e13i	−0.484487	−	0.839156i
$814$	7.98211e12	−	1.38254e13i	0.637247	−	1.10374i
$815$	4.83473e12	−	8.37399e12i	0.383851	−	0.664849i
$816$	7.19724e12			0.568277
$817$	8.28250e10	+	2.07009e11i	0.00650373	+	0.0162551i
$818$	−2.57457e13			−2.01055
$819$	1.41009e12	−	2.44234e12i	0.109514	−	0.189683i
$820$	9.35214e12	−	1.61984e13i	0.722351	−	1.25115i
$821$	−2.18877e12	−	3.79107e12i	−0.168134	−	0.291217i	0.769629	−	0.638491i	$-0.220441\pi$
$821$	−2.18877e12	−	3.79107e12i	−0.168134	−	0.291217i	−0.937764	+	0.347273i	$0.887108\pi$
$822$	−1.29151e12	+	2.23696e12i	−0.0986674	+	0.170897i
$823$	−2.01045e12	−	3.48219e12i	−0.152754	−	0.264578i	0.779485	−	0.626421i	$-0.215481\pi$
$823$	−2.01045e12	−	3.48219e12i	−0.152754	−	0.264578i	−0.932239	+	0.361843i	$0.882148\pi$
$824$	1.76689e12			0.133518
$825$	4.05855e12			0.305020
$826$	1.48688e13	+	2.57535e13i	1.11139	+	1.92498i
$827$	5.67659e12	+	9.83213e12i	0.422000	+	0.730925i	0.996135	−	0.0878353i	$-0.0279949\pi$
$827$	5.67659e12	+	9.83213e12i	0.422000	+	0.730925i	−0.574135	+	0.818761i	$0.694662\pi$
$828$	−7.18738e11			−0.0531416
$829$	2.21298e13			1.62735			0.813676	−	0.581319i	$-0.197463\pi$
$829$	2.21298e13			1.62735			0.813676	+	0.581319i	$0.197463\pi$
$830$	1.26768e13	+	2.19569e13i	0.927170	+	1.60591i
$831$	9.83535e12	−	1.70353e13i	0.715459	−	1.23921i
$832$	−1.21164e13	−	2.09863e13i	−0.876638	−	1.51838i
$833$	1.04406e12	−	1.80836e12i	0.0751313	−	0.130131i
$834$	−1.24833e13	+	2.16217e13i	−0.893474	+	1.54754i
$835$	2.76207e13			1.96628
$836$	1.49789e13	+	2.15675e12i	1.06060	+	0.152711i
$837$	−4.56347e12			−0.321389
$838$	2.53521e11	−	4.39112e11i	0.0177589	−	0.0307594i
$839$	1.80883e12	−	3.13299e12i	0.126029	−	0.218288i	−0.796106	−	0.605157i	$-0.793110\pi$
$839$	1.80883e12	−	3.13299e12i	0.126029	−	0.218288i	0.922135	+	0.386869i	$0.126444\pi$
$840$	1.00666e12	+	1.74358e12i	0.0697629	+	0.120833i
$841$	6.70514e12	−	1.16136e13i	0.462196	−	0.800546i
$842$	1.14191e12	+	1.97785e12i	0.0782941	+	0.135609i
$843$	−1.49213e13			−1.01762
$844$	1.47770e13			1.00241
$845$	−1.11337e13	−	1.92842e13i	−0.751253	−	1.30121i
$846$	2.00162e12	+	3.46690e12i	0.134343	+	0.232688i
$847$	2.96625e11			0.0198031
$848$	2.03276e13			1.34991
$849$	1.59776e12	+	2.76739e12i	0.105542	+	0.182804i
$850$	2.42075e12	−	4.19287e12i	0.159062	−	0.275503i
$851$	2.57003e12	+	4.45142e12i	0.167979	+	0.290948i
$852$	1.29286e13	−	2.23929e13i	0.840567	−	1.45591i
$853$	−4.98910e12	+	8.64137e12i	−0.322665	+	0.558872i	−0.981037	−	0.193821i	$-0.937912\pi$
$853$	−4.98910e12	+	8.64137e12i	−0.322665	+	0.558872i	0.658372	+	0.752693i	$0.271245\pi$
$854$	2.30718e12			0.148430
$855$	1.45316e12	−	1.84707e12i	0.0929961	−	0.118205i
$856$	6.66805e11			0.0424490
$857$	−4.54456e12	+	7.87141e12i	−0.287792	+	0.498470i	−0.973282	−	0.229612i	$-0.926254\pi$
$857$	−4.54456e12	+	7.87141e12i	−0.287792	+	0.498470i	0.685491	+	0.728081i	$0.259588\pi$
$858$	1.60580e13	−	2.78132e13i	1.01157	−	1.75210i
$859$	4.39723e12	+	7.61622e12i	0.275556	+	0.477277i	0.970275	−	0.242004i	$-0.0778048\pi$
$859$	4.39723e12	+	7.61622e12i	0.275556	+	0.477277i	−0.694719	+	0.719281i	$0.744471\pi$
$860$	1.75110e11	−	3.03299e11i	0.0109161	−	0.0189072i
$861$	−9.64070e12	−	1.66982e13i	−0.597853	−	1.03551i
$862$	6.53731e12			0.403289
$863$	−6.67387e12			−0.409571			−0.204786	−	0.978807i	$-0.565650\pi$
$863$	−6.67387e12			−0.409571			−0.204786	+	0.978807i	$0.565650\pi$
$864$	−1.23726e13	−	2.14300e13i	−0.755352	−	1.30831i
$865$	−4.17023e11	−	7.22306e11i	−0.0253272	−	0.0438681i
$866$	−1.89626e13			−1.14569
$867$	−8.58962e12			−0.516283
$868$	3.05089e12	+	5.28430e12i	0.182426	+	0.315972i
$869$	1.16843e13	−	2.02379e13i	0.695048	−	1.20386i
$870$	−3.60452e12	−	6.24321e12i	−0.213310	−	0.369464i
$871$	−1.66118e13	+	2.87725e13i	−0.977992	+	1.69393i
$872$	6.10991e11	−	1.05827e12i	0.0357858	−	0.0619828i
$873$	−2.81142e12			−0.163818
$874$	−5.79917e12	+	7.37116e12i	−0.336174	+	0.427302i
$875$	1.48272e13			0.855114
$876$	−1.10680e13	+	1.91703e13i	−0.635039	+	1.09992i
$877$	−5.87607e12	+	1.01777e13i	−0.335420	+	0.580964i	−0.983565	−	0.180552i	$-0.942212\pi$
$877$	−5.87607e12	+	1.01777e13i	−0.335420	+	0.580964i	0.648145	+	0.761517i	$0.275545\pi$
$878$	−1.72682e13	−	2.99093e13i	−0.980665	−	1.69856i
$879$	−1.05137e13	+	1.82103e13i	−0.594028	+	1.02889i
$880$	9.27299e12	+	1.60613e13i	0.521252	+	0.902835i
$881$	2.57887e10			0.00144224			0.000721122	−	1.00000i	$-0.499770\pi$
$881$	2.57887e10			0.00144224			0.000721122		1.00000i	$0.499770\pi$
$882$	−7.60499e11			−0.0423146
$883$	−4.68221e12	−	8.10982e12i	−0.259195	−	0.448940i	0.706831	−	0.707382i	$-0.250124\pi$
$883$	−4.68221e12	−	8.10982e12i	−0.259195	−	0.448940i	−0.966027	+	0.258443i	$0.916791\pi$
$884$	−9.95182e12	−	1.72371e13i	−0.548109	−	0.949353i
$885$	2.73223e13			1.49718
$886$	−1.92917e13			−1.05176
$887$	4.40696e12	+	7.63309e12i	0.239047	+	0.414041i	0.960441	−	0.278483i	$-0.0898317\pi$
$887$	4.40696e12	+	7.63309e12i	0.239047	+	0.414041i	−0.721394	+	0.692525i	$0.756498\pi$
$888$	9.02799e11	−	1.56369e12i	0.0487228	−	0.0843904i
$889$	−4.18511e10	−	7.24882e10i	−0.00224724	−	0.00389233i
$890$	−2.01014e13	+	3.48166e13i	−1.07392	+	1.86008i
$891$	7.94758e12	−	1.37656e13i	0.422459	−	0.731721i
$892$	−6.65841e12			−0.352151
$893$	2.68621e13	+	3.86776e12i	1.41354	+	0.203530i
$894$	−2.75829e13			−1.44418
$895$	−6.03619e12	+	1.04550e13i	−0.314456	+	0.544653i
$896$	−2.49466e12	+	4.32089e12i	−0.129308	+	0.223968i
$897$	5.17025e12	+	8.95513e12i	0.266652	+	0.461855i
$898$	6.49877e12	−	1.12562e13i	0.333494	−	0.577628i
$899$	−8.20941e11	−	1.42191e12i	−0.0419173	−	0.0726029i
$900$	−9.16069e11			−0.0465411
$901$	1.95589e13			0.988742
$902$	1.64648e13	+	2.85179e13i	0.828185	+	1.43446i
$903$	−1.80513e11	−	3.12657e11i	−0.00903469	−	0.0156485i
$904$	1.24826e12			0.0621654
$905$	−3.62083e13			−1.79428
$906$	9.47209e12	+	1.64061e13i	0.467056	+	0.808965i
$907$	8.48623e12	−	1.46986e13i	0.416372	−	0.721178i	−0.579199	−	0.815186i	$-0.696635\pi$
$907$	8.48623e12	−	1.46986e13i	0.416372	−	0.721178i	0.995571	+	0.0940079i	$0.0299679\pi$
$908$	7.27754e12	+	1.26051e13i	0.355302	+	0.615402i
$909$	−2.23102e12	+	3.86423e12i	−0.108384	+	0.187727i
$910$	−2.89025e13	+	5.00606e13i	−1.39717	+	2.41997i
$911$	−1.00079e13			−0.481404			−0.240702	−	0.970599i	$-0.577378\pi$
$911$	−1.00079e13			−0.481404			−0.240702	+	0.970599i	$0.577378\pi$
$912$	−1.75890e13	−	2.53256e12i	−0.841907	−	0.121223i
$913$	−2.31894e13			−1.10451
$914$	1.93997e13	−	3.36013e13i	0.919470	−	1.59257i
$915$	1.05990e12	−	1.83580e12i	0.0499884	−	0.0865825i
$916$	1.11549e13	+	1.93209e13i	0.523524	+	0.906771i
$917$	1.84217e13	−	3.19073e13i	0.860334	−	1.49014i
$918$	−1.09310e13	−	1.89330e13i	−0.508003	−	0.879888i
$919$	2.66714e12			0.123346			0.0616732	−	0.998096i	$-0.480356\pi$
$919$	2.66714e12			0.123346			0.0616732	+	0.998096i	$0.480356\pi$
$920$	1.10708e12			0.0509489
$921$	1.56188e12	+	2.70526e12i	0.0715287	+	0.123891i
$922$	−2.98598e13	−	5.17187e13i	−1.36081	−	2.35700i
$923$	5.57897e13			2.53015
$924$	−2.45042e13			−1.10590
$925$	3.27564e12	+	5.67357e12i	0.147115	+	0.254811i
$926$	2.53513e12	−	4.39098e12i	0.113306	−	0.196251i
$927$	1.66984e12	+	2.89224e12i	0.0742703	+	0.128640i
$928$	4.45151e12	−	7.71025e12i	0.197034	−	0.341273i
$929$	3.83328e12	−	6.63944e12i	0.168850	−	0.292456i	−0.769166	−	0.639049i	$-0.779328\pi$
$929$	3.83328e12	−	6.63944e12i	0.168850	−	0.292456i	0.938016	+	0.346593i	$0.112661\pi$
$930$	1.07911e13			0.473034
$931$	−3.18784e12	+	4.05197e12i	−0.139067	+	0.176764i
$932$	−2.64859e13			−1.14986
$933$	−8.06014e12	+	1.39606e13i	−0.348237	+	0.603164i
$934$	−1.44115e13	+	2.49614e13i	−0.619651	+	1.07327i
$935$	8.92232e12	+	1.54539e13i	0.381791	+	0.661281i
$936$	−2.72375e11	+	4.71767e11i	−0.0115991	+	0.0200903i
$937$	1.55985e13	+	2.70173e13i	0.661080	+	1.14502i	0.980332	+	0.197354i	$0.0632348\pi$
$937$	1.55985e13	+	2.70173e13i	0.661080	+	1.14502i	−0.319253	+	0.947670i	$0.603432\pi$
$938$	4.87937e13			2.05803
$939$	−4.95650e12			−0.208056
$940$	−2.13144e13	−	3.69176e13i	−0.890426	−	1.54226i
$941$	1.71032e13	+	2.96237e13i	0.711091	+	1.23165i	0.964448	+	0.264273i	$0.0851320\pi$
$941$	1.71032e13	+	2.96237e13i	0.711091	+	1.23165i	−0.253357	+	0.967373i	$0.581535\pi$
$942$	1.87513e13			0.775895
$943$	−1.06025e13			−0.436621
$944$	1.54913e13	+	2.68317e13i	0.634912	+	1.09970i
$945$	−1.64928e13	+	2.85664e13i	−0.672746	+	1.16523i
$946$	3.08288e11	+	5.33970e11i	0.0125154	+	0.0216774i
$947$	−4.04225e12	+	7.00138e12i	−0.163323	+	0.282884i	−0.936059	−	0.351844i	$-0.885555\pi$
$947$	−4.04225e12	+	7.00138e12i	−0.163323	+	0.282884i	0.772735	+	0.634729i	$0.218888\pi$
$948$	1.75856e13	−	3.04592e13i	0.707164	−	1.22484i
$949$	−4.77609e13			−1.91150
$950$	−7.39134e12	+	9.39493e12i	−0.294420	+	0.374229i
$951$	1.91620e12			0.0759677
$952$	−1.09835e12	+	1.90239e12i	−0.0433384	+	0.0750643i
$953$	−6.05633e12	+	1.04899e13i	−0.237844	+	0.411957i	−0.960095	−	0.279673i	$-0.909774\pi$
$953$	−6.05633e12	+	1.04899e13i	−0.237844	+	0.411957i	0.722252	+	0.691630i	$0.243107\pi$
$954$	−3.56172e12	−	6.16908e12i	−0.139217	−	0.241131i
$955$	1.00964e13	−	1.74874e13i	0.392781	−	0.680316i
$956$	−1.12599e13	−	1.95027e13i	−0.435987	−	0.755152i
$957$	6.59365e12			0.254110
$958$	−1.36898e13			−0.525114
$959$	2.12613e12	+	3.68257e12i	0.0811721	+	0.140594i
$960$	1.63495e13	+	2.83181e13i	0.621274	+	1.07608i
$961$	−2.39819e13			−0.907044
$962$	5.18412e13			1.95158
$963$	6.30177e11	+	1.09150e12i	0.0236126	+	0.0408982i
$964$	2.64664e13	−	4.58411e13i	0.987070	−	1.70966i
$965$	−2.83864e13	−	4.91666e13i	−1.05375	−	1.82515i
$966$	7.59326e12	−	1.31519e13i	0.280564	−	0.485950i
$967$	2.35733e13	−	4.08302e13i	0.866964	−	1.50163i	0.00188102	−	0.999998i	$-0.499401\pi$
$967$	2.35733e13	−	4.08302e13i	0.866964	−	1.50163i	0.865083	−	0.501628i	$-0.167265\pi$
$968$	−5.72967e10			−0.00209744
$969$	−1.69238e13	−	2.43679e12i	−0.616654	−	0.0887893i
$970$	5.76255e13			2.08998
$971$	1.21598e13	−	2.10615e13i	0.438977	−	0.760330i	−0.558634	−	0.829414i	$-0.688674\pi$
$971$	1.21598e13	−	2.10615e13i	0.438977	−	0.760330i	0.997611	+	0.0690841i	$0.0220077\pi$
$972$	−3.89792e12	+	6.75140e12i	−0.140067	+	0.242603i
$973$	2.05505e13	+	3.55945e13i	0.735046	+	1.27314i
$974$	−7.52445e12	+	1.30327e13i	−0.267892	+	0.464002i
$975$	6.58975e12	+	1.14138e13i	0.233533	+	0.404491i
$976$	2.40378e12			0.0847950
$977$	−8.81348e12			−0.309472			−0.154736	−	0.987956i	$-0.549453\pi$
$977$	−8.81348e12			−0.309472			−0.154736	+	0.987956i	$0.549453\pi$
$978$	1.28107e13	+	2.21887e13i	0.447761	+	0.775545i
$979$	−1.83855e13	−	3.18445e13i	−0.639664	−	1.10793i
$980$	8.09826e12			0.280462
$981$	2.30971e12			0.0796247
$982$	−3.26300e13	−	5.65168e13i	−1.11974	−	1.93944i
$983$	−2.05991e13	+	3.56787e13i	−0.703651	+	1.21876i	0.263525	+	0.964652i	$0.415115\pi$
$983$	−2.05991e13	+	3.56787e13i	−0.703651	+	1.21876i	−0.967176	+	0.254107i	$0.918219\pi$
$984$	1.86221e12	+	3.22545e12i	0.0633216	+	0.109676i
$985$	3.39114e12	−	5.87363e12i	0.114784	−	0.198812i
$986$	3.93283e12	−	6.81186e12i	0.132513	−	0.229520i
$987$	−4.39441e13			−1.47392
$988$	1.82554e13	+	4.56266e13i	0.609516	+	1.52339i
$989$	−1.98521e11			−0.00659817
$990$	3.24955e12	−	5.62838e12i	0.107514	−	0.186219i
$991$	−1.80619e12	+	3.12841e12i	−0.0594883	+	0.103037i	−0.894236	−	0.447596i	$-0.852280\pi$
$991$	−1.80619e12	+	3.12841e12i	−0.0594883	+	0.103037i	0.834748	+	0.550633i	$0.185614\pi$
$992$	6.66340e12	+	1.15413e13i	0.218471	+	0.378402i
$993$	−2.51064e12	+	4.34855e12i	−0.0819431	+	0.141930i
$994$	−4.09677e13	−	7.09581e13i	−1.33108	−	2.30549i
$995$	4.46745e13			1.44496
$996$	−3.49014e13			−1.12377
$997$	−1.96473e13	−	3.40302e13i	−0.629760	−	1.09078i	−0.987600	−	0.156994i	$-0.949820\pi$
$997$	−1.96473e13	−	3.40302e13i	−0.629760	−	1.09078i	0.357839	−	0.933783i	$-0.383514\pi$
$998$	8.00530e12	+	1.38656e13i	0.255441	+	0.442436i
$999$	2.95824e13			0.939700

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.10.c.a.11.3	yes	28
19.7	even	3	inner	19.10.c.a.7.3	✓	28
19.8	odd	6		361.10.a.f.1.3		14
19.11	even	3		361.10.a.e.1.12		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.10.c.a.7.3	✓	28	19.7	even	3	inner
19.10.c.a.11.3	yes	28	1.1	even	1	trivial
361.10.a.e.1.12		14	19.11	even	3
361.10.a.f.1.3		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+(-16.3218 + 28.2702i) q^{2} +(-65.4143 + 113.301i) q^{3} +(-276.801 - 479.434i) q^{4} +(-805.880 + 1395.83i) q^{5} +(-2135.35 - 3698.54i) q^{6} -7030.62 q^{7} +1358.05 q^{8} +(1283.45 + 2223.00i) q^{9} +(-26306.8 - 45564.7i) q^{10} +48122.3 q^{11} +72427.0 q^{12} +(78134.7 + 135333. i) q^{13} +(114752. - 198757. i) q^{14} +(-105432. - 182614. i) q^{15} +(119556. - 207078. i) q^{16} +(115035. - 199247. i) q^{17} -83792.6 q^{18} +(-351240. + 446451. i) q^{19} +892274. q^{20} +(459903. - 796575. i) q^{21} +(-785442. + 1.36043e6i) q^{22} +(-252892. - 438021. i) q^{23} +(-88835.7 + 153868. i) q^{24} +(-322324. - 558281. i) q^{25} -5.10119e6 q^{26} -2.91092e6 q^{27} +(1.94608e6 + 3.37071e6i) q^{28} +(-523657. - 907001. i) q^{29} +6.88336e6 q^{30} +1.56771e6 q^{31} +(4.25041e6 + 7.36192e6i) q^{32} +(-3.14789e6 + 5.45230e6i) q^{33} +(3.75516e6 + 6.50412e6i) q^{34} +(5.66584e6 - 9.81352e6i) q^{35} +(710519. - 1.23066e6i) q^{36} -1.01626e7 q^{37} +(-6.88838e6 - 1.72165e7i) q^{38} -2.04445e7 q^{39} +(-1.09442e6 + 1.89560e6i) q^{40} +(1.04812e7 - 1.81540e7i) q^{41} +(1.50129e7 + 2.60030e7i) q^{42} +(196251. - 339917. i) q^{43} +(-1.33203e7 - 2.30715e7i) q^{44} -4.13722e6 q^{45} +1.65106e7 q^{46} +(-2.38877e7 - 4.13748e7i) q^{47} +(1.56414e7 + 2.70917e7i) q^{48} +9.07597e6 q^{49} +2.10436e7 q^{50} +(1.50499e7 + 2.60672e7i) q^{51} +(4.32556e7 - 7.49208e7i) q^{52} +(4.25064e7 + 7.36232e7i) q^{53} +(4.75114e7 - 8.22922e7i) q^{54} +(-3.87808e7 + 6.71704e7i) q^{55} -9.54791e6 q^{56} +(-2.76072e7 - 6.90000e7i) q^{57} +3.41881e7 q^{58} +(-6.47865e7 + 1.12214e8i) q^{59} +(-5.83675e7 + 1.01095e8i) q^{60} +(5.02645e6 + 8.70606e6i) q^{61} +(-2.55878e7 + 4.43194e7i) q^{62} +(-9.02343e6 - 1.56290e7i) q^{63} -1.55071e8 q^{64} -2.51869e8 q^{65} +(-1.02758e8 - 1.77982e8i) q^{66} +(1.06302e8 + 1.84121e8i) q^{67} -1.27367e8 q^{68} +6.61709e7 q^{69} +(1.84953e8 + 3.20348e8i) q^{70} +(1.78505e8 - 3.09180e8i) q^{71} +(1.74298e6 + 3.01893e6i) q^{72} +(-1.52816e8 + 2.64685e8i) q^{73} +(1.65871e8 - 2.87297e8i) q^{74} +8.43383e7 q^{75} +(3.11267e8 + 4.48180e7i) q^{76} -3.38330e8 q^{77} +(3.33691e8 - 5.77969e8i) q^{78} +(2.42805e8 - 4.20551e8i) q^{79} +(1.92696e8 + 3.33760e8i) q^{80} +(1.65154e8 - 2.86055e8i) q^{81} +(3.42145e8 + 5.92612e8i) q^{82} -4.81884e8 q^{83} -5.09206e8 q^{84} +(1.85409e8 + 3.21138e8i) q^{85} +(6.40634e6 + 1.10961e7i) q^{86} +1.37019e8 q^{87} +6.53524e7 q^{88} +(-3.82057e8 - 6.61742e8i) q^{89} +(6.75268e7 - 1.16960e8i) q^{90} +(-5.49335e8 - 9.51477e8i) q^{91} +(-1.40001e8 + 2.42490e8i) q^{92} +(-1.02550e8 + 1.77623e8i) q^{93} +1.55956e9 q^{94} +(-3.40110e8 - 8.50055e8i) q^{95} -1.11215e9 q^{96} +(-5.47630e8 + 9.48522e8i) q^{97} +(-1.48136e8 + 2.56579e8i) q^{98} +(6.17625e7 + 1.06976e8i) 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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