Properties

Label 99.8.j.a.8.1
Level $99$
Weight $8$
Character 99.8
Analytic conductor $30.926$
Analytic rank $0$
Dimension $112$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [99,8,Mod(8,99)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(99, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 3]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("99.8");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 99.j (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(30.9261175229\)
Analytic rank: \(0\)
Dimension: \(112\)
Relative dimension: \(28\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 8.1
Character \(\chi\) \(=\) 99.8
Dual form 99.8.j.a.62.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-17.5311 + 12.7371i) q^{2} +(105.552 - 324.855i) q^{4} +(-159.065 + 218.934i) q^{5} +(-1136.60 - 369.305i) q^{7} +(1430.14 + 4401.52i) q^{8} +O(q^{10})\) \(q+(-17.5311 + 12.7371i) q^{2} +(105.552 - 324.855i) q^{4} +(-159.065 + 218.934i) q^{5} +(-1136.60 - 369.305i) q^{7} +(1430.14 + 4401.52i) q^{8} -5864.17i q^{10} +(4216.26 - 1307.78i) q^{11} +(6830.31 + 9401.11i) q^{13} +(24629.8 - 8002.70i) q^{14} +(-45763.1 - 33248.9i) q^{16} +(-4812.95 - 3496.81i) q^{17} +(29060.5 - 9442.31i) q^{19} +(54332.1 + 74781.8i) q^{20} +(-57258.3 + 76629.7i) q^{22} +96563.1i q^{23} +(1511.50 + 4651.91i) q^{25} +(-239485. - 77813.5i) q^{26} +(-239941. + 330250. i) q^{28} +(-24030.4 + 73957.8i) q^{29} +(-127217. + 92428.6i) q^{31} +633383. q^{32} +128915. q^{34} +(261647. - 190098. i) q^{35} +(135597. - 417323. i) q^{37} +(-389194. + 535679. i) q^{38} +(-1.19113e6 - 387020. i) q^{40} +(-7872.79 - 24230.0i) q^{41} -44925.2i q^{43} +(20194.4 - 1.50771e6i) q^{44} +(-1.22993e6 - 1.69286e6i) q^{46} +(208893. - 67873.6i) q^{47} +(489222. + 355441. i) q^{49} +(-85750.0 - 62301.0i) q^{50} +(3.77494e6 - 1.22655e6i) q^{52} +(487319. + 670738. i) q^{53} +(-384341. + 1.13111e6i) q^{55} -5.53094e6i q^{56} +(-520729. - 1.60264e6i) q^{58} +(-1.99174e6 - 647157. i) q^{59} +(500336. - 688653. i) q^{61} +(1.05298e6 - 3.24075e6i) q^{62} +(-5.24622e6 + 3.81160e6i) q^{64} -3.14468e6 q^{65} -2.90295e6 q^{67} +(-1.64397e6 + 1.19441e6i) q^{68} +(-2.16567e6 + 6.66524e6i) q^{70} +(-2.16301e6 + 2.97713e6i) q^{71} +(5.27787e6 + 1.71488e6i) q^{73} +(2.93833e6 + 9.04324e6i) q^{74} -1.04371e7i q^{76} +(-5.27519e6 - 70656.2i) q^{77} +(-4.80416e6 - 6.61236e6i) q^{79} +(1.45586e7 - 4.73038e6i) q^{80} +(446638. + 324501. i) q^{82} +(707866. + 514295. i) q^{83} +(1.53114e6 - 497498. i) q^{85} +(572216. + 787588. i) q^{86} +(1.17861e7 + 1.66876e7i) q^{88} -3.06496e6i q^{89} +(-4.29148e6 - 1.32078e7i) q^{91} +(3.13690e7 + 1.01924e7i) q^{92} +(-2.79762e6 + 3.85059e6i) q^{94} +(-2.55525e6 + 7.86426e6i) q^{95} +(-2.33105e6 + 1.69361e6i) q^{97} -1.31039e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 112 q - 1792 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 112 q - 1792 q^{4} - 134096 q^{16} + 401484 q^{22} - 68552 q^{25} + 1493020 q^{28} - 398144 q^{31} - 729944 q^{34} + 685476 q^{37} - 399360 q^{40} - 1410880 q^{46} + 2923872 q^{49} + 6472520 q^{52} + 1445488 q^{55} + 13215936 q^{58} - 7843440 q^{61} - 12806712 q^{64} + 1864032 q^{67} - 1233728 q^{70} + 53841940 q^{73} - 53845440 q^{79} - 36360204 q^{82} + 41703500 q^{85} + 21474024 q^{88} + 27611736 q^{91} - 94707560 q^{94} - 27695460 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\)
\(\chi(n)\) \(e\left(\frac{3}{10}\right)\) \(-1\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −17.5311 + 12.7371i −1.54954 + 1.12581i −0.605569 + 0.795793i \(0.707054\pi\)
−0.943975 + 0.330016i \(0.892946\pi\)
\(3\) 0 0
\(4\) 105.552 324.855i 0.824622 2.53793i
\(5\) −159.065 + 218.934i −0.569088 + 0.783282i −0.992446 0.122680i \(-0.960851\pi\)
0.423359 + 0.905962i \(0.360851\pi\)
\(6\) 0 0
\(7\) −1136.60 369.305i −1.25247 0.406951i −0.393662 0.919255i \(-0.628792\pi\)
−0.858804 + 0.512304i \(0.828792\pi\)
\(8\) 1430.14 + 4401.52i 0.987560 + 3.03940i
\(9\) 0 0
\(10\) 5864.17i 1.85441i
\(11\) 4216.26 1307.78i 0.955110 0.296252i
\(12\) 0 0
\(13\) 6830.31 + 9401.11i 0.862261 + 1.18680i 0.981026 + 0.193878i \(0.0621064\pi\)
−0.118765 + 0.992922i \(0.537894\pi\)
\(14\) 24629.8 8002.70i 2.39890 0.779450i
\(15\) 0 0
\(16\) −45763.1 33248.9i −2.79316 2.02935i
\(17\) −4812.95 3496.81i −0.237596 0.172624i 0.462615 0.886559i \(-0.346911\pi\)
−0.700212 + 0.713935i \(0.746911\pi\)
\(18\) 0 0
\(19\) 29060.5 9442.31i 0.971997 0.315821i 0.220375 0.975415i \(-0.429272\pi\)
0.751622 + 0.659594i \(0.229272\pi\)
\(20\) 54332.1 + 74781.8i 1.51863 + 2.09021i
\(21\) 0 0
\(22\) −57258.3 + 76629.7i −1.14646 + 1.53433i
\(23\) 96563.1i 1.65487i 0.561561 + 0.827435i \(0.310201\pi\)
−0.561561 + 0.827435i \(0.689799\pi\)
\(24\) 0 0
\(25\) 1511.50 + 4651.91i 0.0193472 + 0.0595445i
\(26\) −239485. 77813.5i −2.67222 0.868257i
\(27\) 0 0
\(28\) −239941. + 330250.i −2.06562 + 2.84309i
\(29\) −24030.4 + 73957.8i −0.182965 + 0.563107i −0.999907 0.0136116i \(-0.995667\pi\)
0.816943 + 0.576719i \(0.195667\pi\)
\(30\) 0 0
\(31\) −127217. + 92428.6i −0.766972 + 0.557238i −0.901041 0.433734i \(-0.857196\pi\)
0.134069 + 0.990972i \(0.457196\pi\)
\(32\) 633383. 3.41697
\(33\) 0 0
\(34\) 128915. 0.562508
\(35\) 261647. 190098.i 1.03152 0.749443i
\(36\) 0 0
\(37\) 135597. 417323.i 0.440091 1.35446i −0.447687 0.894190i \(-0.647752\pi\)
0.887778 0.460271i \(-0.152248\pi\)
\(38\) −389194. + 535679.i −1.15060 + 1.58366i
\(39\) 0 0
\(40\) −1.19113e6 387020.i −2.94271 0.956145i
\(41\) −7872.79 24230.0i −0.0178396 0.0549047i 0.941740 0.336341i \(-0.109189\pi\)
−0.959580 + 0.281436i \(0.909189\pi\)
\(42\) 0 0
\(43\) 44925.2i 0.0861689i −0.999071 0.0430845i \(-0.986282\pi\)
0.999071 0.0430845i \(-0.0137185\pi\)
\(44\) 20194.4 1.50771e6i 0.0357393 2.66829i
\(45\) 0 0
\(46\) −1.22993e6 1.69286e6i −1.86307 2.56429i
\(47\) 208893. 67873.6i 0.293482 0.0953582i −0.158575 0.987347i \(-0.550690\pi\)
0.452058 + 0.891989i \(0.350690\pi\)
\(48\) 0 0
\(49\) 489222. + 355441.i 0.594046 + 0.431599i
\(50\) −85750.0 62301.0i −0.0970150 0.0704855i
\(51\) 0 0
\(52\) 3.77494e6 1.22655e6i 3.72305 1.20969i
\(53\) 487319. + 670738.i 0.449623 + 0.618853i 0.972316 0.233668i \(-0.0750729\pi\)
−0.522694 + 0.852521i \(0.675073\pi\)
\(54\) 0 0
\(55\) −384341. + 1.13111e6i −0.311492 + 0.916714i
\(56\) 5.53094e6i 4.20863i
\(57\) 0 0
\(58\) −520729. 1.60264e6i −0.350440 1.07854i
\(59\) −1.99174e6 647157.i −1.26256 0.410230i −0.400153 0.916448i \(-0.631043\pi\)
−0.862405 + 0.506218i \(0.831043\pi\)
\(60\) 0 0
\(61\) 500336. 688653.i 0.282233 0.388460i −0.644239 0.764824i \(-0.722826\pi\)
0.926472 + 0.376364i \(0.122826\pi\)
\(62\) 1.05298e6 3.24075e6i 0.561113 1.72693i
\(63\) 0 0
\(64\) −5.24622e6 + 3.81160e6i −2.50159 + 1.81751i
\(65\) −3.14468e6 −1.42030
\(66\) 0 0
\(67\) −2.90295e6 −1.17917 −0.589587 0.807705i \(-0.700710\pi\)
−0.589587 + 0.807705i \(0.700710\pi\)
\(68\) −1.64397e6 + 1.19441e6i −0.634034 + 0.460653i
\(69\) 0 0
\(70\) −2.16567e6 + 6.66524e6i −0.754655 + 2.32259i
\(71\) −2.16301e6 + 2.97713e6i −0.717223 + 0.987173i 0.282389 + 0.959300i \(0.408873\pi\)
−0.999611 + 0.0278726i \(0.991127\pi\)
\(72\) 0 0
\(73\) 5.27787e6 + 1.71488e6i 1.58792 + 0.515946i 0.964081 0.265608i \(-0.0855727\pi\)
0.623838 + 0.781554i \(0.285573\pi\)
\(74\) 2.93833e6 + 9.04324e6i 0.842925 + 2.59426i
\(75\) 0 0
\(76\) 1.04371e7i 2.72729i
\(77\) −5.27519e6 70656.2i −1.31680 0.0176373i
\(78\) 0 0
\(79\) −4.80416e6 6.61236e6i −1.09628 1.50890i −0.840221 0.542244i \(-0.817575\pi\)
−0.256062 0.966660i \(-0.582425\pi\)
\(80\) 1.45586e7 4.73038e6i 3.17911 1.03295i
\(81\) 0 0
\(82\) 446638. + 324501.i 0.0894555 + 0.0649932i
\(83\) 707866. + 514295.i 0.135887 + 0.0987276i 0.653652 0.756795i \(-0.273236\pi\)
−0.517765 + 0.855523i \(0.673236\pi\)
\(84\) 0 0
\(85\) 1.53114e6 497498.i 0.270426 0.0878668i
\(86\) 572216. + 787588.i 0.0970098 + 0.133523i
\(87\) 0 0
\(88\) 1.17861e7 + 1.66876e7i 1.84366 + 2.61039i
\(89\) 3.06496e6i 0.460851i −0.973090 0.230425i \(-0.925988\pi\)
0.973090 0.230425i \(-0.0740118\pi\)
\(90\) 0 0
\(91\) −4.29148e6 1.32078e7i −0.596983 1.83732i
\(92\) 3.13690e7 + 1.01924e7i 4.19994 + 1.36464i
\(93\) 0 0
\(94\) −2.79762e6 + 3.85059e6i −0.347409 + 0.478167i
\(95\) −2.55525e6 + 7.86426e6i −0.305775 + 0.941077i
\(96\) 0 0
\(97\) −2.33105e6 + 1.69361e6i −0.259328 + 0.188413i −0.709851 0.704352i \(-0.751238\pi\)
0.450522 + 0.892765i \(0.351238\pi\)
\(98\) −1.31039e7 −1.40640
\(99\) 0 0
\(100\) 1.67074e6 0.167074
\(101\) 1.93406e6 1.40517e6i 0.186786 0.135708i −0.490463 0.871462i \(-0.663172\pi\)
0.677249 + 0.735754i \(0.263172\pi\)
\(102\) 0 0
\(103\) −1.45103e6 + 4.46580e6i −0.130841 + 0.402688i −0.994920 0.100668i \(-0.967902\pi\)
0.864079 + 0.503357i \(0.167902\pi\)
\(104\) −3.16109e7 + 4.35086e7i −2.75562 + 3.79279i
\(105\) 0 0
\(106\) −1.70865e7 5.55173e6i −1.39342 0.452750i
\(107\) −6.16946e6 1.89876e7i −0.486860 1.49840i −0.829269 0.558850i \(-0.811243\pi\)
0.342409 0.939551i \(-0.388757\pi\)
\(108\) 0 0
\(109\) 2.58835e6i 0.191439i 0.995408 + 0.0957196i \(0.0305152\pi\)
−0.995408 + 0.0957196i \(0.969485\pi\)
\(110\) −7.66906e6 2.47249e7i −0.549374 1.77117i
\(111\) 0 0
\(112\) 3.97356e7 + 5.46913e7i 2.67249 + 3.67837i
\(113\) −1.92026e7 + 6.23930e6i −1.25195 + 0.406782i −0.858618 0.512617i \(-0.828676\pi\)
−0.393328 + 0.919398i \(0.628676\pi\)
\(114\) 0 0
\(115\) −2.11409e7 1.53598e7i −1.29623 0.941766i
\(116\) 2.14891e7 + 1.56127e7i 1.27825 + 0.928701i
\(117\) 0 0
\(118\) 4.31603e7 1.40236e7i 2.41823 0.785731i
\(119\) 4.17902e6 + 5.75193e6i 0.227332 + 0.312896i
\(120\) 0 0
\(121\) 1.60666e7 1.10279e7i 0.824470 0.565906i
\(122\) 1.84457e7i 0.919676i
\(123\) 0 0
\(124\) 1.65979e7 + 5.10830e7i 0.781766 + 2.40603i
\(125\) −2.13661e7 6.94227e6i −0.978453 0.317919i
\(126\) 0 0
\(127\) −6.54024e6 + 9.00187e6i −0.283322 + 0.389960i −0.926831 0.375479i \(-0.877478\pi\)
0.643509 + 0.765439i \(0.277478\pi\)
\(128\) 1.83703e7 5.65379e7i 0.774250 2.38290i
\(129\) 0 0
\(130\) 5.51297e7 4.00541e7i 2.20082 1.59899i
\(131\) −4.76925e7 −1.85354 −0.926768 0.375635i \(-0.877425\pi\)
−0.926768 + 0.375635i \(0.877425\pi\)
\(132\) 0 0
\(133\) −3.65173e7 −1.34592
\(134\) 5.08919e7 3.69751e7i 1.82718 1.32753i
\(135\) 0 0
\(136\) 8.50808e6 2.61852e7i 0.290032 0.892626i
\(137\) −1.07934e7 + 1.48558e7i −0.358621 + 0.493599i −0.949764 0.312968i \(-0.898677\pi\)
0.591143 + 0.806567i \(0.298677\pi\)
\(138\) 0 0
\(139\) 2.64308e7 + 8.58790e6i 0.834755 + 0.271228i 0.695047 0.718964i \(-0.255384\pi\)
0.139708 + 0.990193i \(0.455384\pi\)
\(140\) −3.41368e7 1.05062e8i −1.05142 3.23593i
\(141\) 0 0
\(142\) 7.97427e7i 2.33712i
\(143\) 4.10930e7 + 3.07050e7i 1.17515 + 0.878078i
\(144\) 0 0
\(145\) −1.23695e7 1.70251e7i −0.336949 0.463770i
\(146\) −1.14369e8 + 3.71608e7i −3.04141 + 0.988213i
\(147\) 0 0
\(148\) −1.21257e8 8.80983e7i −3.07461 2.23384i
\(149\) 1.17024e7 + 8.50229e6i 0.289816 + 0.210564i 0.723188 0.690651i \(-0.242676\pi\)
−0.433371 + 0.901215i \(0.642676\pi\)
\(150\) 0 0
\(151\) 5.99320e6 1.94731e6i 0.141658 0.0460273i −0.237330 0.971429i \(-0.576272\pi\)
0.378988 + 0.925402i \(0.376272\pi\)
\(152\) 8.31210e7 + 1.14406e8i 1.91981 + 2.64239i
\(153\) 0 0
\(154\) 9.33798e7 6.59519e7i 2.06030 1.45514i
\(155\) 4.25543e7i 0.917873i
\(156\) 0 0
\(157\) 2.93418e7 + 9.03048e7i 0.605115 + 1.86235i 0.495997 + 0.868324i \(0.334803\pi\)
0.109118 + 0.994029i \(0.465197\pi\)
\(158\) 1.68444e8 + 5.47309e7i 3.39748 + 1.10391i
\(159\) 0 0
\(160\) −1.00749e8 + 1.38669e8i −1.94456 + 2.67645i
\(161\) 3.56612e7 1.09754e8i 0.673451 2.07267i
\(162\) 0 0
\(163\) −5.15716e7 + 3.74689e7i −0.932725 + 0.677665i −0.946659 0.322238i \(-0.895565\pi\)
0.0139332 + 0.999903i \(0.495565\pi\)
\(164\) −8.70220e6 −0.154055
\(165\) 0 0
\(166\) −1.89603e7 −0.321711
\(167\) −6.07288e7 + 4.41220e7i −1.00899 + 0.733074i −0.963997 0.265913i \(-0.914327\pi\)
−0.0449932 + 0.998987i \(0.514327\pi\)
\(168\) 0 0
\(169\) −2.23374e7 + 6.87476e7i −0.355984 + 1.09561i
\(170\) −2.05059e7 + 2.82239e7i −0.320116 + 0.440602i
\(171\) 0 0
\(172\) −1.45942e7 4.74193e6i −0.218690 0.0710568i
\(173\) −9.85562e6 3.03325e7i −0.144718 0.445396i 0.852257 0.523124i \(-0.175234\pi\)
−0.996975 + 0.0777277i \(0.975234\pi\)
\(174\) 0 0
\(175\) 5.84558e6i 0.0824508i
\(176\) −2.36432e8 8.03377e7i −3.26897 1.11077i
\(177\) 0 0
\(178\) 3.90387e7 + 5.37322e7i 0.518830 + 0.714109i
\(179\) −1.31379e7 + 4.26878e6i −0.171215 + 0.0556311i −0.393370 0.919380i \(-0.628691\pi\)
0.222155 + 0.975011i \(0.428691\pi\)
\(180\) 0 0
\(181\) 3.71801e7 + 2.70129e7i 0.466054 + 0.338608i 0.795901 0.605426i \(-0.206997\pi\)
−0.329848 + 0.944034i \(0.606997\pi\)
\(182\) 2.43463e8 + 1.76886e8i 2.99353 + 2.17493i
\(183\) 0 0
\(184\) −4.25024e8 + 1.38099e8i −5.02981 + 1.63428i
\(185\) 6.97976e7 + 9.60682e7i 0.810475 + 1.11552i
\(186\) 0 0
\(187\) −2.48657e7 8.44919e6i −0.278071 0.0944864i
\(188\) 7.50241e7i 0.823471i
\(189\) 0 0
\(190\) −5.53714e7 1.70416e8i −0.585663 1.80248i
\(191\) 2.27515e6 + 739241.i 0.0236262 + 0.00767661i 0.320806 0.947145i \(-0.396046\pi\)
−0.297180 + 0.954821i \(0.596046\pi\)
\(192\) 0 0
\(193\) 1.67196e7 2.30126e7i 0.167408 0.230417i −0.717068 0.697003i \(-0.754516\pi\)
0.884476 + 0.466586i \(0.154516\pi\)
\(194\) 1.92942e7 5.93815e7i 0.189724 0.583909i
\(195\) 0 0
\(196\) 1.67105e8 1.21409e8i 1.58523 1.15174i
\(197\) −9.82844e7 −0.915910 −0.457955 0.888975i \(-0.651418\pi\)
−0.457955 + 0.888975i \(0.651418\pi\)
\(198\) 0 0
\(199\) −1.30437e8 −1.17332 −0.586660 0.809833i \(-0.699557\pi\)
−0.586660 + 0.809833i \(0.699557\pi\)
\(200\) −1.83138e7 + 1.33058e7i −0.161873 + 0.117607i
\(201\) 0 0
\(202\) −1.60083e7 + 4.92684e7i −0.136652 + 0.420571i
\(203\) 5.46260e7 7.51862e7i 0.458314 0.630815i
\(204\) 0 0
\(205\) 6.55705e6 + 2.13051e6i 0.0531581 + 0.0172721i
\(206\) −3.14432e7 9.67722e7i −0.250606 0.771286i
\(207\) 0 0
\(208\) 6.57324e8i 5.06475i
\(209\) 1.10178e8 7.78160e7i 0.834801 0.589600i
\(210\) 0 0
\(211\) −1.65709e7 2.28080e7i −0.121439 0.167147i 0.743969 0.668214i \(-0.232941\pi\)
−0.865408 + 0.501067i \(0.832941\pi\)
\(212\) 2.69330e8 8.75105e7i 1.94137 0.630790i
\(213\) 0 0
\(214\) 3.50005e8 + 2.54293e8i 2.44132 + 1.77373i
\(215\) 9.83566e6 + 7.14602e6i 0.0674946 + 0.0490377i
\(216\) 0 0
\(217\) 1.78730e8 5.80728e7i 1.18738 0.385802i
\(218\) −3.29681e7 4.53766e7i −0.215524 0.296643i
\(219\) 0 0
\(220\) 3.26877e8 + 2.44245e8i 2.06969 + 1.54649i
\(221\) 6.91314e7i 0.430826i
\(222\) 0 0
\(223\) 5.23558e7 + 1.61134e8i 0.316153 + 0.973019i 0.975277 + 0.220985i \(0.0709272\pi\)
−0.659124 + 0.752034i \(0.729073\pi\)
\(224\) −7.19906e8 2.33912e8i −4.27965 1.39054i
\(225\) 0 0
\(226\) 2.57172e8 3.53967e8i 1.48199 2.03978i
\(227\) −4.91950e6 + 1.51407e7i −0.0279145 + 0.0859121i −0.964043 0.265746i \(-0.914382\pi\)
0.936129 + 0.351658i \(0.114382\pi\)
\(228\) 0 0
\(229\) −2.53269e8 + 1.84011e8i −1.39366 + 1.01256i −0.398210 + 0.917294i \(0.630369\pi\)
−0.995452 + 0.0952612i \(0.969631\pi\)
\(230\) 5.66263e8 3.06881
\(231\) 0 0
\(232\) −3.59893e8 −1.89219
\(233\) 1.35704e8 9.85944e7i 0.702822 0.510630i −0.178028 0.984025i \(-0.556972\pi\)
0.880850 + 0.473395i \(0.156972\pi\)
\(234\) 0 0
\(235\) −1.83678e7 + 5.65301e7i −0.0923249 + 0.284147i
\(236\) −4.20464e8 + 5.78719e8i −2.08227 + 2.86600i
\(237\) 0 0
\(238\) −1.46526e8 4.76091e7i −0.704522 0.228913i
\(239\) −2.29398e7 7.06015e7i −0.108692 0.334519i 0.881887 0.471460i \(-0.156273\pi\)
−0.990579 + 0.136941i \(0.956273\pi\)
\(240\) 0 0
\(241\) 2.87762e6i 0.0132426i 0.999978 + 0.00662131i \(0.00210764\pi\)
−0.999978 + 0.00662131i \(0.997892\pi\)
\(242\) −1.41201e8 + 3.97973e8i −0.640449 + 1.80509i
\(243\) 0 0
\(244\) −1.70901e8 2.35225e8i −0.753147 1.03662i
\(245\) −1.55636e8 + 5.05692e7i −0.676128 + 0.219687i
\(246\) 0 0
\(247\) 2.87260e8 + 2.08707e8i 1.21293 + 0.881246i
\(248\) −5.88764e8 4.27762e8i −2.45110 1.78083i
\(249\) 0 0
\(250\) 4.62995e8 1.50436e8i 1.87407 0.608923i
\(251\) −4.12073e7 5.67170e7i −0.164481 0.226389i 0.718818 0.695198i \(-0.244683\pi\)
−0.883300 + 0.468809i \(0.844683\pi\)
\(252\) 0 0
\(253\) 1.26284e8 + 4.07136e8i 0.490258 + 1.58058i
\(254\) 2.41116e8i 0.923226i
\(255\) 0 0
\(256\) 1.41581e8 + 4.35741e8i 0.527429 + 1.62326i
\(257\) −1.74191e8 5.65980e7i −0.640116 0.207986i −0.0290651 0.999578i \(-0.509253\pi\)
−0.611051 + 0.791591i \(0.709253\pi\)
\(258\) 0 0
\(259\) −3.08239e8 + 4.24255e8i −1.10240 + 1.51732i
\(260\) −3.31927e8 + 1.02156e9i −1.17121 + 3.60462i
\(261\) 0 0
\(262\) 8.36102e8 6.07464e8i 2.87213 2.08673i
\(263\) 4.22481e8 1.43206 0.716031 0.698069i \(-0.245957\pi\)
0.716031 + 0.698069i \(0.245957\pi\)
\(264\) 0 0
\(265\) −2.24363e8 −0.740611
\(266\) 6.40188e8 4.65124e8i 2.08556 1.51525i
\(267\) 0 0
\(268\) −3.06411e8 + 9.43037e8i −0.972374 + 2.99266i
\(269\) 3.25147e8 4.47527e8i 1.01847 1.40180i 0.105194 0.994452i \(-0.466454\pi\)
0.913273 0.407348i \(-0.133546\pi\)
\(270\) 0 0
\(271\) −1.61700e8 5.25394e7i −0.493534 0.160359i 0.0516669 0.998664i \(-0.483547\pi\)
−0.545201 + 0.838306i \(0.683547\pi\)
\(272\) 1.03991e8 + 3.20050e8i 0.313331 + 0.964332i
\(273\) 0 0
\(274\) 3.97915e8i 1.16859i
\(275\) 1.24566e7 + 1.76370e7i 0.0361188 + 0.0511399i
\(276\) 0 0
\(277\) −2.36819e8 3.25953e8i −0.669479 0.921459i 0.330269 0.943887i \(-0.392860\pi\)
−0.999748 + 0.0224276i \(0.992860\pi\)
\(278\) −5.72746e8 + 1.86096e8i −1.59884 + 0.519495i
\(279\) 0 0
\(280\) 1.21091e9 + 8.79778e8i 3.29654 + 2.39508i
\(281\) −5.61350e6 4.07844e6i −0.0150925 0.0109653i 0.580213 0.814464i \(-0.302969\pi\)
−0.595306 + 0.803499i \(0.702969\pi\)
\(282\) 0 0
\(283\) −2.85926e8 + 9.29028e7i −0.749895 + 0.243656i −0.658936 0.752199i \(-0.728993\pi\)
−0.0909590 + 0.995855i \(0.528993\pi\)
\(284\) 7.38824e8 + 1.01690e9i 1.91393 + 2.63430i
\(285\) 0 0
\(286\) −1.11150e9 1.48875e7i −2.80949 0.0376304i
\(287\) 3.04473e7i 0.0760261i
\(288\) 0 0
\(289\) −1.15865e8 3.56595e8i −0.282364 0.869027i
\(290\) 4.33701e8 + 1.40918e8i 1.04423 + 0.339292i
\(291\) 0 0
\(292\) 1.11417e9 1.53353e9i 2.61887 3.60456i
\(293\) −6.61585e6 + 2.03615e7i −0.0153656 + 0.0472904i −0.958445 0.285276i \(-0.907915\pi\)
0.943080 + 0.332567i \(0.107915\pi\)
\(294\) 0 0
\(295\) 4.58501e8 3.33121e8i 1.03983 0.755482i
\(296\) 2.03078e9 4.55136
\(297\) 0 0
\(298\) −3.13450e8 −0.686138
\(299\) −9.07801e8 + 6.59556e8i −1.96400 + 1.42693i
\(300\) 0 0
\(301\) −1.65911e7 + 5.10622e7i −0.0350665 + 0.107924i
\(302\) −8.02643e7 + 1.10474e8i −0.167687 + 0.230801i
\(303\) 0 0
\(304\) −1.64384e9 5.34117e8i −3.35585 1.09038i
\(305\) 7.11837e7 + 2.19081e8i 0.143659 + 0.442135i
\(306\) 0 0
\(307\) 4.78004e8i 0.942860i −0.881904 0.471430i \(-0.843738\pi\)
0.881904 0.471430i \(-0.156262\pi\)
\(308\) −5.79758e8 + 1.70621e9i −1.13063 + 3.32740i
\(309\) 0 0
\(310\) 5.42017e8 + 7.46023e8i 1.03335 + 1.42228i
\(311\) 3.13450e8 1.01846e8i 0.590891 0.191992i 0.00171734 0.999999i \(-0.499453\pi\)
0.589174 + 0.808006i \(0.299453\pi\)
\(312\) 0 0
\(313\) −3.59369e8 2.61097e8i −0.662422 0.481278i 0.205058 0.978750i \(-0.434262\pi\)
−0.867480 + 0.497472i \(0.834262\pi\)
\(314\) −1.66461e9 1.20941e9i −3.03431 2.20455i
\(315\) 0 0
\(316\) −2.65514e9 + 8.62708e8i −4.73351 + 1.53801i
\(317\) 2.32784e7 + 3.20399e7i 0.0410436 + 0.0564916i 0.829046 0.559181i \(-0.188884\pi\)
−0.788002 + 0.615673i \(0.788884\pi\)
\(318\) 0 0
\(319\) −4.59754e6 + 3.43252e8i −0.00792972 + 0.592033i
\(320\) 1.75487e9i 2.99378i
\(321\) 0 0
\(322\) 7.72766e8 + 2.37833e9i 1.28989 + 3.96987i
\(323\) −1.72884e8 5.61736e7i −0.285461 0.0927520i
\(324\) 0 0
\(325\) −3.34091e7 + 4.59837e7i −0.0539851 + 0.0743041i
\(326\) 4.26861e8 1.31374e9i 0.682378 2.10014i
\(327\) 0 0
\(328\) 9.53894e7 6.93045e7i 0.149259 0.108443i
\(329\) −2.62495e8 −0.406383
\(330\) 0 0
\(331\) 1.19903e9 1.81732 0.908660 0.417536i \(-0.137106\pi\)
0.908660 + 0.417536i \(0.137106\pi\)
\(332\) 2.41787e8 1.75669e8i 0.362619 0.263458i
\(333\) 0 0
\(334\) 5.02656e8 1.54701e9i 0.738173 2.27186i
\(335\) 4.61758e8 6.35555e8i 0.671054 0.923626i
\(336\) 0 0
\(337\) 8.68206e8 + 2.82097e8i 1.23571 + 0.401508i 0.852781 0.522268i \(-0.174914\pi\)
0.382933 + 0.923776i \(0.374914\pi\)
\(338\) −4.84044e8 1.48973e9i −0.681830 2.09846i
\(339\) 0 0
\(340\) 5.49910e8i 0.758779i
\(341\) −4.15504e8 + 5.56076e8i −0.567460 + 0.759440i
\(342\) 0 0
\(343\) 1.53720e8 + 2.11578e8i 0.205684 + 0.283100i
\(344\) 1.97739e8 6.42493e7i 0.261902 0.0850970i
\(345\) 0 0
\(346\) 5.59127e8 + 4.06230e8i 0.725678 + 0.527236i
\(347\) −6.60456e8 4.79850e8i −0.848576 0.616527i 0.0761768 0.997094i \(-0.475729\pi\)
−0.924753 + 0.380568i \(0.875729\pi\)
\(348\) 0 0
\(349\) −8.31786e8 + 2.70264e8i −1.04742 + 0.340329i −0.781657 0.623708i \(-0.785625\pi\)
−0.265767 + 0.964037i \(0.585625\pi\)
\(350\) 7.44557e7 + 1.02479e8i 0.0928239 + 0.127761i
\(351\) 0 0
\(352\) 2.67051e9 8.28328e8i 3.26359 1.01229i
\(353\) 4.10173e8i 0.496313i 0.968720 + 0.248157i \(0.0798248\pi\)
−0.968720 + 0.248157i \(0.920175\pi\)
\(354\) 0 0
\(355\) −3.07735e8 9.47112e8i −0.365072 1.12358i
\(356\) −9.95668e8 3.23512e8i −1.16961 0.380028i
\(357\) 0 0
\(358\) 1.75951e8 2.42175e8i 0.202675 0.278958i
\(359\) −3.25759e8 + 1.00258e9i −0.371592 + 1.14364i 0.574158 + 0.818745i \(0.305330\pi\)
−0.945749 + 0.324897i \(0.894670\pi\)
\(360\) 0 0
\(361\) 3.21954e7 2.33913e7i 0.0360179 0.0261686i
\(362\) −9.95874e8 −1.10338
\(363\) 0 0
\(364\) −4.74359e9 −5.15528
\(365\) −1.21497e9 + 8.82726e8i −1.30780 + 0.950169i
\(366\) 0 0
\(367\) 4.01854e8 1.23678e9i 0.424363 1.30606i −0.479240 0.877684i \(-0.659088\pi\)
0.903603 0.428371i \(-0.140912\pi\)
\(368\) 3.21061e9 4.41903e9i 3.35831 4.62232i
\(369\) 0 0
\(370\) −2.44726e9 7.95162e8i −2.51173 0.816111i
\(371\) −3.06182e8 9.42333e8i −0.311295 0.958066i
\(372\) 0 0
\(373\) 5.29458e8i 0.528263i −0.964487 0.264132i \(-0.914915\pi\)
0.964487 0.264132i \(-0.0850853\pi\)
\(374\) 5.43541e8 1.68593e8i 0.537257 0.166644i
\(375\) 0 0
\(376\) 5.97493e8 + 8.22379e8i 0.579663 + 0.797838i
\(377\) −8.59421e8 + 2.79243e8i −0.826059 + 0.268403i
\(378\) 0 0
\(379\) −5.76636e8 4.18950e8i −0.544082 0.395299i 0.281517 0.959556i \(-0.409162\pi\)
−0.825599 + 0.564258i \(0.809162\pi\)
\(380\) 2.28503e9 + 1.66017e9i 2.13624 + 1.55207i
\(381\) 0 0
\(382\) −4.93016e7 + 1.60191e7i −0.0452522 + 0.0147033i
\(383\) 2.17749e8 + 2.99705e8i 0.198043 + 0.272583i 0.896476 0.443093i \(-0.146119\pi\)
−0.698433 + 0.715676i \(0.746119\pi\)
\(384\) 0 0
\(385\) 8.54567e8 1.14368e9i 0.763191 1.02139i
\(386\) 6.16396e8i 0.545512i
\(387\) 0 0
\(388\) 3.04130e8 + 9.36014e8i 0.264331 + 0.813526i
\(389\) −1.12923e9 3.66909e8i −0.972656 0.316035i −0.220768 0.975326i \(-0.570856\pi\)
−0.751888 + 0.659291i \(0.770856\pi\)
\(390\) 0 0
\(391\) 3.37663e8 4.64753e8i 0.285670 0.393191i
\(392\) −8.64822e8 + 2.66165e9i −0.725146 + 2.23177i
\(393\) 0 0
\(394\) 1.72303e9 1.25186e9i 1.41924 1.03114i
\(395\) 2.21184e9 1.80578
\(396\) 0 0
\(397\) 3.08823e8 0.247709 0.123855 0.992300i \(-0.460474\pi\)
0.123855 + 0.992300i \(0.460474\pi\)
\(398\) 2.28671e9 1.66139e9i 1.81811 1.32093i
\(399\) 0 0
\(400\) 8.54999e7 2.63142e8i 0.0667968 0.205579i
\(401\) −1.11081e9 + 1.52891e9i −0.860273 + 1.18406i 0.121231 + 0.992624i \(0.461316\pi\)
−0.981504 + 0.191440i \(0.938684\pi\)
\(402\) 0 0
\(403\) −1.73786e9 5.64666e8i −1.32266 0.429758i
\(404\) −2.52334e8 7.76605e8i −0.190389 0.585957i
\(405\) 0 0
\(406\) 2.01387e9i 1.49345i
\(407\) 2.59426e7 1.93688e9i 0.0190736 1.42404i
\(408\) 0 0
\(409\) 1.25202e8 + 1.72325e8i 0.0904854 + 0.124542i 0.851860 0.523770i \(-0.175475\pi\)
−0.761374 + 0.648313i \(0.775475\pi\)
\(410\) −1.42089e8 + 4.61674e7i −0.101816 + 0.0330820i
\(411\) 0 0
\(412\) 1.29758e9 + 9.42745e8i 0.914099 + 0.664131i
\(413\) 2.02483e9 + 1.47112e9i 1.41437 + 1.02760i
\(414\) 0 0
\(415\) −2.25193e8 + 7.31697e7i −0.154663 + 0.0502531i
\(416\) 4.32620e9 + 5.95451e9i 2.94632 + 4.05527i
\(417\) 0 0
\(418\) −9.40392e8 + 2.76755e9i −0.629784 + 1.85344i
\(419\) 2.09860e9i 1.39374i −0.717198 0.696869i \(-0.754576\pi\)
0.717198 0.696869i \(-0.245424\pi\)
\(420\) 0 0
\(421\) 4.94540e8 + 1.52204e9i 0.323009 + 0.994118i 0.972331 + 0.233605i \(0.0750524\pi\)
−0.649323 + 0.760513i \(0.724948\pi\)
\(422\) 5.81013e8 + 1.88783e8i 0.376351 + 0.122284i
\(423\) 0 0
\(424\) −2.25533e9 + 3.10419e9i −1.43691 + 1.97774i
\(425\) 8.99210e6 2.76748e7i 0.00568198 0.0174873i
\(426\) 0 0
\(427\) −8.23007e8 + 5.97949e8i −0.511571 + 0.371678i
\(428\) −6.81942e9 −4.20431
\(429\) 0 0
\(430\) −2.63449e8 −0.159793
\(431\) −1.99131e8 + 1.44677e8i −0.119803 + 0.0870419i −0.646073 0.763275i \(-0.723590\pi\)
0.526270 + 0.850317i \(0.323590\pi\)
\(432\) 0 0
\(433\) 3.99678e7 1.23008e8i 0.0236593 0.0728159i −0.938530 0.345198i \(-0.887812\pi\)
0.962189 + 0.272383i \(0.0878116\pi\)
\(434\) −2.39365e9 + 3.29458e9i −1.40555 + 1.93457i
\(435\) 0 0
\(436\) 8.40838e8 + 2.73205e8i 0.485858 + 0.157865i
\(437\) 9.11779e8 + 2.80617e9i 0.522643 + 1.60853i
\(438\) 0 0
\(439\) 2.22822e9i 1.25699i −0.777813 0.628496i \(-0.783671\pi\)
0.777813 0.628496i \(-0.216329\pi\)
\(440\) −5.52824e9 7.40456e7i −3.09387 0.0414395i
\(441\) 0 0
\(442\) 8.80532e8 + 1.21195e9i 0.485028 + 0.667584i
\(443\) −1.97258e8 + 6.40930e7i −0.107801 + 0.0350265i −0.362421 0.932015i \(-0.618050\pi\)
0.254620 + 0.967041i \(0.418050\pi\)
\(444\) 0 0
\(445\) 6.71025e8 + 4.87528e8i 0.360976 + 0.262265i
\(446\) −2.97024e9 2.15800e9i −1.58533 1.15181i
\(447\) 0 0
\(448\) 7.37051e9 2.39483e9i 3.87280 1.25835i
\(449\) −1.16804e9 1.60766e9i −0.608967 0.838171i 0.387525 0.921859i \(-0.373330\pi\)
−0.996492 + 0.0836879i \(0.973330\pi\)
\(450\) 0 0
\(451\) −6.48813e7 9.18640e7i −0.0333044 0.0471550i
\(452\) 6.89662e9i 3.51279i
\(453\) 0 0
\(454\) −1.06604e8 3.28092e8i −0.0534659 0.164551i
\(455\) 3.57426e9 + 1.16135e9i 1.77888 + 0.577993i
\(456\) 0 0
\(457\) −1.15785e9 + 1.59364e9i −0.567473 + 0.781060i −0.992253 0.124237i \(-0.960352\pi\)
0.424779 + 0.905297i \(0.360352\pi\)
\(458\) 2.09632e9 6.45181e9i 1.01960 3.13800i
\(459\) 0 0
\(460\) −7.22116e9 + 5.24648e9i −3.45903 + 2.51313i
\(461\) 2.20731e9 1.04933 0.524663 0.851310i \(-0.324191\pi\)
0.524663 + 0.851310i \(0.324191\pi\)
\(462\) 0 0
\(463\) 1.66274e9 0.778556 0.389278 0.921120i \(-0.372725\pi\)
0.389278 + 0.921120i \(0.372725\pi\)
\(464\) 3.55872e9 2.58556e9i 1.65379 1.20155i
\(465\) 0 0
\(466\) −1.12323e9 + 3.45693e9i −0.514181 + 1.58249i
\(467\) −2.26326e8 + 3.11511e8i −0.102831 + 0.141535i −0.857331 0.514765i \(-0.827879\pi\)
0.754500 + 0.656300i \(0.227879\pi\)
\(468\) 0 0
\(469\) 3.29951e9 + 1.07208e9i 1.47688 + 0.479866i
\(470\) −3.98022e8 1.22499e9i −0.176834 0.544238i
\(471\) 0 0
\(472\) 9.69222e9i 4.24254i
\(473\) −5.87524e7 1.89417e8i −0.0255277 0.0823008i
\(474\) 0 0
\(475\) 8.78496e7 + 1.20915e8i 0.0376108 + 0.0517668i
\(476\) 2.30964e9 7.50449e8i 0.981569 0.318931i
\(477\) 0 0
\(478\) 1.30142e9 + 9.45535e8i 0.545028 + 0.395986i
\(479\) 6.79822e8 + 4.93919e8i 0.282632 + 0.205344i 0.720064 0.693907i \(-0.244112\pi\)
−0.437433 + 0.899251i \(0.644112\pi\)
\(480\) 0 0
\(481\) 4.84947e9 1.57569e9i 1.98695 0.645599i
\(482\) −3.66525e7 5.04478e7i −0.0149087 0.0205200i
\(483\) 0 0
\(484\) −1.88661e9 6.38331e9i −0.756352 2.55910i
\(485\) 7.79739e8i 0.310351i
\(486\) 0 0
\(487\) −3.75506e8 1.15569e9i −0.147321 0.453408i 0.849981 0.526813i \(-0.176613\pi\)
−0.997302 + 0.0734053i \(0.976613\pi\)
\(488\) 3.74667e9 + 1.21737e9i 1.45941 + 0.474190i
\(489\) 0 0
\(490\) 2.08436e9 2.86888e9i 0.800364 1.10161i
\(491\) 2.09309e8 6.44187e8i 0.0797999 0.245599i −0.903195 0.429230i \(-0.858785\pi\)
0.982995 + 0.183631i \(0.0587851\pi\)
\(492\) 0 0
\(493\) 3.74273e8 2.71925e8i 0.140678 0.102208i
\(494\) −7.69430e9 −2.87160
\(495\) 0 0
\(496\) 8.89500e9 3.27311
\(497\) 3.55795e9 2.58500e9i 1.30003 0.944526i
\(498\) 0 0
\(499\) −8.02086e8 + 2.46857e9i −0.288981 + 0.889391i 0.696197 + 0.717851i \(0.254874\pi\)
−0.985177 + 0.171540i \(0.945126\pi\)
\(500\) −4.51045e9 + 6.20811e9i −1.61371 + 2.22108i
\(501\) 0 0
\(502\) 1.44482e9 + 4.69450e8i 0.509742 + 0.165625i
\(503\) 1.50959e9 + 4.64604e9i 0.528897 + 1.62778i 0.756478 + 0.654019i \(0.226919\pi\)
−0.227581 + 0.973759i \(0.573081\pi\)
\(504\) 0 0
\(505\) 6.46944e8i 0.223536i
\(506\) −7.39961e9 5.52905e9i −2.53911 1.89724i
\(507\) 0 0
\(508\) 2.23396e9 + 3.07479e9i 0.756055 + 1.04062i
\(509\) 3.81563e9 1.23977e9i 1.28249 0.416707i 0.413034 0.910716i \(-0.364469\pi\)
0.869457 + 0.494009i \(0.164469\pi\)
\(510\) 0 0
\(511\) −5.36553e9 3.89828e9i −1.77885 1.29241i
\(512\) −1.87609e9 1.36306e9i −0.617746 0.448819i
\(513\) 0 0
\(514\) 3.77464e9 1.22646e9i 1.22604 0.398365i
\(515\) −7.46908e8 1.02803e9i −0.240958 0.331651i
\(516\) 0 0
\(517\) 7.91986e8 5.59360e8i 0.252058 0.178022i
\(518\) 1.13637e10i 3.59225i
\(519\) 0 0
\(520\) −4.49734e9 1.38414e10i −1.40263 4.31686i
\(521\) −3.64272e9 1.18359e9i −1.12848 0.366665i −0.315482 0.948932i \(-0.602166\pi\)
−0.812998 + 0.582266i \(0.802166\pi\)
\(522\) 0 0
\(523\) −5.38305e6 + 7.40914e6i −0.00164540 + 0.00226471i −0.809839 0.586652i \(-0.800446\pi\)
0.808193 + 0.588917i \(0.200446\pi\)
\(524\) −5.03403e9 + 1.54931e10i −1.52847 + 4.70414i
\(525\) 0 0
\(526\) −7.40655e9 + 5.38117e9i −2.21904 + 1.61223i
\(527\) 9.35495e8 0.278422
\(528\) 0 0
\(529\) −5.91961e9 −1.73860
\(530\) 3.93332e9 2.85772e9i 1.14761 0.833787i
\(531\) 0 0
\(532\) −3.85446e9 + 1.18628e10i −1.10987 + 3.41584i
\(533\) 1.74015e8 2.39511e8i 0.0497785 0.0685142i
\(534\) 0 0
\(535\) 5.13839e9 + 1.66956e9i 1.45074 + 0.471373i
\(536\) −4.15163e9 1.27774e10i −1.16451 3.58398i
\(537\) 0 0
\(538\) 1.19871e10i 3.31875i
\(539\) 2.52753e9 + 8.58835e8i 0.695241 + 0.236238i
\(540\) 0 0
\(541\) −3.00104e8 4.13058e8i −0.0814857 0.112155i 0.766328 0.642449i \(-0.222082\pi\)
−0.847814 + 0.530294i \(0.822082\pi\)
\(542\) 3.50397e9 1.13851e9i 0.945286 0.307142i
\(543\) 0 0
\(544\) −3.04844e9 2.21482e9i −0.811861 0.589851i
\(545\) −5.66678e8 4.11716e8i −0.149951 0.108946i
\(546\) 0 0
\(547\) 7.85767e8 2.55311e8i 0.205276 0.0666982i −0.204574 0.978851i \(-0.565581\pi\)
0.409850 + 0.912153i \(0.365581\pi\)
\(548\) 3.68672e9 + 5.07433e9i 0.956991 + 1.31719i
\(549\) 0 0
\(550\) −4.43021e8 1.50535e8i −0.113541 0.0385805i
\(551\) 2.37615e9i 0.605123i
\(552\) 0 0
\(553\) 3.01845e9 + 9.28984e9i 0.759008 + 2.33599i
\(554\) 8.30339e9 + 2.69793e9i 2.07478 + 0.674135i
\(555\) 0 0
\(556\) 5.57964e9 7.67971e9i 1.37672 1.89489i
\(557\) 7.09812e8 2.18458e9i 0.174040 0.535641i −0.825548 0.564332i \(-0.809134\pi\)
0.999588 + 0.0286909i \(0.00913384\pi\)
\(558\) 0 0
\(559\) 4.22347e8 3.06853e8i 0.102265 0.0743001i
\(560\) −1.82943e10 −4.40208
\(561\) 0 0
\(562\) 1.50358e8 0.0357314
\(563\) 1.97074e9 1.43183e9i 0.465426 0.338152i −0.330230 0.943900i \(-0.607126\pi\)
0.795656 + 0.605749i \(0.207126\pi\)
\(564\) 0 0
\(565\) 1.68846e9 5.19655e9i 0.393842 1.21212i
\(566\) 3.82927e9 5.27054e9i 0.887685 1.22179i
\(567\) 0 0
\(568\) −1.61973e10 5.26281e9i −3.70871 1.20503i
\(569\) −5.41073e8 1.66525e9i −0.123130 0.378954i 0.870426 0.492299i \(-0.163843\pi\)
−0.993556 + 0.113345i \(0.963843\pi\)
\(570\) 0 0
\(571\) 1.90437e9i 0.428079i 0.976825 + 0.214039i \(0.0686621\pi\)
−0.976825 + 0.214039i \(0.931338\pi\)
\(572\) 1.43121e10 1.01083e10i 3.19755 2.25835i
\(573\) 0 0
\(574\) −3.87810e8 5.33775e8i −0.0855909 0.117806i
\(575\) −4.49203e8 + 1.45955e8i −0.0985384 + 0.0320171i
\(576\) 0 0
\(577\) −1.77768e9 1.29156e9i −0.385246 0.279898i 0.378258 0.925700i \(-0.376523\pi\)
−0.763505 + 0.645802i \(0.776523\pi\)
\(578\) 6.57322e9 + 4.77572e9i 1.41589 + 1.02871i
\(579\) 0 0
\(580\) −6.83632e9 + 2.22125e9i −1.45487 + 0.472716i
\(581\) −6.14631e8 8.45968e8i −0.130016 0.178952i
\(582\) 0 0
\(583\) 2.93185e9 + 2.19070e9i 0.612775 + 0.457871i
\(584\) 2.56831e10i 5.33584i
\(585\) 0 0
\(586\) −1.43363e8 4.41226e8i −0.0294303 0.0905773i
\(587\) −6.05080e8 1.96602e8i −0.123475 0.0401195i 0.246628 0.969110i \(-0.420678\pi\)
−0.370103 + 0.928991i \(0.620678\pi\)
\(588\) 0 0
\(589\) −2.82425e9 + 3.88724e9i −0.569507 + 0.783859i
\(590\) −3.79504e9 + 1.16799e10i −0.760737 + 2.34131i
\(591\) 0 0
\(592\) −2.00809e10 + 1.45896e10i −3.97792 + 2.89013i
\(593\) −6.60675e9 −1.30106 −0.650528 0.759482i \(-0.725453\pi\)
−0.650528 + 0.759482i \(0.725453\pi\)
\(594\) 0 0
\(595\) −1.92403e9 −0.374457
\(596\) 3.99722e9 2.90415e9i 0.773385 0.561897i
\(597\) 0 0
\(598\) 7.51392e9 2.31255e10i 1.43685 4.42218i
\(599\) −1.24334e9 + 1.71131e9i −0.236372 + 0.325338i −0.910680 0.413112i \(-0.864442\pi\)
0.674309 + 0.738450i \(0.264442\pi\)
\(600\) 0 0
\(601\) 8.93339e9 + 2.90264e9i 1.67863 + 0.545421i 0.984646 0.174566i \(-0.0558522\pi\)
0.693988 + 0.719987i \(0.255852\pi\)
\(602\) −3.59523e8 1.10650e9i −0.0671644 0.206711i
\(603\) 0 0
\(604\) 2.15246e9i 0.397471i
\(605\) −1.41243e8 + 5.27167e9i −0.0259313 + 0.967842i
\(606\) 0 0
\(607\) −2.29038e9 3.15244e9i −0.415669 0.572120i 0.548920 0.835875i \(-0.315039\pi\)
−0.964590 + 0.263755i \(0.915039\pi\)
\(608\) 1.84064e10 5.98061e9i 3.32129 1.07915i
\(609\) 0 0
\(610\) −4.03838e9 2.93406e9i −0.720365 0.523376i
\(611\) 2.06489e9 + 1.50023e9i 0.366229 + 0.266081i
\(612\) 0 0
\(613\) −7.47637e9 + 2.42922e9i −1.31093 + 0.425947i −0.879371 0.476138i \(-0.842036\pi\)
−0.431559 + 0.902085i \(0.642036\pi\)
\(614\) 6.08837e9 + 8.37993e9i 1.06148 + 1.46100i
\(615\) 0 0
\(616\) −7.23327e9 2.33199e10i −1.24681 4.01970i
\(617\) 9.21072e7i 0.0157868i −0.999969 0.00789342i \(-0.997487\pi\)
0.999969 0.00789342i \(-0.00251258\pi\)
\(618\) 0 0
\(619\) −2.79979e8 8.61686e8i −0.0474469 0.146026i 0.924526 0.381118i \(-0.124461\pi\)
−0.971973 + 0.235092i \(0.924461\pi\)
\(620\) −1.38240e10 4.49167e9i −2.32949 0.756898i
\(621\) 0 0
\(622\) −4.19790e9 + 5.77792e9i −0.699465 + 0.962731i
\(623\) −1.13191e9 + 3.48365e9i −0.187544 + 0.577200i
\(624\) 0 0
\(625\) 4.60934e9 3.34888e9i 0.755194 0.548681i
\(626\) 9.62573e9 1.56828
\(627\) 0 0
\(628\) 3.24330e10 5.22551
\(629\) −2.11192e9 + 1.53440e9i −0.338377 + 0.245845i
\(630\) 0 0
\(631\) −4.00569e8 + 1.23282e9i −0.0634708 + 0.195343i −0.977763 0.209712i \(-0.932748\pi\)
0.914292 + 0.405055i \(0.132748\pi\)
\(632\) 2.22338e10 3.06022e10i 3.50351 4.82217i
\(633\) 0 0
\(634\) −8.16190e8 2.65196e8i −0.127198 0.0413290i
\(635\) −9.30492e8 2.86376e9i −0.144213 0.443842i
\(636\) 0 0
\(637\) 7.02700e9i 1.07716i
\(638\) −4.29143e9 6.07614e9i −0.654229 0.926308i
\(639\) 0 0
\(640\) 9.45600e9 + 1.30151e10i 1.42586 + 1.96253i
\(641\) −7.59910e9 + 2.46910e9i −1.13962 + 0.370284i −0.817223 0.576321i \(-0.804488\pi\)
−0.322394 + 0.946605i \(0.604488\pi\)
\(642\) 0 0
\(643\) −6.35425e9 4.61663e9i −0.942597 0.684837i 0.00644744 0.999979i \(-0.497948\pi\)
−0.949044 + 0.315142i \(0.897948\pi\)
\(644\) −3.18900e10 2.31694e10i −4.70494 3.41834i
\(645\) 0 0
\(646\) 3.74634e9 1.21726e9i 0.546756 0.177652i
\(647\) −4.68346e9 6.44623e9i −0.679833 0.935710i 0.320099 0.947384i \(-0.396284\pi\)
−0.999932 + 0.0116744i \(0.996284\pi\)
\(648\) 0 0
\(649\) −9.24406e9 1.23815e8i −1.32741 0.0177795i
\(650\) 1.23168e9i 0.175914i
\(651\) 0 0
\(652\) 6.72849e9 + 2.07082e10i 0.950717 + 2.92601i
\(653\) 6.71408e9 + 2.18154e9i 0.943606 + 0.306596i 0.740115 0.672481i \(-0.234771\pi\)
0.203491 + 0.979077i \(0.434771\pi\)
\(654\) 0 0
\(655\) 7.58621e9 1.04415e10i 1.05482 1.45184i
\(656\) −4.45335e8 + 1.37060e9i −0.0615919 + 0.189560i
\(657\) 0 0
\(658\) 4.60182e9 3.34342e9i 0.629708 0.457510i
\(659\) −9.53571e8 −0.129794 −0.0648969 0.997892i \(-0.520672\pi\)
−0.0648969 + 0.997892i \(0.520672\pi\)
\(660\) 0 0
\(661\) 1.14191e9 0.153790 0.0768950 0.997039i \(-0.475499\pi\)
0.0768950 + 0.997039i \(0.475499\pi\)
\(662\) −2.10203e10 + 1.52721e10i −2.81602 + 2.04596i
\(663\) 0 0
\(664\) −1.25133e9 + 3.85120e9i −0.165876 + 0.510514i
\(665\) 5.80862e9 7.99488e9i 0.765945 1.05423i
\(666\) 0 0
\(667\) −7.14160e9 2.32045e9i −0.931869 0.302783i
\(668\) 7.92322e9 + 2.43852e10i 1.02845 + 3.16525i
\(669\) 0 0
\(670\) 1.70234e10i 2.18668i
\(671\) 1.20894e9 3.55787e9i 0.154481 0.454634i
\(672\) 0 0
\(673\) 4.42077e9 + 6.08466e9i 0.559042 + 0.769456i 0.991204 0.132340i \(-0.0422491\pi\)
−0.432162 + 0.901796i \(0.642249\pi\)
\(674\) −1.88137e10 + 6.11294e9i −2.36682 + 0.769025i
\(675\) 0 0
\(676\) 1.99752e10 + 1.45128e10i 2.48701 + 1.80692i
\(677\) −2.97784e9 2.16353e9i −0.368843 0.267980i 0.387888 0.921706i \(-0.373205\pi\)
−0.756731 + 0.653727i \(0.773205\pi\)
\(678\) 0 0
\(679\) 3.27494e9 1.06409e9i 0.401475 0.130447i
\(680\) 4.37949e9 + 6.02785e9i 0.534124 + 0.735159i
\(681\) 0 0
\(682\) 2.01459e8 1.50409e10i 0.0243188 1.81564i
\(683\) 1.16210e10i 1.39564i −0.716274 0.697819i \(-0.754154\pi\)
0.716274 0.697819i \(-0.245846\pi\)
\(684\) 0 0
\(685\) −1.53559e9 4.72607e9i −0.182541 0.561802i
\(686\) −5.38976e9 1.75124e9i −0.637434 0.207115i
\(687\) 0 0
\(688\) −1.49371e9 + 2.05592e9i −0.174867 + 0.240684i
\(689\) −2.97714e9 + 9.16269e9i −0.346762 + 1.06722i
\(690\) 0 0
\(691\) −8.66267e9 + 6.29380e9i −0.998800 + 0.725671i −0.961831 0.273646i \(-0.911770\pi\)
−0.0369695 + 0.999316i \(0.511770\pi\)
\(692\) −1.08939e10 −1.24972
\(693\) 0 0
\(694\) 1.76904e10 2.00900
\(695\) −6.08440e9 + 4.42057e9i −0.687497 + 0.499496i
\(696\) 0 0
\(697\) −4.68363e7 + 1.44147e8i −0.00523923 + 0.0161247i
\(698\) 1.11397e10 1.53325e10i 1.23988 1.70655i
\(699\) 0 0
\(700\) −1.89896e9 6.17011e8i −0.209254 0.0679907i
\(701\) 1.03788e9 + 3.19426e9i 0.113798 + 0.350233i 0.991694 0.128617i \(-0.0410538\pi\)
−0.877897 + 0.478850i \(0.841054\pi\)
\(702\) 0 0
\(703\) 1.34080e10i 1.45552i
\(704\) −1.71347e10 + 2.29316e10i −1.85085 + 2.47703i
\(705\) 0 0
\(706\) −5.22441e9 7.19078e9i −0.558754 0.769059i
\(707\) −2.71719e9 + 8.82869e8i −0.289170 + 0.0939569i
\(708\) 0 0
\(709\) 6.22477e9 + 4.52256e9i 0.655936 + 0.476565i 0.865288 0.501275i \(-0.167136\pi\)
−0.209352 + 0.977840i \(0.567136\pi\)
\(710\) 1.74584e10 + 1.26843e10i 1.83063 + 1.33003i
\(711\) 0 0
\(712\) 1.34905e10 4.38333e9i 1.40071 0.455118i
\(713\) −8.92520e9 1.22845e10i −0.922156 1.26924i
\(714\) 0 0
\(715\) −1.32588e10 + 4.11256e9i −1.35654 + 0.420767i
\(716\) 4.71850e9i 0.480406i
\(717\) 0 0
\(718\) −7.05908e9 2.17256e10i −0.711725 2.19046i
\(719\) 1.06843e10 + 3.47155e9i 1.07200 + 0.348315i 0.791267 0.611470i \(-0.209422\pi\)
0.280736 + 0.959785i \(0.409422\pi\)
\(720\) 0 0
\(721\) 3.29849e9 4.53998e9i 0.327749 0.451108i
\(722\) −2.66483e8 + 8.20151e8i −0.0263506 + 0.0810987i
\(723\) 0 0
\(724\) 1.26997e10 9.22687e9i 1.24368 0.903586i
\(725\) −3.80367e8 −0.0370698
\(726\) 0 0
\(727\) −1.94517e10 −1.87753 −0.938766 0.344555i \(-0.888030\pi\)
−0.938766 + 0.344555i \(0.888030\pi\)
\(728\) 5.19970e10 3.77780e10i 4.99480 3.62894i
\(729\) 0 0
\(730\) 1.00564e10 3.09503e10i 0.956778 2.94466i
\(731\) −1.57095e8 + 2.16223e8i −0.0148748 + 0.0204734i
\(732\) 0 0
\(733\) 1.07247e10 + 3.48465e9i 1.00582 + 0.326810i 0.765188 0.643807i \(-0.222646\pi\)
0.240630 + 0.970617i \(0.422646\pi\)
\(734\) 8.70803e9 + 2.68006e10i 0.812800 + 2.50154i
\(735\) 0 0
\(736\) 6.11615e10i 5.65465i
\(737\) −1.22396e10 + 3.79643e9i −1.12624 + 0.349333i
\(738\) 0 0
\(739\) −5.56409e9 7.65831e9i −0.507153 0.698036i 0.476283 0.879292i \(-0.341984\pi\)
−0.983436 + 0.181256i \(0.941984\pi\)
\(740\) 3.85754e10 1.25339e10i 3.49945 1.13704i
\(741\) 0 0
\(742\) 1.73703e10 + 1.26202e10i 1.56096 + 1.13411i
\(743\) −1.50128e10 1.09075e10i −1.34277 0.975579i −0.999337 0.0364014i \(-0.988411\pi\)
−0.343432 0.939178i \(-0.611589\pi\)
\(744\) 0 0
\(745\) −3.72288e9 + 1.20964e9i −0.329862 + 0.107179i
\(746\) 6.74374e9 + 9.28197e9i 0.594724 + 0.818567i
\(747\) 0 0
\(748\) −5.36937e9 + 7.18592e9i −0.469103 + 0.627808i
\(749\) 2.38599e10i 2.07482i
\(750\) 0 0
\(751\) 2.23307e9 + 6.87268e9i 0.192381 + 0.592088i 0.999997 + 0.00237963i \(0.000757460\pi\)
−0.807616 + 0.589709i \(0.799243\pi\)
\(752\) −1.18163e10 3.83936e9i −1.01326 0.329228i
\(753\) 0 0
\(754\) 1.15098e10 1.58419e10i 0.977844 1.34589i
\(755\) −5.26976e8 + 1.62186e9i −0.0445632 + 0.137151i
\(756\) 0 0
\(757\) −1.31201e10 + 9.53234e9i −1.09927 + 0.798664i −0.980940 0.194311i \(-0.937753\pi\)
−0.118326 + 0.992975i \(0.537753\pi\)
\(758\) 1.54453e10 1.28811
\(759\) 0 0
\(760\) −3.82690e10 −3.16228
\(761\) −6.76120e9 + 4.91230e9i −0.556131 + 0.404053i −0.830041 0.557702i \(-0.811683\pi\)
0.273910 + 0.961755i \(0.411683\pi\)
\(762\) 0 0
\(763\) 9.55892e8 2.94193e9i 0.0779063 0.239771i
\(764\) 4.80292e8 6.61065e8i 0.0389653 0.0536312i
\(765\) 0 0
\(766\) −7.63474e9 2.48068e9i −0.613753 0.199420i
\(767\) −7.52023e9 2.31449e10i −0.601793 1.85213i
\(768\) 0 0
\(769\) 1.87910e9i 0.149007i −0.997221 0.0745036i \(-0.976263\pi\)
0.997221 0.0745036i \(-0.0237372\pi\)
\(770\) −4.14340e8 + 3.09346e10i −0.0327069 + 2.44190i
\(771\) 0 0
\(772\) −5.71097e9 7.86047e9i −0.446734 0.614877i
\(773\) −1.80238e10 + 5.85629e9i −1.40352 + 0.456031i −0.910327 0.413889i \(-0.864170\pi\)