Properties

Label 192.9.e.d.65.1
Level $192$
Weight $9$
Character 192.65
Analytic conductor $78.217$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [192,9,Mod(65,192)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(192, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("192.65");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 192.e (of order \(2\), degree \(1\), not 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: \(78.2166931317\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{-110}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 110 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2\cdot 3 \)
Twist minimal: no (minimal twist has level 12)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 65.1
Root \(-10.4881i\) of defining polynomial
Character \(\chi\) \(=\) 192.65
Dual form 192.9.e.d.65.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-51.0000 - 62.9285i) q^{3} -1132.71i q^{5} +3094.00 q^{7} +(-1359.00 + 6418.71i) q^{9} +O(q^{10})\) \(q+(-51.0000 - 62.9285i) q^{3} -1132.71i q^{5} +3094.00 q^{7} +(-1359.00 + 6418.71i) q^{9} +1132.71i q^{11} +7294.00 q^{13} +(-71280.0 + 57768.4i) q^{15} -58901.1i q^{17} -80326.0 q^{19} +(-157794. - 194701. i) q^{21} -97413.4i q^{23} -892415. q^{25} +(473229. - 241834. i) q^{27} -864260. i q^{29} -435914. q^{31} +(71280.0 - 57768.4i) q^{33} -3.50462e6i q^{35} -1.15930e6 q^{37} +(-371994. - 459001. i) q^{39} +2.71625e6i q^{41} +990266. q^{43} +(7.27056e6 + 1.53936e6i) q^{45} -6.70113e6i q^{47} +3.80804e6 q^{49} +(-3.70656e6 + 3.00396e6i) q^{51} +1.00710e7i q^{53} +1.28304e6 q^{55} +(4.09663e6 + 5.05480e6i) q^{57} -1.59826e6i q^{59} -1.93692e7 q^{61} +(-4.20475e6 + 1.98595e7i) q^{63} -8.26201e6i q^{65} -2.80243e7 q^{67} +(-6.13008e6 + 4.96808e6i) q^{69} -3.36575e7i q^{71} -2.52301e7 q^{73} +(4.55132e7 + 5.61584e7i) q^{75} +3.50462e6i q^{77} +6.34014e7 q^{79} +(-3.93530e7 - 1.74461e7i) q^{81} -4.75434e7i q^{83} -6.67181e7 q^{85} +(-5.43866e7 + 4.40773e7i) q^{87} +7.82954e7i q^{89} +2.25676e7 q^{91} +(2.22316e7 + 2.74314e7i) q^{93} +9.09863e7i q^{95} +1.95503e7 q^{97} +(-7.27056e6 - 1.53936e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 102 q^{3} + 6188 q^{7} - 2718 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 102 q^{3} + 6188 q^{7} - 2718 q^{9} + 14588 q^{13} - 142560 q^{15} - 160652 q^{19} - 315588 q^{21} - 1784830 q^{25} + 946458 q^{27} - 871828 q^{31} + 142560 q^{33} - 2318596 q^{37} - 743988 q^{39} + 1980532 q^{43} + 14541120 q^{45} + 7616070 q^{49} - 7413120 q^{51} + 2566080 q^{55} + 8193252 q^{57} - 38738308 q^{61} - 8409492 q^{63} - 56048588 q^{67} - 12260160 q^{69} - 50460284 q^{73} + 91026330 q^{75} + 126802796 q^{79} - 78705918 q^{81} - 133436160 q^{85} - 108773280 q^{87} + 45135272 q^{91} + 44463228 q^{93} + 39100612 q^{97} - 14541120 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/192\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(133\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −51.0000 62.9285i −0.629630 0.776895i
\(4\) 0 0
\(5\) 1132.71i 1.81234i −0.422912 0.906171i \(-0.638992\pi\)
0.422912 0.906171i \(-0.361008\pi\)
\(6\) 0 0
\(7\) 3094.00 1.28863 0.644315 0.764760i \(-0.277143\pi\)
0.644315 + 0.764760i \(0.277143\pi\)
\(8\) 0 0
\(9\) −1359.00 + 6418.71i −0.207133 + 0.978313i
\(10\) 0 0
\(11\) 1132.71i 0.0773659i 0.999252 + 0.0386829i \(0.0123162\pi\)
−0.999252 + 0.0386829i \(0.987684\pi\)
\(12\) 0 0
\(13\) 7294.00 0.255383 0.127692 0.991814i \(-0.459243\pi\)
0.127692 + 0.991814i \(0.459243\pi\)
\(14\) 0 0
\(15\) −71280.0 + 57768.4i −1.40800 + 1.14110i
\(16\) 0 0
\(17\) 58901.1i 0.705225i −0.935769 0.352613i \(-0.885293\pi\)
0.935769 0.352613i \(-0.114707\pi\)
\(18\) 0 0
\(19\) −80326.0 −0.616370 −0.308185 0.951326i \(-0.599722\pi\)
−0.308185 + 0.951326i \(0.599722\pi\)
\(20\) 0 0
\(21\) −157794. 194701.i −0.811359 1.00113i
\(22\) 0 0
\(23\) 97413.4i 0.348103i −0.984737 0.174051i \(-0.944314\pi\)
0.984737 0.174051i \(-0.0556858\pi\)
\(24\) 0 0
\(25\) −892415. −2.28458
\(26\) 0 0
\(27\) 473229. 241834.i 0.890464 0.455054i
\(28\) 0 0
\(29\) 864260.i 1.22195i −0.791651 0.610974i \(-0.790778\pi\)
0.791651 0.610974i \(-0.209222\pi\)
\(30\) 0 0
\(31\) −435914. −0.472013 −0.236007 0.971751i \(-0.575839\pi\)
−0.236007 + 0.971751i \(0.575839\pi\)
\(32\) 0 0
\(33\) 71280.0 57768.4i 0.0601052 0.0487118i
\(34\) 0 0
\(35\) 3.50462e6i 2.33544i
\(36\) 0 0
\(37\) −1.15930e6 −0.618569 −0.309285 0.950970i \(-0.600090\pi\)
−0.309285 + 0.950970i \(0.600090\pi\)
\(38\) 0 0
\(39\) −371994. 459001.i −0.160797 0.198406i
\(40\) 0 0
\(41\) 2.71625e6i 0.961244i 0.876928 + 0.480622i \(0.159589\pi\)
−0.876928 + 0.480622i \(0.840411\pi\)
\(42\) 0 0
\(43\) 990266. 0.289653 0.144827 0.989457i \(-0.453738\pi\)
0.144827 + 0.989457i \(0.453738\pi\)
\(44\) 0 0
\(45\) 7.27056e6 + 1.53936e6i 1.77304 + 0.375396i
\(46\) 0 0
\(47\) 6.70113e6i 1.37327i −0.727001 0.686636i \(-0.759086\pi\)
0.727001 0.686636i \(-0.240914\pi\)
\(48\) 0 0
\(49\) 3.80804e6 0.660567
\(50\) 0 0
\(51\) −3.70656e6 + 3.00396e6i −0.547886 + 0.444031i
\(52\) 0 0
\(53\) 1.00710e7i 1.27634i 0.769894 + 0.638171i \(0.220309\pi\)
−0.769894 + 0.638171i \(0.779691\pi\)
\(54\) 0 0
\(55\) 1.28304e6 0.140213
\(56\) 0 0
\(57\) 4.09663e6 + 5.05480e6i 0.388085 + 0.478855i
\(58\) 0 0
\(59\) 1.59826e6i 0.131898i −0.997823 0.0659491i \(-0.978992\pi\)
0.997823 0.0659491i \(-0.0210075\pi\)
\(60\) 0 0
\(61\) −1.93692e7 −1.39891 −0.699457 0.714674i \(-0.746575\pi\)
−0.699457 + 0.714674i \(0.746575\pi\)
\(62\) 0 0
\(63\) −4.20475e6 + 1.98595e7i −0.266918 + 1.26068i
\(64\) 0 0
\(65\) 8.26201e6i 0.462842i
\(66\) 0 0
\(67\) −2.80243e7 −1.39071 −0.695353 0.718668i \(-0.744752\pi\)
−0.695353 + 0.718668i \(0.744752\pi\)
\(68\) 0 0
\(69\) −6.13008e6 + 4.96808e6i −0.270439 + 0.219176i
\(70\) 0 0
\(71\) 3.36575e7i 1.32449i −0.749289 0.662244i \(-0.769604\pi\)
0.749289 0.662244i \(-0.230396\pi\)
\(72\) 0 0
\(73\) −2.52301e7 −0.888440 −0.444220 0.895918i \(-0.646519\pi\)
−0.444220 + 0.895918i \(0.646519\pi\)
\(74\) 0 0
\(75\) 4.55132e7 + 5.61584e7i 1.43844 + 1.77488i
\(76\) 0 0
\(77\) 3.50462e6i 0.0996959i
\(78\) 0 0
\(79\) 6.34014e7 1.62776 0.813880 0.581033i \(-0.197351\pi\)
0.813880 + 0.581033i \(0.197351\pi\)
\(80\) 0 0
\(81\) −3.93530e7 1.74461e7i −0.914192 0.405282i
\(82\) 0 0
\(83\) 4.75434e7i 1.00179i −0.865507 0.500896i \(-0.833004\pi\)
0.865507 0.500896i \(-0.166996\pi\)
\(84\) 0 0
\(85\) −6.67181e7 −1.27811
\(86\) 0 0
\(87\) −5.43866e7 + 4.40773e7i −0.949326 + 0.769375i
\(88\) 0 0
\(89\) 7.82954e7i 1.24789i 0.781468 + 0.623945i \(0.214471\pi\)
−0.781468 + 0.623945i \(0.785529\pi\)
\(90\) 0 0
\(91\) 2.25676e7 0.329094
\(92\) 0 0
\(93\) 2.22316e7 + 2.74314e7i 0.297193 + 0.366705i
\(94\) 0 0
\(95\) 9.09863e7i 1.11707i
\(96\) 0 0
\(97\) 1.95503e7 0.220834 0.110417 0.993885i \(-0.464781\pi\)
0.110417 + 0.993885i \(0.464781\pi\)
\(98\) 0 0
\(99\) −7.27056e6 1.53936e6i −0.0756880 0.0160250i
\(100\) 0 0
\(101\) 4.38847e7i 0.421724i 0.977516 + 0.210862i \(0.0676270\pi\)
−0.977516 + 0.210862i \(0.932373\pi\)
\(102\) 0 0
\(103\) −1.13498e8 −1.00841 −0.504207 0.863583i \(-0.668215\pi\)
−0.504207 + 0.863583i \(0.668215\pi\)
\(104\) 0 0
\(105\) −2.20540e8 + 1.78735e8i −1.81439 + 1.47046i
\(106\) 0 0
\(107\) 5.49966e7i 0.419567i 0.977748 + 0.209783i \(0.0672759\pi\)
−0.977748 + 0.209783i \(0.932724\pi\)
\(108\) 0 0
\(109\) −1.74355e6 −0.0123518 −0.00617589 0.999981i \(-0.501966\pi\)
−0.00617589 + 0.999981i \(0.501966\pi\)
\(110\) 0 0
\(111\) 5.91242e7 + 7.29529e7i 0.389469 + 0.480563i
\(112\) 0 0
\(113\) 1.94469e8i 1.19271i 0.802720 + 0.596357i \(0.203386\pi\)
−0.802720 + 0.596357i \(0.796614\pi\)
\(114\) 0 0
\(115\) −1.10341e8 −0.630881
\(116\) 0 0
\(117\) −9.91255e6 + 4.68181e7i −0.0528983 + 0.249845i
\(118\) 0 0
\(119\) 1.82240e8i 0.908774i
\(120\) 0 0
\(121\) 2.13076e8 0.994015
\(122\) 0 0
\(123\) 1.70929e8 1.38529e8i 0.746786 0.605228i
\(124\) 0 0
\(125\) 5.68384e8i 2.32810i
\(126\) 0 0
\(127\) 1.77121e8 0.680854 0.340427 0.940271i \(-0.389428\pi\)
0.340427 + 0.940271i \(0.389428\pi\)
\(128\) 0 0
\(129\) −5.05036e7 6.23160e7i −0.182374 0.225030i
\(130\) 0 0
\(131\) 1.31133e8i 0.445274i −0.974901 0.222637i \(-0.928534\pi\)
0.974901 0.222637i \(-0.0714664\pi\)
\(132\) 0 0
\(133\) −2.48529e8 −0.794273
\(134\) 0 0
\(135\) −2.73929e8 5.36033e8i −0.824713 1.61382i
\(136\) 0 0
\(137\) 1.76348e8i 0.500596i 0.968169 + 0.250298i \(0.0805286\pi\)
−0.968169 + 0.250298i \(0.919471\pi\)
\(138\) 0 0
\(139\) −2.32285e8 −0.622245 −0.311123 0.950370i \(-0.600705\pi\)
−0.311123 + 0.950370i \(0.600705\pi\)
\(140\) 0 0
\(141\) −4.21692e8 + 3.41758e8i −1.06689 + 0.864653i
\(142\) 0 0
\(143\) 8.26201e6i 0.0197579i
\(144\) 0 0
\(145\) −9.78960e8 −2.21459
\(146\) 0 0
\(147\) −1.94210e8 2.39634e8i −0.415912 0.513191i
\(148\) 0 0
\(149\) 5.85329e8i 1.18756i −0.804628 0.593779i \(-0.797635\pi\)
0.804628 0.593779i \(-0.202365\pi\)
\(150\) 0 0
\(151\) 4.17368e8 0.802808 0.401404 0.915901i \(-0.368522\pi\)
0.401404 + 0.915901i \(0.368522\pi\)
\(152\) 0 0
\(153\) 3.78069e8 + 8.00466e7i 0.689931 + 0.146075i
\(154\) 0 0
\(155\) 4.93766e8i 0.855449i
\(156\) 0 0
\(157\) −8.18571e8 −1.34728 −0.673640 0.739060i \(-0.735270\pi\)
−0.673640 + 0.739060i \(0.735270\pi\)
\(158\) 0 0
\(159\) 6.33750e8 5.13619e8i 0.991585 0.803623i
\(160\) 0 0
\(161\) 3.01397e8i 0.448575i
\(162\) 0 0
\(163\) 3.18429e8 0.451088 0.225544 0.974233i \(-0.427584\pi\)
0.225544 + 0.974233i \(0.427584\pi\)
\(164\) 0 0
\(165\) −6.54350e7 8.07398e7i −0.0882825 0.108931i
\(166\) 0 0
\(167\) 1.16043e9i 1.49195i 0.665976 + 0.745974i \(0.268016\pi\)
−0.665976 + 0.745974i \(0.731984\pi\)
\(168\) 0 0
\(169\) −7.62528e8 −0.934779
\(170\) 0 0
\(171\) 1.09163e8 5.15589e8i 0.127671 0.603003i
\(172\) 0 0
\(173\) 1.41652e9i 1.58139i 0.612213 + 0.790693i \(0.290279\pi\)
−0.612213 + 0.790693i \(0.709721\pi\)
\(174\) 0 0
\(175\) −2.76113e9 −2.94398
\(176\) 0 0
\(177\) −1.00576e8 + 8.15112e7i −0.102471 + 0.0830471i
\(178\) 0 0
\(179\) 1.56828e9i 1.52760i 0.645451 + 0.763802i \(0.276669\pi\)
−0.645451 + 0.763802i \(0.723331\pi\)
\(180\) 0 0
\(181\) 6.19722e8 0.577408 0.288704 0.957418i \(-0.406776\pi\)
0.288704 + 0.957418i \(0.406776\pi\)
\(182\) 0 0
\(183\) 9.87827e8 + 1.21887e9i 0.880798 + 1.08681i
\(184\) 0 0
\(185\) 1.31315e9i 1.12106i
\(186\) 0 0
\(187\) 6.67181e7 0.0545603
\(188\) 0 0
\(189\) 1.46417e9 7.48235e8i 1.14748 0.586396i
\(190\) 0 0
\(191\) 4.87719e8i 0.366468i 0.983069 + 0.183234i \(0.0586567\pi\)
−0.983069 + 0.183234i \(0.941343\pi\)
\(192\) 0 0
\(193\) 1.34577e9 0.969933 0.484967 0.874533i \(-0.338832\pi\)
0.484967 + 0.874533i \(0.338832\pi\)
\(194\) 0 0
\(195\) −5.19916e8 + 4.21363e8i −0.359580 + 0.291419i
\(196\) 0 0
\(197\) 1.60057e9i 1.06270i −0.847153 0.531349i \(-0.821685\pi\)
0.847153 0.531349i \(-0.178315\pi\)
\(198\) 0 0
\(199\) 1.41860e9 0.904579 0.452289 0.891871i \(-0.350607\pi\)
0.452289 + 0.891871i \(0.350607\pi\)
\(200\) 0 0
\(201\) 1.42924e9 + 1.76353e9i 0.875630 + 1.08043i
\(202\) 0 0
\(203\) 2.67402e9i 1.57464i
\(204\) 0 0
\(205\) 3.07673e9 1.74210
\(206\) 0 0
\(207\) 6.25268e8 + 1.32385e8i 0.340553 + 0.0721035i
\(208\) 0 0
\(209\) 9.09863e7i 0.0476860i
\(210\) 0 0
\(211\) 2.70459e9 1.36449 0.682247 0.731122i \(-0.261003\pi\)
0.682247 + 0.731122i \(0.261003\pi\)
\(212\) 0 0
\(213\) −2.11801e9 + 1.71653e9i −1.02899 + 0.833936i
\(214\) 0 0
\(215\) 1.12169e9i 0.524950i
\(216\) 0 0
\(217\) −1.34872e9 −0.608250
\(218\) 0 0
\(219\) 1.28674e9 + 1.58770e9i 0.559388 + 0.690225i
\(220\) 0 0
\(221\) 4.29625e8i 0.180103i
\(222\) 0 0
\(223\) −1.69115e9 −0.683853 −0.341927 0.939727i \(-0.611079\pi\)
−0.341927 + 0.939727i \(0.611079\pi\)
\(224\) 0 0
\(225\) 1.21279e9 5.72815e9i 0.473213 2.23504i
\(226\) 0 0
\(227\) 6.35028e8i 0.239160i −0.992825 0.119580i \(-0.961845\pi\)
0.992825 0.119580i \(-0.0381549\pi\)
\(228\) 0 0
\(229\) −7.90639e7 −0.0287499 −0.0143749 0.999897i \(-0.504576\pi\)
−0.0143749 + 0.999897i \(0.504576\pi\)
\(230\) 0 0
\(231\) 2.20540e8 1.78735e8i 0.0774533 0.0627715i
\(232\) 0 0
\(233\) 5.72051e9i 1.94094i −0.241229 0.970468i \(-0.577550\pi\)
0.241229 0.970468i \(-0.422450\pi\)
\(234\) 0 0
\(235\) −7.59046e9 −2.48884
\(236\) 0 0
\(237\) −3.23347e9 3.98976e9i −1.02489 1.26460i
\(238\) 0 0
\(239\) 4.71043e9i 1.44367i −0.692063 0.721837i \(-0.743298\pi\)
0.692063 0.721837i \(-0.256702\pi\)
\(240\) 0 0
\(241\) 1.11857e9 0.331585 0.165793 0.986161i \(-0.446982\pi\)
0.165793 + 0.986161i \(0.446982\pi\)
\(242\) 0 0
\(243\) 9.09146e8 + 3.36617e9i 0.260741 + 0.965409i
\(244\) 0 0
\(245\) 4.31341e9i 1.19717i
\(246\) 0 0
\(247\) −5.85898e8 −0.157411
\(248\) 0 0
\(249\) −2.99184e9 + 2.42471e9i −0.778288 + 0.630758i
\(250\) 0 0
\(251\) 1.96911e9i 0.496107i −0.968746 0.248054i \(-0.920209\pi\)
0.968746 0.248054i \(-0.0797909\pi\)
\(252\) 0 0
\(253\) 1.10341e8 0.0269313
\(254\) 0 0
\(255\) 3.40262e9 + 4.19847e9i 0.804735 + 0.992957i
\(256\) 0 0
\(257\) 1.87262e9i 0.429257i −0.976696 0.214628i \(-0.931146\pi\)
0.976696 0.214628i \(-0.0688540\pi\)
\(258\) 0 0
\(259\) −3.58687e9 −0.797106
\(260\) 0 0
\(261\) 5.54744e9 + 1.17453e9i 1.19545 + 0.253106i
\(262\) 0 0
\(263\) 5.02882e9i 1.05110i −0.850764 0.525548i \(-0.823860\pi\)
0.850764 0.525548i \(-0.176140\pi\)
\(264\) 0 0
\(265\) 1.14075e10 2.31317
\(266\) 0 0
\(267\) 4.92702e9 3.99307e9i 0.969480 0.785709i
\(268\) 0 0
\(269\) 1.57165e9i 0.300155i 0.988674 + 0.150077i \(0.0479523\pi\)
−0.988674 + 0.150077i \(0.952048\pi\)
\(270\) 0 0
\(271\) −4.27374e9 −0.792375 −0.396188 0.918170i \(-0.629667\pi\)
−0.396188 + 0.918170i \(0.629667\pi\)
\(272\) 0 0
\(273\) −1.15095e9 1.42015e9i −0.207208 0.255672i
\(274\) 0 0
\(275\) 1.01085e9i 0.176749i
\(276\) 0 0
\(277\) 2.43619e9 0.413802 0.206901 0.978362i \(-0.433662\pi\)
0.206901 + 0.978362i \(0.433662\pi\)
\(278\) 0 0
\(279\) 5.92407e8 2.79801e9i 0.0977695 0.461776i
\(280\) 0 0
\(281\) 5.88309e9i 0.943584i −0.881710 0.471792i \(-0.843607\pi\)
0.881710 0.471792i \(-0.156393\pi\)
\(282\) 0 0
\(283\) 5.67732e9 0.885111 0.442555 0.896741i \(-0.354072\pi\)
0.442555 + 0.896741i \(0.354072\pi\)
\(284\) 0 0
\(285\) 5.72564e9 4.64030e9i 0.867849 0.703343i
\(286\) 0 0
\(287\) 8.40407e9i 1.23869i
\(288\) 0 0
\(289\) 3.50642e9 0.502658
\(290\) 0 0
\(291\) −9.97066e8 1.23027e9i −0.139044 0.171565i
\(292\) 0 0
\(293\) 3.58952e9i 0.487041i −0.969896 0.243520i \(-0.921698\pi\)
0.969896 0.243520i \(-0.0783023\pi\)
\(294\) 0 0
\(295\) −1.81037e9 −0.239045
\(296\) 0 0
\(297\) 2.73929e8 + 5.36033e8i 0.0352056 + 0.0688915i
\(298\) 0 0
\(299\) 7.10533e8i 0.0888995i
\(300\) 0 0
\(301\) 3.06388e9 0.373255
\(302\) 0 0
\(303\) 2.76160e9 2.23812e9i 0.327635 0.265530i
\(304\) 0 0
\(305\) 2.19397e10i 2.53531i
\(306\) 0 0
\(307\) −1.43988e10 −1.62096 −0.810480 0.585767i \(-0.800794\pi\)
−0.810480 + 0.585767i \(0.800794\pi\)
\(308\) 0 0
\(309\) 5.78839e9 + 7.14226e9i 0.634927 + 0.783432i
\(310\) 0 0
\(311\) 5.12061e8i 0.0547369i 0.999625 + 0.0273685i \(0.00871274\pi\)
−0.999625 + 0.0273685i \(0.991287\pi\)
\(312\) 0 0
\(313\) −9.70528e9 −1.01118 −0.505592 0.862772i \(-0.668726\pi\)
−0.505592 + 0.862772i \(0.668726\pi\)
\(314\) 0 0
\(315\) 2.24951e10 + 4.76277e9i 2.28479 + 0.483746i
\(316\) 0 0
\(317\) 4.26479e9i 0.422338i −0.977450 0.211169i \(-0.932273\pi\)
0.977450 0.211169i \(-0.0677271\pi\)
\(318\) 0 0
\(319\) 9.78960e8 0.0945370
\(320\) 0 0
\(321\) 3.46086e9 2.80483e9i 0.325959 0.264172i
\(322\) 0 0
\(323\) 4.73129e9i 0.434680i
\(324\) 0 0
\(325\) −6.50928e9 −0.583444
\(326\) 0 0
\(327\) 8.89213e7 + 1.09719e8i 0.00777704 + 0.00959604i
\(328\) 0 0
\(329\) 2.07333e10i 1.76964i
\(330\) 0 0
\(331\) −5.35245e9 −0.445904 −0.222952 0.974829i \(-0.571569\pi\)
−0.222952 + 0.974829i \(0.571569\pi\)
\(332\) 0 0
\(333\) 1.57549e9 7.44120e9i 0.128126 0.605154i
\(334\) 0 0
\(335\) 3.17435e10i 2.52044i
\(336\) 0 0
\(337\) −5.99698e9 −0.464957 −0.232479 0.972602i \(-0.574684\pi\)
−0.232479 + 0.972602i \(0.574684\pi\)
\(338\) 0 0
\(339\) 1.22376e10 9.91791e9i 0.926614 0.750968i
\(340\) 0 0
\(341\) 4.93766e8i 0.0365177i
\(342\) 0 0
\(343\) −6.05423e9 −0.437404
\(344\) 0 0
\(345\) 5.62741e9 + 6.94362e9i 0.397221 + 0.490128i
\(346\) 0 0
\(347\) 2.39763e10i 1.65373i 0.562400 + 0.826865i \(0.309878\pi\)
−0.562400 + 0.826865i \(0.690122\pi\)
\(348\) 0 0
\(349\) −2.80408e10 −1.89011 −0.945057 0.326904i \(-0.893995\pi\)
−0.945057 + 0.326904i \(0.893995\pi\)
\(350\) 0 0
\(351\) 3.45173e9 1.76394e9i 0.227410 0.116213i
\(352\) 0 0
\(353\) 7.50727e9i 0.483485i 0.970340 + 0.241743i \(0.0777190\pi\)
−0.970340 + 0.241743i \(0.922281\pi\)
\(354\) 0 0
\(355\) −3.81243e10 −2.40042
\(356\) 0 0
\(357\) −1.14681e10 + 9.29424e9i −0.706022 + 0.572191i
\(358\) 0 0
\(359\) 1.71973e10i 1.03534i −0.855581 0.517669i \(-0.826800\pi\)
0.855581 0.517669i \(-0.173200\pi\)
\(360\) 0 0
\(361\) −1.05313e10 −0.620088
\(362\) 0 0
\(363\) −1.08669e10 1.34085e10i −0.625861 0.772245i
\(364\) 0 0
\(365\) 2.85785e10i 1.61016i
\(366\) 0 0
\(367\) −1.66397e10 −0.917237 −0.458619 0.888633i \(-0.651656\pi\)
−0.458619 + 0.888633i \(0.651656\pi\)
\(368\) 0 0
\(369\) −1.74348e10 3.69138e9i −0.940398 0.199106i
\(370\) 0 0
\(371\) 3.11595e10i 1.64473i
\(372\) 0 0
\(373\) 1.00036e10 0.516797 0.258398 0.966038i \(-0.416805\pi\)
0.258398 + 0.966038i \(0.416805\pi\)
\(374\) 0 0
\(375\) 3.57676e10 2.89876e10i 1.80869 1.46584i
\(376\) 0 0
\(377\) 6.30392e9i 0.312065i
\(378\) 0 0
\(379\) 3.78010e10 1.83209 0.916044 0.401079i \(-0.131365\pi\)
0.916044 + 0.401079i \(0.131365\pi\)
\(380\) 0 0
\(381\) −9.03315e9 1.11459e10i −0.428686 0.528952i
\(382\) 0 0
\(383\) 2.07214e10i 0.962997i −0.876447 0.481499i \(-0.840093\pi\)
0.876447 0.481499i \(-0.159907\pi\)
\(384\) 0 0
\(385\) 3.96973e9 0.180683
\(386\) 0 0
\(387\) −1.34577e9 + 6.35623e9i −0.0599967 + 0.283371i
\(388\) 0 0
\(389\) 1.34143e10i 0.585826i 0.956139 + 0.292913i \(0.0946246\pi\)
−0.956139 + 0.292913i \(0.905375\pi\)
\(390\) 0 0
\(391\) −5.73775e9 −0.245491
\(392\) 0 0
\(393\) −8.25201e9 + 6.68779e9i −0.345931 + 0.280358i
\(394\) 0 0
\(395\) 7.18156e10i 2.95006i
\(396\) 0 0
\(397\) −8.79600e9 −0.354098 −0.177049 0.984202i \(-0.556655\pi\)
−0.177049 + 0.984202i \(0.556655\pi\)
\(398\) 0 0
\(399\) 1.26750e10 + 1.56395e10i 0.500098 + 0.617067i
\(400\) 0 0
\(401\) 3.60295e10i 1.39342i 0.717355 + 0.696708i \(0.245353\pi\)
−0.717355 + 0.696708i \(0.754647\pi\)
\(402\) 0 0
\(403\) −3.17956e9 −0.120544
\(404\) 0 0
\(405\) −1.97614e10 + 4.45756e10i −0.734509 + 1.65683i
\(406\) 0 0
\(407\) 1.31315e9i 0.0478561i
\(408\) 0 0
\(409\) 9.78141e9 0.349549 0.174775 0.984608i \(-0.444080\pi\)
0.174775 + 0.984608i \(0.444080\pi\)
\(410\) 0 0
\(411\) 1.10973e10 8.99373e9i 0.388911 0.315190i
\(412\) 0 0
\(413\) 4.94501e9i 0.169968i
\(414\) 0 0
\(415\) −5.38530e10 −1.81559
\(416\) 0 0
\(417\) 1.18465e10 + 1.46173e10i 0.391784 + 0.483420i
\(418\) 0 0
\(419\) 2.82806e10i 0.917556i −0.888551 0.458778i \(-0.848287\pi\)
0.888551 0.458778i \(-0.151713\pi\)
\(420\) 0 0
\(421\) 1.94096e10 0.617859 0.308929 0.951085i \(-0.400029\pi\)
0.308929 + 0.951085i \(0.400029\pi\)
\(422\) 0 0
\(423\) 4.30126e10 + 9.10684e9i 1.34349 + 0.284450i
\(424\) 0 0
\(425\) 5.25642e10i 1.61114i
\(426\) 0 0
\(427\) −5.99282e10 −1.80268
\(428\) 0 0
\(429\) 5.19916e8 4.21363e8i 0.0153499 0.0124402i
\(430\) 0 0
\(431\) 5.94440e9i 0.172266i −0.996284 0.0861329i \(-0.972549\pi\)
0.996284 0.0861329i \(-0.0274510\pi\)
\(432\) 0 0
\(433\) −2.32206e10 −0.660573 −0.330287 0.943881i \(-0.607145\pi\)
−0.330287 + 0.943881i \(0.607145\pi\)
\(434\) 0 0
\(435\) 4.99269e10 + 6.16045e10i 1.39437 + 1.72050i
\(436\) 0 0
\(437\) 7.82483e9i 0.214560i
\(438\) 0 0
\(439\) −3.09862e10 −0.834277 −0.417138 0.908843i \(-0.636967\pi\)
−0.417138 + 0.908843i \(0.636967\pi\)
\(440\) 0 0
\(441\) −5.17512e9 + 2.44427e10i −0.136825 + 0.646241i
\(442\) 0 0
\(443\) 3.79891e9i 0.0986379i −0.998783 0.0493189i \(-0.984295\pi\)
0.998783 0.0493189i \(-0.0157051\pi\)
\(444\) 0 0
\(445\) 8.86863e10 2.26160
\(446\) 0 0
\(447\) −3.68339e10 + 2.98518e10i −0.922608 + 0.747721i
\(448\) 0 0
\(449\) 2.65525e10i 0.653310i −0.945144 0.326655i \(-0.894078\pi\)
0.945144 0.326655i \(-0.105922\pi\)
\(450\) 0 0
\(451\) −3.07673e9 −0.0743675
\(452\) 0 0
\(453\) −2.12858e10 2.62644e10i −0.505471 0.623698i
\(454\) 0 0
\(455\) 2.55627e10i 0.596432i
\(456\) 0 0
\(457\) −6.93722e10 −1.59045 −0.795226 0.606313i \(-0.792648\pi\)
−0.795226 + 0.606313i \(0.792648\pi\)
\(458\) 0 0
\(459\) −1.42443e10 2.78737e10i −0.320915 0.627977i
\(460\) 0 0
\(461\) 2.05609e10i 0.455239i 0.973750 + 0.227619i \(0.0730942\pi\)
−0.973750 + 0.227619i \(0.926906\pi\)
\(462\) 0 0
\(463\) −5.34582e9 −0.116330 −0.0581648 0.998307i \(-0.518525\pi\)
−0.0581648 + 0.998307i \(0.518525\pi\)
\(464\) 0 0
\(465\) 3.10719e10 2.51821e10i 0.664594 0.538616i
\(466\) 0 0
\(467\) 6.90921e10i 1.45265i 0.687351 + 0.726325i \(0.258773\pi\)
−0.687351 + 0.726325i \(0.741227\pi\)
\(468\) 0 0
\(469\) −8.67072e10 −1.79211
\(470\) 0 0
\(471\) 4.17471e10 + 5.15115e10i 0.848287 + 1.04670i
\(472\) 0 0
\(473\) 1.12169e9i 0.0224093i
\(474\) 0 0
\(475\) 7.16841e10 1.40815
\(476\) 0 0
\(477\) −6.46425e10 1.36864e10i −1.24866 0.264373i
\(478\) 0 0
\(479\) 5.90567e10i 1.12183i 0.827873 + 0.560915i \(0.189551\pi\)
−0.827873 + 0.560915i \(0.810449\pi\)
\(480\) 0 0
\(481\) −8.45592e9 −0.157972
\(482\) 0 0
\(483\) −1.89665e10 + 1.53712e10i −0.348496 + 0.282436i
\(484\) 0 0
\(485\) 2.21449e10i 0.400227i
\(486\) 0 0
\(487\) 5.63052e10 1.00100 0.500498 0.865738i \(-0.333150\pi\)
0.500498 + 0.865738i \(0.333150\pi\)
\(488\) 0 0
\(489\) −1.62399e10 2.00382e10i −0.284019 0.350449i
\(490\) 0 0
\(491\) 1.03299e11i 1.77733i −0.458555 0.888666i \(-0.651633\pi\)
0.458555 0.888666i \(-0.348367\pi\)
\(492\) 0 0
\(493\) −5.09059e10 −0.861748
\(494\) 0 0
\(495\) −1.74365e9 + 8.23546e9i −0.0290428 + 0.137173i
\(496\) 0 0
\(497\) 1.04136e11i 1.70677i
\(498\) 0 0
\(499\) −6.45656e10 −1.04136 −0.520678 0.853753i \(-0.674321\pi\)
−0.520678 + 0.853753i \(0.674321\pi\)
\(500\) 0 0
\(501\) 7.30242e10 5.91820e10i 1.15909 0.939374i
\(502\) 0 0
\(503\) 8.39308e10i 1.31114i −0.755134 0.655570i \(-0.772428\pi\)
0.755134 0.655570i \(-0.227572\pi\)
\(504\) 0 0
\(505\) 4.97088e10 0.764307
\(506\) 0 0
\(507\) 3.88889e10 + 4.79848e10i 0.588565 + 0.726226i
\(508\) 0 0
\(509\) 7.78937e10i 1.16046i −0.814452 0.580232i \(-0.802962\pi\)
0.814452 0.580232i \(-0.197038\pi\)
\(510\) 0 0
\(511\) −7.80621e10 −1.14487
\(512\) 0 0
\(513\) −3.80126e10 + 1.94256e10i −0.548856 + 0.280482i
\(514\) 0 0
\(515\) 1.28561e11i 1.82759i
\(516\) 0 0
\(517\) 7.59046e9 0.106244
\(518\) 0 0
\(519\) 8.91394e10 7.22424e10i 1.22857 0.995687i
\(520\) 0 0
\(521\) 1.40022e10i 0.190041i 0.995475 + 0.0950203i \(0.0302916\pi\)
−0.995475 + 0.0950203i \(0.969708\pi\)
\(522\) 0 0
\(523\) −2.95062e10 −0.394372 −0.197186 0.980366i \(-0.563180\pi\)
−0.197186 + 0.980366i \(0.563180\pi\)
\(524\) 0 0
\(525\) 1.40818e11 + 1.73754e11i 1.85362 + 2.28717i
\(526\) 0 0
\(527\) 2.56758e10i 0.332875i
\(528\) 0 0
\(529\) 6.88216e10 0.878825
\(530\) 0 0
\(531\) 1.02588e10 + 2.17203e9i 0.129038 + 0.0273205i
\(532\) 0 0
\(533\) 1.98123e10i 0.245486i
\(534\) 0 0
\(535\) 6.22954e10 0.760398
\(536\) 0 0
\(537\) 9.86894e10 7.99821e10i 1.18679 0.961824i
\(538\) 0 0
\(539\) 4.31341e9i 0.0511053i
\(540\) 0 0
\(541\) −7.00056e10 −0.817229 −0.408614 0.912707i \(-0.633988\pi\)
−0.408614 + 0.912707i \(0.633988\pi\)
\(542\) 0 0
\(543\) −3.16058e10 3.89982e10i −0.363553 0.448585i
\(544\) 0 0
\(545\) 1.97495e9i 0.0223856i
\(546\) 0 0
\(547\) −9.25123e10 −1.03336 −0.516678 0.856180i \(-0.672832\pi\)
−0.516678 + 0.856180i \(0.672832\pi\)
\(548\) 0 0
\(549\) 2.63227e10 1.24325e11i 0.289762 1.36858i
\(550\) 0 0
\(551\) 6.94226e10i 0.753172i
\(552\) 0 0
\(553\) 1.96164e11 2.09758
\(554\) 0 0
\(555\) 8.26348e10 6.69708e10i 0.870945 0.705852i
\(556\) 0 0
\(557\) 9.19422e10i 0.955199i 0.878578 + 0.477600i \(0.158493\pi\)
−0.878578 + 0.477600i \(0.841507\pi\)
\(558\) 0 0
\(559\) 7.22300e9 0.0739725
\(560\) 0 0
\(561\) −3.40262e9 4.19847e9i −0.0343528 0.0423877i
\(562\) 0 0
\(563\) 9.45913e10i 0.941494i −0.882268 0.470747i \(-0.843984\pi\)
0.882268 0.470747i \(-0.156016\pi\)
\(564\) 0 0
\(565\) 2.20277e11 2.16160
\(566\) 0 0
\(567\) −1.21758e11 5.39781e10i −1.17805 0.522258i
\(568\) 0 0
\(569\) 3.17728e10i 0.303114i 0.988448 + 0.151557i \(0.0484288\pi\)
−0.988448 + 0.151557i \(0.951571\pi\)
\(570\) 0 0
\(571\) 1.14811e11 1.08003 0.540017 0.841654i \(-0.318418\pi\)
0.540017 + 0.841654i \(0.318418\pi\)
\(572\) 0 0
\(573\) 3.06915e10 2.48737e10i 0.284708 0.230739i
\(574\) 0 0
\(575\) 8.69331e10i 0.795269i
\(576\) 0 0
\(577\) −5.54200e10 −0.499993 −0.249996 0.968247i \(-0.580429\pi\)
−0.249996 + 0.968247i \(0.580429\pi\)
\(578\) 0 0
\(579\) −6.86343e10 8.46874e10i −0.610699 0.753537i
\(580\) 0 0
\(581\) 1.47099e11i 1.29094i
\(582\) 0 0
\(583\) −1.14075e10 −0.0987453
\(584\) 0 0
\(585\) 5.30315e10 + 1.12281e10i 0.452804 + 0.0958698i
\(586\) 0 0
\(587\) 1.60567e11i 1.35240i 0.736718 + 0.676200i \(0.236375\pi\)
−0.736718 + 0.676200i \(0.763625\pi\)
\(588\) 0 0
\(589\) 3.50152e10 0.290935
\(590\) 0 0
\(591\) −1.00722e11 + 8.16291e10i −0.825605 + 0.669106i
\(592\) 0 0
\(593\) 1.47472e11i 1.19259i −0.802767 0.596293i \(-0.796640\pi\)
0.802767 0.596293i \(-0.203360\pi\)
\(594\) 0 0
\(595\) −2.06426e11 −1.64701
\(596\) 0 0
\(597\) −7.23484e10 8.92702e10i −0.569550 0.702763i
\(598\) 0 0
\(599\) 1.76519e11i 1.37115i −0.728002 0.685575i \(-0.759551\pi\)
0.728002 0.685575i \(-0.240449\pi\)
\(600\) 0 0
\(601\) −2.03534e11 −1.56005 −0.780025 0.625749i \(-0.784793\pi\)
−0.780025 + 0.625749i \(0.784793\pi\)
\(602\) 0 0
\(603\) 3.80850e10 1.79880e11i 0.288061 1.36055i
\(604\) 0 0
\(605\) 2.41354e11i 1.80149i
\(606\) 0 0
\(607\) 1.24167e11 0.914639 0.457320 0.889302i \(-0.348810\pi\)
0.457320 + 0.889302i \(0.348810\pi\)
\(608\) 0 0
\(609\) −1.68272e11 + 1.36375e11i −1.22333 + 0.991439i
\(610\) 0 0
\(611\) 4.88781e10i 0.350711i
\(612\) 0 0
\(613\) −3.49779e10 −0.247715 −0.123857 0.992300i \(-0.539527\pi\)
−0.123857 + 0.992300i \(0.539527\pi\)
\(614\) 0 0
\(615\) −1.56913e11 1.93614e11i −1.09688 1.35343i
\(616\) 0 0
\(617\) 3.10618e10i 0.214332i −0.994241 0.107166i \(-0.965822\pi\)
0.994241 0.107166i \(-0.0341776\pi\)
\(618\) 0 0
\(619\) 1.65857e11 1.12972 0.564859 0.825187i \(-0.308931\pi\)
0.564859 + 0.825187i \(0.308931\pi\)
\(620\) 0 0
\(621\) −2.35579e10 4.60988e10i −0.158405 0.309973i
\(622\) 0 0
\(623\) 2.42246e11i 1.60807i
\(624\) 0 0
\(625\) 2.95217e11 1.93473
\(626\) 0 0
\(627\) −5.72564e9 + 4.64030e9i −0.0370471 + 0.0300245i
\(628\) 0 0
\(629\) 6.82839e10i 0.436230i
\(630\) 0 0
\(631\) 1.14663e11 0.723280 0.361640 0.932318i \(-0.382217\pi\)
0.361640 + 0.932318i \(0.382217\pi\)
\(632\) 0 0
\(633\) −1.37934e11 1.70196e11i −0.859126 1.06007i
\(634\) 0 0
\(635\) 2.00627e11i 1.23394i
\(636\) 0 0
\(637\) 2.77758e10 0.168698
\(638\) 0 0
\(639\) 2.16037e11 + 4.57405e10i 1.29576 + 0.274345i
\(640\) 0 0
\(641\) 1.48884e11i 0.881894i −0.897533 0.440947i \(-0.854643\pi\)
0.897533 0.440947i \(-0.145357\pi\)
\(642\) 0 0
\(643\) 2.37607e11 1.39000 0.695000 0.719010i \(-0.255404\pi\)
0.695000 + 0.719010i \(0.255404\pi\)
\(644\) 0 0
\(645\) −7.05862e10 + 5.72061e10i −0.407831 + 0.330524i
\(646\) 0 0
\(647\) 1.40329e11i 0.800814i −0.916337 0.400407i \(-0.868869\pi\)
0.916337 0.400407i \(-0.131131\pi\)
\(648\) 0 0
\(649\) 1.81037e9 0.0102044
\(650\) 0 0
\(651\) 6.87846e10 + 8.48728e10i 0.382972 + 0.472547i
\(652\) 0 0
\(653\) 3.99459e10i 0.219695i 0.993948 + 0.109847i \(0.0350362\pi\)
−0.993948 + 0.109847i \(0.964964\pi\)
\(654\) 0 0
\(655\) −1.48536e11 −0.806988
\(656\) 0 0
\(657\) 3.42878e10 1.61945e11i 0.184025 0.869173i
\(658\) 0 0
\(659\) 2.73467e11i 1.44998i 0.688757 + 0.724992i \(0.258157\pi\)
−0.688757 + 0.724992i \(0.741843\pi\)
\(660\) 0 0
\(661\) −2.01420e11 −1.05511 −0.527554 0.849521i \(-0.676891\pi\)
−0.527554 + 0.849521i \(0.676891\pi\)
\(662\) 0 0
\(663\) −2.70356e10 + 2.19109e10i −0.139921 + 0.113398i
\(664\) 0 0
\(665\) 2.81512e11i 1.43949i
\(666\) 0 0
\(667\) −8.41905e10 −0.425363
\(668\) 0 0
\(669\) 8.62487e10 + 1.06422e11i 0.430574 + 0.531282i
\(670\) 0 0
\(671\) 2.19397e10i 0.108228i
\(672\) 0 0
\(673\) −5.63035e10 −0.274457 −0.137229 0.990539i \(-0.543820\pi\)
−0.137229 + 0.990539i \(0.543820\pi\)
\(674\) 0 0
\(675\) −4.22317e11 + 2.15817e11i −2.03434 + 1.03961i
\(676\) 0 0
\(677\) 2.30376e11i 1.09668i 0.836254 + 0.548342i \(0.184741\pi\)
−0.836254 + 0.548342i \(0.815259\pi\)
\(678\) 0 0
\(679\) 6.04886e10 0.284574
\(680\) 0 0
\(681\) −3.99614e10 + 3.23864e10i −0.185803 + 0.150582i
\(682\) 0 0
\(683\) 6.27237e10i 0.288236i −0.989560 0.144118i \(-0.953965\pi\)
0.989560 0.144118i \(-0.0460345\pi\)
\(684\) 0 0
\(685\) 1.99751e11 0.907251
\(686\) 0 0
\(687\) 4.03226e9 + 4.97537e9i 0.0181018 + 0.0223357i
\(688\) 0 0
\(689\) 7.34576e10i 0.325956i
\(690\) 0 0
\(691\) 2.05762e11 0.902511 0.451256 0.892395i \(-0.350976\pi\)
0.451256 + 0.892395i \(0.350976\pi\)
\(692\) 0 0
\(693\) −2.24951e10 4.76277e9i −0.0975338 0.0206503i
\(694\) 0 0
\(695\) 2.63112e11i 1.12772i
\(696\) 0 0
\(697\) 1.59990e11 0.677894
\(698\) 0 0
\(699\) −3.59984e11 + 2.91746e11i −1.50790 + 1.22207i
\(700\) 0 0
\(701\) 2.57881e11i 1.06794i −0.845504 0.533970i \(-0.820700\pi\)
0.845504 0.533970i \(-0.179300\pi\)
\(702\) 0 0
\(703\) 9.31218e10 0.381268
\(704\) 0 0
\(705\) 3.87114e11 + 4.77657e11i 1.56705 + 1.93357i
\(706\) 0 0
\(707\) 1.35779e11i 0.543446i
\(708\) 0 0
\(709\) 1.09817e11 0.434595 0.217297 0.976105i \(-0.430276\pi\)
0.217297 + 0.976105i \(0.430276\pi\)
\(710\) 0 0
\(711\) −8.61625e10 + 4.06955e11i −0.337163 + 1.59246i
\(712\) 0 0
\(713\) 4.24638e10i 0.164309i
\(714\) 0 0
\(715\) 9.35849e9 0.0358081
\(716\) 0 0
\(717\) −2.96421e11 + 2.40232e11i −1.12158 + 0.908980i
\(718\) 0 0
\(719\) 2.85970e11i 1.07005i −0.844836 0.535025i \(-0.820302\pi\)
0.844836 0.535025i \(-0.179698\pi\)
\(720\) 0 0
\(721\) −3.51162e11 −1.29947
\(722\) 0 0
\(723\) −5.70471e10 7.03900e10i −0.208776 0.257607i
\(724\) 0 0
\(725\) 7.71279e11i 2.79164i
\(726\) 0 0
\(727\) 3.23636e11 1.15856 0.579280 0.815129i \(-0.303334\pi\)
0.579280 + 0.815129i \(0.303334\pi\)
\(728\) 0 0
\(729\) 1.65462e11 2.28886e11i 0.585852 0.810418i
\(730\) 0 0
\(731\) 5.83278e10i 0.204271i
\(732\) 0 0
\(733\) −4.62635e11 −1.60259 −0.801296 0.598269i \(-0.795856\pi\)
−0.801296 + 0.598269i \(0.795856\pi\)
\(734\) 0 0
\(735\) −2.71437e11 + 2.19984e11i −0.930078 + 0.753775i
\(736\) 0 0
\(737\) 3.17435e10i 0.107593i
\(738\) 0 0
\(739\) 4.79772e11 1.60863 0.804317 0.594200i \(-0.202531\pi\)
0.804317 + 0.594200i \(0.202531\pi\)
\(740\) 0 0
\(741\) 2.98808e10 + 3.68697e10i 0.0991104 + 0.122292i
\(742\) 0 0
\(743\) 5.66358e11i 1.85839i −0.369595 0.929193i \(-0.620504\pi\)
0.369595 0.929193i \(-0.379496\pi\)
\(744\) 0 0
\(745\) −6.63010e11 −2.15226
\(746\) 0 0
\(747\) 3.05167e11 + 6.46115e10i 0.980066 + 0.207504i
\(748\) 0 0
\(749\) 1.70160e11i 0.540666i
\(750\) 0 0
\(751\) −1.77971e11 −0.559486 −0.279743 0.960075i \(-0.590249\pi\)
−0.279743 + 0.960075i \(0.590249\pi\)
\(752\) 0 0
\(753\) −1.23913e11 + 1.00425e11i −0.385424 + 0.312364i
\(754\) 0 0
\(755\) 4.72758e11i 1.45496i
\(756\) 0 0
\(757\) 2.17313e11 0.661763 0.330882 0.943672i \(-0.392654\pi\)
0.330882 + 0.943672i \(0.392654\pi\)
\(758\) 0 0
\(759\) −5.62741e9 6.94362e9i −0.0169567 0.0209228i
\(760\) 0 0
\(761\) 2.90514e10i 0.0866220i 0.999062 + 0.0433110i \(0.0137906\pi\)
−0.999062 + 0.0433110i \(0.986209\pi\)
\(762\) 0 0
\(763\) −5.39456e9 −0.0159169
\(764\) 0 0
\(765\) 9.06699e10 4.28244e11i 0.264739 1.25039i
\(766\) 0 0
\(767\) 1.16577e10i 0.0336846i
\(768\) 0 0
\(769\) −1.47894e11 −0.422906 −0.211453 0.977388i \(-0.567820\pi\)
−0.211453 + 0.977388i \(0.567820\pi\)
\(770\) 0 0
\(771\) −1.17841e11 + 9.55036e10i −0.333488 + 0.270273i
\(772\) 0 0
\(773\) 3.53522e11i 0.990144i −0.868852 0.495072i \(-0.835142\pi\)
0.868852 0.495072i \(-0.164858\pi\)
\(774\) 0 0
\(775\) 3.89016e11 1.07835
\(776\) 0 0
\(777\) 1.82930e11 + 2.25716e11i 0.501882 + 0.619268i
\(778\) 0 0
\(779\) 2.18185e11i 0.592483i
\(780\)