Properties

Label 192.9.e.c.65.2
Level $192$
Weight $9$
Character 192.65
Analytic conductor $78.217$
Analytic rank $0$
Dimension $2$
CM no
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: \(\Q(\sqrt{-2}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2}\cdot 3 \)
Twist minimal: no (minimal twist has level 6)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 65.2
Root \(-1.41421i\) of defining polynomial
Character \(\chi\) \(=\) 192.65
Dual form 192.9.e.c.65.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-63.0000 + 50.9117i) q^{3} -576.999i q^{5} -2786.00 q^{7} +(1377.00 - 6414.87i) q^{9} +O(q^{10})\) \(q+(-63.0000 + 50.9117i) q^{3} -576.999i q^{5} -2786.00 q^{7} +(1377.00 - 6414.87i) q^{9} +22435.1i q^{11} +13150.0 q^{13} +(29376.0 + 36350.9i) q^{15} -66388.8i q^{17} +144002. q^{19} +(175518. - 141840. i) q^{21} -49350.4i q^{23} +57697.0 q^{25} +(239841. + 474242. i) q^{27} +627402. i q^{29} -728738. q^{31} +(-1.14221e6 - 1.41341e6i) q^{33} +1.60752e6i q^{35} +1.96445e6 q^{37} +(-828450. + 669489. i) q^{39} +986125. i q^{41} -78142.0 q^{43} +(-3.70138e6 - 794528. i) q^{45} +3.51969e6i q^{47} +1.99700e6 q^{49} +(3.37997e6 + 4.18250e6i) q^{51} -522048. i q^{53} +1.29450e7 q^{55} +(-9.07213e6 + 7.33138e6i) q^{57} -5.00425e6i q^{59} -1.75783e7 q^{61} +(-3.83632e6 + 1.78718e7i) q^{63} -7.58754e6i q^{65} -1.71368e7 q^{67} +(2.51251e6 + 3.10907e6i) q^{69} -2.58906e7i q^{71} +2.81393e7 q^{73} +(-3.63491e6 + 2.93745e6i) q^{75} -6.25041e7i q^{77} -9.18250e6 q^{79} +(-3.92545e7 - 1.76666e7i) q^{81} -8.71084e7i q^{83} -3.83063e7 q^{85} +(-3.19421e7 - 3.95263e7i) q^{87} -8.12528e7i q^{89} -3.66359e7 q^{91} +(4.59105e7 - 3.71013e7i) q^{93} -8.30890e7i q^{95} -1.28723e8 q^{97} +(1.43918e8 + 3.08931e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 126 q^{3} - 5572 q^{7} + 2754 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 126 q^{3} - 5572 q^{7} + 2754 q^{9} + 26300 q^{13} + 58752 q^{15} + 288004 q^{19} + 351036 q^{21} + 115394 q^{25} + 479682 q^{27} - 1457476 q^{31} - 2284416 q^{33} + 3928892 q^{37} - 1656900 q^{39} - 156284 q^{43} - 7402752 q^{45} + 3993990 q^{49} + 6759936 q^{51} + 25890048 q^{55} - 18144252 q^{57} - 35156548 q^{61} - 7672644 q^{63} - 34273532 q^{67} + 5025024 q^{69} + 56278660 q^{73} - 7269822 q^{75} - 18364996 q^{79} - 78508926 q^{81} - 76612608 q^{85} - 63884160 q^{87} - 73271800 q^{91} + 91820988 q^{93} - 257445116 q^{97} + 287836416 q^{99}+O(q^{100}) \) 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
\(3\) −63.0000 + 50.9117i −0.777778 + 0.628539i
\(4\) 0 0
\(5\) 576.999i 0.923199i −0.887089 0.461599i \(-0.847276\pi\)
0.887089 0.461599i \(-0.152724\pi\)
\(6\) 0 0
\(7\) −2786.00 −1.16035 −0.580175 0.814492i \(-0.697016\pi\)
−0.580175 + 0.814492i \(0.697016\pi\)
\(8\) 0 0
\(9\) 1377.00 6414.87i 0.209877 0.977728i
\(10\) 0 0
\(11\) 22435.1i 1.53235i 0.642634 + 0.766173i \(0.277842\pi\)
−0.642634 + 0.766173i \(0.722158\pi\)
\(12\) 0 0
\(13\) 13150.0 0.460418 0.230209 0.973141i \(-0.426059\pi\)
0.230209 + 0.973141i \(0.426059\pi\)
\(14\) 0 0
\(15\) 29376.0 + 36350.9i 0.580267 + 0.718043i
\(16\) 0 0
\(17\) 66388.8i 0.794876i −0.917629 0.397438i \(-0.869899\pi\)
0.917629 0.397438i \(-0.130101\pi\)
\(18\) 0 0
\(19\) 144002. 1.10498 0.552490 0.833520i \(-0.313678\pi\)
0.552490 + 0.833520i \(0.313678\pi\)
\(20\) 0 0
\(21\) 175518. 141840.i 0.902494 0.729326i
\(22\) 0 0
\(23\) 49350.4i 0.176352i −0.996105 0.0881758i \(-0.971896\pi\)
0.996105 0.0881758i \(-0.0281037\pi\)
\(24\) 0 0
\(25\) 57697.0 0.147704
\(26\) 0 0
\(27\) 239841. + 474242.i 0.451303 + 0.892371i
\(28\) 0 0
\(29\) 627402.i 0.887061i 0.896259 + 0.443531i \(0.146274\pi\)
−0.896259 + 0.443531i \(0.853726\pi\)
\(30\) 0 0
\(31\) −728738. −0.789087 −0.394543 0.918877i \(-0.629097\pi\)
−0.394543 + 0.918877i \(0.629097\pi\)
\(32\) 0 0
\(33\) −1.14221e6 1.41341e6i −0.963140 1.19182i
\(34\) 0 0
\(35\) 1.60752e6i 1.07123i
\(36\) 0 0
\(37\) 1.96445e6 1.04817 0.524087 0.851665i \(-0.324407\pi\)
0.524087 + 0.851665i \(0.324407\pi\)
\(38\) 0 0
\(39\) −828450. + 669489.i −0.358103 + 0.289391i
\(40\) 0 0
\(41\) 986125.i 0.348977i 0.984659 + 0.174488i \(0.0558272\pi\)
−0.984659 + 0.174488i \(0.944173\pi\)
\(42\) 0 0
\(43\) −78142.0 −0.0228566 −0.0114283 0.999935i \(-0.503638\pi\)
−0.0114283 + 0.999935i \(0.503638\pi\)
\(44\) 0 0
\(45\) −3.70138e6 794528.i −0.902637 0.193758i
\(46\) 0 0
\(47\) 3.51969e6i 0.721296i 0.932702 + 0.360648i \(0.117444\pi\)
−0.932702 + 0.360648i \(0.882556\pi\)
\(48\) 0 0
\(49\) 1.99700e6 0.346412
\(50\) 0 0
\(51\) 3.37997e6 + 4.18250e6i 0.499611 + 0.618237i
\(52\) 0 0
\(53\) 522048.i 0.0661618i −0.999453 0.0330809i \(-0.989468\pi\)
0.999453 0.0330809i \(-0.0105319\pi\)
\(54\) 0 0
\(55\) 1.29450e7 1.41466
\(56\) 0 0
\(57\) −9.07213e6 + 7.33138e6i −0.859428 + 0.694523i
\(58\) 0 0
\(59\) 5.00425e6i 0.412981i −0.978449 0.206491i \(-0.933796\pi\)
0.978449 0.206491i \(-0.0662043\pi\)
\(60\) 0 0
\(61\) −1.75783e7 −1.26957 −0.634785 0.772689i \(-0.718911\pi\)
−0.634785 + 0.772689i \(0.718911\pi\)
\(62\) 0 0
\(63\) −3.83632e6 + 1.78718e7i −0.243530 + 1.13451i
\(64\) 0 0
\(65\) 7.58754e6i 0.425057i
\(66\) 0 0
\(67\) −1.71368e7 −0.850413 −0.425206 0.905096i \(-0.639798\pi\)
−0.425206 + 0.905096i \(0.639798\pi\)
\(68\) 0 0
\(69\) 2.51251e6 + 3.10907e6i 0.110844 + 0.137162i
\(70\) 0 0
\(71\) 2.58906e7i 1.01885i −0.860516 0.509424i \(-0.829859\pi\)
0.860516 0.509424i \(-0.170141\pi\)
\(72\) 0 0
\(73\) 2.81393e7 0.990883 0.495441 0.868641i \(-0.335006\pi\)
0.495441 + 0.868641i \(0.335006\pi\)
\(74\) 0 0
\(75\) −3.63491e6 + 2.93745e6i −0.114881 + 0.0928380i
\(76\) 0 0
\(77\) 6.25041e7i 1.77806i
\(78\) 0 0
\(79\) −9.18250e6 −0.235750 −0.117875 0.993028i \(-0.537608\pi\)
−0.117875 + 0.993028i \(0.537608\pi\)
\(80\) 0 0
\(81\) −3.92545e7 1.76666e7i −0.911904 0.410404i
\(82\) 0 0
\(83\) 8.71084e7i 1.83547i −0.397190 0.917736i \(-0.630015\pi\)
0.397190 0.917736i \(-0.369985\pi\)
\(84\) 0 0
\(85\) −3.83063e7 −0.733828
\(86\) 0 0
\(87\) −3.19421e7 3.95263e7i −0.557553 0.689937i
\(88\) 0 0
\(89\) 8.12528e7i 1.29503i −0.762055 0.647513i \(-0.775809\pi\)
0.762055 0.647513i \(-0.224191\pi\)
\(90\) 0 0
\(91\) −3.66359e7 −0.534246
\(92\) 0 0
\(93\) 4.59105e7 3.71013e7i 0.613734 0.495972i
\(94\) 0 0
\(95\) 8.30890e7i 1.02012i
\(96\) 0 0
\(97\) −1.28723e8 −1.45401 −0.727006 0.686632i \(-0.759089\pi\)
−0.727006 + 0.686632i \(0.759089\pi\)
\(98\) 0 0
\(99\) 1.43918e8 + 3.08931e7i 1.49822 + 0.321604i
\(100\) 0 0
\(101\) 9.37809e7i 0.901216i 0.892722 + 0.450608i \(0.148793\pi\)
−0.892722 + 0.450608i \(0.851207\pi\)
\(102\) 0 0
\(103\) 5.30322e7 0.471184 0.235592 0.971852i \(-0.424297\pi\)
0.235592 + 0.971852i \(0.424297\pi\)
\(104\) 0 0
\(105\) −8.18415e7 1.01274e8i −0.673312 0.833182i
\(106\) 0 0
\(107\) 1.90801e8i 1.45561i 0.685785 + 0.727804i \(0.259459\pi\)
−0.685785 + 0.727804i \(0.740541\pi\)
\(108\) 0 0
\(109\) −2.71959e8 −1.92662 −0.963312 0.268384i \(-0.913510\pi\)
−0.963312 + 0.268384i \(0.913510\pi\)
\(110\) 0 0
\(111\) −1.23760e8 + 1.00013e8i −0.815246 + 0.658818i
\(112\) 0 0
\(113\) 7.69189e7i 0.471758i 0.971782 + 0.235879i \(0.0757969\pi\)
−0.971782 + 0.235879i \(0.924203\pi\)
\(114\) 0 0
\(115\) −2.84751e7 −0.162808
\(116\) 0 0
\(117\) 1.81076e7 8.43556e7i 0.0966309 0.450164i
\(118\) 0 0
\(119\) 1.84959e8i 0.922334i
\(120\) 0 0
\(121\) −2.88974e8 −1.34809
\(122\) 0 0
\(123\) −5.02053e7 6.21259e7i −0.219346 0.271427i
\(124\) 0 0
\(125\) 2.58681e8i 1.05956i
\(126\) 0 0
\(127\) 1.25417e8 0.482104 0.241052 0.970512i \(-0.422508\pi\)
0.241052 + 0.970512i \(0.422508\pi\)
\(128\) 0 0
\(129\) 4.92295e6 3.97834e6i 0.0177773 0.0143662i
\(130\) 0 0
\(131\) 1.24051e8i 0.421225i −0.977570 0.210612i \(-0.932454\pi\)
0.977570 0.210612i \(-0.0675458\pi\)
\(132\) 0 0
\(133\) −4.01190e8 −1.28216
\(134\) 0 0
\(135\) 2.73637e8 1.38388e8i 0.823835 0.416642i
\(136\) 0 0
\(137\) 5.50746e8i 1.56340i −0.623656 0.781699i \(-0.714353\pi\)
0.623656 0.781699i \(-0.285647\pi\)
\(138\) 0 0
\(139\) −7.59262e7 −0.203391 −0.101696 0.994816i \(-0.532427\pi\)
−0.101696 + 0.994816i \(0.532427\pi\)
\(140\) 0 0
\(141\) −1.79194e8 2.21741e8i −0.453363 0.561008i
\(142\) 0 0
\(143\) 2.95021e8i 0.705520i
\(144\) 0 0
\(145\) 3.62010e8 0.818934
\(146\) 0 0
\(147\) −1.25811e8 + 1.01670e8i −0.269431 + 0.217733i
\(148\) 0 0
\(149\) 7.35143e8i 1.49151i −0.666219 0.745756i \(-0.732088\pi\)
0.666219 0.745756i \(-0.267912\pi\)
\(150\) 0 0
\(151\) −3.01637e8 −0.580198 −0.290099 0.956997i \(-0.593688\pi\)
−0.290099 + 0.956997i \(0.593688\pi\)
\(152\) 0 0
\(153\) −4.25876e8 9.14174e7i −0.777172 0.166826i
\(154\) 0 0
\(155\) 4.20481e8i 0.728484i
\(156\) 0 0
\(157\) 1.61241e8 0.265386 0.132693 0.991157i \(-0.457638\pi\)
0.132693 + 0.991157i \(0.457638\pi\)
\(158\) 0 0
\(159\) 2.65784e7 + 3.28891e7i 0.0415853 + 0.0514592i
\(160\) 0 0
\(161\) 1.37490e8i 0.204630i
\(162\) 0 0
\(163\) −2.21232e8 −0.313399 −0.156700 0.987646i \(-0.550085\pi\)
−0.156700 + 0.987646i \(0.550085\pi\)
\(164\) 0 0
\(165\) −8.15537e8 + 6.59053e8i −1.10029 + 0.889170i
\(166\) 0 0
\(167\) 4.01854e8i 0.516657i 0.966057 + 0.258328i \(0.0831716\pi\)
−0.966057 + 0.258328i \(0.916828\pi\)
\(168\) 0 0
\(169\) −6.42808e8 −0.788015
\(170\) 0 0
\(171\) 1.98291e8 9.23755e8i 0.231909 1.08037i
\(172\) 0 0
\(173\) 1.08224e7i 0.0120820i 0.999982 + 0.00604099i \(0.00192292\pi\)
−0.999982 + 0.00604099i \(0.998077\pi\)
\(174\) 0 0
\(175\) −1.60744e8 −0.171389
\(176\) 0 0
\(177\) 2.54775e8 + 3.15267e8i 0.259575 + 0.321208i
\(178\) 0 0
\(179\) 2.24822e8i 0.218991i 0.993987 + 0.109495i \(0.0349235\pi\)
−0.993987 + 0.109495i \(0.965076\pi\)
\(180\) 0 0
\(181\) 1.31026e9 1.22080 0.610398 0.792095i \(-0.291010\pi\)
0.610398 + 0.792095i \(0.291010\pi\)
\(182\) 0 0
\(183\) 1.10743e9 8.94940e8i 0.987444 0.797975i
\(184\) 0 0
\(185\) 1.13348e9i 0.967672i
\(186\) 0 0
\(187\) 1.48944e9 1.21803
\(188\) 0 0
\(189\) −6.68197e8 1.32124e9i −0.523670 1.03546i
\(190\) 0 0
\(191\) 2.18984e9i 1.64543i −0.568454 0.822715i \(-0.692458\pi\)
0.568454 0.822715i \(-0.307542\pi\)
\(192\) 0 0
\(193\) −1.71183e9 −1.23376 −0.616881 0.787057i \(-0.711604\pi\)
−0.616881 + 0.787057i \(0.711604\pi\)
\(194\) 0 0
\(195\) 3.86294e8 + 4.78015e8i 0.267165 + 0.330600i
\(196\) 0 0
\(197\) 2.63287e9i 1.74810i 0.485840 + 0.874048i \(0.338514\pi\)
−0.485840 + 0.874048i \(0.661486\pi\)
\(198\) 0 0
\(199\) −2.95243e9 −1.88264 −0.941319 0.337517i \(-0.890413\pi\)
−0.941319 + 0.337517i \(0.890413\pi\)
\(200\) 0 0
\(201\) 1.07962e9 8.72462e8i 0.661432 0.534518i
\(202\) 0 0
\(203\) 1.74794e9i 1.02930i
\(204\) 0 0
\(205\) 5.68994e8 0.322175
\(206\) 0 0
\(207\) −3.16577e8 6.79555e7i −0.172424 0.0370121i
\(208\) 0 0
\(209\) 3.23070e9i 1.69321i
\(210\) 0 0
\(211\) −2.66349e9 −1.34376 −0.671880 0.740660i \(-0.734513\pi\)
−0.671880 + 0.740660i \(0.734513\pi\)
\(212\) 0 0
\(213\) 1.31814e9 + 1.63111e9i 0.640386 + 0.792437i
\(214\) 0 0
\(215\) 4.50879e7i 0.0211011i
\(216\) 0 0
\(217\) 2.03026e9 0.915616
\(218\) 0 0
\(219\) −1.77278e9 + 1.43262e9i −0.770687 + 0.622809i
\(220\) 0 0
\(221\) 8.73013e8i 0.365975i
\(222\) 0 0
\(223\) 2.04266e8 0.0825993 0.0412996 0.999147i \(-0.486850\pi\)
0.0412996 + 0.999147i \(0.486850\pi\)
\(224\) 0 0
\(225\) 7.94488e7 3.70119e8i 0.0309997 0.144415i
\(226\) 0 0
\(227\) 4.26163e8i 0.160499i −0.996775 0.0802495i \(-0.974428\pi\)
0.996775 0.0802495i \(-0.0255717\pi\)
\(228\) 0 0
\(229\) 3.05784e8 0.111192 0.0555960 0.998453i \(-0.482294\pi\)
0.0555960 + 0.998453i \(0.482294\pi\)
\(230\) 0 0
\(231\) 3.18219e9 + 3.93776e9i 1.11758 + 1.38293i
\(232\) 0 0
\(233\) 1.40915e9i 0.478117i 0.971005 + 0.239059i \(0.0768388\pi\)
−0.971005 + 0.239059i \(0.923161\pi\)
\(234\) 0 0
\(235\) 2.03086e9 0.665900
\(236\) 0 0
\(237\) 5.78497e8 4.67496e8i 0.183361 0.148178i
\(238\) 0 0
\(239\) 2.28759e9i 0.701109i 0.936542 + 0.350555i \(0.114007\pi\)
−0.936542 + 0.350555i \(0.885993\pi\)
\(240\) 0 0
\(241\) 4.37370e9 1.29653 0.648263 0.761417i \(-0.275496\pi\)
0.648263 + 0.761417i \(0.275496\pi\)
\(242\) 0 0
\(243\) 3.37247e9 8.85518e8i 0.967214 0.253964i
\(244\) 0 0
\(245\) 1.15226e9i 0.319807i
\(246\) 0 0
\(247\) 1.89363e9 0.508752
\(248\) 0 0
\(249\) 4.43484e9 + 5.48783e9i 1.15367 + 1.42759i
\(250\) 0 0
\(251\) 1.78995e9i 0.450969i 0.974247 + 0.225484i \(0.0723965\pi\)
−0.974247 + 0.225484i \(0.927604\pi\)
\(252\) 0 0
\(253\) 1.10718e9 0.270232
\(254\) 0 0
\(255\) 2.41330e9 1.95024e9i 0.570755 0.461240i
\(256\) 0 0
\(257\) 2.20683e9i 0.505867i −0.967484 0.252933i \(-0.918605\pi\)
0.967484 0.252933i \(-0.0813954\pi\)
\(258\) 0 0
\(259\) −5.47295e9 −1.21625
\(260\) 0 0
\(261\) 4.02470e9 + 8.63932e8i 0.867305 + 0.186173i
\(262\) 0 0
\(263\) 1.77804e9i 0.371636i 0.982584 + 0.185818i \(0.0594935\pi\)
−0.982584 + 0.185818i \(0.940506\pi\)
\(264\) 0 0
\(265\) −3.01222e8 −0.0610805
\(266\) 0 0
\(267\) 4.13672e9 + 5.11893e9i 0.813975 + 1.00724i
\(268\) 0 0
\(269\) 5.97276e9i 1.14069i 0.821406 + 0.570343i \(0.193190\pi\)
−0.821406 + 0.570343i \(0.806810\pi\)
\(270\) 0 0
\(271\) −3.24555e9 −0.601744 −0.300872 0.953665i \(-0.597278\pi\)
−0.300872 + 0.953665i \(0.597278\pi\)
\(272\) 0 0
\(273\) 2.30806e9 1.86520e9i 0.415525 0.335795i
\(274\) 0 0
\(275\) 1.29444e9i 0.226334i
\(276\) 0 0
\(277\) 1.34137e9 0.227841 0.113920 0.993490i \(-0.463659\pi\)
0.113920 + 0.993490i \(0.463659\pi\)
\(278\) 0 0
\(279\) −1.00347e9 + 4.67476e9i −0.165611 + 0.771512i
\(280\) 0 0
\(281\) 1.89253e9i 0.303541i 0.988416 + 0.151771i \(0.0484975\pi\)
−0.988416 + 0.151771i \(0.951502\pi\)
\(282\) 0 0
\(283\) −6.88292e9 −1.07307 −0.536534 0.843879i \(-0.680267\pi\)
−0.536534 + 0.843879i \(0.680267\pi\)
\(284\) 0 0
\(285\) 4.23020e9 + 5.23461e9i 0.641183 + 0.793423i
\(286\) 0 0
\(287\) 2.74735e9i 0.404935i
\(288\) 0 0
\(289\) 2.56828e9 0.368172
\(290\) 0 0
\(291\) 8.10952e9 6.55348e9i 1.13090 0.913903i
\(292\) 0 0
\(293\) 4.31371e9i 0.585302i −0.956219 0.292651i \(-0.905463\pi\)
0.956219 0.292651i \(-0.0945375\pi\)
\(294\) 0 0
\(295\) −2.88745e9 −0.381264
\(296\) 0 0
\(297\) −1.06397e10 + 5.38085e9i −1.36742 + 0.691553i
\(298\) 0 0
\(299\) 6.48958e8i 0.0811954i
\(300\) 0 0
\(301\) 2.17704e8 0.0265216
\(302\) 0 0
\(303\) −4.77455e9 5.90820e9i −0.566450 0.700946i
\(304\) 0 0
\(305\) 1.01426e10i 1.17207i
\(306\) 0 0
\(307\) −8.32155e9 −0.936809 −0.468404 0.883514i \(-0.655171\pi\)
−0.468404 + 0.883514i \(0.655171\pi\)
\(308\) 0 0
\(309\) −3.34103e9 + 2.69996e9i −0.366477 + 0.296158i
\(310\) 0 0
\(311\) 1.09184e10i 1.16712i −0.812069 0.583561i \(-0.801659\pi\)
0.812069 0.583561i \(-0.198341\pi\)
\(312\) 0 0
\(313\) 6.19953e9 0.645924 0.322962 0.946412i \(-0.395321\pi\)
0.322962 + 0.946412i \(0.395321\pi\)
\(314\) 0 0
\(315\) 1.03120e10 + 2.21355e9i 1.04737 + 0.224827i
\(316\) 0 0
\(317\) 1.86870e10i 1.85056i 0.379289 + 0.925278i \(0.376169\pi\)
−0.379289 + 0.925278i \(0.623831\pi\)
\(318\) 0 0
\(319\) −1.40758e10 −1.35929
\(320\) 0 0
\(321\) −9.71398e9 1.20204e10i −0.914907 1.13214i
\(322\) 0 0
\(323\) 9.56013e9i 0.878322i
\(324\) 0 0
\(325\) 7.58716e8 0.0680057
\(326\) 0 0
\(327\) 1.71334e10 1.38459e10i 1.49849 1.21096i
\(328\) 0 0
\(329\) 9.80587e9i 0.836956i
\(330\) 0 0
\(331\) 3.24478e9 0.270317 0.135158 0.990824i \(-0.456846\pi\)
0.135158 + 0.990824i \(0.456846\pi\)
\(332\) 0 0
\(333\) 2.70504e9 1.26017e10i 0.219987 1.02483i
\(334\) 0 0
\(335\) 9.88790e9i 0.785100i
\(336\) 0 0
\(337\) 4.89137e9 0.379237 0.189619 0.981858i \(-0.439275\pi\)
0.189619 + 0.981858i \(0.439275\pi\)
\(338\) 0 0
\(339\) −3.91607e9 4.84589e9i −0.296518 0.366923i
\(340\) 0 0
\(341\) 1.63493e10i 1.20915i
\(342\) 0 0
\(343\) 1.04971e10 0.758391
\(344\) 0 0
\(345\) 1.79393e9 1.44972e9i 0.126628 0.102331i
\(346\) 0 0
\(347\) 1.44263e10i 0.995030i 0.867455 + 0.497515i \(0.165754\pi\)
−0.867455 + 0.497515i \(0.834246\pi\)
\(348\) 0 0
\(349\) 5.34169e9 0.360062 0.180031 0.983661i \(-0.442380\pi\)
0.180031 + 0.983661i \(0.442380\pi\)
\(350\) 0 0
\(351\) 3.15391e9 + 6.23629e9i 0.207788 + 0.410864i
\(352\) 0 0
\(353\) 7.82366e9i 0.503861i −0.967745 0.251931i \(-0.918935\pi\)
0.967745 0.251931i \(-0.0810655\pi\)
\(354\) 0 0
\(355\) −1.49389e10 −0.940599
\(356\) 0 0
\(357\) −9.41659e9 1.16524e10i −0.579723 0.717371i
\(358\) 0 0
\(359\) 1.66718e10i 1.00370i 0.864955 + 0.501850i \(0.167347\pi\)
−0.864955 + 0.501850i \(0.832653\pi\)
\(360\) 0 0
\(361\) 3.75301e9 0.220979
\(362\) 0 0
\(363\) 1.82054e10 1.47122e10i 1.04851 0.847325i
\(364\) 0 0
\(365\) 1.62364e10i 0.914782i
\(366\) 0 0
\(367\) −1.86456e10 −1.02781 −0.513905 0.857847i \(-0.671802\pi\)
−0.513905 + 0.857847i \(0.671802\pi\)
\(368\) 0 0
\(369\) 6.32587e9 + 1.35789e9i 0.341205 + 0.0732421i
\(370\) 0 0
\(371\) 1.45443e9i 0.0767708i
\(372\) 0 0
\(373\) −3.38390e10 −1.74817 −0.874083 0.485776i \(-0.838537\pi\)
−0.874083 + 0.485776i \(0.838537\pi\)
\(374\) 0 0
\(375\) 1.31699e10 + 1.62969e10i 0.665975 + 0.824101i
\(376\) 0 0
\(377\) 8.25033e9i 0.408419i
\(378\) 0 0
\(379\) −2.82088e10 −1.36719 −0.683594 0.729863i \(-0.739584\pi\)
−0.683594 + 0.729863i \(0.739584\pi\)
\(380\) 0 0
\(381\) −7.90126e9 + 6.38518e9i −0.374970 + 0.303021i
\(382\) 0 0
\(383\) 1.82405e10i 0.847698i −0.905733 0.423849i \(-0.860679\pi\)
0.905733 0.423849i \(-0.139321\pi\)
\(384\) 0 0
\(385\) −3.60648e10 −1.64150
\(386\) 0 0
\(387\) −1.07602e8 + 5.01271e8i −0.00479705 + 0.0223475i
\(388\) 0 0
\(389\) 1.94375e10i 0.848871i −0.905458 0.424435i \(-0.860473\pi\)
0.905458 0.424435i \(-0.139527\pi\)
\(390\) 0 0
\(391\) −3.27632e9 −0.140178
\(392\) 0 0
\(393\) 6.31563e9 + 7.81519e9i 0.264756 + 0.327619i
\(394\) 0 0
\(395\) 5.29829e9i 0.217644i
\(396\) 0 0
\(397\) −1.66719e10 −0.671157 −0.335578 0.942012i \(-0.608932\pi\)
−0.335578 + 0.942012i \(0.608932\pi\)
\(398\) 0 0
\(399\) 2.52749e10 2.04252e10i 0.997238 0.805890i
\(400\) 0 0
\(401\) 3.30836e10i 1.27949i −0.768589 0.639743i \(-0.779041\pi\)
0.768589 0.639743i \(-0.220959\pi\)
\(402\) 0 0
\(403\) −9.58290e9 −0.363310
\(404\) 0 0
\(405\) −1.01936e10 + 2.26498e10i −0.378885 + 0.841868i
\(406\) 0 0
\(407\) 4.40725e10i 1.60616i
\(408\) 0 0
\(409\) −5.03326e10 −1.79869 −0.899345 0.437240i \(-0.855956\pi\)
−0.899345 + 0.437240i \(0.855956\pi\)
\(410\) 0 0
\(411\) 2.80394e10 + 3.46970e10i 0.982657 + 1.21598i
\(412\) 0 0
\(413\) 1.39418e10i 0.479203i
\(414\) 0 0
\(415\) −5.02615e10 −1.69451
\(416\) 0 0
\(417\) 4.78335e9 3.86553e9i 0.158193 0.127839i
\(418\) 0 0
\(419\) 2.94280e10i 0.954782i −0.878691 0.477391i \(-0.841582\pi\)
0.878691 0.477391i \(-0.158418\pi\)
\(420\) 0 0
\(421\) 3.33243e10 1.06080 0.530399 0.847748i \(-0.322042\pi\)
0.530399 + 0.847748i \(0.322042\pi\)
\(422\) 0 0
\(423\) 2.25784e10 + 4.84662e9i 0.705231 + 0.151383i
\(424\) 0 0
\(425\) 3.83044e9i 0.117407i
\(426\) 0 0
\(427\) 4.89731e10 1.47315
\(428\) 0 0
\(429\) −1.50200e10 1.85863e10i −0.443447 0.548738i
\(430\) 0 0
\(431\) 5.62271e10i 1.62943i −0.579860 0.814716i \(-0.696893\pi\)
0.579860 0.814716i \(-0.303107\pi\)
\(432\) 0 0
\(433\) −2.18807e10 −0.622457 −0.311229 0.950335i \(-0.600740\pi\)
−0.311229 + 0.950335i \(0.600740\pi\)
\(434\) 0 0
\(435\) −2.28066e10 + 1.84306e10i −0.636949 + 0.514732i
\(436\) 0 0
\(437\) 7.10656e9i 0.194865i
\(438\) 0 0
\(439\) −1.87990e10 −0.506146 −0.253073 0.967447i \(-0.581441\pi\)
−0.253073 + 0.967447i \(0.581441\pi\)
\(440\) 0 0
\(441\) 2.74986e9 1.28105e10i 0.0727037 0.338696i
\(442\) 0 0
\(443\) 6.53593e10i 1.69704i 0.529163 + 0.848520i \(0.322506\pi\)
−0.529163 + 0.848520i \(0.677494\pi\)
\(444\) 0 0
\(445\) −4.68828e10 −1.19557
\(446\) 0 0
\(447\) 3.74274e10 + 4.63140e10i 0.937474 + 1.16006i
\(448\) 0 0
\(449\) 1.58084e10i 0.388959i −0.980907 0.194479i \(-0.937698\pi\)
0.980907 0.194479i \(-0.0623017\pi\)
\(450\) 0 0
\(451\) −2.21238e10 −0.534754
\(452\) 0 0
\(453\) 1.90031e10 1.53568e10i 0.451265 0.364677i
\(454\) 0 0
\(455\) 2.11389e10i 0.493215i
\(456\) 0 0
\(457\) 3.30400e9 0.0757486 0.0378743 0.999283i \(-0.487941\pi\)
0.0378743 + 0.999283i \(0.487941\pi\)
\(458\) 0 0
\(459\) 3.14844e10 1.59228e10i 0.709324 0.358730i
\(460\) 0 0
\(461\) 3.30139e10i 0.730960i −0.930819 0.365480i \(-0.880905\pi\)
0.930819 0.365480i \(-0.119095\pi\)
\(462\) 0 0
\(463\) −5.63117e10 −1.22539 −0.612696 0.790319i \(-0.709915\pi\)
−0.612696 + 0.790319i \(0.709915\pi\)
\(464\) 0 0
\(465\) −2.14074e10 2.64903e10i −0.457881 0.566598i
\(466\) 0 0
\(467\) 5.38175e10i 1.13150i −0.824576 0.565752i \(-0.808586\pi\)
0.824576 0.565752i \(-0.191414\pi\)
\(468\) 0 0
\(469\) 4.77430e10 0.986776
\(470\) 0 0
\(471\) −1.01582e10 + 8.20907e9i −0.206411 + 0.166805i
\(472\) 0 0
\(473\) 1.75312e9i 0.0350242i
\(474\) 0 0
\(475\) 8.30848e9 0.163210
\(476\) 0 0
\(477\) −3.34887e9 7.18861e8i −0.0646882 0.0138858i
\(478\) 0 0
\(479\) 8.02692e10i 1.52478i −0.647119 0.762389i \(-0.724026\pi\)
0.647119 0.762389i \(-0.275974\pi\)
\(480\) 0 0
\(481\) 2.58325e10 0.482598
\(482\) 0 0
\(483\) −6.99986e9 8.66188e9i −0.128618 0.159156i
\(484\) 0 0
\(485\) 7.42728e10i 1.34234i
\(486\) 0 0
\(487\) 7.07093e10 1.25707 0.628537 0.777780i \(-0.283654\pi\)
0.628537 + 0.777780i \(0.283654\pi\)
\(488\) 0 0
\(489\) 1.39376e10 1.12633e10i 0.243755 0.196984i
\(490\) 0 0
\(491\) 6.06876e10i 1.04418i −0.852892 0.522088i \(-0.825153\pi\)
0.852892 0.522088i \(-0.174847\pi\)
\(492\) 0 0
\(493\) 4.16525e10 0.705104
\(494\) 0 0
\(495\) 1.78253e10 8.30407e10i 0.296904 1.38315i
\(496\) 0 0
\(497\) 7.21313e10i 1.18222i
\(498\) 0 0
\(499\) −1.04926e11 −1.69232 −0.846158 0.532932i \(-0.821090\pi\)
−0.846158 + 0.532932i \(0.821090\pi\)
\(500\) 0 0
\(501\) −2.04590e10 2.53168e10i −0.324739 0.401844i
\(502\) 0 0
\(503\) 4.73262e9i 0.0739315i 0.999317 + 0.0369657i \(0.0117692\pi\)
−0.999317 + 0.0369657i \(0.988231\pi\)
\(504\) 0 0
\(505\) 5.41115e10 0.832002
\(506\) 0 0
\(507\) 4.04969e10 3.27265e10i 0.612901 0.495299i
\(508\) 0 0
\(509\) 8.34402e7i 0.00124309i 1.00000 0.000621547i \(0.000197845\pi\)
−1.00000 0.000621547i \(0.999802\pi\)
\(510\) 0 0
\(511\) −7.83962e10 −1.14977
\(512\) 0 0
\(513\) 3.45376e10 + 6.82919e10i 0.498681 + 0.986051i
\(514\) 0 0
\(515\) 3.05995e10i 0.434997i
\(516\) 0 0
\(517\) −7.89646e10 −1.10528
\(518\) 0 0
\(519\) −5.50985e8 6.81809e8i −0.00759399 0.00939709i
\(520\) 0 0
\(521\) 3.30179e10i 0.448124i −0.974575 0.224062i \(-0.928068\pi\)
0.974575 0.224062i \(-0.0719318\pi\)
\(522\) 0 0
\(523\) −7.60491e9 −0.101645 −0.0508227 0.998708i \(-0.516184\pi\)
−0.0508227 + 0.998708i \(0.516184\pi\)
\(524\) 0 0
\(525\) 1.01269e10 8.18374e9i 0.133302 0.107725i
\(526\) 0 0
\(527\) 4.83801e10i 0.627226i
\(528\) 0 0
\(529\) 7.58755e10 0.968900
\(530\) 0 0
\(531\) −3.21016e10 6.89085e9i −0.403784 0.0866751i
\(532\) 0 0
\(533\) 1.29675e10i 0.160675i
\(534\) 0 0
\(535\) 1.10092e11 1.34382
\(536\) 0 0
\(537\) −1.14460e10 1.41638e10i −0.137644 0.170326i
\(538\) 0 0
\(539\) 4.48028e10i 0.530823i
\(540\) 0 0
\(541\) 1.18116e11 1.37885 0.689427 0.724355i \(-0.257862\pi\)
0.689427 + 0.724355i \(0.257862\pi\)
\(542\) 0 0
\(543\) −8.25464e10 + 6.67075e10i −0.949508 + 0.767318i
\(544\) 0 0
\(545\) 1.56920e11i 1.77866i
\(546\) 0 0
\(547\) −6.60454e10 −0.737723 −0.368862 0.929484i \(-0.620252\pi\)
−0.368862 + 0.929484i \(0.620252\pi\)
\(548\) 0 0
\(549\) −2.42053e10 + 1.12762e11i −0.266453 + 1.24129i
\(550\) 0 0
\(551\) 9.03471e10i 0.980184i
\(552\) 0 0
\(553\) 2.55824e10 0.273553
\(554\) 0 0
\(555\) 5.77076e10 + 7.14095e10i 0.608220 + 0.752634i
\(556\) 0 0
\(557\) 1.38850e11i 1.44253i −0.692659 0.721265i \(-0.743561\pi\)
0.692659 0.721265i \(-0.256439\pi\)
\(558\) 0 0
\(559\) −1.02757e9 −0.0105236
\(560\) 0 0
\(561\) −9.38347e10 + 7.58299e10i −0.947353 + 0.765577i
\(562\) 0 0
\(563\) 3.29834e10i 0.328294i 0.986436 + 0.164147i \(0.0524871\pi\)
−0.986436 + 0.164147i \(0.947513\pi\)
\(564\) 0 0
\(565\) 4.43821e10 0.435526
\(566\) 0 0
\(567\) 1.09363e11 + 4.92190e10i 1.05813 + 0.476213i
\(568\) 0 0
\(569\) 7.16018e10i 0.683085i −0.939866 0.341543i \(-0.889051\pi\)
0.939866 0.341543i \(-0.110949\pi\)
\(570\) 0 0
\(571\) 4.20250e10 0.395333 0.197667 0.980269i \(-0.436664\pi\)
0.197667 + 0.980269i \(0.436664\pi\)
\(572\) 0 0
\(573\) 1.11489e11 + 1.37960e11i 1.03422 + 1.27978i
\(574\) 0 0
\(575\) 2.84737e9i 0.0260479i
\(576\) 0 0
\(577\) 2.19502e11 1.98032 0.990162 0.139927i \(-0.0446868\pi\)
0.990162 + 0.139927i \(0.0446868\pi\)
\(578\) 0 0
\(579\) 1.07845e11 8.71521e10i 0.959592 0.775468i
\(580\) 0 0
\(581\) 2.42684e11i 2.12979i
\(582\) 0 0
\(583\) 1.17122e10 0.101383
\(584\) 0 0
\(585\) −4.86731e10 1.04480e10i −0.415590 0.0892096i
\(586\) 0 0
\(587\) 2.05299e11i 1.72916i 0.502496 + 0.864580i \(0.332415\pi\)
−0.502496 + 0.864580i \(0.667585\pi\)
\(588\) 0 0
\(589\) −1.04940e11 −0.871924
\(590\) 0 0
\(591\) −1.34044e11 1.65871e11i −1.09875 1.35963i
\(592\) 0 0
\(593\) 1.01405e11i 0.820052i −0.912074 0.410026i \(-0.865520\pi\)
0.912074 0.410026i \(-0.134480\pi\)
\(594\) 0 0
\(595\) 1.06721e11 0.851498
\(596\) 0 0
\(597\) 1.86003e11 1.50313e11i 1.46427 1.18331i
\(598\) 0 0
\(599\) 9.27543e10i 0.720488i −0.932858 0.360244i \(-0.882693\pi\)
0.932858 0.360244i \(-0.117307\pi\)
\(600\) 0 0
\(601\) −1.18263e11 −0.906464 −0.453232 0.891393i \(-0.649729\pi\)
−0.453232 + 0.891393i \(0.649729\pi\)
\(602\) 0 0
\(603\) −2.35973e10 + 1.09930e11i −0.178482 + 0.831472i
\(604\) 0 0
\(605\) 1.66738e11i 1.24455i
\(606\) 0 0
\(607\) 7.78725e10 0.573627 0.286813 0.957986i \(-0.407404\pi\)
0.286813 + 0.957986i \(0.407404\pi\)
\(608\) 0 0
\(609\) 8.89906e10 + 1.10120e11i 0.646957 + 0.800568i
\(610\) 0 0
\(611\) 4.62840e10i 0.332098i
\(612\) 0 0
\(613\) 6.04009e10 0.427761 0.213881 0.976860i \(-0.431390\pi\)
0.213881 + 0.976860i \(0.431390\pi\)
\(614\) 0 0
\(615\) −3.58466e10 + 2.89684e10i −0.250581 + 0.202500i
\(616\) 0 0
\(617\) 1.86030e11i 1.28364i 0.766856 + 0.641819i \(0.221820\pi\)
−0.766856 + 0.641819i \(0.778180\pi\)
\(618\) 0 0
\(619\) 1.54130e11 1.04984 0.524922 0.851151i \(-0.324095\pi\)
0.524922 + 0.851151i \(0.324095\pi\)
\(620\) 0 0
\(621\) 2.34040e10 1.18362e10i 0.157371 0.0795880i
\(622\) 0 0
\(623\) 2.26370e11i 1.50268i
\(624\) 0 0
\(625\) −1.26721e11 −0.830479
\(626\) 0 0
\(627\) −1.64480e11 2.03534e11i −1.06425 1.31694i
\(628\) 0 0
\(629\) 1.30417e11i 0.833168i
\(630\) 0 0
\(631\) −4.35140e10 −0.274480 −0.137240 0.990538i \(-0.543823\pi\)
−0.137240 + 0.990538i \(0.543823\pi\)
\(632\) 0 0
\(633\) 1.67800e11 1.35603e11i 1.04515 0.844606i
\(634\) 0 0
\(635\) 7.23654e10i 0.445078i
\(636\) 0 0
\(637\) 2.62605e10 0.159494
\(638\) 0 0
\(639\) −1.66085e11 3.56514e10i −0.996156 0.213832i
\(640\) 0 0
\(641\) 1.74736e11i 1.03502i −0.855676 0.517512i \(-0.826858\pi\)
0.855676 0.517512i \(-0.173142\pi\)
\(642\) 0 0
\(643\) −2.46091e11 −1.43963 −0.719817 0.694164i \(-0.755774\pi\)
−0.719817 + 0.694164i \(0.755774\pi\)
\(644\) 0 0
\(645\) −2.29550e9 2.84054e9i −0.0132629 0.0164120i
\(646\) 0 0
\(647\) 1.89739e10i 0.108278i 0.998533 + 0.0541390i \(0.0172414\pi\)
−0.998533 + 0.0541390i \(0.982759\pi\)
\(648\) 0 0
\(649\) 1.12271e11 0.632831
\(650\) 0 0
\(651\) −1.27907e11 + 1.03364e11i −0.712146 + 0.575501i
\(652\) 0 0
\(653\) 1.53366e11i 0.843484i −0.906716 0.421742i \(-0.861419\pi\)
0.906716 0.421742i \(-0.138581\pi\)
\(654\) 0 0
\(655\) −7.15771e10 −0.388874
\(656\) 0 0
\(657\) 3.87479e10 1.80510e11i 0.207963 0.968814i
\(658\) 0 0
\(659\) 1.47234e11i 0.780667i −0.920674 0.390333i \(-0.872360\pi\)
0.920674 0.390333i \(-0.127640\pi\)
\(660\) 0 0
\(661\) 6.61159e10 0.346338 0.173169 0.984892i \(-0.444599\pi\)
0.173169 + 0.984892i \(0.444599\pi\)
\(662\) 0 0
\(663\) 4.44466e10 + 5.49998e10i 0.230030 + 0.284647i
\(664\) 0 0
\(665\) 2.31486e11i 1.18369i
\(666\) 0 0
\(667\) 3.09625e10 0.156435
\(668\) 0 0
\(669\) −1.28687e10 + 1.03995e10i −0.0642439 + 0.0519169i
\(670\) 0 0
\(671\) 3.94370e11i 1.94542i
\(672\) 0 0
\(673\) −1.67142e11 −0.814753 −0.407377 0.913260i \(-0.633556\pi\)
−0.407377 + 0.913260i \(0.633556\pi\)
\(674\) 0 0
\(675\) 1.38381e10 + 2.73624e10i 0.0666594 + 0.131807i
\(676\) 0 0
\(677\) 7.82435e10i 0.372472i −0.982505 0.186236i \(-0.940371\pi\)
0.982505 0.186236i \(-0.0596289\pi\)
\(678\) 0 0
\(679\) 3.58621e11 1.68716
\(680\) 0 0
\(681\) 2.16967e10 + 2.68483e10i 0.100880 + 0.124832i
\(682\) 0 0
\(683\) 1.21724e11i 0.559361i −0.960093 0.279681i \(-0.909771\pi\)
0.960093 0.279681i \(-0.0902286\pi\)
\(684\) 0 0
\(685\) −3.17780e11 −1.44333
\(686\) 0 0
\(687\) −1.92644e10 + 1.55680e10i −0.0864827 + 0.0698885i
\(688\) 0 0
\(689\) 6.86494e9i 0.0304621i
\(690\) 0 0
\(691\) 3.71272e11 1.62847 0.814236 0.580535i \(-0.197156\pi\)
0.814236 + 0.580535i \(0.197156\pi\)
\(692\) 0 0
\(693\) −4.00956e11 8.60682e10i −1.73846 0.373173i
\(694\) 0 0
\(695\) 4.38094e10i 0.187771i
\(696\) 0 0
\(697\) 6.54677e10 0.277393
\(698\) 0 0
\(699\) −7.17424e10 8.87767e10i −0.300516 0.371869i
\(700\) 0 0
\(701\) 2.35914e11i 0.976970i 0.872572 + 0.488485i \(0.162450\pi\)
−0.872572 + 0.488485i \(0.837550\pi\)
\(702\) 0 0
\(703\) 2.82884e11 1.15821
\(704\) 0 0
\(705\) −1.27944e11 + 1.03395e11i −0.517922 + 0.418544i
\(706\) 0 0
\(707\) 2.61274e11i 1.04573i
\(708\) 0 0
\(709\) 1.51154e11 0.598184 0.299092 0.954224i \(-0.403316\pi\)
0.299092 + 0.954224i \(0.403316\pi\)
\(710\) 0 0
\(711\) −1.26443e10 + 5.89046e10i −0.0494785 + 0.230500i
\(712\) 0 0
\(713\) 3.59635e10i 0.139157i
\(714\) 0 0
\(715\) 1.70227e11 0.651335
\(716\) 0 0
\(717\) −1.16465e11 1.44118e11i −0.440675 0.545307i
\(718\) 0 0
\(719\) 1.57719e10i 0.0590158i −0.999565 0.0295079i \(-0.990606\pi\)
0.999565 0.0295079i \(-0.00939402\pi\)
\(720\) 0 0
\(721\) −1.47748e11 −0.546739
\(722\) 0 0
\(723\) −2.75543e11 + 2.22673e11i −1.00841 + 0.814918i
\(724\) 0 0
\(725\) 3.61992e10i 0.131023i
\(726\) 0 0
\(727\) −3.61913e11 −1.29559 −0.647794 0.761816i \(-0.724308\pi\)
−0.647794 + 0.761816i \(0.724308\pi\)
\(728\) 0 0
\(729\) −1.67382e11 + 2.27486e11i −0.592651 + 0.805459i
\(730\) 0 0
\(731\) 5.18776e9i 0.0181681i
\(732\) 0 0
\(733\) −5.75659e10 −0.199411 −0.0997056 0.995017i \(-0.531790\pi\)
−0.0997056 + 0.995017i \(0.531790\pi\)
\(734\) 0 0
\(735\) 5.86637e10 + 7.25927e10i 0.201011 + 0.248739i
\(736\) 0 0
\(737\) 3.84465e11i 1.30313i
\(738\) 0 0
\(739\) −2.30778e11 −0.773780 −0.386890 0.922126i \(-0.626451\pi\)
−0.386890 + 0.922126i \(0.626451\pi\)
\(740\) 0 0
\(741\) −1.19298e11 + 9.64077e10i −0.395696 + 0.319771i
\(742\) 0 0
\(743\) 4.84430e10i 0.158956i 0.996837 + 0.0794778i \(0.0253253\pi\)
−0.996837 + 0.0794778i \(0.974675\pi\)
\(744\) 0 0
\(745\) −4.24177e11 −1.37696
\(746\) 0 0
\(747\) −5.58790e11 1.19948e11i −1.79459 0.385223i
\(748\) 0 0
\(749\) 5.31571e11i 1.68902i
\(750\) 0 0
\(751\) −1.03467e11 −0.325269 −0.162635 0.986686i \(-0.551999\pi\)
−0.162635 + 0.986686i \(0.551999\pi\)
\(752\) 0 0
\(753\) −9.11295e10 1.12767e11i −0.283452 0.350753i
\(754\) 0 0
\(755\) 1.74044e11i 0.535638i
\(756\) 0 0
\(757\) −3.09395e11 −0.942170 −0.471085 0.882088i \(-0.656137\pi\)
−0.471085 + 0.882088i \(0.656137\pi\)
\(758\) 0 0
\(759\) −6.97524e10 + 5.63684e10i −0.210180 + 0.169851i
\(760\) 0 0
\(761\) 3.57736e11i 1.06665i −0.845909 0.533327i \(-0.820941\pi\)
0.845909 0.533327i \(-0.179059\pi\)
\(762\) 0 0
\(763\) 7.57677e11 2.23556
\(764\) 0 0
\(765\) −5.27478e10 + 2.45730e11i −0.154013 + 0.717485i
\(766\) 0 0
\(767\) 6.58058e10i 0.190144i
\(768\) 0 0
\(769\) 6.91156e10 0.197638 0.0988190 0.995105i \(-0.468494\pi\)
0.0988190 + 0.995105i \(0.468494\pi\)
\(770\) 0 0
\(771\) 1.12353e11 + 1.39030e11i 0.317957 + 0.393452i
\(772\) 0 0
\(773\) 4.96225e11i 1.38983i −0.719093 0.694914i \(-0.755443\pi\)
0.719093 0.694914i \(-0.244557\pi\)
\(774\) 0 0
\(775\) −4.20460e10 −0.116551
\(776\) 0 0
\(777\) 3.44796e11 2.78637e11i 0.945971 0.764460i
\(778\) 0 0
\(779\) 1.42004e11i 0.385612i
\(780\) 0 0
\(781\)