Properties

Label 48.13.e.d.17.4
Level $48$
Weight $13$
Character 48.17
Analytic conductor $43.872$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [48,13,Mod(17,48)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(48, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 13, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("48.17");
 
S:= CuspForms(chi, 13);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 13 \)
Character orbit: \([\chi]\) \(=\) 48.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: \(43.8717032293\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 4105x^{2} + 385000 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{10}\cdot 3^{7} \)
Twist minimal: no (minimal twist has level 12)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 17.4
Root \(9.79973i\) of defining polynomial
Character \(\chi\) \(=\) 48.17
Dual form 48.13.e.d.17.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(446.724 + 576.089i) q^{3} -11638.0i q^{5} +24223.1 q^{7} +(-132316. + 514706. i) q^{9} +O(q^{10})\) \(q+(446.724 + 576.089i) q^{3} -11638.0i q^{5} +24223.1 q^{7} +(-132316. + 514706. i) q^{9} -1.35468e6i q^{11} -5.79080e6 q^{13} +(6.70454e6 - 5.19899e6i) q^{15} +4.63555e7i q^{17} +3.36159e7 q^{19} +(1.08210e7 + 1.39547e7i) q^{21} +1.86091e8i q^{23} +1.08697e8 q^{25} +(-3.55625e8 + 1.53705e8i) q^{27} -2.36538e8i q^{29} +5.29079e7 q^{31} +(7.80415e8 - 6.05167e8i) q^{33} -2.81909e8i q^{35} -4.83240e9 q^{37} +(-2.58689e9 - 3.33602e9i) q^{39} +6.23992e9i q^{41} +6.78329e9 q^{43} +(5.99016e9 + 1.53990e9i) q^{45} +1.19817e10i q^{47} -1.32545e10 q^{49} +(-2.67049e10 + 2.07081e10i) q^{51} +7.56235e9i q^{53} -1.57658e10 q^{55} +(1.50170e10 + 1.93658e10i) q^{57} +5.06066e10i q^{59} -5.11029e10 q^{61} +(-3.20511e9 + 1.24678e10i) q^{63} +6.73935e10i q^{65} -9.11126e9 q^{67} +(-1.07205e11 + 8.31312e10i) q^{69} -1.39772e11i q^{71} -6.80946e9 q^{73} +(4.85576e10 + 6.26191e10i) q^{75} -3.28145e10i q^{77} -3.21423e11 q^{79} +(-2.47414e11 - 1.36208e11i) q^{81} +5.38395e11i q^{83} +5.39486e11 q^{85} +(1.36267e11 - 1.05667e11i) q^{87} +5.38855e10i q^{89} -1.40271e11 q^{91} +(2.36352e10 + 3.04796e10i) q^{93} -3.91223e11i q^{95} +7.08737e10 q^{97} +(6.97260e11 + 1.79246e11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 300 q^{3} - 15800 q^{7} + 96804 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 300 q^{3} - 15800 q^{7} + 96804 q^{9} + 3432200 q^{13} - 6613920 q^{15} + 2050024 q^{19} + 59979336 q^{21} - 437451260 q^{25} - 508358700 q^{27} + 2519008264 q^{31} + 3795184800 q^{33} - 7466711800 q^{37} - 14132878296 q^{39} + 26119930600 q^{43} + 35876727360 q^{45} - 52127844660 q^{49} - 54522702720 q^{51} + 96029271360 q^{55} + 68929593000 q^{57} - 9307235704 q^{61} - 18020676600 q^{63} - 89055584600 q^{67} - 143365584960 q^{69} + 464142475400 q^{73} + 487877005140 q^{75} - 567022026488 q^{79} - 929051518716 q^{81} + 1015432485120 q^{85} + 976838637600 q^{87} - 762832207984 q^{91} - 1392739649400 q^{93} + 862958525000 q^{97} - 1272066016320 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(31\) \(37\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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
\(3\) 446.724 + 576.089i 0.612790 + 0.790246i
\(4\) 0 0
\(5\) 11638.0i 0.744834i −0.928066 0.372417i \(-0.878529\pi\)
0.928066 0.372417i \(-0.121471\pi\)
\(6\) 0 0
\(7\) 24223.1 0.205893 0.102946 0.994687i \(-0.467173\pi\)
0.102946 + 0.994687i \(0.467173\pi\)
\(8\) 0 0
\(9\) −132316. + 514706.i −0.248976 + 0.968510i
\(10\) 0 0
\(11\) 1.35468e6i 0.764680i −0.924022 0.382340i \(-0.875118\pi\)
0.924022 0.382340i \(-0.124882\pi\)
\(12\) 0 0
\(13\) −5.79080e6 −1.19972 −0.599858 0.800106i \(-0.704776\pi\)
−0.599858 + 0.800106i \(0.704776\pi\)
\(14\) 0 0
\(15\) 6.70454e6 5.19899e6i 0.588602 0.456427i
\(16\) 0 0
\(17\) 4.63555e7i 1.92047i 0.279194 + 0.960235i \(0.409933\pi\)
−0.279194 + 0.960235i \(0.590067\pi\)
\(18\) 0 0
\(19\) 3.36159e7 0.714534 0.357267 0.934002i \(-0.383709\pi\)
0.357267 + 0.934002i \(0.383709\pi\)
\(20\) 0 0
\(21\) 1.08210e7 + 1.39547e7i 0.126169 + 0.162706i
\(22\) 0 0
\(23\) 1.86091e8i 1.25706i 0.777784 + 0.628532i \(0.216344\pi\)
−0.777784 + 0.628532i \(0.783656\pi\)
\(24\) 0 0
\(25\) 1.08697e8 0.445223
\(26\) 0 0
\(27\) −3.55625e8 + 1.53705e8i −0.917931 + 0.396741i
\(28\) 0 0
\(29\) 2.36538e8i 0.397662i −0.980034 0.198831i \(-0.936286\pi\)
0.980034 0.198831i \(-0.0637144\pi\)
\(30\) 0 0
\(31\) 5.29079e7 0.0596142 0.0298071 0.999556i \(-0.490511\pi\)
0.0298071 + 0.999556i \(0.490511\pi\)
\(32\) 0 0
\(33\) 7.80415e8 6.05167e8i 0.604285 0.468589i
\(34\) 0 0
\(35\) 2.81909e8i 0.153356i
\(36\) 0 0
\(37\) −4.83240e9 −1.88344 −0.941722 0.336391i \(-0.890794\pi\)
−0.941722 + 0.336391i \(0.890794\pi\)
\(38\) 0 0
\(39\) −2.58689e9 3.33602e9i −0.735174 0.948071i
\(40\) 0 0
\(41\) 6.23992e9i 1.31364i 0.754048 + 0.656819i \(0.228098\pi\)
−0.754048 + 0.656819i \(0.771902\pi\)
\(42\) 0 0
\(43\) 6.78329e9 1.07307 0.536537 0.843877i \(-0.319732\pi\)
0.536537 + 0.843877i \(0.319732\pi\)
\(44\) 0 0
\(45\) 5.99016e9 + 1.53990e9i 0.721379 + 0.185446i
\(46\) 0 0
\(47\) 1.19817e10i 1.11155i 0.831331 + 0.555777i \(0.187579\pi\)
−0.831331 + 0.555777i \(0.812421\pi\)
\(48\) 0 0
\(49\) −1.32545e10 −0.957608
\(50\) 0 0
\(51\) −2.67049e10 + 2.07081e10i −1.51764 + 1.17684i
\(52\) 0 0
\(53\) 7.56235e9i 0.341194i 0.985341 + 0.170597i \(0.0545696\pi\)
−0.985341 + 0.170597i \(0.945430\pi\)
\(54\) 0 0
\(55\) −1.57658e10 −0.569560
\(56\) 0 0
\(57\) 1.50170e10 + 1.93658e10i 0.437860 + 0.564658i
\(58\) 0 0
\(59\) 5.06066e10i 1.19976i 0.800089 + 0.599881i \(0.204785\pi\)
−0.800089 + 0.599881i \(0.795215\pi\)
\(60\) 0 0
\(61\) −5.11029e10 −0.991897 −0.495948 0.868352i \(-0.665179\pi\)
−0.495948 + 0.868352i \(0.665179\pi\)
\(62\) 0 0
\(63\) −3.20511e9 + 1.24678e10i −0.0512625 + 0.199409i
\(64\) 0 0
\(65\) 6.73935e10i 0.893589i
\(66\) 0 0
\(67\) −9.11126e9 −0.100723 −0.0503616 0.998731i \(-0.516037\pi\)
−0.0503616 + 0.998731i \(0.516037\pi\)
\(68\) 0 0
\(69\) −1.07205e11 + 8.31312e10i −0.993390 + 0.770317i
\(70\) 0 0
\(71\) 1.39772e11i 1.09112i −0.838072 0.545559i \(-0.816317\pi\)
0.838072 0.545559i \(-0.183683\pi\)
\(72\) 0 0
\(73\) −6.80946e9 −0.0449962 −0.0224981 0.999747i \(-0.507162\pi\)
−0.0224981 + 0.999747i \(0.507162\pi\)
\(74\) 0 0
\(75\) 4.85576e10 + 6.26191e10i 0.272828 + 0.351835i
\(76\) 0 0
\(77\) 3.28145e10i 0.157442i
\(78\) 0 0
\(79\) −3.21423e11 −1.32225 −0.661126 0.750274i \(-0.729921\pi\)
−0.661126 + 0.750274i \(0.729921\pi\)
\(80\) 0 0
\(81\) −2.47414e11 1.36208e11i −0.876022 0.482272i
\(82\) 0 0
\(83\) 5.38395e11i 1.64677i 0.567484 + 0.823384i \(0.307917\pi\)
−0.567484 + 0.823384i \(0.692083\pi\)
\(84\) 0 0
\(85\) 5.39486e11 1.43043
\(86\) 0 0
\(87\) 1.36267e11 1.05667e11i 0.314250 0.243683i
\(88\) 0 0
\(89\) 5.38855e10i 0.108426i 0.998529 + 0.0542128i \(0.0172649\pi\)
−0.998529 + 0.0542128i \(0.982735\pi\)
\(90\) 0 0
\(91\) −1.40271e11 −0.247013
\(92\) 0 0
\(93\) 2.36352e10 + 3.04796e10i 0.0365310 + 0.0471099i
\(94\) 0 0
\(95\) 3.91223e11i 0.532209i
\(96\) 0 0
\(97\) 7.08737e10 0.0850853 0.0425426 0.999095i \(-0.486454\pi\)
0.0425426 + 0.999095i \(0.486454\pi\)
\(98\) 0 0
\(99\) 6.97260e11 + 1.79246e11i 0.740600 + 0.190387i
\(100\) 0 0
\(101\) 2.21868e11i 0.209010i 0.994524 + 0.104505i \(0.0333258\pi\)
−0.994524 + 0.104505i \(0.966674\pi\)
\(102\) 0 0
\(103\) 1.71165e12 1.43348 0.716741 0.697340i \(-0.245633\pi\)
0.716741 + 0.697340i \(0.245633\pi\)
\(104\) 0 0
\(105\) 1.62405e11 1.25936e11i 0.121189 0.0939751i
\(106\) 0 0
\(107\) 1.99636e12i 1.33026i −0.746728 0.665130i \(-0.768376\pi\)
0.746728 0.665130i \(-0.231624\pi\)
\(108\) 0 0
\(109\) 8.91772e10 0.0531734 0.0265867 0.999647i \(-0.491536\pi\)
0.0265867 + 0.999647i \(0.491536\pi\)
\(110\) 0 0
\(111\) −2.15875e12 2.78389e12i −1.15416 1.48838i
\(112\) 0 0
\(113\) 2.33608e12i 1.12206i −0.827794 0.561032i \(-0.810405\pi\)
0.827794 0.561032i \(-0.189595\pi\)
\(114\) 0 0
\(115\) 2.16573e12 0.936304
\(116\) 0 0
\(117\) 7.66217e11 2.98056e12i 0.298701 1.16194i
\(118\) 0 0
\(119\) 1.12287e12i 0.395411i
\(120\) 0 0
\(121\) 1.30328e12 0.415264
\(122\) 0 0
\(123\) −3.59475e12 + 2.78752e12i −1.03810 + 0.804984i
\(124\) 0 0
\(125\) 4.10633e12i 1.07645i
\(126\) 0 0
\(127\) 2.60532e12 0.620926 0.310463 0.950586i \(-0.399516\pi\)
0.310463 + 0.950586i \(0.399516\pi\)
\(128\) 0 0
\(129\) 3.03026e12 + 3.90778e12i 0.657569 + 0.847992i
\(130\) 0 0
\(131\) 4.19667e12i 0.830380i −0.909735 0.415190i \(-0.863715\pi\)
0.909735 0.415190i \(-0.136285\pi\)
\(132\) 0 0
\(133\) 8.14281e11 0.147118
\(134\) 0 0
\(135\) 1.78883e12 + 4.13877e12i 0.295506 + 0.683706i
\(136\) 0 0
\(137\) 7.88117e12i 1.19198i 0.802993 + 0.595988i \(0.203239\pi\)
−0.802993 + 0.595988i \(0.796761\pi\)
\(138\) 0 0
\(139\) 4.47638e12 0.620637 0.310319 0.950633i \(-0.399564\pi\)
0.310319 + 0.950633i \(0.399564\pi\)
\(140\) 0 0
\(141\) −6.90252e12 + 5.35251e12i −0.878401 + 0.681150i
\(142\) 0 0
\(143\) 7.84467e12i 0.917399i
\(144\) 0 0
\(145\) −2.75284e12 −0.296192
\(146\) 0 0
\(147\) −5.92112e12 7.63579e12i −0.586813 0.756746i
\(148\) 0 0
\(149\) 5.96655e12i 0.545263i 0.962119 + 0.272631i \(0.0878939\pi\)
−0.962119 + 0.272631i \(0.912106\pi\)
\(150\) 0 0
\(151\) −4.60240e12 −0.388260 −0.194130 0.980976i \(-0.562188\pi\)
−0.194130 + 0.980976i \(0.562188\pi\)
\(152\) 0 0
\(153\) −2.38594e13 6.13358e12i −1.85999 0.478151i
\(154\) 0 0
\(155\) 6.15743e11i 0.0444027i
\(156\) 0 0
\(157\) 2.17935e13 1.45522 0.727610 0.685991i \(-0.240631\pi\)
0.727610 + 0.685991i \(0.240631\pi\)
\(158\) 0 0
\(159\) −4.35659e12 + 3.37828e12i −0.269627 + 0.209080i
\(160\) 0 0
\(161\) 4.50769e12i 0.258821i
\(162\) 0 0
\(163\) −1.76185e13 −0.939382 −0.469691 0.882831i \(-0.655635\pi\)
−0.469691 + 0.882831i \(0.655635\pi\)
\(164\) 0 0
\(165\) −7.04295e12 9.08249e12i −0.349021 0.450092i
\(166\) 0 0
\(167\) 2.77898e13i 1.28111i 0.767912 + 0.640555i \(0.221296\pi\)
−0.767912 + 0.640555i \(0.778704\pi\)
\(168\) 0 0
\(169\) 1.02353e13 0.439319
\(170\) 0 0
\(171\) −4.44793e12 + 1.73023e13i −0.177902 + 0.692033i
\(172\) 0 0
\(173\) 1.66424e13i 0.620784i −0.950609 0.310392i \(-0.899540\pi\)
0.950609 0.310392i \(-0.100460\pi\)
\(174\) 0 0
\(175\) 2.63298e12 0.0916682
\(176\) 0 0
\(177\) −2.91539e13 + 2.26072e13i −0.948107 + 0.735202i
\(178\) 0 0
\(179\) 8.30575e12i 0.252500i −0.991998 0.126250i \(-0.959706\pi\)
0.991998 0.126250i \(-0.0402941\pi\)
\(180\) 0 0
\(181\) 1.61679e13 0.459813 0.229907 0.973213i \(-0.426158\pi\)
0.229907 + 0.973213i \(0.426158\pi\)
\(182\) 0 0
\(183\) −2.28289e13 2.94398e13i −0.607825 0.783842i
\(184\) 0 0
\(185\) 5.62396e13i 1.40285i
\(186\) 0 0
\(187\) 6.27967e13 1.46854
\(188\) 0 0
\(189\) −8.61434e12 + 3.72322e12i −0.188995 + 0.0816861i
\(190\) 0 0
\(191\) 2.73160e13i 0.562622i −0.959617 0.281311i \(-0.909231\pi\)
0.959617 0.281311i \(-0.0907693\pi\)
\(192\) 0 0
\(193\) −1.51524e13 −0.293183 −0.146591 0.989197i \(-0.546830\pi\)
−0.146591 + 0.989197i \(0.546830\pi\)
\(194\) 0 0
\(195\) −3.88247e13 + 3.01063e13i −0.706155 + 0.547583i
\(196\) 0 0
\(197\) 3.49951e13i 0.598701i −0.954143 0.299351i \(-0.903230\pi\)
0.954143 0.299351i \(-0.0967701\pi\)
\(198\) 0 0
\(199\) 1.04733e14 1.68642 0.843209 0.537586i \(-0.180664\pi\)
0.843209 + 0.537586i \(0.180664\pi\)
\(200\) 0 0
\(201\) −4.07022e12 5.24890e12i −0.0617222 0.0795961i
\(202\) 0 0
\(203\) 5.72969e12i 0.0818757i
\(204\) 0 0
\(205\) 7.26203e13 0.978442
\(206\) 0 0
\(207\) −9.57819e13 2.46228e13i −1.21748 0.312979i
\(208\) 0 0
\(209\) 4.55387e13i 0.546390i
\(210\) 0 0
\(211\) 2.91530e13 0.330361 0.165181 0.986263i \(-0.447179\pi\)
0.165181 + 0.986263i \(0.447179\pi\)
\(212\) 0 0
\(213\) 8.05214e13 6.24397e13i 0.862251 0.668626i
\(214\) 0 0
\(215\) 7.89441e13i 0.799261i
\(216\) 0 0
\(217\) 1.28159e12 0.0122742
\(218\) 0 0
\(219\) −3.04195e12 3.92286e12i −0.0275732 0.0355580i
\(220\) 0 0
\(221\) 2.68435e14i 2.30402i
\(222\) 0 0
\(223\) 4.54466e13 0.369549 0.184775 0.982781i \(-0.440845\pi\)
0.184775 + 0.982781i \(0.440845\pi\)
\(224\) 0 0
\(225\) −1.43824e13 + 5.59470e13i −0.110850 + 0.431203i
\(226\) 0 0
\(227\) 4.06919e13i 0.297408i 0.988882 + 0.148704i \(0.0475102\pi\)
−0.988882 + 0.148704i \(0.952490\pi\)
\(228\) 0 0
\(229\) 1.43348e14 0.993983 0.496992 0.867755i \(-0.334438\pi\)
0.496992 + 0.867755i \(0.334438\pi\)
\(230\) 0 0
\(231\) 1.89041e13 1.46590e13i 0.124418 0.0964791i
\(232\) 0 0
\(233\) 2.35348e14i 1.47088i 0.677592 + 0.735438i \(0.263023\pi\)
−0.677592 + 0.735438i \(0.736977\pi\)
\(234\) 0 0
\(235\) 1.39443e14 0.827924
\(236\) 0 0
\(237\) −1.43587e14 1.85168e14i −0.810264 1.04490i
\(238\) 0 0
\(239\) 2.51042e14i 1.34697i −0.739200 0.673486i \(-0.764796\pi\)
0.739200 0.673486i \(-0.235204\pi\)
\(240\) 0 0
\(241\) −1.08817e14 −0.555384 −0.277692 0.960670i \(-0.589569\pi\)
−0.277692 + 0.960670i \(0.589569\pi\)
\(242\) 0 0
\(243\) −3.20581e13 2.03380e14i −0.155704 0.987804i
\(244\) 0 0
\(245\) 1.54257e14i 0.713259i
\(246\) 0 0
\(247\) −1.94663e14 −0.857239
\(248\) 0 0
\(249\) −3.10164e14 + 2.40514e14i −1.30135 + 1.00912i
\(250\) 0 0
\(251\) 3.07316e14i 1.22898i 0.788926 + 0.614488i \(0.210637\pi\)
−0.788926 + 0.614488i \(0.789363\pi\)
\(252\) 0 0
\(253\) 2.52093e14 0.961252
\(254\) 0 0
\(255\) 2.41001e14 + 3.10792e14i 0.876554 + 1.13039i
\(256\) 0 0
\(257\) 1.28066e14i 0.444461i 0.974994 + 0.222231i \(0.0713338\pi\)
−0.974994 + 0.222231i \(0.928666\pi\)
\(258\) 0 0
\(259\) −1.17056e14 −0.387788
\(260\) 0 0
\(261\) 1.21748e14 + 3.12979e13i 0.385139 + 0.0990083i
\(262\) 0 0
\(263\) 5.00513e14i 1.51245i 0.654312 + 0.756225i \(0.272958\pi\)
−0.654312 + 0.756225i \(0.727042\pi\)
\(264\) 0 0
\(265\) 8.80108e13 0.254133
\(266\) 0 0
\(267\) −3.10428e13 + 2.40719e13i −0.0856829 + 0.0664421i
\(268\) 0 0
\(269\) 1.92445e14i 0.507916i −0.967215 0.253958i \(-0.918267\pi\)
0.967215 0.253958i \(-0.0817325\pi\)
\(270\) 0 0
\(271\) −3.48382e14 −0.879507 −0.439754 0.898118i \(-0.644934\pi\)
−0.439754 + 0.898118i \(0.644934\pi\)
\(272\) 0 0
\(273\) −6.26625e13 8.08087e13i −0.151367 0.195201i
\(274\) 0 0
\(275\) 1.47249e14i 0.340453i
\(276\) 0 0
\(277\) −1.79176e13 −0.0396644 −0.0198322 0.999803i \(-0.506313\pi\)
−0.0198322 + 0.999803i \(0.506313\pi\)
\(278\) 0 0
\(279\) −7.00057e12 + 2.72320e13i −0.0148425 + 0.0577370i
\(280\) 0 0
\(281\) 4.57063e14i 0.928407i 0.885728 + 0.464204i \(0.153659\pi\)
−0.885728 + 0.464204i \(0.846341\pi\)
\(282\) 0 0
\(283\) −7.49541e14 −1.45907 −0.729536 0.683942i \(-0.760264\pi\)
−0.729536 + 0.683942i \(0.760264\pi\)
\(284\) 0 0
\(285\) 2.25379e14 1.74769e14i 0.420576 0.326133i
\(286\) 0 0
\(287\) 1.51150e14i 0.270469i
\(288\) 0 0
\(289\) −1.56621e15 −2.68820
\(290\) 0 0
\(291\) 3.16610e13 + 4.08295e13i 0.0521394 + 0.0672383i
\(292\) 0 0
\(293\) 6.11317e14i 0.966185i −0.875569 0.483093i \(-0.839513\pi\)
0.875569 0.483093i \(-0.160487\pi\)
\(294\) 0 0
\(295\) 5.88961e14 0.893623
\(296\) 0 0
\(297\) 2.08221e14 + 4.81757e14i 0.303380 + 0.701923i
\(298\) 0 0
\(299\) 1.07761e15i 1.50812i
\(300\) 0 0
\(301\) 1.64312e14 0.220938
\(302\) 0 0
\(303\) −1.27816e14 + 9.91139e13i −0.165169 + 0.128079i
\(304\) 0 0
\(305\) 5.94737e14i 0.738798i
\(306\) 0 0
\(307\) 7.95312e14 0.949965 0.474982 0.879995i \(-0.342454\pi\)
0.474982 + 0.879995i \(0.342454\pi\)
\(308\) 0 0
\(309\) 7.64636e14 + 9.86064e14i 0.878423 + 1.13280i
\(310\) 0 0
\(311\) 9.04430e13i 0.0999568i −0.998750 0.0499784i \(-0.984085\pi\)
0.998750 0.0499784i \(-0.0159153\pi\)
\(312\) 0 0
\(313\) −5.37834e14 −0.571982 −0.285991 0.958232i \(-0.592323\pi\)
−0.285991 + 0.958232i \(0.592323\pi\)
\(314\) 0 0
\(315\) 1.45100e14 + 3.73011e13i 0.148527 + 0.0381820i
\(316\) 0 0
\(317\) 5.80541e14i 0.572107i −0.958214 0.286054i \(-0.907656\pi\)
0.958214 0.286054i \(-0.0923436\pi\)
\(318\) 0 0
\(319\) −3.20433e14 −0.304084
\(320\) 0 0
\(321\) 1.15008e15 8.91822e14i 1.05123 0.815170i
\(322\) 0 0
\(323\) 1.55828e15i 1.37224i
\(324\) 0 0
\(325\) −6.29443e14 −0.534141
\(326\) 0 0
\(327\) 3.98376e13 + 5.13740e13i 0.0325842 + 0.0420201i
\(328\) 0 0
\(329\) 2.90234e14i 0.228861i
\(330\) 0 0
\(331\) −4.07241e14 −0.309659 −0.154829 0.987941i \(-0.549483\pi\)
−0.154829 + 0.987941i \(0.549483\pi\)
\(332\) 0 0
\(333\) 6.39405e14 2.48727e15i 0.468933 1.82413i
\(334\) 0 0
\(335\) 1.06037e14i 0.0750220i
\(336\) 0 0
\(337\) 2.19833e15 1.50076 0.750382 0.661004i \(-0.229869\pi\)
0.750382 + 0.661004i \(0.229869\pi\)
\(338\) 0 0
\(339\) 1.34579e15 1.04358e15i 0.886706 0.687589i
\(340\) 0 0
\(341\) 7.16731e13i 0.0455858i
\(342\) 0 0
\(343\) −6.56345e14 −0.403058
\(344\) 0 0
\(345\) 9.67483e14 + 1.24765e15i 0.573758 + 0.739910i
\(346\) 0 0
\(347\) 9.94469e14i 0.569658i −0.958578 0.284829i \(-0.908063\pi\)
0.958578 0.284829i \(-0.0919369\pi\)
\(348\) 0 0
\(349\) −1.93671e15 −1.07180 −0.535898 0.844283i \(-0.680027\pi\)
−0.535898 + 0.844283i \(0.680027\pi\)
\(350\) 0 0
\(351\) 2.05935e15 8.90078e14i 1.10126 0.475976i
\(352\) 0 0
\(353\) 2.70230e15i 1.39664i −0.715784 0.698322i \(-0.753930\pi\)
0.715784 0.698322i \(-0.246070\pi\)
\(354\) 0 0
\(355\) −1.62668e15 −0.812701
\(356\) 0 0
\(357\) −6.46875e14 + 5.01614e14i −0.312472 + 0.242304i
\(358\) 0 0
\(359\) 3.96427e15i 1.85181i −0.377753 0.925906i \(-0.623303\pi\)
0.377753 0.925906i \(-0.376697\pi\)
\(360\) 0 0
\(361\) −1.08329e15 −0.489441
\(362\) 0 0
\(363\) 5.82205e14 + 7.50804e14i 0.254470 + 0.328161i
\(364\) 0 0
\(365\) 7.92487e13i 0.0335147i
\(366\) 0 0
\(367\) −4.69175e14 −0.192016 −0.0960082 0.995381i \(-0.530608\pi\)
−0.0960082 + 0.995381i \(0.530608\pi\)
\(368\) 0 0
\(369\) −3.21172e15 8.25642e14i −1.27227 0.327065i
\(370\) 0 0
\(371\) 1.83184e14i 0.0702495i
\(372\) 0 0
\(373\) 4.09671e15 1.52119 0.760593 0.649229i \(-0.224908\pi\)
0.760593 + 0.649229i \(0.224908\pi\)
\(374\) 0 0
\(375\) 2.36561e15 1.83440e15i 0.850660 0.659638i
\(376\) 0 0
\(377\) 1.36975e15i 0.477081i
\(378\) 0 0
\(379\) 2.91887e15 0.984872 0.492436 0.870349i \(-0.336107\pi\)
0.492436 + 0.870349i \(0.336107\pi\)
\(380\) 0 0
\(381\) 1.16386e15 + 1.50090e15i 0.380497 + 0.490684i
\(382\) 0 0
\(383\) 2.39815e15i 0.759772i 0.925033 + 0.379886i \(0.124037\pi\)
−0.925033 + 0.379886i \(0.875963\pi\)
\(384\) 0 0
\(385\) −3.81896e14 −0.117268
\(386\) 0 0
\(387\) −8.97539e14 + 3.49140e15i −0.267170 + 1.03928i
\(388\) 0 0
\(389\) 5.28945e15i 1.52656i 0.646070 + 0.763278i \(0.276411\pi\)
−0.646070 + 0.763278i \(0.723589\pi\)
\(390\) 0 0
\(391\) −8.62632e15 −2.41415
\(392\) 0 0
\(393\) 2.41765e15 1.87475e15i 0.656204 0.508849i
\(394\) 0 0
\(395\) 3.74073e15i 0.984859i
\(396\) 0 0
\(397\) −4.66477e15 −1.19148 −0.595741 0.803176i \(-0.703142\pi\)
−0.595741 + 0.803176i \(0.703142\pi\)
\(398\) 0 0
\(399\) 3.63759e14 + 4.69099e14i 0.0901522 + 0.116259i
\(400\) 0 0
\(401\) 6.11325e15i 1.47030i −0.677905 0.735150i \(-0.737112\pi\)
0.677905 0.735150i \(-0.262888\pi\)
\(402\) 0 0
\(403\) −3.06379e14 −0.0715202
\(404\) 0 0
\(405\) −1.58519e15 + 2.87941e15i −0.359212 + 0.652490i
\(406\) 0 0
\(407\) 6.54635e15i 1.44023i
\(408\) 0 0
\(409\) 2.86429e15 0.611895 0.305948 0.952048i \(-0.401027\pi\)
0.305948 + 0.952048i \(0.401027\pi\)
\(410\) 0 0
\(411\) −4.54026e15 + 3.52071e15i −0.941954 + 0.730431i
\(412\) 0 0
\(413\) 1.22585e15i 0.247023i
\(414\) 0 0
\(415\) 6.26586e15 1.22657
\(416\) 0 0
\(417\) 1.99970e15 + 2.57879e15i 0.380320 + 0.490456i
\(418\) 0 0
\(419\) 8.14846e15i 1.50588i −0.658087 0.752942i \(-0.728634\pi\)
0.658087 0.752942i \(-0.271366\pi\)
\(420\) 0 0
\(421\) −7.15780e15 −1.28554 −0.642772 0.766057i \(-0.722216\pi\)
−0.642772 + 0.766057i \(0.722216\pi\)
\(422\) 0 0
\(423\) −6.16704e15 1.58537e15i −1.07655 0.276751i
\(424\) 0 0
\(425\) 5.03870e15i 0.855037i
\(426\) 0 0
\(427\) −1.23787e15 −0.204225
\(428\) 0 0
\(429\) −4.51923e15 + 3.50440e15i −0.724971 + 0.562173i
\(430\) 0 0
\(431\) 8.34343e13i 0.0130161i −0.999979 0.00650805i \(-0.997928\pi\)
0.999979 0.00650805i \(-0.00207159\pi\)
\(432\) 0 0
\(433\) −1.28270e15 −0.194624 −0.0973121 0.995254i \(-0.531024\pi\)
−0.0973121 + 0.995254i \(0.531024\pi\)
\(434\) 0 0
\(435\) −1.22976e15 1.58588e15i −0.181503 0.234064i
\(436\) 0 0
\(437\) 6.25560e15i 0.898216i
\(438\) 0 0
\(439\) 1.28612e16 1.79678 0.898392 0.439194i \(-0.144736\pi\)
0.898392 + 0.439194i \(0.144736\pi\)
\(440\) 0 0
\(441\) 1.75379e15 6.82218e15i 0.238422 0.927453i
\(442\) 0 0
\(443\) 7.99552e14i 0.105785i −0.998600 0.0528925i \(-0.983156\pi\)
0.998600 0.0528925i \(-0.0168441\pi\)
\(444\) 0 0
\(445\) 6.27121e14 0.0807590
\(446\) 0 0
\(447\) −3.43726e15 + 2.66540e15i −0.430891 + 0.334132i
\(448\) 0 0
\(449\) 6.16075e15i 0.751892i −0.926642 0.375946i \(-0.877318\pi\)
0.926642 0.375946i \(-0.122682\pi\)
\(450\) 0 0
\(451\) 8.45308e15 1.00451
\(452\) 0 0
\(453\) −2.05600e15 2.65139e15i −0.237922 0.306821i
\(454\) 0 0
\(455\) 1.63248e15i 0.183984i
\(456\) 0 0
\(457\) 6.71139e15 0.736742 0.368371 0.929679i \(-0.379916\pi\)
0.368371 + 0.929679i \(0.379916\pi\)
\(458\) 0 0
\(459\) −7.12509e15 1.64852e16i −0.761928 1.76286i
\(460\) 0 0
\(461\) 1.72904e15i 0.180136i −0.995936 0.0900680i \(-0.971292\pi\)
0.995936 0.0900680i \(-0.0287084\pi\)
\(462\) 0 0
\(463\) −1.79448e16 −1.82160 −0.910801 0.412846i \(-0.864535\pi\)
−0.910801 + 0.412846i \(0.864535\pi\)
\(464\) 0 0
\(465\) 3.54723e14 2.75067e14i 0.0350890 0.0272095i
\(466\) 0 0
\(467\) 4.84904e15i 0.467471i 0.972300 + 0.233735i \(0.0750949\pi\)
−0.972300 + 0.233735i \(0.924905\pi\)
\(468\) 0 0
\(469\) −2.20703e14 −0.0207382
\(470\) 0 0
\(471\) 9.73567e15 + 1.25550e16i 0.891745 + 1.14998i
\(472\) 0 0
\(473\) 9.18917e15i 0.820558i
\(474\) 0 0
\(475\) 3.65395e15 0.318127
\(476\) 0 0
\(477\) −3.89238e15 1.00062e15i −0.330450 0.0849493i
\(478\) 0 0
\(479\) 3.53107e15i 0.292343i −0.989259 0.146172i \(-0.953305\pi\)
0.989259 0.146172i \(-0.0466952\pi\)
\(480\) 0 0
\(481\) 2.79835e16 2.25960
\(482\) 0 0
\(483\) −2.59683e15 + 2.01369e15i −0.204532 + 0.158603i
\(484\) 0 0
\(485\) 8.24830e14i 0.0633744i
\(486\) 0 0
\(487\) 1.32795e16 0.995427 0.497713 0.867342i \(-0.334173\pi\)
0.497713 + 0.867342i \(0.334173\pi\)
\(488\) 0 0
\(489\) −7.87059e15 1.01498e16i −0.575644 0.742342i
\(490\) 0 0
\(491\) 3.46645e15i 0.247398i 0.992320 + 0.123699i \(0.0394757\pi\)
−0.992320 + 0.123699i \(0.960524\pi\)
\(492\) 0 0
\(493\) 1.09648e16 0.763697
\(494\) 0 0
\(495\) 2.08607e15 8.11473e15i 0.141807 0.551624i
\(496\) 0 0
\(497\) 3.38572e15i 0.224653i
\(498\) 0 0
\(499\) 6.85958e15 0.444318 0.222159 0.975010i \(-0.428690\pi\)
0.222159 + 0.975010i \(0.428690\pi\)
\(500\) 0 0
\(501\) −1.60094e16 + 1.24144e16i −1.01239 + 0.785052i
\(502\) 0 0
\(503\) 1.86257e16i 1.15002i −0.818148 0.575008i \(-0.804999\pi\)
0.818148 0.575008i \(-0.195001\pi\)
\(504\) 0 0
\(505\) 2.58211e15 0.155678
\(506\) 0 0
\(507\) 4.57235e15 + 5.89644e15i 0.269211 + 0.347170i
\(508\) 0 0
\(509\) 1.83953e16i 1.05779i 0.848686 + 0.528897i \(0.177394\pi\)
−0.848686 + 0.528897i \(0.822606\pi\)
\(510\) 0 0
\(511\) −1.64946e14 −0.00926440
\(512\) 0 0
\(513\) −1.19547e16 + 5.16695e15i −0.655893 + 0.283485i
\(514\) 0 0
\(515\) 1.99202e16i 1.06771i
\(516\) 0 0
\(517\) 1.62313e16 0.849984
\(518\) 0 0
\(519\) 9.58753e15 7.43458e15i 0.490572 0.380410i
\(520\) 0 0
\(521\) 1.10846e16i 0.554237i −0.960836 0.277118i \(-0.910621\pi\)
0.960836 0.277118i \(-0.0893794\pi\)
\(522\) 0 0
\(523\) 1.85778e16 0.907786 0.453893 0.891056i \(-0.350035\pi\)
0.453893 + 0.891056i \(0.350035\pi\)
\(524\) 0 0
\(525\) 1.17621e15 + 1.51683e15i 0.0561734 + 0.0724404i
\(526\) 0 0
\(527\) 2.45257e15i 0.114487i
\(528\) 0 0
\(529\) −1.27151e16 −0.580211
\(530\) 0 0
\(531\) −2.60475e16 6.69607e15i −1.16198 0.298712i
\(532\) 0 0
\(533\) 3.61341e16i 1.57599i
\(534\) 0 0
\(535\) −2.32337e16 −0.990822
\(536\) 0 0
\(537\) 4.78485e15 3.71038e15i 0.199537 0.154729i
\(538\) 0 0
\(539\) 1.79556e16i 0.732264i
\(540\) 0 0
\(541\) −7.82042e15 −0.311922 −0.155961 0.987763i \(-0.549847\pi\)
−0.155961 + 0.987763i \(0.549847\pi\)
\(542\) 0 0
\(543\) 7.22258e15 + 9.31414e15i 0.281769 + 0.363366i
\(544\) 0 0
\(545\) 1.03785e15i 0.0396054i
\(546\) 0 0
\(547\) 7.99398e15 0.298428 0.149214 0.988805i \(-0.452326\pi\)
0.149214 + 0.988805i \(0.452326\pi\)
\(548\) 0 0
\(549\) 6.76174e15 2.63030e16i 0.246959 0.960662i
\(550\) 0 0
\(551\) 7.95145e15i 0.284143i
\(552\) 0 0
\(553\) −7.78586e15 −0.272243
\(554\) 0 0
\(555\) −3.23990e16 + 2.51236e16i −1.10860 + 0.859655i
\(556\) 0 0
\(557\) 4.08661e16i 1.36846i 0.729267 + 0.684229i \(0.239861\pi\)
−0.729267 + 0.684229i \(0.760139\pi\)
\(558\) 0 0
\(559\) −3.92807e16 −1.28738
\(560\) 0 0
\(561\) 2.80528e16 + 3.61765e16i 0.899910 + 1.16051i
\(562\) 0 0
\(563\) 4.26547e16i 1.33942i 0.742624 + 0.669709i \(0.233581\pi\)
−0.742624 + 0.669709i \(0.766419\pi\)
\(564\) 0 0
\(565\) −2.71874e16 −0.835751
\(566\) 0 0
\(567\) −5.99314e15 3.29938e15i −0.180367 0.0992964i
\(568\) 0 0
\(569\) 1.97852e16i 0.582997i 0.956571 + 0.291499i \(0.0941539\pi\)
−0.956571 + 0.291499i \(0.905846\pi\)
\(570\) 0 0
\(571\) 3.60533e16 1.04023 0.520114 0.854097i \(-0.325890\pi\)
0.520114 + 0.854097i \(0.325890\pi\)
\(572\) 0 0
\(573\) 1.57365e16 1.22027e16i 0.444610 0.344770i
\(574\) 0 0
\(575\) 2.02275e16i 0.559674i
\(576\) 0 0
\(577\) −4.01099e16 −1.08692 −0.543459 0.839435i \(-0.682886\pi\)
−0.543459 + 0.839435i \(0.682886\pi\)
\(578\) 0 0
\(579\) −6.76895e15 8.72914e15i −0.179659 0.231686i
\(580\) 0 0
\(581\) 1.30416e16i 0.339058i
\(582\) 0 0
\(583\) 1.02445e16 0.260904
\(584\) 0 0
\(585\) −3.46878e16 8.91725e15i −0.865450 0.222483i
\(586\) 0 0
\(587\) 3.80370e16i 0.929774i 0.885370 + 0.464887i \(0.153905\pi\)
−0.885370 + 0.464887i \(0.846095\pi\)
\(588\) 0 0
\(589\) 1.77855e15 0.0425964
\(590\) 0 0
\(591\) 2.01603e16 1.56332e16i 0.473121 0.366878i
\(592\) 0 0
\(593\) 7.12143e16i 1.63772i 0.573996 + 0.818858i \(0.305393\pi\)
−0.573996 + 0.818858i \(0.694607\pi\)
\(594\) 0 0
\(595\) 1.30680e16 0.294515
\(596\) 0 0
\(597\) 4.67868e16 + 6.03355e16i 1.03342 + 1.33268i
\(598\) 0 0
\(599\) 1.66670e16i 0.360825i −0.983591 0.180412i \(-0.942257\pi\)
0.983591 0.180412i \(-0.0577432\pi\)
\(600\) 0 0
\(601\) −2.65649e16 −0.563717 −0.281859 0.959456i \(-0.590951\pi\)
−0.281859 + 0.959456i \(0.590951\pi\)
\(602\) 0 0
\(603\) 1.20557e15 4.68962e15i 0.0250777 0.0975514i
\(604\) 0 0
\(605\) 1.51676e16i 0.309303i
\(606\) 0 0
\(607\) −5.95925e15 −0.119140 −0.0595702 0.998224i \(-0.518973\pi\)
−0.0595702 + 0.998224i \(0.518973\pi\)
\(608\) 0 0
\(609\) 3.30081e15 2.55959e15i 0.0647019 0.0501726i
\(610\) 0 0
\(611\) 6.93836e16i 1.33355i
\(612\) 0 0
\(613\) −1.45442e16 −0.274111 −0.137056 0.990563i \(-0.543764\pi\)
−0.137056 + 0.990563i \(0.543764\pi\)
\(614\) 0 0
\(615\) 3.24412e16 + 4.18358e16i 0.599579 + 0.773209i
\(616\) 0 0
\(617\) 5.45352e15i 0.0988475i 0.998778 + 0.0494238i \(0.0157385\pi\)
−0.998778 + 0.0494238i \(0.984262\pi\)
\(618\) 0 0
\(619\) −9.81167e16 −1.74421 −0.872106 0.489317i \(-0.837246\pi\)
−0.872106 + 0.489317i \(0.837246\pi\)
\(620\) 0 0
\(621\) −2.86032e16 6.61785e16i −0.498729 1.15390i
\(622\) 0 0
\(623\) 1.30527e15i 0.0223241i
\(624\) 0 0
\(625\) −2.12523e16 −0.356554
\(626\) 0 0
\(627\) 2.62344e16 2.03432e16i 0.431783 0.334823i
\(628\) 0 0
\(629\) 2.24008e17i 3.61710i
\(630\) 0 0
\(631\) −9.73307e16 −1.54196 −0.770981 0.636858i \(-0.780234\pi\)
−0.770981 + 0.636858i \(0.780234\pi\)
\(632\) 0 0
\(633\) 1.30234e16 + 1.67947e16i 0.202442 + 0.261066i
\(634\) 0 0
\(635\) 3.03208e16i 0.462486i
\(636\) 0 0
\(637\) 7.67543e16 1.14886
\(638\) 0 0
\(639\) 7.19417e16 + 1.84942e16i 1.05676 + 0.271662i
\(640\) 0 0
\(641\) 4.66947e16i 0.673161i 0.941655 + 0.336581i \(0.109271\pi\)
−0.941655 + 0.336581i \(0.890729\pi\)
\(642\) 0 0
\(643\) 4.61235e16 0.652614 0.326307 0.945264i \(-0.394196\pi\)
0.326307 + 0.945264i \(0.394196\pi\)
\(644\) 0 0
\(645\) 4.54788e16 3.52662e16i 0.631613 0.489779i
\(646\) 0 0
\(647\) 4.10286e16i 0.559321i 0.960099 + 0.279661i \(0.0902219\pi\)
−0.960099 + 0.279661i \(0.909778\pi\)
\(648\) 0 0
\(649\) 6.85556e16 0.917434
\(650\) 0 0
\(651\) 5.72518e14 + 7.38311e14i 0.00752148 + 0.00969959i
\(652\) 0 0
\(653\) 3.87096e16i 0.499275i 0.968339 + 0.249637i \(0.0803114\pi\)
−0.968339 + 0.249637i \(0.919689\pi\)
\(654\) 0 0
\(655\) −4.88409e16 −0.618495
\(656\) 0 0
\(657\) 9.01002e14 3.50487e15i 0.0112030 0.0435792i
\(658\) 0 0
\(659\) 4.38378e16i 0.535225i −0.963527 0.267612i \(-0.913765\pi\)
0.963527 0.267612i \(-0.0862347\pi\)
\(660\) 0 0
\(661\) −1.36247e16 −0.163350 −0.0816749 0.996659i \(-0.526027\pi\)
−0.0816749 + 0.996659i \(0.526027\pi\)
\(662\) 0 0
\(663\) 1.54643e17 1.19916e17i 1.82074 1.41188i
\(664\) 0 0
\(665\) 9.47663e15i 0.109578i
\(666\) 0 0
\(667\) 4.40176e16 0.499886
\(668\) 0 0
\(669\) 2.03021e16 + 2.61813e16i 0.226456 + 0.292035i
\(670\) 0 0
\(671\) 6.92280e16i 0.758484i
\(672\) 0 0
\(673\) −4.39005e16 −0.472475 −0.236237 0.971695i \(-0.575914\pi\)
−0.236237 + 0.971695i \(0.575914\pi\)
\(674\) 0 0
\(675\) −3.86554e16 + 1.67073e16i −0.408684 + 0.176638i
\(676\) 0 0
\(677\) 3.87725e16i 0.402710i 0.979518 + 0.201355i \(0.0645345\pi\)
−0.979518 + 0.201355i \(0.935466\pi\)
\(678\) 0 0
\(679\) 1.71678e15 0.0175185
\(680\) 0 0
\(681\) −2.34422e16 + 1.81780e16i −0.235025 + 0.182249i
\(682\) 0 0
\(683\) 1.81136e17i 1.78436i −0.451684 0.892178i \(-0.649177\pi\)
0.451684 0.892178i \(-0.350823\pi\)
\(684\) 0 0
\(685\) 9.17213e16 0.887824
\(686\) 0 0
\(687\) 6.40371e16 + 8.25813e16i 0.609103 + 0.785491i
\(688\) 0 0
\(689\) 4.37921e16i 0.409336i
\(690\) 0 0
\(691\) 1.41596e17 1.30072 0.650359 0.759627i \(-0.274619\pi\)
0.650359 + 0.759627i \(0.274619\pi\)
\(692\) 0 0
\(693\) 1.68898e16 + 4.34189e15i 0.152484 + 0.0391994i
\(694\) 0 0
\(695\) 5.20962e16i 0.462271i
\(696\) 0 0
\(697\) −2.89254e17 −2.52280
\(698\) 0 0
\(699\) −1.35582e17 + 1.05136e17i −1.16235 + 0.901338i
\(700\) 0 0
\(701\) 1.22736e16i 0.103434i 0.998662 + 0.0517172i \(0.0164695\pi\)
−0.998662 + 0.0517172i \(0.983531\pi\)
\(702\) 0 0
\(703\) −1.62446e17 −1.34579
\(704\) 0 0
\(705\) 6.22926e16 + 8.03317e16i 0.507343 + 0.654263i
\(706\) 0 0
\(707\) 5.37434e15i 0.0430337i
\(708\) 0 0
\(709\) 8.99842e16 0.708417 0.354208 0.935167i \(-0.384750\pi\)
0.354208 + 0.935167i \(0.384750\pi\)
\(710\) 0 0
\(711\) 4.25295e16 1.65438e17i 0.329210 1.28061i
\(712\) 0 0
\(713\) 9.84566e15i 0.0749389i
\(714\) 0 0
\(715\) 9.12965e16 0.683310
\(716\) 0 0
\(717\) 1.44622e17 1.12146e17i 1.06444 0.825411i
\(718\) 0 0
\(719\) 1.59451e17i 1.15413i 0.816698 + 0.577065i \(0.195802\pi\)
−0.816698 + 0.577065i \(0.804198\pi\)
\(720\) 0 0
\(721\) 4.14615e16 0.295144
\(722\) 0 0
\(723\) −4.86110e16 6.26881e16i −0.340334 0.438890i
\(724\) 0 0
\(725\) 2.57110e16i 0.177048i
\(726\) 0 0
\(727\) −1.01477e17 −0.687324 −0.343662 0.939093i \(-0.611667\pi\)
−0.343662 + 0.939093i \(0.611667\pi\)
\(728\) 0 0
\(729\) 1.02844e17 1.09323e17i 0.685194 0.728361i
\(730\) 0 0
\(731\) 3.14442e17i 2.06080i
\(732\) 0 0
\(733\) −2.48565e17 −1.60257 −0.801283 0.598286i \(-0.795849\pi\)
−0.801283 + 0.598286i \(0.795849\pi\)
\(734\) 0 0
\(735\) −8.88655e16 + 6.89101e16i −0.563650 + 0.437078i
\(736\) 0 0
\(737\) 1.23428e16i 0.0770210i
\(738\) 0 0
\(739\) 5.84812e16 0.359046 0.179523 0.983754i \(-0.442545\pi\)
0.179523 + 0.983754i \(0.442545\pi\)
\(740\) 0 0
\(741\) −8.69606e16 1.12143e17i −0.525307 0.677429i
\(742\) 0 0
\(743\) 1.34165e17i 0.797454i −0.917070 0.398727i \(-0.869452\pi\)
0.917070 0.398727i \(-0.130548\pi\)
\(744\) 0 0
\(745\) 6.94389e16 0.406130
\(746\) 0 0
\(747\) −2.77115e17 7.12384e16i −1.59491 0.410006i
\(748\) 0 0
\(749\) 4.83580e16i 0.273891i
\(750\) 0 0
\(751\) 6.37267e16 0.355207 0.177604 0.984102i \(-0.443165\pi\)
0.177604 + 0.984102i \(0.443165\pi\)
\(752\) 0 0
\(753\) −1.77042e17 + 1.37286e17i −0.971192 + 0.753104i
\(754\) 0 0
\(755\) 5.35629e16i 0.289189i
\(756\) 0 0
\(757\) 9.78521e15 0.0519990 0.0259995 0.999662i \(-0.491723\pi\)
0.0259995 + 0.999662i \(0.491723\pi\)
\(758\) 0 0
\(759\) 1.12616e17 + 1.45228e17i 0.589046 + 0.759625i
\(760\) 0 0
\(761\) 2.53164e17i 1.30345i 0.758456 + 0.651724i \(0.225954\pi\)
−0.758456 + 0.651724i \(0.774046\pi\)
\(762\) 0 0
\(763\) 2.16015e15 0.0109480
\(764\) 0 0
\(765\) −7.13828e16 + 2.77677e17i −0.356143 + 1.38539i
\(766\) 0 0
\(767\) 2.93053e17i 1.43937i
\(768\) 0 0
\(769\) 9.51680e16 0.460185 0.230093 0.973169i \(-0.426097\pi\)
0.230093 + 0.973169i \(0.426097\pi\)
\(770\) 0 0
\(771\) −7.37772e16 + 5.72100e16i −0.351234 + 0.272362i
\(772\) 0 0
\(773\) 3.40819e17i 1.59752i 0.601649 + 0.798761i \(0.294511\pi\)
−0.601649 + 0.798761i \(0.705489\pi\)
\(774\) 0 0
\(775\) 5.75092e15 0.0265416
\(776\) 0 0