Properties

Label 48.19.e.b.17.4
Level $48$
Weight $19$
Character 48.17
Analytic conductor $98.585$
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] = [48,19,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, 19, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("48.17");
 
S:= CuspForms(chi, 19);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 19 \)
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: \(98.5853461007\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.0.601940665.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + 123x^{2} - 1744x + 16016 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{15}\cdot 3^{11} \)
Twist minimal: no (minimal twist has level 3)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 17.4
Root \(-6.07949 + 12.9551i\) of defining polynomial
Character \(\chi\) \(=\) 48.17
Dual form 48.19.e.b.17.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(4234.02 + 19222.2i) q^{3} -1.14247e6i q^{5} +9.81043e6 q^{7} +(-3.51567e8 + 1.62775e8i) q^{9} +O(q^{10})\) \(q+(4234.02 + 19222.2i) q^{3} -1.14247e6i q^{5} +9.81043e6 q^{7} +(-3.51567e8 + 1.62775e8i) q^{9} +2.16393e9i q^{11} -1.47189e10 q^{13} +(2.19608e10 - 4.83724e9i) q^{15} -1.36506e10i q^{17} +2.38919e11 q^{19} +(4.15376e10 + 1.88578e11i) q^{21} -5.70649e11i q^{23} +2.50946e12 q^{25} +(-4.61743e12 - 6.06870e12i) q^{27} +1.35326e13i q^{29} +1.17012e13 q^{31} +(-4.15954e13 + 9.16211e12i) q^{33} -1.12081e13i q^{35} -1.26080e14 q^{37} +(-6.23201e13 - 2.82930e14i) q^{39} -3.28662e14i q^{41} -8.40904e14 q^{43} +(1.85965e14 + 4.01654e14i) q^{45} +9.97479e14i q^{47} -1.53217e15 q^{49} +(2.62395e14 - 5.77971e13i) q^{51} -5.45882e15i q^{53} +2.47222e15 q^{55} +(1.01159e15 + 4.59255e15i) q^{57} -8.03632e14i q^{59} +1.04106e16 q^{61} +(-3.44902e15 + 1.59689e15i) q^{63} +1.68159e16i q^{65} +1.50639e16 q^{67} +(1.09691e16 - 2.41614e15i) q^{69} -4.47214e16i q^{71} -3.92287e16 q^{73} +(1.06251e16 + 4.82374e16i) q^{75} +2.12290e16i q^{77} +7.20817e16 q^{79} +(9.71035e16 - 1.14452e17i) q^{81} -1.02835e17i q^{83} -1.55954e16 q^{85} +(-2.60126e17 + 5.72973e16i) q^{87} -5.12684e17i q^{89} -1.44399e17 q^{91} +(4.95431e16 + 2.24923e17i) q^{93} -2.72957e17i q^{95} -7.28759e17 q^{97} +(-3.52232e17 - 7.60764e17i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 15876 q^{3} + 95744152 q^{7} - 885341340 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 15876 q^{3} + 95744152 q^{7} - 885341340 q^{9} - 5426221528 q^{13} + 68287821120 q^{15} - 191416649480 q^{19} - 843499414296 q^{21} + 11407599454180 q^{25} + 4632207691356 q^{27} - 35728415085608 q^{31} + 12242871023040 q^{33} - 475299833502232 q^{37} - 416909545005096 q^{39} - 15\!\cdots\!92 q^{43}+ \cdots - 30\!\cdots\!60 q^{99}+O(q^{100}) \) 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
\(3\) 4234.02 + 19222.2i 0.215111 + 0.976590i
\(4\) 0 0
\(5\) 1.14247e6i 0.584944i −0.956274 0.292472i \(-0.905522\pi\)
0.956274 0.292472i \(-0.0944779\pi\)
\(6\) 0 0
\(7\) 9.81043e6 0.243112 0.121556 0.992585i \(-0.461212\pi\)
0.121556 + 0.992585i \(0.461212\pi\)
\(8\) 0 0
\(9\) −3.51567e8 + 1.62775e8i −0.907455 + 0.420150i
\(10\) 0 0
\(11\) 2.16393e9i 0.917716i 0.888510 + 0.458858i \(0.151741\pi\)
−0.888510 + 0.458858i \(0.848259\pi\)
\(12\) 0 0
\(13\) −1.47189e10 −1.38799 −0.693993 0.719982i \(-0.744150\pi\)
−0.693993 + 0.719982i \(0.744150\pi\)
\(14\) 0 0
\(15\) 2.19608e10 4.83724e9i 0.571251 0.125828i
\(16\) 0 0
\(17\) 1.36506e10i 0.115110i −0.998342 0.0575549i \(-0.981670\pi\)
0.998342 0.0575549i \(-0.0183304\pi\)
\(18\) 0 0
\(19\) 2.38919e11 0.740402 0.370201 0.928952i \(-0.379289\pi\)
0.370201 + 0.928952i \(0.379289\pi\)
\(20\) 0 0
\(21\) 4.15376e10 + 1.88578e11i 0.0522959 + 0.237420i
\(22\) 0 0
\(23\) 5.70649e11i 0.316824i −0.987373 0.158412i \(-0.949363\pi\)
0.987373 0.158412i \(-0.0506375\pi\)
\(24\) 0 0
\(25\) 2.50946e12 0.657840
\(26\) 0 0
\(27\) −4.61743e12 6.06870e12i −0.605517 0.795832i
\(28\) 0 0
\(29\) 1.35326e13i 0.932823i 0.884568 + 0.466411i \(0.154453\pi\)
−0.884568 + 0.466411i \(0.845547\pi\)
\(30\) 0 0
\(31\) 1.17012e13 0.442562 0.221281 0.975210i \(-0.428976\pi\)
0.221281 + 0.975210i \(0.428976\pi\)
\(32\) 0 0
\(33\) −4.15954e13 + 9.16211e12i −0.896232 + 0.197410i
\(34\) 0 0
\(35\) 1.12081e13i 0.142207i
\(36\) 0 0
\(37\) −1.26080e14 −0.970132 −0.485066 0.874478i \(-0.661204\pi\)
−0.485066 + 0.874478i \(0.661204\pi\)
\(38\) 0 0
\(39\) −6.23201e13 2.82930e14i −0.298571 1.35549i
\(40\) 0 0
\(41\) 3.28662e14i 1.00391i −0.864894 0.501955i \(-0.832614\pi\)
0.864894 0.501955i \(-0.167386\pi\)
\(42\) 0 0
\(43\) −8.40904e14 −1.67313 −0.836566 0.547866i \(-0.815440\pi\)
−0.836566 + 0.547866i \(0.815440\pi\)
\(44\) 0 0
\(45\) 1.85965e14 + 4.01654e14i 0.245764 + 0.530811i
\(46\) 0 0
\(47\) 9.97479e14i 0.891298i 0.895208 + 0.445649i \(0.147027\pi\)
−0.895208 + 0.445649i \(0.852973\pi\)
\(48\) 0 0
\(49\) −1.53217e15 −0.940897
\(50\) 0 0
\(51\) 2.62395e14 5.77971e13i 0.112415 0.0247613i
\(52\) 0 0
\(53\) 5.45882e15i 1.65431i −0.561977 0.827153i \(-0.689959\pi\)
0.561977 0.827153i \(-0.310041\pi\)
\(54\) 0 0
\(55\) 2.47222e15 0.536813
\(56\) 0 0
\(57\) 1.01159e15 + 4.59255e15i 0.159268 + 0.723069i
\(58\) 0 0
\(59\) 8.03632e14i 0.0927660i −0.998924 0.0463830i \(-0.985231\pi\)
0.998924 0.0463830i \(-0.0147695\pi\)
\(60\) 0 0
\(61\) 1.04106e16 0.890243 0.445121 0.895470i \(-0.353161\pi\)
0.445121 + 0.895470i \(0.353161\pi\)
\(62\) 0 0
\(63\) −3.44902e15 + 1.59689e15i −0.220613 + 0.102143i
\(64\) 0 0
\(65\) 1.68159e16i 0.811894i
\(66\) 0 0
\(67\) 1.50639e16 0.553685 0.276843 0.960915i \(-0.410712\pi\)
0.276843 + 0.960915i \(0.410712\pi\)
\(68\) 0 0
\(69\) 1.09691e16 2.41614e15i 0.309407 0.0681523i
\(70\) 0 0
\(71\) 4.47214e16i 0.975417i −0.873007 0.487709i \(-0.837833\pi\)
0.873007 0.487709i \(-0.162167\pi\)
\(72\) 0 0
\(73\) −3.92287e16 −0.666344 −0.333172 0.942866i \(-0.608119\pi\)
−0.333172 + 0.942866i \(0.608119\pi\)
\(74\) 0 0
\(75\) 1.06251e16 + 4.82374e16i 0.141508 + 0.642440i
\(76\) 0 0
\(77\) 2.12290e16i 0.223107i
\(78\) 0 0
\(79\) 7.20817e16 0.601425 0.300712 0.953715i \(-0.402776\pi\)
0.300712 + 0.953715i \(0.402776\pi\)
\(80\) 0 0
\(81\) 9.71035e16 1.14452e17i 0.646948 0.762534i
\(82\) 0 0
\(83\) 1.02835e17i 0.550093i −0.961431 0.275047i \(-0.911307\pi\)
0.961431 0.275047i \(-0.0886933\pi\)
\(84\) 0 0
\(85\) −1.55954e16 −0.0673328
\(86\) 0 0
\(87\) −2.60126e17 + 5.72973e16i −0.910985 + 0.200660i
\(88\) 0 0
\(89\) 5.12684e17i 1.46332i −0.681669 0.731661i \(-0.738746\pi\)
0.681669 0.731661i \(-0.261254\pi\)
\(90\) 0 0
\(91\) −1.44399e17 −0.337435
\(92\) 0 0
\(93\) 4.95431e16 + 2.24923e17i 0.0951999 + 0.432202i
\(94\) 0 0
\(95\) 2.72957e17i 0.433094i
\(96\) 0 0
\(97\) −7.28759e17 −0.958602 −0.479301 0.877651i \(-0.659110\pi\)
−0.479301 + 0.877651i \(0.659110\pi\)
\(98\) 0 0
\(99\) −3.52232e17 7.60764e17i −0.385578 0.832785i
\(100\) 0 0
\(101\) 1.15126e18i 1.05264i −0.850286 0.526321i \(-0.823571\pi\)
0.850286 0.526321i \(-0.176429\pi\)
\(102\) 0 0
\(103\) 1.83618e18 1.40728 0.703638 0.710559i \(-0.251558\pi\)
0.703638 + 0.710559i \(0.251558\pi\)
\(104\) 0 0
\(105\) 2.15445e17 4.74554e16i 0.138878 0.0305902i
\(106\) 0 0
\(107\) 1.30924e18i 0.712140i −0.934459 0.356070i \(-0.884117\pi\)
0.934459 0.356070i \(-0.115883\pi\)
\(108\) 0 0
\(109\) 9.37377e17 0.431594 0.215797 0.976438i \(-0.430765\pi\)
0.215797 + 0.976438i \(0.430765\pi\)
\(110\) 0 0
\(111\) −5.33826e17 2.42354e18i −0.208686 0.947420i
\(112\) 0 0
\(113\) 5.05201e17i 0.168174i 0.996458 + 0.0840868i \(0.0267973\pi\)
−0.996458 + 0.0840868i \(0.973203\pi\)
\(114\) 0 0
\(115\) −6.51949e17 −0.185325
\(116\) 0 0
\(117\) 5.17467e18 2.39586e18i 1.25953 0.583162i
\(118\) 0 0
\(119\) 1.33918e17i 0.0279845i
\(120\) 0 0
\(121\) 8.77344e17 0.157798
\(122\) 0 0
\(123\) 6.31761e18 1.39156e18i 0.980408 0.215952i
\(124\) 0 0
\(125\) 7.22516e18i 0.969744i
\(126\) 0 0
\(127\) 8.86372e18 1.03129 0.515647 0.856801i \(-0.327552\pi\)
0.515647 + 0.856801i \(0.327552\pi\)
\(128\) 0 0
\(129\) −3.56041e18 1.61640e19i −0.359909 1.63396i
\(130\) 0 0
\(131\) 1.50395e19i 1.32371i −0.749632 0.661855i \(-0.769769\pi\)
0.749632 0.661855i \(-0.230231\pi\)
\(132\) 0 0
\(133\) 2.34389e18 0.180000
\(134\) 0 0
\(135\) −6.93330e18 + 5.27527e18i −0.465518 + 0.354194i
\(136\) 0 0
\(137\) 7.91047e18i 0.465283i −0.972563 0.232641i \(-0.925263\pi\)
0.972563 0.232641i \(-0.0747369\pi\)
\(138\) 0 0
\(139\) −2.96560e19 −1.53102 −0.765508 0.643426i \(-0.777512\pi\)
−0.765508 + 0.643426i \(0.777512\pi\)
\(140\) 0 0
\(141\) −1.91738e19 + 4.22335e18i −0.870433 + 0.191728i
\(142\) 0 0
\(143\) 3.18506e19i 1.27378i
\(144\) 0 0
\(145\) 1.54606e19 0.545649
\(146\) 0 0
\(147\) −6.48724e18 2.94517e19i −0.202397 0.918870i
\(148\) 0 0
\(149\) 3.76072e19i 1.03895i −0.854486 0.519475i \(-0.826128\pi\)
0.854486 0.519475i \(-0.173872\pi\)
\(150\) 0 0
\(151\) 3.02438e19 0.741044 0.370522 0.928824i \(-0.379179\pi\)
0.370522 + 0.928824i \(0.379179\pi\)
\(152\) 0 0
\(153\) 2.22198e18 + 4.79910e18i 0.0483633 + 0.104457i
\(154\) 0 0
\(155\) 1.33682e19i 0.258874i
\(156\) 0 0
\(157\) −1.60317e19 −0.276620 −0.138310 0.990389i \(-0.544167\pi\)
−0.138310 + 0.990389i \(0.544167\pi\)
\(158\) 0 0
\(159\) 1.04931e20 2.31128e19i 1.61558 0.355859i
\(160\) 0 0
\(161\) 5.59831e18i 0.0770237i
\(162\) 0 0
\(163\) −4.78329e19 −0.588895 −0.294448 0.955668i \(-0.595136\pi\)
−0.294448 + 0.955668i \(0.595136\pi\)
\(164\) 0 0
\(165\) 1.04674e19 + 4.75215e19i 0.115474 + 0.524246i
\(166\) 0 0
\(167\) 1.25413e20i 1.24135i 0.784067 + 0.620676i \(0.213142\pi\)
−0.784067 + 0.620676i \(0.786858\pi\)
\(168\) 0 0
\(169\) 1.04190e20 0.926503
\(170\) 0 0
\(171\) −8.39958e19 + 3.88899e19i −0.671881 + 0.311080i
\(172\) 0 0
\(173\) 1.32712e19i 0.0956085i −0.998857 0.0478042i \(-0.984778\pi\)
0.998857 0.0478042i \(-0.0152224\pi\)
\(174\) 0 0
\(175\) 2.46189e19 0.159929
\(176\) 0 0
\(177\) 1.54476e19 3.40260e18i 0.0905943 0.0199550i
\(178\) 0 0
\(179\) 3.08776e19i 0.163669i −0.996646 0.0818345i \(-0.973922\pi\)
0.996646 0.0818345i \(-0.0260779\pi\)
\(180\) 0 0
\(181\) 6.94280e18 0.0332987 0.0166494 0.999861i \(-0.494700\pi\)
0.0166494 + 0.999861i \(0.494700\pi\)
\(182\) 0 0
\(183\) 4.40789e19 + 2.00115e20i 0.191501 + 0.869402i
\(184\) 0 0
\(185\) 1.44043e20i 0.567473i
\(186\) 0 0
\(187\) 2.95389e19 0.105638
\(188\) 0 0
\(189\) −4.52990e19 5.95365e19i −0.147208 0.193476i
\(190\) 0 0
\(191\) 3.84936e19i 0.113786i 0.998380 + 0.0568930i \(0.0181194\pi\)
−0.998380 + 0.0568930i \(0.981881\pi\)
\(192\) 0 0
\(193\) −5.08300e20 −1.36806 −0.684028 0.729455i \(-0.739774\pi\)
−0.684028 + 0.729455i \(0.739774\pi\)
\(194\) 0 0
\(195\) −3.23238e20 + 7.11989e19i −0.792887 + 0.174647i
\(196\) 0 0
\(197\) 6.30050e20i 1.40987i 0.709272 + 0.704935i \(0.249024\pi\)
−0.709272 + 0.704935i \(0.750976\pi\)
\(198\) 0 0
\(199\) −1.14335e19 −0.0233615 −0.0116807 0.999932i \(-0.503718\pi\)
−0.0116807 + 0.999932i \(0.503718\pi\)
\(200\) 0 0
\(201\) 6.37807e19 + 2.89561e20i 0.119104 + 0.540723i
\(202\) 0 0
\(203\) 1.32761e20i 0.226780i
\(204\) 0 0
\(205\) −3.75486e20 −0.587231
\(206\) 0 0
\(207\) 9.28872e19 + 2.00621e20i 0.133114 + 0.287504i
\(208\) 0 0
\(209\) 5.17002e20i 0.679479i
\(210\) 0 0
\(211\) −6.41724e20 −0.774117 −0.387058 0.922055i \(-0.626509\pi\)
−0.387058 + 0.922055i \(0.626509\pi\)
\(212\) 0 0
\(213\) 8.59645e20 1.89352e20i 0.952582 0.209823i
\(214\) 0 0
\(215\) 9.60707e20i 0.978690i
\(216\) 0 0
\(217\) 1.14794e20 0.107592
\(218\) 0 0
\(219\) −1.66095e20 7.54063e20i −0.143338 0.650744i
\(220\) 0 0
\(221\) 2.00922e20i 0.159771i
\(222\) 0 0
\(223\) 8.65729e20 0.634802 0.317401 0.948291i \(-0.397190\pi\)
0.317401 + 0.948291i \(0.397190\pi\)
\(224\) 0 0
\(225\) −8.82242e20 + 4.08477e20i −0.596960 + 0.276391i
\(226\) 0 0
\(227\) 2.48692e21i 1.55392i 0.629547 + 0.776962i \(0.283240\pi\)
−0.629547 + 0.776962i \(0.716760\pi\)
\(228\) 0 0
\(229\) −4.47185e20 −0.258207 −0.129103 0.991631i \(-0.541210\pi\)
−0.129103 + 0.991631i \(0.541210\pi\)
\(230\) 0 0
\(231\) −4.08069e20 + 8.98843e19i −0.217884 + 0.0479928i
\(232\) 0 0
\(233\) 2.20802e21i 1.09094i −0.838131 0.545468i \(-0.816352\pi\)
0.838131 0.545468i \(-0.183648\pi\)
\(234\) 0 0
\(235\) 1.13959e21 0.521360
\(236\) 0 0
\(237\) 3.05196e20 + 1.38557e21i 0.129373 + 0.587345i
\(238\) 0 0
\(239\) 1.30522e21i 0.512983i −0.966547 0.256491i \(-0.917434\pi\)
0.966547 0.256491i \(-0.0825665\pi\)
\(240\) 0 0
\(241\) 1.77386e21 0.646795 0.323398 0.946263i \(-0.395175\pi\)
0.323398 + 0.946263i \(0.395175\pi\)
\(242\) 0 0
\(243\) 2.61116e21 + 1.38195e21i 0.883848 + 0.467774i
\(244\) 0 0
\(245\) 1.75046e21i 0.550372i
\(246\) 0 0
\(247\) −3.51662e21 −1.02767
\(248\) 0 0
\(249\) 1.97671e21 4.35404e20i 0.537215 0.118331i
\(250\) 0 0
\(251\) 4.95925e21i 1.25416i −0.778956 0.627079i \(-0.784250\pi\)
0.778956 0.627079i \(-0.215750\pi\)
\(252\) 0 0
\(253\) 1.23484e21 0.290755
\(254\) 0 0
\(255\) −6.60314e19 2.99778e20i −0.0144840 0.0657565i
\(256\) 0 0
\(257\) 7.24122e20i 0.148052i −0.997256 0.0740259i \(-0.976415\pi\)
0.997256 0.0740259i \(-0.0235847\pi\)
\(258\) 0 0
\(259\) −1.23690e21 −0.235850
\(260\) 0 0
\(261\) −2.20276e21 4.75761e21i −0.391925 0.846494i
\(262\) 0 0
\(263\) 1.13671e22i 1.88821i −0.329650 0.944103i \(-0.606931\pi\)
0.329650 0.944103i \(-0.393069\pi\)
\(264\) 0 0
\(265\) −6.23653e21 −0.967676
\(266\) 0 0
\(267\) 9.85492e21 2.17072e21i 1.42906 0.314776i
\(268\) 0 0
\(269\) 9.09091e21i 1.23264i −0.787495 0.616321i \(-0.788623\pi\)
0.787495 0.616321i \(-0.211377\pi\)
\(270\) 0 0
\(271\) −5.59132e21 −0.709235 −0.354618 0.935011i \(-0.615389\pi\)
−0.354618 + 0.935011i \(0.615389\pi\)
\(272\) 0 0
\(273\) −6.11387e20 2.77566e21i −0.0725860 0.329536i
\(274\) 0 0
\(275\) 5.43029e21i 0.603710i
\(276\) 0 0
\(277\) −3.61235e21 −0.376246 −0.188123 0.982145i \(-0.560240\pi\)
−0.188123 + 0.982145i \(0.560240\pi\)
\(278\) 0 0
\(279\) −4.11374e21 + 1.90466e21i −0.401605 + 0.185942i
\(280\) 0 0
\(281\) 3.75694e20i 0.0343936i −0.999852 0.0171968i \(-0.994526\pi\)
0.999852 0.0171968i \(-0.00547418\pi\)
\(282\) 0 0
\(283\) −4.33569e21 −0.372375 −0.186187 0.982514i \(-0.559613\pi\)
−0.186187 + 0.982514i \(0.559613\pi\)
\(284\) 0 0
\(285\) 5.24684e21 1.15571e21i 0.422955 0.0931632i
\(286\) 0 0
\(287\) 3.22431e21i 0.244062i
\(288\) 0 0
\(289\) 1.38767e22 0.986750
\(290\) 0 0
\(291\) −3.08558e21 1.40084e22i −0.206205 0.936160i
\(292\) 0 0
\(293\) 1.01590e22i 0.638326i −0.947700 0.319163i \(-0.896598\pi\)
0.947700 0.319163i \(-0.103402\pi\)
\(294\) 0 0
\(295\) −9.18125e20 −0.0542630
\(296\) 0 0
\(297\) 1.31322e22 9.99178e21i 0.730348 0.555693i
\(298\) 0 0
\(299\) 8.39932e21i 0.439748i
\(300\) 0 0
\(301\) −8.24963e21 −0.406758
\(302\) 0 0
\(303\) 2.21297e22 4.87446e21i 1.02800 0.226434i
\(304\) 0 0
\(305\) 1.18938e22i 0.520742i
\(306\) 0 0
\(307\) 3.56186e22 1.47039 0.735194 0.677857i \(-0.237091\pi\)
0.735194 + 0.677857i \(0.237091\pi\)
\(308\) 0 0
\(309\) 7.77441e21 + 3.52954e22i 0.302720 + 1.37433i
\(310\) 0 0
\(311\) 9.62119e21i 0.353497i 0.984256 + 0.176748i \(0.0565579\pi\)
−0.984256 + 0.176748i \(0.943442\pi\)
\(312\) 0 0
\(313\) −2.06842e22 −0.717364 −0.358682 0.933460i \(-0.616774\pi\)
−0.358682 + 0.933460i \(0.616774\pi\)
\(314\) 0 0
\(315\) 1.82440e21 + 3.94040e21i 0.0597481 + 0.129046i
\(316\) 0 0
\(317\) 4.70774e22i 1.45640i 0.685367 + 0.728198i \(0.259642\pi\)
−0.685367 + 0.728198i \(0.740358\pi\)
\(318\) 0 0
\(319\) −2.92835e22 −0.856066
\(320\) 0 0
\(321\) 2.51665e22 5.54335e21i 0.695468 0.153189i
\(322\) 0 0
\(323\) 3.26139e21i 0.0852275i
\(324\) 0 0
\(325\) −3.69365e22 −0.913072
\(326\) 0 0
\(327\) 3.96888e21 + 1.80185e22i 0.0928406 + 0.421491i
\(328\) 0 0
\(329\) 9.78570e21i 0.216685i
\(330\) 0 0
\(331\) −6.94207e22 −1.45558 −0.727791 0.685799i \(-0.759453\pi\)
−0.727791 + 0.685799i \(0.759453\pi\)
\(332\) 0 0
\(333\) 4.43255e22 2.05226e22i 0.880350 0.407601i
\(334\) 0 0
\(335\) 1.72100e22i 0.323875i
\(336\) 0 0
\(337\) −7.20588e22 −1.28534 −0.642670 0.766143i \(-0.722173\pi\)
−0.642670 + 0.766143i \(0.722173\pi\)
\(338\) 0 0
\(339\) −9.71107e21 + 2.13903e21i −0.164237 + 0.0361759i
\(340\) 0 0
\(341\) 2.53205e22i 0.406146i
\(342\) 0 0
\(343\) −3.10067e22 −0.471854
\(344\) 0 0
\(345\) −2.76037e21 1.25319e22i −0.0398653 0.180986i
\(346\) 0 0
\(347\) 7.97053e22i 1.09275i 0.837540 + 0.546376i \(0.183993\pi\)
−0.837540 + 0.546376i \(0.816007\pi\)
\(348\) 0 0
\(349\) −2.86134e22 −0.372513 −0.186256 0.982501i \(-0.559635\pi\)
−0.186256 + 0.982501i \(0.559635\pi\)
\(350\) 0 0
\(351\) 6.79635e22 + 8.93245e22i 0.840449 + 1.10460i
\(352\) 0 0
\(353\) 4.43974e22i 0.521657i 0.965385 + 0.260829i \(0.0839957\pi\)
−0.965385 + 0.260829i \(0.916004\pi\)
\(354\) 0 0
\(355\) −5.10928e22 −0.570565
\(356\) 0 0
\(357\) 2.57421e21 5.67014e20i 0.0273294 0.00601977i
\(358\) 0 0
\(359\) 4.97330e22i 0.502105i 0.967973 + 0.251052i \(0.0807767\pi\)
−0.967973 + 0.251052i \(0.919223\pi\)
\(360\) 0 0
\(361\) −4.70452e22 −0.451805
\(362\) 0 0
\(363\) 3.71470e21 + 1.68645e22i 0.0339441 + 0.154104i
\(364\) 0 0
\(365\) 4.48176e22i 0.389774i
\(366\) 0 0
\(367\) 6.92177e22 0.573090 0.286545 0.958067i \(-0.407493\pi\)
0.286545 + 0.958067i \(0.407493\pi\)
\(368\) 0 0
\(369\) 5.34978e22 + 1.15547e23i 0.421792 + 0.911003i
\(370\) 0 0
\(371\) 5.35533e22i 0.402181i
\(372\) 0 0
\(373\) 8.88028e22 0.635400 0.317700 0.948191i \(-0.397090\pi\)
0.317700 + 0.948191i \(0.397090\pi\)
\(374\) 0 0
\(375\) 1.38884e23 3.05915e22i 0.947042 0.208602i
\(376\) 0 0
\(377\) 1.99185e23i 1.29474i
\(378\) 0 0
\(379\) −2.92079e23 −1.81028 −0.905142 0.425109i \(-0.860236\pi\)
−0.905142 + 0.425109i \(0.860236\pi\)
\(380\) 0 0
\(381\) 3.75292e22 + 1.70380e23i 0.221842 + 1.00715i
\(382\) 0 0
\(383\) 1.19044e23i 0.671306i 0.941986 + 0.335653i \(0.108957\pi\)
−0.941986 + 0.335653i \(0.891043\pi\)
\(384\) 0 0
\(385\) 2.42535e22 0.130505
\(386\) 0 0
\(387\) 2.95634e23 1.36878e23i 1.51829 0.702966i
\(388\) 0 0
\(389\) 3.20490e23i 1.57133i 0.618650 + 0.785666i \(0.287680\pi\)
−0.618650 + 0.785666i \(0.712320\pi\)
\(390\) 0 0
\(391\) −7.78971e21 −0.0364696
\(392\) 0 0
\(393\) 2.89093e23 6.36778e22i 1.29272 0.284744i
\(394\) 0 0
\(395\) 8.23511e22i 0.351800i
\(396\) 0 0
\(397\) −3.68991e23 −1.50626 −0.753132 0.657870i \(-0.771458\pi\)
−0.753132 + 0.657870i \(0.771458\pi\)
\(398\) 0 0
\(399\) 9.92411e21 + 4.50548e22i 0.0387200 + 0.175786i
\(400\) 0 0
\(401\) 4.34713e23i 1.62145i −0.585429 0.810724i \(-0.699074\pi\)
0.585429 0.810724i \(-0.300926\pi\)
\(402\) 0 0
\(403\) −1.72228e23 −0.614270
\(404\) 0 0
\(405\) −1.30758e23 1.10938e23i −0.446040 0.378429i
\(406\) 0 0
\(407\) 2.72828e23i 0.890305i
\(408\) 0 0
\(409\) 1.61875e22 0.0505440 0.0252720 0.999681i \(-0.491955\pi\)
0.0252720 + 0.999681i \(0.491955\pi\)
\(410\) 0 0
\(411\) 1.52057e23 3.34931e22i 0.454391 0.100087i
\(412\) 0 0
\(413\) 7.88397e21i 0.0225525i
\(414\) 0 0
\(415\) −1.17485e23 −0.321774
\(416\) 0 0
\(417\) −1.25564e23 5.70055e23i −0.329338 1.49518i
\(418\) 0 0
\(419\) 1.48601e23i 0.373333i 0.982423 + 0.186666i \(0.0597684\pi\)
−0.982423 + 0.186666i \(0.940232\pi\)
\(420\) 0 0
\(421\) −2.10694e23 −0.507123 −0.253562 0.967319i \(-0.581602\pi\)
−0.253562 + 0.967319i \(0.581602\pi\)
\(422\) 0 0
\(423\) −1.62364e23 3.50680e23i −0.374479 0.808813i
\(424\) 0 0
\(425\) 3.42557e22i 0.0757238i
\(426\) 0 0
\(427\) 1.02133e23 0.216428
\(428\) 0 0
\(429\) 6.12239e23 1.34856e23i 1.24396 0.274003i
\(430\) 0 0
\(431\) 1.45530e23i 0.283567i −0.989898 0.141783i \(-0.954716\pi\)
0.989898 0.141783i \(-0.0452837\pi\)
\(432\) 0 0
\(433\) 2.76937e23 0.517594 0.258797 0.965932i \(-0.416674\pi\)
0.258797 + 0.965932i \(0.416674\pi\)
\(434\) 0 0
\(435\) 6.54605e22 + 2.97187e23i 0.117375 + 0.532876i
\(436\) 0 0
\(437\) 1.36339e23i 0.234577i
\(438\) 0 0
\(439\) −7.04854e23 −1.16391 −0.581954 0.813222i \(-0.697712\pi\)
−0.581954 + 0.813222i \(0.697712\pi\)
\(440\) 0 0
\(441\) 5.38659e23 2.49398e23i 0.853821 0.395318i
\(442\) 0 0
\(443\) 1.22387e24i 1.86252i −0.364351 0.931262i \(-0.618709\pi\)
0.364351 0.931262i \(-0.381291\pi\)
\(444\) 0 0
\(445\) −5.85726e23 −0.855962
\(446\) 0 0
\(447\) 7.22894e23 1.59230e23i 1.01463 0.223489i
\(448\) 0 0
\(449\) 4.92165e23i 0.663580i −0.943353 0.331790i \(-0.892347\pi\)
0.943353 0.331790i \(-0.107653\pi\)
\(450\) 0 0
\(451\) 7.11200e23 0.921304
\(452\) 0 0
\(453\) 1.28053e23 + 5.81353e23i 0.159407 + 0.723696i
\(454\) 0 0
\(455\) 1.64971e23i 0.197381i
\(456\) 0 0
\(457\) −1.39981e24 −1.60999 −0.804994 0.593284i \(-0.797831\pi\)
−0.804994 + 0.593284i \(0.797831\pi\)
\(458\) 0 0
\(459\) −8.28415e22 + 6.30308e22i −0.0916080 + 0.0697009i
\(460\) 0 0
\(461\) 1.15752e24i 1.23090i 0.788177 + 0.615449i \(0.211025\pi\)
−0.788177 + 0.615449i \(0.788975\pi\)
\(462\) 0 0
\(463\) −1.06888e23 −0.109320 −0.0546602 0.998505i \(-0.517408\pi\)
−0.0546602 + 0.998505i \(0.517408\pi\)
\(464\) 0 0
\(465\) 2.56967e23 5.66015e22i 0.252814 0.0556867i
\(466\) 0 0
\(467\) 1.19933e24i 1.13524i 0.823291 + 0.567619i \(0.192135\pi\)
−0.823291 + 0.567619i \(0.807865\pi\)
\(468\) 0 0
\(469\) 1.47783e23 0.134607
\(470\) 0 0
\(471\) −6.78788e22 3.08165e23i −0.0595039 0.270144i
\(472\) 0 0
\(473\) 1.81965e24i 1.53546i
\(474\) 0 0
\(475\) 5.99557e23 0.487066
\(476\) 0 0
\(477\) 8.88557e23 + 1.91914e24i 0.695056 + 1.50121i
\(478\) 0 0
\(479\) 8.59327e23i 0.647350i −0.946168 0.323675i \(-0.895082\pi\)
0.946168 0.323675i \(-0.104918\pi\)
\(480\) 0 0
\(481\) 1.85576e24 1.34653
\(482\) 0 0
\(483\) 1.07612e23 2.37034e22i 0.0752205 0.0165686i
\(484\) 0 0
\(485\) 8.32585e23i 0.560729i
\(486\) 0 0
\(487\) −9.68317e23 −0.628430 −0.314215 0.949352i \(-0.601741\pi\)
−0.314215 + 0.949352i \(0.601741\pi\)
\(488\) 0 0
\(489\) −2.02526e23 9.19454e23i −0.126678 0.575109i
\(490\) 0 0
\(491\) 1.67063e24i 1.00727i 0.863916 + 0.503635i \(0.168004\pi\)
−0.863916 + 0.503635i \(0.831996\pi\)
\(492\) 0 0
\(493\) 1.84728e23 0.107377
\(494\) 0 0
\(495\) −8.69149e23 + 4.02415e23i −0.487133 + 0.225542i
\(496\) 0 0
\(497\) 4.38736e23i 0.237135i
\(498\) 0 0
\(499\) −3.00033e23 −0.156410 −0.0782050 0.996937i \(-0.524919\pi\)
−0.0782050 + 0.996937i \(0.524919\pi\)
\(500\) 0 0
\(501\) −2.41072e24 + 5.31002e23i −1.21229 + 0.267028i
\(502\) 0 0
\(503\) 3.08864e24i 1.49850i 0.662289 + 0.749248i \(0.269585\pi\)
−0.662289 + 0.749248i \(0.730415\pi\)
\(504\) 0 0
\(505\) −1.31528e24 −0.615737
\(506\) 0 0
\(507\) 4.41144e23 + 2.00277e24i 0.199301 + 0.904813i
\(508\) 0 0
\(509\) 3.85870e24i 1.68260i 0.540569 + 0.841299i \(0.318209\pi\)
−0.540569 + 0.841299i \(0.681791\pi\)
\(510\) 0 0
\(511\) −3.84851e23 −0.161996
\(512\) 0 0
\(513\) −1.10319e24 1.44992e24i −0.448326 0.589236i
\(514\) 0 0
\(515\) 2.09777e24i 0.823178i
\(516\) 0 0
\(517\) −2.15847e24 −0.817958
\(518\) 0 0
\(519\) 2.55103e23 5.61907e22i 0.0933702 0.0205664i
\(520\) 0 0
\(521\) 1.16274e24i 0.411097i −0.978647 0.205549i \(-0.934102\pi\)
0.978647 0.205549i \(-0.0658979\pi\)
\(522\) 0 0
\(523\) −1.12148e24 −0.383069 −0.191534 0.981486i \(-0.561346\pi\)
−0.191534 + 0.981486i \(0.561346\pi\)
\(524\) 0 0
\(525\) 1.04237e23 + 4.73230e23i 0.0344023 + 0.156185i
\(526\) 0 0
\(527\) 1.59728e23i 0.0509432i
\(528\) 0 0
\(529\) 2.91851e24 0.899622
\(530\) 0 0
\(531\) 1.30811e23 + 2.82530e23i 0.0389756 + 0.0841810i
\(532\) 0 0
\(533\) 4.83754e24i 1.39341i
\(534\) 0 0
\(535\) −1.49577e24 −0.416562
\(536\) 0 0
\(537\) 5.93536e23 1.30737e23i 0.159837 0.0352070i
\(538\) 0 0
\(539\) 3.31550e24i 0.863476i
\(540\) 0 0
\(541\) 2.23337e24 0.562582 0.281291 0.959622i \(-0.409237\pi\)
0.281291 + 0.959622i \(0.409237\pi\)
\(542\) 0 0
\(543\) 2.93960e22 + 1.33456e23i 0.00716291 + 0.0325192i
\(544\) 0 0
\(545\) 1.07092e24i 0.252459i
\(546\) 0 0
\(547\) −2.13233e24 −0.486372 −0.243186 0.969980i \(-0.578192\pi\)
−0.243186 + 0.969980i \(0.578192\pi\)
\(548\) 0 0
\(549\) −3.66003e24 + 1.69459e24i −0.807855 + 0.374035i
\(550\) 0 0
\(551\) 3.23319e24i 0.690664i
\(552\) 0 0
\(553\) 7.07152e23 0.146213
\(554\) 0 0
\(555\) −2.76882e24 + 6.09880e23i −0.554188 + 0.122070i
\(556\) 0 0
\(557\) 4.28440e24i 0.830221i 0.909771 + 0.415111i \(0.136257\pi\)
−0.909771 + 0.415111i \(0.863743\pi\)
\(558\) 0 0
\(559\) 1.23772e25 2.32228
\(560\) 0 0
\(561\) 1.25069e23 + 5.67804e23i 0.0227239 + 0.103165i
\(562\) 0 0
\(563\) 6.48683e24i 1.14145i 0.821141 + 0.570725i \(0.193338\pi\)
−0.821141 + 0.570725i \(0.806662\pi\)
\(564\) 0 0
\(565\) 5.77176e23 0.0983722
\(566\) 0 0
\(567\) 9.52627e23 1.12283e24i 0.157281 0.185381i
\(568\) 0 0
\(569\) 1.13256e25i 1.81155i −0.423762 0.905774i \(-0.639291\pi\)
0.423762 0.905774i \(-0.360709\pi\)
\(570\) 0 0
\(571\) −3.22177e23 −0.0499309 −0.0249654 0.999688i \(-0.507948\pi\)
−0.0249654 + 0.999688i \(0.507948\pi\)
\(572\) 0 0
\(573\) −7.39933e23 + 1.62983e23i −0.111122 + 0.0244766i
\(574\) 0 0
\(575\) 1.43202e24i 0.208420i
\(576\) 0 0
\(577\) 1.04474e25 1.47375 0.736877 0.676027i \(-0.236300\pi\)
0.736877 + 0.676027i \(0.236300\pi\)
\(578\) 0 0
\(579\) −2.15215e24 9.77065e24i −0.294284 1.33603i
\(580\) 0 0
\(581\) 1.00885e24i 0.133734i
\(582\) 0 0
\(583\) 1.18125e25 1.51818
\(584\) 0 0
\(585\) −2.73720e24 5.91190e24i −0.341117 0.736757i
\(586\) 0 0
\(587\) 1.94521e24i 0.235084i −0.993068 0.117542i \(-0.962498\pi\)
0.993068 0.117542i \(-0.0375015\pi\)
\(588\) 0 0
\(589\) 2.79563e24 0.327674
\(590\) 0 0
\(591\) −1.21110e25 + 2.66765e24i −1.37686 + 0.303278i
\(592\) 0 0
\(593\) 1.02435e25i 1.12968i −0.825200 0.564841i \(-0.808937\pi\)
0.825200 0.564841i \(-0.191063\pi\)
\(594\) 0 0
\(595\) −1.52998e23 −0.0163694
\(596\) 0 0
\(597\) −4.84096e22 2.19777e23i −0.00502531 0.0228146i
\(598\) 0 0
\(599\) 8.10173e24i 0.816086i −0.912963 0.408043i \(-0.866211\pi\)
0.912963 0.408043i \(-0.133789\pi\)
\(600\) 0 0
\(601\) −4.00759e24 −0.391754 −0.195877 0.980628i \(-0.562755\pi\)
−0.195877 + 0.980628i \(0.562755\pi\)
\(602\) 0 0
\(603\) −5.29595e24 + 2.45201e24i −0.502444 + 0.232631i
\(604\) 0 0
\(605\) 1.00234e24i 0.0923031i
\(606\) 0 0
\(607\) −1.18663e25 −1.06076 −0.530378 0.847761i \(-0.677950\pi\)
−0.530378 + 0.847761i \(0.677950\pi\)
\(608\) 0 0
\(609\) −2.55195e24 + 5.62112e23i −0.221471 + 0.0487828i
\(610\) 0 0
\(611\) 1.46818e25i 1.23711i
\(612\) 0 0
\(613\) −1.12607e25 −0.921345 −0.460673 0.887570i \(-0.652392\pi\)
−0.460673 + 0.887570i \(0.652392\pi\)
\(614\) 0 0
\(615\) −1.58982e24 7.21768e24i −0.126320 0.573484i
\(616\) 0 0
\(617\) 2.90545e23i 0.0224206i −0.999937 0.0112103i \(-0.996432\pi\)
0.999937 0.0112103i \(-0.00356842\pi\)
\(618\) 0 0
\(619\) 1.42594e25 1.06877 0.534385 0.845241i \(-0.320543\pi\)
0.534385 + 0.845241i \(0.320543\pi\)
\(620\) 0 0
\(621\) −3.46310e24 + 2.63493e24i −0.252139 + 0.191843i
\(622\) 0 0
\(623\) 5.02965e24i 0.355750i
\(624\) 0 0
\(625\) 1.31831e24 0.0905936
\(626\) 0 0
\(627\) −9.93793e24 + 2.18900e24i −0.663572 + 0.146163i
\(628\) 0 0
\(629\) 1.72107e24i 0.111672i
\(630\) 0 0
\(631\) 1.34151e25 0.845923 0.422961 0.906148i \(-0.360991\pi\)
0.422961 + 0.906148i \(0.360991\pi\)
\(632\) 0 0
\(633\) −2.71708e24 1.23354e25i −0.166521 0.755995i
\(634\) 0 0
\(635\) 1.01265e25i 0.603249i
\(636\) 0 0
\(637\) 2.25518e25 1.30595
\(638\) 0 0
\(639\) 7.27951e24 + 1.57226e25i 0.409821 + 0.885147i
\(640\) 0 0
\(641\) 5.98895e24i 0.327815i −0.986476 0.163907i \(-0.947590\pi\)
0.986476 0.163907i \(-0.0524098\pi\)
\(642\) 0 0
\(643\) 1.54893e25 0.824391 0.412196 0.911095i \(-0.364762\pi\)
0.412196 + 0.911095i \(0.364762\pi\)
\(644\) 0 0
\(645\) −1.84669e25 + 4.06766e24i −0.955778 + 0.210527i
\(646\) 0 0
\(647\) 1.51080e25i 0.760447i −0.924895 0.380223i \(-0.875847\pi\)
0.924895 0.380223i \(-0.124153\pi\)
\(648\) 0 0
\(649\) 1.73900e24 0.0851328
\(650\) 0 0
\(651\) 4.86039e23 + 2.20659e24i 0.0231442 + 0.105073i
\(652\) 0 0
\(653\) 2.12528e25i 0.984457i 0.870466 + 0.492228i \(0.163818\pi\)
−0.870466 + 0.492228i \(0.836182\pi\)
\(654\) 0 0
\(655\) −1.71822e25 −0.774297
\(656\) 0 0
\(657\) 1.37915e25 6.38544e24i 0.604677 0.279964i
\(658\) 0 0
\(659\) 4.11576e25i 1.75583i 0.478820 + 0.877913i \(0.341064\pi\)
−0.478820 + 0.877913i \(0.658936\pi\)
\(660\) 0 0
\(661\) 3.24714e25 1.34799 0.673996 0.738735i \(-0.264576\pi\)
0.673996 + 0.738735i \(0.264576\pi\)
\(662\) 0 0
\(663\) −3.86217e24 + 8.50709e23i −0.156030 + 0.0343684i
\(664\) 0 0
\(665\) 2.67783e24i 0.105290i
\(666\) 0 0
\(667\) 7.72236e24 0.295541
\(668\) 0 0
\(669\) 3.66552e24 + 1.66412e25i 0.136553 + 0.619941i
\(670\) 0 0
\(671\) 2.25278e25i 0.816990i
\(672\) 0 0
\(673\) 1.10390e25 0.389758 0.194879 0.980827i \(-0.437569\pi\)
0.194879 + 0.980827i \(0.437569\pi\)
\(674\) 0 0
\(675\) −1.15873e25 1.52292e25i −0.398334 0.523530i
\(676\) 0 0
\(677\) 2.74075e25i 0.917427i −0.888584 0.458714i \(-0.848310\pi\)
0.888584 0.458714i \(-0.151690\pi\)
\(678\) 0 0
\(679\) −7.14944e24 −0.233047
\(680\) 0 0
\(681\) −4.78042e25 + 1.05297e25i −1.51755 + 0.334266i
\(682\) 0 0
\(683\) 3.99739e25i 1.23592i 0.786210 + 0.617960i \(0.212041\pi\)
−0.786210 + 0.617960i \(0.787959\pi\)
\(684\) 0 0
\(685\) −9.03747e24 −0.272165
\(686\) 0 0
\(687\) −1.89339e24 8.59589e24i −0.0555431 0.252162i
\(688\) 0 0
\(689\) 8.03477e25i 2.29615i
\(690\) 0 0
\(691\) 1.02801e25 0.286218 0.143109 0.989707i \(-0.454290\pi\)
0.143109 + 0.989707i \(0.454290\pi\)
\(692\) 0 0
\(693\) −3.45555e24 7.46342e24i −0.0937385 0.202460i
\(694\) 0 0
\(695\) 3.38811e25i 0.895560i
\(696\) 0 0
\(697\) −4.48644e24 −0.115560
\(698\) 0 0
\(699\) 4.24430e25 9.34881e24i 1.06540 0.234672i
\(700\) 0 0
\(701\) 2.02392e25i 0.495143i −0.968870 0.247572i \(-0.920367\pi\)
0.968870 0.247572i \(-0.0796325\pi\)
\(702\) 0 0
\(703\) −3.01229e25 −0.718288
\(704\) 0 0
\(705\) 4.82505e24 + 2.19054e25i 0.112150 + 0.509155i
\(706\) 0 0
\(707\) 1.12943e25i 0.255909i
\(708\) 0 0
\(709\) −8.66215e25 −1.91342 −0.956708 0.291048i \(-0.905996\pi\)
−0.956708 + 0.291048i \(0.905996\pi\)
\(710\) 0 0
\(711\) −2.53415e25 + 1.17331e25i −0.545766 + 0.252688i
\(712\) 0 0
\(713\) 6.67727e24i 0.140215i
\(714\) 0 0
\(715\) −3.63883e25 −0.745088
\(716\) 0 0
\(717\) 2.50892e25 5.52633e24i 0.500973 0.110348i
\(718\) 0 0
\(719\) 8.53805e25i 1.66264i −0.555793 0.831320i \(-0.687585\pi\)
0.555793 0.831320i \(-0.312415\pi\)
\(720\) 0 0
\(721\) 1.80137e25 0.342125
\(722\) 0 0
\(723\) 7.51058e24 + 3.40976e25i 0.139133 + 0.631653i
\(724\) 0 0
\(725\) 3.39595e25i 0.613648i
\(726\) 0 0
\(727\) −1.83358e25 −0.323215 −0.161607 0.986855i \(-0.551668\pi\)
−0.161607 + 0.986855i \(0.551668\pi\)
\(728\) 0 0
\(729\) −1.55084e25 + 5.60436e25i −0.266698 + 0.963780i
\(730\) 0 0
\(731\) 1.14789e25i 0.192594i
\(732\) 0 0
\(733\) 9.99901e25 1.63690 0.818449 0.574580i \(-0.194834\pi\)
0.818449 + 0.574580i \(0.194834\pi\)
\(734\) 0 0
\(735\) −3.36476e25 + 7.41148e24i −0.537488 + 0.118391i
\(736\) 0 0
\(737\) 3.25971e25i 0.508126i
\(738\) 0 0
\(739\) −7.21830e24 −0.109808 −0.0549041 0.998492i \(-0.517485\pi\)
−0.0549041 + 0.998492i \(0.517485\pi\)
\(740\) 0 0
\(741\) −1.48894e25 6.75972e25i −0.221062 1.00361i
\(742\) 0 0
\(743\) 4.78088e25i 0.692802i 0.938087 + 0.346401i \(0.112596\pi\)
−0.938087 + 0.346401i \(0.887404\pi\)
\(744\) 0 0
\(745\) −4.29651e25 −0.607728
\(746\) 0 0
\(747\) 1.67389e25 + 3.61532e25i 0.231122 + 0.499185i
\(748\) 0 0
\(749\) 1.28442e25i 0.173129i
\(750\) 0 0
\(751\) 1.09528e26 1.44134 0.720670 0.693278i \(-0.243834\pi\)
0.720670 + 0.693278i \(0.243834\pi\)
\(752\) 0 0
\(753\) 9.53277e25 2.09976e25i 1.22480 0.269783i
\(754\) 0 0
\(755\) 3.45527e25i 0.433470i
\(756\) 0 0
\(757\) −1.54885e26 −1.89734 −0.948670 0.316267i \(-0.897570\pi\)
−0.948670 + 0.316267i \(0.897570\pi\)
\(758\) 0 0
\(759\) 5.22835e24 + 2.37364e25i 0.0625445 + 0.283948i
\(760\) 0 0
\(761\) 2.98795e25i 0.349069i −0.984651 0.174535i \(-0.944158\pi\)
0.984651 0.174535i \(-0.0558421\pi\)
\(762\) 0 0
\(763\) 9.19607e24 0.104926
\(764\) 0 0
\(765\) 5.48283e24 2.53854e24i 0.0611015 0.0282899i
\(766\) 0 0
\(767\) 1.18286e25i 0.128758i
\(768\) 0 0
\(769\) 3.57805e25 0.380461 0.190230 0.981739i \(-0.439077\pi\)
0.190230 + 0.981739i \(0.439077\pi\)
\(770\) 0 0
\(771\)