Properties

Label 48.19.e.b.17.2
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 17.2
Root \(6.57949 - 5.90892i\) of defining polynomial
Character \(\chi\) \(=\) 48.17
Dual form 48.19.e.b.17.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-12172.0 + 15468.1i) q^{3} -787628. i q^{5} +3.80616e7 q^{7} +(-9.11041e7 - 3.76556e8i) q^{9} +O(q^{10})\) \(q+(-12172.0 + 15468.1i) q^{3} -787628. i q^{5} +3.80616e7 q^{7} +(-9.11041e7 - 3.76556e8i) q^{9} -3.08486e9i q^{11} +1.20058e10 q^{13} +(1.21831e10 + 9.58703e9i) q^{15} -1.44261e11i q^{17} -3.34627e11 q^{19} +(-4.63287e11 + 5.88742e11i) q^{21} -1.92274e12i q^{23} +3.19434e12 q^{25} +(6.93353e12 + 3.17425e12i) q^{27} +1.09466e13i q^{29} -2.95654e13 q^{31} +(4.77169e13 + 3.75489e13i) q^{33} -2.99784e13i q^{35} -1.11570e14 q^{37} +(-1.46135e14 + 1.85707e14i) q^{39} +3.22853e14i q^{41} +4.11004e13 q^{43} +(-2.96586e14 + 7.17562e13i) q^{45} +8.18748e14i q^{47} -1.79725e14 q^{49} +(2.23144e15 + 1.75594e15i) q^{51} +7.04145e14i q^{53} -2.42972e15 q^{55} +(4.07309e15 - 5.17605e15i) q^{57} -3.09091e15i q^{59} -1.15143e16 q^{61} +(-3.46757e15 - 1.43324e16i) q^{63} -9.45609e15i q^{65} +5.60191e15 q^{67} +(2.97411e16 + 2.34036e16i) q^{69} -5.38702e16i q^{71} +1.65337e16 q^{73} +(-3.88816e16 + 4.94104e16i) q^{75} -1.17415e17i q^{77} +1.66010e16 q^{79} +(-1.33495e17 + 6.86117e16i) q^{81} +4.84222e16i q^{83} -1.13624e17 q^{85} +(-1.69323e17 - 1.33242e17i) q^{87} +5.03152e16i q^{89} +4.56960e17 q^{91} +(3.59871e17 - 4.57321e17i) q^{93} +2.63562e17i q^{95} -1.01702e18 q^{97} +(-1.16162e18 + 2.81043e17i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 15876 q^{3} + 95744152 q^{7} - 885341340 q^{9}+O(q^{10}) \) 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
\(3\) −12172.0 + 15468.1i −0.618403 + 0.785861i
\(4\) 0 0
\(5\) 787628.i 0.403266i −0.979461 0.201633i \(-0.935375\pi\)
0.979461 0.201633i \(-0.0646248\pi\)
\(6\) 0 0
\(7\) 3.80616e7 0.943203 0.471602 0.881812i \(-0.343676\pi\)
0.471602 + 0.881812i \(0.343676\pi\)
\(8\) 0 0
\(9\) −9.11041e7 3.76556e8i −0.235156 0.971958i
\(10\) 0 0
\(11\) 3.08486e9i 1.30828i −0.756374 0.654140i \(-0.773031\pi\)
0.756374 0.654140i \(-0.226969\pi\)
\(12\) 0 0
\(13\) 1.20058e10 1.13214 0.566070 0.824357i \(-0.308463\pi\)
0.566070 + 0.824357i \(0.308463\pi\)
\(14\) 0 0
\(15\) 1.21831e10 + 9.58703e9i 0.316911 + 0.249381i
\(16\) 0 0
\(17\) 1.44261e11i 1.21649i −0.793751 0.608243i \(-0.791874\pi\)
0.793751 0.608243i \(-0.208126\pi\)
\(18\) 0 0
\(19\) −3.34627e11 −1.03700 −0.518500 0.855078i \(-0.673509\pi\)
−0.518500 + 0.855078i \(0.673509\pi\)
\(20\) 0 0
\(21\) −4.63287e11 + 5.88742e11i −0.583280 + 0.741227i
\(22\) 0 0
\(23\) 1.92274e12i 1.06750i −0.845641 0.533752i \(-0.820781\pi\)
0.845641 0.533752i \(-0.179219\pi\)
\(24\) 0 0
\(25\) 3.19434e12 0.837377
\(26\) 0 0
\(27\) 6.93353e12 + 3.17425e12i 0.909245 + 0.416262i
\(28\) 0 0
\(29\) 1.09466e13i 0.754564i 0.926098 + 0.377282i \(0.123141\pi\)
−0.926098 + 0.377282i \(0.876859\pi\)
\(30\) 0 0
\(31\) −2.95654e13 −1.11822 −0.559111 0.829093i \(-0.688858\pi\)
−0.559111 + 0.829093i \(0.688858\pi\)
\(32\) 0 0
\(33\) 4.77169e13 + 3.75489e13i 1.02813 + 0.809044i
\(34\) 0 0
\(35\) 2.99784e13i 0.380361i
\(36\) 0 0
\(37\) −1.11570e14 −0.858483 −0.429241 0.903190i \(-0.641219\pi\)
−0.429241 + 0.903190i \(0.641219\pi\)
\(38\) 0 0
\(39\) −1.46135e14 + 1.85707e14i −0.700119 + 0.889705i
\(40\) 0 0
\(41\) 3.22853e14i 0.986165i 0.869982 + 0.493083i \(0.164130\pi\)
−0.869982 + 0.493083i \(0.835870\pi\)
\(42\) 0 0
\(43\) 4.11004e13 0.0817769 0.0408884 0.999164i \(-0.486981\pi\)
0.0408884 + 0.999164i \(0.486981\pi\)
\(44\) 0 0
\(45\) −2.96586e14 + 7.17562e13i −0.391957 + 0.0948302i
\(46\) 0 0
\(47\) 8.18748e14i 0.731593i 0.930695 + 0.365796i \(0.119203\pi\)
−0.930695 + 0.365796i \(0.880797\pi\)
\(48\) 0 0
\(49\) −1.79725e14 −0.110368
\(50\) 0 0
\(51\) 2.23144e15 + 1.75594e15i 0.955990 + 0.752279i
\(52\) 0 0
\(53\) 7.04145e14i 0.213393i 0.994292 + 0.106696i \(0.0340273\pi\)
−0.994292 + 0.106696i \(0.965973\pi\)
\(54\) 0 0
\(55\) −2.42972e15 −0.527584
\(56\) 0 0
\(57\) 4.07309e15 5.17605e15i 0.641284 0.814938i
\(58\) 0 0
\(59\) 3.09091e15i 0.356794i −0.983959 0.178397i \(-0.942909\pi\)
0.983959 0.178397i \(-0.0570912\pi\)
\(60\) 0 0
\(61\) −1.15143e16 −0.984618 −0.492309 0.870421i \(-0.663847\pi\)
−0.492309 + 0.870421i \(0.663847\pi\)
\(62\) 0 0
\(63\) −3.46757e15 1.43324e16i −0.221800 0.916754i
\(64\) 0 0
\(65\) 9.45609e15i 0.456553i
\(66\) 0 0
\(67\) 5.60191e15 0.205903 0.102952 0.994686i \(-0.467171\pi\)
0.102952 + 0.994686i \(0.467171\pi\)
\(68\) 0 0
\(69\) 2.97411e16 + 2.34036e16i 0.838910 + 0.660148i
\(70\) 0 0
\(71\) 5.38702e16i 1.17496i −0.809238 0.587481i \(-0.800120\pi\)
0.809238 0.587481i \(-0.199880\pi\)
\(72\) 0 0
\(73\) 1.65337e16 0.280844 0.140422 0.990092i \(-0.455154\pi\)
0.140422 + 0.990092i \(0.455154\pi\)
\(74\) 0 0
\(75\) −3.88816e16 + 4.94104e16i −0.517836 + 0.658062i
\(76\) 0 0
\(77\) 1.17415e17i 1.23397i
\(78\) 0 0
\(79\) 1.66010e16 0.138513 0.0692565 0.997599i \(-0.477937\pi\)
0.0692565 + 0.997599i \(0.477937\pi\)
\(80\) 0 0
\(81\) −1.33495e17 + 6.86117e16i −0.889404 + 0.457123i
\(82\) 0 0
\(83\) 4.84222e16i 0.259025i 0.991578 + 0.129512i \(0.0413412\pi\)
−0.991578 + 0.129512i \(0.958659\pi\)
\(84\) 0 0
\(85\) −1.13624e17 −0.490567
\(86\) 0 0
\(87\) −1.69323e17 1.33242e17i −0.592983 0.466625i
\(88\) 0 0
\(89\) 5.03152e16i 0.143611i 0.997419 + 0.0718057i \(0.0228762\pi\)
−0.997419 + 0.0718057i \(0.977124\pi\)
\(90\) 0 0
\(91\) 4.56960e17 1.06784
\(92\) 0 0
\(93\) 3.59871e17 4.57321e17i 0.691512 0.878768i
\(94\) 0 0
\(95\) 2.63562e17i 0.418186i
\(96\) 0 0
\(97\) −1.01702e18 −1.33778 −0.668891 0.743360i \(-0.733231\pi\)
−0.668891 + 0.743360i \(0.733231\pi\)
\(98\) 0 0
\(99\) −1.16162e18 + 2.81043e17i −1.27159 + 0.307649i
\(100\) 0 0
\(101\) 4.94174e17i 0.451843i 0.974146 + 0.225921i \(0.0725393\pi\)
−0.974146 + 0.225921i \(0.927461\pi\)
\(102\) 0 0
\(103\) −1.21075e18 −0.927939 −0.463970 0.885851i \(-0.653575\pi\)
−0.463970 + 0.885851i \(0.653575\pi\)
\(104\) 0 0
\(105\) 4.63709e17 + 3.64898e17i 0.298911 + 0.235217i
\(106\) 0 0
\(107\) 3.26862e18i 1.77791i −0.457993 0.888956i \(-0.651432\pi\)
0.457993 0.888956i \(-0.348568\pi\)
\(108\) 0 0
\(109\) −6.74802e17 −0.310698 −0.155349 0.987860i \(-0.549650\pi\)
−0.155349 + 0.987860i \(0.549650\pi\)
\(110\) 0 0
\(111\) 1.35803e18 1.72578e18i 0.530888 0.674648i
\(112\) 0 0
\(113\) 5.04400e18i 1.67907i −0.543305 0.839536i \(-0.682827\pi\)
0.543305 0.839536i \(-0.317173\pi\)
\(114\) 0 0
\(115\) −1.51440e18 −0.430488
\(116\) 0 0
\(117\) −1.09378e18 4.52085e18i −0.266229 1.10039i
\(118\) 0 0
\(119\) 5.49080e18i 1.14739i
\(120\) 0 0
\(121\) −3.95642e18 −0.711596
\(122\) 0 0
\(123\) −4.99392e18 3.92977e18i −0.774989 0.609848i
\(124\) 0 0
\(125\) 5.52051e18i 0.740951i
\(126\) 0 0
\(127\) −5.82269e17 −0.0677471 −0.0338735 0.999426i \(-0.510784\pi\)
−0.0338735 + 0.999426i \(0.510784\pi\)
\(128\) 0 0
\(129\) −5.00276e17 + 6.35746e17i −0.0505710 + 0.0642653i
\(130\) 0 0
\(131\) 1.29504e19i 1.13984i 0.821702 + 0.569918i \(0.193025\pi\)
−0.821702 + 0.569918i \(0.806975\pi\)
\(132\) 0 0
\(133\) −1.27365e19 −0.978101
\(134\) 0 0
\(135\) 2.50012e18 5.46105e18i 0.167864 0.366667i
\(136\) 0 0
\(137\) 8.52718e18i 0.501557i −0.968045 0.250778i \(-0.919313\pi\)
0.968045 0.250778i \(-0.0806866\pi\)
\(138\) 0 0
\(139\) −1.94254e19 −1.00285 −0.501425 0.865201i \(-0.667191\pi\)
−0.501425 + 0.865201i \(0.667191\pi\)
\(140\) 0 0
\(141\) −1.26645e19 9.96582e18i −0.574930 0.452419i
\(142\) 0 0
\(143\) 3.70361e19i 1.48116i
\(144\) 0 0
\(145\) 8.62183e18 0.304290
\(146\) 0 0
\(147\) 2.18761e18 2.78000e18i 0.0682519 0.0867339i
\(148\) 0 0
\(149\) 2.52538e19i 0.697669i 0.937184 + 0.348835i \(0.113422\pi\)
−0.937184 + 0.348835i \(0.886578\pi\)
\(150\) 0 0
\(151\) −4.93498e19 −1.20918 −0.604592 0.796535i \(-0.706664\pi\)
−0.604592 + 0.796535i \(0.706664\pi\)
\(152\) 0 0
\(153\) −5.43222e19 + 1.31427e19i −1.18237 + 0.286064i
\(154\) 0 0
\(155\) 2.32865e19i 0.450941i
\(156\) 0 0
\(157\) 4.64830e19 0.802043 0.401021 0.916069i \(-0.368655\pi\)
0.401021 + 0.916069i \(0.368655\pi\)
\(158\) 0 0
\(159\) −1.08918e19 8.57087e18i −0.167697 0.131963i
\(160\) 0 0
\(161\) 7.31826e19i 1.00687i
\(162\) 0 0
\(163\) 5.33167e19 0.656409 0.328205 0.944607i \(-0.393556\pi\)
0.328205 + 0.944607i \(0.393556\pi\)
\(164\) 0 0
\(165\) 2.95746e19 3.75832e19i 0.326260 0.414608i
\(166\) 0 0
\(167\) 1.72019e20i 1.70266i −0.524631 0.851330i \(-0.675797\pi\)
0.524631 0.851330i \(-0.324203\pi\)
\(168\) 0 0
\(169\) 3.16833e19 0.281741
\(170\) 0 0
\(171\) 3.04859e19 + 1.26006e20i 0.243856 + 1.00792i
\(172\) 0 0
\(173\) 4.28816e19i 0.308927i −0.987998 0.154464i \(-0.950635\pi\)
0.987998 0.154464i \(-0.0493649\pi\)
\(174\) 0 0
\(175\) 1.21582e20 0.789816
\(176\) 0 0
\(177\) 4.78105e19 + 3.76226e19i 0.280391 + 0.220643i
\(178\) 0 0
\(179\) 1.99405e20i 1.05696i 0.848946 + 0.528479i \(0.177238\pi\)
−0.848946 + 0.528479i \(0.822762\pi\)
\(180\) 0 0
\(181\) −3.50663e20 −1.68183 −0.840917 0.541164i \(-0.817984\pi\)
−0.840917 + 0.541164i \(0.817984\pi\)
\(182\) 0 0
\(183\) 1.40152e20 1.78104e20i 0.608890 0.773773i
\(184\) 0 0
\(185\) 8.78756e19i 0.346197i
\(186\) 0 0
\(187\) −4.45023e20 −1.59151
\(188\) 0 0
\(189\) 2.63902e20 + 1.20817e20i 0.857603 + 0.392619i
\(190\) 0 0
\(191\) 3.95689e20i 1.16964i 0.811162 + 0.584822i \(0.198836\pi\)
−0.811162 + 0.584822i \(0.801164\pi\)
\(192\) 0 0
\(193\) 5.57447e20 1.50033 0.750167 0.661248i \(-0.229973\pi\)
0.750167 + 0.661248i \(0.229973\pi\)
\(194\) 0 0
\(195\) 1.46268e20 + 1.15100e20i 0.358787 + 0.282334i
\(196\) 0 0
\(197\) 6.09641e20i 1.36420i 0.731259 + 0.682100i \(0.238933\pi\)
−0.731259 + 0.682100i \(0.761067\pi\)
\(198\) 0 0
\(199\) 7.93685e20 1.62170 0.810850 0.585255i \(-0.199005\pi\)
0.810850 + 0.585255i \(0.199005\pi\)
\(200\) 0 0
\(201\) −6.81866e19 + 8.66510e19i −0.127331 + 0.161811i
\(202\) 0 0
\(203\) 4.16645e20i 0.711708i
\(204\) 0 0
\(205\) 2.54288e20 0.397687
\(206\) 0 0
\(207\) −7.24019e20 + 1.75169e20i −1.03757 + 0.251030i
\(208\) 0 0
\(209\) 1.03228e21i 1.35669i
\(210\) 0 0
\(211\) 9.70884e20 1.17118 0.585592 0.810606i \(-0.300862\pi\)
0.585592 + 0.810606i \(0.300862\pi\)
\(212\) 0 0
\(213\) 8.33270e20 + 6.55710e20i 0.923357 + 0.726600i
\(214\) 0 0
\(215\) 3.23719e19i 0.0329778i
\(216\) 0 0
\(217\) −1.12531e21 −1.05471
\(218\) 0 0
\(219\) −2.01249e20 + 2.55746e20i −0.173675 + 0.220704i
\(220\) 0 0
\(221\) 1.73196e21i 1.37723i
\(222\) 0 0
\(223\) −5.41092e20 −0.396759 −0.198380 0.980125i \(-0.563568\pi\)
−0.198380 + 0.980125i \(0.563568\pi\)
\(224\) 0 0
\(225\) −2.91017e20 1.20285e21i −0.196914 0.813895i
\(226\) 0 0
\(227\) 1.06343e19i 0.00664471i 0.999994 + 0.00332235i \(0.00105754\pi\)
−0.999994 + 0.00332235i \(0.998942\pi\)
\(228\) 0 0
\(229\) 8.33519e20 0.481278 0.240639 0.970615i \(-0.422643\pi\)
0.240639 + 0.970615i \(0.422643\pi\)
\(230\) 0 0
\(231\) 1.81618e21 + 1.42917e21i 0.969732 + 0.763093i
\(232\) 0 0
\(233\) 6.48594e20i 0.320457i 0.987080 + 0.160228i \(0.0512231\pi\)
−0.987080 + 0.160228i \(0.948777\pi\)
\(234\) 0 0
\(235\) 6.44869e20 0.295026
\(236\) 0 0
\(237\) −2.02068e20 + 2.56786e20i −0.0856568 + 0.108852i
\(238\) 0 0
\(239\) 1.26828e21i 0.498466i −0.968444 0.249233i \(-0.919821\pi\)
0.968444 0.249233i \(-0.0801785\pi\)
\(240\) 0 0
\(241\) 1.90001e21 0.692791 0.346396 0.938089i \(-0.387405\pi\)
0.346396 + 0.938089i \(0.387405\pi\)
\(242\) 0 0
\(243\) 5.63609e20 2.90005e21i 0.190775 0.981634i
\(244\) 0 0
\(245\) 1.41556e20i 0.0445076i
\(246\) 0 0
\(247\) −4.01746e21 −1.17403
\(248\) 0 0
\(249\) −7.48999e20 5.89396e20i −0.203558 0.160182i
\(250\) 0 0
\(251\) 1.52328e20i 0.0385227i 0.999814 + 0.0192614i \(0.00613146\pi\)
−0.999814 + 0.0192614i \(0.993869\pi\)
\(252\) 0 0
\(253\) −5.93137e21 −1.39659
\(254\) 0 0
\(255\) 1.38303e21 1.75754e21i 0.303368 0.385518i
\(256\) 0 0
\(257\) 2.25211e21i 0.460459i −0.973136 0.230229i \(-0.926052\pi\)
0.973136 0.230229i \(-0.0739477\pi\)
\(258\) 0 0
\(259\) −4.24654e21 −0.809724
\(260\) 0 0
\(261\) 4.12200e21 9.97278e20i 0.733405 0.177440i
\(262\) 0 0
\(263\) 9.39971e20i 0.156139i −0.996948 0.0780697i \(-0.975124\pi\)
0.996948 0.0780697i \(-0.0248757\pi\)
\(264\) 0 0
\(265\) 5.54605e20 0.0860539
\(266\) 0 0
\(267\) −7.78281e20 6.12438e20i −0.112859 0.0888097i
\(268\) 0 0
\(269\) 6.52766e20i 0.0885089i 0.999020 + 0.0442545i \(0.0140912\pi\)
−0.999020 + 0.0442545i \(0.985909\pi\)
\(270\) 0 0
\(271\) −8.01941e21 −1.01723 −0.508615 0.860994i \(-0.669842\pi\)
−0.508615 + 0.860994i \(0.669842\pi\)
\(272\) 0 0
\(273\) −5.56212e21 + 7.06830e21i −0.660354 + 0.839172i
\(274\) 0 0
\(275\) 9.85407e21i 1.09552i
\(276\) 0 0
\(277\) −7.20753e21 −0.750704 −0.375352 0.926882i \(-0.622478\pi\)
−0.375352 + 0.926882i \(0.622478\pi\)
\(278\) 0 0
\(279\) 2.69353e21 + 1.11330e22i 0.262956 + 1.08687i
\(280\) 0 0
\(281\) 2.02613e22i 1.85486i −0.373999 0.927429i \(-0.622014\pi\)
0.373999 0.927429i \(-0.377986\pi\)
\(282\) 0 0
\(283\) −2.45641e21 −0.210971 −0.105485 0.994421i \(-0.533640\pi\)
−0.105485 + 0.994421i \(0.533640\pi\)
\(284\) 0 0
\(285\) −4.07680e21 3.20808e21i −0.328636 0.258608i
\(286\) 0 0
\(287\) 1.22883e22i 0.930154i
\(288\) 0 0
\(289\) −6.74804e21 −0.479840
\(290\) 0 0
\(291\) 1.23792e22 1.57314e22i 0.827288 1.05131i
\(292\) 0 0
\(293\) 1.07510e22i 0.675521i 0.941232 + 0.337761i \(0.109669\pi\)
−0.941232 + 0.337761i \(0.890331\pi\)
\(294\) 0 0
\(295\) −2.43449e21 −0.143883
\(296\) 0 0
\(297\) 9.79209e21 2.13890e22i 0.544587 1.18955i
\(298\) 0 0
\(299\) 2.30840e22i 1.20856i
\(300\) 0 0
\(301\) 1.56435e21 0.0771322
\(302\) 0 0
\(303\) −7.64394e21 6.01510e21i −0.355086 0.279421i
\(304\) 0 0
\(305\) 9.06896e21i 0.397062i
\(306\) 0 0
\(307\) −1.38184e22 −0.570444 −0.285222 0.958461i \(-0.592067\pi\)
−0.285222 + 0.958461i \(0.592067\pi\)
\(308\) 0 0
\(309\) 1.47373e22 1.87280e22i 0.573840 0.729231i
\(310\) 0 0
\(311\) 1.09800e22i 0.403422i −0.979445 0.201711i \(-0.935350\pi\)
0.979445 0.201711i \(-0.0646501\pi\)
\(312\) 0 0
\(313\) −3.70789e22 −1.28596 −0.642981 0.765882i \(-0.722303\pi\)
−0.642981 + 0.765882i \(0.722303\pi\)
\(314\) 0 0
\(315\) −1.12886e22 + 2.73116e21i −0.369695 + 0.0894441i
\(316\) 0 0
\(317\) 1.41066e22i 0.436405i −0.975903 0.218203i \(-0.929981\pi\)
0.975903 0.218203i \(-0.0700194\pi\)
\(318\) 0 0
\(319\) 3.37686e22 0.987181
\(320\) 0 0
\(321\) 5.05593e22 + 3.97857e22i 1.39719 + 1.09947i
\(322\) 0 0
\(323\) 4.82735e22i 1.26150i
\(324\) 0 0
\(325\) 3.83505e22 0.948028
\(326\) 0 0
\(327\) 8.21371e21 1.04379e22i 0.192136 0.244165i
\(328\) 0 0
\(329\) 3.11629e22i 0.690040i
\(330\) 0 0
\(331\) −5.37767e21 −0.112757 −0.0563784 0.998409i \(-0.517955\pi\)
−0.0563784 + 0.998409i \(0.517955\pi\)
\(332\) 0 0
\(333\) 1.01645e22 + 4.20124e22i 0.201877 + 0.834409i
\(334\) 0 0
\(335\) 4.41222e21i 0.0830337i
\(336\) 0 0
\(337\) −7.51619e22 −1.34069 −0.670346 0.742049i \(-0.733854\pi\)
−0.670346 + 0.742049i \(0.733854\pi\)
\(338\) 0 0
\(339\) 7.80211e22 + 6.13957e22i 1.31952 + 1.03834i
\(340\) 0 0
\(341\) 9.12049e22i 1.46295i
\(342\) 0 0
\(343\) −6.88207e22 −1.04730
\(344\) 0 0
\(345\) 1.84334e22 2.34249e22i 0.266215 0.338304i
\(346\) 0 0
\(347\) 1.33632e23i 1.83208i 0.401082 + 0.916042i \(0.368634\pi\)
−0.401082 + 0.916042i \(0.631366\pi\)
\(348\) 0 0
\(349\) −2.64641e22 −0.344531 −0.172265 0.985051i \(-0.555109\pi\)
−0.172265 + 0.985051i \(0.555109\pi\)
\(350\) 0 0
\(351\) 8.32425e22 + 3.81093e22i 1.02939 + 0.471267i
\(352\) 0 0
\(353\) 9.99960e22i 1.17493i −0.809251 0.587463i \(-0.800127\pi\)
0.809251 0.587463i \(-0.199873\pi\)
\(354\) 0 0
\(355\) −4.24297e22 −0.473822
\(356\) 0 0
\(357\) 8.49322e22 + 6.68341e22i 0.901693 + 0.709552i
\(358\) 0 0
\(359\) 5.93683e22i 0.599383i −0.954036 0.299692i \(-0.903116\pi\)
0.954036 0.299692i \(-0.0968838\pi\)
\(360\) 0 0
\(361\) 7.84788e21 0.0753681
\(362\) 0 0
\(363\) 4.81576e22 6.11983e22i 0.440053 0.559216i
\(364\) 0 0
\(365\) 1.30224e22i 0.113255i
\(366\) 0 0
\(367\) 2.37011e22 0.196234 0.0981171 0.995175i \(-0.468718\pi\)
0.0981171 + 0.995175i \(0.468718\pi\)
\(368\) 0 0
\(369\) 1.21572e23 2.94132e22i 0.958511 0.231902i
\(370\) 0 0
\(371\) 2.68009e22i 0.201273i
\(372\) 0 0
\(373\) −3.66833e21 −0.0262476 −0.0131238 0.999914i \(-0.504178\pi\)
−0.0131238 + 0.999914i \(0.504178\pi\)
\(374\) 0 0
\(375\) 8.53919e22 + 6.71958e22i 0.582285 + 0.458206i
\(376\) 0 0
\(377\) 1.31422e23i 0.854273i
\(378\) 0 0
\(379\) 1.36680e22 0.0847133 0.0423566 0.999103i \(-0.486513\pi\)
0.0423566 + 0.999103i \(0.486513\pi\)
\(380\) 0 0
\(381\) 7.08740e21 9.00661e21i 0.0418950 0.0532398i
\(382\) 0 0
\(383\) 2.33776e23i 1.31829i −0.752015 0.659146i \(-0.770918\pi\)
0.752015 0.659146i \(-0.229082\pi\)
\(384\) 0 0
\(385\) −9.24791e22 −0.497619
\(386\) 0 0
\(387\) −3.74442e21 1.54766e22i −0.0192303 0.0794836i
\(388\) 0 0
\(389\) 6.57142e22i 0.322190i 0.986939 + 0.161095i \(0.0515026\pi\)
−0.986939 + 0.161095i \(0.948497\pi\)
\(390\) 0 0
\(391\) −2.77375e23 −1.29861
\(392\) 0 0
\(393\) −2.00318e23 1.57633e23i −0.895752 0.704877i
\(394\) 0 0
\(395\) 1.30754e22i 0.0558575i
\(396\) 0 0
\(397\) 3.05894e23 1.24870 0.624348 0.781146i \(-0.285365\pi\)
0.624348 + 0.781146i \(0.285365\pi\)
\(398\) 0 0
\(399\) 1.55028e23 1.97009e23i 0.604861 0.768652i
\(400\) 0 0
\(401\) 1.87752e23i 0.700301i −0.936693 0.350151i \(-0.886130\pi\)
0.936693 0.350151i \(-0.113870\pi\)
\(402\) 0 0
\(403\) −3.54955e23 −1.26598
\(404\) 0 0
\(405\) 5.40405e22 + 1.05144e23i 0.184342 + 0.358666i
\(406\) 0 0
\(407\) 3.44177e23i 1.12314i
\(408\) 0 0
\(409\) −4.15170e23 −1.29633 −0.648166 0.761499i \(-0.724464\pi\)
−0.648166 + 0.761499i \(0.724464\pi\)
\(410\) 0 0
\(411\) 1.31899e23 + 1.03793e23i 0.394154 + 0.310164i
\(412\) 0 0
\(413\) 1.17645e23i 0.336530i
\(414\) 0 0
\(415\) 3.81387e22 0.104456
\(416\) 0 0
\(417\) 2.36446e23 3.00474e23i 0.620165 0.788101i
\(418\) 0 0
\(419\) 4.77936e23i 1.20072i −0.799728 0.600362i \(-0.795023\pi\)
0.799728 0.600362i \(-0.204977\pi\)
\(420\) 0 0
\(421\) −7.31647e23 −1.76101 −0.880507 0.474034i \(-0.842797\pi\)
−0.880507 + 0.474034i \(0.842797\pi\)
\(422\) 0 0
\(423\) 3.08305e23 7.45913e22i 0.711077 0.172038i
\(424\) 0 0
\(425\) 4.60817e23i 1.01866i
\(426\) 0 0
\(427\) −4.38252e23 −0.928694
\(428\) 0 0
\(429\) 5.72878e23 + 4.50804e23i 1.16398 + 0.915951i
\(430\) 0 0
\(431\) 1.55731e23i 0.303446i 0.988423 + 0.151723i \(0.0484821\pi\)
−0.988423 + 0.151723i \(0.951518\pi\)
\(432\) 0 0
\(433\) −8.73394e23 −1.63237 −0.816186 0.577790i \(-0.803915\pi\)
−0.816186 + 0.577790i \(0.803915\pi\)
\(434\) 0 0
\(435\) −1.04945e23 + 1.33363e23i −0.188174 + 0.239130i
\(436\) 0 0
\(437\) 6.43400e23i 1.10700i
\(438\) 0 0
\(439\) −5.44754e23 −0.899538 −0.449769 0.893145i \(-0.648494\pi\)
−0.449769 + 0.893145i \(0.648494\pi\)
\(440\) 0 0
\(441\) 1.63737e22 + 6.76765e22i 0.0259536 + 0.107273i
\(442\) 0 0
\(443\) 1.37168e23i 0.208747i 0.994538 + 0.104374i \(0.0332838\pi\)
−0.994538 + 0.104374i \(0.966716\pi\)
\(444\) 0 0
\(445\) 3.96297e22 0.0579136
\(446\) 0 0
\(447\) −3.90628e23 3.07389e23i −0.548271 0.431441i
\(448\) 0 0
\(449\) 1.27019e24i 1.71259i −0.516490 0.856294i \(-0.672761\pi\)
0.516490 0.856294i \(-0.327239\pi\)
\(450\) 0 0
\(451\) 9.95954e23 1.29018
\(452\) 0 0
\(453\) 6.00687e23 7.63348e23i 0.747764 0.950252i
\(454\) 0 0
\(455\) 3.59914e23i 0.430622i
\(456\) 0 0
\(457\) 3.24758e23 0.373520 0.186760 0.982406i \(-0.440201\pi\)
0.186760 + 0.982406i \(0.440201\pi\)
\(458\) 0 0
\(459\) 4.57918e23 1.00024e24i 0.506377 1.10608i
\(460\) 0 0
\(461\) 1.03509e24i 1.10070i 0.834933 + 0.550351i \(0.185506\pi\)
−0.834933 + 0.550351i \(0.814494\pi\)
\(462\) 0 0
\(463\) −1.05861e24 −1.08270 −0.541349 0.840798i \(-0.682086\pi\)
−0.541349 + 0.840798i \(0.682086\pi\)
\(464\) 0 0
\(465\) −3.60199e23 2.83444e23i −0.354377 0.278863i
\(466\) 0 0
\(467\) 1.79684e24i 1.70082i −0.526124 0.850408i \(-0.676355\pi\)
0.526124 0.850408i \(-0.323645\pi\)
\(468\) 0 0
\(469\) 2.13218e23 0.194209
\(470\) 0 0
\(471\) −5.65792e23 + 7.19004e23i −0.495985 + 0.630294i
\(472\) 0 0
\(473\) 1.26789e23i 0.106987i
\(474\) 0 0
\(475\) −1.06891e24 −0.868359
\(476\) 0 0
\(477\) 2.65150e23 6.41505e22i 0.207409 0.0501805i
\(478\) 0 0
\(479\) 1.34665e24i 1.01446i 0.861812 + 0.507229i \(0.169330\pi\)
−0.861812 + 0.507229i \(0.830670\pi\)
\(480\) 0 0
\(481\) −1.33948e24 −0.971923
\(482\) 0 0
\(483\) 1.13200e24 + 8.90780e23i 0.791263 + 0.622654i
\(484\) 0 0
\(485\) 8.01036e23i 0.539482i
\(486\) 0 0
\(487\) 2.88392e24 1.87164 0.935819 0.352480i \(-0.114662\pi\)
0.935819 + 0.352480i \(0.114662\pi\)
\(488\) 0 0
\(489\) −6.48972e23 + 8.24708e23i −0.405926 + 0.515847i
\(490\) 0 0
\(491\) 1.45684e24i 0.878372i 0.898396 + 0.439186i \(0.144733\pi\)
−0.898396 + 0.439186i \(0.855267\pi\)
\(492\) 0 0
\(493\) 1.57916e24 0.917918
\(494\) 0 0
\(495\) 2.21357e23 + 9.14926e23i 0.124064 + 0.512790i
\(496\) 0 0
\(497\) 2.05039e24i 1.10823i
\(498\) 0 0
\(499\) 6.62415e23 0.345323 0.172661 0.984981i \(-0.444763\pi\)
0.172661 + 0.984981i \(0.444763\pi\)
\(500\) 0 0
\(501\) 2.66081e24 + 2.09382e24i 1.33805 + 1.05293i
\(502\) 0 0
\(503\) 3.54934e23i 0.172201i −0.996286 0.0861006i \(-0.972559\pi\)
0.996286 0.0861006i \(-0.0274406\pi\)
\(504\) 0 0
\(505\) 3.89225e23 0.182213
\(506\) 0 0
\(507\) −3.85650e23 + 4.90081e23i −0.174229 + 0.221409i
\(508\) 0 0
\(509\) 2.66614e24i 1.16258i 0.813697 + 0.581290i \(0.197452\pi\)
−0.813697 + 0.581290i \(0.802548\pi\)
\(510\) 0 0
\(511\) 6.29301e23 0.264893
\(512\) 0 0
\(513\) −2.32015e24 1.06219e24i −0.942886 0.431663i
\(514\) 0 0
\(515\) 9.53621e23i 0.374206i
\(516\) 0 0
\(517\) 2.52572e24 0.957128
\(518\) 0 0
\(519\) 6.63297e23 + 5.21956e23i 0.242774 + 0.191042i
\(520\) 0 0
\(521\) 6.76943e23i 0.239339i 0.992814 + 0.119669i \(0.0381834\pi\)
−0.992814 + 0.119669i \(0.961817\pi\)
\(522\) 0 0
\(523\) −1.41522e24 −0.483404 −0.241702 0.970351i \(-0.577706\pi\)
−0.241702 + 0.970351i \(0.577706\pi\)
\(524\) 0 0
\(525\) −1.47990e24 + 1.88064e24i −0.488425 + 0.620686i
\(526\) 0 0
\(527\) 4.26512e24i 1.36030i
\(528\) 0 0
\(529\) −4.52773e23 −0.139566
\(530\) 0 0
\(531\) −1.16390e24 + 2.81594e23i −0.346789 + 0.0839022i
\(532\) 0 0
\(533\) 3.87610e24i 1.11648i
\(534\) 0 0
\(535\) −2.57446e24 −0.716971
\(536\) 0 0
\(537\) −3.08441e24 2.42716e24i −0.830623 0.653626i
\(538\) 0 0
\(539\) 5.54425e23i 0.144392i
\(540\) 0 0
\(541\) 5.91029e24 1.48879 0.744395 0.667740i \(-0.232738\pi\)
0.744395 + 0.667740i \(0.232738\pi\)
\(542\) 0 0
\(543\) 4.26828e24 5.42410e24i 1.04005 1.32169i
\(544\) 0 0
\(545\) 5.31493e23i 0.125294i
\(546\) 0 0
\(547\) 2.74589e24 0.626321 0.313160 0.949700i \(-0.398612\pi\)
0.313160 + 0.949700i \(0.398612\pi\)
\(548\) 0 0
\(549\) 1.04900e24 + 4.33577e24i 0.231538 + 0.957007i
\(550\) 0 0
\(551\) 3.66302e24i 0.782483i
\(552\) 0 0
\(553\) 6.31862e23 0.130646
\(554\) 0 0
\(555\) −1.35927e24 1.06962e24i −0.272063 0.214089i
\(556\) 0 0
\(557\) 2.11583e24i 0.410001i −0.978762 0.205000i \(-0.934280\pi\)
0.978762 0.205000i \(-0.0657196\pi\)
\(558\) 0 0
\(559\) 4.93443e23 0.0925829
\(560\) 0 0
\(561\) 5.41683e24 6.88366e24i 0.984192 1.25070i
\(562\) 0 0
\(563\) 3.02777e23i 0.0532779i −0.999645 0.0266389i \(-0.991520\pi\)
0.999645 0.0266389i \(-0.00848044\pi\)
\(564\) 0 0
\(565\) −3.97280e24 −0.677112
\(566\) 0 0
\(567\) −5.08103e24 + 2.61147e24i −0.838888 + 0.431160i
\(568\) 0 0
\(569\) 7.60979e24i 1.21720i −0.793477 0.608600i \(-0.791731\pi\)
0.793477 0.608600i \(-0.208269\pi\)
\(570\) 0 0
\(571\) 8.38957e24 1.30021 0.650106 0.759843i \(-0.274724\pi\)
0.650106 + 0.759843i \(0.274724\pi\)
\(572\) 0 0
\(573\) −6.12056e24 4.81634e24i −0.919178 0.723311i
\(574\) 0 0
\(575\) 6.14188e24i 0.893904i
\(576\) 0 0
\(577\) −3.94794e24 −0.556915 −0.278457 0.960449i \(-0.589823\pi\)
−0.278457 + 0.960449i \(0.589823\pi\)
\(578\) 0 0
\(579\) −6.78526e24 + 8.62265e24i −0.927811 + 1.17905i
\(580\) 0 0
\(581\) 1.84303e24i 0.244313i
\(582\) 0 0
\(583\) 2.17219e24 0.279177
\(584\) 0 0
\(585\) −3.56075e24 + 8.61489e23i −0.443750 + 0.107361i
\(586\) 0 0
\(587\) 1.94436e23i 0.0234981i −0.999931 0.0117491i \(-0.996260\pi\)
0.999931 0.0117491i \(-0.00373993\pi\)
\(588\) 0 0
\(589\) 9.89338e24 1.15960
\(590\) 0 0
\(591\) −9.42999e24 7.42057e24i −1.07207 0.843626i
\(592\) 0 0
\(593\) 1.07663e25i 1.18733i −0.804711 0.593666i \(-0.797680\pi\)
0.804711 0.593666i \(-0.202320\pi\)
\(594\) 0 0
\(595\) −4.32471e24 −0.462705
\(596\) 0 0
\(597\) −9.66075e24 + 1.22768e25i −1.00286 + 1.27443i
\(598\) 0 0
\(599\) 1.06993e25i 1.07774i −0.842388 0.538871i \(-0.818851\pi\)
0.842388 0.538871i \(-0.181149\pi\)
\(600\) 0 0
\(601\) −1.69522e25 −1.65713 −0.828563 0.559896i \(-0.810841\pi\)
−0.828563 + 0.559896i \(0.810841\pi\)
\(602\) 0 0
\(603\) −5.10357e23 2.10944e24i −0.0484193 0.200129i
\(604\) 0 0
\(605\) 3.11619e24i 0.286962i
\(606\) 0 0
\(607\) 7.82318e24 0.699335 0.349667 0.936874i \(-0.386295\pi\)
0.349667 + 0.936874i \(0.386295\pi\)
\(608\) 0 0
\(609\) −6.44470e24 5.07141e24i −0.559303 0.440122i
\(610\) 0 0
\(611\) 9.82970e24i 0.828265i
\(612\) 0 0
\(613\) 1.87651e25 1.53534 0.767672 0.640843i \(-0.221415\pi\)
0.767672 + 0.640843i \(0.221415\pi\)
\(614\) 0 0
\(615\) −3.09520e24 + 3.93335e24i −0.245931 + 0.312526i
\(616\) 0 0
\(617\) 4.89772e24i 0.377944i 0.981983 + 0.188972i \(0.0605155\pi\)
−0.981983 + 0.188972i \(0.939485\pi\)
\(618\) 0 0
\(619\) −3.82122e24 −0.286409 −0.143204 0.989693i \(-0.545741\pi\)
−0.143204 + 0.989693i \(0.545741\pi\)
\(620\) 0 0
\(621\) 6.10324e24 1.33314e25i 0.444361 0.970623i
\(622\) 0 0
\(623\) 1.91508e24i 0.135455i
\(624\) 0 0
\(625\) 7.83732e24 0.538577
\(626\) 0 0
\(627\) −1.59674e25 1.25649e25i −1.06617 0.838978i
\(628\) 0 0
\(629\) 1.60951e25i 1.04433i
\(630\) 0 0
\(631\) 9.88067e24 0.623049 0.311524 0.950238i \(-0.399160\pi\)
0.311524 + 0.950238i \(0.399160\pi\)
\(632\) 0 0
\(633\) −1.18176e25 + 1.50177e25i −0.724264 + 0.920388i
\(634\) 0 0
\(635\) 4.58612e23i 0.0273201i
\(636\) 0 0
\(637\) −2.15773e24 −0.124952
\(638\) 0 0
\(639\) −2.02852e25 + 4.90780e24i −1.14201 + 0.276299i
\(640\) 0 0
\(641\) 1.80423e25i 0.987574i −0.869583 0.493787i \(-0.835612\pi\)
0.869583 0.493787i \(-0.164388\pi\)
\(642\) 0 0
\(643\) −3.02845e24 −0.161184 −0.0805920 0.996747i \(-0.525681\pi\)
−0.0805920 + 0.996747i \(0.525681\pi\)
\(644\) 0 0
\(645\) 5.00732e23 + 3.94031e23i 0.0259160 + 0.0203936i
\(646\) 0 0
\(647\) 1.83814e23i 0.00925209i −0.999989 0.00462604i \(-0.998527\pi\)
0.999989 0.00462604i \(-0.00147252\pi\)
\(648\) 0 0
\(649\) −9.53501e24 −0.466787
\(650\) 0 0
\(651\) 1.36973e25 1.74064e25i 0.652236 0.828857i
\(652\) 0 0
\(653\) 3.87281e25i 1.79394i −0.442092 0.896970i \(-0.645763\pi\)
0.442092 0.896970i \(-0.354237\pi\)
\(654\) 0 0
\(655\) 1.02001e25 0.459656
\(656\) 0 0
\(657\) −1.50629e24 6.22588e24i −0.0660421 0.272969i
\(658\) 0 0
\(659\) 4.07856e25i 1.73996i −0.493090 0.869978i \(-0.664133\pi\)
0.493090 0.869978i \(-0.335867\pi\)
\(660\) 0 0
\(661\) −6.61984e24 −0.274811 −0.137406 0.990515i \(-0.543876\pi\)
−0.137406 + 0.990515i \(0.543876\pi\)
\(662\) 0 0
\(663\) 2.67902e25 + 2.10815e25i 1.08231 + 0.851685i
\(664\) 0 0
\(665\) 1.00316e25i 0.394435i
\(666\) 0 0
\(667\) 2.10474e25 0.805501
\(668\) 0 0
\(669\) 6.58618e24 8.36967e24i 0.245357 0.311798i
\(670\) 0 0
\(671\) 3.55198e25i 1.28816i
\(672\) 0 0
\(673\) 4.79308e25 1.69231 0.846153 0.532941i \(-0.178913\pi\)
0.846153 + 0.532941i \(0.178913\pi\)
\(674\) 0 0
\(675\) 2.21481e25 + 1.01396e25i 0.761381 + 0.348568i
\(676\) 0 0
\(677\) 4.80922e25i 1.60982i 0.593399 + 0.804909i \(0.297786\pi\)
−0.593399 + 0.804909i \(0.702214\pi\)
\(678\) 0 0
\(679\) −3.87096e25 −1.26180
\(680\) 0 0
\(681\) −1.64492e23 1.29441e23i −0.00522182 0.00410911i
\(682\) 0 0
\(683\) 2.51210e25i 0.776695i 0.921513 + 0.388347i \(0.126954\pi\)
−0.921513 + 0.388347i \(0.873046\pi\)
\(684\) 0 0
\(685\) −6.71624e24 −0.202261
\(686\) 0 0
\(687\) −1.01456e25 + 1.28930e25i −0.297624 + 0.378218i
\(688\) 0 0
\(689\) 8.45381e24i 0.241590i
\(690\) 0 0
\(691\) 1.30800e25 0.364171 0.182085 0.983283i \(-0.441715\pi\)
0.182085 + 0.983283i \(0.441715\pi\)
\(692\) 0 0
\(693\) −4.42132e25 + 1.06970e25i −1.19937 + 0.290176i
\(694\) 0 0
\(695\) 1.53000e25i 0.404415i
\(696\) 0 0
\(697\) 4.65749e25 1.19966
\(698\) 0 0
\(699\) −1.00325e25 7.89470e24i −0.251835 0.198172i
\(700\) 0 0
\(701\) 1.51612e24i 0.0370913i 0.999828 + 0.0185456i \(0.00590360\pi\)
−0.999828 + 0.0185456i \(0.994096\pi\)
\(702\) 0 0
\(703\) 3.73343e25 0.890246
\(704\) 0 0
\(705\) −7.84936e24 + 9.97490e24i −0.182445 + 0.231850i
\(706\) 0 0
\(707\) 1.88091e25i 0.426180i
\(708\) 0 0
\(709\) 4.79750e25 1.05974 0.529869 0.848079i \(-0.322241\pi\)
0.529869 + 0.848079i \(0.322241\pi\)
\(710\) 0 0
\(711\) −1.51242e24 6.25121e24i −0.0325721 0.134629i
\(712\) 0 0
\(713\) 5.68465e25i 1.19371i
\(714\) 0 0
\(715\) −2.91707e25 −0.597299
\(716\) 0 0
\(717\) 1.96180e25 + 1.54376e25i 0.391725 + 0.308253i
\(718\) 0 0
\(719\) 1.66163e25i 0.323574i −0.986826 0.161787i \(-0.948274\pi\)
0.986826 0.161787i \(-0.0517257\pi\)
\(720\) 0 0
\(721\) −4.60832e25 −0.875235
\(722\) 0 0
\(723\) −2.31270e25 + 2.93895e25i −0.428424 + 0.544438i
\(724\) 0 0
\(725\) 3.49671e25i 0.631855i
\(726\) 0 0
\(727\) 3.23199e25 0.569718 0.284859 0.958569i \(-0.408053\pi\)
0.284859 + 0.958569i \(0.408053\pi\)
\(728\) 0 0
\(729\) 3.79981e25 + 4.40175e25i 0.653452 + 0.756968i
\(730\) 0 0
\(731\) 5.92917e24i 0.0994805i
\(732\) 0 0
\(733\) −3.49733e25 −0.572533 −0.286266 0.958150i \(-0.592414\pi\)
−0.286266 + 0.958150i \(0.592414\pi\)
\(734\) 0 0
\(735\) −2.18961e24 1.72303e24i −0.0349768 0.0275236i
\(736\) 0 0
\(737\) 1.72811e25i 0.269379i
\(738\) 0 0
\(739\) 6.36670e25 0.968533 0.484267 0.874920i \(-0.339086\pi\)
0.484267 + 0.874920i \(0.339086\pi\)
\(740\) 0 0
\(741\) 4.89006e25 6.21425e25i 0.726023 0.922624i
\(742\) 0 0
\(743\) 4.64497e25i 0.673107i 0.941664 + 0.336553i \(0.109261\pi\)
−0.941664 + 0.336553i \(0.890739\pi\)
\(744\) 0 0
\(745\) 1.98906e25 0.281346
\(746\) 0 0
\(747\) 1.82337e25 4.41146e24i 0.251761 0.0609112i
\(748\) 0 0
\(749\) 1.24409e26i 1.67693i
\(750\) 0 0
\(751\) −8.14117e25 −1.07134 −0.535670 0.844427i \(-0.679941\pi\)
−0.535670 + 0.844427i \(0.679941\pi\)
\(752\) 0 0
\(753\) −2.35623e24 1.85414e24i −0.0302735 0.0238226i
\(754\) 0 0
\(755\) 3.88693e25i 0.487623i
\(756\) 0 0
\(757\) −1.58931e26 −1.94691 −0.973455 0.228879i \(-0.926494\pi\)
−0.973455 + 0.228879i \(0.926494\pi\)
\(758\) 0 0
\(759\) 7.21968e25 9.17471e25i 0.863658 1.09753i
\(760\) 0 0
\(761\) 9.42509e25i 1.10109i 0.834805 + 0.550546i \(0.185580\pi\)
−0.834805 + 0.550546i \(0.814420\pi\)
\(762\) 0 0
\(763\) −2.56841e25 −0.293051
\(764\) 0 0
\(765\) 1.03516e25 + 4.27857e25i 0.115360 + 0.476811i
\(766\) 0 0
\(767\) 3.71088e25i 0.403941i
\(768\) 0 0
\(769\) 1.11441e26 1.18497 0.592484 0.805583i \(-0.298148\pi\)
0.592484 + 0.805583i \(0.298148\pi\)
\(770\) 0 0
\(771\) 3.48358e25 + 2.74127e25i