Properties

Label 1620.4.i.l.541.1
Level $1620$
Weight $4$
Character 1620.541
Analytic conductor $95.583$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1620,4,Mod(541,1620)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1620, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1620.541");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1620.i (of order \(3\), degree \(2\), 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: \(95.5830942093\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 60)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 541.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1620.541
Dual form 1620.4.i.l.1081.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.50000 + 4.33013i) q^{5} +(14.0000 - 24.2487i) q^{7} +(12.0000 - 20.7846i) q^{11} +(35.0000 + 60.6218i) q^{13} +102.000 q^{17} +20.0000 q^{19} +(36.0000 + 62.3538i) q^{23} +(-12.5000 + 21.6506i) q^{25} +(-153.000 + 265.004i) q^{29} +(68.0000 + 117.779i) q^{31} +140.000 q^{35} -214.000 q^{37} +(75.0000 + 129.904i) q^{41} +(146.000 - 252.879i) q^{43} +(36.0000 - 62.3538i) q^{47} +(-220.500 - 381.917i) q^{49} -414.000 q^{53} +120.000 q^{55} +(372.000 + 644.323i) q^{59} +(209.000 - 361.999i) q^{61} +(-175.000 + 303.109i) q^{65} +(-94.0000 - 162.813i) q^{67} +480.000 q^{71} +434.000 q^{73} +(-336.000 - 581.969i) q^{77} +(-676.000 + 1170.87i) q^{79} +(306.000 - 530.008i) q^{83} +(255.000 + 441.673i) q^{85} -30.0000 q^{89} +1960.00 q^{91} +(50.0000 + 86.6025i) q^{95} +(143.000 - 247.683i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 5 q^{5} + 28 q^{7} + 24 q^{11} + 70 q^{13} + 204 q^{17} + 40 q^{19} + 72 q^{23} - 25 q^{25} - 306 q^{29} + 136 q^{31} + 280 q^{35} - 428 q^{37} + 150 q^{41} + 292 q^{43} + 72 q^{47} - 441 q^{49} - 828 q^{53}+ \cdots + 286 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).

\(n\) \(811\) \(1297\) \(1541\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) 2.50000 + 4.33013i 0.223607 + 0.387298i
\(6\) 0 0
\(7\) 14.0000 24.2487i 0.755929 1.30931i −0.188982 0.981981i \(-0.560519\pi\)
0.944911 0.327327i \(-0.106148\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 12.0000 20.7846i 0.328921 0.569709i −0.653377 0.757033i \(-0.726648\pi\)
0.982298 + 0.187324i \(0.0599815\pi\)
\(12\) 0 0
\(13\) 35.0000 + 60.6218i 0.746712 + 1.29334i 0.949391 + 0.314098i \(0.101702\pi\)
−0.202679 + 0.979245i \(0.564965\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 102.000 1.45521 0.727607 0.685994i \(-0.240633\pi\)
0.727607 + 0.685994i \(0.240633\pi\)
\(18\) 0 0
\(19\) 20.0000 0.241490 0.120745 0.992684i \(-0.461472\pi\)
0.120745 + 0.992684i \(0.461472\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 36.0000 + 62.3538i 0.326370 + 0.565290i 0.981789 0.189976i \(-0.0608410\pi\)
−0.655418 + 0.755266i \(0.727508\pi\)
\(24\) 0 0
\(25\) −12.5000 + 21.6506i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −153.000 + 265.004i −0.979703 + 1.69690i −0.316253 + 0.948675i \(0.602425\pi\)
−0.663450 + 0.748220i \(0.730909\pi\)
\(30\) 0 0
\(31\) 68.0000 + 117.779i 0.393973 + 0.682381i 0.992970 0.118370i \(-0.0377670\pi\)
−0.598997 + 0.800752i \(0.704434\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 140.000 0.676123
\(36\) 0 0
\(37\) −214.000 −0.950848 −0.475424 0.879757i \(-0.657705\pi\)
−0.475424 + 0.879757i \(0.657705\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 75.0000 + 129.904i 0.285684 + 0.494819i 0.972775 0.231753i \(-0.0744460\pi\)
−0.687091 + 0.726571i \(0.741113\pi\)
\(42\) 0 0
\(43\) 146.000 252.879i 0.517786 0.896831i −0.482001 0.876171i \(-0.660090\pi\)
0.999787 0.0206606i \(-0.00657693\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 36.0000 62.3538i 0.111726 0.193516i −0.804740 0.593627i \(-0.797695\pi\)
0.916466 + 0.400112i \(0.131029\pi\)
\(48\) 0 0
\(49\) −220.500 381.917i −0.642857 1.11346i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −414.000 −1.07297 −0.536484 0.843911i \(-0.680248\pi\)
−0.536484 + 0.843911i \(0.680248\pi\)
\(54\) 0 0
\(55\) 120.000 0.294196
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 372.000 + 644.323i 0.820852 + 1.42176i 0.905048 + 0.425308i \(0.139834\pi\)
−0.0841964 + 0.996449i \(0.526832\pi\)
\(60\) 0 0
\(61\) 209.000 361.999i 0.438684 0.759823i −0.558905 0.829232i \(-0.688778\pi\)
0.997588 + 0.0694095i \(0.0221115\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −175.000 + 303.109i −0.333940 + 0.578400i
\(66\) 0 0
\(67\) −94.0000 162.813i −0.171402 0.296877i 0.767508 0.641039i \(-0.221496\pi\)
−0.938910 + 0.344162i \(0.888163\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 480.000 0.802331 0.401166 0.916006i \(-0.368605\pi\)
0.401166 + 0.916006i \(0.368605\pi\)
\(72\) 0 0
\(73\) 434.000 0.695834 0.347917 0.937525i \(-0.386889\pi\)
0.347917 + 0.937525i \(0.386889\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −336.000 581.969i −0.497283 0.861319i
\(78\) 0 0
\(79\) −676.000 + 1170.87i −0.962733 + 1.66750i −0.247148 + 0.968978i \(0.579494\pi\)
−0.715585 + 0.698526i \(0.753840\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 306.000 530.008i 0.404673 0.700914i −0.589610 0.807688i \(-0.700719\pi\)
0.994283 + 0.106774i \(0.0340520\pi\)
\(84\) 0 0
\(85\) 255.000 + 441.673i 0.325396 + 0.563602i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −30.0000 −0.0357303 −0.0178651 0.999840i \(-0.505687\pi\)
−0.0178651 + 0.999840i \(0.505687\pi\)
\(90\) 0 0
\(91\) 1960.00 2.25784
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 50.0000 + 86.6025i 0.0539989 + 0.0935288i
\(96\) 0 0
\(97\) 143.000 247.683i 0.149685 0.259262i −0.781426 0.623998i \(-0.785507\pi\)
0.931111 + 0.364736i \(0.118841\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 771.000 1335.41i 0.759578 1.31563i −0.183488 0.983022i \(-0.558739\pi\)
0.943066 0.332606i \(-0.107928\pi\)
\(102\) 0 0
\(103\) −586.000 1014.98i −0.560585 0.970962i −0.997445 0.0714329i \(-0.977243\pi\)
0.436860 0.899530i \(-0.356091\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1956.00 1.76723 0.883615 0.468214i \(-0.155102\pi\)
0.883615 + 0.468214i \(0.155102\pi\)
\(108\) 0 0
\(109\) −1858.00 −1.63270 −0.816349 0.577559i \(-0.804005\pi\)
−0.816349 + 0.577559i \(0.804005\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −87.0000 150.688i −0.0724272 0.125448i 0.827537 0.561411i \(-0.189741\pi\)
−0.899965 + 0.435963i \(0.856408\pi\)
\(114\) 0 0
\(115\) −180.000 + 311.769i −0.145957 + 0.252805i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 1428.00 2473.37i 1.10004 1.90532i
\(120\) 0 0
\(121\) 377.500 + 653.849i 0.283621 + 0.491247i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) −2068.00 −1.44492 −0.722462 0.691411i \(-0.756990\pi\)
−0.722462 + 0.691411i \(0.756990\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −156.000 270.200i −0.104044 0.180210i 0.809303 0.587391i \(-0.199845\pi\)
−0.913347 + 0.407181i \(0.866512\pi\)
\(132\) 0 0
\(133\) 280.000 484.974i 0.182549 0.316185i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1323.00 + 2291.50i −0.825048 + 1.42902i 0.0768354 + 0.997044i \(0.475518\pi\)
−0.901883 + 0.431981i \(0.857815\pi\)
\(138\) 0 0
\(139\) 638.000 + 1105.05i 0.389313 + 0.674309i 0.992357 0.123398i \(-0.0393792\pi\)
−0.603045 + 0.797707i \(0.706046\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 1680.00 0.982438
\(144\) 0 0
\(145\) −1530.00 −0.876273
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1599.00 + 2769.55i 0.879162 + 1.52275i 0.852262 + 0.523116i \(0.175230\pi\)
0.0269006 + 0.999638i \(0.491436\pi\)
\(150\) 0 0
\(151\) 380.000 658.179i 0.204794 0.354714i −0.745273 0.666760i \(-0.767681\pi\)
0.950067 + 0.312045i \(0.101014\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −340.000 + 588.897i −0.176190 + 0.305170i
\(156\) 0 0
\(157\) 83.0000 + 143.760i 0.0421919 + 0.0730784i 0.886350 0.463016i \(-0.153233\pi\)
−0.844158 + 0.536094i \(0.819899\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 2016.00 0.986851
\(162\) 0 0
\(163\) 3020.00 1.45119 0.725597 0.688120i \(-0.241564\pi\)
0.725597 + 0.688120i \(0.241564\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 492.000 + 852.169i 0.227977 + 0.394867i 0.957208 0.289400i \(-0.0934557\pi\)
−0.729232 + 0.684267i \(0.760122\pi\)
\(168\) 0 0
\(169\) −1351.50 + 2340.87i −0.615157 + 1.06548i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −981.000 + 1699.14i −0.431122 + 0.746725i −0.996970 0.0777846i \(-0.975215\pi\)
0.565849 + 0.824509i \(0.308549\pi\)
\(174\) 0 0
\(175\) 350.000 + 606.218i 0.151186 + 0.261861i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 576.000 0.240515 0.120258 0.992743i \(-0.461628\pi\)
0.120258 + 0.992743i \(0.461628\pi\)
\(180\) 0 0
\(181\) −1210.00 −0.496898 −0.248449 0.968645i \(-0.579921\pi\)
−0.248449 + 0.968645i \(0.579921\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −535.000 926.647i −0.212616 0.368262i
\(186\) 0 0
\(187\) 1224.00 2120.03i 0.478651 0.829048i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1692.00 + 2930.63i −0.640989 + 1.11022i 0.344224 + 0.938888i \(0.388142\pi\)
−0.985212 + 0.171337i \(0.945191\pi\)
\(192\) 0 0
\(193\) 1019.00 + 1764.96i 0.380048 + 0.658262i 0.991069 0.133352i \(-0.0425742\pi\)
−0.611021 + 0.791614i \(0.709241\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 4098.00 1.48208 0.741042 0.671459i \(-0.234332\pi\)
0.741042 + 0.671459i \(0.234332\pi\)
\(198\) 0 0
\(199\) −2248.00 −0.800786 −0.400393 0.916343i \(-0.631126\pi\)
−0.400393 + 0.916343i \(0.631126\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 4284.00 + 7420.11i 1.48117 + 2.56546i
\(204\) 0 0
\(205\) −375.000 + 649.519i −0.127762 + 0.221290i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 240.000 415.692i 0.0794313 0.137579i
\(210\) 0 0
\(211\) −1630.00 2823.24i −0.531819 0.921138i −0.999310 0.0371398i \(-0.988175\pi\)
0.467491 0.883998i \(-0.345158\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1460.00 0.463122
\(216\) 0 0
\(217\) 3808.00 1.19126
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 3570.00 + 6183.42i 1.08663 + 1.88209i
\(222\) 0 0
\(223\) 1490.00 2580.76i 0.447434 0.774978i −0.550784 0.834648i \(-0.685671\pi\)
0.998218 + 0.0596693i \(0.0190046\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1590.00 2753.96i 0.464899 0.805228i −0.534298 0.845296i \(-0.679424\pi\)
0.999197 + 0.0400678i \(0.0127574\pi\)
\(228\) 0 0
\(229\) −1687.00 2921.97i −0.486813 0.843184i 0.513072 0.858345i \(-0.328507\pi\)
−0.999885 + 0.0151611i \(0.995174\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1950.00 0.548278 0.274139 0.961690i \(-0.411607\pi\)
0.274139 + 0.961690i \(0.411607\pi\)
\(234\) 0 0
\(235\) 360.000 0.0999311
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −1116.00 1932.97i −0.302042 0.523152i 0.674556 0.738223i \(-0.264335\pi\)
−0.976598 + 0.215071i \(0.931002\pi\)
\(240\) 0 0
\(241\) 911.000 1577.90i 0.243497 0.421748i −0.718211 0.695825i \(-0.755039\pi\)
0.961708 + 0.274077i \(0.0883722\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1102.50 1909.59i 0.287494 0.497955i
\(246\) 0 0
\(247\) 700.000 + 1212.44i 0.180324 + 0.312330i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1488.00 0.374190 0.187095 0.982342i \(-0.440093\pi\)
0.187095 + 0.982342i \(0.440093\pi\)
\(252\) 0 0
\(253\) 1728.00 0.429401
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1497.00 + 2592.88i 0.363347 + 0.629336i 0.988510 0.151159i \(-0.0483005\pi\)
−0.625162 + 0.780495i \(0.714967\pi\)
\(258\) 0 0
\(259\) −2996.00 + 5189.22i −0.718774 + 1.24495i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1236.00 2140.81i 0.289791 0.501933i −0.683969 0.729511i \(-0.739748\pi\)
0.973760 + 0.227579i \(0.0730809\pi\)
\(264\) 0 0
\(265\) −1035.00 1792.67i −0.239923 0.415558i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 3954.00 0.896207 0.448103 0.893982i \(-0.352100\pi\)
0.448103 + 0.893982i \(0.352100\pi\)
\(270\) 0 0
\(271\) −2176.00 −0.487759 −0.243879 0.969806i \(-0.578420\pi\)
−0.243879 + 0.969806i \(0.578420\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 300.000 + 519.615i 0.0657843 + 0.113942i
\(276\) 0 0
\(277\) −517.000 + 895.470i −0.112143 + 0.194237i −0.916634 0.399728i \(-0.869105\pi\)
0.804491 + 0.593964i \(0.202438\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 3327.00 5762.53i 0.706307 1.22336i −0.259911 0.965633i \(-0.583693\pi\)
0.966218 0.257727i \(-0.0829734\pi\)
\(282\) 0 0
\(283\) 878.000 + 1520.74i 0.184423 + 0.319430i 0.943382 0.331709i \(-0.107625\pi\)
−0.758959 + 0.651138i \(0.774292\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 4200.00 0.863826
\(288\) 0 0
\(289\) 5491.00 1.11765
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1617.00 2800.73i −0.322410 0.558431i 0.658575 0.752515i \(-0.271160\pi\)
−0.980985 + 0.194085i \(0.937826\pi\)
\(294\) 0 0
\(295\) −1860.00 + 3221.61i −0.367096 + 0.635829i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −2520.00 + 4364.77i −0.487409 + 0.844218i
\(300\) 0 0
\(301\) −4088.00 7080.62i −0.782819 1.35588i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 2090.00 0.392371
\(306\) 0 0
\(307\) 2036.00 0.378504 0.189252 0.981929i \(-0.439394\pi\)
0.189252 + 0.981929i \(0.439394\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 48.0000 + 83.1384i 0.00875187 + 0.0151587i 0.870368 0.492402i \(-0.163881\pi\)
−0.861616 + 0.507560i \(0.830547\pi\)
\(312\) 0 0
\(313\) −601.000 + 1040.96i −0.108532 + 0.187983i −0.915176 0.403055i \(-0.867948\pi\)
0.806644 + 0.591038i \(0.201282\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1899.00 3289.16i 0.336462 0.582769i −0.647303 0.762233i \(-0.724103\pi\)
0.983765 + 0.179464i \(0.0574363\pi\)
\(318\) 0 0
\(319\) 3672.00 + 6360.09i 0.644491 + 1.11629i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 2040.00 0.351420
\(324\) 0 0
\(325\) −1750.00 −0.298685
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −1008.00 1745.91i −0.168914 0.292568i
\(330\) 0 0
\(331\) 2834.00 4908.63i 0.470606 0.815114i −0.528828 0.848729i \(-0.677369\pi\)
0.999435 + 0.0336145i \(0.0107018\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 470.000 814.064i 0.0766533 0.132767i
\(336\) 0 0
\(337\) 227.000 + 393.176i 0.0366928 + 0.0635538i 0.883789 0.467886i \(-0.154984\pi\)
−0.847096 + 0.531440i \(0.821651\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 3264.00 0.518345
\(342\) 0 0
\(343\) −2744.00 −0.431959
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2802.00 + 4853.21i 0.433485 + 0.750818i 0.997171 0.0751715i \(-0.0239504\pi\)
−0.563686 + 0.825989i \(0.690617\pi\)
\(348\) 0 0
\(349\) 5633.00 9756.64i 0.863976 1.49645i −0.00408463 0.999992i \(-0.501300\pi\)
0.868060 0.496458i \(-0.165366\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 3213.00 5565.08i 0.484450 0.839091i −0.515391 0.856955i \(-0.672353\pi\)
0.999840 + 0.0178638i \(0.00568654\pi\)
\(354\) 0 0
\(355\) 1200.00 + 2078.46i 0.179407 + 0.310742i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 6936.00 1.01969 0.509844 0.860267i \(-0.329703\pi\)
0.509844 + 0.860267i \(0.329703\pi\)
\(360\) 0 0
\(361\) −6459.00 −0.941682
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1085.00 + 1879.28i 0.155593 + 0.269495i
\(366\) 0 0
\(367\) 194.000 336.018i 0.0275932 0.0477929i −0.851899 0.523706i \(-0.824549\pi\)
0.879492 + 0.475913i \(0.157882\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −5796.00 + 10039.0i −0.811087 + 1.40484i
\(372\) 0 0
\(373\) 4031.00 + 6981.90i 0.559564 + 0.969193i 0.997533 + 0.0702027i \(0.0223646\pi\)
−0.437969 + 0.898990i \(0.644302\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −21420.0 −2.92622
\(378\) 0 0
\(379\) −3388.00 −0.459182 −0.229591 0.973287i \(-0.573739\pi\)
−0.229591 + 0.973287i \(0.573739\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −3492.00 6048.32i −0.465882 0.806932i 0.533359 0.845889i \(-0.320930\pi\)
−0.999241 + 0.0389576i \(0.987596\pi\)
\(384\) 0 0
\(385\) 1680.00 2909.85i 0.222392 0.385193i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 1263.00 2187.58i 0.164619 0.285128i −0.771901 0.635743i \(-0.780694\pi\)
0.936520 + 0.350615i \(0.114027\pi\)
\(390\) 0 0
\(391\) 3672.00 + 6360.09i 0.474939 + 0.822618i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −6760.00 −0.861095
\(396\) 0 0
\(397\) 6146.00 0.776975 0.388487 0.921454i \(-0.372998\pi\)
0.388487 + 0.921454i \(0.372998\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −4893.00 8474.92i −0.609339 1.05541i −0.991350 0.131248i \(-0.958102\pi\)
0.382011 0.924158i \(-0.375232\pi\)
\(402\) 0 0
\(403\) −4760.00 + 8244.56i −0.588368 + 1.01908i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −2568.00 + 4447.91i −0.312754 + 0.541706i
\(408\) 0 0
\(409\) 443.000 + 767.299i 0.0535573 + 0.0927640i 0.891561 0.452900i \(-0.149611\pi\)
−0.838004 + 0.545664i \(0.816277\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 20832.0 2.48202
\(414\) 0 0
\(415\) 3060.00 0.361951
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 5676.00 + 9831.12i 0.661792 + 1.14626i 0.980144 + 0.198285i \(0.0635370\pi\)
−0.318353 + 0.947972i \(0.603130\pi\)
\(420\) 0 0
\(421\) −5095.00 + 8824.80i −0.589822 + 1.02160i 0.404433 + 0.914568i \(0.367469\pi\)
−0.994255 + 0.107034i \(0.965865\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1275.00 + 2208.36i −0.145521 + 0.252050i
\(426\) 0 0
\(427\) −5852.00 10136.0i −0.663227 1.14874i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 2448.00 0.273587 0.136794 0.990600i \(-0.456320\pi\)
0.136794 + 0.990600i \(0.456320\pi\)
\(432\) 0 0
\(433\) −7078.00 −0.785559 −0.392779 0.919633i \(-0.628486\pi\)
−0.392779 + 0.919633i \(0.628486\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 720.000 + 1247.08i 0.0788153 + 0.136512i
\(438\) 0 0
\(439\) 9044.00 15664.7i 0.983250 1.70304i 0.333779 0.942651i \(-0.391676\pi\)
0.649470 0.760387i \(-0.274991\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −1926.00 + 3335.93i −0.206562 + 0.357776i −0.950629 0.310329i \(-0.899561\pi\)
0.744067 + 0.668105i \(0.232894\pi\)
\(444\) 0 0
\(445\) −75.0000 129.904i −0.00798953 0.0138383i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 6522.00 0.685506 0.342753 0.939426i \(-0.388641\pi\)
0.342753 + 0.939426i \(0.388641\pi\)
\(450\) 0 0
\(451\) 3600.00 0.375870
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 4900.00 + 8487.05i 0.504869 + 0.874459i
\(456\) 0 0
\(457\) −1045.00 + 1809.99i −0.106965 + 0.185269i −0.914539 0.404497i \(-0.867447\pi\)
0.807574 + 0.589766i \(0.200780\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 4947.00 8568.46i 0.499793 0.865668i −0.500207 0.865906i \(-0.666743\pi\)
1.00000 0.000238537i \(7.59288e-5\pi\)
\(462\) 0 0
\(463\) −1522.00 2636.18i −0.152772 0.264609i 0.779474 0.626435i \(-0.215487\pi\)
−0.932245 + 0.361826i \(0.882153\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 10236.0 1.01427 0.507137 0.861866i \(-0.330704\pi\)
0.507137 + 0.861866i \(0.330704\pi\)
\(468\) 0 0
\(469\) −5264.00 −0.518271
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −3504.00 6069.11i −0.340622 0.589974i
\(474\) 0 0
\(475\) −250.000 + 433.013i −0.0241490 + 0.0418273i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −5748.00 + 9955.83i −0.548294 + 0.949673i 0.450098 + 0.892979i \(0.351389\pi\)
−0.998392 + 0.0566937i \(0.981944\pi\)
\(480\) 0 0
\(481\) −7490.00 12973.1i −0.710010 1.22977i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1430.00 0.133882
\(486\) 0 0
\(487\) −15316.0 −1.42512 −0.712561 0.701610i \(-0.752465\pi\)
−0.712561 + 0.701610i \(0.752465\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 5808.00 + 10059.8i 0.533832 + 0.924624i 0.999219 + 0.0395165i \(0.0125818\pi\)
−0.465387 + 0.885107i \(0.654085\pi\)
\(492\) 0 0
\(493\) −15606.0 + 27030.4i −1.42568 + 2.46935i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 6720.00 11639.4i 0.606505 1.05050i
\(498\) 0 0
\(499\) −7498.00 12986.9i −0.672658 1.16508i −0.977147 0.212563i \(-0.931819\pi\)
0.304489 0.952516i \(-0.401514\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −21648.0 −1.91896 −0.959480 0.281778i \(-0.909076\pi\)
−0.959480 + 0.281778i \(0.909076\pi\)
\(504\) 0 0
\(505\) 7710.00 0.679387
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −1689.00 2925.43i −0.147080 0.254750i 0.783067 0.621937i \(-0.213654\pi\)
−0.930147 + 0.367187i \(0.880321\pi\)
\(510\) 0 0
\(511\) 6076.00 10523.9i 0.526001 0.911060i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 2930.00 5074.91i 0.250701 0.434228i
\(516\) 0 0
\(517\) −864.000 1496.49i −0.0734984 0.127303i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −16158.0 −1.35872 −0.679362 0.733804i \(-0.737743\pi\)
−0.679362 + 0.733804i \(0.737743\pi\)
\(522\) 0 0
\(523\) −76.0000 −0.00635420 −0.00317710 0.999995i \(-0.501011\pi\)
−0.00317710 + 0.999995i \(0.501011\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 6936.00 + 12013.5i 0.573315 + 0.993010i
\(528\) 0 0
\(529\) 3491.50 6047.46i 0.286965 0.497038i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −5250.00 + 9093.27i −0.426647 + 0.738974i
\(534\) 0 0
\(535\) 4890.00 + 8469.73i 0.395165 + 0.684445i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −10584.0 −0.845798
\(540\) 0 0
\(541\) 9278.00 0.737324 0.368662 0.929563i \(-0.379816\pi\)
0.368662 + 0.929563i \(0.379816\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −4645.00 8045.38i −0.365082 0.632341i
\(546\) 0 0
\(547\) −7282.00 + 12612.8i −0.569206 + 0.985894i 0.427438 + 0.904044i \(0.359416\pi\)
−0.996645 + 0.0818497i \(0.973917\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −3060.00 + 5300.08i −0.236589 + 0.409784i
\(552\) 0 0
\(553\) 18928.0 + 32784.3i 1.45552 + 2.52103i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 2154.00 0.163856 0.0819281 0.996638i \(-0.473892\pi\)
0.0819281 + 0.996638i \(0.473892\pi\)
\(558\) 0 0
\(559\) 20440.0 1.54655
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 4350.00 + 7534.42i 0.325632 + 0.564011i 0.981640 0.190743i \(-0.0610897\pi\)
−0.656008 + 0.754754i \(0.727756\pi\)
\(564\) 0 0
\(565\) 435.000 753.442i 0.0323904 0.0561019i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −2097.00 + 3632.11i −0.154501 + 0.267603i −0.932877 0.360195i \(-0.882710\pi\)
0.778377 + 0.627798i \(0.216044\pi\)
\(570\) 0 0
\(571\) 4010.00 + 6945.52i 0.293894 + 0.509039i 0.974727 0.223400i \(-0.0717155\pi\)
−0.680833 + 0.732438i \(0.738382\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1800.00 −0.130548
\(576\) 0 0
\(577\) −2686.00 −0.193795 −0.0968974 0.995294i \(-0.530892\pi\)
−0.0968974 + 0.995294i \(0.530892\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −8568.00 14840.2i −0.611808 1.05968i
\(582\) 0 0
\(583\) −4968.00 + 8604.83i −0.352922 + 0.611279i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1506.00 + 2608.47i −0.105893 + 0.183412i −0.914103 0.405483i \(-0.867103\pi\)
0.808210 + 0.588895i \(0.200437\pi\)
\(588\) 0 0
\(589\) 1360.00 + 2355.59i 0.0951406 + 0.164788i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −15522.0 −1.07489 −0.537447 0.843298i \(-0.680611\pi\)
−0.537447 + 0.843298i \(0.680611\pi\)
\(594\) 0 0
\(595\) 14280.0 0.983904
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −9612.00 16648.5i −0.655652 1.13562i −0.981730 0.190280i \(-0.939060\pi\)
0.326078 0.945343i \(-0.394273\pi\)
\(600\) 0 0
\(601\) 3251.00 5630.90i 0.220651 0.382178i −0.734355 0.678766i \(-0.762515\pi\)
0.955006 + 0.296587i \(0.0958486\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1887.50 + 3269.25i −0.126839 + 0.219692i
\(606\) 0 0
\(607\) −14698.0 25457.7i −0.982823 1.70230i −0.651238 0.758874i \(-0.725750\pi\)
−0.331585 0.943425i \(-0.607583\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 5040.00 0.333710
\(612\) 0 0
\(613\) −10006.0 −0.659280 −0.329640 0.944107i \(-0.606927\pi\)
−0.329640 + 0.944107i \(0.606927\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −11559.0 20020.8i −0.754210 1.30633i −0.945766 0.324849i \(-0.894687\pi\)
0.191556 0.981482i \(-0.438647\pi\)
\(618\) 0 0
\(619\) −7018.00 + 12155.5i −0.455698 + 0.789293i −0.998728 0.0504209i \(-0.983944\pi\)
0.543030 + 0.839713i \(0.317277\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −420.000 + 727.461i −0.0270095 + 0.0467819i
\(624\) 0 0
\(625\) −312.500 541.266i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −21828.0 −1.38369
\(630\) 0 0
\(631\) −4288.00 −0.270527 −0.135264 0.990810i \(-0.543188\pi\)
−0.135264 + 0.990810i \(0.543188\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −5170.00 8954.70i −0.323095 0.559617i
\(636\) 0 0
\(637\) 15435.0 26734.2i 0.960058 1.66287i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −657.000 + 1137.96i −0.0404835 + 0.0701195i −0.885557 0.464530i \(-0.846223\pi\)
0.845074 + 0.534650i \(0.179556\pi\)
\(642\) 0 0
\(643\) 314.000 + 543.864i 0.0192581 + 0.0333560i 0.875494 0.483229i \(-0.160536\pi\)
−0.856236 + 0.516585i \(0.827203\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −10944.0 −0.664997 −0.332498 0.943104i \(-0.607892\pi\)
−0.332498 + 0.943104i \(0.607892\pi\)
\(648\) 0 0
\(649\) 17856.0 1.07998
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −549.000 950.896i −0.0329005 0.0569853i 0.849106 0.528222i \(-0.177141\pi\)
−0.882007 + 0.471237i \(0.843808\pi\)
\(654\) 0 0
\(655\) 780.000 1351.00i 0.0465300 0.0805922i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −156.000 + 270.200i −0.00922139 + 0.0159719i −0.870599 0.491993i \(-0.836269\pi\)
0.861378 + 0.507965i \(0.169602\pi\)
\(660\) 0 0
\(661\) −4339.00 7515.37i −0.255322 0.442230i 0.709661 0.704543i \(-0.248848\pi\)
−0.964983 + 0.262313i \(0.915515\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 2800.00 0.163277
\(666\) 0 0
\(667\) −22032.0 −1.27898
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −5016.00 8687.97i −0.288585 0.499844i
\(672\) 0 0
\(673\) 7235.00 12531.4i 0.414396 0.717756i −0.580969 0.813926i \(-0.697326\pi\)
0.995365 + 0.0961705i \(0.0306594\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 5919.00 10252.0i 0.336020 0.582004i −0.647660 0.761929i \(-0.724252\pi\)
0.983680 + 0.179925i \(0.0575856\pi\)
\(678\) 0 0
\(679\) −4004.00 6935.13i −0.226303 0.391967i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −25548.0 −1.43128 −0.715642 0.698467i \(-0.753866\pi\)
−0.715642 + 0.698467i \(0.753866\pi\)
\(684\) 0 0
\(685\) −13230.0 −0.737945
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −14490.0 25097.4i −0.801197 1.38771i
\(690\) 0 0
\(691\) 9206.00 15945.3i 0.506820 0.877838i −0.493149 0.869945i \(-0.664154\pi\)
0.999969 0.00789325i \(-0.00251253\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −3190.00 + 5525.24i −0.174106 + 0.301560i
\(696\) 0 0
\(697\) 7650.00 + 13250.2i 0.415731 + 0.720067i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −8814.00 −0.474893 −0.237447 0.971401i \(-0.576310\pi\)
−0.237447 + 0.971401i \(0.576310\pi\)
\(702\) 0 0
\(703\) −4280.00 −0.229621
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −21588.0 37391.5i −1.14837 1.98904i
\(708\) 0 0
\(709\) 8657.00 14994.4i 0.458562 0.794253i −0.540323 0.841458i \(-0.681698\pi\)
0.998885 + 0.0472049i \(0.0150314\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −4896.00 + 8480.12i −0.257162 + 0.445418i
\(714\) 0 0
\(715\) 4200.00 + 7274.61i 0.219680 + 0.380497i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −768.000 −0.0398353 −0.0199176 0.999802i \(-0.506340\pi\)
−0.0199176 + 0.999802i \(0.506340\pi\)
\(720\) 0 0
\(721\) −32816.0 −1.69505
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −3825.00 6625.09i −0.195941 0.339379i
\(726\) 0 0
\(727\) 9098.00 15758.2i 0.464135 0.803905i −0.535027 0.844835i \(-0.679699\pi\)
0.999162 + 0.0409295i \(0.0130319\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 14892.0 25793.7i 0.753489 1.30508i
\(732\) 0 0
\(733\) 9071.00 + 15711.4i 0.457087 + 0.791699i 0.998806 0.0488616i \(-0.0155593\pi\)
−0.541718 + 0.840560i \(0.682226\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −4512.00 −0.225511
\(738\) 0 0
\(739\) −13660.0 −0.679961 −0.339981 0.940432i \(-0.610420\pi\)
−0.339981 + 0.940432i \(0.610420\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 6384.00 + 11057.4i 0.315217 + 0.545972i 0.979484 0.201524i \(-0.0645894\pi\)
−0.664267 + 0.747496i \(0.731256\pi\)
\(744\) 0 0
\(745\) −7995.00 + 13847.7i −0.393173 + 0.680996i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 27384.0 47430.5i 1.33590 2.31385i
\(750\) 0 0
\(751\) −11476.0 19877.0i −0.557610 0.965809i −0.997695 0.0678530i \(-0.978385\pi\)
0.440085 0.897956i \(-0.354948\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 3800.00 0.183174
\(756\) 0 0
\(757\) 15818.0 0.759465 0.379732 0.925096i \(-0.376016\pi\)
0.379732 + 0.925096i \(0.376016\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 9279.00 + 16071.7i 0.442002 + 0.765570i 0.997838 0.0657221i \(-0.0209351\pi\)
−0.555836 + 0.831292i \(0.687602\pi\)
\(762\) 0 0
\(763\) −26012.0 + 45054.1i −1.23420 + 2.13770i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −26040.0 + 45102.6i −1.22588 + 2.12329i
\(768\) 0 0
\(769\) −7489.00 12971.3i −0.351184 0.608268i 0.635273 0.772287i \(-0.280887\pi\)
−0.986457 + 0.164019i \(0.947554\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 8946.00 0.416255 0.208128 0.978102i \(-0.433263\pi\)
0.208128 + 0.978102i \(0.433263\pi\)
\(774\) 0 0
\(775\) −3400.00 −0.157589
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1500.00 + 2598.08i 0.0689898 + 0.119494i
\(780\) 0 0
\(781\) 5760.00 9976.61i 0.263904 0.457095i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −415.000 + 718.801i −0.0188688 + 0.0326817i
\(786\) 0 0
\(787\) 9218.00 + 15966.0i 0.417517 + 0.723161i 0.995689 0.0927538i \(-0.0295669\pi\)
−0.578172 + 0.815915i \(0.696234\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −4872.00 −0.218999
\(792\) 0 0
\(793\) 29260.0 1.31028
\(794\) 0 0