Properties

Label 432.4.i.a.289.1
Level $432$
Weight $4$
Character 432.289
Analytic conductor $25.489$
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] = [432,4,Mod(145,432)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(432, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("432.145");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 432.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: \(25.4888251225\)
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 18)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 289.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 432.289
Dual form 432.4.i.a.145.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-4.50000 - 7.79423i) q^{5} +(-15.5000 + 26.8468i) q^{7} +O(q^{10})\) \(q+(-4.50000 - 7.79423i) q^{5} +(-15.5000 + 26.8468i) q^{7} +(7.50000 - 12.9904i) q^{11} +(18.5000 + 32.0429i) q^{13} +42.0000 q^{17} +28.0000 q^{19} +(-97.5000 - 168.875i) q^{23} +(22.0000 - 38.1051i) q^{25} +(55.5000 - 96.1288i) q^{29} +(-102.500 - 177.535i) q^{31} +279.000 q^{35} -166.000 q^{37} +(-130.500 - 226.033i) q^{41} +(-21.5000 + 37.2391i) q^{43} +(-88.5000 + 153.286i) q^{47} +(-309.000 - 535.204i) q^{49} -114.000 q^{53} -135.000 q^{55} +(-79.5000 - 137.698i) q^{59} +(-95.5000 + 165.411i) q^{61} +(166.500 - 288.386i) q^{65} +(-210.500 - 364.597i) q^{67} +156.000 q^{71} +182.000 q^{73} +(232.500 + 402.702i) q^{77} +(566.500 - 981.207i) q^{79} +(541.500 - 937.906i) q^{83} +(-189.000 - 327.358i) q^{85} +1050.00 q^{89} -1147.00 q^{91} +(-126.000 - 218.238i) q^{95} +(450.500 - 780.289i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 9 q^{5} - 31 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 9 q^{5} - 31 q^{7} + 15 q^{11} + 37 q^{13} + 84 q^{17} + 56 q^{19} - 195 q^{23} + 44 q^{25} + 111 q^{29} - 205 q^{31} + 558 q^{35} - 332 q^{37} - 261 q^{41} - 43 q^{43} - 177 q^{47} - 618 q^{49} - 228 q^{53} - 270 q^{55} - 159 q^{59} - 191 q^{61} + 333 q^{65} - 421 q^{67} + 312 q^{71} + 364 q^{73} + 465 q^{77} + 1133 q^{79} + 1083 q^{83} - 378 q^{85} + 2100 q^{89} - 2294 q^{91} - 252 q^{95} + 901 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(5\) −4.50000 7.79423i −0.402492 0.697137i 0.591534 0.806280i \(-0.298523\pi\)
−0.994026 + 0.109143i \(0.965189\pi\)
\(6\) 0 0
\(7\) −15.5000 + 26.8468i −0.836921 + 1.44959i 0.0555351 + 0.998457i \(0.482314\pi\)
−0.892456 + 0.451134i \(0.851020\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 7.50000 12.9904i 0.205576 0.356068i −0.744740 0.667355i \(-0.767427\pi\)
0.950316 + 0.311287i \(0.100760\pi\)
\(12\) 0 0
\(13\) 18.5000 + 32.0429i 0.394691 + 0.683624i 0.993062 0.117595i \(-0.0375185\pi\)
−0.598371 + 0.801219i \(0.704185\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 42.0000 0.599206 0.299603 0.954064i \(-0.403146\pi\)
0.299603 + 0.954064i \(0.403146\pi\)
\(18\) 0 0
\(19\) 28.0000 0.338086 0.169043 0.985609i \(-0.445932\pi\)
0.169043 + 0.985609i \(0.445932\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −97.5000 168.875i −0.883920 1.53099i −0.846947 0.531678i \(-0.821562\pi\)
−0.0369731 0.999316i \(-0.511772\pi\)
\(24\) 0 0
\(25\) 22.0000 38.1051i 0.176000 0.304841i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 55.5000 96.1288i 0.355382 0.615540i −0.631801 0.775131i \(-0.717684\pi\)
0.987183 + 0.159590i \(0.0510173\pi\)
\(30\) 0 0
\(31\) −102.500 177.535i −0.593856 1.02859i −0.993707 0.112009i \(-0.964271\pi\)
0.399851 0.916580i \(-0.369062\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 279.000 1.34742
\(36\) 0 0
\(37\) −166.000 −0.737574 −0.368787 0.929514i \(-0.620227\pi\)
−0.368787 + 0.929514i \(0.620227\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −130.500 226.033i −0.497090 0.860985i 0.502905 0.864342i \(-0.332265\pi\)
−0.999994 + 0.00335732i \(0.998931\pi\)
\(42\) 0 0
\(43\) −21.5000 + 37.2391i −0.0762493 + 0.132068i −0.901629 0.432511i \(-0.857628\pi\)
0.825380 + 0.564578i \(0.190961\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −88.5000 + 153.286i −0.274661 + 0.475726i −0.970049 0.242907i \(-0.921899\pi\)
0.695389 + 0.718634i \(0.255232\pi\)
\(48\) 0 0
\(49\) −309.000 535.204i −0.900875 1.56036i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −114.000 −0.295455 −0.147727 0.989028i \(-0.547196\pi\)
−0.147727 + 0.989028i \(0.547196\pi\)
\(54\) 0 0
\(55\) −135.000 −0.330971
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −79.5000 137.698i −0.175424 0.303843i 0.764884 0.644168i \(-0.222796\pi\)
−0.940308 + 0.340325i \(0.889463\pi\)
\(60\) 0 0
\(61\) −95.5000 + 165.411i −0.200451 + 0.347192i −0.948674 0.316256i \(-0.897574\pi\)
0.748223 + 0.663448i \(0.230907\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 166.500 288.386i 0.317720 0.550307i
\(66\) 0 0
\(67\) −210.500 364.597i −0.383831 0.664815i 0.607775 0.794109i \(-0.292062\pi\)
−0.991606 + 0.129294i \(0.958729\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 156.000 0.260758 0.130379 0.991464i \(-0.458381\pi\)
0.130379 + 0.991464i \(0.458381\pi\)
\(72\) 0 0
\(73\) 182.000 0.291801 0.145901 0.989299i \(-0.453392\pi\)
0.145901 + 0.989299i \(0.453392\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 232.500 + 402.702i 0.344102 + 0.596002i
\(78\) 0 0
\(79\) 566.500 981.207i 0.806788 1.39740i −0.108290 0.994119i \(-0.534537\pi\)
0.915078 0.403278i \(-0.132129\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 541.500 937.906i 0.716113 1.24034i −0.246416 0.969164i \(-0.579253\pi\)
0.962529 0.271179i \(-0.0874136\pi\)
\(84\) 0 0
\(85\) −189.000 327.358i −0.241176 0.417728i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1050.00 1.25056 0.625280 0.780401i \(-0.284985\pi\)
0.625280 + 0.780401i \(0.284985\pi\)
\(90\) 0 0
\(91\) −1147.00 −1.32130
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −126.000 218.238i −0.136077 0.235693i
\(96\) 0 0
\(97\) 450.500 780.289i 0.471560 0.816766i −0.527910 0.849300i \(-0.677024\pi\)
0.999471 + 0.0325338i \(0.0103576\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 193.500 335.152i 0.190633 0.330187i −0.754827 0.655924i \(-0.772279\pi\)
0.945460 + 0.325737i \(0.105613\pi\)
\(102\) 0 0
\(103\) 275.500 + 477.180i 0.263552 + 0.456485i 0.967183 0.254080i \(-0.0817727\pi\)
−0.703631 + 0.710565i \(0.748439\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −12.0000 −0.0108419 −0.00542095 0.999985i \(-0.501726\pi\)
−0.00542095 + 0.999985i \(0.501726\pi\)
\(108\) 0 0
\(109\) −502.000 −0.441127 −0.220564 0.975373i \(-0.570790\pi\)
−0.220564 + 0.975373i \(0.570790\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −700.500 1213.30i −0.583164 1.01007i −0.995102 0.0988572i \(-0.968481\pi\)
0.411938 0.911212i \(-0.364852\pi\)
\(114\) 0 0
\(115\) −877.500 + 1519.87i −0.711542 + 1.23243i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −651.000 + 1127.57i −0.501488 + 0.868603i
\(120\) 0 0
\(121\) 553.000 + 957.824i 0.415477 + 0.719627i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1521.00 −1.08834
\(126\) 0 0
\(127\) 880.000 0.614861 0.307431 0.951571i \(-0.400531\pi\)
0.307431 + 0.951571i \(0.400531\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −751.500 1301.64i −0.501213 0.868126i −0.999999 0.00140084i \(-0.999554\pi\)
0.498786 0.866725i \(-0.333779\pi\)
\(132\) 0 0
\(133\) −434.000 + 751.710i −0.282952 + 0.490087i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1330.50 + 2304.49i −0.829725 + 1.43713i 0.0685295 + 0.997649i \(0.478169\pi\)
−0.898254 + 0.439476i \(0.855164\pi\)
\(138\) 0 0
\(139\) −60.5000 104.789i −0.0369176 0.0639431i 0.846976 0.531631i \(-0.178421\pi\)
−0.883894 + 0.467688i \(0.845087\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 555.000 0.324555
\(144\) 0 0
\(145\) −999.000 −0.572155
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1414.50 2449.99i −0.777721 1.34705i −0.933253 0.359221i \(-0.883043\pi\)
0.155532 0.987831i \(-0.450291\pi\)
\(150\) 0 0
\(151\) 230.500 399.238i 0.124224 0.215162i −0.797205 0.603708i \(-0.793689\pi\)
0.921429 + 0.388546i \(0.127023\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −922.500 + 1597.82i −0.478045 + 0.827998i
\(156\) 0 0
\(157\) 1488.50 + 2578.16i 0.756658 + 1.31057i 0.944546 + 0.328379i \(0.106502\pi\)
−0.187889 + 0.982190i \(0.560164\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 6045.00 2.95909
\(162\) 0 0
\(163\) 3316.00 1.59343 0.796715 0.604355i \(-0.206569\pi\)
0.796715 + 0.604355i \(0.206569\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 340.500 + 589.763i 0.157777 + 0.273277i 0.934067 0.357099i \(-0.116234\pi\)
−0.776290 + 0.630376i \(0.782901\pi\)
\(168\) 0 0
\(169\) 414.000 717.069i 0.188439 0.326386i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1990.50 + 3447.65i −0.874768 + 1.51514i −0.0177589 + 0.999842i \(0.505653\pi\)
−0.857009 + 0.515301i \(0.827680\pi\)
\(174\) 0 0
\(175\) 682.000 + 1181.26i 0.294596 + 0.510256i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 2004.00 0.836793 0.418397 0.908264i \(-0.362592\pi\)
0.418397 + 0.908264i \(0.362592\pi\)
\(180\) 0 0
\(181\) 1274.00 0.523181 0.261590 0.965179i \(-0.415753\pi\)
0.261590 + 0.965179i \(0.415753\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 747.000 + 1293.84i 0.296868 + 0.514190i
\(186\) 0 0
\(187\) 315.000 545.596i 0.123182 0.213358i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −580.500 + 1005.46i −0.219914 + 0.380902i −0.954781 0.297309i \(-0.903911\pi\)
0.734868 + 0.678210i \(0.237244\pi\)
\(192\) 0 0
\(193\) −1805.50 3127.22i −0.673382 1.16633i −0.976939 0.213519i \(-0.931508\pi\)
0.303557 0.952813i \(-0.401826\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −2046.00 −0.739957 −0.369978 0.929040i \(-0.620635\pi\)
−0.369978 + 0.929040i \(0.620635\pi\)
\(198\) 0 0
\(199\) −2996.00 −1.06724 −0.533620 0.845724i \(-0.679169\pi\)
−0.533620 + 0.845724i \(0.679169\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1720.50 + 2979.99i 0.594854 + 1.03032i
\(204\) 0 0
\(205\) −1174.50 + 2034.29i −0.400149 + 0.693079i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 210.000 363.731i 0.0695024 0.120382i
\(210\) 0 0
\(211\) 377.500 + 653.849i 0.123167 + 0.213331i 0.921015 0.389528i \(-0.127362\pi\)
−0.797848 + 0.602858i \(0.794028\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 387.000 0.122759
\(216\) 0 0
\(217\) 6355.00 1.98804
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 777.000 + 1345.80i 0.236501 + 0.409631i
\(222\) 0 0
\(223\) −1731.50 + 2999.05i −0.519954 + 0.900587i 0.479777 + 0.877391i \(0.340718\pi\)
−0.999731 + 0.0231966i \(0.992616\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −3112.50 + 5391.01i −0.910061 + 1.57627i −0.0960856 + 0.995373i \(0.530632\pi\)
−0.813976 + 0.580899i \(0.802701\pi\)
\(228\) 0 0
\(229\) 732.500 + 1268.73i 0.211375 + 0.366113i 0.952145 0.305646i \(-0.0988724\pi\)
−0.740770 + 0.671759i \(0.765539\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −2634.00 −0.740597 −0.370298 0.928913i \(-0.620745\pi\)
−0.370298 + 0.928913i \(0.620745\pi\)
\(234\) 0 0
\(235\) 1593.00 0.442195
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −3457.50 5988.57i −0.935762 1.62079i −0.773270 0.634077i \(-0.781380\pi\)
−0.162492 0.986710i \(-0.551953\pi\)
\(240\) 0 0
\(241\) 744.500 1289.51i 0.198994 0.344667i −0.749209 0.662334i \(-0.769566\pi\)
0.948202 + 0.317667i \(0.102899\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −2781.00 + 4816.83i −0.725190 + 1.25607i
\(246\) 0 0
\(247\) 518.000 + 897.202i 0.133439 + 0.231124i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −4620.00 −1.16180 −0.580900 0.813975i \(-0.697299\pi\)
−0.580900 + 0.813975i \(0.697299\pi\)
\(252\) 0 0
\(253\) −2925.00 −0.726850
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1675.50 + 2902.05i 0.406672 + 0.704377i 0.994515 0.104598i \(-0.0333557\pi\)
−0.587842 + 0.808976i \(0.700022\pi\)
\(258\) 0 0
\(259\) 2573.00 4456.57i 0.617291 1.06918i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 301.500 522.213i 0.0706893 0.122437i −0.828514 0.559968i \(-0.810813\pi\)
0.899204 + 0.437530i \(0.144147\pi\)
\(264\) 0 0
\(265\) 513.000 + 888.542i 0.118918 + 0.205972i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1470.00 0.333188 0.166594 0.986026i \(-0.446723\pi\)
0.166594 + 0.986026i \(0.446723\pi\)
\(270\) 0 0
\(271\) −2072.00 −0.464447 −0.232223 0.972662i \(-0.574600\pi\)
−0.232223 + 0.972662i \(0.574600\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −330.000 571.577i −0.0723627 0.125336i
\(276\) 0 0
\(277\) −3569.50 + 6182.56i −0.774262 + 1.34106i 0.160947 + 0.986963i \(0.448545\pi\)
−0.935209 + 0.354097i \(0.884788\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 4213.50 7298.00i 0.894507 1.54933i 0.0600924 0.998193i \(-0.480860\pi\)
0.834414 0.551138i \(-0.185806\pi\)
\(282\) 0 0
\(283\) −228.500 395.774i −0.0479962 0.0831318i 0.841029 0.540990i \(-0.181950\pi\)
−0.889025 + 0.457858i \(0.848617\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 8091.00 1.66410
\(288\) 0 0
\(289\) −3149.00 −0.640953
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −2944.50 5100.02i −0.587097 1.01688i −0.994610 0.103683i \(-0.966937\pi\)
0.407513 0.913199i \(-0.366396\pi\)
\(294\) 0 0
\(295\) −715.500 + 1239.28i −0.141214 + 0.244589i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 3607.50 6248.37i 0.697750 1.20854i
\(300\) 0 0
\(301\) −666.500 1154.41i −0.127629 0.221060i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1719.00 0.322720
\(306\) 0 0
\(307\) 1204.00 0.223830 0.111915 0.993718i \(-0.464302\pi\)
0.111915 + 0.993718i \(0.464302\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1642.50 + 2844.89i 0.299478 + 0.518711i 0.976017 0.217696i \(-0.0698542\pi\)
−0.676539 + 0.736407i \(0.736521\pi\)
\(312\) 0 0
\(313\) 5028.50 8709.62i 0.908075 1.57283i 0.0913406 0.995820i \(-0.470885\pi\)
0.816735 0.577013i \(-0.195782\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1147.50 1987.53i 0.203312 0.352147i −0.746281 0.665631i \(-0.768163\pi\)
0.949594 + 0.313483i \(0.101496\pi\)
\(318\) 0 0
\(319\) −832.500 1441.93i −0.146116 0.253081i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1176.00 0.202583
\(324\) 0 0
\(325\) 1628.00 0.277862
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −2743.50 4751.88i −0.459739 0.796291i
\(330\) 0 0
\(331\) −3339.50 + 5784.18i −0.554548 + 0.960506i 0.443390 + 0.896329i \(0.353776\pi\)
−0.997939 + 0.0641773i \(0.979558\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −1894.50 + 3281.37i −0.308978 + 0.535165i
\(336\) 0 0
\(337\) −1091.50 1890.53i −0.176433 0.305590i 0.764224 0.644951i \(-0.223122\pi\)
−0.940656 + 0.339361i \(0.889789\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −3075.00 −0.488330
\(342\) 0 0
\(343\) 8525.00 1.34200
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1945.50 3369.70i −0.300980 0.521312i 0.675379 0.737471i \(-0.263980\pi\)
−0.976358 + 0.216159i \(0.930647\pi\)
\(348\) 0 0
\(349\) −1397.50 + 2420.54i −0.214345 + 0.371257i −0.953070 0.302751i \(-0.902095\pi\)
0.738725 + 0.674007i \(0.235428\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2377.50 4117.95i 0.358475 0.620896i −0.629232 0.777218i \(-0.716630\pi\)
0.987706 + 0.156322i \(0.0499636\pi\)
\(354\) 0 0
\(355\) −702.000 1215.90i −0.104953 0.181784i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 4608.00 0.677440 0.338720 0.940887i \(-0.390006\pi\)
0.338720 + 0.940887i \(0.390006\pi\)
\(360\) 0 0
\(361\) −6075.00 −0.885698
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −819.000 1418.55i −0.117448 0.203425i
\(366\) 0 0
\(367\) 1922.50 3329.87i 0.273443 0.473618i −0.696298 0.717753i \(-0.745171\pi\)
0.969741 + 0.244135i \(0.0785041\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1767.00 3060.53i 0.247272 0.428288i
\(372\) 0 0
\(373\) 4158.50 + 7202.73i 0.577263 + 0.999848i 0.995792 + 0.0916449i \(0.0292125\pi\)
−0.418529 + 0.908203i \(0.637454\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 4107.00 0.561064
\(378\) 0 0
\(379\) −12560.0 −1.70228 −0.851140 0.524939i \(-0.824088\pi\)
−0.851140 + 0.524939i \(0.824088\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −6043.50 10467.6i −0.806288 1.39653i −0.915418 0.402505i \(-0.868140\pi\)
0.109130 0.994028i \(-0.465194\pi\)
\(384\) 0 0
\(385\) 2092.50 3624.32i 0.276997 0.479772i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −4270.50 + 7396.72i −0.556614 + 0.964084i 0.441162 + 0.897428i \(0.354567\pi\)
−0.997776 + 0.0666565i \(0.978767\pi\)
\(390\) 0 0
\(391\) −4095.00 7092.75i −0.529650 0.917380i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −10197.0 −1.29890
\(396\) 0 0
\(397\) −13174.0 −1.66545 −0.832726 0.553686i \(-0.813221\pi\)
−0.832726 + 0.553686i \(0.813221\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 4801.50 + 8316.44i 0.597944 + 1.03567i 0.993124 + 0.117066i \(0.0373488\pi\)
−0.395180 + 0.918604i \(0.629318\pi\)
\(402\) 0 0
\(403\) 3792.50 6568.80i 0.468779 0.811949i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −1245.00 + 2156.40i −0.151627 + 0.262626i
\(408\) 0 0
\(409\) −5735.50 9934.18i −0.693404 1.20101i −0.970716 0.240231i \(-0.922777\pi\)
0.277312 0.960780i \(-0.410557\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 4929.00 0.587264
\(414\) 0 0
\(415\) −9747.00 −1.15292
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 2986.50 + 5172.77i 0.348210 + 0.603118i 0.985932 0.167149i \(-0.0534562\pi\)
−0.637721 + 0.770267i \(0.720123\pi\)
\(420\) 0 0
\(421\) 4452.50 7711.96i 0.515443 0.892774i −0.484396 0.874849i \(-0.660961\pi\)
0.999839 0.0179250i \(-0.00570601\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 924.000 1600.41i 0.105460 0.182662i
\(426\) 0 0
\(427\) −2960.50 5127.74i −0.335524 0.581144i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 1416.00 0.158251 0.0791257 0.996865i \(-0.474787\pi\)
0.0791257 + 0.996865i \(0.474787\pi\)
\(432\) 0 0
\(433\) 10766.0 1.19488 0.597438 0.801915i \(-0.296186\pi\)
0.597438 + 0.801915i \(0.296186\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −2730.00 4728.50i −0.298841 0.517608i
\(438\) 0 0
\(439\) 2174.50 3766.34i 0.236408 0.409471i −0.723273 0.690562i \(-0.757363\pi\)
0.959681 + 0.281091i \(0.0906964\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 7273.50 12598.1i 0.780078 1.35113i −0.151818 0.988408i \(-0.548513\pi\)
0.931896 0.362726i \(-0.118154\pi\)
\(444\) 0 0
\(445\) −4725.00 8183.94i −0.503340 0.871811i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 3330.00 0.350005 0.175003 0.984568i \(-0.444007\pi\)
0.175003 + 0.984568i \(0.444007\pi\)
\(450\) 0 0
\(451\) −3915.00 −0.408759
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 5161.50 + 8939.98i 0.531813 + 0.921127i
\(456\) 0 0
\(457\) −4073.50 + 7055.51i −0.416959 + 0.722194i −0.995632 0.0933655i \(-0.970237\pi\)
0.578673 + 0.815560i \(0.303571\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 4015.50 6955.05i 0.405684 0.702666i −0.588717 0.808340i \(-0.700367\pi\)
0.994401 + 0.105674i \(0.0336999\pi\)
\(462\) 0 0
\(463\) 2141.50 + 3709.19i 0.214955 + 0.372312i 0.953259 0.302156i \(-0.0977063\pi\)
−0.738304 + 0.674468i \(0.764373\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 5460.00 0.541025 0.270512 0.962716i \(-0.412807\pi\)
0.270512 + 0.962716i \(0.412807\pi\)
\(468\) 0 0
\(469\) 13051.0 1.28494
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 322.500 + 558.586i 0.0313500 + 0.0542999i
\(474\) 0 0
\(475\) 616.000 1066.94i 0.0595032 0.103063i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −214.500 + 371.525i −0.0204609 + 0.0354393i −0.876075 0.482176i \(-0.839847\pi\)
0.855614 + 0.517615i \(0.173180\pi\)
\(480\) 0 0
\(481\) −3071.00 5319.13i −0.291113 0.504223i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −8109.00 −0.759197
\(486\) 0 0
\(487\) 11296.0 1.05107 0.525535 0.850772i \(-0.323865\pi\)
0.525535 + 0.850772i \(0.323865\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 7336.50 + 12707.2i 0.674321 + 1.16796i 0.976667 + 0.214760i \(0.0688969\pi\)
−0.302346 + 0.953198i \(0.597770\pi\)
\(492\) 0 0
\(493\) 2331.00 4037.41i 0.212947 0.368835i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −2418.00 + 4188.10i −0.218234 + 0.377992i
\(498\) 0 0
\(499\) 6719.50 + 11638.5i 0.602818 + 1.04411i 0.992392 + 0.123116i \(0.0392888\pi\)
−0.389574 + 0.920995i \(0.627378\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −17388.0 −1.54134 −0.770669 0.637236i \(-0.780078\pi\)
−0.770669 + 0.637236i \(0.780078\pi\)
\(504\) 0 0
\(505\) −3483.00 −0.306914
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −1894.50 3281.37i −0.164975 0.285745i 0.771671 0.636021i \(-0.219421\pi\)
−0.936646 + 0.350276i \(0.886088\pi\)
\(510\) 0 0
\(511\) −2821.00 + 4886.12i −0.244215 + 0.422992i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 2479.50 4294.62i 0.212155 0.367463i
\(516\) 0 0
\(517\) 1327.50 + 2299.30i 0.112927 + 0.195596i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −9786.00 −0.822903 −0.411451 0.911432i \(-0.634978\pi\)
−0.411451 + 0.911432i \(0.634978\pi\)
\(522\) 0 0
\(523\) 8008.00 0.669532 0.334766 0.942301i \(-0.391343\pi\)
0.334766 + 0.942301i \(0.391343\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −4305.00 7456.48i −0.355842 0.616336i
\(528\) 0 0
\(529\) −12929.0 + 22393.7i −1.06263 + 1.84053i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 4828.50 8363.21i 0.392393 0.679645i
\(534\) 0 0
\(535\) 54.0000 + 93.5307i 0.00436378 + 0.00755829i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −9270.00 −0.740793
\(540\) 0 0
\(541\) −2938.00 −0.233483 −0.116742 0.993162i \(-0.537245\pi\)
−0.116742 + 0.993162i \(0.537245\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 2259.00 + 3912.70i 0.177550 + 0.307526i
\(546\) 0 0
\(547\) −5187.50 + 8985.01i −0.405487 + 0.702324i −0.994378 0.105888i \(-0.966231\pi\)
0.588891 + 0.808213i \(0.299565\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 1554.00 2691.61i 0.120150 0.208106i
\(552\) 0 0
\(553\) 17561.5 + 30417.4i 1.35044 + 2.33902i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −3306.00 −0.251490 −0.125745 0.992063i \(-0.540132\pi\)
−0.125745 + 0.992063i \(0.540132\pi\)
\(558\) 0 0
\(559\) −1591.00 −0.120379
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 10546.5 + 18267.1i 0.789488 + 1.36743i 0.926281 + 0.376834i \(0.122987\pi\)
−0.136792 + 0.990600i \(0.543679\pi\)
\(564\) 0 0
\(565\) −6304.50 + 10919.7i −0.469438 + 0.813090i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 643.500 1114.57i 0.0474111 0.0821185i −0.841346 0.540497i \(-0.818236\pi\)
0.888757 + 0.458379i \(0.151570\pi\)
\(570\) 0 0
\(571\) 7517.50 + 13020.7i 0.550959 + 0.954289i 0.998206 + 0.0598783i \(0.0190713\pi\)
−0.447247 + 0.894411i \(0.647595\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −8580.00 −0.622280
\(576\) 0 0
\(577\) 1190.00 0.0858585 0.0429292 0.999078i \(-0.486331\pi\)
0.0429292 + 0.999078i \(0.486331\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 16786.5 + 29075.1i 1.19866 + 2.07614i
\(582\) 0 0
\(583\) −855.000 + 1480.90i −0.0607384 + 0.105202i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 8941.50 15487.1i 0.628714 1.08896i −0.359096 0.933301i \(-0.616915\pi\)
0.987810 0.155664i \(-0.0497518\pi\)
\(588\) 0 0
\(589\) −2870.00 4970.99i −0.200775 0.347752i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −20118.0 −1.39317 −0.696583 0.717476i \(-0.745297\pi\)
−0.696583 + 0.717476i \(0.745297\pi\)
\(594\) 0 0
\(595\) 11718.0 0.807380
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 532.500 + 922.317i 0.0363228 + 0.0629129i 0.883615 0.468214i \(-0.155102\pi\)
−0.847293 + 0.531127i \(0.821769\pi\)
\(600\) 0 0
\(601\) 10362.5 17948.4i 0.703320 1.21819i −0.263975 0.964530i \(-0.585034\pi\)
0.967294 0.253656i \(-0.0816331\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 4977.00 8620.42i 0.334453 0.579289i
\(606\) 0 0
\(607\) −7872.50 13635.6i −0.526417 0.911780i −0.999526 0.0307768i \(-0.990202\pi\)
0.473110 0.881004i \(-0.343131\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −6549.00 −0.433624
\(612\) 0 0
\(613\) 5042.00 0.332210 0.166105 0.986108i \(-0.446881\pi\)
0.166105 + 0.986108i \(0.446881\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −5026.50 8706.15i −0.327973 0.568066i 0.654137 0.756376i \(-0.273032\pi\)
−0.982110 + 0.188311i \(0.939699\pi\)
\(618\) 0 0
\(619\) −2991.50 + 5181.43i −0.194246 + 0.336445i −0.946653 0.322254i \(-0.895559\pi\)
0.752407 + 0.658699i \(0.228893\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −16275.0 + 28189.1i −1.04662 + 1.81280i
\(624\) 0 0
\(625\) 4094.50 + 7091.88i 0.262048 + 0.453880i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −6972.00 −0.441958
\(630\) 0 0
\(631\) 19696.0 1.24261 0.621304 0.783570i \(-0.286603\pi\)
0.621304 + 0.783570i \(0.286603\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −3960.00 6858.92i −0.247477 0.428642i
\(636\) 0 0
\(637\) 11433.0 19802.5i 0.711133 1.23172i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −5488.50 + 9506.36i −0.338195 + 0.585770i −0.984093 0.177653i \(-0.943150\pi\)
0.645899 + 0.763423i \(0.276483\pi\)
\(642\) 0 0
\(643\) −7914.50 13708.3i −0.485408 0.840752i 0.514451 0.857520i \(-0.327996\pi\)
−0.999859 + 0.0167681i \(0.994662\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 28224.0 1.71499 0.857496 0.514490i \(-0.172019\pi\)
0.857496 + 0.514490i \(0.172019\pi\)
\(648\) 0 0
\(649\) −2385.00 −0.144252
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 14083.5 + 24393.3i 0.843997 + 1.46185i 0.886490 + 0.462749i \(0.153137\pi\)
−0.0424927 + 0.999097i \(0.513530\pi\)
\(654\) 0 0
\(655\) −6763.50 + 11714.7i −0.403468 + 0.698828i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −5368.50 + 9298.51i −0.317340 + 0.549649i −0.979932 0.199331i \(-0.936123\pi\)
0.662592 + 0.748980i \(0.269456\pi\)
\(660\) 0 0
\(661\) −5063.50 8770.24i −0.297954 0.516071i 0.677714 0.735326i \(-0.262971\pi\)
−0.975668 + 0.219255i \(0.929637\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 7812.00 0.455543
\(666\) 0 0
\(667\) −21645.0 −1.25652
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1432.50 + 2481.16i 0.0824159 + 0.142748i
\(672\) 0 0
\(673\) −125.500 + 217.372i −0.00718822 + 0.0124504i −0.869597 0.493762i \(-0.835621\pi\)
0.862409 + 0.506212i \(0.168955\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 4225.50 7318.78i 0.239881 0.415485i −0.720799 0.693144i \(-0.756225\pi\)
0.960680 + 0.277659i \(0.0895584\pi\)
\(678\) 0 0
\(679\) 13965.5 + 24189.0i 0.789318 + 1.36714i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −25884.0 −1.45011 −0.725054 0.688692i \(-0.758185\pi\)
−0.725054 + 0.688692i \(0.758185\pi\)
\(684\) 0 0
\(685\) 23949.0 1.33583
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −2109.00 3652.90i −0.116613 0.201980i
\(690\) 0 0
\(691\) 3182.50 5512.25i 0.175207 0.303467i −0.765026 0.643999i \(-0.777274\pi\)
0.940233 + 0.340532i \(0.110607\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −544.500 + 943.102i −0.0297181 + 0.0514732i
\(696\) 0 0
\(697\) −5481.00 9493.37i −0.297859 0.515907i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −1122.00 −0.0604527 −0.0302264 0.999543i \(-0.509623\pi\)
−0.0302264 + 0.999543i \(0.509623\pi\)
\(702\) 0 0
\(703\) −4648.00 −0.249364
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 5998.50 + 10389.7i 0.319090 + 0.552681i
\(708\) 0 0
\(709\) −2141.50 + 3709.19i −0.113435 + 0.196476i −0.917153 0.398535i \(-0.869519\pi\)
0.803718 + 0.595011i \(0.202852\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −19987.5 + 34619.4i −1.04984 + 1.81838i
\(714\) 0 0
\(715\) −2497.50 4325.80i −0.130631 0.226260i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 4032.00 0.209135 0.104568 0.994518i \(-0.466654\pi\)
0.104568 + 0.994518i \(0.466654\pi\)
\(720\) 0 0
\(721\) −17081.0 −0.882288
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −2442.00 4229.67i −0.125095 0.216670i
\(726\) 0 0
\(727\) 12002.5 20788.9i 0.612308 1.06055i −0.378542 0.925584i \(-0.623574\pi\)
0.990850 0.134965i \(-0.0430922\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −903.000 + 1564.04i −0.0456890 + 0.0791357i
\(732\) 0 0
\(733\) 18750.5 + 32476.8i 0.944837 + 1.63651i 0.756077 + 0.654482i \(0.227113\pi\)
0.188760 + 0.982023i \(0.439553\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −6315.00 −0.315626
\(738\) 0 0
\(739\) 880.000 0.0438042 0.0219021 0.999760i \(-0.493028\pi\)
0.0219021 + 0.999760i \(0.493028\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −811.500 1405.56i −0.0400687 0.0694010i 0.845296 0.534299i \(-0.179424\pi\)
−0.885364 + 0.464898i \(0.846091\pi\)
\(744\) 0 0
\(745\) −12730.5 + 22049.9i −0.626053 + 1.08436i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 186.000 322.161i 0.00907382 0.0157163i
\(750\) 0 0
\(751\) −3444.50 5966.05i −0.167366 0.289886i 0.770127 0.637890i \(-0.220193\pi\)
−0.937493 + 0.348005i \(0.886859\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −4149.00 −0.199997
\(756\) 0 0
\(757\) −12850.0 −0.616963 −0.308482 0.951230i \(-0.599821\pi\)
−0.308482 + 0.951230i \(0.599821\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 2305.50 + 3993.24i 0.109822 + 0.190217i 0.915698 0.401867i \(-0.131639\pi\)
−0.805876 + 0.592084i \(0.798305\pi\)
\(762\) 0 0
\(763\) 7781.00 13477.1i 0.369189 0.639454i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 2941.50 5094.83i 0.138476 0.239848i
\(768\) 0 0
\(769\) 1152.50 + 1996.19i 0.0540445 + 0.0936078i 0.891782 0.452465i \(-0.149455\pi\)
−0.837737 + 0.546073i \(0.816122\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 34902.0 1.62398 0.811991 0.583670i \(-0.198384\pi\)
0.811991 + 0.583670i \(0.198384\pi\)
\(774\) 0 0
\(775\) −9020.00 −0.418075
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −3654.00 6328.91i −0.168059 0.291087i
\(780\) 0 0
\(781\) 1170.00 2026.50i 0.0536055 0.0928474i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 13396.5 23203.4i 0.609098 1.05499i
\(786\) 0 0
\(787\) 13127.5 + 22737.5i 0.594593 + 1.02987i 0.993604 + 0.112919i \(0.0360202\pi\)
−0.399011 + 0.916946i \(0.630646\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 43431.0 1.95225
\(792\) 0 0