Properties

Label 192.5.e.c.65.2
Level $192$
Weight $5$
Character 192.65
Analytic conductor $19.847$
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] = [192,5,Mod(65,192)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(192, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("192.65");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 192.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: \(19.8470329121\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{-2}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2\cdot 3 \)
Twist minimal: no (minimal twist has level 6)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 65.2
Root \(1.41421i\) of defining polynomial
Character \(\chi\) \(=\) 192.65
Dual form 192.5.e.c.65.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.00000 + 8.48528i) q^{3} +16.9706i q^{5} -26.0000 q^{7} +(-63.0000 - 50.9117i) q^{9} +O(q^{10})\) \(q+(-3.00000 + 8.48528i) q^{3} +16.9706i q^{5} -26.0000 q^{7} +(-63.0000 - 50.9117i) q^{9} +118.794i q^{11} -50.0000 q^{13} +(-144.000 - 50.9117i) q^{15} -203.647i q^{17} -358.000 q^{19} +(78.0000 - 220.617i) q^{21} +373.352i q^{23} +337.000 q^{25} +(621.000 - 381.838i) q^{27} -1442.50i q^{29} +742.000 q^{31} +(-1008.00 - 356.382i) q^{33} -441.235i q^{35} -1874.00 q^{37} +(150.000 - 424.264i) q^{39} -2409.82i q^{41} -262.000 q^{43} +(864.000 - 1069.15i) q^{45} -1697.06i q^{47} -1725.00 q^{49} +(1728.00 + 610.940i) q^{51} -458.205i q^{53} -2016.00 q^{55} +(1074.00 - 3037.73i) q^{57} +1815.85i q^{59} +1486.00 q^{61} +(1638.00 + 1323.70i) q^{63} -848.528i q^{65} -4486.00 q^{67} +(-3168.00 - 1120.06i) q^{69} +3563.82i q^{71} +290.000 q^{73} +(-1011.00 + 2859.54i) q^{75} -3088.64i q^{77} -9818.00 q^{79} +(1377.00 + 6414.87i) q^{81} -7110.67i q^{83} +3456.00 q^{85} +(12240.0 + 4327.49i) q^{87} +7840.40i q^{89} +1300.00 q^{91} +(-2226.00 + 6296.08i) q^{93} -6075.46i q^{95} -478.000 q^{97} +(6048.00 - 7484.02i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 6 q^{3} - 52 q^{7} - 126 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 6 q^{3} - 52 q^{7} - 126 q^{9} - 100 q^{13} - 288 q^{15} - 716 q^{19} + 156 q^{21} + 674 q^{25} + 1242 q^{27} + 1484 q^{31} - 2016 q^{33} - 3748 q^{37} + 300 q^{39} - 524 q^{43} + 1728 q^{45} - 3450 q^{49} + 3456 q^{51} - 4032 q^{55} + 2148 q^{57} + 2972 q^{61} + 3276 q^{63} - 8972 q^{67} - 6336 q^{69} + 580 q^{73} - 2022 q^{75} - 19636 q^{79} + 2754 q^{81} + 6912 q^{85} + 24480 q^{87} + 2600 q^{91} - 4452 q^{93} - 956 q^{97} + 12096 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/192\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(133\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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
\(3\) −3.00000 + 8.48528i −0.333333 + 0.942809i
\(4\) 0 0
\(5\) 16.9706i 0.678823i 0.940638 + 0.339411i \(0.110228\pi\)
−0.940638 + 0.339411i \(0.889772\pi\)
\(6\) 0 0
\(7\) −26.0000 −0.530612 −0.265306 0.964164i \(-0.585473\pi\)
−0.265306 + 0.964164i \(0.585473\pi\)
\(8\) 0 0
\(9\) −63.0000 50.9117i −0.777778 0.628539i
\(10\) 0 0
\(11\) 118.794i 0.981768i 0.871225 + 0.490884i \(0.163326\pi\)
−0.871225 + 0.490884i \(0.836674\pi\)
\(12\) 0 0
\(13\) −50.0000 −0.295858 −0.147929 0.988998i \(-0.547261\pi\)
−0.147929 + 0.988998i \(0.547261\pi\)
\(14\) 0 0
\(15\) −144.000 50.9117i −0.640000 0.226274i
\(16\) 0 0
\(17\) 203.647i 0.704660i −0.935876 0.352330i \(-0.885389\pi\)
0.935876 0.352330i \(-0.114611\pi\)
\(18\) 0 0
\(19\) −358.000 −0.991690 −0.495845 0.868411i \(-0.665142\pi\)
−0.495845 + 0.868411i \(0.665142\pi\)
\(20\) 0 0
\(21\) 78.0000 220.617i 0.176871 0.500266i
\(22\) 0 0
\(23\) 373.352i 0.705770i 0.935667 + 0.352885i \(0.114799\pi\)
−0.935667 + 0.352885i \(0.885201\pi\)
\(24\) 0 0
\(25\) 337.000 0.539200
\(26\) 0 0
\(27\) 621.000 381.838i 0.851852 0.523783i
\(28\) 0 0
\(29\) 1442.50i 1.71522i −0.514303 0.857609i \(-0.671949\pi\)
0.514303 0.857609i \(-0.328051\pi\)
\(30\) 0 0
\(31\) 742.000 0.772112 0.386056 0.922475i \(-0.373837\pi\)
0.386056 + 0.922475i \(0.373837\pi\)
\(32\) 0 0
\(33\) −1008.00 356.382i −0.925620 0.327256i
\(34\) 0 0
\(35\) 441.235i 0.360192i
\(36\) 0 0
\(37\) −1874.00 −1.36888 −0.684441 0.729068i \(-0.739954\pi\)
−0.684441 + 0.729068i \(0.739954\pi\)
\(38\) 0 0
\(39\) 150.000 424.264i 0.0986193 0.278938i
\(40\) 0 0
\(41\) 2409.82i 1.43356i −0.697298 0.716782i \(-0.745614\pi\)
0.697298 0.716782i \(-0.254386\pi\)
\(42\) 0 0
\(43\) −262.000 −0.141698 −0.0708491 0.997487i \(-0.522571\pi\)
−0.0708491 + 0.997487i \(0.522571\pi\)
\(44\) 0 0
\(45\) 864.000 1069.15i 0.426667 0.527973i
\(46\) 0 0
\(47\) 1697.06i 0.768246i −0.923282 0.384123i \(-0.874504\pi\)
0.923282 0.384123i \(-0.125496\pi\)
\(48\) 0 0
\(49\) −1725.00 −0.718451
\(50\) 0 0
\(51\) 1728.00 + 610.940i 0.664360 + 0.234887i
\(52\) 0 0
\(53\) 458.205i 0.163120i −0.996668 0.0815602i \(-0.974010\pi\)
0.996668 0.0815602i \(-0.0259903\pi\)
\(54\) 0 0
\(55\) −2016.00 −0.666446
\(56\) 0 0
\(57\) 1074.00 3037.73i 0.330563 0.934974i
\(58\) 0 0
\(59\) 1815.85i 0.521646i 0.965387 + 0.260823i \(0.0839939\pi\)
−0.965387 + 0.260823i \(0.916006\pi\)
\(60\) 0 0
\(61\) 1486.00 0.399355 0.199678 0.979862i \(-0.436011\pi\)
0.199678 + 0.979862i \(0.436011\pi\)
\(62\) 0 0
\(63\) 1638.00 + 1323.70i 0.412698 + 0.333511i
\(64\) 0 0
\(65\) 848.528i 0.200835i
\(66\) 0 0
\(67\) −4486.00 −0.999332 −0.499666 0.866218i \(-0.666544\pi\)
−0.499666 + 0.866218i \(0.666544\pi\)
\(68\) 0 0
\(69\) −3168.00 1120.06i −0.665406 0.235257i
\(70\) 0 0
\(71\) 3563.82i 0.706967i 0.935441 + 0.353483i \(0.115003\pi\)
−0.935441 + 0.353483i \(0.884997\pi\)
\(72\) 0 0
\(73\) 290.000 0.0544192 0.0272096 0.999630i \(-0.491338\pi\)
0.0272096 + 0.999630i \(0.491338\pi\)
\(74\) 0 0
\(75\) −1011.00 + 2859.54i −0.179733 + 0.508363i
\(76\) 0 0
\(77\) 3088.64i 0.520938i
\(78\) 0 0
\(79\) −9818.00 −1.57315 −0.786573 0.617498i \(-0.788146\pi\)
−0.786573 + 0.617498i \(0.788146\pi\)
\(80\) 0 0
\(81\) 1377.00 + 6414.87i 0.209877 + 0.977728i
\(82\) 0 0
\(83\) 7110.67i 1.03218i −0.856535 0.516088i \(-0.827388\pi\)
0.856535 0.516088i \(-0.172612\pi\)
\(84\) 0 0
\(85\) 3456.00 0.478339
\(86\) 0 0
\(87\) 12240.0 + 4327.49i 1.61712 + 0.571739i
\(88\) 0 0
\(89\) 7840.40i 0.989825i 0.868943 + 0.494912i \(0.164800\pi\)
−0.868943 + 0.494912i \(0.835200\pi\)
\(90\) 0 0
\(91\) 1300.00 0.156986
\(92\) 0 0
\(93\) −2226.00 + 6296.08i −0.257371 + 0.727955i
\(94\) 0 0
\(95\) 6075.46i 0.673181i
\(96\) 0 0
\(97\) −478.000 −0.0508024 −0.0254012 0.999677i \(-0.508086\pi\)
−0.0254012 + 0.999677i \(0.508086\pi\)
\(98\) 0 0
\(99\) 6048.00 7484.02i 0.617080 0.763597i
\(100\) 0 0
\(101\) 13729.2i 1.34587i 0.739703 + 0.672933i \(0.234966\pi\)
−0.739703 + 0.672933i \(0.765034\pi\)
\(102\) 0 0
\(103\) −2138.00 −0.201527 −0.100764 0.994910i \(-0.532129\pi\)
−0.100764 + 0.994910i \(0.532129\pi\)
\(104\) 0 0
\(105\) 3744.00 + 1323.70i 0.339592 + 0.120064i
\(106\) 0 0
\(107\) 10844.2i 0.947174i 0.880747 + 0.473587i \(0.157041\pi\)
−0.880747 + 0.473587i \(0.842959\pi\)
\(108\) 0 0
\(109\) 4750.00 0.399798 0.199899 0.979817i \(-0.435939\pi\)
0.199899 + 0.979817i \(0.435939\pi\)
\(110\) 0 0
\(111\) 5622.00 15901.4i 0.456294 1.29059i
\(112\) 0 0
\(113\) 3190.47i 0.249860i 0.992166 + 0.124930i \(0.0398707\pi\)
−0.992166 + 0.124930i \(0.960129\pi\)
\(114\) 0 0
\(115\) −6336.00 −0.479093
\(116\) 0 0
\(117\) 3150.00 + 2545.58i 0.230112 + 0.185958i
\(118\) 0 0
\(119\) 5294.82i 0.373901i
\(120\) 0 0
\(121\) 529.000 0.0361314
\(122\) 0 0
\(123\) 20448.0 + 7229.46i 1.35158 + 0.477854i
\(124\) 0 0
\(125\) 16325.7i 1.04484i
\(126\) 0 0
\(127\) −8282.00 −0.513485 −0.256743 0.966480i \(-0.582649\pi\)
−0.256743 + 0.966480i \(0.582649\pi\)
\(128\) 0 0
\(129\) 786.000 2223.14i 0.0472327 0.133594i
\(130\) 0 0
\(131\) 5413.61i 0.315460i −0.987482 0.157730i \(-0.949582\pi\)
0.987482 0.157730i \(-0.0504176\pi\)
\(132\) 0 0
\(133\) 9308.00 0.526203
\(134\) 0 0
\(135\) 6480.00 + 10538.7i 0.355556 + 0.578256i
\(136\) 0 0
\(137\) 18090.6i 0.963856i 0.876211 + 0.481928i \(0.160063\pi\)
−0.876211 + 0.481928i \(0.839937\pi\)
\(138\) 0 0
\(139\) −23206.0 −1.20108 −0.600538 0.799596i \(-0.705047\pi\)
−0.600538 + 0.799596i \(0.705047\pi\)
\(140\) 0 0
\(141\) 14400.0 + 5091.17i 0.724310 + 0.256082i
\(142\) 0 0
\(143\) 5939.70i 0.290464i
\(144\) 0 0
\(145\) 24480.0 1.16433
\(146\) 0 0
\(147\) 5175.00 14637.1i 0.239484 0.677362i
\(148\) 0 0
\(149\) 11183.6i 0.503743i −0.967761 0.251872i \(-0.918954\pi\)
0.967761 0.251872i \(-0.0810460\pi\)
\(150\) 0 0
\(151\) −14426.0 −0.632692 −0.316346 0.948644i \(-0.602456\pi\)
−0.316346 + 0.948644i \(0.602456\pi\)
\(152\) 0 0
\(153\) −10368.0 + 12829.7i −0.442907 + 0.548069i
\(154\) 0 0
\(155\) 12592.2i 0.524127i
\(156\) 0 0
\(157\) −49010.0 −1.98832 −0.994158 0.107935i \(-0.965576\pi\)
−0.994158 + 0.107935i \(0.965576\pi\)
\(158\) 0 0
\(159\) 3888.00 + 1374.62i 0.153791 + 0.0543735i
\(160\) 0 0
\(161\) 9707.16i 0.374490i
\(162\) 0 0
\(163\) −42982.0 −1.61775 −0.808875 0.587981i \(-0.799923\pi\)
−0.808875 + 0.587981i \(0.799923\pi\)
\(164\) 0 0
\(165\) 6048.00 17106.3i 0.222149 0.628332i
\(166\) 0 0
\(167\) 44157.4i 1.58333i 0.610957 + 0.791663i \(0.290785\pi\)
−0.610957 + 0.791663i \(0.709215\pi\)
\(168\) 0 0
\(169\) −26061.0 −0.912468
\(170\) 0 0
\(171\) 22554.0 + 18226.4i 0.771314 + 0.623316i
\(172\) 0 0
\(173\) 22418.1i 0.749043i −0.927218 0.374522i \(-0.877807\pi\)
0.927218 0.374522i \(-0.122193\pi\)
\(174\) 0 0
\(175\) −8762.00 −0.286106
\(176\) 0 0
\(177\) −15408.0 5447.55i −0.491813 0.173882i
\(178\) 0 0
\(179\) 30597.9i 0.954962i −0.878642 0.477481i \(-0.841550\pi\)
0.878642 0.477481i \(-0.158450\pi\)
\(180\) 0 0
\(181\) 13102.0 0.399927 0.199963 0.979803i \(-0.435918\pi\)
0.199963 + 0.979803i \(0.435918\pi\)
\(182\) 0 0
\(183\) −4458.00 + 12609.1i −0.133118 + 0.376516i
\(184\) 0 0
\(185\) 31802.8i 0.929228i
\(186\) 0 0
\(187\) 24192.0 0.691813
\(188\) 0 0
\(189\) −16146.0 + 9927.78i −0.452003 + 0.277926i
\(190\) 0 0
\(191\) 70326.0i 1.92774i −0.266367 0.963872i \(-0.585823\pi\)
0.266367 0.963872i \(-0.414177\pi\)
\(192\) 0 0
\(193\) 18050.0 0.484577 0.242288 0.970204i \(-0.422102\pi\)
0.242288 + 0.970204i \(0.422102\pi\)
\(194\) 0 0
\(195\) 7200.00 + 2545.58i 0.189349 + 0.0669450i
\(196\) 0 0
\(197\) 26321.3i 0.678228i −0.940745 0.339114i \(-0.889873\pi\)
0.940745 0.339114i \(-0.110127\pi\)
\(198\) 0 0
\(199\) 37222.0 0.939926 0.469963 0.882686i \(-0.344267\pi\)
0.469963 + 0.882686i \(0.344267\pi\)
\(200\) 0 0
\(201\) 13458.0 38065.0i 0.333111 0.942179i
\(202\) 0 0
\(203\) 37504.9i 0.910115i
\(204\) 0 0
\(205\) 40896.0 0.973135
\(206\) 0 0
\(207\) 19008.0 23521.2i 0.443604 0.548932i
\(208\) 0 0
\(209\) 42528.2i 0.973609i
\(210\) 0 0
\(211\) 15098.0 0.339121 0.169560 0.985520i \(-0.445765\pi\)
0.169560 + 0.985520i \(0.445765\pi\)
\(212\) 0 0
\(213\) −30240.0 10691.5i −0.666534 0.235656i
\(214\) 0 0
\(215\) 4446.29i 0.0961879i
\(216\) 0 0
\(217\) −19292.0 −0.409692
\(218\) 0 0
\(219\) −870.000 + 2460.73i −0.0181397 + 0.0513069i
\(220\) 0 0
\(221\) 10182.3i 0.208479i
\(222\) 0 0
\(223\) −58778.0 −1.18197 −0.590983 0.806684i \(-0.701260\pi\)
−0.590983 + 0.806684i \(0.701260\pi\)
\(224\) 0 0
\(225\) −21231.0 17157.2i −0.419378 0.338908i
\(226\) 0 0
\(227\) 68001.0i 1.31967i −0.751412 0.659833i \(-0.770627\pi\)
0.751412 0.659833i \(-0.229373\pi\)
\(228\) 0 0
\(229\) −28562.0 −0.544650 −0.272325 0.962205i \(-0.587793\pi\)
−0.272325 + 0.962205i \(0.587793\pi\)
\(230\) 0 0
\(231\) 26208.0 + 9265.93i 0.491145 + 0.173646i
\(232\) 0 0
\(233\) 22503.0i 0.414503i −0.978288 0.207252i \(-0.933548\pi\)
0.978288 0.207252i \(-0.0664519\pi\)
\(234\) 0 0
\(235\) 28800.0 0.521503
\(236\) 0 0
\(237\) 29454.0 83308.5i 0.524382 1.48318i
\(238\) 0 0
\(239\) 1289.76i 0.0225795i 0.999936 + 0.0112897i \(0.00359371\pi\)
−0.999936 + 0.0112897i \(0.996406\pi\)
\(240\) 0 0
\(241\) −61246.0 −1.05449 −0.527246 0.849712i \(-0.676776\pi\)
−0.527246 + 0.849712i \(0.676776\pi\)
\(242\) 0 0
\(243\) −58563.0 7560.39i −0.991770 0.128036i
\(244\) 0 0
\(245\) 29274.2i 0.487700i
\(246\) 0 0
\(247\) 17900.0 0.293399
\(248\) 0 0
\(249\) 60336.0 + 21332.0i 0.973146 + 0.344059i
\(250\) 0 0
\(251\) 45260.5i 0.718409i 0.933259 + 0.359205i \(0.116952\pi\)
−0.933259 + 0.359205i \(0.883048\pi\)
\(252\) 0 0
\(253\) −44352.0 −0.692903
\(254\) 0 0
\(255\) −10368.0 + 29325.1i −0.159446 + 0.450982i
\(256\) 0 0
\(257\) 85260.1i 1.29086i 0.763819 + 0.645431i \(0.223322\pi\)
−0.763819 + 0.645431i \(0.776678\pi\)
\(258\) 0 0
\(259\) 48724.0 0.726346
\(260\) 0 0
\(261\) −73440.0 + 90877.4i −1.07808 + 1.33406i
\(262\) 0 0
\(263\) 84751.0i 1.22527i 0.790364 + 0.612637i \(0.209891\pi\)
−0.790364 + 0.612637i \(0.790109\pi\)
\(264\) 0 0
\(265\) 7776.00 0.110730
\(266\) 0 0
\(267\) −66528.0 23521.2i −0.933216 0.329942i
\(268\) 0 0
\(269\) 42918.6i 0.593117i −0.955015 0.296559i \(-0.904161\pi\)
0.955015 0.296559i \(-0.0958390\pi\)
\(270\) 0 0
\(271\) 27430.0 0.373497 0.186749 0.982408i \(-0.440205\pi\)
0.186749 + 0.982408i \(0.440205\pi\)
\(272\) 0 0
\(273\) −3900.00 + 11030.9i −0.0523286 + 0.148008i
\(274\) 0 0
\(275\) 40033.6i 0.529369i
\(276\) 0 0
\(277\) 93934.0 1.22423 0.612115 0.790768i \(-0.290319\pi\)
0.612115 + 0.790768i \(0.290319\pi\)
\(278\) 0 0
\(279\) −46746.0 37776.5i −0.600532 0.485303i
\(280\) 0 0
\(281\) 24471.6i 0.309919i −0.987921 0.154960i \(-0.950475\pi\)
0.987921 0.154960i \(-0.0495248\pi\)
\(282\) 0 0
\(283\) −65830.0 −0.821961 −0.410980 0.911644i \(-0.634813\pi\)
−0.410980 + 0.911644i \(0.634813\pi\)
\(284\) 0 0
\(285\) 51552.0 + 18226.4i 0.634681 + 0.224394i
\(286\) 0 0
\(287\) 62655.3i 0.760666i
\(288\) 0 0
\(289\) 42049.0 0.503454
\(290\) 0 0
\(291\) 1434.00 4055.96i 0.0169341 0.0478970i
\(292\) 0 0
\(293\) 90028.8i 1.04869i 0.851506 + 0.524344i \(0.175689\pi\)
−0.851506 + 0.524344i \(0.824311\pi\)
\(294\) 0 0
\(295\) −30816.0 −0.354105
\(296\) 0 0
\(297\) 45360.0 + 73771.0i 0.514233 + 0.836321i
\(298\) 0 0
\(299\) 18667.6i 0.208808i
\(300\) 0 0
\(301\) 6812.00 0.0751868
\(302\) 0 0
\(303\) −116496. 41187.6i −1.26890 0.448622i
\(304\) 0 0
\(305\) 25218.3i 0.271091i
\(306\) 0 0
\(307\) 67322.0 0.714299 0.357150 0.934047i \(-0.383749\pi\)
0.357150 + 0.934047i \(0.383749\pi\)
\(308\) 0 0
\(309\) 6414.00 18141.5i 0.0671757 0.190001i
\(310\) 0 0
\(311\) 131997.i 1.36472i −0.731017 0.682360i \(-0.760954\pi\)
0.731017 0.682360i \(-0.239046\pi\)
\(312\) 0 0
\(313\) −22078.0 −0.225357 −0.112679 0.993631i \(-0.535943\pi\)
−0.112679 + 0.993631i \(0.535943\pi\)
\(314\) 0 0
\(315\) −22464.0 + 27797.8i −0.226395 + 0.280149i
\(316\) 0 0
\(317\) 117894.i 1.17321i 0.809874 + 0.586604i \(0.199535\pi\)
−0.809874 + 0.586604i \(0.800465\pi\)
\(318\) 0 0
\(319\) 171360. 1.68395
\(320\) 0 0
\(321\) −92016.0 32532.6i −0.893004 0.315725i
\(322\) 0 0
\(323\) 72905.5i 0.698804i
\(324\) 0 0
\(325\) −16850.0 −0.159527
\(326\) 0 0
\(327\) −14250.0 + 40305.1i −0.133266 + 0.376933i
\(328\) 0 0
\(329\) 44123.5i 0.407641i
\(330\) 0 0
\(331\) 167642. 1.53012 0.765062 0.643956i \(-0.222708\pi\)
0.765062 + 0.643956i \(0.222708\pi\)
\(332\) 0 0
\(333\) 118062. + 95408.5i 1.06469 + 0.860396i
\(334\) 0 0
\(335\) 76129.9i 0.678369i
\(336\) 0 0
\(337\) 162914. 1.43449 0.717247 0.696819i \(-0.245402\pi\)
0.717247 + 0.696819i \(0.245402\pi\)
\(338\) 0 0
\(339\) −27072.0 9571.40i −0.235571 0.0832868i
\(340\) 0 0
\(341\) 88145.1i 0.758035i
\(342\) 0 0
\(343\) 107276. 0.911831
\(344\) 0 0
\(345\) 19008.0 53762.7i 0.159698 0.451693i
\(346\) 0 0
\(347\) 132184.i 1.09779i −0.835892 0.548895i \(-0.815049\pi\)
0.835892 0.548895i \(-0.184951\pi\)
\(348\) 0 0
\(349\) −53234.0 −0.437057 −0.218529 0.975831i \(-0.570126\pi\)
−0.218529 + 0.975831i \(0.570126\pi\)
\(350\) 0 0
\(351\) −31050.0 + 19091.9i −0.252027 + 0.154965i
\(352\) 0 0
\(353\) 144861.i 1.16252i 0.813717 + 0.581261i \(0.197440\pi\)
−0.813717 + 0.581261i \(0.802560\pi\)
\(354\) 0 0
\(355\) −60480.0 −0.479905
\(356\) 0 0
\(357\) −44928.0 15884.4i −0.352517 0.124634i
\(358\) 0 0
\(359\) 12931.6i 0.100337i 0.998741 + 0.0501686i \(0.0159759\pi\)
−0.998741 + 0.0501686i \(0.984024\pi\)
\(360\) 0 0
\(361\) −2157.00 −0.0165514
\(362\) 0 0
\(363\) −1587.00 + 4488.71i −0.0120438 + 0.0340650i
\(364\) 0 0
\(365\) 4921.46i 0.0369410i
\(366\) 0 0
\(367\) 44326.0 0.329099 0.164549 0.986369i \(-0.447383\pi\)
0.164549 + 0.986369i \(0.447383\pi\)
\(368\) 0 0
\(369\) −122688. + 151819.i −0.901051 + 1.11499i
\(370\) 0 0
\(371\) 11913.3i 0.0865537i
\(372\) 0 0
\(373\) 60718.0 0.436415 0.218208 0.975902i \(-0.429979\pi\)
0.218208 + 0.975902i \(0.429979\pi\)
\(374\) 0 0
\(375\) −138528. 48977.0i −0.985088 0.348281i
\(376\) 0 0
\(377\) 72124.9i 0.507461i
\(378\) 0 0
\(379\) 30458.0 0.212043 0.106021 0.994364i \(-0.466189\pi\)
0.106021 + 0.994364i \(0.466189\pi\)
\(380\) 0 0
\(381\) 24846.0 70275.1i 0.171162 0.484118i
\(382\) 0 0
\(383\) 235687.i 1.60671i 0.595498 + 0.803357i \(0.296955\pi\)
−0.595498 + 0.803357i \(0.703045\pi\)
\(384\) 0 0
\(385\) 52416.0 0.353625
\(386\) 0 0
\(387\) 16506.0 + 13338.9i 0.110210 + 0.0890629i
\(388\) 0 0
\(389\) 150410.i 0.993980i −0.867756 0.496990i \(-0.834439\pi\)
0.867756 0.496990i \(-0.165561\pi\)
\(390\) 0 0
\(391\) 76032.0 0.497328
\(392\) 0 0
\(393\) 45936.0 + 16240.8i 0.297419 + 0.105153i
\(394\) 0 0
\(395\) 166617.i 1.06789i
\(396\) 0 0
\(397\) −172658. −1.09548 −0.547742 0.836648i \(-0.684512\pi\)
−0.547742 + 0.836648i \(0.684512\pi\)
\(398\) 0 0
\(399\) −27924.0 + 78981.0i −0.175401 + 0.496109i
\(400\) 0 0
\(401\) 167466.i 1.04145i −0.853726 0.520723i \(-0.825662\pi\)
0.853726 0.520723i \(-0.174338\pi\)
\(402\) 0 0
\(403\) −37100.0 −0.228436
\(404\) 0 0
\(405\) −108864. + 23368.5i −0.663704 + 0.142469i
\(406\) 0 0
\(407\) 222620.i 1.34393i
\(408\) 0 0
\(409\) −150430. −0.899265 −0.449633 0.893214i \(-0.648445\pi\)
−0.449633 + 0.893214i \(0.648445\pi\)
\(410\) 0 0
\(411\) −153504. 54271.9i −0.908732 0.321285i
\(412\) 0 0
\(413\) 47212.1i 0.276792i
\(414\) 0 0
\(415\) 120672. 0.700665
\(416\) 0 0
\(417\) 69618.0 196909.i 0.400359 1.13239i
\(418\) 0 0
\(419\) 178276.i 1.01546i 0.861515 + 0.507732i \(0.169516\pi\)
−0.861515 + 0.507732i \(0.830484\pi\)
\(420\) 0 0
\(421\) 216046. 1.21894 0.609470 0.792809i \(-0.291382\pi\)
0.609470 + 0.792809i \(0.291382\pi\)
\(422\) 0 0
\(423\) −86400.0 + 106915.i −0.482873 + 0.597525i
\(424\) 0 0
\(425\) 68629.0i 0.379953i
\(426\) 0 0
\(427\) −38636.0 −0.211903
\(428\) 0 0
\(429\) 50400.0 + 17819.1i 0.273852 + 0.0968213i
\(430\) 0 0
\(431\) 5498.46i 0.0295997i −0.999890 0.0147998i \(-0.995289\pi\)
0.999890 0.0147998i \(-0.00471110\pi\)
\(432\) 0 0
\(433\) 108002. 0.576044 0.288022 0.957624i \(-0.407002\pi\)
0.288022 + 0.957624i \(0.407002\pi\)
\(434\) 0 0
\(435\) −73440.0 + 207720.i −0.388109 + 1.09774i
\(436\) 0 0
\(437\) 133660.i 0.699905i
\(438\) 0 0
\(439\) −357722. −1.85617 −0.928083 0.372374i \(-0.878544\pi\)
−0.928083 + 0.372374i \(0.878544\pi\)
\(440\) 0 0
\(441\) 108675. + 87822.7i 0.558795 + 0.451575i
\(442\) 0 0
\(443\) 86261.4i 0.439551i 0.975551 + 0.219775i \(0.0705324\pi\)
−0.975551 + 0.219775i \(0.929468\pi\)
\(444\) 0 0
\(445\) −133056. −0.671915
\(446\) 0 0
\(447\) 94896.0 + 33550.8i 0.474934 + 0.167914i
\(448\) 0 0
\(449\) 301397.i 1.49502i −0.664251 0.747509i \(-0.731250\pi\)
0.664251 0.747509i \(-0.268750\pi\)
\(450\) 0 0
\(451\) 286272. 1.40743
\(452\) 0 0
\(453\) 43278.0 122409.i 0.210897 0.596507i
\(454\) 0 0
\(455\) 22061.7i 0.106566i
\(456\) 0 0
\(457\) −399070. −1.91081 −0.955403 0.295305i \(-0.904579\pi\)
−0.955403 + 0.295305i \(0.904579\pi\)
\(458\) 0 0
\(459\) −77760.0 126465.i −0.369089 0.600266i
\(460\) 0 0
\(461\) 38268.6i 0.180070i 0.995939 + 0.0900349i \(0.0286979\pi\)
−0.995939 + 0.0900349i \(0.971302\pi\)
\(462\) 0 0
\(463\) −144410. −0.673652 −0.336826 0.941567i \(-0.609353\pi\)
−0.336826 + 0.941567i \(0.609353\pi\)
\(464\) 0 0
\(465\) −106848. 37776.5i −0.494152 0.174709i
\(466\) 0 0
\(467\) 148204.i 0.679557i 0.940505 + 0.339779i \(0.110352\pi\)
−0.940505 + 0.339779i \(0.889648\pi\)
\(468\) 0 0
\(469\) 116636. 0.530258
\(470\) 0 0
\(471\) 147030. 415864.i 0.662772 1.87460i
\(472\) 0 0
\(473\) 31124.0i 0.139115i
\(474\) 0 0
\(475\) −120646. −0.534719
\(476\) 0 0
\(477\) −23328.0 + 28866.9i −0.102528 + 0.126871i
\(478\) 0 0
\(479\) 305606.i 1.33196i 0.745970 + 0.665979i \(0.231986\pi\)
−0.745970 + 0.665979i \(0.768014\pi\)
\(480\) 0 0
\(481\) 93700.0 0.404995
\(482\) 0 0
\(483\) 82368.0 + 29121.5i 0.353073 + 0.124830i
\(484\) 0 0
\(485\) 8111.93i 0.0344858i
\(486\) 0 0
\(487\) 196774. 0.829678 0.414839 0.909895i \(-0.363838\pi\)
0.414839 + 0.909895i \(0.363838\pi\)
\(488\) 0 0
\(489\) 128946. 364714.i 0.539250 1.52523i
\(490\) 0 0
\(491\) 166193.i 0.689365i −0.938719 0.344682i \(-0.887987\pi\)
0.938719 0.344682i \(-0.112013\pi\)
\(492\) 0 0
\(493\) −293760. −1.20865
\(494\) 0 0
\(495\) 127008. + 102638.i 0.518347 + 0.418888i
\(496\) 0 0
\(497\) 92659.3i 0.375125i
\(498\) 0 0
\(499\) 189050. 0.759234 0.379617 0.925144i \(-0.376056\pi\)
0.379617 + 0.925144i \(0.376056\pi\)
\(500\) 0 0
\(501\) −374688. 132472.i −1.49277 0.527776i
\(502\) 0 0
\(503\) 344061.i 1.35988i −0.733269 0.679939i \(-0.762006\pi\)
0.733269 0.679939i \(-0.237994\pi\)
\(504\) 0 0
\(505\) −232992. −0.913605
\(506\) 0 0
\(507\) 78183.0 221135.i 0.304156 0.860283i
\(508\) 0 0
\(509\) 353208.i 1.36331i −0.731673 0.681656i \(-0.761260\pi\)
0.731673 0.681656i \(-0.238740\pi\)
\(510\) 0 0
\(511\) −7540.00 −0.0288755
\(512\) 0 0
\(513\) −222318. + 136698.i −0.844773 + 0.519430i
\(514\) 0 0
\(515\) 36283.1i 0.136801i
\(516\) 0 0
\(517\) 201600. 0.754240
\(518\) 0 0
\(519\) 190224. + 67254.3i 0.706205 + 0.249681i
\(520\) 0 0
\(521\) 276043.i 1.01695i 0.861075 + 0.508477i \(0.169791\pi\)
−0.861075 + 0.508477i \(0.830209\pi\)
\(522\) 0 0
\(523\) −146950. −0.537237 −0.268619 0.963247i \(-0.586567\pi\)
−0.268619 + 0.963247i \(0.586567\pi\)
\(524\) 0 0
\(525\) 26286.0 74348.0i 0.0953687 0.269743i
\(526\) 0 0
\(527\) 151106.i 0.544077i
\(528\) 0 0
\(529\) 140449. 0.501889
\(530\) 0 0
\(531\) 92448.0 114399.i 0.327875 0.405725i
\(532\) 0 0
\(533\) 120491.i 0.424131i
\(534\) 0 0
\(535\) −184032. −0.642963
\(536\) 0 0
\(537\) 259632. + 91793.8i 0.900346 + 0.318321i
\(538\) 0 0
\(539\) 204920.i 0.705352i
\(540\) 0 0
\(541\) 244942. 0.836891 0.418445 0.908242i \(-0.362575\pi\)
0.418445 + 0.908242i \(0.362575\pi\)
\(542\) 0 0
\(543\) −39306.0 + 111174.i −0.133309 + 0.377055i
\(544\) 0 0
\(545\) 80610.2i 0.271392i
\(546\) 0 0
\(547\) −283366. −0.947050 −0.473525 0.880780i \(-0.657019\pi\)
−0.473525 + 0.880780i \(0.657019\pi\)
\(548\) 0 0
\(549\) −93618.0 75654.8i −0.310609 0.251010i
\(550\) 0 0
\(551\) 516414.i 1.70096i
\(552\) 0 0
\(553\) 255268. 0.834730
\(554\) 0 0
\(555\) 269856. + 95408.5i 0.876085 + 0.309743i
\(556\) 0 0
\(557\) 47093.3i 0.151792i 0.997116 + 0.0758960i \(0.0241817\pi\)
−0.997116 + 0.0758960i \(0.975818\pi\)
\(558\) 0 0
\(559\) 13100.0 0.0419225
\(560\) 0 0
\(561\) −72576.0 + 205276.i −0.230604 + 0.652247i
\(562\) 0 0
\(563\) 84.8528i 0.000267701i 1.00000 0.000133850i \(4.26059e-5\pi\)
−1.00000 0.000133850i \(0.999957\pi\)
\(564\) 0 0
\(565\) −54144.0 −0.169611
\(566\) 0 0
\(567\) −35802.0 166787.i −0.111363 0.518794i
\(568\) 0 0
\(569\) 239115.i 0.738555i −0.929319 0.369277i \(-0.879605\pi\)
0.929319 0.369277i \(-0.120395\pi\)
\(570\) 0 0
\(571\) −140710. −0.431571 −0.215786 0.976441i \(-0.569231\pi\)
−0.215786 + 0.976441i \(0.569231\pi\)
\(572\) 0 0
\(573\) 596736. + 210978.i 1.81749 + 0.642581i
\(574\) 0 0
\(575\) 125820.i 0.380551i
\(576\) 0 0
\(577\) 36002.0 0.108137 0.0540686 0.998537i \(-0.482781\pi\)
0.0540686 + 0.998537i \(0.482781\pi\)
\(578\) 0 0
\(579\) −54150.0 + 153159.i −0.161526 + 0.456863i
\(580\) 0 0
\(581\) 184877.i 0.547686i
\(582\) 0 0
\(583\) 54432.0 0.160146
\(584\) 0 0
\(585\) −43200.0 + 53457.3i −0.126233 + 0.156205i
\(586\) 0 0
\(587\) 316179.i 0.917606i 0.888538 + 0.458803i \(0.151722\pi\)
−0.888538 + 0.458803i \(0.848278\pi\)
\(588\) 0 0
\(589\) −265636. −0.765696
\(590\) 0 0
\(591\) 223344. + 78964.0i 0.639439 + 0.226076i
\(592\) 0 0
\(593\) 262093.i 0.745327i 0.927967 + 0.372663i \(0.121555\pi\)
−0.927967 + 0.372663i \(0.878445\pi\)
\(594\) 0 0
\(595\) −89856.0 −0.253813
\(596\) 0 0
\(597\) −111666. + 315839.i −0.313309 + 0.886171i
\(598\) 0 0
\(599\) 606494.i 1.69034i −0.534501 0.845168i \(-0.679501\pi\)
0.534501 0.845168i \(-0.320499\pi\)
\(600\) 0 0
\(601\) 306530. 0.848641 0.424321 0.905512i \(-0.360513\pi\)
0.424321 + 0.905512i \(0.360513\pi\)
\(602\) 0 0
\(603\) 282618. + 228390.i 0.777258 + 0.628119i
\(604\) 0 0
\(605\) 8977.43i 0.0245268i
\(606\) 0 0
\(607\) −563162. −1.52847 −0.764233 0.644940i \(-0.776882\pi\)
−0.764233 + 0.644940i \(0.776882\pi\)
\(608\) 0 0
\(609\) −318240. 112515.i −0.858065 0.303372i
\(610\) 0 0
\(611\) 84852.8i 0.227292i
\(612\) 0 0
\(613\) −111314. −0.296230 −0.148115 0.988970i \(-0.547321\pi\)
−0.148115 + 0.988970i \(0.547321\pi\)
\(614\) 0 0
\(615\) −122688. + 347014.i −0.324378 + 0.917481i
\(616\) 0 0
\(617\) 121340.i 0.318737i −0.987219 0.159368i \(-0.949054\pi\)
0.987219 0.159368i \(-0.0509457\pi\)
\(618\) 0 0
\(619\) −581158. −1.51675 −0.758373 0.651821i \(-0.774005\pi\)
−0.758373 + 0.651821i \(0.774005\pi\)
\(620\) 0 0
\(621\) 142560. + 231852.i 0.369670 + 0.601212i
\(622\) 0 0
\(623\) 203850.i 0.525213i
\(624\) 0 0
\(625\) −66431.0 −0.170063
\(626\) 0 0
\(627\) 360864. + 127585.i 0.917928 + 0.324536i
\(628\) 0 0
\(629\) 381634.i 0.964597i
\(630\) 0 0
\(631\) −232346. −0.583548 −0.291774 0.956487i \(-0.594245\pi\)
−0.291774 + 0.956487i \(0.594245\pi\)
\(632\) 0 0
\(633\) −45294.0 + 128111.i −0.113040 + 0.319726i
\(634\) 0 0
\(635\) 140550.i 0.348565i
\(636\) 0 0
\(637\) 86250.0 0.212559
\(638\) 0 0
\(639\) 181440. 224521.i 0.444356 0.549863i
\(640\) 0 0
\(641\) 653570.i 1.59066i 0.606179 + 0.795328i \(0.292701\pi\)
−0.606179 + 0.795328i \(0.707299\pi\)
\(642\) 0 0
\(643\) −424678. −1.02716 −0.513580 0.858042i \(-0.671681\pi\)
−0.513580 + 0.858042i \(0.671681\pi\)
\(644\) 0 0
\(645\) 37728.0 + 13338.9i 0.0906869 + 0.0320626i
\(646\) 0 0
\(647\) 427964.i 1.02235i 0.859478 + 0.511173i \(0.170789\pi\)
−0.859478 + 0.511173i \(0.829211\pi\)
\(648\) 0 0
\(649\) −215712. −0.512136
\(650\) 0 0
\(651\) 57876.0 163698.i 0.136564 0.386262i
\(652\) 0 0
\(653\) 720621.i 1.68998i 0.534785 + 0.844988i \(0.320393\pi\)
−0.534785 + 0.844988i \(0.679607\pi\)
\(654\) 0 0
\(655\) 91872.0 0.214141
\(656\) 0 0
\(657\) −18270.0 14764.4i −0.0423261 0.0342046i
\(658\) 0 0
\(659\) 40135.4i 0.0924180i 0.998932 + 0.0462090i \(0.0147140\pi\)
−0.998932 + 0.0462090i \(0.985286\pi\)
\(660\) 0 0
\(661\) 358510. 0.820537 0.410269 0.911965i \(-0.365435\pi\)
0.410269 + 0.911965i \(0.365435\pi\)
\(662\) 0 0
\(663\) −86400.0 30547.0i −0.196556 0.0694931i
\(664\) 0 0
\(665\) 157962.i 0.357198i
\(666\) 0 0
\(667\) 538560. 1.21055
\(668\) 0 0
\(669\) 176334. 498748.i 0.393989 1.11437i
\(670\) 0 0
\(671\) 176528.i 0.392074i
\(672\) 0 0
\(673\) 582434. 1.28593 0.642964 0.765896i \(-0.277705\pi\)
0.642964 + 0.765896i \(0.277705\pi\)
\(674\) 0 0
\(675\) 209277. 128679.i 0.459319 0.282424i
\(676\) 0 0
\(677\) 37352.2i 0.0814965i 0.999169 + 0.0407482i \(0.0129742\pi\)
−0.999169 + 0.0407482i \(0.987026\pi\)
\(678\) 0 0
\(679\) 12428.0 0.0269564
\(680\) 0 0
\(681\) 577008. + 204003.i 1.24419 + 0.439889i
\(682\) 0 0
\(683\) 161848.i 0.346950i −0.984838 0.173475i \(-0.944500\pi\)
0.984838 0.173475i \(-0.0554995\pi\)
\(684\) 0 0
\(685\) −307008. −0.654287
\(686\) 0 0
\(687\) 85686.0 242357.i 0.181550 0.513501i
\(688\) 0 0
\(689\) 22910.3i 0.0482605i
\(690\) 0 0
\(691\) −630118. −1.31967 −0.659836 0.751410i \(-0.729374\pi\)
−0.659836 + 0.751410i \(0.729374\pi\)
\(692\) 0 0
\(693\) −157248. + 194584.i −0.327430 + 0.405174i
\(694\) 0 0
\(695\) 393819.i 0.815318i
\(696\) 0 0
\(697\) −490752. −1.01017
\(698\) 0 0
\(699\) 190944. + 67508.9i 0.390797 + 0.138168i
\(700\) 0 0
\(701\) 457747.i 0.931514i −0.884913 0.465757i \(-0.845782\pi\)
0.884913 0.465757i \(-0.154218\pi\)
\(702\) 0 0
\(703\) 670892. 1.35751
\(704\) 0 0
\(705\) −86400.0 + 244376.i −0.173834 + 0.491678i
\(706\) 0 0
\(707\) 356959.i 0.714133i
\(708\) 0 0
\(709\) −274130. −0.545336 −0.272668 0.962108i \(-0.587906\pi\)
−0.272668 + 0.962108i \(0.587906\pi\)
\(710\) 0 0
\(711\) 618534. + 499851.i 1.22356 + 0.988784i
\(712\) 0 0
\(713\) 277027.i 0.544934i
\(714\) 0 0
\(715\) 100800. 0.197173
\(716\) 0 0
\(717\) −10944.0 3869.29i −0.0212881 0.00752650i
\(718\) 0 0
\(719\) 304045.i 0.588138i −0.955784 0.294069i \(-0.904990\pi\)
0.955784 0.294069i \(-0.0950096\pi\)
\(720\) 0 0
\(721\) 55588.0 0.106933
\(722\) 0 0
\(723\) 183738. 519690.i 0.351498 0.994185i
\(724\) 0 0
\(725\) 486122.i 0.924845i
\(726\) 0 0
\(727\) −364058. −0.688814 −0.344407 0.938821i \(-0.611920\pi\)
−0.344407 + 0.938821i \(0.611920\pi\)
\(728\) 0 0
\(729\) 239841. 474242.i 0.451303 0.892371i
\(730\) 0 0
\(731\) 53355.4i 0.0998491i
\(732\) 0 0
\(733\) 301198. 0.560588 0.280294 0.959914i \(-0.409568\pi\)
0.280294 + 0.959914i \(0.409568\pi\)
\(734\) 0 0
\(735\) 248400. + 87822.7i 0.459808 + 0.162567i
\(736\) 0 0
\(737\) 532910.i 0.981112i
\(738\) 0 0
\(739\) 872570. 1.59776 0.798880 0.601491i \(-0.205426\pi\)
0.798880 + 0.601491i \(0.205426\pi\)
\(740\) 0 0
\(741\) −53700.0 + 151887.i −0.0977998 + 0.276620i
\(742\) 0 0
\(743\) 874222.i 1.58359i 0.610784 + 0.791797i \(0.290854\pi\)
−0.610784 + 0.791797i \(0.709146\pi\)
\(744\) 0 0
\(745\) 189792. 0.341952
\(746\) 0 0
\(747\) −362016. + 447972.i −0.648764 + 0.802804i
\(748\) 0 0
\(749\) 281949.i 0.502582i
\(750\) 0 0
\(751\) −916250. −1.62455 −0.812277 0.583272i \(-0.801772\pi\)
−0.812277 + 0.583272i \(0.801772\pi\)
\(752\) 0 0
\(753\) −384048. 135781.i −0.677323 0.239470i
\(754\) 0 0
\(755\) 244817.i 0.429485i
\(756\) 0 0
\(757\) 691630. 1.20693 0.603465 0.797390i \(-0.293786\pi\)
0.603465 + 0.797390i \(0.293786\pi\)
\(758\) 0 0
\(759\) 133056. 376339.i 0.230968 0.653275i
\(760\) 0 0
\(761\) 90249.5i 0.155839i 0.996960 + 0.0779193i \(0.0248277\pi\)
−0.996960 + 0.0779193i \(0.975172\pi\)
\(762\) 0 0
\(763\) −123500. −0.212138
\(764\) 0 0
\(765\) −217728. 175951.i −0.372042 0.300655i
\(766\) 0 0
\(767\) 90792.5i 0.154333i
\(768\) 0 0
\(769\) −515326. −0.871424 −0.435712 0.900086i \(-0.643503\pi\)
−0.435712 + 0.900086i \(0.643503\pi\)
\(770\) 0 0
\(771\) −723456. 255780.i −1.21704 0.430287i
\(772\) 0 0
\(773\) 100449.i 0.168107i −0.996461 0.0840535i \(-0.973213\pi\)
0.996461 0.0840535i \(-0.0267867\pi\)
\(774\) 0 0
\(775\) 250054. 0.416323
\(776\) 0 0
\(777\) −146172. + 413437.i −0.242115 + 0.684805i
\(778\) 0 0
\(779\) 862716.i 1.42165i
\(780\) 0 0
\(781\) −423360. −0.694077
\(782\) 0 0
\(783\) −550800. 895791.i −0.898401 1.46111i
\(784\) 0 0
\(785\) 831727.i 1.34971i
\(786\) 0 0
\(787\) −107878. −0.174174 −0.0870870 0.996201i \(-0.527756\pi\)
−0.0870870 + 0.996201i \(0.527756\pi\)