Properties

Label 76.5.j.a.13.2
Level $76$
Weight $5$
Character 76.13
Analytic conductor $7.856$
Analytic rank $0$
Dimension $42$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 76.j (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.85611719437\)
Analytic rank: \(0\)
Dimension: \(42\)
Relative dimension: \(7\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 13.2
Character \(\chi\) \(=\) 76.13
Dual form 76.5.j.a.41.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-4.13985 + 11.3741i) q^{3} +(-6.25205 - 35.4571i) q^{5} +(-25.8702 + 44.8086i) q^{7} +(-50.1832 - 42.1087i) q^{9} +O(q^{10})\) \(q+(-4.13985 + 11.3741i) q^{3} +(-6.25205 - 35.4571i) q^{5} +(-25.8702 + 44.8086i) q^{7} +(-50.1832 - 42.1087i) q^{9} +(-31.3514 - 54.3022i) q^{11} +(-109.766 - 301.581i) q^{13} +(429.177 + 75.6755i) q^{15} +(342.075 - 287.035i) q^{17} +(-162.907 - 322.153i) q^{19} +(-402.560 - 479.753i) q^{21} +(-90.4845 + 513.163i) q^{23} +(-630.811 + 229.596i) q^{25} +(-162.378 + 93.7490i) q^{27} +(-524.868 + 625.513i) q^{29} +(-1072.59 - 619.262i) q^{31} +(747.431 - 131.792i) q^{33} +(1750.52 + 637.139i) q^{35} +532.840i q^{37} +3884.64 q^{39} +(-355.017 + 975.401i) q^{41} +(-79.7398 - 452.227i) q^{43} +(-1179.31 + 2042.62i) q^{45} +(-2408.38 - 2020.87i) q^{47} +(-138.039 - 239.091i) q^{49} +(1848.64 + 5079.10i) q^{51} +(-1797.47 - 316.942i) q^{53} +(-1729.39 + 1451.13i) q^{55} +(4338.62 - 519.262i) q^{57} +(-365.255 - 435.294i) q^{59} +(93.8036 - 531.987i) q^{61} +(3185.09 - 1159.28i) q^{63} +(-10006.9 + 5777.50i) q^{65} +(4282.23 - 5103.37i) q^{67} +(-5462.20 - 3153.60i) q^{69} +(-1606.46 + 283.262i) q^{71} +(7746.45 + 2819.48i) q^{73} -8125.43i q^{75} +3244.27 q^{77} +(-2379.76 + 6538.35i) q^{79} +(-1315.52 - 7460.68i) q^{81} +(3687.63 - 6387.16i) q^{83} +(-12316.1 - 10334.4i) q^{85} +(-4941.80 - 8559.45i) q^{87} +(2153.49 + 5916.67i) q^{89} +(16353.1 + 2883.49i) q^{91} +(11484.0 - 9636.18i) q^{93} +(-10404.1 + 7790.32i) q^{95} +(-2695.42 - 3212.28i) q^{97} +(-713.283 + 4045.23i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 42q + 12q^{3} - 45q^{7} - 84q^{9} + O(q^{10}) \) \( 42q + 12q^{3} - 45q^{7} - 84q^{9} - 45q^{11} + 33q^{13} - 393q^{15} + 909q^{17} + 1242q^{19} + 1107q^{21} - 360q^{23} - 810q^{25} - 7056q^{27} - 2889q^{29} + 2808q^{31} + 10875q^{33} + 6741q^{35} - 3480q^{39} - 3060q^{41} - 8079q^{43} - 4320q^{45} - 2655q^{47} - 474q^{49} - 12222q^{51} - 6705q^{53} + 4623q^{55} - 8022q^{57} + 24309q^{59} + 7104q^{61} + 12063q^{63} + 25245q^{65} + 15573q^{67} - 10881q^{69} - 25506q^{71} + 3036q^{73} + 12924q^{77} - 16839q^{79} - 2208q^{81} - 6363q^{83} - 37890q^{85} - 21924q^{87} - 22644q^{89} + 17418q^{91} + 8184q^{93} - 82413q^{95} + 13383q^{97} + 23565q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\) \(1\)

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
\(3\) −4.13985 + 11.3741i −0.459983 + 1.26379i 0.465514 + 0.885040i \(0.345869\pi\)
−0.925498 + 0.378754i \(0.876353\pi\)
\(4\) 0 0
\(5\) −6.25205 35.4571i −0.250082 1.41828i −0.808388 0.588650i \(-0.799660\pi\)
0.558306 0.829635i \(-0.311451\pi\)
\(6\) 0 0
\(7\) −25.8702 + 44.8086i −0.527964 + 0.914461i 0.471504 + 0.881864i \(0.343711\pi\)
−0.999469 + 0.0325971i \(0.989622\pi\)
\(8\) 0 0
\(9\) −50.1832 42.1087i −0.619546 0.519861i
\(10\) 0 0
\(11\) −31.3514 54.3022i −0.259102 0.448778i 0.706899 0.707314i \(-0.250093\pi\)
−0.966002 + 0.258536i \(0.916760\pi\)
\(12\) 0 0
\(13\) −109.766 301.581i −0.649506 1.78450i −0.619558 0.784951i \(-0.712688\pi\)
−0.0299481 0.999551i \(-0.509534\pi\)
\(14\) 0 0
\(15\) 429.177 + 75.6755i 1.90745 + 0.336335i
\(16\) 0 0
\(17\) 342.075 287.035i 1.18365 0.993202i 0.183704 0.982982i \(-0.441191\pi\)
0.999948 0.0102204i \(-0.00325333\pi\)
\(18\) 0 0
\(19\) −162.907 322.153i −0.451265 0.892390i
\(20\) 0 0
\(21\) −402.560 479.753i −0.912835 1.08787i
\(22\) 0 0
\(23\) −90.4845 + 513.163i −0.171048 + 0.970062i 0.771559 + 0.636158i \(0.219477\pi\)
−0.942607 + 0.333904i \(0.891634\pi\)
\(24\) 0 0
\(25\) −630.811 + 229.596i −1.00930 + 0.367354i
\(26\) 0 0
\(27\) −162.378 + 93.7490i −0.222741 + 0.128599i
\(28\) 0 0
\(29\) −524.868 + 625.513i −0.624099 + 0.743773i −0.981770 0.190075i \(-0.939127\pi\)
0.357670 + 0.933848i \(0.383571\pi\)
\(30\) 0 0
\(31\) −1072.59 619.262i −1.11612 0.644393i −0.175714 0.984441i \(-0.556223\pi\)
−0.940408 + 0.340048i \(0.889557\pi\)
\(32\) 0 0
\(33\) 747.431 131.792i 0.686346 0.121021i
\(34\) 0 0
\(35\) 1750.52 + 637.139i 1.42900 + 0.520113i
\(36\) 0 0
\(37\) 532.840i 0.389219i 0.980881 + 0.194609i \(0.0623439\pi\)
−0.980881 + 0.194609i \(0.937656\pi\)
\(38\) 0 0
\(39\) 3884.64 2.55401
\(40\) 0 0
\(41\) −355.017 + 975.401i −0.211194 + 0.580251i −0.999381 0.0351853i \(-0.988798\pi\)
0.788187 + 0.615436i \(0.211020\pi\)
\(42\) 0 0
\(43\) −79.7398 452.227i −0.0431259 0.244579i 0.955623 0.294594i \(-0.0951843\pi\)
−0.998748 + 0.0500145i \(0.984073\pi\)
\(44\) 0 0
\(45\) −1179.31 + 2042.62i −0.582374 + 1.00870i
\(46\) 0 0
\(47\) −2408.38 2020.87i −1.09026 0.914836i −0.0935268 0.995617i \(-0.529814\pi\)
−0.996732 + 0.0807812i \(0.974259\pi\)
\(48\) 0 0
\(49\) −138.039 239.091i −0.0574924 0.0995797i
\(50\) 0 0
\(51\) 1848.64 + 5079.10i 0.710742 + 1.95275i
\(52\) 0 0
\(53\) −1797.47 316.942i −0.639895 0.112831i −0.155719 0.987801i \(-0.549769\pi\)
−0.484176 + 0.874971i \(0.660881\pi\)
\(54\) 0 0
\(55\) −1729.39 + 1451.13i −0.571699 + 0.479712i
\(56\) 0 0
\(57\) 4338.62 519.262i 1.33537 0.159822i
\(58\) 0 0
\(59\) −365.255 435.294i −0.104928 0.125049i 0.711024 0.703167i \(-0.248231\pi\)
−0.815953 + 0.578119i \(0.803787\pi\)
\(60\) 0 0
\(61\) 93.8036 531.987i 0.0252093 0.142969i −0.969605 0.244674i \(-0.921319\pi\)
0.994815 + 0.101706i \(0.0324300\pi\)
\(62\) 0 0
\(63\) 3185.09 1159.28i 0.802491 0.292083i
\(64\) 0 0
\(65\) −10006.9 + 5777.50i −2.36850 + 1.36746i
\(66\) 0 0
\(67\) 4282.23 5103.37i 0.953939 1.13686i −0.0365584 0.999332i \(-0.511640\pi\)
0.990498 0.137529i \(-0.0439160\pi\)
\(68\) 0 0
\(69\) −5462.20 3153.60i −1.14728 0.662382i
\(70\) 0 0
\(71\) −1606.46 + 283.262i −0.318678 + 0.0561915i −0.330699 0.943736i \(-0.607285\pi\)
0.0120212 + 0.999928i \(0.496173\pi\)
\(72\) 0 0
\(73\) 7746.45 + 2819.48i 1.45364 + 0.529082i 0.943605 0.331072i \(-0.107410\pi\)
0.510034 + 0.860154i \(0.329633\pi\)
\(74\) 0 0
\(75\) 8125.43i 1.44452i
\(76\) 0 0
\(77\) 3244.27 0.547187
\(78\) 0 0
\(79\) −2379.76 + 6538.35i −0.381311 + 1.04764i 0.589493 + 0.807773i \(0.299327\pi\)
−0.970805 + 0.239871i \(0.922895\pi\)
\(80\) 0 0
\(81\) −1315.52 7460.68i −0.200506 1.13713i
\(82\) 0 0
\(83\) 3687.63 6387.16i 0.535292 0.927153i −0.463857 0.885910i \(-0.653535\pi\)
0.999149 0.0412433i \(-0.0131319\pi\)
\(84\) 0 0
\(85\) −12316.1 10334.4i −1.70465 1.43037i
\(86\) 0 0
\(87\) −4941.80 8559.45i −0.652900 1.13086i
\(88\) 0 0
\(89\) 2153.49 + 5916.67i 0.271871 + 0.746960i 0.998220 + 0.0596339i \(0.0189933\pi\)
−0.726349 + 0.687326i \(0.758784\pi\)
\(90\) 0 0
\(91\) 16353.1 + 2883.49i 1.97477 + 0.348206i
\(92\) 0 0
\(93\) 11484.0 9636.18i 1.32778 1.11414i
\(94\) 0 0
\(95\) −10404.1 + 7790.32i −1.15281 + 0.863193i
\(96\) 0 0
\(97\) −2695.42 3212.28i −0.286473 0.341405i 0.603546 0.797328i \(-0.293754\pi\)
−0.890019 + 0.455923i \(0.849309\pi\)
\(98\) 0 0
\(99\) −713.283 + 4045.23i −0.0727765 + 0.412736i
\(100\) 0 0
\(101\) 3566.13 1297.97i 0.349587 0.127239i −0.161258 0.986912i \(-0.551555\pi\)
0.510844 + 0.859673i \(0.329333\pi\)
\(102\) 0 0
\(103\) 2896.28 1672.17i 0.273003 0.157618i −0.357249 0.934009i \(-0.616285\pi\)
0.630251 + 0.776391i \(0.282952\pi\)
\(104\) 0 0
\(105\) −14493.8 + 17273.1i −1.31463 + 1.56672i
\(106\) 0 0
\(107\) 8891.77 + 5133.67i 0.776642 + 0.448394i 0.835239 0.549887i \(-0.185329\pi\)
−0.0585971 + 0.998282i \(0.518663\pi\)
\(108\) 0 0
\(109\) −20233.7 + 3567.75i −1.70303 + 0.300290i −0.938751 0.344596i \(-0.888016\pi\)
−0.764279 + 0.644886i \(0.776905\pi\)
\(110\) 0 0
\(111\) −6060.61 2205.88i −0.491892 0.179034i
\(112\) 0 0
\(113\) 9155.56i 0.717015i −0.933527 0.358507i \(-0.883286\pi\)
0.933527 0.358507i \(-0.116714\pi\)
\(114\) 0 0
\(115\) 18761.0 1.41860
\(116\) 0 0
\(117\) −7190.75 + 19756.4i −0.525294 + 1.44323i
\(118\) 0 0
\(119\) 4012.07 + 22753.6i 0.283318 + 1.60678i
\(120\) 0 0
\(121\) 5354.68 9274.58i 0.365732 0.633466i
\(122\) 0 0
\(123\) −9624.64 8076.03i −0.636172 0.533811i
\(124\) 0 0
\(125\) 833.406 + 1443.50i 0.0533380 + 0.0923841i
\(126\) 0 0
\(127\) −1123.59 3087.05i −0.0696630 0.191397i 0.899975 0.435941i \(-0.143584\pi\)
−0.969638 + 0.244543i \(0.921362\pi\)
\(128\) 0 0
\(129\) 5473.81 + 965.180i 0.328935 + 0.0580001i
\(130\) 0 0
\(131\) −10134.1 + 8503.54i −0.590532 + 0.495515i −0.888387 0.459096i \(-0.848173\pi\)
0.297855 + 0.954611i \(0.403729\pi\)
\(132\) 0 0
\(133\) 18649.6 + 1034.55i 1.05431 + 0.0584853i
\(134\) 0 0
\(135\) 4339.26 + 5171.33i 0.238094 + 0.283749i
\(136\) 0 0
\(137\) −742.666 + 4211.87i −0.0395688 + 0.224406i −0.998179 0.0603146i \(-0.980790\pi\)
0.958611 + 0.284720i \(0.0919007\pi\)
\(138\) 0 0
\(139\) −6529.51 + 2376.55i −0.337949 + 0.123003i −0.505419 0.862874i \(-0.668662\pi\)
0.167471 + 0.985877i \(0.446440\pi\)
\(140\) 0 0
\(141\) 32956.0 19027.2i 1.65766 0.957053i
\(142\) 0 0
\(143\) −12935.2 + 15415.5i −0.632558 + 0.753853i
\(144\) 0 0
\(145\) 25460.4 + 14699.6i 1.21096 + 0.699147i
\(146\) 0 0
\(147\) 3290.92 580.277i 0.152294 0.0268535i
\(148\) 0 0
\(149\) 41071.4 + 14948.8i 1.84998 + 0.673337i 0.985255 + 0.171090i \(0.0547290\pi\)
0.864724 + 0.502247i \(0.167493\pi\)
\(150\) 0 0
\(151\) 22893.0i 1.00403i −0.864858 0.502017i \(-0.832591\pi\)
0.864858 0.502017i \(-0.167409\pi\)
\(152\) 0 0
\(153\) −29253.1 −1.24965
\(154\) 0 0
\(155\) −15251.3 + 41902.7i −0.634811 + 1.74413i
\(156\) 0 0
\(157\) −4649.04 26366.0i −0.188610 1.06966i −0.921229 0.389021i \(-0.872813\pi\)
0.732619 0.680639i \(-0.238298\pi\)
\(158\) 0 0
\(159\) 11046.2 19132.5i 0.436936 0.756796i
\(160\) 0 0
\(161\) −20653.2 17330.1i −0.796777 0.668575i
\(162\) 0 0
\(163\) −17362.1 30072.0i −0.653472 1.13185i −0.982275 0.187448i \(-0.939978\pi\)
0.328803 0.944399i \(-0.393355\pi\)
\(164\) 0 0
\(165\) −9345.95 25677.8i −0.343285 0.943169i
\(166\) 0 0
\(167\) −45243.1 7977.57i −1.62226 0.286047i −0.712650 0.701520i \(-0.752505\pi\)
−0.909606 + 0.415473i \(0.863616\pi\)
\(168\) 0 0
\(169\) −57023.4 + 47848.3i −1.99655 + 1.67530i
\(170\) 0 0
\(171\) −5390.25 + 23026.5i −0.184339 + 0.787472i
\(172\) 0 0
\(173\) 33628.3 + 40076.7i 1.12360 + 1.33906i 0.934032 + 0.357191i \(0.116265\pi\)
0.189571 + 0.981867i \(0.439290\pi\)
\(174\) 0 0
\(175\) 6031.35 34205.5i 0.196942 1.11691i
\(176\) 0 0
\(177\) 6463.20 2352.41i 0.206301 0.0750874i
\(178\) 0 0
\(179\) −3772.59 + 2178.10i −0.117743 + 0.0679787i −0.557715 0.830033i \(-0.688322\pi\)
0.439972 + 0.898011i \(0.354988\pi\)
\(180\) 0 0
\(181\) 22208.2 26466.7i 0.677886 0.807873i −0.311948 0.950099i \(-0.600982\pi\)
0.989834 + 0.142226i \(0.0454261\pi\)
\(182\) 0 0
\(183\) 5662.56 + 3269.28i 0.169087 + 0.0976226i
\(184\) 0 0
\(185\) 18893.0 3331.34i 0.552023 0.0973365i
\(186\) 0 0
\(187\) −26311.2 9576.49i −0.752415 0.273857i
\(188\) 0 0
\(189\) 9701.24i 0.271584i
\(190\) 0 0
\(191\) 2319.58 0.0635833 0.0317917 0.999495i \(-0.489879\pi\)
0.0317917 + 0.999495i \(0.489879\pi\)
\(192\) 0 0
\(193\) 11685.7 32106.2i 0.313719 0.861935i −0.678179 0.734896i \(-0.737231\pi\)
0.991898 0.127038i \(-0.0405471\pi\)
\(194\) 0 0
\(195\) −24287.0 137738.i −0.638710 3.62231i
\(196\) 0 0
\(197\) 6488.54 11238.5i 0.167192 0.289585i −0.770240 0.637755i \(-0.779863\pi\)
0.937431 + 0.348170i \(0.113197\pi\)
\(198\) 0 0
\(199\) 39079.4 + 32791.5i 0.986828 + 0.828047i 0.985105 0.171952i \(-0.0550074\pi\)
0.00172223 + 0.999999i \(0.499452\pi\)
\(200\) 0 0
\(201\) 40318.6 + 69833.9i 0.997961 + 1.72852i
\(202\) 0 0
\(203\) −14449.9 39700.7i −0.350649 0.963400i
\(204\) 0 0
\(205\) 36804.5 + 6489.63i 0.875776 + 0.154423i
\(206\) 0 0
\(207\) 26149.4 21942.0i 0.610270 0.512077i
\(208\) 0 0
\(209\) −12386.2 + 18946.1i −0.283561 + 0.433738i
\(210\) 0 0
\(211\) 17233.3 + 20537.9i 0.387083 + 0.461308i 0.924037 0.382304i \(-0.124869\pi\)
−0.536953 + 0.843612i \(0.680425\pi\)
\(212\) 0 0
\(213\) 3428.63 19444.7i 0.0755721 0.428591i
\(214\) 0 0
\(215\) −15536.1 + 5654.69i −0.336098 + 0.122330i
\(216\) 0 0
\(217\) 55496.5 32040.9i 1.17854 0.680433i
\(218\) 0 0
\(219\) −64138.3 + 76437.0i −1.33730 + 1.59373i
\(220\) 0 0
\(221\) −124113. 71656.6i −2.54116 1.46714i
\(222\) 0 0
\(223\) 36556.3 6445.86i 0.735110 0.129620i 0.206454 0.978456i \(-0.433808\pi\)
0.528655 + 0.848837i \(0.322696\pi\)
\(224\) 0 0
\(225\) 41324.2 + 15040.8i 0.816280 + 0.297101i
\(226\) 0 0
\(227\) 58042.3i 1.12640i 0.826320 + 0.563200i \(0.190430\pi\)
−0.826320 + 0.563200i \(0.809570\pi\)
\(228\) 0 0
\(229\) −47979.8 −0.914930 −0.457465 0.889228i \(-0.651242\pi\)
−0.457465 + 0.889228i \(0.651242\pi\)
\(230\) 0 0
\(231\) −13430.8 + 36900.8i −0.251697 + 0.691532i
\(232\) 0 0
\(233\) 15332.4 + 86954.6i 0.282422 + 1.60170i 0.714350 + 0.699789i \(0.246723\pi\)
−0.431927 + 0.901909i \(0.642166\pi\)
\(234\) 0 0
\(235\) −56597.0 + 98028.8i −1.02484 + 1.77508i
\(236\) 0 0
\(237\) −64516.3 54135.6i −1.14861 0.963798i
\(238\) 0 0
\(239\) −21266.4 36834.6i −0.372305 0.644851i 0.617615 0.786481i \(-0.288099\pi\)
−0.989920 + 0.141629i \(0.954766\pi\)
\(240\) 0 0
\(241\) −378.914 1041.06i −0.00652390 0.0179243i 0.936388 0.350967i \(-0.114147\pi\)
−0.942912 + 0.333042i \(0.891925\pi\)
\(242\) 0 0
\(243\) 75348.3 + 13285.9i 1.27603 + 0.224999i
\(244\) 0 0
\(245\) −7614.45 + 6389.28i −0.126855 + 0.106444i
\(246\) 0 0
\(247\) −79273.4 + 84491.2i −1.29937 + 1.38490i
\(248\) 0 0
\(249\) 57382.3 + 68385.5i 0.925505 + 1.10297i
\(250\) 0 0
\(251\) −5413.15 + 30699.5i −0.0859217 + 0.487286i 0.911232 + 0.411893i \(0.135132\pi\)
−0.997154 + 0.0753931i \(0.975979\pi\)
\(252\) 0 0
\(253\) 30702.7 11174.9i 0.479662 0.174583i
\(254\) 0 0
\(255\) 168532. 97302.2i 2.59181 1.49638i
\(256\) 0 0
\(257\) 50379.6 60040.0i 0.762760 0.909023i −0.235259 0.971933i \(-0.575594\pi\)
0.998019 + 0.0629103i \(0.0200382\pi\)
\(258\) 0 0
\(259\) −23875.8 13784.7i −0.355925 0.205494i
\(260\) 0 0
\(261\) 52679.1 9288.75i 0.773317 0.136357i
\(262\) 0 0
\(263\) 82030.2 + 29856.6i 1.18594 + 0.431647i 0.858296 0.513155i \(-0.171523\pi\)
0.327643 + 0.944802i \(0.393746\pi\)
\(264\) 0 0
\(265\) 65714.5i 0.935771i
\(266\) 0 0
\(267\) −76212.2 −1.06906
\(268\) 0 0
\(269\) 2186.85 6008.31i 0.0302213 0.0830325i −0.923664 0.383202i \(-0.874821\pi\)
0.953886 + 0.300170i \(0.0970434\pi\)
\(270\) 0 0
\(271\) 718.640 + 4075.61i 0.00978527 + 0.0554950i 0.989309 0.145832i \(-0.0465858\pi\)
−0.979524 + 0.201327i \(0.935475\pi\)
\(272\) 0 0
\(273\) −100497. + 174065.i −1.34842 + 2.33554i
\(274\) 0 0
\(275\) 32244.4 + 27056.3i 0.426372 + 0.357769i
\(276\) 0 0
\(277\) −57251.9 99163.2i −0.746157 1.29238i −0.949652 0.313306i \(-0.898563\pi\)
0.203495 0.979076i \(-0.434770\pi\)
\(278\) 0 0
\(279\) 27749.9 + 76242.1i 0.356494 + 0.979460i
\(280\) 0 0
\(281\) −75809.1 13367.2i −0.960082 0.169288i −0.328420 0.944532i \(-0.606516\pi\)
−0.631663 + 0.775243i \(0.717627\pi\)
\(282\) 0 0
\(283\) 16680.1 13996.3i 0.208270 0.174759i −0.532686 0.846313i \(-0.678817\pi\)
0.740956 + 0.671554i \(0.234373\pi\)
\(284\) 0 0
\(285\) −45536.8 150589.i −0.560625 1.85397i
\(286\) 0 0
\(287\) −34522.0 41141.7i −0.419114 0.499480i
\(288\) 0 0
\(289\) 20123.0 114123.i 0.240934 1.36640i
\(290\) 0 0
\(291\) 47695.6 17359.8i 0.563239 0.205002i
\(292\) 0 0
\(293\) −6337.52 + 3658.97i −0.0738217 + 0.0426210i −0.536456 0.843928i \(-0.680237\pi\)
0.462635 + 0.886549i \(0.346904\pi\)
\(294\) 0 0
\(295\) −13150.7 + 15672.4i −0.151114 + 0.180090i
\(296\) 0 0
\(297\) 10181.6 + 5878.32i 0.115425 + 0.0666408i
\(298\) 0 0
\(299\) 164692. 29039.7i 1.84218 0.324825i
\(300\) 0 0
\(301\) 22326.5 + 8126.20i 0.246427 + 0.0896921i
\(302\) 0 0
\(303\) 45935.1i 0.500333i
\(304\) 0 0
\(305\) −19449.2 −0.209075
\(306\) 0 0
\(307\) 15214.4 41801.2i 0.161428 0.443519i −0.832437 0.554119i \(-0.813055\pi\)
0.993865 + 0.110600i \(0.0352773\pi\)
\(308\) 0 0
\(309\) 7029.33 + 39865.3i 0.0736202 + 0.417521i
\(310\) 0 0
\(311\) −27129.2 + 46989.2i −0.280489 + 0.485822i −0.971505 0.237018i \(-0.923830\pi\)
0.691016 + 0.722840i \(0.257163\pi\)
\(312\) 0 0
\(313\) −133986. 112427.i −1.36763 1.14758i −0.973541 0.228510i \(-0.926614\pi\)
−0.394093 0.919071i \(-0.628941\pi\)
\(314\) 0 0
\(315\) −61017.9 105686.i −0.614945 1.06512i
\(316\) 0 0
\(317\) 17422.9 + 47869.1i 0.173381 + 0.476361i 0.995697 0.0926706i \(-0.0295404\pi\)
−0.822316 + 0.569032i \(0.807318\pi\)
\(318\) 0 0
\(319\) 50422.0 + 8890.77i 0.495495 + 0.0873691i
\(320\) 0 0
\(321\) −95201.7 + 79883.7i −0.923920 + 0.775261i
\(322\) 0 0
\(323\) −148196. 63440.5i −1.42046 0.608081i
\(324\) 0 0
\(325\) 138484. + 165039.i 1.31109 + 1.56250i
\(326\) 0 0
\(327\) 43184.4 244911.i 0.403861 2.29041i
\(328\) 0 0
\(329\) 152858. 55635.7i 1.41220 0.513998i
\(330\) 0 0
\(331\) 42178.2 24351.6i 0.384975 0.222265i −0.295006 0.955495i \(-0.595322\pi\)
0.679980 + 0.733230i \(0.261988\pi\)
\(332\) 0 0
\(333\) 22437.2 26739.7i 0.202340 0.241139i
\(334\) 0 0
\(335\) −207723. 119929.i −1.85095 1.06865i
\(336\) 0 0
\(337\) −172939. + 30493.9i −1.52277 + 0.268505i −0.871520 0.490360i \(-0.836865\pi\)
−0.651248 + 0.758865i \(0.725754\pi\)
\(338\) 0 0
\(339\) 104137. + 37902.7i 0.906159 + 0.329815i
\(340\) 0 0
\(341\) 77658.9i 0.667855i
\(342\) 0 0
\(343\) −109944. −0.934513
\(344\) 0 0
\(345\) −77667.7 + 213390.i −0.652533 + 1.79282i
\(346\) 0 0
\(347\) −35555.2 201644.i −0.295287 1.67466i −0.666034 0.745921i \(-0.732009\pi\)
0.370747 0.928734i \(-0.379102\pi\)
\(348\) 0 0
\(349\) 14177.9 24556.8i 0.116402 0.201614i −0.801937 0.597408i \(-0.796197\pi\)
0.918339 + 0.395794i \(0.129531\pi\)
\(350\) 0 0
\(351\) 46096.6 + 38679.6i 0.374158 + 0.313955i
\(352\) 0 0
\(353\) 31647.8 + 54815.5i 0.253976 + 0.439900i 0.964617 0.263655i \(-0.0849281\pi\)
−0.710641 + 0.703555i \(0.751595\pi\)
\(354\) 0 0
\(355\) 20087.3 + 55189.3i 0.159391 + 0.437924i
\(356\) 0 0
\(357\) −275412. 48562.6i −2.16096 0.381035i
\(358\) 0 0
\(359\) 138189. 115954.i 1.07222 0.899699i 0.0769680 0.997034i \(-0.475476\pi\)
0.995252 + 0.0973344i \(0.0310316\pi\)
\(360\) 0 0
\(361\) −77243.7 + 104962.i −0.592719 + 0.805409i
\(362\) 0 0
\(363\) 83322.9 + 99300.3i 0.632340 + 0.753594i
\(364\) 0 0
\(365\) 51539.3 292294.i 0.386859 2.19399i
\(366\) 0 0
\(367\) 155098. 56451.0i 1.15153 0.419121i 0.305463 0.952204i \(-0.401189\pi\)
0.846063 + 0.533083i \(0.178966\pi\)
\(368\) 0 0
\(369\) 58888.8 33999.5i 0.432494 0.249701i
\(370\) 0 0
\(371\) 60702.6 72342.5i 0.441021 0.525589i
\(372\) 0 0
\(373\) 17104.7 + 9875.42i 0.122942 + 0.0709803i 0.560210 0.828351i \(-0.310721\pi\)
−0.437268 + 0.899331i \(0.644054\pi\)
\(374\) 0 0
\(375\) −19868.8 + 3503.40i −0.141289 + 0.0249131i
\(376\) 0 0
\(377\) 246256. + 89629.7i 1.73262 + 0.630622i
\(378\) 0 0
\(379\) 62884.2i 0.437787i −0.975749 0.218894i \(-0.929755\pi\)
0.975749 0.218894i \(-0.0702448\pi\)
\(380\) 0 0
\(381\) 39764.1 0.273931
\(382\) 0 0
\(383\) −87776.5 + 241164.i −0.598385 + 1.64405i 0.156107 + 0.987740i \(0.450105\pi\)
−0.754492 + 0.656309i \(0.772117\pi\)
\(384\) 0 0
\(385\) −20283.3 115033.i −0.136842 0.776067i
\(386\) 0 0
\(387\) −15041.1 + 26052.0i −0.100429 + 0.173948i
\(388\) 0 0
\(389\) 57339.1 + 48113.2i 0.378924 + 0.317955i 0.812280 0.583268i \(-0.198226\pi\)
−0.433356 + 0.901223i \(0.642671\pi\)
\(390\) 0 0
\(391\) 116343. + 201513.i 0.761006 + 1.31810i
\(392\) 0 0
\(393\) −54766.7 150470.i −0.354594 0.974240i
\(394\) 0 0
\(395\) 246709. + 43501.5i 1.58122 + 0.278811i
\(396\) 0 0
\(397\) 76222.8 63958.5i 0.483619 0.405805i −0.368114 0.929781i \(-0.619996\pi\)
0.851733 + 0.523976i \(0.175552\pi\)
\(398\) 0 0
\(399\) −88973.8 + 207841.i −0.558877 + 1.30553i
\(400\) 0 0
\(401\) −17594.1 20967.9i −0.109416 0.130396i 0.708557 0.705653i \(-0.249346\pi\)
−0.817973 + 0.575257i \(0.804902\pi\)
\(402\) 0 0
\(403\) −69022.8 + 391448.i −0.424994 + 2.41026i
\(404\) 0 0
\(405\) −256309. + 93289.0i −1.56262 + 0.568749i
\(406\) 0 0
\(407\) 28934.4 16705.3i 0.174673 0.100847i
\(408\) 0 0
\(409\) −31610.0 + 37671.3i −0.188963 + 0.225198i −0.852206 0.523207i \(-0.824735\pi\)
0.663242 + 0.748405i \(0.269180\pi\)
\(410\) 0 0
\(411\) −44831.9 25883.7i −0.265402 0.153230i
\(412\) 0 0
\(413\) 28954.1 5105.40i 0.169750 0.0299316i
\(414\) 0 0
\(415\) −249525. 90819.8i −1.44883 0.527333i
\(416\) 0 0
\(417\) 84106.1i 0.483677i
\(418\) 0 0
\(419\) 172898. 0.984829 0.492415 0.870361i \(-0.336114\pi\)
0.492415 + 0.870361i \(0.336114\pi\)
\(420\) 0 0
\(421\) −31024.7 + 85239.6i −0.175042 + 0.480925i −0.995926 0.0901699i \(-0.971259\pi\)
0.820884 + 0.571095i \(0.193481\pi\)
\(422\) 0 0
\(423\) 35764.0 + 202828.i 0.199878 + 1.13357i
\(424\) 0 0
\(425\) −149883. + 259604.i −0.829800 + 1.43726i
\(426\) 0 0
\(427\) 21410.9 + 17965.8i 0.117430 + 0.0985353i
\(428\) 0 0
\(429\) −121789. 210945.i −0.661749 1.14618i
\(430\) 0 0
\(431\) −57800.6 158806.i −0.311156 0.854894i −0.992424 0.122860i \(-0.960793\pi\)
0.681268 0.732034i \(-0.261429\pi\)
\(432\) 0 0
\(433\) 62509.0 + 11022.0i 0.333401 + 0.0587876i 0.337843 0.941203i \(-0.390303\pi\)
−0.00444187 + 0.999990i \(0.501414\pi\)
\(434\) 0 0
\(435\) −272597. + 228736.i −1.44060 + 1.20880i
\(436\) 0 0
\(437\) 180057. 54447.9i 0.942862 0.285114i
\(438\) 0 0
\(439\) 78416.9 + 93453.6i 0.406893 + 0.484916i 0.930109 0.367284i \(-0.119712\pi\)
−0.523216 + 0.852200i \(0.675268\pi\)
\(440\) 0 0
\(441\) −3140.56 + 17811.0i −0.0161484 + 0.0915823i
\(442\) 0 0
\(443\) −39956.5 + 14543.0i −0.203601 + 0.0741047i −0.441808 0.897110i \(-0.645663\pi\)
0.238207 + 0.971214i \(0.423440\pi\)
\(444\) 0 0
\(445\) 196324. 113348.i 0.991411 0.572392i
\(446\) 0 0
\(447\) −340059. + 405266.i −1.70192 + 2.02827i
\(448\) 0 0
\(449\) 244799. + 141335.i 1.21427 + 0.701061i 0.963687 0.267034i \(-0.0860436\pi\)
0.250585 + 0.968094i \(0.419377\pi\)
\(450\) 0 0
\(451\) 64096.7 11302.0i 0.315125 0.0555650i
\(452\) 0 0
\(453\) 260388. + 94773.6i 1.26889 + 0.461839i
\(454\) 0 0
\(455\) 597861.i 2.88787i
\(456\) 0 0
\(457\) −245414. −1.17508 −0.587539 0.809196i \(-0.699903\pi\)
−0.587539 + 0.809196i \(0.699903\pi\)
\(458\) 0 0
\(459\) −28636.3 + 78677.5i −0.135922 + 0.373444i
\(460\) 0 0
\(461\) −54578.8 309532.i −0.256816 1.45648i −0.791368 0.611340i \(-0.790631\pi\)
0.534552 0.845136i \(-0.320480\pi\)
\(462\) 0 0
\(463\) 207033. 358592.i 0.965779 1.67278i 0.258272 0.966072i \(-0.416847\pi\)
0.707507 0.706706i \(-0.249820\pi\)
\(464\) 0 0
\(465\) −413469. 346942.i −1.91222 1.60454i
\(466\) 0 0
\(467\) −126489. 219086.i −0.579990 1.00457i −0.995480 0.0949745i \(-0.969723\pi\)
0.415489 0.909598i \(-0.363610\pi\)
\(468\) 0 0
\(469\) 117892. + 323906.i 0.535969 + 1.47256i
\(470\) 0 0
\(471\) 319138. + 56272.6i 1.43859 + 0.253662i
\(472\) 0 0
\(473\) −22057.0 + 18508.0i −0.0985879 + 0.0827250i
\(474\) 0 0
\(475\) 176729. + 165815.i 0.783284 + 0.734913i
\(476\) 0 0
\(477\) 76856.6 + 91594.2i 0.337788 + 0.402560i
\(478\) 0 0
\(479\) −3378.29 + 19159.3i −0.0147240 + 0.0835040i −0.991284 0.131740i \(-0.957944\pi\)
0.976560 + 0.215244i \(0.0690547\pi\)
\(480\) 0 0
\(481\) 160695. 58488.0i 0.694562 0.252800i
\(482\) 0 0
\(483\) 282617. 163169.i 1.21145 0.699428i
\(484\) 0 0
\(485\) −97046.3 + 115655.i −0.412568 + 0.491679i
\(486\) 0 0
\(487\) −138308. 79852.2i −0.583162 0.336689i 0.179227 0.983808i \(-0.442640\pi\)
−0.762389 + 0.647119i \(0.775974\pi\)
\(488\) 0 0
\(489\) 413920. 72985.3i 1.73101 0.305223i
\(490\) 0 0
\(491\) −61049.3 22220.1i −0.253232 0.0921687i 0.212285 0.977208i \(-0.431909\pi\)
−0.465517 + 0.885039i \(0.654132\pi\)
\(492\) 0 0
\(493\) 364628.i 1.50022i
\(494\) 0 0
\(495\) 147892. 0.603577
\(496\) 0 0
\(497\) 28866.9 79311.1i 0.116866 0.321086i
\(498\) 0 0
\(499\) −10083.2 57184.4i −0.0404944 0.229655i 0.957843 0.287291i \(-0.0927548\pi\)
−0.998338 + 0.0576361i \(0.981644\pi\)
\(500\) 0 0
\(501\) 278038. 481575.i 1.10772 1.91862i
\(502\) 0 0
\(503\) −280926. 235725.i −1.11034 0.931686i −0.112263 0.993678i \(-0.535810\pi\)
−0.998077 + 0.0619926i \(0.980254\pi\)
\(504\) 0 0
\(505\) −68317.8 118330.i −0.267887 0.463993i
\(506\) 0 0
\(507\) −308165. 846677.i −1.19886 3.29384i
\(508\) 0 0
\(509\) −327355. 57721.5i −1.26352 0.222793i −0.498553 0.866859i \(-0.666135\pi\)
−0.764970 + 0.644066i \(0.777246\pi\)
\(510\) 0 0
\(511\) −326739. + 274167.i −1.25129 + 1.04996i
\(512\) 0 0
\(513\) 56654.0 + 37038.2i 0.215276 + 0.140739i
\(514\) 0 0
\(515\) −77398.0 92239.4i −0.291820 0.347778i
\(516\) 0 0
\(517\) −34231.7 + 194137.i −0.128070 + 0.726321i
\(518\) 0 0
\(519\) −595054. + 216582.i −2.20913 + 0.804058i
\(520\) 0 0
\(521\) −154075. + 88955.0i −0.567617 + 0.327714i −0.756197 0.654344i \(-0.772945\pi\)
0.188580 + 0.982058i \(0.439612\pi\)
\(522\) 0 0
\(523\) −7225.72 + 8611.28i −0.0264167 + 0.0314821i −0.779091 0.626911i \(-0.784319\pi\)
0.752674 + 0.658393i \(0.228763\pi\)
\(524\) 0 0
\(525\) 364089. + 210207.i 1.32096 + 0.762655i
\(526\) 0 0
\(527\) −544658. + 96037.9i −1.96111 + 0.345797i
\(528\) 0 0
\(529\) 7815.74 + 2844.70i 0.0279292 + 0.0101654i
\(530\) 0 0
\(531\) 37224.9i 0.132021i
\(532\) 0 0
\(533\) 333131. 1.17263
\(534\) 0 0
\(535\) 126433. 347372.i 0.441727 1.21363i
\(536\) 0 0
\(537\) −9156.13 51927.0i −0.0317514 0.180071i
\(538\) 0 0
\(539\) −8655.44 + 14991.7i −0.0297928 + 0.0516027i
\(540\) 0 0
\(541\) −381628. 320224.i −1.30391 1.09411i −0.989456 0.144833i \(-0.953736\pi\)
−0.314450 0.949274i \(-0.601820\pi\)
\(542\) 0 0
\(543\) 209098. + 362168.i 0.709169 + 1.22832i
\(544\) 0 0
\(545\) 253004. + 695123.i 0.851794 + 2.34028i
\(546\) 0 0
\(547\) 276.343 + 48.7267i 0.000923578 + 0.000162852i 0.174110 0.984726i \(-0.444295\pi\)
−0.173186 + 0.984889i \(0.555406\pi\)
\(548\) 0 0
\(549\) −27108.7 + 22746.9i −0.0899422 + 0.0754704i
\(550\) 0 0
\(551\) 287015. + 67187.2i 0.945370 + 0.221301i
\(552\) 0 0
\(553\) −231409. 275783.i −0.756711 0.901813i
\(554\) 0 0
\(555\) −40323.0 + 228683.i −0.130908 + 0.742416i
\(556\) 0 0
\(557\) 107948. 39289.8i 0.347940 0.126640i −0.162138 0.986768i \(-0.551839\pi\)
0.510078 + 0.860128i \(0.329617\pi\)
\(558\) 0 0
\(559\) −127630. + 73687.4i −0.408442 + 0.235814i
\(560\) 0 0
\(561\) 217849. 259622.i 0.692196 0.824928i
\(562\) 0 0
\(563\) 43650.6 + 25201.7i 0.137713 + 0.0795084i 0.567273 0.823530i \(-0.307998\pi\)
−0.429561 + 0.903038i \(0.641332\pi\)
\(564\) 0 0
\(565\) −324630. + 57241.0i −1.01693 + 0.179312i
\(566\) 0 0
\(567\) 368335. + 134063.i 1.14572 + 0.417007i
\(568\) 0 0
\(569\) 51452.5i 0.158921i −0.996838 0.0794606i \(-0.974680\pi\)
0.996838 0.0794606i \(-0.0253198\pi\)
\(570\) 0 0
\(571\) −313784. −0.962406 −0.481203 0.876609i \(-0.659800\pi\)
−0.481203 + 0.876609i \(0.659800\pi\)
\(572\) 0 0
\(573\) −9602.73 + 26383.3i −0.0292473 + 0.0803562i
\(574\) 0 0
\(575\) −60741.8 344484.i −0.183718 1.04192i
\(576\) 0 0
\(577\) 292982. 507460.i 0.880014 1.52423i 0.0286892 0.999588i \(-0.490867\pi\)
0.851324 0.524640i \(-0.175800\pi\)
\(578\) 0 0
\(579\) 316804. + 265830.i 0.945002 + 0.792951i
\(580\) 0 0
\(581\) 190800. + 330475.i 0.565230 + 0.979008i
\(582\) 0 0
\(583\) 39142.4 + 107543.i 0.115162 + 0.316406i
\(584\) 0 0
\(585\) 745463. + 131445.i 2.17828 + 0.384090i
\(586\) 0 0
\(587\) 86046.8 72201.8i 0.249723 0.209542i −0.509330 0.860571i \(-0.670107\pi\)
0.759053 + 0.651029i \(0.225662\pi\)
\(588\) 0 0
\(589\) −24764.2 + 446421.i −0.0713828 + 1.28681i
\(590\) 0 0
\(591\) 100967. + 120327.i 0.289070 + 0.344500i
\(592\) 0 0
\(593\) 66008.9 374355.i 0.187712 1.06457i −0.734708 0.678383i \(-0.762681\pi\)
0.922421 0.386187i \(-0.126208\pi\)
\(594\) 0 0
\(595\) 781693. 284513.i 2.20802 0.803652i
\(596\) 0 0
\(597\) −534758. + 308743.i −1.50040 + 0.866259i
\(598\) 0 0
\(599\) −37860.1 + 45119.9i −0.105518 + 0.125752i −0.816219 0.577743i \(-0.803934\pi\)
0.710700 + 0.703495i \(0.248378\pi\)
\(600\) 0 0
\(601\) −276837. 159832.i −0.766435 0.442502i 0.0651661 0.997874i \(-0.479242\pi\)
−0.831602 + 0.555373i \(0.812576\pi\)
\(602\) 0 0
\(603\) −429793. + 75784.0i −1.18202 + 0.208422i
\(604\) 0 0
\(605\) −362328. 131876.i −0.989899 0.360294i
\(606\) 0 0
\(607\) 350213.i 0.950507i −0.879849 0.475253i \(-0.842356\pi\)
0.879849 0.475253i \(-0.157644\pi\)
\(608\) 0 0
\(609\) 511382. 1.37883
\(610\) 0 0
\(611\) −345097. + 948146.i −0.924397 + 2.53976i
\(612\) 0 0
\(613\) −12206.6 69227.1i −0.0324844 0.184228i 0.964248 0.265001i \(-0.0853722\pi\)
−0.996733 + 0.0807729i \(0.974261\pi\)
\(614\) 0 0
\(615\) −226179. + 391754.i −0.598002 + 1.03577i
\(616\) 0 0
\(617\) 542281. + 455027.i 1.42447 + 1.19527i 0.948892 + 0.315600i \(0.102206\pi\)
0.475579 + 0.879673i \(0.342239\pi\)
\(618\) 0 0
\(619\) −167678. 290427.i −0.437617 0.757976i 0.559888 0.828568i \(-0.310844\pi\)
−0.997505 + 0.0705929i \(0.977511\pi\)
\(620\) 0 0
\(621\) −33415.8 91809.2i −0.0866501 0.238069i
\(622\) 0 0
\(623\) −320829. 56570.8i −0.826604 0.145753i
\(624\) 0 0
\(625\) −275429. + 231113.i −0.705099 + 0.591648i
\(626\) 0 0
\(627\) −164219. 219317.i −0.417723 0.557876i
\(628\) 0 0
\(629\) 152944. + 182272.i 0.386573 + 0.460700i
\(630\) 0 0
\(631\) −40019.6 + 226962.i −0.100511 + 0.570026i 0.892408 + 0.451230i \(0.149015\pi\)
−0.992919 + 0.118796i \(0.962096\pi\)
\(632\) 0 0
\(633\) −304944. + 110991.i −0.761050 + 0.277000i
\(634\) 0 0
\(635\) −102433. + 59139.8i −0.254035 + 0.146667i
\(636\) 0 0
\(637\) −56953.2 + 67874.2i −0.140359 + 0.167273i
\(638\) 0 0
\(639\) 92545.0 + 53430.9i 0.226648 + 0.130855i
\(640\) 0 0
\(641\) 391871. 69097.5i 0.953734 0.168169i 0.324935 0.945736i \(-0.394658\pi\)
0.628800 + 0.777567i \(0.283547\pi\)
\(642\) 0 0
\(643\) 131116. + 47722.2i 0.317126 + 0.115425i 0.495679 0.868506i \(-0.334919\pi\)
−0.178553 + 0.983930i \(0.557141\pi\)
\(644\) 0 0
\(645\) 200120.i 0.481028i
\(646\) 0 0
\(647\) 27790.7 0.0663883 0.0331941 0.999449i \(-0.489432\pi\)
0.0331941 + 0.999449i \(0.489432\pi\)
\(648\) 0 0
\(649\) −12186.2 + 33481.2i −0.0289320 + 0.0794899i
\(650\) 0 0
\(651\) 134691. + 763870.i 0.317816 + 1.80243i
\(652\) 0 0
\(653\) −319447. + 553298.i −0.749155 + 1.29758i 0.199073 + 0.979985i \(0.436207\pi\)
−0.948228 + 0.317590i \(0.897126\pi\)
\(654\) 0 0
\(655\) 364870. + 306162.i 0.850463 + 0.713623i
\(656\) 0 0
\(657\) −270017. 467683.i −0.625548 1.08348i
\(658\) 0 0
\(659\) 26699.8 + 73357.1i 0.0614805 + 0.168916i 0.966630 0.256178i \(-0.0824632\pi\)
−0.905149 + 0.425094i \(0.860241\pi\)
\(660\) 0 0
\(661\) −49357.5 8703.06i −0.112967 0.0199191i 0.116879 0.993146i \(-0.462711\pi\)
−0.229846 + 0.973227i \(0.573822\pi\)
\(662\) 0 0
\(663\) 1.32884e6 1.11503e6i 3.02305 2.53664i
\(664\) 0 0
\(665\) −79916.4 667731.i −0.180714 1.50993i
\(666\) 0 0
\(667\) −273498. 325942.i −0.614755 0.732636i
\(668\) 0 0
\(669\) −78021.4 + 442481.i −0.174326 + 0.988650i
\(670\) 0 0
\(671\) −31828.9 + 11584.8i −0.0706931 + 0.0257302i
\(672\) 0 0
\(673\) −615226. + 355201.i −1.35833 + 0.784231i −0.989398 0.145227i \(-0.953609\pi\)
−0.368929 + 0.929457i \(0.620276\pi\)
\(674\) 0 0
\(675\) 80905.4 96419.3i 0.177570 0.211620i
\(676\) 0 0
\(677\) −318414. 183836.i −0.694727 0.401101i 0.110653 0.993859i \(-0.464706\pi\)
−0.805380 + 0.592758i \(0.798039\pi\)
\(678\) 0 0
\(679\) 213669. 37675.6i 0.463449 0.0817186i
\(680\) 0 0
\(681\) −660182. 240286.i −1.42354 0.518126i
\(682\) 0 0
\(683\) 47025.2i 0.100807i 0.998729 + 0.0504033i \(0.0160507\pi\)
−0.998729 + 0.0504033i \(0.983949\pi\)
\(684\) 0 0
\(685\) 153984. 0.328167
\(686\) 0 0
\(687\) 198629. 545730.i 0.420853 1.15628i
\(688\) 0 0
\(689\) 101718. + 576871.i 0.214269 + 1.21518i
\(690\) 0 0
\(691\) 153603. 266049.i 0.321695 0.557192i −0.659143 0.752018i \(-0.729081\pi\)
0.980838 + 0.194826i \(0.0624141\pi\)
\(692\) 0 0
\(693\) −162808. 136612.i −0.339008 0.284461i
\(694\) 0 0
\(695\) 125088. + 216659.i 0.258968 + 0.448546i
\(696\) 0 0
\(697\) 158532. + 435563.i 0.326326 + 0.896573i
\(698\) 0 0
\(699\) −1.05251e6 185586.i −2.15413 0.379830i
\(700\) 0 0
\(701\) 46126.4 38704.6i 0.0938671 0.0787639i −0.594646 0.803987i \(-0.702708\pi\)
0.688514 + 0.725223i \(0.258264\pi\)
\(702\) 0 0
\(703\) 171656. 86803.3i 0.347335 0.175641i
\(704\) 0 0
\(705\) −880691. 1.04957e6i −1.77193 2.11170i
\(706\) 0 0
\(707\) −34096.7 + 193372.i −0.0682140 + 0.386861i
\(708\) 0 0
\(709\) 233239. 84891.9i 0.463989 0.168878i −0.0994384 0.995044i \(-0.531705\pi\)
0.563428 + 0.826165i \(0.309482\pi\)
\(710\) 0 0
\(711\) 394746. 227907.i 0.780869 0.450835i
\(712\) 0 0
\(713\) 414835. 494382.i 0.816012 0.972486i
\(714\) 0 0
\(715\) 627462. + 362265.i 1.22737 + 0.708622i
\(716\) 0 0
\(717\) 507002. 89398.1i 0.986214 0.173896i
\(718\) 0 0
\(719\) −520380. 189403.i −1.00661 0.366377i −0.214482 0.976728i \(-0.568806\pi\)
−0.792131 + 0.610351i \(0.791029\pi\)
\(720\) 0 0
\(721\) 173038.i 0.332867i
\(722\) 0 0
\(723\) 13409.8 0.0256535
\(724\) 0 0
\(725\) 187477. 515088.i 0.356674 0.979954i
\(726\) 0 0
\(727\) 67242.9 + 381353.i 0.127226 + 0.721537i 0.979961 + 0.199192i \(0.0638317\pi\)
−0.852734 + 0.522345i \(0.825057\pi\)
\(728\) 0 0
\(729\) −156228. + 270595.i −0.293971 + 0.509172i
\(730\) 0 0
\(731\) −157082. 131808.i −0.293963 0.246664i
\(732\) 0 0
\(733\) 2211.44 + 3830.33i 0.00411593 + 0.00712900i 0.868076 0.496431i \(-0.165357\pi\)
−0.863960 + 0.503560i \(0.832023\pi\)
\(734\) 0 0
\(735\) −41149.9 113059.i −0.0761718 0.209280i
\(736\) 0 0
\(737\) −411378. 72537.0i −0.757366 0.133544i
\(738\) 0 0
\(739\) 305398. 256259.i 0.559213 0.469236i −0.318833 0.947811i \(-0.603291\pi\)
0.878047 + 0.478575i \(0.158847\pi\)
\(740\) 0 0
\(741\) −632835. 1.25145e6i −1.15253 2.27917i
\(742\) 0 0
\(743\) 474303. + 565252.i 0.859168 + 1.02392i 0.999429 + 0.0338014i \(0.0107614\pi\)
−0.140261 + 0.990115i \(0.544794\pi\)
\(744\) 0 0
\(745\) 273260. 1.54973e6i 0.492338 2.79219i
\(746\) 0 0
\(747\) −454012. + 165247.i −0.813629 + 0.296137i
\(748\) 0 0
\(749\) −460065. + 265618.i −0.820078 + 0.473472i
\(750\) 0 0
\(751\) 542438. 646452.i 0.961768 1.14619i −0.0274331 0.999624i \(-0.508733\pi\)
0.989201 0.146567i \(-0.0468222\pi\)
\(752\) 0 0
\(753\) −326771. 188661.i −0.576307 0.332731i
\(754\) 0 0
\(755\) −811720. + 143128.i −1.42401 + 0.251091i
\(756\) 0 0
\(757\) 787851. + 286754.i 1.37484 + 0.500401i 0.920610 0.390483i \(-0.127692\pi\)
0.454231 + 0.890884i \(0.349914\pi\)
\(758\) 0 0
\(759\) 395479.i 0.686499i
\(760\) 0 0
\(761\) 258202. 0.445851 0.222925 0.974836i \(-0.428439\pi\)
0.222925 + 0.974836i \(0.428439\pi\)
\(762\) 0 0
\(763\) 363585. 998942.i 0.624535 1.71590i
\(764\) 0 0
\(765\) 182892. + 1.03723e6i 0.312516 + 1.77236i
\(766\) 0 0
\(767\) −91183.6 + 157935.i −0.154998 + 0.268464i
\(768\) 0 0
\(769\) 202961. + 170305.i 0.343211 + 0.287988i 0.798057 0.602582i \(-0.205861\pi\)
−0.454846 + 0.890570i \(0.650306\pi\)
\(770\) 0 0
\(771\) 474340. + 821581.i 0.797960 + 1.38211i
\(772\) 0 0
\(773\) 66157.2 + 181765.i 0.110718 + 0.304195i 0.982661 0.185413i \(-0.0593622\pi\)
−0.871943 + 0.489608i \(0.837140\pi\)
\(774\) 0 0
\(775\) 818784. + 144374.i 1.36322 + 0.240372i
\(776\) 0 0
\(777\) 255632. 214500.i 0.423421 0.355293i
\(778\) 0 0
\(779\) 372063. 44529.8i 0.613114 0.0733797i
\(780\) 0 0
\(781\) 65746.3 + 78353.4i 0.107788 + 0.128456i
\(782\) 0 0
\(783\) 26585.8 150775.i 0.0433636 0.245927i
\(784\) 0 0
\(785\) −905798. + 329683.i −1.46991 + 0.535005i
\(786\) 0 0
\(787\) 90304.7 52137.4i 0.145801 0.0841783i −0.425325 0.905041i \(-0.639840\pi\)
0.571126 + 0.820862i \(0.306507\pi\)
\(788\) 0 0
\(789\) −679186. + 809422.i −1.09102 + 1.30023i
\(790\) 0 0
\(791\) 410248. + 236857.i 0.655682 + 0.378558i
\(792\) 0 0