Properties

Label 76.5.j.a.41.2
Level $76$
Weight $5$
Character 76.41
Analytic conductor $7.856$
Analytic rank $0$
Dimension $42$
CM no
Inner twists $2$

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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 41.2
Character \(\chi\) \(=\) 76.41
Dual form 76.5.j.a.13.2

$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{13}{18}\right)\) \(1\)

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 −0.925498 0.378754i \(-0.876353\pi\)
0.465514 0.885040i \(-0.345869\pi\)
\(4\) 0 0
\(5\) −6.25205 + 35.4571i −0.250082 + 1.41828i 0.558306 + 0.829635i \(0.311451\pi\)
−0.808388 + 0.588650i \(0.799660\pi\)
\(6\) 0 0
\(7\) −25.8702 44.8086i −0.527964 0.914461i −0.999469 0.0325971i \(-0.989622\pi\)
0.471504 0.881864i \(-0.343711\pi\)
\(8\) 0 0
\(9\) −50.1832 + 42.1087i −0.619546 + 0.519861i
\(10\) 0 0
\(11\) −31.3514 + 54.3022i −0.259102 + 0.448778i −0.966002 0.258536i \(-0.916760\pi\)
0.706899 + 0.707314i \(0.250093\pi\)
\(12\) 0 0
\(13\) −109.766 + 301.581i −0.649506 + 1.78450i −0.0299481 + 0.999551i \(0.509534\pi\)
−0.619558 + 0.784951i \(0.712688\pi\)
\(14\) 0 0
\(15\) 429.177 75.6755i 1.90745 0.336335i
\(16\) 0 0
\(17\) 342.075 + 287.035i 1.18365 + 0.993202i 0.999948 + 0.0102204i \(0.00325333\pi\)
0.183704 + 0.982982i \(0.441191\pi\)
\(18\) 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 −0.942607 0.333904i \(-0.891634\pi\)
0.771559 0.636158i \(-0.219477\pi\)
\(24\) 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 0.357670 0.933848i \(-0.383571\pi\)
−0.981770 + 0.190075i \(0.939127\pi\)
\(30\) 0 0
\(31\) −1072.59 + 619.262i −1.11612 + 0.644393i −0.940408 0.340048i \(-0.889557\pi\)
−0.175714 + 0.984441i \(0.556223\pi\)
\(32\) 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 \(-0.937656\pi\)
0.980881 0.194609i \(-0.0623439\pi\)
\(38\) 0 0
\(39\) 3884.64 2.55401
\(40\) 0 0
\(41\) −355.017 975.401i −0.211194 0.580251i 0.788187 0.615436i \(-0.211020\pi\)
−0.999381 + 0.0351853i \(0.988798\pi\)
\(42\) 0 0
\(43\) −79.7398 + 452.227i −0.0431259 + 0.244579i −0.998748 0.0500145i \(-0.984073\pi\)
0.955623 + 0.294594i \(0.0951843\pi\)
\(44\) 0 0
\(45\) −1179.31 2042.62i −0.582374 1.00870i
\(46\) 0 0
\(47\) −2408.38 + 2020.87i −1.09026 + 0.914836i −0.996732 0.0807812i \(-0.974259\pi\)
−0.0935268 + 0.995617i \(0.529814\pi\)
\(48\) 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 −0.484176 0.874971i \(-0.660881\pi\)
−0.155719 + 0.987801i \(0.549769\pi\)
\(54\) 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 −0.815953 0.578119i \(-0.803787\pi\)
0.711024 + 0.703167i \(0.248231\pi\)
\(60\) 0 0
\(61\) 93.8036 + 531.987i 0.0252093 + 0.142969i 0.994815 0.101706i \(-0.0324300\pi\)
−0.969605 + 0.244674i \(0.921319\pi\)
\(62\) 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 0.990498 + 0.137529i \(0.0439160\pi\)
−0.0365584 + 0.999332i \(0.511640\pi\)
\(68\) 0 0
\(69\) −5462.20 + 3153.60i −1.14728 + 0.662382i
\(70\) 0 0
\(71\) −1606.46 283.262i −0.318678 0.0561915i 0.0120212 0.999928i \(-0.496173\pi\)
−0.330699 + 0.943736i \(0.607285\pi\)
\(72\) 0 0
\(73\) 7746.45 2819.48i 1.45364 0.529082i 0.510034 0.860154i \(-0.329633\pi\)
0.943605 + 0.331072i \(0.107410\pi\)
\(74\) 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 −0.970805 0.239871i \(-0.922895\pi\)
0.589493 0.807773i \(-0.299327\pi\)
\(80\) 0 0
\(81\) −1315.52 + 7460.68i −0.200506 + 1.13713i
\(82\) 0 0
\(83\) 3687.63 + 6387.16i 0.535292 + 0.927153i 0.999149 + 0.0412433i \(0.0131319\pi\)
−0.463857 + 0.885910i \(0.653535\pi\)
\(84\) 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 −0.726349 0.687326i \(-0.758784\pi\)
0.998220 0.0596339i \(-0.0189933\pi\)
\(90\) 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 −0.890019 0.455923i \(-0.849309\pi\)
0.603546 + 0.797328i \(0.293754\pi\)
\(98\) 0 0
\(99\) −713.283 4045.23i −0.0727765 0.412736i
\(100\) 0 0
\(101\) 3566.13 + 1297.97i 0.349587 + 0.127239i 0.510844 0.859673i \(-0.329333\pi\)
−0.161258 + 0.986912i \(0.551555\pi\)
\(102\) 0 0
\(103\) 2896.28 + 1672.17i 0.273003 + 0.157618i 0.630251 0.776391i \(-0.282952\pi\)
−0.357249 + 0.934009i \(0.616285\pi\)
\(104\) 0 0
\(105\) −14493.8 17273.1i −1.31463 1.56672i
\(106\) 0 0
\(107\) 8891.77 5133.67i 0.776642 0.448394i −0.0585971 0.998282i \(-0.518663\pi\)
0.835239 + 0.549887i \(0.185329\pi\)
\(108\) 0 0
\(109\) −20233.7 3567.75i −1.70303 0.300290i −0.764279 0.644886i \(-0.776905\pi\)
−0.938751 + 0.344596i \(0.888016\pi\)
\(110\) 0 0
\(111\) −6060.61 + 2205.88i −0.491892 + 0.179034i
\(112\) 0 0
\(113\) 9155.56i 0.717015i 0.933527 + 0.358507i \(0.116714\pi\)
−0.933527 + 0.358507i \(0.883286\pi\)
\(114\) 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 −0.969638 0.244543i \(-0.921362\pi\)
0.899975 + 0.435941i \(0.143584\pi\)
\(128\) 0 0
\(129\) 5473.81 965.180i 0.328935 0.0580001i
\(130\) 0 0
\(131\) −10134.1 8503.54i −0.590532 0.495515i 0.297855 0.954611i \(-0.403729\pi\)
−0.888387 + 0.459096i \(0.848173\pi\)
\(132\) 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 0.958611 0.284720i \(-0.0919007\pi\)
−0.998179 + 0.0603146i \(0.980790\pi\)
\(138\) 0 0
\(139\) −6529.51 2376.55i −0.337949 0.123003i 0.167471 0.985877i \(-0.446440\pi\)
−0.505419 + 0.862874i \(0.668662\pi\)
\(140\) 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 0.864724 0.502247i \(-0.167493\pi\)
0.985255 0.171090i \(-0.0547290\pi\)
\(150\) 0 0
\(151\) 22893.0i 1.00403i 0.864858 + 0.502017i \(0.167409\pi\)
−0.864858 + 0.502017i \(0.832591\pi\)
\(152\) 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 0.732619 + 0.680639i \(0.238298\pi\)
−0.921229 + 0.389021i \(0.872813\pi\)
\(158\) 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 0.328803 + 0.944399i \(0.393355\pi\)
−0.982275 + 0.187448i \(0.939978\pi\)
\(164\) 0 0
\(165\) −9345.95 + 25677.8i −0.343285 + 0.943169i
\(166\) 0 0
\(167\) −45243.1 + 7977.57i −1.62226 + 0.286047i −0.909606 0.415473i \(-0.863616\pi\)
−0.712650 + 0.701520i \(0.752505\pi\)
\(168\) 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 0.189571 0.981867i \(-0.439290\pi\)
0.934032 0.357191i \(-0.116265\pi\)
\(174\) 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 0.439972 0.898011i \(-0.354988\pi\)
−0.557715 + 0.830033i \(0.688322\pi\)
\(180\) 0 0
\(181\) 22208.2 + 26466.7i 0.677886 + 0.807873i 0.989834 0.142226i \(-0.0454261\pi\)
−0.311948 + 0.950099i \(0.600982\pi\)
\(182\) 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 0.991898 + 0.127038i \(0.0405471\pi\)
−0.678179 + 0.734896i \(0.737231\pi\)
\(194\) 0 0
\(195\) −24287.0 + 137738.i −0.638710 + 3.62231i
\(196\) 0 0
\(197\) 6488.54 + 11238.5i 0.167192 + 0.289585i 0.937431 0.348170i \(-0.113197\pi\)
−0.770240 + 0.637755i \(0.779863\pi\)
\(198\) 0 0
\(199\) 39079.4 32791.5i 0.986828 0.828047i 0.00172223 0.999999i \(-0.499452\pi\)
0.985105 + 0.171952i \(0.0550074\pi\)
\(200\) 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 −0.536953 0.843612i \(-0.680425\pi\)
0.924037 + 0.382304i \(0.124869\pi\)
\(212\) 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 0.528655 0.848837i \(-0.322696\pi\)
0.206454 + 0.978456i \(0.433808\pi\)
\(224\) 0 0
\(225\) 41324.2 15040.8i 0.816280 0.297101i
\(226\) 0 0
\(227\) 58042.3i 1.12640i −0.826320 0.563200i \(-0.809570\pi\)
0.826320 0.563200i \(-0.190430\pi\)
\(228\) 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 −0.431927 0.901909i \(-0.642166\pi\)
0.714350 0.699789i \(-0.246723\pi\)
\(234\) 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 −0.989920 0.141629i \(-0.954766\pi\)
0.617615 + 0.786481i \(0.288099\pi\)
\(240\) 0 0
\(241\) −378.914 + 1041.06i −0.00652390 + 0.0179243i −0.942912 0.333042i \(-0.891925\pi\)
0.936388 + 0.350967i \(0.114147\pi\)
\(242\) 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 −0.997154 0.0753931i \(-0.975979\pi\)
0.911232 0.411893i \(-0.135132\pi\)
\(252\) 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 0.998019 0.0629103i \(-0.0200382\pi\)
−0.235259 + 0.971933i \(0.575594\pi\)
\(258\) 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 0.327643 0.944802i \(-0.393746\pi\)
0.858296 + 0.513155i \(0.171523\pi\)
\(264\) 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 0.953886 0.300170i \(-0.0970434\pi\)
−0.923664 + 0.383202i \(0.874821\pi\)
\(270\) 0 0
\(271\) 718.640 4075.61i 0.00978527 0.0554950i −0.979524 0.201327i \(-0.935475\pi\)
0.989309 + 0.145832i \(0.0465858\pi\)
\(272\) 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 0.203495 + 0.979076i \(0.434770\pi\)
−0.949652 + 0.313306i \(0.898563\pi\)
\(278\) 0 0
\(279\) 27749.9 76242.1i 0.356494 0.979460i
\(280\) 0 0
\(281\) −75809.1 + 13367.2i −0.960082 + 0.169288i −0.631663 0.775243i \(-0.717627\pi\)
−0.328420 + 0.944532i \(0.606516\pi\)
\(282\) 0 0
\(283\) 16680.1 + 13996.3i 0.208270 + 0.174759i 0.740956 0.671554i \(-0.234373\pi\)
−0.532686 + 0.846313i \(0.678817\pi\)
\(284\) 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 0.462635 0.886549i \(-0.346904\pi\)
−0.536456 + 0.843928i \(0.680237\pi\)
\(294\) 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 0.993865 0.110600i \(-0.0352773\pi\)
−0.832437 + 0.554119i \(0.813055\pi\)
\(308\) 0 0
\(309\) 7029.33 39865.3i 0.0736202 0.417521i
\(310\) 0 0
\(311\) −27129.2 46989.2i −0.280489 0.485822i 0.691016 0.722840i \(-0.257163\pi\)
−0.971505 + 0.237018i \(0.923830\pi\)
\(312\) 0 0
\(313\) −133986. + 112427.i −1.36763 + 1.14758i −0.394093 + 0.919071i \(0.628941\pi\)
−0.973541 + 0.228510i \(0.926614\pi\)
\(314\) 0 0
\(315\) −61017.9 + 105686.i −0.614945 + 1.06512i
\(316\) 0 0
\(317\) 17422.9 47869.1i 0.173381 0.476361i −0.822316 0.569032i \(-0.807318\pi\)
0.995697 + 0.0926706i \(0.0295404\pi\)
\(318\) 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 0.679980 0.733230i \(-0.261988\pi\)
−0.295006 + 0.955495i \(0.595322\pi\)
\(332\) 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 −0.651248 0.758865i \(-0.725754\pi\)
−0.871520 + 0.490360i \(0.836865\pi\)
\(338\) 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 0.370747 + 0.928734i \(0.379102\pi\)
−0.666034 + 0.745921i \(0.732009\pi\)
\(348\) 0 0
\(349\) 14177.9 + 24556.8i 0.116402 + 0.201614i 0.918339 0.395794i \(-0.129531\pi\)
−0.801937 + 0.597408i \(0.796197\pi\)
\(350\) 0 0
\(351\) 46096.6 38679.6i 0.374158 0.313955i
\(352\) 0 0
\(353\) 31647.8 54815.5i 0.253976 0.439900i −0.710641 0.703555i \(-0.751595\pi\)
0.964617 + 0.263655i \(0.0849281\pi\)
\(354\) 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 0.995252 0.0973344i \(-0.0310316\pi\)
0.0769680 + 0.997034i \(0.475476\pi\)
\(360\) 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 0.846063 0.533083i \(-0.178966\pi\)
0.305463 + 0.952204i \(0.401189\pi\)
\(368\) 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 −0.437268 0.899331i \(-0.644054\pi\)
0.560210 + 0.828351i \(0.310721\pi\)
\(374\) 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 \(0.0702448\pi\)
−0.975749 + 0.218894i \(0.929755\pi\)
\(380\) 0 0
\(381\) 39764.1 0.273931
\(382\) 0 0
\(383\) −87776.5 241164.i −0.598385 1.64405i −0.754492 0.656309i \(-0.772117\pi\)
0.156107 0.987740i \(-0.450105\pi\)
\(384\) 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 −0.433356 0.901223i \(-0.642671\pi\)
0.812280 + 0.583268i \(0.198226\pi\)
\(390\) 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 0.851733 0.523976i \(-0.175552\pi\)
−0.368114 + 0.929781i \(0.619996\pi\)
\(398\) 0 0
\(399\) −88973.8 207841.i −0.558877 1.30553i
\(400\) 0 0
\(401\) −17594.1 + 20967.9i −0.109416 + 0.130396i −0.817973 0.575257i \(-0.804902\pi\)
0.708557 + 0.705653i \(0.249346\pi\)
\(402\) 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 0.663242 0.748405i \(-0.269180\pi\)
−0.852206 + 0.523207i \(0.824735\pi\)
\(410\) 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 0.820884 0.571095i \(-0.193481\pi\)
−0.995926 + 0.0901699i \(0.971259\pi\)
\(422\) 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 0.681268 + 0.732034i \(0.261429\pi\)
−0.992424 + 0.122860i \(0.960793\pi\)
\(432\) 0 0
\(433\) 62509.0 11022.0i 0.333401 0.0587876i −0.00444187 0.999990i \(-0.501414\pi\)
0.337843 + 0.941203i \(0.390303\pi\)
\(434\) 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 −0.523216 0.852200i \(-0.675268\pi\)
0.930109 + 0.367284i \(0.119712\pi\)
\(440\) 0 0
\(441\) −3140.56 17811.0i −0.0161484 0.0915823i
\(442\) 0 0
\(443\) −39956.5 14543.0i −0.203601 0.0741047i 0.238207 0.971214i \(-0.423440\pi\)
−0.441808 + 0.897110i \(0.645663\pi\)
\(444\) 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 0.250585 0.968094i \(-0.419377\pi\)
0.963687 + 0.267034i \(0.0860436\pi\)
\(450\) 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 0.534552 + 0.845136i \(0.320480\pi\)
−0.791368 + 0.611340i \(0.790631\pi\)
\(462\) 0 0
\(463\) 207033. + 358592.i 0.965779 + 1.67278i 0.707507 + 0.706706i \(0.249820\pi\)
0.258272 + 0.966072i \(0.416847\pi\)
\(464\) 0 0
\(465\) −413469. + 346942.i −1.91222 + 1.60454i
\(466\) 0 0
\(467\) −126489. + 219086.i −0.579990 + 1.00457i 0.415489 + 0.909598i \(0.363610\pi\)
−0.995480 + 0.0949745i \(0.969723\pi\)
\(468\) 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 0.976560 0.215244i \(-0.0690547\pi\)
−0.991284 + 0.131740i \(0.957944\pi\)
\(480\) 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 −0.762389 0.647119i \(-0.775974\pi\)
0.179227 + 0.983808i \(0.442640\pi\)
\(488\) 0 0
\(489\) 413920. + 72985.3i 1.73101 + 0.305223i
\(490\) 0 0
\(491\) −61049.3 + 22220.1i −0.253232 + 0.0921687i −0.465517 0.885039i \(-0.654132\pi\)
0.212285 + 0.977208i \(0.431909\pi\)
\(492\) 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 −0.998338 0.0576361i \(-0.981644\pi\)
0.957843 + 0.287291i \(0.0927548\pi\)
\(500\) 0 0
\(501\) 278038. + 481575.i 1.10772 + 1.91862i
\(502\) 0 0
\(503\) −280926. + 235725.i −1.11034 + 0.931686i −0.998077 0.0619926i \(-0.980254\pi\)
−0.112263 + 0.993678i \(0.535810\pi\)
\(504\) 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 −0.764970 0.644066i \(-0.777246\pi\)
−0.498553 + 0.866859i \(0.666135\pi\)
\(510\) 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 0.188580 0.982058i \(-0.439612\pi\)
−0.756197 + 0.654344i \(0.772945\pi\)
\(522\) 0 0
\(523\) −7225.72 8611.28i −0.0264167 0.0314821i 0.752674 0.658393i \(-0.228763\pi\)
−0.779091 + 0.626911i \(0.784319\pi\)
\(524\) 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 −0.314450 + 0.949274i \(0.601820\pi\)
−0.989456 + 0.144833i \(0.953736\pi\)
\(542\) 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 −0.173186 0.984889i \(-0.555406\pi\)
0.174110 + 0.984726i \(0.444295\pi\)
\(548\) 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 0.510078 0.860128i \(-0.329617\pi\)
−0.162138 + 0.986768i \(0.551839\pi\)
\(558\) 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 −0.429561 0.903038i \(-0.641332\pi\)
0.567273 + 0.823530i \(0.307998\pi\)
\(564\) 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 \(0.0253198\pi\)
−0.996838 + 0.0794606i \(0.974680\pi\)
\(570\) 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 0.851324 + 0.524640i \(0.175800\pi\)
0.0286892 + 0.999588i \(0.490867\pi\)
\(578\) 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 0.759053 0.651029i \(-0.225662\pi\)
−0.509330 + 0.860571i \(0.670107\pi\)
\(588\) 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 0.922421 + 0.386187i \(0.126208\pi\)
−0.734708 + 0.678383i \(0.762681\pi\)
\(594\) 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 0.710700 0.703495i \(-0.248378\pi\)
−0.816219 + 0.577743i \(0.803934\pi\)
\(600\) 0 0
\(601\) −276837. + 159832.i −0.766435 + 0.442502i −0.831602 0.555373i \(-0.812576\pi\)
0.0651661 + 0.997874i \(0.479242\pi\)
\(602\) 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 \(0.157644\pi\)
−0.879849 + 0.475253i \(0.842356\pi\)
\(608\) 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 −0.996733 0.0807729i \(-0.974261\pi\)
0.964248 + 0.265001i \(0.0853722\pi\)
\(614\) 0 0
\(615\) −226179. 391754.i −0.598002 1.03577i
\(616\) 0 0
\(617\) 542281. 455027.i 1.42447 1.19527i 0.475579 0.879673i \(-0.342239\pi\)
0.948892 0.315600i \(-0.102206\pi\)
\(618\) 0 0
\(619\) −167678. + 290427.i −0.437617 + 0.757976i −0.997505 0.0705929i \(-0.977511\pi\)
0.559888 + 0.828568i \(0.310844\pi\)
\(620\) 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 −0.992919 0.118796i \(-0.962096\pi\)
0.892408 0.451230i \(-0.149015\pi\)
\(632\) 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 0.628800 0.777567i \(-0.283547\pi\)
0.324935 + 0.945736i \(0.394658\pi\)
\(642\) 0 0
\(643\) 131116. 47722.2i 0.317126 0.115425i −0.178553 0.983930i \(-0.557141\pi\)
0.495679 + 0.868506i \(0.334919\pi\)
\(644\) 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 −0.948228 0.317590i \(-0.897126\pi\)
0.199073 0.979985i \(-0.436207\pi\)
\(654\) 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 −0.905149 0.425094i \(-0.860241\pi\)
0.966630 + 0.256178i \(0.0824632\pi\)
\(660\) 0 0
\(661\) −49357.5 + 8703.06i −0.112967 + 0.0199191i −0.229846 0.973227i \(-0.573822\pi\)
0.116879 + 0.993146i \(0.462711\pi\)
\(662\) 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 −0.368929 0.929457i \(-0.620276\pi\)
−0.989398 + 0.145227i \(0.953609\pi\)
\(674\) 0 0
\(675\) 80905.4 + 96419.3i 0.177570 + 0.211620i
\(676\) 0 0
\(677\) −318414. + 183836.i −0.694727 + 0.401101i −0.805380 0.592758i \(-0.798039\pi\)
0.110653 + 0.993859i \(0.464706\pi\)
\(678\) 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 \(-0.983949\pi\)
0.998729 0.0504033i \(-0.0160507\pi\)
\(684\) 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 0.980838 0.194826i \(-0.0624141\pi\)
−0.659143 + 0.752018i \(0.729081\pi\)
\(692\) 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 0.688514 0.725223i \(-0.258264\pi\)
−0.594646 + 0.803987i \(0.702708\pi\)
\(702\) 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 0.563428 0.826165i \(-0.309482\pi\)
−0.0994384 + 0.995044i \(0.531705\pi\)
\(710\) 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 −0.792131 0.610351i \(-0.791029\pi\)
−0.214482 + 0.976728i \(0.568806\pi\)
\(720\) 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 −0.852734 0.522345i \(-0.825057\pi\)
0.979961 0.199192i \(-0.0638317\pi\)
\(728\) 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 −0.863960 0.503560i \(-0.832023\pi\)
0.868076 + 0.496431i \(0.165357\pi\)
\(734\) 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 0.878047 0.478575i \(-0.158847\pi\)
−0.318833 + 0.947811i \(0.603291\pi\)
\(740\) 0 0
\(741\) −632835. + 1.25145e6i −1.15253 + 2.27917i
\(742\) 0 0
\(743\) 474303. 565252.i 0.859168 1.02392i −0.140261 0.990115i \(-0.544794\pi\)
0.999429 0.0338014i \(-0.0107614\pi\)
\(744\) 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 0.989201 + 0.146567i \(0.0468222\pi\)
−0.0274331 + 0.999624i \(0.508733\pi\)
\(752\) 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 0.454231 0.890884i \(-0.349914\pi\)
0.920610 + 0.390483i \(0.127692\pi\)
\(758\) 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 −0.454846 0.890570i \(-0.650306\pi\)
0.798057 + 0.602582i \(0.205861\pi\)
\(770\) 0 0
\(771\) 474340. 821581.i 0.797960 1.38211i
\(772\) 0 0
\(773\) 66157.2 181765.i 0.110718 0.304195i −0.871943 0.489608i \(-0.837140\pi\)
0.982661 + 0.185413i \(0.0593622\pi\)
\(774\) 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 0.571126 0.820862i \(-0.306507\pi\)
−0.425325 + 0.905041i \(0.639840\pi\)
\(788\) 0 0
\(789\) −679186. 809422.i −1.09102 1.30023i
\(790\) 0 0
\(791\) 410248. 236857.i 0.655682 0.378558i
\(792\) 0