Properties

Label 108.5.k.a.29.8
Level 108
Weight 5
Character 108.29
Analytic conductor 11.164
Analytic rank 0
Dimension 72
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 108.k (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1639560131\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(12\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 29.8
Character \(\chi\) \(=\) 108.29
Dual form 108.5.k.a.41.8

$q$-expansion

\(f(q)\) \(=\) \(q+(4.39288 + 7.85510i) q^{3} +(6.32074 + 7.53276i) q^{5} +(66.1128 - 24.0631i) q^{7} +(-42.4052 + 69.0131i) q^{9} +O(q^{10})\) \(q+(4.39288 + 7.85510i) q^{3} +(6.32074 + 7.53276i) q^{5} +(66.1128 - 24.0631i) q^{7} +(-42.4052 + 69.0131i) q^{9} +(90.1574 - 107.445i) q^{11} +(37.0033 + 209.856i) q^{13} +(-31.4043 + 82.7405i) q^{15} +(-45.6573 + 26.3602i) q^{17} +(-163.587 + 283.340i) q^{19} +(479.444 + 413.617i) q^{21} +(-193.229 + 530.892i) q^{23} +(91.7393 - 520.280i) q^{25} +(-728.385 - 29.9305i) q^{27} +(109.946 + 19.3864i) q^{29} +(868.674 + 316.171i) q^{31} +(1240.05 + 236.200i) q^{33} +(599.143 + 345.916i) q^{35} +(154.394 + 267.419i) q^{37} +(-1485.89 + 1212.54i) q^{39} +(-478.016 + 84.2871i) q^{41} +(1943.12 + 1630.47i) q^{43} +(-787.891 + 116.785i) q^{45} +(-1391.66 - 3823.56i) q^{47} +(1952.60 - 1638.43i) q^{49} +(-407.629 - 242.845i) q^{51} -4272.88i q^{53} +1379.22 q^{55} +(-2944.28 - 40.3082i) q^{57} +(-3174.41 - 3783.11i) q^{59} +(-1472.97 + 536.118i) q^{61} +(-1142.86 + 5583.05i) q^{63} +(-1346.91 + 1605.18i) q^{65} +(-527.119 - 2989.44i) q^{67} +(-5019.04 + 814.314i) q^{69} +(-5046.35 + 2913.51i) q^{71} +(3497.66 - 6058.12i) q^{73} +(4489.85 - 1564.91i) q^{75} +(3375.09 - 9272.99i) q^{77} +(54.1811 - 307.276i) q^{79} +(-2964.60 - 5853.02i) q^{81} +(11818.7 + 2083.95i) q^{83} +(-487.153 - 177.309i) q^{85} +(330.697 + 948.798i) q^{87} +(-8394.50 - 4846.57i) q^{89} +(7496.17 + 12983.8i) q^{91} +(1332.42 + 8212.42i) q^{93} +(-3168.32 + 558.661i) q^{95} +(3647.23 + 3060.39i) q^{97} +(3592.00 + 10778.3i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72q + 9q^{5} - 102q^{9} + O(q^{10}) \) \( 72q + 9q^{5} - 102q^{9} + 18q^{11} - 225q^{15} - 282q^{21} - 1278q^{23} + 441q^{25} + 54q^{27} + 1854q^{29} - 1665q^{31} - 45q^{33} - 2673q^{35} + 6951q^{39} - 5472q^{41} + 1260q^{43} + 5553q^{45} + 5103q^{47} - 5904q^{49} + 1899q^{51} + 1107q^{57} - 10944q^{59} + 8352q^{61} - 11985q^{63} + 8757q^{65} + 378q^{67} + 5607q^{69} - 19764q^{71} + 6111q^{73} - 3453q^{75} - 5679q^{77} - 5652q^{79} - 20466q^{81} - 20061q^{83} + 26100q^{85} + 40545q^{87} + 15633q^{89} - 6039q^{91} + 40179q^{93} + 48024q^{95} - 37530q^{97} + 12177q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{1}{18}\right)\) \(1\)

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
\(3\) 4.39288 + 7.85510i 0.488098 + 0.872789i
\(4\) 0 0
\(5\) 6.32074 + 7.53276i 0.252829 + 0.301310i 0.877499 0.479579i \(-0.159211\pi\)
−0.624669 + 0.780889i \(0.714766\pi\)
\(6\) 0 0
\(7\) 66.1128 24.0631i 1.34924 0.491084i 0.436531 0.899689i \(-0.356207\pi\)
0.912711 + 0.408606i \(0.133985\pi\)
\(8\) 0 0
\(9\) −42.4052 + 69.0131i −0.523521 + 0.852013i
\(10\) 0 0
\(11\) 90.1574 107.445i 0.745103 0.887979i −0.251706 0.967804i \(-0.580992\pi\)
0.996809 + 0.0798249i \(0.0254361\pi\)
\(12\) 0 0
\(13\) 37.0033 + 209.856i 0.218954 + 1.24175i 0.873912 + 0.486085i \(0.161575\pi\)
−0.654957 + 0.755666i \(0.727313\pi\)
\(14\) 0 0
\(15\) −31.4043 + 82.7405i −0.139575 + 0.367736i
\(16\) 0 0
\(17\) −45.6573 + 26.3602i −0.157984 + 0.0912119i −0.576908 0.816809i \(-0.695741\pi\)
0.418924 + 0.908021i \(0.362407\pi\)
\(18\) 0 0
\(19\) −163.587 + 283.340i −0.453148 + 0.784876i −0.998580 0.0532795i \(-0.983033\pi\)
0.545431 + 0.838156i \(0.316366\pi\)
\(20\) 0 0
\(21\) 479.444 + 413.617i 1.08717 + 0.937906i
\(22\) 0 0
\(23\) −193.229 + 530.892i −0.365272 + 1.00358i 0.611864 + 0.790963i \(0.290420\pi\)
−0.977136 + 0.212614i \(0.931802\pi\)
\(24\) 0 0
\(25\) 91.7393 520.280i 0.146783 0.832447i
\(26\) 0 0
\(27\) −728.385 29.9305i −0.999157 0.0410569i
\(28\) 0 0
\(29\) 109.946 + 19.3864i 0.130732 + 0.0230516i 0.238631 0.971110i \(-0.423301\pi\)
−0.107899 + 0.994162i \(0.534412\pi\)
\(30\) 0 0
\(31\) 868.674 + 316.171i 0.903927 + 0.329002i 0.751825 0.659362i \(-0.229174\pi\)
0.152102 + 0.988365i \(0.451396\pi\)
\(32\) 0 0
\(33\) 1240.05 + 236.200i 1.13870 + 0.216897i
\(34\) 0 0
\(35\) 599.143 + 345.916i 0.489097 + 0.282380i
\(36\) 0 0
\(37\) 154.394 + 267.419i 0.112779 + 0.195339i 0.916890 0.399141i \(-0.130691\pi\)
−0.804111 + 0.594480i \(0.797358\pi\)
\(38\) 0 0
\(39\) −1485.89 + 1212.54i −0.976915 + 0.797197i
\(40\) 0 0
\(41\) −478.016 + 84.2871i −0.284364 + 0.0501411i −0.314011 0.949419i \(-0.601673\pi\)
0.0296468 + 0.999560i \(0.490562\pi\)
\(42\) 0 0
\(43\) 1943.12 + 1630.47i 1.05090 + 0.881813i 0.993188 0.116521i \(-0.0371741\pi\)
0.0577150 + 0.998333i \(0.481619\pi\)
\(44\) 0 0
\(45\) −787.891 + 116.785i −0.389082 + 0.0576718i
\(46\) 0 0
\(47\) −1391.66 3823.56i −0.629997 1.73090i −0.681081 0.732208i \(-0.738490\pi\)
0.0510841 0.998694i \(-0.483732\pi\)
\(48\) 0 0
\(49\) 1952.60 1638.43i 0.813245 0.682394i
\(50\) 0 0
\(51\) −407.629 242.845i −0.156720 0.0933660i
\(52\) 0 0
\(53\) 4272.88i 1.52114i −0.649256 0.760570i \(-0.724920\pi\)
0.649256 0.760570i \(-0.275080\pi\)
\(54\) 0 0
\(55\) 1379.22 0.455941
\(56\) 0 0
\(57\) −2944.28 40.3082i −0.906212 0.0124064i
\(58\) 0 0
\(59\) −3174.41 3783.11i −0.911924 1.08679i −0.995913 0.0903222i \(-0.971210\pi\)
0.0839884 0.996467i \(-0.473234\pi\)
\(60\) 0 0
\(61\) −1472.97 + 536.118i −0.395854 + 0.144079i −0.532274 0.846572i \(-0.678662\pi\)
0.136420 + 0.990651i \(0.456440\pi\)
\(62\) 0 0
\(63\) −1142.86 + 5583.05i −0.287946 + 1.40666i
\(64\) 0 0
\(65\) −1346.91 + 1605.18i −0.318794 + 0.379924i
\(66\) 0 0
\(67\) −527.119 2989.44i −0.117425 0.665948i −0.985521 0.169553i \(-0.945768\pi\)
0.868097 0.496395i \(-0.165343\pi\)
\(68\) 0 0
\(69\) −5019.04 + 814.314i −1.05420 + 0.171039i
\(70\) 0 0
\(71\) −5046.35 + 2913.51i −1.00106 + 0.577963i −0.908562 0.417750i \(-0.862819\pi\)
−0.0924992 + 0.995713i \(0.529486\pi\)
\(72\) 0 0
\(73\) 3497.66 6058.12i 0.656344 1.13682i −0.325211 0.945642i \(-0.605435\pi\)
0.981555 0.191180i \(-0.0612314\pi\)
\(74\) 0 0
\(75\) 4489.85 1564.91i 0.798195 0.278206i
\(76\) 0 0
\(77\) 3375.09 9272.99i 0.569252 1.56401i
\(78\) 0 0
\(79\) 54.1811 307.276i 0.00868148 0.0492351i −0.980159 0.198211i \(-0.936487\pi\)
0.988841 + 0.148976i \(0.0475978\pi\)
\(80\) 0 0
\(81\) −2964.60 5853.02i −0.451852 0.892093i
\(82\) 0 0
\(83\) 11818.7 + 2083.95i 1.71559 + 0.302504i 0.943096 0.332521i \(-0.107899\pi\)
0.772491 + 0.635025i \(0.219010\pi\)
\(84\) 0 0
\(85\) −487.153 177.309i −0.0674260 0.0245411i
\(86\) 0 0
\(87\) 330.697 + 948.798i 0.0436910 + 0.125353i
\(88\) 0 0
\(89\) −8394.50 4846.57i −1.05978 0.611863i −0.134407 0.990926i \(-0.542913\pi\)
−0.925371 + 0.379063i \(0.876246\pi\)
\(90\) 0 0
\(91\) 7496.17 + 12983.8i 0.905226 + 1.56790i
\(92\) 0 0
\(93\) 1332.42 + 8212.42i 0.154055 + 0.949523i
\(94\) 0 0
\(95\) −3168.32 + 558.661i −0.351061 + 0.0619015i
\(96\) 0 0
\(97\) 3647.23 + 3060.39i 0.387632 + 0.325262i 0.815690 0.578490i \(-0.196358\pi\)
−0.428058 + 0.903751i \(0.640802\pi\)
\(98\) 0 0
\(99\) 3592.00 + 10778.3i 0.366493 + 1.09971i
\(100\) 0 0
\(101\) −3495.98 9605.13i −0.342710 0.941587i −0.984605 0.174795i \(-0.944074\pi\)
0.641895 0.766792i \(-0.278148\pi\)
\(102\) 0 0
\(103\) 1825.20 1531.53i 0.172043 0.144361i −0.552701 0.833380i \(-0.686403\pi\)
0.724743 + 0.689019i \(0.241958\pi\)
\(104\) 0 0
\(105\) −85.2347 + 6225.90i −0.00773104 + 0.564707i
\(106\) 0 0
\(107\) 15855.4i 1.38487i 0.721479 + 0.692436i \(0.243462\pi\)
−0.721479 + 0.692436i \(0.756538\pi\)
\(108\) 0 0
\(109\) 18526.7 1.55935 0.779676 0.626183i \(-0.215384\pi\)
0.779676 + 0.626183i \(0.215384\pi\)
\(110\) 0 0
\(111\) −1422.37 + 2387.52i −0.115442 + 0.193777i
\(112\) 0 0
\(113\) −4943.81 5891.80i −0.387173 0.461415i 0.536892 0.843651i \(-0.319598\pi\)
−0.924064 + 0.382237i \(0.875154\pi\)
\(114\) 0 0
\(115\) −5220.43 + 1900.08i −0.394740 + 0.143673i
\(116\) 0 0
\(117\) −16051.9 6345.26i −1.17261 0.463530i
\(118\) 0 0
\(119\) −2384.22 + 2841.41i −0.168365 + 0.200650i
\(120\) 0 0
\(121\) −873.777 4955.44i −0.0596801 0.338463i
\(122\) 0 0
\(123\) −2761.95 3384.60i −0.182560 0.223716i
\(124\) 0 0
\(125\) 9821.44 5670.41i 0.628572 0.362906i
\(126\) 0 0
\(127\) −1907.85 + 3304.49i −0.118287 + 0.204879i −0.919089 0.394050i \(-0.871074\pi\)
0.800802 + 0.598929i \(0.204407\pi\)
\(128\) 0 0
\(129\) −4271.62 + 22425.9i −0.256692 + 1.34763i
\(130\) 0 0
\(131\) −4284.95 + 11772.8i −0.249691 + 0.686021i 0.750006 + 0.661430i \(0.230050\pi\)
−0.999698 + 0.0245903i \(0.992172\pi\)
\(132\) 0 0
\(133\) −3997.13 + 22668.8i −0.225967 + 1.28152i
\(134\) 0 0
\(135\) −4378.47 5675.93i −0.240245 0.311437i
\(136\) 0 0
\(137\) 9048.16 + 1595.44i 0.482080 + 0.0850038i 0.409407 0.912352i \(-0.365736\pi\)
0.0726736 + 0.997356i \(0.476847\pi\)
\(138\) 0 0
\(139\) 38.1456 + 13.8839i 0.00197431 + 0.000718590i 0.343007 0.939333i \(-0.388555\pi\)
−0.341033 + 0.940051i \(0.610777\pi\)
\(140\) 0 0
\(141\) 23921.1 27728.1i 1.20321 1.39470i
\(142\) 0 0
\(143\) 25884.2 + 14944.2i 1.26579 + 0.730805i
\(144\) 0 0
\(145\) 548.906 + 950.732i 0.0261073 + 0.0452191i
\(146\) 0 0
\(147\) 21447.6 + 8140.46i 0.992529 + 0.376716i
\(148\) 0 0
\(149\) −6325.77 + 1115.40i −0.284932 + 0.0502412i −0.314287 0.949328i \(-0.601766\pi\)
0.0293557 + 0.999569i \(0.490654\pi\)
\(150\) 0 0
\(151\) −33859.8 28411.8i −1.48501 1.24608i −0.900621 0.434605i \(-0.856888\pi\)
−0.584394 0.811470i \(-0.698668\pi\)
\(152\) 0 0
\(153\) 116.903 4268.76i 0.00499395 0.182355i
\(154\) 0 0
\(155\) 3109.01 + 8541.94i 0.129407 + 0.355544i
\(156\) 0 0
\(157\) 9697.94 8137.54i 0.393442 0.330137i −0.424511 0.905423i \(-0.639554\pi\)
0.817952 + 0.575286i \(0.195109\pi\)
\(158\) 0 0
\(159\) 33563.9 18770.3i 1.32763 0.742465i
\(160\) 0 0
\(161\) 39748.5i 1.53345i
\(162\) 0 0
\(163\) −34222.6 −1.28806 −0.644032 0.764999i \(-0.722740\pi\)
−0.644032 + 0.764999i \(0.722740\pi\)
\(164\) 0 0
\(165\) 6058.76 + 10833.9i 0.222544 + 0.397940i
\(166\) 0 0
\(167\) −26227.0 31256.2i −0.940407 1.12073i −0.992519 0.122093i \(-0.961039\pi\)
0.0521112 0.998641i \(-0.483405\pi\)
\(168\) 0 0
\(169\) −15831.7 + 5762.26i −0.554311 + 0.201753i
\(170\) 0 0
\(171\) −12617.3 23304.7i −0.431492 0.796987i
\(172\) 0 0
\(173\) 26785.1 31921.3i 0.894956 1.06657i −0.102461 0.994737i \(-0.532672\pi\)
0.997417 0.0718297i \(-0.0228838\pi\)
\(174\) 0 0
\(175\) −6454.40 36604.7i −0.210756 1.19526i
\(176\) 0 0
\(177\) 15771.9 41554.1i 0.503429 1.32638i
\(178\) 0 0
\(179\) −31745.4 + 18328.2i −0.990773 + 0.572023i −0.905505 0.424335i \(-0.860508\pi\)
−0.0852679 + 0.996358i \(0.527175\pi\)
\(180\) 0 0
\(181\) −1763.07 + 3053.72i −0.0538160 + 0.0932121i −0.891678 0.452669i \(-0.850472\pi\)
0.837862 + 0.545881i \(0.183805\pi\)
\(182\) 0 0
\(183\) −10681.8 9215.23i −0.318966 0.275172i
\(184\) 0 0
\(185\) −1038.52 + 2853.30i −0.0303438 + 0.0833689i
\(186\) 0 0
\(187\) −1284.05 + 7282.23i −0.0367198 + 0.208248i
\(188\) 0 0
\(189\) −48875.8 + 15548.4i −1.36827 + 0.435274i
\(190\) 0 0
\(191\) 43588.6 + 7685.85i 1.19483 + 0.210681i 0.735462 0.677565i \(-0.236965\pi\)
0.459368 + 0.888246i \(0.348076\pi\)
\(192\) 0 0
\(193\) −47996.6 17469.3i −1.28853 0.468988i −0.395288 0.918557i \(-0.629355\pi\)
−0.893245 + 0.449570i \(0.851577\pi\)
\(194\) 0 0
\(195\) −18525.6 3528.71i −0.487197 0.0927998i
\(196\) 0 0
\(197\) −17477.7 10090.8i −0.450353 0.260011i 0.257626 0.966245i \(-0.417060\pi\)
−0.707979 + 0.706233i \(0.750393\pi\)
\(198\) 0 0
\(199\) 14185.5 + 24570.0i 0.358211 + 0.620439i 0.987662 0.156601i \(-0.0500536\pi\)
−0.629451 + 0.777040i \(0.716720\pi\)
\(200\) 0 0
\(201\) 21166.8 17272.8i 0.523917 0.427535i
\(202\) 0 0
\(203\) 7735.33 1363.95i 0.187710 0.0330983i
\(204\) 0 0
\(205\) −3656.33 3068.02i −0.0870036 0.0730047i
\(206\) 0 0
\(207\) −28444.6 35847.9i −0.663833 0.836610i
\(208\) 0 0
\(209\) 15695.1 + 43121.9i 0.359311 + 0.987200i
\(210\) 0 0
\(211\) 2986.01 2505.56i 0.0670697 0.0562782i −0.608637 0.793449i \(-0.708283\pi\)
0.675706 + 0.737171i \(0.263839\pi\)
\(212\) 0 0
\(213\) −45053.9 26840.9i −0.993056 0.591612i
\(214\) 0 0
\(215\) 24942.8i 0.539596i
\(216\) 0 0
\(217\) 65038.5 1.38118
\(218\) 0 0
\(219\) 62951.9 + 861.834i 1.31257 + 0.0179695i
\(220\) 0 0
\(221\) −7221.32 8606.03i −0.147854 0.176205i
\(222\) 0 0
\(223\) −87864.5 + 31980.1i −1.76687 + 0.643087i −0.766867 + 0.641806i \(0.778186\pi\)
−0.999999 + 0.00128111i \(0.999592\pi\)
\(224\) 0 0
\(225\) 32015.9 + 28393.8i 0.632412 + 0.560864i
\(226\) 0 0
\(227\) 28076.5 33460.3i 0.544868 0.649349i −0.421404 0.906873i \(-0.638462\pi\)
0.966272 + 0.257525i \(0.0829069\pi\)
\(228\) 0 0
\(229\) −11334.4 64280.4i −0.216136 1.22577i −0.878925 0.476961i \(-0.841738\pi\)
0.662789 0.748806i \(-0.269373\pi\)
\(230\) 0 0
\(231\) 87666.6 14223.5i 1.64290 0.266552i
\(232\) 0 0
\(233\) −65540.1 + 37839.6i −1.20724 + 0.697003i −0.962156 0.272498i \(-0.912150\pi\)
−0.245088 + 0.969501i \(0.578817\pi\)
\(234\) 0 0
\(235\) 20005.6 34650.8i 0.362257 0.627448i
\(236\) 0 0
\(237\) 2651.70 924.231i 0.0472093 0.0164545i
\(238\) 0 0
\(239\) −10375.8 + 28507.3i −0.181646 + 0.499069i −0.996778 0.0802063i \(-0.974442\pi\)
0.815132 + 0.579275i \(0.196664\pi\)
\(240\) 0 0
\(241\) −15861.1 + 89953.0i −0.273087 + 1.54875i 0.471888 + 0.881659i \(0.343573\pi\)
−0.744975 + 0.667093i \(0.767538\pi\)
\(242\) 0 0
\(243\) 32952.9 48998.9i 0.558060 0.829801i
\(244\) 0 0
\(245\) 24683.8 + 4352.41i 0.411225 + 0.0725100i
\(246\) 0 0
\(247\) −65513.9 23845.1i −1.07384 0.390846i
\(248\) 0 0
\(249\) 35548.4 + 101991.i 0.573352 + 1.64500i
\(250\) 0 0
\(251\) 67801.8 + 39145.4i 1.07620 + 0.621346i 0.929869 0.367890i \(-0.119920\pi\)
0.146333 + 0.989235i \(0.453253\pi\)
\(252\) 0 0
\(253\) 39620.9 + 68625.4i 0.618990 + 1.07212i
\(254\) 0 0
\(255\) −747.224 4605.53i −0.0114913 0.0708271i
\(256\) 0 0
\(257\) 5822.68 1026.70i 0.0881570 0.0155445i −0.129396 0.991593i \(-0.541304\pi\)
0.217553 + 0.976049i \(0.430193\pi\)
\(258\) 0 0
\(259\) 16642.4 + 13964.6i 0.248094 + 0.208175i
\(260\) 0 0
\(261\) −6000.19 + 6765.62i −0.0880814 + 0.0993176i
\(262\) 0 0
\(263\) 42306.2 + 116235.i 0.611635 + 1.68045i 0.726581 + 0.687081i \(0.241108\pi\)
−0.114946 + 0.993372i \(0.536670\pi\)
\(264\) 0 0
\(265\) 32186.6 27007.8i 0.458335 0.384589i
\(266\) 0 0
\(267\) 1194.21 87230.0i 0.0167517 1.22361i
\(268\) 0 0
\(269\) 31192.9i 0.431073i 0.976496 + 0.215536i \(0.0691500\pi\)
−0.976496 + 0.215536i \(0.930850\pi\)
\(270\) 0 0
\(271\) 49482.4 0.673770 0.336885 0.941546i \(-0.390627\pi\)
0.336885 + 0.941546i \(0.390627\pi\)
\(272\) 0 0
\(273\) −69058.9 + 115919.i −0.926604 + 1.55536i
\(274\) 0 0
\(275\) −47630.7 56764.0i −0.629827 0.750599i
\(276\) 0 0
\(277\) −53816.5 + 19587.6i −0.701385 + 0.255283i −0.668002 0.744160i \(-0.732850\pi\)
−0.0333826 + 0.999443i \(0.510628\pi\)
\(278\) 0 0
\(279\) −58656.2 + 46542.5i −0.753539 + 0.597918i
\(280\) 0 0
\(281\) 68511.2 81648.5i 0.867659 1.03404i −0.131429 0.991326i \(-0.541956\pi\)
0.999088 0.0427098i \(-0.0135991\pi\)
\(282\) 0 0
\(283\) −8701.95 49351.2i −0.108654 0.616205i −0.989698 0.143171i \(-0.954270\pi\)
0.881044 0.473034i \(-0.156841\pi\)
\(284\) 0 0
\(285\) −18306.4 22433.4i −0.225379 0.276188i
\(286\) 0 0
\(287\) −29574.8 + 17075.0i −0.359052 + 0.207299i
\(288\) 0 0
\(289\) −40370.8 + 69924.2i −0.483361 + 0.837205i
\(290\) 0 0
\(291\) −8017.80 + 42093.3i −0.0946824 + 0.497080i
\(292\) 0 0
\(293\) 32359.9 88908.2i 0.376940 1.03563i −0.595677 0.803224i \(-0.703116\pi\)
0.972618 0.232411i \(-0.0746614\pi\)
\(294\) 0 0
\(295\) 8432.68 47824.1i 0.0968995 0.549544i
\(296\) 0 0
\(297\) −68885.2 + 75563.2i −0.780932 + 0.856638i
\(298\) 0 0
\(299\) −118561. 20905.5i −1.32617 0.233840i
\(300\) 0 0
\(301\) 167699. + 61037.6i 1.85097 + 0.673697i
\(302\) 0 0
\(303\) 60091.8 69655.5i 0.654531 0.758700i
\(304\) 0 0
\(305\) −13348.7 7706.88i −0.143496 0.0828474i
\(306\) 0 0
\(307\) −39692.4 68749.2i −0.421143 0.729442i 0.574908 0.818218i \(-0.305038\pi\)
−0.996052 + 0.0887760i \(0.971704\pi\)
\(308\) 0 0
\(309\) 20048.2 + 7609.33i 0.209970 + 0.0796947i
\(310\) 0 0
\(311\) 7118.06 1255.11i 0.0735937 0.0129766i −0.136730 0.990608i \(-0.543659\pi\)
0.210324 + 0.977632i \(0.432548\pi\)
\(312\) 0 0
\(313\) 63912.8 + 53629.2i 0.652378 + 0.547410i 0.907791 0.419422i \(-0.137767\pi\)
−0.255414 + 0.966832i \(0.582212\pi\)
\(314\) 0 0
\(315\) −49279.5 + 26680.1i −0.496644 + 0.268885i
\(316\) 0 0
\(317\) −34347.7 94369.5i −0.341805 0.939103i −0.984871 0.173291i \(-0.944560\pi\)
0.643065 0.765811i \(-0.277662\pi\)
\(318\) 0 0
\(319\) 11995.4 10065.4i 0.117878 0.0989117i
\(320\) 0 0
\(321\) −124546. + 69650.9i −1.20870 + 0.675953i
\(322\) 0 0
\(323\) 17248.7i 0.165330i
\(324\) 0 0
\(325\) 112578. 1.06583
\(326\) 0 0
\(327\) 81385.5 + 145529.i 0.761117 + 1.36099i
\(328\) 0 0
\(329\) −184014. 219299.i −1.70004 2.02602i
\(330\) 0 0
\(331\) 52213.1 19004.0i 0.476567 0.173456i −0.0925579 0.995707i \(-0.529504\pi\)
0.569125 + 0.822251i \(0.307282\pi\)
\(332\) 0 0
\(333\) −25002.5 684.714i −0.225473 0.00617477i
\(334\) 0 0
\(335\) 19187.0 22866.1i 0.170969 0.203752i
\(336\) 0 0
\(337\) 22332.3 + 126653.i 0.196641 + 1.11520i 0.910063 + 0.414470i \(0.136033\pi\)
−0.713422 + 0.700734i \(0.752856\pi\)
\(338\) 0 0
\(339\) 24563.1 64716.1i 0.213739 0.563136i
\(340\) 0 0
\(341\) 112289. 64829.8i 0.965665 0.557527i
\(342\) 0 0
\(343\) 5204.24 9014.01i 0.0442353 0.0766178i
\(344\) 0 0
\(345\) −37858.1 32660.2i −0.318068 0.274398i
\(346\) 0 0
\(347\) −73160.9 + 201008.i −0.607603 + 1.66938i 0.127844 + 0.991794i \(0.459194\pi\)
−0.735447 + 0.677582i \(0.763028\pi\)
\(348\) 0 0
\(349\) 35289.9 200139.i 0.289734 1.64316i −0.398135 0.917327i \(-0.630343\pi\)
0.687869 0.725835i \(-0.258546\pi\)
\(350\) 0 0
\(351\) −20671.5 153963.i −0.167787 1.24969i
\(352\) 0 0
\(353\) 72699.0 + 12818.8i 0.583417 + 0.102872i 0.457564 0.889177i \(-0.348722\pi\)
0.125853 + 0.992049i \(0.459833\pi\)
\(354\) 0 0
\(355\) −53843.4 19597.4i −0.427244 0.155504i
\(356\) 0 0
\(357\) −32793.1 6246.34i −0.257304 0.0490105i
\(358\) 0 0
\(359\) −40092.8 23147.6i −0.311084 0.179605i 0.336327 0.941745i \(-0.390815\pi\)
−0.647412 + 0.762141i \(0.724148\pi\)
\(360\) 0 0
\(361\) 11639.4 + 20160.0i 0.0893130 + 0.154695i
\(362\) 0 0
\(363\) 35087.0 28632.3i 0.266277 0.217291i
\(364\) 0 0
\(365\) 67742.1 11944.8i 0.508479 0.0896586i
\(366\) 0 0
\(367\) −71661.3 60131.0i −0.532050 0.446443i 0.336758 0.941591i \(-0.390669\pi\)
−0.868809 + 0.495148i \(0.835114\pi\)
\(368\) 0 0
\(369\) 14453.4 36563.6i 0.106150 0.268532i
\(370\) 0 0
\(371\) −102819. 282492.i −0.747007 2.05238i
\(372\) 0 0
\(373\) 62546.6 52482.8i 0.449558 0.377224i −0.389714 0.920936i \(-0.627426\pi\)
0.839272 + 0.543712i \(0.182982\pi\)
\(374\) 0 0
\(375\) 87686.1 + 52238.9i 0.623546 + 0.371477i
\(376\) 0 0
\(377\) 23790.2i 0.167384i
\(378\) 0 0
\(379\) −38147.7 −0.265577 −0.132788 0.991144i \(-0.542393\pi\)
−0.132788 + 0.991144i \(0.542393\pi\)
\(380\) 0 0
\(381\) −34338.0 470.100i −0.236551 0.00323847i
\(382\) 0 0
\(383\) 14867.8 + 17718.8i 0.101356 + 0.120792i 0.814338 0.580391i \(-0.197100\pi\)
−0.712982 + 0.701183i \(0.752656\pi\)
\(384\) 0 0
\(385\) 91184.3 33188.4i 0.615175 0.223905i
\(386\) 0 0
\(387\) −194922. + 64960.3i −1.30149 + 0.433736i
\(388\) 0 0
\(389\) −95185.9 + 113438.i −0.629033 + 0.749652i −0.982595 0.185759i \(-0.940526\pi\)
0.353563 + 0.935411i \(0.384970\pi\)
\(390\) 0 0
\(391\) −5172.14 29332.6i −0.0338311 0.191866i
\(392\) 0 0
\(393\) −111300. + 18057.8i −0.720625 + 0.116918i
\(394\) 0 0
\(395\) 2657.10 1534.08i 0.0170300 0.00983227i
\(396\) 0 0
\(397\) 39001.3 67552.2i 0.247456 0.428606i −0.715363 0.698753i \(-0.753739\pi\)
0.962819 + 0.270146i \(0.0870721\pi\)
\(398\) 0 0
\(399\) −195625. + 68183.7i −1.22879 + 0.428287i
\(400\) 0 0
\(401\) −28243.3 + 77597.8i −0.175641 + 0.482570i −0.996008 0.0892678i \(-0.971547\pi\)
0.820366 + 0.571838i \(0.193770\pi\)
\(402\) 0 0
\(403\) −34206.7 + 193996.i −0.210620 + 1.19449i
\(404\) 0 0
\(405\) 25350.9 59327.0i 0.154555 0.361695i
\(406\) 0 0
\(407\) 42652.7 + 7520.83i 0.257489 + 0.0454022i
\(408\) 0 0
\(409\) −61270.7 22300.7i −0.366274 0.133313i 0.152325 0.988330i \(-0.451324\pi\)
−0.518599 + 0.855018i \(0.673546\pi\)
\(410\) 0 0
\(411\) 27215.2 + 78082.8i 0.161112 + 0.462244i
\(412\) 0 0
\(413\) −300903. 173726.i −1.76411 1.01851i
\(414\) 0 0
\(415\) 59004.8 + 102199.i 0.342603 + 0.593406i
\(416\) 0 0
\(417\) 58.5101 + 360.628i 0.000336479 + 0.00207390i
\(418\) 0 0
\(419\) 269322. 47488.7i 1.53406 0.270497i 0.658121 0.752912i \(-0.271352\pi\)
0.875943 + 0.482415i \(0.160240\pi\)
\(420\) 0 0
\(421\) −18999.3 15942.3i −0.107195 0.0899471i 0.587615 0.809141i \(-0.300067\pi\)
−0.694810 + 0.719194i \(0.744511\pi\)
\(422\) 0 0
\(423\) 322890. + 66095.9i 1.80457 + 0.369397i
\(424\) 0 0
\(425\) 9526.13 + 26172.8i 0.0527398 + 0.144901i
\(426\) 0 0
\(427\) −84481.7 + 70888.5i −0.463347 + 0.388795i
\(428\) 0 0
\(429\) −3682.31 + 268971.i −0.0200081 + 1.46147i
\(430\) 0 0
\(431\) 124866.i 0.672186i −0.941829 0.336093i \(-0.890894\pi\)
0.941829 0.336093i \(-0.109106\pi\)
\(432\) 0 0
\(433\) 125519. 0.669475 0.334738 0.942311i \(-0.391352\pi\)
0.334738 + 0.942311i \(0.391352\pi\)
\(434\) 0 0
\(435\) −5056.82 + 8488.16i −0.0267238 + 0.0448575i
\(436\) 0 0
\(437\) −118813. 141596.i −0.622161 0.741463i
\(438\) 0 0
\(439\) 156512. 56965.8i 0.812118 0.295587i 0.0976196 0.995224i \(-0.468877\pi\)
0.714498 + 0.699637i \(0.246655\pi\)
\(440\) 0 0
\(441\) 30272.5 + 204233.i 0.155658 + 1.05014i
\(442\) 0 0
\(443\) −94109.7 + 112156.i −0.479542 + 0.571496i −0.950526 0.310646i \(-0.899455\pi\)
0.470983 + 0.882142i \(0.343899\pi\)
\(444\) 0 0
\(445\) −16551.4 93867.6i −0.0835824 0.474019i
\(446\) 0 0
\(447\) −36550.0 44789.7i −0.182925 0.224163i
\(448\) 0 0
\(449\) 146812. 84762.1i 0.728231 0.420445i −0.0895434 0.995983i \(-0.528541\pi\)
0.817775 + 0.575538i \(0.195207\pi\)
\(450\) 0 0
\(451\) −34040.4 + 58959.7i −0.167356 + 0.289869i
\(452\) 0 0
\(453\) 74435.0 390782.i 0.362728 1.90431i
\(454\) 0 0
\(455\) −50422.2 + 138534.i −0.243556 + 0.669164i
\(456\) 0 0
\(457\) −58409.4 + 331256.i −0.279673 + 1.58610i 0.444044 + 0.896005i \(0.353543\pi\)
−0.723717 + 0.690097i \(0.757568\pi\)
\(458\) 0 0
\(459\) 34045.1 17833.9i 0.161595 0.0846486i
\(460\) 0 0
\(461\) 97008.3 + 17105.2i 0.456465 + 0.0804870i 0.397153 0.917752i \(-0.369998\pi\)
0.0593118 + 0.998240i \(0.481109\pi\)
\(462\) 0 0
\(463\) 312412. + 113709.i 1.45736 + 0.530434i 0.944635 0.328122i \(-0.106416\pi\)
0.512720 + 0.858556i \(0.328638\pi\)
\(464\) 0 0
\(465\) −53440.3 + 61945.4i −0.247151 + 0.286486i
\(466\) 0 0
\(467\) 311347. + 179756.i 1.42761 + 0.824233i 0.996932 0.0782717i \(-0.0249402\pi\)
0.430681 + 0.902504i \(0.358273\pi\)
\(468\) 0 0
\(469\) −106785. 184956.i −0.485470 0.840859i
\(470\) 0 0
\(471\) 106523. + 40431.0i 0.480178 + 0.182252i
\(472\) 0 0
\(473\) 350373. 61780.3i 1.56606 0.276139i
\(474\) 0 0
\(475\) 132409. + 111104.i 0.586854 + 0.492429i
\(476\) 0 0
\(477\) 294885. + 181192.i 1.29603 + 0.796348i
\(478\) 0 0
\(479\) 100143. + 275140.i 0.436464 + 1.19917i 0.941777 + 0.336238i \(0.109155\pi\)
−0.505313 + 0.862936i \(0.668623\pi\)
\(480\) 0 0
\(481\) −50406.3 + 42295.9i −0.217869 + 0.182814i
\(482\) 0 0
\(483\) −312228. + 174610.i −1.33838 + 0.748472i
\(484\) 0 0
\(485\) 46817.6i 0.199033i
\(486\) 0 0
\(487\) −468342. −1.97472 −0.987359 0.158502i \(-0.949334\pi\)
−0.987359 + 0.158502i \(0.949334\pi\)
\(488\) 0 0
\(489\) −150336. 268822.i −0.628701 1.12421i
\(490\) 0 0
\(491\) 122177. + 145605.i 0.506788 + 0.603967i 0.957404 0.288751i \(-0.0932400\pi\)
−0.450616 + 0.892718i \(0.648796\pi\)
\(492\) 0 0
\(493\) −5530.86 + 2013.07i −0.0227561 + 0.00828256i
\(494\) 0 0
\(495\) −58486.1 + 95184.3i −0.238695 + 0.388468i
\(496\) 0 0
\(497\) −263520. + 314051.i −1.06685 + 1.27142i
\(498\) 0 0
\(499\) 71474.9 + 405354.i 0.287047 + 1.62792i 0.697882 + 0.716213i \(0.254126\pi\)
−0.410836 + 0.911709i \(0.634763\pi\)
\(500\) 0 0
\(501\) 130308. 343320.i 0.519153 1.36781i
\(502\) 0 0
\(503\) −254905. + 147169.i −1.00749 + 0.581676i −0.910457 0.413605i \(-0.864270\pi\)
−0.0970362 + 0.995281i \(0.530936\pi\)
\(504\) 0 0
\(505\) 50256.0 87045.9i 0.197063 0.341323i
\(506\) 0 0
\(507\) −114810. 99046.5i −0.446646 0.385321i
\(508\) 0 0
\(509\) −91361.9 + 251015.i −0.352638 + 0.968866i 0.628881 + 0.777502i \(0.283513\pi\)
−0.981519 + 0.191364i \(0.938709\pi\)
\(510\) 0 0
\(511\) 85462.9 484684.i 0.327292 1.85617i
\(512\) 0 0
\(513\) 127635. 201485.i 0.484991 0.765609i
\(514\) 0 0
\(515\) 23073.2 + 4068.44i 0.0869950 + 0.0153396i
\(516\) 0 0
\(517\) −536293. 195195.i −2.00642 0.730276i
\(518\) 0 0
\(519\) 368409. + 70173.4i 1.36771 + 0.260518i
\(520\) 0 0
\(521\) −32279.1 18636.3i −0.118918 0.0686571i 0.439361 0.898310i \(-0.355205\pi\)
−0.558279 + 0.829653i \(0.688538\pi\)
\(522\) 0 0
\(523\) −237983. 412199.i −0.870048 1.50697i −0.861946 0.507000i \(-0.830754\pi\)
−0.00810215 0.999967i \(-0.502579\pi\)
\(524\) 0 0
\(525\) 259180. 211500.i 0.940336 0.767347i
\(526\) 0 0
\(527\) −47995.6 + 8462.92i −0.172815 + 0.0304719i
\(528\) 0 0
\(529\) −30138.4 25289.1i −0.107698 0.0903695i
\(530\) 0 0
\(531\) 395695. 58652.1i 1.40337 0.208015i
\(532\) 0 0
\(533\) −35376.3 97195.6i −0.124525 0.342131i
\(534\) 0 0
\(535\) −119435. + 100218.i −0.417276 + 0.350136i
\(536\) 0 0
\(537\) −283423. 168849.i −0.982850 0.585532i
\(538\) 0 0
\(539\) 357515.i 1.23060i
\(540\) 0 0
\(541\) −312630. −1.06816 −0.534081 0.845434i \(-0.679342\pi\)
−0.534081 + 0.845434i \(0.679342\pi\)
\(542\) 0 0
\(543\) −31732.2 434.425i −0.107622 0.00147338i
\(544\) 0 0
\(545\) 117102. + 139557.i 0.394250 + 0.469849i
\(546\) 0 0
\(547\) 92448.8 33648.6i 0.308977 0.112459i −0.182878 0.983136i \(-0.558541\pi\)
0.491855 + 0.870677i \(0.336319\pi\)
\(548\) 0 0
\(549\) 25462.5 124388.i 0.0844804 0.412701i
\(550\) 0 0
\(551\) −23478.6 + 27980.7i −0.0773338 + 0.0921629i
\(552\) 0 0
\(553\) −3811.96 21618.7i −0.0124652 0.0706934i
\(554\) 0 0
\(555\) −26975.0 + 4376.56i −0.0875742 + 0.0142085i
\(556\) 0 0
\(557\) 13215.8 7630.14i 0.0425973 0.0245936i −0.478550 0.878060i \(-0.658837\pi\)
0.521147 + 0.853467i \(0.325504\pi\)
\(558\) 0 0
\(559\) −270262. + 468108.i −0.864892 + 1.49804i
\(560\) 0 0
\(561\) −62843.4 + 21903.6i −0.199680 + 0.0695970i
\(562\) 0 0
\(563\) −207977. + 571412.i −0.656143 + 1.80274i −0.0624470 + 0.998048i \(0.519890\pi\)
−0.593696 + 0.804690i \(0.702332\pi\)
\(564\) 0 0
\(565\) 13133.0 74481.1i 0.0411403 0.233318i
\(566\) 0 0
\(567\) −336840. 315622.i −1.04775 0.981751i
\(568\) 0 0
\(569\) −232026. 40912.4i −0.716658 0.126366i −0.196584 0.980487i \(-0.562985\pi\)
−0.520074 + 0.854121i \(0.674096\pi\)
\(570\) 0 0
\(571\) 462951. + 168501.i 1.41992 + 0.516808i 0.934024 0.357210i \(-0.116272\pi\)
0.485894 + 0.874018i \(0.338494\pi\)
\(572\) 0 0
\(573\) 131107. + 376156.i 0.399314 + 1.14567i
\(574\) 0 0
\(575\) 258486. + 149237.i 0.781809 + 0.451378i
\(576\) 0 0
\(577\) 92113.0 + 159544.i 0.276675 + 0.479214i 0.970556 0.240875i \(-0.0774343\pi\)
−0.693882 + 0.720089i \(0.744101\pi\)
\(578\) 0 0
\(579\) −73620.0 453759.i −0.219603 1.35353i
\(580\) 0 0
\(581\) 831513. 146618.i 2.46330 0.434346i
\(582\) 0 0
\(583\) −459102. 385232.i −1.35074 1.13341i
\(584\) 0 0
\(585\) −53662.6 161022.i −0.156805 0.470515i
\(586\) 0 0
\(587\) −172208. 473138.i −0.499779 1.37313i −0.891489 0.453042i \(-0.850339\pi\)
0.391710 0.920089i \(-0.371884\pi\)
\(588\) 0 0
\(589\) −231687. + 194409.i −0.667839 + 0.560384i
\(590\) 0 0
\(591\) 2486.40 181617.i 0.00711862 0.519974i
\(592\) 0 0
\(593\) 427298.i 1.21513i −0.794271 0.607563i \(-0.792147\pi\)
0.794271 0.607563i \(-0.207853\pi\)
\(594\) 0 0
\(595\) −36473.7 −0.103026
\(596\) 0 0
\(597\) −130685. + 219362.i −0.366670 + 0.615478i
\(598\) 0 0
\(599\) −142612. 169958.i −0.397467 0.473683i 0.529779 0.848136i \(-0.322275\pi\)
−0.927246 + 0.374453i \(0.877831\pi\)
\(600\) 0 0
\(601\) 196054. 71357.7i 0.542783 0.197557i −0.0560543 0.998428i \(-0.517852\pi\)
0.598837 + 0.800871i \(0.295630\pi\)
\(602\) 0 0
\(603\) 228663. + 90389.6i 0.628870 + 0.248590i
\(604\) 0 0
\(605\) 31805.2 37904.0i 0.0868935 0.103556i
\(606\) 0 0
\(607\) 37410.2 + 212164.i 0.101534 + 0.575830i 0.992548 + 0.121853i \(0.0388838\pi\)
−0.891014 + 0.453976i \(0.850005\pi\)
\(608\) 0 0
\(609\) 44694.4 + 54770.1i 0.120509 + 0.147676i
\(610\) 0 0
\(611\) 750901. 433533.i 2.01141 1.16129i
\(612\) 0 0
\(613\) 275443. 477081.i 0.733011 1.26961i −0.222579 0.974915i \(-0.571447\pi\)
0.955590 0.294698i \(-0.0952192\pi\)
\(614\) 0 0
\(615\) 8037.81 42198.3i 0.0212514 0.111569i
\(616\) 0 0
\(617\) −236748. + 650459.i −0.621892 + 1.70863i 0.0804154 + 0.996761i \(0.474375\pi\)
−0.702308 + 0.711874i \(0.747847\pi\)
\(618\) 0 0
\(619\) 116854. 662713.i 0.304974 1.72959i −0.318652 0.947872i \(-0.603230\pi\)
0.623626 0.781723i \(-0.285659\pi\)
\(620\) 0 0
\(621\) 156635. 380911.i 0.406168 0.987734i
\(622\) 0 0
\(623\) −671608. 118423.i −1.73037 0.305111i
\(624\) 0 0
\(625\) −205486. 74790.6i −0.526043 0.191464i
\(626\) 0 0
\(627\) −269780. + 312716.i −0.686238 + 0.795453i
\(628\) 0 0
\(629\) −14098.5 8139.74i −0.0356345 0.0205736i
\(630\) 0 0
\(631\) −196798. 340864.i −0.494268 0.856097i 0.505710 0.862703i \(-0.331230\pi\)
−0.999978 + 0.00660642i \(0.997897\pi\)
\(632\) 0 0
\(633\) 32798.6 + 12448.8i 0.0818556 + 0.0310684i
\(634\) 0 0
\(635\) −36950.9 + 6515.45i −0.0916385 + 0.0161583i
\(636\) 0 0
\(637\) 416086. + 349138.i 1.02543 + 0.860435i
\(638\) 0 0
\(639\) 12921.0 471812.i 0.0316441 1.15549i
\(640\) 0 0
\(641\) 240188. + 659912.i 0.584569 + 1.60609i 0.780282 + 0.625428i \(0.215076\pi\)
−0.195713 + 0.980661i \(0.562702\pi\)
\(642\) 0 0
\(643\) −208490. + 174944.i −0.504270 + 0.423133i −0.859107 0.511795i \(-0.828981\pi\)
0.354837 + 0.934928i \(0.384536\pi\)
\(644\) 0 0
\(645\) −195928. + 109571.i −0.470954 + 0.263376i
\(646\) 0 0
\(647\) 337710.i 0.806743i 0.915036 + 0.403372i \(0.132162\pi\)
−0.915036 + 0.403372i \(0.867838\pi\)
\(648\) 0 0
\(649\) −692675. −1.64452
\(650\) 0 0
\(651\) 285707. + 510884.i 0.674153 + 1.20548i
\(652\) 0 0
\(653\) −88035.2 104916.i −0.206457 0.246046i 0.652873 0.757468i \(-0.273564\pi\)
−0.859330 + 0.511421i \(0.829119\pi\)
\(654\) 0 0
\(655\) −115766. + 42135.3i −0.269834 + 0.0982117i
\(656\) 0 0
\(657\) 269771. + 498280.i 0.624977 + 1.15436i
\(658\) 0 0
\(659\) 82186.9 97946.5i 0.189248 0.225537i −0.663075 0.748553i \(-0.730749\pi\)
0.852323 + 0.523016i \(0.175193\pi\)
\(660\) 0 0
\(661\) 59270.9 + 336142.i 0.135656 + 0.769343i 0.974401 + 0.224818i \(0.0721788\pi\)
−0.838745 + 0.544525i \(0.816710\pi\)
\(662\) 0 0
\(663\) 35878.8 94529.4i 0.0816227 0.215050i
\(664\) 0 0
\(665\) −196024. + 113174.i −0.443267 + 0.255920i
\(666\) 0 0
\(667\) −31536.8 + 54623.4i −0.0708870 + 0.122780i
\(668\) 0 0
\(669\) −637185. 549700.i −1.42368 1.22821i
\(670\) 0 0
\(671\) −75195.9 + 206599.i −0.167013 + 0.458863i
\(672\) 0 0
\(673\) 34575.4 196087.i 0.0763375 0.432931i −0.922554 0.385867i \(-0.873902\pi\)
0.998892 0.0470642i \(-0.0149865\pi\)
\(674\) 0 0
\(675\) −82393.8 + 376218.i −0.180837 + 0.825719i
\(676\) 0 0
\(677\) −261985. 46195.1i −0.571609 0.100790i −0.119630 0.992819i \(-0.538171\pi\)
−0.451979 + 0.892028i \(0.649282\pi\)
\(678\) 0 0
\(679\) 314771. + 114567.i 0.682740 + 0.248497i
\(680\) 0 0
\(681\) 386171. + 73556.7i 0.832693 + 0.158609i
\(682\) 0 0
\(683\) −228548. 131952.i −0.489933 0.282863i 0.234614 0.972089i \(-0.424617\pi\)
−0.724547 + 0.689226i \(0.757951\pi\)
\(684\) 0 0
\(685\) 45173.0 + 78242.0i 0.0962716 + 0.166747i
\(686\) 0 0
\(687\) 455139. 371409.i 0.964340 0.786935i
\(688\) 0 0
\(689\) 896689. 158110.i 1.88888 0.333060i
\(690\) 0 0
\(691\) 508520. + 426699.i 1.06501 + 0.893646i 0.994591 0.103872i \(-0.0331233\pi\)
0.0704147 + 0.997518i \(0.477568\pi\)
\(692\) 0 0
\(693\) 496836. + 626148.i 1.03454 + 1.30380i
\(694\) 0 0
\(695\) 136.525 + 375.098i 0.000282645 + 0.000776560i
\(696\) 0 0
\(697\) 19603.1 16448.9i 0.0403514 0.0338588i
\(698\) 0 0
\(699\) −585144. 348599.i −1.19759 0.713464i
\(700\) 0 0
\(701\) 214146.i 0.435788i 0.975972 + 0.217894i \(0.0699186\pi\)
−0.975972 + 0.217894i \(0.930081\pi\)
\(702\) 0 0
\(703\) −101027. −0.204422
\(704\) 0 0
\(705\) 360068. + 4929.45i 0.724446 + 0.00991792i
\(706\) 0 0
\(707\) −462259. 550898.i −0.924797 1.10213i
\(708\) 0 0
\(709\) −283230. + 103087.i −0.563438 + 0.205075i −0.608007 0.793932i \(-0.708031\pi\)
0.0445691 + 0.999006i \(0.485809\pi\)
\(710\) 0 0
\(711\) 18908.5 + 16769.3i 0.0374040 + 0.0331723i
\(712\) 0 0
\(713\) −335706. + 400079.i −0.660358 + 0.786984i
\(714\) 0 0
\(715\) 51035.7 + 289438.i 0.0998302 + 0.566165i
\(716\) 0 0
\(717\) −269508. + 43726.2i −0.524243 + 0.0850558i
\(718\) 0 0
\(719\) 249436. 144012.i 0.482505 0.278574i −0.238955 0.971031i \(-0.576805\pi\)
0.721460 + 0.692456i \(0.243472\pi\)
\(720\) 0 0
\(721\) 83816.0 145174.i 0.161234 0.279265i
\(722\) 0 0
\(723\) −776266. + 270562.i −1.48503 + 0.517596i
\(724\) 0 0
\(725\) 20172.7 55424.1i 0.0383786 0.105444i
\(726\) 0 0
\(727\) −64865.9 + 367873.i −0.122729 + 0.696032i 0.859901 + 0.510460i \(0.170525\pi\)
−0.982631 + 0.185572i \(0.940586\pi\)
\(728\) 0 0
\(729\) 529649. + 43601.9i 0.996629 + 0.0820446i
\(730\) 0 0
\(731\) −131697. 23221.8i −0.246457 0.0434571i
\(732\) 0 0
\(733\) 88629.6 + 32258.5i 0.164957 + 0.0600394i 0.423179 0.906046i \(-0.360914\pi\)
−0.258222 + 0.966086i \(0.583136\pi\)
\(734\) 0 0
\(735\) 74244.2 + 213013.i 0.137432 + 0.394304i
\(736\) 0 0
\(737\) −368725. 212884.i −0.678841 0.391929i
\(738\) 0 0
\(739\) 419686. + 726918.i 0.768486 + 1.33106i 0.938384 + 0.345595i \(0.112323\pi\)
−0.169898 + 0.985462i \(0.554344\pi\)
\(740\) 0 0
\(741\) −100489. 619367.i −0.183013 1.12801i
\(742\) 0 0
\(743\) 565336. 99684.0i 1.02407 0.180571i 0.363703 0.931515i \(-0.381512\pi\)
0.660366 + 0.750944i \(0.270401\pi\)
\(744\) 0 0
\(745\) −48385.6 40600.3i −0.0871773 0.0731505i
\(746\) 0 0
\(747\) −644993. + 727273.i −1.15588 + 1.30334i
\(748\) 0 0
\(749\) 381530. + 1.04825e6i 0.680088 + 1.86853i
\(750\) 0 0
\(751\) 719252. 603524.i 1.27527 1.07008i 0.281388 0.959594i \(-0.409205\pi\)
0.993878 0.110482i \(-0.0352394\pi\)
\(752\) 0 0
\(753\) −9645.55 + 704551.i −0.0170113 + 1.24257i
\(754\) 0 0
\(755\) 434641.i 0.762495i
\(756\) 0 0
\(757\) 980425. 1.71089 0.855446 0.517891i \(-0.173283\pi\)
0.855446 + 0.517891i \(0.173283\pi\)
\(758\) 0 0
\(759\) −365010. + 612690.i −0.633608 + 1.06355i
\(760\) 0 0
\(761\) −326111. 388644.i −0.563113 0.671092i 0.407089 0.913388i \(-0.366544\pi\)
−0.970202 + 0.242296i \(0.922099\pi\)
\(762\) 0 0
\(763\) 1.22485e6 445809.i 2.10394 0.765773i
\(764\) 0 0
\(765\) 32894.4 26101.1i 0.0562082 0.0446001i
\(766\) 0 0
\(767\) 676445. 806156.i 1.14985 1.37034i
\(768\) 0 0
\(769\) −63373.5 359409.i −0.107166 0.607766i −0.990333 0.138709i \(-0.955705\pi\)
0.883168 0.469057i \(-0.155406\pi\)
\(770\) 0 0
\(771\) 33643.2 + 41227.6i 0.0565963 + 0.0693553i
\(772\) 0 0
\(773\) −629772. + 363599.i −1.05396 + 0.608504i −0.923755 0.382983i \(-0.874897\pi\)
−0.130205 + 0.991487i \(0.541563\pi\)
\(774\) 0 0
\(775\) 244189. 422948.i 0.406558 0.704180i
\(776\) 0 0
\(777\) −36585.4 + 192072.i −0.0605991 + 0.318144i
\(778\) 0 0
\(779\) 54315.1 149229.i 0.0895046 0.245912i
\(780\) 0 0
\