Properties

Label 108.4.b.b.107.3
Level 108
Weight 4
Character 108.107
Analytic conductor 6.372
Analytic rank 0
Dimension 12
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 108.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.37220628062\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \(x^{12} + 3 x^{10} - 12 x^{9} + 73 x^{8} - 12 x^{7} + 589 x^{6} + 84 x^{5} + 2452 x^{4} + 852 x^{3} + 6854 x^{2} - 888 x + 9496\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{14}\cdot 3^{12} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 107.3
Root \(-1.29835 - 1.36719i\) of defining polynomial
Character \(\chi\) \(=\) 108.107
Dual form 108.4.b.b.107.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.27435 - 1.68146i) q^{2} +(2.34537 + 7.64848i) q^{4} -5.83890i q^{5} +8.83113i q^{7} +(7.52641 - 21.3390i) q^{8} +O(q^{10})\) \(q+(-2.27435 - 1.68146i) q^{2} +(2.34537 + 7.64848i) q^{4} -5.83890i q^{5} +8.83113i q^{7} +(7.52641 - 21.3390i) q^{8} +(-9.81789 + 13.2797i) q^{10} +23.6146 q^{11} +54.6531 q^{13} +(14.8492 - 20.0851i) q^{14} +(-52.9984 + 35.8771i) q^{16} -117.211i q^{17} -109.576i q^{19} +(44.6587 - 13.6944i) q^{20} +(-53.7080 - 39.7070i) q^{22} -33.5763 q^{23} +90.9072 q^{25} +(-124.300 - 91.8970i) q^{26} +(-67.5447 + 20.7123i) q^{28} +40.0490i q^{29} -292.510i q^{31} +(180.863 + 7.51762i) q^{32} +(-197.086 + 266.580i) q^{34} +51.5641 q^{35} +283.265 q^{37} +(-184.248 + 249.215i) q^{38} +(-124.596 - 43.9460i) q^{40} +367.472i q^{41} +323.337i q^{43} +(55.3851 + 180.616i) q^{44} +(76.3644 + 56.4572i) q^{46} +66.2249 q^{47} +265.011 q^{49} +(-206.755 - 152.857i) q^{50} +(128.182 + 418.013i) q^{52} +158.506i q^{53} -137.883i q^{55} +(188.447 + 66.4667i) q^{56} +(67.3408 - 91.0856i) q^{58} -848.630 q^{59} -348.716 q^{61} +(-491.844 + 665.270i) q^{62} +(-398.706 - 321.212i) q^{64} -319.114i q^{65} -194.285i q^{67} +(896.489 - 274.905i) q^{68} +(-117.275 - 86.7031i) q^{70} +939.761 q^{71} -473.826 q^{73} +(-644.246 - 476.300i) q^{74} +(838.091 - 256.997i) q^{76} +208.544i q^{77} +273.221i q^{79} +(209.483 + 309.453i) q^{80} +(617.890 - 835.761i) q^{82} +338.366 q^{83} -684.386 q^{85} +(543.679 - 735.383i) q^{86} +(177.733 - 503.912i) q^{88} -739.884i q^{89} +482.648i q^{91} +(-78.7490 - 256.807i) q^{92} +(-150.619 - 111.355i) q^{94} -639.805 q^{95} -448.629 q^{97} +(-602.729 - 445.606i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 6q^{4} + O(q^{10}) \) \( 12q + 6q^{4} + 42q^{10} - 72q^{13} + 114q^{16} + 66q^{22} - 384q^{25} - 282q^{28} - 324q^{34} - 240q^{37} + 774q^{40} + 1752q^{46} + 288q^{49} + 924q^{52} - 948q^{58} + 144q^{61} - 3066q^{64} - 3558q^{70} + 156q^{73} + 576q^{76} + 5832q^{82} - 168q^{85} + 5022q^{88} - 3444q^{94} + 516q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.27435 1.68146i −0.804106 0.594486i
\(3\) 0 0
\(4\) 2.34537 + 7.64848i 0.293172 + 0.956060i
\(5\) 5.83890i 0.522247i −0.965305 0.261124i \(-0.915907\pi\)
0.965305 0.261124i \(-0.0840930\pi\)
\(6\) 0 0
\(7\) 8.83113i 0.476836i 0.971163 + 0.238418i \(0.0766288\pi\)
−0.971163 + 0.238418i \(0.923371\pi\)
\(8\) 7.52641 21.3390i 0.332623 0.943060i
\(9\) 0 0
\(10\) −9.81789 + 13.2797i −0.310469 + 0.419942i
\(11\) 23.6146 0.647279 0.323639 0.946180i \(-0.395094\pi\)
0.323639 + 0.946180i \(0.395094\pi\)
\(12\) 0 0
\(13\) 54.6531 1.16600 0.583001 0.812471i \(-0.301878\pi\)
0.583001 + 0.812471i \(0.301878\pi\)
\(14\) 14.8492 20.0851i 0.283473 0.383427i
\(15\) 0 0
\(16\) −52.9984 + 35.8771i −0.828101 + 0.560580i
\(17\) 117.211i 1.67223i −0.548553 0.836116i \(-0.684821\pi\)
0.548553 0.836116i \(-0.315179\pi\)
\(18\) 0 0
\(19\) 109.576i 1.32308i −0.749910 0.661539i \(-0.769903\pi\)
0.749910 0.661539i \(-0.230097\pi\)
\(20\) 44.6587 13.6944i 0.499300 0.153108i
\(21\) 0 0
\(22\) −53.7080 39.7070i −0.520481 0.384799i
\(23\) −33.5763 −0.304397 −0.152199 0.988350i \(-0.548635\pi\)
−0.152199 + 0.988350i \(0.548635\pi\)
\(24\) 0 0
\(25\) 90.9072 0.727258
\(26\) −124.300 91.8970i −0.937589 0.693173i
\(27\) 0 0
\(28\) −67.5447 + 20.7123i −0.455884 + 0.139795i
\(29\) 40.0490i 0.256445i 0.991745 + 0.128223i \(0.0409272\pi\)
−0.991745 + 0.128223i \(0.959073\pi\)
\(30\) 0 0
\(31\) 292.510i 1.69472i −0.531020 0.847359i \(-0.678191\pi\)
0.531020 0.847359i \(-0.321809\pi\)
\(32\) 180.863 + 7.51762i 0.999137 + 0.0415294i
\(33\) 0 0
\(34\) −197.086 + 266.580i −0.994119 + 1.34465i
\(35\) 51.5641 0.249026
\(36\) 0 0
\(37\) 283.265 1.25861 0.629304 0.777159i \(-0.283340\pi\)
0.629304 + 0.777159i \(0.283340\pi\)
\(38\) −184.248 + 249.215i −0.786552 + 1.06390i
\(39\) 0 0
\(40\) −124.596 43.9460i −0.492510 0.173712i
\(41\) 367.472i 1.39974i 0.714269 + 0.699871i \(0.246759\pi\)
−0.714269 + 0.699871i \(0.753241\pi\)
\(42\) 0 0
\(43\) 323.337i 1.14671i 0.819308 + 0.573354i \(0.194358\pi\)
−0.819308 + 0.573354i \(0.805642\pi\)
\(44\) 55.3851 + 180.616i 0.189764 + 0.618837i
\(45\) 0 0
\(46\) 76.3644 + 56.4572i 0.244768 + 0.180960i
\(47\) 66.2249 0.205530 0.102765 0.994706i \(-0.467231\pi\)
0.102765 + 0.994706i \(0.467231\pi\)
\(48\) 0 0
\(49\) 265.011 0.772627
\(50\) −206.755 152.857i −0.584792 0.432345i
\(51\) 0 0
\(52\) 128.182 + 418.013i 0.341839 + 1.11477i
\(53\) 158.506i 0.410801i 0.978678 + 0.205401i \(0.0658498\pi\)
−0.978678 + 0.205401i \(0.934150\pi\)
\(54\) 0 0
\(55\) 137.883i 0.338040i
\(56\) 188.447 + 66.4667i 0.449685 + 0.158607i
\(57\) 0 0
\(58\) 67.3408 91.0856i 0.152453 0.206209i
\(59\) −848.630 −1.87258 −0.936290 0.351228i \(-0.885764\pi\)
−0.936290 + 0.351228i \(0.885764\pi\)
\(60\) 0 0
\(61\) −348.716 −0.731943 −0.365972 0.930626i \(-0.619263\pi\)
−0.365972 + 0.930626i \(0.619263\pi\)
\(62\) −491.844 + 665.270i −1.00749 + 1.36273i
\(63\) 0 0
\(64\) −398.706 321.212i −0.778723 0.627368i
\(65\) 319.114i 0.608942i
\(66\) 0 0
\(67\) 194.285i 0.354264i −0.984187 0.177132i \(-0.943318\pi\)
0.984187 0.177132i \(-0.0566819\pi\)
\(68\) 896.489 274.905i 1.59875 0.490251i
\(69\) 0 0
\(70\) −117.275 86.7031i −0.200244 0.148043i
\(71\) 939.761 1.57083 0.785417 0.618968i \(-0.212449\pi\)
0.785417 + 0.618968i \(0.212449\pi\)
\(72\) 0 0
\(73\) −473.826 −0.759686 −0.379843 0.925051i \(-0.624022\pi\)
−0.379843 + 0.925051i \(0.624022\pi\)
\(74\) −644.246 476.300i −1.01205 0.748226i
\(75\) 0 0
\(76\) 838.091 256.997i 1.26494 0.387889i
\(77\) 208.544i 0.308646i
\(78\) 0 0
\(79\) 273.221i 0.389112i 0.980891 + 0.194556i \(0.0623265\pi\)
−0.980891 + 0.194556i \(0.937673\pi\)
\(80\) 209.483 + 309.453i 0.292761 + 0.432473i
\(81\) 0 0
\(82\) 617.890 835.761i 0.832128 1.12554i
\(83\) 338.366 0.447476 0.223738 0.974649i \(-0.428174\pi\)
0.223738 + 0.974649i \(0.428174\pi\)
\(84\) 0 0
\(85\) −684.386 −0.873318
\(86\) 543.679 735.383i 0.681702 0.922074i
\(87\) 0 0
\(88\) 177.733 503.912i 0.215300 0.610423i
\(89\) 739.884i 0.881208i −0.897702 0.440604i \(-0.854764\pi\)
0.897702 0.440604i \(-0.145236\pi\)
\(90\) 0 0
\(91\) 482.648i 0.555992i
\(92\) −78.7490 256.807i −0.0892407 0.291022i
\(93\) 0 0
\(94\) −150.619 111.355i −0.165268 0.122185i
\(95\) −639.805 −0.690974
\(96\) 0 0
\(97\) −448.629 −0.469602 −0.234801 0.972044i \(-0.575444\pi\)
−0.234801 + 0.972044i \(0.575444\pi\)
\(98\) −602.729 445.606i −0.621274 0.459316i
\(99\) 0 0
\(100\) 213.211 + 695.302i 0.213211 + 0.695302i
\(101\) 1152.87i 1.13580i −0.823099 0.567898i \(-0.807757\pi\)
0.823099 0.567898i \(-0.192243\pi\)
\(102\) 0 0
\(103\) 1389.90i 1.32962i 0.747013 + 0.664809i \(0.231487\pi\)
−0.747013 + 0.664809i \(0.768513\pi\)
\(104\) 411.341 1166.24i 0.387840 1.09961i
\(105\) 0 0
\(106\) 266.522 360.499i 0.244216 0.330328i
\(107\) 245.479 0.221788 0.110894 0.993832i \(-0.464629\pi\)
0.110894 + 0.993832i \(0.464629\pi\)
\(108\) 0 0
\(109\) −644.998 −0.566785 −0.283393 0.959004i \(-0.591460\pi\)
−0.283393 + 0.959004i \(0.591460\pi\)
\(110\) −231.846 + 313.596i −0.200960 + 0.271820i
\(111\) 0 0
\(112\) −316.835 468.036i −0.267305 0.394868i
\(113\) 825.442i 0.687177i 0.939120 + 0.343589i \(0.111643\pi\)
−0.939120 + 0.343589i \(0.888357\pi\)
\(114\) 0 0
\(115\) 196.049i 0.158971i
\(116\) −306.314 + 93.9299i −0.245177 + 0.0751825i
\(117\) 0 0
\(118\) 1930.09 + 1426.94i 1.50575 + 1.11322i
\(119\) 1035.11 0.797380
\(120\) 0 0
\(121\) −773.351 −0.581030
\(122\) 793.104 + 586.353i 0.588560 + 0.435130i
\(123\) 0 0
\(124\) 2237.25 686.044i 1.62025 0.496844i
\(125\) 1260.66i 0.902056i
\(126\) 0 0
\(127\) 754.649i 0.527278i 0.964621 + 0.263639i \(0.0849228\pi\)
−0.964621 + 0.263639i \(0.915077\pi\)
\(128\) 366.694 + 1400.96i 0.253214 + 0.967410i
\(129\) 0 0
\(130\) −536.578 + 725.778i −0.362008 + 0.489654i
\(131\) −2026.43 −1.35153 −0.675765 0.737117i \(-0.736186\pi\)
−0.675765 + 0.737117i \(0.736186\pi\)
\(132\) 0 0
\(133\) 967.681 0.630892
\(134\) −326.682 + 441.873i −0.210605 + 0.284865i
\(135\) 0 0
\(136\) −2501.17 882.181i −1.57701 0.556223i
\(137\) 1882.88i 1.17420i 0.809515 + 0.587099i \(0.199730\pi\)
−0.809515 + 0.587099i \(0.800270\pi\)
\(138\) 0 0
\(139\) 93.7277i 0.0571934i 0.999591 + 0.0285967i \(0.00910385\pi\)
−0.999591 + 0.0285967i \(0.990896\pi\)
\(140\) 120.937 + 394.387i 0.0730075 + 0.238084i
\(141\) 0 0
\(142\) −2137.35 1580.17i −1.26312 0.933839i
\(143\) 1290.61 0.754729
\(144\) 0 0
\(145\) 233.842 0.133928
\(146\) 1077.65 + 796.719i 0.610868 + 0.451623i
\(147\) 0 0
\(148\) 664.363 + 2166.55i 0.368989 + 1.20331i
\(149\) 2764.69i 1.52008i 0.649874 + 0.760042i \(0.274822\pi\)
−0.649874 + 0.760042i \(0.725178\pi\)
\(150\) 0 0
\(151\) 3694.11i 1.99088i −0.0954051 0.995439i \(-0.530415\pi\)
0.0954051 0.995439i \(-0.469585\pi\)
\(152\) −2338.25 824.715i −1.24774 0.440087i
\(153\) 0 0
\(154\) 350.658 474.302i 0.183486 0.248184i
\(155\) −1707.94 −0.885062
\(156\) 0 0
\(157\) 812.401 0.412972 0.206486 0.978450i \(-0.433797\pi\)
0.206486 + 0.978450i \(0.433797\pi\)
\(158\) 459.411 621.402i 0.231322 0.312887i
\(159\) 0 0
\(160\) 43.8947 1056.04i 0.0216886 0.521797i
\(161\) 296.516i 0.145148i
\(162\) 0 0
\(163\) 1034.18i 0.496953i −0.968638 0.248477i \(-0.920070\pi\)
0.968638 0.248477i \(-0.0799299\pi\)
\(164\) −2810.60 + 861.859i −1.33824 + 0.410365i
\(165\) 0 0
\(166\) −769.564 568.949i −0.359818 0.266018i
\(167\) 1453.29 0.673409 0.336704 0.941610i \(-0.390688\pi\)
0.336704 + 0.941610i \(0.390688\pi\)
\(168\) 0 0
\(169\) 789.957 0.359562
\(170\) 1556.54 + 1150.77i 0.702240 + 0.519176i
\(171\) 0 0
\(172\) −2473.04 + 758.346i −1.09632 + 0.336182i
\(173\) 634.902i 0.279022i 0.990221 + 0.139511i \(0.0445530\pi\)
−0.990221 + 0.139511i \(0.955447\pi\)
\(174\) 0 0
\(175\) 802.813i 0.346783i
\(176\) −1251.54 + 847.223i −0.536012 + 0.362851i
\(177\) 0 0
\(178\) −1244.09 + 1682.76i −0.523866 + 0.708584i
\(179\) −2909.35 −1.21483 −0.607417 0.794383i \(-0.707794\pi\)
−0.607417 + 0.794383i \(0.707794\pi\)
\(180\) 0 0
\(181\) 1354.46 0.556222 0.278111 0.960549i \(-0.410292\pi\)
0.278111 + 0.960549i \(0.410292\pi\)
\(182\) 811.554 1097.71i 0.330530 0.447076i
\(183\) 0 0
\(184\) −252.709 + 716.484i −0.101250 + 0.287065i
\(185\) 1653.96i 0.657305i
\(186\) 0 0
\(187\) 2767.90i 1.08240i
\(188\) 155.322 + 506.520i 0.0602555 + 0.196499i
\(189\) 0 0
\(190\) 1455.14 + 1075.81i 0.555616 + 0.410775i
\(191\) 3488.40 1.32153 0.660765 0.750593i \(-0.270232\pi\)
0.660765 + 0.750593i \(0.270232\pi\)
\(192\) 0 0
\(193\) 2912.99 1.08643 0.543217 0.839592i \(-0.317206\pi\)
0.543217 + 0.839592i \(0.317206\pi\)
\(194\) 1020.34 + 754.352i 0.377609 + 0.279172i
\(195\) 0 0
\(196\) 621.550 + 2026.93i 0.226513 + 0.738678i
\(197\) 2432.66i 0.879795i 0.898048 + 0.439897i \(0.144985\pi\)
−0.898048 + 0.439897i \(0.855015\pi\)
\(198\) 0 0
\(199\) 563.190i 0.200621i 0.994956 + 0.100310i \(0.0319836\pi\)
−0.994956 + 0.100310i \(0.968016\pi\)
\(200\) 684.205 1939.87i 0.241903 0.685847i
\(201\) 0 0
\(202\) −1938.51 + 2622.05i −0.675215 + 0.913299i
\(203\) −353.678 −0.122282
\(204\) 0 0
\(205\) 2145.63 0.731012
\(206\) 2337.06 3161.12i 0.790440 1.06915i
\(207\) 0 0
\(208\) −2896.53 + 1960.79i −0.965567 + 0.653637i
\(209\) 2587.60i 0.856401i
\(210\) 0 0
\(211\) 1447.62i 0.472314i −0.971715 0.236157i \(-0.924112\pi\)
0.971715 0.236157i \(-0.0758879\pi\)
\(212\) −1212.33 + 371.756i −0.392751 + 0.120435i
\(213\) 0 0
\(214\) −558.306 412.763i −0.178341 0.131850i
\(215\) 1887.93 0.598865
\(216\) 0 0
\(217\) 2583.19 0.808103
\(218\) 1466.95 + 1084.54i 0.455755 + 0.336946i
\(219\) 0 0
\(220\) 1054.60 323.388i 0.323186 0.0991037i
\(221\) 6405.96i 1.94983i
\(222\) 0 0
\(223\) 5049.28i 1.51625i 0.652107 + 0.758127i \(0.273885\pi\)
−0.652107 + 0.758127i \(0.726115\pi\)
\(224\) −66.3891 + 1597.23i −0.0198027 + 0.476425i
\(225\) 0 0
\(226\) 1387.95 1877.35i 0.408517 0.552563i
\(227\) −5716.54 −1.67145 −0.835727 0.549146i \(-0.814953\pi\)
−0.835727 + 0.549146i \(0.814953\pi\)
\(228\) 0 0
\(229\) −2582.55 −0.745240 −0.372620 0.927984i \(-0.621540\pi\)
−0.372620 + 0.927984i \(0.621540\pi\)
\(230\) 329.648 445.884i 0.0945059 0.127829i
\(231\) 0 0
\(232\) 854.606 + 301.425i 0.241843 + 0.0852997i
\(233\) 587.204i 0.165103i −0.996587 0.0825516i \(-0.973693\pi\)
0.996587 0.0825516i \(-0.0263069\pi\)
\(234\) 0 0
\(235\) 386.681i 0.107337i
\(236\) −1990.35 6490.73i −0.548988 1.79030i
\(237\) 0 0
\(238\) −2354.20 1740.50i −0.641178 0.474032i
\(239\) 5583.00 1.51102 0.755512 0.655135i \(-0.227388\pi\)
0.755512 + 0.655135i \(0.227388\pi\)
\(240\) 0 0
\(241\) −2056.95 −0.549791 −0.274895 0.961474i \(-0.588643\pi\)
−0.274895 + 0.961474i \(0.588643\pi\)
\(242\) 1758.87 + 1300.36i 0.467209 + 0.345414i
\(243\) 0 0
\(244\) −817.870 2667.15i −0.214585 0.699781i
\(245\) 1547.37i 0.403503i
\(246\) 0 0
\(247\) 5988.67i 1.54271i
\(248\) −6241.86 2201.55i −1.59822 0.563703i
\(249\) 0 0
\(250\) −2119.75 + 2867.19i −0.536260 + 0.725348i
\(251\) −1256.79 −0.316047 −0.158023 0.987435i \(-0.550512\pi\)
−0.158023 + 0.987435i \(0.550512\pi\)
\(252\) 0 0
\(253\) −792.890 −0.197030
\(254\) 1268.91 1716.34i 0.313460 0.423987i
\(255\) 0 0
\(256\) 1521.67 3802.86i 0.371501 0.928432i
\(257\) 643.773i 0.156255i 0.996943 + 0.0781273i \(0.0248941\pi\)
−0.996943 + 0.0781273i \(0.975106\pi\)
\(258\) 0 0
\(259\) 2501.55i 0.600150i
\(260\) 2440.74 748.442i 0.582185 0.178525i
\(261\) 0 0
\(262\) 4608.83 + 3407.37i 1.08677 + 0.803466i
\(263\) 917.108 0.215024 0.107512 0.994204i \(-0.465712\pi\)
0.107512 + 0.994204i \(0.465712\pi\)
\(264\) 0 0
\(265\) 925.501 0.214540
\(266\) −2200.85 1627.12i −0.507304 0.375057i
\(267\) 0 0
\(268\) 1485.98 455.671i 0.338697 0.103860i
\(269\) 6577.00i 1.49073i 0.666656 + 0.745366i \(0.267725\pi\)
−0.666656 + 0.745366i \(0.732275\pi\)
\(270\) 0 0
\(271\) 4656.21i 1.04371i −0.853035 0.521854i \(-0.825241\pi\)
0.853035 0.521854i \(-0.174759\pi\)
\(272\) 4205.20 + 6212.02i 0.937419 + 1.38478i
\(273\) 0 0
\(274\) 3165.99 4282.33i 0.698045 0.944179i
\(275\) 2146.74 0.470739
\(276\) 0 0
\(277\) −2881.42 −0.625010 −0.312505 0.949916i \(-0.601168\pi\)
−0.312505 + 0.949916i \(0.601168\pi\)
\(278\) 157.600 213.170i 0.0340007 0.0459895i
\(279\) 0 0
\(280\) 388.093 1100.33i 0.0828320 0.234847i
\(281\) 2604.93i 0.553015i 0.961012 + 0.276507i \(0.0891771\pi\)
−0.961012 + 0.276507i \(0.910823\pi\)
\(282\) 0 0
\(283\) 5786.02i 1.21535i 0.794187 + 0.607674i \(0.207897\pi\)
−0.794187 + 0.607674i \(0.792103\pi\)
\(284\) 2204.09 + 7187.74i 0.460524 + 1.50181i
\(285\) 0 0
\(286\) −2935.30 2170.11i −0.606882 0.448676i
\(287\) −3245.19 −0.667448
\(288\) 0 0
\(289\) −8825.50 −1.79636
\(290\) −531.840 393.197i −0.107692 0.0796183i
\(291\) 0 0
\(292\) −1111.30 3624.04i −0.222719 0.726305i
\(293\) 3279.55i 0.653902i −0.945041 0.326951i \(-0.893979\pi\)
0.945041 0.326951i \(-0.106021\pi\)
\(294\) 0 0
\(295\) 4955.07i 0.977950i
\(296\) 2131.97 6044.60i 0.418643 1.18694i
\(297\) 0 0
\(298\) 4648.73 6287.89i 0.903669 1.22231i
\(299\) −1835.05 −0.354928
\(300\) 0 0
\(301\) −2855.43 −0.546792
\(302\) −6211.50 + 8401.72i −1.18355 + 1.60088i
\(303\) 0 0
\(304\) 3931.27 + 5807.37i 0.741691 + 1.09564i
\(305\) 2036.12i 0.382255i
\(306\) 0 0
\(307\) 3014.47i 0.560407i 0.959941 + 0.280203i \(0.0904019\pi\)
−0.959941 + 0.280203i \(0.909598\pi\)
\(308\) −1595.04 + 489.113i −0.295084 + 0.0904863i
\(309\) 0 0
\(310\) 3884.45 + 2871.83i 0.711684 + 0.526157i
\(311\) 6230.80 1.13606 0.568032 0.823006i \(-0.307705\pi\)
0.568032 + 0.823006i \(0.307705\pi\)
\(312\) 0 0
\(313\) −3922.49 −0.708346 −0.354173 0.935180i \(-0.615238\pi\)
−0.354173 + 0.935180i \(0.615238\pi\)
\(314\) −1847.69 1366.02i −0.332073 0.245506i
\(315\) 0 0
\(316\) −2089.73 + 640.807i −0.372014 + 0.114077i
\(317\) 6882.19i 1.21938i 0.792641 + 0.609689i \(0.208705\pi\)
−0.792641 + 0.609689i \(0.791295\pi\)
\(318\) 0 0
\(319\) 945.741i 0.165992i
\(320\) −1875.53 + 2328.01i −0.327641 + 0.406686i
\(321\) 0 0
\(322\) −498.581 + 674.383i −0.0862883 + 0.116714i
\(323\) −12843.6 −2.21249
\(324\) 0 0
\(325\) 4968.36 0.847984
\(326\) −1738.94 + 2352.10i −0.295432 + 0.399603i
\(327\) 0 0
\(328\) 7841.48 + 2765.74i 1.32004 + 0.465587i
\(329\) 584.841i 0.0980040i
\(330\) 0 0
\(331\) 9489.08i 1.57573i 0.615847 + 0.787866i \(0.288814\pi\)
−0.615847 + 0.787866i \(0.711186\pi\)
\(332\) 793.595 + 2587.98i 0.131187 + 0.427813i
\(333\) 0 0
\(334\) −3305.31 2443.66i −0.541492 0.400332i
\(335\) −1134.41 −0.185013
\(336\) 0 0
\(337\) 4578.52 0.740083 0.370041 0.929015i \(-0.379344\pi\)
0.370041 + 0.929015i \(0.379344\pi\)
\(338\) −1796.64 1328.28i −0.289126 0.213755i
\(339\) 0 0
\(340\) −1605.14 5234.51i −0.256032 0.834945i
\(341\) 6907.50i 1.09696i
\(342\) 0 0
\(343\) 5369.42i 0.845253i
\(344\) 6899.69 + 2433.57i 1.08141 + 0.381422i
\(345\) 0 0
\(346\) 1067.56 1443.99i 0.165875 0.224363i
\(347\) 942.483 0.145807 0.0729037 0.997339i \(-0.476773\pi\)
0.0729037 + 0.997339i \(0.476773\pi\)
\(348\) 0 0
\(349\) −2124.84 −0.325903 −0.162951 0.986634i \(-0.552101\pi\)
−0.162951 + 0.986634i \(0.552101\pi\)
\(350\) 1349.90 1825.88i 0.206158 0.278850i
\(351\) 0 0
\(352\) 4271.01 + 177.526i 0.646721 + 0.0268811i
\(353\) 3881.60i 0.585260i 0.956226 + 0.292630i \(0.0945304\pi\)
−0.956226 + 0.292630i \(0.905470\pi\)
\(354\) 0 0
\(355\) 5487.18i 0.820363i
\(356\) 5658.98 1735.30i 0.842488 0.258345i
\(357\) 0 0
\(358\) 6616.90 + 4891.97i 0.976855 + 0.722202i
\(359\) 8050.44 1.18353 0.591763 0.806112i \(-0.298432\pi\)
0.591763 + 0.806112i \(0.298432\pi\)
\(360\) 0 0
\(361\) −5147.94 −0.750537
\(362\) −3080.52 2277.47i −0.447261 0.330666i
\(363\) 0 0
\(364\) −3691.52 + 1131.99i −0.531562 + 0.163001i
\(365\) 2766.62i 0.396744i
\(366\) 0 0
\(367\) 6890.96i 0.980123i −0.871688 0.490062i \(-0.836974\pi\)
0.871688 0.490062i \(-0.163026\pi\)
\(368\) 1779.49 1204.62i 0.252072 0.170639i
\(369\) 0 0
\(370\) −2781.07 + 3761.69i −0.390759 + 0.528543i
\(371\) −1399.79 −0.195885
\(372\) 0 0
\(373\) −10512.5 −1.45930 −0.729649 0.683822i \(-0.760316\pi\)
−0.729649 + 0.683822i \(0.760316\pi\)
\(374\) −4654.12 + 6295.18i −0.643472 + 0.870364i
\(375\) 0 0
\(376\) 498.436 1413.17i 0.0683640 0.193827i
\(377\) 2188.80i 0.299016i
\(378\) 0 0
\(379\) 3139.69i 0.425528i −0.977104 0.212764i \(-0.931753\pi\)
0.977104 0.212764i \(-0.0682466\pi\)
\(380\) −1500.58 4893.53i −0.202574 0.660613i
\(381\) 0 0
\(382\) −7933.87 5865.62i −1.06265 0.785631i
\(383\) 5117.53 0.682751 0.341375 0.939927i \(-0.389107\pi\)
0.341375 + 0.939927i \(0.389107\pi\)
\(384\) 0 0
\(385\) 1217.67 0.161190
\(386\) −6625.17 4898.08i −0.873607 0.645870i
\(387\) 0 0
\(388\) −1052.20 3431.33i −0.137674 0.448967i
\(389\) 787.004i 0.102578i −0.998684 0.0512888i \(-0.983667\pi\)
0.998684 0.0512888i \(-0.0163329\pi\)
\(390\) 0 0
\(391\) 3935.52i 0.509023i
\(392\) 1994.58 5655.07i 0.256994 0.728634i
\(393\) 0 0
\(394\) 4090.42 5532.72i 0.523026 0.707448i
\(395\) 1595.31 0.203212
\(396\) 0 0
\(397\) 11160.6 1.41092 0.705458 0.708752i \(-0.250741\pi\)
0.705458 + 0.708752i \(0.250741\pi\)
\(398\) 946.983 1280.89i 0.119266 0.161320i
\(399\) 0 0
\(400\) −4817.94 + 3261.49i −0.602242 + 0.407686i
\(401\) 13224.6i 1.64689i −0.567394 0.823447i \(-0.692048\pi\)
0.567394 0.823447i \(-0.307952\pi\)
\(402\) 0 0
\(403\) 15986.5i 1.97605i
\(404\) 8817.74 2703.92i 1.08589 0.332983i
\(405\) 0 0
\(406\) 804.388 + 594.695i 0.0983279 + 0.0726952i
\(407\) 6689.20 0.814671
\(408\) 0 0
\(409\) 8153.09 0.985683 0.492841 0.870119i \(-0.335958\pi\)
0.492841 + 0.870119i \(0.335958\pi\)
\(410\) −4879.93 3607.80i −0.587811 0.434577i
\(411\) 0 0
\(412\) −10630.6 + 3259.83i −1.27119 + 0.389806i
\(413\) 7494.36i 0.892914i
\(414\) 0 0
\(415\) 1975.69i 0.233693i
\(416\) 9884.73 + 410.861i 1.16500 + 0.0484233i
\(417\) 0 0
\(418\) −4350.94 + 5885.11i −0.509119 + 0.688637i
\(419\) −11682.5 −1.36212 −0.681061 0.732226i \(-0.738481\pi\)
−0.681061 + 0.732226i \(0.738481\pi\)
\(420\) 0 0
\(421\) 9595.77 1.11085 0.555426 0.831566i \(-0.312555\pi\)
0.555426 + 0.831566i \(0.312555\pi\)
\(422\) −2434.12 + 3292.40i −0.280784 + 0.379790i
\(423\) 0 0
\(424\) 3382.36 + 1192.98i 0.387410 + 0.136642i
\(425\) 10655.4i 1.21614i
\(426\) 0 0
\(427\) 3079.56i 0.349017i
\(428\) 575.740 + 1877.54i 0.0650220 + 0.212043i
\(429\) 0 0
\(430\) −4293.83 3174.49i −0.481551 0.356017i
\(431\) −4294.48 −0.479948 −0.239974 0.970779i \(-0.577139\pi\)
−0.239974 + 0.970779i \(0.577139\pi\)
\(432\) 0 0
\(433\) 168.392 0.0186892 0.00934460 0.999956i \(-0.497025\pi\)
0.00934460 + 0.999956i \(0.497025\pi\)
\(434\) −5875.09 4343.53i −0.649800 0.480406i
\(435\) 0 0
\(436\) −1512.76 4933.25i −0.166166 0.541881i
\(437\) 3679.16i 0.402742i
\(438\) 0 0
\(439\) 1459.53i 0.158677i −0.996848 0.0793387i \(-0.974719\pi\)
0.996848 0.0793387i \(-0.0252809\pi\)
\(440\) −2942.29 1037.77i −0.318792 0.112440i
\(441\) 0 0
\(442\) −10771.4 + 14569.4i −1.15914 + 1.56787i
\(443\) 333.411 0.0357581 0.0178790 0.999840i \(-0.494309\pi\)
0.0178790 + 0.999840i \(0.494309\pi\)
\(444\) 0 0
\(445\) −4320.11 −0.460209
\(446\) 8490.16 11483.8i 0.901392 1.21923i
\(447\) 0 0
\(448\) 2836.67 3521.03i 0.299152 0.371323i
\(449\) 11454.3i 1.20393i 0.798523 + 0.601964i \(0.205615\pi\)
−0.798523 + 0.601964i \(0.794385\pi\)
\(450\) 0 0
\(451\) 8677.70i 0.906024i
\(452\) −6313.37 + 1935.97i −0.656982 + 0.201461i
\(453\) 0 0
\(454\) 13001.4 + 9612.14i 1.34402 + 0.993656i
\(455\) 2818.14 0.290365
\(456\) 0 0
\(457\) 9680.26 0.990861 0.495431 0.868648i \(-0.335010\pi\)
0.495431 + 0.868648i \(0.335010\pi\)
\(458\) 5873.64 + 4342.46i 0.599252 + 0.443035i
\(459\) 0 0
\(460\) −1499.47 + 459.808i −0.151986 + 0.0466057i
\(461\) 14806.9i 1.49593i −0.663737 0.747966i \(-0.731030\pi\)
0.663737 0.747966i \(-0.268970\pi\)
\(462\) 0 0
\(463\) 3658.08i 0.367183i 0.983003 + 0.183591i \(0.0587723\pi\)
−0.983003 + 0.183591i \(0.941228\pi\)
\(464\) −1436.84 2122.53i −0.143758 0.212362i
\(465\) 0 0
\(466\) −987.361 + 1335.51i −0.0981516 + 0.132760i
\(467\) 9852.37 0.976260 0.488130 0.872771i \(-0.337679\pi\)
0.488130 + 0.872771i \(0.337679\pi\)
\(468\) 0 0
\(469\) 1715.75 0.168926
\(470\) −650.189 + 879.449i −0.0638106 + 0.0863106i
\(471\) 0 0
\(472\) −6387.14 + 18108.9i −0.622864 + 1.76595i
\(473\) 7635.47i 0.742240i
\(474\) 0 0
\(475\) 9961.26i 0.962219i
\(476\) 2427.72 + 7917.01i 0.233769 + 0.762343i
\(477\) 0 0
\(478\) −12697.7 9387.61i −1.21502 0.898283i
\(479\) −11107.9 −1.05957 −0.529784 0.848133i \(-0.677727\pi\)
−0.529784 + 0.848133i \(0.677727\pi\)
\(480\) 0 0
\(481\) 15481.3 1.46754
\(482\) 4678.22 + 3458.68i 0.442090 + 0.326843i
\(483\) 0 0
\(484\) −1813.80 5914.96i −0.170342 0.555499i
\(485\) 2619.50i 0.245248i
\(486\) 0 0
\(487\) 11703.7i 1.08900i −0.838761 0.544500i \(-0.816719\pi\)
0.838761 0.544500i \(-0.183281\pi\)
\(488\) −2624.58 + 7441.26i −0.243461 + 0.690266i
\(489\) 0 0
\(490\) −2601.85 + 3519.28i −0.239877 + 0.324459i
\(491\) 2851.25 0.262067 0.131034 0.991378i \(-0.458170\pi\)
0.131034 + 0.991378i \(0.458170\pi\)
\(492\) 0 0
\(493\) 4694.20 0.428836
\(494\) −10069.7 + 13620.4i −0.917122 + 1.24050i
\(495\) 0 0
\(496\) 10494.4 + 15502.6i 0.950024 + 1.40340i
\(497\) 8299.15i 0.749030i
\(498\) 0 0
\(499\) 14936.0i 1.33994i 0.742389 + 0.669969i \(0.233693\pi\)
−0.742389 + 0.669969i \(0.766307\pi\)
\(500\) 9642.14 2956.72i 0.862419 0.264457i
\(501\) 0 0
\(502\) 2858.38 + 2113.24i 0.254135 + 0.187885i
\(503\) 9047.91 0.802041 0.401020 0.916069i \(-0.368656\pi\)
0.401020 + 0.916069i \(0.368656\pi\)
\(504\) 0 0
\(505\) −6731.52 −0.593166
\(506\) 1803.31 + 1333.21i 0.158433 + 0.117132i
\(507\) 0 0
\(508\) −5771.92 + 1769.94i −0.504109 + 0.154583i
\(509\) 15173.5i 1.32132i 0.750683 + 0.660662i \(0.229724\pi\)
−0.750683 + 0.660662i \(0.770276\pi\)
\(510\) 0 0
\(511\) 4184.41i 0.362246i
\(512\) −9855.18 + 6090.42i −0.850667 + 0.525705i
\(513\) 0 0
\(514\) 1082.48 1464.17i 0.0928913 0.125645i
\(515\) 8115.47 0.694389
\(516\) 0 0
\(517\) 1563.87 0.133035
\(518\) 4206.26 5689.42i 0.356781 0.482584i
\(519\) 0 0
\(520\) −6809.57 2401.78i −0.574268 0.202548i
\(521\) 7375.96i 0.620243i −0.950697 0.310121i \(-0.899630\pi\)
0.950697 0.310121i \(-0.100370\pi\)
\(522\) 0 0
\(523\) 8514.96i 0.711918i −0.934502 0.355959i \(-0.884154\pi\)
0.934502 0.355959i \(-0.115846\pi\)
\(524\) −4752.75 15499.1i −0.396230 1.29214i
\(525\) 0 0
\(526\) −2085.83 1542.08i −0.172902 0.127829i
\(527\) −34285.4 −2.83396
\(528\) 0 0
\(529\) −11039.6 −0.907342
\(530\) −2104.92 1556.19i −0.172513 0.127541i
\(531\) 0 0
\(532\) 2269.57 + 7401.29i 0.184960 + 0.603170i
\(533\) 20083.5i 1.63210i
\(534\) 0 0
\(535\) 1433.33i 0.115828i
\(536\) −4145.84 1462.27i −0.334092 0.117836i
\(537\) 0 0
\(538\) 11059.0 14958.4i 0.886220 1.19871i
\(539\) 6258.13 0.500105
\(540\) 0 0
\(541\) −2214.98 −0.176025 −0.0880125 0.996119i \(-0.528052\pi\)
−0.0880125 + 0.996119i \(0.528052\pi\)
\(542\) −7829.25 + 10589.9i −0.620470 + 0.839252i
\(543\) 0 0
\(544\) 881.150 21199.2i 0.0694467 1.67079i
\(545\) 3766.08i 0.296002i
\(546\) 0 0
\(547\) 3906.55i 0.305360i 0.988276 + 0.152680i \(0.0487904\pi\)
−0.988276 + 0.152680i \(0.951210\pi\)
\(548\) −14401.1 + 4416.05i −1.12260 + 0.344242i
\(549\) 0 0
\(550\) −4882.44 3609.66i −0.378524 0.279848i
\(551\) 4388.41 0.339297
\(552\) 0 0
\(553\) −2412.85 −0.185542
\(554\) 6553.37 + 4844.99i 0.502574 + 0.371560i
\(555\) 0 0
\(556\) −716.874 + 219.827i −0.0546803 + 0.0167675i
\(557\) 2978.14i 0.226549i 0.993564 + 0.113275i \(0.0361340\pi\)
−0.993564 + 0.113275i \(0.963866\pi\)
\(558\) 0 0
\(559\) 17671.4i 1.33706i
\(560\) −2732.82 + 1849.97i −0.206219 + 0.139599i
\(561\) 0 0
\(562\) 4380.09 5924.54i 0.328760 0.444682i
\(563\) −8786.44 −0.657734 −0.328867 0.944376i \(-0.606667\pi\)
−0.328867 + 0.944376i \(0.606667\pi\)
\(564\) 0 0
\(565\) 4819.67 0.358876
\(566\) 9728.97 13159.5i 0.722507 0.977268i
\(567\) 0 0
\(568\) 7073.03 20053.6i 0.522496 1.48139i
\(569\) 19271.0i 1.41983i −0.704288 0.709914i \(-0.748734\pi\)
0.704288 0.709914i \(-0.251266\pi\)
\(570\) 0 0
\(571\) 15535.7i 1.13861i −0.822125 0.569307i \(-0.807212\pi\)
0.822125 0.569307i \(-0.192788\pi\)
\(572\) 3026.96 + 9871.20i 0.221265 + 0.721566i
\(573\) 0 0
\(574\) 7380.71 + 5456.66i 0.536699 + 0.396789i
\(575\) −3052.33 −0.221375
\(576\) 0 0
\(577\) 3783.58 0.272985 0.136493 0.990641i \(-0.456417\pi\)
0.136493 + 0.990641i \(0.456417\pi\)
\(578\) 20072.3 + 14839.7i 1.44446 + 1.06791i
\(579\) 0 0
\(580\) 548.447 + 1788.54i 0.0392639 + 0.128043i
\(581\) 2988.15i 0.213373i
\(582\) 0 0
\(583\) 3743.06i 0.265903i
\(584\) −3566.21 + 10111.0i −0.252689 + 0.716429i
\(585\) 0 0
\(586\) −5514.43 + 7458.85i −0.388736 + 0.525806i
\(587\) 15515.4 1.09095 0.545477 0.838126i \(-0.316349\pi\)
0.545477 + 0.838126i \(0.316349\pi\)
\(588\) 0 0
\(589\) −32052.1 −2.24225
\(590\) 8331.76 11269.6i 0.581378 0.786375i
\(591\) 0 0
\(592\) −15012.6 + 10162.7i −1.04225 + 0.705550i
\(593\) 14098.1i 0.976292i −0.872762 0.488146i \(-0.837673\pi\)
0.872762 0.488146i \(-0.162327\pi\)
\(594\) 0 0
\(595\) 6043.90i 0.416430i
\(596\) −21145.7 + 6484.24i −1.45329 + 0.445646i
\(597\) 0 0
\(598\) 4173.55 + 3085.56i 0.285400 + 0.211000i
\(599\) 572.539 0.0390539 0.0195270 0.999809i \(-0.493784\pi\)
0.0195270 + 0.999809i \(0.493784\pi\)
\(600\) 0 0
\(601\) −23463.4 −1.59250 −0.796249 0.604969i \(-0.793185\pi\)
−0.796249 + 0.604969i \(0.793185\pi\)
\(602\) 6494.26 + 4801.30i 0.439678 + 0.325060i
\(603\) 0 0
\(604\) 28254.3 8664.07i 1.90340 0.583669i
\(605\) 4515.52i 0.303441i
\(606\) 0 0
\(607\) 1980.51i 0.132433i −0.997805 0.0662163i \(-0.978907\pi\)
0.997805 0.0662163i \(-0.0210927\pi\)
\(608\) 823.752 19818.3i 0.0549466 1.32194i
\(609\) 0 0
\(610\) 3423.66 4630.86i 0.227246 0.307374i
\(611\) 3619.39 0.239648
\(612\) 0 0
\(613\) 2479.01 0.163338 0.0816691 0.996660i \(-0.473975\pi\)
0.0816691 + 0.996660i \(0.473975\pi\)
\(614\) 5068.71 6855.97i 0.333154 0.450626i
\(615\) 0 0
\(616\) 4450.11 + 1569.58i 0.291072 + 0.102663i
\(617\) 20002.8i 1.30516i 0.757722 + 0.652578i \(0.226312\pi\)
−0.757722 + 0.652578i \(0.773688\pi\)
\(618\) 0 0
\(619\) 22292.4i 1.44751i 0.690058 + 0.723754i \(0.257585\pi\)
−0.690058 + 0.723754i \(0.742415\pi\)
\(620\) −4005.75 13063.1i −0.259475 0.846172i
\(621\) 0 0
\(622\) −14171.0 10476.8i −0.913516 0.675375i
\(623\) 6534.01 0.420192
\(624\) 0 0
\(625\) 4002.52 0.256161
\(626\) 8921.13 + 6595.52i 0.569585 + 0.421102i
\(627\) 0 0
\(628\) 1905.38 + 6213.63i 0.121072 + 0.394826i
\(629\) 33201.9i 2.10469i
\(630\) 0 0
\(631\) 24203.8i 1.52700i 0.645807 + 0.763501i \(0.276521\pi\)
−0.645807 + 0.763501i \(0.723479\pi\)
\(632\) 5830.27 + 2056.38i 0.366955 + 0.129428i
\(633\) 0 0
\(634\) 11572.1 15652.5i 0.724903 0.980508i
\(635\) 4406.32 0.275370
\(636\) 0 0
\(637\) 14483.7 0.900885
\(638\) 1590.23 2150.95i 0.0986797 0.133475i
\(639\) 0 0
\(640\) 8180.07 2141.09i 0.505227 0.132241i
\(641\) 4423.87i 0.272593i 0.990668 + 0.136297i \(0.0435200\pi\)
−0.990668 + 0.136297i \(0.956480\pi\)
\(642\) 0 0
\(643\) 11961.5i 0.733619i 0.930296 + 0.366810i \(0.119550\pi\)
−0.930296 + 0.366810i \(0.880450\pi\)
\(644\) 2267.90 695.442i 0.138770 0.0425532i
\(645\) 0 0
\(646\) 29210.8 + 21596.0i 1.77908 + 1.31530i
\(647\) −6287.16 −0.382030 −0.191015 0.981587i \(-0.561178\pi\)
−0.191015 + 0.981587i \(0.561178\pi\)
\(648\) 0 0
\(649\) −20040.1 −1.21208
\(650\) −11299.8 8354.10i −0.681869 0.504115i
\(651\) 0 0
\(652\) 7909.92 2425.54i 0.475117 0.145693i
\(653\) 18793.2i 1.12624i −0.826376 0.563119i \(-0.809601\pi\)
0.826376 0.563119i \(-0.190399\pi\)
\(654\) 0 0
\(655\) 11832.2i 0.705833i
\(656\) −13183.8 19475.4i −0.784667 1.15913i
\(657\) 0 0
\(658\) 983.387 1330.14i 0.0582620 0.0788056i
\(659\) −20827.2 −1.23113 −0.615563 0.788088i \(-0.711071\pi\)
−0.615563 + 0.788088i \(0.711071\pi\)
\(660\) 0 0
\(661\) −6038.16 −0.355306 −0.177653 0.984093i \(-0.556850\pi\)
−0.177653 + 0.984093i \(0.556850\pi\)
\(662\) 15955.5 21581.5i 0.936751 1.26705i
\(663\) 0 0
\(664\) 2546.68 7220.39i 0.148841 0.421996i
\(665\) 5650.20i 0.329482i
\(666\) 0 0
\(667\) 1344.70i 0.0780612i
\(668\) 3408.52 + 11115.5i 0.197425 + 0.643819i
\(669\) 0 0
\(670\) 2580.05 + 1907.47i 0.148770 + 0.109988i
\(671\) −8234.79 −0.473771
\(672\) 0 0
\(673\) −19811.5 −1.13474 −0.567368 0.823464i \(-0.692038\pi\)
−0.567368 + 0.823464i \(0.692038\pi\)
\(674\) −10413.2 7698.60i −0.595105 0.439969i
\(675\) 0 0
\(676\) 1852.75 + 6041.97i 0.105413 + 0.343763i
\(677\) 22962.5i 1.30357i −0.758402 0.651787i \(-0.774020\pi\)
0.758402 0.651787i \(-0.225980\pi\)
\(678\) 0 0
\(679\) 3961.90i 0.223923i
\(680\) −5150.97 + 14604.1i −0.290486 + 0.823591i
\(681\) 0 0
\(682\) −11614.7 + 15710.1i −0.652125 + 0.882068i
\(683\) 33097.3 1.85422 0.927109 0.374791i \(-0.122286\pi\)
0.927109 + 0.374791i \(0.122286\pi\)
\(684\) 0 0
\(685\) 10993.9 0.613222
\(686\) 9028.48 12212.0i 0.502491 0.679672i
\(687\) 0 0
\(688\) −11600.4 17136.4i −0.642821 0.949589i
\(689\) 8662.84i 0.478995i
\(690\) 0 0
\(691\) 21151.0i 1.16443i 0.813034 + 0.582216i \(0.197814\pi\)
−0.813034 + 0.582216i \(0.802186\pi\)
\(692\) −4856.04 + 1489.08i −0.266761 + 0.0818012i
\(693\) 0 0
\(694\) −2143.54 1584.75i −0.117244 0.0866805i
\(695\) 547.267 0.0298691
\(696\) 0 0
\(697\) 43071.9 2.34069
\(698\) 4832.63 + 3572.83i 0.262060 + 0.193745i
\(699\) 0 0
\(700\) −6140.30 + 1882.90i −0.331545 + 0.101667i
\(701\) 18752.3i 1.01036i 0.863013 + 0.505182i \(0.168575\pi\)
−0.863013 + 0.505182i \(0.831425\pi\)
\(702\) 0 0
\(703\) 31039.1i 1.66524i
\(704\) −9415.29 7585.30i −0.504051 0.406082i
\(705\) 0 0
\(706\) 6526.76 8828.13i 0.347929 0.470611i
\(707\) 10181.2 0.541588
\(708\) 0 0
\(709\) −25964.1 −1.37532 −0.687660 0.726033i \(-0.741362\pi\)
−0.687660 + 0.726033i \(0.741362\pi\)
\(710\) −9226.47 + 12479.8i −0.487695 + 0.659659i
\(711\) 0 0
\(712\) −15788.4 5568.67i −0.831032 0.293110i
\(713\) 9821.38i 0.515868i
\(714\) 0 0
\(715\) 7535.75i 0.394155i
\(716\) −6823.52 22252.1i −0.356155 1.16145i
\(717\) 0 0
\(718\) −18309.6 13536.5i −0.951681 0.703591i
\(719\) −11741.1 −0.608998 −0.304499 0.952513i \(-0.598489\pi\)
−0.304499 + 0.952513i \(0.598489\pi\)
\(720\) 0 0
\(721\) −12274.4 −0.634010
\(722\) 11708.2 + 8656.06i 0.603511 + 0.446184i
\(723\) 0 0
\(724\) 3176.72 + 10359.6i 0.163069 + 0.531782i
\(725\) 3640.74i 0.186502i
\(726\) 0 0
\(727\) 5637.87i 0.287616i −0.989606 0.143808i \(-0.954065\pi\)
0.989606 0.143808i \(-0.0459348\pi\)
\(728\) 10299.2 + 3632.61i 0.524334 + 0.184936i
\(729\) 0 0
\(730\) 4651.97 6292.28i 0.235859 0.319024i
\(731\) 37898.8 1.91756
\(732\) 0 0
\(733\) −23807.3 −1.19965 −0.599825 0.800131i \(-0.704763\pi\)
−0.599825 + 0.800131i \(0.704763\pi\)
\(734\) −11586.9 + 15672.5i −0.582670 + 0.788123i
\(735\) 0 0
\(736\) −6072.71 252.414i −0.304135 0.0126414i
\(737\) 4587.96i 0.229307i
\(738\) 0 0
\(739\) 3556.31i 0.177024i 0.996075 + 0.0885122i \(0.0282112\pi\)
−0.996075 + 0.0885122i \(0.971789\pi\)
\(740\) 12650.3 3879.15i 0.628423 0.192703i
\(741\) 0 0
\(742\) 3183.61 + 2353.69i 0.157512 + 0.116451i
\(743\) −24054.6 −1.18772 −0.593860 0.804568i \(-0.702397\pi\)
−0.593860 + 0.804568i \(0.702397\pi\)
\(744\) 0 0
\(745\) 16142.8 0.793860
\(746\) 23909.2 + 17676.4i 1.17343 + 0.867533i
\(747\) 0 0
\(748\) 21170.2 6491.76i 1.03484 0.317329i
\(749\) 2167.86i 0.105757i
\(750\) 0 0
\(751\) 15373.0i 0.746960i −0.927638 0.373480i \(-0.878164\pi\)
0.927638 0.373480i \(-0.121836\pi\)
\(752\) −3509.82 + 2375.96i −0.170199 + 0.115216i
\(753\) 0 0
\(754\) 3680.38 4978.11i 0.177761 0.240440i
\(755\) −21569.6 −1.03973
\(756\) 0 0
\(757\) 26000.8 1.24837 0.624184 0.781277i \(-0.285431\pi\)
0.624184 + 0.781277i \(0.285431\pi\)
\(758\) −5279.27 + 7140.77i −0.252971 + 0.342170i
\(759\) 0 0
\(760\) −4815.43 + 13652.8i −0.229834 + 0.651630i
\(761\) 9461.72i 0.450706i −0.974277 0.225353i \(-0.927646\pi\)
0.974277 0.225353i \(-0.0723535\pi\)
\(762\) 0 0
\(763\) 5696.06i 0.270264i
\(764\) 8181.61 + 26681.0i 0.387435 + 1.26346i
\(765\) 0 0
\(766\) −11639.1 8604.93i −0.549004 0.405886i
\(767\) −46380.2 −2.18343
\(768\) 0 0
\(769\) 11196.2 0.525028 0.262514 0.964928i \(-0.415448\pi\)
0.262514 + 0.964928i \(0.415448\pi\)
\(770\) −2769.40 2047.46i −0.129613 0.0958250i
\(771\) 0 0
\(772\) 6832.05 + 22279.9i 0.318512 + 1.03870i
\(773\) 39575.0i 1.84141i 0.390255 + 0.920707i \(0.372387\pi\)
−0.390255 + 0.920707i \(0.627613\pi\)
\(774\) 0 0
\(775\) 26591.2i 1.23250i
\(776\) −3376.56 + 9573.29i −0.156201 + 0.442862i
\(777\) 0 0
\(778\) −1323.32 + 1789.92i −0.0609810 + 0.0824832i
\(779\) 40266.2 1.85197
\(780\) 0 0
\(781\) 22192.1 1.01677
\(782\) 6617.43 8950.77i 0.302607 0.409308i
\(783\) 0 0
\(784\) −14045.2 + 9507.83i −0.639813 + 0.433119i
\(785\) 4743.53i 0.215674i
\(786\) 0 0
\(787\) 25069.2i 1.13548i −0.823209 0.567739i \(-0.807818\pi\)
0.823209 0.567739i \(-0.192182\pi\)
\(788\) −18606.1 + 5705.49i −0.841136 + 0.257931i
\(789\) 0 0
\(790\) −3628.31 2682.46i −0.163404 0.120807i
\(791\) −7289.58 −0.327671
\(792\) 0