Properties

Label 108.4.b.b.107.9
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: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
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 107.9
Root \(0.433705 - 1.36719i\) of \(x^{12} + 3 x^{10} - 12 x^{9} + 73 x^{8} - 12 x^{7} + 589 x^{6} + 84 x^{5} + 2452 x^{4} + 852 x^{3} + 6854 x^{2} - 888 x + 9496\)
Character \(\chi\) \(=\) 108.107
Dual form 108.4.b.b.107.10

$q$-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 \(-0.923371\pi\)
0.971163 0.238418i \(-0.0766288\pi\)
\(8\) −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 \(-0.604906\pi\)
−0.323639 + 0.946180i \(0.604906\pi\)
\(12\) 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 \(0.230097\pi\)
−0.749910 + 0.661539i \(0.769903\pi\)
\(20\) −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 \(-0.451365\pi\)
0.152199 + 0.988350i \(0.451365\pi\)
\(24\) 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 \(0.321809\pi\)
−0.531020 + 0.847359i \(0.678191\pi\)
\(32\) −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 \(-0.805642\pi\)
0.819308 0.573354i \(-0.194358\pi\)
\(44\) −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 \(-0.532769\pi\)
−0.102765 + 0.994706i \(0.532769\pi\)
\(48\) 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 \(-0.114236\pi\)
0.936290 + 0.351228i \(0.114236\pi\)
\(60\) 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 \(0.0566819\pi\)
−0.984187 + 0.177132i \(0.943318\pi\)
\(68\) −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 \(-0.787551\pi\)
−0.785417 + 0.618968i \(0.787551\pi\)
\(72\) 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 \(-0.937673\pi\)
0.980891 0.194556i \(-0.0623265\pi\)
\(80\) −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 \(-0.571826\pi\)
−0.223738 + 0.974649i \(0.571826\pi\)
\(84\) 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 \(-0.768513\pi\)
0.747013 0.664809i \(-0.231487\pi\)
\(104\) −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 \(-0.535371\pi\)
−0.110894 + 0.993832i \(0.535371\pi\)
\(108\) 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 \(-0.915077\pi\)
0.964621 0.263639i \(-0.0849228\pi\)
\(128\) −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 \(-0.263814\pi\)
0.675765 + 0.737117i \(0.263814\pi\)
\(132\) 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 \(-0.990896\pi\)
0.999591 0.0285967i \(-0.00910385\pi\)
\(140\) −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 \(0.469585\pi\)
−0.0954051 + 0.995439i \(0.530415\pi\)
\(152\) 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 \(0.0799299\pi\)
−0.968638 + 0.248477i \(0.920070\pi\)
\(164\) 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 \(-0.609312\pi\)
−0.336704 + 0.941610i \(0.609312\pi\)
\(168\) 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 \(-0.292206\pi\)
0.607417 + 0.794383i \(0.292206\pi\)
\(180\) 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 \(-0.729768\pi\)
−0.660765 + 0.750593i \(0.729768\pi\)
\(192\) 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 \(-0.968016\pi\)
0.994956 0.100310i \(-0.0319836\pi\)
\(200\) −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 \(0.0758879\pi\)
−0.971715 + 0.236157i \(0.924112\pi\)
\(212\) 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 \(-0.726115\pi\)
0.652107 0.758127i \(-0.273885\pi\)
\(224\) 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 \(-0.185047\pi\)
0.835727 + 0.549146i \(0.185047\pi\)
\(228\) 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 \(-0.772612\pi\)
−0.755512 + 0.655135i \(0.772612\pi\)
\(240\) 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 \(-0.449488\pi\)
0.158023 + 0.987435i \(0.449488\pi\)
\(252\) 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 \(-0.534288\pi\)
−0.107512 + 0.994204i \(0.534288\pi\)
\(264\) 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 \(0.174759\pi\)
−0.853035 + 0.521854i \(0.825241\pi\)
\(272\) −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 \(-0.792103\pi\)
0.794187 0.607674i \(-0.207897\pi\)
\(284\) −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 \(-0.909598\pi\)
0.959941 0.280203i \(-0.0904019\pi\)
\(308\) 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 \(-0.692295\pi\)
−0.568032 + 0.823006i \(0.692295\pi\)
\(312\) 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 \(-0.711186\pi\)
0.615847 0.787866i \(-0.288814\pi\)
\(332\) −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 \(-0.523227\pi\)
−0.0729037 + 0.997339i \(0.523227\pi\)
\(348\) 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 \(-0.701568\pi\)
−0.591763 + 0.806112i \(0.701568\pi\)
\(360\) 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 \(0.163026\pi\)
−0.871688 + 0.490062i \(0.836974\pi\)
\(368\) −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 \(0.0682466\pi\)
−0.977104 + 0.212764i \(0.931753\pi\)
\(380\) 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 \(-0.610893\pi\)
−0.341375 + 0.939927i \(0.610893\pi\)
\(384\) 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 \(-0.261519\pi\)
0.681061 + 0.732226i \(0.261519\pi\)
\(420\) 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 \(-0.422861\pi\)
0.239974 + 0.970779i \(0.422861\pi\)
\(432\) 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 \(0.0252809\pi\)
−0.996848 + 0.0793387i \(0.974719\pi\)
\(440\) 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 \(-0.505691\pi\)
−0.0178790 + 0.999840i \(0.505691\pi\)
\(444\) 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 \(-0.941228\pi\)
0.983003 0.183591i \(-0.0587723\pi\)
\(464\) 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 \(-0.662321\pi\)
−0.488130 + 0.872771i \(0.662321\pi\)
\(468\) 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 \(-0.322273\pi\)
0.529784 + 0.848133i \(0.322273\pi\)
\(480\) 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 \(0.183281\pi\)
−0.838761 + 0.544500i \(0.816719\pi\)
\(488\) 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 \(-0.541830\pi\)
−0.131034 + 0.991378i \(0.541830\pi\)
\(492\) 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 \(-0.766307\pi\)
0.742389 0.669969i \(-0.233693\pi\)
\(500\) −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 \(-0.631344\pi\)
−0.401020 + 0.916069i \(0.631344\pi\)
\(504\) 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 \(0.115846\pi\)
−0.934502 + 0.355959i \(0.884154\pi\)
\(524\) 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 \(-0.951210\pi\)
0.988276 0.152680i \(-0.0487904\pi\)
\(548\) 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 \(-0.393333\pi\)
0.328867 + 0.944376i \(0.393333\pi\)
\(564\) 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 \(0.192788\pi\)
−0.822125 + 0.569307i \(0.807212\pi\)
\(572\) −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 \(-0.683651\pi\)
−0.545477 + 0.838126i \(0.683651\pi\)
\(588\) 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 \(-0.506216\pi\)
−0.0195270 + 0.999809i \(0.506216\pi\)
\(600\) 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 \(0.0210927\pi\)
−0.997805 + 0.0662163i \(0.978907\pi\)
\(608\) −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 \(-0.742415\pi\)
0.690058 0.723754i \(-0.257585\pi\)
\(620\) 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 \(-0.723479\pi\)
0.645807 0.763501i \(-0.276521\pi\)
\(632\) −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 \(-0.880450\pi\)
0.930296 0.366810i \(-0.119550\pi\)
\(644\) −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 \(-0.438822\pi\)
0.191015 + 0.981587i \(0.438822\pi\)
\(648\) 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 \(-0.288929\pi\)
0.615563 + 0.788088i \(0.288929\pi\)
\(660\) 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 \(-0.877714\pi\)
−0.927109 + 0.374791i \(0.877714\pi\)
\(684\) 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 \(-0.802186\pi\)
0.813034 0.582216i \(-0.197814\pi\)
\(692\) 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 \(-0.401511\pi\)
0.304499 + 0.952513i \(0.401511\pi\)
\(720\) 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 \(0.0459348\pi\)
−0.989606 + 0.143808i \(0.954065\pi\)
\(728\) −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 \(-0.971789\pi\)
0.996075 0.0885122i \(-0.0282112\pi\)
\(740\) −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 \(-0.297603\pi\)
0.593860 + 0.804568i \(0.297603\pi\)
\(744\) 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 \(0.121836\pi\)
−0.927638 + 0.373480i \(0.878164\pi\)
\(752\) 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 \(0.192182\pi\)
−0.823209 + 0.567739i \(0.807818\pi\)
\(788\) 18606.1 + 5705.49i 0.841136 + 0.257931i
\(789\) 0 0
\(790\) −3628.31 + 2682.46i −0.163404 + 0.120807i