Properties

Label 225.4.f.c.107.5
Level $225$
Weight $4$
Character 225.107
Analytic conductor $13.275$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.f (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 16 x^{10} - 14 x^{8} - 512 x^{6} + 3889 x^{4} + 126224 x^{2} + 506944\)
Coefficient ring: \(\Z[a_1, \ldots, a_{29}]\)
Coefficient ring index: \( 2^{11}\cdot 3^{4} \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 107.5
Root \(0.347140 + 2.27426i\) of defining polynomial
Character \(\chi\) \(=\) 225.107
Dual form 225.4.f.c.143.5

$q$-expansion

\(f(q)\) \(=\) \(q+(2.62140 - 2.62140i) q^{2} -5.74350i q^{4} +(10.8652 + 10.8652i) q^{7} +(5.91519 + 5.91519i) q^{8} +O(q^{10})\) \(q+(2.62140 - 2.62140i) q^{2} -5.74350i q^{4} +(10.8652 + 10.8652i) q^{7} +(5.91519 + 5.91519i) q^{8} -37.8905i q^{11} +(48.1085 - 48.1085i) q^{13} +56.9640 q^{14} +76.9602 q^{16} +(60.3458 - 60.3458i) q^{17} +109.678i q^{19} +(-99.3262 - 99.3262i) q^{22} +(-39.7660 - 39.7660i) q^{23} -252.224i q^{26} +(62.4042 - 62.4042i) q^{28} +90.3553 q^{29} -233.678 q^{31} +(154.422 - 154.422i) q^{32} -316.381i q^{34} +(19.0042 + 19.0042i) q^{37} +(287.509 + 287.509i) q^{38} +260.783i q^{41} +(-176.216 + 176.216i) q^{43} -217.624 q^{44} -208.485 q^{46} +(145.788 - 145.788i) q^{47} -106.896i q^{49} +(-276.311 - 276.311i) q^{52} +(183.285 + 183.285i) q^{53} +128.539i q^{56} +(236.858 - 236.858i) q^{58} +279.564 q^{59} -390.267 q^{61} +(-612.563 + 612.563i) q^{62} -193.924i q^{64} +(-150.444 - 150.444i) q^{67} +(-346.596 - 346.596i) q^{68} -470.042i q^{71} +(-480.765 + 480.765i) q^{73} +99.6355 q^{74} +629.934 q^{76} +(411.687 - 411.687i) q^{77} +1322.44i q^{79} +(683.618 + 683.618i) q^{82} +(-456.192 - 456.192i) q^{83} +923.868i q^{86} +(224.129 - 224.129i) q^{88} -1364.85 q^{89} +1045.41 q^{91} +(-228.396 + 228.396i) q^{92} -764.340i q^{94} +(785.308 + 785.308i) q^{97} +(-280.218 - 280.218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 24 q^{7} + O(q^{10}) \) \( 12 q - 24 q^{7} + 108 q^{13} - 648 q^{16} - 1056 q^{22} + 576 q^{28} - 1248 q^{31} - 828 q^{37} + 96 q^{43} + 672 q^{46} + 312 q^{52} + 3864 q^{58} + 96 q^{61} - 1632 q^{67} - 3972 q^{73} - 480 q^{76} + 7848 q^{82} - 7968 q^{88} + 4752 q^{91} - 2772 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.62140 2.62140i 0.926806 0.926806i −0.0706924 0.997498i \(-0.522521\pi\)
0.997498 + 0.0706924i \(0.0225209\pi\)
\(3\) 0 0
\(4\) 5.74350i 0.717938i
\(5\) 0 0
\(6\) 0 0
\(7\) 10.8652 + 10.8652i 0.586664 + 0.586664i 0.936726 0.350062i \(-0.113840\pi\)
−0.350062 + 0.936726i \(0.613840\pi\)
\(8\) 5.91519 + 5.91519i 0.261417 + 0.261417i
\(9\) 0 0
\(10\) 0 0
\(11\) 37.8905i 1.03858i −0.854597 0.519291i \(-0.826196\pi\)
0.854597 0.519291i \(-0.173804\pi\)
\(12\) 0 0
\(13\) 48.1085 48.1085i 1.02638 1.02638i 0.0267344 0.999643i \(-0.491489\pi\)
0.999643 0.0267344i \(-0.00851083\pi\)
\(14\) 56.9640 1.08745
\(15\) 0 0
\(16\) 76.9602 1.20250
\(17\) 60.3458 60.3458i 0.860942 0.860942i −0.130506 0.991448i \(-0.541660\pi\)
0.991448 + 0.130506i \(0.0416601\pi\)
\(18\) 0 0
\(19\) 109.678i 1.32430i 0.749369 + 0.662152i \(0.230357\pi\)
−0.749369 + 0.662152i \(0.769643\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −99.3262 99.3262i −0.962564 0.962564i
\(23\) −39.7660 39.7660i −0.360512 0.360512i 0.503489 0.864002i \(-0.332049\pi\)
−0.864002 + 0.503489i \(0.832049\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 252.224i 1.90250i
\(27\) 0 0
\(28\) 62.4042 62.4042i 0.421188 0.421188i
\(29\) 90.3553 0.578571 0.289285 0.957243i \(-0.406582\pi\)
0.289285 + 0.957243i \(0.406582\pi\)
\(30\) 0 0
\(31\) −233.678 −1.35386 −0.676932 0.736046i \(-0.736691\pi\)
−0.676932 + 0.736046i \(0.736691\pi\)
\(32\) 154.422 154.422i 0.853070 0.853070i
\(33\) 0 0
\(34\) 316.381i 1.59585i
\(35\) 0 0
\(36\) 0 0
\(37\) 19.0042 + 19.0042i 0.0844399 + 0.0844399i 0.748065 0.663625i \(-0.230983\pi\)
−0.663625 + 0.748065i \(0.730983\pi\)
\(38\) 287.509 + 287.509i 1.22737 + 1.22737i
\(39\) 0 0
\(40\) 0 0
\(41\) 260.783i 0.993354i 0.867935 + 0.496677i \(0.165447\pi\)
−0.867935 + 0.496677i \(0.834553\pi\)
\(42\) 0 0
\(43\) −176.216 + 176.216i −0.624948 + 0.624948i −0.946792 0.321845i \(-0.895697\pi\)
0.321845 + 0.946792i \(0.395697\pi\)
\(44\) −217.624 −0.745638
\(45\) 0 0
\(46\) −208.485 −0.668250
\(47\) 145.788 145.788i 0.452456 0.452456i −0.443713 0.896169i \(-0.646339\pi\)
0.896169 + 0.443713i \(0.146339\pi\)
\(48\) 0 0
\(49\) 106.896i 0.311650i
\(50\) 0 0
\(51\) 0 0
\(52\) −276.311 276.311i −0.736875 0.736875i
\(53\) 183.285 + 183.285i 0.475022 + 0.475022i 0.903535 0.428513i \(-0.140962\pi\)
−0.428513 + 0.903535i \(0.640962\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 128.539i 0.306728i
\(57\) 0 0
\(58\) 236.858 236.858i 0.536223 0.536223i
\(59\) 279.564 0.616883 0.308441 0.951243i \(-0.400193\pi\)
0.308441 + 0.951243i \(0.400193\pi\)
\(60\) 0 0
\(61\) −390.267 −0.819157 −0.409578 0.912275i \(-0.634324\pi\)
−0.409578 + 0.912275i \(0.634324\pi\)
\(62\) −612.563 + 612.563i −1.25477 + 1.25477i
\(63\) 0 0
\(64\) 193.924i 0.378757i
\(65\) 0 0
\(66\) 0 0
\(67\) −150.444 150.444i −0.274324 0.274324i 0.556514 0.830838i \(-0.312139\pi\)
−0.830838 + 0.556514i \(0.812139\pi\)
\(68\) −346.596 346.596i −0.618103 0.618103i
\(69\) 0 0
\(70\) 0 0
\(71\) 470.042i 0.785686i −0.919605 0.392843i \(-0.871492\pi\)
0.919605 0.392843i \(-0.128508\pi\)
\(72\) 0 0
\(73\) −480.765 + 480.765i −0.770812 + 0.770812i −0.978249 0.207436i \(-0.933488\pi\)
0.207436 + 0.978249i \(0.433488\pi\)
\(74\) 99.6355 0.156519
\(75\) 0 0
\(76\) 629.934 0.950769
\(77\) 411.687 411.687i 0.609299 0.609299i
\(78\) 0 0
\(79\) 1322.44i 1.88337i 0.336497 + 0.941685i \(0.390758\pi\)
−0.336497 + 0.941685i \(0.609242\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 683.618 + 683.618i 0.920646 + 0.920646i
\(83\) −456.192 456.192i −0.603296 0.603296i 0.337890 0.941186i \(-0.390287\pi\)
−0.941186 + 0.337890i \(0.890287\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 923.868i 1.15841i
\(87\) 0 0
\(88\) 224.129 224.129i 0.271503 0.271503i
\(89\) −1364.85 −1.62555 −0.812774 0.582580i \(-0.802043\pi\)
−0.812774 + 0.582580i \(0.802043\pi\)
\(90\) 0 0
\(91\) 1045.41 1.20428
\(92\) −228.396 + 228.396i −0.258825 + 0.258825i
\(93\) 0 0
\(94\) 764.340i 0.838677i
\(95\) 0 0
\(96\) 0 0
\(97\) 785.308 + 785.308i 0.822020 + 0.822020i 0.986398 0.164377i \(-0.0525614\pi\)
−0.164377 + 0.986398i \(0.552561\pi\)
\(98\) −280.218 280.218i −0.288839 0.288839i
\(99\) 0 0
\(100\) 0 0
\(101\) 111.555i 0.109902i −0.998489 0.0549510i \(-0.982500\pi\)
0.998489 0.0549510i \(-0.0175003\pi\)
\(102\) 0 0
\(103\) −13.8820 + 13.8820i −0.0132800 + 0.0132800i −0.713716 0.700436i \(-0.752989\pi\)
0.700436 + 0.713716i \(0.252989\pi\)
\(104\) 569.142 0.536624
\(105\) 0 0
\(106\) 960.929 0.880507
\(107\) −776.165 + 776.165i −0.701259 + 0.701259i −0.964681 0.263422i \(-0.915149\pi\)
0.263422 + 0.964681i \(0.415149\pi\)
\(108\) 0 0
\(109\) 410.579i 0.360792i 0.983594 + 0.180396i \(0.0577379\pi\)
−0.983594 + 0.180396i \(0.942262\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 836.186 + 836.186i 0.705465 + 0.705465i
\(113\) −521.328 521.328i −0.434004 0.434004i 0.455984 0.889988i \(-0.349287\pi\)
−0.889988 + 0.455984i \(0.849287\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 518.956i 0.415378i
\(117\) 0 0
\(118\) 732.849 732.849i 0.571730 0.571730i
\(119\) 1311.34 1.01017
\(120\) 0 0
\(121\) −104.688 −0.0786538
\(122\) −1023.05 + 1023.05i −0.759199 + 0.759199i
\(123\) 0 0
\(124\) 1342.13i 0.971990i
\(125\) 0 0
\(126\) 0 0
\(127\) −786.555 786.555i −0.549571 0.549571i 0.376746 0.926317i \(-0.377043\pi\)
−0.926317 + 0.376746i \(0.877043\pi\)
\(128\) 727.025 + 727.025i 0.502036 + 0.502036i
\(129\) 0 0
\(130\) 0 0
\(131\) 448.364i 0.299036i 0.988759 + 0.149518i \(0.0477722\pi\)
−0.988759 + 0.149518i \(0.952228\pi\)
\(132\) 0 0
\(133\) −1191.67 + 1191.67i −0.776922 + 0.776922i
\(134\) −788.751 −0.508490
\(135\) 0 0
\(136\) 713.914 0.450129
\(137\) 950.120 950.120i 0.592512 0.592512i −0.345797 0.938309i \(-0.612391\pi\)
0.938309 + 0.345797i \(0.112391\pi\)
\(138\) 0 0
\(139\) 112.735i 0.0687918i 0.999408 + 0.0343959i \(0.0109507\pi\)
−0.999408 + 0.0343959i \(0.989049\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −1232.17 1232.17i −0.728179 0.728179i
\(143\) −1822.85 1822.85i −1.06598 1.06598i
\(144\) 0 0
\(145\) 0 0
\(146\) 2520.56i 1.42879i
\(147\) 0 0
\(148\) 109.151 109.151i 0.0606226 0.0606226i
\(149\) −1492.95 −0.820852 −0.410426 0.911894i \(-0.634620\pi\)
−0.410426 + 0.911894i \(0.634620\pi\)
\(150\) 0 0
\(151\) −2939.54 −1.58422 −0.792108 0.610381i \(-0.791016\pi\)
−0.792108 + 0.610381i \(0.791016\pi\)
\(152\) −648.764 + 648.764i −0.346196 + 0.346196i
\(153\) 0 0
\(154\) 2158.39i 1.12940i
\(155\) 0 0
\(156\) 0 0
\(157\) −156.386 156.386i −0.0794967 0.0794967i 0.666240 0.745737i \(-0.267902\pi\)
−0.745737 + 0.666240i \(0.767902\pi\)
\(158\) 3466.65 + 3466.65i 1.74552 + 1.74552i
\(159\) 0 0
\(160\) 0 0
\(161\) 864.129i 0.422999i
\(162\) 0 0
\(163\) 239.292 239.292i 0.114986 0.114986i −0.647272 0.762259i \(-0.724090\pi\)
0.762259 + 0.647272i \(0.224090\pi\)
\(164\) 1497.81 0.713167
\(165\) 0 0
\(166\) −2391.72 −1.11828
\(167\) 677.159 677.159i 0.313773 0.313773i −0.532596 0.846369i \(-0.678784\pi\)
0.846369 + 0.532596i \(0.178784\pi\)
\(168\) 0 0
\(169\) 2431.86i 1.10690i
\(170\) 0 0
\(171\) 0 0
\(172\) 1012.10 + 1012.10i 0.448674 + 0.448674i
\(173\) 441.523 + 441.523i 0.194037 + 0.194037i 0.797438 0.603401i \(-0.206188\pi\)
−0.603401 + 0.797438i \(0.706188\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 2916.06i 1.24890i
\(177\) 0 0
\(178\) −3577.82 + 3577.82i −1.50657 + 1.50657i
\(179\) −4724.27 −1.97267 −0.986337 0.164737i \(-0.947322\pi\)
−0.986337 + 0.164737i \(0.947322\pi\)
\(180\) 0 0
\(181\) −1548.35 −0.635847 −0.317923 0.948116i \(-0.602985\pi\)
−0.317923 + 0.948116i \(0.602985\pi\)
\(182\) 2740.45 2740.45i 1.11613 1.11613i
\(183\) 0 0
\(184\) 470.447i 0.188488i
\(185\) 0 0
\(186\) 0 0
\(187\) −2286.53 2286.53i −0.894159 0.894159i
\(188\) −837.336 837.336i −0.324835 0.324835i
\(189\) 0 0
\(190\) 0 0
\(191\) 1090.71i 0.413200i 0.978426 + 0.206600i \(0.0662398\pi\)
−0.978426 + 0.206600i \(0.933760\pi\)
\(192\) 0 0
\(193\) 2825.69 2825.69i 1.05387 1.05387i 0.0554112 0.998464i \(-0.482353\pi\)
0.998464 0.0554112i \(-0.0176470\pi\)
\(194\) 4117.22 1.52371
\(195\) 0 0
\(196\) −613.958 −0.223746
\(197\) 1163.99 1163.99i 0.420969 0.420969i −0.464569 0.885537i \(-0.653791\pi\)
0.885537 + 0.464569i \(0.153791\pi\)
\(198\) 0 0
\(199\) 520.257i 0.185327i −0.995697 0.0926633i \(-0.970462\pi\)
0.995697 0.0926633i \(-0.0295380\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −292.430 292.430i −0.101858 0.101858i
\(203\) 981.726 + 981.726i 0.339427 + 0.339427i
\(204\) 0 0
\(205\) 0 0
\(206\) 72.7808i 0.0246159i
\(207\) 0 0
\(208\) 3702.44 3702.44i 1.23422 1.23422i
\(209\) 4155.74 1.37540
\(210\) 0 0
\(211\) 5524.38 1.80244 0.901219 0.433365i \(-0.142674\pi\)
0.901219 + 0.433365i \(0.142674\pi\)
\(212\) 1052.70 1052.70i 0.341036 0.341036i
\(213\) 0 0
\(214\) 4069.28i 1.29986i
\(215\) 0 0
\(216\) 0 0
\(217\) −2538.95 2538.95i −0.794263 0.794263i
\(218\) 1076.29 + 1076.29i 0.334384 + 0.334384i
\(219\) 0 0
\(220\) 0 0
\(221\) 5806.30i 1.76730i
\(222\) 0 0
\(223\) −323.198 + 323.198i −0.0970537 + 0.0970537i −0.753967 0.656913i \(-0.771862\pi\)
0.656913 + 0.753967i \(0.271862\pi\)
\(224\) 3355.65 1.00093
\(225\) 0 0
\(226\) −2733.22 −0.804474
\(227\) −2739.76 + 2739.76i −0.801077 + 0.801077i −0.983264 0.182187i \(-0.941682\pi\)
0.182187 + 0.983264i \(0.441682\pi\)
\(228\) 0 0
\(229\) 230.334i 0.0664667i 0.999448 + 0.0332333i \(0.0105804\pi\)
−0.999448 + 0.0332333i \(0.989420\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 534.468 + 534.468i 0.151248 + 0.151248i
\(233\) −350.156 350.156i −0.0984526 0.0984526i 0.656165 0.754618i \(-0.272178\pi\)
−0.754618 + 0.656165i \(0.772178\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 1605.67i 0.442883i
\(237\) 0 0
\(238\) 3437.54 3437.54i 0.936229 0.936229i
\(239\) −1013.20 −0.274218 −0.137109 0.990556i \(-0.543781\pi\)
−0.137109 + 0.990556i \(0.543781\pi\)
\(240\) 0 0
\(241\) 2584.30 0.690744 0.345372 0.938466i \(-0.387753\pi\)
0.345372 + 0.938466i \(0.387753\pi\)
\(242\) −274.430 + 274.430i −0.0728968 + 0.0728968i
\(243\) 0 0
\(244\) 2241.50i 0.588104i
\(245\) 0 0
\(246\) 0 0
\(247\) 5276.43 + 5276.43i 1.35924 + 1.35924i
\(248\) −1382.25 1382.25i −0.353923 0.353923i
\(249\) 0 0
\(250\) 0 0
\(251\) 1708.34i 0.429599i −0.976658 0.214800i \(-0.931090\pi\)
0.976658 0.214800i \(-0.0689099\pi\)
\(252\) 0 0
\(253\) −1506.75 + 1506.75i −0.374422 + 0.374422i
\(254\) −4123.76 −1.01869
\(255\) 0 0
\(256\) 5363.04 1.30934
\(257\) 2659.48 2659.48i 0.645500 0.645500i −0.306402 0.951902i \(-0.599125\pi\)
0.951902 + 0.306402i \(0.0991252\pi\)
\(258\) 0 0
\(259\) 412.969i 0.0990757i
\(260\) 0 0
\(261\) 0 0
\(262\) 1175.34 + 1175.34i 0.277148 + 0.277148i
\(263\) −2307.03 2307.03i −0.540903 0.540903i 0.382891 0.923794i \(-0.374929\pi\)
−0.923794 + 0.382891i \(0.874929\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 6247.68i 1.44011i
\(267\) 0 0
\(268\) −864.078 + 864.078i −0.196948 + 0.196948i
\(269\) 447.584 0.101449 0.0507243 0.998713i \(-0.483847\pi\)
0.0507243 + 0.998713i \(0.483847\pi\)
\(270\) 0 0
\(271\) 1573.15 0.352627 0.176314 0.984334i \(-0.443583\pi\)
0.176314 + 0.984334i \(0.443583\pi\)
\(272\) 4644.23 4644.23i 1.03529 1.03529i
\(273\) 0 0
\(274\) 4981.29i 1.09829i
\(275\) 0 0
\(276\) 0 0
\(277\) −5816.91 5816.91i −1.26175 1.26175i −0.950245 0.311504i \(-0.899167\pi\)
−0.311504 0.950245i \(-0.600833\pi\)
\(278\) 295.524 + 295.524i 0.0637566 + 0.0637566i
\(279\) 0 0
\(280\) 0 0
\(281\) 140.032i 0.0297281i 0.999890 + 0.0148640i \(0.00473155\pi\)
−0.999890 + 0.0148640i \(0.995268\pi\)
\(282\) 0 0
\(283\) −4431.85 + 4431.85i −0.930905 + 0.930905i −0.997763 0.0668572i \(-0.978703\pi\)
0.0668572 + 0.997763i \(0.478703\pi\)
\(284\) −2699.69 −0.564074
\(285\) 0 0
\(286\) −9556.87 −1.97591
\(287\) −2833.46 + 2833.46i −0.582765 + 0.582765i
\(288\) 0 0
\(289\) 2370.24i 0.482442i
\(290\) 0 0
\(291\) 0 0
\(292\) 2761.28 + 2761.28i 0.553395 + 0.553395i
\(293\) −1244.45 1244.45i −0.248127 0.248127i 0.572074 0.820202i \(-0.306139\pi\)
−0.820202 + 0.572074i \(0.806139\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 224.827i 0.0441480i
\(297\) 0 0
\(298\) −3913.61 + 3913.61i −0.760771 + 0.760771i
\(299\) −3826.17 −0.740043
\(300\) 0 0
\(301\) −3829.24 −0.733269
\(302\) −7705.73 + 7705.73i −1.46826 + 1.46826i
\(303\) 0 0
\(304\) 8440.82i 1.59248i
\(305\) 0 0
\(306\) 0 0
\(307\) 7327.60 + 7327.60i 1.36224 + 1.36224i 0.871053 + 0.491189i \(0.163437\pi\)
0.491189 + 0.871053i \(0.336563\pi\)
\(308\) −2364.52 2364.52i −0.437439 0.437439i
\(309\) 0 0
\(310\) 0 0
\(311\) 7489.38i 1.36554i 0.730632 + 0.682771i \(0.239225\pi\)
−0.730632 + 0.682771i \(0.760775\pi\)
\(312\) 0 0
\(313\) 2456.04 2456.04i 0.443525 0.443525i −0.449670 0.893195i \(-0.648458\pi\)
0.893195 + 0.449670i \(0.148458\pi\)
\(314\) −819.903 −0.147356
\(315\) 0 0
\(316\) 7595.44 1.35214
\(317\) −6724.30 + 6724.30i −1.19140 + 1.19140i −0.214728 + 0.976674i \(0.568887\pi\)
−0.976674 + 0.214728i \(0.931113\pi\)
\(318\) 0 0
\(319\) 3423.60i 0.600894i
\(320\) 0 0
\(321\) 0 0
\(322\) −2265.23 2265.23i −0.392038 0.392038i
\(323\) 6618.59 + 6618.59i 1.14015 + 1.14015i
\(324\) 0 0
\(325\) 0 0
\(326\) 1254.56i 0.213140i
\(327\) 0 0
\(328\) −1542.58 + 1542.58i −0.259679 + 0.259679i
\(329\) 3168.03 0.530879
\(330\) 0 0
\(331\) −199.080 −0.0330586 −0.0165293 0.999863i \(-0.505262\pi\)
−0.0165293 + 0.999863i \(0.505262\pi\)
\(332\) −2620.14 + 2620.14i −0.433129 + 0.433129i
\(333\) 0 0
\(334\) 3550.21i 0.581614i
\(335\) 0 0
\(336\) 0 0
\(337\) −3308.77 3308.77i −0.534838 0.534838i 0.387170 0.922008i \(-0.373453\pi\)
−0.922008 + 0.387170i \(0.873453\pi\)
\(338\) −6374.88 6374.88i −1.02588 1.02588i
\(339\) 0 0
\(340\) 0 0
\(341\) 8854.16i 1.40610i
\(342\) 0 0
\(343\) 4888.20 4888.20i 0.769498 0.769498i
\(344\) −2084.71 −0.326744
\(345\) 0 0
\(346\) 2314.82 0.359669
\(347\) 2371.68 2371.68i 0.366912 0.366912i −0.499438 0.866350i \(-0.666460\pi\)
0.866350 + 0.499438i \(0.166460\pi\)
\(348\) 0 0
\(349\) 8208.92i 1.25906i 0.776975 + 0.629532i \(0.216753\pi\)
−0.776975 + 0.629532i \(0.783247\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −5851.13 5851.13i −0.885984 0.885984i
\(353\) 6800.98 + 6800.98i 1.02544 + 1.02544i 0.999668 + 0.0257707i \(0.00820398\pi\)
0.0257707 + 0.999668i \(0.491796\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 7839.01i 1.16704i
\(357\) 0 0
\(358\) −12384.2 + 12384.2i −1.82829 + 1.82829i
\(359\) 1778.14 0.261411 0.130705 0.991421i \(-0.458276\pi\)
0.130705 + 0.991421i \(0.458276\pi\)
\(360\) 0 0
\(361\) −5170.20 −0.753783
\(362\) −4058.86 + 4058.86i −0.589306 + 0.589306i
\(363\) 0 0
\(364\) 6004.34i 0.864596i
\(365\) 0 0
\(366\) 0 0
\(367\) 4673.56 + 4673.56i 0.664735 + 0.664735i 0.956492 0.291757i \(-0.0942400\pi\)
−0.291757 + 0.956492i \(0.594240\pi\)
\(368\) −3060.40 3060.40i −0.433517 0.433517i
\(369\) 0 0
\(370\) 0 0
\(371\) 3982.85i 0.557357i
\(372\) 0 0
\(373\) 5729.37 5729.37i 0.795323 0.795323i −0.187031 0.982354i \(-0.559886\pi\)
0.982354 + 0.187031i \(0.0598865\pi\)
\(374\) −11987.8 −1.65742
\(375\) 0 0
\(376\) 1724.73 0.236559
\(377\) 4346.86 4346.86i 0.593832 0.593832i
\(378\) 0 0
\(379\) 153.883i 0.0208561i 0.999946 + 0.0104280i \(0.00331941\pi\)
−0.999946 + 0.0104280i \(0.996681\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 2859.19 + 2859.19i 0.382956 + 0.382956i
\(383\) −4297.76 4297.76i −0.573382 0.573382i 0.359690 0.933072i \(-0.382882\pi\)
−0.933072 + 0.359690i \(0.882882\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 14814.6i 1.95347i
\(387\) 0 0
\(388\) 4510.42 4510.42i 0.590160 0.590160i
\(389\) 7833.00 1.02095 0.510474 0.859893i \(-0.329470\pi\)
0.510474 + 0.859893i \(0.329470\pi\)
\(390\) 0 0
\(391\) −4799.42 −0.620760
\(392\) 632.310 632.310i 0.0814706 0.0814706i
\(393\) 0 0
\(394\) 6102.57i 0.780312i
\(395\) 0 0
\(396\) 0 0
\(397\) 10195.4 + 10195.4i 1.28889 + 1.28889i 0.935459 + 0.353435i \(0.114987\pi\)
0.353435 + 0.935459i \(0.385013\pi\)
\(398\) −1363.80 1363.80i −0.171762 0.171762i
\(399\) 0 0
\(400\) 0 0
\(401\) 10778.3i 1.34226i −0.741341 0.671128i \(-0.765810\pi\)
0.741341 0.671128i \(-0.234190\pi\)
\(402\) 0 0
\(403\) −11241.9 + 11241.9i −1.38957 + 1.38957i
\(404\) −640.714 −0.0789028
\(405\) 0 0
\(406\) 5147.00 0.629165
\(407\) 720.079 720.079i 0.0876978 0.0876978i
\(408\) 0 0
\(409\) 4629.92i 0.559743i 0.960037 + 0.279872i \(0.0902919\pi\)
−0.960037 + 0.279872i \(0.909708\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 79.7315 + 79.7315i 0.00953420 + 0.00953420i
\(413\) 3037.51 + 3037.51i 0.361903 + 0.361903i
\(414\) 0 0
\(415\) 0 0
\(416\) 14858.0i 1.75114i
\(417\) 0 0
\(418\) 10893.9 10893.9i 1.27473 1.27473i
\(419\) 11276.5 1.31478 0.657389 0.753551i \(-0.271661\pi\)
0.657389 + 0.753551i \(0.271661\pi\)
\(420\) 0 0
\(421\) 3387.58 0.392163 0.196082 0.980588i \(-0.437178\pi\)
0.196082 + 0.980588i \(0.437178\pi\)
\(422\) 14481.6 14481.6i 1.67051 1.67051i
\(423\) 0 0
\(424\) 2168.33i 0.248358i
\(425\) 0 0
\(426\) 0 0
\(427\) −4240.32 4240.32i −0.480570 0.480570i
\(428\) 4457.91 + 4457.91i 0.503461 + 0.503461i
\(429\) 0 0
\(430\) 0 0
\(431\) 16161.7i 1.80623i 0.429402 + 0.903113i \(0.358724\pi\)
−0.429402 + 0.903113i \(0.641276\pi\)
\(432\) 0 0
\(433\) 3808.79 3808.79i 0.422722 0.422722i −0.463418 0.886140i \(-0.653377\pi\)
0.886140 + 0.463418i \(0.153377\pi\)
\(434\) −13311.2 −1.47226
\(435\) 0 0
\(436\) 2358.16 0.259026
\(437\) 4361.44 4361.44i 0.477428 0.477428i
\(438\) 0 0
\(439\) 1607.30i 0.174744i 0.996176 + 0.0873718i \(0.0278468\pi\)
−0.996176 + 0.0873718i \(0.972153\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −15220.6 15220.6i −1.63795 1.63795i
\(443\) −8296.60 8296.60i −0.889805 0.889805i 0.104699 0.994504i \(-0.466612\pi\)
−0.994504 + 0.104699i \(0.966612\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 1694.47i 0.179900i
\(447\) 0 0
\(448\) 2107.02 2107.02i 0.222203 0.222203i
\(449\) 15061.8 1.58309 0.791547 0.611108i \(-0.209276\pi\)
0.791547 + 0.611108i \(0.209276\pi\)
\(450\) 0 0
\(451\) 9881.20 1.03168
\(452\) −2994.25 + 2994.25i −0.311588 + 0.311588i
\(453\) 0 0
\(454\) 14364.0i 1.48489i
\(455\) 0 0
\(456\) 0 0
\(457\) −2671.27 2671.27i −0.273428 0.273428i 0.557050 0.830479i \(-0.311933\pi\)
−0.830479 + 0.557050i \(0.811933\pi\)
\(458\) 603.797 + 603.797i 0.0616017 + 0.0616017i
\(459\) 0 0
\(460\) 0 0
\(461\) 12809.1i 1.29410i −0.762449 0.647049i \(-0.776003\pi\)
0.762449 0.647049i \(-0.223997\pi\)
\(462\) 0 0
\(463\) 11154.1 11154.1i 1.11960 1.11960i 0.127804 0.991799i \(-0.459207\pi\)
0.991799 0.127804i \(-0.0407927\pi\)
\(464\) 6953.76 0.695733
\(465\) 0 0
\(466\) −1835.80 −0.182493
\(467\) −7905.44 + 7905.44i −0.783341 + 0.783341i −0.980393 0.197052i \(-0.936863\pi\)
0.197052 + 0.980393i \(0.436863\pi\)
\(468\) 0 0
\(469\) 3269.21i 0.321872i
\(470\) 0 0
\(471\) 0 0
\(472\) 1653.67 + 1653.67i 0.161263 + 0.161263i
\(473\) 6676.92 + 6676.92i 0.649060 + 0.649060i
\(474\) 0 0
\(475\) 0 0
\(476\) 7531.66i 0.725238i
\(477\) 0 0
\(478\) −2655.99 + 2655.99i −0.254147 + 0.254147i
\(479\) −10715.8 −1.02217 −0.511085 0.859530i \(-0.670756\pi\)
−0.511085 + 0.859530i \(0.670756\pi\)
\(480\) 0 0
\(481\) 1828.53 0.173334
\(482\) 6774.48 6774.48i 0.640185 0.640185i
\(483\) 0 0
\(484\) 601.277i 0.0564685i
\(485\) 0 0
\(486\) 0 0
\(487\) 4489.84 + 4489.84i 0.417770 + 0.417770i 0.884435 0.466664i \(-0.154544\pi\)
−0.466664 + 0.884435i \(0.654544\pi\)
\(488\) −2308.50 2308.50i −0.214141 0.214141i
\(489\) 0 0
\(490\) 0 0
\(491\) 15174.1i 1.39470i −0.716729 0.697352i \(-0.754362\pi\)
0.716729 0.697352i \(-0.245638\pi\)
\(492\) 0 0
\(493\) 5452.56 5452.56i 0.498116 0.498116i
\(494\) 27663.3 2.51950
\(495\) 0 0
\(496\) −17983.9 −1.62802
\(497\) 5107.09 5107.09i 0.460934 0.460934i
\(498\) 0 0
\(499\) 8887.20i 0.797286i −0.917106 0.398643i \(-0.869481\pi\)
0.917106 0.398643i \(-0.130519\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −4478.25 4478.25i −0.398155 0.398155i
\(503\) 12740.5 + 12740.5i 1.12936 + 1.12936i 0.990281 + 0.139084i \(0.0444158\pi\)
0.139084 + 0.990281i \(0.455584\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 7899.61i 0.694033i
\(507\) 0 0
\(508\) −4517.58 + 4517.58i −0.394558 + 0.394558i
\(509\) −9257.00 −0.806108 −0.403054 0.915176i \(-0.632051\pi\)
−0.403054 + 0.915176i \(0.632051\pi\)
\(510\) 0 0
\(511\) −10447.2 −0.904416
\(512\) 8242.49 8242.49i 0.711465 0.711465i
\(513\) 0 0
\(514\) 13943.1i 1.19651i
\(515\) 0 0
\(516\) 0 0
\(517\) −5523.99 5523.99i −0.469913 0.469913i
\(518\) 1082.56 + 1082.56i 0.0918240 + 0.0918240i
\(519\) 0 0
\(520\) 0 0
\(521\) 13563.3i 1.14054i 0.821458 + 0.570268i \(0.193161\pi\)
−0.821458 + 0.570268i \(0.806839\pi\)
\(522\) 0 0
\(523\) −11193.8 + 11193.8i −0.935894 + 0.935894i −0.998065 0.0621714i \(-0.980197\pi\)
0.0621714 + 0.998065i \(0.480197\pi\)
\(524\) 2575.18 0.214689
\(525\) 0 0
\(526\) −12095.3 −1.00262
\(527\) −14101.5 + 14101.5i −1.16560 + 1.16560i
\(528\) 0 0
\(529\) 9004.33i 0.740062i
\(530\) 0 0
\(531\) 0 0
\(532\) 6844.34 + 6844.34i 0.557782 + 0.557782i
\(533\) 12545.9 + 12545.9i 1.01956 + 1.01956i
\(534\) 0 0
\(535\) 0 0
\(536\) 1779.81i 0.143426i
\(537\) 0 0
\(538\) 1173.30 1173.30i 0.0940231 0.0940231i
\(539\) −4050.34 −0.323675
\(540\) 0 0
\(541\) 1383.33 0.109934 0.0549668 0.998488i \(-0.482495\pi\)
0.0549668 + 0.998488i \(0.482495\pi\)
\(542\) 4123.86 4123.86i 0.326817 0.326817i
\(543\) 0 0
\(544\) 18637.5i 1.46889i
\(545\) 0 0
\(546\) 0 0
\(547\) −2181.76 2181.76i −0.170540 0.170540i 0.616677 0.787217i \(-0.288479\pi\)
−0.787217 + 0.616677i \(0.788479\pi\)
\(548\) −5457.01 5457.01i −0.425387 0.425387i
\(549\) 0 0
\(550\) 0 0
\(551\) 9909.96i 0.766204i
\(552\) 0 0
\(553\) −14368.5 + 14368.5i −1.10491 + 1.10491i
\(554\) −30496.9 −2.33879
\(555\) 0 0
\(556\) 647.494 0.0493882
\(557\) 15674.9 15674.9i 1.19240 1.19240i 0.216007 0.976392i \(-0.430697\pi\)
0.976392 0.216007i \(-0.0693035\pi\)
\(558\) 0 0
\(559\) 16955.0i 1.28286i
\(560\) 0 0
\(561\) 0 0
\(562\) 367.080 + 367.080i 0.0275522 + 0.0275522i
\(563\) −8213.60 8213.60i −0.614852 0.614852i 0.329354 0.944206i \(-0.393169\pi\)
−0.944206 + 0.329354i \(0.893169\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 23235.3i 1.72554i
\(567\) 0 0
\(568\) 2780.39 2780.39i 0.205392 0.205392i
\(569\) −16902.1 −1.24530 −0.622648 0.782502i \(-0.713943\pi\)
−0.622648 + 0.782502i \(0.713943\pi\)
\(570\) 0 0
\(571\) 6507.12 0.476908 0.238454 0.971154i \(-0.423359\pi\)
0.238454 + 0.971154i \(0.423359\pi\)
\(572\) −10469.6 + 10469.6i −0.765305 + 0.765305i
\(573\) 0 0
\(574\) 14855.3i 1.08022i
\(575\) 0 0
\(576\) 0 0
\(577\) −7884.54 7884.54i −0.568870 0.568870i 0.362942 0.931812i \(-0.381772\pi\)
−0.931812 + 0.362942i \(0.881772\pi\)
\(578\) −6213.35 6213.35i −0.447130 0.447130i
\(579\) 0 0
\(580\) 0 0
\(581\) 9913.20i 0.707864i
\(582\) 0 0
\(583\) 6944.77 6944.77i 0.493350 0.493350i
\(584\) −5687.63 −0.403007
\(585\) 0 0
\(586\) −6524.39 −0.459932
\(587\) −9548.44 + 9548.44i −0.671390 + 0.671390i −0.958037 0.286646i \(-0.907460\pi\)
0.286646 + 0.958037i \(0.407460\pi\)
\(588\) 0 0
\(589\) 25629.2i 1.79293i
\(590\) 0 0
\(591\) 0 0
\(592\) 1462.57 + 1462.57i 0.101539 + 0.101539i
\(593\) −3491.97 3491.97i −0.241818 0.241818i 0.575784 0.817602i \(-0.304697\pi\)
−0.817602 + 0.575784i \(0.804697\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 8574.75i 0.589321i
\(597\) 0 0
\(598\) −10029.9 + 10029.9i −0.685876 + 0.685876i
\(599\) 11203.0 0.764175 0.382087 0.924126i \(-0.375205\pi\)
0.382087 + 0.924126i \(0.375205\pi\)
\(600\) 0 0
\(601\) −13953.5 −0.947048 −0.473524 0.880781i \(-0.657018\pi\)
−0.473524 + 0.880781i \(0.657018\pi\)
\(602\) −10038.0 + 10038.0i −0.679598 + 0.679598i
\(603\) 0 0
\(604\) 16883.3i 1.13737i
\(605\) 0 0
\(606\) 0 0
\(607\) 1292.54 + 1292.54i 0.0864293 + 0.0864293i 0.749000 0.662570i \(-0.230534\pi\)
−0.662570 + 0.749000i \(0.730534\pi\)
\(608\) 16936.7 + 16936.7i 1.12972 + 1.12972i
\(609\) 0 0
\(610\) 0 0
\(611\) 14027.3i 0.928780i
\(612\) 0 0
\(613\) −225.964 + 225.964i −0.0148884 + 0.0148884i −0.714512 0.699623i \(-0.753351\pi\)
0.699623 + 0.714512i \(0.253351\pi\)
\(614\) 38417.2 2.52507
\(615\) 0 0
\(616\) 4870.41 0.318562
\(617\) −2717.41 + 2717.41i −0.177308 + 0.177308i −0.790181 0.612873i \(-0.790014\pi\)
0.612873 + 0.790181i \(0.290014\pi\)
\(618\) 0 0
\(619\) 8870.55i 0.575989i 0.957632 + 0.287995i \(0.0929886\pi\)
−0.957632 + 0.287995i \(0.907011\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 19632.7 + 19632.7i 1.26559 + 1.26559i
\(623\) −14829.3 14829.3i −0.953650 0.953650i
\(624\) 0 0
\(625\) 0 0
\(626\) 12876.5i 0.822123i
\(627\) 0 0
\(628\) −898.205 + 898.205i −0.0570737 + 0.0570737i
\(629\) 2293.65 0.145396
\(630\) 0 0
\(631\) 29762.7 1.87771 0.938853 0.344318i \(-0.111890\pi\)
0.938853 + 0.344318i \(0.111890\pi\)
\(632\) −7822.48 + 7822.48i −0.492344 + 0.492344i
\(633\) 0 0
\(634\) 35254.2i 2.20840i
\(635\) 0 0
\(636\) 0 0
\(637\) −5142.61 5142.61i −0.319871 0.319871i
\(638\) −8974.65 8974.65i −0.556912 0.556912i
\(639\) 0 0
\(640\) 0 0
\(641\) 5168.75i 0.318492i 0.987239 + 0.159246i \(0.0509063\pi\)
−0.987239 + 0.159246i \(0.949094\pi\)
\(642\) 0 0
\(643\) 2078.46 2078.46i 0.127475 0.127475i −0.640491 0.767966i \(-0.721269\pi\)
0.767966 + 0.640491i \(0.221269\pi\)
\(644\) −4963.13 −0.303687
\(645\) 0 0
\(646\) 34700.0 2.11339
\(647\) −10765.7 + 10765.7i −0.654164 + 0.654164i −0.953993 0.299829i \(-0.903070\pi\)
0.299829 + 0.953993i \(0.403070\pi\)
\(648\) 0 0
\(649\) 10592.8i 0.640684i
\(650\) 0 0
\(651\) 0 0
\(652\) −1374.37 1374.37i −0.0825530 0.0825530i
\(653\) −12815.1 12815.1i −0.767984 0.767984i 0.209767 0.977751i \(-0.432729\pi\)
−0.977751 + 0.209767i \(0.932729\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 20069.9i 1.19451i
\(657\) 0 0
\(658\) 8304.68 8304.68i 0.492022 0.492022i
\(659\) −16634.8 −0.983307 −0.491654 0.870791i \(-0.663607\pi\)
−0.491654 + 0.870791i \(0.663607\pi\)
\(660\) 0 0
\(661\) −10835.6 −0.637601 −0.318800 0.947822i \(-0.603280\pi\)
−0.318800 + 0.947822i \(0.603280\pi\)
\(662\) −521.868 + 521.868i −0.0306389 + 0.0306389i
\(663\) 0 0
\(664\) 5396.92i 0.315423i
\(665\) 0 0
\(666\) 0 0
\(667\) −3593.07 3593.07i −0.208582 0.208582i
\(668\) −3889.27 3889.27i −0.225270 0.225270i
\(669\) 0 0
\(670\) 0 0
\(671\) 14787.4i 0.850762i
\(672\) 0 0
\(673\) 16220.3 16220.3i 0.929045 0.929045i −0.0685992 0.997644i \(-0.521853\pi\)
0.997644 + 0.0685992i \(0.0218530\pi\)
\(674\) −17347.3 −0.991382
\(675\) 0 0
\(676\) −13967.4 −0.794685
\(677\) 11196.6 11196.6i 0.635626 0.635626i −0.313847 0.949473i \(-0.601618\pi\)
0.949473 + 0.313847i \(0.101618\pi\)
\(678\) 0 0
\(679\) 17065.0i 0.964500i
\(680\) 0 0
\(681\) 0 0
\(682\) 23210.3 + 23210.3i 1.30318 + 1.30318i
\(683\) −15428.1 15428.1i −0.864331 0.864331i 0.127507 0.991838i \(-0.459303\pi\)
−0.991838 + 0.127507i \(0.959303\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 25627.9i 1.42635i
\(687\) 0 0
\(688\) −13561.6 + 13561.6i −0.751501 + 0.751501i
\(689\) 17635.2 0.975104
\(690\) 0 0
\(691\) 21858.6 1.20339 0.601693 0.798728i \(-0.294493\pi\)
0.601693 + 0.798728i \(0.294493\pi\)
\(692\) 2535.89 2535.89i 0.139307 0.139307i
\(693\) 0 0
\(694\) 12434.2i 0.680112i
\(695\) 0 0
\(696\) 0 0
\(697\) 15737.2 + 15737.2i 0.855220 + 0.855220i
\(698\) 21518.9 + 21518.9i 1.16691 + 1.16691i
\(699\) 0 0
\(700\) 0 0
\(701\) 8846.82i 0.476662i −0.971184 0.238331i \(-0.923400\pi\)
0.971184 0.238331i \(-0.0766002\pi\)
\(702\) 0 0
\(703\) −2084.34 + 2084.34i −0.111824 + 0.111824i
\(704\) −7347.86 −0.393371
\(705\) 0 0
\(706\) 35656.2 1.90076
\(707\) 1212.06 1212.06i 0.0644755 0.0644755i
\(708\) 0 0
\(709\) 23189.8i 1.22837i −0.789163 0.614184i \(-0.789485\pi\)
0.789163 0.614184i \(-0.210515\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −8073.34 8073.34i −0.424945 0.424945i
\(713\) 9292.43 + 9292.43i 0.488084 + 0.488084i
\(714\) 0 0
\(715\) 0 0
\(716\) 27133.9i 1.41626i
\(717\) 0 0
\(718\) 4661.21 4661.21i 0.242277 0.242277i
\(719\) −7005.29 −0.363356 −0.181678 0.983358i \(-0.558153\pi\)
−0.181678 + 0.983358i \(0.558153\pi\)
\(720\) 0 0
\(721\) −301.661 −0.0155818
\(722\) −13553.2 + 13553.2i −0.698611 + 0.698611i
\(723\) 0 0
\(724\) 8892.98i 0.456498i
\(725\) 0 0
\(726\) 0 0
\(727\) 16025.7 + 16025.7i 0.817553 + 0.817553i 0.985753 0.168200i \(-0.0537954\pi\)
−0.168200 + 0.985753i \(0.553795\pi\)
\(728\) 6183.82 + 6183.82i 0.314818 + 0.314818i
\(729\) 0 0
\(730\) 0 0
\(731\) 21267.8i 1.07609i
\(732\) 0 0
\(733\) 3319.43 3319.43i 0.167266 0.167266i −0.618511 0.785777i \(-0.712264\pi\)
0.785777 + 0.618511i \(0.212264\pi\)
\(734\) 24502.5 1.23216
\(735\) 0 0
\(736\) −12281.5 −0.615084
\(737\) −5700.41 + 5700.41i −0.284908 + 0.284908i
\(738\) 0 0
\(739\) 19979.4i 0.994526i 0.867600 + 0.497263i \(0.165662\pi\)
−0.867600 + 0.497263i \(0.834338\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 10440.7 + 10440.7i 0.516562 + 0.516562i
\(743\) −14574.6 14574.6i −0.719637 0.719637i 0.248894 0.968531i \(-0.419933\pi\)
−0.968531 + 0.248894i \(0.919933\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 30038.0i 1.47422i
\(747\) 0 0
\(748\) −13132.7 + 13132.7i −0.641951 + 0.641951i
\(749\) −16866.3 −0.822807
\(750\) 0 0
\(751\) −11620.1 −0.564612 −0.282306 0.959324i \(-0.591099\pi\)
−0.282306 + 0.959324i \(0.591099\pi\)
\(752\) 11219.9 11219.9i 0.544079 0.544079i
\(753\) 0 0
\(754\) 22789.7i 1.10073i
\(755\) 0 0
\(756\) 0 0
\(757\) −10502.0 10502.0i −0.504229 0.504229i 0.408520 0.912749i \(-0.366045\pi\)
−0.912749 + 0.408520i \(0.866045\pi\)
\(758\) 403.390 + 403.390i 0.0193296 + 0.0193296i
\(759\) 0 0
\(760\) 0 0
\(761\) 36489.6i 1.73817i −0.494664 0.869085i \(-0.664709\pi\)
0.494664 0.869085i \(-0.335291\pi\)
\(762\) 0 0
\(763\) −4461.01 + 4461.01i −0.211664 + 0.211664i
\(764\) 6264.50 0.296652
\(765\) 0 0
\(766\) −22532.3 −1.06283
\(767\) 13449.4 13449.4i 0.633154 0.633154i
\(768\) 0 0
\(769\) 30323.9i 1.42199i 0.703198 + 0.710994i \(0.251755\pi\)
−0.703198 + 0.710994i \(0.748245\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −16229.4 16229.4i −0.756617 0.756617i
\(773\) −10327.2 10327.2i −0.480522 0.480522i 0.424777 0.905298i \(-0.360353\pi\)
−0.905298 + 0.424777i \(0.860353\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 9290.49i 0.429780i
\(777\) 0 0
\(778\) 20533.4 20533.4i 0.946220 0.946220i
\(779\) −28602.1 −1.31550
\(780\) 0 0
\(781\) −17810.1 −0.816000
\(782\) −12581.2 + 12581.2i −0.575324 + 0.575324i
\(783\) 0 0
\(784\) 8226.74i 0.374760i
\(785\) 0 0
\(786\) 0 0
\(787\) −21521.8 21521.8i −0.974802 0.974802i 0.0248882 0.999690i \(-0.492077\pi\)
−0.999690 + 0.0248882i \(0.992077\pi\)
\(788\) −6685.38 6685.38i −0.302229 0.302229i
\(789\) 0 0
\(790\) 0 0
\(791\) 11328.6i 0.509229i
\(792\) 0 0
\(793\) −18775.2 + 18775.2i −0.840764 + 0.840764i
\(794\) 53452.3 2.38911