Properties

Label 45.4.f.a.8.2
Level $45$
Weight $4$
Character 45.8
Analytic conductor $2.655$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 45.f (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.65508595026\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \( x^{12} - 16x^{10} - 14x^{8} - 512x^{6} + 3889x^{4} + 126224x^{2} + 506944 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{10}\cdot 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 8.2
Root \(-0.347140 + 2.27426i\) of defining polynomial
Character \(\chi\) \(=\) 45.8
Dual form 45.4.f.a.17.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.62140 - 2.62140i) q^{2} +5.74350i q^{4} +(-8.38994 - 7.38978i) q^{5} +(-10.8652 + 10.8652i) q^{7} +(-5.91519 + 5.91519i) q^{8} +O(q^{10})\) \(q+(-2.62140 - 2.62140i) q^{2} +5.74350i q^{4} +(-8.38994 - 7.38978i) q^{5} +(-10.8652 + 10.8652i) q^{7} +(-5.91519 + 5.91519i) q^{8} +(2.62183 + 41.3650i) q^{10} +37.8905i q^{11} +(-48.1085 - 48.1085i) q^{13} +56.9640 q^{14} +76.9602 q^{16} +(-60.3458 - 60.3458i) q^{17} -109.678i q^{19} +(42.4432 - 48.1877i) q^{20} +(99.3262 - 99.3262i) q^{22} +(39.7660 - 39.7660i) q^{23} +(15.7823 + 124.000i) q^{25} +252.224i q^{26} +(-62.4042 - 62.4042i) q^{28} +90.3553 q^{29} -233.678 q^{31} +(-154.422 - 154.422i) q^{32} +316.381i q^{34} +(171.449 - 10.8670i) q^{35} +(-19.0042 + 19.0042i) q^{37} +(-287.509 + 287.509i) q^{38} +(93.3400 - 5.91616i) q^{40} -260.783i q^{41} +(176.216 + 176.216i) q^{43} -217.624 q^{44} -208.485 q^{46} +(-145.788 - 145.788i) q^{47} +106.896i q^{49} +(283.681 - 366.425i) q^{50} +(276.311 - 276.311i) q^{52} +(-183.285 + 183.285i) q^{53} +(280.002 - 317.899i) q^{55} -128.539i q^{56} +(-236.858 - 236.858i) q^{58} +279.564 q^{59} -390.267 q^{61} +(612.563 + 612.563i) q^{62} +193.924i q^{64} +(48.1164 + 759.139i) q^{65} +(150.444 - 150.444i) q^{67} +(346.596 - 346.596i) q^{68} +(-477.925 - 420.951i) q^{70} +470.042i q^{71} +(480.765 + 480.765i) q^{73} +99.6355 q^{74} +629.934 q^{76} +(-411.687 - 411.687i) q^{77} -1322.44i q^{79} +(-645.692 - 568.719i) q^{80} +(-683.618 + 683.618i) q^{82} +(456.192 - 456.192i) q^{83} +(60.3558 + 952.240i) q^{85} -923.868i q^{86} +(-224.129 - 224.129i) q^{88} -1364.85 q^{89} +1045.41 q^{91} +(228.396 + 228.396i) q^{92} +764.340i q^{94} +(-810.494 + 920.190i) q^{95} +(-785.308 + 785.308i) q^{97} +(280.218 - 280.218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 24 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 24 q^{7} + 192 q^{10} - 108 q^{13} - 648 q^{16} + 1056 q^{22} - 144 q^{25} - 576 q^{28} - 1248 q^{31} + 828 q^{37} + 2568 q^{40} - 96 q^{43} + 672 q^{46} - 312 q^{52} - 1512 q^{55} - 3864 q^{58} + 96 q^{61} + 1632 q^{67} - 1536 q^{70} + 3972 q^{73} - 480 q^{76} - 7848 q^{82} - 1752 q^{85} + 7968 q^{88} + 4752 q^{91} + 2772 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(37\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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 \(-0.477479\pi\)
−0.997498 + 0.0706924i \(0.977479\pi\)
\(3\) 0 0
\(4\) 5.74350i 0.717938i
\(5\) −8.38994 7.38978i −0.750419 0.660962i
\(6\) 0 0
\(7\) −10.8652 + 10.8652i −0.586664 + 0.586664i −0.936726 0.350062i \(-0.886160\pi\)
0.350062 + 0.936726i \(0.386160\pi\)
\(8\) −5.91519 + 5.91519i −0.261417 + 0.261417i
\(9\) 0 0
\(10\) 2.62183 + 41.3650i 0.0829097 + 1.30808i
\(11\) 37.8905i 1.03858i 0.854597 + 0.519291i \(0.173804\pi\)
−0.854597 + 0.519291i \(0.826196\pi\)
\(12\) 0 0
\(13\) −48.1085 48.1085i −1.02638 1.02638i −0.999643 0.0267344i \(-0.991489\pi\)
−0.0267344 0.999643i \(-0.508511\pi\)
\(14\) 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 \(-0.458340\pi\)
−0.991448 + 0.130506i \(0.958340\pi\)
\(18\) 0 0
\(19\) 109.678i 1.32430i −0.749369 0.662152i \(-0.769643\pi\)
0.749369 0.662152i \(-0.230357\pi\)
\(20\) 42.4432 48.1877i 0.474530 0.538755i
\(21\) 0 0
\(22\) 99.3262 99.3262i 0.962564 0.962564i
\(23\) 39.7660 39.7660i 0.360512 0.360512i −0.503489 0.864002i \(-0.667951\pi\)
0.864002 + 0.503489i \(0.167951\pi\)
\(24\) 0 0
\(25\) 15.7823 + 124.000i 0.126259 + 0.991997i
\(26\) 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
\(35\) 171.449 10.8670i 0.828007 0.0524815i
\(36\) 0 0
\(37\) −19.0042 + 19.0042i −0.0844399 + 0.0844399i −0.748065 0.663625i \(-0.769017\pi\)
0.663625 + 0.748065i \(0.269017\pi\)
\(38\) −287.509 + 287.509i −1.22737 + 1.22737i
\(39\) 0 0
\(40\) 93.3400 5.91616i 0.368959 0.0233857i
\(41\) 260.783i 0.993354i −0.867935 0.496677i \(-0.834553\pi\)
0.867935 0.496677i \(-0.165447\pi\)
\(42\) 0 0
\(43\) 176.216 + 176.216i 0.624948 + 0.624948i 0.946792 0.321845i \(-0.104303\pi\)
−0.321845 + 0.946792i \(0.604303\pi\)
\(44\) −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 \(-0.353661\pi\)
−0.896169 + 0.443713i \(0.853661\pi\)
\(48\) 0 0
\(49\) 106.896i 0.311650i
\(50\) 283.681 366.425i 0.802372 1.03641i
\(51\) 0 0
\(52\) 276.311 276.311i 0.736875 0.736875i
\(53\) −183.285 + 183.285i −0.475022 + 0.475022i −0.903535 0.428513i \(-0.859038\pi\)
0.428513 + 0.903535i \(0.359038\pi\)
\(54\) 0 0
\(55\) 280.002 317.899i 0.686464 0.779373i
\(56\) 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
\(65\) 48.1164 + 759.139i 0.0918170 + 1.44861i
\(66\) 0 0
\(67\) 150.444 150.444i 0.274324 0.274324i −0.556514 0.830838i \(-0.687861\pi\)
0.830838 + 0.556514i \(0.187861\pi\)
\(68\) 346.596 346.596i 0.618103 0.618103i
\(69\) 0 0
\(70\) −477.925 420.951i −0.816042 0.718761i
\(71\) 470.042i 0.785686i 0.919605 + 0.392843i \(0.128508\pi\)
−0.919605 + 0.392843i \(0.871492\pi\)
\(72\) 0 0
\(73\) 480.765 + 480.765i 0.770812 + 0.770812i 0.978249 0.207436i \(-0.0665119\pi\)
−0.207436 + 0.978249i \(0.566512\pi\)
\(74\) 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 \(-0.609242\pi\)
0.336497 0.941685i \(-0.390758\pi\)
\(80\) −645.692 568.719i −0.902382 0.794809i
\(81\) 0 0
\(82\) −683.618 + 683.618i −0.920646 + 0.920646i
\(83\) 456.192 456.192i 0.603296 0.603296i −0.337890 0.941186i \(-0.609713\pi\)
0.941186 + 0.337890i \(0.109713\pi\)
\(84\) 0 0
\(85\) 60.3558 + 952.240i 0.0770177 + 1.21512i
\(86\) 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
\(95\) −810.494 + 920.190i −0.875315 + 0.993784i
\(96\) 0 0
\(97\) −785.308 + 785.308i −0.822020 + 0.822020i −0.986398 0.164377i \(-0.947439\pi\)
0.164377 + 0.986398i \(0.447439\pi\)
\(98\) 280.218 280.218i 0.288839 0.288839i
\(99\) 0 0
\(100\) −712.193 + 90.6458i −0.712193 + 0.0906458i
\(101\) 111.555i 0.109902i 0.998489 + 0.0549510i \(0.0175003\pi\)
−0.998489 + 0.0549510i \(0.982500\pi\)
\(102\) 0 0
\(103\) 13.8820 + 13.8820i 0.0132800 + 0.0132800i 0.713716 0.700436i \(-0.247011\pi\)
−0.700436 + 0.713716i \(0.747011\pi\)
\(104\) 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 \(-0.0848510\pi\)
−0.263422 + 0.964681i \(0.584851\pi\)
\(108\) 0 0
\(109\) 410.579i 0.360792i −0.983594 0.180396i \(-0.942262\pi\)
0.983594 0.180396i \(-0.0577379\pi\)
\(110\) −1567.34 + 99.3425i −1.35855 + 0.0861085i
\(111\) 0 0
\(112\) −836.186 + 836.186i −0.705465 + 0.705465i
\(113\) 521.328 521.328i 0.434004 0.434004i −0.455984 0.889988i \(-0.650713\pi\)
0.889988 + 0.455984i \(0.150713\pi\)
\(114\) 0 0
\(115\) −627.496 + 39.7725i −0.508820 + 0.0322505i
\(116\) 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
\(125\) 783.917 1156.98i 0.560926 0.827866i
\(126\) 0 0
\(127\) 786.555 786.555i 0.549571 0.549571i −0.376746 0.926317i \(-0.622957\pi\)
0.926317 + 0.376746i \(0.122957\pi\)
\(128\) −727.025 + 727.025i −0.502036 + 0.502036i
\(129\) 0 0
\(130\) 1863.88 2116.14i 1.25748 1.42768i
\(131\) 448.364i 0.299036i −0.988759 0.149518i \(-0.952228\pi\)
0.988759 0.149518i \(-0.0477722\pi\)
\(132\) 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 \(-0.387609\pi\)
−0.938309 + 0.345797i \(0.887609\pi\)
\(138\) 0 0
\(139\) 112.735i 0.0687918i −0.999408 0.0343959i \(-0.989049\pi\)
0.999408 0.0343959i \(-0.0109507\pi\)
\(140\) 62.4144 + 984.720i 0.0376784 + 0.594458i
\(141\) 0 0
\(142\) 1232.17 1232.17i 0.728179 0.728179i
\(143\) 1822.85 1822.85i 1.06598 1.06598i
\(144\) 0 0
\(145\) −758.076 667.706i −0.434171 0.382413i
\(146\) 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
\(155\) 1960.54 + 1726.83i 1.01597 + 0.894852i
\(156\) 0 0
\(157\) 156.386 156.386i 0.0794967 0.0794967i −0.666240 0.745737i \(-0.732098\pi\)
0.745737 + 0.666240i \(0.232098\pi\)
\(158\) −3466.65 + 3466.65i −1.74552 + 1.74552i
\(159\) 0 0
\(160\) 154.448 + 2436.74i 0.0763135 + 1.20401i
\(161\) 864.129i 0.422999i
\(162\) 0 0
\(163\) −239.292 239.292i −0.114986 0.114986i 0.647272 0.762259i \(-0.275910\pi\)
−0.762259 + 0.647272i \(0.775910\pi\)
\(164\) 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 \(-0.321216\pi\)
−0.846369 + 0.532596i \(0.821216\pi\)
\(168\) 0 0
\(169\) 2431.86i 1.10690i
\(170\) 2337.99 2654.42i 1.05480 1.19756i
\(171\) 0 0
\(172\) −1012.10 + 1012.10i −0.448674 + 0.448674i
\(173\) −441.523 + 441.523i −0.194037 + 0.194037i −0.797438 0.603401i \(-0.793812\pi\)
0.603401 + 0.797438i \(0.293812\pi\)
\(174\) 0 0
\(175\) −1518.76 1175.80i −0.656041 0.507898i
\(176\) 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
\(185\) 299.882 19.0074i 0.119177 0.00755378i
\(186\) 0 0
\(187\) 2286.53 2286.53i 0.894159 0.894159i
\(188\) 837.336 837.336i 0.324835 0.324835i
\(189\) 0 0
\(190\) 4536.82 287.557i 1.73229 0.109798i
\(191\) 1090.71i 0.413200i −0.978426 0.206600i \(-0.933760\pi\)
0.978426 0.206600i \(-0.0662398\pi\)
\(192\) 0 0
\(193\) −2825.69 2825.69i −1.05387 1.05387i −0.998464 0.0554112i \(-0.982353\pi\)
−0.0554112 0.998464i \(-0.517647\pi\)
\(194\) 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 \(-0.346209\pi\)
−0.885537 + 0.464569i \(0.846209\pi\)
\(198\) 0 0
\(199\) 520.257i 0.185327i 0.995697 + 0.0926633i \(0.0295380\pi\)
−0.995697 + 0.0926633i \(0.970462\pi\)
\(200\) −826.837 640.126i −0.292331 0.226319i
\(201\) 0 0
\(202\) 292.430 292.430i 0.101858 0.101858i
\(203\) −981.726 + 981.726i −0.339427 + 0.339427i
\(204\) 0 0
\(205\) −1927.13 + 2187.96i −0.656569 + 0.745432i
\(206\) 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
\(215\) −176.245 2780.65i −0.0559062 0.882039i
\(216\) 0 0
\(217\) 2538.95 2538.95i 0.794263 0.794263i
\(218\) −1076.29 + 1076.29i −0.334384 + 0.334384i
\(219\) 0 0
\(220\) 1825.85 + 1608.19i 0.559541 + 0.492838i
\(221\) 5806.30i 1.76730i
\(222\) 0 0
\(223\) 323.198 + 323.198i 0.0970537 + 0.0970537i 0.753967 0.656913i \(-0.228138\pi\)
−0.656913 + 0.753967i \(0.728138\pi\)
\(224\) 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 \(-0.0583177\pi\)
−0.182187 + 0.983264i \(0.558318\pi\)
\(228\) 0 0
\(229\) 230.334i 0.0664667i −0.999448 0.0332333i \(-0.989420\pi\)
0.999448 0.0332333i \(-0.0105804\pi\)
\(230\) 1749.18 + 1540.66i 0.501468 + 0.441688i
\(231\) 0 0
\(232\) −534.468 + 534.468i −0.151248 + 0.151248i
\(233\) 350.156 350.156i 0.0984526 0.0984526i −0.656165 0.754618i \(-0.727822\pi\)
0.754618 + 0.656165i \(0.227822\pi\)
\(234\) 0 0
\(235\) 145.812 + 2300.50i 0.0404755 + 0.638587i
\(236\) 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
\(245\) 789.938 896.852i 0.205989 0.233868i
\(246\) 0 0
\(247\) −5276.43 + 5276.43i −1.35924 + 1.35924i
\(248\) 1382.25 1382.25i 0.353923 0.353923i
\(249\) 0 0
\(250\) −5087.87 + 977.942i −1.28714 + 0.247402i
\(251\) 1708.34i 0.429599i 0.976658 + 0.214800i \(0.0689099\pi\)
−0.976658 + 0.214800i \(0.931090\pi\)
\(252\) 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 \(-0.400875\pi\)
−0.951902 + 0.306402i \(0.900875\pi\)
\(258\) 0 0
\(259\) 412.969i 0.0990757i
\(260\) −4360.12 + 276.357i −1.04001 + 0.0659189i
\(261\) 0 0
\(262\) −1175.34 + 1175.34i −0.277148 + 0.277148i
\(263\) 2307.03 2307.03i 0.540903 0.540903i −0.382891 0.923794i \(-0.625071\pi\)
0.923794 + 0.382891i \(0.125071\pi\)
\(264\) 0 0
\(265\) 2892.19 183.315i 0.670437 0.0424943i
\(266\) 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
\(275\) −4698.41 + 598.000i −1.03027 + 0.131130i
\(276\) 0 0
\(277\) 5816.91 5816.91i 1.26175 1.26175i 0.311504 0.950245i \(-0.399167\pi\)
0.950245 0.311504i \(-0.100833\pi\)
\(278\) −295.524 + 295.524i −0.0637566 + 0.0637566i
\(279\) 0 0
\(280\) −949.875 + 1078.44i −0.202735 + 0.230174i
\(281\) 140.032i 0.0297281i −0.999890 0.0148640i \(-0.995268\pi\)
0.999890 0.0148640i \(-0.00473155\pi\)
\(282\) 0 0
\(283\) 4431.85 + 4431.85i 0.930905 + 0.930905i 0.997763 0.0668572i \(-0.0212972\pi\)
−0.0668572 + 0.997763i \(0.521297\pi\)
\(284\) −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
\(290\) 236.897 + 3737.55i 0.0479691 + 0.756815i
\(291\) 0 0
\(292\) −2761.28 + 2761.28i −0.553395 + 0.553395i
\(293\) 1244.45 1244.45i 0.248127 0.248127i −0.572074 0.820202i \(-0.693861\pi\)
0.820202 + 0.572074i \(0.193861\pi\)
\(294\) 0 0
\(295\) −2345.52 2065.91i −0.462921 0.407736i
\(296\) 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
\(305\) 3274.32 + 2883.99i 0.614711 + 0.541432i
\(306\) 0 0
\(307\) −7327.60 + 7327.60i −1.36224 + 1.36224i −0.491189 + 0.871053i \(0.663437\pi\)
−0.871053 + 0.491189i \(0.836563\pi\)
\(308\) 2364.52 2364.52i 0.437439 0.437439i
\(309\) 0 0
\(310\) −612.664 9666.08i −0.112248 1.77096i
\(311\) 7489.38i 1.36554i −0.730632 0.682771i \(-0.760775\pi\)
0.730632 0.682771i \(-0.239225\pi\)
\(312\) 0 0
\(313\) −2456.04 2456.04i −0.443525 0.443525i 0.449670 0.893195i \(-0.351542\pi\)
−0.893195 + 0.449670i \(0.851542\pi\)
\(314\) −819.903 −0.147356
\(315\) 0 0
\(316\) 7595.44 1.35214
\(317\) 6724.30 + 6724.30i 1.19140 + 1.19140i 0.976674 + 0.214728i \(0.0688866\pi\)
0.214728 + 0.976674i \(0.431113\pi\)
\(318\) 0 0
\(319\) 3423.60i 0.600894i
\(320\) 1433.05 1627.01i 0.250344 0.284227i
\(321\) 0 0
\(322\) 2265.23 2265.23i 0.392038 0.392038i
\(323\) −6618.59 + 6618.59i −1.14015 + 1.14015i
\(324\) 0 0
\(325\) 5206.18 6724.70i 0.888574 1.14775i
\(326\) 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
\(335\) −2373.97 + 150.469i −0.387176 + 0.0245403i
\(336\) 0 0
\(337\) 3308.77 3308.77i 0.534838 0.534838i −0.387170 0.922008i \(-0.626547\pi\)
0.922008 + 0.387170i \(0.126547\pi\)
\(338\) 6374.88 6374.88i 1.02588 1.02588i
\(339\) 0 0
\(340\) −5469.20 + 346.653i −0.872379 + 0.0552939i
\(341\) 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 \(-0.333540\pi\)
−0.866350 + 0.499438i \(0.833540\pi\)
\(348\) 0 0
\(349\) 8208.92i 1.25906i −0.776975 0.629532i \(-0.783247\pi\)
0.776975 0.629532i \(-0.216753\pi\)
\(350\) 899.024 + 7063.52i 0.137300 + 1.07875i
\(351\) 0 0
\(352\) 5851.13 5851.13i 0.885984 0.885984i
\(353\) −6800.98 + 6800.98i −1.02544 + 1.02544i −0.0257707 + 0.999668i \(0.508204\pi\)
−0.999668 + 0.0257707i \(0.991796\pi\)
\(354\) 0 0
\(355\) 3473.51 3943.63i 0.519309 0.589594i
\(356\) 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
\(365\) −480.844 7586.34i −0.0689549 1.08791i
\(366\) 0 0
\(367\) −4673.56 + 4673.56i −0.664735 + 0.664735i −0.956492 0.291757i \(-0.905760\pi\)
0.291757 + 0.956492i \(0.405760\pi\)
\(368\) 3060.40 3060.40i 0.433517 0.433517i
\(369\) 0 0
\(370\) −835.936 736.284i −0.117455 0.103453i
\(371\) 3982.85i 0.557357i
\(372\) 0 0
\(373\) −5729.37 5729.37i −0.795323 0.795323i 0.187031 0.982354i \(-0.440114\pi\)
−0.982354 + 0.187031i \(0.940114\pi\)
\(374\) −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 \(-0.996681\pi\)
0.999946 0.0104280i \(-0.00331941\pi\)
\(380\) −5285.11 4655.08i −0.713475 0.628422i
\(381\) 0 0
\(382\) −2859.19 + 2859.19i −0.382956 + 0.382956i
\(383\) 4297.76 4297.76i 0.573382 0.573382i −0.359690 0.933072i \(-0.617118\pi\)
0.933072 + 0.359690i \(0.117118\pi\)
\(384\) 0 0
\(385\) 411.754 + 6496.30i 0.0545063 + 0.859954i
\(386\) 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
\(395\) −9772.54 + 11095.2i −1.24484 + 1.41332i
\(396\) 0 0
\(397\) −10195.4 + 10195.4i −1.28889 + 1.28889i −0.353435 + 0.935459i \(0.614987\pi\)
−0.935459 + 0.353435i \(0.885013\pi\)
\(398\) 1363.80 1363.80i 0.171762 0.171762i
\(399\) 0 0
\(400\) 1214.61 + 9543.04i 0.151826 + 1.19288i
\(401\) 10778.3i 1.34226i 0.741341 + 0.671128i \(0.234190\pi\)
−0.741341 + 0.671128i \(0.765810\pi\)
\(402\) 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 \(-0.909708\pi\)
0.960037 0.279872i \(-0.0902919\pi\)
\(410\) 10787.3 683.731i 1.29938 0.0823587i
\(411\) 0 0
\(412\) −79.7315 + 79.7315i −0.00953420 + 0.00953420i
\(413\) −3037.51 + 3037.51i −0.361903 + 0.361903i
\(414\) 0 0
\(415\) −7198.58 + 456.267i −0.851480 + 0.0539693i
\(416\) 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
\(425\) 6530.47 8435.26i 0.745351 0.962753i
\(426\) 0 0
\(427\) 4240.32 4240.32i 0.480570 0.480570i
\(428\) −4457.91 + 4457.91i −0.503461 + 0.503461i
\(429\) 0 0
\(430\) −6827.18 + 7751.20i −0.765665 + 0.869293i
\(431\) 16161.7i 1.80623i −0.429402 0.903113i \(-0.641276\pi\)
0.429402 0.903113i \(-0.358724\pi\)
\(432\) 0 0
\(433\) −3808.79 3808.79i −0.422722 0.422722i 0.463418 0.886140i \(-0.346623\pi\)
−0.886140 + 0.463418i \(0.846623\pi\)
\(434\) −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 \(-0.972153\pi\)
0.996176 0.0873718i \(-0.0278468\pi\)
\(440\) 224.166 + 3536.70i 0.0242880 + 0.383194i
\(441\) 0 0
\(442\) 15220.6 15220.6i 1.63795 1.63795i
\(443\) 8296.60 8296.60i 0.889805 0.889805i −0.104699 0.994504i \(-0.533388\pi\)
0.994504 + 0.104699i \(0.0333880\pi\)
\(444\) 0 0
\(445\) 11451.0 + 10085.9i 1.21984 + 1.07442i
\(446\) 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
\(455\) −8770.97 7725.38i −0.903713 0.795981i
\(456\) 0 0
\(457\) 2671.27 2671.27i 0.273428 0.273428i −0.557050 0.830479i \(-0.688067\pi\)
0.830479 + 0.557050i \(0.188067\pi\)
\(458\) −603.797 + 603.797i −0.0616017 + 0.0616017i
\(459\) 0 0
\(460\) −228.434 3604.03i −0.0231539 0.365301i
\(461\) 12809.1i 1.29410i 0.762449 + 0.647049i \(0.223997\pi\)
−0.762449 + 0.647049i \(0.776003\pi\)
\(462\) 0 0
\(463\) −11154.1 11154.1i −1.11960 1.11960i −0.991799 0.127804i \(-0.959207\pi\)
−0.127804 0.991799i \(-0.540793\pi\)
\(464\) 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 \(-0.0631368\pi\)
−0.197052 + 0.980393i \(0.563137\pi\)
\(468\) 0 0
\(469\) 3269.21i 0.321872i
\(470\) 5648.30 6412.77i 0.554334 0.629360i
\(471\) 0 0
\(472\) −1653.67 + 1653.67i −0.161263 + 0.161263i
\(473\) −6676.92 + 6676.92i −0.649060 + 0.649060i
\(474\) 0 0
\(475\) 13600.0 1730.97i 1.31371 0.167205i
\(476\) 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
\(485\) 12391.9 785.437i 1.16018 0.0735358i
\(486\) 0 0
\(487\) −4489.84 + 4489.84i −0.417770 + 0.417770i −0.884435 0.466664i \(-0.845456\pi\)
0.466664 + 0.884435i \(0.345456\pi\)
\(488\) 2308.50 2308.50i 0.214141 0.214141i
\(489\) 0 0
\(490\) −4421.76 + 280.264i −0.407662 + 0.0258388i
\(491\) 15174.1i 1.39470i 0.716729 + 0.697352i \(0.245638\pi\)
−0.716729 + 0.697352i \(0.754362\pi\)
\(492\) 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 \(0.130519\pi\)
−0.917106 + 0.398643i \(0.869481\pi\)
\(500\) 6645.11 + 4502.43i 0.594357 + 0.402710i
\(501\) 0 0
\(502\) 4478.25 4478.25i 0.398155 0.398155i
\(503\) −12740.5 + 12740.5i −1.12936 + 1.12936i −0.139084 + 0.990281i \(0.544416\pi\)
−0.990281 + 0.139084i \(0.955584\pi\)
\(504\) 0 0
\(505\) 824.364 935.937i 0.0726410 0.0824726i
\(506\) 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
\(515\) −13.8843 219.055i −0.00118799 0.0187431i
\(516\) 0 0
\(517\) 5523.99 5523.99i 0.469913 0.469913i
\(518\) −1082.56 + 1082.56i −0.0918240 + 0.0918240i
\(519\) 0 0
\(520\) −4775.07 4205.83i −0.402693 0.354688i
\(521\) 13563.3i 1.14054i −0.821458 0.570268i \(-0.806839\pi\)
0.821458 0.570268i \(-0.193161\pi\)
\(522\) 0 0
\(523\) 11193.8 + 11193.8i 0.935894 + 0.935894i 0.998065 0.0621714i \(-0.0198026\pi\)
−0.0621714 + 0.998065i \(0.519803\pi\)
\(524\) 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
\(530\) −8062.14 7101.05i −0.660749 0.581981i
\(531\) 0 0
\(532\) −6844.34 + 6844.34i −0.557782 + 0.557782i
\(533\) −12545.9 + 12545.9i −1.01956 + 1.01956i
\(534\) 0 0
\(535\) −776.293 12247.7i −0.0627329 0.989744i
\(536\) 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
\(545\) −3034.09 + 3444.73i −0.238470 + 0.270745i
\(546\) 0 0
\(547\) 2181.76 2181.76i 0.170540 0.170540i −0.616677 0.787217i \(-0.711521\pi\)
0.787217 + 0.616677i \(0.211521\pi\)
\(548\) 5457.01 5457.01i 0.425387 0.425387i
\(549\) 0 0
\(550\) 13884.0 + 10748.8i 1.07639 + 0.833329i
\(551\) 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 −0.976392 0.216007i \(-0.930697\pi\)
−0.216007 0.976392i \(-0.569303\pi\)
\(558\) 0 0
\(559\) 16955.0i 1.28286i
\(560\) 13194.8 836.323i 0.995681 0.0631091i
\(561\) 0 0
\(562\) −367.080 + 367.080i −0.0275522 + 0.0275522i
\(563\) 8213.60 8213.60i 0.614852 0.614852i −0.329354 0.944206i \(-0.606831\pi\)
0.944206 + 0.329354i \(0.106831\pi\)
\(564\) 0 0
\(565\) −8226.41 + 521.414i −0.612545 + 0.0388248i
\(566\) 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
\(575\) 5558.57 + 4303.37i 0.403145 + 0.312109i
\(576\) 0 0
\(577\) 7884.54 7884.54i 0.568870 0.568870i −0.362942 0.931812i \(-0.618228\pi\)
0.931812 + 0.362942i \(0.118228\pi\)
\(578\) 6213.35 6213.35i 0.447130 0.447130i
\(579\) 0 0
\(580\) 3834.97 4354.01i 0.274549 0.311708i
\(581\) 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 \(-0.0925404\pi\)
−0.286646 + 0.958037i \(0.592540\pi\)
\(588\) 0 0
\(589\) 25629.2i 1.79293i
\(590\) 732.969 + 11564.1i 0.0511455 + 0.806930i
\(591\) 0 0
\(592\) −1462.57 + 1462.57i −0.101539 + 0.101539i
\(593\) 3491.97 3491.97i 0.241818 0.241818i −0.575784 0.817602i \(-0.695303\pi\)
0.817602 + 0.575784i \(0.195303\pi\)
\(594\) 0 0
\(595\) −11002.0 9690.48i −0.758049 0.667682i
\(596\) 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
\(605\) 878.328 + 773.622i 0.0590233 + 0.0519871i
\(606\) 0 0
\(607\) −1292.54 + 1292.54i −0.0864293 + 0.0864293i −0.749000 0.662570i \(-0.769466\pi\)
0.662570 + 0.749000i \(0.269466\pi\)
\(608\) −16936.7 + 16936.7i −1.12972 + 1.12972i
\(609\) 0 0
\(610\) −1023.22 16143.4i −0.0679160 1.07152i
\(611\) 14027.3i 0.928780i
\(612\) 0 0
\(613\) 225.964 + 225.964i 0.0148884 + 0.0148884i 0.714512 0.699623i \(-0.246649\pi\)
−0.699623 + 0.714512i \(0.746649\pi\)
\(614\) 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 \(-0.209986\pi\)
−0.612873 + 0.790181i \(0.709986\pi\)
\(618\) 0 0
\(619\) 8870.55i 0.575989i −0.957632 0.287995i \(-0.907011\pi\)
0.957632 0.287995i \(-0.0929886\pi\)
\(620\) −9918.04 + 11260.4i −0.642448 + 0.729400i
\(621\) 0 0
\(622\) −19632.7 + 19632.7i −1.26559 + 1.26559i
\(623\) 14829.3 14829.3i 0.953650 0.953650i
\(624\) 0 0
\(625\) −15126.8 + 3914.00i −0.968118 + 0.250496i
\(626\) 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
\(635\) −12411.6 + 786.685i −0.775654 + 0.0491632i
\(636\) 0 0
\(637\) 5142.61 5142.61i 0.319871 0.319871i
\(638\) 8974.65 8974.65i 0.556912 0.556912i
\(639\) 0 0
\(640\) 11472.3 727.145i 0.708564 0.0449108i
\(641\) 5168.75i 0.318492i −0.987239 0.159246i \(-0.949094\pi\)
0.987239 0.159246i \(-0.0509063\pi\)
\(642\) 0 0
\(643\) −2078.46 2078.46i −0.127475 0.127475i 0.640491 0.767966i \(-0.278731\pi\)
−0.767966 + 0.640491i \(0.778731\pi\)
\(644\) −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 \(-0.0969297\pi\)
−0.299829 + 0.953993i \(0.596930\pi\)
\(648\) 0 0
\(649\) 10592.8i 0.640684i
\(650\) −31275.6 + 3980.67i −1.88728 + 0.240207i
\(651\) 0 0
\(652\) 1374.37 1374.37i 0.0825530 0.0825530i
\(653\) 12815.1 12815.1i 0.767984 0.767984i −0.209767 0.977751i \(-0.567271\pi\)
0.977751 + 0.209767i \(0.0672707\pi\)
\(654\) 0 0
\(655\) −3313.31 + 3761.75i −0.197651 + 0.224402i
\(656\) 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
\(665\) −1191.86 18804.2i −0.0695015 1.09653i
\(666\) 0 0
\(667\) 3593.07 3593.07i 0.208582 0.208582i
\(668\) 3889.27 3889.27i 0.225270 0.225270i
\(669\) 0 0
\(670\) 6617.58 + 5828.70i 0.381581 + 0.336093i
\(671\) 14787.4i 0.850762i
\(672\) 0 0
\(673\) −16220.3 16220.3i −0.929045 0.929045i 0.0685992 0.997644i \(-0.478147\pi\)
−0.997644 + 0.0685992i \(0.978147\pi\)
\(674\) −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 \(-0.398382\pi\)
−0.949473 + 0.313847i \(0.898382\pi\)
\(678\) 0 0
\(679\) 17065.0i 0.964500i
\(680\) −5989.70 5275.66i −0.337786 0.297518i
\(681\) 0 0
\(682\) −23210.3 + 23210.3i −1.30318 + 1.30318i
\(683\) 15428.1 15428.1i 0.864331 0.864331i −0.127507 0.991838i \(-0.540697\pi\)
0.991838 + 0.127507i \(0.0406975\pi\)
\(684\) 0 0
\(685\) 950.276 + 14992.6i 0.0530046 + 0.836261i
\(686\) 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
\(695\) −833.087 + 945.841i −0.0454688 + 0.0516227i
\(696\) 0 0
\(697\) −15737.2 + 15737.2i −0.855220 + 0.855220i
\(698\) −21518.9 + 21518.9i −1.16691 + 1.16691i
\(699\) 0 0
\(700\) 6753.21 8722.98i 0.364639 0.470996i
\(701\) 8846.82i 0.476662i 0.971184 + 0.238331i \(0.0766002\pi\)
−0.971184 + 0.238331i \(0.923400\pi\)
\(702\) 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 \(0.210515\pi\)
−0.789163 + 0.614184i \(0.789485\pi\)
\(710\) −19443.3 + 1232.37i −1.02774 + 0.0651410i
\(711\) 0 0
\(712\) 8073.34 8073.34i 0.424945 0.424945i
\(713\) −9292.43 + 9292.43i −0.488084 + 0.488084i
\(714\) 0 0
\(715\) −28764.1 + 1823.15i −1.50450 + 0.0953596i
\(716\) 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
\(725\) 1426.02 + 11204.0i 0.0730495 + 0.573941i
\(726\) 0 0
\(727\) −16025.7 + 16025.7i −0.817553 + 0.817553i −0.985753 0.168200i \(-0.946205\pi\)
0.168200 + 0.985753i \(0.446205\pi\)
\(728\) −6183.82 + 6183.82i −0.314818 + 0.314818i
\(729\) 0 0
\(730\) −18626.4 + 21147.3i −0.944374 + 1.07219i
\(731\) 21267.8i 1.07609i
\(732\) 0 0
\(733\) −3319.43 3319.43i −0.167266 0.167266i 0.618511 0.785777i \(-0.287736\pi\)
−0.785777 + 0.618511i \(0.787736\pi\)
\(734\) 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 \(-0.834338\pi\)
0.867600 0.497263i \(-0.165662\pi\)
\(740\) 109.169 + 1722.37i 0.00542314 + 0.0855616i
\(741\) 0 0
\(742\) −10440.7 + 10440.7i −0.516562 + 0.516562i
\(743\) 14574.6 14574.6i 0.719637 0.719637i −0.248894 0.968531i \(-0.580067\pi\)
0.968531 + 0.248894i \(0.0800670\pi\)
\(744\) 0 0
\(745\) 12525.7 + 11032.5i 0.615983 + 0.542552i
\(746\) 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
\(755\) 24662.6 + 21722.6i 1.18883 + 1.04711i
\(756\) 0 0
\(757\) 10502.0 10502.0i 0.504229 0.504229i −0.408520 0.912749i \(-0.633955\pi\)
0.912749 + 0.408520i \(0.133955\pi\)
\(758\) −403.390 + 403.390i −0.0193296 + 0.0193296i
\(759\) 0 0
\(760\) −648.871 10237.3i −0.0309698 0.488614i
\(761\) 36489.6i 1.73817i 0.494664 + 0.869085i \(0.335291\pi\)
−0.494664 + 0.869085i \(0.664709\pi\)
\(762\) 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 \(-0.748245\pi\)
0.703198 0.710994i \(-0.251755\pi\)
\(770\) 15950.0 18108.8i 0.746493 0.847527i
\(771\) 0 0
\(772\) 16229.4 16229.4i 0.756617 0.756617i
\(773\) 10327.2 10327.2i 0.480522 0.480522i −0.424777 0.905298i \(-0.639647\pi\)
0.905298 + 0.424777i \(0.139647\pi\)
\(774\) 0 0
\(775\) −3687.98 28976.0i −0.170937 1.34303i
\(776\) 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
\(785\) −2467.73 + 156.412i −0.112200 + 0.00711157i
\(786\)