Properties

Label 45.4.f.a.17.2
Level $45$
Weight $4$
Character 45.17
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 17.2
Root \(-0.347140 - 2.27426i\) of defining polynomial
Character \(\chi\) \(=\) 45.17
Dual form 45.4.f.a.8.2

$q$-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 \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).

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

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 −0.997498 0.0706924i \(-0.977479\pi\)
0.0706924 + 0.997498i \(0.477479\pi\)
\(3\) 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 0.350062 0.936726i \(-0.386160\pi\)
−0.936726 + 0.350062i \(0.886160\pi\)
\(8\) −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 \(-0.826196\pi\)
0.854597 0.519291i \(-0.173804\pi\)
\(12\) 0 0
\(13\) −48.1085 + 48.1085i −1.02638 + 1.02638i −0.0267344 + 0.999643i \(0.508511\pi\)
−0.999643 + 0.0267344i \(0.991489\pi\)
\(14\) 56.9640 1.08745
\(15\) 0 0
\(16\) 76.9602 1.20250
\(17\) −60.3458 + 60.3458i −0.860942 + 0.860942i −0.991448 0.130506i \(-0.958340\pi\)
0.130506 + 0.991448i \(0.458340\pi\)
\(18\) 0 0
\(19\) 109.678i 1.32430i 0.749369 + 0.662152i \(0.230357\pi\)
−0.749369 + 0.662152i \(0.769643\pi\)
\(20\) 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 0.864002 0.503489i \(-0.167951\pi\)
−0.503489 + 0.864002i \(0.667951\pi\)
\(24\) 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 0.663625 0.748065i \(-0.269017\pi\)
−0.748065 + 0.663625i \(0.769017\pi\)
\(38\) −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 \(0.165447\pi\)
−0.867935 + 0.496677i \(0.834553\pi\)
\(42\) 0 0
\(43\) 176.216 176.216i 0.624948 0.624948i −0.321845 0.946792i \(-0.604303\pi\)
0.946792 + 0.321845i \(0.104303\pi\)
\(44\) −217.624 −0.745638
\(45\) 0 0
\(46\) −208.485 −0.668250
\(47\) −145.788 + 145.788i −0.452456 + 0.452456i −0.896169 0.443713i \(-0.853661\pi\)
0.443713 + 0.896169i \(0.353661\pi\)
\(48\) 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 0.428513 0.903535i \(-0.359038\pi\)
−0.903535 + 0.428513i \(0.859038\pi\)
\(54\) 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 0.830838 0.556514i \(-0.187861\pi\)
−0.556514 + 0.830838i \(0.687861\pi\)
\(68\) 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 \(-0.871492\pi\)
0.919605 0.392843i \(-0.128508\pi\)
\(72\) 0 0
\(73\) 480.765 480.765i 0.770812 0.770812i −0.207436 0.978249i \(-0.566512\pi\)
0.978249 + 0.207436i \(0.0665119\pi\)
\(74\) 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 \(0.609242\pi\)
\(80\) −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 0.941186 0.337890i \(-0.109713\pi\)
−0.337890 + 0.941186i \(0.609713\pi\)
\(84\) 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 0.164377 0.986398i \(-0.447439\pi\)
−0.986398 + 0.164377i \(0.947439\pi\)
\(98\) 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 \(-0.982500\pi\)
0.998489 0.0549510i \(-0.0175003\pi\)
\(102\) 0 0
\(103\) 13.8820 13.8820i 0.0132800 0.0132800i −0.700436 0.713716i \(-0.747011\pi\)
0.713716 + 0.700436i \(0.247011\pi\)
\(104\) 569.142 0.536624
\(105\) 0 0
\(106\) 960.929 0.880507
\(107\) 776.165 776.165i 0.701259 0.701259i −0.263422 0.964681i \(-0.584851\pi\)
0.964681 + 0.263422i \(0.0848510\pi\)
\(108\) 0 0
\(109\) 410.579i 0.360792i 0.983594 + 0.180396i \(0.0577379\pi\)
−0.983594 + 0.180396i \(0.942262\pi\)
\(110\) −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 0.889988 0.455984i \(-0.150713\pi\)
−0.455984 + 0.889988i \(0.650713\pi\)
\(114\) 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 0.926317 0.376746i \(-0.122957\pi\)
−0.376746 + 0.926317i \(0.622957\pi\)
\(128\) −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 \(0.0477722\pi\)
−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 −0.938309 0.345797i \(-0.887609\pi\)
0.345797 + 0.938309i \(0.387609\pi\)
\(138\) 0 0
\(139\) 112.735i 0.0687918i 0.999408 + 0.0343959i \(0.0109507\pi\)
−0.999408 + 0.0343959i \(0.989049\pi\)
\(140\) 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 0.745737 0.666240i \(-0.232098\pi\)
−0.666240 + 0.745737i \(0.732098\pi\)
\(158\) −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 −0.762259 0.647272i \(-0.775910\pi\)
0.647272 + 0.762259i \(0.275910\pi\)
\(164\) 1497.81 0.713167
\(165\) 0 0
\(166\) −2391.72 −1.11828
\(167\) −677.159 + 677.159i −0.313773 + 0.313773i −0.846369 0.532596i \(-0.821216\pi\)
0.532596 + 0.846369i \(0.321216\pi\)
\(168\) 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 0.603401 0.797438i \(-0.293812\pi\)
−0.797438 + 0.603401i \(0.793812\pi\)
\(174\) 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 \(0.0662398\pi\)
−0.978426 + 0.206600i \(0.933760\pi\)
\(192\) 0 0
\(193\) −2825.69 + 2825.69i −1.05387 + 1.05387i −0.0554112 + 0.998464i \(0.517647\pi\)
−0.998464 + 0.0554112i \(0.982353\pi\)
\(194\) 4117.22 1.52371
\(195\) 0 0
\(196\) −613.958 −0.223746
\(197\) −1163.99 + 1163.99i −0.420969 + 0.420969i −0.885537 0.464569i \(-0.846209\pi\)
0.464569 + 0.885537i \(0.346209\pi\)
\(198\) 0 0
\(199\) 520.257i 0.185327i −0.995697 0.0926633i \(-0.970462\pi\)
0.995697 0.0926633i \(-0.0295380\pi\)
\(200\) −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 −0.656913 0.753967i \(-0.728138\pi\)
0.753967 + 0.656913i \(0.228138\pi\)
\(224\) 3355.65 1.00093
\(225\) 0 0
\(226\) −2733.22 −0.804474
\(227\) 2739.76 2739.76i 0.801077 0.801077i −0.182187 0.983264i \(-0.558318\pi\)
0.983264 + 0.182187i \(0.0583177\pi\)
\(228\) 0 0
\(229\) 230.334i 0.0664667i 0.999448 + 0.0332333i \(0.0105804\pi\)
−0.999448 + 0.0332333i \(0.989420\pi\)
\(230\) 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 0.754618 0.656165i \(-0.227822\pi\)
−0.656165 + 0.754618i \(0.727822\pi\)
\(234\) 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 \(-0.931090\pi\)
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 −0.951902 0.306402i \(-0.900875\pi\)
0.306402 + 0.951902i \(0.400875\pi\)
\(258\) 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 0.923794 0.382891i \(-0.125071\pi\)
−0.382891 + 0.923794i \(0.625071\pi\)
\(264\) 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 0.950245 + 0.311504i \(0.100833\pi\)
0.311504 + 0.950245i \(0.399167\pi\)
\(278\) −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 \(0.00473155\pi\)
−0.999890 + 0.0148640i \(0.995268\pi\)
\(282\) 0 0
\(283\) 4431.85 4431.85i 0.930905 0.930905i −0.0668572 0.997763i \(-0.521297\pi\)
0.997763 + 0.0668572i \(0.0212972\pi\)
\(284\) −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 0.820202 0.572074i \(-0.193861\pi\)
−0.572074 + 0.820202i \(0.693861\pi\)
\(294\) 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 −0.871053 0.491189i \(-0.836563\pi\)
−0.491189 0.871053i \(-0.663437\pi\)
\(308\) 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 \(0.239225\pi\)
−0.730632 + 0.682771i \(0.760775\pi\)
\(312\) 0 0
\(313\) −2456.04 + 2456.04i −0.443525 + 0.443525i −0.893195 0.449670i \(-0.851542\pi\)
0.449670 + 0.893195i \(0.351542\pi\)
\(314\) −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 \(-0.431113\pi\)
0.976674 0.214728i \(-0.0688866\pi\)
\(318\) 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 0.922008 0.387170i \(-0.126547\pi\)
−0.387170 + 0.922008i \(0.626547\pi\)
\(338\) 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 −0.866350 0.499438i \(-0.833540\pi\)
0.499438 + 0.866350i \(0.333540\pi\)
\(348\) 0 0
\(349\) 8208.92i 1.25906i 0.776975 + 0.629532i \(0.216753\pi\)
−0.776975 + 0.629532i \(0.783247\pi\)
\(350\) 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 −0.999668 0.0257707i \(-0.991796\pi\)
−0.0257707 0.999668i \(-0.508204\pi\)
\(354\) 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 0.291757 0.956492i \(-0.405760\pi\)
−0.956492 + 0.291757i \(0.905760\pi\)
\(368\) 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 −0.982354 0.187031i \(-0.940114\pi\)
0.187031 + 0.982354i \(0.440114\pi\)
\(374\) −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 \(0.996681\pi\)
\(380\) −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 0.933072 0.359690i \(-0.117118\pi\)
−0.359690 + 0.933072i \(0.617118\pi\)
\(384\) 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 −0.935459 0.353435i \(-0.885013\pi\)
−0.353435 0.935459i \(-0.614987\pi\)
\(398\) 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 \(-0.765810\pi\)
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 \(0.909708\pi\)
\(410\) 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 \(0.358724\pi\)
−0.429402 + 0.903113i \(0.641276\pi\)
\(432\) 0 0
\(433\) −3808.79 + 3808.79i −0.422722 + 0.422722i −0.886140 0.463418i \(-0.846623\pi\)
0.463418 + 0.886140i \(0.346623\pi\)
\(434\) −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 \(0.972153\pi\)
\(440\) 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 0.994504 0.104699i \(-0.0333880\pi\)
−0.104699 + 0.994504i \(0.533388\pi\)
\(444\) 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 0.830479 0.557050i \(-0.188067\pi\)
−0.557050 + 0.830479i \(0.688067\pi\)
\(458\) −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 \(-0.776003\pi\)
0.762449 0.647049i \(-0.223997\pi\)
\(462\) 0 0
\(463\) −11154.1 + 11154.1i −1.11960 + 1.11960i −0.127804 + 0.991799i \(0.540793\pi\)
−0.991799 + 0.127804i \(0.959207\pi\)
\(464\) 6953.76 0.695733
\(465\) 0 0
\(466\) −1835.80 −0.182493
\(467\) 7905.44 7905.44i 0.783341 0.783341i −0.197052 0.980393i \(-0.563137\pi\)
0.980393 + 0.197052i \(0.0631368\pi\)
\(468\) 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 0.466664 0.884435i \(-0.345456\pi\)
−0.884435 + 0.466664i \(0.845456\pi\)
\(488\) 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 \(-0.754362\pi\)
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 \(-0.130519\pi\)
\(500\) 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 −0.990281 0.139084i \(-0.955584\pi\)
−0.139084 0.990281i \(-0.544416\pi\)
\(504\) 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 \(0.193161\pi\)
−0.821458 + 0.570268i \(0.806839\pi\)
\(522\) 0 0
\(523\) 11193.8 11193.8i 0.935894 0.935894i −0.0621714 0.998065i \(-0.519803\pi\)
0.998065 + 0.0621714i \(0.0198026\pi\)
\(524\) 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 0.787217 0.616677i \(-0.211521\pi\)
−0.616677 + 0.787217i \(0.711521\pi\)
\(548\) 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 −0.216007 + 0.976392i \(0.569303\pi\)
−0.976392 + 0.216007i \(0.930697\pi\)
\(558\) 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 0.944206 0.329354i \(-0.106831\pi\)
−0.329354 + 0.944206i \(0.606831\pi\)
\(564\) 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 0.931812 0.362942i \(-0.118228\pi\)
−0.362942 + 0.931812i \(0.618228\pi\)
\(578\) 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 −0.286646 0.958037i \(-0.592540\pi\)
0.958037 + 0.286646i \(0.0925404\pi\)
\(588\) 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 0.817602 0.575784i \(-0.195303\pi\)
−0.575784 + 0.817602i \(0.695303\pi\)
\(594\) 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 0.662570 0.749000i \(-0.269466\pi\)
−0.749000 + 0.662570i \(0.769466\pi\)
\(608\) −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 −0.699623 0.714512i \(-0.746649\pi\)
0.714512 + 0.699623i \(0.246649\pi\)
\(614\) 38417.2 2.52507
\(615\) 0 0
\(616\) 4870.41 0.318562
\(617\) 2717.41 2717.41i 0.177308 0.177308i −0.612873 0.790181i \(-0.709986\pi\)
0.790181 + 0.612873i \(0.209986\pi\)
\(618\) 0 0
\(619\) 8870.55i 0.575989i 0.957632 + 0.287995i \(0.0929886\pi\)
−0.957632 + 0.287995i \(0.907011\pi\)
\(620\) −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 \(0.0509063\pi\)
−0.987239 + 0.159246i \(0.949094\pi\)
\(642\) 0 0
\(643\) −2078.46 + 2078.46i −0.127475 + 0.127475i −0.767966 0.640491i \(-0.778731\pi\)
0.640491 + 0.767966i \(0.278731\pi\)
\(644\) −4963.13 −0.303687
\(645\) 0 0
\(646\) 34700.0 2.11339
\(647\) 10765.7 10765.7i 0.654164 0.654164i −0.299829 0.953993i \(-0.596930\pi\)
0.953993 + 0.299829i \(0.0969297\pi\)
\(648\) 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 0.977751 0.209767i \(-0.0672707\pi\)
−0.209767 + 0.977751i \(0.567271\pi\)
\(654\) 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 −0.997644 0.0685992i \(-0.978147\pi\)
0.0685992 + 0.997644i \(0.478147\pi\)
\(674\) −17347.3 −0.991382
\(675\) 0 0
\(676\) −13967.4 −0.794685
\(677\) −11196.6 + 11196.6i −0.635626 + 0.635626i −0.949473 0.313847i \(-0.898382\pi\)
0.313847 + 0.949473i \(0.398382\pi\)
\(678\) 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 0.991838 0.127507i \(-0.0406975\pi\)
−0.127507 + 0.991838i \(0.540697\pi\)
\(684\) 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 \(-0.923400\pi\)
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 \(-0.210515\pi\)
\(710\) −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 0.168200 0.985753i \(-0.446205\pi\)
−0.985753 + 0.168200i \(0.946205\pi\)
\(728\) −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 −0.785777 0.618511i \(-0.787736\pi\)
0.618511 + 0.785777i \(0.287736\pi\)
\(734\) 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 \(0.834338\pi\)
\(740\) 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 0.968531 0.248894i \(-0.0800670\pi\)
−0.248894 + 0.968531i \(0.580067\pi\)
\(744\) 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 0.912749 0.408520i \(-0.133955\pi\)
−0.408520 + 0.912749i \(0.633955\pi\)
\(758\) −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 \(-0.664709\pi\)
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 \(0.748245\pi\)
\(770\) 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 0.905298 0.424777i \(-0.139647\pi\)
−0.424777 + 0.905298i \(0.639647\pi\)
\(774\) 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
\(786\) 0