Properties

Label 261.3.s.a.73.4
Level $261$
Weight $3$
Character 261.73
Analytic conductor $7.112$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 261 = 3^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 261.s (of order \(28\), degree \(12\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.11173489980\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(4\) over \(\Q(\zeta_{28})\)
Twist minimal: no (minimal twist has level 29)
Sato-Tate group: $\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label 73.4
Character \(\chi\) \(=\) 261.73
Dual form 261.3.s.a.118.4

$q$-expansion

\(f(q)\) \(=\) \(q+(3.56136 - 0.401269i) q^{2} +(8.62256 - 1.96804i) q^{4} +(-5.24106 - 4.17960i) q^{5} +(2.11977 - 9.28734i) q^{7} +(16.3872 - 5.73413i) q^{8} +O(q^{10})\) \(q+(3.56136 - 0.401269i) q^{2} +(8.62256 - 1.96804i) q^{4} +(-5.24106 - 4.17960i) q^{5} +(2.11977 - 9.28734i) q^{7} +(16.3872 - 5.73413i) q^{8} +(-20.3424 - 12.7820i) q^{10} +(0.700768 + 0.245209i) q^{11} +(3.39382 + 7.04735i) q^{13} +(3.82256 - 33.9262i) q^{14} +(24.1861 - 11.6474i) q^{16} +(17.4730 + 17.4730i) q^{17} +(-7.96846 + 12.6817i) q^{19} +(-53.4169 - 25.7242i) q^{20} +(2.59408 + 0.592082i) q^{22} +(11.9732 + 15.0139i) q^{23} +(4.43656 + 19.4379i) q^{25} +(14.9145 + 23.7363i) q^{26} -84.2524i q^{28} +(19.7681 - 21.2184i) q^{29} +(0.327624 - 0.0369143i) q^{31} +(22.6600 - 14.2382i) q^{32} +(69.2390 + 55.2162i) q^{34} +(-49.9272 + 39.8156i) q^{35} +(-15.2693 + 5.34296i) q^{37} +(-23.2898 + 48.3617i) q^{38} +(-109.853 - 38.4391i) q^{40} +(-28.0484 + 28.0484i) q^{41} +(0.679170 - 6.02780i) q^{43} +(6.52499 + 0.735190i) q^{44} +(48.6656 + 48.6656i) q^{46} +(-1.43620 + 4.10443i) q^{47} +(-37.6137 - 18.1138i) q^{49} +(23.6000 + 67.4450i) q^{50} +(43.1329 + 54.0870i) q^{52} +(37.6082 - 47.1592i) q^{53} +(-2.64789 - 4.21408i) q^{55} +(-18.5176 - 164.349i) q^{56} +(61.8871 - 83.4988i) q^{58} -91.1542 q^{59} +(6.43745 - 4.04492i) q^{61} +(1.15197 - 0.262930i) q^{62} +(-8.96447 + 7.14893i) q^{64} +(11.6679 - 51.1204i) q^{65} +(29.8663 - 62.0180i) q^{67} +(185.049 + 116.274i) q^{68} +(-161.832 + 161.832i) q^{70} +(38.1572 + 79.2343i) q^{71} +(-29.1293 - 3.28209i) q^{73} +(-52.2355 + 25.1553i) q^{74} +(-43.7503 + 125.031i) q^{76} +(3.76281 - 5.98848i) q^{77} +(7.28322 + 20.8142i) q^{79} +(-175.442 - 40.0435i) q^{80} +(-88.6354 + 111.145i) q^{82} +(-9.19165 - 40.2713i) q^{83} +(-18.5468 - 164.607i) q^{85} -21.7397i q^{86} +12.8897 q^{88} +(-98.0089 + 11.0429i) q^{89} +(72.6452 - 16.5808i) q^{91} +(132.788 + 105.895i) q^{92} +(-3.46785 + 15.1936i) q^{94} +(94.7678 - 33.1607i) q^{95} +(136.891 + 86.0143i) q^{97} +(-141.224 - 49.4166i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} + O(q^{10}) \) \( 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} - 20q^{10} + 8q^{11} - 14q^{13} - 26q^{14} + 18q^{16} + 26q^{17} + 2q^{19} - 46q^{20} + 154q^{22} - 56q^{23} - 34q^{25} - 110q^{26} + 170q^{29} - 88q^{31} + 132q^{32} - 224q^{34} + 210q^{35} - 56q^{37} + 294q^{38} - 492q^{40} + 34q^{41} + 176q^{43} - 126q^{44} + 744q^{46} - 208q^{47} + 506q^{49} - 732q^{50} + 690q^{52} + 14q^{53} + 284q^{55} - 332q^{56} - 508q^{58} + 44q^{59} - 30q^{61} + 504q^{62} - 896q^{64} + 554q^{65} - 574q^{67} + 796q^{68} - 1066q^{70} - 224q^{71} - 22q^{73} - 820q^{74} + 514q^{76} - 436q^{77} + 564q^{79} - 1162q^{80} - 18q^{82} + 126q^{83} + 38q^{85} - 384q^{88} + 160q^{89} - 434q^{91} + 1022q^{92} - 2q^{94} + 642q^{95} + 604q^{97} + 102q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/261\mathbb{Z}\right)^\times\).

\(n\) \(118\) \(146\)
\(\chi(n)\) \(e\left(\frac{27}{28}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.56136 0.401269i 1.78068 0.200634i 0.840616 0.541632i \(-0.182193\pi\)
0.940064 + 0.340997i \(0.110765\pi\)
\(3\) 0 0
\(4\) 8.62256 1.96804i 2.15564 0.492011i
\(5\) −5.24106 4.17960i −1.04821 0.835920i −0.0614515 0.998110i \(-0.519573\pi\)
−0.986760 + 0.162190i \(0.948144\pi\)
\(6\) 0 0
\(7\) 2.11977 9.28734i 0.302825 1.32676i −0.563017 0.826445i \(-0.690360\pi\)
0.865842 0.500317i \(-0.166783\pi\)
\(8\) 16.3872 5.73413i 2.04840 0.716766i
\(9\) 0 0
\(10\) −20.3424 12.7820i −2.03424 1.27820i
\(11\) 0.700768 + 0.245209i 0.0637061 + 0.0222917i 0.361944 0.932200i \(-0.382113\pi\)
−0.298238 + 0.954492i \(0.596399\pi\)
\(12\) 0 0
\(13\) 3.39382 + 7.04735i 0.261063 + 0.542104i 0.989761 0.142731i \(-0.0455885\pi\)
−0.728698 + 0.684835i \(0.759874\pi\)
\(14\) 3.82256 33.9262i 0.273040 2.42330i
\(15\) 0 0
\(16\) 24.1861 11.6474i 1.51163 0.727962i
\(17\) 17.4730 + 17.4730i 1.02782 + 1.02782i 0.999602 + 0.0282209i \(0.00898419\pi\)
0.0282209 + 0.999602i \(0.491016\pi\)
\(18\) 0 0
\(19\) −7.96846 + 12.6817i −0.419393 + 0.667460i −0.987878 0.155234i \(-0.950387\pi\)
0.568485 + 0.822694i \(0.307530\pi\)
\(20\) −53.4169 25.7242i −2.67085 1.28621i
\(21\) 0 0
\(22\) 2.59408 + 0.592082i 0.117913 + 0.0269128i
\(23\) 11.9732 + 15.0139i 0.520575 + 0.652780i 0.970731 0.240170i \(-0.0772031\pi\)
−0.450156 + 0.892950i \(0.648632\pi\)
\(24\) 0 0
\(25\) 4.43656 + 19.4379i 0.177463 + 0.777514i
\(26\) 14.9145 + 23.7363i 0.573635 + 0.912935i
\(27\) 0 0
\(28\) 84.2524i 3.00901i
\(29\) 19.7681 21.2184i 0.681659 0.731670i
\(30\) 0 0
\(31\) 0.327624 0.0369143i 0.0105685 0.00119078i −0.106679 0.994294i \(-0.534022\pi\)
0.117247 + 0.993103i \(0.462593\pi\)
\(32\) 22.6600 14.2382i 0.708124 0.444944i
\(33\) 0 0
\(34\) 69.2390 + 55.2162i 2.03644 + 1.62401i
\(35\) −49.9272 + 39.8156i −1.42649 + 1.13759i
\(36\) 0 0
\(37\) −15.2693 + 5.34296i −0.412684 + 0.144404i −0.528632 0.848851i \(-0.677295\pi\)
0.115949 + 0.993255i \(0.463009\pi\)
\(38\) −23.2898 + 48.3617i −0.612889 + 1.27268i
\(39\) 0 0
\(40\) −109.853 38.4391i −2.74632 0.960978i
\(41\) −28.0484 + 28.0484i −0.684106 + 0.684106i −0.960923 0.276816i \(-0.910721\pi\)
0.276816 + 0.960923i \(0.410721\pi\)
\(42\) 0 0
\(43\) 0.679170 6.02780i 0.0157947 0.140181i −0.983340 0.181776i \(-0.941815\pi\)
0.999135 + 0.0415949i \(0.0132439\pi\)
\(44\) 6.52499 + 0.735190i 0.148295 + 0.0167089i
\(45\) 0 0
\(46\) 48.6656 + 48.6656i 1.05795 + 1.05795i
\(47\) −1.43620 + 4.10443i −0.0305575 + 0.0873282i −0.958152 0.286261i \(-0.907587\pi\)
0.927594 + 0.373590i \(0.121873\pi\)
\(48\) 0 0
\(49\) −37.6137 18.1138i −0.767627 0.369670i
\(50\) 23.6000 + 67.4450i 0.472000 + 1.34890i
\(51\) 0 0
\(52\) 43.1329 + 54.0870i 0.829479 + 1.04013i
\(53\) 37.6082 47.1592i 0.709589 0.889797i −0.288110 0.957597i \(-0.593027\pi\)
0.997699 + 0.0678006i \(0.0215982\pi\)
\(54\) 0 0
\(55\) −2.64789 4.21408i −0.0481434 0.0766197i
\(56\) −18.5176 164.349i −0.330672 2.93480i
\(57\) 0 0
\(58\) 61.8871 83.4988i 1.06702 1.43963i
\(59\) −91.1542 −1.54499 −0.772493 0.635023i \(-0.780991\pi\)
−0.772493 + 0.635023i \(0.780991\pi\)
\(60\) 0 0
\(61\) 6.43745 4.04492i 0.105532 0.0663101i −0.478232 0.878234i \(-0.658722\pi\)
0.583764 + 0.811923i \(0.301579\pi\)
\(62\) 1.15197 0.262930i 0.0185802 0.00424081i
\(63\) 0 0
\(64\) −8.96447 + 7.14893i −0.140070 + 0.111702i
\(65\) 11.6679 51.1204i 0.179506 0.786467i
\(66\) 0 0
\(67\) 29.8663 62.0180i 0.445766 0.925642i −0.550125 0.835082i \(-0.685420\pi\)
0.995891 0.0905598i \(-0.0288656\pi\)
\(68\) 185.049 + 116.274i 2.72131 + 1.70992i
\(69\) 0 0
\(70\) −161.832 + 161.832i −2.31189 + 2.31189i
\(71\) 38.1572 + 79.2343i 0.537426 + 1.11598i 0.976098 + 0.217329i \(0.0697346\pi\)
−0.438672 + 0.898647i \(0.644551\pi\)
\(72\) 0 0
\(73\) −29.1293 3.28209i −0.399032 0.0449601i −0.0898315 0.995957i \(-0.528633\pi\)
−0.309200 + 0.950997i \(0.600061\pi\)
\(74\) −52.2355 + 25.1553i −0.705885 + 0.339936i
\(75\) 0 0
\(76\) −43.7503 + 125.031i −0.575662 + 1.64515i
\(77\) 3.76281 5.98848i 0.0488677 0.0777724i
\(78\) 0 0
\(79\) 7.28322 + 20.8142i 0.0921927 + 0.263472i 0.980741 0.195311i \(-0.0625715\pi\)
−0.888549 + 0.458782i \(0.848286\pi\)
\(80\) −175.442 40.0435i −2.19302 0.500543i
\(81\) 0 0
\(82\) −88.6354 + 111.145i −1.08092 + 1.35543i
\(83\) −9.19165 40.2713i −0.110743 0.485196i −0.999633 0.0270764i \(-0.991380\pi\)
0.888891 0.458120i \(-0.151477\pi\)
\(84\) 0 0
\(85\) −18.5468 164.607i −0.218197 1.93655i
\(86\) 21.7397i 0.252787i
\(87\) 0 0
\(88\) 12.8897 0.146474
\(89\) −98.0089 + 11.0429i −1.10122 + 0.124078i −0.643817 0.765180i \(-0.722650\pi\)
−0.457407 + 0.889258i \(0.651222\pi\)
\(90\) 0 0
\(91\) 72.6452 16.5808i 0.798299 0.182207i
\(92\) 132.788 + 105.895i 1.44335 + 1.15103i
\(93\) 0 0
\(94\) −3.46785 + 15.1936i −0.0368920 + 0.161635i
\(95\) 94.7678 33.1607i 0.997556 0.349060i
\(96\) 0 0
\(97\) 136.891 + 86.0143i 1.41125 + 0.886745i 0.999696 0.0246414i \(-0.00784441\pi\)
0.411551 + 0.911387i \(0.364987\pi\)
\(98\) −141.224 49.4166i −1.44107 0.504251i
\(99\) 0 0
\(100\) 76.5091 + 158.873i 0.765091 + 1.58873i
\(101\) −0.930887 + 8.26185i −0.00921670 + 0.0818005i −0.997478 0.0709693i \(-0.977391\pi\)
0.988262 + 0.152770i \(0.0488193\pi\)
\(102\) 0 0
\(103\) −65.6998 + 31.6393i −0.637862 + 0.307178i −0.724721 0.689043i \(-0.758031\pi\)
0.0868590 + 0.996221i \(0.472317\pi\)
\(104\) 96.0257 + 96.0257i 0.923324 + 0.923324i
\(105\) 0 0
\(106\) 115.013 183.042i 1.08503 1.72681i
\(107\) 73.2735 + 35.2867i 0.684799 + 0.329782i 0.743730 0.668480i \(-0.233055\pi\)
−0.0589308 + 0.998262i \(0.518769\pi\)
\(108\) 0 0
\(109\) 119.739 + 27.3296i 1.09852 + 0.250730i 0.733106 0.680114i \(-0.238070\pi\)
0.365415 + 0.930845i \(0.380927\pi\)
\(110\) −11.1211 13.9454i −0.101100 0.126776i
\(111\) 0 0
\(112\) −56.9043 249.314i −0.508074 2.22602i
\(113\) −84.5371 134.540i −0.748116 1.19062i −0.976178 0.216973i \(-0.930382\pi\)
0.228062 0.973647i \(-0.426761\pi\)
\(114\) 0 0
\(115\) 128.732i 1.11941i
\(116\) 128.693 221.862i 1.10942 1.91260i
\(117\) 0 0
\(118\) −324.633 + 36.5773i −2.75113 + 0.309977i
\(119\) 199.316 125.239i 1.67493 1.05243i
\(120\) 0 0
\(121\) −94.1707 75.0986i −0.778270 0.620650i
\(122\) 21.3030 16.9886i 0.174615 0.139250i
\(123\) 0 0
\(124\) 2.75231 0.963073i 0.0221960 0.00776672i
\(125\) −14.7239 + 30.5745i −0.117791 + 0.244596i
\(126\) 0 0
\(127\) 91.0577 + 31.8625i 0.716990 + 0.250886i 0.664025 0.747711i \(-0.268847\pi\)
0.0529652 + 0.998596i \(0.483133\pi\)
\(128\) −104.751 + 104.751i −0.818369 + 0.818369i
\(129\) 0 0
\(130\) 21.0405 186.740i 0.161850 1.43646i
\(131\) −75.6558 8.52436i −0.577525 0.0650714i −0.181630 0.983367i \(-0.558137\pi\)
−0.395895 + 0.918296i \(0.629566\pi\)
\(132\) 0 0
\(133\) 100.888 + 100.888i 0.758558 + 0.758558i
\(134\) 81.4787 232.853i 0.608050 1.73771i
\(135\) 0 0
\(136\) 386.526 + 186.141i 2.84210 + 1.36868i
\(137\) 50.4454 + 144.165i 0.368215 + 1.05230i 0.967742 + 0.251943i \(0.0810695\pi\)
−0.599528 + 0.800354i \(0.704645\pi\)
\(138\) 0 0
\(139\) −84.2699 105.671i −0.606258 0.760224i 0.380080 0.924953i \(-0.375896\pi\)
−0.986339 + 0.164729i \(0.947325\pi\)
\(140\) −352.142 + 441.572i −2.51530 + 3.15408i
\(141\) 0 0
\(142\) 167.686 + 266.871i 1.18089 + 1.87937i
\(143\) 0.650207 + 5.77075i 0.00454690 + 0.0403549i
\(144\) 0 0
\(145\) −192.290 + 28.5841i −1.32614 + 0.197132i
\(146\) −105.057 −0.719569
\(147\) 0 0
\(148\) −121.145 + 76.1206i −0.818549 + 0.514328i
\(149\) −58.0928 + 13.2593i −0.389885 + 0.0889886i −0.412969 0.910745i \(-0.635508\pi\)
0.0230848 + 0.999734i \(0.492651\pi\)
\(150\) 0 0
\(151\) −203.074 + 161.946i −1.34486 + 1.07249i −0.354340 + 0.935117i \(0.615294\pi\)
−0.990519 + 0.137373i \(0.956134\pi\)
\(152\) −57.8621 + 253.510i −0.380672 + 1.66783i
\(153\) 0 0
\(154\) 10.9977 22.8370i 0.0714138 0.148292i
\(155\) −1.87138 1.17587i −0.0120734 0.00758624i
\(156\) 0 0
\(157\) −132.437 + 132.437i −0.843550 + 0.843550i −0.989319 0.145769i \(-0.953434\pi\)
0.145769 + 0.989319i \(0.453434\pi\)
\(158\) 34.2903 + 71.2045i 0.217027 + 0.450661i
\(159\) 0 0
\(160\) −178.272 20.0865i −1.11420 0.125540i
\(161\) 164.820 79.3732i 1.02373 0.493001i
\(162\) 0 0
\(163\) 84.1241 240.413i 0.516098 1.47492i −0.331073 0.943605i \(-0.607411\pi\)
0.847171 0.531320i \(-0.178304\pi\)
\(164\) −186.648 + 297.049i −1.13810 + 1.81127i
\(165\) 0 0
\(166\) −48.8944 139.732i −0.294545 0.841760i
\(167\) 37.5325 + 8.56655i 0.224746 + 0.0512967i 0.333411 0.942782i \(-0.391800\pi\)
−0.108665 + 0.994078i \(0.534658\pi\)
\(168\) 0 0
\(169\) 67.2227 84.2946i 0.397768 0.498785i
\(170\) −132.103 578.783i −0.777079 3.40460i
\(171\) 0 0
\(172\) −6.00679 53.3117i −0.0349232 0.309952i
\(173\) 38.3828i 0.221866i 0.993828 + 0.110933i \(0.0353839\pi\)
−0.993828 + 0.110933i \(0.964616\pi\)
\(174\) 0 0
\(175\) 189.930 1.08532
\(176\) 19.8048 2.23147i 0.112528 0.0126788i
\(177\) 0 0
\(178\) −344.614 + 78.6558i −1.93603 + 0.441887i
\(179\) −136.077 108.518i −0.760206 0.606244i 0.164742 0.986337i \(-0.447321\pi\)
−0.924949 + 0.380092i \(0.875892\pi\)
\(180\) 0 0
\(181\) 37.8882 165.999i 0.209327 0.917122i −0.755689 0.654931i \(-0.772698\pi\)
0.965016 0.262191i \(-0.0844451\pi\)
\(182\) 252.062 88.2005i 1.38496 0.484618i
\(183\) 0 0
\(184\) 282.300 + 177.381i 1.53424 + 0.964025i
\(185\) 102.359 + 35.8168i 0.553290 + 0.193605i
\(186\) 0 0
\(187\) 7.95997 + 16.5290i 0.0425667 + 0.0883906i
\(188\) −4.30604 + 38.2172i −0.0229045 + 0.203283i
\(189\) 0 0
\(190\) 324.196 156.124i 1.70629 0.821708i
\(191\) 20.1345 + 20.1345i 0.105416 + 0.105416i 0.757848 0.652431i \(-0.226251\pi\)
−0.652431 + 0.757848i \(0.726251\pi\)
\(192\) 0 0
\(193\) −157.961 + 251.393i −0.818449 + 1.30255i 0.131867 + 0.991267i \(0.457903\pi\)
−0.950316 + 0.311287i \(0.899240\pi\)
\(194\) 522.033 + 251.398i 2.69089 + 1.29587i
\(195\) 0 0
\(196\) −359.975 82.1620i −1.83661 0.419194i
\(197\) −152.105 190.734i −0.772108 0.968192i 0.227877 0.973690i \(-0.426822\pi\)
−0.999985 + 0.00549749i \(0.998250\pi\)
\(198\) 0 0
\(199\) −70.5672 309.175i −0.354609 1.55364i −0.766399 0.642365i \(-0.777953\pi\)
0.411789 0.911279i \(-0.364904\pi\)
\(200\) 184.162 + 293.092i 0.920811 + 1.46546i
\(201\) 0 0
\(202\) 29.7970i 0.147510i
\(203\) −155.159 228.571i −0.764329 1.12597i
\(204\) 0 0
\(205\) 264.234 29.7720i 1.28895 0.145229i
\(206\) −221.285 + 139.042i −1.07420 + 0.674963i
\(207\) 0 0
\(208\) 164.166 + 130.918i 0.789261 + 0.629415i
\(209\) −8.69372 + 6.93301i −0.0415967 + 0.0331723i
\(210\) 0 0
\(211\) 353.376 123.652i 1.67477 0.586027i 0.684978 0.728563i \(-0.259812\pi\)
0.989789 + 0.142537i \(0.0455259\pi\)
\(212\) 231.468 480.648i 1.09183 2.26721i
\(213\) 0 0
\(214\) 275.113 + 96.2661i 1.28557 + 0.449842i
\(215\) −28.7534 + 28.7534i −0.133737 + 0.133737i
\(216\) 0 0
\(217\) 0.351652 3.12100i 0.00162052 0.0143825i
\(218\) 437.400 + 49.2831i 2.00642 + 0.226069i
\(219\) 0 0
\(220\) −31.1250 31.1250i −0.141477 0.141477i
\(221\) −63.8380 + 182.438i −0.288860 + 0.825513i
\(222\) 0 0
\(223\) −249.428 120.118i −1.11851 0.538647i −0.219079 0.975707i \(-0.570305\pi\)
−0.899432 + 0.437061i \(0.856020\pi\)
\(224\) −84.2010 240.633i −0.375897 1.07425i
\(225\) 0 0
\(226\) −355.054 445.223i −1.57103 1.97001i
\(227\) 163.809 205.410i 0.721624 0.904888i −0.276805 0.960926i \(-0.589276\pi\)
0.998429 + 0.0560385i \(0.0178470\pi\)
\(228\) 0 0
\(229\) 164.093 + 261.153i 0.716564 + 1.14040i 0.984230 + 0.176893i \(0.0566046\pi\)
−0.267667 + 0.963512i \(0.586253\pi\)
\(230\) −51.6562 458.462i −0.224592 1.99331i
\(231\) 0 0
\(232\) 202.275 461.064i 0.871875 1.98734i
\(233\) −92.4111 −0.396614 −0.198307 0.980140i \(-0.563544\pi\)
−0.198307 + 0.980140i \(0.563544\pi\)
\(234\) 0 0
\(235\) 24.6821 15.5088i 0.105030 0.0659948i
\(236\) −785.982 + 179.395i −3.33043 + 0.760150i
\(237\) 0 0
\(238\) 659.583 526.000i 2.77136 2.21008i
\(239\) 91.6570 401.575i 0.383502 1.68023i −0.302910 0.953019i \(-0.597958\pi\)
0.686412 0.727213i \(-0.259185\pi\)
\(240\) 0 0
\(241\) −53.8613 + 111.844i −0.223491 + 0.464084i −0.982321 0.187205i \(-0.940057\pi\)
0.758830 + 0.651289i \(0.225771\pi\)
\(242\) −365.510 229.665i −1.51037 0.949031i
\(243\) 0 0
\(244\) 47.5467 47.5467i 0.194864 0.194864i
\(245\) 121.427 + 252.146i 0.495621 + 1.02917i
\(246\) 0 0
\(247\) −116.416 13.1169i −0.471320 0.0531051i
\(248\) 5.15717 2.48356i 0.0207950 0.0100144i
\(249\) 0 0
\(250\) −40.1686 + 114.795i −0.160674 + 0.459181i
\(251\) −17.8330 + 28.3810i −0.0710477 + 0.113072i −0.880358 0.474309i \(-0.842698\pi\)
0.809311 + 0.587381i \(0.199841\pi\)
\(252\) 0 0
\(253\) 4.70889 + 13.4572i 0.0186122 + 0.0531906i
\(254\) 337.075 + 76.9351i 1.32707 + 0.302894i
\(255\) 0 0
\(256\) −302.428 + 379.233i −1.18136 + 1.48138i
\(257\) 60.1375 + 263.480i 0.233998 + 1.02521i 0.946287 + 0.323327i \(0.104801\pi\)
−0.712289 + 0.701886i \(0.752342\pi\)
\(258\) 0 0
\(259\) 17.2544 + 153.137i 0.0666193 + 0.591262i
\(260\) 463.751i 1.78366i
\(261\) 0 0
\(262\) −272.858 −1.04144
\(263\) −177.612 + 20.0120i −0.675329 + 0.0760914i −0.442967 0.896538i \(-0.646074\pi\)
−0.232362 + 0.972629i \(0.574646\pi\)
\(264\) 0 0
\(265\) −394.214 + 89.9767i −1.48760 + 0.339535i
\(266\) 399.783 + 318.816i 1.50294 + 1.19856i
\(267\) 0 0
\(268\) 135.470 593.532i 0.505484 2.21467i
\(269\) 369.061 129.140i 1.37197 0.480074i 0.459124 0.888372i \(-0.348163\pi\)
0.912849 + 0.408298i \(0.133878\pi\)
\(270\) 0 0
\(271\) 28.6724 + 18.0161i 0.105802 + 0.0664799i 0.583894 0.811830i \(-0.301528\pi\)
−0.478092 + 0.878310i \(0.658671\pi\)
\(272\) 626.117 + 219.088i 2.30190 + 0.805470i
\(273\) 0 0
\(274\) 237.503 + 493.180i 0.866799 + 1.79993i
\(275\) −1.65734 + 14.7093i −0.00602669 + 0.0534884i
\(276\) 0 0
\(277\) −106.776 + 51.4207i −0.385473 + 0.185634i −0.616576 0.787295i \(-0.711481\pi\)
0.231103 + 0.972929i \(0.425767\pi\)
\(278\) −342.518 342.518i −1.23208 1.23208i
\(279\) 0 0
\(280\) −589.860 + 938.756i −2.10664 + 3.35270i
\(281\) −257.658 124.081i −0.916932 0.441571i −0.0849569 0.996385i \(-0.527075\pi\)
−0.831975 + 0.554814i \(0.812790\pi\)
\(282\) 0 0
\(283\) −221.399 50.5329i −0.782329 0.178561i −0.187340 0.982295i \(-0.559986\pi\)
−0.594989 + 0.803734i \(0.702844\pi\)
\(284\) 484.950 + 608.108i 1.70757 + 2.14122i
\(285\) 0 0
\(286\) 4.63124 + 20.2908i 0.0161932 + 0.0709469i
\(287\) 201.038 + 319.951i 0.700482 + 1.11481i
\(288\) 0 0
\(289\) 321.610i 1.11284i
\(290\) −673.345 + 178.958i −2.32188 + 0.617098i
\(291\) 0 0
\(292\) −257.629 + 29.0278i −0.882290 + 0.0994102i
\(293\) 160.239 100.685i 0.546891 0.343634i −0.230079 0.973172i \(-0.573899\pi\)
0.776970 + 0.629538i \(0.216756\pi\)
\(294\) 0 0
\(295\) 477.744 + 380.988i 1.61947 + 1.29149i
\(296\) −219.584 + 175.112i −0.741837 + 0.591595i
\(297\) 0 0
\(298\) −201.569 + 70.5320i −0.676405 + 0.236685i
\(299\) −65.1735 + 135.334i −0.217971 + 0.452622i
\(300\) 0 0
\(301\) −54.5425 19.0853i −0.181204 0.0634062i
\(302\) −658.235 + 658.235i −2.17959 + 2.17959i
\(303\) 0 0
\(304\) −45.0165 + 399.533i −0.148081 + 1.31425i
\(305\) −50.6452 5.70634i −0.166050 0.0187093i
\(306\) 0 0
\(307\) −287.766 287.766i −0.937349 0.937349i 0.0608010 0.998150i \(-0.480634\pi\)
−0.998150 + 0.0608010i \(0.980634\pi\)
\(308\) 20.6595 59.0414i 0.0670762 0.191693i
\(309\) 0 0
\(310\) −7.13650 3.43676i −0.0230210 0.0110863i
\(311\) 7.89034 + 22.5493i 0.0253709 + 0.0725058i 0.955872 0.293782i \(-0.0949141\pi\)
−0.930501 + 0.366288i \(0.880628\pi\)
\(312\) 0 0
\(313\) 256.380 + 321.491i 0.819107 + 1.02713i 0.999056 + 0.0434514i \(0.0138354\pi\)
−0.179949 + 0.983676i \(0.557593\pi\)
\(314\) −418.514 + 524.800i −1.33285 + 1.67134i
\(315\) 0 0
\(316\) 103.763 + 165.138i 0.328365 + 0.522590i
\(317\) 53.9274 + 478.619i 0.170118 + 1.50984i 0.731248 + 0.682111i \(0.238938\pi\)
−0.561131 + 0.827727i \(0.689633\pi\)
\(318\) 0 0
\(319\) 19.0558 10.0219i 0.0597361 0.0314165i
\(320\) 76.8630 0.240197
\(321\) 0 0
\(322\) 555.134 348.814i 1.72402 1.08327i
\(323\) −360.821 + 82.3550i −1.11709 + 0.254969i
\(324\) 0 0
\(325\) −121.928 + 97.2347i −0.375164 + 0.299184i
\(326\) 203.126 889.953i 0.623086 2.72992i
\(327\) 0 0
\(328\) −298.801 + 620.467i −0.910980 + 1.89167i
\(329\) 35.0748 + 22.0389i 0.106610 + 0.0669877i
\(330\) 0 0
\(331\) −253.593 + 253.593i −0.766142 + 0.766142i −0.977425 0.211283i \(-0.932236\pi\)
0.211283 + 0.977425i \(0.432236\pi\)
\(332\) −158.511 329.152i −0.477443 0.991421i
\(333\) 0 0
\(334\) 137.104 + 15.4479i 0.410492 + 0.0462513i
\(335\) −415.742 + 200.211i −1.24102 + 0.597644i
\(336\) 0 0
\(337\) 7.65449 21.8753i 0.0227136 0.0649118i −0.931968 0.362540i \(-0.881910\pi\)
0.954682 + 0.297628i \(0.0961955\pi\)
\(338\) 205.580 327.178i 0.608223 0.967982i
\(339\) 0 0
\(340\) −483.874 1382.83i −1.42316 4.06716i
\(341\) 0.238640 + 0.0544680i 0.000699823 + 0.000159730i
\(342\) 0 0
\(343\) 43.0726 54.0114i 0.125576 0.157468i
\(344\) −23.4345 102.673i −0.0681236 0.298469i
\(345\) 0 0
\(346\) 15.4018 + 136.695i 0.0445139 + 0.395072i
\(347\) 307.231i 0.885393i 0.896672 + 0.442696i \(0.145978\pi\)
−0.896672 + 0.442696i \(0.854022\pi\)
\(348\) 0 0
\(349\) 81.9545 0.234827 0.117413 0.993083i \(-0.462540\pi\)
0.117413 + 0.993083i \(0.462540\pi\)
\(350\) 676.411 76.2132i 1.93260 0.217752i
\(351\) 0 0
\(352\) 19.3707 4.42124i 0.0550305 0.0125603i
\(353\) −34.5942 27.5880i −0.0980006 0.0781529i 0.573264 0.819371i \(-0.305677\pi\)
−0.671264 + 0.741218i \(0.734248\pi\)
\(354\) 0 0
\(355\) 131.184 574.754i 0.369532 1.61902i
\(356\) −823.354 + 288.104i −2.31279 + 0.809281i
\(357\) 0 0
\(358\) −528.164 331.867i −1.47532 0.927004i
\(359\) 329.635 + 115.344i 0.918204 + 0.321294i 0.747680 0.664060i \(-0.231168\pi\)
0.170525 + 0.985353i \(0.445454\pi\)
\(360\) 0 0
\(361\) 59.3020 + 123.142i 0.164271 + 0.341113i
\(362\) 68.3233 606.386i 0.188738 1.67510i
\(363\) 0 0
\(364\) 593.756 285.938i 1.63120 0.785543i
\(365\) 138.951 + 138.951i 0.380687 + 0.380687i
\(366\) 0 0
\(367\) 117.163 186.464i 0.319246 0.508076i −0.648094 0.761560i \(-0.724434\pi\)
0.967340 + 0.253484i \(0.0815765\pi\)
\(368\) 464.458 + 223.671i 1.26211 + 0.607802i
\(369\) 0 0
\(370\) 378.908 + 86.4833i 1.02408 + 0.233739i
\(371\) −358.263 449.247i −0.965668 1.21091i
\(372\) 0 0
\(373\) 58.3911 + 255.828i 0.156545 + 0.685867i 0.990896 + 0.134633i \(0.0429855\pi\)
−0.834351 + 0.551234i \(0.814157\pi\)
\(374\) 34.9809 + 55.6718i 0.0935318 + 0.148855i
\(375\) 0 0
\(376\) 75.4955i 0.200786i
\(377\) 216.623 + 67.3012i 0.574597 + 0.178518i
\(378\) 0 0
\(379\) −224.710 + 25.3187i −0.592901 + 0.0668039i −0.403317 0.915061i \(-0.632143\pi\)
−0.189584 + 0.981864i \(0.560714\pi\)
\(380\) 751.879 472.437i 1.97863 1.24326i
\(381\) 0 0
\(382\) 79.7857 + 63.6270i 0.208863 + 0.166563i
\(383\) −106.140 + 84.6436i −0.277127 + 0.221002i −0.752183 0.658954i \(-0.770999\pi\)
0.475056 + 0.879956i \(0.342428\pi\)
\(384\) 0 0
\(385\) −44.7505 + 15.6589i −0.116235 + 0.0406724i
\(386\) −461.679 + 958.686i −1.19606 + 2.48364i
\(387\) 0 0
\(388\) 1349.63 + 472.256i 3.47843 + 1.21715i
\(389\) 11.0445 11.0445i 0.0283920 0.0283920i −0.692768 0.721160i \(-0.743609\pi\)
0.721160 + 0.692768i \(0.243609\pi\)
\(390\) 0 0
\(391\) −53.1305 + 471.546i −0.135884 + 1.20600i
\(392\) −720.251 81.1528i −1.83737 0.207022i
\(393\) 0 0
\(394\) −618.237 618.237i −1.56913 1.56913i
\(395\) 48.8235 139.530i 0.123604 0.353240i
\(396\) 0 0
\(397\) −258.406 124.442i −0.650896 0.313455i 0.0791405 0.996863i \(-0.474782\pi\)
−0.730036 + 0.683409i \(0.760497\pi\)
\(398\) −375.378 1072.77i −0.943160 2.69540i
\(399\) 0 0
\(400\) 333.703 + 418.451i 0.834258 + 1.04613i
\(401\) −94.6371 + 118.671i −0.236003 + 0.295938i −0.885703 0.464253i \(-0.846323\pi\)
0.649700 + 0.760191i \(0.274894\pi\)
\(402\) 0 0
\(403\) 1.37204 + 2.18360i 0.00340458 + 0.00541835i
\(404\) 8.23305 + 73.0703i 0.0203788 + 0.180867i
\(405\) 0 0
\(406\) −644.295 751.765i −1.58693 1.85164i
\(407\) −12.0104 −0.0295095
\(408\) 0 0
\(409\) −138.561 + 87.0640i −0.338781 + 0.212870i −0.690668 0.723172i \(-0.742683\pi\)
0.351886 + 0.936043i \(0.385540\pi\)
\(410\) 929.086 212.058i 2.26606 0.517214i
\(411\) 0 0
\(412\) −504.233 + 402.112i −1.22387 + 0.976000i
\(413\) −193.226 + 846.580i −0.467860 + 2.04983i
\(414\) 0 0
\(415\) −120.144 + 249.481i −0.289503 + 0.601160i
\(416\) 177.246 + 111.371i 0.426071 + 0.267718i
\(417\) 0 0
\(418\) −28.1795 + 28.1795i −0.0674150 + 0.0674150i
\(419\) 14.3641 + 29.8274i 0.0342819 + 0.0711870i 0.917406 0.397952i \(-0.130279\pi\)
−0.883125 + 0.469139i \(0.844564\pi\)
\(420\) 0 0
\(421\) −442.876 49.9001i −1.05196 0.118528i −0.430986 0.902358i \(-0.641834\pi\)
−0.620974 + 0.783831i \(0.713263\pi\)
\(422\) 1208.88 582.167i 2.86465 1.37954i
\(423\) 0 0
\(424\) 345.877 988.459i 0.815747 2.33127i
\(425\) −262.117 + 417.157i −0.616747 + 0.981547i
\(426\) 0 0
\(427\) −23.9206 68.3611i −0.0560201 0.160096i
\(428\) 701.251 + 160.056i 1.63844 + 0.373962i
\(429\) 0 0
\(430\) −90.8633 + 113.939i −0.211310 + 0.264974i
\(431\) −56.6584 248.237i −0.131458 0.575955i −0.997154 0.0753857i \(-0.975981\pi\)
0.865696 0.500569i \(-0.166876\pi\)
\(432\) 0 0
\(433\) 41.5408 + 368.685i 0.0959371 + 0.851465i 0.945864 + 0.324564i \(0.105218\pi\)
−0.849927 + 0.526901i \(0.823354\pi\)
\(434\) 11.2561i 0.0259358i
\(435\) 0 0
\(436\) 1086.24 2.49138
\(437\) −285.811 + 32.2032i −0.654030 + 0.0736915i
\(438\) 0 0
\(439\) 472.512 107.848i 1.07634 0.245667i 0.352622 0.935766i \(-0.385290\pi\)
0.723715 + 0.690099i \(0.242433\pi\)
\(440\) −67.5556 53.8738i −0.153535 0.122440i
\(441\) 0 0
\(442\) −154.143 + 675.345i −0.348740 + 1.52793i
\(443\) 133.331 46.6547i 0.300974 0.105315i −0.175567 0.984467i \(-0.556176\pi\)
0.476541 + 0.879152i \(0.341890\pi\)
\(444\) 0 0
\(445\) 559.825 + 351.761i 1.25803 + 0.790475i
\(446\) −936.503 327.696i −2.09978 0.734745i
\(447\) 0 0
\(448\) 47.3918 + 98.4102i 0.105785 + 0.219666i
\(449\) −55.2993 + 490.795i −0.123161 + 1.09309i 0.768332 + 0.640051i \(0.221087\pi\)
−0.891493 + 0.453034i \(0.850342\pi\)
\(450\) 0 0
\(451\) −26.5331 + 12.7777i −0.0588317 + 0.0283319i
\(452\) −993.706 993.706i −2.19847 2.19847i
\(453\) 0 0
\(454\) 500.957 797.269i 1.10343 1.75610i
\(455\) −450.039 216.727i −0.989096 0.476324i
\(456\) 0 0
\(457\) 890.248 + 203.193i 1.94803 + 0.444624i 0.983653 + 0.180077i \(0.0576347\pi\)
0.964373 + 0.264547i \(0.0852225\pi\)
\(458\) 689.187 + 864.213i 1.50478 + 1.88693i
\(459\) 0 0
\(460\) −253.351 1110.00i −0.550762 2.41305i
\(461\) 70.6093 + 112.374i 0.153166 + 0.243762i 0.914489 0.404611i \(-0.132593\pi\)
−0.761323 + 0.648372i \(0.775450\pi\)
\(462\) 0 0
\(463\) 36.6184i 0.0790895i 0.999218 + 0.0395447i \(0.0125908\pi\)
−0.999218 + 0.0395447i \(0.987409\pi\)
\(464\) 230.973 743.437i 0.497788 1.60223i
\(465\) 0 0
\(466\) −329.109 + 37.0817i −0.706243 + 0.0795745i
\(467\) −125.291 + 78.7258i −0.268290 + 0.168578i −0.659458 0.751742i \(-0.729214\pi\)
0.391168 + 0.920319i \(0.372071\pi\)
\(468\) 0 0
\(469\) −512.672 408.843i −1.09312 0.871733i
\(470\) 81.6786 65.1365i 0.173784 0.138588i
\(471\) 0 0
\(472\) −1493.76 + 522.690i −3.16475 + 1.10739i
\(473\) 1.95401 4.05755i 0.00413111 0.00857833i
\(474\) 0 0
\(475\) −281.858 98.6265i −0.593386 0.207635i
\(476\) 1472.14 1472.14i 3.09273 3.09273i
\(477\) 0 0
\(478\) 165.284 1466.93i 0.345782 3.06890i
\(479\) 541.118 + 60.9693i 1.12968 + 0.127285i 0.656959 0.753926i \(-0.271842\pi\)
0.472723 + 0.881211i \(0.343271\pi\)
\(480\) 0 0
\(481\) −89.4749 89.4749i −0.186019 0.186019i
\(482\) −146.940 + 419.930i −0.304855 + 0.871225i
\(483\) 0 0
\(484\) −959.789 462.210i −1.98304 0.954980i
\(485\) −357.948 1022.96i −0.738036 2.10919i
\(486\) 0 0
\(487\) −143.770 180.282i −0.295216 0.370190i 0.611997 0.790860i \(-0.290366\pi\)
−0.907214 + 0.420670i \(0.861795\pi\)
\(488\) 82.2977 103.198i 0.168643 0.211471i
\(489\) 0 0
\(490\) 533.624 + 849.257i 1.08903 + 1.73318i
\(491\) −55.3414 491.168i −0.112712 1.00034i −0.915013 0.403424i \(-0.867820\pi\)
0.802302 0.596919i \(-0.203608\pi\)
\(492\) 0 0
\(493\) 716.157 25.3412i 1.45265 0.0514020i
\(494\) −419.863 −0.849926
\(495\) 0 0
\(496\) 7.49397 4.70877i 0.0151088 0.00949349i
\(497\) 816.761 186.420i 1.64338 0.375091i
\(498\) 0 0
\(499\) 116.986 93.2931i 0.234441 0.186960i −0.499222 0.866474i \(-0.666381\pi\)
0.733663 + 0.679514i \(0.237809\pi\)
\(500\) −66.7859 + 292.608i −0.133572 + 0.585216i
\(501\) 0 0
\(502\) −52.1212 + 108.231i −0.103827 + 0.215599i
\(503\) 579.852 + 364.345i 1.15279 + 0.724344i 0.966124 0.258080i \(-0.0830897\pi\)
0.186664 + 0.982424i \(0.440233\pi\)
\(504\) 0 0
\(505\) 39.4101 39.4101i 0.0780398 0.0780398i
\(506\) 22.1700 + 46.0365i 0.0438143 + 0.0909813i
\(507\) 0 0
\(508\) 847.857 + 95.5305i 1.66901 + 0.188052i
\(509\) 285.063 137.279i 0.560046 0.269704i −0.132372 0.991200i \(-0.542259\pi\)
0.692419 + 0.721496i \(0.256545\pi\)
\(510\) 0 0
\(511\) −92.2295 + 263.577i −0.180488 + 0.515806i
\(512\) −609.618 + 970.201i −1.19066 + 1.89492i
\(513\) 0 0
\(514\) 319.898 + 914.215i 0.622369 + 1.77863i
\(515\) 476.576 + 108.775i 0.925390 + 0.211214i
\(516\) 0 0
\(517\) −2.01289 + 2.52408i −0.00389340 + 0.00488217i
\(518\) 122.898 + 538.452i 0.237255 + 1.03948i
\(519\) 0 0
\(520\) −101.927 904.625i −0.196013 1.73966i
\(521\) 561.548i 1.07783i −0.842361 0.538914i \(-0.818835\pi\)
0.842361 0.538914i \(-0.181165\pi\)
\(522\) 0 0
\(523\) −649.609 −1.24208 −0.621041 0.783778i \(-0.713290\pi\)
−0.621041 + 0.783778i \(0.713290\pi\)
\(524\) −669.123 + 75.3920i −1.27695 + 0.143878i
\(525\) 0 0
\(526\) −624.509 + 142.540i −1.18728 + 0.270989i
\(527\) 6.36957 + 5.07956i 0.0120865 + 0.00963863i
\(528\) 0 0
\(529\) 35.6531 156.206i 0.0673971 0.295286i
\(530\) −1367.83 + 478.625i −2.58082 + 0.903066i
\(531\) 0 0
\(532\) 1068.47 + 671.362i 2.00840 + 1.26196i
\(533\) −292.858 102.475i −0.549452 0.192261i
\(534\) 0 0
\(535\) −236.546 491.193i −0.442143 0.918119i
\(536\) 133.806 1187.56i 0.249638 2.21560i
\(537\) 0 0
\(538\) 1262.54 608.006i 2.34672 1.13012i
\(539\) −21.9168 21.9168i −0.0406620 0.0406620i
\(540\) 0 0
\(541\) 412.119 655.884i 0.761774 1.21236i −0.210290 0.977639i \(-0.567441\pi\)
0.972064 0.234717i \(-0.0754162\pi\)
\(542\) 109.342 + 52.6563i 0.201738 + 0.0971519i
\(543\) 0 0
\(544\) 644.722 + 147.153i 1.18515 + 0.270503i
\(545\) −513.331 643.697i −0.941892 1.18109i
\(546\) 0 0
\(547\) −116.423 510.082i −0.212839 0.932508i −0.962627 0.270830i \(-0.912702\pi\)
0.749788 0.661678i \(-0.230155\pi\)
\(548\) 718.691 + 1143.79i 1.31148 + 2.08721i
\(549\) 0 0
\(550\) 53.0502i 0.0964549i
\(551\) 111.565 + 419.772i 0.202477 + 0.761837i
\(552\) 0 0
\(553\) 208.748 23.5202i 0.377482 0.0425320i
\(554\) −359.635 + 225.973i −0.649160 + 0.407894i
\(555\) 0 0
\(556\) −934.588 745.309i −1.68091 1.34048i
\(557\) 133.141 106.177i 0.239033 0.190622i −0.496645 0.867954i \(-0.665435\pi\)
0.735678 + 0.677331i \(0.236864\pi\)
\(558\) 0 0
\(559\) 44.7850 15.6709i 0.0801163 0.0280339i
\(560\) −743.794 + 1544.50i −1.32820 + 2.75804i
\(561\) 0 0
\(562\) −967.402 338.509i −1.72136 0.602329i
\(563\) 622.112 622.112i 1.10499 1.10499i 0.111195 0.993799i \(-0.464532\pi\)
0.993799 0.111195i \(-0.0354679\pi\)
\(564\) 0 0
\(565\) −119.260 + 1058.46i −0.211080 + 1.87339i
\(566\) −808.759 91.1252i −1.42890 0.160999i
\(567\) 0 0
\(568\) 1079.63 + 1079.63i 1.90076 + 1.90076i
\(569\) −62.1379 + 177.580i −0.109205 + 0.312091i −0.985498 0.169689i \(-0.945724\pi\)
0.876292 + 0.481780i \(0.160010\pi\)
\(570\) 0 0
\(571\) 485.208 + 233.664i 0.849751 + 0.409218i 0.807485 0.589888i \(-0.200828\pi\)
0.0422657 + 0.999106i \(0.486542\pi\)
\(572\) 16.9635 + 48.4790i 0.0296565 + 0.0847535i
\(573\) 0 0
\(574\) 844.356 + 1058.79i 1.47100 + 1.84458i
\(575\) −238.719 + 299.344i −0.415163 + 0.520599i
\(576\) 0 0
\(577\) −276.433 439.941i −0.479087 0.762462i 0.516502 0.856286i \(-0.327234\pi\)
−0.995589 + 0.0938238i \(0.970091\pi\)
\(578\) 129.052 + 1145.37i 0.223274 + 1.98161i
\(579\) 0 0
\(580\) −1601.78 + 624.904i −2.76169 + 1.07742i
\(581\) −393.497 −0.677276
\(582\) 0 0
\(583\) 37.9185 23.8258i 0.0650403 0.0408675i
\(584\) −496.168 + 113.247i −0.849603 + 0.193916i
\(585\) 0 0
\(586\) 530.267 422.874i 0.904893 0.721628i
\(587\) 235.013 1029.66i 0.400363 1.75411i −0.225568 0.974227i \(-0.572424\pi\)
0.625931 0.779878i \(-0.284719\pi\)
\(588\) 0 0
\(589\) −2.14252 + 4.44899i −0.00363755 + 0.00755346i
\(590\) 1854.30 + 1165.13i 3.14288 + 1.97480i
\(591\) 0 0
\(592\) −307.072 + 307.072i −0.518703 + 0.518703i
\(593\) −85.9928 178.566i −0.145013 0.301123i 0.815793 0.578344i \(-0.196301\pi\)
−0.960806 + 0.277221i \(0.910587\pi\)
\(594\) 0 0
\(595\) −1568.08 176.680i −2.63542 0.296941i
\(596\) −474.814 + 228.658i −0.796667 + 0.383655i
\(597\) 0 0
\(598\) −177.801 + 508.126i −0.297326 + 0.849708i
\(599\) 154.573 246.002i 0.258052 0.410687i −0.692421 0.721493i \(-0.743456\pi\)
0.950473 + 0.310806i \(0.100599\pi\)
\(600\) 0 0
\(601\) −168.543 481.670i −0.280438 0.801447i −0.994816 0.101687i \(-0.967576\pi\)
0.714378 0.699760i \(-0.246710\pi\)
\(602\) −201.904 46.0833i −0.335389 0.0765503i
\(603\) 0 0
\(604\) −1432.30 + 1796.05i −2.37136 + 2.97359i
\(605\) 179.671 + 787.192i 0.296978 + 1.30114i
\(606\) 0 0
\(607\) 2.33822 + 20.7523i 0.00385209 + 0.0341883i 0.995491 0.0948538i \(-0.0302384\pi\)
−0.991639 + 0.129042i \(0.958810\pi\)
\(608\) 400.825i 0.659251i
\(609\) 0 0
\(610\) −182.656 −0.299435
\(611\) −33.7995 + 3.80829i −0.0553184 + 0.00623289i
\(612\) 0 0
\(613\) −480.301 + 109.626i −0.783525 + 0.178835i −0.595527 0.803335i \(-0.703057\pi\)
−0.187998 + 0.982169i \(0.560200\pi\)
\(614\) −1140.31 909.367i −1.85718 1.48105i
\(615\) 0 0
\(616\) 27.3232 119.711i 0.0443559 0.194336i
\(617\) −814.785 + 285.105i −1.32056 + 0.462083i −0.896296 0.443456i \(-0.853752\pi\)
−0.424262 + 0.905539i \(0.639467\pi\)
\(618\) 0 0
\(619\) −111.989 70.3677i −0.180920 0.113680i 0.438527 0.898718i \(-0.355500\pi\)
−0.619447 + 0.785038i \(0.712643\pi\)
\(620\) −18.4502 6.45602i −0.0297585 0.0104129i
\(621\) 0 0
\(622\) 37.1487 + 77.1400i 0.0597245 + 0.124019i
\(623\) −105.197 + 933.650i −0.168856 + 1.49864i
\(624\) 0 0
\(625\) 654.040 314.969i 1.04646 0.503951i
\(626\) 1042.07 + 1042.07i 1.66464 + 1.66464i
\(627\) 0 0
\(628\) −881.306 + 1402.59i −1.40335 + 2.23342i
\(629\) −360.157 173.443i −0.572587 0.275744i
\(630\) 0 0
\(631\) 901.413 + 205.742i 1.42855 + 0.326056i 0.865724 0.500522i \(-0.166858\pi\)
0.562822 + 0.826578i \(0.309716\pi\)
\(632\) 238.703 + 299.324i 0.377695 + 0.473615i
\(633\) 0 0
\(634\) 384.110 + 1682.89i 0.605851 + 2.65441i
\(635\) −344.066 547.578i −0.541836 0.862327i
\(636\) 0 0
\(637\) 326.552i 0.512640i
\(638\) 63.8431 43.3380i 0.100068 0.0679278i
\(639\) 0 0
\(640\) 986.826 111.189i 1.54192 0.173732i
\(641\) 836.101 525.357i 1.30437 0.819590i 0.312883 0.949792i \(-0.398705\pi\)
0.991488 + 0.130202i \(0.0415625\pi\)
\(642\) 0 0
\(643\) 597.523 + 476.509i 0.929274 + 0.741071i 0.966078 0.258251i \(-0.0831463\pi\)
−0.0368040 + 0.999323i \(0.511718\pi\)
\(644\) 1264.96 1008.77i 1.96423 1.56642i
\(645\) 0 0
\(646\) −1251.97 + 438.082i −1.93803 + 0.678145i
\(647\) 530.613 1101.83i 0.820112 1.70298i 0.115593 0.993297i \(-0.463123\pi\)
0.704520 0.709684i \(-0.251162\pi\)
\(648\) 0 0
\(649\) −63.8779 22.3518i −0.0984251 0.0344404i
\(650\) −395.214 + 395.214i −0.608021 + 0.608021i
\(651\) 0 0
\(652\) 252.222 2238.53i 0.386844 3.43333i
\(653\) −1154.35 130.064i −1.76777 0.199179i −0.832717 0.553699i \(-0.813216\pi\)
−0.935049 + 0.354520i \(0.884644\pi\)
\(654\) 0 0
\(655\) 360.888 + 360.888i 0.550974 + 0.550974i
\(656\) −351.689 + 1005.07i −0.536111 + 1.53212i
\(657\) 0 0
\(658\) 133.757 + 64.4142i 0.203279 + 0.0978939i
\(659\) 103.295 + 295.200i 0.156745 + 0.447951i 0.995297 0.0968701i \(-0.0308831\pi\)
−0.838552 + 0.544821i \(0.816597\pi\)
\(660\) 0 0
\(661\) −741.803 930.192i −1.12224 1.40725i −0.901963 0.431813i \(-0.857874\pi\)
−0.220281 0.975436i \(-0.570697\pi\)
\(662\) −801.377 + 1004.90i −1.21054 + 1.51797i
\(663\) 0 0
\(664\) −381.546 607.228i −0.574618 0.914499i
\(665\) −107.088 950.433i −0.161035 1.42922i
\(666\) 0 0
\(667\) 555.260 + 42.7445i 0.832474 + 0.0640847i
\(668\) 340.486 0.509709
\(669\) 0 0
\(670\) −1400.27 + 879.846i −2.08995 + 1.31320i
\(671\) 5.50301 1.25603i 0.00820120 0.00187187i
\(672\) 0 0
\(673\) −444.801 + 354.717i −0.660922 + 0.527068i −0.895518 0.445025i \(-0.853195\pi\)
0.234596 + 0.972093i \(0.424623\pi\)
\(674\) 18.4825 80.9772i 0.0274221 0.120144i
\(675\) 0 0
\(676\) 413.736 859.133i 0.612036 1.27091i
\(677\) −157.955 99.2497i −0.233316 0.146602i 0.410300 0.911950i \(-0.365424\pi\)
−0.643616 + 0.765348i \(0.722567\pi\)
\(678\) 0 0
\(679\) 1089.02 1089.02i 1.60386 1.60386i
\(680\) −1247.81 2591.10i −1.83501 3.81044i
\(681\) 0 0
\(682\) 0.871738 + 0.0982213i 0.00127821 + 0.000144020i
\(683\) −102.817 + 49.5142i −0.150538 + 0.0724951i −0.507636 0.861572i \(-0.669480\pi\)
0.357098 + 0.934067i \(0.383766\pi\)
\(684\) 0 0
\(685\) 338.164 966.417i 0.493670 1.41083i
\(686\) 131.724 209.638i 0.192018 0.305594i
\(687\) 0 0
\(688\) −53.7817 153.699i −0.0781711 0.223400i
\(689\) 459.983 + 104.988i 0.667610 + 0.152378i
\(690\) 0 0
\(691\) −301.568 + 378.155i −0.436423 + 0.547257i −0.950597 0.310429i \(-0.899527\pi\)
0.514174 + 0.857686i \(0.328099\pi\)
\(692\) 75.5389 + 330.958i 0.109160 + 0.478263i
\(693\) 0 0
\(694\) 123.282 + 1094.16i 0.177640 + 1.57660i
\(695\) 906.043i 1.30366i
\(696\) 0 0
\(697\) −980.177 −1.40628
\(698\) 291.870 32.8858i 0.418151 0.0471143i
\(699\) 0 0
\(700\) 1637.69 373.791i 2.33955 0.533988i
\(701\) 382.725 + 305.213i 0.545969 + 0.435396i 0.857234 0.514927i \(-0.172181\pi\)
−0.311264 + 0.950323i \(0.600752\pi\)
\(702\) 0 0
\(703\) 53.9148 236.216i 0.0766925 0.336012i
\(704\) −8.03499 + 2.81157i −0.0114133 + 0.00399370i
\(705\) 0 0
\(706\) −134.273 84.3691i −0.190188 0.119503i
\(707\) 74.7573 + 26.1587i 0.105739 + 0.0369996i
\(708\) 0 0
\(709\) 461.431 + 958.172i 0.650820 + 1.35144i 0.921351 + 0.388731i \(0.127086\pi\)
−0.270531 + 0.962711i \(0.587199\pi\)
\(710\) 236.562 2099.54i 0.333186 2.95711i
\(711\) 0 0
\(712\) −1542.77 + 742.959i −2.16681 + 1.04348i
\(713\) 4.47694 + 4.47694i 0.00627902 + 0.00627902i
\(714\) 0 0
\(715\) 20.7117 32.9624i 0.0289674 0.0461013i
\(716\) −1386.90 667.895i −1.93701 0.932815i
\(717\) 0 0
\(718\) 1220.23 + 278.511i 1.69949 + 0.387898i
\(719\) 465.243 + 583.396i 0.647069 + 0.811399i 0.991867 0.127278i \(-0.0406240\pi\)
−0.344798 + 0.938677i \(0.612053\pi\)
\(720\) 0 0
\(721\) 154.577 + 677.244i 0.214392 + 0.939312i
\(722\) 260.609 + 414.757i 0.360954 + 0.574455i
\(723\) 0 0
\(724\) 1505.90i 2.07998i
\(725\) 500.143 + 290.113i 0.689853 + 0.400156i
\(726\) 0 0
\(727\) 137.483 15.4906i 0.189110 0.0213076i −0.0169014 0.999857i \(-0.505380\pi\)
0.206012 + 0.978550i \(0.433952\pi\)
\(728\) 1095.38 688.270i 1.50464 0.945426i
\(729\) 0 0
\(730\) 550.610 + 439.097i 0.754260 + 0.601502i
\(731\) 117.191 93.4566i 0.160316 0.127848i
\(732\) 0 0
\(733\) −96.2298 + 33.6723i −0.131282 + 0.0459376i −0.395121 0.918629i \(-0.629297\pi\)
0.263838 + 0.964567i \(0.415011\pi\)
\(734\) 342.438 711.079i 0.466537 0.968773i
\(735\) 0 0
\(736\) 485.085 + 169.738i 0.659082 + 0.230623i
\(737\) 36.1367 36.1367i 0.0490322 0.0490322i
\(738\) 0 0
\(739\) 77.8075 690.560i 0.105288 0.934452i −0.824376 0.566043i \(-0.808474\pi\)
0.929663 0.368410i \(-0.120098\pi\)
\(740\) 953.082 + 107.387i 1.28795 + 0.145117i
\(741\) 0 0
\(742\) −1456.17 1456.17i −1.96250 1.96250i
\(743\) 213.456 610.021i 0.287289 0.821024i −0.706294 0.707918i \(-0.749634\pi\)
0.993583 0.113106i \(-0.0360799\pi\)
\(744\) 0 0
\(745\) 359.886 + 173.312i 0.483069 + 0.232634i
\(746\) 310.608 + 887.666i 0.416364 + 1.18990i
\(747\) 0 0
\(748\) 101.165 + 126.857i 0.135247 + 0.169595i
\(749\) 483.042 605.716i 0.644916 0.808700i
\(750\) 0 0
\(751\) 203.554 + 323.954i 0.271044 + 0.431364i 0.954316 0.298800i \(-0.0965865\pi\)
−0.683272 + 0.730164i \(0.739444\pi\)
\(752\) 13.0698 + 115.998i 0.0173801 + 0.154253i
\(753\) 0 0
\(754\) 798.479 + 152.760i 1.05899 + 0.202599i
\(755\) 1741.19 2.30621
\(756\) 0 0
\(757\) −572.593 + 359.784i −0.756397 + 0.475276i −0.854210 0.519929i \(-0.825958\pi\)
0.0978121 + 0.995205i \(0.468816\pi\)
\(758\) −790.112 + 180.338i −1.04236 + 0.237913i
\(759\) 0 0
\(760\) 1362.83 1086.82i 1.79320 1.43003i
\(761\) −139.727 + 612.184i −0.183610 + 0.804447i 0.796283 + 0.604924i \(0.206796\pi\)
−0.979893 + 0.199523i \(0.936061\pi\)
\(762\) 0 0
\(763\) 507.639 1054.12i 0.665319 1.38155i
\(764\) 213.237 + 133.986i 0.279106 + 0.175374i
\(765\) 0 0
\(766\) −344.037 + 344.037i −0.449134 + 0.449134i
\(767\) −309.361 642.395i −0.403339 0.837543i
\(768\) 0 0
\(769\) −322.552 36.3428i −0.419443 0.0472599i −0.100279 0.994959i \(-0.531974\pi\)
−0.319164 + 0.947700i \(0.603402\pi\)
\(770\) −153.089 + 73.7240i −0.198817 + 0.0957454i
\(771\) 0 0
\(772\) −867.273 + 2478.52i −1.12341 + 3.21052i
\(773\) 246.656 392.551i 0.319089 0.507828i −0.648211 0.761461i \(-0.724483\pi\)
0.967301 + 0.253633i \(0.0816255\pi\)
\(774\) 0 0
\(775\) 2.17106 + 6.20453i 0.00280137 + 0.00800585i
\(776\) 2736.48 + 624.583i 3.52639 + 0.804875i
\(777\) 0 0
\(778\) 34.9016 43.7652i 0.0448606 0.0562534i
\(779\) −132.200 579.204i −0.169704 0.743523i
\(780\) 0 0
\(781\) 7.31037 + 64.8814i 0.00936027 + 0.0830747i
\(782\) 1700.67i 2.17476i
\(783\) 0 0
\(784\) −1120.71 −1.42947
\(785\) 1247.65 140.576i 1.58936 0.179078i
\(786\) 0 0
\(787\) 1295.68 295.731i 1.64636 0.375770i 0.703953 0.710246i \(-0.251416\pi\)
0.942404 + 0.334476i \(0.108559\pi\)