Properties

Label 261.3.s.a.73.1
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 73.1
Character \(\chi\) \(=\) 261.73
Dual form 261.3.s.a.118.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.58169 + 0.290886i) q^{2} +(2.68078 - 0.611870i) q^{4} +(2.49104 + 1.98654i) q^{5} +(1.30161 - 5.70272i) q^{7} +(3.06598 - 1.07283i) q^{8} +O(q^{10})\) \(q+(-2.58169 + 0.290886i) q^{2} +(2.68078 - 0.611870i) q^{4} +(2.49104 + 1.98654i) q^{5} +(1.30161 - 5.70272i) q^{7} +(3.06598 - 1.07283i) q^{8} +(-7.00893 - 4.40400i) q^{10} +(-16.1070 - 5.63608i) q^{11} +(2.84196 + 5.90140i) q^{13} +(-1.70150 + 15.1013i) q^{14} +(-17.5130 + 8.43380i) q^{16} +(14.7807 + 14.7807i) q^{17} +(9.65814 - 15.3708i) q^{19} +(7.89342 + 3.80127i) q^{20} +(43.2227 + 9.86529i) q^{22} +(-18.5750 - 23.2923i) q^{23} +(-3.30408 - 14.4761i) q^{25} +(-9.05369 - 14.4089i) q^{26} -16.0841i q^{28} +(19.9272 - 21.0691i) q^{29} +(-13.3687 + 1.50629i) q^{31} +(31.7582 - 19.9550i) q^{32} +(-42.4586 - 33.8596i) q^{34} +(14.5710 - 11.6200i) q^{35} +(17.2522 - 6.03682i) q^{37} +(-20.4631 + 42.4921i) q^{38} +(9.76869 + 3.41821i) q^{40} +(44.4102 - 44.4102i) q^{41} +(7.00239 - 62.1479i) q^{43} +(-46.6278 - 5.25369i) q^{44} +(54.7302 + 54.7302i) q^{46} +(16.6790 - 47.6658i) q^{47} +(13.3206 + 6.41487i) q^{49} +(12.7410 + 36.4117i) q^{50} +(11.2296 + 14.0814i) q^{52} +(-12.0961 + 15.1681i) q^{53} +(-28.9269 - 46.0368i) q^{55} +(-2.12736 - 18.8808i) q^{56} +(-45.3170 + 60.1904i) q^{58} -47.9911 q^{59} +(41.0683 - 25.8049i) q^{61} +(34.0756 - 7.77754i) q^{62} +(-15.3963 + 12.2781i) q^{64} +(-4.64390 + 20.3463i) q^{65} +(-6.15092 + 12.7725i) q^{67} +(48.6676 + 30.5799i) q^{68} +(-34.2377 + 34.2377i) q^{70} +(11.6321 + 24.1543i) q^{71} +(-12.2617 - 1.38156i) q^{73} +(-42.7839 + 20.6036i) q^{74} +(16.4864 - 47.1153i) q^{76} +(-53.1060 + 84.5178i) q^{77} +(33.5205 + 95.7961i) q^{79} +(-60.3795 - 13.7812i) q^{80} +(-101.735 + 127.571i) q^{82} +(9.73978 + 42.6728i) q^{83} +(7.45688 + 66.1816i) q^{85} +162.483i q^{86} -55.4303 q^{88} +(-53.9337 + 6.07686i) q^{89} +(37.3532 - 8.52561i) q^{91} +(-64.0472 - 51.0760i) q^{92} +(-29.1946 + 127.910i) q^{94} +(54.5935 - 19.1031i) q^{95} +(-124.213 - 78.0480i) q^{97} +(-36.2556 - 12.6864i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} + O(q^{10}) \) \( 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} - 20q^{10} + 8q^{11} - 14q^{13} - 26q^{14} + 18q^{16} + 26q^{17} + 2q^{19} - 46q^{20} + 154q^{22} - 56q^{23} - 34q^{25} - 110q^{26} + 170q^{29} - 88q^{31} + 132q^{32} - 224q^{34} + 210q^{35} - 56q^{37} + 294q^{38} - 492q^{40} + 34q^{41} + 176q^{43} - 126q^{44} + 744q^{46} - 208q^{47} + 506q^{49} - 732q^{50} + 690q^{52} + 14q^{53} + 284q^{55} - 332q^{56} - 508q^{58} + 44q^{59} - 30q^{61} + 504q^{62} - 896q^{64} + 554q^{65} - 574q^{67} + 796q^{68} - 1066q^{70} - 224q^{71} - 22q^{73} - 820q^{74} + 514q^{76} - 436q^{77} + 564q^{79} - 1162q^{80} - 18q^{82} + 126q^{83} + 38q^{85} - 384q^{88} + 160q^{89} - 434q^{91} + 1022q^{92} - 2q^{94} + 642q^{95} + 604q^{97} + 102q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.58169 + 0.290886i −1.29084 + 0.145443i −0.730554 0.682854i \(-0.760738\pi\)
−0.560289 + 0.828298i \(0.689310\pi\)
\(3\) 0 0
\(4\) 2.68078 0.611870i 0.670194 0.152967i
\(5\) 2.49104 + 1.98654i 0.498207 + 0.397307i 0.840100 0.542432i \(-0.182496\pi\)
−0.341892 + 0.939739i \(0.611068\pi\)
\(6\) 0 0
\(7\) 1.30161 5.70272i 0.185944 0.814675i −0.792782 0.609505i \(-0.791368\pi\)
0.978726 0.205170i \(-0.0657746\pi\)
\(8\) 3.06598 1.07283i 0.383247 0.134104i
\(9\) 0 0
\(10\) −7.00893 4.40400i −0.700893 0.440400i
\(11\) −16.1070 5.63608i −1.46427 0.512371i −0.523682 0.851914i \(-0.675442\pi\)
−0.940591 + 0.339543i \(0.889728\pi\)
\(12\) 0 0
\(13\) 2.84196 + 5.90140i 0.218613 + 0.453954i 0.981216 0.192913i \(-0.0617934\pi\)
−0.762603 + 0.646866i \(0.776079\pi\)
\(14\) −1.70150 + 15.1013i −0.121536 + 1.07866i
\(15\) 0 0
\(16\) −17.5130 + 8.43380i −1.09456 + 0.527112i
\(17\) 14.7807 + 14.7807i 0.869452 + 0.869452i 0.992412 0.122959i \(-0.0392385\pi\)
−0.122959 + 0.992412i \(0.539238\pi\)
\(18\) 0 0
\(19\) 9.65814 15.3708i 0.508323 0.808992i −0.489697 0.871893i \(-0.662892\pi\)
0.998020 + 0.0629012i \(0.0200353\pi\)
\(20\) 7.89342 + 3.80127i 0.394671 + 0.190063i
\(21\) 0 0
\(22\) 43.2227 + 9.86529i 1.96467 + 0.448422i
\(23\) −18.5750 23.2923i −0.807608 1.01271i −0.999510 0.0312943i \(-0.990037\pi\)
0.191902 0.981414i \(-0.438534\pi\)
\(24\) 0 0
\(25\) −3.30408 14.4761i −0.132163 0.579045i
\(26\) −9.05369 14.4089i −0.348219 0.554187i
\(27\) 0 0
\(28\) 16.0841i 0.574434i
\(29\) 19.9272 21.0691i 0.687144 0.726521i
\(30\) 0 0
\(31\) −13.3687 + 1.50629i −0.431249 + 0.0485900i −0.324921 0.945741i \(-0.605338\pi\)
−0.106327 + 0.994331i \(0.533909\pi\)
\(32\) 31.7582 19.9550i 0.992443 0.623593i
\(33\) 0 0
\(34\) −42.4586 33.8596i −1.24878 0.995871i
\(35\) 14.5710 11.6200i 0.416315 0.332000i
\(36\) 0 0
\(37\) 17.2522 6.03682i 0.466277 0.163157i −0.0869071 0.996216i \(-0.527698\pi\)
0.553184 + 0.833059i \(0.313413\pi\)
\(38\) −20.4631 + 42.4921i −0.538503 + 1.11821i
\(39\) 0 0
\(40\) 9.76869 + 3.41821i 0.244217 + 0.0854553i
\(41\) 44.4102 44.4102i 1.08318 1.08318i 0.0869640 0.996211i \(-0.472283\pi\)
0.996211 0.0869640i \(-0.0277165\pi\)
\(42\) 0 0
\(43\) 7.00239 62.1479i 0.162846 1.44530i −0.600663 0.799503i \(-0.705096\pi\)
0.763509 0.645797i \(-0.223475\pi\)
\(44\) −46.6278 5.25369i −1.05972 0.119402i
\(45\) 0 0
\(46\) 54.7302 + 54.7302i 1.18979 + 1.18979i
\(47\) 16.6790 47.6658i 0.354872 1.01417i −0.618668 0.785652i \(-0.712327\pi\)
0.973541 0.228515i \(-0.0733868\pi\)
\(48\) 0 0
\(49\) 13.3206 + 6.41487i 0.271849 + 0.130916i
\(50\) 12.7410 + 36.4117i 0.254820 + 0.728234i
\(51\) 0 0
\(52\) 11.2296 + 14.0814i 0.215953 + 0.270796i
\(53\) −12.0961 + 15.1681i −0.228229 + 0.286190i −0.882739 0.469863i \(-0.844303\pi\)
0.654511 + 0.756053i \(0.272875\pi\)
\(54\) 0 0
\(55\) −28.9269 46.0368i −0.525943 0.837033i
\(56\) −2.12736 18.8808i −0.0379886 0.337158i
\(57\) 0 0
\(58\) −45.3170 + 60.1904i −0.781327 + 1.03777i
\(59\) −47.9911 −0.813408 −0.406704 0.913560i \(-0.633322\pi\)
−0.406704 + 0.913560i \(0.633322\pi\)
\(60\) 0 0
\(61\) 41.0683 25.8049i 0.673251 0.423031i −0.151554 0.988449i \(-0.548428\pi\)
0.824805 + 0.565417i \(0.191285\pi\)
\(62\) 34.0756 7.77754i 0.549607 0.125444i
\(63\) 0 0
\(64\) −15.3963 + 12.2781i −0.240567 + 0.191846i
\(65\) −4.64390 + 20.3463i −0.0714446 + 0.313019i
\(66\) 0 0
\(67\) −6.15092 + 12.7725i −0.0918048 + 0.190635i −0.941815 0.336132i \(-0.890881\pi\)
0.850010 + 0.526766i \(0.176596\pi\)
\(68\) 48.6676 + 30.5799i 0.715700 + 0.449704i
\(69\) 0 0
\(70\) −34.2377 + 34.2377i −0.489110 + 0.489110i
\(71\) 11.6321 + 24.1543i 0.163832 + 0.340202i 0.966682 0.255980i \(-0.0823981\pi\)
−0.802850 + 0.596182i \(0.796684\pi\)
\(72\) 0 0
\(73\) −12.2617 1.38156i −0.167968 0.0189255i 0.0275798 0.999620i \(-0.491220\pi\)
−0.195548 + 0.980694i \(0.562649\pi\)
\(74\) −42.7839 + 20.6036i −0.578160 + 0.278427i
\(75\) 0 0
\(76\) 16.4864 47.1153i 0.216926 0.619938i
\(77\) −53.1060 + 84.5178i −0.689689 + 1.09763i
\(78\) 0 0
\(79\) 33.5205 + 95.7961i 0.424310 + 1.21261i 0.935557 + 0.353175i \(0.114898\pi\)
−0.511247 + 0.859434i \(0.670816\pi\)
\(80\) −60.3795 13.7812i −0.754744 0.172265i
\(81\) 0 0
\(82\) −101.735 + 127.571i −1.24067 + 1.55575i
\(83\) 9.73978 + 42.6728i 0.117347 + 0.514130i 0.999100 + 0.0424187i \(0.0135063\pi\)
−0.881753 + 0.471711i \(0.843637\pi\)
\(84\) 0 0
\(85\) 7.45688 + 66.1816i 0.0877280 + 0.778607i
\(86\) 162.483i 1.88934i
\(87\) 0 0
\(88\) −55.4303 −0.629890
\(89\) −53.9337 + 6.07686i −0.605996 + 0.0682794i −0.409631 0.912251i \(-0.634342\pi\)
−0.196365 + 0.980531i \(0.562914\pi\)
\(90\) 0 0
\(91\) 37.3532 8.52561i 0.410474 0.0936881i
\(92\) −64.0472 51.0760i −0.696165 0.555173i
\(93\) 0 0
\(94\) −29.1946 + 127.910i −0.310581 + 1.36074i
\(95\) 54.5935 19.1031i 0.574669 0.201085i
\(96\) 0 0
\(97\) −124.213 78.0480i −1.28054 0.804619i −0.292126 0.956380i \(-0.594363\pi\)
−0.988417 + 0.151761i \(0.951506\pi\)
\(98\) −36.2556 12.6864i −0.369955 0.129453i
\(99\) 0 0
\(100\) −17.7150 36.7856i −0.177150 0.367856i
\(101\) 15.1390 134.362i 0.149891 1.33032i −0.663314 0.748342i \(-0.730850\pi\)
0.813205 0.581978i \(-0.197721\pi\)
\(102\) 0 0
\(103\) 42.8611 20.6408i 0.416127 0.200396i −0.214092 0.976813i \(-0.568679\pi\)
0.630219 + 0.776417i \(0.282965\pi\)
\(104\) 15.0446 + 15.0446i 0.144660 + 0.144660i
\(105\) 0 0
\(106\) 26.8162 42.6778i 0.252983 0.402620i
\(107\) −119.175 57.3917i −1.11379 0.536371i −0.215818 0.976434i \(-0.569242\pi\)
−0.897967 + 0.440063i \(0.854956\pi\)
\(108\) 0 0
\(109\) −42.9080 9.79348i −0.393652 0.0898485i 0.0211130 0.999777i \(-0.493279\pi\)
−0.414765 + 0.909929i \(0.636136\pi\)
\(110\) 88.0715 + 110.438i 0.800650 + 1.00398i
\(111\) 0 0
\(112\) 25.3006 + 110.849i 0.225898 + 0.989724i
\(113\) 48.1620 + 76.6493i 0.426212 + 0.678313i 0.988938 0.148331i \(-0.0473901\pi\)
−0.562726 + 0.826644i \(0.690247\pi\)
\(114\) 0 0
\(115\) 94.9218i 0.825407i
\(116\) 40.5287 68.6744i 0.349386 0.592021i
\(117\) 0 0
\(118\) 123.898 13.9599i 1.04998 0.118305i
\(119\) 103.529 65.0515i 0.869991 0.546651i
\(120\) 0 0
\(121\) 133.068 + 106.119i 1.09974 + 0.877012i
\(122\) −98.5191 + 78.5664i −0.807534 + 0.643987i
\(123\) 0 0
\(124\) −34.9169 + 12.2179i −0.281588 + 0.0985317i
\(125\) 55.0873 114.390i 0.440698 0.915120i
\(126\) 0 0
\(127\) −198.494 69.4561i −1.56295 0.546898i −0.596244 0.802804i \(-0.703341\pi\)
−0.966702 + 0.255905i \(0.917626\pi\)
\(128\) −69.9093 + 69.9093i −0.546166 + 0.546166i
\(129\) 0 0
\(130\) 6.07065 53.8785i 0.0466973 0.414450i
\(131\) 164.999 + 18.5909i 1.25953 + 0.141915i 0.716375 0.697715i \(-0.245800\pi\)
0.543158 + 0.839631i \(0.317228\pi\)
\(132\) 0 0
\(133\) −75.0845 75.0845i −0.564545 0.564545i
\(134\) 12.1644 34.7638i 0.0907791 0.259432i
\(135\) 0 0
\(136\) 61.1745 + 29.4601i 0.449813 + 0.216618i
\(137\) 56.9427 + 162.733i 0.415640 + 1.18783i 0.941428 + 0.337215i \(0.109485\pi\)
−0.525788 + 0.850616i \(0.676229\pi\)
\(138\) 0 0
\(139\) 97.5376 + 122.308i 0.701709 + 0.879915i 0.997150 0.0754457i \(-0.0240379\pi\)
−0.295441 + 0.955361i \(0.595467\pi\)
\(140\) 31.9517 40.0662i 0.228227 0.286187i
\(141\) 0 0
\(142\) −37.0566 58.9752i −0.260962 0.415319i
\(143\) −12.5147 111.071i −0.0875156 0.776723i
\(144\) 0 0
\(145\) 91.4939 12.8979i 0.630992 0.0889512i
\(146\) 32.0577 0.219573
\(147\) 0 0
\(148\) 42.5557 26.7395i 0.287538 0.180672i
\(149\) −101.993 + 23.2793i −0.684519 + 0.156237i −0.550617 0.834758i \(-0.685608\pi\)
−0.133901 + 0.990995i \(0.542751\pi\)
\(150\) 0 0
\(151\) −87.2999 + 69.6194i −0.578145 + 0.461055i −0.868379 0.495900i \(-0.834838\pi\)
0.290234 + 0.956956i \(0.406267\pi\)
\(152\) 13.1213 57.4883i 0.0863245 0.378212i
\(153\) 0 0
\(154\) 112.518 233.646i 0.730637 1.51718i
\(155\) −36.2942 22.8052i −0.234156 0.147130i
\(156\) 0 0
\(157\) 154.052 154.052i 0.981223 0.981223i −0.0186037 0.999827i \(-0.505922\pi\)
0.999827 + 0.0186037i \(0.00592209\pi\)
\(158\) −114.405 237.565i −0.724083 1.50357i
\(159\) 0 0
\(160\) 118.752 + 13.3801i 0.742201 + 0.0836259i
\(161\) −157.007 + 75.6105i −0.975198 + 0.469631i
\(162\) 0 0
\(163\) −18.9751 + 54.2278i −0.116412 + 0.332686i −0.987316 0.158767i \(-0.949248\pi\)
0.870904 + 0.491453i \(0.163534\pi\)
\(164\) 91.8805 146.227i 0.560247 0.891628i
\(165\) 0 0
\(166\) −37.5580 107.335i −0.226253 0.646594i
\(167\) −131.159 29.9362i −0.785384 0.179259i −0.189020 0.981973i \(-0.560531\pi\)
−0.596364 + 0.802714i \(0.703388\pi\)
\(168\) 0 0
\(169\) 78.6200 98.5864i 0.465207 0.583352i
\(170\) −38.5026 168.691i −0.226486 0.992300i
\(171\) 0 0
\(172\) −19.2546 170.889i −0.111945 0.993542i
\(173\) 21.1826i 0.122443i −0.998124 0.0612213i \(-0.980500\pi\)
0.998124 0.0612213i \(-0.0194995\pi\)
\(174\) 0 0
\(175\) −86.8540 −0.496308
\(176\) 329.615 37.1387i 1.87281 0.211015i
\(177\) 0 0
\(178\) 137.472 31.3771i 0.772315 0.176276i
\(179\) 71.5446 + 57.0549i 0.399690 + 0.318742i 0.802622 0.596487i \(-0.203437\pi\)
−0.402932 + 0.915230i \(0.632009\pi\)
\(180\) 0 0
\(181\) −43.7618 + 191.733i −0.241778 + 1.05930i 0.697620 + 0.716468i \(0.254242\pi\)
−0.939398 + 0.342829i \(0.888615\pi\)
\(182\) −93.9541 + 32.8760i −0.516232 + 0.180637i
\(183\) 0 0
\(184\) −81.9393 51.4858i −0.445322 0.279814i
\(185\) 54.9684 + 19.2343i 0.297126 + 0.103969i
\(186\) 0 0
\(187\) −154.767 321.378i −0.827633 1.71860i
\(188\) 15.5474 137.987i 0.0826988 0.733973i
\(189\) 0 0
\(190\) −135.387 + 65.1987i −0.712561 + 0.343151i
\(191\) 173.129 + 173.129i 0.906436 + 0.906436i 0.995983 0.0895465i \(-0.0285418\pi\)
−0.0895465 + 0.995983i \(0.528542\pi\)
\(192\) 0 0
\(193\) −107.871 + 171.676i −0.558917 + 0.889511i −0.999968 0.00797056i \(-0.997463\pi\)
0.441051 + 0.897482i \(0.354606\pi\)
\(194\) 343.381 + 165.364i 1.77001 + 0.852390i
\(195\) 0 0
\(196\) 39.6346 + 9.04635i 0.202218 + 0.0461548i
\(197\) −39.4510 49.4700i −0.200259 0.251117i 0.671554 0.740956i \(-0.265627\pi\)
−0.871813 + 0.489839i \(0.837056\pi\)
\(198\) 0 0
\(199\) −10.0083 43.8490i −0.0502928 0.220347i 0.943536 0.331269i \(-0.107477\pi\)
−0.993829 + 0.110922i \(0.964620\pi\)
\(200\) −25.6607 40.8388i −0.128304 0.204194i
\(201\) 0 0
\(202\) 351.285i 1.73903i
\(203\) −94.2140 141.063i −0.464108 0.694891i
\(204\) 0 0
\(205\) 198.850 22.4050i 0.970000 0.109293i
\(206\) −104.650 + 65.7557i −0.508008 + 0.319203i
\(207\) 0 0
\(208\) −99.5424 79.3824i −0.478569 0.381646i
\(209\) −242.195 + 193.144i −1.15883 + 0.924134i
\(210\) 0 0
\(211\) 267.044 93.4429i 1.26561 0.442857i 0.387748 0.921765i \(-0.373253\pi\)
0.877865 + 0.478908i \(0.158967\pi\)
\(212\) −23.1461 + 48.0634i −0.109180 + 0.226714i
\(213\) 0 0
\(214\) 324.367 + 113.501i 1.51573 + 0.530378i
\(215\) 140.902 140.902i 0.655359 0.655359i
\(216\) 0 0
\(217\) −8.81087 + 78.1986i −0.0406031 + 0.360362i
\(218\) 113.624 + 12.8023i 0.521210 + 0.0587263i
\(219\) 0 0
\(220\) −105.715 105.715i −0.480523 0.480523i
\(221\) −45.2205 + 129.233i −0.204618 + 0.584764i
\(222\) 0 0
\(223\) −9.38970 4.52184i −0.0421063 0.0202773i 0.412712 0.910862i \(-0.364582\pi\)
−0.454818 + 0.890584i \(0.650296\pi\)
\(224\) −72.4610 207.082i −0.323487 0.924472i
\(225\) 0 0
\(226\) −146.635 183.875i −0.648829 0.813605i
\(227\) −41.9912 + 52.6552i −0.184983 + 0.231961i −0.865673 0.500611i \(-0.833109\pi\)
0.680690 + 0.732572i \(0.261680\pi\)
\(228\) 0 0
\(229\) −137.469 218.781i −0.600303 0.955376i −0.999262 0.0384078i \(-0.987771\pi\)
0.398959 0.916969i \(-0.369371\pi\)
\(230\) 27.6114 + 245.058i 0.120050 + 1.06547i
\(231\) 0 0
\(232\) 38.4927 85.9760i 0.165917 0.370586i
\(233\) −139.905 −0.600452 −0.300226 0.953868i \(-0.597062\pi\)
−0.300226 + 0.953868i \(0.597062\pi\)
\(234\) 0 0
\(235\) 136.238 85.6040i 0.579736 0.364272i
\(236\) −128.653 + 29.3643i −0.545141 + 0.124425i
\(237\) 0 0
\(238\) −248.356 + 198.058i −1.04351 + 0.832175i
\(239\) −22.0091 + 96.4282i −0.0920883 + 0.403465i −0.999872 0.0159726i \(-0.994916\pi\)
0.907784 + 0.419438i \(0.137773\pi\)
\(240\) 0 0
\(241\) −158.413 + 328.947i −0.657314 + 1.36493i 0.259552 + 0.965729i \(0.416425\pi\)
−0.916865 + 0.399197i \(0.869289\pi\)
\(242\) −374.409 235.257i −1.54715 0.972136i
\(243\) 0 0
\(244\) 94.3057 94.3057i 0.386499 0.386499i
\(245\) 20.4388 + 42.4415i 0.0834235 + 0.173231i
\(246\) 0 0
\(247\) 118.158 + 13.3132i 0.478371 + 0.0538994i
\(248\) −39.3722 + 18.9606i −0.158759 + 0.0764542i
\(249\) 0 0
\(250\) −108.944 + 311.343i −0.435775 + 1.24537i
\(251\) −117.710 + 187.335i −0.468965 + 0.746353i −0.994536 0.104396i \(-0.966709\pi\)
0.525571 + 0.850750i \(0.323852\pi\)
\(252\) 0 0
\(253\) 167.910 + 479.859i 0.663676 + 1.89668i
\(254\) 532.653 + 121.575i 2.09706 + 0.478640i
\(255\) 0 0
\(256\) 209.261 262.405i 0.817425 1.02502i
\(257\) 29.0472 + 127.264i 0.113024 + 0.495191i 0.999476 + 0.0323701i \(0.0103055\pi\)
−0.886452 + 0.462821i \(0.846837\pi\)
\(258\) 0 0
\(259\) −11.9706 106.242i −0.0462187 0.410202i
\(260\) 57.3852i 0.220712i
\(261\) 0 0
\(262\) −431.383 −1.64650
\(263\) −53.5898 + 6.03812i −0.203763 + 0.0229586i −0.213256 0.976996i \(-0.568407\pi\)
0.00949275 + 0.999955i \(0.496978\pi\)
\(264\) 0 0
\(265\) −60.2638 + 13.7548i −0.227411 + 0.0519050i
\(266\) 215.686 + 172.004i 0.810849 + 0.646630i
\(267\) 0 0
\(268\) −8.67412 + 38.0038i −0.0323661 + 0.141805i
\(269\) −23.6596 + 8.27885i −0.0879538 + 0.0307764i −0.373897 0.927470i \(-0.621979\pi\)
0.285943 + 0.958246i \(0.407693\pi\)
\(270\) 0 0
\(271\) 261.030 + 164.016i 0.963211 + 0.605226i 0.919194 0.393805i \(-0.128841\pi\)
0.0440174 + 0.999031i \(0.485984\pi\)
\(272\) −383.511 134.196i −1.40997 0.493369i
\(273\) 0 0
\(274\) −194.345 403.561i −0.709288 1.47285i
\(275\) −28.3698 + 251.789i −0.103163 + 0.915596i
\(276\) 0 0
\(277\) −448.792 + 216.127i −1.62019 + 0.780241i −0.999991 0.00420714i \(-0.998661\pi\)
−0.620195 + 0.784448i \(0.712947\pi\)
\(278\) −287.389 287.389i −1.03377 1.03377i
\(279\) 0 0
\(280\) 32.2081 51.2590i 0.115029 0.183068i
\(281\) 360.665 + 173.687i 1.28350 + 0.618103i 0.946288 0.323325i \(-0.104801\pi\)
0.337216 + 0.941427i \(0.390515\pi\)
\(282\) 0 0
\(283\) 72.2136 + 16.4823i 0.255172 + 0.0582413i 0.348193 0.937423i \(-0.386795\pi\)
−0.0930214 + 0.995664i \(0.529652\pi\)
\(284\) 45.9624 + 57.6350i 0.161839 + 0.202940i
\(285\) 0 0
\(286\) 64.6182 + 283.111i 0.225938 + 0.989898i
\(287\) −195.454 311.064i −0.681026 1.08385i
\(288\) 0 0
\(289\) 147.938i 0.511895i
\(290\) −232.457 + 59.9127i −0.801575 + 0.206596i
\(291\) 0 0
\(292\) −33.7161 + 3.79890i −0.115466 + 0.0130099i
\(293\) 381.722 239.852i 1.30281 0.818608i 0.311508 0.950243i \(-0.399166\pi\)
0.991298 + 0.131636i \(0.0420230\pi\)
\(294\) 0 0
\(295\) −119.548 95.3360i −0.405246 0.323173i
\(296\) 46.4185 37.0176i 0.156819 0.125059i
\(297\) 0 0
\(298\) 256.543 89.7683i 0.860882 0.301236i
\(299\) 84.6676 175.814i 0.283169 0.588007i
\(300\) 0 0
\(301\) −345.298 120.825i −1.14717 0.401412i
\(302\) 205.130 205.130i 0.679237 0.679237i
\(303\) 0 0
\(304\) −39.5081 + 350.644i −0.129961 + 1.15343i
\(305\) 153.565 + 17.3026i 0.503492 + 0.0567299i
\(306\) 0 0
\(307\) −14.8497 14.8497i −0.0483703 0.0483703i 0.682508 0.730878i \(-0.260889\pi\)
−0.730878 + 0.682508i \(0.760889\pi\)
\(308\) −90.6515 + 259.067i −0.294323 + 0.841127i
\(309\) 0 0
\(310\) 100.334 + 48.3183i 0.323658 + 0.155866i
\(311\) −51.0039 145.761i −0.164000 0.468684i 0.832330 0.554280i \(-0.187006\pi\)
−0.996330 + 0.0855959i \(0.972721\pi\)
\(312\) 0 0
\(313\) 106.381 + 133.398i 0.339876 + 0.426191i 0.922169 0.386788i \(-0.126416\pi\)
−0.582292 + 0.812979i \(0.697844\pi\)
\(314\) −352.902 + 442.526i −1.12389 + 1.40932i
\(315\) 0 0
\(316\) 148.476 + 236.298i 0.469860 + 0.747777i
\(317\) 4.18683 + 37.1591i 0.0132077 + 0.117221i 0.998586 0.0531589i \(-0.0169290\pi\)
−0.985378 + 0.170380i \(0.945500\pi\)
\(318\) 0 0
\(319\) −439.714 + 227.049i −1.37841 + 0.711753i
\(320\) −62.7436 −0.196074
\(321\) 0 0
\(322\) 383.348 240.874i 1.19052 0.748055i
\(323\) 369.946 84.4377i 1.14534 0.261417i
\(324\) 0 0
\(325\) 76.0393 60.6393i 0.233967 0.186582i
\(326\) 33.2137 145.519i 0.101883 0.446377i
\(327\) 0 0
\(328\) 88.5161 183.805i 0.269866 0.560383i
\(329\) −250.116 157.158i −0.760230 0.477684i
\(330\) 0 0
\(331\) 195.213 195.213i 0.589768 0.589768i −0.347800 0.937569i \(-0.613071\pi\)
0.937569 + 0.347800i \(0.113071\pi\)
\(332\) 52.2204 + 108.437i 0.157290 + 0.326616i
\(333\) 0 0
\(334\) 347.320 + 39.1335i 1.03988 + 0.117166i
\(335\) −40.6952 + 19.5978i −0.121478 + 0.0585009i
\(336\) 0 0
\(337\) 86.0626 245.953i 0.255379 0.729830i −0.742801 0.669513i \(-0.766503\pi\)
0.998179 0.0603174i \(-0.0192113\pi\)
\(338\) −174.295 + 277.389i −0.515665 + 0.820676i
\(339\) 0 0
\(340\) 60.4848 + 172.855i 0.177896 + 0.508398i
\(341\) 223.819 + 51.0853i 0.656362 + 0.149810i
\(342\) 0 0
\(343\) 232.625 291.702i 0.678207 0.850444i
\(344\) −45.2051 198.057i −0.131410 0.575746i
\(345\) 0 0
\(346\) 6.16172 + 54.6867i 0.0178084 + 0.158054i
\(347\) 75.7571i 0.218320i −0.994024 0.109160i \(-0.965184\pi\)
0.994024 0.109160i \(-0.0348161\pi\)
\(348\) 0 0
\(349\) −88.0863 −0.252396 −0.126198 0.992005i \(-0.540277\pi\)
−0.126198 + 0.992005i \(0.540277\pi\)
\(350\) 224.230 25.2646i 0.640656 0.0721846i
\(351\) 0 0
\(352\) −623.997 + 142.423i −1.77272 + 0.404611i
\(353\) −333.963 266.327i −0.946071 0.754467i 0.0233860 0.999727i \(-0.492555\pi\)
−0.969457 + 0.245260i \(0.921127\pi\)
\(354\) 0 0
\(355\) −19.0074 + 83.2769i −0.0535420 + 0.234583i
\(356\) −140.866 + 49.2911i −0.395691 + 0.138458i
\(357\) 0 0
\(358\) −201.302 126.486i −0.562296 0.353314i
\(359\) −396.769 138.835i −1.10521 0.386728i −0.284845 0.958574i \(-0.591942\pi\)
−0.820361 + 0.571845i \(0.806228\pi\)
\(360\) 0 0
\(361\) 13.6489 + 28.3422i 0.0378086 + 0.0785103i
\(362\) 57.2067 507.723i 0.158030 1.40255i
\(363\) 0 0
\(364\) 94.9189 45.7105i 0.260766 0.125578i
\(365\) −27.7998 27.7998i −0.0761638 0.0761638i
\(366\) 0 0
\(367\) −133.333 + 212.198i −0.363305 + 0.578196i −0.977494 0.210962i \(-0.932340\pi\)
0.614189 + 0.789159i \(0.289483\pi\)
\(368\) 521.746 + 251.259i 1.41779 + 0.682770i
\(369\) 0 0
\(370\) −147.506 33.6673i −0.398665 0.0909927i
\(371\) 70.7548 + 88.7237i 0.190714 + 0.239148i
\(372\) 0 0
\(373\) 109.293 + 478.845i 0.293012 + 1.28377i 0.880311 + 0.474397i \(0.157334\pi\)
−0.587299 + 0.809370i \(0.699809\pi\)
\(374\) 493.045 + 784.677i 1.31830 + 2.09807i
\(375\) 0 0
\(376\) 164.036i 0.436267i
\(377\) 180.970 + 57.7205i 0.480025 + 0.153105i
\(378\) 0 0
\(379\) 8.35834 0.941759i 0.0220537 0.00248485i −0.100931 0.994893i \(-0.532182\pi\)
0.122984 + 0.992409i \(0.460753\pi\)
\(380\) 134.664 84.6153i 0.354380 0.222672i
\(381\) 0 0
\(382\) −497.326 396.605i −1.30190 1.03823i
\(383\) 81.7068 65.1590i 0.213334 0.170128i −0.510993 0.859585i \(-0.670722\pi\)
0.724327 + 0.689457i \(0.242151\pi\)
\(384\) 0 0
\(385\) −300.187 + 105.040i −0.779706 + 0.272831i
\(386\) 228.551 474.591i 0.592101 1.22951i
\(387\) 0 0
\(388\) −380.742 133.227i −0.981293 0.343369i
\(389\) −3.30195 + 3.30195i −0.00848831 + 0.00848831i −0.711338 0.702850i \(-0.751911\pi\)
0.702850 + 0.711338i \(0.251911\pi\)
\(390\) 0 0
\(391\) 69.7251 618.827i 0.178325 1.58268i
\(392\) 47.7228 + 5.37707i 0.121742 + 0.0137170i
\(393\) 0 0
\(394\) 116.240 + 116.240i 0.295026 + 0.295026i
\(395\) −106.802 + 305.221i −0.270384 + 0.772712i
\(396\) 0 0
\(397\) 596.541 + 287.279i 1.50262 + 0.723625i 0.990783 0.135457i \(-0.0432503\pi\)
0.511839 + 0.859082i \(0.328965\pi\)
\(398\) 38.5933 + 110.293i 0.0969680 + 0.277119i
\(399\) 0 0
\(400\) 179.953 + 225.654i 0.449883 + 0.564135i
\(401\) 297.015 372.445i 0.740687 0.928792i −0.258622 0.965979i \(-0.583268\pi\)
0.999308 + 0.0371871i \(0.0118398\pi\)
\(402\) 0 0
\(403\) −46.8826 74.6132i −0.116334 0.185144i
\(404\) −41.6279 369.458i −0.103039 0.914501i
\(405\) 0 0
\(406\) 284.264 + 336.775i 0.700158 + 0.829494i
\(407\) −311.906 −0.766354
\(408\) 0 0
\(409\) −245.996 + 154.570i −0.601458 + 0.377921i −0.798074 0.602560i \(-0.794148\pi\)
0.196616 + 0.980481i \(0.437005\pi\)
\(410\) −506.851 + 115.685i −1.23622 + 0.282159i
\(411\) 0 0
\(412\) 102.271 81.5587i 0.248232 0.197958i
\(413\) −62.4657 + 273.680i −0.151249 + 0.662663i
\(414\) 0 0
\(415\) −60.5088 + 125.648i −0.145804 + 0.302766i
\(416\) 208.018 + 130.706i 0.500043 + 0.314198i
\(417\) 0 0
\(418\) 569.089 569.089i 1.36146 1.36146i
\(419\) −148.802 308.990i −0.355135 0.737446i 0.644496 0.764608i \(-0.277067\pi\)
−0.999631 + 0.0271619i \(0.991353\pi\)
\(420\) 0 0
\(421\) 528.745 + 59.5753i 1.25593 + 0.141509i 0.714738 0.699392i \(-0.246546\pi\)
0.541189 + 0.840901i \(0.317974\pi\)
\(422\) −662.244 + 318.920i −1.56930 + 0.755734i
\(423\) 0 0
\(424\) −20.8137 + 59.4821i −0.0490889 + 0.140288i
\(425\) 165.131 262.804i 0.388542 0.618362i
\(426\) 0 0
\(427\) −93.7034 267.789i −0.219446 0.627141i
\(428\) −354.598 80.9346i −0.828500 0.189100i
\(429\) 0 0
\(430\) −322.779 + 404.752i −0.750649 + 0.941284i
\(431\) 125.008 + 547.695i 0.290041 + 1.27075i 0.884467 + 0.466604i \(0.154523\pi\)
−0.594425 + 0.804151i \(0.702620\pi\)
\(432\) 0 0
\(433\) −14.0479 124.679i −0.0324432 0.287942i −0.999449 0.0331877i \(-0.989434\pi\)
0.967006 0.254754i \(-0.0819945\pi\)
\(434\) 204.447i 0.471077i
\(435\) 0 0
\(436\) −121.019 −0.277567
\(437\) −537.422 + 60.5529i −1.22980 + 0.138565i
\(438\) 0 0
\(439\) 505.439 115.363i 1.15134 0.262786i 0.396084 0.918214i \(-0.370369\pi\)
0.755258 + 0.655428i \(0.227512\pi\)
\(440\) −138.079 110.114i −0.313816 0.250260i
\(441\) 0 0
\(442\) 79.1532 346.793i 0.179080 0.784599i
\(443\) −57.1618 + 20.0018i −0.129033 + 0.0451507i −0.394023 0.919100i \(-0.628917\pi\)
0.264990 + 0.964251i \(0.414631\pi\)
\(444\) 0 0
\(445\) −146.423 92.0035i −0.329040 0.206749i
\(446\) 25.5566 + 8.94264i 0.0573018 + 0.0200508i
\(447\) 0 0
\(448\) 49.9788 + 103.782i 0.111560 + 0.231656i
\(449\) 80.2125 711.905i 0.178647 1.58554i −0.509829 0.860276i \(-0.670291\pi\)
0.688476 0.725260i \(-0.258280\pi\)
\(450\) 0 0
\(451\) −965.615 + 465.015i −2.14105 + 1.03108i
\(452\) 176.011 + 176.011i 0.389405 + 0.389405i
\(453\) 0 0
\(454\) 93.0913 148.154i 0.205047 0.326330i
\(455\) 109.985 + 52.9658i 0.241724 + 0.116408i
\(456\) 0 0
\(457\) −533.475 121.762i −1.16734 0.266438i −0.405435 0.914124i \(-0.632880\pi\)
−0.761908 + 0.647686i \(0.775737\pi\)
\(458\) 418.543 + 524.836i 0.913850 + 1.14593i
\(459\) 0 0
\(460\) −58.0798 254.464i −0.126260 0.553183i
\(461\) 313.897 + 499.564i 0.680904 + 1.08365i 0.991118 + 0.132985i \(0.0424564\pi\)
−0.310214 + 0.950667i \(0.600401\pi\)
\(462\) 0 0
\(463\) 75.7339i 0.163572i −0.996650 0.0817861i \(-0.973938\pi\)
0.996650 0.0817861i \(-0.0260624\pi\)
\(464\) −171.291 + 537.045i −0.369162 + 1.15742i
\(465\) 0 0
\(466\) 361.192 40.6965i 0.775090 0.0873316i
\(467\) 146.168 91.8436i 0.312994 0.196667i −0.366369 0.930470i \(-0.619399\pi\)
0.679363 + 0.733803i \(0.262256\pi\)
\(468\) 0 0
\(469\) 64.8320 + 51.7018i 0.138235 + 0.110238i
\(470\) −326.823 + 260.632i −0.695367 + 0.554537i
\(471\) 0 0
\(472\) −147.140 + 51.4864i −0.311737 + 0.109081i
\(473\) −463.058 + 961.550i −0.978981 + 2.03288i
\(474\) 0 0
\(475\) −254.422 89.0260i −0.535624 0.187423i
\(476\) 237.735 237.735i 0.499443 0.499443i
\(477\) 0 0
\(478\) 28.7710 255.349i 0.0601903 0.534204i
\(479\) 14.8101 + 1.66870i 0.0309188 + 0.00348372i 0.127410 0.991850i \(-0.459333\pi\)
−0.0964915 + 0.995334i \(0.530762\pi\)
\(480\) 0 0
\(481\) 84.6559 + 84.6559i 0.176000 + 0.176000i
\(482\) 313.285 895.318i 0.649970 1.85751i
\(483\) 0 0
\(484\) 421.657 + 203.059i 0.871193 + 0.419544i
\(485\) −154.373 441.174i −0.318296 0.909636i
\(486\) 0 0
\(487\) 121.461 + 152.307i 0.249406 + 0.312745i 0.890737 0.454519i \(-0.150189\pi\)
−0.641331 + 0.767264i \(0.721618\pi\)
\(488\) 98.2302 123.177i 0.201291 0.252411i
\(489\) 0 0
\(490\) −65.1121 103.625i −0.132882 0.211480i
\(491\) −4.56914 40.5522i −0.00930578 0.0825911i 0.988201 0.153163i \(-0.0489461\pi\)
−0.997507 + 0.0705722i \(0.977517\pi\)
\(492\) 0 0
\(493\) 605.953 16.8788i 1.22911 0.0342370i
\(494\) −308.918 −0.625341
\(495\) 0 0
\(496\) 221.422 139.129i 0.446415 0.280501i
\(497\) 152.886 34.8952i 0.307617 0.0702116i
\(498\) 0 0
\(499\) 510.903 407.432i 1.02385 0.816497i 0.0406810 0.999172i \(-0.487047\pi\)
0.983173 + 0.182676i \(0.0584758\pi\)
\(500\) 77.6850 340.360i 0.155370 0.680720i
\(501\) 0 0
\(502\) 249.398 517.880i 0.496808 1.03163i
\(503\) 543.585 + 341.557i 1.08069 + 0.679040i 0.949958 0.312379i \(-0.101126\pi\)
0.130728 + 0.991418i \(0.458269\pi\)
\(504\) 0 0
\(505\) 304.627 304.627i 0.603222 0.603222i
\(506\) −573.075 1190.00i −1.13256 2.35178i
\(507\) 0 0
\(508\) −574.616 64.7437i −1.13113 0.127448i
\(509\) 108.052 52.0353i 0.212284 0.102230i −0.324720 0.945810i \(-0.605270\pi\)
0.537004 + 0.843580i \(0.319556\pi\)
\(510\) 0 0
\(511\) −23.8386 + 68.1267i −0.0466508 + 0.133320i
\(512\) −253.515 + 403.466i −0.495146 + 0.788020i
\(513\) 0 0
\(514\) −112.010 320.106i −0.217918 0.622775i
\(515\) 147.772 + 33.7280i 0.286936 + 0.0654913i
\(516\) 0 0
\(517\) −537.297 + 673.750i −1.03926 + 1.30319i
\(518\) 61.8089 + 270.802i 0.119322 + 0.522785i
\(519\) 0 0
\(520\) 7.59003 + 67.3634i 0.0145962 + 0.129545i
\(521\) 424.304i 0.814404i 0.913338 + 0.407202i \(0.133495\pi\)
−0.913338 + 0.407202i \(0.866505\pi\)
\(522\) 0 0
\(523\) 4.61578 0.00882558 0.00441279 0.999990i \(-0.498595\pi\)
0.00441279 + 0.999990i \(0.498595\pi\)
\(524\) 453.700 51.1197i 0.865840 0.0975568i
\(525\) 0 0
\(526\) 136.596 31.1770i 0.259687 0.0592720i
\(527\) −219.863 175.335i −0.417197 0.332703i
\(528\) 0 0
\(529\) −79.7873 + 349.571i −0.150827 + 0.660815i
\(530\) 151.581 53.0405i 0.286002 0.100076i
\(531\) 0 0
\(532\) −247.227 155.343i −0.464712 0.291998i
\(533\) 388.294 + 135.870i 0.728507 + 0.254916i
\(534\) 0 0
\(535\) −182.859 379.710i −0.341792 0.709739i
\(536\) −5.15582 + 45.7592i −0.00961907 + 0.0853716i
\(537\) 0 0
\(538\) 58.6734 28.2556i 0.109058 0.0525198i
\(539\) −178.400 178.400i −0.330984 0.330984i
\(540\) 0 0
\(541\) 160.391 255.261i 0.296472 0.471833i −0.664958 0.746880i \(-0.731551\pi\)
0.961431 + 0.275048i \(0.0886936\pi\)
\(542\) −721.608 347.508i −1.33138 0.641159i
\(543\) 0 0
\(544\) 764.356 + 174.459i 1.40507 + 0.320697i
\(545\) −87.4304 109.634i −0.160423 0.201164i
\(546\) 0 0
\(547\) 33.8389 + 148.258i 0.0618627 + 0.271038i 0.996394 0.0848416i \(-0.0270384\pi\)
−0.934532 + 0.355880i \(0.884181\pi\)
\(548\) 252.222 + 401.409i 0.460259 + 0.732498i
\(549\) 0 0
\(550\) 658.293i 1.19690i
\(551\) −131.391 509.786i −0.238459 0.925201i
\(552\) 0 0
\(553\) 589.929 66.4691i 1.06678 0.120197i
\(554\) 1095.77 688.518i 1.97793 1.24281i
\(555\) 0 0
\(556\) 336.313 + 268.201i 0.604880 + 0.482375i
\(557\) 24.5533 19.5806i 0.0440814 0.0351538i −0.601201 0.799098i \(-0.705311\pi\)
0.645283 + 0.763944i \(0.276740\pi\)
\(558\) 0 0
\(559\) 386.660 135.298i 0.691699 0.242036i
\(560\) −157.181 + 326.390i −0.280680 + 0.582839i
\(561\) 0 0
\(562\) −981.646 343.493i −1.74670 0.611197i
\(563\) 667.667 667.667i 1.18591 1.18591i 0.207721 0.978188i \(-0.433395\pi\)
0.978188 0.207721i \(-0.0666048\pi\)
\(564\) 0 0
\(565\) −32.2934 + 286.612i −0.0571565 + 0.507278i
\(566\) −191.227 21.5461i −0.337857 0.0380674i
\(567\) 0 0
\(568\) 61.5773 + 61.5773i 0.108411 + 0.108411i
\(569\) −296.283 + 846.727i −0.520708 + 1.48810i 0.320428 + 0.947273i \(0.396173\pi\)
−0.841136 + 0.540824i \(0.818112\pi\)
\(570\) 0 0
\(571\) −603.338 290.552i −1.05663 0.508848i −0.176858 0.984236i \(-0.556593\pi\)
−0.879776 + 0.475388i \(0.842308\pi\)
\(572\) −101.510 290.100i −0.177466 0.507168i
\(573\) 0 0
\(574\) 595.086 + 746.214i 1.03673 + 1.30002i
\(575\) −275.809 + 345.853i −0.479668 + 0.601484i
\(576\) 0 0
\(577\) −4.39331 6.99192i −0.00761406 0.0121177i 0.842895 0.538077i \(-0.180849\pi\)
−0.850510 + 0.525960i \(0.823706\pi\)
\(578\) −43.0330 381.928i −0.0744516 0.660776i
\(579\) 0 0
\(580\) 237.383 90.5588i 0.409281 0.156136i
\(581\) 256.028 0.440669
\(582\) 0 0
\(583\) 280.321 176.137i 0.480825 0.302122i
\(584\) −39.0762 + 8.91890i −0.0669114 + 0.0152721i
\(585\) 0 0
\(586\) −915.717 + 730.260i −1.56266 + 1.24618i
\(587\) 68.8550 301.673i 0.117300 0.513924i −0.881805 0.471615i \(-0.843671\pi\)
0.999105 0.0423093i \(-0.0134715\pi\)
\(588\) 0 0
\(589\) −105.964 + 220.036i −0.179905 + 0.373576i
\(590\) 336.366 + 211.353i 0.570112 + 0.358225i
\(591\) 0 0
\(592\) −251.225 + 251.225i −0.424366 + 0.424366i
\(593\) −313.607 651.212i −0.528849 1.09817i −0.978744 0.205084i \(-0.934253\pi\)
0.449896 0.893081i \(-0.351461\pi\)
\(594\) 0 0
\(595\) 387.121 + 43.6181i 0.650624 + 0.0733077i
\(596\) −259.177 + 124.813i −0.434861 + 0.209418i
\(597\) 0 0
\(598\) −167.443 + 478.526i −0.280006 + 0.800210i
\(599\) 202.636 322.493i 0.338290 0.538386i −0.633648 0.773621i \(-0.718443\pi\)
0.971938 + 0.235235i \(0.0755861\pi\)
\(600\) 0 0
\(601\) −311.119 889.126i −0.517668 1.47941i −0.845137 0.534549i \(-0.820481\pi\)
0.327469 0.944862i \(-0.393804\pi\)
\(602\) 926.597 + 211.490i 1.53920 + 0.351312i
\(603\) 0 0
\(604\) −191.434 + 240.050i −0.316943 + 0.397434i
\(605\) 120.670 + 528.690i 0.199455 + 0.873868i
\(606\) 0 0
\(607\) 9.33482 + 82.8488i 0.0153786 + 0.136489i 0.999055 0.0434556i \(-0.0138367\pi\)
−0.983677 + 0.179945i \(0.942408\pi\)
\(608\) 680.878i 1.11986i
\(609\) 0 0
\(610\) −401.490 −0.658180
\(611\) 328.696 37.0352i 0.537964 0.0606140i
\(612\) 0 0
\(613\) −730.866 + 166.815i −1.19228 + 0.272129i −0.772212 0.635365i \(-0.780850\pi\)
−0.420065 + 0.907494i \(0.637993\pi\)
\(614\) 42.6568 + 34.0177i 0.0694737 + 0.0554034i
\(615\) 0 0
\(616\) −72.1486 + 316.104i −0.117124 + 0.513155i
\(617\) −516.148 + 180.608i −0.836544 + 0.292719i −0.714351 0.699787i \(-0.753278\pi\)
−0.122192 + 0.992506i \(0.538992\pi\)
\(618\) 0 0
\(619\) −669.936 420.949i −1.08229 0.680046i −0.131947 0.991257i \(-0.542123\pi\)
−0.950341 + 0.311211i \(0.899266\pi\)
\(620\) −111.251 38.9283i −0.179436 0.0627875i
\(621\) 0 0
\(622\) 174.076 + 361.472i 0.279865 + 0.581145i
\(623\) −35.5459 + 315.478i −0.0570560 + 0.506386i
\(624\) 0 0
\(625\) 30.0154 14.4547i 0.0480247 0.0231275i
\(626\) −313.447 313.447i −0.500713 0.500713i
\(627\) 0 0
\(628\) 318.719 507.239i 0.507515 0.807705i
\(629\) 344.229 + 165.772i 0.547263 + 0.263548i
\(630\) 0 0
\(631\) 305.108 + 69.6389i 0.483531 + 0.110363i 0.457336 0.889294i \(-0.348804\pi\)
0.0261949 + 0.999657i \(0.491661\pi\)
\(632\) 205.546 + 257.747i 0.325232 + 0.407828i
\(633\) 0 0
\(634\) −21.6182 94.7153i −0.0340980 0.149393i
\(635\) −356.479 567.333i −0.561384 0.893438i
\(636\) 0 0
\(637\) 96.8410i 0.152027i
\(638\) 1069.16 714.076i 1.67580 1.11924i
\(639\) 0 0
\(640\) −313.024 + 35.2693i −0.489100 + 0.0551083i
\(641\) −166.181 + 104.418i −0.259253 + 0.162899i −0.655387 0.755293i \(-0.727494\pi\)
0.396134 + 0.918193i \(0.370352\pi\)
\(642\) 0 0
\(643\) −28.9995 23.1263i −0.0451003 0.0359663i 0.600680 0.799489i \(-0.294896\pi\)
−0.645781 + 0.763523i \(0.723468\pi\)
\(644\) −374.636 + 298.763i −0.581734 + 0.463917i
\(645\) 0 0
\(646\) −930.522 + 325.604i −1.44044 + 0.504030i
\(647\) −341.548 + 709.232i −0.527895 + 1.09619i 0.451132 + 0.892457i \(0.351020\pi\)
−0.979027 + 0.203729i \(0.934694\pi\)
\(648\) 0 0
\(649\) 772.992 + 270.482i 1.19105 + 0.416767i
\(650\) −178.670 + 178.670i −0.274878 + 0.274878i
\(651\) 0 0
\(652\) −17.6877 + 156.983i −0.0271284 + 0.240771i
\(653\) −651.771 73.4370i −0.998118 0.112461i −0.402239 0.915535i \(-0.631768\pi\)
−0.595879 + 0.803074i \(0.703196\pi\)
\(654\) 0 0
\(655\) 374.087 + 374.087i 0.571125 + 0.571125i
\(656\) −403.207 + 1152.30i −0.614646 + 1.75656i
\(657\) 0 0
\(658\) 691.435 + 332.978i 1.05081 + 0.506045i
\(659\) 49.7225 + 142.099i 0.0754514 + 0.215628i 0.975431 0.220304i \(-0.0707048\pi\)
−0.899980 + 0.435931i \(0.856419\pi\)
\(660\) 0 0
\(661\) 236.407 + 296.445i 0.357650 + 0.448479i 0.927809 0.373055i \(-0.121690\pi\)
−0.570159 + 0.821534i \(0.693118\pi\)
\(662\) −447.195 + 560.764i −0.675521 + 0.847076i
\(663\) 0 0
\(664\) 75.6427 + 120.385i 0.113920 + 0.181302i
\(665\) −37.8803 336.197i −0.0569628 0.505559i
\(666\) 0 0
\(667\) −860.895 72.7909i −1.29070 0.109132i
\(668\) −369.925 −0.553780
\(669\) 0 0
\(670\) 99.3616 62.4330i 0.148301 0.0931836i
\(671\) −806.926 + 184.176i −1.20257 + 0.274479i
\(672\) 0 0
\(673\) −387.895 + 309.336i −0.576367 + 0.459637i −0.867772 0.496963i \(-0.834449\pi\)
0.291405 + 0.956600i \(0.405877\pi\)
\(674\) −150.642 + 660.007i −0.223505 + 0.979239i
\(675\) 0 0
\(676\) 150.441 312.393i 0.222545 0.462120i
\(677\) 659.147 + 414.170i 0.973630 + 0.611772i 0.922122 0.386900i \(-0.126454\pi\)
0.0515083 + 0.998673i \(0.483597\pi\)
\(678\) 0 0
\(679\) −606.763 + 606.763i −0.893612 + 0.893612i
\(680\) 93.8645 + 194.912i 0.138036 + 0.286635i
\(681\) 0 0
\(682\) −592.691 66.7803i −0.869049 0.0979183i
\(683\) −346.400 + 166.817i −0.507174 + 0.244242i −0.669930 0.742424i \(-0.733676\pi\)
0.162756 + 0.986666i \(0.447962\pi\)
\(684\) 0 0
\(685\) −181.428 + 518.492i −0.264859 + 0.756923i
\(686\) −515.712 + 820.751i −0.751767 + 1.19643i
\(687\) 0 0
\(688\) 401.510 + 1147.45i 0.583591 + 1.66781i
\(689\) −123.889 28.2770i −0.179811 0.0410406i
\(690\) 0 0
\(691\) 654.553 820.783i 0.947254 1.18782i −0.0348332 0.999393i \(-0.511090\pi\)
0.982087 0.188426i \(-0.0603386\pi\)
\(692\) −12.9610 56.7857i −0.0187297 0.0820603i
\(693\) 0 0
\(694\) 22.0367 + 195.581i 0.0317532 + 0.281817i
\(695\) 498.436i 0.717175i
\(696\) 0 0
\(697\) 1312.83 1.88354
\(698\) 227.411 25.6231i 0.325804 0.0367093i
\(699\) 0 0
\(700\) −232.836 + 53.1433i −0.332623 + 0.0759190i
\(701\) −70.4321 56.1677i −0.100474 0.0801252i 0.571964 0.820278i \(-0.306182\pi\)
−0.672438 + 0.740153i \(0.734753\pi\)
\(702\) 0 0
\(703\) 73.8336 323.486i 0.105026 0.460151i
\(704\) 317.188 110.989i 0.450552 0.157655i
\(705\) 0 0
\(706\) 939.659 + 590.427i 1.33096 + 0.836299i
\(707\) −746.526 261.221i −1.05591 0.369478i
\(708\) 0 0
\(709\) −457.420 949.843i −0.645162 1.33969i −0.925118 0.379681i \(-0.876034\pi\)
0.279955 0.960013i \(-0.409680\pi\)
\(710\) 24.8471 220.524i 0.0349959 0.310597i
\(711\) 0 0
\(712\) −158.840 + 76.4933i −0.223090 + 0.107434i
\(713\) 283.408 + 283.408i 0.397487 + 0.397487i
\(714\) 0 0
\(715\) 189.473 301.544i 0.264997 0.421740i
\(716\) 226.705 + 109.175i 0.316627 + 0.152480i
\(717\) 0 0
\(718\) 1064.72 + 243.015i 1.48289 + 0.338461i
\(719\) 375.775 + 471.207i 0.522636 + 0.655364i 0.971166 0.238403i \(-0.0766240\pi\)
−0.448531 + 0.893767i \(0.648053\pi\)
\(720\) 0 0
\(721\) −61.9204 271.291i −0.0858813 0.376270i
\(722\) −43.4815 69.2005i −0.0602237 0.0958455i
\(723\) 0 0
\(724\) 540.769i 0.746919i
\(725\) −370.840 218.854i −0.511504 0.301868i
\(726\) 0 0
\(727\) −652.396 + 73.5073i −0.897380 + 0.101110i −0.548591 0.836091i \(-0.684836\pi\)
−0.348789 + 0.937201i \(0.613407\pi\)
\(728\) 105.377 66.2131i 0.144749 0.0909520i
\(729\) 0 0
\(730\) 79.8569 + 63.6837i 0.109393 + 0.0872380i
\(731\) 1022.09 815.089i 1.39821 1.11503i
\(732\) 0 0
\(733\) −1069.34 + 374.177i −1.45885 + 0.510473i −0.939040 0.343809i \(-0.888283\pi\)
−0.519810 + 0.854282i \(0.673997\pi\)
\(734\) 282.498 586.614i 0.384875 0.799201i
\(735\) 0 0
\(736\) −1054.70 369.057i −1.43302 0.501436i
\(737\) 171.060 171.060i 0.232103 0.232103i
\(738\) 0 0
\(739\) 72.0915 639.830i 0.0975527 0.865805i −0.845684 0.533684i \(-0.820807\pi\)
0.943237 0.332121i \(-0.107764\pi\)
\(740\) 159.127 + 17.9293i 0.215036 + 0.0242288i
\(741\) 0 0
\(742\) −208.475 208.475i −0.280964 0.280964i
\(743\) −147.582 + 421.766i −0.198630 + 0.567653i −0.999514 0.0311669i \(-0.990078\pi\)
0.800884 + 0.598820i \(0.204363\pi\)
\(744\) 0 0
\(745\) −300.314 144.624i −0.403106 0.194126i
\(746\) −421.450 1204.44i −0.564947 1.61453i
\(747\) 0 0
\(748\) −611.538 766.844i −0.817564 1.02519i
\(749\) −482.408 + 604.921i −0.644070 + 0.807638i
\(750\) 0 0
\(751\) 523.385 + 832.962i 0.696917 + 1.10914i 0.988299 + 0.152531i \(0.0487423\pi\)
−0.291381 + 0.956607i \(0.594115\pi\)
\(752\) 109.905 + 975.438i 0.146151 + 1.29712i
\(753\) 0 0
\(754\) −483.997 96.3746i −0.641905 0.127818i
\(755\) −355.769 −0.471217
\(756\) 0 0
\(757\) −315.734 + 198.389i −0.417086 + 0.262073i −0.724186 0.689605i \(-0.757784\pi\)
0.307100 + 0.951677i \(0.400641\pi\)
\(758\) −21.3047 + 4.86265i −0.0281064 + 0.00641511i
\(759\) 0 0
\(760\) 146.888 117.139i 0.193274 0.154131i
\(761\) −0.0873012 + 0.382492i −0.000114719 + 0.000502617i −0.974985 0.222270i \(-0.928653\pi\)
0.974871 + 0.222772i \(0.0715106\pi\)
\(762\) 0 0
\(763\) −111.699 + 231.945i −0.146395 + 0.303991i
\(764\) 570.053 + 358.188i 0.746143 + 0.468833i
\(765\) 0 0
\(766\) −191.987 + 191.987i −0.250636 + 0.250636i
\(767\) −136.389 283.214i −0.177821 0.369250i
\(768\) 0 0
\(769\) 1349.61 + 152.064i 1.75502 + 0.197743i 0.930049 0.367436i \(-0.119764\pi\)
0.824968 + 0.565179i \(0.191193\pi\)
\(770\) 744.433 358.500i 0.966797 0.465585i
\(771\) 0 0
\(772\) −184.135 + 526.227i −0.238517 + 0.681641i
\(773\) −392.849 + 625.216i −0.508214 + 0.808818i −0.998012 0.0630179i \(-0.979927\pi\)
0.489798 + 0.871836i \(0.337070\pi\)
\(774\) 0 0
\(775\) 65.9766 + 188.550i 0.0851310 + 0.243291i
\(776\) −464.566 106.034i −0.598668 0.136642i
\(777\) 0 0
\(778\) 7.56411 9.48510i 0.00972251 0.0121916i
\(779\) −253.702 1111.54i −0.325677 1.42688i
\(780\) 0 0
\(781\) −51.2226 454.613i −0.0655859 0.582091i
\(782\) 1617.90i 2.06893i
\(783\) 0 0
\(784\) −287.385 −0.366563
\(785\) 689.779 77.7195i 0.878700 0.0990057i
\(786\) 0 0
\(787\) 161.929 36.9592i 0.205755 0.0469622i −0.118401