Properties

Label 315.3.ca.b.37.10
Level 315
Weight 3
Character 315.37
Analytic conductor 8.583
Analytic rank 0
Dimension 64
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 315.ca (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.58312832735\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 37.10
Character \(\chi\) \(=\) 315.37
Dual form 315.3.ca.b.298.10

$q$-expansion

\(f(q)\) \(=\) \(q+(0.445275 - 0.119311i) q^{2} +(-3.28007 + 1.89375i) q^{4} +(-4.59550 + 1.97013i) q^{5} +(-0.171680 - 6.99789i) q^{7} +(-2.53844 + 2.53844i) q^{8} +O(q^{10})\) \(q+(0.445275 - 0.119311i) q^{2} +(-3.28007 + 1.89375i) q^{4} +(-4.59550 + 1.97013i) q^{5} +(-0.171680 - 6.99789i) q^{7} +(-2.53844 + 2.53844i) q^{8} +(-1.81120 + 1.42554i) q^{10} +(7.70109 + 13.3387i) q^{11} +(17.1139 - 17.1139i) q^{13} +(-0.911371 - 3.09550i) q^{14} +(6.74755 - 11.6871i) q^{16} +(5.59776 - 20.8911i) q^{17} +(-15.6219 - 9.01929i) q^{19} +(11.3426 - 15.1649i) q^{20} +(5.02055 + 5.02055i) q^{22} +(-2.98781 - 11.1507i) q^{23} +(17.2372 - 18.1075i) q^{25} +(5.57852 - 9.66228i) q^{26} +(13.8154 + 22.6284i) q^{28} +1.87676i q^{29} +(9.52708 + 16.5014i) q^{31} +(5.32665 - 19.8793i) q^{32} -9.97017i q^{34} +(14.5757 + 31.8206i) q^{35} +(-4.95991 + 1.32900i) q^{37} +(-8.03212 - 2.15220i) q^{38} +(6.66433 - 16.6665i) q^{40} +51.4301 q^{41} +(18.4492 - 18.4492i) q^{43} +(-50.5202 - 29.1678i) q^{44} +(-2.66080 - 4.60863i) q^{46} +(-22.4470 + 6.01467i) q^{47} +(-48.9411 + 2.40280i) q^{49} +(5.51485 - 10.1194i) q^{50} +(-23.7254 + 88.5443i) q^{52} +(-75.2491 - 20.1629i) q^{53} +(-61.6693 - 46.1257i) q^{55} +(18.1995 + 17.3279i) q^{56} +(0.223918 + 0.835675i) q^{58} +(40.1729 - 23.1938i) q^{59} +(12.3169 - 21.3335i) q^{61} +(6.21097 + 6.21097i) q^{62} +44.4931i q^{64} +(-44.9303 + 112.364i) q^{65} +(29.9876 - 111.915i) q^{67} +(21.2015 + 79.1251i) q^{68} +(10.2867 + 12.4298i) q^{70} -63.9145 q^{71} +(13.3047 + 3.56497i) q^{73} +(-2.04996 + 1.18354i) q^{74} +68.3210 q^{76} +(92.0205 - 56.1814i) q^{77} +(45.3292 + 26.1708i) q^{79} +(-7.98321 + 67.0016i) q^{80} +(22.9005 - 6.13617i) q^{82} +(34.3710 - 34.3710i) q^{83} +(15.4338 + 107.033i) q^{85} +(6.01376 - 10.4161i) q^{86} +(-53.4082 - 14.3107i) q^{88} +(-44.5648 - 25.7295i) q^{89} +(-122.700 - 116.823i) q^{91} +(30.9168 + 30.9168i) q^{92} +(-9.27748 + 5.35636i) q^{94} +(89.5594 + 10.6710i) q^{95} +(39.0134 + 39.0134i) q^{97} +(-21.5055 + 6.90911i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64q - 4q^{5} - 4q^{7} - 24q^{8} + O(q^{10}) \) \( 64q - 4q^{5} - 4q^{7} - 24q^{8} - 16q^{10} - 16q^{11} + 80q^{16} - 56q^{17} - 96q^{22} - 72q^{23} - 4q^{25} + 288q^{26} - 380q^{28} - 136q^{31} + 48q^{32} - 76q^{35} - 28q^{37} + 68q^{38} + 164q^{40} - 128q^{41} + 344q^{43} + 240q^{46} - 412q^{47} + 72q^{50} + 388q^{52} + 40q^{53} - 8q^{55} + 864q^{56} + 56q^{58} - 216q^{61} + 912q^{62} - 20q^{65} - 368q^{67} + 492q^{68} + 416q^{70} - 784q^{71} - 316q^{73} - 32q^{76} - 844q^{77} - 908q^{80} + 556q^{82} - 1408q^{83} - 536q^{85} - 1024q^{86} + 372q^{88} - 1064q^{91} + 1704q^{92} - 260q^{95} + 352q^{97} - 272q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.445275 0.119311i 0.222637 0.0596555i −0.145776 0.989318i \(-0.546568\pi\)
0.368413 + 0.929662i \(0.379901\pi\)
\(3\) 0 0
\(4\) −3.28007 + 1.89375i −0.820017 + 0.473437i
\(5\) −4.59550 + 1.97013i −0.919099 + 0.394026i
\(6\) 0 0
\(7\) −0.171680 6.99789i −0.0245257 0.999699i
\(8\) −2.53844 + 2.53844i −0.317305 + 0.317305i
\(9\) 0 0
\(10\) −1.81120 + 1.42554i −0.181120 + 0.142554i
\(11\) 7.70109 + 13.3387i 0.700099 + 1.21261i 0.968431 + 0.249280i \(0.0801941\pi\)
−0.268333 + 0.963326i \(0.586473\pi\)
\(12\) 0 0
\(13\) 17.1139 17.1139i 1.31646 1.31646i 0.399894 0.916561i \(-0.369047\pi\)
0.916561 0.399894i \(-0.130953\pi\)
\(14\) −0.911371 3.09550i −0.0650979 0.221107i
\(15\) 0 0
\(16\) 6.74755 11.6871i 0.421722 0.730444i
\(17\) 5.59776 20.8911i 0.329280 1.22889i −0.580658 0.814147i \(-0.697205\pi\)
0.909938 0.414743i \(-0.136129\pi\)
\(18\) 0 0
\(19\) −15.6219 9.01929i −0.822203 0.474699i 0.0289723 0.999580i \(-0.490777\pi\)
−0.851176 + 0.524881i \(0.824110\pi\)
\(20\) 11.3426 15.1649i 0.567130 0.758244i
\(21\) 0 0
\(22\) 5.02055 + 5.02055i 0.228207 + 0.228207i
\(23\) −2.98781 11.1507i −0.129905 0.484812i 0.870062 0.492942i \(-0.164079\pi\)
−0.999967 + 0.00813035i \(0.997412\pi\)
\(24\) 0 0
\(25\) 17.2372 18.1075i 0.689486 0.724299i
\(26\) 5.57852 9.66228i 0.214558 0.371626i
\(27\) 0 0
\(28\) 13.8154 + 22.6284i 0.493406 + 0.808159i
\(29\) 1.87676i 0.0647160i 0.999476 + 0.0323580i \(0.0103017\pi\)
−0.999476 + 0.0323580i \(0.989698\pi\)
\(30\) 0 0
\(31\) 9.52708 + 16.5014i 0.307325 + 0.532303i 0.977776 0.209651i \(-0.0672327\pi\)
−0.670451 + 0.741954i \(0.733899\pi\)
\(32\) 5.32665 19.8793i 0.166458 0.621229i
\(33\) 0 0
\(34\) 9.97017i 0.293240i
\(35\) 14.5757 + 31.8206i 0.416449 + 0.909159i
\(36\) 0 0
\(37\) −4.95991 + 1.32900i −0.134052 + 0.0359190i −0.325221 0.945638i \(-0.605439\pi\)
0.191169 + 0.981557i \(0.438772\pi\)
\(38\) −8.03212 2.15220i −0.211372 0.0566369i
\(39\) 0 0
\(40\) 6.66433 16.6665i 0.166608 0.416661i
\(41\) 51.4301 1.25439 0.627196 0.778861i \(-0.284203\pi\)
0.627196 + 0.778861i \(0.284203\pi\)
\(42\) 0 0
\(43\) 18.4492 18.4492i 0.429051 0.429051i −0.459254 0.888305i \(-0.651883\pi\)
0.888305 + 0.459254i \(0.151883\pi\)
\(44\) −50.5202 29.1678i −1.14819 0.662905i
\(45\) 0 0
\(46\) −2.66080 4.60863i −0.0578434 0.100188i
\(47\) −22.4470 + 6.01467i −0.477597 + 0.127972i −0.489583 0.871957i \(-0.662851\pi\)
0.0119867 + 0.999928i \(0.496184\pi\)
\(48\) 0 0
\(49\) −48.9411 + 2.40280i −0.998797 + 0.0490367i
\(50\) 5.51485 10.1194i 0.110297 0.202388i
\(51\) 0 0
\(52\) −23.7254 + 88.5443i −0.456257 + 1.70277i
\(53\) −75.2491 20.1629i −1.41979 0.380433i −0.534384 0.845242i \(-0.679456\pi\)
−0.885411 + 0.464809i \(0.846123\pi\)
\(54\) 0 0
\(55\) −61.6693 46.1257i −1.12126 0.838648i
\(56\) 18.1995 + 17.3279i 0.324992 + 0.309428i
\(57\) 0 0
\(58\) 0.223918 + 0.835675i 0.00386066 + 0.0144082i
\(59\) 40.1729 23.1938i 0.680897 0.393116i −0.119296 0.992859i \(-0.538064\pi\)
0.800193 + 0.599743i \(0.204730\pi\)
\(60\) 0 0
\(61\) 12.3169 21.3335i 0.201917 0.349730i −0.747229 0.664566i \(-0.768616\pi\)
0.949146 + 0.314836i \(0.101950\pi\)
\(62\) 6.21097 + 6.21097i 0.100177 + 0.100177i
\(63\) 0 0
\(64\) 44.4931i 0.695205i
\(65\) −44.9303 + 112.364i −0.691235 + 1.72867i
\(66\) 0 0
\(67\) 29.9876 111.915i 0.447576 1.67038i −0.261467 0.965212i \(-0.584206\pi\)
0.709043 0.705165i \(-0.249127\pi\)
\(68\) 21.2015 + 79.1251i 0.311787 + 1.16360i
\(69\) 0 0
\(70\) 10.2867 + 12.4298i 0.146954 + 0.177569i
\(71\) −63.9145 −0.900204 −0.450102 0.892977i \(-0.648612\pi\)
−0.450102 + 0.892977i \(0.648612\pi\)
\(72\) 0 0
\(73\) 13.3047 + 3.56497i 0.182256 + 0.0488352i 0.348792 0.937200i \(-0.386592\pi\)
−0.166537 + 0.986035i \(0.553258\pi\)
\(74\) −2.04996 + 1.18354i −0.0277021 + 0.0159938i
\(75\) 0 0
\(76\) 68.3210 0.898961
\(77\) 92.0205 56.1814i 1.19507 0.729628i
\(78\) 0 0
\(79\) 45.3292 + 26.1708i 0.573788 + 0.331276i 0.758661 0.651486i \(-0.225854\pi\)
−0.184873 + 0.982762i \(0.559187\pi\)
\(80\) −7.98321 + 67.0016i −0.0997901 + 0.837520i
\(81\) 0 0
\(82\) 22.9005 6.13617i 0.279274 0.0748314i
\(83\) 34.3710 34.3710i 0.414109 0.414109i −0.469058 0.883167i \(-0.655407\pi\)
0.883167 + 0.469058i \(0.155407\pi\)
\(84\) 0 0
\(85\) 15.4338 + 107.033i 0.181574 + 1.25922i
\(86\) 6.01376 10.4161i 0.0699275 0.121118i
\(87\) 0 0
\(88\) −53.4082 14.3107i −0.606911 0.162621i
\(89\) −44.5648 25.7295i −0.500728 0.289095i 0.228286 0.973594i \(-0.426688\pi\)
−0.729014 + 0.684499i \(0.760021\pi\)
\(90\) 0 0
\(91\) −122.700 116.823i −1.34835 1.28377i
\(92\) 30.9168 + 30.9168i 0.336052 + 0.336052i
\(93\) 0 0
\(94\) −9.27748 + 5.35636i −0.0986966 + 0.0569825i
\(95\) 89.5594 + 10.6710i 0.942731 + 0.112326i
\(96\) 0 0
\(97\) 39.0134 + 39.0134i 0.402200 + 0.402200i 0.879008 0.476808i \(-0.158206\pi\)
−0.476808 + 0.879008i \(0.658206\pi\)
\(98\) −21.5055 + 6.90911i −0.219444 + 0.0705011i
\(99\) 0 0
\(100\) −22.2481 + 92.0365i −0.222481 + 0.920365i
\(101\) −79.6712 137.995i −0.788824 1.36628i −0.926688 0.375832i \(-0.877357\pi\)
0.137864 0.990451i \(-0.455976\pi\)
\(102\) 0 0
\(103\) 26.2481 + 97.9591i 0.254835 + 0.951059i 0.968182 + 0.250247i \(0.0805119\pi\)
−0.713346 + 0.700812i \(0.752821\pi\)
\(104\) 86.8854i 0.835436i
\(105\) 0 0
\(106\) −35.9122 −0.338794
\(107\) 9.51326 2.54907i 0.0889090 0.0238231i −0.214090 0.976814i \(-0.568679\pi\)
0.302999 + 0.952991i \(0.402012\pi\)
\(108\) 0 0
\(109\) −38.6718 + 22.3271i −0.354787 + 0.204836i −0.666792 0.745244i \(-0.732333\pi\)
0.312005 + 0.950081i \(0.399000\pi\)
\(110\) −32.9631 13.1808i −0.299664 0.119825i
\(111\) 0 0
\(112\) −82.9435 45.2122i −0.740567 0.403680i
\(113\) −34.1599 + 34.1599i −0.302300 + 0.302300i −0.841913 0.539613i \(-0.818571\pi\)
0.539613 + 0.841913i \(0.318571\pi\)
\(114\) 0 0
\(115\) 35.6988 + 45.3565i 0.310424 + 0.394404i
\(116\) −3.55412 6.15591i −0.0306389 0.0530682i
\(117\) 0 0
\(118\) 15.1207 15.1207i 0.128141 0.128141i
\(119\) −147.155 35.5860i −1.23660 0.299042i
\(120\) 0 0
\(121\) −58.1135 + 100.655i −0.480277 + 0.831863i
\(122\) 2.93909 10.9688i 0.0240909 0.0899084i
\(123\) 0 0
\(124\) −62.4989 36.0838i −0.504024 0.290998i
\(125\) −43.5392 + 117.172i −0.348314 + 0.937378i
\(126\) 0 0
\(127\) 44.4734 + 44.4734i 0.350184 + 0.350184i 0.860178 0.509994i \(-0.170352\pi\)
−0.509994 + 0.860178i \(0.670352\pi\)
\(128\) 26.6151 + 99.3290i 0.207931 + 0.776008i
\(129\) 0 0
\(130\) −6.60009 + 55.3934i −0.0507700 + 0.426103i
\(131\) 112.718 195.234i 0.860446 1.49034i −0.0110531 0.999939i \(-0.503518\pi\)
0.871499 0.490397i \(-0.163148\pi\)
\(132\) 0 0
\(133\) −60.4341 + 110.869i −0.454391 + 0.833598i
\(134\) 53.4109i 0.398589i
\(135\) 0 0
\(136\) 38.8213 + 67.2405i 0.285451 + 0.494416i
\(137\) −9.15488 + 34.1665i −0.0668239 + 0.249390i −0.991255 0.131958i \(-0.957874\pi\)
0.924431 + 0.381349i \(0.124540\pi\)
\(138\) 0 0
\(139\) 56.7049i 0.407949i 0.978976 + 0.203974i \(0.0653859\pi\)
−0.978976 + 0.203974i \(0.934614\pi\)
\(140\) −108.069 76.7708i −0.771925 0.548363i
\(141\) 0 0
\(142\) −28.4595 + 7.62570i −0.200419 + 0.0537021i
\(143\) 360.073 + 96.4812i 2.51799 + 0.674694i
\(144\) 0 0
\(145\) −3.69747 8.62466i −0.0254998 0.0594804i
\(146\) 6.34957 0.0434902
\(147\) 0 0
\(148\) 13.7520 13.7520i 0.0929191 0.0929191i
\(149\) −79.1387 45.6907i −0.531132 0.306649i 0.210345 0.977627i \(-0.432541\pi\)
−0.741477 + 0.670978i \(0.765875\pi\)
\(150\) 0 0
\(151\) −45.6835 79.1262i −0.302540 0.524015i 0.674171 0.738576i \(-0.264501\pi\)
−0.976711 + 0.214561i \(0.931168\pi\)
\(152\) 62.5501 16.7603i 0.411514 0.110265i
\(153\) 0 0
\(154\) 34.2713 35.9952i 0.222541 0.233735i
\(155\) −76.2916 57.0625i −0.492204 0.368145i
\(156\) 0 0
\(157\) 46.7269 174.387i 0.297623 1.11075i −0.641488 0.767133i \(-0.721683\pi\)
0.939112 0.343613i \(-0.111651\pi\)
\(158\) 23.3064 + 6.24494i 0.147509 + 0.0395249i
\(159\) 0 0
\(160\) 14.6863 + 101.850i 0.0917894 + 0.636560i
\(161\) −77.5183 + 22.8228i −0.481480 + 0.141756i
\(162\) 0 0
\(163\) 20.5517 + 76.7000i 0.126084 + 0.470552i 0.999876 0.0157477i \(-0.00501286\pi\)
−0.873792 + 0.486300i \(0.838346\pi\)
\(164\) −168.694 + 97.3956i −1.02862 + 0.593875i
\(165\) 0 0
\(166\) 11.2037 19.4054i 0.0674922 0.116900i
\(167\) −15.2411 15.2411i −0.0912643 0.0912643i 0.660001 0.751265i \(-0.270556\pi\)
−0.751265 + 0.660001i \(0.770556\pi\)
\(168\) 0 0
\(169\) 416.773i 2.46611i
\(170\) 19.6426 + 45.8179i 0.115544 + 0.269517i
\(171\) 0 0
\(172\) −25.5765 + 95.4527i −0.148700 + 0.554957i
\(173\) −1.14313 4.26621i −0.00660768 0.0246602i 0.962543 0.271128i \(-0.0873967\pi\)
−0.969151 + 0.246468i \(0.920730\pi\)
\(174\) 0 0
\(175\) −129.673 117.515i −0.740991 0.671515i
\(176\) 207.854 1.18099
\(177\) 0 0
\(178\) −22.9134 6.13962i −0.128727 0.0344923i
\(179\) −9.12125 + 5.26616i −0.0509567 + 0.0294199i −0.525262 0.850941i \(-0.676033\pi\)
0.474305 + 0.880360i \(0.342699\pi\)
\(180\) 0 0
\(181\) 325.032 1.79575 0.897877 0.440246i \(-0.145109\pi\)
0.897877 + 0.440246i \(0.145109\pi\)
\(182\) −68.5733 37.3791i −0.376776 0.205379i
\(183\) 0 0
\(184\) 35.8897 + 20.7209i 0.195053 + 0.112614i
\(185\) 20.1749 15.8791i 0.109054 0.0858330i
\(186\) 0 0
\(187\) 321.769 86.2177i 1.72069 0.461057i
\(188\) 62.2375 62.2375i 0.331051 0.331051i
\(189\) 0 0
\(190\) 41.1517 5.93391i 0.216588 0.0312311i
\(191\) −119.545 + 207.058i −0.625891 + 1.08408i 0.362477 + 0.931993i \(0.381931\pi\)
−0.988368 + 0.152082i \(0.951402\pi\)
\(192\) 0 0
\(193\) −184.527 49.4439i −0.956100 0.256186i −0.253151 0.967427i \(-0.581467\pi\)
−0.702949 + 0.711241i \(0.748134\pi\)
\(194\) 22.0264 + 12.7170i 0.113538 + 0.0655513i
\(195\) 0 0
\(196\) 155.980 100.563i 0.795815 0.513078i
\(197\) 60.9439 + 60.9439i 0.309360 + 0.309360i 0.844661 0.535301i \(-0.179802\pi\)
−0.535301 + 0.844661i \(0.679802\pi\)
\(198\) 0 0
\(199\) −48.7356 + 28.1375i −0.244903 + 0.141395i −0.617428 0.786627i \(-0.711825\pi\)
0.372525 + 0.928022i \(0.378492\pi\)
\(200\) 2.20922 + 89.7202i 0.0110461 + 0.448601i
\(201\) 0 0
\(202\) −51.9399 51.9399i −0.257128 0.257128i
\(203\) 13.1334 0.322203i 0.0646965 0.00158721i
\(204\) 0 0
\(205\) −236.347 + 101.324i −1.15291 + 0.494264i
\(206\) 23.3752 + 40.4870i 0.113472 + 0.196539i
\(207\) 0 0
\(208\) −84.5351 315.489i −0.406419 1.51678i
\(209\) 277.833i 1.32935i
\(210\) 0 0
\(211\) −57.8783 −0.274305 −0.137152 0.990550i \(-0.543795\pi\)
−0.137152 + 0.990550i \(0.543795\pi\)
\(212\) 285.006 76.3670i 1.34437 0.360222i
\(213\) 0 0
\(214\) 3.93188 2.27007i 0.0183733 0.0106078i
\(215\) −48.4358 + 121.130i −0.225283 + 0.563398i
\(216\) 0 0
\(217\) 113.839 69.5025i 0.524605 0.320288i
\(218\) −14.5557 + 14.5557i −0.0667692 + 0.0667692i
\(219\) 0 0
\(220\) 289.630 + 34.5092i 1.31650 + 0.156860i
\(221\) −261.730 453.329i −1.18430 2.05126i
\(222\) 0 0
\(223\) 118.966 118.966i 0.533481 0.533481i −0.388125 0.921607i \(-0.626877\pi\)
0.921607 + 0.388125i \(0.126877\pi\)
\(224\) −140.028 33.8624i −0.625125 0.151172i
\(225\) 0 0
\(226\) −11.1349 + 19.2862i −0.0492694 + 0.0853371i
\(227\) −87.4561 + 326.391i −0.385269 + 1.43784i 0.452473 + 0.891778i \(0.350542\pi\)
−0.837742 + 0.546066i \(0.816125\pi\)
\(228\) 0 0
\(229\) −6.66275 3.84674i −0.0290950 0.0167980i 0.485382 0.874302i \(-0.338681\pi\)
−0.514477 + 0.857504i \(0.672014\pi\)
\(230\) 21.3073 + 15.9368i 0.0926404 + 0.0692906i
\(231\) 0 0
\(232\) −4.76405 4.76405i −0.0205347 0.0205347i
\(233\) −66.8075 249.329i −0.286728 1.07008i −0.947568 0.319555i \(-0.896466\pi\)
0.660840 0.750527i \(-0.270200\pi\)
\(234\) 0 0
\(235\) 91.3056 71.8640i 0.388534 0.305804i
\(236\) −87.8465 + 152.155i −0.372231 + 0.644723i
\(237\) 0 0
\(238\) −69.7702 + 1.71168i −0.293152 + 0.00719193i
\(239\) 252.435i 1.05621i 0.849178 + 0.528107i \(0.177098\pi\)
−0.849178 + 0.528107i \(0.822902\pi\)
\(240\) 0 0
\(241\) 7.25757 + 12.5705i 0.0301144 + 0.0521597i 0.880690 0.473693i \(-0.157080\pi\)
−0.850575 + 0.525853i \(0.823746\pi\)
\(242\) −13.8672 + 51.7529i −0.0573023 + 0.213855i
\(243\) 0 0
\(244\) 93.3005i 0.382379i
\(245\) 220.175 107.462i 0.898672 0.438622i
\(246\) 0 0
\(247\) −421.707 + 112.996i −1.70732 + 0.457474i
\(248\) −66.0717 17.7039i −0.266418 0.0713866i
\(249\) 0 0
\(250\) −5.40696 + 57.3685i −0.0216279 + 0.229474i
\(251\) 211.955 0.844443 0.422221 0.906493i \(-0.361251\pi\)
0.422221 + 0.906493i \(0.361251\pi\)
\(252\) 0 0
\(253\) 125.726 125.726i 0.496940 0.496940i
\(254\) 25.1090 + 14.4967i 0.0988545 + 0.0570736i
\(255\) 0 0
\(256\) −65.2842 113.076i −0.255016 0.441701i
\(257\) 309.551 82.9440i 1.20448 0.322739i 0.399886 0.916565i \(-0.369050\pi\)
0.804594 + 0.593825i \(0.202383\pi\)
\(258\) 0 0
\(259\) 10.1517 + 34.4807i 0.0391959 + 0.133130i
\(260\) −65.4141 453.647i −0.251593 1.74480i
\(261\) 0 0
\(262\) 26.8971 100.381i 0.102661 0.383135i
\(263\) −125.573 33.6471i −0.477462 0.127936i 0.0120584 0.999927i \(-0.496162\pi\)
−0.489521 + 0.871992i \(0.662828\pi\)
\(264\) 0 0
\(265\) 385.531 55.5920i 1.45483 0.209781i
\(266\) −13.6819 + 56.5774i −0.0514358 + 0.212697i
\(267\) 0 0
\(268\) 113.578 + 423.879i 0.423798 + 1.58164i
\(269\) −59.9735 + 34.6257i −0.222950 + 0.128720i −0.607315 0.794461i \(-0.707754\pi\)
0.384366 + 0.923181i \(0.374420\pi\)
\(270\) 0 0
\(271\) −207.020 + 358.570i −0.763913 + 1.32314i 0.176907 + 0.984228i \(0.443391\pi\)
−0.940820 + 0.338908i \(0.889943\pi\)
\(272\) −206.386 206.386i −0.758771 0.758771i
\(273\) 0 0
\(274\) 16.3057i 0.0595100i
\(275\) 374.274 + 90.4737i 1.36100 + 0.328995i
\(276\) 0 0
\(277\) −13.5956 + 50.7395i −0.0490816 + 0.183175i −0.986115 0.166065i \(-0.946894\pi\)
0.937033 + 0.349241i \(0.113560\pi\)
\(278\) 6.76551 + 25.2492i 0.0243364 + 0.0908246i
\(279\) 0 0
\(280\) −117.774 43.7750i −0.420622 0.156339i
\(281\) 460.003 1.63702 0.818511 0.574491i \(-0.194800\pi\)
0.818511 + 0.574491i \(0.194800\pi\)
\(282\) 0 0
\(283\) 177.279 + 47.5016i 0.626426 + 0.167850i 0.558047 0.829809i \(-0.311551\pi\)
0.0683786 + 0.997659i \(0.478217\pi\)
\(284\) 209.644 121.038i 0.738182 0.426190i
\(285\) 0 0
\(286\) 171.843 0.600848
\(287\) −8.82952 359.902i −0.0307649 1.25401i
\(288\) 0 0
\(289\) −154.823 89.3874i −0.535721 0.309299i
\(290\) −2.67541 3.39919i −0.00922554 0.0117214i
\(291\) 0 0
\(292\) −50.3913 + 13.5023i −0.172573 + 0.0462408i
\(293\) −2.24023 + 2.24023i −0.00764585 + 0.00764585i −0.710919 0.703274i \(-0.751721\pi\)
0.703274 + 0.710919i \(0.251721\pi\)
\(294\) 0 0
\(295\) −138.919 + 185.733i −0.470913 + 0.629604i
\(296\) 9.21683 15.9640i 0.0311379 0.0539325i
\(297\) 0 0
\(298\) −40.6899 10.9028i −0.136543 0.0365866i
\(299\) −241.965 139.699i −0.809248 0.467219i
\(300\) 0 0
\(301\) −132.273 125.938i −0.439445 0.418399i
\(302\) −29.7823 29.7823i −0.0986170 0.0986170i
\(303\) 0 0
\(304\) −210.819 + 121.716i −0.693482 + 0.400382i
\(305\) −14.5725 + 122.304i −0.0477786 + 0.400997i
\(306\) 0 0
\(307\) 71.4036 + 71.4036i 0.232585 + 0.232585i 0.813771 0.581186i \(-0.197411\pi\)
−0.581186 + 0.813771i \(0.697411\pi\)
\(308\) −195.440 + 358.542i −0.634546 + 1.16410i
\(309\) 0 0
\(310\) −40.7789 16.3060i −0.131545 0.0526001i
\(311\) −47.7241 82.6605i −0.153454 0.265789i 0.779041 0.626973i \(-0.215706\pi\)
−0.932495 + 0.361183i \(0.882373\pi\)
\(312\) 0 0
\(313\) −37.5811 140.255i −0.120067 0.448098i 0.879549 0.475809i \(-0.157845\pi\)
−0.999616 + 0.0277115i \(0.991178\pi\)
\(314\) 83.2252i 0.265048i
\(315\) 0 0
\(316\) −198.244 −0.627354
\(317\) −444.564 + 119.121i −1.40241 + 0.375775i −0.879210 0.476434i \(-0.841929\pi\)
−0.523201 + 0.852209i \(0.675262\pi\)
\(318\) 0 0
\(319\) −25.0335 + 14.4531i −0.0784750 + 0.0453076i
\(320\) −87.6573 204.468i −0.273929 0.638962i
\(321\) 0 0
\(322\) −31.7939 + 19.4112i −0.0987389 + 0.0602832i
\(323\) −275.871 + 275.871i −0.854089 + 0.854089i
\(324\) 0 0
\(325\) −14.8943 604.885i −0.0458287 1.86119i
\(326\) 18.3023 + 31.7005i 0.0561421 + 0.0972409i
\(327\) 0 0
\(328\) −130.552 + 130.552i −0.398025 + 0.398025i
\(329\) 45.9437 + 156.049i 0.139647 + 0.474314i
\(330\) 0 0
\(331\) 23.3963 40.5235i 0.0706836 0.122428i −0.828517 0.559963i \(-0.810815\pi\)
0.899201 + 0.437536i \(0.144149\pi\)
\(332\) −47.6492 + 177.829i −0.143522 + 0.535630i
\(333\) 0 0
\(334\) −8.60493 4.96806i −0.0257633 0.0148744i
\(335\) 82.6799 + 573.386i 0.246806 + 1.71160i
\(336\) 0 0
\(337\) 391.846 + 391.846i 1.16275 + 1.16275i 0.983872 + 0.178877i \(0.0572463\pi\)
0.178877 + 0.983872i \(0.442754\pi\)
\(338\) −49.7256 185.578i −0.147117 0.549048i
\(339\) 0 0
\(340\) −253.318 321.849i −0.745054 0.946616i
\(341\) −146.738 + 254.157i −0.430316 + 0.745329i
\(342\) 0 0
\(343\) 25.2167 + 342.072i 0.0735182 + 0.997294i
\(344\) 93.6643i 0.272280i
\(345\) 0 0
\(346\) −1.01801 1.76325i −0.00294223 0.00509609i
\(347\) 8.37062 31.2396i 0.0241228 0.0900276i −0.952815 0.303552i \(-0.901828\pi\)
0.976938 + 0.213524i \(0.0684942\pi\)
\(348\) 0 0
\(349\) 214.001i 0.613183i −0.951841 0.306592i \(-0.900811\pi\)
0.951841 0.306592i \(-0.0991886\pi\)
\(350\) −71.7611 36.8551i −0.205032 0.105300i
\(351\) 0 0
\(352\) 306.185 82.0420i 0.869843 0.233074i
\(353\) 154.485 + 41.3943i 0.437636 + 0.117264i 0.470908 0.882182i \(-0.343926\pi\)
−0.0332725 + 0.999446i \(0.510593\pi\)
\(354\) 0 0
\(355\) 293.719 125.920i 0.827376 0.354704i
\(356\) 194.901 0.547474
\(357\) 0 0
\(358\) −3.43315 + 3.43315i −0.00958981 + 0.00958981i
\(359\) 422.373 + 243.857i 1.17653 + 0.679267i 0.955208 0.295935i \(-0.0956311\pi\)
0.221317 + 0.975202i \(0.428964\pi\)
\(360\) 0 0
\(361\) −17.8049 30.8390i −0.0493210 0.0854265i
\(362\) 144.728 38.7798i 0.399802 0.107127i
\(363\) 0 0
\(364\) 623.697 + 150.826i 1.71345 + 0.414358i
\(365\) −68.1650 + 9.82912i −0.186753 + 0.0269291i
\(366\) 0 0
\(367\) −67.9239 + 253.495i −0.185079 + 0.690723i 0.809535 + 0.587072i \(0.199719\pi\)
−0.994614 + 0.103652i \(0.966947\pi\)
\(368\) −150.480 40.3209i −0.408912 0.109568i
\(369\) 0 0
\(370\) 7.08883 9.47765i 0.0191590 0.0256153i
\(371\) −128.179 + 530.047i −0.345497 + 1.42870i
\(372\) 0 0
\(373\) −35.7315 133.352i −0.0957949 0.357512i 0.901344 0.433104i \(-0.142582\pi\)
−0.997139 + 0.0755927i \(0.975915\pi\)
\(374\) 132.989 76.7811i 0.355585 0.205297i
\(375\) 0 0
\(376\) 41.7126 72.2484i 0.110938 0.192150i
\(377\) 32.1188 + 32.1188i 0.0851957 + 0.0851957i
\(378\) 0 0
\(379\) 535.154i 1.41202i 0.708204 + 0.706008i \(0.249506\pi\)
−0.708204 + 0.706008i \(0.750494\pi\)
\(380\) −313.969 + 134.601i −0.826234 + 0.354214i
\(381\) 0 0
\(382\) −28.5261 + 106.461i −0.0746757 + 0.278693i
\(383\) −33.3533 124.476i −0.0870845 0.325004i 0.908616 0.417632i \(-0.137140\pi\)
−0.995701 + 0.0926283i \(0.970473\pi\)
\(384\) 0 0
\(385\) −312.195 + 439.474i −0.810896 + 1.14149i
\(386\) −88.0645 −0.228146
\(387\) 0 0
\(388\) −201.848 54.0850i −0.520227 0.139394i
\(389\) 128.234 74.0357i 0.329649 0.190323i −0.326036 0.945357i \(-0.605713\pi\)
0.655685 + 0.755034i \(0.272380\pi\)
\(390\) 0 0
\(391\) −249.675 −0.638556
\(392\) 118.135 130.333i 0.301364 0.332483i
\(393\) 0 0
\(394\) 34.4080 + 19.8655i 0.0873300 + 0.0504200i
\(395\) −259.870 30.9634i −0.657899 0.0783884i
\(396\) 0 0
\(397\) −462.699 + 123.980i −1.16549 + 0.312292i −0.789156 0.614193i \(-0.789482\pi\)
−0.376333 + 0.926485i \(0.622815\pi\)
\(398\) −18.3436 + 18.3436i −0.0460895 + 0.0460895i
\(399\) 0 0
\(400\) −95.3152 323.633i −0.238288 0.809084i
\(401\) −233.401 + 404.263i −0.582048 + 1.00814i 0.413189 + 0.910645i \(0.364415\pi\)
−0.995236 + 0.0974907i \(0.968918\pi\)
\(402\) 0 0
\(403\) 445.449 + 119.358i 1.10533 + 0.296173i
\(404\) 522.654 + 301.754i 1.29370 + 0.746917i
\(405\) 0 0
\(406\) 5.80952 1.71043i 0.0143092 0.00421287i
\(407\) −55.9238 55.9238i −0.137405 0.137405i
\(408\) 0 0
\(409\) −556.548 + 321.323i −1.36075 + 0.785631i −0.989724 0.142990i \(-0.954328\pi\)
−0.371029 + 0.928621i \(0.620995\pi\)
\(410\) −93.1501 + 73.3158i −0.227195 + 0.178819i
\(411\) 0 0
\(412\) −271.605 271.605i −0.659236 0.659236i
\(413\) −169.205 277.144i −0.409697 0.671050i
\(414\) 0 0
\(415\) −90.2364 + 225.667i −0.217437 + 0.543777i
\(416\) −249.053 431.373i −0.598686 1.03695i
\(417\) 0 0
\(418\) −33.1486 123.712i −0.0793028 0.295962i
\(419\) 476.798i 1.13794i −0.822358 0.568971i \(-0.807342\pi\)
0.822358 0.568971i \(-0.192658\pi\)
\(420\) 0 0
\(421\) −478.207 −1.13588 −0.567942 0.823069i \(-0.692260\pi\)
−0.567942 + 0.823069i \(0.692260\pi\)
\(422\) −25.7717 + 6.90552i −0.0610705 + 0.0163638i
\(423\) 0 0
\(424\) 242.198 139.833i 0.571221 0.329795i
\(425\) −281.796 461.465i −0.663050 1.08580i
\(426\) 0 0
\(427\) −151.404 82.5299i −0.354577 0.193279i
\(428\) −26.3768 + 26.3768i −0.0616281 + 0.0616281i
\(429\) 0 0
\(430\) −7.11505 + 59.7153i −0.0165466 + 0.138873i
\(431\) 104.378 + 180.788i 0.242176 + 0.419461i 0.961334 0.275386i \(-0.0888055\pi\)
−0.719158 + 0.694847i \(0.755472\pi\)
\(432\) 0 0
\(433\) −258.656 + 258.656i −0.597358 + 0.597358i −0.939609 0.342251i \(-0.888811\pi\)
0.342251 + 0.939609i \(0.388811\pi\)
\(434\) 42.3974 44.5300i 0.0976898 0.102604i
\(435\) 0 0
\(436\) 84.5640 146.469i 0.193954 0.335938i
\(437\) −53.8959 + 201.142i −0.123332 + 0.460280i
\(438\) 0 0
\(439\) 447.029 + 258.092i 1.01829 + 0.587910i 0.913608 0.406596i \(-0.133284\pi\)
0.104681 + 0.994506i \(0.466618\pi\)
\(440\) 273.631 39.4565i 0.621889 0.0896739i
\(441\) 0 0
\(442\) −170.629 170.629i −0.386038 0.386038i
\(443\) −125.295 467.609i −0.282834 1.05555i −0.950408 0.311007i \(-0.899334\pi\)
0.667574 0.744544i \(-0.267333\pi\)
\(444\) 0 0
\(445\) 255.488 + 30.4413i 0.574130 + 0.0684073i
\(446\) 38.7787 67.1667i 0.0869478 0.150598i
\(447\) 0 0
\(448\) 311.358 7.63858i 0.694996 0.0170504i
\(449\) 290.894i 0.647871i 0.946079 + 0.323936i \(0.105006\pi\)
−0.946079 + 0.323936i \(0.894994\pi\)
\(450\) 0 0
\(451\) 396.067 + 686.009i 0.878198 + 1.52108i
\(452\) 47.3565 176.737i 0.104771 0.391011i
\(453\) 0 0
\(454\) 155.768i 0.343101i
\(455\) 794.023 + 295.127i 1.74510 + 0.648630i
\(456\) 0 0
\(457\) 80.7582 21.6391i 0.176714 0.0473503i −0.169377 0.985551i \(-0.554176\pi\)
0.346091 + 0.938201i \(0.387509\pi\)
\(458\) −3.42571 0.917917i −0.00747972 0.00200419i
\(459\) 0 0
\(460\) −202.988 81.1678i −0.441279 0.176452i
\(461\) −579.921 −1.25796 −0.628982 0.777420i \(-0.716528\pi\)
−0.628982 + 0.777420i \(0.716528\pi\)
\(462\) 0 0
\(463\) 340.706 340.706i 0.735865 0.735865i −0.235910 0.971775i \(-0.575807\pi\)
0.971775 + 0.235910i \(0.0758069\pi\)
\(464\) 21.9339 + 12.6636i 0.0472714 + 0.0272921i
\(465\) 0 0
\(466\) −59.4954 103.049i −0.127673 0.221135i
\(467\) −393.823 + 105.524i −0.843304 + 0.225963i −0.654509 0.756054i \(-0.727125\pi\)
−0.188794 + 0.982017i \(0.560458\pi\)
\(468\) 0 0
\(469\) −788.320 190.636i −1.68085 0.406474i
\(470\) 32.0819 42.8930i 0.0682594 0.0912617i
\(471\) 0 0
\(472\) −43.1004 + 160.853i −0.0913143 + 0.340790i
\(473\) 388.166 + 104.009i 0.820648 + 0.219892i
\(474\) 0 0
\(475\) −432.593 + 127.405i −0.910722 + 0.268222i
\(476\) 550.069 161.950i 1.15561 0.340231i
\(477\) 0 0
\(478\) 30.1183 + 112.403i 0.0630089 + 0.235152i
\(479\) 547.299 315.983i 1.14259 0.659673i 0.195517 0.980700i \(-0.437361\pi\)
0.947070 + 0.321027i \(0.104028\pi\)
\(480\) 0 0
\(481\) −62.1390 + 107.628i −0.129187 + 0.223759i
\(482\) 4.73141 + 4.73141i 0.00981620 + 0.00981620i
\(483\) 0 0
\(484\) 440.209i 0.909523i
\(485\) −256.147 102.424i −0.528139 0.211184i
\(486\) 0 0
\(487\) −14.3646 + 53.6096i −0.0294962 + 0.110081i −0.979104 0.203358i \(-0.934815\pi\)
0.949608 + 0.313439i \(0.101481\pi\)
\(488\) 22.8881 + 85.4196i 0.0469019 + 0.175040i
\(489\) 0 0
\(490\) 85.2167 74.1195i 0.173912 0.151264i
\(491\) −328.623 −0.669293 −0.334646 0.942344i \(-0.608617\pi\)
−0.334646 + 0.942344i \(0.608617\pi\)
\(492\) 0 0
\(493\) 39.2077 + 10.5057i 0.0795288 + 0.0213097i
\(494\) −174.294 + 100.629i −0.352821 + 0.203701i
\(495\) 0 0
\(496\) 257.138 0.518423
\(497\) 10.9728 + 447.267i 0.0220782 + 0.899933i
\(498\) 0 0
\(499\) 794.743 + 458.845i 1.59267 + 0.919529i 0.992846 + 0.119398i \(0.0380965\pi\)
0.599825 + 0.800131i \(0.295237\pi\)
\(500\) −79.0832 466.785i −0.158166 0.933570i
\(501\) 0 0
\(502\) 94.3782 25.2886i 0.188004 0.0503756i
\(503\) −268.947 + 268.947i −0.534685 + 0.534685i −0.921963 0.387278i \(-0.873415\pi\)
0.387278 + 0.921963i \(0.373415\pi\)
\(504\) 0 0
\(505\) 637.996 + 477.191i 1.26336 + 0.944932i
\(506\) 40.9821 70.9830i 0.0809922 0.140283i
\(507\) 0 0
\(508\) −230.097 61.6543i −0.452947 0.121367i
\(509\) 288.616 + 166.632i 0.567025 + 0.327372i 0.755960 0.654618i \(-0.227170\pi\)
−0.188935 + 0.981990i \(0.560504\pi\)
\(510\) 0 0
\(511\) 22.6632 93.7166i 0.0443506 0.183398i
\(512\) −333.416 333.416i −0.651203 0.651203i
\(513\) 0 0
\(514\) 127.939 73.8658i 0.248909 0.143708i
\(515\) −313.615 398.458i −0.608961 0.773706i
\(516\) 0 0
\(517\) −253.094 253.094i −0.489544 0.489544i
\(518\) 8.63424 + 14.1422i 0.0166684 + 0.0273015i
\(519\) 0 0
\(520\) −171.176 399.281i −0.329184 0.767849i
\(521\) −186.745 323.451i −0.358435 0.620828i 0.629264 0.777191i \(-0.283356\pi\)
−0.987700 + 0.156363i \(0.950023\pi\)
\(522\) 0 0
\(523\) −48.0280 179.243i −0.0918317 0.342721i 0.904688 0.426074i \(-0.140104\pi\)
−0.996520 + 0.0833533i \(0.973437\pi\)
\(524\) 853.841i 1.62947i
\(525\) 0 0
\(526\) −59.9288 −0.113933
\(527\) 398.063 106.661i 0.755338 0.202392i
\(528\) 0 0
\(529\) 342.717 197.868i 0.647858 0.374041i
\(530\) 165.034 70.7517i 0.311385 0.133494i
\(531\) 0 0
\(532\) −11.7294 478.103i −0.0220477 0.898690i
\(533\) 880.170 880.170i 1.65135 1.65135i
\(534\) 0 0
\(535\) −38.6962 + 30.4566i −0.0723293 + 0.0569283i
\(536\) 207.969 + 360.212i 0.388001 + 0.672037i
\(537\) 0 0
\(538\) −22.5735 + 22.5735i −0.0419581 + 0.0419581i
\(539\) −408.949 634.305i −0.758719 1.17682i
\(540\) 0 0
\(541\) 493.154 854.168i 0.911560 1.57887i 0.0996992 0.995018i \(-0.468212\pi\)
0.811861 0.583851i \(-0.198455\pi\)
\(542\) −49.3996 + 184.362i −0.0911432 + 0.340151i
\(543\) 0 0
\(544\) −385.484 222.560i −0.708611 0.409117i
\(545\) 133.728 178.793i 0.245373 0.328060i
\(546\) 0 0
\(547\) 414.571 + 414.571i 0.757899 + 0.757899i 0.975940 0.218040i \(-0.0699664\pi\)
−0.218040 + 0.975940i \(0.569966\pi\)
\(548\) −34.6741 129.405i −0.0632738 0.236141i
\(549\) 0 0
\(550\) 177.449 4.36941i 0.322635 0.00794438i
\(551\) 16.9271 29.3185i 0.0307206 0.0532097i
\(552\) 0 0
\(553\) 175.359 321.702i 0.317104 0.581740i
\(554\) 24.2151i 0.0437096i
\(555\) 0 0
\(556\) −107.385 185.996i −0.193138 0.334525i
\(557\) −231.777 + 865.003i −0.416116 + 1.55297i 0.366472 + 0.930429i \(0.380565\pi\)
−0.782589 + 0.622539i \(0.786101\pi\)
\(558\) 0 0
\(559\) 631.476i 1.12965i
\(560\) 470.241 + 44.3628i 0.839715 + 0.0792193i
\(561\) 0 0
\(562\) 204.828 54.8834i 0.364462 0.0976574i
\(563\) 787.593 + 211.035i 1.39892 + 0.374840i 0.877958 0.478738i \(-0.158906\pi\)
0.520964 + 0.853578i \(0.325572\pi\)
\(564\) 0 0
\(565\) 89.6822 224.281i 0.158729 0.396958i
\(566\) 84.6051 0.149479
\(567\) 0 0
\(568\) 162.243 162.243i 0.285639 0.285639i
\(569\) 161.663 + 93.3360i 0.284117 + 0.164035i 0.635286 0.772277i \(-0.280882\pi\)
−0.351169 + 0.936312i \(0.614216\pi\)
\(570\) 0 0
\(571\) 399.962 + 692.755i 0.700459 + 1.21323i 0.968305 + 0.249769i \(0.0803548\pi\)
−0.267846 + 0.963462i \(0.586312\pi\)
\(572\) −1363.77 + 365.422i −2.38422 + 0.638850i
\(573\) 0 0
\(574\) −46.8718 159.202i −0.0816583 0.277355i
\(575\) −253.412 138.104i −0.440716 0.240181i
\(576\) 0 0
\(577\) 38.8655 145.048i 0.0673579 0.251383i −0.924034 0.382310i \(-0.875129\pi\)
0.991392 + 0.130927i \(0.0417953\pi\)
\(578\) −79.6039 21.3298i −0.137723 0.0369027i
\(579\) 0 0
\(580\) 28.4609 + 21.2874i 0.0490705 + 0.0367024i
\(581\) −246.426 234.624i −0.424140 0.403828i
\(582\) 0 0
\(583\) −310.553 1159.00i −0.532681 1.98799i
\(584\) −42.8226 + 24.7236i −0.0733263 + 0.0423350i
\(585\) 0 0
\(586\) −0.730235 + 1.26480i −0.00124613 + 0.00215837i
\(587\) −153.429 153.429i −0.261378 0.261378i 0.564236 0.825614i \(-0.309171\pi\)
−0.825614 + 0.564236i \(0.809171\pi\)
\(588\) 0 0
\(589\) 343.710i 0.583548i
\(590\) −39.6973 + 99.2769i −0.0672836 + 0.168266i
\(591\) 0 0
\(592\) −17.9350 + 66.9344i −0.0302957 + 0.113065i
\(593\) −0.220820 0.824110i −0.000372377 0.00138973i 0.965739 0.259514i \(-0.0835623\pi\)
−0.966112 + 0.258124i \(0.916896\pi\)
\(594\) 0 0
\(595\) 746.359 126.380i 1.25439 0.212403i
\(596\) 346.107 0.580716
\(597\) 0 0
\(598\) −124.408 33.3352i −0.208041 0.0557444i
\(599\) 696.721 402.252i 1.16314 0.671539i 0.211085 0.977468i \(-0.432300\pi\)
0.952054 + 0.305929i \(0.0989669\pi\)
\(600\) 0 0
\(601\) −635.940 −1.05814 −0.529068 0.848579i \(-0.677458\pi\)
−0.529068 + 0.848579i \(0.677458\pi\)
\(602\) −73.9235 40.2954i −0.122797 0.0669360i
\(603\) 0 0
\(604\) 299.690 + 173.026i 0.496176 + 0.286467i
\(605\) 68.7556 577.053i 0.113646 0.953807i
\(606\) 0 0
\(607\) −248.787 + 66.6623i −0.409864 + 0.109823i −0.457859 0.889025i \(-0.651383\pi\)
0.0479951 + 0.998848i \(0.484717\pi\)
\(608\) −262.510 + 262.510i −0.431759 + 0.431759i
\(609\) 0 0
\(610\) 8.10346 + 56.1976i 0.0132844 + 0.0921271i
\(611\) −281.222 + 487.091i −0.460266 + 0.797204i
\(612\) 0 0
\(613\) −1115.56 298.914i −1.81984 0.487624i −0.823069 0.567941i \(-0.807740\pi\)
−0.996769 + 0.0803163i \(0.974407\pi\)
\(614\) 40.3134 + 23.2750i 0.0656571 + 0.0379071i
\(615\) 0 0
\(616\) −90.9755 + 376.202i −0.147687 + 0.610717i
\(617\) 265.010 + 265.010i 0.429514 + 0.429514i 0.888463 0.458949i \(-0.151774\pi\)
−0.458949 + 0.888463i \(0.651774\pi\)
\(618\) 0 0
\(619\) 758.758 438.069i 1.22578 0.707704i 0.259635 0.965707i \(-0.416398\pi\)
0.966144 + 0.258003i \(0.0830643\pi\)
\(620\) 358.303 + 42.6917i 0.577909 + 0.0688576i
\(621\) 0 0
\(622\) −31.1126 31.1126i −0.0500203 0.0500203i
\(623\) −172.401 + 316.277i −0.276728 + 0.507668i
\(624\) 0 0
\(625\) −30.7606 624.243i −0.0492170 0.998788i
\(626\) −33.4678 57.9680i −0.0534630 0.0926006i
\(627\) 0 0
\(628\) 176.978 + 660.490i 0.281812 + 1.05174i
\(629\) 111.058i 0.176562i
\(630\) 0 0
\(631\) 247.281 0.391888 0.195944 0.980615i \(-0.437223\pi\)
0.195944 + 0.980615i \(0.437223\pi\)
\(632\) −181.499 + 48.6324i −0.287181 + 0.0769500i
\(633\) 0 0
\(634\) −183.741 + 106.083i −0.289812 + 0.167323i
\(635\) −291.996 116.759i −0.459836 0.183872i
\(636\) 0 0
\(637\) −796.452 + 878.695i −1.25032 + 1.37943i
\(638\) −9.42238 + 9.42238i −0.0147686 + 0.0147686i
\(639\) 0 0
\(640\) −318.001 404.031i −0.496876 0.631298i
\(641\) 540.040 + 935.377i 0.842497 + 1.45925i 0.887778 + 0.460273i \(0.152248\pi\)
−0.0452811 + 0.998974i \(0.514418\pi\)
\(642\) 0 0
\(643\) −40.2830 + 40.2830i −0.0626485 + 0.0626485i −0.737737 0.675088i \(-0.764105\pi\)
0.675088 + 0.737737i \(0.264105\pi\)
\(644\) 211.045 221.660i 0.327709 0.344193i
\(645\) 0 0
\(646\) −89.9238 + 155.753i −0.139201 + 0.241103i
\(647\) 71.9712 268.600i 0.111238 0.415147i −0.887740 0.460346i \(-0.847725\pi\)
0.998978 + 0.0451988i \(0.0143921\pi\)
\(648\) 0 0
\(649\) 618.750 + 357.235i 0.953390 + 0.550440i
\(650\) −78.8015 267.563i −0.121233 0.411635i
\(651\) 0 0
\(652\) −212.662 212.662i −0.326168 0.326168i
\(653\) −228.842 854.052i −0.350448 1.30789i −0.886117 0.463461i \(-0.846607\pi\)
0.535669 0.844428i \(-0.320059\pi\)
\(654\) 0 0
\(655\) −133.360 + 1119.27i −0.203603 + 1.70881i
\(656\) 347.027 601.068i 0.529005 0.916263i
\(657\) 0 0
\(658\) 39.0760 + 64.0033i 0.0593860 + 0.0972694i
\(659\) 431.384i 0.654604i 0.944920 + 0.327302i \(0.106139\pi\)
−0.944920 + 0.327302i \(0.893861\pi\)
\(660\) 0 0
\(661\) −185.671 321.591i −0.280894 0.486522i 0.690711 0.723130i \(-0.257297\pi\)
−0.971605 + 0.236608i \(0.923964\pi\)
\(662\) 5.58286 20.8355i 0.00843333 0.0314736i
\(663\) 0 0
\(664\) 174.498i 0.262798i
\(665\) 59.2987 628.559i 0.0891710 0.945202i
\(666\) 0 0
\(667\) 20.9272 5.60742i 0.0313751 0.00840693i
\(668\) 78.8548 + 21.1291i 0.118046 + 0.0316304i
\(669\) 0 0
\(670\) 105.227 + 245.450i 0.157054 + 0.366343i
\(671\) 379.414 0.565446
\(672\) 0 0
\(673\) −306.397 + 306.397i −0.455271 + 0.455271i −0.897100 0.441828i \(-0.854330\pi\)
0.441828 + 0.897100i \(0.354330\pi\)
\(674\) 221.231 + 127.728i 0.328235 + 0.189507i
\(675\) 0 0
\(676\) 789.262 + 1367.04i 1.16755 + 2.02225i
\(677\) 1114.67 298.674i 1.64648 0.441173i 0.687856 0.725847i \(-0.258552\pi\)
0.958624 + 0.284674i \(0.0918855\pi\)
\(678\) 0 0
\(679\) 266.314 279.709i 0.392215 0.411943i
\(680\) −310.876 232.520i −0.457170 0.341942i
\(681\) 0 0
\(682\) −35.0149 + 130.677i −0.0513414 + 0.191609i
\(683\) −890.075 238.495i −1.30318 0.349187i −0.460531 0.887644i \(-0.652341\pi\)
−0.842653 + 0.538456i \(0.819008\pi\)
\(684\) 0 0
\(685\) −25.2413 175.048i −0.0368485 0.255545i
\(686\) 52.0413 + 149.307i 0.0758620 + 0.217649i
\(687\) 0 0
\(688\) −91.1307 340.104i −0.132457 0.494338i
\(689\) −1632.87 + 942.741i −2.36992 + 1.36827i
\(690\) 0 0
\(691\) 84.0700 145.613i 0.121664 0.210729i −0.798760 0.601650i \(-0.794510\pi\)
0.920424 + 0.390921i \(0.127844\pi\)
\(692\) 11.8287 + 11.8287i 0.0170934 + 0.0170934i
\(693\) 0 0
\(694\) 14.9089i 0.0214826i
\(695\) −111.716 260.587i −0.160743 0.374945i
\(696\) 0 0
\(697\) 287.893 1074.43i 0.413046 1.54151i
\(698\) −25.5327 95.2892i −0.0365797 0.136517i
\(699\) 0 0
\(700\) 647.882 + 139.889i 0.925545 + 0.199841i
\(701\) −958.494 −1.36732 −0.683662 0.729799i \(-0.739614\pi\)
−0.683662 + 0.729799i \(0.739614\pi\)
\(702\) 0 0
\(703\) 89.4696 + 23.9733i 0.127268 + 0.0341014i
\(704\) −593.479 + 342.645i −0.843010 + 0.486712i
\(705\) 0 0
\(706\) 73.7273 0.104430
\(707\) −951.994 + 581.222i −1.34653 + 0.822096i
\(708\) 0 0
\(709\) 30.6249 + 17.6813i 0.0431945 + 0.0249383i 0.521442 0.853287i \(-0.325394\pi\)
−0.478247 + 0.878225i \(0.658728\pi\)
\(710\) 115.762 91.1128i 0.163045 0.128328i
\(711\) 0 0
\(712\) 178.438 47.8123i 0.250615 0.0671521i
\(713\) 155.537 155.537i 0.218144 0.218144i
\(714\) 0 0
\(715\) −1844.79 + 266.012i −2.58013 + 0.372045i
\(716\) 19.9456 34.5467i 0.0278569 0.0482496i
\(717\) 0 0
\(718\) 217.167 + 58.1896i 0.302460 + 0.0810440i
\(719\) 983.525 + 567.839i 1.36791 + 0.789762i 0.990661 0.136351i \(-0.0435375\pi\)
0.377247 + 0.926113i \(0.376871\pi\)
\(720\) 0 0
\(721\) 681.001 200.499i 0.944523 0.278084i
\(722\) −11.6075 11.6075i −0.0160769 0.0160769i
\(723\) 0 0
\(724\) −1066.13 + 615.528i −1.47255 + 0.850177i
\(725\) 33.9834 + 32.3501i 0.0468737 + 0.0446208i
\(726\) 0 0
\(727\) −12.8697 12.8697i −0.0177025 0.0177025i 0.698200 0.715903i \(-0.253985\pi\)
−0.715903 + 0.698200i \(0.753985\pi\)
\(728\) 608.015 14.9165i 0.835185 0.0204897i
\(729\) 0 0
\(730\) −29.1794 + 12.5095i −0.0399718 + 0.0171363i
\(731\) −282.150 488.699i −0.385979 0.668535i
\(732\) 0 0
\(733\) 141.743 + 528.993i 0.193374 + 0.721682i 0.992682 + 0.120760i \(0.0385332\pi\)
−0.799308 + 0.600922i \(0.794800\pi\)
\(734\) 120.979i 0.164822i
\(735\) 0 0
\(736\) −237.583 −0.322803
\(737\) 1723.74 461.874i 2.33886 0.626695i
\(738\) 0 0
\(739\) −312.563 + 180.459i −0.422955 + 0.244193i −0.696341 0.717711i \(-0.745190\pi\)
0.273386 + 0.961904i \(0.411856\pi\)
\(740\) −36.1041 + 90.2907i −0.0487893 + 0.122014i
\(741\) 0 0
\(742\) 6.16541 + 251.310i 0.00830918 + 0.338692i
\(743\) −416.926 + 416.926i −0.561138 + 0.561138i −0.929631 0.368492i \(-0.879874\pi\)
0.368492 + 0.929631i \(0.379874\pi\)
\(744\) 0 0
\(745\) 453.698 + 54.0579i 0.608991 + 0.0725610i
\(746\) −31.8207 55.1150i −0.0426551 0.0738807i
\(747\) 0 0
\(748\) −892.149 + 892.149i −1.19271 + 1.19271i
\(749\) −19.4714 66.1352i −0.0259965 0.0882980i
\(750\) 0 0
\(751\) −521.992 + 904.116i −0.695062 + 1.20388i 0.275097 + 0.961416i \(0.411290\pi\)
−0.970160 + 0.242467i \(0.922043\pi\)
\(752\) −81.1685 + 302.925i −0.107937 + 0.402826i
\(753\) 0 0
\(754\) 18.1338 + 10.4696i 0.0240501 + 0.0138854i
\(755\) 365.828 + 273.621i 0.484540 + 0.362413i
\(756\) 0 0
\(757\) −691.527 691.527i −0.913510 0.913510i 0.0830364 0.996547i \(-0.473538\pi\)
−0.996547 + 0.0830364i \(0.973538\pi\)
\(758\) 63.8497 + 238.291i 0.0842345 + 0.314367i
\(759\) 0 0
\(760\) −254.429 + 200.254i −0.334775 + 0.263492i
\(761\) −553.925 + 959.427i −0.727891 + 1.26074i 0.229881 + 0.973219i \(0.426166\pi\)
−0.957773 + 0.287526i \(0.907167\pi\)
\(762\) 0 0
\(763\) 162.882 + 266.788i 0.213476 + 0.349656i
\(764\) 905.554i 1.18528i
\(765\) 0 0
\(766\) −29.7028 51.4468i −0.0387765 0.0671629i
\(767\) 290.578 1084.45i 0.378851 1.41389i
\(768\) 0 0
\(769\) 671.432i 0.873124i 0.899674 + 0.436562i \(0.143804\pi\)
−0.899674 + 0.436562i \(0.856196\pi\)
\(770\) −86.5785 + 232.935i −0.112440 + 0.302513i
\(771\) 0 0
\(772\) 698.896 187.269i 0.905306 0.242576i
\(773\) 1110.22 + 297.482i 1.43625 + 0.384841i 0.891217 0.453577i \(-0.149852\pi\)
0.545028 + 0.838418i \(0.316519\pi\)
\(774\) 0 0
\(775\) 463.018 +