Properties

Label 392.3.k.l.67.3
Level 392
Weight 3
Character 392.67
Analytic conductor 10.681
Analytic rank 0
Dimension 12
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 392 = 2^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 392.k (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.6812263629\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 3 x^{11} - 4 x^{10} + 3 x^{9} + 86 x^{8} - 163 x^{7} + 155 x^{6} - 166 x^{5} + 164 x^{4} - 116 x^{3} + 60 x^{2} - 20 x + 4\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 56)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 67.3
Root \(0.378279 + 0.358951i\) of defining polynomial
Character \(\chi\) \(=\) 392.67
Dual form 392.3.k.l.275.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.104798 - 1.99725i) q^{2} +(-1.99052 + 3.44767i) q^{3} +(-3.97803 - 0.418616i) q^{4} +(1.63031 - 0.941260i) q^{5} +(6.67727 + 4.33687i) q^{6} +(-1.25297 + 7.90127i) q^{8} +(-3.42430 - 5.93106i) q^{9} +O(q^{10})\) \(q+(0.104798 - 1.99725i) q^{2} +(-1.99052 + 3.44767i) q^{3} +(-3.97803 - 0.418616i) q^{4} +(1.63031 - 0.941260i) q^{5} +(6.67727 + 4.33687i) q^{6} +(-1.25297 + 7.90127i) q^{8} +(-3.42430 - 5.93106i) q^{9} +(-1.70908 - 3.35478i) q^{10} +(3.93973 - 6.82381i) q^{11} +(9.36159 - 12.8817i) q^{12} +11.4863i q^{13} +7.49437i q^{15} +(15.6495 + 3.33054i) q^{16} +(-1.44921 + 2.51011i) q^{17} +(-12.2047 + 6.21763i) q^{18} +(-15.0223 - 26.0194i) q^{19} +(-6.87946 + 3.06189i) q^{20} +(-13.2160 - 8.58375i) q^{22} +(-33.3838 + 19.2741i) q^{23} +(-24.7469 - 20.0474i) q^{24} +(-10.7281 + 18.5815i) q^{25} +(22.9411 + 1.20374i) q^{26} -8.56478 q^{27} -27.8701i q^{29} +(14.9681 + 0.785394i) q^{30} +(-19.4709 - 11.2416i) q^{31} +(8.29196 - 30.9070i) q^{32} +(15.6842 + 27.1658i) q^{33} +(4.86145 + 3.15750i) q^{34} +(11.1392 + 25.0274i) q^{36} +(-39.4520 + 22.7776i) q^{37} +(-53.5417 + 27.2766i) q^{38} +(-39.6011 - 22.8637i) q^{39} +(5.39442 + 14.0609i) q^{40} +40.6313 q^{41} -47.2806 q^{43} +(-18.5289 + 25.4961i) q^{44} +(-11.1653 - 6.44632i) q^{45} +(34.9968 + 68.6958i) q^{46} +(-71.5172 + 41.2905i) q^{47} +(-42.6332 + 47.3250i) q^{48} +(35.9878 + 23.3739i) q^{50} +(-5.76936 - 9.99283i) q^{51} +(4.80836 - 45.6930i) q^{52} +(-23.2823 - 13.4420i) q^{53} +(-0.897571 + 17.1060i) q^{54} -14.8332i q^{55} +119.609 q^{57} +(-55.6637 - 2.92073i) q^{58} +(-5.20555 + 9.01627i) q^{59} +(3.13726 - 29.8129i) q^{60} +(19.1932 - 11.0812i) q^{61} +(-24.4927 + 37.7103i) q^{62} +(-60.8601 - 19.8001i) q^{64} +(10.8116 + 18.7263i) q^{65} +(55.9006 - 28.4783i) q^{66} +(29.6549 - 51.3639i) q^{67} +(6.81579 - 9.37864i) q^{68} -153.462i q^{69} +38.2541i q^{71} +(51.1535 - 19.6249i) q^{72} +(6.98890 - 12.1051i) q^{73} +(41.3581 + 81.1826i) q^{74} +(-42.7087 - 73.9737i) q^{75} +(48.8672 + 109.795i) q^{76} +(-49.8147 + 76.6974i) q^{78} +(44.3314 - 25.5948i) q^{79} +(28.6485 - 9.30046i) q^{80} +(47.8670 - 82.9081i) q^{81} +(4.25807 - 81.1509i) q^{82} +89.4458 q^{83} +5.45635i q^{85} +(-4.95491 + 94.4313i) q^{86} +(96.0871 + 55.4759i) q^{87} +(48.9804 + 39.6789i) q^{88} +(52.6288 + 91.1558i) q^{89} +(-14.0450 + 21.6245i) q^{90} +(140.870 - 62.6982i) q^{92} +(77.5144 - 44.7530i) q^{93} +(74.9726 + 147.165i) q^{94} +(-48.9821 - 28.2798i) q^{95} +(90.0520 + 90.1088i) q^{96} -55.3301 q^{97} -53.9633 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 2q^{2} + 6q^{3} - 4q^{4} + 56q^{6} + 8q^{8} - 40q^{9} + O(q^{10}) \) \( 12q + 2q^{2} + 6q^{3} - 4q^{4} + 56q^{6} + 8q^{8} - 40q^{9} + 6q^{10} + 30q^{11} - 32q^{12} + 16q^{16} - 30q^{17} - 16q^{18} - 78q^{19} - 48q^{20} + 24q^{22} + 76q^{24} - 92q^{25} + 128q^{26} - 156q^{27} - 16q^{30} + 112q^{32} + 78q^{33} - 76q^{34} - 248q^{36} - 80q^{38} - 44q^{40} + 232q^{41} - 200q^{43} + 132q^{44} - 156q^{46} - 176q^{48} + 48q^{50} + 10q^{51} - 132q^{52} + 36q^{54} + 332q^{57} + 4q^{58} + 110q^{59} + 84q^{60} + 96q^{62} - 160q^{64} - 32q^{65} + 138q^{66} + 434q^{67} - 96q^{68} - 328q^{72} - 102q^{73} - 34q^{74} + 60q^{75} + 168q^{76} + 720q^{78} + 256q^{80} - 82q^{81} + 24q^{82} + 536q^{83} + 240q^{86} - 204q^{88} - 214q^{89} - 440q^{90} + 160q^{92} + 16q^{94} - 48q^{96} + 152q^{97} + 504q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(297\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.104798 1.99725i 0.0523990 0.998626i
\(3\) −1.99052 + 3.44767i −0.663505 + 1.14922i 0.316183 + 0.948698i \(0.397599\pi\)
−0.979688 + 0.200526i \(0.935735\pi\)
\(4\) −3.97803 0.418616i −0.994509 0.104654i
\(5\) 1.63031 0.941260i 0.326062 0.188252i −0.328029 0.944668i \(-0.606384\pi\)
0.654091 + 0.756416i \(0.273051\pi\)
\(6\) 6.67727 + 4.33687i 1.11288 + 0.722812i
\(7\) 0 0
\(8\) −1.25297 + 7.90127i −0.156621 + 0.987659i
\(9\) −3.42430 5.93106i −0.380478 0.659007i
\(10\) −1.70908 3.35478i −0.170908 0.335478i
\(11\) 3.93973 6.82381i 0.358157 0.620346i −0.629496 0.777004i \(-0.716739\pi\)
0.987653 + 0.156658i \(0.0500719\pi\)
\(12\) 9.36159 12.8817i 0.780132 1.07348i
\(13\) 11.4863i 0.883564i 0.897122 + 0.441782i \(0.145654\pi\)
−0.897122 + 0.441782i \(0.854346\pi\)
\(14\) 0 0
\(15\) 7.49437i 0.499625i
\(16\) 15.6495 + 3.33054i 0.978095 + 0.208159i
\(17\) −1.44921 + 2.51011i −0.0852478 + 0.147654i −0.905497 0.424353i \(-0.860502\pi\)
0.820249 + 0.572007i \(0.193835\pi\)
\(18\) −12.2047 + 6.21763i −0.678038 + 0.345424i
\(19\) −15.0223 26.0194i −0.790649 1.36944i −0.925566 0.378587i \(-0.876410\pi\)
0.134916 0.990857i \(-0.456923\pi\)
\(20\) −6.87946 + 3.06189i −0.343973 + 0.153095i
\(21\) 0 0
\(22\) −13.2160 8.58375i −0.600727 0.390171i
\(23\) −33.3838 + 19.2741i −1.45147 + 0.838006i −0.998565 0.0535530i \(-0.982945\pi\)
−0.452904 + 0.891559i \(0.649612\pi\)
\(24\) −24.7469 20.0474i −1.03112 0.835310i
\(25\) −10.7281 + 18.5815i −0.429122 + 0.743262i
\(26\) 22.9411 + 1.20374i 0.882350 + 0.0462978i
\(27\) −8.56478 −0.317214
\(28\) 0 0
\(29\) 27.8701i 0.961039i −0.876984 0.480519i \(-0.840448\pi\)
0.876984 0.480519i \(-0.159552\pi\)
\(30\) 14.9681 + 0.785394i 0.498938 + 0.0261798i
\(31\) −19.4709 11.2416i −0.628095 0.362631i 0.151919 0.988393i \(-0.451455\pi\)
−0.780014 + 0.625762i \(0.784788\pi\)
\(32\) 8.29196 30.9070i 0.259124 0.965844i
\(33\) 15.6842 + 27.1658i 0.475278 + 0.823206i
\(34\) 4.86145 + 3.15750i 0.142984 + 0.0928676i
\(35\) 0 0
\(36\) 11.1392 + 25.0274i 0.309421 + 0.695207i
\(37\) −39.4520 + 22.7776i −1.06627 + 0.615611i −0.927160 0.374666i \(-0.877757\pi\)
−0.139109 + 0.990277i \(0.544424\pi\)
\(38\) −53.5417 + 27.2766i −1.40899 + 0.717805i
\(39\) −39.6011 22.8637i −1.01541 0.586249i
\(40\) 5.39442 + 14.0609i 0.134860 + 0.351522i
\(41\) 40.6313 0.991007 0.495503 0.868606i \(-0.334984\pi\)
0.495503 + 0.868606i \(0.334984\pi\)
\(42\) 0 0
\(43\) −47.2806 −1.09955 −0.549774 0.835313i \(-0.685286\pi\)
−0.549774 + 0.835313i \(0.685286\pi\)
\(44\) −18.5289 + 25.4961i −0.421112 + 0.579457i
\(45\) −11.1653 6.44632i −0.248119 0.143251i
\(46\) 34.9968 + 68.6958i 0.760799 + 1.49339i
\(47\) −71.5172 + 41.2905i −1.52164 + 0.878520i −0.521968 + 0.852965i \(0.674802\pi\)
−0.999673 + 0.0255554i \(0.991865\pi\)
\(48\) −42.6332 + 47.3250i −0.888192 + 0.985937i
\(49\) 0 0
\(50\) 35.9878 + 23.3739i 0.719755 + 0.467479i
\(51\) −5.76936 9.99283i −0.113125 0.195938i
\(52\) 4.80836 45.6930i 0.0924685 0.878712i
\(53\) −23.2823 13.4420i −0.439288 0.253623i 0.264007 0.964521i \(-0.414956\pi\)
−0.703296 + 0.710897i \(0.748289\pi\)
\(54\) −0.897571 + 17.1060i −0.0166217 + 0.316778i
\(55\) 14.8332i 0.269695i
\(56\) 0 0
\(57\) 119.609 2.09840
\(58\) −55.6637 2.92073i −0.959719 0.0503574i
\(59\) −5.20555 + 9.01627i −0.0882296 + 0.152818i −0.906763 0.421641i \(-0.861454\pi\)
0.818533 + 0.574459i \(0.194788\pi\)
\(60\) 3.13726 29.8129i 0.0522877 0.496881i
\(61\) 19.1932 11.0812i 0.314642 0.181659i −0.334360 0.942446i \(-0.608520\pi\)
0.649002 + 0.760787i \(0.275187\pi\)
\(62\) −24.4927 + 37.7103i −0.395044 + 0.608231i
\(63\) 0 0
\(64\) −60.8601 19.8001i −0.950939 0.309377i
\(65\) 10.8116 + 18.7263i 0.166333 + 0.288097i
\(66\) 55.9006 28.4783i 0.846979 0.431490i
\(67\) 29.6549 51.3639i 0.442611 0.766625i −0.555271 0.831669i \(-0.687386\pi\)
0.997882 + 0.0650444i \(0.0207189\pi\)
\(68\) 6.81579 9.37864i 0.100232 0.137921i
\(69\) 153.462i 2.22409i
\(70\) 0 0
\(71\) 38.2541i 0.538791i 0.963030 + 0.269395i \(0.0868238\pi\)
−0.963030 + 0.269395i \(0.913176\pi\)
\(72\) 51.1535 19.6249i 0.710465 0.272568i
\(73\) 6.98890 12.1051i 0.0957383 0.165824i −0.814178 0.580615i \(-0.802812\pi\)
0.909917 + 0.414791i \(0.136145\pi\)
\(74\) 41.3581 + 81.1826i 0.558894 + 1.09706i
\(75\) −42.7087 73.9737i −0.569450 0.986316i
\(76\) 48.8672 + 109.795i 0.642990 + 1.44467i
\(77\) 0 0
\(78\) −49.8147 + 76.6974i −0.638651 + 0.983300i
\(79\) 44.3314 25.5948i 0.561157 0.323984i −0.192453 0.981306i \(-0.561644\pi\)
0.753610 + 0.657322i \(0.228311\pi\)
\(80\) 28.6485 9.30046i 0.358106 0.116256i
\(81\) 47.8670 82.9081i 0.590951 1.02356i
\(82\) 4.25807 81.1509i 0.0519277 0.989646i
\(83\) 89.4458 1.07766 0.538830 0.842414i \(-0.318866\pi\)
0.538830 + 0.842414i \(0.318866\pi\)
\(84\) 0 0
\(85\) 5.45635i 0.0641923i
\(86\) −4.95491 + 94.4313i −0.0576152 + 1.09804i
\(87\) 96.0871 + 55.4759i 1.10445 + 0.637654i
\(88\) 48.9804 + 39.6789i 0.556595 + 0.450896i
\(89\) 52.6288 + 91.1558i 0.591335 + 1.02422i 0.994053 + 0.108898i \(0.0347323\pi\)
−0.402718 + 0.915324i \(0.631934\pi\)
\(90\) −14.0450 + 21.6245i −0.156056 + 0.240272i
\(91\) 0 0
\(92\) 140.870 62.6982i 1.53120 0.681502i
\(93\) 77.5144 44.7530i 0.833488 0.481215i
\(94\) 74.9726 + 147.165i 0.797581 + 1.56558i
\(95\) −48.9821 28.2798i −0.515601 0.297683i
\(96\) 90.0520 + 90.1088i 0.938042 + 0.938634i
\(97\) −55.3301 −0.570413 −0.285206 0.958466i \(-0.592062\pi\)
−0.285206 + 0.958466i \(0.592062\pi\)
\(98\) 0 0
\(99\) −53.9633 −0.545084
\(100\) 50.4551 69.4271i 0.504551 0.694271i
\(101\) −27.2216 15.7164i −0.269521 0.155608i 0.359149 0.933280i \(-0.383067\pi\)
−0.628670 + 0.777672i \(0.716400\pi\)
\(102\) −20.5628 + 10.4756i −0.201596 + 0.102702i
\(103\) −69.2701 + 39.9931i −0.672525 + 0.388283i −0.797033 0.603936i \(-0.793598\pi\)
0.124508 + 0.992219i \(0.460265\pi\)
\(104\) −90.7566 14.3920i −0.872660 0.138385i
\(105\) 0 0
\(106\) −29.2871 + 45.0919i −0.276293 + 0.425395i
\(107\) −24.3817 42.2303i −0.227866 0.394676i 0.729309 0.684184i \(-0.239842\pi\)
−0.957175 + 0.289508i \(0.906508\pi\)
\(108\) 34.0710 + 3.58535i 0.315472 + 0.0331977i
\(109\) −99.6528 57.5346i −0.914246 0.527840i −0.0324509 0.999473i \(-0.510331\pi\)
−0.881795 + 0.471633i \(0.843665\pi\)
\(110\) −29.6257 1.55449i −0.269325 0.0141317i
\(111\) 181.357i 1.63384i
\(112\) 0 0
\(113\) −55.7570 −0.493425 −0.246712 0.969089i \(-0.579350\pi\)
−0.246712 + 0.969089i \(0.579350\pi\)
\(114\) 12.5347 238.889i 0.109954 2.09552i
\(115\) −36.2840 + 62.8457i −0.315513 + 0.546484i
\(116\) −11.6669 + 110.868i −0.100577 + 0.955762i
\(117\) 68.1262 39.3327i 0.582275 0.336177i
\(118\) 17.4622 + 11.3417i 0.147985 + 0.0961159i
\(119\) 0 0
\(120\) −59.2150 9.39023i −0.493459 0.0782519i
\(121\) 29.4571 + 51.0212i 0.243447 + 0.421663i
\(122\) −20.1205 39.4949i −0.164922 0.323729i
\(123\) −80.8772 + 140.083i −0.657538 + 1.13889i
\(124\) 72.7502 + 52.8701i 0.586695 + 0.426372i
\(125\) 87.4546i 0.699637i
\(126\) 0 0
\(127\) 35.6964i 0.281074i −0.990075 0.140537i \(-0.955117\pi\)
0.990075 0.140537i \(-0.0448828\pi\)
\(128\) −45.9239 + 119.478i −0.358780 + 0.933422i
\(129\) 94.1127 163.008i 0.729556 1.26363i
\(130\) 38.5342 19.6311i 0.296417 0.151008i
\(131\) −60.6462 105.042i −0.462948 0.801849i 0.536158 0.844117i \(-0.319875\pi\)
−0.999106 + 0.0422680i \(0.986542\pi\)
\(132\) −51.0202 114.632i −0.386516 0.868425i
\(133\) 0 0
\(134\) −99.4788 64.6112i −0.742379 0.482173i
\(135\) −13.9632 + 8.06168i −0.103431 + 0.0597162i
\(136\) −18.0172 14.5957i −0.132480 0.107321i
\(137\) 4.24835 7.35836i 0.0310099 0.0537107i −0.850104 0.526615i \(-0.823461\pi\)
0.881114 + 0.472904i \(0.156794\pi\)
\(138\) −306.502 16.0825i −2.22103 0.116540i
\(139\) 3.05942 0.0220102 0.0110051 0.999939i \(-0.496497\pi\)
0.0110051 + 0.999939i \(0.496497\pi\)
\(140\) 0 0
\(141\) 328.757i 2.33161i
\(142\) 76.4032 + 4.00895i 0.538050 + 0.0282321i
\(143\) 78.3806 + 45.2530i 0.548116 + 0.316455i
\(144\) −33.8351 104.223i −0.234966 0.723771i
\(145\) −26.2330 45.4370i −0.180918 0.313358i
\(146\) −23.4446 15.2272i −0.160579 0.104296i
\(147\) 0 0
\(148\) 166.476 74.0949i 1.12484 0.500641i
\(149\) 27.4740 15.8621i 0.184389 0.106457i −0.404964 0.914333i \(-0.632716\pi\)
0.589353 + 0.807876i \(0.299383\pi\)
\(150\) −152.220 + 77.5478i −1.01480 + 0.516986i
\(151\) 219.621 + 126.798i 1.45444 + 0.839723i 0.998729 0.0504039i \(-0.0160509\pi\)
0.455713 + 0.890127i \(0.349384\pi\)
\(152\) 224.409 86.0939i 1.47638 0.566407i
\(153\) 19.8502 0.129740
\(154\) 0 0
\(155\) −42.3249 −0.273064
\(156\) 147.964 + 107.530i 0.948484 + 0.689297i
\(157\) 42.7187 + 24.6636i 0.272093 + 0.157093i 0.629839 0.776726i \(-0.283121\pi\)
−0.357745 + 0.933819i \(0.616454\pi\)
\(158\) −46.4734 91.2233i −0.294135 0.577363i
\(159\) 92.6875 53.5132i 0.582940 0.336561i
\(160\) −15.5731 58.1929i −0.0973317 0.363706i
\(161\) 0 0
\(162\) −160.572 104.291i −0.991186 0.643773i
\(163\) −57.8597 100.216i −0.354967 0.614821i 0.632145 0.774850i \(-0.282175\pi\)
−0.987112 + 0.160029i \(0.948841\pi\)
\(164\) −161.633 17.0089i −0.985565 0.103713i
\(165\) 51.1401 + 29.5258i 0.309940 + 0.178944i
\(166\) 9.37373 178.646i 0.0564683 1.07618i
\(167\) 32.3859i 0.193928i 0.995288 + 0.0969639i \(0.0309131\pi\)
−0.995288 + 0.0969639i \(0.969087\pi\)
\(168\) 0 0
\(169\) 37.0641 0.219314
\(170\) 10.8977 + 0.571814i 0.0641041 + 0.00336361i
\(171\) −102.882 + 178.197i −0.601649 + 1.04209i
\(172\) 188.084 + 19.7924i 1.09351 + 0.115072i
\(173\) −179.479 + 103.622i −1.03745 + 0.598973i −0.919110 0.394000i \(-0.871091\pi\)
−0.118341 + 0.992973i \(0.537758\pi\)
\(174\) 120.869 186.096i 0.694650 1.06952i
\(175\) 0 0
\(176\) 84.3818 93.6679i 0.479442 0.532204i
\(177\) −20.7234 35.8941i −0.117082 0.202791i
\(178\) 187.577 95.5601i 1.05380 0.536855i
\(179\) −87.0837 + 150.833i −0.486501 + 0.842644i −0.999880 0.0155178i \(-0.995060\pi\)
0.513379 + 0.858162i \(0.328394\pi\)
\(180\) 41.7176 + 30.3177i 0.231764 + 0.168431i
\(181\) 204.244i 1.12842i 0.825632 + 0.564209i \(0.190819\pi\)
−0.825632 + 0.564209i \(0.809181\pi\)
\(182\) 0 0
\(183\) 88.2291i 0.482126i
\(184\) −110.461 287.924i −0.600333 1.56481i
\(185\) −42.8793 + 74.2691i −0.231780 + 0.401455i
\(186\) −81.2596 159.506i −0.436880 0.857558i
\(187\) 11.4190 + 19.7783i 0.0610642 + 0.105766i
\(188\) 301.783 134.317i 1.60523 0.714450i
\(189\) 0 0
\(190\) −61.6152 + 94.8660i −0.324291 + 0.499295i
\(191\) −258.518 + 149.255i −1.35350 + 0.781442i −0.988737 0.149660i \(-0.952182\pi\)
−0.364759 + 0.931102i \(0.618849\pi\)
\(192\) 189.407 170.413i 0.986497 0.887570i
\(193\) 165.381 286.448i 0.856896 1.48419i −0.0179791 0.999838i \(-0.505723\pi\)
0.874875 0.484349i \(-0.160943\pi\)
\(194\) −5.79847 + 110.508i −0.0298890 + 0.569629i
\(195\) −86.0828 −0.441450
\(196\) 0 0
\(197\) 327.309i 1.66146i 0.556672 + 0.830732i \(0.312078\pi\)
−0.556672 + 0.830732i \(0.687922\pi\)
\(198\) −5.65524 + 107.778i −0.0285618 + 0.544335i
\(199\) −11.0295 6.36789i −0.0554246 0.0319994i 0.472032 0.881582i \(-0.343521\pi\)
−0.527456 + 0.849582i \(0.676854\pi\)
\(200\) −133.376 108.047i −0.666879 0.540237i
\(201\) 118.057 + 204.481i 0.587349 + 1.01732i
\(202\) −34.2424 + 52.7214i −0.169517 + 0.260997i
\(203\) 0 0
\(204\) 18.7676 + 42.1670i 0.0919979 + 0.206701i
\(205\) 66.2416 38.2446i 0.323130 0.186559i
\(206\) 72.6170 + 142.541i 0.352510 + 0.691947i
\(207\) 228.632 + 132.001i 1.10450 + 0.637686i
\(208\) −38.2557 + 179.756i −0.183921 + 0.864210i
\(209\) −236.736 −1.13271
\(210\) 0 0
\(211\) 120.455 0.570875 0.285437 0.958397i \(-0.407861\pi\)
0.285437 + 0.958397i \(0.407861\pi\)
\(212\) 86.9907 + 63.2192i 0.410334 + 0.298204i
\(213\) −131.888 76.1454i −0.619191 0.357490i
\(214\) −86.8997 + 44.2707i −0.406073 + 0.206873i
\(215\) −77.0820 + 44.5033i −0.358521 + 0.206992i
\(216\) 10.7314 67.6726i 0.0496825 0.313299i
\(217\) 0 0
\(218\) −125.354 + 193.002i −0.575020 + 0.885331i
\(219\) 27.8230 + 48.1909i 0.127046 + 0.220050i
\(220\) −6.20943 + 59.0071i −0.0282247 + 0.268214i
\(221\) −28.8320 16.6461i −0.130461 0.0753219i
\(222\) −362.215 19.0058i −1.63160 0.0856117i
\(223\) 372.958i 1.67246i 0.548382 + 0.836228i \(0.315244\pi\)
−0.548382 + 0.836228i \(0.684756\pi\)
\(224\) 0 0
\(225\) 146.944 0.653086
\(226\) −5.84322 + 111.361i −0.0258549 + 0.492747i
\(227\) 36.7128 63.5885i 0.161730 0.280125i −0.773759 0.633480i \(-0.781626\pi\)
0.935489 + 0.353355i \(0.114959\pi\)
\(228\) −475.808 50.0701i −2.08688 0.219606i
\(229\) 367.587 212.226i 1.60518 0.926752i 0.614755 0.788718i \(-0.289255\pi\)
0.990428 0.138034i \(-0.0440783\pi\)
\(230\) 121.716 + 79.0543i 0.529201 + 0.343714i
\(231\) 0 0
\(232\) 220.209 + 34.9205i 0.949179 + 0.150519i
\(233\) 41.7070 + 72.2386i 0.179000 + 0.310037i 0.941538 0.336906i \(-0.109380\pi\)
−0.762538 + 0.646943i \(0.776047\pi\)
\(234\) −71.4178 140.187i −0.305204 0.599090i
\(235\) −77.7301 + 134.632i −0.330766 + 0.572904i
\(236\) 24.4822 33.6879i 0.103738 0.142745i
\(237\) 203.787i 0.859861i
\(238\) 0 0
\(239\) 112.561i 0.470967i 0.971878 + 0.235484i \(0.0756674\pi\)
−0.971878 + 0.235484i \(0.924333\pi\)
\(240\) −24.9603 + 117.283i −0.104001 + 0.488680i
\(241\) 140.216 242.861i 0.581809 1.00772i −0.413455 0.910524i \(-0.635678\pi\)
0.995265 0.0971992i \(-0.0309884\pi\)
\(242\) 104.989 53.4863i 0.433840 0.221018i
\(243\) 152.019 + 263.304i 0.625591 + 1.08356i
\(244\) −80.9899 + 36.0468i −0.331926 + 0.147733i
\(245\) 0 0
\(246\) 271.306 + 176.213i 1.10287 + 0.716311i
\(247\) 298.868 172.552i 1.20999 0.698589i
\(248\) 113.219 139.760i 0.456529 0.563548i
\(249\) −178.043 + 308.380i −0.715033 + 1.23847i
\(250\) 174.669 + 9.16506i 0.698675 + 0.0366602i
\(251\) 32.9560 0.131299 0.0656493 0.997843i \(-0.479088\pi\)
0.0656493 + 0.997843i \(0.479088\pi\)
\(252\) 0 0
\(253\) 303.740i 1.20055i
\(254\) −71.2946 3.74090i −0.280688 0.0147280i
\(255\) −18.8117 10.8609i −0.0737714 0.0425919i
\(256\) 233.815 + 104.243i 0.913340 + 0.407198i
\(257\) −112.109 194.179i −0.436223 0.755561i 0.561172 0.827700i \(-0.310351\pi\)
−0.997395 + 0.0721390i \(0.977017\pi\)
\(258\) −315.705 205.050i −1.22366 0.794767i
\(259\) 0 0
\(260\) −35.1699 79.0197i −0.135269 0.303922i
\(261\) −165.300 + 95.4357i −0.633332 + 0.365654i
\(262\) −216.152 + 110.118i −0.825006 + 0.420296i
\(263\) −147.190 84.9804i −0.559659 0.323119i 0.193350 0.981130i \(-0.438065\pi\)
−0.753009 + 0.658011i \(0.771398\pi\)
\(264\) −234.296 + 89.8870i −0.887485 + 0.340481i
\(265\) −50.6098 −0.190980
\(266\) 0 0
\(267\) −419.034 −1.56942
\(268\) −139.470 + 191.913i −0.520411 + 0.716094i
\(269\) −93.9863 54.2630i −0.349391 0.201721i 0.315026 0.949083i \(-0.397987\pi\)
−0.664417 + 0.747362i \(0.731320\pi\)
\(270\) 14.6379 + 28.7330i 0.0542144 + 0.106418i
\(271\) −16.7690 + 9.68157i −0.0618781 + 0.0357253i −0.530620 0.847610i \(-0.678041\pi\)
0.468742 + 0.883335i \(0.344707\pi\)
\(272\) −31.0395 + 34.4554i −0.114116 + 0.126674i
\(273\) 0 0
\(274\) −14.2513 9.25617i −0.0520120 0.0337817i
\(275\) 84.5313 + 146.412i 0.307386 + 0.532409i
\(276\) −64.2416 + 610.477i −0.232759 + 2.21187i
\(277\) 112.104 + 64.7231i 0.404707 + 0.233658i 0.688513 0.725224i \(-0.258264\pi\)
−0.283806 + 0.958882i \(0.591597\pi\)
\(278\) 0.320621 6.11044i 0.00115331 0.0219800i
\(279\) 153.978i 0.551892i
\(280\) 0 0
\(281\) 83.3608 0.296658 0.148329 0.988938i \(-0.452611\pi\)
0.148329 + 0.988938i \(0.452611\pi\)
\(282\) −656.611 34.4531i −2.32841 0.122174i
\(283\) 14.4646 25.0535i 0.0511118 0.0885282i −0.839338 0.543611i \(-0.817057\pi\)
0.890449 + 0.455082i \(0.150390\pi\)
\(284\) 16.0138 152.176i 0.0563866 0.535832i
\(285\) 194.999 112.583i 0.684208 0.395028i
\(286\) 98.5959 151.803i 0.344741 0.530781i
\(287\) 0 0
\(288\) −211.706 + 56.6548i −0.735089 + 0.196718i
\(289\) 140.300 + 243.006i 0.485466 + 0.840851i
\(290\) −93.4982 + 47.6323i −0.322408 + 0.164249i
\(291\) 110.135 190.760i 0.378472 0.655533i
\(292\) −32.8695 + 45.2290i −0.112567 + 0.154894i
\(293\) 214.613i 0.732468i −0.930523 0.366234i \(-0.880647\pi\)
0.930523 0.366234i \(-0.119353\pi\)
\(294\) 0 0
\(295\) 19.5991i 0.0664376i
\(296\) −130.540 340.260i −0.441013 1.14953i
\(297\) −33.7429 + 58.4444i −0.113612 + 0.196783i
\(298\) −28.8014 56.5347i −0.0966490 0.189714i
\(299\) −221.389 383.457i −0.740432 1.28247i
\(300\) 138.930 + 312.148i 0.463101 + 1.04049i
\(301\) 0 0
\(302\) 276.264 425.350i 0.914780 1.40844i
\(303\) 108.370 62.5675i 0.357657 0.206493i
\(304\) −148.434 457.224i −0.488269 1.50403i
\(305\) 20.8606 36.1316i 0.0683953 0.118464i
\(306\) 2.08026 39.6458i 0.00679822 0.129561i
\(307\) 120.542 0.392644 0.196322 0.980539i \(-0.437100\pi\)
0.196322 + 0.980539i \(0.437100\pi\)
\(308\) 0 0
\(309\) 318.427i 1.03051i
\(310\) −4.43556 + 84.5335i −0.0143083 + 0.272689i
\(311\) −281.771 162.681i −0.906016 0.523089i −0.0268689 0.999639i \(-0.508554\pi\)
−0.879147 + 0.476550i \(0.841887\pi\)
\(312\) 230.272 284.252i 0.738050 0.911063i
\(313\) 228.378 + 395.562i 0.729642 + 1.26378i 0.957034 + 0.289974i \(0.0936467\pi\)
−0.227392 + 0.973803i \(0.573020\pi\)
\(314\) 53.7363 82.7353i 0.171135 0.263488i
\(315\) 0 0
\(316\) −187.066 + 83.2590i −0.591982 + 0.263478i
\(317\) 104.980 60.6102i 0.331167 0.191199i −0.325192 0.945648i \(-0.605429\pi\)
0.656359 + 0.754449i \(0.272096\pi\)
\(318\) −97.1658 190.728i −0.305553 0.599775i
\(319\) −190.180 109.801i −0.596177 0.344203i
\(320\) −117.858 + 25.0049i −0.368306 + 0.0781402i
\(321\) 194.128 0.604761
\(322\) 0 0
\(323\) 87.0822 0.269604
\(324\) −225.123 + 309.774i −0.694825 + 0.956091i
\(325\) −213.434 123.226i −0.656719 0.379157i
\(326\) −206.220 + 105.058i −0.632577 + 0.322264i
\(327\) 396.721 229.047i 1.21321 0.700449i
\(328\) −50.9098 + 321.039i −0.155213 + 0.978777i
\(329\) 0 0
\(330\) 64.3298 99.0455i 0.194939 0.300138i
\(331\) −60.5842 104.935i −0.183034 0.317024i 0.759878 0.650065i \(-0.225258\pi\)
−0.942912 + 0.333041i \(0.891925\pi\)
\(332\) −355.819 37.4434i −1.07174 0.112781i
\(333\) 270.191 + 155.995i 0.811384 + 0.468453i
\(334\) 64.6829 + 3.39398i 0.193661 + 0.0101616i
\(335\) 111.652i 0.333290i
\(336\) 0 0
\(337\) −464.021 −1.37692 −0.688459 0.725275i \(-0.741713\pi\)
−0.688459 + 0.725275i \(0.741713\pi\)
\(338\) 3.88424 74.0264i 0.0114918 0.219013i
\(339\) 110.985 192.232i 0.327390 0.567056i
\(340\) 2.28411 21.7055i 0.00671798 0.0638398i
\(341\) −153.420 + 88.5773i −0.449913 + 0.259758i
\(342\) 345.122 + 224.156i 1.00913 + 0.655427i
\(343\) 0 0
\(344\) 59.2412 373.577i 0.172213 1.08598i
\(345\) −144.448 250.190i −0.418688 0.725190i
\(346\) 188.151 + 369.325i 0.543789 + 1.06741i
\(347\) 185.593 321.457i 0.534851 0.926388i −0.464320 0.885667i \(-0.653701\pi\)
0.999171 0.0407208i \(-0.0129654\pi\)
\(348\) −359.015 260.909i −1.03165 0.749738i
\(349\) 207.871i 0.595619i 0.954625 + 0.297809i \(0.0962560\pi\)
−0.954625 + 0.297809i \(0.903744\pi\)
\(350\) 0 0
\(351\) 98.3779i 0.280279i
\(352\) −178.236 178.348i −0.506351 0.506670i
\(353\) −307.007 + 531.751i −0.869708 + 1.50638i −0.00741211 + 0.999973i \(0.502359\pi\)
−0.862296 + 0.506405i \(0.830974\pi\)
\(354\) −73.8613 + 37.6283i −0.208648 + 0.106295i
\(355\) 36.0071 + 62.3661i 0.101428 + 0.175679i
\(356\) −171.200 384.652i −0.480899 1.08048i
\(357\) 0 0
\(358\) 292.126 + 189.735i 0.815995 + 0.529986i
\(359\) −93.5930 + 54.0359i −0.260705 + 0.150518i −0.624656 0.780900i \(-0.714761\pi\)
0.363951 + 0.931418i \(0.381427\pi\)
\(360\) 64.9239 80.1434i 0.180344 0.222620i
\(361\) −270.841 + 469.110i −0.750252 + 1.29947i
\(362\) 407.926 + 21.4043i 1.12687 + 0.0591280i
\(363\) −234.539 −0.646113
\(364\) 0 0
\(365\) 26.3135i 0.0720917i
\(366\) 176.216 + 9.24623i 0.481464 + 0.0252629i
\(367\) −393.881 227.407i −1.07325 0.619639i −0.144179 0.989552i \(-0.546054\pi\)
−0.929067 + 0.369913i \(0.879388\pi\)
\(368\) −586.634 + 190.445i −1.59411 + 0.517514i
\(369\) −139.134 240.987i −0.377056 0.653081i
\(370\) 143.840 + 93.4240i 0.388758 + 0.252497i
\(371\) 0 0
\(372\) −327.089 + 145.580i −0.879272 + 0.391344i
\(373\) 235.344 135.876i 0.630949 0.364279i −0.150171 0.988660i \(-0.547982\pi\)
0.781119 + 0.624382i \(0.214649\pi\)
\(374\) 40.6990 20.7339i 0.108821 0.0554383i
\(375\) −301.515 174.080i −0.804039 0.464212i
\(376\) −236.638 616.812i −0.629357 1.64046i
\(377\) 320.126 0.849140
\(378\) 0 0
\(379\) 268.351 0.708051 0.354026 0.935236i \(-0.384813\pi\)
0.354026 + 0.935236i \(0.384813\pi\)
\(380\) 183.014 + 133.003i 0.481616 + 0.350008i
\(381\) 123.069 + 71.0541i 0.323017 + 0.186494i
\(382\) 271.008 + 531.967i 0.709446 + 1.39258i
\(383\) −283.718 + 163.805i −0.740779 + 0.427689i −0.822352 0.568979i \(-0.807339\pi\)
0.0815738 + 0.996667i \(0.474005\pi\)
\(384\) −320.509 396.153i −0.834659 1.03165i
\(385\) 0 0
\(386\) −554.778 360.327i −1.43725 0.933489i
\(387\) 161.903 + 280.424i 0.418354 + 0.724610i
\(388\) 220.105 + 23.1620i 0.567281 + 0.0596960i
\(389\) −109.380 63.1506i −0.281183 0.162341i 0.352776 0.935708i \(-0.385238\pi\)
−0.633959 + 0.773367i \(0.718571\pi\)
\(390\) −9.02130 + 171.929i −0.0231315 + 0.440844i
\(391\) 111.729i 0.285753i
\(392\) 0 0
\(393\) 482.869 1.22867
\(394\) 653.718 + 34.3013i 1.65918 + 0.0870590i
\(395\) 48.1826 83.4548i 0.121981 0.211278i
\(396\) 214.668 + 22.5899i 0.542090 + 0.0570451i
\(397\) 110.110 63.5720i 0.277355 0.160131i −0.354870 0.934916i \(-0.615475\pi\)
0.632225 + 0.774784i \(0.282142\pi\)
\(398\) −13.8741 + 21.3614i −0.0348597 + 0.0536718i
\(399\) 0 0
\(400\) −229.775 + 255.062i −0.574439 + 0.637655i
\(401\) −30.0751 52.0916i −0.0750003 0.129904i 0.826086 0.563544i \(-0.190562\pi\)
−0.901086 + 0.433640i \(0.857229\pi\)
\(402\) 420.773 214.361i 1.04670 0.533236i
\(403\) 129.124 223.650i 0.320408 0.554962i
\(404\) 101.709 + 73.9158i 0.251756 + 0.182960i
\(405\) 180.221i 0.444991i
\(406\) 0 0
\(407\) 358.950i 0.881941i
\(408\) 86.1849 33.0646i 0.211237 0.0810406i
\(409\) −34.8873 + 60.4267i −0.0852991 + 0.147742i −0.905519 0.424306i \(-0.860518\pi\)
0.820220 + 0.572049i \(0.193851\pi\)
\(410\) −69.4421 136.309i −0.169371 0.332461i
\(411\) 16.9128 + 29.2939i 0.0411504 + 0.0712746i
\(412\) 292.301 130.096i 0.709467 0.315768i
\(413\) 0 0
\(414\) 287.599 442.803i 0.694685 1.06957i
\(415\) 145.824 84.1918i 0.351384 0.202872i
\(416\) 355.008 + 95.2442i 0.853385 + 0.228952i
\(417\) −6.08982 + 10.5479i −0.0146039 + 0.0252947i
\(418\) −24.8094 + 472.821i −0.0593526 + 1.13115i
\(419\) −714.794 −1.70595 −0.852976 0.521950i \(-0.825205\pi\)
−0.852976 + 0.521950i \(0.825205\pi\)
\(420\) 0 0
\(421\) 303.440i 0.720759i −0.932806 0.360380i \(-0.882647\pi\)
0.932806 0.360380i \(-0.117353\pi\)
\(422\) 12.6234 240.578i 0.0299132 0.570090i
\(423\) 489.793 + 282.782i 1.15790 + 0.668515i
\(424\) 135.381 167.117i 0.319295 0.394144i
\(425\) −31.0945 53.8572i −0.0731635 0.126723i
\(426\) −165.903 + 255.433i −0.389444 + 0.599609i
\(427\) 0 0
\(428\) 79.3129 + 178.200i 0.185310 + 0.416356i
\(429\) −312.035 + 180.154i −0.727355 + 0.419939i
\(430\) 80.8064 + 158.616i 0.187922 + 0.368875i
\(431\) 373.685 + 215.747i 0.867019 + 0.500574i 0.866357 0.499426i \(-0.166456\pi\)
0.000662591 1.00000i \(0.499789\pi\)
\(432\) −134.035 28.5253i −0.310265 0.0660308i
\(433\) −194.875 −0.450057 −0.225029 0.974352i \(-0.572248\pi\)
−0.225029 + 0.974352i \(0.572248\pi\)
\(434\) 0 0
\(435\) 208.869 0.480159
\(436\) 372.337 + 270.591i 0.853985 + 0.620621i
\(437\) 1003.00 + 579.085i 2.29521 + 1.32514i
\(438\) 99.1652 50.5193i 0.226404 0.115341i
\(439\) 264.977 152.985i 0.603593 0.348485i −0.166861 0.985980i \(-0.553363\pi\)
0.770454 + 0.637496i \(0.220030\pi\)
\(440\) 117.201 + 18.5856i 0.266367 + 0.0422400i
\(441\) 0 0
\(442\) −36.2681 + 55.8402i −0.0820545 + 0.126335i
\(443\) −125.099 216.677i −0.282390 0.489113i 0.689583 0.724206i \(-0.257794\pi\)
−0.971973 + 0.235093i \(0.924460\pi\)
\(444\) −75.9187 + 721.443i −0.170988 + 1.62487i
\(445\) 171.603 + 99.0748i 0.385624 + 0.222640i
\(446\) 744.891 + 39.0852i 1.67016 + 0.0876350i
\(447\) 126.295i 0.282539i
\(448\) 0 0
\(449\) −688.681 −1.53381 −0.766905 0.641761i \(-0.778204\pi\)
−0.766905 + 0.641761i \(0.778204\pi\)
\(450\) 15.3995 293.485i 0.0342210 0.652189i
\(451\) 160.076 277.260i 0.354936 0.614768i
\(452\) 221.803 + 23.3408i 0.490715 + 0.0516388i
\(453\) −874.317 + 504.787i −1.93006 + 1.11432i
\(454\) −123.155 79.9887i −0.271266 0.176187i
\(455\) 0 0
\(456\) −149.866 + 945.061i −0.328654 + 2.07250i
\(457\) −402.259 696.733i −0.880217 1.52458i −0.851100 0.525004i \(-0.824064\pi\)
−0.0291166 0.999576i \(-0.509269\pi\)
\(458\) −385.347 756.404i −0.841369 1.65154i
\(459\) 12.4122 21.4985i 0.0270418 0.0468378i
\(460\) 170.647 234.813i 0.370972 0.510463i
\(461\) 693.657i 1.50468i −0.658776 0.752339i \(-0.728926\pi\)
0.658776 0.752339i \(-0.271074\pi\)
\(462\) 0 0
\(463\) 321.194i 0.693724i −0.937916 0.346862i \(-0.887247\pi\)
0.937916 0.346862i \(-0.112753\pi\)
\(464\) 92.8225 436.154i 0.200048 0.939988i
\(465\) 84.2484 145.922i 0.181179 0.313812i
\(466\) 148.650 75.7289i 0.318990 0.162508i
\(467\) 375.937 + 651.142i 0.805005 + 1.39431i 0.916288 + 0.400521i \(0.131171\pi\)
−0.111283 + 0.993789i \(0.535496\pi\)
\(468\) −287.474 + 127.948i −0.614260 + 0.273393i
\(469\) 0 0
\(470\) 260.749 + 169.356i 0.554785 + 0.360332i
\(471\) −170.064 + 98.1867i −0.361071 + 0.208464i
\(472\) −64.7176 52.4276i −0.137114 0.111075i
\(473\) −186.273 + 322.634i −0.393811 + 0.682101i
\(474\) 407.014 + 21.3565i 0.858680 + 0.0450558i
\(475\) 644.642 1.35714
\(476\) 0 0
\(477\) 184.118i 0.385992i
\(478\) 224.813 + 11.7962i 0.470320 + 0.0246782i
\(479\) 625.392 + 361.070i 1.30562 + 0.753800i 0.981362 0.192169i \(-0.0615523\pi\)
0.324257 + 0.945969i \(0.394886\pi\)
\(480\) 231.629 + 62.1430i 0.482559 + 0.129465i
\(481\) −261.631 453.158i −0.543932 0.942117i
\(482\) −470.361 305.498i −0.975853 0.633814i
\(483\) 0 0
\(484\) −95.8230 215.295i −0.197981 0.444825i
\(485\) −90.2052 + 52.0800i −0.185990 + 0.107381i
\(486\) 541.816 276.026i 1.11485 0.567954i
\(487\) −41.4211 23.9145i −0.0850536 0.0491057i 0.456870 0.889533i \(-0.348970\pi\)
−0.541924 + 0.840428i \(0.682304\pi\)
\(488\) 63.5070 + 165.535i 0.130137 + 0.339211i
\(489\) 460.682 0.942090
\(490\) 0 0
\(491\) 44.4724 0.0905752 0.0452876 0.998974i \(-0.485580\pi\)
0.0452876 + 0.998974i \(0.485580\pi\)
\(492\) 380.373 523.400i 0.773117 1.06382i
\(493\) 69.9571 + 40.3898i 0.141901 + 0.0819265i
\(494\) −313.308 614.998i −0.634227 1.24494i
\(495\) −87.9769 + 50.7935i −0.177731 + 0.102613i
\(496\) −267.271 240.774i −0.538852 0.485431i
\(497\) 0 0
\(498\) 597.254 + 387.915i 1.19931 + 0.778945i
\(499\) 250.786 + 434.374i 0.502577 + 0.870489i 0.999996 + 0.00297862i \(0.000948124\pi\)
−0.497418 + 0.867511i \(0.665719\pi\)
\(500\) 36.6099 347.897i 0.0732197 0.695795i
\(501\) −111.656 64.4647i −0.222867 0.128672i
\(502\) 3.45372 65.8214i 0.00687991 0.131118i
\(503\) 462.733i 0.919946i −0.887933 0.459973i \(-0.847859\pi\)
0.887933 0.459973i \(-0.152141\pi\)
\(504\) 0 0
\(505\) −59.1729 −0.117174
\(506\) 606.645 + 31.8313i 1.19890 + 0.0629076i
\(507\) −73.7767 + 127.785i −0.145516 + 0.252041i
\(508\) −14.9431 + 142.001i −0.0294155 + 0.279530i
\(509\) −408.751 + 235.992i −0.803046 + 0.463639i −0.844535 0.535500i \(-0.820123\pi\)
0.0414889 + 0.999139i \(0.486790\pi\)
\(510\) −23.6635 + 36.4335i −0.0463989 + 0.0714382i
\(511\) 0 0
\(512\) 232.702 456.063i 0.454496 0.890749i
\(513\) 128.663 + 222.851i 0.250805 + 0.434407i
\(514\) −399.573 + 203.561i −0.777380 + 0.396033i
\(515\) −75.2878 + 130.402i −0.146190 + 0.253208i
\(516\) −442.621 + 609.055i −0.857794 + 1.18034i
\(517\) 650.693i 1.25859i
\(518\) 0 0
\(519\) 825.047i 1.58969i
\(520\) −161.508 + 61.9621i −0.310593 + 0.119158i
\(521\) −45.3709 + 78.5848i −0.0870843 + 0.150834i −0.906277 0.422683i \(-0.861088\pi\)
0.819193 + 0.573518i \(0.194422\pi\)
\(522\) 173.286 + 340.146i 0.331966 + 0.651621i
\(523\) −180.256 312.213i −0.344658 0.596965i 0.640634 0.767847i \(-0.278672\pi\)
−0.985292 + 0.170882i \(0.945338\pi\)
\(524\) 197.280 + 443.249i 0.376489 + 0.845896i
\(525\) 0 0
\(526\) −185.152 + 285.070i −0.352001 + 0.541959i
\(527\) 56.4351 32.5828i 0.107087 0.0618270i
\(528\) 154.973 + 477.368i 0.293510 + 0.904107i
\(529\) 478.485 828.760i 0.904509 1.56665i
\(530\) −5.30380 + 101.081i −0.0100072 + 0.190718i
\(531\) 71.3014 0.134278
\(532\) 0 0
\(533\) 466.705i 0.875618i
\(534\) −43.9139 + 836.917i −0.0822357 + 1.56726i
\(535\) −79.4994 45.8990i −0.148597 0.0857925i
\(536\) 368.683 + 298.669i 0.687841 + 0.557218i
\(537\) −346.683 600.472i −0.645592 1.11820i
\(538\) −118.226 + 182.028i −0.219752 + 0.338341i
\(539\) 0 0
\(540\) 58.9210 26.2244i 0.109113 0.0485637i
\(541\) −485.969 + 280.574i −0.898278 + 0.518621i −0.876641 0.481145i \(-0.840221\pi\)
−0.0216371 + 0.999766i \(0.506888\pi\)
\(542\) 17.5792 + 34.5065i 0.0324339 + 0.0636651i
\(543\) −704.166 406.550i −1.29681 0.748712i
\(544\) 65.5632 + 65.6046i 0.120521 + 0.120597i
\(545\) −216.620 −0.397468
\(546\) 0 0
\(547\) 1043.62 1.90790 0.953952 0.299960i \(-0.0969733\pi\)
0.953952 + 0.299960i \(0.0969733\pi\)
\(548\) −19.9804 + 27.4934i −0.0364606 + 0.0501704i
\(549\) −131.447 75.8907i −0.239429 0.138234i
\(550\) 301.281 153.487i 0.547784 0.279067i
\(551\) −725.165 + 418.674i −1.31609 + 0.759845i
\(552\) 1212.54 + 192.283i 2.19664 + 0.348339i
\(553\) 0 0
\(554\) 141.017 217.117i 0.254543 0.391907i
\(555\) −170.704 295.667i −0.307574 0.532734i
\(556\) −12.1705 1.28072i −0.0218894 0.00230346i
\(557\) 42.1273 + 24.3222i 0.0756324 + 0.0436664i 0.537339 0.843366i \(-0.319429\pi\)
−0.461707 + 0.887033i \(0.652763\pi\)
\(558\) 307.533 + 16.1366i 0.551134 + 0.0289186i
\(559\) 543.081i 0.971522i
\(560\) 0 0
\(561\) −90.9189 −0.162066
\(562\) 8.73604 166.493i 0.0155446 0.296250i
\(563\) 363.015 628.761i 0.644787 1.11680i −0.339563 0.940583i \(-0.610279\pi\)
0.984351 0.176221i \(-0.0563874\pi\)
\(564\) −137.623 + 1307.81i −0.244012 + 2.31881i
\(565\) −90.9012 + 52.4818i −0.160887 + 0.0928882i
\(566\) −48.5223 31.5151i −0.0857284 0.0556804i
\(567\) 0 0
\(568\) −302.256 47.9313i −0.532141 0.0843861i
\(569\) 240.696 + 416.898i 0.423016 + 0.732685i 0.996233 0.0867185i \(-0.0276381\pi\)
−0.573217 + 0.819404i \(0.694305\pi\)
\(570\) −204.421 401.261i −0.358633 0.703967i
\(571\) −55.0633 + 95.3724i −0.0964331 + 0.167027i −0.910206 0.414156i \(-0.864077\pi\)
0.813773 + 0.581183i \(0.197410\pi\)
\(572\) −292.857 212.829i −0.511988 0.372080i
\(573\) 1188.38i 2.07396i
\(574\) 0 0
\(575\) 827.097i 1.43843i
\(576\) 90.9676 + 428.767i 0.157930 + 0.744387i
\(577\) −101.168 + 175.228i −0.175335 + 0.303688i −0.940277 0.340410i \(-0.889434\pi\)
0.764942 + 0.644099i \(0.222767\pi\)
\(578\) 500.047 254.747i 0.865134 0.440739i
\(579\) 658.386 + 1140.36i 1.13711 + 1.96953i
\(580\) 85.3353 + 191.731i 0.147130 + 0.330571i
\(581\) 0 0
\(582\) −369.454 239.959i −0.634800 0.412301i
\(583\) −183.452 + 105.916i −0.314669 + 0.181674i
\(584\) 86.8890 + 70.3886i 0.148783 + 0.120528i
\(585\) 74.0445 128.249i 0.126572 0.219229i
\(586\) −428.637 22.4910i −0.731462 0.0383806i
\(587\) 568.689 0.968805 0.484403 0.874845i \(-0.339037\pi\)
0.484403 + 0.874845i \(0.339037\pi\)
\(588\) 0 0
\(589\) 675.497i 1.14685i
\(590\) 39.1443 + 2.05394i 0.0663463 + 0.00348126i
\(591\) −1128.45 651.513i −1.90940 1.10239i
\(592\) −693.266 + 225.062i −1.17106 + 0.380173i
\(593\) −342.686 593.550i −0.577886 1.00093i −0.995721 0.0924054i \(-0.970544\pi\)
0.417835 0.908523i \(-0.362789\pi\)
\(594\) 113.192 + 73.5179i 0.190559 + 0.123768i
\(595\) 0 0
\(596\) −115.932 + 51.5989i −0.194518 + 0.0865754i
\(597\) 43.9088 25.3507i 0.0735491 0.0424636i
\(598\) −789.062 + 401.985i −1.31950 + 0.672215i
\(599\) 318.077 + 183.642i 0.531013 + 0.306580i 0.741429 0.671032i \(-0.234149\pi\)
−0.210416 + 0.977612i \(0.567482\pi\)
\(600\) 637.999 244.766i 1.06333 0.407944i
\(601\) −412.344 −0.686097 −0.343049 0.939318i \(-0.611460\pi\)
−0.343049 + 0.939318i \(0.611460\pi\)
\(602\) 0 0
\(603\) −406.190 −0.673615
\(604\) −820.579 596.344i −1.35858 0.987325i
\(605\) 96.0484 + 55.4535i 0.158758 + 0.0916588i
\(606\) −113.606 222.999i −0.187469 0.367986i
\(607\) 1010.46 583.389i 1.66468 0.961102i 0.694241 0.719743i \(-0.255740\pi\)
0.970436 0.241359i \(-0.0775930\pi\)
\(608\) −928.748 + 248.543i −1.52755 + 0.408788i
\(609\) 0 0
\(610\) −69.9777 45.4503i −0.114718 0.0745087i
\(611\) −474.276 821.470i −0.776229 1.34447i
\(612\) −78.9647 8.30959i −0.129027 0.0135778i
\(613\) −373.900 215.871i −0.609951 0.352155i 0.162995 0.986627i \(-0.447885\pi\)
−0.772946 + 0.634471i \(0.781218\pi\)
\(614\) 12.6325 240.752i 0.0205741 0.392105i
\(615\) 304.506i 0.495131i
\(616\) 0 0
\(617\) −333.751 −0.540926 −0.270463 0.962730i \(-0.587177\pi\)
−0.270463 + 0.962730i \(0.587177\pi\)
\(618\) −635.980 33.3705i −1.02909 0.0539976i
\(619\) −488.158 + 845.514i −0.788624 + 1.36594i 0.138187 + 0.990406i \(0.455873\pi\)
−0.926810 + 0.375530i \(0.877461\pi\)
\(620\) 168.370 + 17.7179i 0.271564 + 0.0285772i
\(621\) 285.925 165.079i 0.460426 0.265827i
\(622\) −354.443 + 545.719i −0.569844 + 0.877362i
\(623\) 0 0
\(624\) −543.590 489.699i −0.871138 0.784775i
\(625\) −185.884 321.961i −0.297414 0.515137i
\(626\) 813.971 414.674i 1.30027 0.662419i
\(627\) 471.226 816.187i 0.751556 1.30173i
\(628\) −159.612 115.996i −0.254159 0.184706i
\(629\) 132.038i 0.209918i
\(630\) 0 0
\(631\) 639.885i 1.01408i −0.861922 0.507040i \(-0.830739\pi\)
0.861922 0.507040i \(-0.169261\pi\)
\(632\) 146.685 + 382.344i 0.232097 + 0.604975i
\(633\) −239.767 + 415.288i −0.378778 + 0.656063i
\(634\) −110.052 216.023i −0.173584 0.340731i
\(635\) −33.5995 58.1961i −0.0529127 0.0916474i
\(636\) −391.116 + 174.077i −0.614962 + 0.273706i
\(637\) 0 0
\(638\) −239.230 + 368.332i −0.374969 + 0.577322i
\(639\) 226.888 130.994i 0.355067 0.204998i
\(640\) 37.5898 + 238.013i 0.0587340 + 0.371895i
\(641\) −10.4295 + 18.0645i −0.0162707 + 0.0281817i −0.874046 0.485843i \(-0.838513\pi\)
0.857775 + 0.514025i \(0.171846\pi\)
\(642\) 20.3442 387.723i 0.0316889 0.603931i
\(643\) 69.1348 0.107519 0.0537596 0.998554i \(-0.482880\pi\)
0.0537596 + 0.998554i \(0.482880\pi\)
\(644\) 0 0
\(645\) 354.338i 0.549362i
\(646\) 9.12604 173.925i 0.0141270 0.269234i
\(647\) −310.868 179.480i −0.480476 0.277403i 0.240139 0.970739i \(-0.422807\pi\)
−0.720615 + 0.693336i \(0.756140\pi\)
\(648\) 595.104 + 482.092i 0.918370 + 0.743969i
\(649\) 41.0169 + 71.0433i 0.0632001 + 0.109466i
\(650\) −268.481 + 413.367i −0.413048 + 0.635950i
\(651\) 0 0
\(652\) 188.216 + 422.883i 0.288675 + 0.648594i
\(653\) 32.1227 18.5460i 0.0491925 0.0284013i −0.475202 0.879877i \(-0.657625\pi\)
0.524395 + 0.851475i \(0.324292\pi\)
\(654\) −415.889 816.355i −0.635916 1.24825i
\(655\) −197.744 114.168i −0.301900 0.174302i
\(656\) 635.860 + 135.324i 0.969299 + 0.206287i
\(657\) −95.7284 −0.145705
\(658\) 0 0
\(659\) 197.302 0.299396 0.149698 0.988732i \(-0.452170\pi\)
0.149698 + 0.988732i \(0.452170\pi\)
\(660\) −191.077 138.863i −0.289511 0.210398i
\(661\) −938.626 541.916i −1.42001 0.819843i −0.423710 0.905798i \(-0.639272\pi\)
−0.996299 + 0.0859554i \(0.972606\pi\)
\(662\) −215.931 + 110.005i −0.326179 + 0.166171i
\(663\) 114.781 66.2688i 0.173124 0.0999530i
\(664\) −112.073 + 706.735i −0.168785 + 1.06436i
\(665\) 0 0
\(666\) 339.876 523.291i 0.510325 0.785723i
\(667\) 537.173 + 930.411i 0.805357 + 1.39492i
\(668\) 13.5573 128.832i 0.0202953 0.192863i
\(669\) −1285.84 742.378i −1.92203 1.10968i
\(670\) −222.997 11.7009i −0.332832 0.0174640i
\(671\) 174.628i 0.260250i
\(672\) 0 0
\(673\) −286.066 −0.425061 −0.212530 0.977154i \(-0.568170\pi\)
−0.212530 + 0.977154i \(0.568170\pi\)
\(674\) −48.6285 + 926.768i −0.0721491 + 1.37503i
\(675\) 91.8834 159.147i 0.136124 0.235773i
\(676\) −147.442 15.5156i −0.218110 0.0229521i
\(677\) −433.324 + 250.180i −0.640065 + 0.369542i −0.784640 0.619952i \(-0.787152\pi\)
0.144575 + 0.989494i \(0.453819\pi\)
\(678\) −372.305 241.811i −0.549122 0.356653i
\(679\) 0 0
\(680\) −43.1121 6.83664i −0.0634001 0.0100539i
\(681\) 146.155 + 253.148i 0.214618 + 0.371729i
\(682\) 160.833 + 315.702i 0.235826 + 0.462906i
\(683\) −473.225 + 819.650i −0.692862 + 1.20007i 0.278034 + 0.960571i \(0.410317\pi\)
−0.970896 + 0.239501i \(0.923016\pi\)
\(684\) 483.864 665.805i 0.707404 0.973399i
\(685\) 15.9952i 0.0233507i
\(686\) 0 0
\(687\) 1689.76i 2.45962i
\(688\) −739.919 157.470i −1.07546 0.228880i
\(689\) 154.400 267.428i 0.224092 0.388140i
\(690\) −514.831 + 262.279i −0.746132 + 0.380114i
\(691\) 151.632 + 262.634i 0.219439 + 0.380079i 0.954636 0.297774i \(-0.0962441\pi\)
−0.735198 + 0.677853i \(0.762911\pi\)
\(692\) 757.352 337.080i 1.09444 0.487111i
\(693\) 0 0
\(694\) −622.580 404.364i −0.897090 0.582658i
\(695\) 4.98781 2.87971i 0.00717670 0.00414347i
\(696\) −558.725 + 689.700i −0.802765 + 0.990949i
\(697\) −58.8834 + 101.989i −0.0844812 + 0.146326i
\(698\) 415.171 + 21.7844i 0.594801 + 0.0312098i
\(699\) −332.074 −0.475069
\(700\) 0 0
\(701\) 390.864i 0.557580i 0.960352 + 0.278790i \(0.0899333\pi\)
−0.960352 + 0.278790i \(0.910067\pi\)
\(702\) −196.486 10.3098i −0.279894 0.0146863i
\(703\) 1185.32 + 684.345i 1.68609 + 0.973464i
\(704\) −374.885 + 337.291i −0.532507 + 0.479106i
\(705\) −309.446 535.976i −0.438930 0.760250i
\(706\) 1029.87 + 668.897i 1.45874 + 0.947446i
\(707\) 0 0
\(708\) 67.4128 + 151.463i 0.0952158 + 0.213931i
\(709\) 832.393 480.582i 1.17404 0.677831i 0.219410 0.975633i \(-0.429587\pi\)
0.954628 + 0.297801i \(0.0962533\pi\)
\(710\) 128.334 65.3794i 0.180753 0.0920837i
\(711\) −303.608 175.288i −0.427016 0.246538i
\(712\) −786.189 + 301.619i −1.10420 + 0.423622i
\(713\) 866.685 1.21555
\(714\) 0 0
\(715\) 170.379 0.238293
\(716\) 409.563 563.566i 0.572016 0.787103i
\(717\) −388.074 224.055i −0.541247 0.312489i
\(718\) 98.1151 + 192.592i 0.136650 + 0.268234i
\(719\) 454.773 262.563i 0.632507 0.365178i −0.149215 0.988805i \(-0.547675\pi\)
0.781722 + 0.623627i \(0.214341\pi\)
\(720\) −153.263 138.068i −0.212865 0.191762i
\(721\) 0 0
\(722\) 908.548 + 590.100i 1.25838 + 0.817312i
\(723\) 558.204 + 966.838i 0.772067 + 1.33726i
\(724\) 85.4997 812.489i 0.118093 1.12222i
\(725\) 517.870 + 298.992i 0.714304 + 0.412403i
\(726\) −24.5792 + 468.434i −0.0338557 + 0.645226i
\(727\) 108.633i 0.149426i −0.997205 0.0747131i \(-0.976196\pi\)
0.997205 0.0747131i \(-0.0238041\pi\)
\(728\) 0 0
\(729\) −348.775 −0.478429
\(730\) −52.5547 2.75760i −0.0719927 0.00377753i
\(731\) 68.5197 118.680i 0.0937341 0.162352i
\(732\) 36.9341 350.979i 0.0504564 0.479479i
\(733\) −34.8609 + 20.1270i −0.0475593 + 0.0274584i −0.523591 0.851970i \(-0.675408\pi\)
0.476032 + 0.879428i \(0.342075\pi\)
\(734\) −495.468 + 762.849i −0.675025 + 1.03930i
\(735\) 0 0
\(736\) 318.889 + 1191.61i 0.433273 + 1.61904i
\(737\) −233.665 404.719i −0.317049 0.549144i
\(738\) −495.892 + 252.630i −0.671941 + 0.342318i
\(739\) −498.602 + 863.603i −0.674698 + 1.16861i 0.301859 + 0.953352i \(0.402393\pi\)
−0.976557 + 0.215258i \(0.930941\pi\)
\(740\) 201.665 277.495i 0.272521 0.374993i
\(741\) 1373.87i 1.85407i
\(742\) 0 0
\(743\) 476.575i 0.641420i 0.947177 + 0.320710i \(0.103922\pi\)
−0.947177 + 0.320710i \(0.896078\pi\)
\(744\) 256.482 + 668.536i 0.344734 + 0.898570i
\(745\) 29.8607 51.7203i 0.0400815 0.0694232i
\(746\) −246.715 484.281i −0.330717 0.649170i
\(747\) −306.289 530.509i −0.410026 0.710186i
\(748\) −37.1457 83.4590i −0.0496600 0.111576i
\(749\) 0 0
\(750\) −379.279 + 583.958i −0.505706 + 0.778611i
\(751\) −457.691 + 264.248i −0.609442 + 0.351862i −0.772747 0.634714i \(-0.781118\pi\)
0.163305 + 0.986576i \(0.447785\pi\)
\(752\) −1256.73 + 407.985i −1.67118 + 0.542534i
\(753\) −65.5993 + 113.621i −0.0871173 + 0.150892i
\(754\) 33.5485 639.372i 0.0444940 0.847973i
\(755\) 477.400 0.632318
\(756\) 0 0
\(757\) 455.964i 0.602331i −0.953572 0.301165i \(-0.902624\pi\)
0.953572 0.301165i \(-0.0973756\pi\)
\(758\) 28.1227 535.965i 0.0371011 0.707078i
\(759\) −1047.19 604.598i −1.37970 0.796572i
\(760\) 284.820 351.587i 0.374763 0.462615i
\(761\) 238.325 + 412.791i 0.313174 + 0.542433i 0.979048 0.203632i \(-0.0652745\pi\)
−0.665874 + 0.746064i \(0.731941\pi\)
\(762\) 154.810 238.354i 0.203163 0.312801i
\(763\) 0 0
\(764\) 1090.87 485.523i 1.42784 0.635502i
\(765\) 32.3619 18.6842i 0.0423032 0.0244238i
\(766\) 297.426 + 583.823i 0.388285 + 0.762171i
\(767\) −103.564 59.7927i −0.135025 0.0779565i
\(768\) −824.807 + 598.622i −1.07397 + 0.779455i
\(769\) 568.246 0.738941 0.369471 0.929242i \(-0.379539\pi\)
0.369471 + 0.929242i \(0.379539\pi\)
\(770\) 0 0
\(771\) 892.621 1.15774
\(772\) −777.803 + 1070.27i −1.00752 + 1.38636i
\(773\) 1036.66 + 598.515i 1.34108 + 0.774275i 0.986967 0.160925i \(-0.0514478\pi\)
0.354118 + 0.935201i \(0.384781\pi\)
\(774\) 577.045 293.973i 0.745536 0.379810i
\(775\) 417.771 241.200i 0.539059 0.311226i
\(776\) 69.3270 437.178i 0.0893389 0.563373i
\(777\) 0