Properties

Label 392.3.k.l.67.1
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 67.1
Root \(0.121721 + 0.507075i\) of defining polynomial
Character \(\chi\) \(=\) 392.67
Dual form 392.3.k.l.275.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.78207 - 0.907869i) q^{2} +(-1.99052 + 3.44767i) q^{3} +(2.35155 + 3.23577i) q^{4} +(-1.63031 + 0.941260i) q^{5} +(6.67727 - 4.33687i) q^{6} +(-1.25297 - 7.90127i) q^{8} +(-3.42430 - 5.93106i) q^{9} +O(q^{10})\) \(q+(-1.78207 - 0.907869i) q^{2} +(-1.99052 + 3.44767i) q^{3} +(2.35155 + 3.23577i) 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} +(3.75987 - 0.197284i) q^{10} +(3.93973 - 6.82381i) q^{11} +(-15.8367 + 1.66652i) q^{12} -11.4863i q^{13} -7.49437i q^{15} +(-4.94043 + 15.2182i) q^{16} +(-1.44921 + 2.51011i) q^{17} +(0.717719 + 13.6784i) 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} +(29.7351 + 11.4078i) q^{24} +(-10.7281 + 18.5815i) q^{25} +(-10.4281 + 20.4695i) q^{26} -8.56478 q^{27} +27.8701i q^{29} +(-6.80390 + 13.3555i) q^{30} +(19.4709 + 11.2416i) q^{31} +(22.6203 - 22.6346i) 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} +(3.14862 + 60.0068i) q^{38} +(39.6011 + 22.8637i) q^{39} +(9.47988 + 11.7021i) q^{40} +40.6313 q^{41} -47.2806 q^{43} +(31.3448 - 3.29846i) q^{44} +(11.1653 + 6.44632i) q^{45} +(-76.9907 + 4.03978i) 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} +(37.1672 - 27.0107i) q^{52} +(23.2823 + 13.4420i) q^{53} +(15.2630 + 7.77569i) q^{54} +14.8332i q^{55} +119.609 q^{57} +(25.3024 - 49.6665i) q^{58} +(-5.20555 + 9.01627i) q^{59} +(24.2501 - 17.6234i) 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} +(-3.28734 - 62.6505i) q^{66} +(29.6549 - 51.3639i) q^{67} +(-11.5300 + 1.21333i) q^{68} +153.462i q^{69} -38.2541i q^{71} +(-42.5724 + 34.4878i) q^{72} +(6.98890 - 12.1051i) q^{73} +(-90.9852 + 4.77409i) 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} +(-6.26980 - 29.4605i) q^{80} +(47.8670 - 82.9081i) q^{81} +(-72.4078 - 36.8879i) q^{82} +89.4458 q^{83} -5.45635i q^{85} +(84.2573 + 42.9246i) q^{86} +(-96.0871 - 55.4759i) q^{87} +(-58.8531 - 22.5788i) 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} +(-164.935 + 8.65431i) q^{94} +(48.9821 + 28.2798i) q^{95} +(33.0105 + 123.042i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.78207 0.907869i −0.891035 0.453934i
\(3\) −1.99052 + 3.44767i −0.663505 + 1.14922i 0.316183 + 0.948698i \(0.397599\pi\)
−0.979688 + 0.200526i \(0.935735\pi\)
\(4\) 2.35155 + 3.23577i 0.587887 + 0.808943i
\(5\) −1.63031 + 0.941260i −0.326062 + 0.188252i −0.654091 0.756416i \(-0.726949\pi\)
0.328029 + 0.944668i \(0.393616\pi\)
\(6\) 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
\(10\) 3.75987 0.197284i 0.375987 0.0197284i
\(11\) 3.93973 6.82381i 0.358157 0.620346i −0.629496 0.777004i \(-0.716739\pi\)
0.987653 + 0.156658i \(0.0500719\pi\)
\(12\) −15.8367 + 1.66652i −1.31972 + 0.138877i
\(13\) 11.4863i 0.883564i −0.897122 0.441782i \(-0.854346\pi\)
0.897122 0.441782i \(-0.145654\pi\)
\(14\) 0 0
\(15\) 7.49437i 0.499625i
\(16\) −4.94043 + 15.2182i −0.308777 + 0.951134i
\(17\) −1.44921 + 2.51011i −0.0852478 + 0.147654i −0.905497 0.424353i \(-0.860502\pi\)
0.820249 + 0.572007i \(0.193835\pi\)
\(18\) 0.717719 + 13.6784i 0.0398733 + 0.759910i
\(19\) −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 0.452904 0.891559i \(-0.350388\pi\)
0.998565 + 0.0535530i \(0.0170546\pi\)
\(24\) 29.7351 + 11.4078i 1.23896 + 0.475323i
\(25\) −10.7281 + 18.5815i −0.429122 + 0.743262i
\(26\) −10.4281 + 20.4695i −0.401080 + 0.787287i
\(27\) −8.56478 −0.317214
\(28\) 0 0
\(29\) 27.8701i 0.961039i 0.876984 + 0.480519i \(0.159552\pi\)
−0.876984 + 0.480519i \(0.840448\pi\)
\(30\) −6.80390 + 13.3555i −0.226797 + 0.445183i
\(31\) 19.4709 + 11.2416i 0.628095 + 0.362631i 0.780014 0.625762i \(-0.215212\pi\)
−0.151919 + 0.988393i \(0.548545\pi\)
\(32\) 22.6203 22.6346i 0.706884 0.707330i
\(33\) 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 0.139109 0.990277i \(-0.455576\pi\)
0.927160 + 0.374666i \(0.122243\pi\)
\(38\) 3.14862 + 60.0068i 0.0828584 + 1.57913i
\(39\) 39.6011 + 22.8637i 1.01541 + 0.586249i
\(40\) 9.47988 + 11.7021i 0.236997 + 0.292554i
\(41\) 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 \(0.685286\pi\)
\(44\) 31.3448 3.29846i 0.712381 0.0749651i
\(45\) 11.1653 + 6.44632i 0.248119 + 0.143251i
\(46\) −76.9907 + 4.03978i −1.67371 + 0.0878213i
\(47\) 71.5172 41.2905i 1.52164 0.878520i 0.521968 0.852965i \(-0.325198\pi\)
0.999673 0.0255554i \(-0.00813541\pi\)
\(48\) −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
\(52\) 37.1672 27.0107i 0.714753 0.519436i
\(53\) 23.2823 + 13.4420i 0.439288 + 0.253623i 0.703296 0.710897i \(-0.251711\pi\)
−0.264007 + 0.964521i \(0.585044\pi\)
\(54\) 15.2630 + 7.77569i 0.282649 + 0.143994i
\(55\) 14.8332i 0.269695i
\(56\) 0 0
\(57\) 119.609 2.09840
\(58\) 25.3024 49.6665i 0.436249 0.856320i
\(59\) −5.20555 + 9.01627i −0.0882296 + 0.152818i −0.906763 0.421641i \(-0.861454\pi\)
0.818533 + 0.574459i \(0.194788\pi\)
\(60\) 24.2501 17.6234i 0.404168 0.293723i
\(61\) −19.1932 + 11.0812i −0.314642 + 0.181659i −0.649002 0.760787i \(-0.724813\pi\)
0.334360 + 0.942446i \(0.391480\pi\)
\(62\) −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
\(66\) −3.28734 62.6505i −0.0498082 0.949250i
\(67\) 29.6549 51.3639i 0.442611 0.766625i −0.555271 0.831669i \(-0.687386\pi\)
0.997882 + 0.0650444i \(0.0207189\pi\)
\(68\) −11.5300 + 1.21333i −0.169559 + 0.0178430i
\(69\) 153.462i 2.22409i
\(70\) 0 0
\(71\) 38.2541i 0.538791i −0.963030 0.269395i \(-0.913176\pi\)
0.963030 0.269395i \(-0.0868238\pi\)
\(72\) −42.5724 + 34.4878i −0.591283 + 0.478997i
\(73\) 6.98890 12.1051i 0.0957383 0.165824i −0.814178 0.580615i \(-0.802812\pi\)
0.909917 + 0.414791i \(0.136145\pi\)
\(74\) −90.9852 + 4.77409i −1.22953 + 0.0645147i
\(75\) −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 −0.753610 0.657322i \(-0.771689\pi\)
0.192453 + 0.981306i \(0.438356\pi\)
\(80\) −6.26980 29.4605i −0.0783725 0.368257i
\(81\) 47.8670 82.9081i 0.590951 1.02356i
\(82\) −72.4078 36.8879i −0.883022 0.449852i
\(83\) 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
\(86\) 84.2573 + 42.9246i 0.979737 + 0.499123i
\(87\) −96.0871 55.4759i −1.10445 0.637654i
\(88\) −58.8531 22.5788i −0.668786 0.256578i
\(89\) 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
\(94\) −164.935 + 8.65431i −1.75463 + 0.0920671i
\(95\) 48.9821 + 28.2798i 0.515601 + 0.297683i
\(96\) 33.0105 + 123.042i 0.343860 + 1.28168i
\(97\) −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
\(100\) −85.3532 + 8.98187i −0.853532 + 0.0898187i
\(101\) 27.2216 + 15.7164i 0.269521 + 0.155608i 0.628670 0.777672i \(-0.283600\pi\)
−0.359149 + 0.933280i \(0.616933\pi\)
\(102\) 1.20923 + 23.0457i 0.0118552 + 0.225939i
\(103\) 69.2701 39.9931i 0.672525 0.388283i −0.124508 0.992219i \(-0.539735\pi\)
0.797033 + 0.603936i \(0.206402\pi\)
\(104\) −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 \(0.906508\pi\)
\(108\) −20.1405 27.7137i −0.186486 0.256608i
\(109\) 99.6528 + 57.5346i 0.914246 + 0.527840i 0.881795 0.471633i \(-0.156335\pi\)
0.0324509 + 0.999473i \(0.489669\pi\)
\(110\) 13.4666 26.4339i 0.122424 0.240308i
\(111\) 181.357i 1.63384i
\(112\) 0 0
\(113\) −55.7570 −0.493425 −0.246712 0.969089i \(-0.579350\pi\)
−0.246712 + 0.969089i \(0.579350\pi\)
\(114\) −213.151 108.589i −1.86975 0.952535i
\(115\) −36.2840 + 62.8457i −0.315513 + 0.546484i
\(116\) −90.1814 + 65.5380i −0.777426 + 0.564983i
\(117\) −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
\(122\) 44.2639 2.32257i 0.362819 0.0190375i
\(123\) −80.8772 + 140.083i −0.657538 + 1.13889i
\(124\) 9.41178 + 89.4386i 0.0759015 + 0.721279i
\(125\) 87.4546i 0.699637i
\(126\) 0 0
\(127\) 35.6964i 0.281074i 0.990075 + 0.140537i \(0.0448828\pi\)
−0.990075 + 0.140537i \(0.955117\pi\)
\(128\) 126.433 + 19.9678i 0.987757 + 0.155998i
\(129\) 94.1127 163.008i 0.729556 1.26363i
\(130\) −2.26607 43.1871i −0.0174313 0.332208i
\(131\) −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
\(136\) 21.6489 + 8.30553i 0.159183 + 0.0610701i
\(137\) 4.24835 7.35836i 0.0310099 0.0537107i −0.850104 0.526615i \(-0.823461\pi\)
0.881114 + 0.472904i \(0.156794\pi\)
\(138\) 139.323 273.480i 1.00959 1.98174i
\(139\) 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
\(142\) −34.7297 + 68.1716i −0.244576 + 0.480081i
\(143\) −78.3806 45.2530i −0.548116 0.316455i
\(144\) 107.177 22.8095i 0.744287 0.158399i
\(145\) −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 −0.589353 0.807876i \(-0.700617\pi\)
0.404964 + 0.914333i \(0.367284\pi\)
\(150\) 8.95157 + 170.600i 0.0596771 + 1.13733i
\(151\) −219.621 126.798i −1.45444 0.839723i −0.455713 0.890127i \(-0.650616\pi\)
−0.998729 + 0.0504039i \(0.983949\pi\)
\(152\) −186.764 + 151.297i −1.22871 + 0.995376i
\(153\) 19.8502 0.129740
\(154\) 0 0
\(155\) −42.3249 −0.273064
\(156\) 19.1422 + 181.905i 0.122707 + 1.16606i
\(157\) −42.7187 24.6636i −0.272093 0.157093i 0.357745 0.933819i \(-0.383546\pi\)
−0.629839 + 0.776726i \(0.716879\pi\)
\(158\) 102.238 5.36455i 0.647078 0.0339529i
\(159\) −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 \(0.948841\pi\)
\(164\) 95.5465 + 131.474i 0.582600 + 0.801668i
\(165\) −51.1401 29.5258i −0.309940 0.178944i
\(166\) −159.399 81.2050i −0.960233 0.489187i
\(167\) 32.3859i 0.193928i −0.995288 0.0969639i \(-0.969087\pi\)
0.995288 0.0969639i \(-0.0309131\pi\)
\(168\) 0 0
\(169\) 37.0641 0.219314
\(170\) −4.95364 + 9.72359i −0.0291391 + 0.0571976i
\(171\) −102.882 + 178.197i −0.601649 + 1.04209i
\(172\) −111.183 152.989i −0.646411 0.889472i
\(173\) 179.479 103.622i 1.03745 0.598973i 0.118341 0.992973i \(-0.462242\pi\)
0.919110 + 0.394000i \(0.128909\pi\)
\(174\) 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
\(178\) −11.0308 210.226i −0.0619707 1.18105i
\(179\) −87.0837 + 150.833i −0.486501 + 0.842644i −0.999880 0.0155178i \(-0.995060\pi\)
0.513379 + 0.858162i \(0.328394\pi\)
\(180\) 5.39706 + 51.2873i 0.0299837 + 0.284930i
\(181\) 204.244i 1.12842i −0.825632 0.564209i \(-0.809181\pi\)
0.825632 0.564209i \(-0.190819\pi\)
\(182\) 0 0
\(183\) 88.2291i 0.482126i
\(184\) −194.119 239.624i −1.05500 1.30231i
\(185\) −42.8793 + 74.2691i −0.231780 + 0.401455i
\(186\) 178.766 9.38003i 0.961107 0.0504303i
\(187\) 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 0.364759 0.931102i \(-0.381151\pi\)
0.988737 + 0.149660i \(0.0478180\pi\)
\(192\) 52.8786 249.238i 0.275410 1.29812i
\(193\) 165.381 286.448i 0.856896 1.48419i −0.0179791 0.999838i \(-0.505723\pi\)
0.874875 0.484349i \(-0.160943\pi\)
\(194\) 98.6021 + 50.2324i 0.508258 + 0.258930i
\(195\) −86.0828 −0.441450
\(196\) 0 0
\(197\) 327.309i 1.66146i −0.556672 0.830732i \(-0.687922\pi\)
0.556672 0.830732i \(-0.312078\pi\)
\(198\) 96.1663 + 48.9916i 0.485689 + 0.247432i
\(199\) 11.0295 + 6.36789i 0.0554246 + 0.0319994i 0.527456 0.849582i \(-0.323146\pi\)
−0.472032 + 0.881582i \(0.656479\pi\)
\(200\) 160.260 + 61.4832i 0.801299 + 0.307416i
\(201\) 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
\(206\) −159.753 + 8.38239i −0.775498 + 0.0406912i
\(207\) −228.632 132.001i −1.10450 0.637686i
\(208\) 174.801 + 56.7475i 0.840388 + 0.272824i
\(209\) −236.736 −1.13271
\(210\) 0 0
\(211\) 120.455 0.570875 0.285437 0.958397i \(-0.407861\pi\)
0.285437 + 0.958397i \(0.407861\pi\)
\(212\) 11.2541 + 106.946i 0.0530854 + 0.504461i
\(213\) 131.888 + 76.1454i 0.619191 + 0.357490i
\(214\) 5.11030 + 97.3927i 0.0238799 + 0.455106i
\(215\) 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
\(220\) −47.9970 + 34.8811i −0.218168 + 0.158550i
\(221\) 28.8320 + 16.6461i 0.130461 + 0.0753219i
\(222\) 164.648 323.190i 0.741657 1.45581i
\(223\) 372.958i 1.67246i −0.548382 0.836228i \(-0.684756\pi\)
0.548382 0.836228i \(-0.315244\pi\)
\(224\) 0 0
\(225\) 146.944 0.653086
\(226\) 99.3629 + 50.6200i 0.439659 + 0.223982i
\(227\) 36.7128 63.5885i 0.161730 0.280125i −0.773759 0.633480i \(-0.781626\pi\)
0.935489 + 0.353355i \(0.114959\pi\)
\(228\) 281.266 + 387.026i 1.23362 + 1.69748i
\(229\) −367.587 + 212.226i −1.60518 + 0.926752i −0.614755 + 0.788718i \(0.710745\pi\)
−0.990428 + 0.138034i \(0.955922\pi\)
\(230\) 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 \(0.776047\pi\)
\(234\) 157.115 8.24396i 0.671430 0.0352306i
\(235\) −77.7301 + 134.632i −0.330766 + 0.572904i
\(236\) −41.4157 + 4.35825i −0.175490 + 0.0184672i
\(237\) 203.787i 0.859861i
\(238\) 0 0
\(239\) 112.561i 0.470967i −0.971878 0.235484i \(-0.924333\pi\)
0.971878 0.235484i \(-0.0756674\pi\)
\(240\) 114.050 + 37.0254i 0.475210 + 0.154273i
\(241\) 140.216 242.861i 0.581809 1.00772i −0.413455 0.910524i \(-0.635678\pi\)
0.995265 0.0971992i \(-0.0309884\pi\)
\(242\) −6.17408 117.666i −0.0255127 0.486225i
\(243\) 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
\(248\) 64.4260 167.931i 0.259782 0.677139i
\(249\) −178.043 + 308.380i −0.715033 + 1.23847i
\(250\) −79.3973 + 155.850i −0.317589 + 0.623401i
\(251\) 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
\(254\) 32.4076 63.6134i 0.127589 0.250446i
\(255\) 18.8117 + 10.8609i 0.0737714 + 0.0425919i
\(256\) −207.184 150.368i −0.809314 0.587377i
\(257\) −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
\(262\) 12.7112 + 242.252i 0.0485160 + 0.924624i
\(263\) 147.190 + 84.9804i 0.559659 + 0.323119i 0.753009 0.658011i \(-0.228602\pi\)
−0.193350 + 0.981130i \(0.561935\pi\)
\(264\) 194.992 157.963i 0.738608 0.598344i
\(265\) −50.6098 −0.190980
\(266\) 0 0
\(267\) −419.034 −1.56942
\(268\) 235.937 24.8280i 0.880361 0.0926420i
\(269\) 93.9863 + 54.2630i 0.349391 + 0.201721i 0.664417 0.747362i \(-0.268680\pi\)
−0.315026 + 0.949083i \(0.602013\pi\)
\(270\) −32.2024 + 1.68969i −0.119268 + 0.00625813i
\(271\) 16.7690 9.68157i 0.0618781 0.0357253i −0.468742 0.883335i \(-0.655293\pi\)
0.530620 + 0.847610i \(0.321959\pi\)
\(272\) −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
\(276\) −496.568 + 360.873i −1.79916 + 1.30751i
\(277\) −112.104 64.7231i −0.404707 0.233658i 0.283806 0.958882i \(-0.408403\pi\)
−0.688513 + 0.725224i \(0.741736\pi\)
\(278\) −5.45210 2.77755i −0.0196119 0.00999120i
\(279\) 153.978i 0.551892i
\(280\) 0 0
\(281\) 83.3608 0.296658 0.148329 0.988938i \(-0.452611\pi\)
0.148329 + 0.988938i \(0.452611\pi\)
\(282\) 298.468 585.868i 1.05840 2.07755i
\(283\) 14.4646 25.0535i 0.0511118 0.0885282i −0.839338 0.543611i \(-0.817057\pi\)
0.890449 + 0.455082i \(0.150390\pi\)
\(284\) 123.782 89.9565i 0.435851 0.316748i
\(285\) −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
\(290\) 5.49833 + 104.788i 0.0189598 + 0.361338i
\(291\) 110.135 190.760i 0.378472 0.655533i
\(292\) 55.6042 5.85133i 0.190425 0.0200388i
\(293\) 214.613i 0.732468i 0.930523 + 0.366234i \(0.119353\pi\)
−0.930523 + 0.366234i \(0.880647\pi\)
\(294\) 0 0
\(295\) 19.5991i 0.0664376i
\(296\) −229.404 283.181i −0.775014 0.956692i
\(297\) −33.7429 + 58.4444i −0.113612 + 0.196783i
\(298\) 63.3612 3.32463i 0.212622 0.0111565i
\(299\) −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
\(304\) 470.185 100.065i 1.54666 0.329161i
\(305\) 20.8606 36.1316i 0.0683953 0.118464i
\(306\) −35.3744 18.0213i −0.115603 0.0588933i
\(307\) 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
\(310\) 75.4259 + 38.4254i 0.243309 + 0.123953i
\(311\) 281.771 + 162.681i 0.906016 + 0.523089i 0.879147 0.476550i \(-0.158113\pi\)
0.0268689 + 0.999639i \(0.491446\pi\)
\(312\) 131.033 341.547i 0.419979 1.09470i
\(313\) 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 −0.656359 0.754449i \(-0.727904\pi\)
0.325192 + 0.945648i \(0.394571\pi\)
\(318\) 213.759 11.2161i 0.672197 0.0352709i
\(319\) 190.180 + 109.801i 0.596177 + 0.344203i
\(320\) 80.5838 89.5655i 0.251824 0.279892i
\(321\) 194.128 0.604761
\(322\) 0 0
\(323\) 87.0822 0.269604
\(324\) 380.833 40.0758i 1.17541 0.123691i
\(325\) 213.434 + 123.226i 0.656719 + 0.379157i
\(326\) 12.1271 + 231.121i 0.0371998 + 0.708959i
\(327\) −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 \(0.891925\pi\)
\(332\) 210.336 + 289.426i 0.633543 + 0.871766i
\(333\) −270.191 155.995i −0.811384 0.468453i
\(334\) −29.4022 + 57.7140i −0.0880305 + 0.172797i
\(335\) 111.652i 0.333290i
\(336\) 0 0
\(337\) −464.021 −1.37692 −0.688459 0.725275i \(-0.741713\pi\)
−0.688459 + 0.725275i \(0.741713\pi\)
\(338\) −66.0509 33.6494i −0.195417 0.0995543i
\(339\) 110.985 192.232i 0.327390 0.567056i
\(340\) 17.6555 12.8309i 0.0519279 0.0377378i
\(341\) 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
\(346\) −413.920 + 21.7188i −1.19630 + 0.0627711i
\(347\) 185.593 321.457i 0.534851 0.926388i −0.464320 0.885667i \(-0.653701\pi\)
0.999171 0.0407208i \(-0.0129654\pi\)
\(348\) −46.4462 441.370i −0.133466 1.26831i
\(349\) 207.871i 0.595619i −0.954625 0.297809i \(-0.903744\pi\)
0.954625 0.297809i \(-0.0962560\pi\)
\(350\) 0 0
\(351\) 98.3779i 0.280279i
\(352\) −65.3361 243.530i −0.185614 0.691848i
\(353\) −307.007 + 531.751i −0.869708 + 1.50638i −0.00741211 + 0.999973i \(0.502359\pi\)
−0.862296 + 0.506405i \(0.830974\pi\)
\(354\) 4.34355 + 82.7799i 0.0122699 + 0.233841i
\(355\) 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 −0.363951 0.931418i \(-0.618573\pi\)
0.624656 + 0.780900i \(0.285239\pi\)
\(360\) 36.9442 96.2975i 0.102623 0.267493i
\(361\) −270.841 + 469.110i −0.750252 + 1.29947i
\(362\) −185.427 + 363.977i −0.512228 + 1.00546i
\(363\) −234.539 −0.646113
\(364\) 0 0
\(365\) 26.3135i 0.0720917i
\(366\) −80.1005 + 157.231i −0.218854 + 0.429592i
\(367\) 393.881 + 227.407i 1.07325 + 0.619639i 0.929067 0.369913i \(-0.120612\pi\)
0.144179 + 0.989552i \(0.453946\pi\)
\(368\) 128.386 + 603.262i 0.348876 + 1.63930i
\(369\) −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 −0.781119 0.624382i \(-0.785351\pi\)
0.150171 + 0.988660i \(0.452018\pi\)
\(374\) −2.39338 45.6133i −0.00639940 0.121961i
\(375\) 301.515 + 174.080i 0.804039 + 0.464212i
\(376\) −415.856 513.341i −1.10600 1.36527i
\(377\) 320.126 0.849140
\(378\) 0 0
\(379\) 268.351 0.708051 0.354026 0.935236i \(-0.384813\pi\)
0.354026 + 0.935236i \(0.384813\pi\)
\(380\) 23.6768 + 224.996i 0.0623073 + 0.592096i
\(381\) −123.069 71.0541i −0.323017 0.186494i
\(382\) −596.201 + 31.2833i −1.56074 + 0.0818934i
\(383\) 283.718 163.805i 0.740779 0.427689i −0.0815738 0.996667i \(-0.525995\pi\)
0.822352 + 0.568979i \(0.192661\pi\)
\(384\) −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
\(388\) −130.111 179.035i −0.335339 0.461431i
\(389\) 109.380 + 63.1506i 0.281183 + 0.162341i 0.633959 0.773367i \(-0.281429\pi\)
−0.352776 + 0.935708i \(0.614762\pi\)
\(390\) 153.406 + 78.1519i 0.393348 + 0.200389i
\(391\) 111.729i 0.285753i
\(392\) 0 0
\(393\) 482.869 1.22867
\(394\) −297.153 + 583.287i −0.754196 + 1.48042i
\(395\) 48.1826 83.4548i 0.121981 0.211278i
\(396\) −126.897 174.613i −0.320448 0.440941i
\(397\) −110.110 + 63.5720i −0.277355 + 0.160131i −0.632225 0.774784i \(-0.717858\pi\)
0.354870 + 0.934916i \(0.384525\pi\)
\(398\) −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 \(0.857229\pi\)
\(402\) −24.7443 471.580i −0.0615530 1.17308i
\(403\) 129.124 223.650i 0.320408 0.554962i
\(404\) 13.1583 + 125.041i 0.0325700 + 0.309507i
\(405\) 180.221i 0.444991i
\(406\) 0 0
\(407\) 358.950i 0.881941i
\(408\) −71.7272 + 58.1060i −0.175802 + 0.142417i
\(409\) −34.8873 + 60.4267i −0.0852991 + 0.147742i −0.905519 0.424306i \(-0.860518\pi\)
0.820220 + 0.572049i \(0.193851\pi\)
\(410\) 152.768 8.01591i 0.372605 0.0195510i
\(411\) 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
\(416\) −259.988 259.824i −0.624971 0.624577i
\(417\) −6.08982 + 10.5479i −0.0146039 + 0.0252947i
\(418\) 421.880 + 214.925i 1.00928 + 0.514174i
\(419\) −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 \(0.117353\pi\)
−0.932806 + 0.360380i \(0.882647\pi\)
\(422\) −214.658 109.357i −0.508669 0.259140i
\(423\) −489.793 282.782i −1.15790 0.668515i
\(424\) 77.0371 200.802i 0.181691 0.473590i
\(425\) −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
\(430\) −177.769 + 9.32771i −0.413416 + 0.0216924i
\(431\) −373.685 215.747i −0.867019 0.500574i −0.000662591 1.00000i \(-0.500211\pi\)
−0.866357 + 0.499426i \(0.833544\pi\)
\(432\) 42.3137 130.340i 0.0979484 0.301713i
\(433\) −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
\(436\) 48.1697 + 457.749i 0.110481 + 1.04988i
\(437\) −1003.00 579.085i −2.29521 1.32514i
\(438\) −5.83159 111.139i −0.0133141 0.253742i
\(439\) −264.977 + 152.985i −0.603593 + 0.348485i −0.770454 0.637496i \(-0.779970\pi\)
0.166861 + 0.985980i \(0.446637\pi\)
\(440\) 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 \(0.924460\pi\)
\(444\) −586.828 + 426.469i −1.32169 + 0.960516i
\(445\) −171.603 99.0748i −0.385624 0.222640i
\(446\) −338.597 + 664.637i −0.759185 + 1.49022i
\(447\) 126.295i 0.282539i
\(448\) 0 0
\(449\) −688.681 −1.53381 −0.766905 0.641761i \(-0.778204\pi\)
−0.766905 + 0.641761i \(0.778204\pi\)
\(450\) −261.865 133.406i −0.581923 0.296458i
\(451\) 160.076 277.260i 0.354936 0.614768i
\(452\) −131.115 180.417i −0.290078 0.399152i
\(453\) 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 \(-0.509269\pi\)
\(458\) 847.739 44.4817i 1.85096 0.0971217i
\(459\) 12.4122 21.4985i 0.0270418 0.0468378i
\(460\) −288.678 + 30.3781i −0.627560 + 0.0660393i
\(461\) 693.657i 1.50468i 0.658776 + 0.752339i \(0.271074\pi\)
−0.658776 + 0.752339i \(0.728926\pi\)
\(462\) 0 0
\(463\) 321.194i 0.693724i 0.937916 + 0.346862i \(0.112753\pi\)
−0.937916 + 0.346862i \(0.887247\pi\)
\(464\) −424.132 137.690i −0.914077 0.296747i
\(465\) 84.2484 145.922i 0.181179 0.313812i
\(466\) −8.74161 166.599i −0.0187588 0.357508i
\(467\) 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
\(472\) 77.7624 + 29.8333i 0.164751 + 0.0632062i
\(473\) −186.273 + 322.634i −0.393811 + 0.682101i
\(474\) −185.012 + 363.163i −0.390320 + 0.766166i
\(475\) 644.642 1.35714
\(476\) 0 0
\(477\) 184.118i 0.385992i
\(478\) −102.191 + 200.592i −0.213788 + 0.419648i
\(479\) −625.392 361.070i −1.30562 0.753800i −0.324257 0.945969i \(-0.605114\pi\)
−0.981362 + 0.192169i \(0.938448\pi\)
\(480\) −169.632 169.525i −0.353399 0.353176i
\(481\) −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
\(486\) −31.8625 607.239i −0.0655606 1.24946i
\(487\) 41.4211 + 23.9145i 0.0850536 + 0.0491057i 0.541924 0.840428i \(-0.317696\pi\)
−0.456870 + 0.889533i \(0.651030\pi\)
\(488\) 111.604 + 137.766i 0.228697 + 0.282308i
\(489\) 460.682 0.942090
\(490\) 0 0
\(491\) 44.4724 0.0905752 0.0452876 0.998974i \(-0.485580\pi\)
0.0452876 + 0.998974i \(0.485580\pi\)
\(492\) −643.465 + 67.7129i −1.30785 + 0.137628i
\(493\) −69.9571 40.3898i −0.141901 0.0819265i
\(494\) 689.258 36.1661i 1.39526 0.0732107i
\(495\) 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 \(0.665719\pi\)
\(500\) 282.983 205.654i 0.565966 0.411307i
\(501\) 111.656 + 64.4647i 0.222867 + 0.128672i
\(502\) −58.7298 29.9197i −0.116992 0.0596010i
\(503\) 462.733i 0.919946i 0.887933 + 0.459973i \(0.152141\pi\)
−0.887933 + 0.459973i \(0.847859\pi\)
\(504\) 0 0
\(505\) −59.1729 −0.117174
\(506\) −275.756 + 541.285i −0.544971 + 1.06973i
\(507\) −73.7767 + 127.785i −0.145516 + 0.252041i
\(508\) −115.505 + 83.9417i −0.227372 + 0.165240i
\(509\) 408.751 235.992i 0.803046 0.463639i −0.0414889 0.999139i \(-0.513210\pi\)
0.844535 + 0.535500i \(0.179877\pi\)
\(510\) −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
\(514\) 23.4976 + 447.821i 0.0457153 + 0.871248i
\(515\) −75.2878 + 130.402i −0.146190 + 0.253208i
\(516\) 748.767 78.7941i 1.45110 0.152702i
\(517\) 650.693i 1.25859i
\(518\) 0 0
\(519\) 825.047i 1.58969i
\(520\) 134.415 108.889i 0.258490 0.209402i
\(521\) −45.3709 + 78.5848i −0.0870843 + 0.150834i −0.906277 0.422683i \(-0.861088\pi\)
0.819193 + 0.573518i \(0.194422\pi\)
\(522\) −381.218 + 20.0029i −0.730304 + 0.0383198i
\(523\) −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
\(528\) −490.900 + 104.473i −0.929734 + 0.197866i
\(529\) 478.485 828.760i 0.904509 1.56665i
\(530\) 90.1902 + 45.9470i 0.170170 + 0.0866925i
\(531\) 71.3014 0.134278
\(532\) 0 0
\(533\) 466.705i 0.875618i
\(534\) 746.748 + 380.428i 1.39840 + 0.712412i
\(535\) 79.4994 + 45.8990i 0.148597 + 0.0857925i
\(536\) −442.997 169.954i −0.826486 0.317079i
\(537\) −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 0.0216371 0.999766i \(-0.493112\pi\)
0.876641 + 0.481145i \(0.159779\pi\)
\(542\) −38.6731 + 2.02922i −0.0713525 + 0.00374394i
\(543\) 704.166 + 406.550i 1.29681 + 0.748712i
\(544\) 24.0336 + 89.5817i 0.0441795 + 0.164672i
\(545\) −216.620 −0.397468
\(546\) 0 0
\(547\) 1043.62 1.90790 0.953952 0.299960i \(-0.0969733\pi\)
0.953952 + 0.299960i \(0.0969733\pi\)
\(548\) 33.8002 3.55685i 0.0616792 0.00649061i
\(549\) 131.447 + 75.8907i 0.239429 + 0.138234i
\(550\) −17.7174 337.661i −0.0322135 0.613928i
\(551\) 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
\(556\) 7.19438 + 9.89959i 0.0129395 + 0.0178050i
\(557\) −42.1273 24.3222i −0.0756324 0.0436664i 0.461707 0.887033i \(-0.347237\pi\)
−0.537339 + 0.843366i \(0.680571\pi\)
\(558\) −139.792 + 274.399i −0.250523 + 0.491755i
\(559\) 543.081i 0.971522i
\(560\) 0 0
\(561\) −90.9189 −0.162066
\(562\) −148.555 75.6807i −0.264332 0.134663i
\(563\) 363.015 628.761i 0.644787 1.11680i −0.339563 0.940583i \(-0.610279\pi\)
0.984351 0.176221i \(-0.0563874\pi\)
\(564\) −1063.78 + 773.088i −1.88614 + 1.37072i
\(565\) 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 \(0.694305\pi\)
\(570\) 449.713 23.5969i 0.788970 0.0413981i
\(571\) −55.0633 + 95.3724i −0.0964331 + 0.167027i −0.910206 0.414156i \(-0.864077\pi\)
0.813773 + 0.581183i \(0.197410\pi\)
\(572\) −37.8873 360.036i −0.0662365 0.629434i
\(573\) 1188.38i 2.07396i
\(574\) 0 0
\(575\) 827.097i 1.43843i
\(576\) 325.839 + 293.164i 0.565693 + 0.508965i
\(577\) −101.168 + 175.228i −0.175335 + 0.303688i −0.940277 0.340410i \(-0.889434\pi\)
0.764942 + 0.644099i \(0.222767\pi\)
\(578\) −29.4062 560.427i −0.0508758 0.969597i
\(579\) 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
\(584\) −104.403 40.0538i −0.178772 0.0685853i
\(585\) 74.0445 128.249i 0.126572 0.219229i
\(586\) 194.841 382.456i 0.332492 0.652655i
\(587\) 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
\(590\) −17.7934 + 34.9270i −0.0301583 + 0.0591982i
\(591\) 1128.45 + 651.513i 1.90940 + 1.10239i
\(592\) 151.723 + 712.917i 0.256289 + 1.20425i
\(593\) −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
\(598\) 46.4023 + 884.340i 0.0775957 + 1.47883i
\(599\) −318.077 183.642i −0.531013 0.306580i 0.210416 0.977612i \(-0.432518\pi\)
−0.741429 + 0.671032i \(0.765851\pi\)
\(600\) −530.973 + 430.140i −0.884955 + 0.716900i
\(601\) −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
\(604\) −106.159 1008.81i −0.175761 1.67022i
\(605\) −96.0484 55.4535i −0.158758 0.0916588i
\(606\) 249.926 13.1139i 0.412420 0.0216401i
\(607\) −1010.46 + 583.389i −1.66468 + 0.961102i −0.694241 + 0.719743i \(0.744260\pi\)
−0.970436 + 0.241359i \(0.922407\pi\)
\(608\) −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
\(612\) 46.6787 + 64.2306i 0.0762723 + 0.104952i
\(613\) 373.900 + 215.871i 0.609951 + 0.352155i 0.772946 0.634471i \(-0.218782\pi\)
−0.162995 + 0.986627i \(0.552115\pi\)
\(614\) −214.814 109.436i −0.349860 0.178235i
\(615\) 304.506i 0.495131i
\(616\) 0 0
\(617\) −333.751 −0.540926 −0.270463 0.962730i \(-0.587177\pi\)
−0.270463 + 0.962730i \(0.587177\pi\)
\(618\) 289.090 567.460i 0.467784 0.918220i
\(619\) −488.158 + 845.514i −0.788624 + 1.36594i 0.138187 + 0.990406i \(0.455873\pi\)
−0.926810 + 0.375530i \(0.877461\pi\)
\(620\) −99.5291 136.954i −0.160531 0.220893i
\(621\) −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
\(626\) −47.8671 912.257i −0.0764650 1.45728i
\(627\) 471.226 816.187i 0.751556 1.30173i
\(628\) −20.6492 196.226i −0.0328808 0.312461i
\(629\) 132.038i 0.209918i
\(630\) 0 0
\(631\) 639.885i 1.01408i 0.861922 + 0.507040i \(0.169261\pi\)
−0.861922 + 0.507040i \(0.830739\pi\)
\(632\) 257.777 + 318.205i 0.407875 + 0.503489i
\(633\) −239.767 + 415.288i −0.378778 + 0.656063i
\(634\) 242.108 12.7036i 0.381873 0.0200373i
\(635\) −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
\(640\) −224.920 + 86.4526i −0.351437 + 0.135082i
\(641\) −10.4295 + 18.0645i −0.0162707 + 0.0281817i −0.874046 0.485843i \(-0.838513\pi\)
0.857775 + 0.514025i \(0.171846\pi\)
\(642\) −345.950 176.243i −0.538864 0.274522i
\(643\) 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
\(646\) −155.187 79.0592i −0.240227 0.122383i
\(647\) 310.868 + 179.480i 0.480476 + 0.277403i 0.720615 0.693336i \(-0.243860\pi\)
−0.240139 + 0.970739i \(0.577193\pi\)
\(648\) −715.056 274.329i −1.10348 0.423347i
\(649\) 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 −0.524395 0.851475i \(-0.675708\pi\)
0.475202 + 0.879877i \(0.342375\pi\)
\(654\) 914.929 48.0073i 1.39897 0.0734056i
\(655\) 197.744 + 114.168i 0.301900 + 0.174302i
\(656\) −200.736 + 618.333i −0.306000 + 0.942581i
\(657\) −95.7284 −0.145705
\(658\) 0 0
\(659\) 197.302 0.299396 0.149698 0.988732i \(-0.452170\pi\)
0.149698 + 0.988732i \(0.452170\pi\)
\(660\) −24.7199 234.909i −0.0374544 0.355923i
\(661\) 938.626 + 541.916i 1.42001 + 0.819843i 0.996299 0.0859554i \(-0.0273942\pi\)
0.423710 + 0.905798i \(0.360728\pi\)
\(662\) 12.6982 + 242.004i 0.0191816 + 0.365565i
\(663\) −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
\(668\) 104.794 76.1571i 0.156877 0.114008i
\(669\) 1285.84 + 742.378i 1.92203 + 1.10968i
\(670\) 101.365 198.972i 0.151292 0.296973i
\(671\) 174.628i 0.260250i
\(672\) 0 0
\(673\) −286.066 −0.425061 −0.212530 0.977154i \(-0.568170\pi\)
−0.212530 + 0.977154i \(0.568170\pi\)
\(674\) 826.919 + 421.270i 1.22688 + 0.625030i
\(675\) 91.8834 159.147i 0.136124 0.235773i
\(676\) 87.1581 + 119.931i 0.128932 + 0.177413i
\(677\) 433.324 250.180i 0.640065 0.369542i −0.144575 0.989494i \(-0.546181\pi\)
0.784640 + 0.619952i \(0.212848\pi\)
\(678\) −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
\(682\) −353.823 + 18.5654i −0.518801 + 0.0272221i
\(683\) −473.225 + 819.650i −0.692862 + 1.20007i 0.278034 + 0.960571i \(0.410317\pi\)
−0.970896 + 0.239501i \(0.923016\pi\)
\(684\) −818.536 + 86.1360i −1.19669 + 0.125930i
\(685\) 15.9952i 0.0233507i
\(686\) 0 0
\(687\) 1689.76i 2.45962i
\(688\) 233.587 719.523i 0.339515 1.04582i
\(689\) 154.400 267.428i 0.224092 0.388140i
\(690\) 30.2756 + 576.996i 0.0438777 + 0.836227i
\(691\) 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
\(696\) −317.936 + 828.720i −0.456804 + 1.19069i
\(697\) −58.8834 + 101.989i −0.0844812 + 0.146326i
\(698\) −188.720 + 370.441i −0.270372 + 0.530717i
\(699\) −332.074 −0.475069
\(700\) 0 0
\(701\) 390.864i 0.557580i −0.960352 0.278790i \(-0.910067\pi\)
0.960352 0.278790i \(-0.0899333\pi\)
\(702\) 89.3142 175.316i 0.127228 0.249738i
\(703\) −1185.32 684.345i −1.68609 0.973464i
\(704\) −104.660 + 493.305i −0.148665 + 0.700717i
\(705\) −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 −0.954628 0.297801i \(-0.903747\pi\)
−0.219410 + 0.975633i \(0.570413\pi\)
\(710\) −7.54693 143.830i −0.0106295 0.202578i
\(711\) 303.608 + 175.288i 0.427016 + 0.246538i
\(712\) 654.304 530.050i 0.918967 0.744453i
\(713\) 866.685 1.21555
\(714\) 0 0
\(715\) 170.379 0.238293
\(716\) −692.844 + 72.9092i −0.967659 + 0.101828i
\(717\) 388.074 + 224.055i 0.541247 + 0.312489i
\(718\) −215.847 + 11.3257i −0.300622 + 0.0157740i
\(719\) −454.773 + 262.563i −0.632507 + 0.365178i −0.781722 0.623627i \(-0.785659\pi\)
0.149215 + 0.988805i \(0.452325\pi\)
\(720\) −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
\(724\) 660.886 480.289i 0.912826 0.663383i
\(725\) −517.870 298.992i −0.714304 0.412403i
\(726\) 417.965 + 212.931i 0.575710 + 0.293293i
\(727\) 108.633i 0.149426i 0.997205 + 0.0747131i \(0.0238041\pi\)
−0.997205 + 0.0747131i \(0.976196\pi\)
\(728\) 0 0
\(729\) −348.775 −0.478429
\(730\) 23.8892 46.8925i 0.0327249 0.0642363i
\(731\) 68.5197 118.680i 0.0937341 0.162352i
\(732\) 285.489 207.475i 0.390013 0.283436i
\(733\) 34.8609 20.1270i 0.0475593 0.0274584i −0.476032 0.879428i \(-0.657925\pi\)
0.523591 + 0.851970i \(0.324592\pi\)
\(734\) −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
\(738\) 29.1619 + 555.770i 0.0395147 + 0.753077i
\(739\) −498.602 + 863.603i −0.674698 + 1.16861i 0.301859 + 0.953352i \(0.402393\pi\)
−0.976557 + 0.215258i \(0.930941\pi\)
\(740\) −341.151 + 35.8999i −0.461014 + 0.0485134i
\(741\) 1373.87i 1.85407i
\(742\) 0 0
\(743\) 476.575i 0.641420i −0.947177 0.320710i \(-0.896078\pi\)
0.947177 0.320710i \(-0.103922\pi\)
\(744\) 450.729 + 556.388i 0.605818 + 0.747833i
\(745\) 29.8607 51.7203i 0.0400815 0.0694232i
\(746\) 542.757 28.4790i 0.727556 0.0381756i
\(747\) −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 −0.163305 0.986576i \(-0.552215\pi\)
0.772747 + 0.634714i \(0.218882\pi\)
\(752\) 275.039 + 1292.35i 0.365743 + 1.71855i
\(753\) −65.5993 + 113.621i −0.0871173 + 0.150892i
\(754\) −570.486 290.632i −0.756613 0.385454i
\(755\) 477.400 0.632318
\(756\) 0 0
\(757\) 455.964i 0.602331i 0.953572 + 0.301165i \(0.0973756\pi\)
−0.953572 + 0.301165i \(0.902624\pi\)
\(758\) −478.221 243.628i −0.630898 0.321409i
\(759\) 1047.19 + 604.598i 1.37970 + 0.796572i
\(760\) 162.073 422.455i 0.213255 0.555862i
\(761\) 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
\(766\) −654.319 + 34.3328i −0.854202 + 0.0448209i
\(767\) 103.564 + 59.7927i 0.135025 + 0.0779565i
\(768\) 930.825 414.993i 1.21201 0.540355i
\(769\) 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
\(772\) 1315.78 138.462i 1.70438 0.179355i
\(773\) −1036.66 598.515i −1.34108 0.774275i −0.354118 0.935201i \(-0.615219\pi\)
−0.986967 + 0.160925i \(0.948552\pi\)
\(774\) −33.9342 646.722i −0.0438426 0.835559i
\(775\) −417.771 + 241.200i −0.539059 + 0.311226i
\(776\) 69.3270 + 437.178i 0.0893389 + 0.563373i
\(777\) 0 0