Properties

Label 315.3.ca.b.163.1
Level 315
Weight 3
Character 315.163
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 163.1
Character \(\chi\) \(=\) 315.163
Dual form 315.3.ca.b.172.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.955194 - 3.56483i) q^{2} +(-8.33154 + 4.81021i) q^{4} +(3.70210 - 3.36072i) q^{5} +(3.07429 + 6.28878i) q^{7} +(14.6673 + 14.6673i) q^{8} +O(q^{10})\) \(q+(-0.955194 - 3.56483i) q^{2} +(-8.33154 + 4.81021i) q^{4} +(3.70210 - 3.36072i) q^{5} +(3.07429 + 6.28878i) q^{7} +(14.6673 + 14.6673i) q^{8} +(-15.5166 - 9.98725i) q^{10} +(4.09367 + 7.09045i) q^{11} +(14.0569 + 14.0569i) q^{13} +(19.4819 - 16.9663i) q^{14} +(19.0355 - 32.9704i) q^{16} +(6.76150 + 1.81174i) q^{17} +(18.2350 + 10.5280i) q^{19} +(-14.6784 + 45.8079i) q^{20} +(21.3660 - 21.3660i) q^{22} +(-31.4621 + 8.43024i) q^{23} +(2.41116 - 24.8835i) q^{25} +(36.6833 - 63.5374i) q^{26} +(-55.8639 - 37.6072i) q^{28} -22.1129i q^{29} +(13.7286 + 23.7786i) q^{31} +(-55.5730 - 14.8907i) q^{32} -25.8342i q^{34} +(32.5162 + 12.9499i) q^{35} +(-4.01580 - 14.9872i) q^{37} +(20.1126 - 75.0611i) q^{38} +(103.592 + 5.00723i) q^{40} -0.496183 q^{41} +(-33.4554 - 33.4554i) q^{43} +(-68.2132 - 39.3829i) q^{44} +(60.1048 + 104.105i) q^{46} +(6.46488 + 24.1272i) q^{47} +(-30.0975 + 38.6671i) q^{49} +(-91.0085 + 15.1731i) q^{50} +(-184.732 - 49.4987i) q^{52} +(-9.20667 + 34.3598i) q^{53} +(38.9842 + 12.4919i) q^{55} +(-47.1478 + 137.331i) q^{56} +(-78.8289 + 21.1222i) q^{58} +(-15.5949 + 9.00371i) q^{59} +(13.4849 - 23.3565i) q^{61} +(71.6533 - 71.6533i) q^{62} +60.0481i q^{64} +(99.2811 + 4.79884i) q^{65} +(5.37586 + 1.44046i) q^{67} +(-65.0485 + 17.4297i) q^{68} +(15.1050 - 128.284i) q^{70} +105.010 q^{71} +(21.8814 - 81.6625i) q^{73} +(-49.5909 + 28.6313i) q^{74} -202.568 q^{76} +(-32.0051 + 47.5423i) q^{77} +(86.5708 + 49.9817i) q^{79} +(-40.3329 - 186.033i) q^{80} +(0.473951 + 1.76881i) q^{82} +(-95.6303 - 95.6303i) q^{83} +(31.1205 - 16.0162i) q^{85} +(-87.3064 + 151.219i) q^{86} +(-43.9546 + 164.041i) q^{88} +(54.3480 + 31.3778i) q^{89} +(-45.1856 + 131.615i) q^{91} +(221.576 - 221.576i) q^{92} +(79.8344 - 46.0924i) q^{94} +(102.890 - 22.3070i) q^{95} +(59.0158 - 59.0158i) q^{97} +(166.591 + 70.3578i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64q - 4q^{5} - 4q^{7} - 24q^{8} + O(q^{10}) \) \( 64q - 4q^{5} - 4q^{7} - 24q^{8} - 16q^{10} - 16q^{11} + 80q^{16} - 56q^{17} - 96q^{22} - 72q^{23} - 4q^{25} + 288q^{26} - 380q^{28} - 136q^{31} + 48q^{32} - 76q^{35} - 28q^{37} + 68q^{38} + 164q^{40} - 128q^{41} + 344q^{43} + 240q^{46} - 412q^{47} + 72q^{50} + 388q^{52} + 40q^{53} - 8q^{55} + 864q^{56} + 56q^{58} - 216q^{61} + 912q^{62} - 20q^{65} - 368q^{67} + 492q^{68} + 416q^{70} - 784q^{71} - 316q^{73} - 32q^{76} - 844q^{77} - 908q^{80} + 556q^{82} - 1408q^{83} - 536q^{85} - 1024q^{86} + 372q^{88} - 1064q^{91} + 1704q^{92} - 260q^{95} + 352q^{97} - 272q^{98} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.955194 3.56483i −0.477597 1.78242i −0.611304 0.791396i \(-0.709355\pi\)
0.133707 0.991021i \(-0.457312\pi\)
\(3\) 0 0
\(4\) −8.33154 + 4.81021i −2.08288 + 1.20255i
\(5\) 3.70210 3.36072i 0.740421 0.672143i
\(6\) 0 0
\(7\) 3.07429 + 6.28878i 0.439185 + 0.898397i
\(8\) 14.6673 + 14.6673i 1.83341 + 1.83341i
\(9\) 0 0
\(10\) −15.5166 9.98725i −1.55166 0.998725i
\(11\) 4.09367 + 7.09045i 0.372152 + 0.644586i 0.989896 0.141793i \(-0.0452866\pi\)
−0.617744 + 0.786379i \(0.711953\pi\)
\(12\) 0 0
\(13\) 14.0569 + 14.0569i 1.08130 + 1.08130i 0.996389 + 0.0849086i \(0.0270598\pi\)
0.0849086 + 0.996389i \(0.472940\pi\)
\(14\) 19.4819 16.9663i 1.39156 1.21188i
\(15\) 0 0
\(16\) 19.0355 32.9704i 1.18972 2.06065i
\(17\) 6.76150 + 1.81174i 0.397735 + 0.106573i 0.452142 0.891946i \(-0.350660\pi\)
−0.0544067 + 0.998519i \(0.517327\pi\)
\(18\) 0 0
\(19\) 18.2350 + 10.5280i 0.959739 + 0.554105i 0.896093 0.443867i \(-0.146394\pi\)
0.0636460 + 0.997973i \(0.479727\pi\)
\(20\) −14.6784 + 45.8079i −0.733922 + 2.29039i
\(21\) 0 0
\(22\) 21.3660 21.3660i 0.971183 0.971183i
\(23\) −31.4621 + 8.43024i −1.36792 + 0.366532i −0.866717 0.498800i \(-0.833774\pi\)
−0.501199 + 0.865332i \(0.667108\pi\)
\(24\) 0 0
\(25\) 2.41116 24.8835i 0.0964464 0.995338i
\(26\) 36.6833 63.5374i 1.41090 2.44375i
\(27\) 0 0
\(28\) −55.8639 37.6072i −1.99514 1.34311i
\(29\) 22.1129i 0.762515i −0.924469 0.381258i \(-0.875491\pi\)
0.924469 0.381258i \(-0.124509\pi\)
\(30\) 0 0
\(31\) 13.7286 + 23.7786i 0.442857 + 0.767052i 0.997900 0.0647702i \(-0.0206314\pi\)
−0.555043 + 0.831822i \(0.687298\pi\)
\(32\) −55.5730 14.8907i −1.73666 0.465335i
\(33\) 0 0
\(34\) 25.8342i 0.759829i
\(35\) 32.5162 + 12.9499i 0.929033 + 0.369997i
\(36\) 0 0
\(37\) −4.01580 14.9872i −0.108535 0.405058i 0.890187 0.455595i \(-0.150573\pi\)
−0.998722 + 0.0505367i \(0.983907\pi\)
\(38\) 20.1126 75.0611i 0.529278 1.97529i
\(39\) 0 0
\(40\) 103.592 + 5.00723i 2.58981 + 0.125181i
\(41\) −0.496183 −0.0121020 −0.00605101 0.999982i \(-0.501926\pi\)
−0.00605101 + 0.999982i \(0.501926\pi\)
\(42\) 0 0
\(43\) −33.4554 33.4554i −0.778032 0.778032i 0.201464 0.979496i \(-0.435430\pi\)
−0.979496 + 0.201464i \(0.935430\pi\)
\(44\) −68.2132 39.3829i −1.55030 0.895066i
\(45\) 0 0
\(46\) 60.1048 + 104.105i 1.30663 + 2.26314i
\(47\) 6.46488 + 24.1272i 0.137551 + 0.513346i 0.999974 + 0.00715874i \(0.00227872\pi\)
−0.862424 + 0.506187i \(0.831055\pi\)
\(48\) 0 0
\(49\) −30.0975 + 38.6671i −0.614234 + 0.789124i
\(50\) −91.0085 + 15.1731i −1.82017 + 0.303463i
\(51\) 0 0
\(52\) −184.732 49.4987i −3.55253 0.951899i
\(53\) −9.20667 + 34.3598i −0.173711 + 0.648297i 0.823057 + 0.567959i \(0.192267\pi\)
−0.996768 + 0.0803384i \(0.974400\pi\)
\(54\) 0 0
\(55\) 38.9842 + 12.4919i 0.708804 + 0.227126i
\(56\) −47.1478 + 137.331i −0.841925 + 2.45234i
\(57\) 0 0
\(58\) −78.8289 + 21.1222i −1.35912 + 0.364175i
\(59\) −15.5949 + 9.00371i −0.264320 + 0.152605i −0.626304 0.779579i \(-0.715433\pi\)
0.361984 + 0.932184i \(0.382100\pi\)
\(60\) 0 0
\(61\) 13.4849 23.3565i 0.221064 0.382894i −0.734067 0.679077i \(-0.762380\pi\)
0.955131 + 0.296183i \(0.0957137\pi\)
\(62\) 71.6533 71.6533i 1.15570 1.15570i
\(63\) 0 0
\(64\) 60.0481i 0.938252i
\(65\) 99.2811 + 4.79884i 1.52740 + 0.0738283i
\(66\) 0 0
\(67\) 5.37586 + 1.44046i 0.0802367 + 0.0214993i 0.298714 0.954343i \(-0.403442\pi\)
−0.218477 + 0.975842i \(0.570109\pi\)
\(68\) −65.0485 + 17.4297i −0.956596 + 0.256319i
\(69\) 0 0
\(70\) 15.1050 128.284i 0.215785 1.83263i
\(71\) 105.010 1.47902 0.739509 0.673146i \(-0.235058\pi\)
0.739509 + 0.673146i \(0.235058\pi\)
\(72\) 0 0
\(73\) 21.8814 81.6625i 0.299745 1.11866i −0.637630 0.770343i \(-0.720085\pi\)
0.937375 0.348321i \(-0.113248\pi\)
\(74\) −49.5909 + 28.6313i −0.670147 + 0.386909i
\(75\) 0 0
\(76\) −202.568 −2.66537
\(77\) −32.0051 + 47.5423i −0.415651 + 0.617433i
\(78\) 0 0
\(79\) 86.5708 + 49.9817i 1.09583 + 0.632679i 0.935123 0.354322i \(-0.115288\pi\)
0.160710 + 0.987002i \(0.448622\pi\)
\(80\) −40.3329 186.033i −0.504161 2.32541i
\(81\) 0 0
\(82\) 0.473951 + 1.76881i 0.00577989 + 0.0215708i
\(83\) −95.6303 95.6303i −1.15217 1.15217i −0.986116 0.166057i \(-0.946897\pi\)
−0.166057 0.986116i \(-0.553103\pi\)
\(84\) 0 0
\(85\) 31.1205 16.0162i 0.366124 0.188426i
\(86\) −87.3064 + 151.219i −1.01519 + 1.75836i
\(87\) 0 0
\(88\) −43.9546 + 164.041i −0.499484 + 1.86410i
\(89\) 54.3480 + 31.3778i 0.610651 + 0.352560i 0.773220 0.634137i \(-0.218645\pi\)
−0.162569 + 0.986697i \(0.551978\pi\)
\(90\) 0 0
\(91\) −45.1856 + 131.615i −0.496545 + 1.44632i
\(92\) 221.576 221.576i 2.40844 2.40844i
\(93\) 0 0
\(94\) 79.8344 46.0924i 0.849302 0.490345i
\(95\) 102.890 22.3070i 1.08305 0.234811i
\(96\) 0 0
\(97\) 59.0158 59.0158i 0.608410 0.608410i −0.334120 0.942530i \(-0.608439\pi\)
0.942530 + 0.334120i \(0.108439\pi\)
\(98\) 166.591 + 70.3578i 1.69990 + 0.717937i
\(99\) 0 0
\(100\) 99.6061 + 218.916i 0.996061 + 2.18916i
\(101\) −19.3636 33.5388i −0.191719 0.332067i 0.754101 0.656758i \(-0.228073\pi\)
−0.945820 + 0.324691i \(0.894740\pi\)
\(102\) 0 0
\(103\) 29.9227 8.01775i 0.290511 0.0778422i −0.110620 0.993863i \(-0.535284\pi\)
0.401131 + 0.916021i \(0.368617\pi\)
\(104\) 412.352i 3.96493i
\(105\) 0 0
\(106\) 131.281 1.23850
\(107\) 5.02357 + 18.7482i 0.0469492 + 0.175217i 0.985419 0.170144i \(-0.0544232\pi\)
−0.938470 + 0.345361i \(0.887757\pi\)
\(108\) 0 0
\(109\) 73.5876 42.4858i 0.675116 0.389778i −0.122896 0.992419i \(-0.539218\pi\)
0.798012 + 0.602641i \(0.205885\pi\)
\(110\) 7.29410 150.904i 0.0663100 1.37186i
\(111\) 0 0
\(112\) 265.864 + 18.3492i 2.37379 + 0.163832i
\(113\) 94.3686 + 94.3686i 0.835120 + 0.835120i 0.988212 0.153092i \(-0.0489231\pi\)
−0.153092 + 0.988212i \(0.548923\pi\)
\(114\) 0 0
\(115\) −88.1443 + 136.945i −0.766472 + 1.19082i
\(116\) 106.368 + 184.235i 0.916966 + 1.58823i
\(117\) 0 0
\(118\) 46.9929 + 46.9929i 0.398245 + 0.398245i
\(119\) 9.39320 + 48.0914i 0.0789345 + 0.404129i
\(120\) 0 0
\(121\) 26.9837 46.7371i 0.223006 0.386257i
\(122\) −96.1428 25.7614i −0.788056 0.211159i
\(123\) 0 0
\(124\) −228.760 132.075i −1.84484 1.06512i
\(125\) −74.6999 100.224i −0.597599 0.801795i
\(126\) 0 0
\(127\) −146.532 + 146.532i −1.15380 + 1.15380i −0.168010 + 0.985785i \(0.553734\pi\)
−0.985785 + 0.168010i \(0.946266\pi\)
\(128\) −8.23036 + 2.20532i −0.0642997 + 0.0172290i
\(129\) 0 0
\(130\) −77.7257 358.504i −0.597890 2.75773i
\(131\) 57.4723 99.5449i 0.438720 0.759885i −0.558871 0.829254i \(-0.688765\pi\)
0.997591 + 0.0693695i \(0.0220987\pi\)
\(132\) 0 0
\(133\) −10.1484 + 147.042i −0.0763041 + 1.10558i
\(134\) 20.5399i 0.153283i
\(135\) 0 0
\(136\) 72.5996 + 125.746i 0.533820 + 0.924604i
\(137\) −105.092 28.1594i −0.767096 0.205543i −0.146008 0.989283i \(-0.546643\pi\)
−0.621088 + 0.783741i \(0.713309\pi\)
\(138\) 0 0
\(139\) 188.782i 1.35814i 0.734071 + 0.679072i \(0.237618\pi\)
−0.734071 + 0.679072i \(0.762382\pi\)
\(140\) −333.201 + 48.5172i −2.38001 + 0.346552i
\(141\) 0 0
\(142\) −100.305 374.344i −0.706375 2.63623i
\(143\) −42.1253 + 157.214i −0.294582 + 1.09940i
\(144\) 0 0
\(145\) −74.3154 81.8644i −0.512520 0.564582i
\(146\) −312.014 −2.13708
\(147\) 0 0
\(148\) 105.549 + 105.549i 0.713170 + 0.713170i
\(149\) −102.211 59.0115i −0.685979 0.396050i 0.116125 0.993235i \(-0.462953\pi\)
−0.802104 + 0.597184i \(0.796286\pi\)
\(150\) 0 0
\(151\) −89.3003 154.673i −0.591393 1.02432i −0.994045 0.108969i \(-0.965245\pi\)
0.402653 0.915353i \(-0.368088\pi\)
\(152\) 113.041 + 421.876i 0.743693 + 2.77550i
\(153\) 0 0
\(154\) 200.052 + 68.6808i 1.29904 + 0.445979i
\(155\) 130.738 + 41.8930i 0.843470 + 0.270277i
\(156\) 0 0
\(157\) 57.3089 + 15.3559i 0.365025 + 0.0978081i 0.436669 0.899622i \(-0.356158\pi\)
−0.0716444 + 0.997430i \(0.522825\pi\)
\(158\) 95.4844 356.353i 0.604332 2.25540i
\(159\) 0 0
\(160\) −255.780 + 131.638i −1.59863 + 0.822737i
\(161\) −149.740 171.941i −0.930059 1.06796i
\(162\) 0 0
\(163\) −121.490 + 32.5532i −0.745338 + 0.199713i −0.611449 0.791284i \(-0.709413\pi\)
−0.133889 + 0.990996i \(0.542747\pi\)
\(164\) 4.13396 2.38674i 0.0252071 0.0145533i
\(165\) 0 0
\(166\) −249.561 + 432.252i −1.50338 + 2.60393i
\(167\) 30.2982 30.2982i 0.181427 0.181427i −0.610551 0.791977i \(-0.709052\pi\)
0.791977 + 0.610551i \(0.209052\pi\)
\(168\) 0 0
\(169\) 226.191i 1.33841i
\(170\) −86.8214 95.6408i −0.510714 0.562593i
\(171\) 0 0
\(172\) 439.662 + 117.807i 2.55617 + 0.684925i
\(173\) −34.7961 + 9.32360i −0.201134 + 0.0538936i −0.357979 0.933730i \(-0.616534\pi\)
0.156846 + 0.987623i \(0.449868\pi\)
\(174\) 0 0
\(175\) 163.899 61.3358i 0.936566 0.350490i
\(176\) 311.700 1.77102
\(177\) 0 0
\(178\) 59.9438 223.713i 0.336763 1.25682i
\(179\) 65.4777 37.8036i 0.365797 0.211193i −0.305823 0.952088i \(-0.598932\pi\)
0.671621 + 0.740895i \(0.265598\pi\)
\(180\) 0 0
\(181\) −182.419 −1.00784 −0.503919 0.863751i \(-0.668109\pi\)
−0.503919 + 0.863751i \(0.668109\pi\)
\(182\) 512.348 + 35.3608i 2.81510 + 0.194290i
\(183\) 0 0
\(184\) −585.112 337.815i −3.17996 1.83595i
\(185\) −65.2345 41.9881i −0.352619 0.226963i
\(186\) 0 0
\(187\) 14.8333 + 55.3587i 0.0793226 + 0.296036i
\(188\) −169.920 169.920i −0.903827 0.903827i
\(189\) 0 0
\(190\) −177.800 345.477i −0.935792 1.81830i
\(191\) 7.66297 13.2727i 0.0401203 0.0694904i −0.845268 0.534343i \(-0.820559\pi\)
0.885388 + 0.464852i \(0.153893\pi\)
\(192\) 0 0
\(193\) 58.2576 217.420i 0.301853 1.12653i −0.633768 0.773523i \(-0.718493\pi\)
0.935621 0.353007i \(-0.114841\pi\)
\(194\) −266.753 154.010i −1.37502 0.793865i
\(195\) 0 0
\(196\) 64.7611 466.931i 0.330414 2.38230i
\(197\) −261.191 + 261.191i −1.32584 + 1.32584i −0.416883 + 0.908960i \(0.636878\pi\)
−0.908960 + 0.416883i \(0.863122\pi\)
\(198\) 0 0
\(199\) −57.1020 + 32.9678i −0.286945 + 0.165668i −0.636563 0.771225i \(-0.719645\pi\)
0.349619 + 0.936892i \(0.386311\pi\)
\(200\) 400.338 329.608i 2.00169 1.64804i
\(201\) 0 0
\(202\) −101.064 + 101.064i −0.500317 + 0.500317i
\(203\) 139.063 67.9816i 0.685041 0.334885i
\(204\) 0 0
\(205\) −1.83692 + 1.66753i −0.00896058 + 0.00813429i
\(206\) −57.1639 99.0107i −0.277495 0.480635i
\(207\) 0 0
\(208\) 731.039 195.881i 3.51461 0.941738i
\(209\) 172.393i 0.824846i
\(210\) 0 0
\(211\) 408.766 1.93728 0.968639 0.248472i \(-0.0799283\pi\)
0.968639 + 0.248472i \(0.0799283\pi\)
\(212\) −88.5721 330.556i −0.417793 1.55922i
\(213\) 0 0
\(214\) 62.0357 35.8164i 0.289887 0.167366i
\(215\) −236.289 11.4212i −1.09902 0.0531221i
\(216\) 0 0
\(217\) −107.333 + 159.438i −0.494621 + 0.734739i
\(218\) −221.745 221.745i −1.01718 1.01718i
\(219\) 0 0
\(220\) −384.887 + 83.4456i −1.74949 + 0.379298i
\(221\) 69.5781 + 120.513i 0.314833 + 0.545307i
\(222\) 0 0
\(223\) −180.123 180.123i −0.807725 0.807725i 0.176564 0.984289i \(-0.443502\pi\)
−0.984289 + 0.176564i \(0.943502\pi\)
\(224\) −77.2030 395.264i −0.344656 1.76457i
\(225\) 0 0
\(226\) 246.268 426.548i 1.08968 1.88738i
\(227\) −211.989 56.8024i −0.933874 0.250231i −0.240368 0.970682i \(-0.577268\pi\)
−0.693506 + 0.720451i \(0.743935\pi\)
\(228\) 0 0
\(229\) −292.008 168.591i −1.27515 0.736206i −0.299194 0.954192i \(-0.596718\pi\)
−0.975952 + 0.217986i \(0.930051\pi\)
\(230\) 572.380 + 183.411i 2.48861 + 0.797438i
\(231\) 0 0
\(232\) 324.337 324.337i 1.39800 1.39800i
\(233\) −284.131 + 76.1326i −1.21945 + 0.326749i −0.810461 0.585792i \(-0.800783\pi\)
−0.408984 + 0.912542i \(0.634117\pi\)
\(234\) 0 0
\(235\) 105.018 + 67.5950i 0.446887 + 0.287638i
\(236\) 86.6195 150.029i 0.367032 0.635718i
\(237\) 0 0
\(238\) 162.465 79.4218i 0.682628 0.333705i
\(239\) 191.663i 0.801937i 0.916092 + 0.400968i \(0.131326\pi\)
−0.916092 + 0.400968i \(0.868674\pi\)
\(240\) 0 0
\(241\) −61.5720 106.646i −0.255486 0.442514i 0.709542 0.704663i \(-0.248902\pi\)
−0.965027 + 0.262149i \(0.915569\pi\)
\(242\) −192.385 51.5493i −0.794978 0.213014i
\(243\) 0 0
\(244\) 259.461i 1.06337i
\(245\) 18.5252 + 244.299i 0.0756130 + 0.997137i
\(246\) 0 0
\(247\) 108.337 + 404.318i 0.438610 + 1.63692i
\(248\) −147.407 + 550.129i −0.594381 + 2.21826i
\(249\) 0 0
\(250\) −285.930 + 362.026i −1.14372 + 1.44811i
\(251\) 21.1349 0.0842027 0.0421014 0.999113i \(-0.486595\pi\)
0.0421014 + 0.999113i \(0.486595\pi\)
\(252\) 0 0
\(253\) −188.570 188.570i −0.745335 0.745335i
\(254\) 662.329 + 382.396i 2.60759 + 1.50549i
\(255\) 0 0
\(256\) 135.819 + 235.246i 0.530545 + 0.918930i
\(257\) 48.9113 + 182.539i 0.190316 + 0.710270i 0.993430 + 0.114444i \(0.0365086\pi\)
−0.803114 + 0.595826i \(0.796825\pi\)
\(258\) 0 0
\(259\) 81.9052 71.3294i 0.316236 0.275403i
\(260\) −850.248 + 437.582i −3.27018 + 1.68301i
\(261\) 0 0
\(262\) −409.758 109.794i −1.56396 0.419063i
\(263\) 36.1131 134.776i 0.137312 0.512457i −0.862665 0.505775i \(-0.831207\pi\)
0.999978 0.00668144i \(-0.00212678\pi\)
\(264\) 0 0
\(265\) 81.3894 + 158.144i 0.307130 + 0.596771i
\(266\) 533.875 104.276i 2.00705 0.392016i
\(267\) 0 0
\(268\) −51.7180 + 13.8578i −0.192978 + 0.0517082i
\(269\) 169.522 97.8736i 0.630194 0.363842i −0.150634 0.988590i \(-0.548131\pi\)
0.780827 + 0.624747i \(0.214798\pi\)
\(270\) 0 0
\(271\) 123.964 214.711i 0.457430 0.792292i −0.541394 0.840769i \(-0.682103\pi\)
0.998824 + 0.0484766i \(0.0154366\pi\)
\(272\) 188.442 188.442i 0.692802 0.692802i
\(273\) 0 0
\(274\) 401.534i 1.46545i
\(275\) 186.305 84.7685i 0.677474 0.308249i
\(276\) 0 0
\(277\) −263.603 70.6321i −0.951634 0.254989i −0.250578 0.968096i \(-0.580621\pi\)
−0.701055 + 0.713107i \(0.747287\pi\)
\(278\) 672.977 180.324i 2.42078 0.648646i
\(279\) 0 0
\(280\) 286.984 + 666.864i 1.02494 + 2.38166i
\(281\) 426.012 1.51606 0.758028 0.652222i \(-0.226163\pi\)
0.758028 + 0.652222i \(0.226163\pi\)
\(282\) 0 0
\(283\) −28.5453 + 106.533i −0.100867 + 0.376440i −0.997844 0.0656376i \(-0.979092\pi\)
0.896977 + 0.442078i \(0.145759\pi\)
\(284\) −874.897 + 505.122i −3.08062 + 1.77860i
\(285\) 0 0
\(286\) 600.679 2.10027
\(287\) −1.52541 3.12038i −0.00531502 0.0108724i
\(288\) 0 0
\(289\) −207.846 120.000i −0.719190 0.415224i
\(290\) −220.847 + 343.118i −0.761543 + 1.18317i
\(291\) 0 0
\(292\) 210.508 + 785.628i 0.720919 + 2.69051i
\(293\) −224.196 224.196i −0.765175 0.765175i 0.212078 0.977253i \(-0.431977\pi\)
−0.977253 + 0.212078i \(0.931977\pi\)
\(294\) 0 0
\(295\) −27.4750 + 85.7427i −0.0931355 + 0.290653i
\(296\) 160.920 278.722i 0.543649 0.941628i
\(297\) 0 0
\(298\) −112.735 + 420.732i −0.378305 + 1.41185i
\(299\) −560.761 323.755i −1.87545 1.08279i
\(300\) 0 0
\(301\) 107.542 313.245i 0.357282 1.04068i
\(302\) −466.083 + 466.083i −1.54332 + 1.54332i
\(303\) 0 0
\(304\) 694.225 400.811i 2.28363 1.31846i
\(305\) −28.5722 131.787i −0.0936793 0.432089i
\(306\) 0 0
\(307\) 348.544 348.544i 1.13532 1.13532i 0.146043 0.989278i \(-0.453346\pi\)
0.989278 0.146043i \(-0.0466539\pi\)
\(308\) 37.9631 550.052i 0.123257 1.78588i
\(309\) 0 0
\(310\) 24.4615 506.074i 0.0789082 1.63250i
\(311\) 7.38338 + 12.7884i 0.0237408 + 0.0411202i 0.877652 0.479299i \(-0.159109\pi\)
−0.853911 + 0.520419i \(0.825776\pi\)
\(312\) 0 0
\(313\) −116.758 + 31.2853i −0.373030 + 0.0999530i −0.440463 0.897771i \(-0.645186\pi\)
0.0674334 + 0.997724i \(0.478519\pi\)
\(314\) 218.964i 0.697339i
\(315\) 0 0
\(316\) −961.690 −3.04332
\(317\) −80.4604 300.282i −0.253818 0.947262i −0.968744 0.248062i \(-0.920206\pi\)
0.714926 0.699200i \(-0.246460\pi\)
\(318\) 0 0
\(319\) 156.791 90.5232i 0.491507 0.283772i
\(320\) 201.805 + 222.304i 0.630640 + 0.694701i
\(321\) 0 0
\(322\) −469.911 + 698.033i −1.45935 + 2.16781i
\(323\) 104.222 + 104.222i 0.322669 + 0.322669i
\(324\) 0 0
\(325\) 383.677 315.890i 1.18054 0.971969i
\(326\) 232.093 + 401.998i 0.711943 + 1.23312i
\(327\) 0 0
\(328\) −7.27765 7.27765i −0.0221880 0.0221880i
\(329\) −131.856 + 114.830i −0.400778 + 0.349028i
\(330\) 0 0
\(331\) 64.5929 111.878i 0.195145 0.338001i −0.751803 0.659388i \(-0.770816\pi\)
0.946948 + 0.321387i \(0.104149\pi\)
\(332\) 1256.75 + 336.745i 3.78539 + 1.01429i
\(333\) 0 0
\(334\) −136.949 79.0675i −0.410027 0.236729i
\(335\) 24.7429 12.7340i 0.0738595 0.0380120i
\(336\) 0 0
\(337\) −51.0347 + 51.0347i −0.151438 + 0.151438i −0.778760 0.627322i \(-0.784151\pi\)
0.627322 + 0.778760i \(0.284151\pi\)
\(338\) 806.333 216.056i 2.38560 0.639220i
\(339\) 0 0
\(340\) −182.240 + 283.136i −0.536000 + 0.832754i
\(341\) −112.401 + 194.684i −0.329621 + 0.570920i
\(342\) 0 0
\(343\) −335.697 70.4023i −0.978709 0.205255i
\(344\) 981.399i 2.85290i
\(345\) 0 0
\(346\) 66.4741 + 115.137i 0.192122 + 0.332765i
\(347\) 585.959 + 157.007i 1.68864 + 0.452470i 0.970039 0.242950i \(-0.0781151\pi\)
0.718603 + 0.695420i \(0.244782\pi\)
\(348\) 0 0
\(349\) 82.1983i 0.235525i 0.993042 + 0.117763i \(0.0375722\pi\)
−0.993042 + 0.117763i \(0.962428\pi\)
\(350\) −375.207 525.685i −1.07202 1.50196i
\(351\) 0 0
\(352\) −121.916 454.995i −0.346351 1.29260i
\(353\) −38.0031 + 141.830i −0.107658 + 0.401783i −0.998633 0.0522678i \(-0.983355\pi\)
0.890976 + 0.454051i \(0.150022\pi\)
\(354\) 0 0
\(355\) 388.759 352.910i 1.09510 0.994112i
\(356\) −603.736 −1.69589
\(357\) 0 0
\(358\) −197.307 197.307i −0.551138 0.551138i
\(359\) 175.063 + 101.073i 0.487641 + 0.281539i 0.723595 0.690225i \(-0.242488\pi\)
−0.235955 + 0.971764i \(0.575822\pi\)
\(360\) 0 0
\(361\) 41.1776 + 71.3218i 0.114065 + 0.197567i
\(362\) 174.245 + 650.292i 0.481340 + 1.79639i
\(363\) 0 0
\(364\) −256.633 1313.91i −0.705036 3.60965i
\(365\) −193.437 375.860i −0.529965 1.02975i
\(366\) 0 0
\(367\) 486.132 + 130.259i 1.32461 + 0.354928i 0.850703 0.525647i \(-0.176177\pi\)
0.473907 + 0.880575i \(0.342843\pi\)
\(368\) −320.947 + 1197.79i −0.872139 + 3.25487i
\(369\) 0 0
\(370\) −87.3689 + 272.657i −0.236132 + 0.736911i
\(371\) −244.385 + 47.7332i −0.658719 + 0.128661i
\(372\) 0 0
\(373\) 178.568 47.8471i 0.478735 0.128277i −0.0113788 0.999935i \(-0.503622\pi\)
0.490113 + 0.871659i \(0.336955\pi\)
\(374\) 183.176 105.757i 0.489775 0.282772i
\(375\) 0 0
\(376\) −259.059 + 448.703i −0.688987 + 1.19336i
\(377\) 310.839 310.839i 0.824506 0.824506i
\(378\) 0 0
\(379\) 348.414i 0.919299i 0.888100 + 0.459649i \(0.152025\pi\)
−0.888100 + 0.459649i \(0.847975\pi\)
\(380\) −749.927 + 680.773i −1.97349 + 1.79151i
\(381\) 0 0
\(382\) −54.6344 14.6393i −0.143022 0.0383226i
\(383\) −436.725 + 117.020i −1.14028 + 0.305536i −0.779062 0.626947i \(-0.784304\pi\)
−0.361214 + 0.932483i \(0.617638\pi\)
\(384\) 0 0
\(385\) 41.2900 + 283.567i 0.107247 + 0.736537i
\(386\) −830.714 −2.15211
\(387\) 0 0
\(388\) −207.814 + 775.571i −0.535602 + 1.99889i
\(389\) 565.646 326.576i 1.45410 0.839527i 0.455393 0.890290i \(-0.349499\pi\)
0.998711 + 0.0507630i \(0.0161653\pi\)
\(390\) 0 0
\(391\) −228.004 −0.583131
\(392\) −1008.59 + 125.693i −2.57293 + 0.320646i
\(393\) 0 0
\(394\) 1180.59 + 681.614i 2.99642 + 1.72999i
\(395\) 488.468 105.903i 1.23663 0.268108i
\(396\) 0 0
\(397\) 17.0735 + 63.7193i 0.0430064 + 0.160502i 0.984090 0.177673i \(-0.0568570\pi\)
−0.941083 + 0.338175i \(0.890190\pi\)
\(398\) 172.068 + 172.068i 0.432333 + 0.432333i
\(399\) 0 0
\(400\) −774.520 553.165i −1.93630 1.38291i
\(401\) −54.6685 + 94.6886i −0.136330 + 0.236131i −0.926105 0.377266i \(-0.876864\pi\)
0.789775 + 0.613397i \(0.210198\pi\)
\(402\) 0 0
\(403\) −141.272 + 527.233i −0.350550 + 1.30827i
\(404\) 322.657 + 186.286i 0.798657 + 0.461105i
\(405\) 0 0
\(406\) −375.176 430.802i −0.924078 1.06109i
\(407\) 89.8264 89.8264i 0.220704 0.220704i
\(408\) 0 0
\(409\) −254.528 + 146.952i −0.622318 + 0.359295i −0.777771 0.628548i \(-0.783650\pi\)
0.155453 + 0.987843i \(0.450316\pi\)
\(410\) 7.69908 + 4.95550i 0.0187782 + 0.0120866i
\(411\) 0 0
\(412\) −210.735 + 210.735i −0.511492 + 0.511492i
\(413\) −104.566 70.3927i −0.253185 0.170442i
\(414\) 0 0
\(415\) −675.420 32.6470i −1.62752 0.0786675i
\(416\) −571.865 990.499i −1.37467 2.38101i
\(417\) 0 0
\(418\) 614.552 164.669i 1.47022 0.393944i
\(419\) 234.794i 0.560368i −0.959946 0.280184i \(-0.909605\pi\)
0.959946 0.280184i \(-0.0903955\pi\)
\(420\) 0 0
\(421\) −124.297 −0.295242 −0.147621 0.989044i \(-0.547162\pi\)
−0.147621 + 0.989044i \(0.547162\pi\)
\(422\) −390.451 1457.18i −0.925238 3.45304i
\(423\) 0 0
\(424\) −639.001 + 368.928i −1.50708 + 0.870112i
\(425\) 61.3854 163.881i 0.144436 0.385602i
\(426\) 0 0
\(427\) 188.341 + 12.9987i 0.441079 + 0.0304420i
\(428\) −132.037 132.037i −0.308498 0.308498i
\(429\) 0 0
\(430\) 184.987 + 853.241i 0.430203 + 1.98428i
\(431\) −105.297 182.380i −0.244309 0.423155i 0.717628 0.696426i \(-0.245228\pi\)
−0.961937 + 0.273271i \(0.911894\pi\)
\(432\) 0 0
\(433\) −549.109 549.109i −1.26815 1.26815i −0.947042 0.321109i \(-0.895944\pi\)
−0.321109 0.947042i \(-0.604056\pi\)
\(434\) 670.895 + 230.328i 1.54584 + 0.530711i
\(435\) 0 0
\(436\) −408.732 + 707.944i −0.937459 + 1.62373i
\(437\) −662.466 177.507i −1.51594 0.406195i
\(438\) 0 0
\(439\) 83.0573 + 47.9532i 0.189197 + 0.109233i 0.591606 0.806227i \(-0.298494\pi\)
−0.402410 + 0.915460i \(0.631827\pi\)
\(440\) 388.570 + 755.015i 0.883114 + 1.71594i
\(441\) 0 0
\(442\) 363.148 363.148i 0.821601 0.821601i
\(443\) 96.6633 25.9009i 0.218202 0.0584670i −0.148062 0.988978i \(-0.547304\pi\)
0.366264 + 0.930511i \(0.380637\pi\)
\(444\) 0 0
\(445\) 306.654 66.4842i 0.689110 0.149403i
\(446\) −470.055 + 814.159i −1.05394 + 1.82547i
\(447\) 0 0
\(448\) −377.629 + 184.605i −0.842922 + 0.412066i
\(449\) 344.308i 0.766832i 0.923576 + 0.383416i \(0.125252\pi\)
−0.923576 + 0.383416i \(0.874748\pi\)
\(450\) 0 0
\(451\) −2.03121 3.51816i −0.00450379 0.00780079i
\(452\) −1240.17 332.302i −2.74373 0.735181i
\(453\) 0 0
\(454\) 809.964i 1.78406i
\(455\) 275.040 + 639.110i 0.604484 + 1.40464i
\(456\) 0 0
\(457\) −22.3113 83.2667i −0.0488211 0.182203i 0.937210 0.348767i \(-0.113399\pi\)
−0.986031 + 0.166564i \(0.946733\pi\)
\(458\) −322.074 + 1202.00i −0.703219 + 2.62445i
\(459\) 0 0
\(460\) 75.6434 1564.95i 0.164442 3.40207i
\(461\) 618.594 1.34185 0.670926 0.741524i \(-0.265897\pi\)
0.670926 + 0.741524i \(0.265897\pi\)
\(462\) 0 0
\(463\) 113.717 + 113.717i 0.245610 + 0.245610i 0.819166 0.573556i \(-0.194437\pi\)
−0.573556 + 0.819166i \(0.694437\pi\)
\(464\) −729.073 420.930i −1.57128 0.907177i
\(465\) 0 0
\(466\) 542.800 + 940.157i 1.16481 + 2.01750i
\(467\) −13.0497 48.7023i −0.0279438 0.104288i 0.950545 0.310585i \(-0.100525\pi\)
−0.978489 + 0.206298i \(0.933858\pi\)
\(468\) 0 0
\(469\) 7.46824 + 38.2359i 0.0159238 + 0.0815265i
\(470\) 140.652 438.940i 0.299259 0.933914i
\(471\) 0 0
\(472\) −360.795 96.6746i −0.764395 0.204819i
\(473\) 100.258 374.169i 0.211963 0.791055i
\(474\) 0 0
\(475\) 305.941 428.366i 0.644086 0.901823i
\(476\) −309.590 355.492i −0.650398 0.746831i
\(477\) 0 0
\(478\) 683.246 183.075i 1.42938 0.383003i
\(479\) −152.207 + 87.8766i −0.317760 + 0.183459i −0.650393 0.759597i \(-0.725396\pi\)
0.332634 + 0.943056i \(0.392063\pi\)
\(480\) 0 0
\(481\) 154.223 267.122i 0.320630 0.555347i
\(482\) −321.361 + 321.361i −0.666725 + 0.666725i
\(483\) 0 0
\(484\) 519.189i 1.07270i
\(485\) 20.1473 416.818i 0.0415408 0.859419i
\(486\) 0 0
\(487\) −245.352 65.7419i −0.503803 0.134994i −0.00203876 0.999998i \(-0.500649\pi\)
−0.501765 + 0.865004i \(0.667316\pi\)
\(488\) 540.364 144.790i 1.10730 0.296701i
\(489\) 0 0
\(490\) 853.189 299.392i 1.74120 0.611004i
\(491\) −275.796 −0.561704 −0.280852 0.959751i \(-0.590617\pi\)
−0.280852 + 0.959751i \(0.590617\pi\)
\(492\) 0 0
\(493\) 40.0629 149.517i 0.0812634 0.303279i
\(494\) 1337.84 772.405i 2.70819 1.56357i
\(495\) 0 0
\(496\) 1045.32 2.10750
\(497\) 322.832 + 660.386i 0.649562 + 1.32875i
\(498\) 0 0
\(499\) −520.379 300.441i −1.04284 0.602086i −0.122206 0.992505i \(-0.538997\pi\)
−0.920637 + 0.390419i \(0.872330\pi\)
\(500\) 1104.47 + 475.701i 2.20893 + 0.951401i
\(501\) 0 0
\(502\) −20.1879 75.3423i −0.0402150 0.150084i
\(503\) 513.924 + 513.924i 1.02172 + 1.02172i 0.999759 + 0.0219593i \(0.00699042\pi\)
0.0219593 + 0.999759i \(0.493010\pi\)
\(504\) 0 0
\(505\) −184.401 59.0884i −0.365150 0.117007i
\(506\) −492.099 + 852.340i −0.972527 + 1.68447i
\(507\) 0 0
\(508\) 515.986 1925.69i 1.01572 3.79072i
\(509\) 406.687 + 234.801i 0.798993 + 0.461299i 0.843119 0.537727i \(-0.180717\pi\)
−0.0441259 + 0.999026i \(0.514050\pi\)
\(510\) 0 0
\(511\) 580.827 113.447i 1.13665 0.222010i
\(512\) 684.779 684.779i 1.33746 1.33746i
\(513\) 0 0
\(514\) 604.002 348.721i 1.17510 0.678446i
\(515\) 83.8314 130.244i 0.162779 0.252901i
\(516\) 0 0
\(517\) −144.608 + 144.608i −0.279706 + 0.279706i
\(518\) −332.513 223.845i −0.641916 0.432133i
\(519\) 0 0
\(520\) 1385.80 + 1526.57i 2.66500 + 2.93571i
\(521\) −72.5876 125.725i −0.139324 0.241316i 0.787917 0.615781i \(-0.211160\pi\)
−0.927241 + 0.374466i \(0.877826\pi\)
\(522\) 0 0
\(523\) −809.900 + 217.012i −1.54857 + 0.414937i −0.929022 0.370026i \(-0.879349\pi\)
−0.619543 + 0.784962i \(0.712682\pi\)
\(524\) 1105.82i 2.11034i
\(525\) 0 0
\(526\) −514.949 −0.978991
\(527\) 49.7452 + 185.652i 0.0943932 + 0.352280i
\(528\) 0 0
\(529\) 460.666 265.966i 0.870824 0.502770i
\(530\) 486.016 441.198i 0.917011 0.832449i
\(531\) 0 0
\(532\) −622.753 1273.90i −1.17059 2.39456i
\(533\) −6.97477 6.97477i −0.0130859 0.0130859i
\(534\) 0 0
\(535\) 81.6052 + 52.5250i 0.152533 + 0.0981777i
\(536\) 57.7216 + 99.9768i 0.107690 + 0.186524i
\(537\) 0 0
\(538\) −510.829 510.829i −0.949497 0.949497i
\(539\) −397.376 55.1141i −0.737247 0.102253i
\(540\) 0 0
\(541\) −225.980 + 391.408i −0.417708 + 0.723491i −0.995708 0.0925455i \(-0.970500\pi\)
0.578001 + 0.816036i \(0.303833\pi\)
\(542\) −883.819 236.819i −1.63066 0.436935i
\(543\) 0 0
\(544\) −348.778 201.367i −0.641137 0.370160i
\(545\) 129.646 404.594i 0.237883 0.742375i
\(546\) 0 0
\(547\) 389.492 389.492i 0.712051 0.712051i −0.254913 0.966964i \(-0.582047\pi\)
0.966964 + 0.254913i \(0.0820469\pi\)
\(548\) 1011.03 270.905i 1.84495 0.494353i
\(549\) 0 0
\(550\) −480.143 583.177i −0.872988 1.06032i
\(551\) 232.805 403.230i 0.422514 0.731815i
\(552\) 0 0
\(553\) −48.1797 + 698.083i −0.0871243 + 1.26236i
\(554\) 1007.17i 1.81799i
\(555\) 0 0
\(556\) −908.083 1572.85i −1.63324 2.82886i
\(557\) 950.780 + 254.761i 1.70697 + 0.457380i 0.974678 0.223615i \(-0.0717859\pi\)
0.732288 + 0.680995i \(0.238453\pi\)
\(558\) 0 0
\(559\) 940.555i 1.68257i
\(560\) 1045.92 825.563i 1.86772 1.47422i
\(561\) 0 0
\(562\) −406.924 1518.66i −0.724064 2.70224i
\(563\) 222.762 831.358i 0.395669 1.47666i −0.424968 0.905208i \(-0.639715\pi\)
0.820637 0.571450i \(-0.193619\pi\)
\(564\) 0 0
\(565\) 666.508 + 32.2163i 1.17966 + 0.0570199i
\(566\) 407.037 0.719147
\(567\) 0 0
\(568\) 1540.22 + 1540.22i 2.71165 + 2.71165i
\(569\) −343.723 198.449i −0.604083 0.348768i 0.166563 0.986031i \(-0.446733\pi\)
−0.770646 + 0.637263i \(0.780066\pi\)
\(570\) 0 0
\(571\) 402.947 + 697.924i 0.705686 + 1.22228i 0.966443 + 0.256880i \(0.0826944\pi\)
−0.260757 + 0.965404i \(0.583972\pi\)
\(572\) −405.263 1512.46i −0.708502 2.64417i
\(573\) 0 0
\(574\) −9.66658 + 8.41840i −0.0168407 + 0.0146662i
\(575\) 133.913 + 803.212i 0.232893 + 1.39689i
\(576\) 0 0
\(577\) −1000.77 268.157i −1.73445 0.464743i −0.753246 0.657739i \(-0.771513\pi\)
−0.981200 + 0.192996i \(0.938180\pi\)
\(578\) −229.246 + 855.559i −0.396620 + 1.48021i
\(579\) 0 0
\(580\) 1012.95 + 324.584i 1.74646 + 0.559627i
\(581\) 307.402 895.394i 0.529092 1.54113i
\(582\) 0 0
\(583\) −281.315 + 75.3782i −0.482530 + 0.129294i
\(584\) 1518.71 876.826i 2.60053 1.50141i
\(585\) 0 0
\(586\) −585.071 + 1013.37i −0.998415 + 1.72930i
\(587\) −541.901 + 541.901i −0.923170 + 0.923170i −0.997252 0.0740817i \(-0.976397\pi\)
0.0740817 + 0.997252i \(0.476397\pi\)
\(588\) 0 0
\(589\) 578.138i 0.981559i
\(590\) 331.902 + 16.0428i 0.562546 + 0.0271912i
\(591\) 0 0
\(592\) −570.575 152.885i −0.963810 0.258252i
\(593\) −767.912 + 205.761i −1.29496 + 0.346984i −0.839543 0.543293i \(-0.817177\pi\)
−0.455419 + 0.890277i \(0.650510\pi\)
\(594\) 0 0
\(595\) 196.396 + 146.471i 0.330078 + 0.246170i
\(596\) 1135.43 1.90509
\(597\) 0 0
\(598\) −618.499 + 2308.27i −1.03428 + 3.85998i
\(599\) −357.782 + 206.565i −0.597299 + 0.344850i −0.767978 0.640476i \(-0.778737\pi\)
0.170680 + 0.985327i \(0.445404\pi\)
\(600\) 0 0
\(601\) −439.370 −0.731066 −0.365533 0.930798i \(-0.619113\pi\)
−0.365533 + 0.930798i \(0.619113\pi\)
\(602\) −1219.39 84.1588i −2.02556 0.139799i
\(603\) 0 0
\(604\) 1488.02 + 859.107i 2.46360 + 1.42236i
\(605\) −57.1738 263.710i −0.0945021 0.435884i
\(606\) 0 0
\(607\) 56.8754 + 212.262i 0.0936991 + 0.349690i 0.996819 0.0796986i \(-0.0253958\pi\)
−0.903120 + 0.429388i \(0.858729\pi\)
\(608\) −856.605 856.605i −1.40889 1.40889i
\(609\) 0 0
\(610\) −442.508 + 227.738i −0.725422 + 0.373340i
\(611\) −248.278 + 430.029i −0.406346 + 0.703812i
\(612\) 0 0
\(613\) 253.466 945.946i 0.413484 1.54314i −0.374370 0.927280i \(-0.622141\pi\)
0.787853 0.615863i \(-0.211192\pi\)
\(614\) −1575.43 909.573i −2.56584 1.48139i
\(615\) 0 0
\(616\) −1166.75 + 227.889i −1.89407 + 0.369949i
\(617\) 56.3252 56.3252i 0.0912887 0.0912887i −0.659988 0.751276i \(-0.729439\pi\)
0.751276 + 0.659988i \(0.229439\pi\)
\(618\) 0 0
\(619\) 451.442 260.640i 0.729309 0.421067i −0.0888604 0.996044i \(-0.528323\pi\)
0.818169 + 0.574977i \(0.194989\pi\)
\(620\) −1290.76 + 279.844i −2.08187 + 0.451361i
\(621\) 0 0
\(622\) 38.5359 38.5359i 0.0619548 0.0619548i
\(623\) −30.2466 + 438.247i −0.0485499 + 0.703446i
\(624\) 0 0
\(625\) −613.373 119.996i −0.981396 0.191994i
\(626\) 223.054 + 386.340i 0.356316 + 0.617157i
\(627\) 0 0
\(628\) −551.336 + 147.730i −0.877924 + 0.235239i
\(629\) 108.611i 0.172673i
\(630\) 0 0
\(631\) 606.021 0.960413 0.480207 0.877155i \(-0.340562\pi\)
0.480207 + 0.877155i \(0.340562\pi\)
\(632\) 536.663 + 2002.85i 0.849151 + 3.16907i
\(633\) 0 0
\(634\) −993.601 + 573.656i −1.56719 + 0.904819i
\(635\) −50.0242 + 1034.93i −0.0787783 + 1.62981i
\(636\) 0 0
\(637\) −966.614 + 120.462i −1.51745 + 0.189108i
\(638\) −472.466 472.466i −0.740542 0.740542i
\(639\) 0 0
\(640\) −23.0582 + 35.8242i −0.0360284 + 0.0559753i
\(641\) −552.914 957.675i −0.862580 1.49403i −0.869430 0.494056i \(-0.835514\pi\)
0.00685032 0.999977i \(-0.497819\pi\)
\(642\) 0 0
\(643\) 495.423 + 495.423i 0.770487 + 0.770487i 0.978192 0.207704i \(-0.0665992\pi\)
−0.207704 + 0.978192i \(0.566599\pi\)
\(644\) 2074.63 + 712.253i 3.22148 + 1.10598i
\(645\) 0 0
\(646\) 271.982 471.087i 0.421025 0.729237i
\(647\) 747.117 + 200.190i 1.15474 + 0.309412i 0.784864 0.619669i \(-0.212733\pi\)
0.369877 + 0.929081i \(0.379400\pi\)
\(648\) 0 0
\(649\) −127.681 73.7165i −0.196735 0.113585i
\(650\) −1492.58 1066.01i −2.29628 1.64001i
\(651\) 0 0
\(652\) 855.612 855.612i 1.31229 1.31229i
\(653\) −1045.38 + 280.108i −1.60089 + 0.428956i −0.945310 0.326172i \(-0.894241\pi\)
−0.655576 + 0.755129i \(0.727574\pi\)
\(654\) 0 0
\(655\) −121.774 561.674i −0.185914 0.857517i
\(656\) −9.44507 + 16.3593i −0.0143980 + 0.0249380i
\(657\) 0 0
\(658\) 535.299 + 360.359i 0.813524 + 0.547658i
\(659\) 388.022i 0.588805i −0.955682 0.294402i \(-0.904879\pi\)
0.955682 0.294402i \(-0.0951206\pi\)
\(660\) 0 0
\(661\) −309.552 536.160i −0.468308 0.811134i 0.531036 0.847350i \(-0.321803\pi\)
−0.999344 + 0.0362155i \(0.988470\pi\)
\(662\) −460.526 123.398i −0.695658 0.186401i
\(663\) 0 0
\(664\) 2805.28i 4.22481i
\(665\) 456.597 + 578.472i 0.686612 + 0.869882i
\(666\) 0 0
\(667\) 186.417 + 695.719i 0.279486 + 1.04306i
\(668\) −106.690 + 398.172i −0.159715 + 0.596066i
\(669\) 0 0
\(670\) −69.0289 76.0410i −0.103028 0.113494i
\(671\) 220.811 0.329078
\(672\) 0 0
\(673\) 185.772 + 185.772i 0.276036 + 0.276036i 0.831524 0.555488i \(-0.187469\pi\)
−0.555488 + 0.831524i \(0.687469\pi\)
\(674\) 230.678 + 133.182i 0.342253 + 0.197600i
\(675\) 0 0
\(676\) −1088.03 1884.52i −1.60951 2.78775i
\(677\) −191.084 713.136i −0.282252 1.05338i −0.950824 0.309731i \(-0.899761\pi\)
0.668573 0.743647i \(-0.266906\pi\)
\(678\) 0 0
\(679\) 552.569 + 189.705i 0.813798 + 0.279389i
\(680\) 691.368 + 221.539i 1.01672 + 0.325792i
\(681\) 0 0
\(682\) 801.379 + 214.729i 1.17504 + 0.314852i
\(683\) 135.236 504.707i 0.198003 0.738957i −0.793466 0.608614i \(-0.791726\pi\)
0.991469 0.130342i \(-0.0416077\pi\)
\(684\) 0 0
\(685\) −483.698 + 248.936i −0.706129 + 0.363411i
\(686\) 69.6833 + 1263.95i 0.101579 + 1.84250i
\(687\) 0 0
\(688\) −1739.88 + 466.198i −2.52889 + 0.677614i
\(689\) −612.407 + 353.574i −0.888835 + 0.513169i
\(690\) 0 0
\(691\) −301.546 + 522.293i −0.436391 + 0.755851i −0.997408 0.0719534i \(-0.977077\pi\)
0.561017 + 0.827804i \(0.310410\pi\)
\(692\) 245.057 245.057i 0.354128 0.354128i
\(693\) 0 0
\(694\) 2238.82i 3.22596i
\(695\) 634.443 + 698.891i 0.912868 + 1.00560i
\(696\) 0 0
\(697\) −3.35494 0.898953i −0.00481340 0.00128975i
\(698\) 293.023 78.5153i 0.419804 0.112486i
\(699\) 0 0
\(700\) −1070.49 + 1299.41i −1.52928 + 1.85630i
\(701\) −100.279 −0.143052 −0.0715259 0.997439i \(-0.522787\pi\)
−0.0715259 + 0.997439i \(0.522787\pi\)
\(702\) 0 0
\(703\) 84.5567 315.570i 0.120280 0.448890i
\(704\) −425.768 + 245.817i −0.604784 + 0.349172i
\(705\) 0 0
\(706\) 541.899 0.767562
\(707\) 151.389 224.882i 0.214128 0.318079i
\(708\) 0 0
\(709\) 339.531 + 196.029i 0.478888 + 0.276486i 0.719953 0.694023i \(-0.244163\pi\)
−0.241065 + 0.970509i \(0.577497\pi\)
\(710\) −1629.41 1048.76i −2.29494 1.47713i
\(711\) 0 0
\(712\) 336.910 + 1257.36i 0.473188 + 1.76596i
\(713\) −632.389 632.389i −0.886941 0.886941i
\(714\) 0 0
\(715\) 372.399 + 723.593i 0.520837 + 1.01202i
\(716\) −363.687 + 629.924i −0.507942 + 0.879782i
\(717\) 0 0
\(718\) 193.088 720.614i 0.268925 1.00364i
\(719\) −1001.31 578.104i −1.39264 0.804039i −0.399031 0.916938i \(-0.630653\pi\)
−0.993607 + 0.112898i \(0.963987\pi\)
\(720\) 0 0
\(721\) 142.413 + 163.528i 0.197521 + 0.226807i
\(722\) 214.918 214.918i 0.297670 0.297670i
\(723\) 0 0
\(724\) 1519.83 877.472i 2.09921 1.21198i
\(725\) −550.246 53.3179i −0.758961 0.0735419i
\(726\) 0 0
\(727\) −27.8958 + 27.8958i −0.0383712 + 0.0383712i −0.726032 0.687661i \(-0.758638\pi\)
0.687661 + 0.726032i \(0.258638\pi\)
\(728\) −2593.19 + 1267.69i −3.56208 + 1.74133i
\(729\) 0 0
\(730\) −1155.11 + 1048.59i −1.58234 + 1.43643i
\(731\) −165.596 286.821i −0.226534 0.392368i
\(732\) 0 0
\(733\) 780.690 209.185i 1.06506 0.285382i 0.316599 0.948559i \(-0.397459\pi\)
0.748463 + 0.663177i \(0.230792\pi\)
\(734\) 1857.40i 2.53052i
\(735\) 0 0
\(736\) 1873.97 2.54616
\(737\) 11.7935 + 44.0140i 0.0160021 + 0.0597205i
\(738\) 0 0
\(739\) −452.698 + 261.365i −0.612582 + 0.353674i −0.773975 0.633216i \(-0.781735\pi\)
0.161393 + 0.986890i \(0.448401\pi\)
\(740\) 745.475 + 36.0332i 1.00740 + 0.0486935i
\(741\) 0 0
\(742\) 403.596 + 825.597i 0.543930 + 1.11266i
\(743\) 34.1788 + 34.1788i 0.0460011 + 0.0460011i 0.729733 0.683732i \(-0.239644\pi\)
−0.683732 + 0.729733i \(0.739644\pi\)
\(744\) 0 0
\(745\) −576.717 + 125.035i −0.774116 + 0.167833i
\(746\) −341.134 590.862i −0.457284 0.792040i
\(747\) 0 0
\(748\) −389.872 389.872i −0.521219 0.521219i
\(749\) −102.459 + 89.2296i −0.136795 + 0.119132i
\(750\) 0 0
\(751\) 352.812 611.088i 0.469790 0.813700i −0.529614 0.848239i \(-0.677663\pi\)
0.999403 + 0.0345394i \(0.0109964\pi\)
\(752\) 918.547 + 246.124i 1.22147 + 0.327292i
\(753\) 0 0
\(754\) −1405.00 811.177i −1.86339 1.07583i
\(755\) −850.410 272.501i −1.12637 0.360929i
\(756\) 0 0
\(757\) 395.694 395.694i 0.522713 0.522713i −0.395677 0.918390i \(-0.629490\pi\)
0.918390 + 0.395677i \(0.129490\pi\)
\(758\) 1242.04 332.803i 1.63857 0.439054i
\(759\) 0 0
\(760\) 1836.30 + 1181.93i 2.41618 + 1.55517i
\(761\) 692.529 1199.50i 0.910025 1.57621i 0.0959984 0.995381i \(-0.469396\pi\)
0.814026 0.580828i \(-0.197271\pi\)
\(762\) 0 0
\(763\) 493.414 + 332.162i 0.646676 + 0.435337i
\(764\) 147.442i 0.192987i
\(765\) 0 0
\(766\) 834.315 + 1445.08i 1.08918 + 1.88652i
\(767\) −345.779 92.6512i −0.450820 0.120797i
\(768\) 0 0
\(769\) 907.238i 1.17976i 0.807490 + 0.589882i \(0.200826\pi\)
−0.807490 + 0.589882i \(0.799174\pi\)
\(770\) 971.428 418.053i 1.26160 0.542926i
\(771\) 0 0
\(772\) 560.463 + 2091.68i 0.725988 + 2.70942i
\(773\) −161.404 + 602.366i −0.208802 + 0.779258i 0.779456 + 0.626458i \(0.215496\pi\)
−0.988257 + 0.152800i \(0.951171\pi\)
\(774\) 0 0
\(775\) 624.796 284.281i 0.806188 0.366814i