Properties

Label 315.3.ca.b.37.16
Level 315
Weight 3
Character 315.37
Analytic conductor 8.583
Analytic rank 0
Dimension 64
CM no
Inner twists 4

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 37.16
Character \(\chi\) \(=\) 315.37
Dual form 315.3.ca.b.298.16

$q$-expansion

\(f(q)\) \(=\) \(q+(3.56483 - 0.955194i) q^{2} +(8.33154 - 4.81021i) q^{4} +(1.05941 - 4.88648i) q^{5} +(-6.28878 + 3.07429i) q^{7} +(14.6673 - 14.6673i) q^{8} +O(q^{10})\) \(q+(3.56483 - 0.955194i) q^{2} +(8.33154 - 4.81021i) q^{4} +(1.05941 - 4.88648i) q^{5} +(-6.28878 + 3.07429i) q^{7} +(14.6673 - 14.6673i) q^{8} +(-0.890898 - 18.4314i) q^{10} +(4.09367 + 7.09045i) q^{11} +(14.0569 - 14.0569i) q^{13} +(-19.4819 + 16.9663i) q^{14} +(19.0355 - 32.9704i) q^{16} +(-1.81174 + 6.76150i) q^{17} +(-18.2350 - 10.5280i) q^{19} +(-14.6784 - 45.8079i) q^{20} +(21.3660 + 21.3660i) q^{22} +(8.43024 + 31.4621i) q^{23} +(-22.7553 - 10.3536i) q^{25} +(36.6833 - 63.5374i) q^{26} +(-37.6072 + 55.8639i) q^{28} +22.1129i q^{29} +(13.7286 + 23.7786i) q^{31} +(14.8907 - 55.5730i) q^{32} +25.8342i q^{34} +(8.36003 + 33.9869i) q^{35} +(14.9872 - 4.01580i) q^{37} +(-75.0611 - 20.1126i) q^{38} +(-56.1326 - 87.2101i) q^{40} -0.496183 q^{41} +(-33.4554 + 33.4554i) q^{43} +(68.2132 + 39.3829i) q^{44} +(60.1048 + 104.105i) q^{46} +(-24.1272 + 6.46488i) q^{47} +(30.0975 - 38.6671i) q^{49} +(-91.0085 - 15.1731i) q^{50} +(49.4987 - 184.732i) q^{52} +(34.3598 + 9.20667i) q^{53} +(38.9842 - 12.4919i) q^{55} +(-47.1478 + 137.331i) q^{56} +(21.1222 + 78.8289i) q^{58} +(15.5949 - 9.00371i) q^{59} +(13.4849 - 23.3565i) q^{61} +(71.6533 + 71.6533i) q^{62} -60.0481i q^{64} +(-53.7965 - 83.5806i) q^{65} +(-1.44046 + 5.37586i) q^{67} +(17.4297 + 65.0485i) q^{68} +(62.2662 + 113.172i) q^{70} +105.010 q^{71} +(-81.6625 - 21.8814i) q^{73} +(49.5909 - 28.6313i) q^{74} -202.568 q^{76} +(-47.5423 - 32.0051i) q^{77} +(-86.5708 - 49.9817i) q^{79} +(-140.943 - 127.946i) q^{80} +(-1.76881 + 0.473951i) q^{82} +(-95.6303 + 95.6303i) q^{83} +(31.1205 + 16.0162i) q^{85} +(-87.3064 + 151.219i) q^{86} +(164.041 + 43.9546i) q^{88} +(-54.3480 - 31.3778i) q^{89} +(-45.1856 + 131.615i) q^{91} +(221.576 + 221.576i) q^{92} +(-79.8344 + 46.0924i) q^{94} +(-70.7633 + 77.9515i) q^{95} +(59.0158 + 59.0158i) q^{97} +(70.3578 - 166.591i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64q - 4q^{5} - 4q^{7} - 24q^{8} + O(q^{10}) \) \( 64q - 4q^{5} - 4q^{7} - 24q^{8} - 16q^{10} - 16q^{11} + 80q^{16} - 56q^{17} - 96q^{22} - 72q^{23} - 4q^{25} + 288q^{26} - 380q^{28} - 136q^{31} + 48q^{32} - 76q^{35} - 28q^{37} + 68q^{38} + 164q^{40} - 128q^{41} + 344q^{43} + 240q^{46} - 412q^{47} + 72q^{50} + 388q^{52} + 40q^{53} - 8q^{55} + 864q^{56} + 56q^{58} - 216q^{61} + 912q^{62} - 20q^{65} - 368q^{67} + 492q^{68} + 416q^{70} - 784q^{71} - 316q^{73} - 32q^{76} - 844q^{77} - 908q^{80} + 556q^{82} - 1408q^{83} - 536q^{85} - 1024q^{86} + 372q^{88} - 1064q^{91} + 1704q^{92} - 260q^{95} + 352q^{97} - 272q^{98} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.56483 0.955194i 1.78242 0.477597i 0.791396 0.611304i \(-0.209355\pi\)
0.991021 + 0.133707i \(0.0426882\pi\)
\(3\) 0 0
\(4\) 8.33154 4.81021i 2.08288 1.20255i
\(5\) 1.05941 4.88648i 0.211883 0.977295i
\(6\) 0 0
\(7\) −6.28878 + 3.07429i −0.898397 + 0.439185i
\(8\) 14.6673 14.6673i 1.83341 1.83341i
\(9\) 0 0
\(10\) −0.890898 18.4314i −0.0890898 1.84314i
\(11\) 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 0.0849086 0.996389i \(-0.472940\pi\)
0.996389 0.0849086i \(-0.0270598\pi\)
\(14\) −19.4819 + 16.9663i −1.39156 + 1.21188i
\(15\) 0 0
\(16\) 19.0355 32.9704i 1.18972 2.06065i
\(17\) −1.81174 + 6.76150i −0.106573 + 0.397735i −0.998519 0.0544067i \(-0.982673\pi\)
0.891946 + 0.452142i \(0.149340\pi\)
\(18\) 0 0
\(19\) −18.2350 10.5280i −0.959739 0.554105i −0.0636460 0.997973i \(-0.520273\pi\)
−0.896093 + 0.443867i \(0.853606\pi\)
\(20\) −14.6784 45.8079i −0.733922 2.29039i
\(21\) 0 0
\(22\) 21.3660 + 21.3660i 0.971183 + 0.971183i
\(23\) 8.43024 + 31.4621i 0.366532 + 1.36792i 0.865332 + 0.501199i \(0.167108\pi\)
−0.498800 + 0.866717i \(0.666226\pi\)
\(24\) 0 0
\(25\) −22.7553 10.3536i −0.910211 0.414144i
\(26\) 36.6833 63.5374i 1.41090 2.44375i
\(27\) 0 0
\(28\) −37.6072 + 55.8639i −1.34311 + 1.99514i
\(29\) 22.1129i 0.762515i 0.924469 + 0.381258i \(0.124509\pi\)
−0.924469 + 0.381258i \(0.875491\pi\)
\(30\) 0 0
\(31\) 13.7286 + 23.7786i 0.442857 + 0.767052i 0.997900 0.0647702i \(-0.0206314\pi\)
−0.555043 + 0.831822i \(0.687298\pi\)
\(32\) 14.8907 55.5730i 0.465335 1.73666i
\(33\) 0 0
\(34\) 25.8342i 0.759829i
\(35\) 8.36003 + 33.9869i 0.238858 + 0.971054i
\(36\) 0 0
\(37\) 14.9872 4.01580i 0.405058 0.108535i −0.0505367 0.998722i \(-0.516093\pi\)
0.455595 + 0.890187i \(0.349427\pi\)
\(38\) −75.0611 20.1126i −1.97529 0.529278i
\(39\) 0 0
\(40\) −56.1326 87.2101i −1.40332 2.18025i
\(41\) −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 −0.979496 0.201464i \(-0.935430\pi\)
0.201464 + 0.979496i \(0.435430\pi\)
\(44\) 68.2132 + 39.3829i 1.55030 + 0.895066i
\(45\) 0 0
\(46\) 60.1048 + 104.105i 1.30663 + 2.26314i
\(47\) −24.1272 + 6.46488i −0.513346 + 0.137551i −0.506187 0.862424i \(-0.668945\pi\)
−0.00715874 + 0.999974i \(0.502279\pi\)
\(48\) 0 0
\(49\) 30.0975 38.6671i 0.614234 0.789124i
\(50\) −91.0085 15.1731i −1.82017 0.303463i
\(51\) 0 0
\(52\) 49.4987 184.732i 0.951899 3.55253i
\(53\) 34.3598 + 9.20667i 0.648297 + 0.173711i 0.567959 0.823057i \(-0.307733\pi\)
0.0803384 + 0.996768i \(0.474400\pi\)
\(54\) 0 0
\(55\) 38.9842 12.4919i 0.708804 0.227126i
\(56\) −47.1478 + 137.331i −0.841925 + 2.45234i
\(57\) 0 0
\(58\) 21.1222 + 78.8289i 0.364175 + 1.35912i
\(59\) 15.5949 9.00371i 0.264320 0.152605i −0.361984 0.932184i \(-0.617900\pi\)
0.626304 + 0.779579i \(0.284567\pi\)
\(60\) 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
\(65\) −53.7965 83.5806i −0.827638 1.28585i
\(66\) 0 0
\(67\) −1.44046 + 5.37586i −0.0214993 + 0.0802367i −0.975842 0.218477i \(-0.929891\pi\)
0.954343 + 0.298714i \(0.0965577\pi\)
\(68\) 17.4297 + 65.0485i 0.256319 + 0.956596i
\(69\) 0 0
\(70\) 62.2662 + 113.172i 0.889517 + 1.61675i
\(71\) 105.010 1.47902 0.739509 0.673146i \(-0.235058\pi\)
0.739509 + 0.673146i \(0.235058\pi\)
\(72\) 0 0
\(73\) −81.6625 21.8814i −1.11866 0.299745i −0.348321 0.937375i \(-0.613248\pi\)
−0.770343 + 0.637630i \(0.779915\pi\)
\(74\) 49.5909 28.6313i 0.670147 0.386909i
\(75\) 0 0
\(76\) −202.568 −2.66537
\(77\) −47.5423 32.0051i −0.617433 0.415651i
\(78\) 0 0
\(79\) −86.5708 49.9817i −1.09583 0.632679i −0.160710 0.987002i \(-0.551378\pi\)
−0.935123 + 0.354322i \(0.884712\pi\)
\(80\) −140.943 127.946i −1.76178 1.59932i
\(81\) 0 0
\(82\) −1.76881 + 0.473951i −0.0215708 + 0.00577989i
\(83\) −95.6303 + 95.6303i −1.15217 + 1.15217i −0.166057 + 0.986116i \(0.553103\pi\)
−0.986116 + 0.166057i \(0.946897\pi\)
\(84\) 0 0
\(85\) 31.1205 + 16.0162i 0.366124 + 0.188426i
\(86\) −87.3064 + 151.219i −1.01519 + 1.75836i
\(87\) 0 0
\(88\) 164.041 + 43.9546i 1.86410 + 0.499484i
\(89\) −54.3480 31.3778i −0.610651 0.352560i 0.162569 0.986697i \(-0.448022\pi\)
−0.773220 + 0.634137i \(0.781355\pi\)
\(90\) 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
\(95\) −70.7633 + 77.9515i −0.744877 + 0.820542i
\(96\) 0 0
\(97\) 59.0158 + 59.0158i 0.608410 + 0.608410i 0.942530 0.334120i \(-0.108439\pi\)
−0.334120 + 0.942530i \(0.608439\pi\)
\(98\) 70.3578 166.591i 0.717937 1.69990i
\(99\) 0 0
\(100\) −239.390 + 23.1964i −2.39390 + 0.231964i
\(101\) −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
\(103\) −8.01775 29.9227i −0.0778422 0.290511i 0.916021 0.401131i \(-0.131383\pi\)
−0.993863 + 0.110620i \(0.964716\pi\)
\(104\) 412.352i 3.96493i
\(105\) 0 0
\(106\) 131.281 1.23850
\(107\) −18.7482 + 5.02357i −0.175217 + 0.0469492i −0.345361 0.938470i \(-0.612243\pi\)
0.170144 + 0.985419i \(0.445577\pi\)
\(108\) 0 0
\(109\) −73.5876 + 42.4858i −0.675116 + 0.389778i −0.798012 0.602641i \(-0.794115\pi\)
0.122896 + 0.992419i \(0.460782\pi\)
\(110\) 127.040 81.7691i 1.15491 0.743355i
\(111\) 0 0
\(112\) −18.3492 + 265.864i −0.163832 + 2.37379i
\(113\) 94.3686 94.3686i 0.835120 0.835120i −0.153092 0.988212i \(-0.548923\pi\)
0.988212 + 0.153092i \(0.0489231\pi\)
\(114\) 0 0
\(115\) 162.670 7.86279i 1.41452 0.0683720i
\(116\) 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
\(122\) 25.7614 96.1428i 0.211159 0.788056i
\(123\) 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 −0.985785 0.168010i \(-0.946266\pi\)
−0.168010 0.985785i \(-0.553734\pi\)
\(128\) 2.20532 + 8.23036i 0.0172290 + 0.0642997i
\(129\) 0 0
\(130\) −271.611 246.565i −2.08932 1.89665i
\(131\) 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
\(133\) 147.042 + 10.1484i 1.10558 + 0.0763041i
\(134\) 20.5399i 0.153283i
\(135\) 0 0
\(136\) 72.5996 + 125.746i 0.533820 + 0.924604i
\(137\) 28.1594 105.092i 0.205543 0.767096i −0.783741 0.621088i \(-0.786691\pi\)
0.989283 0.146008i \(-0.0466425\pi\)
\(138\) 0 0
\(139\) 188.782i 1.35814i −0.734071 0.679072i \(-0.762382\pi\)
0.734071 0.679072i \(-0.237618\pi\)
\(140\) 233.136 + 242.950i 1.66526 + 1.73535i
\(141\) 0 0
\(142\) 374.344 100.305i 2.63623 0.706375i
\(143\) 157.214 + 42.1253i 1.09940 + 0.294582i
\(144\) 0 0
\(145\) 108.054 + 23.4268i 0.745202 + 0.161564i
\(146\) −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 0.802104 0.597184i \(-0.203714\pi\)
−0.116125 + 0.993235i \(0.537047\pi\)
\(150\) 0 0
\(151\) −89.3003 154.673i −0.591393 1.02432i −0.994045 0.108969i \(-0.965245\pi\)
0.402653 0.915353i \(-0.368088\pi\)
\(152\) −421.876 + 113.041i −2.77550 + 0.743693i
\(153\) 0 0
\(154\) −200.052 68.6808i −1.29904 0.445979i
\(155\) 130.738 41.8930i 0.843470 0.270277i
\(156\) 0 0
\(157\) −15.3559 + 57.3089i −0.0978081 + 0.365025i −0.997430 0.0716444i \(-0.977175\pi\)
0.899622 + 0.436669i \(0.143842\pi\)
\(158\) −356.353 95.4844i −2.25540 0.604332i
\(159\) 0 0
\(160\) −255.780 131.638i −1.59863 0.822737i
\(161\) −149.740 171.941i −0.930059 1.06796i
\(162\) 0 0
\(163\) 32.5532 + 121.490i 0.199713 + 0.745338i 0.990996 + 0.133889i \(0.0427466\pi\)
−0.791284 + 0.611449i \(0.790587\pi\)
\(164\) −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 0.791977 0.610551i \(-0.209052\pi\)
−0.610551 + 0.791977i \(0.709052\pi\)
\(168\) 0 0
\(169\) 226.191i 1.33841i
\(170\) 126.238 + 27.3691i 0.742577 + 0.160995i
\(171\) 0 0
\(172\) −117.807 + 439.662i −0.684925 + 2.55617i
\(173\) 9.32360 + 34.7961i 0.0538936 + 0.201134i 0.987623 0.156846i \(-0.0501325\pi\)
−0.933730 + 0.357979i \(0.883466\pi\)
\(174\) 0 0
\(175\) 174.933 4.84489i 0.999617 0.0276851i
\(176\) 311.700 1.77102
\(177\) 0 0
\(178\) −223.713 59.9438i −1.25682 0.336763i
\(179\) −65.4777 + 37.8036i −0.365797 + 0.211193i −0.671621 0.740895i \(-0.734402\pi\)
0.305823 + 0.952088i \(0.401068\pi\)
\(180\) 0 0
\(181\) −182.419 −1.00784 −0.503919 0.863751i \(-0.668109\pi\)
−0.503919 + 0.863751i \(0.668109\pi\)
\(182\) −35.3608 + 512.348i −0.194290 + 2.81510i
\(183\) 0 0
\(184\) 585.112 + 337.815i 3.17996 + 1.83595i
\(185\) −3.74549 77.4888i −0.0202459 0.418858i
\(186\) 0 0
\(187\) −55.3587 + 14.8333i −0.296036 + 0.0793226i
\(188\) −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
\(193\) −217.420 58.2576i −1.12653 0.301853i −0.353007 0.935621i \(-0.614841\pi\)
−0.773523 + 0.633768i \(0.781507\pi\)
\(194\) 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 −0.908960 0.416883i \(-0.863122\pi\)
−0.416883 0.908960i \(-0.636878\pi\)
\(198\) 0 0
\(199\) 57.1020 32.9678i 0.286945 0.165668i −0.349619 0.936892i \(-0.613689\pi\)
0.636563 + 0.771225i \(0.280355\pi\)
\(200\) −485.618 + 181.899i −2.42809 + 0.909495i
\(201\) 0 0
\(202\) −101.064 101.064i −0.500317 0.500317i
\(203\) −67.9816 139.063i −0.334885 0.685041i
\(204\) 0 0
\(205\) −0.525663 + 2.42458i −0.00256421 + 0.0118272i
\(206\) −57.1639 99.0107i −0.277495 0.480635i
\(207\) 0 0
\(208\) −195.881 731.039i −0.941738 3.51461i
\(209\) 172.393i 0.824846i
\(210\) 0 0
\(211\) 408.766 1.93728 0.968639 0.248472i \(-0.0799283\pi\)
0.968639 + 0.248472i \(0.0799283\pi\)
\(212\) 330.556 88.5721i 1.55922 0.417793i
\(213\) 0 0
\(214\) −62.0357 + 35.8164i −0.289887 + 0.167366i
\(215\) 128.036 + 198.922i 0.595515 + 0.925218i
\(216\) 0 0
\(217\) −159.438 107.333i −0.734739 0.494621i
\(218\) −221.745 + 221.745i −1.01718 + 1.01718i
\(219\) 0 0
\(220\) 264.710 291.599i 1.20323 1.32545i
\(221\) 69.5781 + 120.513i 0.314833 + 0.545307i
\(222\) 0 0
\(223\) −180.123 + 180.123i −0.807725 + 0.807725i −0.984289 0.176564i \(-0.943502\pi\)
0.176564 + 0.984289i \(0.443502\pi\)
\(224\) 77.2030 + 395.264i 0.344656 + 1.76457i
\(225\) 0 0
\(226\) 246.268 426.548i 1.08968 1.88738i
\(227\) 56.8024 211.989i 0.250231 0.933874i −0.720451 0.693506i \(-0.756065\pi\)
0.970682 0.240368i \(-0.0772681\pi\)
\(228\) 0 0
\(229\) 292.008 + 168.591i 1.27515 + 0.736206i 0.975952 0.217986i \(-0.0699489\pi\)
0.299194 + 0.954192i \(0.403282\pi\)
\(230\) 572.380 183.411i 2.48861 0.797438i
\(231\) 0 0
\(232\) 324.337 + 324.337i 1.39800 + 1.39800i
\(233\) 76.1326 + 284.131i 0.326749 + 1.21945i 0.912542 + 0.408984i \(0.134117\pi\)
−0.585792 + 0.810461i \(0.699217\pi\)
\(234\) 0 0
\(235\) 6.02971 + 124.746i 0.0256584 + 0.530835i
\(236\) 86.6195 150.029i 0.367032 0.635718i
\(237\) 0 0
\(238\) −79.4218 162.465i −0.333705 0.682628i
\(239\) 191.663i 0.801937i −0.916092 0.400968i \(-0.868674\pi\)
0.916092 0.400968i \(-0.131326\pi\)
\(240\) 0 0
\(241\) −61.5720 106.646i −0.255486 0.442514i 0.709542 0.704663i \(-0.248902\pi\)
−0.965027 + 0.262149i \(0.915569\pi\)
\(242\) 51.5493 192.385i 0.213014 0.794978i
\(243\) 0 0
\(244\) 259.461i 1.06337i
\(245\) −157.060 188.035i −0.641062 0.767490i
\(246\) 0 0
\(247\) −404.318 + 108.337i −1.63692 + 0.438610i
\(248\) 550.129 + 147.407i 2.21826 + 0.594381i
\(249\) 0 0
\(250\) −170.559 + 428.636i −0.682235 + 1.71454i
\(251\) 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
\(257\) −182.539 + 48.9113i −0.710270 + 0.190316i −0.595826 0.803114i \(-0.703175\pi\)
−0.114444 + 0.993430i \(0.536509\pi\)
\(258\) 0 0
\(259\) −81.9052 + 71.3294i −0.316236 + 0.275403i
\(260\) −850.248 437.582i −3.27018 1.68301i
\(261\) 0 0
\(262\) 109.794 409.758i 0.419063 1.56396i
\(263\) −134.776 36.1131i −0.512457 0.137312i −0.00668144 0.999978i \(-0.502127\pi\)
−0.505775 + 0.862665i \(0.668793\pi\)
\(264\) 0 0
\(265\) 81.3894 158.144i 0.307130 0.596771i
\(266\) 533.875 104.276i 2.00705 0.392016i
\(267\) 0 0
\(268\) 13.8578 + 51.7180i 0.0517082 + 0.192978i
\(269\) −169.522 + 97.8736i −0.630194 + 0.363842i −0.780827 0.624747i \(-0.785202\pi\)
0.150634 + 0.988590i \(0.451869\pi\)
\(270\) 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
\(275\) −19.7410 203.729i −0.0717855 0.740834i
\(276\) 0 0
\(277\) 70.6321 263.603i 0.254989 0.951634i −0.713107 0.701055i \(-0.752713\pi\)
0.968096 0.250578i \(-0.0806208\pi\)
\(278\) −180.324 672.977i −0.648646 2.42078i
\(279\) 0 0
\(280\) 621.115 + 375.877i 2.21827 + 1.34242i
\(281\) 426.012 1.51606 0.758028 0.652222i \(-0.226163\pi\)
0.758028 + 0.652222i \(0.226163\pi\)
\(282\) 0 0
\(283\) 106.533 + 28.5453i 0.376440 + 0.100867i 0.442078 0.896977i \(-0.354241\pi\)
−0.0656376 + 0.997844i \(0.520908\pi\)
\(284\) 874.897 505.122i 3.08062 1.77860i
\(285\) 0 0
\(286\) 600.679 2.10027
\(287\) 3.12038 1.52541i 0.0108724 0.00531502i
\(288\) 0 0
\(289\) 207.846 + 120.000i 0.719190 + 0.415224i
\(290\) 407.573 19.7004i 1.40542 0.0679324i
\(291\) 0 0
\(292\) −785.628 + 210.508i −2.69051 + 0.720919i
\(293\) −224.196 + 224.196i −0.765175 + 0.765175i −0.977253 0.212078i \(-0.931977\pi\)
0.212078 + 0.977253i \(0.431977\pi\)
\(294\) 0 0
\(295\) −27.4750 85.7427i −0.0931355 0.290653i
\(296\) 160.920 278.722i 0.543649 0.941628i
\(297\) 0 0
\(298\) 420.732 + 112.735i 1.41185 + 0.378305i
\(299\) 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
\(305\) −99.8450 90.6379i −0.327361 0.297173i
\(306\) 0 0
\(307\) 348.544 + 348.544i 1.13532 + 1.13532i 0.989278 + 0.146043i \(0.0466539\pi\)
0.146043 + 0.989278i \(0.453346\pi\)
\(308\) −550.052 37.9631i −1.78588 0.123257i
\(309\) 0 0
\(310\) 426.042 274.221i 1.37433 0.884585i
\(311\) 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
\(313\) 31.2853 + 116.758i 0.0999530 + 0.373030i 0.997724 0.0674334i \(-0.0214810\pi\)
−0.897771 + 0.440463i \(0.854814\pi\)
\(314\) 218.964i 0.697339i
\(315\) 0 0
\(316\) −961.690 −3.04332
\(317\) 300.282 80.4604i 0.947262 0.253818i 0.248062 0.968744i \(-0.420206\pi\)
0.699200 + 0.714926i \(0.253540\pi\)
\(318\) 0 0
\(319\) −156.791 + 90.5232i −0.491507 + 0.283772i
\(320\) −293.424 63.6158i −0.916949 0.198799i
\(321\) 0 0
\(322\) −698.033 469.911i −2.16781 1.45935i
\(323\) 104.222 104.222i 0.322669 0.322669i
\(324\) 0 0
\(325\) −465.407 + 174.329i −1.43202 + 0.536396i
\(326\) 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 \(0.104149\pi\)
\(332\) −336.745 + 1256.75i −1.01429 + 3.78539i
\(333\) 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 0.627322 0.778760i \(-0.284151\pi\)
−0.778760 + 0.627322i \(0.784151\pi\)
\(338\) −216.056 806.333i −0.639220 2.38560i
\(339\) 0 0
\(340\) 336.323 16.2565i 0.989186 0.0478132i
\(341\) −112.401 + 194.684i −0.329621 + 0.570920i
\(342\) 0 0
\(343\) −70.4023 + 335.697i −0.205255 + 0.978709i
\(344\) 981.399i 2.85290i
\(345\) 0 0
\(346\) 66.4741 + 115.137i 0.192122 + 0.332765i
\(347\) −157.007 + 585.959i −0.452470 + 1.68864i 0.242950 + 0.970039i \(0.421885\pi\)
−0.695420 + 0.718603i \(0.744782\pi\)
\(348\) 0 0
\(349\) 82.1983i 0.235525i −0.993042 0.117763i \(-0.962428\pi\)
0.993042 0.117763i \(-0.0375722\pi\)
\(350\) 618.979 184.366i 1.76851 0.526760i
\(351\) 0 0
\(352\) 454.995 121.916i 1.29260 0.346351i
\(353\) 141.830 + 38.0031i 0.401783 + 0.107658i 0.454051 0.890976i \(-0.349978\pi\)
−0.0522678 + 0.998633i \(0.516645\pi\)
\(354\) 0 0
\(355\) 111.249 513.130i 0.313379 1.44544i
\(356\) −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 0.235955 0.971764i \(-0.424178\pi\)
−0.723595 + 0.690225i \(0.757512\pi\)
\(360\) 0 0
\(361\) 41.1776 + 71.3218i 0.114065 + 0.197567i
\(362\) −650.292 + 174.245i −1.79639 + 0.481340i
\(363\) 0 0
\(364\) 256.633 + 1313.91i 0.705036 + 3.60965i
\(365\) −193.437 + 375.860i −0.529965 + 1.02975i
\(366\) 0 0
\(367\) −130.259 + 486.132i −0.354928 + 1.32461i 0.525647 + 0.850703i \(0.323823\pi\)
−0.880575 + 0.473907i \(0.842843\pi\)
\(368\) 1197.79 + 320.947i 3.25487 + 0.872139i
\(369\) 0 0
\(370\) −87.3689 272.657i −0.236132 0.736911i
\(371\) −244.385 + 47.7332i −0.658719 + 0.128661i
\(372\) 0 0
\(373\) −47.8471 178.568i −0.128277 0.478735i 0.871659 0.490113i \(-0.163045\pi\)
−0.999935 + 0.0113788i \(0.996378\pi\)
\(374\) −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 \(-0.847975\pi\)
0.888100 0.459649i \(-0.152025\pi\)
\(380\) −214.603 + 989.842i −0.564745 + 2.60485i
\(381\) 0 0
\(382\) 14.6393 54.6344i 0.0383226 0.143022i
\(383\) 117.020 + 436.725i 0.305536 + 1.14028i 0.932483 + 0.361214i \(0.117638\pi\)
−0.626947 + 0.779062i \(0.715696\pi\)
\(384\) 0 0
\(385\) −206.759 + 198.408i −0.537037 + 0.515345i
\(386\) −830.714 −2.15211
\(387\) 0 0
\(388\) 775.571 + 207.814i 1.99889 + 0.535602i
\(389\) −565.646 + 326.576i −1.45410 + 0.839527i −0.998711 0.0507630i \(-0.983835\pi\)
−0.455393 + 0.890290i \(0.650501\pi\)
\(390\) 0 0
\(391\) −228.004 −0.583131
\(392\) −125.693 1008.59i −0.320646 2.57293i
\(393\) 0 0
\(394\) −1180.59 681.614i −2.99642 1.72999i
\(395\) −335.949 + 370.075i −0.850503 + 0.936898i
\(396\) 0 0
\(397\) −63.7193 + 17.0735i −0.160502 + 0.0430064i −0.338175 0.941083i \(-0.609810\pi\)
0.177673 + 0.984090i \(0.443143\pi\)
\(398\) 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
\(403\) 527.233 + 141.272i 1.30827 + 0.350550i
\(404\) −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 −0.155453 0.987843i \(-0.549684\pi\)
0.777771 + 0.628548i \(0.216350\pi\)
\(410\) 0.442048 + 9.14535i 0.00107817 + 0.0223057i
\(411\) 0 0
\(412\) −210.735 210.735i −0.511492 0.511492i
\(413\) −70.3927 + 104.566i −0.170442 + 0.253185i
\(414\) 0 0
\(415\) 365.983 + 568.607i 0.881887 + 1.37014i
\(416\) −571.865 990.499i −1.37467 2.38101i
\(417\) 0 0
\(418\) −164.669 614.552i −0.393944 1.47022i
\(419\) 234.794i 0.560368i 0.959946 + 0.280184i \(0.0903955\pi\)
−0.959946 + 0.280184i \(0.909605\pi\)
\(420\) 0 0
\(421\) −124.297 −0.295242 −0.147621 0.989044i \(-0.547162\pi\)
−0.147621 + 0.989044i \(0.547162\pi\)
\(422\) 1457.18 390.451i 3.45304 0.925238i
\(423\) 0 0
\(424\) 639.001 368.928i 1.50708 0.870112i
\(425\) 111.232 135.102i 0.261723 0.317887i
\(426\) 0 0
\(427\) −12.9987 + 188.341i −0.0304420 + 0.441079i
\(428\) −132.037 + 132.037i −0.308498 + 0.308498i
\(429\) 0 0
\(430\) 646.435 + 586.824i 1.50334 + 1.36471i
\(431\) −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 −0.321109 + 0.947042i \(0.604056\pi\)
−0.947042 + 0.321109i \(0.895944\pi\)
\(434\) −670.895 230.328i −1.54584 0.530711i
\(435\) 0 0
\(436\) −408.732 + 707.944i −0.937459 + 1.62373i
\(437\) 177.507 662.466i 0.406195 1.51594i
\(438\) 0 0
\(439\) −83.0573 47.9532i −0.189197 0.109233i 0.402410 0.915460i \(-0.368173\pi\)
−0.591606 + 0.806227i \(0.701506\pi\)
\(440\) 388.570 755.015i 0.883114 1.71594i
\(441\) 0 0
\(442\) 363.148 + 363.148i 0.821601 + 0.821601i
\(443\) −25.9009 96.6633i −0.0584670 0.218202i 0.930511 0.366264i \(-0.119363\pi\)
−0.988978 + 0.148062i \(0.952696\pi\)
\(444\) 0 0
\(445\) −210.904 + 232.328i −0.473941 + 0.522085i
\(446\) −470.055 + 814.159i −1.05394 + 1.82547i
\(447\) 0 0
\(448\) 184.605 + 377.629i 0.412066 + 0.842922i
\(449\) 344.308i 0.766832i −0.923576 0.383416i \(-0.874748\pi\)
0.923576 0.383416i \(-0.125252\pi\)
\(450\) 0 0
\(451\) −2.03121 3.51816i −0.00450379 0.00780079i
\(452\) 332.302 1240.17i 0.735181 2.74373i
\(453\) 0 0
\(454\) 809.964i 1.78406i
\(455\) 595.265 + 360.234i 1.30828 + 0.791722i
\(456\) 0 0
\(457\) 83.2667 22.3113i 0.182203 0.0488211i −0.166564 0.986031i \(-0.553267\pi\)
0.348767 + 0.937210i \(0.386601\pi\)
\(458\) 1202.00 + 322.074i 2.62445 + 0.703219i
\(459\) 0 0
\(460\) 1317.47 847.986i 2.86406 1.84345i
\(461\) 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 −0.573556 0.819166i \(-0.694437\pi\)
0.819166 + 0.573556i \(0.194437\pi\)
\(464\) 729.073 + 420.930i 1.57128 + 0.907177i
\(465\) 0 0
\(466\) 542.800 + 940.157i 1.16481 + 2.01750i
\(467\) 48.7023 13.0497i 0.104288 0.0279438i −0.206298 0.978489i \(-0.566142\pi\)
0.310585 + 0.950545i \(0.399475\pi\)
\(468\) 0 0
\(469\) −7.46824 38.2359i −0.0159238 0.0815265i
\(470\) 140.652 + 438.940i 0.299259 + 0.933914i
\(471\) 0 0
\(472\) 96.6746 360.795i 0.204819 0.764395i
\(473\) −374.169 100.258i −0.791055 0.211963i
\(474\) 0 0
\(475\) 305.941 + 428.366i 0.644086 + 0.901823i
\(476\) −309.590 355.492i −0.650398 0.746831i
\(477\) 0 0
\(478\) −183.075 683.246i −0.383003 1.42938i
\(479\) 152.207 87.8766i 0.317760 0.183459i −0.332634 0.943056i \(-0.607937\pi\)
0.650393 + 0.759597i \(0.274604\pi\)
\(480\) 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
\(485\) 350.901 225.857i 0.723508 0.465685i
\(486\) 0 0
\(487\) 65.7419 245.352i 0.134994 0.503803i −0.865004 0.501765i \(-0.832684\pi\)
0.999998 0.00203876i \(-0.000648959\pi\)
\(488\) −144.790 540.364i −0.296701 1.10730i
\(489\) 0 0
\(490\) −739.503 520.290i −1.50919 1.06182i
\(491\) −275.796 −0.561704 −0.280852 0.959751i \(-0.590617\pi\)
−0.280852 + 0.959751i \(0.590617\pi\)
\(492\) 0 0
\(493\) −149.517 40.0629i −0.303279 0.0812634i
\(494\) −1337.84 + 772.405i −2.70819 + 1.56357i
\(495\) 0 0
\(496\) 1045.32 2.10750
\(497\) −660.386 + 322.832i −1.32875 + 0.649562i
\(498\) 0 0
\(499\) 520.379 + 300.441i 1.04284 + 0.602086i 0.920637 0.390419i \(-0.127670\pi\)
0.122206 + 0.992505i \(0.461003\pi\)
\(500\) −140.264 + 1194.35i −0.280528 + 2.38869i
\(501\) 0 0
\(502\) 75.3423 20.1879i 0.150084 0.0402150i
\(503\) 513.924 513.924i 1.02172 1.02172i 0.0219593 0.999759i \(-0.493010\pi\)
0.999759 0.0219593i \(-0.00699042\pi\)
\(504\) 0 0
\(505\) −184.401 + 59.0884i −0.365150 + 0.117007i
\(506\) −492.099 + 852.340i −0.972527 + 1.68447i
\(507\) 0 0
\(508\) −1925.69 515.986i −3.79072 1.01572i
\(509\) −406.687 234.801i −0.798993 0.461299i 0.0441259 0.999026i \(-0.485950\pi\)
−0.843119 + 0.537727i \(0.819283\pi\)
\(510\) 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
\(515\) −154.710 + 7.47806i −0.300409 + 0.0145205i
\(516\) 0 0
\(517\) −144.608 144.608i −0.279706 0.279706i
\(518\) −223.845 + 332.513i −0.432133 + 0.641916i
\(519\) 0 0
\(520\) −2014.95 436.852i −3.87490 0.840099i
\(521\) −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
\(523\) 217.012 + 809.900i 0.414937 + 1.54857i 0.784962 + 0.619543i \(0.212682\pi\)
−0.370026 + 0.929022i \(0.620651\pi\)
\(524\) 1105.82i 2.11034i
\(525\) 0 0
\(526\) −514.949 −0.978991
\(527\) −185.652 + 49.7452i −0.352280 + 0.0943932i
\(528\) 0 0
\(529\) −460.666 + 265.966i −0.870824 + 0.502770i
\(530\) 139.081 641.501i 0.262417 1.21038i
\(531\) 0 0
\(532\) 1273.90 622.753i 2.39456 1.17059i
\(533\) −6.97477 + 6.97477i −0.0130859 + 0.0130859i
\(534\) 0 0
\(535\) 4.68542 + 96.9347i 0.00875780 + 0.181186i
\(536\) 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 \(0.303833\pi\)
\(542\) 236.819 883.819i 0.436935 1.63066i
\(543\) 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 0.966964 0.254913i \(-0.0820469\pi\)
−0.254913 + 0.966964i \(0.582047\pi\)
\(548\) −270.905 1011.03i −0.494353 1.84495i
\(549\) 0 0
\(550\) −264.975 707.405i −0.481772 1.28619i
\(551\) 232.805 403.230i 0.422514 0.731815i
\(552\) 0 0
\(553\) 698.083 + 48.1797i 1.26236 + 0.0871243i
\(554\) 1007.17i 1.81799i
\(555\) 0 0
\(556\) −908.083 1572.85i −1.63324 2.82886i
\(557\) −254.761 + 950.780i −0.457380 + 1.70697i 0.223615 + 0.974678i \(0.428214\pi\)
−0.680995 + 0.732288i \(0.738453\pi\)
\(558\) 0 0
\(559\) 940.555i 1.68257i
\(560\) 1279.70 + 371.323i 2.28518 + 0.663077i
\(561\) 0 0
\(562\) 1518.66 406.924i 2.70224 0.724064i
\(563\) −831.358 222.762i −1.47666 0.395669i −0.571450 0.820637i \(-0.693619\pi\)
−0.905208 + 0.424968i \(0.860285\pi\)
\(564\) 0 0
\(565\) −361.154 561.105i −0.639211 0.993106i
\(566\) 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 0.770646 0.637263i \(-0.219934\pi\)
−0.166563 + 0.986031i \(0.553267\pi\)
\(570\) 0 0
\(571\) 402.947 + 697.924i 0.705686 + 1.22228i 0.966443 + 0.256880i \(0.0826944\pi\)
−0.260757 + 0.965404i \(0.583972\pi\)
\(572\) 1512.46 405.263i 2.64417 0.708502i
\(573\) 0 0
\(574\) 9.66658 8.41840i 0.0168407 0.0146662i
\(575\) 133.913 803.212i 0.232893 1.39689i
\(576\) 0 0
\(577\) 268.157 1000.77i 0.464743 1.73445i −0.192996 0.981200i \(-0.561820\pi\)
0.657739 0.753246i \(-0.271513\pi\)
\(578\) 855.559 + 229.246i 1.48021 + 0.396620i
\(579\) 0 0
\(580\) 1012.95 324.584i 1.74646 0.559627i
\(581\) 307.402 895.394i 0.529092 1.54113i
\(582\) 0 0
\(583\) 75.3782 + 281.315i 0.129294 + 0.482530i
\(584\) −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 0.0740817 0.997252i \(-0.476397\pi\)
−0.997252 + 0.0740817i \(0.976397\pi\)
\(588\) 0 0
\(589\) 578.138i 0.981559i
\(590\) −179.845 279.414i −0.304821 0.473584i
\(591\) 0 0
\(592\) 152.885 570.575i 0.258252 0.963810i
\(593\) 205.761 + 767.912i 0.346984 + 1.29496i 0.890277 + 0.455419i \(0.150510\pi\)
−0.543293 + 0.839543i \(0.682823\pi\)
\(594\) 0 0
\(595\) −244.949 5.04902i −0.411678 0.00848576i
\(596\) 1135.43 1.90509
\(597\) 0 0
\(598\) 2308.27 + 618.499i 3.85998 + 1.03428i
\(599\) 357.782 206.565i 0.597299 0.344850i −0.170680 0.985327i \(-0.554596\pi\)
0.767978 + 0.640476i \(0.221263\pi\)
\(600\) 0 0
\(601\) −439.370 −0.731066 −0.365533 0.930798i \(-0.619113\pi\)
−0.365533 + 0.930798i \(0.619113\pi\)
\(602\) 84.1588 1219.39i 0.139799 2.02556i
\(603\) 0 0
\(604\) −1488.02 859.107i −2.46360 1.42236i
\(605\) −199.793 181.369i −0.330236 0.299783i
\(606\) 0 0
\(607\) −212.262 + 56.8754i −0.349690 + 0.0936991i −0.429388 0.903120i \(-0.641271\pi\)
0.0796986 + 0.996819i \(0.474604\pi\)
\(608\) −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
\(613\) −945.946 253.466i −1.54314 0.413484i −0.615863 0.787853i \(-0.711192\pi\)
−0.927280 + 0.374370i \(0.877859\pi\)
\(614\) 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 0.751276 0.659988i \(-0.229439\pi\)
−0.659988 + 0.751276i \(0.729439\pi\)
\(618\) 0 0
\(619\) −451.442 + 260.640i −0.729309 + 0.421067i −0.818169 0.574977i \(-0.805011\pi\)
0.0888604 + 0.996044i \(0.471677\pi\)
\(620\) 887.732 977.910i 1.43183 1.57727i
\(621\) 0 0
\(622\) 38.5359 + 38.5359i 0.0619548 + 0.0619548i
\(623\) 438.247 + 30.2466i 0.703446 + 0.0485499i
\(624\) 0 0
\(625\) 410.606 + 471.198i 0.656969 + 0.753917i
\(626\) 223.054 + 386.340i 0.356316 + 0.617157i
\(627\) 0 0
\(628\) 147.730 + 551.336i 0.235239 + 0.877924i
\(629\) 108.611i 0.172673i
\(630\) 0 0
\(631\) 606.021 0.960413 0.480207 0.877155i \(-0.340562\pi\)
0.480207 + 0.877155i \(0.340562\pi\)
\(632\) −2002.85 + 536.663i −3.16907 + 0.849151i
\(633\) 0 0
\(634\) 993.601 573.656i 1.56719 0.904819i
\(635\) −871.263 + 560.787i −1.37207 + 0.883129i
\(636\) 0 0
\(637\) −120.462 966.614i −0.189108 1.51745i
\(638\) −472.466 + 472.466i −0.740542 + 0.740542i
\(639\) 0 0
\(640\) 42.5538 2.05687i 0.0664903 0.00321387i
\(641\) −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 −0.207704 0.978192i \(-0.566599\pi\)
0.978192 + 0.207704i \(0.0665992\pi\)
\(644\) −2074.63 712.253i −3.22148 1.10598i
\(645\) 0 0
\(646\) 271.982 471.087i 0.421025 0.729237i
\(647\) −200.190 + 747.117i −0.309412 + 1.15474i 0.619669 + 0.784864i \(0.287267\pi\)
−0.929081 + 0.369877i \(0.879400\pi\)
\(648\) 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
\(653\) 280.108 + 1045.38i 0.428956 + 1.60089i 0.755129 + 0.655576i \(0.227574\pi\)
−0.326172 + 0.945310i \(0.605759\pi\)
\(654\) 0 0
\(655\) −425.537 386.296i −0.649675 0.589765i
\(656\) −9.44507 + 16.3593i −0.0143980 + 0.0249380i
\(657\) 0 0
\(658\) 360.359 535.299i 0.547658 0.813524i
\(659\) 388.022i 0.588805i 0.955682 + 0.294402i \(0.0951206\pi\)
−0.955682 + 0.294402i \(0.904879\pi\)
\(660\) 0 0
\(661\) −309.552 536.160i −0.468308 0.811134i 0.531036 0.847350i \(-0.321803\pi\)
−0.999344 + 0.0362155i \(0.988470\pi\)
\(662\) 123.398 460.526i 0.186401 0.695658i
\(663\) 0 0
\(664\) 2805.28i 4.22481i
\(665\) 205.369 707.767i 0.308825 1.06431i
\(666\) 0 0
\(667\) −695.719 + 186.417i −1.04306 + 0.279486i
\(668\) 398.172 + 106.690i 0.596066 + 0.159715i
\(669\) 0 0
\(670\) 100.368 + 21.7603i 0.149803 + 0.0324781i
\(671\) 220.811 0.329078
\(672\) 0 0
\(673\) 185.772 185.772i 0.276036 0.276036i −0.555488 0.831524i \(-0.687469\pi\)
0.831524 + 0.555488i \(0.187469\pi\)
\(674\) −230.678 133.182i −0.342253 0.197600i
\(675\) 0 0
\(676\) −1088.03 1884.52i −1.60951 2.78775i
\(677\) 713.136 191.084i 1.05338 0.282252i 0.309731 0.950824i \(-0.399761\pi\)
0.743647 + 0.668573i \(0.233094\pi\)
\(678\) 0 0
\(679\) −552.569 189.705i −0.813798 0.279389i
\(680\) 691.368 221.539i 1.01672 0.325792i
\(681\) 0 0
\(682\) −214.729 + 801.379i −0.314852 + 1.17504i
\(683\) −504.707 135.236i −0.738957 0.198003i −0.130342 0.991469i \(-0.541608\pi\)
−0.608614 + 0.793466i \(0.708274\pi\)
\(684\) 0 0
\(685\) −483.698 248.936i −0.706129 0.363411i
\(686\) 69.6833 + 1263.95i 0.101579 + 1.84250i
\(687\) 0 0
\(688\) 466.198 + 1739.88i 0.677614 + 2.52889i
\(689\) 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
\(695\) −922.479 199.998i −1.32731 0.287768i
\(696\) 0 0
\(697\) 0.898953 3.35494i 0.00128975 0.00481340i
\(698\) −78.5153 293.023i −0.112486 0.419804i
\(699\) 0 0
\(700\) 1434.15 881.830i 2.04879 1.25976i
\(701\) −100.279 −0.143052 −0.0715259 0.997439i \(-0.522787\pi\)
−0.0715259 + 0.997439i \(0.522787\pi\)
\(702\) 0 0
\(703\) −315.570 84.5567i −0.448890 0.120280i
\(704\) 425.768 245.817i 0.604784 0.349172i
\(705\) 0 0
\(706\) 541.899 0.767562
\(707\) 224.882 + 151.389i 0.318079 + 0.214128i
\(708\) 0 0
\(709\) −339.531 196.029i −0.478888 0.276486i 0.241065 0.970509i \(-0.422503\pi\)
−0.719953 + 0.694023i \(0.755837\pi\)
\(710\) −93.5535 1935.49i −0.131766 2.72604i
\(711\) 0 0
\(712\) −1257.36 + 336.910i −1.76596 + 0.473188i
\(713\) −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
\(718\) −720.614 193.088i −1.00364 0.268925i
\(719\) 1001.31 + 578.104i 1.39264 + 0.804039i 0.993607 0.112898i \(-0.0360134\pi\)
0.399031 + 0.916938i \(0.369347\pi\)
\(720\) 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
\(725\) 228.949 503.186i 0.315791 0.694050i
\(726\) 0 0
\(727\) −27.8958 27.8958i −0.0383712 0.0383712i 0.687661 0.726032i \(-0.258638\pi\)
−0.726032 + 0.687661i \(0.758638\pi\)
\(728\) 1267.69 + 2593.19i 1.74133 + 3.56208i
\(729\) 0 0
\(730\) −330.552 + 1524.65i −0.452811 + 2.08856i
\(731\) −165.596 286.821i −0.226534 0.392368i
\(732\) 0 0
\(733\) −209.185 780.690i −0.285382 1.06506i −0.948559 0.316599i \(-0.897459\pi\)
0.663177 0.748463i \(-0.269208\pi\)
\(734\) 1857.40i 2.53052i
\(735\) 0 0
\(736\) 1873.97 2.54616
\(737\) −44.0140 + 11.7935i −0.0597205 + 0.0160021i
\(738\) 0 0
\(739\) 452.698 261.365i 0.612582 0.353674i −0.161393 0.986890i \(-0.551599\pi\)
0.773975 + 0.633216i \(0.218265\pi\)
\(740\) −403.943 627.584i −0.545869 0.848086i
\(741\) 0 0
\(742\) −825.597 + 403.596i −1.11266 + 0.543930i
\(743\) 34.1788 34.1788i 0.0460011 0.0460011i −0.683732 0.729733i \(-0.739644\pi\)
0.729733 + 0.683732i \(0.239644\pi\)
\(744\) 0 0
\(745\) 396.642 436.934i 0.532405 0.586488i
\(746\) −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 \(0.0109964\pi\)
\(752\) −246.124 + 918.547i −0.327292 + 1.22147i
\(753\) 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 0.918390 0.395677i \(-0.129490\pi\)
−0.395677 + 0.918390i \(0.629490\pi\)
\(758\) −332.803 1242.04i −0.439054 1.63857i
\(759\) 0 0
\(760\) 105.432 + 2181.24i 0.138727 + 2.87006i
\(761\) 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
\(763\) 332.162 493.414i 0.435337 0.646676i
\(764\) 147.442i 0.192987i
\(765\) 0 0
\(766\) 834.315 + 1445.08i 1.08918 + 1.88652i
\(767\) 92.6512 345.779i 0.120797 0.450820i
\(768\) 0 0
\(769\) 907.238i 1.17976i −0.807490 0.589882i \(-0.799174\pi\)
0.807490 0.589882i \(-0.200826\pi\)
\(770\) −547.544 + 904.786i −0.711096 + 1.17505i
\(771\) 0 0
\(772\) −2091.68 + 560.463i −2.70942 + 0.725988i
\(773\) 602.366 + 161.404i 0.779258 + 0.208802i 0.626458 0.779456i \(-0.284504\pi\)
0.152800 + 0.988257i \(0.451171\pi\)
\(774\) 0 0
\(775\) −66.2036 683.229i −0.0854240 0.881586i