Properties

Label 99.3.l.a.26.6
Level $99$
Weight $3$
Character 99.26
Analytic conductor $2.698$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 99.l (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.69755461717\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 26.6
Character \(\chi\) \(=\) 99.26
Dual form 99.3.l.a.80.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.15480 - 1.58945i) q^{2} +(0.0432885 + 0.133228i) q^{4} +(5.65603 + 7.78486i) q^{5} +(-1.61633 - 4.97456i) q^{7} +(7.73579 + 2.51351i) q^{8} +O(q^{10})\) \(q+(1.15480 - 1.58945i) q^{2} +(0.0432885 + 0.133228i) q^{4} +(5.65603 + 7.78486i) q^{5} +(-1.61633 - 4.97456i) q^{7} +(7.73579 + 2.51351i) q^{8} +18.9052 q^{10} +(-9.06319 - 6.23366i) q^{11} +(-13.9350 - 10.1244i) q^{13} +(-9.77335 - 3.17555i) q^{14} +(12.4751 - 9.06367i) q^{16} +(4.53667 + 6.24419i) q^{17} +(4.33521 - 13.3424i) q^{19} +(-0.792322 + 1.09054i) q^{20} +(-20.3743 + 7.20684i) q^{22} -5.68512i q^{23} +(-20.8879 + 64.2864i) q^{25} +(-32.1844 + 10.4574i) q^{26} +(0.592783 - 0.430682i) q^{28} +(22.9057 - 7.44253i) q^{29} +(-12.1481 - 8.82612i) q^{31} +2.24031i q^{32} +15.1638 q^{34} +(29.5842 - 40.7192i) q^{35} +(-2.36563 - 7.28065i) q^{37} +(-16.2007 - 22.2984i) q^{38} +(24.1865 + 74.4385i) q^{40} +(-17.3048 - 5.62267i) q^{41} -53.6955 q^{43} +(0.438168 - 1.47732i) q^{44} +(-9.03621 - 6.56519i) q^{46} +(-36.9117 - 11.9934i) q^{47} +(17.5081 - 12.7204i) q^{49} +(78.0585 + 107.438i) q^{50} +(0.745630 - 2.29481i) q^{52} +(-47.9715 + 66.0271i) q^{53} +(-2.73355 - 105.813i) q^{55} -42.5448i q^{56} +(14.6221 - 45.0022i) q^{58} +(0.000412921 - 0.000134166i) q^{59} +(-3.86696 + 2.80951i) q^{61} +(-28.0573 + 9.11638i) q^{62} +(53.4611 + 38.8418i) q^{64} -165.746i q^{65} +111.796 q^{67} +(-0.635517 + 0.874715i) q^{68} +(-30.5571 - 94.0452i) q^{70} +(58.5632 + 80.6053i) q^{71} +(-10.5980 - 32.6171i) q^{73} +(-14.3041 - 4.64767i) q^{74} +1.96525 q^{76} +(-16.3606 + 55.1611i) q^{77} +(49.9398 + 36.2834i) q^{79} +(141.119 + 45.8523i) q^{80} +(-28.9205 + 21.0120i) q^{82} +(38.3421 + 52.7733i) q^{83} +(-22.9506 + 70.6347i) q^{85} +(-62.0076 + 85.3462i) q^{86} +(-54.4426 - 71.0027i) q^{88} -92.5976i q^{89} +(-27.8408 + 85.6851i) q^{91} +(0.757419 - 0.246100i) q^{92} +(-61.6886 + 44.8194i) q^{94} +(128.389 - 41.7160i) q^{95} +(42.4116 + 30.8138i) q^{97} -42.5178i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 16 q^{4} - 16 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 16 q^{4} - 16 q^{7} + 48 q^{10} + 8 q^{13} + 96 q^{16} - 40 q^{19} - 60 q^{22} - 188 q^{25} - 348 q^{28} - 164 q^{31} + 296 q^{34} - 36 q^{37} + 48 q^{40} + 544 q^{43} + 296 q^{46} + 196 q^{49} - 640 q^{52} - 440 q^{55} - 208 q^{58} - 432 q^{61} - 328 q^{64} + 48 q^{67} + 112 q^{70} + 712 q^{73} + 2104 q^{76} + 432 q^{79} + 676 q^{82} - 68 q^{85} - 176 q^{88} + 64 q^{91} - 1360 q^{94} + 132 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\)
\(\chi(n)\) \(e\left(\frac{1}{5}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.15480 1.58945i 0.577401 0.794724i −0.416006 0.909362i \(-0.636571\pi\)
0.993407 + 0.114637i \(0.0365706\pi\)
\(3\) 0 0
\(4\) 0.0432885 + 0.133228i 0.0108221 + 0.0333071i
\(5\) 5.65603 + 7.78486i 1.13121 + 1.55697i 0.785758 + 0.618533i \(0.212273\pi\)
0.345448 + 0.938438i \(0.387727\pi\)
\(6\) 0 0
\(7\) −1.61633 4.97456i −0.230905 0.710651i −0.997638 0.0686861i \(-0.978119\pi\)
0.766734 0.641965i \(-0.221881\pi\)
\(8\) 7.73579 + 2.51351i 0.966973 + 0.314189i
\(9\) 0 0
\(10\) 18.9052 1.89052
\(11\) −9.06319 6.23366i −0.823927 0.566696i
\(12\) 0 0
\(13\) −13.9350 10.1244i −1.07193 0.778800i −0.0956692 0.995413i \(-0.530499\pi\)
−0.976258 + 0.216613i \(0.930499\pi\)
\(14\) −9.77335 3.17555i −0.698097 0.226825i
\(15\) 0 0
\(16\) 12.4751 9.06367i 0.779692 0.566479i
\(17\) 4.53667 + 6.24419i 0.266863 + 0.367306i 0.921328 0.388787i \(-0.127106\pi\)
−0.654464 + 0.756093i \(0.727106\pi\)
\(18\) 0 0
\(19\) 4.33521 13.3424i 0.228169 0.702231i −0.769786 0.638302i \(-0.779637\pi\)
0.997954 0.0639288i \(-0.0203630\pi\)
\(20\) −0.792322 + 1.09054i −0.0396161 + 0.0545269i
\(21\) 0 0
\(22\) −20.3743 + 7.20684i −0.926104 + 0.327584i
\(23\) 5.68512i 0.247179i −0.992333 0.123590i \(-0.960559\pi\)
0.992333 0.123590i \(-0.0394407\pi\)
\(24\) 0 0
\(25\) −20.8879 + 64.2864i −0.835516 + 2.57145i
\(26\) −32.1844 + 10.4574i −1.23786 + 0.402206i
\(27\) 0 0
\(28\) 0.592783 0.430682i 0.0211708 0.0153815i
\(29\) 22.9057 7.44253i 0.789853 0.256639i 0.113812 0.993502i \(-0.463694\pi\)
0.676042 + 0.736863i \(0.263694\pi\)
\(30\) 0 0
\(31\) −12.1481 8.82612i −0.391874 0.284713i 0.374349 0.927288i \(-0.377866\pi\)
−0.766223 + 0.642575i \(0.777866\pi\)
\(32\) 2.24031i 0.0700097i
\(33\) 0 0
\(34\) 15.1638 0.445994
\(35\) 29.5842 40.7192i 0.845263 1.16340i
\(36\) 0 0
\(37\) −2.36563 7.28065i −0.0639359 0.196774i 0.913986 0.405746i \(-0.132988\pi\)
−0.977922 + 0.208972i \(0.932988\pi\)
\(38\) −16.2007 22.2984i −0.426335 0.586800i
\(39\) 0 0
\(40\) 24.1865 + 74.4385i 0.604663 + 1.86096i
\(41\) −17.3048 5.62267i −0.422068 0.137138i 0.0902795 0.995916i \(-0.471224\pi\)
−0.512347 + 0.858778i \(0.671224\pi\)
\(42\) 0 0
\(43\) −53.6955 −1.24873 −0.624366 0.781132i \(-0.714642\pi\)
−0.624366 + 0.781132i \(0.714642\pi\)
\(44\) 0.438168 1.47732i 0.00995836 0.0335754i
\(45\) 0 0
\(46\) −9.03621 6.56519i −0.196439 0.142722i
\(47\) −36.9117 11.9934i −0.785356 0.255178i −0.111231 0.993795i \(-0.535479\pi\)
−0.674125 + 0.738617i \(0.735479\pi\)
\(48\) 0 0
\(49\) 17.5081 12.7204i 0.357309 0.259600i
\(50\) 78.0585 + 107.438i 1.56117 + 2.14877i
\(51\) 0 0
\(52\) 0.745630 2.29481i 0.0143390 0.0441310i
\(53\) −47.9715 + 66.0271i −0.905123 + 1.24580i 0.0636816 + 0.997970i \(0.479716\pi\)
−0.968805 + 0.247825i \(0.920284\pi\)
\(54\) 0 0
\(55\) −2.73355 105.813i −0.0497010 1.92388i
\(56\) 42.5448i 0.759728i
\(57\) 0 0
\(58\) 14.6221 45.0022i 0.252105 0.775899i
\(59\) 0.000412921 0 0.000134166i 6.99867e−6 0 2.27400e-6i −0.309013 0.951058i \(-0.599999\pi\)
0.309020 + 0.951055i \(0.399999\pi\)
\(60\) 0 0
\(61\) −3.86696 + 2.80951i −0.0633928 + 0.0460576i −0.619030 0.785367i \(-0.712474\pi\)
0.555638 + 0.831425i \(0.312474\pi\)
\(62\) −28.0573 + 9.11638i −0.452537 + 0.147038i
\(63\) 0 0
\(64\) 53.4611 + 38.8418i 0.835330 + 0.606903i
\(65\) 165.746i 2.54994i
\(66\) 0 0
\(67\) 111.796 1.66860 0.834298 0.551313i \(-0.185873\pi\)
0.834298 + 0.551313i \(0.185873\pi\)
\(68\) −0.635517 + 0.874715i −0.00934585 + 0.0128635i
\(69\) 0 0
\(70\) −30.5571 94.0452i −0.436530 1.34350i
\(71\) 58.5632 + 80.6053i 0.824834 + 1.13529i 0.988863 + 0.148831i \(0.0475509\pi\)
−0.164029 + 0.986456i \(0.552449\pi\)
\(72\) 0 0
\(73\) −10.5980 32.6171i −0.145177 0.446810i 0.851856 0.523775i \(-0.175477\pi\)
−0.997034 + 0.0769653i \(0.975477\pi\)
\(74\) −14.3041 4.64767i −0.193298 0.0628063i
\(75\) 0 0
\(76\) 1.96525 0.0258585
\(77\) −16.3606 + 55.1611i −0.212475 + 0.716377i
\(78\) 0 0
\(79\) 49.9398 + 36.2834i 0.632150 + 0.459284i 0.857144 0.515076i \(-0.172236\pi\)
−0.224995 + 0.974360i \(0.572236\pi\)
\(80\) 141.119 + 45.8523i 1.76398 + 0.573153i
\(81\) 0 0
\(82\) −28.9205 + 21.0120i −0.352690 + 0.256244i
\(83\) 38.3421 + 52.7733i 0.461953 + 0.635823i 0.974912 0.222589i \(-0.0714509\pi\)
−0.512960 + 0.858413i \(0.671451\pi\)
\(84\) 0 0
\(85\) −22.9506 + 70.6347i −0.270007 + 0.830996i
\(86\) −62.0076 + 85.3462i −0.721019 + 0.992397i
\(87\) 0 0
\(88\) −54.4426 71.0027i −0.618666 0.806849i
\(89\) 92.5976i 1.04042i −0.854038 0.520211i \(-0.825853\pi\)
0.854038 0.520211i \(-0.174147\pi\)
\(90\) 0 0
\(91\) −27.8408 + 85.6851i −0.305943 + 0.941595i
\(92\) 0.757419 0.246100i 0.00823282 0.00267500i
\(93\) 0 0
\(94\) −61.6886 + 44.8194i −0.656261 + 0.476802i
\(95\) 128.389 41.7160i 1.35146 0.439116i
\(96\) 0 0
\(97\) 42.4116 + 30.8138i 0.437233 + 0.317668i 0.784534 0.620085i \(-0.212902\pi\)
−0.347302 + 0.937753i \(0.612902\pi\)
\(98\) 42.5178i 0.433855i
\(99\) 0 0
\(100\) −9.46897 −0.0946897
\(101\) −34.6336 + 47.6691i −0.342907 + 0.471971i −0.945288 0.326238i \(-0.894219\pi\)
0.602381 + 0.798209i \(0.294219\pi\)
\(102\) 0 0
\(103\) −29.8866 91.9816i −0.290161 0.893025i −0.984804 0.173670i \(-0.944437\pi\)
0.694642 0.719355i \(-0.255563\pi\)
\(104\) −82.3508 113.346i −0.791834 1.08987i
\(105\) 0 0
\(106\) 49.5491 + 152.497i 0.467445 + 1.43865i
\(107\) −17.4915 5.68333i −0.163472 0.0531152i 0.226138 0.974095i \(-0.427390\pi\)
−0.389610 + 0.920980i \(0.627390\pi\)
\(108\) 0 0
\(109\) 50.6495 0.464674 0.232337 0.972635i \(-0.425363\pi\)
0.232337 + 0.972635i \(0.425363\pi\)
\(110\) −171.342 117.849i −1.55765 1.07135i
\(111\) 0 0
\(112\) −65.2516 47.4081i −0.582604 0.423286i
\(113\) −9.35427 3.03939i −0.0827811 0.0268972i 0.267334 0.963604i \(-0.413857\pi\)
−0.350115 + 0.936707i \(0.613857\pi\)
\(114\) 0 0
\(115\) 44.2579 32.1552i 0.384851 0.279611i
\(116\) 1.98311 + 2.72952i 0.0170958 + 0.0235303i
\(117\) 0 0
\(118\) 0.000263592 0 0.000811253i 2.23383e−6 0 6.87502e-6i
\(119\) 23.7293 32.6606i 0.199406 0.274459i
\(120\) 0 0
\(121\) 43.2830 + 112.994i 0.357711 + 0.933832i
\(122\) 9.39077i 0.0769736i
\(123\) 0 0
\(124\) 0.650015 2.00054i 0.00524206 0.0161334i
\(125\) −389.812 + 126.657i −3.11849 + 1.01326i
\(126\) 0 0
\(127\) −174.328 + 126.656i −1.37266 + 0.997294i −0.375133 + 0.926971i \(0.622403\pi\)
−0.997524 + 0.0703233i \(0.977597\pi\)
\(128\) 114.951 37.3500i 0.898058 0.291797i
\(129\) 0 0
\(130\) −263.445 191.404i −2.02650 1.47234i
\(131\) 166.588i 1.27166i 0.771827 + 0.635832i \(0.219343\pi\)
−0.771827 + 0.635832i \(0.780657\pi\)
\(132\) 0 0
\(133\) −73.3797 −0.551727
\(134\) 129.102 177.694i 0.963450 1.32607i
\(135\) 0 0
\(136\) 19.3999 + 59.7067i 0.142646 + 0.439020i
\(137\) −25.7144 35.3928i −0.187696 0.258342i 0.704790 0.709416i \(-0.251041\pi\)
−0.892487 + 0.451074i \(0.851041\pi\)
\(138\) 0 0
\(139\) −31.8516 98.0291i −0.229148 0.705245i −0.997844 0.0656308i \(-0.979094\pi\)
0.768696 0.639614i \(-0.220906\pi\)
\(140\) 6.70560 + 2.17878i 0.0478972 + 0.0155627i
\(141\) 0 0
\(142\) 195.747 1.37850
\(143\) 63.1840 + 178.626i 0.441846 + 1.24913i
\(144\) 0 0
\(145\) 187.495 + 136.223i 1.29307 + 0.939468i
\(146\) −64.0818 20.8214i −0.438917 0.142613i
\(147\) 0 0
\(148\) 0.867584 0.630337i 0.00586205 0.00425903i
\(149\) 53.1924 + 73.2130i 0.356996 + 0.491363i 0.949309 0.314345i \(-0.101785\pi\)
−0.592313 + 0.805708i \(0.701785\pi\)
\(150\) 0 0
\(151\) 74.2733 228.590i 0.491876 1.51384i −0.329892 0.944019i \(-0.607012\pi\)
0.821769 0.569821i \(-0.192988\pi\)
\(152\) 67.0724 92.3173i 0.441266 0.607351i
\(153\) 0 0
\(154\) 68.7825 + 89.7044i 0.446639 + 0.582496i
\(155\) 144.492i 0.932207i
\(156\) 0 0
\(157\) −9.14801 + 28.1547i −0.0582676 + 0.179329i −0.975954 0.217976i \(-0.930055\pi\)
0.917687 + 0.397305i \(0.130055\pi\)
\(158\) 115.341 37.4766i 0.730008 0.237194i
\(159\) 0 0
\(160\) −17.4405 + 12.6713i −0.109003 + 0.0791953i
\(161\) −28.2810 + 9.18905i −0.175658 + 0.0570748i
\(162\) 0 0
\(163\) −169.962 123.484i −1.04271 0.757573i −0.0718974 0.997412i \(-0.522905\pi\)
−0.970813 + 0.239839i \(0.922905\pi\)
\(164\) 2.54888i 0.0155420i
\(165\) 0 0
\(166\) 128.158 0.772036
\(167\) −8.96158 + 12.3346i −0.0536622 + 0.0738596i −0.835005 0.550243i \(-0.814535\pi\)
0.781343 + 0.624102i \(0.214535\pi\)
\(168\) 0 0
\(169\) 39.4581 + 121.440i 0.233480 + 0.718578i
\(170\) 85.7668 + 118.048i 0.504511 + 0.694399i
\(171\) 0 0
\(172\) −2.32440 7.15375i −0.0135139 0.0415916i
\(173\) 203.903 + 66.2520i 1.17863 + 0.382960i 0.831857 0.554990i \(-0.187278\pi\)
0.346772 + 0.937950i \(0.387278\pi\)
\(174\) 0 0
\(175\) 353.558 2.02033
\(176\) −169.564 + 4.38046i −0.963431 + 0.0248890i
\(177\) 0 0
\(178\) −147.179 106.932i −0.826849 0.600741i
\(179\) 194.582 + 63.2234i 1.08705 + 0.353204i 0.797105 0.603840i \(-0.206364\pi\)
0.289943 + 0.957044i \(0.406364\pi\)
\(180\) 0 0
\(181\) −110.640 + 80.3847i −0.611271 + 0.444114i −0.849862 0.527006i \(-0.823315\pi\)
0.238591 + 0.971120i \(0.423315\pi\)
\(182\) 104.042 + 143.201i 0.571657 + 0.786818i
\(183\) 0 0
\(184\) 14.2896 43.9789i 0.0776609 0.239016i
\(185\) 43.2988 59.5956i 0.234047 0.322139i
\(186\) 0 0
\(187\) −2.19257 84.8724i −0.0117250 0.453863i
\(188\) 5.43686i 0.0289195i
\(189\) 0 0
\(190\) 81.9581 252.241i 0.431358 1.32758i
\(191\) 232.753 75.6261i 1.21860 0.395948i 0.372030 0.928221i \(-0.378662\pi\)
0.846573 + 0.532272i \(0.178662\pi\)
\(192\) 0 0
\(193\) 12.7310 9.24963i 0.0659639 0.0479256i −0.554315 0.832307i \(-0.687020\pi\)
0.620279 + 0.784382i \(0.287020\pi\)
\(194\) 97.9540 31.8272i 0.504918 0.164058i
\(195\) 0 0
\(196\) 2.45262 + 1.78193i 0.0125133 + 0.00909148i
\(197\) 95.4172i 0.484351i 0.970232 + 0.242176i \(0.0778610\pi\)
−0.970232 + 0.242176i \(0.922139\pi\)
\(198\) 0 0
\(199\) −65.2214 −0.327746 −0.163873 0.986481i \(-0.552399\pi\)
−0.163873 + 0.986481i \(0.552399\pi\)
\(200\) −323.169 + 444.804i −1.61584 + 2.22402i
\(201\) 0 0
\(202\) 35.7726 + 110.097i 0.177092 + 0.545033i
\(203\) −74.0466 101.916i −0.364762 0.502051i
\(204\) 0 0
\(205\) −54.1047 166.517i −0.263926 0.812279i
\(206\) −180.713 58.7173i −0.877248 0.285035i
\(207\) 0 0
\(208\) −265.605 −1.27695
\(209\) −122.463 + 93.9005i −0.585946 + 0.449285i
\(210\) 0 0
\(211\) 222.580 + 161.714i 1.05488 + 0.766415i 0.973134 0.230238i \(-0.0739506\pi\)
0.0817453 + 0.996653i \(0.473951\pi\)
\(212\) −10.8733 3.53295i −0.0512891 0.0166649i
\(213\) 0 0
\(214\) −29.2326 + 21.2387i −0.136601 + 0.0992462i
\(215\) −303.703 418.011i −1.41257 1.94424i
\(216\) 0 0
\(217\) −24.2707 + 74.6974i −0.111846 + 0.344228i
\(218\) 58.4902 80.5048i 0.268304 0.369288i
\(219\) 0 0
\(220\) 13.9790 4.94469i 0.0635410 0.0224759i
\(221\) 132.944i 0.601558i
\(222\) 0 0
\(223\) 56.5219 173.956i 0.253461 0.780074i −0.740668 0.671872i \(-0.765491\pi\)
0.994129 0.108202i \(-0.0345094\pi\)
\(224\) 11.1445 3.62108i 0.0497525 0.0161656i
\(225\) 0 0
\(226\) −15.6333 + 11.3582i −0.0691738 + 0.0502577i
\(227\) −238.155 + 77.3812i −1.04914 + 0.340886i −0.782331 0.622863i \(-0.785969\pi\)
−0.266809 + 0.963749i \(0.585969\pi\)
\(228\) 0 0
\(229\) 283.549 + 206.010i 1.23820 + 0.899608i 0.997477 0.0709854i \(-0.0226144\pi\)
0.240726 + 0.970593i \(0.422614\pi\)
\(230\) 107.479i 0.467298i
\(231\) 0 0
\(232\) 195.901 0.844400
\(233\) 214.372 295.058i 0.920052 1.26634i −0.0435636 0.999051i \(-0.513871\pi\)
0.963616 0.267292i \(-0.0861289\pi\)
\(234\) 0 0
\(235\) −115.407 355.187i −0.491095 1.51144i
\(236\) 3.57495e−5 0 4.92049e-5i 1.51481e−7 0 2.08495e-7i
\(237\) 0 0
\(238\) −24.5097 75.4331i −0.102982 0.316946i
\(239\) −230.931 75.0342i −0.966240 0.313951i −0.216943 0.976184i \(-0.569609\pi\)
−0.749297 + 0.662234i \(0.769609\pi\)
\(240\) 0 0
\(241\) −418.345 −1.73587 −0.867935 0.496677i \(-0.834553\pi\)
−0.867935 + 0.496677i \(0.834553\pi\)
\(242\) 229.581 + 61.6893i 0.948682 + 0.254914i
\(243\) 0 0
\(244\) −0.541702 0.393569i −0.00222009 0.00161299i
\(245\) 198.053 + 64.3513i 0.808379 + 0.262658i
\(246\) 0 0
\(247\) −195.495 + 142.036i −0.791478 + 0.575043i
\(248\) −71.7906 98.8113i −0.289478 0.398433i
\(249\) 0 0
\(250\) −248.840 + 765.850i −0.995359 + 3.06340i
\(251\) −162.338 + 223.439i −0.646766 + 0.890197i −0.998954 0.0457326i \(-0.985438\pi\)
0.352188 + 0.935929i \(0.385438\pi\)
\(252\) 0 0
\(253\) −35.4391 + 51.5254i −0.140076 + 0.203658i
\(254\) 423.348i 1.66672i
\(255\) 0 0
\(256\) −8.30108 + 25.5481i −0.0324261 + 0.0997972i
\(257\) −153.309 + 49.8130i −0.596532 + 0.193825i −0.591693 0.806163i \(-0.701540\pi\)
−0.00483877 + 0.999988i \(0.501540\pi\)
\(258\) 0 0
\(259\) −32.3944 + 23.5359i −0.125075 + 0.0908722i
\(260\) 22.0821 7.17491i 0.0849311 0.0275958i
\(261\) 0 0
\(262\) 264.783 + 192.376i 1.01062 + 0.734260i
\(263\) 55.4784i 0.210944i −0.994422 0.105472i \(-0.966365\pi\)
0.994422 0.105472i \(-0.0336354\pi\)
\(264\) 0 0
\(265\) −785.340 −2.96355
\(266\) −84.7390 + 116.633i −0.318568 + 0.438471i
\(267\) 0 0
\(268\) 4.83948 + 14.8944i 0.0180578 + 0.0555761i
\(269\) −34.2101 47.0861i −0.127175 0.175041i 0.740682 0.671856i \(-0.234503\pi\)
−0.867856 + 0.496815i \(0.834503\pi\)
\(270\) 0 0
\(271\) 131.612 + 405.060i 0.485653 + 1.49469i 0.831033 + 0.556223i \(0.187750\pi\)
−0.345380 + 0.938463i \(0.612250\pi\)
\(272\) 113.191 + 36.7779i 0.416142 + 0.135213i
\(273\) 0 0
\(274\) −85.9501 −0.313686
\(275\) 590.050 452.432i 2.14564 1.64521i
\(276\) 0 0
\(277\) 103.461 + 75.1686i 0.373504 + 0.271367i 0.758663 0.651484i \(-0.225853\pi\)
−0.385158 + 0.922851i \(0.625853\pi\)
\(278\) −192.594 62.5777i −0.692786 0.225100i
\(279\) 0 0
\(280\) 331.205 240.635i 1.18288 0.859409i
\(281\) −43.7302 60.1895i −0.155624 0.214198i 0.724085 0.689711i \(-0.242262\pi\)
−0.879709 + 0.475513i \(0.842262\pi\)
\(282\) 0 0
\(283\) 152.758 470.142i 0.539782 1.66128i −0.193301 0.981139i \(-0.561919\pi\)
0.733083 0.680139i \(-0.238081\pi\)
\(284\) −8.20379 + 11.2916i −0.0288866 + 0.0397590i
\(285\) 0 0
\(286\) 356.882 + 105.850i 1.24784 + 0.370104i
\(287\) 95.1718i 0.331609i
\(288\) 0 0
\(289\) 70.8974 218.200i 0.245320 0.755016i
\(290\) 433.038 140.703i 1.49324 0.485182i
\(291\) 0 0
\(292\) 3.88676 2.82389i 0.0133108 0.00967087i
\(293\) −12.9456 + 4.20629i −0.0441831 + 0.0143559i −0.331025 0.943622i \(-0.607394\pi\)
0.286842 + 0.957978i \(0.407394\pi\)
\(294\) 0 0
\(295\) 0.00337996 + 0.00245568i 1.14575e−5 + 8.32436e-6i
\(296\) 62.2676i 0.210363i
\(297\) 0 0
\(298\) 177.795 0.596628
\(299\) −57.5585 + 79.2225i −0.192503 + 0.264958i
\(300\) 0 0
\(301\) 86.7897 + 267.111i 0.288338 + 0.887413i
\(302\) −277.561 382.030i −0.919075 1.26500i
\(303\) 0 0
\(304\) −66.8490 205.740i −0.219898 0.676777i
\(305\) −43.7433 14.2131i −0.143421 0.0466002i
\(306\) 0 0
\(307\) −215.268 −0.701198 −0.350599 0.936526i \(-0.614022\pi\)
−0.350599 + 0.936526i \(0.614022\pi\)
\(308\) −8.05724 + 0.208148i −0.0261599 + 0.000675806i
\(309\) 0 0
\(310\) −229.663 166.860i −0.740847 0.538257i
\(311\) −85.6398 27.8260i −0.275369 0.0894728i 0.168077 0.985774i \(-0.446244\pi\)
−0.443446 + 0.896301i \(0.646244\pi\)
\(312\) 0 0
\(313\) −208.941 + 151.805i −0.667544 + 0.484999i −0.869202 0.494457i \(-0.835367\pi\)
0.201658 + 0.979456i \(0.435367\pi\)
\(314\) 34.1863 + 47.0534i 0.108873 + 0.149851i
\(315\) 0 0
\(316\) −2.67216 + 8.22405i −0.00845619 + 0.0260255i
\(317\) −61.7422 + 84.9808i −0.194770 + 0.268078i −0.895221 0.445623i \(-0.852982\pi\)
0.700451 + 0.713701i \(0.252982\pi\)
\(318\) 0 0
\(319\) −253.993 75.3335i −0.796218 0.236155i
\(320\) 635.878i 1.98712i
\(321\) 0 0
\(322\) −18.0534 + 55.5627i −0.0560665 + 0.172555i
\(323\) 102.980 33.4602i 0.318823 0.103592i
\(324\) 0 0
\(325\) 941.935 684.356i 2.89826 2.10571i
\(326\) −392.544 + 127.545i −1.20412 + 0.391244i
\(327\) 0 0
\(328\) −119.733 86.9915i −0.365041 0.265218i
\(329\) 203.005i 0.617036i
\(330\) 0 0
\(331\) 258.731 0.781664 0.390832 0.920462i \(-0.372187\pi\)
0.390832 + 0.920462i \(0.372187\pi\)
\(332\) −5.37113 + 7.39273i −0.0161781 + 0.0222673i
\(333\) 0 0
\(334\) 9.25629 + 28.4879i 0.0277135 + 0.0852933i
\(335\) 632.321 + 870.316i 1.88753 + 2.59796i
\(336\) 0 0
\(337\) −113.715 349.979i −0.337433 1.03851i −0.965511 0.260362i \(-0.916158\pi\)
0.628078 0.778150i \(-0.283842\pi\)
\(338\) 238.588 + 77.5221i 0.705883 + 0.229355i
\(339\) 0 0
\(340\) −10.4040 −0.0306001
\(341\) 55.0817 + 155.720i 0.161530 + 0.456657i
\(342\) 0 0
\(343\) −298.926 217.183i −0.871505 0.633186i
\(344\) −415.377 134.964i −1.20749 0.392337i
\(345\) 0 0
\(346\) 340.772 247.585i 0.984889 0.715564i
\(347\) −245.149 337.419i −0.706482 0.972388i −0.999866 0.0163937i \(-0.994781\pi\)
0.293384 0.955995i \(-0.405219\pi\)
\(348\) 0 0
\(349\) 86.4724 266.135i 0.247772 0.762564i −0.747396 0.664379i \(-0.768696\pi\)
0.995168 0.0981851i \(-0.0313037\pi\)
\(350\) 408.290 561.963i 1.16654 1.60561i
\(351\) 0 0
\(352\) 13.9653 20.3044i 0.0396742 0.0576828i
\(353\) 333.271i 0.944111i −0.881569 0.472056i \(-0.843512\pi\)
0.881569 0.472056i \(-0.156488\pi\)
\(354\) 0 0
\(355\) −296.266 + 911.812i −0.834551 + 2.56848i
\(356\) 12.3366 4.00841i 0.0346534 0.0112596i
\(357\) 0 0
\(358\) 325.194 236.267i 0.908363 0.659964i
\(359\) −472.450 + 153.508i −1.31602 + 0.427600i −0.881125 0.472883i \(-0.843213\pi\)
−0.434891 + 0.900483i \(0.643213\pi\)
\(360\) 0 0
\(361\) 132.830 + 96.5064i 0.367949 + 0.267331i
\(362\) 268.685i 0.742224i
\(363\) 0 0
\(364\) −12.6209 −0.0346727
\(365\) 193.977 266.987i 0.531445 0.731471i
\(366\) 0 0
\(367\) 51.0462 + 157.104i 0.139090 + 0.428076i 0.996204 0.0870514i \(-0.0277444\pi\)
−0.857113 + 0.515128i \(0.827744\pi\)
\(368\) −51.5281 70.9223i −0.140022 0.192724i
\(369\) 0 0
\(370\) −44.7227 137.642i −0.120872 0.372006i
\(371\) 405.994 + 131.915i 1.09432 + 0.355567i
\(372\) 0 0
\(373\) 393.501 1.05496 0.527481 0.849567i \(-0.323136\pi\)
0.527481 + 0.849567i \(0.323136\pi\)
\(374\) −137.432 94.5259i −0.367466 0.252743i
\(375\) 0 0
\(376\) −255.396 185.556i −0.679245 0.493500i
\(377\) −394.544 128.195i −1.04654 0.340040i
\(378\) 0 0
\(379\) −153.017 + 111.173i −0.403739 + 0.293334i −0.771062 0.636760i \(-0.780274\pi\)
0.367323 + 0.930093i \(0.380274\pi\)
\(380\) 11.1155 + 15.2992i 0.0292513 + 0.0402610i
\(381\) 0 0
\(382\) 148.580 457.282i 0.388953 1.19707i
\(383\) 275.626 379.367i 0.719651 0.990514i −0.279885 0.960034i \(-0.590296\pi\)
0.999535 0.0304804i \(-0.00970371\pi\)
\(384\) 0 0
\(385\) −521.957 + 184.628i −1.35573 + 0.479553i
\(386\) 30.9168i 0.0800954i
\(387\) 0 0
\(388\) −2.26934 + 6.98431i −0.00584881 + 0.0180008i
\(389\) 432.711 140.596i 1.11237 0.361430i 0.305518 0.952186i \(-0.401170\pi\)
0.806850 + 0.590756i \(0.201170\pi\)
\(390\) 0 0
\(391\) 35.4990 25.7915i 0.0907903 0.0659630i
\(392\) 167.412 54.3954i 0.427071 0.138764i
\(393\) 0 0
\(394\) 151.661 + 110.188i 0.384926 + 0.279665i
\(395\) 593.994i 1.50378i
\(396\) 0 0
\(397\) 168.638 0.424782 0.212391 0.977185i \(-0.431875\pi\)
0.212391 + 0.977185i \(0.431875\pi\)
\(398\) −75.3178 + 103.666i −0.189241 + 0.260468i
\(399\) 0 0
\(400\) 322.092 + 991.298i 0.805231 + 2.47825i
\(401\) 41.0252 + 56.4664i 0.102307 + 0.140814i 0.857101 0.515148i \(-0.172263\pi\)
−0.754794 + 0.655962i \(0.772263\pi\)
\(402\) 0 0
\(403\) 79.9253 + 245.985i 0.198326 + 0.610384i
\(404\) −7.85011 2.55066i −0.0194310 0.00631350i
\(405\) 0 0
\(406\) −247.500 −0.609606
\(407\) −23.9450 + 80.7325i −0.0588328 + 0.198360i
\(408\) 0 0
\(409\) −448.126 325.583i −1.09566 0.796046i −0.115317 0.993329i \(-0.536788\pi\)
−0.980347 + 0.197283i \(0.936788\pi\)
\(410\) −327.151 106.298i −0.797929 0.259263i
\(411\) 0 0
\(412\) 10.9608 7.96349i 0.0266039 0.0193289i
\(413\) −0.00133484 0.00183724i −3.23205e−6 4.44853e-6i
\(414\) 0 0
\(415\) −193.969 + 596.975i −0.467395 + 1.43849i
\(416\) 22.6818 31.2188i 0.0545235 0.0750452i
\(417\) 0 0
\(418\) 7.82980 + 303.085i 0.0187316 + 0.725083i
\(419\) 307.485i 0.733855i 0.930250 + 0.366927i \(0.119590\pi\)
−0.930250 + 0.366927i \(0.880410\pi\)
\(420\) 0 0
\(421\) −1.09596 + 3.37301i −0.00260322 + 0.00801189i −0.952350 0.305008i \(-0.901341\pi\)
0.949746 + 0.313020i \(0.101341\pi\)
\(422\) 514.071 167.032i 1.21818 0.395810i
\(423\) 0 0
\(424\) −537.057 + 390.195i −1.26664 + 0.920271i
\(425\) −496.178 + 161.218i −1.16748 + 0.379337i
\(426\) 0 0
\(427\) 20.2264 + 14.6953i 0.0473686 + 0.0344153i
\(428\) 2.57638i 0.00601959i
\(429\) 0 0
\(430\) −1015.12 −2.36076
\(431\) 69.9030 96.2132i 0.162188 0.223232i −0.720187 0.693781i \(-0.755944\pi\)
0.882374 + 0.470548i \(0.155944\pi\)
\(432\) 0 0
\(433\) 61.6340 + 189.690i 0.142342 + 0.438083i 0.996660 0.0816680i \(-0.0260247\pi\)
−0.854318 + 0.519751i \(0.826025\pi\)
\(434\) 90.6999 + 124.838i 0.208986 + 0.287644i
\(435\) 0 0
\(436\) 2.19254 + 6.74795i 0.00502876 + 0.0154769i
\(437\) −75.8532 24.6462i −0.173577 0.0563986i
\(438\) 0 0
\(439\) −7.94474 −0.0180973 −0.00904867 0.999959i \(-0.502880\pi\)
−0.00904867 + 0.999959i \(0.502880\pi\)
\(440\) 244.817 825.421i 0.556402 1.87596i
\(441\) 0 0
\(442\) −211.308 153.524i −0.478073 0.347340i
\(443\) −446.341 145.025i −1.00754 0.327370i −0.241666 0.970359i \(-0.577694\pi\)
−0.765875 + 0.642989i \(0.777694\pi\)
\(444\) 0 0
\(445\) 720.859 523.735i 1.61991 1.17693i
\(446\) −211.223 290.724i −0.473595 0.651847i
\(447\) 0 0
\(448\) 106.810 328.727i 0.238415 0.733765i
\(449\) −434.087 + 597.469i −0.966786 + 1.33067i −0.0231324 + 0.999732i \(0.507364\pi\)
−0.943654 + 0.330935i \(0.892636\pi\)
\(450\) 0 0
\(451\) 121.787 + 158.831i 0.270037 + 0.352176i
\(452\) 1.37782i 0.00304828i
\(453\) 0 0
\(454\) −152.028 + 467.895i −0.334864 + 1.03060i
\(455\) −824.515 + 267.901i −1.81212 + 0.588794i
\(456\) 0 0
\(457\) 146.584 106.500i 0.320753 0.233041i −0.415744 0.909482i \(-0.636479\pi\)
0.736497 + 0.676441i \(0.236479\pi\)
\(458\) 654.885 212.785i 1.42988 0.464596i
\(459\) 0 0
\(460\) 6.19984 + 4.50445i 0.0134779 + 0.00979228i
\(461\) 561.409i 1.21781i −0.793244 0.608903i \(-0.791610\pi\)
0.793244 0.608903i \(-0.208390\pi\)
\(462\) 0 0
\(463\) 379.155 0.818909 0.409454 0.912331i \(-0.365719\pi\)
0.409454 + 0.912331i \(0.365719\pi\)
\(464\) 218.294 300.456i 0.470462 0.647535i
\(465\) 0 0
\(466\) −221.422 681.467i −0.475155 1.46238i
\(467\) −268.209 369.158i −0.574324 0.790489i 0.418735 0.908109i \(-0.362474\pi\)
−0.993059 + 0.117619i \(0.962474\pi\)
\(468\) 0 0
\(469\) −180.699 556.136i −0.385287 1.18579i
\(470\) −697.825 226.737i −1.48473 0.482419i
\(471\) 0 0
\(472\) 0.00353150 7.48199e−6
\(473\) 486.652 + 334.719i 1.02886 + 0.707651i
\(474\) 0 0
\(475\) 767.181 + 557.389i 1.61512 + 1.17345i
\(476\) 5.37853 + 1.74759i 0.0112994 + 0.00367141i
\(477\) 0 0
\(478\) −385.943 + 280.404i −0.807412 + 0.586619i
\(479\) −316.414 435.507i −0.660573 0.909201i 0.338927 0.940813i \(-0.389936\pi\)
−0.999500 + 0.0316118i \(0.989936\pi\)
\(480\) 0 0
\(481\) −40.7471 + 125.407i −0.0847134 + 0.260721i
\(482\) −483.106 + 664.938i −1.00229 + 1.37954i
\(483\) 0 0
\(484\) −13.1803 + 10.6578i −0.0272320 + 0.0220203i
\(485\) 504.452i 1.04011i
\(486\) 0 0
\(487\) 60.1626 185.162i 0.123537 0.380208i −0.870095 0.492885i \(-0.835942\pi\)
0.993632 + 0.112676i \(0.0359424\pi\)
\(488\) −36.9757 + 12.0141i −0.0757700 + 0.0246192i
\(489\) 0 0
\(490\) 330.995 240.482i 0.675500 0.490780i
\(491\) −193.879 + 62.9950i −0.394865 + 0.128299i −0.499717 0.866188i \(-0.666563\pi\)
0.104853 + 0.994488i \(0.466563\pi\)
\(492\) 0 0
\(493\) 150.388 + 109.264i 0.305048 + 0.221630i
\(494\) 474.752i 0.961037i
\(495\) 0 0
\(496\) −231.546 −0.466826
\(497\) 306.318 421.611i 0.616335 0.848312i
\(498\) 0 0
\(499\) −264.246 813.267i −0.529552 1.62979i −0.755135 0.655569i \(-0.772429\pi\)
0.225584 0.974224i \(-0.427571\pi\)
\(500\) −33.7487 46.4511i −0.0674974 0.0929022i
\(501\) 0 0
\(502\) 167.677 + 516.057i 0.334018 + 1.02800i
\(503\) −258.957 84.1401i −0.514824 0.167277i 0.0400708 0.999197i \(-0.487242\pi\)
−0.554895 + 0.831920i \(0.687242\pi\)
\(504\) 0 0
\(505\) −566.986 −1.12274
\(506\) 40.9718 + 115.830i 0.0809719 + 0.228914i
\(507\) 0 0
\(508\) −24.4206 17.7426i −0.0480720 0.0349264i
\(509\) 897.352 + 291.567i 1.76297 + 0.572824i 0.997501 0.0706498i \(-0.0225073\pi\)
0.765468 + 0.643473i \(0.222507\pi\)
\(510\) 0 0
\(511\) −145.126 + 105.440i −0.284004 + 0.206341i
\(512\) 315.197 + 433.831i 0.615619 + 0.847327i
\(513\) 0 0
\(514\) −97.8660 + 301.200i −0.190401 + 0.585993i
\(515\) 547.024 752.914i 1.06218 1.46197i
\(516\) 0 0
\(517\) 259.776 + 338.793i 0.502468 + 0.655306i
\(518\) 78.6685i 0.151870i
\(519\) 0 0
\(520\) 416.605 1282.18i 0.801163 2.46573i
\(521\) 308.494 100.236i 0.592119 0.192391i 0.00239665 0.999997i \(-0.499237\pi\)
0.589722 + 0.807606i \(0.299237\pi\)
\(522\) 0 0
\(523\) −98.0023 + 71.2028i −0.187385 + 0.136143i −0.677523 0.735502i \(-0.736946\pi\)
0.490138 + 0.871645i \(0.336946\pi\)
\(524\) −22.1942 + 7.21135i −0.0423554 + 0.0137621i
\(525\) 0 0
\(526\) −88.1801 64.0666i −0.167643 0.121800i
\(527\) 115.896i 0.219917i
\(528\) 0 0
\(529\) 496.679 0.938902
\(530\) −906.913 + 1248.26i −1.71116 + 2.35520i
\(531\) 0 0
\(532\) −3.17649 9.77624i −0.00597085 0.0183764i
\(533\) 184.217 + 253.553i 0.345623 + 0.475709i
\(534\) 0 0
\(535\) −54.6885 168.314i −0.102221 0.314605i
\(536\) 864.830 + 281.000i 1.61349 + 0.524254i
\(537\) 0 0
\(538\) −114.347 −0.212540
\(539\) −237.974 + 6.14776i −0.441510 + 0.0114059i
\(540\) 0 0
\(541\) 482.965 + 350.895i 0.892727 + 0.648604i 0.936588 0.350433i \(-0.113966\pi\)
−0.0438604 + 0.999038i \(0.513966\pi\)
\(542\) 795.808 + 258.574i 1.46828 + 0.477073i
\(543\) 0 0
\(544\) −13.9889 + 10.1635i −0.0257149 + 0.0186830i
\(545\) 286.475 + 394.299i 0.525643 + 0.723485i
\(546\) 0 0
\(547\) −104.567 + 321.823i −0.191164 + 0.588343i 0.808836 + 0.588035i \(0.200098\pi\)
−1.00000 0.000308188i \(0.999902\pi\)
\(548\) 3.60219 4.95798i 0.00657333 0.00904742i
\(549\) 0 0
\(550\) −37.7256 1460.32i −0.0685920 2.65513i
\(551\) 337.882i 0.613217i
\(552\) 0 0
\(553\) 99.7746 307.075i 0.180424 0.555289i
\(554\) 238.953 77.6406i 0.431324 0.140146i
\(555\) 0 0
\(556\) 11.6814 8.48706i 0.0210098 0.0152645i
\(557\) 454.284 147.606i 0.815590 0.265001i 0.128627 0.991693i \(-0.458943\pi\)
0.686964 + 0.726692i \(0.258943\pi\)
\(558\) 0 0
\(559\) 748.249 + 543.635i 1.33855 + 0.972513i
\(560\) 776.116i 1.38592i
\(561\) 0 0
\(562\) −146.168 −0.260085
\(563\) −277.409 + 381.820i −0.492733 + 0.678189i −0.980889 0.194567i \(-0.937670\pi\)
0.488156 + 0.872756i \(0.337670\pi\)
\(564\) 0 0
\(565\) −29.2468 90.0125i −0.0517643 0.159314i
\(566\) −570.861 785.722i −1.00859 1.38820i
\(567\) 0 0
\(568\) 250.430 + 770.745i 0.440898 + 1.35694i
\(569\) 122.262 + 39.7253i 0.214871 + 0.0698159i 0.414475 0.910061i \(-0.363965\pi\)
−0.199603 + 0.979877i \(0.563965\pi\)
\(570\) 0 0
\(571\) 266.234 0.466259 0.233130 0.972446i \(-0.425103\pi\)
0.233130 + 0.972446i \(0.425103\pi\)
\(572\) −21.0629 + 16.1503i −0.0368232 + 0.0282348i
\(573\) 0 0
\(574\) 151.271 + 109.905i 0.263538 + 0.191471i
\(575\) 365.476 + 118.750i 0.635610 + 0.206522i
\(576\) 0 0
\(577\) −583.296 + 423.789i −1.01091 + 0.734470i −0.964400 0.264448i \(-0.914810\pi\)
−0.0465112 + 0.998918i \(0.514810\pi\)
\(578\) −264.945 364.665i −0.458382 0.630908i
\(579\) 0 0
\(580\) −10.0324 + 30.8765i −0.0172972 + 0.0532353i
\(581\) 200.551 276.034i 0.345182 0.475102i
\(582\) 0 0
\(583\) 846.366 299.379i 1.45174 0.513514i
\(584\) 278.957i 0.477667i
\(585\) 0 0
\(586\) −8.26396 + 25.4339i −0.0141023 + 0.0434025i
\(587\) −391.709 + 127.274i −0.667307 + 0.216821i −0.623030 0.782198i \(-0.714098\pi\)
−0.0442770 + 0.999019i \(0.514098\pi\)
\(588\) 0 0
\(589\) −170.426 + 123.822i −0.289348 + 0.210224i
\(590\) 0.00780637 0.00253644i 1.32311e−5 4.29906e-6i
\(591\) 0 0
\(592\) −95.5008 69.3854i −0.161319 0.117205i
\(593\) 750.336i 1.26532i −0.774429 0.632661i \(-0.781963\pi\)
0.774429 0.632661i \(-0.218037\pi\)
\(594\) 0 0
\(595\) 388.472 0.652895
\(596\) −7.45143 + 10.2560i −0.0125024 + 0.0172081i
\(597\) 0 0
\(598\) 59.4514 + 182.973i 0.0994171 + 0.305974i
\(599\) 319.528 + 439.793i 0.533436 + 0.734211i 0.987649 0.156682i \(-0.0500796\pi\)
−0.454213 + 0.890893i \(0.650080\pi\)
\(600\) 0 0
\(601\) −227.497 700.163i −0.378530 1.16500i −0.941066 0.338224i \(-0.890174\pi\)
0.562535 0.826773i \(-0.309826\pi\)
\(602\) 524.785 + 170.513i 0.871735 + 0.283244i
\(603\) 0 0
\(604\) 33.6698 0.0557447
\(605\) −634.830 + 976.048i −1.04931 + 1.61330i
\(606\) 0 0
\(607\) −452.759 328.949i −0.745896 0.541925i 0.148656 0.988889i \(-0.452505\pi\)
−0.894552 + 0.446964i \(0.852505\pi\)
\(608\) 29.8911 + 9.71220i 0.0491630 + 0.0159740i
\(609\) 0 0
\(610\) −73.1058 + 53.1145i −0.119846 + 0.0870729i
\(611\) 392.941 + 540.837i 0.643112 + 0.885168i
\(612\) 0 0
\(613\) −33.9655 + 104.535i −0.0554086 + 0.170530i −0.974931 0.222508i \(-0.928576\pi\)
0.919522 + 0.393038i \(0.128576\pi\)
\(614\) −248.592 + 342.157i −0.404872 + 0.557259i
\(615\) 0 0
\(616\) −265.210 + 385.592i −0.430535 + 0.625961i
\(617\) 61.1594i 0.0991238i −0.998771 0.0495619i \(-0.984217\pi\)
0.998771 0.0495619i \(-0.0157825\pi\)
\(618\) 0 0
\(619\) 25.2833 77.8139i 0.0408454 0.125709i −0.928555 0.371196i \(-0.878948\pi\)
0.969400 + 0.245487i \(0.0789478\pi\)
\(620\) 19.2504 6.25484i 0.0310491 0.0100885i
\(621\) 0 0
\(622\) −143.125 + 103.986i −0.230105 + 0.167181i
\(623\) −460.632 + 149.668i −0.739377 + 0.240238i
\(624\) 0 0
\(625\) −1823.67 1324.97i −2.91786 2.11995i
\(626\) 507.406i 0.810553i
\(627\) 0 0
\(628\) −4.14700 −0.00660351
\(629\) 34.7297 47.8014i 0.0552142 0.0759958i
\(630\) 0 0
\(631\) 2.87142 + 8.83732i 0.00455058 + 0.0140053i 0.953306 0.302006i \(-0.0976563\pi\)
−0.948755 + 0.316011i \(0.897656\pi\)
\(632\) 295.125 + 406.205i 0.466970 + 0.642729i
\(633\) 0 0
\(634\) 63.7726 + 196.272i 0.100588 + 0.309577i
\(635\) −1972.00 640.743i −3.10552 1.00904i
\(636\) 0 0
\(637\) −372.763 −0.585185
\(638\) −413.051 + 316.714i −0.647415 + 0.496417i
\(639\) 0 0
\(640\) 940.933 + 683.628i 1.47021 + 1.06817i
\(641\) 331.957 + 107.859i 0.517874 + 0.168268i 0.556280 0.830995i \(-0.312228\pi\)
−0.0384062 + 0.999262i \(0.512228\pi\)
\(642\) 0 0
\(643\) −733.104 + 532.631i −1.14013 + 0.828353i −0.987137 0.159874i \(-0.948891\pi\)
−0.152993 + 0.988227i \(0.548891\pi\)
\(644\) −2.44848 3.37005i −0.00380199 0.00523299i
\(645\) 0 0
\(646\) 65.7381 202.321i 0.101762 0.313191i
\(647\) 33.2345 45.7434i 0.0513671 0.0707007i −0.782561 0.622574i \(-0.786087\pi\)
0.833928 + 0.551874i \(0.186087\pi\)
\(648\) 0 0
\(649\) −0.00457873 0.00135804i −7.05506e−6 2.09250e-6i
\(650\) 2287.45i 3.51916i
\(651\) 0 0
\(652\) 9.09423 27.9892i 0.0139482 0.0429282i
\(653\) −540.720 + 175.691i −0.828055 + 0.269051i −0.692226 0.721681i \(-0.743370\pi\)
−0.135829 + 0.990732i \(0.543370\pi\)
\(654\) 0 0
\(655\) −1296.86 + 942.227i −1.97995 + 1.43851i
\(656\) −266.840 + 86.7017i −0.406769 + 0.132167i
\(657\) 0 0
\(658\) 322.666 + 234.430i 0.490374 + 0.356277i
\(659\) 380.801i 0.577847i −0.957352 0.288923i \(-0.906703\pi\)
0.957352 0.288923i \(-0.0932973\pi\)
\(660\) 0 0
\(661\) 350.773 0.530671 0.265335 0.964156i \(-0.414517\pi\)
0.265335 + 0.964156i \(0.414517\pi\)
\(662\) 298.783 411.239i 0.451333 0.621207i
\(663\) 0 0
\(664\) 163.960 + 504.616i 0.246927 + 0.759965i
\(665\) −415.038 571.250i −0.624117 0.859023i
\(666\) 0 0
\(667\) −42.3117 130.222i −0.0634358 0.195235i
\(668\) −2.03125 0.659992i −0.00304079 0.000988011i
\(669\) 0 0
\(670\) 2113.53 3.15452
\(671\) 52.5606 1.35784i 0.0783317 0.00202360i
\(672\) 0 0
\(673\) 390.671 + 283.839i 0.580491 + 0.421752i 0.838901 0.544284i \(-0.183198\pi\)
−0.258410 + 0.966035i \(0.583198\pi\)
\(674\) −687.591 223.412i −1.02017 0.331472i
\(675\) 0 0
\(676\) −14.4711 + 10.5139i −0.0214070 + 0.0155531i
\(677\) −499.429 687.405i −0.737709 1.01537i −0.998747 0.0500409i \(-0.984065\pi\)
0.261038 0.965328i \(-0.415935\pi\)
\(678\) 0 0
\(679\) 84.7340 260.784i 0.124792 0.384071i
\(680\) −355.082 + 488.728i −0.522179 + 0.718718i
\(681\) 0 0
\(682\) 311.117 + 92.2763i 0.456184 + 0.135302i
\(683\) 831.602i 1.21757i 0.793334 + 0.608786i \(0.208343\pi\)
−0.793334 + 0.608786i \(0.791657\pi\)
\(684\) 0 0
\(685\) 130.087 400.366i 0.189908 0.584475i
\(686\) −690.402 + 224.325i −1.00642 + 0.327004i
\(687\) 0 0
\(688\) −669.855 + 486.678i −0.973626 + 0.707381i
\(689\) 1336.97 434.408i 1.94045 0.630491i
\(690\) 0 0
\(691\) −736.820 535.331i −1.06631 0.774719i −0.0910643 0.995845i \(-0.529027\pi\)
−0.975245 + 0.221126i \(0.929027\pi\)
\(692\) 30.0336i 0.0434011i
\(693\) 0 0
\(694\) −819.409 −1.18070
\(695\) 582.989 802.415i 0.838833 1.15455i
\(696\) 0 0
\(697\) −43.3971 133.563i −0.0622627 0.191625i
\(698\) −323.149 444.776i −0.462964 0.637216i
\(699\) 0 0
\(700\) 15.3050 + 47.1039i 0.0218643 + 0.0672913i
\(701\) 856.342 + 278.242i 1.22160 + 0.396922i 0.847665 0.530532i \(-0.178008\pi\)
0.373936 + 0.927454i \(0.378008\pi\)
\(702\) 0 0
\(703\) −107.397 −0.152769
\(704\) −242.402 685.289i −0.344321 0.973422i
\(705\) 0 0
\(706\) −529.718 384.862i −0.750308 0.545131i
\(707\) 293.112 + 95.2379i 0.414586 + 0.134707i
\(708\) 0 0
\(709\) 746.154 542.113i 1.05240 0.764616i 0.0797356 0.996816i \(-0.474592\pi\)
0.972668 + 0.232200i \(0.0745924\pi\)
\(710\) 1107.15 + 1523.86i 1.55937 + 2.14628i
\(711\) 0 0
\(712\) 232.745 716.315i 0.326889 1.00606i
\(713\) −50.1776 + 69.0635i −0.0703753 + 0.0968632i
\(714\) 0 0
\(715\) −1033.21 + 1502.19i −1.44504 + 2.10097i
\(716\) 28.6606i 0.0400288i
\(717\) 0 0
\(718\) −301.593 + 928.206i −0.420045 + 1.29277i
\(719\) −9.82994 + 3.19394i −0.0136717 + 0.00444220i −0.315845 0.948811i \(-0.602288\pi\)
0.302173 + 0.953253i \(0.402288\pi\)
\(720\) 0 0
\(721\) −409.261 + 297.346i −0.567630 + 0.412407i
\(722\) 306.784 99.6802i 0.424909 0.138061i
\(723\) 0 0
\(724\) −15.4989 11.2606i −0.0214074 0.0155534i
\(725\) 1627.99i 2.24550i
\(726\) 0 0
\(727\) 119.809 0.164799 0.0823995 0.996599i \(-0.473742\pi\)
0.0823995 + 0.996599i \(0.473742\pi\)
\(728\) −430.741 + 592.864i −0.591677 + 0.814373i
\(729\) 0 0
\(730\) −200.357 616.635i −0.274461 0.844705i
\(731\) −243.599 335.285i −0.333240 0.458666i
\(732\) 0 0
\(733\) 393.151 + 1210.00i 0.536359 + 1.65074i 0.740693 + 0.671843i \(0.234497\pi\)
−0.204334 + 0.978901i \(0.565503\pi\)
\(734\) 308.657 + 100.289i 0.420514 + 0.136633i
\(735\) 0 0
\(736\) 12.7364 0.0173049
\(737\) −1013.23 696.898i −1.37480 0.945588i
\(738\) 0 0
\(739\) 136.706 + 99.3227i 0.184988 + 0.134402i 0.676425 0.736511i \(-0.263528\pi\)
−0.491437 + 0.870913i \(0.663528\pi\)
\(740\) 9.81416 + 3.18882i 0.0132624 + 0.00430921i
\(741\) 0 0
\(742\) 678.515 492.970i 0.914441 0.664380i
\(743\) 566.208 + 779.319i 0.762057 + 1.04888i 0.997040 + 0.0768822i \(0.0244965\pi\)
−0.234983 + 0.971999i \(0.575503\pi\)
\(744\) 0 0
\(745\) −269.095 + 828.190i −0.361202 + 1.11167i
\(746\) 454.416 625.450i 0.609137 0.838405i
\(747\) 0 0
\(748\) 11.2125 3.96611i 0.0149900 0.00530229i
\(749\) 96.1986i 0.128436i
\(750\) 0 0
\(751\) −127.573 + 392.629i −0.169871 + 0.522808i −0.999362 0.0357111i \(-0.988630\pi\)
0.829491 + 0.558519i \(0.188630\pi\)
\(752\) −569.180 + 184.938i −0.756889 + 0.245928i
\(753\) 0 0
\(754\) −659.380 + 479.067i −0.874509 + 0.635368i
\(755\) 2199.63 714.704i 2.91342 0.946627i
\(756\) 0 0
\(757\) −729.792 530.225i −0.964058 0.700429i −0.00996868 0.999950i \(-0.503173\pi\)
−0.954090 + 0.299521i \(0.903173\pi\)
\(758\) 371.596i 0.490233i
\(759\) 0 0
\(760\) 1098.04 1.44479
\(761\) 571.395 786.458i 0.750848 1.03345i −0.247073 0.968997i \(-0.579469\pi\)
0.997921 0.0644566i \(-0.0205314\pi\)
\(762\) 0 0
\(763\) −81.8665 251.959i −0.107295 0.330222i
\(764\) 20.1511 + 27.7356i 0.0263757 + 0.0363031i
\(765\) 0 0
\(766\) −284.691 876.187i −0.371659 1.14385i
\(767\) −0.00711243 0.00231097i −9.27305e−6 3.01300e-6i
\(768\) 0 0
\(769\) 1404.29 1.82613 0.913064 0.407817i \(-0.133710\pi\)
0.913064 + 0.407817i \(0.133710\pi\)
\(770\) −309.300 + 1042.83i −0.401689 + 1.35433i
\(771\) 0 0
\(772\) 1.78342 + 1.29573i 0.00231013 + 0.00167841i
\(773\) −138.598 45.0331i −0.179298 0.0582576i 0.217992 0.975951i \(-0.430049\pi\)
−0.397290 + 0.917693i \(0.630049\pi\)
\(774\) 0 0
\(775\) 821.147 596.599i 1.05955 0.769805i
\(776\) 250.636 + 344.971i 0.322985 + 0.444550i
\(777\) 0 0
\(778\) 276.225 850.133i 0.355045 1.09272i
\(779\) −150.040 + 206.512i −0.192605 + 0.265099i
\(780\) 0 0
\(781\) −28.3035 1095.60i −0.0362401 1.40282i
\(782\) 86.2080i 0.110240i
\(783\) 0 0
\(784\) 103.122 317.376i 0.131533 0.404816i
\(785\) −270.921 + 88.0277i −0.345123 + 0.112137i
\(786\) 0 0
\(787\)