Properties

Label 76.3.b.b.39.13
Level $76$
Weight $3$
Character 76.39
Analytic conductor $2.071$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 76.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.07085000914\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Defining polynomial: \(x^{14} - 2 x^{13} + x^{12} + 14 x^{11} - 42 x^{10} + 28 x^{9} + 132 x^{8} - 440 x^{7} + 528 x^{6} + 448 x^{5} - 2688 x^{4} + 3584 x^{3} + 1024 x^{2} - 8192 x + 16384\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{12} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 39.13
Root \(1.94929 + 0.447510i\) of defining polynomial
Character \(\chi\) \(=\) 76.39
Dual form 76.3.b.b.39.14

$q$-expansion

\(f(q)\) \(=\) \(q+(1.94929 - 0.447510i) q^{2} -3.19988i q^{3} +(3.59947 - 1.74465i) q^{4} -3.90374 q^{5} +(-1.43198 - 6.23749i) q^{6} +2.64664i q^{7} +(6.23566 - 5.01164i) q^{8} -1.23921 q^{9} +O(q^{10})\) \(q+(1.94929 - 0.447510i) q^{2} -3.19988i q^{3} +(3.59947 - 1.74465i) q^{4} -3.90374 q^{5} +(-1.43198 - 6.23749i) q^{6} +2.64664i q^{7} +(6.23566 - 5.01164i) q^{8} -1.23921 q^{9} +(-7.60953 + 1.74696i) q^{10} +13.2532i q^{11} +(-5.58268 - 11.5179i) q^{12} +1.60050 q^{13} +(1.18440 + 5.15907i) q^{14} +12.4915i q^{15} +(9.91236 - 12.5597i) q^{16} +8.10013 q^{17} +(-2.41559 + 0.554561i) q^{18} -4.35890i q^{19} +(-14.0514 + 6.81068i) q^{20} +8.46893 q^{21} +(5.93094 + 25.8343i) q^{22} +38.2047i q^{23} +(-16.0366 - 19.9534i) q^{24} -9.76079 q^{25} +(3.11984 - 0.716239i) q^{26} -24.8336i q^{27} +(4.61747 + 9.52650i) q^{28} -51.1656 q^{29} +(5.59007 + 24.3496i) q^{30} -13.6518i q^{31} +(13.7015 - 28.9183i) q^{32} +42.4086 q^{33} +(15.7895 - 3.62489i) q^{34} -10.3318i q^{35} +(-4.46052 + 2.16200i) q^{36} -35.3910 q^{37} +(-1.95065 - 8.49676i) q^{38} -5.12140i q^{39} +(-24.3424 + 19.5641i) q^{40} +8.06155 q^{41} +(16.5084 - 3.78993i) q^{42} -16.2115i q^{43} +(23.1223 + 47.7045i) q^{44} +4.83758 q^{45} +(17.0970 + 74.4721i) q^{46} -1.59429i q^{47} +(-40.1894 - 31.7183i) q^{48} +41.9953 q^{49} +(-19.0266 + 4.36805i) q^{50} -25.9194i q^{51} +(5.76095 - 2.79232i) q^{52} +56.8772 q^{53} +(-11.1133 - 48.4078i) q^{54} -51.7371i q^{55} +(13.2640 + 16.5036i) q^{56} -13.9479 q^{57} +(-99.7366 + 22.8971i) q^{58} -106.526i q^{59} +(21.7934 + 44.9628i) q^{60} -35.9021 q^{61} +(-6.10933 - 26.6114i) q^{62} -3.27976i q^{63} +(13.7670 - 62.5018i) q^{64} -6.24794 q^{65} +(82.6667 - 18.9783i) q^{66} -47.5191i q^{67} +(29.1562 - 14.1319i) q^{68} +122.250 q^{69} +(-4.62359 - 20.1397i) q^{70} +125.941i q^{71} +(-7.72733 + 6.21050i) q^{72} +34.2172 q^{73} +(-68.9874 + 15.8378i) q^{74} +31.2333i q^{75} +(-7.60477 - 15.6897i) q^{76} -35.0765 q^{77} +(-2.29188 - 9.98310i) q^{78} -71.1726i q^{79} +(-38.6953 + 49.0297i) q^{80} -90.6173 q^{81} +(15.7143 - 3.60763i) q^{82} +149.310i q^{83} +(30.4836 - 14.7754i) q^{84} -31.6208 q^{85} +(-7.25479 - 31.6008i) q^{86} +163.724i q^{87} +(66.4202 + 82.6425i) q^{88} -169.809 q^{89} +(9.42984 - 2.16486i) q^{90} +4.23595i q^{91} +(66.6541 + 137.517i) q^{92} -43.6841 q^{93} +(-0.713460 - 3.10773i) q^{94} +17.0160i q^{95} +(-92.5351 - 43.8431i) q^{96} +109.526 q^{97} +(81.8610 - 18.7933i) q^{98} -16.4236i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q + 2q^{2} + 2q^{4} - 40q^{8} - 68q^{9} + O(q^{10}) \) \( 14q + 2q^{2} + 2q^{4} - 40q^{8} - 68q^{9} - 12q^{10} + 4q^{12} + 54q^{13} + 30q^{14} + 58q^{16} + 34q^{17} + 36q^{18} + 32q^{20} - 38q^{21} + 36q^{22} - 98q^{24} - 86q^{25} - 16q^{26} + 18q^{28} + 54q^{29} - 204q^{30} + 72q^{32} + 20q^{33} - 82q^{34} + 96q^{36} + 100q^{37} - 148q^{40} + 224q^{41} + 224q^{42} - 96q^{44} - 168q^{45} + 46q^{46} + 296q^{48} - 220q^{49} - 58q^{50} - 288q^{52} + 14q^{53} - 128q^{54} + 12q^{56} + 38q^{57} - 72q^{58} + 188q^{60} + 28q^{61} + 396q^{62} - 118q^{64} - 472q^{65} - 32q^{66} + 30q^{68} + 122q^{69} + 156q^{70} + 80q^{72} + 70q^{73} - 224q^{74} + 228q^{77} + 274q^{78} - 348q^{80} + 334q^{81} - 400q^{82} - 216q^{84} + 48q^{85} - 124q^{86} + 472q^{88} + 416q^{90} + 126q^{92} - 176q^{93} - 88q^{94} - 106q^{96} + 308q^{97} + 68q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.94929 0.447510i 0.974645 0.223755i
\(3\) 3.19988i 1.06663i −0.845918 0.533313i \(-0.820947\pi\)
0.845918 0.533313i \(-0.179053\pi\)
\(4\) 3.59947 1.74465i 0.899867 0.436164i
\(5\) −3.90374 −0.780749 −0.390374 0.920656i \(-0.627654\pi\)
−0.390374 + 0.920656i \(0.627654\pi\)
\(6\) −1.43198 6.23749i −0.238663 1.03958i
\(7\) 2.64664i 0.378092i 0.981968 + 0.189046i \(0.0605395\pi\)
−0.981968 + 0.189046i \(0.939461\pi\)
\(8\) 6.23566 5.01164i 0.779458 0.626455i
\(9\) −1.23921 −0.137691
\(10\) −7.60953 + 1.74696i −0.760953 + 0.174696i
\(11\) 13.2532i 1.20484i 0.798181 + 0.602418i \(0.205796\pi\)
−0.798181 + 0.602418i \(0.794204\pi\)
\(12\) −5.58268 11.5179i −0.465223 0.959822i
\(13\) 1.60050 0.123115 0.0615576 0.998104i \(-0.480393\pi\)
0.0615576 + 0.998104i \(0.480393\pi\)
\(14\) 1.18440 + 5.15907i 0.0845999 + 0.368505i
\(15\) 12.4915i 0.832767i
\(16\) 9.91236 12.5597i 0.619523 0.784979i
\(17\) 8.10013 0.476478 0.238239 0.971207i \(-0.423430\pi\)
0.238239 + 0.971207i \(0.423430\pi\)
\(18\) −2.41559 + 0.554561i −0.134199 + 0.0308089i
\(19\) 4.35890i 0.229416i
\(20\) −14.0514 + 6.81068i −0.702570 + 0.340534i
\(21\) 8.46893 0.403282
\(22\) 5.93094 + 25.8343i 0.269588 + 1.17429i
\(23\) 38.2047i 1.66108i 0.556962 + 0.830538i \(0.311967\pi\)
−0.556962 + 0.830538i \(0.688033\pi\)
\(24\) −16.0366 19.9534i −0.668193 0.831390i
\(25\) −9.76079 −0.390431
\(26\) 3.11984 0.716239i 0.119994 0.0275477i
\(27\) 24.8336i 0.919762i
\(28\) 4.61747 + 9.52650i 0.164910 + 0.340232i
\(29\) −51.1656 −1.76433 −0.882165 0.470940i \(-0.843915\pi\)
−0.882165 + 0.470940i \(0.843915\pi\)
\(30\) 5.59007 + 24.3496i 0.186336 + 0.811652i
\(31\) 13.6518i 0.440381i −0.975457 0.220191i \(-0.929332\pi\)
0.975457 0.220191i \(-0.0706679\pi\)
\(32\) 13.7015 28.9183i 0.428172 0.903697i
\(33\) 42.4086 1.28511
\(34\) 15.7895 3.62489i 0.464397 0.106614i
\(35\) 10.3318i 0.295195i
\(36\) −4.46052 + 2.16200i −0.123903 + 0.0600556i
\(37\) −35.3910 −0.956514 −0.478257 0.878220i \(-0.658731\pi\)
−0.478257 + 0.878220i \(0.658731\pi\)
\(38\) −1.95065 8.49676i −0.0513329 0.223599i
\(39\) 5.12140i 0.131318i
\(40\) −24.3424 + 19.5641i −0.608561 + 0.489104i
\(41\) 8.06155 0.196623 0.0983116 0.995156i \(-0.468656\pi\)
0.0983116 + 0.995156i \(0.468656\pi\)
\(42\) 16.5084 3.78993i 0.393057 0.0902364i
\(43\) 16.2115i 0.377010i −0.982072 0.188505i \(-0.939636\pi\)
0.982072 0.188505i \(-0.0603643\pi\)
\(44\) 23.1223 + 47.7045i 0.525506 + 1.08419i
\(45\) 4.83758 0.107502
\(46\) 17.0970 + 74.4721i 0.371674 + 1.61896i
\(47\) 1.59429i 0.0339210i −0.999856 0.0169605i \(-0.994601\pi\)
0.999856 0.0169605i \(-0.00539895\pi\)
\(48\) −40.1894 31.7183i −0.837279 0.660799i
\(49\) 41.9953 0.857047
\(50\) −19.0266 + 4.36805i −0.380532 + 0.0873610i
\(51\) 25.9194i 0.508224i
\(52\) 5.76095 2.79232i 0.110787 0.0536984i
\(53\) 56.8772 1.07315 0.536577 0.843851i \(-0.319717\pi\)
0.536577 + 0.843851i \(0.319717\pi\)
\(54\) −11.1133 48.4078i −0.205801 0.896441i
\(55\) 51.7371i 0.940675i
\(56\) 13.2640 + 16.5036i 0.236857 + 0.294706i
\(57\) −13.9479 −0.244701
\(58\) −99.7366 + 22.8971i −1.71960 + 0.394778i
\(59\) 106.526i 1.80553i −0.430135 0.902765i \(-0.641534\pi\)
0.430135 0.902765i \(-0.358466\pi\)
\(60\) 21.7934 + 44.9628i 0.363223 + 0.749380i
\(61\) −35.9021 −0.588558 −0.294279 0.955720i \(-0.595080\pi\)
−0.294279 + 0.955720i \(0.595080\pi\)
\(62\) −6.10933 26.6114i −0.0985375 0.429216i
\(63\) 3.27976i 0.0520596i
\(64\) 13.7670 62.5018i 0.215109 0.976590i
\(65\) −6.24794 −0.0961221
\(66\) 82.6667 18.9783i 1.25253 0.287550i
\(67\) 47.5191i 0.709240i −0.935011 0.354620i \(-0.884610\pi\)
0.935011 0.354620i \(-0.115390\pi\)
\(68\) 29.1562 14.1319i 0.428767 0.207822i
\(69\) 122.250 1.77175
\(70\) −4.62359 20.1397i −0.0660513 0.287710i
\(71\) 125.941i 1.77382i 0.461941 + 0.886911i \(0.347153\pi\)
−0.461941 + 0.886911i \(0.652847\pi\)
\(72\) −7.72733 + 6.21050i −0.107324 + 0.0862569i
\(73\) 34.2172 0.468729 0.234364 0.972149i \(-0.424699\pi\)
0.234364 + 0.972149i \(0.424699\pi\)
\(74\) −68.9874 + 15.8378i −0.932262 + 0.214025i
\(75\) 31.2333i 0.416444i
\(76\) −7.60477 15.6897i −0.100063 0.206444i
\(77\) −35.0765 −0.455539
\(78\) −2.29188 9.98310i −0.0293830 0.127988i
\(79\) 71.1726i 0.900919i −0.892797 0.450460i \(-0.851260\pi\)
0.892797 0.450460i \(-0.148740\pi\)
\(80\) −38.6953 + 49.0297i −0.483692 + 0.612871i
\(81\) −90.6173 −1.11873
\(82\) 15.7143 3.60763i 0.191638 0.0439954i
\(83\) 149.310i 1.79891i 0.437010 + 0.899457i \(0.356038\pi\)
−0.437010 + 0.899457i \(0.643962\pi\)
\(84\) 30.4836 14.7754i 0.362901 0.175897i
\(85\) −31.6208 −0.372010
\(86\) −7.25479 31.6008i −0.0843580 0.367452i
\(87\) 163.724i 1.88188i
\(88\) 66.4202 + 82.6425i 0.754776 + 0.939119i
\(89\) −169.809 −1.90797 −0.953983 0.299861i \(-0.903060\pi\)
−0.953983 + 0.299861i \(0.903060\pi\)
\(90\) 9.42984 2.16486i 0.104776 0.0240540i
\(91\) 4.23595i 0.0465488i
\(92\) 66.6541 + 137.517i 0.724501 + 1.49475i
\(93\) −43.6841 −0.469722
\(94\) −0.713460 3.10773i −0.00758999 0.0330610i
\(95\) 17.0160i 0.179116i
\(96\) −92.5351 43.8431i −0.963907 0.456699i
\(97\) 109.526 1.12914 0.564569 0.825386i \(-0.309042\pi\)
0.564569 + 0.825386i \(0.309042\pi\)
\(98\) 81.8610 18.7933i 0.835317 0.191769i
\(99\) 16.4236i 0.165895i
\(100\) −35.1336 + 17.0292i −0.351336 + 0.170292i
\(101\) −118.435 −1.17263 −0.586313 0.810084i \(-0.699421\pi\)
−0.586313 + 0.810084i \(0.699421\pi\)
\(102\) −11.5992 50.5245i −0.113718 0.495338i
\(103\) 34.5985i 0.335908i −0.985795 0.167954i \(-0.946284\pi\)
0.985795 0.167954i \(-0.0537160\pi\)
\(104\) 9.98017 8.02112i 0.0959632 0.0771261i
\(105\) −33.0605 −0.314862
\(106\) 110.870 25.4531i 1.04595 0.240124i
\(107\) 85.2253i 0.796498i 0.917277 + 0.398249i \(0.130382\pi\)
−0.917277 + 0.398249i \(0.869618\pi\)
\(108\) −43.3260 89.3876i −0.401166 0.827663i
\(109\) 146.541 1.34442 0.672208 0.740362i \(-0.265346\pi\)
0.672208 + 0.740362i \(0.265346\pi\)
\(110\) −23.1529 100.851i −0.210481 0.916824i
\(111\) 113.247i 1.02024i
\(112\) 33.2409 + 26.2345i 0.296794 + 0.234236i
\(113\) 36.0565 0.319084 0.159542 0.987191i \(-0.448998\pi\)
0.159542 + 0.987191i \(0.448998\pi\)
\(114\) −27.1886 + 6.24184i −0.238496 + 0.0547530i
\(115\) 149.141i 1.29688i
\(116\) −184.169 + 89.2662i −1.58766 + 0.769537i
\(117\) −1.98336 −0.0169518
\(118\) −47.6716 207.651i −0.403996 1.75975i
\(119\) 21.4381i 0.180152i
\(120\) 62.6029 + 77.8928i 0.521691 + 0.649107i
\(121\) −54.6474 −0.451631
\(122\) −69.9836 + 16.0665i −0.573636 + 0.131693i
\(123\) 25.7960i 0.209723i
\(124\) −23.8177 49.1393i −0.192078 0.396285i
\(125\) 135.697 1.08558
\(126\) −1.46772 6.39320i −0.0116486 0.0507397i
\(127\) 103.364i 0.813890i 0.913453 + 0.406945i \(0.133406\pi\)
−0.913453 + 0.406945i \(0.866594\pi\)
\(128\) −1.13432 127.995i −0.00886188 0.999961i
\(129\) −51.8747 −0.402129
\(130\) −12.1790 + 2.79601i −0.0936850 + 0.0215078i
\(131\) 85.6520i 0.653832i −0.945053 0.326916i \(-0.893991\pi\)
0.945053 0.326916i \(-0.106009\pi\)
\(132\) 152.649 73.9884i 1.15643 0.560518i
\(133\) 11.5364 0.0867402
\(134\) −21.2653 92.6285i −0.158696 0.691257i
\(135\) 96.9439i 0.718103i
\(136\) 50.5097 40.5949i 0.371395 0.298492i
\(137\) 89.4114 0.652638 0.326319 0.945260i \(-0.394192\pi\)
0.326319 + 0.945260i \(0.394192\pi\)
\(138\) 238.302 54.7083i 1.72682 0.396437i
\(139\) 175.314i 1.26125i −0.776087 0.630625i \(-0.782799\pi\)
0.776087 0.630625i \(-0.217201\pi\)
\(140\) −18.0254 37.1890i −0.128753 0.265636i
\(141\) −5.10152 −0.0361810
\(142\) 56.3600 + 245.496i 0.396901 + 1.72885i
\(143\) 21.2117i 0.148334i
\(144\) −12.2835 + 15.5641i −0.0853024 + 0.108084i
\(145\) 199.737 1.37750
\(146\) 66.6993 15.3125i 0.456844 0.104880i
\(147\) 134.380i 0.914148i
\(148\) −127.389 + 61.7451i −0.860736 + 0.417197i
\(149\) 207.665 1.39372 0.696862 0.717205i \(-0.254579\pi\)
0.696862 + 0.717205i \(0.254579\pi\)
\(150\) 13.9772 + 60.8828i 0.0931815 + 0.405885i
\(151\) 33.2962i 0.220504i −0.993904 0.110252i \(-0.964834\pi\)
0.993904 0.110252i \(-0.0351659\pi\)
\(152\) −21.8452 27.1806i −0.143719 0.178820i
\(153\) −10.0378 −0.0656065
\(154\) −68.3742 + 15.6971i −0.443989 + 0.101929i
\(155\) 53.2932i 0.343827i
\(156\) −8.93507 18.4343i −0.0572761 0.118169i
\(157\) −232.843 −1.48308 −0.741539 0.670910i \(-0.765904\pi\)
−0.741539 + 0.670910i \(0.765904\pi\)
\(158\) −31.8505 138.736i −0.201585 0.878077i
\(159\) 182.000i 1.14465i
\(160\) −53.4872 + 112.890i −0.334295 + 0.705561i
\(161\) −101.114 −0.628039
\(162\) −176.639 + 40.5521i −1.09037 + 0.250322i
\(163\) 133.148i 0.816858i −0.912790 0.408429i \(-0.866077\pi\)
0.912790 0.408429i \(-0.133923\pi\)
\(164\) 29.0173 14.0646i 0.176935 0.0857599i
\(165\) −165.552 −1.00335
\(166\) 66.8177 + 291.048i 0.402516 + 1.75330i
\(167\) 84.0944i 0.503559i 0.967785 + 0.251780i \(0.0810158\pi\)
−0.967785 + 0.251780i \(0.918984\pi\)
\(168\) 52.8094 42.4432i 0.314341 0.252638i
\(169\) −166.438 −0.984843
\(170\) −61.6382 + 14.1506i −0.362578 + 0.0832390i
\(171\) 5.40161i 0.0315884i
\(172\) −28.2834 58.3526i −0.164438 0.339259i
\(173\) 40.8353 0.236042 0.118021 0.993011i \(-0.462345\pi\)
0.118021 + 0.993011i \(0.462345\pi\)
\(174\) 73.2679 + 319.145i 0.421080 + 1.83417i
\(175\) 25.8333i 0.147619i
\(176\) 166.456 + 131.371i 0.945771 + 0.746424i
\(177\) −340.871 −1.92582
\(178\) −331.007 + 75.9912i −1.85959 + 0.426917i
\(179\) 94.3723i 0.527219i −0.964629 0.263610i \(-0.915087\pi\)
0.964629 0.263610i \(-0.0849131\pi\)
\(180\) 17.4127 8.43990i 0.0967373 0.0468883i
\(181\) 101.869 0.562811 0.281405 0.959589i \(-0.409199\pi\)
0.281405 + 0.959589i \(0.409199\pi\)
\(182\) 1.89563 + 8.25709i 0.0104155 + 0.0453686i
\(183\) 114.882i 0.627772i
\(184\) 191.468 + 238.232i 1.04059 + 1.29474i
\(185\) 138.157 0.746797
\(186\) −85.1531 + 19.5491i −0.457812 + 0.105103i
\(187\) 107.353i 0.574078i
\(188\) −2.78148 5.73859i −0.0147951 0.0305244i
\(189\) 65.7255 0.347754
\(190\) 7.61484 + 33.1692i 0.0400781 + 0.174575i
\(191\) 96.9894i 0.507798i −0.967231 0.253899i \(-0.918287\pi\)
0.967231 0.253899i \(-0.0817131\pi\)
\(192\) −199.998 44.0526i −1.04166 0.229441i
\(193\) 218.158 1.13035 0.565177 0.824970i \(-0.308808\pi\)
0.565177 + 0.824970i \(0.308808\pi\)
\(194\) 213.499 49.0142i 1.10051 0.252650i
\(195\) 19.9926i 0.102526i
\(196\) 151.161 73.2673i 0.771228 0.373813i
\(197\) −0.646370 −0.00328107 −0.00164053 0.999999i \(-0.500522\pi\)
−0.00164053 + 0.999999i \(0.500522\pi\)
\(198\) −7.34971 32.0143i −0.0371197 0.161688i
\(199\) 20.5908i 0.103471i 0.998661 + 0.0517356i \(0.0164753\pi\)
−0.998661 + 0.0517356i \(0.983525\pi\)
\(200\) −60.8650 + 48.9175i −0.304325 + 0.244588i
\(201\) −152.055 −0.756494
\(202\) −230.865 + 53.0010i −1.14290 + 0.262381i
\(203\) 135.417i 0.667078i
\(204\) −45.2204 93.2961i −0.221669 0.457334i
\(205\) −31.4702 −0.153513
\(206\) −15.4832 67.4426i −0.0751611 0.327391i
\(207\) 47.3439i 0.228714i
\(208\) 15.8647 20.1017i 0.0762727 0.0966429i
\(209\) 57.7694 0.276408
\(210\) −64.4446 + 14.7949i −0.306879 + 0.0704520i
\(211\) 161.772i 0.766690i 0.923605 + 0.383345i \(0.125228\pi\)
−0.923605 + 0.383345i \(0.874772\pi\)
\(212\) 204.728 99.2311i 0.965697 0.468071i
\(213\) 402.997 1.89200
\(214\) 38.1392 + 166.129i 0.178221 + 0.776303i
\(215\) 63.2854i 0.294350i
\(216\) −124.457 154.854i −0.576189 0.716915i
\(217\) 36.1315 0.166504
\(218\) 285.652 65.5787i 1.31033 0.300820i
\(219\) 109.491i 0.499958i
\(220\) −90.2634 186.226i −0.410288 0.846482i
\(221\) 12.9642 0.0586617
\(222\) 50.6791 + 220.751i 0.228284 + 0.994375i
\(223\) 171.167i 0.767567i 0.923423 + 0.383784i \(0.125379\pi\)
−0.923423 + 0.383784i \(0.874621\pi\)
\(224\) 76.5364 + 36.2630i 0.341680 + 0.161888i
\(225\) 12.0957 0.0537587
\(226\) 70.2845 16.1356i 0.310994 0.0713966i
\(227\) 110.173i 0.485343i −0.970109 0.242672i \(-0.921976\pi\)
0.970109 0.242672i \(-0.0780237\pi\)
\(228\) −50.2052 + 24.3343i −0.220198 + 0.106730i
\(229\) 184.830 0.807120 0.403560 0.914953i \(-0.367773\pi\)
0.403560 + 0.914953i \(0.367773\pi\)
\(230\) −66.7423 290.720i −0.290184 1.26400i
\(231\) 112.240i 0.485889i
\(232\) −319.051 + 256.423i −1.37522 + 1.10527i
\(233\) −226.138 −0.970550 −0.485275 0.874362i \(-0.661281\pi\)
−0.485275 + 0.874362i \(0.661281\pi\)
\(234\) −3.86615 + 0.887574i −0.0165220 + 0.00379305i
\(235\) 6.22369i 0.0264838i
\(236\) −185.851 383.438i −0.787506 1.62474i
\(237\) −227.744 −0.960944
\(238\) 9.59378 + 41.7891i 0.0403100 + 0.175585i
\(239\) 282.285i 1.18111i −0.806999 0.590553i \(-0.798910\pi\)
0.806999 0.590553i \(-0.201090\pi\)
\(240\) 156.889 + 123.820i 0.653704 + 0.515918i
\(241\) −8.68875 −0.0360529 −0.0180265 0.999838i \(-0.505738\pi\)
−0.0180265 + 0.999838i \(0.505738\pi\)
\(242\) −106.524 + 24.4552i −0.440180 + 0.101055i
\(243\) 66.4621i 0.273507i
\(244\) −129.228 + 62.6367i −0.529624 + 0.256708i
\(245\) −163.939 −0.669138
\(246\) −11.5440 50.2839i −0.0469267 0.204406i
\(247\) 6.97641i 0.0282446i
\(248\) −68.4180 85.1281i −0.275879 0.343259i
\(249\) 477.773 1.91877
\(250\) 264.513 60.7259i 1.05805 0.242903i
\(251\) 273.275i 1.08874i 0.838844 + 0.544372i \(0.183232\pi\)
−0.838844 + 0.544372i \(0.816768\pi\)
\(252\) −5.72204 11.8054i −0.0227065 0.0468468i
\(253\) −506.335 −2.00132
\(254\) 46.2565 + 201.487i 0.182112 + 0.793255i
\(255\) 101.183i 0.396795i
\(256\) −59.4902 248.992i −0.232383 0.972624i
\(257\) 225.614 0.877877 0.438938 0.898517i \(-0.355355\pi\)
0.438938 + 0.898517i \(0.355355\pi\)
\(258\) −101.119 + 23.2144i −0.391933 + 0.0899784i
\(259\) 93.6673i 0.361650i
\(260\) −22.4893 + 10.9005i −0.0864971 + 0.0419250i
\(261\) 63.4051 0.242932
\(262\) −38.3301 166.961i −0.146298 0.637255i
\(263\) 153.711i 0.584454i −0.956349 0.292227i \(-0.905604\pi\)
0.956349 0.292227i \(-0.0943962\pi\)
\(264\) 264.446 212.537i 1.00169 0.805063i
\(265\) −222.034 −0.837864
\(266\) 22.4879 5.16267i 0.0845409 0.0194085i
\(267\) 543.368i 2.03509i
\(268\) −82.9044 171.043i −0.309345 0.638222i
\(269\) −266.196 −0.989575 −0.494788 0.869014i \(-0.664754\pi\)
−0.494788 + 0.869014i \(0.664754\pi\)
\(270\) 43.3833 + 188.972i 0.160679 + 0.699895i
\(271\) 420.472i 1.55156i −0.631005 0.775778i \(-0.717357\pi\)
0.631005 0.775778i \(-0.282643\pi\)
\(272\) 80.2914 101.735i 0.295189 0.374025i
\(273\) 13.5545 0.0496502
\(274\) 174.289 40.0125i 0.636091 0.146031i
\(275\) 129.362i 0.470406i
\(276\) 440.037 213.285i 1.59434 0.772771i
\(277\) −51.6625 −0.186507 −0.0932536 0.995642i \(-0.529727\pi\)
−0.0932536 + 0.995642i \(0.529727\pi\)
\(278\) −78.4547 341.738i −0.282211 1.22927i
\(279\) 16.9175i 0.0606363i
\(280\) −51.7793 64.4257i −0.184926 0.230092i
\(281\) 412.087 1.46650 0.733251 0.679958i \(-0.238002\pi\)
0.733251 + 0.679958i \(0.238002\pi\)
\(282\) −9.94435 + 2.28298i −0.0352637 + 0.00809568i
\(283\) 492.048i 1.73868i 0.494211 + 0.869342i \(0.335457\pi\)
−0.494211 + 0.869342i \(0.664543\pi\)
\(284\) 219.724 + 453.322i 0.773676 + 1.59620i
\(285\) 54.4492 0.191050
\(286\) 9.49246 + 41.3478i 0.0331904 + 0.144573i
\(287\) 21.3360i 0.0743416i
\(288\) −16.9791 + 35.8360i −0.0589552 + 0.124431i
\(289\) −223.388 −0.772969
\(290\) 389.346 89.3844i 1.34257 0.308222i
\(291\) 350.471i 1.20437i
\(292\) 123.164 59.6972i 0.421794 0.204442i
\(293\) −462.881 −1.57980 −0.789899 0.613237i \(-0.789867\pi\)
−0.789899 + 0.613237i \(0.789867\pi\)
\(294\) −60.1363 261.945i −0.204545 0.890970i
\(295\) 415.851i 1.40966i
\(296\) −220.686 + 177.367i −0.745562 + 0.599213i
\(297\) 329.124 1.10816
\(298\) 404.799 92.9321i 1.35839 0.311853i
\(299\) 61.1466i 0.204504i
\(300\) 54.4913 + 112.423i 0.181638 + 0.374745i
\(301\) 42.9059 0.142544
\(302\) −14.9004 64.9039i −0.0493390 0.214914i
\(303\) 378.978i 1.25075i
\(304\) −54.7463 43.2070i −0.180086 0.142128i
\(305\) 140.152 0.459516
\(306\) −19.5666 + 4.49201i −0.0639431 + 0.0146798i
\(307\) 477.735i 1.55614i 0.628178 + 0.778070i \(0.283801\pi\)
−0.628178 + 0.778070i \(0.716199\pi\)
\(308\) −126.257 + 61.1963i −0.409924 + 0.198689i
\(309\) −110.711 −0.358288
\(310\) 23.8492 + 103.884i 0.0769330 + 0.335109i
\(311\) 397.518i 1.27819i −0.769127 0.639096i \(-0.779309\pi\)
0.769127 0.639096i \(-0.220691\pi\)
\(312\) −25.6666 31.9353i −0.0822647 0.102357i
\(313\) −249.717 −0.797818 −0.398909 0.916991i \(-0.630611\pi\)
−0.398909 + 0.916991i \(0.630611\pi\)
\(314\) −453.879 + 104.200i −1.44548 + 0.331846i
\(315\) 12.8033i 0.0406455i
\(316\) −124.172 256.184i −0.392948 0.810708i
\(317\) 17.5401 0.0553317 0.0276658 0.999617i \(-0.491193\pi\)
0.0276658 + 0.999617i \(0.491193\pi\)
\(318\) −81.4469 354.771i −0.256122 1.11563i
\(319\) 678.108i 2.12573i
\(320\) −53.7428 + 243.991i −0.167946 + 0.762471i
\(321\) 272.711 0.849566
\(322\) −197.101 + 45.2496i −0.612115 + 0.140527i
\(323\) 35.3076i 0.109312i
\(324\) −326.174 + 158.096i −1.00671 + 0.487950i
\(325\) −15.6221 −0.0480681
\(326\) −59.5850 259.544i −0.182776 0.796147i
\(327\) 468.914i 1.43399i
\(328\) 50.2691 40.4016i 0.153260 0.123176i
\(329\) 4.21951 0.0128252
\(330\) −322.710 + 74.0864i −0.977908 + 0.224504i
\(331\) 524.291i 1.58396i 0.610546 + 0.791981i \(0.290950\pi\)
−0.610546 + 0.791981i \(0.709050\pi\)
\(332\) 260.494 + 537.436i 0.784621 + 1.61878i
\(333\) 43.8571 0.131703
\(334\) 37.6331 + 163.924i 0.112674 + 0.490792i
\(335\) 185.502i 0.553738i
\(336\) 83.9471 106.367i 0.249842 0.316568i
\(337\) −10.3787 −0.0307974 −0.0153987 0.999881i \(-0.504902\pi\)
−0.0153987 + 0.999881i \(0.504902\pi\)
\(338\) −324.437 + 74.4829i −0.959872 + 0.220363i
\(339\) 115.376i 0.340343i
\(340\) −113.818 + 55.1674i −0.334759 + 0.162257i
\(341\) 180.930 0.530587
\(342\) 2.41728 + 10.5293i 0.00706806 + 0.0307875i
\(343\) 240.832i 0.702134i
\(344\) −81.2459 101.089i −0.236180 0.293864i
\(345\) −477.234 −1.38329
\(346\) 79.5998 18.2742i 0.230057 0.0528156i
\(347\) 140.835i 0.405864i 0.979193 + 0.202932i \(0.0650470\pi\)
−0.979193 + 0.202932i \(0.934953\pi\)
\(348\) 285.641 + 589.318i 0.820808 + 1.69344i
\(349\) 588.176 1.68532 0.842659 0.538447i \(-0.180989\pi\)
0.842659 + 0.538447i \(0.180989\pi\)
\(350\) −11.5607 50.3566i −0.0330305 0.143876i
\(351\) 39.7461i 0.113237i
\(352\) 383.260 + 181.589i 1.08881 + 0.515877i
\(353\) −67.7579 −0.191949 −0.0959744 0.995384i \(-0.530597\pi\)
−0.0959744 + 0.995384i \(0.530597\pi\)
\(354\) −664.456 + 152.543i −1.87700 + 0.430913i
\(355\) 491.643i 1.38491i
\(356\) −611.222 + 296.258i −1.71692 + 0.832185i
\(357\) 68.5994 0.192155
\(358\) −42.2325 183.959i −0.117968 0.513852i
\(359\) 136.276i 0.379598i 0.981823 + 0.189799i \(0.0607836\pi\)
−0.981823 + 0.189799i \(0.939216\pi\)
\(360\) 30.1655 24.2442i 0.0837930 0.0673449i
\(361\) −19.0000 −0.0526316
\(362\) 198.572 45.5873i 0.548541 0.125932i
\(363\) 174.865i 0.481721i
\(364\) 7.39026 + 15.2472i 0.0203029 + 0.0418878i
\(365\) −133.575 −0.365959
\(366\) 51.4109 + 223.939i 0.140467 + 0.611855i
\(367\) 274.645i 0.748352i 0.927358 + 0.374176i \(0.122074\pi\)
−0.927358 + 0.374176i \(0.877926\pi\)
\(368\) 479.838 + 378.699i 1.30391 + 1.02907i
\(369\) −9.99000 −0.0270732
\(370\) 269.309 61.8268i 0.727862 0.167100i
\(371\) 150.534i 0.405751i
\(372\) −157.240 + 76.2137i −0.422687 + 0.204876i
\(373\) 7.96701 0.0213593 0.0106796 0.999943i \(-0.496601\pi\)
0.0106796 + 0.999943i \(0.496601\pi\)
\(374\) 48.0414 + 209.261i 0.128453 + 0.559523i
\(375\) 434.214i 1.15791i
\(376\) −7.98999 9.94144i −0.0212500 0.0264400i
\(377\) −81.8904 −0.217216
\(378\) 128.118 29.4128i 0.338937 0.0778117i
\(379\) 514.957i 1.35873i −0.733803 0.679363i \(-0.762256\pi\)
0.733803 0.679363i \(-0.237744\pi\)
\(380\) 29.6871 + 61.2487i 0.0781239 + 0.161181i
\(381\) 330.752 0.868116
\(382\) −43.4037 189.061i −0.113622 0.494923i
\(383\) 669.698i 1.74856i −0.485424 0.874279i \(-0.661335\pi\)
0.485424 0.874279i \(-0.338665\pi\)
\(384\) −409.568 + 3.62969i −1.06658 + 0.00945231i
\(385\) 136.930 0.355661
\(386\) 425.254 97.6280i 1.10169 0.252922i
\(387\) 20.0895i 0.0519108i
\(388\) 394.237 191.086i 1.01607 0.492489i
\(389\) −374.922 −0.963809 −0.481905 0.876224i \(-0.660055\pi\)
−0.481905 + 0.876224i \(0.660055\pi\)
\(390\) 8.94690 + 38.9714i 0.0229408 + 0.0999268i
\(391\) 309.463i 0.791466i
\(392\) 261.868 210.465i 0.668032 0.536901i
\(393\) −274.076 −0.697394
\(394\) −1.25996 + 0.289257i −0.00319788 + 0.000734155i
\(395\) 277.840i 0.703391i
\(396\) −28.6534 59.1161i −0.0723572 0.149283i
\(397\) −32.0134 −0.0806384 −0.0403192 0.999187i \(-0.512837\pi\)
−0.0403192 + 0.999187i \(0.512837\pi\)
\(398\) 9.21458 + 40.1374i 0.0231522 + 0.100848i
\(399\) 36.9152i 0.0925193i
\(400\) −96.7524 + 122.592i −0.241881 + 0.306480i
\(401\) 380.066 0.947796 0.473898 0.880580i \(-0.342847\pi\)
0.473898 + 0.880580i \(0.342847\pi\)
\(402\) −296.400 + 68.0462i −0.737313 + 0.169269i
\(403\) 21.8497i 0.0542177i
\(404\) −426.304 + 206.629i −1.05521 + 0.511457i
\(405\) 353.747 0.873448
\(406\) −60.6004 263.967i −0.149262 0.650165i
\(407\) 469.044i 1.15244i
\(408\) −129.899 161.625i −0.318379 0.396139i
\(409\) 116.916 0.285858 0.142929 0.989733i \(-0.454348\pi\)
0.142929 + 0.989733i \(0.454348\pi\)
\(410\) −61.3446 + 14.0832i −0.149621 + 0.0343494i
\(411\) 286.106i 0.696121i
\(412\) −60.3625 124.536i −0.146511 0.302273i
\(413\) 281.937 0.682655
\(414\) −21.1869 92.2870i −0.0511760 0.222915i
\(415\) 582.867i 1.40450i
\(416\) 21.9292 46.2837i 0.0527145 0.111259i
\(417\) −560.983 −1.34528
\(418\) 112.609 25.8524i 0.269400 0.0618478i
\(419\) 0.146671i 0.000350050i −1.00000 0.000175025i \(-0.999944\pi\)
1.00000 0.000175025i \(-5.57122e-5\pi\)
\(420\) −119.000 + 57.6792i −0.283334 + 0.137331i
\(421\) −613.336 −1.45686 −0.728428 0.685123i \(-0.759749\pi\)
−0.728428 + 0.685123i \(0.759749\pi\)
\(422\) 72.3944 + 315.340i 0.171551 + 0.747251i
\(423\) 1.97566i 0.00467060i
\(424\) 354.667 285.048i 0.836479 0.672283i
\(425\) −79.0636 −0.186032
\(426\) 785.558 180.345i 1.84403 0.423345i
\(427\) 95.0199i 0.222529i
\(428\) 148.689 + 306.766i 0.347404 + 0.716743i
\(429\) 67.8749 0.158217
\(430\) 28.3208 + 123.362i 0.0658624 + 0.286887i
\(431\) 310.234i 0.719800i −0.932991 0.359900i \(-0.882811\pi\)
0.932991 0.359900i \(-0.117189\pi\)
\(432\) −311.901 246.159i −0.721993 0.569813i
\(433\) −194.780 −0.449838 −0.224919 0.974378i \(-0.572212\pi\)
−0.224919 + 0.974378i \(0.572212\pi\)
\(434\) 70.4307 16.1692i 0.162283 0.0372562i
\(435\) 639.135i 1.46928i
\(436\) 527.471 255.664i 1.20980 0.586385i
\(437\) 166.531 0.381077
\(438\) −48.9982 213.429i −0.111868 0.487282i
\(439\) 340.063i 0.774631i 0.921947 + 0.387315i \(0.126598\pi\)
−0.921947 + 0.387315i \(0.873402\pi\)
\(440\) −259.288 322.615i −0.589290 0.733216i
\(441\) −52.0412 −0.118007
\(442\) 25.2711 5.80163i 0.0571744 0.0131259i
\(443\) 643.348i 1.45225i 0.687561 + 0.726127i \(0.258682\pi\)
−0.687561 + 0.726127i \(0.741318\pi\)
\(444\) 197.577 + 407.629i 0.444993 + 0.918083i
\(445\) 662.891 1.48964
\(446\) 76.5992 + 333.655i 0.171747 + 0.748106i
\(447\) 664.502i 1.48658i
\(448\) 165.420 + 36.4363i 0.369240 + 0.0813309i
\(449\) −416.379 −0.927348 −0.463674 0.886006i \(-0.653469\pi\)
−0.463674 + 0.886006i \(0.653469\pi\)
\(450\) 23.5781 5.41295i 0.0523957 0.0120288i
\(451\) 106.841i 0.236899i
\(452\) 129.784 62.9061i 0.287133 0.139173i
\(453\) −106.544 −0.235196
\(454\) −49.3035 214.759i −0.108598 0.473037i
\(455\) 16.5360i 0.0363430i
\(456\) −86.9747 + 69.9020i −0.190734 + 0.153294i
\(457\) 814.576 1.78244 0.891221 0.453568i \(-0.149849\pi\)
0.891221 + 0.453568i \(0.149849\pi\)
\(458\) 360.288 82.7134i 0.786655 0.180597i
\(459\) 201.155i 0.438246i
\(460\) −260.200 536.830i −0.565653 1.16702i
\(461\) 122.745 0.266259 0.133129 0.991099i \(-0.457497\pi\)
0.133129 + 0.991099i \(0.457497\pi\)
\(462\) 50.2287 + 218.789i 0.108720 + 0.473570i
\(463\) 348.734i 0.753206i 0.926375 + 0.376603i \(0.122908\pi\)
−0.926375 + 0.376603i \(0.877092\pi\)
\(464\) −507.172 + 642.622i −1.09304 + 1.38496i
\(465\) 170.532 0.366735
\(466\) −440.809 + 101.199i −0.945942 + 0.217165i
\(467\) 41.9400i 0.0898072i −0.998991 0.0449036i \(-0.985702\pi\)
0.998991 0.0449036i \(-0.0142981\pi\)
\(468\) −7.13905 + 3.46028i −0.0152544 + 0.00739376i
\(469\) 125.766 0.268158
\(470\) 2.78516 + 12.1318i 0.00592588 + 0.0258123i
\(471\) 745.070i 1.58189i
\(472\) −533.871 664.262i −1.13108 1.40733i
\(473\) 214.854 0.454236
\(474\) −443.939 + 101.918i −0.936579 + 0.215016i
\(475\) 42.5463i 0.0895711i
\(476\) 37.4021 + 77.1659i 0.0785759 + 0.162113i
\(477\) −70.4831 −0.147763
\(478\) −126.325 550.255i −0.264279 1.15116i
\(479\) 257.365i 0.537297i 0.963238 + 0.268648i \(0.0865770\pi\)
−0.963238 + 0.268648i \(0.913423\pi\)
\(480\) 361.233 + 171.152i 0.752569 + 0.356567i
\(481\) −56.6433 −0.117761
\(482\) −16.9369 + 3.88830i −0.0351388 + 0.00806702i
\(483\) 323.553i 0.669882i
\(484\) −196.702 + 95.3408i −0.406408 + 0.196985i
\(485\) −427.563 −0.881573
\(486\) 29.7425 + 129.554i 0.0611985 + 0.266572i
\(487\) 312.131i 0.640927i 0.947261 + 0.320463i \(0.103839\pi\)
−0.947261 + 0.320463i \(0.896161\pi\)
\(488\) −223.873 + 179.928i −0.458756 + 0.368705i
\(489\) −426.057 −0.871282
\(490\) −319.565 + 73.3643i −0.652172 + 0.149723i
\(491\) 855.711i 1.74279i 0.490581 + 0.871396i \(0.336785\pi\)
−0.490581 + 0.871396i \(0.663215\pi\)
\(492\) −45.0051 92.8519i −0.0914737 0.188723i
\(493\) −414.448 −0.840665
\(494\) −3.12201 13.5991i −0.00631987 0.0275285i
\(495\) 64.1134i 0.129522i
\(496\) −171.462 135.322i −0.345690 0.272826i
\(497\) −333.321 −0.670667
\(498\) 931.319 213.808i 1.87012 0.429334i
\(499\) 437.337i 0.876427i 0.898871 + 0.438214i \(0.144389\pi\)
−0.898871 + 0.438214i \(0.855611\pi\)
\(500\) 488.438 236.745i 0.976876 0.473489i
\(501\) 269.092 0.537109
\(502\) 122.293 + 532.692i 0.243612 + 1.06114i
\(503\) 454.628i 0.903834i 0.892060 + 0.451917i \(0.149260\pi\)
−0.892060 + 0.451917i \(0.850740\pi\)
\(504\) −16.4370 20.4515i −0.0326130 0.0405783i
\(505\) 462.341 0.915527
\(506\) −986.994 + 226.590i −1.95058 + 0.447806i
\(507\) 532.582i 1.05046i
\(508\) 180.335 + 372.056i 0.354989 + 0.732393i
\(509\) 330.296 0.648912 0.324456 0.945901i \(-0.394819\pi\)
0.324456 + 0.945901i \(0.394819\pi\)
\(510\) 45.2803 + 197.235i 0.0887849 + 0.386735i
\(511\) 90.5606i 0.177222i
\(512\) −227.390 458.735i −0.444121 0.895967i
\(513\) −108.247 −0.211008
\(514\) 439.788 100.965i 0.855619 0.196429i
\(515\) 135.064i 0.262260i
\(516\) −186.721 + 90.5033i −0.361863 + 0.175394i
\(517\) 21.1294 0.0408693
\(518\) −41.9171 182.585i −0.0809210 0.352480i
\(519\) 130.668i 0.251768i
\(520\) −38.9600 + 31.3124i −0.0749231 + 0.0602161i
\(521\) −156.351 −0.300098 −0.150049 0.988679i \(-0.547943\pi\)
−0.150049 + 0.988679i \(0.547943\pi\)
\(522\) 123.595 28.3744i 0.236772 0.0543572i
\(523\) 383.630i 0.733518i 0.930316 + 0.366759i \(0.119533\pi\)
−0.930316 + 0.366759i \(0.880467\pi\)
\(524\) −149.433 308.302i −0.285178 0.588362i
\(525\) −82.6634 −0.157454
\(526\) −68.7874 299.628i −0.130774 0.569635i
\(527\) 110.581i 0.209832i
\(528\) 420.370 532.638i 0.796155 1.00878i
\(529\) −930.602 −1.75917
\(530\) −432.809 + 99.3624i −0.816620 + 0.187476i
\(531\) 132.009i 0.248604i
\(532\) 41.5251 20.1271i 0.0780546 0.0378329i
\(533\) 12.9025 0.0242073
\(534\) 243.163 + 1059.18i 0.455361 + 1.98349i
\(535\) 332.698i 0.621865i
\(536\) −238.148 296.313i −0.444307 0.552823i
\(537\) −301.980 −0.562346
\(538\) −518.893 + 119.125i −0.964485 + 0.221422i
\(539\) 556.572i 1.03260i
\(540\) 169.134 + 348.946i 0.313210 + 0.646197i
\(541\) −167.893 −0.310337 −0.155169 0.987888i \(-0.549592\pi\)
−0.155169 + 0.987888i \(0.549592\pi\)
\(542\) −188.165 819.622i −0.347169 1.51222i
\(543\) 325.968i 0.600309i
\(544\) 110.984 234.242i 0.204015 0.430592i
\(545\) −572.060 −1.04965
\(546\) 26.4217 6.06578i 0.0483913 0.0111095i
\(547\) 93.9282i 0.171715i −0.996307 0.0858576i \(-0.972637\pi\)
0.996307 0.0858576i \(-0.0273630\pi\)
\(548\) 321.834 155.992i 0.587288 0.284657i
\(549\) 44.4904 0.0810389
\(550\) −57.8906 252.164i −0.105256 0.458479i
\(551\) 223.026i 0.404765i
\(552\) 762.313 612.675i 1.38100 1.10992i
\(553\) 188.368 0.340630
\(554\) −100.705 + 23.1195i −0.181778 + 0.0417319i
\(555\) 442.087i 0.796553i
\(556\) −305.862 631.037i −0.550112 1.13496i
\(557\) 658.999 1.18312 0.591561 0.806260i \(-0.298512\pi\)
0.591561 + 0.806260i \(0.298512\pi\)
\(558\) 7.57077 + 32.9772i 0.0135677 + 0.0590989i
\(559\) 25.9464i 0.0464158i
\(560\) −129.764 102.413i −0.231721 0.182880i
\(561\) 343.515 0.612327
\(562\) 803.277 184.413i 1.42932 0.328137i
\(563\) 709.470i 1.26016i −0.776531 0.630079i \(-0.783022\pi\)
0.776531 0.630079i \(-0.216978\pi\)
\(564\) −18.3628 + 8.90040i −0.0325581 + 0.0157808i
\(565\) −140.755 −0.249124
\(566\) 220.196 + 959.144i 0.389039 + 1.69460i
\(567\) 239.831i 0.422983i
\(568\) 631.172 + 785.328i 1.11122 + 1.38262i
\(569\) 613.773 1.07869 0.539344 0.842086i \(-0.318672\pi\)
0.539344 + 0.842086i \(0.318672\pi\)
\(570\) 106.137 24.3666i 0.186206 0.0427483i
\(571\) 436.257i 0.764022i −0.924158 0.382011i \(-0.875232\pi\)
0.924158 0.382011i \(-0.124768\pi\)
\(572\) 37.0071 + 76.3510i 0.0646978 + 0.133481i
\(573\) −310.354 −0.541631
\(574\) 9.54809 + 41.5901i 0.0166343 + 0.0724567i
\(575\) 372.908i 0.648536i
\(576\) −17.0602 + 77.4531i −0.0296185 + 0.134467i
\(577\) 356.629 0.618074 0.309037 0.951050i \(-0.399993\pi\)
0.309037 + 0.951050i \(0.399993\pi\)
\(578\) −435.448 + 99.9683i −0.753370 + 0.172956i
\(579\) 698.080i 1.20566i
\(580\) 718.948 348.473i 1.23957 0.600815i
\(581\) −395.170 −0.680154
\(582\) −156.839 683.170i −0.269483 1.17383i
\(583\) 753.805i 1.29298i
\(584\) 213.367 171.484i 0.365354 0.293637i
\(585\) 7.74253 0.0132351
\(586\) −902.290 + 207.144i −1.53974 + 0.353488i
\(587\) 411.394i 0.700842i 0.936592 + 0.350421i \(0.113961\pi\)
−0.936592 + 0.350421i \(0.886039\pi\)
\(588\) −234.446 483.696i −0.398718 0.822612i
\(589\) −59.5069 −0.101030
\(590\) 186.098 + 810.615i 0.315420 + 1.37392i
\(591\) 2.06831i 0.00349967i
\(592\) −350.809 + 444.499i −0.592582 + 0.750843i
\(593\) 110.332 0.186057 0.0930285 0.995663i \(-0.470345\pi\)
0.0930285 + 0.995663i \(0.470345\pi\)
\(594\) 641.559 147.286i 1.08007 0.247957i
\(595\) 83.6890i 0.140654i
\(596\) 747.483 362.303i 1.25417 0.607892i
\(597\) 65.8880 0.110365
\(598\) 27.3637 + 119.193i 0.0457587 + 0.199319i
\(599\) 679.317i 1.13408i −0.823689 0.567042i \(-0.808088\pi\)
0.823689 0.567042i \(-0.191912\pi\)
\(600\) 156.530 + 194.760i 0.260883 + 0.324601i
\(601\) −873.422 −1.45328 −0.726641 0.687018i \(-0.758920\pi\)
−0.726641 + 0.687018i \(0.758920\pi\)
\(602\) 83.6361 19.2008i 0.138930 0.0318950i
\(603\) 58.8863i 0.0976556i
\(604\) −58.0903 119.849i −0.0961760 0.198425i
\(605\) 213.329 0.352610
\(606\) 169.597 + 738.739i 0.279862 + 1.21904i
\(607\) 14.0258i 0.0231067i −0.999933 0.0115534i \(-0.996322\pi\)
0.999933 0.0115534i \(-0.00367763\pi\)
\(608\) −126.052 59.7235i −0.207322 0.0982294i
\(609\) −433.318 −0.711523
\(610\) 273.198 62.7196i 0.447865 0.102819i
\(611\) 2.55165i 0.00417619i
\(612\) −36.1307 + 17.5125i −0.0590372 + 0.0286152i
\(613\) 22.8620 0.0372953 0.0186477 0.999826i \(-0.494064\pi\)
0.0186477 + 0.999826i \(0.494064\pi\)
\(614\) 213.791 + 931.244i 0.348194 + 1.51668i
\(615\) 100.701i 0.163741i
\(616\) −218.725 + 175.791i −0.355073 + 0.285374i
\(617\) 935.677 1.51649 0.758247 0.651968i \(-0.226056\pi\)
0.758247 + 0.651968i \(0.226056\pi\)
\(618\) −215.808 + 49.5443i −0.349204 + 0.0801688i
\(619\) 256.561i 0.414476i 0.978291 + 0.207238i \(0.0664475\pi\)
−0.978291 + 0.207238i \(0.933553\pi\)
\(620\) 92.9782 + 191.827i 0.149965 + 0.309399i
\(621\) 948.760 1.52779
\(622\) −177.893 774.877i −0.286002 1.24578i
\(623\) 449.423i 0.721386i
\(624\) −64.3230 50.7652i −0.103082 0.0813544i
\(625\) −285.707 −0.457132
\(626\) −486.771 + 111.751i −0.777589 + 0.178516i
\(627\) 184.855i 0.294824i
\(628\) −838.112 + 406.231i −1.33457 + 0.646865i
\(629\) −286.672 −0.455758
\(630\) 5.72962 + 24.9574i 0.00909463 + 0.0396149i
\(631\) 530.971i 0.841476i 0.907182 + 0.420738i \(0.138229\pi\)
−0.907182 + 0.420738i \(0.861771\pi\)
\(632\) −356.691 443.808i −0.564385 0.702228i
\(633\) 517.649 0.817771
\(634\) 34.1908 7.84939i 0.0539288 0.0123807i
\(635\) 403.507i 0.635444i
\(636\) −317.527 655.104i −0.499257 1.03004i
\(637\) 67.2134 0.105516
\(638\) −303.460 1321.83i −0.475643 2.07183i
\(639\) 156.068i 0.244238i
\(640\) 4.42810 + 499.660i 0.00691890 + 0.780718i
\(641\) −394.362 −0.615230 −0.307615 0.951511i \(-0.599531\pi\)
−0.307615 + 0.951511i \(0.599531\pi\)
\(642\) 531.592 122.041i 0.828025 0.190095i
\(643\) 4.02353i 0.00625743i −0.999995 0.00312871i \(-0.999004\pi\)
0.999995 0.00312871i \(-0.000995902\pi\)
\(644\) −363.958 + 176.409i −0.565151 + 0.273928i
\(645\) 202.505 0.313962
\(646\) −15.8005 68.8249i −0.0244590 0.106540i
\(647\) 627.845i 0.970394i −0.874405 0.485197i \(-0.838748\pi\)
0.874405 0.485197i \(-0.161252\pi\)
\(648\) −565.059 + 454.141i −0.872004 + 0.700835i
\(649\) 1411.81 2.17537
\(650\) −30.4521 + 6.99106i −0.0468493 + 0.0107555i
\(651\) 115.616i 0.177598i
\(652\) −232.297 479.262i −0.356284 0.735064i
\(653\) −548.722 −0.840309 −0.420155 0.907453i \(-0.638024\pi\)
−0.420155 + 0.907453i \(0.638024\pi\)
\(654\) −209.844 914.051i −0.320862 1.39763i
\(655\) 334.364i 0.510479i
\(656\) 79.9090 101.250i 0.121813 0.154345i
\(657\) −42.4025 −0.0645395
\(658\) 8.22504 1.88827i 0.0125001 0.00286971i
\(659\) 499.633i 0.758168i 0.925362 + 0.379084i \(0.123761\pi\)
−0.925362 + 0.379084i \(0.876239\pi\)
\(660\) −595.901 + 288.832i −0.902880 + 0.437624i
\(661\) −655.267 −0.991326 −0.495663 0.868515i \(-0.665075\pi\)
−0.495663 + 0.868515i \(0.665075\pi\)
\(662\) 234.626 + 1022.00i 0.354419 + 1.54380i
\(663\) 41.4840i 0.0625701i
\(664\) 748.287 + 931.046i 1.12694 + 1.40218i
\(665\) −45.0353 −0.0677223
\(666\) 85.4902 19.6265i 0.128364 0.0294692i
\(667\) 1954.77i 2.93069i
\(668\) 146.716 + 302.695i 0.219634 + 0.453136i
\(669\) 547.715 0.818707
\(670\) 83.0141 + 361.598i 0.123902 + 0.539698i
\(671\) 475.817i 0.709117i
\(672\) 116.037 244.907i 0.172674 0.364445i
\(673\) 686.513 1.02008 0.510039 0.860151i \(-0.329631\pi\)
0.510039 + 0.860151i \(0.329631\pi\)
\(674\) −20.2311 + 4.64458i −0.0300165 + 0.00689107i
\(675\) 242.395i 0.359104i
\(676\) −599.090 + 290.377i −0.886228 + 0.429553i
\(677\) −639.146 −0.944085 −0.472043 0.881576i \(-0.656483\pi\)
−0.472043 + 0.881576i \(0.656483\pi\)
\(678\) −51.6320 224.902i −0.0761535 0.331714i
\(679\) 289.877i 0.426918i
\(680\) −197.177 + 158.472i −0.289966 + 0.233047i
\(681\) −352.540 −0.517679
\(682\) 352.686 80.9681i 0.517135 0.118722i
\(683\) 839.655i 1.22936i −0.788775 0.614682i \(-0.789284\pi\)
0.788775 0.614682i \(-0.210716\pi\)
\(684\) 9.42395 + 19.4429i 0.0137777 + 0.0284253i
\(685\) −349.039 −0.509546
\(686\) 107.775 + 469.451i 0.157106 + 0.684331i
\(687\) 591.435i 0.860894i
\(688\) −203.610 160.694i −0.295945 0.233567i
\(689\) 91.0319 0.132122
\(690\) −930.269 + 213.567i −1.34822 + 0.309518i
\(691\) 1091.05i 1.57895i 0.613783 + 0.789475i \(0.289647\pi\)
−0.613783 + 0.789475i \(0.710353\pi\)
\(692\) 146.985 71.2434i 0.212406 0.102953i
\(693\) 43.4673 0.0627233
\(694\) 63.0249 + 274.528i 0.0908140 + 0.395573i
\(695\) 684.380i 0.984720i
\(696\) 820.523 + 1020.92i 1.17891 + 1.46685i
\(697\) 65.2996 0.0936867
\(698\) 1146.53 263.215i 1.64259 0.377098i
\(699\) 723.614i 1.03521i
\(700\) −45.0702 92.9862i −0.0643860 0.132837i
\(701\) 431.165 0.615071 0.307536 0.951537i \(-0.400496\pi\)
0.307536 + 0.951537i \(0.400496\pi\)
\(702\) −17.7868 77.4767i −0.0253373 0.110366i
\(703\) 154.266i 0.219439i
\(704\) 828.349 + 182.457i 1.17663 + 0.259171i
\(705\) 19.9150 0.0282483
\(706\) −132.080 + 30.3223i −0.187082 + 0.0429495i
\(707\) 313.456i 0.443360i
\(708\) −1226.95 + 594.702i −1.73299 + 0.839974i
\(709\) −197.989 −0.279251 −0.139626 0.990204i \(-0.544590\pi\)
−0.139626 + 0.990204i \(0.544590\pi\)
\(710\) −220.015 958.355i −0.309880 1.34980i
\(711\) 88.1982i 0.124048i
\(712\) −1058.87 + 851.021i −1.48718 + 1.19525i
\(713\) 521.564 0.731506
\(714\) 133.720 30.6989i 0.187283 0.0429957i
\(715\) 82.8052i 0.115811i
\(716\) −164.647 339.690i −0.229954 0.474427i
\(717\) −903.276 −1.25980
\(718\) 60.9847 + 265.641i 0.0849369 + 0.369973i
\(719\) 555.460i 0.772545i −0.922385 0.386273i \(-0.873762\pi\)
0.922385 0.386273i \(-0.126238\pi\)
\(720\) 47.9518 60.7583i 0.0665997 0.0843866i
\(721\) 91.5699 0.127004
\(722\) −37.0365 + 8.50269i −0.0512971 + 0.0117766i
\(723\) 27.8029i 0.0384550i
\(724\) 366.674 177.726i 0.506455 0.245478i
\(725\) 499.416 0.688850
\(726\) 78.2538 + 340.863i 0.107788 + 0.469508i
\(727\) 8.18995i 0.0112654i 0.999984 + 0.00563271i \(0.00179296\pi\)
−0.999984 + 0.00563271i \(0.998207\pi\)
\(728\) 21.2290 + 26.4139i 0.0291607 + 0.0362829i
\(729\) −602.885 −0.827003
\(730\) −260.377 + 59.7762i −0.356681 + 0.0818852i
\(731\) 131.315i 0.179637i
\(732\) 200.430 + 413.515i 0.273811 + 0.564911i
\(733\) −491.152 −0.670058 −0.335029 0.942208i \(-0.608746\pi\)
−0.335029 + 0.942208i \(0.608746\pi\)
\(734\) 122.907 + 535.364i 0.167448 + 0.729378i
\(735\) 524.584i 0.713720i
\(736\) 1104.82 + 523.462i 1.50111 + 0.711226i
\(737\) 629.780 0.854518
\(738\) −19.4734 + 4.47062i −0.0263867 + 0.00605776i
\(739\) 1037.82i 1.40436i −0.712000 0.702180i \(-0.752210\pi\)
0.712000 0.702180i \(-0.247790\pi\)
\(740\) 497.294 241.037i 0.672018 0.325726i
\(741\) −22.3237 −0.0301264
\(742\) 67.3653 + 293.434i 0.0907888 + 0.395463i
\(743\) 148.421i 0.199759i −0.995000 0.0998795i \(-0.968154\pi\)
0.995000 0.0998795i \(-0.0318457\pi\)
\(744\) −272.400 + 218.929i −0.366128 + 0.294260i
\(745\) −810.670 −1.08815
\(746\) 15.5300 3.56532i 0.0208177 0.00477925i
\(747\) 185.027i 0.247693i
\(748\) 187.293 + 386.413i 0.250392 + 0.516594i
\(749\) −225.561 −0.301149
\(750\) −194.315 846.410i −0.259087 1.12855i
\(751\) 443.027i 0.589916i 0.955510 + 0.294958i \(0.0953056\pi\)
−0.955510 + 0.294958i \(0.904694\pi\)
\(752\) −20.0237 15.8032i −0.0266273 0.0210148i
\(753\) 874.445 1.16128
\(754\) −159.628 + 36.6468i −0.211709 + 0.0486032i
\(755\) 129.980i 0.172159i
\(756\) 236.577 114.668i 0.312933 0.151678i
\(757\) 878.626 1.16067 0.580334 0.814379i \(-0.302922\pi\)
0.580334 + 0.814379i \(0.302922\pi\)
\(758\) −230.448 1003.80i −0.304022 1.32428i
\(759\) 1620.21i 2.13466i
\(760\) 85.2781 + 106.106i 0.112208 + 0.139613i
\(761\) −750.924 −0.986760 −0.493380 0.869814i \(-0.664239\pi\)
−0.493380 + 0.869814i \(0.664239\pi\)
\(762\) 644.733 148.015i 0.846106 0.194245i
\(763\) 387.842i 0.508312i
\(764\) −169.213 349.111i −0.221483 0.456951i
\(765\) 39.1850 0.0512222
\(766\) −299.696 1305.44i −0.391249 1.70422i
\(767\) 170.495i 0.222288i
\(768\) −796.743 + 190.361i −1.03743 + 0.247866i
\(769\) −315.536 −0.410319 −0.205160 0.978729i \(-0.565771\pi\)
−0.205160 + 0.978729i \(0.565771\pi\)
\(770\) 266.916 61.2773i 0.346644 0.0795810i
\(771\) 721.938i 0.936366i
\(772\) 785.254 380.611i 1.01717 0.493019i
\(773\) −110.053 −0.142371 −0.0711853 0.997463i \(-0.522678\pi\)
−0.0711853 + 0.997463i \(0.522678\pi\)
\(774\) 8.99024 + 39.1602i 0.0116153 + 0.0505946i
\(775\) 133.252i 0.171939i
\(776\) 682.970 548.907i 0.880116 0.707354i
\(777\) −299.724 −0.385745
\(778\) −730.832 + 167.781i −0.939372 + 0.215657i
\(779\) 35.1395i