Properties

Label 177.4.d.c.176.9
Level $177$
Weight $4$
Character 177.176
Analytic conductor $10.443$
Analytic rank $0$
Dimension $52$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 177.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.4433380710\)
Analytic rank: \(0\)
Dimension: \(52\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 176.9
Character \(\chi\) \(=\) 177.176
Dual form 177.4.d.c.176.10

$q$-expansion

\(f(q)\) \(=\) \(q-4.28707 q^{2} +(0.191639 - 5.19262i) q^{3} +10.3790 q^{4} +4.91692i q^{5} +(-0.821572 + 22.2611i) q^{6} +31.8159 q^{7} -10.1988 q^{8} +(-26.9265 - 1.99022i) q^{9} +O(q^{10})\) \(q-4.28707 q^{2} +(0.191639 - 5.19262i) q^{3} +10.3790 q^{4} +4.91692i q^{5} +(-0.821572 + 22.2611i) q^{6} +31.8159 q^{7} -10.1988 q^{8} +(-26.9265 - 1.99022i) q^{9} -21.0792i q^{10} -38.0073 q^{11} +(1.98902 - 53.8940i) q^{12} +69.1147i q^{13} -136.397 q^{14} +(25.5317 + 0.942275i) q^{15} -39.3088 q^{16} +38.2553i q^{17} +(115.436 + 8.53221i) q^{18} -79.5969 q^{19} +51.0325i q^{20} +(6.09719 - 165.208i) q^{21} +162.940 q^{22} +61.2479 q^{23} +(-1.95449 + 52.9584i) q^{24} +100.824 q^{25} -296.300i q^{26} +(-15.4946 + 139.438i) q^{27} +330.216 q^{28} +168.216i q^{29} +(-109.456 - 4.03960i) q^{30} +22.7122i q^{31} +250.110 q^{32} +(-7.28369 + 197.357i) q^{33} -164.003i q^{34} +156.436i q^{35} +(-279.470 - 20.6564i) q^{36} +197.816i q^{37} +341.237 q^{38} +(358.886 + 13.2451i) q^{39} -50.1466i q^{40} +415.087i q^{41} +(-26.1391 + 708.258i) q^{42} -429.319i q^{43} -394.476 q^{44} +(9.78575 - 132.396i) q^{45} -262.574 q^{46} +90.7688 q^{47} +(-7.53312 + 204.116i) q^{48} +669.253 q^{49} -432.239 q^{50} +(198.645 + 7.33123i) q^{51} +717.339i q^{52} -4.32567i q^{53} +(66.4266 - 597.780i) q^{54} -186.879i q^{55} -324.484 q^{56} +(-15.2539 + 413.316i) q^{57} -721.152i q^{58} +(314.804 + 326.002i) q^{59} +(264.992 + 9.77984i) q^{60} +230.891i q^{61} -97.3686i q^{62} +(-856.693 - 63.3207i) q^{63} -757.768 q^{64} -339.832 q^{65} +(31.2257 - 846.084i) q^{66} -803.305i q^{67} +397.051i q^{68} +(11.7375 - 318.037i) q^{69} -670.653i q^{70} -606.858i q^{71} +(274.618 + 20.2978i) q^{72} +723.253i q^{73} -848.050i q^{74} +(19.3218 - 523.540i) q^{75} -826.133 q^{76} -1209.24 q^{77} +(-1538.57 - 56.7827i) q^{78} -282.277 q^{79} -193.278i q^{80} +(721.078 + 107.180i) q^{81} -1779.51i q^{82} -375.995 q^{83} +(63.2825 - 1714.69i) q^{84} -188.098 q^{85} +1840.52i q^{86} +(873.480 + 32.2368i) q^{87} +387.628 q^{88} +1445.90 q^{89} +(-41.9522 + 567.589i) q^{90} +2198.95i q^{91} +635.690 q^{92} +(117.936 + 4.35254i) q^{93} -389.132 q^{94} -391.371i q^{95} +(47.9309 - 1298.73i) q^{96} +1440.25i q^{97} -2869.14 q^{98} +(1023.40 + 75.6428i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q - 8q^{3} + 268q^{4} - 16q^{7} - 4q^{9} + O(q^{10}) \) \( 52q - 8q^{3} + 268q^{4} - 16q^{7} - 4q^{9} + 28q^{12} + 114q^{15} + 484q^{16} - 184q^{19} - 758q^{21} - 60q^{22} + 36q^{25} + 742q^{27} - 4q^{28} - 888q^{36} + 1402q^{45} - 660q^{46} - 488q^{48} - 924q^{49} - 1772q^{51} - 630q^{57} - 1880q^{60} - 212q^{63} + 7648q^{64} + 1316q^{66} - 1556q^{75} - 5680q^{76} + 3224q^{78} - 1504q^{79} - 276q^{81} + 1228q^{84} - 848q^{85} + 3598q^{87} + 5760q^{88} + 888q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.28707 −1.51571 −0.757854 0.652424i \(-0.773752\pi\)
−0.757854 + 0.652424i \(0.773752\pi\)
\(3\) 0.191639 5.19262i 0.0368810 0.999320i
\(4\) 10.3790 1.29737
\(5\) 4.91692i 0.439783i 0.975524 + 0.219891i \(0.0705703\pi\)
−0.975524 + 0.219891i \(0.929430\pi\)
\(6\) −0.821572 + 22.2611i −0.0559009 + 1.51468i
\(7\) 31.8159 1.71790 0.858949 0.512060i \(-0.171118\pi\)
0.858949 + 0.512060i \(0.171118\pi\)
\(8\) −10.1988 −0.450727
\(9\) −26.9265 1.99022i −0.997280 0.0737119i
\(10\) 21.0792i 0.666582i
\(11\) −38.0073 −1.04178 −0.520892 0.853623i \(-0.674401\pi\)
−0.520892 + 0.853623i \(0.674401\pi\)
\(12\) 1.98902 53.8940i 0.0478484 1.29649i
\(13\) 69.1147i 1.47454i 0.675600 + 0.737269i \(0.263885\pi\)
−0.675600 + 0.737269i \(0.736115\pi\)
\(14\) −136.397 −2.60383
\(15\) 25.5317 + 0.942275i 0.439483 + 0.0162196i
\(16\) −39.3088 −0.614200
\(17\) 38.2553i 0.545781i 0.962045 + 0.272891i \(0.0879797\pi\)
−0.962045 + 0.272891i \(0.912020\pi\)
\(18\) 115.436 + 8.53221i 1.51158 + 0.111726i
\(19\) −79.5969 −0.961093 −0.480547 0.876969i \(-0.659562\pi\)
−0.480547 + 0.876969i \(0.659562\pi\)
\(20\) 51.0325i 0.570561i
\(21\) 6.09719 165.208i 0.0633579 1.71673i
\(22\) 162.940 1.57904
\(23\) 61.2479 0.555264 0.277632 0.960687i \(-0.410450\pi\)
0.277632 + 0.960687i \(0.410450\pi\)
\(24\) −1.95449 + 52.9584i −0.0166233 + 0.450420i
\(25\) 100.824 0.806591
\(26\) 296.300i 2.23497i
\(27\) −15.4946 + 139.438i −0.110442 + 0.993883i
\(28\) 330.216 2.22875
\(29\) 168.216i 1.07713i 0.842583 + 0.538567i \(0.181034\pi\)
−0.842583 + 0.538567i \(0.818966\pi\)
\(30\) −109.456 4.03960i −0.666128 0.0245842i
\(31\) 22.7122i 0.131588i 0.997833 + 0.0657939i \(0.0209580\pi\)
−0.997833 + 0.0657939i \(0.979042\pi\)
\(32\) 250.110 1.38168
\(33\) −7.28369 + 197.357i −0.0384220 + 1.04107i
\(34\) 164.003i 0.827245i
\(35\) 156.436i 0.755502i
\(36\) −279.470 20.6564i −1.29384 0.0956316i
\(37\) 197.816i 0.878938i 0.898258 + 0.439469i \(0.144833\pi\)
−0.898258 + 0.439469i \(0.855167\pi\)
\(38\) 341.237 1.45674
\(39\) 358.886 + 13.2451i 1.47353 + 0.0543824i
\(40\) 50.1466i 0.198222i
\(41\) 415.087i 1.58111i 0.612389 + 0.790557i \(0.290209\pi\)
−0.612389 + 0.790557i \(0.709791\pi\)
\(42\) −26.1391 + 708.258i −0.0960320 + 2.60206i
\(43\) 429.319i 1.52257i −0.648417 0.761286i \(-0.724569\pi\)
0.648417 0.761286i \(-0.275431\pi\)
\(44\) −394.476 −1.35158
\(45\) 9.78575 132.396i 0.0324172 0.438586i
\(46\) −262.574 −0.841618
\(47\) 90.7688 0.281702 0.140851 0.990031i \(-0.455016\pi\)
0.140851 + 0.990031i \(0.455016\pi\)
\(48\) −7.53312 + 204.116i −0.0226523 + 0.613782i
\(49\) 669.253 1.95118
\(50\) −432.239 −1.22256
\(51\) 198.645 + 7.33123i 0.545410 + 0.0201290i
\(52\) 717.339i 1.91302i
\(53\) 4.32567i 0.0112109i −0.999984 0.00560544i \(-0.998216\pi\)
0.999984 0.00560544i \(-0.00178428\pi\)
\(54\) 66.4266 597.780i 0.167398 1.50644i
\(55\) 186.879i 0.458158i
\(56\) −324.484 −0.774303
\(57\) −15.2539 + 413.316i −0.0354461 + 0.960440i
\(58\) 721.152i 1.63262i
\(59\) 314.804 + 326.002i 0.694644 + 0.719354i
\(60\) 264.992 + 9.77984i 0.570173 + 0.0210429i
\(61\) 230.891i 0.484633i 0.970197 + 0.242317i \(0.0779072\pi\)
−0.970197 + 0.242317i \(0.922093\pi\)
\(62\) 97.3686i 0.199449i
\(63\) −856.693 63.3207i −1.71323 0.126630i
\(64\) −757.768 −1.48002
\(65\) −339.832 −0.648476
\(66\) 31.2257 846.084i 0.0582366 1.57797i
\(67\) 803.305i 1.46477i −0.680893 0.732383i \(-0.738408\pi\)
0.680893 0.732383i \(-0.261592\pi\)
\(68\) 397.051i 0.708081i
\(69\) 11.7375 318.037i 0.0204787 0.554886i
\(70\) 670.653i 1.14512i
\(71\) 606.858i 1.01438i −0.861835 0.507189i \(-0.830685\pi\)
0.861835 0.507189i \(-0.169315\pi\)
\(72\) 274.618 + 20.2978i 0.449501 + 0.0332239i
\(73\) 723.253i 1.15959i 0.814761 + 0.579797i \(0.196868\pi\)
−0.814761 + 0.579797i \(0.803132\pi\)
\(74\) 848.050i 1.33221i
\(75\) 19.3218 523.540i 0.0297479 0.806043i
\(76\) −826.133 −1.24689
\(77\) −1209.24 −1.78968
\(78\) −1538.57 56.7827i −2.23345 0.0824279i
\(79\) −282.277 −0.402009 −0.201004 0.979590i \(-0.564421\pi\)
−0.201004 + 0.979590i \(0.564421\pi\)
\(80\) 193.278i 0.270115i
\(81\) 721.078 + 107.180i 0.989133 + 0.147023i
\(82\) 1779.51i 2.39651i
\(83\) −375.995 −0.497238 −0.248619 0.968601i \(-0.579977\pi\)
−0.248619 + 0.968601i \(0.579977\pi\)
\(84\) 63.2825 1714.69i 0.0821986 2.22723i
\(85\) −188.098 −0.240025
\(86\) 1840.52i 2.30777i
\(87\) 873.480 + 32.2368i 1.07640 + 0.0397258i
\(88\) 387.628 0.469560
\(89\) 1445.90 1.72208 0.861041 0.508535i \(-0.169813\pi\)
0.861041 + 0.508535i \(0.169813\pi\)
\(90\) −41.9522 + 567.589i −0.0491350 + 0.664769i
\(91\) 2198.95i 2.53311i
\(92\) 635.690 0.720383
\(93\) 117.936 + 4.35254i 0.131498 + 0.00485309i
\(94\) −389.132 −0.426978
\(95\) 391.371i 0.422672i
\(96\) 47.9309 1298.73i 0.0509576 1.38074i
\(97\) 1440.25i 1.50758i 0.657116 + 0.753789i \(0.271776\pi\)
−0.657116 + 0.753789i \(0.728224\pi\)
\(98\) −2869.14 −2.95741
\(99\) 1023.40 + 75.6428i 1.03895 + 0.0767918i
\(100\) 1046.45 1.04645
\(101\) 509.974 0.502419 0.251210 0.967933i \(-0.419172\pi\)
0.251210 + 0.967933i \(0.419172\pi\)
\(102\) −851.606 31.4295i −0.826682 0.0305096i
\(103\) 1404.56i 1.34364i 0.740712 + 0.671822i \(0.234488\pi\)
−0.740712 + 0.671822i \(0.765512\pi\)
\(104\) 704.886i 0.664613i
\(105\) 812.314 + 29.9794i 0.754988 + 0.0278637i
\(106\) 18.5444i 0.0169924i
\(107\) 671.679i 0.606857i −0.952854 0.303429i \(-0.901869\pi\)
0.952854 0.303429i \(-0.0981314\pi\)
\(108\) −160.818 + 1447.22i −0.143285 + 1.28943i
\(109\) 1588.02i 1.39545i −0.716365 0.697726i \(-0.754195\pi\)
0.716365 0.697726i \(-0.245805\pi\)
\(110\) 801.162i 0.694434i
\(111\) 1027.18 + 37.9093i 0.878340 + 0.0324161i
\(112\) −1250.65 −1.05513
\(113\) 417.004 0.347154 0.173577 0.984820i \(-0.444467\pi\)
0.173577 + 0.984820i \(0.444467\pi\)
\(114\) 65.3945 1771.91i 0.0537260 1.45575i
\(115\) 301.151i 0.244195i
\(116\) 1745.90i 1.39744i
\(117\) 137.554 1861.02i 0.108691 1.47053i
\(118\) −1349.59 1397.59i −1.05288 1.09033i
\(119\) 1217.13i 0.937597i
\(120\) −260.392 9.61006i −0.198087 0.00731062i
\(121\) 113.552 0.0853131
\(122\) 989.848i 0.734562i
\(123\) 2155.39 + 79.5470i 1.58004 + 0.0583131i
\(124\) 235.729i 0.170718i
\(125\) 1110.36i 0.794507i
\(126\) 3672.70 + 271.460i 2.59675 + 0.191933i
\(127\) −739.133 −0.516437 −0.258218 0.966087i \(-0.583135\pi\)
−0.258218 + 0.966087i \(0.583135\pi\)
\(128\) 1247.72 0.861596
\(129\) −2229.29 82.2745i −1.52154 0.0561540i
\(130\) 1456.88 0.982900
\(131\) −1517.87 −1.01234 −0.506172 0.862432i \(-0.668940\pi\)
−0.506172 + 0.862432i \(0.668940\pi\)
\(132\) −75.5971 + 2048.36i −0.0498476 + 1.35066i
\(133\) −2532.45 −1.65106
\(134\) 3443.83i 2.22016i
\(135\) −685.605 76.1859i −0.437092 0.0485706i
\(136\) 390.158i 0.245998i
\(137\) 450.679i 0.281052i 0.990077 + 0.140526i \(0.0448793\pi\)
−0.990077 + 0.140526i \(0.955121\pi\)
\(138\) −50.3195 + 1363.45i −0.0310397 + 0.841046i
\(139\) 733.381 0.447515 0.223757 0.974645i \(-0.428168\pi\)
0.223757 + 0.974645i \(0.428168\pi\)
\(140\) 1623.65i 0.980166i
\(141\) 17.3949 471.328i 0.0103895 0.281510i
\(142\) 2601.64i 1.53750i
\(143\) 2626.86i 1.53615i
\(144\) 1058.45 + 78.2332i 0.612529 + 0.0452739i
\(145\) −827.103 −0.473705
\(146\) 3100.64i 1.75761i
\(147\) 128.255 3475.18i 0.0719614 1.94985i
\(148\) 2053.12i 1.14031i
\(149\) −854.020 −0.469557 −0.234779 0.972049i \(-0.575437\pi\)
−0.234779 + 0.972049i \(0.575437\pi\)
\(150\) −82.8341 + 2244.45i −0.0450891 + 1.22173i
\(151\) 1524.51i 0.821607i 0.911724 + 0.410803i \(0.134752\pi\)
−0.911724 + 0.410803i \(0.865248\pi\)
\(152\) 811.791 0.433191
\(153\) 76.1366 1030.08i 0.0402306 0.544297i
\(154\) 5184.08 2.71263
\(155\) −111.674 −0.0578700
\(156\) 3724.87 + 137.471i 1.91172 + 0.0705542i
\(157\) 1263.83i 0.642449i 0.947003 + 0.321224i \(0.104094\pi\)
−0.947003 + 0.321224i \(0.895906\pi\)
\(158\) 1210.14 0.609328
\(159\) −22.4615 0.828969i −0.0112032 0.000413469i
\(160\) 1229.77i 0.607637i
\(161\) 1948.66 0.953888
\(162\) −3091.31 459.486i −1.49924 0.222843i
\(163\) 3122.87 1.50063 0.750313 0.661083i \(-0.229903\pi\)
0.750313 + 0.661083i \(0.229903\pi\)
\(164\) 4308.17i 2.05129i
\(165\) −970.389 35.8133i −0.457847 0.0168973i
\(166\) 1611.91 0.753668
\(167\) 893.505i 0.414021i −0.978339 0.207010i \(-0.933627\pi\)
0.978339 0.207010i \(-0.0663734\pi\)
\(168\) −62.1839 + 1684.92i −0.0285571 + 0.773776i
\(169\) −2579.85 −1.17426
\(170\) 806.391 0.363808
\(171\) 2143.27 + 158.415i 0.958479 + 0.0708440i
\(172\) 4455.89i 1.97534i
\(173\) −4487.65 −1.97220 −0.986098 0.166162i \(-0.946863\pi\)
−0.986098 + 0.166162i \(0.946863\pi\)
\(174\) −3744.67 138.201i −1.63151 0.0602127i
\(175\) 3207.81 1.38564
\(176\) 1494.02 0.639864
\(177\) 1753.13 1572.18i 0.744483 0.667641i
\(178\) −6198.69 −2.61017
\(179\) 2508.10 1.04729 0.523643 0.851938i \(-0.324573\pi\)
0.523643 + 0.851938i \(0.324573\pi\)
\(180\) 101.566 1374.13i 0.0420571 0.569009i
\(181\) −32.6715 −0.0134169 −0.00670844 0.999977i \(-0.502135\pi\)
−0.00670844 + 0.999977i \(0.502135\pi\)
\(182\) 9427.05i 3.83945i
\(183\) 1198.93 + 44.2479i 0.484303 + 0.0178738i
\(184\) −624.654 −0.250272
\(185\) −972.644 −0.386542
\(186\) −505.598 18.6597i −0.199313 0.00735587i
\(187\) 1453.98i 0.568586i
\(188\) 942.086 0.365472
\(189\) −492.976 + 4436.35i −0.189729 + 1.70739i
\(190\) 1677.84i 0.640648i
\(191\) −3696.45 −1.40034 −0.700172 0.713974i \(-0.746893\pi\)
−0.700172 + 0.713974i \(0.746893\pi\)
\(192\) −145.218 + 3934.80i −0.0545845 + 1.47901i
\(193\) 2075.49 0.774078 0.387039 0.922063i \(-0.373498\pi\)
0.387039 + 0.922063i \(0.373498\pi\)
\(194\) 6174.45i 2.28505i
\(195\) −65.1251 + 1764.62i −0.0239164 + 0.648035i
\(196\) 6946.16 2.53140
\(197\) 4360.73i 1.57710i −0.614968 0.788552i \(-0.710831\pi\)
0.614968 0.788552i \(-0.289169\pi\)
\(198\) −4387.41 324.286i −1.57474 0.116394i
\(199\) −3431.73 −1.22246 −0.611228 0.791454i \(-0.709324\pi\)
−0.611228 + 0.791454i \(0.709324\pi\)
\(200\) −1028.28 −0.363552
\(201\) −4171.26 153.945i −1.46377 0.0540221i
\(202\) −2186.29 −0.761520
\(203\) 5351.94i 1.85041i
\(204\) 2061.73 + 76.0906i 0.707599 + 0.0261147i
\(205\) −2040.95 −0.695346
\(206\) 6021.44i 2.03657i
\(207\) −1649.20 121.897i −0.553754 0.0409296i
\(208\) 2716.82i 0.905661i
\(209\) 3025.26 1.00125
\(210\) −3482.45 128.524i −1.14434 0.0422332i
\(211\) 926.630i 0.302331i 0.988508 + 0.151166i \(0.0483026\pi\)
−0.988508 + 0.151166i \(0.951697\pi\)
\(212\) 44.8960i 0.0145447i
\(213\) −3151.18 116.298i −1.01369 0.0374113i
\(214\) 2879.54i 0.919818i
\(215\) 2110.93 0.669600
\(216\) 158.026 1422.10i 0.0497794 0.447969i
\(217\) 722.608i 0.226055i
\(218\) 6807.93i 2.11510i
\(219\) 3755.58 + 138.604i 1.15881 + 0.0427670i
\(220\) 1939.61i 0.594401i
\(221\) −2644.01 −0.804775
\(222\) −4403.60 162.520i −1.33131 0.0491334i
\(223\) 4090.39 1.22831 0.614154 0.789186i \(-0.289497\pi\)
0.614154 + 0.789186i \(0.289497\pi\)
\(224\) 7957.48 2.37358
\(225\) −2714.84 200.662i −0.804397 0.0594553i
\(226\) −1787.72 −0.526184
\(227\) −3062.19 −0.895351 −0.447676 0.894196i \(-0.647748\pi\)
−0.447676 + 0.894196i \(0.647748\pi\)
\(228\) −158.320 + 4289.79i −0.0459867 + 1.24605i
\(229\) 5907.73i 1.70478i −0.522910 0.852388i \(-0.675154\pi\)
0.522910 0.852388i \(-0.324846\pi\)
\(230\) 1291.06i 0.370129i
\(231\) −231.737 + 6279.10i −0.0660052 + 1.78846i
\(232\) 1715.60i 0.485493i
\(233\) 1083.45 0.304631 0.152316 0.988332i \(-0.451327\pi\)
0.152316 + 0.988332i \(0.451327\pi\)
\(234\) −589.702 + 7978.33i −0.164744 + 2.22889i
\(235\) 446.303i 0.123888i
\(236\) 3267.34 + 3383.56i 0.901211 + 0.933268i
\(237\) −54.0955 + 1465.76i −0.0148265 + 0.401735i
\(238\) 5217.92i 1.42112i
\(239\) 790.173i 0.213858i 0.994267 + 0.106929i \(0.0341017\pi\)
−0.994267 + 0.106929i \(0.965898\pi\)
\(240\) −1003.62 37.0397i −0.269931 0.00996210i
\(241\) 111.874 0.0299022 0.0149511 0.999888i \(-0.495241\pi\)
0.0149511 + 0.999888i \(0.495241\pi\)
\(242\) −486.804 −0.129310
\(243\) 694.729 3723.74i 0.183403 0.983038i
\(244\) 2396.41i 0.628749i
\(245\) 3290.66i 0.858093i
\(246\) −9240.29 341.023i −2.39488 0.0883856i
\(247\) 5501.32i 1.41717i
\(248\) 231.636i 0.0593102i
\(249\) −72.0554 + 1952.40i −0.0183386 + 0.496900i
\(250\) 4760.18i 1.20424i
\(251\) 3259.06i 0.819563i −0.912184 0.409781i \(-0.865605\pi\)
0.912184 0.409781i \(-0.134395\pi\)
\(252\) −8891.59 657.203i −2.22269 0.164285i
\(253\) −2327.87 −0.578465
\(254\) 3168.72 0.782767
\(255\) −36.0471 + 976.723i −0.00885237 + 0.239862i
\(256\) 713.062 0.174087
\(257\) 3474.54i 0.843330i −0.906752 0.421665i \(-0.861446\pi\)
0.906752 0.421665i \(-0.138554\pi\)
\(258\) 9557.12 + 352.716i 2.30620 + 0.0851130i
\(259\) 6293.69i 1.50993i
\(260\) −3527.10 −0.841313
\(261\) 334.786 4529.47i 0.0793975 1.07420i
\(262\) 6507.22 1.53442
\(263\) 6207.65i 1.45544i 0.685875 + 0.727719i \(0.259420\pi\)
−0.685875 + 0.727719i \(0.740580\pi\)
\(264\) 74.2848 2012.80i 0.0173178 0.469240i
\(265\) 21.2690 0.00493035
\(266\) 10856.8 2.50253
\(267\) 277.092 7508.02i 0.0635122 1.72091i
\(268\) 8337.48i 1.90034i
\(269\) 978.321 0.221745 0.110872 0.993835i \(-0.464636\pi\)
0.110872 + 0.993835i \(0.464636\pi\)
\(270\) 2939.23 + 326.614i 0.662504 + 0.0736189i
\(271\) −5102.58 −1.14376 −0.571882 0.820336i \(-0.693786\pi\)
−0.571882 + 0.820336i \(0.693786\pi\)
\(272\) 1503.77i 0.335219i
\(273\) 11418.3 + 421.406i 2.53138 + 0.0934235i
\(274\) 1932.09i 0.425992i
\(275\) −3832.04 −0.840294
\(276\) 121.823 3300.89i 0.0265685 0.719893i
\(277\) −3823.63 −0.829386 −0.414693 0.909961i \(-0.636111\pi\)
−0.414693 + 0.909961i \(0.636111\pi\)
\(278\) −3144.06 −0.678302
\(279\) 45.2022 611.560i 0.00969959 0.131230i
\(280\) 1595.46i 0.340525i
\(281\) 2999.43i 0.636764i 0.947962 + 0.318382i \(0.103140\pi\)
−0.947962 + 0.318382i \(0.896860\pi\)
\(282\) −74.5731 + 2020.61i −0.0157474 + 0.426687i
\(283\) 4002.87i 0.840799i 0.907339 + 0.420399i \(0.138110\pi\)
−0.907339 + 0.420399i \(0.861890\pi\)
\(284\) 6298.56i 1.31602i
\(285\) −2032.24 75.0022i −0.422385 0.0155886i
\(286\) 11261.5i 2.32835i
\(287\) 13206.4i 2.71619i
\(288\) −6734.60 497.774i −1.37792 0.101846i
\(289\) 3449.53 0.702123
\(290\) 3545.85 0.717998
\(291\) 7478.66 + 276.009i 1.50655 + 0.0556011i
\(292\) 7506.62i 1.50442i
\(293\) 5009.72i 0.998878i 0.866349 + 0.499439i \(0.166460\pi\)
−0.866349 + 0.499439i \(0.833540\pi\)
\(294\) −549.840 + 14898.3i −0.109072 + 2.95540i
\(295\) −1602.93 + 1547.87i −0.316359 + 0.305492i
\(296\) 2017.48i 0.396161i
\(297\) 588.909 5299.65i 0.115057 1.03541i
\(298\) 3661.24 0.711712
\(299\) 4233.13i 0.818757i
\(300\) 200.541 5433.80i 0.0385941 1.04574i
\(301\) 13659.2i 2.61562i
\(302\) 6535.67i 1.24532i
\(303\) 97.7311 2648.10i 0.0185297 0.502077i
\(304\) 3128.86 0.590304
\(305\) −1135.27 −0.213133
\(306\) −326.403 + 4416.04i −0.0609778 + 0.824995i
\(307\) −5297.78 −0.984887 −0.492443 0.870344i \(-0.663896\pi\)
−0.492443 + 0.870344i \(0.663896\pi\)
\(308\) −12550.6 −2.32188
\(309\) 7293.34 + 269.169i 1.34273 + 0.0495550i
\(310\) 478.753 0.0877141
\(311\) 8054.46i 1.46857i −0.678839 0.734287i \(-0.737517\pi\)
0.678839 0.734287i \(-0.262483\pi\)
\(312\) −3660.20 135.084i −0.664161 0.0245116i
\(313\) 3832.10i 0.692023i 0.938230 + 0.346012i \(0.112464\pi\)
−0.938230 + 0.346012i \(0.887536\pi\)
\(314\) 5418.12i 0.973765i
\(315\) 311.343 4212.29i 0.0556895 0.753447i
\(316\) −2929.75 −0.521554
\(317\) 5852.55i 1.03695i −0.855094 0.518473i \(-0.826501\pi\)
0.855094 0.518473i \(-0.173499\pi\)
\(318\) 96.2942 + 3.55385i 0.0169809 + 0.000626698i
\(319\) 6393.42i 1.12214i
\(320\) 3725.88i 0.650885i
\(321\) −3487.77 128.720i −0.606444 0.0223815i
\(322\) −8354.04 −1.44581
\(323\) 3045.01i 0.524547i
\(324\) 7484.04 + 1112.41i 1.28327 + 0.190743i
\(325\) 6968.42i 1.18935i
\(326\) −13388.0 −2.27451
\(327\) −8245.95 304.326i −1.39450 0.0514657i
\(328\) 4233.38i 0.712650i
\(329\) 2887.89 0.483935
\(330\) 4160.13 + 153.534i 0.693962 + 0.0256114i
\(331\) −8698.99 −1.44453 −0.722266 0.691616i \(-0.756899\pi\)
−0.722266 + 0.691616i \(0.756899\pi\)
\(332\) −3902.43 −0.645102
\(333\) 393.697 5326.50i 0.0647882 0.876547i
\(334\) 3830.52i 0.627534i
\(335\) 3949.79 0.644179
\(336\) −239.673 + 6494.13i −0.0389144 + 1.05442i
\(337\) 10431.4i 1.68616i −0.537786 0.843081i \(-0.680739\pi\)
0.537786 0.843081i \(-0.319261\pi\)
\(338\) 11060.0 1.77983
\(339\) 79.9143 2165.34i 0.0128034 0.346918i
\(340\) −1952.27 −0.311401
\(341\) 863.227i 0.137086i
\(342\) −9188.34 679.137i −1.45277 0.107379i
\(343\) 10380.1 1.63402
\(344\) 4378.53i 0.686264i
\(345\) 1563.76 + 57.7124i 0.244029 + 0.00900618i
\(346\) 19238.9 2.98927
\(347\) 9324.88 1.44261 0.721305 0.692617i \(-0.243543\pi\)
0.721305 + 0.692617i \(0.243543\pi\)
\(348\) 9065.82 + 334.584i 1.39649 + 0.0515391i
\(349\) 7070.35i 1.08443i 0.840239 + 0.542217i \(0.182415\pi\)
−0.840239 + 0.542217i \(0.817585\pi\)
\(350\) −13752.1 −2.10023
\(351\) −9637.21 1070.91i −1.46552 0.162851i
\(352\) −9505.99 −1.43941
\(353\) −3887.06 −0.586083 −0.293042 0.956100i \(-0.594667\pi\)
−0.293042 + 0.956100i \(0.594667\pi\)
\(354\) −7515.80 + 6740.05i −1.12842 + 1.01195i
\(355\) 2983.87 0.446106
\(356\) 15007.0 2.23418
\(357\) 6320.09 + 233.250i 0.936959 + 0.0345795i
\(358\) −10752.4 −1.58738
\(359\) 5264.51i 0.773956i 0.922089 + 0.386978i \(0.126481\pi\)
−0.922089 + 0.386978i \(0.873519\pi\)
\(360\) −99.8028 + 1350.27i −0.0146113 + 0.197683i
\(361\) −523.337 −0.0762993
\(362\) 140.065 0.0203361
\(363\) 21.7610 589.631i 0.00314644 0.0852551i
\(364\) 22822.8i 3.28638i
\(365\) −3556.18 −0.509969
\(366\) −5139.90 189.694i −0.734062 0.0270914i
\(367\) 5255.81i 0.747550i 0.927519 + 0.373775i \(0.121937\pi\)
−0.927519 + 0.373775i \(0.878063\pi\)
\(368\) −2407.58 −0.341043
\(369\) 826.114 11176.8i 0.116547 1.57681i
\(370\) 4169.79 0.585884
\(371\) 137.625i 0.0192591i
\(372\) 1224.05 + 45.1749i 0.170602 + 0.00629626i
\(373\) 938.194 0.130236 0.0651178 0.997878i \(-0.479258\pi\)
0.0651178 + 0.997878i \(0.479258\pi\)
\(374\) 6233.32i 0.861810i
\(375\) 5765.66 + 212.788i 0.793967 + 0.0293022i
\(376\) −925.731 −0.126971
\(377\) −11626.2 −1.58827
\(378\) 2113.42 19018.9i 0.287574 2.58790i
\(379\) −1139.89 −0.154491 −0.0772454 0.997012i \(-0.524612\pi\)
−0.0772454 + 0.997012i \(0.524612\pi\)
\(380\) 4062.03i 0.548362i
\(381\) −141.647 + 3838.04i −0.0190467 + 0.516085i
\(382\) 15846.9 2.12251
\(383\) 10055.5i 1.34154i −0.741665 0.670770i \(-0.765964\pi\)
0.741665 0.670770i \(-0.234036\pi\)
\(384\) 239.113 6478.96i 0.0317765 0.861010i
\(385\) 5945.72i 0.787070i
\(386\) −8897.77 −1.17328
\(387\) −854.440 + 11560.1i −0.112232 + 1.51843i
\(388\) 14948.3i 1.95589i
\(389\) 4162.74i 0.542569i 0.962499 + 0.271285i \(0.0874485\pi\)
−0.962499 + 0.271285i \(0.912552\pi\)
\(390\) 279.196 7565.03i 0.0362503 0.982231i
\(391\) 2343.06i 0.303053i
\(392\) −6825.57 −0.879447
\(393\) −290.884 + 7881.73i −0.0373363 + 1.01166i
\(394\) 18694.8i 2.39043i
\(395\) 1387.93i 0.176796i
\(396\) 10621.9 + 785.094i 1.34790 + 0.0996274i
\(397\) 2409.59i 0.304619i 0.988333 + 0.152310i \(0.0486711\pi\)
−0.988333 + 0.152310i \(0.951329\pi\)
\(398\) 14712.1 1.85289
\(399\) −485.317 + 13150.0i −0.0608928 + 1.64994i
\(400\) −3963.27 −0.495409
\(401\) 11702.0 1.45728 0.728641 0.684896i \(-0.240152\pi\)
0.728641 + 0.684896i \(0.240152\pi\)
\(402\) 17882.5 + 659.973i 2.21865 + 0.0818817i
\(403\) −1569.74 −0.194031
\(404\) 5293.00 0.651824
\(405\) −526.993 + 3545.48i −0.0646580 + 0.435003i
\(406\) 22944.1i 2.80468i
\(407\) 7518.44i 0.915664i
\(408\) −2025.94 74.7696i −0.245831 0.00907267i
\(409\) 6683.54i 0.808019i 0.914755 + 0.404010i \(0.132384\pi\)
−0.914755 + 0.404010i \(0.867616\pi\)
\(410\) 8749.68 1.05394
\(411\) 2340.20 + 86.3678i 0.280860 + 0.0103655i
\(412\) 14577.9i 1.74320i
\(413\) 10015.8 + 10372.1i 1.19333 + 1.23578i
\(414\) 7070.21 + 522.580i 0.839329 + 0.0620372i
\(415\) 1848.73i 0.218677i
\(416\) 17286.3i 2.03733i
\(417\) 140.545 3808.17i 0.0165048 0.447210i
\(418\) −12969.5 −1.51760
\(419\) 1833.55 0.213782 0.106891 0.994271i \(-0.465910\pi\)
0.106891 + 0.994271i \(0.465910\pi\)
\(420\) 8430.98 + 311.155i 0.979499 + 0.0361495i
\(421\) 7484.92i 0.866491i −0.901276 0.433245i \(-0.857368\pi\)
0.901276 0.433245i \(-0.142632\pi\)
\(422\) 3972.53i 0.458246i
\(423\) −2444.09 180.650i −0.280936 0.0207648i
\(424\) 44.1166i 0.00505304i
\(425\) 3857.05i 0.440222i
\(426\) 13509.3 + 498.578i 1.53645 + 0.0567046i
\(427\) 7346.03i 0.832551i
\(428\) 6971.34i 0.787318i
\(429\) −13640.3 503.410i −1.53510 0.0566547i
\(430\) −9049.69 −1.01492
\(431\) 10125.3 1.13159 0.565796 0.824545i \(-0.308569\pi\)
0.565796 + 0.824545i \(0.308569\pi\)
\(432\) 609.076 5481.14i 0.0678338 0.610443i
\(433\) 5496.52 0.610037 0.305018 0.952346i \(-0.401337\pi\)
0.305018 + 0.952346i \(0.401337\pi\)
\(434\) 3097.87i 0.342633i
\(435\) −158.506 + 4294.83i −0.0174707 + 0.473382i
\(436\) 16482.0i 1.81042i
\(437\) −4875.14 −0.533661
\(438\) −16100.4 594.204i −1.75641 0.0648223i
\(439\) 17145.2 1.86400 0.932000 0.362457i \(-0.118062\pi\)
0.932000 + 0.362457i \(0.118062\pi\)
\(440\) 1905.93i 0.206504i
\(441\) −18020.7 1331.96i −1.94587 0.143825i
\(442\) 11335.0 1.21980
\(443\) −6312.63 −0.677025 −0.338513 0.940962i \(-0.609924\pi\)
−0.338513 + 0.940962i \(0.609924\pi\)
\(444\) 10661.1 + 393.459i 1.13953 + 0.0420557i
\(445\) 7109.39i 0.757342i
\(446\) −17535.8 −1.86176
\(447\) −163.664 + 4434.60i −0.0173178 + 0.469238i
\(448\) −24109.1 −2.54252
\(449\) 6493.80i 0.682542i −0.939965 0.341271i \(-0.889143\pi\)
0.939965 0.341271i \(-0.110857\pi\)
\(450\) 11638.7 + 860.251i 1.21923 + 0.0901169i
\(451\) 15776.3i 1.64718i
\(452\) 4328.06 0.450387
\(453\) 7916.18 + 292.156i 0.821048 + 0.0303017i
\(454\) 13127.8 1.35709
\(455\) −10812.1 −1.11402
\(456\) 155.571 4215.32i 0.0159765 0.432896i
\(457\) 4963.65i 0.508074i −0.967195 0.254037i \(-0.918242\pi\)
0.967195 0.254037i \(-0.0817585\pi\)
\(458\) 25326.8i 2.58394i
\(459\) −5334.24 592.753i −0.542443 0.0602774i
\(460\) 3125.64i 0.316812i
\(461\) 3552.52i 0.358910i 0.983766 + 0.179455i \(0.0574334\pi\)
−0.983766 + 0.179455i \(0.942567\pi\)
\(462\) 993.474 26918.9i 0.100045 2.71078i
\(463\) 2281.21i 0.228978i −0.993425 0.114489i \(-0.963477\pi\)
0.993425 0.114489i \(-0.0365231\pi\)
\(464\) 6612.36i 0.661576i
\(465\) −21.4011 + 579.879i −0.00213431 + 0.0578307i
\(466\) −4644.82 −0.461732
\(467\) −16620.8 −1.64694 −0.823468 0.567363i \(-0.807964\pi\)
−0.823468 + 0.567363i \(0.807964\pi\)
\(468\) 1427.66 19315.5i 0.141012 1.90782i
\(469\) 25557.9i 2.51632i
\(470\) 1913.33i 0.187777i
\(471\) 6562.58 + 242.199i 0.642012 + 0.0236942i
\(472\) −3210.62 3324.82i −0.313095 0.324232i
\(473\) 16317.2i 1.58619i
\(474\) 231.911 6283.81i 0.0224726 0.608913i
\(475\) −8025.27 −0.775210
\(476\) 12632.5i 1.21641i
\(477\) −8.60903 + 116.475i −0.000826374 + 0.0111804i
\(478\) 3387.53i 0.324146i
\(479\) 5318.13i 0.507289i −0.967298 0.253645i \(-0.918371\pi\)
0.967298 0.253645i \(-0.0816293\pi\)
\(480\) 6385.73 + 235.672i 0.607223 + 0.0224103i
\(481\) −13672.0 −1.29603
\(482\) −479.612 −0.0453231
\(483\) 373.440 10118.6i 0.0351803 0.953239i
\(484\) 1178.55 0.110683
\(485\) −7081.59 −0.663007
\(486\) −2978.35 + 15963.9i −0.277985 + 1.49000i
\(487\) 13000.8 1.20970 0.604851 0.796339i \(-0.293233\pi\)
0.604851 + 0.796339i \(0.293233\pi\)
\(488\) 2354.81i 0.218437i
\(489\) 598.465 16215.9i 0.0553446 1.49960i
\(490\) 14107.3i 1.30062i
\(491\) 16541.6i 1.52039i 0.649692 + 0.760197i \(0.274898\pi\)
−0.649692 + 0.760197i \(0.725102\pi\)
\(492\) 22370.7 + 825.615i 2.04989 + 0.0756537i
\(493\) −6435.15 −0.587879
\(494\) 23584.5i 2.14801i
\(495\) −371.930 + 5032.00i −0.0337717 + 0.456912i
\(496\) 892.788i 0.0808213i
\(497\) 19307.8i 1.74260i
\(498\) 308.906 8370.06i 0.0277960 0.753155i
\(499\) 123.162 0.0110491 0.00552454 0.999985i \(-0.498241\pi\)
0.00552454 + 0.999985i \(0.498241\pi\)
\(500\) 11524.4i 1.03077i
\(501\) −4639.63 171.231i −0.413739 0.0152695i
\(502\) 13971.8i 1.24222i
\(503\) 3911.31 0.346713 0.173356 0.984859i \(-0.444539\pi\)
0.173356 + 0.984859i \(0.444539\pi\)
\(504\) 8737.23 + 645.794i 0.772197 + 0.0570753i
\(505\) 2507.50i 0.220955i
\(506\) 9979.72 0.876784
\(507\) −494.401 + 13396.2i −0.0433079 + 1.17346i
\(508\) −7671.44 −0.670010
\(509\) −5694.55 −0.495887 −0.247943 0.968775i \(-0.579755\pi\)
−0.247943 + 0.968775i \(0.579755\pi\)
\(510\) 154.536 4187.28i 0.0134176 0.363560i
\(511\) 23011.0i 1.99207i
\(512\) −13038.7 −1.12546
\(513\) 1233.33 11098.8i 0.106145 0.955214i
\(514\) 14895.6i 1.27824i
\(515\) −6906.11 −0.590911
\(516\) −23137.7 853.924i −1.97399 0.0728525i
\(517\) −3449.87 −0.293472
\(518\) 26981.5i 2.28861i
\(519\) −860.012 + 23302.7i −0.0727366 + 1.97086i
\(520\) 3465.87 0.292285
\(521\) 4865.16i 0.409111i −0.978855 0.204555i \(-0.934425\pi\)
0.978855 0.204555i \(-0.0655748\pi\)
\(522\) −1435.25 + 19418.1i −0.120343 + 1.62818i
\(523\) 14048.1 1.17454 0.587268 0.809392i \(-0.300203\pi\)
0.587268 + 0.809392i \(0.300203\pi\)
\(524\) −15753.9 −1.31339
\(525\) 614.742 16656.9i 0.0511039 1.38470i
\(526\) 26612.6i 2.20602i
\(527\) −868.861 −0.0718182
\(528\) 286.313 7757.88i 0.0235988 0.639429i
\(529\) −8415.69 −0.691682
\(530\) −91.1815 −0.00747297
\(531\) −7827.77 9404.64i −0.639729 0.768600i
\(532\) −26284.2 −2.14204
\(533\) −28688.6 −2.33141
\(534\) −1187.91 + 32187.4i −0.0962659 + 2.60840i
\(535\) 3302.59 0.266885
\(536\) 8192.74i 0.660210i
\(537\) 480.651 13023.6i 0.0386250 1.04657i
\(538\) −4194.13 −0.336100
\(539\) −25436.5 −2.03270
\(540\) −7115.87 790.731i −0.567071 0.0630141i
\(541\) 5515.05i 0.438282i −0.975693 0.219141i \(-0.929675\pi\)
0.975693 0.219141i \(-0.0703254\pi\)
\(542\) 21875.1 1.73361
\(543\) −6.26115 + 169.651i −0.000494829 + 0.0134078i
\(544\) 9568.04i 0.754092i
\(545\) 7808.14 0.613695
\(546\) −48951.1 1806.59i −3.83684 0.141603i
\(547\) 5840.48 0.456528 0.228264 0.973599i \(-0.426695\pi\)
0.228264 + 0.973599i \(0.426695\pi\)
\(548\) 4677.58i 0.364628i
\(549\) 459.525 6217.11i 0.0357232 0.483315i
\(550\) 16428.2 1.27364
\(551\) 13389.4i 1.03523i
\(552\) −119.708 + 3243.59i −0.00923030 + 0.250102i
\(553\) −8980.92 −0.690610
\(554\) 16392.2 1.25711
\(555\) −186.397 + 5050.57i −0.0142561 + 0.386279i
\(556\) 7611.74 0.580593
\(557\) 7717.58i 0.587082i 0.955947 + 0.293541i \(0.0948337\pi\)
−0.955947 + 0.293541i \(0.905166\pi\)
\(558\) −193.785 + 2621.80i −0.0147017 + 0.198906i
\(559\) 29672.3 2.24509
\(560\) 6149.33i 0.464030i
\(561\) −7549.96 278.640i −0.568199 0.0209700i
\(562\) 12858.7i 0.965149i
\(563\) 16512.6 1.23609 0.618047 0.786141i \(-0.287924\pi\)
0.618047 + 0.786141i \(0.287924\pi\)
\(564\) 180.541 4891.89i 0.0134790 0.365223i
\(565\) 2050.37i 0.152672i
\(566\) 17160.6i 1.27441i
\(567\) 22941.8 + 3410.02i 1.69923 + 0.252570i
\(568\) 6189.22i 0.457207i
\(569\) 7065.54 0.520567 0.260284 0.965532i \(-0.416184\pi\)
0.260284 + 0.965532i \(0.416184\pi\)
\(570\) 8712.36 + 321.540i 0.640212 + 0.0236277i
\(571\) 9513.95i 0.697279i 0.937257 + 0.348640i \(0.113356\pi\)
−0.937257 + 0.348640i \(0.886644\pi\)
\(572\) 27264.1i 1.99295i
\(573\) −708.385 + 19194.2i −0.0516461 + 1.39939i
\(574\) 56616.6i 4.11695i
\(575\) 6175.25 0.447871
\(576\) 20404.1 + 1508.13i 1.47599 + 0.109095i
\(577\) 9897.10 0.714075 0.357038 0.934090i \(-0.383787\pi\)
0.357038 + 0.934090i \(0.383787\pi\)
\(578\) −14788.4 −1.06421
\(579\) 397.746 10777.2i 0.0285488 0.773551i
\(580\) −8584.47 −0.614570
\(581\) −11962.6 −0.854205
\(582\) −32061.5 1183.27i −2.28349 0.0842750i
\(583\) 164.407i 0.0116793i
\(584\) 7376.30i 0.522660i
\(585\) 9150.49 + 676.340i 0.646712 + 0.0478004i
\(586\) 21477.0i 1.51401i
\(587\) 10651.2 0.748934 0.374467 0.927240i \(-0.377826\pi\)
0.374467 + 0.927240i \(0.377826\pi\)
\(588\) 1331.16 36068.7i 0.0933606 2.52968i
\(589\) 1807.82i 0.126468i
\(590\) 6871.85 6635.81i 0.479508 0.463037i
\(591\) −22643.6 835.689i −1.57603 0.0581652i
\(592\) 7775.91i 0.539844i
\(593\) 2803.21i 0.194122i 0.995278 + 0.0970608i \(0.0309441\pi\)
−0.995278 + 0.0970608i \(0.969056\pi\)
\(594\) −2524.69 + 22720.0i −0.174393 + 1.56938i
\(595\) −5984.53 −0.412339
\(596\) −8863.84 −0.609190
\(597\) −657.654 + 17819.7i −0.0450854 + 1.22162i
\(598\) 18147.7i 1.24100i
\(599\) 16913.9i 1.15373i −0.816840 0.576864i \(-0.804276\pi\)
0.816840 0.576864i \(-0.195724\pi\)
\(600\) −197.059 + 5339.47i −0.0134082 + 0.363305i
\(601\) 27268.4i 1.85075i −0.379050 0.925376i \(-0.623749\pi\)
0.379050 0.925376i \(-0.376251\pi\)
\(602\) 58557.9i 3.96452i
\(603\) −1598.75 + 21630.2i −0.107971 + 1.46078i
\(604\) 15822.8i 1.06593i
\(605\) 558.325i 0.0375192i
\(606\) −418.980 + 11352.6i −0.0280857 + 0.761002i
\(607\) −9888.87 −0.661247 −0.330624 0.943763i \(-0.607259\pi\)
−0.330624 + 0.943763i \(0.607259\pi\)
\(608\) −19908.0 −1.32792
\(609\) 27790.6 + 1025.64i 1.84915 + 0.0682449i
\(610\) 4867.00 0.323048
\(611\) 6273.46i 0.415380i
\(612\) 790.219 10691.2i 0.0521939 0.706154i
\(613\) 16594.8i 1.09341i −0.837327 0.546703i \(-0.815883\pi\)
0.837327 0.546703i \(-0.184117\pi\)
\(614\) 22712.0 1.49280
\(615\) −391.126 + 10597.9i −0.0256451 + 0.694873i
\(616\) 12332.7 0.806656
\(617\) 4880.08i 0.318419i −0.987245 0.159210i \(-0.949105\pi\)
0.987245 0.159210i \(-0.0508946\pi\)
\(618\) −31267.1 1153.95i −2.03519 0.0751109i
\(619\) 16459.3 1.06875 0.534373 0.845249i \(-0.320548\pi\)
0.534373 + 0.845249i \(0.320548\pi\)
\(620\) −1159.06 −0.0750789
\(621\) −949.015 + 8540.28i −0.0613247 + 0.551867i
\(622\) 34530.0i 2.22593i
\(623\) 46002.7 2.95836
\(624\) −14107.4 520.650i −0.905045 0.0334017i
\(625\) 7143.45 0.457181
\(626\) 16428.5i 1.04890i
\(627\) 579.759 15709.0i 0.0369272 1.00057i
\(628\) 13117.2i 0.833494i
\(629\) −7567.51 −0.479708
\(630\) −1334.75 + 18058.4i −0.0844090 + 1.14201i
\(631\) 7718.51 0.486956 0.243478 0.969906i \(-0.421712\pi\)
0.243478 + 0.969906i \(0.421712\pi\)
\(632\) 2878.89 0.181196
\(633\) 4811.64 + 177.579i 0.302125 + 0.0111503i
\(634\) 25090.3i 1.57171i
\(635\) 3634.26i 0.227120i
\(636\) −233.128 8.60384i −0.0145348 0.000536422i
\(637\) 46255.3i 2.87708i
\(638\) 27409.0i 1.70084i
\(639\) −1207.78 + 16340.6i −0.0747717 + 1.01162i
\(640\) 6134.96i 0.378915i
\(641\) 18008.9i 1.10969i 0.831955 + 0.554843i \(0.187222\pi\)
−0.831955 + 0.554843i \(0.812778\pi\)
\(642\) 14952.3 + 551.833i 0.919192 + 0.0339238i
\(643\) −4243.70 −0.260272 −0.130136 0.991496i \(-0.541541\pi\)
−0.130136 + 0.991496i \(0.541541\pi\)
\(644\) 20225.1 1.23755
\(645\) 404.537 10961.2i 0.0246955 0.669145i
\(646\) 13054.2i 0.795060i
\(647\) 17795.9i 1.08134i −0.841233 0.540672i \(-0.818170\pi\)
0.841233 0.540672i \(-0.181830\pi\)
\(648\) −7354.12 1093.10i −0.445829 0.0662671i
\(649\) −11964.8 12390.4i −0.723669 0.749411i
\(650\) 29874.1i 1.80271i
\(651\) 3752.23 + 138.480i 0.225901 + 0.00833713i
\(652\) 32412.1 1.94687
\(653\) 23188.2i 1.38963i 0.719190 + 0.694813i \(0.244513\pi\)
−0.719190 + 0.694813i \(0.755487\pi\)
\(654\) 35351.0 + 1304.67i 2.11366 + 0.0780070i
\(655\) 7463.25i 0.445211i
\(656\) 16316.6i 0.971120i
\(657\) 1439.43 19474.7i 0.0854759 1.15644i
\(658\) −12380.6 −0.733505
\(659\) 17654.2 1.04356 0.521782 0.853079i \(-0.325268\pi\)
0.521782 + 0.853079i \(0.325268\pi\)
\(660\) −10071.6 371.705i −0.593997 0.0219221i
\(661\) 26614.0 1.56606 0.783028 0.621986i \(-0.213674\pi\)
0.783028 + 0.621986i \(0.213674\pi\)
\(662\) 37293.2 2.18949
\(663\) −506.696 + 13729.3i −0.0296809 + 0.804227i
\(664\) 3834.69 0.224119
\(665\) 12451.8i 0.726108i
\(666\) −1687.81 + 22835.1i −0.0982000 + 1.32859i
\(667\) 10302.9i 0.598094i
\(668\) 9273.65i 0.537138i
\(669\) 783.879 21239.8i 0.0453012 1.22747i
\(670\) −16933.0 −0.976387
\(671\) 8775.55i 0.504883i
\(672\) 1524.97 41320.1i 0.0875400 2.37196i
\(673\) 8452.89i 0.484153i −0.970257 0.242077i \(-0.922171\pi\)
0.970257 0.242077i \(-0.0778285\pi\)
\(674\) 44720.3i 2.55573i
\(675\) −1562.23 + 14058.7i −0.0890819 + 0.801657i
\(676\) −26776.2 −1.52345
\(677\) 18022.6i 1.02314i 0.859243 + 0.511568i \(0.170935\pi\)
−0.859243 + 0.511568i \(0.829065\pi\)
\(678\) −342.598 + 9282.96i −0.0194062 + 0.525826i
\(679\) 45822.9i 2.58987i
\(680\) 1918.37 0.108186
\(681\) −586.836 + 15900.8i −0.0330215 + 0.894742i
\(682\) 3700.71i 0.207782i
\(683\) −9737.81 −0.545545 −0.272772 0.962079i \(-0.587941\pi\)
−0.272772 + 0.962079i \(0.587941\pi\)
\(684\) 22244.9 + 1644.19i 1.24350 + 0.0919109i
\(685\) −2215.95 −0.123602
\(686\) −44500.0 −2.47670
\(687\) −30676.6 1132.15i −1.70362 0.0628739i
\(688\) 16876.0i 0.935164i
\(689\) 298.968 0.0165308
\(690\) −6703.96 247.417i −0.369877 0.0136507i
\(691\) 634.088i 0.0349086i −0.999848 0.0174543i \(-0.994444\pi\)
0.999848 0.0174543i \(-0.00555616\pi\)
\(692\) −46577.2 −2.55867
\(693\) 32560.6 + 2406.65i 1.78481 + 0.131921i
\(694\) −39976.4 −2.18658
\(695\) 3605.97i 0.196809i
\(696\) −8908.43 328.776i −0.485163 0.0179055i
\(697\) −15879.3 −0.862942
\(698\) 30311.1i 1.64368i
\(699\) 207.631 5625.93i 0.0112351 0.304424i
\(700\) 33293.7 1.79769
\(701\) 20373.9 1.09773 0.548867 0.835910i \(-0.315059\pi\)
0.548867 + 0.835910i \(0.315059\pi\)
\(702\) 41315.4 + 4591.06i 2.22130 + 0.246835i
\(703\) 15745.5i 0.844742i
\(704\) 28800.7 1.54186
\(705\) 2317.48 + 85.5292i 0.123803 + 0.00456910i
\(706\) 16664.1 0.888331
\(707\) 16225.3 0.863105
\(708\) 18195.7 16317.6i 0.965871 0.866178i
\(709\) 4574.90 0.242333 0.121166 0.992632i \(-0.461337\pi\)
0.121166 + 0.992632i \(0.461337\pi\)
\(710\) −12792.1 −0.676166
\(711\) 7600.76 + 561.794i 0.400915 + 0.0296328i
\(712\) −14746.4 −0.776189
\(713\) 1391.07i 0.0730660i
\(714\) −27094.6 999.959i −1.42016 0.0524125i
\(715\) 12916.1 0.675571
\(716\) 26031.5 1.35872
\(717\) 4103.07 + 151.428i 0.213712 + 0.00788730i
\(718\) 22569.3i 1.17309i
\(719\) −21858.7 −1.13379 −0.566894 0.823791i \(-0.691855\pi\)
−0.566894 + 0.823791i \(0.691855\pi\)
\(720\) −384.666 + 5204.32i −0.0199107 + 0.269380i
\(721\) 44687.4i 2.30825i
\(722\) 2243.58 0.115647
\(723\) 21.4395 580.919i 0.00110283 0.0298819i
\(724\) −339.097 −0.0174067
\(725\) 16960.2i 0.868807i
\(726\) −93.2909 + 2527.79i −0.00476908 + 0.129222i
\(727\) −34829.9 −1.77685 −0.888424 0.459024i \(-0.848199\pi\)
−0.888424 + 0.459024i \(0.848199\pi\)
\(728\) 22426.6i 1.14174i
\(729\) −19202.8 4321.08i −0.975605 0.219534i
\(730\) 15245.6 0.772965
\(731\) 16423.7 0.830991
\(732\) 12443.7 + 459.247i 0.628321 + 0.0231889i
\(733\) 5419.55 0.273091 0.136545 0.990634i \(-0.456400\pi\)
0.136545 + 0.990634i \(0.456400\pi\)
\(734\) 22532.0i 1.13307i
\(735\) 17087.2 + 630.621i 0.857510 + 0.0316474i
\(736\) 15318.7 0.767195
\(737\) 30531.4i 1.52597i
\(738\) −3541.61 + 47915.9i −0.176651 + 2.38999i
\(739\) 3453.34i 0.171899i −0.996300 0.0859493i \(-0.972608\pi\)
0.996300 0.0859493i \(-0.0273923\pi\)
\(740\) −10095.0 −0.501488
\(741\) −28566.2 1054.27i −1.41620 0.0522666i
\(742\) 590.009i 0.0291912i
\(743\) 12096.3i 0.597267i −0.954368 0.298633i \(-0.903469\pi\)
0.954368 0.298633i \(-0.0965308\pi\)
\(744\) −1202.80 44.3906i −0.0592698 0.00218742i
\(745\) 4199.15i 0.206503i
\(746\) −4022.10 −0.197399
\(747\) 10124.2 + 748.312i 0.495885 + 0.0366523i
\(748\) 15090.8i 0.737667i
\(749\) 21370.1i 1.04252i
\(750\) −24717.8 912.238i −1.20342 0.0444136i
\(751\) 537.734i 0.0261281i 0.999915 + 0.0130640i \(0.00415853\pi\)
−0.999915 + 0.0130640i \(0.995841\pi\)
\(752\) −3568.01 −0.173021
\(753\) −16923.1 624.565i −0.819005 0.0302263i
\(754\) 49842.3 2.40736
\(755\) −7495.88 −0.361328
\(756\) −5116.58 + 46044.7i −0.246149 + 2.21512i
\(757\) 12016.6 0.576951 0.288476 0.957487i \(-0.406852\pi\)
0.288476 + 0.957487i \(0.406852\pi\)
\(758\) 4886.77 0.234163
\(759\) −446.111 + 12087.7i −0.0213344 + 0.578071i
\(760\) 3991.51i 0.190510i
\(761\) 26602.2i 1.26719i −0.773666 0.633593i \(-0.781579\pi\)
0.773666 0.633593i \(-0.218421\pi\)
\(762\) 607.251 16453.9i 0.0288693 0.782235i
\(763\) 50524.2i 2.39725i
\(764\) −38365.3 −1.81676
\(765\) 5064.84 + 374.357i 0.239372 + 0.0176927i
\(766\) 43108.4i 2.03338i
\(767\) −22531.6 + 21757.6i −1.06071 + 1.02428i
\(768\) 136.651 3702.66i 0.00642052 0.173969i
\(769\) 18705.9i 0.877183i −0.898687 0.438591i \(-0.855478\pi\)
0.898687 0.438591i \(-0.144522\pi\)
\(770\) 25489.7i 1.19297i
\(771\) −18042.0 665.859i −0.842757 0.0311029i
\(772\) 21541.4 1.00427
\(773\) 31143.8 1.44911 0.724556 0.689216i \(-0.242045\pi\)
0.724556 + 0.689216i \(0.242045\pi\)
\(774\) 3663.04 49558.9i 0.170110 2.30149i
\(775\) 2289.93i 0.106138i
\(776\) 14688.8i 0.679506i
\(777\) 32680.7 + 1206.12i 1.50890 + 0.0556877i
\(778\) 17846.0i 0.822376i
\(779\) 33039.6i 1.51960i
\(780\) −675.931 + 18314.9i −0.0310285 + 0.840741i
\(781\) 23065.0i 1.05676i
\(782\) 10044.9i 0.459339i
\(783\) −23455.6 2606.44i −1.07054 0.118961i
\(784\) −26307.6