Properties

Label 147.4.c.b.146.15
Level $147$
Weight $4$
Character 147.146
Analytic conductor $8.673$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 147.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.67328077084\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 146.15
Character \(\chi\) \(=\) 147.146
Dual form 147.4.c.b.146.9

$q$-expansion

\(f(q)\) \(=\) \(q+1.05015i q^{2} +(-4.50851 - 2.58329i) q^{3} +6.89718 q^{4} -10.2305 q^{5} +(2.71285 - 4.73462i) q^{6} +15.6443i q^{8} +(13.6533 + 23.2935i) q^{9} +O(q^{10})\) \(q+1.05015i q^{2} +(-4.50851 - 2.58329i) q^{3} +6.89718 q^{4} -10.2305 q^{5} +(2.71285 - 4.73462i) q^{6} +15.6443i q^{8} +(13.6533 + 23.2935i) q^{9} -10.7436i q^{10} -24.0632i q^{11} +(-31.0960 - 17.8174i) q^{12} +49.4354i q^{13} +(46.1243 + 26.4283i) q^{15} +38.7485 q^{16} +125.761 q^{17} +(-24.4618 + 14.3380i) q^{18} +95.5681i q^{19} -70.5616 q^{20} +25.2700 q^{22} +185.716i q^{23} +(40.4138 - 70.5325i) q^{24} -20.3367 q^{25} -51.9147 q^{26} +(-1.38202 - 140.289i) q^{27} +40.6873i q^{29} +(-27.7538 + 48.4376i) q^{30} +37.5677i q^{31} +165.846i q^{32} +(-62.1620 + 108.489i) q^{33} +132.069i q^{34} +(94.1690 + 160.660i) q^{36} +283.290 q^{37} -100.361 q^{38} +(127.706 - 222.880i) q^{39} -160.049i q^{40} +166.685 q^{41} -411.667 q^{43} -165.968i q^{44} +(-139.680 - 238.305i) q^{45} -195.030 q^{46} +15.1056 q^{47} +(-174.698 - 100.098i) q^{48} -21.3567i q^{50} +(-566.996 - 324.878i) q^{51} +340.964i q^{52} -190.230i q^{53} +(147.325 - 1.45133i) q^{54} +246.178i q^{55} +(246.880 - 430.869i) q^{57} -42.7279 q^{58} -94.7330 q^{59} +(318.128 + 182.281i) q^{60} -412.161i q^{61} -39.4518 q^{62} +135.824 q^{64} -505.749i q^{65} +(-113.930 - 65.2797i) q^{66} -88.7656 q^{67} +867.398 q^{68} +(479.756 - 837.300i) q^{69} -1064.80i q^{71} +(-364.411 + 213.596i) q^{72} +828.400i q^{73} +297.497i q^{74} +(91.6883 + 52.5356i) q^{75} +659.150i q^{76} +(234.058 + 134.111i) q^{78} +256.515 q^{79} -396.417 q^{80} +(-356.177 + 636.065i) q^{81} +175.045i q^{82} +97.2939 q^{83} -1286.60 q^{85} -432.314i q^{86} +(105.107 - 183.439i) q^{87} +376.452 q^{88} -899.046 q^{89} +(250.256 - 146.685i) q^{90} +1280.91i q^{92} +(97.0480 - 169.374i) q^{93} +15.8632i q^{94} -977.710i q^{95} +(428.429 - 747.720i) q^{96} +398.892i q^{97} +(560.516 - 328.541i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 96 q^{4} - 64 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 96 q^{4} - 64 q^{9} + 256 q^{15} + 864 q^{16} - 32 q^{18} - 384 q^{22} + 744 q^{25} - 1704 q^{30} + 584 q^{36} + 432 q^{37} - 2368 q^{39} - 624 q^{43} + 3744 q^{46} - 2160 q^{51} + 2032 q^{57} + 6384 q^{58} - 5832 q^{60} - 3504 q^{64} + 3792 q^{67} - 7472 q^{72} + 2248 q^{78} + 2784 q^{79} - 1968 q^{81} - 3744 q^{85} - 624 q^{88} - 3232 q^{93} + 1320 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).

\(n\) \(50\) \(52\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.05015i 0.371285i 0.982617 + 0.185643i \(0.0594367\pi\)
−0.982617 + 0.185643i \(0.940563\pi\)
\(3\) −4.50851 2.58329i −0.867663 0.497154i
\(4\) 6.89718 0.862147
\(5\) −10.2305 −0.915044 −0.457522 0.889198i \(-0.651263\pi\)
−0.457522 + 0.889198i \(0.651263\pi\)
\(6\) 2.71285 4.73462i 0.184586 0.322150i
\(7\) 0 0
\(8\) 15.6443i 0.691388i
\(9\) 13.6533 + 23.2935i 0.505677 + 0.862723i
\(10\) 10.7436i 0.339742i
\(11\) 24.0632i 0.659574i −0.944055 0.329787i \(-0.893023\pi\)
0.944055 0.329787i \(-0.106977\pi\)
\(12\) −31.0960 17.8174i −0.748053 0.428620i
\(13\) 49.4354i 1.05468i 0.849653 + 0.527342i \(0.176811\pi\)
−0.849653 + 0.527342i \(0.823189\pi\)
\(14\) 0 0
\(15\) 46.1243 + 26.4283i 0.793950 + 0.454918i
\(16\) 38.7485 0.605445
\(17\) 125.761 1.79421 0.897106 0.441815i \(-0.145665\pi\)
0.897106 + 0.441815i \(0.145665\pi\)
\(18\) −24.4618 + 14.3380i −0.320316 + 0.187750i
\(19\) 95.5681i 1.15394i 0.816766 + 0.576969i \(0.195765\pi\)
−0.816766 + 0.576969i \(0.804235\pi\)
\(20\) −70.5616 −0.788903
\(21\) 0 0
\(22\) 25.2700 0.244890
\(23\) 185.716i 1.68367i 0.539736 + 0.841834i \(0.318524\pi\)
−0.539736 + 0.841834i \(0.681476\pi\)
\(24\) 40.4138 70.5325i 0.343726 0.599891i
\(25\) −20.3367 −0.162694
\(26\) −51.9147 −0.391589
\(27\) −1.38202 140.289i −0.00985074 0.999951i
\(28\) 0 0
\(29\) 40.6873i 0.260533i 0.991479 + 0.130266i \(0.0415832\pi\)
−0.991479 + 0.130266i \(0.958417\pi\)
\(30\) −27.7538 + 48.4376i −0.168904 + 0.294782i
\(31\) 37.5677i 0.217656i 0.994061 + 0.108828i \(0.0347098\pi\)
−0.994061 + 0.108828i \(0.965290\pi\)
\(32\) 165.846i 0.916181i
\(33\) −62.1620 + 108.489i −0.327910 + 0.572288i
\(34\) 132.069i 0.666165i
\(35\) 0 0
\(36\) 94.1690 + 160.660i 0.435968 + 0.743794i
\(37\) 283.290 1.25872 0.629358 0.777115i \(-0.283318\pi\)
0.629358 + 0.777115i \(0.283318\pi\)
\(38\) −100.361 −0.428440
\(39\) 127.706 222.880i 0.524340 0.915110i
\(40\) 160.049i 0.632651i
\(41\) 166.685 0.634923 0.317462 0.948271i \(-0.397170\pi\)
0.317462 + 0.948271i \(0.397170\pi\)
\(42\) 0 0
\(43\) −411.667 −1.45997 −0.729984 0.683464i \(-0.760473\pi\)
−0.729984 + 0.683464i \(0.760473\pi\)
\(44\) 165.968i 0.568650i
\(45\) −139.680 238.305i −0.462716 0.789430i
\(46\) −195.030 −0.625121
\(47\) 15.1056 0.0468805 0.0234402 0.999725i \(-0.492538\pi\)
0.0234402 + 0.999725i \(0.492538\pi\)
\(48\) −174.698 100.098i −0.525322 0.300999i
\(49\) 0 0
\(50\) 21.3567i 0.0604058i
\(51\) −566.996 324.878i −1.55677 0.891999i
\(52\) 340.964i 0.909293i
\(53\) 190.230i 0.493020i −0.969140 0.246510i \(-0.920716\pi\)
0.969140 0.246510i \(-0.0792838\pi\)
\(54\) 147.325 1.45133i 0.371267 0.00365744i
\(55\) 246.178i 0.603540i
\(56\) 0 0
\(57\) 246.880 430.869i 0.573684 1.00123i
\(58\) −42.7279 −0.0967320
\(59\) −94.7330 −0.209037 −0.104519 0.994523i \(-0.533330\pi\)
−0.104519 + 0.994523i \(0.533330\pi\)
\(60\) 318.128 + 182.281i 0.684502 + 0.392206i
\(61\) 412.161i 0.865111i −0.901607 0.432555i \(-0.857612\pi\)
0.901607 0.432555i \(-0.142388\pi\)
\(62\) −39.4518 −0.0808126
\(63\) 0 0
\(64\) 135.824 0.265281
\(65\) 505.749i 0.965083i
\(66\) −113.930 65.2797i −0.212482 0.121748i
\(67\) −88.7656 −0.161857 −0.0809287 0.996720i \(-0.525789\pi\)
−0.0809287 + 0.996720i \(0.525789\pi\)
\(68\) 867.398 1.54688
\(69\) 479.756 837.300i 0.837042 1.46086i
\(70\) 0 0
\(71\) 1064.80i 1.77984i −0.456118 0.889920i \(-0.650760\pi\)
0.456118 0.889920i \(-0.349240\pi\)
\(72\) −364.411 + 213.596i −0.596476 + 0.349619i
\(73\) 828.400i 1.32818i 0.747654 + 0.664088i \(0.231180\pi\)
−0.747654 + 0.664088i \(0.768820\pi\)
\(74\) 297.497i 0.467343i
\(75\) 91.6883 + 52.5356i 0.141163 + 0.0808839i
\(76\) 659.150i 0.994864i
\(77\) 0 0
\(78\) 234.058 + 134.111i 0.339767 + 0.194680i
\(79\) 256.515 0.365319 0.182659 0.983176i \(-0.441529\pi\)
0.182659 + 0.983176i \(0.441529\pi\)
\(80\) −396.417 −0.554009
\(81\) −356.177 + 636.065i −0.488582 + 0.872518i
\(82\) 175.045i 0.235738i
\(83\) 97.2939 0.128667 0.0643337 0.997928i \(-0.479508\pi\)
0.0643337 + 0.997928i \(0.479508\pi\)
\(84\) 0 0
\(85\) −1286.60 −1.64178
\(86\) 432.314i 0.542065i
\(87\) 105.107 183.439i 0.129525 0.226054i
\(88\) 376.452 0.456022
\(89\) −899.046 −1.07077 −0.535386 0.844608i \(-0.679834\pi\)
−0.535386 + 0.844608i \(0.679834\pi\)
\(90\) 250.256 146.685i 0.293104 0.171800i
\(91\) 0 0
\(92\) 1280.91i 1.45157i
\(93\) 97.0480 169.374i 0.108209 0.188852i
\(94\) 15.8632i 0.0174060i
\(95\) 977.710i 1.05590i
\(96\) 428.429 747.720i 0.455483 0.794936i
\(97\) 398.892i 0.417540i 0.977965 + 0.208770i \(0.0669460\pi\)
−0.977965 + 0.208770i \(0.933054\pi\)
\(98\) 0 0
\(99\) 560.516 328.541i 0.569030 0.333531i
\(100\) −140.266 −0.140266
\(101\) −57.2539 −0.0564057 −0.0282028 0.999602i \(-0.508978\pi\)
−0.0282028 + 0.999602i \(0.508978\pi\)
\(102\) 341.171 595.433i 0.331186 0.578006i
\(103\) 740.200i 0.708098i 0.935227 + 0.354049i \(0.115195\pi\)
−0.935227 + 0.354049i \(0.884805\pi\)
\(104\) −773.383 −0.729196
\(105\) 0 0
\(106\) 199.770 0.183051
\(107\) 862.638i 0.779386i 0.920945 + 0.389693i \(0.127419\pi\)
−0.920945 + 0.389693i \(0.872581\pi\)
\(108\) −9.53205 967.600i −0.00849279 0.862105i
\(109\) −657.058 −0.577383 −0.288691 0.957422i \(-0.593220\pi\)
−0.288691 + 0.957422i \(0.593220\pi\)
\(110\) −258.525 −0.224085
\(111\) −1277.21 731.818i −1.09214 0.625776i
\(112\) 0 0
\(113\) 884.317i 0.736190i 0.929788 + 0.368095i \(0.119990\pi\)
−0.929788 + 0.368095i \(0.880010\pi\)
\(114\) 452.479 + 259.262i 0.371742 + 0.213001i
\(115\) 1899.96i 1.54063i
\(116\) 280.628i 0.224618i
\(117\) −1151.52 + 674.954i −0.909901 + 0.533329i
\(118\) 99.4842i 0.0776124i
\(119\) 0 0
\(120\) −413.453 + 721.584i −0.314524 + 0.548927i
\(121\) 751.964 0.564962
\(122\) 432.832 0.321203
\(123\) −751.501 430.595i −0.550899 0.315654i
\(124\) 259.111i 0.187652i
\(125\) 1486.87 1.06392
\(126\) 0 0
\(127\) 1004.76 0.702028 0.351014 0.936370i \(-0.385837\pi\)
0.351014 + 0.936370i \(0.385837\pi\)
\(128\) 1469.41i 1.01468i
\(129\) 1856.00 + 1063.45i 1.26676 + 0.725829i
\(130\) 531.114 0.358321
\(131\) −712.639 −0.475294 −0.237647 0.971352i \(-0.576376\pi\)
−0.237647 + 0.971352i \(0.576376\pi\)
\(132\) −428.743 + 748.268i −0.282706 + 0.493396i
\(133\) 0 0
\(134\) 93.2175i 0.0600953i
\(135\) 14.1388 + 1435.23i 0.00901387 + 0.915000i
\(136\) 1967.45i 1.24050i
\(137\) 1359.68i 0.847921i 0.905681 + 0.423961i \(0.139361\pi\)
−0.905681 + 0.423961i \(0.860639\pi\)
\(138\) 879.293 + 503.818i 0.542394 + 0.310781i
\(139\) 213.266i 0.130137i −0.997881 0.0650684i \(-0.979273\pi\)
0.997881 0.0650684i \(-0.0207266\pi\)
\(140\) 0 0
\(141\) −68.1039 39.0222i −0.0406765 0.0233068i
\(142\) 1118.20 0.660828
\(143\) 1189.57 0.695643
\(144\) 529.043 + 902.589i 0.306159 + 0.522331i
\(145\) 416.252i 0.238399i
\(146\) −869.947 −0.493132
\(147\) 0 0
\(148\) 1953.90 1.08520
\(149\) 1522.90i 0.837319i 0.908143 + 0.418660i \(0.137500\pi\)
−0.908143 + 0.418660i \(0.862500\pi\)
\(150\) −55.1704 + 96.2868i −0.0300310 + 0.0524119i
\(151\) 410.715 0.221348 0.110674 0.993857i \(-0.464699\pi\)
0.110674 + 0.993857i \(0.464699\pi\)
\(152\) −1495.10 −0.797819
\(153\) 1717.05 + 2929.43i 0.907291 + 1.54791i
\(154\) 0 0
\(155\) 384.336i 0.199165i
\(156\) 880.809 1537.24i 0.452059 0.788960i
\(157\) 2184.75i 1.11059i −0.831655 0.555293i \(-0.812606\pi\)
0.831655 0.555293i \(-0.187394\pi\)
\(158\) 269.380i 0.135637i
\(159\) −491.417 + 857.651i −0.245107 + 0.427775i
\(160\) 1696.69i 0.838346i
\(161\) 0 0
\(162\) −667.966 374.040i −0.323953 0.181403i
\(163\) −1593.25 −0.765600 −0.382800 0.923831i \(-0.625040\pi\)
−0.382800 + 0.923831i \(0.625040\pi\)
\(164\) 1149.66 0.547397
\(165\) 635.949 1109.90i 0.300052 0.523669i
\(166\) 102.173i 0.0477723i
\(167\) −1297.31 −0.601129 −0.300564 0.953762i \(-0.597175\pi\)
−0.300564 + 0.953762i \(0.597175\pi\)
\(168\) 0 0
\(169\) −246.854 −0.112360
\(170\) 1351.13i 0.609570i
\(171\) −2226.12 + 1304.82i −0.995529 + 0.583519i
\(172\) −2839.34 −1.25871
\(173\) 3229.49 1.41927 0.709635 0.704570i \(-0.248860\pi\)
0.709635 + 0.704570i \(0.248860\pi\)
\(174\) 192.639 + 110.378i 0.0839307 + 0.0480906i
\(175\) 0 0
\(176\) 932.411i 0.399336i
\(177\) 427.104 + 244.722i 0.181374 + 0.103924i
\(178\) 944.136i 0.397562i
\(179\) 3521.41i 1.47040i −0.677848 0.735202i \(-0.737087\pi\)
0.677848 0.735202i \(-0.262913\pi\)
\(180\) −963.397 1643.63i −0.398930 0.680605i
\(181\) 3143.01i 1.29071i −0.763883 0.645354i \(-0.776710\pi\)
0.763883 0.645354i \(-0.223290\pi\)
\(182\) 0 0
\(183\) −1064.73 + 1858.23i −0.430093 + 0.750624i
\(184\) −2905.39 −1.16407
\(185\) −2898.20 −1.15178
\(186\) 177.869 + 101.915i 0.0701181 + 0.0401763i
\(187\) 3026.22i 1.18342i
\(188\) 104.186 0.0404179
\(189\) 0 0
\(190\) 1026.75 0.392042
\(191\) 4480.24i 1.69727i −0.528978 0.848636i \(-0.677424\pi\)
0.528978 0.848636i \(-0.322576\pi\)
\(192\) −612.362 350.871i −0.230174 0.131885i
\(193\) 5217.77 1.94603 0.973013 0.230751i \(-0.0741182\pi\)
0.973013 + 0.230751i \(0.0741182\pi\)
\(194\) −418.898 −0.155026
\(195\) −1306.49 + 2280.17i −0.479795 + 0.837367i
\(196\) 0 0
\(197\) 474.082i 0.171457i −0.996319 0.0857283i \(-0.972678\pi\)
0.996319 0.0857283i \(-0.0273217\pi\)
\(198\) 345.018 + 588.628i 0.123835 + 0.211272i
\(199\) 1055.13i 0.375860i −0.982182 0.187930i \(-0.939822\pi\)
0.982182 0.187930i \(-0.0601778\pi\)
\(200\) 318.154i 0.112485i
\(201\) 400.200 + 229.307i 0.140438 + 0.0804680i
\(202\) 60.1253i 0.0209426i
\(203\) 0 0
\(204\) −3910.67 2240.74i −1.34217 0.769035i
\(205\) −1705.27 −0.580983
\(206\) −777.324 −0.262906
\(207\) −4325.97 + 2535.62i −1.45254 + 0.851392i
\(208\) 1915.55i 0.638554i
\(209\) 2299.67 0.761108
\(210\) 0 0
\(211\) −1367.40 −0.446141 −0.223070 0.974802i \(-0.571608\pi\)
−0.223070 + 0.974802i \(0.571608\pi\)
\(212\) 1312.05i 0.425056i
\(213\) −2750.68 + 4800.66i −0.884853 + 1.54430i
\(214\) −905.902 −0.289375
\(215\) 4211.56 1.33594
\(216\) 2194.73 21.6208i 0.691354 0.00681069i
\(217\) 0 0
\(218\) 690.012i 0.214374i
\(219\) 2139.99 3734.85i 0.660308 1.15241i
\(220\) 1697.94i 0.520340i
\(221\) 6217.06i 1.89233i
\(222\) 768.521 1341.27i 0.232341 0.405496i
\(223\) 1165.04i 0.349852i −0.984582 0.174926i \(-0.944031\pi\)
0.984582 0.174926i \(-0.0559686\pi\)
\(224\) 0 0
\(225\) −277.663 473.714i −0.0822705 0.140360i
\(226\) −928.668 −0.273337
\(227\) 1508.20 0.440981 0.220491 0.975389i \(-0.429234\pi\)
0.220491 + 0.975389i \(0.429234\pi\)
\(228\) 1702.77 2971.78i 0.494600 0.863207i
\(229\) 2678.95i 0.773056i 0.922278 + 0.386528i \(0.126326\pi\)
−0.922278 + 0.386528i \(0.873674\pi\)
\(230\) 1995.25 0.572014
\(231\) 0 0
\(232\) −636.526 −0.180129
\(233\) 1651.83i 0.464443i 0.972663 + 0.232221i \(0.0745994\pi\)
−0.972663 + 0.232221i \(0.925401\pi\)
\(234\) −708.805 1209.28i −0.198017 0.337833i
\(235\) −154.538 −0.0428977
\(236\) −653.390 −0.180221
\(237\) −1156.50 662.651i −0.316973 0.181620i
\(238\) 0 0
\(239\) 1945.85i 0.526638i −0.964709 0.263319i \(-0.915183\pi\)
0.964709 0.263319i \(-0.0848172\pi\)
\(240\) 1787.25 + 1024.06i 0.480693 + 0.275428i
\(241\) 480.849i 0.128524i −0.997933 0.0642618i \(-0.979531\pi\)
0.997933 0.0642618i \(-0.0204693\pi\)
\(242\) 789.678i 0.209762i
\(243\) 3248.96 1947.60i 0.857700 0.514151i
\(244\) 2842.74i 0.745853i
\(245\) 0 0
\(246\) 452.191 789.192i 0.117198 0.204541i
\(247\) −4724.44 −1.21704
\(248\) −587.720 −0.150485
\(249\) −438.650 251.338i −0.111640 0.0639674i
\(250\) 1561.44i 0.395017i
\(251\) −5108.84 −1.28473 −0.642364 0.766400i \(-0.722046\pi\)
−0.642364 + 0.766400i \(0.722046\pi\)
\(252\) 0 0
\(253\) 4468.90 1.11050
\(254\) 1055.15i 0.260653i
\(255\) 5800.66 + 3323.66i 1.42451 + 0.816219i
\(256\) −456.513 −0.111453
\(257\) −1656.10 −0.401963 −0.200982 0.979595i \(-0.564413\pi\)
−0.200982 + 0.979595i \(0.564413\pi\)
\(258\) −1116.79 + 1949.09i −0.269489 + 0.470329i
\(259\) 0 0
\(260\) 3488.24i 0.832044i
\(261\) −947.751 + 555.515i −0.224768 + 0.131745i
\(262\) 748.380i 0.176470i
\(263\) 1496.85i 0.350950i −0.984484 0.175475i \(-0.943854\pi\)
0.984484 0.175475i \(-0.0561462\pi\)
\(264\) −1697.24 972.483i −0.395673 0.226713i
\(265\) 1946.15i 0.451135i
\(266\) 0 0
\(267\) 4053.35 + 2322.49i 0.929068 + 0.532338i
\(268\) −612.232 −0.139545
\(269\) −2373.66 −0.538009 −0.269005 0.963139i \(-0.586695\pi\)
−0.269005 + 0.963139i \(0.586695\pi\)
\(270\) −1507.21 + 14.8479i −0.339726 + 0.00334672i
\(271\) 5846.44i 1.31050i −0.755412 0.655251i \(-0.772563\pi\)
0.755412 0.655251i \(-0.227437\pi\)
\(272\) 4873.06 1.08630
\(273\) 0 0
\(274\) −1427.87 −0.314821
\(275\) 489.366i 0.107309i
\(276\) 3308.97 5775.01i 0.721653 1.25947i
\(277\) 2501.87 0.542681 0.271341 0.962483i \(-0.412533\pi\)
0.271341 + 0.962483i \(0.412533\pi\)
\(278\) 223.962 0.0483179
\(279\) −875.083 + 512.921i −0.187777 + 0.110064i
\(280\) 0 0
\(281\) 8088.74i 1.71720i 0.512645 + 0.858601i \(0.328666\pi\)
−0.512645 + 0.858601i \(0.671334\pi\)
\(282\) 40.9793 71.5195i 0.00865347 0.0151026i
\(283\) 4331.83i 0.909895i −0.890518 0.454947i \(-0.849658\pi\)
0.890518 0.454947i \(-0.150342\pi\)
\(284\) 7344.12i 1.53448i
\(285\) −2525.70 + 4408.01i −0.524947 + 0.916169i
\(286\) 1249.23i 0.258282i
\(287\) 0 0
\(288\) −3863.15 + 2264.35i −0.790410 + 0.463291i
\(289\) 10902.9 2.21920
\(290\) 437.128 0.0885140
\(291\) 1030.45 1798.41i 0.207581 0.362284i
\(292\) 5713.62i 1.14508i
\(293\) −4715.26 −0.940164 −0.470082 0.882623i \(-0.655776\pi\)
−0.470082 + 0.882623i \(0.655776\pi\)
\(294\) 0 0
\(295\) 969.166 0.191278
\(296\) 4431.87i 0.870261i
\(297\) −3375.81 + 33.2558i −0.659542 + 0.00649730i
\(298\) −1599.28 −0.310884
\(299\) −9180.91 −1.77574
\(300\) 632.391 + 362.347i 0.121704 + 0.0697338i
\(301\) 0 0
\(302\) 431.314i 0.0821832i
\(303\) 258.129 + 147.903i 0.0489411 + 0.0280423i
\(304\) 3703.12i 0.698646i
\(305\) 4216.61i 0.791615i
\(306\) −3076.35 + 1803.17i −0.574716 + 0.336864i
\(307\) 4540.05i 0.844020i 0.906591 + 0.422010i \(0.138675\pi\)
−0.906591 + 0.422010i \(0.861325\pi\)
\(308\) 0 0
\(309\) 1912.15 3337.20i 0.352033 0.614390i
\(310\) 403.612 0.0739471
\(311\) 5248.33 0.956932 0.478466 0.878106i \(-0.341193\pi\)
0.478466 + 0.878106i \(0.341193\pi\)
\(312\) 3486.80 + 1997.87i 0.632696 + 0.362522i
\(313\) 6079.22i 1.09782i −0.835881 0.548910i \(-0.815043\pi\)
0.835881 0.548910i \(-0.184957\pi\)
\(314\) 2294.32 0.412344
\(315\) 0 0
\(316\) 1769.23 0.314959
\(317\) 4335.82i 0.768215i 0.923288 + 0.384107i \(0.125491\pi\)
−0.923288 + 0.384107i \(0.874509\pi\)
\(318\) −900.666 516.064i −0.158826 0.0910044i
\(319\) 979.066 0.171841
\(320\) −1389.55 −0.242744
\(321\) 2228.44 3889.21i 0.387475 0.676244i
\(322\) 0 0
\(323\) 12018.8i 2.07041i
\(324\) −2456.61 + 4387.06i −0.421230 + 0.752239i
\(325\) 1005.35i 0.171591i
\(326\) 1673.16i 0.284256i
\(327\) 2962.35 + 1697.37i 0.500974 + 0.287048i
\(328\) 2607.68i 0.438978i
\(329\) 0 0
\(330\) 1165.56 + 667.844i 0.194431 + 0.111405i
\(331\) 6270.17 1.04121 0.520603 0.853799i \(-0.325707\pi\)
0.520603 + 0.853799i \(0.325707\pi\)
\(332\) 671.053 0.110930
\(333\) 3867.83 + 6598.81i 0.636504 + 1.08592i
\(334\) 1362.37i 0.223190i
\(335\) 908.117 0.148107
\(336\) 0 0
\(337\) −5320.37 −0.859997 −0.429999 0.902830i \(-0.641486\pi\)
−0.429999 + 0.902830i \(0.641486\pi\)
\(338\) 259.235i 0.0417175i
\(339\) 2284.44 3986.95i 0.366000 0.638765i
\(340\) −8873.93 −1.41546
\(341\) 903.997 0.143561
\(342\) −1370.26 2337.76i −0.216652 0.369625i
\(343\) 0 0
\(344\) 6440.25i 1.00940i
\(345\) −4908.15 + 8566.00i −0.765930 + 1.33675i
\(346\) 3391.46i 0.526954i
\(347\) 4815.66i 0.745009i −0.928030 0.372504i \(-0.878499\pi\)
0.928030 0.372504i \(-0.121501\pi\)
\(348\) 724.942 1265.21i 0.111669 0.194892i
\(349\) 5201.69i 0.797822i −0.916990 0.398911i \(-0.869388\pi\)
0.916990 0.398911i \(-0.130612\pi\)
\(350\) 0 0
\(351\) 6935.25 68.3207i 1.05463 0.0103894i
\(352\) 3990.79 0.604289
\(353\) 637.734 0.0961563 0.0480782 0.998844i \(-0.484690\pi\)
0.0480782 + 0.998844i \(0.484690\pi\)
\(354\) −256.996 + 448.525i −0.0385853 + 0.0673413i
\(355\) 10893.4i 1.62863i
\(356\) −6200.88 −0.923163
\(357\) 0 0
\(358\) 3698.02 0.545939
\(359\) 5518.37i 0.811277i −0.914034 0.405638i \(-0.867049\pi\)
0.914034 0.405638i \(-0.132951\pi\)
\(360\) 3728.11 2185.20i 0.545802 0.319917i
\(361\) −2274.26 −0.331573
\(362\) 3300.64 0.479221
\(363\) −3390.23 1942.54i −0.490196 0.280873i
\(364\) 0 0
\(365\) 8474.95i 1.21534i
\(366\) −1951.42 1118.13i −0.278696 0.159687i
\(367\) 2594.14i 0.368973i 0.982835 + 0.184486i \(0.0590622\pi\)
−0.982835 + 0.184486i \(0.940938\pi\)
\(368\) 7196.20i 1.01937i
\(369\) 2275.80 + 3882.69i 0.321066 + 0.547763i
\(370\) 3043.55i 0.427640i
\(371\) 0 0
\(372\) 669.357 1168.20i 0.0932918 0.162819i
\(373\) −5173.83 −0.718206 −0.359103 0.933298i \(-0.616917\pi\)
−0.359103 + 0.933298i \(0.616917\pi\)
\(374\) 3177.99 0.439385
\(375\) −6703.56 3841.01i −0.923120 0.528930i
\(376\) 236.317i 0.0324126i
\(377\) −2011.39 −0.274780
\(378\) 0 0
\(379\) −14088.2 −1.90940 −0.954700 0.297568i \(-0.903824\pi\)
−0.954700 + 0.297568i \(0.903824\pi\)
\(380\) 6743.44i 0.910345i
\(381\) −4529.95 2595.57i −0.609124 0.349016i
\(382\) 4704.94 0.630172
\(383\) 7732.32 1.03160 0.515801 0.856709i \(-0.327495\pi\)
0.515801 + 0.856709i \(0.327495\pi\)
\(384\) 3795.90 6624.83i 0.504450 0.880396i
\(385\) 0 0
\(386\) 5479.45i 0.722531i
\(387\) −5620.60 9589.18i −0.738272 1.25955i
\(388\) 2751.23i 0.359981i
\(389\) 731.955i 0.0954025i −0.998862 0.0477013i \(-0.984810\pi\)
0.998862 0.0477013i \(-0.0151895\pi\)
\(390\) −2394.53 1372.02i −0.310902 0.178141i
\(391\) 23355.8i 3.02086i
\(392\) 0 0
\(393\) 3212.94 + 1840.95i 0.412395 + 0.236294i
\(394\) 497.859 0.0636593
\(395\) −2624.28 −0.334283
\(396\) 3865.98 2266.00i 0.490588 0.287553i
\(397\) 14564.1i 1.84119i −0.390518 0.920595i \(-0.627704\pi\)
0.390518 0.920595i \(-0.372296\pi\)
\(398\) 1108.05 0.139551
\(399\) 0 0
\(400\) −788.018 −0.0985022
\(401\) 5909.89i 0.735975i 0.929831 + 0.367988i \(0.119953\pi\)
−0.929831 + 0.367988i \(0.880047\pi\)
\(402\) −240.807 + 420.272i −0.0298766 + 0.0521424i
\(403\) −1857.17 −0.229559
\(404\) −394.890 −0.0486300
\(405\) 3643.87 6507.27i 0.447075 0.798392i
\(406\) 0 0
\(407\) 6816.84i 0.830217i
\(408\) 5082.49 8870.27i 0.616717 1.07633i
\(409\) 8054.46i 0.973759i 0.873469 + 0.486880i \(0.161865\pi\)
−0.873469 + 0.486880i \(0.838135\pi\)
\(410\) 1790.80i 0.215710i
\(411\) 3512.44 6130.12i 0.421547 0.735709i
\(412\) 5105.29i 0.610485i
\(413\) 0 0
\(414\) −2662.79 4542.93i −0.316109 0.539307i
\(415\) −995.366 −0.117736
\(416\) −8198.68 −0.966282
\(417\) −550.928 + 961.513i −0.0646980 + 0.112915i
\(418\) 2415.01i 0.282588i
\(419\) 13850.2 1.61486 0.807428 0.589966i \(-0.200859\pi\)
0.807428 + 0.589966i \(0.200859\pi\)
\(420\) 0 0
\(421\) −2365.25 −0.273813 −0.136906 0.990584i \(-0.543716\pi\)
−0.136906 + 0.990584i \(0.543716\pi\)
\(422\) 1435.98i 0.165645i
\(423\) 206.241 + 351.863i 0.0237064 + 0.0404449i
\(424\) 2976.01 0.340868
\(425\) −2557.58 −0.291907
\(426\) −5041.43 2888.64i −0.573376 0.328533i
\(427\) 0 0
\(428\) 5949.77i 0.671946i
\(429\) −5363.19 3073.00i −0.603583 0.345841i
\(430\) 4422.79i 0.496013i
\(431\) 194.891i 0.0217809i −0.999941 0.0108905i \(-0.996533\pi\)
0.999941 0.0108905i \(-0.00346661\pi\)
\(432\) −53.5512 5436.00i −0.00596409 0.605416i
\(433\) 7716.01i 0.856369i −0.903691 0.428185i \(-0.859153\pi\)
0.903691 0.428185i \(-0.140847\pi\)
\(434\) 0 0
\(435\) −1075.30 + 1876.68i −0.118521 + 0.206850i
\(436\) −4531.85 −0.497789
\(437\) −17748.5 −1.94285
\(438\) 3922.16 + 2247.32i 0.427873 + 0.245163i
\(439\) 7595.59i 0.825781i 0.910781 + 0.412891i \(0.135481\pi\)
−0.910781 + 0.412891i \(0.864519\pi\)
\(440\) −3851.29 −0.417280
\(441\) 0 0
\(442\) −6528.86 −0.702594
\(443\) 10116.7i 1.08501i −0.840053 0.542505i \(-0.817476\pi\)
0.840053 0.542505i \(-0.182524\pi\)
\(444\) −8809.16 5047.48i −0.941587 0.539511i
\(445\) 9197.69 0.979803
\(446\) 1223.47 0.129895
\(447\) 3934.08 6865.99i 0.416276 0.726511i
\(448\) 0 0
\(449\) 18315.5i 1.92509i −0.271131 0.962543i \(-0.587398\pi\)
0.271131 0.962543i \(-0.412602\pi\)
\(450\) 497.473 291.589i 0.0521135 0.0305458i
\(451\) 4010.97i 0.418779i
\(452\) 6099.29i 0.634705i
\(453\) −1851.71 1061.00i −0.192055 0.110044i
\(454\) 1583.84i 0.163730i
\(455\) 0 0
\(456\) 6740.66 + 3862.26i 0.692237 + 0.396638i
\(457\) 5171.83 0.529383 0.264692 0.964333i \(-0.414730\pi\)
0.264692 + 0.964333i \(0.414730\pi\)
\(458\) −2813.31 −0.287024
\(459\) −173.805 17643.0i −0.0176743 1.79413i
\(460\) 13104.4i 1.32825i
\(461\) 7960.73 0.804269 0.402135 0.915581i \(-0.368268\pi\)
0.402135 + 0.915581i \(0.368268\pi\)
\(462\) 0 0
\(463\) 1659.53 0.166577 0.0832883 0.996525i \(-0.473458\pi\)
0.0832883 + 0.996525i \(0.473458\pi\)
\(464\) 1576.57i 0.157738i
\(465\) −992.850 + 1732.78i −0.0990157 + 0.172808i
\(466\) −1734.68 −0.172441
\(467\) 6925.40 0.686230 0.343115 0.939293i \(-0.388518\pi\)
0.343115 + 0.939293i \(0.388518\pi\)
\(468\) −7942.26 + 4655.28i −0.784468 + 0.459808i
\(469\) 0 0
\(470\) 162.289i 0.0159273i
\(471\) −5643.83 + 9849.95i −0.552131 + 0.963613i
\(472\) 1482.03i 0.144526i
\(473\) 9906.01i 0.962958i
\(474\) 695.885 1214.50i 0.0674327 0.117688i
\(475\) 1943.54i 0.187739i
\(476\) 0 0
\(477\) 4431.12 2597.26i 0.425339 0.249309i
\(478\) 2043.44 0.195533
\(479\) 19425.3 1.85295 0.926474 0.376358i \(-0.122824\pi\)
0.926474 + 0.376358i \(0.122824\pi\)
\(480\) −4383.04 + 7649.55i −0.416787 + 0.727401i
\(481\) 14004.5i 1.32755i
\(482\) 504.965 0.0477190
\(483\) 0 0
\(484\) 5186.43 0.487080
\(485\) 4080.87i 0.382067i
\(486\) 2045.28 + 3411.91i 0.190897 + 0.318451i
\(487\) −9624.35 −0.895525 −0.447763 0.894152i \(-0.647779\pi\)
−0.447763 + 0.894152i \(0.647779\pi\)
\(488\) 6447.97 0.598127
\(489\) 7183.17 + 4115.82i 0.664283 + 0.380621i
\(490\) 0 0
\(491\) 448.247i 0.0411998i −0.999788 0.0205999i \(-0.993442\pi\)
0.999788 0.0205999i \(-0.00655762\pi\)
\(492\) −5183.24 2969.89i −0.474956 0.272141i
\(493\) 5116.89i 0.467451i
\(494\) 4961.39i 0.451869i
\(495\) −5734.36 + 3361.14i −0.520688 + 0.305196i
\(496\) 1455.69i 0.131779i
\(497\) 0 0
\(498\) 263.943 460.650i 0.0237502 0.0414502i
\(499\) −13858.2 −1.24324 −0.621620 0.783319i \(-0.713525\pi\)
−0.621620 + 0.783319i \(0.713525\pi\)
\(500\) 10255.2 0.917253
\(501\) 5848.91 + 3351.31i 0.521577 + 0.298853i
\(502\) 5365.06i 0.477001i
\(503\) −17853.2 −1.58258 −0.791288 0.611443i \(-0.790589\pi\)
−0.791288 + 0.611443i \(0.790589\pi\)
\(504\) 0 0
\(505\) 585.736 0.0516137
\(506\) 4693.04i 0.412314i
\(507\) 1112.94 + 637.695i 0.0974903 + 0.0558600i
\(508\) 6929.98 0.605252
\(509\) −9982.92 −0.869322 −0.434661 0.900594i \(-0.643132\pi\)
−0.434661 + 0.900594i \(0.643132\pi\)
\(510\) −3490.35 + 6091.58i −0.303050 + 0.528901i
\(511\) 0 0
\(512\) 11275.8i 0.973295i
\(513\) 13407.2 132.077i 1.15388 0.0113671i
\(514\) 1739.16i 0.149243i
\(515\) 7572.62i 0.647941i
\(516\) 12801.2 + 7334.83i 1.09213 + 0.625771i
\(517\) 363.489i 0.0309212i
\(518\) 0 0
\(519\) −14560.2 8342.70i −1.23145 0.705595i
\(520\) 7912.10 0.667247
\(521\) 12630.5 1.06210 0.531048 0.847342i \(-0.321798\pi\)
0.531048 + 0.847342i \(0.321798\pi\)
\(522\) −583.376 995.284i −0.0489151 0.0834529i
\(523\) 11669.0i 0.975622i −0.872949 0.487811i \(-0.837795\pi\)
0.872949 0.487811i \(-0.162205\pi\)
\(524\) −4915.20 −0.409774
\(525\) 0 0
\(526\) 1571.93 0.130303
\(527\) 4724.56i 0.390522i
\(528\) −2408.68 + 4203.78i −0.198531 + 0.346489i
\(529\) −22323.3 −1.83474
\(530\) −2043.75 −0.167500
\(531\) −1293.41 2206.67i −0.105705 0.180341i
\(532\) 0 0
\(533\) 8240.14i 0.669644i
\(534\) −2438.97 + 4256.64i −0.197649 + 0.344949i
\(535\) 8825.22i 0.713173i
\(536\) 1388.68i 0.111906i
\(537\) −9096.80 + 15876.3i −0.731016 + 1.27581i
\(538\) 2492.71i 0.199755i
\(539\) 0 0
\(540\) 97.5177 + 9899.04i 0.00777128 + 0.788865i
\(541\) 19740.4 1.56877 0.784385 0.620274i \(-0.212979\pi\)
0.784385 + 0.620274i \(0.212979\pi\)
\(542\) 6139.66 0.486570
\(543\) −8119.30 + 14170.3i −0.641680 + 1.11990i
\(544\) 20857.1i 1.64382i
\(545\) 6722.04 0.528331
\(546\) 0 0
\(547\) 7949.55 0.621386 0.310693 0.950510i \(-0.399439\pi\)
0.310693 + 0.950510i \(0.399439\pi\)
\(548\) 9377.95i 0.731033i
\(549\) 9600.67 5627.34i 0.746351 0.437466i
\(550\) −513.910 −0.0398421
\(551\) −3888.41 −0.300639
\(552\) 13099.0 + 7505.46i 1.01002 + 0.578721i
\(553\) 0 0
\(554\) 2627.34i 0.201489i
\(555\) 13066.5 + 7486.87i 0.999358 + 0.572612i
\(556\) 1470.94i 0.112197i
\(557\) 9866.11i 0.750522i −0.926919 0.375261i \(-0.877553\pi\)
0.926919 0.375261i \(-0.122447\pi\)
\(558\) −538.646 918.971i −0.0408651 0.0697189i
\(559\) 20350.9i 1.53981i
\(560\) 0 0
\(561\) −7817.58 + 13643.7i −0.588340 + 1.02681i
\(562\) −8494.42 −0.637572
\(563\) −9237.69 −0.691514 −0.345757 0.938324i \(-0.612378\pi\)
−0.345757 + 0.938324i \(0.612378\pi\)
\(564\) −469.724 269.143i −0.0350691 0.0200939i
\(565\) 9047.01i 0.673647i
\(566\) 4549.08 0.337831
\(567\) 0 0
\(568\) 16658.1 1.23056
\(569\) 12586.1i 0.927308i 0.886016 + 0.463654i \(0.153462\pi\)
−0.886016 + 0.463654i \(0.846538\pi\)
\(570\) −4629.09 2652.38i −0.340160 0.194905i
\(571\) 20675.9 1.51534 0.757669 0.652640i \(-0.226338\pi\)
0.757669 + 0.652640i \(0.226338\pi\)
\(572\) 8204.68 0.599747
\(573\) −11573.7 + 20199.2i −0.843805 + 1.47266i
\(574\) 0 0
\(575\) 3776.85i 0.273923i
\(576\) 1854.44 + 3163.81i 0.134146 + 0.228864i
\(577\) 15543.6i 1.12147i −0.827996 0.560734i \(-0.810519\pi\)
0.827996 0.560734i \(-0.189481\pi\)
\(578\) 11449.7i 0.823955i
\(579\) −23524.3 13479.0i −1.68849 0.967474i
\(580\) 2870.96i 0.205535i
\(581\) 0 0
\(582\) 1888.60 + 1082.13i 0.134511 + 0.0770719i
\(583\) −4577.53 −0.325183
\(584\) −12959.8 −0.918285
\(585\) 11780.7 6905.12i 0.832600 0.488020i
\(586\) 4951.74i 0.349069i
\(587\) −13650.3 −0.959811 −0.479905 0.877320i \(-0.659329\pi\)
−0.479905 + 0.877320i \(0.659329\pi\)
\(588\) 0 0
\(589\) −3590.27 −0.251162
\(590\) 1017.77i 0.0710188i
\(591\) −1224.69 + 2137.40i −0.0852402 + 0.148766i
\(592\) 10977.0 0.762084
\(593\) −24799.6 −1.71736 −0.858682 0.512508i \(-0.828716\pi\)
−0.858682 + 0.512508i \(0.828716\pi\)
\(594\) −34.9237 3545.11i −0.00241235 0.244878i
\(595\) 0 0
\(596\) 10503.7i 0.721892i
\(597\) −2725.70 + 4757.06i −0.186860 + 0.326120i
\(598\) 9641.37i 0.659306i
\(599\) 7543.35i 0.514545i −0.966339 0.257273i \(-0.917176\pi\)
0.966339 0.257273i \(-0.0828239\pi\)
\(600\) −821.884 + 1434.40i −0.0559221 + 0.0975987i
\(601\) 17481.2i 1.18648i −0.805027 0.593239i \(-0.797849\pi\)
0.805027 0.593239i \(-0.202151\pi\)
\(602\) 0 0
\(603\) −1211.94 2067.66i −0.0818475 0.139638i
\(604\) 2832.78 0.190835
\(605\) −7692.97 −0.516965
\(606\) −155.321 + 271.075i −0.0104117 + 0.0181711i
\(607\) 25695.5i 1.71820i 0.511806 + 0.859101i \(0.328977\pi\)
−0.511806 + 0.859101i \(0.671023\pi\)
\(608\) −15849.6 −1.05722
\(609\) 0 0
\(610\) −4428.09 −0.293915
\(611\) 746.752i 0.0494441i
\(612\) 11842.8 + 20204.8i 0.782219 + 1.33452i
\(613\) −7168.60 −0.472328 −0.236164 0.971713i \(-0.575890\pi\)
−0.236164 + 0.971713i \(0.575890\pi\)
\(614\) −4767.75 −0.313372
\(615\) 7688.24 + 4405.21i 0.504097 + 0.288838i
\(616\) 0 0
\(617\) 10280.7i 0.670805i 0.942075 + 0.335402i \(0.108872\pi\)
−0.942075 + 0.335402i \(0.891128\pi\)
\(618\) 3504.57 + 2008.05i 0.228114 + 0.130705i
\(619\) 4548.35i 0.295337i −0.989037 0.147668i \(-0.952823\pi\)
0.989037 0.147668i \(-0.0471769\pi\)
\(620\) 2650.83i 0.171710i
\(621\) 26053.9 256.663i 1.68359 0.0165854i
\(622\) 5511.56i 0.355295i
\(623\) 0 0
\(624\) 4948.40 8636.25i 0.317459 0.554049i
\(625\) −12669.3 −0.810837
\(626\) 6384.11 0.407605
\(627\) −10368.1 5940.71i −0.660385 0.378388i
\(628\) 15068.6i 0.957488i
\(629\) 35626.9 2.25840
\(630\) 0 0
\(631\) 18015.7 1.13660 0.568298 0.822823i \(-0.307602\pi\)
0.568298 + 0.822823i \(0.307602\pi\)
\(632\) 4013.00i 0.252577i
\(633\) 6164.93 + 3532.38i 0.387099 + 0.221800i
\(634\) −4553.28 −0.285227
\(635\) −10279.2 −0.642387
\(636\) −3389.39 + 5915.37i −0.211318 + 0.368805i
\(637\) 0 0
\(638\) 1028.17i 0.0638019i
\(639\) 24803.0 14538.0i 1.53551 0.900023i
\(640\) 15032.8i 0.928473i
\(641\) 1117.06i 0.0688321i 0.999408 + 0.0344161i \(0.0109571\pi\)
−0.999408 + 0.0344161i \(0.989043\pi\)
\(642\) 4084.27 + 2340.20i 0.251080 + 0.143864i
\(643\) 11689.0i 0.716907i 0.933548 + 0.358453i \(0.116696\pi\)
−0.933548 + 0.358453i \(0.883304\pi\)
\(644\) 0 0
\(645\) −18987.9 10879.7i −1.15914 0.664165i
\(646\) −12621.6 −0.768713
\(647\) 10088.7 0.613025 0.306513 0.951867i \(-0.400838\pi\)
0.306513 + 0.951867i \(0.400838\pi\)
\(648\) −9950.81 5572.14i −0.603248 0.337800i
\(649\) 2279.58i 0.137875i
\(650\) 1055.78 0.0637091
\(651\) 0 0
\(652\) −10988.9 −0.660060
\(653\) 20037.7i 1.20082i −0.799693 0.600409i \(-0.795005\pi\)
0.799693 0.600409i \(-0.204995\pi\)
\(654\) −1782.50 + 3110.92i −0.106577 + 0.186004i
\(655\) 7290.66 0.434915
\(656\) 6458.80 0.384411
\(657\) −19296.4 + 11310.4i −1.14585 + 0.671628i
\(658\) 0 0
\(659\) 11752.2i 0.694691i −0.937737 0.347345i \(-0.887083\pi\)
0.937737 0.347345i \(-0.112917\pi\)
\(660\) 4386.25 7655.16i 0.258689 0.451480i
\(661\) 22013.0i 1.29532i 0.761930 + 0.647659i \(0.224252\pi\)
−0.761930 + 0.647659i \(0.775748\pi\)
\(662\) 6584.64i 0.386585i
\(663\) 16060.4 28029.6i 0.940778 1.64190i
\(664\) 1522.10i 0.0889590i
\(665\) 0 0
\(666\) −6929.76 + 4061.81i −0.403188 + 0.236324i
\(667\) −7556.27 −0.438651
\(668\) −8947.75 −0.518262
\(669\) −3009.63 + 5252.60i −0.173930 + 0.303553i
\(670\) 953.662i 0.0549898i
\(671\) −9917.89 −0.570605
\(672\) 0 0
\(673\) 24243.2 1.38857 0.694283 0.719702i \(-0.255721\pi\)
0.694283 + 0.719702i \(0.255721\pi\)
\(674\) 5587.20i 0.319304i
\(675\) 28.1058 + 2853.03i 0.00160266 + 0.162686i
\(676\) −1702.60 −0.0968706
\(677\) 29061.2 1.64979 0.824897 0.565283i \(-0.191233\pi\)
0.824897 + 0.565283i \(0.191233\pi\)
\(678\) 4186.91 + 2399.02i 0.237164 + 0.135890i
\(679\) 0 0
\(680\) 20128.0i 1.13511i
\(681\) −6799.73 3896.11i −0.382623 0.219235i
\(682\) 949.335i 0.0533019i
\(683\) 12078.4i 0.676673i 0.941025 + 0.338337i \(0.109864\pi\)
−0.941025 + 0.338337i \(0.890136\pi\)
\(684\) −15353.9 + 8999.55i −0.858293 + 0.503080i
\(685\) 13910.2i 0.775886i
\(686\) 0 0
\(687\) 6920.49 12078.1i 0.384328 0.670752i
\(688\) −15951.5 −0.883931
\(689\) 9404.07 0.519980
\(690\) −8995.62 5154.31i −0.496315 0.284379i
\(691\) 5338.80i 0.293918i 0.989143 + 0.146959i \(0.0469486\pi\)
−0.989143 + 0.146959i \(0.953051\pi\)
\(692\) 22274.4 1.22362
\(693\) 0 0
\(694\) 5057.18 0.276611
\(695\) 2181.82i 0.119081i
\(696\) 2869.78 + 1644.33i 0.156291 + 0.0895518i
\(697\) 20962.6 1.13919
\(698\) 5462.57 0.296220
\(699\) 4267.16 7447.30i 0.230899 0.402980i
\(700\) 0 0
\(701\) 11322.3i 0.610038i −0.952346 0.305019i \(-0.901337\pi\)
0.952346 0.305019i \(-0.0986628\pi\)
\(702\) 71.7472 + 7283.08i 0.00385744 + 0.391570i
\(703\) 27073.4i 1.45248i
\(704\) 3268.35i 0.174972i
\(705\) 696.737 + 399.217i 0.0372208 + 0.0213268i
\(706\) 669.719i 0.0357014i
\(707\) 0 0
\(708\) 2945.81 + 1687.89i 0.156371 + 0.0895974i
\(709\) −16036.7 −0.849466 −0.424733 0.905319i \(-0.639632\pi\)
−0.424733 + 0.905319i \(0.639632\pi\)
\(710\) −11439.8 −0.604687
\(711\) 3502.27 + 5975.14i 0.184733 + 0.315169i
\(712\) 14065.0i 0.740318i
\(713\) −6976.90 −0.366461
\(714\) 0 0
\(715\) −12169.9 −0.636544
\(716\) 24287.8i 1.26770i
\(717\) −5026.68 + 8772.87i −0.261820 + 0.456944i
\(718\) 5795.13 0.301215
\(719\) 20243.8 1.05002 0.525011 0.851096i \(-0.324061\pi\)
0.525011 + 0.851096i \(0.324061\pi\)
\(720\) −5412.38 9233.94i −0.280149 0.477956i
\(721\) 0 0
\(722\) 2388.32i 0.123108i
\(723\) −1242.17 + 2167.91i −0.0638960 + 0.111515i
\(724\) 21677.9i 1.11278i
\(725\) 827.448i 0.0423871i
\(726\) 2039.96 3560.27i 0.104284 0.182003i
\(727\) 23697.2i 1.20892i −0.796637 0.604458i \(-0.793390\pi\)
0.796637 0.604458i \(-0.206610\pi\)
\(728\) 0 0
\(729\) −19679.2 + 387.766i −0.999806 + 0.0197005i
\(730\) 8900.00 0.451238
\(731\) −51771.8 −2.61949
\(732\) −7343.62 + 12816.5i −0.370803 + 0.647148i
\(733\) 7895.50i 0.397854i 0.980014 + 0.198927i \(0.0637457\pi\)
−0.980014 + 0.198927i \(0.936254\pi\)
\(734\) −2724.24 −0.136994
\(735\) 0 0
\(736\) −30800.3 −1.54254
\(737\) 2135.98i 0.106757i
\(738\) −4077.42 + 2389.94i −0.203376 + 0.119207i
\(739\) −23190.3 −1.15436 −0.577178 0.816619i \(-0.695846\pi\)
−0.577178 + 0.816619i \(0.695846\pi\)
\(740\) −19989.4 −0.993005
\(741\) 21300.2 + 12204.6i 1.05598 + 0.605056i
\(742\) 0 0
\(743\) 24811.0i 1.22507i 0.790443 + 0.612536i \(0.209850\pi\)
−0.790443 + 0.612536i \(0.790150\pi\)
\(744\) 2649.74 + 1518.25i 0.130570 + 0.0748142i
\(745\) 15580.0i 0.766184i
\(746\) 5433.32i 0.266659i
\(747\) 1328.38 + 2266.32i 0.0650641 + 0.111004i
\(748\) 20872.4i 1.02028i
\(749\) 0 0
\(750\) 4033.65 7039.76i 0.196384 0.342741i
\(751\) −26673.5 −1.29605 −0.648023 0.761621i \(-0.724404\pi\)
−0.648023 + 0.761621i \(0.724404\pi\)
\(752\) 585.321 0.0283836
\(753\) 23033.2 + 13197.6i 1.11471 + 0.638707i
\(754\) 2112.27i 0.102022i
\(755\) −4201.83 −0.202543
\(756\) 0 0
\(757\) −1543.03 −0.0740853 −0.0370426 0.999314i \(-0.511794\pi\)
−0.0370426 + 0.999314i \(0.511794\pi\)
\(758\) 14794.8i 0.708932i
\(759\) −20148.1 11544.5i −0.963543 0.552091i
\(760\) 15295.6 0.730039
\(761\) 15291.5 0.728405 0.364202 0.931320i \(-0.381342\pi\)
0.364202 + 0.931320i \(0.381342\pi\)
\(762\) 2725.75 4757.14i 0.129584 0.226159i
\(763\) 0 0
\(764\) 30901.0i 1.46330i
\(765\) −17566.3 29969.5i −0.830212 1.41640i
\(766\) 8120.13i 0.383018i
\(767\) 4683.16i 0.220468i
\(768\) 2058.19 + 1179.30i 0.0967039 + 0.0554095i
\(769\) 30749.1i 1.44193i 0.692973 + 0.720963i \(0.256300\pi\)
−0.692973 + 0.720963i \(0.743700\pi\)
\(770\) 0 0
\(771\) 7466.53 + 4278.17i 0.348768 + 0.199837i
\(772\) 35987.9 1.67776
\(773\) 16417.4 0.763899 0.381949 0.924183i \(-0.375253\pi\)
0.381949 + 0.924183i \(0.375253\pi\)
\(774\) 10070.1 5902.49i 0.467652 0.274109i
\(775\) 764.003i 0.0354114i
\(776\) −6240.40 −0.288682
\(777\) 0 0
\(778\) 768.665 0.0354216
\(779\) 15929.8i 0.732662i
\(780\) −9011.12 + 15726.7i −0.413654 + 0.721933i
\(781\) −25622.5 −1.17394
\(782\) −24527.2 −1.12160
\(783\) 5708.00 56.2308i 0.260520 0.00256644i
\(784\) 0 0
\(785\) 22351.1i 1.01623i
\(786\) −1933.28 + 3374.08i