Properties

Label 441.4.p.c.215.2
Level $441$
Weight $4$
Character 441.215
Analytic conductor $26.020$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 441.p (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(26.0198423125\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 48 x^{14} + 1647 x^{12} - 27620 x^{10} + 336765 x^{8} - 1200006 x^{6} + 3242464 x^{4} - 1762200 x^{2} + 810000\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{4}\cdot 3^{8} \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 215.2
Root \(-3.91663 - 2.26127i\) of defining polynomial
Character \(\chi\) \(=\) 441.215
Dual form 441.4.p.c.80.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.91663 - 2.26127i) q^{2} +(6.22668 + 10.7849i) q^{4} +(0.632851 - 1.09613i) q^{5} -20.1405i q^{8} +O(q^{10})\) \(q+(-3.91663 - 2.26127i) q^{2} +(6.22668 + 10.7849i) q^{4} +(0.632851 - 1.09613i) q^{5} -20.1405i q^{8} +(-4.95730 + 2.86210i) q^{10} +(36.0248 - 20.7989i) q^{11} +85.7355i q^{13} +(4.27028 - 7.39634i) q^{16} +(-38.8929 - 67.3645i) q^{17} +(-42.1638 - 24.3433i) q^{19} +15.7623 q^{20} -188.128 q^{22} +(78.7639 + 45.4743i) q^{23} +(61.6990 + 106.866i) q^{25} +(193.871 - 335.795i) q^{26} -151.196i q^{29} +(-76.3661 + 44.0900i) q^{31} +(-172.988 + 99.8747i) q^{32} +351.790i q^{34} +(-45.2914 + 78.4470i) q^{37} +(110.093 + 190.687i) q^{38} +(-22.0767 - 12.7460i) q^{40} -383.530 q^{41} -227.894 q^{43} +(448.630 + 259.017i) q^{44} +(-205.660 - 356.213i) q^{46} +(-69.5529 + 120.469i) q^{47} -558.072i q^{50} +(-924.652 + 533.848i) q^{52} +(-289.749 + 167.287i) q^{53} -52.6505i q^{55} +(-341.895 + 592.179i) q^{58} +(440.050 + 762.189i) q^{59} +(-11.3944 - 6.57854i) q^{61} +398.797 q^{62} +835.050 q^{64} +(93.9774 + 54.2579i) q^{65} +(221.212 + 383.151i) q^{67} +(484.348 - 838.915i) q^{68} +341.552i q^{71} +(798.218 - 460.851i) q^{73} +(354.780 - 204.832i) q^{74} -606.311i q^{76} +(206.564 - 357.780i) q^{79} +(-5.40490 - 9.36157i) q^{80} +(1502.15 + 867.265i) q^{82} +954.307 q^{83} -98.4538 q^{85} +(892.579 + 515.331i) q^{86} +(-418.901 - 725.558i) q^{88} +(14.8490 - 25.7193i) q^{89} +1132.62i q^{92} +(544.826 - 314.556i) q^{94} +(-53.3668 + 30.8113i) q^{95} +1199.63i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 32q^{4} + O(q^{10}) \) \( 16q + 32q^{4} + 72q^{10} - 188q^{16} + 612q^{19} + 528q^{22} - 20q^{25} - 1128q^{31} - 1196q^{37} + 3204q^{40} + 328q^{43} - 1392q^{46} - 4452q^{52} - 3372q^{58} + 1632q^{61} + 5432q^{64} + 308q^{67} - 4068q^{73} - 2176q^{79} + 10188q^{82} - 4608q^{85} + 708q^{88} + 2916q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.91663 2.26127i −1.38474 0.799480i −0.392023 0.919955i \(-0.628225\pi\)
−0.992716 + 0.120476i \(0.961558\pi\)
\(3\) 0 0
\(4\) 6.22668 + 10.7849i 0.778336 + 1.34812i
\(5\) 0.632851 1.09613i 0.0566040 0.0980409i −0.836335 0.548219i \(-0.815306\pi\)
0.892939 + 0.450178i \(0.148639\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 20.1405i 0.890094i
\(9\) 0 0
\(10\) −4.95730 + 2.86210i −0.156763 + 0.0905074i
\(11\) 36.0248 20.7989i 0.987443 0.570101i 0.0829344 0.996555i \(-0.473571\pi\)
0.904509 + 0.426454i \(0.140237\pi\)
\(12\) 0 0
\(13\) 85.7355i 1.82914i 0.404433 + 0.914568i \(0.367469\pi\)
−0.404433 + 0.914568i \(0.632531\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 4.27028 7.39634i 0.0667231 0.115568i
\(17\) −38.8929 67.3645i −0.554878 0.961076i −0.997913 0.0645722i \(-0.979432\pi\)
0.443035 0.896504i \(-0.353902\pi\)
\(18\) 0 0
\(19\) −42.1638 24.3433i −0.509107 0.293933i 0.223360 0.974736i \(-0.428298\pi\)
−0.732466 + 0.680803i \(0.761631\pi\)
\(20\) 15.7623 0.176227
\(21\) 0 0
\(22\) −188.128 −1.82314
\(23\) 78.7639 + 45.4743i 0.714061 + 0.412263i 0.812563 0.582874i \(-0.198072\pi\)
−0.0985019 + 0.995137i \(0.531405\pi\)
\(24\) 0 0
\(25\) 61.6990 + 106.866i 0.493592 + 0.854926i
\(26\) 193.871 335.795i 1.46236 2.53288i
\(27\) 0 0
\(28\) 0 0
\(29\) 151.196i 0.968151i −0.875026 0.484075i \(-0.839156\pi\)
0.875026 0.484075i \(-0.160844\pi\)
\(30\) 0 0
\(31\) −76.3661 + 44.0900i −0.442444 + 0.255445i −0.704634 0.709571i \(-0.748889\pi\)
0.262190 + 0.965016i \(0.415555\pi\)
\(32\) −172.988 + 99.8747i −0.955633 + 0.551735i
\(33\) 0 0
\(34\) 351.790i 1.77445i
\(35\) 0 0
\(36\) 0 0
\(37\) −45.2914 + 78.4470i −0.201239 + 0.348557i −0.948928 0.315493i \(-0.897830\pi\)
0.747689 + 0.664050i \(0.231164\pi\)
\(38\) 110.093 + 190.687i 0.469987 + 0.814041i
\(39\) 0 0
\(40\) −22.0767 12.7460i −0.0872657 0.0503829i
\(41\) −383.530 −1.46091 −0.730455 0.682961i \(-0.760692\pi\)
−0.730455 + 0.682961i \(0.760692\pi\)
\(42\) 0 0
\(43\) −227.894 −0.808222 −0.404111 0.914710i \(-0.632419\pi\)
−0.404111 + 0.914710i \(0.632419\pi\)
\(44\) 448.630 + 259.017i 1.53712 + 0.887459i
\(45\) 0 0
\(46\) −205.660 356.213i −0.659192 1.14175i
\(47\) −69.5529 + 120.469i −0.215858 + 0.373877i −0.953538 0.301274i \(-0.902588\pi\)
0.737680 + 0.675151i \(0.235922\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 558.072i 1.57847i
\(51\) 0 0
\(52\) −924.652 + 533.848i −2.46589 + 1.42368i
\(53\) −289.749 + 167.287i −0.750945 + 0.433558i −0.826035 0.563619i \(-0.809409\pi\)
0.0750904 + 0.997177i \(0.476075\pi\)
\(54\) 0 0
\(55\) 52.6505i 0.129080i
\(56\) 0 0
\(57\) 0 0
\(58\) −341.895 + 592.179i −0.774017 + 1.34064i
\(59\) 440.050 + 762.189i 0.971010 + 1.68184i 0.692518 + 0.721401i \(0.256501\pi\)
0.278493 + 0.960438i \(0.410165\pi\)
\(60\) 0 0
\(61\) −11.3944 6.57854i −0.0239164 0.0138081i 0.487994 0.872847i \(-0.337729\pi\)
−0.511911 + 0.859039i \(0.671062\pi\)
\(62\) 398.797 0.816892
\(63\) 0 0
\(64\) 835.050 1.63096
\(65\) 93.9774 + 54.2579i 0.179330 + 0.103536i
\(66\) 0 0
\(67\) 221.212 + 383.151i 0.403364 + 0.698647i 0.994130 0.108197i \(-0.0345076\pi\)
−0.590766 + 0.806843i \(0.701174\pi\)
\(68\) 484.348 838.915i 0.863762 1.49608i
\(69\) 0 0
\(70\) 0 0
\(71\) 341.552i 0.570912i 0.958392 + 0.285456i \(0.0921450\pi\)
−0.958392 + 0.285456i \(0.907855\pi\)
\(72\) 0 0
\(73\) 798.218 460.851i 1.27979 0.738885i 0.302977 0.952998i \(-0.402019\pi\)
0.976809 + 0.214113i \(0.0686862\pi\)
\(74\) 354.780 204.832i 0.557328 0.321774i
\(75\) 0 0
\(76\) 606.311i 0.915114i
\(77\) 0 0
\(78\) 0 0
\(79\) 206.564 357.780i 0.294181 0.509537i −0.680613 0.732643i \(-0.738286\pi\)
0.974794 + 0.223107i \(0.0716198\pi\)
\(80\) −5.40490 9.36157i −0.00755358 0.0130832i
\(81\) 0 0
\(82\) 1502.15 + 867.265i 2.02298 + 1.16797i
\(83\) 954.307 1.26203 0.631017 0.775769i \(-0.282638\pi\)
0.631017 + 0.775769i \(0.282638\pi\)
\(84\) 0 0
\(85\) −98.4538 −0.125633
\(86\) 892.579 + 515.331i 1.11918 + 0.646157i
\(87\) 0 0
\(88\) −418.901 725.558i −0.507444 0.878918i
\(89\) 14.8490 25.7193i 0.0176853 0.0306319i −0.857047 0.515238i \(-0.827704\pi\)
0.874733 + 0.484606i \(0.161037\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 1132.62i 1.28352i
\(93\) 0 0
\(94\) 544.826 314.556i 0.597814 0.345148i
\(95\) −53.3668 + 30.8113i −0.0576349 + 0.0332755i
\(96\) 0 0
\(97\) 1199.63i 1.25572i 0.778328 + 0.627858i \(0.216068\pi\)
−0.778328 + 0.627858i \(0.783932\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −768.360 + 1330.84i −0.768360 + 1.33084i
\(101\) −327.422 567.111i −0.322571 0.558710i 0.658447 0.752628i \(-0.271214\pi\)
−0.981018 + 0.193918i \(0.937881\pi\)
\(102\) 0 0
\(103\) 1186.01 + 684.744i 1.13457 + 0.655047i 0.945081 0.326836i \(-0.105982\pi\)
0.189493 + 0.981882i \(0.439316\pi\)
\(104\) 1726.76 1.62810
\(105\) 0 0
\(106\) 1513.12 1.38648
\(107\) −371.311 214.377i −0.335477 0.193688i 0.322793 0.946470i \(-0.395378\pi\)
−0.658270 + 0.752782i \(0.728711\pi\)
\(108\) 0 0
\(109\) 334.261 + 578.957i 0.293728 + 0.508752i 0.974688 0.223568i \(-0.0717706\pi\)
−0.680960 + 0.732321i \(0.738437\pi\)
\(110\) −119.057 + 206.213i −0.103197 + 0.178742i
\(111\) 0 0
\(112\) 0 0
\(113\) 914.837i 0.761598i 0.924658 + 0.380799i \(0.124351\pi\)
−0.924658 + 0.380799i \(0.875649\pi\)
\(114\) 0 0
\(115\) 99.6917 57.5570i 0.0808374 0.0466715i
\(116\) 1630.64 941.449i 1.30518 0.753546i
\(117\) 0 0
\(118\) 3980.29i 3.10521i
\(119\) 0 0
\(120\) 0 0
\(121\) 199.690 345.873i 0.150030 0.259859i
\(122\) 29.7517 + 51.5314i 0.0220786 + 0.0382413i
\(123\) 0 0
\(124\) −951.015 549.069i −0.688739 0.397644i
\(125\) 314.398 0.224965
\(126\) 0 0
\(127\) 1260.95 0.881034 0.440517 0.897744i \(-0.354795\pi\)
0.440517 + 0.897744i \(0.354795\pi\)
\(128\) −1886.68 1089.28i −1.30282 0.752182i
\(129\) 0 0
\(130\) −245.383 425.016i −0.165550 0.286742i
\(131\) −683.600 + 1184.03i −0.455926 + 0.789688i −0.998741 0.0501648i \(-0.984025\pi\)
0.542814 + 0.839853i \(0.317359\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 2000.88i 1.28992i
\(135\) 0 0
\(136\) −1356.76 + 783.325i −0.855449 + 0.493894i
\(137\) −953.631 + 550.579i −0.594702 + 0.343351i −0.766955 0.641701i \(-0.778229\pi\)
0.172252 + 0.985053i \(0.444896\pi\)
\(138\) 0 0
\(139\) 2306.56i 1.40748i 0.710458 + 0.703739i \(0.248488\pi\)
−0.710458 + 0.703739i \(0.751512\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 772.341 1337.73i 0.456432 0.790564i
\(143\) 1783.21 + 3088.60i 1.04279 + 1.80617i
\(144\) 0 0
\(145\) −165.730 95.6845i −0.0949184 0.0548012i
\(146\) −4168.44 −2.36289
\(147\) 0 0
\(148\) −1128.06 −0.626527
\(149\) 1520.57 + 877.901i 0.836040 + 0.482688i 0.855916 0.517115i \(-0.172994\pi\)
−0.0198764 + 0.999802i \(0.506327\pi\)
\(150\) 0 0
\(151\) 262.491 + 454.647i 0.141465 + 0.245024i 0.928048 0.372460i \(-0.121485\pi\)
−0.786584 + 0.617484i \(0.788152\pi\)
\(152\) −490.286 + 849.201i −0.261628 + 0.453153i
\(153\) 0 0
\(154\) 0 0
\(155\) 111.610i 0.0578368i
\(156\) 0 0
\(157\) 1141.44 659.009i 0.580233 0.334998i −0.180993 0.983484i \(-0.557931\pi\)
0.761226 + 0.648487i \(0.224598\pi\)
\(158\) −1618.07 + 934.195i −0.814728 + 0.470384i
\(159\) 0 0
\(160\) 252.823i 0.124921i
\(161\) 0 0
\(162\) 0 0
\(163\) 223.916 387.834i 0.107598 0.186365i −0.807199 0.590280i \(-0.799017\pi\)
0.914797 + 0.403915i \(0.132351\pi\)
\(164\) −2388.12 4136.35i −1.13708 1.96948i
\(165\) 0 0
\(166\) −3737.67 2157.95i −1.74759 1.00897i
\(167\) −811.124 −0.375848 −0.187924 0.982184i \(-0.560176\pi\)
−0.187924 + 0.982184i \(0.560176\pi\)
\(168\) 0 0
\(169\) −5153.58 −2.34574
\(170\) 385.608 + 222.631i 0.173969 + 0.100441i
\(171\) 0 0
\(172\) −1419.03 2457.82i −0.629068 1.08958i
\(173\) −1121.24 + 1942.04i −0.492751 + 0.853470i −0.999965 0.00834994i \(-0.997342\pi\)
0.507214 + 0.861820i \(0.330675\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 355.269i 0.152156i
\(177\) 0 0
\(178\) −116.317 + 67.1554i −0.0489792 + 0.0282781i
\(179\) −2531.77 + 1461.72i −1.05717 + 0.610357i −0.924648 0.380824i \(-0.875641\pi\)
−0.132521 + 0.991180i \(0.542307\pi\)
\(180\) 0 0
\(181\) 282.859i 0.116159i −0.998312 0.0580794i \(-0.981502\pi\)
0.998312 0.0580794i \(-0.0184977\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 915.878 1586.35i 0.366953 0.635582i
\(185\) 57.3255 + 99.2906i 0.0227819 + 0.0394594i
\(186\) 0 0
\(187\) −2802.22 1617.86i −1.09582 0.632672i
\(188\) −1732.34 −0.672040
\(189\) 0 0
\(190\) 278.691 0.106412
\(191\) −3998.63 2308.61i −1.51482 0.874582i −0.999849 0.0173741i \(-0.994469\pi\)
−0.514971 0.857208i \(-0.672197\pi\)
\(192\) 0 0
\(193\) 2077.73 + 3598.73i 0.774912 + 1.34219i 0.934844 + 0.355058i \(0.115539\pi\)
−0.159933 + 0.987128i \(0.551128\pi\)
\(194\) 2712.70 4698.53i 1.00392 1.73884i
\(195\) 0 0
\(196\) 0 0
\(197\) 1626.36i 0.588190i 0.955776 + 0.294095i \(0.0950183\pi\)
−0.955776 + 0.294095i \(0.904982\pi\)
\(198\) 0 0
\(199\) −150.861 + 87.0995i −0.0537399 + 0.0310267i −0.526629 0.850095i \(-0.676544\pi\)
0.472889 + 0.881122i \(0.343211\pi\)
\(200\) 2152.33 1242.65i 0.760965 0.439344i
\(201\) 0 0
\(202\) 2961.56i 1.03156i
\(203\) 0 0
\(204\) 0 0
\(205\) −242.718 + 420.399i −0.0826933 + 0.143229i
\(206\) −3096.78 5363.78i −1.04739 1.81414i
\(207\) 0 0
\(208\) 634.129 + 366.115i 0.211389 + 0.122046i
\(209\) −2025.25 −0.670286
\(210\) 0 0
\(211\) −2942.35 −0.959999 −0.479999 0.877269i \(-0.659363\pi\)
−0.479999 + 0.877269i \(0.659363\pi\)
\(212\) −3608.35 2083.28i −1.16897 0.674907i
\(213\) 0 0
\(214\) 969.527 + 1679.27i 0.309699 + 0.536414i
\(215\) −144.223 + 249.802i −0.0457486 + 0.0792389i
\(216\) 0 0
\(217\) 0 0
\(218\) 3023.42i 0.939319i
\(219\) 0 0
\(220\) 567.832 327.838i 0.174015 0.100467i
\(221\) 5775.53 3334.51i 1.75794 1.01495i
\(222\) 0 0
\(223\) 3374.75i 1.01341i 0.862120 + 0.506704i \(0.169136\pi\)
−0.862120 + 0.506704i \(0.830864\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 2068.69 3583.08i 0.608882 1.05461i
\(227\) −1515.43 2624.79i −0.443094 0.767461i 0.554823 0.831968i \(-0.312786\pi\)
−0.997917 + 0.0645069i \(0.979453\pi\)
\(228\) 0 0
\(229\) −960.030 554.274i −0.277033 0.159945i 0.355046 0.934849i \(-0.384465\pi\)
−0.632080 + 0.774904i \(0.717798\pi\)
\(230\) −520.608 −0.149252
\(231\) 0 0
\(232\) −3045.17 −0.861746
\(233\) 2684.57 + 1549.94i 0.754815 + 0.435793i 0.827431 0.561567i \(-0.189801\pi\)
−0.0726160 + 0.997360i \(0.523135\pi\)
\(234\) 0 0
\(235\) 88.0333 + 152.478i 0.0244368 + 0.0423259i
\(236\) −5480.10 + 9491.82i −1.51154 + 2.61807i
\(237\) 0 0
\(238\) 0 0
\(239\) 1735.25i 0.469640i −0.972039 0.234820i \(-0.924550\pi\)
0.972039 0.234820i \(-0.0754501\pi\)
\(240\) 0 0
\(241\) 1039.26 600.019i 0.277779 0.160376i −0.354638 0.935004i \(-0.615396\pi\)
0.632418 + 0.774628i \(0.282063\pi\)
\(242\) −1564.22 + 903.104i −0.415504 + 0.239892i
\(243\) 0 0
\(244\) 163.850i 0.0429894i
\(245\) 0 0
\(246\) 0 0
\(247\) 2087.08 3614.93i 0.537643 0.931225i
\(248\) 887.996 + 1538.05i 0.227370 + 0.393817i
\(249\) 0 0
\(250\) −1231.38 710.939i −0.311518 0.179855i
\(251\) 3712.56 0.933603 0.466802 0.884362i \(-0.345406\pi\)
0.466802 + 0.884362i \(0.345406\pi\)
\(252\) 0 0
\(253\) 3783.27 0.940126
\(254\) −4938.69 2851.35i −1.22000 0.704369i
\(255\) 0 0
\(256\) 1586.09 + 2747.20i 0.387230 + 0.670702i
\(257\) 389.574 674.762i 0.0945563 0.163776i −0.814867 0.579648i \(-0.803190\pi\)
0.909423 + 0.415872i \(0.136523\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 1351.39i 0.322344i
\(261\) 0 0
\(262\) 5354.82 3091.61i 1.26268 0.729008i
\(263\) 1702.07 982.690i 0.399065 0.230400i −0.287015 0.957926i \(-0.592663\pi\)
0.686080 + 0.727526i \(0.259330\pi\)
\(264\) 0 0
\(265\) 423.470i 0.0981644i
\(266\) 0 0
\(267\) 0 0
\(268\) −2754.84 + 4771.52i −0.627905 + 1.08756i
\(269\) 1236.41 + 2141.53i 0.280243 + 0.485395i 0.971444 0.237267i \(-0.0762516\pi\)
−0.691201 + 0.722662i \(0.742918\pi\)
\(270\) 0 0
\(271\) −4095.79 2364.71i −0.918088 0.530058i −0.0350633 0.999385i \(-0.511163\pi\)
−0.883025 + 0.469327i \(0.844497\pi\)
\(272\) −664.334 −0.148093
\(273\) 0 0
\(274\) 4980.03 1.09801
\(275\) 4445.39 + 2566.54i 0.974788 + 0.562794i
\(276\) 0 0
\(277\) −586.579 1015.98i −0.127235 0.220378i 0.795369 0.606125i \(-0.207277\pi\)
−0.922604 + 0.385747i \(0.873944\pi\)
\(278\) 5215.74 9033.93i 1.12525 1.94899i
\(279\) 0 0
\(280\) 0 0
\(281\) 8195.18i 1.73980i 0.493229 + 0.869899i \(0.335816\pi\)
−0.493229 + 0.869899i \(0.664184\pi\)
\(282\) 0 0
\(283\) −2242.44 + 1294.67i −0.471021 + 0.271944i −0.716667 0.697415i \(-0.754333\pi\)
0.245646 + 0.969360i \(0.421000\pi\)
\(284\) −3683.61 + 2126.74i −0.769656 + 0.444361i
\(285\) 0 0
\(286\) 16129.2i 3.33476i
\(287\) 0 0
\(288\) 0 0
\(289\) −568.820 + 985.225i −0.115779 + 0.200534i
\(290\) 432.737 + 749.523i 0.0876248 + 0.151771i
\(291\) 0 0
\(292\) 9940.50 + 5739.15i 1.99221 + 1.15020i
\(293\) 8871.16 1.76880 0.884400 0.466729i \(-0.154568\pi\)
0.884400 + 0.466729i \(0.154568\pi\)
\(294\) 0 0
\(295\) 1113.94 0.219852
\(296\) 1579.96 + 912.193i 0.310249 + 0.179122i
\(297\) 0 0
\(298\) −3970.34 6876.84i −0.771798 1.33679i
\(299\) −3898.77 + 6752.86i −0.754085 + 1.30611i
\(300\) 0 0
\(301\) 0 0
\(302\) 2374.25i 0.452393i
\(303\) 0 0
\(304\) −360.102 + 207.905i −0.0679383 + 0.0392242i
\(305\) −14.4219 + 8.32647i −0.00270752 + 0.00156319i
\(306\) 0 0
\(307\) 2707.52i 0.503344i −0.967813 0.251672i \(-0.919020\pi\)
0.967813 0.251672i \(-0.0809804\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 252.379 437.134i 0.0462393 0.0800889i
\(311\) 1080.55 + 1871.56i 0.197017 + 0.341243i 0.947560 0.319579i \(-0.103541\pi\)
−0.750543 + 0.660822i \(0.770208\pi\)
\(312\) 0 0
\(313\) 7300.25 + 4214.80i 1.31832 + 0.761133i 0.983459 0.181133i \(-0.0579766\pi\)
0.334863 + 0.942267i \(0.391310\pi\)
\(314\) −5960.79 −1.07130
\(315\) 0 0
\(316\) 5144.84 0.915886
\(317\) −8310.07 4797.82i −1.47237 0.850071i −0.472848 0.881144i \(-0.656774\pi\)
−0.999517 + 0.0310734i \(0.990107\pi\)
\(318\) 0 0
\(319\) −3144.71 5446.80i −0.551943 0.955994i
\(320\) 528.463 915.324i 0.0923186 0.159901i
\(321\) 0 0
\(322\) 0 0
\(323\) 3787.12i 0.652387i
\(324\) 0 0
\(325\) −9162.20 + 5289.80i −1.56378 + 0.902847i
\(326\) −1753.99 + 1012.67i −0.297990 + 0.172045i
\(327\) 0 0
\(328\) 7724.50i 1.30035i
\(329\) 0 0
\(330\) 0 0
\(331\) −4271.96 + 7399.25i −0.709390 + 1.22870i 0.255694 + 0.966758i \(0.417696\pi\)
−0.965084 + 0.261941i \(0.915637\pi\)
\(332\) 5942.17 + 10292.1i 0.982286 + 1.70137i
\(333\) 0 0
\(334\) 3176.88 + 1834.17i 0.520452 + 0.300483i
\(335\) 559.978 0.0913280
\(336\) 0 0
\(337\) 598.875 0.0968036 0.0484018 0.998828i \(-0.484587\pi\)
0.0484018 + 0.998828i \(0.484587\pi\)
\(338\) 20184.7 + 11653.6i 3.24823 + 1.87537i
\(339\) 0 0
\(340\) −613.041 1061.82i −0.0977847 0.169368i
\(341\) −1834.05 + 3176.66i −0.291259 + 0.504475i
\(342\) 0 0
\(343\) 0 0
\(344\) 4589.91i 0.719394i
\(345\) 0 0
\(346\) 8782.94 5070.83i 1.36466 0.787889i
\(347\) −6149.62 + 3550.49i −0.951381 + 0.549280i −0.893510 0.449044i \(-0.851765\pi\)
−0.0578712 + 0.998324i \(0.518431\pi\)
\(348\) 0 0
\(349\) 3620.71i 0.555336i −0.960677 0.277668i \(-0.910438\pi\)
0.960677 0.277668i \(-0.0895616\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −4154.57 + 7195.92i −0.629089 + 1.08961i
\(353\) −1164.89 2017.64i −0.175639 0.304216i 0.764743 0.644335i \(-0.222866\pi\)
−0.940382 + 0.340119i \(0.889533\pi\)
\(354\) 0 0
\(355\) 374.386 + 216.152i 0.0559727 + 0.0323159i
\(356\) 369.841 0.0550605
\(357\) 0 0
\(358\) 13221.3 1.95187
\(359\) −1522.43 878.975i −0.223818 0.129222i 0.383899 0.923375i \(-0.374581\pi\)
−0.607717 + 0.794154i \(0.707914\pi\)
\(360\) 0 0
\(361\) −2244.31 3887.26i −0.327207 0.566739i
\(362\) −639.621 + 1107.86i −0.0928667 + 0.160850i
\(363\) 0 0
\(364\) 0 0
\(365\) 1166.60i 0.167295i
\(366\) 0 0
\(367\) −1458.89 + 842.290i −0.207503 + 0.119802i −0.600150 0.799887i \(-0.704893\pi\)
0.392648 + 0.919689i \(0.371559\pi\)
\(368\) 672.687 388.376i 0.0952887 0.0550150i
\(369\) 0 0
\(370\) 518.513i 0.0728547i
\(371\) 0 0
\(372\) 0 0
\(373\) 148.646 257.462i 0.0206343 0.0357397i −0.855524 0.517763i \(-0.826765\pi\)
0.876158 + 0.482024i \(0.160098\pi\)
\(374\) 7316.84 + 12673.1i 1.01162 + 1.75217i
\(375\) 0 0
\(376\) 2426.31 + 1400.83i 0.332786 + 0.192134i
\(377\) 12962.9 1.77088
\(378\) 0 0
\(379\) −7402.78 −1.00331 −0.501656 0.865067i \(-0.667276\pi\)
−0.501656 + 0.865067i \(0.667276\pi\)
\(380\) −664.596 383.705i −0.0897186 0.0517991i
\(381\) 0 0
\(382\) 10440.8 + 18084.0i 1.39842 + 2.42214i
\(383\) 6263.77 10849.2i 0.835676 1.44743i −0.0578031 0.998328i \(-0.518410\pi\)
0.893479 0.449105i \(-0.148257\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 18793.2i 2.47810i
\(387\) 0 0
\(388\) −12938.0 + 7469.75i −1.69285 + 0.977368i
\(389\) 6904.14 3986.11i 0.899881 0.519547i 0.0227196 0.999742i \(-0.492767\pi\)
0.877162 + 0.480195i \(0.159434\pi\)
\(390\) 0 0
\(391\) 7074.52i 0.915023i
\(392\) 0 0
\(393\) 0 0
\(394\) 3677.64 6369.87i 0.470246 0.814491i
\(395\) −261.449 452.843i −0.0333036 0.0576836i
\(396\) 0 0
\(397\) −10832.5 6254.16i −1.36944 0.790648i −0.378586 0.925566i \(-0.623590\pi\)
−0.990857 + 0.134918i \(0.956923\pi\)
\(398\) 787.822 0.0992210
\(399\) 0 0
\(400\) 1053.89 0.131736
\(401\) −6943.55 4008.86i −0.864699 0.499234i 0.000883860 1.00000i \(-0.499719\pi\)
−0.865583 + 0.500765i \(0.833052\pi\)
\(402\) 0 0
\(403\) −3780.08 6547.29i −0.467243 0.809289i
\(404\) 4077.51 7062.45i 0.502137 0.869728i
\(405\) 0 0
\(406\) 0 0
\(407\) 3768.05i 0.458907i
\(408\) 0 0
\(409\) 7566.04 4368.26i 0.914711 0.528109i 0.0327670 0.999463i \(-0.489568\pi\)
0.881944 + 0.471354i \(0.156235\pi\)
\(410\) 1901.27 1097.70i 0.229017 0.132223i
\(411\) 0 0
\(412\) 17054.7i 2.03938i
\(413\) 0 0
\(414\) 0 0
\(415\) 603.935 1046.05i 0.0714361 0.123731i
\(416\) −8562.81 14831.2i −1.00920 1.74798i
\(417\) 0 0
\(418\) 7932.18 + 4579.64i 0.928171 + 0.535880i
\(419\) −3926.67 −0.457829 −0.228914 0.973447i \(-0.573518\pi\)
−0.228914 + 0.973447i \(0.573518\pi\)
\(420\) 0 0
\(421\) 1443.44 0.167100 0.0835499 0.996504i \(-0.473374\pi\)
0.0835499 + 0.996504i \(0.473374\pi\)
\(422\) 11524.1 + 6653.45i 1.32935 + 0.767500i
\(423\) 0 0
\(424\) 3369.24 + 5835.70i 0.385908 + 0.668412i
\(425\) 4799.31 8312.65i 0.547766 0.948759i
\(426\) 0 0
\(427\) 0 0
\(428\) 5339.42i 0.603016i
\(429\) 0 0
\(430\) 1129.74 652.255i 0.126700 0.0731501i
\(431\) 12820.5 7401.92i 1.43281 0.827234i 0.435477 0.900200i \(-0.356580\pi\)
0.997334 + 0.0729655i \(0.0232463\pi\)
\(432\) 0 0
\(433\) 15872.1i 1.76158i 0.473508 + 0.880790i \(0.342988\pi\)
−0.473508 + 0.880790i \(0.657012\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −4162.67 + 7209.96i −0.457238 + 0.791960i
\(437\) −2213.99 3834.74i −0.242356 0.419772i
\(438\) 0 0
\(439\) 2626.58 + 1516.45i 0.285557 + 0.164867i 0.635937 0.771741i \(-0.280614\pi\)
−0.350379 + 0.936608i \(0.613947\pi\)
\(440\) −1060.41 −0.114893
\(441\) 0 0
\(442\) −30160.9 −3.24572
\(443\) 11126.8 + 6424.08i 1.19334 + 0.688978i 0.959064 0.283191i \(-0.0913930\pi\)
0.234281 + 0.972169i \(0.424726\pi\)
\(444\) 0 0
\(445\) −18.7945 32.5530i −0.00200212 0.00346777i
\(446\) 7631.22 13217.7i 0.810199 1.40331i
\(447\) 0 0
\(448\) 0 0
\(449\) 107.668i 0.0113166i 0.999984 + 0.00565831i \(0.00180111\pi\)
−0.999984 + 0.00565831i \(0.998199\pi\)
\(450\) 0 0
\(451\) −13816.6 + 7977.01i −1.44257 + 0.832866i
\(452\) −9866.45 + 5696.40i −1.02672 + 0.592779i
\(453\) 0 0
\(454\) 13707.1i 1.41698i
\(455\) 0 0
\(456\) 0 0
\(457\) 4888.53 8467.18i 0.500385 0.866691i −0.499615 0.866247i \(-0.666525\pi\)
1.00000 0.000444115i \(-0.000141366\pi\)
\(458\) 2506.72 + 4341.77i 0.255746 + 0.442965i
\(459\) 0 0
\(460\) 1241.50 + 716.779i 0.125837 + 0.0726521i
\(461\) 638.874 0.0645452 0.0322726 0.999479i \(-0.489726\pi\)
0.0322726 + 0.999479i \(0.489726\pi\)
\(462\) 0 0
\(463\) −5602.26 −0.562331 −0.281165 0.959659i \(-0.590721\pi\)
−0.281165 + 0.959659i \(0.590721\pi\)
\(464\) −1118.30 645.648i −0.111887 0.0645980i
\(465\) 0 0
\(466\) −7009.65 12141.1i −0.696815 1.20692i
\(467\) −2759.44 + 4779.49i −0.273430 + 0.473594i −0.969738 0.244149i \(-0.921491\pi\)
0.696308 + 0.717743i \(0.254825\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 796.268i 0.0781470i
\(471\) 0 0
\(472\) 15350.9 8862.84i 1.49700 0.864291i
\(473\) −8209.84 + 4739.95i −0.798074 + 0.460768i
\(474\) 0 0
\(475\) 6007.82i 0.580332i
\(476\) 0 0
\(477\) 0 0
\(478\) −3923.87 + 6796.34i −0.375468 + 0.650329i
\(479\) −2734.40 4736.11i −0.260830 0.451771i 0.705632 0.708578i \(-0.250663\pi\)
−0.966463 + 0.256807i \(0.917330\pi\)
\(480\) 0 0
\(481\) −6725.70 3883.08i −0.637558 0.368094i
\(482\) −5427.22 −0.512869
\(483\) 0 0
\(484\) 4973.62 0.467094
\(485\) 1314.96 + 759.190i 0.123112 + 0.0710785i
\(486\) 0 0
\(487\) 5866.72 + 10161.5i 0.545886 + 0.945502i 0.998551 + 0.0538213i \(0.0171401\pi\)
−0.452665 + 0.891681i \(0.649527\pi\)
\(488\) −132.495 + 229.489i −0.0122905 + 0.0212878i
\(489\) 0 0
\(490\) 0 0
\(491\) 3514.92i 0.323068i 0.986867 + 0.161534i \(0.0516441\pi\)
−0.986867 + 0.161534i \(0.948356\pi\)
\(492\) 0 0
\(493\) −10185.2 + 5880.45i −0.930467 + 0.537205i
\(494\) −16348.7 + 9438.91i −1.48899 + 0.859670i
\(495\) 0 0
\(496\) 753.106i 0.0681763i
\(497\) 0 0
\(498\) 0 0
\(499\) −4944.49 + 8564.11i −0.443579 + 0.768301i −0.997952 0.0639672i \(-0.979625\pi\)
0.554373 + 0.832268i \(0.312958\pi\)
\(500\) 1957.66 + 3390.76i 0.175098 + 0.303279i
\(501\) 0 0
\(502\) −14540.7 8395.09i −1.29280 0.746397i
\(503\) −10172.2 −0.901698 −0.450849 0.892600i \(-0.648879\pi\)
−0.450849 + 0.892600i \(0.648879\pi\)
\(504\) 0 0
\(505\) −828.838 −0.0730353
\(506\) −14817.7 8554.99i −1.30183 0.751612i
\(507\) 0 0
\(508\) 7851.55 + 13599.3i 0.685740 + 1.18774i
\(509\) −2149.56 + 3723.15i −0.187186 + 0.324216i −0.944311 0.329054i \(-0.893270\pi\)
0.757125 + 0.653270i \(0.226603\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 3082.06i 0.266033i
\(513\) 0 0
\(514\) −3051.64 + 1761.86i −0.261872 + 0.151192i
\(515\) 1501.14 866.682i 0.128443 0.0741565i
\(516\) 0 0
\(517\) 5786.50i 0.492243i
\(518\) 0 0
\(519\) 0 0
\(520\) 1092.78 1892.76i 0.0921571 0.159621i
\(521\) −5496.48 9520.18i −0.462198 0.800550i 0.536872 0.843664i \(-0.319606\pi\)
−0.999070 + 0.0431133i \(0.986272\pi\)
\(522\) 0 0
\(523\) −7386.80 4264.77i −0.617595 0.356569i 0.158337 0.987385i \(-0.449387\pi\)
−0.775932 + 0.630817i \(0.782720\pi\)
\(524\) −17026.2 −1.41946
\(525\) 0 0
\(526\) −8888.51 −0.736801
\(527\) 5940.20 + 3429.58i 0.491004 + 0.283481i
\(528\) 0 0
\(529\) −1947.67 3373.46i −0.160078 0.277263i
\(530\) 957.581 1658.58i 0.0784805 0.135932i
\(531\) 0 0
\(532\) 0 0
\(533\) 32882.2i 2.67220i
\(534\) 0 0
\(535\) −469.970 + 271.337i −0.0379786 + 0.0219270i
\(536\) 7716.86 4455.33i 0.621862 0.359032i
\(537\) 0 0
\(538\) 11183.4i 0.896195i
\(539\) 0 0
\(540\) 0 0
\(541\) 4352.93 7539.49i 0.345928 0.599165i −0.639594 0.768713i \(-0.720897\pi\)
0.985522 + 0.169548i \(0.0542308\pi\)
\(542\) 10694.5 + 18523.4i 0.847542 + 1.46799i
\(543\) 0 0
\(544\) 13456.0 + 7768.84i 1.06052 + 0.612291i
\(545\) 846.150 0.0665047
\(546\) 0 0
\(547\) 17183.8 1.34319 0.671596 0.740917i \(-0.265609\pi\)
0.671596 + 0.740917i \(0.265609\pi\)
\(548\) −11875.9 6856.56i −0.925756 0.534485i
\(549\) 0 0
\(550\) −11607.3 20104.4i −0.899885 1.55865i
\(551\) −3680.60 + 6374.99i −0.284571 + 0.492892i
\(552\) 0 0
\(553\) 0 0
\(554\) 5305.66i 0.406888i
\(555\) 0 0
\(556\) −24876.0 + 14362.2i −1.89744 + 1.09549i
\(557\) 8989.79 5190.26i 0.683859 0.394826i −0.117448 0.993079i \(-0.537471\pi\)
0.801307 + 0.598253i \(0.204138\pi\)
\(558\) 0 0
\(559\) 19538.6i 1.47835i
\(560\) 0 0
\(561\) 0 0
\(562\) 18531.5 32097.5i 1.39093 2.40917i
\(563\) 9248.22 + 16018.4i 0.692302 + 1.19910i 0.971082 + 0.238747i \(0.0767366\pi\)
−0.278780 + 0.960355i \(0.589930\pi\)
\(564\) 0 0
\(565\) 1002.78 + 578.956i 0.0746678 + 0.0431095i
\(566\) 11710.4 0.869656
\(567\) 0 0
\(568\) 6879.04 0.508166
\(569\) 3493.45 + 2016.94i 0.257386 + 0.148602i 0.623142 0.782109i \(-0.285856\pi\)
−0.365755 + 0.930711i \(0.619189\pi\)
\(570\) 0 0
\(571\) −6430.01 11137.1i −0.471257 0.816241i 0.528203 0.849118i \(-0.322866\pi\)
−0.999459 + 0.0328777i \(0.989533\pi\)
\(572\) −22206.9 + 38463.5i −1.62328 + 2.81161i
\(573\) 0 0
\(574\) 0 0
\(575\) 11222.9i 0.813959i
\(576\) 0 0
\(577\) 17669.2 10201.3i 1.27483 0.736026i 0.298940 0.954272i \(-0.403367\pi\)
0.975894 + 0.218246i \(0.0700335\pi\)
\(578\) 4455.72 2572.51i 0.320646 0.185125i
\(579\) 0 0
\(580\) 2383.19i 0.170615i
\(581\) 0 0
\(582\) 0 0
\(583\) −6958.76 + 12052.9i −0.494344 + 0.856228i
\(584\) −9281.80 16076.5i −0.657677 1.13913i
\(585\) 0 0
\(586\) −34745.1 20060.1i −2.44933 1.41412i
\(587\) −16279.7 −1.14470 −0.572348 0.820011i \(-0.693967\pi\)
−0.572348 + 0.820011i \(0.693967\pi\)
\(588\) 0 0
\(589\) 4293.17 0.300335
\(590\) −4362.91 2518.93i −0.304438 0.175767i
\(591\) 0 0
\(592\) 386.814 + 669.981i 0.0268546 + 0.0465136i
\(593\) 1342.16 2324.68i 0.0929440 0.160984i −0.815805 0.578328i \(-0.803706\pi\)
0.908749 + 0.417344i \(0.137039\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 21865.7i 1.50277i
\(597\) 0 0
\(598\) 30540.1 17632.3i 2.08842 1.20575i
\(599\) −12224.6 + 7057.90i −0.833865 + 0.481432i −0.855174 0.518341i \(-0.826550\pi\)
0.0213091 + 0.999773i \(0.493217\pi\)
\(600\) 0 0
\(601\) 11096.1i 0.753109i −0.926394 0.376555i \(-0.877109\pi\)
0.926394 0.376555i \(-0.122891\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −3268.89 + 5661.89i −0.220214 + 0.381422i
\(605\) −252.748 437.772i −0.0169846 0.0294181i
\(606\) 0 0
\(607\) 9592.70 + 5538.35i 0.641442 + 0.370337i 0.785170 0.619280i \(-0.212576\pi\)
−0.143728 + 0.989617i \(0.545909\pi\)
\(608\) 9725.10 0.648692
\(609\) 0 0
\(610\) 75.3136 0.00499895
\(611\) −10328.5 5963.15i −0.683872 0.394834i
\(612\) 0 0
\(613\) 3801.34 + 6584.11i 0.250464 + 0.433817i 0.963654 0.267154i \(-0.0860834\pi\)
−0.713189 + 0.700971i \(0.752750\pi\)
\(614\) −6122.44 + 10604.4i −0.402413 + 0.697000i
\(615\) 0 0
\(616\) 0 0
\(617\) 11325.9i 0.738998i 0.929231 + 0.369499i \(0.120471\pi\)
−0.929231 + 0.369499i \(0.879529\pi\)
\(618\) 0 0
\(619\) 16595.2 9581.22i 1.07757 0.622136i 0.147330 0.989087i \(-0.452932\pi\)
0.930240 + 0.366952i \(0.119599\pi\)
\(620\) −1203.70 + 694.958i −0.0779707 + 0.0450164i
\(621\) 0 0
\(622\) 9773.64i 0.630044i
\(623\) 0 0
\(624\) 0 0
\(625\) −7513.41 + 13013.6i −0.480858 + 0.832871i
\(626\) −19061.6 33015.7i −1.21702 2.10794i
\(627\) 0 0
\(628\) 14214.7 + 8206.88i 0.903232 + 0.521481i
\(629\) 7046.06 0.446653
\(630\) 0 0
\(631\) 10140.7 0.639768 0.319884 0.947457i \(-0.396356\pi\)
0.319884 + 0.947457i \(0.396356\pi\)
\(632\) −7205.88 4160.32i −0.453536 0.261849i
\(633\) 0 0
\(634\) 21698.3 + 37582.6i 1.35923 + 2.35425i
\(635\) 797.995 1382.17i 0.0498700 0.0863774i
\(636\) 0 0
\(637\) 0 0
\(638\) 28444.2i 1.76507i
\(639\) 0 0
\(640\) −2387.98 + 1378.70i −0.147489 + 0.0851530i
\(641\) 2950.66 1703.56i 0.181816 0.104972i −0.406330 0.913727i \(-0.633192\pi\)
0.588146 + 0.808755i \(0.299858\pi\)
\(642\) 0 0
\(643\) 659.110i 0.0404242i −0.999796 0.0202121i \(-0.993566\pi\)
0.999796 0.0202121i \(-0.00643415\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 8563.71 14832.8i 0.521570 0.903386i
\(647\) 3303.47 + 5721.78i 0.200731 + 0.347676i 0.948764 0.315985i \(-0.102335\pi\)
−0.748033 + 0.663661i \(0.769002\pi\)
\(648\) 0 0
\(649\) 31705.4 + 18305.1i 1.91764 + 1.10715i
\(650\) 47846.6 2.88723
\(651\) 0 0
\(652\) 5577.01 0.334989
\(653\) −22417.1 12942.5i −1.34342 0.775622i −0.356109 0.934444i \(-0.615897\pi\)
−0.987307 + 0.158823i \(0.949230\pi\)
\(654\) 0 0
\(655\) 865.234 + 1498.63i 0.0516145 + 0.0893989i
\(656\) −1637.78 + 2836.72i −0.0974764 + 0.168834i
\(657\) 0 0
\(658\) 0 0
\(659\) 7468.86i 0.441495i −0.975331 0.220748i \(-0.929150\pi\)
0.975331 0.220748i \(-0.0708497\pi\)
\(660\) 0 0
\(661\) 5501.96 3176.56i 0.323754 0.186919i −0.329311 0.944222i \(-0.606816\pi\)
0.653065 + 0.757302i \(0.273483\pi\)
\(662\) 33463.4 19320.1i 1.96464 1.13429i
\(663\) 0 0
\(664\) 19220.3i 1.12333i
\(665\) 0 0
\(666\) 0 0
\(667\) 6875.53 11908.8i 0.399133 0.691319i
\(668\) −5050.61 8747.92i −0.292536 0.506687i
\(669\) 0 0
\(670\) −2193.23 1266.26i −0.126465 0.0730148i
\(671\) −547.306 −0.0314881
\(672\) 0 0
\(673\) −20238.2 −1.15918 −0.579589 0.814909i \(-0.696787\pi\)
−0.579589 + 0.814909i \(0.696787\pi\)
\(674\) −2345.58 1354.22i −0.134048 0.0773925i
\(675\) 0 0
\(676\) −32089.7 55581.1i −1.82577 3.16233i
\(677\) 5658.37 9800.59i 0.321224 0.556377i −0.659516 0.751690i \(-0.729239\pi\)
0.980741 + 0.195313i \(0.0625723\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 1982.91i 0.111825i
\(681\) 0 0
\(682\) 14366.6 8294.55i 0.806635 0.465711i
\(683\) −14869.4 + 8584.87i −0.833035 + 0.480953i −0.854891 0.518808i \(-0.826376\pi\)
0.0218557 + 0.999761i \(0.493043\pi\)
\(684\) 0 0
\(685\) 1393.74i 0.0777402i
\(686\) 0 0
\(687\) 0 0
\(688\) −973.172 + 1685.58i −0.0539271 + 0.0934044i
\(689\) −14342.4 24841.8i −0.793037 1.37358i
\(690\) 0 0
\(691\) 7238.59 + 4179.20i 0.398508 + 0.230079i 0.685840 0.727752i \(-0.259435\pi\)
−0.287332 + 0.957831i \(0.592768\pi\)
\(692\) −27926.3 −1.53410
\(693\) 0 0
\(694\) 32114.4 1.75655
\(695\) 2528.29 + 1459.71i 0.137990 + 0.0796688i
\(696\) 0 0
\(697\) 14916.6 + 25836.3i 0.810627 + 1.40405i
\(698\) −8187.41 + 14181.0i −0.443980 + 0.768996i
\(699\) 0 0
\(700\) 0 0
\(701\) 19235.8i 1.03641i 0.855256 + 0.518206i \(0.173400\pi\)
−0.855256 + 0.518206i \(0.826600\pi\)
\(702\) 0 0
\(703\) 3819.31 2205.08i 0.204905 0.118302i
\(704\) 30082.5 17368.1i 1.61048 0.929810i
\(705\) 0 0
\(706\) 10536.5i 0.561680i
\(707\) 0 0
\(708\) 0 0
\(709\) 5160.17 8937.67i 0.273334 0.473429i −0.696379 0.717674i \(-0.745207\pi\)
0.969714 + 0.244245i \(0.0785401\pi\)
\(710\) −977.554 1693.17i −0.0516718 0.0894981i
\(711\) 0 0
\(712\) −518.001 299.068i −0.0272653 0.0157416i
\(713\) −8019.85 −0.421242
\(714\) 0 0
\(715\) 4514.02 0.236105
\(716\) −31529.0 18203.3i −1.64566 0.950124i
\(717\) 0 0
\(718\) 3975.20 + 6885.25i 0.206620 + 0.357876i
\(719\) −11679.8 + 20229.9i −0.605815 + 1.04930i 0.386107 + 0.922454i \(0.373820\pi\)
−0.991922 + 0.126849i \(0.959514\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 20300.0i 1.04638i
\(723\) 0 0
\(724\) 3050.62 1761.28i 0.156596 0.0904106i
\(725\) 16157.7 9328.63i 0.827698 0.477871i
\(726\) 0 0
\(727\) 22260.4i 1.13561i 0.823162 + 0.567807i \(0.192208\pi\)
−0.823162 + 0.567807i \(0.807792\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −2638.00 + 4569.15i −0.133749 + 0.231660i
\(731\) 8863.48 + 15352.0i 0.448464 + 0.776763i
\(732\) 0 0
\(733\) −9047.84 5223.77i −0.455920 0.263226i 0.254407 0.967097i \(-0.418120\pi\)
−0.710327 + 0.703872i \(0.751453\pi\)
\(734\) 7618.58 0.383116
\(735\) 0 0
\(736\) −18166.9 −0.909840
\(737\) 15938.2 + 9201.95i 0.796598 + 0.459916i
\(738\) 0 0
\(739\) −6595.44 11423.6i −0.328304 0.568640i 0.653871 0.756606i \(-0.273144\pi\)
−0.982176 + 0.187966i \(0.939811\pi\)
\(740\) −713.895 + 1236.50i −0.0354639 + 0.0614253i
\(741\) 0 0
\(742\) 0 0
\(743\) 35382.2i 1.74703i −0.486795 0.873517i \(-0.661834\pi\)
0.486795 0.873517i \(-0.338166\pi\)
\(744\) 0 0
\(745\) 1924.59 1111.16i 0.0946463 0.0546441i
\(746\) −1164.38 + 672.258i −0.0571463 + 0.0329934i
\(747\) 0 0
\(748\) 40295.6i 1.96973i
\(749\) 0 0
\(750\) 0 0
\(751\) 14692.3 25447.8i 0.713888 1.23649i −0.249498 0.968375i \(-0.580266\pi\)
0.963387 0.268116i \(-0.0864010\pi\)
\(752\) 594.020 + 1028.87i 0.0288054 + 0.0498925i
\(753\) 0 0
\(754\) −50770.8 29312.5i −2.45221 1.41578i
\(755\) 664.470 0.0320299
\(756\) 0 0
\(757\) 11329.1 0.543939 0.271969 0.962306i \(-0.412325\pi\)
0.271969 + 0.962306i \(0.412325\pi\)
\(758\) 28994.0 + 16739.7i 1.38932 + 0.802127i
\(759\) 0 0
\(760\) 620.557 + 1074.84i 0.0296184 + 0.0513005i
\(761\) 12696.5 21990.9i 0.604792 1.04753i −0.387292 0.921957i \(-0.626589\pi\)
0.992084 0.125574i \(-0.0400772\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 57499.9i 2.72287i
\(765\) 0 0
\(766\) −49065.8 + 28328.2i −2.31439 + 1.33621i
\(767\) −65346.7 + 37727.9i −3.07631 + 1.77611i
\(768\) 0 0
\(769\) 18120.8i 0.849744i 0.905253 + 0.424872i \(0.139681\pi\)
−0.905253 + 0.424872i \(0.860319\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −25874.7 + 44816.3i −1.20628 + 2.08934i
\(773\) 8673.05 + 15022.2i 0.403555 + 0.698978i 0.994152 0.107989i \(-0.0344410\pi\)
−0.590597 + 0.806967i \(0.701108\pi\)
\(774\) 0 0
\(775\) −9423.42 5440.61i −0.436773 0.252171i
\(776\) 24161.3 1.11771
\(777\) 0 0
\(778\) −36054.7 −1.66147
\(779\) 16171.1 + 9336.37i 0.743759 + 0.429410i
\(780\) 0 0
\(781\) 7103.91 + 12304.3i 0.325477 + 0.563743i
\(782\) −15997.4 + 27708.3i −0.731542 + 1.26707i
\(783\) 0 0
\(784\) 0 0
\(785\) 1668.22i 0.0758488i
\(786\) 0 0
\(787\) −1801.52 + 1040.11i −0.0815977 + 0.0471104i −0.540244 0.841509i \(-0.681668\pi\)
0.458646 + 0.888619i \(0.348335\pi\)
\(788\) −17540.2 + 10126.8i −0.792949 + 0.457810i
\(789\) 0 0
\(790\) 2364.83i 0.106502i