Properties

Label 441.4.p.c.80.7
Level $441$
Weight $4$
Character 441.80
Analytic conductor $26.020$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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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 80.7
Root \(3.91663 - 2.26127i\) of defining polynomial
Character \(\chi\) \(=\) 441.80
Dual form 441.4.p.c.215.7

$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

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

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 \(-0.371775\pi\)
0.992716 + 0.120476i \(0.0384420\pi\)
\(3\) 0 0
\(4\) 6.22668 10.7849i 0.778336 1.34812i
\(5\) −0.632851 1.09613i −0.0566040 0.0980409i 0.836335 0.548219i \(-0.184694\pi\)
−0.892939 + 0.450178i \(0.851361\pi\)
\(6\) 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 \(-0.526429\pi\)
−0.904509 + 0.426454i \(0.859763\pi\)
\(12\) 0 0
\(13\) 85.7355i 1.82914i −0.404433 0.914568i \(-0.632531\pi\)
0.404433 0.914568i \(-0.367469\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 4.27028 + 7.39634i 0.0667231 + 0.115568i
\(17\) 38.8929 67.3645i 0.554878 0.961076i −0.443035 0.896504i \(-0.646098\pi\)
0.997913 0.0645722i \(-0.0205683\pi\)
\(18\) 0 0
\(19\) −42.1638 + 24.3433i −0.509107 + 0.293933i −0.732466 0.680803i \(-0.761631\pi\)
0.223360 + 0.974736i \(0.428298\pi\)
\(20\) −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 \(-0.801928\pi\)
0.0985019 + 0.995137i \(0.468595\pi\)
\(24\) 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 0.262190 0.965016i \(-0.415555\pi\)
−0.704634 + 0.709571i \(0.748889\pi\)
\(32\) 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 0.747689 0.664050i \(-0.231164\pi\)
−0.948928 + 0.315493i \(0.897830\pi\)
\(38\) −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 \(-0.239308\pi\)
0.730455 + 0.682961i \(0.239308\pi\)
\(42\) 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 \(-0.0974118\pi\)
−0.737680 + 0.675151i \(0.764078\pi\)
\(48\) 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 \(-0.190591\pi\)
−0.0750904 + 0.997177i \(0.523925\pi\)
\(54\) 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 −0.278493 + 0.960438i \(0.589835\pi\)
−0.692518 + 0.721401i \(0.743499\pi\)
\(60\) 0 0
\(61\) −11.3944 + 6.57854i −0.0239164 + 0.0138081i −0.511911 0.859039i \(-0.671062\pi\)
0.487994 + 0.872847i \(0.337729\pi\)
\(62\) −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 −0.590766 0.806843i \(-0.701174\pi\)
0.994130 + 0.108197i \(0.0345076\pi\)
\(68\) −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 0.976809 0.214113i \(-0.0686862\pi\)
0.302977 + 0.952998i \(0.402019\pi\)
\(74\) −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 0.974794 0.223107i \(-0.0716198\pi\)
−0.680613 + 0.732643i \(0.738286\pi\)
\(80\) 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 \(-0.717362\pi\)
−0.631017 + 0.775769i \(0.717362\pi\)
\(84\) 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 \(-0.172296\pi\)
−0.874733 + 0.484606i \(0.838963\pi\)
\(90\) 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 \(-0.783932\pi\)
0.778328 0.627858i \(-0.216068\pi\)
\(98\) 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 \(-0.728786\pi\)
0.981018 + 0.193918i \(0.0621195\pi\)
\(102\) 0 0
\(103\) 1186.01 684.744i 1.13457 0.655047i 0.189493 0.981882i \(-0.439316\pi\)
0.945081 + 0.326836i \(0.105982\pi\)
\(104\) −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 \(-0.604622\pi\)
0.658270 + 0.752782i \(0.271289\pi\)
\(108\) 0 0
\(109\) 334.261 578.957i 0.293728 0.508752i −0.680960 0.732321i \(-0.738437\pi\)
0.974688 + 0.223568i \(0.0717706\pi\)
\(110\) 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 \(-0.0159747\pi\)
−0.542814 + 0.839853i \(0.682641\pi\)
\(132\) 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 \(-0.221771\pi\)
−0.172252 + 0.985053i \(0.555104\pi\)
\(138\) 0 0
\(139\) 2306.56i 1.40748i −0.710458 0.703739i \(-0.751512\pi\)
0.710458 0.703739i \(-0.248488\pi\)
\(140\) 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 \(-0.827006\pi\)
0.0198764 + 0.999802i \(0.493673\pi\)
\(150\) 0 0
\(151\) 262.491 454.647i 0.141465 0.245024i −0.786584 0.617484i \(-0.788152\pi\)
0.928048 + 0.372460i \(0.121485\pi\)
\(152\) 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 0.761226 0.648487i \(-0.224598\pi\)
−0.180993 + 0.983484i \(0.557931\pi\)
\(158\) 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 0.914797 0.403915i \(-0.132351\pi\)
−0.807199 + 0.590280i \(0.799017\pi\)
\(164\) 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 \(-0.439824\pi\)
0.187924 + 0.982184i \(0.439824\pi\)
\(168\) 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 \(-0.00265790\pi\)
−0.507214 + 0.861820i \(0.669325\pi\)
\(174\) 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 \(-0.124359\pi\)
0.132521 + 0.991180i \(0.457693\pi\)
\(180\) 0 0
\(181\) 282.859i 0.116159i 0.998312 + 0.0580794i \(0.0184977\pi\)
−0.998312 + 0.0580794i \(0.981502\pi\)
\(182\) 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 0.514971 0.857208i \(-0.327803\pi\)
0.999849 0.0173741i \(-0.00553064\pi\)
\(192\) 0 0
\(193\) 2077.73 3598.73i 0.774912 1.34219i −0.159933 0.987128i \(-0.551128\pi\)
0.934844 0.355058i \(-0.115539\pi\)
\(194\) −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 0.472889 0.881122i \(-0.343211\pi\)
−0.526629 + 0.850095i \(0.676544\pi\)
\(200\) −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 \(-0.830864\pi\)
0.862120 0.506704i \(-0.169136\pi\)
\(224\) 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 \(-0.687214\pi\)
0.997917 + 0.0645069i \(0.0205475\pi\)
\(228\) 0 0
\(229\) −960.030 + 554.274i −0.277033 + 0.159945i −0.632080 0.774904i \(-0.717798\pi\)
0.355046 + 0.934849i \(0.384465\pi\)
\(230\) 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 \(-0.810199\pi\)
0.0726160 + 0.997360i \(0.476865\pi\)
\(234\) 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 0.632418 0.774628i \(-0.282063\pi\)
−0.354638 + 0.935004i \(0.615396\pi\)
\(242\) 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 \(-0.654594\pi\)
−0.466802 + 0.884362i \(0.654594\pi\)
\(252\) 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 \(-0.196810\pi\)
−0.909423 + 0.415872i \(0.863477\pi\)
\(258\) 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 \(-0.407337\pi\)
−0.686080 + 0.727526i \(0.740670\pi\)
\(264\) 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 \(-0.923748\pi\)
0.691201 + 0.722662i \(0.257082\pi\)
\(270\) 0 0
\(271\) −4095.79 + 2364.71i −0.918088 + 0.530058i −0.883025 0.469327i \(-0.844497\pi\)
−0.0350633 + 0.999385i \(0.511163\pi\)
\(272\) 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 −0.922604 0.385747i \(-0.873944\pi\)
0.795369 + 0.606125i \(0.207277\pi\)
\(278\) −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 0.245646 0.969360i \(-0.421000\pi\)
−0.716667 + 0.697415i \(0.754333\pi\)
\(284\) 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 \(-0.845432\pi\)
−0.884400 + 0.466729i \(0.845432\pi\)
\(294\) 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 \(0.0809804\pi\)
−0.967813 + 0.251672i \(0.919020\pi\)
\(308\) 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 \(-0.896459\pi\)
0.750543 + 0.660822i \(0.229792\pi\)
\(312\) 0 0
\(313\) 7300.25 4214.80i 1.31832 0.761133i 0.334863 0.942267i \(-0.391310\pi\)
0.983459 + 0.181133i \(0.0579766\pi\)
\(314\) 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 \(-0.343226\pi\)
0.999517 + 0.0310734i \(0.00989256\pi\)
\(318\) 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 −0.965084 0.261941i \(-0.915637\pi\)
0.255694 0.966758i \(-0.417696\pi\)
\(332\) −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 \(-0.148235\pi\)
0.0578712 + 0.998324i \(0.481569\pi\)
\(348\) 0 0
\(349\) 3620.71i 0.555336i 0.960677 + 0.277668i \(0.0895616\pi\)
−0.960677 + 0.277668i \(0.910438\pi\)
\(350\) 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 \(-0.777134\pi\)
0.940382 + 0.340119i \(0.110467\pi\)
\(354\) 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 \(-0.625419\pi\)
0.607717 + 0.794154i \(0.292086\pi\)
\(360\) 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 0.392648 0.919689i \(-0.371559\pi\)
−0.600150 + 0.799887i \(0.704893\pi\)
\(368\) −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 0.876158 0.482024i \(-0.160098\pi\)
−0.855524 + 0.517763i \(0.826765\pi\)
\(374\) −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 −0.893479 0.449105i \(-0.851743\pi\)
0.0578031 0.998328i \(-0.481590\pi\)
\(384\) 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 \(-0.507233\pi\)
−0.877162 + 0.480195i \(0.840566\pi\)
\(390\) 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 −0.990857 0.134918i \(-0.956923\pi\)
−0.378586 + 0.925566i \(0.623590\pi\)
\(398\) −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 \(-0.500281\pi\)
0.865583 + 0.500765i \(0.166948\pi\)
\(402\) 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 0.881944 0.471354i \(-0.156235\pi\)
0.0327670 + 0.999463i \(0.489568\pi\)
\(410\) −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 \(-0.426482\pi\)
0.228914 + 0.973447i \(0.426482\pi\)
\(420\) 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 \(-0.643420\pi\)
−0.997334 + 0.0729655i \(0.976754\pi\)
\(432\) 0 0
\(433\) 15872.1i 1.76158i −0.473508 0.880790i \(-0.657012\pi\)
0.473508 0.880790i \(-0.342988\pi\)
\(434\) 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 −0.350379 0.936608i \(-0.613947\pi\)
0.635937 + 0.771741i \(0.280614\pi\)
\(440\) 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 \(-0.908607\pi\)
−0.234281 + 0.972169i \(0.575274\pi\)
\(444\) 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 1.00000 0.000444115i \(0.000141366\pi\)
−0.499615 + 0.866247i \(0.666525\pi\)
\(458\) −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 \(-0.510274\pi\)
−0.0322726 + 0.999479i \(0.510274\pi\)
\(462\) 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 \(-0.0785086\pi\)
−0.696308 + 0.717743i \(0.745175\pi\)
\(468\) 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 \(-0.749337\pi\)
0.966463 + 0.256807i \(0.0826703\pi\)
\(480\) 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 −0.452665 0.891681i \(-0.649527\pi\)
0.998551 0.0538213i \(-0.0171401\pi\)
\(488\) 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 0.554373 0.832268i \(-0.312958\pi\)
−0.997952 + 0.0639672i \(0.979625\pi\)
\(500\) −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 \(-0.351121\pi\)
0.450849 + 0.892600i \(0.351121\pi\)
\(504\) 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 \(-0.106730\pi\)
−0.757125 + 0.653270i \(0.773397\pi\)
\(510\) 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 \(-0.680394\pi\)
0.999070 + 0.0431133i \(0.0137276\pi\)
\(522\) 0 0
\(523\) −7386.80 + 4264.77i −0.617595 + 0.356569i −0.775932 0.630817i \(-0.782720\pi\)
0.158337 + 0.987385i \(0.449387\pi\)
\(524\) 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 0.985522 0.169548i \(-0.0542308\pi\)
−0.639594 + 0.768713i \(0.720897\pi\)
\(542\) −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 \(-0.462529\pi\)
−0.801307 + 0.598253i \(0.795862\pi\)
\(558\) 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 0.278780 + 0.960355i \(0.410070\pi\)
−0.971082 + 0.238747i \(0.923263\pi\)
\(564\) 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 \(-0.714144\pi\)
0.365755 + 0.930711i \(0.380811\pi\)
\(570\) 0 0
\(571\) −6430.01 + 11137.1i −0.471257 + 0.816241i −0.999459 0.0328777i \(-0.989533\pi\)
0.528203 + 0.849118i \(0.322866\pi\)
\(572\) 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 0.975894 0.218246i \(-0.0700335\pi\)
0.298940 + 0.954272i \(0.403367\pi\)
\(578\) −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 \(-0.306033\pi\)
0.572348 + 0.820011i \(0.306033\pi\)
\(588\) 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 \(-0.196294\pi\)
−0.908749 + 0.417344i \(0.862961\pi\)
\(594\) 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 \(-0.173450\pi\)
−0.0213091 + 0.999773i \(0.506783\pi\)
\(600\) 0 0
\(601\) 11096.1i 0.753109i 0.926394 + 0.376555i \(0.122891\pi\)
−0.926394 + 0.376555i \(0.877109\pi\)
\(602\) 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 −0.143728 0.989617i \(-0.545909\pi\)
0.785170 + 0.619280i \(0.212576\pi\)
\(608\) −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 −0.713189 0.700971i \(-0.752750\pi\)
0.963654 + 0.267154i \(0.0860834\pi\)
\(614\) 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 0.930240 0.366952i \(-0.119599\pi\)
0.147330 + 0.989087i \(0.452932\pi\)
\(620\) 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 \(-0.366808\pi\)
−0.588146 + 0.808755i \(0.700142\pi\)
\(642\) 0 0
\(643\) 659.110i 0.0404242i 0.999796 + 0.0202121i \(0.00643415\pi\)
−0.999796 + 0.0202121i \(0.993566\pi\)
\(644\) 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 \(-0.897665\pi\)
0.748033 + 0.663661i \(0.230998\pi\)
\(648\) 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 \(-0.384103\pi\)
0.987307 + 0.158823i \(0.0507698\pi\)
\(654\) 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 0.653065 0.757302i \(-0.273483\pi\)
−0.329311 + 0.944222i \(0.606816\pi\)
\(662\) −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 \(-0.270761\pi\)
−0.980741 + 0.195313i \(0.937428\pi\)
\(678\) 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 \(-0.173624\pi\)
−0.0218557 + 0.999761i \(0.506957\pi\)
\(684\) 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 −0.287332 0.957831i \(-0.592768\pi\)
0.685840 + 0.727752i \(0.259435\pi\)
\(692\) 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 0.969714 0.244245i \(-0.0785401\pi\)
−0.696379 + 0.717674i \(0.745207\pi\)
\(710\) 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 0.991922 + 0.126849i \(0.0404864\pi\)
−0.386107 + 0.922454i \(0.626180\pi\)
\(720\) 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 \(-0.807792\pi\)
0.823162 0.567807i \(-0.192208\pi\)
\(728\) 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 −0.710327 0.703872i \(-0.751453\pi\)
0.254407 + 0.967097i \(0.418120\pi\)
\(734\) −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 −0.982176 0.187966i \(-0.939811\pi\)
0.653871 + 0.756606i \(0.273144\pi\)
\(740\) 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 0.963387 + 0.268116i \(0.0864010\pi\)
−0.249498 + 0.968375i \(0.580266\pi\)
\(752\) −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 −0.992084 0.125574i \(-0.959923\pi\)
0.387292 0.921957i \(-0.373411\pi\)
\(762\) 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 \(-0.860319\pi\)
0.905253 0.424872i \(-0.139681\pi\)
\(770\) 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 \(-0.965559\pi\)
0.590597 + 0.806967i \(0.298892\pi\)
\(774\) 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 0.458646 0.888619i \(-0.348335\pi\)
−0.540244 + 0.841509i \(0.681668\pi\)
\(788\) 17540.2 + 10126.8i 0.792949 + 0.457810i
\(789\) 0 0
\(790\) 2364.83i 0.106502i
\(791\)