Properties

Label 441.4.e.z.226.7
Level $441$
Weight $4$
Character 441.226
Analytic conductor $26.020$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(26.0198423125\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 74 x^{14} + 4007 x^{12} + 91050 x^{10} + 1502189 x^{8} + 12598332 x^{6} + 74261084 x^{4} + 22070000 x^{2} + 6250000\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 2^{8}\cdot 7^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 226.7
Root \(3.40706 - 5.90120i\) of defining polynomial
Character \(\chi\) \(=\) 441.226
Dual form 441.4.e.z.361.7

$q$-expansion

\(f(q)\) \(=\) \(q+(2.69995 - 4.67646i) q^{2} +(-10.5795 - 18.3242i) q^{4} +(-7.78839 + 13.4899i) q^{5} -71.0573 q^{8} +O(q^{10})\) \(q+(2.69995 - 4.67646i) q^{2} +(-10.5795 - 18.3242i) q^{4} +(-7.78839 + 13.4899i) q^{5} -71.0573 q^{8} +(42.0566 + 72.8441i) q^{10} +(15.9851 + 27.6870i) q^{11} +72.5746 q^{13} +(-107.215 + 185.703i) q^{16} +(14.5144 + 25.1397i) q^{17} +(-54.4146 + 94.2489i) q^{19} +329.589 q^{20} +172.636 q^{22} +(-27.6434 + 47.8798i) q^{23} +(-58.8180 - 101.876i) q^{25} +(195.948 - 339.392i) q^{26} -17.7363 q^{29} +(-28.0594 - 48.6004i) q^{31} +(294.724 + 510.477i) q^{32} +156.753 q^{34} +(147.908 - 256.184i) q^{37} +(293.834 + 508.935i) q^{38} +(553.422 - 958.555i) q^{40} +238.605 q^{41} +16.8202 q^{43} +(338.228 - 585.829i) q^{44} +(149.272 + 258.547i) q^{46} +(-255.954 + 443.326i) q^{47} -635.223 q^{50} +(-767.802 - 1329.87i) q^{52} +(132.603 + 229.674i) q^{53} -497.992 q^{55} +(-47.8871 + 82.9429i) q^{58} +(127.091 + 220.128i) q^{59} +(36.4176 - 63.0771i) q^{61} -303.037 q^{62} +1467.52 q^{64} +(-565.239 + 979.023i) q^{65} +(253.180 + 438.520i) q^{67} +(307.110 - 531.930i) q^{68} +827.722 q^{71} +(186.288 + 322.661i) q^{73} +(-798.689 - 1383.37i) q^{74} +2302.72 q^{76} +(-514.226 + 890.665i) q^{79} +(-1670.07 - 2892.65i) q^{80} +(644.222 - 1115.82i) q^{82} +453.148 q^{83} -452.175 q^{85} +(45.4138 - 78.6590i) q^{86} +(-1135.86 - 1967.36i) q^{88} +(-166.033 + 287.577i) q^{89} +1169.81 q^{92} +(1382.13 + 2393.92i) q^{94} +(-847.605 - 1468.09i) q^{95} -1164.54 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 68q^{4} + O(q^{10}) \) \( 16q - 68q^{4} - 804q^{16} + 1952q^{22} - 536q^{25} - 64q^{37} + 4320q^{43} + 768q^{46} - 2184q^{58} + 15176q^{64} - 5392q^{79} + 5728q^{85} - 5616q^{88} + O(q^{100}) \)

Character values

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

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.69995 4.67646i 0.954578 1.65338i 0.219246 0.975670i \(-0.429640\pi\)
0.735332 0.677707i \(-0.237026\pi\)
\(3\) 0 0
\(4\) −10.5795 18.3242i −1.32244 2.29053i
\(5\) −7.78839 + 13.4899i −0.696615 + 1.20657i 0.273019 + 0.962009i \(0.411978\pi\)
−0.969633 + 0.244563i \(0.921355\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −71.0573 −3.14032
\(9\) 0 0
\(10\) 42.0566 + 72.8441i 1.32995 + 2.30353i
\(11\) 15.9851 + 27.6870i 0.438153 + 0.758904i 0.997547 0.0699983i \(-0.0222994\pi\)
−0.559394 + 0.828902i \(0.688966\pi\)
\(12\) 0 0
\(13\) 72.5746 1.54835 0.774176 0.632971i \(-0.218165\pi\)
0.774176 + 0.632971i \(0.218165\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −107.215 + 185.703i −1.67524 + 2.90160i
\(17\) 14.5144 + 25.1397i 0.207074 + 0.358663i 0.950792 0.309831i \(-0.100273\pi\)
−0.743717 + 0.668494i \(0.766939\pi\)
\(18\) 0 0
\(19\) −54.4146 + 94.2489i −0.657030 + 1.13801i 0.324350 + 0.945937i \(0.394854\pi\)
−0.981381 + 0.192073i \(0.938479\pi\)
\(20\) 329.589 3.68492
\(21\) 0 0
\(22\) 172.636 1.67300
\(23\) −27.6434 + 47.8798i −0.250611 + 0.434071i −0.963694 0.267008i \(-0.913965\pi\)
0.713083 + 0.701079i \(0.247298\pi\)
\(24\) 0 0
\(25\) −58.8180 101.876i −0.470544 0.815006i
\(26\) 195.948 339.392i 1.47802 2.56001i
\(27\) 0 0
\(28\) 0 0
\(29\) −17.7363 −0.113570 −0.0567852 0.998386i \(-0.518085\pi\)
−0.0567852 + 0.998386i \(0.518085\pi\)
\(30\) 0 0
\(31\) −28.0594 48.6004i −0.162568 0.281577i 0.773221 0.634137i \(-0.218644\pi\)
−0.935789 + 0.352560i \(0.885311\pi\)
\(32\) 294.724 + 510.477i 1.62814 + 2.82001i
\(33\) 0 0
\(34\) 156.753 0.790673
\(35\) 0 0
\(36\) 0 0
\(37\) 147.908 256.184i 0.657187 1.13828i −0.324154 0.946004i \(-0.605080\pi\)
0.981341 0.192276i \(-0.0615870\pi\)
\(38\) 293.834 + 508.935i 1.25437 + 2.17264i
\(39\) 0 0
\(40\) 553.422 958.555i 2.18759 3.78902i
\(41\) 238.605 0.908873 0.454437 0.890779i \(-0.349841\pi\)
0.454437 + 0.890779i \(0.349841\pi\)
\(42\) 0 0
\(43\) 16.8202 0.0596526 0.0298263 0.999555i \(-0.490505\pi\)
0.0298263 + 0.999555i \(0.490505\pi\)
\(44\) 338.228 585.829i 1.15886 2.00720i
\(45\) 0 0
\(46\) 149.272 + 258.547i 0.478455 + 0.828709i
\(47\) −255.954 + 443.326i −0.794357 + 1.37587i 0.128889 + 0.991659i \(0.458859\pi\)
−0.923246 + 0.384208i \(0.874474\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −635.223 −1.79668
\(51\) 0 0
\(52\) −767.802 1329.87i −2.04760 3.54654i
\(53\) 132.603 + 229.674i 0.343667 + 0.595249i 0.985111 0.171921i \(-0.0549974\pi\)
−0.641443 + 0.767170i \(0.721664\pi\)
\(54\) 0 0
\(55\) −497.992 −1.22090
\(56\) 0 0
\(57\) 0 0
\(58\) −47.8871 + 82.9429i −0.108412 + 0.187775i
\(59\) 127.091 + 220.128i 0.280437 + 0.485732i 0.971493 0.237070i \(-0.0761872\pi\)
−0.691055 + 0.722802i \(0.742854\pi\)
\(60\) 0 0
\(61\) 36.4176 63.0771i 0.0764392 0.132397i −0.825272 0.564735i \(-0.808978\pi\)
0.901711 + 0.432339i \(0.142312\pi\)
\(62\) −303.037 −0.620737
\(63\) 0 0
\(64\) 1467.52 2.86625
\(65\) −565.239 + 979.023i −1.07860 + 1.86820i
\(66\) 0 0
\(67\) 253.180 + 438.520i 0.461654 + 0.799609i 0.999044 0.0437257i \(-0.0139228\pi\)
−0.537389 + 0.843334i \(0.680589\pi\)
\(68\) 307.110 531.930i 0.547685 0.948618i
\(69\) 0 0
\(70\) 0 0
\(71\) 827.722 1.38356 0.691779 0.722110i \(-0.256827\pi\)
0.691779 + 0.722110i \(0.256827\pi\)
\(72\) 0 0
\(73\) 186.288 + 322.661i 0.298677 + 0.517324i 0.975834 0.218515i \(-0.0701214\pi\)
−0.677157 + 0.735839i \(0.736788\pi\)
\(74\) −798.689 1383.37i −1.25467 2.17315i
\(75\) 0 0
\(76\) 2302.72 3.47552
\(77\) 0 0
\(78\) 0 0
\(79\) −514.226 + 890.665i −0.732341 + 1.26845i 0.223539 + 0.974695i \(0.428239\pi\)
−0.955880 + 0.293757i \(0.905094\pi\)
\(80\) −1670.07 2892.65i −2.33400 4.04260i
\(81\) 0 0
\(82\) 644.222 1115.82i 0.867590 1.50271i
\(83\) 453.148 0.599270 0.299635 0.954054i \(-0.403135\pi\)
0.299635 + 0.954054i \(0.403135\pi\)
\(84\) 0 0
\(85\) −452.175 −0.577003
\(86\) 45.4138 78.6590i 0.0569430 0.0986282i
\(87\) 0 0
\(88\) −1135.86 1967.36i −1.37594 2.38320i
\(89\) −166.033 + 287.577i −0.197746 + 0.342507i −0.947797 0.318873i \(-0.896696\pi\)
0.750051 + 0.661380i \(0.230029\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 1169.81 1.32567
\(93\) 0 0
\(94\) 1382.13 + 2393.92i 1.51655 + 2.62674i
\(95\) −847.605 1468.09i −0.915394 1.58551i
\(96\) 0 0
\(97\) −1164.54 −1.21898 −0.609489 0.792795i \(-0.708625\pi\)
−0.609489 + 0.792795i \(0.708625\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −1244.53 + 2155.59i −1.24453 + 2.15559i
\(101\) 931.771 + 1613.88i 0.917967 + 1.58997i 0.802498 + 0.596655i \(0.203504\pi\)
0.115470 + 0.993311i \(0.463163\pi\)
\(102\) 0 0
\(103\) −493.140 + 854.144i −0.471753 + 0.817100i −0.999478 0.0323154i \(-0.989712\pi\)
0.527725 + 0.849415i \(0.323045\pi\)
\(104\) −5156.95 −4.86232
\(105\) 0 0
\(106\) 1432.08 1.31223
\(107\) −347.843 + 602.481i −0.314273 + 0.544337i −0.979283 0.202498i \(-0.935094\pi\)
0.665010 + 0.746835i \(0.268427\pi\)
\(108\) 0 0
\(109\) −857.498 1485.23i −0.753517 1.30513i −0.946108 0.323851i \(-0.895022\pi\)
0.192591 0.981279i \(-0.438311\pi\)
\(110\) −1344.56 + 2328.84i −1.16544 + 2.01860i
\(111\) 0 0
\(112\) 0 0
\(113\) −877.721 −0.730700 −0.365350 0.930870i \(-0.619051\pi\)
−0.365350 + 0.930870i \(0.619051\pi\)
\(114\) 0 0
\(115\) −430.595 745.813i −0.349159 0.604760i
\(116\) 187.641 + 325.003i 0.150190 + 0.260136i
\(117\) 0 0
\(118\) 1372.56 1.07080
\(119\) 0 0
\(120\) 0 0
\(121\) 154.454 267.522i 0.116044 0.200993i
\(122\) −196.652 340.610i −0.145934 0.252766i
\(123\) 0 0
\(124\) −593.709 + 1028.33i −0.429973 + 0.744735i
\(125\) −114.708 −0.0820784
\(126\) 0 0
\(127\) 781.088 0.545751 0.272875 0.962049i \(-0.412025\pi\)
0.272875 + 0.962049i \(0.412025\pi\)
\(128\) 1604.44 2778.97i 1.10792 1.91897i
\(129\) 0 0
\(130\) 3052.24 + 5286.63i 2.05922 + 3.56668i
\(131\) −980.619 + 1698.48i −0.654024 + 1.13280i 0.328114 + 0.944638i \(0.393587\pi\)
−0.982138 + 0.188164i \(0.939746\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 2734.29 1.76274
\(135\) 0 0
\(136\) −1031.35 1786.36i −0.650279 1.12632i
\(137\) −610.155 1056.82i −0.380504 0.659053i 0.610630 0.791916i \(-0.290916\pi\)
−0.991134 + 0.132863i \(0.957583\pi\)
\(138\) 0 0
\(139\) 1068.10 0.651765 0.325882 0.945410i \(-0.394339\pi\)
0.325882 + 0.945410i \(0.394339\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 2234.81 3870.81i 1.32071 2.28754i
\(143\) 1160.11 + 2009.37i 0.678415 + 1.17505i
\(144\) 0 0
\(145\) 138.137 239.260i 0.0791148 0.137031i
\(146\) 2011.88 1.14044
\(147\) 0 0
\(148\) −6259.16 −3.47635
\(149\) −1295.41 + 2243.72i −0.712243 + 1.23364i 0.251770 + 0.967787i \(0.418987\pi\)
−0.964013 + 0.265855i \(0.914346\pi\)
\(150\) 0 0
\(151\) −964.770 1671.03i −0.519946 0.900573i −0.999731 0.0231868i \(-0.992619\pi\)
0.479785 0.877386i \(-0.340715\pi\)
\(152\) 3866.56 6697.08i 2.06328 3.57371i
\(153\) 0 0
\(154\) 0 0
\(155\) 874.151 0.452990
\(156\) 0 0
\(157\) −1312.87 2273.95i −0.667377 1.15593i −0.978635 0.205605i \(-0.934084\pi\)
0.311259 0.950325i \(-0.399249\pi\)
\(158\) 2776.77 + 4809.51i 1.39815 + 2.42167i
\(159\) 0 0
\(160\) −9181.70 −4.53673
\(161\) 0 0
\(162\) 0 0
\(163\) 1550.08 2684.82i 0.744858 1.29013i −0.205403 0.978678i \(-0.565850\pi\)
0.950261 0.311455i \(-0.100816\pi\)
\(164\) −2524.32 4372.25i −1.20193 2.08180i
\(165\) 0 0
\(166\) 1223.48 2119.13i 0.572050 0.990819i
\(167\) 3264.73 1.51277 0.756386 0.654126i \(-0.226963\pi\)
0.756386 + 0.654126i \(0.226963\pi\)
\(168\) 0 0
\(169\) 3070.07 1.39739
\(170\) −1220.85 + 2114.58i −0.550795 + 0.954004i
\(171\) 0 0
\(172\) −177.949 308.217i −0.0788867 0.136636i
\(173\) 1018.15 1763.49i 0.447450 0.775006i −0.550769 0.834657i \(-0.685666\pi\)
0.998219 + 0.0596516i \(0.0189990\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −6855.39 −2.93605
\(177\) 0 0
\(178\) 896.561 + 1552.89i 0.377529 + 0.653899i
\(179\) −1791.17 3102.40i −0.747925 1.29544i −0.948816 0.315831i \(-0.897717\pi\)
0.200890 0.979614i \(-0.435617\pi\)
\(180\) 0 0
\(181\) −1637.35 −0.672392 −0.336196 0.941792i \(-0.609140\pi\)
−0.336196 + 0.941792i \(0.609140\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 1964.27 3402.21i 0.786998 1.36312i
\(185\) 2303.93 + 3990.52i 0.915612 + 1.58589i
\(186\) 0 0
\(187\) −464.028 + 803.720i −0.181460 + 0.314299i
\(188\) 10831.5 4.20195
\(189\) 0 0
\(190\) −9153.97 −3.49526
\(191\) 1412.39 2446.33i 0.535063 0.926756i −0.464098 0.885784i \(-0.653621\pi\)
0.999160 0.0409717i \(-0.0130454\pi\)
\(192\) 0 0
\(193\) 828.765 + 1435.46i 0.309098 + 0.535373i 0.978165 0.207829i \(-0.0666397\pi\)
−0.669068 + 0.743201i \(0.733306\pi\)
\(194\) −3144.19 + 5445.90i −1.16361 + 2.01543i
\(195\) 0 0
\(196\) 0 0
\(197\) −1890.78 −0.683819 −0.341909 0.939733i \(-0.611074\pi\)
−0.341909 + 0.939733i \(0.611074\pi\)
\(198\) 0 0
\(199\) 696.373 + 1206.15i 0.248063 + 0.429658i 0.962988 0.269543i \(-0.0868726\pi\)
−0.714925 + 0.699201i \(0.753539\pi\)
\(200\) 4179.45 + 7239.01i 1.47766 + 2.55938i
\(201\) 0 0
\(202\) 10063.0 3.50508
\(203\) 0 0
\(204\) 0 0
\(205\) −1858.35 + 3218.75i −0.633134 + 1.09662i
\(206\) 2662.91 + 4612.30i 0.900650 + 1.55997i
\(207\) 0 0
\(208\) −7781.12 + 13477.3i −2.59386 + 4.49270i
\(209\) −3479.29 −1.15152
\(210\) 0 0
\(211\) 3314.53 1.08143 0.540714 0.841206i \(-0.318154\pi\)
0.540714 + 0.841206i \(0.318154\pi\)
\(212\) 2805.74 4859.68i 0.908957 1.57436i
\(213\) 0 0
\(214\) 1878.32 + 3253.34i 0.599996 + 1.03922i
\(215\) −131.002 + 226.903i −0.0415548 + 0.0719751i
\(216\) 0 0
\(217\) 0 0
\(218\) −9260.82 −2.87716
\(219\) 0 0
\(220\) 5268.51 + 9125.32i 1.61456 + 2.79650i
\(221\) 1053.38 + 1824.50i 0.320624 + 0.555336i
\(222\) 0 0
\(223\) −5576.50 −1.67457 −0.837287 0.546764i \(-0.815860\pi\)
−0.837287 + 0.546764i \(0.815860\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −2369.81 + 4104.63i −0.697510 + 1.20812i
\(227\) −723.961 1253.94i −0.211678 0.366638i 0.740562 0.671989i \(-0.234560\pi\)
−0.952240 + 0.305351i \(0.901226\pi\)
\(228\) 0 0
\(229\) −808.774 + 1400.84i −0.233385 + 0.404235i −0.958802 0.284074i \(-0.908314\pi\)
0.725417 + 0.688310i \(0.241647\pi\)
\(230\) −4650.35 −1.33320
\(231\) 0 0
\(232\) 1260.29 0.356647
\(233\) −3046.05 + 5275.92i −0.856454 + 1.48342i 0.0188365 + 0.999823i \(0.494004\pi\)
−0.875290 + 0.483598i \(0.839330\pi\)
\(234\) 0 0
\(235\) −3986.94 6905.59i −1.10672 1.91690i
\(236\) 2689.11 4657.68i 0.741721 1.28470i
\(237\) 0 0
\(238\) 0 0
\(239\) 1595.90 0.431927 0.215963 0.976401i \(-0.430711\pi\)
0.215963 + 0.976401i \(0.430711\pi\)
\(240\) 0 0
\(241\) −1094.42 1895.58i −0.292521 0.506661i 0.681884 0.731460i \(-0.261161\pi\)
−0.974405 + 0.224799i \(0.927827\pi\)
\(242\) −834.037 1444.59i −0.221545 0.383727i
\(243\) 0 0
\(244\) −1541.12 −0.404344
\(245\) 0 0
\(246\) 0 0
\(247\) −3949.12 + 6840.08i −1.01731 + 1.76204i
\(248\) 1993.83 + 3453.41i 0.510517 + 0.884241i
\(249\) 0 0
\(250\) −309.706 + 536.427i −0.0783502 + 0.135707i
\(251\) 6203.07 1.55990 0.779949 0.625843i \(-0.215245\pi\)
0.779949 + 0.625843i \(0.215245\pi\)
\(252\) 0 0
\(253\) −1767.53 −0.439224
\(254\) 2108.90 3652.72i 0.520961 0.902331i
\(255\) 0 0
\(256\) −2793.74 4838.90i −0.682066 1.18137i
\(257\) −134.162 + 232.375i −0.0325633 + 0.0564013i −0.881848 0.471534i \(-0.843700\pi\)
0.849284 + 0.527935i \(0.177034\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 23919.8 5.70554
\(261\) 0 0
\(262\) 5295.25 + 9171.65i 1.24863 + 2.16270i
\(263\) 1862.48 + 3225.91i 0.436675 + 0.756343i 0.997431 0.0716384i \(-0.0228228\pi\)
−0.560756 + 0.827981i \(0.689489\pi\)
\(264\) 0 0
\(265\) −4131.04 −0.957615
\(266\) 0 0
\(267\) 0 0
\(268\) 5357.03 9278.64i 1.22102 2.11486i
\(269\) −4278.63 7410.80i −0.969786 1.67972i −0.696167 0.717880i \(-0.745112\pi\)
−0.273619 0.961838i \(-0.588221\pi\)
\(270\) 0 0
\(271\) 2639.83 4572.32i 0.591728 1.02490i −0.402271 0.915521i \(-0.631779\pi\)
0.994000 0.109383i \(-0.0348875\pi\)
\(272\) −6224.67 −1.38760
\(273\) 0 0
\(274\) −6589.56 −1.45288
\(275\) 1880.42 3256.98i 0.412341 0.714195i
\(276\) 0 0
\(277\) 220.774 + 382.392i 0.0478882 + 0.0829448i 0.888976 0.457954i \(-0.151418\pi\)
−0.841088 + 0.540899i \(0.818084\pi\)
\(278\) 2883.83 4994.94i 0.622160 1.07761i
\(279\) 0 0
\(280\) 0 0
\(281\) 3766.49 0.799609 0.399804 0.916601i \(-0.369078\pi\)
0.399804 + 0.916601i \(0.369078\pi\)
\(282\) 0 0
\(283\) −905.511 1568.39i −0.190201 0.329439i 0.755115 0.655592i \(-0.227581\pi\)
−0.945317 + 0.326153i \(0.894247\pi\)
\(284\) −8756.88 15167.4i −1.82967 3.16908i
\(285\) 0 0
\(286\) 12529.0 2.59040
\(287\) 0 0
\(288\) 0 0
\(289\) 2035.16 3525.01i 0.414241 0.717486i
\(290\) −745.926 1291.98i −0.151042 0.261613i
\(291\) 0 0
\(292\) 3941.68 6827.18i 0.789963 1.36826i
\(293\) −5815.74 −1.15959 −0.579794 0.814763i \(-0.696867\pi\)
−0.579794 + 0.814763i \(0.696867\pi\)
\(294\) 0 0
\(295\) −3959.33 −0.781427
\(296\) −10509.9 + 18203.7i −2.06378 + 3.57456i
\(297\) 0 0
\(298\) 6995.10 + 12115.9i 1.35978 + 2.35521i
\(299\) −2006.21 + 3474.86i −0.388034 + 0.672094i
\(300\) 0 0
\(301\) 0 0
\(302\) −10419.3 −1.98532
\(303\) 0 0
\(304\) −11668.2 20209.9i −2.20137 3.81288i
\(305\) 567.269 + 982.538i 0.106497 + 0.184459i
\(306\) 0 0
\(307\) −1974.93 −0.367150 −0.183575 0.983006i \(-0.558767\pi\)
−0.183575 + 0.983006i \(0.558767\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 2360.17 4087.93i 0.432414 0.748964i
\(311\) −579.535 1003.78i −0.105667 0.183020i 0.808344 0.588711i \(-0.200364\pi\)
−0.914010 + 0.405691i \(0.867031\pi\)
\(312\) 0 0
\(313\) −2246.84 + 3891.64i −0.405747 + 0.702774i −0.994408 0.105606i \(-0.966322\pi\)
0.588661 + 0.808380i \(0.299655\pi\)
\(314\) −14178.7 −2.54825
\(315\) 0 0
\(316\) 21761.0 3.87390
\(317\) 2338.75 4050.83i 0.414376 0.717721i −0.580987 0.813913i \(-0.697333\pi\)
0.995363 + 0.0961925i \(0.0306664\pi\)
\(318\) 0 0
\(319\) −283.516 491.064i −0.0497612 0.0861890i
\(320\) −11429.6 + 19796.7i −1.99667 + 3.45833i
\(321\) 0 0
\(322\) 0 0
\(323\) −3159.19 −0.544216
\(324\) 0 0
\(325\) −4268.69 7393.59i −0.728567 1.26192i
\(326\) −8370.30 14497.8i −1.42205 2.46306i
\(327\) 0 0
\(328\) −16954.6 −2.85415
\(329\) 0 0
\(330\) 0 0
\(331\) 1491.36 2583.10i 0.247650 0.428943i −0.715223 0.698896i \(-0.753675\pi\)
0.962873 + 0.269953i \(0.0870082\pi\)
\(332\) −4794.07 8303.58i −0.792497 1.37264i
\(333\) 0 0
\(334\) 8814.63 15267.4i 1.44406 2.50118i
\(335\) −7887.45 −1.28638
\(336\) 0 0
\(337\) 7328.53 1.18460 0.592301 0.805717i \(-0.298220\pi\)
0.592301 + 0.805717i \(0.298220\pi\)
\(338\) 8289.04 14357.0i 1.33392 2.31042i
\(339\) 0 0
\(340\) 4783.79 + 8285.76i 0.763051 + 1.32164i
\(341\) 897.065 1553.76i 0.142460 0.246748i
\(342\) 0 0
\(343\) 0 0
\(344\) −1195.20 −0.187328
\(345\) 0 0
\(346\) −5497.94 9522.71i −0.854251 1.47961i
\(347\) 4154.66 + 7196.09i 0.642749 + 1.11327i 0.984816 + 0.173599i \(0.0555397\pi\)
−0.342067 + 0.939676i \(0.611127\pi\)
\(348\) 0 0
\(349\) 334.303 0.0512745 0.0256373 0.999671i \(-0.491839\pi\)
0.0256373 + 0.999671i \(0.491839\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −9422.38 + 16320.0i −1.42675 + 2.47120i
\(353\) −2729.09 4726.93i −0.411487 0.712717i 0.583565 0.812066i \(-0.301657\pi\)
−0.995053 + 0.0993491i \(0.968324\pi\)
\(354\) 0 0
\(355\) −6446.62 + 11165.9i −0.963806 + 1.66936i
\(356\) 7026.17 1.04603
\(357\) 0 0
\(358\) −19344.3 −2.85581
\(359\) 3598.45 6232.70i 0.529022 0.916293i −0.470405 0.882451i \(-0.655892\pi\)
0.999427 0.0338425i \(-0.0107745\pi\)
\(360\) 0 0
\(361\) −2492.41 4316.98i −0.363378 0.629389i
\(362\) −4420.76 + 7656.98i −0.641851 + 1.11172i
\(363\) 0 0
\(364\) 0 0
\(365\) −5803.55 −0.832251
\(366\) 0 0
\(367\) 3162.21 + 5477.12i 0.449772 + 0.779028i 0.998371 0.0570579i \(-0.0181720\pi\)
−0.548599 + 0.836086i \(0.684839\pi\)
\(368\) −5927.60 10266.9i −0.839668 1.45435i
\(369\) 0 0
\(370\) 24882.0 3.49609
\(371\) 0 0
\(372\) 0 0
\(373\) 5465.88 9467.18i 0.758746 1.31419i −0.184744 0.982787i \(-0.559146\pi\)
0.943490 0.331400i \(-0.107521\pi\)
\(374\) 2505.71 + 4340.01i 0.346436 + 0.600045i
\(375\) 0 0
\(376\) 18187.4 31501.6i 2.49454 4.32066i
\(377\) −1287.20 −0.175847
\(378\) 0 0
\(379\) 6024.02 0.816446 0.408223 0.912882i \(-0.366149\pi\)
0.408223 + 0.912882i \(0.366149\pi\)
\(380\) −17934.5 + 31063.4i −2.42110 + 4.19347i
\(381\) 0 0
\(382\) −7626.78 13210.0i −1.02152 1.76932i
\(383\) 3424.05 5930.63i 0.456816 0.791229i −0.541974 0.840395i \(-0.682323\pi\)
0.998791 + 0.0491658i \(0.0156563\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 8950.51 1.18023
\(387\) 0 0
\(388\) 12320.2 + 21339.2i 1.61202 + 2.79210i
\(389\) 2580.94 + 4470.32i 0.336398 + 0.582659i 0.983752 0.179531i \(-0.0574579\pi\)
−0.647354 + 0.762189i \(0.724125\pi\)
\(390\) 0 0
\(391\) −1604.91 −0.207580
\(392\) 0 0
\(393\) 0 0
\(394\) −5105.01 + 8842.14i −0.652758 + 1.13061i
\(395\) −8009.98 13873.7i −1.02032 1.76724i
\(396\) 0 0
\(397\) 172.384 298.578i 0.0217927 0.0377461i −0.854923 0.518754i \(-0.826396\pi\)
0.876716 + 0.481008i \(0.159729\pi\)
\(398\) 7520.70 0.947182
\(399\) 0 0
\(400\) 25224.8 3.15310
\(401\) 2549.42 4415.72i 0.317486 0.549902i −0.662477 0.749083i \(-0.730495\pi\)
0.979963 + 0.199180i \(0.0638280\pi\)
\(402\) 0 0
\(403\) −2036.40 3527.15i −0.251713 0.435980i
\(404\) 19715.3 34148.0i 2.42791 4.20526i
\(405\) 0 0
\(406\) 0 0
\(407\) 9457.28 1.15179
\(408\) 0 0
\(409\) −161.562 279.834i −0.0195323 0.0338310i 0.856094 0.516820i \(-0.172884\pi\)
−0.875626 + 0.482989i \(0.839551\pi\)
\(410\) 10034.9 + 17380.9i 1.20875 + 2.09362i
\(411\) 0 0
\(412\) 20868.7 2.49545
\(413\) 0 0
\(414\) 0 0
\(415\) −3529.29 + 6112.91i −0.417460 + 0.723062i
\(416\) 21389.5 + 37047.7i 2.52093 + 4.36637i
\(417\) 0 0
\(418\) −9393.92 + 16270.8i −1.09922 + 1.90390i
\(419\) 4415.98 0.514880 0.257440 0.966294i \(-0.417121\pi\)
0.257440 + 0.966294i \(0.417121\pi\)
\(420\) 0 0
\(421\) 1379.37 0.159683 0.0798415 0.996808i \(-0.474559\pi\)
0.0798415 + 0.996808i \(0.474559\pi\)
\(422\) 8949.06 15500.2i 1.03231 1.78801i
\(423\) 0 0
\(424\) −9422.38 16320.0i −1.07922 1.86927i
\(425\) 1707.42 2957.33i 0.194875 0.337533i
\(426\) 0 0
\(427\) 0 0
\(428\) 14720.0 1.66243
\(429\) 0 0
\(430\) 707.401 + 1225.25i 0.0793346 + 0.137412i
\(431\) 827.893 + 1433.95i 0.0925248 + 0.160258i 0.908573 0.417726i \(-0.137173\pi\)
−0.816048 + 0.577984i \(0.803840\pi\)
\(432\) 0 0
\(433\) −8612.65 −0.955883 −0.477942 0.878392i \(-0.658617\pi\)
−0.477942 + 0.878392i \(0.658617\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −18143.8 + 31426.0i −1.99296 + 3.45190i
\(437\) −3008.41 5210.73i −0.329318 0.570396i
\(438\) 0 0
\(439\) −2987.69 + 5174.84i −0.324817 + 0.562600i −0.981475 0.191588i \(-0.938636\pi\)
0.656658 + 0.754188i \(0.271969\pi\)
\(440\) 35386.0 3.83400
\(441\) 0 0
\(442\) 11376.3 1.22424
\(443\) 403.266 698.477i 0.0432500 0.0749112i −0.843590 0.536988i \(-0.819562\pi\)
0.886840 + 0.462077i \(0.152895\pi\)
\(444\) 0 0
\(445\) −2586.25 4479.52i −0.275506 0.477190i
\(446\) −15056.3 + 26078.2i −1.59851 + 2.76870i
\(447\) 0 0
\(448\) 0 0
\(449\) −6253.04 −0.657237 −0.328618 0.944463i \(-0.606583\pi\)
−0.328618 + 0.944463i \(0.606583\pi\)
\(450\) 0 0
\(451\) 3814.12 + 6606.24i 0.398226 + 0.689747i
\(452\) 9285.85 + 16083.6i 0.966304 + 1.67369i
\(453\) 0 0
\(454\) −7818.65 −0.808254
\(455\) 0 0
\(456\) 0 0
\(457\) −80.1439 + 138.813i −0.00820344 + 0.0142088i −0.870098 0.492879i \(-0.835945\pi\)
0.861895 + 0.507088i \(0.169278\pi\)
\(458\) 4367.30 + 7564.39i 0.445569 + 0.771748i
\(459\) 0 0
\(460\) −9110.96 + 15780.7i −0.923480 + 1.59951i
\(461\) −2408.80 −0.243360 −0.121680 0.992569i \(-0.538828\pi\)
−0.121680 + 0.992569i \(0.538828\pi\)
\(462\) 0 0
\(463\) −1092.89 −0.109699 −0.0548496 0.998495i \(-0.517468\pi\)
−0.0548496 + 0.998495i \(0.517468\pi\)
\(464\) 1901.60 3293.67i 0.190258 0.329536i
\(465\) 0 0
\(466\) 16448.4 + 28489.5i 1.63510 + 2.83208i
\(467\) 7527.42 13037.9i 0.745884 1.29191i −0.203897 0.978992i \(-0.565361\pi\)
0.949781 0.312916i \(-0.101306\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −43058.3 −4.22581
\(471\) 0 0
\(472\) −9030.73 15641.7i −0.880663 1.52535i
\(473\) 268.873 + 465.701i 0.0261370 + 0.0452705i
\(474\) 0 0
\(475\) 12802.2 1.23665
\(476\) 0 0
\(477\) 0 0
\(478\) 4308.87 7463.18i 0.412308 0.714138i
\(479\) 5227.80 + 9054.82i 0.498673 + 0.863727i 0.999999 0.00153157i \(-0.000487513\pi\)
−0.501326 + 0.865259i \(0.667154\pi\)
\(480\) 0 0
\(481\) 10734.4 18592.4i 1.01756 1.76246i
\(482\) −11819.5 −1.11693
\(483\) 0 0
\(484\) −6536.18 −0.613841
\(485\) 9069.86 15709.5i 0.849157 1.47078i
\(486\) 0 0
\(487\) 6358.83 + 11013.8i 0.591675 + 1.02481i 0.994007 + 0.109318i \(0.0348666\pi\)
−0.402331 + 0.915494i \(0.631800\pi\)
\(488\) −2587.74 + 4482.09i −0.240044 + 0.415768i
\(489\) 0 0
\(490\) 0 0
\(491\) −20983.1 −1.92863 −0.964313 0.264763i \(-0.914706\pi\)
−0.964313 + 0.264763i \(0.914706\pi\)
\(492\) 0 0
\(493\) −257.431 445.884i −0.0235175 0.0407335i
\(494\) 21324.9 + 36935.8i 1.94221 + 3.36401i
\(495\) 0 0
\(496\) 12033.6 1.08937
\(497\) 0 0
\(498\) 0 0
\(499\) −6359.04 + 11014.2i −0.570480 + 0.988101i 0.426036 + 0.904706i \(0.359910\pi\)
−0.996517 + 0.0833946i \(0.973424\pi\)
\(500\) 1213.55 + 2101.94i 0.108544 + 0.188003i
\(501\) 0 0
\(502\) 16748.0 29008.4i 1.48904 2.57910i
\(503\) −15675.9 −1.38957 −0.694785 0.719218i \(-0.744500\pi\)
−0.694785 + 0.719218i \(0.744500\pi\)
\(504\) 0 0
\(505\) −29028.0 −2.55788
\(506\) −4772.25 + 8265.78i −0.419273 + 0.726203i
\(507\) 0 0
\(508\) −8263.51 14312.8i −0.721721 1.25006i
\(509\) 5109.15 8849.30i 0.444910 0.770606i −0.553136 0.833091i \(-0.686569\pi\)
0.998046 + 0.0624847i \(0.0199025\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −4500.87 −0.388501
\(513\) 0 0
\(514\) 724.460 + 1254.80i 0.0621684 + 0.107679i
\(515\) −7681.54 13304.8i −0.657260 1.13841i
\(516\) 0 0
\(517\) −16365.8 −1.39220
\(518\) 0 0
\(519\) 0 0
\(520\) 40164.4 69566.7i 3.38716 5.86674i
\(521\) 2404.07 + 4163.96i 0.202157 + 0.350147i 0.949223 0.314603i \(-0.101871\pi\)
−0.747066 + 0.664750i \(0.768538\pi\)
\(522\) 0 0
\(523\) −4968.09 + 8604.99i −0.415372 + 0.719445i −0.995467 0.0951032i \(-0.969682\pi\)
0.580095 + 0.814548i \(0.303015\pi\)
\(524\) 41497.8 3.45962
\(525\) 0 0
\(526\) 20114.4 1.66736
\(527\) 814.532 1410.81i 0.0673274 0.116615i
\(528\) 0 0
\(529\) 4555.18 + 7889.81i 0.374388 + 0.648459i
\(530\) −11153.6 + 19318.6i −0.914117 + 1.58330i
\(531\) 0 0
\(532\) 0 0
\(533\) 17316.6 1.40725
\(534\) 0 0
\(535\) −5418.27 9384.72i −0.437854 0.758386i
\(536\) −17990.3 31160.1i −1.44974 2.51103i
\(537\) 0 0
\(538\) −46208.4 −3.70294
\(539\) 0 0
\(540\) 0 0
\(541\) 1024.33 1774.19i 0.0814038 0.140995i −0.822449 0.568838i \(-0.807393\pi\)
0.903853 + 0.427843i \(0.140726\pi\)
\(542\) −14254.8 24690.1i −1.12970 1.95670i
\(543\) 0 0
\(544\) −8555.49 + 14818.5i −0.674290 + 1.16790i
\(545\) 26714.1 2.09964
\(546\) 0 0
\(547\) 6154.72 0.481091 0.240546 0.970638i \(-0.422674\pi\)
0.240546 + 0.970638i \(0.422674\pi\)
\(548\) −12910.3 + 22361.2i −1.00639 + 1.74311i
\(549\) 0 0
\(550\) −10154.1 17587.4i −0.787222 1.36351i
\(551\) 965.112 1671.62i 0.0746192 0.129244i
\(552\) 0 0
\(553\) 0 0
\(554\) 2384.32 0.182852
\(555\) 0 0
\(556\) −11300.0 19572.2i −0.861918 1.49289i
\(557\) −2223.38 3851.00i −0.169134 0.292948i 0.768982 0.639271i \(-0.220764\pi\)
−0.938116 + 0.346322i \(0.887430\pi\)
\(558\) 0 0
\(559\) 1220.72 0.0923631
\(560\) 0 0
\(561\) 0 0
\(562\) 10169.3 17613.8i 0.763288 1.32205i
\(563\) −4843.29 8388.83i −0.362559 0.627970i 0.625823 0.779965i \(-0.284763\pi\)
−0.988381 + 0.151996i \(0.951430\pi\)
\(564\) 0 0
\(565\) 6836.04 11840.4i 0.509016 0.881642i
\(566\) −9779.35 −0.726248
\(567\) 0 0
\(568\) −58815.7 −4.34481
\(569\) 3653.46 6327.98i 0.269176 0.466226i −0.699473 0.714659i \(-0.746582\pi\)
0.968649 + 0.248433i \(0.0799154\pi\)
\(570\) 0 0
\(571\) −4554.67 7888.92i −0.333813 0.578180i 0.649443 0.760410i \(-0.275002\pi\)
−0.983256 + 0.182230i \(0.941669\pi\)
\(572\) 24546.8 42516.3i 1.79432 3.10786i
\(573\) 0 0
\(574\) 0 0
\(575\) 6503.72 0.471694
\(576\) 0 0
\(577\) −9353.85 16201.3i −0.674880 1.16893i −0.976504 0.215500i \(-0.930862\pi\)
0.301624 0.953427i \(-0.402471\pi\)
\(578\) −10989.7 19034.7i −0.790850 1.36979i
\(579\) 0 0
\(580\) −5845.67 −0.418497
\(581\) 0 0
\(582\) 0 0
\(583\) −4239.33 + 7342.73i −0.301158 + 0.521621i
\(584\) −13237.2 22927.4i −0.937941 1.62456i
\(585\) 0 0
\(586\) −15702.2 + 27197.0i −1.10692 + 1.91723i
\(587\) −24610.4 −1.73046 −0.865230 0.501375i \(-0.832828\pi\)
−0.865230 + 0.501375i \(0.832828\pi\)
\(588\) 0 0
\(589\) 6107.38 0.427250
\(590\) −10690.0 + 18515.6i −0.745933 + 1.29199i
\(591\) 0 0
\(592\) 31716.0 + 54933.8i 2.20189 + 3.81379i
\(593\) −9420.00 + 16315.9i −0.652332 + 1.12987i 0.330223 + 0.943903i \(0.392876\pi\)
−0.982555 + 0.185970i \(0.940457\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 54819.2 3.76759
\(597\) 0 0
\(598\) 10833.3 + 18763.9i 0.740817 + 1.28313i
\(599\) 10323.8 + 17881.4i 0.704206 + 1.21972i 0.966977 + 0.254862i \(0.0820301\pi\)
−0.262771 + 0.964858i \(0.584637\pi\)
\(600\) 0 0
\(601\) 15772.8 1.07053 0.535264 0.844685i \(-0.320212\pi\)
0.535264 + 0.844685i \(0.320212\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −20413.6 + 35357.3i −1.37519 + 2.38190i
\(605\) 2405.89 + 4167.13i 0.161675 + 0.280030i
\(606\) 0 0
\(607\) 2591.32 4488.30i 0.173276 0.300123i −0.766287 0.642498i \(-0.777898\pi\)
0.939563 + 0.342375i \(0.111231\pi\)
\(608\) −64149.2 −4.27894
\(609\) 0 0
\(610\) 6126.39 0.406640
\(611\) −18575.8 + 32174.2i −1.22994 + 2.13033i
\(612\) 0 0
\(613\) 14419.5 + 24975.4i 0.950081 + 1.64559i 0.745244 + 0.666792i \(0.232333\pi\)
0.204837 + 0.978796i \(0.434333\pi\)
\(614\) −5332.21 + 9235.66i −0.350473 + 0.607037i
\(615\) 0 0
\(616\) 0 0
\(617\) −5114.80 −0.333734 −0.166867 0.985979i \(-0.553365\pi\)
−0.166867 + 0.985979i \(0.553365\pi\)
\(618\) 0 0
\(619\) 14607.0 + 25300.0i 0.948471 + 1.64280i 0.748648 + 0.662968i \(0.230703\pi\)
0.199823 + 0.979832i \(0.435963\pi\)
\(620\) −9248.07 16018.1i −0.599051 1.03759i
\(621\) 0 0
\(622\) −6258.87 −0.403469
\(623\) 0 0
\(624\) 0 0
\(625\) 8245.64 14281.9i 0.527721 0.914039i
\(626\) 12132.7 + 21014.5i 0.774634 + 1.34170i
\(627\) 0 0
\(628\) −27778.9 + 48114.5i −1.76513 + 3.05729i
\(629\) 8587.18 0.544345
\(630\) 0 0
\(631\) 19557.5 1.23387 0.616934 0.787015i \(-0.288374\pi\)
0.616934 + 0.787015i \(0.288374\pi\)
\(632\) 36539.5 63288.3i 2.29978 3.98334i
\(633\) 0 0
\(634\) −12629.0 21874.1i −0.791108 1.37024i
\(635\) −6083.41 + 10536.8i −0.380178 + 0.658487i
\(636\) 0 0
\(637\) 0 0
\(638\) −3061.92 −0.190004
\(639\) 0 0
\(640\) 24992.0 + 43287.4i 1.54359 + 2.67357i
\(641\) −7316.15 12671.9i −0.450812 0.780829i 0.547625 0.836724i \(-0.315532\pi\)
−0.998437 + 0.0558950i \(0.982199\pi\)
\(642\) 0 0
\(643\) 23808.1 1.46019 0.730094 0.683347i \(-0.239476\pi\)
0.730094 + 0.683347i \(0.239476\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −8529.65 + 14773.8i −0.519496 + 0.899794i
\(647\) 8661.08 + 15001.4i 0.526279 + 0.911541i 0.999531 + 0.0306145i \(0.00974643\pi\)
−0.473253 + 0.880927i \(0.656920\pi\)
\(648\) 0 0
\(649\) −4063.11 + 7037.52i −0.245749 + 0.425650i
\(650\) −46101.1 −2.78190
\(651\) 0 0
\(652\) −65596.4 −3.94011
\(653\) 1620.84 2807.38i 0.0971338 0.168241i −0.813363 0.581756i \(-0.802366\pi\)
0.910497 + 0.413515i \(0.135699\pi\)
\(654\) 0 0
\(655\) −15274.9 26456.9i −0.911205 1.57825i
\(656\) −25582.1 + 44309.5i −1.52258 + 2.63719i
\(657\) 0 0
\(658\) 0 0
\(659\) −16358.2 −0.966958 −0.483479 0.875356i \(-0.660627\pi\)
−0.483479 + 0.875356i \(0.660627\pi\)
\(660\) 0 0
\(661\) 6286.30 + 10888.2i 0.369907 + 0.640698i 0.989551 0.144185i \(-0.0460562\pi\)
−0.619644 + 0.784883i \(0.712723\pi\)
\(662\) −8053.18 13948.5i −0.472803 0.818919i
\(663\) 0 0
\(664\) −32199.5 −1.88190
\(665\) 0 0
\(666\) 0 0
\(667\) 490.291 849.209i 0.0284620 0.0492976i
\(668\) −34539.2 59823.7i −2.00054 3.46504i
\(669\) 0 0
\(670\) −21295.7 + 36885.3i −1.22795 + 2.12687i
\(671\) 2328.55 0.133968
\(672\) 0 0
\(673\) 13130.7 0.752082 0.376041 0.926603i \(-0.377285\pi\)
0.376041 + 0.926603i \(0.377285\pi\)
\(674\) 19786.7 34271.6i 1.13079 1.95859i
\(675\) 0 0
\(676\) −32479.8 56256.6i −1.84796 3.20076i
\(677\) −9312.08 + 16129.0i −0.528644 + 0.915639i 0.470798 + 0.882241i \(0.343966\pi\)
−0.999442 + 0.0333977i \(0.989367\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 32130.4 1.81198
\(681\) 0 0
\(682\) −4844.07 8390.17i −0.271978 0.471079i
\(683\) −12688.5 21977.1i −0.710852 1.23123i −0.964538 0.263946i \(-0.914976\pi\)
0.253685 0.967287i \(-0.418357\pi\)
\(684\) 0 0
\(685\) 19008.5 1.06026
\(686\) 0 0
\(687\) 0 0
\(688\) −1803.39 + 3123.56i −0.0999324 + 0.173088i
\(689\) 9623.58 + 16668.5i 0.532118 + 0.921655i
\(690\) 0 0
\(691\) 1067.71 1849.33i 0.0587810 0.101812i −0.835137 0.550041i \(-0.814612\pi\)
0.893918 + 0.448230i \(0.147945\pi\)
\(692\) −43086.2 −2.36690
\(693\) 0 0
\(694\) 44869.6 2.45422
\(695\) −8318.80 + 14408.6i −0.454029 + 0.786401i
\(696\) 0 0
\(697\) 3463.21 + 5998.45i 0.188204 + 0.325979i
\(698\) 902.602 1563.35i 0.0489455 0.0847761i
\(699\) 0 0
\(700\) 0 0
\(701\) 9679.27 0.521513 0.260757 0.965405i \(-0.416028\pi\)
0.260757 + 0.965405i \(0.416028\pi\)
\(702\) 0 0
\(703\) 16096.7 + 27880.3i 0.863583 + 1.49577i
\(704\) 23458.4 + 40631.2i 1.25586 + 2.17521i
\(705\) 0 0
\(706\) −29473.7 −1.57119
\(707\) 0 0
\(708\) 0 0
\(709\) 12871.6 22294.2i 0.681809 1.18093i −0.292619 0.956229i \(-0.594527\pi\)
0.974428 0.224699i \(-0.0721399\pi\)
\(710\) 34811.2 + 60294.7i 1.84006 + 3.18707i
\(711\) 0 0
\(712\) 11797.8 20434.5i 0.620987 1.07558i
\(713\) 3102.63 0.162966
\(714\) 0 0
\(715\) −36141.6 −1.89038
\(716\) −37899.4 + 65643.7i −1.97817 + 3.42629i
\(717\) 0 0
\(718\) −19431.3 33656.0i −1.00999 1.74935i
\(719\) −5254.26 + 9100.64i −0.272532 + 0.472040i −0.969510 0.245053i \(-0.921194\pi\)
0.696977 + 0.717093i \(0.254528\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −26917.5 −1.38749
\(723\) 0 0
\(724\) 17322.3 + 30003.1i 0.889196 + 1.54013i
\(725\) 1043.21 + 1806.89i 0.0534398 + 0.0925605i
\(726\) 0 0
\(727\) 24259.4 1.23759 0.618797 0.785551i \(-0.287620\pi\)
0.618797 + 0.785551i \(0.287620\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −15669.3 + 27140.0i −0.794448 + 1.37602i
\(731\) 244.136 + 422.855i 0.0123525 + 0.0213952i
\(732\) 0 0
\(733\) 9816.08 17001.9i 0.494632 0.856727i −0.505349 0.862915i \(-0.668636\pi\)
0.999981 + 0.00618771i \(0.00196962\pi\)
\(734\) 34151.3 1.71737
\(735\) 0 0
\(736\) −32588.7 −1.63212
\(737\) −8094.20 + 14019.6i −0.404551 + 0.700702i
\(738\) 0 0
\(739\) 13176.8 + 22822.9i 0.655909 + 1.13607i 0.981665 + 0.190614i \(0.0610478\pi\)
−0.325756 + 0.945454i \(0.605619\pi\)
\(740\) 48748.8 84435.4i 2.42168 4.19447i
\(741\) 0 0
\(742\) 0 0
\(743\) 31464.6 1.55360 0.776799 0.629749i \(-0.216842\pi\)
0.776799 + 0.629749i \(0.216842\pi\)
\(744\) 0 0
\(745\) −20178.3 34949.9i −0.992318 1.71875i
\(746\) −29515.2 51121.9i −1.44856 2.50899i
\(747\) 0 0
\(748\) 19636.7 0.959880
\(749\) 0 0
\(750\) 0 0
\(751\) −2705.76 + 4686.51i −0.131471 + 0.227714i −0.924244 0.381803i \(-0.875303\pi\)
0.792773 + 0.609517i \(0.208637\pi\)
\(752\) −54884.5 95062.8i −2.66148 4.60982i
\(753\) 0 0
\(754\) −3475.38 + 6019.54i −0.167859 + 0.290741i
\(755\) 30056.0 1.44881
\(756\) 0 0
\(757\) 3607.94 0.173227 0.0866135 0.996242i \(-0.472395\pi\)
0.0866135 + 0.996242i \(0.472395\pi\)
\(758\) 16264.6 28171.1i 0.779361 1.34989i
\(759\) 0 0
\(760\) 60228.5 + 104319.i 2.87463 + 4.97900i
\(761\) 2331.85 4038.89i 0.111077 0.192391i −0.805128 0.593101i \(-0.797903\pi\)
0.916205 + 0.400710i \(0.131237\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −59769.5 −2.83035
\(765\) 0 0
\(766\) −18489.5 32024.8i −0.872134 1.51058i
\(767\) 9223.56 + 15975.7i 0.434216 + 0.752083i
\(768\) 0 0
\(769\) 9725.21 0.456047 0.228023 0.973656i \(-0.426774\pi\)
0.228023 + 0.973656i \(0.426774\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 17535.8 30373.0i 0.817524 1.41599i
\(773\) −1546.40 2678.44i −0.0719536 0.124627i 0.827804 0.561018i \(-0.189590\pi\)
−0.899757 + 0.436390i \(0.856257\pi\)
\(774\) 0 0
\(775\) −3300.80 + 5717.15i −0.152991 + 0.264988i
\(776\) 82748.8 3.82798
\(777\) 0 0
\(778\) 27873.7 1.28447
\(779\) −12983.6 + 22488.2i −0.597157 + 1.03431i
\(780\) 0 0
\(781\) 13231.2 + 22917.1i 0.606210 + 1.04999i
\(782\) −4333.19 + 7505.30i −0.198151 + 0.343208i
\(783\) 0 0
\(784\) 0 0
\(785\) 40900.4 1.85962
\(786\) 0 0
\(787\) 11406.4 + 19756.5i 0.516640 + 0.894846i 0.999813 + 0.0193216i \(0.00615065\pi\)
−0.483174 + 0.875525i \(0.660516\pi\)
\(788\) 20003.5 + 34647.0i 0.904307 + 1.56631i
\(789\) 0 0
\(790\) −86506.3 −3.89589
\(791\) 0 0