Properties

Label 441.4.e.z.226.8
Level $441$
Weight $4$
Character 441.226
Analytic conductor $26.020$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

Related objects

Downloads

Learn more about

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 226.8
Root \(1.99285 - 3.45171i\) of defining polynomial
Character \(\chi\) \(=\) 441.226
Dual form 441.4.e.z.361.8

$q$-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 \(-0.588022\pi\)
0.969633 0.244563i \(-0.0786446\pi\)
\(6\) 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 \(-0.781835\pi\)
−0.774176 + 0.632971i \(0.781835\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −107.215 + 185.703i −1.67524 + 2.90160i
\(17\) −14.5144 25.1397i −0.207074 0.358663i 0.743717 0.668494i \(-0.233061\pi\)
−0.950792 + 0.309831i \(0.899727\pi\)
\(18\) 0 0
\(19\) 54.4146 94.2489i 0.657030 1.13801i −0.324350 0.945937i \(-0.605146\pi\)
0.981381 0.192073i \(-0.0615210\pi\)
\(20\) −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 0.935789 0.352560i \(-0.114689\pi\)
−0.773221 + 0.634137i \(0.781356\pi\)
\(32\) 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 \(-0.650159\pi\)
−0.454437 + 0.890779i \(0.650159\pi\)
\(42\) 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 \(-0.541141\pi\)
0.923246 0.384208i \(-0.125526\pi\)
\(48\) 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 0.691055 0.722802i \(-0.257146\pi\)
−0.971493 + 0.237070i \(0.923813\pi\)
\(60\) 0 0
\(61\) −36.4176 + 63.0771i −0.0764392 + 0.132397i −0.901711 0.432339i \(-0.857688\pi\)
0.825272 + 0.564735i \(0.191022\pi\)
\(62\) 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 0.677157 0.735839i \(-0.263212\pi\)
−0.975834 + 0.218515i \(0.929879\pi\)
\(74\) −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 \(-0.596865\pi\)
−0.299635 + 0.954054i \(0.596865\pi\)
\(84\) 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 −0.750051 0.661380i \(-0.769971\pi\)
0.947797 + 0.318873i \(0.103304\pi\)
\(90\) 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 \(-0.291375\pi\)
0.609489 + 0.792795i \(0.291375\pi\)
\(98\) 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 \(-0.796496\pi\)
−0.115470 0.993311i \(-0.536837\pi\)
\(102\) 0 0
\(103\) 493.140 854.144i 0.471753 0.817100i −0.527725 0.849415i \(-0.676955\pi\)
0.999478 + 0.0323154i \(0.0102881\pi\)
\(104\) 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 \(-0.606413\pi\)
0.982138 0.188164i \(-0.0602537\pi\)
\(132\) 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 \(-0.605661\pi\)
−0.325882 + 0.945410i \(0.605661\pi\)
\(140\) 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 \(0.0659162\pi\)
−0.311259 + 0.950325i \(0.600751\pi\)
\(158\) 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 \(-0.773037\pi\)
−0.756386 + 0.654126i \(0.773037\pi\)
\(168\) 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 −0.998219 0.0596516i \(-0.981001\pi\)
0.550769 + 0.834657i \(0.314334\pi\)
\(174\) 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 \(-0.390860\pi\)
0.336196 + 0.941792i \(0.390860\pi\)
\(182\) 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 0.714925 0.699201i \(-0.246461\pi\)
−0.962988 + 0.269543i \(0.913127\pi\)
\(200\) 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 \(-0.184140\pi\)
0.837287 + 0.546764i \(0.184140\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −2369.81 + 4104.63i −0.697510 + 1.20812i
\(227\) 723.961 + 1253.94i 0.211678 + 0.366638i 0.952240 0.305351i \(-0.0987737\pi\)
−0.740562 + 0.671989i \(0.765440\pi\)
\(228\) 0 0
\(229\) 808.774 1400.84i 0.233385 0.404235i −0.725417 0.688310i \(-0.758353\pi\)
0.958802 + 0.284074i \(0.0916863\pi\)
\(230\) 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 0.974405 0.224799i \(-0.0721726\pi\)
−0.681884 + 0.731460i \(0.738839\pi\)
\(242\) −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 \(-0.784755\pi\)
−0.779949 + 0.625843i \(0.784755\pi\)
\(252\) 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 −0.849284 0.527935i \(-0.822966\pi\)
0.881848 + 0.471534i \(0.156300\pi\)
\(258\) 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 \(0.254888\pi\)
0.273619 + 0.961838i \(0.411779\pi\)
\(270\) 0 0
\(271\) −2639.83 + 4572.32i −0.591728 + 1.02490i 0.402271 + 0.915521i \(0.368221\pi\)
−0.994000 + 0.109383i \(0.965112\pi\)
\(272\) 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 0.945317 0.326153i \(-0.105753\pi\)
−0.755115 + 0.655592i \(0.772419\pi\)
\(284\) −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 \(-0.303133\pi\)
0.579794 + 0.814763i \(0.303133\pi\)
\(294\) 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 \(-0.441233\pi\)
0.183575 + 0.983006i \(0.441233\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 2360.17 4087.93i 0.432414 0.748964i
\(311\) 579.535 + 1003.78i 0.105667 + 0.183020i 0.914010 0.405691i \(-0.132969\pi\)
−0.808344 + 0.588711i \(0.799636\pi\)
\(312\) 0 0
\(313\) 2246.84 3891.64i 0.405747 0.702774i −0.588661 0.808380i \(-0.700345\pi\)
0.994408 + 0.105606i \(0.0336781\pi\)
\(314\) 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 \(-0.508161\pi\)
−0.0256373 + 0.999671i \(0.508161\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −9422.38 + 16320.0i −1.42675 + 2.47120i
\(353\) 2729.09 + 4726.93i 0.411487 + 0.712717i 0.995053 0.0993491i \(-0.0316761\pi\)
−0.583565 + 0.812066i \(0.698343\pi\)
\(354\) 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 0.548599 0.836086i \(-0.315161\pi\)
−0.998371 + 0.0570579i \(0.981828\pi\)
\(368\) −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 −0.998791 0.0491658i \(-0.984344\pi\)
0.541974 + 0.840395i \(0.317677\pi\)
\(384\) 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 −0.876716 0.481008i \(-0.840271\pi\)
0.854923 + 0.518754i \(0.173604\pi\)
\(398\) −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 0.875626 0.482989i \(-0.160449\pi\)
−0.856094 + 0.516820i \(0.827116\pi\)
\(410\) 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 \(-0.582879\pi\)
−0.257440 + 0.966294i \(0.582879\pi\)
\(420\) 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 \(-0.341383\pi\)
0.477942 + 0.878392i \(0.341383\pi\)
\(434\) 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 −0.656658 0.754188i \(-0.728031\pi\)
0.981475 + 0.191588i \(0.0613638\pi\)
\(440\) −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 \(-0.461172\pi\)
0.121680 + 0.992569i \(0.461172\pi\)
\(462\) 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 \(0.434639\pi\)
−0.949781 + 0.312916i \(0.898694\pi\)
\(468\) 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 0.501326 0.865259i \(-0.332846\pi\)
−0.999999 + 0.00153157i \(0.999512\pi\)
\(480\) 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 \(-0.255500\pi\)
0.694785 + 0.719218i \(0.255500\pi\)
\(504\) 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 −0.998046 0.0624847i \(-0.980098\pi\)
0.553136 + 0.833091i \(0.313431\pi\)
\(510\) 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 0.747066 0.664750i \(-0.231462\pi\)
−0.949223 + 0.314603i \(0.898129\pi\)
\(522\) 0 0
\(523\) 4968.09 8604.99i 0.415372 0.719445i −0.580095 0.814548i \(-0.696985\pi\)
0.995467 + 0.0951032i \(0.0303181\pi\)
\(524\) −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 0.988381 0.151996i \(-0.0485699\pi\)
−0.625823 + 0.779965i \(0.715237\pi\)
\(564\) 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 \(0.0691380\pi\)
−0.301624 + 0.953427i \(0.597529\pi\)
\(578\) −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 \(-0.167172\pi\)
0.865230 + 0.501375i \(0.167172\pi\)
\(588\) 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 \(-0.607124\pi\)
0.982555 0.185970i \(-0.0595427\pi\)
\(594\) 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 \(-0.679788\pi\)
−0.535264 + 0.844685i \(0.679788\pi\)
\(602\) 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 −0.939563 0.342375i \(-0.888769\pi\)
0.766287 + 0.642498i \(0.222102\pi\)
\(608\) 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 \(-0.769297\pi\)
−0.199823 0.979832i \(-0.564037\pi\)
\(620\) −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 \(-0.760524\pi\)
−0.730094 + 0.683347i \(0.760524\pi\)
\(644\) 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 \(-0.990254\pi\)
0.473253 0.880927i \(-0.343080\pi\)
\(648\) 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 0.619644 0.784883i \(-0.287277\pi\)
−0.989551 + 0.144185i \(0.953944\pi\)
\(662\) −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 \(-0.656034\pi\)
0.999442 0.0333977i \(-0.0106328\pi\)
\(678\) 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 −0.893918 0.448230i \(-0.852055\pi\)
0.835137 + 0.550041i \(0.185388\pi\)
\(692\) 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 −0.696977 0.717093i \(-0.745472\pi\)
0.969510 + 0.245053i \(0.0788055\pi\)
\(720\) 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 \(-0.712380\pi\)
−0.618797 + 0.785551i \(0.712380\pi\)
\(728\) 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 −0.999981 0.00618771i \(-0.998030\pi\)
0.505349 + 0.862915i \(0.331364\pi\)
\(734\) −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 −0.916205 0.400710i \(-0.868763\pi\)
0.805128 + 0.593101i \(0.202097\pi\)
\(762\) 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 \(-0.573226\pi\)
−0.228023 + 0.973656i \(0.573226\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 17535.8 30373.0i 0.817524 1.41599i
\(773\) 1546.40 + 2678.44i 0.0719536 + 0.124627i 0.899757 0.436390i \(-0.143743\pi\)
−0.827804 + 0.561018i \(0.810410\pi\)
\(774\) 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 \(-0.993849\pi\)
0.483174 0.875525i \(-0.339484\pi\)
\(788\) 20003.5 + 34647.0i 0.904307 + 1.56631i
\(789\) 0 0
\(790\) 86506.3 3.89589
\(791\) 0